Properties

Label 8023.2.a.c.1.16
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.47274 q^{2}\) \(-2.32483 q^{3}\) \(+4.11444 q^{4}\) \(-0.448444 q^{5}\) \(+5.74869 q^{6}\) \(+4.71625 q^{7}\) \(-5.22846 q^{8}\) \(+2.40481 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.47274 q^{2}\) \(-2.32483 q^{3}\) \(+4.11444 q^{4}\) \(-0.448444 q^{5}\) \(+5.74869 q^{6}\) \(+4.71625 q^{7}\) \(-5.22846 q^{8}\) \(+2.40481 q^{9}\) \(+1.10889 q^{10}\) \(-3.11738 q^{11}\) \(-9.56535 q^{12}\) \(+1.13805 q^{13}\) \(-11.6621 q^{14}\) \(+1.04255 q^{15}\) \(+4.69974 q^{16}\) \(-5.01853 q^{17}\) \(-5.94648 q^{18}\) \(-7.46652 q^{19}\) \(-1.84510 q^{20}\) \(-10.9645 q^{21}\) \(+7.70847 q^{22}\) \(-4.64694 q^{23}\) \(+12.1553 q^{24}\) \(-4.79890 q^{25}\) \(-2.81410 q^{26}\) \(+1.38371 q^{27}\) \(+19.4047 q^{28}\) \(-5.28273 q^{29}\) \(-2.57797 q^{30}\) \(+9.31388 q^{31}\) \(-1.16430 q^{32}\) \(+7.24737 q^{33}\) \(+12.4095 q^{34}\) \(-2.11498 q^{35}\) \(+9.89446 q^{36}\) \(+1.67683 q^{37}\) \(+18.4628 q^{38}\) \(-2.64577 q^{39}\) \(+2.34467 q^{40}\) \(+11.3768 q^{41}\) \(+27.1123 q^{42}\) \(+11.6479 q^{43}\) \(-12.8263 q^{44}\) \(-1.07842 q^{45}\) \(+11.4907 q^{46}\) \(-10.6614 q^{47}\) \(-10.9261 q^{48}\) \(+15.2430 q^{49}\) \(+11.8664 q^{50}\) \(+11.6672 q^{51}\) \(+4.68244 q^{52}\) \(+9.13629 q^{53}\) \(-3.42154 q^{54}\) \(+1.39797 q^{55}\) \(-24.6587 q^{56}\) \(+17.3584 q^{57}\) \(+13.0628 q^{58}\) \(-5.36263 q^{59}\) \(+4.28953 q^{60}\) \(-2.46830 q^{61}\) \(-23.0308 q^{62}\) \(+11.3417 q^{63}\) \(-6.52045 q^{64}\) \(-0.510352 q^{65}\) \(-17.9209 q^{66}\) \(+2.51918 q^{67}\) \(-20.6484 q^{68}\) \(+10.8033 q^{69}\) \(+5.22978 q^{70}\) \(-1.00000 q^{71}\) \(-12.5735 q^{72}\) \(-0.446884 q^{73}\) \(-4.14635 q^{74}\) \(+11.1566 q^{75}\) \(-30.7205 q^{76}\) \(-14.7024 q^{77}\) \(+6.54230 q^{78}\) \(-0.650824 q^{79}\) \(-2.10757 q^{80}\) \(-10.4313 q^{81}\) \(-28.1319 q^{82}\) \(+11.8608 q^{83}\) \(-45.1126 q^{84}\) \(+2.25053 q^{85}\) \(-28.8023 q^{86}\) \(+12.2814 q^{87}\) \(+16.2991 q^{88}\) \(-14.4211 q^{89}\) \(+2.66666 q^{90}\) \(+5.36734 q^{91}\) \(-19.1196 q^{92}\) \(-21.6531 q^{93}\) \(+26.3629 q^{94}\) \(+3.34832 q^{95}\) \(+2.70680 q^{96}\) \(+8.52789 q^{97}\) \(-37.6921 q^{98}\) \(-7.49672 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47274 −1.74849 −0.874245 0.485484i \(-0.838643\pi\)
−0.874245 + 0.485484i \(0.838643\pi\)
\(3\) −2.32483 −1.34224 −0.671119 0.741349i \(-0.734186\pi\)
−0.671119 + 0.741349i \(0.734186\pi\)
\(4\) 4.11444 2.05722
\(5\) −0.448444 −0.200550 −0.100275 0.994960i \(-0.531972\pi\)
−0.100275 + 0.994960i \(0.531972\pi\)
\(6\) 5.74869 2.34689
\(7\) 4.71625 1.78258 0.891288 0.453437i \(-0.149802\pi\)
0.891288 + 0.453437i \(0.149802\pi\)
\(8\) −5.22846 −1.84854
\(9\) 2.40481 0.801604
\(10\) 1.10889 0.350660
\(11\) −3.11738 −0.939926 −0.469963 0.882686i \(-0.655733\pi\)
−0.469963 + 0.882686i \(0.655733\pi\)
\(12\) −9.56535 −2.76128
\(13\) 1.13805 0.315638 0.157819 0.987468i \(-0.449554\pi\)
0.157819 + 0.987468i \(0.449554\pi\)
\(14\) −11.6621 −3.11682
\(15\) 1.04255 0.269186
\(16\) 4.69974 1.17493
\(17\) −5.01853 −1.21717 −0.608586 0.793488i \(-0.708263\pi\)
−0.608586 + 0.793488i \(0.708263\pi\)
\(18\) −5.94648 −1.40160
\(19\) −7.46652 −1.71294 −0.856468 0.516199i \(-0.827346\pi\)
−0.856468 + 0.516199i \(0.827346\pi\)
\(20\) −1.84510 −0.412576
\(21\) −10.9645 −2.39264
\(22\) 7.70847 1.64345
\(23\) −4.64694 −0.968954 −0.484477 0.874804i \(-0.660990\pi\)
−0.484477 + 0.874804i \(0.660990\pi\)
\(24\) 12.1553 2.48118
\(25\) −4.79890 −0.959780
\(26\) −2.81410 −0.551891
\(27\) 1.38371 0.266294
\(28\) 19.4047 3.66715
\(29\) −5.28273 −0.980979 −0.490489 0.871447i \(-0.663182\pi\)
−0.490489 + 0.871447i \(0.663182\pi\)
\(30\) −2.57797 −0.470670
\(31\) 9.31388 1.67282 0.836411 0.548103i \(-0.184650\pi\)
0.836411 + 0.548103i \(0.184650\pi\)
\(32\) −1.16430 −0.205822
\(33\) 7.24737 1.26161
\(34\) 12.4095 2.12821
\(35\) −2.11498 −0.357496
\(36\) 9.89446 1.64908
\(37\) 1.67683 0.275669 0.137834 0.990455i \(-0.455986\pi\)
0.137834 + 0.990455i \(0.455986\pi\)
\(38\) 18.4628 2.99505
\(39\) −2.64577 −0.423662
\(40\) 2.34467 0.370725
\(41\) 11.3768 1.77676 0.888381 0.459107i \(-0.151831\pi\)
0.888381 + 0.459107i \(0.151831\pi\)
\(42\) 27.1123 4.18351
\(43\) 11.6479 1.77629 0.888146 0.459562i \(-0.151994\pi\)
0.888146 + 0.459562i \(0.151994\pi\)
\(44\) −12.8263 −1.93363
\(45\) −1.07842 −0.160762
\(46\) 11.4907 1.69421
\(47\) −10.6614 −1.55513 −0.777564 0.628804i \(-0.783545\pi\)
−0.777564 + 0.628804i \(0.783545\pi\)
\(48\) −10.9261 −1.57704
\(49\) 15.2430 2.17758
\(50\) 11.8664 1.67817
\(51\) 11.6672 1.63373
\(52\) 4.68244 0.649338
\(53\) 9.13629 1.25497 0.627483 0.778630i \(-0.284085\pi\)
0.627483 + 0.778630i \(0.284085\pi\)
\(54\) −3.42154 −0.465613
\(55\) 1.39797 0.188502
\(56\) −24.6587 −3.29516
\(57\) 17.3584 2.29917
\(58\) 13.0628 1.71523
\(59\) −5.36263 −0.698155 −0.349078 0.937094i \(-0.613505\pi\)
−0.349078 + 0.937094i \(0.613505\pi\)
\(60\) 4.28953 0.553776
\(61\) −2.46830 −0.316033 −0.158016 0.987436i \(-0.550510\pi\)
−0.158016 + 0.987436i \(0.550510\pi\)
\(62\) −23.0308 −2.92491
\(63\) 11.3417 1.42892
\(64\) −6.52045 −0.815056
\(65\) −0.510352 −0.0633014
\(66\) −17.9209 −2.20590
\(67\) 2.51918 0.307767 0.153883 0.988089i \(-0.450822\pi\)
0.153883 + 0.988089i \(0.450822\pi\)
\(68\) −20.6484 −2.50399
\(69\) 10.8033 1.30057
\(70\) 5.22978 0.625079
\(71\) −1.00000 −0.118678
\(72\) −12.5735 −1.48180
\(73\) −0.446884 −0.0523038 −0.0261519 0.999658i \(-0.508325\pi\)
−0.0261519 + 0.999658i \(0.508325\pi\)
\(74\) −4.14635 −0.482004
\(75\) 11.1566 1.28825
\(76\) −30.7205 −3.52389
\(77\) −14.7024 −1.67549
\(78\) 6.54230 0.740769
\(79\) −0.650824 −0.0732235 −0.0366117 0.999330i \(-0.511656\pi\)
−0.0366117 + 0.999330i \(0.511656\pi\)
\(80\) −2.10757 −0.235633
\(81\) −10.4313 −1.15903
\(82\) −28.1319 −3.10665
\(83\) 11.8608 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(84\) −45.1126 −4.92219
\(85\) 2.25053 0.244104
\(86\) −28.8023 −3.10583
\(87\) 12.2814 1.31671
\(88\) 16.2991 1.73749
\(89\) −14.4211 −1.52863 −0.764317 0.644840i \(-0.776924\pi\)
−0.764317 + 0.644840i \(0.776924\pi\)
\(90\) 2.66666 0.281091
\(91\) 5.36734 0.562650
\(92\) −19.1196 −1.99335
\(93\) −21.6531 −2.24533
\(94\) 26.3629 2.71913
\(95\) 3.34832 0.343530
\(96\) 2.70680 0.276262
\(97\) 8.52789 0.865876 0.432938 0.901424i \(-0.357477\pi\)
0.432938 + 0.901424i \(0.357477\pi\)
\(98\) −37.6921 −3.80747
\(99\) −7.49672 −0.753449
\(100\) −19.7448 −1.97448
\(101\) 12.5797 1.25172 0.625862 0.779933i \(-0.284747\pi\)
0.625862 + 0.779933i \(0.284747\pi\)
\(102\) −28.8499 −2.85657
\(103\) −17.2770 −1.70236 −0.851179 0.524876i \(-0.824112\pi\)
−0.851179 + 0.524876i \(0.824112\pi\)
\(104\) −5.95025 −0.583470
\(105\) 4.91695 0.479845
\(106\) −22.5917 −2.19430
\(107\) 13.5058 1.30566 0.652829 0.757505i \(-0.273582\pi\)
0.652829 + 0.757505i \(0.273582\pi\)
\(108\) 5.69317 0.547826
\(109\) 10.8420 1.03848 0.519238 0.854630i \(-0.326216\pi\)
0.519238 + 0.854630i \(0.326216\pi\)
\(110\) −3.45682 −0.329595
\(111\) −3.89833 −0.370013
\(112\) 22.1651 2.09441
\(113\) −1.00000 −0.0940721
\(114\) −42.9227 −4.02008
\(115\) 2.08389 0.194324
\(116\) −21.7355 −2.01809
\(117\) 2.73680 0.253017
\(118\) 13.2604 1.22072
\(119\) −23.6686 −2.16970
\(120\) −5.45095 −0.497602
\(121\) −1.28193 −0.116539
\(122\) 6.10345 0.552581
\(123\) −26.4491 −2.38484
\(124\) 38.3214 3.44136
\(125\) 4.39426 0.393034
\(126\) −28.0451 −2.49846
\(127\) 10.3746 0.920600 0.460300 0.887764i \(-0.347742\pi\)
0.460300 + 0.887764i \(0.347742\pi\)
\(128\) 18.4520 1.63094
\(129\) −27.0794 −2.38421
\(130\) 1.26197 0.110682
\(131\) 6.13464 0.535986 0.267993 0.963421i \(-0.413640\pi\)
0.267993 + 0.963421i \(0.413640\pi\)
\(132\) 29.8189 2.59540
\(133\) −35.2140 −3.05344
\(134\) −6.22928 −0.538127
\(135\) −0.620514 −0.0534054
\(136\) 26.2392 2.24999
\(137\) −0.215788 −0.0184360 −0.00921800 0.999958i \(-0.502934\pi\)
−0.00921800 + 0.999958i \(0.502934\pi\)
\(138\) −26.7138 −2.27403
\(139\) 17.6972 1.50106 0.750530 0.660836i \(-0.229798\pi\)
0.750530 + 0.660836i \(0.229798\pi\)
\(140\) −8.70194 −0.735448
\(141\) 24.7859 2.08735
\(142\) 2.47274 0.207508
\(143\) −3.54774 −0.296677
\(144\) 11.3020 0.941832
\(145\) 2.36901 0.196736
\(146\) 1.10503 0.0914528
\(147\) −35.4374 −2.92283
\(148\) 6.89920 0.567111
\(149\) 23.2012 1.90072 0.950358 0.311157i \(-0.100717\pi\)
0.950358 + 0.311157i \(0.100717\pi\)
\(150\) −27.5874 −2.25250
\(151\) 18.2579 1.48581 0.742904 0.669397i \(-0.233448\pi\)
0.742904 + 0.669397i \(0.233448\pi\)
\(152\) 39.0384 3.16643
\(153\) −12.0686 −0.975690
\(154\) 36.3551 2.92958
\(155\) −4.17675 −0.335485
\(156\) −10.8859 −0.871566
\(157\) −18.9435 −1.51186 −0.755928 0.654654i \(-0.772814\pi\)
−0.755928 + 0.654654i \(0.772814\pi\)
\(158\) 1.60932 0.128031
\(159\) −21.2403 −1.68446
\(160\) 0.522125 0.0412776
\(161\) −21.9162 −1.72723
\(162\) 25.7939 2.02656
\(163\) −10.2360 −0.801745 −0.400872 0.916134i \(-0.631293\pi\)
−0.400872 + 0.916134i \(0.631293\pi\)
\(164\) 46.8093 3.65519
\(165\) −3.25004 −0.253015
\(166\) −29.3286 −2.27634
\(167\) 15.1748 1.17426 0.587132 0.809491i \(-0.300257\pi\)
0.587132 + 0.809491i \(0.300257\pi\)
\(168\) 57.3273 4.42289
\(169\) −11.7048 −0.900372
\(170\) −5.56497 −0.426814
\(171\) −17.9556 −1.37310
\(172\) 47.9247 3.65422
\(173\) −3.34857 −0.254587 −0.127294 0.991865i \(-0.540629\pi\)
−0.127294 + 0.991865i \(0.540629\pi\)
\(174\) −30.3688 −2.30225
\(175\) −22.6328 −1.71088
\(176\) −14.6509 −1.10435
\(177\) 12.4672 0.937091
\(178\) 35.6597 2.67280
\(179\) 1.64435 0.122904 0.0614522 0.998110i \(-0.480427\pi\)
0.0614522 + 0.998110i \(0.480427\pi\)
\(180\) −4.43711 −0.330723
\(181\) 23.9239 1.77825 0.889124 0.457666i \(-0.151314\pi\)
0.889124 + 0.457666i \(0.151314\pi\)
\(182\) −13.2720 −0.983788
\(183\) 5.73836 0.424192
\(184\) 24.2963 1.79115
\(185\) −0.751963 −0.0552854
\(186\) 53.5426 3.92593
\(187\) 15.6447 1.14405
\(188\) −43.8658 −3.19924
\(189\) 6.52590 0.474690
\(190\) −8.27951 −0.600659
\(191\) −12.8964 −0.933154 −0.466577 0.884481i \(-0.654513\pi\)
−0.466577 + 0.884481i \(0.654513\pi\)
\(192\) 15.1589 1.09400
\(193\) −6.77538 −0.487702 −0.243851 0.969813i \(-0.578411\pi\)
−0.243851 + 0.969813i \(0.578411\pi\)
\(194\) −21.0873 −1.51398
\(195\) 1.18648 0.0849656
\(196\) 62.7166 4.47976
\(197\) 3.03452 0.216200 0.108100 0.994140i \(-0.465523\pi\)
0.108100 + 0.994140i \(0.465523\pi\)
\(198\) 18.5374 1.31740
\(199\) −11.9810 −0.849314 −0.424657 0.905354i \(-0.639605\pi\)
−0.424657 + 0.905354i \(0.639605\pi\)
\(200\) 25.0908 1.77419
\(201\) −5.85665 −0.413097
\(202\) −31.1063 −2.18863
\(203\) −24.9147 −1.74867
\(204\) 48.0040 3.36095
\(205\) −5.10187 −0.356330
\(206\) 42.7216 2.97656
\(207\) −11.1750 −0.776718
\(208\) 5.34854 0.370854
\(209\) 23.2760 1.61003
\(210\) −12.1583 −0.839005
\(211\) −20.2056 −1.39101 −0.695504 0.718522i \(-0.744819\pi\)
−0.695504 + 0.718522i \(0.744819\pi\)
\(212\) 37.5907 2.58174
\(213\) 2.32483 0.159294
\(214\) −33.3964 −2.28293
\(215\) −5.22344 −0.356236
\(216\) −7.23464 −0.492255
\(217\) 43.9266 2.98193
\(218\) −26.8095 −1.81577
\(219\) 1.03893 0.0702042
\(220\) 5.75187 0.387791
\(221\) −5.71134 −0.384186
\(222\) 9.63955 0.646964
\(223\) −20.6600 −1.38349 −0.691747 0.722140i \(-0.743159\pi\)
−0.691747 + 0.722140i \(0.743159\pi\)
\(224\) −5.49115 −0.366893
\(225\) −11.5405 −0.769364
\(226\) 2.47274 0.164484
\(227\) −29.7519 −1.97471 −0.987353 0.158538i \(-0.949322\pi\)
−0.987353 + 0.158538i \(0.949322\pi\)
\(228\) 71.4199 4.72990
\(229\) −15.5414 −1.02700 −0.513502 0.858088i \(-0.671652\pi\)
−0.513502 + 0.858088i \(0.671652\pi\)
\(230\) −5.15293 −0.339774
\(231\) 34.1804 2.24891
\(232\) 27.6205 1.81338
\(233\) −4.66988 −0.305934 −0.152967 0.988231i \(-0.548883\pi\)
−0.152967 + 0.988231i \(0.548883\pi\)
\(234\) −6.76739 −0.442398
\(235\) 4.78105 0.311881
\(236\) −22.0642 −1.43626
\(237\) 1.51305 0.0982834
\(238\) 58.5264 3.79370
\(239\) 10.1608 0.657246 0.328623 0.944461i \(-0.393415\pi\)
0.328623 + 0.944461i \(0.393415\pi\)
\(240\) 4.89973 0.316276
\(241\) 10.3195 0.664735 0.332367 0.943150i \(-0.392153\pi\)
0.332367 + 0.943150i \(0.392153\pi\)
\(242\) 3.16987 0.203767
\(243\) 20.0999 1.28941
\(244\) −10.1557 −0.650149
\(245\) −6.83565 −0.436714
\(246\) 65.4018 4.16987
\(247\) −8.49728 −0.540669
\(248\) −48.6972 −3.09228
\(249\) −27.5743 −1.74745
\(250\) −10.8659 −0.687217
\(251\) −7.99047 −0.504354 −0.252177 0.967681i \(-0.581147\pi\)
−0.252177 + 0.967681i \(0.581147\pi\)
\(252\) 46.6648 2.93960
\(253\) 14.4863 0.910745
\(254\) −25.6538 −1.60966
\(255\) −5.23209 −0.327646
\(256\) −32.5860 −2.03663
\(257\) −12.8385 −0.800846 −0.400423 0.916330i \(-0.631137\pi\)
−0.400423 + 0.916330i \(0.631137\pi\)
\(258\) 66.9602 4.16876
\(259\) 7.90834 0.491400
\(260\) −2.09981 −0.130225
\(261\) −12.7040 −0.786357
\(262\) −15.1694 −0.937166
\(263\) −16.3684 −1.00932 −0.504659 0.863318i \(-0.668382\pi\)
−0.504659 + 0.863318i \(0.668382\pi\)
\(264\) −37.8926 −2.33213
\(265\) −4.09712 −0.251684
\(266\) 87.0750 5.33891
\(267\) 33.5266 2.05179
\(268\) 10.3650 0.633144
\(269\) 14.7533 0.899523 0.449762 0.893149i \(-0.351509\pi\)
0.449762 + 0.893149i \(0.351509\pi\)
\(270\) 1.53437 0.0933788
\(271\) 11.6153 0.705582 0.352791 0.935702i \(-0.385233\pi\)
0.352791 + 0.935702i \(0.385233\pi\)
\(272\) −23.5858 −1.43010
\(273\) −12.4781 −0.755210
\(274\) 0.533587 0.0322352
\(275\) 14.9600 0.902122
\(276\) 44.4496 2.67555
\(277\) −18.2270 −1.09515 −0.547576 0.836756i \(-0.684449\pi\)
−0.547576 + 0.836756i \(0.684449\pi\)
\(278\) −43.7607 −2.62459
\(279\) 22.3981 1.34094
\(280\) 11.0581 0.660846
\(281\) −15.1613 −0.904450 −0.452225 0.891904i \(-0.649370\pi\)
−0.452225 + 0.891904i \(0.649370\pi\)
\(282\) −61.2892 −3.64972
\(283\) −9.99210 −0.593969 −0.296984 0.954882i \(-0.595981\pi\)
−0.296984 + 0.954882i \(0.595981\pi\)
\(284\) −4.11444 −0.244147
\(285\) −7.78425 −0.461099
\(286\) 8.77263 0.518737
\(287\) 53.6560 3.16721
\(288\) −2.79993 −0.164988
\(289\) 8.18562 0.481507
\(290\) −5.85795 −0.343990
\(291\) −19.8259 −1.16221
\(292\) −1.83868 −0.107600
\(293\) 8.74560 0.510923 0.255462 0.966819i \(-0.417773\pi\)
0.255462 + 0.966819i \(0.417773\pi\)
\(294\) 87.6275 5.11054
\(295\) 2.40484 0.140015
\(296\) −8.76722 −0.509584
\(297\) −4.31354 −0.250297
\(298\) −57.3705 −3.32339
\(299\) −5.28845 −0.305839
\(300\) 45.9032 2.65022
\(301\) 54.9345 3.16637
\(302\) −45.1471 −2.59792
\(303\) −29.2456 −1.68011
\(304\) −35.0907 −2.01259
\(305\) 1.10689 0.0633805
\(306\) 29.8426 1.70599
\(307\) 12.1528 0.693600 0.346800 0.937939i \(-0.387268\pi\)
0.346800 + 0.937939i \(0.387268\pi\)
\(308\) −60.4920 −3.44685
\(309\) 40.1661 2.28497
\(310\) 10.3280 0.586592
\(311\) 12.5209 0.709997 0.354999 0.934867i \(-0.384481\pi\)
0.354999 + 0.934867i \(0.384481\pi\)
\(312\) 13.8333 0.783156
\(313\) −2.53594 −0.143340 −0.0716700 0.997428i \(-0.522833\pi\)
−0.0716700 + 0.997428i \(0.522833\pi\)
\(314\) 46.8424 2.64347
\(315\) −5.08612 −0.286571
\(316\) −2.67778 −0.150637
\(317\) −13.7755 −0.773709 −0.386854 0.922141i \(-0.626438\pi\)
−0.386854 + 0.922141i \(0.626438\pi\)
\(318\) 52.5217 2.94527
\(319\) 16.4683 0.922048
\(320\) 2.92406 0.163460
\(321\) −31.3987 −1.75250
\(322\) 54.1929 3.02005
\(323\) 37.4709 2.08494
\(324\) −42.9190 −2.38439
\(325\) −5.46139 −0.302943
\(326\) 25.3109 1.40184
\(327\) −25.2058 −1.39388
\(328\) −59.4833 −3.28441
\(329\) −50.2820 −2.77213
\(330\) 8.03650 0.442395
\(331\) −17.7862 −0.977620 −0.488810 0.872390i \(-0.662569\pi\)
−0.488810 + 0.872390i \(0.662569\pi\)
\(332\) 48.8005 2.67827
\(333\) 4.03245 0.220977
\(334\) −37.5234 −2.05319
\(335\) −1.12971 −0.0617227
\(336\) −51.5301 −2.81120
\(337\) −25.2938 −1.37784 −0.688921 0.724837i \(-0.741915\pi\)
−0.688921 + 0.724837i \(0.741915\pi\)
\(338\) 28.9430 1.57429
\(339\) 2.32483 0.126267
\(340\) 9.25967 0.502176
\(341\) −29.0349 −1.57233
\(342\) 44.3995 2.40085
\(343\) 38.8763 2.09912
\(344\) −60.9007 −3.28354
\(345\) −4.84469 −0.260829
\(346\) 8.28014 0.445143
\(347\) 3.98979 0.214183 0.107092 0.994249i \(-0.465846\pi\)
0.107092 + 0.994249i \(0.465846\pi\)
\(348\) 50.5312 2.70876
\(349\) −8.14040 −0.435745 −0.217873 0.975977i \(-0.569912\pi\)
−0.217873 + 0.975977i \(0.569912\pi\)
\(350\) 55.9651 2.99146
\(351\) 1.57473 0.0840527
\(352\) 3.62958 0.193457
\(353\) 15.1185 0.804676 0.402338 0.915491i \(-0.368198\pi\)
0.402338 + 0.915491i \(0.368198\pi\)
\(354\) −30.8281 −1.63849
\(355\) 0.448444 0.0238009
\(356\) −59.3348 −3.14474
\(357\) 55.0255 2.91226
\(358\) −4.06605 −0.214897
\(359\) 21.7516 1.14800 0.574001 0.818854i \(-0.305390\pi\)
0.574001 + 0.818854i \(0.305390\pi\)
\(360\) 5.63850 0.297175
\(361\) 36.7489 1.93415
\(362\) −59.1575 −3.10925
\(363\) 2.98026 0.156423
\(364\) 22.0836 1.15749
\(365\) 0.200403 0.0104895
\(366\) −14.1895 −0.741695
\(367\) 27.5662 1.43894 0.719471 0.694523i \(-0.244384\pi\)
0.719471 + 0.694523i \(0.244384\pi\)
\(368\) −21.8394 −1.13846
\(369\) 27.3591 1.42426
\(370\) 1.85941 0.0966660
\(371\) 43.0891 2.23707
\(372\) −89.0905 −4.61913
\(373\) 8.10130 0.419469 0.209735 0.977758i \(-0.432740\pi\)
0.209735 + 0.977758i \(0.432740\pi\)
\(374\) −38.6852 −2.00036
\(375\) −10.2159 −0.527546
\(376\) 55.7428 2.87472
\(377\) −6.01202 −0.309635
\(378\) −16.1369 −0.829990
\(379\) −32.6199 −1.67557 −0.837787 0.545998i \(-0.816151\pi\)
−0.837787 + 0.545998i \(0.816151\pi\)
\(380\) 13.7764 0.706717
\(381\) −24.1192 −1.23566
\(382\) 31.8896 1.63161
\(383\) −19.9370 −1.01873 −0.509367 0.860549i \(-0.670121\pi\)
−0.509367 + 0.860549i \(0.670121\pi\)
\(384\) −42.8976 −2.18911
\(385\) 6.59319 0.336020
\(386\) 16.7537 0.852743
\(387\) 28.0111 1.42388
\(388\) 35.0875 1.78130
\(389\) −15.0917 −0.765178 −0.382589 0.923919i \(-0.624967\pi\)
−0.382589 + 0.923919i \(0.624967\pi\)
\(390\) −2.93386 −0.148562
\(391\) 23.3208 1.17938
\(392\) −79.6976 −4.02534
\(393\) −14.2620 −0.719421
\(394\) −7.50356 −0.378024
\(395\) 0.291858 0.0146850
\(396\) −30.8448 −1.55001
\(397\) 8.86894 0.445120 0.222560 0.974919i \(-0.428559\pi\)
0.222560 + 0.974919i \(0.428559\pi\)
\(398\) 29.6260 1.48502
\(399\) 81.8664 4.09845
\(400\) −22.5536 −1.12768
\(401\) −16.9797 −0.847926 −0.423963 0.905679i \(-0.639361\pi\)
−0.423963 + 0.905679i \(0.639361\pi\)
\(402\) 14.4820 0.722295
\(403\) 10.5997 0.528007
\(404\) 51.7583 2.57507
\(405\) 4.67786 0.232445
\(406\) 61.6076 3.05753
\(407\) −5.22731 −0.259108
\(408\) −61.0015 −3.02002
\(409\) −11.7547 −0.581231 −0.290616 0.956840i \(-0.593860\pi\)
−0.290616 + 0.956840i \(0.593860\pi\)
\(410\) 12.6156 0.623040
\(411\) 0.501669 0.0247455
\(412\) −71.0853 −3.50212
\(413\) −25.2915 −1.24452
\(414\) 27.6329 1.35808
\(415\) −5.31890 −0.261095
\(416\) −1.32504 −0.0649653
\(417\) −41.1430 −2.01478
\(418\) −57.5555 −2.81513
\(419\) −6.78611 −0.331523 −0.165762 0.986166i \(-0.553008\pi\)
−0.165762 + 0.986166i \(0.553008\pi\)
\(420\) 20.2305 0.987147
\(421\) −2.79379 −0.136161 −0.0680806 0.997680i \(-0.521688\pi\)
−0.0680806 + 0.997680i \(0.521688\pi\)
\(422\) 49.9631 2.43217
\(423\) −25.6387 −1.24660
\(424\) −47.7687 −2.31985
\(425\) 24.0834 1.16822
\(426\) −5.74869 −0.278525
\(427\) −11.6411 −0.563353
\(428\) 55.5689 2.68603
\(429\) 8.24787 0.398211
\(430\) 12.9162 0.622875
\(431\) 9.36821 0.451251 0.225625 0.974214i \(-0.427557\pi\)
0.225625 + 0.974214i \(0.427557\pi\)
\(432\) 6.50305 0.312878
\(433\) −15.7728 −0.757993 −0.378996 0.925398i \(-0.623731\pi\)
−0.378996 + 0.925398i \(0.623731\pi\)
\(434\) −108.619 −5.21388
\(435\) −5.50754 −0.264066
\(436\) 44.6088 2.13637
\(437\) 34.6965 1.65976
\(438\) −2.56900 −0.122751
\(439\) −18.1870 −0.868017 −0.434008 0.900909i \(-0.642901\pi\)
−0.434008 + 0.900909i \(0.642901\pi\)
\(440\) −7.30924 −0.348454
\(441\) 36.6567 1.74556
\(442\) 14.1227 0.671746
\(443\) 8.37092 0.397714 0.198857 0.980028i \(-0.436277\pi\)
0.198857 + 0.980028i \(0.436277\pi\)
\(444\) −16.0394 −0.761198
\(445\) 6.46706 0.306568
\(446\) 51.0867 2.41903
\(447\) −53.9388 −2.55122
\(448\) −30.7521 −1.45290
\(449\) 12.9745 0.612306 0.306153 0.951982i \(-0.400958\pi\)
0.306153 + 0.951982i \(0.400958\pi\)
\(450\) 28.5365 1.34523
\(451\) −35.4659 −1.67003
\(452\) −4.11444 −0.193527
\(453\) −42.4465 −1.99431
\(454\) 73.5688 3.45275
\(455\) −2.40695 −0.112840
\(456\) −90.7574 −4.25011
\(457\) 5.55422 0.259815 0.129908 0.991526i \(-0.458532\pi\)
0.129908 + 0.991526i \(0.458532\pi\)
\(458\) 38.4298 1.79571
\(459\) −6.94416 −0.324126
\(460\) 8.57405 0.399767
\(461\) 4.06514 0.189333 0.0946663 0.995509i \(-0.469822\pi\)
0.0946663 + 0.995509i \(0.469822\pi\)
\(462\) −84.5193 −3.93219
\(463\) 1.41528 0.0657737 0.0328868 0.999459i \(-0.489530\pi\)
0.0328868 + 0.999459i \(0.489530\pi\)
\(464\) −24.8274 −1.15259
\(465\) 9.71022 0.450301
\(466\) 11.5474 0.534923
\(467\) −39.1503 −1.81166 −0.905830 0.423640i \(-0.860752\pi\)
−0.905830 + 0.423640i \(0.860752\pi\)
\(468\) 11.2604 0.520512
\(469\) 11.8811 0.548618
\(470\) −11.8223 −0.545322
\(471\) 44.0404 2.02927
\(472\) 28.0383 1.29057
\(473\) −36.3110 −1.66958
\(474\) −3.74139 −0.171848
\(475\) 35.8311 1.64404
\(476\) −97.3832 −4.46355
\(477\) 21.9711 1.00599
\(478\) −25.1250 −1.14919
\(479\) −13.0730 −0.597322 −0.298661 0.954359i \(-0.596540\pi\)
−0.298661 + 0.954359i \(0.596540\pi\)
\(480\) −1.21385 −0.0554044
\(481\) 1.90831 0.0870116
\(482\) −25.5173 −1.16228
\(483\) 50.9512 2.31836
\(484\) −5.27442 −0.239746
\(485\) −3.82428 −0.173652
\(486\) −49.7017 −2.25452
\(487\) −2.76391 −0.125245 −0.0626223 0.998037i \(-0.519946\pi\)
−0.0626223 + 0.998037i \(0.519946\pi\)
\(488\) 12.9054 0.584199
\(489\) 23.7969 1.07613
\(490\) 16.9028 0.763590
\(491\) −1.93759 −0.0874423 −0.0437212 0.999044i \(-0.513921\pi\)
−0.0437212 + 0.999044i \(0.513921\pi\)
\(492\) −108.823 −4.90614
\(493\) 26.5115 1.19402
\(494\) 21.0116 0.945354
\(495\) 3.36186 0.151104
\(496\) 43.7728 1.96546
\(497\) −4.71625 −0.211553
\(498\) 68.1839 3.05540
\(499\) 15.2449 0.682457 0.341228 0.939980i \(-0.389157\pi\)
0.341228 + 0.939980i \(0.389157\pi\)
\(500\) 18.0799 0.808558
\(501\) −35.2789 −1.57614
\(502\) 19.7584 0.881859
\(503\) −10.9172 −0.486775 −0.243388 0.969929i \(-0.578259\pi\)
−0.243388 + 0.969929i \(0.578259\pi\)
\(504\) −59.2997 −2.64142
\(505\) −5.64128 −0.251034
\(506\) −35.8208 −1.59243
\(507\) 27.2117 1.20851
\(508\) 42.6858 1.89388
\(509\) 15.9153 0.705435 0.352717 0.935730i \(-0.385258\pi\)
0.352717 + 0.935730i \(0.385258\pi\)
\(510\) 12.9376 0.572886
\(511\) −2.10762 −0.0932356
\(512\) 43.6728 1.93008
\(513\) −10.3315 −0.456145
\(514\) 31.7464 1.40027
\(515\) 7.74779 0.341408
\(516\) −111.416 −4.90484
\(517\) 33.2357 1.46171
\(518\) −19.5553 −0.859209
\(519\) 7.78484 0.341717
\(520\) 2.66836 0.117015
\(521\) 2.98286 0.130681 0.0653407 0.997863i \(-0.479187\pi\)
0.0653407 + 0.997863i \(0.479187\pi\)
\(522\) 31.4136 1.37494
\(523\) 21.4568 0.938242 0.469121 0.883134i \(-0.344571\pi\)
0.469121 + 0.883134i \(0.344571\pi\)
\(524\) 25.2406 1.10264
\(525\) 52.6174 2.29641
\(526\) 40.4748 1.76478
\(527\) −46.7420 −2.03611
\(528\) 34.0607 1.48230
\(529\) −1.40594 −0.0611277
\(530\) 10.1311 0.440067
\(531\) −12.8961 −0.559644
\(532\) −144.886 −6.28160
\(533\) 12.9474 0.560814
\(534\) −82.9025 −3.58754
\(535\) −6.05661 −0.261850
\(536\) −13.1714 −0.568919
\(537\) −3.82283 −0.164967
\(538\) −36.4810 −1.57281
\(539\) −47.5184 −2.04676
\(540\) −2.55307 −0.109867
\(541\) 27.0603 1.16341 0.581706 0.813399i \(-0.302386\pi\)
0.581706 + 0.813399i \(0.302386\pi\)
\(542\) −28.7217 −1.23370
\(543\) −55.6189 −2.38683
\(544\) 5.84309 0.250520
\(545\) −4.86204 −0.208267
\(546\) 30.8551 1.32048
\(547\) 0.931059 0.0398092 0.0199046 0.999802i \(-0.493664\pi\)
0.0199046 + 0.999802i \(0.493664\pi\)
\(548\) −0.887846 −0.0379269
\(549\) −5.93579 −0.253333
\(550\) −36.9922 −1.57735
\(551\) 39.4436 1.68035
\(552\) −56.4847 −2.40415
\(553\) −3.06945 −0.130526
\(554\) 45.0705 1.91486
\(555\) 1.74818 0.0742062
\(556\) 72.8142 3.08801
\(557\) −25.9303 −1.09870 −0.549351 0.835591i \(-0.685125\pi\)
−0.549351 + 0.835591i \(0.685125\pi\)
\(558\) −55.3848 −2.34462
\(559\) 13.2559 0.560666
\(560\) −9.93983 −0.420034
\(561\) −36.3711 −1.53559
\(562\) 37.4900 1.58142
\(563\) −16.6768 −0.702845 −0.351423 0.936217i \(-0.614302\pi\)
−0.351423 + 0.936217i \(0.614302\pi\)
\(564\) 101.980 4.29414
\(565\) 0.448444 0.0188662
\(566\) 24.7079 1.03855
\(567\) −49.1967 −2.06607
\(568\) 5.22846 0.219381
\(569\) 18.4139 0.771952 0.385976 0.922509i \(-0.373865\pi\)
0.385976 + 0.922509i \(0.373865\pi\)
\(570\) 19.2484 0.806228
\(571\) 39.1999 1.64046 0.820232 0.572032i \(-0.193845\pi\)
0.820232 + 0.572032i \(0.193845\pi\)
\(572\) −14.5970 −0.610329
\(573\) 29.9820 1.25252
\(574\) −132.677 −5.53784
\(575\) 22.3002 0.929982
\(576\) −15.6805 −0.653353
\(577\) −10.1310 −0.421759 −0.210879 0.977512i \(-0.567633\pi\)
−0.210879 + 0.977512i \(0.567633\pi\)
\(578\) −20.2409 −0.841910
\(579\) 15.7516 0.654613
\(580\) 9.74715 0.404728
\(581\) 55.9385 2.32072
\(582\) 49.0242 2.03212
\(583\) −28.4813 −1.17958
\(584\) 2.33652 0.0966857
\(585\) −1.22730 −0.0507427
\(586\) −21.6256 −0.893345
\(587\) −39.3123 −1.62259 −0.811296 0.584636i \(-0.801237\pi\)
−0.811296 + 0.584636i \(0.801237\pi\)
\(588\) −145.805 −6.01290
\(589\) −69.5422 −2.86544
\(590\) −5.94655 −0.244815
\(591\) −7.05472 −0.290192
\(592\) 7.88064 0.323892
\(593\) 16.8202 0.690723 0.345361 0.938470i \(-0.387756\pi\)
0.345361 + 0.938470i \(0.387756\pi\)
\(594\) 10.6663 0.437642
\(595\) 10.6141 0.435134
\(596\) 95.4600 3.91019
\(597\) 27.8538 1.13998
\(598\) 13.0770 0.534757
\(599\) 27.5468 1.12553 0.562766 0.826616i \(-0.309737\pi\)
0.562766 + 0.826616i \(0.309737\pi\)
\(600\) −58.3318 −2.38139
\(601\) −30.8954 −1.26025 −0.630124 0.776495i \(-0.716996\pi\)
−0.630124 + 0.776495i \(0.716996\pi\)
\(602\) −135.839 −5.53638
\(603\) 6.05816 0.246707
\(604\) 75.1211 3.05664
\(605\) 0.574873 0.0233719
\(606\) 72.3166 2.93766
\(607\) −17.5847 −0.713742 −0.356871 0.934154i \(-0.616156\pi\)
−0.356871 + 0.934154i \(0.616156\pi\)
\(608\) 8.69330 0.352560
\(609\) 57.9223 2.34713
\(610\) −2.73706 −0.110820
\(611\) −12.1332 −0.490858
\(612\) −49.6556 −2.00721
\(613\) −25.2380 −1.01935 −0.509676 0.860366i \(-0.670235\pi\)
−0.509676 + 0.860366i \(0.670235\pi\)
\(614\) −30.0508 −1.21275
\(615\) 11.8610 0.478280
\(616\) 76.8707 3.09721
\(617\) −42.2751 −1.70193 −0.850966 0.525220i \(-0.823983\pi\)
−0.850966 + 0.525220i \(0.823983\pi\)
\(618\) −99.3203 −3.99525
\(619\) 18.8517 0.757713 0.378856 0.925455i \(-0.376317\pi\)
0.378856 + 0.925455i \(0.376317\pi\)
\(620\) −17.1850 −0.690166
\(621\) −6.43000 −0.258027
\(622\) −30.9610 −1.24142
\(623\) −68.0136 −2.72491
\(624\) −12.4344 −0.497775
\(625\) 22.0239 0.880956
\(626\) 6.27073 0.250629
\(627\) −54.1126 −2.16105
\(628\) −77.9419 −3.11022
\(629\) −8.41520 −0.335536
\(630\) 12.5767 0.501066
\(631\) −5.31278 −0.211498 −0.105749 0.994393i \(-0.533724\pi\)
−0.105749 + 0.994393i \(0.533724\pi\)
\(632\) 3.40281 0.135356
\(633\) 46.9744 1.86707
\(634\) 34.0632 1.35282
\(635\) −4.65244 −0.184627
\(636\) −87.3919 −3.46531
\(637\) 17.3474 0.687327
\(638\) −40.7218 −1.61219
\(639\) −2.40481 −0.0951329
\(640\) −8.27468 −0.327086
\(641\) −21.3290 −0.842447 −0.421223 0.906957i \(-0.638399\pi\)
−0.421223 + 0.906957i \(0.638399\pi\)
\(642\) 77.6408 3.06424
\(643\) −10.5159 −0.414706 −0.207353 0.978266i \(-0.566485\pi\)
−0.207353 + 0.978266i \(0.566485\pi\)
\(644\) −90.1727 −3.55330
\(645\) 12.1436 0.478153
\(646\) −92.6558 −3.64550
\(647\) 20.2878 0.797595 0.398798 0.917039i \(-0.369428\pi\)
0.398798 + 0.917039i \(0.369428\pi\)
\(648\) 54.5397 2.14252
\(649\) 16.7174 0.656214
\(650\) 13.5046 0.529694
\(651\) −102.122 −4.00247
\(652\) −42.1154 −1.64937
\(653\) 0.520755 0.0203787 0.0101894 0.999948i \(-0.496757\pi\)
0.0101894 + 0.999948i \(0.496757\pi\)
\(654\) 62.3273 2.43719
\(655\) −2.75104 −0.107492
\(656\) 53.4681 2.08758
\(657\) −1.07467 −0.0419270
\(658\) 124.334 4.84705
\(659\) −8.45241 −0.329259 −0.164630 0.986355i \(-0.552643\pi\)
−0.164630 + 0.986355i \(0.552643\pi\)
\(660\) −13.3721 −0.520508
\(661\) −4.42208 −0.171999 −0.0859994 0.996295i \(-0.527408\pi\)
−0.0859994 + 0.996295i \(0.527408\pi\)
\(662\) 43.9807 1.70936
\(663\) 13.2779 0.515670
\(664\) −62.0136 −2.40660
\(665\) 15.7915 0.612368
\(666\) −9.97121 −0.386376
\(667\) 24.5485 0.950523
\(668\) 62.4360 2.41572
\(669\) 48.0308 1.85698
\(670\) 2.79348 0.107922
\(671\) 7.69462 0.297048
\(672\) 12.7660 0.492458
\(673\) −39.6119 −1.52693 −0.763464 0.645851i \(-0.776503\pi\)
−0.763464 + 0.645851i \(0.776503\pi\)
\(674\) 62.5450 2.40914
\(675\) −6.64026 −0.255584
\(676\) −48.1589 −1.85226
\(677\) −5.69647 −0.218933 −0.109467 0.993990i \(-0.534914\pi\)
−0.109467 + 0.993990i \(0.534914\pi\)
\(678\) −5.74869 −0.220777
\(679\) 40.2197 1.54349
\(680\) −11.7668 −0.451236
\(681\) 69.1681 2.65053
\(682\) 71.7958 2.74920
\(683\) 15.2851 0.584869 0.292434 0.956286i \(-0.405535\pi\)
0.292434 + 0.956286i \(0.405535\pi\)
\(684\) −73.8772 −2.82476
\(685\) 0.0967688 0.00369735
\(686\) −96.1309 −3.67030
\(687\) 36.1310 1.37848
\(688\) 54.7421 2.08702
\(689\) 10.3976 0.396116
\(690\) 11.9797 0.456058
\(691\) −1.50943 −0.0574215 −0.0287107 0.999588i \(-0.509140\pi\)
−0.0287107 + 0.999588i \(0.509140\pi\)
\(692\) −13.7775 −0.523742
\(693\) −35.3564 −1.34308
\(694\) −9.86572 −0.374498
\(695\) −7.93623 −0.301038
\(696\) −64.2129 −2.43399
\(697\) −57.0949 −2.16262
\(698\) 20.1291 0.761897
\(699\) 10.8567 0.410636
\(700\) −93.1214 −3.51966
\(701\) −4.31140 −0.162839 −0.0814197 0.996680i \(-0.525945\pi\)
−0.0814197 + 0.996680i \(0.525945\pi\)
\(702\) −3.89389 −0.146965
\(703\) −12.5201 −0.472203
\(704\) 20.3267 0.766093
\(705\) −11.1151 −0.418619
\(706\) −37.3841 −1.40697
\(707\) 59.3290 2.23129
\(708\) 51.2955 1.92780
\(709\) −23.9421 −0.899165 −0.449582 0.893239i \(-0.648427\pi\)
−0.449582 + 0.893239i \(0.648427\pi\)
\(710\) −1.10889 −0.0416157
\(711\) −1.56511 −0.0586963
\(712\) 75.4002 2.82574
\(713\) −43.2810 −1.62089
\(714\) −136.064 −5.09205
\(715\) 1.59096 0.0594986
\(716\) 6.76558 0.252842
\(717\) −23.6220 −0.882181
\(718\) −53.7859 −2.00727
\(719\) −44.0363 −1.64228 −0.821138 0.570730i \(-0.806660\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(720\) −5.06831 −0.188885
\(721\) −81.4829 −3.03458
\(722\) −90.8705 −3.38185
\(723\) −23.9909 −0.892233
\(724\) 98.4334 3.65825
\(725\) 25.3513 0.941523
\(726\) −7.36940 −0.273504
\(727\) 8.40336 0.311663 0.155832 0.987784i \(-0.450194\pi\)
0.155832 + 0.987784i \(0.450194\pi\)
\(728\) −28.0629 −1.04008
\(729\) −15.4347 −0.571657
\(730\) −0.495543 −0.0183409
\(731\) −58.4554 −2.16205
\(732\) 23.6101 0.872655
\(733\) 26.5469 0.980532 0.490266 0.871573i \(-0.336900\pi\)
0.490266 + 0.871573i \(0.336900\pi\)
\(734\) −68.1639 −2.51598
\(735\) 15.8917 0.586174
\(736\) 5.41045 0.199432
\(737\) −7.85325 −0.289278
\(738\) −67.6520 −2.49031
\(739\) 10.8180 0.397947 0.198974 0.980005i \(-0.436239\pi\)
0.198974 + 0.980005i \(0.436239\pi\)
\(740\) −3.09391 −0.113734
\(741\) 19.7547 0.725706
\(742\) −106.548 −3.91150
\(743\) −7.84366 −0.287756 −0.143878 0.989595i \(-0.545957\pi\)
−0.143878 + 0.989595i \(0.545957\pi\)
\(744\) 113.213 4.15057
\(745\) −10.4044 −0.381189
\(746\) −20.0324 −0.733438
\(747\) 28.5230 1.04360
\(748\) 64.3690 2.35357
\(749\) 63.6969 2.32744
\(750\) 25.2612 0.922409
\(751\) 20.7755 0.758110 0.379055 0.925374i \(-0.376249\pi\)
0.379055 + 0.925374i \(0.376249\pi\)
\(752\) −50.1059 −1.82717
\(753\) 18.5765 0.676964
\(754\) 14.8662 0.541393
\(755\) −8.18766 −0.297979
\(756\) 26.8504 0.976541
\(757\) −26.3390 −0.957305 −0.478653 0.878004i \(-0.658875\pi\)
−0.478653 + 0.878004i \(0.658875\pi\)
\(758\) 80.6606 2.92972
\(759\) −33.6781 −1.22244
\(760\) −17.5065 −0.635029
\(761\) 27.3512 0.991482 0.495741 0.868470i \(-0.334897\pi\)
0.495741 + 0.868470i \(0.334897\pi\)
\(762\) 59.6405 2.16055
\(763\) 51.1337 1.85116
\(764\) −53.0617 −1.91970
\(765\) 5.41210 0.195675
\(766\) 49.2991 1.78125
\(767\) −6.10295 −0.220365
\(768\) 75.7569 2.73364
\(769\) −6.35042 −0.229002 −0.114501 0.993423i \(-0.536527\pi\)
−0.114501 + 0.993423i \(0.536527\pi\)
\(770\) −16.3032 −0.587528
\(771\) 29.8474 1.07493
\(772\) −27.8769 −1.00331
\(773\) 41.9948 1.51045 0.755223 0.655468i \(-0.227528\pi\)
0.755223 + 0.655468i \(0.227528\pi\)
\(774\) −69.2641 −2.48965
\(775\) −44.6964 −1.60554
\(776\) −44.5877 −1.60061
\(777\) −18.3855 −0.659576
\(778\) 37.3177 1.33791
\(779\) −84.9453 −3.04348
\(780\) 4.88170 0.174793
\(781\) 3.11738 0.111549
\(782\) −57.6663 −2.06214
\(783\) −7.30974 −0.261229
\(784\) 71.6383 2.55851
\(785\) 8.49511 0.303203
\(786\) 35.2661 1.25790
\(787\) 14.1240 0.503467 0.251734 0.967797i \(-0.418999\pi\)
0.251734 + 0.967797i \(0.418999\pi\)
\(788\) 12.4853 0.444771
\(789\) 38.0537 1.35475
\(790\) −0.721690 −0.0256766
\(791\) −4.71625 −0.167691
\(792\) 39.1963 1.39278
\(793\) −2.80905 −0.0997521
\(794\) −21.9306 −0.778287
\(795\) 9.52508 0.337820
\(796\) −49.2953 −1.74723
\(797\) −15.9738 −0.565821 −0.282910 0.959146i \(-0.591300\pi\)
−0.282910 + 0.959146i \(0.591300\pi\)
\(798\) −202.434 −7.16609
\(799\) 53.5046 1.89286
\(800\) 5.58738 0.197544
\(801\) −34.6801 −1.22536
\(802\) 41.9864 1.48259
\(803\) 1.39311 0.0491617
\(804\) −24.0969 −0.849830
\(805\) 9.82817 0.346397
\(806\) −26.2102 −0.923215
\(807\) −34.2988 −1.20738
\(808\) −65.7723 −2.31386
\(809\) 32.8254 1.15408 0.577040 0.816716i \(-0.304208\pi\)
0.577040 + 0.816716i \(0.304208\pi\)
\(810\) −11.5671 −0.406428
\(811\) −2.95930 −0.103915 −0.0519576 0.998649i \(-0.516546\pi\)
−0.0519576 + 0.998649i \(0.516546\pi\)
\(812\) −102.510 −3.59740
\(813\) −27.0037 −0.947060
\(814\) 12.9258 0.453048
\(815\) 4.59027 0.160790
\(816\) 54.8328 1.91953
\(817\) −86.9694 −3.04267
\(818\) 29.0663 1.01628
\(819\) 12.9074 0.451022
\(820\) −20.9913 −0.733050
\(821\) 37.0895 1.29443 0.647217 0.762306i \(-0.275933\pi\)
0.647217 + 0.762306i \(0.275933\pi\)
\(822\) −1.24050 −0.0432673
\(823\) −17.2461 −0.601160 −0.300580 0.953757i \(-0.597180\pi\)
−0.300580 + 0.953757i \(0.597180\pi\)
\(824\) 90.3323 3.14687
\(825\) −34.7794 −1.21086
\(826\) 62.5394 2.17602
\(827\) −36.7882 −1.27925 −0.639626 0.768686i \(-0.720911\pi\)
−0.639626 + 0.768686i \(0.720911\pi\)
\(828\) −45.9790 −1.59788
\(829\) 4.40770 0.153086 0.0765429 0.997066i \(-0.475612\pi\)
0.0765429 + 0.997066i \(0.475612\pi\)
\(830\) 13.1523 0.456521
\(831\) 42.3745 1.46996
\(832\) −7.42060 −0.257263
\(833\) −76.4976 −2.65049
\(834\) 101.736 3.52283
\(835\) −6.80507 −0.235499
\(836\) 95.7677 3.31219
\(837\) 12.8877 0.445463
\(838\) 16.7803 0.579665
\(839\) −51.6154 −1.78196 −0.890981 0.454040i \(-0.849982\pi\)
−0.890981 + 0.454040i \(0.849982\pi\)
\(840\) −25.7081 −0.887013
\(841\) −1.09274 −0.0376807
\(842\) 6.90833 0.238077
\(843\) 35.2475 1.21399
\(844\) −83.1346 −2.86161
\(845\) 5.24897 0.180570
\(846\) 63.3979 2.17966
\(847\) −6.04590 −0.207739
\(848\) 42.9382 1.47450
\(849\) 23.2299 0.797247
\(850\) −59.5520 −2.04262
\(851\) −7.79211 −0.267110
\(852\) 9.56535 0.327704
\(853\) −27.8865 −0.954817 −0.477408 0.878682i \(-0.658424\pi\)
−0.477408 + 0.878682i \(0.658424\pi\)
\(854\) 28.7854 0.985017
\(855\) 8.05208 0.275375
\(856\) −70.6147 −2.41356
\(857\) 6.93319 0.236833 0.118417 0.992964i \(-0.462218\pi\)
0.118417 + 0.992964i \(0.462218\pi\)
\(858\) −20.3948 −0.696268
\(859\) 26.3868 0.900305 0.450152 0.892952i \(-0.351370\pi\)
0.450152 + 0.892952i \(0.351370\pi\)
\(860\) −21.4915 −0.732855
\(861\) −124.741 −4.25116
\(862\) −23.1651 −0.789007
\(863\) 35.6393 1.21318 0.606588 0.795017i \(-0.292538\pi\)
0.606588 + 0.795017i \(0.292538\pi\)
\(864\) −1.61105 −0.0548091
\(865\) 1.50165 0.0510575
\(866\) 39.0020 1.32534
\(867\) −19.0301 −0.646297
\(868\) 180.733 6.13449
\(869\) 2.02887 0.0688246
\(870\) 13.6187 0.461717
\(871\) 2.86695 0.0971430
\(872\) −56.6870 −1.91966
\(873\) 20.5080 0.694090
\(874\) −85.7953 −2.90207
\(875\) 20.7244 0.700614
\(876\) 4.27460 0.144426
\(877\) −26.9121 −0.908756 −0.454378 0.890809i \(-0.650138\pi\)
−0.454378 + 0.890809i \(0.650138\pi\)
\(878\) 44.9716 1.51772
\(879\) −20.3320 −0.685781
\(880\) 6.57010 0.221478
\(881\) −41.5155 −1.39869 −0.699347 0.714782i \(-0.746526\pi\)
−0.699347 + 0.714782i \(0.746526\pi\)
\(882\) −90.6424 −3.05209
\(883\) 45.6593 1.53656 0.768278 0.640116i \(-0.221114\pi\)
0.768278 + 0.640116i \(0.221114\pi\)
\(884\) −23.4990 −0.790355
\(885\) −5.59084 −0.187934
\(886\) −20.6991 −0.695400
\(887\) −58.9336 −1.97880 −0.989399 0.145226i \(-0.953609\pi\)
−0.989399 + 0.145226i \(0.953609\pi\)
\(888\) 20.3822 0.683983
\(889\) 48.9294 1.64104
\(890\) −15.9914 −0.536032
\(891\) 32.5184 1.08941
\(892\) −85.0042 −2.84615
\(893\) 79.6037 2.66384
\(894\) 133.376 4.46078
\(895\) −0.737399 −0.0246485
\(896\) 87.0242 2.90728
\(897\) 12.2947 0.410509
\(898\) −32.0826 −1.07061
\(899\) −49.2027 −1.64100
\(900\) −47.4825 −1.58275
\(901\) −45.8507 −1.52751
\(902\) 87.6980 2.92002
\(903\) −127.713 −4.25003
\(904\) 5.22846 0.173896
\(905\) −10.7285 −0.356628
\(906\) 104.959 3.48703
\(907\) −55.5112 −1.84322 −0.921609 0.388120i \(-0.873125\pi\)
−0.921609 + 0.388120i \(0.873125\pi\)
\(908\) −122.413 −4.06240
\(909\) 30.2518 1.00339
\(910\) 5.95176 0.197299
\(911\) −12.8600 −0.426069 −0.213035 0.977045i \(-0.568335\pi\)
−0.213035 + 0.977045i \(0.568335\pi\)
\(912\) 81.5797 2.70137
\(913\) −36.9746 −1.22368
\(914\) −13.7341 −0.454285
\(915\) −2.57333 −0.0850717
\(916\) −63.9441 −2.11277
\(917\) 28.9325 0.955436
\(918\) 17.1711 0.566731
\(919\) 45.9234 1.51487 0.757437 0.652908i \(-0.226451\pi\)
0.757437 + 0.652908i \(0.226451\pi\)
\(920\) −10.8956 −0.359216
\(921\) −28.2533 −0.930976
\(922\) −10.0520 −0.331046
\(923\) −1.13805 −0.0374594
\(924\) 140.633 4.62650
\(925\) −8.04692 −0.264581
\(926\) −3.49962 −0.115005
\(927\) −41.5481 −1.36462
\(928\) 6.15071 0.201907
\(929\) 12.4602 0.408805 0.204403 0.978887i \(-0.434475\pi\)
0.204403 + 0.978887i \(0.434475\pi\)
\(930\) −24.0109 −0.787347
\(931\) −113.812 −3.73005
\(932\) −19.2139 −0.629373
\(933\) −29.1090 −0.952986
\(934\) 96.8085 3.16767
\(935\) −7.01576 −0.229440
\(936\) −14.3092 −0.467712
\(937\) −0.216022 −0.00705713 −0.00352857 0.999994i \(-0.501123\pi\)
−0.00352857 + 0.999994i \(0.501123\pi\)
\(938\) −29.3788 −0.959253
\(939\) 5.89562 0.192396
\(940\) 19.6714 0.641609
\(941\) −19.2443 −0.627347 −0.313674 0.949531i \(-0.601560\pi\)
−0.313674 + 0.949531i \(0.601560\pi\)
\(942\) −108.900 −3.54816
\(943\) −52.8675 −1.72160
\(944\) −25.2030 −0.820286
\(945\) −2.92650 −0.0951992
\(946\) 89.7877 2.91925
\(947\) 24.3233 0.790402 0.395201 0.918595i \(-0.370675\pi\)
0.395201 + 0.918595i \(0.370675\pi\)
\(948\) 6.22537 0.202190
\(949\) −0.508577 −0.0165091
\(950\) −88.6009 −2.87459
\(951\) 32.0256 1.03850
\(952\) 123.751 4.01078
\(953\) −4.24632 −0.137552 −0.0687759 0.997632i \(-0.521909\pi\)
−0.0687759 + 0.997632i \(0.521909\pi\)
\(954\) −54.3288 −1.75896
\(955\) 5.78334 0.187144
\(956\) 41.8059 1.35210
\(957\) −38.2859 −1.23761
\(958\) 32.3262 1.04441
\(959\) −1.01771 −0.0328636
\(960\) −6.79792 −0.219402
\(961\) 55.7483 1.79833
\(962\) −4.71876 −0.152139
\(963\) 32.4790 1.04662
\(964\) 42.4588 1.36751
\(965\) 3.03838 0.0978089
\(966\) −125.989 −4.05363
\(967\) −9.02839 −0.290333 −0.145167 0.989407i \(-0.546372\pi\)
−0.145167 + 0.989407i \(0.546372\pi\)
\(968\) 6.70251 0.215427
\(969\) −87.1134 −2.79848
\(970\) 9.45646 0.303629
\(971\) 45.7744 1.46897 0.734485 0.678625i \(-0.237424\pi\)
0.734485 + 0.678625i \(0.237424\pi\)
\(972\) 82.6997 2.65259
\(973\) 83.4647 2.67575
\(974\) 6.83442 0.218989
\(975\) 12.6968 0.406622
\(976\) −11.6003 −0.371318
\(977\) −24.5663 −0.785945 −0.392973 0.919550i \(-0.628553\pi\)
−0.392973 + 0.919550i \(0.628553\pi\)
\(978\) −58.8435 −1.88161
\(979\) 44.9561 1.43680
\(980\) −28.1249 −0.898417
\(981\) 26.0730 0.832447
\(982\) 4.79116 0.152892
\(983\) 0.806857 0.0257347 0.0128674 0.999917i \(-0.495904\pi\)
0.0128674 + 0.999917i \(0.495904\pi\)
\(984\) 138.288 4.40847
\(985\) −1.36081 −0.0433590
\(986\) −65.5561 −2.08773
\(987\) 116.897 3.72087
\(988\) −34.9615 −1.11227
\(989\) −54.1272 −1.72114
\(990\) −8.31301 −0.264205
\(991\) 13.9277 0.442428 0.221214 0.975225i \(-0.428998\pi\)
0.221214 + 0.975225i \(0.428998\pi\)
\(992\) −10.8442 −0.344303
\(993\) 41.3499 1.31220
\(994\) 11.6621 0.369898
\(995\) 5.37283 0.170330
\(996\) −113.453 −3.59488
\(997\) −48.7826 −1.54496 −0.772480 0.635039i \(-0.780984\pi\)
−0.772480 + 0.635039i \(0.780984\pi\)
\(998\) −37.6967 −1.19327
\(999\) 2.32023 0.0734089
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 \(a_p\))