Properties

Label 4008.2.a.i.1.4
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.482381\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.48238 q^{5}\) \(-1.03908 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.48238 q^{5}\) \(-1.03908 q^{7}\) \(+1.00000 q^{9}\) \(+5.64105 q^{11}\) \(-4.47983 q^{13}\) \(-1.48238 q^{15}\) \(-6.13922 q^{17}\) \(+5.87154 q^{19}\) \(-1.03908 q^{21}\) \(-1.22710 q^{23}\) \(-2.80255 q^{25}\) \(+1.00000 q^{27}\) \(-6.91991 q^{29}\) \(+3.70123 q^{31}\) \(+5.64105 q^{33}\) \(+1.54031 q^{35}\) \(-6.62294 q^{37}\) \(-4.47983 q^{39}\) \(+1.85846 q^{41}\) \(-2.29781 q^{43}\) \(-1.48238 q^{45}\) \(+3.59229 q^{47}\) \(-5.92031 q^{49}\) \(-6.13922 q^{51}\) \(-0.299721 q^{53}\) \(-8.36218 q^{55}\) \(+5.87154 q^{57}\) \(+0.102376 q^{59}\) \(+3.64463 q^{61}\) \(-1.03908 q^{63}\) \(+6.64082 q^{65}\) \(-5.27810 q^{67}\) \(-1.22710 q^{69}\) \(+2.00339 q^{71}\) \(+9.34023 q^{73}\) \(-2.80255 q^{75}\) \(-5.86150 q^{77}\) \(-3.92469 q^{79}\) \(+1.00000 q^{81}\) \(-11.4441 q^{83}\) \(+9.10067 q^{85}\) \(-6.91991 q^{87}\) \(-10.4583 q^{89}\) \(+4.65490 q^{91}\) \(+3.70123 q^{93}\) \(-8.70385 q^{95}\) \(-3.40524 q^{97}\) \(+5.64105 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.48238 −0.662941 −0.331470 0.943466i \(-0.607545\pi\)
−0.331470 + 0.943466i \(0.607545\pi\)
\(6\) 0 0
\(7\) −1.03908 −0.392735 −0.196368 0.980530i \(-0.562915\pi\)
−0.196368 + 0.980530i \(0.562915\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.64105 1.70084 0.850420 0.526105i \(-0.176348\pi\)
0.850420 + 0.526105i \(0.176348\pi\)
\(12\) 0 0
\(13\) −4.47983 −1.24248 −0.621241 0.783620i \(-0.713371\pi\)
−0.621241 + 0.783620i \(0.713371\pi\)
\(14\) 0 0
\(15\) −1.48238 −0.382749
\(16\) 0 0
\(17\) −6.13922 −1.48898 −0.744490 0.667634i \(-0.767307\pi\)
−0.744490 + 0.667634i \(0.767307\pi\)
\(18\) 0 0
\(19\) 5.87154 1.34702 0.673511 0.739177i \(-0.264785\pi\)
0.673511 + 0.739177i \(0.264785\pi\)
\(20\) 0 0
\(21\) −1.03908 −0.226746
\(22\) 0 0
\(23\) −1.22710 −0.255869 −0.127934 0.991783i \(-0.540835\pi\)
−0.127934 + 0.991783i \(0.540835\pi\)
\(24\) 0 0
\(25\) −2.80255 −0.560509
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.91991 −1.28500 −0.642498 0.766288i \(-0.722102\pi\)
−0.642498 + 0.766288i \(0.722102\pi\)
\(30\) 0 0
\(31\) 3.70123 0.664760 0.332380 0.943146i \(-0.392148\pi\)
0.332380 + 0.943146i \(0.392148\pi\)
\(32\) 0 0
\(33\) 5.64105 0.981980
\(34\) 0 0
\(35\) 1.54031 0.260360
\(36\) 0 0
\(37\) −6.62294 −1.08880 −0.544402 0.838824i \(-0.683244\pi\)
−0.544402 + 0.838824i \(0.683244\pi\)
\(38\) 0 0
\(39\) −4.47983 −0.717347
\(40\) 0 0
\(41\) 1.85846 0.290242 0.145121 0.989414i \(-0.453643\pi\)
0.145121 + 0.989414i \(0.453643\pi\)
\(42\) 0 0
\(43\) −2.29781 −0.350413 −0.175207 0.984532i \(-0.556059\pi\)
−0.175207 + 0.984532i \(0.556059\pi\)
\(44\) 0 0
\(45\) −1.48238 −0.220980
\(46\) 0 0
\(47\) 3.59229 0.523990 0.261995 0.965069i \(-0.415620\pi\)
0.261995 + 0.965069i \(0.415620\pi\)
\(48\) 0 0
\(49\) −5.92031 −0.845759
\(50\) 0 0
\(51\) −6.13922 −0.859663
\(52\) 0 0
\(53\) −0.299721 −0.0411699 −0.0205849 0.999788i \(-0.506553\pi\)
−0.0205849 + 0.999788i \(0.506553\pi\)
\(54\) 0 0
\(55\) −8.36218 −1.12756
\(56\) 0 0
\(57\) 5.87154 0.777704
\(58\) 0 0
\(59\) 0.102376 0.0133282 0.00666409 0.999978i \(-0.497879\pi\)
0.00666409 + 0.999978i \(0.497879\pi\)
\(60\) 0 0
\(61\) 3.64463 0.466647 0.233323 0.972399i \(-0.425040\pi\)
0.233323 + 0.972399i \(0.425040\pi\)
\(62\) 0 0
\(63\) −1.03908 −0.130912
\(64\) 0 0
\(65\) 6.64082 0.823692
\(66\) 0 0
\(67\) −5.27810 −0.644823 −0.322412 0.946600i \(-0.604493\pi\)
−0.322412 + 0.946600i \(0.604493\pi\)
\(68\) 0 0
\(69\) −1.22710 −0.147726
\(70\) 0 0
\(71\) 2.00339 0.237759 0.118879 0.992909i \(-0.462070\pi\)
0.118879 + 0.992909i \(0.462070\pi\)
\(72\) 0 0
\(73\) 9.34023 1.09319 0.546596 0.837397i \(-0.315923\pi\)
0.546596 + 0.837397i \(0.315923\pi\)
\(74\) 0 0
\(75\) −2.80255 −0.323610
\(76\) 0 0
\(77\) −5.86150 −0.667979
\(78\) 0 0
\(79\) −3.92469 −0.441562 −0.220781 0.975323i \(-0.570861\pi\)
−0.220781 + 0.975323i \(0.570861\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.4441 −1.25615 −0.628075 0.778153i \(-0.716157\pi\)
−0.628075 + 0.778153i \(0.716157\pi\)
\(84\) 0 0
\(85\) 9.10067 0.987106
\(86\) 0 0
\(87\) −6.91991 −0.741893
\(88\) 0 0
\(89\) −10.4583 −1.10858 −0.554290 0.832324i \(-0.687010\pi\)
−0.554290 + 0.832324i \(0.687010\pi\)
\(90\) 0 0
\(91\) 4.65490 0.487966
\(92\) 0 0
\(93\) 3.70123 0.383799
\(94\) 0 0
\(95\) −8.70385 −0.892997
\(96\) 0 0
\(97\) −3.40524 −0.345749 −0.172875 0.984944i \(-0.555306\pi\)
−0.172875 + 0.984944i \(0.555306\pi\)
\(98\) 0 0
\(99\) 5.64105 0.566947
\(100\) 0 0
\(101\) −12.6052 −1.25426 −0.627132 0.778913i \(-0.715771\pi\)
−0.627132 + 0.778913i \(0.715771\pi\)
\(102\) 0 0
\(103\) −15.3704 −1.51449 −0.757245 0.653131i \(-0.773455\pi\)
−0.757245 + 0.653131i \(0.773455\pi\)
\(104\) 0 0
\(105\) 1.54031 0.150319
\(106\) 0 0
\(107\) 6.62482 0.640446 0.320223 0.947342i \(-0.396242\pi\)
0.320223 + 0.947342i \(0.396242\pi\)
\(108\) 0 0
\(109\) −18.9911 −1.81901 −0.909507 0.415690i \(-0.863540\pi\)
−0.909507 + 0.415690i \(0.863540\pi\)
\(110\) 0 0
\(111\) −6.62294 −0.628622
\(112\) 0 0
\(113\) 16.3656 1.53955 0.769774 0.638316i \(-0.220369\pi\)
0.769774 + 0.638316i \(0.220369\pi\)
\(114\) 0 0
\(115\) 1.81903 0.169626
\(116\) 0 0
\(117\) −4.47983 −0.414160
\(118\) 0 0
\(119\) 6.37914 0.584775
\(120\) 0 0
\(121\) 20.8214 1.89286
\(122\) 0 0
\(123\) 1.85846 0.167571
\(124\) 0 0
\(125\) 11.5663 1.03453
\(126\) 0 0
\(127\) 17.6141 1.56300 0.781499 0.623906i \(-0.214455\pi\)
0.781499 + 0.623906i \(0.214455\pi\)
\(128\) 0 0
\(129\) −2.29781 −0.202311
\(130\) 0 0
\(131\) 9.79697 0.855965 0.427982 0.903787i \(-0.359224\pi\)
0.427982 + 0.903787i \(0.359224\pi\)
\(132\) 0 0
\(133\) −6.10099 −0.529023
\(134\) 0 0
\(135\) −1.48238 −0.127583
\(136\) 0 0
\(137\) −6.81856 −0.582549 −0.291274 0.956640i \(-0.594079\pi\)
−0.291274 + 0.956640i \(0.594079\pi\)
\(138\) 0 0
\(139\) −5.34794 −0.453606 −0.226803 0.973941i \(-0.572827\pi\)
−0.226803 + 0.973941i \(0.572827\pi\)
\(140\) 0 0
\(141\) 3.59229 0.302526
\(142\) 0 0
\(143\) −25.2709 −2.11326
\(144\) 0 0
\(145\) 10.2579 0.851876
\(146\) 0 0
\(147\) −5.92031 −0.488299
\(148\) 0 0
\(149\) −20.0944 −1.64620 −0.823100 0.567896i \(-0.807757\pi\)
−0.823100 + 0.567896i \(0.807757\pi\)
\(150\) 0 0
\(151\) −15.4596 −1.25808 −0.629041 0.777372i \(-0.716552\pi\)
−0.629041 + 0.777372i \(0.716552\pi\)
\(152\) 0 0
\(153\) −6.13922 −0.496327
\(154\) 0 0
\(155\) −5.48663 −0.440696
\(156\) 0 0
\(157\) 10.6576 0.850568 0.425284 0.905060i \(-0.360174\pi\)
0.425284 + 0.905060i \(0.360174\pi\)
\(158\) 0 0
\(159\) −0.299721 −0.0237694
\(160\) 0 0
\(161\) 1.27506 0.100489
\(162\) 0 0
\(163\) −21.2802 −1.66680 −0.833399 0.552672i \(-0.813608\pi\)
−0.833399 + 0.552672i \(0.813608\pi\)
\(164\) 0 0
\(165\) −8.36218 −0.650995
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 7.06888 0.543760
\(170\) 0 0
\(171\) 5.87154 0.449008
\(172\) 0 0
\(173\) −16.4057 −1.24730 −0.623650 0.781704i \(-0.714351\pi\)
−0.623650 + 0.781704i \(0.714351\pi\)
\(174\) 0 0
\(175\) 2.91207 0.220132
\(176\) 0 0
\(177\) 0.102376 0.00769503
\(178\) 0 0
\(179\) 1.21604 0.0908913 0.0454456 0.998967i \(-0.485529\pi\)
0.0454456 + 0.998967i \(0.485529\pi\)
\(180\) 0 0
\(181\) −6.24694 −0.464331 −0.232166 0.972676i \(-0.574581\pi\)
−0.232166 + 0.972676i \(0.574581\pi\)
\(182\) 0 0
\(183\) 3.64463 0.269419
\(184\) 0 0
\(185\) 9.81772 0.721813
\(186\) 0 0
\(187\) −34.6316 −2.53252
\(188\) 0 0
\(189\) −1.03908 −0.0755819
\(190\) 0 0
\(191\) 16.2291 1.17429 0.587146 0.809481i \(-0.300251\pi\)
0.587146 + 0.809481i \(0.300251\pi\)
\(192\) 0 0
\(193\) −8.97087 −0.645737 −0.322869 0.946444i \(-0.604647\pi\)
−0.322869 + 0.946444i \(0.604647\pi\)
\(194\) 0 0
\(195\) 6.64082 0.475559
\(196\) 0 0
\(197\) −23.1926 −1.65240 −0.826201 0.563376i \(-0.809502\pi\)
−0.826201 + 0.563376i \(0.809502\pi\)
\(198\) 0 0
\(199\) −13.8934 −0.984876 −0.492438 0.870348i \(-0.663894\pi\)
−0.492438 + 0.870348i \(0.663894\pi\)
\(200\) 0 0
\(201\) −5.27810 −0.372289
\(202\) 0 0
\(203\) 7.19034 0.504663
\(204\) 0 0
\(205\) −2.75494 −0.192413
\(206\) 0 0
\(207\) −1.22710 −0.0852895
\(208\) 0 0
\(209\) 33.1216 2.29107
\(210\) 0 0
\(211\) −11.9560 −0.823082 −0.411541 0.911391i \(-0.635009\pi\)
−0.411541 + 0.911391i \(0.635009\pi\)
\(212\) 0 0
\(213\) 2.00339 0.137270
\(214\) 0 0
\(215\) 3.40623 0.232303
\(216\) 0 0
\(217\) −3.84587 −0.261074
\(218\) 0 0
\(219\) 9.34023 0.631155
\(220\) 0 0
\(221\) 27.5027 1.85003
\(222\) 0 0
\(223\) −25.7496 −1.72432 −0.862159 0.506638i \(-0.830888\pi\)
−0.862159 + 0.506638i \(0.830888\pi\)
\(224\) 0 0
\(225\) −2.80255 −0.186836
\(226\) 0 0
\(227\) 23.2899 1.54580 0.772901 0.634527i \(-0.218805\pi\)
0.772901 + 0.634527i \(0.218805\pi\)
\(228\) 0 0
\(229\) −10.4690 −0.691813 −0.345906 0.938269i \(-0.612429\pi\)
−0.345906 + 0.938269i \(0.612429\pi\)
\(230\) 0 0
\(231\) −5.86150 −0.385658
\(232\) 0 0
\(233\) −19.6195 −1.28532 −0.642658 0.766153i \(-0.722168\pi\)
−0.642658 + 0.766153i \(0.722168\pi\)
\(234\) 0 0
\(235\) −5.32515 −0.347374
\(236\) 0 0
\(237\) −3.92469 −0.254936
\(238\) 0 0
\(239\) 15.5821 1.00793 0.503963 0.863725i \(-0.331875\pi\)
0.503963 + 0.863725i \(0.331875\pi\)
\(240\) 0 0
\(241\) −30.8313 −1.98602 −0.993011 0.118025i \(-0.962344\pi\)
−0.993011 + 0.118025i \(0.962344\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 8.77616 0.560688
\(246\) 0 0
\(247\) −26.3035 −1.67365
\(248\) 0 0
\(249\) −11.4441 −0.725238
\(250\) 0 0
\(251\) −5.66860 −0.357799 −0.178899 0.983867i \(-0.557254\pi\)
−0.178899 + 0.983867i \(0.557254\pi\)
\(252\) 0 0
\(253\) −6.92214 −0.435191
\(254\) 0 0
\(255\) 9.10067 0.569906
\(256\) 0 0
\(257\) −6.81618 −0.425182 −0.212591 0.977141i \(-0.568190\pi\)
−0.212591 + 0.977141i \(0.568190\pi\)
\(258\) 0 0
\(259\) 6.88176 0.427612
\(260\) 0 0
\(261\) −6.91991 −0.428332
\(262\) 0 0
\(263\) 4.22632 0.260606 0.130303 0.991474i \(-0.458405\pi\)
0.130303 + 0.991474i \(0.458405\pi\)
\(264\) 0 0
\(265\) 0.444301 0.0272932
\(266\) 0 0
\(267\) −10.4583 −0.640039
\(268\) 0 0
\(269\) 20.5783 1.25468 0.627340 0.778745i \(-0.284144\pi\)
0.627340 + 0.778745i \(0.284144\pi\)
\(270\) 0 0
\(271\) −6.93172 −0.421072 −0.210536 0.977586i \(-0.567521\pi\)
−0.210536 + 0.977586i \(0.567521\pi\)
\(272\) 0 0
\(273\) 4.65490 0.281727
\(274\) 0 0
\(275\) −15.8093 −0.953336
\(276\) 0 0
\(277\) 22.5380 1.35418 0.677088 0.735902i \(-0.263242\pi\)
0.677088 + 0.735902i \(0.263242\pi\)
\(278\) 0 0
\(279\) 3.70123 0.221587
\(280\) 0 0
\(281\) 20.5684 1.22701 0.613504 0.789691i \(-0.289759\pi\)
0.613504 + 0.789691i \(0.289759\pi\)
\(282\) 0 0
\(283\) 29.4021 1.74777 0.873886 0.486131i \(-0.161592\pi\)
0.873886 + 0.486131i \(0.161592\pi\)
\(284\) 0 0
\(285\) −8.70385 −0.515572
\(286\) 0 0
\(287\) −1.93108 −0.113988
\(288\) 0 0
\(289\) 20.6900 1.21706
\(290\) 0 0
\(291\) −3.40524 −0.199618
\(292\) 0 0
\(293\) 20.2839 1.18500 0.592500 0.805571i \(-0.298141\pi\)
0.592500 + 0.805571i \(0.298141\pi\)
\(294\) 0 0
\(295\) −0.151760 −0.00883580
\(296\) 0 0
\(297\) 5.64105 0.327327
\(298\) 0 0
\(299\) 5.49721 0.317912
\(300\) 0 0
\(301\) 2.38761 0.137619
\(302\) 0 0
\(303\) −12.6052 −0.724149
\(304\) 0 0
\(305\) −5.40273 −0.309359
\(306\) 0 0
\(307\) 10.9899 0.627224 0.313612 0.949551i \(-0.398461\pi\)
0.313612 + 0.949551i \(0.398461\pi\)
\(308\) 0 0
\(309\) −15.3704 −0.874391
\(310\) 0 0
\(311\) 26.9703 1.52935 0.764673 0.644418i \(-0.222900\pi\)
0.764673 + 0.644418i \(0.222900\pi\)
\(312\) 0 0
\(313\) −32.1109 −1.81501 −0.907507 0.420036i \(-0.862017\pi\)
−0.907507 + 0.420036i \(0.862017\pi\)
\(314\) 0 0
\(315\) 1.54031 0.0867867
\(316\) 0 0
\(317\) −21.3657 −1.20002 −0.600008 0.799994i \(-0.704836\pi\)
−0.600008 + 0.799994i \(0.704836\pi\)
\(318\) 0 0
\(319\) −39.0356 −2.18557
\(320\) 0 0
\(321\) 6.62482 0.369761
\(322\) 0 0
\(323\) −36.0467 −2.00569
\(324\) 0 0
\(325\) 12.5549 0.696422
\(326\) 0 0
\(327\) −18.9911 −1.05021
\(328\) 0 0
\(329\) −3.73268 −0.205789
\(330\) 0 0
\(331\) 23.6701 1.30102 0.650512 0.759496i \(-0.274554\pi\)
0.650512 + 0.759496i \(0.274554\pi\)
\(332\) 0 0
\(333\) −6.62294 −0.362935
\(334\) 0 0
\(335\) 7.82416 0.427480
\(336\) 0 0
\(337\) −23.6003 −1.28559 −0.642796 0.766037i \(-0.722226\pi\)
−0.642796 + 0.766037i \(0.722226\pi\)
\(338\) 0 0
\(339\) 16.3656 0.888859
\(340\) 0 0
\(341\) 20.8788 1.13065
\(342\) 0 0
\(343\) 13.4252 0.724894
\(344\) 0 0
\(345\) 1.81903 0.0979335
\(346\) 0 0
\(347\) 17.2073 0.923736 0.461868 0.886949i \(-0.347179\pi\)
0.461868 + 0.886949i \(0.347179\pi\)
\(348\) 0 0
\(349\) 20.7148 1.10884 0.554419 0.832238i \(-0.312941\pi\)
0.554419 + 0.832238i \(0.312941\pi\)
\(350\) 0 0
\(351\) −4.47983 −0.239116
\(352\) 0 0
\(353\) 1.81530 0.0966187 0.0483094 0.998832i \(-0.484617\pi\)
0.0483094 + 0.998832i \(0.484617\pi\)
\(354\) 0 0
\(355\) −2.96979 −0.157620
\(356\) 0 0
\(357\) 6.37914 0.337620
\(358\) 0 0
\(359\) −7.55958 −0.398979 −0.199490 0.979900i \(-0.563928\pi\)
−0.199490 + 0.979900i \(0.563928\pi\)
\(360\) 0 0
\(361\) 15.4749 0.814471
\(362\) 0 0
\(363\) 20.8214 1.09284
\(364\) 0 0
\(365\) −13.8458 −0.724722
\(366\) 0 0
\(367\) −24.2242 −1.26449 −0.632247 0.774767i \(-0.717867\pi\)
−0.632247 + 0.774767i \(0.717867\pi\)
\(368\) 0 0
\(369\) 1.85846 0.0967473
\(370\) 0 0
\(371\) 0.311434 0.0161689
\(372\) 0 0
\(373\) 8.50121 0.440176 0.220088 0.975480i \(-0.429366\pi\)
0.220088 + 0.975480i \(0.429366\pi\)
\(374\) 0 0
\(375\) 11.5663 0.597284
\(376\) 0 0
\(377\) 31.0000 1.59658
\(378\) 0 0
\(379\) −4.72626 −0.242772 −0.121386 0.992605i \(-0.538734\pi\)
−0.121386 + 0.992605i \(0.538734\pi\)
\(380\) 0 0
\(381\) 17.6141 0.902398
\(382\) 0 0
\(383\) 22.7605 1.16301 0.581505 0.813543i \(-0.302464\pi\)
0.581505 + 0.813543i \(0.302464\pi\)
\(384\) 0 0
\(385\) 8.68897 0.442831
\(386\) 0 0
\(387\) −2.29781 −0.116804
\(388\) 0 0
\(389\) 26.2141 1.32911 0.664554 0.747241i \(-0.268622\pi\)
0.664554 + 0.747241i \(0.268622\pi\)
\(390\) 0 0
\(391\) 7.53346 0.380983
\(392\) 0 0
\(393\) 9.79697 0.494192
\(394\) 0 0
\(395\) 5.81789 0.292730
\(396\) 0 0
\(397\) 8.99098 0.451244 0.225622 0.974215i \(-0.427559\pi\)
0.225622 + 0.974215i \(0.427559\pi\)
\(398\) 0 0
\(399\) −6.10099 −0.305432
\(400\) 0 0
\(401\) 4.85669 0.242531 0.121266 0.992620i \(-0.461305\pi\)
0.121266 + 0.992620i \(0.461305\pi\)
\(402\) 0 0
\(403\) −16.5809 −0.825952
\(404\) 0 0
\(405\) −1.48238 −0.0736601
\(406\) 0 0
\(407\) −37.3603 −1.85188
\(408\) 0 0
\(409\) 28.4764 1.40807 0.704034 0.710166i \(-0.251380\pi\)
0.704034 + 0.710166i \(0.251380\pi\)
\(410\) 0 0
\(411\) −6.81856 −0.336335
\(412\) 0 0
\(413\) −0.106376 −0.00523444
\(414\) 0 0
\(415\) 16.9645 0.832753
\(416\) 0 0
\(417\) −5.34794 −0.261890
\(418\) 0 0
\(419\) 22.7505 1.11143 0.555717 0.831371i \(-0.312444\pi\)
0.555717 + 0.831371i \(0.312444\pi\)
\(420\) 0 0
\(421\) 9.05605 0.441365 0.220682 0.975346i \(-0.429172\pi\)
0.220682 + 0.975346i \(0.429172\pi\)
\(422\) 0 0
\(423\) 3.59229 0.174663
\(424\) 0 0
\(425\) 17.2055 0.834587
\(426\) 0 0
\(427\) −3.78706 −0.183269
\(428\) 0 0
\(429\) −25.2709 −1.22009
\(430\) 0 0
\(431\) 7.21053 0.347319 0.173660 0.984806i \(-0.444441\pi\)
0.173660 + 0.984806i \(0.444441\pi\)
\(432\) 0 0
\(433\) −26.9366 −1.29449 −0.647246 0.762281i \(-0.724079\pi\)
−0.647246 + 0.762281i \(0.724079\pi\)
\(434\) 0 0
\(435\) 10.2579 0.491831
\(436\) 0 0
\(437\) −7.20498 −0.344661
\(438\) 0 0
\(439\) −24.4736 −1.16806 −0.584031 0.811731i \(-0.698525\pi\)
−0.584031 + 0.811731i \(0.698525\pi\)
\(440\) 0 0
\(441\) −5.92031 −0.281920
\(442\) 0 0
\(443\) 32.1730 1.52858 0.764292 0.644870i \(-0.223088\pi\)
0.764292 + 0.644870i \(0.223088\pi\)
\(444\) 0 0
\(445\) 15.5032 0.734923
\(446\) 0 0
\(447\) −20.0944 −0.950434
\(448\) 0 0
\(449\) 37.2697 1.75887 0.879434 0.476021i \(-0.157921\pi\)
0.879434 + 0.476021i \(0.157921\pi\)
\(450\) 0 0
\(451\) 10.4836 0.493655
\(452\) 0 0
\(453\) −15.4596 −0.726354
\(454\) 0 0
\(455\) −6.90033 −0.323493
\(456\) 0 0
\(457\) −3.52936 −0.165096 −0.0825482 0.996587i \(-0.526306\pi\)
−0.0825482 + 0.996587i \(0.526306\pi\)
\(458\) 0 0
\(459\) −6.13922 −0.286554
\(460\) 0 0
\(461\) −5.01289 −0.233474 −0.116737 0.993163i \(-0.537243\pi\)
−0.116737 + 0.993163i \(0.537243\pi\)
\(462\) 0 0
\(463\) −11.8928 −0.552707 −0.276353 0.961056i \(-0.589126\pi\)
−0.276353 + 0.961056i \(0.589126\pi\)
\(464\) 0 0
\(465\) −5.48663 −0.254436
\(466\) 0 0
\(467\) −8.68147 −0.401730 −0.200865 0.979619i \(-0.564375\pi\)
−0.200865 + 0.979619i \(0.564375\pi\)
\(468\) 0 0
\(469\) 5.48437 0.253245
\(470\) 0 0
\(471\) 10.6576 0.491076
\(472\) 0 0
\(473\) −12.9621 −0.595996
\(474\) 0 0
\(475\) −16.4553 −0.755019
\(476\) 0 0
\(477\) −0.299721 −0.0137233
\(478\) 0 0
\(479\) −11.9188 −0.544585 −0.272293 0.962215i \(-0.587782\pi\)
−0.272293 + 0.962215i \(0.587782\pi\)
\(480\) 0 0
\(481\) 29.6697 1.35282
\(482\) 0 0
\(483\) 1.27506 0.0580171
\(484\) 0 0
\(485\) 5.04786 0.229211
\(486\) 0 0
\(487\) 34.7303 1.57378 0.786889 0.617095i \(-0.211690\pi\)
0.786889 + 0.617095i \(0.211690\pi\)
\(488\) 0 0
\(489\) −21.2802 −0.962326
\(490\) 0 0
\(491\) −8.62022 −0.389025 −0.194513 0.980900i \(-0.562313\pi\)
−0.194513 + 0.980900i \(0.562313\pi\)
\(492\) 0 0
\(493\) 42.4829 1.91333
\(494\) 0 0
\(495\) −8.36218 −0.375852
\(496\) 0 0
\(497\) −2.08168 −0.0933762
\(498\) 0 0
\(499\) 19.1457 0.857080 0.428540 0.903523i \(-0.359028\pi\)
0.428540 + 0.903523i \(0.359028\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −24.8619 −1.10854 −0.554269 0.832337i \(-0.687002\pi\)
−0.554269 + 0.832337i \(0.687002\pi\)
\(504\) 0 0
\(505\) 18.6857 0.831502
\(506\) 0 0
\(507\) 7.06888 0.313940
\(508\) 0 0
\(509\) 2.12427 0.0941567 0.0470783 0.998891i \(-0.485009\pi\)
0.0470783 + 0.998891i \(0.485009\pi\)
\(510\) 0 0
\(511\) −9.70525 −0.429335
\(512\) 0 0
\(513\) 5.87154 0.259235
\(514\) 0 0
\(515\) 22.7848 1.00402
\(516\) 0 0
\(517\) 20.2643 0.891222
\(518\) 0 0
\(519\) −16.4057 −0.720129
\(520\) 0 0
\(521\) −2.08693 −0.0914302 −0.0457151 0.998955i \(-0.514557\pi\)
−0.0457151 + 0.998955i \(0.514557\pi\)
\(522\) 0 0
\(523\) −21.6413 −0.946306 −0.473153 0.880980i \(-0.656884\pi\)
−0.473153 + 0.880980i \(0.656884\pi\)
\(524\) 0 0
\(525\) 2.91207 0.127093
\(526\) 0 0
\(527\) −22.7226 −0.989814
\(528\) 0 0
\(529\) −21.4942 −0.934531
\(530\) 0 0
\(531\) 0.102376 0.00444273
\(532\) 0 0
\(533\) −8.32556 −0.360620
\(534\) 0 0
\(535\) −9.82051 −0.424578
\(536\) 0 0
\(537\) 1.21604 0.0524761
\(538\) 0 0
\(539\) −33.3968 −1.43850
\(540\) 0 0
\(541\) 24.7817 1.06545 0.532725 0.846289i \(-0.321168\pi\)
0.532725 + 0.846289i \(0.321168\pi\)
\(542\) 0 0
\(543\) −6.24694 −0.268082
\(544\) 0 0
\(545\) 28.1520 1.20590
\(546\) 0 0
\(547\) 2.13808 0.0914179 0.0457089 0.998955i \(-0.485445\pi\)
0.0457089 + 0.998955i \(0.485445\pi\)
\(548\) 0 0
\(549\) 3.64463 0.155549
\(550\) 0 0
\(551\) −40.6305 −1.73092
\(552\) 0 0
\(553\) 4.07807 0.173417
\(554\) 0 0
\(555\) 9.81772 0.416739
\(556\) 0 0
\(557\) −11.7687 −0.498656 −0.249328 0.968419i \(-0.580210\pi\)
−0.249328 + 0.968419i \(0.580210\pi\)
\(558\) 0 0
\(559\) 10.2938 0.435382
\(560\) 0 0
\(561\) −34.6316 −1.46215
\(562\) 0 0
\(563\) 14.6893 0.619079 0.309540 0.950887i \(-0.399825\pi\)
0.309540 + 0.950887i \(0.399825\pi\)
\(564\) 0 0
\(565\) −24.2601 −1.02063
\(566\) 0 0
\(567\) −1.03908 −0.0436372
\(568\) 0 0
\(569\) −16.2827 −0.682608 −0.341304 0.939953i \(-0.610869\pi\)
−0.341304 + 0.939953i \(0.610869\pi\)
\(570\) 0 0
\(571\) 14.0677 0.588714 0.294357 0.955696i \(-0.404895\pi\)
0.294357 + 0.955696i \(0.404895\pi\)
\(572\) 0 0
\(573\) 16.2291 0.677978
\(574\) 0 0
\(575\) 3.43901 0.143417
\(576\) 0 0
\(577\) 15.5023 0.645369 0.322684 0.946507i \(-0.395415\pi\)
0.322684 + 0.946507i \(0.395415\pi\)
\(578\) 0 0
\(579\) −8.97087 −0.372816
\(580\) 0 0
\(581\) 11.8913 0.493334
\(582\) 0 0
\(583\) −1.69074 −0.0700234
\(584\) 0 0
\(585\) 6.64082 0.274564
\(586\) 0 0
\(587\) −22.7257 −0.937989 −0.468995 0.883201i \(-0.655384\pi\)
−0.468995 + 0.883201i \(0.655384\pi\)
\(588\) 0 0
\(589\) 21.7319 0.895447
\(590\) 0 0
\(591\) −23.1926 −0.954015
\(592\) 0 0
\(593\) −34.1852 −1.40382 −0.701909 0.712267i \(-0.747669\pi\)
−0.701909 + 0.712267i \(0.747669\pi\)
\(594\) 0 0
\(595\) −9.45631 −0.387671
\(596\) 0 0
\(597\) −13.8934 −0.568618
\(598\) 0 0
\(599\) 5.88943 0.240636 0.120318 0.992735i \(-0.461609\pi\)
0.120318 + 0.992735i \(0.461609\pi\)
\(600\) 0 0
\(601\) −39.0125 −1.59135 −0.795676 0.605723i \(-0.792884\pi\)
−0.795676 + 0.605723i \(0.792884\pi\)
\(602\) 0 0
\(603\) −5.27810 −0.214941
\(604\) 0 0
\(605\) −30.8653 −1.25485
\(606\) 0 0
\(607\) −5.36469 −0.217746 −0.108873 0.994056i \(-0.534724\pi\)
−0.108873 + 0.994056i \(0.534724\pi\)
\(608\) 0 0
\(609\) 7.19034 0.291367
\(610\) 0 0
\(611\) −16.0929 −0.651047
\(612\) 0 0
\(613\) −44.6516 −1.80346 −0.901731 0.432297i \(-0.857703\pi\)
−0.901731 + 0.432297i \(0.857703\pi\)
\(614\) 0 0
\(615\) −2.75494 −0.111090
\(616\) 0 0
\(617\) −15.1280 −0.609030 −0.304515 0.952508i \(-0.598494\pi\)
−0.304515 + 0.952508i \(0.598494\pi\)
\(618\) 0 0
\(619\) −38.8437 −1.56126 −0.780631 0.624992i \(-0.785102\pi\)
−0.780631 + 0.624992i \(0.785102\pi\)
\(620\) 0 0
\(621\) −1.22710 −0.0492419
\(622\) 0 0
\(623\) 10.8670 0.435378
\(624\) 0 0
\(625\) −3.13300 −0.125320
\(626\) 0 0
\(627\) 33.1216 1.32275
\(628\) 0 0
\(629\) 40.6597 1.62121
\(630\) 0 0
\(631\) 23.0968 0.919470 0.459735 0.888056i \(-0.347944\pi\)
0.459735 + 0.888056i \(0.347944\pi\)
\(632\) 0 0
\(633\) −11.9560 −0.475207
\(634\) 0 0
\(635\) −26.1108 −1.03618
\(636\) 0 0
\(637\) 26.5220 1.05084
\(638\) 0 0
\(639\) 2.00339 0.0792529
\(640\) 0 0
\(641\) 28.3497 1.11974 0.559872 0.828579i \(-0.310850\pi\)
0.559872 + 0.828579i \(0.310850\pi\)
\(642\) 0 0
\(643\) −40.8208 −1.60981 −0.804907 0.593401i \(-0.797785\pi\)
−0.804907 + 0.593401i \(0.797785\pi\)
\(644\) 0 0
\(645\) 3.40623 0.134120
\(646\) 0 0
\(647\) −31.6874 −1.24576 −0.622881 0.782317i \(-0.714038\pi\)
−0.622881 + 0.782317i \(0.714038\pi\)
\(648\) 0 0
\(649\) 0.577506 0.0226691
\(650\) 0 0
\(651\) −3.84587 −0.150731
\(652\) 0 0
\(653\) 17.1808 0.672337 0.336169 0.941802i \(-0.390869\pi\)
0.336169 + 0.941802i \(0.390869\pi\)
\(654\) 0 0
\(655\) −14.5228 −0.567454
\(656\) 0 0
\(657\) 9.34023 0.364397
\(658\) 0 0
\(659\) 29.0908 1.13322 0.566608 0.823988i \(-0.308255\pi\)
0.566608 + 0.823988i \(0.308255\pi\)
\(660\) 0 0
\(661\) 2.34936 0.0913794 0.0456897 0.998956i \(-0.485451\pi\)
0.0456897 + 0.998956i \(0.485451\pi\)
\(662\) 0 0
\(663\) 27.5027 1.06812
\(664\) 0 0
\(665\) 9.04400 0.350711
\(666\) 0 0
\(667\) 8.49144 0.328790
\(668\) 0 0
\(669\) −25.7496 −0.995535
\(670\) 0 0
\(671\) 20.5595 0.793691
\(672\) 0 0
\(673\) 19.7107 0.759792 0.379896 0.925029i \(-0.375960\pi\)
0.379896 + 0.925029i \(0.375960\pi\)
\(674\) 0 0
\(675\) −2.80255 −0.107870
\(676\) 0 0
\(677\) 13.2631 0.509744 0.254872 0.966975i \(-0.417967\pi\)
0.254872 + 0.966975i \(0.417967\pi\)
\(678\) 0 0
\(679\) 3.53831 0.135788
\(680\) 0 0
\(681\) 23.2899 0.892469
\(682\) 0 0
\(683\) −32.2080 −1.23241 −0.616203 0.787587i \(-0.711330\pi\)
−0.616203 + 0.787587i \(0.711330\pi\)
\(684\) 0 0
\(685\) 10.1077 0.386195
\(686\) 0 0
\(687\) −10.4690 −0.399418
\(688\) 0 0
\(689\) 1.34270 0.0511528
\(690\) 0 0
\(691\) −18.3513 −0.698115 −0.349058 0.937101i \(-0.613498\pi\)
−0.349058 + 0.937101i \(0.613498\pi\)
\(692\) 0 0
\(693\) −5.86150 −0.222660
\(694\) 0 0
\(695\) 7.92768 0.300714
\(696\) 0 0
\(697\) −11.4095 −0.432164
\(698\) 0 0
\(699\) −19.6195 −0.742078
\(700\) 0 0
\(701\) −15.0603 −0.568821 −0.284411 0.958703i \(-0.591798\pi\)
−0.284411 + 0.958703i \(0.591798\pi\)
\(702\) 0 0
\(703\) −38.8868 −1.46665
\(704\) 0 0
\(705\) −5.32515 −0.200557
\(706\) 0 0
\(707\) 13.0978 0.492593
\(708\) 0 0
\(709\) 22.7311 0.853684 0.426842 0.904326i \(-0.359626\pi\)
0.426842 + 0.904326i \(0.359626\pi\)
\(710\) 0 0
\(711\) −3.92469 −0.147187
\(712\) 0 0
\(713\) −4.54178 −0.170091
\(714\) 0 0
\(715\) 37.4611 1.40097
\(716\) 0 0
\(717\) 15.5821 0.581926
\(718\) 0 0
\(719\) 22.0804 0.823460 0.411730 0.911306i \(-0.364925\pi\)
0.411730 + 0.911306i \(0.364925\pi\)
\(720\) 0 0
\(721\) 15.9711 0.594793
\(722\) 0 0
\(723\) −30.8313 −1.14663
\(724\) 0 0
\(725\) 19.3934 0.720252
\(726\) 0 0
\(727\) −1.19378 −0.0442749 −0.0221374 0.999755i \(-0.507047\pi\)
−0.0221374 + 0.999755i \(0.507047\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 14.1068 0.521758
\(732\) 0 0
\(733\) −40.8588 −1.50915 −0.754577 0.656212i \(-0.772158\pi\)
−0.754577 + 0.656212i \(0.772158\pi\)
\(734\) 0 0
\(735\) 8.77616 0.323714
\(736\) 0 0
\(737\) −29.7740 −1.09674
\(738\) 0 0
\(739\) 43.2993 1.59279 0.796396 0.604776i \(-0.206737\pi\)
0.796396 + 0.604776i \(0.206737\pi\)
\(740\) 0 0
\(741\) −26.3035 −0.966283
\(742\) 0 0
\(743\) 30.6987 1.12622 0.563112 0.826380i \(-0.309604\pi\)
0.563112 + 0.826380i \(0.309604\pi\)
\(744\) 0 0
\(745\) 29.7876 1.09133
\(746\) 0 0
\(747\) −11.4441 −0.418717
\(748\) 0 0
\(749\) −6.88372 −0.251525
\(750\) 0 0
\(751\) 38.3723 1.40022 0.700112 0.714033i \(-0.253133\pi\)
0.700112 + 0.714033i \(0.253133\pi\)
\(752\) 0 0
\(753\) −5.66860 −0.206575
\(754\) 0 0
\(755\) 22.9170 0.834034
\(756\) 0 0
\(757\) 15.5003 0.563367 0.281684 0.959507i \(-0.409107\pi\)
0.281684 + 0.959507i \(0.409107\pi\)
\(758\) 0 0
\(759\) −6.92214 −0.251258
\(760\) 0 0
\(761\) 41.5796 1.50726 0.753629 0.657300i \(-0.228301\pi\)
0.753629 + 0.657300i \(0.228301\pi\)
\(762\) 0 0
\(763\) 19.7332 0.714390
\(764\) 0 0
\(765\) 9.10067 0.329035
\(766\) 0 0
\(767\) −0.458626 −0.0165600
\(768\) 0 0
\(769\) 42.7687 1.54228 0.771140 0.636666i \(-0.219687\pi\)
0.771140 + 0.636666i \(0.219687\pi\)
\(770\) 0 0
\(771\) −6.81618 −0.245479
\(772\) 0 0
\(773\) 32.3512 1.16359 0.581795 0.813335i \(-0.302350\pi\)
0.581795 + 0.813335i \(0.302350\pi\)
\(774\) 0 0
\(775\) −10.3729 −0.372604
\(776\) 0 0
\(777\) 6.88176 0.246882
\(778\) 0 0
\(779\) 10.9120 0.390963
\(780\) 0 0
\(781\) 11.3012 0.404389
\(782\) 0 0
\(783\) −6.91991 −0.247298
\(784\) 0 0
\(785\) −15.7986 −0.563877
\(786\) 0 0
\(787\) 0.830709 0.0296116 0.0148058 0.999890i \(-0.495287\pi\)
0.0148058 + 0.999890i \(0.495287\pi\)
\(788\) 0 0
\(789\) 4.22632 0.150461
\(790\) 0 0
\(791\) −17.0052 −0.604635
\(792\) 0 0
\(793\) −16.3273 −0.579800
\(794\) 0 0
\(795\) 0.444301 0.0157577
\(796\) 0 0
\(797\) 44.9143 1.59095 0.795473 0.605988i \(-0.207222\pi\)
0.795473 + 0.605988i \(0.207222\pi\)
\(798\) 0 0
\(799\) −22.0539 −0.780210
\(800\) 0 0
\(801\) −10.4583 −0.369527
\(802\) 0 0
\(803\) 52.6887 1.85934
\(804\) 0 0
\(805\) −1.89012 −0.0666180
\(806\) 0 0
\(807\) 20.5783 0.724390
\(808\) 0 0
\(809\) −25.0553 −0.880897 −0.440449 0.897778i \(-0.645181\pi\)
−0.440449 + 0.897778i \(0.645181\pi\)
\(810\) 0 0
\(811\) 30.9063 1.08527 0.542634 0.839969i \(-0.317427\pi\)
0.542634 + 0.839969i \(0.317427\pi\)
\(812\) 0 0
\(813\) −6.93172 −0.243106
\(814\) 0 0
\(815\) 31.5454 1.10499
\(816\) 0 0
\(817\) −13.4917 −0.472014
\(818\) 0 0
\(819\) 4.65490 0.162655
\(820\) 0 0
\(821\) 4.78573 0.167023 0.0835115 0.996507i \(-0.473386\pi\)
0.0835115 + 0.996507i \(0.473386\pi\)
\(822\) 0 0
\(823\) 21.7901 0.759555 0.379778 0.925078i \(-0.376001\pi\)
0.379778 + 0.925078i \(0.376001\pi\)
\(824\) 0 0
\(825\) −15.8093 −0.550409
\(826\) 0 0
\(827\) 37.7470 1.31259 0.656295 0.754504i \(-0.272123\pi\)
0.656295 + 0.754504i \(0.272123\pi\)
\(828\) 0 0
\(829\) −13.6115 −0.472748 −0.236374 0.971662i \(-0.575959\pi\)
−0.236374 + 0.971662i \(0.575959\pi\)
\(830\) 0 0
\(831\) 22.5380 0.781833
\(832\) 0 0
\(833\) 36.3461 1.25932
\(834\) 0 0
\(835\) 1.48238 0.0512999
\(836\) 0 0
\(837\) 3.70123 0.127933
\(838\) 0 0
\(839\) −20.7228 −0.715431 −0.357715 0.933831i \(-0.616444\pi\)
−0.357715 + 0.933831i \(0.616444\pi\)
\(840\) 0 0
\(841\) 18.8852 0.651214
\(842\) 0 0
\(843\) 20.5684 0.708414
\(844\) 0 0
\(845\) −10.4788 −0.360481
\(846\) 0 0
\(847\) −21.6351 −0.743391
\(848\) 0 0
\(849\) 29.4021 1.00908
\(850\) 0 0
\(851\) 8.12703 0.278591
\(852\) 0 0
\(853\) −18.7796 −0.643001 −0.321501 0.946909i \(-0.604187\pi\)
−0.321501 + 0.946909i \(0.604187\pi\)
\(854\) 0 0
\(855\) −8.70385 −0.297666
\(856\) 0 0
\(857\) −47.7602 −1.63146 −0.815729 0.578434i \(-0.803664\pi\)
−0.815729 + 0.578434i \(0.803664\pi\)
\(858\) 0 0
\(859\) 41.5608 1.41804 0.709018 0.705190i \(-0.249138\pi\)
0.709018 + 0.705190i \(0.249138\pi\)
\(860\) 0 0
\(861\) −1.93108 −0.0658111
\(862\) 0 0
\(863\) 0.525151 0.0178764 0.00893818 0.999960i \(-0.497155\pi\)
0.00893818 + 0.999960i \(0.497155\pi\)
\(864\) 0 0
\(865\) 24.3194 0.826886
\(866\) 0 0
\(867\) 20.6900 0.702671
\(868\) 0 0
\(869\) −22.1394 −0.751027
\(870\) 0 0
\(871\) 23.6450 0.801181
\(872\) 0 0
\(873\) −3.40524 −0.115250
\(874\) 0 0
\(875\) −12.0184 −0.406294
\(876\) 0 0
\(877\) −3.76515 −0.127140 −0.0635701 0.997977i \(-0.520249\pi\)
−0.0635701 + 0.997977i \(0.520249\pi\)
\(878\) 0 0
\(879\) 20.2839 0.684160
\(880\) 0 0
\(881\) −30.4381 −1.02549 −0.512743 0.858542i \(-0.671371\pi\)
−0.512743 + 0.858542i \(0.671371\pi\)
\(882\) 0 0
\(883\) −3.63578 −0.122354 −0.0611768 0.998127i \(-0.519485\pi\)
−0.0611768 + 0.998127i \(0.519485\pi\)
\(884\) 0 0
\(885\) −0.151760 −0.00510135
\(886\) 0 0
\(887\) −19.9846 −0.671018 −0.335509 0.942037i \(-0.608908\pi\)
−0.335509 + 0.942037i \(0.608908\pi\)
\(888\) 0 0
\(889\) −18.3024 −0.613844
\(890\) 0 0
\(891\) 5.64105 0.188982
\(892\) 0 0
\(893\) 21.0923 0.705826
\(894\) 0 0
\(895\) −1.80264 −0.0602555
\(896\) 0 0
\(897\) 5.49721 0.183547
\(898\) 0 0
\(899\) −25.6122 −0.854213
\(900\) 0 0
\(901\) 1.84006 0.0613011
\(902\) 0 0
\(903\) 2.38761 0.0794547
\(904\) 0 0
\(905\) 9.26035 0.307824
\(906\) 0 0
\(907\) −20.7963 −0.690529 −0.345264 0.938505i \(-0.612211\pi\)
−0.345264 + 0.938505i \(0.612211\pi\)
\(908\) 0 0
\(909\) −12.6052 −0.418088
\(910\) 0 0
\(911\) 54.5814 1.80836 0.904181 0.427150i \(-0.140482\pi\)
0.904181 + 0.427150i \(0.140482\pi\)
\(912\) 0 0
\(913\) −64.5565 −2.13651
\(914\) 0 0
\(915\) −5.40273 −0.178609
\(916\) 0 0
\(917\) −10.1798 −0.336168
\(918\) 0 0
\(919\) 8.31975 0.274443 0.137222 0.990540i \(-0.456183\pi\)
0.137222 + 0.990540i \(0.456183\pi\)
\(920\) 0 0
\(921\) 10.9899 0.362128
\(922\) 0 0
\(923\) −8.97485 −0.295411
\(924\) 0 0
\(925\) 18.5611 0.610285
\(926\) 0 0
\(927\) −15.3704 −0.504830
\(928\) 0 0
\(929\) 14.6371 0.480229 0.240114 0.970745i \(-0.422815\pi\)
0.240114 + 0.970745i \(0.422815\pi\)
\(930\) 0 0
\(931\) −34.7613 −1.13926
\(932\) 0 0
\(933\) 26.9703 0.882969
\(934\) 0 0
\(935\) 51.3373 1.67891
\(936\) 0 0
\(937\) 10.0788 0.329260 0.164630 0.986355i \(-0.447357\pi\)
0.164630 + 0.986355i \(0.447357\pi\)
\(938\) 0 0
\(939\) −32.1109 −1.04790
\(940\) 0 0
\(941\) 12.5806 0.410116 0.205058 0.978750i \(-0.434262\pi\)
0.205058 + 0.978750i \(0.434262\pi\)
\(942\) 0 0
\(943\) −2.28052 −0.0742638
\(944\) 0 0
\(945\) 1.54031 0.0501063
\(946\) 0 0
\(947\) 15.0438 0.488858 0.244429 0.969667i \(-0.421399\pi\)
0.244429 + 0.969667i \(0.421399\pi\)
\(948\) 0 0
\(949\) −41.8427 −1.35827
\(950\) 0 0
\(951\) −21.3657 −0.692830
\(952\) 0 0
\(953\) 61.0466 1.97749 0.988746 0.149603i \(-0.0477996\pi\)
0.988746 + 0.149603i \(0.0477996\pi\)
\(954\) 0 0
\(955\) −24.0576 −0.778487
\(956\) 0 0
\(957\) −39.0356 −1.26184
\(958\) 0 0
\(959\) 7.08502 0.228787
\(960\) 0 0
\(961\) −17.3009 −0.558095
\(962\) 0 0
\(963\) 6.62482 0.213482
\(964\) 0 0
\(965\) 13.2982 0.428085
\(966\) 0 0
\(967\) 6.42784 0.206705 0.103353 0.994645i \(-0.467043\pi\)
0.103353 + 0.994645i \(0.467043\pi\)
\(968\) 0 0
\(969\) −36.0467 −1.15799
\(970\) 0 0
\(971\) 28.9135 0.927879 0.463940 0.885867i \(-0.346435\pi\)
0.463940 + 0.885867i \(0.346435\pi\)
\(972\) 0 0
\(973\) 5.55693 0.178147
\(974\) 0 0
\(975\) 12.5549 0.402080
\(976\) 0 0
\(977\) −5.12031 −0.163813 −0.0819066 0.996640i \(-0.526101\pi\)
−0.0819066 + 0.996640i \(0.526101\pi\)
\(978\) 0 0
\(979\) −58.9959 −1.88552
\(980\) 0 0
\(981\) −18.9911 −0.606338
\(982\) 0 0
\(983\) −15.0970 −0.481518 −0.240759 0.970585i \(-0.577396\pi\)
−0.240759 + 0.970585i \(0.577396\pi\)
\(984\) 0 0
\(985\) 34.3802 1.09544
\(986\) 0 0
\(987\) −3.73268 −0.118812
\(988\) 0 0
\(989\) 2.81965 0.0896597
\(990\) 0 0
\(991\) −24.5344 −0.779360 −0.389680 0.920950i \(-0.627414\pi\)
−0.389680 + 0.920950i \(0.627414\pi\)
\(992\) 0 0
\(993\) 23.6701 0.751147
\(994\) 0 0
\(995\) 20.5953 0.652915
\(996\) 0 0
\(997\) −2.08691 −0.0660930 −0.0330465 0.999454i \(-0.510521\pi\)
−0.0330465 + 0.999454i \(0.510521\pi\)
\(998\) 0 0
\(999\) −6.62294 −0.209541
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 \(a_p\))