Properties

Label 8018.2.a.d.1.11
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.44219 q^{3}\) \(+1.00000 q^{4}\) \(-1.29569 q^{5}\) \(-1.44219 q^{6}\) \(+1.46621 q^{7}\) \(+1.00000 q^{8}\) \(-0.920075 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.44219 q^{3}\) \(+1.00000 q^{4}\) \(-1.29569 q^{5}\) \(-1.44219 q^{6}\) \(+1.46621 q^{7}\) \(+1.00000 q^{8}\) \(-0.920075 q^{9}\) \(-1.29569 q^{10}\) \(+4.03083 q^{11}\) \(-1.44219 q^{12}\) \(-4.55842 q^{13}\) \(+1.46621 q^{14}\) \(+1.86864 q^{15}\) \(+1.00000 q^{16}\) \(+4.46505 q^{17}\) \(-0.920075 q^{18}\) \(+1.00000 q^{19}\) \(-1.29569 q^{20}\) \(-2.11456 q^{21}\) \(+4.03083 q^{22}\) \(-5.71583 q^{23}\) \(-1.44219 q^{24}\) \(-3.32118 q^{25}\) \(-4.55842 q^{26}\) \(+5.65351 q^{27}\) \(+1.46621 q^{28}\) \(-2.18737 q^{29}\) \(+1.86864 q^{30}\) \(+2.09464 q^{31}\) \(+1.00000 q^{32}\) \(-5.81323 q^{33}\) \(+4.46505 q^{34}\) \(-1.89976 q^{35}\) \(-0.920075 q^{36}\) \(+0.932881 q^{37}\) \(+1.00000 q^{38}\) \(+6.57413 q^{39}\) \(-1.29569 q^{40}\) \(-5.12241 q^{41}\) \(-2.11456 q^{42}\) \(-5.26177 q^{43}\) \(+4.03083 q^{44}\) \(+1.19214 q^{45}\) \(-5.71583 q^{46}\) \(-4.83158 q^{47}\) \(-1.44219 q^{48}\) \(-4.85023 q^{49}\) \(-3.32118 q^{50}\) \(-6.43946 q^{51}\) \(-4.55842 q^{52}\) \(+11.7170 q^{53}\) \(+5.65351 q^{54}\) \(-5.22271 q^{55}\) \(+1.46621 q^{56}\) \(-1.44219 q^{57}\) \(-2.18737 q^{58}\) \(+6.23967 q^{59}\) \(+1.86864 q^{60}\) \(+7.92789 q^{61}\) \(+2.09464 q^{62}\) \(-1.34902 q^{63}\) \(+1.00000 q^{64}\) \(+5.90632 q^{65}\) \(-5.81323 q^{66}\) \(-5.85180 q^{67}\) \(+4.46505 q^{68}\) \(+8.24333 q^{69}\) \(-1.89976 q^{70}\) \(-9.87136 q^{71}\) \(-0.920075 q^{72}\) \(-1.85006 q^{73}\) \(+0.932881 q^{74}\) \(+4.78979 q^{75}\) \(+1.00000 q^{76}\) \(+5.91004 q^{77}\) \(+6.57413 q^{78}\) \(+15.3599 q^{79}\) \(-1.29569 q^{80}\) \(-5.39324 q^{81}\) \(-5.12241 q^{82}\) \(-6.53807 q^{83}\) \(-2.11456 q^{84}\) \(-5.78533 q^{85}\) \(-5.26177 q^{86}\) \(+3.15461 q^{87}\) \(+4.03083 q^{88}\) \(-14.9426 q^{89}\) \(+1.19214 q^{90}\) \(-6.68361 q^{91}\) \(-5.71583 q^{92}\) \(-3.02088 q^{93}\) \(-4.83158 q^{94}\) \(-1.29569 q^{95}\) \(-1.44219 q^{96}\) \(+14.1798 q^{97}\) \(-4.85023 q^{98}\) \(-3.70866 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.44219 −0.832651 −0.416326 0.909216i \(-0.636682\pi\)
−0.416326 + 0.909216i \(0.636682\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.29569 −0.579451 −0.289726 0.957110i \(-0.593564\pi\)
−0.289726 + 0.957110i \(0.593564\pi\)
\(6\) −1.44219 −0.588773
\(7\) 1.46621 0.554175 0.277088 0.960845i \(-0.410631\pi\)
0.277088 + 0.960845i \(0.410631\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.920075 −0.306692
\(10\) −1.29569 −0.409734
\(11\) 4.03083 1.21534 0.607670 0.794190i \(-0.292104\pi\)
0.607670 + 0.794190i \(0.292104\pi\)
\(12\) −1.44219 −0.416326
\(13\) −4.55842 −1.26428 −0.632140 0.774855i \(-0.717823\pi\)
−0.632140 + 0.774855i \(0.717823\pi\)
\(14\) 1.46621 0.391861
\(15\) 1.86864 0.482481
\(16\) 1.00000 0.250000
\(17\) 4.46505 1.08293 0.541466 0.840722i \(-0.317869\pi\)
0.541466 + 0.840722i \(0.317869\pi\)
\(18\) −0.920075 −0.216864
\(19\) 1.00000 0.229416
\(20\) −1.29569 −0.289726
\(21\) −2.11456 −0.461435
\(22\) 4.03083 0.859375
\(23\) −5.71583 −1.19183 −0.595916 0.803047i \(-0.703211\pi\)
−0.595916 + 0.803047i \(0.703211\pi\)
\(24\) −1.44219 −0.294387
\(25\) −3.32118 −0.664236
\(26\) −4.55842 −0.893980
\(27\) 5.65351 1.08802
\(28\) 1.46621 0.277088
\(29\) −2.18737 −0.406184 −0.203092 0.979160i \(-0.565099\pi\)
−0.203092 + 0.979160i \(0.565099\pi\)
\(30\) 1.86864 0.341166
\(31\) 2.09464 0.376209 0.188104 0.982149i \(-0.439766\pi\)
0.188104 + 0.982149i \(0.439766\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.81323 −1.01195
\(34\) 4.46505 0.765749
\(35\) −1.89976 −0.321118
\(36\) −0.920075 −0.153346
\(37\) 0.932881 0.153365 0.0766824 0.997056i \(-0.475567\pi\)
0.0766824 + 0.997056i \(0.475567\pi\)
\(38\) 1.00000 0.162221
\(39\) 6.57413 1.05270
\(40\) −1.29569 −0.204867
\(41\) −5.12241 −0.799986 −0.399993 0.916518i \(-0.630987\pi\)
−0.399993 + 0.916518i \(0.630987\pi\)
\(42\) −2.11456 −0.326284
\(43\) −5.26177 −0.802413 −0.401206 0.915988i \(-0.631409\pi\)
−0.401206 + 0.915988i \(0.631409\pi\)
\(44\) 4.03083 0.607670
\(45\) 1.19214 0.177713
\(46\) −5.71583 −0.842753
\(47\) −4.83158 −0.704758 −0.352379 0.935857i \(-0.614627\pi\)
−0.352379 + 0.935857i \(0.614627\pi\)
\(48\) −1.44219 −0.208163
\(49\) −4.85023 −0.692890
\(50\) −3.32118 −0.469686
\(51\) −6.43946 −0.901705
\(52\) −4.55842 −0.632140
\(53\) 11.7170 1.60946 0.804728 0.593644i \(-0.202311\pi\)
0.804728 + 0.593644i \(0.202311\pi\)
\(54\) 5.65351 0.769345
\(55\) −5.22271 −0.704230
\(56\) 1.46621 0.195931
\(57\) −1.44219 −0.191023
\(58\) −2.18737 −0.287216
\(59\) 6.23967 0.812335 0.406168 0.913799i \(-0.366865\pi\)
0.406168 + 0.913799i \(0.366865\pi\)
\(60\) 1.86864 0.241241
\(61\) 7.92789 1.01506 0.507531 0.861634i \(-0.330558\pi\)
0.507531 + 0.861634i \(0.330558\pi\)
\(62\) 2.09464 0.266020
\(63\) −1.34902 −0.169961
\(64\) 1.00000 0.125000
\(65\) 5.90632 0.732588
\(66\) −5.81323 −0.715560
\(67\) −5.85180 −0.714912 −0.357456 0.933930i \(-0.616356\pi\)
−0.357456 + 0.933930i \(0.616356\pi\)
\(68\) 4.46505 0.541466
\(69\) 8.24333 0.992381
\(70\) −1.89976 −0.227065
\(71\) −9.87136 −1.17152 −0.585758 0.810486i \(-0.699203\pi\)
−0.585758 + 0.810486i \(0.699203\pi\)
\(72\) −0.920075 −0.108432
\(73\) −1.85006 −0.216533 −0.108266 0.994122i \(-0.534530\pi\)
−0.108266 + 0.994122i \(0.534530\pi\)
\(74\) 0.932881 0.108445
\(75\) 4.78979 0.553077
\(76\) 1.00000 0.114708
\(77\) 5.91004 0.673511
\(78\) 6.57413 0.744374
\(79\) 15.3599 1.72812 0.864062 0.503385i \(-0.167912\pi\)
0.864062 + 0.503385i \(0.167912\pi\)
\(80\) −1.29569 −0.144863
\(81\) −5.39324 −0.599248
\(82\) −5.12241 −0.565675
\(83\) −6.53807 −0.717646 −0.358823 0.933406i \(-0.616822\pi\)
−0.358823 + 0.933406i \(0.616822\pi\)
\(84\) −2.11456 −0.230717
\(85\) −5.78533 −0.627507
\(86\) −5.26177 −0.567391
\(87\) 3.15461 0.338210
\(88\) 4.03083 0.429687
\(89\) −14.9426 −1.58392 −0.791958 0.610576i \(-0.790938\pi\)
−0.791958 + 0.610576i \(0.790938\pi\)
\(90\) 1.19214 0.125662
\(91\) −6.68361 −0.700632
\(92\) −5.71583 −0.595916
\(93\) −3.02088 −0.313251
\(94\) −4.83158 −0.498339
\(95\) −1.29569 −0.132935
\(96\) −1.44219 −0.147193
\(97\) 14.1798 1.43975 0.719873 0.694106i \(-0.244200\pi\)
0.719873 + 0.694106i \(0.244200\pi\)
\(98\) −4.85023 −0.489947
\(99\) −3.70866 −0.372735
\(100\) −3.32118 −0.332118
\(101\) −3.84467 −0.382559 −0.191279 0.981536i \(-0.561264\pi\)
−0.191279 + 0.981536i \(0.561264\pi\)
\(102\) −6.43946 −0.637602
\(103\) −12.3069 −1.21263 −0.606316 0.795224i \(-0.707353\pi\)
−0.606316 + 0.795224i \(0.707353\pi\)
\(104\) −4.55842 −0.446990
\(105\) 2.73982 0.267379
\(106\) 11.7170 1.13806
\(107\) −7.27339 −0.703146 −0.351573 0.936161i \(-0.614353\pi\)
−0.351573 + 0.936161i \(0.614353\pi\)
\(108\) 5.65351 0.544009
\(109\) 6.98340 0.668889 0.334444 0.942416i \(-0.391451\pi\)
0.334444 + 0.942416i \(0.391451\pi\)
\(110\) −5.22271 −0.497966
\(111\) −1.34540 −0.127699
\(112\) 1.46621 0.138544
\(113\) 12.9632 1.21948 0.609738 0.792603i \(-0.291275\pi\)
0.609738 + 0.792603i \(0.291275\pi\)
\(114\) −1.44219 −0.135074
\(115\) 7.40596 0.690609
\(116\) −2.18737 −0.203092
\(117\) 4.19409 0.387744
\(118\) 6.23967 0.574408
\(119\) 6.54670 0.600135
\(120\) 1.86864 0.170583
\(121\) 5.24755 0.477050
\(122\) 7.92789 0.717757
\(123\) 7.38751 0.666109
\(124\) 2.09464 0.188104
\(125\) 10.7817 0.964344
\(126\) −1.34902 −0.120181
\(127\) −11.4260 −1.01390 −0.506948 0.861977i \(-0.669226\pi\)
−0.506948 + 0.861977i \(0.669226\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.58850 0.668130
\(130\) 5.90632 0.518018
\(131\) −9.61613 −0.840165 −0.420082 0.907486i \(-0.637999\pi\)
−0.420082 + 0.907486i \(0.637999\pi\)
\(132\) −5.81323 −0.505977
\(133\) 1.46621 0.127137
\(134\) −5.85180 −0.505519
\(135\) −7.32521 −0.630454
\(136\) 4.46505 0.382875
\(137\) −2.34078 −0.199986 −0.0999931 0.994988i \(-0.531882\pi\)
−0.0999931 + 0.994988i \(0.531882\pi\)
\(138\) 8.24333 0.701719
\(139\) 8.56107 0.726141 0.363070 0.931762i \(-0.381728\pi\)
0.363070 + 0.931762i \(0.381728\pi\)
\(140\) −1.89976 −0.160559
\(141\) 6.96808 0.586818
\(142\) −9.87136 −0.828386
\(143\) −18.3742 −1.53653
\(144\) −0.920075 −0.0766729
\(145\) 2.83416 0.235364
\(146\) −1.85006 −0.153112
\(147\) 6.99497 0.576935
\(148\) 0.932881 0.0766824
\(149\) 7.47949 0.612743 0.306372 0.951912i \(-0.400885\pi\)
0.306372 + 0.951912i \(0.400885\pi\)
\(150\) 4.78979 0.391084
\(151\) −12.5443 −1.02084 −0.510420 0.859926i \(-0.670510\pi\)
−0.510420 + 0.859926i \(0.670510\pi\)
\(152\) 1.00000 0.0811107
\(153\) −4.10818 −0.332127
\(154\) 5.91004 0.476244
\(155\) −2.71401 −0.217995
\(156\) 6.57413 0.526352
\(157\) 1.84383 0.147154 0.0735769 0.997290i \(-0.476559\pi\)
0.0735769 + 0.997290i \(0.476559\pi\)
\(158\) 15.3599 1.22197
\(159\) −16.8982 −1.34012
\(160\) −1.29569 −0.102434
\(161\) −8.38060 −0.660484
\(162\) −5.39324 −0.423733
\(163\) −1.90813 −0.149456 −0.0747281 0.997204i \(-0.523809\pi\)
−0.0747281 + 0.997204i \(0.523809\pi\)
\(164\) −5.12241 −0.399993
\(165\) 7.53216 0.586378
\(166\) −6.53807 −0.507452
\(167\) −10.1117 −0.782470 −0.391235 0.920291i \(-0.627952\pi\)
−0.391235 + 0.920291i \(0.627952\pi\)
\(168\) −2.11456 −0.163142
\(169\) 7.77922 0.598401
\(170\) −5.78533 −0.443714
\(171\) −0.920075 −0.0703599
\(172\) −5.26177 −0.401206
\(173\) 3.14349 0.238995 0.119498 0.992834i \(-0.461872\pi\)
0.119498 + 0.992834i \(0.461872\pi\)
\(174\) 3.15461 0.239150
\(175\) −4.86955 −0.368103
\(176\) 4.03083 0.303835
\(177\) −8.99881 −0.676392
\(178\) −14.9426 −1.12000
\(179\) −7.22917 −0.540334 −0.270167 0.962814i \(-0.587079\pi\)
−0.270167 + 0.962814i \(0.587079\pi\)
\(180\) 1.19214 0.0888565
\(181\) −18.0301 −1.34017 −0.670085 0.742285i \(-0.733742\pi\)
−0.670085 + 0.742285i \(0.733742\pi\)
\(182\) −6.68361 −0.495422
\(183\) −11.4336 −0.845193
\(184\) −5.71583 −0.421376
\(185\) −1.20873 −0.0888674
\(186\) −3.02088 −0.221502
\(187\) 17.9978 1.31613
\(188\) −4.83158 −0.352379
\(189\) 8.28923 0.602953
\(190\) −1.29569 −0.0939994
\(191\) −14.0248 −1.01480 −0.507398 0.861712i \(-0.669393\pi\)
−0.507398 + 0.861712i \(0.669393\pi\)
\(192\) −1.44219 −0.104081
\(193\) −24.0917 −1.73416 −0.867079 0.498171i \(-0.834005\pi\)
−0.867079 + 0.498171i \(0.834005\pi\)
\(194\) 14.1798 1.01805
\(195\) −8.51806 −0.609991
\(196\) −4.85023 −0.346445
\(197\) −19.3440 −1.37820 −0.689101 0.724665i \(-0.741995\pi\)
−0.689101 + 0.724665i \(0.741995\pi\)
\(198\) −3.70866 −0.263563
\(199\) 3.68411 0.261160 0.130580 0.991438i \(-0.458316\pi\)
0.130580 + 0.991438i \(0.458316\pi\)
\(200\) −3.32118 −0.234843
\(201\) 8.43944 0.595272
\(202\) −3.84467 −0.270510
\(203\) −3.20714 −0.225097
\(204\) −6.43946 −0.450853
\(205\) 6.63707 0.463553
\(206\) −12.3069 −0.857460
\(207\) 5.25899 0.365525
\(208\) −4.55842 −0.316070
\(209\) 4.03083 0.278818
\(210\) 2.73982 0.189066
\(211\) −1.00000 −0.0688428
\(212\) 11.7170 0.804728
\(213\) 14.2364 0.975464
\(214\) −7.27339 −0.497199
\(215\) 6.81764 0.464959
\(216\) 5.65351 0.384673
\(217\) 3.07119 0.208486
\(218\) 6.98340 0.472976
\(219\) 2.66814 0.180296
\(220\) −5.22271 −0.352115
\(221\) −20.3536 −1.36913
\(222\) −1.34540 −0.0902971
\(223\) −8.59346 −0.575461 −0.287730 0.957711i \(-0.592901\pi\)
−0.287730 + 0.957711i \(0.592901\pi\)
\(224\) 1.46621 0.0979653
\(225\) 3.05574 0.203716
\(226\) 12.9632 0.862300
\(227\) 18.1353 1.20368 0.601840 0.798616i \(-0.294434\pi\)
0.601840 + 0.798616i \(0.294434\pi\)
\(228\) −1.44219 −0.0955117
\(229\) 6.68049 0.441459 0.220729 0.975335i \(-0.429156\pi\)
0.220729 + 0.975335i \(0.429156\pi\)
\(230\) 7.40596 0.488334
\(231\) −8.52342 −0.560800
\(232\) −2.18737 −0.143608
\(233\) 24.7884 1.62394 0.811972 0.583696i \(-0.198394\pi\)
0.811972 + 0.583696i \(0.198394\pi\)
\(234\) 4.19409 0.274176
\(235\) 6.26024 0.408373
\(236\) 6.23967 0.406168
\(237\) −22.1520 −1.43893
\(238\) 6.54670 0.424359
\(239\) −1.48248 −0.0958934 −0.0479467 0.998850i \(-0.515268\pi\)
−0.0479467 + 0.998850i \(0.515268\pi\)
\(240\) 1.86864 0.120620
\(241\) 3.49549 0.225164 0.112582 0.993642i \(-0.464088\pi\)
0.112582 + 0.993642i \(0.464088\pi\)
\(242\) 5.24755 0.337325
\(243\) −9.18244 −0.589054
\(244\) 7.92789 0.507531
\(245\) 6.28441 0.401496
\(246\) 7.38751 0.471010
\(247\) −4.55842 −0.290045
\(248\) 2.09464 0.133010
\(249\) 9.42916 0.597549
\(250\) 10.7817 0.681894
\(251\) −30.2344 −1.90838 −0.954189 0.299203i \(-0.903279\pi\)
−0.954189 + 0.299203i \(0.903279\pi\)
\(252\) −1.34902 −0.0849805
\(253\) −23.0395 −1.44848
\(254\) −11.4260 −0.716933
\(255\) 8.34357 0.522494
\(256\) 1.00000 0.0625000
\(257\) −20.9504 −1.30685 −0.653425 0.756991i \(-0.726668\pi\)
−0.653425 + 0.756991i \(0.726668\pi\)
\(258\) 7.58850 0.472439
\(259\) 1.36780 0.0849910
\(260\) 5.90632 0.366294
\(261\) 2.01254 0.124573
\(262\) −9.61613 −0.594086
\(263\) 25.0769 1.54631 0.773155 0.634217i \(-0.218677\pi\)
0.773155 + 0.634217i \(0.218677\pi\)
\(264\) −5.81323 −0.357780
\(265\) −15.1816 −0.932601
\(266\) 1.46621 0.0898991
\(267\) 21.5502 1.31885
\(268\) −5.85180 −0.357456
\(269\) −16.6717 −1.01649 −0.508245 0.861213i \(-0.669705\pi\)
−0.508245 + 0.861213i \(0.669705\pi\)
\(270\) −7.32521 −0.445798
\(271\) 21.2874 1.29311 0.646557 0.762865i \(-0.276208\pi\)
0.646557 + 0.762865i \(0.276208\pi\)
\(272\) 4.46505 0.270733
\(273\) 9.63906 0.583382
\(274\) −2.34078 −0.141412
\(275\) −13.3871 −0.807272
\(276\) 8.24333 0.496190
\(277\) −28.5155 −1.71333 −0.856665 0.515873i \(-0.827468\pi\)
−0.856665 + 0.515873i \(0.827468\pi\)
\(278\) 8.56107 0.513459
\(279\) −1.92723 −0.115380
\(280\) −1.89976 −0.113532
\(281\) −4.77555 −0.284886 −0.142443 0.989803i \(-0.545496\pi\)
−0.142443 + 0.989803i \(0.545496\pi\)
\(282\) 6.96808 0.414943
\(283\) −8.53132 −0.507134 −0.253567 0.967318i \(-0.581604\pi\)
−0.253567 + 0.967318i \(0.581604\pi\)
\(284\) −9.87136 −0.585758
\(285\) 1.86864 0.110689
\(286\) −18.3742 −1.08649
\(287\) −7.51053 −0.443332
\(288\) −0.920075 −0.0542160
\(289\) 2.93664 0.172743
\(290\) 2.83416 0.166427
\(291\) −20.4501 −1.19881
\(292\) −1.85006 −0.108266
\(293\) −15.6409 −0.913754 −0.456877 0.889530i \(-0.651032\pi\)
−0.456877 + 0.889530i \(0.651032\pi\)
\(294\) 6.99497 0.407955
\(295\) −8.08469 −0.470709
\(296\) 0.932881 0.0542226
\(297\) 22.7883 1.32231
\(298\) 7.47949 0.433275
\(299\) 26.0552 1.50681
\(300\) 4.78979 0.276538
\(301\) −7.71486 −0.444677
\(302\) −12.5443 −0.721842
\(303\) 5.54476 0.318538
\(304\) 1.00000 0.0573539
\(305\) −10.2721 −0.588179
\(306\) −4.10818 −0.234849
\(307\) −6.75740 −0.385665 −0.192832 0.981232i \(-0.561767\pi\)
−0.192832 + 0.981232i \(0.561767\pi\)
\(308\) 5.91004 0.336756
\(309\) 17.7489 1.00970
\(310\) −2.71401 −0.154146
\(311\) 5.51261 0.312591 0.156296 0.987710i \(-0.450045\pi\)
0.156296 + 0.987710i \(0.450045\pi\)
\(312\) 6.57413 0.372187
\(313\) −7.64779 −0.432278 −0.216139 0.976363i \(-0.569347\pi\)
−0.216139 + 0.976363i \(0.569347\pi\)
\(314\) 1.84383 0.104053
\(315\) 1.74792 0.0984842
\(316\) 15.3599 0.864062
\(317\) −14.7299 −0.827312 −0.413656 0.910433i \(-0.635748\pi\)
−0.413656 + 0.910433i \(0.635748\pi\)
\(318\) −16.8982 −0.947605
\(319\) −8.81690 −0.493652
\(320\) −1.29569 −0.0724314
\(321\) 10.4896 0.585475
\(322\) −8.38060 −0.467033
\(323\) 4.46505 0.248442
\(324\) −5.39324 −0.299624
\(325\) 15.1393 0.839780
\(326\) −1.90813 −0.105681
\(327\) −10.0714 −0.556951
\(328\) −5.12241 −0.282838
\(329\) −7.08411 −0.390560
\(330\) 7.53216 0.414632
\(331\) −9.21502 −0.506503 −0.253252 0.967400i \(-0.581500\pi\)
−0.253252 + 0.967400i \(0.581500\pi\)
\(332\) −6.53807 −0.358823
\(333\) −0.858321 −0.0470357
\(334\) −10.1117 −0.553290
\(335\) 7.58214 0.414257
\(336\) −2.11456 −0.115359
\(337\) −25.1254 −1.36867 −0.684333 0.729170i \(-0.739906\pi\)
−0.684333 + 0.729170i \(0.739906\pi\)
\(338\) 7.77922 0.423134
\(339\) −18.6955 −1.01540
\(340\) −5.78533 −0.313753
\(341\) 8.44314 0.457222
\(342\) −0.920075 −0.0497520
\(343\) −17.3749 −0.938158
\(344\) −5.26177 −0.283696
\(345\) −10.6808 −0.575036
\(346\) 3.14349 0.168995
\(347\) −36.3139 −1.94943 −0.974716 0.223448i \(-0.928269\pi\)
−0.974716 + 0.223448i \(0.928269\pi\)
\(348\) 3.15461 0.169105
\(349\) −29.8919 −1.60008 −0.800039 0.599948i \(-0.795188\pi\)
−0.800039 + 0.599948i \(0.795188\pi\)
\(350\) −4.86955 −0.260288
\(351\) −25.7711 −1.37556
\(352\) 4.03083 0.214844
\(353\) 34.5369 1.83821 0.919107 0.394009i \(-0.128912\pi\)
0.919107 + 0.394009i \(0.128912\pi\)
\(354\) −8.99881 −0.478281
\(355\) 12.7903 0.678836
\(356\) −14.9426 −0.791958
\(357\) −9.44161 −0.499703
\(358\) −7.22917 −0.382074
\(359\) −33.5032 −1.76823 −0.884115 0.467269i \(-0.845238\pi\)
−0.884115 + 0.467269i \(0.845238\pi\)
\(360\) 1.19214 0.0628310
\(361\) 1.00000 0.0526316
\(362\) −18.0301 −0.947643
\(363\) −7.56799 −0.397216
\(364\) −6.68361 −0.350316
\(365\) 2.39711 0.125470
\(366\) −11.4336 −0.597641
\(367\) 6.31709 0.329750 0.164875 0.986315i \(-0.447278\pi\)
0.164875 + 0.986315i \(0.447278\pi\)
\(368\) −5.71583 −0.297958
\(369\) 4.71300 0.245349
\(370\) −1.20873 −0.0628388
\(371\) 17.1796 0.891921
\(372\) −3.02088 −0.156625
\(373\) −3.26221 −0.168911 −0.0844553 0.996427i \(-0.526915\pi\)
−0.0844553 + 0.996427i \(0.526915\pi\)
\(374\) 17.9978 0.930645
\(375\) −15.5493 −0.802962
\(376\) −4.83158 −0.249170
\(377\) 9.97095 0.513530
\(378\) 8.28923 0.426352
\(379\) 24.5061 1.25879 0.629397 0.777084i \(-0.283302\pi\)
0.629397 + 0.777084i \(0.283302\pi\)
\(380\) −1.29569 −0.0664676
\(381\) 16.4786 0.844222
\(382\) −14.0248 −0.717569
\(383\) −1.79746 −0.0918457 −0.0459229 0.998945i \(-0.514623\pi\)
−0.0459229 + 0.998945i \(0.514623\pi\)
\(384\) −1.44219 −0.0735967
\(385\) −7.65759 −0.390267
\(386\) −24.0917 −1.22623
\(387\) 4.84123 0.246093
\(388\) 14.1798 0.719873
\(389\) 12.5599 0.636812 0.318406 0.947954i \(-0.396852\pi\)
0.318406 + 0.947954i \(0.396852\pi\)
\(390\) −8.51806 −0.431328
\(391\) −25.5214 −1.29067
\(392\) −4.85023 −0.244973
\(393\) 13.8683 0.699564
\(394\) −19.3440 −0.974536
\(395\) −19.9017 −1.00136
\(396\) −3.70866 −0.186367
\(397\) 14.9495 0.750293 0.375146 0.926966i \(-0.377592\pi\)
0.375146 + 0.926966i \(0.377592\pi\)
\(398\) 3.68411 0.184668
\(399\) −2.11456 −0.105860
\(400\) −3.32118 −0.166059
\(401\) 15.2745 0.762775 0.381387 0.924415i \(-0.375446\pi\)
0.381387 + 0.924415i \(0.375446\pi\)
\(402\) 8.43944 0.420921
\(403\) −9.54827 −0.475633
\(404\) −3.84467 −0.191279
\(405\) 6.98798 0.347235
\(406\) −3.20714 −0.159168
\(407\) 3.76028 0.186390
\(408\) −6.43946 −0.318801
\(409\) 14.6745 0.725605 0.362803 0.931866i \(-0.381820\pi\)
0.362803 + 0.931866i \(0.381820\pi\)
\(410\) 6.63707 0.327781
\(411\) 3.37586 0.166519
\(412\) −12.3069 −0.606316
\(413\) 9.14866 0.450176
\(414\) 5.25899 0.258465
\(415\) 8.47133 0.415841
\(416\) −4.55842 −0.223495
\(417\) −12.3467 −0.604622
\(418\) 4.03083 0.197154
\(419\) 17.0859 0.834701 0.417351 0.908746i \(-0.362959\pi\)
0.417351 + 0.908746i \(0.362959\pi\)
\(420\) 2.73982 0.133690
\(421\) −6.92230 −0.337373 −0.168686 0.985670i \(-0.553952\pi\)
−0.168686 + 0.985670i \(0.553952\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 4.44542 0.216144
\(424\) 11.7170 0.569028
\(425\) −14.8292 −0.719323
\(426\) 14.2364 0.689757
\(427\) 11.6239 0.562522
\(428\) −7.27339 −0.351573
\(429\) 26.4992 1.27939
\(430\) 6.81764 0.328776
\(431\) 27.7113 1.33481 0.667404 0.744696i \(-0.267405\pi\)
0.667404 + 0.744696i \(0.267405\pi\)
\(432\) 5.65351 0.272005
\(433\) −8.07997 −0.388298 −0.194149 0.980972i \(-0.562195\pi\)
−0.194149 + 0.980972i \(0.562195\pi\)
\(434\) 3.07119 0.147422
\(435\) −4.08741 −0.195976
\(436\) 6.98340 0.334444
\(437\) −5.71583 −0.273425
\(438\) 2.66814 0.127489
\(439\) 41.2004 1.96639 0.983194 0.182566i \(-0.0584404\pi\)
0.983194 + 0.182566i \(0.0584404\pi\)
\(440\) −5.22271 −0.248983
\(441\) 4.46258 0.212504
\(442\) −20.3536 −0.968120
\(443\) −11.8945 −0.565125 −0.282562 0.959249i \(-0.591184\pi\)
−0.282562 + 0.959249i \(0.591184\pi\)
\(444\) −1.34540 −0.0638497
\(445\) 19.3611 0.917802
\(446\) −8.59346 −0.406912
\(447\) −10.7869 −0.510202
\(448\) 1.46621 0.0692719
\(449\) −17.5206 −0.826849 −0.413425 0.910538i \(-0.635667\pi\)
−0.413425 + 0.910538i \(0.635667\pi\)
\(450\) 3.05574 0.144049
\(451\) −20.6475 −0.972254
\(452\) 12.9632 0.609738
\(453\) 18.0913 0.850003
\(454\) 18.1353 0.851131
\(455\) 8.65990 0.405982
\(456\) −1.44219 −0.0675369
\(457\) −19.6238 −0.917963 −0.458982 0.888446i \(-0.651786\pi\)
−0.458982 + 0.888446i \(0.651786\pi\)
\(458\) 6.68049 0.312159
\(459\) 25.2432 1.17825
\(460\) 7.40596 0.345304
\(461\) −42.1904 −1.96500 −0.982502 0.186250i \(-0.940366\pi\)
−0.982502 + 0.186250i \(0.940366\pi\)
\(462\) −8.52342 −0.396545
\(463\) 8.95400 0.416128 0.208064 0.978115i \(-0.433284\pi\)
0.208064 + 0.978115i \(0.433284\pi\)
\(464\) −2.18737 −0.101546
\(465\) 3.91413 0.181514
\(466\) 24.7884 1.14830
\(467\) −26.9179 −1.24561 −0.622806 0.782376i \(-0.714008\pi\)
−0.622806 + 0.782376i \(0.714008\pi\)
\(468\) 4.19409 0.193872
\(469\) −8.57998 −0.396186
\(470\) 6.26024 0.288763
\(471\) −2.65916 −0.122528
\(472\) 6.23967 0.287204
\(473\) −21.2093 −0.975204
\(474\) −22.1520 −1.01747
\(475\) −3.32118 −0.152386
\(476\) 6.54670 0.300067
\(477\) −10.7805 −0.493607
\(478\) −1.48248 −0.0678068
\(479\) 29.4731 1.34666 0.673331 0.739341i \(-0.264863\pi\)
0.673331 + 0.739341i \(0.264863\pi\)
\(480\) 1.86864 0.0852914
\(481\) −4.25247 −0.193896
\(482\) 3.49549 0.159215
\(483\) 12.0865 0.549953
\(484\) 5.24755 0.238525
\(485\) −18.3727 −0.834262
\(486\) −9.18244 −0.416524
\(487\) 20.4895 0.928469 0.464234 0.885712i \(-0.346330\pi\)
0.464234 + 0.885712i \(0.346330\pi\)
\(488\) 7.92789 0.358879
\(489\) 2.75189 0.124445
\(490\) 6.28441 0.283900
\(491\) −21.2564 −0.959288 −0.479644 0.877463i \(-0.659234\pi\)
−0.479644 + 0.877463i \(0.659234\pi\)
\(492\) 7.38751 0.333055
\(493\) −9.76670 −0.439870
\(494\) −4.55842 −0.205093
\(495\) 4.80529 0.215982
\(496\) 2.09464 0.0940522
\(497\) −14.4735 −0.649225
\(498\) 9.42916 0.422531
\(499\) −39.8369 −1.78334 −0.891672 0.452682i \(-0.850467\pi\)
−0.891672 + 0.452682i \(0.850467\pi\)
\(500\) 10.7817 0.482172
\(501\) 14.5831 0.651525
\(502\) −30.2344 −1.34943
\(503\) 32.5936 1.45328 0.726639 0.687020i \(-0.241081\pi\)
0.726639 + 0.687020i \(0.241081\pi\)
\(504\) −1.34902 −0.0600903
\(505\) 4.98151 0.221674
\(506\) −23.0395 −1.02423
\(507\) −11.2191 −0.498260
\(508\) −11.4260 −0.506948
\(509\) −4.79494 −0.212532 −0.106266 0.994338i \(-0.533889\pi\)
−0.106266 + 0.994338i \(0.533889\pi\)
\(510\) 8.34357 0.369459
\(511\) −2.71257 −0.119997
\(512\) 1.00000 0.0441942
\(513\) 5.65351 0.249609
\(514\) −20.9504 −0.924082
\(515\) 15.9459 0.702661
\(516\) 7.58850 0.334065
\(517\) −19.4753 −0.856521
\(518\) 1.36780 0.0600977
\(519\) −4.53353 −0.199000
\(520\) 5.90632 0.259009
\(521\) 17.4637 0.765097 0.382549 0.923935i \(-0.375046\pi\)
0.382549 + 0.923935i \(0.375046\pi\)
\(522\) 2.01254 0.0880866
\(523\) −2.20374 −0.0963629 −0.0481814 0.998839i \(-0.515343\pi\)
−0.0481814 + 0.998839i \(0.515343\pi\)
\(524\) −9.61613 −0.420082
\(525\) 7.02283 0.306502
\(526\) 25.0769 1.09341
\(527\) 9.35268 0.407409
\(528\) −5.81323 −0.252989
\(529\) 9.67068 0.420464
\(530\) −15.1816 −0.659449
\(531\) −5.74096 −0.249137
\(532\) 1.46621 0.0635683
\(533\) 23.3501 1.01141
\(534\) 21.5502 0.932567
\(535\) 9.42408 0.407439
\(536\) −5.85180 −0.252759
\(537\) 10.4259 0.449910
\(538\) −16.6717 −0.718766
\(539\) −19.5504 −0.842096
\(540\) −7.32521 −0.315227
\(541\) −21.6585 −0.931173 −0.465586 0.885003i \(-0.654156\pi\)
−0.465586 + 0.885003i \(0.654156\pi\)
\(542\) 21.2874 0.914370
\(543\) 26.0030 1.11589
\(544\) 4.46505 0.191437
\(545\) −9.04834 −0.387588
\(546\) 9.63906 0.412514
\(547\) −8.55169 −0.365644 −0.182822 0.983146i \(-0.558523\pi\)
−0.182822 + 0.983146i \(0.558523\pi\)
\(548\) −2.34078 −0.0999931
\(549\) −7.29425 −0.311311
\(550\) −13.3871 −0.570828
\(551\) −2.18737 −0.0931850
\(552\) 8.24333 0.350860
\(553\) 22.5209 0.957684
\(554\) −28.5155 −1.21151
\(555\) 1.74322 0.0739956
\(556\) 8.56107 0.363070
\(557\) −11.3959 −0.482858 −0.241429 0.970419i \(-0.577616\pi\)
−0.241429 + 0.970419i \(0.577616\pi\)
\(558\) −1.92723 −0.0815861
\(559\) 23.9854 1.01447
\(560\) −1.89976 −0.0802794
\(561\) −25.9564 −1.09588
\(562\) −4.77555 −0.201445
\(563\) −37.7400 −1.59055 −0.795276 0.606247i \(-0.792674\pi\)
−0.795276 + 0.606247i \(0.792674\pi\)
\(564\) 6.96808 0.293409
\(565\) −16.7963 −0.706627
\(566\) −8.53132 −0.358598
\(567\) −7.90762 −0.332089
\(568\) −9.87136 −0.414193
\(569\) −0.998313 −0.0418515 −0.0209257 0.999781i \(-0.506661\pi\)
−0.0209257 + 0.999781i \(0.506661\pi\)
\(570\) 1.86864 0.0782688
\(571\) 34.2041 1.43140 0.715698 0.698410i \(-0.246109\pi\)
0.715698 + 0.698410i \(0.246109\pi\)
\(572\) −18.3742 −0.768264
\(573\) 20.2264 0.844971
\(574\) −7.51053 −0.313483
\(575\) 18.9833 0.791658
\(576\) −0.920075 −0.0383365
\(577\) −39.0794 −1.62690 −0.813449 0.581637i \(-0.802412\pi\)
−0.813449 + 0.581637i \(0.802412\pi\)
\(578\) 2.93664 0.122148
\(579\) 34.7449 1.44395
\(580\) 2.83416 0.117682
\(581\) −9.58618 −0.397702
\(582\) −20.4501 −0.847684
\(583\) 47.2292 1.95603
\(584\) −1.85006 −0.0765560
\(585\) −5.43426 −0.224679
\(586\) −15.6409 −0.646122
\(587\) 29.4932 1.21731 0.608656 0.793434i \(-0.291709\pi\)
0.608656 + 0.793434i \(0.291709\pi\)
\(588\) 6.99497 0.288468
\(589\) 2.09464 0.0863082
\(590\) −8.08469 −0.332841
\(591\) 27.8978 1.14756
\(592\) 0.932881 0.0383412
\(593\) −10.4827 −0.430471 −0.215236 0.976562i \(-0.569052\pi\)
−0.215236 + 0.976562i \(0.569052\pi\)
\(594\) 22.7883 0.935016
\(595\) −8.48251 −0.347749
\(596\) 7.47949 0.306372
\(597\) −5.31320 −0.217455
\(598\) 26.0552 1.06547
\(599\) −30.3920 −1.24178 −0.620892 0.783896i \(-0.713229\pi\)
−0.620892 + 0.783896i \(0.713229\pi\)
\(600\) 4.78979 0.195542
\(601\) 31.7564 1.29537 0.647686 0.761907i \(-0.275737\pi\)
0.647686 + 0.761907i \(0.275737\pi\)
\(602\) −7.71486 −0.314434
\(603\) 5.38410 0.219258
\(604\) −12.5443 −0.510420
\(605\) −6.79921 −0.276427
\(606\) 5.54476 0.225240
\(607\) 14.0798 0.571483 0.285742 0.958307i \(-0.407760\pi\)
0.285742 + 0.958307i \(0.407760\pi\)
\(608\) 1.00000 0.0405554
\(609\) 4.62532 0.187427
\(610\) −10.2721 −0.415905
\(611\) 22.0244 0.891011
\(612\) −4.10818 −0.166063
\(613\) 13.4374 0.542733 0.271366 0.962476i \(-0.412524\pi\)
0.271366 + 0.962476i \(0.412524\pi\)
\(614\) −6.75740 −0.272706
\(615\) −9.57194 −0.385978
\(616\) 5.91004 0.238122
\(617\) −40.8722 −1.64545 −0.822726 0.568438i \(-0.807548\pi\)
−0.822726 + 0.568438i \(0.807548\pi\)
\(618\) 17.7489 0.713965
\(619\) 8.68986 0.349275 0.174637 0.984633i \(-0.444125\pi\)
0.174637 + 0.984633i \(0.444125\pi\)
\(620\) −2.71401 −0.108997
\(621\) −32.3145 −1.29674
\(622\) 5.51261 0.221035
\(623\) −21.9090 −0.877767
\(624\) 6.57413 0.263176
\(625\) 2.63614 0.105446
\(626\) −7.64779 −0.305667
\(627\) −5.81323 −0.232158
\(628\) 1.84383 0.0735769
\(629\) 4.16536 0.166084
\(630\) 1.74792 0.0696388
\(631\) −37.9916 −1.51242 −0.756211 0.654328i \(-0.772952\pi\)
−0.756211 + 0.654328i \(0.772952\pi\)
\(632\) 15.3599 0.610984
\(633\) 1.44219 0.0573221
\(634\) −14.7299 −0.584998
\(635\) 14.8046 0.587504
\(636\) −16.8982 −0.670058
\(637\) 22.1094 0.876006
\(638\) −8.81690 −0.349064
\(639\) 9.08240 0.359294
\(640\) −1.29569 −0.0512168
\(641\) −22.4366 −0.886193 −0.443096 0.896474i \(-0.646120\pi\)
−0.443096 + 0.896474i \(0.646120\pi\)
\(642\) 10.4896 0.413993
\(643\) −47.1543 −1.85959 −0.929793 0.368083i \(-0.880014\pi\)
−0.929793 + 0.368083i \(0.880014\pi\)
\(644\) −8.38060 −0.330242
\(645\) −9.83236 −0.387149
\(646\) 4.46505 0.175675
\(647\) −32.5549 −1.27987 −0.639933 0.768431i \(-0.721038\pi\)
−0.639933 + 0.768431i \(0.721038\pi\)
\(648\) −5.39324 −0.211866
\(649\) 25.1510 0.987263
\(650\) 15.1393 0.593814
\(651\) −4.42925 −0.173596
\(652\) −1.90813 −0.0747281
\(653\) 38.4206 1.50351 0.751757 0.659440i \(-0.229207\pi\)
0.751757 + 0.659440i \(0.229207\pi\)
\(654\) −10.0714 −0.393824
\(655\) 12.4595 0.486835
\(656\) −5.12241 −0.199996
\(657\) 1.70219 0.0664089
\(658\) −7.08411 −0.276167
\(659\) 14.8950 0.580225 0.290112 0.956993i \(-0.406307\pi\)
0.290112 + 0.956993i \(0.406307\pi\)
\(660\) 7.53216 0.293189
\(661\) 26.9981 1.05011 0.525053 0.851070i \(-0.324046\pi\)
0.525053 + 0.851070i \(0.324046\pi\)
\(662\) −9.21502 −0.358152
\(663\) 29.3538 1.14001
\(664\) −6.53807 −0.253726
\(665\) −1.89976 −0.0736695
\(666\) −0.858321 −0.0332593
\(667\) 12.5026 0.484103
\(668\) −10.1117 −0.391235
\(669\) 12.3934 0.479158
\(670\) 7.58214 0.292924
\(671\) 31.9559 1.23364
\(672\) −2.11456 −0.0815709
\(673\) 11.5558 0.445442 0.222721 0.974882i \(-0.428506\pi\)
0.222721 + 0.974882i \(0.428506\pi\)
\(674\) −25.1254 −0.967793
\(675\) −18.7763 −0.722701
\(676\) 7.77922 0.299201
\(677\) −4.27317 −0.164231 −0.0821157 0.996623i \(-0.526168\pi\)
−0.0821157 + 0.996623i \(0.526168\pi\)
\(678\) −18.6955 −0.717995
\(679\) 20.7906 0.797871
\(680\) −5.78533 −0.221857
\(681\) −26.1546 −1.00225
\(682\) 8.44314 0.323304
\(683\) 17.9501 0.686841 0.343421 0.939182i \(-0.388414\pi\)
0.343421 + 0.939182i \(0.388414\pi\)
\(684\) −0.920075 −0.0351800
\(685\) 3.03293 0.115882
\(686\) −17.3749 −0.663378
\(687\) −9.63456 −0.367581
\(688\) −5.26177 −0.200603
\(689\) −53.4111 −2.03480
\(690\) −10.6808 −0.406612
\(691\) −4.46973 −0.170037 −0.0850183 0.996379i \(-0.527095\pi\)
−0.0850183 + 0.996379i \(0.527095\pi\)
\(692\) 3.14349 0.119498
\(693\) −5.43768 −0.206560
\(694\) −36.3139 −1.37846
\(695\) −11.0925 −0.420763
\(696\) 3.15461 0.119575
\(697\) −22.8718 −0.866331
\(698\) −29.8919 −1.13143
\(699\) −35.7497 −1.35218
\(700\) −4.86955 −0.184052
\(701\) −13.9807 −0.528043 −0.264022 0.964517i \(-0.585049\pi\)
−0.264022 + 0.964517i \(0.585049\pi\)
\(702\) −25.7711 −0.972667
\(703\) 0.932881 0.0351843
\(704\) 4.03083 0.151917
\(705\) −9.02849 −0.340033
\(706\) 34.5369 1.29981
\(707\) −5.63709 −0.212005
\(708\) −8.99881 −0.338196
\(709\) 30.6789 1.15217 0.576085 0.817390i \(-0.304580\pi\)
0.576085 + 0.817390i \(0.304580\pi\)
\(710\) 12.7903 0.480010
\(711\) −14.1323 −0.530002
\(712\) −14.9426 −0.559999
\(713\) −11.9726 −0.448378
\(714\) −9.44161 −0.353343
\(715\) 23.8073 0.890343
\(716\) −7.22917 −0.270167
\(717\) 2.13802 0.0798457
\(718\) −33.5032 −1.25033
\(719\) 20.2745 0.756112 0.378056 0.925783i \(-0.376593\pi\)
0.378056 + 0.925783i \(0.376593\pi\)
\(720\) 1.19214 0.0444283
\(721\) −18.0445 −0.672011
\(722\) 1.00000 0.0372161
\(723\) −5.04118 −0.187483
\(724\) −18.0301 −0.670085
\(725\) 7.26464 0.269802
\(726\) −7.56799 −0.280874
\(727\) −13.6242 −0.505295 −0.252647 0.967558i \(-0.581301\pi\)
−0.252647 + 0.967558i \(0.581301\pi\)
\(728\) −6.68361 −0.247711
\(729\) 29.4226 1.08972
\(730\) 2.39711 0.0887209
\(731\) −23.4941 −0.868959
\(732\) −11.4336 −0.422596
\(733\) −41.9111 −1.54802 −0.774011 0.633173i \(-0.781752\pi\)
−0.774011 + 0.633173i \(0.781752\pi\)
\(734\) 6.31709 0.233168
\(735\) −9.06333 −0.334306
\(736\) −5.71583 −0.210688
\(737\) −23.5876 −0.868860
\(738\) 4.71300 0.173488
\(739\) 8.66340 0.318688 0.159344 0.987223i \(-0.449062\pi\)
0.159344 + 0.987223i \(0.449062\pi\)
\(740\) −1.20873 −0.0444337
\(741\) 6.57413 0.241507
\(742\) 17.1796 0.630683
\(743\) 34.8007 1.27671 0.638356 0.769741i \(-0.279615\pi\)
0.638356 + 0.769741i \(0.279615\pi\)
\(744\) −3.02088 −0.110751
\(745\) −9.69112 −0.355055
\(746\) −3.26221 −0.119438
\(747\) 6.01551 0.220096
\(748\) 17.9978 0.658065
\(749\) −10.6643 −0.389666
\(750\) −15.5493 −0.567780
\(751\) 24.4616 0.892616 0.446308 0.894879i \(-0.352739\pi\)
0.446308 + 0.894879i \(0.352739\pi\)
\(752\) −4.83158 −0.176190
\(753\) 43.6039 1.58901
\(754\) 9.97095 0.363121
\(755\) 16.2535 0.591527
\(756\) 8.28923 0.301477
\(757\) −16.7086 −0.607284 −0.303642 0.952786i \(-0.598203\pi\)
−0.303642 + 0.952786i \(0.598203\pi\)
\(758\) 24.5061 0.890102
\(759\) 33.2274 1.20608
\(760\) −1.29569 −0.0469997
\(761\) 39.3146 1.42515 0.712576 0.701595i \(-0.247528\pi\)
0.712576 + 0.701595i \(0.247528\pi\)
\(762\) 16.4786 0.596955
\(763\) 10.2391 0.370682
\(764\) −14.0248 −0.507398
\(765\) 5.32294 0.192451
\(766\) −1.79746 −0.0649448
\(767\) −28.4430 −1.02702
\(768\) −1.44219 −0.0520407
\(769\) 51.5686 1.85961 0.929806 0.368051i \(-0.119975\pi\)
0.929806 + 0.368051i \(0.119975\pi\)
\(770\) −7.65759 −0.275960
\(771\) 30.2145 1.08815
\(772\) −24.0917 −0.867079
\(773\) 11.0151 0.396187 0.198093 0.980183i \(-0.436525\pi\)
0.198093 + 0.980183i \(0.436525\pi\)
\(774\) 4.84123 0.174014
\(775\) −6.95669 −0.249892
\(776\) 14.1798 0.509027
\(777\) −1.97263 −0.0707678
\(778\) 12.5599 0.450294
\(779\) −5.12241 −0.183529
\(780\) −8.51806 −0.304995
\(781\) −39.7897 −1.42379
\(782\) −25.5214 −0.912644
\(783\) −12.3663 −0.441936
\(784\) −4.85023 −0.173222
\(785\) −2.38904 −0.0852685
\(786\) 13.8683 0.494667
\(787\) 10.1016 0.360083 0.180041 0.983659i \(-0.442377\pi\)
0.180041 + 0.983659i \(0.442377\pi\)
\(788\) −19.3440 −0.689101
\(789\) −36.1658 −1.28754
\(790\) −19.9017 −0.708071
\(791\) 19.0068 0.675804
\(792\) −3.70866 −0.131782
\(793\) −36.1387 −1.28332
\(794\) 14.9495 0.530537
\(795\) 21.8949 0.776532
\(796\) 3.68411 0.130580
\(797\) 43.1521 1.52853 0.764263 0.644904i \(-0.223103\pi\)
0.764263 + 0.644904i \(0.223103\pi\)
\(798\) −2.11456 −0.0748546
\(799\) −21.5732 −0.763206
\(800\) −3.32118 −0.117421
\(801\) 13.7483 0.485774
\(802\) 15.2745 0.539363
\(803\) −7.45726 −0.263161
\(804\) 8.43944 0.297636
\(805\) 10.8587 0.382718
\(806\) −9.54827 −0.336323
\(807\) 24.0438 0.846381
\(808\) −3.84467 −0.135255
\(809\) −3.43427 −0.120742 −0.0603712 0.998176i \(-0.519228\pi\)
−0.0603712 + 0.998176i \(0.519228\pi\)
\(810\) 6.98798 0.245532
\(811\) −24.6057 −0.864025 −0.432012 0.901868i \(-0.642196\pi\)
−0.432012 + 0.901868i \(0.642196\pi\)
\(812\) −3.20714 −0.112549
\(813\) −30.7005 −1.07671
\(814\) 3.76028 0.131798
\(815\) 2.47235 0.0866026
\(816\) −6.43946 −0.225426
\(817\) −5.26177 −0.184086
\(818\) 14.6745 0.513080
\(819\) 6.14942 0.214878
\(820\) 6.63707 0.231776
\(821\) 8.57105 0.299132 0.149566 0.988752i \(-0.452212\pi\)
0.149566 + 0.988752i \(0.452212\pi\)
\(822\) 3.37586 0.117747
\(823\) 40.9895 1.42880 0.714402 0.699735i \(-0.246699\pi\)
0.714402 + 0.699735i \(0.246699\pi\)
\(824\) −12.3069 −0.428730
\(825\) 19.3068 0.672176
\(826\) 9.14866 0.318323
\(827\) −35.2591 −1.22608 −0.613039 0.790053i \(-0.710053\pi\)
−0.613039 + 0.790053i \(0.710053\pi\)
\(828\) 5.25899 0.182763
\(829\) 2.49867 0.0867823 0.0433912 0.999058i \(-0.486184\pi\)
0.0433912 + 0.999058i \(0.486184\pi\)
\(830\) 8.47133 0.294044
\(831\) 41.1249 1.42661
\(832\) −4.55842 −0.158035
\(833\) −21.6565 −0.750353
\(834\) −12.3467 −0.427532
\(835\) 13.1017 0.453404
\(836\) 4.03083 0.139409
\(837\) 11.8421 0.409322
\(838\) 17.0859 0.590223
\(839\) 9.19702 0.317516 0.158758 0.987317i \(-0.449251\pi\)
0.158758 + 0.987317i \(0.449251\pi\)
\(840\) 2.73982 0.0945328
\(841\) −24.2154 −0.835014
\(842\) −6.92230 −0.238558
\(843\) 6.88728 0.237210
\(844\) −1.00000 −0.0344214
\(845\) −10.0795 −0.346745
\(846\) 4.44542 0.152837
\(847\) 7.69401 0.264369
\(848\) 11.7170 0.402364
\(849\) 12.3038 0.422266
\(850\) −14.8292 −0.508638
\(851\) −5.33219 −0.182785
\(852\) 14.2364 0.487732
\(853\) −0.381396 −0.0130588 −0.00652938 0.999979i \(-0.502078\pi\)
−0.00652938 + 0.999979i \(0.502078\pi\)
\(854\) 11.6239 0.397763
\(855\) 1.19214 0.0407702
\(856\) −7.27339 −0.248600
\(857\) 14.9111 0.509354 0.254677 0.967026i \(-0.418031\pi\)
0.254677 + 0.967026i \(0.418031\pi\)
\(858\) 26.4992 0.904667
\(859\) −51.9534 −1.77263 −0.886313 0.463087i \(-0.846742\pi\)
−0.886313 + 0.463087i \(0.846742\pi\)
\(860\) 6.81764 0.232480
\(861\) 10.8316 0.369141
\(862\) 27.7113 0.943852
\(863\) 2.88329 0.0981483 0.0490742 0.998795i \(-0.484373\pi\)
0.0490742 + 0.998795i \(0.484373\pi\)
\(864\) 5.65351 0.192336
\(865\) −4.07300 −0.138486
\(866\) −8.07997 −0.274568
\(867\) −4.23520 −0.143835
\(868\) 3.07119 0.104243
\(869\) 61.9131 2.10026
\(870\) −4.08741 −0.138576
\(871\) 26.6750 0.903848
\(872\) 6.98340 0.236488
\(873\) −13.0465 −0.441558
\(874\) −5.71583 −0.193341
\(875\) 15.8082 0.534416
\(876\) 2.66814 0.0901482
\(877\) −13.8427 −0.467435 −0.233717 0.972305i \(-0.575089\pi\)
−0.233717 + 0.972305i \(0.575089\pi\)
\(878\) 41.2004 1.39045
\(879\) 22.5573 0.760838
\(880\) −5.22271 −0.176058
\(881\) 32.3180 1.08882 0.544410 0.838819i \(-0.316754\pi\)
0.544410 + 0.838819i \(0.316754\pi\)
\(882\) 4.46258 0.150263
\(883\) 28.2011 0.949042 0.474521 0.880244i \(-0.342621\pi\)
0.474521 + 0.880244i \(0.342621\pi\)
\(884\) −20.3536 −0.684565
\(885\) 11.6597 0.391936
\(886\) −11.8945 −0.399603
\(887\) 20.5494 0.689980 0.344990 0.938606i \(-0.387882\pi\)
0.344990 + 0.938606i \(0.387882\pi\)
\(888\) −1.34540 −0.0451485
\(889\) −16.7530 −0.561876
\(890\) 19.3611 0.648984
\(891\) −21.7392 −0.728290
\(892\) −8.59346 −0.287730
\(893\) −4.83158 −0.161683
\(894\) −10.7869 −0.360767
\(895\) 9.36679 0.313097
\(896\) 1.46621 0.0489826
\(897\) −37.5766 −1.25465
\(898\) −17.5206 −0.584671
\(899\) −4.58175 −0.152810
\(900\) 3.05574 0.101858
\(901\) 52.3170 1.74293
\(902\) −20.6475 −0.687488
\(903\) 11.1263 0.370261
\(904\) 12.9632 0.431150
\(905\) 23.3615 0.776563
\(906\) 18.0913 0.601043
\(907\) 38.3338 1.27285 0.636427 0.771337i \(-0.280412\pi\)
0.636427 + 0.771337i \(0.280412\pi\)
\(908\) 18.1353 0.601840
\(909\) 3.53738 0.117328
\(910\) 8.65990 0.287073
\(911\) −31.3294 −1.03799 −0.518995 0.854777i \(-0.673694\pi\)
−0.518995 + 0.854777i \(0.673694\pi\)
\(912\) −1.44219 −0.0477558
\(913\) −26.3538 −0.872184
\(914\) −19.6238 −0.649098
\(915\) 14.8144 0.489748
\(916\) 6.68049 0.220729
\(917\) −14.0993 −0.465599
\(918\) 25.2432 0.833149
\(919\) −1.28254 −0.0423072 −0.0211536 0.999776i \(-0.506734\pi\)
−0.0211536 + 0.999776i \(0.506734\pi\)
\(920\) 7.40596 0.244167
\(921\) 9.74548 0.321124
\(922\) −42.1904 −1.38947
\(923\) 44.9979 1.48112
\(924\) −8.52342 −0.280400
\(925\) −3.09827 −0.101870
\(926\) 8.95400 0.294247
\(927\) 11.3232 0.371904
\(928\) −2.18737 −0.0718039
\(929\) −18.3101 −0.600734 −0.300367 0.953824i \(-0.597109\pi\)
−0.300367 + 0.953824i \(0.597109\pi\)
\(930\) 3.91413 0.128350
\(931\) −4.85023 −0.158960
\(932\) 24.7884 0.811972
\(933\) −7.95025 −0.260280
\(934\) −26.9179 −0.880781
\(935\) −23.3196 −0.762634
\(936\) 4.19409 0.137088
\(937\) −34.3194 −1.12117 −0.560584 0.828098i \(-0.689423\pi\)
−0.560584 + 0.828098i \(0.689423\pi\)
\(938\) −8.57998 −0.280146
\(939\) 11.0296 0.359937
\(940\) 6.26024 0.204187
\(941\) 8.89780 0.290060 0.145030 0.989427i \(-0.453672\pi\)
0.145030 + 0.989427i \(0.453672\pi\)
\(942\) −2.65916 −0.0866403
\(943\) 29.2788 0.953449
\(944\) 6.23967 0.203084
\(945\) −10.7403 −0.349382
\(946\) −21.2093 −0.689573
\(947\) −49.3282 −1.60295 −0.801475 0.598029i \(-0.795951\pi\)
−0.801475 + 0.598029i \(0.795951\pi\)
\(948\) −22.1520 −0.719463
\(949\) 8.43335 0.273758
\(950\) −3.32118 −0.107753
\(951\) 21.2433 0.688862
\(952\) 6.54670 0.212180
\(953\) 37.3774 1.21077 0.605387 0.795932i \(-0.293019\pi\)
0.605387 + 0.795932i \(0.293019\pi\)
\(954\) −10.7805 −0.349033
\(955\) 18.1718 0.588025
\(956\) −1.48248 −0.0479467
\(957\) 12.7157 0.411040
\(958\) 29.4731 0.952234
\(959\) −3.43207 −0.110827
\(960\) 1.86864 0.0603101
\(961\) −26.6125 −0.858467
\(962\) −4.25247 −0.137105
\(963\) 6.69207 0.215649
\(964\) 3.49549 0.112582
\(965\) 31.2154 1.00486
\(966\) 12.0865 0.388875
\(967\) 22.0195 0.708100 0.354050 0.935227i \(-0.384804\pi\)
0.354050 + 0.935227i \(0.384804\pi\)
\(968\) 5.24755 0.168663
\(969\) −6.43946 −0.206865
\(970\) −18.3727 −0.589913
\(971\) 35.7902 1.14856 0.574281 0.818658i \(-0.305282\pi\)
0.574281 + 0.818658i \(0.305282\pi\)
\(972\) −9.18244 −0.294527
\(973\) 12.5523 0.402409
\(974\) 20.4895 0.656526
\(975\) −21.8339 −0.699244
\(976\) 7.92789 0.253765
\(977\) 22.9157 0.733139 0.366570 0.930391i \(-0.380532\pi\)
0.366570 + 0.930391i \(0.380532\pi\)
\(978\) 2.75189 0.0879958
\(979\) −60.2311 −1.92500
\(980\) 6.28441 0.200748
\(981\) −6.42526 −0.205143
\(982\) −21.2564 −0.678319
\(983\) 30.4755 0.972017 0.486008 0.873954i \(-0.338452\pi\)
0.486008 + 0.873954i \(0.338452\pi\)
\(984\) 7.38751 0.235505
\(985\) 25.0639 0.798602
\(986\) −9.76670 −0.311035
\(987\) 10.2167 0.325200
\(988\) −4.55842 −0.145023
\(989\) 30.0754 0.956341
\(990\) 4.80529 0.152722
\(991\) −18.9649 −0.602441 −0.301221 0.953554i \(-0.597394\pi\)
−0.301221 + 0.953554i \(0.597394\pi\)
\(992\) 2.09464 0.0665050
\(993\) 13.2898 0.421740
\(994\) −14.4735 −0.459071
\(995\) −4.77347 −0.151329
\(996\) 9.42916 0.298775
\(997\) −47.1509 −1.49328 −0.746642 0.665226i \(-0.768335\pi\)
−0.746642 + 0.665226i \(0.768335\pi\)
\(998\) −39.8369 −1.26101
\(999\) 5.27406 0.166864
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 \(a_p\))