Properties

Label 8042.2.a.a.1.7
Level 8042
Weight 2
Character 8042.1
Self dual Yes
Analytic conductor 64.216
Analytic rank 1
Dimension 67
CM No

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Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(1\)
Dimension: \(67\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.60646 q^{3}\) \(+1.00000 q^{4}\) \(-0.616826 q^{5}\) \(-2.60646 q^{6}\) \(-3.04419 q^{7}\) \(+1.00000 q^{8}\) \(+3.79362 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.60646 q^{3}\) \(+1.00000 q^{4}\) \(-0.616826 q^{5}\) \(-2.60646 q^{6}\) \(-3.04419 q^{7}\) \(+1.00000 q^{8}\) \(+3.79362 q^{9}\) \(-0.616826 q^{10}\) \(-0.708752 q^{11}\) \(-2.60646 q^{12}\) \(+4.52204 q^{13}\) \(-3.04419 q^{14}\) \(+1.60773 q^{15}\) \(+1.00000 q^{16}\) \(-7.53136 q^{17}\) \(+3.79362 q^{18}\) \(+1.15378 q^{19}\) \(-0.616826 q^{20}\) \(+7.93454 q^{21}\) \(-0.708752 q^{22}\) \(+6.01283 q^{23}\) \(-2.60646 q^{24}\) \(-4.61953 q^{25}\) \(+4.52204 q^{26}\) \(-2.06853 q^{27}\) \(-3.04419 q^{28}\) \(+3.05269 q^{29}\) \(+1.60773 q^{30}\) \(-4.59808 q^{31}\) \(+1.00000 q^{32}\) \(+1.84733 q^{33}\) \(-7.53136 q^{34}\) \(+1.87773 q^{35}\) \(+3.79362 q^{36}\) \(+0.716683 q^{37}\) \(+1.15378 q^{38}\) \(-11.7865 q^{39}\) \(-0.616826 q^{40}\) \(+5.61551 q^{41}\) \(+7.93454 q^{42}\) \(+1.06760 q^{43}\) \(-0.708752 q^{44}\) \(-2.34000 q^{45}\) \(+6.01283 q^{46}\) \(+5.03724 q^{47}\) \(-2.60646 q^{48}\) \(+2.26707 q^{49}\) \(-4.61953 q^{50}\) \(+19.6302 q^{51}\) \(+4.52204 q^{52}\) \(-6.45049 q^{53}\) \(-2.06853 q^{54}\) \(+0.437177 q^{55}\) \(-3.04419 q^{56}\) \(-3.00729 q^{57}\) \(+3.05269 q^{58}\) \(+1.48533 q^{59}\) \(+1.60773 q^{60}\) \(-1.93080 q^{61}\) \(-4.59808 q^{62}\) \(-11.5485 q^{63}\) \(+1.00000 q^{64}\) \(-2.78932 q^{65}\) \(+1.84733 q^{66}\) \(-2.98628 q^{67}\) \(-7.53136 q^{68}\) \(-15.6722 q^{69}\) \(+1.87773 q^{70}\) \(+11.7144 q^{71}\) \(+3.79362 q^{72}\) \(+5.50758 q^{73}\) \(+0.716683 q^{74}\) \(+12.0406 q^{75}\) \(+1.15378 q^{76}\) \(+2.15757 q^{77}\) \(-11.7865 q^{78}\) \(+10.9722 q^{79}\) \(-0.616826 q^{80}\) \(-5.98931 q^{81}\) \(+5.61551 q^{82}\) \(-1.61518 q^{83}\) \(+7.93454 q^{84}\) \(+4.64554 q^{85}\) \(+1.06760 q^{86}\) \(-7.95672 q^{87}\) \(-0.708752 q^{88}\) \(+2.45925 q^{89}\) \(-2.34000 q^{90}\) \(-13.7659 q^{91}\) \(+6.01283 q^{92}\) \(+11.9847 q^{93}\) \(+5.03724 q^{94}\) \(-0.711684 q^{95}\) \(-2.60646 q^{96}\) \(+12.5402 q^{97}\) \(+2.26707 q^{98}\) \(-2.68873 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.60646 −1.50484 −0.752419 0.658684i \(-0.771113\pi\)
−0.752419 + 0.658684i \(0.771113\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.616826 −0.275853 −0.137927 0.990442i \(-0.544044\pi\)
−0.137927 + 0.990442i \(0.544044\pi\)
\(6\) −2.60646 −1.06408
\(7\) −3.04419 −1.15059 −0.575297 0.817944i \(-0.695114\pi\)
−0.575297 + 0.817944i \(0.695114\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.79362 1.26454
\(10\) −0.616826 −0.195058
\(11\) −0.708752 −0.213697 −0.106848 0.994275i \(-0.534076\pi\)
−0.106848 + 0.994275i \(0.534076\pi\)
\(12\) −2.60646 −0.752419
\(13\) 4.52204 1.25419 0.627095 0.778943i \(-0.284244\pi\)
0.627095 + 0.778943i \(0.284244\pi\)
\(14\) −3.04419 −0.813593
\(15\) 1.60773 0.415114
\(16\) 1.00000 0.250000
\(17\) −7.53136 −1.82662 −0.913311 0.407263i \(-0.866483\pi\)
−0.913311 + 0.407263i \(0.866483\pi\)
\(18\) 3.79362 0.894165
\(19\) 1.15378 0.264696 0.132348 0.991203i \(-0.457748\pi\)
0.132348 + 0.991203i \(0.457748\pi\)
\(20\) −0.616826 −0.137927
\(21\) 7.93454 1.73146
\(22\) −0.708752 −0.151106
\(23\) 6.01283 1.25376 0.626881 0.779115i \(-0.284331\pi\)
0.626881 + 0.779115i \(0.284331\pi\)
\(24\) −2.60646 −0.532041
\(25\) −4.61953 −0.923905
\(26\) 4.52204 0.886846
\(27\) −2.06853 −0.398090
\(28\) −3.04419 −0.575297
\(29\) 3.05269 0.566871 0.283436 0.958991i \(-0.408526\pi\)
0.283436 + 0.958991i \(0.408526\pi\)
\(30\) 1.60773 0.293530
\(31\) −4.59808 −0.825839 −0.412920 0.910767i \(-0.635491\pi\)
−0.412920 + 0.910767i \(0.635491\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.84733 0.321579
\(34\) −7.53136 −1.29162
\(35\) 1.87773 0.317395
\(36\) 3.79362 0.632270
\(37\) 0.716683 0.117822 0.0589110 0.998263i \(-0.481237\pi\)
0.0589110 + 0.998263i \(0.481237\pi\)
\(38\) 1.15378 0.187168
\(39\) −11.7865 −1.88735
\(40\) −0.616826 −0.0975288
\(41\) 5.61551 0.876996 0.438498 0.898732i \(-0.355511\pi\)
0.438498 + 0.898732i \(0.355511\pi\)
\(42\) 7.93454 1.22433
\(43\) 1.06760 0.162807 0.0814035 0.996681i \(-0.474060\pi\)
0.0814035 + 0.996681i \(0.474060\pi\)
\(44\) −0.708752 −0.106848
\(45\) −2.34000 −0.348827
\(46\) 6.01283 0.886544
\(47\) 5.03724 0.734757 0.367378 0.930072i \(-0.380255\pi\)
0.367378 + 0.930072i \(0.380255\pi\)
\(48\) −2.60646 −0.376210
\(49\) 2.26707 0.323868
\(50\) −4.61953 −0.653300
\(51\) 19.6302 2.74877
\(52\) 4.52204 0.627095
\(53\) −6.45049 −0.886043 −0.443021 0.896511i \(-0.646093\pi\)
−0.443021 + 0.896511i \(0.646093\pi\)
\(54\) −2.06853 −0.281492
\(55\) 0.437177 0.0589489
\(56\) −3.04419 −0.406797
\(57\) −3.00729 −0.398325
\(58\) 3.05269 0.400838
\(59\) 1.48533 0.193373 0.0966866 0.995315i \(-0.469176\pi\)
0.0966866 + 0.995315i \(0.469176\pi\)
\(60\) 1.60773 0.207557
\(61\) −1.93080 −0.247214 −0.123607 0.992331i \(-0.539446\pi\)
−0.123607 + 0.992331i \(0.539446\pi\)
\(62\) −4.59808 −0.583957
\(63\) −11.5485 −1.45497
\(64\) 1.00000 0.125000
\(65\) −2.78932 −0.345972
\(66\) 1.84733 0.227391
\(67\) −2.98628 −0.364832 −0.182416 0.983221i \(-0.558392\pi\)
−0.182416 + 0.983221i \(0.558392\pi\)
\(68\) −7.53136 −0.913311
\(69\) −15.6722 −1.88671
\(70\) 1.87773 0.224432
\(71\) 11.7144 1.39025 0.695124 0.718890i \(-0.255349\pi\)
0.695124 + 0.718890i \(0.255349\pi\)
\(72\) 3.79362 0.447082
\(73\) 5.50758 0.644614 0.322307 0.946635i \(-0.395542\pi\)
0.322307 + 0.946635i \(0.395542\pi\)
\(74\) 0.716683 0.0833127
\(75\) 12.0406 1.39033
\(76\) 1.15378 0.132348
\(77\) 2.15757 0.245878
\(78\) −11.7865 −1.33456
\(79\) 10.9722 1.23447 0.617236 0.786778i \(-0.288252\pi\)
0.617236 + 0.786778i \(0.288252\pi\)
\(80\) −0.616826 −0.0689633
\(81\) −5.98931 −0.665479
\(82\) 5.61551 0.620130
\(83\) −1.61518 −0.177289 −0.0886443 0.996063i \(-0.528253\pi\)
−0.0886443 + 0.996063i \(0.528253\pi\)
\(84\) 7.93454 0.865730
\(85\) 4.64554 0.503879
\(86\) 1.06760 0.115122
\(87\) −7.95672 −0.853050
\(88\) −0.708752 −0.0755532
\(89\) 2.45925 0.260680 0.130340 0.991469i \(-0.458393\pi\)
0.130340 + 0.991469i \(0.458393\pi\)
\(90\) −2.34000 −0.246658
\(91\) −13.7659 −1.44306
\(92\) 6.01283 0.626881
\(93\) 11.9847 1.24275
\(94\) 5.03724 0.519552
\(95\) −0.711684 −0.0730173
\(96\) −2.60646 −0.266020
\(97\) 12.5402 1.27326 0.636632 0.771168i \(-0.280327\pi\)
0.636632 + 0.771168i \(0.280327\pi\)
\(98\) 2.26707 0.229009
\(99\) −2.68873 −0.270228
\(100\) −4.61953 −0.461953
\(101\) −13.5576 −1.34904 −0.674518 0.738258i \(-0.735648\pi\)
−0.674518 + 0.738258i \(0.735648\pi\)
\(102\) 19.6302 1.94367
\(103\) 19.5165 1.92302 0.961508 0.274778i \(-0.0886042\pi\)
0.961508 + 0.274778i \(0.0886042\pi\)
\(104\) 4.52204 0.443423
\(105\) −4.89423 −0.477628
\(106\) −6.45049 −0.626527
\(107\) −12.9180 −1.24883 −0.624417 0.781091i \(-0.714664\pi\)
−0.624417 + 0.781091i \(0.714664\pi\)
\(108\) −2.06853 −0.199045
\(109\) −3.93185 −0.376603 −0.188301 0.982111i \(-0.560298\pi\)
−0.188301 + 0.982111i \(0.560298\pi\)
\(110\) 0.437177 0.0416832
\(111\) −1.86800 −0.177303
\(112\) −3.04419 −0.287649
\(113\) −18.6937 −1.75856 −0.879279 0.476307i \(-0.841975\pi\)
−0.879279 + 0.476307i \(0.841975\pi\)
\(114\) −3.00729 −0.281658
\(115\) −3.70887 −0.345854
\(116\) 3.05269 0.283436
\(117\) 17.1549 1.58597
\(118\) 1.48533 0.136735
\(119\) 22.9269 2.10170
\(120\) 1.60773 0.146765
\(121\) −10.4977 −0.954334
\(122\) −1.93080 −0.174807
\(123\) −14.6366 −1.31974
\(124\) −4.59808 −0.412920
\(125\) 5.93358 0.530715
\(126\) −11.5485 −1.02882
\(127\) −5.47636 −0.485949 −0.242974 0.970033i \(-0.578123\pi\)
−0.242974 + 0.970033i \(0.578123\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.78265 −0.244998
\(130\) −2.78932 −0.244639
\(131\) 19.0650 1.66572 0.832859 0.553485i \(-0.186702\pi\)
0.832859 + 0.553485i \(0.186702\pi\)
\(132\) 1.84733 0.160790
\(133\) −3.51233 −0.304558
\(134\) −2.98628 −0.257976
\(135\) 1.27593 0.109814
\(136\) −7.53136 −0.645808
\(137\) −15.1802 −1.29693 −0.648466 0.761244i \(-0.724589\pi\)
−0.648466 + 0.761244i \(0.724589\pi\)
\(138\) −15.6722 −1.33411
\(139\) −6.26425 −0.531327 −0.265664 0.964066i \(-0.585591\pi\)
−0.265664 + 0.964066i \(0.585591\pi\)
\(140\) 1.87773 0.158698
\(141\) −13.1293 −1.10569
\(142\) 11.7144 0.983054
\(143\) −3.20501 −0.268016
\(144\) 3.79362 0.316135
\(145\) −1.88298 −0.156373
\(146\) 5.50758 0.455811
\(147\) −5.90903 −0.487368
\(148\) 0.716683 0.0589110
\(149\) 14.4738 1.18574 0.592872 0.805297i \(-0.297994\pi\)
0.592872 + 0.805297i \(0.297994\pi\)
\(150\) 12.0406 0.983110
\(151\) −0.119120 −0.00969382 −0.00484691 0.999988i \(-0.501543\pi\)
−0.00484691 + 0.999988i \(0.501543\pi\)
\(152\) 1.15378 0.0935842
\(153\) −28.5711 −2.30984
\(154\) 2.15757 0.173862
\(155\) 2.83622 0.227810
\(156\) −11.7865 −0.943676
\(157\) 15.5116 1.23796 0.618978 0.785408i \(-0.287547\pi\)
0.618978 + 0.785408i \(0.287547\pi\)
\(158\) 10.9722 0.872904
\(159\) 16.8129 1.33335
\(160\) −0.616826 −0.0487644
\(161\) −18.3042 −1.44257
\(162\) −5.98931 −0.470565
\(163\) −15.0880 −1.18178 −0.590890 0.806752i \(-0.701223\pi\)
−0.590890 + 0.806752i \(0.701223\pi\)
\(164\) 5.61551 0.438498
\(165\) −1.13948 −0.0887086
\(166\) −1.61518 −0.125362
\(167\) 14.4544 1.11851 0.559257 0.828994i \(-0.311086\pi\)
0.559257 + 0.828994i \(0.311086\pi\)
\(168\) 7.93454 0.612163
\(169\) 7.44888 0.572991
\(170\) 4.64554 0.356296
\(171\) 4.37702 0.334719
\(172\) 1.06760 0.0814035
\(173\) −13.1084 −0.996610 −0.498305 0.867002i \(-0.666044\pi\)
−0.498305 + 0.867002i \(0.666044\pi\)
\(174\) −7.95672 −0.603197
\(175\) 14.0627 1.06304
\(176\) −0.708752 −0.0534242
\(177\) −3.87144 −0.290995
\(178\) 2.45925 0.184329
\(179\) −5.73901 −0.428954 −0.214477 0.976729i \(-0.568805\pi\)
−0.214477 + 0.976729i \(0.568805\pi\)
\(180\) −2.34000 −0.174414
\(181\) −4.15790 −0.309054 −0.154527 0.987989i \(-0.549385\pi\)
−0.154527 + 0.987989i \(0.549385\pi\)
\(182\) −13.7659 −1.02040
\(183\) 5.03255 0.372017
\(184\) 6.01283 0.443272
\(185\) −0.442069 −0.0325016
\(186\) 11.9847 0.878760
\(187\) 5.33786 0.390343
\(188\) 5.03724 0.367378
\(189\) 6.29700 0.458040
\(190\) −0.711684 −0.0516310
\(191\) −10.2417 −0.741062 −0.370531 0.928820i \(-0.620824\pi\)
−0.370531 + 0.928820i \(0.620824\pi\)
\(192\) −2.60646 −0.188105
\(193\) −1.58131 −0.113825 −0.0569127 0.998379i \(-0.518126\pi\)
−0.0569127 + 0.998379i \(0.518126\pi\)
\(194\) 12.5402 0.900334
\(195\) 7.27023 0.520632
\(196\) 2.26707 0.161934
\(197\) 0.465375 0.0331566 0.0165783 0.999863i \(-0.494723\pi\)
0.0165783 + 0.999863i \(0.494723\pi\)
\(198\) −2.68873 −0.191080
\(199\) 0.780673 0.0553404 0.0276702 0.999617i \(-0.491191\pi\)
0.0276702 + 0.999617i \(0.491191\pi\)
\(200\) −4.61953 −0.326650
\(201\) 7.78362 0.549014
\(202\) −13.5576 −0.953912
\(203\) −9.29297 −0.652239
\(204\) 19.6302 1.37439
\(205\) −3.46380 −0.241922
\(206\) 19.5165 1.35978
\(207\) 22.8104 1.58543
\(208\) 4.52204 0.313547
\(209\) −0.817747 −0.0565647
\(210\) −4.89423 −0.337734
\(211\) −24.0924 −1.65859 −0.829296 0.558809i \(-0.811258\pi\)
−0.829296 + 0.558809i \(0.811258\pi\)
\(212\) −6.45049 −0.443021
\(213\) −30.5332 −2.09210
\(214\) −12.9180 −0.883059
\(215\) −0.658522 −0.0449108
\(216\) −2.06853 −0.140746
\(217\) 13.9974 0.950206
\(218\) −3.93185 −0.266299
\(219\) −14.3553 −0.970040
\(220\) 0.437177 0.0294745
\(221\) −34.0571 −2.29093
\(222\) −1.86800 −0.125372
\(223\) −18.9446 −1.26862 −0.634312 0.773077i \(-0.718716\pi\)
−0.634312 + 0.773077i \(0.718716\pi\)
\(224\) −3.04419 −0.203398
\(225\) −17.5247 −1.16831
\(226\) −18.6937 −1.24349
\(227\) −21.2732 −1.41195 −0.705975 0.708237i \(-0.749491\pi\)
−0.705975 + 0.708237i \(0.749491\pi\)
\(228\) −3.00729 −0.199163
\(229\) 9.46496 0.625462 0.312731 0.949842i \(-0.398756\pi\)
0.312731 + 0.949842i \(0.398756\pi\)
\(230\) −3.70887 −0.244556
\(231\) −5.62362 −0.370007
\(232\) 3.05269 0.200419
\(233\) −7.44251 −0.487575 −0.243787 0.969829i \(-0.578390\pi\)
−0.243787 + 0.969829i \(0.578390\pi\)
\(234\) 17.1549 1.12145
\(235\) −3.10710 −0.202685
\(236\) 1.48533 0.0966866
\(237\) −28.5986 −1.85768
\(238\) 22.9269 1.48613
\(239\) 23.9371 1.54837 0.774183 0.632962i \(-0.218161\pi\)
0.774183 + 0.632962i \(0.218161\pi\)
\(240\) 1.60773 0.103779
\(241\) −7.34849 −0.473358 −0.236679 0.971588i \(-0.576059\pi\)
−0.236679 + 0.971588i \(0.576059\pi\)
\(242\) −10.4977 −0.674816
\(243\) 21.8165 1.39953
\(244\) −1.93080 −0.123607
\(245\) −1.39839 −0.0893399
\(246\) −14.6366 −0.933195
\(247\) 5.21746 0.331979
\(248\) −4.59808 −0.291978
\(249\) 4.20989 0.266791
\(250\) 5.93358 0.375272
\(251\) 23.0951 1.45775 0.728876 0.684646i \(-0.240043\pi\)
0.728876 + 0.684646i \(0.240043\pi\)
\(252\) −11.5485 −0.727486
\(253\) −4.26161 −0.267925
\(254\) −5.47636 −0.343618
\(255\) −12.1084 −0.758257
\(256\) 1.00000 0.0625000
\(257\) −15.9746 −0.996469 −0.498235 0.867042i \(-0.666018\pi\)
−0.498235 + 0.867042i \(0.666018\pi\)
\(258\) −2.78265 −0.173240
\(259\) −2.18172 −0.135565
\(260\) −2.78932 −0.172986
\(261\) 11.5808 0.716831
\(262\) 19.0650 1.17784
\(263\) −20.7078 −1.27690 −0.638450 0.769663i \(-0.720424\pi\)
−0.638450 + 0.769663i \(0.720424\pi\)
\(264\) 1.84733 0.113695
\(265\) 3.97883 0.244418
\(266\) −3.51233 −0.215355
\(267\) −6.40994 −0.392282
\(268\) −2.98628 −0.182416
\(269\) −30.4598 −1.85716 −0.928582 0.371127i \(-0.878972\pi\)
−0.928582 + 0.371127i \(0.878972\pi\)
\(270\) 1.27593 0.0776504
\(271\) −21.4757 −1.30456 −0.652278 0.757980i \(-0.726186\pi\)
−0.652278 + 0.757980i \(0.726186\pi\)
\(272\) −7.53136 −0.456655
\(273\) 35.8804 2.17158
\(274\) −15.1802 −0.917069
\(275\) 3.27410 0.197436
\(276\) −15.6722 −0.943355
\(277\) −13.6355 −0.819276 −0.409638 0.912248i \(-0.634345\pi\)
−0.409638 + 0.912248i \(0.634345\pi\)
\(278\) −6.26425 −0.375705
\(279\) −17.4434 −1.04431
\(280\) 1.87773 0.112216
\(281\) −6.77677 −0.404268 −0.202134 0.979358i \(-0.564788\pi\)
−0.202134 + 0.979358i \(0.564788\pi\)
\(282\) −13.1293 −0.781841
\(283\) 5.42191 0.322299 0.161150 0.986930i \(-0.448480\pi\)
0.161150 + 0.986930i \(0.448480\pi\)
\(284\) 11.7144 0.695124
\(285\) 1.85497 0.109879
\(286\) −3.20501 −0.189516
\(287\) −17.0947 −1.00907
\(288\) 3.79362 0.223541
\(289\) 39.7213 2.33655
\(290\) −1.88298 −0.110573
\(291\) −32.6855 −1.91606
\(292\) 5.50758 0.322307
\(293\) 2.48853 0.145382 0.0726908 0.997355i \(-0.476841\pi\)
0.0726908 + 0.997355i \(0.476841\pi\)
\(294\) −5.90903 −0.344622
\(295\) −0.916189 −0.0533426
\(296\) 0.716683 0.0416564
\(297\) 1.46608 0.0850704
\(298\) 14.4738 0.838447
\(299\) 27.1903 1.57246
\(300\) 12.0406 0.695164
\(301\) −3.24996 −0.187325
\(302\) −0.119120 −0.00685457
\(303\) 35.3374 2.03008
\(304\) 1.15378 0.0661740
\(305\) 1.19097 0.0681947
\(306\) −28.5711 −1.63330
\(307\) −14.6098 −0.833828 −0.416914 0.908946i \(-0.636888\pi\)
−0.416914 + 0.908946i \(0.636888\pi\)
\(308\) 2.15757 0.122939
\(309\) −50.8689 −2.89383
\(310\) 2.83622 0.161086
\(311\) −11.7922 −0.668677 −0.334338 0.942453i \(-0.608513\pi\)
−0.334338 + 0.942453i \(0.608513\pi\)
\(312\) −11.7865 −0.667280
\(313\) −5.04499 −0.285160 −0.142580 0.989783i \(-0.545540\pi\)
−0.142580 + 0.989783i \(0.545540\pi\)
\(314\) 15.5116 0.875368
\(315\) 7.12341 0.401359
\(316\) 10.9722 0.617236
\(317\) −11.4506 −0.643131 −0.321566 0.946887i \(-0.604209\pi\)
−0.321566 + 0.946887i \(0.604209\pi\)
\(318\) 16.8129 0.942822
\(319\) −2.16360 −0.121139
\(320\) −0.616826 −0.0344816
\(321\) 33.6703 1.87929
\(322\) −18.3042 −1.02005
\(323\) −8.68956 −0.483500
\(324\) −5.98931 −0.332740
\(325\) −20.8897 −1.15875
\(326\) −15.0880 −0.835645
\(327\) 10.2482 0.566727
\(328\) 5.61551 0.310065
\(329\) −15.3343 −0.845407
\(330\) −1.13948 −0.0627265
\(331\) −23.9042 −1.31390 −0.656948 0.753936i \(-0.728153\pi\)
−0.656948 + 0.753936i \(0.728153\pi\)
\(332\) −1.61518 −0.0886443
\(333\) 2.71882 0.148991
\(334\) 14.4544 0.790909
\(335\) 1.84202 0.100640
\(336\) 7.93454 0.432865
\(337\) −17.9843 −0.979667 −0.489833 0.871816i \(-0.662942\pi\)
−0.489833 + 0.871816i \(0.662942\pi\)
\(338\) 7.44888 0.405166
\(339\) 48.7244 2.64635
\(340\) 4.64554 0.251940
\(341\) 3.25890 0.176479
\(342\) 4.37702 0.236682
\(343\) 14.4079 0.777954
\(344\) 1.06760 0.0575610
\(345\) 9.66702 0.520455
\(346\) −13.1084 −0.704710
\(347\) 17.4068 0.934447 0.467224 0.884139i \(-0.345254\pi\)
0.467224 + 0.884139i \(0.345254\pi\)
\(348\) −7.95672 −0.426525
\(349\) −29.2073 −1.56343 −0.781716 0.623635i \(-0.785655\pi\)
−0.781716 + 0.623635i \(0.785655\pi\)
\(350\) 14.0627 0.751683
\(351\) −9.35400 −0.499280
\(352\) −0.708752 −0.0377766
\(353\) −18.7365 −0.997242 −0.498621 0.866820i \(-0.666160\pi\)
−0.498621 + 0.866820i \(0.666160\pi\)
\(354\) −3.87144 −0.205765
\(355\) −7.22578 −0.383504
\(356\) 2.45925 0.130340
\(357\) −59.7579 −3.16272
\(358\) −5.73901 −0.303316
\(359\) 26.8376 1.41643 0.708216 0.705995i \(-0.249500\pi\)
0.708216 + 0.705995i \(0.249500\pi\)
\(360\) −2.34000 −0.123329
\(361\) −17.6688 −0.929936
\(362\) −4.15790 −0.218535
\(363\) 27.3617 1.43612
\(364\) −13.7659 −0.721532
\(365\) −3.39722 −0.177819
\(366\) 5.03255 0.263056
\(367\) 17.6152 0.919505 0.459752 0.888047i \(-0.347938\pi\)
0.459752 + 0.888047i \(0.347938\pi\)
\(368\) 6.01283 0.313441
\(369\) 21.3031 1.10900
\(370\) −0.442069 −0.0229821
\(371\) 19.6365 1.01948
\(372\) 11.9847 0.621377
\(373\) 37.0947 1.92069 0.960346 0.278811i \(-0.0899404\pi\)
0.960346 + 0.278811i \(0.0899404\pi\)
\(374\) 5.33786 0.276014
\(375\) −15.4656 −0.798641
\(376\) 5.03724 0.259776
\(377\) 13.8044 0.710964
\(378\) 6.29700 0.323883
\(379\) 11.6444 0.598131 0.299065 0.954233i \(-0.403325\pi\)
0.299065 + 0.954233i \(0.403325\pi\)
\(380\) −0.711684 −0.0365086
\(381\) 14.2739 0.731275
\(382\) −10.2417 −0.524010
\(383\) 7.91835 0.404609 0.202304 0.979323i \(-0.435157\pi\)
0.202304 + 0.979323i \(0.435157\pi\)
\(384\) −2.60646 −0.133010
\(385\) −1.33085 −0.0678263
\(386\) −1.58131 −0.0804867
\(387\) 4.05006 0.205876
\(388\) 12.5402 0.636632
\(389\) 22.7545 1.15370 0.576849 0.816851i \(-0.304282\pi\)
0.576849 + 0.816851i \(0.304282\pi\)
\(390\) 7.27023 0.368143
\(391\) −45.2848 −2.29015
\(392\) 2.26707 0.114504
\(393\) −49.6922 −2.50664
\(394\) 0.465375 0.0234453
\(395\) −6.76796 −0.340533
\(396\) −2.68873 −0.135114
\(397\) −20.7737 −1.04260 −0.521302 0.853372i \(-0.674553\pi\)
−0.521302 + 0.853372i \(0.674553\pi\)
\(398\) 0.780673 0.0391316
\(399\) 9.15475 0.458311
\(400\) −4.61953 −0.230976
\(401\) −23.2179 −1.15945 −0.579724 0.814813i \(-0.696840\pi\)
−0.579724 + 0.814813i \(0.696840\pi\)
\(402\) 7.78362 0.388212
\(403\) −20.7927 −1.03576
\(404\) −13.5576 −0.674518
\(405\) 3.69437 0.183574
\(406\) −9.29297 −0.461202
\(407\) −0.507951 −0.0251782
\(408\) 19.6302 0.971837
\(409\) −11.9253 −0.589669 −0.294835 0.955548i \(-0.595265\pi\)
−0.294835 + 0.955548i \(0.595265\pi\)
\(410\) −3.46380 −0.171065
\(411\) 39.5665 1.95167
\(412\) 19.5165 0.961508
\(413\) −4.52161 −0.222494
\(414\) 22.8104 1.12107
\(415\) 0.996283 0.0489056
\(416\) 4.52204 0.221711
\(417\) 16.3275 0.799562
\(418\) −0.817747 −0.0399973
\(419\) 27.7954 1.35790 0.678948 0.734187i \(-0.262436\pi\)
0.678948 + 0.734187i \(0.262436\pi\)
\(420\) −4.89423 −0.238814
\(421\) −34.8715 −1.69953 −0.849765 0.527161i \(-0.823256\pi\)
−0.849765 + 0.527161i \(0.823256\pi\)
\(422\) −24.0924 −1.17280
\(423\) 19.1094 0.929129
\(424\) −6.45049 −0.313264
\(425\) 34.7913 1.68763
\(426\) −30.5332 −1.47934
\(427\) 5.87772 0.284443
\(428\) −12.9180 −0.624417
\(429\) 8.35372 0.403321
\(430\) −0.658522 −0.0317567
\(431\) −14.4154 −0.694365 −0.347183 0.937798i \(-0.612862\pi\)
−0.347183 + 0.937798i \(0.612862\pi\)
\(432\) −2.06853 −0.0995224
\(433\) −13.7117 −0.658940 −0.329470 0.944166i \(-0.606870\pi\)
−0.329470 + 0.944166i \(0.606870\pi\)
\(434\) 13.9974 0.671897
\(435\) 4.90791 0.235316
\(436\) −3.93185 −0.188301
\(437\) 6.93751 0.331866
\(438\) −14.3553 −0.685922
\(439\) 14.5141 0.692721 0.346360 0.938102i \(-0.387417\pi\)
0.346360 + 0.938102i \(0.387417\pi\)
\(440\) 0.437177 0.0208416
\(441\) 8.60041 0.409543
\(442\) −34.0571 −1.61993
\(443\) −34.0471 −1.61762 −0.808812 0.588067i \(-0.799889\pi\)
−0.808812 + 0.588067i \(0.799889\pi\)
\(444\) −1.86800 −0.0886515
\(445\) −1.51693 −0.0719095
\(446\) −18.9446 −0.897052
\(447\) −37.7255 −1.78435
\(448\) −3.04419 −0.143824
\(449\) 14.4308 0.681032 0.340516 0.940239i \(-0.389398\pi\)
0.340516 + 0.940239i \(0.389398\pi\)
\(450\) −17.5247 −0.826123
\(451\) −3.98001 −0.187411
\(452\) −18.6937 −0.879279
\(453\) 0.310480 0.0145876
\(454\) −21.2732 −0.998399
\(455\) 8.49120 0.398074
\(456\) −3.00729 −0.140829
\(457\) −17.7909 −0.832223 −0.416111 0.909314i \(-0.636607\pi\)
−0.416111 + 0.909314i \(0.636607\pi\)
\(458\) 9.46496 0.442269
\(459\) 15.5789 0.727159
\(460\) −3.70887 −0.172927
\(461\) 27.0926 1.26183 0.630915 0.775852i \(-0.282680\pi\)
0.630915 + 0.775852i \(0.282680\pi\)
\(462\) −5.62362 −0.261635
\(463\) −32.5408 −1.51230 −0.756150 0.654398i \(-0.772922\pi\)
−0.756150 + 0.654398i \(0.772922\pi\)
\(464\) 3.05269 0.141718
\(465\) −7.39247 −0.342818
\(466\) −7.44251 −0.344767
\(467\) −4.16093 −0.192545 −0.0962724 0.995355i \(-0.530692\pi\)
−0.0962724 + 0.995355i \(0.530692\pi\)
\(468\) 17.1549 0.792986
\(469\) 9.09080 0.419774
\(470\) −3.10710 −0.143320
\(471\) −40.4302 −1.86293
\(472\) 1.48533 0.0683677
\(473\) −0.756661 −0.0347913
\(474\) −28.5986 −1.31358
\(475\) −5.32993 −0.244554
\(476\) 22.9269 1.05085
\(477\) −24.4707 −1.12044
\(478\) 23.9371 1.09486
\(479\) −29.7519 −1.35940 −0.679698 0.733492i \(-0.737889\pi\)
−0.679698 + 0.733492i \(0.737889\pi\)
\(480\) 1.60773 0.0733826
\(481\) 3.24087 0.147771
\(482\) −7.34849 −0.334714
\(483\) 47.7091 2.17084
\(484\) −10.4977 −0.477167
\(485\) −7.73513 −0.351234
\(486\) 21.8165 0.989616
\(487\) 31.3125 1.41890 0.709452 0.704754i \(-0.248943\pi\)
0.709452 + 0.704754i \(0.248943\pi\)
\(488\) −1.93080 −0.0874033
\(489\) 39.3261 1.77839
\(490\) −1.39839 −0.0631728
\(491\) 2.57433 0.116178 0.0580889 0.998311i \(-0.481499\pi\)
0.0580889 + 0.998311i \(0.481499\pi\)
\(492\) −14.6366 −0.659869
\(493\) −22.9909 −1.03546
\(494\) 5.21746 0.234745
\(495\) 1.65848 0.0745432
\(496\) −4.59808 −0.206460
\(497\) −35.6610 −1.59961
\(498\) 4.20989 0.188649
\(499\) −31.6113 −1.41512 −0.707559 0.706654i \(-0.750204\pi\)
−0.707559 + 0.706654i \(0.750204\pi\)
\(500\) 5.93358 0.265358
\(501\) −37.6748 −1.68318
\(502\) 23.0951 1.03079
\(503\) −14.2842 −0.636902 −0.318451 0.947939i \(-0.603163\pi\)
−0.318451 + 0.947939i \(0.603163\pi\)
\(504\) −11.5485 −0.514410
\(505\) 8.36271 0.372136
\(506\) −4.26161 −0.189452
\(507\) −19.4152 −0.862259
\(508\) −5.47636 −0.242974
\(509\) 13.2359 0.586672 0.293336 0.956009i \(-0.405235\pi\)
0.293336 + 0.956009i \(0.405235\pi\)
\(510\) −12.1084 −0.536169
\(511\) −16.7661 −0.741689
\(512\) 1.00000 0.0441942
\(513\) −2.38664 −0.105373
\(514\) −15.9746 −0.704610
\(515\) −12.0383 −0.530470
\(516\) −2.78265 −0.122499
\(517\) −3.57015 −0.157015
\(518\) −2.18172 −0.0958591
\(519\) 34.1664 1.49974
\(520\) −2.78932 −0.122320
\(521\) 34.4885 1.51097 0.755485 0.655166i \(-0.227401\pi\)
0.755485 + 0.655166i \(0.227401\pi\)
\(522\) 11.5808 0.506876
\(523\) −31.6562 −1.38423 −0.692114 0.721788i \(-0.743321\pi\)
−0.692114 + 0.721788i \(0.743321\pi\)
\(524\) 19.0650 0.832859
\(525\) −36.6538 −1.59970
\(526\) −20.7078 −0.902905
\(527\) 34.6298 1.50850
\(528\) 1.84733 0.0803948
\(529\) 13.1542 0.571921
\(530\) 3.97883 0.172829
\(531\) 5.63477 0.244528
\(532\) −3.51233 −0.152279
\(533\) 25.3936 1.09992
\(534\) −6.40994 −0.277385
\(535\) 7.96819 0.344495
\(536\) −2.98628 −0.128988
\(537\) 14.9585 0.645507
\(538\) −30.4598 −1.31321
\(539\) −1.60679 −0.0692094
\(540\) 1.27593 0.0549071
\(541\) 9.22216 0.396492 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(542\) −21.4757 −0.922460
\(543\) 10.8374 0.465077
\(544\) −7.53136 −0.322904
\(545\) 2.42527 0.103887
\(546\) 35.8804 1.53554
\(547\) −16.5514 −0.707688 −0.353844 0.935305i \(-0.615126\pi\)
−0.353844 + 0.935305i \(0.615126\pi\)
\(548\) −15.1802 −0.648466
\(549\) −7.32473 −0.312612
\(550\) 3.27410 0.139608
\(551\) 3.52215 0.150049
\(552\) −15.6722 −0.667053
\(553\) −33.4015 −1.42038
\(554\) −13.6355 −0.579316
\(555\) 1.15223 0.0489096
\(556\) −6.26425 −0.265664
\(557\) 6.47071 0.274173 0.137086 0.990559i \(-0.456226\pi\)
0.137086 + 0.990559i \(0.456226\pi\)
\(558\) −17.4434 −0.738436
\(559\) 4.82772 0.204191
\(560\) 1.87773 0.0793488
\(561\) −13.9129 −0.587404
\(562\) −6.77677 −0.285861
\(563\) −23.4795 −0.989541 −0.494771 0.869024i \(-0.664748\pi\)
−0.494771 + 0.869024i \(0.664748\pi\)
\(564\) −13.1293 −0.552845
\(565\) 11.5308 0.485104
\(566\) 5.42191 0.227900
\(567\) 18.2326 0.765697
\(568\) 11.7144 0.491527
\(569\) −21.4300 −0.898392 −0.449196 0.893433i \(-0.648290\pi\)
−0.449196 + 0.893433i \(0.648290\pi\)
\(570\) 1.85497 0.0776963
\(571\) 3.52308 0.147437 0.0737183 0.997279i \(-0.476513\pi\)
0.0737183 + 0.997279i \(0.476513\pi\)
\(572\) −3.20501 −0.134008
\(573\) 26.6945 1.11518
\(574\) −17.0947 −0.713518
\(575\) −27.7764 −1.15836
\(576\) 3.79362 0.158067
\(577\) −37.5094 −1.56154 −0.780769 0.624820i \(-0.785173\pi\)
−0.780769 + 0.624820i \(0.785173\pi\)
\(578\) 39.7213 1.65219
\(579\) 4.12162 0.171289
\(580\) −1.88298 −0.0781866
\(581\) 4.91690 0.203987
\(582\) −32.6855 −1.35486
\(583\) 4.57180 0.189345
\(584\) 5.50758 0.227905
\(585\) −10.5816 −0.437495
\(586\) 2.48853 0.102800
\(587\) −0.295064 −0.0121786 −0.00608929 0.999981i \(-0.501938\pi\)
−0.00608929 + 0.999981i \(0.501938\pi\)
\(588\) −5.90903 −0.243684
\(589\) −5.30519 −0.218596
\(590\) −0.916189 −0.0377189
\(591\) −1.21298 −0.0498953
\(592\) 0.716683 0.0294555
\(593\) −19.9916 −0.820956 −0.410478 0.911870i \(-0.634638\pi\)
−0.410478 + 0.911870i \(0.634638\pi\)
\(594\) 1.46608 0.0601539
\(595\) −14.1419 −0.579761
\(596\) 14.4738 0.592872
\(597\) −2.03479 −0.0832784
\(598\) 27.1903 1.11189
\(599\) −5.06602 −0.206992 −0.103496 0.994630i \(-0.533003\pi\)
−0.103496 + 0.994630i \(0.533003\pi\)
\(600\) 12.0406 0.491555
\(601\) 33.4515 1.36451 0.682257 0.731113i \(-0.260999\pi\)
0.682257 + 0.731113i \(0.260999\pi\)
\(602\) −3.24996 −0.132459
\(603\) −11.3288 −0.461345
\(604\) −0.119120 −0.00484691
\(605\) 6.47524 0.263256
\(606\) 35.3374 1.43548
\(607\) 41.9650 1.70331 0.851654 0.524105i \(-0.175600\pi\)
0.851654 + 0.524105i \(0.175600\pi\)
\(608\) 1.15378 0.0467921
\(609\) 24.2217 0.981514
\(610\) 1.19097 0.0482209
\(611\) 22.7786 0.921524
\(612\) −28.5711 −1.15492
\(613\) −47.6468 −1.92444 −0.962219 0.272278i \(-0.912223\pi\)
−0.962219 + 0.272278i \(0.912223\pi\)
\(614\) −14.6098 −0.589605
\(615\) 9.02824 0.364054
\(616\) 2.15757 0.0869311
\(617\) 12.0943 0.486897 0.243449 0.969914i \(-0.421721\pi\)
0.243449 + 0.969914i \(0.421721\pi\)
\(618\) −50.8689 −2.04625
\(619\) 13.4894 0.542185 0.271093 0.962553i \(-0.412615\pi\)
0.271093 + 0.962553i \(0.412615\pi\)
\(620\) 2.83622 0.113905
\(621\) −12.4378 −0.499110
\(622\) −11.7922 −0.472826
\(623\) −7.48643 −0.299937
\(624\) −11.7865 −0.471838
\(625\) 19.4376 0.777506
\(626\) −5.04499 −0.201639
\(627\) 2.13142 0.0851208
\(628\) 15.5116 0.618978
\(629\) −5.39759 −0.215216
\(630\) 7.12341 0.283803
\(631\) 5.65521 0.225130 0.112565 0.993644i \(-0.464093\pi\)
0.112565 + 0.993644i \(0.464093\pi\)
\(632\) 10.9722 0.436452
\(633\) 62.7959 2.49591
\(634\) −11.4506 −0.454762
\(635\) 3.37797 0.134050
\(636\) 16.8129 0.666676
\(637\) 10.2518 0.406191
\(638\) −2.16360 −0.0856579
\(639\) 44.4401 1.75802
\(640\) −0.616826 −0.0243822
\(641\) 16.8022 0.663646 0.331823 0.943342i \(-0.392336\pi\)
0.331823 + 0.943342i \(0.392336\pi\)
\(642\) 33.6703 1.32886
\(643\) −7.13022 −0.281188 −0.140594 0.990067i \(-0.544901\pi\)
−0.140594 + 0.990067i \(0.544901\pi\)
\(644\) −18.3042 −0.721286
\(645\) 1.71641 0.0675835
\(646\) −8.68956 −0.341886
\(647\) −1.18914 −0.0467498 −0.0233749 0.999727i \(-0.507441\pi\)
−0.0233749 + 0.999727i \(0.507441\pi\)
\(648\) −5.98931 −0.235282
\(649\) −1.05273 −0.0413232
\(650\) −20.8897 −0.819361
\(651\) −36.4836 −1.42991
\(652\) −15.0880 −0.590890
\(653\) 26.7321 1.04611 0.523054 0.852299i \(-0.324793\pi\)
0.523054 + 0.852299i \(0.324793\pi\)
\(654\) 10.2482 0.400736
\(655\) −11.7598 −0.459494
\(656\) 5.61551 0.219249
\(657\) 20.8937 0.815140
\(658\) −15.3343 −0.597793
\(659\) −19.3339 −0.753141 −0.376570 0.926388i \(-0.622897\pi\)
−0.376570 + 0.926388i \(0.622897\pi\)
\(660\) −1.13948 −0.0443543
\(661\) 43.1667 1.67899 0.839495 0.543368i \(-0.182851\pi\)
0.839495 + 0.543368i \(0.182851\pi\)
\(662\) −23.9042 −0.929064
\(663\) 88.7684 3.44748
\(664\) −1.61518 −0.0626810
\(665\) 2.16650 0.0840133
\(666\) 2.71882 0.105352
\(667\) 18.3553 0.710722
\(668\) 14.4544 0.559257
\(669\) 49.3783 1.90907
\(670\) 1.84202 0.0711634
\(671\) 1.36846 0.0528288
\(672\) 7.93454 0.306082
\(673\) −41.2219 −1.58899 −0.794493 0.607273i \(-0.792264\pi\)
−0.794493 + 0.607273i \(0.792264\pi\)
\(674\) −17.9843 −0.692729
\(675\) 9.55564 0.367797
\(676\) 7.44888 0.286496
\(677\) 3.56036 0.136836 0.0684179 0.997657i \(-0.478205\pi\)
0.0684179 + 0.997657i \(0.478205\pi\)
\(678\) 48.7244 1.87125
\(679\) −38.1747 −1.46501
\(680\) 4.64554 0.178148
\(681\) 55.4476 2.12476
\(682\) 3.25890 0.124790
\(683\) 33.8031 1.29344 0.646720 0.762727i \(-0.276140\pi\)
0.646720 + 0.762727i \(0.276140\pi\)
\(684\) 4.37702 0.167359
\(685\) 9.36354 0.357763
\(686\) 14.4079 0.550097
\(687\) −24.6700 −0.941220
\(688\) 1.06760 0.0407017
\(689\) −29.1694 −1.11127
\(690\) 9.66702 0.368017
\(691\) 30.5921 1.16378 0.581890 0.813268i \(-0.302313\pi\)
0.581890 + 0.813268i \(0.302313\pi\)
\(692\) −13.1084 −0.498305
\(693\) 8.18501 0.310923
\(694\) 17.4068 0.660754
\(695\) 3.86396 0.146568
\(696\) −7.95672 −0.301599
\(697\) −42.2924 −1.60194
\(698\) −29.2073 −1.10551
\(699\) 19.3986 0.733721
\(700\) 14.0627 0.531520
\(701\) −34.9799 −1.32117 −0.660587 0.750750i \(-0.729693\pi\)
−0.660587 + 0.750750i \(0.729693\pi\)
\(702\) −9.35400 −0.353044
\(703\) 0.826897 0.0311870
\(704\) −0.708752 −0.0267121
\(705\) 8.09853 0.305008
\(706\) −18.7365 −0.705157
\(707\) 41.2720 1.55219
\(708\) −3.87144 −0.145498
\(709\) 13.4455 0.504955 0.252477 0.967603i \(-0.418755\pi\)
0.252477 + 0.967603i \(0.418755\pi\)
\(710\) −7.22578 −0.271179
\(711\) 41.6245 1.56104
\(712\) 2.45925 0.0921644
\(713\) −27.6475 −1.03541
\(714\) −59.7579 −2.23638
\(715\) 1.97693 0.0739331
\(716\) −5.73901 −0.214477
\(717\) −62.3912 −2.33004
\(718\) 26.8376 1.00157
\(719\) −21.6499 −0.807403 −0.403702 0.914891i \(-0.632277\pi\)
−0.403702 + 0.914891i \(0.632277\pi\)
\(720\) −2.34000 −0.0872068
\(721\) −59.4118 −2.21261
\(722\) −17.6688 −0.657564
\(723\) 19.1535 0.712327
\(724\) −4.15790 −0.154527
\(725\) −14.1020 −0.523735
\(726\) 27.3617 1.01549
\(727\) −30.9286 −1.14708 −0.573540 0.819178i \(-0.694430\pi\)
−0.573540 + 0.819178i \(0.694430\pi\)
\(728\) −13.7659 −0.510200
\(729\) −38.8958 −1.44059
\(730\) −3.39722 −0.125737
\(731\) −8.04045 −0.297387
\(732\) 5.03255 0.186008
\(733\) 2.35799 0.0870945 0.0435472 0.999051i \(-0.486134\pi\)
0.0435472 + 0.999051i \(0.486134\pi\)
\(734\) 17.6152 0.650188
\(735\) 3.64484 0.134442
\(736\) 6.01283 0.221636
\(737\) 2.11653 0.0779635
\(738\) 21.3031 0.784179
\(739\) 6.06474 0.223095 0.111548 0.993759i \(-0.464419\pi\)
0.111548 + 0.993759i \(0.464419\pi\)
\(740\) −0.442069 −0.0162508
\(741\) −13.5991 −0.499575
\(742\) 19.6365 0.720878
\(743\) −15.9695 −0.585862 −0.292931 0.956134i \(-0.594631\pi\)
−0.292931 + 0.956134i \(0.594631\pi\)
\(744\) 11.9847 0.439380
\(745\) −8.92785 −0.327091
\(746\) 37.0947 1.35813
\(747\) −6.12736 −0.224188
\(748\) 5.33786 0.195172
\(749\) 39.3249 1.43690
\(750\) −15.4656 −0.564724
\(751\) 10.5346 0.384412 0.192206 0.981355i \(-0.438436\pi\)
0.192206 + 0.981355i \(0.438436\pi\)
\(752\) 5.03724 0.183689
\(753\) −60.1965 −2.19368
\(754\) 13.8044 0.502727
\(755\) 0.0734761 0.00267407
\(756\) 6.29700 0.229020
\(757\) −16.0653 −0.583904 −0.291952 0.956433i \(-0.594305\pi\)
−0.291952 + 0.956433i \(0.594305\pi\)
\(758\) 11.6444 0.422942
\(759\) 11.1077 0.403184
\(760\) −0.711684 −0.0258155
\(761\) −4.11506 −0.149171 −0.0745853 0.997215i \(-0.523763\pi\)
−0.0745853 + 0.997215i \(0.523763\pi\)
\(762\) 14.2739 0.517089
\(763\) 11.9693 0.433317
\(764\) −10.2417 −0.370531
\(765\) 17.6234 0.637175
\(766\) 7.91835 0.286102
\(767\) 6.71672 0.242527
\(768\) −2.60646 −0.0940524
\(769\) −30.3888 −1.09585 −0.547924 0.836528i \(-0.684582\pi\)
−0.547924 + 0.836528i \(0.684582\pi\)
\(770\) −1.33085 −0.0479604
\(771\) 41.6372 1.49953
\(772\) −1.58131 −0.0569127
\(773\) 24.3087 0.874324 0.437162 0.899383i \(-0.355984\pi\)
0.437162 + 0.899383i \(0.355984\pi\)
\(774\) 4.05006 0.145576
\(775\) 21.2409 0.762997
\(776\) 12.5402 0.450167
\(777\) 5.68655 0.204004
\(778\) 22.7545 0.815788
\(779\) 6.47909 0.232137
\(780\) 7.27023 0.260316
\(781\) −8.30263 −0.297092
\(782\) −45.2848 −1.61938
\(783\) −6.31460 −0.225665
\(784\) 2.26707 0.0809669
\(785\) −9.56794 −0.341494
\(786\) −49.6922 −1.77246
\(787\) −5.87991 −0.209596 −0.104798 0.994494i \(-0.533420\pi\)
−0.104798 + 0.994494i \(0.533420\pi\)
\(788\) 0.465375 0.0165783
\(789\) 53.9741 1.92153
\(790\) −6.76796 −0.240793
\(791\) 56.9072 2.02339
\(792\) −2.68873 −0.0955400
\(793\) −8.73117 −0.310053
\(794\) −20.7737 −0.737232
\(795\) −10.3707 −0.367809
\(796\) 0.780673 0.0276702
\(797\) 21.1411 0.748857 0.374428 0.927256i \(-0.377839\pi\)
0.374428 + 0.927256i \(0.377839\pi\)
\(798\) 9.15475 0.324075
\(799\) −37.9372 −1.34212
\(800\) −4.61953 −0.163325
\(801\) 9.32947 0.329641
\(802\) −23.2179 −0.819854
\(803\) −3.90351 −0.137752
\(804\) 7.78362 0.274507
\(805\) 11.2905 0.397938
\(806\) −20.7927 −0.732392
\(807\) 79.3921 2.79473
\(808\) −13.5576 −0.476956
\(809\) −30.7131 −1.07982 −0.539908 0.841724i \(-0.681541\pi\)
−0.539908 + 0.841724i \(0.681541\pi\)
\(810\) 3.69437 0.129807
\(811\) 27.2339 0.956311 0.478156 0.878275i \(-0.341305\pi\)
0.478156 + 0.878275i \(0.341305\pi\)
\(812\) −9.29297 −0.326119
\(813\) 55.9755 1.96315
\(814\) −0.507951 −0.0178037
\(815\) 9.30665 0.325998
\(816\) 19.6302 0.687193
\(817\) 1.23178 0.0430944
\(818\) −11.9253 −0.416959
\(819\) −52.2228 −1.82481
\(820\) −3.46380 −0.120961
\(821\) −35.8648 −1.25169 −0.625845 0.779947i \(-0.715246\pi\)
−0.625845 + 0.779947i \(0.715246\pi\)
\(822\) 39.5665 1.38004
\(823\) −1.25030 −0.0435827 −0.0217913 0.999763i \(-0.506937\pi\)
−0.0217913 + 0.999763i \(0.506937\pi\)
\(824\) 19.5165 0.679889
\(825\) −8.53380 −0.297109
\(826\) −4.52161 −0.157327
\(827\) −3.16554 −0.110077 −0.0550383 0.998484i \(-0.517528\pi\)
−0.0550383 + 0.998484i \(0.517528\pi\)
\(828\) 22.8104 0.792716
\(829\) 35.8011 1.24342 0.621712 0.783246i \(-0.286438\pi\)
0.621712 + 0.783246i \(0.286438\pi\)
\(830\) 0.996283 0.0345815
\(831\) 35.5403 1.23288
\(832\) 4.52204 0.156774
\(833\) −17.0741 −0.591584
\(834\) 16.3275 0.565375
\(835\) −8.91585 −0.308546
\(836\) −0.817747 −0.0282824
\(837\) 9.51128 0.328758
\(838\) 27.7954 0.960177
\(839\) 56.8969 1.96430 0.982150 0.188101i \(-0.0602334\pi\)
0.982150 + 0.188101i \(0.0602334\pi\)
\(840\) −4.89423 −0.168867
\(841\) −19.6811 −0.678657
\(842\) −34.8715 −1.20175
\(843\) 17.6634 0.608359
\(844\) −24.0924 −0.829296
\(845\) −4.59467 −0.158061
\(846\) 19.1094 0.656994
\(847\) 31.9569 1.09805
\(848\) −6.45049 −0.221511
\(849\) −14.1320 −0.485008
\(850\) 34.7913 1.19333
\(851\) 4.30930 0.147721
\(852\) −30.5332 −1.04605
\(853\) 44.9664 1.53962 0.769810 0.638273i \(-0.220351\pi\)
0.769810 + 0.638273i \(0.220351\pi\)
\(854\) 5.87772 0.201131
\(855\) −2.69986 −0.0923332
\(856\) −12.9180 −0.441530
\(857\) 16.0390 0.547880 0.273940 0.961747i \(-0.411673\pi\)
0.273940 + 0.961747i \(0.411673\pi\)
\(858\) 8.35372 0.285191
\(859\) −50.5465 −1.72462 −0.862311 0.506378i \(-0.830984\pi\)
−0.862311 + 0.506378i \(0.830984\pi\)
\(860\) −0.658522 −0.0224554
\(861\) 44.5565 1.51848
\(862\) −14.4154 −0.490990
\(863\) −22.6391 −0.770645 −0.385322 0.922782i \(-0.625910\pi\)
−0.385322 + 0.922782i \(0.625910\pi\)
\(864\) −2.06853 −0.0703729
\(865\) 8.08558 0.274918
\(866\) −13.7117 −0.465941
\(867\) −103.532 −3.51613
\(868\) 13.9974 0.475103
\(869\) −7.77659 −0.263803
\(870\) 4.90791 0.166394
\(871\) −13.5041 −0.457569
\(872\) −3.93185 −0.133149
\(873\) 47.5727 1.61009
\(874\) 6.93751 0.234665
\(875\) −18.0629 −0.610638
\(876\) −14.3553 −0.485020
\(877\) −9.68447 −0.327021 −0.163511 0.986542i \(-0.552282\pi\)
−0.163511 + 0.986542i \(0.552282\pi\)
\(878\) 14.5141 0.489827
\(879\) −6.48625 −0.218776
\(880\) 0.437177 0.0147372
\(881\) −3.67703 −0.123882 −0.0619411 0.998080i \(-0.519729\pi\)
−0.0619411 + 0.998080i \(0.519729\pi\)
\(882\) 8.60041 0.289591
\(883\) 6.80588 0.229036 0.114518 0.993421i \(-0.463468\pi\)
0.114518 + 0.993421i \(0.463468\pi\)
\(884\) −34.0571 −1.14546
\(885\) 2.38801 0.0802720
\(886\) −34.0471 −1.14383
\(887\) 12.8262 0.430661 0.215331 0.976541i \(-0.430917\pi\)
0.215331 + 0.976541i \(0.430917\pi\)
\(888\) −1.86800 −0.0626861
\(889\) 16.6711 0.559130
\(890\) −1.51693 −0.0508477
\(891\) 4.24494 0.142211
\(892\) −18.9446 −0.634312
\(893\) 5.81189 0.194487
\(894\) −37.7255 −1.26173
\(895\) 3.53997 0.118328
\(896\) −3.04419 −0.101699
\(897\) −70.8704 −2.36629
\(898\) 14.4308 0.481562
\(899\) −14.0365 −0.468144
\(900\) −17.5247 −0.584157
\(901\) 48.5809 1.61847
\(902\) −3.98001 −0.132520
\(903\) 8.47089 0.281894
\(904\) −18.6937 −0.621744
\(905\) 2.56470 0.0852536
\(906\) 0.310480 0.0103150
\(907\) −3.84368 −0.127627 −0.0638136 0.997962i \(-0.520326\pi\)
−0.0638136 + 0.997962i \(0.520326\pi\)
\(908\) −21.2732 −0.705975
\(909\) −51.4325 −1.70591
\(910\) 8.49120 0.281480
\(911\) 29.0050 0.960979 0.480490 0.877000i \(-0.340459\pi\)
0.480490 + 0.877000i \(0.340459\pi\)
\(912\) −3.00729 −0.0995813
\(913\) 1.14476 0.0378860
\(914\) −17.7909 −0.588470
\(915\) −3.10421 −0.102622
\(916\) 9.46496 0.312731
\(917\) −58.0375 −1.91657
\(918\) 15.5789 0.514179
\(919\) 38.3305 1.26441 0.632204 0.774802i \(-0.282151\pi\)
0.632204 + 0.774802i \(0.282151\pi\)
\(920\) −3.70887 −0.122278
\(921\) 38.0799 1.25478
\(922\) 27.0926 0.892249
\(923\) 52.9732 1.74364
\(924\) −5.62362 −0.185004
\(925\) −3.31074 −0.108856
\(926\) −32.5408 −1.06936
\(927\) 74.0381 2.43173
\(928\) 3.05269 0.100210
\(929\) 4.34903 0.142687 0.0713435 0.997452i \(-0.477271\pi\)
0.0713435 + 0.997452i \(0.477271\pi\)
\(930\) −7.39247 −0.242409
\(931\) 2.61571 0.0857265
\(932\) −7.44251 −0.243787
\(933\) 30.7360 1.00625
\(934\) −4.16093 −0.136150
\(935\) −3.29253 −0.107677
\(936\) 17.1549 0.560726
\(937\) 10.1199 0.330602 0.165301 0.986243i \(-0.447140\pi\)
0.165301 + 0.986243i \(0.447140\pi\)
\(938\) 9.09080 0.296825
\(939\) 13.1496 0.429120
\(940\) −3.10710 −0.101342
\(941\) −7.66545 −0.249887 −0.124943 0.992164i \(-0.539875\pi\)
−0.124943 + 0.992164i \(0.539875\pi\)
\(942\) −40.4302 −1.31729
\(943\) 33.7651 1.09954
\(944\) 1.48533 0.0483433
\(945\) −3.88416 −0.126352
\(946\) −0.756661 −0.0246012
\(947\) −17.1425 −0.557056 −0.278528 0.960428i \(-0.589846\pi\)
−0.278528 + 0.960428i \(0.589846\pi\)
\(948\) −28.5986 −0.928841
\(949\) 24.9055 0.808468
\(950\) −5.32993 −0.172926
\(951\) 29.8456 0.967809
\(952\) 22.9269 0.743064
\(953\) 1.31656 0.0426477 0.0213239 0.999773i \(-0.493212\pi\)
0.0213239 + 0.999773i \(0.493212\pi\)
\(954\) −24.4707 −0.792268
\(955\) 6.31734 0.204424
\(956\) 23.9371 0.774183
\(957\) 5.63934 0.182294
\(958\) −29.7519 −0.961239
\(959\) 46.2114 1.49224
\(960\) 1.60773 0.0518893
\(961\) −9.85768 −0.317990
\(962\) 3.24087 0.104490
\(963\) −49.0061 −1.57920
\(964\) −7.34849 −0.236679
\(965\) 0.975396 0.0313991
\(966\) 47.7091 1.53501
\(967\) 60.6103 1.94910 0.974549 0.224176i \(-0.0719690\pi\)
0.974549 + 0.224176i \(0.0719690\pi\)
\(968\) −10.4977 −0.337408
\(969\) 22.6490 0.727589
\(970\) −7.73513 −0.248360
\(971\) −41.5176 −1.33236 −0.666182 0.745789i \(-0.732073\pi\)
−0.666182 + 0.745789i \(0.732073\pi\)
\(972\) 21.8165 0.699764
\(973\) 19.0696 0.611342
\(974\) 31.3125 1.00332
\(975\) 54.4481 1.74373
\(976\) −1.93080 −0.0618035
\(977\) −3.73681 −0.119551 −0.0597755 0.998212i \(-0.519038\pi\)
−0.0597755 + 0.998212i \(0.519038\pi\)
\(978\) 39.3261 1.25751
\(979\) −1.74300 −0.0557065
\(980\) −1.39839 −0.0446699
\(981\) −14.9159 −0.476229
\(982\) 2.57433 0.0821501
\(983\) 43.9104 1.40053 0.700263 0.713885i \(-0.253066\pi\)
0.700263 + 0.713885i \(0.253066\pi\)
\(984\) −14.6366 −0.466598
\(985\) −0.287056 −0.00914635
\(986\) −22.9909 −0.732180
\(987\) 39.9682 1.27220
\(988\) 5.21746 0.165990
\(989\) 6.41928 0.204121
\(990\) 1.65848 0.0527100
\(991\) −22.1178 −0.702595 −0.351298 0.936264i \(-0.614259\pi\)
−0.351298 + 0.936264i \(0.614259\pi\)
\(992\) −4.59808 −0.145989
\(993\) 62.3053 1.97720
\(994\) −35.6610 −1.13110
\(995\) −0.481539 −0.0152658
\(996\) 4.20989 0.133395
\(997\) 13.8301 0.438004 0.219002 0.975724i \(-0.429720\pi\)
0.219002 + 0.975724i \(0.429720\pi\)
\(998\) −31.6113 −1.00064
\(999\) −1.48248 −0.0469037
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 \(a_p\))