Properties

Label 8042.2.a.a.1.4
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 1.4
Character \(\chi\) = 8042.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.05107 q^{3}\) \(+1.00000 q^{4}\) \(-1.41145 q^{5}\) \(-3.05107 q^{6}\) \(-1.76739 q^{7}\) \(+1.00000 q^{8}\) \(+6.30900 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.05107 q^{3}\) \(+1.00000 q^{4}\) \(-1.41145 q^{5}\) \(-3.05107 q^{6}\) \(-1.76739 q^{7}\) \(+1.00000 q^{8}\) \(+6.30900 q^{9}\) \(-1.41145 q^{10}\) \(+0.990488 q^{11}\) \(-3.05107 q^{12}\) \(+2.81976 q^{13}\) \(-1.76739 q^{14}\) \(+4.30643 q^{15}\) \(+1.00000 q^{16}\) \(-1.33739 q^{17}\) \(+6.30900 q^{18}\) \(-3.59035 q^{19}\) \(-1.41145 q^{20}\) \(+5.39244 q^{21}\) \(+0.990488 q^{22}\) \(-1.70994 q^{23}\) \(-3.05107 q^{24}\) \(-3.00780 q^{25}\) \(+2.81976 q^{26}\) \(-10.0960 q^{27}\) \(-1.76739 q^{28}\) \(-7.08295 q^{29}\) \(+4.30643 q^{30}\) \(+8.88408 q^{31}\) \(+1.00000 q^{32}\) \(-3.02205 q^{33}\) \(-1.33739 q^{34}\) \(+2.49459 q^{35}\) \(+6.30900 q^{36}\) \(-3.20982 q^{37}\) \(-3.59035 q^{38}\) \(-8.60327 q^{39}\) \(-1.41145 q^{40}\) \(+8.34664 q^{41}\) \(+5.39244 q^{42}\) \(+4.65492 q^{43}\) \(+0.990488 q^{44}\) \(-8.90485 q^{45}\) \(-1.70994 q^{46}\) \(+6.28260 q^{47}\) \(-3.05107 q^{48}\) \(-3.87632 q^{49}\) \(-3.00780 q^{50}\) \(+4.08047 q^{51}\) \(+2.81976 q^{52}\) \(+3.23255 q^{53}\) \(-10.0960 q^{54}\) \(-1.39803 q^{55}\) \(-1.76739 q^{56}\) \(+10.9544 q^{57}\) \(-7.08295 q^{58}\) \(-6.97108 q^{59}\) \(+4.30643 q^{60}\) \(+3.30534 q^{61}\) \(+8.88408 q^{62}\) \(-11.1505 q^{63}\) \(+1.00000 q^{64}\) \(-3.97995 q^{65}\) \(-3.02205 q^{66}\) \(+7.59227 q^{67}\) \(-1.33739 q^{68}\) \(+5.21715 q^{69}\) \(+2.49459 q^{70}\) \(+2.97748 q^{71}\) \(+6.30900 q^{72}\) \(-7.64838 q^{73}\) \(-3.20982 q^{74}\) \(+9.17701 q^{75}\) \(-3.59035 q^{76}\) \(-1.75058 q^{77}\) \(-8.60327 q^{78}\) \(+1.60053 q^{79}\) \(-1.41145 q^{80}\) \(+11.8765 q^{81}\) \(+8.34664 q^{82}\) \(-3.29857 q^{83}\) \(+5.39244 q^{84}\) \(+1.88766 q^{85}\) \(+4.65492 q^{86}\) \(+21.6106 q^{87}\) \(+0.990488 q^{88}\) \(-9.31347 q^{89}\) \(-8.90485 q^{90}\) \(-4.98362 q^{91}\) \(-1.70994 q^{92}\) \(-27.1059 q^{93}\) \(+6.28260 q^{94}\) \(+5.06761 q^{95}\) \(-3.05107 q^{96}\) \(-10.1265 q^{97}\) \(-3.87632 q^{98}\) \(+6.24899 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(67q \) \(\mathstrut +\mathstrut 67q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 67q^{4} \) \(\mathstrut -\mathstrut 20q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 40q^{7} \) \(\mathstrut +\mathstrut 67q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 31q^{15} \) \(\mathstrut +\mathstrut 67q^{16} \) \(\mathstrut -\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut -\mathstrut 33q^{19} \) \(\mathstrut -\mathstrut 20q^{20} \) \(\mathstrut -\mathstrut 39q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 43q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 51q^{26} \) \(\mathstrut -\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut -\mathstrut 63q^{29} \) \(\mathstrut -\mathstrut 31q^{30} \) \(\mathstrut -\mathstrut 43q^{31} \) \(\mathstrut +\mathstrut 67q^{32} \) \(\mathstrut -\mathstrut 49q^{33} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 50q^{41} \) \(\mathstrut -\mathstrut 39q^{42} \) \(\mathstrut -\mathstrut 56q^{43} \) \(\mathstrut -\mathstrut 13q^{44} \) \(\mathstrut -\mathstrut 48q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 9q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 51q^{52} \) \(\mathstrut -\mathstrut 91q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{56} \) \(\mathstrut -\mathstrut 65q^{57} \) \(\mathstrut -\mathstrut 63q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut -\mathstrut 31q^{60} \) \(\mathstrut -\mathstrut 45q^{61} \) \(\mathstrut -\mathstrut 43q^{62} \) \(\mathstrut -\mathstrut 67q^{63} \) \(\mathstrut +\mathstrut 67q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 112q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 75q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut -\mathstrut 77q^{74} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 33q^{76} \) \(\mathstrut -\mathstrut 85q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 80q^{79} \) \(\mathstrut -\mathstrut 20q^{80} \) \(\mathstrut -\mathstrut 77q^{81} \) \(\mathstrut -\mathstrut 50q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 39q^{84} \) \(\mathstrut -\mathstrut 134q^{85} \) \(\mathstrut -\mathstrut 56q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 48q^{90} \) \(\mathstrut -\mathstrut 17q^{91} \) \(\mathstrut -\mathstrut 43q^{92} \) \(\mathstrut -\mathstrut 97q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 87q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.05107 −1.76153 −0.880767 0.473550i \(-0.842972\pi\)
−0.880767 + 0.473550i \(0.842972\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.41145 −0.631220 −0.315610 0.948889i \(-0.602209\pi\)
−0.315610 + 0.948889i \(0.602209\pi\)
\(6\) −3.05107 −1.24559
\(7\) −1.76739 −0.668012 −0.334006 0.942571i \(-0.608401\pi\)
−0.334006 + 0.942571i \(0.608401\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.30900 2.10300
\(10\) −1.41145 −0.446340
\(11\) 0.990488 0.298644 0.149322 0.988789i \(-0.452291\pi\)
0.149322 + 0.988789i \(0.452291\pi\)
\(12\) −3.05107 −0.880767
\(13\) 2.81976 0.782060 0.391030 0.920378i \(-0.372119\pi\)
0.391030 + 0.920378i \(0.372119\pi\)
\(14\) −1.76739 −0.472356
\(15\) 4.30643 1.11192
\(16\) 1.00000 0.250000
\(17\) −1.33739 −0.324365 −0.162182 0.986761i \(-0.551853\pi\)
−0.162182 + 0.986761i \(0.551853\pi\)
\(18\) 6.30900 1.48705
\(19\) −3.59035 −0.823683 −0.411842 0.911255i \(-0.635114\pi\)
−0.411842 + 0.911255i \(0.635114\pi\)
\(20\) −1.41145 −0.315610
\(21\) 5.39244 1.17673
\(22\) 0.990488 0.211173
\(23\) −1.70994 −0.356548 −0.178274 0.983981i \(-0.557051\pi\)
−0.178274 + 0.983981i \(0.557051\pi\)
\(24\) −3.05107 −0.622796
\(25\) −3.00780 −0.601561
\(26\) 2.81976 0.553000
\(27\) −10.0960 −1.94297
\(28\) −1.76739 −0.334006
\(29\) −7.08295 −1.31527 −0.657636 0.753336i \(-0.728443\pi\)
−0.657636 + 0.753336i \(0.728443\pi\)
\(30\) 4.30643 0.786243
\(31\) 8.88408 1.59563 0.797814 0.602904i \(-0.205990\pi\)
0.797814 + 0.602904i \(0.205990\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.02205 −0.526071
\(34\) −1.33739 −0.229361
\(35\) 2.49459 0.421663
\(36\) 6.30900 1.05150
\(37\) −3.20982 −0.527691 −0.263845 0.964565i \(-0.584991\pi\)
−0.263845 + 0.964565i \(0.584991\pi\)
\(38\) −3.59035 −0.582432
\(39\) −8.60327 −1.37763
\(40\) −1.41145 −0.223170
\(41\) 8.34664 1.30353 0.651763 0.758423i \(-0.274030\pi\)
0.651763 + 0.758423i \(0.274030\pi\)
\(42\) 5.39244 0.832071
\(43\) 4.65492 0.709869 0.354934 0.934891i \(-0.384503\pi\)
0.354934 + 0.934891i \(0.384503\pi\)
\(44\) 0.990488 0.149322
\(45\) −8.90485 −1.32746
\(46\) −1.70994 −0.252117
\(47\) 6.28260 0.916411 0.458206 0.888846i \(-0.348492\pi\)
0.458206 + 0.888846i \(0.348492\pi\)
\(48\) −3.05107 −0.440383
\(49\) −3.87632 −0.553760
\(50\) −3.00780 −0.425368
\(51\) 4.08047 0.571379
\(52\) 2.81976 0.391030
\(53\) 3.23255 0.444024 0.222012 0.975044i \(-0.428738\pi\)
0.222012 + 0.975044i \(0.428738\pi\)
\(54\) −10.0960 −1.37389
\(55\) −1.39803 −0.188510
\(56\) −1.76739 −0.236178
\(57\) 10.9544 1.45095
\(58\) −7.08295 −0.930037
\(59\) −6.97108 −0.907557 −0.453779 0.891114i \(-0.649924\pi\)
−0.453779 + 0.891114i \(0.649924\pi\)
\(60\) 4.30643 0.555958
\(61\) 3.30534 0.423206 0.211603 0.977356i \(-0.432132\pi\)
0.211603 + 0.977356i \(0.432132\pi\)
\(62\) 8.88408 1.12828
\(63\) −11.1505 −1.40483
\(64\) 1.00000 0.125000
\(65\) −3.97995 −0.493652
\(66\) −3.02205 −0.371988
\(67\) 7.59227 0.927544 0.463772 0.885955i \(-0.346496\pi\)
0.463772 + 0.885955i \(0.346496\pi\)
\(68\) −1.33739 −0.162182
\(69\) 5.21715 0.628071
\(70\) 2.49459 0.298161
\(71\) 2.97748 0.353362 0.176681 0.984268i \(-0.443464\pi\)
0.176681 + 0.984268i \(0.443464\pi\)
\(72\) 6.30900 0.743523
\(73\) −7.64838 −0.895175 −0.447588 0.894240i \(-0.647717\pi\)
−0.447588 + 0.894240i \(0.647717\pi\)
\(74\) −3.20982 −0.373134
\(75\) 9.17701 1.05967
\(76\) −3.59035 −0.411842
\(77\) −1.75058 −0.199497
\(78\) −8.60327 −0.974128
\(79\) 1.60053 0.180074 0.0900370 0.995938i \(-0.471301\pi\)
0.0900370 + 0.995938i \(0.471301\pi\)
\(80\) −1.41145 −0.157805
\(81\) 11.8765 1.31961
\(82\) 8.34664 0.921732
\(83\) −3.29857 −0.362065 −0.181032 0.983477i \(-0.557944\pi\)
−0.181032 + 0.983477i \(0.557944\pi\)
\(84\) 5.39244 0.588363
\(85\) 1.88766 0.204746
\(86\) 4.65492 0.501953
\(87\) 21.6106 2.31689
\(88\) 0.990488 0.105586
\(89\) −9.31347 −0.987226 −0.493613 0.869682i \(-0.664324\pi\)
−0.493613 + 0.869682i \(0.664324\pi\)
\(90\) −8.90485 −0.938654
\(91\) −4.98362 −0.522426
\(92\) −1.70994 −0.178274
\(93\) −27.1059 −2.81075
\(94\) 6.28260 0.648001
\(95\) 5.06761 0.519926
\(96\) −3.05107 −0.311398
\(97\) −10.1265 −1.02819 −0.514095 0.857733i \(-0.671872\pi\)
−0.514095 + 0.857733i \(0.671872\pi\)
\(98\) −3.87632 −0.391567
\(99\) 6.24899 0.628048
\(100\) −3.00780 −0.300780
\(101\) 18.6082 1.85159 0.925793 0.378032i \(-0.123399\pi\)
0.925793 + 0.378032i \(0.123399\pi\)
\(102\) 4.08047 0.404026
\(103\) −1.10760 −0.109136 −0.0545678 0.998510i \(-0.517378\pi\)
−0.0545678 + 0.998510i \(0.517378\pi\)
\(104\) 2.81976 0.276500
\(105\) −7.61116 −0.742773
\(106\) 3.23255 0.313973
\(107\) 17.0999 1.65311 0.826557 0.562853i \(-0.190296\pi\)
0.826557 + 0.562853i \(0.190296\pi\)
\(108\) −10.0960 −0.971487
\(109\) 13.9731 1.33838 0.669190 0.743092i \(-0.266641\pi\)
0.669190 + 0.743092i \(0.266641\pi\)
\(110\) −1.39803 −0.133297
\(111\) 9.79337 0.929545
\(112\) −1.76739 −0.167003
\(113\) −1.22548 −0.115284 −0.0576419 0.998337i \(-0.518358\pi\)
−0.0576419 + 0.998337i \(0.518358\pi\)
\(114\) 10.9544 1.02597
\(115\) 2.41350 0.225060
\(116\) −7.08295 −0.657636
\(117\) 17.7899 1.64467
\(118\) −6.97108 −0.641740
\(119\) 2.36370 0.216680
\(120\) 4.30643 0.393122
\(121\) −10.0189 −0.910812
\(122\) 3.30534 0.299252
\(123\) −25.4662 −2.29621
\(124\) 8.88408 0.797814
\(125\) 11.3026 1.01094
\(126\) −11.1505 −0.993365
\(127\) 0.638189 0.0566301 0.0283151 0.999599i \(-0.490986\pi\)
0.0283151 + 0.999599i \(0.490986\pi\)
\(128\) 1.00000 0.0883883
\(129\) −14.2025 −1.25046
\(130\) −3.97995 −0.349065
\(131\) 0.391940 0.0342440 0.0171220 0.999853i \(-0.494550\pi\)
0.0171220 + 0.999853i \(0.494550\pi\)
\(132\) −3.02205 −0.263035
\(133\) 6.34557 0.550231
\(134\) 7.59227 0.655872
\(135\) 14.2500 1.22644
\(136\) −1.33739 −0.114680
\(137\) −18.3245 −1.56557 −0.782786 0.622291i \(-0.786202\pi\)
−0.782786 + 0.622291i \(0.786202\pi\)
\(138\) 5.21715 0.444113
\(139\) 14.1675 1.20167 0.600836 0.799372i \(-0.294834\pi\)
0.600836 + 0.799372i \(0.294834\pi\)
\(140\) 2.49459 0.210831
\(141\) −19.1686 −1.61429
\(142\) 2.97748 0.249865
\(143\) 2.79294 0.233557
\(144\) 6.30900 0.525750
\(145\) 9.99724 0.830226
\(146\) −7.64838 −0.632985
\(147\) 11.8269 0.975466
\(148\) −3.20982 −0.263845
\(149\) −15.3214 −1.25518 −0.627588 0.778545i \(-0.715958\pi\)
−0.627588 + 0.778545i \(0.715958\pi\)
\(150\) 9.17701 0.749300
\(151\) 1.77251 0.144245 0.0721223 0.997396i \(-0.477023\pi\)
0.0721223 + 0.997396i \(0.477023\pi\)
\(152\) −3.59035 −0.291216
\(153\) −8.43760 −0.682139
\(154\) −1.75058 −0.141066
\(155\) −12.5394 −1.00719
\(156\) −8.60327 −0.688813
\(157\) 4.77543 0.381121 0.190561 0.981675i \(-0.438969\pi\)
0.190561 + 0.981675i \(0.438969\pi\)
\(158\) 1.60053 0.127332
\(159\) −9.86271 −0.782164
\(160\) −1.41145 −0.111585
\(161\) 3.02214 0.238178
\(162\) 11.8765 0.933107
\(163\) 0.156336 0.0122452 0.00612258 0.999981i \(-0.498051\pi\)
0.00612258 + 0.999981i \(0.498051\pi\)
\(164\) 8.34664 0.651763
\(165\) 4.26547 0.332066
\(166\) −3.29857 −0.256019
\(167\) 17.1656 1.32831 0.664157 0.747593i \(-0.268791\pi\)
0.664157 + 0.747593i \(0.268791\pi\)
\(168\) 5.39244 0.416035
\(169\) −5.04896 −0.388382
\(170\) 1.88766 0.144777
\(171\) −22.6515 −1.73221
\(172\) 4.65492 0.354934
\(173\) 6.81045 0.517789 0.258894 0.965906i \(-0.416642\pi\)
0.258894 + 0.965906i \(0.416642\pi\)
\(174\) 21.6106 1.63829
\(175\) 5.31598 0.401850
\(176\) 0.990488 0.0746609
\(177\) 21.2692 1.59869
\(178\) −9.31347 −0.698074
\(179\) −1.76346 −0.131807 −0.0659034 0.997826i \(-0.520993\pi\)
−0.0659034 + 0.997826i \(0.520993\pi\)
\(180\) −8.90485 −0.663728
\(181\) −0.379324 −0.0281949 −0.0140975 0.999901i \(-0.504488\pi\)
−0.0140975 + 0.999901i \(0.504488\pi\)
\(182\) −4.98362 −0.369411
\(183\) −10.0848 −0.745491
\(184\) −1.70994 −0.126059
\(185\) 4.53050 0.333089
\(186\) −27.1059 −1.98750
\(187\) −1.32467 −0.0968694
\(188\) 6.28260 0.458206
\(189\) 17.8436 1.29793
\(190\) 5.06761 0.367643
\(191\) 13.9413 1.00876 0.504379 0.863482i \(-0.331721\pi\)
0.504379 + 0.863482i \(0.331721\pi\)
\(192\) −3.05107 −0.220192
\(193\) −14.6097 −1.05163 −0.525815 0.850599i \(-0.676240\pi\)
−0.525815 + 0.850599i \(0.676240\pi\)
\(194\) −10.1265 −0.727041
\(195\) 12.1431 0.869585
\(196\) −3.87632 −0.276880
\(197\) −22.9184 −1.63287 −0.816433 0.577441i \(-0.804051\pi\)
−0.816433 + 0.577441i \(0.804051\pi\)
\(198\) 6.24899 0.444097
\(199\) 14.7608 1.04636 0.523182 0.852221i \(-0.324745\pi\)
0.523182 + 0.852221i \(0.324745\pi\)
\(200\) −3.00780 −0.212684
\(201\) −23.1645 −1.63390
\(202\) 18.6082 1.30927
\(203\) 12.5184 0.878617
\(204\) 4.08047 0.285690
\(205\) −11.7809 −0.822812
\(206\) −1.10760 −0.0771705
\(207\) −10.7880 −0.749820
\(208\) 2.81976 0.195515
\(209\) −3.55620 −0.245988
\(210\) −7.61116 −0.525220
\(211\) −23.7895 −1.63774 −0.818869 0.573981i \(-0.805399\pi\)
−0.818869 + 0.573981i \(0.805399\pi\)
\(212\) 3.23255 0.222012
\(213\) −9.08449 −0.622459
\(214\) 17.0999 1.16893
\(215\) −6.57019 −0.448084
\(216\) −10.0960 −0.686945
\(217\) −15.7017 −1.06590
\(218\) 13.9731 0.946377
\(219\) 23.3357 1.57688
\(220\) −1.39803 −0.0942549
\(221\) −3.77112 −0.253673
\(222\) 9.79337 0.657288
\(223\) −28.4792 −1.90711 −0.953555 0.301219i \(-0.902606\pi\)
−0.953555 + 0.301219i \(0.902606\pi\)
\(224\) −1.76739 −0.118089
\(225\) −18.9762 −1.26508
\(226\) −1.22548 −0.0815180
\(227\) 15.0721 1.00037 0.500185 0.865919i \(-0.333265\pi\)
0.500185 + 0.865919i \(0.333265\pi\)
\(228\) 10.9544 0.725473
\(229\) 19.3331 1.27757 0.638785 0.769385i \(-0.279437\pi\)
0.638785 + 0.769385i \(0.279437\pi\)
\(230\) 2.41350 0.159142
\(231\) 5.34115 0.351422
\(232\) −7.08295 −0.465019
\(233\) −27.3546 −1.79206 −0.896029 0.443995i \(-0.853561\pi\)
−0.896029 + 0.443995i \(0.853561\pi\)
\(234\) 17.7899 1.16296
\(235\) −8.86758 −0.578457
\(236\) −6.97108 −0.453779
\(237\) −4.88333 −0.317206
\(238\) 2.36370 0.153216
\(239\) −26.4726 −1.71237 −0.856185 0.516669i \(-0.827172\pi\)
−0.856185 + 0.516669i \(0.827172\pi\)
\(240\) 4.30643 0.277979
\(241\) −11.3914 −0.733783 −0.366892 0.930264i \(-0.619578\pi\)
−0.366892 + 0.930264i \(0.619578\pi\)
\(242\) −10.0189 −0.644041
\(243\) −5.94806 −0.381568
\(244\) 3.30534 0.211603
\(245\) 5.47124 0.349544
\(246\) −25.4662 −1.62366
\(247\) −10.1239 −0.644170
\(248\) 8.88408 0.564139
\(249\) 10.0641 0.637789
\(250\) 11.3026 0.714841
\(251\) −3.90272 −0.246338 −0.123169 0.992386i \(-0.539306\pi\)
−0.123169 + 0.992386i \(0.539306\pi\)
\(252\) −11.1505 −0.702415
\(253\) −1.69368 −0.106481
\(254\) 0.638189 0.0400435
\(255\) −5.75938 −0.360666
\(256\) 1.00000 0.0625000
\(257\) 7.26231 0.453010 0.226505 0.974010i \(-0.427270\pi\)
0.226505 + 0.974010i \(0.427270\pi\)
\(258\) −14.2025 −0.884207
\(259\) 5.67301 0.352504
\(260\) −3.97995 −0.246826
\(261\) −44.6864 −2.76602
\(262\) 0.391940 0.0242142
\(263\) −8.73603 −0.538687 −0.269343 0.963044i \(-0.586807\pi\)
−0.269343 + 0.963044i \(0.586807\pi\)
\(264\) −3.02205 −0.185994
\(265\) −4.56258 −0.280277
\(266\) 6.34557 0.389072
\(267\) 28.4160 1.73903
\(268\) 7.59227 0.463772
\(269\) 24.1705 1.47370 0.736851 0.676056i \(-0.236312\pi\)
0.736851 + 0.676056i \(0.236312\pi\)
\(270\) 14.2500 0.867227
\(271\) −20.6518 −1.25451 −0.627253 0.778815i \(-0.715821\pi\)
−0.627253 + 0.778815i \(0.715821\pi\)
\(272\) −1.33739 −0.0810912
\(273\) 15.2054 0.920271
\(274\) −18.3245 −1.10703
\(275\) −2.97920 −0.179652
\(276\) 5.21715 0.314035
\(277\) −13.1585 −0.790620 −0.395310 0.918548i \(-0.629363\pi\)
−0.395310 + 0.918548i \(0.629363\pi\)
\(278\) 14.1675 0.849710
\(279\) 56.0497 3.35561
\(280\) 2.49459 0.149080
\(281\) −13.0492 −0.778451 −0.389226 0.921142i \(-0.627257\pi\)
−0.389226 + 0.921142i \(0.627257\pi\)
\(282\) −19.1686 −1.14148
\(283\) −13.1308 −0.780546 −0.390273 0.920699i \(-0.627619\pi\)
−0.390273 + 0.920699i \(0.627619\pi\)
\(284\) 2.97748 0.176681
\(285\) −15.4616 −0.915867
\(286\) 2.79294 0.165150
\(287\) −14.7518 −0.870771
\(288\) 6.30900 0.371762
\(289\) −15.2114 −0.894788
\(290\) 9.99724 0.587058
\(291\) 30.8966 1.81119
\(292\) −7.64838 −0.447588
\(293\) −26.2268 −1.53218 −0.766092 0.642731i \(-0.777801\pi\)
−0.766092 + 0.642731i \(0.777801\pi\)
\(294\) 11.8269 0.689759
\(295\) 9.83934 0.572869
\(296\) −3.20982 −0.186567
\(297\) −9.99996 −0.580256
\(298\) −15.3214 −0.887544
\(299\) −4.82163 −0.278842
\(300\) 9.17701 0.529835
\(301\) −8.22708 −0.474201
\(302\) 1.77251 0.101996
\(303\) −56.7748 −3.26163
\(304\) −3.59035 −0.205921
\(305\) −4.66533 −0.267136
\(306\) −8.43760 −0.482345
\(307\) −34.2440 −1.95441 −0.977204 0.212301i \(-0.931904\pi\)
−0.977204 + 0.212301i \(0.931904\pi\)
\(308\) −1.75058 −0.0997487
\(309\) 3.37937 0.192246
\(310\) −12.5394 −0.712193
\(311\) 4.91937 0.278952 0.139476 0.990225i \(-0.455458\pi\)
0.139476 + 0.990225i \(0.455458\pi\)
\(312\) −8.60327 −0.487064
\(313\) −4.99586 −0.282383 −0.141191 0.989982i \(-0.545093\pi\)
−0.141191 + 0.989982i \(0.545093\pi\)
\(314\) 4.77543 0.269493
\(315\) 15.7384 0.886757
\(316\) 1.60053 0.0900370
\(317\) −3.70493 −0.208090 −0.104045 0.994573i \(-0.533179\pi\)
−0.104045 + 0.994573i \(0.533179\pi\)
\(318\) −9.86271 −0.553073
\(319\) −7.01558 −0.392797
\(320\) −1.41145 −0.0789025
\(321\) −52.1731 −2.91202
\(322\) 3.02214 0.168417
\(323\) 4.80170 0.267174
\(324\) 11.8765 0.659806
\(325\) −8.48128 −0.470457
\(326\) 0.156336 0.00865864
\(327\) −42.6328 −2.35760
\(328\) 8.34664 0.460866
\(329\) −11.1038 −0.612174
\(330\) 4.26547 0.234806
\(331\) 7.27379 0.399804 0.199902 0.979816i \(-0.435938\pi\)
0.199902 + 0.979816i \(0.435938\pi\)
\(332\) −3.29857 −0.181032
\(333\) −20.2508 −1.10973
\(334\) 17.1656 0.939260
\(335\) −10.7161 −0.585484
\(336\) 5.39244 0.294181
\(337\) 20.5115 1.11733 0.558666 0.829393i \(-0.311313\pi\)
0.558666 + 0.829393i \(0.311313\pi\)
\(338\) −5.04896 −0.274627
\(339\) 3.73903 0.203076
\(340\) 1.88766 0.102373
\(341\) 8.79958 0.476524
\(342\) −22.6515 −1.22486
\(343\) 19.2227 1.03793
\(344\) 4.65492 0.250976
\(345\) −7.36375 −0.396451
\(346\) 6.81045 0.366132
\(347\) −19.7865 −1.06219 −0.531097 0.847311i \(-0.678220\pi\)
−0.531097 + 0.847311i \(0.678220\pi\)
\(348\) 21.6106 1.15845
\(349\) 17.9510 0.960897 0.480448 0.877023i \(-0.340474\pi\)
0.480448 + 0.877023i \(0.340474\pi\)
\(350\) 5.31598 0.284151
\(351\) −28.4682 −1.51952
\(352\) 0.990488 0.0527932
\(353\) −12.0914 −0.643562 −0.321781 0.946814i \(-0.604282\pi\)
−0.321781 + 0.946814i \(0.604282\pi\)
\(354\) 21.2692 1.13045
\(355\) −4.20257 −0.223049
\(356\) −9.31347 −0.493613
\(357\) −7.21179 −0.381688
\(358\) −1.76346 −0.0932015
\(359\) −23.2548 −1.22734 −0.613671 0.789562i \(-0.710308\pi\)
−0.613671 + 0.789562i \(0.710308\pi\)
\(360\) −8.90485 −0.469327
\(361\) −6.10937 −0.321546
\(362\) −0.379324 −0.0199368
\(363\) 30.5684 1.60443
\(364\) −4.98362 −0.261213
\(365\) 10.7953 0.565053
\(366\) −10.0848 −0.527142
\(367\) −20.2384 −1.05643 −0.528217 0.849109i \(-0.677139\pi\)
−0.528217 + 0.849109i \(0.677139\pi\)
\(368\) −1.70994 −0.0891369
\(369\) 52.6590 2.74132
\(370\) 4.53050 0.235530
\(371\) −5.71318 −0.296614
\(372\) −27.1059 −1.40538
\(373\) −20.4964 −1.06126 −0.530631 0.847603i \(-0.678045\pi\)
−0.530631 + 0.847603i \(0.678045\pi\)
\(374\) −1.32467 −0.0684970
\(375\) −34.4851 −1.78080
\(376\) 6.28260 0.324000
\(377\) −19.9722 −1.02862
\(378\) 17.8436 0.917775
\(379\) −32.9203 −1.69100 −0.845500 0.533975i \(-0.820698\pi\)
−0.845500 + 0.533975i \(0.820698\pi\)
\(380\) 5.06761 0.259963
\(381\) −1.94716 −0.0997559
\(382\) 13.9413 0.713300
\(383\) 14.0638 0.718628 0.359314 0.933217i \(-0.383011\pi\)
0.359314 + 0.933217i \(0.383011\pi\)
\(384\) −3.05107 −0.155699
\(385\) 2.47086 0.125927
\(386\) −14.6097 −0.743615
\(387\) 29.3679 1.49285
\(388\) −10.1265 −0.514095
\(389\) −25.6156 −1.29876 −0.649381 0.760464i \(-0.724972\pi\)
−0.649381 + 0.760464i \(0.724972\pi\)
\(390\) 12.1431 0.614890
\(391\) 2.28686 0.115652
\(392\) −3.87632 −0.195784
\(393\) −1.19584 −0.0603219
\(394\) −22.9184 −1.15461
\(395\) −2.25907 −0.113666
\(396\) 6.24899 0.314024
\(397\) −22.3461 −1.12152 −0.560760 0.827978i \(-0.689491\pi\)
−0.560760 + 0.827978i \(0.689491\pi\)
\(398\) 14.7608 0.739892
\(399\) −19.3607 −0.969250
\(400\) −3.00780 −0.150390
\(401\) 39.6643 1.98074 0.990370 0.138449i \(-0.0442116\pi\)
0.990370 + 0.138449i \(0.0442116\pi\)
\(402\) −23.1645 −1.15534
\(403\) 25.0510 1.24788
\(404\) 18.6082 0.925793
\(405\) −16.7631 −0.832966
\(406\) 12.5184 0.621276
\(407\) −3.17929 −0.157591
\(408\) 4.08047 0.202013
\(409\) −7.75325 −0.383373 −0.191687 0.981456i \(-0.561396\pi\)
−0.191687 + 0.981456i \(0.561396\pi\)
\(410\) −11.7809 −0.581816
\(411\) 55.9094 2.75781
\(412\) −1.10760 −0.0545678
\(413\) 12.3206 0.606259
\(414\) −10.7880 −0.530203
\(415\) 4.65577 0.228543
\(416\) 2.81976 0.138250
\(417\) −43.2260 −2.11679
\(418\) −3.55620 −0.173940
\(419\) −15.5207 −0.758235 −0.379118 0.925348i \(-0.623772\pi\)
−0.379118 + 0.925348i \(0.623772\pi\)
\(420\) −7.61116 −0.371387
\(421\) 7.02289 0.342275 0.171137 0.985247i \(-0.445256\pi\)
0.171137 + 0.985247i \(0.445256\pi\)
\(422\) −23.7895 −1.15806
\(423\) 39.6369 1.92721
\(424\) 3.23255 0.156986
\(425\) 4.02261 0.195125
\(426\) −9.08449 −0.440145
\(427\) −5.84184 −0.282707
\(428\) 17.0999 0.826557
\(429\) −8.52144 −0.411419
\(430\) −6.57019 −0.316843
\(431\) 38.2424 1.84207 0.921035 0.389480i \(-0.127345\pi\)
0.921035 + 0.389480i \(0.127345\pi\)
\(432\) −10.0960 −0.485743
\(433\) −5.15882 −0.247917 −0.123958 0.992287i \(-0.539559\pi\)
−0.123958 + 0.992287i \(0.539559\pi\)
\(434\) −15.7017 −0.753704
\(435\) −30.5023 −1.46247
\(436\) 13.9731 0.669190
\(437\) 6.13930 0.293682
\(438\) 23.3357 1.11502
\(439\) 20.4598 0.976493 0.488246 0.872706i \(-0.337637\pi\)
0.488246 + 0.872706i \(0.337637\pi\)
\(440\) −1.39803 −0.0666483
\(441\) −24.4557 −1.16456
\(442\) −3.77112 −0.179374
\(443\) −26.2999 −1.24955 −0.624773 0.780806i \(-0.714809\pi\)
−0.624773 + 0.780806i \(0.714809\pi\)
\(444\) 9.79337 0.464773
\(445\) 13.1455 0.623157
\(446\) −28.4792 −1.34853
\(447\) 46.7465 2.21104
\(448\) −1.76739 −0.0835015
\(449\) −7.78811 −0.367544 −0.183772 0.982969i \(-0.558831\pi\)
−0.183772 + 0.982969i \(0.558831\pi\)
\(450\) −18.9762 −0.894549
\(451\) 8.26725 0.389290
\(452\) −1.22548 −0.0576419
\(453\) −5.40804 −0.254092
\(454\) 15.0721 0.707368
\(455\) 7.03414 0.329766
\(456\) 10.9544 0.512987
\(457\) 12.5807 0.588500 0.294250 0.955728i \(-0.404930\pi\)
0.294250 + 0.955728i \(0.404930\pi\)
\(458\) 19.3331 0.903378
\(459\) 13.5023 0.630232
\(460\) 2.41350 0.112530
\(461\) −5.98896 −0.278934 −0.139467 0.990227i \(-0.544539\pi\)
−0.139467 + 0.990227i \(0.544539\pi\)
\(462\) 5.34115 0.248493
\(463\) 14.9361 0.694140 0.347070 0.937839i \(-0.387177\pi\)
0.347070 + 0.937839i \(0.387177\pi\)
\(464\) −7.08295 −0.328818
\(465\) 38.2587 1.77420
\(466\) −27.3546 −1.26718
\(467\) 22.9564 1.06230 0.531149 0.847279i \(-0.321761\pi\)
0.531149 + 0.847279i \(0.321761\pi\)
\(468\) 17.7899 0.822337
\(469\) −13.4185 −0.619610
\(470\) −8.86758 −0.409031
\(471\) −14.5702 −0.671358
\(472\) −6.97108 −0.320870
\(473\) 4.61064 0.211998
\(474\) −4.88333 −0.224299
\(475\) 10.7991 0.495496
\(476\) 2.36370 0.108340
\(477\) 20.3941 0.933784
\(478\) −26.4726 −1.21083
\(479\) −4.91130 −0.224403 −0.112201 0.993685i \(-0.535790\pi\)
−0.112201 + 0.993685i \(0.535790\pi\)
\(480\) 4.30643 0.196561
\(481\) −9.05091 −0.412686
\(482\) −11.3914 −0.518863
\(483\) −9.22076 −0.419559
\(484\) −10.0189 −0.455406
\(485\) 14.2931 0.649015
\(486\) −5.94806 −0.269809
\(487\) −26.5750 −1.20423 −0.602115 0.798409i \(-0.705675\pi\)
−0.602115 + 0.798409i \(0.705675\pi\)
\(488\) 3.30534 0.149626
\(489\) −0.476991 −0.0215703
\(490\) 5.47124 0.247165
\(491\) 24.0414 1.08497 0.542486 0.840065i \(-0.317483\pi\)
0.542486 + 0.840065i \(0.317483\pi\)
\(492\) −25.4662 −1.14810
\(493\) 9.47267 0.426628
\(494\) −10.1239 −0.455497
\(495\) −8.82015 −0.396436
\(496\) 8.88408 0.398907
\(497\) −5.26238 −0.236050
\(498\) 10.0641 0.450985
\(499\) 27.9188 1.24982 0.624908 0.780698i \(-0.285136\pi\)
0.624908 + 0.780698i \(0.285136\pi\)
\(500\) 11.3026 0.505469
\(501\) −52.3734 −2.33987
\(502\) −3.90272 −0.174187
\(503\) −29.9901 −1.33719 −0.668596 0.743626i \(-0.733104\pi\)
−0.668596 + 0.743626i \(0.733104\pi\)
\(504\) −11.1505 −0.496682
\(505\) −26.2646 −1.16876
\(506\) −1.69368 −0.0752932
\(507\) 15.4047 0.684147
\(508\) 0.638189 0.0283151
\(509\) −9.34356 −0.414146 −0.207073 0.978325i \(-0.566394\pi\)
−0.207073 + 0.978325i \(0.566394\pi\)
\(510\) −5.75938 −0.255030
\(511\) 13.5177 0.597988
\(512\) 1.00000 0.0441942
\(513\) 36.2482 1.60039
\(514\) 7.26231 0.320327
\(515\) 1.56333 0.0688886
\(516\) −14.2025 −0.625229
\(517\) 6.22284 0.273680
\(518\) 5.67301 0.249258
\(519\) −20.7791 −0.912103
\(520\) −3.97995 −0.174532
\(521\) −15.1620 −0.664259 −0.332130 0.943234i \(-0.607767\pi\)
−0.332130 + 0.943234i \(0.607767\pi\)
\(522\) −44.6864 −1.95587
\(523\) −5.22631 −0.228531 −0.114265 0.993450i \(-0.536451\pi\)
−0.114265 + 0.993450i \(0.536451\pi\)
\(524\) 0.391940 0.0171220
\(525\) −16.2194 −0.707872
\(526\) −8.73603 −0.380909
\(527\) −11.8815 −0.517565
\(528\) −3.02205 −0.131518
\(529\) −20.0761 −0.872874
\(530\) −4.56258 −0.198186
\(531\) −43.9806 −1.90859
\(532\) 6.34557 0.275115
\(533\) 23.5355 1.01944
\(534\) 28.4160 1.22968
\(535\) −24.1357 −1.04348
\(536\) 7.59227 0.327936
\(537\) 5.38042 0.232182
\(538\) 24.1705 1.04206
\(539\) −3.83945 −0.165377
\(540\) 14.2500 0.613222
\(541\) −5.57200 −0.239559 −0.119779 0.992801i \(-0.538219\pi\)
−0.119779 + 0.992801i \(0.538219\pi\)
\(542\) −20.6518 −0.887070
\(543\) 1.15734 0.0496663
\(544\) −1.33739 −0.0573401
\(545\) −19.7223 −0.844812
\(546\) 15.2054 0.650730
\(547\) −0.0877621 −0.00375244 −0.00187622 0.999998i \(-0.500597\pi\)
−0.00187622 + 0.999998i \(0.500597\pi\)
\(548\) −18.3245 −0.782786
\(549\) 20.8534 0.890002
\(550\) −2.97920 −0.127033
\(551\) 25.4303 1.08337
\(552\) 5.21715 0.222057
\(553\) −2.82877 −0.120292
\(554\) −13.1585 −0.559053
\(555\) −13.8229 −0.586748
\(556\) 14.1675 0.600836
\(557\) 21.3248 0.903559 0.451780 0.892130i \(-0.350789\pi\)
0.451780 + 0.892130i \(0.350789\pi\)
\(558\) 56.0497 2.37277
\(559\) 13.1258 0.555160
\(560\) 2.49459 0.105416
\(561\) 4.04165 0.170639
\(562\) −13.0492 −0.550448
\(563\) −20.6875 −0.871876 −0.435938 0.899977i \(-0.643583\pi\)
−0.435938 + 0.899977i \(0.643583\pi\)
\(564\) −19.1686 −0.807145
\(565\) 1.72971 0.0727695
\(566\) −13.1308 −0.551930
\(567\) −20.9905 −0.881517
\(568\) 2.97748 0.124932
\(569\) −11.0933 −0.465056 −0.232528 0.972590i \(-0.574700\pi\)
−0.232528 + 0.972590i \(0.574700\pi\)
\(570\) −15.4616 −0.647615
\(571\) 19.3218 0.808594 0.404297 0.914628i \(-0.367516\pi\)
0.404297 + 0.914628i \(0.367516\pi\)
\(572\) 2.79294 0.116779
\(573\) −42.5359 −1.77696
\(574\) −14.7518 −0.615728
\(575\) 5.14317 0.214485
\(576\) 6.30900 0.262875
\(577\) 1.00605 0.0418825 0.0209413 0.999781i \(-0.493334\pi\)
0.0209413 + 0.999781i \(0.493334\pi\)
\(578\) −15.2114 −0.632710
\(579\) 44.5752 1.85248
\(580\) 9.99724 0.415113
\(581\) 5.82987 0.241864
\(582\) 30.8966 1.28071
\(583\) 3.20180 0.132605
\(584\) −7.64838 −0.316492
\(585\) −25.1095 −1.03815
\(586\) −26.2268 −1.08342
\(587\) 14.1937 0.585836 0.292918 0.956138i \(-0.405374\pi\)
0.292918 + 0.956138i \(0.405374\pi\)
\(588\) 11.8269 0.487733
\(589\) −31.8970 −1.31429
\(590\) 9.83934 0.405079
\(591\) 69.9254 2.87635
\(592\) −3.20982 −0.131923
\(593\) 16.2398 0.666889 0.333445 0.942770i \(-0.391789\pi\)
0.333445 + 0.942770i \(0.391789\pi\)
\(594\) −9.99996 −0.410303
\(595\) −3.33624 −0.136773
\(596\) −15.3214 −0.627588
\(597\) −45.0361 −1.84321
\(598\) −4.82163 −0.197171
\(599\) 25.4165 1.03849 0.519245 0.854626i \(-0.326213\pi\)
0.519245 + 0.854626i \(0.326213\pi\)
\(600\) 9.17701 0.374650
\(601\) 29.4047 1.19944 0.599721 0.800209i \(-0.295278\pi\)
0.599721 + 0.800209i \(0.295278\pi\)
\(602\) −8.22708 −0.335311
\(603\) 47.8997 1.95062
\(604\) 1.77251 0.0721223
\(605\) 14.1412 0.574923
\(606\) −56.7748 −2.30632
\(607\) 11.3300 0.459872 0.229936 0.973206i \(-0.426148\pi\)
0.229936 + 0.973206i \(0.426148\pi\)
\(608\) −3.59035 −0.145608
\(609\) −38.1944 −1.54771
\(610\) −4.66533 −0.188894
\(611\) 17.7154 0.716689
\(612\) −8.43760 −0.341070
\(613\) −45.0699 −1.82036 −0.910178 0.414218i \(-0.864055\pi\)
−0.910178 + 0.414218i \(0.864055\pi\)
\(614\) −34.2440 −1.38198
\(615\) 35.9442 1.44941
\(616\) −1.75058 −0.0705330
\(617\) 21.9085 0.882004 0.441002 0.897506i \(-0.354623\pi\)
0.441002 + 0.897506i \(0.354623\pi\)
\(618\) 3.37937 0.135938
\(619\) 6.95192 0.279421 0.139711 0.990192i \(-0.455383\pi\)
0.139711 + 0.990192i \(0.455383\pi\)
\(620\) −12.5394 −0.503596
\(621\) 17.2636 0.692763
\(622\) 4.91937 0.197249
\(623\) 16.4606 0.659479
\(624\) −8.60327 −0.344406
\(625\) −0.914088 −0.0365635
\(626\) −4.99586 −0.199675
\(627\) 10.8502 0.433316
\(628\) 4.77543 0.190561
\(629\) 4.29278 0.171164
\(630\) 15.7384 0.627032
\(631\) −46.4204 −1.84796 −0.923982 0.382435i \(-0.875086\pi\)
−0.923982 + 0.382435i \(0.875086\pi\)
\(632\) 1.60053 0.0636658
\(633\) 72.5834 2.88493
\(634\) −3.70493 −0.147142
\(635\) −0.900773 −0.0357461
\(636\) −9.86271 −0.391082
\(637\) −10.9303 −0.433074
\(638\) −7.01558 −0.277750
\(639\) 18.7849 0.743121
\(640\) −1.41145 −0.0557925
\(641\) −20.9759 −0.828498 −0.414249 0.910164i \(-0.635956\pi\)
−0.414249 + 0.910164i \(0.635956\pi\)
\(642\) −52.1731 −2.05911
\(643\) −3.99573 −0.157576 −0.0787880 0.996891i \(-0.525105\pi\)
−0.0787880 + 0.996891i \(0.525105\pi\)
\(644\) 3.02214 0.119089
\(645\) 20.0461 0.789314
\(646\) 4.80170 0.188920
\(647\) −23.5850 −0.927221 −0.463610 0.886039i \(-0.653446\pi\)
−0.463610 + 0.886039i \(0.653446\pi\)
\(648\) 11.8765 0.466553
\(649\) −6.90477 −0.271036
\(650\) −8.48128 −0.332663
\(651\) 47.9068 1.87762
\(652\) 0.156336 0.00612258
\(653\) −19.3043 −0.755436 −0.377718 0.925921i \(-0.623291\pi\)
−0.377718 + 0.925921i \(0.623291\pi\)
\(654\) −42.6328 −1.66707
\(655\) −0.553205 −0.0216155
\(656\) 8.34664 0.325882
\(657\) −48.2537 −1.88255
\(658\) −11.1038 −0.432872
\(659\) −39.2456 −1.52879 −0.764396 0.644747i \(-0.776963\pi\)
−0.764396 + 0.644747i \(0.776963\pi\)
\(660\) 4.26547 0.166033
\(661\) −35.8195 −1.39322 −0.696608 0.717452i \(-0.745308\pi\)
−0.696608 + 0.717452i \(0.745308\pi\)
\(662\) 7.27379 0.282704
\(663\) 11.5059 0.446853
\(664\) −3.29857 −0.128009
\(665\) −8.95646 −0.347317
\(666\) −20.2508 −0.784701
\(667\) 12.1114 0.468957
\(668\) 17.1656 0.664157
\(669\) 86.8920 3.35944
\(670\) −10.7161 −0.414000
\(671\) 3.27390 0.126388
\(672\) 5.39244 0.208018
\(673\) −18.9883 −0.731945 −0.365973 0.930626i \(-0.619264\pi\)
−0.365973 + 0.930626i \(0.619264\pi\)
\(674\) 20.5115 0.790073
\(675\) 30.3668 1.16882
\(676\) −5.04896 −0.194191
\(677\) −9.51894 −0.365843 −0.182921 0.983128i \(-0.558555\pi\)
−0.182921 + 0.983128i \(0.558555\pi\)
\(678\) 3.73903 0.143597
\(679\) 17.8975 0.686844
\(680\) 1.88766 0.0723885
\(681\) −45.9859 −1.76218
\(682\) 8.79958 0.336953
\(683\) −9.13741 −0.349633 −0.174817 0.984601i \(-0.555933\pi\)
−0.174817 + 0.984601i \(0.555933\pi\)
\(684\) −22.6515 −0.866103
\(685\) 25.8642 0.988221
\(686\) 19.2227 0.733928
\(687\) −58.9867 −2.25048
\(688\) 4.65492 0.177467
\(689\) 9.11500 0.347254
\(690\) −7.36375 −0.280333
\(691\) −14.9149 −0.567390 −0.283695 0.958915i \(-0.591560\pi\)
−0.283695 + 0.958915i \(0.591560\pi\)
\(692\) 6.81045 0.258894
\(693\) −11.0444 −0.419543
\(694\) −19.7865 −0.751084
\(695\) −19.9967 −0.758520
\(696\) 21.6106 0.819146
\(697\) −11.1627 −0.422818
\(698\) 17.9510 0.679457
\(699\) 83.4607 3.15677
\(700\) 5.31598 0.200925
\(701\) 25.5660 0.965614 0.482807 0.875727i \(-0.339617\pi\)
0.482807 + 0.875727i \(0.339617\pi\)
\(702\) −28.4682 −1.07446
\(703\) 11.5244 0.434650
\(704\) 0.990488 0.0373304
\(705\) 27.0556 1.01897
\(706\) −12.0914 −0.455067
\(707\) −32.8880 −1.23688
\(708\) 21.2692 0.799346
\(709\) 39.1418 1.47000 0.735000 0.678067i \(-0.237182\pi\)
0.735000 + 0.678067i \(0.237182\pi\)
\(710\) −4.20257 −0.157720
\(711\) 10.0978 0.378696
\(712\) −9.31347 −0.349037
\(713\) −15.1913 −0.568917
\(714\) −7.21179 −0.269894
\(715\) −3.94210 −0.147426
\(716\) −1.76346 −0.0659034
\(717\) 80.7696 3.01640
\(718\) −23.2548 −0.867862
\(719\) 15.9034 0.593095 0.296548 0.955018i \(-0.404165\pi\)
0.296548 + 0.955018i \(0.404165\pi\)
\(720\) −8.90485 −0.331864
\(721\) 1.95757 0.0729039
\(722\) −6.10937 −0.227367
\(723\) 34.7558 1.29258
\(724\) −0.379324 −0.0140975
\(725\) 21.3041 0.791216
\(726\) 30.5684 1.13450
\(727\) 3.70503 0.137412 0.0687059 0.997637i \(-0.478113\pi\)
0.0687059 + 0.997637i \(0.478113\pi\)
\(728\) −4.98362 −0.184705
\(729\) −17.4816 −0.647467
\(730\) 10.7953 0.399553
\(731\) −6.22544 −0.230256
\(732\) −10.0848 −0.372746
\(733\) −11.0908 −0.409647 −0.204823 0.978799i \(-0.565662\pi\)
−0.204823 + 0.978799i \(0.565662\pi\)
\(734\) −20.2384 −0.747011
\(735\) −16.6931 −0.615734
\(736\) −1.70994 −0.0630293
\(737\) 7.52006 0.277005
\(738\) 52.6590 1.93840
\(739\) 21.9608 0.807840 0.403920 0.914794i \(-0.367647\pi\)
0.403920 + 0.914794i \(0.367647\pi\)
\(740\) 4.53050 0.166545
\(741\) 30.8888 1.13473
\(742\) −5.71318 −0.209738
\(743\) 9.16532 0.336243 0.168121 0.985766i \(-0.446230\pi\)
0.168121 + 0.985766i \(0.446230\pi\)
\(744\) −27.1059 −0.993751
\(745\) 21.6254 0.792293
\(746\) −20.4964 −0.750426
\(747\) −20.8107 −0.761423
\(748\) −1.32467 −0.0484347
\(749\) −30.2223 −1.10430
\(750\) −34.4851 −1.25922
\(751\) −40.4684 −1.47671 −0.738357 0.674410i \(-0.764398\pi\)
−0.738357 + 0.674410i \(0.764398\pi\)
\(752\) 6.28260 0.229103
\(753\) 11.9075 0.433932
\(754\) −19.9722 −0.727345
\(755\) −2.50181 −0.0910501
\(756\) 17.8436 0.648965
\(757\) 6.71012 0.243883 0.121942 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(758\) −32.9203 −1.19572
\(759\) 5.16752 0.187569
\(760\) 5.06761 0.183821
\(761\) −21.8030 −0.790357 −0.395179 0.918604i \(-0.629317\pi\)
−0.395179 + 0.918604i \(0.629317\pi\)
\(762\) −1.94716 −0.0705380
\(763\) −24.6960 −0.894054
\(764\) 13.9413 0.504379
\(765\) 11.9093 0.430580
\(766\) 14.0638 0.508147
\(767\) −19.6568 −0.709764
\(768\) −3.05107 −0.110096
\(769\) −12.0805 −0.435636 −0.217818 0.975989i \(-0.569894\pi\)
−0.217818 + 0.975989i \(0.569894\pi\)
\(770\) 2.47086 0.0890437
\(771\) −22.1578 −0.797993
\(772\) −14.6097 −0.525815
\(773\) −14.0036 −0.503675 −0.251837 0.967770i \(-0.581035\pi\)
−0.251837 + 0.967770i \(0.581035\pi\)
\(774\) 29.3679 1.05561
\(775\) −26.7216 −0.959867
\(776\) −10.1265 −0.363520
\(777\) −17.3087 −0.620948
\(778\) −25.6156 −0.918363
\(779\) −29.9674 −1.07369
\(780\) 12.1431 0.434793
\(781\) 2.94916 0.105529
\(782\) 2.28686 0.0817780
\(783\) 71.5094 2.55554
\(784\) −3.87632 −0.138440
\(785\) −6.74029 −0.240571
\(786\) −1.19584 −0.0426541
\(787\) 6.43181 0.229269 0.114635 0.993408i \(-0.463430\pi\)
0.114635 + 0.993408i \(0.463430\pi\)
\(788\) −22.9184 −0.816433
\(789\) 26.6542 0.948915
\(790\) −2.25907 −0.0803743
\(791\) 2.16591 0.0770110
\(792\) 6.24899 0.222048
\(793\) 9.32027 0.330973
\(794\) −22.3461 −0.793035
\(795\) 13.9207 0.493718
\(796\) 14.7608 0.523182
\(797\) 11.0103 0.390005 0.195003 0.980803i \(-0.437528\pi\)
0.195003 + 0.980803i \(0.437528\pi\)
\(798\) −19.3607 −0.685363
\(799\) −8.40229 −0.297252
\(800\) −3.00780 −0.106342
\(801\) −58.7587 −2.07614
\(802\) 39.6643 1.40059
\(803\) −7.57563 −0.267338
\(804\) −23.1645 −0.816950
\(805\) −4.26561 −0.150343
\(806\) 25.0510 0.882382
\(807\) −73.7458 −2.59597
\(808\) 18.6082 0.654634
\(809\) 40.3635 1.41911 0.709553 0.704652i \(-0.248897\pi\)
0.709553 + 0.704652i \(0.248897\pi\)
\(810\) −16.7631 −0.588996
\(811\) 33.1330 1.16346 0.581728 0.813384i \(-0.302377\pi\)
0.581728 + 0.813384i \(0.302377\pi\)
\(812\) 12.5184 0.439309
\(813\) 63.0099 2.20986
\(814\) −3.17929 −0.111434
\(815\) −0.220660 −0.00772940
\(816\) 4.08047 0.142845
\(817\) −16.7128 −0.584707
\(818\) −7.75325 −0.271086
\(819\) −31.4417 −1.09866
\(820\) −11.7809 −0.411406
\(821\) 26.2748 0.916997 0.458499 0.888695i \(-0.348387\pi\)
0.458499 + 0.888695i \(0.348387\pi\)
\(822\) 55.9094 1.95006
\(823\) 15.7803 0.550066 0.275033 0.961435i \(-0.411311\pi\)
0.275033 + 0.961435i \(0.411311\pi\)
\(824\) −1.10760 −0.0385852
\(825\) 9.08972 0.316464
\(826\) 12.3206 0.428690
\(827\) 27.4534 0.954647 0.477324 0.878728i \(-0.341607\pi\)
0.477324 + 0.878728i \(0.341607\pi\)
\(828\) −10.7880 −0.374910
\(829\) 20.8442 0.723949 0.361974 0.932188i \(-0.382103\pi\)
0.361974 + 0.932188i \(0.382103\pi\)
\(830\) 4.65577 0.161604
\(831\) 40.1476 1.39270
\(832\) 2.81976 0.0977575
\(833\) 5.18415 0.179620
\(834\) −43.2260 −1.49679
\(835\) −24.2284 −0.838459
\(836\) −3.55620 −0.122994
\(837\) −89.6935 −3.10026
\(838\) −15.5207 −0.536153
\(839\) −3.90126 −0.134686 −0.0673432 0.997730i \(-0.521452\pi\)
−0.0673432 + 0.997730i \(0.521452\pi\)
\(840\) −7.61116 −0.262610
\(841\) 21.1682 0.729939
\(842\) 7.02289 0.242025
\(843\) 39.8140 1.37127
\(844\) −23.7895 −0.818869
\(845\) 7.12636 0.245154
\(846\) 39.6369 1.36275
\(847\) 17.7074 0.608434
\(848\) 3.23255 0.111006
\(849\) 40.0630 1.37496
\(850\) 4.02261 0.137974
\(851\) 5.48861 0.188147
\(852\) −9.08449 −0.311229
\(853\) 23.7078 0.811738 0.405869 0.913931i \(-0.366969\pi\)
0.405869 + 0.913931i \(0.366969\pi\)
\(854\) −5.84184 −0.199904
\(855\) 31.9716 1.09340
\(856\) 17.0999 0.584464
\(857\) −16.0872 −0.549527 −0.274764 0.961512i \(-0.588600\pi\)
−0.274764 + 0.961512i \(0.588600\pi\)
\(858\) −8.52144 −0.290917
\(859\) 48.9156 1.66898 0.834489 0.551024i \(-0.185763\pi\)
0.834489 + 0.551024i \(0.185763\pi\)
\(860\) −6.57019 −0.224042
\(861\) 45.0087 1.53389
\(862\) 38.2424 1.30254
\(863\) 30.8015 1.04849 0.524247 0.851566i \(-0.324347\pi\)
0.524247 + 0.851566i \(0.324347\pi\)
\(864\) −10.0960 −0.343472
\(865\) −9.61262 −0.326839
\(866\) −5.15882 −0.175304
\(867\) 46.4109 1.57620
\(868\) −15.7017 −0.532949
\(869\) 1.58531 0.0537779
\(870\) −30.5023 −1.03412
\(871\) 21.4084 0.725395
\(872\) 13.9731 0.473188
\(873\) −63.8882 −2.16229
\(874\) 6.13930 0.207665
\(875\) −19.9762 −0.675319
\(876\) 23.3357 0.788441
\(877\) 28.0998 0.948864 0.474432 0.880292i \(-0.342653\pi\)
0.474432 + 0.880292i \(0.342653\pi\)
\(878\) 20.4598 0.690485
\(879\) 80.0196 2.69899
\(880\) −1.39803 −0.0471275
\(881\) 3.00848 0.101358 0.0506791 0.998715i \(-0.483861\pi\)
0.0506791 + 0.998715i \(0.483861\pi\)
\(882\) −24.4557 −0.823466
\(883\) −23.5000 −0.790837 −0.395418 0.918501i \(-0.629400\pi\)
−0.395418 + 0.918501i \(0.629400\pi\)
\(884\) −3.77112 −0.126836
\(885\) −30.0205 −1.00913
\(886\) −26.2999 −0.883563
\(887\) 24.9535 0.837857 0.418929 0.908019i \(-0.362406\pi\)
0.418929 + 0.908019i \(0.362406\pi\)
\(888\) 9.79337 0.328644
\(889\) −1.12793 −0.0378296
\(890\) 13.1455 0.440639
\(891\) 11.7635 0.394094
\(892\) −28.4792 −0.953555
\(893\) −22.5567 −0.754833
\(894\) 46.7465 1.56344
\(895\) 2.48903 0.0831992
\(896\) −1.76739 −0.0590445
\(897\) 14.7111 0.491189
\(898\) −7.78811 −0.259893
\(899\) −62.9255 −2.09868
\(900\) −18.9762 −0.632542
\(901\) −4.32318 −0.144026
\(902\) 8.26725 0.275269
\(903\) 25.1014 0.835321
\(904\) −1.22548 −0.0407590
\(905\) 0.535397 0.0177972
\(906\) −5.40804 −0.179670
\(907\) −19.1289 −0.635165 −0.317583 0.948231i \(-0.602871\pi\)
−0.317583 + 0.948231i \(0.602871\pi\)
\(908\) 15.0721 0.500185
\(909\) 117.399 3.89389
\(910\) 7.03414 0.233180
\(911\) 35.4600 1.17484 0.587421 0.809282i \(-0.300143\pi\)
0.587421 + 0.809282i \(0.300143\pi\)
\(912\) 10.9544 0.362737
\(913\) −3.26719 −0.108128
\(914\) 12.5807 0.416133
\(915\) 14.2342 0.470569
\(916\) 19.3331 0.638785
\(917\) −0.692713 −0.0228754
\(918\) 13.5023 0.445641
\(919\) 7.46159 0.246135 0.123067 0.992398i \(-0.460727\pi\)
0.123067 + 0.992398i \(0.460727\pi\)
\(920\) 2.41350 0.0795708
\(921\) 104.481 3.44276
\(922\) −5.98896 −0.197236
\(923\) 8.39578 0.276350
\(924\) 5.34115 0.175711
\(925\) 9.65451 0.317438
\(926\) 14.9361 0.490831
\(927\) −6.98788 −0.229512
\(928\) −7.08295 −0.232509
\(929\) −45.1928 −1.48273 −0.741364 0.671103i \(-0.765821\pi\)
−0.741364 + 0.671103i \(0.765821\pi\)
\(930\) 38.2587 1.25455
\(931\) 13.9173 0.456123
\(932\) −27.3546 −0.896029
\(933\) −15.0093 −0.491383
\(934\) 22.9564 0.751157
\(935\) 1.86971 0.0611459
\(936\) 17.7899 0.581480
\(937\) −50.5444 −1.65122 −0.825608 0.564245i \(-0.809167\pi\)
−0.825608 + 0.564245i \(0.809167\pi\)
\(938\) −13.4185 −0.438131
\(939\) 15.2427 0.497427
\(940\) −8.86758 −0.289229
\(941\) −34.3366 −1.11934 −0.559670 0.828716i \(-0.689072\pi\)
−0.559670 + 0.828716i \(0.689072\pi\)
\(942\) −14.5702 −0.474721
\(943\) −14.2723 −0.464769
\(944\) −6.97108 −0.226889
\(945\) −25.1854 −0.819280
\(946\) 4.61064 0.149905
\(947\) −50.1975 −1.63120 −0.815600 0.578616i \(-0.803593\pi\)
−0.815600 + 0.578616i \(0.803593\pi\)
\(948\) −4.88333 −0.158603
\(949\) −21.5666 −0.700081
\(950\) 10.7991 0.350368
\(951\) 11.3040 0.366557
\(952\) 2.36370 0.0766078
\(953\) −46.6564 −1.51135 −0.755675 0.654947i \(-0.772691\pi\)
−0.755675 + 0.654947i \(0.772691\pi\)
\(954\) 20.3941 0.660285
\(955\) −19.6775 −0.636749
\(956\) −26.4726 −0.856185
\(957\) 21.4050 0.691926
\(958\) −4.91130 −0.158677
\(959\) 32.3867 1.04582
\(960\) 4.30643 0.138989
\(961\) 47.9268 1.54603
\(962\) −9.05091 −0.291813
\(963\) 107.884 3.47650
\(964\) −11.3914 −0.366892
\(965\) 20.6209 0.663811
\(966\) −9.22076 −0.296673
\(967\) −58.7466 −1.88916 −0.944581 0.328278i \(-0.893532\pi\)
−0.944581 + 0.328278i \(0.893532\pi\)
\(968\) −10.0189 −0.322021
\(969\) −14.6503 −0.470636
\(970\) 14.2931 0.458923
\(971\) 41.5009 1.33183 0.665914 0.746028i \(-0.268042\pi\)
0.665914 + 0.746028i \(0.268042\pi\)
\(972\) −5.94806 −0.190784
\(973\) −25.0396 −0.802731
\(974\) −26.5750 −0.851519
\(975\) 25.8770 0.828726
\(976\) 3.30534 0.105801
\(977\) 26.0602 0.833739 0.416870 0.908966i \(-0.363127\pi\)
0.416870 + 0.908966i \(0.363127\pi\)
\(978\) −0.476991 −0.0152525
\(979\) −9.22489 −0.294829
\(980\) 5.47124 0.174772
\(981\) 88.1563 2.81461
\(982\) 24.0414 0.767191
\(983\) −26.7644 −0.853653 −0.426826 0.904334i \(-0.640368\pi\)
−0.426826 + 0.904334i \(0.640368\pi\)
\(984\) −25.4662 −0.811831
\(985\) 32.3481 1.03070
\(986\) 9.47267 0.301671
\(987\) 33.8785 1.07836
\(988\) −10.1239 −0.322085
\(989\) −7.95965 −0.253102
\(990\) −8.82015 −0.280323
\(991\) −15.1316 −0.480671 −0.240336 0.970690i \(-0.577257\pi\)
−0.240336 + 0.970690i \(0.577257\pi\)
\(992\) 8.88408 0.282070
\(993\) −22.1928 −0.704267
\(994\) −5.26238 −0.166913
\(995\) −20.8341 −0.660487
\(996\) 10.0641 0.318895
\(997\) 6.59747 0.208944 0.104472 0.994528i \(-0.466685\pi\)
0.104472 + 0.994528i \(0.466685\pi\)
\(998\) 27.9188 0.883754
\(999\) 32.4063 1.02529
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 \(a_p\))