Properties

Label 6026.2.a.i.1.4
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(25\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} -1.46275 q^{10} +3.06412 q^{11} -2.39972 q^{12} +2.86180 q^{13} -0.813594 q^{14} -3.51019 q^{15} +1.00000 q^{16} +0.904748 q^{17} -2.75865 q^{18} -1.54618 q^{19} +1.46275 q^{20} -1.95240 q^{21} -3.06412 q^{22} +1.00000 q^{23} +2.39972 q^{24} -2.86036 q^{25} -2.86180 q^{26} +0.579184 q^{27} +0.813594 q^{28} +1.89799 q^{29} +3.51019 q^{30} -4.44494 q^{31} -1.00000 q^{32} -7.35302 q^{33} -0.904748 q^{34} +1.19009 q^{35} +2.75865 q^{36} -3.09637 q^{37} +1.54618 q^{38} -6.86752 q^{39} -1.46275 q^{40} -3.00239 q^{41} +1.95240 q^{42} -1.65231 q^{43} +3.06412 q^{44} +4.03521 q^{45} -1.00000 q^{46} -7.73379 q^{47} -2.39972 q^{48} -6.33806 q^{49} +2.86036 q^{50} -2.17114 q^{51} +2.86180 q^{52} -4.92913 q^{53} -0.579184 q^{54} +4.48205 q^{55} -0.813594 q^{56} +3.71040 q^{57} -1.89799 q^{58} -9.37352 q^{59} -3.51019 q^{60} +9.96319 q^{61} +4.44494 q^{62} +2.24442 q^{63} +1.00000 q^{64} +4.18611 q^{65} +7.35302 q^{66} +3.71486 q^{67} +0.904748 q^{68} -2.39972 q^{69} -1.19009 q^{70} -12.1090 q^{71} -2.75865 q^{72} +1.67829 q^{73} +3.09637 q^{74} +6.86405 q^{75} -1.54618 q^{76} +2.49295 q^{77} +6.86752 q^{78} -11.4921 q^{79} +1.46275 q^{80} -9.66581 q^{81} +3.00239 q^{82} -4.73564 q^{83} -1.95240 q^{84} +1.32342 q^{85} +1.65231 q^{86} -4.55463 q^{87} -3.06412 q^{88} +6.25332 q^{89} -4.03521 q^{90} +2.32835 q^{91} +1.00000 q^{92} +10.6666 q^{93} +7.73379 q^{94} -2.26168 q^{95} +2.39972 q^{96} +4.11638 q^{97} +6.33806 q^{98} +8.45282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + O(q^{10}) \) \( 25q - 25q^{2} - 4q^{3} + 25q^{4} - 3q^{5} + 4q^{6} - 11q^{7} - 25q^{8} + 19q^{9} + 3q^{10} - 12q^{11} - 4q^{12} - 6q^{13} + 11q^{14} + 25q^{16} + 8q^{17} - 19q^{18} - 23q^{19} - 3q^{20} - 16q^{21} + 12q^{22} + 25q^{23} + 4q^{24} + 4q^{25} + 6q^{26} - 13q^{27} - 11q^{28} - 7q^{29} - 7q^{31} - 25q^{32} + 3q^{33} - 8q^{34} - 18q^{35} + 19q^{36} - 7q^{37} + 23q^{38} - 2q^{39} + 3q^{40} - 10q^{41} + 16q^{42} - 26q^{43} - 12q^{44} + 20q^{45} - 25q^{46} - 2q^{47} - 4q^{48} + 2q^{49} - 4q^{50} - 28q^{51} - 6q^{52} + 47q^{53} + 13q^{54} - 38q^{55} + 11q^{56} - 4q^{57} + 7q^{58} - 19q^{59} - 26q^{61} + 7q^{62} - 15q^{63} + 25q^{64} + 13q^{65} - 3q^{66} - 34q^{67} + 8q^{68} - 4q^{69} + 18q^{70} - 10q^{71} - 19q^{72} - 22q^{73} + 7q^{74} - 8q^{75} - 23q^{76} + 28q^{77} + 2q^{78} - 21q^{79} - 3q^{80} - 27q^{81} + 10q^{82} - 16q^{83} - 16q^{84} - 42q^{85} + 26q^{86} - 17q^{87} + 12q^{88} + 27q^{89} - 20q^{90} - 26q^{91} + 25q^{92} - 27q^{93} + 2q^{94} + 4q^{96} + 4q^{97} - 2q^{98} - 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.39972 −1.38548 −0.692739 0.721189i \(-0.743596\pi\)
−0.692739 + 0.721189i \(0.743596\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.46275 0.654163 0.327081 0.944996i \(-0.393935\pi\)
0.327081 + 0.944996i \(0.393935\pi\)
\(6\) 2.39972 0.979681
\(7\) 0.813594 0.307510 0.153755 0.988109i \(-0.450863\pi\)
0.153755 + 0.988109i \(0.450863\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.75865 0.919548
\(10\) −1.46275 −0.462563
\(11\) 3.06412 0.923867 0.461933 0.886915i \(-0.347156\pi\)
0.461933 + 0.886915i \(0.347156\pi\)
\(12\) −2.39972 −0.692739
\(13\) 2.86180 0.793721 0.396861 0.917879i \(-0.370100\pi\)
0.396861 + 0.917879i \(0.370100\pi\)
\(14\) −0.813594 −0.217442
\(15\) −3.51019 −0.906328
\(16\) 1.00000 0.250000
\(17\) 0.904748 0.219434 0.109717 0.993963i \(-0.465006\pi\)
0.109717 + 0.993963i \(0.465006\pi\)
\(18\) −2.75865 −0.650219
\(19\) −1.54618 −0.354719 −0.177359 0.984146i \(-0.556755\pi\)
−0.177359 + 0.984146i \(0.556755\pi\)
\(20\) 1.46275 0.327081
\(21\) −1.95240 −0.426048
\(22\) −3.06412 −0.653272
\(23\) 1.00000 0.208514
\(24\) 2.39972 0.489840
\(25\) −2.86036 −0.572071
\(26\) −2.86180 −0.561246
\(27\) 0.579184 0.111464
\(28\) 0.813594 0.153755
\(29\) 1.89799 0.352447 0.176224 0.984350i \(-0.443612\pi\)
0.176224 + 0.984350i \(0.443612\pi\)
\(30\) 3.51019 0.640870
\(31\) −4.44494 −0.798335 −0.399167 0.916878i \(-0.630701\pi\)
−0.399167 + 0.916878i \(0.630701\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.35302 −1.28000
\(34\) −0.904748 −0.155163
\(35\) 1.19009 0.201161
\(36\) 2.75865 0.459774
\(37\) −3.09637 −0.509040 −0.254520 0.967068i \(-0.581917\pi\)
−0.254520 + 0.967068i \(0.581917\pi\)
\(38\) 1.54618 0.250824
\(39\) −6.86752 −1.09968
\(40\) −1.46275 −0.231281
\(41\) −3.00239 −0.468895 −0.234447 0.972129i \(-0.575328\pi\)
−0.234447 + 0.972129i \(0.575328\pi\)
\(42\) 1.95240 0.301261
\(43\) −1.65231 −0.251976 −0.125988 0.992032i \(-0.540210\pi\)
−0.125988 + 0.992032i \(0.540210\pi\)
\(44\) 3.06412 0.461933
\(45\) 4.03521 0.601534
\(46\) −1.00000 −0.147442
\(47\) −7.73379 −1.12809 −0.564045 0.825744i \(-0.690756\pi\)
−0.564045 + 0.825744i \(0.690756\pi\)
\(48\) −2.39972 −0.346369
\(49\) −6.33806 −0.905438
\(50\) 2.86036 0.404515
\(51\) −2.17114 −0.304021
\(52\) 2.86180 0.396861
\(53\) −4.92913 −0.677068 −0.338534 0.940954i \(-0.609931\pi\)
−0.338534 + 0.940954i \(0.609931\pi\)
\(54\) −0.579184 −0.0788169
\(55\) 4.48205 0.604359
\(56\) −0.813594 −0.108721
\(57\) 3.71040 0.491455
\(58\) −1.89799 −0.249218
\(59\) −9.37352 −1.22033 −0.610164 0.792275i \(-0.708897\pi\)
−0.610164 + 0.792275i \(0.708897\pi\)
\(60\) −3.51019 −0.453164
\(61\) 9.96319 1.27566 0.637828 0.770179i \(-0.279833\pi\)
0.637828 + 0.770179i \(0.279833\pi\)
\(62\) 4.44494 0.564508
\(63\) 2.24442 0.282770
\(64\) 1.00000 0.125000
\(65\) 4.18611 0.519223
\(66\) 7.35302 0.905094
\(67\) 3.71486 0.453843 0.226921 0.973913i \(-0.427134\pi\)
0.226921 + 0.973913i \(0.427134\pi\)
\(68\) 0.904748 0.109717
\(69\) −2.39972 −0.288892
\(70\) −1.19009 −0.142243
\(71\) −12.1090 −1.43708 −0.718538 0.695488i \(-0.755188\pi\)
−0.718538 + 0.695488i \(0.755188\pi\)
\(72\) −2.75865 −0.325109
\(73\) 1.67829 0.196429 0.0982145 0.995165i \(-0.468687\pi\)
0.0982145 + 0.995165i \(0.468687\pi\)
\(74\) 3.09637 0.359946
\(75\) 6.86405 0.792592
\(76\) −1.54618 −0.177359
\(77\) 2.49295 0.284098
\(78\) 6.86752 0.777593
\(79\) −11.4921 −1.29296 −0.646480 0.762931i \(-0.723760\pi\)
−0.646480 + 0.762931i \(0.723760\pi\)
\(80\) 1.46275 0.163541
\(81\) −9.66581 −1.07398
\(82\) 3.00239 0.331559
\(83\) −4.73564 −0.519804 −0.259902 0.965635i \(-0.583690\pi\)
−0.259902 + 0.965635i \(0.583690\pi\)
\(84\) −1.95240 −0.213024
\(85\) 1.32342 0.143545
\(86\) 1.65231 0.178174
\(87\) −4.55463 −0.488308
\(88\) −3.06412 −0.326636
\(89\) 6.25332 0.662851 0.331425 0.943481i \(-0.392470\pi\)
0.331425 + 0.943481i \(0.392470\pi\)
\(90\) −4.03521 −0.425349
\(91\) 2.32835 0.244077
\(92\) 1.00000 0.104257
\(93\) 10.6666 1.10608
\(94\) 7.73379 0.797680
\(95\) −2.26168 −0.232044
\(96\) 2.39972 0.244920
\(97\) 4.11638 0.417955 0.208977 0.977920i \(-0.432987\pi\)
0.208977 + 0.977920i \(0.432987\pi\)
\(98\) 6.33806 0.640241
\(99\) 8.45282 0.849540
\(100\) −2.86036 −0.286036
\(101\) −0.635708 −0.0632554 −0.0316277 0.999500i \(-0.510069\pi\)
−0.0316277 + 0.999500i \(0.510069\pi\)
\(102\) 2.17114 0.214975
\(103\) −3.18439 −0.313767 −0.156883 0.987617i \(-0.550145\pi\)
−0.156883 + 0.987617i \(0.550145\pi\)
\(104\) −2.86180 −0.280623
\(105\) −2.85587 −0.278705
\(106\) 4.92913 0.478759
\(107\) −7.80643 −0.754676 −0.377338 0.926076i \(-0.623161\pi\)
−0.377338 + 0.926076i \(0.623161\pi\)
\(108\) 0.579184 0.0557320
\(109\) 9.57356 0.916981 0.458490 0.888699i \(-0.348390\pi\)
0.458490 + 0.888699i \(0.348390\pi\)
\(110\) −4.48205 −0.427346
\(111\) 7.43041 0.705263
\(112\) 0.813594 0.0768774
\(113\) −14.3790 −1.35266 −0.676332 0.736597i \(-0.736432\pi\)
−0.676332 + 0.736597i \(0.736432\pi\)
\(114\) −3.71040 −0.347511
\(115\) 1.46275 0.136402
\(116\) 1.89799 0.176224
\(117\) 7.89470 0.729865
\(118\) 9.37352 0.862902
\(119\) 0.736098 0.0674780
\(120\) 3.51019 0.320435
\(121\) −1.61118 −0.146471
\(122\) −9.96319 −0.902025
\(123\) 7.20489 0.649643
\(124\) −4.44494 −0.399167
\(125\) −11.4978 −1.02839
\(126\) −2.24442 −0.199949
\(127\) −1.50464 −0.133515 −0.0667575 0.997769i \(-0.521265\pi\)
−0.0667575 + 0.997769i \(0.521265\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.96509 0.349107
\(130\) −4.18611 −0.367146
\(131\) 1.00000 0.0873704
\(132\) −7.35302 −0.639998
\(133\) −1.25797 −0.109079
\(134\) −3.71486 −0.320915
\(135\) 0.847202 0.0729155
\(136\) −0.904748 −0.0775815
\(137\) 0.999989 0.0854349 0.0427174 0.999087i \(-0.486398\pi\)
0.0427174 + 0.999087i \(0.486398\pi\)
\(138\) 2.39972 0.204278
\(139\) −11.6809 −0.990764 −0.495382 0.868675i \(-0.664972\pi\)
−0.495382 + 0.868675i \(0.664972\pi\)
\(140\) 1.19009 0.100581
\(141\) 18.5589 1.56294
\(142\) 12.1090 1.01617
\(143\) 8.76890 0.733292
\(144\) 2.75865 0.229887
\(145\) 2.77628 0.230558
\(146\) −1.67829 −0.138896
\(147\) 15.2096 1.25446
\(148\) −3.09637 −0.254520
\(149\) 0.487928 0.0399726 0.0199863 0.999800i \(-0.493638\pi\)
0.0199863 + 0.999800i \(0.493638\pi\)
\(150\) −6.86405 −0.560447
\(151\) 10.9684 0.892592 0.446296 0.894885i \(-0.352743\pi\)
0.446296 + 0.894885i \(0.352743\pi\)
\(152\) 1.54618 0.125412
\(153\) 2.49588 0.201780
\(154\) −2.49295 −0.200888
\(155\) −6.50185 −0.522241
\(156\) −6.86752 −0.549841
\(157\) −11.1294 −0.888224 −0.444112 0.895971i \(-0.646481\pi\)
−0.444112 + 0.895971i \(0.646481\pi\)
\(158\) 11.4921 0.914261
\(159\) 11.8285 0.938062
\(160\) −1.46275 −0.115641
\(161\) 0.813594 0.0641202
\(162\) 9.66581 0.759418
\(163\) 1.59275 0.124754 0.0623768 0.998053i \(-0.480132\pi\)
0.0623768 + 0.998053i \(0.480132\pi\)
\(164\) −3.00239 −0.234447
\(165\) −10.7556 −0.837326
\(166\) 4.73564 0.367557
\(167\) 2.58158 0.199769 0.0998843 0.994999i \(-0.468153\pi\)
0.0998843 + 0.994999i \(0.468153\pi\)
\(168\) 1.95240 0.150631
\(169\) −4.81009 −0.370007
\(170\) −1.32342 −0.101502
\(171\) −4.26537 −0.326181
\(172\) −1.65231 −0.125988
\(173\) 4.05919 0.308615 0.154307 0.988023i \(-0.450685\pi\)
0.154307 + 0.988023i \(0.450685\pi\)
\(174\) 4.55463 0.345286
\(175\) −2.32717 −0.175917
\(176\) 3.06412 0.230967
\(177\) 22.4938 1.69074
\(178\) −6.25332 −0.468706
\(179\) 23.3718 1.74689 0.873447 0.486919i \(-0.161879\pi\)
0.873447 + 0.486919i \(0.161879\pi\)
\(180\) 4.03521 0.300767
\(181\) −19.1396 −1.42263 −0.711317 0.702871i \(-0.751901\pi\)
−0.711317 + 0.702871i \(0.751901\pi\)
\(182\) −2.32835 −0.172588
\(183\) −23.9089 −1.76739
\(184\) −1.00000 −0.0737210
\(185\) −4.52922 −0.332995
\(186\) −10.6666 −0.782113
\(187\) 2.77226 0.202727
\(188\) −7.73379 −0.564045
\(189\) 0.471220 0.0342762
\(190\) 2.26168 0.164080
\(191\) 10.6728 0.772255 0.386127 0.922445i \(-0.373813\pi\)
0.386127 + 0.922445i \(0.373813\pi\)
\(192\) −2.39972 −0.173185
\(193\) 22.2628 1.60251 0.801255 0.598323i \(-0.204166\pi\)
0.801255 + 0.598323i \(0.204166\pi\)
\(194\) −4.11638 −0.295539
\(195\) −10.0455 −0.719371
\(196\) −6.33806 −0.452719
\(197\) 26.9338 1.91895 0.959477 0.281786i \(-0.0909268\pi\)
0.959477 + 0.281786i \(0.0909268\pi\)
\(198\) −8.45282 −0.600715
\(199\) −7.31007 −0.518197 −0.259099 0.965851i \(-0.583425\pi\)
−0.259099 + 0.965851i \(0.583425\pi\)
\(200\) 2.86036 0.202258
\(201\) −8.91462 −0.628789
\(202\) 0.635708 0.0447283
\(203\) 1.54419 0.108381
\(204\) −2.17114 −0.152010
\(205\) −4.39175 −0.306733
\(206\) 3.18439 0.221867
\(207\) 2.75865 0.191739
\(208\) 2.86180 0.198430
\(209\) −4.73769 −0.327713
\(210\) 2.85587 0.197074
\(211\) 4.26394 0.293542 0.146771 0.989171i \(-0.453112\pi\)
0.146771 + 0.989171i \(0.453112\pi\)
\(212\) −4.92913 −0.338534
\(213\) 29.0582 1.99104
\(214\) 7.80643 0.533637
\(215\) −2.41693 −0.164833
\(216\) −0.579184 −0.0394084
\(217\) −3.61638 −0.245496
\(218\) −9.57356 −0.648403
\(219\) −4.02742 −0.272148
\(220\) 4.48205 0.302179
\(221\) 2.58921 0.174169
\(222\) −7.43041 −0.498697
\(223\) 24.7642 1.65834 0.829168 0.558999i \(-0.188814\pi\)
0.829168 + 0.558999i \(0.188814\pi\)
\(224\) −0.813594 −0.0543605
\(225\) −7.89071 −0.526047
\(226\) 14.3790 0.956478
\(227\) 17.4784 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(228\) 3.71040 0.245727
\(229\) −5.44225 −0.359634 −0.179817 0.983700i \(-0.557551\pi\)
−0.179817 + 0.983700i \(0.557551\pi\)
\(230\) −1.46275 −0.0964510
\(231\) −5.98237 −0.393611
\(232\) −1.89799 −0.124609
\(233\) −10.4212 −0.682717 −0.341358 0.939933i \(-0.610887\pi\)
−0.341358 + 0.939933i \(0.610887\pi\)
\(234\) −7.89470 −0.516092
\(235\) −11.3126 −0.737954
\(236\) −9.37352 −0.610164
\(237\) 27.5778 1.79137
\(238\) −0.736098 −0.0477141
\(239\) −21.2310 −1.37332 −0.686660 0.726978i \(-0.740924\pi\)
−0.686660 + 0.726978i \(0.740924\pi\)
\(240\) −3.51019 −0.226582
\(241\) 24.5765 1.58311 0.791557 0.611095i \(-0.209271\pi\)
0.791557 + 0.611095i \(0.209271\pi\)
\(242\) 1.61118 0.103570
\(243\) 21.4577 1.37651
\(244\) 9.96319 0.637828
\(245\) −9.27102 −0.592304
\(246\) −7.20489 −0.459367
\(247\) −4.42487 −0.281548
\(248\) 4.44494 0.282254
\(249\) 11.3642 0.720177
\(250\) 11.4978 0.727182
\(251\) −10.9984 −0.694213 −0.347107 0.937826i \(-0.612836\pi\)
−0.347107 + 0.937826i \(0.612836\pi\)
\(252\) 2.24442 0.141385
\(253\) 3.06412 0.192639
\(254\) 1.50464 0.0944093
\(255\) −3.17584 −0.198879
\(256\) 1.00000 0.0625000
\(257\) 5.98703 0.373460 0.186730 0.982411i \(-0.440211\pi\)
0.186730 + 0.982411i \(0.440211\pi\)
\(258\) −3.96509 −0.246856
\(259\) −2.51919 −0.156535
\(260\) 4.18611 0.259611
\(261\) 5.23587 0.324092
\(262\) −1.00000 −0.0617802
\(263\) −6.34520 −0.391262 −0.195631 0.980678i \(-0.562675\pi\)
−0.195631 + 0.980678i \(0.562675\pi\)
\(264\) 7.35302 0.452547
\(265\) −7.21009 −0.442912
\(266\) 1.25797 0.0771308
\(267\) −15.0062 −0.918365
\(268\) 3.71486 0.226921
\(269\) −14.4617 −0.881745 −0.440873 0.897570i \(-0.645331\pi\)
−0.440873 + 0.897570i \(0.645331\pi\)
\(270\) −0.847202 −0.0515591
\(271\) −29.1109 −1.76836 −0.884180 0.467147i \(-0.845282\pi\)
−0.884180 + 0.467147i \(0.845282\pi\)
\(272\) 0.904748 0.0548584
\(273\) −5.58737 −0.338163
\(274\) −0.999989 −0.0604116
\(275\) −8.76447 −0.528518
\(276\) −2.39972 −0.144446
\(277\) −8.96632 −0.538734 −0.269367 0.963038i \(-0.586814\pi\)
−0.269367 + 0.963038i \(0.586814\pi\)
\(278\) 11.6809 0.700576
\(279\) −12.2620 −0.734107
\(280\) −1.19009 −0.0711213
\(281\) 18.2968 1.09149 0.545746 0.837950i \(-0.316246\pi\)
0.545746 + 0.837950i \(0.316246\pi\)
\(282\) −18.5589 −1.10517
\(283\) −22.0620 −1.31145 −0.655725 0.754999i \(-0.727637\pi\)
−0.655725 + 0.754999i \(0.727637\pi\)
\(284\) −12.1090 −0.718538
\(285\) 5.42740 0.321491
\(286\) −8.76890 −0.518516
\(287\) −2.44273 −0.144190
\(288\) −2.75865 −0.162555
\(289\) −16.1814 −0.951849
\(290\) −2.77628 −0.163029
\(291\) −9.87814 −0.579067
\(292\) 1.67829 0.0982145
\(293\) 19.7031 1.15107 0.575534 0.817778i \(-0.304794\pi\)
0.575534 + 0.817778i \(0.304794\pi\)
\(294\) −15.2096 −0.887040
\(295\) −13.7111 −0.798293
\(296\) 3.09637 0.179973
\(297\) 1.77469 0.102978
\(298\) −0.487928 −0.0282649
\(299\) 2.86180 0.165502
\(300\) 6.86405 0.396296
\(301\) −1.34431 −0.0774849
\(302\) −10.9684 −0.631158
\(303\) 1.52552 0.0876389
\(304\) −1.54618 −0.0886797
\(305\) 14.5737 0.834487
\(306\) −2.49588 −0.142680
\(307\) −11.3388 −0.647138 −0.323569 0.946205i \(-0.604883\pi\)
−0.323569 + 0.946205i \(0.604883\pi\)
\(308\) 2.49295 0.142049
\(309\) 7.64163 0.434717
\(310\) 6.50185 0.369280
\(311\) 3.59044 0.203595 0.101798 0.994805i \(-0.467541\pi\)
0.101798 + 0.994805i \(0.467541\pi\)
\(312\) 6.86752 0.388797
\(313\) −27.1652 −1.53547 −0.767735 0.640767i \(-0.778616\pi\)
−0.767735 + 0.640767i \(0.778616\pi\)
\(314\) 11.1294 0.628069
\(315\) 3.28303 0.184978
\(316\) −11.4921 −0.646480
\(317\) 7.90363 0.443912 0.221956 0.975057i \(-0.428756\pi\)
0.221956 + 0.975057i \(0.428756\pi\)
\(318\) −11.8285 −0.663310
\(319\) 5.81565 0.325614
\(320\) 1.46275 0.0817703
\(321\) 18.7332 1.04559
\(322\) −0.813594 −0.0453398
\(323\) −1.39891 −0.0778372
\(324\) −9.66581 −0.536990
\(325\) −8.18577 −0.454065
\(326\) −1.59275 −0.0882141
\(327\) −22.9738 −1.27046
\(328\) 3.00239 0.165779
\(329\) −6.29217 −0.346899
\(330\) 10.7556 0.592079
\(331\) −27.3514 −1.50337 −0.751684 0.659523i \(-0.770758\pi\)
−0.751684 + 0.659523i \(0.770758\pi\)
\(332\) −4.73564 −0.259902
\(333\) −8.54178 −0.468087
\(334\) −2.58158 −0.141258
\(335\) 5.43392 0.296887
\(336\) −1.95240 −0.106512
\(337\) −11.1571 −0.607766 −0.303883 0.952709i \(-0.598283\pi\)
−0.303883 + 0.952709i \(0.598283\pi\)
\(338\) 4.81009 0.261634
\(339\) 34.5056 1.87409
\(340\) 1.32342 0.0717727
\(341\) −13.6198 −0.737555
\(342\) 4.26537 0.230645
\(343\) −10.8518 −0.585941
\(344\) 1.65231 0.0890868
\(345\) −3.51019 −0.188982
\(346\) −4.05919 −0.218223
\(347\) 4.08794 0.219452 0.109726 0.993962i \(-0.465003\pi\)
0.109726 + 0.993962i \(0.465003\pi\)
\(348\) −4.55463 −0.244154
\(349\) 27.7722 1.48661 0.743305 0.668953i \(-0.233257\pi\)
0.743305 + 0.668953i \(0.233257\pi\)
\(350\) 2.32717 0.124392
\(351\) 1.65751 0.0884713
\(352\) −3.06412 −0.163318
\(353\) −3.21943 −0.171353 −0.0856764 0.996323i \(-0.527305\pi\)
−0.0856764 + 0.996323i \(0.527305\pi\)
\(354\) −22.4938 −1.19553
\(355\) −17.7125 −0.940081
\(356\) 6.25332 0.331425
\(357\) −1.76643 −0.0934892
\(358\) −23.3718 −1.23524
\(359\) −7.93004 −0.418531 −0.209266 0.977859i \(-0.567107\pi\)
−0.209266 + 0.977859i \(0.567107\pi\)
\(360\) −4.03521 −0.212674
\(361\) −16.6093 −0.874175
\(362\) 19.1396 1.00595
\(363\) 3.86637 0.202932
\(364\) 2.32835 0.122038
\(365\) 2.45492 0.128496
\(366\) 23.9089 1.24974
\(367\) −35.5396 −1.85515 −0.927575 0.373637i \(-0.878111\pi\)
−0.927575 + 0.373637i \(0.878111\pi\)
\(368\) 1.00000 0.0521286
\(369\) −8.28253 −0.431171
\(370\) 4.52922 0.235463
\(371\) −4.01031 −0.208205
\(372\) 10.6666 0.553038
\(373\) 27.2806 1.41253 0.706267 0.707945i \(-0.250378\pi\)
0.706267 + 0.707945i \(0.250378\pi\)
\(374\) −2.77226 −0.143350
\(375\) 27.5914 1.42481
\(376\) 7.73379 0.398840
\(377\) 5.43166 0.279745
\(378\) −0.471220 −0.0242370
\(379\) −1.29574 −0.0665575 −0.0332788 0.999446i \(-0.510595\pi\)
−0.0332788 + 0.999446i \(0.510595\pi\)
\(380\) −2.26168 −0.116022
\(381\) 3.61070 0.184982
\(382\) −10.6728 −0.546067
\(383\) −0.0745281 −0.00380821 −0.00190410 0.999998i \(-0.500606\pi\)
−0.00190410 + 0.999998i \(0.500606\pi\)
\(384\) 2.39972 0.122460
\(385\) 3.64657 0.185846
\(386\) −22.2628 −1.13315
\(387\) −4.55815 −0.231704
\(388\) 4.11638 0.208977
\(389\) 25.9727 1.31687 0.658434 0.752639i \(-0.271219\pi\)
0.658434 + 0.752639i \(0.271219\pi\)
\(390\) 10.0455 0.508672
\(391\) 0.904748 0.0457551
\(392\) 6.33806 0.320121
\(393\) −2.39972 −0.121050
\(394\) −26.9338 −1.35691
\(395\) −16.8101 −0.845806
\(396\) 8.45282 0.424770
\(397\) 4.73923 0.237855 0.118928 0.992903i \(-0.462054\pi\)
0.118928 + 0.992903i \(0.462054\pi\)
\(398\) 7.31007 0.366421
\(399\) 3.01876 0.151127
\(400\) −2.86036 −0.143018
\(401\) 32.2131 1.60864 0.804322 0.594194i \(-0.202529\pi\)
0.804322 + 0.594194i \(0.202529\pi\)
\(402\) 8.91462 0.444621
\(403\) −12.7205 −0.633655
\(404\) −0.635708 −0.0316277
\(405\) −14.1387 −0.702557
\(406\) −1.54419 −0.0766369
\(407\) −9.48764 −0.470285
\(408\) 2.17114 0.107487
\(409\) −28.0134 −1.38517 −0.692586 0.721335i \(-0.743529\pi\)
−0.692586 + 0.721335i \(0.743529\pi\)
\(410\) 4.39175 0.216893
\(411\) −2.39969 −0.118368
\(412\) −3.18439 −0.156883
\(413\) −7.62624 −0.375263
\(414\) −2.75865 −0.135580
\(415\) −6.92706 −0.340036
\(416\) −2.86180 −0.140311
\(417\) 28.0309 1.37268
\(418\) 4.73769 0.231728
\(419\) −39.3205 −1.92093 −0.960467 0.278394i \(-0.910198\pi\)
−0.960467 + 0.278394i \(0.910198\pi\)
\(420\) −2.85587 −0.139352
\(421\) −29.7676 −1.45078 −0.725391 0.688337i \(-0.758341\pi\)
−0.725391 + 0.688337i \(0.758341\pi\)
\(422\) −4.26394 −0.207565
\(423\) −21.3348 −1.03733
\(424\) 4.92913 0.239380
\(425\) −2.58790 −0.125532
\(426\) −29.0582 −1.40788
\(427\) 8.10600 0.392277
\(428\) −7.80643 −0.377338
\(429\) −21.0429 −1.01596
\(430\) 2.41693 0.116555
\(431\) −31.8325 −1.53332 −0.766658 0.642056i \(-0.778082\pi\)
−0.766658 + 0.642056i \(0.778082\pi\)
\(432\) 0.579184 0.0278660
\(433\) 17.8782 0.859174 0.429587 0.903026i \(-0.358659\pi\)
0.429587 + 0.903026i \(0.358659\pi\)
\(434\) 3.61638 0.173592
\(435\) −6.66229 −0.319433
\(436\) 9.57356 0.458490
\(437\) −1.54618 −0.0739639
\(438\) 4.02742 0.192438
\(439\) −5.09555 −0.243197 −0.121599 0.992579i \(-0.538802\pi\)
−0.121599 + 0.992579i \(0.538802\pi\)
\(440\) −4.48205 −0.213673
\(441\) −17.4845 −0.832594
\(442\) −2.58921 −0.123156
\(443\) 16.2288 0.771054 0.385527 0.922697i \(-0.374020\pi\)
0.385527 + 0.922697i \(0.374020\pi\)
\(444\) 7.43041 0.352632
\(445\) 9.14706 0.433612
\(446\) −24.7642 −1.17262
\(447\) −1.17089 −0.0553811
\(448\) 0.813594 0.0384387
\(449\) −25.0366 −1.18155 −0.590775 0.806836i \(-0.701178\pi\)
−0.590775 + 0.806836i \(0.701178\pi\)
\(450\) 7.89071 0.371972
\(451\) −9.19968 −0.433196
\(452\) −14.3790 −0.676332
\(453\) −26.3210 −1.23667
\(454\) −17.4784 −0.820303
\(455\) 3.40579 0.159666
\(456\) −3.71040 −0.173755
\(457\) 12.8166 0.599534 0.299767 0.954012i \(-0.403091\pi\)
0.299767 + 0.954012i \(0.403091\pi\)
\(458\) 5.44225 0.254300
\(459\) 0.524015 0.0244589
\(460\) 1.46275 0.0682012
\(461\) 3.21953 0.149948 0.0749742 0.997185i \(-0.476113\pi\)
0.0749742 + 0.997185i \(0.476113\pi\)
\(462\) 5.98237 0.278325
\(463\) −31.5623 −1.46682 −0.733412 0.679784i \(-0.762073\pi\)
−0.733412 + 0.679784i \(0.762073\pi\)
\(464\) 1.89799 0.0881118
\(465\) 15.6026 0.723553
\(466\) 10.4212 0.482754
\(467\) 17.8579 0.826367 0.413184 0.910648i \(-0.364417\pi\)
0.413184 + 0.910648i \(0.364417\pi\)
\(468\) 7.89470 0.364933
\(469\) 3.02239 0.139561
\(470\) 11.3126 0.521812
\(471\) 26.7075 1.23061
\(472\) 9.37352 0.431451
\(473\) −5.06289 −0.232792
\(474\) −27.5778 −1.26669
\(475\) 4.42263 0.202924
\(476\) 0.736098 0.0337390
\(477\) −13.5977 −0.622596
\(478\) 21.2310 0.971084
\(479\) 14.6987 0.671601 0.335800 0.941933i \(-0.390993\pi\)
0.335800 + 0.941933i \(0.390993\pi\)
\(480\) 3.51019 0.160218
\(481\) −8.86120 −0.404036
\(482\) −24.5765 −1.11943
\(483\) −1.95240 −0.0888371
\(484\) −1.61118 −0.0732353
\(485\) 6.02124 0.273410
\(486\) −21.4577 −0.973340
\(487\) 26.7250 1.21103 0.605513 0.795836i \(-0.292968\pi\)
0.605513 + 0.795836i \(0.292968\pi\)
\(488\) −9.96319 −0.451013
\(489\) −3.82214 −0.172843
\(490\) 9.27102 0.418822
\(491\) −24.3950 −1.10093 −0.550465 0.834858i \(-0.685549\pi\)
−0.550465 + 0.834858i \(0.685549\pi\)
\(492\) 7.20489 0.324822
\(493\) 1.71720 0.0773388
\(494\) 4.42487 0.199084
\(495\) 12.3644 0.555737
\(496\) −4.44494 −0.199584
\(497\) −9.85183 −0.441915
\(498\) −11.3642 −0.509242
\(499\) −33.1929 −1.48592 −0.742959 0.669337i \(-0.766578\pi\)
−0.742959 + 0.669337i \(0.766578\pi\)
\(500\) −11.4978 −0.514195
\(501\) −6.19506 −0.276775
\(502\) 10.9984 0.490883
\(503\) −8.45644 −0.377054 −0.188527 0.982068i \(-0.560371\pi\)
−0.188527 + 0.982068i \(0.560371\pi\)
\(504\) −2.24442 −0.0999743
\(505\) −0.929884 −0.0413793
\(506\) −3.06412 −0.136217
\(507\) 11.5429 0.512636
\(508\) −1.50464 −0.0667575
\(509\) −20.0036 −0.886645 −0.443323 0.896362i \(-0.646200\pi\)
−0.443323 + 0.896362i \(0.646200\pi\)
\(510\) 3.17584 0.140629
\(511\) 1.36545 0.0604038
\(512\) −1.00000 −0.0441942
\(513\) −0.895524 −0.0395383
\(514\) −5.98703 −0.264076
\(515\) −4.65797 −0.205255
\(516\) 3.96509 0.174553
\(517\) −23.6973 −1.04220
\(518\) 2.51919 0.110687
\(519\) −9.74091 −0.427579
\(520\) −4.18611 −0.183573
\(521\) 32.2500 1.41290 0.706450 0.707763i \(-0.250296\pi\)
0.706450 + 0.707763i \(0.250296\pi\)
\(522\) −5.23587 −0.229168
\(523\) −1.40551 −0.0614587 −0.0307294 0.999528i \(-0.509783\pi\)
−0.0307294 + 0.999528i \(0.509783\pi\)
\(524\) 1.00000 0.0436852
\(525\) 5.58455 0.243730
\(526\) 6.34520 0.276664
\(527\) −4.02155 −0.175182
\(528\) −7.35302 −0.319999
\(529\) 1.00000 0.0434783
\(530\) 7.21009 0.313186
\(531\) −25.8582 −1.12215
\(532\) −1.25797 −0.0545397
\(533\) −8.59225 −0.372172
\(534\) 15.0062 0.649382
\(535\) −11.4189 −0.493681
\(536\) −3.71486 −0.160458
\(537\) −56.0858 −2.42028
\(538\) 14.4617 0.623488
\(539\) −19.4206 −0.836504
\(540\) 0.847202 0.0364578
\(541\) 32.8351 1.41169 0.705845 0.708367i \(-0.250568\pi\)
0.705845 + 0.708367i \(0.250568\pi\)
\(542\) 29.1109 1.25042
\(543\) 45.9296 1.97103
\(544\) −0.904748 −0.0387908
\(545\) 14.0037 0.599854
\(546\) 5.58737 0.239117
\(547\) −25.5926 −1.09426 −0.547131 0.837047i \(-0.684280\pi\)
−0.547131 + 0.837047i \(0.684280\pi\)
\(548\) 0.999989 0.0427174
\(549\) 27.4849 1.17303
\(550\) 8.76447 0.373718
\(551\) −2.93463 −0.125020
\(552\) 2.39972 0.102139
\(553\) −9.34989 −0.397598
\(554\) 8.96632 0.380943
\(555\) 10.8688 0.461357
\(556\) −11.6809 −0.495382
\(557\) −26.3568 −1.11677 −0.558386 0.829581i \(-0.688579\pi\)
−0.558386 + 0.829581i \(0.688579\pi\)
\(558\) 12.2620 0.519092
\(559\) −4.72860 −0.199998
\(560\) 1.19009 0.0502903
\(561\) −6.65263 −0.280874
\(562\) −18.2968 −0.771802
\(563\) 2.49675 0.105225 0.0526127 0.998615i \(-0.483245\pi\)
0.0526127 + 0.998615i \(0.483245\pi\)
\(564\) 18.5589 0.781472
\(565\) −21.0329 −0.884863
\(566\) 22.0620 0.927336
\(567\) −7.86405 −0.330259
\(568\) 12.1090 0.508083
\(569\) 5.96413 0.250029 0.125015 0.992155i \(-0.460102\pi\)
0.125015 + 0.992155i \(0.460102\pi\)
\(570\) −5.42740 −0.227329
\(571\) 8.39480 0.351311 0.175656 0.984452i \(-0.443795\pi\)
0.175656 + 0.984452i \(0.443795\pi\)
\(572\) 8.76890 0.366646
\(573\) −25.6116 −1.06994
\(574\) 2.44273 0.101957
\(575\) −2.86036 −0.119285
\(576\) 2.75865 0.114944
\(577\) −3.29637 −0.137230 −0.0686149 0.997643i \(-0.521858\pi\)
−0.0686149 + 0.997643i \(0.521858\pi\)
\(578\) 16.1814 0.673059
\(579\) −53.4244 −2.22024
\(580\) 2.77628 0.115279
\(581\) −3.85289 −0.159845
\(582\) 9.87814 0.409462
\(583\) −15.1034 −0.625520
\(584\) −1.67829 −0.0694481
\(585\) 11.5480 0.477450
\(586\) −19.7031 −0.813928
\(587\) −13.1105 −0.541130 −0.270565 0.962702i \(-0.587210\pi\)
−0.270565 + 0.962702i \(0.587210\pi\)
\(588\) 15.2096 0.627232
\(589\) 6.87269 0.283184
\(590\) 13.7111 0.564479
\(591\) −64.6335 −2.65867
\(592\) −3.09637 −0.127260
\(593\) 27.6631 1.13599 0.567994 0.823033i \(-0.307720\pi\)
0.567994 + 0.823033i \(0.307720\pi\)
\(594\) −1.77469 −0.0728163
\(595\) 1.07673 0.0441416
\(596\) 0.487928 0.0199863
\(597\) 17.5421 0.717950
\(598\) −2.86180 −0.117028
\(599\) 8.01598 0.327524 0.163762 0.986500i \(-0.447637\pi\)
0.163762 + 0.986500i \(0.447637\pi\)
\(600\) −6.86405 −0.280224
\(601\) 2.38505 0.0972882 0.0486441 0.998816i \(-0.484510\pi\)
0.0486441 + 0.998816i \(0.484510\pi\)
\(602\) 1.34431 0.0547901
\(603\) 10.2480 0.417330
\(604\) 10.9684 0.446296
\(605\) −2.35675 −0.0958156
\(606\) −1.52552 −0.0619701
\(607\) 1.14297 0.0463918 0.0231959 0.999731i \(-0.492616\pi\)
0.0231959 + 0.999731i \(0.492616\pi\)
\(608\) 1.54618 0.0627060
\(609\) −3.70562 −0.150159
\(610\) −14.5737 −0.590071
\(611\) −22.1326 −0.895389
\(612\) 2.49588 0.100890
\(613\) 10.0729 0.406839 0.203419 0.979092i \(-0.434795\pi\)
0.203419 + 0.979092i \(0.434795\pi\)
\(614\) 11.3388 0.457595
\(615\) 10.5390 0.424972
\(616\) −2.49295 −0.100444
\(617\) 40.3538 1.62458 0.812292 0.583251i \(-0.198220\pi\)
0.812292 + 0.583251i \(0.198220\pi\)
\(618\) −7.64163 −0.307391
\(619\) −11.2636 −0.452721 −0.226361 0.974044i \(-0.572683\pi\)
−0.226361 + 0.974044i \(0.572683\pi\)
\(620\) −6.50185 −0.261120
\(621\) 0.579184 0.0232418
\(622\) −3.59044 −0.143964
\(623\) 5.08767 0.203833
\(624\) −6.86752 −0.274921
\(625\) −2.51658 −0.100663
\(626\) 27.1652 1.08574
\(627\) 11.3691 0.454039
\(628\) −11.1294 −0.444112
\(629\) −2.80143 −0.111701
\(630\) −3.28303 −0.130799
\(631\) −38.7095 −1.54100 −0.770500 0.637440i \(-0.779993\pi\)
−0.770500 + 0.637440i \(0.779993\pi\)
\(632\) 11.4921 0.457130
\(633\) −10.2322 −0.406695
\(634\) −7.90363 −0.313893
\(635\) −2.20091 −0.0873405
\(636\) 11.8285 0.469031
\(637\) −18.1383 −0.718665
\(638\) −5.81565 −0.230244
\(639\) −33.4045 −1.32146
\(640\) −1.46275 −0.0578204
\(641\) −27.4830 −1.08551 −0.542757 0.839890i \(-0.682620\pi\)
−0.542757 + 0.839890i \(0.682620\pi\)
\(642\) −18.7332 −0.739342
\(643\) −15.8256 −0.624100 −0.312050 0.950066i \(-0.601016\pi\)
−0.312050 + 0.950066i \(0.601016\pi\)
\(644\) 0.813594 0.0320601
\(645\) 5.79994 0.228372
\(646\) 1.39891 0.0550392
\(647\) 25.4030 0.998696 0.499348 0.866402i \(-0.333573\pi\)
0.499348 + 0.866402i \(0.333573\pi\)
\(648\) 9.66581 0.379709
\(649\) −28.7216 −1.12742
\(650\) 8.18577 0.321073
\(651\) 8.67828 0.340129
\(652\) 1.59275 0.0623768
\(653\) −33.5484 −1.31285 −0.656424 0.754392i \(-0.727932\pi\)
−0.656424 + 0.754392i \(0.727932\pi\)
\(654\) 22.9738 0.898348
\(655\) 1.46275 0.0571545
\(656\) −3.00239 −0.117224
\(657\) 4.62980 0.180626
\(658\) 6.29217 0.245294
\(659\) −31.3720 −1.22208 −0.611039 0.791600i \(-0.709248\pi\)
−0.611039 + 0.791600i \(0.709248\pi\)
\(660\) −10.7556 −0.418663
\(661\) −25.8043 −1.00367 −0.501836 0.864963i \(-0.667342\pi\)
−0.501836 + 0.864963i \(0.667342\pi\)
\(662\) 27.3514 1.06304
\(663\) −6.21338 −0.241308
\(664\) 4.73564 0.183778
\(665\) −1.84009 −0.0713557
\(666\) 8.54178 0.330987
\(667\) 1.89799 0.0734903
\(668\) 2.58158 0.0998843
\(669\) −59.4272 −2.29759
\(670\) −5.43392 −0.209931
\(671\) 30.5284 1.17854
\(672\) 1.95240 0.0753153
\(673\) 34.0308 1.31179 0.655895 0.754852i \(-0.272292\pi\)
0.655895 + 0.754852i \(0.272292\pi\)
\(674\) 11.1571 0.429755
\(675\) −1.65667 −0.0637653
\(676\) −4.81009 −0.185003
\(677\) 24.5707 0.944330 0.472165 0.881510i \(-0.343473\pi\)
0.472165 + 0.881510i \(0.343473\pi\)
\(678\) −34.5056 −1.32518
\(679\) 3.34906 0.128525
\(680\) −1.32342 −0.0507509
\(681\) −41.9433 −1.60727
\(682\) 13.6198 0.521530
\(683\) 22.0909 0.845286 0.422643 0.906296i \(-0.361102\pi\)
0.422643 + 0.906296i \(0.361102\pi\)
\(684\) −4.26537 −0.163090
\(685\) 1.46274 0.0558883
\(686\) 10.8518 0.414323
\(687\) 13.0599 0.498265
\(688\) −1.65231 −0.0629939
\(689\) −14.1062 −0.537403
\(690\) 3.51019 0.133631
\(691\) −39.4704 −1.50152 −0.750762 0.660572i \(-0.770314\pi\)
−0.750762 + 0.660572i \(0.770314\pi\)
\(692\) 4.05919 0.154307
\(693\) 6.87716 0.261242
\(694\) −4.08794 −0.155176
\(695\) −17.0863 −0.648120
\(696\) 4.55463 0.172643
\(697\) −2.71641 −0.102891
\(698\) −27.7722 −1.05119
\(699\) 25.0080 0.945889
\(700\) −2.32717 −0.0879587
\(701\) −28.1663 −1.06383 −0.531913 0.846799i \(-0.678527\pi\)
−0.531913 + 0.846799i \(0.678527\pi\)
\(702\) −1.65751 −0.0625586
\(703\) 4.78755 0.180566
\(704\) 3.06412 0.115483
\(705\) 27.1471 1.02242
\(706\) 3.21943 0.121165
\(707\) −0.517209 −0.0194516
\(708\) 22.4938 0.845369
\(709\) −31.5986 −1.18671 −0.593355 0.804941i \(-0.702197\pi\)
−0.593355 + 0.804941i \(0.702197\pi\)
\(710\) 17.7125 0.664738
\(711\) −31.7026 −1.18894
\(712\) −6.25332 −0.234353
\(713\) −4.44494 −0.166464
\(714\) 1.76643 0.0661069
\(715\) 12.8267 0.479692
\(716\) 23.3718 0.873447
\(717\) 50.9485 1.90270
\(718\) 7.93004 0.295946
\(719\) 5.90943 0.220385 0.110192 0.993910i \(-0.464853\pi\)
0.110192 + 0.993910i \(0.464853\pi\)
\(720\) 4.03521 0.150384
\(721\) −2.59080 −0.0964864
\(722\) 16.6093 0.618135
\(723\) −58.9768 −2.19337
\(724\) −19.1396 −0.711317
\(725\) −5.42892 −0.201625
\(726\) −3.86637 −0.143494
\(727\) −2.00384 −0.0743185 −0.0371592 0.999309i \(-0.511831\pi\)
−0.0371592 + 0.999309i \(0.511831\pi\)
\(728\) −2.32835 −0.0862942
\(729\) −22.4949 −0.833145
\(730\) −2.45492 −0.0908607
\(731\) −1.49493 −0.0552919
\(732\) −23.9089 −0.883697
\(733\) 15.6155 0.576772 0.288386 0.957514i \(-0.406881\pi\)
0.288386 + 0.957514i \(0.406881\pi\)
\(734\) 35.5396 1.31179
\(735\) 22.2478 0.820623
\(736\) −1.00000 −0.0368605
\(737\) 11.3828 0.419290
\(738\) 8.28253 0.304884
\(739\) 21.6004 0.794584 0.397292 0.917692i \(-0.369950\pi\)
0.397292 + 0.917692i \(0.369950\pi\)
\(740\) −4.52922 −0.166497
\(741\) 10.6184 0.390078
\(742\) 4.01031 0.147223
\(743\) 44.6605 1.63843 0.819217 0.573483i \(-0.194408\pi\)
0.819217 + 0.573483i \(0.194408\pi\)
\(744\) −10.6666 −0.391057
\(745\) 0.713717 0.0261486
\(746\) −27.2806 −0.998813
\(747\) −13.0639 −0.477985
\(748\) 2.77226 0.101364
\(749\) −6.35127 −0.232070
\(750\) −27.5914 −1.00749
\(751\) −22.4340 −0.818630 −0.409315 0.912393i \(-0.634232\pi\)
−0.409315 + 0.912393i \(0.634232\pi\)
\(752\) −7.73379 −0.282022
\(753\) 26.3931 0.961817
\(754\) −5.43166 −0.197809
\(755\) 16.0440 0.583901
\(756\) 0.471220 0.0171381
\(757\) −23.7009 −0.861425 −0.430712 0.902489i \(-0.641738\pi\)
−0.430712 + 0.902489i \(0.641738\pi\)
\(758\) 1.29574 0.0470633
\(759\) −7.35302 −0.266898
\(760\) 2.26168 0.0820398
\(761\) −22.7413 −0.824372 −0.412186 0.911100i \(-0.635235\pi\)
−0.412186 + 0.911100i \(0.635235\pi\)
\(762\) −3.61070 −0.130802
\(763\) 7.78899 0.281980
\(764\) 10.6728 0.386127
\(765\) 3.65085 0.131997
\(766\) 0.0745281 0.00269281
\(767\) −26.8252 −0.968600
\(768\) −2.39972 −0.0865924
\(769\) 9.26088 0.333956 0.166978 0.985961i \(-0.446599\pi\)
0.166978 + 0.985961i \(0.446599\pi\)
\(770\) −3.64657 −0.131413
\(771\) −14.3672 −0.517421
\(772\) 22.2628 0.801255
\(773\) −11.1153 −0.399790 −0.199895 0.979817i \(-0.564060\pi\)
−0.199895 + 0.979817i \(0.564060\pi\)
\(774\) 4.55815 0.163839
\(775\) 12.7141 0.456704
\(776\) −4.11638 −0.147769
\(777\) 6.04534 0.216875
\(778\) −25.9727 −0.931166
\(779\) 4.64224 0.166326
\(780\) −10.0455 −0.359686
\(781\) −37.1035 −1.32767
\(782\) −0.904748 −0.0323537
\(783\) 1.09928 0.0392851
\(784\) −6.33806 −0.226359
\(785\) −16.2796 −0.581043
\(786\) 2.39972 0.0855951
\(787\) 13.2209 0.471274 0.235637 0.971841i \(-0.424282\pi\)
0.235637 + 0.971841i \(0.424282\pi\)
\(788\) 26.9338 0.959477
\(789\) 15.2267 0.542084
\(790\) 16.8101 0.598075
\(791\) −11.6987 −0.415957
\(792\) −8.45282 −0.300358
\(793\) 28.5127 1.01252
\(794\) −4.73923 −0.168189
\(795\) 17.3022 0.613645
\(796\) −7.31007 −0.259099
\(797\) 28.4079 1.00626 0.503129 0.864211i \(-0.332182\pi\)
0.503129 + 0.864211i \(0.332182\pi\)
\(798\) −3.01876 −0.106863
\(799\) −6.99714 −0.247541
\(800\) 2.86036 0.101129
\(801\) 17.2507 0.609523
\(802\) −32.2131 −1.13748
\(803\) 5.14248 0.181474
\(804\) −8.91462 −0.314395
\(805\) 1.19009 0.0419450
\(806\) 12.7205 0.448062
\(807\) 34.7040 1.22164
\(808\) 0.635708 0.0223641
\(809\) −3.29101 −0.115706 −0.0578529 0.998325i \(-0.518425\pi\)
−0.0578529 + 0.998325i \(0.518425\pi\)
\(810\) 14.1387 0.496783
\(811\) 30.5075 1.07126 0.535632 0.844451i \(-0.320073\pi\)
0.535632 + 0.844451i \(0.320073\pi\)
\(812\) 1.54419 0.0541904
\(813\) 69.8579 2.45002
\(814\) 9.48764 0.332542
\(815\) 2.32979 0.0816092
\(816\) −2.17114 −0.0760051
\(817\) 2.55478 0.0893805
\(818\) 28.0134 0.979465
\(819\) 6.42308 0.224441
\(820\) −4.39175 −0.153367
\(821\) 6.94957 0.242542 0.121271 0.992619i \(-0.461303\pi\)
0.121271 + 0.992619i \(0.461303\pi\)
\(822\) 2.39969 0.0836989
\(823\) −30.9266 −1.07803 −0.539017 0.842295i \(-0.681204\pi\)
−0.539017 + 0.842295i \(0.681204\pi\)
\(824\) 3.18439 0.110933
\(825\) 21.0323 0.732249
\(826\) 7.62624 0.265351
\(827\) −25.4075 −0.883506 −0.441753 0.897137i \(-0.645643\pi\)
−0.441753 + 0.897137i \(0.645643\pi\)
\(828\) 2.75865 0.0958695
\(829\) 11.1445 0.387066 0.193533 0.981094i \(-0.438005\pi\)
0.193533 + 0.981094i \(0.438005\pi\)
\(830\) 6.92706 0.240442
\(831\) 21.5166 0.746404
\(832\) 2.86180 0.0992151
\(833\) −5.73435 −0.198684
\(834\) −28.0309 −0.970632
\(835\) 3.77621 0.130681
\(836\) −4.73769 −0.163856
\(837\) −2.57444 −0.0889855
\(838\) 39.3205 1.35831
\(839\) −29.8408 −1.03022 −0.515110 0.857124i \(-0.672249\pi\)
−0.515110 + 0.857124i \(0.672249\pi\)
\(840\) 2.85587 0.0985369
\(841\) −25.3977 −0.875781
\(842\) 29.7676 1.02586
\(843\) −43.9070 −1.51224
\(844\) 4.26394 0.146771
\(845\) −7.03596 −0.242045
\(846\) 21.3348 0.733505
\(847\) −1.31084 −0.0450411
\(848\) −4.92913 −0.169267
\(849\) 52.9426 1.81699
\(850\) 2.58790 0.0887643
\(851\) −3.09637 −0.106142
\(852\) 29.0582 0.995518
\(853\) −44.3501 −1.51852 −0.759259 0.650789i \(-0.774438\pi\)
−0.759259 + 0.650789i \(0.774438\pi\)
\(854\) −8.10600 −0.277381
\(855\) −6.23918 −0.213375
\(856\) 7.80643 0.266818
\(857\) 1.22977 0.0420083 0.0210041 0.999779i \(-0.493314\pi\)
0.0210041 + 0.999779i \(0.493314\pi\)
\(858\) 21.0429 0.718392
\(859\) 44.6251 1.52259 0.761294 0.648407i \(-0.224565\pi\)
0.761294 + 0.648407i \(0.224565\pi\)
\(860\) −2.41693 −0.0824165
\(861\) 5.86186 0.199772
\(862\) 31.8325 1.08422
\(863\) −36.8766 −1.25529 −0.627647 0.778498i \(-0.715982\pi\)
−0.627647 + 0.778498i \(0.715982\pi\)
\(864\) −0.579184 −0.0197042
\(865\) 5.93759 0.201884
\(866\) −17.8782 −0.607528
\(867\) 38.8309 1.31877
\(868\) −3.61638 −0.122748
\(869\) −35.2131 −1.19452
\(870\) 6.66229 0.225873
\(871\) 10.6312 0.360225
\(872\) −9.57356 −0.324202
\(873\) 11.3556 0.384330
\(874\) 1.54618 0.0523004
\(875\) −9.35450 −0.316240
\(876\) −4.02742 −0.136074
\(877\) 36.0441 1.21712 0.608561 0.793507i \(-0.291747\pi\)
0.608561 + 0.793507i \(0.291747\pi\)
\(878\) 5.09555 0.171967
\(879\) −47.2819 −1.59478
\(880\) 4.48205 0.151090
\(881\) 49.4966 1.66758 0.833791 0.552081i \(-0.186166\pi\)
0.833791 + 0.552081i \(0.186166\pi\)
\(882\) 17.4845 0.588733
\(883\) −42.8645 −1.44251 −0.721253 0.692672i \(-0.756433\pi\)
−0.721253 + 0.692672i \(0.756433\pi\)
\(884\) 2.58921 0.0870846
\(885\) 32.9029 1.10602
\(886\) −16.2288 −0.545218
\(887\) 36.4516 1.22393 0.611963 0.790887i \(-0.290380\pi\)
0.611963 + 0.790887i \(0.290380\pi\)
\(888\) −7.43041 −0.249348
\(889\) −1.22416 −0.0410571
\(890\) −9.14706 −0.306610
\(891\) −29.6172 −0.992213
\(892\) 24.7642 0.829168
\(893\) 11.9579 0.400154
\(894\) 1.17089 0.0391604
\(895\) 34.1872 1.14275
\(896\) −0.813594 −0.0271803
\(897\) −6.86752 −0.229300
\(898\) 25.0366 0.835482
\(899\) −8.43643 −0.281371
\(900\) −7.89071 −0.263024
\(901\) −4.45962 −0.148571
\(902\) 9.19968 0.306316
\(903\) 3.22597 0.107354
\(904\) 14.3790 0.478239
\(905\) −27.9965 −0.930634
\(906\) 26.3210 0.874456
\(907\) −35.9212 −1.19274 −0.596372 0.802708i \(-0.703392\pi\)
−0.596372 + 0.802708i \(0.703392\pi\)
\(908\) 17.4784 0.580042
\(909\) −1.75369 −0.0581664
\(910\) −3.40579 −0.112901
\(911\) −24.6376 −0.816278 −0.408139 0.912920i \(-0.633822\pi\)
−0.408139 + 0.912920i \(0.633822\pi\)
\(912\) 3.71040 0.122864
\(913\) −14.5106 −0.480229
\(914\) −12.8166 −0.423935
\(915\) −34.9727 −1.15616
\(916\) −5.44225 −0.179817
\(917\) 0.813594 0.0268672
\(918\) −0.524015 −0.0172951
\(919\) 40.7959 1.34573 0.672866 0.739764i \(-0.265063\pi\)
0.672866 + 0.739764i \(0.265063\pi\)
\(920\) −1.46275 −0.0482255
\(921\) 27.2098 0.896595
\(922\) −3.21953 −0.106029
\(923\) −34.6536 −1.14064
\(924\) −5.98237 −0.196806
\(925\) 8.85672 0.291207
\(926\) 31.5623 1.03720
\(927\) −8.78459 −0.288524
\(928\) −1.89799 −0.0623044
\(929\) −14.1678 −0.464831 −0.232416 0.972617i \(-0.574663\pi\)
−0.232416 + 0.972617i \(0.574663\pi\)
\(930\) −15.6026 −0.511629
\(931\) 9.79981 0.321176
\(932\) −10.4212 −0.341358
\(933\) −8.61605 −0.282077
\(934\) −17.8579 −0.584330
\(935\) 4.05512 0.132617
\(936\) −7.89470 −0.258046
\(937\) 8.00799 0.261610 0.130805 0.991408i \(-0.458244\pi\)
0.130805 + 0.991408i \(0.458244\pi\)
\(938\) −3.02239 −0.0986846
\(939\) 65.1889 2.12736
\(940\) −11.3126 −0.368977
\(941\) −30.2572 −0.986356 −0.493178 0.869928i \(-0.664165\pi\)
−0.493178 + 0.869928i \(0.664165\pi\)
\(942\) −26.7075 −0.870176
\(943\) −3.00239 −0.0977713
\(944\) −9.37352 −0.305082
\(945\) 0.689278 0.0224222
\(946\) 5.06289 0.164609
\(947\) −17.0199 −0.553073 −0.276537 0.961003i \(-0.589187\pi\)
−0.276537 + 0.961003i \(0.589187\pi\)
\(948\) 27.5778 0.895684
\(949\) 4.80293 0.155910
\(950\) −4.42263 −0.143489
\(951\) −18.9665 −0.615030
\(952\) −0.736098 −0.0238571
\(953\) −18.4305 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(954\) 13.5977 0.440242
\(955\) 15.6116 0.505180
\(956\) −21.2310 −0.686660
\(957\) −13.9559 −0.451131
\(958\) −14.6987 −0.474894
\(959\) 0.813585 0.0262720
\(960\) −3.51019 −0.113291
\(961\) −11.2425 −0.362662
\(962\) 8.86120 0.285696
\(963\) −21.5352 −0.693961
\(964\) 24.5765 0.791557
\(965\) 32.5649 1.04830
\(966\) 1.95240 0.0628173
\(967\) 39.9945 1.28614 0.643069 0.765808i \(-0.277661\pi\)
0.643069 + 0.765808i \(0.277661\pi\)
\(968\) 1.61118 0.0517852
\(969\) 3.35698 0.107842
\(970\) −6.02124 −0.193330
\(971\) 56.3989 1.80993 0.904963 0.425490i \(-0.139898\pi\)
0.904963 + 0.425490i \(0.139898\pi\)
\(972\) 21.4577 0.688255
\(973\) −9.50354 −0.304669
\(974\) −26.7250 −0.856324
\(975\) 19.6435 0.629097
\(976\) 9.96319 0.318914
\(977\) 16.0810 0.514478 0.257239 0.966348i \(-0.417187\pi\)
0.257239 + 0.966348i \(0.417187\pi\)
\(978\) 3.82214 0.122219
\(979\) 19.1609 0.612386
\(980\) −9.27102 −0.296152
\(981\) 26.4101 0.843208
\(982\) 24.3950 0.778475
\(983\) 7.09242 0.226213 0.113107 0.993583i \(-0.463920\pi\)
0.113107 + 0.993583i \(0.463920\pi\)
\(984\) −7.20489 −0.229684
\(985\) 39.3975 1.25531
\(986\) −1.71720 −0.0546868
\(987\) 15.0994 0.480620
\(988\) −4.42487 −0.140774
\(989\) −1.65231 −0.0525406
\(990\) −12.3644 −0.392966
\(991\) −30.5461 −0.970329 −0.485165 0.874423i \(-0.661240\pi\)
−0.485165 + 0.874423i \(0.661240\pi\)
\(992\) 4.44494 0.141127
\(993\) 65.6356 2.08288
\(994\) 9.85183 0.312481
\(995\) −10.6928 −0.338985
\(996\) 11.3642 0.360088
\(997\) 27.9063 0.883802 0.441901 0.897064i \(-0.354304\pi\)
0.441901 + 0.897064i \(0.354304\pi\)
\(998\) 33.1929 1.05070
\(999\) −1.79337 −0.0567396
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 \(a_p\))