Properties

Label 4008.2.a.i.1.3
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 1.3
Root \(-0.985991\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.98599 q^{5}\) \(-0.0909950 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.98599 q^{5}\) \(-0.0909950 q^{7}\) \(+1.00000 q^{9}\) \(-2.35607 q^{11}\) \(+0.834094 q^{13}\) \(-1.98599 q^{15}\) \(+7.08503 q^{17}\) \(-1.66738 q^{19}\) \(-0.0909950 q^{21}\) \(-2.49969 q^{23}\) \(-1.05584 q^{25}\) \(+1.00000 q^{27}\) \(-3.96700 q^{29}\) \(-3.52738 q^{31}\) \(-2.35607 q^{33}\) \(+0.180715 q^{35}\) \(-1.64278 q^{37}\) \(+0.834094 q^{39}\) \(+0.142888 q^{41}\) \(-5.36216 q^{43}\) \(-1.98599 q^{45}\) \(-6.35086 q^{47}\) \(-6.99172 q^{49}\) \(+7.08503 q^{51}\) \(+13.4619 q^{53}\) \(+4.67913 q^{55}\) \(-1.66738 q^{57}\) \(+4.39116 q^{59}\) \(+0.0766485 q^{61}\) \(-0.0909950 q^{63}\) \(-1.65650 q^{65}\) \(+4.51021 q^{67}\) \(-2.49969 q^{69}\) \(+3.17932 q^{71}\) \(+9.30247 q^{73}\) \(-1.05584 q^{75}\) \(+0.214390 q^{77}\) \(-17.3241 q^{79}\) \(+1.00000 q^{81}\) \(+0.0141153 q^{83}\) \(-14.0708 q^{85}\) \(-3.96700 q^{87}\) \(-7.96099 q^{89}\) \(-0.0758984 q^{91}\) \(-3.52738 q^{93}\) \(+3.31139 q^{95}\) \(-12.8801 q^{97}\) \(-2.35607 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 7q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 9q^{29} \) \(\mathstrut -\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 26q^{53} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 11q^{63} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut -\mathstrut 7q^{69} \) \(\mathstrut -\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 20q^{77} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 9q^{87} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut -\mathstrut 4q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −1.98599 −0.888162 −0.444081 0.895987i \(-0.646470\pi\)
−0.444081 + 0.895987i \(0.646470\pi\)
\(6\) 0 0
\(7\) −0.0909950 −0.0343929 −0.0171964 0.999852i \(-0.505474\pi\)
−0.0171964 + 0.999852i \(0.505474\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.35607 −0.710380 −0.355190 0.934794i \(-0.615584\pi\)
−0.355190 + 0.934794i \(0.615584\pi\)
\(12\) 0 0
\(13\) 0.834094 0.231336 0.115668 0.993288i \(-0.463099\pi\)
0.115668 + 0.993288i \(0.463099\pi\)
\(14\) 0 0
\(15\) −1.98599 −0.512781
\(16\) 0 0
\(17\) 7.08503 1.71837 0.859186 0.511663i \(-0.170970\pi\)
0.859186 + 0.511663i \(0.170970\pi\)
\(18\) 0 0
\(19\) −1.66738 −0.382522 −0.191261 0.981539i \(-0.561258\pi\)
−0.191261 + 0.981539i \(0.561258\pi\)
\(20\) 0 0
\(21\) −0.0909950 −0.0198567
\(22\) 0 0
\(23\) −2.49969 −0.521221 −0.260611 0.965444i \(-0.583924\pi\)
−0.260611 + 0.965444i \(0.583924\pi\)
\(24\) 0 0
\(25\) −1.05584 −0.211168
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −3.96700 −0.736652 −0.368326 0.929697i \(-0.620069\pi\)
−0.368326 + 0.929697i \(0.620069\pi\)
\(30\) 0 0
\(31\) −3.52738 −0.633535 −0.316768 0.948503i \(-0.602598\pi\)
−0.316768 + 0.948503i \(0.602598\pi\)
\(32\) 0 0
\(33\) −2.35607 −0.410138
\(34\) 0 0
\(35\) 0.180715 0.0305465
\(36\) 0 0
\(37\) −1.64278 −0.270071 −0.135036 0.990841i \(-0.543115\pi\)
−0.135036 + 0.990841i \(0.543115\pi\)
\(38\) 0 0
\(39\) 0.834094 0.133562
\(40\) 0 0
\(41\) 0.142888 0.0223154 0.0111577 0.999938i \(-0.496448\pi\)
0.0111577 + 0.999938i \(0.496448\pi\)
\(42\) 0 0
\(43\) −5.36216 −0.817721 −0.408861 0.912597i \(-0.634074\pi\)
−0.408861 + 0.912597i \(0.634074\pi\)
\(44\) 0 0
\(45\) −1.98599 −0.296054
\(46\) 0 0
\(47\) −6.35086 −0.926369 −0.463184 0.886262i \(-0.653293\pi\)
−0.463184 + 0.886262i \(0.653293\pi\)
\(48\) 0 0
\(49\) −6.99172 −0.998817
\(50\) 0 0
\(51\) 7.08503 0.992103
\(52\) 0 0
\(53\) 13.4619 1.84914 0.924569 0.381015i \(-0.124425\pi\)
0.924569 + 0.381015i \(0.124425\pi\)
\(54\) 0 0
\(55\) 4.67913 0.630933
\(56\) 0 0
\(57\) −1.66738 −0.220849
\(58\) 0 0
\(59\) 4.39116 0.571680 0.285840 0.958277i \(-0.407727\pi\)
0.285840 + 0.958277i \(0.407727\pi\)
\(60\) 0 0
\(61\) 0.0766485 0.00981383 0.00490692 0.999988i \(-0.498438\pi\)
0.00490692 + 0.999988i \(0.498438\pi\)
\(62\) 0 0
\(63\) −0.0909950 −0.0114643
\(64\) 0 0
\(65\) −1.65650 −0.205464
\(66\) 0 0
\(67\) 4.51021 0.551010 0.275505 0.961300i \(-0.411155\pi\)
0.275505 + 0.961300i \(0.411155\pi\)
\(68\) 0 0
\(69\) −2.49969 −0.300927
\(70\) 0 0
\(71\) 3.17932 0.377316 0.188658 0.982043i \(-0.439586\pi\)
0.188658 + 0.982043i \(0.439586\pi\)
\(72\) 0 0
\(73\) 9.30247 1.08877 0.544386 0.838835i \(-0.316763\pi\)
0.544386 + 0.838835i \(0.316763\pi\)
\(74\) 0 0
\(75\) −1.05584 −0.121918
\(76\) 0 0
\(77\) 0.214390 0.0244320
\(78\) 0 0
\(79\) −17.3241 −1.94912 −0.974558 0.224137i \(-0.928044\pi\)
−0.974558 + 0.224137i \(0.928044\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.0141153 0.00154936 0.000774679 1.00000i \(-0.499753\pi\)
0.000774679 1.00000i \(0.499753\pi\)
\(84\) 0 0
\(85\) −14.0708 −1.52619
\(86\) 0 0
\(87\) −3.96700 −0.425307
\(88\) 0 0
\(89\) −7.96099 −0.843863 −0.421932 0.906628i \(-0.638648\pi\)
−0.421932 + 0.906628i \(0.638648\pi\)
\(90\) 0 0
\(91\) −0.0758984 −0.00795631
\(92\) 0 0
\(93\) −3.52738 −0.365772
\(94\) 0 0
\(95\) 3.31139 0.339742
\(96\) 0 0
\(97\) −12.8801 −1.30778 −0.653888 0.756591i \(-0.726863\pi\)
−0.653888 + 0.756591i \(0.726863\pi\)
\(98\) 0 0
\(99\) −2.35607 −0.236793
\(100\) 0 0
\(101\) −14.6926 −1.46197 −0.730983 0.682396i \(-0.760938\pi\)
−0.730983 + 0.682396i \(0.760938\pi\)
\(102\) 0 0
\(103\) −4.05118 −0.399174 −0.199587 0.979880i \(-0.563960\pi\)
−0.199587 + 0.979880i \(0.563960\pi\)
\(104\) 0 0
\(105\) 0.180715 0.0176360
\(106\) 0 0
\(107\) 10.1492 0.981161 0.490581 0.871396i \(-0.336785\pi\)
0.490581 + 0.871396i \(0.336785\pi\)
\(108\) 0 0
\(109\) −4.51988 −0.432926 −0.216463 0.976291i \(-0.569452\pi\)
−0.216463 + 0.976291i \(0.569452\pi\)
\(110\) 0 0
\(111\) −1.64278 −0.155926
\(112\) 0 0
\(113\) −14.4542 −1.35974 −0.679869 0.733333i \(-0.737963\pi\)
−0.679869 + 0.733333i \(0.737963\pi\)
\(114\) 0 0
\(115\) 4.96436 0.462929
\(116\) 0 0
\(117\) 0.834094 0.0771120
\(118\) 0 0
\(119\) −0.644702 −0.0590998
\(120\) 0 0
\(121\) −5.44896 −0.495360
\(122\) 0 0
\(123\) 0.142888 0.0128838
\(124\) 0 0
\(125\) 12.0268 1.07571
\(126\) 0 0
\(127\) −18.7384 −1.66277 −0.831383 0.555700i \(-0.812450\pi\)
−0.831383 + 0.555700i \(0.812450\pi\)
\(128\) 0 0
\(129\) −5.36216 −0.472112
\(130\) 0 0
\(131\) 6.50104 0.567998 0.283999 0.958825i \(-0.408339\pi\)
0.283999 + 0.958825i \(0.408339\pi\)
\(132\) 0 0
\(133\) 0.151723 0.0131560
\(134\) 0 0
\(135\) −1.98599 −0.170927
\(136\) 0 0
\(137\) −4.41640 −0.377319 −0.188659 0.982043i \(-0.560414\pi\)
−0.188659 + 0.982043i \(0.560414\pi\)
\(138\) 0 0
\(139\) 3.57252 0.303017 0.151508 0.988456i \(-0.451587\pi\)
0.151508 + 0.988456i \(0.451587\pi\)
\(140\) 0 0
\(141\) −6.35086 −0.534839
\(142\) 0 0
\(143\) −1.96518 −0.164337
\(144\) 0 0
\(145\) 7.87842 0.654267
\(146\) 0 0
\(147\) −6.99172 −0.576667
\(148\) 0 0
\(149\) −3.73856 −0.306275 −0.153137 0.988205i \(-0.548938\pi\)
−0.153137 + 0.988205i \(0.548938\pi\)
\(150\) 0 0
\(151\) −9.88374 −0.804327 −0.402164 0.915568i \(-0.631742\pi\)
−0.402164 + 0.915568i \(0.631742\pi\)
\(152\) 0 0
\(153\) 7.08503 0.572791
\(154\) 0 0
\(155\) 7.00534 0.562682
\(156\) 0 0
\(157\) −0.704086 −0.0561922 −0.0280961 0.999605i \(-0.508944\pi\)
−0.0280961 + 0.999605i \(0.508944\pi\)
\(158\) 0 0
\(159\) 13.4619 1.06760
\(160\) 0 0
\(161\) 0.227459 0.0179263
\(162\) 0 0
\(163\) −3.79586 −0.297315 −0.148658 0.988889i \(-0.547495\pi\)
−0.148658 + 0.988889i \(0.547495\pi\)
\(164\) 0 0
\(165\) 4.67913 0.364269
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −12.3043 −0.946484
\(170\) 0 0
\(171\) −1.66738 −0.127507
\(172\) 0 0
\(173\) −5.35209 −0.406912 −0.203456 0.979084i \(-0.565217\pi\)
−0.203456 + 0.979084i \(0.565217\pi\)
\(174\) 0 0
\(175\) 0.0960759 0.00726266
\(176\) 0 0
\(177\) 4.39116 0.330060
\(178\) 0 0
\(179\) −2.68131 −0.200410 −0.100205 0.994967i \(-0.531950\pi\)
−0.100205 + 0.994967i \(0.531950\pi\)
\(180\) 0 0
\(181\) −21.8000 −1.62038 −0.810189 0.586169i \(-0.800635\pi\)
−0.810189 + 0.586169i \(0.800635\pi\)
\(182\) 0 0
\(183\) 0.0766485 0.00566602
\(184\) 0 0
\(185\) 3.26255 0.239867
\(186\) 0 0
\(187\) −16.6928 −1.22070
\(188\) 0 0
\(189\) −0.0909950 −0.00661891
\(190\) 0 0
\(191\) −26.2790 −1.90148 −0.950740 0.309989i \(-0.899675\pi\)
−0.950740 + 0.309989i \(0.899675\pi\)
\(192\) 0 0
\(193\) 18.3316 1.31953 0.659767 0.751470i \(-0.270655\pi\)
0.659767 + 0.751470i \(0.270655\pi\)
\(194\) 0 0
\(195\) −1.65650 −0.118625
\(196\) 0 0
\(197\) 14.1522 1.00830 0.504150 0.863616i \(-0.331806\pi\)
0.504150 + 0.863616i \(0.331806\pi\)
\(198\) 0 0
\(199\) −17.7862 −1.26083 −0.630414 0.776259i \(-0.717115\pi\)
−0.630414 + 0.776259i \(0.717115\pi\)
\(200\) 0 0
\(201\) 4.51021 0.318126
\(202\) 0 0
\(203\) 0.360977 0.0253356
\(204\) 0 0
\(205\) −0.283775 −0.0198197
\(206\) 0 0
\(207\) −2.49969 −0.173740
\(208\) 0 0
\(209\) 3.92845 0.271736
\(210\) 0 0
\(211\) 2.74876 0.189232 0.0946161 0.995514i \(-0.469838\pi\)
0.0946161 + 0.995514i \(0.469838\pi\)
\(212\) 0 0
\(213\) 3.17932 0.217843
\(214\) 0 0
\(215\) 10.6492 0.726269
\(216\) 0 0
\(217\) 0.320973 0.0217891
\(218\) 0 0
\(219\) 9.30247 0.628602
\(220\) 0 0
\(221\) 5.90958 0.397522
\(222\) 0 0
\(223\) −5.97542 −0.400143 −0.200072 0.979781i \(-0.564118\pi\)
−0.200072 + 0.979781i \(0.564118\pi\)
\(224\) 0 0
\(225\) −1.05584 −0.0703892
\(226\) 0 0
\(227\) 0.438914 0.0291318 0.0145659 0.999894i \(-0.495363\pi\)
0.0145659 + 0.999894i \(0.495363\pi\)
\(228\) 0 0
\(229\) 1.49354 0.0986960 0.0493480 0.998782i \(-0.484286\pi\)
0.0493480 + 0.998782i \(0.484286\pi\)
\(230\) 0 0
\(231\) 0.214390 0.0141058
\(232\) 0 0
\(233\) −17.5018 −1.14658 −0.573291 0.819352i \(-0.694333\pi\)
−0.573291 + 0.819352i \(0.694333\pi\)
\(234\) 0 0
\(235\) 12.6128 0.822766
\(236\) 0 0
\(237\) −17.3241 −1.12532
\(238\) 0 0
\(239\) −3.14251 −0.203272 −0.101636 0.994822i \(-0.532408\pi\)
−0.101636 + 0.994822i \(0.532408\pi\)
\(240\) 0 0
\(241\) 18.6616 1.20210 0.601050 0.799211i \(-0.294749\pi\)
0.601050 + 0.799211i \(0.294749\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 13.8855 0.887112
\(246\) 0 0
\(247\) −1.39075 −0.0884912
\(248\) 0 0
\(249\) 0.0141153 0.000894522 0
\(250\) 0 0
\(251\) 3.34821 0.211337 0.105668 0.994401i \(-0.466302\pi\)
0.105668 + 0.994401i \(0.466302\pi\)
\(252\) 0 0
\(253\) 5.88943 0.370265
\(254\) 0 0
\(255\) −14.0708 −0.881148
\(256\) 0 0
\(257\) 7.22045 0.450399 0.225200 0.974313i \(-0.427697\pi\)
0.225200 + 0.974313i \(0.427697\pi\)
\(258\) 0 0
\(259\) 0.149485 0.00928853
\(260\) 0 0
\(261\) −3.96700 −0.245551
\(262\) 0 0
\(263\) 7.01628 0.432642 0.216321 0.976322i \(-0.430594\pi\)
0.216321 + 0.976322i \(0.430594\pi\)
\(264\) 0 0
\(265\) −26.7353 −1.64233
\(266\) 0 0
\(267\) −7.96099 −0.487205
\(268\) 0 0
\(269\) 17.2316 1.05063 0.525316 0.850907i \(-0.323947\pi\)
0.525316 + 0.850907i \(0.323947\pi\)
\(270\) 0 0
\(271\) −27.6572 −1.68005 −0.840027 0.542545i \(-0.817461\pi\)
−0.840027 + 0.542545i \(0.817461\pi\)
\(272\) 0 0
\(273\) −0.0758984 −0.00459358
\(274\) 0 0
\(275\) 2.48762 0.150009
\(276\) 0 0
\(277\) 24.7248 1.48557 0.742785 0.669529i \(-0.233504\pi\)
0.742785 + 0.669529i \(0.233504\pi\)
\(278\) 0 0
\(279\) −3.52738 −0.211178
\(280\) 0 0
\(281\) −1.24892 −0.0745041 −0.0372520 0.999306i \(-0.511860\pi\)
−0.0372520 + 0.999306i \(0.511860\pi\)
\(282\) 0 0
\(283\) −26.7744 −1.59158 −0.795788 0.605576i \(-0.792943\pi\)
−0.795788 + 0.605576i \(0.792943\pi\)
\(284\) 0 0
\(285\) 3.31139 0.196150
\(286\) 0 0
\(287\) −0.0130021 −0.000767491 0
\(288\) 0 0
\(289\) 33.1977 1.95280
\(290\) 0 0
\(291\) −12.8801 −0.755045
\(292\) 0 0
\(293\) 25.2333 1.47414 0.737072 0.675814i \(-0.236208\pi\)
0.737072 + 0.675814i \(0.236208\pi\)
\(294\) 0 0
\(295\) −8.72080 −0.507745
\(296\) 0 0
\(297\) −2.35607 −0.136713
\(298\) 0 0
\(299\) −2.08498 −0.120577
\(300\) 0 0
\(301\) 0.487929 0.0281238
\(302\) 0 0
\(303\) −14.6926 −0.844066
\(304\) 0 0
\(305\) −0.152223 −0.00871628
\(306\) 0 0
\(307\) 3.20268 0.182786 0.0913932 0.995815i \(-0.470868\pi\)
0.0913932 + 0.995815i \(0.470868\pi\)
\(308\) 0 0
\(309\) −4.05118 −0.230463
\(310\) 0 0
\(311\) −3.45554 −0.195946 −0.0979729 0.995189i \(-0.531236\pi\)
−0.0979729 + 0.995189i \(0.531236\pi\)
\(312\) 0 0
\(313\) 31.7617 1.79528 0.897638 0.440734i \(-0.145282\pi\)
0.897638 + 0.440734i \(0.145282\pi\)
\(314\) 0 0
\(315\) 0.180715 0.0101822
\(316\) 0 0
\(317\) −25.1696 −1.41367 −0.706834 0.707380i \(-0.749877\pi\)
−0.706834 + 0.707380i \(0.749877\pi\)
\(318\) 0 0
\(319\) 9.34650 0.523304
\(320\) 0 0
\(321\) 10.1492 0.566474
\(322\) 0 0
\(323\) −11.8134 −0.657316
\(324\) 0 0
\(325\) −0.880668 −0.0488507
\(326\) 0 0
\(327\) −4.51988 −0.249950
\(328\) 0 0
\(329\) 0.577897 0.0318605
\(330\) 0 0
\(331\) −8.94004 −0.491389 −0.245694 0.969347i \(-0.579016\pi\)
−0.245694 + 0.969347i \(0.579016\pi\)
\(332\) 0 0
\(333\) −1.64278 −0.0900238
\(334\) 0 0
\(335\) −8.95724 −0.489387
\(336\) 0 0
\(337\) −2.25049 −0.122592 −0.0612959 0.998120i \(-0.519523\pi\)
−0.0612959 + 0.998120i \(0.519523\pi\)
\(338\) 0 0
\(339\) −14.4542 −0.785045
\(340\) 0 0
\(341\) 8.31073 0.450051
\(342\) 0 0
\(343\) 1.27318 0.0687451
\(344\) 0 0
\(345\) 4.96436 0.267272
\(346\) 0 0
\(347\) 4.88275 0.262119 0.131060 0.991374i \(-0.458162\pi\)
0.131060 + 0.991374i \(0.458162\pi\)
\(348\) 0 0
\(349\) 6.94280 0.371639 0.185820 0.982584i \(-0.440506\pi\)
0.185820 + 0.982584i \(0.440506\pi\)
\(350\) 0 0
\(351\) 0.834094 0.0445207
\(352\) 0 0
\(353\) −12.9864 −0.691199 −0.345599 0.938382i \(-0.612324\pi\)
−0.345599 + 0.938382i \(0.612324\pi\)
\(354\) 0 0
\(355\) −6.31410 −0.335118
\(356\) 0 0
\(357\) −0.644702 −0.0341213
\(358\) 0 0
\(359\) −2.00276 −0.105702 −0.0528509 0.998602i \(-0.516831\pi\)
−0.0528509 + 0.998602i \(0.516831\pi\)
\(360\) 0 0
\(361\) −16.2199 −0.853677
\(362\) 0 0
\(363\) −5.44896 −0.285996
\(364\) 0 0
\(365\) −18.4746 −0.967006
\(366\) 0 0
\(367\) 28.1645 1.47017 0.735087 0.677973i \(-0.237141\pi\)
0.735087 + 0.677973i \(0.237141\pi\)
\(368\) 0 0
\(369\) 0.142888 0.00743848
\(370\) 0 0
\(371\) −1.22497 −0.0635971
\(372\) 0 0
\(373\) −0.470865 −0.0243804 −0.0121902 0.999926i \(-0.503880\pi\)
−0.0121902 + 0.999926i \(0.503880\pi\)
\(374\) 0 0
\(375\) 12.0268 0.621063
\(376\) 0 0
\(377\) −3.30885 −0.170414
\(378\) 0 0
\(379\) −16.1101 −0.827519 −0.413760 0.910386i \(-0.635785\pi\)
−0.413760 + 0.910386i \(0.635785\pi\)
\(380\) 0 0
\(381\) −18.7384 −0.959999
\(382\) 0 0
\(383\) 37.3788 1.90997 0.954984 0.296656i \(-0.0958716\pi\)
0.954984 + 0.296656i \(0.0958716\pi\)
\(384\) 0 0
\(385\) −0.425777 −0.0216996
\(386\) 0 0
\(387\) −5.36216 −0.272574
\(388\) 0 0
\(389\) 8.93497 0.453021 0.226511 0.974009i \(-0.427268\pi\)
0.226511 + 0.974009i \(0.427268\pi\)
\(390\) 0 0
\(391\) −17.7104 −0.895652
\(392\) 0 0
\(393\) 6.50104 0.327934
\(394\) 0 0
\(395\) 34.4055 1.73113
\(396\) 0 0
\(397\) 0.164468 0.00825442 0.00412721 0.999991i \(-0.498686\pi\)
0.00412721 + 0.999991i \(0.498686\pi\)
\(398\) 0 0
\(399\) 0.151723 0.00759564
\(400\) 0 0
\(401\) 5.07799 0.253583 0.126791 0.991929i \(-0.459532\pi\)
0.126791 + 0.991929i \(0.459532\pi\)
\(402\) 0 0
\(403\) −2.94216 −0.146560
\(404\) 0 0
\(405\) −1.98599 −0.0986847
\(406\) 0 0
\(407\) 3.87050 0.191853
\(408\) 0 0
\(409\) 31.1261 1.53909 0.769544 0.638594i \(-0.220484\pi\)
0.769544 + 0.638594i \(0.220484\pi\)
\(410\) 0 0
\(411\) −4.41640 −0.217845
\(412\) 0 0
\(413\) −0.399573 −0.0196617
\(414\) 0 0
\(415\) −0.0280329 −0.00137608
\(416\) 0 0
\(417\) 3.57252 0.174947
\(418\) 0 0
\(419\) −23.9570 −1.17037 −0.585187 0.810898i \(-0.698979\pi\)
−0.585187 + 0.810898i \(0.698979\pi\)
\(420\) 0 0
\(421\) 19.3408 0.942612 0.471306 0.881970i \(-0.343783\pi\)
0.471306 + 0.881970i \(0.343783\pi\)
\(422\) 0 0
\(423\) −6.35086 −0.308790
\(424\) 0 0
\(425\) −7.48064 −0.362865
\(426\) 0 0
\(427\) −0.00697463 −0.000337526 0
\(428\) 0 0
\(429\) −1.96518 −0.0948798
\(430\) 0 0
\(431\) −7.52144 −0.362295 −0.181147 0.983456i \(-0.557981\pi\)
−0.181147 + 0.983456i \(0.557981\pi\)
\(432\) 0 0
\(433\) 35.3240 1.69756 0.848781 0.528745i \(-0.177337\pi\)
0.848781 + 0.528745i \(0.177337\pi\)
\(434\) 0 0
\(435\) 7.87842 0.377741
\(436\) 0 0
\(437\) 4.16792 0.199379
\(438\) 0 0
\(439\) −3.59035 −0.171358 −0.0856790 0.996323i \(-0.527306\pi\)
−0.0856790 + 0.996323i \(0.527306\pi\)
\(440\) 0 0
\(441\) −6.99172 −0.332939
\(442\) 0 0
\(443\) 11.2209 0.533121 0.266560 0.963818i \(-0.414113\pi\)
0.266560 + 0.963818i \(0.414113\pi\)
\(444\) 0 0
\(445\) 15.8105 0.749488
\(446\) 0 0
\(447\) −3.73856 −0.176828
\(448\) 0 0
\(449\) −14.4857 −0.683622 −0.341811 0.939769i \(-0.611040\pi\)
−0.341811 + 0.939769i \(0.611040\pi\)
\(450\) 0 0
\(451\) −0.336655 −0.0158524
\(452\) 0 0
\(453\) −9.88374 −0.464379
\(454\) 0 0
\(455\) 0.150734 0.00706650
\(456\) 0 0
\(457\) 18.0839 0.845929 0.422965 0.906146i \(-0.360989\pi\)
0.422965 + 0.906146i \(0.360989\pi\)
\(458\) 0 0
\(459\) 7.08503 0.330701
\(460\) 0 0
\(461\) −11.4205 −0.531904 −0.265952 0.963986i \(-0.585686\pi\)
−0.265952 + 0.963986i \(0.585686\pi\)
\(462\) 0 0
\(463\) 11.4961 0.534268 0.267134 0.963659i \(-0.413923\pi\)
0.267134 + 0.963659i \(0.413923\pi\)
\(464\) 0 0
\(465\) 7.00534 0.324865
\(466\) 0 0
\(467\) 28.3176 1.31038 0.655191 0.755463i \(-0.272588\pi\)
0.655191 + 0.755463i \(0.272588\pi\)
\(468\) 0 0
\(469\) −0.410407 −0.0189508
\(470\) 0 0
\(471\) −0.704086 −0.0324426
\(472\) 0 0
\(473\) 12.6336 0.580893
\(474\) 0 0
\(475\) 1.76048 0.0807763
\(476\) 0 0
\(477\) 13.4619 0.616379
\(478\) 0 0
\(479\) 0.851972 0.0389276 0.0194638 0.999811i \(-0.493804\pi\)
0.0194638 + 0.999811i \(0.493804\pi\)
\(480\) 0 0
\(481\) −1.37023 −0.0624772
\(482\) 0 0
\(483\) 0.227459 0.0103498
\(484\) 0 0
\(485\) 25.5798 1.16152
\(486\) 0 0
\(487\) −16.8841 −0.765091 −0.382546 0.923937i \(-0.624953\pi\)
−0.382546 + 0.923937i \(0.624953\pi\)
\(488\) 0 0
\(489\) −3.79586 −0.171655
\(490\) 0 0
\(491\) 40.5909 1.83184 0.915921 0.401359i \(-0.131462\pi\)
0.915921 + 0.401359i \(0.131462\pi\)
\(492\) 0 0
\(493\) −28.1063 −1.26584
\(494\) 0 0
\(495\) 4.67913 0.210311
\(496\) 0 0
\(497\) −0.289302 −0.0129770
\(498\) 0 0
\(499\) 1.31828 0.0590143 0.0295071 0.999565i \(-0.490606\pi\)
0.0295071 + 0.999565i \(0.490606\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −20.3191 −0.905983 −0.452991 0.891515i \(-0.649643\pi\)
−0.452991 + 0.891515i \(0.649643\pi\)
\(504\) 0 0
\(505\) 29.1793 1.29846
\(506\) 0 0
\(507\) −12.3043 −0.546453
\(508\) 0 0
\(509\) 39.7984 1.76403 0.882016 0.471219i \(-0.156186\pi\)
0.882016 + 0.471219i \(0.156186\pi\)
\(510\) 0 0
\(511\) −0.846478 −0.0374460
\(512\) 0 0
\(513\) −1.66738 −0.0736164
\(514\) 0 0
\(515\) 8.04560 0.354532
\(516\) 0 0
\(517\) 14.9631 0.658074
\(518\) 0 0
\(519\) −5.35209 −0.234931
\(520\) 0 0
\(521\) 8.30626 0.363904 0.181952 0.983307i \(-0.441758\pi\)
0.181952 + 0.983307i \(0.441758\pi\)
\(522\) 0 0
\(523\) −26.3330 −1.15146 −0.575731 0.817639i \(-0.695283\pi\)
−0.575731 + 0.817639i \(0.695283\pi\)
\(524\) 0 0
\(525\) 0.0960759 0.00419310
\(526\) 0 0
\(527\) −24.9916 −1.08865
\(528\) 0 0
\(529\) −16.7516 −0.728328
\(530\) 0 0
\(531\) 4.39116 0.190560
\(532\) 0 0
\(533\) 0.119182 0.00516236
\(534\) 0 0
\(535\) −20.1562 −0.871431
\(536\) 0 0
\(537\) −2.68131 −0.115707
\(538\) 0 0
\(539\) 16.4729 0.709540
\(540\) 0 0
\(541\) −14.1502 −0.608365 −0.304182 0.952614i \(-0.598383\pi\)
−0.304182 + 0.952614i \(0.598383\pi\)
\(542\) 0 0
\(543\) −21.8000 −0.935525
\(544\) 0 0
\(545\) 8.97645 0.384509
\(546\) 0 0
\(547\) −24.6028 −1.05194 −0.525971 0.850503i \(-0.676298\pi\)
−0.525971 + 0.850503i \(0.676298\pi\)
\(548\) 0 0
\(549\) 0.0766485 0.00327128
\(550\) 0 0
\(551\) 6.61447 0.281786
\(552\) 0 0
\(553\) 1.57641 0.0670357
\(554\) 0 0
\(555\) 3.26255 0.138487
\(556\) 0 0
\(557\) −23.1405 −0.980493 −0.490246 0.871584i \(-0.663093\pi\)
−0.490246 + 0.871584i \(0.663093\pi\)
\(558\) 0 0
\(559\) −4.47254 −0.189168
\(560\) 0 0
\(561\) −16.6928 −0.704770
\(562\) 0 0
\(563\) 18.8347 0.793787 0.396894 0.917865i \(-0.370088\pi\)
0.396894 + 0.917865i \(0.370088\pi\)
\(564\) 0 0
\(565\) 28.7060 1.20767
\(566\) 0 0
\(567\) −0.0909950 −0.00382143
\(568\) 0 0
\(569\) 38.2495 1.60350 0.801752 0.597657i \(-0.203901\pi\)
0.801752 + 0.597657i \(0.203901\pi\)
\(570\) 0 0
\(571\) 28.5374 1.19425 0.597126 0.802148i \(-0.296309\pi\)
0.597126 + 0.802148i \(0.296309\pi\)
\(572\) 0 0
\(573\) −26.2790 −1.09782
\(574\) 0 0
\(575\) 2.63927 0.110065
\(576\) 0 0
\(577\) −11.7985 −0.491178 −0.245589 0.969374i \(-0.578981\pi\)
−0.245589 + 0.969374i \(0.578981\pi\)
\(578\) 0 0
\(579\) 18.3316 0.761833
\(580\) 0 0
\(581\) −0.00128442 −5.32868e−5 0
\(582\) 0 0
\(583\) −31.7172 −1.31359
\(584\) 0 0
\(585\) −1.65650 −0.0684880
\(586\) 0 0
\(587\) −1.16607 −0.0481287 −0.0240644 0.999710i \(-0.507661\pi\)
−0.0240644 + 0.999710i \(0.507661\pi\)
\(588\) 0 0
\(589\) 5.88146 0.242341
\(590\) 0 0
\(591\) 14.1522 0.582142
\(592\) 0 0
\(593\) 20.2574 0.831870 0.415935 0.909394i \(-0.363454\pi\)
0.415935 + 0.909394i \(0.363454\pi\)
\(594\) 0 0
\(595\) 1.28037 0.0524902
\(596\) 0 0
\(597\) −17.7862 −0.727940
\(598\) 0 0
\(599\) −35.8580 −1.46512 −0.732559 0.680703i \(-0.761674\pi\)
−0.732559 + 0.680703i \(0.761674\pi\)
\(600\) 0 0
\(601\) −29.0525 −1.18507 −0.592537 0.805543i \(-0.701874\pi\)
−0.592537 + 0.805543i \(0.701874\pi\)
\(602\) 0 0
\(603\) 4.51021 0.183670
\(604\) 0 0
\(605\) 10.8216 0.439960
\(606\) 0 0
\(607\) −18.0950 −0.734455 −0.367227 0.930131i \(-0.619693\pi\)
−0.367227 + 0.930131i \(0.619693\pi\)
\(608\) 0 0
\(609\) 0.360977 0.0146275
\(610\) 0 0
\(611\) −5.29722 −0.214303
\(612\) 0 0
\(613\) 36.0458 1.45588 0.727939 0.685642i \(-0.240478\pi\)
0.727939 + 0.685642i \(0.240478\pi\)
\(614\) 0 0
\(615\) −0.283775 −0.0114429
\(616\) 0 0
\(617\) 24.3584 0.980632 0.490316 0.871545i \(-0.336881\pi\)
0.490316 + 0.871545i \(0.336881\pi\)
\(618\) 0 0
\(619\) −26.2196 −1.05386 −0.526928 0.849910i \(-0.676656\pi\)
−0.526928 + 0.849910i \(0.676656\pi\)
\(620\) 0 0
\(621\) −2.49969 −0.100309
\(622\) 0 0
\(623\) 0.724410 0.0290229
\(624\) 0 0
\(625\) −18.6060 −0.744241
\(626\) 0 0
\(627\) 3.92845 0.156887
\(628\) 0 0
\(629\) −11.6391 −0.464083
\(630\) 0 0
\(631\) 39.0723 1.55544 0.777722 0.628609i \(-0.216375\pi\)
0.777722 + 0.628609i \(0.216375\pi\)
\(632\) 0 0
\(633\) 2.74876 0.109253
\(634\) 0 0
\(635\) 37.2144 1.47681
\(636\) 0 0
\(637\) −5.83175 −0.231062
\(638\) 0 0
\(639\) 3.17932 0.125772
\(640\) 0 0
\(641\) 13.3708 0.528116 0.264058 0.964507i \(-0.414939\pi\)
0.264058 + 0.964507i \(0.414939\pi\)
\(642\) 0 0
\(643\) 28.3204 1.11685 0.558424 0.829555i \(-0.311406\pi\)
0.558424 + 0.829555i \(0.311406\pi\)
\(644\) 0 0
\(645\) 10.6492 0.419312
\(646\) 0 0
\(647\) 13.7492 0.540539 0.270269 0.962785i \(-0.412887\pi\)
0.270269 + 0.962785i \(0.412887\pi\)
\(648\) 0 0
\(649\) −10.3459 −0.406110
\(650\) 0 0
\(651\) 0.320973 0.0125799
\(652\) 0 0
\(653\) −23.5266 −0.920667 −0.460334 0.887746i \(-0.652270\pi\)
−0.460334 + 0.887746i \(0.652270\pi\)
\(654\) 0 0
\(655\) −12.9110 −0.504475
\(656\) 0 0
\(657\) 9.30247 0.362924
\(658\) 0 0
\(659\) −37.7144 −1.46914 −0.734571 0.678531i \(-0.762617\pi\)
−0.734571 + 0.678531i \(0.762617\pi\)
\(660\) 0 0
\(661\) −22.3286 −0.868483 −0.434241 0.900797i \(-0.642984\pi\)
−0.434241 + 0.900797i \(0.642984\pi\)
\(662\) 0 0
\(663\) 5.90958 0.229509
\(664\) 0 0
\(665\) −0.301320 −0.0116847
\(666\) 0 0
\(667\) 9.91626 0.383959
\(668\) 0 0
\(669\) −5.97542 −0.231023
\(670\) 0 0
\(671\) −0.180589 −0.00697155
\(672\) 0 0
\(673\) −1.89185 −0.0729256 −0.0364628 0.999335i \(-0.511609\pi\)
−0.0364628 + 0.999335i \(0.511609\pi\)
\(674\) 0 0
\(675\) −1.05584 −0.0406392
\(676\) 0 0
\(677\) 31.6117 1.21494 0.607468 0.794344i \(-0.292185\pi\)
0.607468 + 0.794344i \(0.292185\pi\)
\(678\) 0 0
\(679\) 1.17202 0.0449782
\(680\) 0 0
\(681\) 0.438914 0.0168192
\(682\) 0 0
\(683\) 19.1816 0.733962 0.366981 0.930228i \(-0.380391\pi\)
0.366981 + 0.930228i \(0.380391\pi\)
\(684\) 0 0
\(685\) 8.77094 0.335120
\(686\) 0 0
\(687\) 1.49354 0.0569822
\(688\) 0 0
\(689\) 11.2285 0.427772
\(690\) 0 0
\(691\) 19.4533 0.740037 0.370019 0.929024i \(-0.379351\pi\)
0.370019 + 0.929024i \(0.379351\pi\)
\(692\) 0 0
\(693\) 0.214390 0.00814401
\(694\) 0 0
\(695\) −7.09499 −0.269128
\(696\) 0 0
\(697\) 1.01237 0.0383462
\(698\) 0 0
\(699\) −17.5018 −0.661979
\(700\) 0 0
\(701\) −2.81290 −0.106242 −0.0531208 0.998588i \(-0.516917\pi\)
−0.0531208 + 0.998588i \(0.516917\pi\)
\(702\) 0 0
\(703\) 2.73913 0.103308
\(704\) 0 0
\(705\) 12.6128 0.475024
\(706\) 0 0
\(707\) 1.33695 0.0502812
\(708\) 0 0
\(709\) −33.0623 −1.24168 −0.620841 0.783936i \(-0.713209\pi\)
−0.620841 + 0.783936i \(0.713209\pi\)
\(710\) 0 0
\(711\) −17.3241 −0.649705
\(712\) 0 0
\(713\) 8.81734 0.330212
\(714\) 0 0
\(715\) 3.90283 0.145958
\(716\) 0 0
\(717\) −3.14251 −0.117359
\(718\) 0 0
\(719\) −46.3189 −1.72740 −0.863701 0.504004i \(-0.831860\pi\)
−0.863701 + 0.504004i \(0.831860\pi\)
\(720\) 0 0
\(721\) 0.368637 0.0137287
\(722\) 0 0
\(723\) 18.6616 0.694033
\(724\) 0 0
\(725\) 4.18850 0.155557
\(726\) 0 0
\(727\) 22.5142 0.835004 0.417502 0.908676i \(-0.362906\pi\)
0.417502 + 0.908676i \(0.362906\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −37.9910 −1.40515
\(732\) 0 0
\(733\) −22.7476 −0.840202 −0.420101 0.907477i \(-0.638005\pi\)
−0.420101 + 0.907477i \(0.638005\pi\)
\(734\) 0 0
\(735\) 13.8855 0.512174
\(736\) 0 0
\(737\) −10.6264 −0.391427
\(738\) 0 0
\(739\) −50.1147 −1.84350 −0.921750 0.387785i \(-0.873240\pi\)
−0.921750 + 0.387785i \(0.873240\pi\)
\(740\) 0 0
\(741\) −1.39075 −0.0510904
\(742\) 0 0
\(743\) −29.3798 −1.07784 −0.538920 0.842357i \(-0.681167\pi\)
−0.538920 + 0.842357i \(0.681167\pi\)
\(744\) 0 0
\(745\) 7.42474 0.272022
\(746\) 0 0
\(747\) 0.0141153 0.000516452 0
\(748\) 0 0
\(749\) −0.923527 −0.0337449
\(750\) 0 0
\(751\) −45.8288 −1.67232 −0.836159 0.548487i \(-0.815204\pi\)
−0.836159 + 0.548487i \(0.815204\pi\)
\(752\) 0 0
\(753\) 3.34821 0.122015
\(754\) 0 0
\(755\) 19.6290 0.714373
\(756\) 0 0
\(757\) −1.36638 −0.0496621 −0.0248310 0.999692i \(-0.507905\pi\)
−0.0248310 + 0.999692i \(0.507905\pi\)
\(758\) 0 0
\(759\) 5.88943 0.213773
\(760\) 0 0
\(761\) 41.1549 1.49187 0.745933 0.666021i \(-0.232004\pi\)
0.745933 + 0.666021i \(0.232004\pi\)
\(762\) 0 0
\(763\) 0.411287 0.0148896
\(764\) 0 0
\(765\) −14.0708 −0.508731
\(766\) 0 0
\(767\) 3.66264 0.132250
\(768\) 0 0
\(769\) −6.65538 −0.239999 −0.120000 0.992774i \(-0.538289\pi\)
−0.120000 + 0.992774i \(0.538289\pi\)
\(770\) 0 0
\(771\) 7.22045 0.260038
\(772\) 0 0
\(773\) −30.8303 −1.10889 −0.554444 0.832221i \(-0.687069\pi\)
−0.554444 + 0.832221i \(0.687069\pi\)
\(774\) 0 0
\(775\) 3.72434 0.133782
\(776\) 0 0
\(777\) 0.149485 0.00536273
\(778\) 0 0
\(779\) −0.238249 −0.00853615
\(780\) 0 0
\(781\) −7.49068 −0.268038
\(782\) 0 0
\(783\) −3.96700 −0.141769
\(784\) 0 0
\(785\) 1.39831 0.0499078
\(786\) 0 0
\(787\) 9.92617 0.353830 0.176915 0.984226i \(-0.443388\pi\)
0.176915 + 0.984226i \(0.443388\pi\)
\(788\) 0 0
\(789\) 7.01628 0.249786
\(790\) 0 0
\(791\) 1.31526 0.0467653
\(792\) 0 0
\(793\) 0.0639321 0.00227029
\(794\) 0 0
\(795\) −26.7353 −0.948202
\(796\) 0 0
\(797\) −20.4507 −0.724402 −0.362201 0.932100i \(-0.617975\pi\)
−0.362201 + 0.932100i \(0.617975\pi\)
\(798\) 0 0
\(799\) −44.9961 −1.59185
\(800\) 0 0
\(801\) −7.96099 −0.281288
\(802\) 0 0
\(803\) −21.9172 −0.773442
\(804\) 0 0
\(805\) −0.451732 −0.0159215
\(806\) 0 0
\(807\) 17.2316 0.606582
\(808\) 0 0
\(809\) −11.0254 −0.387631 −0.193815 0.981038i \(-0.562086\pi\)
−0.193815 + 0.981038i \(0.562086\pi\)
\(810\) 0 0
\(811\) 39.7185 1.39471 0.697353 0.716728i \(-0.254361\pi\)
0.697353 + 0.716728i \(0.254361\pi\)
\(812\) 0 0
\(813\) −27.6572 −0.969979
\(814\) 0 0
\(815\) 7.53855 0.264064
\(816\) 0 0
\(817\) 8.94073 0.312797
\(818\) 0 0
\(819\) −0.0758984 −0.00265210
\(820\) 0 0
\(821\) 4.78084 0.166853 0.0834263 0.996514i \(-0.473414\pi\)
0.0834263 + 0.996514i \(0.473414\pi\)
\(822\) 0 0
\(823\) 11.8312 0.412408 0.206204 0.978509i \(-0.433889\pi\)
0.206204 + 0.978509i \(0.433889\pi\)
\(824\) 0 0
\(825\) 2.48762 0.0866079
\(826\) 0 0
\(827\) 25.7394 0.895045 0.447523 0.894273i \(-0.352306\pi\)
0.447523 + 0.894273i \(0.352306\pi\)
\(828\) 0 0
\(829\) 6.37091 0.221271 0.110636 0.993861i \(-0.464711\pi\)
0.110636 + 0.993861i \(0.464711\pi\)
\(830\) 0 0
\(831\) 24.7248 0.857695
\(832\) 0 0
\(833\) −49.5366 −1.71634
\(834\) 0 0
\(835\) 1.98599 0.0687281
\(836\) 0 0
\(837\) −3.52738 −0.121924
\(838\) 0 0
\(839\) 35.3021 1.21876 0.609381 0.792877i \(-0.291418\pi\)
0.609381 + 0.792877i \(0.291418\pi\)
\(840\) 0 0
\(841\) −13.2630 −0.457343
\(842\) 0 0
\(843\) −1.24892 −0.0430150
\(844\) 0 0
\(845\) 24.4362 0.840631
\(846\) 0 0
\(847\) 0.495828 0.0170368
\(848\) 0 0
\(849\) −26.7744 −0.918897
\(850\) 0 0
\(851\) 4.10644 0.140767
\(852\) 0 0
\(853\) 6.70883 0.229706 0.114853 0.993383i \(-0.463360\pi\)
0.114853 + 0.993383i \(0.463360\pi\)
\(854\) 0 0
\(855\) 3.31139 0.113247
\(856\) 0 0
\(857\) 25.0043 0.854130 0.427065 0.904221i \(-0.359548\pi\)
0.427065 + 0.904221i \(0.359548\pi\)
\(858\) 0 0
\(859\) −21.4079 −0.730429 −0.365214 0.930923i \(-0.619004\pi\)
−0.365214 + 0.930923i \(0.619004\pi\)
\(860\) 0 0
\(861\) −0.0130021 −0.000443111 0
\(862\) 0 0
\(863\) 23.1799 0.789053 0.394527 0.918885i \(-0.370909\pi\)
0.394527 + 0.918885i \(0.370909\pi\)
\(864\) 0 0
\(865\) 10.6292 0.361404
\(866\) 0 0
\(867\) 33.1977 1.12745
\(868\) 0 0
\(869\) 40.8167 1.38461
\(870\) 0 0
\(871\) 3.76194 0.127469
\(872\) 0 0
\(873\) −12.8801 −0.435926
\(874\) 0 0
\(875\) −1.09438 −0.0369969
\(876\) 0 0
\(877\) −19.9817 −0.674734 −0.337367 0.941373i \(-0.609536\pi\)
−0.337367 + 0.941373i \(0.609536\pi\)
\(878\) 0 0
\(879\) 25.2333 0.851098
\(880\) 0 0
\(881\) 31.0252 1.04527 0.522633 0.852557i \(-0.324950\pi\)
0.522633 + 0.852557i \(0.324950\pi\)
\(882\) 0 0
\(883\) −6.97713 −0.234799 −0.117400 0.993085i \(-0.537456\pi\)
−0.117400 + 0.993085i \(0.537456\pi\)
\(884\) 0 0
\(885\) −8.72080 −0.293147
\(886\) 0 0
\(887\) 31.9000 1.07110 0.535549 0.844504i \(-0.320105\pi\)
0.535549 + 0.844504i \(0.320105\pi\)
\(888\) 0 0
\(889\) 1.70510 0.0571873
\(890\) 0 0
\(891\) −2.35607 −0.0789312
\(892\) 0 0
\(893\) 10.5893 0.354357
\(894\) 0 0
\(895\) 5.32506 0.177997
\(896\) 0 0
\(897\) −2.08498 −0.0696153
\(898\) 0 0
\(899\) 13.9931 0.466695
\(900\) 0 0
\(901\) 95.3782 3.17751
\(902\) 0 0
\(903\) 0.487929 0.0162373
\(904\) 0 0
\(905\) 43.2945 1.43916
\(906\) 0 0
\(907\) −9.59465 −0.318585 −0.159293 0.987231i \(-0.550921\pi\)
−0.159293 + 0.987231i \(0.550921\pi\)
\(908\) 0 0
\(909\) −14.6926 −0.487322
\(910\) 0 0
\(911\) 26.1540 0.866520 0.433260 0.901269i \(-0.357363\pi\)
0.433260 + 0.901269i \(0.357363\pi\)
\(912\) 0 0
\(913\) −0.0332566 −0.00110063
\(914\) 0 0
\(915\) −0.152223 −0.00503234
\(916\) 0 0
\(917\) −0.591562 −0.0195351
\(918\) 0 0
\(919\) 1.18144 0.0389722 0.0194861 0.999810i \(-0.493797\pi\)
0.0194861 + 0.999810i \(0.493797\pi\)
\(920\) 0 0
\(921\) 3.20268 0.105532
\(922\) 0 0
\(923\) 2.65185 0.0872867
\(924\) 0 0
\(925\) 1.73451 0.0570303
\(926\) 0 0
\(927\) −4.05118 −0.133058
\(928\) 0 0
\(929\) 43.5999 1.43046 0.715232 0.698887i \(-0.246321\pi\)
0.715232 + 0.698887i \(0.246321\pi\)
\(930\) 0 0
\(931\) 11.6578 0.382070
\(932\) 0 0
\(933\) −3.45554 −0.113129
\(934\) 0 0
\(935\) 33.1518 1.08418
\(936\) 0 0
\(937\) 15.5235 0.507130 0.253565 0.967318i \(-0.418397\pi\)
0.253565 + 0.967318i \(0.418397\pi\)
\(938\) 0 0
\(939\) 31.7617 1.03650
\(940\) 0 0
\(941\) −15.1806 −0.494874 −0.247437 0.968904i \(-0.579588\pi\)
−0.247437 + 0.968904i \(0.579588\pi\)
\(942\) 0 0
\(943\) −0.357177 −0.0116313
\(944\) 0 0
\(945\) 0.180715 0.00587867
\(946\) 0 0
\(947\) −22.6669 −0.736574 −0.368287 0.929712i \(-0.620056\pi\)
−0.368287 + 0.929712i \(0.620056\pi\)
\(948\) 0 0
\(949\) 7.75913 0.251872
\(950\) 0 0
\(951\) −25.1696 −0.816181
\(952\) 0 0
\(953\) −56.4316 −1.82800 −0.914000 0.405715i \(-0.867022\pi\)
−0.914000 + 0.405715i \(0.867022\pi\)
\(954\) 0 0
\(955\) 52.1898 1.68882
\(956\) 0 0
\(957\) 9.34650 0.302129
\(958\) 0 0
\(959\) 0.401871 0.0129771
\(960\) 0 0
\(961\) −18.5576 −0.598633
\(962\) 0 0
\(963\) 10.1492 0.327054
\(964\) 0 0
\(965\) −36.4063 −1.17196
\(966\) 0 0
\(967\) 14.1287 0.454349 0.227174 0.973854i \(-0.427051\pi\)
0.227174 + 0.973854i \(0.427051\pi\)
\(968\) 0 0
\(969\) −11.8134 −0.379501
\(970\) 0 0
\(971\) −16.4175 −0.526863 −0.263431 0.964678i \(-0.584854\pi\)
−0.263431 + 0.964678i \(0.584854\pi\)
\(972\) 0 0
\(973\) −0.325081 −0.0104216
\(974\) 0 0
\(975\) −0.880668 −0.0282040
\(976\) 0 0
\(977\) −15.1986 −0.486248 −0.243124 0.969995i \(-0.578172\pi\)
−0.243124 + 0.969995i \(0.578172\pi\)
\(978\) 0 0
\(979\) 18.7566 0.599464
\(980\) 0 0
\(981\) −4.51988 −0.144309
\(982\) 0 0
\(983\) −11.0518 −0.352499 −0.176249 0.984346i \(-0.556397\pi\)
−0.176249 + 0.984346i \(0.556397\pi\)
\(984\) 0 0
\(985\) −28.1061 −0.895534
\(986\) 0 0
\(987\) 0.577897 0.0183947
\(988\) 0 0
\(989\) 13.4037 0.426214
\(990\) 0 0
\(991\) 13.0573 0.414780 0.207390 0.978258i \(-0.433503\pi\)
0.207390 + 0.978258i \(0.433503\pi\)
\(992\) 0 0
\(993\) −8.94004 −0.283703
\(994\) 0 0
\(995\) 35.3232 1.11982
\(996\) 0 0
\(997\) 40.9089 1.29560 0.647799 0.761811i \(-0.275690\pi\)
0.647799 + 0.761811i \(0.275690\pi\)
\(998\) 0 0
\(999\) −1.64278 −0.0519752
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 \(a_p\))