Properties

Label 8001.2.a.u.1.12
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 1.12
Root \(1.52505\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.52505 q^{2}\) \(+0.325779 q^{4}\) \(+1.71268 q^{5}\) \(+1.00000 q^{7}\) \(-2.55327 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.52505 q^{2}\) \(+0.325779 q^{4}\) \(+1.71268 q^{5}\) \(+1.00000 q^{7}\) \(-2.55327 q^{8}\) \(+2.61192 q^{10}\) \(+1.69211 q^{11}\) \(-1.16748 q^{13}\) \(+1.52505 q^{14}\) \(-4.54543 q^{16}\) \(-5.50471 q^{17}\) \(-0.828520 q^{19}\) \(+0.557955 q^{20}\) \(+2.58056 q^{22}\) \(+6.42297 q^{23}\) \(-2.06673 q^{25}\) \(-1.78047 q^{26}\) \(+0.325779 q^{28}\) \(+2.43481 q^{29}\) \(-0.583990 q^{31}\) \(-1.82546 q^{32}\) \(-8.39496 q^{34}\) \(+1.71268 q^{35}\) \(+11.0189 q^{37}\) \(-1.26353 q^{38}\) \(-4.37293 q^{40}\) \(+0.0442353 q^{41}\) \(+12.9529 q^{43}\) \(+0.551255 q^{44}\) \(+9.79535 q^{46}\) \(-3.58595 q^{47}\) \(+1.00000 q^{49}\) \(-3.15187 q^{50}\) \(-0.380341 q^{52}\) \(+12.7616 q^{53}\) \(+2.89805 q^{55}\) \(-2.55327 q^{56}\) \(+3.71321 q^{58}\) \(-1.61982 q^{59}\) \(-5.74621 q^{61}\) \(-0.890614 q^{62}\) \(+6.30693 q^{64}\) \(-1.99952 q^{65}\) \(-0.393750 q^{67}\) \(-1.79332 q^{68}\) \(+2.61192 q^{70}\) \(-10.0573 q^{71}\) \(+7.94732 q^{73}\) \(+16.8044 q^{74}\) \(-0.269914 q^{76}\) \(+1.69211 q^{77}\) \(+3.92230 q^{79}\) \(-7.78485 q^{80}\) \(+0.0674610 q^{82}\) \(-6.36257 q^{83}\) \(-9.42780 q^{85}\) \(+19.7538 q^{86}\) \(-4.32042 q^{88}\) \(+5.77339 q^{89}\) \(-1.16748 q^{91}\) \(+2.09247 q^{92}\) \(-5.46876 q^{94}\) \(-1.41899 q^{95}\) \(+15.1754 q^{97}\) \(+1.52505 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52505 1.07837 0.539187 0.842186i \(-0.318732\pi\)
0.539187 + 0.842186i \(0.318732\pi\)
\(3\) 0 0
\(4\) 0.325779 0.162890
\(5\) 1.71268 0.765933 0.382966 0.923762i \(-0.374902\pi\)
0.382966 + 0.923762i \(0.374902\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.55327 −0.902718
\(9\) 0 0
\(10\) 2.61192 0.825962
\(11\) 1.69211 0.510191 0.255096 0.966916i \(-0.417893\pi\)
0.255096 + 0.966916i \(0.417893\pi\)
\(12\) 0 0
\(13\) −1.16748 −0.323801 −0.161901 0.986807i \(-0.551762\pi\)
−0.161901 + 0.986807i \(0.551762\pi\)
\(14\) 1.52505 0.407587
\(15\) 0 0
\(16\) −4.54543 −1.13636
\(17\) −5.50471 −1.33509 −0.667544 0.744570i \(-0.732655\pi\)
−0.667544 + 0.744570i \(0.732655\pi\)
\(18\) 0 0
\(19\) −0.828520 −0.190075 −0.0950377 0.995474i \(-0.530297\pi\)
−0.0950377 + 0.995474i \(0.530297\pi\)
\(20\) 0.557955 0.124762
\(21\) 0 0
\(22\) 2.58056 0.550177
\(23\) 6.42297 1.33928 0.669641 0.742685i \(-0.266448\pi\)
0.669641 + 0.742685i \(0.266448\pi\)
\(24\) 0 0
\(25\) −2.06673 −0.413347
\(26\) −1.78047 −0.349179
\(27\) 0 0
\(28\) 0.325779 0.0615664
\(29\) 2.43481 0.452133 0.226066 0.974112i \(-0.427413\pi\)
0.226066 + 0.974112i \(0.427413\pi\)
\(30\) 0 0
\(31\) −0.583990 −0.104888 −0.0524438 0.998624i \(-0.516701\pi\)
−0.0524438 + 0.998624i \(0.516701\pi\)
\(32\) −1.82546 −0.322699
\(33\) 0 0
\(34\) −8.39496 −1.43972
\(35\) 1.71268 0.289495
\(36\) 0 0
\(37\) 11.0189 1.81150 0.905749 0.423814i \(-0.139309\pi\)
0.905749 + 0.423814i \(0.139309\pi\)
\(38\) −1.26353 −0.204972
\(39\) 0 0
\(40\) −4.37293 −0.691421
\(41\) 0.0442353 0.00690839 0.00345419 0.999994i \(-0.498900\pi\)
0.00345419 + 0.999994i \(0.498900\pi\)
\(42\) 0 0
\(43\) 12.9529 1.97529 0.987647 0.156695i \(-0.0500839\pi\)
0.987647 + 0.156695i \(0.0500839\pi\)
\(44\) 0.551255 0.0831048
\(45\) 0 0
\(46\) 9.79535 1.44425
\(47\) −3.58595 −0.523065 −0.261533 0.965195i \(-0.584228\pi\)
−0.261533 + 0.965195i \(0.584228\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −3.15187 −0.445742
\(51\) 0 0
\(52\) −0.380341 −0.0527439
\(53\) 12.7616 1.75295 0.876473 0.481451i \(-0.159890\pi\)
0.876473 + 0.481451i \(0.159890\pi\)
\(54\) 0 0
\(55\) 2.89805 0.390772
\(56\) −2.55327 −0.341195
\(57\) 0 0
\(58\) 3.71321 0.487568
\(59\) −1.61982 −0.210883 −0.105442 0.994426i \(-0.533626\pi\)
−0.105442 + 0.994426i \(0.533626\pi\)
\(60\) 0 0
\(61\) −5.74621 −0.735727 −0.367864 0.929880i \(-0.619911\pi\)
−0.367864 + 0.929880i \(0.619911\pi\)
\(62\) −0.890614 −0.113108
\(63\) 0 0
\(64\) 6.30693 0.788366
\(65\) −1.99952 −0.248010
\(66\) 0 0
\(67\) −0.393750 −0.0481042 −0.0240521 0.999711i \(-0.507657\pi\)
−0.0240521 + 0.999711i \(0.507657\pi\)
\(68\) −1.79332 −0.217472
\(69\) 0 0
\(70\) 2.61192 0.312184
\(71\) −10.0573 −1.19358 −0.596792 0.802396i \(-0.703558\pi\)
−0.596792 + 0.802396i \(0.703558\pi\)
\(72\) 0 0
\(73\) 7.94732 0.930163 0.465081 0.885268i \(-0.346025\pi\)
0.465081 + 0.885268i \(0.346025\pi\)
\(74\) 16.8044 1.95347
\(75\) 0 0
\(76\) −0.269914 −0.0309613
\(77\) 1.69211 0.192834
\(78\) 0 0
\(79\) 3.92230 0.441293 0.220647 0.975354i \(-0.429183\pi\)
0.220647 + 0.975354i \(0.429183\pi\)
\(80\) −7.78485 −0.870373
\(81\) 0 0
\(82\) 0.0674610 0.00744982
\(83\) −6.36257 −0.698382 −0.349191 0.937051i \(-0.613544\pi\)
−0.349191 + 0.937051i \(0.613544\pi\)
\(84\) 0 0
\(85\) −9.42780 −1.02259
\(86\) 19.7538 2.13010
\(87\) 0 0
\(88\) −4.32042 −0.460559
\(89\) 5.77339 0.611978 0.305989 0.952035i \(-0.401013\pi\)
0.305989 + 0.952035i \(0.401013\pi\)
\(90\) 0 0
\(91\) −1.16748 −0.122385
\(92\) 2.09247 0.218155
\(93\) 0 0
\(94\) −5.46876 −0.564060
\(95\) −1.41899 −0.145585
\(96\) 0 0
\(97\) 15.1754 1.54083 0.770415 0.637542i \(-0.220049\pi\)
0.770415 + 0.637542i \(0.220049\pi\)
\(98\) 1.52505 0.154053
\(99\) 0 0
\(100\) −0.673298 −0.0673298
\(101\) 16.9988 1.69144 0.845722 0.533624i \(-0.179170\pi\)
0.845722 + 0.533624i \(0.179170\pi\)
\(102\) 0 0
\(103\) 0.475453 0.0468478 0.0234239 0.999726i \(-0.492543\pi\)
0.0234239 + 0.999726i \(0.492543\pi\)
\(104\) 2.98090 0.292301
\(105\) 0 0
\(106\) 19.4621 1.89033
\(107\) 16.9210 1.63582 0.817908 0.575349i \(-0.195134\pi\)
0.817908 + 0.575349i \(0.195134\pi\)
\(108\) 0 0
\(109\) 3.98507 0.381700 0.190850 0.981619i \(-0.438876\pi\)
0.190850 + 0.981619i \(0.438876\pi\)
\(110\) 4.41967 0.421399
\(111\) 0 0
\(112\) −4.54543 −0.429502
\(113\) 18.6198 1.75160 0.875802 0.482670i \(-0.160333\pi\)
0.875802 + 0.482670i \(0.160333\pi\)
\(114\) 0 0
\(115\) 11.0005 1.02580
\(116\) 0.793210 0.0736477
\(117\) 0 0
\(118\) −2.47031 −0.227411
\(119\) −5.50471 −0.504616
\(120\) 0 0
\(121\) −8.13675 −0.739705
\(122\) −8.76327 −0.793389
\(123\) 0 0
\(124\) −0.190252 −0.0170851
\(125\) −12.1030 −1.08253
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 13.2693 1.17285
\(129\) 0 0
\(130\) −3.04937 −0.267448
\(131\) 10.2394 0.894622 0.447311 0.894379i \(-0.352382\pi\)
0.447311 + 0.894379i \(0.352382\pi\)
\(132\) 0 0
\(133\) −0.828520 −0.0718418
\(134\) −0.600488 −0.0518743
\(135\) 0 0
\(136\) 14.0550 1.20521
\(137\) −14.4173 −1.23175 −0.615874 0.787844i \(-0.711197\pi\)
−0.615874 + 0.787844i \(0.711197\pi\)
\(138\) 0 0
\(139\) 2.41938 0.205209 0.102605 0.994722i \(-0.467282\pi\)
0.102605 + 0.994722i \(0.467282\pi\)
\(140\) 0.557955 0.0471558
\(141\) 0 0
\(142\) −15.3379 −1.28713
\(143\) −1.97551 −0.165201
\(144\) 0 0
\(145\) 4.17004 0.346303
\(146\) 12.1201 1.00306
\(147\) 0 0
\(148\) 3.58973 0.295074
\(149\) −13.8882 −1.13776 −0.568882 0.822419i \(-0.692624\pi\)
−0.568882 + 0.822419i \(0.692624\pi\)
\(150\) 0 0
\(151\) 15.9548 1.29839 0.649193 0.760624i \(-0.275107\pi\)
0.649193 + 0.760624i \(0.275107\pi\)
\(152\) 2.11544 0.171584
\(153\) 0 0
\(154\) 2.58056 0.207947
\(155\) −1.00019 −0.0803369
\(156\) 0 0
\(157\) −8.84694 −0.706063 −0.353031 0.935611i \(-0.614849\pi\)
−0.353031 + 0.935611i \(0.614849\pi\)
\(158\) 5.98171 0.475879
\(159\) 0 0
\(160\) −3.12643 −0.247166
\(161\) 6.42297 0.506201
\(162\) 0 0
\(163\) −14.1224 −1.10615 −0.553077 0.833130i \(-0.686547\pi\)
−0.553077 + 0.833130i \(0.686547\pi\)
\(164\) 0.0144109 0.00112530
\(165\) 0 0
\(166\) −9.70323 −0.753117
\(167\) 18.7284 1.44925 0.724624 0.689144i \(-0.242013\pi\)
0.724624 + 0.689144i \(0.242013\pi\)
\(168\) 0 0
\(169\) −11.6370 −0.895153
\(170\) −14.3779 −1.10273
\(171\) 0 0
\(172\) 4.21977 0.321755
\(173\) 22.7424 1.72907 0.864535 0.502573i \(-0.167613\pi\)
0.864535 + 0.502573i \(0.167613\pi\)
\(174\) 0 0
\(175\) −2.06673 −0.156230
\(176\) −7.69138 −0.579759
\(177\) 0 0
\(178\) 8.80471 0.659941
\(179\) −4.09159 −0.305820 −0.152910 0.988240i \(-0.548864\pi\)
−0.152910 + 0.988240i \(0.548864\pi\)
\(180\) 0 0
\(181\) −23.9770 −1.78220 −0.891099 0.453810i \(-0.850065\pi\)
−0.891099 + 0.453810i \(0.850065\pi\)
\(182\) −1.78047 −0.131977
\(183\) 0 0
\(184\) −16.3996 −1.20899
\(185\) 18.8719 1.38749
\(186\) 0 0
\(187\) −9.31460 −0.681151
\(188\) −1.16823 −0.0852018
\(189\) 0 0
\(190\) −2.16403 −0.156995
\(191\) 5.39625 0.390459 0.195229 0.980758i \(-0.437455\pi\)
0.195229 + 0.980758i \(0.437455\pi\)
\(192\) 0 0
\(193\) −9.73030 −0.700402 −0.350201 0.936675i \(-0.613887\pi\)
−0.350201 + 0.936675i \(0.613887\pi\)
\(194\) 23.1433 1.66159
\(195\) 0 0
\(196\) 0.325779 0.0232699
\(197\) 0.142596 0.0101595 0.00507976 0.999987i \(-0.498383\pi\)
0.00507976 + 0.999987i \(0.498383\pi\)
\(198\) 0 0
\(199\) −11.8974 −0.843386 −0.421693 0.906739i \(-0.638564\pi\)
−0.421693 + 0.906739i \(0.638564\pi\)
\(200\) 5.27693 0.373135
\(201\) 0 0
\(202\) 25.9240 1.82401
\(203\) 2.43481 0.170890
\(204\) 0 0
\(205\) 0.0757608 0.00529136
\(206\) 0.725090 0.0505194
\(207\) 0 0
\(208\) 5.30671 0.367954
\(209\) −1.40195 −0.0969748
\(210\) 0 0
\(211\) 7.02643 0.483720 0.241860 0.970311i \(-0.422243\pi\)
0.241860 + 0.970311i \(0.422243\pi\)
\(212\) 4.15747 0.285537
\(213\) 0 0
\(214\) 25.8054 1.76402
\(215\) 22.1841 1.51294
\(216\) 0 0
\(217\) −0.583990 −0.0396438
\(218\) 6.07743 0.411615
\(219\) 0 0
\(220\) 0.944122 0.0636527
\(221\) 6.42666 0.432304
\(222\) 0 0
\(223\) −8.33132 −0.557907 −0.278953 0.960305i \(-0.589987\pi\)
−0.278953 + 0.960305i \(0.589987\pi\)
\(224\) −1.82546 −0.121969
\(225\) 0 0
\(226\) 28.3961 1.88888
\(227\) −7.54679 −0.500898 −0.250449 0.968130i \(-0.580578\pi\)
−0.250449 + 0.968130i \(0.580578\pi\)
\(228\) 0 0
\(229\) −13.3110 −0.879614 −0.439807 0.898092i \(-0.644953\pi\)
−0.439807 + 0.898092i \(0.644953\pi\)
\(230\) 16.7763 1.10620
\(231\) 0 0
\(232\) −6.21673 −0.408148
\(233\) −26.4435 −1.73237 −0.866187 0.499720i \(-0.833436\pi\)
−0.866187 + 0.499720i \(0.833436\pi\)
\(234\) 0 0
\(235\) −6.14159 −0.400633
\(236\) −0.527705 −0.0343506
\(237\) 0 0
\(238\) −8.39496 −0.544165
\(239\) −13.5322 −0.875328 −0.437664 0.899139i \(-0.644194\pi\)
−0.437664 + 0.899139i \(0.644194\pi\)
\(240\) 0 0
\(241\) 4.26598 0.274796 0.137398 0.990516i \(-0.456126\pi\)
0.137398 + 0.990516i \(0.456126\pi\)
\(242\) −12.4090 −0.797678
\(243\) 0 0
\(244\) −1.87200 −0.119842
\(245\) 1.71268 0.109419
\(246\) 0 0
\(247\) 0.967283 0.0615467
\(248\) 1.49108 0.0946840
\(249\) 0 0
\(250\) −18.4577 −1.16737
\(251\) −11.6345 −0.734363 −0.367182 0.930149i \(-0.619677\pi\)
−0.367182 + 0.930149i \(0.619677\pi\)
\(252\) 0 0
\(253\) 10.8684 0.683290
\(254\) 1.52505 0.0956902
\(255\) 0 0
\(256\) 7.62251 0.476407
\(257\) 21.3143 1.32955 0.664774 0.747044i \(-0.268528\pi\)
0.664774 + 0.747044i \(0.268528\pi\)
\(258\) 0 0
\(259\) 11.0189 0.684682
\(260\) −0.651402 −0.0403983
\(261\) 0 0
\(262\) 15.6156 0.964737
\(263\) 18.8019 1.15938 0.579688 0.814839i \(-0.303175\pi\)
0.579688 + 0.814839i \(0.303175\pi\)
\(264\) 0 0
\(265\) 21.8566 1.34264
\(266\) −1.26353 −0.0774723
\(267\) 0 0
\(268\) −0.128275 −0.00783566
\(269\) 19.1251 1.16608 0.583038 0.812445i \(-0.301864\pi\)
0.583038 + 0.812445i \(0.301864\pi\)
\(270\) 0 0
\(271\) −24.9073 −1.51301 −0.756507 0.653986i \(-0.773095\pi\)
−0.756507 + 0.653986i \(0.773095\pi\)
\(272\) 25.0213 1.51714
\(273\) 0 0
\(274\) −21.9870 −1.32829
\(275\) −3.49715 −0.210886
\(276\) 0 0
\(277\) 16.2979 0.979245 0.489623 0.871934i \(-0.337135\pi\)
0.489623 + 0.871934i \(0.337135\pi\)
\(278\) 3.68968 0.221292
\(279\) 0 0
\(280\) −4.37293 −0.261333
\(281\) −18.9557 −1.13080 −0.565401 0.824816i \(-0.691279\pi\)
−0.565401 + 0.824816i \(0.691279\pi\)
\(282\) 0 0
\(283\) −2.71943 −0.161654 −0.0808268 0.996728i \(-0.525756\pi\)
−0.0808268 + 0.996728i \(0.525756\pi\)
\(284\) −3.27646 −0.194422
\(285\) 0 0
\(286\) −3.01276 −0.178148
\(287\) 0.0442353 0.00261113
\(288\) 0 0
\(289\) 13.3019 0.782462
\(290\) 6.35953 0.373444
\(291\) 0 0
\(292\) 2.58907 0.151514
\(293\) 1.50441 0.0878883 0.0439442 0.999034i \(-0.486008\pi\)
0.0439442 + 0.999034i \(0.486008\pi\)
\(294\) 0 0
\(295\) −2.77424 −0.161522
\(296\) −28.1343 −1.63527
\(297\) 0 0
\(298\) −21.1802 −1.22693
\(299\) −7.49870 −0.433661
\(300\) 0 0
\(301\) 12.9529 0.746591
\(302\) 24.3319 1.40015
\(303\) 0 0
\(304\) 3.76597 0.215993
\(305\) −9.84142 −0.563518
\(306\) 0 0
\(307\) −14.8091 −0.845197 −0.422599 0.906317i \(-0.638882\pi\)
−0.422599 + 0.906317i \(0.638882\pi\)
\(308\) 0.551255 0.0314107
\(309\) 0 0
\(310\) −1.52534 −0.0866332
\(311\) −18.8186 −1.06711 −0.533554 0.845766i \(-0.679144\pi\)
−0.533554 + 0.845766i \(0.679144\pi\)
\(312\) 0 0
\(313\) −13.1089 −0.740961 −0.370480 0.928840i \(-0.620807\pi\)
−0.370480 + 0.928840i \(0.620807\pi\)
\(314\) −13.4920 −0.761400
\(315\) 0 0
\(316\) 1.27780 0.0718820
\(317\) 26.8211 1.50642 0.753210 0.657780i \(-0.228504\pi\)
0.753210 + 0.657780i \(0.228504\pi\)
\(318\) 0 0
\(319\) 4.11997 0.230674
\(320\) 10.8017 0.603836
\(321\) 0 0
\(322\) 9.79535 0.545873
\(323\) 4.56076 0.253768
\(324\) 0 0
\(325\) 2.41288 0.133842
\(326\) −21.5374 −1.19285
\(327\) 0 0
\(328\) −0.112945 −0.00623633
\(329\) −3.58595 −0.197700
\(330\) 0 0
\(331\) 1.70474 0.0937009 0.0468505 0.998902i \(-0.485082\pi\)
0.0468505 + 0.998902i \(0.485082\pi\)
\(332\) −2.07279 −0.113759
\(333\) 0 0
\(334\) 28.5618 1.56283
\(335\) −0.674366 −0.0368446
\(336\) 0 0
\(337\) 4.03114 0.219590 0.109795 0.993954i \(-0.464981\pi\)
0.109795 + 0.993954i \(0.464981\pi\)
\(338\) −17.7470 −0.965309
\(339\) 0 0
\(340\) −3.07138 −0.166569
\(341\) −0.988177 −0.0535128
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −33.0722 −1.78313
\(345\) 0 0
\(346\) 34.6833 1.86458
\(347\) 28.9241 1.55272 0.776362 0.630287i \(-0.217063\pi\)
0.776362 + 0.630287i \(0.217063\pi\)
\(348\) 0 0
\(349\) −28.0120 −1.49945 −0.749723 0.661752i \(-0.769813\pi\)
−0.749723 + 0.661752i \(0.769813\pi\)
\(350\) −3.15187 −0.168475
\(351\) 0 0
\(352\) −3.08889 −0.164638
\(353\) 13.4125 0.713874 0.356937 0.934129i \(-0.383821\pi\)
0.356937 + 0.934129i \(0.383821\pi\)
\(354\) 0 0
\(355\) −17.2249 −0.914205
\(356\) 1.88085 0.0996848
\(357\) 0 0
\(358\) −6.23988 −0.329788
\(359\) 14.1328 0.745901 0.372951 0.927851i \(-0.378346\pi\)
0.372951 + 0.927851i \(0.378346\pi\)
\(360\) 0 0
\(361\) −18.3136 −0.963871
\(362\) −36.5662 −1.92187
\(363\) 0 0
\(364\) −0.380341 −0.0199353
\(365\) 13.6112 0.712442
\(366\) 0 0
\(367\) −0.149960 −0.00782787 −0.00391393 0.999992i \(-0.501246\pi\)
−0.00391393 + 0.999992i \(0.501246\pi\)
\(368\) −29.1951 −1.52190
\(369\) 0 0
\(370\) 28.7805 1.49623
\(371\) 12.7616 0.662551
\(372\) 0 0
\(373\) 32.4335 1.67934 0.839672 0.543093i \(-0.182747\pi\)
0.839672 + 0.543093i \(0.182747\pi\)
\(374\) −14.2052 −0.734535
\(375\) 0 0
\(376\) 9.15592 0.472180
\(377\) −2.84260 −0.146401
\(378\) 0 0
\(379\) −3.44284 −0.176847 −0.0884234 0.996083i \(-0.528183\pi\)
−0.0884234 + 0.996083i \(0.528183\pi\)
\(380\) −0.462276 −0.0237143
\(381\) 0 0
\(382\) 8.22955 0.421060
\(383\) 33.4195 1.70766 0.853828 0.520556i \(-0.174275\pi\)
0.853828 + 0.520556i \(0.174275\pi\)
\(384\) 0 0
\(385\) 2.89805 0.147698
\(386\) −14.8392 −0.755295
\(387\) 0 0
\(388\) 4.94383 0.250985
\(389\) 29.8748 1.51471 0.757356 0.653002i \(-0.226491\pi\)
0.757356 + 0.653002i \(0.226491\pi\)
\(390\) 0 0
\(391\) −35.3566 −1.78806
\(392\) −2.55327 −0.128960
\(393\) 0 0
\(394\) 0.217466 0.0109558
\(395\) 6.71764 0.338001
\(396\) 0 0
\(397\) 20.8790 1.04788 0.523942 0.851754i \(-0.324461\pi\)
0.523942 + 0.851754i \(0.324461\pi\)
\(398\) −18.1442 −0.909486
\(399\) 0 0
\(400\) 9.39418 0.469709
\(401\) 26.7500 1.33583 0.667915 0.744237i \(-0.267187\pi\)
0.667915 + 0.744237i \(0.267187\pi\)
\(402\) 0 0
\(403\) 0.681798 0.0339628
\(404\) 5.53785 0.275518
\(405\) 0 0
\(406\) 3.71321 0.184283
\(407\) 18.6453 0.924211
\(408\) 0 0
\(409\) 19.3447 0.956535 0.478267 0.878214i \(-0.341265\pi\)
0.478267 + 0.878214i \(0.341265\pi\)
\(410\) 0.115539 0.00570607
\(411\) 0 0
\(412\) 0.154893 0.00763101
\(413\) −1.61982 −0.0797063
\(414\) 0 0
\(415\) −10.8970 −0.534914
\(416\) 2.13119 0.104490
\(417\) 0 0
\(418\) −2.13804 −0.104575
\(419\) 2.14664 0.104870 0.0524351 0.998624i \(-0.483302\pi\)
0.0524351 + 0.998624i \(0.483302\pi\)
\(420\) 0 0
\(421\) −0.674689 −0.0328823 −0.0164412 0.999865i \(-0.505234\pi\)
−0.0164412 + 0.999865i \(0.505234\pi\)
\(422\) 10.7157 0.521630
\(423\) 0 0
\(424\) −32.5839 −1.58242
\(425\) 11.3768 0.551855
\(426\) 0 0
\(427\) −5.74621 −0.278079
\(428\) 5.51251 0.266457
\(429\) 0 0
\(430\) 33.8319 1.63152
\(431\) −7.06226 −0.340177 −0.170089 0.985429i \(-0.554405\pi\)
−0.170089 + 0.985429i \(0.554405\pi\)
\(432\) 0 0
\(433\) 6.73974 0.323891 0.161946 0.986800i \(-0.448223\pi\)
0.161946 + 0.986800i \(0.448223\pi\)
\(434\) −0.890614 −0.0427508
\(435\) 0 0
\(436\) 1.29825 0.0621749
\(437\) −5.32155 −0.254564
\(438\) 0 0
\(439\) 2.65835 0.126876 0.0634380 0.997986i \(-0.479793\pi\)
0.0634380 + 0.997986i \(0.479793\pi\)
\(440\) −7.39950 −0.352757
\(441\) 0 0
\(442\) 9.80098 0.466185
\(443\) −5.02361 −0.238679 −0.119339 0.992854i \(-0.538078\pi\)
−0.119339 + 0.992854i \(0.538078\pi\)
\(444\) 0 0
\(445\) 9.88795 0.468734
\(446\) −12.7057 −0.601632
\(447\) 0 0
\(448\) 6.30693 0.297975
\(449\) −16.7743 −0.791626 −0.395813 0.918331i \(-0.629537\pi\)
−0.395813 + 0.918331i \(0.629537\pi\)
\(450\) 0 0
\(451\) 0.0748511 0.00352460
\(452\) 6.06594 0.285318
\(453\) 0 0
\(454\) −11.5092 −0.540155
\(455\) −1.99952 −0.0937391
\(456\) 0 0
\(457\) −17.6220 −0.824320 −0.412160 0.911111i \(-0.635226\pi\)
−0.412160 + 0.911111i \(0.635226\pi\)
\(458\) −20.2999 −0.948552
\(459\) 0 0
\(460\) 3.58372 0.167092
\(461\) 0.380299 0.0177123 0.00885614 0.999961i \(-0.497181\pi\)
0.00885614 + 0.999961i \(0.497181\pi\)
\(462\) 0 0
\(463\) −8.78153 −0.408112 −0.204056 0.978959i \(-0.565413\pi\)
−0.204056 + 0.978959i \(0.565413\pi\)
\(464\) −11.0672 −0.513784
\(465\) 0 0
\(466\) −40.3277 −1.86815
\(467\) 19.8468 0.918400 0.459200 0.888333i \(-0.348136\pi\)
0.459200 + 0.888333i \(0.348136\pi\)
\(468\) 0 0
\(469\) −0.393750 −0.0181817
\(470\) −9.36623 −0.432032
\(471\) 0 0
\(472\) 4.13585 0.190368
\(473\) 21.9177 1.00778
\(474\) 0 0
\(475\) 1.71233 0.0785671
\(476\) −1.79332 −0.0821967
\(477\) 0 0
\(478\) −20.6374 −0.943930
\(479\) −1.39194 −0.0635993 −0.0317997 0.999494i \(-0.510124\pi\)
−0.0317997 + 0.999494i \(0.510124\pi\)
\(480\) 0 0
\(481\) −12.8644 −0.586566
\(482\) 6.50584 0.296333
\(483\) 0 0
\(484\) −2.65078 −0.120490
\(485\) 25.9906 1.18017
\(486\) 0 0
\(487\) −5.98929 −0.271401 −0.135700 0.990750i \(-0.543328\pi\)
−0.135700 + 0.990750i \(0.543328\pi\)
\(488\) 14.6716 0.664154
\(489\) 0 0
\(490\) 2.61192 0.117995
\(491\) 1.88645 0.0851344 0.0425672 0.999094i \(-0.486446\pi\)
0.0425672 + 0.999094i \(0.486446\pi\)
\(492\) 0 0
\(493\) −13.4029 −0.603637
\(494\) 1.47515 0.0663703
\(495\) 0 0
\(496\) 2.65448 0.119190
\(497\) −10.0573 −0.451132
\(498\) 0 0
\(499\) 18.0508 0.808066 0.404033 0.914744i \(-0.367608\pi\)
0.404033 + 0.914744i \(0.367608\pi\)
\(500\) −3.94292 −0.176333
\(501\) 0 0
\(502\) −17.7432 −0.791918
\(503\) −40.4303 −1.80270 −0.901348 0.433095i \(-0.857421\pi\)
−0.901348 + 0.433095i \(0.857421\pi\)
\(504\) 0 0
\(505\) 29.1135 1.29553
\(506\) 16.5748 0.736841
\(507\) 0 0
\(508\) 0.325779 0.0144541
\(509\) 28.8945 1.28072 0.640362 0.768073i \(-0.278784\pi\)
0.640362 + 0.768073i \(0.278784\pi\)
\(510\) 0 0
\(511\) 7.94732 0.351569
\(512\) −14.9139 −0.659108
\(513\) 0 0
\(514\) 32.5054 1.43375
\(515\) 0.814298 0.0358823
\(516\) 0 0
\(517\) −6.06784 −0.266863
\(518\) 16.8044 0.738343
\(519\) 0 0
\(520\) 5.10532 0.223883
\(521\) 11.5348 0.505348 0.252674 0.967551i \(-0.418690\pi\)
0.252674 + 0.967551i \(0.418690\pi\)
\(522\) 0 0
\(523\) 8.32409 0.363987 0.181993 0.983300i \(-0.441745\pi\)
0.181993 + 0.983300i \(0.441745\pi\)
\(524\) 3.33579 0.145725
\(525\) 0 0
\(526\) 28.6739 1.25024
\(527\) 3.21470 0.140034
\(528\) 0 0
\(529\) 18.2545 0.793674
\(530\) 33.3324 1.44787
\(531\) 0 0
\(532\) −0.269914 −0.0117023
\(533\) −0.0516439 −0.00223695
\(534\) 0 0
\(535\) 28.9803 1.25293
\(536\) 1.00535 0.0434245
\(537\) 0 0
\(538\) 29.1667 1.25746
\(539\) 1.69211 0.0728845
\(540\) 0 0
\(541\) 28.0228 1.20479 0.602396 0.798197i \(-0.294213\pi\)
0.602396 + 0.798197i \(0.294213\pi\)
\(542\) −37.9850 −1.63159
\(543\) 0 0
\(544\) 10.0486 0.430832
\(545\) 6.82514 0.292357
\(546\) 0 0
\(547\) 0.859530 0.0367509 0.0183754 0.999831i \(-0.494151\pi\)
0.0183754 + 0.999831i \(0.494151\pi\)
\(548\) −4.69684 −0.200639
\(549\) 0 0
\(550\) −5.33333 −0.227414
\(551\) −2.01729 −0.0859393
\(552\) 0 0
\(553\) 3.92230 0.166793
\(554\) 24.8551 1.05599
\(555\) 0 0
\(556\) 0.788183 0.0334264
\(557\) 34.8987 1.47871 0.739354 0.673317i \(-0.235131\pi\)
0.739354 + 0.673317i \(0.235131\pi\)
\(558\) 0 0
\(559\) −15.1223 −0.639603
\(560\) −7.78485 −0.328970
\(561\) 0 0
\(562\) −28.9084 −1.21943
\(563\) −13.3554 −0.562865 −0.281432 0.959581i \(-0.590810\pi\)
−0.281432 + 0.959581i \(0.590810\pi\)
\(564\) 0 0
\(565\) 31.8897 1.34161
\(566\) −4.14727 −0.174323
\(567\) 0 0
\(568\) 25.6790 1.07747
\(569\) 3.71560 0.155766 0.0778831 0.996962i \(-0.475184\pi\)
0.0778831 + 0.996962i \(0.475184\pi\)
\(570\) 0 0
\(571\) −5.10153 −0.213492 −0.106746 0.994286i \(-0.534043\pi\)
−0.106746 + 0.994286i \(0.534043\pi\)
\(572\) −0.643581 −0.0269095
\(573\) 0 0
\(574\) 0.0674610 0.00281577
\(575\) −13.2746 −0.553587
\(576\) 0 0
\(577\) −13.8444 −0.576349 −0.288174 0.957578i \(-0.593048\pi\)
−0.288174 + 0.957578i \(0.593048\pi\)
\(578\) 20.2860 0.843786
\(579\) 0 0
\(580\) 1.35851 0.0564092
\(581\) −6.36257 −0.263964
\(582\) 0 0
\(583\) 21.5941 0.894338
\(584\) −20.2917 −0.839675
\(585\) 0 0
\(586\) 2.29429 0.0947764
\(587\) 42.5391 1.75578 0.877888 0.478866i \(-0.158952\pi\)
0.877888 + 0.478866i \(0.158952\pi\)
\(588\) 0 0
\(589\) 0.483847 0.0199366
\(590\) −4.23085 −0.174181
\(591\) 0 0
\(592\) −50.0857 −2.05851
\(593\) −14.6580 −0.601933 −0.300966 0.953635i \(-0.597309\pi\)
−0.300966 + 0.953635i \(0.597309\pi\)
\(594\) 0 0
\(595\) −9.42780 −0.386502
\(596\) −4.52448 −0.185330
\(597\) 0 0
\(598\) −11.4359 −0.467649
\(599\) −40.4992 −1.65475 −0.827377 0.561647i \(-0.810168\pi\)
−0.827377 + 0.561647i \(0.810168\pi\)
\(600\) 0 0
\(601\) 13.8489 0.564908 0.282454 0.959281i \(-0.408851\pi\)
0.282454 + 0.959281i \(0.408851\pi\)
\(602\) 19.7538 0.805104
\(603\) 0 0
\(604\) 5.19775 0.211494
\(605\) −13.9356 −0.566564
\(606\) 0 0
\(607\) −43.2955 −1.75731 −0.878656 0.477456i \(-0.841559\pi\)
−0.878656 + 0.477456i \(0.841559\pi\)
\(608\) 1.51243 0.0613372
\(609\) 0 0
\(610\) −15.0087 −0.607683
\(611\) 4.18654 0.169369
\(612\) 0 0
\(613\) −10.6948 −0.431959 −0.215980 0.976398i \(-0.569295\pi\)
−0.215980 + 0.976398i \(0.569295\pi\)
\(614\) −22.5846 −0.911439
\(615\) 0 0
\(616\) −4.32042 −0.174075
\(617\) −14.2139 −0.572230 −0.286115 0.958195i \(-0.592364\pi\)
−0.286115 + 0.958195i \(0.592364\pi\)
\(618\) 0 0
\(619\) −4.95554 −0.199180 −0.0995899 0.995029i \(-0.531753\pi\)
−0.0995899 + 0.995029i \(0.531753\pi\)
\(620\) −0.325840 −0.0130860
\(621\) 0 0
\(622\) −28.6994 −1.15074
\(623\) 5.77339 0.231306
\(624\) 0 0
\(625\) −10.3949 −0.415798
\(626\) −19.9918 −0.799032
\(627\) 0 0
\(628\) −2.88215 −0.115010
\(629\) −60.6560 −2.41851
\(630\) 0 0
\(631\) 9.86390 0.392675 0.196338 0.980536i \(-0.437095\pi\)
0.196338 + 0.980536i \(0.437095\pi\)
\(632\) −10.0147 −0.398363
\(633\) 0 0
\(634\) 40.9035 1.62448
\(635\) 1.71268 0.0679656
\(636\) 0 0
\(637\) −1.16748 −0.0462574
\(638\) 6.28317 0.248753
\(639\) 0 0
\(640\) 22.7261 0.898326
\(641\) −22.0104 −0.869358 −0.434679 0.900585i \(-0.643138\pi\)
−0.434679 + 0.900585i \(0.643138\pi\)
\(642\) 0 0
\(643\) 34.9113 1.37677 0.688383 0.725347i \(-0.258321\pi\)
0.688383 + 0.725347i \(0.258321\pi\)
\(644\) 2.09247 0.0824548
\(645\) 0 0
\(646\) 6.95539 0.273656
\(647\) −5.34394 −0.210092 −0.105046 0.994467i \(-0.533499\pi\)
−0.105046 + 0.994467i \(0.533499\pi\)
\(648\) 0 0
\(649\) −2.74093 −0.107591
\(650\) 3.67976 0.144332
\(651\) 0 0
\(652\) −4.60079 −0.180181
\(653\) −17.7216 −0.693500 −0.346750 0.937958i \(-0.612715\pi\)
−0.346750 + 0.937958i \(0.612715\pi\)
\(654\) 0 0
\(655\) 17.5368 0.685220
\(656\) −0.201068 −0.00785039
\(657\) 0 0
\(658\) −5.46876 −0.213195
\(659\) −47.9307 −1.86711 −0.933557 0.358429i \(-0.883312\pi\)
−0.933557 + 0.358429i \(0.883312\pi\)
\(660\) 0 0
\(661\) −33.4838 −1.30237 −0.651184 0.758920i \(-0.725727\pi\)
−0.651184 + 0.758920i \(0.725727\pi\)
\(662\) 2.59981 0.101045
\(663\) 0 0
\(664\) 16.2454 0.630442
\(665\) −1.41899 −0.0550260
\(666\) 0 0
\(667\) 15.6387 0.605533
\(668\) 6.10133 0.236067
\(669\) 0 0
\(670\) −1.02844 −0.0397322
\(671\) −9.72325 −0.375362
\(672\) 0 0
\(673\) −25.9171 −0.999031 −0.499515 0.866305i \(-0.666489\pi\)
−0.499515 + 0.866305i \(0.666489\pi\)
\(674\) 6.14769 0.236800
\(675\) 0 0
\(676\) −3.79109 −0.145811
\(677\) −42.5126 −1.63389 −0.816946 0.576714i \(-0.804335\pi\)
−0.816946 + 0.576714i \(0.804335\pi\)
\(678\) 0 0
\(679\) 15.1754 0.582379
\(680\) 24.0717 0.923109
\(681\) 0 0
\(682\) −1.50702 −0.0577068
\(683\) 33.7802 1.29257 0.646283 0.763098i \(-0.276323\pi\)
0.646283 + 0.763098i \(0.276323\pi\)
\(684\) 0 0
\(685\) −24.6921 −0.943437
\(686\) 1.52505 0.0582267
\(687\) 0 0
\(688\) −58.8763 −2.24464
\(689\) −14.8990 −0.567607
\(690\) 0 0
\(691\) 17.2866 0.657611 0.328806 0.944398i \(-0.393354\pi\)
0.328806 + 0.944398i \(0.393354\pi\)
\(692\) 7.40899 0.281647
\(693\) 0 0
\(694\) 44.1106 1.67442
\(695\) 4.14362 0.157176
\(696\) 0 0
\(697\) −0.243502 −0.00922331
\(698\) −42.7196 −1.61696
\(699\) 0 0
\(700\) −0.673298 −0.0254483
\(701\) −10.5109 −0.396991 −0.198495 0.980102i \(-0.563605\pi\)
−0.198495 + 0.980102i \(0.563605\pi\)
\(702\) 0 0
\(703\) −9.12939 −0.344321
\(704\) 10.6720 0.402218
\(705\) 0 0
\(706\) 20.4547 0.769823
\(707\) 16.9988 0.639306
\(708\) 0 0
\(709\) −0.557852 −0.0209506 −0.0104753 0.999945i \(-0.503334\pi\)
−0.0104753 + 0.999945i \(0.503334\pi\)
\(710\) −26.2689 −0.985854
\(711\) 0 0
\(712\) −14.7410 −0.552443
\(713\) −3.75095 −0.140474
\(714\) 0 0
\(715\) −3.38342 −0.126533
\(716\) −1.33295 −0.0498148
\(717\) 0 0
\(718\) 21.5532 0.804360
\(719\) −31.7055 −1.18242 −0.591209 0.806519i \(-0.701349\pi\)
−0.591209 + 0.806519i \(0.701349\pi\)
\(720\) 0 0
\(721\) 0.475453 0.0177068
\(722\) −27.9291 −1.03941
\(723\) 0 0
\(724\) −7.81121 −0.290301
\(725\) −5.03210 −0.186888
\(726\) 0 0
\(727\) −23.0045 −0.853190 −0.426595 0.904443i \(-0.640287\pi\)
−0.426595 + 0.904443i \(0.640287\pi\)
\(728\) 2.98090 0.110480
\(729\) 0 0
\(730\) 20.7578 0.768279
\(731\) −71.3018 −2.63719
\(732\) 0 0
\(733\) −35.5374 −1.31260 −0.656302 0.754498i \(-0.727880\pi\)
−0.656302 + 0.754498i \(0.727880\pi\)
\(734\) −0.228697 −0.00844136
\(735\) 0 0
\(736\) −11.7249 −0.432185
\(737\) −0.666269 −0.0245423
\(738\) 0 0
\(739\) 30.4169 1.11890 0.559451 0.828863i \(-0.311012\pi\)
0.559451 + 0.828863i \(0.311012\pi\)
\(740\) 6.14806 0.226007
\(741\) 0 0
\(742\) 19.4621 0.714478
\(743\) −43.1393 −1.58263 −0.791313 0.611411i \(-0.790602\pi\)
−0.791313 + 0.611411i \(0.790602\pi\)
\(744\) 0 0
\(745\) −23.7860 −0.871451
\(746\) 49.4628 1.81096
\(747\) 0 0
\(748\) −3.03450 −0.110952
\(749\) 16.9210 0.618280
\(750\) 0 0
\(751\) −36.1332 −1.31852 −0.659260 0.751915i \(-0.729130\pi\)
−0.659260 + 0.751915i \(0.729130\pi\)
\(752\) 16.2997 0.594389
\(753\) 0 0
\(754\) −4.33511 −0.157875
\(755\) 27.3255 0.994477
\(756\) 0 0
\(757\) −34.0480 −1.23750 −0.618748 0.785590i \(-0.712360\pi\)
−0.618748 + 0.785590i \(0.712360\pi\)
\(758\) −5.25050 −0.190707
\(759\) 0 0
\(760\) 3.62306 0.131422
\(761\) −49.9432 −1.81044 −0.905219 0.424945i \(-0.860293\pi\)
−0.905219 + 0.424945i \(0.860293\pi\)
\(762\) 0 0
\(763\) 3.98507 0.144269
\(764\) 1.75798 0.0636016
\(765\) 0 0
\(766\) 50.9664 1.84149
\(767\) 1.89112 0.0682843
\(768\) 0 0
\(769\) −40.4520 −1.45874 −0.729368 0.684121i \(-0.760186\pi\)
−0.729368 + 0.684121i \(0.760186\pi\)
\(770\) 4.41967 0.159274
\(771\) 0 0
\(772\) −3.16993 −0.114088
\(773\) 27.5266 0.990063 0.495032 0.868875i \(-0.335156\pi\)
0.495032 + 0.868875i \(0.335156\pi\)
\(774\) 0 0
\(775\) 1.20695 0.0433550
\(776\) −38.7470 −1.39094
\(777\) 0 0
\(778\) 45.5606 1.63343
\(779\) −0.0366498 −0.00131312
\(780\) 0 0
\(781\) −17.0181 −0.608956
\(782\) −53.9206 −1.92820
\(783\) 0 0
\(784\) −4.54543 −0.162337
\(785\) −15.1520 −0.540797
\(786\) 0 0
\(787\) −40.4724 −1.44269 −0.721343 0.692578i \(-0.756475\pi\)
−0.721343 + 0.692578i \(0.756475\pi\)
\(788\) 0.0464547 0.00165488
\(789\) 0 0
\(790\) 10.2447 0.364491
\(791\) 18.6198 0.662044
\(792\) 0 0
\(793\) 6.70861 0.238230
\(794\) 31.8415 1.13001
\(795\) 0 0
\(796\) −3.87593 −0.137379
\(797\) 42.8646 1.51834 0.759170 0.650892i \(-0.225605\pi\)
0.759170 + 0.650892i \(0.225605\pi\)
\(798\) 0 0
\(799\) 19.7396 0.698338
\(800\) 3.77274 0.133387
\(801\) 0 0
\(802\) 40.7951 1.44052
\(803\) 13.4478 0.474561
\(804\) 0 0
\(805\) 11.0005 0.387716
\(806\) 1.03978 0.0366246
\(807\) 0 0
\(808\) −43.4025 −1.52690
\(809\) 24.1197 0.848003 0.424001 0.905662i \(-0.360625\pi\)
0.424001 + 0.905662i \(0.360625\pi\)
\(810\) 0 0
\(811\) −4.65144 −0.163334 −0.0816670 0.996660i \(-0.526024\pi\)
−0.0816670 + 0.996660i \(0.526024\pi\)
\(812\) 0.793210 0.0278362
\(813\) 0 0
\(814\) 28.4350 0.996645
\(815\) −24.1872 −0.847240
\(816\) 0 0
\(817\) −10.7317 −0.375455
\(818\) 29.5017 1.03150
\(819\) 0 0
\(820\) 0.0246813 0.000861908 0
\(821\) −11.1947 −0.390697 −0.195349 0.980734i \(-0.562584\pi\)
−0.195349 + 0.980734i \(0.562584\pi\)
\(822\) 0 0
\(823\) 47.6002 1.65924 0.829619 0.558330i \(-0.188558\pi\)
0.829619 + 0.558330i \(0.188558\pi\)
\(824\) −1.21396 −0.0422903
\(825\) 0 0
\(826\) −2.47031 −0.0859532
\(827\) 32.7249 1.13796 0.568979 0.822352i \(-0.307339\pi\)
0.568979 + 0.822352i \(0.307339\pi\)
\(828\) 0 0
\(829\) 31.8180 1.10508 0.552542 0.833485i \(-0.313658\pi\)
0.552542 + 0.833485i \(0.313658\pi\)
\(830\) −16.6185 −0.576837
\(831\) 0 0
\(832\) −7.36323 −0.255274
\(833\) −5.50471 −0.190727
\(834\) 0 0
\(835\) 32.0758 1.11003
\(836\) −0.456726 −0.0157962
\(837\) 0 0
\(838\) 3.27374 0.113089
\(839\) 4.50320 0.155468 0.0777338 0.996974i \(-0.475232\pi\)
0.0777338 + 0.996974i \(0.475232\pi\)
\(840\) 0 0
\(841\) −23.0717 −0.795576
\(842\) −1.02894 −0.0354594
\(843\) 0 0
\(844\) 2.28906 0.0787928
\(845\) −19.9304 −0.685627
\(846\) 0 0
\(847\) −8.13675 −0.279582
\(848\) −58.0071 −1.99197
\(849\) 0 0
\(850\) 17.3502 0.595105
\(851\) 70.7741 2.42611
\(852\) 0 0
\(853\) −43.9321 −1.50421 −0.752103 0.659046i \(-0.770960\pi\)
−0.752103 + 0.659046i \(0.770960\pi\)
\(854\) −8.76327 −0.299873
\(855\) 0 0
\(856\) −43.2039 −1.47668
\(857\) 8.78489 0.300086 0.150043 0.988679i \(-0.452059\pi\)
0.150043 + 0.988679i \(0.452059\pi\)
\(858\) 0 0
\(859\) 40.0693 1.36715 0.683573 0.729883i \(-0.260425\pi\)
0.683573 + 0.729883i \(0.260425\pi\)
\(860\) 7.22711 0.246443
\(861\) 0 0
\(862\) −10.7703 −0.366838
\(863\) −38.3279 −1.30470 −0.652348 0.757919i \(-0.726216\pi\)
−0.652348 + 0.757919i \(0.726216\pi\)
\(864\) 0 0
\(865\) 38.9504 1.32435
\(866\) 10.2784 0.349276
\(867\) 0 0
\(868\) −0.190252 −0.00645756
\(869\) 6.63698 0.225144
\(870\) 0 0
\(871\) 0.459696 0.0155762
\(872\) −10.1750 −0.344567
\(873\) 0 0
\(874\) −8.11564 −0.274516
\(875\) −12.1030 −0.409157
\(876\) 0 0
\(877\) 23.4617 0.792245 0.396122 0.918198i \(-0.370356\pi\)
0.396122 + 0.918198i \(0.370356\pi\)
\(878\) 4.05412 0.136820
\(879\) 0 0
\(880\) −13.1729 −0.444057
\(881\) 38.6863 1.30338 0.651688 0.758487i \(-0.274061\pi\)
0.651688 + 0.758487i \(0.274061\pi\)
\(882\) 0 0
\(883\) −8.55080 −0.287757 −0.143879 0.989595i \(-0.545958\pi\)
−0.143879 + 0.989595i \(0.545958\pi\)
\(884\) 2.09367 0.0704177
\(885\) 0 0
\(886\) −7.66126 −0.257385
\(887\) −53.2942 −1.78944 −0.894722 0.446623i \(-0.852627\pi\)
−0.894722 + 0.446623i \(0.852627\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 15.0796 0.505470
\(891\) 0 0
\(892\) −2.71417 −0.0908772
\(893\) 2.97103 0.0994219
\(894\) 0 0
\(895\) −7.00758 −0.234237
\(896\) 13.2693 0.443297
\(897\) 0 0
\(898\) −25.5816 −0.853669
\(899\) −1.42190 −0.0474231
\(900\) 0 0
\(901\) −70.2492 −2.34034
\(902\) 0.114152 0.00380084
\(903\) 0 0
\(904\) −47.5414 −1.58120
\(905\) −41.0649 −1.36504
\(906\) 0 0
\(907\) 24.0792 0.799536 0.399768 0.916616i \(-0.369091\pi\)
0.399768 + 0.916616i \(0.369091\pi\)
\(908\) −2.45859 −0.0815911
\(909\) 0 0
\(910\) −3.04937 −0.101086
\(911\) 43.2252 1.43212 0.716058 0.698041i \(-0.245945\pi\)
0.716058 + 0.698041i \(0.245945\pi\)
\(912\) 0 0
\(913\) −10.7662 −0.356309
\(914\) −26.8744 −0.888925
\(915\) 0 0
\(916\) −4.33644 −0.143280
\(917\) 10.2394 0.338135
\(918\) 0 0
\(919\) 41.5792 1.37157 0.685786 0.727803i \(-0.259459\pi\)
0.685786 + 0.727803i \(0.259459\pi\)
\(920\) −28.0872 −0.926007
\(921\) 0 0
\(922\) 0.579975 0.0191005
\(923\) 11.7417 0.386484
\(924\) 0 0
\(925\) −22.7732 −0.748777
\(926\) −13.3923 −0.440098
\(927\) 0 0
\(928\) −4.44465 −0.145903
\(929\) 0.613766 0.0201370 0.0100685 0.999949i \(-0.496795\pi\)
0.0100685 + 0.999949i \(0.496795\pi\)
\(930\) 0 0
\(931\) −0.828520 −0.0271536
\(932\) −8.61475 −0.282185
\(933\) 0 0
\(934\) 30.2674 0.990378
\(935\) −15.9529 −0.521716
\(936\) 0 0
\(937\) 46.1622 1.50805 0.754026 0.656845i \(-0.228109\pi\)
0.754026 + 0.656845i \(0.228109\pi\)
\(938\) −0.600488 −0.0196066
\(939\) 0 0
\(940\) −2.00080 −0.0652589
\(941\) −6.85694 −0.223530 −0.111765 0.993735i \(-0.535650\pi\)
−0.111765 + 0.993735i \(0.535650\pi\)
\(942\) 0 0
\(943\) 0.284122 0.00925227
\(944\) 7.36279 0.239638
\(945\) 0 0
\(946\) 33.4256 1.08676
\(947\) −15.9566 −0.518519 −0.259259 0.965808i \(-0.583478\pi\)
−0.259259 + 0.965808i \(0.583478\pi\)
\(948\) 0 0
\(949\) −9.27835 −0.301188
\(950\) 2.61139 0.0847246
\(951\) 0 0
\(952\) 14.0550 0.455526
\(953\) −3.19350 −0.103447 −0.0517237 0.998661i \(-0.516472\pi\)
−0.0517237 + 0.998661i \(0.516472\pi\)
\(954\) 0 0
\(955\) 9.24203 0.299065
\(956\) −4.40852 −0.142582
\(957\) 0 0
\(958\) −2.12278 −0.0685838
\(959\) −14.4173 −0.465557
\(960\) 0 0
\(961\) −30.6590 −0.988999
\(962\) −19.6189 −0.632537
\(963\) 0 0
\(964\) 1.38977 0.0447614
\(965\) −16.6649 −0.536461
\(966\) 0 0
\(967\) −32.8839 −1.05747 −0.528737 0.848786i \(-0.677334\pi\)
−0.528737 + 0.848786i \(0.677334\pi\)
\(968\) 20.7753 0.667745
\(969\) 0 0
\(970\) 39.6370 1.27267
\(971\) 49.2552 1.58068 0.790338 0.612671i \(-0.209905\pi\)
0.790338 + 0.612671i \(0.209905\pi\)
\(972\) 0 0
\(973\) 2.41938 0.0775618
\(974\) −9.13397 −0.292671
\(975\) 0 0
\(976\) 26.1190 0.836049
\(977\) 16.7606 0.536220 0.268110 0.963388i \(-0.413601\pi\)
0.268110 + 0.963388i \(0.413601\pi\)
\(978\) 0 0
\(979\) 9.76923 0.312226
\(980\) 0.557955 0.0178232
\(981\) 0 0
\(982\) 2.87694 0.0918067
\(983\) 49.5398 1.58007 0.790037 0.613059i \(-0.210061\pi\)
0.790037 + 0.613059i \(0.210061\pi\)
\(984\) 0 0
\(985\) 0.244221 0.00778151
\(986\) −20.4401 −0.650946
\(987\) 0 0
\(988\) 0.315120 0.0100253
\(989\) 83.1958 2.64547
\(990\) 0 0
\(991\) −31.0914 −0.987652 −0.493826 0.869561i \(-0.664402\pi\)
−0.493826 + 0.869561i \(0.664402\pi\)
\(992\) 1.06605 0.0338471
\(993\) 0 0
\(994\) −15.3379 −0.486489
\(995\) −20.3765 −0.645977
\(996\) 0 0
\(997\) −53.4798 −1.69372 −0.846861 0.531814i \(-0.821510\pi\)
−0.846861 + 0.531814i \(0.821510\pi\)
\(998\) 27.5284 0.871397
\(999\) 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 \(a_p\))