Properties

Label 4008.2.a.l.1.8
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
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: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.56937\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+1.56937 q^{5}\) \(+3.21458 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+1.56937 q^{5}\) \(+3.21458 q^{7}\) \(+1.00000 q^{9}\) \(-5.96544 q^{11}\) \(+2.81457 q^{13}\) \(+1.56937 q^{15}\) \(+4.33096 q^{17}\) \(+4.82798 q^{19}\) \(+3.21458 q^{21}\) \(+3.36422 q^{23}\) \(-2.53708 q^{25}\) \(+1.00000 q^{27}\) \(-8.76511 q^{29}\) \(+2.34104 q^{31}\) \(-5.96544 q^{33}\) \(+5.04486 q^{35}\) \(+7.28651 q^{37}\) \(+2.81457 q^{39}\) \(-1.39154 q^{41}\) \(+2.86513 q^{43}\) \(+1.56937 q^{45}\) \(+9.87896 q^{47}\) \(+3.33349 q^{49}\) \(+4.33096 q^{51}\) \(-11.2692 q^{53}\) \(-9.36199 q^{55}\) \(+4.82798 q^{57}\) \(-1.96751 q^{59}\) \(-3.76751 q^{61}\) \(+3.21458 q^{63}\) \(+4.41711 q^{65}\) \(+11.6949 q^{67}\) \(+3.36422 q^{69}\) \(-4.01255 q^{71}\) \(+8.49415 q^{73}\) \(-2.53708 q^{75}\) \(-19.1764 q^{77}\) \(+3.69376 q^{79}\) \(+1.00000 q^{81}\) \(+8.33948 q^{83}\) \(+6.79689 q^{85}\) \(-8.76511 q^{87}\) \(+12.3598 q^{89}\) \(+9.04765 q^{91}\) \(+2.34104 q^{93}\) \(+7.57689 q^{95}\) \(+0.582982 q^{97}\) \(-5.96544 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.56937 0.701844 0.350922 0.936405i \(-0.385868\pi\)
0.350922 + 0.936405i \(0.385868\pi\)
\(6\) 0 0
\(7\) 3.21458 1.21500 0.607498 0.794321i \(-0.292173\pi\)
0.607498 + 0.794321i \(0.292173\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.96544 −1.79865 −0.899325 0.437282i \(-0.855941\pi\)
−0.899325 + 0.437282i \(0.855941\pi\)
\(12\) 0 0
\(13\) 2.81457 0.780622 0.390311 0.920683i \(-0.372368\pi\)
0.390311 + 0.920683i \(0.372368\pi\)
\(14\) 0 0
\(15\) 1.56937 0.405210
\(16\) 0 0
\(17\) 4.33096 1.05041 0.525207 0.850975i \(-0.323988\pi\)
0.525207 + 0.850975i \(0.323988\pi\)
\(18\) 0 0
\(19\) 4.82798 1.10761 0.553807 0.832645i \(-0.313175\pi\)
0.553807 + 0.832645i \(0.313175\pi\)
\(20\) 0 0
\(21\) 3.21458 0.701478
\(22\) 0 0
\(23\) 3.36422 0.701489 0.350744 0.936471i \(-0.385929\pi\)
0.350744 + 0.936471i \(0.385929\pi\)
\(24\) 0 0
\(25\) −2.53708 −0.507415
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.76511 −1.62764 −0.813820 0.581117i \(-0.802616\pi\)
−0.813820 + 0.581117i \(0.802616\pi\)
\(30\) 0 0
\(31\) 2.34104 0.420463 0.210231 0.977652i \(-0.432578\pi\)
0.210231 + 0.977652i \(0.432578\pi\)
\(32\) 0 0
\(33\) −5.96544 −1.03845
\(34\) 0 0
\(35\) 5.04486 0.852737
\(36\) 0 0
\(37\) 7.28651 1.19789 0.598947 0.800788i \(-0.295586\pi\)
0.598947 + 0.800788i \(0.295586\pi\)
\(38\) 0 0
\(39\) 2.81457 0.450692
\(40\) 0 0
\(41\) −1.39154 −0.217322 −0.108661 0.994079i \(-0.534656\pi\)
−0.108661 + 0.994079i \(0.534656\pi\)
\(42\) 0 0
\(43\) 2.86513 0.436928 0.218464 0.975845i \(-0.429895\pi\)
0.218464 + 0.975845i \(0.429895\pi\)
\(44\) 0 0
\(45\) 1.56937 0.233948
\(46\) 0 0
\(47\) 9.87896 1.44099 0.720497 0.693458i \(-0.243914\pi\)
0.720497 + 0.693458i \(0.243914\pi\)
\(48\) 0 0
\(49\) 3.33349 0.476213
\(50\) 0 0
\(51\) 4.33096 0.606456
\(52\) 0 0
\(53\) −11.2692 −1.54794 −0.773970 0.633223i \(-0.781732\pi\)
−0.773970 + 0.633223i \(0.781732\pi\)
\(54\) 0 0
\(55\) −9.36199 −1.26237
\(56\) 0 0
\(57\) 4.82798 0.639481
\(58\) 0 0
\(59\) −1.96751 −0.256148 −0.128074 0.991765i \(-0.540879\pi\)
−0.128074 + 0.991765i \(0.540879\pi\)
\(60\) 0 0
\(61\) −3.76751 −0.482381 −0.241190 0.970478i \(-0.577538\pi\)
−0.241190 + 0.970478i \(0.577538\pi\)
\(62\) 0 0
\(63\) 3.21458 0.404998
\(64\) 0 0
\(65\) 4.41711 0.547875
\(66\) 0 0
\(67\) 11.6949 1.42875 0.714377 0.699761i \(-0.246710\pi\)
0.714377 + 0.699761i \(0.246710\pi\)
\(68\) 0 0
\(69\) 3.36422 0.405005
\(70\) 0 0
\(71\) −4.01255 −0.476202 −0.238101 0.971240i \(-0.576525\pi\)
−0.238101 + 0.971240i \(0.576525\pi\)
\(72\) 0 0
\(73\) 8.49415 0.994165 0.497082 0.867703i \(-0.334405\pi\)
0.497082 + 0.867703i \(0.334405\pi\)
\(74\) 0 0
\(75\) −2.53708 −0.292956
\(76\) 0 0
\(77\) −19.1764 −2.18535
\(78\) 0 0
\(79\) 3.69376 0.415580 0.207790 0.978173i \(-0.433373\pi\)
0.207790 + 0.978173i \(0.433373\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 8.33948 0.915377 0.457688 0.889113i \(-0.348677\pi\)
0.457688 + 0.889113i \(0.348677\pi\)
\(84\) 0 0
\(85\) 6.79689 0.737226
\(86\) 0 0
\(87\) −8.76511 −0.939718
\(88\) 0 0
\(89\) 12.3598 1.31013 0.655067 0.755571i \(-0.272640\pi\)
0.655067 + 0.755571i \(0.272640\pi\)
\(90\) 0 0
\(91\) 9.04765 0.948452
\(92\) 0 0
\(93\) 2.34104 0.242754
\(94\) 0 0
\(95\) 7.57689 0.777372
\(96\) 0 0
\(97\) 0.582982 0.0591929 0.0295964 0.999562i \(-0.490578\pi\)
0.0295964 + 0.999562i \(0.490578\pi\)
\(98\) 0 0
\(99\) −5.96544 −0.599550
\(100\) 0 0
\(101\) 1.44938 0.144218 0.0721091 0.997397i \(-0.477027\pi\)
0.0721091 + 0.997397i \(0.477027\pi\)
\(102\) 0 0
\(103\) −14.7825 −1.45657 −0.728284 0.685276i \(-0.759682\pi\)
−0.728284 + 0.685276i \(0.759682\pi\)
\(104\) 0 0
\(105\) 5.04486 0.492328
\(106\) 0 0
\(107\) −10.3485 −1.00043 −0.500214 0.865902i \(-0.666745\pi\)
−0.500214 + 0.865902i \(0.666745\pi\)
\(108\) 0 0
\(109\) −2.71160 −0.259724 −0.129862 0.991532i \(-0.541453\pi\)
−0.129862 + 0.991532i \(0.541453\pi\)
\(110\) 0 0
\(111\) 7.28651 0.691605
\(112\) 0 0
\(113\) −0.419192 −0.0394343 −0.0197171 0.999806i \(-0.506277\pi\)
−0.0197171 + 0.999806i \(0.506277\pi\)
\(114\) 0 0
\(115\) 5.27971 0.492336
\(116\) 0 0
\(117\) 2.81457 0.260207
\(118\) 0 0
\(119\) 13.9222 1.27625
\(120\) 0 0
\(121\) 24.5865 2.23514
\(122\) 0 0
\(123\) −1.39154 −0.125471
\(124\) 0 0
\(125\) −11.8285 −1.05797
\(126\) 0 0
\(127\) −14.5074 −1.28733 −0.643663 0.765309i \(-0.722586\pi\)
−0.643663 + 0.765309i \(0.722586\pi\)
\(128\) 0 0
\(129\) 2.86513 0.252260
\(130\) 0 0
\(131\) 19.6189 1.71411 0.857054 0.515226i \(-0.172292\pi\)
0.857054 + 0.515226i \(0.172292\pi\)
\(132\) 0 0
\(133\) 15.5199 1.34575
\(134\) 0 0
\(135\) 1.56937 0.135070
\(136\) 0 0
\(137\) −7.89669 −0.674660 −0.337330 0.941387i \(-0.609524\pi\)
−0.337330 + 0.941387i \(0.609524\pi\)
\(138\) 0 0
\(139\) −6.36468 −0.539845 −0.269923 0.962882i \(-0.586998\pi\)
−0.269923 + 0.962882i \(0.586998\pi\)
\(140\) 0 0
\(141\) 9.87896 0.831958
\(142\) 0 0
\(143\) −16.7902 −1.40406
\(144\) 0 0
\(145\) −13.7557 −1.14235
\(146\) 0 0
\(147\) 3.33349 0.274942
\(148\) 0 0
\(149\) 9.16385 0.750732 0.375366 0.926877i \(-0.377517\pi\)
0.375366 + 0.926877i \(0.377517\pi\)
\(150\) 0 0
\(151\) 16.2998 1.32646 0.663228 0.748418i \(-0.269186\pi\)
0.663228 + 0.748418i \(0.269186\pi\)
\(152\) 0 0
\(153\) 4.33096 0.350138
\(154\) 0 0
\(155\) 3.67396 0.295099
\(156\) 0 0
\(157\) 18.2988 1.46040 0.730200 0.683233i \(-0.239427\pi\)
0.730200 + 0.683233i \(0.239427\pi\)
\(158\) 0 0
\(159\) −11.2692 −0.893703
\(160\) 0 0
\(161\) 10.8145 0.852306
\(162\) 0 0
\(163\) −9.82475 −0.769534 −0.384767 0.923014i \(-0.625718\pi\)
−0.384767 + 0.923014i \(0.625718\pi\)
\(164\) 0 0
\(165\) −9.36199 −0.728830
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −5.07819 −0.390630
\(170\) 0 0
\(171\) 4.82798 0.369205
\(172\) 0 0
\(173\) −19.1154 −1.45332 −0.726658 0.687000i \(-0.758927\pi\)
−0.726658 + 0.687000i \(0.758927\pi\)
\(174\) 0 0
\(175\) −8.15562 −0.616507
\(176\) 0 0
\(177\) −1.96751 −0.147887
\(178\) 0 0
\(179\) −8.40836 −0.628471 −0.314235 0.949345i \(-0.601748\pi\)
−0.314235 + 0.949345i \(0.601748\pi\)
\(180\) 0 0
\(181\) −20.3287 −1.51102 −0.755510 0.655137i \(-0.772611\pi\)
−0.755510 + 0.655137i \(0.772611\pi\)
\(182\) 0 0
\(183\) −3.76751 −0.278503
\(184\) 0 0
\(185\) 11.4352 0.840735
\(186\) 0 0
\(187\) −25.8361 −1.88932
\(188\) 0 0
\(189\) 3.21458 0.233826
\(190\) 0 0
\(191\) 24.2261 1.75294 0.876471 0.481454i \(-0.159891\pi\)
0.876471 + 0.481454i \(0.159891\pi\)
\(192\) 0 0
\(193\) −12.2851 −0.884301 −0.442151 0.896941i \(-0.645784\pi\)
−0.442151 + 0.896941i \(0.645784\pi\)
\(194\) 0 0
\(195\) 4.41711 0.316316
\(196\) 0 0
\(197\) −15.3618 −1.09448 −0.547240 0.836976i \(-0.684322\pi\)
−0.547240 + 0.836976i \(0.684322\pi\)
\(198\) 0 0
\(199\) 8.14641 0.577483 0.288742 0.957407i \(-0.406763\pi\)
0.288742 + 0.957407i \(0.406763\pi\)
\(200\) 0 0
\(201\) 11.6949 0.824892
\(202\) 0 0
\(203\) −28.1761 −1.97757
\(204\) 0 0
\(205\) −2.18384 −0.152526
\(206\) 0 0
\(207\) 3.36422 0.233830
\(208\) 0 0
\(209\) −28.8010 −1.99221
\(210\) 0 0
\(211\) −12.7610 −0.878503 −0.439251 0.898364i \(-0.644756\pi\)
−0.439251 + 0.898364i \(0.644756\pi\)
\(212\) 0 0
\(213\) −4.01255 −0.274936
\(214\) 0 0
\(215\) 4.49645 0.306655
\(216\) 0 0
\(217\) 7.52544 0.510860
\(218\) 0 0
\(219\) 8.49415 0.573981
\(220\) 0 0
\(221\) 12.1898 0.819975
\(222\) 0 0
\(223\) 9.88563 0.661991 0.330995 0.943632i \(-0.392616\pi\)
0.330995 + 0.943632i \(0.392616\pi\)
\(224\) 0 0
\(225\) −2.53708 −0.169138
\(226\) 0 0
\(227\) −0.485281 −0.0322093 −0.0161046 0.999870i \(-0.505126\pi\)
−0.0161046 + 0.999870i \(0.505126\pi\)
\(228\) 0 0
\(229\) −28.3959 −1.87646 −0.938228 0.346019i \(-0.887533\pi\)
−0.938228 + 0.346019i \(0.887533\pi\)
\(230\) 0 0
\(231\) −19.1764 −1.26171
\(232\) 0 0
\(233\) −26.5196 −1.73736 −0.868679 0.495376i \(-0.835030\pi\)
−0.868679 + 0.495376i \(0.835030\pi\)
\(234\) 0 0
\(235\) 15.5037 1.01135
\(236\) 0 0
\(237\) 3.69376 0.239935
\(238\) 0 0
\(239\) 13.4261 0.868464 0.434232 0.900801i \(-0.357020\pi\)
0.434232 + 0.900801i \(0.357020\pi\)
\(240\) 0 0
\(241\) 11.4392 0.736865 0.368432 0.929655i \(-0.379895\pi\)
0.368432 + 0.929655i \(0.379895\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 5.23149 0.334228
\(246\) 0 0
\(247\) 13.5887 0.864627
\(248\) 0 0
\(249\) 8.33948 0.528493
\(250\) 0 0
\(251\) −16.4258 −1.03679 −0.518395 0.855141i \(-0.673470\pi\)
−0.518395 + 0.855141i \(0.673470\pi\)
\(252\) 0 0
\(253\) −20.0691 −1.26173
\(254\) 0 0
\(255\) 6.79689 0.425638
\(256\) 0 0
\(257\) 17.6649 1.10190 0.550952 0.834537i \(-0.314265\pi\)
0.550952 + 0.834537i \(0.314265\pi\)
\(258\) 0 0
\(259\) 23.4230 1.45544
\(260\) 0 0
\(261\) −8.76511 −0.542547
\(262\) 0 0
\(263\) 7.60215 0.468768 0.234384 0.972144i \(-0.424693\pi\)
0.234384 + 0.972144i \(0.424693\pi\)
\(264\) 0 0
\(265\) −17.6855 −1.08641
\(266\) 0 0
\(267\) 12.3598 0.756406
\(268\) 0 0
\(269\) −7.33835 −0.447427 −0.223714 0.974655i \(-0.571818\pi\)
−0.223714 + 0.974655i \(0.571818\pi\)
\(270\) 0 0
\(271\) 30.7629 1.86871 0.934356 0.356340i \(-0.115975\pi\)
0.934356 + 0.356340i \(0.115975\pi\)
\(272\) 0 0
\(273\) 9.04765 0.547589
\(274\) 0 0
\(275\) 15.1348 0.912662
\(276\) 0 0
\(277\) 15.0041 0.901508 0.450754 0.892648i \(-0.351155\pi\)
0.450754 + 0.892648i \(0.351155\pi\)
\(278\) 0 0
\(279\) 2.34104 0.140154
\(280\) 0 0
\(281\) 10.2001 0.608488 0.304244 0.952594i \(-0.401596\pi\)
0.304244 + 0.952594i \(0.401596\pi\)
\(282\) 0 0
\(283\) 2.65541 0.157847 0.0789237 0.996881i \(-0.474852\pi\)
0.0789237 + 0.996881i \(0.474852\pi\)
\(284\) 0 0
\(285\) 7.57689 0.448816
\(286\) 0 0
\(287\) −4.47321 −0.264045
\(288\) 0 0
\(289\) 1.75725 0.103368
\(290\) 0 0
\(291\) 0.582982 0.0341750
\(292\) 0 0
\(293\) 19.0956 1.11558 0.557789 0.829983i \(-0.311650\pi\)
0.557789 + 0.829983i \(0.311650\pi\)
\(294\) 0 0
\(295\) −3.08775 −0.179776
\(296\) 0 0
\(297\) −5.96544 −0.346150
\(298\) 0 0
\(299\) 9.46885 0.547597
\(300\) 0 0
\(301\) 9.21017 0.530865
\(302\) 0 0
\(303\) 1.44938 0.0832644
\(304\) 0 0
\(305\) −5.91263 −0.338556
\(306\) 0 0
\(307\) 2.29511 0.130989 0.0654944 0.997853i \(-0.479138\pi\)
0.0654944 + 0.997853i \(0.479138\pi\)
\(308\) 0 0
\(309\) −14.7825 −0.840950
\(310\) 0 0
\(311\) −0.877859 −0.0497788 −0.0248894 0.999690i \(-0.507923\pi\)
−0.0248894 + 0.999690i \(0.507923\pi\)
\(312\) 0 0
\(313\) −18.9459 −1.07089 −0.535443 0.844571i \(-0.679855\pi\)
−0.535443 + 0.844571i \(0.679855\pi\)
\(314\) 0 0
\(315\) 5.04486 0.284246
\(316\) 0 0
\(317\) 32.8653 1.84590 0.922950 0.384920i \(-0.125771\pi\)
0.922950 + 0.384920i \(0.125771\pi\)
\(318\) 0 0
\(319\) 52.2878 2.92755
\(320\) 0 0
\(321\) −10.3485 −0.577598
\(322\) 0 0
\(323\) 20.9098 1.16345
\(324\) 0 0
\(325\) −7.14078 −0.396099
\(326\) 0 0
\(327\) −2.71160 −0.149952
\(328\) 0 0
\(329\) 31.7566 1.75080
\(330\) 0 0
\(331\) 6.81707 0.374700 0.187350 0.982293i \(-0.440010\pi\)
0.187350 + 0.982293i \(0.440010\pi\)
\(332\) 0 0
\(333\) 7.28651 0.399298
\(334\) 0 0
\(335\) 18.3536 1.00276
\(336\) 0 0
\(337\) −14.6194 −0.796372 −0.398186 0.917305i \(-0.630360\pi\)
−0.398186 + 0.917305i \(0.630360\pi\)
\(338\) 0 0
\(339\) −0.419192 −0.0227674
\(340\) 0 0
\(341\) −13.9653 −0.756265
\(342\) 0 0
\(343\) −11.7863 −0.636398
\(344\) 0 0
\(345\) 5.27971 0.284250
\(346\) 0 0
\(347\) 18.2051 0.977301 0.488651 0.872480i \(-0.337489\pi\)
0.488651 + 0.872480i \(0.337489\pi\)
\(348\) 0 0
\(349\) 12.8709 0.688964 0.344482 0.938793i \(-0.388055\pi\)
0.344482 + 0.938793i \(0.388055\pi\)
\(350\) 0 0
\(351\) 2.81457 0.150231
\(352\) 0 0
\(353\) 12.9234 0.687841 0.343921 0.938999i \(-0.388245\pi\)
0.343921 + 0.938999i \(0.388245\pi\)
\(354\) 0 0
\(355\) −6.29718 −0.334220
\(356\) 0 0
\(357\) 13.9222 0.736841
\(358\) 0 0
\(359\) −21.7806 −1.14954 −0.574769 0.818316i \(-0.694908\pi\)
−0.574769 + 0.818316i \(0.694908\pi\)
\(360\) 0 0
\(361\) 4.30936 0.226808
\(362\) 0 0
\(363\) 24.5865 1.29046
\(364\) 0 0
\(365\) 13.3305 0.697749
\(366\) 0 0
\(367\) −18.0839 −0.943970 −0.471985 0.881607i \(-0.656462\pi\)
−0.471985 + 0.881607i \(0.656462\pi\)
\(368\) 0 0
\(369\) −1.39154 −0.0724407
\(370\) 0 0
\(371\) −36.2256 −1.88074
\(372\) 0 0
\(373\) −28.5524 −1.47839 −0.739193 0.673494i \(-0.764793\pi\)
−0.739193 + 0.673494i \(0.764793\pi\)
\(374\) 0 0
\(375\) −11.8285 −0.610819
\(376\) 0 0
\(377\) −24.6700 −1.27057
\(378\) 0 0
\(379\) 29.6698 1.52404 0.762019 0.647555i \(-0.224208\pi\)
0.762019 + 0.647555i \(0.224208\pi\)
\(380\) 0 0
\(381\) −14.5074 −0.743237
\(382\) 0 0
\(383\) 26.8107 1.36996 0.684982 0.728560i \(-0.259810\pi\)
0.684982 + 0.728560i \(0.259810\pi\)
\(384\) 0 0
\(385\) −30.0948 −1.53377
\(386\) 0 0
\(387\) 2.86513 0.145643
\(388\) 0 0
\(389\) −27.5430 −1.39649 −0.698243 0.715861i \(-0.746035\pi\)
−0.698243 + 0.715861i \(0.746035\pi\)
\(390\) 0 0
\(391\) 14.5703 0.736853
\(392\) 0 0
\(393\) 19.6189 0.989641
\(394\) 0 0
\(395\) 5.79687 0.291672
\(396\) 0 0
\(397\) −15.7322 −0.789575 −0.394787 0.918772i \(-0.629182\pi\)
−0.394787 + 0.918772i \(0.629182\pi\)
\(398\) 0 0
\(399\) 15.5199 0.776966
\(400\) 0 0
\(401\) −6.71138 −0.335150 −0.167575 0.985859i \(-0.553594\pi\)
−0.167575 + 0.985859i \(0.553594\pi\)
\(402\) 0 0
\(403\) 6.58902 0.328222
\(404\) 0 0
\(405\) 1.56937 0.0779827
\(406\) 0 0
\(407\) −43.4673 −2.15459
\(408\) 0 0
\(409\) −25.3626 −1.25410 −0.627049 0.778980i \(-0.715737\pi\)
−0.627049 + 0.778980i \(0.715737\pi\)
\(410\) 0 0
\(411\) −7.89669 −0.389515
\(412\) 0 0
\(413\) −6.32470 −0.311218
\(414\) 0 0
\(415\) 13.0877 0.642452
\(416\) 0 0
\(417\) −6.36468 −0.311680
\(418\) 0 0
\(419\) −4.52335 −0.220980 −0.110490 0.993877i \(-0.535242\pi\)
−0.110490 + 0.993877i \(0.535242\pi\)
\(420\) 0 0
\(421\) 25.4294 1.23935 0.619677 0.784857i \(-0.287264\pi\)
0.619677 + 0.784857i \(0.287264\pi\)
\(422\) 0 0
\(423\) 9.87896 0.480331
\(424\) 0 0
\(425\) −10.9880 −0.532995
\(426\) 0 0
\(427\) −12.1110 −0.586090
\(428\) 0 0
\(429\) −16.7902 −0.810637
\(430\) 0 0
\(431\) −29.8778 −1.43917 −0.719583 0.694407i \(-0.755667\pi\)
−0.719583 + 0.694407i \(0.755667\pi\)
\(432\) 0 0
\(433\) 17.1484 0.824100 0.412050 0.911161i \(-0.364813\pi\)
0.412050 + 0.911161i \(0.364813\pi\)
\(434\) 0 0
\(435\) −13.7557 −0.659536
\(436\) 0 0
\(437\) 16.2424 0.776979
\(438\) 0 0
\(439\) −15.7954 −0.753872 −0.376936 0.926239i \(-0.623022\pi\)
−0.376936 + 0.926239i \(0.623022\pi\)
\(440\) 0 0
\(441\) 3.33349 0.158738
\(442\) 0 0
\(443\) 22.8494 1.08561 0.542804 0.839860i \(-0.317363\pi\)
0.542804 + 0.839860i \(0.317363\pi\)
\(444\) 0 0
\(445\) 19.3971 0.919509
\(446\) 0 0
\(447\) 9.16385 0.433435
\(448\) 0 0
\(449\) −15.5104 −0.731982 −0.365991 0.930618i \(-0.619270\pi\)
−0.365991 + 0.930618i \(0.619270\pi\)
\(450\) 0 0
\(451\) 8.30116 0.390886
\(452\) 0 0
\(453\) 16.2998 0.765830
\(454\) 0 0
\(455\) 14.1991 0.665665
\(456\) 0 0
\(457\) 36.1847 1.69265 0.846325 0.532666i \(-0.178810\pi\)
0.846325 + 0.532666i \(0.178810\pi\)
\(458\) 0 0
\(459\) 4.33096 0.202152
\(460\) 0 0
\(461\) −12.1329 −0.565085 −0.282542 0.959255i \(-0.591178\pi\)
−0.282542 + 0.959255i \(0.591178\pi\)
\(462\) 0 0
\(463\) 24.5598 1.14139 0.570696 0.821161i \(-0.306673\pi\)
0.570696 + 0.821161i \(0.306673\pi\)
\(464\) 0 0
\(465\) 3.67396 0.170376
\(466\) 0 0
\(467\) −22.6629 −1.04872 −0.524358 0.851498i \(-0.675695\pi\)
−0.524358 + 0.851498i \(0.675695\pi\)
\(468\) 0 0
\(469\) 37.5940 1.73593
\(470\) 0 0
\(471\) 18.2988 0.843163
\(472\) 0 0
\(473\) −17.0918 −0.785880
\(474\) 0 0
\(475\) −12.2489 −0.562020
\(476\) 0 0
\(477\) −11.2692 −0.515980
\(478\) 0 0
\(479\) 11.5978 0.529915 0.264958 0.964260i \(-0.414642\pi\)
0.264958 + 0.964260i \(0.414642\pi\)
\(480\) 0 0
\(481\) 20.5084 0.935102
\(482\) 0 0
\(483\) 10.8145 0.492079
\(484\) 0 0
\(485\) 0.914916 0.0415442
\(486\) 0 0
\(487\) −28.9911 −1.31371 −0.656856 0.754016i \(-0.728114\pi\)
−0.656856 + 0.754016i \(0.728114\pi\)
\(488\) 0 0
\(489\) −9.82475 −0.444291
\(490\) 0 0
\(491\) −37.7088 −1.70177 −0.850887 0.525349i \(-0.823935\pi\)
−0.850887 + 0.525349i \(0.823935\pi\)
\(492\) 0 0
\(493\) −37.9614 −1.70969
\(494\) 0 0
\(495\) −9.36199 −0.420790
\(496\) 0 0
\(497\) −12.8987 −0.578584
\(498\) 0 0
\(499\) 22.0629 0.987669 0.493835 0.869556i \(-0.335595\pi\)
0.493835 + 0.869556i \(0.335595\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −32.1216 −1.43223 −0.716117 0.697981i \(-0.754082\pi\)
−0.716117 + 0.697981i \(0.754082\pi\)
\(504\) 0 0
\(505\) 2.27461 0.101219
\(506\) 0 0
\(507\) −5.07819 −0.225530
\(508\) 0 0
\(509\) −21.3655 −0.947009 −0.473504 0.880791i \(-0.657011\pi\)
−0.473504 + 0.880791i \(0.657011\pi\)
\(510\) 0 0
\(511\) 27.3051 1.20791
\(512\) 0 0
\(513\) 4.82798 0.213160
\(514\) 0 0
\(515\) −23.1993 −1.02228
\(516\) 0 0
\(517\) −58.9324 −2.59184
\(518\) 0 0
\(519\) −19.1154 −0.839072
\(520\) 0 0
\(521\) 4.55492 0.199555 0.0997774 0.995010i \(-0.468187\pi\)
0.0997774 + 0.995010i \(0.468187\pi\)
\(522\) 0 0
\(523\) 2.01218 0.0879864 0.0439932 0.999032i \(-0.485992\pi\)
0.0439932 + 0.999032i \(0.485992\pi\)
\(524\) 0 0
\(525\) −8.15562 −0.355940
\(526\) 0 0
\(527\) 10.1389 0.441660
\(528\) 0 0
\(529\) −11.6820 −0.507913
\(530\) 0 0
\(531\) −1.96751 −0.0853826
\(532\) 0 0
\(533\) −3.91659 −0.169646
\(534\) 0 0
\(535\) −16.2407 −0.702145
\(536\) 0 0
\(537\) −8.40836 −0.362848
\(538\) 0 0
\(539\) −19.8858 −0.856541
\(540\) 0 0
\(541\) 17.1502 0.737343 0.368672 0.929560i \(-0.379813\pi\)
0.368672 + 0.929560i \(0.379813\pi\)
\(542\) 0 0
\(543\) −20.3287 −0.872388
\(544\) 0 0
\(545\) −4.25550 −0.182286
\(546\) 0 0
\(547\) −5.92215 −0.253213 −0.126606 0.991953i \(-0.540408\pi\)
−0.126606 + 0.991953i \(0.540408\pi\)
\(548\) 0 0
\(549\) −3.76751 −0.160794
\(550\) 0 0
\(551\) −42.3177 −1.80280
\(552\) 0 0
\(553\) 11.8739 0.504928
\(554\) 0 0
\(555\) 11.4352 0.485399
\(556\) 0 0
\(557\) 20.1694 0.854603 0.427301 0.904109i \(-0.359464\pi\)
0.427301 + 0.904109i \(0.359464\pi\)
\(558\) 0 0
\(559\) 8.06410 0.341075
\(560\) 0 0
\(561\) −25.8361 −1.09080
\(562\) 0 0
\(563\) −35.6864 −1.50400 −0.752002 0.659161i \(-0.770911\pi\)
−0.752002 + 0.659161i \(0.770911\pi\)
\(564\) 0 0
\(565\) −0.657868 −0.0276767
\(566\) 0 0
\(567\) 3.21458 0.134999
\(568\) 0 0
\(569\) −34.0630 −1.42800 −0.713998 0.700148i \(-0.753117\pi\)
−0.713998 + 0.700148i \(0.753117\pi\)
\(570\) 0 0
\(571\) 34.9133 1.46108 0.730538 0.682872i \(-0.239270\pi\)
0.730538 + 0.682872i \(0.239270\pi\)
\(572\) 0 0
\(573\) 24.2261 1.01206
\(574\) 0 0
\(575\) −8.53529 −0.355946
\(576\) 0 0
\(577\) 15.2801 0.636117 0.318059 0.948071i \(-0.396969\pi\)
0.318059 + 0.948071i \(0.396969\pi\)
\(578\) 0 0
\(579\) −12.2851 −0.510552
\(580\) 0 0
\(581\) 26.8079 1.11218
\(582\) 0 0
\(583\) 67.2256 2.78420
\(584\) 0 0
\(585\) 4.41711 0.182625
\(586\) 0 0
\(587\) 4.37405 0.180536 0.0902682 0.995917i \(-0.471228\pi\)
0.0902682 + 0.995917i \(0.471228\pi\)
\(588\) 0 0
\(589\) 11.3025 0.465710
\(590\) 0 0
\(591\) −15.3618 −0.631899
\(592\) 0 0
\(593\) −33.2932 −1.36719 −0.683595 0.729862i \(-0.739584\pi\)
−0.683595 + 0.729862i \(0.739584\pi\)
\(594\) 0 0
\(595\) 21.8491 0.895726
\(596\) 0 0
\(597\) 8.14641 0.333410
\(598\) 0 0
\(599\) 8.35724 0.341468 0.170734 0.985317i \(-0.445386\pi\)
0.170734 + 0.985317i \(0.445386\pi\)
\(600\) 0 0
\(601\) −33.2266 −1.35534 −0.677671 0.735365i \(-0.737011\pi\)
−0.677671 + 0.735365i \(0.737011\pi\)
\(602\) 0 0
\(603\) 11.6949 0.476251
\(604\) 0 0
\(605\) 38.5854 1.56872
\(606\) 0 0
\(607\) −17.0042 −0.690180 −0.345090 0.938570i \(-0.612152\pi\)
−0.345090 + 0.938570i \(0.612152\pi\)
\(608\) 0 0
\(609\) −28.1761 −1.14175
\(610\) 0 0
\(611\) 27.8050 1.12487
\(612\) 0 0
\(613\) −4.21522 −0.170251 −0.0851255 0.996370i \(-0.527129\pi\)
−0.0851255 + 0.996370i \(0.527129\pi\)
\(614\) 0 0
\(615\) −2.18384 −0.0880610
\(616\) 0 0
\(617\) −45.4867 −1.83123 −0.915613 0.402061i \(-0.868294\pi\)
−0.915613 + 0.402061i \(0.868294\pi\)
\(618\) 0 0
\(619\) 17.5216 0.704252 0.352126 0.935953i \(-0.385459\pi\)
0.352126 + 0.935953i \(0.385459\pi\)
\(620\) 0 0
\(621\) 3.36422 0.135002
\(622\) 0 0
\(623\) 39.7314 1.59181
\(624\) 0 0
\(625\) −5.87787 −0.235115
\(626\) 0 0
\(627\) −28.8010 −1.15020
\(628\) 0 0
\(629\) 31.5576 1.25828
\(630\) 0 0
\(631\) −26.8300 −1.06809 −0.534043 0.845458i \(-0.679328\pi\)
−0.534043 + 0.845458i \(0.679328\pi\)
\(632\) 0 0
\(633\) −12.7610 −0.507204
\(634\) 0 0
\(635\) −22.7675 −0.903501
\(636\) 0 0
\(637\) 9.38236 0.371743
\(638\) 0 0
\(639\) −4.01255 −0.158734
\(640\) 0 0
\(641\) 2.25848 0.0892044 0.0446022 0.999005i \(-0.485798\pi\)
0.0446022 + 0.999005i \(0.485798\pi\)
\(642\) 0 0
\(643\) −14.0840 −0.555418 −0.277709 0.960665i \(-0.589575\pi\)
−0.277709 + 0.960665i \(0.589575\pi\)
\(644\) 0 0
\(645\) 4.49645 0.177047
\(646\) 0 0
\(647\) 18.9010 0.743076 0.371538 0.928418i \(-0.378831\pi\)
0.371538 + 0.928418i \(0.378831\pi\)
\(648\) 0 0
\(649\) 11.7371 0.460720
\(650\) 0 0
\(651\) 7.52544 0.294945
\(652\) 0 0
\(653\) −19.4383 −0.760680 −0.380340 0.924847i \(-0.624193\pi\)
−0.380340 + 0.924847i \(0.624193\pi\)
\(654\) 0 0
\(655\) 30.7893 1.20304
\(656\) 0 0
\(657\) 8.49415 0.331388
\(658\) 0 0
\(659\) −21.8476 −0.851061 −0.425531 0.904944i \(-0.639912\pi\)
−0.425531 + 0.904944i \(0.639912\pi\)
\(660\) 0 0
\(661\) −8.02092 −0.311978 −0.155989 0.987759i \(-0.549856\pi\)
−0.155989 + 0.987759i \(0.549856\pi\)
\(662\) 0 0
\(663\) 12.1898 0.473413
\(664\) 0 0
\(665\) 24.3565 0.944503
\(666\) 0 0
\(667\) −29.4878 −1.14177
\(668\) 0 0
\(669\) 9.88563 0.382201
\(670\) 0 0
\(671\) 22.4749 0.867634
\(672\) 0 0
\(673\) 8.07660 0.311330 0.155665 0.987810i \(-0.450248\pi\)
0.155665 + 0.987810i \(0.450248\pi\)
\(674\) 0 0
\(675\) −2.53708 −0.0976521
\(676\) 0 0
\(677\) −26.4185 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(678\) 0 0
\(679\) 1.87404 0.0719191
\(680\) 0 0
\(681\) −0.485281 −0.0185960
\(682\) 0 0
\(683\) −50.8346 −1.94513 −0.972565 0.232630i \(-0.925267\pi\)
−0.972565 + 0.232630i \(0.925267\pi\)
\(684\) 0 0
\(685\) −12.3928 −0.473506
\(686\) 0 0
\(687\) −28.3959 −1.08337
\(688\) 0 0
\(689\) −31.7179 −1.20836
\(690\) 0 0
\(691\) 1.96602 0.0747910 0.0373955 0.999301i \(-0.488094\pi\)
0.0373955 + 0.999301i \(0.488094\pi\)
\(692\) 0 0
\(693\) −19.1764 −0.728450
\(694\) 0 0
\(695\) −9.98855 −0.378887
\(696\) 0 0
\(697\) −6.02671 −0.228278
\(698\) 0 0
\(699\) −26.5196 −1.00306
\(700\) 0 0
\(701\) 42.9796 1.62332 0.811659 0.584132i \(-0.198565\pi\)
0.811659 + 0.584132i \(0.198565\pi\)
\(702\) 0 0
\(703\) 35.1791 1.32680
\(704\) 0 0
\(705\) 15.5037 0.583905
\(706\) 0 0
\(707\) 4.65913 0.175224
\(708\) 0 0
\(709\) 17.9765 0.675121 0.337561 0.941304i \(-0.390398\pi\)
0.337561 + 0.941304i \(0.390398\pi\)
\(710\) 0 0
\(711\) 3.69376 0.138527
\(712\) 0 0
\(713\) 7.87577 0.294950
\(714\) 0 0
\(715\) −26.3500 −0.985434
\(716\) 0 0
\(717\) 13.4261 0.501408
\(718\) 0 0
\(719\) −51.1045 −1.90588 −0.952938 0.303165i \(-0.901957\pi\)
−0.952938 + 0.303165i \(0.901957\pi\)
\(720\) 0 0
\(721\) −47.5196 −1.76972
\(722\) 0 0
\(723\) 11.4392 0.425429
\(724\) 0 0
\(725\) 22.2377 0.825889
\(726\) 0 0
\(727\) −21.8541 −0.810523 −0.405262 0.914201i \(-0.632820\pi\)
−0.405262 + 0.914201i \(0.632820\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.4088 0.458955
\(732\) 0 0
\(733\) −26.5674 −0.981290 −0.490645 0.871360i \(-0.663239\pi\)
−0.490645 + 0.871360i \(0.663239\pi\)
\(734\) 0 0
\(735\) 5.23149 0.192966
\(736\) 0 0
\(737\) −69.7650 −2.56983
\(738\) 0 0
\(739\) 48.6605 1.79001 0.895003 0.446060i \(-0.147173\pi\)
0.895003 + 0.446060i \(0.147173\pi\)
\(740\) 0 0
\(741\) 13.5887 0.499193
\(742\) 0 0
\(743\) 7.70496 0.282668 0.141334 0.989962i \(-0.454861\pi\)
0.141334 + 0.989962i \(0.454861\pi\)
\(744\) 0 0
\(745\) 14.3815 0.526896
\(746\) 0 0
\(747\) 8.33948 0.305126
\(748\) 0 0
\(749\) −33.2661 −1.21552
\(750\) 0 0
\(751\) −8.01994 −0.292652 −0.146326 0.989236i \(-0.546745\pi\)
−0.146326 + 0.989236i \(0.546745\pi\)
\(752\) 0 0
\(753\) −16.4258 −0.598591
\(754\) 0 0
\(755\) 25.5804 0.930965
\(756\) 0 0
\(757\) 23.5836 0.857161 0.428580 0.903504i \(-0.359014\pi\)
0.428580 + 0.903504i \(0.359014\pi\)
\(758\) 0 0
\(759\) −20.0691 −0.728462
\(760\) 0 0
\(761\) −34.8994 −1.26510 −0.632551 0.774518i \(-0.717992\pi\)
−0.632551 + 0.774518i \(0.717992\pi\)
\(762\) 0 0
\(763\) −8.71663 −0.315563
\(764\) 0 0
\(765\) 6.79689 0.245742
\(766\) 0 0
\(767\) −5.53769 −0.199954
\(768\) 0 0
\(769\) 13.0487 0.470549 0.235275 0.971929i \(-0.424401\pi\)
0.235275 + 0.971929i \(0.424401\pi\)
\(770\) 0 0
\(771\) 17.6649 0.636185
\(772\) 0 0
\(773\) 7.14375 0.256943 0.128471 0.991713i \(-0.458993\pi\)
0.128471 + 0.991713i \(0.458993\pi\)
\(774\) 0 0
\(775\) −5.93939 −0.213349
\(776\) 0 0
\(777\) 23.4230 0.840296
\(778\) 0 0
\(779\) −6.71832 −0.240709
\(780\) 0 0
\(781\) 23.9367 0.856521
\(782\) 0 0
\(783\) −8.76511 −0.313239
\(784\) 0 0
\(785\) 28.7176 1.02497
\(786\) 0 0
\(787\) −7.36950 −0.262694 −0.131347 0.991336i \(-0.541930\pi\)
−0.131347 + 0.991336i \(0.541930\pi\)
\(788\) 0 0
\(789\) 7.60215 0.270644
\(790\) 0 0
\(791\) −1.34752 −0.0479124
\(792\) 0 0
\(793\) −10.6039 −0.376557
\(794\) 0 0
\(795\) −17.6855 −0.627240
\(796\) 0 0
\(797\) −11.3558 −0.402243 −0.201122 0.979566i \(-0.564459\pi\)
−0.201122 + 0.979566i \(0.564459\pi\)
\(798\) 0 0
\(799\) 42.7854 1.51364
\(800\) 0 0
\(801\) 12.3598 0.436711
\(802\) 0 0
\(803\) −50.6714 −1.78815
\(804\) 0 0
\(805\) 16.9720 0.598186
\(806\) 0 0
\(807\) −7.33835 −0.258322
\(808\) 0 0
\(809\) 40.4208 1.42112 0.710560 0.703637i \(-0.248442\pi\)
0.710560 + 0.703637i \(0.248442\pi\)
\(810\) 0 0
\(811\) −38.6275 −1.35639 −0.678197 0.734880i \(-0.737238\pi\)
−0.678197 + 0.734880i \(0.737238\pi\)
\(812\) 0 0
\(813\) 30.7629 1.07890
\(814\) 0 0
\(815\) −15.4187 −0.540093
\(816\) 0 0
\(817\) 13.8328 0.483947
\(818\) 0 0
\(819\) 9.04765 0.316151
\(820\) 0 0
\(821\) 12.1383 0.423631 0.211815 0.977310i \(-0.432062\pi\)
0.211815 + 0.977310i \(0.432062\pi\)
\(822\) 0 0
\(823\) 36.6833 1.27870 0.639350 0.768915i \(-0.279203\pi\)
0.639350 + 0.768915i \(0.279203\pi\)
\(824\) 0 0
\(825\) 15.1348 0.526925
\(826\) 0 0
\(827\) −29.4355 −1.02357 −0.511787 0.859113i \(-0.671016\pi\)
−0.511787 + 0.859113i \(0.671016\pi\)
\(828\) 0 0
\(829\) −8.55858 −0.297252 −0.148626 0.988894i \(-0.547485\pi\)
−0.148626 + 0.988894i \(0.547485\pi\)
\(830\) 0 0
\(831\) 15.0041 0.520486
\(832\) 0 0
\(833\) 14.4372 0.500221
\(834\) 0 0
\(835\) 1.56937 0.0543103
\(836\) 0 0
\(837\) 2.34104 0.0809181
\(838\) 0 0
\(839\) 49.4086 1.70578 0.852888 0.522094i \(-0.174849\pi\)
0.852888 + 0.522094i \(0.174849\pi\)
\(840\) 0 0
\(841\) 47.8271 1.64921
\(842\) 0 0
\(843\) 10.2001 0.351311
\(844\) 0 0
\(845\) −7.96956 −0.274161
\(846\) 0 0
\(847\) 79.0352 2.71568
\(848\) 0 0
\(849\) 2.65541 0.0911333
\(850\) 0 0
\(851\) 24.5134 0.840310
\(852\) 0 0
\(853\) −28.6271 −0.980173 −0.490087 0.871674i \(-0.663035\pi\)
−0.490087 + 0.871674i \(0.663035\pi\)
\(854\) 0 0
\(855\) 7.57689 0.259124
\(856\) 0 0
\(857\) −25.9474 −0.886346 −0.443173 0.896436i \(-0.646147\pi\)
−0.443173 + 0.896436i \(0.646147\pi\)
\(858\) 0 0
\(859\) −31.5220 −1.07552 −0.537758 0.843099i \(-0.680729\pi\)
−0.537758 + 0.843099i \(0.680729\pi\)
\(860\) 0 0
\(861\) −4.47321 −0.152447
\(862\) 0 0
\(863\) 24.3259 0.828065 0.414032 0.910262i \(-0.364120\pi\)
0.414032 + 0.910262i \(0.364120\pi\)
\(864\) 0 0
\(865\) −29.9991 −1.02000
\(866\) 0 0
\(867\) 1.75725 0.0596793
\(868\) 0 0
\(869\) −22.0349 −0.747483
\(870\) 0 0
\(871\) 32.9160 1.11532
\(872\) 0 0
\(873\) 0.582982 0.0197310
\(874\) 0 0
\(875\) −38.0235 −1.28543
\(876\) 0 0
\(877\) −33.5288 −1.13219 −0.566094 0.824341i \(-0.691546\pi\)
−0.566094 + 0.824341i \(0.691546\pi\)
\(878\) 0 0
\(879\) 19.0956 0.644079
\(880\) 0 0
\(881\) 30.6148 1.03144 0.515719 0.856758i \(-0.327525\pi\)
0.515719 + 0.856758i \(0.327525\pi\)
\(882\) 0 0
\(883\) −25.0058 −0.841511 −0.420756 0.907174i \(-0.638235\pi\)
−0.420756 + 0.907174i \(0.638235\pi\)
\(884\) 0 0
\(885\) −3.08775 −0.103794
\(886\) 0 0
\(887\) 13.2595 0.445212 0.222606 0.974909i \(-0.428544\pi\)
0.222606 + 0.974909i \(0.428544\pi\)
\(888\) 0 0
\(889\) −46.6352 −1.56409
\(890\) 0 0
\(891\) −5.96544 −0.199850
\(892\) 0 0
\(893\) 47.6954 1.59606
\(894\) 0 0
\(895\) −13.1958 −0.441088
\(896\) 0 0
\(897\) 9.46885 0.316156
\(898\) 0 0
\(899\) −20.5194 −0.684362
\(900\) 0 0
\(901\) −48.8064 −1.62598
\(902\) 0 0
\(903\) 9.21017 0.306495
\(904\) 0 0
\(905\) −31.9033 −1.06050
\(906\) 0 0
\(907\) −22.6968 −0.753636 −0.376818 0.926287i \(-0.622982\pi\)
−0.376818 + 0.926287i \(0.622982\pi\)
\(908\) 0 0
\(909\) 1.44938 0.0480727
\(910\) 0 0
\(911\) 2.15372 0.0713559 0.0356780 0.999363i \(-0.488641\pi\)
0.0356780 + 0.999363i \(0.488641\pi\)
\(912\) 0 0
\(913\) −49.7487 −1.64644
\(914\) 0 0
\(915\) −5.91263 −0.195465
\(916\) 0 0
\(917\) 63.0663 2.08263
\(918\) 0 0
\(919\) 9.83614 0.324464 0.162232 0.986753i \(-0.448131\pi\)
0.162232 + 0.986753i \(0.448131\pi\)
\(920\) 0 0
\(921\) 2.29511 0.0756264
\(922\) 0 0
\(923\) −11.2936 −0.371734
\(924\) 0 0
\(925\) −18.4864 −0.607830
\(926\) 0 0
\(927\) −14.7825 −0.485523
\(928\) 0 0
\(929\) 14.1814 0.465277 0.232639 0.972563i \(-0.425264\pi\)
0.232639 + 0.972563i \(0.425264\pi\)
\(930\) 0 0
\(931\) 16.0940 0.527461
\(932\) 0 0
\(933\) −0.877859 −0.0287398
\(934\) 0 0
\(935\) −40.5465 −1.32601
\(936\) 0 0
\(937\) −7.82726 −0.255705 −0.127853 0.991793i \(-0.540808\pi\)
−0.127853 + 0.991793i \(0.540808\pi\)
\(938\) 0 0
\(939\) −18.9459 −0.618276
\(940\) 0 0
\(941\) −41.7609 −1.36137 −0.680683 0.732578i \(-0.738317\pi\)
−0.680683 + 0.732578i \(0.738317\pi\)
\(942\) 0 0
\(943\) −4.68145 −0.152449
\(944\) 0 0
\(945\) 5.04486 0.164109
\(946\) 0 0
\(947\) 27.7498 0.901747 0.450874 0.892588i \(-0.351113\pi\)
0.450874 + 0.892588i \(0.351113\pi\)
\(948\) 0 0
\(949\) 23.9074 0.776067
\(950\) 0 0
\(951\) 32.8653 1.06573
\(952\) 0 0
\(953\) −24.8241 −0.804130 −0.402065 0.915611i \(-0.631707\pi\)
−0.402065 + 0.915611i \(0.631707\pi\)
\(954\) 0 0
\(955\) 38.0198 1.23029
\(956\) 0 0
\(957\) 52.2878 1.69022
\(958\) 0 0
\(959\) −25.3845 −0.819708
\(960\) 0 0
\(961\) −25.5195 −0.823211
\(962\) 0 0
\(963\) −10.3485 −0.333476
\(964\) 0 0
\(965\) −19.2799 −0.620641
\(966\) 0 0
\(967\) 21.3164 0.685489 0.342744 0.939429i \(-0.388644\pi\)
0.342744 + 0.939429i \(0.388644\pi\)
\(968\) 0 0
\(969\) 20.9098 0.671719
\(970\) 0 0
\(971\) 36.8650 1.18305 0.591527 0.806285i \(-0.298525\pi\)
0.591527 + 0.806285i \(0.298525\pi\)
\(972\) 0 0
\(973\) −20.4597 −0.655909
\(974\) 0 0
\(975\) −7.14078 −0.228688
\(976\) 0 0
\(977\) 17.1237 0.547837 0.273918 0.961753i \(-0.411680\pi\)
0.273918 + 0.961753i \(0.411680\pi\)
\(978\) 0 0
\(979\) −73.7316 −2.35647
\(980\) 0 0
\(981\) −2.71160 −0.0865746
\(982\) 0 0
\(983\) −19.0292 −0.606936 −0.303468 0.952842i \(-0.598145\pi\)
−0.303468 + 0.952842i \(0.598145\pi\)
\(984\) 0 0
\(985\) −24.1083 −0.768155
\(986\) 0 0
\(987\) 31.7566 1.01083
\(988\) 0 0
\(989\) 9.63893 0.306500
\(990\) 0 0
\(991\) 28.2266 0.896648 0.448324 0.893871i \(-0.352021\pi\)
0.448324 + 0.893871i \(0.352021\pi\)
\(992\) 0 0
\(993\) 6.81707 0.216333
\(994\) 0 0
\(995\) 12.7847 0.405303
\(996\) 0 0
\(997\) −30.3558 −0.961379 −0.480689 0.876891i \(-0.659613\pi\)
−0.480689 + 0.876891i \(0.659613\pi\)
\(998\) 0 0
\(999\) 7.28651 0.230535
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 \(a_p\))