Properties

Label 8040.2.a.t.1.1
Level 8040
Weight 2
Character 8040.1
Self dual Yes
Analytic conductor 64.200
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1997232251\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.70642\)
Character \(\chi\) = 8040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(-2.80016 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.00000 q^{5}\) \(-2.80016 q^{7}\) \(+1.00000 q^{9}\) \(+0.770919 q^{11}\) \(-3.59031 q^{13}\) \(-1.00000 q^{15}\) \(-0.618268 q^{17}\) \(-6.93864 q^{19}\) \(-2.80016 q^{21}\) \(+1.25243 q^{23}\) \(+1.00000 q^{25}\) \(+1.00000 q^{27}\) \(+3.30276 q^{29}\) \(+3.43206 q^{31}\) \(+0.770919 q^{33}\) \(+2.80016 q^{35}\) \(-5.13260 q^{37}\) \(-3.59031 q^{39}\) \(-1.43206 q^{41}\) \(-4.84274 q^{43}\) \(-1.00000 q^{45}\) \(+10.8741 q^{47}\) \(+0.840913 q^{49}\) \(-0.618268 q^{51}\) \(+12.6800 q^{53}\) \(-0.770919 q^{55}\) \(-6.93864 q^{57}\) \(+0.397624 q^{59}\) \(-12.9478 q^{61}\) \(-2.80016 q^{63}\) \(+3.59031 q^{65}\) \(+1.00000 q^{67}\) \(+1.25243 q^{69}\) \(-1.10374 q^{71}\) \(-2.18458 q^{73}\) \(+1.00000 q^{75}\) \(-2.15870 q^{77}\) \(+9.90420 q^{79}\) \(+1.00000 q^{81}\) \(-15.1850 q^{83}\) \(+0.618268 q^{85}\) \(+3.30276 q^{87}\) \(+10.2586 q^{89}\) \(+10.0535 q^{91}\) \(+3.43206 q^{93}\) \(+6.93864 q^{95}\) \(+18.2174 q^{97}\) \(+0.770919 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 7q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut +\mathstrut 13q^{53} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut +\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 25q^{79} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 29q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut q^{87} \) \(\mathstrut +\mathstrut 7q^{89} \) \(\mathstrut +\mathstrut 27q^{91} \) \(\mathstrut +\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 9q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.80016 −1.05836 −0.529181 0.848509i \(-0.677501\pi\)
−0.529181 + 0.848509i \(0.677501\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.770919 0.232441 0.116220 0.993223i \(-0.462922\pi\)
0.116220 + 0.993223i \(0.462922\pi\)
\(12\) 0 0
\(13\) −3.59031 −0.995774 −0.497887 0.867242i \(-0.665891\pi\)
−0.497887 + 0.867242i \(0.665891\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −0.618268 −0.149952 −0.0749760 0.997185i \(-0.523888\pi\)
−0.0749760 + 0.997185i \(0.523888\pi\)
\(18\) 0 0
\(19\) −6.93864 −1.59183 −0.795917 0.605406i \(-0.793011\pi\)
−0.795917 + 0.605406i \(0.793011\pi\)
\(20\) 0 0
\(21\) −2.80016 −0.611046
\(22\) 0 0
\(23\) 1.25243 0.261150 0.130575 0.991438i \(-0.458318\pi\)
0.130575 + 0.991438i \(0.458318\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.30276 0.613307 0.306654 0.951821i \(-0.400791\pi\)
0.306654 + 0.951821i \(0.400791\pi\)
\(30\) 0 0
\(31\) 3.43206 0.616417 0.308208 0.951319i \(-0.400271\pi\)
0.308208 + 0.951319i \(0.400271\pi\)
\(32\) 0 0
\(33\) 0.770919 0.134200
\(34\) 0 0
\(35\) 2.80016 0.473314
\(36\) 0 0
\(37\) −5.13260 −0.843794 −0.421897 0.906644i \(-0.638636\pi\)
−0.421897 + 0.906644i \(0.638636\pi\)
\(38\) 0 0
\(39\) −3.59031 −0.574910
\(40\) 0 0
\(41\) −1.43206 −0.223651 −0.111825 0.993728i \(-0.535670\pi\)
−0.111825 + 0.993728i \(0.535670\pi\)
\(42\) 0 0
\(43\) −4.84274 −0.738512 −0.369256 0.929328i \(-0.620387\pi\)
−0.369256 + 0.929328i \(0.620387\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 10.8741 1.58616 0.793078 0.609120i \(-0.208477\pi\)
0.793078 + 0.609120i \(0.208477\pi\)
\(48\) 0 0
\(49\) 0.840913 0.120130
\(50\) 0 0
\(51\) −0.618268 −0.0865748
\(52\) 0 0
\(53\) 12.6800 1.74174 0.870868 0.491516i \(-0.163557\pi\)
0.870868 + 0.491516i \(0.163557\pi\)
\(54\) 0 0
\(55\) −0.770919 −0.103951
\(56\) 0 0
\(57\) −6.93864 −0.919046
\(58\) 0 0
\(59\) 0.397624 0.0517662 0.0258831 0.999665i \(-0.491760\pi\)
0.0258831 + 0.999665i \(0.491760\pi\)
\(60\) 0 0
\(61\) −12.9478 −1.65780 −0.828899 0.559398i \(-0.811032\pi\)
−0.828899 + 0.559398i \(0.811032\pi\)
\(62\) 0 0
\(63\) −2.80016 −0.352787
\(64\) 0 0
\(65\) 3.59031 0.445324
\(66\) 0 0
\(67\) 1.00000 0.122169
\(68\) 0 0
\(69\) 1.25243 0.150775
\(70\) 0 0
\(71\) −1.10374 −0.130990 −0.0654951 0.997853i \(-0.520863\pi\)
−0.0654951 + 0.997853i \(0.520863\pi\)
\(72\) 0 0
\(73\) −2.18458 −0.255686 −0.127843 0.991794i \(-0.540805\pi\)
−0.127843 + 0.991794i \(0.540805\pi\)
\(74\) 0 0
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) −2.15870 −0.246006
\(78\) 0 0
\(79\) 9.90420 1.11431 0.557155 0.830409i \(-0.311893\pi\)
0.557155 + 0.830409i \(0.311893\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −15.1850 −1.66677 −0.833387 0.552689i \(-0.813602\pi\)
−0.833387 + 0.552689i \(0.813602\pi\)
\(84\) 0 0
\(85\) 0.618268 0.0670606
\(86\) 0 0
\(87\) 3.30276 0.354093
\(88\) 0 0
\(89\) 10.2586 1.08741 0.543703 0.839278i \(-0.317022\pi\)
0.543703 + 0.839278i \(0.317022\pi\)
\(90\) 0 0
\(91\) 10.0535 1.05389
\(92\) 0 0
\(93\) 3.43206 0.355888
\(94\) 0 0
\(95\) 6.93864 0.711890
\(96\) 0 0
\(97\) 18.2174 1.84969 0.924847 0.380340i \(-0.124193\pi\)
0.924847 + 0.380340i \(0.124193\pi\)
\(98\) 0 0
\(99\) 0.770919 0.0774802
\(100\) 0 0
\(101\) −5.98598 −0.595627 −0.297814 0.954624i \(-0.596257\pi\)
−0.297814 + 0.954624i \(0.596257\pi\)
\(102\) 0 0
\(103\) 17.8331 1.75715 0.878573 0.477607i \(-0.158496\pi\)
0.878573 + 0.477607i \(0.158496\pi\)
\(104\) 0 0
\(105\) 2.80016 0.273268
\(106\) 0 0
\(107\) −4.03839 −0.390406 −0.195203 0.980763i \(-0.562537\pi\)
−0.195203 + 0.980763i \(0.562537\pi\)
\(108\) 0 0
\(109\) 4.95193 0.474309 0.237154 0.971472i \(-0.423785\pi\)
0.237154 + 0.971472i \(0.423785\pi\)
\(110\) 0 0
\(111\) −5.13260 −0.487165
\(112\) 0 0
\(113\) −2.11233 −0.198711 −0.0993557 0.995052i \(-0.531678\pi\)
−0.0993557 + 0.995052i \(0.531678\pi\)
\(114\) 0 0
\(115\) −1.25243 −0.116790
\(116\) 0 0
\(117\) −3.59031 −0.331925
\(118\) 0 0
\(119\) 1.73125 0.158704
\(120\) 0 0
\(121\) −10.4057 −0.945971
\(122\) 0 0
\(123\) −1.43206 −0.129125
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.97601 0.619021 0.309510 0.950896i \(-0.399835\pi\)
0.309510 + 0.950896i \(0.399835\pi\)
\(128\) 0 0
\(129\) −4.84274 −0.426380
\(130\) 0 0
\(131\) 19.5046 1.70413 0.852064 0.523437i \(-0.175350\pi\)
0.852064 + 0.523437i \(0.175350\pi\)
\(132\) 0 0
\(133\) 19.4293 1.68474
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) 0 0
\(137\) 2.24286 0.191621 0.0958103 0.995400i \(-0.469456\pi\)
0.0958103 + 0.995400i \(0.469456\pi\)
\(138\) 0 0
\(139\) 16.5268 1.40179 0.700894 0.713265i \(-0.252784\pi\)
0.700894 + 0.713265i \(0.252784\pi\)
\(140\) 0 0
\(141\) 10.8741 0.915768
\(142\) 0 0
\(143\) −2.76784 −0.231458
\(144\) 0 0
\(145\) −3.30276 −0.274279
\(146\) 0 0
\(147\) 0.840913 0.0693574
\(148\) 0 0
\(149\) 4.86809 0.398810 0.199405 0.979917i \(-0.436099\pi\)
0.199405 + 0.979917i \(0.436099\pi\)
\(150\) 0 0
\(151\) −5.59330 −0.455176 −0.227588 0.973757i \(-0.573084\pi\)
−0.227588 + 0.973757i \(0.573084\pi\)
\(152\) 0 0
\(153\) −0.618268 −0.0499840
\(154\) 0 0
\(155\) −3.43206 −0.275670
\(156\) 0 0
\(157\) −1.77705 −0.141824 −0.0709120 0.997483i \(-0.522591\pi\)
−0.0709120 + 0.997483i \(0.522591\pi\)
\(158\) 0 0
\(159\) 12.6800 1.00559
\(160\) 0 0
\(161\) −3.50701 −0.276391
\(162\) 0 0
\(163\) 18.1332 1.42030 0.710149 0.704051i \(-0.248628\pi\)
0.710149 + 0.704051i \(0.248628\pi\)
\(164\) 0 0
\(165\) −0.770919 −0.0600159
\(166\) 0 0
\(167\) −2.83587 −0.219446 −0.109723 0.993962i \(-0.534996\pi\)
−0.109723 + 0.993962i \(0.534996\pi\)
\(168\) 0 0
\(169\) −0.109639 −0.00843381
\(170\) 0 0
\(171\) −6.93864 −0.530611
\(172\) 0 0
\(173\) 17.5907 1.33739 0.668696 0.743535i \(-0.266853\pi\)
0.668696 + 0.743535i \(0.266853\pi\)
\(174\) 0 0
\(175\) −2.80016 −0.211672
\(176\) 0 0
\(177\) 0.397624 0.0298872
\(178\) 0 0
\(179\) −21.0294 −1.57181 −0.785904 0.618348i \(-0.787802\pi\)
−0.785904 + 0.618348i \(0.787802\pi\)
\(180\) 0 0
\(181\) −14.9936 −1.11447 −0.557234 0.830356i \(-0.688137\pi\)
−0.557234 + 0.830356i \(0.688137\pi\)
\(182\) 0 0
\(183\) −12.9478 −0.957130
\(184\) 0 0
\(185\) 5.13260 0.377356
\(186\) 0 0
\(187\) −0.476634 −0.0348549
\(188\) 0 0
\(189\) −2.80016 −0.203682
\(190\) 0 0
\(191\) 2.98651 0.216097 0.108048 0.994146i \(-0.465540\pi\)
0.108048 + 0.994146i \(0.465540\pi\)
\(192\) 0 0
\(193\) 11.9299 0.858735 0.429367 0.903130i \(-0.358737\pi\)
0.429367 + 0.903130i \(0.358737\pi\)
\(194\) 0 0
\(195\) 3.59031 0.257108
\(196\) 0 0
\(197\) 23.3272 1.66199 0.830996 0.556279i \(-0.187771\pi\)
0.830996 + 0.556279i \(0.187771\pi\)
\(198\) 0 0
\(199\) 10.3504 0.733717 0.366859 0.930277i \(-0.380433\pi\)
0.366859 + 0.930277i \(0.380433\pi\)
\(200\) 0 0
\(201\) 1.00000 0.0705346
\(202\) 0 0
\(203\) −9.24827 −0.649101
\(204\) 0 0
\(205\) 1.43206 0.100020
\(206\) 0 0
\(207\) 1.25243 0.0870499
\(208\) 0 0
\(209\) −5.34913 −0.370007
\(210\) 0 0
\(211\) −27.0627 −1.86307 −0.931536 0.363650i \(-0.881531\pi\)
−0.931536 + 0.363650i \(0.881531\pi\)
\(212\) 0 0
\(213\) −1.10374 −0.0756272
\(214\) 0 0
\(215\) 4.84274 0.330272
\(216\) 0 0
\(217\) −9.61034 −0.652392
\(218\) 0 0
\(219\) −2.18458 −0.147621
\(220\) 0 0
\(221\) 2.21978 0.149318
\(222\) 0 0
\(223\) 18.1399 1.21474 0.607369 0.794420i \(-0.292225\pi\)
0.607369 + 0.794420i \(0.292225\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 10.8027 0.716997 0.358499 0.933530i \(-0.383289\pi\)
0.358499 + 0.933530i \(0.383289\pi\)
\(228\) 0 0
\(229\) −21.9118 −1.44797 −0.723987 0.689813i \(-0.757693\pi\)
−0.723987 + 0.689813i \(0.757693\pi\)
\(230\) 0 0
\(231\) −2.15870 −0.142032
\(232\) 0 0
\(233\) −2.19444 −0.143762 −0.0718811 0.997413i \(-0.522900\pi\)
−0.0718811 + 0.997413i \(0.522900\pi\)
\(234\) 0 0
\(235\) −10.8741 −0.709351
\(236\) 0 0
\(237\) 9.90420 0.643347
\(238\) 0 0
\(239\) 21.6147 1.39814 0.699070 0.715053i \(-0.253598\pi\)
0.699070 + 0.715053i \(0.253598\pi\)
\(240\) 0 0
\(241\) 19.7227 1.27045 0.635226 0.772326i \(-0.280907\pi\)
0.635226 + 0.772326i \(0.280907\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −0.840913 −0.0537240
\(246\) 0 0
\(247\) 24.9119 1.58511
\(248\) 0 0
\(249\) −15.1850 −0.962313
\(250\) 0 0
\(251\) 12.8631 0.811911 0.405956 0.913893i \(-0.366939\pi\)
0.405956 + 0.913893i \(0.366939\pi\)
\(252\) 0 0
\(253\) 0.965521 0.0607018
\(254\) 0 0
\(255\) 0.618268 0.0387174
\(256\) 0 0
\(257\) −14.3381 −0.894384 −0.447192 0.894438i \(-0.647576\pi\)
−0.447192 + 0.894438i \(0.647576\pi\)
\(258\) 0 0
\(259\) 14.3721 0.893040
\(260\) 0 0
\(261\) 3.30276 0.204436
\(262\) 0 0
\(263\) −16.7140 −1.03063 −0.515314 0.857001i \(-0.672325\pi\)
−0.515314 + 0.857001i \(0.672325\pi\)
\(264\) 0 0
\(265\) −12.6800 −0.778928
\(266\) 0 0
\(267\) 10.2586 0.627814
\(268\) 0 0
\(269\) 10.2574 0.625405 0.312702 0.949851i \(-0.398766\pi\)
0.312702 + 0.949851i \(0.398766\pi\)
\(270\) 0 0
\(271\) 0.523534 0.0318024 0.0159012 0.999874i \(-0.494938\pi\)
0.0159012 + 0.999874i \(0.494938\pi\)
\(272\) 0 0
\(273\) 10.0535 0.608464
\(274\) 0 0
\(275\) 0.770919 0.0464881
\(276\) 0 0
\(277\) 4.58867 0.275706 0.137853 0.990453i \(-0.455980\pi\)
0.137853 + 0.990453i \(0.455980\pi\)
\(278\) 0 0
\(279\) 3.43206 0.205472
\(280\) 0 0
\(281\) −5.89896 −0.351902 −0.175951 0.984399i \(-0.556300\pi\)
−0.175951 + 0.984399i \(0.556300\pi\)
\(282\) 0 0
\(283\) 4.28874 0.254939 0.127469 0.991842i \(-0.459315\pi\)
0.127469 + 0.991842i \(0.459315\pi\)
\(284\) 0 0
\(285\) 6.93864 0.411010
\(286\) 0 0
\(287\) 4.01001 0.236703
\(288\) 0 0
\(289\) −16.6177 −0.977514
\(290\) 0 0
\(291\) 18.2174 1.06792
\(292\) 0 0
\(293\) 11.5034 0.672038 0.336019 0.941855i \(-0.390919\pi\)
0.336019 + 0.941855i \(0.390919\pi\)
\(294\) 0 0
\(295\) −0.397624 −0.0231505
\(296\) 0 0
\(297\) 0.770919 0.0447332
\(298\) 0 0
\(299\) −4.49662 −0.260046
\(300\) 0 0
\(301\) 13.5605 0.781613
\(302\) 0 0
\(303\) −5.98598 −0.343885
\(304\) 0 0
\(305\) 12.9478 0.741390
\(306\) 0 0
\(307\) −18.3432 −1.04690 −0.523451 0.852056i \(-0.675356\pi\)
−0.523451 + 0.852056i \(0.675356\pi\)
\(308\) 0 0
\(309\) 17.8331 1.01449
\(310\) 0 0
\(311\) −21.8167 −1.23711 −0.618555 0.785742i \(-0.712281\pi\)
−0.618555 + 0.785742i \(0.712281\pi\)
\(312\) 0 0
\(313\) 15.8966 0.898526 0.449263 0.893400i \(-0.351687\pi\)
0.449263 + 0.893400i \(0.351687\pi\)
\(314\) 0 0
\(315\) 2.80016 0.157771
\(316\) 0 0
\(317\) −14.6686 −0.823870 −0.411935 0.911213i \(-0.635147\pi\)
−0.411935 + 0.911213i \(0.635147\pi\)
\(318\) 0 0
\(319\) 2.54616 0.142558
\(320\) 0 0
\(321\) −4.03839 −0.225401
\(322\) 0 0
\(323\) 4.28994 0.238699
\(324\) 0 0
\(325\) −3.59031 −0.199155
\(326\) 0 0
\(327\) 4.95193 0.273842
\(328\) 0 0
\(329\) −30.4494 −1.67873
\(330\) 0 0
\(331\) −5.88278 −0.323347 −0.161674 0.986844i \(-0.551689\pi\)
−0.161674 + 0.986844i \(0.551689\pi\)
\(332\) 0 0
\(333\) −5.13260 −0.281265
\(334\) 0 0
\(335\) −1.00000 −0.0546358
\(336\) 0 0
\(337\) −17.3684 −0.946117 −0.473059 0.881031i \(-0.656850\pi\)
−0.473059 + 0.881031i \(0.656850\pi\)
\(338\) 0 0
\(339\) −2.11233 −0.114726
\(340\) 0 0
\(341\) 2.64584 0.143280
\(342\) 0 0
\(343\) 17.2464 0.931221
\(344\) 0 0
\(345\) −1.25243 −0.0674285
\(346\) 0 0
\(347\) −12.1492 −0.652203 −0.326102 0.945335i \(-0.605735\pi\)
−0.326102 + 0.945335i \(0.605735\pi\)
\(348\) 0 0
\(349\) −3.61774 −0.193653 −0.0968267 0.995301i \(-0.530869\pi\)
−0.0968267 + 0.995301i \(0.530869\pi\)
\(350\) 0 0
\(351\) −3.59031 −0.191637
\(352\) 0 0
\(353\) −7.48416 −0.398341 −0.199171 0.979965i \(-0.563825\pi\)
−0.199171 + 0.979965i \(0.563825\pi\)
\(354\) 0 0
\(355\) 1.10374 0.0585806
\(356\) 0 0
\(357\) 1.73125 0.0916275
\(358\) 0 0
\(359\) 13.5067 0.712856 0.356428 0.934323i \(-0.383995\pi\)
0.356428 + 0.934323i \(0.383995\pi\)
\(360\) 0 0
\(361\) 29.1447 1.53393
\(362\) 0 0
\(363\) −10.4057 −0.546157
\(364\) 0 0
\(365\) 2.18458 0.114346
\(366\) 0 0
\(367\) 17.2686 0.901414 0.450707 0.892672i \(-0.351172\pi\)
0.450707 + 0.892672i \(0.351172\pi\)
\(368\) 0 0
\(369\) −1.43206 −0.0745502
\(370\) 0 0
\(371\) −35.5062 −1.84339
\(372\) 0 0
\(373\) 30.7796 1.59371 0.796853 0.604173i \(-0.206497\pi\)
0.796853 + 0.604173i \(0.206497\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −11.8580 −0.610716
\(378\) 0 0
\(379\) 22.8477 1.17361 0.586804 0.809729i \(-0.300386\pi\)
0.586804 + 0.809729i \(0.300386\pi\)
\(380\) 0 0
\(381\) 6.97601 0.357392
\(382\) 0 0
\(383\) 32.0531 1.63783 0.818917 0.573912i \(-0.194575\pi\)
0.818917 + 0.573912i \(0.194575\pi\)
\(384\) 0 0
\(385\) 2.15870 0.110017
\(386\) 0 0
\(387\) −4.84274 −0.246171
\(388\) 0 0
\(389\) −7.36726 −0.373535 −0.186768 0.982404i \(-0.559801\pi\)
−0.186768 + 0.982404i \(0.559801\pi\)
\(390\) 0 0
\(391\) −0.774337 −0.0391599
\(392\) 0 0
\(393\) 19.5046 0.983879
\(394\) 0 0
\(395\) −9.90420 −0.498334
\(396\) 0 0
\(397\) 5.39602 0.270819 0.135409 0.990790i \(-0.456765\pi\)
0.135409 + 0.990790i \(0.456765\pi\)
\(398\) 0 0
\(399\) 19.4293 0.972683
\(400\) 0 0
\(401\) −9.41085 −0.469955 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(402\) 0 0
\(403\) −12.3222 −0.613812
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −3.95682 −0.196132
\(408\) 0 0
\(409\) 21.0386 1.04029 0.520145 0.854078i \(-0.325878\pi\)
0.520145 + 0.854078i \(0.325878\pi\)
\(410\) 0 0
\(411\) 2.24286 0.110632
\(412\) 0 0
\(413\) −1.11341 −0.0547874
\(414\) 0 0
\(415\) 15.1850 0.745404
\(416\) 0 0
\(417\) 16.5268 0.809323
\(418\) 0 0
\(419\) 28.8120 1.40756 0.703779 0.710419i \(-0.251495\pi\)
0.703779 + 0.710419i \(0.251495\pi\)
\(420\) 0 0
\(421\) −7.54037 −0.367495 −0.183748 0.982973i \(-0.558823\pi\)
−0.183748 + 0.982973i \(0.558823\pi\)
\(422\) 0 0
\(423\) 10.8741 0.528719
\(424\) 0 0
\(425\) −0.618268 −0.0299904
\(426\) 0 0
\(427\) 36.2560 1.75455
\(428\) 0 0
\(429\) −2.76784 −0.133633
\(430\) 0 0
\(431\) 20.2233 0.974124 0.487062 0.873367i \(-0.338069\pi\)
0.487062 + 0.873367i \(0.338069\pi\)
\(432\) 0 0
\(433\) 22.3192 1.07259 0.536297 0.844029i \(-0.319823\pi\)
0.536297 + 0.844029i \(0.319823\pi\)
\(434\) 0 0
\(435\) −3.30276 −0.158355
\(436\) 0 0
\(437\) −8.69016 −0.415707
\(438\) 0 0
\(439\) 37.2371 1.77723 0.888616 0.458653i \(-0.151668\pi\)
0.888616 + 0.458653i \(0.151668\pi\)
\(440\) 0 0
\(441\) 0.840913 0.0400435
\(442\) 0 0
\(443\) 2.59870 0.123468 0.0617339 0.998093i \(-0.480337\pi\)
0.0617339 + 0.998093i \(0.480337\pi\)
\(444\) 0 0
\(445\) −10.2586 −0.486302
\(446\) 0 0
\(447\) 4.86809 0.230253
\(448\) 0 0
\(449\) −10.8092 −0.510117 −0.255059 0.966926i \(-0.582095\pi\)
−0.255059 + 0.966926i \(0.582095\pi\)
\(450\) 0 0
\(451\) −1.10400 −0.0519855
\(452\) 0 0
\(453\) −5.59330 −0.262796
\(454\) 0 0
\(455\) −10.0535 −0.471314
\(456\) 0 0
\(457\) 1.08113 0.0505732 0.0252866 0.999680i \(-0.491950\pi\)
0.0252866 + 0.999680i \(0.491950\pi\)
\(458\) 0 0
\(459\) −0.618268 −0.0288583
\(460\) 0 0
\(461\) 20.8420 0.970710 0.485355 0.874317i \(-0.338690\pi\)
0.485355 + 0.874317i \(0.338690\pi\)
\(462\) 0 0
\(463\) 39.2230 1.82285 0.911423 0.411471i \(-0.134985\pi\)
0.911423 + 0.411471i \(0.134985\pi\)
\(464\) 0 0
\(465\) −3.43206 −0.159158
\(466\) 0 0
\(467\) 14.6977 0.680127 0.340064 0.940402i \(-0.389551\pi\)
0.340064 + 0.940402i \(0.389551\pi\)
\(468\) 0 0
\(469\) −2.80016 −0.129300
\(470\) 0 0
\(471\) −1.77705 −0.0818821
\(472\) 0 0
\(473\) −3.73336 −0.171660
\(474\) 0 0
\(475\) −6.93864 −0.318367
\(476\) 0 0
\(477\) 12.6800 0.580579
\(478\) 0 0
\(479\) −36.0434 −1.64687 −0.823433 0.567413i \(-0.807944\pi\)
−0.823433 + 0.567413i \(0.807944\pi\)
\(480\) 0 0
\(481\) 18.4276 0.840228
\(482\) 0 0
\(483\) −3.50701 −0.159574
\(484\) 0 0
\(485\) −18.2174 −0.827208
\(486\) 0 0
\(487\) −14.5604 −0.659794 −0.329897 0.944017i \(-0.607014\pi\)
−0.329897 + 0.944017i \(0.607014\pi\)
\(488\) 0 0
\(489\) 18.1332 0.820010
\(490\) 0 0
\(491\) −29.3926 −1.32647 −0.663234 0.748412i \(-0.730816\pi\)
−0.663234 + 0.748412i \(0.730816\pi\)
\(492\) 0 0
\(493\) −2.04199 −0.0919666
\(494\) 0 0
\(495\) −0.770919 −0.0346502
\(496\) 0 0
\(497\) 3.09066 0.138635
\(498\) 0 0
\(499\) 0.0999720 0.00447536 0.00223768 0.999997i \(-0.499288\pi\)
0.00223768 + 0.999997i \(0.499288\pi\)
\(500\) 0 0
\(501\) −2.83587 −0.126697
\(502\) 0 0
\(503\) 4.73233 0.211004 0.105502 0.994419i \(-0.466355\pi\)
0.105502 + 0.994419i \(0.466355\pi\)
\(504\) 0 0
\(505\) 5.98598 0.266373
\(506\) 0 0
\(507\) −0.109639 −0.00486926
\(508\) 0 0
\(509\) 29.6276 1.31322 0.656610 0.754231i \(-0.271990\pi\)
0.656610 + 0.754231i \(0.271990\pi\)
\(510\) 0 0
\(511\) 6.11719 0.270609
\(512\) 0 0
\(513\) −6.93864 −0.306349
\(514\) 0 0
\(515\) −17.8331 −0.785820
\(516\) 0 0
\(517\) 8.38308 0.368687
\(518\) 0 0
\(519\) 17.5907 0.772144
\(520\) 0 0
\(521\) −27.5380 −1.20646 −0.603232 0.797566i \(-0.706121\pi\)
−0.603232 + 0.797566i \(0.706121\pi\)
\(522\) 0 0
\(523\) −16.7245 −0.731310 −0.365655 0.930750i \(-0.619155\pi\)
−0.365655 + 0.930750i \(0.619155\pi\)
\(524\) 0 0
\(525\) −2.80016 −0.122209
\(526\) 0 0
\(527\) −2.12193 −0.0924329
\(528\) 0 0
\(529\) −21.4314 −0.931801
\(530\) 0 0
\(531\) 0.397624 0.0172554
\(532\) 0 0
\(533\) 5.14156 0.222706
\(534\) 0 0
\(535\) 4.03839 0.174595
\(536\) 0 0
\(537\) −21.0294 −0.907484
\(538\) 0 0
\(539\) 0.648276 0.0279232
\(540\) 0 0
\(541\) −12.0047 −0.516122 −0.258061 0.966129i \(-0.583084\pi\)
−0.258061 + 0.966129i \(0.583084\pi\)
\(542\) 0 0
\(543\) −14.9936 −0.643438
\(544\) 0 0
\(545\) −4.95193 −0.212117
\(546\) 0 0
\(547\) −17.1256 −0.732239 −0.366120 0.930568i \(-0.619314\pi\)
−0.366120 + 0.930568i \(0.619314\pi\)
\(548\) 0 0
\(549\) −12.9478 −0.552599
\(550\) 0 0
\(551\) −22.9167 −0.976283
\(552\) 0 0
\(553\) −27.7334 −1.17934
\(554\) 0 0
\(555\) 5.13260 0.217867
\(556\) 0 0
\(557\) −25.4222 −1.07717 −0.538586 0.842571i \(-0.681041\pi\)
−0.538586 + 0.842571i \(0.681041\pi\)
\(558\) 0 0
\(559\) 17.3870 0.735391
\(560\) 0 0
\(561\) −0.476634 −0.0201235
\(562\) 0 0
\(563\) 15.1871 0.640060 0.320030 0.947407i \(-0.396307\pi\)
0.320030 + 0.947407i \(0.396307\pi\)
\(564\) 0 0
\(565\) 2.11233 0.0888664
\(566\) 0 0
\(567\) −2.80016 −0.117596
\(568\) 0 0
\(569\) −4.93336 −0.206817 −0.103409 0.994639i \(-0.532975\pi\)
−0.103409 + 0.994639i \(0.532975\pi\)
\(570\) 0 0
\(571\) 2.91412 0.121952 0.0609761 0.998139i \(-0.480579\pi\)
0.0609761 + 0.998139i \(0.480579\pi\)
\(572\) 0 0
\(573\) 2.98651 0.124763
\(574\) 0 0
\(575\) 1.25243 0.0522299
\(576\) 0 0
\(577\) −18.7838 −0.781981 −0.390991 0.920395i \(-0.627868\pi\)
−0.390991 + 0.920395i \(0.627868\pi\)
\(578\) 0 0
\(579\) 11.9299 0.495791
\(580\) 0 0
\(581\) 42.5206 1.76405
\(582\) 0 0
\(583\) 9.77528 0.404851
\(584\) 0 0
\(585\) 3.59031 0.148441
\(586\) 0 0
\(587\) 36.0169 1.48658 0.743288 0.668972i \(-0.233265\pi\)
0.743288 + 0.668972i \(0.233265\pi\)
\(588\) 0 0
\(589\) −23.8139 −0.981233
\(590\) 0 0
\(591\) 23.3272 0.959551
\(592\) 0 0
\(593\) −6.75562 −0.277420 −0.138710 0.990333i \(-0.544296\pi\)
−0.138710 + 0.990333i \(0.544296\pi\)
\(594\) 0 0
\(595\) −1.73125 −0.0709744
\(596\) 0 0
\(597\) 10.3504 0.423612
\(598\) 0 0
\(599\) −0.367910 −0.0150324 −0.00751619 0.999972i \(-0.502393\pi\)
−0.00751619 + 0.999972i \(0.502393\pi\)
\(600\) 0 0
\(601\) −47.7932 −1.94953 −0.974764 0.223240i \(-0.928337\pi\)
−0.974764 + 0.223240i \(0.928337\pi\)
\(602\) 0 0
\(603\) 1.00000 0.0407231
\(604\) 0 0
\(605\) 10.4057 0.423051
\(606\) 0 0
\(607\) −41.7573 −1.69488 −0.847438 0.530895i \(-0.821856\pi\)
−0.847438 + 0.530895i \(0.821856\pi\)
\(608\) 0 0
\(609\) −9.24827 −0.374759
\(610\) 0 0
\(611\) −39.0416 −1.57945
\(612\) 0 0
\(613\) −0.687236 −0.0277572 −0.0138786 0.999904i \(-0.504418\pi\)
−0.0138786 + 0.999904i \(0.504418\pi\)
\(614\) 0 0
\(615\) 1.43206 0.0577464
\(616\) 0 0
\(617\) 39.4001 1.58619 0.793094 0.609099i \(-0.208469\pi\)
0.793094 + 0.609099i \(0.208469\pi\)
\(618\) 0 0
\(619\) 45.9164 1.84554 0.922768 0.385356i \(-0.125921\pi\)
0.922768 + 0.385356i \(0.125921\pi\)
\(620\) 0 0
\(621\) 1.25243 0.0502583
\(622\) 0 0
\(623\) −28.7256 −1.15087
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −5.34913 −0.213624
\(628\) 0 0
\(629\) 3.17332 0.126529
\(630\) 0 0
\(631\) −16.1120 −0.641409 −0.320705 0.947179i \(-0.603920\pi\)
−0.320705 + 0.947179i \(0.603920\pi\)
\(632\) 0 0
\(633\) −27.0627 −1.07564
\(634\) 0 0
\(635\) −6.97601 −0.276835
\(636\) 0 0
\(637\) −3.01914 −0.119623
\(638\) 0 0
\(639\) −1.10374 −0.0436634
\(640\) 0 0
\(641\) −6.04522 −0.238772 −0.119386 0.992848i \(-0.538093\pi\)
−0.119386 + 0.992848i \(0.538093\pi\)
\(642\) 0 0
\(643\) 36.2149 1.42817 0.714087 0.700056i \(-0.246842\pi\)
0.714087 + 0.700056i \(0.246842\pi\)
\(644\) 0 0
\(645\) 4.84274 0.190683
\(646\) 0 0
\(647\) −30.5047 −1.19926 −0.599632 0.800276i \(-0.704686\pi\)
−0.599632 + 0.800276i \(0.704686\pi\)
\(648\) 0 0
\(649\) 0.306535 0.0120326
\(650\) 0 0
\(651\) −9.61034 −0.376659
\(652\) 0 0
\(653\) −8.39308 −0.328446 −0.164223 0.986423i \(-0.552512\pi\)
−0.164223 + 0.986423i \(0.552512\pi\)
\(654\) 0 0
\(655\) −19.5046 −0.762110
\(656\) 0 0
\(657\) −2.18458 −0.0852288
\(658\) 0 0
\(659\) −19.0519 −0.742157 −0.371078 0.928602i \(-0.621012\pi\)
−0.371078 + 0.928602i \(0.621012\pi\)
\(660\) 0 0
\(661\) 11.3170 0.440182 0.220091 0.975479i \(-0.429365\pi\)
0.220091 + 0.975479i \(0.429365\pi\)
\(662\) 0 0
\(663\) 2.21978 0.0862090
\(664\) 0 0
\(665\) −19.4293 −0.753437
\(666\) 0 0
\(667\) 4.13647 0.160165
\(668\) 0 0
\(669\) 18.1399 0.701330
\(670\) 0 0
\(671\) −9.98171 −0.385340
\(672\) 0 0
\(673\) −35.8117 −1.38044 −0.690219 0.723600i \(-0.742486\pi\)
−0.690219 + 0.723600i \(0.742486\pi\)
\(674\) 0 0
\(675\) 1.00000 0.0384900
\(676\) 0 0
\(677\) 5.01871 0.192885 0.0964423 0.995339i \(-0.469254\pi\)
0.0964423 + 0.995339i \(0.469254\pi\)
\(678\) 0 0
\(679\) −51.0116 −1.95765
\(680\) 0 0
\(681\) 10.8027 0.413959
\(682\) 0 0
\(683\) −37.0204 −1.41655 −0.708274 0.705938i \(-0.750526\pi\)
−0.708274 + 0.705938i \(0.750526\pi\)
\(684\) 0 0
\(685\) −2.24286 −0.0856954
\(686\) 0 0
\(687\) −21.9118 −0.835989
\(688\) 0 0
\(689\) −45.5253 −1.73438
\(690\) 0 0
\(691\) −11.0593 −0.420716 −0.210358 0.977624i \(-0.567463\pi\)
−0.210358 + 0.977624i \(0.567463\pi\)
\(692\) 0 0
\(693\) −2.15870 −0.0820021
\(694\) 0 0
\(695\) −16.5268 −0.626899
\(696\) 0 0
\(697\) 0.885399 0.0335369
\(698\) 0 0
\(699\) −2.19444 −0.0830012
\(700\) 0 0
\(701\) −6.85470 −0.258898 −0.129449 0.991586i \(-0.541321\pi\)
−0.129449 + 0.991586i \(0.541321\pi\)
\(702\) 0 0
\(703\) 35.6133 1.34318
\(704\) 0 0
\(705\) −10.8741 −0.409544
\(706\) 0 0
\(707\) 16.7617 0.630389
\(708\) 0 0
\(709\) 52.0169 1.95354 0.976768 0.214298i \(-0.0687463\pi\)
0.976768 + 0.214298i \(0.0687463\pi\)
\(710\) 0 0
\(711\) 9.90420 0.371437
\(712\) 0 0
\(713\) 4.29842 0.160977
\(714\) 0 0
\(715\) 2.76784 0.103511
\(716\) 0 0
\(717\) 21.6147 0.807216
\(718\) 0 0
\(719\) −7.65778 −0.285587 −0.142794 0.989752i \(-0.545609\pi\)
−0.142794 + 0.989752i \(0.545609\pi\)
\(720\) 0 0
\(721\) −49.9356 −1.85970
\(722\) 0 0
\(723\) 19.7227 0.733496
\(724\) 0 0
\(725\) 3.30276 0.122661
\(726\) 0 0
\(727\) 28.0287 1.03953 0.519764 0.854310i \(-0.326020\pi\)
0.519764 + 0.854310i \(0.326020\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 2.99411 0.110741
\(732\) 0 0
\(733\) −17.5927 −0.649802 −0.324901 0.945748i \(-0.605331\pi\)
−0.324901 + 0.945748i \(0.605331\pi\)
\(734\) 0 0
\(735\) −0.840913 −0.0310176
\(736\) 0 0
\(737\) 0.770919 0.0283972
\(738\) 0 0
\(739\) −11.5493 −0.424846 −0.212423 0.977178i \(-0.568136\pi\)
−0.212423 + 0.977178i \(0.568136\pi\)
\(740\) 0 0
\(741\) 24.9119 0.915162
\(742\) 0 0
\(743\) 51.2577 1.88046 0.940232 0.340535i \(-0.110608\pi\)
0.940232 + 0.340535i \(0.110608\pi\)
\(744\) 0 0
\(745\) −4.86809 −0.178353
\(746\) 0 0
\(747\) −15.1850 −0.555592
\(748\) 0 0
\(749\) 11.3082 0.413191
\(750\) 0 0
\(751\) 1.34401 0.0490438 0.0245219 0.999699i \(-0.492194\pi\)
0.0245219 + 0.999699i \(0.492194\pi\)
\(752\) 0 0
\(753\) 12.8631 0.468757
\(754\) 0 0
\(755\) 5.59330 0.203561
\(756\) 0 0
\(757\) −13.0627 −0.474770 −0.237385 0.971416i \(-0.576290\pi\)
−0.237385 + 0.971416i \(0.576290\pi\)
\(758\) 0 0
\(759\) 0.965521 0.0350462
\(760\) 0 0
\(761\) −41.9765 −1.52165 −0.760823 0.648959i \(-0.775205\pi\)
−0.760823 + 0.648959i \(0.775205\pi\)
\(762\) 0 0
\(763\) −13.8662 −0.501990
\(764\) 0 0
\(765\) 0.618268 0.0223535
\(766\) 0 0
\(767\) −1.42759 −0.0515474
\(768\) 0 0
\(769\) −23.7149 −0.855182 −0.427591 0.903972i \(-0.640638\pi\)
−0.427591 + 0.903972i \(0.640638\pi\)
\(770\) 0 0
\(771\) −14.3381 −0.516373
\(772\) 0 0
\(773\) −14.6775 −0.527912 −0.263956 0.964535i \(-0.585027\pi\)
−0.263956 + 0.964535i \(0.585027\pi\)
\(774\) 0 0
\(775\) 3.43206 0.123283
\(776\) 0 0
\(777\) 14.3721 0.515597
\(778\) 0 0
\(779\) 9.93658 0.356015
\(780\) 0 0
\(781\) −0.850896 −0.0304475
\(782\) 0 0
\(783\) 3.30276 0.118031
\(784\) 0 0
\(785\) 1.77705 0.0634256
\(786\) 0 0
\(787\) 10.7688 0.383865 0.191932 0.981408i \(-0.438525\pi\)
0.191932 + 0.981408i \(0.438525\pi\)
\(788\) 0 0
\(789\) −16.7140 −0.595033
\(790\) 0 0
\(791\) 5.91487 0.210309
\(792\) 0 0
\(793\) 46.4867 1.65079
\(794\) 0 0
\(795\) −12.6800 −0.449715
\(796\) 0 0
\(797\) −16.0887 −0.569892 −0.284946 0.958544i \(-0.591976\pi\)
−0.284946 + 0.958544i \(0.591976\pi\)
\(798\) 0 0
\(799\) −6.72313 −0.237847
\(800\) 0 0
\(801\) 10.2586 0.362468
\(802\) 0 0
\(803\) −1.68414 −0.0594319
\(804\) 0 0
\(805\) 3.50701 0.123606
\(806\) 0 0
\(807\) 10.2574 0.361078
\(808\) 0 0
\(809\) 4.31327 0.151647 0.0758233 0.997121i \(-0.475842\pi\)
0.0758233 + 0.997121i \(0.475842\pi\)
\(810\) 0 0
\(811\) 52.3909 1.83969 0.919847 0.392278i \(-0.128313\pi\)
0.919847 + 0.392278i \(0.128313\pi\)
\(812\) 0 0
\(813\) 0.523534 0.0183611
\(814\) 0 0
\(815\) −18.1332 −0.635177
\(816\) 0 0
\(817\) 33.6021 1.17559
\(818\) 0 0
\(819\) 10.0535 0.351297
\(820\) 0 0
\(821\) −26.3661 −0.920184 −0.460092 0.887871i \(-0.652184\pi\)
−0.460092 + 0.887871i \(0.652184\pi\)
\(822\) 0 0
\(823\) −44.2733 −1.54327 −0.771635 0.636065i \(-0.780561\pi\)
−0.771635 + 0.636065i \(0.780561\pi\)
\(824\) 0 0
\(825\) 0.770919 0.0268399
\(826\) 0 0
\(827\) 17.8720 0.621469 0.310734 0.950497i \(-0.399425\pi\)
0.310734 + 0.950497i \(0.399425\pi\)
\(828\) 0 0
\(829\) 37.7800 1.31215 0.656077 0.754694i \(-0.272215\pi\)
0.656077 + 0.754694i \(0.272215\pi\)
\(830\) 0 0
\(831\) 4.58867 0.159179
\(832\) 0 0
\(833\) −0.519910 −0.0180138
\(834\) 0 0
\(835\) 2.83587 0.0981393
\(836\) 0 0
\(837\) 3.43206 0.118629
\(838\) 0 0
\(839\) 31.4349 1.08525 0.542627 0.839974i \(-0.317430\pi\)
0.542627 + 0.839974i \(0.317430\pi\)
\(840\) 0 0
\(841\) −18.0918 −0.623854
\(842\) 0 0
\(843\) −5.89896 −0.203171
\(844\) 0 0
\(845\) 0.109639 0.00377171
\(846\) 0 0
\(847\) 29.1376 1.00118
\(848\) 0 0
\(849\) 4.28874 0.147189
\(850\) 0 0
\(851\) −6.42822 −0.220356
\(852\) 0 0
\(853\) 13.6990 0.469044 0.234522 0.972111i \(-0.424647\pi\)
0.234522 + 0.972111i \(0.424647\pi\)
\(854\) 0 0
\(855\) 6.93864 0.237297
\(856\) 0 0
\(857\) 48.3392 1.65124 0.825618 0.564230i \(-0.190827\pi\)
0.825618 + 0.564230i \(0.190827\pi\)
\(858\) 0 0
\(859\) 22.8014 0.777973 0.388986 0.921244i \(-0.372825\pi\)
0.388986 + 0.921244i \(0.372825\pi\)
\(860\) 0 0
\(861\) 4.01001 0.136661
\(862\) 0 0
\(863\) 55.5191 1.88989 0.944946 0.327227i \(-0.106114\pi\)
0.944946 + 0.327227i \(0.106114\pi\)
\(864\) 0 0
\(865\) −17.5907 −0.598100
\(866\) 0 0
\(867\) −16.6177 −0.564368
\(868\) 0 0
\(869\) 7.63533 0.259011
\(870\) 0 0
\(871\) −3.59031 −0.121653
\(872\) 0 0
\(873\) 18.2174 0.616565
\(874\) 0 0
\(875\) 2.80016 0.0946628
\(876\) 0 0
\(877\) −10.8801 −0.367393 −0.183697 0.982983i \(-0.558806\pi\)
−0.183697 + 0.982983i \(0.558806\pi\)
\(878\) 0 0
\(879\) 11.5034 0.388001
\(880\) 0 0
\(881\) 10.9986 0.370553 0.185277 0.982686i \(-0.440682\pi\)
0.185277 + 0.982686i \(0.440682\pi\)
\(882\) 0 0
\(883\) 24.0520 0.809414 0.404707 0.914446i \(-0.367374\pi\)
0.404707 + 0.914446i \(0.367374\pi\)
\(884\) 0 0
\(885\) −0.397624 −0.0133660
\(886\) 0 0
\(887\) −18.1313 −0.608790 −0.304395 0.952546i \(-0.598454\pi\)
−0.304395 + 0.952546i \(0.598454\pi\)
\(888\) 0 0
\(889\) −19.5340 −0.655148
\(890\) 0 0
\(891\) 0.770919 0.0258267
\(892\) 0 0
\(893\) −75.4518 −2.52490
\(894\) 0 0
\(895\) 21.0294 0.702934
\(896\) 0 0
\(897\) −4.49662 −0.150138
\(898\) 0 0
\(899\) 11.3353 0.378053
\(900\) 0 0
\(901\) −7.83966 −0.261177
\(902\) 0 0
\(903\) 13.5605 0.451264
\(904\) 0 0
\(905\) 14.9936 0.498405
\(906\) 0 0
\(907\) −25.6799 −0.852686 −0.426343 0.904562i \(-0.640198\pi\)
−0.426343 + 0.904562i \(0.640198\pi\)
\(908\) 0 0
\(909\) −5.98598 −0.198542
\(910\) 0 0
\(911\) 26.1355 0.865909 0.432954 0.901416i \(-0.357471\pi\)
0.432954 + 0.901416i \(0.357471\pi\)
\(912\) 0 0
\(913\) −11.7064 −0.387426
\(914\) 0 0
\(915\) 12.9478 0.428042
\(916\) 0 0
\(917\) −54.6162 −1.80359
\(918\) 0 0
\(919\) −6.71219 −0.221415 −0.110707 0.993853i \(-0.535312\pi\)
−0.110707 + 0.993853i \(0.535312\pi\)
\(920\) 0 0
\(921\) −18.3432 −0.604429
\(922\) 0 0
\(923\) 3.96278 0.130437
\(924\) 0 0
\(925\) −5.13260 −0.168759
\(926\) 0 0
\(927\) 17.8331 0.585716
\(928\) 0 0
\(929\) 29.1764 0.957248 0.478624 0.878020i \(-0.341136\pi\)
0.478624 + 0.878020i \(0.341136\pi\)
\(930\) 0 0
\(931\) −5.83480 −0.191228
\(932\) 0 0
\(933\) −21.8167 −0.714245
\(934\) 0 0
\(935\) 0.476634 0.0155876
\(936\) 0 0
\(937\) 41.9706 1.37112 0.685559 0.728017i \(-0.259558\pi\)
0.685559 + 0.728017i \(0.259558\pi\)
\(938\) 0 0
\(939\) 15.8966 0.518764
\(940\) 0 0
\(941\) −15.9652 −0.520451 −0.260225 0.965548i \(-0.583797\pi\)
−0.260225 + 0.965548i \(0.583797\pi\)
\(942\) 0 0
\(943\) −1.79356 −0.0584063
\(944\) 0 0
\(945\) 2.80016 0.0910893
\(946\) 0 0
\(947\) −20.1280 −0.654073 −0.327037 0.945012i \(-0.606050\pi\)
−0.327037 + 0.945012i \(0.606050\pi\)
\(948\) 0 0
\(949\) 7.84335 0.254606
\(950\) 0 0
\(951\) −14.6686 −0.475662
\(952\) 0 0
\(953\) −3.96459 −0.128426 −0.0642128 0.997936i \(-0.520454\pi\)
−0.0642128 + 0.997936i \(0.520454\pi\)
\(954\) 0 0
\(955\) −2.98651 −0.0966414
\(956\) 0 0
\(957\) 2.54616 0.0823057
\(958\) 0 0
\(959\) −6.28038 −0.202804
\(960\) 0 0
\(961\) −19.2209 −0.620030
\(962\) 0 0
\(963\) −4.03839 −0.130135
\(964\) 0 0
\(965\) −11.9299 −0.384038
\(966\) 0 0
\(967\) 34.1500 1.09819 0.549096 0.835759i \(-0.314972\pi\)
0.549096 + 0.835759i \(0.314972\pi\)
\(968\) 0 0
\(969\) 4.28994 0.137813
\(970\) 0 0
\(971\) −49.4362 −1.58648 −0.793242 0.608907i \(-0.791608\pi\)
−0.793242 + 0.608907i \(0.791608\pi\)
\(972\) 0 0
\(973\) −46.2779 −1.48360
\(974\) 0 0
\(975\) −3.59031 −0.114982
\(976\) 0 0
\(977\) −52.4778 −1.67891 −0.839457 0.543426i \(-0.817127\pi\)
−0.839457 + 0.543426i \(0.817127\pi\)
\(978\) 0 0
\(979\) 7.90851 0.252757
\(980\) 0 0
\(981\) 4.95193 0.158103
\(982\) 0 0
\(983\) −15.7583 −0.502611 −0.251306 0.967908i \(-0.580860\pi\)
−0.251306 + 0.967908i \(0.580860\pi\)
\(984\) 0 0
\(985\) −23.3272 −0.743265
\(986\) 0 0
\(987\) −30.4494 −0.969214
\(988\) 0 0
\(989\) −6.06519 −0.192862
\(990\) 0 0
\(991\) 30.7377 0.976414 0.488207 0.872728i \(-0.337651\pi\)
0.488207 + 0.872728i \(0.337651\pi\)
\(992\) 0 0
\(993\) −5.88278 −0.186685
\(994\) 0 0
\(995\) −10.3504 −0.328128
\(996\) 0 0
\(997\) −25.6134 −0.811184 −0.405592 0.914054i \(-0.632935\pi\)
−0.405592 + 0.914054i \(0.632935\pi\)
\(998\) 0 0
\(999\) −5.13260 −0.162388
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 \(a_p\))