Properties

Label 4031.2.a.c.1.7
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 1.7
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25610 q^{2}\) \(+3.35950 q^{3}\) \(+3.09001 q^{4}\) \(-1.55616 q^{5}\) \(-7.57937 q^{6}\) \(-0.413231 q^{7}\) \(-2.45917 q^{8}\) \(+8.28621 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25610 q^{2}\) \(+3.35950 q^{3}\) \(+3.09001 q^{4}\) \(-1.55616 q^{5}\) \(-7.57937 q^{6}\) \(-0.413231 q^{7}\) \(-2.45917 q^{8}\) \(+8.28621 q^{9}\) \(+3.51085 q^{10}\) \(+0.250216 q^{11}\) \(+10.3809 q^{12}\) \(-1.55530 q^{13}\) \(+0.932291 q^{14}\) \(-5.22790 q^{15}\) \(-0.631871 q^{16}\) \(-4.51173 q^{17}\) \(-18.6946 q^{18}\) \(-2.98698 q^{19}\) \(-4.80853 q^{20}\) \(-1.38825 q^{21}\) \(-0.564513 q^{22}\) \(+0.223324 q^{23}\) \(-8.26157 q^{24}\) \(-2.57838 q^{25}\) \(+3.50893 q^{26}\) \(+17.7590 q^{27}\) \(-1.27689 q^{28}\) \(-1.00000 q^{29}\) \(+11.7947 q^{30}\) \(-0.373345 q^{31}\) \(+6.34391 q^{32}\) \(+0.840598 q^{33}\) \(+10.1789 q^{34}\) \(+0.643051 q^{35}\) \(+25.6044 q^{36}\) \(-0.987923 q^{37}\) \(+6.73895 q^{38}\) \(-5.22504 q^{39}\) \(+3.82685 q^{40}\) \(-4.17015 q^{41}\) \(+3.13203 q^{42}\) \(-7.46817 q^{43}\) \(+0.773168 q^{44}\) \(-12.8946 q^{45}\) \(-0.503841 q^{46}\) \(+0.634544 q^{47}\) \(-2.12277 q^{48}\) \(-6.82924 q^{49}\) \(+5.81709 q^{50}\) \(-15.1571 q^{51}\) \(-4.80590 q^{52}\) \(-3.25573 q^{53}\) \(-40.0662 q^{54}\) \(-0.389375 q^{55}\) \(+1.01620 q^{56}\) \(-10.0348 q^{57}\) \(+2.25610 q^{58}\) \(-1.92616 q^{59}\) \(-16.1543 q^{60}\) \(-5.84392 q^{61}\) \(+0.842305 q^{62}\) \(-3.42411 q^{63}\) \(-13.0488 q^{64}\) \(+2.42030 q^{65}\) \(-1.89648 q^{66}\) \(+1.28993 q^{67}\) \(-13.9413 q^{68}\) \(+0.750255 q^{69}\) \(-1.45079 q^{70}\) \(+9.07160 q^{71}\) \(-20.3772 q^{72}\) \(+1.62996 q^{73}\) \(+2.22886 q^{74}\) \(-8.66204 q^{75}\) \(-9.22980 q^{76}\) \(-0.103397 q^{77}\) \(+11.7882 q^{78}\) \(-4.82190 q^{79}\) \(+0.983289 q^{80}\) \(+34.8026 q^{81}\) \(+9.40829 q^{82}\) \(-12.1516 q^{83}\) \(-4.28969 q^{84}\) \(+7.02096 q^{85}\) \(+16.8490 q^{86}\) \(-3.35950 q^{87}\) \(-0.615323 q^{88}\) \(+4.25177 q^{89}\) \(+29.0917 q^{90}\) \(+0.642699 q^{91}\) \(+0.690071 q^{92}\) \(-1.25425 q^{93}\) \(-1.43160 q^{94}\) \(+4.64821 q^{95}\) \(+21.3123 q^{96}\) \(-3.46406 q^{97}\) \(+15.4075 q^{98}\) \(+2.07334 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25610 −1.59531 −0.797653 0.603116i \(-0.793926\pi\)
−0.797653 + 0.603116i \(0.793926\pi\)
\(3\) 3.35950 1.93961 0.969803 0.243890i \(-0.0784237\pi\)
0.969803 + 0.243890i \(0.0784237\pi\)
\(4\) 3.09001 1.54500
\(5\) −1.55616 −0.695934 −0.347967 0.937507i \(-0.613128\pi\)
−0.347967 + 0.937507i \(0.613128\pi\)
\(6\) −7.57937 −3.09427
\(7\) −0.413231 −0.156186 −0.0780932 0.996946i \(-0.524883\pi\)
−0.0780932 + 0.996946i \(0.524883\pi\)
\(8\) −2.45917 −0.869448
\(9\) 8.28621 2.76207
\(10\) 3.51085 1.11023
\(11\) 0.250216 0.0754429 0.0377214 0.999288i \(-0.487990\pi\)
0.0377214 + 0.999288i \(0.487990\pi\)
\(12\) 10.3809 2.99670
\(13\) −1.55530 −0.431364 −0.215682 0.976464i \(-0.569197\pi\)
−0.215682 + 0.976464i \(0.569197\pi\)
\(14\) 0.932291 0.249165
\(15\) −5.22790 −1.34984
\(16\) −0.631871 −0.157968
\(17\) −4.51173 −1.09426 −0.547128 0.837049i \(-0.684279\pi\)
−0.547128 + 0.837049i \(0.684279\pi\)
\(18\) −18.6946 −4.40635
\(19\) −2.98698 −0.685261 −0.342630 0.939470i \(-0.611318\pi\)
−0.342630 + 0.939470i \(0.611318\pi\)
\(20\) −4.80853 −1.07522
\(21\) −1.38825 −0.302940
\(22\) −0.564513 −0.120355
\(23\) 0.223324 0.0465662 0.0232831 0.999729i \(-0.492588\pi\)
0.0232831 + 0.999729i \(0.492588\pi\)
\(24\) −8.26157 −1.68639
\(25\) −2.57838 −0.515675
\(26\) 3.50893 0.688157
\(27\) 17.7590 3.41772
\(28\) −1.27689 −0.241309
\(29\) −1.00000 −0.185695
\(30\) 11.7947 2.15341
\(31\) −0.373345 −0.0670547 −0.0335274 0.999438i \(-0.510674\pi\)
−0.0335274 + 0.999438i \(0.510674\pi\)
\(32\) 6.34391 1.12145
\(33\) 0.840598 0.146329
\(34\) 10.1789 1.74567
\(35\) 0.643051 0.108696
\(36\) 25.6044 4.26741
\(37\) −0.987923 −0.162414 −0.0812068 0.996697i \(-0.525877\pi\)
−0.0812068 + 0.996697i \(0.525877\pi\)
\(38\) 6.73895 1.09320
\(39\) −5.22504 −0.836675
\(40\) 3.82685 0.605079
\(41\) −4.17015 −0.651268 −0.325634 0.945496i \(-0.605578\pi\)
−0.325634 + 0.945496i \(0.605578\pi\)
\(42\) 3.13203 0.483282
\(43\) −7.46817 −1.13889 −0.569443 0.822031i \(-0.692841\pi\)
−0.569443 + 0.822031i \(0.692841\pi\)
\(44\) 0.773168 0.116560
\(45\) −12.8946 −1.92222
\(46\) −0.503841 −0.0742874
\(47\) 0.634544 0.0925578 0.0462789 0.998929i \(-0.485264\pi\)
0.0462789 + 0.998929i \(0.485264\pi\)
\(48\) −2.12277 −0.306395
\(49\) −6.82924 −0.975606
\(50\) 5.81709 0.822660
\(51\) −15.1571 −2.12242
\(52\) −4.80590 −0.666458
\(53\) −3.25573 −0.447210 −0.223605 0.974680i \(-0.571782\pi\)
−0.223605 + 0.974680i \(0.571782\pi\)
\(54\) −40.0662 −5.45231
\(55\) −0.389375 −0.0525033
\(56\) 1.01620 0.135796
\(57\) −10.0348 −1.32914
\(58\) 2.25610 0.296241
\(59\) −1.92616 −0.250765 −0.125383 0.992108i \(-0.540016\pi\)
−0.125383 + 0.992108i \(0.540016\pi\)
\(60\) −16.1543 −2.08550
\(61\) −5.84392 −0.748237 −0.374119 0.927381i \(-0.622055\pi\)
−0.374119 + 0.927381i \(0.622055\pi\)
\(62\) 0.842305 0.106973
\(63\) −3.42411 −0.431398
\(64\) −13.0488 −1.63110
\(65\) 2.42030 0.300201
\(66\) −1.89648 −0.233440
\(67\) 1.28993 0.157590 0.0787948 0.996891i \(-0.474893\pi\)
0.0787948 + 0.996891i \(0.474893\pi\)
\(68\) −13.9413 −1.69063
\(69\) 0.750255 0.0903200
\(70\) −1.45079 −0.173403
\(71\) 9.07160 1.07660 0.538300 0.842753i \(-0.319067\pi\)
0.538300 + 0.842753i \(0.319067\pi\)
\(72\) −20.3772 −2.40148
\(73\) 1.62996 0.190772 0.0953861 0.995440i \(-0.469591\pi\)
0.0953861 + 0.995440i \(0.469591\pi\)
\(74\) 2.22886 0.259099
\(75\) −8.66204 −1.00021
\(76\) −9.22980 −1.05873
\(77\) −0.103397 −0.0117832
\(78\) 11.7882 1.33475
\(79\) −4.82190 −0.542507 −0.271253 0.962508i \(-0.587438\pi\)
−0.271253 + 0.962508i \(0.587438\pi\)
\(80\) 0.983289 0.109935
\(81\) 34.8026 3.86696
\(82\) 9.40829 1.03897
\(83\) −12.1516 −1.33381 −0.666905 0.745143i \(-0.732381\pi\)
−0.666905 + 0.745143i \(0.732381\pi\)
\(84\) −4.28969 −0.468044
\(85\) 7.02096 0.761530
\(86\) 16.8490 1.81687
\(87\) −3.35950 −0.360176
\(88\) −0.615323 −0.0655936
\(89\) 4.25177 0.450686 0.225343 0.974279i \(-0.427650\pi\)
0.225343 + 0.974279i \(0.427650\pi\)
\(90\) 29.0917 3.06653
\(91\) 0.642699 0.0673732
\(92\) 0.690071 0.0719449
\(93\) −1.25425 −0.130060
\(94\) −1.43160 −0.147658
\(95\) 4.64821 0.476897
\(96\) 21.3123 2.17518
\(97\) −3.46406 −0.351722 −0.175861 0.984415i \(-0.556271\pi\)
−0.175861 + 0.984415i \(0.556271\pi\)
\(98\) 15.4075 1.55639
\(99\) 2.07334 0.208378
\(100\) −7.96720 −0.796720
\(101\) 3.44608 0.342898 0.171449 0.985193i \(-0.445155\pi\)
0.171449 + 0.985193i \(0.445155\pi\)
\(102\) 34.1961 3.38592
\(103\) −7.79628 −0.768190 −0.384095 0.923294i \(-0.625487\pi\)
−0.384095 + 0.923294i \(0.625487\pi\)
\(104\) 3.82476 0.375048
\(105\) 2.16033 0.210826
\(106\) 7.34528 0.713436
\(107\) −2.76546 −0.267347 −0.133674 0.991025i \(-0.542677\pi\)
−0.133674 + 0.991025i \(0.542677\pi\)
\(108\) 54.8754 5.28039
\(109\) 1.47146 0.140941 0.0704703 0.997514i \(-0.477550\pi\)
0.0704703 + 0.997514i \(0.477550\pi\)
\(110\) 0.878470 0.0837588
\(111\) −3.31892 −0.315018
\(112\) 0.261108 0.0246724
\(113\) −4.32034 −0.406423 −0.203211 0.979135i \(-0.565138\pi\)
−0.203211 + 0.979135i \(0.565138\pi\)
\(114\) 22.6395 2.12038
\(115\) −0.347526 −0.0324070
\(116\) −3.09001 −0.286900
\(117\) −12.8876 −1.19146
\(118\) 4.34563 0.400047
\(119\) 1.86439 0.170908
\(120\) 12.8563 1.17361
\(121\) −10.9374 −0.994308
\(122\) 13.1845 1.19367
\(123\) −14.0096 −1.26320
\(124\) −1.15364 −0.103600
\(125\) 11.7931 1.05481
\(126\) 7.72516 0.688212
\(127\) −6.91921 −0.613980 −0.306990 0.951713i \(-0.599322\pi\)
−0.306990 + 0.951713i \(0.599322\pi\)
\(128\) 16.7516 1.48064
\(129\) −25.0893 −2.20899
\(130\) −5.46044 −0.478912
\(131\) −5.49425 −0.480035 −0.240017 0.970769i \(-0.577153\pi\)
−0.240017 + 0.970769i \(0.577153\pi\)
\(132\) 2.59746 0.226079
\(133\) 1.23431 0.107028
\(134\) −2.91021 −0.251404
\(135\) −27.6358 −2.37851
\(136\) 11.0951 0.951398
\(137\) 18.0414 1.54138 0.770691 0.637209i \(-0.219911\pi\)
0.770691 + 0.637209i \(0.219911\pi\)
\(138\) −1.69265 −0.144088
\(139\) −1.00000 −0.0848189
\(140\) 1.98703 0.167935
\(141\) 2.13175 0.179526
\(142\) −20.4665 −1.71751
\(143\) −0.389161 −0.0325433
\(144\) −5.23581 −0.436318
\(145\) 1.55616 0.129232
\(146\) −3.67735 −0.304340
\(147\) −22.9428 −1.89229
\(148\) −3.05269 −0.250930
\(149\) −6.44860 −0.528290 −0.264145 0.964483i \(-0.585090\pi\)
−0.264145 + 0.964483i \(0.585090\pi\)
\(150\) 19.5425 1.59564
\(151\) 14.1605 1.15236 0.576182 0.817321i \(-0.304542\pi\)
0.576182 + 0.817321i \(0.304542\pi\)
\(152\) 7.34550 0.595799
\(153\) −37.3852 −3.02241
\(154\) 0.233274 0.0187977
\(155\) 0.580983 0.0466657
\(156\) −16.1454 −1.29267
\(157\) −10.6403 −0.849192 −0.424596 0.905383i \(-0.639584\pi\)
−0.424596 + 0.905383i \(0.639584\pi\)
\(158\) 10.8787 0.865465
\(159\) −10.9376 −0.867410
\(160\) −9.87211 −0.780459
\(161\) −0.0922841 −0.00727301
\(162\) −78.5184 −6.16899
\(163\) 9.43979 0.739381 0.369691 0.929155i \(-0.379464\pi\)
0.369691 + 0.929155i \(0.379464\pi\)
\(164\) −12.8858 −1.00621
\(165\) −1.30810 −0.101836
\(166\) 27.4152 2.12784
\(167\) 10.9575 0.847919 0.423960 0.905681i \(-0.360640\pi\)
0.423960 + 0.905681i \(0.360640\pi\)
\(168\) 3.41393 0.263391
\(169\) −10.5810 −0.813925
\(170\) −15.8400 −1.21487
\(171\) −24.7508 −1.89274
\(172\) −23.0767 −1.75958
\(173\) 18.8647 1.43426 0.717130 0.696940i \(-0.245456\pi\)
0.717130 + 0.696940i \(0.245456\pi\)
\(174\) 7.57937 0.574591
\(175\) 1.06546 0.0805415
\(176\) −0.158104 −0.0119175
\(177\) −6.47094 −0.486385
\(178\) −9.59243 −0.718983
\(179\) −13.2746 −0.992191 −0.496095 0.868268i \(-0.665233\pi\)
−0.496095 + 0.868268i \(0.665233\pi\)
\(180\) −39.8445 −2.96984
\(181\) −1.82540 −0.135681 −0.0678405 0.997696i \(-0.521611\pi\)
−0.0678405 + 0.997696i \(0.521611\pi\)
\(182\) −1.45000 −0.107481
\(183\) −19.6326 −1.45129
\(184\) −0.549191 −0.0404869
\(185\) 1.53736 0.113029
\(186\) 2.82972 0.207485
\(187\) −1.12891 −0.0825538
\(188\) 1.96075 0.143002
\(189\) −7.33856 −0.533802
\(190\) −10.4869 −0.760796
\(191\) −14.3122 −1.03560 −0.517799 0.855502i \(-0.673248\pi\)
−0.517799 + 0.855502i \(0.673248\pi\)
\(192\) −43.8373 −3.16368
\(193\) −5.46134 −0.393116 −0.196558 0.980492i \(-0.562976\pi\)
−0.196558 + 0.980492i \(0.562976\pi\)
\(194\) 7.81529 0.561105
\(195\) 8.13097 0.582271
\(196\) −21.1024 −1.50731
\(197\) 17.4367 1.24231 0.621156 0.783687i \(-0.286663\pi\)
0.621156 + 0.783687i \(0.286663\pi\)
\(198\) −4.67767 −0.332428
\(199\) −12.0648 −0.855253 −0.427627 0.903955i \(-0.640650\pi\)
−0.427627 + 0.903955i \(0.640650\pi\)
\(200\) 6.34067 0.448353
\(201\) 4.33350 0.305662
\(202\) −7.77471 −0.547027
\(203\) 0.413231 0.0290031
\(204\) −46.8357 −3.27915
\(205\) 6.48940 0.453239
\(206\) 17.5892 1.22550
\(207\) 1.85051 0.128619
\(208\) 0.982751 0.0681415
\(209\) −0.747390 −0.0516980
\(210\) −4.87393 −0.336333
\(211\) −0.887919 −0.0611269 −0.0305634 0.999533i \(-0.509730\pi\)
−0.0305634 + 0.999533i \(0.509730\pi\)
\(212\) −10.0602 −0.690940
\(213\) 30.4760 2.08818
\(214\) 6.23917 0.426501
\(215\) 11.6216 0.792589
\(216\) −43.6724 −2.97153
\(217\) 0.154278 0.0104730
\(218\) −3.31977 −0.224843
\(219\) 5.47584 0.370023
\(220\) −1.20317 −0.0811178
\(221\) 7.01711 0.472022
\(222\) 7.48784 0.502551
\(223\) 2.77689 0.185954 0.0929771 0.995668i \(-0.470362\pi\)
0.0929771 + 0.995668i \(0.470362\pi\)
\(224\) −2.62150 −0.175156
\(225\) −21.3650 −1.42433
\(226\) 9.74713 0.648369
\(227\) −7.55978 −0.501760 −0.250880 0.968018i \(-0.580720\pi\)
−0.250880 + 0.968018i \(0.580720\pi\)
\(228\) −31.0075 −2.05352
\(229\) 13.5788 0.897316 0.448658 0.893704i \(-0.351902\pi\)
0.448658 + 0.893704i \(0.351902\pi\)
\(230\) 0.784056 0.0516991
\(231\) −0.347361 −0.0228547
\(232\) 2.45917 0.161452
\(233\) −20.4627 −1.34055 −0.670277 0.742111i \(-0.733825\pi\)
−0.670277 + 0.742111i \(0.733825\pi\)
\(234\) 29.0757 1.90074
\(235\) −0.987450 −0.0644142
\(236\) −5.95186 −0.387433
\(237\) −16.1992 −1.05225
\(238\) −4.20625 −0.272651
\(239\) 1.06422 0.0688389 0.0344195 0.999407i \(-0.489042\pi\)
0.0344195 + 0.999407i \(0.489042\pi\)
\(240\) 3.30336 0.213231
\(241\) 8.01794 0.516481 0.258240 0.966081i \(-0.416857\pi\)
0.258240 + 0.966081i \(0.416857\pi\)
\(242\) 24.6759 1.58623
\(243\) 63.6423 4.08266
\(244\) −18.0578 −1.15603
\(245\) 10.6274 0.678958
\(246\) 31.6071 2.01519
\(247\) 4.64567 0.295597
\(248\) 0.918119 0.0583006
\(249\) −40.8232 −2.58706
\(250\) −26.6066 −1.68275
\(251\) 20.8340 1.31503 0.657514 0.753442i \(-0.271608\pi\)
0.657514 + 0.753442i \(0.271608\pi\)
\(252\) −10.5805 −0.666511
\(253\) 0.0558791 0.00351309
\(254\) 15.6105 0.979487
\(255\) 23.5869 1.47707
\(256\) −11.6958 −0.730986
\(257\) −4.19939 −0.261951 −0.130975 0.991386i \(-0.541811\pi\)
−0.130975 + 0.991386i \(0.541811\pi\)
\(258\) 56.6040 3.52401
\(259\) 0.408240 0.0253668
\(260\) 7.47873 0.463811
\(261\) −8.28621 −0.512904
\(262\) 12.3956 0.765803
\(263\) 16.0862 0.991917 0.495959 0.868346i \(-0.334817\pi\)
0.495959 + 0.868346i \(0.334817\pi\)
\(264\) −2.06717 −0.127226
\(265\) 5.06643 0.311229
\(266\) −2.78474 −0.170743
\(267\) 14.2838 0.874154
\(268\) 3.98588 0.243476
\(269\) 10.4027 0.634262 0.317131 0.948382i \(-0.397280\pi\)
0.317131 + 0.948382i \(0.397280\pi\)
\(270\) 62.3492 3.79445
\(271\) −7.66997 −0.465917 −0.232959 0.972487i \(-0.574841\pi\)
−0.232959 + 0.972487i \(0.574841\pi\)
\(272\) 2.85083 0.172857
\(273\) 2.15914 0.130677
\(274\) −40.7033 −2.45898
\(275\) −0.645150 −0.0389040
\(276\) 2.31829 0.139545
\(277\) −9.06701 −0.544784 −0.272392 0.962186i \(-0.587815\pi\)
−0.272392 + 0.962186i \(0.587815\pi\)
\(278\) 2.25610 0.135312
\(279\) −3.09362 −0.185210
\(280\) −1.58137 −0.0945051
\(281\) −26.0106 −1.55166 −0.775831 0.630941i \(-0.782669\pi\)
−0.775831 + 0.630941i \(0.782669\pi\)
\(282\) −4.80945 −0.286398
\(283\) −23.4918 −1.39644 −0.698221 0.715883i \(-0.746025\pi\)
−0.698221 + 0.715883i \(0.746025\pi\)
\(284\) 28.0313 1.66335
\(285\) 15.6157 0.924991
\(286\) 0.877989 0.0519166
\(287\) 1.72323 0.101719
\(288\) 52.5669 3.09754
\(289\) 3.35572 0.197395
\(290\) −3.51085 −0.206164
\(291\) −11.6375 −0.682203
\(292\) 5.03658 0.294744
\(293\) −7.18232 −0.419596 −0.209798 0.977745i \(-0.567281\pi\)
−0.209798 + 0.977745i \(0.567281\pi\)
\(294\) 51.7614 3.01878
\(295\) 2.99741 0.174516
\(296\) 2.42947 0.141210
\(297\) 4.44358 0.257843
\(298\) 14.5487 0.842785
\(299\) −0.347336 −0.0200870
\(300\) −26.7658 −1.54532
\(301\) 3.08608 0.177878
\(302\) −31.9476 −1.83838
\(303\) 11.5771 0.665086
\(304\) 1.88739 0.108249
\(305\) 9.09406 0.520724
\(306\) 84.3448 4.82167
\(307\) −33.4233 −1.90757 −0.953785 0.300489i \(-0.902850\pi\)
−0.953785 + 0.300489i \(0.902850\pi\)
\(308\) −0.319497 −0.0182050
\(309\) −26.1916 −1.48999
\(310\) −1.31076 −0.0744461
\(311\) 21.6668 1.22861 0.614306 0.789068i \(-0.289436\pi\)
0.614306 + 0.789068i \(0.289436\pi\)
\(312\) 12.8493 0.727446
\(313\) 28.9297 1.63520 0.817601 0.575785i \(-0.195303\pi\)
0.817601 + 0.575785i \(0.195303\pi\)
\(314\) 24.0057 1.35472
\(315\) 5.32846 0.300225
\(316\) −14.8997 −0.838175
\(317\) 18.3891 1.03283 0.516417 0.856337i \(-0.327265\pi\)
0.516417 + 0.856337i \(0.327265\pi\)
\(318\) 24.6764 1.38379
\(319\) −0.250216 −0.0140094
\(320\) 20.3059 1.13514
\(321\) −9.29055 −0.518548
\(322\) 0.208203 0.0116027
\(323\) 13.4765 0.749851
\(324\) 107.540 5.97447
\(325\) 4.01016 0.222444
\(326\) −21.2972 −1.17954
\(327\) 4.94337 0.273369
\(328\) 10.2551 0.566243
\(329\) −0.262213 −0.0144563
\(330\) 2.95122 0.162459
\(331\) −2.58939 −0.142326 −0.0711628 0.997465i \(-0.522671\pi\)
−0.0711628 + 0.997465i \(0.522671\pi\)
\(332\) −37.5485 −2.06074
\(333\) −8.18614 −0.448598
\(334\) −24.7213 −1.35269
\(335\) −2.00733 −0.109672
\(336\) 0.877192 0.0478547
\(337\) −11.8572 −0.645905 −0.322952 0.946415i \(-0.604675\pi\)
−0.322952 + 0.946415i \(0.604675\pi\)
\(338\) 23.8719 1.29846
\(339\) −14.5141 −0.788300
\(340\) 21.6948 1.17657
\(341\) −0.0934168 −0.00505880
\(342\) 55.8403 3.01950
\(343\) 5.71466 0.308563
\(344\) 18.3655 0.990201
\(345\) −1.16751 −0.0628568
\(346\) −42.5608 −2.28808
\(347\) −9.29621 −0.499047 −0.249523 0.968369i \(-0.580274\pi\)
−0.249523 + 0.968369i \(0.580274\pi\)
\(348\) −10.3809 −0.556473
\(349\) −1.94740 −0.104242 −0.0521210 0.998641i \(-0.516598\pi\)
−0.0521210 + 0.998641i \(0.516598\pi\)
\(350\) −2.40380 −0.128488
\(351\) −27.6206 −1.47428
\(352\) 1.58734 0.0846058
\(353\) −3.21178 −0.170946 −0.0854729 0.996340i \(-0.527240\pi\)
−0.0854729 + 0.996340i \(0.527240\pi\)
\(354\) 14.5991 0.775934
\(355\) −14.1168 −0.749243
\(356\) 13.1380 0.696312
\(357\) 6.26339 0.331494
\(358\) 29.9489 1.58285
\(359\) −4.38504 −0.231434 −0.115717 0.993282i \(-0.536917\pi\)
−0.115717 + 0.993282i \(0.536917\pi\)
\(360\) 31.7101 1.67127
\(361\) −10.0779 −0.530418
\(362\) 4.11829 0.216453
\(363\) −36.7441 −1.92857
\(364\) 1.98594 0.104092
\(365\) −2.53647 −0.132765
\(366\) 44.2932 2.31525
\(367\) −1.18970 −0.0621019 −0.0310509 0.999518i \(-0.509885\pi\)
−0.0310509 + 0.999518i \(0.509885\pi\)
\(368\) −0.141112 −0.00735595
\(369\) −34.5547 −1.79885
\(370\) −3.46845 −0.180316
\(371\) 1.34537 0.0698481
\(372\) −3.87564 −0.200943
\(373\) 29.1202 1.50778 0.753892 0.656998i \(-0.228174\pi\)
0.753892 + 0.656998i \(0.228174\pi\)
\(374\) 2.54693 0.131699
\(375\) 39.6190 2.04592
\(376\) −1.56045 −0.0804742
\(377\) 1.55530 0.0801022
\(378\) 16.5566 0.851577
\(379\) 17.5786 0.902952 0.451476 0.892283i \(-0.350898\pi\)
0.451476 + 0.892283i \(0.350898\pi\)
\(380\) 14.3630 0.736807
\(381\) −23.2450 −1.19088
\(382\) 32.2899 1.65210
\(383\) 12.8616 0.657198 0.328599 0.944470i \(-0.393424\pi\)
0.328599 + 0.944470i \(0.393424\pi\)
\(384\) 56.2769 2.87187
\(385\) 0.160902 0.00820030
\(386\) 12.3214 0.627140
\(387\) −61.8828 −3.14568
\(388\) −10.7040 −0.543412
\(389\) −32.8841 −1.66729 −0.833646 0.552299i \(-0.813751\pi\)
−0.833646 + 0.552299i \(0.813751\pi\)
\(390\) −18.3443 −0.928901
\(391\) −1.00758 −0.0509553
\(392\) 16.7943 0.848238
\(393\) −18.4579 −0.931078
\(394\) −39.3390 −1.98187
\(395\) 7.50364 0.377549
\(396\) 6.40663 0.321945
\(397\) 25.6068 1.28517 0.642585 0.766214i \(-0.277862\pi\)
0.642585 + 0.766214i \(0.277862\pi\)
\(398\) 27.2195 1.36439
\(399\) 4.14667 0.207593
\(400\) 1.62920 0.0814600
\(401\) 0.170413 0.00851003 0.00425501 0.999991i \(-0.498646\pi\)
0.00425501 + 0.999991i \(0.498646\pi\)
\(402\) −9.77683 −0.487624
\(403\) 0.580665 0.0289250
\(404\) 10.6484 0.529778
\(405\) −54.1584 −2.69115
\(406\) −0.932291 −0.0462688
\(407\) −0.247194 −0.0122529
\(408\) 37.2740 1.84534
\(409\) −32.2587 −1.59509 −0.797545 0.603259i \(-0.793868\pi\)
−0.797545 + 0.603259i \(0.793868\pi\)
\(410\) −14.6408 −0.723056
\(411\) 60.6101 2.98967
\(412\) −24.0906 −1.18686
\(413\) 0.795949 0.0391661
\(414\) −4.17493 −0.205187
\(415\) 18.9098 0.928244
\(416\) −9.86670 −0.483755
\(417\) −3.35950 −0.164515
\(418\) 1.68619 0.0824742
\(419\) 10.9531 0.535095 0.267548 0.963545i \(-0.413787\pi\)
0.267548 + 0.963545i \(0.413787\pi\)
\(420\) 6.67543 0.325728
\(421\) −35.8916 −1.74925 −0.874624 0.484801i \(-0.838892\pi\)
−0.874624 + 0.484801i \(0.838892\pi\)
\(422\) 2.00324 0.0975161
\(423\) 5.25797 0.255651
\(424\) 8.00640 0.388825
\(425\) 11.6329 0.564281
\(426\) −68.7570 −3.33129
\(427\) 2.41489 0.116865
\(428\) −8.54529 −0.413052
\(429\) −1.30739 −0.0631212
\(430\) −26.2196 −1.26442
\(431\) 3.63849 0.175260 0.0876298 0.996153i \(-0.472071\pi\)
0.0876298 + 0.996153i \(0.472071\pi\)
\(432\) −11.2214 −0.539889
\(433\) −4.75224 −0.228378 −0.114189 0.993459i \(-0.536427\pi\)
−0.114189 + 0.993459i \(0.536427\pi\)
\(434\) −0.348066 −0.0167077
\(435\) 5.22790 0.250659
\(436\) 4.54683 0.217754
\(437\) −0.667064 −0.0319100
\(438\) −12.3541 −0.590300
\(439\) 9.36206 0.446827 0.223413 0.974724i \(-0.428280\pi\)
0.223413 + 0.974724i \(0.428280\pi\)
\(440\) 0.957539 0.0456489
\(441\) −56.5885 −2.69469
\(442\) −15.8313 −0.753020
\(443\) 35.3297 1.67856 0.839282 0.543697i \(-0.182976\pi\)
0.839282 + 0.543697i \(0.182976\pi\)
\(444\) −10.2555 −0.486704
\(445\) −6.61642 −0.313648
\(446\) −6.26495 −0.296654
\(447\) −21.6641 −1.02467
\(448\) 5.39215 0.254755
\(449\) 23.8751 1.12674 0.563369 0.826206i \(-0.309505\pi\)
0.563369 + 0.826206i \(0.309505\pi\)
\(450\) 48.2016 2.27225
\(451\) −1.04344 −0.0491335
\(452\) −13.3499 −0.627925
\(453\) 47.5721 2.23513
\(454\) 17.0556 0.800461
\(455\) −1.00014 −0.0468873
\(456\) 24.6772 1.15561
\(457\) 8.90014 0.416331 0.208165 0.978094i \(-0.433251\pi\)
0.208165 + 0.978094i \(0.433251\pi\)
\(458\) −30.6353 −1.43149
\(459\) −80.1238 −3.73986
\(460\) −1.07386 −0.0500689
\(461\) −2.85095 −0.132782 −0.0663910 0.997794i \(-0.521148\pi\)
−0.0663910 + 0.997794i \(0.521148\pi\)
\(462\) 0.783683 0.0364602
\(463\) 11.3826 0.528992 0.264496 0.964387i \(-0.414794\pi\)
0.264496 + 0.964387i \(0.414794\pi\)
\(464\) 0.631871 0.0293339
\(465\) 1.95181 0.0905131
\(466\) 46.1659 2.13860
\(467\) −18.0902 −0.837113 −0.418556 0.908191i \(-0.637464\pi\)
−0.418556 + 0.908191i \(0.637464\pi\)
\(468\) −39.8227 −1.84080
\(469\) −0.533037 −0.0246134
\(470\) 2.22779 0.102760
\(471\) −35.7462 −1.64710
\(472\) 4.73676 0.218027
\(473\) −1.86865 −0.0859208
\(474\) 36.5470 1.67866
\(475\) 7.70157 0.353372
\(476\) 5.76096 0.264053
\(477\) −26.9777 −1.23522
\(478\) −2.40100 −0.109819
\(479\) −22.7085 −1.03758 −0.518789 0.854902i \(-0.673617\pi\)
−0.518789 + 0.854902i \(0.673617\pi\)
\(480\) −33.1653 −1.51378
\(481\) 1.53652 0.0700593
\(482\) −18.0893 −0.823945
\(483\) −0.310028 −0.0141068
\(484\) −33.7966 −1.53621
\(485\) 5.39063 0.244776
\(486\) −143.584 −6.51309
\(487\) −10.9068 −0.494234 −0.247117 0.968986i \(-0.579483\pi\)
−0.247117 + 0.968986i \(0.579483\pi\)
\(488\) 14.3712 0.650553
\(489\) 31.7129 1.43411
\(490\) −23.9765 −1.08315
\(491\) 6.78283 0.306105 0.153052 0.988218i \(-0.451090\pi\)
0.153052 + 0.988218i \(0.451090\pi\)
\(492\) −43.2897 −1.95165
\(493\) 4.51173 0.203198
\(494\) −10.4811 −0.471567
\(495\) −3.22644 −0.145018
\(496\) 0.235906 0.0105925
\(497\) −3.74866 −0.168150
\(498\) 92.1014 4.12716
\(499\) −31.2779 −1.40019 −0.700095 0.714050i \(-0.746859\pi\)
−0.700095 + 0.714050i \(0.746859\pi\)
\(500\) 36.4409 1.62969
\(501\) 36.8118 1.64463
\(502\) −47.0036 −2.09787
\(503\) −27.5427 −1.22807 −0.614034 0.789279i \(-0.710454\pi\)
−0.614034 + 0.789279i \(0.710454\pi\)
\(504\) 8.42048 0.375078
\(505\) −5.36264 −0.238634
\(506\) −0.126069 −0.00560445
\(507\) −35.5469 −1.57869
\(508\) −21.3804 −0.948602
\(509\) 6.79862 0.301343 0.150672 0.988584i \(-0.451856\pi\)
0.150672 + 0.988584i \(0.451856\pi\)
\(510\) −53.2145 −2.35638
\(511\) −0.673548 −0.0297960
\(512\) −7.11628 −0.314498
\(513\) −53.0458 −2.34203
\(514\) 9.47426 0.417892
\(515\) 12.1322 0.534610
\(516\) −77.5260 −3.41289
\(517\) 0.158773 0.00698283
\(518\) −0.921032 −0.0404678
\(519\) 63.3760 2.78190
\(520\) −5.95192 −0.261009
\(521\) −22.0090 −0.964234 −0.482117 0.876107i \(-0.660132\pi\)
−0.482117 + 0.876107i \(0.660132\pi\)
\(522\) 18.6946 0.818238
\(523\) 21.4224 0.936734 0.468367 0.883534i \(-0.344842\pi\)
0.468367 + 0.883534i \(0.344842\pi\)
\(524\) −16.9773 −0.741655
\(525\) 3.57942 0.156219
\(526\) −36.2921 −1.58241
\(527\) 1.68443 0.0733750
\(528\) −0.531149 −0.0231153
\(529\) −22.9501 −0.997832
\(530\) −11.4304 −0.496505
\(531\) −15.9606 −0.692631
\(532\) 3.81403 0.165359
\(533\) 6.48585 0.280933
\(534\) −32.2257 −1.39454
\(535\) 4.30349 0.186056
\(536\) −3.17215 −0.137016
\(537\) −44.5960 −1.92446
\(538\) −23.4695 −1.01184
\(539\) −1.70878 −0.0736025
\(540\) −85.3948 −3.67481
\(541\) 18.6035 0.799827 0.399913 0.916553i \(-0.369040\pi\)
0.399913 + 0.916553i \(0.369040\pi\)
\(542\) 17.3043 0.743281
\(543\) −6.13243 −0.263168
\(544\) −28.6220 −1.22716
\(545\) −2.28983 −0.0980853
\(546\) −4.87126 −0.208470
\(547\) 2.18929 0.0936073 0.0468036 0.998904i \(-0.485096\pi\)
0.0468036 + 0.998904i \(0.485096\pi\)
\(548\) 55.7481 2.38144
\(549\) −48.4239 −2.06668
\(550\) 1.45553 0.0620639
\(551\) 2.98698 0.127250
\(552\) −1.84500 −0.0785286
\(553\) 1.99256 0.0847322
\(554\) 20.4561 0.869097
\(555\) 5.16476 0.219232
\(556\) −3.09001 −0.131045
\(557\) −31.9389 −1.35329 −0.676647 0.736307i \(-0.736568\pi\)
−0.676647 + 0.736307i \(0.736568\pi\)
\(558\) 6.97952 0.295467
\(559\) 11.6153 0.491274
\(560\) −0.406325 −0.0171704
\(561\) −3.79255 −0.160122
\(562\) 58.6826 2.47538
\(563\) 27.9843 1.17940 0.589699 0.807623i \(-0.299246\pi\)
0.589699 + 0.807623i \(0.299246\pi\)
\(564\) 6.58712 0.277368
\(565\) 6.72312 0.282844
\(566\) 52.9999 2.22775
\(567\) −14.3815 −0.603967
\(568\) −22.3086 −0.936048
\(569\) 37.8338 1.58608 0.793038 0.609173i \(-0.208498\pi\)
0.793038 + 0.609173i \(0.208498\pi\)
\(570\) −35.2305 −1.47564
\(571\) −1.69522 −0.0709428 −0.0354714 0.999371i \(-0.511293\pi\)
−0.0354714 + 0.999371i \(0.511293\pi\)
\(572\) −1.20251 −0.0502795
\(573\) −48.0819 −2.00865
\(574\) −3.88779 −0.162273
\(575\) −0.575812 −0.0240130
\(576\) −108.125 −4.50520
\(577\) 6.26135 0.260663 0.130332 0.991470i \(-0.458396\pi\)
0.130332 + 0.991470i \(0.458396\pi\)
\(578\) −7.57086 −0.314906
\(579\) −18.3473 −0.762490
\(580\) 4.80853 0.199664
\(581\) 5.02141 0.208323
\(582\) 26.2554 1.08832
\(583\) −0.814636 −0.0337388
\(584\) −4.00834 −0.165866
\(585\) 20.0551 0.829176
\(586\) 16.2041 0.669384
\(587\) −13.5915 −0.560981 −0.280490 0.959857i \(-0.590497\pi\)
−0.280490 + 0.959857i \(0.590497\pi\)
\(588\) −70.8934 −2.92360
\(589\) 1.11518 0.0459500
\(590\) −6.76247 −0.278407
\(591\) 58.5785 2.40960
\(592\) 0.624239 0.0256561
\(593\) 32.1721 1.32115 0.660574 0.750761i \(-0.270313\pi\)
0.660574 + 0.750761i \(0.270313\pi\)
\(594\) −10.0252 −0.411338
\(595\) −2.90128 −0.118941
\(596\) −19.9262 −0.816210
\(597\) −40.5318 −1.65885
\(598\) 0.783626 0.0320449
\(599\) −27.4145 −1.12013 −0.560063 0.828450i \(-0.689223\pi\)
−0.560063 + 0.828450i \(0.689223\pi\)
\(600\) 21.3014 0.869628
\(601\) −16.8326 −0.686616 −0.343308 0.939223i \(-0.611547\pi\)
−0.343308 + 0.939223i \(0.611547\pi\)
\(602\) −6.96251 −0.283771
\(603\) 10.6886 0.435273
\(604\) 43.7560 1.78041
\(605\) 17.0203 0.691973
\(606\) −26.1191 −1.06102
\(607\) −9.35585 −0.379742 −0.189871 0.981809i \(-0.560807\pi\)
−0.189871 + 0.981809i \(0.560807\pi\)
\(608\) −18.9491 −0.768489
\(609\) 1.38825 0.0562546
\(610\) −20.5171 −0.830715
\(611\) −0.986909 −0.0399261
\(612\) −115.520 −4.66964
\(613\) 30.4582 1.23019 0.615097 0.788451i \(-0.289117\pi\)
0.615097 + 0.788451i \(0.289117\pi\)
\(614\) 75.4065 3.04316
\(615\) 21.8011 0.879106
\(616\) 0.254270 0.0102448
\(617\) −10.1551 −0.408827 −0.204414 0.978885i \(-0.565529\pi\)
−0.204414 + 0.978885i \(0.565529\pi\)
\(618\) 59.0909 2.37698
\(619\) 24.7782 0.995919 0.497959 0.867200i \(-0.334083\pi\)
0.497959 + 0.867200i \(0.334083\pi\)
\(620\) 1.79524 0.0720987
\(621\) 3.96600 0.159150
\(622\) −48.8826 −1.96001
\(623\) −1.75696 −0.0703911
\(624\) 3.30155 0.132168
\(625\) −5.46009 −0.218404
\(626\) −65.2684 −2.60865
\(627\) −2.51085 −0.100274
\(628\) −32.8787 −1.31200
\(629\) 4.45724 0.177722
\(630\) −12.0216 −0.478950
\(631\) −8.66640 −0.345004 −0.172502 0.985009i \(-0.555185\pi\)
−0.172502 + 0.985009i \(0.555185\pi\)
\(632\) 11.8579 0.471681
\(633\) −2.98296 −0.118562
\(634\) −41.4877 −1.64769
\(635\) 10.7674 0.427290
\(636\) −33.7973 −1.34015
\(637\) 10.6215 0.420841
\(638\) 0.564513 0.0223493
\(639\) 75.1692 2.97365
\(640\) −26.0681 −1.03043
\(641\) 3.44575 0.136099 0.0680494 0.997682i \(-0.478322\pi\)
0.0680494 + 0.997682i \(0.478322\pi\)
\(642\) 20.9605 0.827243
\(643\) −26.0210 −1.02617 −0.513084 0.858338i \(-0.671497\pi\)
−0.513084 + 0.858338i \(0.671497\pi\)
\(644\) −0.285159 −0.0112368
\(645\) 39.0428 1.53731
\(646\) −30.4043 −1.19624
\(647\) −32.4488 −1.27570 −0.637848 0.770162i \(-0.720175\pi\)
−0.637848 + 0.770162i \(0.720175\pi\)
\(648\) −85.5856 −3.36212
\(649\) −0.481956 −0.0189184
\(650\) −9.04734 −0.354866
\(651\) 0.518295 0.0203136
\(652\) 29.1690 1.14235
\(653\) −28.1788 −1.10272 −0.551361 0.834267i \(-0.685891\pi\)
−0.551361 + 0.834267i \(0.685891\pi\)
\(654\) −11.1528 −0.436107
\(655\) 8.54991 0.334073
\(656\) 2.63499 0.102879
\(657\) 13.5062 0.526926
\(658\) 0.591580 0.0230622
\(659\) −30.7963 −1.19965 −0.599827 0.800130i \(-0.704764\pi\)
−0.599827 + 0.800130i \(0.704764\pi\)
\(660\) −4.04205 −0.157336
\(661\) −4.96027 −0.192932 −0.0964660 0.995336i \(-0.530754\pi\)
−0.0964660 + 0.995336i \(0.530754\pi\)
\(662\) 5.84193 0.227053
\(663\) 23.5740 0.915537
\(664\) 29.8828 1.15968
\(665\) −1.92078 −0.0744848
\(666\) 18.4688 0.715651
\(667\) −0.223324 −0.00864712
\(668\) 33.8588 1.31004
\(669\) 9.32895 0.360678
\(670\) 4.52874 0.174961
\(671\) −1.46224 −0.0564492
\(672\) −8.80690 −0.339734
\(673\) −17.9449 −0.691726 −0.345863 0.938285i \(-0.612414\pi\)
−0.345863 + 0.938285i \(0.612414\pi\)
\(674\) 26.7512 1.03042
\(675\) −45.7894 −1.76243
\(676\) −32.6955 −1.25752
\(677\) 33.7057 1.29541 0.647707 0.761889i \(-0.275728\pi\)
0.647707 + 0.761889i \(0.275728\pi\)
\(678\) 32.7454 1.25758
\(679\) 1.43146 0.0549343
\(680\) −17.2657 −0.662111
\(681\) −25.3970 −0.973216
\(682\) 0.210758 0.00807034
\(683\) −28.1066 −1.07547 −0.537735 0.843114i \(-0.680720\pi\)
−0.537735 + 0.843114i \(0.680720\pi\)
\(684\) −76.4800 −2.92429
\(685\) −28.0753 −1.07270
\(686\) −12.8929 −0.492252
\(687\) 45.6181 1.74044
\(688\) 4.71892 0.179907
\(689\) 5.06366 0.192910
\(690\) 2.63403 0.100276
\(691\) 27.7331 1.05502 0.527508 0.849550i \(-0.323127\pi\)
0.527508 + 0.849550i \(0.323127\pi\)
\(692\) 58.2922 2.21594
\(693\) −0.856767 −0.0325459
\(694\) 20.9732 0.796133
\(695\) 1.55616 0.0590284
\(696\) 8.26157 0.313154
\(697\) 18.8146 0.712653
\(698\) 4.39354 0.166298
\(699\) −68.7443 −2.60015
\(700\) 3.29229 0.124437
\(701\) 40.4834 1.52904 0.764518 0.644603i \(-0.222977\pi\)
0.764518 + 0.644603i \(0.222977\pi\)
\(702\) 62.3150 2.35193
\(703\) 2.95091 0.111296
\(704\) −3.26501 −0.123055
\(705\) −3.31734 −0.124938
\(706\) 7.24611 0.272711
\(707\) −1.42403 −0.0535560
\(708\) −19.9952 −0.751467
\(709\) −20.7895 −0.780768 −0.390384 0.920652i \(-0.627658\pi\)
−0.390384 + 0.920652i \(0.627658\pi\)
\(710\) 31.8490 1.19527
\(711\) −39.9553 −1.49844
\(712\) −10.4558 −0.391848
\(713\) −0.0833768 −0.00312248
\(714\) −14.1309 −0.528835
\(715\) 0.605596 0.0226480
\(716\) −41.0186 −1.53294
\(717\) 3.57525 0.133520
\(718\) 9.89311 0.369208
\(719\) 24.2014 0.902561 0.451280 0.892382i \(-0.350967\pi\)
0.451280 + 0.892382i \(0.350967\pi\)
\(720\) 8.14774 0.303648
\(721\) 3.22166 0.119981
\(722\) 22.7369 0.846179
\(723\) 26.9362 1.00177
\(724\) −5.64050 −0.209628
\(725\) 2.57838 0.0957585
\(726\) 82.8986 3.07665
\(727\) 28.3421 1.05115 0.525574 0.850748i \(-0.323850\pi\)
0.525574 + 0.850748i \(0.323850\pi\)
\(728\) −1.58051 −0.0585775
\(729\) 109.398 4.05178
\(730\) 5.72254 0.211801
\(731\) 33.6944 1.24623
\(732\) −60.6649 −2.24224
\(733\) −40.4279 −1.49324 −0.746620 0.665251i \(-0.768325\pi\)
−0.746620 + 0.665251i \(0.768325\pi\)
\(734\) 2.68409 0.0990715
\(735\) 35.7026 1.31691
\(736\) 1.41674 0.0522219
\(737\) 0.322760 0.0118890
\(738\) 77.9590 2.86971
\(739\) −30.9896 −1.13997 −0.569986 0.821654i \(-0.693051\pi\)
−0.569986 + 0.821654i \(0.693051\pi\)
\(740\) 4.75046 0.174630
\(741\) 15.6071 0.573341
\(742\) −3.03529 −0.111429
\(743\) −6.37955 −0.234043 −0.117022 0.993129i \(-0.537335\pi\)
−0.117022 + 0.993129i \(0.537335\pi\)
\(744\) 3.08442 0.113080
\(745\) 10.0350 0.367655
\(746\) −65.6981 −2.40538
\(747\) −100.691 −3.68408
\(748\) −3.48833 −0.127546
\(749\) 1.14277 0.0417560
\(750\) −89.3846 −3.26386
\(751\) −9.74559 −0.355621 −0.177811 0.984065i \(-0.556901\pi\)
−0.177811 + 0.984065i \(0.556901\pi\)
\(752\) −0.400950 −0.0146211
\(753\) 69.9916 2.55064
\(754\) −3.50893 −0.127788
\(755\) −22.0360 −0.801970
\(756\) −22.6762 −0.824726
\(757\) −21.5351 −0.782708 −0.391354 0.920240i \(-0.627993\pi\)
−0.391354 + 0.920240i \(0.627993\pi\)
\(758\) −39.6592 −1.44049
\(759\) 0.187725 0.00681400
\(760\) −11.4307 −0.414637
\(761\) 46.1491 1.67290 0.836452 0.548040i \(-0.184626\pi\)
0.836452 + 0.548040i \(0.184626\pi\)
\(762\) 52.4433 1.89982
\(763\) −0.608053 −0.0220130
\(764\) −44.2249 −1.60000
\(765\) 58.1772 2.10340
\(766\) −29.0172 −1.04843
\(767\) 2.99577 0.108171
\(768\) −39.2919 −1.41782
\(769\) 31.3719 1.13130 0.565650 0.824645i \(-0.308625\pi\)
0.565650 + 0.824645i \(0.308625\pi\)
\(770\) −0.363011 −0.0130820
\(771\) −14.1078 −0.508081
\(772\) −16.8756 −0.607365
\(773\) 11.8930 0.427762 0.213881 0.976860i \(-0.431390\pi\)
0.213881 + 0.976860i \(0.431390\pi\)
\(774\) 139.614 5.01832
\(775\) 0.962624 0.0345785
\(776\) 8.51872 0.305804
\(777\) 1.37148 0.0492016
\(778\) 74.1901 2.65984
\(779\) 12.4562 0.446288
\(780\) 25.1248 0.899611
\(781\) 2.26986 0.0812218
\(782\) 2.27320 0.0812894
\(783\) −17.7590 −0.634655
\(784\) 4.31520 0.154114
\(785\) 16.5580 0.590982
\(786\) 41.6430 1.48536
\(787\) −42.5188 −1.51563 −0.757817 0.652468i \(-0.773734\pi\)
−0.757817 + 0.652468i \(0.773734\pi\)
\(788\) 53.8795 1.91938
\(789\) 54.0415 1.92393
\(790\) −16.9290 −0.602307
\(791\) 1.78529 0.0634778
\(792\) −5.09869 −0.181174
\(793\) 9.08907 0.322762
\(794\) −57.7717 −2.05024
\(795\) 17.0207 0.603661
\(796\) −37.2804 −1.32137
\(797\) 16.1339 0.571492 0.285746 0.958305i \(-0.407759\pi\)
0.285746 + 0.958305i \(0.407759\pi\)
\(798\) −9.35531 −0.331175
\(799\) −2.86289 −0.101282
\(800\) −16.3570 −0.578306
\(801\) 35.2310 1.24483
\(802\) −0.384470 −0.0135761
\(803\) 0.407841 0.0143924
\(804\) 13.3906 0.472248
\(805\) 0.143609 0.00506154
\(806\) −1.31004 −0.0461442
\(807\) 34.9477 1.23022
\(808\) −8.47449 −0.298132
\(809\) 21.6191 0.760086 0.380043 0.924969i \(-0.375909\pi\)
0.380043 + 0.924969i \(0.375909\pi\)
\(810\) 122.187 4.29321
\(811\) −45.7438 −1.60628 −0.803141 0.595789i \(-0.796840\pi\)
−0.803141 + 0.595789i \(0.796840\pi\)
\(812\) 1.27689 0.0448099
\(813\) −25.7672 −0.903696
\(814\) 0.557695 0.0195472
\(815\) −14.6898 −0.514561
\(816\) 9.57735 0.335274
\(817\) 22.3073 0.780433
\(818\) 72.7790 2.54466
\(819\) 5.32554 0.186089
\(820\) 20.0523 0.700257
\(821\) −41.2344 −1.43909 −0.719546 0.694445i \(-0.755650\pi\)
−0.719546 + 0.694445i \(0.755650\pi\)
\(822\) −136.743 −4.76945
\(823\) 17.3970 0.606420 0.303210 0.952924i \(-0.401942\pi\)
0.303210 + 0.952924i \(0.401942\pi\)
\(824\) 19.1724 0.667901
\(825\) −2.16738 −0.0754585
\(826\) −1.79574 −0.0624820
\(827\) −37.4316 −1.30162 −0.650812 0.759239i \(-0.725572\pi\)
−0.650812 + 0.759239i \(0.725572\pi\)
\(828\) 5.71808 0.198717
\(829\) 11.3391 0.393824 0.196912 0.980421i \(-0.436909\pi\)
0.196912 + 0.980421i \(0.436909\pi\)
\(830\) −42.6624 −1.48083
\(831\) −30.4606 −1.05667
\(832\) 20.2948 0.703596
\(833\) 30.8117 1.06756
\(834\) 7.57937 0.262452
\(835\) −17.0516 −0.590096
\(836\) −2.30944 −0.0798737
\(837\) −6.63023 −0.229174
\(838\) −24.7114 −0.853641
\(839\) −46.9007 −1.61919 −0.809597 0.586987i \(-0.800314\pi\)
−0.809597 + 0.586987i \(0.800314\pi\)
\(840\) −5.31261 −0.183303
\(841\) 1.00000 0.0344828
\(842\) 80.9752 2.79059
\(843\) −87.3825 −3.00961
\(844\) −2.74368 −0.0944412
\(845\) 16.4657 0.566439
\(846\) −11.8625 −0.407842
\(847\) 4.51966 0.155298
\(848\) 2.05720 0.0706446
\(849\) −78.9205 −2.70855
\(850\) −26.2451 −0.900201
\(851\) −0.220627 −0.00756298
\(852\) 94.1710 3.22625
\(853\) −11.4520 −0.392110 −0.196055 0.980593i \(-0.562813\pi\)
−0.196055 + 0.980593i \(0.562813\pi\)
\(854\) −5.44824 −0.186435
\(855\) 38.5161 1.31722
\(856\) 6.80074 0.232444
\(857\) 15.8471 0.541325 0.270663 0.962674i \(-0.412757\pi\)
0.270663 + 0.962674i \(0.412757\pi\)
\(858\) 2.94960 0.100698
\(859\) −4.51658 −0.154104 −0.0770518 0.997027i \(-0.524551\pi\)
−0.0770518 + 0.997027i \(0.524551\pi\)
\(860\) 35.9110 1.22455
\(861\) 5.78919 0.197295
\(862\) −8.20880 −0.279593
\(863\) 37.4000 1.27311 0.636555 0.771231i \(-0.280359\pi\)
0.636555 + 0.771231i \(0.280359\pi\)
\(864\) 112.661 3.83282
\(865\) −29.3565 −0.998150
\(866\) 10.7215 0.364333
\(867\) 11.2735 0.382869
\(868\) 0.476719 0.0161809
\(869\) −1.20652 −0.0409283
\(870\) −11.7947 −0.399877
\(871\) −2.00623 −0.0679784
\(872\) −3.61857 −0.122540
\(873\) −28.7040 −0.971482
\(874\) 1.50497 0.0509062
\(875\) −4.87329 −0.164747
\(876\) 16.9204 0.571686
\(877\) −5.10815 −0.172490 −0.0862449 0.996274i \(-0.527487\pi\)
−0.0862449 + 0.996274i \(0.527487\pi\)
\(878\) −21.1218 −0.712826
\(879\) −24.1290 −0.813850
\(880\) 0.246034 0.00829382
\(881\) −16.1333 −0.543545 −0.271772 0.962362i \(-0.587610\pi\)
−0.271772 + 0.962362i \(0.587610\pi\)
\(882\) 127.670 4.29886
\(883\) 48.6925 1.63863 0.819316 0.573342i \(-0.194353\pi\)
0.819316 + 0.573342i \(0.194353\pi\)
\(884\) 21.6829 0.729276
\(885\) 10.0698 0.338492
\(886\) −79.7074 −2.67782
\(887\) −25.6603 −0.861589 −0.430794 0.902450i \(-0.641767\pi\)
−0.430794 + 0.902450i \(0.641767\pi\)
\(888\) 8.16179 0.273892
\(889\) 2.85923 0.0958954
\(890\) 14.9273 0.500365
\(891\) 8.70817 0.291735
\(892\) 8.58061 0.287300
\(893\) −1.89537 −0.0634262
\(894\) 48.8764 1.63467
\(895\) 20.6574 0.690500
\(896\) −6.92226 −0.231257
\(897\) −1.16687 −0.0389608
\(898\) −53.8648 −1.79749
\(899\) 0.373345 0.0124518
\(900\) −66.0179 −2.20060
\(901\) 14.6890 0.489362
\(902\) 2.35410 0.0783830
\(903\) 10.3677 0.345014
\(904\) 10.6244 0.353364
\(905\) 2.84061 0.0944251
\(906\) −107.328 −3.56572
\(907\) 2.10111 0.0697661 0.0348831 0.999391i \(-0.488894\pi\)
0.0348831 + 0.999391i \(0.488894\pi\)
\(908\) −23.3598 −0.775221
\(909\) 28.5549 0.947107
\(910\) 2.25642 0.0747996
\(911\) 15.1720 0.502670 0.251335 0.967900i \(-0.419130\pi\)
0.251335 + 0.967900i \(0.419130\pi\)
\(912\) 6.34067 0.209960
\(913\) −3.04052 −0.100626
\(914\) −20.0796 −0.664176
\(915\) 30.5514 1.01000
\(916\) 41.9587 1.38636
\(917\) 2.27039 0.0749749
\(918\) 180.768 5.96622
\(919\) 47.4119 1.56398 0.781988 0.623294i \(-0.214206\pi\)
0.781988 + 0.623294i \(0.214206\pi\)
\(920\) 0.854627 0.0281762
\(921\) −112.286 −3.69993
\(922\) 6.43204 0.211828
\(923\) −14.1091 −0.464406
\(924\) −1.07335 −0.0353106
\(925\) 2.54724 0.0837527
\(926\) −25.6802 −0.843905
\(927\) −64.6016 −2.12180
\(928\) −6.34391 −0.208249
\(929\) −10.5277 −0.345401 −0.172701 0.984974i \(-0.555249\pi\)
−0.172701 + 0.984974i \(0.555249\pi\)
\(930\) −4.40349 −0.144396
\(931\) 20.3988 0.668544
\(932\) −63.2298 −2.07116
\(933\) 72.7895 2.38302
\(934\) 40.8133 1.33545
\(935\) 1.75675 0.0574520
\(936\) 31.6927 1.03591
\(937\) 13.1703 0.430255 0.215128 0.976586i \(-0.430983\pi\)
0.215128 + 0.976586i \(0.430983\pi\)
\(938\) 1.20259 0.0392659
\(939\) 97.1892 3.17165
\(940\) −3.05123 −0.0995201
\(941\) −25.9490 −0.845914 −0.422957 0.906150i \(-0.639008\pi\)
−0.422957 + 0.906150i \(0.639008\pi\)
\(942\) 80.6471 2.62763
\(943\) −0.931292 −0.0303270
\(944\) 1.21709 0.0396128
\(945\) 11.4199 0.371491
\(946\) 4.21588 0.137070
\(947\) 2.29053 0.0744322 0.0372161 0.999307i \(-0.488151\pi\)
0.0372161 + 0.999307i \(0.488151\pi\)
\(948\) −50.0555 −1.62573
\(949\) −2.53508 −0.0822922
\(950\) −17.3755 −0.563737
\(951\) 61.7780 2.00329
\(952\) −4.58484 −0.148596
\(953\) 1.11519 0.0361246 0.0180623 0.999837i \(-0.494250\pi\)
0.0180623 + 0.999837i \(0.494250\pi\)
\(954\) 60.8645 1.97056
\(955\) 22.2721 0.720708
\(956\) 3.28846 0.106356
\(957\) −0.840598 −0.0271727
\(958\) 51.2327 1.65525
\(959\) −7.45526 −0.240743
\(960\) 68.2177 2.20172
\(961\) −30.8606 −0.995504
\(962\) −3.46655 −0.111766
\(963\) −22.9152 −0.738432
\(964\) 24.7755 0.797965
\(965\) 8.49870 0.273583
\(966\) 0.699456 0.0225046
\(967\) 12.7902 0.411304 0.205652 0.978625i \(-0.434069\pi\)
0.205652 + 0.978625i \(0.434069\pi\)
\(968\) 26.8969 0.864499
\(969\) 45.2741 1.45441
\(970\) −12.1618 −0.390492
\(971\) −0.833662 −0.0267535 −0.0133767 0.999911i \(-0.504258\pi\)
−0.0133767 + 0.999911i \(0.504258\pi\)
\(972\) 196.655 6.30772
\(973\) 0.413231 0.0132476
\(974\) 24.6069 0.788455
\(975\) 13.4721 0.431453
\(976\) 3.69260 0.118197
\(977\) 17.8345 0.570575 0.285288 0.958442i \(-0.407911\pi\)
0.285288 + 0.958442i \(0.407911\pi\)
\(978\) −71.5477 −2.28784
\(979\) 1.06386 0.0340011
\(980\) 32.8386 1.04899
\(981\) 12.1928 0.389288
\(982\) −15.3028 −0.488331
\(983\) −36.6560 −1.16915 −0.584573 0.811341i \(-0.698738\pi\)
−0.584573 + 0.811341i \(0.698738\pi\)
\(984\) 34.4520 1.09829
\(985\) −27.1342 −0.864568
\(986\) −10.1789 −0.324163
\(987\) −0.880904 −0.0280395
\(988\) 14.3551 0.456698
\(989\) −1.66782 −0.0530335
\(990\) 7.27919 0.231348
\(991\) 51.0415 1.62139 0.810693 0.585471i \(-0.199090\pi\)
0.810693 + 0.585471i \(0.199090\pi\)
\(992\) −2.36847 −0.0751989
\(993\) −8.69904 −0.276056
\(994\) 8.45737 0.268252
\(995\) 18.7748 0.595200
\(996\) −126.144 −3.99702
\(997\) 0.221157 0.00700412 0.00350206 0.999994i \(-0.498885\pi\)
0.00350206 + 0.999994i \(0.498885\pi\)
\(998\) 70.5662 2.23373
\(999\) −17.5445 −0.555084
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 \(a_p\))