Properties

Label 8015.2.a.l.1.12
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.90469 q^{2}\) \(-0.920285 q^{3}\) \(+1.62783 q^{4}\) \(-1.00000 q^{5}\) \(+1.75286 q^{6}\) \(-1.00000 q^{7}\) \(+0.708859 q^{8}\) \(-2.15308 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.90469 q^{2}\) \(-0.920285 q^{3}\) \(+1.62783 q^{4}\) \(-1.00000 q^{5}\) \(+1.75286 q^{6}\) \(-1.00000 q^{7}\) \(+0.708859 q^{8}\) \(-2.15308 q^{9}\) \(+1.90469 q^{10}\) \(-0.398461 q^{11}\) \(-1.49807 q^{12}\) \(+1.34448 q^{13}\) \(+1.90469 q^{14}\) \(+0.920285 q^{15}\) \(-4.60582 q^{16}\) \(-0.909012 q^{17}\) \(+4.10094 q^{18}\) \(+2.01853 q^{19}\) \(-1.62783 q^{20}\) \(+0.920285 q^{21}\) \(+0.758945 q^{22}\) \(+5.88511 q^{23}\) \(-0.652353 q^{24}\) \(+1.00000 q^{25}\) \(-2.56081 q^{26}\) \(+4.74230 q^{27}\) \(-1.62783 q^{28}\) \(+3.75365 q^{29}\) \(-1.75286 q^{30}\) \(+9.43024 q^{31}\) \(+7.35494 q^{32}\) \(+0.366698 q^{33}\) \(+1.73138 q^{34}\) \(+1.00000 q^{35}\) \(-3.50485 q^{36}\) \(-1.76743 q^{37}\) \(-3.84467 q^{38}\) \(-1.23730 q^{39}\) \(-0.708859 q^{40}\) \(+9.35609 q^{41}\) \(-1.75286 q^{42}\) \(+9.16701 q^{43}\) \(-0.648629 q^{44}\) \(+2.15308 q^{45}\) \(-11.2093 q^{46}\) \(-6.01265 q^{47}\) \(+4.23867 q^{48}\) \(+1.00000 q^{49}\) \(-1.90469 q^{50}\) \(+0.836550 q^{51}\) \(+2.18859 q^{52}\) \(-11.2152 q^{53}\) \(-9.03260 q^{54}\) \(+0.398461 q^{55}\) \(-0.708859 q^{56}\) \(-1.85762 q^{57}\) \(-7.14953 q^{58}\) \(-12.2949 q^{59}\) \(+1.49807 q^{60}\) \(-9.26880 q^{61}\) \(-17.9617 q^{62}\) \(+2.15308 q^{63}\) \(-4.79721 q^{64}\) \(-1.34448 q^{65}\) \(-0.698445 q^{66}\) \(-3.26366 q^{67}\) \(-1.47972 q^{68}\) \(-5.41598 q^{69}\) \(-1.90469 q^{70}\) \(-2.06582 q^{71}\) \(-1.52623 q^{72}\) \(-10.8291 q^{73}\) \(+3.36641 q^{74}\) \(-0.920285 q^{75}\) \(+3.28583 q^{76}\) \(+0.398461 q^{77}\) \(+2.35667 q^{78}\) \(+13.4409 q^{79}\) \(+4.60582 q^{80}\) \(+2.09496 q^{81}\) \(-17.8204 q^{82}\) \(+6.72692 q^{83}\) \(+1.49807 q^{84}\) \(+0.909012 q^{85}\) \(-17.4603 q^{86}\) \(-3.45443 q^{87}\) \(-0.282453 q^{88}\) \(+8.30386 q^{89}\) \(-4.10094 q^{90}\) \(-1.34448 q^{91}\) \(+9.57999 q^{92}\) \(-8.67851 q^{93}\) \(+11.4522 q^{94}\) \(-2.01853 q^{95}\) \(-6.76864 q^{96}\) \(+8.69125 q^{97}\) \(-1.90469 q^{98}\) \(+0.857918 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90469 −1.34682 −0.673409 0.739270i \(-0.735171\pi\)
−0.673409 + 0.739270i \(0.735171\pi\)
\(3\) −0.920285 −0.531327 −0.265663 0.964066i \(-0.585591\pi\)
−0.265663 + 0.964066i \(0.585591\pi\)
\(4\) 1.62783 0.813917
\(5\) −1.00000 −0.447214
\(6\) 1.75286 0.715600
\(7\) −1.00000 −0.377964
\(8\) 0.708859 0.250620
\(9\) −2.15308 −0.717692
\(10\) 1.90469 0.602315
\(11\) −0.398461 −0.120141 −0.0600703 0.998194i \(-0.519132\pi\)
−0.0600703 + 0.998194i \(0.519132\pi\)
\(12\) −1.49807 −0.432456
\(13\) 1.34448 0.372891 0.186445 0.982465i \(-0.440303\pi\)
0.186445 + 0.982465i \(0.440303\pi\)
\(14\) 1.90469 0.509049
\(15\) 0.920285 0.237617
\(16\) −4.60582 −1.15146
\(17\) −0.909012 −0.220468 −0.110234 0.993906i \(-0.535160\pi\)
−0.110234 + 0.993906i \(0.535160\pi\)
\(18\) 4.10094 0.966600
\(19\) 2.01853 0.463083 0.231541 0.972825i \(-0.425623\pi\)
0.231541 + 0.972825i \(0.425623\pi\)
\(20\) −1.62783 −0.363995
\(21\) 0.920285 0.200823
\(22\) 0.758945 0.161808
\(23\) 5.88511 1.22713 0.613565 0.789644i \(-0.289735\pi\)
0.613565 + 0.789644i \(0.289735\pi\)
\(24\) −0.652353 −0.133161
\(25\) 1.00000 0.200000
\(26\) −2.56081 −0.502216
\(27\) 4.74230 0.912656
\(28\) −1.62783 −0.307632
\(29\) 3.75365 0.697035 0.348518 0.937302i \(-0.386685\pi\)
0.348518 + 0.937302i \(0.386685\pi\)
\(30\) −1.75286 −0.320026
\(31\) 9.43024 1.69372 0.846860 0.531815i \(-0.178490\pi\)
0.846860 + 0.531815i \(0.178490\pi\)
\(32\) 7.35494 1.30018
\(33\) 0.366698 0.0638340
\(34\) 1.73138 0.296930
\(35\) 1.00000 0.169031
\(36\) −3.50485 −0.584142
\(37\) −1.76743 −0.290564 −0.145282 0.989390i \(-0.546409\pi\)
−0.145282 + 0.989390i \(0.546409\pi\)
\(38\) −3.84467 −0.623688
\(39\) −1.23730 −0.198127
\(40\) −0.708859 −0.112080
\(41\) 9.35609 1.46118 0.730588 0.682819i \(-0.239246\pi\)
0.730588 + 0.682819i \(0.239246\pi\)
\(42\) −1.75286 −0.270471
\(43\) 9.16701 1.39796 0.698978 0.715143i \(-0.253639\pi\)
0.698978 + 0.715143i \(0.253639\pi\)
\(44\) −0.648629 −0.0977845
\(45\) 2.15308 0.320962
\(46\) −11.2093 −1.65272
\(47\) −6.01265 −0.877035 −0.438518 0.898723i \(-0.644496\pi\)
−0.438518 + 0.898723i \(0.644496\pi\)
\(48\) 4.23867 0.611799
\(49\) 1.00000 0.142857
\(50\) −1.90469 −0.269363
\(51\) 0.836550 0.117140
\(52\) 2.18859 0.303502
\(53\) −11.2152 −1.54053 −0.770264 0.637725i \(-0.779876\pi\)
−0.770264 + 0.637725i \(0.779876\pi\)
\(54\) −9.03260 −1.22918
\(55\) 0.398461 0.0537285
\(56\) −0.708859 −0.0947253
\(57\) −1.85762 −0.246048
\(58\) −7.14953 −0.938779
\(59\) −12.2949 −1.60066 −0.800332 0.599557i \(-0.795344\pi\)
−0.800332 + 0.599557i \(0.795344\pi\)
\(60\) 1.49807 0.193400
\(61\) −9.26880 −1.18675 −0.593374 0.804927i \(-0.702205\pi\)
−0.593374 + 0.804927i \(0.702205\pi\)
\(62\) −17.9617 −2.28113
\(63\) 2.15308 0.271262
\(64\) −4.79721 −0.599651
\(65\) −1.34448 −0.166762
\(66\) −0.698445 −0.0859727
\(67\) −3.26366 −0.398719 −0.199360 0.979926i \(-0.563886\pi\)
−0.199360 + 0.979926i \(0.563886\pi\)
\(68\) −1.47972 −0.179442
\(69\) −5.41598 −0.652008
\(70\) −1.90469 −0.227654
\(71\) −2.06582 −0.245168 −0.122584 0.992458i \(-0.539118\pi\)
−0.122584 + 0.992458i \(0.539118\pi\)
\(72\) −1.52623 −0.179868
\(73\) −10.8291 −1.26745 −0.633725 0.773558i \(-0.718475\pi\)
−0.633725 + 0.773558i \(0.718475\pi\)
\(74\) 3.36641 0.391337
\(75\) −0.920285 −0.106265
\(76\) 3.28583 0.376911
\(77\) 0.398461 0.0454089
\(78\) 2.35667 0.266841
\(79\) 13.4409 1.51221 0.756107 0.654448i \(-0.227099\pi\)
0.756107 + 0.654448i \(0.227099\pi\)
\(80\) 4.60582 0.514947
\(81\) 2.09496 0.232773
\(82\) −17.8204 −1.96794
\(83\) 6.72692 0.738375 0.369188 0.929355i \(-0.379636\pi\)
0.369188 + 0.929355i \(0.379636\pi\)
\(84\) 1.49807 0.163453
\(85\) 0.909012 0.0985962
\(86\) −17.4603 −1.88279
\(87\) −3.45443 −0.370354
\(88\) −0.282453 −0.0301096
\(89\) 8.30386 0.880208 0.440104 0.897947i \(-0.354942\pi\)
0.440104 + 0.897947i \(0.354942\pi\)
\(90\) −4.10094 −0.432277
\(91\) −1.34448 −0.140939
\(92\) 9.57999 0.998783
\(93\) −8.67851 −0.899919
\(94\) 11.4522 1.18121
\(95\) −2.01853 −0.207097
\(96\) −6.76864 −0.690821
\(97\) 8.69125 0.882463 0.441231 0.897393i \(-0.354542\pi\)
0.441231 + 0.897393i \(0.354542\pi\)
\(98\) −1.90469 −0.192402
\(99\) 0.857918 0.0862240
\(100\) 1.62783 0.162783
\(101\) −6.43641 −0.640447 −0.320223 0.947342i \(-0.603758\pi\)
−0.320223 + 0.947342i \(0.603758\pi\)
\(102\) −1.59337 −0.157767
\(103\) 19.6516 1.93632 0.968162 0.250323i \(-0.0805368\pi\)
0.968162 + 0.250323i \(0.0805368\pi\)
\(104\) 0.953045 0.0934537
\(105\) −0.920285 −0.0898106
\(106\) 21.3615 2.07481
\(107\) −0.137896 −0.0133309 −0.00666545 0.999978i \(-0.502122\pi\)
−0.00666545 + 0.999978i \(0.502122\pi\)
\(108\) 7.71968 0.742826
\(109\) −14.3916 −1.37847 −0.689234 0.724539i \(-0.742053\pi\)
−0.689234 + 0.724539i \(0.742053\pi\)
\(110\) −0.758945 −0.0723625
\(111\) 1.62654 0.154385
\(112\) 4.60582 0.435209
\(113\) 5.06663 0.476629 0.238314 0.971188i \(-0.423405\pi\)
0.238314 + 0.971188i \(0.423405\pi\)
\(114\) 3.53819 0.331382
\(115\) −5.88511 −0.548790
\(116\) 6.11032 0.567329
\(117\) −2.89476 −0.267621
\(118\) 23.4180 2.15580
\(119\) 0.909012 0.0833290
\(120\) 0.652353 0.0595514
\(121\) −10.8412 −0.985566
\(122\) 17.6542 1.59833
\(123\) −8.61027 −0.776362
\(124\) 15.3509 1.37855
\(125\) −1.00000 −0.0894427
\(126\) −4.10094 −0.365340
\(127\) 9.07603 0.805368 0.402684 0.915339i \(-0.368077\pi\)
0.402684 + 0.915339i \(0.368077\pi\)
\(128\) −5.57269 −0.492561
\(129\) −8.43626 −0.742771
\(130\) 2.56081 0.224598
\(131\) 19.6266 1.71479 0.857393 0.514662i \(-0.172082\pi\)
0.857393 + 0.514662i \(0.172082\pi\)
\(132\) 0.596924 0.0519556
\(133\) −2.01853 −0.175029
\(134\) 6.21625 0.537002
\(135\) −4.74230 −0.408152
\(136\) −0.644361 −0.0552535
\(137\) 9.72757 0.831082 0.415541 0.909574i \(-0.363592\pi\)
0.415541 + 0.909574i \(0.363592\pi\)
\(138\) 10.3158 0.878135
\(139\) −21.3393 −1.80997 −0.904986 0.425442i \(-0.860119\pi\)
−0.904986 + 0.425442i \(0.860119\pi\)
\(140\) 1.62783 0.137577
\(141\) 5.53335 0.465992
\(142\) 3.93474 0.330196
\(143\) −0.535722 −0.0447994
\(144\) 9.91669 0.826391
\(145\) −3.75365 −0.311724
\(146\) 20.6261 1.70702
\(147\) −0.920285 −0.0759038
\(148\) −2.87709 −0.236495
\(149\) −9.23239 −0.756347 −0.378173 0.925735i \(-0.623448\pi\)
−0.378173 + 0.925735i \(0.623448\pi\)
\(150\) 1.75286 0.143120
\(151\) −8.79112 −0.715412 −0.357706 0.933834i \(-0.616441\pi\)
−0.357706 + 0.933834i \(0.616441\pi\)
\(152\) 1.43085 0.116058
\(153\) 1.95717 0.158228
\(154\) −0.758945 −0.0611575
\(155\) −9.43024 −0.757455
\(156\) −2.01412 −0.161259
\(157\) −22.0034 −1.75606 −0.878030 0.478606i \(-0.841142\pi\)
−0.878030 + 0.478606i \(0.841142\pi\)
\(158\) −25.6006 −2.03668
\(159\) 10.3212 0.818524
\(160\) −7.35494 −0.581459
\(161\) −5.88511 −0.463812
\(162\) −3.99024 −0.313503
\(163\) 15.0074 1.17547 0.587737 0.809052i \(-0.300019\pi\)
0.587737 + 0.809052i \(0.300019\pi\)
\(164\) 15.2302 1.18928
\(165\) −0.366698 −0.0285474
\(166\) −12.8127 −0.994456
\(167\) −19.1886 −1.48486 −0.742429 0.669924i \(-0.766326\pi\)
−0.742429 + 0.669924i \(0.766326\pi\)
\(168\) 0.652353 0.0503301
\(169\) −11.1924 −0.860952
\(170\) −1.73138 −0.132791
\(171\) −4.34605 −0.332351
\(172\) 14.9224 1.13782
\(173\) 5.28611 0.401896 0.200948 0.979602i \(-0.435598\pi\)
0.200948 + 0.979602i \(0.435598\pi\)
\(174\) 6.57961 0.498799
\(175\) −1.00000 −0.0755929
\(176\) 1.83524 0.138337
\(177\) 11.3148 0.850476
\(178\) −15.8163 −1.18548
\(179\) −6.54213 −0.488982 −0.244491 0.969652i \(-0.578621\pi\)
−0.244491 + 0.969652i \(0.578621\pi\)
\(180\) 3.50485 0.261236
\(181\) 3.34882 0.248916 0.124458 0.992225i \(-0.460281\pi\)
0.124458 + 0.992225i \(0.460281\pi\)
\(182\) 2.56081 0.189820
\(183\) 8.52994 0.630551
\(184\) 4.17172 0.307543
\(185\) 1.76743 0.129944
\(186\) 16.5298 1.21203
\(187\) 0.362206 0.0264871
\(188\) −9.78760 −0.713834
\(189\) −4.74230 −0.344951
\(190\) 3.84467 0.278922
\(191\) 2.04324 0.147844 0.0739219 0.997264i \(-0.476448\pi\)
0.0739219 + 0.997264i \(0.476448\pi\)
\(192\) 4.41480 0.318611
\(193\) 25.7380 1.85266 0.926330 0.376712i \(-0.122945\pi\)
0.926330 + 0.376712i \(0.122945\pi\)
\(194\) −16.5541 −1.18852
\(195\) 1.23730 0.0886050
\(196\) 1.62783 0.116274
\(197\) −0.889561 −0.0633786 −0.0316893 0.999498i \(-0.510089\pi\)
−0.0316893 + 0.999498i \(0.510089\pi\)
\(198\) −1.63406 −0.116128
\(199\) −0.177669 −0.0125946 −0.00629731 0.999980i \(-0.502005\pi\)
−0.00629731 + 0.999980i \(0.502005\pi\)
\(200\) 0.708859 0.0501239
\(201\) 3.00349 0.211850
\(202\) 12.2593 0.862565
\(203\) −3.75365 −0.263455
\(204\) 1.36176 0.0953426
\(205\) −9.35609 −0.653458
\(206\) −37.4301 −2.60788
\(207\) −12.6711 −0.880702
\(208\) −6.19242 −0.429367
\(209\) −0.804307 −0.0556350
\(210\) 1.75286 0.120959
\(211\) −25.3607 −1.74590 −0.872950 0.487809i \(-0.837796\pi\)
−0.872950 + 0.487809i \(0.837796\pi\)
\(212\) −18.2565 −1.25386
\(213\) 1.90114 0.130264
\(214\) 0.262649 0.0179543
\(215\) −9.16701 −0.625185
\(216\) 3.36162 0.228729
\(217\) −9.43024 −0.640166
\(218\) 27.4115 1.85654
\(219\) 9.96586 0.673430
\(220\) 0.648629 0.0437306
\(221\) −1.22215 −0.0822104
\(222\) −3.09806 −0.207928
\(223\) 17.9830 1.20423 0.602115 0.798409i \(-0.294325\pi\)
0.602115 + 0.798409i \(0.294325\pi\)
\(224\) −7.35494 −0.491422
\(225\) −2.15308 −0.143538
\(226\) −9.65035 −0.641932
\(227\) −8.88987 −0.590041 −0.295021 0.955491i \(-0.595326\pi\)
−0.295021 + 0.955491i \(0.595326\pi\)
\(228\) −3.02390 −0.200263
\(229\) 1.00000 0.0660819
\(230\) 11.2093 0.739119
\(231\) −0.366698 −0.0241270
\(232\) 2.66081 0.174691
\(233\) 3.64991 0.239114 0.119557 0.992827i \(-0.461853\pi\)
0.119557 + 0.992827i \(0.461853\pi\)
\(234\) 5.51361 0.360436
\(235\) 6.01265 0.392222
\(236\) −20.0141 −1.30281
\(237\) −12.3694 −0.803480
\(238\) −1.73138 −0.112229
\(239\) 16.1757 1.04632 0.523159 0.852235i \(-0.324753\pi\)
0.523159 + 0.852235i \(0.324753\pi\)
\(240\) −4.23867 −0.273605
\(241\) 7.71156 0.496745 0.248373 0.968665i \(-0.420104\pi\)
0.248373 + 0.968665i \(0.420104\pi\)
\(242\) 20.6492 1.32738
\(243\) −16.1549 −1.03633
\(244\) −15.0881 −0.965915
\(245\) −1.00000 −0.0638877
\(246\) 16.3999 1.04562
\(247\) 2.71387 0.172679
\(248\) 6.68471 0.424480
\(249\) −6.19068 −0.392318
\(250\) 1.90469 0.120463
\(251\) −16.6835 −1.05305 −0.526526 0.850159i \(-0.676506\pi\)
−0.526526 + 0.850159i \(0.676506\pi\)
\(252\) 3.50485 0.220785
\(253\) −2.34499 −0.147428
\(254\) −17.2870 −1.08468
\(255\) −0.836550 −0.0523868
\(256\) 20.2087 1.26304
\(257\) 6.17137 0.384960 0.192480 0.981301i \(-0.438347\pi\)
0.192480 + 0.981301i \(0.438347\pi\)
\(258\) 16.0684 1.00038
\(259\) 1.76743 0.109823
\(260\) −2.18859 −0.135730
\(261\) −8.08189 −0.500256
\(262\) −37.3826 −2.30950
\(263\) 8.12510 0.501015 0.250508 0.968115i \(-0.419402\pi\)
0.250508 + 0.968115i \(0.419402\pi\)
\(264\) 0.259937 0.0159980
\(265\) 11.2152 0.688945
\(266\) 3.84467 0.235732
\(267\) −7.64192 −0.467678
\(268\) −5.31269 −0.324524
\(269\) −0.627679 −0.0382702 −0.0191351 0.999817i \(-0.506091\pi\)
−0.0191351 + 0.999817i \(0.506091\pi\)
\(270\) 9.03260 0.549706
\(271\) 8.17038 0.496315 0.248158 0.968720i \(-0.420175\pi\)
0.248158 + 0.968720i \(0.420175\pi\)
\(272\) 4.18675 0.253859
\(273\) 1.23730 0.0748849
\(274\) −18.5280 −1.11932
\(275\) −0.398461 −0.0240281
\(276\) −8.81632 −0.530680
\(277\) 23.8768 1.43462 0.717309 0.696756i \(-0.245374\pi\)
0.717309 + 0.696756i \(0.245374\pi\)
\(278\) 40.6446 2.43770
\(279\) −20.3040 −1.21557
\(280\) 0.708859 0.0423624
\(281\) −2.41049 −0.143798 −0.0718988 0.997412i \(-0.522906\pi\)
−0.0718988 + 0.997412i \(0.522906\pi\)
\(282\) −10.5393 −0.627607
\(283\) 11.9779 0.712013 0.356007 0.934483i \(-0.384138\pi\)
0.356007 + 0.934483i \(0.384138\pi\)
\(284\) −3.36281 −0.199546
\(285\) 1.85762 0.110036
\(286\) 1.02038 0.0603365
\(287\) −9.35609 −0.552273
\(288\) −15.8357 −0.933130
\(289\) −16.1737 −0.951394
\(290\) 7.14953 0.419835
\(291\) −7.99843 −0.468876
\(292\) −17.6280 −1.03160
\(293\) −14.2163 −0.830526 −0.415263 0.909701i \(-0.636310\pi\)
−0.415263 + 0.909701i \(0.636310\pi\)
\(294\) 1.75286 0.102229
\(295\) 12.2949 0.715839
\(296\) −1.25286 −0.0728211
\(297\) −1.88962 −0.109647
\(298\) 17.5848 1.01866
\(299\) 7.91240 0.457586
\(300\) −1.49807 −0.0864912
\(301\) −9.16701 −0.528377
\(302\) 16.7443 0.963529
\(303\) 5.92333 0.340287
\(304\) −9.29700 −0.533219
\(305\) 9.26880 0.530730
\(306\) −3.72780 −0.213104
\(307\) 15.2743 0.871750 0.435875 0.900007i \(-0.356439\pi\)
0.435875 + 0.900007i \(0.356439\pi\)
\(308\) 0.648629 0.0369591
\(309\) −18.0850 −1.02882
\(310\) 17.9617 1.02015
\(311\) −12.3173 −0.698452 −0.349226 0.937038i \(-0.613556\pi\)
−0.349226 + 0.937038i \(0.613556\pi\)
\(312\) −0.877073 −0.0496545
\(313\) −0.226117 −0.0127809 −0.00639045 0.999980i \(-0.502034\pi\)
−0.00639045 + 0.999980i \(0.502034\pi\)
\(314\) 41.9095 2.36509
\(315\) −2.15308 −0.121312
\(316\) 21.8795 1.23082
\(317\) −7.51201 −0.421916 −0.210958 0.977495i \(-0.567658\pi\)
−0.210958 + 0.977495i \(0.567658\pi\)
\(318\) −19.6586 −1.10240
\(319\) −1.49568 −0.0837423
\(320\) 4.79721 0.268172
\(321\) 0.126904 0.00708306
\(322\) 11.2093 0.624670
\(323\) −1.83487 −0.102095
\(324\) 3.41025 0.189458
\(325\) 1.34448 0.0745782
\(326\) −28.5845 −1.58315
\(327\) 13.2444 0.732417
\(328\) 6.63215 0.366199
\(329\) 6.01265 0.331488
\(330\) 0.698445 0.0384482
\(331\) −18.5413 −1.01912 −0.509561 0.860434i \(-0.670192\pi\)
−0.509561 + 0.860434i \(0.670192\pi\)
\(332\) 10.9503 0.600976
\(333\) 3.80542 0.208536
\(334\) 36.5483 1.99983
\(335\) 3.26366 0.178313
\(336\) −4.23867 −0.231238
\(337\) 32.0037 1.74335 0.871677 0.490081i \(-0.163033\pi\)
0.871677 + 0.490081i \(0.163033\pi\)
\(338\) 21.3180 1.15955
\(339\) −4.66275 −0.253246
\(340\) 1.47972 0.0802491
\(341\) −3.75759 −0.203485
\(342\) 8.27786 0.447616
\(343\) −1.00000 −0.0539949
\(344\) 6.49812 0.350355
\(345\) 5.41598 0.291587
\(346\) −10.0684 −0.541280
\(347\) 12.3514 0.663060 0.331530 0.943445i \(-0.392435\pi\)
0.331530 + 0.943445i \(0.392435\pi\)
\(348\) −5.62324 −0.301437
\(349\) 4.63875 0.248307 0.124153 0.992263i \(-0.460379\pi\)
0.124153 + 0.992263i \(0.460379\pi\)
\(350\) 1.90469 0.101810
\(351\) 6.37591 0.340321
\(352\) −2.93066 −0.156205
\(353\) 32.9707 1.75485 0.877427 0.479710i \(-0.159258\pi\)
0.877427 + 0.479710i \(0.159258\pi\)
\(354\) −21.5513 −1.14544
\(355\) 2.06582 0.109642
\(356\) 13.5173 0.716416
\(357\) −0.836550 −0.0442749
\(358\) 12.4607 0.658569
\(359\) −18.5144 −0.977152 −0.488576 0.872521i \(-0.662483\pi\)
−0.488576 + 0.872521i \(0.662483\pi\)
\(360\) 1.52623 0.0804392
\(361\) −14.9255 −0.785555
\(362\) −6.37846 −0.335244
\(363\) 9.97702 0.523658
\(364\) −2.18859 −0.114713
\(365\) 10.8291 0.566821
\(366\) −16.2469 −0.849238
\(367\) −23.4491 −1.22403 −0.612017 0.790844i \(-0.709642\pi\)
−0.612017 + 0.790844i \(0.709642\pi\)
\(368\) −27.1058 −1.41299
\(369\) −20.1444 −1.04867
\(370\) −3.36641 −0.175011
\(371\) 11.2152 0.582265
\(372\) −14.1272 −0.732460
\(373\) −18.0580 −0.935006 −0.467503 0.883991i \(-0.654846\pi\)
−0.467503 + 0.883991i \(0.654846\pi\)
\(374\) −0.689890 −0.0356733
\(375\) 0.920285 0.0475233
\(376\) −4.26212 −0.219802
\(377\) 5.04670 0.259918
\(378\) 9.03260 0.464587
\(379\) −6.96985 −0.358017 −0.179009 0.983847i \(-0.557289\pi\)
−0.179009 + 0.983847i \(0.557289\pi\)
\(380\) −3.28583 −0.168560
\(381\) −8.35254 −0.427913
\(382\) −3.89174 −0.199119
\(383\) −33.5228 −1.71294 −0.856468 0.516200i \(-0.827346\pi\)
−0.856468 + 0.516200i \(0.827346\pi\)
\(384\) 5.12847 0.261711
\(385\) −0.398461 −0.0203075
\(386\) −49.0228 −2.49520
\(387\) −19.7373 −1.00330
\(388\) 14.1479 0.718251
\(389\) −21.8847 −1.10960 −0.554798 0.831985i \(-0.687204\pi\)
−0.554798 + 0.831985i \(0.687204\pi\)
\(390\) −2.35667 −0.119335
\(391\) −5.34964 −0.270543
\(392\) 0.708859 0.0358028
\(393\) −18.0621 −0.911112
\(394\) 1.69434 0.0853594
\(395\) −13.4409 −0.676283
\(396\) 1.39655 0.0701792
\(397\) 26.9346 1.35181 0.675905 0.736989i \(-0.263753\pi\)
0.675905 + 0.736989i \(0.263753\pi\)
\(398\) 0.338404 0.0169627
\(399\) 1.85762 0.0929975
\(400\) −4.60582 −0.230291
\(401\) −24.8204 −1.23947 −0.619736 0.784810i \(-0.712760\pi\)
−0.619736 + 0.784810i \(0.712760\pi\)
\(402\) −5.72072 −0.285323
\(403\) 12.6787 0.631573
\(404\) −10.4774 −0.521271
\(405\) −2.09496 −0.104099
\(406\) 7.14953 0.354825
\(407\) 0.704254 0.0349086
\(408\) 0.592996 0.0293577
\(409\) 9.15483 0.452677 0.226339 0.974049i \(-0.427324\pi\)
0.226339 + 0.974049i \(0.427324\pi\)
\(410\) 17.8204 0.880088
\(411\) −8.95213 −0.441576
\(412\) 31.9895 1.57601
\(413\) 12.2949 0.604994
\(414\) 24.1345 1.18614
\(415\) −6.72692 −0.330211
\(416\) 9.88854 0.484826
\(417\) 19.6382 0.961687
\(418\) 1.53195 0.0749303
\(419\) 5.65783 0.276403 0.138202 0.990404i \(-0.455868\pi\)
0.138202 + 0.990404i \(0.455868\pi\)
\(420\) −1.49807 −0.0730984
\(421\) 27.9693 1.36314 0.681569 0.731754i \(-0.261298\pi\)
0.681569 + 0.731754i \(0.261298\pi\)
\(422\) 48.3041 2.35141
\(423\) 12.9457 0.629441
\(424\) −7.95001 −0.386086
\(425\) −0.909012 −0.0440935
\(426\) −3.62108 −0.175442
\(427\) 9.26880 0.448549
\(428\) −0.224472 −0.0108502
\(429\) 0.493017 0.0238031
\(430\) 17.4603 0.842010
\(431\) −22.3715 −1.07760 −0.538799 0.842434i \(-0.681122\pi\)
−0.538799 + 0.842434i \(0.681122\pi\)
\(432\) −21.8422 −1.05088
\(433\) −9.00623 −0.432812 −0.216406 0.976303i \(-0.569433\pi\)
−0.216406 + 0.976303i \(0.569433\pi\)
\(434\) 17.9617 0.862187
\(435\) 3.45443 0.165627
\(436\) −23.4272 −1.12196
\(437\) 11.8793 0.568263
\(438\) −18.9818 −0.906988
\(439\) 23.2754 1.11087 0.555437 0.831559i \(-0.312551\pi\)
0.555437 + 0.831559i \(0.312551\pi\)
\(440\) 0.282453 0.0134654
\(441\) −2.15308 −0.102527
\(442\) 2.32780 0.110722
\(443\) −9.18886 −0.436576 −0.218288 0.975884i \(-0.570047\pi\)
−0.218288 + 0.975884i \(0.570047\pi\)
\(444\) 2.64774 0.125656
\(445\) −8.30386 −0.393641
\(446\) −34.2520 −1.62188
\(447\) 8.49643 0.401867
\(448\) 4.79721 0.226647
\(449\) −1.68311 −0.0794311 −0.0397155 0.999211i \(-0.512645\pi\)
−0.0397155 + 0.999211i \(0.512645\pi\)
\(450\) 4.10094 0.193320
\(451\) −3.72804 −0.175547
\(452\) 8.24764 0.387936
\(453\) 8.09034 0.380117
\(454\) 16.9324 0.794678
\(455\) 1.34448 0.0630301
\(456\) −1.31679 −0.0616645
\(457\) 6.44068 0.301282 0.150641 0.988589i \(-0.451866\pi\)
0.150641 + 0.988589i \(0.451866\pi\)
\(458\) −1.90469 −0.0890002
\(459\) −4.31080 −0.201211
\(460\) −9.57999 −0.446669
\(461\) −3.35278 −0.156154 −0.0780772 0.996947i \(-0.524878\pi\)
−0.0780772 + 0.996947i \(0.524878\pi\)
\(462\) 0.698445 0.0324946
\(463\) 39.1145 1.81781 0.908903 0.417007i \(-0.136921\pi\)
0.908903 + 0.417007i \(0.136921\pi\)
\(464\) −17.2886 −0.802605
\(465\) 8.67851 0.402456
\(466\) −6.95195 −0.322043
\(467\) 16.5803 0.767247 0.383624 0.923490i \(-0.374676\pi\)
0.383624 + 0.923490i \(0.374676\pi\)
\(468\) −4.71219 −0.217821
\(469\) 3.26366 0.150702
\(470\) −11.4522 −0.528251
\(471\) 20.2494 0.933041
\(472\) −8.71538 −0.401158
\(473\) −3.65270 −0.167951
\(474\) 23.5599 1.08214
\(475\) 2.01853 0.0926165
\(476\) 1.47972 0.0678229
\(477\) 24.1472 1.10562
\(478\) −30.8096 −1.40920
\(479\) 30.9952 1.41621 0.708104 0.706108i \(-0.249551\pi\)
0.708104 + 0.706108i \(0.249551\pi\)
\(480\) 6.76864 0.308945
\(481\) −2.37627 −0.108349
\(482\) −14.6881 −0.669025
\(483\) 5.41598 0.246436
\(484\) −17.6477 −0.802169
\(485\) −8.69125 −0.394649
\(486\) 30.7700 1.39575
\(487\) 9.34362 0.423400 0.211700 0.977335i \(-0.432100\pi\)
0.211700 + 0.977335i \(0.432100\pi\)
\(488\) −6.57028 −0.297422
\(489\) −13.8111 −0.624561
\(490\) 1.90469 0.0860450
\(491\) −0.588749 −0.0265699 −0.0132849 0.999912i \(-0.504229\pi\)
−0.0132849 + 0.999912i \(0.504229\pi\)
\(492\) −14.0161 −0.631894
\(493\) −3.41211 −0.153674
\(494\) −5.16907 −0.232567
\(495\) −0.857918 −0.0385605
\(496\) −43.4340 −1.95024
\(497\) 2.06582 0.0926646
\(498\) 11.7913 0.528381
\(499\) 35.2498 1.57800 0.788998 0.614395i \(-0.210600\pi\)
0.788998 + 0.614395i \(0.210600\pi\)
\(500\) −1.62783 −0.0727990
\(501\) 17.6590 0.788945
\(502\) 31.7768 1.41827
\(503\) −32.7118 −1.45855 −0.729274 0.684222i \(-0.760142\pi\)
−0.729274 + 0.684222i \(0.760142\pi\)
\(504\) 1.52623 0.0679836
\(505\) 6.43641 0.286416
\(506\) 4.46647 0.198559
\(507\) 10.3002 0.457447
\(508\) 14.7743 0.655502
\(509\) 18.6501 0.826650 0.413325 0.910583i \(-0.364367\pi\)
0.413325 + 0.910583i \(0.364367\pi\)
\(510\) 1.59337 0.0705554
\(511\) 10.8291 0.479051
\(512\) −27.3458 −1.20852
\(513\) 9.57247 0.422635
\(514\) −11.7545 −0.518470
\(515\) −19.6516 −0.865951
\(516\) −13.7328 −0.604554
\(517\) 2.39581 0.105368
\(518\) −3.36641 −0.147911
\(519\) −4.86473 −0.213538
\(520\) −0.953045 −0.0417938
\(521\) −4.55655 −0.199626 −0.0998130 0.995006i \(-0.531824\pi\)
−0.0998130 + 0.995006i \(0.531824\pi\)
\(522\) 15.3935 0.673754
\(523\) 11.7941 0.515720 0.257860 0.966182i \(-0.416983\pi\)
0.257860 + 0.966182i \(0.416983\pi\)
\(524\) 31.9489 1.39569
\(525\) 0.920285 0.0401645
\(526\) −15.4758 −0.674776
\(527\) −8.57220 −0.373411
\(528\) −1.68895 −0.0735020
\(529\) 11.6346 0.505850
\(530\) −21.3615 −0.927883
\(531\) 26.4719 1.14878
\(532\) −3.28583 −0.142459
\(533\) 12.5790 0.544859
\(534\) 14.5555 0.629877
\(535\) 0.137896 0.00596176
\(536\) −2.31347 −0.0999268
\(537\) 6.02062 0.259809
\(538\) 1.19553 0.0515430
\(539\) −0.398461 −0.0171630
\(540\) −7.71968 −0.332202
\(541\) 25.1765 1.08242 0.541211 0.840887i \(-0.317966\pi\)
0.541211 + 0.840887i \(0.317966\pi\)
\(542\) −15.5620 −0.668446
\(543\) −3.08187 −0.132256
\(544\) −6.68572 −0.286648
\(545\) 14.3916 0.616469
\(546\) −2.35667 −0.100856
\(547\) 20.4919 0.876170 0.438085 0.898934i \(-0.355657\pi\)
0.438085 + 0.898934i \(0.355657\pi\)
\(548\) 15.8349 0.676432
\(549\) 19.9564 0.851720
\(550\) 0.758945 0.0323615
\(551\) 7.57686 0.322785
\(552\) −3.83917 −0.163406
\(553\) −13.4409 −0.571563
\(554\) −45.4778 −1.93217
\(555\) −1.62654 −0.0690429
\(556\) −34.7368 −1.47317
\(557\) 10.5002 0.444907 0.222454 0.974943i \(-0.428593\pi\)
0.222454 + 0.974943i \(0.428593\pi\)
\(558\) 38.6728 1.63715
\(559\) 12.3248 0.521285
\(560\) −4.60582 −0.194632
\(561\) −0.333333 −0.0140733
\(562\) 4.59122 0.193669
\(563\) 22.5202 0.949114 0.474557 0.880225i \(-0.342608\pi\)
0.474557 + 0.880225i \(0.342608\pi\)
\(564\) 9.00738 0.379279
\(565\) −5.06663 −0.213155
\(566\) −22.8142 −0.958952
\(567\) −2.09496 −0.0879800
\(568\) −1.46437 −0.0614438
\(569\) −34.2086 −1.43410 −0.717051 0.697021i \(-0.754508\pi\)
−0.717051 + 0.697021i \(0.754508\pi\)
\(570\) −3.53819 −0.148199
\(571\) 24.8438 1.03968 0.519840 0.854264i \(-0.325992\pi\)
0.519840 + 0.854264i \(0.325992\pi\)
\(572\) −0.872067 −0.0364630
\(573\) −1.88037 −0.0785534
\(574\) 17.8204 0.743810
\(575\) 5.88511 0.245426
\(576\) 10.3288 0.430365
\(577\) −13.7575 −0.572734 −0.286367 0.958120i \(-0.592448\pi\)
−0.286367 + 0.958120i \(0.592448\pi\)
\(578\) 30.8058 1.28135
\(579\) −23.6863 −0.984369
\(580\) −6.11032 −0.253717
\(581\) −6.72692 −0.279080
\(582\) 15.2345 0.631490
\(583\) 4.46883 0.185080
\(584\) −7.67631 −0.317648
\(585\) 2.89476 0.119684
\(586\) 27.0776 1.11857
\(587\) 2.86817 0.118382 0.0591911 0.998247i \(-0.481148\pi\)
0.0591911 + 0.998247i \(0.481148\pi\)
\(588\) −1.49807 −0.0617794
\(589\) 19.0352 0.784333
\(590\) −23.4180 −0.964105
\(591\) 0.818649 0.0336747
\(592\) 8.14049 0.334572
\(593\) −13.9782 −0.574015 −0.287007 0.957928i \(-0.592660\pi\)
−0.287007 + 0.957928i \(0.592660\pi\)
\(594\) 3.59914 0.147675
\(595\) −0.909012 −0.0372658
\(596\) −15.0288 −0.615604
\(597\) 0.163506 0.00669186
\(598\) −15.0706 −0.616285
\(599\) −26.0883 −1.06594 −0.532969 0.846135i \(-0.678924\pi\)
−0.532969 + 0.846135i \(0.678924\pi\)
\(600\) −0.652353 −0.0266322
\(601\) 10.5552 0.430557 0.215278 0.976553i \(-0.430934\pi\)
0.215278 + 0.976553i \(0.430934\pi\)
\(602\) 17.4603 0.711628
\(603\) 7.02690 0.286157
\(604\) −14.3105 −0.582286
\(605\) 10.8412 0.440759
\(606\) −11.2821 −0.458304
\(607\) 16.1986 0.657482 0.328741 0.944420i \(-0.393376\pi\)
0.328741 + 0.944420i \(0.393376\pi\)
\(608\) 14.8462 0.602091
\(609\) 3.45443 0.139980
\(610\) −17.6542 −0.714797
\(611\) −8.08387 −0.327038
\(612\) 3.18595 0.128784
\(613\) 44.0509 1.77920 0.889599 0.456742i \(-0.150984\pi\)
0.889599 + 0.456742i \(0.150984\pi\)
\(614\) −29.0928 −1.17409
\(615\) 8.61027 0.347200
\(616\) 0.282453 0.0113804
\(617\) −40.3143 −1.62299 −0.811497 0.584357i \(-0.801347\pi\)
−0.811497 + 0.584357i \(0.801347\pi\)
\(618\) 34.4463 1.38563
\(619\) 10.5871 0.425532 0.212766 0.977103i \(-0.431753\pi\)
0.212766 + 0.977103i \(0.431753\pi\)
\(620\) −15.3509 −0.616506
\(621\) 27.9090 1.11995
\(622\) 23.4607 0.940688
\(623\) −8.30386 −0.332687
\(624\) 5.69880 0.228134
\(625\) 1.00000 0.0400000
\(626\) 0.430683 0.0172135
\(627\) 0.740191 0.0295604
\(628\) −35.8178 −1.42929
\(629\) 1.60662 0.0640600
\(630\) 4.10094 0.163385
\(631\) 41.6578 1.65837 0.829186 0.558973i \(-0.188805\pi\)
0.829186 + 0.558973i \(0.188805\pi\)
\(632\) 9.52767 0.378990
\(633\) 23.3390 0.927644
\(634\) 14.3080 0.568244
\(635\) −9.07603 −0.360171
\(636\) 16.8012 0.666211
\(637\) 1.34448 0.0532701
\(638\) 2.84881 0.112786
\(639\) 4.44786 0.175955
\(640\) 5.57269 0.220280
\(641\) 39.4518 1.55825 0.779127 0.626866i \(-0.215663\pi\)
0.779127 + 0.626866i \(0.215663\pi\)
\(642\) −0.241712 −0.00953959
\(643\) −37.5137 −1.47940 −0.739698 0.672939i \(-0.765032\pi\)
−0.739698 + 0.672939i \(0.765032\pi\)
\(644\) −9.57999 −0.377504
\(645\) 8.43626 0.332177
\(646\) 3.49485 0.137503
\(647\) −15.7621 −0.619674 −0.309837 0.950790i \(-0.600274\pi\)
−0.309837 + 0.950790i \(0.600274\pi\)
\(648\) 1.48503 0.0583375
\(649\) 4.89906 0.192305
\(650\) −2.56081 −0.100443
\(651\) 8.67851 0.340138
\(652\) 24.4296 0.956738
\(653\) −16.5984 −0.649547 −0.324773 0.945792i \(-0.605288\pi\)
−0.324773 + 0.945792i \(0.605288\pi\)
\(654\) −25.2264 −0.986432
\(655\) −19.6266 −0.766876
\(656\) −43.0925 −1.68248
\(657\) 23.3159 0.909639
\(658\) −11.4522 −0.446454
\(659\) 11.2084 0.436617 0.218309 0.975880i \(-0.429946\pi\)
0.218309 + 0.975880i \(0.429946\pi\)
\(660\) −0.596924 −0.0232352
\(661\) −18.4365 −0.717098 −0.358549 0.933511i \(-0.616728\pi\)
−0.358549 + 0.933511i \(0.616728\pi\)
\(662\) 35.3154 1.37257
\(663\) 1.12472 0.0436806
\(664\) 4.76844 0.185051
\(665\) 2.01853 0.0782752
\(666\) −7.24813 −0.280859
\(667\) 22.0907 0.855353
\(668\) −31.2359 −1.20855
\(669\) −16.5495 −0.639840
\(670\) −6.21625 −0.240155
\(671\) 3.69326 0.142577
\(672\) 6.76864 0.261106
\(673\) 26.8214 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(674\) −60.9571 −2.34798
\(675\) 4.74230 0.182531
\(676\) −18.2193 −0.700744
\(677\) −20.1774 −0.775480 −0.387740 0.921769i \(-0.626744\pi\)
−0.387740 + 0.921769i \(0.626744\pi\)
\(678\) 8.88108 0.341076
\(679\) −8.69125 −0.333540
\(680\) 0.644361 0.0247101
\(681\) 8.18121 0.313505
\(682\) 7.15703 0.274057
\(683\) 11.2952 0.432198 0.216099 0.976372i \(-0.430667\pi\)
0.216099 + 0.976372i \(0.430667\pi\)
\(684\) −7.07465 −0.270506
\(685\) −9.72757 −0.371671
\(686\) 1.90469 0.0727213
\(687\) −0.920285 −0.0351111
\(688\) −42.2216 −1.60968
\(689\) −15.0786 −0.574449
\(690\) −10.3158 −0.392714
\(691\) −11.3159 −0.430477 −0.215238 0.976562i \(-0.569053\pi\)
−0.215238 + 0.976562i \(0.569053\pi\)
\(692\) 8.60492 0.327110
\(693\) −0.857918 −0.0325896
\(694\) −23.5256 −0.893021
\(695\) 21.3393 0.809444
\(696\) −2.44870 −0.0928178
\(697\) −8.50480 −0.322142
\(698\) −8.83537 −0.334424
\(699\) −3.35896 −0.127048
\(700\) −1.62783 −0.0615264
\(701\) 3.49963 0.132179 0.0660896 0.997814i \(-0.478948\pi\)
0.0660896 + 0.997814i \(0.478948\pi\)
\(702\) −12.1441 −0.458350
\(703\) −3.56762 −0.134555
\(704\) 1.91150 0.0720425
\(705\) −5.53335 −0.208398
\(706\) −62.7989 −2.36347
\(707\) 6.43641 0.242066
\(708\) 18.4187 0.692217
\(709\) −14.4654 −0.543259 −0.271629 0.962402i \(-0.587562\pi\)
−0.271629 + 0.962402i \(0.587562\pi\)
\(710\) −3.93474 −0.147668
\(711\) −28.9392 −1.08530
\(712\) 5.88627 0.220597
\(713\) 55.4980 2.07842
\(714\) 1.59337 0.0596302
\(715\) 0.535722 0.0200349
\(716\) −10.6495 −0.397990
\(717\) −14.8862 −0.555937
\(718\) 35.2641 1.31604
\(719\) 35.8740 1.33787 0.668937 0.743319i \(-0.266750\pi\)
0.668937 + 0.743319i \(0.266750\pi\)
\(720\) −9.91669 −0.369573
\(721\) −19.6516 −0.731862
\(722\) 28.4285 1.05800
\(723\) −7.09683 −0.263934
\(724\) 5.45133 0.202597
\(725\) 3.75365 0.139407
\(726\) −19.0031 −0.705271
\(727\) 12.3345 0.457461 0.228731 0.973490i \(-0.426542\pi\)
0.228731 + 0.973490i \(0.426542\pi\)
\(728\) −0.953045 −0.0353222
\(729\) 8.58219 0.317859
\(730\) −20.6261 −0.763404
\(731\) −8.33292 −0.308204
\(732\) 13.8853 0.513217
\(733\) −26.3479 −0.973180 −0.486590 0.873630i \(-0.661759\pi\)
−0.486590 + 0.873630i \(0.661759\pi\)
\(734\) 44.6633 1.64855
\(735\) 0.920285 0.0339452
\(736\) 43.2846 1.59549
\(737\) 1.30044 0.0479024
\(738\) 38.3687 1.41237
\(739\) 29.8292 1.09729 0.548643 0.836057i \(-0.315145\pi\)
0.548643 + 0.836057i \(0.315145\pi\)
\(740\) 2.87709 0.105764
\(741\) −2.49753 −0.0917491
\(742\) −21.3615 −0.784204
\(743\) 26.9180 0.987525 0.493762 0.869597i \(-0.335621\pi\)
0.493762 + 0.869597i \(0.335621\pi\)
\(744\) −6.15184 −0.225537
\(745\) 9.23239 0.338249
\(746\) 34.3948 1.25928
\(747\) −14.4836 −0.529926
\(748\) 0.589612 0.0215583
\(749\) 0.137896 0.00503861
\(750\) −1.75286 −0.0640052
\(751\) −2.07072 −0.0755617 −0.0377808 0.999286i \(-0.512029\pi\)
−0.0377808 + 0.999286i \(0.512029\pi\)
\(752\) 27.6932 1.00987
\(753\) 15.3536 0.559515
\(754\) −9.61238 −0.350062
\(755\) 8.79112 0.319942
\(756\) −7.71968 −0.280762
\(757\) −7.20119 −0.261732 −0.130866 0.991400i \(-0.541776\pi\)
−0.130866 + 0.991400i \(0.541776\pi\)
\(758\) 13.2754 0.482184
\(759\) 2.15806 0.0783326
\(760\) −1.43085 −0.0519025
\(761\) −21.6954 −0.786458 −0.393229 0.919441i \(-0.628642\pi\)
−0.393229 + 0.919441i \(0.628642\pi\)
\(762\) 15.9090 0.576321
\(763\) 14.3916 0.521012
\(764\) 3.32606 0.120333
\(765\) −1.95717 −0.0707617
\(766\) 63.8505 2.30701
\(767\) −16.5303 −0.596873
\(768\) −18.5977 −0.671087
\(769\) −18.2013 −0.656354 −0.328177 0.944616i \(-0.606434\pi\)
−0.328177 + 0.944616i \(0.606434\pi\)
\(770\) 0.758945 0.0273505
\(771\) −5.67942 −0.204539
\(772\) 41.8972 1.50791
\(773\) 45.5355 1.63780 0.818899 0.573938i \(-0.194585\pi\)
0.818899 + 0.573938i \(0.194585\pi\)
\(774\) 37.5933 1.35126
\(775\) 9.43024 0.338744
\(776\) 6.16087 0.221162
\(777\) −1.62654 −0.0583519
\(778\) 41.6834 1.49442
\(779\) 18.8856 0.676645
\(780\) 2.01412 0.0721172
\(781\) 0.823149 0.0294546
\(782\) 10.1894 0.364372
\(783\) 17.8009 0.636153
\(784\) −4.60582 −0.164494
\(785\) 22.0034 0.785334
\(786\) 34.4027 1.22710
\(787\) −11.1476 −0.397370 −0.198685 0.980063i \(-0.563667\pi\)
−0.198685 + 0.980063i \(0.563667\pi\)
\(788\) −1.44806 −0.0515849
\(789\) −7.47741 −0.266203
\(790\) 25.6006 0.910829
\(791\) −5.06663 −0.180149
\(792\) 0.608143 0.0216094
\(793\) −12.4617 −0.442528
\(794\) −51.3021 −1.82064
\(795\) −10.3212 −0.366055
\(796\) −0.289216 −0.0102510
\(797\) 11.2450 0.398319 0.199159 0.979967i \(-0.436179\pi\)
0.199159 + 0.979967i \(0.436179\pi\)
\(798\) −3.53819 −0.125251
\(799\) 5.46557 0.193358
\(800\) 7.35494 0.260036
\(801\) −17.8788 −0.631718
\(802\) 47.2751 1.66934
\(803\) 4.31498 0.152272
\(804\) 4.88919 0.172428
\(805\) 5.88511 0.207423
\(806\) −24.1490 −0.850613
\(807\) 0.577643 0.0203340
\(808\) −4.56251 −0.160508
\(809\) −12.3035 −0.432568 −0.216284 0.976331i \(-0.569394\pi\)
−0.216284 + 0.976331i \(0.569394\pi\)
\(810\) 3.99024 0.140203
\(811\) 22.7724 0.799648 0.399824 0.916592i \(-0.369071\pi\)
0.399824 + 0.916592i \(0.369071\pi\)
\(812\) −6.11032 −0.214430
\(813\) −7.51908 −0.263706
\(814\) −1.34138 −0.0470155
\(815\) −15.0074 −0.525688
\(816\) −3.85300 −0.134882
\(817\) 18.5039 0.647369
\(818\) −17.4371 −0.609673
\(819\) 2.89476 0.101151
\(820\) −15.2302 −0.531860
\(821\) −3.96660 −0.138435 −0.0692176 0.997602i \(-0.522050\pi\)
−0.0692176 + 0.997602i \(0.522050\pi\)
\(822\) 17.0510 0.594723
\(823\) 47.3231 1.64958 0.824790 0.565440i \(-0.191293\pi\)
0.824790 + 0.565440i \(0.191293\pi\)
\(824\) 13.9302 0.485281
\(825\) 0.366698 0.0127668
\(826\) −23.4180 −0.814817
\(827\) −0.00803216 −0.000279306 0 −0.000139653 1.00000i \(-0.500044\pi\)
−0.000139653 1.00000i \(0.500044\pi\)
\(828\) −20.6264 −0.716818
\(829\) 12.4919 0.433860 0.216930 0.976187i \(-0.430396\pi\)
0.216930 + 0.976187i \(0.430396\pi\)
\(830\) 12.8127 0.444734
\(831\) −21.9735 −0.762251
\(832\) −6.44974 −0.223604
\(833\) −0.909012 −0.0314954
\(834\) −37.4046 −1.29522
\(835\) 19.1886 0.664049
\(836\) −1.30928 −0.0452823
\(837\) 44.7210 1.54578
\(838\) −10.7764 −0.372264
\(839\) −3.90842 −0.134933 −0.0674667 0.997722i \(-0.521492\pi\)
−0.0674667 + 0.997722i \(0.521492\pi\)
\(840\) −0.652353 −0.0225083
\(841\) −14.9101 −0.514142
\(842\) −53.2727 −1.83590
\(843\) 2.21833 0.0764035
\(844\) −41.2830 −1.42102
\(845\) 11.1924 0.385030
\(846\) −24.6575 −0.847742
\(847\) 10.8412 0.372509
\(848\) 51.6553 1.77385
\(849\) −11.0231 −0.378312
\(850\) 1.73138 0.0593860
\(851\) −10.4015 −0.356560
\(852\) 3.09474 0.106024
\(853\) 50.2791 1.72152 0.860761 0.509009i \(-0.169988\pi\)
0.860761 + 0.509009i \(0.169988\pi\)
\(854\) −17.6542 −0.604113
\(855\) 4.34605 0.148632
\(856\) −0.0977488 −0.00334098
\(857\) 48.7011 1.66360 0.831798 0.555078i \(-0.187312\pi\)
0.831798 + 0.555078i \(0.187312\pi\)
\(858\) −0.939044 −0.0320584
\(859\) 27.9745 0.954476 0.477238 0.878774i \(-0.341638\pi\)
0.477238 + 0.878774i \(0.341638\pi\)
\(860\) −14.9224 −0.508849
\(861\) 8.61027 0.293437
\(862\) 42.6107 1.45133
\(863\) −25.2616 −0.859913 −0.429957 0.902850i \(-0.641471\pi\)
−0.429957 + 0.902850i \(0.641471\pi\)
\(864\) 34.8793 1.18662
\(865\) −5.28611 −0.179733
\(866\) 17.1541 0.582919
\(867\) 14.8844 0.505501
\(868\) −15.3509 −0.521042
\(869\) −5.35566 −0.181678
\(870\) −6.57961 −0.223070
\(871\) −4.38791 −0.148679
\(872\) −10.2016 −0.345471
\(873\) −18.7129 −0.633336
\(874\) −22.6263 −0.765346
\(875\) 1.00000 0.0338062
\(876\) 16.2228 0.548117
\(877\) −13.6423 −0.460667 −0.230333 0.973112i \(-0.573982\pi\)
−0.230333 + 0.973112i \(0.573982\pi\)
\(878\) −44.3324 −1.49614
\(879\) 13.0831 0.441281
\(880\) −1.83524 −0.0618660
\(881\) 46.3001 1.55989 0.779945 0.625848i \(-0.215247\pi\)
0.779945 + 0.625848i \(0.215247\pi\)
\(882\) 4.10094 0.138086
\(883\) −3.72856 −0.125476 −0.0627379 0.998030i \(-0.519983\pi\)
−0.0627379 + 0.998030i \(0.519983\pi\)
\(884\) −1.98945 −0.0669124
\(885\) −11.3148 −0.380345
\(886\) 17.5019 0.587988
\(887\) −50.5947 −1.69880 −0.849402 0.527746i \(-0.823037\pi\)
−0.849402 + 0.527746i \(0.823037\pi\)
\(888\) 1.15299 0.0386918
\(889\) −9.07603 −0.304400
\(890\) 15.8163 0.530162
\(891\) −0.834761 −0.0279655
\(892\) 29.2733 0.980144
\(893\) −12.1367 −0.406140
\(894\) −16.1830 −0.541242
\(895\) 6.54213 0.218679
\(896\) 5.57269 0.186171
\(897\) −7.28166 −0.243128
\(898\) 3.20581 0.106979
\(899\) 35.3978 1.18058
\(900\) −3.50485 −0.116828
\(901\) 10.1948 0.339637
\(902\) 7.10075 0.236429
\(903\) 8.43626 0.280741
\(904\) 3.59153 0.119453
\(905\) −3.34882 −0.111319
\(906\) −15.4096 −0.511949
\(907\) −14.2959 −0.474686 −0.237343 0.971426i \(-0.576277\pi\)
−0.237343 + 0.971426i \(0.576277\pi\)
\(908\) −14.4712 −0.480245
\(909\) 13.8581 0.459643
\(910\) −2.56081 −0.0848900
\(911\) −47.5830 −1.57650 −0.788248 0.615358i \(-0.789012\pi\)
−0.788248 + 0.615358i \(0.789012\pi\)
\(912\) 8.55589 0.283314
\(913\) −2.68042 −0.0887089
\(914\) −12.2675 −0.405772
\(915\) −8.52994 −0.281991
\(916\) 1.62783 0.0537852
\(917\) −19.6266 −0.648129
\(918\) 8.21074 0.270995
\(919\) 38.1996 1.26009 0.630044 0.776559i \(-0.283037\pi\)
0.630044 + 0.776559i \(0.283037\pi\)
\(920\) −4.17172 −0.137537
\(921\) −14.0567 −0.463184
\(922\) 6.38599 0.210311
\(923\) −2.77745 −0.0914207
\(924\) −0.596924 −0.0196374
\(925\) −1.76743 −0.0581128
\(926\) −74.5010 −2.44825
\(927\) −42.3113 −1.38968
\(928\) 27.6079 0.906272
\(929\) 36.5202 1.19819 0.599095 0.800678i \(-0.295527\pi\)
0.599095 + 0.800678i \(0.295527\pi\)
\(930\) −16.5298 −0.542035
\(931\) 2.01853 0.0661547
\(932\) 5.94146 0.194619
\(933\) 11.3355 0.371107
\(934\) −31.5804 −1.03334
\(935\) −0.362206 −0.0118454
\(936\) −2.05198 −0.0670710
\(937\) 21.2960 0.695709 0.347855 0.937548i \(-0.386910\pi\)
0.347855 + 0.937548i \(0.386910\pi\)
\(938\) −6.21625 −0.202968
\(939\) 0.208092 0.00679084
\(940\) 9.78760 0.319236
\(941\) 5.09091 0.165959 0.0829794 0.996551i \(-0.473556\pi\)
0.0829794 + 0.996551i \(0.473556\pi\)
\(942\) −38.5687 −1.25664
\(943\) 55.0616 1.79305
\(944\) 56.6283 1.84310
\(945\) 4.74230 0.154267
\(946\) 6.95725 0.226200
\(947\) −6.81255 −0.221378 −0.110689 0.993855i \(-0.535306\pi\)
−0.110689 + 0.993855i \(0.535306\pi\)
\(948\) −20.1354 −0.653966
\(949\) −14.5595 −0.472621
\(950\) −3.84467 −0.124738
\(951\) 6.91319 0.224175
\(952\) 0.644361 0.0208839
\(953\) 7.53218 0.243991 0.121996 0.992531i \(-0.461071\pi\)
0.121996 + 0.992531i \(0.461071\pi\)
\(954\) −45.9929 −1.48907
\(955\) −2.04324 −0.0661178
\(956\) 26.3313 0.851617
\(957\) 1.37646 0.0444945
\(958\) −59.0362 −1.90737
\(959\) −9.72757 −0.314120
\(960\) −4.41480 −0.142487
\(961\) 57.9294 1.86869
\(962\) 4.52606 0.145926
\(963\) 0.296900 0.00956748
\(964\) 12.5531 0.404309
\(965\) −25.7380 −0.828535
\(966\) −10.3158 −0.331904
\(967\) −37.9642 −1.22085 −0.610424 0.792075i \(-0.709001\pi\)
−0.610424 + 0.792075i \(0.709001\pi\)
\(968\) −7.68490 −0.247002
\(969\) 1.68860 0.0542457
\(970\) 16.5541 0.531521
\(971\) −38.0010 −1.21951 −0.609756 0.792590i \(-0.708732\pi\)
−0.609756 + 0.792590i \(0.708732\pi\)
\(972\) −26.2974 −0.843490
\(973\) 21.3393 0.684105
\(974\) −17.7967 −0.570242
\(975\) −1.23730 −0.0396254
\(976\) 42.6905 1.36649
\(977\) 5.03368 0.161042 0.0805208 0.996753i \(-0.474342\pi\)
0.0805208 + 0.996753i \(0.474342\pi\)
\(978\) 26.3059 0.841169
\(979\) −3.30877 −0.105749
\(980\) −1.62783 −0.0519993
\(981\) 30.9862 0.989315
\(982\) 1.12138 0.0357848
\(983\) 9.52341 0.303749 0.151875 0.988400i \(-0.451469\pi\)
0.151875 + 0.988400i \(0.451469\pi\)
\(984\) −6.10347 −0.194572
\(985\) 0.889561 0.0283438
\(986\) 6.49901 0.206970
\(987\) −5.53335 −0.176129
\(988\) 4.41773 0.140547
\(989\) 53.9489 1.71547
\(990\) 1.63406 0.0519340
\(991\) 22.4828 0.714190 0.357095 0.934068i \(-0.383767\pi\)
0.357095 + 0.934068i \(0.383767\pi\)
\(992\) 69.3588 2.20214
\(993\) 17.0633 0.541487
\(994\) −3.93474 −0.124802
\(995\) 0.177669 0.00563249
\(996\) −10.0774 −0.319315
\(997\) 16.5381 0.523766 0.261883 0.965100i \(-0.415657\pi\)
0.261883 + 0.965100i \(0.415657\pi\)
\(998\) −67.1398 −2.12527
\(999\) −8.38170 −0.265185
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 \(a_p\))