Properties

Label 8001.2.a.u.1.8
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-0.375443\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.375443 q^{2}\) \(-1.85904 q^{4}\) \(-2.49678 q^{5}\) \(+1.00000 q^{7}\) \(+1.44885 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.375443 q^{2}\) \(-1.85904 q^{4}\) \(-2.49678 q^{5}\) \(+1.00000 q^{7}\) \(+1.44885 q^{8}\) \(+0.937397 q^{10}\) \(+0.0439826 q^{11}\) \(+1.23685 q^{13}\) \(-0.375443 q^{14}\) \(+3.17413 q^{16}\) \(+4.66254 q^{17}\) \(-4.55600 q^{19}\) \(+4.64162 q^{20}\) \(-0.0165129 q^{22}\) \(+5.31043 q^{23}\) \(+1.23390 q^{25}\) \(-0.464365 q^{26}\) \(-1.85904 q^{28}\) \(+5.23792 q^{29}\) \(+0.715277 q^{31}\) \(-4.08940 q^{32}\) \(-1.75052 q^{34}\) \(-2.49678 q^{35}\) \(+7.90706 q^{37}\) \(+1.71052 q^{38}\) \(-3.61746 q^{40}\) \(+4.97134 q^{41}\) \(+0.341392 q^{43}\) \(-0.0817655 q^{44}\) \(-1.99376 q^{46}\) \(-11.4407 q^{47}\) \(+1.00000 q^{49}\) \(-0.463260 q^{50}\) \(-2.29935 q^{52}\) \(+4.41842 q^{53}\) \(-0.109815 q^{55}\) \(+1.44885 q^{56}\) \(-1.96654 q^{58}\) \(-9.78565 q^{59}\) \(-9.42399 q^{61}\) \(-0.268546 q^{62}\) \(-4.81291 q^{64}\) \(-3.08813 q^{65}\) \(+0.00811780 q^{67}\) \(-8.66785 q^{68}\) \(+0.937397 q^{70}\) \(+4.91418 q^{71}\) \(-11.8395 q^{73}\) \(-2.96865 q^{74}\) \(+8.46980 q^{76}\) \(+0.0439826 q^{77}\) \(-1.44620 q^{79}\) \(-7.92509 q^{80}\) \(-1.86645 q^{82}\) \(+7.62022 q^{83}\) \(-11.6413 q^{85}\) \(-0.128173 q^{86}\) \(+0.0637241 q^{88}\) \(+11.8328 q^{89}\) \(+1.23685 q^{91}\) \(-9.87232 q^{92}\) \(+4.29534 q^{94}\) \(+11.3753 q^{95}\) \(-8.97251 q^{97}\) \(-0.375443 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.375443 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(3\) 0 0
\(4\) −1.85904 −0.929521
\(5\) −2.49678 −1.11659 −0.558297 0.829641i \(-0.688545\pi\)
−0.558297 + 0.829641i \(0.688545\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.44885 0.512246
\(9\) 0 0
\(10\) 0.937397 0.296431
\(11\) 0.0439826 0.0132612 0.00663062 0.999978i \(-0.497889\pi\)
0.00663062 + 0.999978i \(0.497889\pi\)
\(12\) 0 0
\(13\) 1.23685 0.343039 0.171520 0.985181i \(-0.445132\pi\)
0.171520 + 0.985181i \(0.445132\pi\)
\(14\) −0.375443 −0.100341
\(15\) 0 0
\(16\) 3.17413 0.793531
\(17\) 4.66254 1.13083 0.565416 0.824806i \(-0.308716\pi\)
0.565416 + 0.824806i \(0.308716\pi\)
\(18\) 0 0
\(19\) −4.55600 −1.04522 −0.522609 0.852572i \(-0.675041\pi\)
−0.522609 + 0.852572i \(0.675041\pi\)
\(20\) 4.64162 1.03790
\(21\) 0 0
\(22\) −0.0165129 −0.00352057
\(23\) 5.31043 1.10730 0.553651 0.832749i \(-0.313234\pi\)
0.553651 + 0.832749i \(0.313234\pi\)
\(24\) 0 0
\(25\) 1.23390 0.246780
\(26\) −0.464365 −0.0910694
\(27\) 0 0
\(28\) −1.85904 −0.351326
\(29\) 5.23792 0.972657 0.486329 0.873776i \(-0.338336\pi\)
0.486329 + 0.873776i \(0.338336\pi\)
\(30\) 0 0
\(31\) 0.715277 0.128468 0.0642338 0.997935i \(-0.479540\pi\)
0.0642338 + 0.997935i \(0.479540\pi\)
\(32\) −4.08940 −0.722911
\(33\) 0 0
\(34\) −1.75052 −0.300211
\(35\) −2.49678 −0.422033
\(36\) 0 0
\(37\) 7.90706 1.29991 0.649956 0.759972i \(-0.274787\pi\)
0.649956 + 0.759972i \(0.274787\pi\)
\(38\) 1.71052 0.277483
\(39\) 0 0
\(40\) −3.61746 −0.571970
\(41\) 4.97134 0.776393 0.388197 0.921577i \(-0.373098\pi\)
0.388197 + 0.921577i \(0.373098\pi\)
\(42\) 0 0
\(43\) 0.341392 0.0520618 0.0260309 0.999661i \(-0.491713\pi\)
0.0260309 + 0.999661i \(0.491713\pi\)
\(44\) −0.0817655 −0.0123266
\(45\) 0 0
\(46\) −1.99376 −0.293964
\(47\) −11.4407 −1.66880 −0.834402 0.551157i \(-0.814187\pi\)
−0.834402 + 0.551157i \(0.814187\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.463260 −0.0655148
\(51\) 0 0
\(52\) −2.29935 −0.318862
\(53\) 4.41842 0.606916 0.303458 0.952845i \(-0.401859\pi\)
0.303458 + 0.952845i \(0.401859\pi\)
\(54\) 0 0
\(55\) −0.109815 −0.0148074
\(56\) 1.44885 0.193611
\(57\) 0 0
\(58\) −1.96654 −0.258219
\(59\) −9.78565 −1.27398 −0.636991 0.770871i \(-0.719821\pi\)
−0.636991 + 0.770871i \(0.719821\pi\)
\(60\) 0 0
\(61\) −9.42399 −1.20662 −0.603309 0.797508i \(-0.706151\pi\)
−0.603309 + 0.797508i \(0.706151\pi\)
\(62\) −0.268546 −0.0341053
\(63\) 0 0
\(64\) −4.81291 −0.601614
\(65\) −3.08813 −0.383035
\(66\) 0 0
\(67\) 0.00811780 0.000991748 0 0.000495874 1.00000i \(-0.499842\pi\)
0.000495874 1.00000i \(0.499842\pi\)
\(68\) −8.66785 −1.05113
\(69\) 0 0
\(70\) 0.937397 0.112040
\(71\) 4.91418 0.583206 0.291603 0.956539i \(-0.405811\pi\)
0.291603 + 0.956539i \(0.405811\pi\)
\(72\) 0 0
\(73\) −11.8395 −1.38571 −0.692856 0.721076i \(-0.743648\pi\)
−0.692856 + 0.721076i \(0.743648\pi\)
\(74\) −2.96865 −0.345098
\(75\) 0 0
\(76\) 8.46980 0.971553
\(77\) 0.0439826 0.00501228
\(78\) 0 0
\(79\) −1.44620 −0.162710 −0.0813552 0.996685i \(-0.525925\pi\)
−0.0813552 + 0.996685i \(0.525925\pi\)
\(80\) −7.92509 −0.886052
\(81\) 0 0
\(82\) −1.86645 −0.206115
\(83\) 7.62022 0.836428 0.418214 0.908349i \(-0.362656\pi\)
0.418214 + 0.908349i \(0.362656\pi\)
\(84\) 0 0
\(85\) −11.6413 −1.26268
\(86\) −0.128173 −0.0138213
\(87\) 0 0
\(88\) 0.0637241 0.00679301
\(89\) 11.8328 1.25427 0.627137 0.778909i \(-0.284227\pi\)
0.627137 + 0.778909i \(0.284227\pi\)
\(90\) 0 0
\(91\) 1.23685 0.129657
\(92\) −9.87232 −1.02926
\(93\) 0 0
\(94\) 4.29534 0.443031
\(95\) 11.3753 1.16708
\(96\) 0 0
\(97\) −8.97251 −0.911020 −0.455510 0.890231i \(-0.650543\pi\)
−0.455510 + 0.890231i \(0.650543\pi\)
\(98\) −0.375443 −0.0379255
\(99\) 0 0
\(100\) −2.29388 −0.229388
\(101\) −11.8979 −1.18389 −0.591943 0.805980i \(-0.701639\pi\)
−0.591943 + 0.805980i \(0.701639\pi\)
\(102\) 0 0
\(103\) 3.32884 0.328000 0.164000 0.986460i \(-0.447560\pi\)
0.164000 + 0.986460i \(0.447560\pi\)
\(104\) 1.79200 0.175720
\(105\) 0 0
\(106\) −1.65886 −0.161123
\(107\) 11.7272 1.13371 0.566856 0.823817i \(-0.308159\pi\)
0.566856 + 0.823817i \(0.308159\pi\)
\(108\) 0 0
\(109\) −12.3647 −1.18432 −0.592161 0.805820i \(-0.701725\pi\)
−0.592161 + 0.805820i \(0.701725\pi\)
\(110\) 0.0412291 0.00393104
\(111\) 0 0
\(112\) 3.17413 0.299927
\(113\) 11.5463 1.08618 0.543092 0.839673i \(-0.317253\pi\)
0.543092 + 0.839673i \(0.317253\pi\)
\(114\) 0 0
\(115\) −13.2590 −1.23641
\(116\) −9.73752 −0.904106
\(117\) 0 0
\(118\) 3.67395 0.338215
\(119\) 4.66254 0.427414
\(120\) 0 0
\(121\) −10.9981 −0.999824
\(122\) 3.53817 0.320331
\(123\) 0 0
\(124\) −1.32973 −0.119413
\(125\) 9.40311 0.841040
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 9.98578 0.882626
\(129\) 0 0
\(130\) 1.15942 0.101688
\(131\) −1.63563 −0.142906 −0.0714529 0.997444i \(-0.522764\pi\)
−0.0714529 + 0.997444i \(0.522764\pi\)
\(132\) 0 0
\(133\) −4.55600 −0.395056
\(134\) −0.00304777 −0.000263287 0
\(135\) 0 0
\(136\) 6.75531 0.579263
\(137\) −4.20337 −0.359118 −0.179559 0.983747i \(-0.557467\pi\)
−0.179559 + 0.983747i \(0.557467\pi\)
\(138\) 0 0
\(139\) −1.83457 −0.155606 −0.0778030 0.996969i \(-0.524791\pi\)
−0.0778030 + 0.996969i \(0.524791\pi\)
\(140\) 4.64162 0.392288
\(141\) 0 0
\(142\) −1.84499 −0.154828
\(143\) 0.0543996 0.00454913
\(144\) 0 0
\(145\) −13.0779 −1.08606
\(146\) 4.44506 0.367876
\(147\) 0 0
\(148\) −14.6996 −1.20830
\(149\) 14.6708 1.20188 0.600940 0.799294i \(-0.294793\pi\)
0.600940 + 0.799294i \(0.294793\pi\)
\(150\) 0 0
\(151\) 7.31356 0.595169 0.297585 0.954695i \(-0.403819\pi\)
0.297585 + 0.954695i \(0.403819\pi\)
\(152\) −6.60096 −0.535409
\(153\) 0 0
\(154\) −0.0165129 −0.00133065
\(155\) −1.78589 −0.143446
\(156\) 0 0
\(157\) 5.65707 0.451483 0.225742 0.974187i \(-0.427519\pi\)
0.225742 + 0.974187i \(0.427519\pi\)
\(158\) 0.542966 0.0431961
\(159\) 0 0
\(160\) 10.2103 0.807198
\(161\) 5.31043 0.418521
\(162\) 0 0
\(163\) 16.3284 1.27894 0.639470 0.768816i \(-0.279154\pi\)
0.639470 + 0.768816i \(0.279154\pi\)
\(164\) −9.24194 −0.721674
\(165\) 0 0
\(166\) −2.86096 −0.222053
\(167\) 12.9310 1.00063 0.500314 0.865844i \(-0.333218\pi\)
0.500314 + 0.865844i \(0.333218\pi\)
\(168\) 0 0
\(169\) −11.4702 −0.882324
\(170\) 4.37065 0.335213
\(171\) 0 0
\(172\) −0.634663 −0.0483926
\(173\) −9.17036 −0.697209 −0.348605 0.937270i \(-0.613344\pi\)
−0.348605 + 0.937270i \(0.613344\pi\)
\(174\) 0 0
\(175\) 1.23390 0.0932742
\(176\) 0.139606 0.0105232
\(177\) 0 0
\(178\) −4.44254 −0.332982
\(179\) 4.47476 0.334459 0.167230 0.985918i \(-0.446518\pi\)
0.167230 + 0.985918i \(0.446518\pi\)
\(180\) 0 0
\(181\) −10.6152 −0.789023 −0.394511 0.918891i \(-0.629086\pi\)
−0.394511 + 0.918891i \(0.629086\pi\)
\(182\) −0.464365 −0.0344210
\(183\) 0 0
\(184\) 7.69402 0.567210
\(185\) −19.7422 −1.45147
\(186\) 0 0
\(187\) 0.205070 0.0149962
\(188\) 21.2688 1.55119
\(189\) 0 0
\(190\) −4.27079 −0.309835
\(191\) −10.6972 −0.774020 −0.387010 0.922075i \(-0.626492\pi\)
−0.387010 + 0.922075i \(0.626492\pi\)
\(192\) 0 0
\(193\) 3.42294 0.246388 0.123194 0.992383i \(-0.460686\pi\)
0.123194 + 0.992383i \(0.460686\pi\)
\(194\) 3.36866 0.241856
\(195\) 0 0
\(196\) −1.85904 −0.132789
\(197\) −12.6206 −0.899181 −0.449591 0.893235i \(-0.648430\pi\)
−0.449591 + 0.893235i \(0.648430\pi\)
\(198\) 0 0
\(199\) 21.2114 1.50364 0.751819 0.659369i \(-0.229177\pi\)
0.751819 + 0.659369i \(0.229177\pi\)
\(200\) 1.78774 0.126412
\(201\) 0 0
\(202\) 4.46699 0.314296
\(203\) 5.23792 0.367630
\(204\) 0 0
\(205\) −12.4123 −0.866915
\(206\) −1.24979 −0.0870769
\(207\) 0 0
\(208\) 3.92590 0.272212
\(209\) −0.200385 −0.0138609
\(210\) 0 0
\(211\) 1.41420 0.0973575 0.0486788 0.998814i \(-0.484499\pi\)
0.0486788 + 0.998814i \(0.484499\pi\)
\(212\) −8.21403 −0.564142
\(213\) 0 0
\(214\) −4.40290 −0.300976
\(215\) −0.852381 −0.0581319
\(216\) 0 0
\(217\) 0.715277 0.0485562
\(218\) 4.64223 0.314411
\(219\) 0 0
\(220\) 0.204150 0.0137638
\(221\) 5.76684 0.387919
\(222\) 0 0
\(223\) −11.6705 −0.781512 −0.390756 0.920494i \(-0.627786\pi\)
−0.390756 + 0.920494i \(0.627786\pi\)
\(224\) −4.08940 −0.273235
\(225\) 0 0
\(226\) −4.33497 −0.288358
\(227\) 6.98427 0.463562 0.231781 0.972768i \(-0.425545\pi\)
0.231781 + 0.972768i \(0.425545\pi\)
\(228\) 0 0
\(229\) 3.76335 0.248689 0.124345 0.992239i \(-0.460317\pi\)
0.124345 + 0.992239i \(0.460317\pi\)
\(230\) 4.97798 0.328239
\(231\) 0 0
\(232\) 7.58896 0.498240
\(233\) 6.17050 0.404243 0.202121 0.979360i \(-0.435216\pi\)
0.202121 + 0.979360i \(0.435216\pi\)
\(234\) 0 0
\(235\) 28.5650 1.86337
\(236\) 18.1919 1.18419
\(237\) 0 0
\(238\) −1.75052 −0.113469
\(239\) −5.01726 −0.324540 −0.162270 0.986746i \(-0.551882\pi\)
−0.162270 + 0.986746i \(0.551882\pi\)
\(240\) 0 0
\(241\) −4.66693 −0.300623 −0.150312 0.988639i \(-0.548028\pi\)
−0.150312 + 0.988639i \(0.548028\pi\)
\(242\) 4.12914 0.265431
\(243\) 0 0
\(244\) 17.5196 1.12158
\(245\) −2.49678 −0.159513
\(246\) 0 0
\(247\) −5.63507 −0.358551
\(248\) 1.03633 0.0658070
\(249\) 0 0
\(250\) −3.53033 −0.223278
\(251\) 14.9362 0.942765 0.471382 0.881929i \(-0.343755\pi\)
0.471382 + 0.881929i \(0.343755\pi\)
\(252\) 0 0
\(253\) 0.233566 0.0146842
\(254\) −0.375443 −0.0235574
\(255\) 0 0
\(256\) 5.87674 0.367296
\(257\) −2.50206 −0.156074 −0.0780370 0.996950i \(-0.524865\pi\)
−0.0780370 + 0.996950i \(0.524865\pi\)
\(258\) 0 0
\(259\) 7.90706 0.491321
\(260\) 5.74096 0.356040
\(261\) 0 0
\(262\) 0.614086 0.0379383
\(263\) 3.74847 0.231141 0.115570 0.993299i \(-0.463130\pi\)
0.115570 + 0.993299i \(0.463130\pi\)
\(264\) 0 0
\(265\) −11.0318 −0.677679
\(266\) 1.71052 0.104879
\(267\) 0 0
\(268\) −0.0150913 −0.000921851 0
\(269\) −8.16292 −0.497702 −0.248851 0.968542i \(-0.580053\pi\)
−0.248851 + 0.968542i \(0.580053\pi\)
\(270\) 0 0
\(271\) −8.16035 −0.495706 −0.247853 0.968798i \(-0.579725\pi\)
−0.247853 + 0.968798i \(0.579725\pi\)
\(272\) 14.7995 0.897350
\(273\) 0 0
\(274\) 1.57812 0.0953380
\(275\) 0.0542702 0.00327261
\(276\) 0 0
\(277\) −19.5232 −1.17304 −0.586519 0.809935i \(-0.699502\pi\)
−0.586519 + 0.809935i \(0.699502\pi\)
\(278\) 0.688775 0.0413100
\(279\) 0 0
\(280\) −3.61746 −0.216184
\(281\) 13.5957 0.811052 0.405526 0.914084i \(-0.367088\pi\)
0.405526 + 0.914084i \(0.367088\pi\)
\(282\) 0 0
\(283\) 24.0199 1.42783 0.713917 0.700230i \(-0.246919\pi\)
0.713917 + 0.700230i \(0.246919\pi\)
\(284\) −9.13567 −0.542102
\(285\) 0 0
\(286\) −0.0204240 −0.00120769
\(287\) 4.97134 0.293449
\(288\) 0 0
\(289\) 4.73924 0.278779
\(290\) 4.91001 0.288326
\(291\) 0 0
\(292\) 22.0102 1.28805
\(293\) 27.5825 1.61138 0.805692 0.592334i \(-0.201794\pi\)
0.805692 + 0.592334i \(0.201794\pi\)
\(294\) 0 0
\(295\) 24.4326 1.42252
\(296\) 11.4561 0.665875
\(297\) 0 0
\(298\) −5.50806 −0.319073
\(299\) 6.56818 0.379848
\(300\) 0 0
\(301\) 0.341392 0.0196775
\(302\) −2.74582 −0.158004
\(303\) 0 0
\(304\) −14.4613 −0.829414
\(305\) 23.5296 1.34730
\(306\) 0 0
\(307\) −24.8153 −1.41629 −0.708143 0.706069i \(-0.750467\pi\)
−0.708143 + 0.706069i \(0.750467\pi\)
\(308\) −0.0817655 −0.00465902
\(309\) 0 0
\(310\) 0.670499 0.0380818
\(311\) 0.788961 0.0447379 0.0223689 0.999750i \(-0.492879\pi\)
0.0223689 + 0.999750i \(0.492879\pi\)
\(312\) 0 0
\(313\) 16.4791 0.931453 0.465727 0.884929i \(-0.345793\pi\)
0.465727 + 0.884929i \(0.345793\pi\)
\(314\) −2.12391 −0.119859
\(315\) 0 0
\(316\) 2.68855 0.151243
\(317\) −15.2893 −0.858735 −0.429367 0.903130i \(-0.641263\pi\)
−0.429367 + 0.903130i \(0.641263\pi\)
\(318\) 0 0
\(319\) 0.230377 0.0128986
\(320\) 12.0168 0.671758
\(321\) 0 0
\(322\) −1.99376 −0.111108
\(323\) −21.2425 −1.18197
\(324\) 0 0
\(325\) 1.52615 0.0846554
\(326\) −6.13039 −0.339531
\(327\) 0 0
\(328\) 7.20273 0.397704
\(329\) −11.4407 −0.630748
\(330\) 0 0
\(331\) −8.79412 −0.483369 −0.241684 0.970355i \(-0.577700\pi\)
−0.241684 + 0.970355i \(0.577700\pi\)
\(332\) −14.1663 −0.777477
\(333\) 0 0
\(334\) −4.85484 −0.265645
\(335\) −0.0202684 −0.00110738
\(336\) 0 0
\(337\) 10.3907 0.566015 0.283008 0.959118i \(-0.408668\pi\)
0.283008 + 0.959118i \(0.408668\pi\)
\(338\) 4.30641 0.234238
\(339\) 0 0
\(340\) 21.6417 1.17369
\(341\) 0.0314597 0.00170364
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.494626 0.0266684
\(345\) 0 0
\(346\) 3.44294 0.185094
\(347\) 3.73798 0.200665 0.100333 0.994954i \(-0.468009\pi\)
0.100333 + 0.994954i \(0.468009\pi\)
\(348\) 0 0
\(349\) 13.8895 0.743487 0.371744 0.928335i \(-0.378760\pi\)
0.371744 + 0.928335i \(0.378760\pi\)
\(350\) −0.463260 −0.0247623
\(351\) 0 0
\(352\) −0.179862 −0.00958670
\(353\) 29.3769 1.56357 0.781787 0.623546i \(-0.214309\pi\)
0.781787 + 0.623546i \(0.214309\pi\)
\(354\) 0 0
\(355\) −12.2696 −0.651204
\(356\) −21.9977 −1.16587
\(357\) 0 0
\(358\) −1.68002 −0.0887917
\(359\) 3.99547 0.210873 0.105436 0.994426i \(-0.466376\pi\)
0.105436 + 0.994426i \(0.466376\pi\)
\(360\) 0 0
\(361\) 1.75716 0.0924823
\(362\) 3.98541 0.209468
\(363\) 0 0
\(364\) −2.29935 −0.120519
\(365\) 29.5607 1.54728
\(366\) 0 0
\(367\) −15.8689 −0.828348 −0.414174 0.910198i \(-0.635929\pi\)
−0.414174 + 0.910198i \(0.635929\pi\)
\(368\) 16.8560 0.878678
\(369\) 0 0
\(370\) 7.41206 0.385335
\(371\) 4.41842 0.229393
\(372\) 0 0
\(373\) −1.79342 −0.0928595 −0.0464298 0.998922i \(-0.514784\pi\)
−0.0464298 + 0.998922i \(0.514784\pi\)
\(374\) −0.0769922 −0.00398117
\(375\) 0 0
\(376\) −16.5759 −0.854837
\(377\) 6.47850 0.333660
\(378\) 0 0
\(379\) 30.6924 1.57656 0.788280 0.615316i \(-0.210972\pi\)
0.788280 + 0.615316i \(0.210972\pi\)
\(380\) −21.1472 −1.08483
\(381\) 0 0
\(382\) 4.01618 0.205485
\(383\) 13.9575 0.713194 0.356597 0.934258i \(-0.383937\pi\)
0.356597 + 0.934258i \(0.383937\pi\)
\(384\) 0 0
\(385\) −0.109815 −0.00559668
\(386\) −1.28512 −0.0654107
\(387\) 0 0
\(388\) 16.6803 0.846813
\(389\) −31.4166 −1.59288 −0.796442 0.604715i \(-0.793287\pi\)
−0.796442 + 0.604715i \(0.793287\pi\)
\(390\) 0 0
\(391\) 24.7601 1.25217
\(392\) 1.44885 0.0731780
\(393\) 0 0
\(394\) 4.73832 0.238713
\(395\) 3.61085 0.181681
\(396\) 0 0
\(397\) 4.14664 0.208114 0.104057 0.994571i \(-0.466818\pi\)
0.104057 + 0.994571i \(0.466818\pi\)
\(398\) −7.96368 −0.399183
\(399\) 0 0
\(400\) 3.91656 0.195828
\(401\) −23.0458 −1.15085 −0.575427 0.817853i \(-0.695164\pi\)
−0.575427 + 0.817853i \(0.695164\pi\)
\(402\) 0 0
\(403\) 0.884688 0.0440694
\(404\) 22.1187 1.10045
\(405\) 0 0
\(406\) −1.96654 −0.0975977
\(407\) 0.347773 0.0172385
\(408\) 0 0
\(409\) 10.6304 0.525639 0.262819 0.964845i \(-0.415348\pi\)
0.262819 + 0.964845i \(0.415348\pi\)
\(410\) 4.66012 0.230147
\(411\) 0 0
\(412\) −6.18845 −0.304883
\(413\) −9.78565 −0.481520
\(414\) 0 0
\(415\) −19.0260 −0.933950
\(416\) −5.05796 −0.247987
\(417\) 0 0
\(418\) 0.0752330 0.00367977
\(419\) −0.439830 −0.0214871 −0.0107436 0.999942i \(-0.503420\pi\)
−0.0107436 + 0.999942i \(0.503420\pi\)
\(420\) 0 0
\(421\) 30.3492 1.47913 0.739564 0.673087i \(-0.235032\pi\)
0.739564 + 0.673087i \(0.235032\pi\)
\(422\) −0.530951 −0.0258463
\(423\) 0 0
\(424\) 6.40162 0.310890
\(425\) 5.75311 0.279067
\(426\) 0 0
\(427\) −9.42399 −0.456059
\(428\) −21.8014 −1.05381
\(429\) 0 0
\(430\) 0.320020 0.0154327
\(431\) −8.63673 −0.416017 −0.208008 0.978127i \(-0.566698\pi\)
−0.208008 + 0.978127i \(0.566698\pi\)
\(432\) 0 0
\(433\) 9.34002 0.448853 0.224426 0.974491i \(-0.427949\pi\)
0.224426 + 0.974491i \(0.427949\pi\)
\(434\) −0.268546 −0.0128906
\(435\) 0 0
\(436\) 22.9865 1.10085
\(437\) −24.1943 −1.15737
\(438\) 0 0
\(439\) 4.79533 0.228869 0.114434 0.993431i \(-0.463494\pi\)
0.114434 + 0.993431i \(0.463494\pi\)
\(440\) −0.159105 −0.00758503
\(441\) 0 0
\(442\) −2.16512 −0.102984
\(443\) 9.57969 0.455145 0.227572 0.973761i \(-0.426921\pi\)
0.227572 + 0.973761i \(0.426921\pi\)
\(444\) 0 0
\(445\) −29.5439 −1.40051
\(446\) 4.38159 0.207474
\(447\) 0 0
\(448\) −4.81291 −0.227389
\(449\) 22.2178 1.04852 0.524262 0.851557i \(-0.324341\pi\)
0.524262 + 0.851557i \(0.324341\pi\)
\(450\) 0 0
\(451\) 0.218652 0.0102959
\(452\) −21.4651 −1.00963
\(453\) 0 0
\(454\) −2.62219 −0.123066
\(455\) −3.08813 −0.144774
\(456\) 0 0
\(457\) 32.8310 1.53577 0.767884 0.640589i \(-0.221310\pi\)
0.767884 + 0.640589i \(0.221310\pi\)
\(458\) −1.41292 −0.0660216
\(459\) 0 0
\(460\) 24.6490 1.14927
\(461\) 7.65926 0.356727 0.178364 0.983965i \(-0.442920\pi\)
0.178364 + 0.983965i \(0.442920\pi\)
\(462\) 0 0
\(463\) 38.3105 1.78044 0.890220 0.455530i \(-0.150550\pi\)
0.890220 + 0.455530i \(0.150550\pi\)
\(464\) 16.6258 0.771834
\(465\) 0 0
\(466\) −2.31667 −0.107318
\(467\) 35.9613 1.66409 0.832046 0.554707i \(-0.187170\pi\)
0.832046 + 0.554707i \(0.187170\pi\)
\(468\) 0 0
\(469\) 0.00811780 0.000374845 0
\(470\) −10.7245 −0.494685
\(471\) 0 0
\(472\) −14.1779 −0.652592
\(473\) 0.0150153 0.000690404 0
\(474\) 0 0
\(475\) −5.62166 −0.257939
\(476\) −8.66785 −0.397290
\(477\) 0 0
\(478\) 1.88370 0.0861582
\(479\) −9.37274 −0.428251 −0.214126 0.976806i \(-0.568690\pi\)
−0.214126 + 0.976806i \(0.568690\pi\)
\(480\) 0 0
\(481\) 9.77981 0.445921
\(482\) 1.75217 0.0798089
\(483\) 0 0
\(484\) 20.4459 0.929358
\(485\) 22.4024 1.01724
\(486\) 0 0
\(487\) 41.8227 1.89517 0.947584 0.319507i \(-0.103517\pi\)
0.947584 + 0.319507i \(0.103517\pi\)
\(488\) −13.6539 −0.618085
\(489\) 0 0
\(490\) 0.937397 0.0423473
\(491\) −15.2407 −0.687802 −0.343901 0.939006i \(-0.611748\pi\)
−0.343901 + 0.939006i \(0.611748\pi\)
\(492\) 0 0
\(493\) 24.4220 1.09991
\(494\) 2.11565 0.0951875
\(495\) 0 0
\(496\) 2.27038 0.101943
\(497\) 4.91418 0.220431
\(498\) 0 0
\(499\) 18.6214 0.833608 0.416804 0.908996i \(-0.363150\pi\)
0.416804 + 0.908996i \(0.363150\pi\)
\(500\) −17.4808 −0.781765
\(501\) 0 0
\(502\) −5.60769 −0.250283
\(503\) 40.6766 1.81368 0.906841 0.421474i \(-0.138487\pi\)
0.906841 + 0.421474i \(0.138487\pi\)
\(504\) 0 0
\(505\) 29.7064 1.32192
\(506\) −0.0876908 −0.00389833
\(507\) 0 0
\(508\) −1.85904 −0.0824817
\(509\) −33.9922 −1.50668 −0.753340 0.657631i \(-0.771558\pi\)
−0.753340 + 0.657631i \(0.771558\pi\)
\(510\) 0 0
\(511\) −11.8395 −0.523750
\(512\) −22.1779 −0.980136
\(513\) 0 0
\(514\) 0.939379 0.0414342
\(515\) −8.31137 −0.366243
\(516\) 0 0
\(517\) −0.503193 −0.0221304
\(518\) −2.96865 −0.130435
\(519\) 0 0
\(520\) −4.47424 −0.196208
\(521\) 1.31867 0.0577722 0.0288861 0.999583i \(-0.490804\pi\)
0.0288861 + 0.999583i \(0.490804\pi\)
\(522\) 0 0
\(523\) −30.7412 −1.34422 −0.672109 0.740452i \(-0.734611\pi\)
−0.672109 + 0.740452i \(0.734611\pi\)
\(524\) 3.04071 0.132834
\(525\) 0 0
\(526\) −1.40734 −0.0613628
\(527\) 3.33501 0.145275
\(528\) 0 0
\(529\) 5.20068 0.226116
\(530\) 4.14181 0.179909
\(531\) 0 0
\(532\) 8.46980 0.367213
\(533\) 6.14878 0.266333
\(534\) 0 0
\(535\) −29.2803 −1.26590
\(536\) 0.0117615 0.000508019 0
\(537\) 0 0
\(538\) 3.06471 0.132129
\(539\) 0.0439826 0.00189446
\(540\) 0 0
\(541\) 16.8366 0.723860 0.361930 0.932205i \(-0.382118\pi\)
0.361930 + 0.932205i \(0.382118\pi\)
\(542\) 3.06374 0.131599
\(543\) 0 0
\(544\) −19.0670 −0.817490
\(545\) 30.8719 1.32241
\(546\) 0 0
\(547\) 16.8752 0.721531 0.360766 0.932656i \(-0.382515\pi\)
0.360766 + 0.932656i \(0.382515\pi\)
\(548\) 7.81424 0.333808
\(549\) 0 0
\(550\) −0.0203753 −0.000868807 0
\(551\) −23.8640 −1.01664
\(552\) 0 0
\(553\) −1.44620 −0.0614988
\(554\) 7.32986 0.311416
\(555\) 0 0
\(556\) 3.41054 0.144639
\(557\) 31.2255 1.32307 0.661534 0.749915i \(-0.269906\pi\)
0.661534 + 0.749915i \(0.269906\pi\)
\(558\) 0 0
\(559\) 0.422249 0.0178592
\(560\) −7.92509 −0.334896
\(561\) 0 0
\(562\) −5.10441 −0.215317
\(563\) 12.2339 0.515595 0.257798 0.966199i \(-0.417003\pi\)
0.257798 + 0.966199i \(0.417003\pi\)
\(564\) 0 0
\(565\) −28.8285 −1.21283
\(566\) −9.01810 −0.379059
\(567\) 0 0
\(568\) 7.11991 0.298745
\(569\) 16.3199 0.684164 0.342082 0.939670i \(-0.388868\pi\)
0.342082 + 0.939670i \(0.388868\pi\)
\(570\) 0 0
\(571\) 0.774915 0.0324292 0.0162146 0.999869i \(-0.494839\pi\)
0.0162146 + 0.999869i \(0.494839\pi\)
\(572\) −0.101131 −0.00422851
\(573\) 0 0
\(574\) −1.86645 −0.0779043
\(575\) 6.55255 0.273260
\(576\) 0 0
\(577\) 13.3038 0.553845 0.276922 0.960892i \(-0.410685\pi\)
0.276922 + 0.960892i \(0.410685\pi\)
\(578\) −1.77931 −0.0740097
\(579\) 0 0
\(580\) 24.3124 1.00952
\(581\) 7.62022 0.316140
\(582\) 0 0
\(583\) 0.194333 0.00804846
\(584\) −17.1537 −0.709825
\(585\) 0 0
\(586\) −10.3556 −0.427787
\(587\) −1.02046 −0.0421187 −0.0210594 0.999778i \(-0.506704\pi\)
−0.0210594 + 0.999778i \(0.506704\pi\)
\(588\) 0 0
\(589\) −3.25881 −0.134277
\(590\) −9.17304 −0.377648
\(591\) 0 0
\(592\) 25.0980 1.03152
\(593\) 22.7116 0.932655 0.466327 0.884612i \(-0.345577\pi\)
0.466327 + 0.884612i \(0.345577\pi\)
\(594\) 0 0
\(595\) −11.6413 −0.477248
\(596\) −27.2737 −1.11717
\(597\) 0 0
\(598\) −2.46598 −0.100841
\(599\) −25.5601 −1.04436 −0.522180 0.852835i \(-0.674881\pi\)
−0.522180 + 0.852835i \(0.674881\pi\)
\(600\) 0 0
\(601\) −26.9352 −1.09871 −0.549355 0.835589i \(-0.685127\pi\)
−0.549355 + 0.835589i \(0.685127\pi\)
\(602\) −0.128173 −0.00522395
\(603\) 0 0
\(604\) −13.5962 −0.553222
\(605\) 27.4597 1.11640
\(606\) 0 0
\(607\) 37.3334 1.51532 0.757659 0.652651i \(-0.226343\pi\)
0.757659 + 0.652651i \(0.226343\pi\)
\(608\) 18.6313 0.755600
\(609\) 0 0
\(610\) −8.83402 −0.357679
\(611\) −14.1504 −0.572465
\(612\) 0 0
\(613\) 24.7374 0.999135 0.499568 0.866275i \(-0.333492\pi\)
0.499568 + 0.866275i \(0.333492\pi\)
\(614\) 9.31674 0.375993
\(615\) 0 0
\(616\) 0.0637241 0.00256752
\(617\) −1.99796 −0.0804347 −0.0402173 0.999191i \(-0.512805\pi\)
−0.0402173 + 0.999191i \(0.512805\pi\)
\(618\) 0 0
\(619\) −12.8044 −0.514654 −0.257327 0.966324i \(-0.582842\pi\)
−0.257327 + 0.966324i \(0.582842\pi\)
\(620\) 3.32004 0.133336
\(621\) 0 0
\(622\) −0.296210 −0.0118769
\(623\) 11.8328 0.474071
\(624\) 0 0
\(625\) −29.6470 −1.18588
\(626\) −6.18696 −0.247280
\(627\) 0 0
\(628\) −10.5167 −0.419663
\(629\) 36.8670 1.46998
\(630\) 0 0
\(631\) 48.1211 1.91567 0.957836 0.287315i \(-0.0927625\pi\)
0.957836 + 0.287315i \(0.0927625\pi\)
\(632\) −2.09533 −0.0833477
\(633\) 0 0
\(634\) 5.74027 0.227975
\(635\) −2.49678 −0.0990816
\(636\) 0 0
\(637\) 1.23685 0.0490056
\(638\) −0.0864934 −0.00342431
\(639\) 0 0
\(640\) −24.9323 −0.985535
\(641\) 27.7591 1.09642 0.548209 0.836341i \(-0.315310\pi\)
0.548209 + 0.836341i \(0.315310\pi\)
\(642\) 0 0
\(643\) 10.3622 0.408647 0.204323 0.978903i \(-0.434501\pi\)
0.204323 + 0.978903i \(0.434501\pi\)
\(644\) −9.87232 −0.389024
\(645\) 0 0
\(646\) 7.97535 0.313786
\(647\) −27.9465 −1.09869 −0.549345 0.835596i \(-0.685123\pi\)
−0.549345 + 0.835596i \(0.685123\pi\)
\(648\) 0 0
\(649\) −0.430398 −0.0168946
\(650\) −0.572981 −0.0224741
\(651\) 0 0
\(652\) −30.3552 −1.18880
\(653\) −28.5640 −1.11780 −0.558898 0.829237i \(-0.688775\pi\)
−0.558898 + 0.829237i \(0.688775\pi\)
\(654\) 0 0
\(655\) 4.08381 0.159568
\(656\) 15.7797 0.616092
\(657\) 0 0
\(658\) 4.29534 0.167450
\(659\) 21.4088 0.833967 0.416983 0.908914i \(-0.363087\pi\)
0.416983 + 0.908914i \(0.363087\pi\)
\(660\) 0 0
\(661\) −9.97679 −0.388052 −0.194026 0.980996i \(-0.562155\pi\)
−0.194026 + 0.980996i \(0.562155\pi\)
\(662\) 3.30169 0.128324
\(663\) 0 0
\(664\) 11.0406 0.428457
\(665\) 11.3753 0.441116
\(666\) 0 0
\(667\) 27.8156 1.07702
\(668\) −24.0392 −0.930105
\(669\) 0 0
\(670\) 0.00760961 0.000293985 0
\(671\) −0.414491 −0.0160012
\(672\) 0 0
\(673\) 13.9270 0.536846 0.268423 0.963301i \(-0.413498\pi\)
0.268423 + 0.963301i \(0.413498\pi\)
\(674\) −3.90110 −0.150265
\(675\) 0 0
\(676\) 21.3236 0.820139
\(677\) −36.3413 −1.39671 −0.698355 0.715752i \(-0.746084\pi\)
−0.698355 + 0.715752i \(0.746084\pi\)
\(678\) 0 0
\(679\) −8.97251 −0.344333
\(680\) −16.8665 −0.646802
\(681\) 0 0
\(682\) −0.0118113 −0.000452279 0
\(683\) −29.4074 −1.12524 −0.562621 0.826715i \(-0.690207\pi\)
−0.562621 + 0.826715i \(0.690207\pi\)
\(684\) 0 0
\(685\) 10.4949 0.400989
\(686\) −0.375443 −0.0143345
\(687\) 0 0
\(688\) 1.08362 0.0413127
\(689\) 5.46490 0.208196
\(690\) 0 0
\(691\) −30.7917 −1.17137 −0.585685 0.810539i \(-0.699175\pi\)
−0.585685 + 0.810539i \(0.699175\pi\)
\(692\) 17.0481 0.648071
\(693\) 0 0
\(694\) −1.40340 −0.0532722
\(695\) 4.58051 0.173749
\(696\) 0 0
\(697\) 23.1791 0.877970
\(698\) −5.21471 −0.197380
\(699\) 0 0
\(700\) −2.29388 −0.0867004
\(701\) −18.0737 −0.682636 −0.341318 0.939948i \(-0.610873\pi\)
−0.341318 + 0.939948i \(0.610873\pi\)
\(702\) 0 0
\(703\) −36.0246 −1.35869
\(704\) −0.211684 −0.00797815
\(705\) 0 0
\(706\) −11.0293 −0.415095
\(707\) −11.8979 −0.447467
\(708\) 0 0
\(709\) −16.5066 −0.619919 −0.309960 0.950750i \(-0.600316\pi\)
−0.309960 + 0.950750i \(0.600316\pi\)
\(710\) 4.60654 0.172880
\(711\) 0 0
\(712\) 17.1439 0.642496
\(713\) 3.79843 0.142252
\(714\) 0 0
\(715\) −0.135824 −0.00507952
\(716\) −8.31878 −0.310887
\(717\) 0 0
\(718\) −1.50007 −0.0559821
\(719\) 28.8143 1.07459 0.537296 0.843394i \(-0.319446\pi\)
0.537296 + 0.843394i \(0.319446\pi\)
\(720\) 0 0
\(721\) 3.32884 0.123972
\(722\) −0.659715 −0.0245520
\(723\) 0 0
\(724\) 19.7341 0.733413
\(725\) 6.46308 0.240033
\(726\) 0 0
\(727\) 37.2045 1.37984 0.689920 0.723886i \(-0.257646\pi\)
0.689920 + 0.723886i \(0.257646\pi\)
\(728\) 1.79200 0.0664161
\(729\) 0 0
\(730\) −11.0983 −0.410768
\(731\) 1.59175 0.0588731
\(732\) 0 0
\(733\) 17.7329 0.654980 0.327490 0.944855i \(-0.393797\pi\)
0.327490 + 0.944855i \(0.393797\pi\)
\(734\) 5.95785 0.219908
\(735\) 0 0
\(736\) −21.7165 −0.800480
\(737\) 0.000357042 0 1.31518e−5 0
\(738\) 0 0
\(739\) −15.1053 −0.555658 −0.277829 0.960631i \(-0.589615\pi\)
−0.277829 + 0.960631i \(0.589615\pi\)
\(740\) 36.7015 1.34918
\(741\) 0 0
\(742\) −1.65886 −0.0608988
\(743\) 47.6088 1.74660 0.873299 0.487184i \(-0.161976\pi\)
0.873299 + 0.487184i \(0.161976\pi\)
\(744\) 0 0
\(745\) −36.6298 −1.34201
\(746\) 0.673325 0.0246522
\(747\) 0 0
\(748\) −0.381234 −0.0139393
\(749\) 11.7272 0.428503
\(750\) 0 0
\(751\) 7.36875 0.268890 0.134445 0.990921i \(-0.457075\pi\)
0.134445 + 0.990921i \(0.457075\pi\)
\(752\) −36.3143 −1.32425
\(753\) 0 0
\(754\) −2.43231 −0.0885793
\(755\) −18.2603 −0.664562
\(756\) 0 0
\(757\) −2.31274 −0.0840581 −0.0420291 0.999116i \(-0.513382\pi\)
−0.0420291 + 0.999116i \(0.513382\pi\)
\(758\) −11.5232 −0.418543
\(759\) 0 0
\(760\) 16.4811 0.597834
\(761\) 34.4910 1.25030 0.625149 0.780506i \(-0.285038\pi\)
0.625149 + 0.780506i \(0.285038\pi\)
\(762\) 0 0
\(763\) −12.3647 −0.447631
\(764\) 19.8865 0.719468
\(765\) 0 0
\(766\) −5.24024 −0.189337
\(767\) −12.1033 −0.437026
\(768\) 0 0
\(769\) −42.3387 −1.52677 −0.763387 0.645941i \(-0.776465\pi\)
−0.763387 + 0.645941i \(0.776465\pi\)
\(770\) 0.0412291 0.00148580
\(771\) 0 0
\(772\) −6.36339 −0.229023
\(773\) 35.6992 1.28401 0.642006 0.766700i \(-0.278102\pi\)
0.642006 + 0.766700i \(0.278102\pi\)
\(774\) 0 0
\(775\) 0.882582 0.0317033
\(776\) −12.9998 −0.466666
\(777\) 0 0
\(778\) 11.7951 0.422876
\(779\) −22.6495 −0.811501
\(780\) 0 0
\(781\) 0.216138 0.00773404
\(782\) −9.29599 −0.332424
\(783\) 0 0
\(784\) 3.17413 0.113362
\(785\) −14.1244 −0.504123
\(786\) 0 0
\(787\) −43.8015 −1.56135 −0.780677 0.624935i \(-0.785125\pi\)
−0.780677 + 0.624935i \(0.785125\pi\)
\(788\) 23.4623 0.835808
\(789\) 0 0
\(790\) −1.35567 −0.0482324
\(791\) 11.5463 0.410539
\(792\) 0 0
\(793\) −11.6560 −0.413917
\(794\) −1.55683 −0.0552497
\(795\) 0 0
\(796\) −39.4329 −1.39766
\(797\) 31.2751 1.10782 0.553910 0.832577i \(-0.313135\pi\)
0.553910 + 0.832577i \(0.313135\pi\)
\(798\) 0 0
\(799\) −53.3428 −1.88713
\(800\) −5.04592 −0.178400
\(801\) 0 0
\(802\) 8.65240 0.305527
\(803\) −0.520733 −0.0183763
\(804\) 0 0
\(805\) −13.2590 −0.467317
\(806\) −0.332150 −0.0116995
\(807\) 0 0
\(808\) −17.2383 −0.606441
\(809\) −15.2691 −0.536834 −0.268417 0.963303i \(-0.586501\pi\)
−0.268417 + 0.963303i \(0.586501\pi\)
\(810\) 0 0
\(811\) 12.6537 0.444332 0.222166 0.975009i \(-0.428687\pi\)
0.222166 + 0.975009i \(0.428687\pi\)
\(812\) −9.73752 −0.341720
\(813\) 0 0
\(814\) −0.130569 −0.00457643
\(815\) −40.7684 −1.42806
\(816\) 0 0
\(817\) −1.55538 −0.0544160
\(818\) −3.99110 −0.139546
\(819\) 0 0
\(820\) 23.0751 0.805816
\(821\) −34.4322 −1.20169 −0.600846 0.799365i \(-0.705169\pi\)
−0.600846 + 0.799365i \(0.705169\pi\)
\(822\) 0 0
\(823\) −37.0847 −1.29269 −0.646346 0.763044i \(-0.723704\pi\)
−0.646346 + 0.763044i \(0.723704\pi\)
\(824\) 4.82299 0.168017
\(825\) 0 0
\(826\) 3.67395 0.127833
\(827\) −40.9578 −1.42424 −0.712120 0.702057i \(-0.752265\pi\)
−0.712120 + 0.702057i \(0.752265\pi\)
\(828\) 0 0
\(829\) 38.7169 1.34469 0.672346 0.740237i \(-0.265287\pi\)
0.672346 + 0.740237i \(0.265287\pi\)
\(830\) 7.14317 0.247943
\(831\) 0 0
\(832\) −5.95283 −0.206377
\(833\) 4.66254 0.161547
\(834\) 0 0
\(835\) −32.2857 −1.11729
\(836\) 0.372524 0.0128840
\(837\) 0 0
\(838\) 0.165131 0.00570436
\(839\) −41.1323 −1.42005 −0.710023 0.704179i \(-0.751315\pi\)
−0.710023 + 0.704179i \(0.751315\pi\)
\(840\) 0 0
\(841\) −1.56420 −0.0539380
\(842\) −11.3944 −0.392676
\(843\) 0 0
\(844\) −2.62906 −0.0904959
\(845\) 28.6386 0.985197
\(846\) 0 0
\(847\) −10.9981 −0.377898
\(848\) 14.0246 0.481607
\(849\) 0 0
\(850\) −2.15996 −0.0740862
\(851\) 41.9899 1.43940
\(852\) 0 0
\(853\) −17.8259 −0.610348 −0.305174 0.952297i \(-0.598715\pi\)
−0.305174 + 0.952297i \(0.598715\pi\)
\(854\) 3.53817 0.121074
\(855\) 0 0
\(856\) 16.9910 0.580739
\(857\) 52.7623 1.80233 0.901164 0.433479i \(-0.142714\pi\)
0.901164 + 0.433479i \(0.142714\pi\)
\(858\) 0 0
\(859\) −52.2180 −1.78166 −0.890828 0.454341i \(-0.849875\pi\)
−0.890828 + 0.454341i \(0.849875\pi\)
\(860\) 1.58461 0.0540348
\(861\) 0 0
\(862\) 3.24260 0.110443
\(863\) 16.7285 0.569446 0.284723 0.958610i \(-0.408098\pi\)
0.284723 + 0.958610i \(0.408098\pi\)
\(864\) 0 0
\(865\) 22.8963 0.778499
\(866\) −3.50664 −0.119161
\(867\) 0 0
\(868\) −1.32973 −0.0451340
\(869\) −0.0636077 −0.00215774
\(870\) 0 0
\(871\) 0.0100405 0.000340208 0
\(872\) −17.9146 −0.606664
\(873\) 0 0
\(874\) 9.08359 0.307257
\(875\) 9.40311 0.317883
\(876\) 0 0
\(877\) −3.86764 −0.130601 −0.0653005 0.997866i \(-0.520801\pi\)
−0.0653005 + 0.997866i \(0.520801\pi\)
\(878\) −1.80037 −0.0607596
\(879\) 0 0
\(880\) −0.348566 −0.0117501
\(881\) −22.2193 −0.748586 −0.374293 0.927311i \(-0.622115\pi\)
−0.374293 + 0.927311i \(0.622115\pi\)
\(882\) 0 0
\(883\) −3.75514 −0.126370 −0.0631852 0.998002i \(-0.520126\pi\)
−0.0631852 + 0.998002i \(0.520126\pi\)
\(884\) −10.7208 −0.360579
\(885\) 0 0
\(886\) −3.59662 −0.120831
\(887\) −54.5326 −1.83102 −0.915512 0.402291i \(-0.868214\pi\)
−0.915512 + 0.402291i \(0.868214\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 11.0920 0.371806
\(891\) 0 0
\(892\) 21.6959 0.726432
\(893\) 52.1240 1.74426
\(894\) 0 0
\(895\) −11.1725 −0.373455
\(896\) 9.98578 0.333601
\(897\) 0 0
\(898\) −8.34152 −0.278360
\(899\) 3.74657 0.124955
\(900\) 0 0
\(901\) 20.6010 0.686320
\(902\) −0.0820915 −0.00273335
\(903\) 0 0
\(904\) 16.7288 0.556393
\(905\) 26.5038 0.881017
\(906\) 0 0
\(907\) 42.1002 1.39791 0.698957 0.715163i \(-0.253648\pi\)
0.698957 + 0.715163i \(0.253648\pi\)
\(908\) −12.9841 −0.430891
\(909\) 0 0
\(910\) 1.15942 0.0384343
\(911\) −25.1777 −0.834173 −0.417086 0.908867i \(-0.636949\pi\)
−0.417086 + 0.908867i \(0.636949\pi\)
\(912\) 0 0
\(913\) 0.335157 0.0110921
\(914\) −12.3261 −0.407713
\(915\) 0 0
\(916\) −6.99624 −0.231162
\(917\) −1.63563 −0.0540133
\(918\) 0 0
\(919\) 3.16307 0.104340 0.0521699 0.998638i \(-0.483386\pi\)
0.0521699 + 0.998638i \(0.483386\pi\)
\(920\) −19.2103 −0.633343
\(921\) 0 0
\(922\) −2.87561 −0.0947033
\(923\) 6.07808 0.200063
\(924\) 0 0
\(925\) 9.75654 0.320793
\(926\) −14.3834 −0.472668
\(927\) 0 0
\(928\) −21.4200 −0.703145
\(929\) −14.3412 −0.470519 −0.235260 0.971933i \(-0.575594\pi\)
−0.235260 + 0.971933i \(0.575594\pi\)
\(930\) 0 0
\(931\) −4.55600 −0.149317
\(932\) −11.4712 −0.375752
\(933\) 0 0
\(934\) −13.5014 −0.441780
\(935\) −0.512015 −0.0167447
\(936\) 0 0
\(937\) 42.7371 1.39616 0.698080 0.716020i \(-0.254038\pi\)
0.698080 + 0.716020i \(0.254038\pi\)
\(938\) −0.00304777 −9.95133e−5 0
\(939\) 0 0
\(940\) −53.1035 −1.73205
\(941\) 4.82197 0.157192 0.0785958 0.996907i \(-0.474956\pi\)
0.0785958 + 0.996907i \(0.474956\pi\)
\(942\) 0 0
\(943\) 26.4000 0.859701
\(944\) −31.0609 −1.01095
\(945\) 0 0
\(946\) −0.00563739 −0.000183287 0
\(947\) −14.0659 −0.457080 −0.228540 0.973535i \(-0.573395\pi\)
−0.228540 + 0.973535i \(0.573395\pi\)
\(948\) 0 0
\(949\) −14.6437 −0.475354
\(950\) 2.11061 0.0684773
\(951\) 0 0
\(952\) 6.75531 0.218941
\(953\) −37.8805 −1.22707 −0.613534 0.789668i \(-0.710253\pi\)
−0.613534 + 0.789668i \(0.710253\pi\)
\(954\) 0 0
\(955\) 26.7085 0.864266
\(956\) 9.32731 0.301667
\(957\) 0 0
\(958\) 3.51893 0.113691
\(959\) −4.20337 −0.135734
\(960\) 0 0
\(961\) −30.4884 −0.983496
\(962\) −3.67176 −0.118382
\(963\) 0 0
\(964\) 8.67602 0.279436
\(965\) −8.54631 −0.275116
\(966\) 0 0
\(967\) −4.19261 −0.134825 −0.0674126 0.997725i \(-0.521474\pi\)
−0.0674126 + 0.997725i \(0.521474\pi\)
\(968\) −15.9345 −0.512156
\(969\) 0 0
\(970\) −8.41081 −0.270055
\(971\) −48.6618 −1.56163 −0.780815 0.624762i \(-0.785196\pi\)
−0.780815 + 0.624762i \(0.785196\pi\)
\(972\) 0 0
\(973\) −1.83457 −0.0588135
\(974\) −15.7020 −0.503126
\(975\) 0 0
\(976\) −29.9129 −0.957489
\(977\) 9.44891 0.302297 0.151149 0.988511i \(-0.451703\pi\)
0.151149 + 0.988511i \(0.451703\pi\)
\(978\) 0 0
\(979\) 0.520437 0.0166332
\(980\) 4.64162 0.148271
\(981\) 0 0
\(982\) 5.72200 0.182596
\(983\) 41.1626 1.31288 0.656441 0.754377i \(-0.272061\pi\)
0.656441 + 0.754377i \(0.272061\pi\)
\(984\) 0 0
\(985\) 31.5109 1.00402
\(986\) −9.16906 −0.292002
\(987\) 0 0
\(988\) 10.4758 0.333281
\(989\) 1.81294 0.0576481
\(990\) 0 0
\(991\) −24.3889 −0.774740 −0.387370 0.921924i \(-0.626616\pi\)
−0.387370 + 0.921924i \(0.626616\pi\)
\(992\) −2.92506 −0.0928707
\(993\) 0 0
\(994\) −1.84499 −0.0585197
\(995\) −52.9602 −1.67895
\(996\) 0 0
\(997\) 2.58240 0.0817855 0.0408927 0.999164i \(-0.486980\pi\)
0.0408927 + 0.999164i \(0.486980\pi\)
\(998\) −6.99127 −0.221305
\(999\) 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 \(a_p\))