Properties

Label 4012.2.a.f.1.3
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 3
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: \(3\)
Coefficient field: 3.3.321.1
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.69963\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+4.39926 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+4.39926 q^{5}\) \(+1.00000 q^{7}\) \(-2.00000 q^{9}\) \(-2.00000 q^{11}\) \(-3.39926 q^{13}\) \(-4.39926 q^{15}\) \(+1.00000 q^{17}\) \(-6.39926 q^{19}\) \(-1.00000 q^{21}\) \(+0.222528 q^{23}\) \(+14.3535 q^{25}\) \(+5.00000 q^{27}\) \(+2.39926 q^{29}\) \(-6.57598 q^{31}\) \(+2.00000 q^{33}\) \(+4.39926 q^{35}\) \(-9.97524 q^{37}\) \(+3.39926 q^{39}\) \(-6.39926 q^{41}\) \(-10.5760 q^{43}\) \(-8.79851 q^{45}\) \(-4.22253 q^{47}\) \(-6.00000 q^{49}\) \(-1.00000 q^{51}\) \(+13.3535 q^{53}\) \(-8.79851 q^{55}\) \(+6.39926 q^{57}\) \(-1.00000 q^{59}\) \(+1.39926 q^{61}\) \(-2.00000 q^{63}\) \(-14.9542 q^{65}\) \(-2.44506 q^{67}\) \(-0.222528 q^{69}\) \(+6.35346 q^{71}\) \(+2.00000 q^{73}\) \(-14.3535 q^{75}\) \(-2.00000 q^{77}\) \(-5.00000 q^{79}\) \(+1.00000 q^{81}\) \(-13.9752 q^{83}\) \(+4.39926 q^{85}\) \(-2.39926 q^{87}\) \(-4.57598 q^{89}\) \(-3.39926 q^{91}\) \(+6.57598 q^{93}\) \(-28.1520 q^{95}\) \(-15.7527 q^{97}\) \(+4.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 3q^{21} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut -\mathstrut 7q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 7q^{57} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 34q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut -\mathstrut 20q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 6q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 37q^{95} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) 4.39926 1.96741 0.983704 0.179798i \(-0.0575443\pi\)
0.983704 + 0.179798i \(0.0575443\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −3.39926 −0.942784 −0.471392 0.881924i \(-0.656248\pi\)
−0.471392 + 0.881924i \(0.656248\pi\)
\(14\) 0 0
\(15\) −4.39926 −1.13588
\(16\) 0 0
\(17\) 1.00000 0.242536
\(18\) 0 0
\(19\) −6.39926 −1.46809 −0.734045 0.679101i \(-0.762370\pi\)
−0.734045 + 0.679101i \(0.762370\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 0.222528 0.0464004 0.0232002 0.999731i \(-0.492614\pi\)
0.0232002 + 0.999731i \(0.492614\pi\)
\(24\) 0 0
\(25\) 14.3535 2.87069
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 2.39926 0.445531 0.222765 0.974872i \(-0.428492\pi\)
0.222765 + 0.974872i \(0.428492\pi\)
\(30\) 0 0
\(31\) −6.57598 −1.18108 −0.590541 0.807008i \(-0.701086\pi\)
−0.590541 + 0.807008i \(0.701086\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 4.39926 0.743610
\(36\) 0 0
\(37\) −9.97524 −1.63992 −0.819960 0.572421i \(-0.806004\pi\)
−0.819960 + 0.572421i \(0.806004\pi\)
\(38\) 0 0
\(39\) 3.39926 0.544317
\(40\) 0 0
\(41\) −6.39926 −0.999396 −0.499698 0.866200i \(-0.666556\pi\)
−0.499698 + 0.866200i \(0.666556\pi\)
\(42\) 0 0
\(43\) −10.5760 −1.61282 −0.806411 0.591355i \(-0.798593\pi\)
−0.806411 + 0.591355i \(0.798593\pi\)
\(44\) 0 0
\(45\) −8.79851 −1.31160
\(46\) 0 0
\(47\) −4.22253 −0.615919 −0.307960 0.951399i \(-0.599646\pi\)
−0.307960 + 0.951399i \(0.599646\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) 13.3535 1.83424 0.917119 0.398613i \(-0.130508\pi\)
0.917119 + 0.398613i \(0.130508\pi\)
\(54\) 0 0
\(55\) −8.79851 −1.18639
\(56\) 0 0
\(57\) 6.39926 0.847602
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) 1.39926 0.179156 0.0895782 0.995980i \(-0.471448\pi\)
0.0895782 + 0.995980i \(0.471448\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) −14.9542 −1.85484
\(66\) 0 0
\(67\) −2.44506 −0.298711 −0.149356 0.988784i \(-0.547720\pi\)
−0.149356 + 0.988784i \(0.547720\pi\)
\(68\) 0 0
\(69\) −0.222528 −0.0267893
\(70\) 0 0
\(71\) 6.35346 0.754017 0.377008 0.926210i \(-0.376953\pi\)
0.377008 + 0.926210i \(0.376953\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) −14.3535 −1.65739
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.9752 −1.53398 −0.766991 0.641658i \(-0.778247\pi\)
−0.766991 + 0.641658i \(0.778247\pi\)
\(84\) 0 0
\(85\) 4.39926 0.477166
\(86\) 0 0
\(87\) −2.39926 −0.257227
\(88\) 0 0
\(89\) −4.57598 −0.485053 −0.242527 0.970145i \(-0.577976\pi\)
−0.242527 + 0.970145i \(0.577976\pi\)
\(90\) 0 0
\(91\) −3.39926 −0.356339
\(92\) 0 0
\(93\) 6.57598 0.681898
\(94\) 0 0
\(95\) −28.1520 −2.88833
\(96\) 0 0
\(97\) −15.7527 −1.59945 −0.799723 0.600369i \(-0.795020\pi\)
−0.799723 + 0.600369i \(0.795020\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −2.37822 −0.236641 −0.118321 0.992975i \(-0.537751\pi\)
−0.118321 + 0.992975i \(0.537751\pi\)
\(102\) 0 0
\(103\) −11.8443 −1.16705 −0.583527 0.812093i \(-0.698328\pi\)
−0.583527 + 0.812093i \(0.698328\pi\)
\(104\) 0 0
\(105\) −4.39926 −0.429323
\(106\) 0 0
\(107\) 9.79851 0.947258 0.473629 0.880724i \(-0.342944\pi\)
0.473629 + 0.880724i \(0.342944\pi\)
\(108\) 0 0
\(109\) 6.44506 0.617324 0.308662 0.951172i \(-0.400119\pi\)
0.308662 + 0.951172i \(0.400119\pi\)
\(110\) 0 0
\(111\) 9.97524 0.946808
\(112\) 0 0
\(113\) 3.84431 0.361643 0.180821 0.983516i \(-0.442124\pi\)
0.180821 + 0.983516i \(0.442124\pi\)
\(114\) 0 0
\(115\) 0.978959 0.0912884
\(116\) 0 0
\(117\) 6.79851 0.628523
\(118\) 0 0
\(119\) 1.00000 0.0916698
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 6.39926 0.577002
\(124\) 0 0
\(125\) 41.1483 3.68041
\(126\) 0 0
\(127\) 19.1978 1.70353 0.851763 0.523927i \(-0.175533\pi\)
0.851763 + 0.523927i \(0.175533\pi\)
\(128\) 0 0
\(129\) 10.5760 0.931163
\(130\) 0 0
\(131\) 5.15197 0.450130 0.225065 0.974344i \(-0.427741\pi\)
0.225065 + 0.974344i \(0.427741\pi\)
\(132\) 0 0
\(133\) −6.39926 −0.554886
\(134\) 0 0
\(135\) 21.9963 1.89314
\(136\) 0 0
\(137\) 13.7985 1.17889 0.589443 0.807810i \(-0.299347\pi\)
0.589443 + 0.807810i \(0.299347\pi\)
\(138\) 0 0
\(139\) 6.35346 0.538893 0.269447 0.963015i \(-0.413159\pi\)
0.269447 + 0.963015i \(0.413159\pi\)
\(140\) 0 0
\(141\) 4.22253 0.355601
\(142\) 0 0
\(143\) 6.79851 0.568520
\(144\) 0 0
\(145\) 10.5549 0.876540
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) −9.39926 −0.770017 −0.385009 0.922913i \(-0.625802\pi\)
−0.385009 + 0.922913i \(0.625802\pi\)
\(150\) 0 0
\(151\) −6.82327 −0.555270 −0.277635 0.960687i \(-0.589551\pi\)
−0.277635 + 0.960687i \(0.589551\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −28.9294 −2.32367
\(156\) 0 0
\(157\) −13.7527 −1.09759 −0.548793 0.835958i \(-0.684912\pi\)
−0.548793 + 0.835958i \(0.684912\pi\)
\(158\) 0 0
\(159\) −13.3535 −1.05900
\(160\) 0 0
\(161\) 0.222528 0.0175377
\(162\) 0 0
\(163\) 11.2436 0.880664 0.440332 0.897835i \(-0.354861\pi\)
0.440332 + 0.897835i \(0.354861\pi\)
\(164\) 0 0
\(165\) 8.79851 0.684963
\(166\) 0 0
\(167\) −3.44506 −0.266586 −0.133293 0.991077i \(-0.542555\pi\)
−0.133293 + 0.991077i \(0.542555\pi\)
\(168\) 0 0
\(169\) −1.44506 −0.111158
\(170\) 0 0
\(171\) 12.7985 0.978727
\(172\) 0 0
\(173\) 12.9542 0.984890 0.492445 0.870344i \(-0.336103\pi\)
0.492445 + 0.870344i \(0.336103\pi\)
\(174\) 0 0
\(175\) 14.3535 1.08502
\(176\) 0 0
\(177\) 1.00000 0.0751646
\(178\) 0 0
\(179\) −4.60074 −0.343876 −0.171938 0.985108i \(-0.555003\pi\)
−0.171938 + 0.985108i \(0.555003\pi\)
\(180\) 0 0
\(181\) 19.1062 1.42015 0.710075 0.704126i \(-0.248661\pi\)
0.710075 + 0.704126i \(0.248661\pi\)
\(182\) 0 0
\(183\) −1.39926 −0.103436
\(184\) 0 0
\(185\) −43.8836 −3.22639
\(186\) 0 0
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 0 0
\(191\) 7.37450 0.533600 0.266800 0.963752i \(-0.414034\pi\)
0.266800 + 0.963752i \(0.414034\pi\)
\(192\) 0 0
\(193\) 11.1978 0.806033 0.403017 0.915193i \(-0.367962\pi\)
0.403017 + 0.915193i \(0.367962\pi\)
\(194\) 0 0
\(195\) 14.9542 1.07089
\(196\) 0 0
\(197\) 7.90840 0.563450 0.281725 0.959495i \(-0.409093\pi\)
0.281725 + 0.959495i \(0.409093\pi\)
\(198\) 0 0
\(199\) −17.3535 −1.23015 −0.615077 0.788467i \(-0.710875\pi\)
−0.615077 + 0.788467i \(0.710875\pi\)
\(200\) 0 0
\(201\) 2.44506 0.172461
\(202\) 0 0
\(203\) 2.39926 0.168395
\(204\) 0 0
\(205\) −28.1520 −1.96622
\(206\) 0 0
\(207\) −0.445057 −0.0309336
\(208\) 0 0
\(209\) 12.7985 0.885292
\(210\) 0 0
\(211\) −9.02104 −0.621034 −0.310517 0.950568i \(-0.600502\pi\)
−0.310517 + 0.950568i \(0.600502\pi\)
\(212\) 0 0
\(213\) −6.35346 −0.435332
\(214\) 0 0
\(215\) −46.5265 −3.17308
\(216\) 0 0
\(217\) −6.57598 −0.446407
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −3.39926 −0.228659
\(222\) 0 0
\(223\) 1.15197 0.0771415 0.0385708 0.999256i \(-0.487719\pi\)
0.0385708 + 0.999256i \(0.487719\pi\)
\(224\) 0 0
\(225\) −28.7069 −1.91379
\(226\) 0 0
\(227\) 21.6218 1.43509 0.717544 0.696513i \(-0.245266\pi\)
0.717544 + 0.696513i \(0.245266\pi\)
\(228\) 0 0
\(229\) −19.5302 −1.29059 −0.645295 0.763933i \(-0.723266\pi\)
−0.645295 + 0.763933i \(0.723266\pi\)
\(230\) 0 0
\(231\) 2.00000 0.131590
\(232\) 0 0
\(233\) 12.7738 0.836836 0.418418 0.908254i \(-0.362585\pi\)
0.418418 + 0.908254i \(0.362585\pi\)
\(234\) 0 0
\(235\) −18.5760 −1.21176
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) −8.39926 −0.543303 −0.271651 0.962396i \(-0.587570\pi\)
−0.271651 + 0.962396i \(0.587570\pi\)
\(240\) 0 0
\(241\) −27.1978 −1.75196 −0.875981 0.482345i \(-0.839785\pi\)
−0.875981 + 0.482345i \(0.839785\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) −26.3955 −1.68635
\(246\) 0 0
\(247\) 21.7527 1.38409
\(248\) 0 0
\(249\) 13.9752 0.885645
\(250\) 0 0
\(251\) −17.5512 −1.10782 −0.553912 0.832575i \(-0.686866\pi\)
−0.553912 + 0.832575i \(0.686866\pi\)
\(252\) 0 0
\(253\) −0.445057 −0.0279805
\(254\) 0 0
\(255\) −4.39926 −0.275492
\(256\) 0 0
\(257\) −8.15197 −0.508506 −0.254253 0.967138i \(-0.581830\pi\)
−0.254253 + 0.967138i \(0.581830\pi\)
\(258\) 0 0
\(259\) −9.97524 −0.619831
\(260\) 0 0
\(261\) −4.79851 −0.297020
\(262\) 0 0
\(263\) −4.39926 −0.271270 −0.135635 0.990759i \(-0.543307\pi\)
−0.135635 + 0.990759i \(0.543307\pi\)
\(264\) 0 0
\(265\) 58.7453 3.60869
\(266\) 0 0
\(267\) 4.57598 0.280046
\(268\) 0 0
\(269\) 10.7317 0.654322 0.327161 0.944969i \(-0.393908\pi\)
0.327161 + 0.944969i \(0.393908\pi\)
\(270\) 0 0
\(271\) −13.5091 −0.820622 −0.410311 0.911946i \(-0.634580\pi\)
−0.410311 + 0.911946i \(0.634580\pi\)
\(272\) 0 0
\(273\) 3.39926 0.205732
\(274\) 0 0
\(275\) −28.7069 −1.73109
\(276\) 0 0
\(277\) 5.60074 0.336516 0.168258 0.985743i \(-0.446186\pi\)
0.168258 + 0.985743i \(0.446186\pi\)
\(278\) 0 0
\(279\) 13.1520 0.787388
\(280\) 0 0
\(281\) 30.0604 1.79325 0.896626 0.442789i \(-0.146011\pi\)
0.896626 + 0.442789i \(0.146011\pi\)
\(282\) 0 0
\(283\) −13.3077 −0.791058 −0.395529 0.918453i \(-0.629439\pi\)
−0.395529 + 0.918453i \(0.629439\pi\)
\(284\) 0 0
\(285\) 28.1520 1.66758
\(286\) 0 0
\(287\) −6.39926 −0.377736
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 15.7527 0.923440
\(292\) 0 0
\(293\) −29.0421 −1.69666 −0.848328 0.529471i \(-0.822391\pi\)
−0.848328 + 0.529471i \(0.822391\pi\)
\(294\) 0 0
\(295\) −4.39926 −0.256135
\(296\) 0 0
\(297\) −10.0000 −0.580259
\(298\) 0 0
\(299\) −0.756431 −0.0437455
\(300\) 0 0
\(301\) −10.5760 −0.609590
\(302\) 0 0
\(303\) 2.37822 0.136625
\(304\) 0 0
\(305\) 6.15569 0.352474
\(306\) 0 0
\(307\) 5.24729 0.299479 0.149739 0.988726i \(-0.452157\pi\)
0.149739 + 0.988726i \(0.452157\pi\)
\(308\) 0 0
\(309\) 11.8443 0.673799
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 0 0
\(313\) 6.60074 0.373096 0.186548 0.982446i \(-0.440270\pi\)
0.186548 + 0.982446i \(0.440270\pi\)
\(314\) 0 0
\(315\) −8.79851 −0.495740
\(316\) 0 0
\(317\) 13.2436 0.743833 0.371916 0.928266i \(-0.378701\pi\)
0.371916 + 0.928266i \(0.378701\pi\)
\(318\) 0 0
\(319\) −4.79851 −0.268665
\(320\) 0 0
\(321\) −9.79851 −0.546900
\(322\) 0 0
\(323\) −6.39926 −0.356064
\(324\) 0 0
\(325\) −48.7911 −2.70644
\(326\) 0 0
\(327\) −6.44506 −0.356412
\(328\) 0 0
\(329\) −4.22253 −0.232796
\(330\) 0 0
\(331\) −26.3993 −1.45103 −0.725517 0.688204i \(-0.758399\pi\)
−0.725517 + 0.688204i \(0.758399\pi\)
\(332\) 0 0
\(333\) 19.9505 1.09328
\(334\) 0 0
\(335\) −10.7564 −0.587687
\(336\) 0 0
\(337\) 23.9505 1.30467 0.652333 0.757933i \(-0.273790\pi\)
0.652333 + 0.757933i \(0.273790\pi\)
\(338\) 0 0
\(339\) −3.84431 −0.208794
\(340\) 0 0
\(341\) 13.1520 0.712219
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) 0 0
\(345\) −0.978959 −0.0527054
\(346\) 0 0
\(347\) 11.8836 0.637947 0.318974 0.947764i \(-0.396662\pi\)
0.318974 + 0.947764i \(0.396662\pi\)
\(348\) 0 0
\(349\) −3.62178 −0.193870 −0.0969348 0.995291i \(-0.530904\pi\)
−0.0969348 + 0.995291i \(0.530904\pi\)
\(350\) 0 0
\(351\) −16.9963 −0.907194
\(352\) 0 0
\(353\) −16.7738 −0.892777 −0.446388 0.894839i \(-0.647290\pi\)
−0.446388 + 0.894839i \(0.647290\pi\)
\(354\) 0 0
\(355\) 27.9505 1.48346
\(356\) 0 0
\(357\) −1.00000 −0.0529256
\(358\) 0 0
\(359\) −0.0458003 −0.00241725 −0.00120862 0.999999i \(-0.500385\pi\)
−0.00120862 + 0.999999i \(0.500385\pi\)
\(360\) 0 0
\(361\) 21.9505 1.15529
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 8.79851 0.460535
\(366\) 0 0
\(367\) −31.8836 −1.66431 −0.832156 0.554541i \(-0.812894\pi\)
−0.832156 + 0.554541i \(0.812894\pi\)
\(368\) 0 0
\(369\) 12.7985 0.666264
\(370\) 0 0
\(371\) 13.3535 0.693277
\(372\) 0 0
\(373\) −12.3535 −0.639638 −0.319819 0.947479i \(-0.603622\pi\)
−0.319819 + 0.947479i \(0.603622\pi\)
\(374\) 0 0
\(375\) −41.1483 −2.12489
\(376\) 0 0
\(377\) −8.15569 −0.420039
\(378\) 0 0
\(379\) −28.5970 −1.46893 −0.734465 0.678646i \(-0.762567\pi\)
−0.734465 + 0.678646i \(0.762567\pi\)
\(380\) 0 0
\(381\) −19.1978 −0.983531
\(382\) 0 0
\(383\) −13.9084 −0.710686 −0.355343 0.934736i \(-0.615636\pi\)
−0.355343 + 0.934736i \(0.615636\pi\)
\(384\) 0 0
\(385\) −8.79851 −0.448414
\(386\) 0 0
\(387\) 21.1520 1.07521
\(388\) 0 0
\(389\) 11.1520 0.565427 0.282714 0.959204i \(-0.408765\pi\)
0.282714 + 0.959204i \(0.408765\pi\)
\(390\) 0 0
\(391\) 0.222528 0.0112537
\(392\) 0 0
\(393\) −5.15197 −0.259882
\(394\) 0 0
\(395\) −21.9963 −1.10675
\(396\) 0 0
\(397\) 0.692344 0.0347478 0.0173739 0.999849i \(-0.494469\pi\)
0.0173739 + 0.999849i \(0.494469\pi\)
\(398\) 0 0
\(399\) 6.39926 0.320364
\(400\) 0 0
\(401\) −5.04580 −0.251975 −0.125988 0.992032i \(-0.540210\pi\)
−0.125988 + 0.992032i \(0.540210\pi\)
\(402\) 0 0
\(403\) 22.3535 1.11350
\(404\) 0 0
\(405\) 4.39926 0.218601
\(406\) 0 0
\(407\) 19.9505 0.988909
\(408\) 0 0
\(409\) 9.04580 0.447286 0.223643 0.974671i \(-0.428205\pi\)
0.223643 + 0.974671i \(0.428205\pi\)
\(410\) 0 0
\(411\) −13.7985 −0.680630
\(412\) 0 0
\(413\) −1.00000 −0.0492068
\(414\) 0 0
\(415\) −61.4807 −3.01797
\(416\) 0 0
\(417\) −6.35346 −0.311130
\(418\) 0 0
\(419\) −10.2473 −0.500613 −0.250306 0.968167i \(-0.580531\pi\)
−0.250306 + 0.968167i \(0.580531\pi\)
\(420\) 0 0
\(421\) −12.4844 −0.608452 −0.304226 0.952600i \(-0.598398\pi\)
−0.304226 + 0.952600i \(0.598398\pi\)
\(422\) 0 0
\(423\) 8.44506 0.410613
\(424\) 0 0
\(425\) 14.3535 0.696245
\(426\) 0 0
\(427\) 1.39926 0.0677148
\(428\) 0 0
\(429\) −6.79851 −0.328235
\(430\) 0 0
\(431\) 23.5549 1.13460 0.567301 0.823511i \(-0.307988\pi\)
0.567301 + 0.823511i \(0.307988\pi\)
\(432\) 0 0
\(433\) 0.151969 0.00730314 0.00365157 0.999993i \(-0.498838\pi\)
0.00365157 + 0.999993i \(0.498838\pi\)
\(434\) 0 0
\(435\) −10.5549 −0.506071
\(436\) 0 0
\(437\) −1.42402 −0.0681199
\(438\) 0 0
\(439\) −14.3535 −0.685053 −0.342527 0.939508i \(-0.611283\pi\)
−0.342527 + 0.939508i \(0.611283\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) −8.17301 −0.388311 −0.194156 0.980971i \(-0.562197\pi\)
−0.194156 + 0.980971i \(0.562197\pi\)
\(444\) 0 0
\(445\) −20.1309 −0.954297
\(446\) 0 0
\(447\) 9.39926 0.444570
\(448\) 0 0
\(449\) 20.3077 0.958378 0.479189 0.877712i \(-0.340931\pi\)
0.479189 + 0.877712i \(0.340931\pi\)
\(450\) 0 0
\(451\) 12.7985 0.602658
\(452\) 0 0
\(453\) 6.82327 0.320585
\(454\) 0 0
\(455\) −14.9542 −0.701064
\(456\) 0 0
\(457\) 42.3708 1.98202 0.991011 0.133783i \(-0.0427124\pi\)
0.991011 + 0.133783i \(0.0427124\pi\)
\(458\) 0 0
\(459\) 5.00000 0.233380
\(460\) 0 0
\(461\) 8.84803 0.412094 0.206047 0.978542i \(-0.433940\pi\)
0.206047 + 0.978542i \(0.433940\pi\)
\(462\) 0 0
\(463\) −35.4166 −1.64595 −0.822974 0.568079i \(-0.807687\pi\)
−0.822974 + 0.568079i \(0.807687\pi\)
\(464\) 0 0
\(465\) 28.9294 1.34157
\(466\) 0 0
\(467\) 16.7985 0.777342 0.388671 0.921377i \(-0.372934\pi\)
0.388671 + 0.921377i \(0.372934\pi\)
\(468\) 0 0
\(469\) −2.44506 −0.112902
\(470\) 0 0
\(471\) 13.7527 0.633692
\(472\) 0 0
\(473\) 21.1520 0.972569
\(474\) 0 0
\(475\) −91.8514 −4.21443
\(476\) 0 0
\(477\) −26.7069 −1.22283
\(478\) 0 0
\(479\) 18.7490 0.856663 0.428332 0.903622i \(-0.359101\pi\)
0.428332 + 0.903622i \(0.359101\pi\)
\(480\) 0 0
\(481\) 33.9084 1.54609
\(482\) 0 0
\(483\) −0.222528 −0.0101254
\(484\) 0 0
\(485\) −69.3002 −3.14676
\(486\) 0 0
\(487\) 13.2619 0.600952 0.300476 0.953789i \(-0.402854\pi\)
0.300476 + 0.953789i \(0.402854\pi\)
\(488\) 0 0
\(489\) −11.2436 −0.508452
\(490\) 0 0
\(491\) 41.1483 1.85699 0.928497 0.371339i \(-0.121101\pi\)
0.928497 + 0.371339i \(0.121101\pi\)
\(492\) 0 0
\(493\) 2.39926 0.108057
\(494\) 0 0
\(495\) 17.5970 0.790927
\(496\) 0 0
\(497\) 6.35346 0.284991
\(498\) 0 0
\(499\) 3.44506 0.154222 0.0771110 0.997023i \(-0.475430\pi\)
0.0771110 + 0.997023i \(0.475430\pi\)
\(500\) 0 0
\(501\) 3.44506 0.153914
\(502\) 0 0
\(503\) 1.12721 0.0502598 0.0251299 0.999684i \(-0.492000\pi\)
0.0251299 + 0.999684i \(0.492000\pi\)
\(504\) 0 0
\(505\) −10.4624 −0.465570
\(506\) 0 0
\(507\) 1.44506 0.0641772
\(508\) 0 0
\(509\) 24.9963 1.10794 0.553970 0.832536i \(-0.313112\pi\)
0.553970 + 0.832536i \(0.313112\pi\)
\(510\) 0 0
\(511\) 2.00000 0.0884748
\(512\) 0 0
\(513\) −31.9963 −1.41267
\(514\) 0 0
\(515\) −52.1062 −2.29607
\(516\) 0 0
\(517\) 8.44506 0.371413
\(518\) 0 0
\(519\) −12.9542 −0.568626
\(520\) 0 0
\(521\) −7.15197 −0.313333 −0.156667 0.987652i \(-0.550075\pi\)
−0.156667 + 0.987652i \(0.550075\pi\)
\(522\) 0 0
\(523\) −21.2894 −0.930919 −0.465460 0.885069i \(-0.654111\pi\)
−0.465460 + 0.885069i \(0.654111\pi\)
\(524\) 0 0
\(525\) −14.3535 −0.626436
\(526\) 0 0
\(527\) −6.57598 −0.286454
\(528\) 0 0
\(529\) −22.9505 −0.997847
\(530\) 0 0
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) 21.7527 0.942215
\(534\) 0 0
\(535\) 43.1062 1.86364
\(536\) 0 0
\(537\) 4.60074 0.198537
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) −29.6364 −1.27417 −0.637083 0.770795i \(-0.719859\pi\)
−0.637083 + 0.770795i \(0.719859\pi\)
\(542\) 0 0
\(543\) −19.1062 −0.819924
\(544\) 0 0
\(545\) 28.3535 1.21453
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) −2.79851 −0.119438
\(550\) 0 0
\(551\) −15.3535 −0.654079
\(552\) 0 0
\(553\) −5.00000 −0.212622
\(554\) 0 0
\(555\) 43.8836 1.86276
\(556\) 0 0
\(557\) −9.39554 −0.398102 −0.199051 0.979989i \(-0.563786\pi\)
−0.199051 + 0.979989i \(0.563786\pi\)
\(558\) 0 0
\(559\) 35.9505 1.52054
\(560\) 0 0
\(561\) 2.00000 0.0844401
\(562\) 0 0
\(563\) 13.1520 0.554289 0.277145 0.960828i \(-0.410612\pi\)
0.277145 + 0.960828i \(0.410612\pi\)
\(564\) 0 0
\(565\) 16.9121 0.711498
\(566\) 0 0
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −11.8836 −0.498188 −0.249094 0.968479i \(-0.580133\pi\)
−0.249094 + 0.968479i \(0.580133\pi\)
\(570\) 0 0
\(571\) 43.7920 1.83264 0.916320 0.400447i \(-0.131145\pi\)
0.916320 + 0.400447i \(0.131145\pi\)
\(572\) 0 0
\(573\) −7.37450 −0.308074
\(574\) 0 0
\(575\) 3.19405 0.133201
\(576\) 0 0
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) 0 0
\(579\) −11.1978 −0.465363
\(580\) 0 0
\(581\) −13.9752 −0.579791
\(582\) 0 0
\(583\) −26.7069 −1.10609
\(584\) 0 0
\(585\) 29.9084 1.23656
\(586\) 0 0
\(587\) 21.4661 0.886001 0.443000 0.896521i \(-0.353914\pi\)
0.443000 + 0.896521i \(0.353914\pi\)
\(588\) 0 0
\(589\) 42.0814 1.73393
\(590\) 0 0
\(591\) −7.90840 −0.325308
\(592\) 0 0
\(593\) 6.46334 0.265418 0.132709 0.991155i \(-0.457632\pi\)
0.132709 + 0.991155i \(0.457632\pi\)
\(594\) 0 0
\(595\) 4.39926 0.180352
\(596\) 0 0
\(597\) 17.3535 0.710230
\(598\) 0 0
\(599\) 10.3077 0.421159 0.210580 0.977577i \(-0.432465\pi\)
0.210580 + 0.977577i \(0.432465\pi\)
\(600\) 0 0
\(601\) 33.2857 1.35775 0.678875 0.734254i \(-0.262468\pi\)
0.678875 + 0.734254i \(0.262468\pi\)
\(602\) 0 0
\(603\) 4.89011 0.199141
\(604\) 0 0
\(605\) −30.7948 −1.25199
\(606\) 0 0
\(607\) 31.4871 1.27802 0.639012 0.769197i \(-0.279344\pi\)
0.639012 + 0.769197i \(0.279344\pi\)
\(608\) 0 0
\(609\) −2.39926 −0.0972228
\(610\) 0 0
\(611\) 14.3535 0.580679
\(612\) 0 0
\(613\) −38.1730 −1.54179 −0.770897 0.636960i \(-0.780192\pi\)
−0.770897 + 0.636960i \(0.780192\pi\)
\(614\) 0 0
\(615\) 28.1520 1.13520
\(616\) 0 0
\(617\) −26.3077 −1.05911 −0.529553 0.848277i \(-0.677640\pi\)
−0.529553 + 0.848277i \(0.677640\pi\)
\(618\) 0 0
\(619\) 20.2436 0.813658 0.406829 0.913504i \(-0.366635\pi\)
0.406829 + 0.913504i \(0.366635\pi\)
\(620\) 0 0
\(621\) 1.11264 0.0446488
\(622\) 0 0
\(623\) −4.57598 −0.183333
\(624\) 0 0
\(625\) 109.254 4.37018
\(626\) 0 0
\(627\) −12.7985 −0.511123
\(628\) 0 0
\(629\) −9.97524 −0.397739
\(630\) 0 0
\(631\) −24.2619 −0.965849 −0.482925 0.875662i \(-0.660425\pi\)
−0.482925 + 0.875662i \(0.660425\pi\)
\(632\) 0 0
\(633\) 9.02104 0.358554
\(634\) 0 0
\(635\) 84.4559 3.35153
\(636\) 0 0
\(637\) 20.3955 0.808101
\(638\) 0 0
\(639\) −12.7069 −0.502678
\(640\) 0 0
\(641\) −5.50542 −0.217451 −0.108726 0.994072i \(-0.534677\pi\)
−0.108726 + 0.994072i \(0.534677\pi\)
\(642\) 0 0
\(643\) 34.4559 1.35881 0.679404 0.733764i \(-0.262238\pi\)
0.679404 + 0.733764i \(0.262238\pi\)
\(644\) 0 0
\(645\) 46.5265 1.83198
\(646\) 0 0
\(647\) −38.4413 −1.51128 −0.755642 0.654984i \(-0.772675\pi\)
−0.755642 + 0.654984i \(0.772675\pi\)
\(648\) 0 0
\(649\) 2.00000 0.0785069
\(650\) 0 0
\(651\) 6.57598 0.257733
\(652\) 0 0
\(653\) −41.5933 −1.62767 −0.813836 0.581095i \(-0.802625\pi\)
−0.813836 + 0.581095i \(0.802625\pi\)
\(654\) 0 0
\(655\) 22.6648 0.885588
\(656\) 0 0
\(657\) −4.00000 −0.156055
\(658\) 0 0
\(659\) 31.6639 1.23345 0.616725 0.787179i \(-0.288459\pi\)
0.616725 + 0.787179i \(0.288459\pi\)
\(660\) 0 0
\(661\) −31.7490 −1.23489 −0.617446 0.786613i \(-0.711833\pi\)
−0.617446 + 0.786613i \(0.711833\pi\)
\(662\) 0 0
\(663\) 3.39926 0.132016
\(664\) 0 0
\(665\) −28.1520 −1.09169
\(666\) 0 0
\(667\) 0.533902 0.0206728
\(668\) 0 0
\(669\) −1.15197 −0.0445377
\(670\) 0 0
\(671\) −2.79851 −0.108035
\(672\) 0 0
\(673\) −7.24081 −0.279113 −0.139556 0.990214i \(-0.544568\pi\)
−0.139556 + 0.990214i \(0.544568\pi\)
\(674\) 0 0
\(675\) 71.7673 2.76232
\(676\) 0 0
\(677\) −8.09160 −0.310985 −0.155493 0.987837i \(-0.549697\pi\)
−0.155493 + 0.987837i \(0.549697\pi\)
\(678\) 0 0
\(679\) −15.7527 −0.604534
\(680\) 0 0
\(681\) −21.6218 −0.828549
\(682\) 0 0
\(683\) −40.4596 −1.54814 −0.774072 0.633097i \(-0.781783\pi\)
−0.774072 + 0.633097i \(0.781783\pi\)
\(684\) 0 0
\(685\) 60.7032 2.31935
\(686\) 0 0
\(687\) 19.5302 0.745123
\(688\) 0 0
\(689\) −45.3918 −1.72929
\(690\) 0 0
\(691\) 34.0814 1.29652 0.648259 0.761420i \(-0.275497\pi\)
0.648259 + 0.761420i \(0.275497\pi\)
\(692\) 0 0
\(693\) 4.00000 0.151947
\(694\) 0 0
\(695\) 27.9505 1.06022
\(696\) 0 0
\(697\) −6.39926 −0.242389
\(698\) 0 0
\(699\) −12.7738 −0.483148
\(700\) 0 0
\(701\) −15.2829 −0.577227 −0.288614 0.957446i \(-0.593194\pi\)
−0.288614 + 0.957446i \(0.593194\pi\)
\(702\) 0 0
\(703\) 63.8341 2.40755
\(704\) 0 0
\(705\) 18.5760 0.699612
\(706\) 0 0
\(707\) −2.37822 −0.0894420
\(708\) 0 0
\(709\) 29.9542 1.12495 0.562477 0.826813i \(-0.309849\pi\)
0.562477 + 0.826813i \(0.309849\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) −1.46334 −0.0548026
\(714\) 0 0
\(715\) 29.9084 1.11851
\(716\) 0 0
\(717\) 8.39926 0.313676
\(718\) 0 0
\(719\) 47.3918 1.76742 0.883708 0.468038i \(-0.155039\pi\)
0.883708 + 0.468038i \(0.155039\pi\)
\(720\) 0 0
\(721\) −11.8443 −0.441105
\(722\) 0 0
\(723\) 27.1978 1.01150
\(724\) 0 0
\(725\) 34.4376 1.27898
\(726\) 0 0
\(727\) −9.90840 −0.367482 −0.183741 0.982975i \(-0.558821\pi\)
−0.183741 + 0.982975i \(0.558821\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −10.5760 −0.391167
\(732\) 0 0
\(733\) 17.0604 0.630139 0.315070 0.949069i \(-0.397972\pi\)
0.315070 + 0.949069i \(0.397972\pi\)
\(734\) 0 0
\(735\) 26.3955 0.973614
\(736\) 0 0
\(737\) 4.89011 0.180130
\(738\) 0 0
\(739\) 11.5329 0.424246 0.212123 0.977243i \(-0.431962\pi\)
0.212123 + 0.977243i \(0.431962\pi\)
\(740\) 0 0
\(741\) −21.7527 −0.799106
\(742\) 0 0
\(743\) −50.3039 −1.84547 −0.922736 0.385432i \(-0.874052\pi\)
−0.922736 + 0.385432i \(0.874052\pi\)
\(744\) 0 0
\(745\) −41.3497 −1.51494
\(746\) 0 0
\(747\) 27.9505 1.02265
\(748\) 0 0
\(749\) 9.79851 0.358030
\(750\) 0 0
\(751\) −12.8480 −0.468831 −0.234416 0.972136i \(-0.575318\pi\)
−0.234416 + 0.972136i \(0.575318\pi\)
\(752\) 0 0
\(753\) 17.5512 0.639602
\(754\) 0 0
\(755\) −30.0173 −1.09244
\(756\) 0 0
\(757\) −42.2436 −1.53537 −0.767684 0.640828i \(-0.778591\pi\)
−0.767684 + 0.640828i \(0.778591\pi\)
\(758\) 0 0
\(759\) 0.445057 0.0161545
\(760\) 0 0
\(761\) −23.2619 −0.843242 −0.421621 0.906772i \(-0.638539\pi\)
−0.421621 + 0.906772i \(0.638539\pi\)
\(762\) 0 0
\(763\) 6.44506 0.233327
\(764\) 0 0
\(765\) −8.79851 −0.318111
\(766\) 0 0
\(767\) 3.39926 0.122740
\(768\) 0 0
\(769\) 13.3993 0.483190 0.241595 0.970377i \(-0.422330\pi\)
0.241595 + 0.970377i \(0.422330\pi\)
\(770\) 0 0
\(771\) 8.15197 0.293586
\(772\) 0 0
\(773\) −33.4386 −1.20270 −0.601351 0.798985i \(-0.705371\pi\)
−0.601351 + 0.798985i \(0.705371\pi\)
\(774\) 0 0
\(775\) −94.3881 −3.39052
\(776\) 0 0
\(777\) 9.97524 0.357860
\(778\) 0 0
\(779\) 40.9505 1.46720
\(780\) 0 0
\(781\) −12.7069 −0.454689
\(782\) 0 0
\(783\) 11.9963 0.428712
\(784\) 0 0
\(785\) −60.5017 −2.15940
\(786\) 0 0
\(787\) −25.9084 −0.923535 −0.461767 0.887001i \(-0.652785\pi\)
−0.461767 + 0.887001i \(0.652785\pi\)
\(788\) 0 0
\(789\) 4.39926 0.156618
\(790\) 0 0
\(791\) 3.84431 0.136688
\(792\) 0 0
\(793\) −4.75643 −0.168906
\(794\) 0 0
\(795\) −58.7453 −2.08348
\(796\) 0 0
\(797\) 36.1483 1.28044 0.640218 0.768193i \(-0.278844\pi\)
0.640218 + 0.768193i \(0.278844\pi\)
\(798\) 0 0
\(799\) −4.22253 −0.149382
\(800\) 0 0
\(801\) 9.15197 0.323369
\(802\) 0 0
\(803\) −4.00000 −0.141157
\(804\) 0 0
\(805\) 0.978959 0.0345038
\(806\) 0 0
\(807\) −10.7317 −0.377773
\(808\) 0 0
\(809\) −5.08513 −0.178784 −0.0893918 0.995997i \(-0.528492\pi\)
−0.0893918 + 0.995997i \(0.528492\pi\)
\(810\) 0 0
\(811\) −44.2792 −1.55485 −0.777426 0.628974i \(-0.783475\pi\)
−0.777426 + 0.628974i \(0.783475\pi\)
\(812\) 0 0
\(813\) 13.5091 0.473786
\(814\) 0 0
\(815\) 49.4633 1.73263
\(816\) 0 0
\(817\) 67.6784 2.36777
\(818\) 0 0
\(819\) 6.79851 0.237559
\(820\) 0 0
\(821\) 26.3287 0.918878 0.459439 0.888209i \(-0.348051\pi\)
0.459439 + 0.888209i \(0.348051\pi\)
\(822\) 0 0
\(823\) 16.2473 0.566345 0.283172 0.959069i \(-0.408613\pi\)
0.283172 + 0.959069i \(0.408613\pi\)
\(824\) 0 0
\(825\) 28.7069 0.999446
\(826\) 0 0
\(827\) −19.2436 −0.669164 −0.334582 0.942367i \(-0.608595\pi\)
−0.334582 + 0.942367i \(0.608595\pi\)
\(828\) 0 0
\(829\) 49.6574 1.72467 0.862336 0.506336i \(-0.169000\pi\)
0.862336 + 0.506336i \(0.169000\pi\)
\(830\) 0 0
\(831\) −5.60074 −0.194288
\(832\) 0 0
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) −15.1557 −0.524484
\(836\) 0 0
\(837\) −32.8799 −1.13650
\(838\) 0 0
\(839\) −7.57970 −0.261680 −0.130840 0.991403i \(-0.541767\pi\)
−0.130840 + 0.991403i \(0.541767\pi\)
\(840\) 0 0
\(841\) −23.2436 −0.801502
\(842\) 0 0
\(843\) −30.0604 −1.03533
\(844\) 0 0
\(845\) −6.35717 −0.218693
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 13.3077 0.456718
\(850\) 0 0
\(851\) −2.21977 −0.0760929
\(852\) 0 0
\(853\) −29.9468 −1.02536 −0.512679 0.858580i \(-0.671347\pi\)
−0.512679 + 0.858580i \(0.671347\pi\)
\(854\) 0 0
\(855\) 56.3039 1.92555
\(856\) 0 0
\(857\) 1.07056 0.0365696 0.0182848 0.999833i \(-0.494179\pi\)
0.0182848 + 0.999833i \(0.494179\pi\)
\(858\) 0 0
\(859\) 11.9112 0.406403 0.203202 0.979137i \(-0.434865\pi\)
0.203202 + 0.979137i \(0.434865\pi\)
\(860\) 0 0
\(861\) 6.39926 0.218086
\(862\) 0 0
\(863\) 31.9084 1.08617 0.543087 0.839676i \(-0.317255\pi\)
0.543087 + 0.839676i \(0.317255\pi\)
\(864\) 0 0
\(865\) 56.9888 1.93768
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 10.0000 0.339227
\(870\) 0 0
\(871\) 8.31137 0.281620
\(872\) 0 0
\(873\) 31.5054 1.06630
\(874\) 0 0
\(875\) 41.1483 1.39106
\(876\) 0 0
\(877\) −6.44134 −0.217509 −0.108754 0.994069i \(-0.534686\pi\)
−0.108754 + 0.994069i \(0.534686\pi\)
\(878\) 0 0
\(879\) 29.0421 0.979565
\(880\) 0 0
\(881\) −33.6639 −1.13416 −0.567082 0.823661i \(-0.691928\pi\)
−0.567082 + 0.823661i \(0.691928\pi\)
\(882\) 0 0
\(883\) −47.4596 −1.59714 −0.798572 0.601900i \(-0.794411\pi\)
−0.798572 + 0.601900i \(0.794411\pi\)
\(884\) 0 0
\(885\) 4.39926 0.147879
\(886\) 0 0
\(887\) −18.8406 −0.632605 −0.316303 0.948658i \(-0.602441\pi\)
−0.316303 + 0.948658i \(0.602441\pi\)
\(888\) 0 0
\(889\) 19.1978 0.643873
\(890\) 0 0
\(891\) −2.00000 −0.0670025
\(892\) 0 0
\(893\) 27.0210 0.904225
\(894\) 0 0
\(895\) −20.2399 −0.676544
\(896\) 0 0
\(897\) 0.756431 0.0252565
\(898\) 0 0
\(899\) −15.7775 −0.526208
\(900\) 0 0
\(901\) 13.3535 0.444868
\(902\) 0 0
\(903\) 10.5760 0.351947
\(904\) 0 0
\(905\) 84.0529 2.79401
\(906\) 0 0
\(907\) 9.40297 0.312221 0.156110 0.987740i \(-0.450104\pi\)
0.156110 + 0.987740i \(0.450104\pi\)
\(908\) 0 0
\(909\) 4.75643 0.157761
\(910\) 0 0
\(911\) 30.7307 1.01815 0.509077 0.860721i \(-0.329987\pi\)
0.509077 + 0.860721i \(0.329987\pi\)
\(912\) 0 0
\(913\) 27.9505 0.925026
\(914\) 0 0
\(915\) −6.15569 −0.203501
\(916\) 0 0
\(917\) 5.15197 0.170133
\(918\) 0 0
\(919\) 47.8836 1.57954 0.789768 0.613406i \(-0.210201\pi\)
0.789768 + 0.613406i \(0.210201\pi\)
\(920\) 0 0
\(921\) −5.24729 −0.172904
\(922\) 0 0
\(923\) −21.5970 −0.710875
\(924\) 0 0
\(925\) −143.179 −4.70770
\(926\) 0 0
\(927\) 23.6886 0.778037
\(928\) 0 0
\(929\) −49.9505 −1.63882 −0.819411 0.573206i \(-0.805699\pi\)
−0.819411 + 0.573206i \(0.805699\pi\)
\(930\) 0 0
\(931\) 38.3955 1.25836
\(932\) 0 0
\(933\) 15.0000 0.491078
\(934\) 0 0
\(935\) −8.79851 −0.287742
\(936\) 0 0
\(937\) 48.7911 1.59393 0.796967 0.604022i \(-0.206436\pi\)
0.796967 + 0.604022i \(0.206436\pi\)
\(938\) 0 0
\(939\) −6.60074 −0.215407
\(940\) 0 0
\(941\) 58.8552 1.91862 0.959312 0.282349i \(-0.0911136\pi\)
0.959312 + 0.282349i \(0.0911136\pi\)
\(942\) 0 0
\(943\) −1.42402 −0.0463723
\(944\) 0 0
\(945\) 21.9963 0.715539
\(946\) 0 0
\(947\) −33.3955 −1.08521 −0.542605 0.839988i \(-0.682562\pi\)
−0.542605 + 0.839988i \(0.682562\pi\)
\(948\) 0 0
\(949\) −6.79851 −0.220689
\(950\) 0 0
\(951\) −13.2436 −0.429452
\(952\) 0 0
\(953\) −5.73814 −0.185877 −0.0929384 0.995672i \(-0.529626\pi\)
−0.0929384 + 0.995672i \(0.529626\pi\)
\(954\) 0 0
\(955\) 32.4423 1.04981
\(956\) 0 0
\(957\) 4.79851 0.155114
\(958\) 0 0
\(959\) 13.7985 0.445577
\(960\) 0 0
\(961\) 12.2436 0.394954
\(962\) 0 0
\(963\) −19.5970 −0.631505
\(964\) 0 0
\(965\) 49.2619 1.58580
\(966\) 0 0
\(967\) 20.0668 0.645306 0.322653 0.946517i \(-0.395425\pi\)
0.322653 + 0.946517i \(0.395425\pi\)
\(968\) 0 0
\(969\) 6.39926 0.205574
\(970\) 0 0
\(971\) 28.3077 0.908436 0.454218 0.890891i \(-0.349919\pi\)
0.454218 + 0.890891i \(0.349919\pi\)
\(972\) 0 0
\(973\) 6.35346 0.203682
\(974\) 0 0
\(975\) 48.7911 1.56256
\(976\) 0 0
\(977\) −51.0631 −1.63365 −0.816827 0.576883i \(-0.804269\pi\)
−0.816827 + 0.576883i \(0.804269\pi\)
\(978\) 0 0
\(979\) 9.15197 0.292498
\(980\) 0 0
\(981\) −12.8901 −0.411550
\(982\) 0 0
\(983\) 30.8406 0.983662 0.491831 0.870691i \(-0.336328\pi\)
0.491831 + 0.870691i \(0.336328\pi\)
\(984\) 0 0
\(985\) 34.7911 1.10854
\(986\) 0 0
\(987\) 4.22253 0.134405
\(988\) 0 0
\(989\) −2.35346 −0.0748355
\(990\) 0 0
\(991\) 32.4203 1.02986 0.514932 0.857231i \(-0.327817\pi\)
0.514932 + 0.857231i \(0.327817\pi\)
\(992\) 0 0
\(993\) 26.3993 0.837755
\(994\) 0 0
\(995\) −76.3423 −2.42021
\(996\) 0 0
\(997\) 47.1903 1.49453 0.747266 0.664525i \(-0.231366\pi\)
0.747266 + 0.664525i \(0.231366\pi\)
\(998\) 0 0
\(999\) −49.8762 −1.57801
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 \(a_p\))