Properties

Label 8001.2.a.z.1.18
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.242500 q^{2}\) \(-1.94119 q^{4}\) \(-2.79671 q^{5}\) \(-1.00000 q^{7}\) \(-0.955741 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.242500 q^{2}\) \(-1.94119 q^{4}\) \(-2.79671 q^{5}\) \(-1.00000 q^{7}\) \(-0.955741 q^{8}\) \(-0.678204 q^{10}\) \(-4.59836 q^{11}\) \(-4.92098 q^{13}\) \(-0.242500 q^{14}\) \(+3.65062 q^{16}\) \(+2.21339 q^{17}\) \(+0.299740 q^{19}\) \(+5.42896 q^{20}\) \(-1.11510 q^{22}\) \(+2.16929 q^{23}\) \(+2.82161 q^{25}\) \(-1.19334 q^{26}\) \(+1.94119 q^{28}\) \(+5.57762 q^{29}\) \(+6.00125 q^{31}\) \(+2.79676 q^{32}\) \(+0.536748 q^{34}\) \(+2.79671 q^{35}\) \(+8.81952 q^{37}\) \(+0.0726869 q^{38}\) \(+2.67293 q^{40}\) \(+10.5020 q^{41}\) \(-6.69985 q^{43}\) \(+8.92631 q^{44}\) \(+0.526055 q^{46}\) \(-7.58321 q^{47}\) \(+1.00000 q^{49}\) \(+0.684241 q^{50}\) \(+9.55257 q^{52}\) \(+1.04200 q^{53}\) \(+12.8603 q^{55}\) \(+0.955741 q^{56}\) \(+1.35257 q^{58}\) \(+5.65706 q^{59}\) \(+0.161967 q^{61}\) \(+1.45530 q^{62}\) \(-6.62302 q^{64}\) \(+13.7626 q^{65}\) \(+2.60257 q^{67}\) \(-4.29662 q^{68}\) \(+0.678204 q^{70}\) \(+2.49985 q^{71}\) \(-5.94931 q^{73}\) \(+2.13874 q^{74}\) \(-0.581853 q^{76}\) \(+4.59836 q^{77}\) \(-13.1275 q^{79}\) \(-10.2097 q^{80}\) \(+2.54675 q^{82}\) \(+9.40919 q^{83}\) \(-6.19022 q^{85}\) \(-1.62472 q^{86}\) \(+4.39484 q^{88}\) \(-9.33298 q^{89}\) \(+4.92098 q^{91}\) \(-4.21102 q^{92}\) \(-1.83893 q^{94}\) \(-0.838286 q^{95}\) \(-11.8534 q^{97}\) \(+0.242500 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.242500 0.171474 0.0857368 0.996318i \(-0.472676\pi\)
0.0857368 + 0.996318i \(0.472676\pi\)
\(3\) 0 0
\(4\) −1.94119 −0.970597
\(5\) −2.79671 −1.25073 −0.625364 0.780333i \(-0.715050\pi\)
−0.625364 + 0.780333i \(0.715050\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −0.955741 −0.337905
\(9\) 0 0
\(10\) −0.678204 −0.214467
\(11\) −4.59836 −1.38646 −0.693229 0.720718i \(-0.743812\pi\)
−0.693229 + 0.720718i \(0.743812\pi\)
\(12\) 0 0
\(13\) −4.92098 −1.36483 −0.682417 0.730963i \(-0.739071\pi\)
−0.682417 + 0.730963i \(0.739071\pi\)
\(14\) −0.242500 −0.0648109
\(15\) 0 0
\(16\) 3.65062 0.912655
\(17\) 2.21339 0.536826 0.268413 0.963304i \(-0.413501\pi\)
0.268413 + 0.963304i \(0.413501\pi\)
\(18\) 0 0
\(19\) 0.299740 0.0687650 0.0343825 0.999409i \(-0.489054\pi\)
0.0343825 + 0.999409i \(0.489054\pi\)
\(20\) 5.42896 1.21395
\(21\) 0 0
\(22\) −1.11510 −0.237741
\(23\) 2.16929 0.452329 0.226165 0.974089i \(-0.427381\pi\)
0.226165 + 0.974089i \(0.427381\pi\)
\(24\) 0 0
\(25\) 2.82161 0.564321
\(26\) −1.19334 −0.234033
\(27\) 0 0
\(28\) 1.94119 0.366851
\(29\) 5.57762 1.03574 0.517869 0.855460i \(-0.326726\pi\)
0.517869 + 0.855460i \(0.326726\pi\)
\(30\) 0 0
\(31\) 6.00125 1.07786 0.538928 0.842352i \(-0.318829\pi\)
0.538928 + 0.842352i \(0.318829\pi\)
\(32\) 2.79676 0.494402
\(33\) 0 0
\(34\) 0.536748 0.0920515
\(35\) 2.79671 0.472731
\(36\) 0 0
\(37\) 8.81952 1.44992 0.724960 0.688791i \(-0.241858\pi\)
0.724960 + 0.688791i \(0.241858\pi\)
\(38\) 0.0726869 0.0117914
\(39\) 0 0
\(40\) 2.67293 0.422628
\(41\) 10.5020 1.64014 0.820071 0.572262i \(-0.193934\pi\)
0.820071 + 0.572262i \(0.193934\pi\)
\(42\) 0 0
\(43\) −6.69985 −1.02172 −0.510859 0.859665i \(-0.670673\pi\)
−0.510859 + 0.859665i \(0.670673\pi\)
\(44\) 8.92631 1.34569
\(45\) 0 0
\(46\) 0.526055 0.0775625
\(47\) −7.58321 −1.10613 −0.553063 0.833140i \(-0.686541\pi\)
−0.553063 + 0.833140i \(0.686541\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.684241 0.0967662
\(51\) 0 0
\(52\) 9.55257 1.32470
\(53\) 1.04200 0.143130 0.0715649 0.997436i \(-0.477201\pi\)
0.0715649 + 0.997436i \(0.477201\pi\)
\(54\) 0 0
\(55\) 12.8603 1.73408
\(56\) 0.955741 0.127716
\(57\) 0 0
\(58\) 1.35257 0.177602
\(59\) 5.65706 0.736487 0.368243 0.929729i \(-0.379959\pi\)
0.368243 + 0.929729i \(0.379959\pi\)
\(60\) 0 0
\(61\) 0.161967 0.0207378 0.0103689 0.999946i \(-0.496699\pi\)
0.0103689 + 0.999946i \(0.496699\pi\)
\(62\) 1.45530 0.184824
\(63\) 0 0
\(64\) −6.62302 −0.827878
\(65\) 13.7626 1.70704
\(66\) 0 0
\(67\) 2.60257 0.317954 0.158977 0.987282i \(-0.449180\pi\)
0.158977 + 0.987282i \(0.449180\pi\)
\(68\) −4.29662 −0.521041
\(69\) 0 0
\(70\) 0.678204 0.0810609
\(71\) 2.49985 0.296678 0.148339 0.988937i \(-0.452607\pi\)
0.148339 + 0.988937i \(0.452607\pi\)
\(72\) 0 0
\(73\) −5.94931 −0.696314 −0.348157 0.937436i \(-0.613192\pi\)
−0.348157 + 0.937436i \(0.613192\pi\)
\(74\) 2.13874 0.248623
\(75\) 0 0
\(76\) −0.581853 −0.0667431
\(77\) 4.59836 0.524032
\(78\) 0 0
\(79\) −13.1275 −1.47696 −0.738482 0.674273i \(-0.764457\pi\)
−0.738482 + 0.674273i \(0.764457\pi\)
\(80\) −10.2097 −1.14148
\(81\) 0 0
\(82\) 2.54675 0.281241
\(83\) 9.40919 1.03279 0.516396 0.856350i \(-0.327273\pi\)
0.516396 + 0.856350i \(0.327273\pi\)
\(84\) 0 0
\(85\) −6.19022 −0.671423
\(86\) −1.62472 −0.175198
\(87\) 0 0
\(88\) 4.39484 0.468492
\(89\) −9.33298 −0.989294 −0.494647 0.869094i \(-0.664703\pi\)
−0.494647 + 0.869094i \(0.664703\pi\)
\(90\) 0 0
\(91\) 4.92098 0.515859
\(92\) −4.21102 −0.439029
\(93\) 0 0
\(94\) −1.83893 −0.189671
\(95\) −0.838286 −0.0860063
\(96\) 0 0
\(97\) −11.8534 −1.20353 −0.601767 0.798672i \(-0.705536\pi\)
−0.601767 + 0.798672i \(0.705536\pi\)
\(98\) 0.242500 0.0244962
\(99\) 0 0
\(100\) −5.47729 −0.547729
\(101\) 5.46441 0.543729 0.271864 0.962336i \(-0.412360\pi\)
0.271864 + 0.962336i \(0.412360\pi\)
\(102\) 0 0
\(103\) 0.754962 0.0743886 0.0371943 0.999308i \(-0.488158\pi\)
0.0371943 + 0.999308i \(0.488158\pi\)
\(104\) 4.70318 0.461185
\(105\) 0 0
\(106\) 0.252685 0.0245430
\(107\) −10.6424 −1.02884 −0.514419 0.857539i \(-0.671992\pi\)
−0.514419 + 0.857539i \(0.671992\pi\)
\(108\) 0 0
\(109\) 6.61161 0.633277 0.316639 0.948546i \(-0.397446\pi\)
0.316639 + 0.948546i \(0.397446\pi\)
\(110\) 3.11863 0.297349
\(111\) 0 0
\(112\) −3.65062 −0.344951
\(113\) 3.73009 0.350897 0.175449 0.984489i \(-0.443862\pi\)
0.175449 + 0.984489i \(0.443862\pi\)
\(114\) 0 0
\(115\) −6.06690 −0.565741
\(116\) −10.8272 −1.00528
\(117\) 0 0
\(118\) 1.37184 0.126288
\(119\) −2.21339 −0.202901
\(120\) 0 0
\(121\) 10.1449 0.922265
\(122\) 0.0392771 0.00355598
\(123\) 0 0
\(124\) −11.6496 −1.04616
\(125\) 6.09234 0.544916
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −7.19960 −0.636361
\(129\) 0 0
\(130\) 3.33743 0.292712
\(131\) −4.24308 −0.370720 −0.185360 0.982671i \(-0.559345\pi\)
−0.185360 + 0.982671i \(0.559345\pi\)
\(132\) 0 0
\(133\) −0.299740 −0.0259907
\(134\) 0.631124 0.0545208
\(135\) 0 0
\(136\) −2.11543 −0.181396
\(137\) 6.12330 0.523148 0.261574 0.965183i \(-0.415758\pi\)
0.261574 + 0.965183i \(0.415758\pi\)
\(138\) 0 0
\(139\) −5.79278 −0.491337 −0.245668 0.969354i \(-0.579007\pi\)
−0.245668 + 0.969354i \(0.579007\pi\)
\(140\) −5.42896 −0.458831
\(141\) 0 0
\(142\) 0.606215 0.0508725
\(143\) 22.6284 1.89228
\(144\) 0 0
\(145\) −15.5990 −1.29543
\(146\) −1.44271 −0.119399
\(147\) 0 0
\(148\) −17.1204 −1.40729
\(149\) 8.83924 0.724139 0.362070 0.932151i \(-0.382070\pi\)
0.362070 + 0.932151i \(0.382070\pi\)
\(150\) 0 0
\(151\) −8.09628 −0.658866 −0.329433 0.944179i \(-0.606858\pi\)
−0.329433 + 0.944179i \(0.606858\pi\)
\(152\) −0.286473 −0.0232361
\(153\) 0 0
\(154\) 1.11510 0.0898576
\(155\) −16.7838 −1.34811
\(156\) 0 0
\(157\) −0.0956181 −0.00763116 −0.00381558 0.999993i \(-0.501215\pi\)
−0.00381558 + 0.999993i \(0.501215\pi\)
\(158\) −3.18344 −0.253260
\(159\) 0 0
\(160\) −7.82173 −0.618362
\(161\) −2.16929 −0.170964
\(162\) 0 0
\(163\) 15.4482 1.21000 0.604998 0.796227i \(-0.293174\pi\)
0.604998 + 0.796227i \(0.293174\pi\)
\(164\) −20.3865 −1.59192
\(165\) 0 0
\(166\) 2.28173 0.177097
\(167\) −15.5614 −1.20418 −0.602089 0.798429i \(-0.705665\pi\)
−0.602089 + 0.798429i \(0.705665\pi\)
\(168\) 0 0
\(169\) 11.2160 0.862772
\(170\) −1.50113 −0.115131
\(171\) 0 0
\(172\) 13.0057 0.991676
\(173\) −3.17589 −0.241459 −0.120729 0.992685i \(-0.538523\pi\)
−0.120729 + 0.992685i \(0.538523\pi\)
\(174\) 0 0
\(175\) −2.82161 −0.213293
\(176\) −16.7869 −1.26536
\(177\) 0 0
\(178\) −2.26325 −0.169638
\(179\) 0.645010 0.0482103 0.0241051 0.999709i \(-0.492326\pi\)
0.0241051 + 0.999709i \(0.492326\pi\)
\(180\) 0 0
\(181\) 1.26616 0.0941132 0.0470566 0.998892i \(-0.485016\pi\)
0.0470566 + 0.998892i \(0.485016\pi\)
\(182\) 1.19334 0.0884562
\(183\) 0 0
\(184\) −2.07328 −0.152845
\(185\) −24.6657 −1.81346
\(186\) 0 0
\(187\) −10.1780 −0.744286
\(188\) 14.7205 1.07360
\(189\) 0 0
\(190\) −0.203285 −0.0147478
\(191\) −18.1421 −1.31272 −0.656359 0.754449i \(-0.727904\pi\)
−0.656359 + 0.754449i \(0.727904\pi\)
\(192\) 0 0
\(193\) 20.8712 1.50234 0.751170 0.660109i \(-0.229490\pi\)
0.751170 + 0.660109i \(0.229490\pi\)
\(194\) −2.87446 −0.206374
\(195\) 0 0
\(196\) −1.94119 −0.138657
\(197\) 14.1011 1.00466 0.502331 0.864676i \(-0.332476\pi\)
0.502331 + 0.864676i \(0.332476\pi\)
\(198\) 0 0
\(199\) −21.2186 −1.50415 −0.752073 0.659080i \(-0.770946\pi\)
−0.752073 + 0.659080i \(0.770946\pi\)
\(200\) −2.69672 −0.190687
\(201\) 0 0
\(202\) 1.32512 0.0932352
\(203\) −5.57762 −0.391472
\(204\) 0 0
\(205\) −29.3712 −2.05137
\(206\) 0.183079 0.0127557
\(207\) 0 0
\(208\) −17.9646 −1.24562
\(209\) −1.37831 −0.0953397
\(210\) 0 0
\(211\) −1.78981 −0.123215 −0.0616077 0.998100i \(-0.519623\pi\)
−0.0616077 + 0.998100i \(0.519623\pi\)
\(212\) −2.02272 −0.138921
\(213\) 0 0
\(214\) −2.58078 −0.176419
\(215\) 18.7376 1.27789
\(216\) 0 0
\(217\) −6.00125 −0.407391
\(218\) 1.60332 0.108590
\(219\) 0 0
\(220\) −24.9643 −1.68309
\(221\) −10.8920 −0.732678
\(222\) 0 0
\(223\) −2.33108 −0.156101 −0.0780504 0.996949i \(-0.524870\pi\)
−0.0780504 + 0.996949i \(0.524870\pi\)
\(224\) −2.79676 −0.186866
\(225\) 0 0
\(226\) 0.904548 0.0601696
\(227\) 17.3413 1.15098 0.575490 0.817809i \(-0.304811\pi\)
0.575490 + 0.817809i \(0.304811\pi\)
\(228\) 0 0
\(229\) −11.1731 −0.738342 −0.369171 0.929361i \(-0.620358\pi\)
−0.369171 + 0.929361i \(0.620358\pi\)
\(230\) −1.47122 −0.0970097
\(231\) 0 0
\(232\) −5.33076 −0.349981
\(233\) 12.6112 0.826189 0.413094 0.910688i \(-0.364448\pi\)
0.413094 + 0.910688i \(0.364448\pi\)
\(234\) 0 0
\(235\) 21.2081 1.38346
\(236\) −10.9815 −0.714832
\(237\) 0 0
\(238\) −0.536748 −0.0347922
\(239\) −6.93025 −0.448280 −0.224140 0.974557i \(-0.571957\pi\)
−0.224140 + 0.974557i \(0.571957\pi\)
\(240\) 0 0
\(241\) −9.07372 −0.584489 −0.292245 0.956344i \(-0.594402\pi\)
−0.292245 + 0.956344i \(0.594402\pi\)
\(242\) 2.46015 0.158144
\(243\) 0 0
\(244\) −0.314410 −0.0201280
\(245\) −2.79671 −0.178675
\(246\) 0 0
\(247\) −1.47501 −0.0938528
\(248\) −5.73564 −0.364213
\(249\) 0 0
\(250\) 1.47739 0.0934387
\(251\) 17.1122 1.08011 0.540057 0.841628i \(-0.318403\pi\)
0.540057 + 0.841628i \(0.318403\pi\)
\(252\) 0 0
\(253\) −9.97520 −0.627135
\(254\) −0.242500 −0.0152158
\(255\) 0 0
\(256\) 11.5001 0.718759
\(257\) 9.41351 0.587199 0.293599 0.955929i \(-0.405147\pi\)
0.293599 + 0.955929i \(0.405147\pi\)
\(258\) 0 0
\(259\) −8.81952 −0.548018
\(260\) −26.7158 −1.65684
\(261\) 0 0
\(262\) −1.02895 −0.0635686
\(263\) −6.64471 −0.409730 −0.204865 0.978790i \(-0.565676\pi\)
−0.204865 + 0.978790i \(0.565676\pi\)
\(264\) 0 0
\(265\) −2.91418 −0.179016
\(266\) −0.0726869 −0.00445672
\(267\) 0 0
\(268\) −5.05209 −0.308605
\(269\) −16.0652 −0.979514 −0.489757 0.871859i \(-0.662915\pi\)
−0.489757 + 0.871859i \(0.662915\pi\)
\(270\) 0 0
\(271\) 29.0605 1.76530 0.882651 0.470030i \(-0.155757\pi\)
0.882651 + 0.470030i \(0.155757\pi\)
\(272\) 8.08024 0.489937
\(273\) 0 0
\(274\) 1.48490 0.0897062
\(275\) −12.9748 −0.782408
\(276\) 0 0
\(277\) 12.0489 0.723950 0.361975 0.932188i \(-0.382103\pi\)
0.361975 + 0.932188i \(0.382103\pi\)
\(278\) −1.40475 −0.0842513
\(279\) 0 0
\(280\) −2.67293 −0.159738
\(281\) 0.729114 0.0434953 0.0217476 0.999763i \(-0.493077\pi\)
0.0217476 + 0.999763i \(0.493077\pi\)
\(282\) 0 0
\(283\) 5.70007 0.338834 0.169417 0.985544i \(-0.445811\pi\)
0.169417 + 0.985544i \(0.445811\pi\)
\(284\) −4.85270 −0.287955
\(285\) 0 0
\(286\) 5.48740 0.324477
\(287\) −10.5020 −0.619915
\(288\) 0 0
\(289\) −12.1009 −0.711818
\(290\) −3.78276 −0.222131
\(291\) 0 0
\(292\) 11.5488 0.675840
\(293\) 16.3296 0.953983 0.476991 0.878908i \(-0.341727\pi\)
0.476991 + 0.878908i \(0.341727\pi\)
\(294\) 0 0
\(295\) −15.8212 −0.921145
\(296\) −8.42918 −0.489936
\(297\) 0 0
\(298\) 2.14352 0.124171
\(299\) −10.6751 −0.617354
\(300\) 0 0
\(301\) 6.69985 0.386173
\(302\) −1.96335 −0.112978
\(303\) 0 0
\(304\) 1.09424 0.0627587
\(305\) −0.452976 −0.0259373
\(306\) 0 0
\(307\) 3.16022 0.180363 0.0901816 0.995925i \(-0.471255\pi\)
0.0901816 + 0.995925i \(0.471255\pi\)
\(308\) −8.92631 −0.508624
\(309\) 0 0
\(310\) −4.07007 −0.231165
\(311\) 27.0887 1.53606 0.768029 0.640415i \(-0.221237\pi\)
0.768029 + 0.640415i \(0.221237\pi\)
\(312\) 0 0
\(313\) −18.0755 −1.02169 −0.510844 0.859673i \(-0.670667\pi\)
−0.510844 + 0.859673i \(0.670667\pi\)
\(314\) −0.0231874 −0.00130854
\(315\) 0 0
\(316\) 25.4831 1.43354
\(317\) 14.8515 0.834142 0.417071 0.908874i \(-0.363057\pi\)
0.417071 + 0.908874i \(0.363057\pi\)
\(318\) 0 0
\(319\) −25.6479 −1.43601
\(320\) 18.5227 1.03545
\(321\) 0 0
\(322\) −0.526055 −0.0293159
\(323\) 0.663440 0.0369148
\(324\) 0 0
\(325\) −13.8851 −0.770205
\(326\) 3.74620 0.207483
\(327\) 0 0
\(328\) −10.0372 −0.554213
\(329\) 7.58321 0.418076
\(330\) 0 0
\(331\) −29.7585 −1.63568 −0.817839 0.575447i \(-0.804828\pi\)
−0.817839 + 0.575447i \(0.804828\pi\)
\(332\) −18.2651 −1.00243
\(333\) 0 0
\(334\) −3.77365 −0.206485
\(335\) −7.27864 −0.397675
\(336\) 0 0
\(337\) 17.3368 0.944397 0.472198 0.881492i \(-0.343461\pi\)
0.472198 + 0.881492i \(0.343461\pi\)
\(338\) 2.71989 0.147943
\(339\) 0 0
\(340\) 12.0164 0.651681
\(341\) −27.5959 −1.49440
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 6.40332 0.345244
\(345\) 0 0
\(346\) −0.770156 −0.0414038
\(347\) −13.4672 −0.722959 −0.361479 0.932380i \(-0.617728\pi\)
−0.361479 + 0.932380i \(0.617728\pi\)
\(348\) 0 0
\(349\) −16.6140 −0.889328 −0.444664 0.895697i \(-0.646677\pi\)
−0.444664 + 0.895697i \(0.646677\pi\)
\(350\) −0.684241 −0.0365742
\(351\) 0 0
\(352\) −12.8605 −0.685467
\(353\) −0.705030 −0.0375249 −0.0187625 0.999824i \(-0.505973\pi\)
−0.0187625 + 0.999824i \(0.505973\pi\)
\(354\) 0 0
\(355\) −6.99137 −0.371064
\(356\) 18.1171 0.960205
\(357\) 0 0
\(358\) 0.156415 0.00826679
\(359\) 6.08609 0.321211 0.160606 0.987019i \(-0.448655\pi\)
0.160606 + 0.987019i \(0.448655\pi\)
\(360\) 0 0
\(361\) −18.9102 −0.995271
\(362\) 0.307045 0.0161379
\(363\) 0 0
\(364\) −9.55257 −0.500691
\(365\) 16.6385 0.870900
\(366\) 0 0
\(367\) 0.822218 0.0429194 0.0214597 0.999770i \(-0.493169\pi\)
0.0214597 + 0.999770i \(0.493169\pi\)
\(368\) 7.91927 0.412821
\(369\) 0 0
\(370\) −5.98143 −0.310960
\(371\) −1.04200 −0.0540980
\(372\) 0 0
\(373\) −3.32058 −0.171933 −0.0859665 0.996298i \(-0.527398\pi\)
−0.0859665 + 0.996298i \(0.527398\pi\)
\(374\) −2.46816 −0.127625
\(375\) 0 0
\(376\) 7.24759 0.373766
\(377\) −27.4473 −1.41361
\(378\) 0 0
\(379\) 8.11526 0.416853 0.208426 0.978038i \(-0.433166\pi\)
0.208426 + 0.978038i \(0.433166\pi\)
\(380\) 1.62727 0.0834774
\(381\) 0 0
\(382\) −4.39947 −0.225096
\(383\) −6.77315 −0.346092 −0.173046 0.984914i \(-0.555361\pi\)
−0.173046 + 0.984914i \(0.555361\pi\)
\(384\) 0 0
\(385\) −12.8603 −0.655421
\(386\) 5.06127 0.257612
\(387\) 0 0
\(388\) 23.0098 1.16815
\(389\) 8.89791 0.451142 0.225571 0.974227i \(-0.427575\pi\)
0.225571 + 0.974227i \(0.427575\pi\)
\(390\) 0 0
\(391\) 4.80149 0.242822
\(392\) −0.955741 −0.0482722
\(393\) 0 0
\(394\) 3.41952 0.172273
\(395\) 36.7140 1.84728
\(396\) 0 0
\(397\) 6.55375 0.328923 0.164462 0.986383i \(-0.447411\pi\)
0.164462 + 0.986383i \(0.447411\pi\)
\(398\) −5.14551 −0.257921
\(399\) 0 0
\(400\) 10.3006 0.515031
\(401\) 2.19709 0.109717 0.0548586 0.998494i \(-0.482529\pi\)
0.0548586 + 0.998494i \(0.482529\pi\)
\(402\) 0 0
\(403\) −29.5320 −1.47109
\(404\) −10.6075 −0.527742
\(405\) 0 0
\(406\) −1.35257 −0.0671271
\(407\) −40.5553 −2.01025
\(408\) 0 0
\(409\) −38.3816 −1.89785 −0.948923 0.315507i \(-0.897825\pi\)
−0.948923 + 0.315507i \(0.897825\pi\)
\(410\) −7.12252 −0.351756
\(411\) 0 0
\(412\) −1.46553 −0.0722014
\(413\) −5.65706 −0.278366
\(414\) 0 0
\(415\) −26.3148 −1.29174
\(416\) −13.7628 −0.674776
\(417\) 0 0
\(418\) −0.334241 −0.0163482
\(419\) 22.1140 1.08034 0.540169 0.841556i \(-0.318360\pi\)
0.540169 + 0.841556i \(0.318360\pi\)
\(420\) 0 0
\(421\) 22.8139 1.11188 0.555940 0.831223i \(-0.312359\pi\)
0.555940 + 0.831223i \(0.312359\pi\)
\(422\) −0.434029 −0.0211282
\(423\) 0 0
\(424\) −0.995882 −0.0483643
\(425\) 6.24531 0.302942
\(426\) 0 0
\(427\) −0.161967 −0.00783815
\(428\) 20.6589 0.998587
\(429\) 0 0
\(430\) 4.54387 0.219125
\(431\) 31.7123 1.52753 0.763764 0.645495i \(-0.223349\pi\)
0.763764 + 0.645495i \(0.223349\pi\)
\(432\) 0 0
\(433\) 30.3802 1.45998 0.729988 0.683459i \(-0.239525\pi\)
0.729988 + 0.683459i \(0.239525\pi\)
\(434\) −1.45530 −0.0698569
\(435\) 0 0
\(436\) −12.8344 −0.614657
\(437\) 0.650224 0.0311044
\(438\) 0 0
\(439\) −27.8747 −1.33038 −0.665192 0.746672i \(-0.731650\pi\)
−0.665192 + 0.746672i \(0.731650\pi\)
\(440\) −12.2911 −0.585956
\(441\) 0 0
\(442\) −2.64132 −0.125635
\(443\) 33.6373 1.59816 0.799078 0.601227i \(-0.205321\pi\)
0.799078 + 0.601227i \(0.205321\pi\)
\(444\) 0 0
\(445\) 26.1017 1.23734
\(446\) −0.565289 −0.0267672
\(447\) 0 0
\(448\) 6.62302 0.312908
\(449\) −2.86855 −0.135375 −0.0676876 0.997707i \(-0.521562\pi\)
−0.0676876 + 0.997707i \(0.521562\pi\)
\(450\) 0 0
\(451\) −48.2921 −2.27399
\(452\) −7.24082 −0.340580
\(453\) 0 0
\(454\) 4.20526 0.197363
\(455\) −13.7626 −0.645199
\(456\) 0 0
\(457\) −27.3334 −1.27860 −0.639301 0.768957i \(-0.720776\pi\)
−0.639301 + 0.768957i \(0.720776\pi\)
\(458\) −2.70949 −0.126606
\(459\) 0 0
\(460\) 11.7770 0.549106
\(461\) 3.54928 0.165306 0.0826531 0.996578i \(-0.473661\pi\)
0.0826531 + 0.996578i \(0.473661\pi\)
\(462\) 0 0
\(463\) −26.7780 −1.24448 −0.622239 0.782828i \(-0.713777\pi\)
−0.622239 + 0.782828i \(0.713777\pi\)
\(464\) 20.3618 0.945271
\(465\) 0 0
\(466\) 3.05823 0.141670
\(467\) −13.4294 −0.621438 −0.310719 0.950502i \(-0.600570\pi\)
−0.310719 + 0.950502i \(0.600570\pi\)
\(468\) 0 0
\(469\) −2.60257 −0.120175
\(470\) 5.14297 0.237227
\(471\) 0 0
\(472\) −5.40668 −0.248863
\(473\) 30.8083 1.41657
\(474\) 0 0
\(475\) 0.845747 0.0388055
\(476\) 4.29662 0.196935
\(477\) 0 0
\(478\) −1.68059 −0.0768683
\(479\) −24.0582 −1.09925 −0.549624 0.835412i \(-0.685229\pi\)
−0.549624 + 0.835412i \(0.685229\pi\)
\(480\) 0 0
\(481\) −43.4007 −1.97890
\(482\) −2.20038 −0.100225
\(483\) 0 0
\(484\) −19.6932 −0.895147
\(485\) 33.1507 1.50529
\(486\) 0 0
\(487\) 1.40323 0.0635864 0.0317932 0.999494i \(-0.489878\pi\)
0.0317932 + 0.999494i \(0.489878\pi\)
\(488\) −0.154799 −0.00700741
\(489\) 0 0
\(490\) −0.678204 −0.0306381
\(491\) 18.9765 0.856398 0.428199 0.903684i \(-0.359148\pi\)
0.428199 + 0.903684i \(0.359148\pi\)
\(492\) 0 0
\(493\) 12.3454 0.556011
\(494\) −0.357691 −0.0160933
\(495\) 0 0
\(496\) 21.9083 0.983711
\(497\) −2.49985 −0.112134
\(498\) 0 0
\(499\) −3.91564 −0.175288 −0.0876441 0.996152i \(-0.527934\pi\)
−0.0876441 + 0.996152i \(0.527934\pi\)
\(500\) −11.8264 −0.528893
\(501\) 0 0
\(502\) 4.14972 0.185211
\(503\) −4.39051 −0.195763 −0.0978815 0.995198i \(-0.531207\pi\)
−0.0978815 + 0.995198i \(0.531207\pi\)
\(504\) 0 0
\(505\) −15.2824 −0.680057
\(506\) −2.41899 −0.107537
\(507\) 0 0
\(508\) 1.94119 0.0861265
\(509\) −3.77299 −0.167235 −0.0836175 0.996498i \(-0.526647\pi\)
−0.0836175 + 0.996498i \(0.526647\pi\)
\(510\) 0 0
\(511\) 5.94931 0.263182
\(512\) 17.1880 0.759609
\(513\) 0 0
\(514\) 2.28278 0.100689
\(515\) −2.11141 −0.0930400
\(516\) 0 0
\(517\) 34.8703 1.53360
\(518\) −2.13874 −0.0939707
\(519\) 0 0
\(520\) −13.1534 −0.576817
\(521\) 40.5257 1.77546 0.887731 0.460362i \(-0.152281\pi\)
0.887731 + 0.460362i \(0.152281\pi\)
\(522\) 0 0
\(523\) 1.15256 0.0503979 0.0251990 0.999682i \(-0.491978\pi\)
0.0251990 + 0.999682i \(0.491978\pi\)
\(524\) 8.23664 0.359819
\(525\) 0 0
\(526\) −1.61134 −0.0702580
\(527\) 13.2831 0.578621
\(528\) 0 0
\(529\) −18.2942 −0.795398
\(530\) −0.706689 −0.0306966
\(531\) 0 0
\(532\) 0.581853 0.0252265
\(533\) −51.6803 −2.23852
\(534\) 0 0
\(535\) 29.7637 1.28680
\(536\) −2.48738 −0.107438
\(537\) 0 0
\(538\) −3.89582 −0.167961
\(539\) −4.59836 −0.198065
\(540\) 0 0
\(541\) 23.7874 1.02270 0.511349 0.859373i \(-0.329146\pi\)
0.511349 + 0.859373i \(0.329146\pi\)
\(542\) 7.04719 0.302703
\(543\) 0 0
\(544\) 6.19031 0.265408
\(545\) −18.4908 −0.792058
\(546\) 0 0
\(547\) −11.2951 −0.482945 −0.241473 0.970408i \(-0.577630\pi\)
−0.241473 + 0.970408i \(0.577630\pi\)
\(548\) −11.8865 −0.507766
\(549\) 0 0
\(550\) −3.14638 −0.134162
\(551\) 1.67183 0.0712225
\(552\) 0 0
\(553\) 13.1275 0.558240
\(554\) 2.92187 0.124138
\(555\) 0 0
\(556\) 11.2449 0.476890
\(557\) −13.6757 −0.579459 −0.289730 0.957109i \(-0.593565\pi\)
−0.289730 + 0.957109i \(0.593565\pi\)
\(558\) 0 0
\(559\) 32.9698 1.39448
\(560\) 10.2097 0.431440
\(561\) 0 0
\(562\) 0.176810 0.00745829
\(563\) −23.5207 −0.991278 −0.495639 0.868529i \(-0.665066\pi\)
−0.495639 + 0.868529i \(0.665066\pi\)
\(564\) 0 0
\(565\) −10.4320 −0.438877
\(566\) 1.38227 0.0581011
\(567\) 0 0
\(568\) −2.38921 −0.100249
\(569\) 4.30680 0.180550 0.0902752 0.995917i \(-0.471225\pi\)
0.0902752 + 0.995917i \(0.471225\pi\)
\(570\) 0 0
\(571\) −17.3440 −0.725822 −0.362911 0.931824i \(-0.618217\pi\)
−0.362911 + 0.931824i \(0.618217\pi\)
\(572\) −43.9262 −1.83665
\(573\) 0 0
\(574\) −2.54675 −0.106299
\(575\) 6.12090 0.255259
\(576\) 0 0
\(577\) −2.97581 −0.123885 −0.0619423 0.998080i \(-0.519729\pi\)
−0.0619423 + 0.998080i \(0.519729\pi\)
\(578\) −2.93447 −0.122058
\(579\) 0 0
\(580\) 30.2807 1.25734
\(581\) −9.40919 −0.390359
\(582\) 0 0
\(583\) −4.79149 −0.198443
\(584\) 5.68600 0.235288
\(585\) 0 0
\(586\) 3.95992 0.163583
\(587\) −35.0446 −1.44645 −0.723224 0.690614i \(-0.757340\pi\)
−0.723224 + 0.690614i \(0.757340\pi\)
\(588\) 0 0
\(589\) 1.79881 0.0741187
\(590\) −3.83664 −0.157952
\(591\) 0 0
\(592\) 32.1967 1.32328
\(593\) −13.3444 −0.547988 −0.273994 0.961731i \(-0.588345\pi\)
−0.273994 + 0.961731i \(0.588345\pi\)
\(594\) 0 0
\(595\) 6.19022 0.253774
\(596\) −17.1587 −0.702847
\(597\) 0 0
\(598\) −2.58870 −0.105860
\(599\) −25.1804 −1.02884 −0.514421 0.857538i \(-0.671993\pi\)
−0.514421 + 0.857538i \(0.671993\pi\)
\(600\) 0 0
\(601\) −31.7897 −1.29673 −0.648364 0.761331i \(-0.724546\pi\)
−0.648364 + 0.761331i \(0.724546\pi\)
\(602\) 1.62472 0.0662185
\(603\) 0 0
\(604\) 15.7164 0.639493
\(605\) −28.3724 −1.15350
\(606\) 0 0
\(607\) −27.3805 −1.11134 −0.555669 0.831403i \(-0.687538\pi\)
−0.555669 + 0.831403i \(0.687538\pi\)
\(608\) 0.838299 0.0339975
\(609\) 0 0
\(610\) −0.109847 −0.00444757
\(611\) 37.3168 1.50968
\(612\) 0 0
\(613\) −47.9879 −1.93821 −0.969107 0.246642i \(-0.920673\pi\)
−0.969107 + 0.246642i \(0.920673\pi\)
\(614\) 0.766355 0.0309276
\(615\) 0 0
\(616\) −4.39484 −0.177073
\(617\) −23.4031 −0.942174 −0.471087 0.882087i \(-0.656138\pi\)
−0.471087 + 0.882087i \(0.656138\pi\)
\(618\) 0 0
\(619\) −3.26112 −0.131076 −0.0655378 0.997850i \(-0.520876\pi\)
−0.0655378 + 0.997850i \(0.520876\pi\)
\(620\) 32.5806 1.30847
\(621\) 0 0
\(622\) 6.56902 0.263394
\(623\) 9.33298 0.373918
\(624\) 0 0
\(625\) −31.1466 −1.24586
\(626\) −4.38332 −0.175193
\(627\) 0 0
\(628\) 0.185613 0.00740678
\(629\) 19.5210 0.778355
\(630\) 0 0
\(631\) −19.8046 −0.788407 −0.394203 0.919023i \(-0.628979\pi\)
−0.394203 + 0.919023i \(0.628979\pi\)
\(632\) 12.5465 0.499074
\(633\) 0 0
\(634\) 3.60149 0.143033
\(635\) 2.79671 0.110984
\(636\) 0 0
\(637\) −4.92098 −0.194976
\(638\) −6.21962 −0.246237
\(639\) 0 0
\(640\) 20.1352 0.795915
\(641\) −45.0976 −1.78125 −0.890624 0.454741i \(-0.849732\pi\)
−0.890624 + 0.454741i \(0.849732\pi\)
\(642\) 0 0
\(643\) 6.19892 0.244461 0.122231 0.992502i \(-0.460995\pi\)
0.122231 + 0.992502i \(0.460995\pi\)
\(644\) 4.21102 0.165937
\(645\) 0 0
\(646\) 0.160885 0.00632992
\(647\) −12.8151 −0.503815 −0.251907 0.967751i \(-0.581058\pi\)
−0.251907 + 0.967751i \(0.581058\pi\)
\(648\) 0 0
\(649\) −26.0132 −1.02111
\(650\) −3.36713 −0.132070
\(651\) 0 0
\(652\) −29.9880 −1.17442
\(653\) −6.35355 −0.248633 −0.124317 0.992243i \(-0.539674\pi\)
−0.124317 + 0.992243i \(0.539674\pi\)
\(654\) 0 0
\(655\) 11.8667 0.463669
\(656\) 38.3389 1.49688
\(657\) 0 0
\(658\) 1.83893 0.0716890
\(659\) 29.5580 1.15141 0.575707 0.817656i \(-0.304727\pi\)
0.575707 + 0.817656i \(0.304727\pi\)
\(660\) 0 0
\(661\) −30.8995 −1.20185 −0.600926 0.799305i \(-0.705201\pi\)
−0.600926 + 0.799305i \(0.705201\pi\)
\(662\) −7.21646 −0.280476
\(663\) 0 0
\(664\) −8.99275 −0.348986
\(665\) 0.838286 0.0325073
\(666\) 0 0
\(667\) 12.0995 0.468494
\(668\) 30.2077 1.16877
\(669\) 0 0
\(670\) −1.76507 −0.0681907
\(671\) −0.744784 −0.0287521
\(672\) 0 0
\(673\) 37.1773 1.43308 0.716540 0.697546i \(-0.245725\pi\)
0.716540 + 0.697546i \(0.245725\pi\)
\(674\) 4.20418 0.161939
\(675\) 0 0
\(676\) −21.7725 −0.837404
\(677\) −0.0588742 −0.00226272 −0.00113136 0.999999i \(-0.500360\pi\)
−0.00113136 + 0.999999i \(0.500360\pi\)
\(678\) 0 0
\(679\) 11.8534 0.454893
\(680\) 5.91624 0.226878
\(681\) 0 0
\(682\) −6.69202 −0.256251
\(683\) −7.13511 −0.273018 −0.136509 0.990639i \(-0.543588\pi\)
−0.136509 + 0.990639i \(0.543588\pi\)
\(684\) 0 0
\(685\) −17.1251 −0.654317
\(686\) −0.242500 −0.00925871
\(687\) 0 0
\(688\) −24.4586 −0.932476
\(689\) −5.12766 −0.195348
\(690\) 0 0
\(691\) −23.8916 −0.908878 −0.454439 0.890778i \(-0.650160\pi\)
−0.454439 + 0.890778i \(0.650160\pi\)
\(692\) 6.16503 0.234359
\(693\) 0 0
\(694\) −3.26581 −0.123968
\(695\) 16.2007 0.614529
\(696\) 0 0
\(697\) 23.2451 0.880470
\(698\) −4.02891 −0.152496
\(699\) 0 0
\(700\) 5.47729 0.207022
\(701\) −42.6818 −1.61207 −0.806034 0.591869i \(-0.798390\pi\)
−0.806034 + 0.591869i \(0.798390\pi\)
\(702\) 0 0
\(703\) 2.64356 0.0997037
\(704\) 30.4551 1.14782
\(705\) 0 0
\(706\) −0.170970 −0.00643454
\(707\) −5.46441 −0.205510
\(708\) 0 0
\(709\) −29.4112 −1.10456 −0.552280 0.833658i \(-0.686242\pi\)
−0.552280 + 0.833658i \(0.686242\pi\)
\(710\) −1.69541 −0.0636276
\(711\) 0 0
\(712\) 8.91991 0.334288
\(713\) 13.0185 0.487546
\(714\) 0 0
\(715\) −63.2852 −2.36673
\(716\) −1.25209 −0.0467927
\(717\) 0 0
\(718\) 1.47588 0.0550793
\(719\) −48.1805 −1.79683 −0.898416 0.439146i \(-0.855281\pi\)
−0.898416 + 0.439146i \(0.855281\pi\)
\(720\) 0 0
\(721\) −0.754962 −0.0281163
\(722\) −4.58572 −0.170663
\(723\) 0 0
\(724\) −2.45787 −0.0913459
\(725\) 15.7378 0.584489
\(726\) 0 0
\(727\) 41.1964 1.52789 0.763944 0.645282i \(-0.223260\pi\)
0.763944 + 0.645282i \(0.223260\pi\)
\(728\) −4.70318 −0.174311
\(729\) 0 0
\(730\) 4.03485 0.149336
\(731\) −14.8294 −0.548484
\(732\) 0 0
\(733\) −51.8699 −1.91586 −0.957929 0.287004i \(-0.907341\pi\)
−0.957929 + 0.287004i \(0.907341\pi\)
\(734\) 0.199388 0.00735955
\(735\) 0 0
\(736\) 6.06699 0.223632
\(737\) −11.9675 −0.440830
\(738\) 0 0
\(739\) 25.1518 0.925222 0.462611 0.886561i \(-0.346913\pi\)
0.462611 + 0.886561i \(0.346913\pi\)
\(740\) 47.8808 1.76013
\(741\) 0 0
\(742\) −0.252685 −0.00927637
\(743\) 39.8449 1.46177 0.730884 0.682502i \(-0.239108\pi\)
0.730884 + 0.682502i \(0.239108\pi\)
\(744\) 0 0
\(745\) −24.7208 −0.905701
\(746\) −0.805242 −0.0294820
\(747\) 0 0
\(748\) 19.7574 0.722402
\(749\) 10.6424 0.388864
\(750\) 0 0
\(751\) 13.6188 0.496958 0.248479 0.968637i \(-0.420069\pi\)
0.248479 + 0.968637i \(0.420069\pi\)
\(752\) −27.6834 −1.00951
\(753\) 0 0
\(754\) −6.65599 −0.242397
\(755\) 22.6430 0.824062
\(756\) 0 0
\(757\) 37.3375 1.35705 0.678527 0.734576i \(-0.262619\pi\)
0.678527 + 0.734576i \(0.262619\pi\)
\(758\) 1.96795 0.0714793
\(759\) 0 0
\(760\) 0.801184 0.0290620
\(761\) 7.96910 0.288880 0.144440 0.989514i \(-0.453862\pi\)
0.144440 + 0.989514i \(0.453862\pi\)
\(762\) 0 0
\(763\) −6.61161 −0.239356
\(764\) 35.2174 1.27412
\(765\) 0 0
\(766\) −1.64249 −0.0593456
\(767\) −27.8383 −1.00518
\(768\) 0 0
\(769\) 32.8938 1.18618 0.593091 0.805136i \(-0.297908\pi\)
0.593091 + 0.805136i \(0.297908\pi\)
\(770\) −3.11863 −0.112387
\(771\) 0 0
\(772\) −40.5150 −1.45817
\(773\) 3.09221 0.111219 0.0556095 0.998453i \(-0.482290\pi\)
0.0556095 + 0.998453i \(0.482290\pi\)
\(774\) 0 0
\(775\) 16.9332 0.608257
\(776\) 11.3288 0.406681
\(777\) 0 0
\(778\) 2.15775 0.0773590
\(779\) 3.14787 0.112784
\(780\) 0 0
\(781\) −11.4952 −0.411332
\(782\) 1.16436 0.0416376
\(783\) 0 0
\(784\) 3.65062 0.130379
\(785\) 0.267416 0.00954450
\(786\) 0 0
\(787\) −18.1780 −0.647975 −0.323987 0.946061i \(-0.605024\pi\)
−0.323987 + 0.946061i \(0.605024\pi\)
\(788\) −27.3730 −0.975121
\(789\) 0 0
\(790\) 8.90316 0.316760
\(791\) −3.73009 −0.132627
\(792\) 0 0
\(793\) −0.797038 −0.0283036
\(794\) 1.58929 0.0564017
\(795\) 0 0
\(796\) 41.1894 1.45992
\(797\) 12.4294 0.440273 0.220136 0.975469i \(-0.429350\pi\)
0.220136 + 0.975469i \(0.429350\pi\)
\(798\) 0 0
\(799\) −16.7846 −0.593797
\(800\) 7.89135 0.279001
\(801\) 0 0
\(802\) 0.532794 0.0188136
\(803\) 27.3571 0.965410
\(804\) 0 0
\(805\) 6.06690 0.213830
\(806\) −7.16153 −0.252254
\(807\) 0 0
\(808\) −5.22256 −0.183729
\(809\) 38.2936 1.34633 0.673165 0.739492i \(-0.264934\pi\)
0.673165 + 0.739492i \(0.264934\pi\)
\(810\) 0 0
\(811\) −43.5810 −1.53034 −0.765168 0.643830i \(-0.777344\pi\)
−0.765168 + 0.643830i \(0.777344\pi\)
\(812\) 10.8272 0.379962
\(813\) 0 0
\(814\) −9.83468 −0.344705
\(815\) −43.2042 −1.51338
\(816\) 0 0
\(817\) −2.00821 −0.0702584
\(818\) −9.30754 −0.325431
\(819\) 0 0
\(820\) 57.0151 1.99105
\(821\) −34.7141 −1.21153 −0.605765 0.795644i \(-0.707133\pi\)
−0.605765 + 0.795644i \(0.707133\pi\)
\(822\) 0 0
\(823\) −30.6184 −1.06729 −0.533645 0.845708i \(-0.679178\pi\)
−0.533645 + 0.845708i \(0.679178\pi\)
\(824\) −0.721548 −0.0251363
\(825\) 0 0
\(826\) −1.37184 −0.0477324
\(827\) 48.9512 1.70220 0.851099 0.525005i \(-0.175936\pi\)
0.851099 + 0.525005i \(0.175936\pi\)
\(828\) 0 0
\(829\) −3.52359 −0.122379 −0.0611897 0.998126i \(-0.519489\pi\)
−0.0611897 + 0.998126i \(0.519489\pi\)
\(830\) −6.38135 −0.221500
\(831\) 0 0
\(832\) 32.5918 1.12992
\(833\) 2.21339 0.0766894
\(834\) 0 0
\(835\) 43.5208 1.50610
\(836\) 2.67557 0.0925364
\(837\) 0 0
\(838\) 5.36265 0.185250
\(839\) 11.5384 0.398349 0.199175 0.979964i \(-0.436174\pi\)
0.199175 + 0.979964i \(0.436174\pi\)
\(840\) 0 0
\(841\) 2.10982 0.0727525
\(842\) 5.53237 0.190658
\(843\) 0 0
\(844\) 3.47436 0.119592
\(845\) −31.3680 −1.07909
\(846\) 0 0
\(847\) −10.1449 −0.348583
\(848\) 3.80395 0.130628
\(849\) 0 0
\(850\) 1.51449 0.0519466
\(851\) 19.1321 0.655841
\(852\) 0 0
\(853\) 5.47685 0.187524 0.0937618 0.995595i \(-0.470111\pi\)
0.0937618 + 0.995595i \(0.470111\pi\)
\(854\) −0.0392771 −0.00134404
\(855\) 0 0
\(856\) 10.1714 0.347650
\(857\) 9.38512 0.320590 0.160295 0.987069i \(-0.448756\pi\)
0.160295 + 0.987069i \(0.448756\pi\)
\(858\) 0 0
\(859\) −8.15150 −0.278126 −0.139063 0.990284i \(-0.544409\pi\)
−0.139063 + 0.990284i \(0.544409\pi\)
\(860\) −36.3732 −1.24032
\(861\) 0 0
\(862\) 7.69025 0.261931
\(863\) 17.5317 0.596784 0.298392 0.954443i \(-0.403550\pi\)
0.298392 + 0.954443i \(0.403550\pi\)
\(864\) 0 0
\(865\) 8.88207 0.301999
\(866\) 7.36720 0.250348
\(867\) 0 0
\(868\) 11.6496 0.395413
\(869\) 60.3652 2.04775
\(870\) 0 0
\(871\) −12.8072 −0.433955
\(872\) −6.31898 −0.213988
\(873\) 0 0
\(874\) 0.157679 0.00533359
\(875\) −6.09234 −0.205959
\(876\) 0 0
\(877\) 25.2611 0.853008 0.426504 0.904486i \(-0.359745\pi\)
0.426504 + 0.904486i \(0.359745\pi\)
\(878\) −6.75961 −0.228126
\(879\) 0 0
\(880\) 46.9480 1.58262
\(881\) 8.27215 0.278696 0.139348 0.990243i \(-0.455499\pi\)
0.139348 + 0.990243i \(0.455499\pi\)
\(882\) 0 0
\(883\) 53.8500 1.81220 0.906099 0.423066i \(-0.139046\pi\)
0.906099 + 0.423066i \(0.139046\pi\)
\(884\) 21.1436 0.711135
\(885\) 0 0
\(886\) 8.15706 0.274042
\(887\) 26.0125 0.873414 0.436707 0.899604i \(-0.356145\pi\)
0.436707 + 0.899604i \(0.356145\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 6.32966 0.212171
\(891\) 0 0
\(892\) 4.52508 0.151511
\(893\) −2.27299 −0.0760627
\(894\) 0 0
\(895\) −1.80391 −0.0602980
\(896\) 7.19960 0.240522
\(897\) 0 0
\(898\) −0.695624 −0.0232133
\(899\) 33.4727 1.11638
\(900\) 0 0
\(901\) 2.30635 0.0768357
\(902\) −11.7109 −0.389929
\(903\) 0 0
\(904\) −3.56500 −0.118570
\(905\) −3.54110 −0.117710
\(906\) 0 0
\(907\) 43.7207 1.45172 0.725861 0.687842i \(-0.241442\pi\)
0.725861 + 0.687842i \(0.241442\pi\)
\(908\) −33.6628 −1.11714
\(909\) 0 0
\(910\) −3.33743 −0.110635
\(911\) 56.2800 1.86464 0.932320 0.361634i \(-0.117781\pi\)
0.932320 + 0.361634i \(0.117781\pi\)
\(912\) 0 0
\(913\) −43.2669 −1.43192
\(914\) −6.62836 −0.219247
\(915\) 0 0
\(916\) 21.6892 0.716633
\(917\) 4.24308 0.140119
\(918\) 0 0
\(919\) −49.1675 −1.62189 −0.810943 0.585125i \(-0.801045\pi\)
−0.810943 + 0.585125i \(0.801045\pi\)
\(920\) 5.79838 0.191167
\(921\) 0 0
\(922\) 0.860701 0.0283457
\(923\) −12.3017 −0.404916
\(924\) 0 0
\(925\) 24.8852 0.818221
\(926\) −6.49367 −0.213395
\(927\) 0 0
\(928\) 15.5992 0.512070
\(929\) −18.0024 −0.590640 −0.295320 0.955398i \(-0.595426\pi\)
−0.295320 + 0.955398i \(0.595426\pi\)
\(930\) 0 0
\(931\) 0.299740 0.00982357
\(932\) −24.4808 −0.801896
\(933\) 0 0
\(934\) −3.25663 −0.106560
\(935\) 28.4648 0.930900
\(936\) 0 0
\(937\) 6.11724 0.199842 0.0999208 0.994995i \(-0.468141\pi\)
0.0999208 + 0.994995i \(0.468141\pi\)
\(938\) −0.631124 −0.0206069
\(939\) 0 0
\(940\) −41.1690 −1.34278
\(941\) 39.7665 1.29635 0.648175 0.761492i \(-0.275533\pi\)
0.648175 + 0.761492i \(0.275533\pi\)
\(942\) 0 0
\(943\) 22.7820 0.741884
\(944\) 20.6518 0.672158
\(945\) 0 0
\(946\) 7.47103 0.242904
\(947\) 17.0699 0.554698 0.277349 0.960769i \(-0.410544\pi\)
0.277349 + 0.960769i \(0.410544\pi\)
\(948\) 0 0
\(949\) 29.2764 0.950353
\(950\) 0.205094 0.00665413
\(951\) 0 0
\(952\) 2.11543 0.0685614
\(953\) 14.4999 0.469698 0.234849 0.972032i \(-0.424540\pi\)
0.234849 + 0.972032i \(0.424540\pi\)
\(954\) 0 0
\(955\) 50.7383 1.64185
\(956\) 13.4529 0.435099
\(957\) 0 0
\(958\) −5.83412 −0.188492
\(959\) −6.12330 −0.197732
\(960\) 0 0
\(961\) 5.01499 0.161774
\(962\) −10.5247 −0.339329
\(963\) 0 0
\(964\) 17.6138 0.567304
\(965\) −58.3707 −1.87902
\(966\) 0 0
\(967\) −19.8725 −0.639056 −0.319528 0.947577i \(-0.603524\pi\)
−0.319528 + 0.947577i \(0.603524\pi\)
\(968\) −9.69591 −0.311638
\(969\) 0 0
\(970\) 8.03905 0.258118
\(971\) −16.7784 −0.538446 −0.269223 0.963078i \(-0.586767\pi\)
−0.269223 + 0.963078i \(0.586767\pi\)
\(972\) 0 0
\(973\) 5.79278 0.185708
\(974\) 0.340284 0.0109034
\(975\) 0 0
\(976\) 0.591281 0.0189264
\(977\) −58.6614 −1.87675 −0.938373 0.345625i \(-0.887667\pi\)
−0.938373 + 0.345625i \(0.887667\pi\)
\(978\) 0 0
\(979\) 42.9164 1.37161
\(980\) 5.42896 0.173422
\(981\) 0 0
\(982\) 4.60181 0.146850
\(983\) −4.99877 −0.159436 −0.0797181 0.996817i \(-0.525402\pi\)
−0.0797181 + 0.996817i \(0.525402\pi\)
\(984\) 0 0
\(985\) −39.4367 −1.25656
\(986\) 2.99377 0.0953412
\(987\) 0 0
\(988\) 2.86328 0.0910932
\(989\) −14.5340 −0.462153
\(990\) 0 0
\(991\) −1.62682 −0.0516775 −0.0258388 0.999666i \(-0.508226\pi\)
−0.0258388 + 0.999666i \(0.508226\pi\)
\(992\) 16.7840 0.532894
\(993\) 0 0
\(994\) −0.606215 −0.0192280
\(995\) 59.3423 1.88128
\(996\) 0 0
\(997\) 34.8421 1.10346 0.551730 0.834023i \(-0.313968\pi\)
0.551730 + 0.834023i \(0.313968\pi\)
\(998\) −0.949544 −0.0300573
\(999\) 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 \(a_p\))