Properties

Label 4031.2.a.c.1.2
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62306 q^{2}\) \(+1.48834 q^{3}\) \(+4.88043 q^{4}\) \(+0.915377 q^{5}\) \(-3.90400 q^{6}\) \(-2.34390 q^{7}\) \(-7.55555 q^{8}\) \(-0.784847 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62306 q^{2}\) \(+1.48834 q^{3}\) \(+4.88043 q^{4}\) \(+0.915377 q^{5}\) \(-3.90400 q^{6}\) \(-2.34390 q^{7}\) \(-7.55555 q^{8}\) \(-0.784847 q^{9}\) \(-2.40109 q^{10}\) \(-2.86549 q^{11}\) \(+7.26374 q^{12}\) \(+4.85001 q^{13}\) \(+6.14819 q^{14}\) \(+1.36239 q^{15}\) \(+10.0578 q^{16}\) \(+2.11615 q^{17}\) \(+2.05870 q^{18}\) \(-1.70430 q^{19}\) \(+4.46744 q^{20}\) \(-3.48852 q^{21}\) \(+7.51634 q^{22}\) \(+2.87531 q^{23}\) \(-11.2452 q^{24}\) \(-4.16208 q^{25}\) \(-12.7219 q^{26}\) \(-5.63314 q^{27}\) \(-11.4393 q^{28}\) \(-1.00000 q^{29}\) \(-3.57363 q^{30}\) \(+4.12414 q^{31}\) \(-11.2710 q^{32}\) \(-4.26482 q^{33}\) \(-5.55078 q^{34}\) \(-2.14555 q^{35}\) \(-3.83039 q^{36}\) \(-9.79358 q^{37}\) \(+4.47047 q^{38}\) \(+7.21846 q^{39}\) \(-6.91618 q^{40}\) \(+10.6933 q^{41}\) \(+9.15059 q^{42}\) \(-4.66701 q^{43}\) \(-13.9848 q^{44}\) \(-0.718431 q^{45}\) \(-7.54210 q^{46}\) \(+10.4466 q^{47}\) \(+14.9694 q^{48}\) \(-1.50613 q^{49}\) \(+10.9174 q^{50}\) \(+3.14955 q^{51}\) \(+23.6702 q^{52}\) \(-4.88080 q^{53}\) \(+14.7760 q^{54}\) \(-2.62300 q^{55}\) \(+17.7094 q^{56}\) \(-2.53657 q^{57}\) \(+2.62306 q^{58}\) \(-2.10982 q^{59}\) \(+6.64906 q^{60}\) \(+1.94878 q^{61}\) \(-10.8178 q^{62}\) \(+1.83960 q^{63}\) \(+9.44900 q^{64}\) \(+4.43959 q^{65}\) \(+11.1869 q^{66}\) \(+2.44695 q^{67}\) \(+10.3277 q^{68}\) \(+4.27943 q^{69}\) \(+5.62791 q^{70}\) \(+6.20279 q^{71}\) \(+5.92995 q^{72}\) \(-6.92011 q^{73}\) \(+25.6891 q^{74}\) \(-6.19459 q^{75}\) \(-8.31771 q^{76}\) \(+6.71642 q^{77}\) \(-18.9344 q^{78}\) \(-3.33388 q^{79}\) \(+9.20665 q^{80}\) \(-6.02947 q^{81}\) \(-28.0490 q^{82}\) \(-4.26583 q^{83}\) \(-17.0255 q^{84}\) \(+1.93708 q^{85}\) \(+12.2418 q^{86}\) \(-1.48834 q^{87}\) \(+21.6503 q^{88}\) \(+5.49919 q^{89}\) \(+1.88449 q^{90}\) \(-11.3679 q^{91}\) \(+14.0327 q^{92}\) \(+6.13811 q^{93}\) \(-27.4021 q^{94}\) \(-1.56007 q^{95}\) \(-16.7751 q^{96}\) \(+7.50513 q^{97}\) \(+3.95067 q^{98}\) \(+2.24897 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62306 −1.85478 −0.927391 0.374093i \(-0.877954\pi\)
−0.927391 + 0.374093i \(0.877954\pi\)
\(3\) 1.48834 0.859293 0.429646 0.902997i \(-0.358638\pi\)
0.429646 + 0.902997i \(0.358638\pi\)
\(4\) 4.88043 2.44022
\(5\) 0.915377 0.409369 0.204685 0.978828i \(-0.434383\pi\)
0.204685 + 0.978828i \(0.434383\pi\)
\(6\) −3.90400 −1.59380
\(7\) −2.34390 −0.885911 −0.442956 0.896544i \(-0.646070\pi\)
−0.442956 + 0.896544i \(0.646070\pi\)
\(8\) −7.55555 −2.67129
\(9\) −0.784847 −0.261616
\(10\) −2.40109 −0.759291
\(11\) −2.86549 −0.863977 −0.431988 0.901879i \(-0.642188\pi\)
−0.431988 + 0.901879i \(0.642188\pi\)
\(12\) 7.26374 2.09686
\(13\) 4.85001 1.34515 0.672575 0.740029i \(-0.265188\pi\)
0.672575 + 0.740029i \(0.265188\pi\)
\(14\) 6.14819 1.64317
\(15\) 1.36239 0.351768
\(16\) 10.0578 2.51444
\(17\) 2.11615 0.513242 0.256621 0.966512i \(-0.417391\pi\)
0.256621 + 0.966512i \(0.417391\pi\)
\(18\) 2.05870 0.485240
\(19\) −1.70430 −0.390992 −0.195496 0.980704i \(-0.562632\pi\)
−0.195496 + 0.980704i \(0.562632\pi\)
\(20\) 4.46744 0.998950
\(21\) −3.48852 −0.761257
\(22\) 7.51634 1.60249
\(23\) 2.87531 0.599543 0.299772 0.954011i \(-0.403090\pi\)
0.299772 + 0.954011i \(0.403090\pi\)
\(24\) −11.2452 −2.29542
\(25\) −4.16208 −0.832417
\(26\) −12.7219 −2.49496
\(27\) −5.63314 −1.08410
\(28\) −11.4393 −2.16182
\(29\) −1.00000 −0.185695
\(30\) −3.57363 −0.652453
\(31\) 4.12414 0.740717 0.370358 0.928889i \(-0.379235\pi\)
0.370358 + 0.928889i \(0.379235\pi\)
\(32\) −11.2710 −1.99245
\(33\) −4.26482 −0.742409
\(34\) −5.55078 −0.951951
\(35\) −2.14555 −0.362665
\(36\) −3.83039 −0.638399
\(37\) −9.79358 −1.61005 −0.805027 0.593238i \(-0.797849\pi\)
−0.805027 + 0.593238i \(0.797849\pi\)
\(38\) 4.47047 0.725206
\(39\) 7.21846 1.15588
\(40\) −6.91618 −1.09354
\(41\) 10.6933 1.67001 0.835003 0.550245i \(-0.185466\pi\)
0.835003 + 0.550245i \(0.185466\pi\)
\(42\) 9.15059 1.41197
\(43\) −4.66701 −0.711712 −0.355856 0.934541i \(-0.615811\pi\)
−0.355856 + 0.934541i \(0.615811\pi\)
\(44\) −13.9848 −2.10829
\(45\) −0.718431 −0.107097
\(46\) −7.54210 −1.11202
\(47\) 10.4466 1.52380 0.761899 0.647695i \(-0.224267\pi\)
0.761899 + 0.647695i \(0.224267\pi\)
\(48\) 14.9694 2.16064
\(49\) −1.50613 −0.215162
\(50\) 10.9174 1.54395
\(51\) 3.14955 0.441025
\(52\) 23.6702 3.28246
\(53\) −4.88080 −0.670429 −0.335215 0.942142i \(-0.608809\pi\)
−0.335215 + 0.942142i \(0.608809\pi\)
\(54\) 14.7760 2.01076
\(55\) −2.62300 −0.353686
\(56\) 17.7094 2.36652
\(57\) −2.53657 −0.335977
\(58\) 2.62306 0.344424
\(59\) −2.10982 −0.274675 −0.137338 0.990524i \(-0.543855\pi\)
−0.137338 + 0.990524i \(0.543855\pi\)
\(60\) 6.64906 0.858390
\(61\) 1.94878 0.249516 0.124758 0.992187i \(-0.460185\pi\)
0.124758 + 0.992187i \(0.460185\pi\)
\(62\) −10.8178 −1.37387
\(63\) 1.83960 0.231768
\(64\) 9.44900 1.18112
\(65\) 4.43959 0.550663
\(66\) 11.1869 1.37701
\(67\) 2.44695 0.298943 0.149471 0.988766i \(-0.452243\pi\)
0.149471 + 0.988766i \(0.452243\pi\)
\(68\) 10.3277 1.25242
\(69\) 4.27943 0.515183
\(70\) 5.62791 0.672664
\(71\) 6.20279 0.736135 0.368068 0.929799i \(-0.380019\pi\)
0.368068 + 0.929799i \(0.380019\pi\)
\(72\) 5.92995 0.698851
\(73\) −6.92011 −0.809938 −0.404969 0.914330i \(-0.632718\pi\)
−0.404969 + 0.914330i \(0.632718\pi\)
\(74\) 25.6891 2.98630
\(75\) −6.19459 −0.715290
\(76\) −8.31771 −0.954106
\(77\) 6.71642 0.765407
\(78\) −18.9344 −2.14390
\(79\) −3.33388 −0.375091 −0.187545 0.982256i \(-0.560053\pi\)
−0.187545 + 0.982256i \(0.560053\pi\)
\(80\) 9.20665 1.02934
\(81\) −6.02947 −0.669941
\(82\) −28.0490 −3.09750
\(83\) −4.26583 −0.468236 −0.234118 0.972208i \(-0.575220\pi\)
−0.234118 + 0.972208i \(0.575220\pi\)
\(84\) −17.0255 −1.85763
\(85\) 1.93708 0.210105
\(86\) 12.2418 1.32007
\(87\) −1.48834 −0.159567
\(88\) 21.6503 2.30793
\(89\) 5.49919 0.582913 0.291456 0.956584i \(-0.405860\pi\)
0.291456 + 0.956584i \(0.405860\pi\)
\(90\) 1.88449 0.198642
\(91\) −11.3679 −1.19168
\(92\) 14.0327 1.46302
\(93\) 6.13811 0.636493
\(94\) −27.4021 −2.82631
\(95\) −1.56007 −0.160060
\(96\) −16.7751 −1.71210
\(97\) 7.50513 0.762031 0.381015 0.924569i \(-0.375575\pi\)
0.381015 + 0.924569i \(0.375575\pi\)
\(98\) 3.95067 0.399078
\(99\) 2.24897 0.226030
\(100\) −20.3128 −2.03128
\(101\) −5.27766 −0.525147 −0.262574 0.964912i \(-0.584571\pi\)
−0.262574 + 0.964912i \(0.584571\pi\)
\(102\) −8.26145 −0.818005
\(103\) −10.8229 −1.06641 −0.533207 0.845985i \(-0.679013\pi\)
−0.533207 + 0.845985i \(0.679013\pi\)
\(104\) −36.6445 −3.59329
\(105\) −3.19331 −0.311635
\(106\) 12.8026 1.24350
\(107\) −11.6751 −1.12868 −0.564339 0.825543i \(-0.690869\pi\)
−0.564339 + 0.825543i \(0.690869\pi\)
\(108\) −27.4921 −2.64543
\(109\) −15.1364 −1.44980 −0.724902 0.688852i \(-0.758115\pi\)
−0.724902 + 0.688852i \(0.758115\pi\)
\(110\) 6.88029 0.656010
\(111\) −14.5762 −1.38351
\(112\) −23.5744 −2.22757
\(113\) −2.19835 −0.206804 −0.103402 0.994640i \(-0.532973\pi\)
−0.103402 + 0.994640i \(0.532973\pi\)
\(114\) 6.65357 0.623164
\(115\) 2.63199 0.245434
\(116\) −4.88043 −0.453137
\(117\) −3.80652 −0.351913
\(118\) 5.53419 0.509463
\(119\) −4.96004 −0.454686
\(120\) −10.2936 −0.939674
\(121\) −2.78898 −0.253544
\(122\) −5.11177 −0.462798
\(123\) 15.9152 1.43502
\(124\) 20.1276 1.80751
\(125\) −8.38676 −0.750135
\(126\) −4.82539 −0.429880
\(127\) −4.63282 −0.411096 −0.205548 0.978647i \(-0.565898\pi\)
−0.205548 + 0.978647i \(0.565898\pi\)
\(128\) −2.24324 −0.198276
\(129\) −6.94609 −0.611569
\(130\) −11.6453 −1.02136
\(131\) −0.229703 −0.0200692 −0.0100346 0.999950i \(-0.503194\pi\)
−0.0100346 + 0.999950i \(0.503194\pi\)
\(132\) −20.8142 −1.81164
\(133\) 3.99470 0.346385
\(134\) −6.41850 −0.554474
\(135\) −5.15645 −0.443796
\(136\) −15.9887 −1.37102
\(137\) −2.52853 −0.216027 −0.108013 0.994149i \(-0.534449\pi\)
−0.108013 + 0.994149i \(0.534449\pi\)
\(138\) −11.2252 −0.955552
\(139\) −1.00000 −0.0848189
\(140\) −10.4712 −0.884981
\(141\) 15.5481 1.30939
\(142\) −16.2703 −1.36537
\(143\) −13.8976 −1.16218
\(144\) −7.89381 −0.657818
\(145\) −0.915377 −0.0760180
\(146\) 18.1519 1.50226
\(147\) −2.24163 −0.184887
\(148\) −47.7969 −3.92888
\(149\) −18.9421 −1.55180 −0.775898 0.630858i \(-0.782703\pi\)
−0.775898 + 0.630858i \(0.782703\pi\)
\(150\) 16.2488 1.32671
\(151\) −21.1079 −1.71774 −0.858870 0.512194i \(-0.828833\pi\)
−0.858870 + 0.512194i \(0.828833\pi\)
\(152\) 12.8769 1.04445
\(153\) −1.66085 −0.134272
\(154\) −17.6176 −1.41966
\(155\) 3.77514 0.303227
\(156\) 35.2292 2.82059
\(157\) 2.85108 0.227541 0.113770 0.993507i \(-0.463707\pi\)
0.113770 + 0.993507i \(0.463707\pi\)
\(158\) 8.74496 0.695712
\(159\) −7.26428 −0.576095
\(160\) −10.3172 −0.815649
\(161\) −6.73943 −0.531142
\(162\) 15.8157 1.24260
\(163\) 21.6563 1.69625 0.848125 0.529796i \(-0.177732\pi\)
0.848125 + 0.529796i \(0.177732\pi\)
\(164\) 52.1877 4.07518
\(165\) −3.90392 −0.303919
\(166\) 11.1895 0.868475
\(167\) 4.31008 0.333524 0.166762 0.985997i \(-0.446669\pi\)
0.166762 + 0.985997i \(0.446669\pi\)
\(168\) 26.3577 2.03354
\(169\) 10.5226 0.809431
\(170\) −5.08106 −0.389700
\(171\) 1.33761 0.102290
\(172\) −22.7770 −1.73673
\(173\) −4.02159 −0.305756 −0.152878 0.988245i \(-0.548854\pi\)
−0.152878 + 0.988245i \(0.548854\pi\)
\(174\) 3.90400 0.295961
\(175\) 9.75551 0.737447
\(176\) −28.8204 −2.17242
\(177\) −3.14013 −0.236027
\(178\) −14.4247 −1.08118
\(179\) 11.8116 0.882844 0.441422 0.897300i \(-0.354474\pi\)
0.441422 + 0.897300i \(0.354474\pi\)
\(180\) −3.50626 −0.261341
\(181\) 6.72152 0.499606 0.249803 0.968297i \(-0.419634\pi\)
0.249803 + 0.968297i \(0.419634\pi\)
\(182\) 29.8188 2.21031
\(183\) 2.90045 0.214407
\(184\) −21.7245 −1.60155
\(185\) −8.96482 −0.659107
\(186\) −16.1006 −1.18056
\(187\) −6.06380 −0.443429
\(188\) 50.9841 3.71840
\(189\) 13.2035 0.960414
\(190\) 4.09217 0.296877
\(191\) −11.3992 −0.824815 −0.412408 0.910999i \(-0.635312\pi\)
−0.412408 + 0.910999i \(0.635312\pi\)
\(192\) 14.0633 1.01493
\(193\) −20.5310 −1.47786 −0.738928 0.673784i \(-0.764668\pi\)
−0.738928 + 0.673784i \(0.764668\pi\)
\(194\) −19.6864 −1.41340
\(195\) 6.60761 0.473181
\(196\) −7.35057 −0.525041
\(197\) −7.02343 −0.500399 −0.250200 0.968194i \(-0.580496\pi\)
−0.250200 + 0.968194i \(0.580496\pi\)
\(198\) −5.89918 −0.419236
\(199\) −2.17144 −0.153929 −0.0769647 0.997034i \(-0.524523\pi\)
−0.0769647 + 0.997034i \(0.524523\pi\)
\(200\) 31.4468 2.22363
\(201\) 3.64189 0.256879
\(202\) 13.8436 0.974034
\(203\) 2.34390 0.164510
\(204\) 15.3712 1.07620
\(205\) 9.78837 0.683649
\(206\) 28.3892 1.97797
\(207\) −2.25668 −0.156850
\(208\) 48.7803 3.38230
\(209\) 4.88364 0.337808
\(210\) 8.37624 0.578015
\(211\) −0.727573 −0.0500882 −0.0250441 0.999686i \(-0.507973\pi\)
−0.0250441 + 0.999686i \(0.507973\pi\)
\(212\) −23.8204 −1.63599
\(213\) 9.23185 0.632556
\(214\) 30.6246 2.09345
\(215\) −4.27208 −0.291353
\(216\) 42.5614 2.89594
\(217\) −9.66656 −0.656209
\(218\) 39.7036 2.68907
\(219\) −10.2995 −0.695974
\(220\) −12.8014 −0.863070
\(221\) 10.2633 0.690387
\(222\) 38.2341 2.56611
\(223\) −14.7702 −0.989083 −0.494542 0.869154i \(-0.664664\pi\)
−0.494542 + 0.869154i \(0.664664\pi\)
\(224\) 26.4181 1.76514
\(225\) 3.26660 0.217773
\(226\) 5.76641 0.383576
\(227\) 24.4236 1.62105 0.810525 0.585705i \(-0.199182\pi\)
0.810525 + 0.585705i \(0.199182\pi\)
\(228\) −12.3796 −0.819857
\(229\) −22.7679 −1.50455 −0.752273 0.658852i \(-0.771043\pi\)
−0.752273 + 0.658852i \(0.771043\pi\)
\(230\) −6.90387 −0.455228
\(231\) 9.99630 0.657709
\(232\) 7.55555 0.496046
\(233\) 6.41975 0.420572 0.210286 0.977640i \(-0.432560\pi\)
0.210286 + 0.977640i \(0.432560\pi\)
\(234\) 9.98471 0.652721
\(235\) 9.56262 0.623796
\(236\) −10.2968 −0.670268
\(237\) −4.96195 −0.322313
\(238\) 13.0105 0.843344
\(239\) −16.0960 −1.04116 −0.520582 0.853812i \(-0.674285\pi\)
−0.520582 + 0.853812i \(0.674285\pi\)
\(240\) 13.7026 0.884500
\(241\) −5.06697 −0.326392 −0.163196 0.986594i \(-0.552180\pi\)
−0.163196 + 0.986594i \(0.552180\pi\)
\(242\) 7.31566 0.470269
\(243\) 7.92551 0.508421
\(244\) 9.51090 0.608873
\(245\) −1.37868 −0.0880805
\(246\) −41.7465 −2.66166
\(247\) −8.26586 −0.525944
\(248\) −31.1601 −1.97867
\(249\) −6.34900 −0.402352
\(250\) 21.9990 1.39134
\(251\) 14.9398 0.942995 0.471497 0.881868i \(-0.343714\pi\)
0.471497 + 0.881868i \(0.343714\pi\)
\(252\) 8.97806 0.565565
\(253\) −8.23916 −0.517991
\(254\) 12.1522 0.762494
\(255\) 2.88302 0.180542
\(256\) −13.0139 −0.813366
\(257\) −15.2828 −0.953318 −0.476659 0.879088i \(-0.658152\pi\)
−0.476659 + 0.879088i \(0.658152\pi\)
\(258\) 18.2200 1.13433
\(259\) 22.9552 1.42637
\(260\) 21.6671 1.34374
\(261\) 0.784847 0.0485808
\(262\) 0.602524 0.0372240
\(263\) −6.21287 −0.383102 −0.191551 0.981483i \(-0.561352\pi\)
−0.191551 + 0.981483i \(0.561352\pi\)
\(264\) 32.2230 1.98319
\(265\) −4.46777 −0.274453
\(266\) −10.4783 −0.642468
\(267\) 8.18465 0.500893
\(268\) 11.9422 0.729485
\(269\) −14.6538 −0.893456 −0.446728 0.894670i \(-0.647411\pi\)
−0.446728 + 0.894670i \(0.647411\pi\)
\(270\) 13.5257 0.823145
\(271\) 1.04771 0.0636438 0.0318219 0.999494i \(-0.489869\pi\)
0.0318219 + 0.999494i \(0.489869\pi\)
\(272\) 21.2837 1.29052
\(273\) −16.9193 −1.02401
\(274\) 6.63247 0.400682
\(275\) 11.9264 0.719189
\(276\) 20.8855 1.25716
\(277\) −7.66740 −0.460690 −0.230345 0.973109i \(-0.573985\pi\)
−0.230345 + 0.973109i \(0.573985\pi\)
\(278\) 2.62306 0.157321
\(279\) −3.23682 −0.193783
\(280\) 16.2108 0.968782
\(281\) −23.1368 −1.38022 −0.690112 0.723703i \(-0.742439\pi\)
−0.690112 + 0.723703i \(0.742439\pi\)
\(282\) −40.7837 −2.42863
\(283\) 6.53094 0.388224 0.194112 0.980979i \(-0.437817\pi\)
0.194112 + 0.980979i \(0.437817\pi\)
\(284\) 30.2723 1.79633
\(285\) −2.32192 −0.137539
\(286\) 36.4543 2.15559
\(287\) −25.0639 −1.47948
\(288\) 8.84603 0.521257
\(289\) −12.5219 −0.736583
\(290\) 2.40109 0.140997
\(291\) 11.1702 0.654808
\(292\) −33.7731 −1.97642
\(293\) −7.03906 −0.411226 −0.205613 0.978633i \(-0.565919\pi\)
−0.205613 + 0.978633i \(0.565919\pi\)
\(294\) 5.87994 0.342925
\(295\) −1.93128 −0.112444
\(296\) 73.9958 4.30092
\(297\) 16.1417 0.936635
\(298\) 49.6862 2.87824
\(299\) 13.9453 0.806476
\(300\) −30.2323 −1.74546
\(301\) 10.9390 0.630514
\(302\) 55.3673 3.18603
\(303\) −7.85495 −0.451255
\(304\) −17.1414 −0.983128
\(305\) 1.78387 0.102144
\(306\) 4.35652 0.249045
\(307\) 8.21476 0.468841 0.234421 0.972135i \(-0.424681\pi\)
0.234421 + 0.972135i \(0.424681\pi\)
\(308\) 32.7790 1.86776
\(309\) −16.1082 −0.916363
\(310\) −9.90241 −0.562419
\(311\) −13.9130 −0.788935 −0.394468 0.918910i \(-0.629071\pi\)
−0.394468 + 0.918910i \(0.629071\pi\)
\(312\) −54.5394 −3.08769
\(313\) 28.4028 1.60542 0.802712 0.596367i \(-0.203390\pi\)
0.802712 + 0.596367i \(0.203390\pi\)
\(314\) −7.47854 −0.422039
\(315\) 1.68393 0.0948788
\(316\) −16.2708 −0.915303
\(317\) 4.92573 0.276656 0.138328 0.990386i \(-0.455827\pi\)
0.138328 + 0.990386i \(0.455827\pi\)
\(318\) 19.0546 1.06853
\(319\) 2.86549 0.160436
\(320\) 8.64940 0.483516
\(321\) −17.3766 −0.969865
\(322\) 17.6779 0.985152
\(323\) −3.60655 −0.200674
\(324\) −29.4264 −1.63480
\(325\) −20.1862 −1.11973
\(326\) −56.8056 −3.14617
\(327\) −22.5281 −1.24581
\(328\) −80.7934 −4.46107
\(329\) −24.4859 −1.34995
\(330\) 10.2402 0.563704
\(331\) 29.9712 1.64737 0.823683 0.567051i \(-0.191916\pi\)
0.823683 + 0.567051i \(0.191916\pi\)
\(332\) −20.8191 −1.14260
\(333\) 7.68646 0.421216
\(334\) −11.3056 −0.618614
\(335\) 2.23988 0.122378
\(336\) −35.0867 −1.91414
\(337\) −5.77862 −0.314781 −0.157391 0.987536i \(-0.550308\pi\)
−0.157391 + 0.987536i \(0.550308\pi\)
\(338\) −27.6014 −1.50132
\(339\) −3.27190 −0.177705
\(340\) 9.45377 0.512703
\(341\) −11.8177 −0.639962
\(342\) −3.50864 −0.189725
\(343\) 19.9375 1.07653
\(344\) 35.2618 1.90119
\(345\) 3.91730 0.210900
\(346\) 10.5489 0.567110
\(347\) −34.2569 −1.83900 −0.919502 0.393085i \(-0.871408\pi\)
−0.919502 + 0.393085i \(0.871408\pi\)
\(348\) −7.26374 −0.389377
\(349\) −3.58106 −0.191690 −0.0958450 0.995396i \(-0.530555\pi\)
−0.0958450 + 0.995396i \(0.530555\pi\)
\(350\) −25.5893 −1.36780
\(351\) −27.3208 −1.45827
\(352\) 32.2970 1.72143
\(353\) −0.368654 −0.0196215 −0.00981074 0.999952i \(-0.503123\pi\)
−0.00981074 + 0.999952i \(0.503123\pi\)
\(354\) 8.23674 0.437778
\(355\) 5.67789 0.301351
\(356\) 26.8384 1.42243
\(357\) −7.38223 −0.390709
\(358\) −30.9826 −1.63748
\(359\) 13.8984 0.733531 0.366766 0.930313i \(-0.380465\pi\)
0.366766 + 0.930313i \(0.380465\pi\)
\(360\) 5.42814 0.286088
\(361\) −16.0954 −0.847125
\(362\) −17.6309 −0.926661
\(363\) −4.15095 −0.217868
\(364\) −55.4805 −2.90797
\(365\) −6.33451 −0.331564
\(366\) −7.60804 −0.397679
\(367\) −20.3413 −1.06181 −0.530904 0.847432i \(-0.678148\pi\)
−0.530904 + 0.847432i \(0.678148\pi\)
\(368\) 28.9192 1.50752
\(369\) −8.39257 −0.436900
\(370\) 23.5152 1.22250
\(371\) 11.4401 0.593941
\(372\) 29.9567 1.55318
\(373\) −14.8871 −0.770824 −0.385412 0.922745i \(-0.625941\pi\)
−0.385412 + 0.922745i \(0.625941\pi\)
\(374\) 15.9057 0.822464
\(375\) −12.4823 −0.644586
\(376\) −78.9300 −4.07051
\(377\) −4.85001 −0.249788
\(378\) −34.6336 −1.78136
\(379\) −5.94730 −0.305493 −0.152746 0.988265i \(-0.548812\pi\)
−0.152746 + 0.988265i \(0.548812\pi\)
\(380\) −7.61384 −0.390582
\(381\) −6.89521 −0.353252
\(382\) 29.9007 1.52985
\(383\) 25.1310 1.28414 0.642068 0.766647i \(-0.278077\pi\)
0.642068 + 0.766647i \(0.278077\pi\)
\(384\) −3.33870 −0.170377
\(385\) 6.14806 0.313334
\(386\) 53.8541 2.74110
\(387\) 3.66289 0.186195
\(388\) 36.6283 1.85952
\(389\) 29.3804 1.48965 0.744824 0.667261i \(-0.232534\pi\)
0.744824 + 0.667261i \(0.232534\pi\)
\(390\) −17.3322 −0.877648
\(391\) 6.08458 0.307710
\(392\) 11.3796 0.574759
\(393\) −0.341876 −0.0172453
\(394\) 18.4229 0.928131
\(395\) −3.05176 −0.153551
\(396\) 10.9759 0.551562
\(397\) 5.34593 0.268304 0.134152 0.990961i \(-0.457169\pi\)
0.134152 + 0.990961i \(0.457169\pi\)
\(398\) 5.69582 0.285506
\(399\) 5.94547 0.297646
\(400\) −41.8613 −2.09306
\(401\) 31.7714 1.58659 0.793294 0.608838i \(-0.208364\pi\)
0.793294 + 0.608838i \(0.208364\pi\)
\(402\) −9.55290 −0.476455
\(403\) 20.0021 0.996376
\(404\) −25.7573 −1.28147
\(405\) −5.51924 −0.274253
\(406\) −6.14819 −0.305129
\(407\) 28.0634 1.39105
\(408\) −23.7966 −1.17810
\(409\) −14.3410 −0.709117 −0.354558 0.935034i \(-0.615369\pi\)
−0.354558 + 0.935034i \(0.615369\pi\)
\(410\) −25.6755 −1.26802
\(411\) −3.76330 −0.185630
\(412\) −52.8206 −2.60228
\(413\) 4.94521 0.243338
\(414\) 5.91940 0.290922
\(415\) −3.90485 −0.191681
\(416\) −54.6645 −2.68015
\(417\) −1.48834 −0.0728843
\(418\) −12.8101 −0.626561
\(419\) 0.753347 0.0368034 0.0184017 0.999831i \(-0.494142\pi\)
0.0184017 + 0.999831i \(0.494142\pi\)
\(420\) −15.5847 −0.760458
\(421\) 7.09072 0.345580 0.172790 0.984959i \(-0.444722\pi\)
0.172790 + 0.984959i \(0.444722\pi\)
\(422\) 1.90847 0.0929027
\(423\) −8.19901 −0.398650
\(424\) 36.8771 1.79091
\(425\) −8.80759 −0.427231
\(426\) −24.2157 −1.17325
\(427\) −4.56775 −0.221049
\(428\) −56.9797 −2.75422
\(429\) −20.6844 −0.998652
\(430\) 11.2059 0.540397
\(431\) −13.9586 −0.672361 −0.336180 0.941798i \(-0.609135\pi\)
−0.336180 + 0.941798i \(0.609135\pi\)
\(432\) −56.6568 −2.72590
\(433\) −32.0601 −1.54071 −0.770356 0.637615i \(-0.779921\pi\)
−0.770356 + 0.637615i \(0.779921\pi\)
\(434\) 25.3560 1.21712
\(435\) −1.36239 −0.0653217
\(436\) −73.8722 −3.53783
\(437\) −4.90038 −0.234417
\(438\) 27.0161 1.29088
\(439\) 22.2163 1.06033 0.530164 0.847895i \(-0.322131\pi\)
0.530164 + 0.847895i \(0.322131\pi\)
\(440\) 19.8182 0.944796
\(441\) 1.18208 0.0562897
\(442\) −26.9214 −1.28052
\(443\) 39.4190 1.87285 0.936427 0.350863i \(-0.114112\pi\)
0.936427 + 0.350863i \(0.114112\pi\)
\(444\) −71.1380 −3.37606
\(445\) 5.03383 0.238627
\(446\) 38.7430 1.83453
\(447\) −28.1922 −1.33345
\(448\) −22.1475 −1.04637
\(449\) −25.6917 −1.21247 −0.606234 0.795286i \(-0.707321\pi\)
−0.606234 + 0.795286i \(0.707321\pi\)
\(450\) −8.56848 −0.403922
\(451\) −30.6414 −1.44285
\(452\) −10.7289 −0.504646
\(453\) −31.4158 −1.47604
\(454\) −64.0644 −3.00669
\(455\) −10.4060 −0.487839
\(456\) 19.1652 0.897492
\(457\) 16.1178 0.753959 0.376979 0.926222i \(-0.376963\pi\)
0.376979 + 0.926222i \(0.376963\pi\)
\(458\) 59.7216 2.79060
\(459\) −11.9206 −0.556404
\(460\) 12.8453 0.598913
\(461\) −22.4907 −1.04749 −0.523747 0.851874i \(-0.675466\pi\)
−0.523747 + 0.851874i \(0.675466\pi\)
\(462\) −26.2209 −1.21991
\(463\) −0.544971 −0.0253270 −0.0126635 0.999920i \(-0.504031\pi\)
−0.0126635 + 0.999920i \(0.504031\pi\)
\(464\) −10.0578 −0.466920
\(465\) 5.61869 0.260560
\(466\) −16.8394 −0.780069
\(467\) 17.0702 0.789915 0.394958 0.918699i \(-0.370759\pi\)
0.394958 + 0.918699i \(0.370759\pi\)
\(468\) −18.5775 −0.858743
\(469\) −5.73541 −0.264837
\(470\) −25.0833 −1.15701
\(471\) 4.24337 0.195524
\(472\) 15.9409 0.733737
\(473\) 13.3733 0.614903
\(474\) 13.0155 0.597820
\(475\) 7.09343 0.325469
\(476\) −24.2072 −1.10953
\(477\) 3.83068 0.175395
\(478\) 42.2207 1.93113
\(479\) 1.64739 0.0752710 0.0376355 0.999292i \(-0.488017\pi\)
0.0376355 + 0.999292i \(0.488017\pi\)
\(480\) −15.3555 −0.700881
\(481\) −47.4990 −2.16577
\(482\) 13.2909 0.605386
\(483\) −10.0306 −0.456406
\(484\) −13.6114 −0.618702
\(485\) 6.87003 0.311952
\(486\) −20.7891 −0.943011
\(487\) 18.3500 0.831518 0.415759 0.909475i \(-0.363516\pi\)
0.415759 + 0.909475i \(0.363516\pi\)
\(488\) −14.7241 −0.666529
\(489\) 32.2319 1.45758
\(490\) 3.61635 0.163370
\(491\) −1.79664 −0.0810812 −0.0405406 0.999178i \(-0.512908\pi\)
−0.0405406 + 0.999178i \(0.512908\pi\)
\(492\) 77.6730 3.50177
\(493\) −2.11615 −0.0953066
\(494\) 21.6818 0.975511
\(495\) 2.05866 0.0925297
\(496\) 41.4796 1.86249
\(497\) −14.5387 −0.652150
\(498\) 16.6538 0.746275
\(499\) −6.50403 −0.291161 −0.145580 0.989346i \(-0.546505\pi\)
−0.145580 + 0.989346i \(0.546505\pi\)
\(500\) −40.9311 −1.83049
\(501\) 6.41485 0.286595
\(502\) −39.1881 −1.74905
\(503\) 6.20492 0.276664 0.138332 0.990386i \(-0.455826\pi\)
0.138332 + 0.990386i \(0.455826\pi\)
\(504\) −13.8992 −0.619120
\(505\) −4.83105 −0.214979
\(506\) 21.6118 0.960761
\(507\) 15.6612 0.695538
\(508\) −22.6102 −1.00316
\(509\) 3.74128 0.165829 0.0829147 0.996557i \(-0.473577\pi\)
0.0829147 + 0.996557i \(0.473577\pi\)
\(510\) −7.56234 −0.334866
\(511\) 16.2201 0.717533
\(512\) 38.6226 1.70689
\(513\) 9.60053 0.423874
\(514\) 40.0878 1.76820
\(515\) −9.90707 −0.436557
\(516\) −33.8999 −1.49236
\(517\) −29.9347 −1.31653
\(518\) −60.2128 −2.64560
\(519\) −5.98548 −0.262734
\(520\) −33.5435 −1.47098
\(521\) −20.8778 −0.914673 −0.457337 0.889294i \(-0.651197\pi\)
−0.457337 + 0.889294i \(0.651197\pi\)
\(522\) −2.05870 −0.0901068
\(523\) 1.23932 0.0541916 0.0270958 0.999633i \(-0.491374\pi\)
0.0270958 + 0.999633i \(0.491374\pi\)
\(524\) −1.12105 −0.0489733
\(525\) 14.5195 0.633683
\(526\) 16.2967 0.710571
\(527\) 8.72729 0.380167
\(528\) −42.8945 −1.86674
\(529\) −14.7326 −0.640548
\(530\) 11.7192 0.509051
\(531\) 1.65589 0.0718594
\(532\) 19.4959 0.845253
\(533\) 51.8624 2.24641
\(534\) −21.4688 −0.929047
\(535\) −10.6872 −0.462046
\(536\) −18.4881 −0.798562
\(537\) 17.5797 0.758621
\(538\) 38.4377 1.65717
\(539\) 4.31580 0.185895
\(540\) −25.1657 −1.08296
\(541\) −31.7533 −1.36518 −0.682591 0.730801i \(-0.739147\pi\)
−0.682591 + 0.730801i \(0.739147\pi\)
\(542\) −2.74820 −0.118045
\(543\) 10.0039 0.429308
\(544\) −23.8512 −1.02261
\(545\) −13.8555 −0.593505
\(546\) 44.3804 1.89931
\(547\) −33.9854 −1.45311 −0.726556 0.687107i \(-0.758880\pi\)
−0.726556 + 0.687107i \(0.758880\pi\)
\(548\) −12.3403 −0.527152
\(549\) −1.52950 −0.0652773
\(550\) −31.2836 −1.33394
\(551\) 1.70430 0.0726055
\(552\) −32.3334 −1.37620
\(553\) 7.81429 0.332297
\(554\) 20.1120 0.854479
\(555\) −13.3427 −0.566366
\(556\) −4.88043 −0.206977
\(557\) −11.5342 −0.488719 −0.244360 0.969685i \(-0.578578\pi\)
−0.244360 + 0.969685i \(0.578578\pi\)
\(558\) 8.49036 0.359426
\(559\) −22.6350 −0.957360
\(560\) −21.5795 −0.911899
\(561\) −9.02499 −0.381035
\(562\) 60.6891 2.56001
\(563\) 2.14007 0.0901931 0.0450966 0.998983i \(-0.485640\pi\)
0.0450966 + 0.998983i \(0.485640\pi\)
\(564\) 75.8817 3.19519
\(565\) −2.01232 −0.0846591
\(566\) −17.1310 −0.720071
\(567\) 14.1325 0.593509
\(568\) −46.8654 −1.96643
\(569\) −8.51745 −0.357070 −0.178535 0.983934i \(-0.557136\pi\)
−0.178535 + 0.983934i \(0.557136\pi\)
\(570\) 6.09053 0.255104
\(571\) −32.3728 −1.35476 −0.677381 0.735633i \(-0.736885\pi\)
−0.677381 + 0.735633i \(0.736885\pi\)
\(572\) −67.8265 −2.83597
\(573\) −16.9658 −0.708758
\(574\) 65.7441 2.74411
\(575\) −11.9673 −0.499070
\(576\) −7.41602 −0.309001
\(577\) 3.38068 0.140739 0.0703697 0.997521i \(-0.477582\pi\)
0.0703697 + 0.997521i \(0.477582\pi\)
\(578\) 32.8457 1.36620
\(579\) −30.5571 −1.26991
\(580\) −4.46744 −0.185500
\(581\) 9.99868 0.414815
\(582\) −29.3000 −1.21453
\(583\) 13.9859 0.579235
\(584\) 52.2852 2.16358
\(585\) −3.48440 −0.144062
\(586\) 18.4639 0.762735
\(587\) 0.405404 0.0167328 0.00836642 0.999965i \(-0.497337\pi\)
0.00836642 + 0.999965i \(0.497337\pi\)
\(588\) −10.9401 −0.451164
\(589\) −7.02875 −0.289615
\(590\) 5.06587 0.208558
\(591\) −10.4533 −0.429989
\(592\) −98.5015 −4.04839
\(593\) −16.8671 −0.692649 −0.346325 0.938115i \(-0.612570\pi\)
−0.346325 + 0.938115i \(0.612570\pi\)
\(594\) −42.3406 −1.73725
\(595\) −4.54031 −0.186135
\(596\) −92.4456 −3.78672
\(597\) −3.23184 −0.132271
\(598\) −36.5793 −1.49584
\(599\) −16.9366 −0.692013 −0.346006 0.938232i \(-0.612462\pi\)
−0.346006 + 0.938232i \(0.612462\pi\)
\(600\) 46.8035 1.91075
\(601\) 6.15835 0.251204 0.125602 0.992081i \(-0.459914\pi\)
0.125602 + 0.992081i \(0.459914\pi\)
\(602\) −28.6937 −1.16947
\(603\) −1.92048 −0.0782081
\(604\) −103.016 −4.19166
\(605\) −2.55297 −0.103793
\(606\) 20.6040 0.836980
\(607\) −12.3246 −0.500242 −0.250121 0.968215i \(-0.580470\pi\)
−0.250121 + 0.968215i \(0.580470\pi\)
\(608\) 19.2092 0.779034
\(609\) 3.48852 0.141362
\(610\) −4.67920 −0.189455
\(611\) 50.6663 2.04974
\(612\) −8.10569 −0.327653
\(613\) 30.0916 1.21539 0.607693 0.794172i \(-0.292095\pi\)
0.607693 + 0.794172i \(0.292095\pi\)
\(614\) −21.5478 −0.869598
\(615\) 14.5684 0.587455
\(616\) −50.7462 −2.04462
\(617\) −12.7070 −0.511563 −0.255781 0.966735i \(-0.582333\pi\)
−0.255781 + 0.966735i \(0.582333\pi\)
\(618\) 42.2527 1.69965
\(619\) −9.32837 −0.374939 −0.187470 0.982270i \(-0.560029\pi\)
−0.187470 + 0.982270i \(0.560029\pi\)
\(620\) 18.4243 0.739939
\(621\) −16.1970 −0.649963
\(622\) 36.4947 1.46330
\(623\) −12.8895 −0.516409
\(624\) 72.6016 2.90639
\(625\) 13.1334 0.525335
\(626\) −74.5023 −2.97771
\(627\) 7.26851 0.290276
\(628\) 13.9145 0.555249
\(629\) −20.7247 −0.826347
\(630\) −4.41705 −0.175979
\(631\) 10.7719 0.428821 0.214410 0.976744i \(-0.431217\pi\)
0.214410 + 0.976744i \(0.431217\pi\)
\(632\) 25.1893 1.00198
\(633\) −1.08288 −0.0430404
\(634\) −12.9205 −0.513137
\(635\) −4.24078 −0.168290
\(636\) −35.4528 −1.40580
\(637\) −7.30475 −0.289425
\(638\) −7.51634 −0.297575
\(639\) −4.86824 −0.192585
\(640\) −2.05341 −0.0811681
\(641\) −18.1401 −0.716489 −0.358245 0.933628i \(-0.616625\pi\)
−0.358245 + 0.933628i \(0.616625\pi\)
\(642\) 45.5797 1.79889
\(643\) 24.8009 0.978052 0.489026 0.872269i \(-0.337352\pi\)
0.489026 + 0.872269i \(0.337352\pi\)
\(644\) −32.8914 −1.29610
\(645\) −6.35830 −0.250358
\(646\) 9.46018 0.372206
\(647\) −23.4154 −0.920556 −0.460278 0.887775i \(-0.652250\pi\)
−0.460278 + 0.887775i \(0.652250\pi\)
\(648\) 45.5560 1.78961
\(649\) 6.04567 0.237313
\(650\) 52.9494 2.07685
\(651\) −14.3871 −0.563876
\(652\) 105.692 4.13922
\(653\) 30.5678 1.19621 0.598105 0.801418i \(-0.295921\pi\)
0.598105 + 0.801418i \(0.295921\pi\)
\(654\) 59.0925 2.31070
\(655\) −0.210265 −0.00821572
\(656\) 107.550 4.19913
\(657\) 5.43123 0.211892
\(658\) 64.2279 2.50386
\(659\) −0.707816 −0.0275726 −0.0137863 0.999905i \(-0.504388\pi\)
−0.0137863 + 0.999905i \(0.504388\pi\)
\(660\) −19.0528 −0.741630
\(661\) 9.90137 0.385119 0.192559 0.981285i \(-0.438321\pi\)
0.192559 + 0.981285i \(0.438321\pi\)
\(662\) −78.6162 −3.05550
\(663\) 15.2753 0.593245
\(664\) 32.2307 1.25079
\(665\) 3.65666 0.141799
\(666\) −20.1620 −0.781263
\(667\) −2.87531 −0.111332
\(668\) 21.0350 0.813870
\(669\) −21.9830 −0.849912
\(670\) −5.87535 −0.226984
\(671\) −5.58421 −0.215576
\(672\) 39.3191 1.51677
\(673\) 5.85484 0.225688 0.112844 0.993613i \(-0.464004\pi\)
0.112844 + 0.993613i \(0.464004\pi\)
\(674\) 15.1576 0.583851
\(675\) 23.4456 0.902421
\(676\) 51.3548 1.97519
\(677\) −19.2989 −0.741718 −0.370859 0.928689i \(-0.620937\pi\)
−0.370859 + 0.928689i \(0.620937\pi\)
\(678\) 8.58237 0.329604
\(679\) −17.5913 −0.675091
\(680\) −14.6357 −0.561252
\(681\) 36.3505 1.39296
\(682\) 30.9984 1.18699
\(683\) −16.9564 −0.648820 −0.324410 0.945917i \(-0.605166\pi\)
−0.324410 + 0.945917i \(0.605166\pi\)
\(684\) 6.52813 0.249609
\(685\) −2.31456 −0.0884346
\(686\) −52.2973 −1.99672
\(687\) −33.8864 −1.29285
\(688\) −46.9397 −1.78956
\(689\) −23.6719 −0.901828
\(690\) −10.2753 −0.391174
\(691\) −43.1034 −1.63973 −0.819865 0.572558i \(-0.805951\pi\)
−0.819865 + 0.572558i \(0.805951\pi\)
\(692\) −19.6271 −0.746110
\(693\) −5.27136 −0.200242
\(694\) 89.8577 3.41095
\(695\) −0.915377 −0.0347222
\(696\) 11.2452 0.426249
\(697\) 22.6285 0.857117
\(698\) 9.39334 0.355543
\(699\) 9.55477 0.361394
\(700\) 47.6111 1.79953
\(701\) 32.9783 1.24557 0.622786 0.782392i \(-0.286001\pi\)
0.622786 + 0.782392i \(0.286001\pi\)
\(702\) 71.6640 2.70478
\(703\) 16.6912 0.629519
\(704\) −27.0760 −1.02046
\(705\) 14.2324 0.536024
\(706\) 0.967001 0.0363936
\(707\) 12.3703 0.465234
\(708\) −15.3252 −0.575956
\(709\) −0.0267051 −0.00100293 −0.000501465 1.00000i \(-0.500160\pi\)
−0.000501465 1.00000i \(0.500160\pi\)
\(710\) −14.8934 −0.558941
\(711\) 2.61659 0.0981297
\(712\) −41.5494 −1.55713
\(713\) 11.8582 0.444092
\(714\) 19.3640 0.724680
\(715\) −12.7216 −0.475760
\(716\) 57.6459 2.15433
\(717\) −23.9563 −0.894665
\(718\) −36.4564 −1.36054
\(719\) 25.0500 0.934206 0.467103 0.884203i \(-0.345298\pi\)
0.467103 + 0.884203i \(0.345298\pi\)
\(720\) −7.22582 −0.269290
\(721\) 25.3679 0.944749
\(722\) 42.2191 1.57123
\(723\) −7.54136 −0.280466
\(724\) 32.8039 1.21915
\(725\) 4.16208 0.154576
\(726\) 10.8882 0.404098
\(727\) −16.3071 −0.604797 −0.302399 0.953182i \(-0.597787\pi\)
−0.302399 + 0.953182i \(0.597787\pi\)
\(728\) 85.8910 3.18333
\(729\) 29.8843 1.10682
\(730\) 16.6158 0.614978
\(731\) −9.87609 −0.365280
\(732\) 14.1554 0.523200
\(733\) 43.4785 1.60592 0.802958 0.596036i \(-0.203258\pi\)
0.802958 + 0.596036i \(0.203258\pi\)
\(734\) 53.3565 1.96942
\(735\) −2.05194 −0.0756870
\(736\) −32.4076 −1.19456
\(737\) −7.01171 −0.258280
\(738\) 22.0142 0.810354
\(739\) −7.19993 −0.264854 −0.132427 0.991193i \(-0.542277\pi\)
−0.132427 + 0.991193i \(0.542277\pi\)
\(740\) −43.7522 −1.60836
\(741\) −12.3024 −0.451940
\(742\) −30.0081 −1.10163
\(743\) 42.7231 1.56736 0.783679 0.621166i \(-0.213341\pi\)
0.783679 + 0.621166i \(0.213341\pi\)
\(744\) −46.3768 −1.70026
\(745\) −17.3392 −0.635258
\(746\) 39.0497 1.42971
\(747\) 3.34803 0.122498
\(748\) −29.5940 −1.08206
\(749\) 27.3654 0.999908
\(750\) 32.7419 1.19557
\(751\) 1.07082 0.0390748 0.0195374 0.999809i \(-0.493781\pi\)
0.0195374 + 0.999809i \(0.493781\pi\)
\(752\) 105.070 3.83150
\(753\) 22.2356 0.810309
\(754\) 12.7219 0.463303
\(755\) −19.3217 −0.703190
\(756\) 64.4388 2.34362
\(757\) −5.17697 −0.188160 −0.0940800 0.995565i \(-0.529991\pi\)
−0.0940800 + 0.995565i \(0.529991\pi\)
\(758\) 15.6001 0.566622
\(759\) −12.2627 −0.445106
\(760\) 11.7872 0.427567
\(761\) 31.3871 1.13778 0.568890 0.822414i \(-0.307373\pi\)
0.568890 + 0.822414i \(0.307373\pi\)
\(762\) 18.0865 0.655206
\(763\) 35.4782 1.28440
\(764\) −55.6329 −2.01273
\(765\) −1.52031 −0.0549669
\(766\) −65.9202 −2.38179
\(767\) −10.2327 −0.369480
\(768\) −19.3690 −0.698919
\(769\) 29.2998 1.05658 0.528289 0.849065i \(-0.322834\pi\)
0.528289 + 0.849065i \(0.322834\pi\)
\(770\) −16.1267 −0.581166
\(771\) −22.7461 −0.819179
\(772\) −100.200 −3.60629
\(773\) 35.5761 1.27958 0.639792 0.768548i \(-0.279020\pi\)
0.639792 + 0.768548i \(0.279020\pi\)
\(774\) −9.60797 −0.345351
\(775\) −17.1650 −0.616585
\(776\) −56.7054 −2.03560
\(777\) 34.1651 1.22567
\(778\) −77.0666 −2.76297
\(779\) −18.2245 −0.652960
\(780\) 32.2480 1.15466
\(781\) −17.7740 −0.636004
\(782\) −15.9602 −0.570736
\(783\) 5.63314 0.201312
\(784\) −15.1483 −0.541011
\(785\) 2.60981 0.0931482
\(786\) 0.896759 0.0319863
\(787\) 2.22740 0.0793981 0.0396990 0.999212i \(-0.487360\pi\)
0.0396990 + 0.999212i \(0.487360\pi\)
\(788\) −34.2774 −1.22108
\(789\) −9.24686 −0.329197
\(790\) 8.00494 0.284803
\(791\) 5.15272 0.183210
\(792\) −16.9922 −0.603791
\(793\) 9.45161 0.335636
\(794\) −14.0227 −0.497646
\(795\) −6.64956 −0.235836
\(796\) −10.5976 −0.375621
\(797\) 13.4700 0.477133 0.238567 0.971126i \(-0.423322\pi\)
0.238567 + 0.971126i \(0.423322\pi\)
\(798\) −15.5953 −0.552068
\(799\) 22.1066 0.782077
\(800\) 46.9109 1.65855
\(801\) −4.31602 −0.152499
\(802\) −83.3383 −2.94278
\(803\) 19.8295 0.699768
\(804\) 17.7740 0.626841
\(805\) −6.16913 −0.217433
\(806\) −52.4667 −1.84806
\(807\) −21.8098 −0.767740
\(808\) 39.8756 1.40282
\(809\) −41.5677 −1.46144 −0.730722 0.682676i \(-0.760816\pi\)
−0.730722 + 0.682676i \(0.760816\pi\)
\(810\) 14.4773 0.508680
\(811\) −32.2720 −1.13322 −0.566612 0.823984i \(-0.691746\pi\)
−0.566612 + 0.823984i \(0.691746\pi\)
\(812\) 11.4393 0.401439
\(813\) 1.55935 0.0546886
\(814\) −73.6119 −2.58009
\(815\) 19.8237 0.694392
\(816\) 31.6774 1.10893
\(817\) 7.95397 0.278274
\(818\) 37.6173 1.31526
\(819\) 8.92210 0.311763
\(820\) 47.7715 1.66825
\(821\) −26.5092 −0.925178 −0.462589 0.886573i \(-0.653079\pi\)
−0.462589 + 0.886573i \(0.653079\pi\)
\(822\) 9.87136 0.344303
\(823\) 38.1358 1.32933 0.664664 0.747142i \(-0.268575\pi\)
0.664664 + 0.747142i \(0.268575\pi\)
\(824\) 81.7731 2.84870
\(825\) 17.7505 0.617994
\(826\) −12.9716 −0.451339
\(827\) 36.0350 1.25306 0.626530 0.779397i \(-0.284475\pi\)
0.626530 + 0.779397i \(0.284475\pi\)
\(828\) −11.0136 −0.382748
\(829\) −28.7597 −0.998865 −0.499432 0.866353i \(-0.666458\pi\)
−0.499432 + 0.866353i \(0.666458\pi\)
\(830\) 10.2426 0.355527
\(831\) −11.4117 −0.395867
\(832\) 45.8277 1.58879
\(833\) −3.18720 −0.110430
\(834\) 3.90400 0.135184
\(835\) 3.94535 0.136534
\(836\) 23.8343 0.824326
\(837\) −23.2318 −0.803009
\(838\) −1.97607 −0.0682623
\(839\) −24.4262 −0.843286 −0.421643 0.906762i \(-0.638546\pi\)
−0.421643 + 0.906762i \(0.638546\pi\)
\(840\) 24.1272 0.832468
\(841\) 1.00000 0.0344828
\(842\) −18.5994 −0.640977
\(843\) −34.4353 −1.18602
\(844\) −3.55087 −0.122226
\(845\) 9.63215 0.331356
\(846\) 21.5065 0.739408
\(847\) 6.53710 0.224617
\(848\) −49.0899 −1.68575
\(849\) 9.72025 0.333598
\(850\) 23.1028 0.792420
\(851\) −28.1596 −0.965297
\(852\) 45.0554 1.54357
\(853\) 48.8276 1.67183 0.835913 0.548862i \(-0.184939\pi\)
0.835913 + 0.548862i \(0.184939\pi\)
\(854\) 11.9815 0.409997
\(855\) 1.22442 0.0418743
\(856\) 88.2120 3.01503
\(857\) −55.9134 −1.90997 −0.954983 0.296659i \(-0.904127\pi\)
−0.954983 + 0.296659i \(0.904127\pi\)
\(858\) 54.2564 1.85228
\(859\) 36.3786 1.24122 0.620611 0.784118i \(-0.286885\pi\)
0.620611 + 0.784118i \(0.286885\pi\)
\(860\) −20.8496 −0.710965
\(861\) −37.3036 −1.27130
\(862\) 36.6141 1.24708
\(863\) 51.8008 1.76332 0.881660 0.471885i \(-0.156426\pi\)
0.881660 + 0.471885i \(0.156426\pi\)
\(864\) 63.4912 2.16001
\(865\) −3.68127 −0.125167
\(866\) 84.0956 2.85768
\(867\) −18.6368 −0.632941
\(868\) −47.1770 −1.60129
\(869\) 9.55319 0.324070
\(870\) 3.57363 0.121158
\(871\) 11.8677 0.402123
\(872\) 114.364 3.87284
\(873\) −5.89038 −0.199359
\(874\) 12.8540 0.434792
\(875\) 19.6577 0.664553
\(876\) −50.2659 −1.69833
\(877\) −18.9152 −0.638721 −0.319361 0.947633i \(-0.603468\pi\)
−0.319361 + 0.947633i \(0.603468\pi\)
\(878\) −58.2747 −1.96668
\(879\) −10.4765 −0.353364
\(880\) −26.3815 −0.889322
\(881\) −24.5575 −0.827363 −0.413681 0.910422i \(-0.635757\pi\)
−0.413681 + 0.910422i \(0.635757\pi\)
\(882\) −3.10067 −0.104405
\(883\) −54.1537 −1.82242 −0.911209 0.411944i \(-0.864850\pi\)
−0.911209 + 0.411944i \(0.864850\pi\)
\(884\) 50.0896 1.68469
\(885\) −2.87440 −0.0966220
\(886\) −103.398 −3.47374
\(887\) −47.6484 −1.59988 −0.799938 0.600082i \(-0.795135\pi\)
−0.799938 + 0.600082i \(0.795135\pi\)
\(888\) 110.131 3.69575
\(889\) 10.8589 0.364195
\(890\) −13.2040 −0.442600
\(891\) 17.2774 0.578814
\(892\) −72.0848 −2.41358
\(893\) −17.8042 −0.595794
\(894\) 73.9499 2.47325
\(895\) 10.8121 0.361409
\(896\) 5.25793 0.175655
\(897\) 20.7553 0.692999
\(898\) 67.3909 2.24886
\(899\) −4.12414 −0.137548
\(900\) 15.9424 0.531414
\(901\) −10.3285 −0.344092
\(902\) 80.3741 2.67617
\(903\) 16.2810 0.541796
\(904\) 16.6098 0.552432
\(905\) 6.15272 0.204523
\(906\) 82.4054 2.73773
\(907\) −47.5465 −1.57876 −0.789379 0.613907i \(-0.789597\pi\)
−0.789379 + 0.613907i \(0.789597\pi\)
\(908\) 119.198 3.95571
\(909\) 4.14216 0.137387
\(910\) 27.2954 0.904835
\(911\) −10.4122 −0.344972 −0.172486 0.985012i \(-0.555180\pi\)
−0.172486 + 0.985012i \(0.555180\pi\)
\(912\) −25.5122 −0.844795
\(913\) 12.2237 0.404545
\(914\) −42.2779 −1.39843
\(915\) 2.65500 0.0877717
\(916\) −111.117 −3.67142
\(917\) 0.538400 0.0177795
\(918\) 31.2683 1.03201
\(919\) −45.3542 −1.49610 −0.748049 0.663644i \(-0.769009\pi\)
−0.748049 + 0.663644i \(0.769009\pi\)
\(920\) −19.8861 −0.655626
\(921\) 12.2263 0.402872
\(922\) 58.9943 1.94287
\(923\) 30.0836 0.990213
\(924\) 48.7863 1.60495
\(925\) 40.7617 1.34024
\(926\) 1.42949 0.0469760
\(927\) 8.49435 0.278991
\(928\) 11.2710 0.369989
\(929\) −18.2898 −0.600070 −0.300035 0.953928i \(-0.596998\pi\)
−0.300035 + 0.953928i \(0.596998\pi\)
\(930\) −14.7381 −0.483283
\(931\) 2.56689 0.0841266
\(932\) 31.3312 1.02629
\(933\) −20.7073 −0.677926
\(934\) −44.7762 −1.46512
\(935\) −5.55067 −0.181526
\(936\) 28.7603 0.940060
\(937\) −54.3968 −1.77707 −0.888533 0.458812i \(-0.848275\pi\)
−0.888533 + 0.458812i \(0.848275\pi\)
\(938\) 15.0443 0.491214
\(939\) 42.2731 1.37953
\(940\) 46.6697 1.52220
\(941\) 45.5995 1.48650 0.743251 0.669013i \(-0.233283\pi\)
0.743251 + 0.669013i \(0.233283\pi\)
\(942\) −11.1306 −0.362655
\(943\) 30.7464 1.00124
\(944\) −21.2201 −0.690655
\(945\) 12.0862 0.393164
\(946\) −35.0788 −1.14051
\(947\) 59.3017 1.92705 0.963524 0.267623i \(-0.0862381\pi\)
0.963524 + 0.267623i \(0.0862381\pi\)
\(948\) −24.2164 −0.786514
\(949\) −33.5626 −1.08949
\(950\) −18.6065 −0.603674
\(951\) 7.33115 0.237729
\(952\) 37.4758 1.21460
\(953\) 31.2359 1.01183 0.505915 0.862583i \(-0.331155\pi\)
0.505915 + 0.862583i \(0.331155\pi\)
\(954\) −10.0481 −0.325319
\(955\) −10.4345 −0.337654
\(956\) −78.5555 −2.54067
\(957\) 4.26482 0.137862
\(958\) −4.32119 −0.139611
\(959\) 5.92661 0.191380
\(960\) 12.8732 0.415482
\(961\) −13.9915 −0.451339
\(962\) 124.593 4.01702
\(963\) 9.16320 0.295280
\(964\) −24.7290 −0.796467
\(965\) −18.7936 −0.604989
\(966\) 26.3107 0.846534
\(967\) 27.1569 0.873308 0.436654 0.899629i \(-0.356163\pi\)
0.436654 + 0.899629i \(0.356163\pi\)
\(968\) 21.0723 0.677289
\(969\) −5.36776 −0.172437
\(970\) −18.0205 −0.578603
\(971\) −26.1244 −0.838372 −0.419186 0.907900i \(-0.637684\pi\)
−0.419186 + 0.907900i \(0.637684\pi\)
\(972\) 38.6799 1.24066
\(973\) 2.34390 0.0751420
\(974\) −48.1331 −1.54228
\(975\) −30.0438 −0.962173
\(976\) 19.6004 0.627393
\(977\) 37.4883 1.19936 0.599678 0.800241i \(-0.295295\pi\)
0.599678 + 0.800241i \(0.295295\pi\)
\(978\) −84.5461 −2.70348
\(979\) −15.7579 −0.503623
\(980\) −6.72855 −0.214936
\(981\) 11.8798 0.379291
\(982\) 4.71269 0.150388
\(983\) 38.0740 1.21437 0.607186 0.794560i \(-0.292298\pi\)
0.607186 + 0.794560i \(0.292298\pi\)
\(984\) −120.248 −3.83336
\(985\) −6.42909 −0.204848
\(986\) 5.55078 0.176773
\(987\) −36.4433 −1.16000
\(988\) −40.3410 −1.28342
\(989\) −13.4191 −0.426702
\(990\) −5.39997 −0.171622
\(991\) −55.9117 −1.77609 −0.888047 0.459752i \(-0.847938\pi\)
−0.888047 + 0.459752i \(0.847938\pi\)
\(992\) −46.4832 −1.47584
\(993\) 44.6073 1.41557
\(994\) 38.1359 1.20960
\(995\) −1.98769 −0.0630140
\(996\) −30.9859 −0.981825
\(997\) −4.07868 −0.129173 −0.0645865 0.997912i \(-0.520573\pi\)
−0.0645865 + 0.997912i \(0.520573\pi\)
\(998\) 17.0605 0.540039
\(999\) 55.1686 1.74546
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 \(a_p\))