Properties

Label 6023.2.a.b.1.2
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.66510 q^{2}\) \(-2.16013 q^{3}\) \(+5.10274 q^{4}\) \(-2.11668 q^{5}\) \(+5.75694 q^{6}\) \(-1.28803 q^{7}\) \(-8.26911 q^{8}\) \(+1.66614 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.66510 q^{2}\) \(-2.16013 q^{3}\) \(+5.10274 q^{4}\) \(-2.11668 q^{5}\) \(+5.75694 q^{6}\) \(-1.28803 q^{7}\) \(-8.26911 q^{8}\) \(+1.66614 q^{9}\) \(+5.64116 q^{10}\) \(+1.13374 q^{11}\) \(-11.0226 q^{12}\) \(-5.51617 q^{13}\) \(+3.43272 q^{14}\) \(+4.57229 q^{15}\) \(+11.8325 q^{16}\) \(-5.20723 q^{17}\) \(-4.44043 q^{18}\) \(-1.00000 q^{19}\) \(-10.8009 q^{20}\) \(+2.78231 q^{21}\) \(-3.02153 q^{22}\) \(+2.25246 q^{23}\) \(+17.8623 q^{24}\) \(-0.519665 q^{25}\) \(+14.7011 q^{26}\) \(+2.88130 q^{27}\) \(-6.57249 q^{28}\) \(-0.811861 q^{29}\) \(-12.1856 q^{30}\) \(-5.44363 q^{31}\) \(-14.9966 q^{32}\) \(-2.44902 q^{33}\) \(+13.8778 q^{34}\) \(+2.72635 q^{35}\) \(+8.50190 q^{36}\) \(+0.251172 q^{37}\) \(+2.66510 q^{38}\) \(+11.9156 q^{39}\) \(+17.5031 q^{40}\) \(+10.9994 q^{41}\) \(-7.41512 q^{42}\) \(-7.08776 q^{43}\) \(+5.78519 q^{44}\) \(-3.52669 q^{45}\) \(-6.00304 q^{46}\) \(-3.71970 q^{47}\) \(-25.5597 q^{48}\) \(-5.34098 q^{49}\) \(+1.38496 q^{50}\) \(+11.2483 q^{51}\) \(-28.1476 q^{52}\) \(+12.9405 q^{53}\) \(-7.67895 q^{54}\) \(-2.39977 q^{55}\) \(+10.6509 q^{56}\) \(+2.16013 q^{57}\) \(+2.16369 q^{58}\) \(+9.55609 q^{59}\) \(+23.3313 q^{60}\) \(-3.20670 q^{61}\) \(+14.5078 q^{62}\) \(-2.14604 q^{63}\) \(+16.3023 q^{64}\) \(+11.6760 q^{65}\) \(+6.52688 q^{66}\) \(-2.36386 q^{67}\) \(-26.5712 q^{68}\) \(-4.86561 q^{69}\) \(-7.26598 q^{70}\) \(-11.1520 q^{71}\) \(-13.7775 q^{72}\) \(+11.4137 q^{73}\) \(-0.669398 q^{74}\) \(+1.12254 q^{75}\) \(-5.10274 q^{76}\) \(-1.46029 q^{77}\) \(-31.7563 q^{78}\) \(+14.4162 q^{79}\) \(-25.0456 q^{80}\) \(-11.2224 q^{81}\) \(-29.3144 q^{82}\) \(-9.77277 q^{83}\) \(+14.1974 q^{84}\) \(+11.0221 q^{85}\) \(+18.8896 q^{86}\) \(+1.75372 q^{87}\) \(-9.37503 q^{88}\) \(+3.64462 q^{89}\) \(+9.39897 q^{90}\) \(+7.10499 q^{91}\) \(+11.4937 q^{92}\) \(+11.7589 q^{93}\) \(+9.91335 q^{94}\) \(+2.11668 q^{95}\) \(+32.3944 q^{96}\) \(+14.3639 q^{97}\) \(+14.2342 q^{98}\) \(+1.88897 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66510 −1.88451 −0.942254 0.334899i \(-0.891298\pi\)
−0.942254 + 0.334899i \(0.891298\pi\)
\(3\) −2.16013 −1.24715 −0.623575 0.781764i \(-0.714320\pi\)
−0.623575 + 0.781764i \(0.714320\pi\)
\(4\) 5.10274 2.55137
\(5\) −2.11668 −0.946608 −0.473304 0.880899i \(-0.656939\pi\)
−0.473304 + 0.880899i \(0.656939\pi\)
\(6\) 5.75694 2.35026
\(7\) −1.28803 −0.486829 −0.243415 0.969922i \(-0.578268\pi\)
−0.243415 + 0.969922i \(0.578268\pi\)
\(8\) −8.26911 −2.92357
\(9\) 1.66614 0.555381
\(10\) 5.64116 1.78389
\(11\) 1.13374 0.341835 0.170918 0.985285i \(-0.445327\pi\)
0.170918 + 0.985285i \(0.445327\pi\)
\(12\) −11.0226 −3.18194
\(13\) −5.51617 −1.52991 −0.764955 0.644083i \(-0.777239\pi\)
−0.764955 + 0.644083i \(0.777239\pi\)
\(14\) 3.43272 0.917434
\(15\) 4.57229 1.18056
\(16\) 11.8325 2.95813
\(17\) −5.20723 −1.26294 −0.631470 0.775400i \(-0.717548\pi\)
−0.631470 + 0.775400i \(0.717548\pi\)
\(18\) −4.44043 −1.04662
\(19\) −1.00000 −0.229416
\(20\) −10.8009 −2.41515
\(21\) 2.78231 0.607149
\(22\) −3.02153 −0.644192
\(23\) 2.25246 0.469671 0.234836 0.972035i \(-0.424545\pi\)
0.234836 + 0.972035i \(0.424545\pi\)
\(24\) 17.8623 3.64613
\(25\) −0.519665 −0.103933
\(26\) 14.7011 2.88313
\(27\) 2.88130 0.554507
\(28\) −6.57249 −1.24208
\(29\) −0.811861 −0.150759 −0.0753794 0.997155i \(-0.524017\pi\)
−0.0753794 + 0.997155i \(0.524017\pi\)
\(30\) −12.1856 −2.22478
\(31\) −5.44363 −0.977705 −0.488852 0.872366i \(-0.662584\pi\)
−0.488852 + 0.872366i \(0.662584\pi\)
\(32\) −14.9966 −2.65104
\(33\) −2.44902 −0.426320
\(34\) 13.8778 2.38002
\(35\) 2.72635 0.460837
\(36\) 8.50190 1.41698
\(37\) 0.251172 0.0412924 0.0206462 0.999787i \(-0.493428\pi\)
0.0206462 + 0.999787i \(0.493428\pi\)
\(38\) 2.66510 0.432336
\(39\) 11.9156 1.90803
\(40\) 17.5031 2.76748
\(41\) 10.9994 1.71781 0.858906 0.512133i \(-0.171145\pi\)
0.858906 + 0.512133i \(0.171145\pi\)
\(42\) −7.41512 −1.14418
\(43\) −7.08776 −1.08087 −0.540437 0.841385i \(-0.681741\pi\)
−0.540437 + 0.841385i \(0.681741\pi\)
\(44\) 5.78519 0.872149
\(45\) −3.52669 −0.525728
\(46\) −6.00304 −0.885099
\(47\) −3.71970 −0.542573 −0.271287 0.962499i \(-0.587449\pi\)
−0.271287 + 0.962499i \(0.587449\pi\)
\(48\) −25.5597 −3.68923
\(49\) −5.34098 −0.762997
\(50\) 1.38496 0.195863
\(51\) 11.2483 1.57507
\(52\) −28.1476 −3.90337
\(53\) 12.9405 1.77752 0.888759 0.458375i \(-0.151568\pi\)
0.888759 + 0.458375i \(0.151568\pi\)
\(54\) −7.67895 −1.04497
\(55\) −2.39977 −0.323584
\(56\) 10.6509 1.42328
\(57\) 2.16013 0.286116
\(58\) 2.16369 0.284106
\(59\) 9.55609 1.24410 0.622048 0.782979i \(-0.286301\pi\)
0.622048 + 0.782979i \(0.286301\pi\)
\(60\) 23.3313 3.01205
\(61\) −3.20670 −0.410576 −0.205288 0.978702i \(-0.565813\pi\)
−0.205288 + 0.978702i \(0.565813\pi\)
\(62\) 14.5078 1.84249
\(63\) −2.14604 −0.270376
\(64\) 16.3023 2.03778
\(65\) 11.6760 1.44823
\(66\) 6.52688 0.803403
\(67\) −2.36386 −0.288792 −0.144396 0.989520i \(-0.546124\pi\)
−0.144396 + 0.989520i \(0.546124\pi\)
\(68\) −26.5712 −3.22223
\(69\) −4.86561 −0.585750
\(70\) −7.26598 −0.868451
\(71\) −11.1520 −1.32350 −0.661752 0.749723i \(-0.730187\pi\)
−0.661752 + 0.749723i \(0.730187\pi\)
\(72\) −13.7775 −1.62370
\(73\) 11.4137 1.33588 0.667938 0.744217i \(-0.267177\pi\)
0.667938 + 0.744217i \(0.267177\pi\)
\(74\) −0.669398 −0.0778159
\(75\) 1.12254 0.129620
\(76\) −5.10274 −0.585325
\(77\) −1.46029 −0.166416
\(78\) −31.7563 −3.59569
\(79\) 14.4162 1.62195 0.810973 0.585084i \(-0.198938\pi\)
0.810973 + 0.585084i \(0.198938\pi\)
\(80\) −25.0456 −2.80019
\(81\) −11.2224 −1.24693
\(82\) −29.3144 −3.23723
\(83\) −9.77277 −1.07270 −0.536350 0.843996i \(-0.680197\pi\)
−0.536350 + 0.843996i \(0.680197\pi\)
\(84\) 14.1974 1.54906
\(85\) 11.0221 1.19551
\(86\) 18.8896 2.03692
\(87\) 1.75372 0.188019
\(88\) −9.37503 −0.999381
\(89\) 3.64462 0.386329 0.193164 0.981166i \(-0.438125\pi\)
0.193164 + 0.981166i \(0.438125\pi\)
\(90\) 9.39897 0.990739
\(91\) 7.10499 0.744805
\(92\) 11.4937 1.19831
\(93\) 11.7589 1.21934
\(94\) 9.91335 1.02248
\(95\) 2.11668 0.217167
\(96\) 32.3944 3.30624
\(97\) 14.3639 1.45843 0.729216 0.684283i \(-0.239885\pi\)
0.729216 + 0.684283i \(0.239885\pi\)
\(98\) 14.2342 1.43787
\(99\) 1.88897 0.189849
\(100\) −2.65172 −0.265172
\(101\) −3.43360 −0.341656 −0.170828 0.985301i \(-0.554644\pi\)
−0.170828 + 0.985301i \(0.554644\pi\)
\(102\) −29.9778 −2.96824
\(103\) −5.18007 −0.510408 −0.255204 0.966887i \(-0.582143\pi\)
−0.255204 + 0.966887i \(0.582143\pi\)
\(104\) 45.6138 4.47281
\(105\) −5.88925 −0.574732
\(106\) −34.4878 −3.34975
\(107\) −11.9883 −1.15895 −0.579476 0.814989i \(-0.696743\pi\)
−0.579476 + 0.814989i \(0.696743\pi\)
\(108\) 14.7025 1.41475
\(109\) −6.14742 −0.588816 −0.294408 0.955680i \(-0.595122\pi\)
−0.294408 + 0.955680i \(0.595122\pi\)
\(110\) 6.39561 0.609797
\(111\) −0.542563 −0.0514978
\(112\) −15.2406 −1.44010
\(113\) −3.09976 −0.291601 −0.145800 0.989314i \(-0.546576\pi\)
−0.145800 + 0.989314i \(0.546576\pi\)
\(114\) −5.75694 −0.539187
\(115\) −4.76775 −0.444595
\(116\) −4.14272 −0.384642
\(117\) −9.19072 −0.849683
\(118\) −25.4679 −2.34451
\(119\) 6.70707 0.614836
\(120\) −37.8088 −3.45146
\(121\) −9.71463 −0.883149
\(122\) 8.54616 0.773733
\(123\) −23.7600 −2.14237
\(124\) −27.7775 −2.49449
\(125\) 11.6834 1.04499
\(126\) 5.71941 0.509525
\(127\) −9.51038 −0.843910 −0.421955 0.906617i \(-0.638656\pi\)
−0.421955 + 0.906617i \(0.638656\pi\)
\(128\) −13.4540 −1.18918
\(129\) 15.3105 1.34801
\(130\) −31.1176 −2.72919
\(131\) 19.9467 1.74275 0.871375 0.490618i \(-0.163229\pi\)
0.871375 + 0.490618i \(0.163229\pi\)
\(132\) −12.4967 −1.08770
\(133\) 1.28803 0.111686
\(134\) 6.29993 0.544231
\(135\) −6.09879 −0.524900
\(136\) 43.0592 3.69230
\(137\) 1.35425 0.115701 0.0578505 0.998325i \(-0.481575\pi\)
0.0578505 + 0.998325i \(0.481575\pi\)
\(138\) 12.9673 1.10385
\(139\) 20.4970 1.73854 0.869268 0.494341i \(-0.164591\pi\)
0.869268 + 0.494341i \(0.164591\pi\)
\(140\) 13.9118 1.17577
\(141\) 8.03501 0.676670
\(142\) 29.7213 2.49415
\(143\) −6.25390 −0.522978
\(144\) 19.7146 1.64289
\(145\) 1.71845 0.142710
\(146\) −30.4187 −2.51747
\(147\) 11.5372 0.951571
\(148\) 1.28167 0.105352
\(149\) 4.60765 0.377474 0.188737 0.982028i \(-0.439561\pi\)
0.188737 + 0.982028i \(0.439561\pi\)
\(150\) −2.99168 −0.244270
\(151\) 8.41519 0.684818 0.342409 0.939551i \(-0.388757\pi\)
0.342409 + 0.939551i \(0.388757\pi\)
\(152\) 8.26911 0.670714
\(153\) −8.67599 −0.701413
\(154\) 3.89182 0.313612
\(155\) 11.5224 0.925503
\(156\) 60.8024 4.86809
\(157\) −13.6514 −1.08950 −0.544749 0.838599i \(-0.683375\pi\)
−0.544749 + 0.838599i \(0.683375\pi\)
\(158\) −38.4205 −3.05657
\(159\) −27.9532 −2.21683
\(160\) 31.7429 2.50950
\(161\) −2.90124 −0.228650
\(162\) 29.9088 2.34986
\(163\) −19.9915 −1.56586 −0.782929 0.622111i \(-0.786275\pi\)
−0.782929 + 0.622111i \(0.786275\pi\)
\(164\) 56.1269 4.38278
\(165\) 5.18379 0.403558
\(166\) 26.0454 2.02151
\(167\) 17.2844 1.33751 0.668755 0.743483i \(-0.266828\pi\)
0.668755 + 0.743483i \(0.266828\pi\)
\(168\) −23.0072 −1.77504
\(169\) 17.4281 1.34063
\(170\) −29.3748 −2.25295
\(171\) −1.66614 −0.127413
\(172\) −36.1670 −2.75771
\(173\) 11.7380 0.892423 0.446212 0.894928i \(-0.352773\pi\)
0.446212 + 0.894928i \(0.352773\pi\)
\(174\) −4.67384 −0.354323
\(175\) 0.669344 0.0505976
\(176\) 13.4150 1.01119
\(177\) −20.6424 −1.55157
\(178\) −9.71326 −0.728040
\(179\) 9.77774 0.730822 0.365411 0.930846i \(-0.380928\pi\)
0.365411 + 0.930846i \(0.380928\pi\)
\(180\) −17.9958 −1.34133
\(181\) 22.6480 1.68341 0.841705 0.539937i \(-0.181552\pi\)
0.841705 + 0.539937i \(0.181552\pi\)
\(182\) −18.9355 −1.40359
\(183\) 6.92687 0.512049
\(184\) −18.6259 −1.37312
\(185\) −0.531651 −0.0390877
\(186\) −31.3387 −2.29786
\(187\) −5.90365 −0.431718
\(188\) −18.9807 −1.38431
\(189\) −3.71120 −0.269950
\(190\) −5.64116 −0.409253
\(191\) 2.65359 0.192007 0.0960035 0.995381i \(-0.469394\pi\)
0.0960035 + 0.995381i \(0.469394\pi\)
\(192\) −35.2149 −2.54142
\(193\) −14.6977 −1.05797 −0.528983 0.848633i \(-0.677426\pi\)
−0.528983 + 0.848633i \(0.677426\pi\)
\(194\) −38.2812 −2.74843
\(195\) −25.2216 −1.80615
\(196\) −27.2537 −1.94669
\(197\) 3.30679 0.235599 0.117800 0.993037i \(-0.462416\pi\)
0.117800 + 0.993037i \(0.462416\pi\)
\(198\) −5.03429 −0.357772
\(199\) −14.4777 −1.02630 −0.513148 0.858300i \(-0.671521\pi\)
−0.513148 + 0.858300i \(0.671521\pi\)
\(200\) 4.29717 0.303856
\(201\) 5.10624 0.360167
\(202\) 9.15088 0.643854
\(203\) 1.04570 0.0733938
\(204\) 57.3971 4.01860
\(205\) −23.2821 −1.62609
\(206\) 13.8054 0.961868
\(207\) 3.75293 0.260846
\(208\) −65.2701 −4.52567
\(209\) −1.13374 −0.0784224
\(210\) 15.6954 1.08309
\(211\) −9.02851 −0.621549 −0.310774 0.950484i \(-0.600588\pi\)
−0.310774 + 0.950484i \(0.600588\pi\)
\(212\) 66.0322 4.53511
\(213\) 24.0898 1.65061
\(214\) 31.9500 2.18406
\(215\) 15.0025 1.02316
\(216\) −23.8258 −1.62114
\(217\) 7.01156 0.475976
\(218\) 16.3835 1.10963
\(219\) −24.6551 −1.66604
\(220\) −12.2454 −0.825584
\(221\) 28.7240 1.93219
\(222\) 1.44598 0.0970480
\(223\) 22.6655 1.51779 0.758897 0.651211i \(-0.225739\pi\)
0.758897 + 0.651211i \(0.225739\pi\)
\(224\) 19.3160 1.29061
\(225\) −0.865835 −0.0577224
\(226\) 8.26116 0.549524
\(227\) 9.38550 0.622937 0.311469 0.950256i \(-0.399179\pi\)
0.311469 + 0.950256i \(0.399179\pi\)
\(228\) 11.0226 0.729987
\(229\) −18.6712 −1.23383 −0.616913 0.787031i \(-0.711617\pi\)
−0.616913 + 0.787031i \(0.711617\pi\)
\(230\) 12.7065 0.837842
\(231\) 3.15441 0.207545
\(232\) 6.71337 0.440754
\(233\) 9.72636 0.637195 0.318598 0.947890i \(-0.396788\pi\)
0.318598 + 0.947890i \(0.396788\pi\)
\(234\) 24.4942 1.60123
\(235\) 7.87341 0.513604
\(236\) 48.7623 3.17415
\(237\) −31.1407 −2.02281
\(238\) −17.8750 −1.15866
\(239\) −8.34790 −0.539981 −0.269990 0.962863i \(-0.587021\pi\)
−0.269990 + 0.962863i \(0.587021\pi\)
\(240\) 54.1017 3.49225
\(241\) 10.2528 0.660441 0.330220 0.943904i \(-0.392877\pi\)
0.330220 + 0.943904i \(0.392877\pi\)
\(242\) 25.8904 1.66430
\(243\) 15.5979 1.00060
\(244\) −16.3630 −1.04753
\(245\) 11.3051 0.722259
\(246\) 63.3227 4.03731
\(247\) 5.51617 0.350986
\(248\) 45.0140 2.85839
\(249\) 21.1104 1.33782
\(250\) −31.1373 −1.96930
\(251\) 10.1227 0.638938 0.319469 0.947597i \(-0.396496\pi\)
0.319469 + 0.947597i \(0.396496\pi\)
\(252\) −10.9507 −0.689829
\(253\) 2.55371 0.160550
\(254\) 25.3461 1.59036
\(255\) −23.8090 −1.49098
\(256\) 3.25173 0.203233
\(257\) 7.38387 0.460593 0.230297 0.973120i \(-0.426030\pi\)
0.230297 + 0.973120i \(0.426030\pi\)
\(258\) −40.8039 −2.54034
\(259\) −0.323517 −0.0201024
\(260\) 59.5795 3.69496
\(261\) −1.35268 −0.0837285
\(262\) −53.1599 −3.28423
\(263\) 14.9247 0.920297 0.460149 0.887842i \(-0.347796\pi\)
0.460149 + 0.887842i \(0.347796\pi\)
\(264\) 20.2512 1.24638
\(265\) −27.3909 −1.68261
\(266\) −3.43272 −0.210474
\(267\) −7.87283 −0.481810
\(268\) −12.0622 −0.736816
\(269\) −1.33679 −0.0815058 −0.0407529 0.999169i \(-0.512976\pi\)
−0.0407529 + 0.999169i \(0.512976\pi\)
\(270\) 16.2539 0.989179
\(271\) −3.95979 −0.240540 −0.120270 0.992741i \(-0.538376\pi\)
−0.120270 + 0.992741i \(0.538376\pi\)
\(272\) −61.6146 −3.73594
\(273\) −15.3477 −0.928883
\(274\) −3.60920 −0.218040
\(275\) −0.589165 −0.0355280
\(276\) −24.8279 −1.49447
\(277\) 24.8188 1.49122 0.745609 0.666384i \(-0.232159\pi\)
0.745609 + 0.666384i \(0.232159\pi\)
\(278\) −54.6266 −3.27629
\(279\) −9.06986 −0.542998
\(280\) −22.5445 −1.34729
\(281\) −7.29784 −0.435353 −0.217676 0.976021i \(-0.569848\pi\)
−0.217676 + 0.976021i \(0.569848\pi\)
\(282\) −21.4141 −1.27519
\(283\) 10.0871 0.599615 0.299808 0.954000i \(-0.403078\pi\)
0.299808 + 0.954000i \(0.403078\pi\)
\(284\) −56.9060 −3.37675
\(285\) −4.57229 −0.270839
\(286\) 16.6673 0.985556
\(287\) −14.1675 −0.836281
\(288\) −24.9864 −1.47234
\(289\) 10.1153 0.595017
\(290\) −4.57984 −0.268937
\(291\) −31.0278 −1.81888
\(292\) 58.2414 3.40832
\(293\) 25.0879 1.46565 0.732825 0.680418i \(-0.238202\pi\)
0.732825 + 0.680418i \(0.238202\pi\)
\(294\) −30.7477 −1.79324
\(295\) −20.2272 −1.17767
\(296\) −2.07697 −0.120721
\(297\) 3.26665 0.189550
\(298\) −12.2798 −0.711352
\(299\) −12.4250 −0.718555
\(300\) 5.72804 0.330709
\(301\) 9.12925 0.526201
\(302\) −22.4273 −1.29055
\(303\) 7.41701 0.426096
\(304\) −11.8325 −0.678641
\(305\) 6.78755 0.388654
\(306\) 23.1224 1.32182
\(307\) −10.6235 −0.606318 −0.303159 0.952940i \(-0.598041\pi\)
−0.303159 + 0.952940i \(0.598041\pi\)
\(308\) −7.45149 −0.424588
\(309\) 11.1896 0.636555
\(310\) −30.7084 −1.74412
\(311\) 32.0432 1.81700 0.908502 0.417880i \(-0.137227\pi\)
0.908502 + 0.417880i \(0.137227\pi\)
\(312\) −98.5316 −5.57826
\(313\) 5.68624 0.321405 0.160703 0.987003i \(-0.448624\pi\)
0.160703 + 0.987003i \(0.448624\pi\)
\(314\) 36.3823 2.05317
\(315\) 4.54248 0.255940
\(316\) 73.5620 4.13819
\(317\) −1.00000 −0.0561656
\(318\) 74.4979 4.17763
\(319\) −0.920439 −0.0515347
\(320\) −34.5067 −1.92898
\(321\) 25.8962 1.44539
\(322\) 7.73209 0.430892
\(323\) 5.20723 0.289738
\(324\) −57.2650 −3.18139
\(325\) 2.86656 0.159008
\(326\) 53.2794 2.95087
\(327\) 13.2792 0.734341
\(328\) −90.9550 −5.02215
\(329\) 4.79108 0.264141
\(330\) −13.8153 −0.760508
\(331\) −13.2602 −0.728848 −0.364424 0.931233i \(-0.618734\pi\)
−0.364424 + 0.931233i \(0.618734\pi\)
\(332\) −49.8679 −2.73686
\(333\) 0.418488 0.0229330
\(334\) −46.0647 −2.52055
\(335\) 5.00354 0.273373
\(336\) 32.9217 1.79602
\(337\) 22.8459 1.24449 0.622247 0.782821i \(-0.286220\pi\)
0.622247 + 0.782821i \(0.286220\pi\)
\(338\) −46.4477 −2.52642
\(339\) 6.69587 0.363670
\(340\) 56.2427 3.05019
\(341\) −6.17166 −0.334214
\(342\) 4.44043 0.240111
\(343\) 15.8955 0.858279
\(344\) 58.6095 3.16001
\(345\) 10.2989 0.554476
\(346\) −31.2829 −1.68178
\(347\) −4.62374 −0.248216 −0.124108 0.992269i \(-0.539607\pi\)
−0.124108 + 0.992269i \(0.539607\pi\)
\(348\) 8.94879 0.479706
\(349\) 0.205524 0.0110015 0.00550074 0.999985i \(-0.498249\pi\)
0.00550074 + 0.999985i \(0.498249\pi\)
\(350\) −1.78387 −0.0953516
\(351\) −15.8937 −0.848345
\(352\) −17.0022 −0.906220
\(353\) −34.2168 −1.82118 −0.910588 0.413315i \(-0.864371\pi\)
−0.910588 + 0.413315i \(0.864371\pi\)
\(354\) 55.0139 2.92395
\(355\) 23.6053 1.25284
\(356\) 18.5976 0.985669
\(357\) −14.4881 −0.766793
\(358\) −26.0586 −1.37724
\(359\) 32.1419 1.69638 0.848191 0.529690i \(-0.177692\pi\)
0.848191 + 0.529690i \(0.177692\pi\)
\(360\) 29.1626 1.53700
\(361\) 1.00000 0.0526316
\(362\) −60.3591 −3.17240
\(363\) 20.9848 1.10142
\(364\) 36.2550 1.90028
\(365\) −24.1592 −1.26455
\(366\) −18.4608 −0.964960
\(367\) −13.5515 −0.707384 −0.353692 0.935362i \(-0.615074\pi\)
−0.353692 + 0.935362i \(0.615074\pi\)
\(368\) 26.6523 1.38935
\(369\) 18.3265 0.954040
\(370\) 1.41690 0.0736612
\(371\) −16.6678 −0.865348
\(372\) 60.0028 3.11100
\(373\) 20.5316 1.06309 0.531543 0.847031i \(-0.321612\pi\)
0.531543 + 0.847031i \(0.321612\pi\)
\(374\) 15.7338 0.813576
\(375\) −25.2375 −1.30326
\(376\) 30.7586 1.58625
\(377\) 4.47836 0.230647
\(378\) 9.89071 0.508723
\(379\) 20.7868 1.06775 0.533873 0.845565i \(-0.320736\pi\)
0.533873 + 0.845565i \(0.320736\pi\)
\(380\) 10.8009 0.554073
\(381\) 20.5436 1.05248
\(382\) −7.07208 −0.361839
\(383\) −25.6335 −1.30981 −0.654906 0.755710i \(-0.727292\pi\)
−0.654906 + 0.755710i \(0.727292\pi\)
\(384\) 29.0624 1.48308
\(385\) 3.09097 0.157530
\(386\) 39.1709 1.99374
\(387\) −11.8092 −0.600296
\(388\) 73.2953 3.72100
\(389\) 25.1849 1.27692 0.638462 0.769653i \(-0.279571\pi\)
0.638462 + 0.769653i \(0.279571\pi\)
\(390\) 67.2179 3.40371
\(391\) −11.7291 −0.593167
\(392\) 44.1652 2.23068
\(393\) −43.0873 −2.17347
\(394\) −8.81292 −0.443989
\(395\) −30.5144 −1.53535
\(396\) 9.63894 0.484375
\(397\) 25.1340 1.26144 0.630719 0.776011i \(-0.282760\pi\)
0.630719 + 0.776011i \(0.282760\pi\)
\(398\) 38.5844 1.93406
\(399\) −2.78231 −0.139290
\(400\) −6.14894 −0.307447
\(401\) −14.4617 −0.722181 −0.361090 0.932531i \(-0.617595\pi\)
−0.361090 + 0.932531i \(0.617595\pi\)
\(402\) −13.6086 −0.678737
\(403\) 30.0280 1.49580
\(404\) −17.5208 −0.871692
\(405\) 23.7542 1.18036
\(406\) −2.78690 −0.138311
\(407\) 0.284764 0.0141152
\(408\) −93.0133 −4.60485
\(409\) −29.7013 −1.46864 −0.734318 0.678806i \(-0.762498\pi\)
−0.734318 + 0.678806i \(0.762498\pi\)
\(410\) 62.0492 3.06439
\(411\) −2.92534 −0.144296
\(412\) −26.4326 −1.30224
\(413\) −12.3085 −0.605663
\(414\) −10.0019 −0.491567
\(415\) 20.6858 1.01543
\(416\) 82.7236 4.05586
\(417\) −44.2762 −2.16821
\(418\) 3.02153 0.147788
\(419\) 9.91093 0.484180 0.242090 0.970254i \(-0.422167\pi\)
0.242090 + 0.970254i \(0.422167\pi\)
\(420\) −30.0513 −1.46636
\(421\) −26.8130 −1.30678 −0.653392 0.757020i \(-0.726655\pi\)
−0.653392 + 0.757020i \(0.726655\pi\)
\(422\) 24.0619 1.17131
\(423\) −6.19754 −0.301335
\(424\) −107.007 −5.19670
\(425\) 2.70602 0.131261
\(426\) −64.2017 −3.11058
\(427\) 4.13032 0.199880
\(428\) −61.1732 −2.95692
\(429\) 13.5092 0.652231
\(430\) −39.9832 −1.92816
\(431\) −6.02751 −0.290335 −0.145168 0.989407i \(-0.546372\pi\)
−0.145168 + 0.989407i \(0.546372\pi\)
\(432\) 34.0930 1.64030
\(433\) 1.48776 0.0714972 0.0357486 0.999361i \(-0.488618\pi\)
0.0357486 + 0.999361i \(0.488618\pi\)
\(434\) −18.6865 −0.896980
\(435\) −3.71207 −0.177980
\(436\) −31.3687 −1.50229
\(437\) −2.25246 −0.107750
\(438\) 65.7082 3.13966
\(439\) −8.68655 −0.414586 −0.207293 0.978279i \(-0.566465\pi\)
−0.207293 + 0.978279i \(0.566465\pi\)
\(440\) 19.8439 0.946022
\(441\) −8.89883 −0.423754
\(442\) −76.5522 −3.64122
\(443\) −15.0969 −0.717274 −0.358637 0.933477i \(-0.616758\pi\)
−0.358637 + 0.933477i \(0.616758\pi\)
\(444\) −2.76856 −0.131390
\(445\) −7.71449 −0.365702
\(446\) −60.4058 −2.86030
\(447\) −9.95311 −0.470766
\(448\) −20.9978 −0.992053
\(449\) −3.49420 −0.164901 −0.0824507 0.996595i \(-0.526275\pi\)
−0.0824507 + 0.996595i \(0.526275\pi\)
\(450\) 2.30754 0.108778
\(451\) 12.4704 0.587209
\(452\) −15.8173 −0.743982
\(453\) −18.1779 −0.854070
\(454\) −25.0133 −1.17393
\(455\) −15.0390 −0.705039
\(456\) −17.8623 −0.836480
\(457\) 0.171259 0.00801114 0.00400557 0.999992i \(-0.498725\pi\)
0.00400557 + 0.999992i \(0.498725\pi\)
\(458\) 49.7605 2.32516
\(459\) −15.0036 −0.700308
\(460\) −24.3286 −1.13433
\(461\) −1.56470 −0.0728753 −0.0364377 0.999336i \(-0.511601\pi\)
−0.0364377 + 0.999336i \(0.511601\pi\)
\(462\) −8.40681 −0.391120
\(463\) −21.2788 −0.988909 −0.494454 0.869204i \(-0.664632\pi\)
−0.494454 + 0.869204i \(0.664632\pi\)
\(464\) −9.60635 −0.445964
\(465\) −24.8899 −1.15424
\(466\) −25.9217 −1.20080
\(467\) −14.9933 −0.693808 −0.346904 0.937901i \(-0.612767\pi\)
−0.346904 + 0.937901i \(0.612767\pi\)
\(468\) −46.8979 −2.16786
\(469\) 3.04473 0.140592
\(470\) −20.9834 −0.967892
\(471\) 29.4887 1.35877
\(472\) −79.0204 −3.63721
\(473\) −8.03568 −0.369481
\(474\) 82.9931 3.81200
\(475\) 0.519665 0.0238439
\(476\) 34.2245 1.56868
\(477\) 21.5608 0.987199
\(478\) 22.2480 1.01760
\(479\) 15.9817 0.730224 0.365112 0.930964i \(-0.381031\pi\)
0.365112 + 0.930964i \(0.381031\pi\)
\(480\) −68.5687 −3.12972
\(481\) −1.38551 −0.0631737
\(482\) −27.3247 −1.24461
\(483\) 6.26704 0.285160
\(484\) −49.5713 −2.25324
\(485\) −30.4038 −1.38056
\(486\) −41.5699 −1.88565
\(487\) 36.8545 1.67004 0.835019 0.550221i \(-0.185456\pi\)
0.835019 + 0.550221i \(0.185456\pi\)
\(488\) 26.5165 1.20035
\(489\) 43.1842 1.95286
\(490\) −30.1293 −1.36110
\(491\) 21.3811 0.964914 0.482457 0.875920i \(-0.339744\pi\)
0.482457 + 0.875920i \(0.339744\pi\)
\(492\) −121.241 −5.46598
\(493\) 4.22755 0.190399
\(494\) −14.7011 −0.661435
\(495\) −3.99835 −0.179712
\(496\) −64.4118 −2.89218
\(497\) 14.3642 0.644321
\(498\) −56.2613 −2.52113
\(499\) 6.61563 0.296156 0.148078 0.988976i \(-0.452691\pi\)
0.148078 + 0.988976i \(0.452691\pi\)
\(500\) 59.6172 2.66616
\(501\) −37.3366 −1.66807
\(502\) −26.9779 −1.20408
\(503\) −12.9262 −0.576349 −0.288175 0.957578i \(-0.593048\pi\)
−0.288175 + 0.957578i \(0.593048\pi\)
\(504\) 17.7459 0.790463
\(505\) 7.26783 0.323414
\(506\) −6.80588 −0.302558
\(507\) −37.6470 −1.67196
\(508\) −48.5291 −2.15313
\(509\) −40.3289 −1.78755 −0.893773 0.448519i \(-0.851952\pi\)
−0.893773 + 0.448519i \(0.851952\pi\)
\(510\) 63.4533 2.80976
\(511\) −14.7012 −0.650344
\(512\) 18.2419 0.806184
\(513\) −2.88130 −0.127213
\(514\) −19.6787 −0.867992
\(515\) 10.9646 0.483156
\(516\) 78.1253 3.43928
\(517\) −4.21717 −0.185471
\(518\) 0.862204 0.0378831
\(519\) −25.3555 −1.11298
\(520\) −96.5499 −4.23399
\(521\) 30.9177 1.35453 0.677264 0.735740i \(-0.263165\pi\)
0.677264 + 0.735740i \(0.263165\pi\)
\(522\) 3.60501 0.157787
\(523\) −2.19294 −0.0958908 −0.0479454 0.998850i \(-0.515267\pi\)
−0.0479454 + 0.998850i \(0.515267\pi\)
\(524\) 101.783 4.44640
\(525\) −1.44587 −0.0631028
\(526\) −39.7758 −1.73431
\(527\) 28.3463 1.23478
\(528\) −28.9781 −1.26111
\(529\) −17.9264 −0.779409
\(530\) 72.9995 3.17090
\(531\) 15.9218 0.690947
\(532\) 6.57249 0.284953
\(533\) −60.6744 −2.62810
\(534\) 20.9819 0.907974
\(535\) 25.3754 1.09707
\(536\) 19.5471 0.844304
\(537\) −21.1211 −0.911445
\(538\) 3.56269 0.153598
\(539\) −6.05528 −0.260819
\(540\) −31.1206 −1.33922
\(541\) −7.03350 −0.302394 −0.151197 0.988504i \(-0.548313\pi\)
−0.151197 + 0.988504i \(0.548313\pi\)
\(542\) 10.5532 0.453300
\(543\) −48.9225 −2.09946
\(544\) 78.0906 3.34811
\(545\) 13.0121 0.557378
\(546\) 40.9030 1.75049
\(547\) −46.2931 −1.97935 −0.989675 0.143329i \(-0.954219\pi\)
−0.989675 + 0.143329i \(0.954219\pi\)
\(548\) 6.91037 0.295196
\(549\) −5.34281 −0.228026
\(550\) 1.57018 0.0669528
\(551\) 0.811861 0.0345864
\(552\) 40.2342 1.71248
\(553\) −18.5685 −0.789611
\(554\) −66.1445 −2.81021
\(555\) 1.14843 0.0487482
\(556\) 104.591 4.43565
\(557\) 5.11845 0.216876 0.108438 0.994103i \(-0.465415\pi\)
0.108438 + 0.994103i \(0.465415\pi\)
\(558\) 24.1721 1.02329
\(559\) 39.0973 1.65364
\(560\) 32.2595 1.36321
\(561\) 12.7526 0.538416
\(562\) 19.4495 0.820426
\(563\) 24.0977 1.01560 0.507799 0.861475i \(-0.330459\pi\)
0.507799 + 0.861475i \(0.330459\pi\)
\(564\) 41.0006 1.72644
\(565\) 6.56120 0.276032
\(566\) −26.8831 −1.12998
\(567\) 14.4548 0.607044
\(568\) 92.2175 3.86936
\(569\) −25.8258 −1.08267 −0.541337 0.840806i \(-0.682082\pi\)
−0.541337 + 0.840806i \(0.682082\pi\)
\(570\) 12.1856 0.510399
\(571\) −3.41890 −0.143076 −0.0715382 0.997438i \(-0.522791\pi\)
−0.0715382 + 0.997438i \(0.522791\pi\)
\(572\) −31.9121 −1.33431
\(573\) −5.73209 −0.239461
\(574\) 37.7578 1.57598
\(575\) −1.17053 −0.0488143
\(576\) 27.1619 1.13175
\(577\) 8.84613 0.368269 0.184135 0.982901i \(-0.441052\pi\)
0.184135 + 0.982901i \(0.441052\pi\)
\(578\) −26.9582 −1.12132
\(579\) 31.7489 1.31944
\(580\) 8.76881 0.364105
\(581\) 12.5876 0.522222
\(582\) 82.6921 3.42770
\(583\) 14.6712 0.607619
\(584\) −94.3815 −3.90553
\(585\) 19.4538 0.804317
\(586\) −66.8616 −2.76203
\(587\) −31.5012 −1.30019 −0.650097 0.759852i \(-0.725272\pi\)
−0.650097 + 0.759852i \(0.725272\pi\)
\(588\) 58.8713 2.42781
\(589\) 5.44363 0.224301
\(590\) 53.9074 2.21933
\(591\) −7.14309 −0.293827
\(592\) 2.97199 0.122148
\(593\) −40.5085 −1.66349 −0.831743 0.555161i \(-0.812656\pi\)
−0.831743 + 0.555161i \(0.812656\pi\)
\(594\) −8.70593 −0.357209
\(595\) −14.1967 −0.582009
\(596\) 23.5117 0.963076
\(597\) 31.2736 1.27994
\(598\) 33.1138 1.35412
\(599\) −38.8679 −1.58810 −0.794050 0.607853i \(-0.792031\pi\)
−0.794050 + 0.607853i \(0.792031\pi\)
\(600\) −9.28242 −0.378953
\(601\) 0.147424 0.00601355 0.00300678 0.999995i \(-0.499043\pi\)
0.00300678 + 0.999995i \(0.499043\pi\)
\(602\) −24.3303 −0.991630
\(603\) −3.93853 −0.160389
\(604\) 42.9405 1.74723
\(605\) 20.5628 0.835996
\(606\) −19.7670 −0.802982
\(607\) 13.2080 0.536095 0.268048 0.963406i \(-0.413622\pi\)
0.268048 + 0.963406i \(0.413622\pi\)
\(608\) 14.9966 0.608191
\(609\) −2.25885 −0.0915330
\(610\) −18.0895 −0.732422
\(611\) 20.5185 0.830089
\(612\) −44.2714 −1.78956
\(613\) 37.9037 1.53091 0.765457 0.643487i \(-0.222513\pi\)
0.765457 + 0.643487i \(0.222513\pi\)
\(614\) 28.3128 1.14261
\(615\) 50.2923 2.02798
\(616\) 12.0753 0.486528
\(617\) −21.9074 −0.881957 −0.440979 0.897518i \(-0.645369\pi\)
−0.440979 + 0.897518i \(0.645369\pi\)
\(618\) −29.8214 −1.19959
\(619\) −20.2383 −0.813447 −0.406724 0.913551i \(-0.633329\pi\)
−0.406724 + 0.913551i \(0.633329\pi\)
\(620\) 58.7960 2.36130
\(621\) 6.49003 0.260436
\(622\) −85.3983 −3.42416
\(623\) −4.69438 −0.188076
\(624\) 140.992 5.64418
\(625\) −22.1316 −0.885265
\(626\) −15.1544 −0.605691
\(627\) 2.44902 0.0978045
\(628\) −69.6595 −2.77972
\(629\) −1.30791 −0.0521499
\(630\) −12.1062 −0.482321
\(631\) −38.8755 −1.54761 −0.773804 0.633425i \(-0.781649\pi\)
−0.773804 + 0.633425i \(0.781649\pi\)
\(632\) −119.209 −4.74188
\(633\) 19.5027 0.775164
\(634\) 2.66510 0.105845
\(635\) 20.1304 0.798852
\(636\) −142.638 −5.65596
\(637\) 29.4618 1.16732
\(638\) 2.45306 0.0971176
\(639\) −18.5809 −0.735049
\(640\) 28.4778 1.12569
\(641\) −20.2943 −0.801578 −0.400789 0.916170i \(-0.631264\pi\)
−0.400789 + 0.916170i \(0.631264\pi\)
\(642\) −69.0160 −2.72384
\(643\) 13.2161 0.521194 0.260597 0.965448i \(-0.416081\pi\)
0.260597 + 0.965448i \(0.416081\pi\)
\(644\) −14.8043 −0.583371
\(645\) −32.4073 −1.27604
\(646\) −13.8778 −0.546014
\(647\) −20.4200 −0.802794 −0.401397 0.915904i \(-0.631475\pi\)
−0.401397 + 0.915904i \(0.631475\pi\)
\(648\) 92.7993 3.64550
\(649\) 10.8341 0.425276
\(650\) −7.63966 −0.299652
\(651\) −15.1458 −0.593612
\(652\) −102.012 −3.99509
\(653\) −42.6650 −1.66961 −0.834806 0.550544i \(-0.814420\pi\)
−0.834806 + 0.550544i \(0.814420\pi\)
\(654\) −35.3904 −1.38387
\(655\) −42.2208 −1.64970
\(656\) 130.150 5.08151
\(657\) 19.0169 0.741920
\(658\) −12.7687 −0.497775
\(659\) −35.3479 −1.37696 −0.688480 0.725255i \(-0.741722\pi\)
−0.688480 + 0.725255i \(0.741722\pi\)
\(660\) 26.4516 1.02963
\(661\) 41.5329 1.61544 0.807721 0.589564i \(-0.200701\pi\)
0.807721 + 0.589564i \(0.200701\pi\)
\(662\) 35.3398 1.37352
\(663\) −62.0474 −2.40972
\(664\) 80.8121 3.13612
\(665\) −2.72635 −0.105723
\(666\) −1.11531 −0.0432175
\(667\) −1.82869 −0.0708071
\(668\) 88.1981 3.41249
\(669\) −48.9603 −1.89292
\(670\) −13.3349 −0.515173
\(671\) −3.63556 −0.140349
\(672\) −41.7250 −1.60958
\(673\) −42.0973 −1.62273 −0.811367 0.584538i \(-0.801276\pi\)
−0.811367 + 0.584538i \(0.801276\pi\)
\(674\) −60.8864 −2.34526
\(675\) −1.49731 −0.0576315
\(676\) 88.9313 3.42044
\(677\) 7.26154 0.279084 0.139542 0.990216i \(-0.455437\pi\)
0.139542 + 0.990216i \(0.455437\pi\)
\(678\) −17.8451 −0.685338
\(679\) −18.5011 −0.710008
\(680\) −91.1426 −3.49516
\(681\) −20.2738 −0.776896
\(682\) 16.4481 0.629830
\(683\) −27.1348 −1.03828 −0.519142 0.854688i \(-0.673748\pi\)
−0.519142 + 0.854688i \(0.673748\pi\)
\(684\) −8.50190 −0.325078
\(685\) −2.86651 −0.109524
\(686\) −42.3632 −1.61743
\(687\) 40.3321 1.53877
\(688\) −83.8660 −3.19736
\(689\) −71.3821 −2.71944
\(690\) −27.4477 −1.04491
\(691\) 38.8184 1.47672 0.738360 0.674407i \(-0.235600\pi\)
0.738360 + 0.674407i \(0.235600\pi\)
\(692\) 59.8960 2.27690
\(693\) −2.43305 −0.0924240
\(694\) 12.3227 0.467764
\(695\) −43.3857 −1.64571
\(696\) −14.5017 −0.549686
\(697\) −57.2763 −2.16949
\(698\) −0.547743 −0.0207324
\(699\) −21.0102 −0.794677
\(700\) 3.41549 0.129093
\(701\) −33.3425 −1.25933 −0.629665 0.776867i \(-0.716808\pi\)
−0.629665 + 0.776867i \(0.716808\pi\)
\(702\) 42.3584 1.59871
\(703\) −0.251172 −0.00947313
\(704\) 18.4825 0.696587
\(705\) −17.0075 −0.640541
\(706\) 91.1911 3.43202
\(707\) 4.42258 0.166328
\(708\) −105.333 −3.95864
\(709\) −7.67433 −0.288216 −0.144108 0.989562i \(-0.546031\pi\)
−0.144108 + 0.989562i \(0.546031\pi\)
\(710\) −62.9105 −2.36099
\(711\) 24.0194 0.900797
\(712\) −30.1378 −1.12946
\(713\) −12.2616 −0.459200
\(714\) 38.6122 1.44503
\(715\) 13.2375 0.495055
\(716\) 49.8933 1.86460
\(717\) 18.0325 0.673436
\(718\) −85.6612 −3.19685
\(719\) 0.832825 0.0310592 0.0155296 0.999879i \(-0.495057\pi\)
0.0155296 + 0.999879i \(0.495057\pi\)
\(720\) −41.7296 −1.55517
\(721\) 6.67209 0.248482
\(722\) −2.66510 −0.0991847
\(723\) −22.1473 −0.823668
\(724\) 115.567 4.29501
\(725\) 0.421896 0.0156688
\(726\) −55.9266 −2.07563
\(727\) −1.84849 −0.0685567 −0.0342783 0.999412i \(-0.510913\pi\)
−0.0342783 + 0.999412i \(0.510913\pi\)
\(728\) −58.7520 −2.17749
\(729\) −0.0261975 −0.000970278 0
\(730\) 64.3867 2.38306
\(731\) 36.9076 1.36508
\(732\) 35.3460 1.30643
\(733\) −22.9763 −0.848647 −0.424324 0.905511i \(-0.639488\pi\)
−0.424324 + 0.905511i \(0.639488\pi\)
\(734\) 36.1161 1.33307
\(735\) −24.4205 −0.900765
\(736\) −33.7792 −1.24512
\(737\) −2.68001 −0.0987193
\(738\) −48.8419 −1.79790
\(739\) 9.17308 0.337437 0.168719 0.985664i \(-0.446037\pi\)
0.168719 + 0.985664i \(0.446037\pi\)
\(740\) −2.71288 −0.0997274
\(741\) −11.9156 −0.437731
\(742\) 44.4212 1.63076
\(743\) −6.33557 −0.232430 −0.116215 0.993224i \(-0.537076\pi\)
−0.116215 + 0.993224i \(0.537076\pi\)
\(744\) −97.2359 −3.56484
\(745\) −9.75293 −0.357320
\(746\) −54.7187 −2.00340
\(747\) −16.2828 −0.595757
\(748\) −30.1248 −1.10147
\(749\) 15.4413 0.564212
\(750\) 67.2605 2.45601
\(751\) 39.8102 1.45269 0.726347 0.687329i \(-0.241217\pi\)
0.726347 + 0.687329i \(0.241217\pi\)
\(752\) −44.0133 −1.60500
\(753\) −21.8663 −0.796851
\(754\) −11.9353 −0.434657
\(755\) −17.8123 −0.648254
\(756\) −18.9373 −0.688743
\(757\) −33.4508 −1.21579 −0.607894 0.794018i \(-0.707986\pi\)
−0.607894 + 0.794018i \(0.707986\pi\)
\(758\) −55.3989 −2.01218
\(759\) −5.51633 −0.200230
\(760\) −17.5031 −0.634903
\(761\) 34.6852 1.25734 0.628669 0.777673i \(-0.283600\pi\)
0.628669 + 0.777673i \(0.283600\pi\)
\(762\) −54.7508 −1.98341
\(763\) 7.91806 0.286653
\(764\) 13.5406 0.489881
\(765\) 18.3643 0.663963
\(766\) 68.3159 2.46835
\(767\) −52.7130 −1.90336
\(768\) −7.02414 −0.253462
\(769\) −41.5571 −1.49859 −0.749293 0.662239i \(-0.769607\pi\)
−0.749293 + 0.662239i \(0.769607\pi\)
\(770\) −8.23773 −0.296867
\(771\) −15.9501 −0.574428
\(772\) −74.9987 −2.69926
\(773\) −43.1392 −1.55161 −0.775804 0.630974i \(-0.782656\pi\)
−0.775804 + 0.630974i \(0.782656\pi\)
\(774\) 31.4727 1.13126
\(775\) 2.82886 0.101616
\(776\) −118.777 −4.26383
\(777\) 0.698837 0.0250706
\(778\) −67.1202 −2.40638
\(779\) −10.9994 −0.394093
\(780\) −128.699 −4.60817
\(781\) −12.6435 −0.452421
\(782\) 31.2592 1.11783
\(783\) −2.33922 −0.0835967
\(784\) −63.1972 −2.25704
\(785\) 28.8956 1.03133
\(786\) 114.832 4.09592
\(787\) −30.6130 −1.09124 −0.545618 0.838034i \(-0.683705\pi\)
−0.545618 + 0.838034i \(0.683705\pi\)
\(788\) 16.8737 0.601101
\(789\) −32.2392 −1.14775
\(790\) 81.3239 2.89337
\(791\) 3.99258 0.141960
\(792\) −15.6201 −0.555037
\(793\) 17.6887 0.628144
\(794\) −66.9845 −2.37719
\(795\) 59.1679 2.09847
\(796\) −73.8759 −2.61846
\(797\) −11.8243 −0.418837 −0.209419 0.977826i \(-0.567157\pi\)
−0.209419 + 0.977826i \(0.567157\pi\)
\(798\) 7.41512 0.262492
\(799\) 19.3693 0.685238
\(800\) 7.79318 0.275531
\(801\) 6.07245 0.214560
\(802\) 38.5417 1.36096
\(803\) 12.9402 0.456650
\(804\) 26.0558 0.918919
\(805\) 6.14100 0.216442
\(806\) −80.0275 −2.81885
\(807\) 2.88764 0.101650
\(808\) 28.3928 0.998857
\(809\) −54.5986 −1.91958 −0.959792 0.280711i \(-0.909430\pi\)
−0.959792 + 0.280711i \(0.909430\pi\)
\(810\) −63.3073 −2.22439
\(811\) 31.1110 1.09246 0.546228 0.837637i \(-0.316063\pi\)
0.546228 + 0.837637i \(0.316063\pi\)
\(812\) 5.33594 0.187255
\(813\) 8.55365 0.299990
\(814\) −0.758923 −0.0266002
\(815\) 42.3157 1.48225
\(816\) 133.095 4.65927
\(817\) 7.08776 0.247969
\(818\) 79.1569 2.76766
\(819\) 11.8379 0.413651
\(820\) −118.803 −4.14877
\(821\) −5.72089 −0.199661 −0.0998303 0.995004i \(-0.531830\pi\)
−0.0998303 + 0.995004i \(0.531830\pi\)
\(822\) 7.79632 0.271928
\(823\) −5.34762 −0.186406 −0.0932032 0.995647i \(-0.529711\pi\)
−0.0932032 + 0.995647i \(0.529711\pi\)
\(824\) 42.8346 1.49221
\(825\) 1.27267 0.0443087
\(826\) 32.8034 1.14138
\(827\) 0.888069 0.0308812 0.0154406 0.999881i \(-0.495085\pi\)
0.0154406 + 0.999881i \(0.495085\pi\)
\(828\) 19.1502 0.665516
\(829\) −9.47067 −0.328930 −0.164465 0.986383i \(-0.552590\pi\)
−0.164465 + 0.986383i \(0.552590\pi\)
\(830\) −55.1297 −1.91358
\(831\) −53.6117 −1.85977
\(832\) −89.9261 −3.11763
\(833\) 27.8117 0.963620
\(834\) 118.000 4.08602
\(835\) −36.5856 −1.26610
\(836\) −5.78519 −0.200085
\(837\) −15.6847 −0.542144
\(838\) −26.4136 −0.912442
\(839\) −2.93726 −0.101405 −0.0507027 0.998714i \(-0.516146\pi\)
−0.0507027 + 0.998714i \(0.516146\pi\)
\(840\) 48.6989 1.68027
\(841\) −28.3409 −0.977272
\(842\) 71.4592 2.46265
\(843\) 15.7642 0.542950
\(844\) −46.0702 −1.58580
\(845\) −36.8898 −1.26905
\(846\) 16.5171 0.567868
\(847\) 12.5127 0.429943
\(848\) 153.119 5.25812
\(849\) −21.7894 −0.747810
\(850\) −7.21180 −0.247363
\(851\) 0.565756 0.0193939
\(852\) 122.924 4.21131
\(853\) 47.3306 1.62057 0.810284 0.586037i \(-0.199313\pi\)
0.810284 + 0.586037i \(0.199313\pi\)
\(854\) −11.0077 −0.376676
\(855\) 3.52669 0.120610
\(856\) 99.1326 3.38828
\(857\) 33.8740 1.15711 0.578557 0.815642i \(-0.303616\pi\)
0.578557 + 0.815642i \(0.303616\pi\)
\(858\) −36.0034 −1.22914
\(859\) 42.0471 1.43463 0.717314 0.696750i \(-0.245371\pi\)
0.717314 + 0.696750i \(0.245371\pi\)
\(860\) 76.5541 2.61047
\(861\) 30.6036 1.04297
\(862\) 16.0639 0.547139
\(863\) 24.1978 0.823702 0.411851 0.911251i \(-0.364882\pi\)
0.411851 + 0.911251i \(0.364882\pi\)
\(864\) −43.2096 −1.47002
\(865\) −24.8456 −0.844775
\(866\) −3.96503 −0.134737
\(867\) −21.8503 −0.742075
\(868\) 35.7782 1.21439
\(869\) 16.3442 0.554439
\(870\) 9.89302 0.335405
\(871\) 13.0395 0.441826
\(872\) 50.8337 1.72145
\(873\) 23.9323 0.809985
\(874\) 6.00304 0.203056
\(875\) −15.0485 −0.508733
\(876\) −125.809 −4.25068
\(877\) 15.6802 0.529483 0.264741 0.964319i \(-0.414713\pi\)
0.264741 + 0.964319i \(0.414713\pi\)
\(878\) 23.1505 0.781291
\(879\) −54.1930 −1.82788
\(880\) −28.3952 −0.957203
\(881\) −5.57300 −0.187759 −0.0938795 0.995584i \(-0.529927\pi\)
−0.0938795 + 0.995584i \(0.529927\pi\)
\(882\) 23.7163 0.798568
\(883\) −5.75533 −0.193682 −0.0968412 0.995300i \(-0.530874\pi\)
−0.0968412 + 0.995300i \(0.530874\pi\)
\(884\) 146.571 4.92972
\(885\) 43.6933 1.46873
\(886\) 40.2346 1.35171
\(887\) 15.0163 0.504199 0.252099 0.967701i \(-0.418879\pi\)
0.252099 + 0.967701i \(0.418879\pi\)
\(888\) 4.48652 0.150558
\(889\) 12.2497 0.410840
\(890\) 20.5599 0.689169
\(891\) −12.7233 −0.426246
\(892\) 115.656 3.87246
\(893\) 3.71970 0.124475
\(894\) 26.5260 0.887163
\(895\) −20.6963 −0.691803
\(896\) 17.3292 0.578927
\(897\) 26.8395 0.896145
\(898\) 9.31238 0.310758
\(899\) 4.41947 0.147398
\(900\) −4.41814 −0.147271
\(901\) −67.3843 −2.24490
\(902\) −33.2349 −1.10660
\(903\) −19.7203 −0.656251
\(904\) 25.6323 0.852516
\(905\) −47.9385 −1.59353
\(906\) 48.4458 1.60950
\(907\) 18.8258 0.625101 0.312551 0.949901i \(-0.398817\pi\)
0.312551 + 0.949901i \(0.398817\pi\)
\(908\) 47.8918 1.58934
\(909\) −5.72087 −0.189749
\(910\) 40.0804 1.32865
\(911\) −27.5160 −0.911645 −0.455823 0.890071i \(-0.650655\pi\)
−0.455823 + 0.890071i \(0.650655\pi\)
\(912\) 25.5597 0.846366
\(913\) −11.0798 −0.366687
\(914\) −0.456421 −0.0150971
\(915\) −14.6620 −0.484710
\(916\) −95.2743 −3.14795
\(917\) −25.6919 −0.848422
\(918\) 39.9861 1.31974
\(919\) 22.8308 0.753117 0.376559 0.926393i \(-0.377107\pi\)
0.376559 + 0.926393i \(0.377107\pi\)
\(920\) 39.4250 1.29981
\(921\) 22.9482 0.756168
\(922\) 4.17008 0.137334
\(923\) 61.5166 2.02484
\(924\) 16.0962 0.529525
\(925\) −0.130525 −0.00429164
\(926\) 56.7100 1.86361
\(927\) −8.63074 −0.283471
\(928\) 12.1751 0.399668
\(929\) −7.37174 −0.241859 −0.120929 0.992661i \(-0.538587\pi\)
−0.120929 + 0.992661i \(0.538587\pi\)
\(930\) 66.3340 2.17518
\(931\) 5.34098 0.175044
\(932\) 49.6311 1.62572
\(933\) −69.2174 −2.26608
\(934\) 39.9586 1.30749
\(935\) 12.4961 0.408668
\(936\) 75.9992 2.48411
\(937\) −48.2688 −1.57687 −0.788436 0.615117i \(-0.789109\pi\)
−0.788436 + 0.615117i \(0.789109\pi\)
\(938\) −8.11449 −0.264948
\(939\) −12.2830 −0.400840
\(940\) 40.1760 1.31040
\(941\) −12.8826 −0.419960 −0.209980 0.977706i \(-0.567340\pi\)
−0.209980 + 0.977706i \(0.567340\pi\)
\(942\) −78.5902 −2.56061
\(943\) 24.7757 0.806807
\(944\) 113.073 3.68020
\(945\) 7.85542 0.255537
\(946\) 21.4159 0.696290
\(947\) 20.7214 0.673356 0.336678 0.941620i \(-0.390697\pi\)
0.336678 + 0.941620i \(0.390697\pi\)
\(948\) −158.903 −5.16094
\(949\) −62.9601 −2.04377
\(950\) −1.38496 −0.0449339
\(951\) 2.16013 0.0700469
\(952\) −55.4616 −1.79752
\(953\) 29.0265 0.940260 0.470130 0.882597i \(-0.344207\pi\)
0.470130 + 0.882597i \(0.344207\pi\)
\(954\) −57.4615 −1.86038
\(955\) −5.61680 −0.181755
\(956\) −42.5972 −1.37769
\(957\) 1.98826 0.0642715
\(958\) −42.5928 −1.37611
\(959\) −1.74431 −0.0563267
\(960\) 74.5388 2.40573
\(961\) −1.36689 −0.0440931
\(962\) 3.69251 0.119051
\(963\) −19.9742 −0.643660
\(964\) 52.3174 1.68503
\(965\) 31.1104 1.00148
\(966\) −16.7023 −0.537387
\(967\) 38.1007 1.22523 0.612617 0.790380i \(-0.290117\pi\)
0.612617 + 0.790380i \(0.290117\pi\)
\(968\) 80.3314 2.58195
\(969\) −11.2483 −0.361347
\(970\) 81.0290 2.60168
\(971\) −19.7835 −0.634883 −0.317442 0.948278i \(-0.602824\pi\)
−0.317442 + 0.948278i \(0.602824\pi\)
\(972\) 79.5920 2.55291
\(973\) −26.4008 −0.846371
\(974\) −98.2209 −3.14720
\(975\) −6.19213 −0.198307
\(976\) −37.9433 −1.21453
\(977\) 41.2109 1.31845 0.659227 0.751944i \(-0.270884\pi\)
0.659227 + 0.751944i \(0.270884\pi\)
\(978\) −115.090 −3.68018
\(979\) 4.13205 0.132061
\(980\) 57.6873 1.84275
\(981\) −10.2425 −0.327017
\(982\) −56.9826 −1.81839
\(983\) 49.7244 1.58596 0.792981 0.609246i \(-0.208528\pi\)
0.792981 + 0.609246i \(0.208528\pi\)
\(984\) 196.474 6.26337
\(985\) −6.99942 −0.223020
\(986\) −11.2668 −0.358809
\(987\) −10.3493 −0.329423
\(988\) 28.1476 0.895495
\(989\) −15.9649 −0.507655
\(990\) 10.6560 0.338670
\(991\) −48.5414 −1.54197 −0.770984 0.636855i \(-0.780235\pi\)
−0.770984 + 0.636855i \(0.780235\pi\)
\(992\) 81.6357 2.59194
\(993\) 28.6438 0.908982
\(994\) −38.2819 −1.21423
\(995\) 30.6446 0.971500
\(996\) 107.721 3.41327
\(997\) 58.6056 1.85606 0.928030 0.372506i \(-0.121502\pi\)
0.928030 + 0.372506i \(0.121502\pi\)
\(998\) −17.6313 −0.558109
\(999\) 0.723702 0.0228969
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 \(a_p\))