Properties

Label 4019.2.a.b.1.12
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56992 q^{2}\) \(-0.512548 q^{3}\) \(+4.60446 q^{4}\) \(-4.01178 q^{5}\) \(+1.31721 q^{6}\) \(+0.174790 q^{7}\) \(-6.69325 q^{8}\) \(-2.73729 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56992 q^{2}\) \(-0.512548 q^{3}\) \(+4.60446 q^{4}\) \(-4.01178 q^{5}\) \(+1.31721 q^{6}\) \(+0.174790 q^{7}\) \(-6.69325 q^{8}\) \(-2.73729 q^{9}\) \(+10.3099 q^{10}\) \(-2.58944 q^{11}\) \(-2.36001 q^{12}\) \(+0.398828 q^{13}\) \(-0.449196 q^{14}\) \(+2.05623 q^{15}\) \(+7.99217 q^{16}\) \(+2.25702 q^{17}\) \(+7.03461 q^{18}\) \(+4.68238 q^{19}\) \(-18.4721 q^{20}\) \(-0.0895884 q^{21}\) \(+6.65465 q^{22}\) \(-6.94815 q^{23}\) \(+3.43062 q^{24}\) \(+11.0944 q^{25}\) \(-1.02496 q^{26}\) \(+2.94064 q^{27}\) \(+0.804815 q^{28}\) \(+0.630382 q^{29}\) \(-5.28434 q^{30}\) \(-1.13200 q^{31}\) \(-7.15268 q^{32}\) \(+1.32722 q^{33}\) \(-5.80034 q^{34}\) \(-0.701220 q^{35}\) \(-12.6038 q^{36}\) \(-5.41546 q^{37}\) \(-12.0333 q^{38}\) \(-0.204419 q^{39}\) \(+26.8519 q^{40}\) \(-0.895817 q^{41}\) \(+0.230235 q^{42}\) \(-7.33763 q^{43}\) \(-11.9230 q^{44}\) \(+10.9814 q^{45}\) \(+17.8562 q^{46}\) \(-5.63962 q^{47}\) \(-4.09637 q^{48}\) \(-6.96945 q^{49}\) \(-28.5116 q^{50}\) \(-1.15683 q^{51}\) \(+1.83639 q^{52}\) \(-4.48874 q^{53}\) \(-7.55720 q^{54}\) \(+10.3883 q^{55}\) \(-1.16991 q^{56}\) \(-2.39995 q^{57}\) \(-1.62003 q^{58}\) \(-1.04664 q^{59}\) \(+9.46784 q^{60}\) \(-12.2950 q^{61}\) \(+2.90914 q^{62}\) \(-0.478452 q^{63}\) \(+2.39745 q^{64}\) \(-1.60001 q^{65}\) \(-3.41083 q^{66}\) \(-0.160326 q^{67}\) \(+10.3923 q^{68}\) \(+3.56126 q^{69}\) \(+1.80207 q^{70}\) \(-1.67171 q^{71}\) \(+18.3214 q^{72}\) \(-4.74138 q^{73}\) \(+13.9173 q^{74}\) \(-5.68640 q^{75}\) \(+21.5598 q^{76}\) \(-0.452609 q^{77}\) \(+0.525339 q^{78}\) \(-11.5976 q^{79}\) \(-32.0628 q^{80}\) \(+6.70466 q^{81}\) \(+2.30217 q^{82}\) \(-13.2985 q^{83}\) \(-0.412507 q^{84}\) \(-9.05465 q^{85}\) \(+18.8571 q^{86}\) \(-0.323101 q^{87}\) \(+17.3318 q^{88}\) \(-5.97171 q^{89}\) \(-28.2213 q^{90}\) \(+0.0697113 q^{91}\) \(-31.9925 q^{92}\) \(+0.580204 q^{93}\) \(+14.4933 q^{94}\) \(-18.7847 q^{95}\) \(+3.66610 q^{96}\) \(+19.2705 q^{97}\) \(+17.9109 q^{98}\) \(+7.08807 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56992 −1.81720 −0.908602 0.417662i \(-0.862849\pi\)
−0.908602 + 0.417662i \(0.862849\pi\)
\(3\) −0.512548 −0.295920 −0.147960 0.988993i \(-0.547271\pi\)
−0.147960 + 0.988993i \(0.547271\pi\)
\(4\) 4.60446 2.30223
\(5\) −4.01178 −1.79412 −0.897061 0.441906i \(-0.854302\pi\)
−0.897061 + 0.441906i \(0.854302\pi\)
\(6\) 1.31721 0.537747
\(7\) 0.174790 0.0660645 0.0330322 0.999454i \(-0.489484\pi\)
0.0330322 + 0.999454i \(0.489484\pi\)
\(8\) −6.69325 −2.36642
\(9\) −2.73729 −0.912431
\(10\) 10.3099 3.26029
\(11\) −2.58944 −0.780747 −0.390373 0.920657i \(-0.627654\pi\)
−0.390373 + 0.920657i \(0.627654\pi\)
\(12\) −2.36001 −0.681276
\(13\) 0.398828 0.110615 0.0553075 0.998469i \(-0.482386\pi\)
0.0553075 + 0.998469i \(0.482386\pi\)
\(14\) −0.449196 −0.120053
\(15\) 2.05623 0.530917
\(16\) 7.99217 1.99804
\(17\) 2.25702 0.547407 0.273703 0.961814i \(-0.411751\pi\)
0.273703 + 0.961814i \(0.411751\pi\)
\(18\) 7.03461 1.65807
\(19\) 4.68238 1.07421 0.537106 0.843515i \(-0.319518\pi\)
0.537106 + 0.843515i \(0.319518\pi\)
\(20\) −18.4721 −4.13049
\(21\) −0.0895884 −0.0195498
\(22\) 6.65465 1.41878
\(23\) −6.94815 −1.44879 −0.724395 0.689385i \(-0.757881\pi\)
−0.724395 + 0.689385i \(0.757881\pi\)
\(24\) 3.43062 0.700272
\(25\) 11.0944 2.21888
\(26\) −1.02496 −0.201010
\(27\) 2.94064 0.565927
\(28\) 0.804815 0.152096
\(29\) 0.630382 0.117059 0.0585295 0.998286i \(-0.481359\pi\)
0.0585295 + 0.998286i \(0.481359\pi\)
\(30\) −5.28434 −0.964784
\(31\) −1.13200 −0.203313 −0.101656 0.994820i \(-0.532414\pi\)
−0.101656 + 0.994820i \(0.532414\pi\)
\(32\) −7.15268 −1.26443
\(33\) 1.32722 0.231039
\(34\) −5.80034 −0.994750
\(35\) −0.701220 −0.118528
\(36\) −12.6038 −2.10063
\(37\) −5.41546 −0.890296 −0.445148 0.895457i \(-0.646849\pi\)
−0.445148 + 0.895457i \(0.646849\pi\)
\(38\) −12.0333 −1.95206
\(39\) −0.204419 −0.0327332
\(40\) 26.8519 4.24565
\(41\) −0.895817 −0.139903 −0.0699516 0.997550i \(-0.522284\pi\)
−0.0699516 + 0.997550i \(0.522284\pi\)
\(42\) 0.230235 0.0355260
\(43\) −7.33763 −1.11898 −0.559489 0.828838i \(-0.689003\pi\)
−0.559489 + 0.828838i \(0.689003\pi\)
\(44\) −11.9230 −1.79746
\(45\) 10.9814 1.63701
\(46\) 17.8562 2.63275
\(47\) −5.63962 −0.822623 −0.411311 0.911495i \(-0.634929\pi\)
−0.411311 + 0.911495i \(0.634929\pi\)
\(48\) −4.09637 −0.591260
\(49\) −6.96945 −0.995635
\(50\) −28.5116 −4.03215
\(51\) −1.15683 −0.161989
\(52\) 1.83639 0.254662
\(53\) −4.48874 −0.616576 −0.308288 0.951293i \(-0.599756\pi\)
−0.308288 + 0.951293i \(0.599756\pi\)
\(54\) −7.55720 −1.02840
\(55\) 10.3883 1.40076
\(56\) −1.16991 −0.156336
\(57\) −2.39995 −0.317881
\(58\) −1.62003 −0.212720
\(59\) −1.04664 −0.136260 −0.0681302 0.997676i \(-0.521703\pi\)
−0.0681302 + 0.997676i \(0.521703\pi\)
\(60\) 9.46784 1.22229
\(61\) −12.2950 −1.57422 −0.787108 0.616815i \(-0.788423\pi\)
−0.787108 + 0.616815i \(0.788423\pi\)
\(62\) 2.90914 0.369461
\(63\) −0.478452 −0.0602793
\(64\) 2.39745 0.299682
\(65\) −1.60001 −0.198457
\(66\) −3.41083 −0.419844
\(67\) −0.160326 −0.0195869 −0.00979345 0.999952i \(-0.503117\pi\)
−0.00979345 + 0.999952i \(0.503117\pi\)
\(68\) 10.3923 1.26026
\(69\) 3.56126 0.428726
\(70\) 1.80207 0.215389
\(71\) −1.67171 −0.198395 −0.0991977 0.995068i \(-0.531628\pi\)
−0.0991977 + 0.995068i \(0.531628\pi\)
\(72\) 18.3214 2.15920
\(73\) −4.74138 −0.554937 −0.277468 0.960735i \(-0.589495\pi\)
−0.277468 + 0.960735i \(0.589495\pi\)
\(74\) 13.9173 1.61785
\(75\) −5.68640 −0.656609
\(76\) 21.5598 2.47308
\(77\) −0.452609 −0.0515796
\(78\) 0.525339 0.0594829
\(79\) −11.5976 −1.30483 −0.652416 0.757861i \(-0.726245\pi\)
−0.652416 + 0.757861i \(0.726245\pi\)
\(80\) −32.0628 −3.58473
\(81\) 6.70466 0.744962
\(82\) 2.30217 0.254233
\(83\) −13.2985 −1.45970 −0.729848 0.683610i \(-0.760409\pi\)
−0.729848 + 0.683610i \(0.760409\pi\)
\(84\) −0.412507 −0.0450082
\(85\) −9.05465 −0.982115
\(86\) 18.8571 2.03341
\(87\) −0.323101 −0.0346401
\(88\) 17.3318 1.84758
\(89\) −5.97171 −0.633000 −0.316500 0.948592i \(-0.602508\pi\)
−0.316500 + 0.948592i \(0.602508\pi\)
\(90\) −28.2213 −2.97479
\(91\) 0.0697113 0.00730773
\(92\) −31.9925 −3.33545
\(93\) 0.580204 0.0601643
\(94\) 14.4933 1.49487
\(95\) −18.7847 −1.92727
\(96\) 3.66610 0.374169
\(97\) 19.2705 1.95662 0.978309 0.207150i \(-0.0664189\pi\)
0.978309 + 0.207150i \(0.0664189\pi\)
\(98\) 17.9109 1.80927
\(99\) 7.08807 0.712378
\(100\) 51.0837 5.10837
\(101\) 11.8236 1.17649 0.588244 0.808683i \(-0.299819\pi\)
0.588244 + 0.808683i \(0.299819\pi\)
\(102\) 2.97295 0.294366
\(103\) −11.3188 −1.11528 −0.557639 0.830084i \(-0.688293\pi\)
−0.557639 + 0.830084i \(0.688293\pi\)
\(104\) −2.66946 −0.261762
\(105\) 0.359409 0.0350747
\(106\) 11.5357 1.12044
\(107\) −8.45807 −0.817672 −0.408836 0.912608i \(-0.634065\pi\)
−0.408836 + 0.912608i \(0.634065\pi\)
\(108\) 13.5401 1.30289
\(109\) 4.42938 0.424258 0.212129 0.977242i \(-0.431960\pi\)
0.212129 + 0.977242i \(0.431960\pi\)
\(110\) −26.6970 −2.54546
\(111\) 2.77569 0.263456
\(112\) 1.39695 0.132000
\(113\) −3.80020 −0.357492 −0.178746 0.983895i \(-0.557204\pi\)
−0.178746 + 0.983895i \(0.557204\pi\)
\(114\) 6.16766 0.577654
\(115\) 27.8745 2.59931
\(116\) 2.90257 0.269497
\(117\) −1.09171 −0.100929
\(118\) 2.68977 0.247613
\(119\) 0.394504 0.0361641
\(120\) −13.7629 −1.25637
\(121\) −4.29478 −0.390434
\(122\) 31.5972 2.86067
\(123\) 0.459150 0.0414001
\(124\) −5.21224 −0.468073
\(125\) −24.4493 −2.18681
\(126\) 1.22958 0.109540
\(127\) 19.0502 1.69043 0.845216 0.534425i \(-0.179472\pi\)
0.845216 + 0.534425i \(0.179472\pi\)
\(128\) 8.14411 0.719844
\(129\) 3.76089 0.331128
\(130\) 4.11189 0.360637
\(131\) −13.8019 −1.20587 −0.602937 0.797789i \(-0.706003\pi\)
−0.602937 + 0.797789i \(0.706003\pi\)
\(132\) 6.11112 0.531904
\(133\) 0.818434 0.0709672
\(134\) 0.412024 0.0355934
\(135\) −11.7972 −1.01534
\(136\) −15.1068 −1.29540
\(137\) −14.0926 −1.20401 −0.602005 0.798492i \(-0.705631\pi\)
−0.602005 + 0.798492i \(0.705631\pi\)
\(138\) −9.15215 −0.779083
\(139\) −10.8242 −0.918100 −0.459050 0.888410i \(-0.651810\pi\)
−0.459050 + 0.888410i \(0.651810\pi\)
\(140\) −3.22874 −0.272878
\(141\) 2.89058 0.243431
\(142\) 4.29615 0.360525
\(143\) −1.03274 −0.0863624
\(144\) −21.8769 −1.82308
\(145\) −2.52895 −0.210018
\(146\) 12.1849 1.00843
\(147\) 3.57218 0.294628
\(148\) −24.9353 −2.04967
\(149\) 21.9810 1.80076 0.900379 0.435107i \(-0.143289\pi\)
0.900379 + 0.435107i \(0.143289\pi\)
\(150\) 14.6136 1.19319
\(151\) 8.92831 0.726576 0.363288 0.931677i \(-0.381654\pi\)
0.363288 + 0.931677i \(0.381654\pi\)
\(152\) −31.3404 −2.54204
\(153\) −6.17812 −0.499471
\(154\) 1.16317 0.0937307
\(155\) 4.54133 0.364768
\(156\) −0.941239 −0.0753594
\(157\) −18.2329 −1.45514 −0.727572 0.686032i \(-0.759351\pi\)
−0.727572 + 0.686032i \(0.759351\pi\)
\(158\) 29.8049 2.37115
\(159\) 2.30070 0.182457
\(160\) 28.6950 2.26854
\(161\) −1.21447 −0.0957136
\(162\) −17.2304 −1.35375
\(163\) 10.7884 0.845013 0.422507 0.906360i \(-0.361150\pi\)
0.422507 + 0.906360i \(0.361150\pi\)
\(164\) −4.12476 −0.322090
\(165\) −5.32450 −0.414512
\(166\) 34.1759 2.65256
\(167\) −9.11401 −0.705263 −0.352632 0.935762i \(-0.614713\pi\)
−0.352632 + 0.935762i \(0.614713\pi\)
\(168\) 0.599638 0.0462631
\(169\) −12.8409 −0.987764
\(170\) 23.2697 1.78470
\(171\) −12.8170 −0.980144
\(172\) −33.7859 −2.57615
\(173\) 17.8845 1.35974 0.679868 0.733334i \(-0.262037\pi\)
0.679868 + 0.733334i \(0.262037\pi\)
\(174\) 0.830343 0.0629482
\(175\) 1.93919 0.146589
\(176\) −20.6953 −1.55996
\(177\) 0.536452 0.0403222
\(178\) 15.3468 1.15029
\(179\) 8.01910 0.599376 0.299688 0.954037i \(-0.403117\pi\)
0.299688 + 0.954037i \(0.403117\pi\)
\(180\) 50.5636 3.76879
\(181\) 13.0832 0.972465 0.486232 0.873830i \(-0.338371\pi\)
0.486232 + 0.873830i \(0.338371\pi\)
\(182\) −0.179152 −0.0132796
\(183\) 6.30179 0.465842
\(184\) 46.5058 3.42845
\(185\) 21.7256 1.59730
\(186\) −1.49107 −0.109331
\(187\) −5.84442 −0.427386
\(188\) −25.9674 −1.89387
\(189\) 0.513995 0.0373876
\(190\) 48.2750 3.50224
\(191\) 13.0640 0.945278 0.472639 0.881256i \(-0.343301\pi\)
0.472639 + 0.881256i \(0.343301\pi\)
\(192\) −1.22881 −0.0886818
\(193\) −24.3629 −1.75368 −0.876840 0.480782i \(-0.840353\pi\)
−0.876840 + 0.480782i \(0.840353\pi\)
\(194\) −49.5234 −3.55558
\(195\) 0.820083 0.0587274
\(196\) −32.0906 −2.29218
\(197\) −4.09035 −0.291426 −0.145713 0.989327i \(-0.546548\pi\)
−0.145713 + 0.989327i \(0.546548\pi\)
\(198\) −18.2157 −1.29454
\(199\) −1.09274 −0.0774623 −0.0387312 0.999250i \(-0.512332\pi\)
−0.0387312 + 0.999250i \(0.512332\pi\)
\(200\) −74.2575 −5.25080
\(201\) 0.0821747 0.00579616
\(202\) −30.3856 −2.13792
\(203\) 0.110185 0.00773344
\(204\) −5.32658 −0.372935
\(205\) 3.59382 0.251003
\(206\) 29.0884 2.02669
\(207\) 19.0191 1.32192
\(208\) 3.18750 0.221013
\(209\) −12.1248 −0.838687
\(210\) −0.923651 −0.0637379
\(211\) −0.793960 −0.0546585 −0.0273292 0.999626i \(-0.508700\pi\)
−0.0273292 + 0.999626i \(0.508700\pi\)
\(212\) −20.6682 −1.41950
\(213\) 0.856831 0.0587091
\(214\) 21.7365 1.48588
\(215\) 29.4370 2.00758
\(216\) −19.6825 −1.33922
\(217\) −0.197862 −0.0134318
\(218\) −11.3831 −0.770963
\(219\) 2.43019 0.164217
\(220\) 47.8325 3.22486
\(221\) 0.900162 0.0605514
\(222\) −7.13328 −0.478754
\(223\) 12.6126 0.844604 0.422302 0.906455i \(-0.361222\pi\)
0.422302 + 0.906455i \(0.361222\pi\)
\(224\) −1.25022 −0.0835337
\(225\) −30.3686 −2.02457
\(226\) 9.76618 0.649637
\(227\) −0.0602946 −0.00400189 −0.00200095 0.999998i \(-0.500637\pi\)
−0.00200095 + 0.999998i \(0.500637\pi\)
\(228\) −11.0505 −0.731835
\(229\) −12.6478 −0.835790 −0.417895 0.908495i \(-0.637232\pi\)
−0.417895 + 0.908495i \(0.637232\pi\)
\(230\) −71.6350 −4.72347
\(231\) 0.231984 0.0152634
\(232\) −4.21931 −0.277011
\(233\) −20.1291 −1.31870 −0.659349 0.751837i \(-0.729168\pi\)
−0.659349 + 0.751837i \(0.729168\pi\)
\(234\) 2.80560 0.183408
\(235\) 22.6249 1.47589
\(236\) −4.81920 −0.313703
\(237\) 5.94433 0.386126
\(238\) −1.01384 −0.0657176
\(239\) 1.78805 0.115659 0.0578296 0.998326i \(-0.481582\pi\)
0.0578296 + 0.998326i \(0.481582\pi\)
\(240\) 16.4337 1.06079
\(241\) −5.20792 −0.335471 −0.167736 0.985832i \(-0.553646\pi\)
−0.167736 + 0.985832i \(0.553646\pi\)
\(242\) 11.0372 0.709499
\(243\) −12.2584 −0.786376
\(244\) −56.6120 −3.62421
\(245\) 27.9599 1.78629
\(246\) −1.17998 −0.0752325
\(247\) 1.86747 0.118824
\(248\) 7.57675 0.481124
\(249\) 6.81610 0.431953
\(250\) 62.8326 3.97388
\(251\) −2.36503 −0.149279 −0.0746397 0.997211i \(-0.523781\pi\)
−0.0746397 + 0.997211i \(0.523781\pi\)
\(252\) −2.20302 −0.138777
\(253\) 17.9919 1.13114
\(254\) −48.9574 −3.07186
\(255\) 4.64095 0.290627
\(256\) −25.7246 −1.60779
\(257\) −16.6165 −1.03651 −0.518254 0.855227i \(-0.673418\pi\)
−0.518254 + 0.855227i \(0.673418\pi\)
\(258\) −9.66517 −0.601727
\(259\) −0.946569 −0.0588170
\(260\) −7.36720 −0.456894
\(261\) −1.72554 −0.106808
\(262\) 35.4696 2.19132
\(263\) 2.31251 0.142595 0.0712976 0.997455i \(-0.477286\pi\)
0.0712976 + 0.997455i \(0.477286\pi\)
\(264\) −8.88339 −0.546735
\(265\) 18.0078 1.10621
\(266\) −2.10331 −0.128962
\(267\) 3.06079 0.187317
\(268\) −0.738214 −0.0450936
\(269\) 21.4277 1.30647 0.653235 0.757155i \(-0.273411\pi\)
0.653235 + 0.757155i \(0.273411\pi\)
\(270\) 30.3178 1.84508
\(271\) −7.55774 −0.459100 −0.229550 0.973297i \(-0.573725\pi\)
−0.229550 + 0.973297i \(0.573725\pi\)
\(272\) 18.0384 1.09374
\(273\) −0.0357304 −0.00216250
\(274\) 36.2167 2.18793
\(275\) −28.7283 −1.73238
\(276\) 16.3977 0.987027
\(277\) 20.5725 1.23608 0.618041 0.786146i \(-0.287927\pi\)
0.618041 + 0.786146i \(0.287927\pi\)
\(278\) 27.8174 1.66838
\(279\) 3.09861 0.185509
\(280\) 4.69344 0.280487
\(281\) 5.75989 0.343606 0.171803 0.985131i \(-0.445041\pi\)
0.171803 + 0.985131i \(0.445041\pi\)
\(282\) −7.42854 −0.442363
\(283\) −7.06564 −0.420009 −0.210004 0.977700i \(-0.567348\pi\)
−0.210004 + 0.977700i \(0.567348\pi\)
\(284\) −7.69732 −0.456752
\(285\) 9.62805 0.570317
\(286\) 2.65406 0.156938
\(287\) −0.156580 −0.00924263
\(288\) 19.5790 1.15370
\(289\) −11.9059 −0.700346
\(290\) 6.49920 0.381646
\(291\) −9.87704 −0.579002
\(292\) −21.8315 −1.27759
\(293\) −18.5086 −1.08129 −0.540643 0.841252i \(-0.681819\pi\)
−0.540643 + 0.841252i \(0.681819\pi\)
\(294\) −9.18020 −0.535400
\(295\) 4.19887 0.244468
\(296\) 36.2471 2.10682
\(297\) −7.61463 −0.441845
\(298\) −56.4894 −3.27234
\(299\) −2.77112 −0.160258
\(300\) −26.1828 −1.51167
\(301\) −1.28255 −0.0739247
\(302\) −22.9450 −1.32034
\(303\) −6.06015 −0.348146
\(304\) 37.4223 2.14632
\(305\) 49.3249 2.82434
\(306\) 15.8772 0.907641
\(307\) −27.4308 −1.56556 −0.782779 0.622300i \(-0.786199\pi\)
−0.782779 + 0.622300i \(0.786199\pi\)
\(308\) −2.08402 −0.118748
\(309\) 5.80145 0.330033
\(310\) −11.6708 −0.662858
\(311\) 27.2558 1.54554 0.772768 0.634688i \(-0.218872\pi\)
0.772768 + 0.634688i \(0.218872\pi\)
\(312\) 1.36823 0.0774606
\(313\) −20.6383 −1.16655 −0.583273 0.812276i \(-0.698228\pi\)
−0.583273 + 0.812276i \(0.698228\pi\)
\(314\) 46.8570 2.64429
\(315\) 1.91944 0.108148
\(316\) −53.4008 −3.00403
\(317\) 32.0421 1.79966 0.899832 0.436236i \(-0.143689\pi\)
0.899832 + 0.436236i \(0.143689\pi\)
\(318\) −5.91259 −0.331562
\(319\) −1.63234 −0.0913935
\(320\) −9.61806 −0.537666
\(321\) 4.33517 0.241965
\(322\) 3.12108 0.173931
\(323\) 10.5682 0.588031
\(324\) 30.8714 1.71508
\(325\) 4.42475 0.245441
\(326\) −27.7253 −1.53556
\(327\) −2.27027 −0.125546
\(328\) 5.99593 0.331070
\(329\) −0.985750 −0.0543461
\(330\) 13.6835 0.753252
\(331\) 4.50548 0.247644 0.123822 0.992304i \(-0.460485\pi\)
0.123822 + 0.992304i \(0.460485\pi\)
\(332\) −61.2323 −3.36056
\(333\) 14.8237 0.812334
\(334\) 23.4222 1.28161
\(335\) 0.643192 0.0351413
\(336\) −0.716005 −0.0390613
\(337\) 19.3280 1.05286 0.526431 0.850218i \(-0.323530\pi\)
0.526431 + 0.850218i \(0.323530\pi\)
\(338\) 33.0001 1.79497
\(339\) 1.94778 0.105789
\(340\) −41.6918 −2.26106
\(341\) 2.93125 0.158736
\(342\) 32.9387 1.78112
\(343\) −2.44172 −0.131841
\(344\) 49.1126 2.64798
\(345\) −14.2870 −0.769187
\(346\) −45.9617 −2.47092
\(347\) −1.13051 −0.0606888 −0.0303444 0.999540i \(-0.509660\pi\)
−0.0303444 + 0.999540i \(0.509660\pi\)
\(348\) −1.48771 −0.0797496
\(349\) 4.63733 0.248230 0.124115 0.992268i \(-0.460391\pi\)
0.124115 + 0.992268i \(0.460391\pi\)
\(350\) −4.98355 −0.266382
\(351\) 1.17281 0.0626000
\(352\) 18.5215 0.987198
\(353\) −31.6375 −1.68390 −0.841948 0.539559i \(-0.818591\pi\)
−0.841948 + 0.539559i \(0.818591\pi\)
\(354\) −1.37864 −0.0732736
\(355\) 6.70653 0.355945
\(356\) −27.4965 −1.45731
\(357\) −0.202202 −0.0107017
\(358\) −20.6084 −1.08919
\(359\) −31.5339 −1.66429 −0.832147 0.554555i \(-0.812888\pi\)
−0.832147 + 0.554555i \(0.812888\pi\)
\(360\) −73.5014 −3.87387
\(361\) 2.92467 0.153930
\(362\) −33.6227 −1.76717
\(363\) 2.20128 0.115537
\(364\) 0.320983 0.0168241
\(365\) 19.0214 0.995624
\(366\) −16.1951 −0.846530
\(367\) 3.92030 0.204638 0.102319 0.994752i \(-0.467374\pi\)
0.102319 + 0.994752i \(0.467374\pi\)
\(368\) −55.5308 −2.89474
\(369\) 2.45212 0.127652
\(370\) −55.8331 −2.90262
\(371\) −0.784587 −0.0407337
\(372\) 2.67153 0.138512
\(373\) 0.304601 0.0157717 0.00788583 0.999969i \(-0.497490\pi\)
0.00788583 + 0.999969i \(0.497490\pi\)
\(374\) 15.0197 0.776648
\(375\) 12.5314 0.647121
\(376\) 37.7474 1.94667
\(377\) 0.251414 0.0129485
\(378\) −1.32092 −0.0679410
\(379\) 11.4602 0.588673 0.294336 0.955702i \(-0.404901\pi\)
0.294336 + 0.955702i \(0.404901\pi\)
\(380\) −86.4934 −4.43702
\(381\) −9.76415 −0.500232
\(382\) −33.5734 −1.71776
\(383\) −4.60659 −0.235386 −0.117693 0.993050i \(-0.537550\pi\)
−0.117693 + 0.993050i \(0.537550\pi\)
\(384\) −4.17425 −0.213016
\(385\) 1.81577 0.0925402
\(386\) 62.6106 3.18680
\(387\) 20.0853 1.02099
\(388\) 88.7301 4.50459
\(389\) 25.8731 1.31182 0.655909 0.754840i \(-0.272285\pi\)
0.655909 + 0.754840i \(0.272285\pi\)
\(390\) −2.10754 −0.106720
\(391\) −15.6821 −0.793078
\(392\) 46.6483 2.35609
\(393\) 7.07412 0.356842
\(394\) 10.5119 0.529580
\(395\) 46.5270 2.34103
\(396\) 32.6368 1.64006
\(397\) −14.3705 −0.721234 −0.360617 0.932714i \(-0.617434\pi\)
−0.360617 + 0.932714i \(0.617434\pi\)
\(398\) 2.80825 0.140765
\(399\) −0.419487 −0.0210006
\(400\) 88.6681 4.43340
\(401\) 31.0413 1.55013 0.775065 0.631882i \(-0.217717\pi\)
0.775065 + 0.631882i \(0.217717\pi\)
\(402\) −0.211182 −0.0105328
\(403\) −0.451473 −0.0224895
\(404\) 54.4412 2.70855
\(405\) −26.8976 −1.33655
\(406\) −0.283165 −0.0140532
\(407\) 14.0230 0.695096
\(408\) 7.74295 0.383333
\(409\) −0.951862 −0.0470666 −0.0235333 0.999723i \(-0.507492\pi\)
−0.0235333 + 0.999723i \(0.507492\pi\)
\(410\) −9.23582 −0.456125
\(411\) 7.22313 0.356291
\(412\) −52.1172 −2.56763
\(413\) −0.182942 −0.00900197
\(414\) −48.8776 −2.40220
\(415\) 53.3505 2.61887
\(416\) −2.85269 −0.139865
\(417\) 5.54794 0.271684
\(418\) 31.1596 1.52407
\(419\) 22.8013 1.11391 0.556957 0.830541i \(-0.311969\pi\)
0.556957 + 0.830541i \(0.311969\pi\)
\(420\) 1.65489 0.0807502
\(421\) 20.6793 1.00785 0.503924 0.863748i \(-0.331889\pi\)
0.503924 + 0.863748i \(0.331889\pi\)
\(422\) 2.04041 0.0993256
\(423\) 15.4373 0.750587
\(424\) 30.0443 1.45908
\(425\) 25.0402 1.21463
\(426\) −2.20198 −0.106686
\(427\) −2.14905 −0.104000
\(428\) −38.9449 −1.88247
\(429\) 0.529331 0.0255563
\(430\) −75.6505 −3.64819
\(431\) 30.6022 1.47405 0.737027 0.675863i \(-0.236229\pi\)
0.737027 + 0.675863i \(0.236229\pi\)
\(432\) 23.5021 1.13074
\(433\) −10.9444 −0.525953 −0.262976 0.964802i \(-0.584704\pi\)
−0.262976 + 0.964802i \(0.584704\pi\)
\(434\) 0.508489 0.0244082
\(435\) 1.29621 0.0621486
\(436\) 20.3949 0.976739
\(437\) −32.5339 −1.55631
\(438\) −6.24538 −0.298416
\(439\) 17.6597 0.842852 0.421426 0.906863i \(-0.361530\pi\)
0.421426 + 0.906863i \(0.361530\pi\)
\(440\) −69.5314 −3.31478
\(441\) 19.0774 0.908449
\(442\) −2.31334 −0.110034
\(443\) 18.6611 0.886615 0.443307 0.896370i \(-0.353805\pi\)
0.443307 + 0.896370i \(0.353805\pi\)
\(444\) 12.7805 0.606538
\(445\) 23.9572 1.13568
\(446\) −32.4134 −1.53482
\(447\) −11.2663 −0.532880
\(448\) 0.419051 0.0197983
\(449\) 24.8067 1.17070 0.585351 0.810780i \(-0.300957\pi\)
0.585351 + 0.810780i \(0.300957\pi\)
\(450\) 78.0447 3.67906
\(451\) 2.31967 0.109229
\(452\) −17.4979 −0.823030
\(453\) −4.57619 −0.215008
\(454\) 0.154952 0.00727226
\(455\) −0.279666 −0.0131110
\(456\) 16.0634 0.752240
\(457\) −15.3687 −0.718915 −0.359458 0.933161i \(-0.617038\pi\)
−0.359458 + 0.933161i \(0.617038\pi\)
\(458\) 32.5038 1.51880
\(459\) 6.63707 0.309792
\(460\) 128.347 5.98421
\(461\) 4.68495 0.218200 0.109100 0.994031i \(-0.465203\pi\)
0.109100 + 0.994031i \(0.465203\pi\)
\(462\) −0.596180 −0.0277368
\(463\) −1.49220 −0.0693483 −0.0346741 0.999399i \(-0.511039\pi\)
−0.0346741 + 0.999399i \(0.511039\pi\)
\(464\) 5.03812 0.233889
\(465\) −2.32765 −0.107942
\(466\) 51.7300 2.39634
\(467\) −19.2068 −0.888785 −0.444393 0.895832i \(-0.646580\pi\)
−0.444393 + 0.895832i \(0.646580\pi\)
\(468\) −5.02674 −0.232361
\(469\) −0.0280234 −0.00129400
\(470\) −58.1441 −2.68199
\(471\) 9.34524 0.430606
\(472\) 7.00540 0.322450
\(473\) 19.0004 0.873639
\(474\) −15.2764 −0.701670
\(475\) 51.9481 2.38354
\(476\) 1.81648 0.0832582
\(477\) 12.2870 0.562583
\(478\) −4.59513 −0.210176
\(479\) 3.24121 0.148095 0.0740474 0.997255i \(-0.476408\pi\)
0.0740474 + 0.997255i \(0.476408\pi\)
\(480\) −14.7076 −0.671305
\(481\) −2.15984 −0.0984802
\(482\) 13.3839 0.609620
\(483\) 0.622474 0.0283235
\(484\) −19.7751 −0.898870
\(485\) −77.3088 −3.51041
\(486\) 31.5030 1.42901
\(487\) 27.7722 1.25848 0.629240 0.777211i \(-0.283366\pi\)
0.629240 + 0.777211i \(0.283366\pi\)
\(488\) 82.2937 3.72526
\(489\) −5.52958 −0.250056
\(490\) −71.8546 −3.24606
\(491\) 6.44648 0.290925 0.145463 0.989364i \(-0.453533\pi\)
0.145463 + 0.989364i \(0.453533\pi\)
\(492\) 2.11414 0.0953127
\(493\) 1.42278 0.0640789
\(494\) −4.79923 −0.215927
\(495\) −28.4358 −1.27809
\(496\) −9.04711 −0.406227
\(497\) −0.292198 −0.0131069
\(498\) −17.5168 −0.784947
\(499\) 27.7902 1.24406 0.622031 0.782993i \(-0.286308\pi\)
0.622031 + 0.782993i \(0.286308\pi\)
\(500\) −112.576 −5.03455
\(501\) 4.67137 0.208701
\(502\) 6.07793 0.271271
\(503\) −10.2084 −0.455171 −0.227586 0.973758i \(-0.573083\pi\)
−0.227586 + 0.973758i \(0.573083\pi\)
\(504\) 3.20240 0.142646
\(505\) −47.4335 −2.11076
\(506\) −46.2376 −2.05551
\(507\) 6.58160 0.292299
\(508\) 87.7160 3.89177
\(509\) 12.3770 0.548603 0.274301 0.961644i \(-0.411553\pi\)
0.274301 + 0.961644i \(0.411553\pi\)
\(510\) −11.9268 −0.528129
\(511\) −0.828747 −0.0366616
\(512\) 49.8218 2.20183
\(513\) 13.7692 0.607925
\(514\) 42.7030 1.88355
\(515\) 45.4087 2.00094
\(516\) 17.3169 0.762334
\(517\) 14.6035 0.642260
\(518\) 2.43260 0.106882
\(519\) −9.16669 −0.402373
\(520\) 10.7093 0.469633
\(521\) 7.79555 0.341529 0.170765 0.985312i \(-0.445376\pi\)
0.170765 + 0.985312i \(0.445376\pi\)
\(522\) 4.43450 0.194093
\(523\) 24.1473 1.05589 0.527944 0.849279i \(-0.322963\pi\)
0.527944 + 0.849279i \(0.322963\pi\)
\(524\) −63.5502 −2.77620
\(525\) −0.993928 −0.0433786
\(526\) −5.94295 −0.259125
\(527\) −2.55494 −0.111295
\(528\) 10.6073 0.461625
\(529\) 25.2768 1.09899
\(530\) −46.2786 −2.01021
\(531\) 2.86495 0.124328
\(532\) 3.76845 0.163383
\(533\) −0.357277 −0.0154754
\(534\) −7.86598 −0.340394
\(535\) 33.9319 1.46700
\(536\) 1.07310 0.0463509
\(537\) −4.11018 −0.177367
\(538\) −55.0674 −2.37412
\(539\) 18.0470 0.777339
\(540\) −54.3198 −2.33755
\(541\) 15.3824 0.661341 0.330670 0.943746i \(-0.392725\pi\)
0.330670 + 0.943746i \(0.392725\pi\)
\(542\) 19.4227 0.834278
\(543\) −6.70576 −0.287772
\(544\) −16.1437 −0.692156
\(545\) −17.7697 −0.761170
\(546\) 0.0918241 0.00392971
\(547\) −19.1251 −0.817732 −0.408866 0.912594i \(-0.634076\pi\)
−0.408866 + 0.912594i \(0.634076\pi\)
\(548\) −64.8888 −2.77191
\(549\) 33.6551 1.43636
\(550\) 73.8292 3.14809
\(551\) 2.95169 0.125746
\(552\) −23.8364 −1.01455
\(553\) −2.02715 −0.0862031
\(554\) −52.8696 −2.24621
\(555\) −11.1354 −0.472673
\(556\) −49.8398 −2.11368
\(557\) −12.1660 −0.515491 −0.257745 0.966213i \(-0.582980\pi\)
−0.257745 + 0.966213i \(0.582980\pi\)
\(558\) −7.96317 −0.337108
\(559\) −2.92646 −0.123776
\(560\) −5.60426 −0.236823
\(561\) 2.99555 0.126472
\(562\) −14.8024 −0.624403
\(563\) 25.6074 1.07922 0.539611 0.841915i \(-0.318571\pi\)
0.539611 + 0.841915i \(0.318571\pi\)
\(564\) 13.3096 0.560434
\(565\) 15.2455 0.641385
\(566\) 18.1581 0.763242
\(567\) 1.17191 0.0492155
\(568\) 11.1892 0.469487
\(569\) −25.5284 −1.07021 −0.535103 0.844787i \(-0.679727\pi\)
−0.535103 + 0.844787i \(0.679727\pi\)
\(570\) −24.7433 −1.03638
\(571\) −14.7060 −0.615428 −0.307714 0.951479i \(-0.599564\pi\)
−0.307714 + 0.951479i \(0.599564\pi\)
\(572\) −4.75523 −0.198826
\(573\) −6.69593 −0.279727
\(574\) 0.402397 0.0167957
\(575\) −77.0854 −3.21469
\(576\) −6.56254 −0.273439
\(577\) 47.4299 1.97453 0.987266 0.159076i \(-0.0508514\pi\)
0.987266 + 0.159076i \(0.0508514\pi\)
\(578\) 30.5971 1.27267
\(579\) 12.4872 0.518949
\(580\) −11.6445 −0.483511
\(581\) −2.32444 −0.0964340
\(582\) 25.3832 1.05217
\(583\) 11.6233 0.481389
\(584\) 31.7353 1.31321
\(585\) 4.37970 0.181078
\(586\) 47.5656 1.96492
\(587\) −7.17019 −0.295945 −0.147973 0.988991i \(-0.547275\pi\)
−0.147973 + 0.988991i \(0.547275\pi\)
\(588\) 16.4480 0.678303
\(589\) −5.30044 −0.218401
\(590\) −10.7907 −0.444248
\(591\) 2.09650 0.0862386
\(592\) −43.2813 −1.77885
\(593\) −23.6639 −0.971761 −0.485881 0.874025i \(-0.661501\pi\)
−0.485881 + 0.874025i \(0.661501\pi\)
\(594\) 19.5689 0.802924
\(595\) −1.58266 −0.0648829
\(596\) 101.211 4.14576
\(597\) 0.560083 0.0229227
\(598\) 7.12155 0.291222
\(599\) −23.6792 −0.967508 −0.483754 0.875204i \(-0.660727\pi\)
−0.483754 + 0.875204i \(0.660727\pi\)
\(600\) 38.0605 1.55382
\(601\) −22.2412 −0.907236 −0.453618 0.891196i \(-0.649867\pi\)
−0.453618 + 0.891196i \(0.649867\pi\)
\(602\) 3.29603 0.134336
\(603\) 0.438859 0.0178717
\(604\) 41.1101 1.67275
\(605\) 17.2297 0.700487
\(606\) 15.5741 0.632653
\(607\) −18.0900 −0.734251 −0.367126 0.930171i \(-0.619658\pi\)
−0.367126 + 0.930171i \(0.619658\pi\)
\(608\) −33.4916 −1.35826
\(609\) −0.0564749 −0.00228848
\(610\) −126.761 −5.13240
\(611\) −2.24924 −0.0909945
\(612\) −28.4469 −1.14990
\(613\) −2.00063 −0.0808047 −0.0404024 0.999183i \(-0.512864\pi\)
−0.0404024 + 0.999183i \(0.512864\pi\)
\(614\) 70.4948 2.84494
\(615\) −1.84201 −0.0742769
\(616\) 3.02943 0.122059
\(617\) 8.84164 0.355951 0.177975 0.984035i \(-0.443045\pi\)
0.177975 + 0.984035i \(0.443045\pi\)
\(618\) −14.9092 −0.599737
\(619\) 0.000980310 0 3.94020e−5 0 1.97010e−5 1.00000i \(-0.499994\pi\)
1.97010e−5 1.00000i \(0.499994\pi\)
\(620\) 20.9104 0.839781
\(621\) −20.4320 −0.819909
\(622\) −70.0452 −2.80856
\(623\) −1.04380 −0.0418188
\(624\) −1.63375 −0.0654023
\(625\) 42.6133 1.70453
\(626\) 53.0387 2.11985
\(627\) 6.21453 0.248184
\(628\) −83.9527 −3.35008
\(629\) −12.2228 −0.487354
\(630\) −4.93281 −0.196528
\(631\) 9.38662 0.373676 0.186838 0.982391i \(-0.440176\pi\)
0.186838 + 0.982391i \(0.440176\pi\)
\(632\) 77.6257 3.08778
\(633\) 0.406943 0.0161745
\(634\) −82.3455 −3.27036
\(635\) −76.4252 −3.03284
\(636\) 10.5935 0.420058
\(637\) −2.77961 −0.110132
\(638\) 4.19498 0.166081
\(639\) 4.57596 0.181022
\(640\) −32.6724 −1.29149
\(641\) −37.6904 −1.48868 −0.744341 0.667800i \(-0.767236\pi\)
−0.744341 + 0.667800i \(0.767236\pi\)
\(642\) −11.1410 −0.439701
\(643\) 6.82903 0.269311 0.134655 0.990892i \(-0.457007\pi\)
0.134655 + 0.990892i \(0.457007\pi\)
\(644\) −5.59198 −0.220355
\(645\) −15.0879 −0.594084
\(646\) −27.1594 −1.06857
\(647\) −6.28402 −0.247050 −0.123525 0.992341i \(-0.539420\pi\)
−0.123525 + 0.992341i \(0.539420\pi\)
\(648\) −44.8760 −1.76290
\(649\) 2.71021 0.106385
\(650\) −11.3712 −0.446017
\(651\) 0.101414 0.00397472
\(652\) 49.6748 1.94542
\(653\) −17.1976 −0.672995 −0.336497 0.941684i \(-0.609242\pi\)
−0.336497 + 0.941684i \(0.609242\pi\)
\(654\) 5.83440 0.228143
\(655\) 55.3700 2.16349
\(656\) −7.15952 −0.279532
\(657\) 12.9786 0.506342
\(658\) 2.53329 0.0987581
\(659\) −4.88317 −0.190221 −0.0951106 0.995467i \(-0.530320\pi\)
−0.0951106 + 0.995467i \(0.530320\pi\)
\(660\) −24.5165 −0.954302
\(661\) −34.3667 −1.33671 −0.668355 0.743843i \(-0.733001\pi\)
−0.668355 + 0.743843i \(0.733001\pi\)
\(662\) −11.5787 −0.450019
\(663\) −0.461376 −0.0179184
\(664\) 89.0099 3.45426
\(665\) −3.28338 −0.127324
\(666\) −38.0957 −1.47618
\(667\) −4.37999 −0.169594
\(668\) −41.9651 −1.62368
\(669\) −6.46458 −0.249935
\(670\) −1.65295 −0.0638589
\(671\) 31.8373 1.22906
\(672\) 0.640797 0.0247193
\(673\) 15.1142 0.582611 0.291305 0.956630i \(-0.405910\pi\)
0.291305 + 0.956630i \(0.405910\pi\)
\(674\) −49.6713 −1.91327
\(675\) 32.6246 1.25572
\(676\) −59.1256 −2.27406
\(677\) −7.83617 −0.301169 −0.150584 0.988597i \(-0.548115\pi\)
−0.150584 + 0.988597i \(0.548115\pi\)
\(678\) −5.00564 −0.192240
\(679\) 3.36829 0.129263
\(680\) 60.6051 2.32410
\(681\) 0.0309039 0.00118424
\(682\) −7.53305 −0.288456
\(683\) 29.5937 1.13237 0.566186 0.824278i \(-0.308419\pi\)
0.566186 + 0.824278i \(0.308419\pi\)
\(684\) −59.0156 −2.25652
\(685\) 56.5363 2.16014
\(686\) 6.27502 0.239581
\(687\) 6.48261 0.247327
\(688\) −58.6436 −2.23577
\(689\) −1.79024 −0.0682026
\(690\) 36.7164 1.39777
\(691\) 9.26567 0.352483 0.176241 0.984347i \(-0.443606\pi\)
0.176241 + 0.984347i \(0.443606\pi\)
\(692\) 82.3487 3.13043
\(693\) 1.23893 0.0470629
\(694\) 2.90531 0.110284
\(695\) 43.4245 1.64718
\(696\) 2.16260 0.0819731
\(697\) −2.02187 −0.0765839
\(698\) −11.9175 −0.451085
\(699\) 10.3171 0.390229
\(700\) 8.92892 0.337482
\(701\) −38.6769 −1.46081 −0.730403 0.683016i \(-0.760668\pi\)
−0.730403 + 0.683016i \(0.760668\pi\)
\(702\) −3.01402 −0.113757
\(703\) −25.3572 −0.956367
\(704\) −6.20807 −0.233976
\(705\) −11.5964 −0.436744
\(706\) 81.3058 3.05998
\(707\) 2.06664 0.0777241
\(708\) 2.47007 0.0928310
\(709\) 31.4982 1.18294 0.591470 0.806327i \(-0.298548\pi\)
0.591470 + 0.806327i \(0.298548\pi\)
\(710\) −17.2352 −0.646826
\(711\) 31.7461 1.19057
\(712\) 39.9702 1.49795
\(713\) 7.86530 0.294558
\(714\) 0.519643 0.0194472
\(715\) 4.14314 0.154945
\(716\) 36.9237 1.37990
\(717\) −0.916461 −0.0342259
\(718\) 81.0394 3.02436
\(719\) 40.6575 1.51627 0.758134 0.652099i \(-0.226111\pi\)
0.758134 + 0.652099i \(0.226111\pi\)
\(720\) 87.7653 3.27082
\(721\) −1.97842 −0.0736802
\(722\) −7.51616 −0.279723
\(723\) 2.66931 0.0992727
\(724\) 60.2410 2.23884
\(725\) 6.99370 0.259739
\(726\) −5.65710 −0.209955
\(727\) −22.3344 −0.828336 −0.414168 0.910200i \(-0.635927\pi\)
−0.414168 + 0.910200i \(0.635927\pi\)
\(728\) −0.466595 −0.0172932
\(729\) −13.8310 −0.512258
\(730\) −48.8833 −1.80925
\(731\) −16.5612 −0.612536
\(732\) 29.0164 1.07248
\(733\) 35.8980 1.32592 0.662962 0.748653i \(-0.269299\pi\)
0.662962 + 0.748653i \(0.269299\pi\)
\(734\) −10.0748 −0.371869
\(735\) −14.3308 −0.528599
\(736\) 49.6979 1.83189
\(737\) 0.415155 0.0152924
\(738\) −6.30173 −0.231970
\(739\) 5.85171 0.215259 0.107629 0.994191i \(-0.465674\pi\)
0.107629 + 0.994191i \(0.465674\pi\)
\(740\) 100.035 3.67736
\(741\) −0.957166 −0.0351624
\(742\) 2.01632 0.0740215
\(743\) 11.2665 0.413327 0.206664 0.978412i \(-0.433739\pi\)
0.206664 + 0.978412i \(0.433739\pi\)
\(744\) −3.88345 −0.142374
\(745\) −88.1831 −3.23078
\(746\) −0.782800 −0.0286603
\(747\) 36.4018 1.33187
\(748\) −26.9104 −0.983942
\(749\) −1.47839 −0.0540191
\(750\) −32.2048 −1.17595
\(751\) 31.2868 1.14167 0.570835 0.821065i \(-0.306619\pi\)
0.570835 + 0.821065i \(0.306619\pi\)
\(752\) −45.0728 −1.64363
\(753\) 1.21219 0.0441747
\(754\) −0.646113 −0.0235301
\(755\) −35.8184 −1.30357
\(756\) 2.36667 0.0860750
\(757\) −23.4806 −0.853416 −0.426708 0.904390i \(-0.640327\pi\)
−0.426708 + 0.904390i \(0.640327\pi\)
\(758\) −29.4518 −1.06974
\(759\) −9.22170 −0.334726
\(760\) 125.731 4.56073
\(761\) 35.2910 1.27930 0.639648 0.768668i \(-0.279080\pi\)
0.639648 + 0.768668i \(0.279080\pi\)
\(762\) 25.0930 0.909025
\(763\) 0.774212 0.0280283
\(764\) 60.1527 2.17625
\(765\) 24.7852 0.896112
\(766\) 11.8386 0.427744
\(767\) −0.417428 −0.0150725
\(768\) 13.1851 0.475776
\(769\) 0.278809 0.0100541 0.00502706 0.999987i \(-0.498400\pi\)
0.00502706 + 0.999987i \(0.498400\pi\)
\(770\) −4.66637 −0.168164
\(771\) 8.51676 0.306724
\(772\) −112.178 −4.03738
\(773\) −19.5739 −0.704024 −0.352012 0.935995i \(-0.614502\pi\)
−0.352012 + 0.935995i \(0.614502\pi\)
\(774\) −51.6174 −1.85535
\(775\) −12.5588 −0.451126
\(776\) −128.982 −4.63019
\(777\) 0.485163 0.0174051
\(778\) −66.4917 −2.38384
\(779\) −4.19456 −0.150286
\(780\) 3.77604 0.135204
\(781\) 4.32880 0.154897
\(782\) 40.3017 1.44118
\(783\) 1.85373 0.0662468
\(784\) −55.7010 −1.98932
\(785\) 73.1464 2.61071
\(786\) −18.1799 −0.648455
\(787\) 5.09792 0.181721 0.0908606 0.995864i \(-0.471038\pi\)
0.0908606 + 0.995864i \(0.471038\pi\)
\(788\) −18.8339 −0.670929
\(789\) −1.18527 −0.0421968
\(790\) −119.571 −4.25413
\(791\) −0.664237 −0.0236175
\(792\) −47.4423 −1.68579
\(793\) −4.90360 −0.174132
\(794\) 36.9309 1.31063
\(795\) −9.22988 −0.327350
\(796\) −5.03149 −0.178336
\(797\) −5.29812 −0.187669 −0.0938346 0.995588i \(-0.529912\pi\)
−0.0938346 + 0.995588i \(0.529912\pi\)
\(798\) 1.07805 0.0381624
\(799\) −12.7287 −0.450309
\(800\) −79.3545 −2.80561
\(801\) 16.3463 0.577569
\(802\) −79.7735 −2.81690
\(803\) 12.2775 0.433265
\(804\) 0.378370 0.0133441
\(805\) 4.87218 0.171722
\(806\) 1.16025 0.0408680
\(807\) −10.9827 −0.386610
\(808\) −79.1381 −2.78407
\(809\) 4.13007 0.145206 0.0726028 0.997361i \(-0.476869\pi\)
0.0726028 + 0.997361i \(0.476869\pi\)
\(810\) 69.1246 2.42879
\(811\) 32.2044 1.13085 0.565424 0.824800i \(-0.308713\pi\)
0.565424 + 0.824800i \(0.308713\pi\)
\(812\) 0.507341 0.0178042
\(813\) 3.87370 0.135857
\(814\) −36.0380 −1.26313
\(815\) −43.2807 −1.51606
\(816\) −9.24557 −0.323660
\(817\) −34.3576 −1.20202
\(818\) 2.44621 0.0855296
\(819\) −0.190820 −0.00666780
\(820\) 16.5476 0.577868
\(821\) −19.2471 −0.671729 −0.335865 0.941910i \(-0.609028\pi\)
−0.335865 + 0.941910i \(0.609028\pi\)
\(822\) −18.5628 −0.647453
\(823\) −36.9838 −1.28917 −0.644587 0.764531i \(-0.722971\pi\)
−0.644587 + 0.764531i \(0.722971\pi\)
\(824\) 75.7598 2.63922
\(825\) 14.7246 0.512646
\(826\) 0.470145 0.0163584
\(827\) −39.0561 −1.35811 −0.679057 0.734086i \(-0.737611\pi\)
−0.679057 + 0.734086i \(0.737611\pi\)
\(828\) 87.5730 3.04337
\(829\) 9.43066 0.327540 0.163770 0.986499i \(-0.447634\pi\)
0.163770 + 0.986499i \(0.447634\pi\)
\(830\) −137.106 −4.75903
\(831\) −10.5444 −0.365781
\(832\) 0.956173 0.0331493
\(833\) −15.7302 −0.545018
\(834\) −14.2577 −0.493705
\(835\) 36.5634 1.26533
\(836\) −55.8280 −1.93085
\(837\) −3.32880 −0.115060
\(838\) −58.5973 −2.02421
\(839\) 19.8435 0.685074 0.342537 0.939504i \(-0.388714\pi\)
0.342537 + 0.939504i \(0.388714\pi\)
\(840\) −2.40562 −0.0830016
\(841\) −28.6026 −0.986297
\(842\) −53.1441 −1.83147
\(843\) −2.95222 −0.101680
\(844\) −3.65576 −0.125837
\(845\) 51.5150 1.77217
\(846\) −39.6725 −1.36397
\(847\) −0.750685 −0.0257938
\(848\) −35.8747 −1.23194
\(849\) 3.62148 0.124289
\(850\) −64.3512 −2.20723
\(851\) 37.6275 1.28985
\(852\) 3.94525 0.135162
\(853\) 25.1405 0.860795 0.430397 0.902640i \(-0.358373\pi\)
0.430397 + 0.902640i \(0.358373\pi\)
\(854\) 5.52287 0.188989
\(855\) 51.4192 1.75850
\(856\) 56.6120 1.93496
\(857\) −37.9056 −1.29483 −0.647416 0.762137i \(-0.724150\pi\)
−0.647416 + 0.762137i \(0.724150\pi\)
\(858\) −1.36034 −0.0464411
\(859\) −35.5986 −1.21461 −0.607304 0.794469i \(-0.707749\pi\)
−0.607304 + 0.794469i \(0.707749\pi\)
\(860\) 135.541 4.62193
\(861\) 0.0802548 0.00273508
\(862\) −78.6449 −2.67866
\(863\) 19.1710 0.652589 0.326295 0.945268i \(-0.394200\pi\)
0.326295 + 0.945268i \(0.394200\pi\)
\(864\) −21.0335 −0.715573
\(865\) −71.7488 −2.43953
\(866\) 28.1261 0.955764
\(867\) 6.10234 0.207246
\(868\) −0.911049 −0.0309230
\(869\) 30.0314 1.01874
\(870\) −3.33115 −0.112937
\(871\) −0.0639424 −0.00216661
\(872\) −29.6470 −1.00397
\(873\) −52.7489 −1.78528
\(874\) 83.6093 2.82813
\(875\) −4.27350 −0.144471
\(876\) 11.1897 0.378065
\(877\) 55.1035 1.86071 0.930357 0.366655i \(-0.119497\pi\)
0.930357 + 0.366655i \(0.119497\pi\)
\(878\) −45.3840 −1.53163
\(879\) 9.48657 0.319974
\(880\) 83.0249 2.79877
\(881\) 51.0073 1.71848 0.859240 0.511573i \(-0.170937\pi\)
0.859240 + 0.511573i \(0.170937\pi\)
\(882\) −49.0274 −1.65084
\(883\) −56.1603 −1.88995 −0.944973 0.327148i \(-0.893912\pi\)
−0.944973 + 0.327148i \(0.893912\pi\)
\(884\) 4.14476 0.139403
\(885\) −2.15213 −0.0723429
\(886\) −47.9574 −1.61116
\(887\) −15.4881 −0.520041 −0.260020 0.965603i \(-0.583729\pi\)
−0.260020 + 0.965603i \(0.583729\pi\)
\(888\) −18.5784 −0.623449
\(889\) 3.32979 0.111677
\(890\) −61.5680 −2.06376
\(891\) −17.3614 −0.581627
\(892\) 58.0744 1.94448
\(893\) −26.4068 −0.883671
\(894\) 28.9536 0.968352
\(895\) −32.1709 −1.07535
\(896\) 1.42351 0.0475561
\(897\) 1.42033 0.0474235
\(898\) −63.7512 −2.12741
\(899\) −0.713591 −0.0237996
\(900\) −139.831 −4.66103
\(901\) −10.1312 −0.337518
\(902\) −5.96135 −0.198491
\(903\) 0.657367 0.0218758
\(904\) 25.4357 0.845978
\(905\) −52.4868 −1.74472
\(906\) 11.7604 0.390714
\(907\) −39.2318 −1.30267 −0.651335 0.758790i \(-0.725791\pi\)
−0.651335 + 0.758790i \(0.725791\pi\)
\(908\) −0.277624 −0.00921329
\(909\) −32.3646 −1.07347
\(910\) 0.718719 0.0238253
\(911\) −5.76089 −0.190867 −0.0954335 0.995436i \(-0.530424\pi\)
−0.0954335 + 0.995436i \(0.530424\pi\)
\(912\) −19.1808 −0.635139
\(913\) 34.4356 1.13965
\(914\) 39.4961 1.30642
\(915\) −25.2814 −0.835778
\(916\) −58.2364 −1.92418
\(917\) −2.41243 −0.0796654
\(918\) −17.0567 −0.562955
\(919\) 0.140223 0.00462552 0.00231276 0.999997i \(-0.499264\pi\)
0.00231276 + 0.999997i \(0.499264\pi\)
\(920\) −186.571 −6.15106
\(921\) 14.0596 0.463280
\(922\) −12.0399 −0.396514
\(923\) −0.666725 −0.0219455
\(924\) 1.06816 0.0351400
\(925\) −60.0812 −1.97546
\(926\) 3.83482 0.126020
\(927\) 30.9830 1.01761
\(928\) −4.50892 −0.148013
\(929\) −47.0006 −1.54204 −0.771020 0.636811i \(-0.780253\pi\)
−0.771020 + 0.636811i \(0.780253\pi\)
\(930\) 5.98186 0.196153
\(931\) −32.6336 −1.06952
\(932\) −92.6835 −3.03595
\(933\) −13.9699 −0.457355
\(934\) 49.3599 1.61510
\(935\) 23.4465 0.766783
\(936\) 7.30710 0.238840
\(937\) 5.30514 0.173311 0.0866557 0.996238i \(-0.472382\pi\)
0.0866557 + 0.996238i \(0.472382\pi\)
\(938\) 0.0720177 0.00235146
\(939\) 10.5781 0.345204
\(940\) 104.176 3.39783
\(941\) −28.6096 −0.932645 −0.466322 0.884615i \(-0.654421\pi\)
−0.466322 + 0.884615i \(0.654421\pi\)
\(942\) −24.0165 −0.782499
\(943\) 6.22428 0.202690
\(944\) −8.36489 −0.272254
\(945\) −2.06203 −0.0670780
\(946\) −48.8294 −1.58758
\(947\) −4.16170 −0.135237 −0.0676186 0.997711i \(-0.521540\pi\)
−0.0676186 + 0.997711i \(0.521540\pi\)
\(948\) 27.3705 0.888952
\(949\) −1.89100 −0.0613844
\(950\) −133.502 −4.33138
\(951\) −16.4231 −0.532557
\(952\) −2.64052 −0.0855796
\(953\) −12.1201 −0.392607 −0.196304 0.980543i \(-0.562894\pi\)
−0.196304 + 0.980543i \(0.562894\pi\)
\(954\) −31.5765 −1.02233
\(955\) −52.4099 −1.69594
\(956\) 8.23300 0.266274
\(957\) 0.836653 0.0270452
\(958\) −8.32964 −0.269118
\(959\) −2.46324 −0.0795423
\(960\) 4.92972 0.159106
\(961\) −29.7186 −0.958664
\(962\) 5.55060 0.178959
\(963\) 23.1522 0.746070
\(964\) −23.9797 −0.772333
\(965\) 97.7386 3.14632
\(966\) −1.59971 −0.0514697
\(967\) −25.0274 −0.804828 −0.402414 0.915458i \(-0.631829\pi\)
−0.402414 + 0.915458i \(0.631829\pi\)
\(968\) 28.7460 0.923932
\(969\) −5.41672 −0.174010
\(970\) 198.677 6.37914
\(971\) 8.47180 0.271873 0.135937 0.990718i \(-0.456596\pi\)
0.135937 + 0.990718i \(0.456596\pi\)
\(972\) −56.4433 −1.81042
\(973\) −1.89197 −0.0606538
\(974\) −71.3723 −2.28692
\(975\) −2.26790 −0.0726309
\(976\) −98.2639 −3.14535
\(977\) 41.4737 1.32686 0.663431 0.748237i \(-0.269099\pi\)
0.663431 + 0.748237i \(0.269099\pi\)
\(978\) 14.2106 0.454403
\(979\) 15.4634 0.494213
\(980\) 128.740 4.11246
\(981\) −12.1245 −0.387106
\(982\) −16.5669 −0.528671
\(983\) 12.2387 0.390354 0.195177 0.980768i \(-0.437472\pi\)
0.195177 + 0.980768i \(0.437472\pi\)
\(984\) −3.07321 −0.0979702
\(985\) 16.4096 0.522853
\(986\) −3.65643 −0.116444
\(987\) 0.505244 0.0160821
\(988\) 8.59868 0.273560
\(989\) 50.9830 1.62116
\(990\) 73.0776 2.32256
\(991\) 19.8732 0.631294 0.315647 0.948877i \(-0.397778\pi\)
0.315647 + 0.948877i \(0.397778\pi\)
\(992\) 8.09682 0.257074
\(993\) −2.30928 −0.0732827
\(994\) 0.750925 0.0238179
\(995\) 4.38384 0.138977
\(996\) 31.3845 0.994456
\(997\) 18.4035 0.582844 0.291422 0.956595i \(-0.405872\pi\)
0.291422 + 0.956595i \(0.405872\pi\)
\(998\) −71.4185 −2.26071
\(999\) −15.9249 −0.503842
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 \(a_p\))