Properties

Label 8015.2.a.l.1.1
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 1.1
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.78055 q^{2}\) \(+0.298033 q^{3}\) \(+5.73146 q^{4}\) \(-1.00000 q^{5}\) \(-0.828697 q^{6}\) \(-1.00000 q^{7}\) \(-10.3755 q^{8}\) \(-2.91118 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.78055 q^{2}\) \(+0.298033 q^{3}\) \(+5.73146 q^{4}\) \(-1.00000 q^{5}\) \(-0.828697 q^{6}\) \(-1.00000 q^{7}\) \(-10.3755 q^{8}\) \(-2.91118 q^{9}\) \(+2.78055 q^{10}\) \(+1.93021 q^{11}\) \(+1.70817 q^{12}\) \(+0.800858 q^{13}\) \(+2.78055 q^{14}\) \(-0.298033 q^{15}\) \(+17.3867 q^{16}\) \(+0.984021 q^{17}\) \(+8.09467 q^{18}\) \(-7.86576 q^{19}\) \(-5.73146 q^{20}\) \(-0.298033 q^{21}\) \(-5.36704 q^{22}\) \(+3.94812 q^{23}\) \(-3.09225 q^{24}\) \(+1.00000 q^{25}\) \(-2.22683 q^{26}\) \(-1.76173 q^{27}\) \(-5.73146 q^{28}\) \(-9.46879 q^{29}\) \(+0.828697 q^{30}\) \(-2.41133 q^{31}\) \(-27.5937 q^{32}\) \(+0.575266 q^{33}\) \(-2.73612 q^{34}\) \(+1.00000 q^{35}\) \(-16.6853 q^{36}\) \(+9.35326 q^{37}\) \(+21.8711 q^{38}\) \(+0.238682 q^{39}\) \(+10.3755 q^{40}\) \(-4.16333 q^{41}\) \(+0.828697 q^{42}\) \(-6.96297 q^{43}\) \(+11.0629 q^{44}\) \(+2.91118 q^{45}\) \(-10.9779 q^{46}\) \(-8.50129 q^{47}\) \(+5.18183 q^{48}\) \(+1.00000 q^{49}\) \(-2.78055 q^{50}\) \(+0.293271 q^{51}\) \(+4.59009 q^{52}\) \(+5.63325 q^{53}\) \(+4.89857 q^{54}\) \(-1.93021 q^{55}\) \(+10.3755 q^{56}\) \(-2.34426 q^{57}\) \(+26.3285 q^{58}\) \(+1.48487 q^{59}\) \(-1.70817 q^{60}\) \(+8.07188 q^{61}\) \(+6.70483 q^{62}\) \(+2.91118 q^{63}\) \(+41.9521 q^{64}\) \(-0.800858 q^{65}\) \(-1.59956 q^{66}\) \(-13.2763 q^{67}\) \(+5.63988 q^{68}\) \(+1.17667 q^{69}\) \(-2.78055 q^{70}\) \(-3.56191 q^{71}\) \(+30.2050 q^{72}\) \(+13.7107 q^{73}\) \(-26.0072 q^{74}\) \(+0.298033 q^{75}\) \(-45.0823 q^{76}\) \(-1.93021 q^{77}\) \(-0.663669 q^{78}\) \(-4.47244 q^{79}\) \(-17.3867 q^{80}\) \(+8.20847 q^{81}\) \(+11.5764 q^{82}\) \(-7.65176 q^{83}\) \(-1.70817 q^{84}\) \(-0.984021 q^{85}\) \(+19.3609 q^{86}\) \(-2.82202 q^{87}\) \(-20.0269 q^{88}\) \(+5.62676 q^{89}\) \(-8.09467 q^{90}\) \(-0.800858 q^{91}\) \(+22.6285 q^{92}\) \(-0.718657 q^{93}\) \(+23.6383 q^{94}\) \(+7.86576 q^{95}\) \(-8.22384 q^{96}\) \(+18.7585 q^{97}\) \(-2.78055 q^{98}\) \(-5.61917 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78055 −1.96615 −0.983073 0.183213i \(-0.941350\pi\)
−0.983073 + 0.183213i \(0.941350\pi\)
\(3\) 0.298033 0.172070 0.0860348 0.996292i \(-0.472580\pi\)
0.0860348 + 0.996292i \(0.472580\pi\)
\(4\) 5.73146 2.86573
\(5\) −1.00000 −0.447214
\(6\) −0.828697 −0.338314
\(7\) −1.00000 −0.377964
\(8\) −10.3755 −3.66830
\(9\) −2.91118 −0.970392
\(10\) 2.78055 0.879287
\(11\) 1.93021 0.581979 0.290990 0.956726i \(-0.406015\pi\)
0.290990 + 0.956726i \(0.406015\pi\)
\(12\) 1.70817 0.493105
\(13\) 0.800858 0.222118 0.111059 0.993814i \(-0.464576\pi\)
0.111059 + 0.993814i \(0.464576\pi\)
\(14\) 2.78055 0.743133
\(15\) −0.298033 −0.0769519
\(16\) 17.3867 4.34668
\(17\) 0.984021 0.238660 0.119330 0.992855i \(-0.461925\pi\)
0.119330 + 0.992855i \(0.461925\pi\)
\(18\) 8.09467 1.90793
\(19\) −7.86576 −1.80453 −0.902264 0.431183i \(-0.858096\pi\)
−0.902264 + 0.431183i \(0.858096\pi\)
\(20\) −5.73146 −1.28159
\(21\) −0.298033 −0.0650362
\(22\) −5.36704 −1.14426
\(23\) 3.94812 0.823239 0.411620 0.911356i \(-0.364963\pi\)
0.411620 + 0.911356i \(0.364963\pi\)
\(24\) −3.09225 −0.631203
\(25\) 1.00000 0.200000
\(26\) −2.22683 −0.436717
\(27\) −1.76173 −0.339045
\(28\) −5.73146 −1.08314
\(29\) −9.46879 −1.75831 −0.879155 0.476535i \(-0.841892\pi\)
−0.879155 + 0.476535i \(0.841892\pi\)
\(30\) 0.828697 0.151299
\(31\) −2.41133 −0.433088 −0.216544 0.976273i \(-0.569478\pi\)
−0.216544 + 0.976273i \(0.569478\pi\)
\(32\) −27.5937 −4.87792
\(33\) 0.575266 0.100141
\(34\) −2.73612 −0.469241
\(35\) 1.00000 0.169031
\(36\) −16.6853 −2.78088
\(37\) 9.35326 1.53767 0.768833 0.639449i \(-0.220838\pi\)
0.768833 + 0.639449i \(0.220838\pi\)
\(38\) 21.8711 3.54797
\(39\) 0.238682 0.0382198
\(40\) 10.3755 1.64051
\(41\) −4.16333 −0.650203 −0.325102 0.945679i \(-0.605398\pi\)
−0.325102 + 0.945679i \(0.605398\pi\)
\(42\) 0.828697 0.127871
\(43\) −6.96297 −1.06184 −0.530922 0.847421i \(-0.678154\pi\)
−0.530922 + 0.847421i \(0.678154\pi\)
\(44\) 11.0629 1.66780
\(45\) 2.91118 0.433973
\(46\) −10.9779 −1.61861
\(47\) −8.50129 −1.24004 −0.620020 0.784586i \(-0.712876\pi\)
−0.620020 + 0.784586i \(0.712876\pi\)
\(48\) 5.18183 0.747933
\(49\) 1.00000 0.142857
\(50\) −2.78055 −0.393229
\(51\) 0.293271 0.0410662
\(52\) 4.59009 0.636531
\(53\) 5.63325 0.773786 0.386893 0.922125i \(-0.373548\pi\)
0.386893 + 0.922125i \(0.373548\pi\)
\(54\) 4.89857 0.666612
\(55\) −1.93021 −0.260269
\(56\) 10.3755 1.38649
\(57\) −2.34426 −0.310505
\(58\) 26.3285 3.45710
\(59\) 1.48487 0.193313 0.0966567 0.995318i \(-0.469185\pi\)
0.0966567 + 0.995318i \(0.469185\pi\)
\(60\) −1.70817 −0.220523
\(61\) 8.07188 1.03350 0.516749 0.856137i \(-0.327142\pi\)
0.516749 + 0.856137i \(0.327142\pi\)
\(62\) 6.70483 0.851514
\(63\) 2.91118 0.366774
\(64\) 41.9521 5.24401
\(65\) −0.800858 −0.0993342
\(66\) −1.59956 −0.196892
\(67\) −13.2763 −1.62196 −0.810982 0.585071i \(-0.801066\pi\)
−0.810982 + 0.585071i \(0.801066\pi\)
\(68\) 5.63988 0.683936
\(69\) 1.17667 0.141655
\(70\) −2.78055 −0.332339
\(71\) −3.56191 −0.422720 −0.211360 0.977408i \(-0.567789\pi\)
−0.211360 + 0.977408i \(0.567789\pi\)
\(72\) 30.2050 3.55969
\(73\) 13.7107 1.60471 0.802357 0.596844i \(-0.203579\pi\)
0.802357 + 0.596844i \(0.203579\pi\)
\(74\) −26.0072 −3.02328
\(75\) 0.298033 0.0344139
\(76\) −45.0823 −5.17130
\(77\) −1.93021 −0.219968
\(78\) −0.663669 −0.0751457
\(79\) −4.47244 −0.503189 −0.251594 0.967833i \(-0.580955\pi\)
−0.251594 + 0.967833i \(0.580955\pi\)
\(80\) −17.3867 −1.94390
\(81\) 8.20847 0.912053
\(82\) 11.5764 1.27839
\(83\) −7.65176 −0.839890 −0.419945 0.907549i \(-0.637951\pi\)
−0.419945 + 0.907549i \(0.637951\pi\)
\(84\) −1.70817 −0.186376
\(85\) −0.984021 −0.106732
\(86\) 19.3609 2.08774
\(87\) −2.82202 −0.302552
\(88\) −20.0269 −2.13488
\(89\) 5.62676 0.596436 0.298218 0.954498i \(-0.403608\pi\)
0.298218 + 0.954498i \(0.403608\pi\)
\(90\) −8.09467 −0.853253
\(91\) −0.800858 −0.0839527
\(92\) 22.6285 2.35918
\(93\) −0.718657 −0.0745213
\(94\) 23.6383 2.43810
\(95\) 7.86576 0.807010
\(96\) −8.22384 −0.839342
\(97\) 18.7585 1.90464 0.952319 0.305104i \(-0.0986913\pi\)
0.952319 + 0.305104i \(0.0986913\pi\)
\(98\) −2.78055 −0.280878
\(99\) −5.61917 −0.564748
\(100\) 5.73146 0.573146
\(101\) −15.0894 −1.50145 −0.750724 0.660616i \(-0.770295\pi\)
−0.750724 + 0.660616i \(0.770295\pi\)
\(102\) −0.815455 −0.0807421
\(103\) 3.53153 0.347972 0.173986 0.984748i \(-0.444335\pi\)
0.173986 + 0.984748i \(0.444335\pi\)
\(104\) −8.30932 −0.814796
\(105\) 0.298033 0.0290851
\(106\) −15.6635 −1.52138
\(107\) −19.6309 −1.89779 −0.948894 0.315595i \(-0.897796\pi\)
−0.948894 + 0.315595i \(0.897796\pi\)
\(108\) −10.0973 −0.971611
\(109\) 1.25448 0.120157 0.0600787 0.998194i \(-0.480865\pi\)
0.0600787 + 0.998194i \(0.480865\pi\)
\(110\) 5.36704 0.511727
\(111\) 2.78758 0.264586
\(112\) −17.3867 −1.64289
\(113\) −5.15218 −0.484676 −0.242338 0.970192i \(-0.577914\pi\)
−0.242338 + 0.970192i \(0.577914\pi\)
\(114\) 6.51833 0.610498
\(115\) −3.94812 −0.368164
\(116\) −54.2700 −5.03885
\(117\) −2.33144 −0.215542
\(118\) −4.12875 −0.380082
\(119\) −0.984021 −0.0902050
\(120\) 3.09225 0.282283
\(121\) −7.27430 −0.661300
\(122\) −22.4443 −2.03201
\(123\) −1.24081 −0.111880
\(124\) −13.8204 −1.24111
\(125\) −1.00000 −0.0894427
\(126\) −8.09467 −0.721131
\(127\) 14.0867 1.24999 0.624995 0.780629i \(-0.285101\pi\)
0.624995 + 0.780629i \(0.285101\pi\)
\(128\) −61.4626 −5.43258
\(129\) −2.07520 −0.182711
\(130\) 2.22683 0.195306
\(131\) −19.8616 −1.73532 −0.867660 0.497158i \(-0.834377\pi\)
−0.867660 + 0.497158i \(0.834377\pi\)
\(132\) 3.29712 0.286977
\(133\) 7.86576 0.682048
\(134\) 36.9155 3.18902
\(135\) 1.76173 0.151625
\(136\) −10.2097 −0.875477
\(137\) 14.7868 1.26332 0.631662 0.775244i \(-0.282373\pi\)
0.631662 + 0.775244i \(0.282373\pi\)
\(138\) −3.27179 −0.278514
\(139\) −21.9510 −1.86186 −0.930931 0.365196i \(-0.881002\pi\)
−0.930931 + 0.365196i \(0.881002\pi\)
\(140\) 5.73146 0.484397
\(141\) −2.53367 −0.213373
\(142\) 9.90406 0.831130
\(143\) 1.54582 0.129268
\(144\) −50.6159 −4.21799
\(145\) 9.46879 0.786341
\(146\) −38.1233 −3.15510
\(147\) 0.298033 0.0245814
\(148\) 53.6079 4.40654
\(149\) 13.3356 1.09250 0.546249 0.837623i \(-0.316055\pi\)
0.546249 + 0.837623i \(0.316055\pi\)
\(150\) −0.828697 −0.0676628
\(151\) −1.52962 −0.124479 −0.0622395 0.998061i \(-0.519824\pi\)
−0.0622395 + 0.998061i \(0.519824\pi\)
\(152\) 81.6114 6.61955
\(153\) −2.86466 −0.231594
\(154\) 5.36704 0.432488
\(155\) 2.41133 0.193683
\(156\) 1.36800 0.109528
\(157\) −13.7258 −1.09543 −0.547717 0.836663i \(-0.684503\pi\)
−0.547717 + 0.836663i \(0.684503\pi\)
\(158\) 12.4358 0.989343
\(159\) 1.67890 0.133145
\(160\) 27.5937 2.18147
\(161\) −3.94812 −0.311155
\(162\) −22.8241 −1.79323
\(163\) 13.3747 1.04759 0.523795 0.851845i \(-0.324516\pi\)
0.523795 + 0.851845i \(0.324516\pi\)
\(164\) −23.8620 −1.86331
\(165\) −0.575266 −0.0447844
\(166\) 21.2761 1.65135
\(167\) 2.92099 0.226033 0.113017 0.993593i \(-0.463949\pi\)
0.113017 + 0.993593i \(0.463949\pi\)
\(168\) 3.09225 0.238572
\(169\) −12.3586 −0.950664
\(170\) 2.73612 0.209851
\(171\) 22.8986 1.75110
\(172\) −39.9080 −3.04296
\(173\) 11.8602 0.901711 0.450856 0.892597i \(-0.351119\pi\)
0.450856 + 0.892597i \(0.351119\pi\)
\(174\) 7.84676 0.594861
\(175\) −1.00000 −0.0755929
\(176\) 33.5600 2.52968
\(177\) 0.442540 0.0332634
\(178\) −15.6455 −1.17268
\(179\) −6.68431 −0.499609 −0.249805 0.968296i \(-0.580366\pi\)
−0.249805 + 0.968296i \(0.580366\pi\)
\(180\) 16.6853 1.24365
\(181\) 16.3937 1.21854 0.609268 0.792965i \(-0.291463\pi\)
0.609268 + 0.792965i \(0.291463\pi\)
\(182\) 2.22683 0.165063
\(183\) 2.40569 0.177834
\(184\) −40.9638 −3.01989
\(185\) −9.35326 −0.687665
\(186\) 1.99826 0.146520
\(187\) 1.89936 0.138895
\(188\) −48.7248 −3.55362
\(189\) 1.76173 0.128147
\(190\) −21.8711 −1.58670
\(191\) 10.8073 0.781986 0.390993 0.920394i \(-0.372132\pi\)
0.390993 + 0.920394i \(0.372132\pi\)
\(192\) 12.5031 0.902336
\(193\) 3.27495 0.235736 0.117868 0.993029i \(-0.462394\pi\)
0.117868 + 0.993029i \(0.462394\pi\)
\(194\) −52.1590 −3.74480
\(195\) −0.238682 −0.0170924
\(196\) 5.73146 0.409390
\(197\) −3.98985 −0.284265 −0.142132 0.989848i \(-0.545396\pi\)
−0.142132 + 0.989848i \(0.545396\pi\)
\(198\) 15.6244 1.11038
\(199\) 9.65928 0.684728 0.342364 0.939567i \(-0.388772\pi\)
0.342364 + 0.939567i \(0.388772\pi\)
\(200\) −10.3755 −0.733660
\(201\) −3.95679 −0.279091
\(202\) 41.9567 2.95207
\(203\) 9.46879 0.664579
\(204\) 1.68087 0.117685
\(205\) 4.16333 0.290780
\(206\) −9.81960 −0.684164
\(207\) −11.4937 −0.798865
\(208\) 13.9243 0.965477
\(209\) −15.1825 −1.05020
\(210\) −0.828697 −0.0571855
\(211\) −20.8322 −1.43415 −0.717075 0.696996i \(-0.754519\pi\)
−0.717075 + 0.696996i \(0.754519\pi\)
\(212\) 32.2867 2.21746
\(213\) −1.06157 −0.0727374
\(214\) 54.5846 3.73133
\(215\) 6.96297 0.474871
\(216\) 18.2788 1.24372
\(217\) 2.41133 0.163692
\(218\) −3.48815 −0.236247
\(219\) 4.08624 0.276123
\(220\) −11.0629 −0.745861
\(221\) 0.788061 0.0530107
\(222\) −7.75102 −0.520214
\(223\) 5.42935 0.363576 0.181788 0.983338i \(-0.441812\pi\)
0.181788 + 0.983338i \(0.441812\pi\)
\(224\) 27.5937 1.84368
\(225\) −2.91118 −0.194078
\(226\) 14.3259 0.952945
\(227\) 7.57562 0.502812 0.251406 0.967882i \(-0.419107\pi\)
0.251406 + 0.967882i \(0.419107\pi\)
\(228\) −13.4360 −0.889823
\(229\) 1.00000 0.0660819
\(230\) 10.9779 0.723864
\(231\) −0.575266 −0.0378497
\(232\) 98.2437 6.45001
\(233\) −22.7454 −1.49010 −0.745050 0.667008i \(-0.767575\pi\)
−0.745050 + 0.667008i \(0.767575\pi\)
\(234\) 6.48268 0.423786
\(235\) 8.50129 0.554563
\(236\) 8.51046 0.553984
\(237\) −1.33294 −0.0865835
\(238\) 2.73612 0.177356
\(239\) 9.30016 0.601578 0.300789 0.953691i \(-0.402750\pi\)
0.300789 + 0.953691i \(0.402750\pi\)
\(240\) −5.18183 −0.334486
\(241\) 0.572380 0.0368703 0.0184351 0.999830i \(-0.494132\pi\)
0.0184351 + 0.999830i \(0.494132\pi\)
\(242\) 20.2266 1.30021
\(243\) 7.73158 0.495981
\(244\) 46.2637 2.96173
\(245\) −1.00000 −0.0638877
\(246\) 3.45014 0.219973
\(247\) −6.29936 −0.400818
\(248\) 25.0188 1.58870
\(249\) −2.28048 −0.144520
\(250\) 2.78055 0.175857
\(251\) −14.2096 −0.896903 −0.448451 0.893807i \(-0.648024\pi\)
−0.448451 + 0.893807i \(0.648024\pi\)
\(252\) 16.6853 1.05107
\(253\) 7.62069 0.479108
\(254\) −39.1687 −2.45766
\(255\) −0.293271 −0.0183653
\(256\) 86.9958 5.43724
\(257\) 6.65911 0.415384 0.207692 0.978194i \(-0.433405\pi\)
0.207692 + 0.978194i \(0.433405\pi\)
\(258\) 5.77020 0.359237
\(259\) −9.35326 −0.581183
\(260\) −4.59009 −0.284665
\(261\) 27.5653 1.70625
\(262\) 55.2263 3.41189
\(263\) 26.6547 1.64360 0.821799 0.569777i \(-0.192970\pi\)
0.821799 + 0.569777i \(0.192970\pi\)
\(264\) −5.96869 −0.367347
\(265\) −5.63325 −0.346048
\(266\) −21.8711 −1.34101
\(267\) 1.67696 0.102629
\(268\) −76.0929 −4.64811
\(269\) −5.50963 −0.335928 −0.167964 0.985793i \(-0.553719\pi\)
−0.167964 + 0.985793i \(0.553719\pi\)
\(270\) −4.89857 −0.298118
\(271\) 19.3282 1.17411 0.587053 0.809549i \(-0.300288\pi\)
0.587053 + 0.809549i \(0.300288\pi\)
\(272\) 17.1089 1.03738
\(273\) −0.238682 −0.0144457
\(274\) −41.1155 −2.48388
\(275\) 1.93021 0.116396
\(276\) 6.74405 0.405944
\(277\) 9.36540 0.562712 0.281356 0.959603i \(-0.409216\pi\)
0.281356 + 0.959603i \(0.409216\pi\)
\(278\) 61.0359 3.66069
\(279\) 7.01981 0.420265
\(280\) −10.3755 −0.620056
\(281\) 27.6185 1.64758 0.823792 0.566892i \(-0.191854\pi\)
0.823792 + 0.566892i \(0.191854\pi\)
\(282\) 7.04500 0.419523
\(283\) 26.9369 1.60123 0.800617 0.599176i \(-0.204505\pi\)
0.800617 + 0.599176i \(0.204505\pi\)
\(284\) −20.4149 −1.21140
\(285\) 2.34426 0.138862
\(286\) −4.29824 −0.254160
\(287\) 4.16333 0.245754
\(288\) 80.3300 4.73349
\(289\) −16.0317 −0.943041
\(290\) −26.3285 −1.54606
\(291\) 5.59066 0.327730
\(292\) 78.5823 4.59868
\(293\) −14.5291 −0.848797 −0.424398 0.905476i \(-0.639514\pi\)
−0.424398 + 0.905476i \(0.639514\pi\)
\(294\) −0.828697 −0.0483306
\(295\) −1.48487 −0.0864523
\(296\) −97.0449 −5.64062
\(297\) −3.40050 −0.197317
\(298\) −37.0804 −2.14801
\(299\) 3.16188 0.182856
\(300\) 1.70817 0.0986211
\(301\) 6.96297 0.401339
\(302\) 4.25319 0.244744
\(303\) −4.49714 −0.258354
\(304\) −136.760 −7.84372
\(305\) −8.07188 −0.462195
\(306\) 7.96533 0.455347
\(307\) 32.6927 1.86587 0.932935 0.360044i \(-0.117238\pi\)
0.932935 + 0.360044i \(0.117238\pi\)
\(308\) −11.0629 −0.630368
\(309\) 1.05251 0.0598754
\(310\) −6.70483 −0.380808
\(311\) −26.4579 −1.50029 −0.750145 0.661274i \(-0.770016\pi\)
−0.750145 + 0.661274i \(0.770016\pi\)
\(312\) −2.47646 −0.140202
\(313\) 31.1423 1.76027 0.880135 0.474724i \(-0.157452\pi\)
0.880135 + 0.474724i \(0.157452\pi\)
\(314\) 38.1652 2.15378
\(315\) −2.91118 −0.164026
\(316\) −25.6336 −1.44200
\(317\) −14.3876 −0.808085 −0.404043 0.914740i \(-0.632395\pi\)
−0.404043 + 0.914740i \(0.632395\pi\)
\(318\) −4.66825 −0.261783
\(319\) −18.2767 −1.02330
\(320\) −41.9521 −2.34519
\(321\) −5.85066 −0.326552
\(322\) 10.9779 0.611777
\(323\) −7.74007 −0.430669
\(324\) 47.0466 2.61370
\(325\) 0.800858 0.0444236
\(326\) −37.1891 −2.05971
\(327\) 0.373877 0.0206754
\(328\) 43.1967 2.38514
\(329\) 8.50129 0.468691
\(330\) 1.59956 0.0880527
\(331\) 2.76125 0.151772 0.0758859 0.997117i \(-0.475822\pi\)
0.0758859 + 0.997117i \(0.475822\pi\)
\(332\) −43.8558 −2.40690
\(333\) −27.2290 −1.49214
\(334\) −8.12197 −0.444414
\(335\) 13.2763 0.725364
\(336\) −5.18183 −0.282692
\(337\) −31.0714 −1.69257 −0.846284 0.532732i \(-0.821165\pi\)
−0.846284 + 0.532732i \(0.821165\pi\)
\(338\) 34.3638 1.86914
\(339\) −1.53552 −0.0833981
\(340\) −5.63988 −0.305865
\(341\) −4.65437 −0.252048
\(342\) −63.6707 −3.44292
\(343\) −1.00000 −0.0539949
\(344\) 72.2445 3.89516
\(345\) −1.17667 −0.0633498
\(346\) −32.9778 −1.77290
\(347\) −29.2759 −1.57161 −0.785806 0.618473i \(-0.787752\pi\)
−0.785806 + 0.618473i \(0.787752\pi\)
\(348\) −16.1743 −0.867033
\(349\) 10.6770 0.571528 0.285764 0.958300i \(-0.407753\pi\)
0.285764 + 0.958300i \(0.407753\pi\)
\(350\) 2.78055 0.148627
\(351\) −1.41089 −0.0753080
\(352\) −53.2615 −2.83885
\(353\) −9.63726 −0.512940 −0.256470 0.966552i \(-0.582559\pi\)
−0.256470 + 0.966552i \(0.582559\pi\)
\(354\) −1.23051 −0.0654006
\(355\) 3.56191 0.189046
\(356\) 32.2496 1.70922
\(357\) −0.293271 −0.0155216
\(358\) 18.5861 0.982304
\(359\) 19.4085 1.02434 0.512171 0.858883i \(-0.328841\pi\)
0.512171 + 0.858883i \(0.328841\pi\)
\(360\) −30.2050 −1.59194
\(361\) 42.8702 2.25632
\(362\) −45.5836 −2.39582
\(363\) −2.16798 −0.113790
\(364\) −4.59009 −0.240586
\(365\) −13.7107 −0.717650
\(366\) −6.68915 −0.349647
\(367\) 12.5807 0.656709 0.328354 0.944555i \(-0.393506\pi\)
0.328354 + 0.944555i \(0.393506\pi\)
\(368\) 68.6449 3.57836
\(369\) 12.1202 0.630952
\(370\) 26.0072 1.35205
\(371\) −5.63325 −0.292464
\(372\) −4.11896 −0.213558
\(373\) −27.3935 −1.41838 −0.709192 0.705016i \(-0.750940\pi\)
−0.709192 + 0.705016i \(0.750940\pi\)
\(374\) −5.28128 −0.273088
\(375\) −0.298033 −0.0153904
\(376\) 88.2053 4.54884
\(377\) −7.58316 −0.390553
\(378\) −4.89857 −0.251955
\(379\) −19.5606 −1.00476 −0.502381 0.864646i \(-0.667542\pi\)
−0.502381 + 0.864646i \(0.667542\pi\)
\(380\) 45.0823 2.31267
\(381\) 4.19830 0.215085
\(382\) −30.0501 −1.53750
\(383\) 22.0264 1.12549 0.562747 0.826629i \(-0.309744\pi\)
0.562747 + 0.826629i \(0.309744\pi\)
\(384\) −18.3179 −0.934783
\(385\) 1.93021 0.0983725
\(386\) −9.10616 −0.463491
\(387\) 20.2704 1.03040
\(388\) 107.514 5.45818
\(389\) −39.1240 −1.98367 −0.991833 0.127546i \(-0.959290\pi\)
−0.991833 + 0.127546i \(0.959290\pi\)
\(390\) 0.663669 0.0336062
\(391\) 3.88503 0.196474
\(392\) −10.3755 −0.524043
\(393\) −5.91943 −0.298596
\(394\) 11.0940 0.558906
\(395\) 4.47244 0.225033
\(396\) −32.2061 −1.61842
\(397\) 2.21011 0.110922 0.0554611 0.998461i \(-0.482337\pi\)
0.0554611 + 0.998461i \(0.482337\pi\)
\(398\) −26.8581 −1.34628
\(399\) 2.34426 0.117360
\(400\) 17.3867 0.869337
\(401\) −7.74623 −0.386828 −0.193414 0.981117i \(-0.561956\pi\)
−0.193414 + 0.981117i \(0.561956\pi\)
\(402\) 11.0021 0.548733
\(403\) −1.93113 −0.0961966
\(404\) −86.4841 −4.30275
\(405\) −8.20847 −0.407882
\(406\) −26.3285 −1.30666
\(407\) 18.0537 0.894890
\(408\) −3.04284 −0.150643
\(409\) 0.843997 0.0417329 0.0208665 0.999782i \(-0.493358\pi\)
0.0208665 + 0.999782i \(0.493358\pi\)
\(410\) −11.5764 −0.571715
\(411\) 4.40697 0.217380
\(412\) 20.2408 0.997194
\(413\) −1.48487 −0.0730656
\(414\) 31.9587 1.57069
\(415\) 7.65176 0.375610
\(416\) −22.0986 −1.08347
\(417\) −6.54214 −0.320370
\(418\) 42.2158 2.06484
\(419\) 13.5588 0.662391 0.331196 0.943562i \(-0.392548\pi\)
0.331196 + 0.943562i \(0.392548\pi\)
\(420\) 1.70817 0.0833500
\(421\) 34.5469 1.68371 0.841855 0.539703i \(-0.181464\pi\)
0.841855 + 0.539703i \(0.181464\pi\)
\(422\) 57.9251 2.81975
\(423\) 24.7488 1.20333
\(424\) −58.4479 −2.83848
\(425\) 0.984021 0.0477320
\(426\) 2.95174 0.143012
\(427\) −8.07188 −0.390626
\(428\) −112.514 −5.43855
\(429\) 0.460707 0.0222431
\(430\) −19.3609 −0.933666
\(431\) −16.4036 −0.790134 −0.395067 0.918652i \(-0.629279\pi\)
−0.395067 + 0.918652i \(0.629279\pi\)
\(432\) −30.6307 −1.47372
\(433\) 7.60672 0.365555 0.182778 0.983154i \(-0.441491\pi\)
0.182778 + 0.983154i \(0.441491\pi\)
\(434\) −6.70483 −0.321842
\(435\) 2.82202 0.135305
\(436\) 7.19001 0.344339
\(437\) −31.0549 −1.48556
\(438\) −11.3620 −0.542898
\(439\) −18.1859 −0.867964 −0.433982 0.900921i \(-0.642892\pi\)
−0.433982 + 0.900921i \(0.642892\pi\)
\(440\) 20.0269 0.954745
\(441\) −2.91118 −0.138627
\(442\) −2.19124 −0.104227
\(443\) −11.7409 −0.557826 −0.278913 0.960316i \(-0.589974\pi\)
−0.278913 + 0.960316i \(0.589974\pi\)
\(444\) 15.9769 0.758232
\(445\) −5.62676 −0.266734
\(446\) −15.0966 −0.714843
\(447\) 3.97447 0.187986
\(448\) −41.9521 −1.98205
\(449\) −7.45839 −0.351983 −0.175992 0.984392i \(-0.556313\pi\)
−0.175992 + 0.984392i \(0.556313\pi\)
\(450\) 8.09467 0.381587
\(451\) −8.03609 −0.378405
\(452\) −29.5295 −1.38895
\(453\) −0.455879 −0.0214191
\(454\) −21.0644 −0.988602
\(455\) 0.800858 0.0375448
\(456\) 24.3229 1.13902
\(457\) −21.8356 −1.02143 −0.510714 0.859751i \(-0.670619\pi\)
−0.510714 + 0.859751i \(0.670619\pi\)
\(458\) −2.78055 −0.129927
\(459\) −1.73358 −0.0809164
\(460\) −22.6285 −1.05506
\(461\) 15.6388 0.728371 0.364185 0.931327i \(-0.381347\pi\)
0.364185 + 0.931327i \(0.381347\pi\)
\(462\) 1.59956 0.0744181
\(463\) 29.1462 1.35454 0.677269 0.735736i \(-0.263164\pi\)
0.677269 + 0.735736i \(0.263164\pi\)
\(464\) −164.631 −7.64282
\(465\) 0.718657 0.0333269
\(466\) 63.2447 2.92976
\(467\) −3.70976 −0.171667 −0.0858337 0.996309i \(-0.527355\pi\)
−0.0858337 + 0.996309i \(0.527355\pi\)
\(468\) −13.3626 −0.617684
\(469\) 13.2763 0.613045
\(470\) −23.6383 −1.09035
\(471\) −4.09073 −0.188491
\(472\) −15.4063 −0.709131
\(473\) −13.4400 −0.617971
\(474\) 3.70630 0.170236
\(475\) −7.86576 −0.360906
\(476\) −5.63988 −0.258503
\(477\) −16.3994 −0.750876
\(478\) −25.8596 −1.18279
\(479\) −28.0449 −1.28140 −0.640701 0.767790i \(-0.721356\pi\)
−0.640701 + 0.767790i \(0.721356\pi\)
\(480\) 8.22384 0.375365
\(481\) 7.49063 0.341543
\(482\) −1.59153 −0.0724923
\(483\) −1.17667 −0.0535404
\(484\) −41.6924 −1.89511
\(485\) −18.7585 −0.851780
\(486\) −21.4981 −0.975172
\(487\) −21.3870 −0.969139 −0.484569 0.874753i \(-0.661024\pi\)
−0.484569 + 0.874753i \(0.661024\pi\)
\(488\) −83.7500 −3.79118
\(489\) 3.98612 0.180258
\(490\) 2.78055 0.125612
\(491\) 13.6251 0.614892 0.307446 0.951566i \(-0.400526\pi\)
0.307446 + 0.951566i \(0.400526\pi\)
\(492\) −7.11167 −0.320619
\(493\) −9.31749 −0.419639
\(494\) 17.5157 0.788068
\(495\) 5.61917 0.252563
\(496\) −41.9252 −1.88250
\(497\) 3.56191 0.159773
\(498\) 6.34100 0.284147
\(499\) 9.29854 0.416260 0.208130 0.978101i \(-0.433262\pi\)
0.208130 + 0.978101i \(0.433262\pi\)
\(500\) −5.73146 −0.256319
\(501\) 0.870553 0.0388935
\(502\) 39.5105 1.76344
\(503\) −11.1887 −0.498879 −0.249439 0.968390i \(-0.580246\pi\)
−0.249439 + 0.968390i \(0.580246\pi\)
\(504\) −30.2050 −1.34544
\(505\) 15.0894 0.671468
\(506\) −21.1897 −0.941997
\(507\) −3.68328 −0.163580
\(508\) 80.7372 3.58213
\(509\) 42.8827 1.90074 0.950371 0.311118i \(-0.100704\pi\)
0.950371 + 0.311118i \(0.100704\pi\)
\(510\) 0.815455 0.0361090
\(511\) −13.7107 −0.606525
\(512\) −118.971 −5.25782
\(513\) 13.8573 0.611816
\(514\) −18.5160 −0.816705
\(515\) −3.53153 −0.155618
\(516\) −11.8939 −0.523601
\(517\) −16.4093 −0.721678
\(518\) 26.0072 1.14269
\(519\) 3.53472 0.155157
\(520\) 8.30932 0.364388
\(521\) 19.0920 0.836434 0.418217 0.908347i \(-0.362655\pi\)
0.418217 + 0.908347i \(0.362655\pi\)
\(522\) −76.6468 −3.35474
\(523\) 0.946269 0.0413775 0.0206887 0.999786i \(-0.493414\pi\)
0.0206887 + 0.999786i \(0.493414\pi\)
\(524\) −113.836 −4.97296
\(525\) −0.298033 −0.0130072
\(526\) −74.1147 −3.23156
\(527\) −2.37280 −0.103361
\(528\) 10.0020 0.435281
\(529\) −7.41237 −0.322277
\(530\) 15.6635 0.680380
\(531\) −4.32271 −0.187590
\(532\) 45.0823 1.95457
\(533\) −3.33424 −0.144422
\(534\) −4.66288 −0.201783
\(535\) 19.6309 0.848717
\(536\) 137.749 5.94985
\(537\) −1.99215 −0.0859676
\(538\) 15.3198 0.660484
\(539\) 1.93021 0.0831399
\(540\) 10.0973 0.434518
\(541\) 6.05878 0.260487 0.130244 0.991482i \(-0.458424\pi\)
0.130244 + 0.991482i \(0.458424\pi\)
\(542\) −53.7431 −2.30846
\(543\) 4.88588 0.209673
\(544\) −27.1527 −1.16416
\(545\) −1.25448 −0.0537360
\(546\) 0.663669 0.0284024
\(547\) 22.3395 0.955167 0.477584 0.878586i \(-0.341513\pi\)
0.477584 + 0.878586i \(0.341513\pi\)
\(548\) 84.7501 3.62035
\(549\) −23.4987 −1.00290
\(550\) −5.36704 −0.228851
\(551\) 74.4793 3.17292
\(552\) −12.2086 −0.519632
\(553\) 4.47244 0.190187
\(554\) −26.0410 −1.10637
\(555\) −2.78758 −0.118326
\(556\) −125.811 −5.33560
\(557\) −28.3183 −1.19988 −0.599942 0.800044i \(-0.704810\pi\)
−0.599942 + 0.800044i \(0.704810\pi\)
\(558\) −19.5189 −0.826302
\(559\) −5.57635 −0.235855
\(560\) 17.3867 0.734724
\(561\) 0.566074 0.0238997
\(562\) −76.7948 −3.23939
\(563\) 34.7133 1.46299 0.731495 0.681847i \(-0.238823\pi\)
0.731495 + 0.681847i \(0.238823\pi\)
\(564\) −14.5216 −0.611471
\(565\) 5.15218 0.216754
\(566\) −74.8995 −3.14826
\(567\) −8.20847 −0.344724
\(568\) 36.9566 1.55067
\(569\) 32.8004 1.37506 0.687532 0.726154i \(-0.258694\pi\)
0.687532 + 0.726154i \(0.258694\pi\)
\(570\) −6.51833 −0.273023
\(571\) 28.7894 1.20480 0.602398 0.798196i \(-0.294212\pi\)
0.602398 + 0.798196i \(0.294212\pi\)
\(572\) 8.85982 0.370448
\(573\) 3.22092 0.134556
\(574\) −11.5764 −0.483188
\(575\) 3.94812 0.164648
\(576\) −122.130 −5.08875
\(577\) 18.8693 0.785540 0.392770 0.919637i \(-0.371517\pi\)
0.392770 + 0.919637i \(0.371517\pi\)
\(578\) 44.5770 1.85416
\(579\) 0.976044 0.0405630
\(580\) 54.2700 2.25344
\(581\) 7.65176 0.317449
\(582\) −15.5451 −0.644366
\(583\) 10.8733 0.450327
\(584\) −142.256 −5.88658
\(585\) 2.33144 0.0963931
\(586\) 40.3988 1.66886
\(587\) −20.2809 −0.837081 −0.418540 0.908198i \(-0.637458\pi\)
−0.418540 + 0.908198i \(0.637458\pi\)
\(588\) 1.70817 0.0704436
\(589\) 18.9669 0.781519
\(590\) 4.12875 0.169978
\(591\) −1.18911 −0.0489134
\(592\) 162.623 6.68375
\(593\) 41.7801 1.71570 0.857852 0.513897i \(-0.171799\pi\)
0.857852 + 0.513897i \(0.171799\pi\)
\(594\) 9.45526 0.387954
\(595\) 0.984021 0.0403409
\(596\) 76.4328 3.13081
\(597\) 2.87879 0.117821
\(598\) −8.79177 −0.359522
\(599\) 12.7717 0.521836 0.260918 0.965361i \(-0.415975\pi\)
0.260918 + 0.965361i \(0.415975\pi\)
\(600\) −3.09225 −0.126241
\(601\) 20.7937 0.848192 0.424096 0.905617i \(-0.360592\pi\)
0.424096 + 0.905617i \(0.360592\pi\)
\(602\) −19.3609 −0.789091
\(603\) 38.6498 1.57394
\(604\) −8.76698 −0.356723
\(605\) 7.27430 0.295742
\(606\) 12.5045 0.507961
\(607\) −30.7120 −1.24656 −0.623280 0.781999i \(-0.714200\pi\)
−0.623280 + 0.781999i \(0.714200\pi\)
\(608\) 217.045 8.80234
\(609\) 2.82202 0.114354
\(610\) 22.4443 0.908742
\(611\) −6.80833 −0.275435
\(612\) −16.4187 −0.663686
\(613\) −31.8057 −1.28462 −0.642310 0.766445i \(-0.722024\pi\)
−0.642310 + 0.766445i \(0.722024\pi\)
\(614\) −90.9037 −3.66857
\(615\) 1.24081 0.0500344
\(616\) 20.0269 0.806907
\(617\) 13.5320 0.544778 0.272389 0.962187i \(-0.412186\pi\)
0.272389 + 0.962187i \(0.412186\pi\)
\(618\) −2.92657 −0.117724
\(619\) 6.94027 0.278953 0.139477 0.990225i \(-0.455458\pi\)
0.139477 + 0.990225i \(0.455458\pi\)
\(620\) 13.8204 0.555043
\(621\) −6.95551 −0.279115
\(622\) 73.5675 2.94979
\(623\) −5.62676 −0.225432
\(624\) 4.14991 0.166129
\(625\) 1.00000 0.0400000
\(626\) −86.5929 −3.46095
\(627\) −4.52491 −0.180707
\(628\) −78.6687 −3.13922
\(629\) 9.20380 0.366980
\(630\) 8.09467 0.322499
\(631\) 16.5062 0.657102 0.328551 0.944486i \(-0.393440\pi\)
0.328551 + 0.944486i \(0.393440\pi\)
\(632\) 46.4039 1.84585
\(633\) −6.20870 −0.246774
\(634\) 40.0053 1.58881
\(635\) −14.0867 −0.559012
\(636\) 9.62253 0.381558
\(637\) 0.800858 0.0317312
\(638\) 50.8194 2.01196
\(639\) 10.3693 0.410205
\(640\) 61.4626 2.42952
\(641\) 2.48703 0.0982320 0.0491160 0.998793i \(-0.484360\pi\)
0.0491160 + 0.998793i \(0.484360\pi\)
\(642\) 16.2680 0.642049
\(643\) −40.9647 −1.61549 −0.807745 0.589532i \(-0.799312\pi\)
−0.807745 + 0.589532i \(0.799312\pi\)
\(644\) −22.6285 −0.891687
\(645\) 2.07520 0.0817109
\(646\) 21.5217 0.846758
\(647\) −15.3833 −0.604780 −0.302390 0.953184i \(-0.597785\pi\)
−0.302390 + 0.953184i \(0.597785\pi\)
\(648\) −85.1672 −3.34568
\(649\) 2.86610 0.112504
\(650\) −2.22683 −0.0873433
\(651\) 0.718657 0.0281664
\(652\) 76.6567 3.00211
\(653\) 31.0434 1.21482 0.607411 0.794388i \(-0.292208\pi\)
0.607411 + 0.794388i \(0.292208\pi\)
\(654\) −1.03958 −0.0406510
\(655\) 19.8616 0.776059
\(656\) −72.3868 −2.82623
\(657\) −39.9142 −1.55720
\(658\) −23.6383 −0.921516
\(659\) 45.5061 1.77266 0.886332 0.463049i \(-0.153245\pi\)
0.886332 + 0.463049i \(0.153245\pi\)
\(660\) −3.29712 −0.128340
\(661\) 34.7740 1.35255 0.676276 0.736648i \(-0.263592\pi\)
0.676276 + 0.736648i \(0.263592\pi\)
\(662\) −7.67779 −0.298406
\(663\) 0.234868 0.00912154
\(664\) 79.3910 3.08097
\(665\) −7.86576 −0.305021
\(666\) 75.7116 2.93376
\(667\) −37.3839 −1.44751
\(668\) 16.7416 0.647750
\(669\) 1.61813 0.0625604
\(670\) −36.9155 −1.42617
\(671\) 15.5804 0.601475
\(672\) 8.22384 0.317241
\(673\) 33.1060 1.27614 0.638072 0.769977i \(-0.279732\pi\)
0.638072 + 0.769977i \(0.279732\pi\)
\(674\) 86.3957 3.32784
\(675\) −1.76173 −0.0678089
\(676\) −70.8330 −2.72435
\(677\) 2.59983 0.0999196 0.0499598 0.998751i \(-0.484091\pi\)
0.0499598 + 0.998751i \(0.484091\pi\)
\(678\) 4.26960 0.163973
\(679\) −18.7585 −0.719886
\(680\) 10.2097 0.391525
\(681\) 2.25779 0.0865187
\(682\) 12.9417 0.495563
\(683\) −6.29909 −0.241028 −0.120514 0.992712i \(-0.538454\pi\)
−0.120514 + 0.992712i \(0.538454\pi\)
\(684\) 131.243 5.01818
\(685\) −14.7868 −0.564975
\(686\) 2.78055 0.106162
\(687\) 0.298033 0.0113707
\(688\) −121.063 −4.61550
\(689\) 4.51143 0.171872
\(690\) 3.27179 0.124555
\(691\) 6.69528 0.254701 0.127350 0.991858i \(-0.459353\pi\)
0.127350 + 0.991858i \(0.459353\pi\)
\(692\) 67.9761 2.58406
\(693\) 5.61917 0.213455
\(694\) 81.4031 3.09002
\(695\) 21.9510 0.832650
\(696\) 29.2799 1.10985
\(697\) −4.09680 −0.155178
\(698\) −29.6880 −1.12371
\(699\) −6.77889 −0.256401
\(700\) −5.73146 −0.216629
\(701\) 19.6673 0.742823 0.371411 0.928468i \(-0.378874\pi\)
0.371411 + 0.928468i \(0.378874\pi\)
\(702\) 3.92306 0.148066
\(703\) −73.5705 −2.77476
\(704\) 80.9763 3.05191
\(705\) 2.53367 0.0954235
\(706\) 26.7969 1.00851
\(707\) 15.0894 0.567494
\(708\) 2.53640 0.0953239
\(709\) −15.2843 −0.574015 −0.287007 0.957928i \(-0.592660\pi\)
−0.287007 + 0.957928i \(0.592660\pi\)
\(710\) −9.90406 −0.371693
\(711\) 13.0201 0.488290
\(712\) −58.3806 −2.18791
\(713\) −9.52022 −0.356535
\(714\) 0.815455 0.0305176
\(715\) −1.54582 −0.0578105
\(716\) −38.3109 −1.43175
\(717\) 2.77176 0.103513
\(718\) −53.9664 −2.01401
\(719\) −35.5503 −1.32580 −0.662902 0.748706i \(-0.730675\pi\)
−0.662902 + 0.748706i \(0.730675\pi\)
\(720\) 50.6159 1.88634
\(721\) −3.53153 −0.131521
\(722\) −119.203 −4.43626
\(723\) 0.170589 0.00634425
\(724\) 93.9600 3.49200
\(725\) −9.46879 −0.351662
\(726\) 6.02819 0.223727
\(727\) −13.6884 −0.507675 −0.253837 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(728\) 8.30932 0.307964
\(729\) −22.3212 −0.826709
\(730\) 38.1233 1.41101
\(731\) −6.85171 −0.253420
\(732\) 13.7881 0.509624
\(733\) 48.7271 1.79978 0.899889 0.436120i \(-0.143648\pi\)
0.899889 + 0.436120i \(0.143648\pi\)
\(734\) −34.9814 −1.29119
\(735\) −0.298033 −0.0109931
\(736\) −108.943 −4.01569
\(737\) −25.6261 −0.943949
\(738\) −33.7008 −1.24054
\(739\) 20.4498 0.752258 0.376129 0.926567i \(-0.377255\pi\)
0.376129 + 0.926567i \(0.377255\pi\)
\(740\) −53.6079 −1.97066
\(741\) −1.87742 −0.0689687
\(742\) 15.6635 0.575026
\(743\) 28.5780 1.04842 0.524212 0.851588i \(-0.324360\pi\)
0.524212 + 0.851588i \(0.324360\pi\)
\(744\) 7.45644 0.273366
\(745\) −13.3356 −0.488580
\(746\) 76.1691 2.78875
\(747\) 22.2756 0.815023
\(748\) 10.8861 0.398036
\(749\) 19.6309 0.717296
\(750\) 0.828697 0.0302597
\(751\) −3.69614 −0.134874 −0.0674370 0.997724i \(-0.521482\pi\)
−0.0674370 + 0.997724i \(0.521482\pi\)
\(752\) −147.810 −5.39007
\(753\) −4.23494 −0.154330
\(754\) 21.0854 0.767884
\(755\) 1.52962 0.0556687
\(756\) 10.0973 0.367234
\(757\) −35.7776 −1.30036 −0.650179 0.759781i \(-0.725306\pi\)
−0.650179 + 0.759781i \(0.725306\pi\)
\(758\) 54.3893 1.97551
\(759\) 2.27122 0.0824400
\(760\) −81.6114 −2.96035
\(761\) 13.1374 0.476231 0.238116 0.971237i \(-0.423470\pi\)
0.238116 + 0.971237i \(0.423470\pi\)
\(762\) −11.6736 −0.422889
\(763\) −1.25448 −0.0454152
\(764\) 61.9414 2.24096
\(765\) 2.86466 0.103572
\(766\) −61.2454 −2.21289
\(767\) 1.18917 0.0429384
\(768\) 25.9277 0.935584
\(769\) 46.7354 1.68532 0.842661 0.538444i \(-0.180988\pi\)
0.842661 + 0.538444i \(0.180988\pi\)
\(770\) −5.36704 −0.193415
\(771\) 1.98464 0.0714749
\(772\) 18.7702 0.675556
\(773\) −36.9751 −1.32990 −0.664950 0.746888i \(-0.731547\pi\)
−0.664950 + 0.746888i \(0.731547\pi\)
\(774\) −56.3630 −2.02593
\(775\) −2.41133 −0.0866175
\(776\) −194.629 −6.98679
\(777\) −2.78758 −0.100004
\(778\) 108.786 3.90018
\(779\) 32.7478 1.17331
\(780\) −1.36800 −0.0489822
\(781\) −6.87522 −0.246015
\(782\) −10.8025 −0.386297
\(783\) 16.6814 0.596146
\(784\) 17.3867 0.620955
\(785\) 13.7258 0.489893
\(786\) 16.4593 0.587083
\(787\) 31.8596 1.13567 0.567836 0.823142i \(-0.307781\pi\)
0.567836 + 0.823142i \(0.307781\pi\)
\(788\) −22.8677 −0.814627
\(789\) 7.94399 0.282814
\(790\) −12.4358 −0.442447
\(791\) 5.15218 0.183190
\(792\) 58.3019 2.07167
\(793\) 6.46443 0.229559
\(794\) −6.14532 −0.218089
\(795\) −1.67890 −0.0595443
\(796\) 55.3618 1.96225
\(797\) 0.294649 0.0104370 0.00521850 0.999986i \(-0.498339\pi\)
0.00521850 + 0.999986i \(0.498339\pi\)
\(798\) −6.51833 −0.230746
\(799\) −8.36545 −0.295948
\(800\) −27.5937 −0.975583
\(801\) −16.3805 −0.578777
\(802\) 21.5388 0.760561
\(803\) 26.4645 0.933911
\(804\) −22.6782 −0.799799
\(805\) 3.94812 0.139153
\(806\) 5.36961 0.189137
\(807\) −1.64205 −0.0578031
\(808\) 156.560 5.50776
\(809\) −47.6044 −1.67368 −0.836841 0.547446i \(-0.815600\pi\)
−0.836841 + 0.547446i \(0.815600\pi\)
\(810\) 22.8241 0.801956
\(811\) −23.3322 −0.819305 −0.409652 0.912242i \(-0.634350\pi\)
−0.409652 + 0.912242i \(0.634350\pi\)
\(812\) 54.2700 1.90450
\(813\) 5.76045 0.202028
\(814\) −50.1993 −1.75948
\(815\) −13.3747 −0.468496
\(816\) 5.09903 0.178502
\(817\) 54.7691 1.91613
\(818\) −2.34678 −0.0820531
\(819\) 2.33144 0.0814671
\(820\) 23.8620 0.833296
\(821\) 28.6336 0.999320 0.499660 0.866222i \(-0.333458\pi\)
0.499660 + 0.866222i \(0.333458\pi\)
\(822\) −12.2538 −0.427400
\(823\) 47.1786 1.64454 0.822271 0.569096i \(-0.192707\pi\)
0.822271 + 0.569096i \(0.192707\pi\)
\(824\) −36.6415 −1.27647
\(825\) 0.575266 0.0200282
\(826\) 4.12875 0.143658
\(827\) −33.4694 −1.16384 −0.581922 0.813244i \(-0.697699\pi\)
−0.581922 + 0.813244i \(0.697699\pi\)
\(828\) −65.8755 −2.28933
\(829\) 11.2550 0.390902 0.195451 0.980713i \(-0.437383\pi\)
0.195451 + 0.980713i \(0.437383\pi\)
\(830\) −21.2761 −0.738505
\(831\) 2.79120 0.0968257
\(832\) 33.5977 1.16479
\(833\) 0.984021 0.0340943
\(834\) 18.1908 0.629894
\(835\) −2.92099 −0.101085
\(836\) −87.0182 −3.00959
\(837\) 4.24811 0.146836
\(838\) −37.7010 −1.30236
\(839\) 22.1711 0.765431 0.382715 0.923866i \(-0.374989\pi\)
0.382715 + 0.923866i \(0.374989\pi\)
\(840\) −3.09225 −0.106693
\(841\) 60.6581 2.09166
\(842\) −96.0593 −3.31042
\(843\) 8.23125 0.283499
\(844\) −119.399 −4.10989
\(845\) 12.3586 0.425150
\(846\) −68.8152 −2.36591
\(847\) 7.27430 0.249948
\(848\) 97.9438 3.36340
\(849\) 8.02811 0.275524
\(850\) −2.73612 −0.0938481
\(851\) 36.9278 1.26587
\(852\) −6.08433 −0.208446
\(853\) −13.6775 −0.468309 −0.234155 0.972199i \(-0.575232\pi\)
−0.234155 + 0.972199i \(0.575232\pi\)
\(854\) 22.4443 0.768027
\(855\) −22.8986 −0.783116
\(856\) 203.681 6.96166
\(857\) 42.9241 1.46626 0.733130 0.680088i \(-0.238059\pi\)
0.733130 + 0.680088i \(0.238059\pi\)
\(858\) −1.28102 −0.0437332
\(859\) −37.0842 −1.26530 −0.632649 0.774439i \(-0.718032\pi\)
−0.632649 + 0.774439i \(0.718032\pi\)
\(860\) 39.9080 1.36085
\(861\) 1.24081 0.0422868
\(862\) 45.6111 1.55352
\(863\) 19.8413 0.675406 0.337703 0.941253i \(-0.390350\pi\)
0.337703 + 0.941253i \(0.390350\pi\)
\(864\) 48.6125 1.65383
\(865\) −11.8602 −0.403258
\(866\) −21.1509 −0.718735
\(867\) −4.77798 −0.162269
\(868\) 13.8204 0.469097
\(869\) −8.63273 −0.292845
\(870\) −7.84676 −0.266030
\(871\) −10.6325 −0.360267
\(872\) −13.0159 −0.440774
\(873\) −54.6093 −1.84825
\(874\) 86.3499 2.92083
\(875\) 1.00000 0.0338062
\(876\) 23.4201 0.791294
\(877\) 30.8011 1.04008 0.520040 0.854142i \(-0.325917\pi\)
0.520040 + 0.854142i \(0.325917\pi\)
\(878\) 50.5667 1.70654
\(879\) −4.33015 −0.146052
\(880\) −33.5600 −1.13131
\(881\) −3.35327 −0.112974 −0.0564872 0.998403i \(-0.517990\pi\)
−0.0564872 + 0.998403i \(0.517990\pi\)
\(882\) 8.09467 0.272562
\(883\) −19.9101 −0.670027 −0.335014 0.942213i \(-0.608741\pi\)
−0.335014 + 0.942213i \(0.608741\pi\)
\(884\) 4.51674 0.151914
\(885\) −0.442540 −0.0148758
\(886\) 32.6461 1.09677
\(887\) 38.0937 1.27906 0.639530 0.768766i \(-0.279129\pi\)
0.639530 + 0.768766i \(0.279129\pi\)
\(888\) −28.9226 −0.970580
\(889\) −14.0867 −0.472452
\(890\) 15.6455 0.524438
\(891\) 15.8441 0.530796
\(892\) 31.1181 1.04191
\(893\) 66.8691 2.23769
\(894\) −11.0512 −0.369608
\(895\) 6.68431 0.223432
\(896\) 61.4626 2.05332
\(897\) 0.942347 0.0314640
\(898\) 20.7384 0.692051
\(899\) 22.8324 0.761503
\(900\) −16.6853 −0.556177
\(901\) 5.54323 0.184672
\(902\) 22.3448 0.743999
\(903\) 2.07520 0.0690583
\(904\) 53.4566 1.77794
\(905\) −16.3937 −0.544946
\(906\) 1.26759 0.0421130
\(907\) 21.5946 0.717037 0.358518 0.933523i \(-0.383282\pi\)
0.358518 + 0.933523i \(0.383282\pi\)
\(908\) 43.4194 1.44092
\(909\) 43.9278 1.45699
\(910\) −2.22683 −0.0738186
\(911\) 43.0329 1.42574 0.712872 0.701294i \(-0.247394\pi\)
0.712872 + 0.701294i \(0.247394\pi\)
\(912\) −40.7590 −1.34967
\(913\) −14.7695 −0.488799
\(914\) 60.7151 2.00828
\(915\) −2.40569 −0.0795297
\(916\) 5.73146 0.189373
\(917\) 19.8616 0.655889
\(918\) 4.82030 0.159094
\(919\) −3.59329 −0.118532 −0.0592658 0.998242i \(-0.518876\pi\)
−0.0592658 + 0.998242i \(0.518876\pi\)
\(920\) 40.9638 1.35054
\(921\) 9.74352 0.321060
\(922\) −43.4844 −1.43208
\(923\) −2.85258 −0.0938938
\(924\) −3.29712 −0.108467
\(925\) 9.35326 0.307533
\(926\) −81.0424 −2.66322
\(927\) −10.2809 −0.337669
\(928\) 261.279 8.57689
\(929\) 6.21078 0.203769 0.101885 0.994796i \(-0.467513\pi\)
0.101885 + 0.994796i \(0.467513\pi\)
\(930\) −1.99826 −0.0655256
\(931\) −7.86576 −0.257790
\(932\) −130.364 −4.27023
\(933\) −7.88534 −0.258154
\(934\) 10.3152 0.337523
\(935\) −1.89936 −0.0621158
\(936\) 24.1899 0.790671
\(937\) −32.9998 −1.07806 −0.539028 0.842288i \(-0.681208\pi\)
−0.539028 + 0.842288i \(0.681208\pi\)
\(938\) −36.9155 −1.20534
\(939\) 9.28146 0.302889
\(940\) 48.7248 1.58923
\(941\) −22.3146 −0.727436 −0.363718 0.931509i \(-0.618493\pi\)
−0.363718 + 0.931509i \(0.618493\pi\)
\(942\) 11.3745 0.370601
\(943\) −16.4373 −0.535273
\(944\) 25.8170 0.840272
\(945\) −1.76173 −0.0573090
\(946\) 37.3706 1.21502
\(947\) 35.2445 1.14529 0.572646 0.819802i \(-0.305917\pi\)
0.572646 + 0.819802i \(0.305917\pi\)
\(948\) −7.63967 −0.248125
\(949\) 10.9803 0.356436
\(950\) 21.8711 0.709594
\(951\) −4.28797 −0.139047
\(952\) 10.2097 0.330899
\(953\) −25.9978 −0.842150 −0.421075 0.907026i \(-0.638347\pi\)
−0.421075 + 0.907026i \(0.638347\pi\)
\(954\) 45.5993 1.47633
\(955\) −10.8073 −0.349715
\(956\) 53.3035 1.72396
\(957\) −5.44708 −0.176079
\(958\) 77.9802 2.51943
\(959\) −14.7868 −0.477491
\(960\) −12.5031 −0.403537
\(961\) −25.1855 −0.812435
\(962\) −20.8281 −0.671524
\(963\) 57.1489 1.84160
\(964\) 3.28058 0.105660
\(965\) −3.27495 −0.105424
\(966\) 3.27179 0.105268
\(967\) −27.8976 −0.897127 −0.448564 0.893751i \(-0.648064\pi\)
−0.448564 + 0.893751i \(0.648064\pi\)
\(968\) 75.4747 2.42585
\(969\) −2.30680 −0.0741051
\(970\) 52.1590 1.67472
\(971\) 8.17443 0.262330 0.131165 0.991361i \(-0.458128\pi\)
0.131165 + 0.991361i \(0.458128\pi\)
\(972\) 44.3133 1.42135
\(973\) 21.9510 0.703718
\(974\) 59.4677 1.90547
\(975\) 0.238682 0.00764396
\(976\) 140.344 4.49229
\(977\) 54.1255 1.73163 0.865814 0.500365i \(-0.166801\pi\)
0.865814 + 0.500365i \(0.166801\pi\)
\(978\) −11.0836 −0.354414
\(979\) 10.8608 0.347113
\(980\) −5.73146 −0.183085
\(981\) −3.65201 −0.116600
\(982\) −37.8853 −1.20897
\(983\) −27.7172 −0.884043 −0.442021 0.897005i \(-0.645738\pi\)
−0.442021 + 0.897005i \(0.645738\pi\)
\(984\) 12.8741 0.410410
\(985\) 3.98985 0.127127
\(986\) 25.9078 0.825071
\(987\) 2.53367 0.0806476
\(988\) −36.1045 −1.14864
\(989\) −27.4906 −0.874152
\(990\) −15.6244 −0.496576
\(991\) 24.2773 0.771193 0.385596 0.922668i \(-0.373996\pi\)
0.385596 + 0.922668i \(0.373996\pi\)
\(992\) 66.5374 2.11257
\(993\) 0.822944 0.0261153
\(994\) −9.90406 −0.314138
\(995\) −9.65928 −0.306220
\(996\) −13.0705 −0.414155
\(997\) 32.3716 1.02522 0.512610 0.858622i \(-0.328679\pi\)
0.512610 + 0.858622i \(0.328679\pi\)
\(998\) −25.8551 −0.818428
\(999\) −16.4779 −0.521338
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 \(a_p\))