Properties

Label 4019.2.a.b.1.14
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.55030 q^{2}\) \(+3.02512 q^{3}\) \(+4.50404 q^{4}\) \(-1.05624 q^{5}\) \(-7.71496 q^{6}\) \(+5.05580 q^{7}\) \(-6.38607 q^{8}\) \(+6.15132 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.55030 q^{2}\) \(+3.02512 q^{3}\) \(+4.50404 q^{4}\) \(-1.05624 q^{5}\) \(-7.71496 q^{6}\) \(+5.05580 q^{7}\) \(-6.38607 q^{8}\) \(+6.15132 q^{9}\) \(+2.69374 q^{10}\) \(-0.831588 q^{11}\) \(+13.6253 q^{12}\) \(+4.92701 q^{13}\) \(-12.8938 q^{14}\) \(-3.19526 q^{15}\) \(+7.27832 q^{16}\) \(+2.01746 q^{17}\) \(-15.6877 q^{18}\) \(+1.20792 q^{19}\) \(-4.75737 q^{20}\) \(+15.2944 q^{21}\) \(+2.12080 q^{22}\) \(-1.13685 q^{23}\) \(-19.3186 q^{24}\) \(-3.88435 q^{25}\) \(-12.5654 q^{26}\) \(+9.53312 q^{27}\) \(+22.7715 q^{28}\) \(+0.739150 q^{29}\) \(+8.14889 q^{30}\) \(+6.03259 q^{31}\) \(-5.78979 q^{32}\) \(-2.51565 q^{33}\) \(-5.14513 q^{34}\) \(-5.34016 q^{35}\) \(+27.7058 q^{36}\) \(-4.84051 q^{37}\) \(-3.08057 q^{38}\) \(+14.9048 q^{39}\) \(+6.74525 q^{40}\) \(-8.88368 q^{41}\) \(-39.0053 q^{42}\) \(+0.443812 q^{43}\) \(-3.74551 q^{44}\) \(-6.49730 q^{45}\) \(+2.89932 q^{46}\) \(+5.43952 q^{47}\) \(+22.0178 q^{48}\) \(+18.5611 q^{49}\) \(+9.90626 q^{50}\) \(+6.10304 q^{51}\) \(+22.1915 q^{52}\) \(+2.61411 q^{53}\) \(-24.3123 q^{54}\) \(+0.878361 q^{55}\) \(-32.2867 q^{56}\) \(+3.65410 q^{57}\) \(-1.88506 q^{58}\) \(+9.90028 q^{59}\) \(-14.3916 q^{60}\) \(-3.30195 q^{61}\) \(-15.3849 q^{62}\) \(+31.0999 q^{63}\) \(+0.209065 q^{64}\) \(-5.20413 q^{65}\) \(+6.41567 q^{66}\) \(+8.70028 q^{67}\) \(+9.08672 q^{68}\) \(-3.43911 q^{69}\) \(+13.6190 q^{70}\) \(-8.26681 q^{71}\) \(-39.2828 q^{72}\) \(-6.47664 q^{73}\) \(+12.3448 q^{74}\) \(-11.7506 q^{75}\) \(+5.44053 q^{76}\) \(-4.20434 q^{77}\) \(-38.0117 q^{78}\) \(-6.44420 q^{79}\) \(-7.68769 q^{80}\) \(+10.3848 q^{81}\) \(+22.6561 q^{82}\) \(-0.268665 q^{83}\) \(+68.8866 q^{84}\) \(-2.13093 q^{85}\) \(-1.13185 q^{86}\) \(+2.23602 q^{87}\) \(+5.31058 q^{88}\) \(-3.30186 q^{89}\) \(+16.5701 q^{90}\) \(+24.9100 q^{91}\) \(-5.12043 q^{92}\) \(+18.2493 q^{93}\) \(-13.8724 q^{94}\) \(-1.27586 q^{95}\) \(-17.5148 q^{96}\) \(+6.16415 q^{97}\) \(-47.3365 q^{98}\) \(-5.11537 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55030 −1.80334 −0.901668 0.432429i \(-0.857657\pi\)
−0.901668 + 0.432429i \(0.857657\pi\)
\(3\) 3.02512 1.74655 0.873276 0.487227i \(-0.161991\pi\)
0.873276 + 0.487227i \(0.161991\pi\)
\(4\) 4.50404 2.25202
\(5\) −1.05624 −0.472367 −0.236184 0.971708i \(-0.575897\pi\)
−0.236184 + 0.971708i \(0.575897\pi\)
\(6\) −7.71496 −3.14962
\(7\) 5.05580 1.91091 0.955456 0.295132i \(-0.0953636\pi\)
0.955456 + 0.295132i \(0.0953636\pi\)
\(8\) −6.38607 −2.25782
\(9\) 6.15132 2.05044
\(10\) 2.69374 0.851837
\(11\) −0.831588 −0.250733 −0.125367 0.992110i \(-0.540011\pi\)
−0.125367 + 0.992110i \(0.540011\pi\)
\(12\) 13.6253 3.93327
\(13\) 4.92701 1.36651 0.683253 0.730182i \(-0.260565\pi\)
0.683253 + 0.730182i \(0.260565\pi\)
\(14\) −12.8938 −3.44602
\(15\) −3.19526 −0.825013
\(16\) 7.27832 1.81958
\(17\) 2.01746 0.489305 0.244653 0.969611i \(-0.421326\pi\)
0.244653 + 0.969611i \(0.421326\pi\)
\(18\) −15.6877 −3.69763
\(19\) 1.20792 0.277116 0.138558 0.990354i \(-0.455753\pi\)
0.138558 + 0.990354i \(0.455753\pi\)
\(20\) −4.75737 −1.06378
\(21\) 15.2944 3.33751
\(22\) 2.12080 0.452156
\(23\) −1.13685 −0.237050 −0.118525 0.992951i \(-0.537817\pi\)
−0.118525 + 0.992951i \(0.537817\pi\)
\(24\) −19.3186 −3.94339
\(25\) −3.88435 −0.776869
\(26\) −12.5654 −2.46427
\(27\) 9.53312 1.83465
\(28\) 22.7715 4.30342
\(29\) 0.739150 0.137257 0.0686284 0.997642i \(-0.478138\pi\)
0.0686284 + 0.997642i \(0.478138\pi\)
\(30\) 8.14889 1.48778
\(31\) 6.03259 1.08349 0.541743 0.840544i \(-0.317765\pi\)
0.541743 + 0.840544i \(0.317765\pi\)
\(32\) −5.78979 −1.02350
\(33\) −2.51565 −0.437918
\(34\) −5.14513 −0.882382
\(35\) −5.34016 −0.902652
\(36\) 27.7058 4.61764
\(37\) −4.84051 −0.795775 −0.397887 0.917434i \(-0.630256\pi\)
−0.397887 + 0.917434i \(0.630256\pi\)
\(38\) −3.08057 −0.499734
\(39\) 14.9048 2.38667
\(40\) 6.74525 1.06652
\(41\) −8.88368 −1.38740 −0.693699 0.720265i \(-0.744020\pi\)
−0.693699 + 0.720265i \(0.744020\pi\)
\(42\) −39.0053 −6.01865
\(43\) 0.443812 0.0676807 0.0338403 0.999427i \(-0.489226\pi\)
0.0338403 + 0.999427i \(0.489226\pi\)
\(44\) −3.74551 −0.564657
\(45\) −6.49730 −0.968561
\(46\) 2.89932 0.427481
\(47\) 5.43952 0.793435 0.396718 0.917941i \(-0.370149\pi\)
0.396718 + 0.917941i \(0.370149\pi\)
\(48\) 22.0178 3.17799
\(49\) 18.5611 2.65159
\(50\) 9.90626 1.40096
\(51\) 6.10304 0.854597
\(52\) 22.1915 3.07740
\(53\) 2.61411 0.359076 0.179538 0.983751i \(-0.442540\pi\)
0.179538 + 0.983751i \(0.442540\pi\)
\(54\) −24.3123 −3.30849
\(55\) 0.878361 0.118438
\(56\) −32.2867 −4.31449
\(57\) 3.65410 0.483998
\(58\) −1.88506 −0.247520
\(59\) 9.90028 1.28891 0.644453 0.764644i \(-0.277085\pi\)
0.644453 + 0.764644i \(0.277085\pi\)
\(60\) −14.3916 −1.85795
\(61\) −3.30195 −0.422771 −0.211385 0.977403i \(-0.567798\pi\)
−0.211385 + 0.977403i \(0.567798\pi\)
\(62\) −15.3849 −1.95389
\(63\) 31.0999 3.91821
\(64\) 0.209065 0.0261331
\(65\) −5.20413 −0.645493
\(66\) 6.41567 0.789714
\(67\) 8.70028 1.06291 0.531454 0.847087i \(-0.321646\pi\)
0.531454 + 0.847087i \(0.321646\pi\)
\(68\) 9.08672 1.10193
\(69\) −3.43911 −0.414020
\(70\) 13.6190 1.62779
\(71\) −8.26681 −0.981090 −0.490545 0.871416i \(-0.663202\pi\)
−0.490545 + 0.871416i \(0.663202\pi\)
\(72\) −39.2828 −4.62952
\(73\) −6.47664 −0.758034 −0.379017 0.925390i \(-0.623738\pi\)
−0.379017 + 0.925390i \(0.623738\pi\)
\(74\) 12.3448 1.43505
\(75\) −11.7506 −1.35684
\(76\) 5.44053 0.624072
\(77\) −4.20434 −0.479129
\(78\) −38.0117 −4.30397
\(79\) −6.44420 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(80\) −7.68769 −0.859510
\(81\) 10.3848 1.15387
\(82\) 22.6561 2.50194
\(83\) −0.268665 −0.0294898 −0.0147449 0.999891i \(-0.504694\pi\)
−0.0147449 + 0.999891i \(0.504694\pi\)
\(84\) 68.8866 7.51614
\(85\) −2.13093 −0.231132
\(86\) −1.13185 −0.122051
\(87\) 2.23602 0.239726
\(88\) 5.31058 0.566110
\(89\) −3.30186 −0.349997 −0.174998 0.984569i \(-0.555992\pi\)
−0.174998 + 0.984569i \(0.555992\pi\)
\(90\) 16.5701 1.74664
\(91\) 24.9100 2.61127
\(92\) −5.12043 −0.533842
\(93\) 18.2493 1.89236
\(94\) −13.8724 −1.43083
\(95\) −1.27586 −0.130901
\(96\) −17.5148 −1.78759
\(97\) 6.16415 0.625874 0.312937 0.949774i \(-0.398687\pi\)
0.312937 + 0.949774i \(0.398687\pi\)
\(98\) −47.3365 −4.78171
\(99\) −5.11537 −0.514114
\(100\) −17.4953 −1.74953
\(101\) −7.76806 −0.772951 −0.386475 0.922300i \(-0.626308\pi\)
−0.386475 + 0.922300i \(0.626308\pi\)
\(102\) −15.5646 −1.54113
\(103\) −13.5708 −1.33717 −0.668587 0.743634i \(-0.733101\pi\)
−0.668587 + 0.743634i \(0.733101\pi\)
\(104\) −31.4642 −3.08532
\(105\) −16.1546 −1.57653
\(106\) −6.66677 −0.647534
\(107\) −10.6971 −1.03413 −0.517066 0.855946i \(-0.672976\pi\)
−0.517066 + 0.855946i \(0.672976\pi\)
\(108\) 42.9376 4.13167
\(109\) −16.3758 −1.56852 −0.784260 0.620433i \(-0.786957\pi\)
−0.784260 + 0.620433i \(0.786957\pi\)
\(110\) −2.24009 −0.213584
\(111\) −14.6431 −1.38986
\(112\) 36.7978 3.47706
\(113\) 15.0452 1.41534 0.707668 0.706545i \(-0.249747\pi\)
0.707668 + 0.706545i \(0.249747\pi\)
\(114\) −9.31907 −0.872810
\(115\) 1.20079 0.111975
\(116\) 3.32917 0.309105
\(117\) 30.3076 2.80194
\(118\) −25.2487 −2.32433
\(119\) 10.1999 0.935020
\(120\) 20.4052 1.86273
\(121\) −10.3085 −0.937133
\(122\) 8.42096 0.762398
\(123\) −26.8741 −2.42316
\(124\) 27.1711 2.44003
\(125\) 9.38405 0.839335
\(126\) −79.3141 −7.06586
\(127\) 20.7453 1.84085 0.920426 0.390917i \(-0.127842\pi\)
0.920426 + 0.390917i \(0.127842\pi\)
\(128\) 11.0464 0.976373
\(129\) 1.34258 0.118208
\(130\) 13.2721 1.16404
\(131\) 1.65756 0.144821 0.0724107 0.997375i \(-0.476931\pi\)
0.0724107 + 0.997375i \(0.476931\pi\)
\(132\) −11.3306 −0.986202
\(133\) 6.10701 0.529545
\(134\) −22.1883 −1.91678
\(135\) −10.0693 −0.866628
\(136\) −12.8836 −1.10476
\(137\) 7.25442 0.619787 0.309893 0.950771i \(-0.399707\pi\)
0.309893 + 0.950771i \(0.399707\pi\)
\(138\) 8.77076 0.746617
\(139\) 11.3032 0.958726 0.479363 0.877617i \(-0.340868\pi\)
0.479363 + 0.877617i \(0.340868\pi\)
\(140\) −24.0523 −2.03279
\(141\) 16.4552 1.38578
\(142\) 21.0829 1.76924
\(143\) −4.09724 −0.342629
\(144\) 44.7713 3.73094
\(145\) −0.780724 −0.0648356
\(146\) 16.5174 1.36699
\(147\) 56.1495 4.63113
\(148\) −21.8019 −1.79210
\(149\) −9.28543 −0.760692 −0.380346 0.924844i \(-0.624195\pi\)
−0.380346 + 0.924844i \(0.624195\pi\)
\(150\) 29.9676 2.44684
\(151\) 14.6454 1.19182 0.595912 0.803050i \(-0.296791\pi\)
0.595912 + 0.803050i \(0.296791\pi\)
\(152\) −7.71387 −0.625678
\(153\) 12.4100 1.00329
\(154\) 10.7223 0.864032
\(155\) −6.37189 −0.511803
\(156\) 67.1317 5.37484
\(157\) −21.1198 −1.68554 −0.842770 0.538274i \(-0.819077\pi\)
−0.842770 + 0.538274i \(0.819077\pi\)
\(158\) 16.4347 1.30747
\(159\) 7.90798 0.627144
\(160\) 6.11543 0.483468
\(161\) −5.74769 −0.452982
\(162\) −26.4844 −2.08081
\(163\) −0.0323757 −0.00253586 −0.00126793 0.999999i \(-0.500404\pi\)
−0.00126793 + 0.999999i \(0.500404\pi\)
\(164\) −40.0125 −3.12445
\(165\) 2.65714 0.206858
\(166\) 0.685176 0.0531800
\(167\) 5.42944 0.420143 0.210071 0.977686i \(-0.432630\pi\)
0.210071 + 0.977686i \(0.432630\pi\)
\(168\) −97.6710 −7.53548
\(169\) 11.2754 0.867339
\(170\) 5.43452 0.416808
\(171\) 7.43031 0.568210
\(172\) 1.99895 0.152418
\(173\) 2.26187 0.171967 0.0859836 0.996297i \(-0.472597\pi\)
0.0859836 + 0.996297i \(0.472597\pi\)
\(174\) −5.70252 −0.432307
\(175\) −19.6385 −1.48453
\(176\) −6.05257 −0.456229
\(177\) 29.9495 2.25114
\(178\) 8.42076 0.631162
\(179\) −13.2548 −0.990713 −0.495357 0.868690i \(-0.664963\pi\)
−0.495357 + 0.868690i \(0.664963\pi\)
\(180\) −29.2641 −2.18122
\(181\) −6.79274 −0.504900 −0.252450 0.967610i \(-0.581236\pi\)
−0.252450 + 0.967610i \(0.581236\pi\)
\(182\) −63.5280 −4.70901
\(183\) −9.98877 −0.738391
\(184\) 7.26001 0.535215
\(185\) 5.11276 0.375898
\(186\) −46.5412 −3.41257
\(187\) −1.67769 −0.122685
\(188\) 24.4998 1.78683
\(189\) 48.1975 3.50585
\(190\) 3.25383 0.236058
\(191\) 1.50280 0.108739 0.0543693 0.998521i \(-0.482685\pi\)
0.0543693 + 0.998521i \(0.482685\pi\)
\(192\) 0.632446 0.0456428
\(193\) −17.5018 −1.25981 −0.629903 0.776674i \(-0.716905\pi\)
−0.629903 + 0.776674i \(0.716905\pi\)
\(194\) −15.7204 −1.12866
\(195\) −15.7431 −1.12739
\(196\) 83.6001 5.97144
\(197\) 15.9733 1.13805 0.569027 0.822319i \(-0.307320\pi\)
0.569027 + 0.822319i \(0.307320\pi\)
\(198\) 13.0457 0.927120
\(199\) −21.6866 −1.53732 −0.768660 0.639658i \(-0.779076\pi\)
−0.768660 + 0.639658i \(0.779076\pi\)
\(200\) 24.8057 1.75403
\(201\) 26.3193 1.85642
\(202\) 19.8109 1.39389
\(203\) 3.73700 0.262286
\(204\) 27.4884 1.92457
\(205\) 9.38334 0.655361
\(206\) 34.6097 2.41137
\(207\) −6.99314 −0.486057
\(208\) 35.8604 2.48647
\(209\) −1.00449 −0.0694822
\(210\) 41.1991 2.84301
\(211\) 18.1257 1.24783 0.623914 0.781493i \(-0.285542\pi\)
0.623914 + 0.781493i \(0.285542\pi\)
\(212\) 11.7741 0.808646
\(213\) −25.0081 −1.71352
\(214\) 27.2810 1.86489
\(215\) −0.468774 −0.0319701
\(216\) −60.8791 −4.14230
\(217\) 30.4996 2.07045
\(218\) 41.7633 2.82857
\(219\) −19.5926 −1.32394
\(220\) 3.95618 0.266725
\(221\) 9.94003 0.668639
\(222\) 37.3443 2.50639
\(223\) 1.80127 0.120622 0.0603109 0.998180i \(-0.480791\pi\)
0.0603109 + 0.998180i \(0.480791\pi\)
\(224\) −29.2720 −1.95582
\(225\) −23.8939 −1.59292
\(226\) −38.3699 −2.55233
\(227\) −19.4560 −1.29134 −0.645668 0.763618i \(-0.723421\pi\)
−0.645668 + 0.763618i \(0.723421\pi\)
\(228\) 16.4582 1.08997
\(229\) 0.781120 0.0516179 0.0258089 0.999667i \(-0.491784\pi\)
0.0258089 + 0.999667i \(0.491784\pi\)
\(230\) −3.06239 −0.201928
\(231\) −12.7186 −0.836824
\(232\) −4.72027 −0.309901
\(233\) −21.8208 −1.42953 −0.714765 0.699365i \(-0.753466\pi\)
−0.714765 + 0.699365i \(0.753466\pi\)
\(234\) −77.2936 −5.05284
\(235\) −5.74547 −0.374793
\(236\) 44.5913 2.90264
\(237\) −19.4945 −1.26630
\(238\) −26.0127 −1.68616
\(239\) −14.6206 −0.945725 −0.472863 0.881136i \(-0.656779\pi\)
−0.472863 + 0.881136i \(0.656779\pi\)
\(240\) −23.2562 −1.50118
\(241\) 13.0234 0.838914 0.419457 0.907775i \(-0.362221\pi\)
0.419457 + 0.907775i \(0.362221\pi\)
\(242\) 26.2897 1.68997
\(243\) 2.81589 0.180639
\(244\) −14.8721 −0.952089
\(245\) −19.6051 −1.25252
\(246\) 68.5372 4.36977
\(247\) 5.95144 0.378681
\(248\) −38.5246 −2.44631
\(249\) −0.812742 −0.0515054
\(250\) −23.9322 −1.51360
\(251\) 8.00408 0.505213 0.252607 0.967569i \(-0.418712\pi\)
0.252607 + 0.967569i \(0.418712\pi\)
\(252\) 140.075 8.82390
\(253\) 0.945392 0.0594363
\(254\) −52.9069 −3.31967
\(255\) −6.44631 −0.403683
\(256\) −28.5898 −1.78686
\(257\) 1.01470 0.0632952 0.0316476 0.999499i \(-0.489925\pi\)
0.0316476 + 0.999499i \(0.489925\pi\)
\(258\) −3.42399 −0.213168
\(259\) −24.4726 −1.52066
\(260\) −23.4396 −1.45366
\(261\) 4.54675 0.281437
\(262\) −4.22727 −0.261162
\(263\) 4.09619 0.252582 0.126291 0.991993i \(-0.459693\pi\)
0.126291 + 0.991993i \(0.459693\pi\)
\(264\) 16.0651 0.988740
\(265\) −2.76114 −0.169616
\(266\) −15.5747 −0.954948
\(267\) −9.98852 −0.611288
\(268\) 39.1864 2.39369
\(269\) −5.41150 −0.329945 −0.164973 0.986298i \(-0.552754\pi\)
−0.164973 + 0.986298i \(0.552754\pi\)
\(270\) 25.6798 1.56282
\(271\) −9.60792 −0.583640 −0.291820 0.956473i \(-0.594261\pi\)
−0.291820 + 0.956473i \(0.594261\pi\)
\(272\) 14.6837 0.890331
\(273\) 75.3555 4.56072
\(274\) −18.5010 −1.11768
\(275\) 3.23018 0.194787
\(276\) −15.4899 −0.932382
\(277\) 2.34209 0.140723 0.0703613 0.997522i \(-0.477585\pi\)
0.0703613 + 0.997522i \(0.477585\pi\)
\(278\) −28.8266 −1.72891
\(279\) 37.1084 2.22162
\(280\) 34.1027 2.03802
\(281\) −26.7765 −1.59735 −0.798675 0.601762i \(-0.794465\pi\)
−0.798675 + 0.601762i \(0.794465\pi\)
\(282\) −41.9657 −2.49902
\(283\) 13.5206 0.803715 0.401857 0.915702i \(-0.368365\pi\)
0.401857 + 0.915702i \(0.368365\pi\)
\(284\) −37.2341 −2.20944
\(285\) −3.85963 −0.228625
\(286\) 10.4492 0.617875
\(287\) −44.9141 −2.65120
\(288\) −35.6149 −2.09863
\(289\) −12.9299 −0.760580
\(290\) 1.99108 0.116920
\(291\) 18.6473 1.09312
\(292\) −29.1711 −1.70711
\(293\) 23.7477 1.38736 0.693679 0.720284i \(-0.255989\pi\)
0.693679 + 0.720284i \(0.255989\pi\)
\(294\) −143.198 −8.35149
\(295\) −10.4571 −0.608837
\(296\) 30.9118 1.79671
\(297\) −7.92763 −0.460008
\(298\) 23.6807 1.37178
\(299\) −5.60128 −0.323930
\(300\) −52.9252 −3.05564
\(301\) 2.24382 0.129332
\(302\) −37.3501 −2.14926
\(303\) −23.4993 −1.35000
\(304\) 8.79164 0.504235
\(305\) 3.48766 0.199703
\(306\) −31.6493 −1.80927
\(307\) 13.1993 0.753322 0.376661 0.926351i \(-0.377072\pi\)
0.376661 + 0.926351i \(0.377072\pi\)
\(308\) −18.9365 −1.07901
\(309\) −41.0533 −2.33544
\(310\) 16.2503 0.922953
\(311\) −10.3552 −0.587188 −0.293594 0.955930i \(-0.594851\pi\)
−0.293594 + 0.955930i \(0.594851\pi\)
\(312\) −95.1829 −5.38867
\(313\) −17.1686 −0.970429 −0.485214 0.874395i \(-0.661258\pi\)
−0.485214 + 0.874395i \(0.661258\pi\)
\(314\) 53.8618 3.03960
\(315\) −32.8491 −1.85084
\(316\) −29.0250 −1.63278
\(317\) −6.95538 −0.390653 −0.195327 0.980738i \(-0.562577\pi\)
−0.195327 + 0.980738i \(0.562577\pi\)
\(318\) −20.1678 −1.13095
\(319\) −0.614669 −0.0344148
\(320\) −0.220824 −0.0123444
\(321\) −32.3601 −1.80616
\(322\) 14.6584 0.816878
\(323\) 2.43693 0.135594
\(324\) 46.7736 2.59853
\(325\) −19.1382 −1.06160
\(326\) 0.0825679 0.00457301
\(327\) −49.5388 −2.73950
\(328\) 56.7318 3.13249
\(329\) 27.5011 1.51619
\(330\) −6.77652 −0.373035
\(331\) −32.6708 −1.79575 −0.897876 0.440249i \(-0.854890\pi\)
−0.897876 + 0.440249i \(0.854890\pi\)
\(332\) −1.21008 −0.0664116
\(333\) −29.7755 −1.63169
\(334\) −13.8467 −0.757659
\(335\) −9.18963 −0.502083
\(336\) 111.317 6.07286
\(337\) 24.3683 1.32743 0.663714 0.747986i \(-0.268979\pi\)
0.663714 + 0.747986i \(0.268979\pi\)
\(338\) −28.7557 −1.56410
\(339\) 45.5136 2.47196
\(340\) −9.59780 −0.520514
\(341\) −5.01663 −0.271666
\(342\) −18.9496 −1.02467
\(343\) 58.4507 3.15604
\(344\) −2.83421 −0.152810
\(345\) 3.63254 0.195569
\(346\) −5.76846 −0.310115
\(347\) 29.3887 1.57767 0.788834 0.614607i \(-0.210685\pi\)
0.788834 + 0.614607i \(0.210685\pi\)
\(348\) 10.0711 0.539868
\(349\) 6.76226 0.361976 0.180988 0.983485i \(-0.442071\pi\)
0.180988 + 0.983485i \(0.442071\pi\)
\(350\) 50.0841 2.67711
\(351\) 46.9697 2.50706
\(352\) 4.81472 0.256625
\(353\) 23.5015 1.25086 0.625429 0.780281i \(-0.284924\pi\)
0.625429 + 0.780281i \(0.284924\pi\)
\(354\) −76.3802 −4.05956
\(355\) 8.73178 0.463435
\(356\) −14.8717 −0.788201
\(357\) 30.8558 1.63306
\(358\) 33.8039 1.78659
\(359\) −9.69587 −0.511728 −0.255864 0.966713i \(-0.582360\pi\)
−0.255864 + 0.966713i \(0.582360\pi\)
\(360\) 41.4922 2.18683
\(361\) −17.5409 −0.923207
\(362\) 17.3235 0.910505
\(363\) −31.1843 −1.63675
\(364\) 112.196 5.88065
\(365\) 6.84092 0.358070
\(366\) 25.4744 1.33157
\(367\) −32.2254 −1.68215 −0.841075 0.540918i \(-0.818077\pi\)
−0.841075 + 0.540918i \(0.818077\pi\)
\(368\) −8.27437 −0.431331
\(369\) −54.6464 −2.84478
\(370\) −13.0391 −0.677870
\(371\) 13.2164 0.686162
\(372\) 82.1956 4.26164
\(373\) −9.86625 −0.510855 −0.255428 0.966828i \(-0.582216\pi\)
−0.255428 + 0.966828i \(0.582216\pi\)
\(374\) 4.27863 0.221243
\(375\) 28.3878 1.46594
\(376\) −34.7372 −1.79143
\(377\) 3.64180 0.187562
\(378\) −122.918 −6.32223
\(379\) −24.0192 −1.23378 −0.616892 0.787048i \(-0.711608\pi\)
−0.616892 + 0.787048i \(0.711608\pi\)
\(380\) −5.74653 −0.294791
\(381\) 62.7571 3.21514
\(382\) −3.83259 −0.196092
\(383\) −5.06507 −0.258813 −0.129406 0.991592i \(-0.541307\pi\)
−0.129406 + 0.991592i \(0.541307\pi\)
\(384\) 33.4166 1.70528
\(385\) 4.44082 0.226325
\(386\) 44.6349 2.27185
\(387\) 2.73003 0.138775
\(388\) 27.7636 1.40948
\(389\) −26.4390 −1.34051 −0.670255 0.742131i \(-0.733815\pi\)
−0.670255 + 0.742131i \(0.733815\pi\)
\(390\) 40.1496 2.03306
\(391\) −2.29355 −0.115990
\(392\) −118.533 −5.98680
\(393\) 5.01430 0.252938
\(394\) −40.7368 −2.05229
\(395\) 6.80666 0.342480
\(396\) −23.0398 −1.15780
\(397\) 13.9593 0.700597 0.350299 0.936638i \(-0.386080\pi\)
0.350299 + 0.936638i \(0.386080\pi\)
\(398\) 55.3073 2.77230
\(399\) 18.4744 0.924877
\(400\) −28.2715 −1.41358
\(401\) 7.25195 0.362145 0.181073 0.983470i \(-0.442043\pi\)
0.181073 + 0.983470i \(0.442043\pi\)
\(402\) −67.1223 −3.34776
\(403\) 29.7226 1.48059
\(404\) −34.9877 −1.74070
\(405\) −10.9689 −0.545049
\(406\) −9.53047 −0.472989
\(407\) 4.02531 0.199527
\(408\) −38.9745 −1.92952
\(409\) 36.2281 1.79136 0.895682 0.444695i \(-0.146688\pi\)
0.895682 + 0.444695i \(0.146688\pi\)
\(410\) −23.9304 −1.18184
\(411\) 21.9455 1.08249
\(412\) −61.1236 −3.01135
\(413\) 50.0538 2.46299
\(414\) 17.8346 0.876524
\(415\) 0.283776 0.0139300
\(416\) −28.5263 −1.39862
\(417\) 34.1935 1.67446
\(418\) 2.56176 0.125300
\(419\) −29.9845 −1.46484 −0.732420 0.680853i \(-0.761609\pi\)
−0.732420 + 0.680853i \(0.761609\pi\)
\(420\) −72.7611 −3.55038
\(421\) 36.9650 1.80156 0.900782 0.434272i \(-0.142994\pi\)
0.900782 + 0.434272i \(0.142994\pi\)
\(422\) −46.2261 −2.25025
\(423\) 33.4602 1.62689
\(424\) −16.6939 −0.810727
\(425\) −7.83650 −0.380126
\(426\) 63.7781 3.09006
\(427\) −16.6940 −0.807878
\(428\) −48.1804 −2.32889
\(429\) −12.3946 −0.598418
\(430\) 1.19552 0.0576529
\(431\) 8.86994 0.427250 0.213625 0.976916i \(-0.431473\pi\)
0.213625 + 0.976916i \(0.431473\pi\)
\(432\) 69.3851 3.33829
\(433\) −37.2294 −1.78913 −0.894566 0.446936i \(-0.852515\pi\)
−0.894566 + 0.446936i \(0.852515\pi\)
\(434\) −77.7832 −3.73371
\(435\) −2.36178 −0.113239
\(436\) −73.7574 −3.53234
\(437\) −1.37323 −0.0656904
\(438\) 49.9670 2.38752
\(439\) 7.36865 0.351687 0.175843 0.984418i \(-0.443735\pi\)
0.175843 + 0.984418i \(0.443735\pi\)
\(440\) −5.60927 −0.267412
\(441\) 114.175 5.43693
\(442\) −25.3501 −1.20578
\(443\) 28.4203 1.35029 0.675144 0.737686i \(-0.264081\pi\)
0.675144 + 0.737686i \(0.264081\pi\)
\(444\) −65.9531 −3.13000
\(445\) 3.48758 0.165327
\(446\) −4.59378 −0.217522
\(447\) −28.0895 −1.32859
\(448\) 1.05699 0.0499381
\(449\) 35.3313 1.66739 0.833693 0.552228i \(-0.186222\pi\)
0.833693 + 0.552228i \(0.186222\pi\)
\(450\) 60.9366 2.87258
\(451\) 7.38756 0.347867
\(452\) 67.7644 3.18737
\(453\) 44.3039 2.08158
\(454\) 49.6186 2.32871
\(455\) −26.3110 −1.23348
\(456\) −23.3353 −1.09278
\(457\) −29.8255 −1.39518 −0.697589 0.716498i \(-0.745744\pi\)
−0.697589 + 0.716498i \(0.745744\pi\)
\(458\) −1.99209 −0.0930844
\(459\) 19.2327 0.897704
\(460\) 5.40843 0.252169
\(461\) 9.39211 0.437434 0.218717 0.975788i \(-0.429813\pi\)
0.218717 + 0.975788i \(0.429813\pi\)
\(462\) 32.4363 1.50908
\(463\) 26.1182 1.21382 0.606908 0.794772i \(-0.292409\pi\)
0.606908 + 0.794772i \(0.292409\pi\)
\(464\) 5.37978 0.249750
\(465\) −19.2757 −0.893890
\(466\) 55.6497 2.57792
\(467\) 16.5982 0.768073 0.384036 0.923318i \(-0.374534\pi\)
0.384036 + 0.923318i \(0.374534\pi\)
\(468\) 136.507 6.31003
\(469\) 43.9869 2.03113
\(470\) 14.6527 0.675878
\(471\) −63.8897 −2.94388
\(472\) −63.2238 −2.91011
\(473\) −0.369069 −0.0169698
\(474\) 49.7168 2.28357
\(475\) −4.69199 −0.215283
\(476\) 45.9406 2.10569
\(477\) 16.0802 0.736263
\(478\) 37.2868 1.70546
\(479\) 28.9355 1.32210 0.661049 0.750343i \(-0.270112\pi\)
0.661049 + 0.750343i \(0.270112\pi\)
\(480\) 18.4999 0.844401
\(481\) −23.8492 −1.08743
\(482\) −33.2137 −1.51284
\(483\) −17.3874 −0.791156
\(484\) −46.4298 −2.11044
\(485\) −6.51085 −0.295642
\(486\) −7.18137 −0.325754
\(487\) 41.1160 1.86314 0.931571 0.363558i \(-0.118438\pi\)
0.931571 + 0.363558i \(0.118438\pi\)
\(488\) 21.0865 0.954539
\(489\) −0.0979403 −0.00442901
\(490\) 49.9989 2.25872
\(491\) 2.08265 0.0939886 0.0469943 0.998895i \(-0.485036\pi\)
0.0469943 + 0.998895i \(0.485036\pi\)
\(492\) −121.042 −5.45701
\(493\) 1.49120 0.0671605
\(494\) −15.1780 −0.682889
\(495\) 5.40308 0.242850
\(496\) 43.9072 1.97149
\(497\) −41.7954 −1.87478
\(498\) 2.07274 0.0928816
\(499\) −25.7710 −1.15367 −0.576835 0.816861i \(-0.695712\pi\)
−0.576835 + 0.816861i \(0.695712\pi\)
\(500\) 42.2662 1.89020
\(501\) 16.4247 0.733801
\(502\) −20.4128 −0.911070
\(503\) 41.7507 1.86157 0.930787 0.365563i \(-0.119124\pi\)
0.930787 + 0.365563i \(0.119124\pi\)
\(504\) −198.606 −8.84661
\(505\) 8.20497 0.365117
\(506\) −2.41104 −0.107184
\(507\) 34.1094 1.51485
\(508\) 93.4379 4.14564
\(509\) −2.88878 −0.128043 −0.0640215 0.997949i \(-0.520393\pi\)
−0.0640215 + 0.997949i \(0.520393\pi\)
\(510\) 16.4400 0.727977
\(511\) −32.7446 −1.44854
\(512\) 50.8198 2.24594
\(513\) 11.5153 0.508411
\(514\) −2.58779 −0.114143
\(515\) 14.3341 0.631637
\(516\) 6.04705 0.266206
\(517\) −4.52344 −0.198941
\(518\) 62.4126 2.74225
\(519\) 6.84243 0.300349
\(520\) 33.2339 1.45740
\(521\) 27.2437 1.19357 0.596785 0.802401i \(-0.296445\pi\)
0.596785 + 0.802401i \(0.296445\pi\)
\(522\) −11.5956 −0.507525
\(523\) 31.5756 1.38070 0.690352 0.723474i \(-0.257456\pi\)
0.690352 + 0.723474i \(0.257456\pi\)
\(524\) 7.46570 0.326141
\(525\) −59.4087 −2.59281
\(526\) −10.4465 −0.455491
\(527\) 12.1705 0.530155
\(528\) −18.3097 −0.796828
\(529\) −21.7076 −0.943807
\(530\) 7.04174 0.305874
\(531\) 60.8998 2.64283
\(532\) 27.5062 1.19255
\(533\) −43.7699 −1.89589
\(534\) 25.4738 1.10236
\(535\) 11.2988 0.488490
\(536\) −55.5606 −2.39985
\(537\) −40.0974 −1.73033
\(538\) 13.8010 0.595002
\(539\) −15.4352 −0.664841
\(540\) −45.3526 −1.95166
\(541\) −24.7602 −1.06452 −0.532262 0.846580i \(-0.678658\pi\)
−0.532262 + 0.846580i \(0.678658\pi\)
\(542\) 24.5031 1.05250
\(543\) −20.5488 −0.881834
\(544\) −11.6807 −0.500804
\(545\) 17.2969 0.740917
\(546\) −192.179 −8.22452
\(547\) −7.69428 −0.328984 −0.164492 0.986378i \(-0.552598\pi\)
−0.164492 + 0.986378i \(0.552598\pi\)
\(548\) 32.6742 1.39577
\(549\) −20.3113 −0.866867
\(550\) −8.23793 −0.351266
\(551\) 0.892836 0.0380361
\(552\) 21.9624 0.934781
\(553\) −32.5806 −1.38547
\(554\) −5.97304 −0.253770
\(555\) 15.4667 0.656525
\(556\) 50.9102 2.15907
\(557\) 5.65253 0.239505 0.119753 0.992804i \(-0.461790\pi\)
0.119753 + 0.992804i \(0.461790\pi\)
\(558\) −94.6377 −4.00633
\(559\) 2.18666 0.0924860
\(560\) −38.8674 −1.64245
\(561\) −5.07522 −0.214276
\(562\) 68.2881 2.88056
\(563\) −15.6464 −0.659417 −0.329708 0.944083i \(-0.606950\pi\)
−0.329708 + 0.944083i \(0.606950\pi\)
\(564\) 74.1148 3.12080
\(565\) −15.8915 −0.668558
\(566\) −34.4816 −1.44937
\(567\) 52.5035 2.20494
\(568\) 52.7924 2.21512
\(569\) −29.6485 −1.24293 −0.621464 0.783443i \(-0.713462\pi\)
−0.621464 + 0.783443i \(0.713462\pi\)
\(570\) 9.84322 0.412287
\(571\) −8.03446 −0.336232 −0.168116 0.985767i \(-0.553768\pi\)
−0.168116 + 0.985767i \(0.553768\pi\)
\(572\) −18.4542 −0.771607
\(573\) 4.54613 0.189917
\(574\) 114.545 4.78100
\(575\) 4.41592 0.184157
\(576\) 1.28603 0.0535844
\(577\) −15.7770 −0.656806 −0.328403 0.944538i \(-0.606510\pi\)
−0.328403 + 0.944538i \(0.606510\pi\)
\(578\) 32.9751 1.37158
\(579\) −52.9449 −2.20032
\(580\) −3.51641 −0.146011
\(581\) −1.35832 −0.0563524
\(582\) −47.5561 −1.97127
\(583\) −2.17386 −0.0900322
\(584\) 41.3603 1.71150
\(585\) −32.0123 −1.32354
\(586\) −60.5639 −2.50187
\(587\) 34.2653 1.41428 0.707140 0.707073i \(-0.249985\pi\)
0.707140 + 0.707073i \(0.249985\pi\)
\(588\) 252.900 10.4294
\(589\) 7.28690 0.300251
\(590\) 26.6688 1.09794
\(591\) 48.3212 1.98767
\(592\) −35.2308 −1.44798
\(593\) 35.5934 1.46165 0.730823 0.682567i \(-0.239137\pi\)
0.730823 + 0.682567i \(0.239137\pi\)
\(594\) 20.2178 0.829548
\(595\) −10.7736 −0.441673
\(596\) −41.8220 −1.71309
\(597\) −65.6044 −2.68501
\(598\) 14.2850 0.584155
\(599\) 20.3031 0.829562 0.414781 0.909921i \(-0.363858\pi\)
0.414781 + 0.909921i \(0.363858\pi\)
\(600\) 75.0401 3.06350
\(601\) 40.5653 1.65469 0.827347 0.561691i \(-0.189849\pi\)
0.827347 + 0.561691i \(0.189849\pi\)
\(602\) −5.72243 −0.233229
\(603\) 53.5182 2.17943
\(604\) 65.9634 2.68401
\(605\) 10.8883 0.442671
\(606\) 59.9303 2.43450
\(607\) −2.13219 −0.0865430 −0.0432715 0.999063i \(-0.513778\pi\)
−0.0432715 + 0.999063i \(0.513778\pi\)
\(608\) −6.99361 −0.283628
\(609\) 11.3048 0.458096
\(610\) −8.89460 −0.360132
\(611\) 26.8006 1.08423
\(612\) 55.8953 2.25944
\(613\) −25.8368 −1.04354 −0.521770 0.853086i \(-0.674728\pi\)
−0.521770 + 0.853086i \(0.674728\pi\)
\(614\) −33.6621 −1.35849
\(615\) 28.3857 1.14462
\(616\) 26.8492 1.08179
\(617\) 4.94025 0.198887 0.0994435 0.995043i \(-0.468294\pi\)
0.0994435 + 0.995043i \(0.468294\pi\)
\(618\) 104.698 4.21159
\(619\) 16.7361 0.672681 0.336341 0.941740i \(-0.390811\pi\)
0.336341 + 0.941740i \(0.390811\pi\)
\(620\) −28.6993 −1.15259
\(621\) −10.8377 −0.434903
\(622\) 26.4088 1.05890
\(623\) −16.6936 −0.668814
\(624\) 108.482 4.34274
\(625\) 9.50988 0.380395
\(626\) 43.7852 1.75001
\(627\) −3.03871 −0.121354
\(628\) −95.1243 −3.79587
\(629\) −9.76552 −0.389377
\(630\) 83.7751 3.33768
\(631\) 22.9817 0.914887 0.457443 0.889239i \(-0.348765\pi\)
0.457443 + 0.889239i \(0.348765\pi\)
\(632\) 41.1531 1.63698
\(633\) 54.8325 2.17939
\(634\) 17.7383 0.704479
\(635\) −21.9122 −0.869558
\(636\) 35.6179 1.41234
\(637\) 91.4508 3.62341
\(638\) 1.56759 0.0620615
\(639\) −50.8518 −2.01167
\(640\) −11.6677 −0.461206
\(641\) −27.2333 −1.07565 −0.537825 0.843057i \(-0.680754\pi\)
−0.537825 + 0.843057i \(0.680754\pi\)
\(642\) 82.5280 3.25712
\(643\) 6.11953 0.241331 0.120665 0.992693i \(-0.461497\pi\)
0.120665 + 0.992693i \(0.461497\pi\)
\(644\) −25.8879 −1.02012
\(645\) −1.41810 −0.0558374
\(646\) −6.21491 −0.244522
\(647\) 36.6537 1.44100 0.720502 0.693453i \(-0.243911\pi\)
0.720502 + 0.693453i \(0.243911\pi\)
\(648\) −66.3181 −2.60522
\(649\) −8.23295 −0.323172
\(650\) 48.8082 1.91442
\(651\) 92.2647 3.61614
\(652\) −0.145822 −0.00571082
\(653\) −38.9767 −1.52528 −0.762638 0.646825i \(-0.776096\pi\)
−0.762638 + 0.646825i \(0.776096\pi\)
\(654\) 126.339 4.94024
\(655\) −1.75079 −0.0684088
\(656\) −64.6583 −2.52448
\(657\) −39.8399 −1.55430
\(658\) −70.1362 −2.73419
\(659\) 20.2941 0.790547 0.395273 0.918564i \(-0.370650\pi\)
0.395273 + 0.918564i \(0.370650\pi\)
\(660\) 11.9679 0.465849
\(661\) 5.45987 0.212364 0.106182 0.994347i \(-0.466137\pi\)
0.106182 + 0.994347i \(0.466137\pi\)
\(662\) 83.3205 3.23834
\(663\) 30.0697 1.16781
\(664\) 1.71571 0.0665825
\(665\) −6.45050 −0.250140
\(666\) 75.9366 2.94248
\(667\) −0.840304 −0.0325367
\(668\) 24.4545 0.946171
\(669\) 5.44904 0.210672
\(670\) 23.4363 0.905424
\(671\) 2.74586 0.106003
\(672\) −88.5512 −3.41594
\(673\) −34.4977 −1.32979 −0.664894 0.746938i \(-0.731523\pi\)
−0.664894 + 0.746938i \(0.731523\pi\)
\(674\) −62.1467 −2.39380
\(675\) −37.0299 −1.42528
\(676\) 50.7849 1.95327
\(677\) −26.7164 −1.02679 −0.513397 0.858151i \(-0.671613\pi\)
−0.513397 + 0.858151i \(0.671613\pi\)
\(678\) −116.073 −4.45777
\(679\) 31.1647 1.19599
\(680\) 13.6083 0.521853
\(681\) −58.8565 −2.25539
\(682\) 12.7939 0.489905
\(683\) 1.97540 0.0755867 0.0377933 0.999286i \(-0.487967\pi\)
0.0377933 + 0.999286i \(0.487967\pi\)
\(684\) 33.4665 1.27962
\(685\) −7.66245 −0.292767
\(686\) −149.067 −5.69140
\(687\) 2.36298 0.0901532
\(688\) 3.23021 0.123150
\(689\) 12.8797 0.490679
\(690\) −9.26407 −0.352677
\(691\) 8.19996 0.311941 0.155971 0.987762i \(-0.450149\pi\)
0.155971 + 0.987762i \(0.450149\pi\)
\(692\) 10.1876 0.387274
\(693\) −25.8623 −0.982427
\(694\) −74.9500 −2.84506
\(695\) −11.9390 −0.452871
\(696\) −14.2793 −0.541257
\(697\) −17.9224 −0.678861
\(698\) −17.2458 −0.652764
\(699\) −66.0105 −2.49675
\(700\) −88.4526 −3.34319
\(701\) 4.35411 0.164452 0.0822262 0.996614i \(-0.473797\pi\)
0.0822262 + 0.996614i \(0.473797\pi\)
\(702\) −119.787 −4.52107
\(703\) −5.84695 −0.220522
\(704\) −0.173856 −0.00655244
\(705\) −17.3807 −0.654595
\(706\) −59.9359 −2.25572
\(707\) −39.2738 −1.47704
\(708\) 134.894 5.06962
\(709\) 48.9389 1.83794 0.918969 0.394329i \(-0.129023\pi\)
0.918969 + 0.394329i \(0.129023\pi\)
\(710\) −22.2687 −0.835729
\(711\) −39.6404 −1.48663
\(712\) 21.0859 0.790229
\(713\) −6.85816 −0.256840
\(714\) −78.6915 −2.94496
\(715\) 4.32769 0.161846
\(716\) −59.7004 −2.23111
\(717\) −44.2289 −1.65176
\(718\) 24.7274 0.922818
\(719\) −28.0566 −1.04634 −0.523168 0.852230i \(-0.675250\pi\)
−0.523168 + 0.852230i \(0.675250\pi\)
\(720\) −47.2895 −1.76237
\(721\) −68.6114 −2.55522
\(722\) 44.7347 1.66485
\(723\) 39.3974 1.46521
\(724\) −30.5948 −1.13705
\(725\) −2.87112 −0.106631
\(726\) 79.5294 2.95161
\(727\) 7.17863 0.266241 0.133120 0.991100i \(-0.457500\pi\)
0.133120 + 0.991100i \(0.457500\pi\)
\(728\) −159.077 −5.89578
\(729\) −22.6360 −0.838371
\(730\) −17.4464 −0.645721
\(731\) 0.895371 0.0331165
\(732\) −44.9899 −1.66287
\(733\) −28.3097 −1.04564 −0.522821 0.852442i \(-0.675121\pi\)
−0.522821 + 0.852442i \(0.675121\pi\)
\(734\) 82.1844 3.03348
\(735\) −59.3077 −2.18760
\(736\) 6.58213 0.242620
\(737\) −7.23505 −0.266506
\(738\) 139.365 5.13009
\(739\) 1.04107 0.0382963 0.0191482 0.999817i \(-0.493905\pi\)
0.0191482 + 0.999817i \(0.493905\pi\)
\(740\) 23.0281 0.846530
\(741\) 18.0038 0.661386
\(742\) −33.7059 −1.23738
\(743\) −32.4274 −1.18964 −0.594822 0.803857i \(-0.702778\pi\)
−0.594822 + 0.803857i \(0.702778\pi\)
\(744\) −116.541 −4.27261
\(745\) 9.80769 0.359326
\(746\) 25.1619 0.921244
\(747\) −1.65264 −0.0604671
\(748\) −7.55641 −0.276290
\(749\) −54.0826 −1.97614
\(750\) −72.3975 −2.64358
\(751\) 28.6356 1.04493 0.522463 0.852662i \(-0.325013\pi\)
0.522463 + 0.852662i \(0.325013\pi\)
\(752\) 39.5906 1.44372
\(753\) 24.2133 0.882381
\(754\) −9.28769 −0.338238
\(755\) −15.4691 −0.562978
\(756\) 217.084 7.89526
\(757\) −43.4264 −1.57836 −0.789180 0.614162i \(-0.789494\pi\)
−0.789180 + 0.614162i \(0.789494\pi\)
\(758\) 61.2563 2.22493
\(759\) 2.85992 0.103809
\(760\) 8.14774 0.295549
\(761\) 8.48133 0.307448 0.153724 0.988114i \(-0.450873\pi\)
0.153724 + 0.988114i \(0.450873\pi\)
\(762\) −160.049 −5.79798
\(763\) −82.7929 −2.99730
\(764\) 6.76866 0.244882
\(765\) −13.1080 −0.473922
\(766\) 12.9175 0.466727
\(767\) 48.7787 1.76130
\(768\) −86.4874 −3.12085
\(769\) 33.2714 1.19980 0.599899 0.800076i \(-0.295207\pi\)
0.599899 + 0.800076i \(0.295207\pi\)
\(770\) −11.3254 −0.408140
\(771\) 3.06958 0.110548
\(772\) −78.8288 −2.83711
\(773\) −32.8369 −1.18106 −0.590530 0.807016i \(-0.701081\pi\)
−0.590530 + 0.807016i \(0.701081\pi\)
\(774\) −6.96240 −0.250258
\(775\) −23.4327 −0.841727
\(776\) −39.3647 −1.41311
\(777\) −74.0326 −2.65590
\(778\) 67.4274 2.41739
\(779\) −10.7308 −0.384470
\(780\) −70.9076 −2.53890
\(781\) 6.87458 0.245992
\(782\) 5.84925 0.209169
\(783\) 7.04641 0.251818
\(784\) 135.094 4.82478
\(785\) 22.3076 0.796194
\(786\) −12.7880 −0.456132
\(787\) −52.1213 −1.85792 −0.928962 0.370175i \(-0.879298\pi\)
−0.928962 + 0.370175i \(0.879298\pi\)
\(788\) 71.9446 2.56292
\(789\) 12.3915 0.441148
\(790\) −17.3590 −0.617607
\(791\) 76.0657 2.70459
\(792\) 32.6671 1.16077
\(793\) −16.2687 −0.577719
\(794\) −35.6005 −1.26341
\(795\) −8.35277 −0.296242
\(796\) −97.6772 −3.46208
\(797\) 21.9823 0.778653 0.389327 0.921100i \(-0.372708\pi\)
0.389327 + 0.921100i \(0.372708\pi\)
\(798\) −47.1153 −1.66786
\(799\) 10.9740 0.388232
\(800\) 22.4895 0.795125
\(801\) −20.3108 −0.717648
\(802\) −18.4947 −0.653070
\(803\) 5.38590 0.190064
\(804\) 118.543 4.18071
\(805\) 6.07097 0.213974
\(806\) −75.8017 −2.67000
\(807\) −16.3704 −0.576266
\(808\) 49.6074 1.74518
\(809\) −3.84048 −0.135024 −0.0675120 0.997718i \(-0.521506\pi\)
−0.0675120 + 0.997718i \(0.521506\pi\)
\(810\) 27.9740 0.982907
\(811\) −6.03522 −0.211925 −0.105963 0.994370i \(-0.533792\pi\)
−0.105963 + 0.994370i \(0.533792\pi\)
\(812\) 16.8316 0.590673
\(813\) −29.0651 −1.01936
\(814\) −10.2658 −0.359815
\(815\) 0.0341967 0.00119786
\(816\) 44.4199 1.55501
\(817\) 0.536090 0.0187554
\(818\) −92.3926 −3.23043
\(819\) 153.229 5.35426
\(820\) 42.2630 1.47589
\(821\) 49.9607 1.74364 0.871820 0.489827i \(-0.162940\pi\)
0.871820 + 0.489827i \(0.162940\pi\)
\(822\) −55.9676 −1.95209
\(823\) 24.7304 0.862047 0.431024 0.902341i \(-0.358153\pi\)
0.431024 + 0.902341i \(0.358153\pi\)
\(824\) 86.6643 3.01909
\(825\) 9.77166 0.340205
\(826\) −127.652 −4.44159
\(827\) 24.4754 0.851093 0.425546 0.904937i \(-0.360082\pi\)
0.425546 + 0.904937i \(0.360082\pi\)
\(828\) −31.4974 −1.09461
\(829\) −19.9422 −0.692623 −0.346311 0.938120i \(-0.612566\pi\)
−0.346311 + 0.938120i \(0.612566\pi\)
\(830\) −0.723714 −0.0251205
\(831\) 7.08509 0.245779
\(832\) 1.03007 0.0357111
\(833\) 37.4463 1.29744
\(834\) −87.2038 −3.01962
\(835\) −5.73482 −0.198462
\(836\) −4.52428 −0.156476
\(837\) 57.5094 1.98782
\(838\) 76.4697 2.64160
\(839\) 41.1323 1.42004 0.710022 0.704180i \(-0.248685\pi\)
0.710022 + 0.704180i \(0.248685\pi\)
\(840\) 103.164 3.55951
\(841\) −28.4537 −0.981161
\(842\) −94.2719 −3.24882
\(843\) −81.0019 −2.78985
\(844\) 81.6391 2.81013
\(845\) −11.9096 −0.409703
\(846\) −85.3337 −2.93383
\(847\) −52.1175 −1.79078
\(848\) 19.0263 0.653367
\(849\) 40.9013 1.40373
\(850\) 19.9855 0.685496
\(851\) 5.50294 0.188638
\(852\) −112.637 −3.85889
\(853\) −7.31763 −0.250551 −0.125275 0.992122i \(-0.539981\pi\)
−0.125275 + 0.992122i \(0.539981\pi\)
\(854\) 42.5747 1.45688
\(855\) −7.84823 −0.268404
\(856\) 68.3127 2.33488
\(857\) −31.4283 −1.07357 −0.536786 0.843719i \(-0.680362\pi\)
−0.536786 + 0.843719i \(0.680362\pi\)
\(858\) 31.6101 1.07915
\(859\) 42.4709 1.44909 0.724544 0.689229i \(-0.242051\pi\)
0.724544 + 0.689229i \(0.242051\pi\)
\(860\) −2.11138 −0.0719974
\(861\) −135.870 −4.63045
\(862\) −22.6210 −0.770476
\(863\) −42.6371 −1.45138 −0.725691 0.688021i \(-0.758480\pi\)
−0.725691 + 0.688021i \(0.758480\pi\)
\(864\) −55.1947 −1.87776
\(865\) −2.38909 −0.0812316
\(866\) 94.9463 3.22641
\(867\) −39.1143 −1.32839
\(868\) 137.371 4.66269
\(869\) 5.35892 0.181789
\(870\) 6.02325 0.204207
\(871\) 42.8663 1.45247
\(872\) 104.577 3.54143
\(873\) 37.9177 1.28332
\(874\) 3.50214 0.118462
\(875\) 47.4439 1.60390
\(876\) −88.2459 −2.98155
\(877\) 17.7564 0.599590 0.299795 0.954004i \(-0.403082\pi\)
0.299795 + 0.954004i \(0.403082\pi\)
\(878\) −18.7923 −0.634209
\(879\) 71.8397 2.42309
\(880\) 6.39299 0.215508
\(881\) −27.2594 −0.918394 −0.459197 0.888334i \(-0.651863\pi\)
−0.459197 + 0.888334i \(0.651863\pi\)
\(882\) −291.182 −9.80461
\(883\) 32.9514 1.10890 0.554451 0.832216i \(-0.312928\pi\)
0.554451 + 0.832216i \(0.312928\pi\)
\(884\) 44.7703 1.50579
\(885\) −31.6340 −1.06336
\(886\) −72.4803 −2.43502
\(887\) −44.6601 −1.49954 −0.749770 0.661698i \(-0.769836\pi\)
−0.749770 + 0.661698i \(0.769836\pi\)
\(888\) 93.5118 3.13805
\(889\) 104.884 3.51771
\(890\) −8.89438 −0.298140
\(891\) −8.63588 −0.289313
\(892\) 8.11299 0.271643
\(893\) 6.57051 0.219874
\(894\) 71.6367 2.39589
\(895\) 14.0004 0.467980
\(896\) 55.8484 1.86576
\(897\) −16.9445 −0.565761
\(898\) −90.1054 −3.00686
\(899\) 4.45899 0.148716
\(900\) −107.619 −3.58730
\(901\) 5.27386 0.175698
\(902\) −18.8405 −0.627320
\(903\) 6.78782 0.225885
\(904\) −96.0799 −3.19557
\(905\) 7.17479 0.238498
\(906\) −112.988 −3.75379
\(907\) 0.178068 0.00591264 0.00295632 0.999996i \(-0.499059\pi\)
0.00295632 + 0.999996i \(0.499059\pi\)
\(908\) −87.6305 −2.90812
\(909\) −47.7838 −1.58489
\(910\) 67.1011 2.22438
\(911\) 24.6164 0.815577 0.407788 0.913076i \(-0.366300\pi\)
0.407788 + 0.913076i \(0.366300\pi\)
\(912\) 26.5957 0.880673
\(913\) 0.223418 0.00739407
\(914\) 76.0641 2.51598
\(915\) 10.5506 0.348792
\(916\) 3.51820 0.116245
\(917\) 8.38027 0.276741
\(918\) −49.0491 −1.61886
\(919\) 49.6531 1.63790 0.818952 0.573862i \(-0.194556\pi\)
0.818952 + 0.573862i \(0.194556\pi\)
\(920\) −7.66835 −0.252818
\(921\) 39.9293 1.31572
\(922\) −23.9527 −0.788841
\(923\) −40.7307 −1.34067
\(924\) −57.2852 −1.88455
\(925\) 18.8022 0.618213
\(926\) −66.6094 −2.18892
\(927\) −83.4786 −2.74180
\(928\) −4.27952 −0.140482
\(929\) −42.7766 −1.40345 −0.701727 0.712446i \(-0.747587\pi\)
−0.701727 + 0.712446i \(0.747587\pi\)
\(930\) 49.1589 1.61198
\(931\) 22.4204 0.734798
\(932\) −98.2820 −3.21933
\(933\) −31.3256 −1.02555
\(934\) −42.3304 −1.38509
\(935\) 1.77206 0.0579524
\(936\) −193.547 −6.32627
\(937\) −22.9731 −0.750498 −0.375249 0.926924i \(-0.622443\pi\)
−0.375249 + 0.926924i \(0.622443\pi\)
\(938\) −112.180 −3.66280
\(939\) −51.9371 −1.69490
\(940\) −25.8778 −0.844042
\(941\) −15.9610 −0.520313 −0.260156 0.965566i \(-0.583774\pi\)
−0.260156 + 0.965566i \(0.583774\pi\)
\(942\) 162.938 5.30881
\(943\) 10.0994 0.328882
\(944\) 72.0574 2.34527
\(945\) −50.9084 −1.65605
\(946\) 0.941237 0.0306022
\(947\) −26.8821 −0.873550 −0.436775 0.899571i \(-0.643879\pi\)
−0.436775 + 0.899571i \(0.643879\pi\)
\(948\) −87.8039 −2.85174
\(949\) −31.9105 −1.03586
\(950\) 11.9660 0.388228
\(951\) −21.0408 −0.682296
\(952\) −65.1370 −2.11110
\(953\) 46.0112 1.49045 0.745225 0.666813i \(-0.232342\pi\)
0.745225 + 0.666813i \(0.232342\pi\)
\(954\) −41.0095 −1.32773
\(955\) −1.58732 −0.0513645
\(956\) −65.8516 −2.12979
\(957\) −1.85944 −0.0601073
\(958\) −73.7943 −2.38419
\(959\) 36.6769 1.18436
\(960\) −0.668018 −0.0215602
\(961\) 5.39216 0.173941
\(962\) 60.8227 1.96100
\(963\) −65.8016 −2.12043
\(964\) 58.6582 1.88925
\(965\) 18.4862 0.595091
\(966\) 44.3432 1.42672
\(967\) 39.4790 1.26956 0.634780 0.772693i \(-0.281091\pi\)
0.634780 + 0.772693i \(0.281091\pi\)
\(968\) 65.8306 2.11587
\(969\) 7.37200 0.236823
\(970\) 16.6046 0.533143
\(971\) −35.2173 −1.13018 −0.565088 0.825031i \(-0.691158\pi\)
−0.565088 + 0.825031i \(0.691158\pi\)
\(972\) 12.6829 0.406804
\(973\) 57.1468 1.83204
\(974\) −104.858 −3.35987
\(975\) −57.8953 −1.85413
\(976\) −24.0326 −0.769266
\(977\) −30.2323 −0.967218 −0.483609 0.875284i \(-0.660674\pi\)
−0.483609 + 0.875284i \(0.660674\pi\)
\(978\) 0.249777 0.00798700
\(979\) 2.74579 0.0877559
\(980\) −88.3022 −2.82071
\(981\) −100.733 −3.21616
\(982\) −5.31138 −0.169493
\(983\) −29.8130 −0.950886 −0.475443 0.879746i \(-0.657712\pi\)
−0.475443 + 0.879746i \(0.657712\pi\)
\(984\) 171.620 5.47105
\(985\) −16.8718 −0.537579
\(986\) −3.80302 −0.121113
\(987\) 83.1941 2.64810
\(988\) 26.8055 0.852798
\(989\) −0.504548 −0.0160437
\(990\) −13.7795 −0.437941
\(991\) 29.9722 0.952098 0.476049 0.879419i \(-0.342069\pi\)
0.476049 + 0.879419i \(0.342069\pi\)
\(992\) −34.9274 −1.10895
\(993\) −98.8330 −3.13637
\(994\) 106.591 3.38086
\(995\) 22.9063 0.726179
\(996\) −3.66062 −0.115991
\(997\) −33.3667 −1.05673 −0.528367 0.849016i \(-0.677195\pi\)
−0.528367 + 0.849016i \(0.677195\pi\)
\(998\) 65.7239 2.08045
\(999\) −46.1451 −1.45997
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 \(a_p\))