Properties

Label 6036.2.a.i.1.2
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-3.83715 q^{5}\) \(+0.0390685 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-3.83715 q^{5}\) \(+0.0390685 q^{7}\) \(+1.00000 q^{9}\) \(-3.02930 q^{11}\) \(+2.65520 q^{13}\) \(+3.83715 q^{15}\) \(-1.40342 q^{17}\) \(-6.22877 q^{19}\) \(-0.0390685 q^{21}\) \(-6.84008 q^{23}\) \(+9.72369 q^{25}\) \(-1.00000 q^{27}\) \(-6.49534 q^{29}\) \(+5.46543 q^{31}\) \(+3.02930 q^{33}\) \(-0.149912 q^{35}\) \(+5.51070 q^{37}\) \(-2.65520 q^{39}\) \(+1.57053 q^{41}\) \(-7.27143 q^{43}\) \(-3.83715 q^{45}\) \(-8.27547 q^{47}\) \(-6.99847 q^{49}\) \(+1.40342 q^{51}\) \(+1.95739 q^{53}\) \(+11.6239 q^{55}\) \(+6.22877 q^{57}\) \(-7.20540 q^{59}\) \(-11.8372 q^{61}\) \(+0.0390685 q^{63}\) \(-10.1884 q^{65}\) \(-4.49442 q^{67}\) \(+6.84008 q^{69}\) \(-14.1096 q^{71}\) \(+10.5600 q^{73}\) \(-9.72369 q^{75}\) \(-0.118350 q^{77}\) \(+14.1134 q^{79}\) \(+1.00000 q^{81}\) \(-2.15120 q^{83}\) \(+5.38512 q^{85}\) \(+6.49534 q^{87}\) \(+14.6325 q^{89}\) \(+0.103735 q^{91}\) \(-5.46543 q^{93}\) \(+23.9007 q^{95}\) \(-10.8990 q^{97}\) \(-3.02930 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −3.83715 −1.71602 −0.858012 0.513630i \(-0.828301\pi\)
−0.858012 + 0.513630i \(0.828301\pi\)
\(6\) 0 0
\(7\) 0.0390685 0.0147665 0.00738326 0.999973i \(-0.497650\pi\)
0.00738326 + 0.999973i \(0.497650\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.02930 −0.913368 −0.456684 0.889629i \(-0.650963\pi\)
−0.456684 + 0.889629i \(0.650963\pi\)
\(12\) 0 0
\(13\) 2.65520 0.736421 0.368210 0.929743i \(-0.379971\pi\)
0.368210 + 0.929743i \(0.379971\pi\)
\(14\) 0 0
\(15\) 3.83715 0.990747
\(16\) 0 0
\(17\) −1.40342 −0.340379 −0.170189 0.985411i \(-0.554438\pi\)
−0.170189 + 0.985411i \(0.554438\pi\)
\(18\) 0 0
\(19\) −6.22877 −1.42898 −0.714489 0.699646i \(-0.753341\pi\)
−0.714489 + 0.699646i \(0.753341\pi\)
\(20\) 0 0
\(21\) −0.0390685 −0.00852545
\(22\) 0 0
\(23\) −6.84008 −1.42626 −0.713128 0.701034i \(-0.752722\pi\)
−0.713128 + 0.701034i \(0.752722\pi\)
\(24\) 0 0
\(25\) 9.72369 1.94474
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.49534 −1.20615 −0.603077 0.797683i \(-0.706059\pi\)
−0.603077 + 0.797683i \(0.706059\pi\)
\(30\) 0 0
\(31\) 5.46543 0.981620 0.490810 0.871267i \(-0.336701\pi\)
0.490810 + 0.871267i \(0.336701\pi\)
\(32\) 0 0
\(33\) 3.02930 0.527333
\(34\) 0 0
\(35\) −0.149912 −0.0253397
\(36\) 0 0
\(37\) 5.51070 0.905953 0.452977 0.891522i \(-0.350362\pi\)
0.452977 + 0.891522i \(0.350362\pi\)
\(38\) 0 0
\(39\) −2.65520 −0.425173
\(40\) 0 0
\(41\) 1.57053 0.245275 0.122638 0.992452i \(-0.460865\pi\)
0.122638 + 0.992452i \(0.460865\pi\)
\(42\) 0 0
\(43\) −7.27143 −1.10888 −0.554442 0.832223i \(-0.687068\pi\)
−0.554442 + 0.832223i \(0.687068\pi\)
\(44\) 0 0
\(45\) −3.83715 −0.572008
\(46\) 0 0
\(47\) −8.27547 −1.20710 −0.603551 0.797325i \(-0.706248\pi\)
−0.603551 + 0.797325i \(0.706248\pi\)
\(48\) 0 0
\(49\) −6.99847 −0.999782
\(50\) 0 0
\(51\) 1.40342 0.196518
\(52\) 0 0
\(53\) 1.95739 0.268869 0.134434 0.990923i \(-0.457078\pi\)
0.134434 + 0.990923i \(0.457078\pi\)
\(54\) 0 0
\(55\) 11.6239 1.56736
\(56\) 0 0
\(57\) 6.22877 0.825021
\(58\) 0 0
\(59\) −7.20540 −0.938063 −0.469031 0.883182i \(-0.655397\pi\)
−0.469031 + 0.883182i \(0.655397\pi\)
\(60\) 0 0
\(61\) −11.8372 −1.51559 −0.757797 0.652491i \(-0.773724\pi\)
−0.757797 + 0.652491i \(0.773724\pi\)
\(62\) 0 0
\(63\) 0.0390685 0.00492217
\(64\) 0 0
\(65\) −10.1884 −1.26372
\(66\) 0 0
\(67\) −4.49442 −0.549081 −0.274541 0.961576i \(-0.588526\pi\)
−0.274541 + 0.961576i \(0.588526\pi\)
\(68\) 0 0
\(69\) 6.84008 0.823449
\(70\) 0 0
\(71\) −14.1096 −1.67450 −0.837252 0.546817i \(-0.815840\pi\)
−0.837252 + 0.546817i \(0.815840\pi\)
\(72\) 0 0
\(73\) 10.5600 1.23595 0.617976 0.786197i \(-0.287953\pi\)
0.617976 + 0.786197i \(0.287953\pi\)
\(74\) 0 0
\(75\) −9.72369 −1.12279
\(76\) 0 0
\(77\) −0.118350 −0.0134873
\(78\) 0 0
\(79\) 14.1134 1.58788 0.793940 0.607997i \(-0.208027\pi\)
0.793940 + 0.607997i \(0.208027\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.15120 −0.236125 −0.118062 0.993006i \(-0.537668\pi\)
−0.118062 + 0.993006i \(0.537668\pi\)
\(84\) 0 0
\(85\) 5.38512 0.584098
\(86\) 0 0
\(87\) 6.49534 0.696373
\(88\) 0 0
\(89\) 14.6325 1.55104 0.775521 0.631322i \(-0.217487\pi\)
0.775521 + 0.631322i \(0.217487\pi\)
\(90\) 0 0
\(91\) 0.103735 0.0108744
\(92\) 0 0
\(93\) −5.46543 −0.566738
\(94\) 0 0
\(95\) 23.9007 2.45216
\(96\) 0 0
\(97\) −10.8990 −1.10663 −0.553314 0.832973i \(-0.686637\pi\)
−0.553314 + 0.832973i \(0.686637\pi\)
\(98\) 0 0
\(99\) −3.02930 −0.304456
\(100\) 0 0
\(101\) 0.205647 0.0204626 0.0102313 0.999948i \(-0.496743\pi\)
0.0102313 + 0.999948i \(0.496743\pi\)
\(102\) 0 0
\(103\) −12.4002 −1.22183 −0.610916 0.791696i \(-0.709199\pi\)
−0.610916 + 0.791696i \(0.709199\pi\)
\(104\) 0 0
\(105\) 0.149912 0.0146299
\(106\) 0 0
\(107\) −2.40725 −0.232718 −0.116359 0.993207i \(-0.537122\pi\)
−0.116359 + 0.993207i \(0.537122\pi\)
\(108\) 0 0
\(109\) −7.79279 −0.746414 −0.373207 0.927748i \(-0.621742\pi\)
−0.373207 + 0.927748i \(0.621742\pi\)
\(110\) 0 0
\(111\) −5.51070 −0.523052
\(112\) 0 0
\(113\) 2.79544 0.262973 0.131487 0.991318i \(-0.458025\pi\)
0.131487 + 0.991318i \(0.458025\pi\)
\(114\) 0 0
\(115\) 26.2464 2.44749
\(116\) 0 0
\(117\) 2.65520 0.245474
\(118\) 0 0
\(119\) −0.0548295 −0.00502621
\(120\) 0 0
\(121\) −1.82335 −0.165759
\(122\) 0 0
\(123\) −1.57053 −0.141610
\(124\) 0 0
\(125\) −18.1255 −1.62119
\(126\) 0 0
\(127\) 0.615625 0.0546279 0.0273139 0.999627i \(-0.491305\pi\)
0.0273139 + 0.999627i \(0.491305\pi\)
\(128\) 0 0
\(129\) 7.27143 0.640214
\(130\) 0 0
\(131\) 1.72461 0.150680 0.0753398 0.997158i \(-0.475996\pi\)
0.0753398 + 0.997158i \(0.475996\pi\)
\(132\) 0 0
\(133\) −0.243349 −0.0211010
\(134\) 0 0
\(135\) 3.83715 0.330249
\(136\) 0 0
\(137\) 5.88340 0.502653 0.251326 0.967902i \(-0.419133\pi\)
0.251326 + 0.967902i \(0.419133\pi\)
\(138\) 0 0
\(139\) 0.606430 0.0514367 0.0257184 0.999669i \(-0.491813\pi\)
0.0257184 + 0.999669i \(0.491813\pi\)
\(140\) 0 0
\(141\) 8.27547 0.696920
\(142\) 0 0
\(143\) −8.04340 −0.672623
\(144\) 0 0
\(145\) 24.9236 2.06979
\(146\) 0 0
\(147\) 6.99847 0.577224
\(148\) 0 0
\(149\) −8.74814 −0.716676 −0.358338 0.933592i \(-0.616656\pi\)
−0.358338 + 0.933592i \(0.616656\pi\)
\(150\) 0 0
\(151\) −5.73638 −0.466820 −0.233410 0.972378i \(-0.574988\pi\)
−0.233410 + 0.972378i \(0.574988\pi\)
\(152\) 0 0
\(153\) −1.40342 −0.113460
\(154\) 0 0
\(155\) −20.9716 −1.68448
\(156\) 0 0
\(157\) −6.84099 −0.545970 −0.272985 0.962018i \(-0.588011\pi\)
−0.272985 + 0.962018i \(0.588011\pi\)
\(158\) 0 0
\(159\) −1.95739 −0.155231
\(160\) 0 0
\(161\) −0.267232 −0.0210608
\(162\) 0 0
\(163\) 9.56041 0.748829 0.374414 0.927261i \(-0.377844\pi\)
0.374414 + 0.927261i \(0.377844\pi\)
\(164\) 0 0
\(165\) −11.6239 −0.904916
\(166\) 0 0
\(167\) 6.47894 0.501355 0.250678 0.968071i \(-0.419347\pi\)
0.250678 + 0.968071i \(0.419347\pi\)
\(168\) 0 0
\(169\) −5.94990 −0.457684
\(170\) 0 0
\(171\) −6.22877 −0.476326
\(172\) 0 0
\(173\) 18.7896 1.42855 0.714274 0.699866i \(-0.246757\pi\)
0.714274 + 0.699866i \(0.246757\pi\)
\(174\) 0 0
\(175\) 0.379890 0.0287170
\(176\) 0 0
\(177\) 7.20540 0.541591
\(178\) 0 0
\(179\) −3.42836 −0.256248 −0.128124 0.991758i \(-0.540896\pi\)
−0.128124 + 0.991758i \(0.540896\pi\)
\(180\) 0 0
\(181\) −24.1458 −1.79474 −0.897370 0.441279i \(-0.854525\pi\)
−0.897370 + 0.441279i \(0.854525\pi\)
\(182\) 0 0
\(183\) 11.8372 0.875028
\(184\) 0 0
\(185\) −21.1454 −1.55464
\(186\) 0 0
\(187\) 4.25137 0.310891
\(188\) 0 0
\(189\) −0.0390685 −0.00284182
\(190\) 0 0
\(191\) 1.90983 0.138191 0.0690953 0.997610i \(-0.477989\pi\)
0.0690953 + 0.997610i \(0.477989\pi\)
\(192\) 0 0
\(193\) 11.8675 0.854243 0.427121 0.904194i \(-0.359528\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(194\) 0 0
\(195\) 10.1884 0.729607
\(196\) 0 0
\(197\) 12.4184 0.884775 0.442387 0.896824i \(-0.354132\pi\)
0.442387 + 0.896824i \(0.354132\pi\)
\(198\) 0 0
\(199\) 23.2061 1.64504 0.822519 0.568737i \(-0.192568\pi\)
0.822519 + 0.568737i \(0.192568\pi\)
\(200\) 0 0
\(201\) 4.49442 0.317012
\(202\) 0 0
\(203\) −0.253763 −0.0178107
\(204\) 0 0
\(205\) −6.02634 −0.420898
\(206\) 0 0
\(207\) −6.84008 −0.475418
\(208\) 0 0
\(209\) 18.8688 1.30518
\(210\) 0 0
\(211\) 24.9393 1.71689 0.858446 0.512904i \(-0.171430\pi\)
0.858446 + 0.512904i \(0.171430\pi\)
\(212\) 0 0
\(213\) 14.1096 0.966776
\(214\) 0 0
\(215\) 27.9015 1.90287
\(216\) 0 0
\(217\) 0.213526 0.0144951
\(218\) 0 0
\(219\) −10.5600 −0.713577
\(220\) 0 0
\(221\) −3.72636 −0.250662
\(222\) 0 0
\(223\) 3.56656 0.238834 0.119417 0.992844i \(-0.461897\pi\)
0.119417 + 0.992844i \(0.461897\pi\)
\(224\) 0 0
\(225\) 9.72369 0.648246
\(226\) 0 0
\(227\) −18.7918 −1.24726 −0.623629 0.781721i \(-0.714342\pi\)
−0.623629 + 0.781721i \(0.714342\pi\)
\(228\) 0 0
\(229\) 27.8157 1.83811 0.919057 0.394124i \(-0.128952\pi\)
0.919057 + 0.394124i \(0.128952\pi\)
\(230\) 0 0
\(231\) 0.118350 0.00778687
\(232\) 0 0
\(233\) −20.3547 −1.33348 −0.666741 0.745290i \(-0.732311\pi\)
−0.666741 + 0.745290i \(0.732311\pi\)
\(234\) 0 0
\(235\) 31.7542 2.07142
\(236\) 0 0
\(237\) −14.1134 −0.916763
\(238\) 0 0
\(239\) 5.41325 0.350154 0.175077 0.984555i \(-0.443983\pi\)
0.175077 + 0.984555i \(0.443983\pi\)
\(240\) 0 0
\(241\) −10.0541 −0.647643 −0.323821 0.946118i \(-0.604968\pi\)
−0.323821 + 0.946118i \(0.604968\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 26.8542 1.71565
\(246\) 0 0
\(247\) −16.5387 −1.05233
\(248\) 0 0
\(249\) 2.15120 0.136327
\(250\) 0 0
\(251\) 6.24106 0.393932 0.196966 0.980410i \(-0.436891\pi\)
0.196966 + 0.980410i \(0.436891\pi\)
\(252\) 0 0
\(253\) 20.7206 1.30270
\(254\) 0 0
\(255\) −5.38512 −0.337229
\(256\) 0 0
\(257\) 20.4905 1.27817 0.639083 0.769138i \(-0.279314\pi\)
0.639083 + 0.769138i \(0.279314\pi\)
\(258\) 0 0
\(259\) 0.215295 0.0133778
\(260\) 0 0
\(261\) −6.49534 −0.402051
\(262\) 0 0
\(263\) 24.3112 1.49909 0.749547 0.661951i \(-0.230271\pi\)
0.749547 + 0.661951i \(0.230271\pi\)
\(264\) 0 0
\(265\) −7.51080 −0.461385
\(266\) 0 0
\(267\) −14.6325 −0.895494
\(268\) 0 0
\(269\) 0.374620 0.0228410 0.0114205 0.999935i \(-0.496365\pi\)
0.0114205 + 0.999935i \(0.496365\pi\)
\(270\) 0 0
\(271\) 4.25550 0.258503 0.129252 0.991612i \(-0.458742\pi\)
0.129252 + 0.991612i \(0.458742\pi\)
\(272\) 0 0
\(273\) −0.103735 −0.00627832
\(274\) 0 0
\(275\) −29.4560 −1.77626
\(276\) 0 0
\(277\) −4.55446 −0.273651 −0.136826 0.990595i \(-0.543690\pi\)
−0.136826 + 0.990595i \(0.543690\pi\)
\(278\) 0 0
\(279\) 5.46543 0.327207
\(280\) 0 0
\(281\) 29.1317 1.73785 0.868924 0.494945i \(-0.164812\pi\)
0.868924 + 0.494945i \(0.164812\pi\)
\(282\) 0 0
\(283\) 22.7994 1.35529 0.677643 0.735391i \(-0.263001\pi\)
0.677643 + 0.735391i \(0.263001\pi\)
\(284\) 0 0
\(285\) −23.9007 −1.41576
\(286\) 0 0
\(287\) 0.0613582 0.00362186
\(288\) 0 0
\(289\) −15.0304 −0.884142
\(290\) 0 0
\(291\) 10.8990 0.638912
\(292\) 0 0
\(293\) 22.1807 1.29581 0.647906 0.761720i \(-0.275645\pi\)
0.647906 + 0.761720i \(0.275645\pi\)
\(294\) 0 0
\(295\) 27.6482 1.60974
\(296\) 0 0
\(297\) 3.02930 0.175778
\(298\) 0 0
\(299\) −18.1618 −1.05032
\(300\) 0 0
\(301\) −0.284084 −0.0163743
\(302\) 0 0
\(303\) −0.205647 −0.0118141
\(304\) 0 0
\(305\) 45.4209 2.60079
\(306\) 0 0
\(307\) 17.2511 0.984570 0.492285 0.870434i \(-0.336162\pi\)
0.492285 + 0.870434i \(0.336162\pi\)
\(308\) 0 0
\(309\) 12.4002 0.705425
\(310\) 0 0
\(311\) 6.72157 0.381145 0.190573 0.981673i \(-0.438966\pi\)
0.190573 + 0.981673i \(0.438966\pi\)
\(312\) 0 0
\(313\) −17.7539 −1.00351 −0.501756 0.865009i \(-0.667312\pi\)
−0.501756 + 0.865009i \(0.667312\pi\)
\(314\) 0 0
\(315\) −0.149912 −0.00844656
\(316\) 0 0
\(317\) −24.9958 −1.40390 −0.701951 0.712225i \(-0.747687\pi\)
−0.701951 + 0.712225i \(0.747687\pi\)
\(318\) 0 0
\(319\) 19.6763 1.10166
\(320\) 0 0
\(321\) 2.40725 0.134360
\(322\) 0 0
\(323\) 8.74157 0.486394
\(324\) 0 0
\(325\) 25.8184 1.43215
\(326\) 0 0
\(327\) 7.79279 0.430942
\(328\) 0 0
\(329\) −0.323310 −0.0178247
\(330\) 0 0
\(331\) 8.54725 0.469799 0.234900 0.972020i \(-0.424524\pi\)
0.234900 + 0.972020i \(0.424524\pi\)
\(332\) 0 0
\(333\) 5.51070 0.301984
\(334\) 0 0
\(335\) 17.2458 0.942236
\(336\) 0 0
\(337\) 30.7198 1.67342 0.836708 0.547649i \(-0.184477\pi\)
0.836708 + 0.547649i \(0.184477\pi\)
\(338\) 0 0
\(339\) −2.79544 −0.151828
\(340\) 0 0
\(341\) −16.5564 −0.896580
\(342\) 0 0
\(343\) −0.546900 −0.0295298
\(344\) 0 0
\(345\) −26.2464 −1.41306
\(346\) 0 0
\(347\) 0.299088 0.0160559 0.00802795 0.999968i \(-0.497445\pi\)
0.00802795 + 0.999968i \(0.497445\pi\)
\(348\) 0 0
\(349\) −0.665481 −0.0356224 −0.0178112 0.999841i \(-0.505670\pi\)
−0.0178112 + 0.999841i \(0.505670\pi\)
\(350\) 0 0
\(351\) −2.65520 −0.141724
\(352\) 0 0
\(353\) 0.411030 0.0218769 0.0109385 0.999940i \(-0.496518\pi\)
0.0109385 + 0.999940i \(0.496518\pi\)
\(354\) 0 0
\(355\) 54.1407 2.87349
\(356\) 0 0
\(357\) 0.0548295 0.00290188
\(358\) 0 0
\(359\) 7.60341 0.401293 0.200646 0.979664i \(-0.435696\pi\)
0.200646 + 0.979664i \(0.435696\pi\)
\(360\) 0 0
\(361\) 19.7976 1.04198
\(362\) 0 0
\(363\) 1.82335 0.0957011
\(364\) 0 0
\(365\) −40.5202 −2.12092
\(366\) 0 0
\(367\) −30.9614 −1.61617 −0.808085 0.589066i \(-0.799496\pi\)
−0.808085 + 0.589066i \(0.799496\pi\)
\(368\) 0 0
\(369\) 1.57053 0.0817584
\(370\) 0 0
\(371\) 0.0764724 0.00397025
\(372\) 0 0
\(373\) 3.33616 0.172740 0.0863699 0.996263i \(-0.472473\pi\)
0.0863699 + 0.996263i \(0.472473\pi\)
\(374\) 0 0
\(375\) 18.1255 0.935996
\(376\) 0 0
\(377\) −17.2464 −0.888237
\(378\) 0 0
\(379\) −27.6981 −1.42276 −0.711379 0.702809i \(-0.751929\pi\)
−0.711379 + 0.702809i \(0.751929\pi\)
\(380\) 0 0
\(381\) −0.615625 −0.0315394
\(382\) 0 0
\(383\) 10.3897 0.530890 0.265445 0.964126i \(-0.414481\pi\)
0.265445 + 0.964126i \(0.414481\pi\)
\(384\) 0 0
\(385\) 0.454127 0.0231445
\(386\) 0 0
\(387\) −7.27143 −0.369628
\(388\) 0 0
\(389\) 24.8787 1.26140 0.630701 0.776026i \(-0.282767\pi\)
0.630701 + 0.776026i \(0.282767\pi\)
\(390\) 0 0
\(391\) 9.59949 0.485467
\(392\) 0 0
\(393\) −1.72461 −0.0869949
\(394\) 0 0
\(395\) −54.1551 −2.72484
\(396\) 0 0
\(397\) 18.6566 0.936348 0.468174 0.883636i \(-0.344912\pi\)
0.468174 + 0.883636i \(0.344912\pi\)
\(398\) 0 0
\(399\) 0.243349 0.0121827
\(400\) 0 0
\(401\) −38.3355 −1.91439 −0.957193 0.289451i \(-0.906527\pi\)
−0.957193 + 0.289451i \(0.906527\pi\)
\(402\) 0 0
\(403\) 14.5118 0.722885
\(404\) 0 0
\(405\) −3.83715 −0.190669
\(406\) 0 0
\(407\) −16.6936 −0.827469
\(408\) 0 0
\(409\) 31.5485 1.55997 0.779986 0.625797i \(-0.215226\pi\)
0.779986 + 0.625797i \(0.215226\pi\)
\(410\) 0 0
\(411\) −5.88340 −0.290207
\(412\) 0 0
\(413\) −0.281504 −0.0138519
\(414\) 0 0
\(415\) 8.25446 0.405195
\(416\) 0 0
\(417\) −0.606430 −0.0296970
\(418\) 0 0
\(419\) −37.9946 −1.85616 −0.928078 0.372386i \(-0.878540\pi\)
−0.928078 + 0.372386i \(0.878540\pi\)
\(420\) 0 0
\(421\) −3.56960 −0.173972 −0.0869858 0.996210i \(-0.527723\pi\)
−0.0869858 + 0.996210i \(0.527723\pi\)
\(422\) 0 0
\(423\) −8.27547 −0.402367
\(424\) 0 0
\(425\) −13.6464 −0.661948
\(426\) 0 0
\(427\) −0.462460 −0.0223800
\(428\) 0 0
\(429\) 8.04340 0.388339
\(430\) 0 0
\(431\) −8.73333 −0.420670 −0.210335 0.977629i \(-0.567455\pi\)
−0.210335 + 0.977629i \(0.567455\pi\)
\(432\) 0 0
\(433\) −0.385145 −0.0185089 −0.00925443 0.999957i \(-0.502946\pi\)
−0.00925443 + 0.999957i \(0.502946\pi\)
\(434\) 0 0
\(435\) −24.9236 −1.19499
\(436\) 0 0
\(437\) 42.6053 2.03809
\(438\) 0 0
\(439\) 12.5407 0.598534 0.299267 0.954169i \(-0.403258\pi\)
0.299267 + 0.954169i \(0.403258\pi\)
\(440\) 0 0
\(441\) −6.99847 −0.333261
\(442\) 0 0
\(443\) 3.95596 0.187953 0.0939766 0.995574i \(-0.470042\pi\)
0.0939766 + 0.995574i \(0.470042\pi\)
\(444\) 0 0
\(445\) −56.1470 −2.66162
\(446\) 0 0
\(447\) 8.74814 0.413773
\(448\) 0 0
\(449\) −28.8450 −1.36128 −0.680639 0.732619i \(-0.738298\pi\)
−0.680639 + 0.732619i \(0.738298\pi\)
\(450\) 0 0
\(451\) −4.75760 −0.224026
\(452\) 0 0
\(453\) 5.73638 0.269519
\(454\) 0 0
\(455\) −0.398046 −0.0186607
\(456\) 0 0
\(457\) 11.9524 0.559112 0.279556 0.960129i \(-0.409813\pi\)
0.279556 + 0.960129i \(0.409813\pi\)
\(458\) 0 0
\(459\) 1.40342 0.0655059
\(460\) 0 0
\(461\) 0.157915 0.00735484 0.00367742 0.999993i \(-0.498829\pi\)
0.00367742 + 0.999993i \(0.498829\pi\)
\(462\) 0 0
\(463\) −25.9683 −1.20685 −0.603424 0.797421i \(-0.706197\pi\)
−0.603424 + 0.797421i \(0.706197\pi\)
\(464\) 0 0
\(465\) 20.9716 0.972537
\(466\) 0 0
\(467\) −8.43023 −0.390104 −0.195052 0.980793i \(-0.562488\pi\)
−0.195052 + 0.980793i \(0.562488\pi\)
\(468\) 0 0
\(469\) −0.175590 −0.00810801
\(470\) 0 0
\(471\) 6.84099 0.315216
\(472\) 0 0
\(473\) 22.0273 1.01282
\(474\) 0 0
\(475\) −60.5667 −2.77899
\(476\) 0 0
\(477\) 1.95739 0.0896228
\(478\) 0 0
\(479\) 13.2764 0.606615 0.303307 0.952893i \(-0.401909\pi\)
0.303307 + 0.952893i \(0.401909\pi\)
\(480\) 0 0
\(481\) 14.6320 0.667163
\(482\) 0 0
\(483\) 0.267232 0.0121595
\(484\) 0 0
\(485\) 41.8212 1.89900
\(486\) 0 0
\(487\) −18.0896 −0.819718 −0.409859 0.912149i \(-0.634422\pi\)
−0.409859 + 0.912149i \(0.634422\pi\)
\(488\) 0 0
\(489\) −9.56041 −0.432337
\(490\) 0 0
\(491\) −27.7182 −1.25091 −0.625453 0.780262i \(-0.715086\pi\)
−0.625453 + 0.780262i \(0.715086\pi\)
\(492\) 0 0
\(493\) 9.11567 0.410549
\(494\) 0 0
\(495\) 11.6239 0.522454
\(496\) 0 0
\(497\) −0.551242 −0.0247266
\(498\) 0 0
\(499\) 21.6472 0.969064 0.484532 0.874774i \(-0.338990\pi\)
0.484532 + 0.874774i \(0.338990\pi\)
\(500\) 0 0
\(501\) −6.47894 −0.289458
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −0.789097 −0.0351144
\(506\) 0 0
\(507\) 5.94990 0.264244
\(508\) 0 0
\(509\) 14.9445 0.662402 0.331201 0.943560i \(-0.392546\pi\)
0.331201 + 0.943560i \(0.392546\pi\)
\(510\) 0 0
\(511\) 0.412563 0.0182507
\(512\) 0 0
\(513\) 6.22877 0.275007
\(514\) 0 0
\(515\) 47.5815 2.09669
\(516\) 0 0
\(517\) 25.0689 1.10253
\(518\) 0 0
\(519\) −18.7896 −0.824772
\(520\) 0 0
\(521\) 32.0317 1.40334 0.701668 0.712504i \(-0.252439\pi\)
0.701668 + 0.712504i \(0.252439\pi\)
\(522\) 0 0
\(523\) −44.7550 −1.95700 −0.978500 0.206245i \(-0.933876\pi\)
−0.978500 + 0.206245i \(0.933876\pi\)
\(524\) 0 0
\(525\) −0.379890 −0.0165798
\(526\) 0 0
\(527\) −7.67028 −0.334123
\(528\) 0 0
\(529\) 23.7867 1.03420
\(530\) 0 0
\(531\) −7.20540 −0.312688
\(532\) 0 0
\(533\) 4.17007 0.180626
\(534\) 0 0
\(535\) 9.23698 0.399349
\(536\) 0 0
\(537\) 3.42836 0.147945
\(538\) 0 0
\(539\) 21.2005 0.913169
\(540\) 0 0
\(541\) −30.9371 −1.33009 −0.665046 0.746802i \(-0.731588\pi\)
−0.665046 + 0.746802i \(0.731588\pi\)
\(542\) 0 0
\(543\) 24.1458 1.03619
\(544\) 0 0
\(545\) 29.9021 1.28086
\(546\) 0 0
\(547\) −24.9499 −1.06678 −0.533390 0.845869i \(-0.679082\pi\)
−0.533390 + 0.845869i \(0.679082\pi\)
\(548\) 0 0
\(549\) −11.8372 −0.505198
\(550\) 0 0
\(551\) 40.4580 1.72357
\(552\) 0 0
\(553\) 0.551389 0.0234474
\(554\) 0 0
\(555\) 21.1454 0.897570
\(556\) 0 0
\(557\) 4.82451 0.204421 0.102210 0.994763i \(-0.467408\pi\)
0.102210 + 0.994763i \(0.467408\pi\)
\(558\) 0 0
\(559\) −19.3071 −0.816604
\(560\) 0 0
\(561\) −4.25137 −0.179493
\(562\) 0 0
\(563\) 36.5910 1.54213 0.771063 0.636759i \(-0.219725\pi\)
0.771063 + 0.636759i \(0.219725\pi\)
\(564\) 0 0
\(565\) −10.7265 −0.451268
\(566\) 0 0
\(567\) 0.0390685 0.00164072
\(568\) 0 0
\(569\) 22.7838 0.955148 0.477574 0.878592i \(-0.341516\pi\)
0.477574 + 0.878592i \(0.341516\pi\)
\(570\) 0 0
\(571\) 14.9495 0.625616 0.312808 0.949816i \(-0.398730\pi\)
0.312808 + 0.949816i \(0.398730\pi\)
\(572\) 0 0
\(573\) −1.90983 −0.0797844
\(574\) 0 0
\(575\) −66.5108 −2.77369
\(576\) 0 0
\(577\) 25.1589 1.04738 0.523690 0.851909i \(-0.324555\pi\)
0.523690 + 0.851909i \(0.324555\pi\)
\(578\) 0 0
\(579\) −11.8675 −0.493197
\(580\) 0 0
\(581\) −0.0840441 −0.00348674
\(582\) 0 0
\(583\) −5.92953 −0.245576
\(584\) 0 0
\(585\) −10.1884 −0.421239
\(586\) 0 0
\(587\) 6.76003 0.279016 0.139508 0.990221i \(-0.455448\pi\)
0.139508 + 0.990221i \(0.455448\pi\)
\(588\) 0 0
\(589\) −34.0429 −1.40271
\(590\) 0 0
\(591\) −12.4184 −0.510825
\(592\) 0 0
\(593\) −6.25925 −0.257037 −0.128518 0.991707i \(-0.541022\pi\)
−0.128518 + 0.991707i \(0.541022\pi\)
\(594\) 0 0
\(595\) 0.210389 0.00862509
\(596\) 0 0
\(597\) −23.2061 −0.949763
\(598\) 0 0
\(599\) 10.4362 0.426413 0.213207 0.977007i \(-0.431609\pi\)
0.213207 + 0.977007i \(0.431609\pi\)
\(600\) 0 0
\(601\) −29.3706 −1.19805 −0.599026 0.800730i \(-0.704445\pi\)
−0.599026 + 0.800730i \(0.704445\pi\)
\(602\) 0 0
\(603\) −4.49442 −0.183027
\(604\) 0 0
\(605\) 6.99646 0.284447
\(606\) 0 0
\(607\) 28.4328 1.15405 0.577026 0.816726i \(-0.304213\pi\)
0.577026 + 0.816726i \(0.304213\pi\)
\(608\) 0 0
\(609\) 0.253763 0.0102830
\(610\) 0 0
\(611\) −21.9731 −0.888935
\(612\) 0 0
\(613\) 26.1123 1.05467 0.527333 0.849659i \(-0.323192\pi\)
0.527333 + 0.849659i \(0.323192\pi\)
\(614\) 0 0
\(615\) 6.02634 0.243006
\(616\) 0 0
\(617\) −7.73815 −0.311526 −0.155763 0.987794i \(-0.549784\pi\)
−0.155763 + 0.987794i \(0.549784\pi\)
\(618\) 0 0
\(619\) 42.1463 1.69400 0.847002 0.531590i \(-0.178405\pi\)
0.847002 + 0.531590i \(0.178405\pi\)
\(620\) 0 0
\(621\) 6.84008 0.274483
\(622\) 0 0
\(623\) 0.571670 0.0229035
\(624\) 0 0
\(625\) 20.9317 0.837268
\(626\) 0 0
\(627\) −18.8688 −0.753548
\(628\) 0 0
\(629\) −7.73381 −0.308367
\(630\) 0 0
\(631\) −42.0497 −1.67397 −0.836986 0.547224i \(-0.815685\pi\)
−0.836986 + 0.547224i \(0.815685\pi\)
\(632\) 0 0
\(633\) −24.9393 −0.991248
\(634\) 0 0
\(635\) −2.36224 −0.0937427
\(636\) 0 0
\(637\) −18.5824 −0.736260
\(638\) 0 0
\(639\) −14.1096 −0.558168
\(640\) 0 0
\(641\) 6.13011 0.242125 0.121062 0.992645i \(-0.461370\pi\)
0.121062 + 0.992645i \(0.461370\pi\)
\(642\) 0 0
\(643\) −35.9585 −1.41807 −0.709033 0.705176i \(-0.750868\pi\)
−0.709033 + 0.705176i \(0.750868\pi\)
\(644\) 0 0
\(645\) −27.9015 −1.09862
\(646\) 0 0
\(647\) −15.1620 −0.596080 −0.298040 0.954553i \(-0.596333\pi\)
−0.298040 + 0.954553i \(0.596333\pi\)
\(648\) 0 0
\(649\) 21.8273 0.856796
\(650\) 0 0
\(651\) −0.213526 −0.00836875
\(652\) 0 0
\(653\) −6.79559 −0.265932 −0.132966 0.991121i \(-0.542450\pi\)
−0.132966 + 0.991121i \(0.542450\pi\)
\(654\) 0 0
\(655\) −6.61757 −0.258570
\(656\) 0 0
\(657\) 10.5600 0.411984
\(658\) 0 0
\(659\) 6.81047 0.265298 0.132649 0.991163i \(-0.457652\pi\)
0.132649 + 0.991163i \(0.457652\pi\)
\(660\) 0 0
\(661\) −18.7175 −0.728026 −0.364013 0.931394i \(-0.618594\pi\)
−0.364013 + 0.931394i \(0.618594\pi\)
\(662\) 0 0
\(663\) 3.72636 0.144720
\(664\) 0 0
\(665\) 0.933766 0.0362099
\(666\) 0 0
\(667\) 44.4286 1.72028
\(668\) 0 0
\(669\) −3.56656 −0.137891
\(670\) 0 0
\(671\) 35.8583 1.38429
\(672\) 0 0
\(673\) 22.3181 0.860298 0.430149 0.902758i \(-0.358461\pi\)
0.430149 + 0.902758i \(0.358461\pi\)
\(674\) 0 0
\(675\) −9.72369 −0.374265
\(676\) 0 0
\(677\) −10.8892 −0.418504 −0.209252 0.977862i \(-0.567103\pi\)
−0.209252 + 0.977862i \(0.567103\pi\)
\(678\) 0 0
\(679\) −0.425809 −0.0163410
\(680\) 0 0
\(681\) 18.7918 0.720105
\(682\) 0 0
\(683\) −42.9652 −1.64402 −0.822009 0.569475i \(-0.807147\pi\)
−0.822009 + 0.569475i \(0.807147\pi\)
\(684\) 0 0
\(685\) −22.5755 −0.862564
\(686\) 0 0
\(687\) −27.8157 −1.06124
\(688\) 0 0
\(689\) 5.19727 0.198000
\(690\) 0 0
\(691\) −38.1065 −1.44964 −0.724819 0.688939i \(-0.758077\pi\)
−0.724819 + 0.688939i \(0.758077\pi\)
\(692\) 0 0
\(693\) −0.118350 −0.00449575
\(694\) 0 0
\(695\) −2.32696 −0.0882666
\(696\) 0 0
\(697\) −2.20411 −0.0834865
\(698\) 0 0
\(699\) 20.3547 0.769886
\(700\) 0 0
\(701\) 15.6026 0.589303 0.294652 0.955605i \(-0.404796\pi\)
0.294652 + 0.955605i \(0.404796\pi\)
\(702\) 0 0
\(703\) −34.3249 −1.29459
\(704\) 0 0
\(705\) −31.7542 −1.19593
\(706\) 0 0
\(707\) 0.00803432 0.000302162 0
\(708\) 0 0
\(709\) 17.2373 0.647362 0.323681 0.946166i \(-0.395080\pi\)
0.323681 + 0.946166i \(0.395080\pi\)
\(710\) 0 0
\(711\) 14.1134 0.529293
\(712\) 0 0
\(713\) −37.3840 −1.40004
\(714\) 0 0
\(715\) 30.8637 1.15424
\(716\) 0 0
\(717\) −5.41325 −0.202161
\(718\) 0 0
\(719\) −8.81684 −0.328813 −0.164406 0.986393i \(-0.552571\pi\)
−0.164406 + 0.986393i \(0.552571\pi\)
\(720\) 0 0
\(721\) −0.484459 −0.0180422
\(722\) 0 0
\(723\) 10.0541 0.373917
\(724\) 0 0
\(725\) −63.1586 −2.34565
\(726\) 0 0
\(727\) −34.0589 −1.26317 −0.631587 0.775305i \(-0.717596\pi\)
−0.631587 + 0.775305i \(0.717596\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 10.2049 0.377440
\(732\) 0 0
\(733\) 5.26116 0.194325 0.0971627 0.995269i \(-0.469023\pi\)
0.0971627 + 0.995269i \(0.469023\pi\)
\(734\) 0 0
\(735\) −26.8542 −0.990531
\(736\) 0 0
\(737\) 13.6149 0.501513
\(738\) 0 0
\(739\) −6.79365 −0.249909 −0.124954 0.992162i \(-0.539878\pi\)
−0.124954 + 0.992162i \(0.539878\pi\)
\(740\) 0 0
\(741\) 16.5387 0.607563
\(742\) 0 0
\(743\) 22.8291 0.837520 0.418760 0.908097i \(-0.362465\pi\)
0.418760 + 0.908097i \(0.362465\pi\)
\(744\) 0 0
\(745\) 33.5679 1.22983
\(746\) 0 0
\(747\) −2.15120 −0.0787082
\(748\) 0 0
\(749\) −0.0940478 −0.00343643
\(750\) 0 0
\(751\) 30.3210 1.10643 0.553214 0.833039i \(-0.313401\pi\)
0.553214 + 0.833039i \(0.313401\pi\)
\(752\) 0 0
\(753\) −6.24106 −0.227437
\(754\) 0 0
\(755\) 22.0113 0.801075
\(756\) 0 0
\(757\) 31.2068 1.13423 0.567115 0.823639i \(-0.308059\pi\)
0.567115 + 0.823639i \(0.308059\pi\)
\(758\) 0 0
\(759\) −20.7206 −0.752112
\(760\) 0 0
\(761\) 18.9250 0.686031 0.343015 0.939330i \(-0.388552\pi\)
0.343015 + 0.939330i \(0.388552\pi\)
\(762\) 0 0
\(763\) −0.304453 −0.0110219
\(764\) 0 0
\(765\) 5.38512 0.194699
\(766\) 0 0
\(767\) −19.1318 −0.690809
\(768\) 0 0
\(769\) −16.8294 −0.606884 −0.303442 0.952850i \(-0.598136\pi\)
−0.303442 + 0.952850i \(0.598136\pi\)
\(770\) 0 0
\(771\) −20.4905 −0.737949
\(772\) 0 0
\(773\) 3.45996 0.124446 0.0622230 0.998062i \(-0.480181\pi\)
0.0622230 + 0.998062i \(0.480181\pi\)
\(774\) 0 0
\(775\) 53.1441 1.90899
\(776\) 0 0
\(777\) −0.215295 −0.00772366
\(778\) 0 0
\(779\) −9.78246 −0.350493
\(780\) 0 0
\(781\) 42.7423 1.52944
\(782\) 0 0
\(783\) 6.49534 0.232124
\(784\) 0 0
\(785\) 26.2499 0.936898
\(786\) 0 0
\(787\) −25.5238 −0.909823 −0.454912 0.890537i \(-0.650329\pi\)
−0.454912 + 0.890537i \(0.650329\pi\)
\(788\) 0 0
\(789\) −24.3112 −0.865503
\(790\) 0 0
\(791\) 0.109214 0.00388319
\(792\) 0 0
\(793\) −31.4301 −1.11611
\(794\) 0 0
\(795\) 7.51080 0.266381
\(796\) 0 0
\(797\) −12.6053 −0.446503 −0.223251 0.974761i \(-0.571667\pi\)
−0.223251 + 0.974761i \(0.571667\pi\)
\(798\) 0 0
\(799\) 11.6139 0.410872
\(800\) 0 0
\(801\) 14.6325 0.517014
\(802\) 0 0
\(803\) −31.9893 −1.12888
\(804\) 0 0
\(805\) 1.02541 0.0361409
\(806\) 0 0
\(807\) −0.374620 −0.0131873
\(808\) 0 0
\(809\) 7.50905 0.264004 0.132002 0.991249i \(-0.457859\pi\)
0.132002 + 0.991249i \(0.457859\pi\)
\(810\) 0 0
\(811\) 3.46364 0.121625 0.0608125 0.998149i \(-0.480631\pi\)
0.0608125 + 0.998149i \(0.480631\pi\)
\(812\) 0 0
\(813\) −4.25550 −0.149247
\(814\) 0 0
\(815\) −36.6847 −1.28501
\(816\) 0 0
\(817\) 45.2921 1.58457
\(818\) 0 0
\(819\) 0.103735 0.00362479
\(820\) 0 0
\(821\) −14.7887 −0.516130 −0.258065 0.966128i \(-0.583085\pi\)
−0.258065 + 0.966128i \(0.583085\pi\)
\(822\) 0 0
\(823\) −20.8351 −0.726265 −0.363133 0.931737i \(-0.618293\pi\)
−0.363133 + 0.931737i \(0.618293\pi\)
\(824\) 0 0
\(825\) 29.4560 1.02552
\(826\) 0 0
\(827\) −38.1692 −1.32727 −0.663637 0.748055i \(-0.730988\pi\)
−0.663637 + 0.748055i \(0.730988\pi\)
\(828\) 0 0
\(829\) 45.9228 1.59497 0.797483 0.603342i \(-0.206165\pi\)
0.797483 + 0.603342i \(0.206165\pi\)
\(830\) 0 0
\(831\) 4.55446 0.157993
\(832\) 0 0
\(833\) 9.82178 0.340305
\(834\) 0 0
\(835\) −24.8606 −0.860338
\(836\) 0 0
\(837\) −5.46543 −0.188913
\(838\) 0 0
\(839\) −21.7693 −0.751561 −0.375781 0.926709i \(-0.622625\pi\)
−0.375781 + 0.926709i \(0.622625\pi\)
\(840\) 0 0
\(841\) 13.1894 0.454807
\(842\) 0 0
\(843\) −29.1317 −1.00335
\(844\) 0 0
\(845\) 22.8306 0.785397
\(846\) 0 0
\(847\) −0.0712356 −0.00244768
\(848\) 0 0
\(849\) −22.7994 −0.782475
\(850\) 0 0
\(851\) −37.6936 −1.29212
\(852\) 0 0
\(853\) 15.0715 0.516037 0.258019 0.966140i \(-0.416930\pi\)
0.258019 + 0.966140i \(0.416930\pi\)
\(854\) 0 0
\(855\) 23.9007 0.817387
\(856\) 0 0
\(857\) 19.6455 0.671077 0.335539 0.942026i \(-0.391082\pi\)
0.335539 + 0.942026i \(0.391082\pi\)
\(858\) 0 0
\(859\) −3.56535 −0.121648 −0.0608241 0.998149i \(-0.519373\pi\)
−0.0608241 + 0.998149i \(0.519373\pi\)
\(860\) 0 0
\(861\) −0.0613582 −0.00209108
\(862\) 0 0
\(863\) −30.1135 −1.02508 −0.512538 0.858665i \(-0.671294\pi\)
−0.512538 + 0.858665i \(0.671294\pi\)
\(864\) 0 0
\(865\) −72.0985 −2.45142
\(866\) 0 0
\(867\) 15.0304 0.510460
\(868\) 0 0
\(869\) −42.7536 −1.45032
\(870\) 0 0
\(871\) −11.9336 −0.404355
\(872\) 0 0
\(873\) −10.8990 −0.368876
\(874\) 0 0
\(875\) −0.708136 −0.0239394
\(876\) 0 0
\(877\) −41.5131 −1.40180 −0.700899 0.713260i \(-0.747218\pi\)
−0.700899 + 0.713260i \(0.747218\pi\)
\(878\) 0 0
\(879\) −22.1807 −0.748138
\(880\) 0 0
\(881\) −45.2698 −1.52518 −0.762590 0.646883i \(-0.776072\pi\)
−0.762590 + 0.646883i \(0.776072\pi\)
\(882\) 0 0
\(883\) −29.5916 −0.995836 −0.497918 0.867224i \(-0.665902\pi\)
−0.497918 + 0.867224i \(0.665902\pi\)
\(884\) 0 0
\(885\) −27.6482 −0.929383
\(886\) 0 0
\(887\) 43.6404 1.46530 0.732650 0.680606i \(-0.238283\pi\)
0.732650 + 0.680606i \(0.238283\pi\)
\(888\) 0 0
\(889\) 0.0240516 0.000806663 0
\(890\) 0 0
\(891\) −3.02930 −0.101485
\(892\) 0 0
\(893\) 51.5460 1.72492
\(894\) 0 0
\(895\) 13.1551 0.439727
\(896\) 0 0
\(897\) 18.1618 0.606405
\(898\) 0 0
\(899\) −35.4998 −1.18398
\(900\) 0 0
\(901\) −2.74704 −0.0915172
\(902\) 0 0
\(903\) 0.284084 0.00945373
\(904\) 0 0
\(905\) 92.6508 3.07982
\(906\) 0 0
\(907\) −40.6209 −1.34879 −0.674397 0.738369i \(-0.735596\pi\)
−0.674397 + 0.738369i \(0.735596\pi\)
\(908\) 0 0
\(909\) 0.205647 0.00682088
\(910\) 0 0
\(911\) 30.9835 1.02653 0.513264 0.858231i \(-0.328436\pi\)
0.513264 + 0.858231i \(0.328436\pi\)
\(912\) 0 0
\(913\) 6.51662 0.215669
\(914\) 0 0
\(915\) −45.4209 −1.50157
\(916\) 0 0
\(917\) 0.0673779 0.00222501
\(918\) 0 0
\(919\) −16.8095 −0.554494 −0.277247 0.960799i \(-0.589422\pi\)
−0.277247 + 0.960799i \(0.589422\pi\)
\(920\) 0 0
\(921\) −17.2511 −0.568442
\(922\) 0 0
\(923\) −37.4639 −1.23314
\(924\) 0 0
\(925\) 53.5843 1.76184
\(926\) 0 0
\(927\) −12.4002 −0.407277
\(928\) 0 0
\(929\) −19.3104 −0.633554 −0.316777 0.948500i \(-0.602601\pi\)
−0.316777 + 0.948500i \(0.602601\pi\)
\(930\) 0 0
\(931\) 43.5919 1.42867
\(932\) 0 0
\(933\) −6.72157 −0.220054
\(934\) 0 0
\(935\) −16.3131 −0.533497
\(936\) 0 0
\(937\) −1.83866 −0.0600665 −0.0300332 0.999549i \(-0.509561\pi\)
−0.0300332 + 0.999549i \(0.509561\pi\)
\(938\) 0 0
\(939\) 17.7539 0.579378
\(940\) 0 0
\(941\) 7.94424 0.258975 0.129487 0.991581i \(-0.458667\pi\)
0.129487 + 0.991581i \(0.458667\pi\)
\(942\) 0 0
\(943\) −10.7425 −0.349825
\(944\) 0 0
\(945\) 0.149912 0.00487663
\(946\) 0 0
\(947\) 21.4344 0.696525 0.348262 0.937397i \(-0.386772\pi\)
0.348262 + 0.937397i \(0.386772\pi\)
\(948\) 0 0
\(949\) 28.0389 0.910181
\(950\) 0 0
\(951\) 24.9958 0.810543
\(952\) 0 0
\(953\) −41.9229 −1.35802 −0.679009 0.734130i \(-0.737590\pi\)
−0.679009 + 0.734130i \(0.737590\pi\)
\(954\) 0 0
\(955\) −7.32830 −0.237138
\(956\) 0 0
\(957\) −19.6763 −0.636045
\(958\) 0 0
\(959\) 0.229856 0.00742243
\(960\) 0 0
\(961\) −1.12911 −0.0364229
\(962\) 0 0
\(963\) −2.40725 −0.0775726
\(964\) 0 0
\(965\) −45.5374 −1.46590
\(966\) 0 0
\(967\) 43.0934 1.38579 0.692896 0.721038i \(-0.256335\pi\)
0.692896 + 0.721038i \(0.256335\pi\)
\(968\) 0 0
\(969\) −8.74157 −0.280820
\(970\) 0 0
\(971\) 13.0155 0.417688 0.208844 0.977949i \(-0.433030\pi\)
0.208844 + 0.977949i \(0.433030\pi\)
\(972\) 0 0
\(973\) 0.0236923 0.000759541 0
\(974\) 0 0
\(975\) −25.8184 −0.826849
\(976\) 0 0
\(977\) −11.7460 −0.375789 −0.187895 0.982189i \(-0.560166\pi\)
−0.187895 + 0.982189i \(0.560166\pi\)
\(978\) 0 0
\(979\) −44.3262 −1.41667
\(980\) 0 0
\(981\) −7.79279 −0.248805
\(982\) 0 0
\(983\) −35.5071 −1.13250 −0.566250 0.824233i \(-0.691606\pi\)
−0.566250 + 0.824233i \(0.691606\pi\)
\(984\) 0 0
\(985\) −47.6512 −1.51829
\(986\) 0 0
\(987\) 0.323310 0.0102911
\(988\) 0 0
\(989\) 49.7372 1.58155
\(990\) 0 0
\(991\) 51.6990 1.64227 0.821136 0.570733i \(-0.193341\pi\)
0.821136 + 0.570733i \(0.193341\pi\)
\(992\) 0 0
\(993\) −8.54725 −0.271239
\(994\) 0 0
\(995\) −89.0453 −2.82293
\(996\) 0 0
\(997\) −54.0780 −1.71267 −0.856333 0.516423i \(-0.827263\pi\)
−0.856333 + 0.516423i \(0.827263\pi\)
\(998\) 0 0
\(999\) −5.51070 −0.174351
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 \(a_p\))