Properties

Label 4031.2.a.c.1.9
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.10281 q^{2}\) \(-1.04272 q^{3}\) \(+2.42182 q^{4}\) \(+3.50696 q^{5}\) \(+2.19264 q^{6}\) \(-3.91864 q^{7}\) \(-0.887016 q^{8}\) \(-1.91274 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.10281 q^{2}\) \(-1.04272 q^{3}\) \(+2.42182 q^{4}\) \(+3.50696 q^{5}\) \(+2.19264 q^{6}\) \(-3.91864 q^{7}\) \(-0.887016 q^{8}\) \(-1.91274 q^{9}\) \(-7.37448 q^{10}\) \(-0.686935 q^{11}\) \(-2.52528 q^{12}\) \(-0.0835199 q^{13}\) \(+8.24017 q^{14}\) \(-3.65677 q^{15}\) \(-2.97842 q^{16}\) \(-6.13443 q^{17}\) \(+4.02213 q^{18}\) \(-2.60752 q^{19}\) \(+8.49323 q^{20}\) \(+4.08604 q^{21}\) \(+1.44450 q^{22}\) \(+6.11523 q^{23}\) \(+0.924909 q^{24}\) \(+7.29875 q^{25}\) \(+0.175627 q^{26}\) \(+5.12260 q^{27}\) \(-9.49026 q^{28}\) \(-1.00000 q^{29}\) \(+7.68951 q^{30}\) \(+8.22281 q^{31}\) \(+8.03709 q^{32}\) \(+0.716281 q^{33}\) \(+12.8996 q^{34}\) \(-13.7425 q^{35}\) \(-4.63231 q^{36}\) \(+3.10413 q^{37}\) \(+5.48312 q^{38}\) \(+0.0870878 q^{39}\) \(-3.11073 q^{40}\) \(+2.48308 q^{41}\) \(-8.59219 q^{42}\) \(+3.60914 q^{43}\) \(-1.66364 q^{44}\) \(-6.70789 q^{45}\) \(-12.8592 q^{46}\) \(+4.95268 q^{47}\) \(+3.10565 q^{48}\) \(+8.35576 q^{49}\) \(-15.3479 q^{50}\) \(+6.39649 q^{51}\) \(-0.202271 q^{52}\) \(+2.09829 q^{53}\) \(-10.7719 q^{54}\) \(-2.40905 q^{55}\) \(+3.47590 q^{56}\) \(+2.71891 q^{57}\) \(+2.10281 q^{58}\) \(+0.107135 q^{59}\) \(-8.85606 q^{60}\) \(+5.60696 q^{61}\) \(-17.2910 q^{62}\) \(+7.49533 q^{63}\) \(-10.9437 q^{64}\) \(-0.292901 q^{65}\) \(-1.50620 q^{66}\) \(+4.35469 q^{67}\) \(-14.8565 q^{68}\) \(-6.37647 q^{69}\) \(+28.8979 q^{70}\) \(-13.1621 q^{71}\) \(+1.69663 q^{72}\) \(-6.23169 q^{73}\) \(-6.52740 q^{74}\) \(-7.61055 q^{75}\) \(-6.31495 q^{76}\) \(+2.69185 q^{77}\) \(-0.183129 q^{78}\) \(+7.29203 q^{79}\) \(-10.4452 q^{80}\) \(+0.396773 q^{81}\) \(-5.22146 q^{82}\) \(+0.984862 q^{83}\) \(+9.89568 q^{84}\) \(-21.5132 q^{85}\) \(-7.58935 q^{86}\) \(+1.04272 q^{87}\) \(+0.609323 q^{88}\) \(-12.9439 q^{89}\) \(+14.1054 q^{90}\) \(+0.327285 q^{91}\) \(+14.8100 q^{92}\) \(-8.57408 q^{93}\) \(-10.4146 q^{94}\) \(-9.14446 q^{95}\) \(-8.38043 q^{96}\) \(-10.0691 q^{97}\) \(-17.5706 q^{98}\) \(+1.31393 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10281 −1.48691 −0.743457 0.668784i \(-0.766815\pi\)
−0.743457 + 0.668784i \(0.766815\pi\)
\(3\) −1.04272 −0.602014 −0.301007 0.953622i \(-0.597323\pi\)
−0.301007 + 0.953622i \(0.597323\pi\)
\(4\) 2.42182 1.21091
\(5\) 3.50696 1.56836 0.784180 0.620534i \(-0.213084\pi\)
0.784180 + 0.620534i \(0.213084\pi\)
\(6\) 2.19264 0.895143
\(7\) −3.91864 −1.48111 −0.740554 0.671997i \(-0.765437\pi\)
−0.740554 + 0.671997i \(0.765437\pi\)
\(8\) −0.887016 −0.313608
\(9\) −1.91274 −0.637579
\(10\) −7.37448 −2.33201
\(11\) −0.686935 −0.207119 −0.103559 0.994623i \(-0.533023\pi\)
−0.103559 + 0.994623i \(0.533023\pi\)
\(12\) −2.52528 −0.728986
\(13\) −0.0835199 −0.0231643 −0.0115821 0.999933i \(-0.503687\pi\)
−0.0115821 + 0.999933i \(0.503687\pi\)
\(14\) 8.24017 2.20228
\(15\) −3.65677 −0.944174
\(16\) −2.97842 −0.744604
\(17\) −6.13443 −1.48782 −0.743909 0.668281i \(-0.767030\pi\)
−0.743909 + 0.668281i \(0.767030\pi\)
\(18\) 4.02213 0.948025
\(19\) −2.60752 −0.598206 −0.299103 0.954221i \(-0.596687\pi\)
−0.299103 + 0.954221i \(0.596687\pi\)
\(20\) 8.49323 1.89914
\(21\) 4.08604 0.891648
\(22\) 1.44450 0.307968
\(23\) 6.11523 1.27511 0.637557 0.770403i \(-0.279945\pi\)
0.637557 + 0.770403i \(0.279945\pi\)
\(24\) 0.924909 0.188796
\(25\) 7.29875 1.45975
\(26\) 0.175627 0.0344433
\(27\) 5.12260 0.985846
\(28\) −9.49026 −1.79349
\(29\) −1.00000 −0.185695
\(30\) 7.68951 1.40391
\(31\) 8.22281 1.47686 0.738430 0.674330i \(-0.235567\pi\)
0.738430 + 0.674330i \(0.235567\pi\)
\(32\) 8.03709 1.42077
\(33\) 0.716281 0.124688
\(34\) 12.8996 2.21226
\(35\) −13.7425 −2.32291
\(36\) −4.63231 −0.772052
\(37\) 3.10413 0.510315 0.255158 0.966899i \(-0.417873\pi\)
0.255158 + 0.966899i \(0.417873\pi\)
\(38\) 5.48312 0.889480
\(39\) 0.0870878 0.0139452
\(40\) −3.11073 −0.491849
\(41\) 2.48308 0.387792 0.193896 0.981022i \(-0.437888\pi\)
0.193896 + 0.981022i \(0.437888\pi\)
\(42\) −8.59219 −1.32580
\(43\) 3.60914 0.550389 0.275194 0.961389i \(-0.411258\pi\)
0.275194 + 0.961389i \(0.411258\pi\)
\(44\) −1.66364 −0.250803
\(45\) −6.70789 −0.999953
\(46\) −12.8592 −1.89598
\(47\) 4.95268 0.722422 0.361211 0.932484i \(-0.382363\pi\)
0.361211 + 0.932484i \(0.382363\pi\)
\(48\) 3.10565 0.448262
\(49\) 8.35576 1.19368
\(50\) −15.3479 −2.17052
\(51\) 6.39649 0.895688
\(52\) −0.202271 −0.0280499
\(53\) 2.09829 0.288222 0.144111 0.989562i \(-0.453968\pi\)
0.144111 + 0.989562i \(0.453968\pi\)
\(54\) −10.7719 −1.46587
\(55\) −2.40905 −0.324837
\(56\) 3.47590 0.464487
\(57\) 2.71891 0.360128
\(58\) 2.10281 0.276113
\(59\) 0.107135 0.0139479 0.00697393 0.999976i \(-0.497780\pi\)
0.00697393 + 0.999976i \(0.497780\pi\)
\(60\) −8.85606 −1.14331
\(61\) 5.60696 0.717898 0.358949 0.933357i \(-0.383135\pi\)
0.358949 + 0.933357i \(0.383135\pi\)
\(62\) −17.2910 −2.19596
\(63\) 7.49533 0.944323
\(64\) −10.9437 −1.36796
\(65\) −0.292901 −0.0363299
\(66\) −1.50620 −0.185401
\(67\) 4.35469 0.532010 0.266005 0.963972i \(-0.414296\pi\)
0.266005 + 0.963972i \(0.414296\pi\)
\(68\) −14.8565 −1.80162
\(69\) −6.37647 −0.767637
\(70\) 28.8979 3.45396
\(71\) −13.1621 −1.56205 −0.781027 0.624497i \(-0.785304\pi\)
−0.781027 + 0.624497i \(0.785304\pi\)
\(72\) 1.69663 0.199950
\(73\) −6.23169 −0.729364 −0.364682 0.931132i \(-0.618822\pi\)
−0.364682 + 0.931132i \(0.618822\pi\)
\(74\) −6.52740 −0.758795
\(75\) −7.61055 −0.878791
\(76\) −6.31495 −0.724374
\(77\) 2.69185 0.306765
\(78\) −0.183129 −0.0207353
\(79\) 7.29203 0.820417 0.410209 0.911992i \(-0.365456\pi\)
0.410209 + 0.911992i \(0.365456\pi\)
\(80\) −10.4452 −1.16781
\(81\) 0.396773 0.0440858
\(82\) −5.22146 −0.576614
\(83\) 0.984862 0.108103 0.0540513 0.998538i \(-0.482787\pi\)
0.0540513 + 0.998538i \(0.482787\pi\)
\(84\) 9.89568 1.07971
\(85\) −21.5132 −2.33343
\(86\) −7.58935 −0.818381
\(87\) 1.04272 0.111791
\(88\) 0.609323 0.0649541
\(89\) −12.9439 −1.37205 −0.686026 0.727577i \(-0.740646\pi\)
−0.686026 + 0.727577i \(0.740646\pi\)
\(90\) 14.1054 1.48684
\(91\) 0.327285 0.0343088
\(92\) 14.8100 1.54405
\(93\) −8.57408 −0.889091
\(94\) −10.4146 −1.07418
\(95\) −9.14446 −0.938202
\(96\) −8.38043 −0.855324
\(97\) −10.0691 −1.02236 −0.511179 0.859475i \(-0.670791\pi\)
−0.511179 + 0.859475i \(0.670791\pi\)
\(98\) −17.5706 −1.77490
\(99\) 1.31393 0.132055
\(100\) 17.6763 1.76763
\(101\) −7.28969 −0.725351 −0.362675 0.931916i \(-0.618137\pi\)
−0.362675 + 0.931916i \(0.618137\pi\)
\(102\) −13.4506 −1.33181
\(103\) 0.147878 0.0145708 0.00728542 0.999973i \(-0.497681\pi\)
0.00728542 + 0.999973i \(0.497681\pi\)
\(104\) 0.0740836 0.00726449
\(105\) 14.3296 1.39842
\(106\) −4.41231 −0.428562
\(107\) −0.866579 −0.0837754 −0.0418877 0.999122i \(-0.513337\pi\)
−0.0418877 + 0.999122i \(0.513337\pi\)
\(108\) 12.4060 1.19377
\(109\) −1.24876 −0.119610 −0.0598048 0.998210i \(-0.519048\pi\)
−0.0598048 + 0.998210i \(0.519048\pi\)
\(110\) 5.06579 0.483004
\(111\) −3.23673 −0.307217
\(112\) 11.6714 1.10284
\(113\) −8.99068 −0.845772 −0.422886 0.906183i \(-0.638983\pi\)
−0.422886 + 0.906183i \(0.638983\pi\)
\(114\) −5.71736 −0.535480
\(115\) 21.4459 1.99984
\(116\) −2.42182 −0.224861
\(117\) 0.159752 0.0147690
\(118\) −0.225286 −0.0207392
\(119\) 24.0386 2.20362
\(120\) 3.24362 0.296100
\(121\) −10.5281 −0.957102
\(122\) −11.7904 −1.06745
\(123\) −2.58916 −0.233456
\(124\) 19.9142 1.78835
\(125\) 8.06163 0.721054
\(126\) −15.7613 −1.40413
\(127\) 3.40450 0.302101 0.151050 0.988526i \(-0.451734\pi\)
0.151050 + 0.988526i \(0.451734\pi\)
\(128\) 6.93830 0.613265
\(129\) −3.76332 −0.331342
\(130\) 0.615916 0.0540194
\(131\) −3.71368 −0.324465 −0.162233 0.986753i \(-0.551870\pi\)
−0.162233 + 0.986753i \(0.551870\pi\)
\(132\) 1.73471 0.150987
\(133\) 10.2179 0.886007
\(134\) −9.15710 −0.791053
\(135\) 17.9648 1.54616
\(136\) 5.44134 0.466591
\(137\) 19.8097 1.69245 0.846227 0.532823i \(-0.178869\pi\)
0.846227 + 0.532823i \(0.178869\pi\)
\(138\) 13.4085 1.14141
\(139\) −1.00000 −0.0848189
\(140\) −33.2819 −2.81284
\(141\) −5.16425 −0.434908
\(142\) 27.6774 2.32264
\(143\) 0.0573728 0.00479776
\(144\) 5.69693 0.474744
\(145\) −3.50696 −0.291237
\(146\) 13.1041 1.08450
\(147\) −8.71271 −0.718612
\(148\) 7.51765 0.617947
\(149\) −5.54235 −0.454047 −0.227023 0.973889i \(-0.572899\pi\)
−0.227023 + 0.973889i \(0.572899\pi\)
\(150\) 16.0036 1.30669
\(151\) −9.93145 −0.808210 −0.404105 0.914713i \(-0.632417\pi\)
−0.404105 + 0.914713i \(0.632417\pi\)
\(152\) 2.31291 0.187602
\(153\) 11.7336 0.948602
\(154\) −5.66047 −0.456133
\(155\) 28.8370 2.31625
\(156\) 0.210911 0.0168864
\(157\) −8.23938 −0.657574 −0.328787 0.944404i \(-0.606640\pi\)
−0.328787 + 0.944404i \(0.606640\pi\)
\(158\) −15.3338 −1.21989
\(159\) −2.18793 −0.173514
\(160\) 28.1857 2.22828
\(161\) −23.9634 −1.88858
\(162\) −0.834339 −0.0655518
\(163\) 5.27298 0.413012 0.206506 0.978445i \(-0.433791\pi\)
0.206506 + 0.978445i \(0.433791\pi\)
\(164\) 6.01359 0.469582
\(165\) 2.51197 0.195556
\(166\) −2.07098 −0.160739
\(167\) −7.03096 −0.544072 −0.272036 0.962287i \(-0.587697\pi\)
−0.272036 + 0.962287i \(0.587697\pi\)
\(168\) −3.62439 −0.279628
\(169\) −12.9930 −0.999463
\(170\) 45.2382 3.46961
\(171\) 4.98750 0.381403
\(172\) 8.74070 0.666472
\(173\) −12.9429 −0.984028 −0.492014 0.870587i \(-0.663739\pi\)
−0.492014 + 0.870587i \(0.663739\pi\)
\(174\) −2.19264 −0.166224
\(175\) −28.6012 −2.16205
\(176\) 2.04598 0.154222
\(177\) −0.111712 −0.00839680
\(178\) 27.2186 2.04012
\(179\) −8.23835 −0.615763 −0.307882 0.951425i \(-0.599620\pi\)
−0.307882 + 0.951425i \(0.599620\pi\)
\(180\) −16.2453 −1.21085
\(181\) −2.63754 −0.196047 −0.0980234 0.995184i \(-0.531252\pi\)
−0.0980234 + 0.995184i \(0.531252\pi\)
\(182\) −0.688219 −0.0510142
\(183\) −5.84649 −0.432185
\(184\) −5.42431 −0.399886
\(185\) 10.8860 0.800358
\(186\) 18.0297 1.32200
\(187\) 4.21396 0.308155
\(188\) 11.9945 0.874790
\(189\) −20.0737 −1.46014
\(190\) 19.2291 1.39502
\(191\) −9.09683 −0.658223 −0.329112 0.944291i \(-0.606749\pi\)
−0.329112 + 0.944291i \(0.606749\pi\)
\(192\) 11.4112 0.823530
\(193\) 4.90942 0.353388 0.176694 0.984266i \(-0.443460\pi\)
0.176694 + 0.984266i \(0.443460\pi\)
\(194\) 21.1733 1.52016
\(195\) 0.305413 0.0218711
\(196\) 20.2362 1.44544
\(197\) −10.4899 −0.747376 −0.373688 0.927554i \(-0.621907\pi\)
−0.373688 + 0.927554i \(0.621907\pi\)
\(198\) −2.76294 −0.196354
\(199\) −6.71681 −0.476142 −0.238071 0.971248i \(-0.576515\pi\)
−0.238071 + 0.971248i \(0.576515\pi\)
\(200\) −6.47411 −0.457789
\(201\) −4.54072 −0.320277
\(202\) 15.3288 1.07853
\(203\) 3.91864 0.275035
\(204\) 15.4912 1.08460
\(205\) 8.70806 0.608198
\(206\) −0.310960 −0.0216656
\(207\) −11.6968 −0.812986
\(208\) 0.248757 0.0172482
\(209\) 1.79120 0.123900
\(210\) −30.1324 −2.07934
\(211\) −10.4311 −0.718108 −0.359054 0.933317i \(-0.616901\pi\)
−0.359054 + 0.933317i \(0.616901\pi\)
\(212\) 5.08169 0.349012
\(213\) 13.7244 0.940379
\(214\) 1.82225 0.124567
\(215\) 12.6571 0.863207
\(216\) −4.54383 −0.309169
\(217\) −32.2222 −2.18739
\(218\) 2.62591 0.177849
\(219\) 6.49790 0.439087
\(220\) −5.83430 −0.393349
\(221\) 0.512347 0.0344642
\(222\) 6.80625 0.456805
\(223\) 18.0043 1.20566 0.602828 0.797871i \(-0.294040\pi\)
0.602828 + 0.797871i \(0.294040\pi\)
\(224\) −31.4945 −2.10431
\(225\) −13.9606 −0.930706
\(226\) 18.9057 1.25759
\(227\) 23.4123 1.55393 0.776963 0.629546i \(-0.216759\pi\)
0.776963 + 0.629546i \(0.216759\pi\)
\(228\) 6.58472 0.436084
\(229\) 16.6858 1.10263 0.551314 0.834298i \(-0.314127\pi\)
0.551314 + 0.834298i \(0.314127\pi\)
\(230\) −45.0967 −2.97359
\(231\) −2.80685 −0.184677
\(232\) 0.887016 0.0582355
\(233\) −3.34132 −0.218897 −0.109449 0.993992i \(-0.534909\pi\)
−0.109449 + 0.993992i \(0.534909\pi\)
\(234\) −0.335928 −0.0219603
\(235\) 17.3688 1.13302
\(236\) 0.259463 0.0168896
\(237\) −7.60354 −0.493903
\(238\) −50.5488 −3.27659
\(239\) 18.0675 1.16869 0.584344 0.811506i \(-0.301352\pi\)
0.584344 + 0.811506i \(0.301352\pi\)
\(240\) 10.8914 0.703036
\(241\) −17.7528 −1.14356 −0.571779 0.820407i \(-0.693747\pi\)
−0.571779 + 0.820407i \(0.693747\pi\)
\(242\) 22.1387 1.42313
\(243\) −15.7815 −1.01239
\(244\) 13.5791 0.869311
\(245\) 29.3033 1.87212
\(246\) 5.44451 0.347130
\(247\) 0.217780 0.0138570
\(248\) −7.29377 −0.463155
\(249\) −1.02693 −0.0650793
\(250\) −16.9521 −1.07215
\(251\) 9.22426 0.582230 0.291115 0.956688i \(-0.405974\pi\)
0.291115 + 0.956688i \(0.405974\pi\)
\(252\) 18.1524 1.14349
\(253\) −4.20077 −0.264100
\(254\) −7.15903 −0.449198
\(255\) 22.4322 1.40476
\(256\) 7.29737 0.456086
\(257\) −5.31611 −0.331610 −0.165805 0.986159i \(-0.553022\pi\)
−0.165805 + 0.986159i \(0.553022\pi\)
\(258\) 7.91356 0.492677
\(259\) −12.1640 −0.755832
\(260\) −0.709354 −0.0439923
\(261\) 1.91274 0.118395
\(262\) 7.80917 0.482452
\(263\) −0.378874 −0.0233624 −0.0116812 0.999932i \(-0.503718\pi\)
−0.0116812 + 0.999932i \(0.503718\pi\)
\(264\) −0.635353 −0.0391033
\(265\) 7.35862 0.452036
\(266\) −21.4864 −1.31742
\(267\) 13.4969 0.825994
\(268\) 10.5463 0.644217
\(269\) 19.8767 1.21190 0.605952 0.795501i \(-0.292792\pi\)
0.605952 + 0.795501i \(0.292792\pi\)
\(270\) −37.7765 −2.29901
\(271\) −15.6441 −0.950311 −0.475155 0.879902i \(-0.657608\pi\)
−0.475155 + 0.879902i \(0.657608\pi\)
\(272\) 18.2709 1.10784
\(273\) −0.341266 −0.0206544
\(274\) −41.6560 −2.51653
\(275\) −5.01377 −0.302342
\(276\) −15.4427 −0.929541
\(277\) 11.8379 0.711271 0.355635 0.934625i \(-0.384264\pi\)
0.355635 + 0.934625i \(0.384264\pi\)
\(278\) 2.10281 0.126118
\(279\) −15.7281 −0.941615
\(280\) 12.1898 0.728482
\(281\) −25.6727 −1.53150 −0.765752 0.643136i \(-0.777633\pi\)
−0.765752 + 0.643136i \(0.777633\pi\)
\(282\) 10.8595 0.646671
\(283\) −13.2895 −0.789979 −0.394989 0.918686i \(-0.629252\pi\)
−0.394989 + 0.918686i \(0.629252\pi\)
\(284\) −31.8763 −1.89151
\(285\) 9.53510 0.564811
\(286\) −0.120644 −0.00713385
\(287\) −9.73031 −0.574362
\(288\) −15.3728 −0.905853
\(289\) 20.6313 1.21360
\(290\) 7.37448 0.433044
\(291\) 10.4992 0.615474
\(292\) −15.0920 −0.883195
\(293\) 1.18986 0.0695124 0.0347562 0.999396i \(-0.488935\pi\)
0.0347562 + 0.999396i \(0.488935\pi\)
\(294\) 18.3212 1.06851
\(295\) 0.375720 0.0218752
\(296\) −2.75341 −0.160039
\(297\) −3.51890 −0.204187
\(298\) 11.6545 0.675128
\(299\) −0.510744 −0.0295371
\(300\) −18.4314 −1.06414
\(301\) −14.1429 −0.815185
\(302\) 20.8840 1.20174
\(303\) 7.60109 0.436671
\(304\) 7.76628 0.445427
\(305\) 19.6634 1.12592
\(306\) −24.6735 −1.41049
\(307\) 7.28607 0.415838 0.207919 0.978146i \(-0.433331\pi\)
0.207919 + 0.978146i \(0.433331\pi\)
\(308\) 6.51920 0.371466
\(309\) −0.154195 −0.00877185
\(310\) −60.6389 −3.44406
\(311\) −2.83001 −0.160475 −0.0802375 0.996776i \(-0.525568\pi\)
−0.0802375 + 0.996776i \(0.525568\pi\)
\(312\) −0.0772484 −0.00437333
\(313\) −22.1222 −1.25042 −0.625211 0.780456i \(-0.714987\pi\)
−0.625211 + 0.780456i \(0.714987\pi\)
\(314\) 17.3259 0.977756
\(315\) 26.2858 1.48104
\(316\) 17.6600 0.993453
\(317\) 3.17373 0.178254 0.0891272 0.996020i \(-0.471592\pi\)
0.0891272 + 0.996020i \(0.471592\pi\)
\(318\) 4.60080 0.258000
\(319\) 0.686935 0.0384610
\(320\) −38.3790 −2.14545
\(321\) 0.903599 0.0504340
\(322\) 50.3906 2.80816
\(323\) 15.9956 0.890021
\(324\) 0.960913 0.0533841
\(325\) −0.609591 −0.0338141
\(326\) −11.0881 −0.614113
\(327\) 1.30211 0.0720067
\(328\) −2.20253 −0.121615
\(329\) −19.4078 −1.06999
\(330\) −5.28220 −0.290775
\(331\) −36.1564 −1.98734 −0.993668 0.112358i \(-0.964160\pi\)
−0.993668 + 0.112358i \(0.964160\pi\)
\(332\) 2.38516 0.130903
\(333\) −5.93738 −0.325366
\(334\) 14.7848 0.808988
\(335\) 15.2717 0.834383
\(336\) −12.1699 −0.663925
\(337\) −17.4664 −0.951455 −0.475728 0.879593i \(-0.657815\pi\)
−0.475728 + 0.879593i \(0.657815\pi\)
\(338\) 27.3219 1.48612
\(339\) 9.37475 0.509167
\(340\) −52.1012 −2.82558
\(341\) −5.64854 −0.305886
\(342\) −10.4878 −0.567114
\(343\) −5.31273 −0.286860
\(344\) −3.20137 −0.172606
\(345\) −22.3620 −1.20393
\(346\) 27.2164 1.46316
\(347\) −19.8394 −1.06503 −0.532517 0.846419i \(-0.678754\pi\)
−0.532517 + 0.846419i \(0.678754\pi\)
\(348\) 2.52528 0.135369
\(349\) −27.3702 −1.46509 −0.732547 0.680717i \(-0.761668\pi\)
−0.732547 + 0.680717i \(0.761668\pi\)
\(350\) 60.1430 3.21478
\(351\) −0.427840 −0.0228364
\(352\) −5.52096 −0.294268
\(353\) 7.01146 0.373182 0.186591 0.982438i \(-0.440256\pi\)
0.186591 + 0.982438i \(0.440256\pi\)
\(354\) 0.234910 0.0124853
\(355\) −46.1589 −2.44986
\(356\) −31.3479 −1.66143
\(357\) −25.0656 −1.32661
\(358\) 17.3237 0.915587
\(359\) −26.2224 −1.38397 −0.691983 0.721913i \(-0.743263\pi\)
−0.691983 + 0.721913i \(0.743263\pi\)
\(360\) 5.95001 0.313593
\(361\) −12.2008 −0.642150
\(362\) 5.54626 0.291505
\(363\) 10.9779 0.576189
\(364\) 0.792626 0.0415449
\(365\) −21.8543 −1.14390
\(366\) 12.2941 0.642621
\(367\) −8.27547 −0.431976 −0.215988 0.976396i \(-0.569297\pi\)
−0.215988 + 0.976396i \(0.569297\pi\)
\(368\) −18.2137 −0.949456
\(369\) −4.74948 −0.247248
\(370\) −22.8913 −1.19006
\(371\) −8.22245 −0.426888
\(372\) −20.7649 −1.07661
\(373\) −23.9075 −1.23788 −0.618942 0.785437i \(-0.712438\pi\)
−0.618942 + 0.785437i \(0.712438\pi\)
\(374\) −8.86117 −0.458200
\(375\) −8.40602 −0.434085
\(376\) −4.39311 −0.226557
\(377\) 0.0835199 0.00430150
\(378\) 42.2111 2.17111
\(379\) −5.46090 −0.280508 −0.140254 0.990116i \(-0.544792\pi\)
−0.140254 + 0.990116i \(0.544792\pi\)
\(380\) −22.1463 −1.13608
\(381\) −3.54994 −0.181869
\(382\) 19.1289 0.978721
\(383\) −25.3897 −1.29735 −0.648677 0.761064i \(-0.724677\pi\)
−0.648677 + 0.761064i \(0.724677\pi\)
\(384\) −7.23470 −0.369194
\(385\) 9.44022 0.481118
\(386\) −10.3236 −0.525457
\(387\) −6.90334 −0.350916
\(388\) −24.3855 −1.23798
\(389\) 12.6637 0.642076 0.321038 0.947066i \(-0.395968\pi\)
0.321038 + 0.947066i \(0.395968\pi\)
\(390\) −0.642227 −0.0325204
\(391\) −37.5135 −1.89714
\(392\) −7.41169 −0.374347
\(393\) 3.87232 0.195333
\(394\) 22.0583 1.11128
\(395\) 25.5728 1.28671
\(396\) 3.18210 0.159906
\(397\) −17.3326 −0.869900 −0.434950 0.900455i \(-0.643234\pi\)
−0.434950 + 0.900455i \(0.643234\pi\)
\(398\) 14.1242 0.707982
\(399\) −10.6544 −0.533389
\(400\) −21.7387 −1.08694
\(401\) 3.45185 0.172377 0.0861885 0.996279i \(-0.472531\pi\)
0.0861885 + 0.996279i \(0.472531\pi\)
\(402\) 9.54828 0.476225
\(403\) −0.686769 −0.0342104
\(404\) −17.6543 −0.878336
\(405\) 1.39146 0.0691424
\(406\) −8.24017 −0.408953
\(407\) −2.13234 −0.105696
\(408\) −5.67379 −0.280895
\(409\) 27.1946 1.34469 0.672343 0.740240i \(-0.265288\pi\)
0.672343 + 0.740240i \(0.265288\pi\)
\(410\) −18.3114 −0.904337
\(411\) −20.6559 −1.01888
\(412\) 0.358134 0.0176440
\(413\) −0.419826 −0.0206583
\(414\) 24.5963 1.20884
\(415\) 3.45387 0.169544
\(416\) −0.671257 −0.0329111
\(417\) 1.04272 0.0510622
\(418\) −3.76655 −0.184228
\(419\) 35.8510 1.75143 0.875717 0.482824i \(-0.160389\pi\)
0.875717 + 0.482824i \(0.160389\pi\)
\(420\) 34.7037 1.69337
\(421\) −36.3630 −1.77222 −0.886111 0.463473i \(-0.846603\pi\)
−0.886111 + 0.463473i \(0.846603\pi\)
\(422\) 21.9347 1.06776
\(423\) −9.47317 −0.460601
\(424\) −1.86122 −0.0903887
\(425\) −44.7737 −2.17184
\(426\) −28.8598 −1.39826
\(427\) −21.9717 −1.06328
\(428\) −2.09870 −0.101445
\(429\) −0.0598237 −0.00288832
\(430\) −26.6155 −1.28351
\(431\) 0.321407 0.0154816 0.00774081 0.999970i \(-0.497536\pi\)
0.00774081 + 0.999970i \(0.497536\pi\)
\(432\) −15.2573 −0.734065
\(433\) 29.1376 1.40027 0.700133 0.714012i \(-0.253124\pi\)
0.700133 + 0.714012i \(0.253124\pi\)
\(434\) 67.7574 3.25246
\(435\) 3.65677 0.175329
\(436\) −3.02428 −0.144837
\(437\) −15.9456 −0.762781
\(438\) −13.6639 −0.652885
\(439\) −18.5092 −0.883395 −0.441697 0.897164i \(-0.645624\pi\)
−0.441697 + 0.897164i \(0.645624\pi\)
\(440\) 2.13687 0.101871
\(441\) −15.9824 −0.761065
\(442\) −1.07737 −0.0512453
\(443\) 22.5793 1.07277 0.536387 0.843972i \(-0.319789\pi\)
0.536387 + 0.843972i \(0.319789\pi\)
\(444\) −7.83880 −0.372013
\(445\) −45.3937 −2.15187
\(446\) −37.8597 −1.79271
\(447\) 5.77911 0.273343
\(448\) 42.8843 2.02609
\(449\) 19.2916 0.910429 0.455215 0.890382i \(-0.349563\pi\)
0.455215 + 0.890382i \(0.349563\pi\)
\(450\) 29.3565 1.38388
\(451\) −1.70572 −0.0803191
\(452\) −21.7738 −1.02416
\(453\) 10.3557 0.486554
\(454\) −49.2316 −2.31055
\(455\) 1.14777 0.0538085
\(456\) −2.41172 −0.112939
\(457\) 10.7219 0.501550 0.250775 0.968045i \(-0.419315\pi\)
0.250775 + 0.968045i \(0.419315\pi\)
\(458\) −35.0871 −1.63951
\(459\) −31.4243 −1.46676
\(460\) 51.9381 2.42163
\(461\) −16.9188 −0.787988 −0.393994 0.919113i \(-0.628907\pi\)
−0.393994 + 0.919113i \(0.628907\pi\)
\(462\) 5.90228 0.274599
\(463\) 34.7591 1.61539 0.807697 0.589598i \(-0.200714\pi\)
0.807697 + 0.589598i \(0.200714\pi\)
\(464\) 2.97842 0.138270
\(465\) −30.0689 −1.39441
\(466\) 7.02618 0.325481
\(467\) 6.99023 0.323469 0.161735 0.986834i \(-0.448291\pi\)
0.161735 + 0.986834i \(0.448291\pi\)
\(468\) 0.386890 0.0178840
\(469\) −17.0645 −0.787964
\(470\) −36.5234 −1.68470
\(471\) 8.59136 0.395869
\(472\) −0.0950309 −0.00437415
\(473\) −2.47925 −0.113996
\(474\) 15.9888 0.734391
\(475\) −19.0316 −0.873231
\(476\) 58.2174 2.66839
\(477\) −4.01348 −0.183765
\(478\) −37.9925 −1.73774
\(479\) 29.5808 1.35158 0.675790 0.737095i \(-0.263803\pi\)
0.675790 + 0.737095i \(0.263803\pi\)
\(480\) −29.3898 −1.34145
\(481\) −0.259257 −0.0118211
\(482\) 37.3308 1.70037
\(483\) 24.9871 1.13695
\(484\) −25.4972 −1.15897
\(485\) −35.3117 −1.60342
\(486\) 33.1856 1.50533
\(487\) −35.9514 −1.62911 −0.814556 0.580085i \(-0.803019\pi\)
−0.814556 + 0.580085i \(0.803019\pi\)
\(488\) −4.97347 −0.225138
\(489\) −5.49824 −0.248639
\(490\) −61.6193 −2.78368
\(491\) −0.944071 −0.0426053 −0.0213027 0.999773i \(-0.506781\pi\)
−0.0213027 + 0.999773i \(0.506781\pi\)
\(492\) −6.27048 −0.282695
\(493\) 6.13443 0.276281
\(494\) −0.457950 −0.0206042
\(495\) 4.60789 0.207109
\(496\) −24.4910 −1.09968
\(497\) 51.5776 2.31357
\(498\) 2.15945 0.0967673
\(499\) 17.6273 0.789107 0.394553 0.918873i \(-0.370899\pi\)
0.394553 + 0.918873i \(0.370899\pi\)
\(500\) 19.5238 0.873133
\(501\) 7.33132 0.327539
\(502\) −19.3969 −0.865726
\(503\) −9.28633 −0.414057 −0.207028 0.978335i \(-0.566379\pi\)
−0.207028 + 0.978335i \(0.566379\pi\)
\(504\) −6.64848 −0.296147
\(505\) −25.5646 −1.13761
\(506\) 8.83344 0.392694
\(507\) 13.5481 0.601691
\(508\) 8.24510 0.365817
\(509\) −32.2608 −1.42994 −0.714968 0.699157i \(-0.753559\pi\)
−0.714968 + 0.699157i \(0.753559\pi\)
\(510\) −47.1708 −2.08876
\(511\) 24.4197 1.08027
\(512\) −29.2216 −1.29143
\(513\) −13.3573 −0.589739
\(514\) 11.1788 0.493075
\(515\) 0.518602 0.0228523
\(516\) −9.11410 −0.401226
\(517\) −3.40217 −0.149627
\(518\) 25.5785 1.12386
\(519\) 13.4958 0.592399
\(520\) 0.259808 0.0113933
\(521\) −6.49922 −0.284736 −0.142368 0.989814i \(-0.545472\pi\)
−0.142368 + 0.989814i \(0.545472\pi\)
\(522\) −4.02213 −0.176044
\(523\) −2.79653 −0.122284 −0.0611419 0.998129i \(-0.519474\pi\)
−0.0611419 + 0.998129i \(0.519474\pi\)
\(524\) −8.99387 −0.392899
\(525\) 29.8230 1.30158
\(526\) 0.796701 0.0347378
\(527\) −50.4423 −2.19730
\(528\) −2.13338 −0.0928436
\(529\) 14.3961 0.625916
\(530\) −15.4738 −0.672139
\(531\) −0.204922 −0.00889286
\(532\) 24.7460 1.07288
\(533\) −0.207387 −0.00898292
\(534\) −28.3814 −1.22818
\(535\) −3.03906 −0.131390
\(536\) −3.86268 −0.166842
\(537\) 8.59029 0.370698
\(538\) −41.7970 −1.80200
\(539\) −5.73987 −0.247234
\(540\) 43.5075 1.87226
\(541\) −13.7229 −0.589996 −0.294998 0.955498i \(-0.595319\pi\)
−0.294998 + 0.955498i \(0.595319\pi\)
\(542\) 32.8966 1.41303
\(543\) 2.75021 0.118023
\(544\) −49.3030 −2.11385
\(545\) −4.37935 −0.187591
\(546\) 0.717619 0.0307113
\(547\) 2.06811 0.0884258 0.0442129 0.999022i \(-0.485922\pi\)
0.0442129 + 0.999022i \(0.485922\pi\)
\(548\) 47.9755 2.04941
\(549\) −10.7246 −0.457717
\(550\) 10.5430 0.449556
\(551\) 2.60752 0.111084
\(552\) 5.65603 0.240737
\(553\) −28.5749 −1.21513
\(554\) −24.8929 −1.05760
\(555\) −11.3511 −0.481827
\(556\) −2.42182 −0.102708
\(557\) −36.6618 −1.55341 −0.776705 0.629864i \(-0.783110\pi\)
−0.776705 + 0.629864i \(0.783110\pi\)
\(558\) 33.0732 1.40010
\(559\) −0.301435 −0.0127494
\(560\) 40.9309 1.72965
\(561\) −4.39398 −0.185514
\(562\) 53.9849 2.27721
\(563\) 0.432140 0.0182125 0.00910626 0.999959i \(-0.497101\pi\)
0.00910626 + 0.999959i \(0.497101\pi\)
\(564\) −12.5069 −0.526636
\(565\) −31.5299 −1.32647
\(566\) 27.9453 1.17463
\(567\) −1.55481 −0.0652959
\(568\) 11.6750 0.489872
\(569\) 8.64233 0.362305 0.181153 0.983455i \(-0.442017\pi\)
0.181153 + 0.983455i \(0.442017\pi\)
\(570\) −20.0505 −0.839825
\(571\) −8.99945 −0.376615 −0.188308 0.982110i \(-0.560300\pi\)
−0.188308 + 0.982110i \(0.560300\pi\)
\(572\) 0.138947 0.00580966
\(573\) 9.48544 0.396260
\(574\) 20.4610 0.854027
\(575\) 44.6336 1.86135
\(576\) 20.9323 0.872181
\(577\) 22.2843 0.927709 0.463855 0.885911i \(-0.346466\pi\)
0.463855 + 0.885911i \(0.346466\pi\)
\(578\) −43.3837 −1.80452
\(579\) −5.11914 −0.212744
\(580\) −8.49323 −0.352662
\(581\) −3.85932 −0.160112
\(582\) −22.0778 −0.915156
\(583\) −1.44139 −0.0596963
\(584\) 5.52761 0.228734
\(585\) 0.560242 0.0231632
\(586\) −2.50206 −0.103359
\(587\) −29.8291 −1.23118 −0.615590 0.788067i \(-0.711082\pi\)
−0.615590 + 0.788067i \(0.711082\pi\)
\(588\) −21.1006 −0.870176
\(589\) −21.4411 −0.883466
\(590\) −0.790068 −0.0325266
\(591\) 10.9380 0.449931
\(592\) −9.24539 −0.379983
\(593\) 17.0650 0.700777 0.350388 0.936604i \(-0.386050\pi\)
0.350388 + 0.936604i \(0.386050\pi\)
\(594\) 7.39959 0.303609
\(595\) 84.3025 3.45607
\(596\) −13.4226 −0.549811
\(597\) 7.00375 0.286644
\(598\) 1.07400 0.0439191
\(599\) −5.31383 −0.217117 −0.108559 0.994090i \(-0.534624\pi\)
−0.108559 + 0.994090i \(0.534624\pi\)
\(600\) 6.75068 0.275595
\(601\) −25.0796 −1.02302 −0.511509 0.859278i \(-0.670913\pi\)
−0.511509 + 0.859278i \(0.670913\pi\)
\(602\) 29.7399 1.21211
\(603\) −8.32937 −0.339198
\(604\) −24.0522 −0.978671
\(605\) −36.9217 −1.50108
\(606\) −15.9837 −0.649293
\(607\) 47.4201 1.92472 0.962360 0.271776i \(-0.0876111\pi\)
0.962360 + 0.271776i \(0.0876111\pi\)
\(608\) −20.9569 −0.849913
\(609\) −4.08604 −0.165575
\(610\) −41.3484 −1.67415
\(611\) −0.413647 −0.0167344
\(612\) 28.4166 1.14867
\(613\) 28.8690 1.16601 0.583004 0.812470i \(-0.301877\pi\)
0.583004 + 0.812470i \(0.301877\pi\)
\(614\) −15.3212 −0.618315
\(615\) −9.08007 −0.366144
\(616\) −2.38772 −0.0962039
\(617\) 39.7252 1.59928 0.799638 0.600483i \(-0.205025\pi\)
0.799638 + 0.600483i \(0.205025\pi\)
\(618\) 0.324244 0.0130430
\(619\) −9.67869 −0.389019 −0.194510 0.980901i \(-0.562312\pi\)
−0.194510 + 0.980901i \(0.562312\pi\)
\(620\) 69.8382 2.80477
\(621\) 31.3259 1.25707
\(622\) 5.95097 0.238612
\(623\) 50.7225 2.03216
\(624\) −0.259384 −0.0103837
\(625\) −8.22197 −0.328879
\(626\) 46.5189 1.85927
\(627\) −1.86772 −0.0745894
\(628\) −19.9543 −0.796264
\(629\) −19.0421 −0.759257
\(630\) −55.2742 −2.20217
\(631\) −14.5200 −0.578031 −0.289015 0.957324i \(-0.593328\pi\)
−0.289015 + 0.957324i \(0.593328\pi\)
\(632\) −6.46815 −0.257289
\(633\) 10.8767 0.432311
\(634\) −6.67376 −0.265049
\(635\) 11.9394 0.473802
\(636\) −5.29877 −0.210110
\(637\) −0.697872 −0.0276507
\(638\) −1.44450 −0.0571882
\(639\) 25.1756 0.995933
\(640\) 24.3323 0.961820
\(641\) 9.89790 0.390944 0.195472 0.980709i \(-0.437376\pi\)
0.195472 + 0.980709i \(0.437376\pi\)
\(642\) −1.90010 −0.0749909
\(643\) 15.5904 0.614826 0.307413 0.951576i \(-0.400537\pi\)
0.307413 + 0.951576i \(0.400537\pi\)
\(644\) −58.0352 −2.28691
\(645\) −13.1978 −0.519663
\(646\) −33.6359 −1.32338
\(647\) 42.4093 1.66728 0.833641 0.552307i \(-0.186252\pi\)
0.833641 + 0.552307i \(0.186252\pi\)
\(648\) −0.351944 −0.0138257
\(649\) −0.0735952 −0.00288886
\(650\) 1.28186 0.0502786
\(651\) 33.5988 1.31684
\(652\) 12.7702 0.500121
\(653\) 27.8273 1.08897 0.544483 0.838772i \(-0.316726\pi\)
0.544483 + 0.838772i \(0.316726\pi\)
\(654\) −2.73809 −0.107068
\(655\) −13.0237 −0.508878
\(656\) −7.39565 −0.288752
\(657\) 11.9196 0.465027
\(658\) 40.8109 1.59098
\(659\) 25.8774 1.00804 0.504021 0.863691i \(-0.331853\pi\)
0.504021 + 0.863691i \(0.331853\pi\)
\(660\) 6.08354 0.236801
\(661\) −30.2353 −1.17602 −0.588008 0.808855i \(-0.700088\pi\)
−0.588008 + 0.808855i \(0.700088\pi\)
\(662\) 76.0302 2.95500
\(663\) −0.534234 −0.0207479
\(664\) −0.873589 −0.0339018
\(665\) 35.8339 1.38958
\(666\) 12.4852 0.483792
\(667\) −6.11523 −0.236783
\(668\) −17.0277 −0.658823
\(669\) −18.7734 −0.725822
\(670\) −32.1136 −1.24065
\(671\) −3.85162 −0.148690
\(672\) 32.8399 1.26683
\(673\) −2.51537 −0.0969604 −0.0484802 0.998824i \(-0.515438\pi\)
−0.0484802 + 0.998824i \(0.515438\pi\)
\(674\) 36.7286 1.41473
\(675\) 37.3886 1.43909
\(676\) −31.4668 −1.21026
\(677\) −2.60433 −0.100093 −0.0500463 0.998747i \(-0.515937\pi\)
−0.0500463 + 0.998747i \(0.515937\pi\)
\(678\) −19.7134 −0.757087
\(679\) 39.4570 1.51422
\(680\) 19.0826 0.731783
\(681\) −24.4124 −0.935486
\(682\) 11.8778 0.454825
\(683\) 19.2096 0.735035 0.367518 0.930017i \(-0.380208\pi\)
0.367518 + 0.930017i \(0.380208\pi\)
\(684\) 12.0788 0.461846
\(685\) 69.4716 2.65437
\(686\) 11.1717 0.426537
\(687\) −17.3986 −0.663797
\(688\) −10.7495 −0.409822
\(689\) −0.175249 −0.00667646
\(690\) 47.0231 1.79014
\(691\) −38.0600 −1.44787 −0.723936 0.689867i \(-0.757669\pi\)
−0.723936 + 0.689867i \(0.757669\pi\)
\(692\) −31.3453 −1.19157
\(693\) −5.14881 −0.195587
\(694\) 41.7185 1.58361
\(695\) −3.50696 −0.133026
\(696\) −0.924909 −0.0350586
\(697\) −15.2323 −0.576964
\(698\) 57.5544 2.17847
\(699\) 3.48406 0.131779
\(700\) −69.2671 −2.61805
\(701\) −39.8972 −1.50689 −0.753447 0.657508i \(-0.771610\pi\)
−0.753447 + 0.657508i \(0.771610\pi\)
\(702\) 0.899667 0.0339557
\(703\) −8.09407 −0.305274
\(704\) 7.51759 0.283330
\(705\) −18.1108 −0.682093
\(706\) −14.7438 −0.554890
\(707\) 28.5657 1.07432
\(708\) −0.270547 −0.0101678
\(709\) 39.0083 1.46499 0.732494 0.680773i \(-0.238356\pi\)
0.732494 + 0.680773i \(0.238356\pi\)
\(710\) 97.0636 3.64273
\(711\) −13.9477 −0.523081
\(712\) 11.4815 0.430286
\(713\) 50.2844 1.88317
\(714\) 52.7082 1.97255
\(715\) 0.201204 0.00752460
\(716\) −19.9518 −0.745635
\(717\) −18.8393 −0.703567
\(718\) 55.1409 2.05784
\(719\) 4.19148 0.156316 0.0781579 0.996941i \(-0.475096\pi\)
0.0781579 + 0.996941i \(0.475096\pi\)
\(720\) 19.9789 0.744569
\(721\) −0.579481 −0.0215810
\(722\) 25.6561 0.954821
\(723\) 18.5112 0.688438
\(724\) −6.38766 −0.237395
\(725\) −7.29875 −0.271069
\(726\) −23.0844 −0.856743
\(727\) 20.7800 0.770689 0.385344 0.922773i \(-0.374083\pi\)
0.385344 + 0.922773i \(0.374083\pi\)
\(728\) −0.290307 −0.0107595
\(729\) 15.2654 0.565385
\(730\) 45.9554 1.70089
\(731\) −22.1400 −0.818878
\(732\) −14.1592 −0.523338
\(733\) −12.7192 −0.469794 −0.234897 0.972020i \(-0.575475\pi\)
−0.234897 + 0.972020i \(0.575475\pi\)
\(734\) 17.4018 0.642311
\(735\) −30.5551 −1.12704
\(736\) 49.1487 1.81164
\(737\) −2.99139 −0.110189
\(738\) 9.98727 0.367637
\(739\) 40.3992 1.48611 0.743055 0.669231i \(-0.233376\pi\)
0.743055 + 0.669231i \(0.233376\pi\)
\(740\) 26.3641 0.969163
\(741\) −0.227083 −0.00834211
\(742\) 17.2903 0.634746
\(743\) 43.4824 1.59521 0.797607 0.603178i \(-0.206099\pi\)
0.797607 + 0.603178i \(0.206099\pi\)
\(744\) 7.60535 0.278826
\(745\) −19.4368 −0.712109
\(746\) 50.2730 1.84063
\(747\) −1.88378 −0.0689240
\(748\) 10.2055 0.373149
\(749\) 3.39581 0.124080
\(750\) 17.6763 0.645447
\(751\) −13.5066 −0.492864 −0.246432 0.969160i \(-0.579258\pi\)
−0.246432 + 0.969160i \(0.579258\pi\)
\(752\) −14.7511 −0.537919
\(753\) −9.61831 −0.350511
\(754\) −0.175627 −0.00639595
\(755\) −34.8292 −1.26756
\(756\) −48.6149 −1.76811
\(757\) 1.47513 0.0536144 0.0268072 0.999641i \(-0.491466\pi\)
0.0268072 + 0.999641i \(0.491466\pi\)
\(758\) 11.4833 0.417091
\(759\) 4.38022 0.158992
\(760\) 8.11128 0.294227
\(761\) 22.4140 0.812506 0.406253 0.913761i \(-0.366835\pi\)
0.406253 + 0.913761i \(0.366835\pi\)
\(762\) 7.46486 0.270423
\(763\) 4.89345 0.177155
\(764\) −22.0309 −0.797050
\(765\) 41.1491 1.48775
\(766\) 53.3899 1.92905
\(767\) −0.00894795 −0.000323092 0
\(768\) −7.60911 −0.274570
\(769\) −37.8544 −1.36506 −0.682532 0.730856i \(-0.739121\pi\)
−0.682532 + 0.730856i \(0.739121\pi\)
\(770\) −19.8510 −0.715381
\(771\) 5.54321 0.199634
\(772\) 11.8897 0.427921
\(773\) 6.70940 0.241320 0.120660 0.992694i \(-0.461499\pi\)
0.120660 + 0.992694i \(0.461499\pi\)
\(774\) 14.5164 0.521782
\(775\) 60.0163 2.15585
\(776\) 8.93141 0.320619
\(777\) 12.6836 0.455022
\(778\) −26.6294 −0.954712
\(779\) −6.47468 −0.231980
\(780\) 0.739657 0.0264840
\(781\) 9.04151 0.323531
\(782\) 78.8838 2.82088
\(783\) −5.12260 −0.183067
\(784\) −24.8869 −0.888819
\(785\) −28.8952 −1.03131
\(786\) −8.14277 −0.290443
\(787\) 20.7250 0.738765 0.369382 0.929277i \(-0.379569\pi\)
0.369382 + 0.929277i \(0.379569\pi\)
\(788\) −25.4047 −0.905006
\(789\) 0.395059 0.0140645
\(790\) −53.7749 −1.91323
\(791\) 35.2313 1.25268
\(792\) −1.16547 −0.0414133
\(793\) −0.468293 −0.0166296
\(794\) 36.4473 1.29347
\(795\) −7.67297 −0.272132
\(796\) −16.2669 −0.576566
\(797\) −2.54925 −0.0902991 −0.0451495 0.998980i \(-0.514376\pi\)
−0.0451495 + 0.998980i \(0.514376\pi\)
\(798\) 22.4043 0.793103
\(799\) −30.3819 −1.07483
\(800\) 58.6607 2.07397
\(801\) 24.7583 0.874791
\(802\) −7.25859 −0.256310
\(803\) 4.28077 0.151065
\(804\) −10.9968 −0.387828
\(805\) −84.0387 −2.96197
\(806\) 1.44415 0.0508679
\(807\) −20.7258 −0.729584
\(808\) 6.46607 0.227476
\(809\) 43.2595 1.52092 0.760462 0.649383i \(-0.224973\pi\)
0.760462 + 0.649383i \(0.224973\pi\)
\(810\) −2.92599 −0.102809
\(811\) 22.8573 0.802630 0.401315 0.915940i \(-0.368553\pi\)
0.401315 + 0.915940i \(0.368553\pi\)
\(812\) 9.49026 0.333043
\(813\) 16.3124 0.572101
\(814\) 4.48390 0.157161
\(815\) 18.4921 0.647751
\(816\) −19.0514 −0.666933
\(817\) −9.41090 −0.329246
\(818\) −57.1852 −1.99943
\(819\) −0.626010 −0.0218745
\(820\) 21.0894 0.736474
\(821\) −18.6341 −0.650334 −0.325167 0.945657i \(-0.605421\pi\)
−0.325167 + 0.945657i \(0.605421\pi\)
\(822\) 43.4355 1.51499
\(823\) −22.0827 −0.769754 −0.384877 0.922968i \(-0.625756\pi\)
−0.384877 + 0.922968i \(0.625756\pi\)
\(824\) −0.131170 −0.00456953
\(825\) 5.22796 0.182014
\(826\) 0.882815 0.0307171
\(827\) −35.4039 −1.23112 −0.615558 0.788092i \(-0.711069\pi\)
−0.615558 + 0.788092i \(0.711069\pi\)
\(828\) −28.3277 −0.984454
\(829\) −51.9060 −1.80277 −0.901385 0.433018i \(-0.857449\pi\)
−0.901385 + 0.433018i \(0.857449\pi\)
\(830\) −7.26284 −0.252097
\(831\) −12.3436 −0.428195
\(832\) 0.914014 0.0316877
\(833\) −51.2578 −1.77598
\(834\) −2.19264 −0.0759250
\(835\) −24.6573 −0.853300
\(836\) 4.33796 0.150032
\(837\) 42.1222 1.45596
\(838\) −75.3879 −2.60423
\(839\) −32.9816 −1.13865 −0.569326 0.822112i \(-0.692796\pi\)
−0.569326 + 0.822112i \(0.692796\pi\)
\(840\) −12.7106 −0.438556
\(841\) 1.00000 0.0344828
\(842\) 76.4645 2.63514
\(843\) 26.7694 0.921987
\(844\) −25.2623 −0.869566
\(845\) −45.5660 −1.56752
\(846\) 19.9203 0.684874
\(847\) 41.2559 1.41757
\(848\) −6.24958 −0.214612
\(849\) 13.8572 0.475578
\(850\) 94.1507 3.22934
\(851\) 18.9825 0.650711
\(852\) 33.2380 1.13872
\(853\) −40.7871 −1.39652 −0.698261 0.715843i \(-0.746043\pi\)
−0.698261 + 0.715843i \(0.746043\pi\)
\(854\) 46.2023 1.58101
\(855\) 17.4909 0.598178
\(856\) 0.768670 0.0262726
\(857\) 46.5297 1.58942 0.794711 0.606987i \(-0.207622\pi\)
0.794711 + 0.606987i \(0.207622\pi\)
\(858\) 0.125798 0.00429468
\(859\) 31.4868 1.07432 0.537158 0.843481i \(-0.319498\pi\)
0.537158 + 0.843481i \(0.319498\pi\)
\(860\) 30.6533 1.04527
\(861\) 10.1460 0.345774
\(862\) −0.675859 −0.0230198
\(863\) 13.7283 0.467316 0.233658 0.972319i \(-0.424930\pi\)
0.233658 + 0.972319i \(0.424930\pi\)
\(864\) 41.1708 1.40066
\(865\) −45.3901 −1.54331
\(866\) −61.2710 −2.08207
\(867\) −21.5126 −0.730606
\(868\) −78.0366 −2.64873
\(869\) −5.00915 −0.169924
\(870\) −7.68951 −0.260699
\(871\) −0.363703 −0.0123236
\(872\) 1.10767 0.0375105
\(873\) 19.2594 0.651833
\(874\) 33.5306 1.13419
\(875\) −31.5906 −1.06796
\(876\) 15.7368 0.531696
\(877\) 8.48767 0.286608 0.143304 0.989679i \(-0.454227\pi\)
0.143304 + 0.989679i \(0.454227\pi\)
\(878\) 38.9213 1.31353
\(879\) −1.24069 −0.0418475
\(880\) 7.17517 0.241875
\(881\) 34.8625 1.17455 0.587274 0.809388i \(-0.300201\pi\)
0.587274 + 0.809388i \(0.300201\pi\)
\(882\) 33.6079 1.13164
\(883\) −30.4512 −1.02476 −0.512382 0.858758i \(-0.671237\pi\)
−0.512382 + 0.858758i \(0.671237\pi\)
\(884\) 1.24082 0.0417331
\(885\) −0.391770 −0.0131692
\(886\) −47.4801 −1.59512
\(887\) −22.8188 −0.766180 −0.383090 0.923711i \(-0.625140\pi\)
−0.383090 + 0.923711i \(0.625140\pi\)
\(888\) 2.87104 0.0963456
\(889\) −13.3410 −0.447444
\(890\) 95.4546 3.19964
\(891\) −0.272557 −0.00913101
\(892\) 43.6032 1.45994
\(893\) −12.9142 −0.432157
\(894\) −12.1524 −0.406437
\(895\) −28.8916 −0.965738
\(896\) −27.1887 −0.908311
\(897\) 0.532563 0.0177817
\(898\) −40.5667 −1.35373
\(899\) −8.22281 −0.274246
\(900\) −33.8101 −1.12700
\(901\) −12.8718 −0.428822
\(902\) 3.58680 0.119428
\(903\) 14.7471 0.490753
\(904\) 7.97488 0.265241
\(905\) −9.24974 −0.307472
\(906\) −21.7761 −0.723463
\(907\) −51.2352 −1.70124 −0.850619 0.525783i \(-0.823772\pi\)
−0.850619 + 0.525783i \(0.823772\pi\)
\(908\) 56.7004 1.88167
\(909\) 13.9433 0.462468
\(910\) −2.41355 −0.0800086
\(911\) 43.8551 1.45298 0.726492 0.687175i \(-0.241149\pi\)
0.726492 + 0.687175i \(0.241149\pi\)
\(912\) −8.09805 −0.268153
\(913\) −0.676537 −0.0223901
\(914\) −22.5462 −0.745761
\(915\) −20.5034 −0.677821
\(916\) 40.4100 1.33518
\(917\) 14.5526 0.480568
\(918\) 66.0794 2.18094
\(919\) −37.0033 −1.22063 −0.610313 0.792160i \(-0.708956\pi\)
−0.610313 + 0.792160i \(0.708956\pi\)
\(920\) −19.0228 −0.627164
\(921\) −7.59732 −0.250340
\(922\) 35.5771 1.17167
\(923\) 1.09930 0.0361838
\(924\) −6.79769 −0.223628
\(925\) 22.6563 0.744933
\(926\) −73.0920 −2.40195
\(927\) −0.282851 −0.00929006
\(928\) −8.03709 −0.263830
\(929\) −47.8652 −1.57041 −0.785203 0.619239i \(-0.787441\pi\)
−0.785203 + 0.619239i \(0.787441\pi\)
\(930\) 63.2294 2.07337
\(931\) −21.7878 −0.714066
\(932\) −8.09209 −0.265065
\(933\) 2.95090 0.0966082
\(934\) −14.6991 −0.480971
\(935\) 14.7782 0.483298
\(936\) −0.141702 −0.00463169
\(937\) −10.2772 −0.335741 −0.167870 0.985809i \(-0.553689\pi\)
−0.167870 + 0.985809i \(0.553689\pi\)
\(938\) 35.8834 1.17163
\(939\) 23.0673 0.752771
\(940\) 42.0642 1.37198
\(941\) 11.6758 0.380619 0.190309 0.981724i \(-0.439051\pi\)
0.190309 + 0.981724i \(0.439051\pi\)
\(942\) −18.0660 −0.588623
\(943\) 15.1846 0.494479
\(944\) −0.319094 −0.0103856
\(945\) −70.3975 −2.29003
\(946\) 5.21339 0.169502
\(947\) −26.1893 −0.851037 −0.425518 0.904950i \(-0.639908\pi\)
−0.425518 + 0.904950i \(0.639908\pi\)
\(948\) −18.4144 −0.598073
\(949\) 0.520470 0.0168952
\(950\) 40.0200 1.29842
\(951\) −3.30931 −0.107312
\(952\) −21.3227 −0.691072
\(953\) −54.0727 −1.75159 −0.875794 0.482685i \(-0.839662\pi\)
−0.875794 + 0.482685i \(0.839662\pi\)
\(954\) 8.43959 0.273242
\(955\) −31.9022 −1.03233
\(956\) 43.7563 1.41518
\(957\) −0.716281 −0.0231541
\(958\) −62.2028 −2.00968
\(959\) −77.6270 −2.50671
\(960\) 40.0185 1.29159
\(961\) 36.6146 1.18112
\(962\) 0.545168 0.0175769
\(963\) 1.65754 0.0534134
\(964\) −42.9942 −1.38475
\(965\) 17.2171 0.554239
\(966\) −52.5432 −1.69055
\(967\) 27.0777 0.870761 0.435381 0.900247i \(-0.356614\pi\)
0.435381 + 0.900247i \(0.356614\pi\)
\(968\) 9.33862 0.300154
\(969\) −16.6790 −0.535806
\(970\) 74.2540 2.38415
\(971\) −53.2776 −1.70976 −0.854880 0.518825i \(-0.826370\pi\)
−0.854880 + 0.518825i \(0.826370\pi\)
\(972\) −38.2201 −1.22591
\(973\) 3.91864 0.125626
\(974\) 75.5990 2.42235
\(975\) 0.635633 0.0203565
\(976\) −16.6999 −0.534550
\(977\) −55.1915 −1.76573 −0.882866 0.469625i \(-0.844389\pi\)
−0.882866 + 0.469625i \(0.844389\pi\)
\(978\) 11.5618 0.369705
\(979\) 8.89163 0.284178
\(980\) 70.9674 2.26697
\(981\) 2.38855 0.0762606
\(982\) 1.98521 0.0633505
\(983\) −12.5933 −0.401664 −0.200832 0.979626i \(-0.564365\pi\)
−0.200832 + 0.979626i \(0.564365\pi\)
\(984\) 2.29662 0.0732137
\(985\) −36.7877 −1.17215
\(986\) −12.8996 −0.410806
\(987\) 20.2369 0.644146
\(988\) 0.527424 0.0167796
\(989\) 22.0707 0.701809
\(990\) −9.68952 −0.307953
\(991\) 52.1016 1.65506 0.827532 0.561419i \(-0.189744\pi\)
0.827532 + 0.561419i \(0.189744\pi\)
\(992\) 66.0874 2.09828
\(993\) 37.7010 1.19640
\(994\) −108.458 −3.44008
\(995\) −23.5556 −0.746762
\(996\) −2.48705 −0.0788053
\(997\) 20.6417 0.653729 0.326864 0.945071i \(-0.394008\pi\)
0.326864 + 0.945071i \(0.394008\pi\)
\(998\) −37.0670 −1.17333
\(999\) 15.9012 0.503092
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 \(a_p\))