Properties

Label 8016.2.a.bg.1.13
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(4.20017\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+4.20017 q^{5}\) \(+0.497670 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+4.20017 q^{5}\) \(+0.497670 q^{7}\) \(+1.00000 q^{9}\) \(+0.310660 q^{11}\) \(-0.223370 q^{13}\) \(-4.20017 q^{15}\) \(+3.33328 q^{17}\) \(+0.261095 q^{19}\) \(-0.497670 q^{21}\) \(+9.01998 q^{23}\) \(+12.6414 q^{25}\) \(-1.00000 q^{27}\) \(+3.87692 q^{29}\) \(-0.329778 q^{31}\) \(-0.310660 q^{33}\) \(+2.09030 q^{35}\) \(-0.490531 q^{37}\) \(+0.223370 q^{39}\) \(+9.61488 q^{41}\) \(-2.34275 q^{43}\) \(+4.20017 q^{45}\) \(-9.94428 q^{47}\) \(-6.75232 q^{49}\) \(-3.33328 q^{51}\) \(+2.93441 q^{53}\) \(+1.30482 q^{55}\) \(-0.261095 q^{57}\) \(-2.69784 q^{59}\) \(-1.23520 q^{61}\) \(+0.497670 q^{63}\) \(-0.938191 q^{65}\) \(-11.6982 q^{67}\) \(-9.01998 q^{69}\) \(+3.61858 q^{71}\) \(-4.33699 q^{73}\) \(-12.6414 q^{75}\) \(+0.154606 q^{77}\) \(+2.59750 q^{79}\) \(+1.00000 q^{81}\) \(-3.06581 q^{83}\) \(+14.0003 q^{85}\) \(-3.87692 q^{87}\) \(+14.4181 q^{89}\) \(-0.111164 q^{91}\) \(+0.329778 q^{93}\) \(+1.09664 q^{95}\) \(-0.603712 q^{97}\) \(+0.310660 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 4.20017 1.87837 0.939186 0.343409i \(-0.111582\pi\)
0.939186 + 0.343409i \(0.111582\pi\)
\(6\) 0 0
\(7\) 0.497670 0.188101 0.0940507 0.995567i \(-0.470018\pi\)
0.0940507 + 0.995567i \(0.470018\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.310660 0.0936674 0.0468337 0.998903i \(-0.485087\pi\)
0.0468337 + 0.998903i \(0.485087\pi\)
\(12\) 0 0
\(13\) −0.223370 −0.0619517 −0.0309758 0.999520i \(-0.509861\pi\)
−0.0309758 + 0.999520i \(0.509861\pi\)
\(14\) 0 0
\(15\) −4.20017 −1.08448
\(16\) 0 0
\(17\) 3.33328 0.808438 0.404219 0.914662i \(-0.367543\pi\)
0.404219 + 0.914662i \(0.367543\pi\)
\(18\) 0 0
\(19\) 0.261095 0.0598993 0.0299496 0.999551i \(-0.490465\pi\)
0.0299496 + 0.999551i \(0.490465\pi\)
\(20\) 0 0
\(21\) −0.497670 −0.108600
\(22\) 0 0
\(23\) 9.01998 1.88080 0.940398 0.340075i \(-0.110452\pi\)
0.940398 + 0.340075i \(0.110452\pi\)
\(24\) 0 0
\(25\) 12.6414 2.52828
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.87692 0.719927 0.359963 0.932966i \(-0.382789\pi\)
0.359963 + 0.932966i \(0.382789\pi\)
\(30\) 0 0
\(31\) −0.329778 −0.0592299 −0.0296150 0.999561i \(-0.509428\pi\)
−0.0296150 + 0.999561i \(0.509428\pi\)
\(32\) 0 0
\(33\) −0.310660 −0.0540789
\(34\) 0 0
\(35\) 2.09030 0.353325
\(36\) 0 0
\(37\) −0.490531 −0.0806428 −0.0403214 0.999187i \(-0.512838\pi\)
−0.0403214 + 0.999187i \(0.512838\pi\)
\(38\) 0 0
\(39\) 0.223370 0.0357678
\(40\) 0 0
\(41\) 9.61488 1.50159 0.750796 0.660534i \(-0.229670\pi\)
0.750796 + 0.660534i \(0.229670\pi\)
\(42\) 0 0
\(43\) −2.34275 −0.357267 −0.178633 0.983916i \(-0.557168\pi\)
−0.178633 + 0.983916i \(0.557168\pi\)
\(44\) 0 0
\(45\) 4.20017 0.626124
\(46\) 0 0
\(47\) −9.94428 −1.45052 −0.725261 0.688474i \(-0.758281\pi\)
−0.725261 + 0.688474i \(0.758281\pi\)
\(48\) 0 0
\(49\) −6.75232 −0.964618
\(50\) 0 0
\(51\) −3.33328 −0.466752
\(52\) 0 0
\(53\) 2.93441 0.403073 0.201536 0.979481i \(-0.435407\pi\)
0.201536 + 0.979481i \(0.435407\pi\)
\(54\) 0 0
\(55\) 1.30482 0.175942
\(56\) 0 0
\(57\) −0.261095 −0.0345829
\(58\) 0 0
\(59\) −2.69784 −0.351228 −0.175614 0.984459i \(-0.556191\pi\)
−0.175614 + 0.984459i \(0.556191\pi\)
\(60\) 0 0
\(61\) −1.23520 −0.158152 −0.0790759 0.996869i \(-0.525197\pi\)
−0.0790759 + 0.996869i \(0.525197\pi\)
\(62\) 0 0
\(63\) 0.497670 0.0627005
\(64\) 0 0
\(65\) −0.938191 −0.116368
\(66\) 0 0
\(67\) −11.6982 −1.42916 −0.714582 0.699552i \(-0.753383\pi\)
−0.714582 + 0.699552i \(0.753383\pi\)
\(68\) 0 0
\(69\) −9.01998 −1.08588
\(70\) 0 0
\(71\) 3.61858 0.429446 0.214723 0.976675i \(-0.431115\pi\)
0.214723 + 0.976675i \(0.431115\pi\)
\(72\) 0 0
\(73\) −4.33699 −0.507607 −0.253803 0.967256i \(-0.581682\pi\)
−0.253803 + 0.967256i \(0.581682\pi\)
\(74\) 0 0
\(75\) −12.6414 −1.45970
\(76\) 0 0
\(77\) 0.154606 0.0176190
\(78\) 0 0
\(79\) 2.59750 0.292241 0.146121 0.989267i \(-0.453321\pi\)
0.146121 + 0.989267i \(0.453321\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.06581 −0.336517 −0.168258 0.985743i \(-0.553814\pi\)
−0.168258 + 0.985743i \(0.553814\pi\)
\(84\) 0 0
\(85\) 14.0003 1.51855
\(86\) 0 0
\(87\) −3.87692 −0.415650
\(88\) 0 0
\(89\) 14.4181 1.52832 0.764158 0.645029i \(-0.223155\pi\)
0.764158 + 0.645029i \(0.223155\pi\)
\(90\) 0 0
\(91\) −0.111164 −0.0116532
\(92\) 0 0
\(93\) 0.329778 0.0341964
\(94\) 0 0
\(95\) 1.09664 0.112513
\(96\) 0 0
\(97\) −0.603712 −0.0612977 −0.0306489 0.999530i \(-0.509757\pi\)
−0.0306489 + 0.999530i \(0.509757\pi\)
\(98\) 0 0
\(99\) 0.310660 0.0312225
\(100\) 0 0
\(101\) −1.25046 −0.124425 −0.0622126 0.998063i \(-0.519816\pi\)
−0.0622126 + 0.998063i \(0.519816\pi\)
\(102\) 0 0
\(103\) 15.1837 1.49610 0.748049 0.663643i \(-0.230991\pi\)
0.748049 + 0.663643i \(0.230991\pi\)
\(104\) 0 0
\(105\) −2.09030 −0.203992
\(106\) 0 0
\(107\) 6.86387 0.663556 0.331778 0.943358i \(-0.392352\pi\)
0.331778 + 0.943358i \(0.392352\pi\)
\(108\) 0 0
\(109\) 6.48328 0.620985 0.310493 0.950576i \(-0.399506\pi\)
0.310493 + 0.950576i \(0.399506\pi\)
\(110\) 0 0
\(111\) 0.490531 0.0465592
\(112\) 0 0
\(113\) −3.94499 −0.371113 −0.185556 0.982634i \(-0.559409\pi\)
−0.185556 + 0.982634i \(0.559409\pi\)
\(114\) 0 0
\(115\) 37.8854 3.53284
\(116\) 0 0
\(117\) −0.223370 −0.0206506
\(118\) 0 0
\(119\) 1.65887 0.152068
\(120\) 0 0
\(121\) −10.9035 −0.991226
\(122\) 0 0
\(123\) −9.61488 −0.866945
\(124\) 0 0
\(125\) 32.0952 2.87068
\(126\) 0 0
\(127\) −15.9104 −1.41182 −0.705911 0.708300i \(-0.749462\pi\)
−0.705911 + 0.708300i \(0.749462\pi\)
\(128\) 0 0
\(129\) 2.34275 0.206268
\(130\) 0 0
\(131\) −5.83534 −0.509836 −0.254918 0.966963i \(-0.582048\pi\)
−0.254918 + 0.966963i \(0.582048\pi\)
\(132\) 0 0
\(133\) 0.129939 0.0112671
\(134\) 0 0
\(135\) −4.20017 −0.361493
\(136\) 0 0
\(137\) 18.0709 1.54390 0.771949 0.635684i \(-0.219282\pi\)
0.771949 + 0.635684i \(0.219282\pi\)
\(138\) 0 0
\(139\) −1.08854 −0.0923285 −0.0461642 0.998934i \(-0.514700\pi\)
−0.0461642 + 0.998934i \(0.514700\pi\)
\(140\) 0 0
\(141\) 9.94428 0.837459
\(142\) 0 0
\(143\) −0.0693920 −0.00580285
\(144\) 0 0
\(145\) 16.2837 1.35229
\(146\) 0 0
\(147\) 6.75232 0.556922
\(148\) 0 0
\(149\) −7.57620 −0.620667 −0.310333 0.950628i \(-0.600441\pi\)
−0.310333 + 0.950628i \(0.600441\pi\)
\(150\) 0 0
\(151\) 6.06300 0.493400 0.246700 0.969092i \(-0.420654\pi\)
0.246700 + 0.969092i \(0.420654\pi\)
\(152\) 0 0
\(153\) 3.33328 0.269479
\(154\) 0 0
\(155\) −1.38512 −0.111256
\(156\) 0 0
\(157\) −6.55015 −0.522759 −0.261379 0.965236i \(-0.584177\pi\)
−0.261379 + 0.965236i \(0.584177\pi\)
\(158\) 0 0
\(159\) −2.93441 −0.232714
\(160\) 0 0
\(161\) 4.48897 0.353781
\(162\) 0 0
\(163\) 4.61424 0.361415 0.180708 0.983537i \(-0.442161\pi\)
0.180708 + 0.983537i \(0.442161\pi\)
\(164\) 0 0
\(165\) −1.30482 −0.101580
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.9501 −0.996162
\(170\) 0 0
\(171\) 0.261095 0.0199664
\(172\) 0 0
\(173\) −18.3229 −1.39306 −0.696531 0.717526i \(-0.745274\pi\)
−0.696531 + 0.717526i \(0.745274\pi\)
\(174\) 0 0
\(175\) 6.29125 0.475574
\(176\) 0 0
\(177\) 2.69784 0.202782
\(178\) 0 0
\(179\) 15.8576 1.18525 0.592625 0.805478i \(-0.298092\pi\)
0.592625 + 0.805478i \(0.298092\pi\)
\(180\) 0 0
\(181\) −6.26382 −0.465586 −0.232793 0.972526i \(-0.574786\pi\)
−0.232793 + 0.972526i \(0.574786\pi\)
\(182\) 0 0
\(183\) 1.23520 0.0913089
\(184\) 0 0
\(185\) −2.06031 −0.151477
\(186\) 0 0
\(187\) 1.03551 0.0757243
\(188\) 0 0
\(189\) −0.497670 −0.0362001
\(190\) 0 0
\(191\) 11.8669 0.858661 0.429331 0.903147i \(-0.358750\pi\)
0.429331 + 0.903147i \(0.358750\pi\)
\(192\) 0 0
\(193\) −12.0978 −0.870818 −0.435409 0.900233i \(-0.643396\pi\)
−0.435409 + 0.900233i \(0.643396\pi\)
\(194\) 0 0
\(195\) 0.938191 0.0671853
\(196\) 0 0
\(197\) −16.3800 −1.16703 −0.583513 0.812104i \(-0.698322\pi\)
−0.583513 + 0.812104i \(0.698322\pi\)
\(198\) 0 0
\(199\) −13.9684 −0.990190 −0.495095 0.868839i \(-0.664867\pi\)
−0.495095 + 0.868839i \(0.664867\pi\)
\(200\) 0 0
\(201\) 11.6982 0.825128
\(202\) 0 0
\(203\) 1.92943 0.135419
\(204\) 0 0
\(205\) 40.3841 2.82055
\(206\) 0 0
\(207\) 9.01998 0.626932
\(208\) 0 0
\(209\) 0.0811117 0.00561061
\(210\) 0 0
\(211\) 8.16435 0.562057 0.281028 0.959699i \(-0.409324\pi\)
0.281028 + 0.959699i \(0.409324\pi\)
\(212\) 0 0
\(213\) −3.61858 −0.247941
\(214\) 0 0
\(215\) −9.83996 −0.671080
\(216\) 0 0
\(217\) −0.164121 −0.0111412
\(218\) 0 0
\(219\) 4.33699 0.293067
\(220\) 0 0
\(221\) −0.744554 −0.0500841
\(222\) 0 0
\(223\) −23.9773 −1.60564 −0.802819 0.596222i \(-0.796668\pi\)
−0.802819 + 0.596222i \(0.796668\pi\)
\(224\) 0 0
\(225\) 12.6414 0.842761
\(226\) 0 0
\(227\) 19.9052 1.32115 0.660576 0.750759i \(-0.270312\pi\)
0.660576 + 0.750759i \(0.270312\pi\)
\(228\) 0 0
\(229\) −4.53054 −0.299387 −0.149693 0.988732i \(-0.547829\pi\)
−0.149693 + 0.988732i \(0.547829\pi\)
\(230\) 0 0
\(231\) −0.154606 −0.0101723
\(232\) 0 0
\(233\) 5.30087 0.347272 0.173636 0.984810i \(-0.444448\pi\)
0.173636 + 0.984810i \(0.444448\pi\)
\(234\) 0 0
\(235\) −41.7676 −2.72462
\(236\) 0 0
\(237\) −2.59750 −0.168725
\(238\) 0 0
\(239\) −7.02390 −0.454338 −0.227169 0.973855i \(-0.572947\pi\)
−0.227169 + 0.973855i \(0.572947\pi\)
\(240\) 0 0
\(241\) −6.34486 −0.408708 −0.204354 0.978897i \(-0.565509\pi\)
−0.204354 + 0.978897i \(0.565509\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −28.3609 −1.81191
\(246\) 0 0
\(247\) −0.0583208 −0.00371086
\(248\) 0 0
\(249\) 3.06581 0.194288
\(250\) 0 0
\(251\) 25.3005 1.59695 0.798476 0.602026i \(-0.205640\pi\)
0.798476 + 0.602026i \(0.205640\pi\)
\(252\) 0 0
\(253\) 2.80215 0.176169
\(254\) 0 0
\(255\) −14.0003 −0.876734
\(256\) 0 0
\(257\) −3.70489 −0.231105 −0.115552 0.993301i \(-0.536864\pi\)
−0.115552 + 0.993301i \(0.536864\pi\)
\(258\) 0 0
\(259\) −0.244122 −0.0151690
\(260\) 0 0
\(261\) 3.87692 0.239976
\(262\) 0 0
\(263\) 11.5558 0.712563 0.356282 0.934379i \(-0.384044\pi\)
0.356282 + 0.934379i \(0.384044\pi\)
\(264\) 0 0
\(265\) 12.3250 0.757120
\(266\) 0 0
\(267\) −14.4181 −0.882374
\(268\) 0 0
\(269\) −27.8733 −1.69946 −0.849731 0.527216i \(-0.823236\pi\)
−0.849731 + 0.527216i \(0.823236\pi\)
\(270\) 0 0
\(271\) 3.26815 0.198526 0.0992631 0.995061i \(-0.468351\pi\)
0.0992631 + 0.995061i \(0.468351\pi\)
\(272\) 0 0
\(273\) 0.111164 0.00672798
\(274\) 0 0
\(275\) 3.92718 0.236818
\(276\) 0 0
\(277\) −3.68912 −0.221658 −0.110829 0.993840i \(-0.535351\pi\)
−0.110829 + 0.993840i \(0.535351\pi\)
\(278\) 0 0
\(279\) −0.329778 −0.0197433
\(280\) 0 0
\(281\) −11.1453 −0.664874 −0.332437 0.943126i \(-0.607871\pi\)
−0.332437 + 0.943126i \(0.607871\pi\)
\(282\) 0 0
\(283\) 25.0956 1.49178 0.745890 0.666070i \(-0.232025\pi\)
0.745890 + 0.666070i \(0.232025\pi\)
\(284\) 0 0
\(285\) −1.09664 −0.0649595
\(286\) 0 0
\(287\) 4.78504 0.282452
\(288\) 0 0
\(289\) −5.88927 −0.346428
\(290\) 0 0
\(291\) 0.603712 0.0353902
\(292\) 0 0
\(293\) 27.4221 1.60201 0.801007 0.598655i \(-0.204298\pi\)
0.801007 + 0.598655i \(0.204298\pi\)
\(294\) 0 0
\(295\) −11.3314 −0.659738
\(296\) 0 0
\(297\) −0.310660 −0.0180263
\(298\) 0 0
\(299\) −2.01479 −0.116518
\(300\) 0 0
\(301\) −1.16592 −0.0672024
\(302\) 0 0
\(303\) 1.25046 0.0718370
\(304\) 0 0
\(305\) −5.18807 −0.297068
\(306\) 0 0
\(307\) −30.7027 −1.75229 −0.876147 0.482044i \(-0.839894\pi\)
−0.876147 + 0.482044i \(0.839894\pi\)
\(308\) 0 0
\(309\) −15.1837 −0.863773
\(310\) 0 0
\(311\) 1.33888 0.0759212 0.0379606 0.999279i \(-0.487914\pi\)
0.0379606 + 0.999279i \(0.487914\pi\)
\(312\) 0 0
\(313\) 10.5418 0.595856 0.297928 0.954588i \(-0.403704\pi\)
0.297928 + 0.954588i \(0.403704\pi\)
\(314\) 0 0
\(315\) 2.09030 0.117775
\(316\) 0 0
\(317\) −4.08789 −0.229599 −0.114800 0.993389i \(-0.536623\pi\)
−0.114800 + 0.993389i \(0.536623\pi\)
\(318\) 0 0
\(319\) 1.20440 0.0674337
\(320\) 0 0
\(321\) −6.86387 −0.383104
\(322\) 0 0
\(323\) 0.870302 0.0484249
\(324\) 0 0
\(325\) −2.82371 −0.156631
\(326\) 0 0
\(327\) −6.48328 −0.358526
\(328\) 0 0
\(329\) −4.94897 −0.272845
\(330\) 0 0
\(331\) −18.5164 −1.01776 −0.508878 0.860839i \(-0.669939\pi\)
−0.508878 + 0.860839i \(0.669939\pi\)
\(332\) 0 0
\(333\) −0.490531 −0.0268809
\(334\) 0 0
\(335\) −49.1344 −2.68450
\(336\) 0 0
\(337\) 18.2998 0.996851 0.498425 0.866933i \(-0.333912\pi\)
0.498425 + 0.866933i \(0.333912\pi\)
\(338\) 0 0
\(339\) 3.94499 0.214262
\(340\) 0 0
\(341\) −0.102449 −0.00554791
\(342\) 0 0
\(343\) −6.84412 −0.369548
\(344\) 0 0
\(345\) −37.8854 −2.03968
\(346\) 0 0
\(347\) 0.00397972 0.000213642 0 0.000106821 1.00000i \(-0.499966\pi\)
0.000106821 1.00000i \(0.499966\pi\)
\(348\) 0 0
\(349\) 7.38445 0.395280 0.197640 0.980275i \(-0.436672\pi\)
0.197640 + 0.980275i \(0.436672\pi\)
\(350\) 0 0
\(351\) 0.223370 0.0119226
\(352\) 0 0
\(353\) 13.3841 0.712362 0.356181 0.934417i \(-0.384079\pi\)
0.356181 + 0.934417i \(0.384079\pi\)
\(354\) 0 0
\(355\) 15.1986 0.806659
\(356\) 0 0
\(357\) −1.65887 −0.0877967
\(358\) 0 0
\(359\) −5.16101 −0.272388 −0.136194 0.990682i \(-0.543487\pi\)
−0.136194 + 0.990682i \(0.543487\pi\)
\(360\) 0 0
\(361\) −18.9318 −0.996412
\(362\) 0 0
\(363\) 10.9035 0.572285
\(364\) 0 0
\(365\) −18.2161 −0.953474
\(366\) 0 0
\(367\) −2.97797 −0.155449 −0.0777244 0.996975i \(-0.524765\pi\)
−0.0777244 + 0.996975i \(0.524765\pi\)
\(368\) 0 0
\(369\) 9.61488 0.500531
\(370\) 0 0
\(371\) 1.46037 0.0758185
\(372\) 0 0
\(373\) 34.4777 1.78519 0.892595 0.450860i \(-0.148883\pi\)
0.892595 + 0.450860i \(0.148883\pi\)
\(374\) 0 0
\(375\) −32.0952 −1.65739
\(376\) 0 0
\(377\) −0.865988 −0.0446007
\(378\) 0 0
\(379\) 12.8223 0.658639 0.329320 0.944218i \(-0.393181\pi\)
0.329320 + 0.944218i \(0.393181\pi\)
\(380\) 0 0
\(381\) 15.9104 0.815116
\(382\) 0 0
\(383\) 17.6965 0.904246 0.452123 0.891955i \(-0.350667\pi\)
0.452123 + 0.891955i \(0.350667\pi\)
\(384\) 0 0
\(385\) 0.649371 0.0330950
\(386\) 0 0
\(387\) −2.34275 −0.119089
\(388\) 0 0
\(389\) −1.00428 −0.0509189 −0.0254594 0.999676i \(-0.508105\pi\)
−0.0254594 + 0.999676i \(0.508105\pi\)
\(390\) 0 0
\(391\) 30.0661 1.52051
\(392\) 0 0
\(393\) 5.83534 0.294354
\(394\) 0 0
\(395\) 10.9099 0.548937
\(396\) 0 0
\(397\) 3.25402 0.163315 0.0816573 0.996660i \(-0.473979\pi\)
0.0816573 + 0.996660i \(0.473979\pi\)
\(398\) 0 0
\(399\) −0.129939 −0.00650509
\(400\) 0 0
\(401\) 7.93586 0.396298 0.198149 0.980172i \(-0.436507\pi\)
0.198149 + 0.980172i \(0.436507\pi\)
\(402\) 0 0
\(403\) 0.0736626 0.00366939
\(404\) 0 0
\(405\) 4.20017 0.208708
\(406\) 0 0
\(407\) −0.152388 −0.00755360
\(408\) 0 0
\(409\) 16.2683 0.804417 0.402208 0.915548i \(-0.368243\pi\)
0.402208 + 0.915548i \(0.368243\pi\)
\(410\) 0 0
\(411\) −18.0709 −0.891370
\(412\) 0 0
\(413\) −1.34263 −0.0660666
\(414\) 0 0
\(415\) −12.8769 −0.632104
\(416\) 0 0
\(417\) 1.08854 0.0533059
\(418\) 0 0
\(419\) 10.0257 0.489788 0.244894 0.969550i \(-0.421247\pi\)
0.244894 + 0.969550i \(0.421247\pi\)
\(420\) 0 0
\(421\) 33.3083 1.62335 0.811673 0.584112i \(-0.198557\pi\)
0.811673 + 0.584112i \(0.198557\pi\)
\(422\) 0 0
\(423\) −9.94428 −0.483507
\(424\) 0 0
\(425\) 42.1373 2.04396
\(426\) 0 0
\(427\) −0.614724 −0.0297486
\(428\) 0 0
\(429\) 0.0693920 0.00335028
\(430\) 0 0
\(431\) −29.2930 −1.41099 −0.705496 0.708714i \(-0.749276\pi\)
−0.705496 + 0.708714i \(0.749276\pi\)
\(432\) 0 0
\(433\) −29.8885 −1.43635 −0.718175 0.695862i \(-0.755022\pi\)
−0.718175 + 0.695862i \(0.755022\pi\)
\(434\) 0 0
\(435\) −16.2837 −0.780745
\(436\) 0 0
\(437\) 2.35507 0.112658
\(438\) 0 0
\(439\) 12.7837 0.610131 0.305065 0.952331i \(-0.401322\pi\)
0.305065 + 0.952331i \(0.401322\pi\)
\(440\) 0 0
\(441\) −6.75232 −0.321539
\(442\) 0 0
\(443\) 1.03002 0.0489375 0.0244688 0.999701i \(-0.492211\pi\)
0.0244688 + 0.999701i \(0.492211\pi\)
\(444\) 0 0
\(445\) 60.5585 2.87075
\(446\) 0 0
\(447\) 7.57620 0.358342
\(448\) 0 0
\(449\) 13.9295 0.657374 0.328687 0.944439i \(-0.393394\pi\)
0.328687 + 0.944439i \(0.393394\pi\)
\(450\) 0 0
\(451\) 2.98696 0.140650
\(452\) 0 0
\(453\) −6.06300 −0.284865
\(454\) 0 0
\(455\) −0.466909 −0.0218890
\(456\) 0 0
\(457\) 9.59714 0.448935 0.224468 0.974482i \(-0.427936\pi\)
0.224468 + 0.974482i \(0.427936\pi\)
\(458\) 0 0
\(459\) −3.33328 −0.155584
\(460\) 0 0
\(461\) 5.35477 0.249396 0.124698 0.992195i \(-0.460204\pi\)
0.124698 + 0.992195i \(0.460204\pi\)
\(462\) 0 0
\(463\) −17.9012 −0.831941 −0.415970 0.909378i \(-0.636558\pi\)
−0.415970 + 0.909378i \(0.636558\pi\)
\(464\) 0 0
\(465\) 1.38512 0.0642336
\(466\) 0 0
\(467\) 24.5496 1.13602 0.568010 0.823022i \(-0.307714\pi\)
0.568010 + 0.823022i \(0.307714\pi\)
\(468\) 0 0
\(469\) −5.82184 −0.268828
\(470\) 0 0
\(471\) 6.55015 0.301815
\(472\) 0 0
\(473\) −0.727799 −0.0334642
\(474\) 0 0
\(475\) 3.30061 0.151442
\(476\) 0 0
\(477\) 2.93441 0.134358
\(478\) 0 0
\(479\) 4.06290 0.185639 0.0928194 0.995683i \(-0.470412\pi\)
0.0928194 + 0.995683i \(0.470412\pi\)
\(480\) 0 0
\(481\) 0.109570 0.00499596
\(482\) 0 0
\(483\) −4.48897 −0.204255
\(484\) 0 0
\(485\) −2.53569 −0.115140
\(486\) 0 0
\(487\) 15.8338 0.717496 0.358748 0.933434i \(-0.383204\pi\)
0.358748 + 0.933434i \(0.383204\pi\)
\(488\) 0 0
\(489\) −4.61424 −0.208663
\(490\) 0 0
\(491\) −12.9595 −0.584856 −0.292428 0.956288i \(-0.594463\pi\)
−0.292428 + 0.956288i \(0.594463\pi\)
\(492\) 0 0
\(493\) 12.9229 0.582016
\(494\) 0 0
\(495\) 1.30482 0.0586474
\(496\) 0 0
\(497\) 1.80086 0.0807794
\(498\) 0 0
\(499\) −12.9159 −0.578194 −0.289097 0.957300i \(-0.593355\pi\)
−0.289097 + 0.957300i \(0.593355\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 0.878522 0.0391713 0.0195857 0.999808i \(-0.493765\pi\)
0.0195857 + 0.999808i \(0.493765\pi\)
\(504\) 0 0
\(505\) −5.25214 −0.233717
\(506\) 0 0
\(507\) 12.9501 0.575134
\(508\) 0 0
\(509\) −15.7414 −0.697727 −0.348864 0.937173i \(-0.613432\pi\)
−0.348864 + 0.937173i \(0.613432\pi\)
\(510\) 0 0
\(511\) −2.15839 −0.0954815
\(512\) 0 0
\(513\) −0.261095 −0.0115276
\(514\) 0 0
\(515\) 63.7743 2.81023
\(516\) 0 0
\(517\) −3.08928 −0.135867
\(518\) 0 0
\(519\) 18.3229 0.804285
\(520\) 0 0
\(521\) 7.29423 0.319566 0.159783 0.987152i \(-0.448921\pi\)
0.159783 + 0.987152i \(0.448921\pi\)
\(522\) 0 0
\(523\) 30.5868 1.33747 0.668734 0.743501i \(-0.266836\pi\)
0.668734 + 0.743501i \(0.266836\pi\)
\(524\) 0 0
\(525\) −6.29125 −0.274573
\(526\) 0 0
\(527\) −1.09924 −0.0478837
\(528\) 0 0
\(529\) 58.3601 2.53740
\(530\) 0 0
\(531\) −2.69784 −0.117076
\(532\) 0 0
\(533\) −2.14768 −0.0930262
\(534\) 0 0
\(535\) 28.8294 1.24640
\(536\) 0 0
\(537\) −15.8576 −0.684305
\(538\) 0 0
\(539\) −2.09767 −0.0903532
\(540\) 0 0
\(541\) −14.8053 −0.636531 −0.318265 0.948002i \(-0.603100\pi\)
−0.318265 + 0.948002i \(0.603100\pi\)
\(542\) 0 0
\(543\) 6.26382 0.268806
\(544\) 0 0
\(545\) 27.2308 1.16644
\(546\) 0 0
\(547\) −18.2584 −0.780673 −0.390337 0.920672i \(-0.627641\pi\)
−0.390337 + 0.920672i \(0.627641\pi\)
\(548\) 0 0
\(549\) −1.23520 −0.0527172
\(550\) 0 0
\(551\) 1.01225 0.0431231
\(552\) 0 0
\(553\) 1.29269 0.0549710
\(554\) 0 0
\(555\) 2.06031 0.0874554
\(556\) 0 0
\(557\) −46.3035 −1.96194 −0.980972 0.194150i \(-0.937805\pi\)
−0.980972 + 0.194150i \(0.937805\pi\)
\(558\) 0 0
\(559\) 0.523301 0.0221333
\(560\) 0 0
\(561\) −1.03551 −0.0437194
\(562\) 0 0
\(563\) −23.0152 −0.969975 −0.484987 0.874521i \(-0.661176\pi\)
−0.484987 + 0.874521i \(0.661176\pi\)
\(564\) 0 0
\(565\) −16.5696 −0.697088
\(566\) 0 0
\(567\) 0.497670 0.0209002
\(568\) 0 0
\(569\) −16.9171 −0.709203 −0.354602 0.935017i \(-0.615384\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(570\) 0 0
\(571\) −19.9472 −0.834762 −0.417381 0.908732i \(-0.637052\pi\)
−0.417381 + 0.908732i \(0.637052\pi\)
\(572\) 0 0
\(573\) −11.8669 −0.495748
\(574\) 0 0
\(575\) 114.025 4.75518
\(576\) 0 0
\(577\) 37.0310 1.54162 0.770811 0.637064i \(-0.219851\pi\)
0.770811 + 0.637064i \(0.219851\pi\)
\(578\) 0 0
\(579\) 12.0978 0.502767
\(580\) 0 0
\(581\) −1.52576 −0.0632993
\(582\) 0 0
\(583\) 0.911603 0.0377548
\(584\) 0 0
\(585\) −0.938191 −0.0387894
\(586\) 0 0
\(587\) −10.8741 −0.448821 −0.224411 0.974495i \(-0.572046\pi\)
−0.224411 + 0.974495i \(0.572046\pi\)
\(588\) 0 0
\(589\) −0.0861035 −0.00354783
\(590\) 0 0
\(591\) 16.3800 0.673783
\(592\) 0 0
\(593\) 29.4695 1.21017 0.605084 0.796162i \(-0.293140\pi\)
0.605084 + 0.796162i \(0.293140\pi\)
\(594\) 0 0
\(595\) 6.96754 0.285641
\(596\) 0 0
\(597\) 13.9684 0.571687
\(598\) 0 0
\(599\) 46.1804 1.88688 0.943441 0.331542i \(-0.107569\pi\)
0.943441 + 0.331542i \(0.107569\pi\)
\(600\) 0 0
\(601\) −13.9636 −0.569587 −0.284793 0.958589i \(-0.591925\pi\)
−0.284793 + 0.958589i \(0.591925\pi\)
\(602\) 0 0
\(603\) −11.6982 −0.476388
\(604\) 0 0
\(605\) −45.7965 −1.86189
\(606\) 0 0
\(607\) 24.4257 0.991410 0.495705 0.868491i \(-0.334910\pi\)
0.495705 + 0.868491i \(0.334910\pi\)
\(608\) 0 0
\(609\) −1.92943 −0.0781844
\(610\) 0 0
\(611\) 2.22125 0.0898622
\(612\) 0 0
\(613\) −27.1745 −1.09757 −0.548785 0.835964i \(-0.684909\pi\)
−0.548785 + 0.835964i \(0.684909\pi\)
\(614\) 0 0
\(615\) −40.3841 −1.62845
\(616\) 0 0
\(617\) −26.1446 −1.05254 −0.526271 0.850317i \(-0.676410\pi\)
−0.526271 + 0.850317i \(0.676410\pi\)
\(618\) 0 0
\(619\) 24.1844 0.972052 0.486026 0.873944i \(-0.338446\pi\)
0.486026 + 0.873944i \(0.338446\pi\)
\(620\) 0 0
\(621\) −9.01998 −0.361960
\(622\) 0 0
\(623\) 7.17545 0.287479
\(624\) 0 0
\(625\) 71.5982 2.86393
\(626\) 0 0
\(627\) −0.0811117 −0.00323929
\(628\) 0 0
\(629\) −1.63508 −0.0651947
\(630\) 0 0
\(631\) 13.0814 0.520764 0.260382 0.965506i \(-0.416152\pi\)
0.260382 + 0.965506i \(0.416152\pi\)
\(632\) 0 0
\(633\) −8.16435 −0.324504
\(634\) 0 0
\(635\) −66.8265 −2.65193
\(636\) 0 0
\(637\) 1.50827 0.0597597
\(638\) 0 0
\(639\) 3.61858 0.143149
\(640\) 0 0
\(641\) −35.8151 −1.41461 −0.707306 0.706908i \(-0.750090\pi\)
−0.707306 + 0.706908i \(0.750090\pi\)
\(642\) 0 0
\(643\) −16.5618 −0.653133 −0.326567 0.945174i \(-0.605892\pi\)
−0.326567 + 0.945174i \(0.605892\pi\)
\(644\) 0 0
\(645\) 9.83996 0.387448
\(646\) 0 0
\(647\) 37.4892 1.47385 0.736927 0.675972i \(-0.236276\pi\)
0.736927 + 0.675972i \(0.236276\pi\)
\(648\) 0 0
\(649\) −0.838109 −0.0328987
\(650\) 0 0
\(651\) 0.164121 0.00643240
\(652\) 0 0
\(653\) 5.82610 0.227993 0.113996 0.993481i \(-0.463635\pi\)
0.113996 + 0.993481i \(0.463635\pi\)
\(654\) 0 0
\(655\) −24.5094 −0.957661
\(656\) 0 0
\(657\) −4.33699 −0.169202
\(658\) 0 0
\(659\) 8.71072 0.339321 0.169661 0.985503i \(-0.445733\pi\)
0.169661 + 0.985503i \(0.445733\pi\)
\(660\) 0 0
\(661\) 3.84867 0.149696 0.0748480 0.997195i \(-0.476153\pi\)
0.0748480 + 0.997195i \(0.476153\pi\)
\(662\) 0 0
\(663\) 0.744554 0.0289161
\(664\) 0 0
\(665\) 0.545766 0.0211639
\(666\) 0 0
\(667\) 34.9698 1.35404
\(668\) 0 0
\(669\) 23.9773 0.927016
\(670\) 0 0
\(671\) −0.383728 −0.0148137
\(672\) 0 0
\(673\) 37.8497 1.45900 0.729499 0.683982i \(-0.239753\pi\)
0.729499 + 0.683982i \(0.239753\pi\)
\(674\) 0 0
\(675\) −12.6414 −0.486568
\(676\) 0 0
\(677\) −31.2208 −1.19991 −0.599955 0.800033i \(-0.704815\pi\)
−0.599955 + 0.800033i \(0.704815\pi\)
\(678\) 0 0
\(679\) −0.300449 −0.0115302
\(680\) 0 0
\(681\) −19.9052 −0.762768
\(682\) 0 0
\(683\) −0.186306 −0.00712880 −0.00356440 0.999994i \(-0.501135\pi\)
−0.00356440 + 0.999994i \(0.501135\pi\)
\(684\) 0 0
\(685\) 75.9007 2.90002
\(686\) 0 0
\(687\) 4.53054 0.172851
\(688\) 0 0
\(689\) −0.655459 −0.0249710
\(690\) 0 0
\(691\) −8.85083 −0.336702 −0.168351 0.985727i \(-0.553844\pi\)
−0.168351 + 0.985727i \(0.553844\pi\)
\(692\) 0 0
\(693\) 0.154606 0.00587299
\(694\) 0 0
\(695\) −4.57204 −0.173427
\(696\) 0 0
\(697\) 32.0491 1.21394
\(698\) 0 0
\(699\) −5.30087 −0.200497
\(700\) 0 0
\(701\) −27.7316 −1.04741 −0.523704 0.851900i \(-0.675450\pi\)
−0.523704 + 0.851900i \(0.675450\pi\)
\(702\) 0 0
\(703\) −0.128075 −0.00483045
\(704\) 0 0
\(705\) 41.7676 1.57306
\(706\) 0 0
\(707\) −0.622315 −0.0234046
\(708\) 0 0
\(709\) −43.2925 −1.62588 −0.812941 0.582345i \(-0.802135\pi\)
−0.812941 + 0.582345i \(0.802135\pi\)
\(710\) 0 0
\(711\) 2.59750 0.0974137
\(712\) 0 0
\(713\) −2.97460 −0.111399
\(714\) 0 0
\(715\) −0.291458 −0.0108999
\(716\) 0 0
\(717\) 7.02390 0.262312
\(718\) 0 0
\(719\) −3.05404 −0.113896 −0.0569482 0.998377i \(-0.518137\pi\)
−0.0569482 + 0.998377i \(0.518137\pi\)
\(720\) 0 0
\(721\) 7.55649 0.281418
\(722\) 0 0
\(723\) 6.34486 0.235968
\(724\) 0 0
\(725\) 49.0098 1.82018
\(726\) 0 0
\(727\) 26.7202 0.990998 0.495499 0.868608i \(-0.334985\pi\)
0.495499 + 0.868608i \(0.334985\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.80905 −0.288828
\(732\) 0 0
\(733\) −41.1754 −1.52085 −0.760424 0.649427i \(-0.775009\pi\)
−0.760424 + 0.649427i \(0.775009\pi\)
\(734\) 0 0
\(735\) 28.3609 1.04611
\(736\) 0 0
\(737\) −3.63416 −0.133866
\(738\) 0 0
\(739\) −20.4446 −0.752067 −0.376033 0.926606i \(-0.622712\pi\)
−0.376033 + 0.926606i \(0.622712\pi\)
\(740\) 0 0
\(741\) 0.0583208 0.00214247
\(742\) 0 0
\(743\) −33.6474 −1.23440 −0.617202 0.786805i \(-0.711734\pi\)
−0.617202 + 0.786805i \(0.711734\pi\)
\(744\) 0 0
\(745\) −31.8213 −1.16584
\(746\) 0 0
\(747\) −3.06581 −0.112172
\(748\) 0 0
\(749\) 3.41594 0.124816
\(750\) 0 0
\(751\) 17.6170 0.642853 0.321426 0.946935i \(-0.395838\pi\)
0.321426 + 0.946935i \(0.395838\pi\)
\(752\) 0 0
\(753\) −25.3005 −0.922001
\(754\) 0 0
\(755\) 25.4656 0.926789
\(756\) 0 0
\(757\) −33.9209 −1.23288 −0.616438 0.787404i \(-0.711425\pi\)
−0.616438 + 0.787404i \(0.711425\pi\)
\(758\) 0 0
\(759\) −2.80215 −0.101711
\(760\) 0 0
\(761\) −17.8074 −0.645519 −0.322760 0.946481i \(-0.604611\pi\)
−0.322760 + 0.946481i \(0.604611\pi\)
\(762\) 0 0
\(763\) 3.22653 0.116808
\(764\) 0 0
\(765\) 14.0003 0.506183
\(766\) 0 0
\(767\) 0.602616 0.0217592
\(768\) 0 0
\(769\) 38.5232 1.38918 0.694592 0.719404i \(-0.255585\pi\)
0.694592 + 0.719404i \(0.255585\pi\)
\(770\) 0 0
\(771\) 3.70489 0.133428
\(772\) 0 0
\(773\) −40.8426 −1.46901 −0.734504 0.678605i \(-0.762585\pi\)
−0.734504 + 0.678605i \(0.762585\pi\)
\(774\) 0 0
\(775\) −4.16886 −0.149750
\(776\) 0 0
\(777\) 0.244122 0.00875785
\(778\) 0 0
\(779\) 2.51040 0.0899443
\(780\) 0 0
\(781\) 1.12415 0.0402251
\(782\) 0 0
\(783\) −3.87692 −0.138550
\(784\) 0 0
\(785\) −27.5117 −0.981935
\(786\) 0 0
\(787\) 8.76921 0.312589 0.156294 0.987711i \(-0.450045\pi\)
0.156294 + 0.987711i \(0.450045\pi\)
\(788\) 0 0
\(789\) −11.5558 −0.411399
\(790\) 0 0
\(791\) −1.96330 −0.0698069
\(792\) 0 0
\(793\) 0.275907 0.00979776
\(794\) 0 0
\(795\) −12.3250 −0.437124
\(796\) 0 0
\(797\) 7.40598 0.262333 0.131167 0.991360i \(-0.458128\pi\)
0.131167 + 0.991360i \(0.458128\pi\)
\(798\) 0 0
\(799\) −33.1470 −1.17266
\(800\) 0 0
\(801\) 14.4181 0.509439
\(802\) 0 0
\(803\) −1.34733 −0.0475462
\(804\) 0 0
\(805\) 18.8544 0.664532
\(806\) 0 0
\(807\) 27.8733 0.981185
\(808\) 0 0
\(809\) 31.6141 1.11149 0.555746 0.831352i \(-0.312433\pi\)
0.555746 + 0.831352i \(0.312433\pi\)
\(810\) 0 0
\(811\) 46.7943 1.64317 0.821585 0.570086i \(-0.193090\pi\)
0.821585 + 0.570086i \(0.193090\pi\)
\(812\) 0 0
\(813\) −3.26815 −0.114619
\(814\) 0 0
\(815\) 19.3806 0.678872
\(816\) 0 0
\(817\) −0.611681 −0.0214000
\(818\) 0 0
\(819\) −0.111164 −0.00388440
\(820\) 0 0
\(821\) −44.5791 −1.55582 −0.777911 0.628374i \(-0.783721\pi\)
−0.777911 + 0.628374i \(0.783721\pi\)
\(822\) 0 0
\(823\) −27.2960 −0.951479 −0.475739 0.879586i \(-0.657819\pi\)
−0.475739 + 0.879586i \(0.657819\pi\)
\(824\) 0 0
\(825\) −3.92718 −0.136727
\(826\) 0 0
\(827\) −37.4769 −1.30320 −0.651600 0.758562i \(-0.725902\pi\)
−0.651600 + 0.758562i \(0.725902\pi\)
\(828\) 0 0
\(829\) 18.1688 0.631027 0.315514 0.948921i \(-0.397823\pi\)
0.315514 + 0.948921i \(0.397823\pi\)
\(830\) 0 0
\(831\) 3.68912 0.127974
\(832\) 0 0
\(833\) −22.5074 −0.779834
\(834\) 0 0
\(835\) 4.20017 0.145353
\(836\) 0 0
\(837\) 0.329778 0.0113988
\(838\) 0 0
\(839\) 46.6415 1.61024 0.805122 0.593109i \(-0.202100\pi\)
0.805122 + 0.593109i \(0.202100\pi\)
\(840\) 0 0
\(841\) −13.9695 −0.481705
\(842\) 0 0
\(843\) 11.1453 0.383865
\(844\) 0 0
\(845\) −54.3926 −1.87116
\(846\) 0 0
\(847\) −5.42634 −0.186451
\(848\) 0 0
\(849\) −25.0956 −0.861279
\(850\) 0 0
\(851\) −4.42458 −0.151673
\(852\) 0 0
\(853\) 24.9860 0.855504 0.427752 0.903896i \(-0.359306\pi\)
0.427752 + 0.903896i \(0.359306\pi\)
\(854\) 0 0
\(855\) 1.09664 0.0375044
\(856\) 0 0
\(857\) −15.9695 −0.545508 −0.272754 0.962084i \(-0.587935\pi\)
−0.272754 + 0.962084i \(0.587935\pi\)
\(858\) 0 0
\(859\) −32.7854 −1.11862 −0.559312 0.828957i \(-0.688935\pi\)
−0.559312 + 0.828957i \(0.688935\pi\)
\(860\) 0 0
\(861\) −4.78504 −0.163074
\(862\) 0 0
\(863\) 13.0578 0.444492 0.222246 0.974991i \(-0.428661\pi\)
0.222246 + 0.974991i \(0.428661\pi\)
\(864\) 0 0
\(865\) −76.9592 −2.61669
\(866\) 0 0
\(867\) 5.88927 0.200010
\(868\) 0 0
\(869\) 0.806937 0.0273735
\(870\) 0 0
\(871\) 2.61303 0.0885390
\(872\) 0 0
\(873\) −0.603712 −0.0204326
\(874\) 0 0
\(875\) 15.9728 0.539980
\(876\) 0 0
\(877\) 10.8855 0.367578 0.183789 0.982966i \(-0.441164\pi\)
0.183789 + 0.982966i \(0.441164\pi\)
\(878\) 0 0
\(879\) −27.4221 −0.924923
\(880\) 0 0
\(881\) 8.00765 0.269785 0.134892 0.990860i \(-0.456931\pi\)
0.134892 + 0.990860i \(0.456931\pi\)
\(882\) 0 0
\(883\) −8.54999 −0.287730 −0.143865 0.989597i \(-0.545953\pi\)
−0.143865 + 0.989597i \(0.545953\pi\)
\(884\) 0 0
\(885\) 11.3314 0.380900
\(886\) 0 0
\(887\) 5.88800 0.197700 0.0988499 0.995102i \(-0.468484\pi\)
0.0988499 + 0.995102i \(0.468484\pi\)
\(888\) 0 0
\(889\) −7.91814 −0.265566
\(890\) 0 0
\(891\) 0.310660 0.0104075
\(892\) 0 0
\(893\) −2.59640 −0.0868852
\(894\) 0 0
\(895\) 66.6045 2.22634
\(896\) 0 0
\(897\) 2.01479 0.0672720
\(898\) 0 0
\(899\) −1.27853 −0.0426412
\(900\) 0 0
\(901\) 9.78121 0.325859
\(902\) 0 0
\(903\) 1.16592 0.0387993
\(904\) 0 0
\(905\) −26.3091 −0.874544
\(906\) 0 0
\(907\) 28.9433 0.961048 0.480524 0.876982i \(-0.340447\pi\)
0.480524 + 0.876982i \(0.340447\pi\)
\(908\) 0 0
\(909\) −1.25046 −0.0414751
\(910\) 0 0
\(911\) 31.7063 1.05048 0.525239 0.850955i \(-0.323976\pi\)
0.525239 + 0.850955i \(0.323976\pi\)
\(912\) 0 0
\(913\) −0.952424 −0.0315206
\(914\) 0 0
\(915\) 5.18807 0.171512
\(916\) 0 0
\(917\) −2.90407 −0.0959009
\(918\) 0 0
\(919\) −47.1347 −1.55483 −0.777415 0.628989i \(-0.783469\pi\)
−0.777415 + 0.628989i \(0.783469\pi\)
\(920\) 0 0
\(921\) 30.7027 1.01169
\(922\) 0 0
\(923\) −0.808281 −0.0266049
\(924\) 0 0
\(925\) −6.20100 −0.203888
\(926\) 0 0
\(927\) 15.1837 0.498700
\(928\) 0 0
\(929\) 26.7815 0.878674 0.439337 0.898322i \(-0.355213\pi\)
0.439337 + 0.898322i \(0.355213\pi\)
\(930\) 0 0
\(931\) −1.76300 −0.0577799
\(932\) 0 0
\(933\) −1.33888 −0.0438331
\(934\) 0 0
\(935\) 4.34933 0.142238
\(936\) 0 0
\(937\) −9.24100 −0.301890 −0.150945 0.988542i \(-0.548232\pi\)
−0.150945 + 0.988542i \(0.548232\pi\)
\(938\) 0 0
\(939\) −10.5418 −0.344018
\(940\) 0 0
\(941\) 38.3552 1.25034 0.625172 0.780487i \(-0.285029\pi\)
0.625172 + 0.780487i \(0.285029\pi\)
\(942\) 0 0
\(943\) 86.7261 2.82419
\(944\) 0 0
\(945\) −2.09030 −0.0679973
\(946\) 0 0
\(947\) 42.5887 1.38395 0.691973 0.721923i \(-0.256742\pi\)
0.691973 + 0.721923i \(0.256742\pi\)
\(948\) 0 0
\(949\) 0.968753 0.0314471
\(950\) 0 0
\(951\) 4.08789 0.132559
\(952\) 0 0
\(953\) −44.5963 −1.44462 −0.722308 0.691572i \(-0.756919\pi\)
−0.722308 + 0.691572i \(0.756919\pi\)
\(954\) 0 0
\(955\) 49.8431 1.61289
\(956\) 0 0
\(957\) −1.20440 −0.0389328
\(958\) 0 0
\(959\) 8.99332 0.290410
\(960\) 0 0
\(961\) −30.8912 −0.996492
\(962\) 0 0
\(963\) 6.86387 0.221185
\(964\) 0 0
\(965\) −50.8128 −1.63572
\(966\) 0 0
\(967\) 23.0774 0.742118 0.371059 0.928609i \(-0.378995\pi\)
0.371059 + 0.928609i \(0.378995\pi\)
\(968\) 0 0
\(969\) −0.870302 −0.0279581
\(970\) 0 0
\(971\) −45.8648 −1.47187 −0.735936 0.677051i \(-0.763257\pi\)
−0.735936 + 0.677051i \(0.763257\pi\)
\(972\) 0 0
\(973\) −0.541732 −0.0173671
\(974\) 0 0
\(975\) 2.82371 0.0904311
\(976\) 0 0
\(977\) 47.0962 1.50674 0.753370 0.657597i \(-0.228427\pi\)
0.753370 + 0.657597i \(0.228427\pi\)
\(978\) 0 0
\(979\) 4.47912 0.143153
\(980\) 0 0
\(981\) 6.48328 0.206995
\(982\) 0 0
\(983\) 46.6561 1.48810 0.744049 0.668125i \(-0.232903\pi\)
0.744049 + 0.668125i \(0.232903\pi\)
\(984\) 0 0
\(985\) −68.7987 −2.19211
\(986\) 0 0
\(987\) 4.94897 0.157527
\(988\) 0 0
\(989\) −21.1316 −0.671946
\(990\) 0 0
\(991\) 59.1922 1.88030 0.940150 0.340760i \(-0.110684\pi\)
0.940150 + 0.340760i \(0.110684\pi\)
\(992\) 0 0
\(993\) 18.5164 0.587601
\(994\) 0 0
\(995\) −58.6694 −1.85995
\(996\) 0 0
\(997\) 58.9614 1.86733 0.933664 0.358150i \(-0.116593\pi\)
0.933664 + 0.358150i \(0.116593\pi\)
\(998\) 0 0
\(999\) 0.490531 0.0155197
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 \(a_p\))