Properties

Label 8001.2.a.v.1.8
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
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: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.20823\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.20823 q^{2}\) \(-0.540168 q^{4}\) \(-0.486834 q^{5}\) \(+1.00000 q^{7}\) \(+3.06912 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.20823 q^{2}\) \(-0.540168 q^{4}\) \(-0.486834 q^{5}\) \(+1.00000 q^{7}\) \(+3.06912 q^{8}\) \(+0.588209 q^{10}\) \(-3.33645 q^{11}\) \(+2.96046 q^{13}\) \(-1.20823 q^{14}\) \(-2.62788 q^{16}\) \(-0.691924 q^{17}\) \(+0.556445 q^{19}\) \(+0.262972 q^{20}\) \(+4.03122 q^{22}\) \(-4.97719 q^{23}\) \(-4.76299 q^{25}\) \(-3.57693 q^{26}\) \(-0.540168 q^{28}\) \(-1.54090 q^{29}\) \(-1.24157 q^{31}\) \(-2.96314 q^{32}\) \(+0.836007 q^{34}\) \(-0.486834 q^{35}\) \(-7.43380 q^{37}\) \(-0.672316 q^{38}\) \(-1.49415 q^{40}\) \(+5.74868 q^{41}\) \(+9.66027 q^{43}\) \(+1.80225 q^{44}\) \(+6.01361 q^{46}\) \(-4.42787 q^{47}\) \(+1.00000 q^{49}\) \(+5.75481 q^{50}\) \(-1.59915 q^{52}\) \(+3.25257 q^{53}\) \(+1.62430 q^{55}\) \(+3.06912 q^{56}\) \(+1.86177 q^{58}\) \(-10.8233 q^{59}\) \(+9.14746 q^{61}\) \(+1.50011 q^{62}\) \(+8.83593 q^{64}\) \(-1.44125 q^{65}\) \(+10.3697 q^{67}\) \(+0.373756 q^{68}\) \(+0.588209 q^{70}\) \(+2.82644 q^{71}\) \(-4.24827 q^{73}\) \(+8.98178 q^{74}\) \(-0.300574 q^{76}\) \(-3.33645 q^{77}\) \(+13.7939 q^{79}\) \(+1.27934 q^{80}\) \(-6.94576 q^{82}\) \(-0.539810 q^{83}\) \(+0.336852 q^{85}\) \(-11.6719 q^{86}\) \(-10.2400 q^{88}\) \(+9.15032 q^{89}\) \(+2.96046 q^{91}\) \(+2.68852 q^{92}\) \(+5.34991 q^{94}\) \(-0.270896 q^{95}\) \(+11.8201 q^{97}\) \(-1.20823 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20823 −0.854351 −0.427176 0.904169i \(-0.640491\pi\)
−0.427176 + 0.904169i \(0.640491\pi\)
\(3\) 0 0
\(4\) −0.540168 −0.270084
\(5\) −0.486834 −0.217719 −0.108859 0.994057i \(-0.534720\pi\)
−0.108859 + 0.994057i \(0.534720\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 3.06912 1.08510
\(9\) 0 0
\(10\) 0.588209 0.186008
\(11\) −3.33645 −1.00598 −0.502989 0.864293i \(-0.667766\pi\)
−0.502989 + 0.864293i \(0.667766\pi\)
\(12\) 0 0
\(13\) 2.96046 0.821085 0.410542 0.911842i \(-0.365339\pi\)
0.410542 + 0.911842i \(0.365339\pi\)
\(14\) −1.20823 −0.322914
\(15\) 0 0
\(16\) −2.62788 −0.656970
\(17\) −0.691924 −0.167816 −0.0839081 0.996473i \(-0.526740\pi\)
−0.0839081 + 0.996473i \(0.526740\pi\)
\(18\) 0 0
\(19\) 0.556445 0.127657 0.0638286 0.997961i \(-0.479669\pi\)
0.0638286 + 0.997961i \(0.479669\pi\)
\(20\) 0.262972 0.0588024
\(21\) 0 0
\(22\) 4.03122 0.859459
\(23\) −4.97719 −1.03782 −0.518908 0.854830i \(-0.673661\pi\)
−0.518908 + 0.854830i \(0.673661\pi\)
\(24\) 0 0
\(25\) −4.76299 −0.952599
\(26\) −3.57693 −0.701495
\(27\) 0 0
\(28\) −0.540168 −0.102082
\(29\) −1.54090 −0.286138 −0.143069 0.989713i \(-0.545697\pi\)
−0.143069 + 0.989713i \(0.545697\pi\)
\(30\) 0 0
\(31\) −1.24157 −0.222993 −0.111497 0.993765i \(-0.535564\pi\)
−0.111497 + 0.993765i \(0.535564\pi\)
\(32\) −2.96314 −0.523814
\(33\) 0 0
\(34\) 0.836007 0.143374
\(35\) −0.486834 −0.0822899
\(36\) 0 0
\(37\) −7.43380 −1.22211 −0.611055 0.791588i \(-0.709254\pi\)
−0.611055 + 0.791588i \(0.709254\pi\)
\(38\) −0.672316 −0.109064
\(39\) 0 0
\(40\) −1.49415 −0.236246
\(41\) 5.74868 0.897793 0.448897 0.893584i \(-0.351817\pi\)
0.448897 + 0.893584i \(0.351817\pi\)
\(42\) 0 0
\(43\) 9.66027 1.47318 0.736588 0.676341i \(-0.236436\pi\)
0.736588 + 0.676341i \(0.236436\pi\)
\(44\) 1.80225 0.271699
\(45\) 0 0
\(46\) 6.01361 0.886659
\(47\) −4.42787 −0.645872 −0.322936 0.946421i \(-0.604670\pi\)
−0.322936 + 0.946421i \(0.604670\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 5.75481 0.813854
\(51\) 0 0
\(52\) −1.59915 −0.221762
\(53\) 3.25257 0.446775 0.223388 0.974730i \(-0.428288\pi\)
0.223388 + 0.974730i \(0.428288\pi\)
\(54\) 0 0
\(55\) 1.62430 0.219020
\(56\) 3.06912 0.410128
\(57\) 0 0
\(58\) 1.86177 0.244462
\(59\) −10.8233 −1.40907 −0.704535 0.709669i \(-0.748844\pi\)
−0.704535 + 0.709669i \(0.748844\pi\)
\(60\) 0 0
\(61\) 9.14746 1.17121 0.585606 0.810596i \(-0.300856\pi\)
0.585606 + 0.810596i \(0.300856\pi\)
\(62\) 1.50011 0.190515
\(63\) 0 0
\(64\) 8.83593 1.10449
\(65\) −1.44125 −0.178765
\(66\) 0 0
\(67\) 10.3697 1.26686 0.633430 0.773800i \(-0.281647\pi\)
0.633430 + 0.773800i \(0.281647\pi\)
\(68\) 0.373756 0.0453245
\(69\) 0 0
\(70\) 0.588209 0.0703045
\(71\) 2.82644 0.335437 0.167718 0.985835i \(-0.446360\pi\)
0.167718 + 0.985835i \(0.446360\pi\)
\(72\) 0 0
\(73\) −4.24827 −0.497222 −0.248611 0.968603i \(-0.579974\pi\)
−0.248611 + 0.968603i \(0.579974\pi\)
\(74\) 8.98178 1.04411
\(75\) 0 0
\(76\) −0.300574 −0.0344782
\(77\) −3.33645 −0.380224
\(78\) 0 0
\(79\) 13.7939 1.55193 0.775965 0.630776i \(-0.217263\pi\)
0.775965 + 0.630776i \(0.217263\pi\)
\(80\) 1.27934 0.143035
\(81\) 0 0
\(82\) −6.94576 −0.767031
\(83\) −0.539810 −0.0592519 −0.0296259 0.999561i \(-0.509432\pi\)
−0.0296259 + 0.999561i \(0.509432\pi\)
\(84\) 0 0
\(85\) 0.336852 0.0365367
\(86\) −11.6719 −1.25861
\(87\) 0 0
\(88\) −10.2400 −1.09158
\(89\) 9.15032 0.969932 0.484966 0.874533i \(-0.338832\pi\)
0.484966 + 0.874533i \(0.338832\pi\)
\(90\) 0 0
\(91\) 2.96046 0.310341
\(92\) 2.68852 0.280297
\(93\) 0 0
\(94\) 5.34991 0.551801
\(95\) −0.270896 −0.0277933
\(96\) 0 0
\(97\) 11.8201 1.20015 0.600075 0.799944i \(-0.295137\pi\)
0.600075 + 0.799944i \(0.295137\pi\)
\(98\) −1.20823 −0.122050
\(99\) 0 0
\(100\) 2.57282 0.257282
\(101\) −11.7839 −1.17255 −0.586273 0.810113i \(-0.699405\pi\)
−0.586273 + 0.810113i \(0.699405\pi\)
\(102\) 0 0
\(103\) −6.48469 −0.638955 −0.319478 0.947594i \(-0.603507\pi\)
−0.319478 + 0.947594i \(0.603507\pi\)
\(104\) 9.08602 0.890957
\(105\) 0 0
\(106\) −3.92987 −0.381703
\(107\) −7.40352 −0.715725 −0.357863 0.933774i \(-0.616494\pi\)
−0.357863 + 0.933774i \(0.616494\pi\)
\(108\) 0 0
\(109\) −14.4941 −1.38828 −0.694141 0.719839i \(-0.744216\pi\)
−0.694141 + 0.719839i \(0.744216\pi\)
\(110\) −1.96253 −0.187120
\(111\) 0 0
\(112\) −2.62788 −0.248311
\(113\) −12.1032 −1.13858 −0.569289 0.822138i \(-0.692781\pi\)
−0.569289 + 0.822138i \(0.692781\pi\)
\(114\) 0 0
\(115\) 2.42306 0.225952
\(116\) 0.832346 0.0772814
\(117\) 0 0
\(118\) 13.0771 1.20384
\(119\) −0.691924 −0.0634286
\(120\) 0 0
\(121\) 0.131916 0.0119924
\(122\) −11.0523 −1.00063
\(123\) 0 0
\(124\) 0.670660 0.0602270
\(125\) 4.75295 0.425117
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −4.74960 −0.419809
\(129\) 0 0
\(130\) 1.74137 0.152728
\(131\) 11.3196 0.988996 0.494498 0.869179i \(-0.335352\pi\)
0.494498 + 0.869179i \(0.335352\pi\)
\(132\) 0 0
\(133\) 0.556445 0.0482499
\(134\) −12.5290 −1.08234
\(135\) 0 0
\(136\) −2.12360 −0.182097
\(137\) −1.75217 −0.149698 −0.0748490 0.997195i \(-0.523847\pi\)
−0.0748490 + 0.997195i \(0.523847\pi\)
\(138\) 0 0
\(139\) −12.3362 −1.04634 −0.523169 0.852229i \(-0.675251\pi\)
−0.523169 + 0.852229i \(0.675251\pi\)
\(140\) 0.262972 0.0222252
\(141\) 0 0
\(142\) −3.41500 −0.286581
\(143\) −9.87744 −0.825993
\(144\) 0 0
\(145\) 0.750163 0.0622976
\(146\) 5.13290 0.424802
\(147\) 0 0
\(148\) 4.01550 0.330072
\(149\) −0.292352 −0.0239504 −0.0119752 0.999928i \(-0.503812\pi\)
−0.0119752 + 0.999928i \(0.503812\pi\)
\(150\) 0 0
\(151\) 11.0695 0.900821 0.450411 0.892822i \(-0.351278\pi\)
0.450411 + 0.892822i \(0.351278\pi\)
\(152\) 1.70780 0.138521
\(153\) 0 0
\(154\) 4.03122 0.324845
\(155\) 0.604441 0.0485498
\(156\) 0 0
\(157\) −9.72904 −0.776462 −0.388231 0.921562i \(-0.626914\pi\)
−0.388231 + 0.921562i \(0.626914\pi\)
\(158\) −16.6662 −1.32589
\(159\) 0 0
\(160\) 1.44256 0.114044
\(161\) −4.97719 −0.392257
\(162\) 0 0
\(163\) −23.7172 −1.85768 −0.928839 0.370484i \(-0.879192\pi\)
−0.928839 + 0.370484i \(0.879192\pi\)
\(164\) −3.10526 −0.242480
\(165\) 0 0
\(166\) 0.652217 0.0506219
\(167\) 12.0490 0.932380 0.466190 0.884685i \(-0.345626\pi\)
0.466190 + 0.884685i \(0.345626\pi\)
\(168\) 0 0
\(169\) −4.23566 −0.325820
\(170\) −0.406996 −0.0312152
\(171\) 0 0
\(172\) −5.21817 −0.397882
\(173\) 13.0592 0.992872 0.496436 0.868073i \(-0.334642\pi\)
0.496436 + 0.868073i \(0.334642\pi\)
\(174\) 0 0
\(175\) −4.76299 −0.360048
\(176\) 8.76780 0.660898
\(177\) 0 0
\(178\) −11.0557 −0.828662
\(179\) 11.7072 0.875040 0.437520 0.899209i \(-0.355857\pi\)
0.437520 + 0.899209i \(0.355857\pi\)
\(180\) 0 0
\(181\) 23.3643 1.73666 0.868329 0.495988i \(-0.165194\pi\)
0.868329 + 0.495988i \(0.165194\pi\)
\(182\) −3.57693 −0.265140
\(183\) 0 0
\(184\) −15.2756 −1.12613
\(185\) 3.61903 0.266076
\(186\) 0 0
\(187\) 2.30857 0.168820
\(188\) 2.39180 0.174440
\(189\) 0 0
\(190\) 0.327306 0.0237453
\(191\) −7.47087 −0.540573 −0.270287 0.962780i \(-0.587118\pi\)
−0.270287 + 0.962780i \(0.587118\pi\)
\(192\) 0 0
\(193\) 2.23193 0.160658 0.0803291 0.996768i \(-0.474403\pi\)
0.0803291 + 0.996768i \(0.474403\pi\)
\(194\) −14.2815 −1.02535
\(195\) 0 0
\(196\) −0.540168 −0.0385835
\(197\) 24.6516 1.75636 0.878179 0.478333i \(-0.158759\pi\)
0.878179 + 0.478333i \(0.158759\pi\)
\(198\) 0 0
\(199\) 5.25622 0.372604 0.186302 0.982493i \(-0.440350\pi\)
0.186302 + 0.982493i \(0.440350\pi\)
\(200\) −14.6182 −1.03366
\(201\) 0 0
\(202\) 14.2378 1.00177
\(203\) −1.54090 −0.108150
\(204\) 0 0
\(205\) −2.79865 −0.195466
\(206\) 7.83502 0.545892
\(207\) 0 0
\(208\) −7.77974 −0.539428
\(209\) −1.85655 −0.128420
\(210\) 0 0
\(211\) −25.9511 −1.78655 −0.893274 0.449513i \(-0.851598\pi\)
−0.893274 + 0.449513i \(0.851598\pi\)
\(212\) −1.75694 −0.120667
\(213\) 0 0
\(214\) 8.94519 0.611481
\(215\) −4.70294 −0.320738
\(216\) 0 0
\(217\) −1.24157 −0.0842836
\(218\) 17.5123 1.18608
\(219\) 0 0
\(220\) −0.877394 −0.0591539
\(221\) −2.04842 −0.137791
\(222\) 0 0
\(223\) −5.08231 −0.340337 −0.170168 0.985415i \(-0.554431\pi\)
−0.170168 + 0.985415i \(0.554431\pi\)
\(224\) −2.96314 −0.197983
\(225\) 0 0
\(226\) 14.6236 0.972745
\(227\) 27.3641 1.81622 0.908111 0.418729i \(-0.137524\pi\)
0.908111 + 0.418729i \(0.137524\pi\)
\(228\) 0 0
\(229\) −19.5981 −1.29508 −0.647540 0.762031i \(-0.724202\pi\)
−0.647540 + 0.762031i \(0.724202\pi\)
\(230\) −2.92763 −0.193042
\(231\) 0 0
\(232\) −4.72921 −0.310488
\(233\) 1.12255 0.0735409 0.0367705 0.999324i \(-0.488293\pi\)
0.0367705 + 0.999324i \(0.488293\pi\)
\(234\) 0 0
\(235\) 2.15564 0.140618
\(236\) 5.84639 0.380568
\(237\) 0 0
\(238\) 0.836007 0.0541903
\(239\) −20.6348 −1.33476 −0.667378 0.744719i \(-0.732584\pi\)
−0.667378 + 0.744719i \(0.732584\pi\)
\(240\) 0 0
\(241\) 16.6369 1.07168 0.535838 0.844321i \(-0.319996\pi\)
0.535838 + 0.844321i \(0.319996\pi\)
\(242\) −0.159386 −0.0102457
\(243\) 0 0
\(244\) −4.94117 −0.316326
\(245\) −0.486834 −0.0311027
\(246\) 0 0
\(247\) 1.64733 0.104817
\(248\) −3.81054 −0.241970
\(249\) 0 0
\(250\) −5.74268 −0.363199
\(251\) 9.39146 0.592784 0.296392 0.955066i \(-0.404217\pi\)
0.296392 + 0.955066i \(0.404217\pi\)
\(252\) 0 0
\(253\) 16.6061 1.04402
\(254\) −1.20823 −0.0758114
\(255\) 0 0
\(256\) −11.9332 −0.745827
\(257\) 16.5814 1.03432 0.517159 0.855889i \(-0.326990\pi\)
0.517159 + 0.855889i \(0.326990\pi\)
\(258\) 0 0
\(259\) −7.43380 −0.461914
\(260\) 0.778519 0.0482817
\(261\) 0 0
\(262\) −13.6767 −0.844950
\(263\) 29.0182 1.78934 0.894668 0.446731i \(-0.147412\pi\)
0.894668 + 0.446731i \(0.147412\pi\)
\(264\) 0 0
\(265\) −1.58346 −0.0972714
\(266\) −0.672316 −0.0412223
\(267\) 0 0
\(268\) −5.60138 −0.342159
\(269\) 1.32881 0.0810187 0.0405093 0.999179i \(-0.487102\pi\)
0.0405093 + 0.999179i \(0.487102\pi\)
\(270\) 0 0
\(271\) 17.7182 1.07630 0.538152 0.842848i \(-0.319122\pi\)
0.538152 + 0.842848i \(0.319122\pi\)
\(272\) 1.81829 0.110250
\(273\) 0 0
\(274\) 2.11703 0.127895
\(275\) 15.8915 0.958294
\(276\) 0 0
\(277\) −24.1077 −1.44849 −0.724247 0.689540i \(-0.757813\pi\)
−0.724247 + 0.689540i \(0.757813\pi\)
\(278\) 14.9050 0.893941
\(279\) 0 0
\(280\) −1.49415 −0.0892926
\(281\) −13.8431 −0.825810 −0.412905 0.910774i \(-0.635486\pi\)
−0.412905 + 0.910774i \(0.635486\pi\)
\(282\) 0 0
\(283\) 15.6326 0.929260 0.464630 0.885505i \(-0.346187\pi\)
0.464630 + 0.885505i \(0.346187\pi\)
\(284\) −1.52675 −0.0905961
\(285\) 0 0
\(286\) 11.9343 0.705688
\(287\) 5.74868 0.339334
\(288\) 0 0
\(289\) −16.5212 −0.971838
\(290\) −0.906373 −0.0532240
\(291\) 0 0
\(292\) 2.29478 0.134292
\(293\) −10.3552 −0.604955 −0.302477 0.953157i \(-0.597814\pi\)
−0.302477 + 0.953157i \(0.597814\pi\)
\(294\) 0 0
\(295\) 5.26913 0.306781
\(296\) −22.8152 −1.32611
\(297\) 0 0
\(298\) 0.353230 0.0204620
\(299\) −14.7348 −0.852134
\(300\) 0 0
\(301\) 9.66027 0.556808
\(302\) −13.3745 −0.769618
\(303\) 0 0
\(304\) −1.46227 −0.0838670
\(305\) −4.45329 −0.254995
\(306\) 0 0
\(307\) 7.23631 0.412998 0.206499 0.978447i \(-0.433793\pi\)
0.206499 + 0.978447i \(0.433793\pi\)
\(308\) 1.80225 0.102693
\(309\) 0 0
\(310\) −0.730306 −0.0414786
\(311\) 23.7205 1.34507 0.672533 0.740068i \(-0.265207\pi\)
0.672533 + 0.740068i \(0.265207\pi\)
\(312\) 0 0
\(313\) 30.9911 1.75172 0.875860 0.482566i \(-0.160295\pi\)
0.875860 + 0.482566i \(0.160295\pi\)
\(314\) 11.7550 0.663371
\(315\) 0 0
\(316\) −7.45100 −0.419152
\(317\) −5.13371 −0.288338 −0.144169 0.989553i \(-0.546051\pi\)
−0.144169 + 0.989553i \(0.546051\pi\)
\(318\) 0 0
\(319\) 5.14114 0.287849
\(320\) −4.30163 −0.240468
\(321\) 0 0
\(322\) 6.01361 0.335125
\(323\) −0.385018 −0.0214229
\(324\) 0 0
\(325\) −14.1007 −0.782164
\(326\) 28.6560 1.58711
\(327\) 0 0
\(328\) 17.6434 0.974193
\(329\) −4.42787 −0.244117
\(330\) 0 0
\(331\) 25.3612 1.39398 0.696989 0.717082i \(-0.254523\pi\)
0.696989 + 0.717082i \(0.254523\pi\)
\(332\) 0.291588 0.0160030
\(333\) 0 0
\(334\) −14.5580 −0.796580
\(335\) −5.04831 −0.275819
\(336\) 0 0
\(337\) −30.9030 −1.68339 −0.841696 0.539952i \(-0.818442\pi\)
−0.841696 + 0.539952i \(0.818442\pi\)
\(338\) 5.11767 0.278365
\(339\) 0 0
\(340\) −0.181957 −0.00986799
\(341\) 4.14246 0.224327
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 29.6485 1.59854
\(345\) 0 0
\(346\) −15.7786 −0.848261
\(347\) 12.4171 0.666587 0.333293 0.942823i \(-0.391840\pi\)
0.333293 + 0.942823i \(0.391840\pi\)
\(348\) 0 0
\(349\) 17.2201 0.921768 0.460884 0.887460i \(-0.347532\pi\)
0.460884 + 0.887460i \(0.347532\pi\)
\(350\) 5.75481 0.307608
\(351\) 0 0
\(352\) 9.88638 0.526946
\(353\) −12.0591 −0.641841 −0.320921 0.947106i \(-0.603992\pi\)
−0.320921 + 0.947106i \(0.603992\pi\)
\(354\) 0 0
\(355\) −1.37601 −0.0730308
\(356\) −4.94271 −0.261963
\(357\) 0 0
\(358\) −14.1451 −0.747592
\(359\) 3.14917 0.166207 0.0831035 0.996541i \(-0.473517\pi\)
0.0831035 + 0.996541i \(0.473517\pi\)
\(360\) 0 0
\(361\) −18.6904 −0.983704
\(362\) −28.2296 −1.48372
\(363\) 0 0
\(364\) −1.59915 −0.0838181
\(365\) 2.06820 0.108254
\(366\) 0 0
\(367\) −18.4980 −0.965589 −0.482794 0.875734i \(-0.660378\pi\)
−0.482794 + 0.875734i \(0.660378\pi\)
\(368\) 13.0795 0.681814
\(369\) 0 0
\(370\) −4.37263 −0.227322
\(371\) 3.25257 0.168865
\(372\) 0 0
\(373\) 3.34770 0.173337 0.0866686 0.996237i \(-0.472378\pi\)
0.0866686 + 0.996237i \(0.472378\pi\)
\(374\) −2.78930 −0.144231
\(375\) 0 0
\(376\) −13.5897 −0.700834
\(377\) −4.56178 −0.234944
\(378\) 0 0
\(379\) 6.87229 0.353006 0.176503 0.984300i \(-0.443522\pi\)
0.176503 + 0.984300i \(0.443522\pi\)
\(380\) 0.146329 0.00750654
\(381\) 0 0
\(382\) 9.02657 0.461839
\(383\) −3.87185 −0.197842 −0.0989210 0.995095i \(-0.531539\pi\)
−0.0989210 + 0.995095i \(0.531539\pi\)
\(384\) 0 0
\(385\) 1.62430 0.0827819
\(386\) −2.69670 −0.137258
\(387\) 0 0
\(388\) −6.38485 −0.324142
\(389\) 23.9772 1.21569 0.607847 0.794054i \(-0.292034\pi\)
0.607847 + 0.794054i \(0.292034\pi\)
\(390\) 0 0
\(391\) 3.44384 0.174162
\(392\) 3.06912 0.155014
\(393\) 0 0
\(394\) −29.7850 −1.50055
\(395\) −6.71531 −0.337884
\(396\) 0 0
\(397\) 9.65076 0.484358 0.242179 0.970232i \(-0.422138\pi\)
0.242179 + 0.970232i \(0.422138\pi\)
\(398\) −6.35075 −0.318334
\(399\) 0 0
\(400\) 12.5166 0.625829
\(401\) 2.46700 0.123196 0.0615981 0.998101i \(-0.480380\pi\)
0.0615981 + 0.998101i \(0.480380\pi\)
\(402\) 0 0
\(403\) −3.67564 −0.183096
\(404\) 6.36531 0.316686
\(405\) 0 0
\(406\) 1.86177 0.0923981
\(407\) 24.8025 1.22942
\(408\) 0 0
\(409\) −21.4104 −1.05867 −0.529337 0.848412i \(-0.677559\pi\)
−0.529337 + 0.848412i \(0.677559\pi\)
\(410\) 3.38143 0.166997
\(411\) 0 0
\(412\) 3.50282 0.172572
\(413\) −10.8233 −0.532578
\(414\) 0 0
\(415\) 0.262798 0.0129002
\(416\) −8.77227 −0.430096
\(417\) 0 0
\(418\) 2.24315 0.109716
\(419\) −31.1401 −1.52129 −0.760646 0.649167i \(-0.775118\pi\)
−0.760646 + 0.649167i \(0.775118\pi\)
\(420\) 0 0
\(421\) −4.42223 −0.215526 −0.107763 0.994177i \(-0.534369\pi\)
−0.107763 + 0.994177i \(0.534369\pi\)
\(422\) 31.3550 1.52634
\(423\) 0 0
\(424\) 9.98254 0.484795
\(425\) 3.29563 0.159862
\(426\) 0 0
\(427\) 9.14746 0.442677
\(428\) 3.99915 0.193306
\(429\) 0 0
\(430\) 5.68226 0.274023
\(431\) 17.2618 0.831473 0.415737 0.909485i \(-0.363524\pi\)
0.415737 + 0.909485i \(0.363524\pi\)
\(432\) 0 0
\(433\) 36.4416 1.75127 0.875635 0.482973i \(-0.160443\pi\)
0.875635 + 0.482973i \(0.160443\pi\)
\(434\) 1.50011 0.0720078
\(435\) 0 0
\(436\) 7.82925 0.374953
\(437\) −2.76953 −0.132485
\(438\) 0 0
\(439\) −13.2699 −0.633337 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(440\) 4.98516 0.237658
\(441\) 0 0
\(442\) 2.47497 0.117722
\(443\) −13.3154 −0.632635 −0.316318 0.948653i \(-0.602447\pi\)
−0.316318 + 0.948653i \(0.602447\pi\)
\(444\) 0 0
\(445\) −4.45468 −0.211172
\(446\) 6.14063 0.290767
\(447\) 0 0
\(448\) 8.83593 0.417459
\(449\) 30.8559 1.45618 0.728089 0.685483i \(-0.240409\pi\)
0.728089 + 0.685483i \(0.240409\pi\)
\(450\) 0 0
\(451\) −19.1802 −0.903161
\(452\) 6.53779 0.307512
\(453\) 0 0
\(454\) −33.0623 −1.55169
\(455\) −1.44125 −0.0675670
\(456\) 0 0
\(457\) 14.5223 0.679323 0.339662 0.940548i \(-0.389687\pi\)
0.339662 + 0.940548i \(0.389687\pi\)
\(458\) 23.6791 1.10645
\(459\) 0 0
\(460\) −1.30886 −0.0610260
\(461\) −19.4555 −0.906135 −0.453068 0.891476i \(-0.649670\pi\)
−0.453068 + 0.891476i \(0.649670\pi\)
\(462\) 0 0
\(463\) 40.8834 1.90001 0.950007 0.312229i \(-0.101076\pi\)
0.950007 + 0.312229i \(0.101076\pi\)
\(464\) 4.04931 0.187984
\(465\) 0 0
\(466\) −1.35631 −0.0628298
\(467\) 22.7282 1.05174 0.525869 0.850566i \(-0.323740\pi\)
0.525869 + 0.850566i \(0.323740\pi\)
\(468\) 0 0
\(469\) 10.3697 0.478828
\(470\) −2.60452 −0.120137
\(471\) 0 0
\(472\) −33.2179 −1.52898
\(473\) −32.2310 −1.48198
\(474\) 0 0
\(475\) −2.65034 −0.121606
\(476\) 0.373756 0.0171311
\(477\) 0 0
\(478\) 24.9317 1.14035
\(479\) 20.8734 0.953729 0.476865 0.878977i \(-0.341773\pi\)
0.476865 + 0.878977i \(0.341773\pi\)
\(480\) 0 0
\(481\) −22.0075 −1.00346
\(482\) −20.1012 −0.915587
\(483\) 0 0
\(484\) −0.0712570 −0.00323896
\(485\) −5.75443 −0.261295
\(486\) 0 0
\(487\) −9.56100 −0.433250 −0.216625 0.976255i \(-0.569505\pi\)
−0.216625 + 0.976255i \(0.569505\pi\)
\(488\) 28.0747 1.27088
\(489\) 0 0
\(490\) 0.588209 0.0265726
\(491\) 33.1329 1.49527 0.747634 0.664111i \(-0.231190\pi\)
0.747634 + 0.664111i \(0.231190\pi\)
\(492\) 0 0
\(493\) 1.06619 0.0480186
\(494\) −1.99037 −0.0895508
\(495\) 0 0
\(496\) 3.26271 0.146500
\(497\) 2.82644 0.126783
\(498\) 0 0
\(499\) −3.65216 −0.163493 −0.0817467 0.996653i \(-0.526050\pi\)
−0.0817467 + 0.996653i \(0.526050\pi\)
\(500\) −2.56740 −0.114817
\(501\) 0 0
\(502\) −11.3471 −0.506445
\(503\) 21.5098 0.959075 0.479537 0.877521i \(-0.340805\pi\)
0.479537 + 0.877521i \(0.340805\pi\)
\(504\) 0 0
\(505\) 5.73682 0.255285
\(506\) −20.0641 −0.891959
\(507\) 0 0
\(508\) −0.540168 −0.0239661
\(509\) −0.500742 −0.0221950 −0.0110975 0.999938i \(-0.503533\pi\)
−0.0110975 + 0.999938i \(0.503533\pi\)
\(510\) 0 0
\(511\) −4.24827 −0.187932
\(512\) 23.9174 1.05701
\(513\) 0 0
\(514\) −20.0342 −0.883671
\(515\) 3.15696 0.139112
\(516\) 0 0
\(517\) 14.7734 0.649733
\(518\) 8.98178 0.394637
\(519\) 0 0
\(520\) −4.42338 −0.193978
\(521\) 38.1592 1.67179 0.835893 0.548893i \(-0.184950\pi\)
0.835893 + 0.548893i \(0.184950\pi\)
\(522\) 0 0
\(523\) 34.7513 1.51957 0.759783 0.650176i \(-0.225305\pi\)
0.759783 + 0.650176i \(0.225305\pi\)
\(524\) −6.11448 −0.267112
\(525\) 0 0
\(526\) −35.0608 −1.52872
\(527\) 0.859076 0.0374219
\(528\) 0 0
\(529\) 1.77239 0.0770606
\(530\) 1.91320 0.0831039
\(531\) 0 0
\(532\) −0.300574 −0.0130315
\(533\) 17.0188 0.737164
\(534\) 0 0
\(535\) 3.60428 0.155827
\(536\) 31.8258 1.37467
\(537\) 0 0
\(538\) −1.60551 −0.0692184
\(539\) −3.33645 −0.143711
\(540\) 0 0
\(541\) −24.4412 −1.05081 −0.525405 0.850852i \(-0.676086\pi\)
−0.525405 + 0.850852i \(0.676086\pi\)
\(542\) −21.4078 −0.919542
\(543\) 0 0
\(544\) 2.05027 0.0879046
\(545\) 7.05621 0.302255
\(546\) 0 0
\(547\) 0.0873940 0.00373670 0.00186835 0.999998i \(-0.499405\pi\)
0.00186835 + 0.999998i \(0.499405\pi\)
\(548\) 0.946467 0.0404311
\(549\) 0 0
\(550\) −19.2007 −0.818719
\(551\) −0.857426 −0.0365276
\(552\) 0 0
\(553\) 13.7939 0.586574
\(554\) 29.1278 1.23752
\(555\) 0 0
\(556\) 6.66360 0.282600
\(557\) 33.8597 1.43468 0.717342 0.696721i \(-0.245359\pi\)
0.717342 + 0.696721i \(0.245359\pi\)
\(558\) 0 0
\(559\) 28.5989 1.20960
\(560\) 1.27934 0.0540620
\(561\) 0 0
\(562\) 16.7257 0.705532
\(563\) −13.7648 −0.580116 −0.290058 0.957009i \(-0.593675\pi\)
−0.290058 + 0.957009i \(0.593675\pi\)
\(564\) 0 0
\(565\) 5.89227 0.247890
\(566\) −18.8878 −0.793914
\(567\) 0 0
\(568\) 8.67468 0.363982
\(569\) −22.2522 −0.932861 −0.466431 0.884558i \(-0.654460\pi\)
−0.466431 + 0.884558i \(0.654460\pi\)
\(570\) 0 0
\(571\) 15.4552 0.646779 0.323389 0.946266i \(-0.395178\pi\)
0.323389 + 0.946266i \(0.395178\pi\)
\(572\) 5.33548 0.223088
\(573\) 0 0
\(574\) −6.94576 −0.289910
\(575\) 23.7063 0.988621
\(576\) 0 0
\(577\) 38.8006 1.61529 0.807645 0.589670i \(-0.200742\pi\)
0.807645 + 0.589670i \(0.200742\pi\)
\(578\) 19.9615 0.830291
\(579\) 0 0
\(580\) −0.405214 −0.0168256
\(581\) −0.539810 −0.0223951
\(582\) 0 0
\(583\) −10.8521 −0.449446
\(584\) −13.0384 −0.539534
\(585\) 0 0
\(586\) 12.5115 0.516844
\(587\) −0.382995 −0.0158079 −0.00790394 0.999969i \(-0.502516\pi\)
−0.00790394 + 0.999969i \(0.502516\pi\)
\(588\) 0 0
\(589\) −0.690868 −0.0284667
\(590\) −6.36635 −0.262099
\(591\) 0 0
\(592\) 19.5351 0.802890
\(593\) −16.2475 −0.667205 −0.333602 0.942714i \(-0.608264\pi\)
−0.333602 + 0.942714i \(0.608264\pi\)
\(594\) 0 0
\(595\) 0.336852 0.0138096
\(596\) 0.157919 0.00646862
\(597\) 0 0
\(598\) 17.8031 0.728022
\(599\) −18.6566 −0.762289 −0.381144 0.924516i \(-0.624470\pi\)
−0.381144 + 0.924516i \(0.624470\pi\)
\(600\) 0 0
\(601\) 9.10957 0.371587 0.185794 0.982589i \(-0.440514\pi\)
0.185794 + 0.982589i \(0.440514\pi\)
\(602\) −11.6719 −0.475710
\(603\) 0 0
\(604\) −5.97938 −0.243298
\(605\) −0.0642213 −0.00261097
\(606\) 0 0
\(607\) 26.7513 1.08580 0.542902 0.839796i \(-0.317326\pi\)
0.542902 + 0.839796i \(0.317326\pi\)
\(608\) −1.64882 −0.0668687
\(609\) 0 0
\(610\) 5.38063 0.217855
\(611\) −13.1086 −0.530315
\(612\) 0 0
\(613\) 35.0822 1.41696 0.708478 0.705733i \(-0.249382\pi\)
0.708478 + 0.705733i \(0.249382\pi\)
\(614\) −8.74317 −0.352845
\(615\) 0 0
\(616\) −10.2400 −0.412580
\(617\) 2.43811 0.0981545 0.0490773 0.998795i \(-0.484372\pi\)
0.0490773 + 0.998795i \(0.484372\pi\)
\(618\) 0 0
\(619\) 15.1723 0.609828 0.304914 0.952380i \(-0.401372\pi\)
0.304914 + 0.952380i \(0.401372\pi\)
\(620\) −0.326500 −0.0131125
\(621\) 0 0
\(622\) −28.6599 −1.14916
\(623\) 9.15032 0.366600
\(624\) 0 0
\(625\) 21.5011 0.860043
\(626\) −37.4445 −1.49658
\(627\) 0 0
\(628\) 5.25532 0.209710
\(629\) 5.14363 0.205090
\(630\) 0 0
\(631\) −10.2068 −0.406325 −0.203162 0.979145i \(-0.565122\pi\)
−0.203162 + 0.979145i \(0.565122\pi\)
\(632\) 42.3350 1.68400
\(633\) 0 0
\(634\) 6.20273 0.246342
\(635\) −0.486834 −0.0193194
\(636\) 0 0
\(637\) 2.96046 0.117298
\(638\) −6.21171 −0.245924
\(639\) 0 0
\(640\) 2.31227 0.0914003
\(641\) 26.5871 1.05013 0.525063 0.851063i \(-0.324042\pi\)
0.525063 + 0.851063i \(0.324042\pi\)
\(642\) 0 0
\(643\) 18.5503 0.731552 0.365776 0.930703i \(-0.380804\pi\)
0.365776 + 0.930703i \(0.380804\pi\)
\(644\) 2.68852 0.105942
\(645\) 0 0
\(646\) 0.465192 0.0183027
\(647\) −29.1301 −1.14522 −0.572612 0.819826i \(-0.694070\pi\)
−0.572612 + 0.819826i \(0.694070\pi\)
\(648\) 0 0
\(649\) 36.1113 1.41749
\(650\) 17.0369 0.668243
\(651\) 0 0
\(652\) 12.8113 0.501729
\(653\) −11.0653 −0.433020 −0.216510 0.976280i \(-0.569467\pi\)
−0.216510 + 0.976280i \(0.569467\pi\)
\(654\) 0 0
\(655\) −5.51075 −0.215323
\(656\) −15.1069 −0.589824
\(657\) 0 0
\(658\) 5.34991 0.208561
\(659\) 23.4739 0.914414 0.457207 0.889360i \(-0.348850\pi\)
0.457207 + 0.889360i \(0.348850\pi\)
\(660\) 0 0
\(661\) 23.1407 0.900069 0.450035 0.893011i \(-0.351412\pi\)
0.450035 + 0.893011i \(0.351412\pi\)
\(662\) −30.6423 −1.19095
\(663\) 0 0
\(664\) −1.65674 −0.0642941
\(665\) −0.270896 −0.0105049
\(666\) 0 0
\(667\) 7.66935 0.296959
\(668\) −6.50849 −0.251821
\(669\) 0 0
\(670\) 6.09955 0.235646
\(671\) −30.5201 −1.17821
\(672\) 0 0
\(673\) −49.6462 −1.91372 −0.956860 0.290551i \(-0.906162\pi\)
−0.956860 + 0.290551i \(0.906162\pi\)
\(674\) 37.3380 1.43821
\(675\) 0 0
\(676\) 2.28797 0.0879989
\(677\) 28.5588 1.09760 0.548802 0.835952i \(-0.315084\pi\)
0.548802 + 0.835952i \(0.315084\pi\)
\(678\) 0 0
\(679\) 11.8201 0.453614
\(680\) 1.03384 0.0396459
\(681\) 0 0
\(682\) −5.00506 −0.191654
\(683\) 29.1869 1.11680 0.558402 0.829570i \(-0.311415\pi\)
0.558402 + 0.829570i \(0.311415\pi\)
\(684\) 0 0
\(685\) 0.853016 0.0325921
\(686\) −1.20823 −0.0461306
\(687\) 0 0
\(688\) −25.3860 −0.967833
\(689\) 9.62913 0.366840
\(690\) 0 0
\(691\) −32.1744 −1.22397 −0.611986 0.790868i \(-0.709629\pi\)
−0.611986 + 0.790868i \(0.709629\pi\)
\(692\) −7.05416 −0.268159
\(693\) 0 0
\(694\) −15.0028 −0.569499
\(695\) 6.00566 0.227807
\(696\) 0 0
\(697\) −3.97765 −0.150664
\(698\) −20.8059 −0.787514
\(699\) 0 0
\(700\) 2.57282 0.0972434
\(701\) −18.0672 −0.682388 −0.341194 0.939993i \(-0.610831\pi\)
−0.341194 + 0.939993i \(0.610831\pi\)
\(702\) 0 0
\(703\) −4.13650 −0.156011
\(704\) −29.4807 −1.11109
\(705\) 0 0
\(706\) 14.5702 0.548358
\(707\) −11.7839 −0.443181
\(708\) 0 0
\(709\) 15.1868 0.570353 0.285176 0.958475i \(-0.407948\pi\)
0.285176 + 0.958475i \(0.407948\pi\)
\(710\) 1.66254 0.0623940
\(711\) 0 0
\(712\) 28.0834 1.05247
\(713\) 6.17955 0.231426
\(714\) 0 0
\(715\) 4.80867 0.179834
\(716\) −6.32388 −0.236335
\(717\) 0 0
\(718\) −3.80494 −0.141999
\(719\) −19.6906 −0.734335 −0.367168 0.930155i \(-0.619672\pi\)
−0.367168 + 0.930155i \(0.619672\pi\)
\(720\) 0 0
\(721\) −6.48469 −0.241502
\(722\) 22.5824 0.840428
\(723\) 0 0
\(724\) −12.6207 −0.469044
\(725\) 7.33930 0.272575
\(726\) 0 0
\(727\) −35.5316 −1.31779 −0.658897 0.752233i \(-0.728977\pi\)
−0.658897 + 0.752233i \(0.728977\pi\)
\(728\) 9.08602 0.336750
\(729\) 0 0
\(730\) −2.49887 −0.0924873
\(731\) −6.68417 −0.247223
\(732\) 0 0
\(733\) −13.6230 −0.503178 −0.251589 0.967834i \(-0.580953\pi\)
−0.251589 + 0.967834i \(0.580953\pi\)
\(734\) 22.3499 0.824952
\(735\) 0 0
\(736\) 14.7481 0.543623
\(737\) −34.5980 −1.27443
\(738\) 0 0
\(739\) −46.3582 −1.70531 −0.852656 0.522472i \(-0.825010\pi\)
−0.852656 + 0.522472i \(0.825010\pi\)
\(740\) −1.95488 −0.0718629
\(741\) 0 0
\(742\) −3.92987 −0.144270
\(743\) 11.2265 0.411859 0.205930 0.978567i \(-0.433978\pi\)
0.205930 + 0.978567i \(0.433978\pi\)
\(744\) 0 0
\(745\) 0.142327 0.00521445
\(746\) −4.04481 −0.148091
\(747\) 0 0
\(748\) −1.24702 −0.0455955
\(749\) −7.40352 −0.270519
\(750\) 0 0
\(751\) 44.8285 1.63582 0.817908 0.575349i \(-0.195134\pi\)
0.817908 + 0.575349i \(0.195134\pi\)
\(752\) 11.6359 0.424318
\(753\) 0 0
\(754\) 5.51170 0.200724
\(755\) −5.38899 −0.196126
\(756\) 0 0
\(757\) 30.5896 1.11180 0.555898 0.831250i \(-0.312374\pi\)
0.555898 + 0.831250i \(0.312374\pi\)
\(758\) −8.30334 −0.301591
\(759\) 0 0
\(760\) −0.831412 −0.0301585
\(761\) −45.8271 −1.66123 −0.830616 0.556846i \(-0.812011\pi\)
−0.830616 + 0.556846i \(0.812011\pi\)
\(762\) 0 0
\(763\) −14.4941 −0.524721
\(764\) 4.03553 0.146000
\(765\) 0 0
\(766\) 4.67810 0.169027
\(767\) −32.0419 −1.15697
\(768\) 0 0
\(769\) 18.1925 0.656037 0.328019 0.944671i \(-0.393619\pi\)
0.328019 + 0.944671i \(0.393619\pi\)
\(770\) −1.96253 −0.0707248
\(771\) 0 0
\(772\) −1.20562 −0.0433912
\(773\) −27.5311 −0.990227 −0.495113 0.868828i \(-0.664873\pi\)
−0.495113 + 0.868828i \(0.664873\pi\)
\(774\) 0 0
\(775\) 5.91361 0.212423
\(776\) 36.2773 1.30228
\(777\) 0 0
\(778\) −28.9701 −1.03863
\(779\) 3.19882 0.114610
\(780\) 0 0
\(781\) −9.43028 −0.337442
\(782\) −4.16096 −0.148796
\(783\) 0 0
\(784\) −2.62788 −0.0938529
\(785\) 4.73642 0.169050
\(786\) 0 0
\(787\) −30.5551 −1.08917 −0.544586 0.838705i \(-0.683313\pi\)
−0.544586 + 0.838705i \(0.683313\pi\)
\(788\) −13.3160 −0.474364
\(789\) 0 0
\(790\) 8.11367 0.288672
\(791\) −12.1032 −0.430342
\(792\) 0 0
\(793\) 27.0807 0.961665
\(794\) −11.6604 −0.413812
\(795\) 0 0
\(796\) −2.83924 −0.100634
\(797\) 37.6677 1.33426 0.667129 0.744943i \(-0.267523\pi\)
0.667129 + 0.744943i \(0.267523\pi\)
\(798\) 0 0
\(799\) 3.06375 0.108388
\(800\) 14.1134 0.498985
\(801\) 0 0
\(802\) −2.98072 −0.105253
\(803\) 14.1741 0.500194
\(804\) 0 0
\(805\) 2.42306 0.0854017
\(806\) 4.44103 0.156429
\(807\) 0 0
\(808\) −36.1663 −1.27233
\(809\) 12.1123 0.425845 0.212923 0.977069i \(-0.431702\pi\)
0.212923 + 0.977069i \(0.431702\pi\)
\(810\) 0 0
\(811\) 43.5325 1.52863 0.764317 0.644841i \(-0.223076\pi\)
0.764317 + 0.644841i \(0.223076\pi\)
\(812\) 0.832346 0.0292096
\(813\) 0 0
\(814\) −29.9673 −1.05035
\(815\) 11.5464 0.404451
\(816\) 0 0
\(817\) 5.37540 0.188062
\(818\) 25.8687 0.904479
\(819\) 0 0
\(820\) 1.51174 0.0527924
\(821\) 23.3163 0.813745 0.406873 0.913485i \(-0.366619\pi\)
0.406873 + 0.913485i \(0.366619\pi\)
\(822\) 0 0
\(823\) −2.59914 −0.0906004 −0.0453002 0.998973i \(-0.514424\pi\)
−0.0453002 + 0.998973i \(0.514424\pi\)
\(824\) −19.9023 −0.693329
\(825\) 0 0
\(826\) 13.0771 0.455009
\(827\) 12.6692 0.440550 0.220275 0.975438i \(-0.429305\pi\)
0.220275 + 0.975438i \(0.429305\pi\)
\(828\) 0 0
\(829\) −6.91219 −0.240070 −0.120035 0.992770i \(-0.538301\pi\)
−0.120035 + 0.992770i \(0.538301\pi\)
\(830\) −0.317521 −0.0110213
\(831\) 0 0
\(832\) 26.1585 0.906881
\(833\) −0.691924 −0.0239738
\(834\) 0 0
\(835\) −5.86586 −0.202997
\(836\) 1.00285 0.0346843
\(837\) 0 0
\(838\) 37.6245 1.29972
\(839\) −0.427700 −0.0147658 −0.00738292 0.999973i \(-0.502350\pi\)
−0.00738292 + 0.999973i \(0.502350\pi\)
\(840\) 0 0
\(841\) −26.6256 −0.918125
\(842\) 5.34310 0.184135
\(843\) 0 0
\(844\) 14.0180 0.482518
\(845\) 2.06206 0.0709371
\(846\) 0 0
\(847\) 0.131916 0.00453270
\(848\) −8.54738 −0.293518
\(849\) 0 0
\(850\) −3.98190 −0.136578
\(851\) 36.9994 1.26832
\(852\) 0 0
\(853\) −16.3166 −0.558668 −0.279334 0.960194i \(-0.590114\pi\)
−0.279334 + 0.960194i \(0.590114\pi\)
\(854\) −11.0523 −0.378201
\(855\) 0 0
\(856\) −22.7223 −0.776632
\(857\) −5.34493 −0.182579 −0.0912897 0.995824i \(-0.529099\pi\)
−0.0912897 + 0.995824i \(0.529099\pi\)
\(858\) 0 0
\(859\) 32.6604 1.11436 0.557179 0.830392i \(-0.311884\pi\)
0.557179 + 0.830392i \(0.311884\pi\)
\(860\) 2.54038 0.0866263
\(861\) 0 0
\(862\) −20.8563 −0.710370
\(863\) 23.4800 0.799268 0.399634 0.916675i \(-0.369137\pi\)
0.399634 + 0.916675i \(0.369137\pi\)
\(864\) 0 0
\(865\) −6.35765 −0.216167
\(866\) −44.0300 −1.49620
\(867\) 0 0
\(868\) 0.670660 0.0227637
\(869\) −46.0225 −1.56121
\(870\) 0 0
\(871\) 30.6991 1.04020
\(872\) −44.4841 −1.50642
\(873\) 0 0
\(874\) 3.34624 0.113188
\(875\) 4.75295 0.160679
\(876\) 0 0
\(877\) −23.4223 −0.790916 −0.395458 0.918484i \(-0.629414\pi\)
−0.395458 + 0.918484i \(0.629414\pi\)
\(878\) 16.0331 0.541092
\(879\) 0 0
\(880\) −4.26846 −0.143890
\(881\) −3.19683 −0.107704 −0.0538520 0.998549i \(-0.517150\pi\)
−0.0538520 + 0.998549i \(0.517150\pi\)
\(882\) 0 0
\(883\) −2.91600 −0.0981312 −0.0490656 0.998796i \(-0.515624\pi\)
−0.0490656 + 0.998796i \(0.515624\pi\)
\(884\) 1.10649 0.0372153
\(885\) 0 0
\(886\) 16.0882 0.540492
\(887\) 30.6363 1.02867 0.514334 0.857590i \(-0.328039\pi\)
0.514334 + 0.857590i \(0.328039\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 5.38230 0.180415
\(891\) 0 0
\(892\) 2.74530 0.0919196
\(893\) −2.46387 −0.0824501
\(894\) 0 0
\(895\) −5.69948 −0.190513
\(896\) −4.74960 −0.158673
\(897\) 0 0
\(898\) −37.2811 −1.24409
\(899\) 1.91314 0.0638069
\(900\) 0 0
\(901\) −2.25053 −0.0749762
\(902\) 23.1742 0.771616
\(903\) 0 0
\(904\) −37.1463 −1.23547
\(905\) −11.3746 −0.378103
\(906\) 0 0
\(907\) −28.0303 −0.930732 −0.465366 0.885118i \(-0.654077\pi\)
−0.465366 + 0.885118i \(0.654077\pi\)
\(908\) −14.7812 −0.490533
\(909\) 0 0
\(910\) 1.74137 0.0577259
\(911\) 49.5167 1.64056 0.820280 0.571962i \(-0.193817\pi\)
0.820280 + 0.571962i \(0.193817\pi\)
\(912\) 0 0
\(913\) 1.80105 0.0596061
\(914\) −17.5463 −0.580381
\(915\) 0 0
\(916\) 10.5863 0.349781
\(917\) 11.3196 0.373805
\(918\) 0 0
\(919\) 34.0996 1.12484 0.562420 0.826851i \(-0.309870\pi\)
0.562420 + 0.826851i \(0.309870\pi\)
\(920\) 7.43667 0.245180
\(921\) 0 0
\(922\) 23.5069 0.774158
\(923\) 8.36757 0.275422
\(924\) 0 0
\(925\) 35.4071 1.16418
\(926\) −49.3968 −1.62328
\(927\) 0 0
\(928\) 4.56591 0.149883
\(929\) 36.7891 1.20701 0.603506 0.797359i \(-0.293770\pi\)
0.603506 + 0.797359i \(0.293770\pi\)
\(930\) 0 0
\(931\) 0.556445 0.0182367
\(932\) −0.606368 −0.0198622
\(933\) 0 0
\(934\) −27.4611 −0.898553
\(935\) −1.12389 −0.0367552
\(936\) 0 0
\(937\) −8.71731 −0.284782 −0.142391 0.989810i \(-0.545479\pi\)
−0.142391 + 0.989810i \(0.545479\pi\)
\(938\) −12.5290 −0.409087
\(939\) 0 0
\(940\) −1.16441 −0.0379788
\(941\) −14.2029 −0.463001 −0.231500 0.972835i \(-0.574363\pi\)
−0.231500 + 0.972835i \(0.574363\pi\)
\(942\) 0 0
\(943\) −28.6123 −0.931744
\(944\) 28.4423 0.925717
\(945\) 0 0
\(946\) 38.9426 1.26613
\(947\) 47.6944 1.54986 0.774930 0.632047i \(-0.217785\pi\)
0.774930 + 0.632047i \(0.217785\pi\)
\(948\) 0 0
\(949\) −12.5768 −0.408261
\(950\) 3.20224 0.103894
\(951\) 0 0
\(952\) −2.12360 −0.0688262
\(953\) −27.4401 −0.888873 −0.444436 0.895810i \(-0.646596\pi\)
−0.444436 + 0.895810i \(0.646596\pi\)
\(954\) 0 0
\(955\) 3.63707 0.117693
\(956\) 11.1463 0.360497
\(957\) 0 0
\(958\) −25.2199 −0.814820
\(959\) −1.75217 −0.0565805
\(960\) 0 0
\(961\) −29.4585 −0.950274
\(962\) 26.5902 0.857303
\(963\) 0 0
\(964\) −8.98671 −0.289442
\(965\) −1.08658 −0.0349783
\(966\) 0 0
\(967\) 11.3899 0.366275 0.183138 0.983087i \(-0.441375\pi\)
0.183138 + 0.983087i \(0.441375\pi\)
\(968\) 0.404867 0.0130129
\(969\) 0 0
\(970\) 6.95270 0.223238
\(971\) 56.1074 1.80057 0.900286 0.435299i \(-0.143358\pi\)
0.900286 + 0.435299i \(0.143358\pi\)
\(972\) 0 0
\(973\) −12.3362 −0.395479
\(974\) 11.5519 0.370148
\(975\) 0 0
\(976\) −24.0385 −0.769452
\(977\) 29.0159 0.928300 0.464150 0.885757i \(-0.346360\pi\)
0.464150 + 0.885757i \(0.346360\pi\)
\(978\) 0 0
\(979\) −30.5296 −0.975730
\(980\) 0.262972 0.00840034
\(981\) 0 0
\(982\) −40.0324 −1.27748
\(983\) −32.9269 −1.05020 −0.525102 0.851039i \(-0.675973\pi\)
−0.525102 + 0.851039i \(0.675973\pi\)
\(984\) 0 0
\(985\) −12.0013 −0.382392
\(986\) −1.28820 −0.0410248
\(987\) 0 0
\(988\) −0.889838 −0.0283095
\(989\) −48.0810 −1.52889
\(990\) 0 0
\(991\) −13.4717 −0.427944 −0.213972 0.976840i \(-0.568640\pi\)
−0.213972 + 0.976840i \(0.568640\pi\)
\(992\) 3.67896 0.116807
\(993\) 0 0
\(994\) −3.41500 −0.108317
\(995\) −2.55890 −0.0811227
\(996\) 0 0
\(997\) −5.54506 −0.175614 −0.0878069 0.996138i \(-0.527986\pi\)
−0.0878069 + 0.996138i \(0.527986\pi\)
\(998\) 4.41267 0.139681
\(999\) 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 \(a_p\))