Properties

Label 6001.2.a.b.1.19
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.10824 q^{2}\) \(-2.66682 q^{3}\) \(+2.44469 q^{4}\) \(-3.46040 q^{5}\) \(+5.62230 q^{6}\) \(-1.09952 q^{7}\) \(-0.937516 q^{8}\) \(+4.11192 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.10824 q^{2}\) \(-2.66682 q^{3}\) \(+2.44469 q^{4}\) \(-3.46040 q^{5}\) \(+5.62230 q^{6}\) \(-1.09952 q^{7}\) \(-0.937516 q^{8}\) \(+4.11192 q^{9}\) \(+7.29537 q^{10}\) \(-2.77755 q^{11}\) \(-6.51955 q^{12}\) \(+4.41425 q^{13}\) \(+2.31806 q^{14}\) \(+9.22827 q^{15}\) \(-2.91287 q^{16}\) \(+1.00000 q^{17}\) \(-8.66894 q^{18}\) \(+7.84839 q^{19}\) \(-8.45961 q^{20}\) \(+2.93223 q^{21}\) \(+5.85576 q^{22}\) \(-5.90976 q^{23}\) \(+2.50019 q^{24}\) \(+6.97438 q^{25}\) \(-9.30632 q^{26}\) \(-2.96530 q^{27}\) \(-2.68800 q^{28}\) \(-9.04005 q^{29}\) \(-19.4554 q^{30}\) \(-8.72445 q^{31}\) \(+8.01607 q^{32}\) \(+7.40723 q^{33}\) \(-2.10824 q^{34}\) \(+3.80479 q^{35}\) \(+10.0524 q^{36}\) \(-8.47027 q^{37}\) \(-16.5463 q^{38}\) \(-11.7720 q^{39}\) \(+3.24418 q^{40}\) \(+5.14486 q^{41}\) \(-6.18186 q^{42}\) \(-4.00114 q^{43}\) \(-6.79026 q^{44}\) \(-14.2289 q^{45}\) \(+12.4592 q^{46}\) \(+9.30498 q^{47}\) \(+7.76810 q^{48}\) \(-5.79105 q^{49}\) \(-14.7037 q^{50}\) \(-2.66682 q^{51}\) \(+10.7915 q^{52}\) \(-13.3821 q^{53}\) \(+6.25157 q^{54}\) \(+9.61145 q^{55}\) \(+1.03082 q^{56}\) \(-20.9302 q^{57}\) \(+19.0586 q^{58}\) \(-7.54072 q^{59}\) \(+22.5603 q^{60}\) \(+15.1285 q^{61}\) \(+18.3933 q^{62}\) \(-4.52116 q^{63}\) \(-11.0741 q^{64}\) \(-15.2751 q^{65}\) \(-15.6162 q^{66}\) \(+1.64619 q^{67}\) \(+2.44469 q^{68}\) \(+15.7603 q^{69}\) \(-8.02143 q^{70}\) \(+0.983333 q^{71}\) \(-3.85499 q^{72}\) \(+8.86134 q^{73}\) \(+17.8574 q^{74}\) \(-18.5994 q^{75}\) \(+19.1869 q^{76}\) \(+3.05399 q^{77}\) \(+24.8183 q^{78}\) \(+11.9057 q^{79}\) \(+10.0797 q^{80}\) \(-4.42785 q^{81}\) \(-10.8466 q^{82}\) \(+16.2677 q^{83}\) \(+7.16840 q^{84}\) \(-3.46040 q^{85}\) \(+8.43538 q^{86}\) \(+24.1082 q^{87}\) \(+2.60400 q^{88}\) \(-12.3401 q^{89}\) \(+29.9980 q^{90}\) \(-4.85358 q^{91}\) \(-14.4475 q^{92}\) \(+23.2665 q^{93}\) \(-19.6172 q^{94}\) \(-27.1586 q^{95}\) \(-21.3774 q^{96}\) \(+2.51011 q^{97}\) \(+12.2089 q^{98}\) \(-11.4211 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10824 −1.49075 −0.745377 0.666644i \(-0.767730\pi\)
−0.745377 + 0.666644i \(0.767730\pi\)
\(3\) −2.66682 −1.53969 −0.769844 0.638232i \(-0.779666\pi\)
−0.769844 + 0.638232i \(0.779666\pi\)
\(4\) 2.44469 1.22235
\(5\) −3.46040 −1.54754 −0.773770 0.633467i \(-0.781631\pi\)
−0.773770 + 0.633467i \(0.781631\pi\)
\(6\) 5.62230 2.29530
\(7\) −1.09952 −0.415581 −0.207790 0.978173i \(-0.566627\pi\)
−0.207790 + 0.978173i \(0.566627\pi\)
\(8\) −0.937516 −0.331462
\(9\) 4.11192 1.37064
\(10\) 7.29537 2.30700
\(11\) −2.77755 −0.837464 −0.418732 0.908110i \(-0.637525\pi\)
−0.418732 + 0.908110i \(0.637525\pi\)
\(12\) −6.51955 −1.88203
\(13\) 4.41425 1.22429 0.612147 0.790744i \(-0.290306\pi\)
0.612147 + 0.790744i \(0.290306\pi\)
\(14\) 2.31806 0.619529
\(15\) 9.22827 2.38273
\(16\) −2.91287 −0.728217
\(17\) 1.00000 0.242536
\(18\) −8.66894 −2.04329
\(19\) 7.84839 1.80054 0.900272 0.435328i \(-0.143367\pi\)
0.900272 + 0.435328i \(0.143367\pi\)
\(20\) −8.45961 −1.89163
\(21\) 2.93223 0.639865
\(22\) 5.85576 1.24845
\(23\) −5.90976 −1.23227 −0.616135 0.787640i \(-0.711303\pi\)
−0.616135 + 0.787640i \(0.711303\pi\)
\(24\) 2.50019 0.510348
\(25\) 6.97438 1.39488
\(26\) −9.30632 −1.82512
\(27\) −2.96530 −0.570672
\(28\) −2.68800 −0.507983
\(29\) −9.04005 −1.67870 −0.839348 0.543594i \(-0.817063\pi\)
−0.839348 + 0.543594i \(0.817063\pi\)
\(30\) −19.4554 −3.55206
\(31\) −8.72445 −1.56696 −0.783479 0.621418i \(-0.786557\pi\)
−0.783479 + 0.621418i \(0.786557\pi\)
\(32\) 8.01607 1.41705
\(33\) 7.40723 1.28943
\(34\) −2.10824 −0.361561
\(35\) 3.80479 0.643128
\(36\) 10.0524 1.67540
\(37\) −8.47027 −1.39250 −0.696252 0.717797i \(-0.745151\pi\)
−0.696252 + 0.717797i \(0.745151\pi\)
\(38\) −16.5463 −2.68417
\(39\) −11.7720 −1.88503
\(40\) 3.24418 0.512950
\(41\) 5.14486 0.803493 0.401746 0.915751i \(-0.368403\pi\)
0.401746 + 0.915751i \(0.368403\pi\)
\(42\) −6.18186 −0.953881
\(43\) −4.00114 −0.610169 −0.305084 0.952325i \(-0.598685\pi\)
−0.305084 + 0.952325i \(0.598685\pi\)
\(44\) −6.79026 −1.02367
\(45\) −14.2289 −2.12112
\(46\) 12.4592 1.83701
\(47\) 9.30498 1.35727 0.678635 0.734475i \(-0.262572\pi\)
0.678635 + 0.734475i \(0.262572\pi\)
\(48\) 7.76810 1.12123
\(49\) −5.79105 −0.827292
\(50\) −14.7037 −2.07942
\(51\) −2.66682 −0.373429
\(52\) 10.7915 1.49651
\(53\) −13.3821 −1.83817 −0.919087 0.394054i \(-0.871072\pi\)
−0.919087 + 0.394054i \(0.871072\pi\)
\(54\) 6.25157 0.850732
\(55\) 9.61145 1.29601
\(56\) 1.03082 0.137749
\(57\) −20.9302 −2.77228
\(58\) 19.0586 2.50252
\(59\) −7.54072 −0.981718 −0.490859 0.871239i \(-0.663317\pi\)
−0.490859 + 0.871239i \(0.663317\pi\)
\(60\) 22.5603 2.91252
\(61\) 15.1285 1.93701 0.968506 0.248991i \(-0.0800990\pi\)
0.968506 + 0.248991i \(0.0800990\pi\)
\(62\) 18.3933 2.33595
\(63\) −4.52116 −0.569612
\(64\) −11.0741 −1.38426
\(65\) −15.2751 −1.89464
\(66\) −15.6162 −1.92223
\(67\) 1.64619 0.201115 0.100557 0.994931i \(-0.467937\pi\)
0.100557 + 0.994931i \(0.467937\pi\)
\(68\) 2.44469 0.296462
\(69\) 15.7603 1.89731
\(70\) −8.02143 −0.958745
\(71\) 0.983333 0.116700 0.0583501 0.998296i \(-0.481416\pi\)
0.0583501 + 0.998296i \(0.481416\pi\)
\(72\) −3.85499 −0.454315
\(73\) 8.86134 1.03714 0.518571 0.855035i \(-0.326464\pi\)
0.518571 + 0.855035i \(0.326464\pi\)
\(74\) 17.8574 2.07588
\(75\) −18.5994 −2.14768
\(76\) 19.1869 2.20089
\(77\) 3.05399 0.348034
\(78\) 24.8183 2.81012
\(79\) 11.9057 1.33950 0.669749 0.742587i \(-0.266402\pi\)
0.669749 + 0.742587i \(0.266402\pi\)
\(80\) 10.0797 1.12694
\(81\) −4.42785 −0.491984
\(82\) −10.8466 −1.19781
\(83\) 16.2677 1.78561 0.892806 0.450442i \(-0.148734\pi\)
0.892806 + 0.450442i \(0.148734\pi\)
\(84\) 7.16840 0.782136
\(85\) −3.46040 −0.375333
\(86\) 8.43538 0.909611
\(87\) 24.1082 2.58467
\(88\) 2.60400 0.277587
\(89\) −12.3401 −1.30805 −0.654024 0.756474i \(-0.726920\pi\)
−0.654024 + 0.756474i \(0.726920\pi\)
\(90\) 29.9980 3.16207
\(91\) −4.85358 −0.508793
\(92\) −14.4475 −1.50626
\(93\) 23.2665 2.41263
\(94\) −19.6172 −2.02336
\(95\) −27.1586 −2.78641
\(96\) −21.3774 −2.18182
\(97\) 2.51011 0.254864 0.127432 0.991847i \(-0.459327\pi\)
0.127432 + 0.991847i \(0.459327\pi\)
\(98\) 12.2089 1.23329
\(99\) −11.4211 −1.14786
\(100\) 17.0502 1.70502
\(101\) 7.78793 0.774928 0.387464 0.921885i \(-0.373351\pi\)
0.387464 + 0.921885i \(0.373351\pi\)
\(102\) 5.62230 0.556691
\(103\) −11.5730 −1.14032 −0.570161 0.821533i \(-0.693119\pi\)
−0.570161 + 0.821533i \(0.693119\pi\)
\(104\) −4.13843 −0.405807
\(105\) −10.1467 −0.990216
\(106\) 28.2128 2.74027
\(107\) −6.57110 −0.635252 −0.317626 0.948216i \(-0.602886\pi\)
−0.317626 + 0.948216i \(0.602886\pi\)
\(108\) −7.24924 −0.697559
\(109\) 4.20640 0.402901 0.201450 0.979499i \(-0.435435\pi\)
0.201450 + 0.979499i \(0.435435\pi\)
\(110\) −20.2633 −1.93203
\(111\) 22.5887 2.14402
\(112\) 3.20277 0.302633
\(113\) −0.987392 −0.0928860 −0.0464430 0.998921i \(-0.514789\pi\)
−0.0464430 + 0.998921i \(0.514789\pi\)
\(114\) 44.1260 4.13278
\(115\) 20.4502 1.90699
\(116\) −22.1001 −2.05195
\(117\) 18.1511 1.67807
\(118\) 15.8977 1.46350
\(119\) −1.09952 −0.100793
\(120\) −8.65165 −0.789784
\(121\) −3.28520 −0.298654
\(122\) −31.8947 −2.88761
\(123\) −13.7204 −1.23713
\(124\) −21.3286 −1.91536
\(125\) −6.83217 −0.611088
\(126\) 9.53170 0.849152
\(127\) 7.07572 0.627869 0.313934 0.949445i \(-0.398353\pi\)
0.313934 + 0.949445i \(0.398353\pi\)
\(128\) 7.31473 0.646537
\(129\) 10.6703 0.939470
\(130\) 32.2036 2.82444
\(131\) −0.989227 −0.0864292 −0.0432146 0.999066i \(-0.513760\pi\)
−0.0432146 + 0.999066i \(0.513760\pi\)
\(132\) 18.1084 1.57613
\(133\) −8.62949 −0.748272
\(134\) −3.47058 −0.299812
\(135\) 10.2611 0.883138
\(136\) −0.937516 −0.0803913
\(137\) 3.90498 0.333625 0.166813 0.985989i \(-0.446652\pi\)
0.166813 + 0.985989i \(0.446652\pi\)
\(138\) −33.2265 −2.82843
\(139\) 3.31759 0.281394 0.140697 0.990053i \(-0.455066\pi\)
0.140697 + 0.990053i \(0.455066\pi\)
\(140\) 9.30155 0.786124
\(141\) −24.8147 −2.08977
\(142\) −2.07311 −0.173971
\(143\) −12.2608 −1.02530
\(144\) −11.9775 −0.998125
\(145\) 31.2822 2.59785
\(146\) −18.6819 −1.54612
\(147\) 15.4437 1.27377
\(148\) −20.7072 −1.70212
\(149\) 13.0474 1.06888 0.534442 0.845205i \(-0.320522\pi\)
0.534442 + 0.845205i \(0.320522\pi\)
\(150\) 39.2121 3.20166
\(151\) −16.5677 −1.34826 −0.674129 0.738614i \(-0.735481\pi\)
−0.674129 + 0.738614i \(0.735481\pi\)
\(152\) −7.35799 −0.596812
\(153\) 4.11192 0.332429
\(154\) −6.43855 −0.518833
\(155\) 30.1901 2.42493
\(156\) −28.7789 −2.30416
\(157\) 12.6183 1.00705 0.503523 0.863982i \(-0.332037\pi\)
0.503523 + 0.863982i \(0.332037\pi\)
\(158\) −25.1002 −1.99686
\(159\) 35.6877 2.83022
\(160\) −27.7388 −2.19295
\(161\) 6.49793 0.512108
\(162\) 9.33499 0.733426
\(163\) 14.2228 1.11402 0.557009 0.830507i \(-0.311949\pi\)
0.557009 + 0.830507i \(0.311949\pi\)
\(164\) 12.5776 0.982146
\(165\) −25.6320 −1.99545
\(166\) −34.2963 −2.66191
\(167\) −11.3087 −0.875097 −0.437548 0.899195i \(-0.644153\pi\)
−0.437548 + 0.899195i \(0.644153\pi\)
\(168\) −2.74901 −0.212091
\(169\) 6.48563 0.498895
\(170\) 7.29537 0.559529
\(171\) 32.2720 2.46790
\(172\) −9.78156 −0.745837
\(173\) 18.4774 1.40481 0.702404 0.711779i \(-0.252110\pi\)
0.702404 + 0.711779i \(0.252110\pi\)
\(174\) −50.8259 −3.85310
\(175\) −7.66850 −0.579684
\(176\) 8.09065 0.609856
\(177\) 20.1097 1.51154
\(178\) 26.0159 1.94998
\(179\) −20.0292 −1.49705 −0.748526 0.663106i \(-0.769238\pi\)
−0.748526 + 0.663106i \(0.769238\pi\)
\(180\) −34.7853 −2.59274
\(181\) 7.58523 0.563806 0.281903 0.959443i \(-0.409034\pi\)
0.281903 + 0.959443i \(0.409034\pi\)
\(182\) 10.2325 0.758485
\(183\) −40.3451 −2.98239
\(184\) 5.54050 0.408451
\(185\) 29.3106 2.15496
\(186\) −49.0515 −3.59663
\(187\) −2.77755 −0.203115
\(188\) 22.7478 1.65905
\(189\) 3.26042 0.237161
\(190\) 57.2569 4.15385
\(191\) −18.8268 −1.36226 −0.681128 0.732164i \(-0.738510\pi\)
−0.681128 + 0.732164i \(0.738510\pi\)
\(192\) 29.5326 2.13133
\(193\) 1.46391 0.105374 0.0526872 0.998611i \(-0.483221\pi\)
0.0526872 + 0.998611i \(0.483221\pi\)
\(194\) −5.29193 −0.379939
\(195\) 40.7359 2.91716
\(196\) −14.1573 −1.01124
\(197\) 12.9636 0.923618 0.461809 0.886979i \(-0.347200\pi\)
0.461809 + 0.886979i \(0.347200\pi\)
\(198\) 24.0784 1.71118
\(199\) 16.9078 1.19856 0.599281 0.800539i \(-0.295453\pi\)
0.599281 + 0.800539i \(0.295453\pi\)
\(200\) −6.53860 −0.462349
\(201\) −4.39010 −0.309654
\(202\) −16.4189 −1.15523
\(203\) 9.93975 0.697634
\(204\) −6.51955 −0.456460
\(205\) −17.8033 −1.24344
\(206\) 24.3987 1.69994
\(207\) −24.3005 −1.68900
\(208\) −12.8581 −0.891552
\(209\) −21.7993 −1.50789
\(210\) 21.3917 1.47617
\(211\) 0.663214 0.0456576 0.0228288 0.999739i \(-0.492733\pi\)
0.0228288 + 0.999739i \(0.492733\pi\)
\(212\) −32.7151 −2.24688
\(213\) −2.62237 −0.179682
\(214\) 13.8535 0.947004
\(215\) 13.8456 0.944260
\(216\) 2.78002 0.189156
\(217\) 9.59274 0.651198
\(218\) −8.86813 −0.600625
\(219\) −23.6316 −1.59687
\(220\) 23.4970 1.58417
\(221\) 4.41425 0.296935
\(222\) −47.6225 −3.19621
\(223\) 17.5812 1.17732 0.588661 0.808380i \(-0.299655\pi\)
0.588661 + 0.808380i \(0.299655\pi\)
\(224\) −8.81386 −0.588901
\(225\) 28.6781 1.91188
\(226\) 2.08166 0.138470
\(227\) 0.310250 0.0205920 0.0102960 0.999947i \(-0.496723\pi\)
0.0102960 + 0.999947i \(0.496723\pi\)
\(228\) −51.1680 −3.38868
\(229\) −1.53337 −0.101328 −0.0506641 0.998716i \(-0.516134\pi\)
−0.0506641 + 0.998716i \(0.516134\pi\)
\(230\) −43.1139 −2.84285
\(231\) −8.14443 −0.535864
\(232\) 8.47520 0.556424
\(233\) 30.3026 1.98519 0.992596 0.121461i \(-0.0387580\pi\)
0.992596 + 0.121461i \(0.0387580\pi\)
\(234\) −38.2669 −2.50158
\(235\) −32.1990 −2.10043
\(236\) −18.4347 −1.20000
\(237\) −31.7504 −2.06241
\(238\) 2.31806 0.150258
\(239\) −19.8755 −1.28564 −0.642821 0.766017i \(-0.722236\pi\)
−0.642821 + 0.766017i \(0.722236\pi\)
\(240\) −26.8807 −1.73514
\(241\) −11.2526 −0.724846 −0.362423 0.932014i \(-0.618050\pi\)
−0.362423 + 0.932014i \(0.618050\pi\)
\(242\) 6.92600 0.445220
\(243\) 20.7042 1.32817
\(244\) 36.9846 2.36770
\(245\) 20.0394 1.28027
\(246\) 28.9260 1.84425
\(247\) 34.6448 2.20439
\(248\) 8.17931 0.519387
\(249\) −43.3830 −2.74929
\(250\) 14.4039 0.910981
\(251\) 7.74777 0.489035 0.244517 0.969645i \(-0.421370\pi\)
0.244517 + 0.969645i \(0.421370\pi\)
\(252\) −11.0528 −0.696263
\(253\) 16.4147 1.03198
\(254\) −14.9173 −0.935997
\(255\) 9.22827 0.577897
\(256\) 6.72693 0.420433
\(257\) 24.2754 1.51426 0.757129 0.653266i \(-0.226602\pi\)
0.757129 + 0.653266i \(0.226602\pi\)
\(258\) −22.4956 −1.40052
\(259\) 9.31327 0.578698
\(260\) −37.3429 −2.31591
\(261\) −37.1720 −2.30089
\(262\) 2.08553 0.128845
\(263\) 12.5628 0.774657 0.387328 0.921942i \(-0.373398\pi\)
0.387328 + 0.921942i \(0.373398\pi\)
\(264\) −6.94440 −0.427398
\(265\) 46.3075 2.84465
\(266\) 18.1931 1.11549
\(267\) 32.9088 2.01399
\(268\) 4.02444 0.245832
\(269\) −17.0970 −1.04242 −0.521211 0.853428i \(-0.674520\pi\)
−0.521211 + 0.853428i \(0.674520\pi\)
\(270\) −21.6330 −1.31654
\(271\) −7.68225 −0.466664 −0.233332 0.972397i \(-0.574963\pi\)
−0.233332 + 0.972397i \(0.574963\pi\)
\(272\) −2.91287 −0.176619
\(273\) 12.9436 0.783383
\(274\) −8.23266 −0.497353
\(275\) −19.3717 −1.16816
\(276\) 38.5290 2.31917
\(277\) 6.57498 0.395052 0.197526 0.980298i \(-0.436709\pi\)
0.197526 + 0.980298i \(0.436709\pi\)
\(278\) −6.99428 −0.419489
\(279\) −35.8743 −2.14774
\(280\) −3.56706 −0.213172
\(281\) −6.03721 −0.360150 −0.180075 0.983653i \(-0.557634\pi\)
−0.180075 + 0.983653i \(0.557634\pi\)
\(282\) 52.3154 3.11534
\(283\) 10.0544 0.597673 0.298836 0.954304i \(-0.403401\pi\)
0.298836 + 0.954304i \(0.403401\pi\)
\(284\) 2.40395 0.142648
\(285\) 72.4270 4.29021
\(286\) 25.8488 1.52847
\(287\) −5.65690 −0.333916
\(288\) 32.9615 1.94227
\(289\) 1.00000 0.0588235
\(290\) −65.9505 −3.87275
\(291\) −6.69402 −0.392410
\(292\) 21.6632 1.26774
\(293\) 17.7221 1.03534 0.517669 0.855581i \(-0.326800\pi\)
0.517669 + 0.855581i \(0.326800\pi\)
\(294\) −32.5590 −1.89888
\(295\) 26.0939 1.51925
\(296\) 7.94102 0.461562
\(297\) 8.23628 0.477917
\(298\) −27.5071 −1.59344
\(299\) −26.0872 −1.50866
\(300\) −45.4698 −2.62520
\(301\) 4.39935 0.253574
\(302\) 34.9287 2.00992
\(303\) −20.7690 −1.19315
\(304\) −22.8613 −1.31119
\(305\) −52.3509 −2.99760
\(306\) −8.66894 −0.495570
\(307\) −25.8245 −1.47388 −0.736941 0.675957i \(-0.763731\pi\)
−0.736941 + 0.675957i \(0.763731\pi\)
\(308\) 7.46605 0.425418
\(309\) 30.8631 1.75574
\(310\) −63.6481 −3.61497
\(311\) −12.6362 −0.716532 −0.358266 0.933620i \(-0.616632\pi\)
−0.358266 + 0.933620i \(0.616632\pi\)
\(312\) 11.0365 0.624816
\(313\) −10.5786 −0.597936 −0.298968 0.954263i \(-0.596642\pi\)
−0.298968 + 0.954263i \(0.596642\pi\)
\(314\) −26.6023 −1.50126
\(315\) 15.6450 0.881497
\(316\) 29.1058 1.63733
\(317\) 14.2061 0.797893 0.398947 0.916974i \(-0.369376\pi\)
0.398947 + 0.916974i \(0.369376\pi\)
\(318\) −75.2383 −4.21916
\(319\) 25.1092 1.40585
\(320\) 38.3208 2.14220
\(321\) 17.5239 0.978091
\(322\) −13.6992 −0.763427
\(323\) 7.84839 0.436696
\(324\) −10.8247 −0.601374
\(325\) 30.7867 1.70774
\(326\) −29.9852 −1.66072
\(327\) −11.2177 −0.620341
\(328\) −4.82339 −0.266327
\(329\) −10.2310 −0.564056
\(330\) 54.0385 2.97472
\(331\) 19.2837 1.05993 0.529965 0.848020i \(-0.322205\pi\)
0.529965 + 0.848020i \(0.322205\pi\)
\(332\) 39.7695 2.18263
\(333\) −34.8291 −1.90862
\(334\) 23.8416 1.30455
\(335\) −5.69649 −0.311233
\(336\) −8.54121 −0.465961
\(337\) −4.51321 −0.245850 −0.122925 0.992416i \(-0.539227\pi\)
−0.122925 + 0.992416i \(0.539227\pi\)
\(338\) −13.6733 −0.743729
\(339\) 2.63320 0.143016
\(340\) −8.45961 −0.458787
\(341\) 24.2326 1.31227
\(342\) −68.0372 −3.67903
\(343\) 14.0641 0.759388
\(344\) 3.75114 0.202248
\(345\) −54.5369 −2.93617
\(346\) −38.9548 −2.09422
\(347\) −14.4680 −0.776685 −0.388342 0.921515i \(-0.626952\pi\)
−0.388342 + 0.921515i \(0.626952\pi\)
\(348\) 58.9371 3.15936
\(349\) 15.8445 0.848136 0.424068 0.905630i \(-0.360602\pi\)
0.424068 + 0.905630i \(0.360602\pi\)
\(350\) 16.1671 0.864166
\(351\) −13.0896 −0.698670
\(352\) −22.2651 −1.18673
\(353\) 1.00000 0.0532246
\(354\) −42.3962 −2.25333
\(355\) −3.40273 −0.180598
\(356\) −30.1677 −1.59889
\(357\) 2.93223 0.155190
\(358\) 42.2264 2.23173
\(359\) 17.1219 0.903658 0.451829 0.892105i \(-0.350772\pi\)
0.451829 + 0.892105i \(0.350772\pi\)
\(360\) 13.3398 0.703071
\(361\) 42.5972 2.24196
\(362\) −15.9915 −0.840496
\(363\) 8.76103 0.459835
\(364\) −11.8655 −0.621921
\(365\) −30.6638 −1.60502
\(366\) 85.0573 4.44601
\(367\) −13.4138 −0.700192 −0.350096 0.936714i \(-0.613851\pi\)
−0.350096 + 0.936714i \(0.613851\pi\)
\(368\) 17.2144 0.897361
\(369\) 21.1553 1.10130
\(370\) −61.7938 −3.21251
\(371\) 14.7140 0.763910
\(372\) 56.8795 2.94906
\(373\) −32.5154 −1.68358 −0.841792 0.539802i \(-0.818499\pi\)
−0.841792 + 0.539802i \(0.818499\pi\)
\(374\) 5.85576 0.302794
\(375\) 18.2202 0.940885
\(376\) −8.72357 −0.449884
\(377\) −39.9051 −2.05522
\(378\) −6.87376 −0.353548
\(379\) −0.0410933 −0.00211082 −0.00105541 0.999999i \(-0.500336\pi\)
−0.00105541 + 0.999999i \(0.500336\pi\)
\(380\) −66.3943 −3.40596
\(381\) −18.8697 −0.966722
\(382\) 39.6914 2.03079
\(383\) −5.36933 −0.274360 −0.137180 0.990546i \(-0.543804\pi\)
−0.137180 + 0.990546i \(0.543804\pi\)
\(384\) −19.5071 −0.995466
\(385\) −10.5680 −0.538596
\(386\) −3.08627 −0.157087
\(387\) −16.4524 −0.836322
\(388\) 6.13645 0.311531
\(389\) 18.2017 0.922864 0.461432 0.887176i \(-0.347336\pi\)
0.461432 + 0.887176i \(0.347336\pi\)
\(390\) −85.8812 −4.34876
\(391\) −5.90976 −0.298870
\(392\) 5.42920 0.274216
\(393\) 2.63809 0.133074
\(394\) −27.3304 −1.37689
\(395\) −41.1986 −2.07293
\(396\) −27.9210 −1.40308
\(397\) −14.8207 −0.743830 −0.371915 0.928267i \(-0.621299\pi\)
−0.371915 + 0.928267i \(0.621299\pi\)
\(398\) −35.6457 −1.78676
\(399\) 23.0133 1.15211
\(400\) −20.3155 −1.01577
\(401\) 14.2644 0.712331 0.356165 0.934423i \(-0.384084\pi\)
0.356165 + 0.934423i \(0.384084\pi\)
\(402\) 9.25540 0.461618
\(403\) −38.5119 −1.91842
\(404\) 19.0391 0.947230
\(405\) 15.3222 0.761364
\(406\) −20.9554 −1.04000
\(407\) 23.5266 1.16617
\(408\) 2.50019 0.123778
\(409\) 29.1103 1.43941 0.719706 0.694279i \(-0.244277\pi\)
0.719706 + 0.694279i \(0.244277\pi\)
\(410\) 37.5337 1.85366
\(411\) −10.4139 −0.513679
\(412\) −28.2924 −1.39387
\(413\) 8.29120 0.407983
\(414\) 51.2314 2.51788
\(415\) −56.2928 −2.76330
\(416\) 35.3850 1.73489
\(417\) −8.84741 −0.433259
\(418\) 45.9583 2.24789
\(419\) −11.8324 −0.578052 −0.289026 0.957321i \(-0.593331\pi\)
−0.289026 + 0.957321i \(0.593331\pi\)
\(420\) −24.8055 −1.21039
\(421\) 31.6285 1.54148 0.770739 0.637151i \(-0.219887\pi\)
0.770739 + 0.637151i \(0.219887\pi\)
\(422\) −1.39822 −0.0680642
\(423\) 38.2614 1.86033
\(424\) 12.5459 0.609285
\(425\) 6.97438 0.338307
\(426\) 5.52860 0.267861
\(427\) −16.6342 −0.804985
\(428\) −16.0643 −0.776498
\(429\) 32.6974 1.57865
\(430\) −29.1898 −1.40766
\(431\) −24.6588 −1.18777 −0.593885 0.804550i \(-0.702407\pi\)
−0.593885 + 0.804550i \(0.702407\pi\)
\(432\) 8.63753 0.415573
\(433\) −32.2412 −1.54942 −0.774708 0.632320i \(-0.782103\pi\)
−0.774708 + 0.632320i \(0.782103\pi\)
\(434\) −20.2238 −0.970775
\(435\) −83.4240 −3.99988
\(436\) 10.2834 0.492484
\(437\) −46.3821 −2.21876
\(438\) 49.8211 2.38055
\(439\) 1.41788 0.0676716 0.0338358 0.999427i \(-0.489228\pi\)
0.0338358 + 0.999427i \(0.489228\pi\)
\(440\) −9.01089 −0.429577
\(441\) −23.8123 −1.13392
\(442\) −9.30632 −0.442657
\(443\) 36.7112 1.74420 0.872100 0.489327i \(-0.162758\pi\)
0.872100 + 0.489327i \(0.162758\pi\)
\(444\) 55.2224 2.62074
\(445\) 42.7017 2.02426
\(446\) −37.0654 −1.75510
\(447\) −34.7950 −1.64575
\(448\) 12.1762 0.575272
\(449\) −8.69800 −0.410484 −0.205242 0.978711i \(-0.565798\pi\)
−0.205242 + 0.978711i \(0.565798\pi\)
\(450\) −60.4605 −2.85014
\(451\) −14.2901 −0.672896
\(452\) −2.41387 −0.113539
\(453\) 44.1830 2.07590
\(454\) −0.654083 −0.0306976
\(455\) 16.7953 0.787377
\(456\) 19.6224 0.918905
\(457\) −4.73505 −0.221496 −0.110748 0.993849i \(-0.535325\pi\)
−0.110748 + 0.993849i \(0.535325\pi\)
\(458\) 3.23272 0.151055
\(459\) −2.96530 −0.138408
\(460\) 49.9943 2.33100
\(461\) 20.3578 0.948155 0.474078 0.880483i \(-0.342782\pi\)
0.474078 + 0.880483i \(0.342782\pi\)
\(462\) 17.1704 0.798841
\(463\) −4.92241 −0.228764 −0.114382 0.993437i \(-0.536489\pi\)
−0.114382 + 0.993437i \(0.536489\pi\)
\(464\) 26.3325 1.22246
\(465\) −80.5116 −3.73364
\(466\) −63.8854 −2.95943
\(467\) 3.38256 0.156526 0.0782630 0.996933i \(-0.475063\pi\)
0.0782630 + 0.996933i \(0.475063\pi\)
\(468\) 44.3738 2.05118
\(469\) −1.81003 −0.0835794
\(470\) 67.8833 3.13122
\(471\) −33.6506 −1.55054
\(472\) 7.06955 0.325402
\(473\) 11.1134 0.510994
\(474\) 66.9376 3.07455
\(475\) 54.7377 2.51154
\(476\) −2.68800 −0.123204
\(477\) −55.0262 −2.51948
\(478\) 41.9025 1.91657
\(479\) 6.21983 0.284191 0.142096 0.989853i \(-0.454616\pi\)
0.142096 + 0.989853i \(0.454616\pi\)
\(480\) 73.9744 3.37646
\(481\) −37.3899 −1.70483
\(482\) 23.7233 1.08057
\(483\) −17.3288 −0.788487
\(484\) −8.03130 −0.365059
\(485\) −8.68601 −0.394411
\(486\) −43.6495 −1.97998
\(487\) −33.6068 −1.52287 −0.761435 0.648241i \(-0.775505\pi\)
−0.761435 + 0.648241i \(0.775505\pi\)
\(488\) −14.1833 −0.642046
\(489\) −37.9297 −1.71524
\(490\) −42.2478 −1.90856
\(491\) −16.2926 −0.735277 −0.367638 0.929969i \(-0.619834\pi\)
−0.367638 + 0.929969i \(0.619834\pi\)
\(492\) −33.5422 −1.51220
\(493\) −9.04005 −0.407144
\(494\) −73.0396 −3.28621
\(495\) 39.5216 1.77636
\(496\) 25.4132 1.14109
\(497\) −1.08120 −0.0484984
\(498\) 91.4619 4.09851
\(499\) −14.9769 −0.670457 −0.335228 0.942137i \(-0.608813\pi\)
−0.335228 + 0.942137i \(0.608813\pi\)
\(500\) −16.7025 −0.746960
\(501\) 30.1584 1.34738
\(502\) −16.3342 −0.729030
\(503\) 40.6196 1.81114 0.905569 0.424199i \(-0.139444\pi\)
0.905569 + 0.424199i \(0.139444\pi\)
\(504\) 4.23866 0.188805
\(505\) −26.9494 −1.19923
\(506\) −34.6061 −1.53843
\(507\) −17.2960 −0.768143
\(508\) 17.2979 0.767472
\(509\) −13.5307 −0.599740 −0.299870 0.953980i \(-0.596943\pi\)
−0.299870 + 0.953980i \(0.596943\pi\)
\(510\) −19.4554 −0.861501
\(511\) −9.74325 −0.431016
\(512\) −28.8115 −1.27330
\(513\) −23.2728 −1.02752
\(514\) −51.1784 −2.25738
\(515\) 40.0472 1.76469
\(516\) 26.0856 1.14836
\(517\) −25.8451 −1.13667
\(518\) −19.6346 −0.862696
\(519\) −49.2758 −2.16297
\(520\) 14.3206 0.628002
\(521\) −19.5015 −0.854378 −0.427189 0.904162i \(-0.640496\pi\)
−0.427189 + 0.904162i \(0.640496\pi\)
\(522\) 78.3677 3.43006
\(523\) −26.6832 −1.16677 −0.583387 0.812194i \(-0.698273\pi\)
−0.583387 + 0.812194i \(0.698273\pi\)
\(524\) −2.41835 −0.105646
\(525\) 20.4505 0.892533
\(526\) −26.4855 −1.15482
\(527\) −8.72445 −0.380043
\(528\) −21.5763 −0.938988
\(529\) 11.9253 0.518492
\(530\) −97.6275 −4.24067
\(531\) −31.0069 −1.34558
\(532\) −21.0964 −0.914647
\(533\) 22.7107 0.983711
\(534\) −69.3798 −3.00236
\(535\) 22.7386 0.983078
\(536\) −1.54333 −0.0666618
\(537\) 53.4142 2.30499
\(538\) 36.0446 1.55399
\(539\) 16.0849 0.692827
\(540\) 25.0853 1.07950
\(541\) −16.9566 −0.729021 −0.364511 0.931199i \(-0.618764\pi\)
−0.364511 + 0.931199i \(0.618764\pi\)
\(542\) 16.1961 0.695680
\(543\) −20.2284 −0.868086
\(544\) 8.01607 0.343686
\(545\) −14.5559 −0.623504
\(546\) −27.2883 −1.16783
\(547\) −10.0239 −0.428591 −0.214296 0.976769i \(-0.568746\pi\)
−0.214296 + 0.976769i \(0.568746\pi\)
\(548\) 9.54648 0.407805
\(549\) 62.2074 2.65495
\(550\) 40.8403 1.74144
\(551\) −70.9499 −3.02257
\(552\) −14.7755 −0.628887
\(553\) −13.0906 −0.556670
\(554\) −13.8617 −0.588925
\(555\) −78.1660 −3.31796
\(556\) 8.11048 0.343961
\(557\) 29.4122 1.24624 0.623118 0.782128i \(-0.285866\pi\)
0.623118 + 0.782128i \(0.285866\pi\)
\(558\) 75.6317 3.20175
\(559\) −17.6621 −0.747025
\(560\) −11.0829 −0.468337
\(561\) 7.40723 0.312734
\(562\) 12.7279 0.536894
\(563\) 39.2636 1.65477 0.827383 0.561639i \(-0.189829\pi\)
0.827383 + 0.561639i \(0.189829\pi\)
\(564\) −60.6643 −2.55443
\(565\) 3.41677 0.143745
\(566\) −21.1972 −0.890983
\(567\) 4.86853 0.204459
\(568\) −0.921890 −0.0386817
\(569\) 27.7414 1.16298 0.581489 0.813554i \(-0.302470\pi\)
0.581489 + 0.813554i \(0.302470\pi\)
\(570\) −152.694 −6.39564
\(571\) −33.0550 −1.38331 −0.691655 0.722228i \(-0.743118\pi\)
−0.691655 + 0.722228i \(0.743118\pi\)
\(572\) −29.9739 −1.25327
\(573\) 50.2075 2.09745
\(574\) 11.9261 0.497787
\(575\) −41.2170 −1.71887
\(576\) −45.5358 −1.89733
\(577\) 36.2137 1.50760 0.753798 0.657106i \(-0.228219\pi\)
0.753798 + 0.657106i \(0.228219\pi\)
\(578\) −2.10824 −0.0876914
\(579\) −3.90397 −0.162244
\(580\) 76.4754 3.17547
\(581\) −17.8867 −0.742066
\(582\) 14.1126 0.584987
\(583\) 37.1695 1.53940
\(584\) −8.30765 −0.343773
\(585\) −62.8100 −2.59687
\(586\) −37.3626 −1.54343
\(587\) −20.6469 −0.852187 −0.426094 0.904679i \(-0.640111\pi\)
−0.426094 + 0.904679i \(0.640111\pi\)
\(588\) 37.7550 1.55699
\(589\) −68.4729 −2.82138
\(590\) −55.0124 −2.26482
\(591\) −34.5716 −1.42208
\(592\) 24.6728 1.01405
\(593\) 13.6932 0.562311 0.281155 0.959662i \(-0.409282\pi\)
0.281155 + 0.959662i \(0.409282\pi\)
\(594\) −17.3641 −0.712457
\(595\) 3.80479 0.155981
\(596\) 31.8968 1.30654
\(597\) −45.0900 −1.84541
\(598\) 54.9982 2.24904
\(599\) −5.80474 −0.237175 −0.118588 0.992944i \(-0.537837\pi\)
−0.118588 + 0.992944i \(0.537837\pi\)
\(600\) 17.4373 0.711873
\(601\) 1.65581 0.0675420 0.0337710 0.999430i \(-0.489248\pi\)
0.0337710 + 0.999430i \(0.489248\pi\)
\(602\) −9.27490 −0.378017
\(603\) 6.76903 0.275656
\(604\) −40.5028 −1.64804
\(605\) 11.3681 0.462179
\(606\) 43.7861 1.77869
\(607\) 31.5026 1.27865 0.639327 0.768935i \(-0.279213\pi\)
0.639327 + 0.768935i \(0.279213\pi\)
\(608\) 62.9132 2.55147
\(609\) −26.5075 −1.07414
\(610\) 110.368 4.46868
\(611\) 41.0745 1.66170
\(612\) 10.0524 0.406343
\(613\) 17.3656 0.701389 0.350695 0.936490i \(-0.385945\pi\)
0.350695 + 0.936490i \(0.385945\pi\)
\(614\) 54.4444 2.19720
\(615\) 47.4782 1.91451
\(616\) −2.86316 −0.115360
\(617\) 24.3412 0.979941 0.489971 0.871739i \(-0.337007\pi\)
0.489971 + 0.871739i \(0.337007\pi\)
\(618\) −65.0669 −2.61738
\(619\) 19.0596 0.766068 0.383034 0.923734i \(-0.374879\pi\)
0.383034 + 0.923734i \(0.374879\pi\)
\(620\) 73.8055 2.96410
\(621\) 17.5242 0.703223
\(622\) 26.6401 1.06817
\(623\) 13.5682 0.543600
\(624\) 34.2903 1.37271
\(625\) −11.2299 −0.449195
\(626\) 22.3022 0.891375
\(627\) 58.1348 2.32168
\(628\) 30.8477 1.23096
\(629\) −8.47027 −0.337732
\(630\) −32.9835 −1.31410
\(631\) 10.8712 0.432777 0.216389 0.976307i \(-0.430572\pi\)
0.216389 + 0.976307i \(0.430572\pi\)
\(632\) −11.1618 −0.443993
\(633\) −1.76867 −0.0702984
\(634\) −29.9499 −1.18946
\(635\) −24.4848 −0.971651
\(636\) 87.2453 3.45950
\(637\) −25.5631 −1.01285
\(638\) −52.9364 −2.09577
\(639\) 4.04339 0.159954
\(640\) −25.3119 −1.00054
\(641\) −14.3699 −0.567577 −0.283788 0.958887i \(-0.591591\pi\)
−0.283788 + 0.958887i \(0.591591\pi\)
\(642\) −36.9447 −1.45809
\(643\) 32.9196 1.29822 0.649112 0.760693i \(-0.275141\pi\)
0.649112 + 0.760693i \(0.275141\pi\)
\(644\) 15.8854 0.625973
\(645\) −36.9236 −1.45387
\(646\) −16.5463 −0.651006
\(647\) −45.6054 −1.79293 −0.896467 0.443110i \(-0.853875\pi\)
−0.896467 + 0.443110i \(0.853875\pi\)
\(648\) 4.15118 0.163074
\(649\) 20.9448 0.822153
\(650\) −64.9059 −2.54582
\(651\) −25.5821 −1.00264
\(652\) 34.7704 1.36171
\(653\) −4.55485 −0.178245 −0.0891225 0.996021i \(-0.528406\pi\)
−0.0891225 + 0.996021i \(0.528406\pi\)
\(654\) 23.6497 0.924776
\(655\) 3.42312 0.133753
\(656\) −14.9863 −0.585117
\(657\) 36.4372 1.42155
\(658\) 21.5695 0.840868
\(659\) −7.90075 −0.307769 −0.153885 0.988089i \(-0.549178\pi\)
−0.153885 + 0.988089i \(0.549178\pi\)
\(660\) −62.6623 −2.43913
\(661\) 8.81131 0.342720 0.171360 0.985208i \(-0.445184\pi\)
0.171360 + 0.985208i \(0.445184\pi\)
\(662\) −40.6548 −1.58009
\(663\) −11.7720 −0.457187
\(664\) −15.2512 −0.591862
\(665\) 29.8615 1.15798
\(666\) 73.4283 2.84529
\(667\) 53.4246 2.06861
\(668\) −27.6464 −1.06967
\(669\) −46.8858 −1.81271
\(670\) 12.0096 0.463971
\(671\) −42.0203 −1.62218
\(672\) 23.5050 0.906724
\(673\) 6.46726 0.249294 0.124647 0.992201i \(-0.460220\pi\)
0.124647 + 0.992201i \(0.460220\pi\)
\(674\) 9.51494 0.366502
\(675\) −20.6811 −0.796018
\(676\) 15.8554 0.609822
\(677\) 33.1350 1.27348 0.636741 0.771078i \(-0.280282\pi\)
0.636741 + 0.771078i \(0.280282\pi\)
\(678\) −5.55142 −0.213201
\(679\) −2.75993 −0.105916
\(680\) 3.24418 0.124409
\(681\) −0.827381 −0.0317053
\(682\) −51.0883 −1.95627
\(683\) 2.33896 0.0894980 0.0447490 0.998998i \(-0.485751\pi\)
0.0447490 + 0.998998i \(0.485751\pi\)
\(684\) 78.8950 3.01663
\(685\) −13.5128 −0.516298
\(686\) −29.6505 −1.13206
\(687\) 4.08923 0.156014
\(688\) 11.6548 0.444335
\(689\) −59.0720 −2.25047
\(690\) 114.977 4.37710
\(691\) 37.1582 1.41356 0.706781 0.707432i \(-0.250146\pi\)
0.706781 + 0.707432i \(0.250146\pi\)
\(692\) 45.1714 1.71716
\(693\) 12.5578 0.477030
\(694\) 30.5021 1.15785
\(695\) −11.4802 −0.435468
\(696\) −22.6018 −0.856720
\(697\) 5.14486 0.194876
\(698\) −33.4041 −1.26436
\(699\) −80.8117 −3.05658
\(700\) −18.7471 −0.708574
\(701\) −7.28344 −0.275092 −0.137546 0.990495i \(-0.543921\pi\)
−0.137546 + 0.990495i \(0.543921\pi\)
\(702\) 27.5960 1.04155
\(703\) −66.4780 −2.50727
\(704\) 30.7589 1.15927
\(705\) 85.8688 3.23401
\(706\) −2.10824 −0.0793448
\(707\) −8.56302 −0.322045
\(708\) 49.1621 1.84762
\(709\) −49.1251 −1.84493 −0.922467 0.386077i \(-0.873830\pi\)
−0.922467 + 0.386077i \(0.873830\pi\)
\(710\) 7.17378 0.269227
\(711\) 48.9554 1.83597
\(712\) 11.5690 0.433568
\(713\) 51.5595 1.93092
\(714\) −6.18186 −0.231350
\(715\) 42.4274 1.58669
\(716\) −48.9652 −1.82991
\(717\) 53.0045 1.97949
\(718\) −36.0971 −1.34713
\(719\) −39.6517 −1.47876 −0.739380 0.673288i \(-0.764881\pi\)
−0.739380 + 0.673288i \(0.764881\pi\)
\(720\) 41.4470 1.54464
\(721\) 12.7248 0.473896
\(722\) −89.8053 −3.34221
\(723\) 30.0087 1.11604
\(724\) 18.5436 0.689166
\(725\) −63.0488 −2.34157
\(726\) −18.4704 −0.685500
\(727\) 9.13797 0.338909 0.169454 0.985538i \(-0.445800\pi\)
0.169454 + 0.985538i \(0.445800\pi\)
\(728\) 4.55031 0.168646
\(729\) −41.9308 −1.55299
\(730\) 64.6468 2.39268
\(731\) −4.00114 −0.147988
\(732\) −98.6313 −3.64552
\(733\) −4.18278 −0.154495 −0.0772473 0.997012i \(-0.524613\pi\)
−0.0772473 + 0.997012i \(0.524613\pi\)
\(734\) 28.2795 1.04381
\(735\) −53.4413 −1.97121
\(736\) −47.3731 −1.74619
\(737\) −4.57239 −0.168426
\(738\) −44.6005 −1.64177
\(739\) −43.2103 −1.58952 −0.794758 0.606926i \(-0.792402\pi\)
−0.794758 + 0.606926i \(0.792402\pi\)
\(740\) 71.6552 2.63410
\(741\) −92.3914 −3.39408
\(742\) −31.0206 −1.13880
\(743\) −21.7408 −0.797593 −0.398796 0.917040i \(-0.630572\pi\)
−0.398796 + 0.917040i \(0.630572\pi\)
\(744\) −21.8128 −0.799694
\(745\) −45.1492 −1.65414
\(746\) 68.5504 2.50981
\(747\) 66.8915 2.44743
\(748\) −6.79026 −0.248276
\(749\) 7.22508 0.263999
\(750\) −38.4125 −1.40263
\(751\) −23.1640 −0.845265 −0.422632 0.906301i \(-0.638894\pi\)
−0.422632 + 0.906301i \(0.638894\pi\)
\(752\) −27.1042 −0.988388
\(753\) −20.6619 −0.752961
\(754\) 84.1296 3.06382
\(755\) 57.3308 2.08648
\(756\) 7.97071 0.289892
\(757\) −8.33446 −0.302921 −0.151461 0.988463i \(-0.548398\pi\)
−0.151461 + 0.988463i \(0.548398\pi\)
\(758\) 0.0866347 0.00314671
\(759\) −43.7750 −1.58893
\(760\) 25.4616 0.923590
\(761\) −37.8193 −1.37095 −0.685474 0.728097i \(-0.740405\pi\)
−0.685474 + 0.728097i \(0.740405\pi\)
\(762\) 39.7819 1.44114
\(763\) −4.62504 −0.167438
\(764\) −46.0256 −1.66515
\(765\) −14.2289 −0.514447
\(766\) 11.3199 0.409003
\(767\) −33.2867 −1.20191
\(768\) −17.9395 −0.647337
\(769\) 40.3994 1.45684 0.728420 0.685131i \(-0.240255\pi\)
0.728420 + 0.685131i \(0.240255\pi\)
\(770\) 22.2800 0.802914
\(771\) −64.7381 −2.33149
\(772\) 3.57880 0.128804
\(773\) −32.7166 −1.17673 −0.588367 0.808594i \(-0.700229\pi\)
−0.588367 + 0.808594i \(0.700229\pi\)
\(774\) 34.6857 1.24675
\(775\) −60.8477 −2.18571
\(776\) −2.35327 −0.0844776
\(777\) −24.8368 −0.891015
\(778\) −38.3737 −1.37576
\(779\) 40.3789 1.44672
\(780\) 99.5867 3.56578
\(781\) −2.73126 −0.0977322
\(782\) 12.4592 0.445541
\(783\) 26.8065 0.957985
\(784\) 16.8686 0.602449
\(785\) −43.6642 −1.55844
\(786\) −5.56173 −0.198381
\(787\) 25.4707 0.907932 0.453966 0.891019i \(-0.350009\pi\)
0.453966 + 0.891019i \(0.350009\pi\)
\(788\) 31.6920 1.12898
\(789\) −33.5028 −1.19273
\(790\) 86.8567 3.09022
\(791\) 1.08566 0.0386017
\(792\) 10.7075 0.380473
\(793\) 66.7812 2.37147
\(794\) 31.2457 1.10887
\(795\) −123.494 −4.37987
\(796\) 41.3343 1.46506
\(797\) −2.37704 −0.0841991 −0.0420996 0.999113i \(-0.513405\pi\)
−0.0420996 + 0.999113i \(0.513405\pi\)
\(798\) −48.5176 −1.71751
\(799\) 9.30498 0.329187
\(800\) 55.9072 1.97662
\(801\) −50.7416 −1.79286
\(802\) −30.0729 −1.06191
\(803\) −24.6128 −0.868568
\(804\) −10.7324 −0.378504
\(805\) −22.4854 −0.792508
\(806\) 81.1926 2.85989
\(807\) 45.5946 1.60501
\(808\) −7.30131 −0.256859
\(809\) −14.7344 −0.518035 −0.259017 0.965873i \(-0.583399\pi\)
−0.259017 + 0.965873i \(0.583399\pi\)
\(810\) −32.3028 −1.13501
\(811\) −7.21156 −0.253232 −0.126616 0.991952i \(-0.540412\pi\)
−0.126616 + 0.991952i \(0.540412\pi\)
\(812\) 24.2996 0.852750
\(813\) 20.4872 0.718517
\(814\) −49.5999 −1.73847
\(815\) −49.2167 −1.72399
\(816\) 7.76810 0.271938
\(817\) −31.4025 −1.09864
\(818\) −61.3716 −2.14581
\(819\) −19.9575 −0.697373
\(820\) −43.5236 −1.51991
\(821\) 22.7725 0.794765 0.397383 0.917653i \(-0.369919\pi\)
0.397383 + 0.917653i \(0.369919\pi\)
\(822\) 21.9550 0.765769
\(823\) −36.5536 −1.27418 −0.637089 0.770790i \(-0.719862\pi\)
−0.637089 + 0.770790i \(0.719862\pi\)
\(824\) 10.8499 0.377973
\(825\) 51.6609 1.79860
\(826\) −17.4799 −0.608203
\(827\) 3.65442 0.127077 0.0635383 0.997979i \(-0.479761\pi\)
0.0635383 + 0.997979i \(0.479761\pi\)
\(828\) −59.4072 −2.06454
\(829\) −46.8615 −1.62757 −0.813784 0.581168i \(-0.802596\pi\)
−0.813784 + 0.581168i \(0.802596\pi\)
\(830\) 118.679 4.11940
\(831\) −17.5343 −0.608257
\(832\) −48.8838 −1.69474
\(833\) −5.79105 −0.200648
\(834\) 18.6525 0.645883
\(835\) 39.1328 1.35425
\(836\) −53.2926 −1.84316
\(837\) 25.8706 0.894219
\(838\) 24.9456 0.861733
\(839\) −18.8861 −0.652022 −0.326011 0.945366i \(-0.605705\pi\)
−0.326011 + 0.945366i \(0.605705\pi\)
\(840\) 9.51269 0.328219
\(841\) 52.7226 1.81802
\(842\) −66.6805 −2.29796
\(843\) 16.1001 0.554518
\(844\) 1.62135 0.0558093
\(845\) −22.4429 −0.772059
\(846\) −80.6643 −2.77330
\(847\) 3.61215 0.124115
\(848\) 38.9804 1.33859
\(849\) −26.8133 −0.920230
\(850\) −14.7037 −0.504333
\(851\) 50.0573 1.71594
\(852\) −6.41089 −0.219633
\(853\) −18.3337 −0.627733 −0.313867 0.949467i \(-0.601624\pi\)
−0.313867 + 0.949467i \(0.601624\pi\)
\(854\) 35.0689 1.20003
\(855\) −111.674 −3.81917
\(856\) 6.16051 0.210562
\(857\) 12.6696 0.432786 0.216393 0.976306i \(-0.430571\pi\)
0.216393 + 0.976306i \(0.430571\pi\)
\(858\) −68.9341 −2.35337
\(859\) 56.8643 1.94018 0.970092 0.242738i \(-0.0780456\pi\)
0.970092 + 0.242738i \(0.0780456\pi\)
\(860\) 33.8481 1.15421
\(861\) 15.0859 0.514127
\(862\) 51.9867 1.77067
\(863\) −6.18825 −0.210650 −0.105325 0.994438i \(-0.533588\pi\)
−0.105325 + 0.994438i \(0.533588\pi\)
\(864\) −23.7701 −0.808674
\(865\) −63.9391 −2.17399
\(866\) 67.9724 2.30980
\(867\) −2.66682 −0.0905699
\(868\) 23.4513 0.795989
\(869\) −33.0688 −1.12178
\(870\) 175.878 5.96283
\(871\) 7.26672 0.246223
\(872\) −3.94357 −0.133546
\(873\) 10.3214 0.349326
\(874\) 97.7848 3.30762
\(875\) 7.51213 0.253956
\(876\) −57.7719 −1.95193
\(877\) 13.6697 0.461593 0.230796 0.973002i \(-0.425867\pi\)
0.230796 + 0.973002i \(0.425867\pi\)
\(878\) −2.98923 −0.100882
\(879\) −47.2618 −1.59410
\(880\) −27.9969 −0.943775
\(881\) 39.2014 1.32073 0.660365 0.750945i \(-0.270402\pi\)
0.660365 + 0.750945i \(0.270402\pi\)
\(882\) 50.2022 1.69040
\(883\) 30.2275 1.01724 0.508618 0.860992i \(-0.330156\pi\)
0.508618 + 0.860992i \(0.330156\pi\)
\(884\) 10.7915 0.362957
\(885\) −69.5878 −2.33917
\(886\) −77.3961 −2.60017
\(887\) −14.4501 −0.485189 −0.242594 0.970128i \(-0.577998\pi\)
−0.242594 + 0.970128i \(0.577998\pi\)
\(888\) −21.1773 −0.710662
\(889\) −7.77992 −0.260930
\(890\) −90.0256 −3.01767
\(891\) 12.2986 0.412018
\(892\) 42.9805 1.43909
\(893\) 73.0291 2.44383
\(894\) 73.3563 2.45340
\(895\) 69.3090 2.31675
\(896\) −8.04272 −0.268689
\(897\) 69.5698 2.32287
\(898\) 18.3375 0.611931
\(899\) 78.8695 2.63045
\(900\) 70.1092 2.33697
\(901\) −13.3821 −0.445823
\(902\) 30.1271 1.00312
\(903\) −11.7323 −0.390426
\(904\) 0.925696 0.0307882
\(905\) −26.2480 −0.872512
\(906\) −93.1484 −3.09465
\(907\) 20.7556 0.689179 0.344589 0.938754i \(-0.388018\pi\)
0.344589 + 0.938754i \(0.388018\pi\)
\(908\) 0.758466 0.0251706
\(909\) 32.0234 1.06215
\(910\) −35.4086 −1.17378
\(911\) 3.11546 0.103220 0.0516099 0.998667i \(-0.483565\pi\)
0.0516099 + 0.998667i \(0.483565\pi\)
\(912\) 60.9670 2.01882
\(913\) −45.1844 −1.49538
\(914\) 9.98263 0.330196
\(915\) 139.610 4.61537
\(916\) −3.74862 −0.123858
\(917\) 1.08768 0.0359183
\(918\) 6.25157 0.206333
\(919\) 21.3465 0.704154 0.352077 0.935971i \(-0.385475\pi\)
0.352077 + 0.935971i \(0.385475\pi\)
\(920\) −19.1724 −0.632094
\(921\) 68.8693 2.26932
\(922\) −42.9191 −1.41347
\(923\) 4.34068 0.142875
\(924\) −19.9106 −0.655011
\(925\) −59.0750 −1.94237
\(926\) 10.3776 0.341031
\(927\) −47.5873 −1.56297
\(928\) −72.4657 −2.37880
\(929\) 15.1055 0.495596 0.247798 0.968812i \(-0.420293\pi\)
0.247798 + 0.968812i \(0.420293\pi\)
\(930\) 169.738 5.56593
\(931\) −45.4504 −1.48958
\(932\) 74.0806 2.42659
\(933\) 33.6984 1.10324
\(934\) −7.13125 −0.233342
\(935\) 9.61145 0.314328
\(936\) −17.0169 −0.556215
\(937\) −25.4242 −0.830571 −0.415286 0.909691i \(-0.636318\pi\)
−0.415286 + 0.909691i \(0.636318\pi\)
\(938\) 3.81598 0.124596
\(939\) 28.2111 0.920636
\(940\) −78.7165 −2.56745
\(941\) −30.1292 −0.982185 −0.491093 0.871107i \(-0.663402\pi\)
−0.491093 + 0.871107i \(0.663402\pi\)
\(942\) 70.9437 2.31147
\(943\) −30.4049 −0.990121
\(944\) 21.9651 0.714904
\(945\) −11.2824 −0.367015
\(946\) −23.4297 −0.761766
\(947\) 4.17795 0.135765 0.0678825 0.997693i \(-0.478376\pi\)
0.0678825 + 0.997693i \(0.478376\pi\)
\(948\) −77.6199 −2.52098
\(949\) 39.1162 1.26977
\(950\) −115.400 −3.74408
\(951\) −37.8851 −1.22851
\(952\) 1.03082 0.0334091
\(953\) −42.2006 −1.36701 −0.683505 0.729946i \(-0.739545\pi\)
−0.683505 + 0.729946i \(0.739545\pi\)
\(954\) 116.009 3.75592
\(955\) 65.1481 2.10814
\(956\) −48.5895 −1.57150
\(957\) −66.9618 −2.16457
\(958\) −13.1129 −0.423659
\(959\) −4.29362 −0.138648
\(960\) −102.195 −3.29832
\(961\) 45.1161 1.45536
\(962\) 78.8271 2.54149
\(963\) −27.0199 −0.870703
\(964\) −27.5092 −0.886012
\(965\) −5.06571 −0.163071
\(966\) 36.5333 1.17544
\(967\) 17.9202 0.576274 0.288137 0.957589i \(-0.406964\pi\)
0.288137 + 0.957589i \(0.406964\pi\)
\(968\) 3.07993 0.0989926
\(969\) −20.9302 −0.672376
\(970\) 18.3122 0.587970
\(971\) −17.7063 −0.568224 −0.284112 0.958791i \(-0.591699\pi\)
−0.284112 + 0.958791i \(0.591699\pi\)
\(972\) 50.6153 1.62349
\(973\) −3.64777 −0.116942
\(974\) 70.8514 2.27022
\(975\) −82.1026 −2.62939
\(976\) −44.0675 −1.41057
\(977\) −5.91382 −0.189200 −0.0945999 0.995515i \(-0.530157\pi\)
−0.0945999 + 0.995515i \(0.530157\pi\)
\(978\) 79.9650 2.55700
\(979\) 34.2753 1.09544
\(980\) 48.9900 1.56493
\(981\) 17.2964 0.552232
\(982\) 34.3489 1.09612
\(983\) 37.5704 1.19831 0.599155 0.800633i \(-0.295503\pi\)
0.599155 + 0.800633i \(0.295503\pi\)
\(984\) 12.8631 0.410061
\(985\) −44.8593 −1.42934
\(986\) 19.0586 0.606951
\(987\) 27.2844 0.868470
\(988\) 84.6958 2.69453
\(989\) 23.6458 0.751893
\(990\) −83.3211 −2.64812
\(991\) −27.0336 −0.858751 −0.429375 0.903126i \(-0.641266\pi\)
−0.429375 + 0.903126i \(0.641266\pi\)
\(992\) −69.9358 −2.22046
\(993\) −51.4262 −1.63196
\(994\) 2.27943 0.0722991
\(995\) −58.5078 −1.85482
\(996\) −106.058 −3.36058
\(997\) 24.3875 0.772361 0.386180 0.922423i \(-0.373794\pi\)
0.386180 + 0.922423i \(0.373794\pi\)
\(998\) 31.5749 0.999485
\(999\) 25.1169 0.794664
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 \(a_p\))