Properties

Label 8001.2.a.v.1.17
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 1.17
Root \(-1.94177\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.94177 q^{2}\) \(+1.77048 q^{4}\) \(-3.66642 q^{5}\) \(+1.00000 q^{7}\) \(-0.445683 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.94177 q^{2}\) \(+1.77048 q^{4}\) \(-3.66642 q^{5}\) \(+1.00000 q^{7}\) \(-0.445683 q^{8}\) \(-7.11935 q^{10}\) \(-2.76439 q^{11}\) \(-3.90363 q^{13}\) \(+1.94177 q^{14}\) \(-4.40637 q^{16}\) \(-3.65343 q^{17}\) \(-2.93631 q^{19}\) \(-6.49131 q^{20}\) \(-5.36782 q^{22}\) \(+5.90239 q^{23}\) \(+8.44263 q^{25}\) \(-7.57996 q^{26}\) \(+1.77048 q^{28}\) \(-1.00996 q^{29}\) \(-0.885070 q^{31}\) \(-7.66479 q^{32}\) \(-7.09412 q^{34}\) \(-3.66642 q^{35}\) \(+5.97192 q^{37}\) \(-5.70165 q^{38}\) \(+1.63406 q^{40}\) \(-7.04246 q^{41}\) \(+5.95501 q^{43}\) \(-4.89429 q^{44}\) \(+11.4611 q^{46}\) \(+5.51094 q^{47}\) \(+1.00000 q^{49}\) \(+16.3937 q^{50}\) \(-6.91129 q^{52}\) \(-4.27470 q^{53}\) \(+10.1354 q^{55}\) \(-0.445683 q^{56}\) \(-1.96110 q^{58}\) \(+7.36890 q^{59}\) \(+11.9371 q^{61}\) \(-1.71860 q^{62}\) \(-6.07054 q^{64}\) \(+14.3124 q^{65}\) \(+8.14451 q^{67}\) \(-6.46831 q^{68}\) \(-7.11935 q^{70}\) \(-4.06599 q^{71}\) \(+1.01678 q^{73}\) \(+11.5961 q^{74}\) \(-5.19867 q^{76}\) \(-2.76439 q^{77}\) \(+1.03997 q^{79}\) \(+16.1556 q^{80}\) \(-13.6748 q^{82}\) \(-3.97794 q^{83}\) \(+13.3950 q^{85}\) \(+11.5633 q^{86}\) \(+1.23204 q^{88}\) \(-10.8011 q^{89}\) \(-3.90363 q^{91}\) \(+10.4501 q^{92}\) \(+10.7010 q^{94}\) \(+10.7658 q^{95}\) \(+13.1382 q^{97}\) \(+1.94177 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.94177 1.37304 0.686520 0.727111i \(-0.259137\pi\)
0.686520 + 0.727111i \(0.259137\pi\)
\(3\) 0 0
\(4\) 1.77048 0.885238
\(5\) −3.66642 −1.63967 −0.819836 0.572598i \(-0.805936\pi\)
−0.819836 + 0.572598i \(0.805936\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.445683 −0.157573
\(9\) 0 0
\(10\) −7.11935 −2.25134
\(11\) −2.76439 −0.833496 −0.416748 0.909022i \(-0.636830\pi\)
−0.416748 + 0.909022i \(0.636830\pi\)
\(12\) 0 0
\(13\) −3.90363 −1.08267 −0.541336 0.840806i \(-0.682081\pi\)
−0.541336 + 0.840806i \(0.682081\pi\)
\(14\) 1.94177 0.518960
\(15\) 0 0
\(16\) −4.40637 −1.10159
\(17\) −3.65343 −0.886087 −0.443043 0.896500i \(-0.646101\pi\)
−0.443043 + 0.896500i \(0.646101\pi\)
\(18\) 0 0
\(19\) −2.93631 −0.673636 −0.336818 0.941570i \(-0.609351\pi\)
−0.336818 + 0.941570i \(0.609351\pi\)
\(20\) −6.49131 −1.45150
\(21\) 0 0
\(22\) −5.36782 −1.14442
\(23\) 5.90239 1.23073 0.615367 0.788241i \(-0.289008\pi\)
0.615367 + 0.788241i \(0.289008\pi\)
\(24\) 0 0
\(25\) 8.44263 1.68853
\(26\) −7.57996 −1.48655
\(27\) 0 0
\(28\) 1.77048 0.334589
\(29\) −1.00996 −0.187544 −0.0937720 0.995594i \(-0.529892\pi\)
−0.0937720 + 0.995594i \(0.529892\pi\)
\(30\) 0 0
\(31\) −0.885070 −0.158963 −0.0794817 0.996836i \(-0.525327\pi\)
−0.0794817 + 0.996836i \(0.525327\pi\)
\(32\) −7.66479 −1.35496
\(33\) 0 0
\(34\) −7.09412 −1.21663
\(35\) −3.66642 −0.619738
\(36\) 0 0
\(37\) 5.97192 0.981778 0.490889 0.871222i \(-0.336672\pi\)
0.490889 + 0.871222i \(0.336672\pi\)
\(38\) −5.70165 −0.924929
\(39\) 0 0
\(40\) 1.63406 0.258368
\(41\) −7.04246 −1.09985 −0.549924 0.835215i \(-0.685343\pi\)
−0.549924 + 0.835215i \(0.685343\pi\)
\(42\) 0 0
\(43\) 5.95501 0.908130 0.454065 0.890969i \(-0.349973\pi\)
0.454065 + 0.890969i \(0.349973\pi\)
\(44\) −4.89429 −0.737843
\(45\) 0 0
\(46\) 11.4611 1.68985
\(47\) 5.51094 0.803853 0.401927 0.915672i \(-0.368341\pi\)
0.401927 + 0.915672i \(0.368341\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 16.3937 2.31841
\(51\) 0 0
\(52\) −6.91129 −0.958423
\(53\) −4.27470 −0.587176 −0.293588 0.955932i \(-0.594849\pi\)
−0.293588 + 0.955932i \(0.594849\pi\)
\(54\) 0 0
\(55\) 10.1354 1.36666
\(56\) −0.445683 −0.0595568
\(57\) 0 0
\(58\) −1.96110 −0.257505
\(59\) 7.36890 0.959349 0.479675 0.877446i \(-0.340755\pi\)
0.479675 + 0.877446i \(0.340755\pi\)
\(60\) 0 0
\(61\) 11.9371 1.52839 0.764197 0.644983i \(-0.223136\pi\)
0.764197 + 0.644983i \(0.223136\pi\)
\(62\) −1.71860 −0.218263
\(63\) 0 0
\(64\) −6.07054 −0.758817
\(65\) 14.3124 1.77523
\(66\) 0 0
\(67\) 8.14451 0.995011 0.497505 0.867461i \(-0.334249\pi\)
0.497505 + 0.867461i \(0.334249\pi\)
\(68\) −6.46831 −0.784398
\(69\) 0 0
\(70\) −7.11935 −0.850925
\(71\) −4.06599 −0.482545 −0.241272 0.970457i \(-0.577565\pi\)
−0.241272 + 0.970457i \(0.577565\pi\)
\(72\) 0 0
\(73\) 1.01678 0.119005 0.0595027 0.998228i \(-0.481049\pi\)
0.0595027 + 0.998228i \(0.481049\pi\)
\(74\) 11.5961 1.34802
\(75\) 0 0
\(76\) −5.19867 −0.596329
\(77\) −2.76439 −0.315032
\(78\) 0 0
\(79\) 1.03997 0.117006 0.0585029 0.998287i \(-0.481367\pi\)
0.0585029 + 0.998287i \(0.481367\pi\)
\(80\) 16.1556 1.80625
\(81\) 0 0
\(82\) −13.6748 −1.51013
\(83\) −3.97794 −0.436636 −0.218318 0.975878i \(-0.570057\pi\)
−0.218318 + 0.975878i \(0.570057\pi\)
\(84\) 0 0
\(85\) 13.3950 1.45289
\(86\) 11.5633 1.24690
\(87\) 0 0
\(88\) 1.23204 0.131336
\(89\) −10.8011 −1.14492 −0.572458 0.819934i \(-0.694010\pi\)
−0.572458 + 0.819934i \(0.694010\pi\)
\(90\) 0 0
\(91\) −3.90363 −0.409212
\(92\) 10.4501 1.08949
\(93\) 0 0
\(94\) 10.7010 1.10372
\(95\) 10.7658 1.10454
\(96\) 0 0
\(97\) 13.1382 1.33398 0.666991 0.745065i \(-0.267582\pi\)
0.666991 + 0.745065i \(0.267582\pi\)
\(98\) 1.94177 0.196149
\(99\) 0 0
\(100\) 14.9475 1.49475
\(101\) 1.59877 0.159083 0.0795415 0.996832i \(-0.474654\pi\)
0.0795415 + 0.996832i \(0.474654\pi\)
\(102\) 0 0
\(103\) 1.33183 0.131229 0.0656144 0.997845i \(-0.479099\pi\)
0.0656144 + 0.997845i \(0.479099\pi\)
\(104\) 1.73978 0.170600
\(105\) 0 0
\(106\) −8.30050 −0.806215
\(107\) 4.41836 0.427139 0.213570 0.976928i \(-0.431491\pi\)
0.213570 + 0.976928i \(0.431491\pi\)
\(108\) 0 0
\(109\) −6.80353 −0.651660 −0.325830 0.945428i \(-0.605644\pi\)
−0.325830 + 0.945428i \(0.605644\pi\)
\(110\) 19.6807 1.87648
\(111\) 0 0
\(112\) −4.40637 −0.416362
\(113\) 11.6660 1.09744 0.548720 0.836006i \(-0.315115\pi\)
0.548720 + 0.836006i \(0.315115\pi\)
\(114\) 0 0
\(115\) −21.6407 −2.01800
\(116\) −1.78810 −0.166021
\(117\) 0 0
\(118\) 14.3087 1.31722
\(119\) −3.65343 −0.334909
\(120\) 0 0
\(121\) −3.35813 −0.305284
\(122\) 23.1792 2.09855
\(123\) 0 0
\(124\) −1.56700 −0.140720
\(125\) −12.6221 −1.12896
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 3.54198 0.313070
\(129\) 0 0
\(130\) 27.7913 2.43746
\(131\) −5.62011 −0.491032 −0.245516 0.969393i \(-0.578957\pi\)
−0.245516 + 0.969393i \(0.578957\pi\)
\(132\) 0 0
\(133\) −2.93631 −0.254611
\(134\) 15.8148 1.36619
\(135\) 0 0
\(136\) 1.62827 0.139623
\(137\) 7.90120 0.675045 0.337523 0.941317i \(-0.390411\pi\)
0.337523 + 0.941317i \(0.390411\pi\)
\(138\) 0 0
\(139\) −21.4360 −1.81818 −0.909089 0.416601i \(-0.863221\pi\)
−0.909089 + 0.416601i \(0.863221\pi\)
\(140\) −6.49131 −0.548616
\(141\) 0 0
\(142\) −7.89523 −0.662553
\(143\) 10.7912 0.902404
\(144\) 0 0
\(145\) 3.70292 0.307511
\(146\) 1.97436 0.163399
\(147\) 0 0
\(148\) 10.5731 0.869107
\(149\) 1.21636 0.0996478 0.0498239 0.998758i \(-0.484134\pi\)
0.0498239 + 0.998758i \(0.484134\pi\)
\(150\) 0 0
\(151\) 0.654350 0.0532502 0.0266251 0.999645i \(-0.491524\pi\)
0.0266251 + 0.999645i \(0.491524\pi\)
\(152\) 1.30866 0.106147
\(153\) 0 0
\(154\) −5.36782 −0.432551
\(155\) 3.24504 0.260648
\(156\) 0 0
\(157\) 12.1435 0.969158 0.484579 0.874747i \(-0.338973\pi\)
0.484579 + 0.874747i \(0.338973\pi\)
\(158\) 2.01938 0.160654
\(159\) 0 0
\(160\) 28.1023 2.22169
\(161\) 5.90239 0.465174
\(162\) 0 0
\(163\) −11.1369 −0.872307 −0.436154 0.899872i \(-0.643660\pi\)
−0.436154 + 0.899872i \(0.643660\pi\)
\(164\) −12.4685 −0.973627
\(165\) 0 0
\(166\) −7.72426 −0.599519
\(167\) −14.8250 −1.14719 −0.573597 0.819137i \(-0.694453\pi\)
−0.573597 + 0.819137i \(0.694453\pi\)
\(168\) 0 0
\(169\) 2.23835 0.172181
\(170\) 26.0100 1.99488
\(171\) 0 0
\(172\) 10.5432 0.803911
\(173\) −10.9026 −0.828907 −0.414453 0.910071i \(-0.636027\pi\)
−0.414453 + 0.910071i \(0.636027\pi\)
\(174\) 0 0
\(175\) 8.44263 0.638203
\(176\) 12.1809 0.918172
\(177\) 0 0
\(178\) −20.9733 −1.57202
\(179\) −1.82536 −0.136434 −0.0682168 0.997671i \(-0.521731\pi\)
−0.0682168 + 0.997671i \(0.521731\pi\)
\(180\) 0 0
\(181\) −21.5199 −1.59956 −0.799781 0.600292i \(-0.795051\pi\)
−0.799781 + 0.600292i \(0.795051\pi\)
\(182\) −7.57996 −0.561864
\(183\) 0 0
\(184\) −2.63059 −0.193930
\(185\) −21.8956 −1.60979
\(186\) 0 0
\(187\) 10.0995 0.738550
\(188\) 9.75699 0.711602
\(189\) 0 0
\(190\) 20.9046 1.51658
\(191\) 4.98503 0.360704 0.180352 0.983602i \(-0.442276\pi\)
0.180352 + 0.983602i \(0.442276\pi\)
\(192\) 0 0
\(193\) 14.6773 1.05649 0.528247 0.849091i \(-0.322850\pi\)
0.528247 + 0.849091i \(0.322850\pi\)
\(194\) 25.5114 1.83161
\(195\) 0 0
\(196\) 1.77048 0.126463
\(197\) 17.4312 1.24192 0.620960 0.783843i \(-0.286743\pi\)
0.620960 + 0.783843i \(0.286743\pi\)
\(198\) 0 0
\(199\) 25.4374 1.80321 0.901606 0.432558i \(-0.142389\pi\)
0.901606 + 0.432558i \(0.142389\pi\)
\(200\) −3.76274 −0.266066
\(201\) 0 0
\(202\) 3.10444 0.218427
\(203\) −1.00996 −0.0708850
\(204\) 0 0
\(205\) 25.8206 1.80339
\(206\) 2.58610 0.180182
\(207\) 0 0
\(208\) 17.2008 1.19266
\(209\) 8.11713 0.561473
\(210\) 0 0
\(211\) 4.97851 0.342735 0.171367 0.985207i \(-0.445182\pi\)
0.171367 + 0.985207i \(0.445182\pi\)
\(212\) −7.56826 −0.519790
\(213\) 0 0
\(214\) 8.57945 0.586479
\(215\) −21.8335 −1.48904
\(216\) 0 0
\(217\) −0.885070 −0.0600825
\(218\) −13.2109 −0.894755
\(219\) 0 0
\(220\) 17.9445 1.20982
\(221\) 14.2616 0.959342
\(222\) 0 0
\(223\) −1.48750 −0.0996106 −0.0498053 0.998759i \(-0.515860\pi\)
−0.0498053 + 0.998759i \(0.515860\pi\)
\(224\) −7.66479 −0.512125
\(225\) 0 0
\(226\) 22.6526 1.50683
\(227\) 19.5282 1.29613 0.648066 0.761584i \(-0.275578\pi\)
0.648066 + 0.761584i \(0.275578\pi\)
\(228\) 0 0
\(229\) −8.26693 −0.546294 −0.273147 0.961972i \(-0.588065\pi\)
−0.273147 + 0.961972i \(0.588065\pi\)
\(230\) −42.0212 −2.77080
\(231\) 0 0
\(232\) 0.450119 0.0295518
\(233\) 23.3515 1.52981 0.764905 0.644143i \(-0.222786\pi\)
0.764905 + 0.644143i \(0.222786\pi\)
\(234\) 0 0
\(235\) −20.2054 −1.31806
\(236\) 13.0465 0.849252
\(237\) 0 0
\(238\) −7.09412 −0.459844
\(239\) −14.2016 −0.918625 −0.459313 0.888275i \(-0.651904\pi\)
−0.459313 + 0.888275i \(0.651904\pi\)
\(240\) 0 0
\(241\) 4.08805 0.263335 0.131667 0.991294i \(-0.457967\pi\)
0.131667 + 0.991294i \(0.457967\pi\)
\(242\) −6.52071 −0.419167
\(243\) 0 0
\(244\) 21.1344 1.35299
\(245\) −3.66642 −0.234239
\(246\) 0 0
\(247\) 11.4623 0.729328
\(248\) 0.394461 0.0250483
\(249\) 0 0
\(250\) −24.5093 −1.55011
\(251\) 24.8954 1.57138 0.785690 0.618620i \(-0.212308\pi\)
0.785690 + 0.618620i \(0.212308\pi\)
\(252\) 0 0
\(253\) −16.3165 −1.02581
\(254\) 1.94177 0.121838
\(255\) 0 0
\(256\) 19.0188 1.18867
\(257\) 12.2395 0.763481 0.381740 0.924270i \(-0.375325\pi\)
0.381740 + 0.924270i \(0.375325\pi\)
\(258\) 0 0
\(259\) 5.97192 0.371077
\(260\) 25.3397 1.57150
\(261\) 0 0
\(262\) −10.9130 −0.674206
\(263\) 1.56340 0.0964035 0.0482018 0.998838i \(-0.484651\pi\)
0.0482018 + 0.998838i \(0.484651\pi\)
\(264\) 0 0
\(265\) 15.6729 0.962776
\(266\) −5.70165 −0.349590
\(267\) 0 0
\(268\) 14.4197 0.880821
\(269\) −21.2587 −1.29616 −0.648082 0.761571i \(-0.724428\pi\)
−0.648082 + 0.761571i \(0.724428\pi\)
\(270\) 0 0
\(271\) 4.59026 0.278838 0.139419 0.990233i \(-0.455476\pi\)
0.139419 + 0.990233i \(0.455476\pi\)
\(272\) 16.0983 0.976106
\(273\) 0 0
\(274\) 15.3423 0.926864
\(275\) −23.3388 −1.40738
\(276\) 0 0
\(277\) 13.4342 0.807183 0.403592 0.914939i \(-0.367762\pi\)
0.403592 + 0.914939i \(0.367762\pi\)
\(278\) −41.6238 −2.49643
\(279\) 0 0
\(280\) 1.63406 0.0976537
\(281\) 20.7151 1.23576 0.617879 0.786273i \(-0.287992\pi\)
0.617879 + 0.786273i \(0.287992\pi\)
\(282\) 0 0
\(283\) 6.68438 0.397345 0.198673 0.980066i \(-0.436337\pi\)
0.198673 + 0.980066i \(0.436337\pi\)
\(284\) −7.19874 −0.427167
\(285\) 0 0
\(286\) 20.9540 1.23904
\(287\) −7.04246 −0.415703
\(288\) 0 0
\(289\) −3.65245 −0.214850
\(290\) 7.19022 0.422224
\(291\) 0 0
\(292\) 1.80019 0.105348
\(293\) 1.67899 0.0980877 0.0490438 0.998797i \(-0.484383\pi\)
0.0490438 + 0.998797i \(0.484383\pi\)
\(294\) 0 0
\(295\) −27.0175 −1.57302
\(296\) −2.66158 −0.154701
\(297\) 0 0
\(298\) 2.36189 0.136820
\(299\) −23.0408 −1.33248
\(300\) 0 0
\(301\) 5.95501 0.343241
\(302\) 1.27060 0.0731147
\(303\) 0 0
\(304\) 12.9385 0.742072
\(305\) −43.7666 −2.50607
\(306\) 0 0
\(307\) 0.815036 0.0465166 0.0232583 0.999729i \(-0.492596\pi\)
0.0232583 + 0.999729i \(0.492596\pi\)
\(308\) −4.89429 −0.278878
\(309\) 0 0
\(310\) 6.30113 0.357880
\(311\) −6.64455 −0.376778 −0.188389 0.982095i \(-0.560327\pi\)
−0.188389 + 0.982095i \(0.560327\pi\)
\(312\) 0 0
\(313\) 0.290004 0.0163920 0.00819599 0.999966i \(-0.497391\pi\)
0.00819599 + 0.999966i \(0.497391\pi\)
\(314\) 23.5799 1.33069
\(315\) 0 0
\(316\) 1.84124 0.103578
\(317\) −33.6696 −1.89107 −0.945536 0.325518i \(-0.894461\pi\)
−0.945536 + 0.325518i \(0.894461\pi\)
\(318\) 0 0
\(319\) 2.79191 0.156317
\(320\) 22.2571 1.24421
\(321\) 0 0
\(322\) 11.4611 0.638702
\(323\) 10.7276 0.596900
\(324\) 0 0
\(325\) −32.9569 −1.82812
\(326\) −21.6253 −1.19771
\(327\) 0 0
\(328\) 3.13870 0.173306
\(329\) 5.51094 0.303828
\(330\) 0 0
\(331\) 18.1886 0.999734 0.499867 0.866102i \(-0.333382\pi\)
0.499867 + 0.866102i \(0.333382\pi\)
\(332\) −7.04285 −0.386527
\(333\) 0 0
\(334\) −28.7868 −1.57514
\(335\) −29.8612 −1.63149
\(336\) 0 0
\(337\) 5.22052 0.284380 0.142190 0.989839i \(-0.454586\pi\)
0.142190 + 0.989839i \(0.454586\pi\)
\(338\) 4.34636 0.236411
\(339\) 0 0
\(340\) 23.7155 1.28616
\(341\) 2.44668 0.132495
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −2.65404 −0.143096
\(345\) 0 0
\(346\) −21.1703 −1.13812
\(347\) −25.6219 −1.37546 −0.687728 0.725968i \(-0.741392\pi\)
−0.687728 + 0.725968i \(0.741392\pi\)
\(348\) 0 0
\(349\) −8.47632 −0.453727 −0.226863 0.973927i \(-0.572847\pi\)
−0.226863 + 0.973927i \(0.572847\pi\)
\(350\) 16.3937 0.876278
\(351\) 0 0
\(352\) 21.1885 1.12935
\(353\) 29.0703 1.54725 0.773627 0.633641i \(-0.218440\pi\)
0.773627 + 0.633641i \(0.218440\pi\)
\(354\) 0 0
\(355\) 14.9076 0.791215
\(356\) −19.1231 −1.01352
\(357\) 0 0
\(358\) −3.54443 −0.187329
\(359\) −16.1630 −0.853049 −0.426525 0.904476i \(-0.640262\pi\)
−0.426525 + 0.904476i \(0.640262\pi\)
\(360\) 0 0
\(361\) −10.3781 −0.546214
\(362\) −41.7868 −2.19626
\(363\) 0 0
\(364\) −6.91129 −0.362250
\(365\) −3.72795 −0.195130
\(366\) 0 0
\(367\) −8.02538 −0.418921 −0.209461 0.977817i \(-0.567171\pi\)
−0.209461 + 0.977817i \(0.567171\pi\)
\(368\) −26.0081 −1.35577
\(369\) 0 0
\(370\) −42.5162 −2.21031
\(371\) −4.27470 −0.221932
\(372\) 0 0
\(373\) 22.5329 1.16671 0.583355 0.812217i \(-0.301740\pi\)
0.583355 + 0.812217i \(0.301740\pi\)
\(374\) 19.6110 1.01406
\(375\) 0 0
\(376\) −2.45613 −0.126665
\(377\) 3.94249 0.203049
\(378\) 0 0
\(379\) −15.2331 −0.782471 −0.391235 0.920291i \(-0.627952\pi\)
−0.391235 + 0.920291i \(0.627952\pi\)
\(380\) 19.0605 0.977784
\(381\) 0 0
\(382\) 9.67979 0.495261
\(383\) 12.0870 0.617618 0.308809 0.951124i \(-0.400070\pi\)
0.308809 + 0.951124i \(0.400070\pi\)
\(384\) 0 0
\(385\) 10.1354 0.516549
\(386\) 28.4999 1.45061
\(387\) 0 0
\(388\) 23.2609 1.18089
\(389\) −32.5350 −1.64959 −0.824795 0.565431i \(-0.808710\pi\)
−0.824795 + 0.565431i \(0.808710\pi\)
\(390\) 0 0
\(391\) −21.5640 −1.09054
\(392\) −0.445683 −0.0225104
\(393\) 0 0
\(394\) 33.8473 1.70520
\(395\) −3.81297 −0.191851
\(396\) 0 0
\(397\) −8.54787 −0.429005 −0.214503 0.976723i \(-0.568813\pi\)
−0.214503 + 0.976723i \(0.568813\pi\)
\(398\) 49.3937 2.47588
\(399\) 0 0
\(400\) −37.2013 −1.86007
\(401\) 28.8363 1.44002 0.720009 0.693965i \(-0.244138\pi\)
0.720009 + 0.693965i \(0.244138\pi\)
\(402\) 0 0
\(403\) 3.45499 0.172105
\(404\) 2.83058 0.140826
\(405\) 0 0
\(406\) −1.96110 −0.0973279
\(407\) −16.5087 −0.818308
\(408\) 0 0
\(409\) 1.26809 0.0627028 0.0313514 0.999508i \(-0.490019\pi\)
0.0313514 + 0.999508i \(0.490019\pi\)
\(410\) 50.1377 2.47613
\(411\) 0 0
\(412\) 2.35797 0.116169
\(413\) 7.36890 0.362600
\(414\) 0 0
\(415\) 14.5848 0.715940
\(416\) 29.9205 1.46697
\(417\) 0 0
\(418\) 15.7616 0.770925
\(419\) 31.3924 1.53362 0.766808 0.641876i \(-0.221844\pi\)
0.766808 + 0.641876i \(0.221844\pi\)
\(420\) 0 0
\(421\) −2.31725 −0.112936 −0.0564679 0.998404i \(-0.517984\pi\)
−0.0564679 + 0.998404i \(0.517984\pi\)
\(422\) 9.66712 0.470588
\(423\) 0 0
\(424\) 1.90516 0.0925228
\(425\) −30.8446 −1.49618
\(426\) 0 0
\(427\) 11.9371 0.577679
\(428\) 7.82261 0.378120
\(429\) 0 0
\(430\) −42.3958 −2.04451
\(431\) 17.0872 0.823062 0.411531 0.911396i \(-0.364994\pi\)
0.411531 + 0.911396i \(0.364994\pi\)
\(432\) 0 0
\(433\) −24.3684 −1.17107 −0.585534 0.810648i \(-0.699115\pi\)
−0.585534 + 0.810648i \(0.699115\pi\)
\(434\) −1.71860 −0.0824957
\(435\) 0 0
\(436\) −12.0455 −0.576874
\(437\) −17.3313 −0.829067
\(438\) 0 0
\(439\) 7.89424 0.376771 0.188386 0.982095i \(-0.439675\pi\)
0.188386 + 0.982095i \(0.439675\pi\)
\(440\) −4.51718 −0.215348
\(441\) 0 0
\(442\) 27.6929 1.31721
\(443\) −20.7191 −0.984393 −0.492197 0.870484i \(-0.663806\pi\)
−0.492197 + 0.870484i \(0.663806\pi\)
\(444\) 0 0
\(445\) 39.6015 1.87729
\(446\) −2.88839 −0.136769
\(447\) 0 0
\(448\) −6.07054 −0.286806
\(449\) 30.8777 1.45721 0.728604 0.684936i \(-0.240170\pi\)
0.728604 + 0.684936i \(0.240170\pi\)
\(450\) 0 0
\(451\) 19.4681 0.916718
\(452\) 20.6543 0.971496
\(453\) 0 0
\(454\) 37.9193 1.77964
\(455\) 14.3124 0.670974
\(456\) 0 0
\(457\) 19.3189 0.903702 0.451851 0.892094i \(-0.350764\pi\)
0.451851 + 0.892094i \(0.350764\pi\)
\(458\) −16.0525 −0.750083
\(459\) 0 0
\(460\) −38.3143 −1.78641
\(461\) −4.01040 −0.186783 −0.0933915 0.995629i \(-0.529771\pi\)
−0.0933915 + 0.995629i \(0.529771\pi\)
\(462\) 0 0
\(463\) 4.67124 0.217091 0.108546 0.994091i \(-0.465381\pi\)
0.108546 + 0.994091i \(0.465381\pi\)
\(464\) 4.45023 0.206597
\(465\) 0 0
\(466\) 45.3433 2.10049
\(467\) −12.3374 −0.570909 −0.285454 0.958392i \(-0.592144\pi\)
−0.285454 + 0.958392i \(0.592144\pi\)
\(468\) 0 0
\(469\) 8.14451 0.376079
\(470\) −39.2343 −1.80974
\(471\) 0 0
\(472\) −3.28419 −0.151167
\(473\) −16.4620 −0.756923
\(474\) 0 0
\(475\) −24.7902 −1.13745
\(476\) −6.46831 −0.296474
\(477\) 0 0
\(478\) −27.5763 −1.26131
\(479\) 2.70152 0.123436 0.0617178 0.998094i \(-0.480342\pi\)
0.0617178 + 0.998094i \(0.480342\pi\)
\(480\) 0 0
\(481\) −23.3122 −1.06294
\(482\) 7.93807 0.361569
\(483\) 0 0
\(484\) −5.94548 −0.270249
\(485\) −48.1702 −2.18730
\(486\) 0 0
\(487\) −26.9996 −1.22347 −0.611734 0.791064i \(-0.709528\pi\)
−0.611734 + 0.791064i \(0.709528\pi\)
\(488\) −5.32018 −0.240833
\(489\) 0 0
\(490\) −7.11935 −0.321619
\(491\) 25.4643 1.14919 0.574593 0.818439i \(-0.305160\pi\)
0.574593 + 0.818439i \(0.305160\pi\)
\(492\) 0 0
\(493\) 3.68980 0.166180
\(494\) 22.2571 1.00140
\(495\) 0 0
\(496\) 3.89994 0.175113
\(497\) −4.06599 −0.182385
\(498\) 0 0
\(499\) −25.8156 −1.15566 −0.577831 0.816156i \(-0.696101\pi\)
−0.577831 + 0.816156i \(0.696101\pi\)
\(500\) −22.3472 −0.999397
\(501\) 0 0
\(502\) 48.3411 2.15757
\(503\) 37.1572 1.65676 0.828378 0.560170i \(-0.189264\pi\)
0.828378 + 0.560170i \(0.189264\pi\)
\(504\) 0 0
\(505\) −5.86174 −0.260844
\(506\) −31.6830 −1.40848
\(507\) 0 0
\(508\) 1.77048 0.0785522
\(509\) 27.2527 1.20796 0.603978 0.797001i \(-0.293582\pi\)
0.603978 + 0.797001i \(0.293582\pi\)
\(510\) 0 0
\(511\) 1.01678 0.0449798
\(512\) 29.8462 1.31903
\(513\) 0 0
\(514\) 23.7664 1.04829
\(515\) −4.88304 −0.215172
\(516\) 0 0
\(517\) −15.2344 −0.670009
\(518\) 11.5961 0.509504
\(519\) 0 0
\(520\) −6.37877 −0.279727
\(521\) 11.6168 0.508943 0.254471 0.967080i \(-0.418099\pi\)
0.254471 + 0.967080i \(0.418099\pi\)
\(522\) 0 0
\(523\) −29.2279 −1.27805 −0.639023 0.769188i \(-0.720661\pi\)
−0.639023 + 0.769188i \(0.720661\pi\)
\(524\) −9.95028 −0.434680
\(525\) 0 0
\(526\) 3.03577 0.132366
\(527\) 3.23354 0.140855
\(528\) 0 0
\(529\) 11.8383 0.514707
\(530\) 30.4331 1.32193
\(531\) 0 0
\(532\) −5.19867 −0.225391
\(533\) 27.4912 1.19077
\(534\) 0 0
\(535\) −16.1996 −0.700369
\(536\) −3.62987 −0.156786
\(537\) 0 0
\(538\) −41.2794 −1.77968
\(539\) −2.76439 −0.119071
\(540\) 0 0
\(541\) 9.52150 0.409361 0.204681 0.978829i \(-0.434384\pi\)
0.204681 + 0.978829i \(0.434384\pi\)
\(542\) 8.91323 0.382856
\(543\) 0 0
\(544\) 28.0028 1.20061
\(545\) 24.9446 1.06851
\(546\) 0 0
\(547\) 39.7437 1.69932 0.849658 0.527333i \(-0.176808\pi\)
0.849658 + 0.527333i \(0.176808\pi\)
\(548\) 13.9889 0.597576
\(549\) 0 0
\(550\) −45.3186 −1.93239
\(551\) 2.96554 0.126336
\(552\) 0 0
\(553\) 1.03997 0.0442240
\(554\) 26.0862 1.10829
\(555\) 0 0
\(556\) −37.9520 −1.60952
\(557\) 11.1132 0.470879 0.235440 0.971889i \(-0.424347\pi\)
0.235440 + 0.971889i \(0.424347\pi\)
\(558\) 0 0
\(559\) −23.2462 −0.983207
\(560\) 16.1556 0.682698
\(561\) 0 0
\(562\) 40.2239 1.69674
\(563\) −39.4772 −1.66377 −0.831883 0.554950i \(-0.812737\pi\)
−0.831883 + 0.554950i \(0.812737\pi\)
\(564\) 0 0
\(565\) −42.7723 −1.79944
\(566\) 12.9795 0.545571
\(567\) 0 0
\(568\) 1.81214 0.0760358
\(569\) −36.1926 −1.51727 −0.758637 0.651513i \(-0.774134\pi\)
−0.758637 + 0.651513i \(0.774134\pi\)
\(570\) 0 0
\(571\) −28.8322 −1.20659 −0.603295 0.797518i \(-0.706146\pi\)
−0.603295 + 0.797518i \(0.706146\pi\)
\(572\) 19.1055 0.798842
\(573\) 0 0
\(574\) −13.6748 −0.570777
\(575\) 49.8318 2.07813
\(576\) 0 0
\(577\) 32.6307 1.35843 0.679217 0.733937i \(-0.262319\pi\)
0.679217 + 0.733937i \(0.262319\pi\)
\(578\) −7.09223 −0.294998
\(579\) 0 0
\(580\) 6.55593 0.272220
\(581\) −3.97794 −0.165033
\(582\) 0 0
\(583\) 11.8170 0.489409
\(584\) −0.453162 −0.0187520
\(585\) 0 0
\(586\) 3.26022 0.134678
\(587\) 41.8690 1.72812 0.864059 0.503391i \(-0.167914\pi\)
0.864059 + 0.503391i \(0.167914\pi\)
\(588\) 0 0
\(589\) 2.59884 0.107083
\(590\) −52.4618 −2.15982
\(591\) 0 0
\(592\) −26.3145 −1.08152
\(593\) −17.7488 −0.728855 −0.364428 0.931232i \(-0.618735\pi\)
−0.364428 + 0.931232i \(0.618735\pi\)
\(594\) 0 0
\(595\) 13.3950 0.549142
\(596\) 2.15353 0.0882120
\(597\) 0 0
\(598\) −44.7399 −1.82955
\(599\) 11.2278 0.458757 0.229379 0.973337i \(-0.426331\pi\)
0.229379 + 0.973337i \(0.426331\pi\)
\(600\) 0 0
\(601\) 17.2339 0.702987 0.351494 0.936190i \(-0.385674\pi\)
0.351494 + 0.936190i \(0.385674\pi\)
\(602\) 11.5633 0.471283
\(603\) 0 0
\(604\) 1.15851 0.0471391
\(605\) 12.3123 0.500566
\(606\) 0 0
\(607\) −31.1843 −1.26573 −0.632865 0.774262i \(-0.718121\pi\)
−0.632865 + 0.774262i \(0.718121\pi\)
\(608\) 22.5062 0.912748
\(609\) 0 0
\(610\) −84.9847 −3.44093
\(611\) −21.5127 −0.870310
\(612\) 0 0
\(613\) 1.58057 0.0638387 0.0319193 0.999490i \(-0.489838\pi\)
0.0319193 + 0.999490i \(0.489838\pi\)
\(614\) 1.58261 0.0638691
\(615\) 0 0
\(616\) 1.23204 0.0496404
\(617\) 43.3219 1.74408 0.872038 0.489439i \(-0.162798\pi\)
0.872038 + 0.489439i \(0.162798\pi\)
\(618\) 0 0
\(619\) −36.0264 −1.44802 −0.724011 0.689789i \(-0.757703\pi\)
−0.724011 + 0.689789i \(0.757703\pi\)
\(620\) 5.74527 0.230735
\(621\) 0 0
\(622\) −12.9022 −0.517331
\(623\) −10.8011 −0.432738
\(624\) 0 0
\(625\) 4.06490 0.162596
\(626\) 0.563121 0.0225069
\(627\) 0 0
\(628\) 21.4998 0.857936
\(629\) −21.8180 −0.869940
\(630\) 0 0
\(631\) −19.6150 −0.780862 −0.390431 0.920632i \(-0.627674\pi\)
−0.390431 + 0.920632i \(0.627674\pi\)
\(632\) −0.463496 −0.0184369
\(633\) 0 0
\(634\) −65.3786 −2.59652
\(635\) −3.66642 −0.145497
\(636\) 0 0
\(637\) −3.90363 −0.154668
\(638\) 5.42126 0.214630
\(639\) 0 0
\(640\) −12.9864 −0.513332
\(641\) −37.3289 −1.47440 −0.737202 0.675672i \(-0.763854\pi\)
−0.737202 + 0.675672i \(0.763854\pi\)
\(642\) 0 0
\(643\) 15.2063 0.599677 0.299839 0.953990i \(-0.403067\pi\)
0.299839 + 0.953990i \(0.403067\pi\)
\(644\) 10.4501 0.411790
\(645\) 0 0
\(646\) 20.8306 0.819568
\(647\) 33.1334 1.30261 0.651304 0.758817i \(-0.274222\pi\)
0.651304 + 0.758817i \(0.274222\pi\)
\(648\) 0 0
\(649\) −20.3705 −0.799614
\(650\) −63.9948 −2.51008
\(651\) 0 0
\(652\) −19.7176 −0.772199
\(653\) 2.29910 0.0899709 0.0449854 0.998988i \(-0.485676\pi\)
0.0449854 + 0.998988i \(0.485676\pi\)
\(654\) 0 0
\(655\) 20.6057 0.805131
\(656\) 31.0316 1.21158
\(657\) 0 0
\(658\) 10.7010 0.417168
\(659\) 42.2286 1.64499 0.822496 0.568771i \(-0.192581\pi\)
0.822496 + 0.568771i \(0.192581\pi\)
\(660\) 0 0
\(661\) 25.4775 0.990960 0.495480 0.868619i \(-0.334992\pi\)
0.495480 + 0.868619i \(0.334992\pi\)
\(662\) 35.3180 1.37267
\(663\) 0 0
\(664\) 1.77290 0.0688019
\(665\) 10.7658 0.417478
\(666\) 0 0
\(667\) −5.96115 −0.230817
\(668\) −26.2474 −1.01554
\(669\) 0 0
\(670\) −57.9836 −2.24010
\(671\) −32.9990 −1.27391
\(672\) 0 0
\(673\) 22.1340 0.853204 0.426602 0.904439i \(-0.359710\pi\)
0.426602 + 0.904439i \(0.359710\pi\)
\(674\) 10.1371 0.390465
\(675\) 0 0
\(676\) 3.96294 0.152421
\(677\) −30.8690 −1.18639 −0.593195 0.805059i \(-0.702134\pi\)
−0.593195 + 0.805059i \(0.702134\pi\)
\(678\) 0 0
\(679\) 13.1382 0.504198
\(680\) −5.96992 −0.228936
\(681\) 0 0
\(682\) 4.75090 0.181921
\(683\) 49.1676 1.88135 0.940673 0.339315i \(-0.110195\pi\)
0.940673 + 0.339315i \(0.110195\pi\)
\(684\) 0 0
\(685\) −28.9691 −1.10685
\(686\) 1.94177 0.0741372
\(687\) 0 0
\(688\) −26.2399 −1.00039
\(689\) 16.6869 0.635719
\(690\) 0 0
\(691\) −16.7873 −0.638621 −0.319310 0.947650i \(-0.603451\pi\)
−0.319310 + 0.947650i \(0.603451\pi\)
\(692\) −19.3027 −0.733780
\(693\) 0 0
\(694\) −49.7519 −1.88856
\(695\) 78.5934 2.98122
\(696\) 0 0
\(697\) 25.7291 0.974560
\(698\) −16.4591 −0.622985
\(699\) 0 0
\(700\) 14.9475 0.564962
\(701\) −3.96675 −0.149822 −0.0749110 0.997190i \(-0.523867\pi\)
−0.0749110 + 0.997190i \(0.523867\pi\)
\(702\) 0 0
\(703\) −17.5354 −0.661361
\(704\) 16.7814 0.632471
\(705\) 0 0
\(706\) 56.4478 2.12444
\(707\) 1.59877 0.0601278
\(708\) 0 0
\(709\) −12.6827 −0.476309 −0.238154 0.971227i \(-0.576542\pi\)
−0.238154 + 0.971227i \(0.576542\pi\)
\(710\) 28.9472 1.08637
\(711\) 0 0
\(712\) 4.81387 0.180408
\(713\) −5.22404 −0.195642
\(714\) 0 0
\(715\) −39.5650 −1.47965
\(716\) −3.23175 −0.120776
\(717\) 0 0
\(718\) −31.3848 −1.17127
\(719\) −37.0747 −1.38265 −0.691327 0.722542i \(-0.742973\pi\)
−0.691327 + 0.722542i \(0.742973\pi\)
\(720\) 0 0
\(721\) 1.33183 0.0495999
\(722\) −20.1518 −0.749974
\(723\) 0 0
\(724\) −38.1005 −1.41599
\(725\) −8.52668 −0.316673
\(726\) 0 0
\(727\) 30.7092 1.13894 0.569471 0.822011i \(-0.307148\pi\)
0.569471 + 0.822011i \(0.307148\pi\)
\(728\) 1.73978 0.0644806
\(729\) 0 0
\(730\) −7.23883 −0.267921
\(731\) −21.7562 −0.804682
\(732\) 0 0
\(733\) 43.0346 1.58952 0.794761 0.606923i \(-0.207596\pi\)
0.794761 + 0.606923i \(0.207596\pi\)
\(734\) −15.5834 −0.575195
\(735\) 0 0
\(736\) −45.2406 −1.66759
\(737\) −22.5146 −0.829338
\(738\) 0 0
\(739\) −19.5287 −0.718376 −0.359188 0.933265i \(-0.616946\pi\)
−0.359188 + 0.933265i \(0.616946\pi\)
\(740\) −38.7656 −1.42505
\(741\) 0 0
\(742\) −8.30050 −0.304721
\(743\) 39.5429 1.45069 0.725345 0.688386i \(-0.241680\pi\)
0.725345 + 0.688386i \(0.241680\pi\)
\(744\) 0 0
\(745\) −4.45967 −0.163390
\(746\) 43.7538 1.60194
\(747\) 0 0
\(748\) 17.8810 0.653793
\(749\) 4.41836 0.161444
\(750\) 0 0
\(751\) 5.05959 0.184627 0.0923136 0.995730i \(-0.470574\pi\)
0.0923136 + 0.995730i \(0.470574\pi\)
\(752\) −24.2832 −0.885518
\(753\) 0 0
\(754\) 7.65542 0.278794
\(755\) −2.39912 −0.0873129
\(756\) 0 0
\(757\) −3.35286 −0.121862 −0.0609309 0.998142i \(-0.519407\pi\)
−0.0609309 + 0.998142i \(0.519407\pi\)
\(758\) −29.5792 −1.07436
\(759\) 0 0
\(760\) −4.79811 −0.174046
\(761\) −9.15947 −0.332030 −0.166015 0.986123i \(-0.553090\pi\)
−0.166015 + 0.986123i \(0.553090\pi\)
\(762\) 0 0
\(763\) −6.80353 −0.246304
\(764\) 8.82588 0.319309
\(765\) 0 0
\(766\) 23.4702 0.848014
\(767\) −28.7655 −1.03866
\(768\) 0 0
\(769\) −13.6579 −0.492517 −0.246258 0.969204i \(-0.579201\pi\)
−0.246258 + 0.969204i \(0.579201\pi\)
\(770\) 19.6807 0.709243
\(771\) 0 0
\(772\) 25.9858 0.935248
\(773\) −2.38910 −0.0859301 −0.0429651 0.999077i \(-0.513680\pi\)
−0.0429651 + 0.999077i \(0.513680\pi\)
\(774\) 0 0
\(775\) −7.47233 −0.268414
\(776\) −5.85547 −0.210199
\(777\) 0 0
\(778\) −63.1756 −2.26495
\(779\) 20.6789 0.740897
\(780\) 0 0
\(781\) 11.2400 0.402199
\(782\) −41.8723 −1.49735
\(783\) 0 0
\(784\) −4.40637 −0.157370
\(785\) −44.5232 −1.58910
\(786\) 0 0
\(787\) −11.6553 −0.415465 −0.207733 0.978186i \(-0.566608\pi\)
−0.207733 + 0.978186i \(0.566608\pi\)
\(788\) 30.8615 1.09939
\(789\) 0 0
\(790\) −7.40391 −0.263419
\(791\) 11.6660 0.414794
\(792\) 0 0
\(793\) −46.5982 −1.65475
\(794\) −16.5980 −0.589041
\(795\) 0 0
\(796\) 45.0364 1.59627
\(797\) 52.8237 1.87111 0.935556 0.353179i \(-0.114899\pi\)
0.935556 + 0.353179i \(0.114899\pi\)
\(798\) 0 0
\(799\) −20.1338 −0.712284
\(800\) −64.7110 −2.28788
\(801\) 0 0
\(802\) 55.9935 1.97720
\(803\) −2.81079 −0.0991905
\(804\) 0 0
\(805\) −21.6407 −0.762733
\(806\) 6.70880 0.236307
\(807\) 0 0
\(808\) −0.712542 −0.0250671
\(809\) 14.9711 0.526356 0.263178 0.964747i \(-0.415229\pi\)
0.263178 + 0.964747i \(0.415229\pi\)
\(810\) 0 0
\(811\) −18.8772 −0.662869 −0.331434 0.943478i \(-0.607533\pi\)
−0.331434 + 0.943478i \(0.607533\pi\)
\(812\) −1.78810 −0.0627501
\(813\) 0 0
\(814\) −32.0562 −1.12357
\(815\) 40.8324 1.43030
\(816\) 0 0
\(817\) −17.4858 −0.611749
\(818\) 2.46233 0.0860935
\(819\) 0 0
\(820\) 45.7148 1.59643
\(821\) 46.1335 1.61007 0.805035 0.593227i \(-0.202146\pi\)
0.805035 + 0.593227i \(0.202146\pi\)
\(822\) 0 0
\(823\) −42.7137 −1.48891 −0.744453 0.667674i \(-0.767290\pi\)
−0.744453 + 0.667674i \(0.767290\pi\)
\(824\) −0.593572 −0.0206781
\(825\) 0 0
\(826\) 14.3087 0.497864
\(827\) −23.2513 −0.808527 −0.404263 0.914643i \(-0.632472\pi\)
−0.404263 + 0.914643i \(0.632472\pi\)
\(828\) 0 0
\(829\) 19.6651 0.682996 0.341498 0.939883i \(-0.389066\pi\)
0.341498 + 0.939883i \(0.389066\pi\)
\(830\) 28.3204 0.983014
\(831\) 0 0
\(832\) 23.6972 0.821551
\(833\) −3.65343 −0.126584
\(834\) 0 0
\(835\) 54.3548 1.88102
\(836\) 14.3712 0.497038
\(837\) 0 0
\(838\) 60.9568 2.10572
\(839\) −28.3518 −0.978812 −0.489406 0.872056i \(-0.662786\pi\)
−0.489406 + 0.872056i \(0.662786\pi\)
\(840\) 0 0
\(841\) −27.9800 −0.964827
\(842\) −4.49957 −0.155065
\(843\) 0 0
\(844\) 8.81433 0.303402
\(845\) −8.20672 −0.282320
\(846\) 0 0
\(847\) −3.35813 −0.115387
\(848\) 18.8359 0.646828
\(849\) 0 0
\(850\) −59.8931 −2.05432
\(851\) 35.2486 1.20831
\(852\) 0 0
\(853\) 13.4795 0.461530 0.230765 0.973009i \(-0.425877\pi\)
0.230765 + 0.973009i \(0.425877\pi\)
\(854\) 23.1792 0.793176
\(855\) 0 0
\(856\) −1.96919 −0.0673055
\(857\) −40.5096 −1.38378 −0.691891 0.722002i \(-0.743222\pi\)
−0.691891 + 0.722002i \(0.743222\pi\)
\(858\) 0 0
\(859\) −53.5206 −1.82610 −0.913049 0.407850i \(-0.866279\pi\)
−0.913049 + 0.407850i \(0.866279\pi\)
\(860\) −38.6558 −1.31815
\(861\) 0 0
\(862\) 33.1795 1.13010
\(863\) 18.8826 0.642772 0.321386 0.946948i \(-0.395851\pi\)
0.321386 + 0.946948i \(0.395851\pi\)
\(864\) 0 0
\(865\) 39.9734 1.35914
\(866\) −47.3178 −1.60792
\(867\) 0 0
\(868\) −1.56700 −0.0531873
\(869\) −2.87489 −0.0975238
\(870\) 0 0
\(871\) −31.7932 −1.07727
\(872\) 3.03221 0.102684
\(873\) 0 0
\(874\) −33.6534 −1.13834
\(875\) −12.6221 −0.426706
\(876\) 0 0
\(877\) 11.9075 0.402089 0.201044 0.979582i \(-0.435566\pi\)
0.201044 + 0.979582i \(0.435566\pi\)
\(878\) 15.3288 0.517322
\(879\) 0 0
\(880\) −44.6604 −1.50550
\(881\) 21.5448 0.725863 0.362931 0.931816i \(-0.381776\pi\)
0.362931 + 0.931816i \(0.381776\pi\)
\(882\) 0 0
\(883\) 10.8753 0.365985 0.182992 0.983114i \(-0.441422\pi\)
0.182992 + 0.983114i \(0.441422\pi\)
\(884\) 25.2499 0.849246
\(885\) 0 0
\(886\) −40.2317 −1.35161
\(887\) 4.35531 0.146237 0.0731186 0.997323i \(-0.476705\pi\)
0.0731186 + 0.997323i \(0.476705\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 76.8970 2.57759
\(891\) 0 0
\(892\) −2.63359 −0.0881791
\(893\) −16.1818 −0.541505
\(894\) 0 0
\(895\) 6.69252 0.223706
\(896\) 3.54198 0.118329
\(897\) 0 0
\(898\) 59.9574 2.00080
\(899\) 0.893881 0.0298126
\(900\) 0 0
\(901\) 15.6173 0.520288
\(902\) 37.8027 1.25869
\(903\) 0 0
\(904\) −5.19931 −0.172927
\(905\) 78.9010 2.62276
\(906\) 0 0
\(907\) 8.60721 0.285798 0.142899 0.989737i \(-0.454358\pi\)
0.142899 + 0.989737i \(0.454358\pi\)
\(908\) 34.5742 1.14739
\(909\) 0 0
\(910\) 27.7913 0.921273
\(911\) −48.0894 −1.59327 −0.796637 0.604458i \(-0.793390\pi\)
−0.796637 + 0.604458i \(0.793390\pi\)
\(912\) 0 0
\(913\) 10.9966 0.363934
\(914\) 37.5130 1.24082
\(915\) 0 0
\(916\) −14.6364 −0.483600
\(917\) −5.62011 −0.185592
\(918\) 0 0
\(919\) 2.97332 0.0980807 0.0490404 0.998797i \(-0.484384\pi\)
0.0490404 + 0.998797i \(0.484384\pi\)
\(920\) 9.64487 0.317982
\(921\) 0 0
\(922\) −7.78728 −0.256460
\(923\) 15.8721 0.522438
\(924\) 0 0
\(925\) 50.4187 1.65776
\(926\) 9.07049 0.298075
\(927\) 0 0
\(928\) 7.74110 0.254114
\(929\) 9.52563 0.312526 0.156263 0.987715i \(-0.450055\pi\)
0.156263 + 0.987715i \(0.450055\pi\)
\(930\) 0 0
\(931\) −2.93631 −0.0962338
\(932\) 41.3433 1.35425
\(933\) 0 0
\(934\) −23.9565 −0.783880
\(935\) −37.0291 −1.21098
\(936\) 0 0
\(937\) 44.8037 1.46367 0.731836 0.681481i \(-0.238664\pi\)
0.731836 + 0.681481i \(0.238664\pi\)
\(938\) 15.8148 0.516371
\(939\) 0 0
\(940\) −35.7732 −1.16679
\(941\) 24.5478 0.800236 0.400118 0.916464i \(-0.368969\pi\)
0.400118 + 0.916464i \(0.368969\pi\)
\(942\) 0 0
\(943\) −41.5674 −1.35362
\(944\) −32.4701 −1.05681
\(945\) 0 0
\(946\) −31.9654 −1.03928
\(947\) 44.5523 1.44775 0.723877 0.689929i \(-0.242358\pi\)
0.723877 + 0.689929i \(0.242358\pi\)
\(948\) 0 0
\(949\) −3.96914 −0.128844
\(950\) −48.1369 −1.56177
\(951\) 0 0
\(952\) 1.62827 0.0527725
\(953\) 9.81808 0.318039 0.159019 0.987275i \(-0.449167\pi\)
0.159019 + 0.987275i \(0.449167\pi\)
\(954\) 0 0
\(955\) −18.2772 −0.591437
\(956\) −25.1436 −0.813202
\(957\) 0 0
\(958\) 5.24573 0.169482
\(959\) 7.90120 0.255143
\(960\) 0 0
\(961\) −30.2167 −0.974731
\(962\) −45.2669 −1.45946
\(963\) 0 0
\(964\) 7.23780 0.233114
\(965\) −53.8131 −1.73230
\(966\) 0 0
\(967\) 48.7733 1.56844 0.784222 0.620480i \(-0.213062\pi\)
0.784222 + 0.620480i \(0.213062\pi\)
\(968\) 1.49666 0.0481044
\(969\) 0 0
\(970\) −93.5355 −3.00324
\(971\) −27.9521 −0.897027 −0.448514 0.893776i \(-0.648046\pi\)
−0.448514 + 0.893776i \(0.648046\pi\)
\(972\) 0 0
\(973\) −21.4360 −0.687207
\(974\) −52.4270 −1.67987
\(975\) 0 0
\(976\) −52.5994 −1.68367
\(977\) −9.88220 −0.316160 −0.158080 0.987426i \(-0.550530\pi\)
−0.158080 + 0.987426i \(0.550530\pi\)
\(978\) 0 0
\(979\) 29.8586 0.954284
\(980\) −6.49131 −0.207357
\(981\) 0 0
\(982\) 49.4458 1.57788
\(983\) −35.8839 −1.14452 −0.572260 0.820073i \(-0.693933\pi\)
−0.572260 + 0.820073i \(0.693933\pi\)
\(984\) 0 0
\(985\) −63.9100 −2.03634
\(986\) 7.16475 0.228172
\(987\) 0 0
\(988\) 20.2937 0.645629
\(989\) 35.1488 1.11767
\(990\) 0 0
\(991\) 19.8528 0.630646 0.315323 0.948984i \(-0.397887\pi\)
0.315323 + 0.948984i \(0.397887\pi\)
\(992\) 6.78388 0.215388
\(993\) 0 0
\(994\) −7.89523 −0.250421
\(995\) −93.2643 −2.95668
\(996\) 0 0
\(997\) 24.8307 0.786398 0.393199 0.919453i \(-0.371368\pi\)
0.393199 + 0.919453i \(0.371368\pi\)
\(998\) −50.1279 −1.58677
\(999\) 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 \(a_p\))