Properties

Label 8001.2.a.o.1.7
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.307326\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.307326 q^{2}\) \(-1.90555 q^{4}\) \(+0.988649 q^{5}\) \(+1.00000 q^{7}\) \(+1.20028 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.307326 q^{2}\) \(-1.90555 q^{4}\) \(+0.988649 q^{5}\) \(+1.00000 q^{7}\) \(+1.20028 q^{8}\) \(-0.303838 q^{10}\) \(-2.00682 q^{11}\) \(-0.289737 q^{13}\) \(-0.307326 q^{14}\) \(+3.44222 q^{16}\) \(-0.186210 q^{17}\) \(+0.852422 q^{19}\) \(-1.88392 q^{20}\) \(+0.616750 q^{22}\) \(+3.33599 q^{23}\) \(-4.02257 q^{25}\) \(+0.0890436 q^{26}\) \(-1.90555 q^{28}\) \(+4.37763 q^{29}\) \(-5.73898 q^{31}\) \(-3.45844 q^{32}\) \(+0.0572272 q^{34}\) \(+0.988649 q^{35}\) \(-7.05580 q^{37}\) \(-0.261972 q^{38}\) \(+1.18665 q^{40}\) \(-3.81974 q^{41}\) \(+9.06384 q^{43}\) \(+3.82411 q^{44}\) \(-1.02524 q^{46}\) \(-1.34856 q^{47}\) \(+1.00000 q^{49}\) \(+1.23624 q^{50}\) \(+0.552108 q^{52}\) \(-3.75486 q^{53}\) \(-1.98405 q^{55}\) \(+1.20028 q^{56}\) \(-1.34536 q^{58}\) \(+4.26624 q^{59}\) \(+3.08411 q^{61}\) \(+1.76374 q^{62}\) \(-5.82158 q^{64}\) \(-0.286448 q^{65}\) \(-10.8349 q^{67}\) \(+0.354832 q^{68}\) \(-0.303838 q^{70}\) \(-13.0932 q^{71}\) \(+14.9066 q^{73}\) \(+2.16843 q^{74}\) \(-1.62433 q^{76}\) \(-2.00682 q^{77}\) \(+16.7593 q^{79}\) \(+3.40315 q^{80}\) \(+1.17391 q^{82}\) \(-15.1974 q^{83}\) \(-0.184096 q^{85}\) \(-2.78556 q^{86}\) \(-2.40875 q^{88}\) \(+0.526198 q^{89}\) \(-0.289737 q^{91}\) \(-6.35689 q^{92}\) \(+0.414448 q^{94}\) \(+0.842746 q^{95}\) \(+6.83150 q^{97}\) \(-0.307326 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.307326 −0.217312 −0.108656 0.994079i \(-0.534655\pi\)
−0.108656 + 0.994079i \(0.534655\pi\)
\(3\) 0 0
\(4\) −1.90555 −0.952775
\(5\) 0.988649 0.442137 0.221069 0.975258i \(-0.429046\pi\)
0.221069 + 0.975258i \(0.429046\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.20028 0.424362
\(9\) 0 0
\(10\) −0.303838 −0.0960819
\(11\) −2.00682 −0.605081 −0.302540 0.953137i \(-0.597835\pi\)
−0.302540 + 0.953137i \(0.597835\pi\)
\(12\) 0 0
\(13\) −0.289737 −0.0803585 −0.0401792 0.999192i \(-0.512793\pi\)
−0.0401792 + 0.999192i \(0.512793\pi\)
\(14\) −0.307326 −0.0821364
\(15\) 0 0
\(16\) 3.44222 0.860556
\(17\) −0.186210 −0.0451625 −0.0225813 0.999745i \(-0.507188\pi\)
−0.0225813 + 0.999745i \(0.507188\pi\)
\(18\) 0 0
\(19\) 0.852422 0.195559 0.0977795 0.995208i \(-0.468826\pi\)
0.0977795 + 0.995208i \(0.468826\pi\)
\(20\) −1.88392 −0.421257
\(21\) 0 0
\(22\) 0.616750 0.131491
\(23\) 3.33599 0.695601 0.347801 0.937569i \(-0.386929\pi\)
0.347801 + 0.937569i \(0.386929\pi\)
\(24\) 0 0
\(25\) −4.02257 −0.804515
\(26\) 0.0890436 0.0174629
\(27\) 0 0
\(28\) −1.90555 −0.360115
\(29\) 4.37763 0.812905 0.406452 0.913672i \(-0.366766\pi\)
0.406452 + 0.913672i \(0.366766\pi\)
\(30\) 0 0
\(31\) −5.73898 −1.03075 −0.515376 0.856964i \(-0.672348\pi\)
−0.515376 + 0.856964i \(0.672348\pi\)
\(32\) −3.45844 −0.611372
\(33\) 0 0
\(34\) 0.0572272 0.00981438
\(35\) 0.988649 0.167112
\(36\) 0 0
\(37\) −7.05580 −1.15997 −0.579983 0.814629i \(-0.696941\pi\)
−0.579983 + 0.814629i \(0.696941\pi\)
\(38\) −0.261972 −0.0424974
\(39\) 0 0
\(40\) 1.18665 0.187626
\(41\) −3.81974 −0.596544 −0.298272 0.954481i \(-0.596410\pi\)
−0.298272 + 0.954481i \(0.596410\pi\)
\(42\) 0 0
\(43\) 9.06384 1.38222 0.691112 0.722748i \(-0.257121\pi\)
0.691112 + 0.722748i \(0.257121\pi\)
\(44\) 3.82411 0.576506
\(45\) 0 0
\(46\) −1.02524 −0.151163
\(47\) −1.34856 −0.196708 −0.0983540 0.995151i \(-0.531358\pi\)
−0.0983540 + 0.995151i \(0.531358\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.23624 0.174831
\(51\) 0 0
\(52\) 0.552108 0.0765636
\(53\) −3.75486 −0.515770 −0.257885 0.966176i \(-0.583026\pi\)
−0.257885 + 0.966176i \(0.583026\pi\)
\(54\) 0 0
\(55\) −1.98405 −0.267529
\(56\) 1.20028 0.160394
\(57\) 0 0
\(58\) −1.34536 −0.176654
\(59\) 4.26624 0.555418 0.277709 0.960665i \(-0.410425\pi\)
0.277709 + 0.960665i \(0.410425\pi\)
\(60\) 0 0
\(61\) 3.08411 0.394880 0.197440 0.980315i \(-0.436737\pi\)
0.197440 + 0.980315i \(0.436737\pi\)
\(62\) 1.76374 0.223995
\(63\) 0 0
\(64\) −5.82158 −0.727698
\(65\) −0.286448 −0.0355295
\(66\) 0 0
\(67\) −10.8349 −1.32370 −0.661850 0.749636i \(-0.730228\pi\)
−0.661850 + 0.749636i \(0.730228\pi\)
\(68\) 0.354832 0.0430297
\(69\) 0 0
\(70\) −0.303838 −0.0363155
\(71\) −13.0932 −1.55387 −0.776937 0.629579i \(-0.783227\pi\)
−0.776937 + 0.629579i \(0.783227\pi\)
\(72\) 0 0
\(73\) 14.9066 1.74469 0.872343 0.488894i \(-0.162600\pi\)
0.872343 + 0.488894i \(0.162600\pi\)
\(74\) 2.16843 0.252075
\(75\) 0 0
\(76\) −1.62433 −0.186324
\(77\) −2.00682 −0.228699
\(78\) 0 0
\(79\) 16.7593 1.88557 0.942785 0.333400i \(-0.108196\pi\)
0.942785 + 0.333400i \(0.108196\pi\)
\(80\) 3.40315 0.380484
\(81\) 0 0
\(82\) 1.17391 0.129636
\(83\) −15.1974 −1.66813 −0.834067 0.551663i \(-0.813993\pi\)
−0.834067 + 0.551663i \(0.813993\pi\)
\(84\) 0 0
\(85\) −0.184096 −0.0199680
\(86\) −2.78556 −0.300374
\(87\) 0 0
\(88\) −2.40875 −0.256773
\(89\) 0.526198 0.0557769 0.0278884 0.999611i \(-0.491122\pi\)
0.0278884 + 0.999611i \(0.491122\pi\)
\(90\) 0 0
\(91\) −0.289737 −0.0303726
\(92\) −6.35689 −0.662752
\(93\) 0 0
\(94\) 0.414448 0.0427471
\(95\) 0.842746 0.0864639
\(96\) 0 0
\(97\) 6.83150 0.693634 0.346817 0.937933i \(-0.387262\pi\)
0.346817 + 0.937933i \(0.387262\pi\)
\(98\) −0.307326 −0.0310446
\(99\) 0 0
\(100\) 7.66522 0.766522
\(101\) −13.4337 −1.33670 −0.668350 0.743847i \(-0.732999\pi\)
−0.668350 + 0.743847i \(0.732999\pi\)
\(102\) 0 0
\(103\) −2.29311 −0.225947 −0.112973 0.993598i \(-0.536037\pi\)
−0.112973 + 0.993598i \(0.536037\pi\)
\(104\) −0.347764 −0.0341011
\(105\) 0 0
\(106\) 1.15397 0.112083
\(107\) −4.90083 −0.473781 −0.236890 0.971536i \(-0.576128\pi\)
−0.236890 + 0.971536i \(0.576128\pi\)
\(108\) 0 0
\(109\) 2.58229 0.247339 0.123669 0.992323i \(-0.460534\pi\)
0.123669 + 0.992323i \(0.460534\pi\)
\(110\) 0.609749 0.0581373
\(111\) 0 0
\(112\) 3.44222 0.325260
\(113\) 1.77268 0.166760 0.0833799 0.996518i \(-0.473428\pi\)
0.0833799 + 0.996518i \(0.473428\pi\)
\(114\) 0 0
\(115\) 3.29812 0.307551
\(116\) −8.34179 −0.774516
\(117\) 0 0
\(118\) −1.31113 −0.120699
\(119\) −0.186210 −0.0170698
\(120\) 0 0
\(121\) −6.97265 −0.633878
\(122\) −0.947829 −0.0858124
\(123\) 0 0
\(124\) 10.9359 0.982075
\(125\) −8.92016 −0.797843
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 8.70601 0.769509
\(129\) 0 0
\(130\) 0.0880329 0.00772099
\(131\) 11.9789 1.04661 0.523303 0.852147i \(-0.324700\pi\)
0.523303 + 0.852147i \(0.324700\pi\)
\(132\) 0 0
\(133\) 0.852422 0.0739144
\(134\) 3.32986 0.287656
\(135\) 0 0
\(136\) −0.223504 −0.0191653
\(137\) 13.4775 1.15146 0.575731 0.817639i \(-0.304718\pi\)
0.575731 + 0.817639i \(0.304718\pi\)
\(138\) 0 0
\(139\) 6.28920 0.533443 0.266721 0.963774i \(-0.414060\pi\)
0.266721 + 0.963774i \(0.414060\pi\)
\(140\) −1.88392 −0.159220
\(141\) 0 0
\(142\) 4.02387 0.337676
\(143\) 0.581451 0.0486233
\(144\) 0 0
\(145\) 4.32794 0.359416
\(146\) −4.58119 −0.379142
\(147\) 0 0
\(148\) 13.4452 1.10519
\(149\) −2.21608 −0.181548 −0.0907740 0.995872i \(-0.528934\pi\)
−0.0907740 + 0.995872i \(0.528934\pi\)
\(150\) 0 0
\(151\) −11.7145 −0.953316 −0.476658 0.879089i \(-0.658152\pi\)
−0.476658 + 0.879089i \(0.658152\pi\)
\(152\) 1.02314 0.0829879
\(153\) 0 0
\(154\) 0.616750 0.0496991
\(155\) −5.67384 −0.455734
\(156\) 0 0
\(157\) −3.95965 −0.316014 −0.158007 0.987438i \(-0.550507\pi\)
−0.158007 + 0.987438i \(0.550507\pi\)
\(158\) −5.15058 −0.409758
\(159\) 0 0
\(160\) −3.41918 −0.270310
\(161\) 3.33599 0.262913
\(162\) 0 0
\(163\) 22.5680 1.76766 0.883832 0.467805i \(-0.154955\pi\)
0.883832 + 0.467805i \(0.154955\pi\)
\(164\) 7.27872 0.568372
\(165\) 0 0
\(166\) 4.67056 0.362506
\(167\) −15.6225 −1.20891 −0.604453 0.796641i \(-0.706608\pi\)
−0.604453 + 0.796641i \(0.706608\pi\)
\(168\) 0 0
\(169\) −12.9161 −0.993543
\(170\) 0.0565776 0.00433930
\(171\) 0 0
\(172\) −17.2716 −1.31695
\(173\) −16.8019 −1.27743 −0.638713 0.769445i \(-0.720533\pi\)
−0.638713 + 0.769445i \(0.720533\pi\)
\(174\) 0 0
\(175\) −4.02257 −0.304078
\(176\) −6.90794 −0.520706
\(177\) 0 0
\(178\) −0.161714 −0.0121210
\(179\) −18.5086 −1.38340 −0.691699 0.722186i \(-0.743138\pi\)
−0.691699 + 0.722186i \(0.743138\pi\)
\(180\) 0 0
\(181\) 5.16665 0.384034 0.192017 0.981392i \(-0.438497\pi\)
0.192017 + 0.981392i \(0.438497\pi\)
\(182\) 0.0890436 0.00660035
\(183\) 0 0
\(184\) 4.00411 0.295187
\(185\) −6.97571 −0.512864
\(186\) 0 0
\(187\) 0.373691 0.0273270
\(188\) 2.56975 0.187418
\(189\) 0 0
\(190\) −0.258998 −0.0187897
\(191\) 1.27980 0.0926027 0.0463014 0.998928i \(-0.485257\pi\)
0.0463014 + 0.998928i \(0.485257\pi\)
\(192\) 0 0
\(193\) 5.02979 0.362052 0.181026 0.983478i \(-0.442058\pi\)
0.181026 + 0.983478i \(0.442058\pi\)
\(194\) −2.09950 −0.150735
\(195\) 0 0
\(196\) −1.90555 −0.136111
\(197\) 5.69293 0.405604 0.202802 0.979220i \(-0.434995\pi\)
0.202802 + 0.979220i \(0.434995\pi\)
\(198\) 0 0
\(199\) 0.823780 0.0583962 0.0291981 0.999574i \(-0.490705\pi\)
0.0291981 + 0.999574i \(0.490705\pi\)
\(200\) −4.82820 −0.341406
\(201\) 0 0
\(202\) 4.12852 0.290482
\(203\) 4.37763 0.307249
\(204\) 0 0
\(205\) −3.77639 −0.263754
\(206\) 0.704732 0.0491010
\(207\) 0 0
\(208\) −0.997338 −0.0691530
\(209\) −1.71066 −0.118329
\(210\) 0 0
\(211\) −15.1264 −1.04135 −0.520674 0.853756i \(-0.674319\pi\)
−0.520674 + 0.853756i \(0.674319\pi\)
\(212\) 7.15508 0.491413
\(213\) 0 0
\(214\) 1.50615 0.102958
\(215\) 8.96096 0.611132
\(216\) 0 0
\(217\) −5.73898 −0.389587
\(218\) −0.793606 −0.0537498
\(219\) 0 0
\(220\) 3.78070 0.254895
\(221\) 0.0539518 0.00362919
\(222\) 0 0
\(223\) 4.14354 0.277472 0.138736 0.990329i \(-0.455696\pi\)
0.138736 + 0.990329i \(0.455696\pi\)
\(224\) −3.45844 −0.231077
\(225\) 0 0
\(226\) −0.544791 −0.0362390
\(227\) 17.7163 1.17587 0.587935 0.808908i \(-0.299941\pi\)
0.587935 + 0.808908i \(0.299941\pi\)
\(228\) 0 0
\(229\) 27.6285 1.82574 0.912871 0.408249i \(-0.133860\pi\)
0.912871 + 0.408249i \(0.133860\pi\)
\(230\) −1.01360 −0.0668347
\(231\) 0 0
\(232\) 5.25437 0.344966
\(233\) −21.6658 −1.41937 −0.709687 0.704517i \(-0.751164\pi\)
−0.709687 + 0.704517i \(0.751164\pi\)
\(234\) 0 0
\(235\) −1.33325 −0.0869719
\(236\) −8.12954 −0.529188
\(237\) 0 0
\(238\) 0.0572272 0.00370949
\(239\) −3.33796 −0.215915 −0.107957 0.994156i \(-0.534431\pi\)
−0.107957 + 0.994156i \(0.534431\pi\)
\(240\) 0 0
\(241\) −13.4703 −0.867701 −0.433851 0.900985i \(-0.642845\pi\)
−0.433851 + 0.900985i \(0.642845\pi\)
\(242\) 2.14288 0.137749
\(243\) 0 0
\(244\) −5.87693 −0.376232
\(245\) 0.988649 0.0631625
\(246\) 0 0
\(247\) −0.246978 −0.0157148
\(248\) −6.88837 −0.437412
\(249\) 0 0
\(250\) 2.74140 0.173381
\(251\) −3.19071 −0.201396 −0.100698 0.994917i \(-0.532108\pi\)
−0.100698 + 0.994917i \(0.532108\pi\)
\(252\) 0 0
\(253\) −6.69474 −0.420895
\(254\) 0.307326 0.0192834
\(255\) 0 0
\(256\) 8.96758 0.560474
\(257\) −9.04475 −0.564196 −0.282098 0.959386i \(-0.591030\pi\)
−0.282098 + 0.959386i \(0.591030\pi\)
\(258\) 0 0
\(259\) −7.05580 −0.438426
\(260\) 0.545841 0.0338516
\(261\) 0 0
\(262\) −3.68144 −0.227440
\(263\) −28.1759 −1.73740 −0.868700 0.495339i \(-0.835044\pi\)
−0.868700 + 0.495339i \(0.835044\pi\)
\(264\) 0 0
\(265\) −3.71224 −0.228041
\(266\) −0.261972 −0.0160625
\(267\) 0 0
\(268\) 20.6465 1.26119
\(269\) −28.9671 −1.76616 −0.883078 0.469226i \(-0.844533\pi\)
−0.883078 + 0.469226i \(0.844533\pi\)
\(270\) 0 0
\(271\) −2.61077 −0.158593 −0.0792964 0.996851i \(-0.525267\pi\)
−0.0792964 + 0.996851i \(0.525267\pi\)
\(272\) −0.640976 −0.0388649
\(273\) 0 0
\(274\) −4.14199 −0.250227
\(275\) 8.07260 0.486796
\(276\) 0 0
\(277\) −15.2284 −0.914988 −0.457494 0.889213i \(-0.651253\pi\)
−0.457494 + 0.889213i \(0.651253\pi\)
\(278\) −1.93283 −0.115924
\(279\) 0 0
\(280\) 1.18665 0.0709161
\(281\) 16.7836 1.00122 0.500612 0.865672i \(-0.333108\pi\)
0.500612 + 0.865672i \(0.333108\pi\)
\(282\) 0 0
\(283\) −5.84420 −0.347401 −0.173701 0.984798i \(-0.555573\pi\)
−0.173701 + 0.984798i \(0.555573\pi\)
\(284\) 24.9497 1.48049
\(285\) 0 0
\(286\) −0.178695 −0.0105665
\(287\) −3.81974 −0.225472
\(288\) 0 0
\(289\) −16.9653 −0.997960
\(290\) −1.33009 −0.0781054
\(291\) 0 0
\(292\) −28.4053 −1.66229
\(293\) −2.88058 −0.168285 −0.0841427 0.996454i \(-0.526815\pi\)
−0.0841427 + 0.996454i \(0.526815\pi\)
\(294\) 0 0
\(295\) 4.21782 0.245571
\(296\) −8.46892 −0.492246
\(297\) 0 0
\(298\) 0.681058 0.0394526
\(299\) −0.966557 −0.0558974
\(300\) 0 0
\(301\) 9.06384 0.522431
\(302\) 3.60018 0.207167
\(303\) 0 0
\(304\) 2.93423 0.168290
\(305\) 3.04911 0.174591
\(306\) 0 0
\(307\) 2.95818 0.168832 0.0844161 0.996431i \(-0.473098\pi\)
0.0844161 + 0.996431i \(0.473098\pi\)
\(308\) 3.82411 0.217899
\(309\) 0 0
\(310\) 1.74372 0.0990366
\(311\) 7.79466 0.441995 0.220997 0.975274i \(-0.429069\pi\)
0.220997 + 0.975274i \(0.429069\pi\)
\(312\) 0 0
\(313\) 7.56008 0.427321 0.213660 0.976908i \(-0.431461\pi\)
0.213660 + 0.976908i \(0.431461\pi\)
\(314\) 1.21690 0.0686738
\(315\) 0 0
\(316\) −31.9357 −1.79653
\(317\) −31.2502 −1.75519 −0.877593 0.479406i \(-0.840852\pi\)
−0.877593 + 0.479406i \(0.840852\pi\)
\(318\) 0 0
\(319\) −8.78513 −0.491873
\(320\) −5.75550 −0.321742
\(321\) 0 0
\(322\) −1.02524 −0.0571341
\(323\) −0.158729 −0.00883194
\(324\) 0 0
\(325\) 1.16549 0.0646496
\(326\) −6.93574 −0.384135
\(327\) 0 0
\(328\) −4.58475 −0.253151
\(329\) −1.34856 −0.0743486
\(330\) 0 0
\(331\) 12.3799 0.680461 0.340230 0.940342i \(-0.389495\pi\)
0.340230 + 0.940342i \(0.389495\pi\)
\(332\) 28.9595 1.58936
\(333\) 0 0
\(334\) 4.80120 0.262710
\(335\) −10.7120 −0.585257
\(336\) 0 0
\(337\) 24.7975 1.35081 0.675403 0.737448i \(-0.263970\pi\)
0.675403 + 0.737448i \(0.263970\pi\)
\(338\) 3.96944 0.215909
\(339\) 0 0
\(340\) 0.350805 0.0190251
\(341\) 11.5171 0.623688
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 10.8791 0.586563
\(345\) 0 0
\(346\) 5.16367 0.277601
\(347\) 36.3026 1.94883 0.974413 0.224763i \(-0.0721608\pi\)
0.974413 + 0.224763i \(0.0721608\pi\)
\(348\) 0 0
\(349\) 11.0963 0.593973 0.296986 0.954882i \(-0.404018\pi\)
0.296986 + 0.954882i \(0.404018\pi\)
\(350\) 1.23624 0.0660799
\(351\) 0 0
\(352\) 6.94049 0.369929
\(353\) −10.7528 −0.572312 −0.286156 0.958183i \(-0.592378\pi\)
−0.286156 + 0.958183i \(0.592378\pi\)
\(354\) 0 0
\(355\) −12.9445 −0.687025
\(356\) −1.00270 −0.0531428
\(357\) 0 0
\(358\) 5.68818 0.300630
\(359\) 4.97551 0.262598 0.131299 0.991343i \(-0.458085\pi\)
0.131299 + 0.991343i \(0.458085\pi\)
\(360\) 0 0
\(361\) −18.2734 −0.961757
\(362\) −1.58785 −0.0834554
\(363\) 0 0
\(364\) 0.552108 0.0289383
\(365\) 14.7374 0.771391
\(366\) 0 0
\(367\) −21.4750 −1.12099 −0.560493 0.828159i \(-0.689388\pi\)
−0.560493 + 0.828159i \(0.689388\pi\)
\(368\) 11.4832 0.598604
\(369\) 0 0
\(370\) 2.14382 0.111452
\(371\) −3.75486 −0.194943
\(372\) 0 0
\(373\) 19.7237 1.02125 0.510627 0.859803i \(-0.329413\pi\)
0.510627 + 0.859803i \(0.329413\pi\)
\(374\) −0.114845 −0.00593849
\(375\) 0 0
\(376\) −1.61865 −0.0834754
\(377\) −1.26836 −0.0653238
\(378\) 0 0
\(379\) −0.520876 −0.0267556 −0.0133778 0.999911i \(-0.504258\pi\)
−0.0133778 + 0.999911i \(0.504258\pi\)
\(380\) −1.60590 −0.0823807
\(381\) 0 0
\(382\) −0.393314 −0.0201237
\(383\) −24.9559 −1.27519 −0.637594 0.770372i \(-0.720070\pi\)
−0.637594 + 0.770372i \(0.720070\pi\)
\(384\) 0 0
\(385\) −1.98405 −0.101116
\(386\) −1.54579 −0.0786785
\(387\) 0 0
\(388\) −13.0178 −0.660877
\(389\) −14.5891 −0.739696 −0.369848 0.929092i \(-0.620590\pi\)
−0.369848 + 0.929092i \(0.620590\pi\)
\(390\) 0 0
\(391\) −0.621194 −0.0314151
\(392\) 1.20028 0.0606232
\(393\) 0 0
\(394\) −1.74959 −0.0881429
\(395\) 16.5691 0.833681
\(396\) 0 0
\(397\) −5.87002 −0.294608 −0.147304 0.989091i \(-0.547060\pi\)
−0.147304 + 0.989091i \(0.547060\pi\)
\(398\) −0.253169 −0.0126902
\(399\) 0 0
\(400\) −13.8466 −0.692330
\(401\) −5.35527 −0.267429 −0.133715 0.991020i \(-0.542691\pi\)
−0.133715 + 0.991020i \(0.542691\pi\)
\(402\) 0 0
\(403\) 1.66279 0.0828296
\(404\) 25.5985 1.27358
\(405\) 0 0
\(406\) −1.34536 −0.0667690
\(407\) 14.1598 0.701873
\(408\) 0 0
\(409\) −35.4278 −1.75179 −0.875896 0.482500i \(-0.839729\pi\)
−0.875896 + 0.482500i \(0.839729\pi\)
\(410\) 1.16058 0.0573171
\(411\) 0 0
\(412\) 4.36963 0.215276
\(413\) 4.26624 0.209928
\(414\) 0 0
\(415\) −15.0249 −0.737544
\(416\) 1.00204 0.0491289
\(417\) 0 0
\(418\) 0.525731 0.0257143
\(419\) −15.6038 −0.762293 −0.381147 0.924515i \(-0.624471\pi\)
−0.381147 + 0.924515i \(0.624471\pi\)
\(420\) 0 0
\(421\) 25.4791 1.24177 0.620887 0.783900i \(-0.286773\pi\)
0.620887 + 0.783900i \(0.286773\pi\)
\(422\) 4.64875 0.226298
\(423\) 0 0
\(424\) −4.50688 −0.218873
\(425\) 0.749043 0.0363339
\(426\) 0 0
\(427\) 3.08411 0.149251
\(428\) 9.33878 0.451407
\(429\) 0 0
\(430\) −2.75394 −0.132807
\(431\) −2.51062 −0.120932 −0.0604661 0.998170i \(-0.519259\pi\)
−0.0604661 + 0.998170i \(0.519259\pi\)
\(432\) 0 0
\(433\) −26.5601 −1.27640 −0.638198 0.769872i \(-0.720320\pi\)
−0.638198 + 0.769872i \(0.720320\pi\)
\(434\) 1.76374 0.0846622
\(435\) 0 0
\(436\) −4.92069 −0.235658
\(437\) 2.84367 0.136031
\(438\) 0 0
\(439\) 2.59419 0.123814 0.0619070 0.998082i \(-0.480282\pi\)
0.0619070 + 0.998082i \(0.480282\pi\)
\(440\) −2.38141 −0.113529
\(441\) 0 0
\(442\) −0.0165808 −0.000788668 0
\(443\) −24.0954 −1.14481 −0.572404 0.819972i \(-0.693989\pi\)
−0.572404 + 0.819972i \(0.693989\pi\)
\(444\) 0 0
\(445\) 0.520225 0.0246610
\(446\) −1.27342 −0.0602981
\(447\) 0 0
\(448\) −5.82158 −0.275044
\(449\) 11.0719 0.522514 0.261257 0.965269i \(-0.415863\pi\)
0.261257 + 0.965269i \(0.415863\pi\)
\(450\) 0 0
\(451\) 7.66556 0.360957
\(452\) −3.37793 −0.158885
\(453\) 0 0
\(454\) −5.44467 −0.255531
\(455\) −0.286448 −0.0134289
\(456\) 0 0
\(457\) 7.11118 0.332647 0.166324 0.986071i \(-0.446810\pi\)
0.166324 + 0.986071i \(0.446810\pi\)
\(458\) −8.49095 −0.396756
\(459\) 0 0
\(460\) −6.28473 −0.293027
\(461\) −24.0587 −1.12052 −0.560262 0.828315i \(-0.689300\pi\)
−0.560262 + 0.828315i \(0.689300\pi\)
\(462\) 0 0
\(463\) −18.9750 −0.881842 −0.440921 0.897546i \(-0.645348\pi\)
−0.440921 + 0.897546i \(0.645348\pi\)
\(464\) 15.0688 0.699550
\(465\) 0 0
\(466\) 6.65847 0.308448
\(467\) −7.40649 −0.342732 −0.171366 0.985207i \(-0.554818\pi\)
−0.171366 + 0.985207i \(0.554818\pi\)
\(468\) 0 0
\(469\) −10.8349 −0.500311
\(470\) 0.409744 0.0189001
\(471\) 0 0
\(472\) 5.12068 0.235698
\(473\) −18.1895 −0.836356
\(474\) 0 0
\(475\) −3.42893 −0.157330
\(476\) 0.354832 0.0162637
\(477\) 0 0
\(478\) 1.02584 0.0469209
\(479\) 4.92351 0.224961 0.112481 0.993654i \(-0.464120\pi\)
0.112481 + 0.993654i \(0.464120\pi\)
\(480\) 0 0
\(481\) 2.04432 0.0932131
\(482\) 4.13979 0.188562
\(483\) 0 0
\(484\) 13.2867 0.603943
\(485\) 6.75396 0.306681
\(486\) 0 0
\(487\) 9.85082 0.446383 0.223192 0.974775i \(-0.428352\pi\)
0.223192 + 0.974775i \(0.428352\pi\)
\(488\) 3.70179 0.167572
\(489\) 0 0
\(490\) −0.303838 −0.0137260
\(491\) 31.4542 1.41951 0.709755 0.704449i \(-0.248806\pi\)
0.709755 + 0.704449i \(0.248806\pi\)
\(492\) 0 0
\(493\) −0.815157 −0.0367128
\(494\) 0.0759027 0.00341503
\(495\) 0 0
\(496\) −19.7549 −0.887020
\(497\) −13.0932 −0.587309
\(498\) 0 0
\(499\) −15.4537 −0.691801 −0.345900 0.938271i \(-0.612426\pi\)
−0.345900 + 0.938271i \(0.612426\pi\)
\(500\) 16.9978 0.760165
\(501\) 0 0
\(502\) 0.980590 0.0437659
\(503\) −34.8449 −1.55366 −0.776829 0.629712i \(-0.783173\pi\)
−0.776829 + 0.629712i \(0.783173\pi\)
\(504\) 0 0
\(505\) −13.2812 −0.591005
\(506\) 2.05747 0.0914656
\(507\) 0 0
\(508\) 1.90555 0.0845451
\(509\) −22.9563 −1.01752 −0.508761 0.860908i \(-0.669896\pi\)
−0.508761 + 0.860908i \(0.669896\pi\)
\(510\) 0 0
\(511\) 14.9066 0.659429
\(512\) −20.1680 −0.891307
\(513\) 0 0
\(514\) 2.77969 0.122607
\(515\) −2.26708 −0.0998994
\(516\) 0 0
\(517\) 2.70633 0.119024
\(518\) 2.16843 0.0952754
\(519\) 0 0
\(520\) −0.343817 −0.0150774
\(521\) −23.8812 −1.04625 −0.523127 0.852255i \(-0.675235\pi\)
−0.523127 + 0.852255i \(0.675235\pi\)
\(522\) 0 0
\(523\) −42.3363 −1.85124 −0.925620 0.378455i \(-0.876455\pi\)
−0.925620 + 0.378455i \(0.876455\pi\)
\(524\) −22.8265 −0.997180
\(525\) 0 0
\(526\) 8.65919 0.377558
\(527\) 1.06866 0.0465514
\(528\) 0 0
\(529\) −11.8712 −0.516139
\(530\) 1.14087 0.0495561
\(531\) 0 0
\(532\) −1.62433 −0.0704238
\(533\) 1.10672 0.0479373
\(534\) 0 0
\(535\) −4.84520 −0.209476
\(536\) −13.0049 −0.561728
\(537\) 0 0
\(538\) 8.90235 0.383808
\(539\) −2.00682 −0.0864401
\(540\) 0 0
\(541\) −10.0291 −0.431186 −0.215593 0.976483i \(-0.569168\pi\)
−0.215593 + 0.976483i \(0.569168\pi\)
\(542\) 0.802357 0.0344642
\(543\) 0 0
\(544\) 0.643996 0.0276111
\(545\) 2.55298 0.109358
\(546\) 0 0
\(547\) −38.5584 −1.64864 −0.824318 0.566127i \(-0.808441\pi\)
−0.824318 + 0.566127i \(0.808441\pi\)
\(548\) −25.6821 −1.09708
\(549\) 0 0
\(550\) −2.48092 −0.105787
\(551\) 3.73159 0.158971
\(552\) 0 0
\(553\) 16.7593 0.712679
\(554\) 4.68010 0.198838
\(555\) 0 0
\(556\) −11.9844 −0.508251
\(557\) 27.3968 1.16084 0.580420 0.814317i \(-0.302888\pi\)
0.580420 + 0.814317i \(0.302888\pi\)
\(558\) 0 0
\(559\) −2.62613 −0.111073
\(560\) 3.40315 0.143809
\(561\) 0 0
\(562\) −5.15803 −0.217578
\(563\) 39.9956 1.68561 0.842807 0.538216i \(-0.180902\pi\)
0.842807 + 0.538216i \(0.180902\pi\)
\(564\) 0 0
\(565\) 1.75256 0.0737307
\(566\) 1.79607 0.0754946
\(567\) 0 0
\(568\) −15.7154 −0.659405
\(569\) 39.2508 1.64548 0.822740 0.568418i \(-0.192444\pi\)
0.822740 + 0.568418i \(0.192444\pi\)
\(570\) 0 0
\(571\) −14.5997 −0.610978 −0.305489 0.952196i \(-0.598820\pi\)
−0.305489 + 0.952196i \(0.598820\pi\)
\(572\) −1.10798 −0.0463271
\(573\) 0 0
\(574\) 1.17391 0.0489979
\(575\) −13.4192 −0.559621
\(576\) 0 0
\(577\) 22.3677 0.931181 0.465591 0.885000i \(-0.345842\pi\)
0.465591 + 0.885000i \(0.345842\pi\)
\(578\) 5.21389 0.216869
\(579\) 0 0
\(580\) −8.24710 −0.342442
\(581\) −15.1974 −0.630495
\(582\) 0 0
\(583\) 7.53535 0.312082
\(584\) 17.8921 0.740379
\(585\) 0 0
\(586\) 0.885278 0.0365705
\(587\) −37.4645 −1.54633 −0.773164 0.634207i \(-0.781327\pi\)
−0.773164 + 0.634207i \(0.781327\pi\)
\(588\) 0 0
\(589\) −4.89204 −0.201573
\(590\) −1.29625 −0.0533656
\(591\) 0 0
\(592\) −24.2876 −0.998216
\(593\) −48.5027 −1.99177 −0.995883 0.0906456i \(-0.971107\pi\)
−0.995883 + 0.0906456i \(0.971107\pi\)
\(594\) 0 0
\(595\) −0.184096 −0.00754721
\(596\) 4.22284 0.172974
\(597\) 0 0
\(598\) 0.297048 0.0121472
\(599\) −26.4798 −1.08194 −0.540968 0.841043i \(-0.681942\pi\)
−0.540968 + 0.841043i \(0.681942\pi\)
\(600\) 0 0
\(601\) 44.0904 1.79849 0.899243 0.437449i \(-0.144118\pi\)
0.899243 + 0.437449i \(0.144118\pi\)
\(602\) −2.78556 −0.113531
\(603\) 0 0
\(604\) 22.3227 0.908296
\(605\) −6.89351 −0.280261
\(606\) 0 0
\(607\) 36.8393 1.49526 0.747630 0.664116i \(-0.231192\pi\)
0.747630 + 0.664116i \(0.231192\pi\)
\(608\) −2.94805 −0.119559
\(609\) 0 0
\(610\) −0.937070 −0.0379408
\(611\) 0.390728 0.0158071
\(612\) 0 0
\(613\) −43.1987 −1.74478 −0.872389 0.488812i \(-0.837430\pi\)
−0.872389 + 0.488812i \(0.837430\pi\)
\(614\) −0.909125 −0.0366893
\(615\) 0 0
\(616\) −2.40875 −0.0970512
\(617\) −8.35601 −0.336400 −0.168200 0.985753i \(-0.553795\pi\)
−0.168200 + 0.985753i \(0.553795\pi\)
\(618\) 0 0
\(619\) −33.1859 −1.33385 −0.666927 0.745123i \(-0.732391\pi\)
−0.666927 + 0.745123i \(0.732391\pi\)
\(620\) 10.8118 0.434212
\(621\) 0 0
\(622\) −2.39550 −0.0960509
\(623\) 0.526198 0.0210817
\(624\) 0 0
\(625\) 11.2940 0.451758
\(626\) −2.32341 −0.0928621
\(627\) 0 0
\(628\) 7.54531 0.301091
\(629\) 1.31386 0.0523870
\(630\) 0 0
\(631\) −33.3707 −1.32847 −0.664234 0.747525i \(-0.731242\pi\)
−0.664234 + 0.747525i \(0.731242\pi\)
\(632\) 20.1158 0.800165
\(633\) 0 0
\(634\) 9.60400 0.381424
\(635\) −0.988649 −0.0392333
\(636\) 0 0
\(637\) −0.289737 −0.0114798
\(638\) 2.69990 0.106890
\(639\) 0 0
\(640\) 8.60718 0.340229
\(641\) −11.9243 −0.470982 −0.235491 0.971877i \(-0.575670\pi\)
−0.235491 + 0.971877i \(0.575670\pi\)
\(642\) 0 0
\(643\) −28.5011 −1.12397 −0.561987 0.827146i \(-0.689963\pi\)
−0.561987 + 0.827146i \(0.689963\pi\)
\(644\) −6.35689 −0.250497
\(645\) 0 0
\(646\) 0.0487817 0.00191929
\(647\) 13.0053 0.511291 0.255645 0.966771i \(-0.417712\pi\)
0.255645 + 0.966771i \(0.417712\pi\)
\(648\) 0 0
\(649\) −8.56161 −0.336072
\(650\) −0.358184 −0.0140491
\(651\) 0 0
\(652\) −43.0045 −1.68419
\(653\) 25.3698 0.992797 0.496398 0.868095i \(-0.334656\pi\)
0.496398 + 0.868095i \(0.334656\pi\)
\(654\) 0 0
\(655\) 11.8430 0.462743
\(656\) −13.1484 −0.513359
\(657\) 0 0
\(658\) 0.414448 0.0161569
\(659\) −38.0906 −1.48380 −0.741899 0.670511i \(-0.766075\pi\)
−0.741899 + 0.670511i \(0.766075\pi\)
\(660\) 0 0
\(661\) 29.6423 1.15295 0.576477 0.817114i \(-0.304427\pi\)
0.576477 + 0.817114i \(0.304427\pi\)
\(662\) −3.80467 −0.147873
\(663\) 0 0
\(664\) −18.2411 −0.707893
\(665\) 0.842746 0.0326803
\(666\) 0 0
\(667\) 14.6037 0.565458
\(668\) 29.7695 1.15182
\(669\) 0 0
\(670\) 3.29207 0.127184
\(671\) −6.18928 −0.238934
\(672\) 0 0
\(673\) 13.5428 0.522038 0.261019 0.965334i \(-0.415941\pi\)
0.261019 + 0.965334i \(0.415941\pi\)
\(674\) −7.62092 −0.293547
\(675\) 0 0
\(676\) 24.6122 0.946623
\(677\) −15.8075 −0.607533 −0.303767 0.952746i \(-0.598244\pi\)
−0.303767 + 0.952746i \(0.598244\pi\)
\(678\) 0 0
\(679\) 6.83150 0.262169
\(680\) −0.220967 −0.00847368
\(681\) 0 0
\(682\) −3.53952 −0.135535
\(683\) 3.33700 0.127687 0.0638433 0.997960i \(-0.479664\pi\)
0.0638433 + 0.997960i \(0.479664\pi\)
\(684\) 0 0
\(685\) 13.3245 0.509104
\(686\) −0.307326 −0.0117338
\(687\) 0 0
\(688\) 31.1998 1.18948
\(689\) 1.08792 0.0414465
\(690\) 0 0
\(691\) 18.9842 0.722191 0.361096 0.932529i \(-0.382403\pi\)
0.361096 + 0.932529i \(0.382403\pi\)
\(692\) 32.0169 1.21710
\(693\) 0 0
\(694\) −11.1567 −0.423504
\(695\) 6.21781 0.235855
\(696\) 0 0
\(697\) 0.711274 0.0269414
\(698\) −3.41019 −0.129078
\(699\) 0 0
\(700\) 7.66522 0.289718
\(701\) −6.87293 −0.259587 −0.129793 0.991541i \(-0.541431\pi\)
−0.129793 + 0.991541i \(0.541431\pi\)
\(702\) 0 0
\(703\) −6.01452 −0.226842
\(704\) 11.6829 0.440316
\(705\) 0 0
\(706\) 3.30461 0.124371
\(707\) −13.4337 −0.505225
\(708\) 0 0
\(709\) 15.3156 0.575188 0.287594 0.957752i \(-0.407145\pi\)
0.287594 + 0.957752i \(0.407145\pi\)
\(710\) 3.97820 0.149299
\(711\) 0 0
\(712\) 0.631584 0.0236696
\(713\) −19.1452 −0.716992
\(714\) 0 0
\(715\) 0.574851 0.0214982
\(716\) 35.2691 1.31807
\(717\) 0 0
\(718\) −1.52911 −0.0570657
\(719\) −28.3904 −1.05878 −0.529391 0.848378i \(-0.677579\pi\)
−0.529391 + 0.848378i \(0.677579\pi\)
\(720\) 0 0
\(721\) −2.29311 −0.0853998
\(722\) 5.61589 0.209002
\(723\) 0 0
\(724\) −9.84532 −0.365898
\(725\) −17.6093 −0.653994
\(726\) 0 0
\(727\) 3.08701 0.114491 0.0572454 0.998360i \(-0.481768\pi\)
0.0572454 + 0.998360i \(0.481768\pi\)
\(728\) −0.347764 −0.0128890
\(729\) 0 0
\(730\) −4.52919 −0.167633
\(731\) −1.68778 −0.0624247
\(732\) 0 0
\(733\) −35.7181 −1.31928 −0.659638 0.751583i \(-0.729291\pi\)
−0.659638 + 0.751583i \(0.729291\pi\)
\(734\) 6.59983 0.243604
\(735\) 0 0
\(736\) −11.5373 −0.425271
\(737\) 21.7438 0.800945
\(738\) 0 0
\(739\) −19.6678 −0.723490 −0.361745 0.932277i \(-0.617819\pi\)
−0.361745 + 0.932277i \(0.617819\pi\)
\(740\) 13.2926 0.488644
\(741\) 0 0
\(742\) 1.15397 0.0423634
\(743\) −38.7753 −1.42253 −0.711264 0.702925i \(-0.751877\pi\)
−0.711264 + 0.702925i \(0.751877\pi\)
\(744\) 0 0
\(745\) −2.19092 −0.0802691
\(746\) −6.06160 −0.221931
\(747\) 0 0
\(748\) −0.712086 −0.0260365
\(749\) −4.90083 −0.179072
\(750\) 0 0
\(751\) −14.9648 −0.546074 −0.273037 0.962003i \(-0.588028\pi\)
−0.273037 + 0.962003i \(0.588028\pi\)
\(752\) −4.64205 −0.169278
\(753\) 0 0
\(754\) 0.389800 0.0141957
\(755\) −11.5816 −0.421497
\(756\) 0 0
\(757\) −54.7349 −1.98937 −0.994687 0.102946i \(-0.967173\pi\)
−0.994687 + 0.102946i \(0.967173\pi\)
\(758\) 0.160079 0.00581432
\(759\) 0 0
\(760\) 1.01153 0.0366920
\(761\) 16.9679 0.615087 0.307543 0.951534i \(-0.400493\pi\)
0.307543 + 0.951534i \(0.400493\pi\)
\(762\) 0 0
\(763\) 2.58229 0.0934853
\(764\) −2.43871 −0.0882296
\(765\) 0 0
\(766\) 7.66961 0.277114
\(767\) −1.23609 −0.0446325
\(768\) 0 0
\(769\) −12.4821 −0.450116 −0.225058 0.974345i \(-0.572257\pi\)
−0.225058 + 0.974345i \(0.572257\pi\)
\(770\) 0.609749 0.0219738
\(771\) 0 0
\(772\) −9.58452 −0.344955
\(773\) 7.72207 0.277744 0.138872 0.990310i \(-0.455652\pi\)
0.138872 + 0.990310i \(0.455652\pi\)
\(774\) 0 0
\(775\) 23.0855 0.829255
\(776\) 8.19970 0.294352
\(777\) 0 0
\(778\) 4.48361 0.160745
\(779\) −3.25603 −0.116660
\(780\) 0 0
\(781\) 26.2757 0.940218
\(782\) 0.190909 0.00682689
\(783\) 0 0
\(784\) 3.44222 0.122937
\(785\) −3.91470 −0.139722
\(786\) 0 0
\(787\) 4.74326 0.169079 0.0845396 0.996420i \(-0.473058\pi\)
0.0845396 + 0.996420i \(0.473058\pi\)
\(788\) −10.8482 −0.386450
\(789\) 0 0
\(790\) −5.09211 −0.181169
\(791\) 1.77268 0.0630293
\(792\) 0 0
\(793\) −0.893580 −0.0317320
\(794\) 1.80401 0.0640220
\(795\) 0 0
\(796\) −1.56975 −0.0556385
\(797\) −46.3762 −1.64273 −0.821365 0.570403i \(-0.806787\pi\)
−0.821365 + 0.570403i \(0.806787\pi\)
\(798\) 0 0
\(799\) 0.251116 0.00888383
\(800\) 13.9118 0.491858
\(801\) 0 0
\(802\) 1.64581 0.0581157
\(803\) −29.9149 −1.05568
\(804\) 0 0
\(805\) 3.29812 0.116243
\(806\) −0.511020 −0.0179999
\(807\) 0 0
\(808\) −16.1241 −0.567245
\(809\) 38.5949 1.35693 0.678463 0.734635i \(-0.262646\pi\)
0.678463 + 0.734635i \(0.262646\pi\)
\(810\) 0 0
\(811\) 6.69385 0.235053 0.117527 0.993070i \(-0.462503\pi\)
0.117527 + 0.993070i \(0.462503\pi\)
\(812\) −8.34179 −0.292739
\(813\) 0 0
\(814\) −4.35166 −0.152526
\(815\) 22.3119 0.781550
\(816\) 0 0
\(817\) 7.72622 0.270306
\(818\) 10.8879 0.380686
\(819\) 0 0
\(820\) 7.19610 0.251299
\(821\) 27.8784 0.972964 0.486482 0.873690i \(-0.338280\pi\)
0.486482 + 0.873690i \(0.338280\pi\)
\(822\) 0 0
\(823\) −22.7329 −0.792419 −0.396209 0.918160i \(-0.629675\pi\)
−0.396209 + 0.918160i \(0.629675\pi\)
\(824\) −2.75237 −0.0958832
\(825\) 0 0
\(826\) −1.31113 −0.0456200
\(827\) 5.40384 0.187910 0.0939549 0.995576i \(-0.470049\pi\)
0.0939549 + 0.995576i \(0.470049\pi\)
\(828\) 0 0
\(829\) 38.4471 1.33532 0.667661 0.744466i \(-0.267296\pi\)
0.667661 + 0.744466i \(0.267296\pi\)
\(830\) 4.61755 0.160277
\(831\) 0 0
\(832\) 1.68672 0.0584767
\(833\) −0.186210 −0.00645179
\(834\) 0 0
\(835\) −15.4452 −0.534502
\(836\) 3.25975 0.112741
\(837\) 0 0
\(838\) 4.79544 0.165656
\(839\) 22.6601 0.782313 0.391157 0.920324i \(-0.372075\pi\)
0.391157 + 0.920324i \(0.372075\pi\)
\(840\) 0 0
\(841\) −9.83638 −0.339186
\(842\) −7.83038 −0.269853
\(843\) 0 0
\(844\) 28.8242 0.992170
\(845\) −12.7694 −0.439282
\(846\) 0 0
\(847\) −6.97265 −0.239583
\(848\) −12.9251 −0.443849
\(849\) 0 0
\(850\) −0.230200 −0.00789581
\(851\) −23.5380 −0.806874
\(852\) 0 0
\(853\) 22.6319 0.774902 0.387451 0.921890i \(-0.373356\pi\)
0.387451 + 0.921890i \(0.373356\pi\)
\(854\) −0.947829 −0.0324340
\(855\) 0 0
\(856\) −5.88235 −0.201055
\(857\) 38.6289 1.31954 0.659770 0.751468i \(-0.270654\pi\)
0.659770 + 0.751468i \(0.270654\pi\)
\(858\) 0 0
\(859\) −2.75056 −0.0938481 −0.0469240 0.998898i \(-0.514942\pi\)
−0.0469240 + 0.998898i \(0.514942\pi\)
\(860\) −17.0756 −0.582272
\(861\) 0 0
\(862\) 0.771579 0.0262801
\(863\) 18.8268 0.640871 0.320435 0.947270i \(-0.396171\pi\)
0.320435 + 0.947270i \(0.396171\pi\)
\(864\) 0 0
\(865\) −16.6112 −0.564798
\(866\) 8.16261 0.277377
\(867\) 0 0
\(868\) 10.9359 0.371189
\(869\) −33.6330 −1.14092
\(870\) 0 0
\(871\) 3.13928 0.106370
\(872\) 3.09947 0.104961
\(873\) 0 0
\(874\) −0.873933 −0.0295612
\(875\) −8.92016 −0.301556
\(876\) 0 0
\(877\) 5.91209 0.199637 0.0998186 0.995006i \(-0.468174\pi\)
0.0998186 + 0.995006i \(0.468174\pi\)
\(878\) −0.797262 −0.0269063
\(879\) 0 0
\(880\) −6.82953 −0.230223
\(881\) −23.3170 −0.785569 −0.392785 0.919630i \(-0.628488\pi\)
−0.392785 + 0.919630i \(0.628488\pi\)
\(882\) 0 0
\(883\) −20.2527 −0.681558 −0.340779 0.940143i \(-0.610691\pi\)
−0.340779 + 0.940143i \(0.610691\pi\)
\(884\) −0.102808 −0.00345780
\(885\) 0 0
\(886\) 7.40515 0.248781
\(887\) 59.2402 1.98909 0.994545 0.104309i \(-0.0332631\pi\)
0.994545 + 0.104309i \(0.0332631\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −0.159879 −0.00535915
\(891\) 0 0
\(892\) −7.89572 −0.264368
\(893\) −1.14954 −0.0384680
\(894\) 0 0
\(895\) −18.2985 −0.611652
\(896\) 8.70601 0.290847
\(897\) 0 0
\(898\) −3.40268 −0.113549
\(899\) −25.1231 −0.837903
\(900\) 0 0
\(901\) 0.699192 0.0232935
\(902\) −2.35583 −0.0784404
\(903\) 0 0
\(904\) 2.12771 0.0707666
\(905\) 5.10801 0.169796
\(906\) 0 0
\(907\) 3.28126 0.108953 0.0544763 0.998515i \(-0.482651\pi\)
0.0544763 + 0.998515i \(0.482651\pi\)
\(908\) −33.7592 −1.12034
\(909\) 0 0
\(910\) 0.0880329 0.00291826
\(911\) 53.0856 1.75880 0.879402 0.476080i \(-0.157943\pi\)
0.879402 + 0.476080i \(0.157943\pi\)
\(912\) 0 0
\(913\) 30.4986 1.00936
\(914\) −2.18545 −0.0722883
\(915\) 0 0
\(916\) −52.6475 −1.73952
\(917\) 11.9789 0.395580
\(918\) 0 0
\(919\) −10.1491 −0.334787 −0.167394 0.985890i \(-0.553535\pi\)
−0.167394 + 0.985890i \(0.553535\pi\)
\(920\) 3.95866 0.130513
\(921\) 0 0
\(922\) 7.39386 0.243504
\(923\) 3.79357 0.124867
\(924\) 0 0
\(925\) 28.3825 0.933210
\(926\) 5.83151 0.191635
\(927\) 0 0
\(928\) −15.1398 −0.496987
\(929\) 26.8433 0.880699 0.440350 0.897826i \(-0.354855\pi\)
0.440350 + 0.897826i \(0.354855\pi\)
\(930\) 0 0
\(931\) 0.852422 0.0279370
\(932\) 41.2853 1.35235
\(933\) 0 0
\(934\) 2.27621 0.0744798
\(935\) 0.369449 0.0120823
\(936\) 0 0
\(937\) 43.6904 1.42730 0.713651 0.700501i \(-0.247040\pi\)
0.713651 + 0.700501i \(0.247040\pi\)
\(938\) 3.32986 0.108724
\(939\) 0 0
\(940\) 2.54058 0.0828647
\(941\) 9.59031 0.312635 0.156318 0.987707i \(-0.450038\pi\)
0.156318 + 0.987707i \(0.450038\pi\)
\(942\) 0 0
\(943\) −12.7426 −0.414957
\(944\) 14.6854 0.477968
\(945\) 0 0
\(946\) 5.59012 0.181751
\(947\) −3.89541 −0.126584 −0.0632918 0.997995i \(-0.520160\pi\)
−0.0632918 + 0.997995i \(0.520160\pi\)
\(948\) 0 0
\(949\) −4.31899 −0.140200
\(950\) 1.05380 0.0341898
\(951\) 0 0
\(952\) −0.223504 −0.00724379
\(953\) 0.685511 0.0222059 0.0111029 0.999938i \(-0.496466\pi\)
0.0111029 + 0.999938i \(0.496466\pi\)
\(954\) 0 0
\(955\) 1.26527 0.0409431
\(956\) 6.36065 0.205718
\(957\) 0 0
\(958\) −1.51312 −0.0488868
\(959\) 13.4775 0.435212
\(960\) 0 0
\(961\) 1.93592 0.0624489
\(962\) −0.628274 −0.0202564
\(963\) 0 0
\(964\) 25.6684 0.826724
\(965\) 4.97270 0.160077
\(966\) 0 0
\(967\) −38.2729 −1.23077 −0.615386 0.788226i \(-0.711000\pi\)
−0.615386 + 0.788226i \(0.711000\pi\)
\(968\) −8.36912 −0.268994
\(969\) 0 0
\(970\) −2.07567 −0.0666457
\(971\) −2.76859 −0.0888482 −0.0444241 0.999013i \(-0.514145\pi\)
−0.0444241 + 0.999013i \(0.514145\pi\)
\(972\) 0 0
\(973\) 6.28920 0.201622
\(974\) −3.02741 −0.0970046
\(975\) 0 0
\(976\) 10.6162 0.339817
\(977\) −25.2322 −0.807249 −0.403625 0.914925i \(-0.632250\pi\)
−0.403625 + 0.914925i \(0.632250\pi\)
\(978\) 0 0
\(979\) −1.05599 −0.0337495
\(980\) −1.88392 −0.0601796
\(981\) 0 0
\(982\) −9.66671 −0.308477
\(983\) −27.4799 −0.876472 −0.438236 0.898860i \(-0.644397\pi\)
−0.438236 + 0.898860i \(0.644397\pi\)
\(984\) 0 0
\(985\) 5.62831 0.179333
\(986\) 0.250519 0.00797816
\(987\) 0 0
\(988\) 0.470629 0.0149727
\(989\) 30.2369 0.961476
\(990\) 0 0
\(991\) −26.6965 −0.848043 −0.424021 0.905652i \(-0.639382\pi\)
−0.424021 + 0.905652i \(0.639382\pi\)
\(992\) 19.8479 0.630172
\(993\) 0 0
\(994\) 4.02387 0.127629
\(995\) 0.814429 0.0258191
\(996\) 0 0
\(997\) −4.92865 −0.156092 −0.0780459 0.996950i \(-0.524868\pi\)
−0.0780459 + 0.996950i \(0.524868\pi\)
\(998\) 4.74931 0.150337
\(999\) 0 0
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 \(a_p\))