Properties

Label 6001.2.a.b.1.18
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 1.18
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.12375 q^{2}\) \(+2.77384 q^{3}\) \(+2.51031 q^{4}\) \(-3.45627 q^{5}\) \(-5.89093 q^{6}\) \(+3.25214 q^{7}\) \(-1.08377 q^{8}\) \(+4.69417 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.12375 q^{2}\) \(+2.77384 q^{3}\) \(+2.51031 q^{4}\) \(-3.45627 q^{5}\) \(-5.89093 q^{6}\) \(+3.25214 q^{7}\) \(-1.08377 q^{8}\) \(+4.69417 q^{9}\) \(+7.34024 q^{10}\) \(-5.33496 q^{11}\) \(+6.96319 q^{12}\) \(+2.17050 q^{13}\) \(-6.90672 q^{14}\) \(-9.58712 q^{15}\) \(-2.71896 q^{16}\) \(+1.00000 q^{17}\) \(-9.96923 q^{18}\) \(+2.09406 q^{19}\) \(-8.67630 q^{20}\) \(+9.02090 q^{21}\) \(+11.3301 q^{22}\) \(-5.48026 q^{23}\) \(-3.00620 q^{24}\) \(+6.94578 q^{25}\) \(-4.60959 q^{26}\) \(+4.69934 q^{27}\) \(+8.16387 q^{28}\) \(-2.09170 q^{29}\) \(+20.3606 q^{30}\) \(-0.138192 q^{31}\) \(+7.94194 q^{32}\) \(-14.7983 q^{33}\) \(-2.12375 q^{34}\) \(-11.2403 q^{35}\) \(+11.7838 q^{36}\) \(-5.49802 q^{37}\) \(-4.44725 q^{38}\) \(+6.02061 q^{39}\) \(+3.74580 q^{40}\) \(-0.386277 q^{41}\) \(-19.1581 q^{42}\) \(+4.98086 q^{43}\) \(-13.3924 q^{44}\) \(-16.2243 q^{45}\) \(+11.6387 q^{46}\) \(+8.26855 q^{47}\) \(-7.54196 q^{48}\) \(+3.57640 q^{49}\) \(-14.7511 q^{50}\) \(+2.77384 q^{51}\) \(+5.44862 q^{52}\) \(-3.34813 q^{53}\) \(-9.98022 q^{54}\) \(+18.4391 q^{55}\) \(-3.52457 q^{56}\) \(+5.80857 q^{57}\) \(+4.44225 q^{58}\) \(+0.787488 q^{59}\) \(-24.0666 q^{60}\) \(-3.36097 q^{61}\) \(+0.293485 q^{62}\) \(+15.2661 q^{63}\) \(-11.4288 q^{64}\) \(-7.50182 q^{65}\) \(+31.4279 q^{66}\) \(+13.5469 q^{67}\) \(+2.51031 q^{68}\) \(-15.2013 q^{69}\) \(+23.8715 q^{70}\) \(-10.4534 q^{71}\) \(-5.08740 q^{72}\) \(-11.8049 q^{73}\) \(+11.6764 q^{74}\) \(+19.2664 q^{75}\) \(+5.25673 q^{76}\) \(-17.3500 q^{77}\) \(-12.7863 q^{78}\) \(+1.66029 q^{79}\) \(+9.39746 q^{80}\) \(-1.04730 q^{81}\) \(+0.820356 q^{82}\) \(-7.83301 q^{83}\) \(+22.6452 q^{84}\) \(-3.45627 q^{85}\) \(-10.5781 q^{86}\) \(-5.80203 q^{87}\) \(+5.78187 q^{88}\) \(-2.30221 q^{89}\) \(+34.4563 q^{90}\) \(+7.05876 q^{91}\) \(-13.7571 q^{92}\) \(-0.383322 q^{93}\) \(-17.5603 q^{94}\) \(-7.23762 q^{95}\) \(+22.0296 q^{96}\) \(-10.9355 q^{97}\) \(-7.59537 q^{98}\) \(-25.0432 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.12375 −1.50172 −0.750859 0.660463i \(-0.770360\pi\)
−0.750859 + 0.660463i \(0.770360\pi\)
\(3\) 2.77384 1.60148 0.800738 0.599015i \(-0.204441\pi\)
0.800738 + 0.599015i \(0.204441\pi\)
\(4\) 2.51031 1.25515
\(5\) −3.45627 −1.54569 −0.772845 0.634595i \(-0.781167\pi\)
−0.772845 + 0.634595i \(0.781167\pi\)
\(6\) −5.89093 −2.40496
\(7\) 3.25214 1.22919 0.614596 0.788842i \(-0.289319\pi\)
0.614596 + 0.788842i \(0.289319\pi\)
\(8\) −1.08377 −0.383171
\(9\) 4.69417 1.56472
\(10\) 7.34024 2.32119
\(11\) −5.33496 −1.60855 −0.804276 0.594256i \(-0.797447\pi\)
−0.804276 + 0.594256i \(0.797447\pi\)
\(12\) 6.96319 2.01010
\(13\) 2.17050 0.601988 0.300994 0.953626i \(-0.402682\pi\)
0.300994 + 0.953626i \(0.402682\pi\)
\(14\) −6.90672 −1.84590
\(15\) −9.58712 −2.47538
\(16\) −2.71896 −0.679741
\(17\) 1.00000 0.242536
\(18\) −9.96923 −2.34977
\(19\) 2.09406 0.480409 0.240205 0.970722i \(-0.422785\pi\)
0.240205 + 0.970722i \(0.422785\pi\)
\(20\) −8.67630 −1.94008
\(21\) 9.02090 1.96852
\(22\) 11.3301 2.41559
\(23\) −5.48026 −1.14271 −0.571356 0.820702i \(-0.693582\pi\)
−0.571356 + 0.820702i \(0.693582\pi\)
\(24\) −3.00620 −0.613638
\(25\) 6.94578 1.38916
\(26\) −4.60959 −0.904016
\(27\) 4.69934 0.904389
\(28\) 8.16387 1.54283
\(29\) −2.09170 −0.388419 −0.194209 0.980960i \(-0.562214\pi\)
−0.194209 + 0.980960i \(0.562214\pi\)
\(30\) 20.3606 3.71733
\(31\) −0.138192 −0.0248200 −0.0124100 0.999923i \(-0.503950\pi\)
−0.0124100 + 0.999923i \(0.503950\pi\)
\(32\) 7.94194 1.40395
\(33\) −14.7983 −2.57606
\(34\) −2.12375 −0.364220
\(35\) −11.2403 −1.89995
\(36\) 11.7838 1.96397
\(37\) −5.49802 −0.903869 −0.451934 0.892051i \(-0.649266\pi\)
−0.451934 + 0.892051i \(0.649266\pi\)
\(38\) −4.44725 −0.721439
\(39\) 6.02061 0.964069
\(40\) 3.74580 0.592263
\(41\) −0.386277 −0.0603264 −0.0301632 0.999545i \(-0.509603\pi\)
−0.0301632 + 0.999545i \(0.509603\pi\)
\(42\) −19.1581 −2.95616
\(43\) 4.98086 0.759574 0.379787 0.925074i \(-0.375997\pi\)
0.379787 + 0.925074i \(0.375997\pi\)
\(44\) −13.3924 −2.01898
\(45\) −16.2243 −2.41857
\(46\) 11.6387 1.71603
\(47\) 8.26855 1.20609 0.603046 0.797706i \(-0.293954\pi\)
0.603046 + 0.797706i \(0.293954\pi\)
\(48\) −7.54196 −1.08859
\(49\) 3.57640 0.510914
\(50\) −14.7511 −2.08612
\(51\) 2.77384 0.388415
\(52\) 5.44862 0.755588
\(53\) −3.34813 −0.459901 −0.229950 0.973202i \(-0.573856\pi\)
−0.229950 + 0.973202i \(0.573856\pi\)
\(54\) −9.98022 −1.35814
\(55\) 18.4391 2.48632
\(56\) −3.52457 −0.470990
\(57\) 5.80857 0.769364
\(58\) 4.44225 0.583295
\(59\) 0.787488 0.102522 0.0512611 0.998685i \(-0.483676\pi\)
0.0512611 + 0.998685i \(0.483676\pi\)
\(60\) −24.0666 −3.10699
\(61\) −3.36097 −0.430329 −0.215164 0.976578i \(-0.569029\pi\)
−0.215164 + 0.976578i \(0.569029\pi\)
\(62\) 0.293485 0.0372727
\(63\) 15.2661 1.92334
\(64\) −11.4288 −1.42859
\(65\) −7.50182 −0.930487
\(66\) 31.4279 3.86851
\(67\) 13.5469 1.65502 0.827508 0.561454i \(-0.189758\pi\)
0.827508 + 0.561454i \(0.189758\pi\)
\(68\) 2.51031 0.304420
\(69\) −15.2013 −1.83003
\(70\) 23.8715 2.85319
\(71\) −10.4534 −1.24059 −0.620294 0.784370i \(-0.712987\pi\)
−0.620294 + 0.784370i \(0.712987\pi\)
\(72\) −5.08740 −0.599555
\(73\) −11.8049 −1.38166 −0.690828 0.723019i \(-0.742754\pi\)
−0.690828 + 0.723019i \(0.742754\pi\)
\(74\) 11.6764 1.35736
\(75\) 19.2664 2.22470
\(76\) 5.25673 0.602988
\(77\) −17.3500 −1.97722
\(78\) −12.7863 −1.44776
\(79\) 1.66029 0.186797 0.0933987 0.995629i \(-0.470227\pi\)
0.0933987 + 0.995629i \(0.470227\pi\)
\(80\) 9.39746 1.05067
\(81\) −1.04730 −0.116367
\(82\) 0.820356 0.0905932
\(83\) −7.83301 −0.859785 −0.429892 0.902880i \(-0.641449\pi\)
−0.429892 + 0.902880i \(0.641449\pi\)
\(84\) 22.6452 2.47080
\(85\) −3.45627 −0.374885
\(86\) −10.5781 −1.14067
\(87\) −5.80203 −0.622043
\(88\) 5.78187 0.616350
\(89\) −2.30221 −0.244034 −0.122017 0.992528i \(-0.538936\pi\)
−0.122017 + 0.992528i \(0.538936\pi\)
\(90\) 34.4563 3.63201
\(91\) 7.05876 0.739959
\(92\) −13.7571 −1.43428
\(93\) −0.383322 −0.0397486
\(94\) −17.5603 −1.81121
\(95\) −7.23762 −0.742564
\(96\) 22.0296 2.24839
\(97\) −10.9355 −1.11034 −0.555168 0.831738i \(-0.687346\pi\)
−0.555168 + 0.831738i \(0.687346\pi\)
\(98\) −7.59537 −0.767249
\(99\) −25.0432 −2.51694
\(100\) 17.4360 1.74360
\(101\) −6.17367 −0.614303 −0.307152 0.951661i \(-0.599376\pi\)
−0.307152 + 0.951661i \(0.599376\pi\)
\(102\) −5.89093 −0.583289
\(103\) −8.54660 −0.842122 −0.421061 0.907032i \(-0.638342\pi\)
−0.421061 + 0.907032i \(0.638342\pi\)
\(104\) −2.35232 −0.230664
\(105\) −31.1786 −3.04272
\(106\) 7.11059 0.690641
\(107\) 13.6454 1.31915 0.659575 0.751639i \(-0.270736\pi\)
0.659575 + 0.751639i \(0.270736\pi\)
\(108\) 11.7968 1.13515
\(109\) −18.5972 −1.78129 −0.890646 0.454698i \(-0.849747\pi\)
−0.890646 + 0.454698i \(0.849747\pi\)
\(110\) −39.1599 −3.73375
\(111\) −15.2506 −1.44752
\(112\) −8.84245 −0.835533
\(113\) −0.859000 −0.0808079 −0.0404039 0.999183i \(-0.512864\pi\)
−0.0404039 + 0.999183i \(0.512864\pi\)
\(114\) −12.3359 −1.15537
\(115\) 18.9412 1.76628
\(116\) −5.25081 −0.487526
\(117\) 10.1887 0.941944
\(118\) −1.67243 −0.153959
\(119\) 3.25214 0.298123
\(120\) 10.3902 0.948494
\(121\) 17.4618 1.58744
\(122\) 7.13787 0.646232
\(123\) −1.07147 −0.0966112
\(124\) −0.346905 −0.0311530
\(125\) −6.72512 −0.601513
\(126\) −32.4213 −2.88832
\(127\) 4.76165 0.422528 0.211264 0.977429i \(-0.432242\pi\)
0.211264 + 0.977429i \(0.432242\pi\)
\(128\) 8.38793 0.741395
\(129\) 13.8161 1.21644
\(130\) 15.9320 1.39733
\(131\) −7.60287 −0.664266 −0.332133 0.943233i \(-0.607768\pi\)
−0.332133 + 0.943233i \(0.607768\pi\)
\(132\) −37.1484 −3.23335
\(133\) 6.81016 0.590516
\(134\) −28.7702 −2.48537
\(135\) −16.2422 −1.39790
\(136\) −1.08377 −0.0929325
\(137\) 2.73494 0.233662 0.116831 0.993152i \(-0.462726\pi\)
0.116831 + 0.993152i \(0.462726\pi\)
\(138\) 32.2838 2.74818
\(139\) 0.258845 0.0219549 0.0109775 0.999940i \(-0.496506\pi\)
0.0109775 + 0.999940i \(0.496506\pi\)
\(140\) −28.2165 −2.38473
\(141\) 22.9356 1.93153
\(142\) 22.2003 1.86301
\(143\) −11.5795 −0.968329
\(144\) −12.7633 −1.06361
\(145\) 7.22947 0.600375
\(146\) 25.0706 2.07486
\(147\) 9.92034 0.818216
\(148\) −13.8017 −1.13450
\(149\) 1.20004 0.0983114 0.0491557 0.998791i \(-0.484347\pi\)
0.0491557 + 0.998791i \(0.484347\pi\)
\(150\) −40.9171 −3.34087
\(151\) 3.05105 0.248291 0.124146 0.992264i \(-0.460381\pi\)
0.124146 + 0.992264i \(0.460381\pi\)
\(152\) −2.26948 −0.184079
\(153\) 4.69417 0.379501
\(154\) 36.8471 2.96923
\(155\) 0.477628 0.0383640
\(156\) 15.1136 1.21006
\(157\) 5.87738 0.469066 0.234533 0.972108i \(-0.424644\pi\)
0.234533 + 0.972108i \(0.424644\pi\)
\(158\) −3.52604 −0.280517
\(159\) −9.28716 −0.736520
\(160\) −27.4495 −2.17007
\(161\) −17.8225 −1.40461
\(162\) 2.22420 0.174750
\(163\) −1.60461 −0.125683 −0.0628413 0.998024i \(-0.520016\pi\)
−0.0628413 + 0.998024i \(0.520016\pi\)
\(164\) −0.969676 −0.0757190
\(165\) 51.1469 3.98178
\(166\) 16.6354 1.29115
\(167\) 12.1562 0.940671 0.470336 0.882488i \(-0.344133\pi\)
0.470336 + 0.882488i \(0.344133\pi\)
\(168\) −9.77658 −0.754279
\(169\) −8.28893 −0.637610
\(170\) 7.34024 0.562971
\(171\) 9.82985 0.751707
\(172\) 12.5035 0.953383
\(173\) −11.2445 −0.854901 −0.427450 0.904039i \(-0.640588\pi\)
−0.427450 + 0.904039i \(0.640588\pi\)
\(174\) 12.3221 0.934133
\(175\) 22.5886 1.70754
\(176\) 14.5056 1.09340
\(177\) 2.18436 0.164187
\(178\) 4.88932 0.366470
\(179\) 25.7743 1.92646 0.963232 0.268671i \(-0.0865846\pi\)
0.963232 + 0.268671i \(0.0865846\pi\)
\(180\) −40.7280 −3.03569
\(181\) −9.62684 −0.715557 −0.357779 0.933806i \(-0.616466\pi\)
−0.357779 + 0.933806i \(0.616466\pi\)
\(182\) −14.9910 −1.11121
\(183\) −9.32279 −0.689161
\(184\) 5.93934 0.437854
\(185\) 19.0026 1.39710
\(186\) 0.814080 0.0596912
\(187\) −5.33496 −0.390131
\(188\) 20.7566 1.51383
\(189\) 15.2829 1.11167
\(190\) 15.3709 1.11512
\(191\) 11.9297 0.863205 0.431603 0.902064i \(-0.357948\pi\)
0.431603 + 0.902064i \(0.357948\pi\)
\(192\) −31.7015 −2.28786
\(193\) −8.62887 −0.621119 −0.310560 0.950554i \(-0.600516\pi\)
−0.310560 + 0.950554i \(0.600516\pi\)
\(194\) 23.2243 1.66741
\(195\) −20.8088 −1.49015
\(196\) 8.97787 0.641276
\(197\) −11.3723 −0.810241 −0.405120 0.914263i \(-0.632770\pi\)
−0.405120 + 0.914263i \(0.632770\pi\)
\(198\) 53.1855 3.77973
\(199\) −6.68690 −0.474022 −0.237011 0.971507i \(-0.576168\pi\)
−0.237011 + 0.971507i \(0.576168\pi\)
\(200\) −7.52762 −0.532283
\(201\) 37.5769 2.65047
\(202\) 13.1113 0.922510
\(203\) −6.80250 −0.477442
\(204\) 6.96319 0.487521
\(205\) 1.33508 0.0932459
\(206\) 18.1508 1.26463
\(207\) −25.7252 −1.78803
\(208\) −5.90151 −0.409196
\(209\) −11.1717 −0.772764
\(210\) 66.2156 4.56931
\(211\) −26.7490 −1.84148 −0.920738 0.390182i \(-0.872412\pi\)
−0.920738 + 0.390182i \(0.872412\pi\)
\(212\) −8.40484 −0.577247
\(213\) −28.9960 −1.98677
\(214\) −28.9794 −1.98099
\(215\) −17.2152 −1.17407
\(216\) −5.09300 −0.346535
\(217\) −0.449419 −0.0305086
\(218\) 39.4958 2.67500
\(219\) −32.7448 −2.21269
\(220\) 46.2877 3.12072
\(221\) 2.17050 0.146004
\(222\) 32.3885 2.17377
\(223\) −14.6372 −0.980177 −0.490089 0.871673i \(-0.663036\pi\)
−0.490089 + 0.871673i \(0.663036\pi\)
\(224\) 25.8283 1.72572
\(225\) 32.6046 2.17364
\(226\) 1.82430 0.121351
\(227\) −9.01583 −0.598402 −0.299201 0.954190i \(-0.596720\pi\)
−0.299201 + 0.954190i \(0.596720\pi\)
\(228\) 14.5813 0.965671
\(229\) 9.90426 0.654492 0.327246 0.944939i \(-0.393879\pi\)
0.327246 + 0.944939i \(0.393879\pi\)
\(230\) −40.2264 −2.65245
\(231\) −48.1262 −3.16647
\(232\) 2.26692 0.148831
\(233\) −20.1515 −1.32017 −0.660085 0.751191i \(-0.729480\pi\)
−0.660085 + 0.751191i \(0.729480\pi\)
\(234\) −21.6382 −1.41453
\(235\) −28.5783 −1.86424
\(236\) 1.97684 0.128681
\(237\) 4.60538 0.299151
\(238\) −6.90672 −0.447696
\(239\) −20.8975 −1.35175 −0.675873 0.737018i \(-0.736233\pi\)
−0.675873 + 0.737018i \(0.736233\pi\)
\(240\) 26.0670 1.68262
\(241\) 21.2359 1.36793 0.683963 0.729517i \(-0.260255\pi\)
0.683963 + 0.729517i \(0.260255\pi\)
\(242\) −37.0845 −2.38389
\(243\) −17.0031 −1.09075
\(244\) −8.43709 −0.540129
\(245\) −12.3610 −0.789714
\(246\) 2.27553 0.145083
\(247\) 4.54515 0.289201
\(248\) 0.149768 0.00951030
\(249\) −21.7275 −1.37692
\(250\) 14.2825 0.903303
\(251\) 10.8205 0.682987 0.341493 0.939884i \(-0.389067\pi\)
0.341493 + 0.939884i \(0.389067\pi\)
\(252\) 38.3226 2.41410
\(253\) 29.2370 1.83811
\(254\) −10.1125 −0.634518
\(255\) −9.58712 −0.600368
\(256\) 5.04365 0.315228
\(257\) −24.3139 −1.51666 −0.758329 0.651872i \(-0.773984\pi\)
−0.758329 + 0.651872i \(0.773984\pi\)
\(258\) −29.3419 −1.82675
\(259\) −17.8803 −1.11103
\(260\) −18.8319 −1.16790
\(261\) −9.81879 −0.607768
\(262\) 16.1466 0.997540
\(263\) 11.0228 0.679693 0.339847 0.940481i \(-0.389625\pi\)
0.339847 + 0.940481i \(0.389625\pi\)
\(264\) 16.0380 0.987069
\(265\) 11.5720 0.710864
\(266\) −14.4631 −0.886788
\(267\) −6.38596 −0.390815
\(268\) 34.0069 2.07730
\(269\) 31.6610 1.93040 0.965202 0.261505i \(-0.0842189\pi\)
0.965202 + 0.261505i \(0.0842189\pi\)
\(270\) 34.4943 2.09926
\(271\) 16.2337 0.986125 0.493063 0.869994i \(-0.335877\pi\)
0.493063 + 0.869994i \(0.335877\pi\)
\(272\) −2.71896 −0.164861
\(273\) 19.5798 1.18503
\(274\) −5.80833 −0.350894
\(275\) −37.0555 −2.23453
\(276\) −38.1600 −2.29697
\(277\) 9.75341 0.586026 0.293013 0.956108i \(-0.405342\pi\)
0.293013 + 0.956108i \(0.405342\pi\)
\(278\) −0.549721 −0.0329701
\(279\) −0.648696 −0.0388364
\(280\) 12.1818 0.728005
\(281\) −30.9772 −1.84794 −0.923971 0.382462i \(-0.875076\pi\)
−0.923971 + 0.382462i \(0.875076\pi\)
\(282\) −48.7095 −2.90061
\(283\) −22.1500 −1.31668 −0.658339 0.752721i \(-0.728741\pi\)
−0.658339 + 0.752721i \(0.728741\pi\)
\(284\) −26.2412 −1.55713
\(285\) −20.0760 −1.18920
\(286\) 24.5920 1.45416
\(287\) −1.25623 −0.0741528
\(288\) 37.2808 2.19679
\(289\) 1.00000 0.0588235
\(290\) −15.3536 −0.901593
\(291\) −30.3334 −1.77818
\(292\) −29.6339 −1.73419
\(293\) −11.4551 −0.669215 −0.334608 0.942358i \(-0.608604\pi\)
−0.334608 + 0.942358i \(0.608604\pi\)
\(294\) −21.0683 −1.22873
\(295\) −2.72177 −0.158467
\(296\) 5.95859 0.346336
\(297\) −25.0708 −1.45476
\(298\) −2.54859 −0.147636
\(299\) −11.8949 −0.687899
\(300\) 48.3647 2.79234
\(301\) 16.1984 0.933663
\(302\) −6.47967 −0.372863
\(303\) −17.1247 −0.983791
\(304\) −5.69366 −0.326554
\(305\) 11.6164 0.665154
\(306\) −9.96923 −0.569903
\(307\) 0.681164 0.0388761 0.0194381 0.999811i \(-0.493812\pi\)
0.0194381 + 0.999811i \(0.493812\pi\)
\(308\) −43.5540 −2.48172
\(309\) −23.7069 −1.34864
\(310\) −1.01436 −0.0576119
\(311\) 10.1569 0.575946 0.287973 0.957639i \(-0.407019\pi\)
0.287973 + 0.957639i \(0.407019\pi\)
\(312\) −6.52495 −0.369403
\(313\) 18.9282 1.06988 0.534942 0.844889i \(-0.320334\pi\)
0.534942 + 0.844889i \(0.320334\pi\)
\(314\) −12.4821 −0.704405
\(315\) −52.7636 −2.97289
\(316\) 4.16785 0.234460
\(317\) −23.7066 −1.33149 −0.665747 0.746178i \(-0.731887\pi\)
−0.665747 + 0.746178i \(0.731887\pi\)
\(318\) 19.7236 1.10604
\(319\) 11.1591 0.624792
\(320\) 39.5008 2.20816
\(321\) 37.8501 2.11259
\(322\) 37.8506 2.10933
\(323\) 2.09406 0.116516
\(324\) −2.62904 −0.146058
\(325\) 15.0758 0.836255
\(326\) 3.40778 0.188740
\(327\) −51.5857 −2.85269
\(328\) 0.418636 0.0231153
\(329\) 26.8905 1.48252
\(330\) −108.623 −5.97951
\(331\) 15.5842 0.856587 0.428294 0.903640i \(-0.359115\pi\)
0.428294 + 0.903640i \(0.359115\pi\)
\(332\) −19.6633 −1.07916
\(333\) −25.8086 −1.41430
\(334\) −25.8166 −1.41262
\(335\) −46.8217 −2.55814
\(336\) −24.5275 −1.33808
\(337\) −16.8724 −0.919099 −0.459549 0.888152i \(-0.651989\pi\)
−0.459549 + 0.888152i \(0.651989\pi\)
\(338\) 17.6036 0.957510
\(339\) −2.38272 −0.129412
\(340\) −8.67630 −0.470538
\(341\) 0.737249 0.0399243
\(342\) −20.8761 −1.12885
\(343\) −11.1340 −0.601181
\(344\) −5.39811 −0.291046
\(345\) 52.5398 2.82865
\(346\) 23.8804 1.28382
\(347\) 33.8328 1.81624 0.908119 0.418712i \(-0.137518\pi\)
0.908119 + 0.418712i \(0.137518\pi\)
\(348\) −14.5649 −0.780761
\(349\) −15.0963 −0.808088 −0.404044 0.914739i \(-0.632396\pi\)
−0.404044 + 0.914739i \(0.632396\pi\)
\(350\) −47.9726 −2.56424
\(351\) 10.1999 0.544431
\(352\) −42.3699 −2.25833
\(353\) 1.00000 0.0532246
\(354\) −4.63904 −0.246562
\(355\) 36.1297 1.91756
\(356\) −5.77927 −0.306301
\(357\) 9.02090 0.477436
\(358\) −54.7382 −2.89300
\(359\) −32.1092 −1.69466 −0.847328 0.531069i \(-0.821790\pi\)
−0.847328 + 0.531069i \(0.821790\pi\)
\(360\) 17.5834 0.926726
\(361\) −14.6149 −0.769207
\(362\) 20.4450 1.07456
\(363\) 48.4363 2.54224
\(364\) 17.7197 0.928763
\(365\) 40.8008 2.13561
\(366\) 19.7993 1.03492
\(367\) −16.7185 −0.872701 −0.436350 0.899777i \(-0.643729\pi\)
−0.436350 + 0.899777i \(0.643729\pi\)
\(368\) 14.9006 0.776749
\(369\) −1.81325 −0.0943941
\(370\) −40.3568 −2.09805
\(371\) −10.8886 −0.565307
\(372\) −0.962257 −0.0498907
\(373\) −8.86264 −0.458890 −0.229445 0.973322i \(-0.573691\pi\)
−0.229445 + 0.973322i \(0.573691\pi\)
\(374\) 11.3301 0.585867
\(375\) −18.6544 −0.963308
\(376\) −8.96121 −0.462139
\(377\) −4.54003 −0.233824
\(378\) −32.4571 −1.66941
\(379\) 17.5325 0.900586 0.450293 0.892881i \(-0.351320\pi\)
0.450293 + 0.892881i \(0.351320\pi\)
\(380\) −18.1687 −0.932032
\(381\) 13.2080 0.676668
\(382\) −25.3358 −1.29629
\(383\) −16.5227 −0.844268 −0.422134 0.906533i \(-0.638719\pi\)
−0.422134 + 0.906533i \(0.638719\pi\)
\(384\) 23.2667 1.18733
\(385\) 59.9663 3.05617
\(386\) 18.3255 0.932746
\(387\) 23.3810 1.18852
\(388\) −27.4516 −1.39364
\(389\) 25.5025 1.29303 0.646514 0.762902i \(-0.276226\pi\)
0.646514 + 0.762902i \(0.276226\pi\)
\(390\) 44.1927 2.23779
\(391\) −5.48026 −0.277148
\(392\) −3.87599 −0.195767
\(393\) −21.0891 −1.06381
\(394\) 24.1518 1.21675
\(395\) −5.73841 −0.288731
\(396\) −62.8662 −3.15915
\(397\) −27.7984 −1.39516 −0.697581 0.716506i \(-0.745740\pi\)
−0.697581 + 0.716506i \(0.745740\pi\)
\(398\) 14.2013 0.711847
\(399\) 18.8903 0.945696
\(400\) −18.8853 −0.944266
\(401\) −36.1883 −1.80716 −0.903578 0.428423i \(-0.859069\pi\)
−0.903578 + 0.428423i \(0.859069\pi\)
\(402\) −79.8038 −3.98025
\(403\) −0.299946 −0.0149414
\(404\) −15.4978 −0.771045
\(405\) 3.61974 0.179866
\(406\) 14.4468 0.716982
\(407\) 29.3317 1.45392
\(408\) −3.00620 −0.148829
\(409\) −9.40959 −0.465274 −0.232637 0.972564i \(-0.574735\pi\)
−0.232637 + 0.972564i \(0.574735\pi\)
\(410\) −2.83537 −0.140029
\(411\) 7.58628 0.374203
\(412\) −21.4546 −1.05699
\(413\) 2.56102 0.126019
\(414\) 54.6339 2.68511
\(415\) 27.0730 1.32896
\(416\) 17.2380 0.845161
\(417\) 0.717993 0.0351603
\(418\) 23.7259 1.16047
\(419\) 33.4725 1.63524 0.817619 0.575759i \(-0.195293\pi\)
0.817619 + 0.575759i \(0.195293\pi\)
\(420\) −78.2680 −3.81909
\(421\) −8.50570 −0.414542 −0.207271 0.978284i \(-0.566458\pi\)
−0.207271 + 0.978284i \(0.566458\pi\)
\(422\) 56.8081 2.76538
\(423\) 38.8140 1.88720
\(424\) 3.62860 0.176220
\(425\) 6.94578 0.336920
\(426\) 61.5801 2.98357
\(427\) −10.9304 −0.528957
\(428\) 34.2542 1.65574
\(429\) −32.1197 −1.55075
\(430\) 36.5607 1.76311
\(431\) 8.98731 0.432903 0.216452 0.976293i \(-0.430552\pi\)
0.216452 + 0.976293i \(0.430552\pi\)
\(432\) −12.7773 −0.614750
\(433\) 25.3643 1.21893 0.609464 0.792813i \(-0.291385\pi\)
0.609464 + 0.792813i \(0.291385\pi\)
\(434\) 0.954454 0.0458153
\(435\) 20.0534 0.961485
\(436\) −46.6848 −2.23580
\(437\) −11.4760 −0.548970
\(438\) 69.5417 3.32283
\(439\) −6.48964 −0.309734 −0.154867 0.987935i \(-0.549495\pi\)
−0.154867 + 0.987935i \(0.549495\pi\)
\(440\) −19.9837 −0.952685
\(441\) 16.7882 0.799439
\(442\) −4.60959 −0.219256
\(443\) 6.52882 0.310193 0.155097 0.987899i \(-0.450431\pi\)
0.155097 + 0.987899i \(0.450431\pi\)
\(444\) −38.2837 −1.81687
\(445\) 7.95706 0.377201
\(446\) 31.0857 1.47195
\(447\) 3.32873 0.157443
\(448\) −37.1679 −1.75602
\(449\) 15.5154 0.732216 0.366108 0.930572i \(-0.380690\pi\)
0.366108 + 0.930572i \(0.380690\pi\)
\(450\) −69.2441 −3.26420
\(451\) 2.06078 0.0970382
\(452\) −2.15636 −0.101426
\(453\) 8.46313 0.397632
\(454\) 19.1474 0.898631
\(455\) −24.3970 −1.14375
\(456\) −6.29515 −0.294797
\(457\) −7.17015 −0.335405 −0.167703 0.985838i \(-0.553635\pi\)
−0.167703 + 0.985838i \(0.553635\pi\)
\(458\) −21.0342 −0.982862
\(459\) 4.69934 0.219346
\(460\) 47.5483 2.21695
\(461\) 11.8457 0.551710 0.275855 0.961199i \(-0.411039\pi\)
0.275855 + 0.961199i \(0.411039\pi\)
\(462\) 102.208 4.75514
\(463\) 0.272759 0.0126762 0.00633809 0.999980i \(-0.497983\pi\)
0.00633809 + 0.999980i \(0.497983\pi\)
\(464\) 5.68726 0.264024
\(465\) 1.32486 0.0614390
\(466\) 42.7968 1.98252
\(467\) −15.0793 −0.697786 −0.348893 0.937163i \(-0.613442\pi\)
−0.348893 + 0.937163i \(0.613442\pi\)
\(468\) 25.5768 1.18229
\(469\) 44.0564 2.03433
\(470\) 60.6932 2.79957
\(471\) 16.3029 0.751198
\(472\) −0.853455 −0.0392835
\(473\) −26.5727 −1.22181
\(474\) −9.78066 −0.449241
\(475\) 14.5448 0.667363
\(476\) 8.16387 0.374190
\(477\) −15.7167 −0.719617
\(478\) 44.3810 2.02994
\(479\) −22.2481 −1.01654 −0.508270 0.861198i \(-0.669715\pi\)
−0.508270 + 0.861198i \(0.669715\pi\)
\(480\) −76.1403 −3.47531
\(481\) −11.9334 −0.544118
\(482\) −45.0998 −2.05424
\(483\) −49.4368 −2.24945
\(484\) 43.8346 1.99248
\(485\) 37.7961 1.71623
\(486\) 36.1102 1.63799
\(487\) −43.2599 −1.96029 −0.980147 0.198270i \(-0.936468\pi\)
−0.980147 + 0.198270i \(0.936468\pi\)
\(488\) 3.64252 0.164889
\(489\) −4.45092 −0.201277
\(490\) 26.2516 1.18593
\(491\) 14.2569 0.643404 0.321702 0.946841i \(-0.395745\pi\)
0.321702 + 0.946841i \(0.395745\pi\)
\(492\) −2.68972 −0.121262
\(493\) −2.09170 −0.0942054
\(494\) −9.65275 −0.434298
\(495\) 86.5560 3.89040
\(496\) 0.375739 0.0168712
\(497\) −33.9958 −1.52492
\(498\) 46.1437 2.06775
\(499\) −33.3879 −1.49465 −0.747323 0.664461i \(-0.768661\pi\)
−0.747323 + 0.664461i \(0.768661\pi\)
\(500\) −16.8821 −0.754992
\(501\) 33.7192 1.50646
\(502\) −22.9801 −1.02565
\(503\) −7.96211 −0.355013 −0.177506 0.984120i \(-0.556803\pi\)
−0.177506 + 0.984120i \(0.556803\pi\)
\(504\) −16.5449 −0.736969
\(505\) 21.3378 0.949522
\(506\) −62.0920 −2.76032
\(507\) −22.9921 −1.02112
\(508\) 11.9532 0.530338
\(509\) −0.0505329 −0.00223983 −0.00111992 0.999999i \(-0.500356\pi\)
−0.00111992 + 0.999999i \(0.500356\pi\)
\(510\) 20.3606 0.901584
\(511\) −38.3911 −1.69832
\(512\) −27.4873 −1.21478
\(513\) 9.84068 0.434477
\(514\) 51.6366 2.27759
\(515\) 29.5393 1.30166
\(516\) 34.6827 1.52682
\(517\) −44.1124 −1.94006
\(518\) 37.9733 1.66845
\(519\) −31.1903 −1.36910
\(520\) 8.13025 0.356535
\(521\) −28.7497 −1.25955 −0.629773 0.776779i \(-0.716852\pi\)
−0.629773 + 0.776779i \(0.716852\pi\)
\(522\) 20.8526 0.912695
\(523\) 17.0733 0.746565 0.373283 0.927718i \(-0.378232\pi\)
0.373283 + 0.927718i \(0.378232\pi\)
\(524\) −19.0856 −0.833757
\(525\) 62.6571 2.73458
\(526\) −23.4096 −1.02071
\(527\) −0.138192 −0.00601974
\(528\) 40.2361 1.75105
\(529\) 7.03320 0.305791
\(530\) −24.5761 −1.06752
\(531\) 3.69660 0.160419
\(532\) 17.0956 0.741189
\(533\) −0.838415 −0.0363158
\(534\) 13.5622 0.586893
\(535\) −47.1621 −2.03900
\(536\) −14.6817 −0.634153
\(537\) 71.4938 3.08518
\(538\) −67.2400 −2.89892
\(539\) −19.0800 −0.821832
\(540\) −40.7729 −1.75459
\(541\) 29.5546 1.27065 0.635325 0.772245i \(-0.280866\pi\)
0.635325 + 0.772245i \(0.280866\pi\)
\(542\) −34.4762 −1.48088
\(543\) −26.7033 −1.14595
\(544\) 7.94194 0.340508
\(545\) 64.2770 2.75332
\(546\) −41.5827 −1.77957
\(547\) −27.0705 −1.15745 −0.578727 0.815522i \(-0.696450\pi\)
−0.578727 + 0.815522i \(0.696450\pi\)
\(548\) 6.86555 0.293282
\(549\) −15.7770 −0.673345
\(550\) 78.6965 3.35563
\(551\) −4.38014 −0.186600
\(552\) 16.4747 0.701212
\(553\) 5.39950 0.229610
\(554\) −20.7138 −0.880045
\(555\) 52.7101 2.23742
\(556\) 0.649780 0.0275568
\(557\) 1.65013 0.0699183 0.0349592 0.999389i \(-0.488870\pi\)
0.0349592 + 0.999389i \(0.488870\pi\)
\(558\) 1.37767 0.0583213
\(559\) 10.8110 0.457255
\(560\) 30.5618 1.29147
\(561\) −14.7983 −0.624785
\(562\) 65.7877 2.77509
\(563\) 17.7696 0.748898 0.374449 0.927247i \(-0.377832\pi\)
0.374449 + 0.927247i \(0.377832\pi\)
\(564\) 57.5755 2.42436
\(565\) 2.96893 0.124904
\(566\) 47.0410 1.97728
\(567\) −3.40596 −0.143037
\(568\) 11.3291 0.475357
\(569\) −8.77672 −0.367939 −0.183970 0.982932i \(-0.558895\pi\)
−0.183970 + 0.982932i \(0.558895\pi\)
\(570\) 42.6363 1.78584
\(571\) 19.0828 0.798591 0.399296 0.916822i \(-0.369255\pi\)
0.399296 + 0.916822i \(0.369255\pi\)
\(572\) −29.0682 −1.21540
\(573\) 33.0911 1.38240
\(574\) 2.66791 0.111356
\(575\) −38.0646 −1.58740
\(576\) −53.6485 −2.23535
\(577\) 21.3664 0.889497 0.444748 0.895656i \(-0.353293\pi\)
0.444748 + 0.895656i \(0.353293\pi\)
\(578\) −2.12375 −0.0883363
\(579\) −23.9351 −0.994707
\(580\) 18.1482 0.753564
\(581\) −25.4740 −1.05684
\(582\) 64.4205 2.67032
\(583\) 17.8621 0.739774
\(584\) 12.7938 0.529410
\(585\) −35.2148 −1.45595
\(586\) 24.3278 1.00497
\(587\) −2.40200 −0.0991411 −0.0495705 0.998771i \(-0.515785\pi\)
−0.0495705 + 0.998771i \(0.515785\pi\)
\(588\) 24.9031 1.02699
\(589\) −0.289382 −0.0119238
\(590\) 5.78035 0.237973
\(591\) −31.5448 −1.29758
\(592\) 14.9489 0.614397
\(593\) 8.23432 0.338143 0.169072 0.985604i \(-0.445923\pi\)
0.169072 + 0.985604i \(0.445923\pi\)
\(594\) 53.2441 2.18463
\(595\) −11.2403 −0.460805
\(596\) 3.01248 0.123396
\(597\) −18.5484 −0.759134
\(598\) 25.2618 1.03303
\(599\) 3.74730 0.153110 0.0765552 0.997065i \(-0.475608\pi\)
0.0765552 + 0.997065i \(0.475608\pi\)
\(600\) −20.8804 −0.852438
\(601\) 38.8161 1.58334 0.791671 0.610947i \(-0.209211\pi\)
0.791671 + 0.610947i \(0.209211\pi\)
\(602\) −34.4014 −1.40210
\(603\) 63.5914 2.58964
\(604\) 7.65909 0.311644
\(605\) −60.3527 −2.45369
\(606\) 36.3687 1.47738
\(607\) 6.46851 0.262549 0.131274 0.991346i \(-0.458093\pi\)
0.131274 + 0.991346i \(0.458093\pi\)
\(608\) 16.6309 0.674471
\(609\) −18.8690 −0.764611
\(610\) −24.6704 −0.998874
\(611\) 17.9469 0.726053
\(612\) 11.7838 0.476332
\(613\) −8.22936 −0.332381 −0.166190 0.986094i \(-0.553147\pi\)
−0.166190 + 0.986094i \(0.553147\pi\)
\(614\) −1.44662 −0.0583809
\(615\) 3.70329 0.149331
\(616\) 18.8034 0.757612
\(617\) −34.4999 −1.38891 −0.694457 0.719534i \(-0.744355\pi\)
−0.694457 + 0.719534i \(0.744355\pi\)
\(618\) 50.3474 2.02527
\(619\) −10.3352 −0.415407 −0.207704 0.978192i \(-0.566599\pi\)
−0.207704 + 0.978192i \(0.566599\pi\)
\(620\) 1.19900 0.0481528
\(621\) −25.7536 −1.03346
\(622\) −21.5707 −0.864908
\(623\) −7.48711 −0.299965
\(624\) −16.3698 −0.655317
\(625\) −11.4851 −0.459403
\(626\) −40.1987 −1.60666
\(627\) −30.9885 −1.23756
\(628\) 14.7540 0.588751
\(629\) −5.49802 −0.219220
\(630\) 112.057 4.46445
\(631\) −14.6205 −0.582033 −0.291016 0.956718i \(-0.593993\pi\)
−0.291016 + 0.956718i \(0.593993\pi\)
\(632\) −1.79937 −0.0715752
\(633\) −74.1973 −2.94908
\(634\) 50.3468 1.99953
\(635\) −16.4575 −0.653097
\(636\) −23.3137 −0.924446
\(637\) 7.76257 0.307564
\(638\) −23.6992 −0.938261
\(639\) −49.0699 −1.94118
\(640\) −28.9909 −1.14597
\(641\) 32.2579 1.27411 0.637055 0.770819i \(-0.280153\pi\)
0.637055 + 0.770819i \(0.280153\pi\)
\(642\) −80.3841 −3.17251
\(643\) −2.10214 −0.0829004 −0.0414502 0.999141i \(-0.513198\pi\)
−0.0414502 + 0.999141i \(0.513198\pi\)
\(644\) −44.7401 −1.76301
\(645\) −47.7521 −1.88024
\(646\) −4.44725 −0.174975
\(647\) −1.97648 −0.0777036 −0.0388518 0.999245i \(-0.512370\pi\)
−0.0388518 + 0.999245i \(0.512370\pi\)
\(648\) 1.13503 0.0445882
\(649\) −4.20122 −0.164912
\(650\) −32.0172 −1.25582
\(651\) −1.24662 −0.0488587
\(652\) −4.02806 −0.157751
\(653\) −32.0659 −1.25483 −0.627417 0.778683i \(-0.715888\pi\)
−0.627417 + 0.778683i \(0.715888\pi\)
\(654\) 109.555 4.28394
\(655\) 26.2776 1.02675
\(656\) 1.05027 0.0410063
\(657\) −55.4141 −2.16191
\(658\) −57.1086 −2.22632
\(659\) 30.5102 1.18851 0.594254 0.804277i \(-0.297447\pi\)
0.594254 + 0.804277i \(0.297447\pi\)
\(660\) 128.395 4.99775
\(661\) −29.5973 −1.15120 −0.575600 0.817731i \(-0.695232\pi\)
−0.575600 + 0.817731i \(0.695232\pi\)
\(662\) −33.0970 −1.28635
\(663\) 6.02061 0.233821
\(664\) 8.48918 0.329444
\(665\) −23.5377 −0.912754
\(666\) 54.8110 2.12388
\(667\) 11.4630 0.443851
\(668\) 30.5157 1.18069
\(669\) −40.6011 −1.56973
\(670\) 99.4375 3.84160
\(671\) 17.9307 0.692206
\(672\) 71.6434 2.76370
\(673\) −36.7815 −1.41782 −0.708912 0.705297i \(-0.750814\pi\)
−0.708912 + 0.705297i \(0.750814\pi\)
\(674\) 35.8328 1.38023
\(675\) 32.6406 1.25634
\(676\) −20.8078 −0.800300
\(677\) 4.43458 0.170435 0.0852173 0.996362i \(-0.472842\pi\)
0.0852173 + 0.996362i \(0.472842\pi\)
\(678\) 5.06031 0.194340
\(679\) −35.5639 −1.36482
\(680\) 3.74580 0.143645
\(681\) −25.0084 −0.958326
\(682\) −1.56573 −0.0599550
\(683\) 29.1217 1.11431 0.557155 0.830409i \(-0.311893\pi\)
0.557155 + 0.830409i \(0.311893\pi\)
\(684\) 24.6760 0.943509
\(685\) −9.45268 −0.361168
\(686\) 23.6459 0.902803
\(687\) 27.4728 1.04815
\(688\) −13.5428 −0.516314
\(689\) −7.26711 −0.276855
\(690\) −111.581 −4.24783
\(691\) −10.0907 −0.383867 −0.191933 0.981408i \(-0.561476\pi\)
−0.191933 + 0.981408i \(0.561476\pi\)
\(692\) −28.2271 −1.07303
\(693\) −81.4440 −3.09380
\(694\) −71.8523 −2.72748
\(695\) −0.894636 −0.0339355
\(696\) 6.28807 0.238349
\(697\) −0.386277 −0.0146313
\(698\) 32.0608 1.21352
\(699\) −55.8970 −2.11422
\(700\) 56.7044 2.14323
\(701\) 13.5832 0.513031 0.256516 0.966540i \(-0.417426\pi\)
0.256516 + 0.966540i \(0.417426\pi\)
\(702\) −21.6621 −0.817582
\(703\) −11.5132 −0.434227
\(704\) 60.9720 2.29797
\(705\) −79.2716 −2.98554
\(706\) −2.12375 −0.0799283
\(707\) −20.0776 −0.755097
\(708\) 5.48342 0.206080
\(709\) 31.6082 1.18707 0.593535 0.804808i \(-0.297732\pi\)
0.593535 + 0.804808i \(0.297732\pi\)
\(710\) −76.7303 −2.87964
\(711\) 7.79368 0.292286
\(712\) 2.49507 0.0935067
\(713\) 0.757328 0.0283621
\(714\) −19.1581 −0.716975
\(715\) 40.0219 1.49674
\(716\) 64.7015 2.41801
\(717\) −57.9662 −2.16479
\(718\) 68.1918 2.54490
\(719\) 43.4527 1.62051 0.810257 0.586075i \(-0.199328\pi\)
0.810257 + 0.586075i \(0.199328\pi\)
\(720\) 44.1133 1.64400
\(721\) −27.7947 −1.03513
\(722\) 31.0384 1.15513
\(723\) 58.9050 2.19070
\(724\) −24.1663 −0.898135
\(725\) −14.5285 −0.539574
\(726\) −102.866 −3.81773
\(727\) 7.15838 0.265490 0.132745 0.991150i \(-0.457621\pi\)
0.132745 + 0.991150i \(0.457621\pi\)
\(728\) −7.65007 −0.283531
\(729\) −44.0218 −1.63044
\(730\) −86.6507 −3.20709
\(731\) 4.98086 0.184224
\(732\) −23.4031 −0.865003
\(733\) −22.2259 −0.820931 −0.410465 0.911876i \(-0.634634\pi\)
−0.410465 + 0.911876i \(0.634634\pi\)
\(734\) 35.5060 1.31055
\(735\) −34.2873 −1.26471
\(736\) −43.5238 −1.60431
\(737\) −72.2722 −2.66218
\(738\) 3.85089 0.141753
\(739\) 9.10012 0.334753 0.167377 0.985893i \(-0.446470\pi\)
0.167377 + 0.985893i \(0.446470\pi\)
\(740\) 47.7025 1.75358
\(741\) 12.6075 0.463148
\(742\) 23.1246 0.848931
\(743\) 2.62523 0.0963105 0.0481552 0.998840i \(-0.484666\pi\)
0.0481552 + 0.998840i \(0.484666\pi\)
\(744\) 0.415433 0.0152305
\(745\) −4.14767 −0.151959
\(746\) 18.8220 0.689124
\(747\) −36.7695 −1.34532
\(748\) −13.3924 −0.489675
\(749\) 44.3767 1.62149
\(750\) 39.6172 1.44662
\(751\) −20.3009 −0.740790 −0.370395 0.928874i \(-0.620778\pi\)
−0.370395 + 0.928874i \(0.620778\pi\)
\(752\) −22.4819 −0.819830
\(753\) 30.0144 1.09379
\(754\) 9.64189 0.351137
\(755\) −10.5453 −0.383781
\(756\) 38.3648 1.39532
\(757\) −16.3892 −0.595677 −0.297838 0.954616i \(-0.596266\pi\)
−0.297838 + 0.954616i \(0.596266\pi\)
\(758\) −37.2347 −1.35243
\(759\) 81.0985 2.94369
\(760\) 7.84391 0.284529
\(761\) −43.8451 −1.58938 −0.794692 0.607013i \(-0.792368\pi\)
−0.794692 + 0.607013i \(0.792368\pi\)
\(762\) −28.0505 −1.01616
\(763\) −60.4807 −2.18955
\(764\) 29.9473 1.08346
\(765\) −16.2243 −0.586590
\(766\) 35.0900 1.26785
\(767\) 1.70924 0.0617171
\(768\) 13.9903 0.504830
\(769\) 20.6350 0.744118 0.372059 0.928209i \(-0.378652\pi\)
0.372059 + 0.928209i \(0.378652\pi\)
\(770\) −127.353 −4.58950
\(771\) −67.4427 −2.42889
\(772\) −21.6611 −0.779601
\(773\) −27.5680 −0.991552 −0.495776 0.868450i \(-0.665116\pi\)
−0.495776 + 0.868450i \(0.665116\pi\)
\(774\) −49.6554 −1.78482
\(775\) −0.959851 −0.0344789
\(776\) 11.8516 0.425448
\(777\) −49.5971 −1.77928
\(778\) −54.1609 −1.94176
\(779\) −0.808887 −0.0289814
\(780\) −52.2366 −1.87037
\(781\) 55.7684 1.99555
\(782\) 11.6387 0.416199
\(783\) −9.82961 −0.351282
\(784\) −9.72410 −0.347289
\(785\) −20.3138 −0.725030
\(786\) 44.7880 1.59754
\(787\) 20.1260 0.717413 0.358707 0.933450i \(-0.383218\pi\)
0.358707 + 0.933450i \(0.383218\pi\)
\(788\) −28.5479 −1.01698
\(789\) 30.5754 1.08851
\(790\) 12.1869 0.433592
\(791\) −2.79359 −0.0993285
\(792\) 27.1411 0.964416
\(793\) −7.29499 −0.259053
\(794\) 59.0368 2.09514
\(795\) 32.0989 1.13843
\(796\) −16.7862 −0.594971
\(797\) −15.6676 −0.554973 −0.277487 0.960729i \(-0.589501\pi\)
−0.277487 + 0.960729i \(0.589501\pi\)
\(798\) −40.1182 −1.42017
\(799\) 8.26855 0.292520
\(800\) 55.1629 1.95030
\(801\) −10.8070 −0.381846
\(802\) 76.8548 2.71384
\(803\) 62.9786 2.22247
\(804\) 94.3295 3.32675
\(805\) 61.5995 2.17110
\(806\) 0.637009 0.0224377
\(807\) 87.8224 3.09149
\(808\) 6.69084 0.235383
\(809\) 25.4862 0.896047 0.448023 0.894022i \(-0.352128\pi\)
0.448023 + 0.894022i \(0.352128\pi\)
\(810\) −7.68743 −0.270109
\(811\) −12.6195 −0.443132 −0.221566 0.975145i \(-0.571117\pi\)
−0.221566 + 0.975145i \(0.571117\pi\)
\(812\) −17.0764 −0.599263
\(813\) 45.0295 1.57926
\(814\) −62.2932 −2.18338
\(815\) 5.54595 0.194266
\(816\) −7.54196 −0.264021
\(817\) 10.4302 0.364907
\(818\) 19.9836 0.698711
\(819\) 33.1350 1.15783
\(820\) 3.35146 0.117038
\(821\) 35.6448 1.24401 0.622006 0.783012i \(-0.286318\pi\)
0.622006 + 0.783012i \(0.286318\pi\)
\(822\) −16.1113 −0.561948
\(823\) −10.0908 −0.351745 −0.175872 0.984413i \(-0.556275\pi\)
−0.175872 + 0.984413i \(0.556275\pi\)
\(824\) 9.26255 0.322676
\(825\) −102.786 −3.57854
\(826\) −5.43896 −0.189246
\(827\) −3.64299 −0.126679 −0.0633396 0.997992i \(-0.520175\pi\)
−0.0633396 + 0.997992i \(0.520175\pi\)
\(828\) −64.5783 −2.24425
\(829\) −24.2726 −0.843022 −0.421511 0.906823i \(-0.638500\pi\)
−0.421511 + 0.906823i \(0.638500\pi\)
\(830\) −57.4962 −1.99572
\(831\) 27.0544 0.938506
\(832\) −24.8061 −0.859997
\(833\) 3.57640 0.123915
\(834\) −1.52484 −0.0528008
\(835\) −42.0149 −1.45399
\(836\) −28.0445 −0.969938
\(837\) −0.649411 −0.0224469
\(838\) −71.0872 −2.45567
\(839\) 8.70905 0.300670 0.150335 0.988635i \(-0.451965\pi\)
0.150335 + 0.988635i \(0.451965\pi\)
\(840\) 33.7904 1.16588
\(841\) −24.6248 −0.849131
\(842\) 18.0640 0.622525
\(843\) −85.9255 −2.95943
\(844\) −67.1482 −2.31134
\(845\) 28.6488 0.985547
\(846\) −82.4311 −2.83404
\(847\) 56.7883 1.95127
\(848\) 9.10344 0.312614
\(849\) −61.4404 −2.10863
\(850\) −14.7511 −0.505958
\(851\) 30.1305 1.03286
\(852\) −72.7888 −2.49370
\(853\) 1.95559 0.0669583 0.0334791 0.999439i \(-0.489341\pi\)
0.0334791 + 0.999439i \(0.489341\pi\)
\(854\) 23.2133 0.794343
\(855\) −33.9746 −1.16191
\(856\) −14.7885 −0.505459
\(857\) −19.5164 −0.666669 −0.333334 0.942809i \(-0.608174\pi\)
−0.333334 + 0.942809i \(0.608174\pi\)
\(858\) 68.2142 2.32880
\(859\) −24.8796 −0.848883 −0.424441 0.905455i \(-0.639529\pi\)
−0.424441 + 0.905455i \(0.639529\pi\)
\(860\) −43.2154 −1.47363
\(861\) −3.48457 −0.118754
\(862\) −19.0868 −0.650098
\(863\) −34.7878 −1.18419 −0.592095 0.805868i \(-0.701699\pi\)
−0.592095 + 0.805868i \(0.701699\pi\)
\(864\) 37.3219 1.26972
\(865\) 38.8639 1.32141
\(866\) −53.8673 −1.83049
\(867\) 2.77384 0.0942044
\(868\) −1.12818 −0.0382930
\(869\) −8.85759 −0.300473
\(870\) −42.5883 −1.44388
\(871\) 29.4035 0.996300
\(872\) 20.1551 0.682538
\(873\) −51.3333 −1.73737
\(874\) 24.3721 0.824397
\(875\) −21.8710 −0.739375
\(876\) −82.1996 −2.77727
\(877\) −13.9567 −0.471285 −0.235643 0.971840i \(-0.575719\pi\)
−0.235643 + 0.971840i \(0.575719\pi\)
\(878\) 13.7824 0.465133
\(879\) −31.7746 −1.07173
\(880\) −50.1351 −1.69005
\(881\) 22.0636 0.743341 0.371671 0.928365i \(-0.378785\pi\)
0.371671 + 0.928365i \(0.378785\pi\)
\(882\) −35.6539 −1.20053
\(883\) 10.2822 0.346024 0.173012 0.984920i \(-0.444650\pi\)
0.173012 + 0.984920i \(0.444650\pi\)
\(884\) 5.44862 0.183257
\(885\) −7.54973 −0.253782
\(886\) −13.8656 −0.465823
\(887\) −25.0117 −0.839809 −0.419905 0.907568i \(-0.637936\pi\)
−0.419905 + 0.907568i \(0.637936\pi\)
\(888\) 16.5281 0.554648
\(889\) 15.4855 0.519368
\(890\) −16.8988 −0.566449
\(891\) 5.58730 0.187182
\(892\) −36.7438 −1.23027
\(893\) 17.3148 0.579418
\(894\) −7.06938 −0.236435
\(895\) −89.0829 −2.97771
\(896\) 27.2787 0.911317
\(897\) −32.9945 −1.10165
\(898\) −32.9508 −1.09958
\(899\) 0.289056 0.00964056
\(900\) 81.8477 2.72826
\(901\) −3.34813 −0.111542
\(902\) −4.37657 −0.145724
\(903\) 44.9318 1.49524
\(904\) 0.930958 0.0309632
\(905\) 33.2729 1.10603
\(906\) −17.9736 −0.597131
\(907\) 43.5721 1.44679 0.723394 0.690435i \(-0.242581\pi\)
0.723394 + 0.690435i \(0.242581\pi\)
\(908\) −22.6325 −0.751087
\(909\) −28.9802 −0.961214
\(910\) 51.8130 1.71758
\(911\) 49.6188 1.64394 0.821972 0.569528i \(-0.192874\pi\)
0.821972 + 0.569528i \(0.192874\pi\)
\(912\) −15.7933 −0.522968
\(913\) 41.7888 1.38301
\(914\) 15.2276 0.503684
\(915\) 32.2220 1.06523
\(916\) 24.8628 0.821489
\(917\) −24.7256 −0.816511
\(918\) −9.98022 −0.329396
\(919\) 23.4578 0.773802 0.386901 0.922121i \(-0.373546\pi\)
0.386901 + 0.922121i \(0.373546\pi\)
\(920\) −20.5279 −0.676786
\(921\) 1.88944 0.0622591
\(922\) −25.1573 −0.828513
\(923\) −22.6890 −0.746819
\(924\) −120.812 −3.97441
\(925\) −38.1880 −1.25561
\(926\) −0.579272 −0.0190361
\(927\) −40.1192 −1.31769
\(928\) −16.6121 −0.545321
\(929\) −13.1018 −0.429857 −0.214928 0.976630i \(-0.568952\pi\)
−0.214928 + 0.976630i \(0.568952\pi\)
\(930\) −2.81368 −0.0922641
\(931\) 7.48918 0.245448
\(932\) −50.5866 −1.65702
\(933\) 28.1736 0.922363
\(934\) 32.0246 1.04788
\(935\) 18.4391 0.603022
\(936\) −11.0422 −0.360925
\(937\) −50.8397 −1.66086 −0.830430 0.557123i \(-0.811905\pi\)
−0.830430 + 0.557123i \(0.811905\pi\)
\(938\) −93.5646 −3.05499
\(939\) 52.5037 1.71339
\(940\) −71.7404 −2.33991
\(941\) −43.5663 −1.42022 −0.710111 0.704090i \(-0.751355\pi\)
−0.710111 + 0.704090i \(0.751355\pi\)
\(942\) −34.6232 −1.12809
\(943\) 2.11690 0.0689357
\(944\) −2.14115 −0.0696885
\(945\) −52.8218 −1.71829
\(946\) 56.4338 1.83482
\(947\) −17.9416 −0.583024 −0.291512 0.956567i \(-0.594158\pi\)
−0.291512 + 0.956567i \(0.594158\pi\)
\(948\) 11.5609 0.375481
\(949\) −25.6225 −0.831741
\(950\) −30.8896 −1.00219
\(951\) −65.7582 −2.13235
\(952\) −3.52457 −0.114232
\(953\) −13.1344 −0.425467 −0.212733 0.977110i \(-0.568237\pi\)
−0.212733 + 0.977110i \(0.568237\pi\)
\(954\) 33.3783 1.08066
\(955\) −41.2323 −1.33425
\(956\) −52.4592 −1.69665
\(957\) 30.9536 1.00059
\(958\) 47.2493 1.52656
\(959\) 8.89440 0.287215
\(960\) 109.569 3.53632
\(961\) −30.9809 −0.999384
\(962\) 25.3436 0.817112
\(963\) 64.0538 2.06410
\(964\) 53.3087 1.71696
\(965\) 29.8237 0.960058
\(966\) 104.991 3.37804
\(967\) 4.39456 0.141320 0.0706598 0.997500i \(-0.477490\pi\)
0.0706598 + 0.997500i \(0.477490\pi\)
\(968\) −18.9246 −0.608260
\(969\) 5.80857 0.186598
\(970\) −80.2695 −2.57730
\(971\) −40.0968 −1.28677 −0.643384 0.765543i \(-0.722470\pi\)
−0.643384 + 0.765543i \(0.722470\pi\)
\(972\) −42.6829 −1.36906
\(973\) 0.841798 0.0269868
\(974\) 91.8733 2.94381
\(975\) 41.8178 1.33924
\(976\) 9.13837 0.292512
\(977\) 45.2401 1.44736 0.723679 0.690136i \(-0.242449\pi\)
0.723679 + 0.690136i \(0.242449\pi\)
\(978\) 9.45263 0.302262
\(979\) 12.2822 0.392542
\(980\) −31.0299 −0.991214
\(981\) −87.2985 −2.78723
\(982\) −30.2780 −0.966211
\(983\) −60.4109 −1.92681 −0.963404 0.268052i \(-0.913620\pi\)
−0.963404 + 0.268052i \(0.913620\pi\)
\(984\) 1.16123 0.0370186
\(985\) 39.3056 1.25238
\(986\) 4.44225 0.141470
\(987\) 74.5897 2.37422
\(988\) 11.4097 0.362992
\(989\) −27.2964 −0.867975
\(990\) −183.823 −5.84228
\(991\) 58.5089 1.85860 0.929298 0.369330i \(-0.120413\pi\)
0.929298 + 0.369330i \(0.120413\pi\)
\(992\) −1.09751 −0.0348461
\(993\) 43.2281 1.37180
\(994\) 72.1986 2.29000
\(995\) 23.1117 0.732691
\(996\) −54.5427 −1.72825
\(997\) 5.56772 0.176332 0.0881658 0.996106i \(-0.471899\pi\)
0.0881658 + 0.996106i \(0.471899\pi\)
\(998\) 70.9074 2.24454
\(999\) −25.8371 −0.817449
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 \(a_p\))