Properties

Label 4031.2.a.c.1.1
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 1.1
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62831 q^{2}\) \(+0.935172 q^{3}\) \(+4.90799 q^{4}\) \(-2.36331 q^{5}\) \(-2.45792 q^{6}\) \(+0.343928 q^{7}\) \(-7.64309 q^{8}\) \(-2.12545 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62831 q^{2}\) \(+0.935172 q^{3}\) \(+4.90799 q^{4}\) \(-2.36331 q^{5}\) \(-2.45792 q^{6}\) \(+0.343928 q^{7}\) \(-7.64309 q^{8}\) \(-2.12545 q^{9}\) \(+6.21151 q^{10}\) \(+4.42731 q^{11}\) \(+4.58982 q^{12}\) \(-2.43651 q^{13}\) \(-0.903949 q^{14}\) \(-2.21010 q^{15}\) \(+10.2724 q^{16}\) \(+5.05811 q^{17}\) \(+5.58634 q^{18}\) \(-1.41236 q^{19}\) \(-11.5991 q^{20}\) \(+0.321632 q^{21}\) \(-11.6363 q^{22}\) \(+1.96514 q^{23}\) \(-7.14761 q^{24}\) \(+0.585242 q^{25}\) \(+6.40390 q^{26}\) \(-4.79318 q^{27}\) \(+1.68800 q^{28}\) \(-1.00000 q^{29}\) \(+5.80883 q^{30}\) \(+0.410917 q^{31}\) \(-11.7128 q^{32}\) \(+4.14030 q^{33}\) \(-13.2943 q^{34}\) \(-0.812810 q^{35}\) \(-10.4317 q^{36}\) \(-1.20366 q^{37}\) \(+3.71210 q^{38}\) \(-2.27856 q^{39}\) \(+18.0630 q^{40}\) \(-8.28410 q^{41}\) \(-0.845348 q^{42}\) \(-1.27377 q^{43}\) \(+21.7292 q^{44}\) \(+5.02311 q^{45}\) \(-5.16500 q^{46}\) \(-1.89543 q^{47}\) \(+9.60647 q^{48}\) \(-6.88171 q^{49}\) \(-1.53820 q^{50}\) \(+4.73020 q^{51}\) \(-11.9584 q^{52}\) \(+11.0684 q^{53}\) \(+12.5979 q^{54}\) \(-10.4631 q^{55}\) \(-2.62868 q^{56}\) \(-1.32080 q^{57}\) \(+2.62831 q^{58}\) \(+8.43741 q^{59}\) \(-10.8472 q^{60}\) \(-4.77283 q^{61}\) \(-1.08001 q^{62}\) \(-0.731004 q^{63}\) \(+10.2401 q^{64}\) \(+5.75824 q^{65}\) \(-10.8820 q^{66}\) \(-3.01761 q^{67}\) \(+24.8252 q^{68}\) \(+1.83775 q^{69}\) \(+2.13631 q^{70}\) \(+8.62206 q^{71}\) \(+16.2450 q^{72}\) \(+1.28534 q^{73}\) \(+3.16359 q^{74}\) \(+0.547302 q^{75}\) \(-6.93183 q^{76}\) \(+1.52268 q^{77}\) \(+5.98875 q^{78}\) \(+1.49943 q^{79}\) \(-24.2769 q^{80}\) \(+1.89391 q^{81}\) \(+21.7732 q^{82}\) \(+3.80481 q^{83}\) \(+1.57857 q^{84}\) \(-11.9539 q^{85}\) \(+3.34785 q^{86}\) \(-0.935172 q^{87}\) \(-33.8384 q^{88}\) \(+15.3927 q^{89}\) \(-13.2023 q^{90}\) \(-0.837985 q^{91}\) \(+9.64491 q^{92}\) \(+0.384278 q^{93}\) \(+4.98176 q^{94}\) \(+3.33784 q^{95}\) \(-10.9535 q^{96}\) \(-2.47142 q^{97}\) \(+18.0872 q^{98}\) \(-9.41005 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62831 −1.85849 −0.929247 0.369460i \(-0.879543\pi\)
−0.929247 + 0.369460i \(0.879543\pi\)
\(3\) 0.935172 0.539922 0.269961 0.962871i \(-0.412989\pi\)
0.269961 + 0.962871i \(0.412989\pi\)
\(4\) 4.90799 2.45400
\(5\) −2.36331 −1.05691 −0.528453 0.848963i \(-0.677228\pi\)
−0.528453 + 0.848963i \(0.677228\pi\)
\(6\) −2.45792 −1.00344
\(7\) 0.343928 0.129993 0.0649964 0.997886i \(-0.479296\pi\)
0.0649964 + 0.997886i \(0.479296\pi\)
\(8\) −7.64309 −2.70224
\(9\) −2.12545 −0.708484
\(10\) 6.21151 1.96425
\(11\) 4.42731 1.33489 0.667443 0.744661i \(-0.267389\pi\)
0.667443 + 0.744661i \(0.267389\pi\)
\(12\) 4.58982 1.32497
\(13\) −2.43651 −0.675767 −0.337883 0.941188i \(-0.609711\pi\)
−0.337883 + 0.941188i \(0.609711\pi\)
\(14\) −0.903949 −0.241591
\(15\) −2.21010 −0.570646
\(16\) 10.2724 2.56810
\(17\) 5.05811 1.22677 0.613386 0.789783i \(-0.289807\pi\)
0.613386 + 0.789783i \(0.289807\pi\)
\(18\) 5.58634 1.31671
\(19\) −1.41236 −0.324017 −0.162008 0.986789i \(-0.551797\pi\)
−0.162008 + 0.986789i \(0.551797\pi\)
\(20\) −11.5991 −2.59364
\(21\) 0.321632 0.0701859
\(22\) −11.6363 −2.48087
\(23\) 1.96514 0.409761 0.204880 0.978787i \(-0.434319\pi\)
0.204880 + 0.978787i \(0.434319\pi\)
\(24\) −7.14761 −1.45900
\(25\) 0.585242 0.117048
\(26\) 6.40390 1.25591
\(27\) −4.79318 −0.922448
\(28\) 1.68800 0.319002
\(29\) −1.00000 −0.185695
\(30\) 5.80883 1.06054
\(31\) 0.410917 0.0738028 0.0369014 0.999319i \(-0.488251\pi\)
0.0369014 + 0.999319i \(0.488251\pi\)
\(32\) −11.7128 −2.07056
\(33\) 4.14030 0.720734
\(34\) −13.2943 −2.27995
\(35\) −0.812810 −0.137390
\(36\) −10.4317 −1.73862
\(37\) −1.20366 −0.197880 −0.0989402 0.995093i \(-0.531545\pi\)
−0.0989402 + 0.995093i \(0.531545\pi\)
\(38\) 3.71210 0.602183
\(39\) −2.27856 −0.364861
\(40\) 18.0630 2.85601
\(41\) −8.28410 −1.29376 −0.646880 0.762592i \(-0.723926\pi\)
−0.646880 + 0.762592i \(0.723926\pi\)
\(42\) −0.845348 −0.130440
\(43\) −1.27377 −0.194248 −0.0971240 0.995272i \(-0.530964\pi\)
−0.0971240 + 0.995272i \(0.530964\pi\)
\(44\) 21.7292 3.27580
\(45\) 5.02311 0.748801
\(46\) −5.16500 −0.761537
\(47\) −1.89543 −0.276476 −0.138238 0.990399i \(-0.544144\pi\)
−0.138238 + 0.990399i \(0.544144\pi\)
\(48\) 9.60647 1.38657
\(49\) −6.88171 −0.983102
\(50\) −1.53820 −0.217534
\(51\) 4.73020 0.662361
\(52\) −11.9584 −1.65833
\(53\) 11.0684 1.52036 0.760178 0.649715i \(-0.225112\pi\)
0.760178 + 0.649715i \(0.225112\pi\)
\(54\) 12.5979 1.71436
\(55\) −10.4631 −1.41085
\(56\) −2.62868 −0.351272
\(57\) −1.32080 −0.174944
\(58\) 2.62831 0.345113
\(59\) 8.43741 1.09846 0.549229 0.835672i \(-0.314922\pi\)
0.549229 + 0.835672i \(0.314922\pi\)
\(60\) −10.8472 −1.40036
\(61\) −4.77283 −0.611098 −0.305549 0.952176i \(-0.598840\pi\)
−0.305549 + 0.952176i \(0.598840\pi\)
\(62\) −1.08001 −0.137162
\(63\) −0.731004 −0.0920978
\(64\) 10.2401 1.28001
\(65\) 5.75824 0.714221
\(66\) −10.8820 −1.33948
\(67\) −3.01761 −0.368660 −0.184330 0.982864i \(-0.559011\pi\)
−0.184330 + 0.982864i \(0.559011\pi\)
\(68\) 24.8252 3.01049
\(69\) 1.83775 0.221239
\(70\) 2.13631 0.255338
\(71\) 8.62206 1.02325 0.511625 0.859209i \(-0.329044\pi\)
0.511625 + 0.859209i \(0.329044\pi\)
\(72\) 16.2450 1.91450
\(73\) 1.28534 0.150437 0.0752185 0.997167i \(-0.476035\pi\)
0.0752185 + 0.997167i \(0.476035\pi\)
\(74\) 3.16359 0.367759
\(75\) 0.547302 0.0631970
\(76\) −6.93183 −0.795136
\(77\) 1.52268 0.173525
\(78\) 5.98875 0.678092
\(79\) 1.49943 0.168699 0.0843493 0.996436i \(-0.473119\pi\)
0.0843493 + 0.996436i \(0.473119\pi\)
\(80\) −24.2769 −2.71424
\(81\) 1.89391 0.210435
\(82\) 21.7732 2.40444
\(83\) 3.80481 0.417632 0.208816 0.977955i \(-0.433039\pi\)
0.208816 + 0.977955i \(0.433039\pi\)
\(84\) 1.57857 0.172236
\(85\) −11.9539 −1.29658
\(86\) 3.34785 0.361008
\(87\) −0.935172 −0.100261
\(88\) −33.8384 −3.60718
\(89\) 15.3927 1.63163 0.815814 0.578315i \(-0.196289\pi\)
0.815814 + 0.578315i \(0.196289\pi\)
\(90\) −13.2023 −1.39164
\(91\) −0.837985 −0.0878447
\(92\) 9.64491 1.00555
\(93\) 0.384278 0.0398478
\(94\) 4.98176 0.513829
\(95\) 3.33784 0.342455
\(96\) −10.9535 −1.11794
\(97\) −2.47142 −0.250935 −0.125467 0.992098i \(-0.540043\pi\)
−0.125467 + 0.992098i \(0.540043\pi\)
\(98\) 18.0872 1.82709
\(99\) −9.41005 −0.945745
\(100\) 2.87237 0.287237
\(101\) −8.65643 −0.861347 −0.430673 0.902508i \(-0.641724\pi\)
−0.430673 + 0.902508i \(0.641724\pi\)
\(102\) −12.4324 −1.23099
\(103\) −0.934989 −0.0921272 −0.0460636 0.998939i \(-0.514668\pi\)
−0.0460636 + 0.998939i \(0.514668\pi\)
\(104\) 18.6225 1.82609
\(105\) −0.760117 −0.0741798
\(106\) −29.0910 −2.82557
\(107\) −2.56781 −0.248239 −0.124120 0.992267i \(-0.539611\pi\)
−0.124120 + 0.992267i \(0.539611\pi\)
\(108\) −23.5249 −2.26368
\(109\) −9.54608 −0.914349 −0.457174 0.889377i \(-0.651138\pi\)
−0.457174 + 0.889377i \(0.651138\pi\)
\(110\) 27.5003 2.62205
\(111\) −1.12563 −0.106840
\(112\) 3.53297 0.333834
\(113\) −14.0861 −1.32511 −0.662557 0.749012i \(-0.730529\pi\)
−0.662557 + 0.749012i \(0.730529\pi\)
\(114\) 3.47146 0.325132
\(115\) −4.64425 −0.433078
\(116\) −4.90799 −0.455696
\(117\) 5.17869 0.478770
\(118\) −22.1761 −2.04148
\(119\) 1.73963 0.159471
\(120\) 16.8920 1.54202
\(121\) 8.60110 0.781918
\(122\) 12.5445 1.13572
\(123\) −7.74706 −0.698529
\(124\) 2.01678 0.181112
\(125\) 10.4334 0.933196
\(126\) 1.92130 0.171163
\(127\) 17.5443 1.55681 0.778405 0.627763i \(-0.216029\pi\)
0.778405 + 0.627763i \(0.216029\pi\)
\(128\) −3.48847 −0.308341
\(129\) −1.19119 −0.104879
\(130\) −15.1344 −1.32738
\(131\) −15.7016 −1.37185 −0.685926 0.727671i \(-0.740603\pi\)
−0.685926 + 0.727671i \(0.740603\pi\)
\(132\) 20.3206 1.76868
\(133\) −0.485749 −0.0421198
\(134\) 7.93121 0.685152
\(135\) 11.3278 0.974940
\(136\) −38.6596 −3.31503
\(137\) −13.8369 −1.18217 −0.591084 0.806610i \(-0.701300\pi\)
−0.591084 + 0.806610i \(0.701300\pi\)
\(138\) −4.83016 −0.411171
\(139\) −1.00000 −0.0848189
\(140\) −3.98927 −0.337154
\(141\) −1.77255 −0.149276
\(142\) −22.6614 −1.90170
\(143\) −10.7872 −0.902071
\(144\) −21.8335 −1.81946
\(145\) 2.36331 0.196262
\(146\) −3.37825 −0.279586
\(147\) −6.43559 −0.530798
\(148\) −5.90755 −0.485598
\(149\) 11.0049 0.901558 0.450779 0.892636i \(-0.351146\pi\)
0.450779 + 0.892636i \(0.351146\pi\)
\(150\) −1.43848 −0.117451
\(151\) −10.7938 −0.878390 −0.439195 0.898392i \(-0.644736\pi\)
−0.439195 + 0.898392i \(0.644736\pi\)
\(152\) 10.7948 0.875572
\(153\) −10.7508 −0.869149
\(154\) −4.00207 −0.322496
\(155\) −0.971124 −0.0780026
\(156\) −11.1831 −0.895368
\(157\) 6.44625 0.514466 0.257233 0.966349i \(-0.417189\pi\)
0.257233 + 0.966349i \(0.417189\pi\)
\(158\) −3.94095 −0.313525
\(159\) 10.3508 0.820873
\(160\) 27.6811 2.18838
\(161\) 0.675868 0.0532659
\(162\) −4.97778 −0.391091
\(163\) −11.8070 −0.924797 −0.462399 0.886672i \(-0.653011\pi\)
−0.462399 + 0.886672i \(0.653011\pi\)
\(164\) −40.6583 −3.17488
\(165\) −9.78482 −0.761747
\(166\) −10.0002 −0.776167
\(167\) −1.37241 −0.106201 −0.0531003 0.998589i \(-0.516910\pi\)
−0.0531003 + 0.998589i \(0.516910\pi\)
\(168\) −2.45827 −0.189659
\(169\) −7.06341 −0.543339
\(170\) 31.4185 2.40969
\(171\) 3.00190 0.229561
\(172\) −6.25165 −0.476684
\(173\) −11.4830 −0.873035 −0.436517 0.899696i \(-0.643788\pi\)
−0.436517 + 0.899696i \(0.643788\pi\)
\(174\) 2.45792 0.186334
\(175\) 0.201281 0.0152155
\(176\) 45.4792 3.42812
\(177\) 7.89043 0.593081
\(178\) −40.4568 −3.03237
\(179\) −0.618466 −0.0462263 −0.0231132 0.999733i \(-0.507358\pi\)
−0.0231132 + 0.999733i \(0.507358\pi\)
\(180\) 24.6534 1.83755
\(181\) −14.7884 −1.09921 −0.549607 0.835423i \(-0.685223\pi\)
−0.549607 + 0.835423i \(0.685223\pi\)
\(182\) 2.20248 0.163259
\(183\) −4.46341 −0.329945
\(184\) −15.0198 −1.10727
\(185\) 2.84462 0.209141
\(186\) −1.01000 −0.0740568
\(187\) 22.3938 1.63760
\(188\) −9.30274 −0.678472
\(189\) −1.64851 −0.119912
\(190\) −8.77286 −0.636450
\(191\) −22.4065 −1.62128 −0.810638 0.585547i \(-0.800880\pi\)
−0.810638 + 0.585547i \(0.800880\pi\)
\(192\) 9.57627 0.691108
\(193\) 13.6778 0.984550 0.492275 0.870440i \(-0.336165\pi\)
0.492275 + 0.870440i \(0.336165\pi\)
\(194\) 6.49565 0.466360
\(195\) 5.38494 0.385624
\(196\) −33.7754 −2.41253
\(197\) 9.69504 0.690743 0.345372 0.938466i \(-0.387753\pi\)
0.345372 + 0.938466i \(0.387753\pi\)
\(198\) 24.7325 1.75766
\(199\) −7.34376 −0.520585 −0.260293 0.965530i \(-0.583819\pi\)
−0.260293 + 0.965530i \(0.583819\pi\)
\(200\) −4.47306 −0.316293
\(201\) −2.82199 −0.199048
\(202\) 22.7517 1.60081
\(203\) −0.343928 −0.0241390
\(204\) 23.2158 1.62543
\(205\) 19.5779 1.36738
\(206\) 2.45744 0.171218
\(207\) −4.17682 −0.290309
\(208\) −25.0288 −1.73544
\(209\) −6.25294 −0.432525
\(210\) 1.99782 0.137863
\(211\) −5.79229 −0.398758 −0.199379 0.979922i \(-0.563892\pi\)
−0.199379 + 0.979922i \(0.563892\pi\)
\(212\) 54.3234 3.73095
\(213\) 8.06311 0.552475
\(214\) 6.74898 0.461351
\(215\) 3.01031 0.205302
\(216\) 36.6347 2.49268
\(217\) 0.141326 0.00959383
\(218\) 25.0900 1.69931
\(219\) 1.20201 0.0812243
\(220\) −51.3529 −3.46221
\(221\) −12.3241 −0.829011
\(222\) 2.95850 0.198561
\(223\) −1.39323 −0.0932978 −0.0466489 0.998911i \(-0.514854\pi\)
−0.0466489 + 0.998911i \(0.514854\pi\)
\(224\) −4.02838 −0.269157
\(225\) −1.24391 −0.0829270
\(226\) 37.0227 2.46271
\(227\) 4.47162 0.296792 0.148396 0.988928i \(-0.452589\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(228\) −6.48246 −0.429311
\(229\) 12.0981 0.799465 0.399732 0.916632i \(-0.369103\pi\)
0.399732 + 0.916632i \(0.369103\pi\)
\(230\) 12.2065 0.804873
\(231\) 1.42397 0.0936901
\(232\) 7.64309 0.501794
\(233\) 13.2664 0.869111 0.434555 0.900645i \(-0.356906\pi\)
0.434555 + 0.900645i \(0.356906\pi\)
\(234\) −13.6112 −0.889791
\(235\) 4.47948 0.292209
\(236\) 41.4108 2.69561
\(237\) 1.40222 0.0910841
\(238\) −4.57227 −0.296376
\(239\) −15.6568 −1.01275 −0.506377 0.862312i \(-0.669016\pi\)
−0.506377 + 0.862312i \(0.669016\pi\)
\(240\) −22.7031 −1.46548
\(241\) −2.14541 −0.138198 −0.0690990 0.997610i \(-0.522012\pi\)
−0.0690990 + 0.997610i \(0.522012\pi\)
\(242\) −22.6063 −1.45319
\(243\) 16.1507 1.03607
\(244\) −23.4250 −1.49963
\(245\) 16.2636 1.03905
\(246\) 20.3616 1.29821
\(247\) 3.44122 0.218960
\(248\) −3.14068 −0.199433
\(249\) 3.55815 0.225489
\(250\) −27.4223 −1.73434
\(251\) 0.600131 0.0378799 0.0189400 0.999821i \(-0.493971\pi\)
0.0189400 + 0.999821i \(0.493971\pi\)
\(252\) −3.58776 −0.226008
\(253\) 8.70030 0.546983
\(254\) −46.1119 −2.89332
\(255\) −11.1789 −0.700052
\(256\) −11.3114 −0.706966
\(257\) −6.48982 −0.404824 −0.202412 0.979300i \(-0.564878\pi\)
−0.202412 + 0.979300i \(0.564878\pi\)
\(258\) 3.13082 0.194916
\(259\) −0.413973 −0.0257230
\(260\) 28.2614 1.75270
\(261\) 2.12545 0.131562
\(262\) 41.2685 2.54958
\(263\) −5.76283 −0.355352 −0.177676 0.984089i \(-0.556858\pi\)
−0.177676 + 0.984089i \(0.556858\pi\)
\(264\) −31.6447 −1.94760
\(265\) −26.1580 −1.60687
\(266\) 1.27670 0.0782794
\(267\) 14.3949 0.880951
\(268\) −14.8104 −0.904690
\(269\) −3.31761 −0.202278 −0.101139 0.994872i \(-0.532249\pi\)
−0.101139 + 0.994872i \(0.532249\pi\)
\(270\) −29.7729 −1.81192
\(271\) −2.88698 −0.175372 −0.0876859 0.996148i \(-0.527947\pi\)
−0.0876859 + 0.996148i \(0.527947\pi\)
\(272\) 51.9590 3.15047
\(273\) −0.783661 −0.0474293
\(274\) 36.3677 2.19705
\(275\) 2.59105 0.156246
\(276\) 9.01965 0.542919
\(277\) 14.3044 0.859469 0.429734 0.902955i \(-0.358607\pi\)
0.429734 + 0.902955i \(0.358607\pi\)
\(278\) 2.62831 0.157635
\(279\) −0.873384 −0.0522882
\(280\) 6.21238 0.371261
\(281\) −19.6101 −1.16984 −0.584919 0.811092i \(-0.698874\pi\)
−0.584919 + 0.811092i \(0.698874\pi\)
\(282\) 4.65880 0.277428
\(283\) −6.04611 −0.359404 −0.179702 0.983721i \(-0.557513\pi\)
−0.179702 + 0.983721i \(0.557513\pi\)
\(284\) 42.3170 2.51105
\(285\) 3.12145 0.184899
\(286\) 28.3521 1.67649
\(287\) −2.84914 −0.168179
\(288\) 24.8951 1.46696
\(289\) 8.58446 0.504968
\(290\) −6.21151 −0.364752
\(291\) −2.31120 −0.135485
\(292\) 6.30842 0.369172
\(293\) 7.13013 0.416547 0.208273 0.978071i \(-0.433216\pi\)
0.208273 + 0.978071i \(0.433216\pi\)
\(294\) 16.9147 0.986485
\(295\) −19.9402 −1.16097
\(296\) 9.19968 0.534721
\(297\) −21.2209 −1.23136
\(298\) −28.9243 −1.67554
\(299\) −4.78809 −0.276903
\(300\) 2.68616 0.155085
\(301\) −0.438085 −0.0252508
\(302\) 28.3695 1.63248
\(303\) −8.09525 −0.465060
\(304\) −14.5083 −0.832108
\(305\) 11.2797 0.645873
\(306\) 28.2563 1.61531
\(307\) −21.6699 −1.23677 −0.618384 0.785876i \(-0.712212\pi\)
−0.618384 + 0.785876i \(0.712212\pi\)
\(308\) 7.47330 0.425831
\(309\) −0.874376 −0.0497415
\(310\) 2.55241 0.144967
\(311\) 8.99244 0.509915 0.254957 0.966952i \(-0.417939\pi\)
0.254957 + 0.966952i \(0.417939\pi\)
\(312\) 17.4152 0.985943
\(313\) 9.51385 0.537755 0.268877 0.963174i \(-0.413347\pi\)
0.268877 + 0.963174i \(0.413347\pi\)
\(314\) −16.9427 −0.956132
\(315\) 1.72759 0.0973386
\(316\) 7.35917 0.413986
\(317\) −12.8457 −0.721484 −0.360742 0.932666i \(-0.617476\pi\)
−0.360742 + 0.932666i \(0.617476\pi\)
\(318\) −27.2051 −1.52559
\(319\) −4.42731 −0.247882
\(320\) −24.2006 −1.35285
\(321\) −2.40134 −0.134030
\(322\) −1.77639 −0.0989943
\(323\) −7.14385 −0.397495
\(324\) 9.29530 0.516406
\(325\) −1.42595 −0.0790975
\(326\) 31.0325 1.71873
\(327\) −8.92723 −0.493677
\(328\) 63.3162 3.49605
\(329\) −0.651891 −0.0359399
\(330\) 25.7175 1.41570
\(331\) −23.5705 −1.29555 −0.647777 0.761830i \(-0.724301\pi\)
−0.647777 + 0.761830i \(0.724301\pi\)
\(332\) 18.6740 1.02487
\(333\) 2.55832 0.140195
\(334\) 3.60713 0.197373
\(335\) 7.13156 0.389639
\(336\) 3.30394 0.180245
\(337\) −12.3825 −0.674516 −0.337258 0.941412i \(-0.609499\pi\)
−0.337258 + 0.941412i \(0.609499\pi\)
\(338\) 18.5648 1.00979
\(339\) −13.1730 −0.715458
\(340\) −58.6696 −3.18181
\(341\) 1.81926 0.0985183
\(342\) −7.88990 −0.426637
\(343\) −4.77431 −0.257789
\(344\) 9.73554 0.524905
\(345\) −4.34317 −0.233828
\(346\) 30.1808 1.62253
\(347\) −29.4210 −1.57940 −0.789700 0.613493i \(-0.789764\pi\)
−0.789700 + 0.613493i \(0.789764\pi\)
\(348\) −4.58982 −0.246040
\(349\) 23.9935 1.28434 0.642171 0.766561i \(-0.278034\pi\)
0.642171 + 0.766561i \(0.278034\pi\)
\(350\) −0.529029 −0.0282778
\(351\) 11.6786 0.623360
\(352\) −51.8564 −2.76396
\(353\) 10.9643 0.583569 0.291785 0.956484i \(-0.405751\pi\)
0.291785 + 0.956484i \(0.405751\pi\)
\(354\) −20.7385 −1.10224
\(355\) −20.3766 −1.08148
\(356\) 75.5475 4.00401
\(357\) 1.62685 0.0861021
\(358\) 1.62552 0.0859113
\(359\) 13.2791 0.700845 0.350422 0.936592i \(-0.386038\pi\)
0.350422 + 0.936592i \(0.386038\pi\)
\(360\) −38.3921 −2.02344
\(361\) −17.0052 −0.895013
\(362\) 38.8685 2.04288
\(363\) 8.04351 0.422175
\(364\) −4.11283 −0.215571
\(365\) −3.03765 −0.158998
\(366\) 11.7312 0.613201
\(367\) −13.5100 −0.705214 −0.352607 0.935772i \(-0.614705\pi\)
−0.352607 + 0.935772i \(0.614705\pi\)
\(368\) 20.1868 1.05231
\(369\) 17.6075 0.916608
\(370\) −7.47654 −0.388687
\(371\) 3.80672 0.197635
\(372\) 1.88603 0.0977863
\(373\) 1.16663 0.0604059 0.0302030 0.999544i \(-0.490385\pi\)
0.0302030 + 0.999544i \(0.490385\pi\)
\(374\) −58.8578 −3.04347
\(375\) 9.75707 0.503853
\(376\) 14.4869 0.747106
\(377\) 2.43651 0.125487
\(378\) 4.33279 0.222855
\(379\) −14.0363 −0.720997 −0.360498 0.932760i \(-0.617393\pi\)
−0.360498 + 0.932760i \(0.617393\pi\)
\(380\) 16.3821 0.840383
\(381\) 16.4070 0.840555
\(382\) 58.8911 3.01313
\(383\) 8.90894 0.455226 0.227613 0.973752i \(-0.426908\pi\)
0.227613 + 0.973752i \(0.426908\pi\)
\(384\) −3.26232 −0.166480
\(385\) −3.59856 −0.183400
\(386\) −35.9495 −1.82978
\(387\) 2.70734 0.137622
\(388\) −12.1297 −0.615793
\(389\) −12.5763 −0.637642 −0.318821 0.947815i \(-0.603287\pi\)
−0.318821 + 0.947815i \(0.603287\pi\)
\(390\) −14.1533 −0.716679
\(391\) 9.93991 0.502683
\(392\) 52.5976 2.65658
\(393\) −14.6837 −0.740693
\(394\) −25.4815 −1.28374
\(395\) −3.54361 −0.178298
\(396\) −46.1844 −2.32086
\(397\) −29.2307 −1.46705 −0.733524 0.679664i \(-0.762126\pi\)
−0.733524 + 0.679664i \(0.762126\pi\)
\(398\) 19.3016 0.967504
\(399\) −0.454259 −0.0227414
\(400\) 6.01185 0.300592
\(401\) −33.4939 −1.67260 −0.836302 0.548269i \(-0.815287\pi\)
−0.836302 + 0.548269i \(0.815287\pi\)
\(402\) 7.41704 0.369928
\(403\) −1.00120 −0.0498735
\(404\) −42.4857 −2.11374
\(405\) −4.47590 −0.222409
\(406\) 0.903949 0.0448622
\(407\) −5.32898 −0.264148
\(408\) −36.1534 −1.78986
\(409\) −2.18589 −0.108085 −0.0540426 0.998539i \(-0.517211\pi\)
−0.0540426 + 0.998539i \(0.517211\pi\)
\(410\) −51.4568 −2.54127
\(411\) −12.9399 −0.638279
\(412\) −4.58892 −0.226080
\(413\) 2.90187 0.142791
\(414\) 10.9780 0.539537
\(415\) −8.99196 −0.441398
\(416\) 28.5385 1.39921
\(417\) −0.935172 −0.0457956
\(418\) 16.4346 0.803845
\(419\) −20.3932 −0.996271 −0.498135 0.867099i \(-0.665982\pi\)
−0.498135 + 0.867099i \(0.665982\pi\)
\(420\) −3.73065 −0.182037
\(421\) −7.13279 −0.347631 −0.173816 0.984778i \(-0.555610\pi\)
−0.173816 + 0.984778i \(0.555610\pi\)
\(422\) 15.2239 0.741089
\(423\) 4.02864 0.195879
\(424\) −84.5965 −4.10837
\(425\) 2.96022 0.143592
\(426\) −21.1923 −1.02677
\(427\) −1.64151 −0.0794383
\(428\) −12.6028 −0.609178
\(429\) −10.0879 −0.487048
\(430\) −7.91202 −0.381552
\(431\) −20.0149 −0.964084 −0.482042 0.876148i \(-0.660105\pi\)
−0.482042 + 0.876148i \(0.660105\pi\)
\(432\) −49.2375 −2.36894
\(433\) 4.12398 0.198186 0.0990928 0.995078i \(-0.468406\pi\)
0.0990928 + 0.995078i \(0.468406\pi\)
\(434\) −0.371448 −0.0178301
\(435\) 2.21010 0.105966
\(436\) −46.8521 −2.24381
\(437\) −2.77548 −0.132769
\(438\) −3.15925 −0.150955
\(439\) −30.0141 −1.43249 −0.716247 0.697847i \(-0.754142\pi\)
−0.716247 + 0.697847i \(0.754142\pi\)
\(440\) 79.9706 3.81245
\(441\) 14.6268 0.696512
\(442\) 32.3916 1.54071
\(443\) −4.56016 −0.216660 −0.108330 0.994115i \(-0.534550\pi\)
−0.108330 + 0.994115i \(0.534550\pi\)
\(444\) −5.52458 −0.262185
\(445\) −36.3778 −1.72448
\(446\) 3.66184 0.173393
\(447\) 10.2915 0.486771
\(448\) 3.52187 0.166393
\(449\) 8.95557 0.422640 0.211320 0.977417i \(-0.432224\pi\)
0.211320 + 0.977417i \(0.432224\pi\)
\(450\) 3.26936 0.154119
\(451\) −36.6763 −1.72702
\(452\) −69.1347 −3.25182
\(453\) −10.0941 −0.474262
\(454\) −11.7528 −0.551586
\(455\) 1.98042 0.0928436
\(456\) 10.0950 0.472740
\(457\) 22.5126 1.05310 0.526549 0.850145i \(-0.323486\pi\)
0.526549 + 0.850145i \(0.323486\pi\)
\(458\) −31.7975 −1.48580
\(459\) −24.2444 −1.13163
\(460\) −22.7939 −1.06277
\(461\) −3.32266 −0.154752 −0.0773758 0.997002i \(-0.524654\pi\)
−0.0773758 + 0.997002i \(0.524654\pi\)
\(462\) −3.74262 −0.174122
\(463\) −8.73764 −0.406073 −0.203036 0.979171i \(-0.565081\pi\)
−0.203036 + 0.979171i \(0.565081\pi\)
\(464\) −10.2724 −0.476885
\(465\) −0.908168 −0.0421153
\(466\) −34.8682 −1.61524
\(467\) −17.8064 −0.823980 −0.411990 0.911188i \(-0.635166\pi\)
−0.411990 + 0.911188i \(0.635166\pi\)
\(468\) 25.4170 1.17490
\(469\) −1.03784 −0.0479231
\(470\) −11.7735 −0.543069
\(471\) 6.02835 0.277772
\(472\) −64.4879 −2.96830
\(473\) −5.63937 −0.259299
\(474\) −3.68547 −0.169279
\(475\) −0.826571 −0.0379257
\(476\) 8.53808 0.391342
\(477\) −23.5253 −1.07715
\(478\) 41.1509 1.88220
\(479\) −41.4867 −1.89558 −0.947788 0.318900i \(-0.896687\pi\)
−0.947788 + 0.318900i \(0.896687\pi\)
\(480\) 25.8866 1.18156
\(481\) 2.93273 0.133721
\(482\) 5.63879 0.256840
\(483\) 0.632053 0.0287594
\(484\) 42.2141 1.91882
\(485\) 5.84074 0.265214
\(486\) −42.4489 −1.92552
\(487\) −16.1437 −0.731539 −0.365770 0.930705i \(-0.619194\pi\)
−0.365770 + 0.930705i \(0.619194\pi\)
\(488\) 36.4792 1.65133
\(489\) −11.0416 −0.499318
\(490\) −42.7458 −1.93106
\(491\) −10.5206 −0.474790 −0.237395 0.971413i \(-0.576294\pi\)
−0.237395 + 0.971413i \(0.576294\pi\)
\(492\) −38.0225 −1.71419
\(493\) −5.05811 −0.227806
\(494\) −9.04459 −0.406935
\(495\) 22.2389 0.999563
\(496\) 4.22110 0.189533
\(497\) 2.96537 0.133015
\(498\) −9.35192 −0.419069
\(499\) 14.0505 0.628986 0.314493 0.949260i \(-0.398165\pi\)
0.314493 + 0.949260i \(0.398165\pi\)
\(500\) 51.2073 2.29006
\(501\) −1.28344 −0.0573401
\(502\) −1.57733 −0.0703995
\(503\) 34.6649 1.54563 0.772815 0.634632i \(-0.218848\pi\)
0.772815 + 0.634632i \(0.218848\pi\)
\(504\) 5.58713 0.248871
\(505\) 20.4578 0.910362
\(506\) −22.8671 −1.01656
\(507\) −6.60550 −0.293361
\(508\) 86.1075 3.82040
\(509\) −7.33670 −0.325194 −0.162597 0.986693i \(-0.551987\pi\)
−0.162597 + 0.986693i \(0.551987\pi\)
\(510\) 29.3817 1.30104
\(511\) 0.442063 0.0195557
\(512\) 36.7069 1.62223
\(513\) 6.76968 0.298889
\(514\) 17.0572 0.752362
\(515\) 2.20967 0.0973697
\(516\) −5.84637 −0.257372
\(517\) −8.39165 −0.369064
\(518\) 1.08805 0.0478060
\(519\) −10.7386 −0.471370
\(520\) −44.0107 −1.93000
\(521\) 40.0828 1.75606 0.878029 0.478608i \(-0.158858\pi\)
0.878029 + 0.478608i \(0.158858\pi\)
\(522\) −5.58634 −0.244508
\(523\) −14.3247 −0.626374 −0.313187 0.949691i \(-0.601397\pi\)
−0.313187 + 0.949691i \(0.601397\pi\)
\(524\) −77.0632 −3.36652
\(525\) 0.188233 0.00821515
\(526\) 15.1465 0.660419
\(527\) 2.07846 0.0905392
\(528\) 42.5308 1.85092
\(529\) −19.1382 −0.832096
\(530\) 68.7511 2.98636
\(531\) −17.9333 −0.778240
\(532\) −2.38405 −0.103362
\(533\) 20.1843 0.874279
\(534\) −37.8341 −1.63724
\(535\) 6.06853 0.262365
\(536\) 23.0639 0.996208
\(537\) −0.578372 −0.0249586
\(538\) 8.71968 0.375932
\(539\) −30.4675 −1.31233
\(540\) 55.5967 2.39250
\(541\) 29.7731 1.28004 0.640022 0.768356i \(-0.278925\pi\)
0.640022 + 0.768356i \(0.278925\pi\)
\(542\) 7.58787 0.325927
\(543\) −13.8297 −0.593490
\(544\) −59.2448 −2.54010
\(545\) 22.5604 0.966380
\(546\) 2.05970 0.0881470
\(547\) 7.00405 0.299472 0.149736 0.988726i \(-0.452158\pi\)
0.149736 + 0.988726i \(0.452158\pi\)
\(548\) −67.9115 −2.90104
\(549\) 10.1444 0.432953
\(550\) −6.81008 −0.290383
\(551\) 1.41236 0.0601684
\(552\) −14.0461 −0.597841
\(553\) 0.515695 0.0219296
\(554\) −37.5964 −1.59732
\(555\) 2.66021 0.112920
\(556\) −4.90799 −0.208145
\(557\) −17.8046 −0.754407 −0.377204 0.926130i \(-0.623114\pi\)
−0.377204 + 0.926130i \(0.623114\pi\)
\(558\) 2.29552 0.0971772
\(559\) 3.10355 0.131266
\(560\) −8.34951 −0.352831
\(561\) 20.9421 0.884175
\(562\) 51.5413 2.17414
\(563\) −1.26512 −0.0533185 −0.0266592 0.999645i \(-0.508487\pi\)
−0.0266592 + 0.999645i \(0.508487\pi\)
\(564\) −8.69966 −0.366322
\(565\) 33.2900 1.40052
\(566\) 15.8910 0.667950
\(567\) 0.651370 0.0273550
\(568\) −65.8993 −2.76507
\(569\) −42.2205 −1.76998 −0.884988 0.465614i \(-0.845834\pi\)
−0.884988 + 0.465614i \(0.845834\pi\)
\(570\) −8.20413 −0.343633
\(571\) −16.3627 −0.684757 −0.342379 0.939562i \(-0.611233\pi\)
−0.342379 + 0.939562i \(0.611233\pi\)
\(572\) −52.9435 −2.21368
\(573\) −20.9539 −0.875362
\(574\) 7.48841 0.312560
\(575\) 1.15009 0.0479619
\(576\) −21.7649 −0.906870
\(577\) −1.54929 −0.0644980 −0.0322490 0.999480i \(-0.510267\pi\)
−0.0322490 + 0.999480i \(0.510267\pi\)
\(578\) −22.5626 −0.938480
\(579\) 12.7911 0.531580
\(580\) 11.5991 0.481627
\(581\) 1.30858 0.0542892
\(582\) 6.07455 0.251798
\(583\) 49.0031 2.02950
\(584\) −9.82394 −0.406517
\(585\) −12.2389 −0.506015
\(586\) −18.7402 −0.774149
\(587\) 24.9553 1.03002 0.515009 0.857185i \(-0.327789\pi\)
0.515009 + 0.857185i \(0.327789\pi\)
\(588\) −31.5858 −1.30258
\(589\) −0.580361 −0.0239134
\(590\) 52.4090 2.15765
\(591\) 9.06653 0.372947
\(592\) −12.3645 −0.508177
\(593\) −19.8936 −0.816932 −0.408466 0.912773i \(-0.633936\pi\)
−0.408466 + 0.912773i \(0.633936\pi\)
\(594\) 55.7750 2.28848
\(595\) −4.11128 −0.168546
\(596\) 54.0120 2.21242
\(597\) −6.86768 −0.281075
\(598\) 12.5846 0.514622
\(599\) 10.1041 0.412843 0.206422 0.978463i \(-0.433818\pi\)
0.206422 + 0.978463i \(0.433818\pi\)
\(600\) −4.18308 −0.170774
\(601\) −48.6642 −1.98505 −0.992527 0.122029i \(-0.961060\pi\)
−0.992527 + 0.122029i \(0.961060\pi\)
\(602\) 1.15142 0.0469285
\(603\) 6.41379 0.261190
\(604\) −52.9761 −2.15557
\(605\) −20.3271 −0.826413
\(606\) 21.2768 0.864311
\(607\) 9.53920 0.387184 0.193592 0.981082i \(-0.437986\pi\)
0.193592 + 0.981082i \(0.437986\pi\)
\(608\) 16.5427 0.670895
\(609\) −0.321632 −0.0130332
\(610\) −29.6464 −1.20035
\(611\) 4.61823 0.186834
\(612\) −52.7647 −2.13289
\(613\) −20.2305 −0.817104 −0.408552 0.912735i \(-0.633966\pi\)
−0.408552 + 0.912735i \(0.633966\pi\)
\(614\) 56.9552 2.29853
\(615\) 18.3087 0.738279
\(616\) −11.6380 −0.468907
\(617\) 48.8716 1.96750 0.983749 0.179550i \(-0.0574640\pi\)
0.983749 + 0.179550i \(0.0574640\pi\)
\(618\) 2.29813 0.0924442
\(619\) −13.2726 −0.533472 −0.266736 0.963770i \(-0.585945\pi\)
−0.266736 + 0.963770i \(0.585945\pi\)
\(620\) −4.76627 −0.191418
\(621\) −9.41929 −0.377983
\(622\) −23.6349 −0.947673
\(623\) 5.29400 0.212100
\(624\) −23.4063 −0.937001
\(625\) −27.5837 −1.10335
\(626\) −25.0053 −0.999413
\(627\) −5.84758 −0.233530
\(628\) 31.6381 1.26250
\(629\) −6.08824 −0.242754
\(630\) −4.54063 −0.180903
\(631\) −35.5430 −1.41494 −0.707472 0.706742i \(-0.750164\pi\)
−0.707472 + 0.706742i \(0.750164\pi\)
\(632\) −11.4603 −0.455865
\(633\) −5.41679 −0.215298
\(634\) 33.7623 1.34087
\(635\) −41.4628 −1.64540
\(636\) 50.8017 2.01442
\(637\) 16.7674 0.664348
\(638\) 11.6363 0.460687
\(639\) −18.3258 −0.724957
\(640\) 8.24435 0.325887
\(641\) 35.3938 1.39797 0.698986 0.715135i \(-0.253635\pi\)
0.698986 + 0.715135i \(0.253635\pi\)
\(642\) 6.31146 0.249093
\(643\) −15.6360 −0.616625 −0.308312 0.951285i \(-0.599764\pi\)
−0.308312 + 0.951285i \(0.599764\pi\)
\(644\) 3.31716 0.130714
\(645\) 2.81516 0.110847
\(646\) 18.7762 0.738741
\(647\) 1.57843 0.0620546 0.0310273 0.999519i \(-0.490122\pi\)
0.0310273 + 0.999519i \(0.490122\pi\)
\(648\) −14.4753 −0.568645
\(649\) 37.3551 1.46631
\(650\) 3.74783 0.147002
\(651\) 0.132164 0.00517992
\(652\) −57.9488 −2.26945
\(653\) 34.7245 1.35887 0.679437 0.733734i \(-0.262224\pi\)
0.679437 + 0.733734i \(0.262224\pi\)
\(654\) 23.4635 0.917495
\(655\) 37.1077 1.44992
\(656\) −85.0977 −3.32251
\(657\) −2.73192 −0.106582
\(658\) 1.71337 0.0667941
\(659\) −43.3835 −1.68998 −0.844991 0.534781i \(-0.820394\pi\)
−0.844991 + 0.534781i \(0.820394\pi\)
\(660\) −48.0238 −1.86932
\(661\) 19.3222 0.751548 0.375774 0.926711i \(-0.377377\pi\)
0.375774 + 0.926711i \(0.377377\pi\)
\(662\) 61.9506 2.40778
\(663\) −11.5252 −0.447601
\(664\) −29.0805 −1.12854
\(665\) 1.14798 0.0445166
\(666\) −6.72405 −0.260552
\(667\) −1.96514 −0.0760906
\(668\) −6.73580 −0.260616
\(669\) −1.30291 −0.0503735
\(670\) −18.7439 −0.724140
\(671\) −21.1308 −0.815746
\(672\) −3.76723 −0.145324
\(673\) −35.9844 −1.38710 −0.693549 0.720410i \(-0.743954\pi\)
−0.693549 + 0.720410i \(0.743954\pi\)
\(674\) 32.5449 1.25358
\(675\) −2.80517 −0.107971
\(676\) −34.6672 −1.33335
\(677\) 25.4825 0.979372 0.489686 0.871899i \(-0.337111\pi\)
0.489686 + 0.871899i \(0.337111\pi\)
\(678\) 34.6226 1.32967
\(679\) −0.849991 −0.0326197
\(680\) 91.3647 3.50368
\(681\) 4.18174 0.160244
\(682\) −4.78156 −0.183096
\(683\) −6.35577 −0.243197 −0.121598 0.992579i \(-0.538802\pi\)
−0.121598 + 0.992579i \(0.538802\pi\)
\(684\) 14.7333 0.563341
\(685\) 32.7010 1.24944
\(686\) 12.5484 0.479099
\(687\) 11.3138 0.431648
\(688\) −13.0847 −0.498848
\(689\) −26.9682 −1.02741
\(690\) 11.4152 0.434568
\(691\) 7.41721 0.282164 0.141082 0.989998i \(-0.454942\pi\)
0.141082 + 0.989998i \(0.454942\pi\)
\(692\) −56.3584 −2.14242
\(693\) −3.23638 −0.122940
\(694\) 77.3273 2.93530
\(695\) 2.36331 0.0896455
\(696\) 7.14761 0.270929
\(697\) −41.9019 −1.58715
\(698\) −63.0622 −2.38694
\(699\) 12.4064 0.469252
\(700\) 0.987888 0.0373387
\(701\) −50.4375 −1.90500 −0.952499 0.304543i \(-0.901496\pi\)
−0.952499 + 0.304543i \(0.901496\pi\)
\(702\) −30.6950 −1.15851
\(703\) 1.70000 0.0641166
\(704\) 45.3362 1.70867
\(705\) 4.18909 0.157770
\(706\) −28.8175 −1.08456
\(707\) −2.97719 −0.111969
\(708\) 38.7262 1.45542
\(709\) −8.75843 −0.328930 −0.164465 0.986383i \(-0.552590\pi\)
−0.164465 + 0.986383i \(0.552590\pi\)
\(710\) 53.5560 2.00992
\(711\) −3.18696 −0.119520
\(712\) −117.648 −4.40905
\(713\) 0.807510 0.0302415
\(714\) −4.27586 −0.160020
\(715\) 25.4935 0.953403
\(716\) −3.03543 −0.113439
\(717\) −14.6418 −0.546808
\(718\) −34.9016 −1.30251
\(719\) −22.9135 −0.854528 −0.427264 0.904127i \(-0.640523\pi\)
−0.427264 + 0.904127i \(0.640523\pi\)
\(720\) 51.5994 1.92300
\(721\) −0.321569 −0.0119759
\(722\) 44.6950 1.66338
\(723\) −2.00633 −0.0746161
\(724\) −72.5814 −2.69747
\(725\) −0.585242 −0.0217354
\(726\) −21.1408 −0.784609
\(727\) −36.8514 −1.36674 −0.683371 0.730071i \(-0.739487\pi\)
−0.683371 + 0.730071i \(0.739487\pi\)
\(728\) 6.40480 0.237378
\(729\) 9.42192 0.348960
\(730\) 7.98387 0.295496
\(731\) −6.44286 −0.238298
\(732\) −21.9064 −0.809684
\(733\) 18.6553 0.689048 0.344524 0.938778i \(-0.388040\pi\)
0.344524 + 0.938778i \(0.388040\pi\)
\(734\) 35.5083 1.31064
\(735\) 15.2093 0.561003
\(736\) −23.0174 −0.848433
\(737\) −13.3599 −0.492119
\(738\) −46.2778 −1.70351
\(739\) −23.8037 −0.875632 −0.437816 0.899065i \(-0.644248\pi\)
−0.437816 + 0.899065i \(0.644248\pi\)
\(740\) 13.9614 0.513231
\(741\) 3.21813 0.118221
\(742\) −10.0052 −0.367303
\(743\) 23.7484 0.871244 0.435622 0.900130i \(-0.356528\pi\)
0.435622 + 0.900130i \(0.356528\pi\)
\(744\) −2.93707 −0.107678
\(745\) −26.0080 −0.952861
\(746\) −3.06627 −0.112264
\(747\) −8.08695 −0.295886
\(748\) 109.909 4.01866
\(749\) −0.883141 −0.0322693
\(750\) −25.6446 −0.936407
\(751\) 25.7950 0.941274 0.470637 0.882327i \(-0.344024\pi\)
0.470637 + 0.882327i \(0.344024\pi\)
\(752\) −19.4706 −0.710019
\(753\) 0.561225 0.0204522
\(754\) −6.40390 −0.233216
\(755\) 25.5092 0.928375
\(756\) −8.09088 −0.294262
\(757\) −20.3783 −0.740662 −0.370331 0.928900i \(-0.620756\pi\)
−0.370331 + 0.928900i \(0.620756\pi\)
\(758\) 36.8917 1.33997
\(759\) 8.13628 0.295328
\(760\) −25.5114 −0.925396
\(761\) −5.83281 −0.211439 −0.105720 0.994396i \(-0.533715\pi\)
−0.105720 + 0.994396i \(0.533715\pi\)
\(762\) −43.1226 −1.56217
\(763\) −3.28317 −0.118859
\(764\) −109.971 −3.97861
\(765\) 25.4074 0.918608
\(766\) −23.4154 −0.846033
\(767\) −20.5579 −0.742301
\(768\) −10.5782 −0.381706
\(769\) 36.2613 1.30762 0.653808 0.756660i \(-0.273170\pi\)
0.653808 + 0.756660i \(0.273170\pi\)
\(770\) 9.45813 0.340847
\(771\) −6.06910 −0.218573
\(772\) 67.1306 2.41608
\(773\) 40.8478 1.46919 0.734597 0.678504i \(-0.237371\pi\)
0.734597 + 0.678504i \(0.237371\pi\)
\(774\) −7.11571 −0.255769
\(775\) 0.240486 0.00863851
\(776\) 18.8893 0.678086
\(777\) −0.387136 −0.0138884
\(778\) 33.0543 1.18505
\(779\) 11.7001 0.419200
\(780\) 26.4293 0.946319
\(781\) 38.1726 1.36592
\(782\) −26.1251 −0.934232
\(783\) 4.79318 0.171294
\(784\) −70.6918 −2.52471
\(785\) −15.2345 −0.543742
\(786\) 38.5932 1.37657
\(787\) 38.3941 1.36860 0.684301 0.729200i \(-0.260108\pi\)
0.684301 + 0.729200i \(0.260108\pi\)
\(788\) 47.5832 1.69508
\(789\) −5.38924 −0.191862
\(790\) 9.31370 0.331366
\(791\) −4.84463 −0.172255
\(792\) 71.9219 2.55563
\(793\) 11.6290 0.412960
\(794\) 76.8272 2.72650
\(795\) −24.4622 −0.867585
\(796\) −36.0431 −1.27751
\(797\) −15.1324 −0.536017 −0.268009 0.963417i \(-0.586366\pi\)
−0.268009 + 0.963417i \(0.586366\pi\)
\(798\) 1.19393 0.0422647
\(799\) −9.58727 −0.339173
\(800\) −6.85485 −0.242356
\(801\) −32.7166 −1.15598
\(802\) 88.0321 3.10852
\(803\) 5.69058 0.200816
\(804\) −13.8503 −0.488462
\(805\) −1.59729 −0.0562970
\(806\) 2.63147 0.0926895
\(807\) −3.10253 −0.109214
\(808\) 66.1619 2.32757
\(809\) 22.5955 0.794415 0.397207 0.917729i \(-0.369979\pi\)
0.397207 + 0.917729i \(0.369979\pi\)
\(810\) 11.7640 0.413346
\(811\) 45.2936 1.59047 0.795237 0.606299i \(-0.207347\pi\)
0.795237 + 0.606299i \(0.207347\pi\)
\(812\) −1.68800 −0.0592371
\(813\) −2.69983 −0.0946870
\(814\) 14.0062 0.490917
\(815\) 27.9037 0.977423
\(816\) 48.5906 1.70101
\(817\) 1.79902 0.0629396
\(818\) 5.74519 0.200876
\(819\) 1.78110 0.0622366
\(820\) 96.0883 3.35555
\(821\) 31.2674 1.09124 0.545620 0.838033i \(-0.316294\pi\)
0.545620 + 0.838033i \(0.316294\pi\)
\(822\) 34.0100 1.18624
\(823\) −24.5296 −0.855050 −0.427525 0.904004i \(-0.640614\pi\)
−0.427525 + 0.904004i \(0.640614\pi\)
\(824\) 7.14621 0.248950
\(825\) 2.42308 0.0843608
\(826\) −7.62699 −0.265377
\(827\) −36.6656 −1.27499 −0.637493 0.770456i \(-0.720029\pi\)
−0.637493 + 0.770456i \(0.720029\pi\)
\(828\) −20.4998 −0.712417
\(829\) 38.4943 1.33696 0.668482 0.743729i \(-0.266944\pi\)
0.668482 + 0.743729i \(0.266944\pi\)
\(830\) 23.6336 0.820335
\(831\) 13.3771 0.464046
\(832\) −24.9502 −0.864991
\(833\) −34.8085 −1.20604
\(834\) 2.45792 0.0851108
\(835\) 3.24344 0.112244
\(836\) −30.6894 −1.06142
\(837\) −1.96960 −0.0680793
\(838\) 53.5994 1.85156
\(839\) 27.3836 0.945388 0.472694 0.881227i \(-0.343282\pi\)
0.472694 + 0.881227i \(0.343282\pi\)
\(840\) 5.80965 0.200452
\(841\) 1.00000 0.0344828
\(842\) 18.7472 0.646070
\(843\) −18.3388 −0.631621
\(844\) −28.4285 −0.978551
\(845\) 16.6930 0.574258
\(846\) −10.5885 −0.364040
\(847\) 2.95816 0.101644
\(848\) 113.699 3.90443
\(849\) −5.65415 −0.194050
\(850\) −7.78036 −0.266864
\(851\) −2.36536 −0.0810836
\(852\) 39.5737 1.35577
\(853\) −4.82861 −0.165329 −0.0826643 0.996577i \(-0.526343\pi\)
−0.0826643 + 0.996577i \(0.526343\pi\)
\(854\) 4.31439 0.147635
\(855\) −7.09442 −0.242624
\(856\) 19.6260 0.670802
\(857\) −10.9199 −0.373018 −0.186509 0.982453i \(-0.559717\pi\)
−0.186509 + 0.982453i \(0.559717\pi\)
\(858\) 26.5141 0.905175
\(859\) 34.0506 1.16179 0.580896 0.813978i \(-0.302702\pi\)
0.580896 + 0.813978i \(0.302702\pi\)
\(860\) 14.7746 0.503809
\(861\) −2.66443 −0.0908037
\(862\) 52.6053 1.79174
\(863\) 0.410447 0.0139718 0.00698589 0.999976i \(-0.497776\pi\)
0.00698589 + 0.999976i \(0.497776\pi\)
\(864\) 56.1418 1.90998
\(865\) 27.1379 0.922715
\(866\) −10.8391 −0.368327
\(867\) 8.02795 0.272643
\(868\) 0.693627 0.0235432
\(869\) 6.63843 0.225193
\(870\) −5.80883 −0.196938
\(871\) 7.35244 0.249128
\(872\) 72.9616 2.47079
\(873\) 5.25289 0.177783
\(874\) 7.29482 0.246751
\(875\) 3.58836 0.121309
\(876\) 5.89945 0.199324
\(877\) 36.6213 1.23661 0.618307 0.785936i \(-0.287819\pi\)
0.618307 + 0.785936i \(0.287819\pi\)
\(878\) 78.8862 2.66228
\(879\) 6.66790 0.224903
\(880\) −107.481 −3.62320
\(881\) −13.7395 −0.462897 −0.231448 0.972847i \(-0.574346\pi\)
−0.231448 + 0.972847i \(0.574346\pi\)
\(882\) −38.4436 −1.29446
\(883\) −14.6612 −0.493389 −0.246694 0.969093i \(-0.579344\pi\)
−0.246694 + 0.969093i \(0.579344\pi\)
\(884\) −60.4868 −2.03439
\(885\) −18.6475 −0.626831
\(886\) 11.9855 0.402661
\(887\) −41.9019 −1.40693 −0.703465 0.710730i \(-0.748365\pi\)
−0.703465 + 0.710730i \(0.748365\pi\)
\(888\) 8.60329 0.288707
\(889\) 6.03400 0.202374
\(890\) 95.6121 3.20493
\(891\) 8.38494 0.280906
\(892\) −6.83798 −0.228952
\(893\) 2.67702 0.0895830
\(894\) −27.0492 −0.904660
\(895\) 1.46163 0.0488568
\(896\) −1.19979 −0.0400820
\(897\) −4.47769 −0.149506
\(898\) −23.5380 −0.785473
\(899\) −0.410917 −0.0137048
\(900\) −6.10508 −0.203503
\(901\) 55.9849 1.86513
\(902\) 96.3966 3.20965
\(903\) −0.409685 −0.0136335
\(904\) 107.662 3.58078
\(905\) 34.9496 1.16176
\(906\) 26.5304 0.881413
\(907\) 39.4420 1.30965 0.654824 0.755781i \(-0.272743\pi\)
0.654824 + 0.755781i \(0.272743\pi\)
\(908\) 21.9467 0.728326
\(909\) 18.3988 0.610251
\(910\) −5.20515 −0.172549
\(911\) −8.13213 −0.269430 −0.134715 0.990884i \(-0.543012\pi\)
−0.134715 + 0.990884i \(0.543012\pi\)
\(912\) −13.5678 −0.449273
\(913\) 16.8451 0.557491
\(914\) −59.1701 −1.95717
\(915\) 10.5484 0.348721
\(916\) 59.3774 1.96188
\(917\) −5.40022 −0.178331
\(918\) 63.7218 2.10313
\(919\) 16.2567 0.536261 0.268130 0.963383i \(-0.413594\pi\)
0.268130 + 0.963383i \(0.413594\pi\)
\(920\) 35.4964 1.17028
\(921\) −20.2651 −0.667758
\(922\) 8.73296 0.287605
\(923\) −21.0078 −0.691479
\(924\) 6.98882 0.229915
\(925\) −0.704433 −0.0231616
\(926\) 22.9652 0.754683
\(927\) 1.98728 0.0652707
\(928\) 11.7128 0.384493
\(929\) −3.14680 −0.103243 −0.0516215 0.998667i \(-0.516439\pi\)
−0.0516215 + 0.998667i \(0.516439\pi\)
\(930\) 2.38694 0.0782710
\(931\) 9.71943 0.318541
\(932\) 65.1114 2.13279
\(933\) 8.40948 0.275314
\(934\) 46.8006 1.53136
\(935\) −52.9236 −1.73079
\(936\) −39.5812 −1.29375
\(937\) −44.5215 −1.45445 −0.727226 0.686398i \(-0.759191\pi\)
−0.727226 + 0.686398i \(0.759191\pi\)
\(938\) 2.72777 0.0890647
\(939\) 8.89709 0.290346
\(940\) 21.9853 0.717081
\(941\) −5.28426 −0.172262 −0.0861309 0.996284i \(-0.527450\pi\)
−0.0861309 + 0.996284i \(0.527450\pi\)
\(942\) −15.8443 −0.516237
\(943\) −16.2794 −0.530132
\(944\) 86.6725 2.82095
\(945\) 3.89594 0.126735
\(946\) 14.8220 0.481905
\(947\) −4.63559 −0.150636 −0.0753182 0.997160i \(-0.523997\pi\)
−0.0753182 + 0.997160i \(0.523997\pi\)
\(948\) 6.88209 0.223520
\(949\) −3.13173 −0.101660
\(950\) 2.17248 0.0704846
\(951\) −12.0129 −0.389545
\(952\) −13.2961 −0.430930
\(953\) −14.9103 −0.482992 −0.241496 0.970402i \(-0.577638\pi\)
−0.241496 + 0.970402i \(0.577638\pi\)
\(954\) 61.8316 2.00187
\(955\) 52.9535 1.71354
\(956\) −76.8434 −2.48529
\(957\) −4.14030 −0.133837
\(958\) 109.040 3.52292
\(959\) −4.75891 −0.153673
\(960\) −22.6317 −0.730435
\(961\) −30.8311 −0.994553
\(962\) −7.70811 −0.248520
\(963\) 5.45775 0.175874
\(964\) −10.5297 −0.339137
\(965\) −32.3249 −1.04058
\(966\) −1.66123 −0.0534492
\(967\) 40.2853 1.29549 0.647744 0.761858i \(-0.275713\pi\)
0.647744 + 0.761858i \(0.275713\pi\)
\(968\) −65.7390 −2.11293
\(969\) −6.68073 −0.214616
\(970\) −15.3512 −0.492899
\(971\) 12.9114 0.414346 0.207173 0.978304i \(-0.433574\pi\)
0.207173 + 0.978304i \(0.433574\pi\)
\(972\) 79.2674 2.54250
\(973\) −0.343928 −0.0110258
\(974\) 42.4305 1.35956
\(975\) −1.33351 −0.0427065
\(976\) −49.0284 −1.56936
\(977\) −1.55018 −0.0495947 −0.0247974 0.999692i \(-0.507894\pi\)
−0.0247974 + 0.999692i \(0.507894\pi\)
\(978\) 29.0207 0.927979
\(979\) 68.1485 2.17804
\(980\) 79.8218 2.54981
\(981\) 20.2897 0.647802
\(982\) 27.6515 0.882393
\(983\) 52.7948 1.68389 0.841946 0.539561i \(-0.181410\pi\)
0.841946 + 0.539561i \(0.181410\pi\)
\(984\) 59.2115 1.88759
\(985\) −22.9124 −0.730050
\(986\) 13.2943 0.423375
\(987\) −0.609630 −0.0194047
\(988\) 16.8895 0.537326
\(989\) −2.50314 −0.0795952
\(990\) −58.4506 −1.85768
\(991\) 20.7288 0.658472 0.329236 0.944248i \(-0.393209\pi\)
0.329236 + 0.944248i \(0.393209\pi\)
\(992\) −4.81300 −0.152813
\(993\) −22.0425 −0.699498
\(994\) −7.79391 −0.247208
\(995\) 17.3556 0.550209
\(996\) 17.4634 0.553349
\(997\) −12.4077 −0.392955 −0.196477 0.980508i \(-0.562950\pi\)
−0.196477 + 0.980508i \(0.562950\pi\)
\(998\) −36.9290 −1.16897
\(999\) 5.76936 0.182534
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 \(a_p\))