Properties

Label 4017.2.a.j.1.18
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.59660 q^{2} -1.00000 q^{3} +0.549133 q^{4} -3.22334 q^{5} -1.59660 q^{6} +2.57812 q^{7} -2.31645 q^{8} +1.00000 q^{9} -5.14639 q^{10} -3.57802 q^{11} -0.549133 q^{12} +1.00000 q^{13} +4.11623 q^{14} +3.22334 q^{15} -4.79672 q^{16} +6.66029 q^{17} +1.59660 q^{18} -5.80781 q^{19} -1.77005 q^{20} -2.57812 q^{21} -5.71266 q^{22} -1.56970 q^{23} +2.31645 q^{24} +5.38994 q^{25} +1.59660 q^{26} -1.00000 q^{27} +1.41573 q^{28} -3.85916 q^{29} +5.14639 q^{30} -2.09496 q^{31} -3.02554 q^{32} +3.57802 q^{33} +10.6338 q^{34} -8.31016 q^{35} +0.549133 q^{36} -3.49607 q^{37} -9.27276 q^{38} -1.00000 q^{39} +7.46673 q^{40} +8.46980 q^{41} -4.11623 q^{42} -4.32621 q^{43} -1.96481 q^{44} -3.22334 q^{45} -2.50619 q^{46} +8.30395 q^{47} +4.79672 q^{48} -0.353301 q^{49} +8.60558 q^{50} -6.66029 q^{51} +0.549133 q^{52} +5.20081 q^{53} -1.59660 q^{54} +11.5332 q^{55} -5.97210 q^{56} +5.80781 q^{57} -6.16153 q^{58} +7.94515 q^{59} +1.77005 q^{60} -0.135083 q^{61} -3.34481 q^{62} +2.57812 q^{63} +4.76287 q^{64} -3.22334 q^{65} +5.71266 q^{66} +6.03238 q^{67} +3.65739 q^{68} +1.56970 q^{69} -13.2680 q^{70} +6.61908 q^{71} -2.31645 q^{72} -6.56636 q^{73} -5.58183 q^{74} -5.38994 q^{75} -3.18926 q^{76} -9.22455 q^{77} -1.59660 q^{78} +10.9360 q^{79} +15.4615 q^{80} +1.00000 q^{81} +13.5229 q^{82} +3.61033 q^{83} -1.41573 q^{84} -21.4684 q^{85} -6.90723 q^{86} +3.85916 q^{87} +8.28831 q^{88} +1.01165 q^{89} -5.14639 q^{90} +2.57812 q^{91} -0.861976 q^{92} +2.09496 q^{93} +13.2581 q^{94} +18.7206 q^{95} +3.02554 q^{96} +7.20505 q^{97} -0.564081 q^{98} -3.57802 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.59660 1.12897 0.564484 0.825444i \(-0.309075\pi\)
0.564484 + 0.825444i \(0.309075\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.549133 0.274567
\(5\) −3.22334 −1.44152 −0.720761 0.693183i \(-0.756208\pi\)
−0.720761 + 0.693183i \(0.756208\pi\)
\(6\) −1.59660 −0.651809
\(7\) 2.57812 0.974437 0.487219 0.873280i \(-0.338011\pi\)
0.487219 + 0.873280i \(0.338011\pi\)
\(8\) −2.31645 −0.818990
\(9\) 1.00000 0.333333
\(10\) −5.14639 −1.62743
\(11\) −3.57802 −1.07881 −0.539406 0.842046i \(-0.681351\pi\)
−0.539406 + 0.842046i \(0.681351\pi\)
\(12\) −0.549133 −0.158521
\(13\) 1.00000 0.277350
\(14\) 4.11623 1.10011
\(15\) 3.22334 0.832264
\(16\) −4.79672 −1.19918
\(17\) 6.66029 1.61536 0.807679 0.589623i \(-0.200724\pi\)
0.807679 + 0.589623i \(0.200724\pi\)
\(18\) 1.59660 0.376322
\(19\) −5.80781 −1.33240 −0.666202 0.745772i \(-0.732081\pi\)
−0.666202 + 0.745772i \(0.732081\pi\)
\(20\) −1.77005 −0.395794
\(21\) −2.57812 −0.562592
\(22\) −5.71266 −1.21794
\(23\) −1.56970 −0.327305 −0.163653 0.986518i \(-0.552328\pi\)
−0.163653 + 0.986518i \(0.552328\pi\)
\(24\) 2.31645 0.472844
\(25\) 5.38994 1.07799
\(26\) 1.59660 0.313119
\(27\) −1.00000 −0.192450
\(28\) 1.41573 0.267548
\(29\) −3.85916 −0.716627 −0.358314 0.933601i \(-0.616648\pi\)
−0.358314 + 0.933601i \(0.616648\pi\)
\(30\) 5.14639 0.939598
\(31\) −2.09496 −0.376266 −0.188133 0.982144i \(-0.560244\pi\)
−0.188133 + 0.982144i \(0.560244\pi\)
\(32\) −3.02554 −0.534844
\(33\) 3.57802 0.622853
\(34\) 10.6338 1.82369
\(35\) −8.31016 −1.40467
\(36\) 0.549133 0.0915222
\(37\) −3.49607 −0.574751 −0.287375 0.957818i \(-0.592783\pi\)
−0.287375 + 0.957818i \(0.592783\pi\)
\(38\) −9.27276 −1.50424
\(39\) −1.00000 −0.160128
\(40\) 7.46673 1.18059
\(41\) 8.46980 1.32276 0.661380 0.750051i \(-0.269971\pi\)
0.661380 + 0.750051i \(0.269971\pi\)
\(42\) −4.11623 −0.635148
\(43\) −4.32621 −0.659741 −0.329871 0.944026i \(-0.607005\pi\)
−0.329871 + 0.944026i \(0.607005\pi\)
\(44\) −1.96481 −0.296206
\(45\) −3.22334 −0.480508
\(46\) −2.50619 −0.369517
\(47\) 8.30395 1.21126 0.605628 0.795748i \(-0.292922\pi\)
0.605628 + 0.795748i \(0.292922\pi\)
\(48\) 4.79672 0.692347
\(49\) −0.353301 −0.0504716
\(50\) 8.60558 1.21701
\(51\) −6.66029 −0.932627
\(52\) 0.549133 0.0761511
\(53\) 5.20081 0.714387 0.357193 0.934030i \(-0.383734\pi\)
0.357193 + 0.934030i \(0.383734\pi\)
\(54\) −1.59660 −0.217270
\(55\) 11.5332 1.55513
\(56\) −5.97210 −0.798055
\(57\) 5.80781 0.769264
\(58\) −6.16153 −0.809048
\(59\) 7.94515 1.03437 0.517185 0.855874i \(-0.326980\pi\)
0.517185 + 0.855874i \(0.326980\pi\)
\(60\) 1.77005 0.228512
\(61\) −0.135083 −0.0172957 −0.00864783 0.999963i \(-0.502753\pi\)
−0.00864783 + 0.999963i \(0.502753\pi\)
\(62\) −3.34481 −0.424792
\(63\) 2.57812 0.324812
\(64\) 4.76287 0.595358
\(65\) −3.22334 −0.399806
\(66\) 5.71266 0.703180
\(67\) 6.03238 0.736972 0.368486 0.929633i \(-0.379876\pi\)
0.368486 + 0.929633i \(0.379876\pi\)
\(68\) 3.65739 0.443523
\(69\) 1.56970 0.188970
\(70\) −13.2680 −1.58583
\(71\) 6.61908 0.785540 0.392770 0.919637i \(-0.371517\pi\)
0.392770 + 0.919637i \(0.371517\pi\)
\(72\) −2.31645 −0.272997
\(73\) −6.56636 −0.768534 −0.384267 0.923222i \(-0.625546\pi\)
−0.384267 + 0.923222i \(0.625546\pi\)
\(74\) −5.58183 −0.648875
\(75\) −5.38994 −0.622377
\(76\) −3.18926 −0.365834
\(77\) −9.22455 −1.05124
\(78\) −1.59660 −0.180779
\(79\) 10.9360 1.23040 0.615198 0.788372i \(-0.289076\pi\)
0.615198 + 0.788372i \(0.289076\pi\)
\(80\) 15.4615 1.72865
\(81\) 1.00000 0.111111
\(82\) 13.5229 1.49335
\(83\) 3.61033 0.396285 0.198142 0.980173i \(-0.436509\pi\)
0.198142 + 0.980173i \(0.436509\pi\)
\(84\) −1.41573 −0.154469
\(85\) −21.4684 −2.32857
\(86\) −6.90723 −0.744826
\(87\) 3.85916 0.413745
\(88\) 8.28831 0.883537
\(89\) 1.01165 0.107234 0.0536171 0.998562i \(-0.482925\pi\)
0.0536171 + 0.998562i \(0.482925\pi\)
\(90\) −5.14639 −0.542477
\(91\) 2.57812 0.270260
\(92\) −0.861976 −0.0898672
\(93\) 2.09496 0.217237
\(94\) 13.2581 1.36747
\(95\) 18.7206 1.92069
\(96\) 3.02554 0.308792
\(97\) 7.20505 0.731562 0.365781 0.930701i \(-0.380802\pi\)
0.365781 + 0.930701i \(0.380802\pi\)
\(98\) −0.564081 −0.0569807
\(99\) −3.57802 −0.359604
\(100\) 2.95980 0.295980
\(101\) −1.41011 −0.140311 −0.0701557 0.997536i \(-0.522350\pi\)
−0.0701557 + 0.997536i \(0.522350\pi\)
\(102\) −10.6338 −1.05291
\(103\) −1.00000 −0.0985329
\(104\) −2.31645 −0.227147
\(105\) 8.31016 0.810989
\(106\) 8.30362 0.806519
\(107\) 9.96774 0.963618 0.481809 0.876276i \(-0.339980\pi\)
0.481809 + 0.876276i \(0.339980\pi\)
\(108\) −0.549133 −0.0528404
\(109\) −2.14955 −0.205889 −0.102945 0.994687i \(-0.532826\pi\)
−0.102945 + 0.994687i \(0.532826\pi\)
\(110\) 18.4139 1.75569
\(111\) 3.49607 0.331833
\(112\) −12.3665 −1.16853
\(113\) 6.79670 0.639380 0.319690 0.947522i \(-0.396421\pi\)
0.319690 + 0.947522i \(0.396421\pi\)
\(114\) 9.27276 0.868473
\(115\) 5.05969 0.471818
\(116\) −2.11919 −0.196762
\(117\) 1.00000 0.0924500
\(118\) 12.6852 1.16777
\(119\) 17.1710 1.57407
\(120\) −7.46673 −0.681616
\(121\) 1.80219 0.163836
\(122\) −0.215674 −0.0195262
\(123\) −8.46980 −0.763696
\(124\) −1.15041 −0.103310
\(125\) −1.25691 −0.112422
\(126\) 4.11623 0.366703
\(127\) 9.75142 0.865299 0.432649 0.901562i \(-0.357579\pi\)
0.432649 + 0.901562i \(0.357579\pi\)
\(128\) 13.6555 1.20698
\(129\) 4.32621 0.380902
\(130\) −5.14639 −0.451368
\(131\) 16.1198 1.40839 0.704196 0.710005i \(-0.251308\pi\)
0.704196 + 0.710005i \(0.251308\pi\)
\(132\) 1.96481 0.171015
\(133\) −14.9732 −1.29834
\(134\) 9.63130 0.832017
\(135\) 3.22334 0.277421
\(136\) −15.4283 −1.32296
\(137\) −13.4521 −1.14929 −0.574645 0.818403i \(-0.694860\pi\)
−0.574645 + 0.818403i \(0.694860\pi\)
\(138\) 2.50619 0.213341
\(139\) −3.42243 −0.290287 −0.145143 0.989411i \(-0.546364\pi\)
−0.145143 + 0.989411i \(0.546364\pi\)
\(140\) −4.56339 −0.385677
\(141\) −8.30395 −0.699319
\(142\) 10.5680 0.886849
\(143\) −3.57802 −0.299209
\(144\) −4.79672 −0.399727
\(145\) 12.4394 1.03303
\(146\) −10.4838 −0.867649
\(147\) 0.353301 0.0291398
\(148\) −1.91981 −0.157807
\(149\) 10.8433 0.888317 0.444159 0.895948i \(-0.353503\pi\)
0.444159 + 0.895948i \(0.353503\pi\)
\(150\) −8.60558 −0.702643
\(151\) 8.34496 0.679103 0.339552 0.940587i \(-0.389725\pi\)
0.339552 + 0.940587i \(0.389725\pi\)
\(152\) 13.4535 1.09123
\(153\) 6.66029 0.538453
\(154\) −14.7279 −1.18681
\(155\) 6.75277 0.542396
\(156\) −0.549133 −0.0439659
\(157\) −16.8485 −1.34466 −0.672330 0.740252i \(-0.734706\pi\)
−0.672330 + 0.740252i \(0.734706\pi\)
\(158\) 17.4604 1.38908
\(159\) −5.20081 −0.412451
\(160\) 9.75234 0.770990
\(161\) −4.04688 −0.318939
\(162\) 1.59660 0.125441
\(163\) −4.67365 −0.366068 −0.183034 0.983107i \(-0.558592\pi\)
−0.183034 + 0.983107i \(0.558592\pi\)
\(164\) 4.65105 0.363186
\(165\) −11.5332 −0.897856
\(166\) 5.76425 0.447393
\(167\) 22.9189 1.77352 0.886760 0.462231i \(-0.152951\pi\)
0.886760 + 0.462231i \(0.152951\pi\)
\(168\) 5.97210 0.460757
\(169\) 1.00000 0.0769231
\(170\) −34.2765 −2.62888
\(171\) −5.80781 −0.444134
\(172\) −2.37567 −0.181143
\(173\) 14.7285 1.11979 0.559893 0.828565i \(-0.310842\pi\)
0.559893 + 0.828565i \(0.310842\pi\)
\(174\) 6.16153 0.467104
\(175\) 13.8959 1.05043
\(176\) 17.1627 1.29369
\(177\) −7.94515 −0.597194
\(178\) 1.61519 0.121064
\(179\) 17.5602 1.31251 0.656256 0.754538i \(-0.272139\pi\)
0.656256 + 0.754538i \(0.272139\pi\)
\(180\) −1.77005 −0.131931
\(181\) −15.4511 −1.14847 −0.574236 0.818690i \(-0.694701\pi\)
−0.574236 + 0.818690i \(0.694701\pi\)
\(182\) 4.11623 0.305115
\(183\) 0.135083 0.00998565
\(184\) 3.63614 0.268060
\(185\) 11.2690 0.828516
\(186\) 3.34481 0.245254
\(187\) −23.8306 −1.74267
\(188\) 4.55998 0.332571
\(189\) −2.57812 −0.187531
\(190\) 29.8893 2.16840
\(191\) 0.231028 0.0167166 0.00835828 0.999965i \(-0.497339\pi\)
0.00835828 + 0.999965i \(0.497339\pi\)
\(192\) −4.76287 −0.343730
\(193\) 21.8826 1.57514 0.787571 0.616224i \(-0.211338\pi\)
0.787571 + 0.616224i \(0.211338\pi\)
\(194\) 11.5036 0.825909
\(195\) 3.22334 0.230828
\(196\) −0.194009 −0.0138578
\(197\) 13.7099 0.976788 0.488394 0.872623i \(-0.337583\pi\)
0.488394 + 0.872623i \(0.337583\pi\)
\(198\) −5.71266 −0.405981
\(199\) −8.14665 −0.577501 −0.288750 0.957404i \(-0.593240\pi\)
−0.288750 + 0.957404i \(0.593240\pi\)
\(200\) −12.4856 −0.882862
\(201\) −6.03238 −0.425491
\(202\) −2.25139 −0.158407
\(203\) −9.94936 −0.698308
\(204\) −3.65739 −0.256068
\(205\) −27.3011 −1.90679
\(206\) −1.59660 −0.111240
\(207\) −1.56970 −0.109102
\(208\) −4.79672 −0.332593
\(209\) 20.7804 1.43741
\(210\) 13.2680 0.915580
\(211\) −24.5469 −1.68988 −0.844940 0.534860i \(-0.820364\pi\)
−0.844940 + 0.534860i \(0.820364\pi\)
\(212\) 2.85594 0.196147
\(213\) −6.61908 −0.453532
\(214\) 15.9145 1.08789
\(215\) 13.9449 0.951032
\(216\) 2.31645 0.157615
\(217\) −5.40106 −0.366648
\(218\) −3.43197 −0.232442
\(219\) 6.56636 0.443713
\(220\) 6.33325 0.426988
\(221\) 6.66029 0.448020
\(222\) 5.58183 0.374628
\(223\) −5.62517 −0.376689 −0.188345 0.982103i \(-0.560312\pi\)
−0.188345 + 0.982103i \(0.560312\pi\)
\(224\) −7.80019 −0.521172
\(225\) 5.38994 0.359329
\(226\) 10.8516 0.721839
\(227\) 6.41165 0.425556 0.212778 0.977101i \(-0.431749\pi\)
0.212778 + 0.977101i \(0.431749\pi\)
\(228\) 3.18926 0.211214
\(229\) −3.01587 −0.199295 −0.0996473 0.995023i \(-0.531771\pi\)
−0.0996473 + 0.995023i \(0.531771\pi\)
\(230\) 8.07830 0.532667
\(231\) 9.22455 0.606931
\(232\) 8.93956 0.586911
\(233\) −14.0535 −0.920679 −0.460339 0.887743i \(-0.652272\pi\)
−0.460339 + 0.887743i \(0.652272\pi\)
\(234\) 1.59660 0.104373
\(235\) −26.7665 −1.74605
\(236\) 4.36295 0.284004
\(237\) −10.9360 −0.710370
\(238\) 27.4153 1.77707
\(239\) 0.749192 0.0484612 0.0242306 0.999706i \(-0.492286\pi\)
0.0242306 + 0.999706i \(0.492286\pi\)
\(240\) −15.4615 −0.998034
\(241\) −7.65457 −0.493074 −0.246537 0.969133i \(-0.579293\pi\)
−0.246537 + 0.969133i \(0.579293\pi\)
\(242\) 2.87738 0.184965
\(243\) −1.00000 −0.0641500
\(244\) −0.0741788 −0.00474881
\(245\) 1.13881 0.0727559
\(246\) −13.5229 −0.862188
\(247\) −5.80781 −0.369542
\(248\) 4.85288 0.308158
\(249\) −3.61033 −0.228795
\(250\) −2.00678 −0.126920
\(251\) 14.2662 0.900475 0.450237 0.892909i \(-0.351339\pi\)
0.450237 + 0.892909i \(0.351339\pi\)
\(252\) 1.41573 0.0891827
\(253\) 5.61642 0.353101
\(254\) 15.5691 0.976894
\(255\) 21.4684 1.34440
\(256\) 12.2766 0.767287
\(257\) −30.8369 −1.92356 −0.961778 0.273831i \(-0.911709\pi\)
−0.961778 + 0.273831i \(0.911709\pi\)
\(258\) 6.90723 0.430026
\(259\) −9.01329 −0.560059
\(260\) −1.77005 −0.109774
\(261\) −3.85916 −0.238876
\(262\) 25.7369 1.59003
\(263\) −23.5911 −1.45469 −0.727345 0.686272i \(-0.759246\pi\)
−0.727345 + 0.686272i \(0.759246\pi\)
\(264\) −8.28831 −0.510110
\(265\) −16.7640 −1.02980
\(266\) −23.9063 −1.46579
\(267\) −1.01165 −0.0619117
\(268\) 3.31258 0.202348
\(269\) −1.96246 −0.119654 −0.0598268 0.998209i \(-0.519055\pi\)
−0.0598268 + 0.998209i \(0.519055\pi\)
\(270\) 5.14639 0.313199
\(271\) 23.6062 1.43398 0.716989 0.697085i \(-0.245520\pi\)
0.716989 + 0.697085i \(0.245520\pi\)
\(272\) −31.9475 −1.93710
\(273\) −2.57812 −0.156035
\(274\) −21.4776 −1.29751
\(275\) −19.2853 −1.16295
\(276\) 0.861976 0.0518848
\(277\) −10.4327 −0.626839 −0.313420 0.949615i \(-0.601475\pi\)
−0.313420 + 0.949615i \(0.601475\pi\)
\(278\) −5.46426 −0.327724
\(279\) −2.09496 −0.125422
\(280\) 19.2501 1.15041
\(281\) −12.7137 −0.758434 −0.379217 0.925308i \(-0.623807\pi\)
−0.379217 + 0.925308i \(0.623807\pi\)
\(282\) −13.2581 −0.789508
\(283\) −26.7437 −1.58975 −0.794875 0.606773i \(-0.792464\pi\)
−0.794875 + 0.606773i \(0.792464\pi\)
\(284\) 3.63476 0.215683
\(285\) −18.7206 −1.10891
\(286\) −5.71266 −0.337797
\(287\) 21.8362 1.28895
\(288\) −3.02554 −0.178281
\(289\) 27.3595 1.60938
\(290\) 19.8607 1.16626
\(291\) −7.20505 −0.422367
\(292\) −3.60581 −0.211014
\(293\) −17.6685 −1.03221 −0.516104 0.856526i \(-0.672618\pi\)
−0.516104 + 0.856526i \(0.672618\pi\)
\(294\) 0.564081 0.0328978
\(295\) −25.6099 −1.49107
\(296\) 8.09849 0.470715
\(297\) 3.57802 0.207618
\(298\) 17.3124 1.00288
\(299\) −1.56970 −0.0907782
\(300\) −2.95980 −0.170884
\(301\) −11.1535 −0.642877
\(302\) 13.3236 0.766685
\(303\) 1.41011 0.0810088
\(304\) 27.8584 1.59779
\(305\) 0.435420 0.0249321
\(306\) 10.6338 0.607895
\(307\) 31.5625 1.80137 0.900683 0.434476i \(-0.143066\pi\)
0.900683 + 0.434476i \(0.143066\pi\)
\(308\) −5.06551 −0.288634
\(309\) 1.00000 0.0568880
\(310\) 10.7815 0.612347
\(311\) −28.3939 −1.61007 −0.805035 0.593227i \(-0.797854\pi\)
−0.805035 + 0.593227i \(0.797854\pi\)
\(312\) 2.31645 0.131143
\(313\) 16.8316 0.951376 0.475688 0.879614i \(-0.342199\pi\)
0.475688 + 0.879614i \(0.342199\pi\)
\(314\) −26.9004 −1.51808
\(315\) −8.31016 −0.468225
\(316\) 6.00532 0.337826
\(317\) 5.44697 0.305932 0.152966 0.988231i \(-0.451117\pi\)
0.152966 + 0.988231i \(0.451117\pi\)
\(318\) −8.30362 −0.465644
\(319\) 13.8081 0.773106
\(320\) −15.3524 −0.858223
\(321\) −9.96774 −0.556345
\(322\) −6.46125 −0.360071
\(323\) −38.6817 −2.15231
\(324\) 0.549133 0.0305074
\(325\) 5.38994 0.298980
\(326\) −7.46194 −0.413279
\(327\) 2.14955 0.118870
\(328\) −19.6199 −1.08333
\(329\) 21.4086 1.18029
\(330\) −18.4139 −1.01365
\(331\) 7.06715 0.388445 0.194223 0.980957i \(-0.437782\pi\)
0.194223 + 0.980957i \(0.437782\pi\)
\(332\) 1.98255 0.108807
\(333\) −3.49607 −0.191584
\(334\) 36.5924 2.00224
\(335\) −19.4444 −1.06236
\(336\) 12.3665 0.674649
\(337\) 1.23801 0.0674389 0.0337195 0.999431i \(-0.489265\pi\)
0.0337195 + 0.999431i \(0.489265\pi\)
\(338\) 1.59660 0.0868436
\(339\) −6.79670 −0.369146
\(340\) −11.7890 −0.639349
\(341\) 7.49580 0.405920
\(342\) −9.27276 −0.501413
\(343\) −18.9577 −1.02362
\(344\) 10.0215 0.540322
\(345\) −5.05969 −0.272404
\(346\) 23.5155 1.26420
\(347\) 6.32481 0.339533 0.169767 0.985484i \(-0.445699\pi\)
0.169767 + 0.985484i \(0.445699\pi\)
\(348\) 2.11919 0.113601
\(349\) 33.6754 1.80260 0.901301 0.433194i \(-0.142614\pi\)
0.901301 + 0.433194i \(0.142614\pi\)
\(350\) 22.1862 1.18590
\(351\) −1.00000 −0.0533761
\(352\) 10.8254 0.576996
\(353\) 11.7523 0.625510 0.312755 0.949834i \(-0.398748\pi\)
0.312755 + 0.949834i \(0.398748\pi\)
\(354\) −12.6852 −0.674212
\(355\) −21.3356 −1.13237
\(356\) 0.555528 0.0294429
\(357\) −17.1710 −0.908787
\(358\) 28.0367 1.48178
\(359\) −18.6150 −0.982461 −0.491230 0.871030i \(-0.663453\pi\)
−0.491230 + 0.871030i \(0.663453\pi\)
\(360\) 7.46673 0.393531
\(361\) 14.7307 0.775299
\(362\) −24.6692 −1.29659
\(363\) −1.80219 −0.0945906
\(364\) 1.41573 0.0742045
\(365\) 21.1656 1.10786
\(366\) 0.215674 0.0112735
\(367\) −11.1980 −0.584531 −0.292265 0.956337i \(-0.594409\pi\)
−0.292265 + 0.956337i \(0.594409\pi\)
\(368\) 7.52942 0.392498
\(369\) 8.46980 0.440920
\(370\) 17.9922 0.935368
\(371\) 13.4083 0.696125
\(372\) 1.15041 0.0596461
\(373\) 29.1863 1.51121 0.755605 0.655027i \(-0.227343\pi\)
0.755605 + 0.655027i \(0.227343\pi\)
\(374\) −38.0480 −1.96741
\(375\) 1.25691 0.0649066
\(376\) −19.2357 −0.992007
\(377\) −3.85916 −0.198757
\(378\) −4.11623 −0.211716
\(379\) 24.9563 1.28192 0.640960 0.767574i \(-0.278537\pi\)
0.640960 + 0.767574i \(0.278537\pi\)
\(380\) 10.2801 0.527357
\(381\) −9.75142 −0.499580
\(382\) 0.368859 0.0188725
\(383\) 7.05811 0.360653 0.180326 0.983607i \(-0.442285\pi\)
0.180326 + 0.983607i \(0.442285\pi\)
\(384\) −13.6555 −0.696853
\(385\) 29.7339 1.51538
\(386\) 34.9377 1.77828
\(387\) −4.32621 −0.219914
\(388\) 3.95653 0.200863
\(389\) −20.7027 −1.04967 −0.524833 0.851205i \(-0.675872\pi\)
−0.524833 + 0.851205i \(0.675872\pi\)
\(390\) 5.14639 0.260598
\(391\) −10.4547 −0.528715
\(392\) 0.818406 0.0413357
\(393\) −16.1198 −0.813136
\(394\) 21.8892 1.10276
\(395\) −35.2505 −1.77364
\(396\) −1.96481 −0.0987353
\(397\) 0.775127 0.0389025 0.0194513 0.999811i \(-0.493808\pi\)
0.0194513 + 0.999811i \(0.493808\pi\)
\(398\) −13.0069 −0.651979
\(399\) 14.9732 0.749599
\(400\) −25.8540 −1.29270
\(401\) 7.14144 0.356627 0.178313 0.983974i \(-0.442936\pi\)
0.178313 + 0.983974i \(0.442936\pi\)
\(402\) −9.63130 −0.480365
\(403\) −2.09496 −0.104357
\(404\) −0.774340 −0.0385248
\(405\) −3.22334 −0.160169
\(406\) −15.8852 −0.788367
\(407\) 12.5090 0.620048
\(408\) 15.4283 0.763813
\(409\) 3.01082 0.148875 0.0744377 0.997226i \(-0.476284\pi\)
0.0744377 + 0.997226i \(0.476284\pi\)
\(410\) −43.5889 −2.15270
\(411\) 13.4521 0.663542
\(412\) −0.549133 −0.0270539
\(413\) 20.4835 1.00793
\(414\) −2.50619 −0.123172
\(415\) −11.6373 −0.571254
\(416\) −3.02554 −0.148339
\(417\) 3.42243 0.167597
\(418\) 33.1781 1.62279
\(419\) −3.59360 −0.175559 −0.0877794 0.996140i \(-0.527977\pi\)
−0.0877794 + 0.996140i \(0.527977\pi\)
\(420\) 4.56339 0.222671
\(421\) 4.05623 0.197688 0.0988442 0.995103i \(-0.468485\pi\)
0.0988442 + 0.995103i \(0.468485\pi\)
\(422\) −39.1917 −1.90782
\(423\) 8.30395 0.403752
\(424\) −12.0474 −0.585076
\(425\) 35.8986 1.74134
\(426\) −10.5680 −0.512023
\(427\) −0.348261 −0.0168535
\(428\) 5.47362 0.264577
\(429\) 3.57802 0.172748
\(430\) 22.2644 1.07368
\(431\) 7.57357 0.364806 0.182403 0.983224i \(-0.441612\pi\)
0.182403 + 0.983224i \(0.441612\pi\)
\(432\) 4.79672 0.230782
\(433\) −8.51732 −0.409316 −0.204658 0.978834i \(-0.565608\pi\)
−0.204658 + 0.978834i \(0.565608\pi\)
\(434\) −8.62333 −0.413933
\(435\) −12.4394 −0.596423
\(436\) −1.18039 −0.0565303
\(437\) 9.11653 0.436103
\(438\) 10.4838 0.500938
\(439\) 39.2208 1.87191 0.935954 0.352122i \(-0.114540\pi\)
0.935954 + 0.352122i \(0.114540\pi\)
\(440\) −26.7161 −1.27364
\(441\) −0.353301 −0.0168239
\(442\) 10.6338 0.505799
\(443\) −16.7432 −0.795491 −0.397746 0.917496i \(-0.630207\pi\)
−0.397746 + 0.917496i \(0.630207\pi\)
\(444\) 1.91981 0.0911102
\(445\) −3.26088 −0.154581
\(446\) −8.98115 −0.425270
\(447\) −10.8433 −0.512870
\(448\) 12.2792 0.580139
\(449\) 35.5172 1.67616 0.838080 0.545548i \(-0.183678\pi\)
0.838080 + 0.545548i \(0.183678\pi\)
\(450\) 8.60558 0.405671
\(451\) −30.3051 −1.42701
\(452\) 3.73230 0.175552
\(453\) −8.34496 −0.392080
\(454\) 10.2368 0.480439
\(455\) −8.31016 −0.389586
\(456\) −13.4535 −0.630019
\(457\) −13.7067 −0.641174 −0.320587 0.947219i \(-0.603880\pi\)
−0.320587 + 0.947219i \(0.603880\pi\)
\(458\) −4.81515 −0.224997
\(459\) −6.66029 −0.310876
\(460\) 2.77844 0.129546
\(461\) 3.90957 0.182087 0.0910435 0.995847i \(-0.470980\pi\)
0.0910435 + 0.995847i \(0.470980\pi\)
\(462\) 14.7279 0.685205
\(463\) −9.73352 −0.452355 −0.226178 0.974086i \(-0.572623\pi\)
−0.226178 + 0.974086i \(0.572623\pi\)
\(464\) 18.5113 0.859365
\(465\) −6.75277 −0.313152
\(466\) −22.4379 −1.03942
\(467\) 9.33894 0.432155 0.216077 0.976376i \(-0.430674\pi\)
0.216077 + 0.976376i \(0.430674\pi\)
\(468\) 0.549133 0.0253837
\(469\) 15.5522 0.718133
\(470\) −42.7354 −1.97124
\(471\) 16.8485 0.776340
\(472\) −18.4046 −0.847139
\(473\) 15.4793 0.711737
\(474\) −17.4604 −0.801984
\(475\) −31.3038 −1.43632
\(476\) 9.42918 0.432186
\(477\) 5.20081 0.238129
\(478\) 1.19616 0.0547111
\(479\) −0.416598 −0.0190349 −0.00951743 0.999955i \(-0.503030\pi\)
−0.00951743 + 0.999955i \(0.503030\pi\)
\(480\) −9.75234 −0.445131
\(481\) −3.49607 −0.159407
\(482\) −12.2213 −0.556665
\(483\) 4.04688 0.184139
\(484\) 0.989645 0.0449838
\(485\) −23.2243 −1.05456
\(486\) −1.59660 −0.0724233
\(487\) 24.9793 1.13192 0.565960 0.824433i \(-0.308506\pi\)
0.565960 + 0.824433i \(0.308506\pi\)
\(488\) 0.312914 0.0141650
\(489\) 4.67365 0.211350
\(490\) 1.81823 0.0821390
\(491\) 3.95448 0.178463 0.0892315 0.996011i \(-0.471559\pi\)
0.0892315 + 0.996011i \(0.471559\pi\)
\(492\) −4.65105 −0.209686
\(493\) −25.7031 −1.15761
\(494\) −9.27276 −0.417201
\(495\) 11.5332 0.518377
\(496\) 10.0489 0.451210
\(497\) 17.0648 0.765460
\(498\) −5.76425 −0.258302
\(499\) 23.5092 1.05241 0.526207 0.850356i \(-0.323614\pi\)
0.526207 + 0.850356i \(0.323614\pi\)
\(500\) −0.690212 −0.0308672
\(501\) −22.9189 −1.02394
\(502\) 22.7774 1.01661
\(503\) −3.54033 −0.157856 −0.0789278 0.996880i \(-0.525150\pi\)
−0.0789278 + 0.996880i \(0.525150\pi\)
\(504\) −5.97210 −0.266018
\(505\) 4.54527 0.202262
\(506\) 8.96717 0.398640
\(507\) −1.00000 −0.0444116
\(508\) 5.35483 0.237582
\(509\) −9.55862 −0.423679 −0.211839 0.977305i \(-0.567945\pi\)
−0.211839 + 0.977305i \(0.567945\pi\)
\(510\) 34.2765 1.51779
\(511\) −16.9288 −0.748888
\(512\) −7.71012 −0.340742
\(513\) 5.80781 0.256421
\(514\) −49.2343 −2.17163
\(515\) 3.22334 0.142037
\(516\) 2.37567 0.104583
\(517\) −29.7117 −1.30672
\(518\) −14.3906 −0.632288
\(519\) −14.7285 −0.646509
\(520\) 7.46673 0.327438
\(521\) −22.9877 −1.00711 −0.503554 0.863964i \(-0.667975\pi\)
−0.503554 + 0.863964i \(0.667975\pi\)
\(522\) −6.16153 −0.269683
\(523\) −3.41642 −0.149390 −0.0746948 0.997206i \(-0.523798\pi\)
−0.0746948 + 0.997206i \(0.523798\pi\)
\(524\) 8.85191 0.386698
\(525\) −13.8959 −0.606467
\(526\) −37.6656 −1.64230
\(527\) −13.9530 −0.607804
\(528\) −17.1627 −0.746912
\(529\) −20.5360 −0.892871
\(530\) −26.7654 −1.16262
\(531\) 7.94515 0.344790
\(532\) −8.22230 −0.356482
\(533\) 8.46980 0.366868
\(534\) −1.61519 −0.0698963
\(535\) −32.1295 −1.38908
\(536\) −13.9737 −0.603573
\(537\) −17.5602 −0.757780
\(538\) −3.13327 −0.135085
\(539\) 1.26412 0.0544493
\(540\) 1.77005 0.0761706
\(541\) −11.8510 −0.509514 −0.254757 0.967005i \(-0.581996\pi\)
−0.254757 + 0.967005i \(0.581996\pi\)
\(542\) 37.6897 1.61891
\(543\) 15.4511 0.663070
\(544\) −20.1509 −0.863965
\(545\) 6.92872 0.296794
\(546\) −4.11623 −0.176158
\(547\) 10.4548 0.447015 0.223507 0.974702i \(-0.428249\pi\)
0.223507 + 0.974702i \(0.428249\pi\)
\(548\) −7.38699 −0.315557
\(549\) −0.135083 −0.00576522
\(550\) −30.7909 −1.31293
\(551\) 22.4132 0.954836
\(552\) −3.63614 −0.154765
\(553\) 28.1943 1.19894
\(554\) −16.6568 −0.707681
\(555\) −11.2690 −0.478344
\(556\) −1.87937 −0.0797031
\(557\) −29.1013 −1.23306 −0.616530 0.787331i \(-0.711462\pi\)
−0.616530 + 0.787331i \(0.711462\pi\)
\(558\) −3.34481 −0.141597
\(559\) −4.32621 −0.182979
\(560\) 39.8615 1.68446
\(561\) 23.8306 1.00613
\(562\) −20.2986 −0.856247
\(563\) −29.4468 −1.24103 −0.620517 0.784193i \(-0.713077\pi\)
−0.620517 + 0.784193i \(0.713077\pi\)
\(564\) −4.55998 −0.192010
\(565\) −21.9081 −0.921681
\(566\) −42.6991 −1.79478
\(567\) 2.57812 0.108271
\(568\) −15.3328 −0.643350
\(569\) 1.01936 0.0427336 0.0213668 0.999772i \(-0.493198\pi\)
0.0213668 + 0.999772i \(0.493198\pi\)
\(570\) −29.8893 −1.25192
\(571\) −2.07941 −0.0870206 −0.0435103 0.999053i \(-0.513854\pi\)
−0.0435103 + 0.999053i \(0.513854\pi\)
\(572\) −1.96481 −0.0821527
\(573\) −0.231028 −0.00965131
\(574\) 34.8636 1.45518
\(575\) −8.46060 −0.352831
\(576\) 4.76287 0.198453
\(577\) −42.8261 −1.78287 −0.891437 0.453145i \(-0.850302\pi\)
−0.891437 + 0.453145i \(0.850302\pi\)
\(578\) 43.6821 1.81694
\(579\) −21.8826 −0.909409
\(580\) 6.83088 0.283637
\(581\) 9.30786 0.386155
\(582\) −11.5036 −0.476839
\(583\) −18.6086 −0.770689
\(584\) 15.2107 0.629422
\(585\) −3.22334 −0.133269
\(586\) −28.2096 −1.16533
\(587\) −9.35303 −0.386041 −0.193020 0.981195i \(-0.561828\pi\)
−0.193020 + 0.981195i \(0.561828\pi\)
\(588\) 0.194009 0.00800081
\(589\) 12.1671 0.501338
\(590\) −40.8888 −1.68337
\(591\) −13.7099 −0.563949
\(592\) 16.7697 0.689230
\(593\) 0.260122 0.0106819 0.00534096 0.999986i \(-0.498300\pi\)
0.00534096 + 0.999986i \(0.498300\pi\)
\(594\) 5.71266 0.234393
\(595\) −55.3481 −2.26905
\(596\) 5.95441 0.243902
\(597\) 8.14665 0.333420
\(598\) −2.50619 −0.102486
\(599\) 10.6170 0.433798 0.216899 0.976194i \(-0.430406\pi\)
0.216899 + 0.976194i \(0.430406\pi\)
\(600\) 12.4856 0.509720
\(601\) 35.8306 1.46156 0.730780 0.682613i \(-0.239157\pi\)
0.730780 + 0.682613i \(0.239157\pi\)
\(602\) −17.8077 −0.725787
\(603\) 6.03238 0.245657
\(604\) 4.58249 0.186459
\(605\) −5.80909 −0.236173
\(606\) 2.25139 0.0914563
\(607\) −27.2341 −1.10540 −0.552699 0.833381i \(-0.686402\pi\)
−0.552699 + 0.833381i \(0.686402\pi\)
\(608\) 17.5717 0.712628
\(609\) 9.94936 0.403169
\(610\) 0.695192 0.0281475
\(611\) 8.30395 0.335942
\(612\) 3.65739 0.147841
\(613\) 15.5878 0.629587 0.314793 0.949160i \(-0.398065\pi\)
0.314793 + 0.949160i \(0.398065\pi\)
\(614\) 50.3927 2.03368
\(615\) 27.3011 1.10089
\(616\) 21.3683 0.860951
\(617\) −7.16142 −0.288308 −0.144154 0.989555i \(-0.546046\pi\)
−0.144154 + 0.989555i \(0.546046\pi\)
\(618\) 1.59660 0.0642247
\(619\) 41.2809 1.65922 0.829610 0.558343i \(-0.188563\pi\)
0.829610 + 0.558343i \(0.188563\pi\)
\(620\) 3.70817 0.148924
\(621\) 1.56970 0.0629900
\(622\) −45.3337 −1.81772
\(623\) 2.60814 0.104493
\(624\) 4.79672 0.192022
\(625\) −22.8982 −0.915930
\(626\) 26.8733 1.07407
\(627\) −20.7804 −0.829891
\(628\) −9.25210 −0.369199
\(629\) −23.2849 −0.928428
\(630\) −13.2680 −0.528610
\(631\) 7.14149 0.284298 0.142149 0.989845i \(-0.454599\pi\)
0.142149 + 0.989845i \(0.454599\pi\)
\(632\) −25.3328 −1.00768
\(633\) 24.5469 0.975653
\(634\) 8.69663 0.345387
\(635\) −31.4322 −1.24735
\(636\) −2.85594 −0.113245
\(637\) −0.353301 −0.0139983
\(638\) 22.0460 0.872811
\(639\) 6.61908 0.261847
\(640\) −44.0163 −1.73990
\(641\) −4.34844 −0.171753 −0.0858765 0.996306i \(-0.527369\pi\)
−0.0858765 + 0.996306i \(0.527369\pi\)
\(642\) −15.9145 −0.628095
\(643\) −29.0148 −1.14423 −0.572117 0.820172i \(-0.693878\pi\)
−0.572117 + 0.820172i \(0.693878\pi\)
\(644\) −2.22228 −0.0875699
\(645\) −13.9449 −0.549079
\(646\) −61.7592 −2.42988
\(647\) −11.5206 −0.452922 −0.226461 0.974020i \(-0.572716\pi\)
−0.226461 + 0.974020i \(0.572716\pi\)
\(648\) −2.31645 −0.0909989
\(649\) −28.4279 −1.11589
\(650\) 8.60558 0.337539
\(651\) 5.40106 0.211684
\(652\) −2.56645 −0.100510
\(653\) 3.87607 0.151682 0.0758411 0.997120i \(-0.475836\pi\)
0.0758411 + 0.997120i \(0.475836\pi\)
\(654\) 3.43197 0.134200
\(655\) −51.9596 −2.03023
\(656\) −40.6273 −1.58623
\(657\) −6.56636 −0.256178
\(658\) 34.1810 1.33251
\(659\) 29.7929 1.16057 0.580284 0.814414i \(-0.302942\pi\)
0.580284 + 0.814414i \(0.302942\pi\)
\(660\) −6.33325 −0.246521
\(661\) 19.9665 0.776607 0.388303 0.921532i \(-0.373061\pi\)
0.388303 + 0.921532i \(0.373061\pi\)
\(662\) 11.2834 0.438542
\(663\) −6.66029 −0.258664
\(664\) −8.36316 −0.324554
\(665\) 48.2639 1.87159
\(666\) −5.58183 −0.216292
\(667\) 6.05772 0.234556
\(668\) 12.5855 0.486949
\(669\) 5.62517 0.217482
\(670\) −31.0450 −1.19937
\(671\) 0.483330 0.0186588
\(672\) 7.80019 0.300899
\(673\) −39.5360 −1.52400 −0.762001 0.647576i \(-0.775783\pi\)
−0.762001 + 0.647576i \(0.775783\pi\)
\(674\) 1.97661 0.0761363
\(675\) −5.38994 −0.207459
\(676\) 0.549133 0.0211205
\(677\) −10.6400 −0.408928 −0.204464 0.978874i \(-0.565545\pi\)
−0.204464 + 0.978874i \(0.565545\pi\)
\(678\) −10.8516 −0.416754
\(679\) 18.5755 0.712861
\(680\) 49.7306 1.90708
\(681\) −6.41165 −0.245695
\(682\) 11.9678 0.458271
\(683\) 17.6970 0.677158 0.338579 0.940938i \(-0.390054\pi\)
0.338579 + 0.940938i \(0.390054\pi\)
\(684\) −3.18926 −0.121945
\(685\) 43.3607 1.65673
\(686\) −30.2679 −1.15563
\(687\) 3.01587 0.115063
\(688\) 20.7516 0.791149
\(689\) 5.20081 0.198135
\(690\) −8.07830 −0.307536
\(691\) −33.3799 −1.26983 −0.634916 0.772581i \(-0.718965\pi\)
−0.634916 + 0.772581i \(0.718965\pi\)
\(692\) 8.08791 0.307456
\(693\) −9.22455 −0.350412
\(694\) 10.0982 0.383322
\(695\) 11.0317 0.418455
\(696\) −8.93956 −0.338853
\(697\) 56.4113 2.13673
\(698\) 53.7661 2.03508
\(699\) 14.0535 0.531554
\(700\) 7.63071 0.288414
\(701\) 44.5997 1.68451 0.842254 0.539080i \(-0.181228\pi\)
0.842254 + 0.539080i \(0.181228\pi\)
\(702\) −1.59660 −0.0602598
\(703\) 20.3045 0.765800
\(704\) −17.0416 −0.642280
\(705\) 26.7665 1.00808
\(706\) 18.7637 0.706181
\(707\) −3.63544 −0.136725
\(708\) −4.36295 −0.163970
\(709\) 39.5936 1.48697 0.743485 0.668753i \(-0.233172\pi\)
0.743485 + 0.668753i \(0.233172\pi\)
\(710\) −34.0644 −1.27841
\(711\) 10.9360 0.410132
\(712\) −2.34343 −0.0878238
\(713\) 3.28846 0.123154
\(714\) −27.4153 −1.02599
\(715\) 11.5332 0.431316
\(716\) 9.64291 0.360372
\(717\) −0.749192 −0.0279791
\(718\) −29.7207 −1.10917
\(719\) −43.7690 −1.63231 −0.816155 0.577834i \(-0.803898\pi\)
−0.816155 + 0.577834i \(0.803898\pi\)
\(720\) 15.4615 0.576215
\(721\) −2.57812 −0.0960142
\(722\) 23.5190 0.875287
\(723\) 7.65457 0.284677
\(724\) −8.48472 −0.315332
\(725\) −20.8006 −0.772515
\(726\) −2.87738 −0.106790
\(727\) 19.3339 0.717054 0.358527 0.933519i \(-0.383279\pi\)
0.358527 + 0.933519i \(0.383279\pi\)
\(728\) −5.97210 −0.221341
\(729\) 1.00000 0.0370370
\(730\) 33.7930 1.25074
\(731\) −28.8138 −1.06572
\(732\) 0.0741788 0.00274173
\(733\) −44.5155 −1.64422 −0.822109 0.569331i \(-0.807202\pi\)
−0.822109 + 0.569331i \(0.807202\pi\)
\(734\) −17.8787 −0.659916
\(735\) −1.13881 −0.0420056
\(736\) 4.74919 0.175057
\(737\) −21.5839 −0.795055
\(738\) 13.5229 0.497785
\(739\) 36.4258 1.33995 0.669973 0.742386i \(-0.266306\pi\)
0.669973 + 0.742386i \(0.266306\pi\)
\(740\) 6.18821 0.227483
\(741\) 5.80781 0.213355
\(742\) 21.4077 0.785902
\(743\) 18.2327 0.668893 0.334446 0.942415i \(-0.391451\pi\)
0.334446 + 0.942415i \(0.391451\pi\)
\(744\) −4.85288 −0.177915
\(745\) −34.9517 −1.28053
\(746\) 46.5989 1.70611
\(747\) 3.61033 0.132095
\(748\) −13.0862 −0.478478
\(749\) 25.6980 0.938986
\(750\) 2.00678 0.0732774
\(751\) 49.1586 1.79382 0.896911 0.442212i \(-0.145806\pi\)
0.896911 + 0.442212i \(0.145806\pi\)
\(752\) −39.8317 −1.45251
\(753\) −14.2662 −0.519889
\(754\) −6.16153 −0.224390
\(755\) −26.8987 −0.978943
\(756\) −1.41573 −0.0514897
\(757\) 36.2067 1.31596 0.657978 0.753038i \(-0.271412\pi\)
0.657978 + 0.753038i \(0.271412\pi\)
\(758\) 39.8453 1.44725
\(759\) −5.61642 −0.203863
\(760\) −43.3653 −1.57303
\(761\) −9.92457 −0.359766 −0.179883 0.983688i \(-0.557572\pi\)
−0.179883 + 0.983688i \(0.557572\pi\)
\(762\) −15.5691 −0.564010
\(763\) −5.54179 −0.200626
\(764\) 0.126865 0.00458981
\(765\) −21.4684 −0.776192
\(766\) 11.2690 0.407165
\(767\) 7.94515 0.286883
\(768\) −12.2766 −0.442993
\(769\) 17.7053 0.638469 0.319234 0.947676i \(-0.396574\pi\)
0.319234 + 0.947676i \(0.396574\pi\)
\(770\) 47.4731 1.71081
\(771\) 30.8369 1.11057
\(772\) 12.0165 0.432482
\(773\) −10.7427 −0.386389 −0.193194 0.981160i \(-0.561885\pi\)
−0.193194 + 0.981160i \(0.561885\pi\)
\(774\) −6.90723 −0.248275
\(775\) −11.2917 −0.405610
\(776\) −16.6902 −0.599142
\(777\) 9.01329 0.323350
\(778\) −33.0539 −1.18504
\(779\) −49.1910 −1.76245
\(780\) 1.77005 0.0633778
\(781\) −23.6832 −0.847450
\(782\) −16.6919 −0.596902
\(783\) 3.85916 0.137915
\(784\) 1.69469 0.0605245
\(785\) 54.3086 1.93836
\(786\) −25.7369 −0.918004
\(787\) 50.1564 1.78788 0.893941 0.448184i \(-0.147929\pi\)
0.893941 + 0.448184i \(0.147929\pi\)
\(788\) 7.52855 0.268193
\(789\) 23.5911 0.839865
\(790\) −56.2810 −2.00239
\(791\) 17.5227 0.623036
\(792\) 8.28831 0.294512
\(793\) −0.135083 −0.00479695
\(794\) 1.23757 0.0439197
\(795\) 16.7640 0.594558
\(796\) −4.47360 −0.158562
\(797\) −17.6046 −0.623586 −0.311793 0.950150i \(-0.600930\pi\)
−0.311793 + 0.950150i \(0.600930\pi\)
\(798\) 23.9063 0.846273
\(799\) 55.3067 1.95661
\(800\) −16.3075 −0.576556
\(801\) 1.01165 0.0357447
\(802\) 11.4020 0.402620
\(803\) 23.4945 0.829104
\(804\) −3.31258 −0.116826
\(805\) 13.0445 0.459757
\(806\) −3.34481 −0.117816
\(807\) 1.96246 0.0690820
\(808\) 3.26646 0.114914
\(809\) 32.4891 1.14225 0.571127 0.820862i \(-0.306506\pi\)
0.571127 + 0.820862i \(0.306506\pi\)
\(810\) −5.14639 −0.180826
\(811\) −12.1576 −0.426911 −0.213456 0.976953i \(-0.568472\pi\)
−0.213456 + 0.976953i \(0.568472\pi\)
\(812\) −5.46353 −0.191732
\(813\) −23.6062 −0.827907
\(814\) 19.9719 0.700014
\(815\) 15.0648 0.527696
\(816\) 31.9475 1.11839
\(817\) 25.1258 0.879042
\(818\) 4.80707 0.168075
\(819\) 2.57812 0.0900868
\(820\) −14.9919 −0.523541
\(821\) −8.88825 −0.310202 −0.155101 0.987899i \(-0.549570\pi\)
−0.155101 + 0.987899i \(0.549570\pi\)
\(822\) 21.4776 0.749118
\(823\) 27.7821 0.968424 0.484212 0.874951i \(-0.339106\pi\)
0.484212 + 0.874951i \(0.339106\pi\)
\(824\) 2.31645 0.0806975
\(825\) 19.2853 0.671428
\(826\) 32.7040 1.13792
\(827\) −9.07084 −0.315424 −0.157712 0.987485i \(-0.550412\pi\)
−0.157712 + 0.987485i \(0.550412\pi\)
\(828\) −0.861976 −0.0299557
\(829\) 11.9161 0.413864 0.206932 0.978355i \(-0.433652\pi\)
0.206932 + 0.978355i \(0.433652\pi\)
\(830\) −18.5802 −0.644927
\(831\) 10.4327 0.361906
\(832\) 4.76287 0.165123
\(833\) −2.35309 −0.0815296
\(834\) 5.46426 0.189212
\(835\) −73.8755 −2.55657
\(836\) 11.4112 0.394666
\(837\) 2.09496 0.0724124
\(838\) −5.73754 −0.198200
\(839\) 46.7223 1.61303 0.806516 0.591212i \(-0.201350\pi\)
0.806516 + 0.591212i \(0.201350\pi\)
\(840\) −19.2501 −0.664192
\(841\) −14.1069 −0.486446
\(842\) 6.47617 0.223184
\(843\) 12.7137 0.437882
\(844\) −13.4795 −0.463985
\(845\) −3.22334 −0.110886
\(846\) 13.2581 0.455823
\(847\) 4.64627 0.159648
\(848\) −24.9468 −0.856678
\(849\) 26.7437 0.917843
\(850\) 57.3157 1.96591
\(851\) 5.48779 0.188119
\(852\) −3.63476 −0.124525
\(853\) 6.58574 0.225491 0.112746 0.993624i \(-0.464035\pi\)
0.112746 + 0.993624i \(0.464035\pi\)
\(854\) −0.556034 −0.0190271
\(855\) 18.7206 0.640230
\(856\) −23.0898 −0.789194
\(857\) 2.26160 0.0772547 0.0386274 0.999254i \(-0.487701\pi\)
0.0386274 + 0.999254i \(0.487701\pi\)
\(858\) 5.71266 0.195027
\(859\) −26.8486 −0.916064 −0.458032 0.888936i \(-0.651445\pi\)
−0.458032 + 0.888936i \(0.651445\pi\)
\(860\) 7.65759 0.261122
\(861\) −21.8362 −0.744174
\(862\) 12.0920 0.411854
\(863\) 47.5016 1.61697 0.808487 0.588515i \(-0.200287\pi\)
0.808487 + 0.588515i \(0.200287\pi\)
\(864\) 3.02554 0.102931
\(865\) −47.4750 −1.61420
\(866\) −13.5988 −0.462104
\(867\) −27.3595 −0.929176
\(868\) −2.96590 −0.100669
\(869\) −39.1292 −1.32737
\(870\) −19.8607 −0.673342
\(871\) 6.03238 0.204399
\(872\) 4.97933 0.168621
\(873\) 7.20505 0.243854
\(874\) 14.5555 0.492346
\(875\) −3.24047 −0.109548
\(876\) 3.60581 0.121829
\(877\) −15.2072 −0.513512 −0.256756 0.966476i \(-0.582654\pi\)
−0.256756 + 0.966476i \(0.582654\pi\)
\(878\) 62.6200 2.11332
\(879\) 17.6685 0.595945
\(880\) −55.3214 −1.86488
\(881\) 34.6385 1.16700 0.583501 0.812113i \(-0.301683\pi\)
0.583501 + 0.812113i \(0.301683\pi\)
\(882\) −0.564081 −0.0189936
\(883\) 11.1299 0.374551 0.187276 0.982307i \(-0.440034\pi\)
0.187276 + 0.982307i \(0.440034\pi\)
\(884\) 3.65739 0.123011
\(885\) 25.6099 0.860869
\(886\) −26.7321 −0.898084
\(887\) −14.1441 −0.474912 −0.237456 0.971398i \(-0.576313\pi\)
−0.237456 + 0.971398i \(0.576313\pi\)
\(888\) −8.09849 −0.271768
\(889\) 25.1403 0.843179
\(890\) −5.20632 −0.174516
\(891\) −3.57802 −0.119868
\(892\) −3.08897 −0.103426
\(893\) −48.2278 −1.61388
\(894\) −17.3124 −0.579014
\(895\) −56.6026 −1.89202
\(896\) 35.2054 1.17613
\(897\) 1.56970 0.0524108
\(898\) 56.7068 1.89233
\(899\) 8.08477 0.269642
\(900\) 2.95980 0.0986599
\(901\) 34.6389 1.15399
\(902\) −48.3851 −1.61105
\(903\) 11.1535 0.371165
\(904\) −15.7443 −0.523646
\(905\) 49.8042 1.65555
\(906\) −13.3236 −0.442646
\(907\) 2.69785 0.0895808 0.0447904 0.998996i \(-0.485738\pi\)
0.0447904 + 0.998996i \(0.485738\pi\)
\(908\) 3.52085 0.116844
\(909\) −1.41011 −0.0467705
\(910\) −13.2680 −0.439830
\(911\) 54.5279 1.80659 0.903295 0.429019i \(-0.141141\pi\)
0.903295 + 0.429019i \(0.141141\pi\)
\(912\) −27.8584 −0.922485
\(913\) −12.9178 −0.427517
\(914\) −21.8842 −0.723864
\(915\) −0.435420 −0.0143945
\(916\) −1.65612 −0.0547196
\(917\) 41.5587 1.37239
\(918\) −10.6338 −0.350968
\(919\) 56.2695 1.85616 0.928079 0.372383i \(-0.121459\pi\)
0.928079 + 0.372383i \(0.121459\pi\)
\(920\) −11.7205 −0.386415
\(921\) −31.5625 −1.04002
\(922\) 6.24203 0.205570
\(923\) 6.61908 0.217870
\(924\) 5.06551 0.166643
\(925\) −18.8436 −0.619574
\(926\) −15.5406 −0.510694
\(927\) −1.00000 −0.0328443
\(928\) 11.6760 0.383284
\(929\) −45.0044 −1.47655 −0.738273 0.674503i \(-0.764358\pi\)
−0.738273 + 0.674503i \(0.764358\pi\)
\(930\) −10.7815 −0.353539
\(931\) 2.05191 0.0672485
\(932\) −7.71727 −0.252788
\(933\) 28.3939 0.929575
\(934\) 14.9106 0.487889
\(935\) 76.8143 2.51209
\(936\) −2.31645 −0.0757157
\(937\) −33.4371 −1.09234 −0.546171 0.837674i \(-0.683915\pi\)
−0.546171 + 0.837674i \(0.683915\pi\)
\(938\) 24.8306 0.810749
\(939\) −16.8316 −0.549277
\(940\) −14.6984 −0.479408
\(941\) −26.7502 −0.872031 −0.436016 0.899939i \(-0.643611\pi\)
−0.436016 + 0.899939i \(0.643611\pi\)
\(942\) 26.9004 0.876462
\(943\) −13.2951 −0.432947
\(944\) −38.1106 −1.24040
\(945\) 8.31016 0.270330
\(946\) 24.7142 0.803528
\(947\) −7.84123 −0.254806 −0.127403 0.991851i \(-0.540664\pi\)
−0.127403 + 0.991851i \(0.540664\pi\)
\(948\) −6.00532 −0.195044
\(949\) −6.56636 −0.213153
\(950\) −49.9796 −1.62155
\(951\) −5.44697 −0.176630
\(952\) −39.7759 −1.28914
\(953\) 52.2893 1.69382 0.846909 0.531739i \(-0.178461\pi\)
0.846909 + 0.531739i \(0.178461\pi\)
\(954\) 8.30362 0.268840
\(955\) −0.744681 −0.0240973
\(956\) 0.411406 0.0133058
\(957\) −13.8081 −0.446353
\(958\) −0.665141 −0.0214897
\(959\) −34.6811 −1.11991
\(960\) 15.3524 0.495495
\(961\) −26.6111 −0.858424
\(962\) −5.58183 −0.179965
\(963\) 9.96774 0.321206
\(964\) −4.20338 −0.135382
\(965\) −70.5350 −2.27060
\(966\) 6.46125 0.207887
\(967\) −14.6150 −0.469988 −0.234994 0.971997i \(-0.575507\pi\)
−0.234994 + 0.971997i \(0.575507\pi\)
\(968\) −4.17470 −0.134180
\(969\) 38.6817 1.24264
\(970\) −37.0800 −1.19057
\(971\) −29.8225 −0.957050 −0.478525 0.878074i \(-0.658828\pi\)
−0.478525 + 0.878074i \(0.658828\pi\)
\(972\) −0.549133 −0.0176135
\(973\) −8.82344 −0.282866
\(974\) 39.8819 1.27790
\(975\) −5.38994 −0.172616
\(976\) 0.647957 0.0207406
\(977\) 14.0118 0.448276 0.224138 0.974557i \(-0.428043\pi\)
0.224138 + 0.974557i \(0.428043\pi\)
\(978\) 7.46194 0.238607
\(979\) −3.61968 −0.115686
\(980\) 0.625359 0.0199764
\(981\) −2.14955 −0.0686297
\(982\) 6.31372 0.201479
\(983\) 35.4476 1.13060 0.565302 0.824884i \(-0.308760\pi\)
0.565302 + 0.824884i \(0.308760\pi\)
\(984\) 19.6199 0.625460
\(985\) −44.1916 −1.40806
\(986\) −41.0376 −1.30690
\(987\) −21.4086 −0.681443
\(988\) −3.18926 −0.101464
\(989\) 6.79087 0.215937
\(990\) 18.4139 0.585231
\(991\) −61.6821 −1.95940 −0.979698 0.200478i \(-0.935751\pi\)
−0.979698 + 0.200478i \(0.935751\pi\)
\(992\) 6.33837 0.201244
\(993\) −7.06715 −0.224269
\(994\) 27.2456 0.864179
\(995\) 26.2595 0.832481
\(996\) −1.98255 −0.0628196
\(997\) −46.2017 −1.46322 −0.731611 0.681722i \(-0.761231\pi\)
−0.731611 + 0.681722i \(0.761231\pi\)
\(998\) 37.5347 1.18814
\(999\) 3.49607 0.110611
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 \(a_p\))