Properties

Label 8021.2.a.a.1.19
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.13613 q^{2}\) \(-0.639809 q^{3}\) \(+2.56307 q^{4}\) \(+0.116719 q^{5}\) \(+1.36672 q^{6}\) \(-4.16794 q^{7}\) \(-1.20279 q^{8}\) \(-2.59064 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.13613 q^{2}\) \(-0.639809 q^{3}\) \(+2.56307 q^{4}\) \(+0.116719 q^{5}\) \(+1.36672 q^{6}\) \(-4.16794 q^{7}\) \(-1.20279 q^{8}\) \(-2.59064 q^{9}\) \(-0.249327 q^{10}\) \(-2.18943 q^{11}\) \(-1.63987 q^{12}\) \(+1.00000 q^{13}\) \(+8.90327 q^{14}\) \(-0.0746777 q^{15}\) \(-2.55682 q^{16}\) \(-5.42435 q^{17}\) \(+5.53396 q^{18}\) \(-4.50627 q^{19}\) \(+0.299158 q^{20}\) \(+2.66669 q^{21}\) \(+4.67691 q^{22}\) \(+0.268865 q^{23}\) \(+0.769553 q^{24}\) \(-4.98638 q^{25}\) \(-2.13613 q^{26}\) \(+3.57695 q^{27}\) \(-10.6827 q^{28}\) \(+0.610255 q^{29}\) \(+0.159522 q^{30}\) \(+3.63934 q^{31}\) \(+7.86729 q^{32}\) \(+1.40082 q^{33}\) \(+11.5871 q^{34}\) \(-0.486476 q^{35}\) \(-6.63999 q^{36}\) \(+4.94383 q^{37}\) \(+9.62600 q^{38}\) \(-0.639809 q^{39}\) \(-0.140388 q^{40}\) \(+8.74980 q^{41}\) \(-5.69640 q^{42}\) \(+5.96416 q^{43}\) \(-5.61165 q^{44}\) \(-0.302377 q^{45}\) \(-0.574332 q^{46}\) \(-10.1139 q^{47}\) \(+1.63588 q^{48}\) \(+10.3717 q^{49}\) \(+10.6516 q^{50}\) \(+3.47055 q^{51}\) \(+2.56307 q^{52}\) \(+9.56348 q^{53}\) \(-7.64084 q^{54}\) \(-0.255547 q^{55}\) \(+5.01314 q^{56}\) \(+2.88316 q^{57}\) \(-1.30359 q^{58}\) \(+1.41872 q^{59}\) \(-0.191404 q^{60}\) \(+2.18256 q^{61}\) \(-7.77411 q^{62}\) \(+10.7976 q^{63}\) \(-11.6919 q^{64}\) \(+0.116719 q^{65}\) \(-2.99233 q^{66}\) \(+10.5917 q^{67}\) \(-13.9030 q^{68}\) \(-0.172022 q^{69}\) \(+1.03918 q^{70}\) \(+4.72003 q^{71}\) \(+3.11599 q^{72}\) \(+0.843058 q^{73}\) \(-10.5607 q^{74}\) \(+3.19033 q^{75}\) \(-11.5499 q^{76}\) \(+9.12541 q^{77}\) \(+1.36672 q^{78}\) \(-1.95170 q^{79}\) \(-0.298429 q^{80}\) \(+5.48337 q^{81}\) \(-18.6907 q^{82}\) \(-11.1761 q^{83}\) \(+6.83490 q^{84}\) \(-0.633123 q^{85}\) \(-12.7402 q^{86}\) \(-0.390447 q^{87}\) \(+2.63341 q^{88}\) \(+3.22727 q^{89}\) \(+0.645917 q^{90}\) \(-4.16794 q^{91}\) \(+0.689119 q^{92}\) \(-2.32848 q^{93}\) \(+21.6046 q^{94}\) \(-0.525967 q^{95}\) \(-5.03356 q^{96}\) \(+7.57684 q^{97}\) \(-22.1554 q^{98}\) \(+5.67203 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.13613 −1.51047 −0.755237 0.655452i \(-0.772478\pi\)
−0.755237 + 0.655452i \(0.772478\pi\)
\(3\) −0.639809 −0.369394 −0.184697 0.982795i \(-0.559130\pi\)
−0.184697 + 0.982795i \(0.559130\pi\)
\(4\) 2.56307 1.28153
\(5\) 0.116719 0.0521982 0.0260991 0.999659i \(-0.491691\pi\)
0.0260991 + 0.999659i \(0.491691\pi\)
\(6\) 1.36672 0.557960
\(7\) −4.16794 −1.57533 −0.787666 0.616102i \(-0.788711\pi\)
−0.787666 + 0.616102i \(0.788711\pi\)
\(8\) −1.20279 −0.425249
\(9\) −2.59064 −0.863548
\(10\) −0.249327 −0.0788440
\(11\) −2.18943 −0.660138 −0.330069 0.943957i \(-0.607072\pi\)
−0.330069 + 0.943957i \(0.607072\pi\)
\(12\) −1.63987 −0.473391
\(13\) 1.00000 0.277350
\(14\) 8.90327 2.37950
\(15\) −0.0746777 −0.0192817
\(16\) −2.55682 −0.639206
\(17\) −5.42435 −1.31560 −0.657799 0.753194i \(-0.728512\pi\)
−0.657799 + 0.753194i \(0.728512\pi\)
\(18\) 5.53396 1.30437
\(19\) −4.50627 −1.03381 −0.516905 0.856043i \(-0.672916\pi\)
−0.516905 + 0.856043i \(0.672916\pi\)
\(20\) 0.299158 0.0668937
\(21\) 2.66669 0.581919
\(22\) 4.67691 0.997121
\(23\) 0.268865 0.0560622 0.0280311 0.999607i \(-0.491076\pi\)
0.0280311 + 0.999607i \(0.491076\pi\)
\(24\) 0.769553 0.157084
\(25\) −4.98638 −0.997275
\(26\) −2.13613 −0.418930
\(27\) 3.57695 0.688384
\(28\) −10.6827 −2.01884
\(29\) 0.610255 0.113322 0.0566608 0.998393i \(-0.481955\pi\)
0.0566608 + 0.998393i \(0.481955\pi\)
\(30\) 0.159522 0.0291245
\(31\) 3.63934 0.653644 0.326822 0.945086i \(-0.394022\pi\)
0.326822 + 0.945086i \(0.394022\pi\)
\(32\) 7.86729 1.39075
\(33\) 1.40082 0.243851
\(34\) 11.5871 1.98718
\(35\) −0.486476 −0.0822295
\(36\) −6.63999 −1.10667
\(37\) 4.94383 0.812761 0.406381 0.913704i \(-0.366791\pi\)
0.406381 + 0.913704i \(0.366791\pi\)
\(38\) 9.62600 1.56154
\(39\) −0.639809 −0.102452
\(40\) −0.140388 −0.0221972
\(41\) 8.74980 1.36649 0.683244 0.730190i \(-0.260568\pi\)
0.683244 + 0.730190i \(0.260568\pi\)
\(42\) −5.69640 −0.878974
\(43\) 5.96416 0.909526 0.454763 0.890613i \(-0.349724\pi\)
0.454763 + 0.890613i \(0.349724\pi\)
\(44\) −5.61165 −0.845989
\(45\) −0.302377 −0.0450756
\(46\) −0.574332 −0.0846806
\(47\) −10.1139 −1.47526 −0.737631 0.675204i \(-0.764055\pi\)
−0.737631 + 0.675204i \(0.764055\pi\)
\(48\) 1.63588 0.236119
\(49\) 10.3717 1.48167
\(50\) 10.6516 1.50636
\(51\) 3.47055 0.485974
\(52\) 2.56307 0.355433
\(53\) 9.56348 1.31364 0.656822 0.754046i \(-0.271900\pi\)
0.656822 + 0.754046i \(0.271900\pi\)
\(54\) −7.64084 −1.03979
\(55\) −0.255547 −0.0344580
\(56\) 5.01314 0.669908
\(57\) 2.88316 0.381884
\(58\) −1.30359 −0.171169
\(59\) 1.41872 0.184702 0.0923510 0.995727i \(-0.470562\pi\)
0.0923510 + 0.995727i \(0.470562\pi\)
\(60\) −0.191404 −0.0247102
\(61\) 2.18256 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(62\) −7.77411 −0.987313
\(63\) 10.7976 1.36038
\(64\) −11.6919 −1.46149
\(65\) 0.116719 0.0144772
\(66\) −2.99233 −0.368331
\(67\) 10.5917 1.29398 0.646988 0.762500i \(-0.276028\pi\)
0.646988 + 0.762500i \(0.276028\pi\)
\(68\) −13.9030 −1.68598
\(69\) −0.172022 −0.0207091
\(70\) 1.03918 0.124206
\(71\) 4.72003 0.560164 0.280082 0.959976i \(-0.409638\pi\)
0.280082 + 0.959976i \(0.409638\pi\)
\(72\) 3.11599 0.367223
\(73\) 0.843058 0.0986725 0.0493362 0.998782i \(-0.484289\pi\)
0.0493362 + 0.998782i \(0.484289\pi\)
\(74\) −10.5607 −1.22766
\(75\) 3.19033 0.368388
\(76\) −11.5499 −1.32486
\(77\) 9.12541 1.03994
\(78\) 1.36672 0.154750
\(79\) −1.95170 −0.219583 −0.109792 0.993955i \(-0.535018\pi\)
−0.109792 + 0.993955i \(0.535018\pi\)
\(80\) −0.298429 −0.0333654
\(81\) 5.48337 0.609263
\(82\) −18.6907 −2.06405
\(83\) −11.1761 −1.22673 −0.613366 0.789799i \(-0.710185\pi\)
−0.613366 + 0.789799i \(0.710185\pi\)
\(84\) 6.83490 0.745748
\(85\) −0.633123 −0.0686718
\(86\) −12.7402 −1.37382
\(87\) −0.390447 −0.0418603
\(88\) 2.63341 0.280723
\(89\) 3.22727 0.342090 0.171045 0.985263i \(-0.445286\pi\)
0.171045 + 0.985263i \(0.445286\pi\)
\(90\) 0.645917 0.0680856
\(91\) −4.16794 −0.436919
\(92\) 0.689119 0.0718456
\(93\) −2.32848 −0.241452
\(94\) 21.6046 2.22834
\(95\) −0.525967 −0.0539630
\(96\) −5.03356 −0.513736
\(97\) 7.57684 0.769311 0.384656 0.923060i \(-0.374320\pi\)
0.384656 + 0.923060i \(0.374320\pi\)
\(98\) −22.1554 −2.23803
\(99\) 5.67203 0.570061
\(100\) −12.7804 −1.27804
\(101\) 9.84619 0.979733 0.489866 0.871798i \(-0.337046\pi\)
0.489866 + 0.871798i \(0.337046\pi\)
\(102\) −7.41355 −0.734051
\(103\) 6.82986 0.672966 0.336483 0.941690i \(-0.390763\pi\)
0.336483 + 0.941690i \(0.390763\pi\)
\(104\) −1.20279 −0.117943
\(105\) 0.311252 0.0303751
\(106\) −20.4289 −1.98423
\(107\) −15.6351 −1.51150 −0.755750 0.654860i \(-0.772728\pi\)
−0.755750 + 0.654860i \(0.772728\pi\)
\(108\) 9.16795 0.882187
\(109\) 2.38803 0.228732 0.114366 0.993439i \(-0.463516\pi\)
0.114366 + 0.993439i \(0.463516\pi\)
\(110\) 0.545883 0.0520479
\(111\) −3.16311 −0.300229
\(112\) 10.6567 1.00696
\(113\) 19.0073 1.78805 0.894027 0.448013i \(-0.147868\pi\)
0.894027 + 0.448013i \(0.147868\pi\)
\(114\) −6.15881 −0.576825
\(115\) 0.0313816 0.00292635
\(116\) 1.56412 0.145225
\(117\) −2.59064 −0.239505
\(118\) −3.03058 −0.278988
\(119\) 22.6083 2.07250
\(120\) 0.0898213 0.00819952
\(121\) −6.20640 −0.564218
\(122\) −4.66224 −0.422100
\(123\) −5.59820 −0.504773
\(124\) 9.32786 0.837667
\(125\) −1.16560 −0.104254
\(126\) −23.0652 −2.05481
\(127\) 8.19019 0.726762 0.363381 0.931641i \(-0.381622\pi\)
0.363381 + 0.931641i \(0.381622\pi\)
\(128\) 9.24095 0.816792
\(129\) −3.81593 −0.335974
\(130\) −0.249327 −0.0218674
\(131\) −2.51100 −0.219387 −0.109693 0.993965i \(-0.534987\pi\)
−0.109693 + 0.993965i \(0.534987\pi\)
\(132\) 3.59039 0.312503
\(133\) 18.7819 1.62860
\(134\) −22.6252 −1.95452
\(135\) 0.417497 0.0359324
\(136\) 6.52432 0.559456
\(137\) −17.8505 −1.52507 −0.762537 0.646944i \(-0.776047\pi\)
−0.762537 + 0.646944i \(0.776047\pi\)
\(138\) 0.367463 0.0312805
\(139\) 5.60718 0.475595 0.237798 0.971315i \(-0.423575\pi\)
0.237798 + 0.971315i \(0.423575\pi\)
\(140\) −1.24687 −0.105380
\(141\) 6.47096 0.544953
\(142\) −10.0826 −0.846113
\(143\) −2.18943 −0.183089
\(144\) 6.62382 0.551985
\(145\) 0.0712282 0.00591518
\(146\) −1.80088 −0.149042
\(147\) −6.63592 −0.547322
\(148\) 12.6714 1.04158
\(149\) 3.99332 0.327146 0.163573 0.986531i \(-0.447698\pi\)
0.163573 + 0.986531i \(0.447698\pi\)
\(150\) −6.81497 −0.556440
\(151\) −15.5900 −1.26870 −0.634349 0.773046i \(-0.718732\pi\)
−0.634349 + 0.773046i \(0.718732\pi\)
\(152\) 5.42008 0.439627
\(153\) 14.0525 1.13608
\(154\) −19.4931 −1.57080
\(155\) 0.424779 0.0341190
\(156\) −1.63987 −0.131295
\(157\) −7.17438 −0.572578 −0.286289 0.958143i \(-0.592422\pi\)
−0.286289 + 0.958143i \(0.592422\pi\)
\(158\) 4.16909 0.331675
\(159\) −6.11880 −0.485253
\(160\) 0.918260 0.0725948
\(161\) −1.12061 −0.0883167
\(162\) −11.7132 −0.920276
\(163\) −16.2187 −1.27035 −0.635173 0.772370i \(-0.719071\pi\)
−0.635173 + 0.772370i \(0.719071\pi\)
\(164\) 22.4263 1.75120
\(165\) 0.163502 0.0127286
\(166\) 23.8736 1.85295
\(167\) 21.4210 1.65761 0.828804 0.559538i \(-0.189022\pi\)
0.828804 + 0.559538i \(0.189022\pi\)
\(168\) −3.20745 −0.247460
\(169\) 1.00000 0.0769231
\(170\) 1.35243 0.103727
\(171\) 11.6742 0.892745
\(172\) 15.2865 1.16559
\(173\) −3.76276 −0.286077 −0.143039 0.989717i \(-0.545687\pi\)
−0.143039 + 0.989717i \(0.545687\pi\)
\(174\) 0.834047 0.0632290
\(175\) 20.7829 1.57104
\(176\) 5.59798 0.421964
\(177\) −0.907712 −0.0682278
\(178\) −6.89388 −0.516718
\(179\) −0.867106 −0.0648105 −0.0324053 0.999475i \(-0.510317\pi\)
−0.0324053 + 0.999475i \(0.510317\pi\)
\(180\) −0.775011 −0.0577659
\(181\) 5.36722 0.398942 0.199471 0.979904i \(-0.436078\pi\)
0.199471 + 0.979904i \(0.436078\pi\)
\(182\) 8.90327 0.659955
\(183\) −1.39642 −0.103227
\(184\) −0.323387 −0.0238404
\(185\) 0.577038 0.0424247
\(186\) 4.97395 0.364708
\(187\) 11.8762 0.868475
\(188\) −25.9226 −1.89060
\(189\) −14.9085 −1.08443
\(190\) 1.12353 0.0815098
\(191\) −22.7940 −1.64932 −0.824659 0.565630i \(-0.808633\pi\)
−0.824659 + 0.565630i \(0.808633\pi\)
\(192\) 7.48061 0.539866
\(193\) −9.98339 −0.718620 −0.359310 0.933218i \(-0.616988\pi\)
−0.359310 + 0.933218i \(0.616988\pi\)
\(194\) −16.1851 −1.16202
\(195\) −0.0746777 −0.00534778
\(196\) 26.5834 1.89881
\(197\) −8.58741 −0.611828 −0.305914 0.952059i \(-0.598962\pi\)
−0.305914 + 0.952059i \(0.598962\pi\)
\(198\) −12.1162 −0.861062
\(199\) −21.1283 −1.49775 −0.748874 0.662713i \(-0.769405\pi\)
−0.748874 + 0.662713i \(0.769405\pi\)
\(200\) 5.99754 0.424090
\(201\) −6.77664 −0.477987
\(202\) −21.0328 −1.47986
\(203\) −2.54351 −0.178519
\(204\) 8.89525 0.622792
\(205\) 1.02126 0.0713282
\(206\) −14.5895 −1.01650
\(207\) −0.696533 −0.0484124
\(208\) −2.55682 −0.177284
\(209\) 9.86617 0.682457
\(210\) −0.664876 −0.0458808
\(211\) 2.90551 0.200023 0.100012 0.994986i \(-0.468112\pi\)
0.100012 + 0.994986i \(0.468112\pi\)
\(212\) 24.5118 1.68348
\(213\) −3.01992 −0.206921
\(214\) 33.3986 2.28308
\(215\) 0.696129 0.0474756
\(216\) −4.30230 −0.292734
\(217\) −15.1685 −1.02971
\(218\) −5.10116 −0.345494
\(219\) −0.539396 −0.0364490
\(220\) −0.654985 −0.0441591
\(221\) −5.42435 −0.364881
\(222\) 6.75683 0.453489
\(223\) −8.13499 −0.544759 −0.272380 0.962190i \(-0.587811\pi\)
−0.272380 + 0.962190i \(0.587811\pi\)
\(224\) −32.7904 −2.19090
\(225\) 12.9179 0.861195
\(226\) −40.6021 −2.70081
\(227\) 25.9451 1.72204 0.861020 0.508571i \(-0.169826\pi\)
0.861020 + 0.508571i \(0.169826\pi\)
\(228\) 7.38972 0.489396
\(229\) 4.12978 0.272903 0.136452 0.990647i \(-0.456430\pi\)
0.136452 + 0.990647i \(0.456430\pi\)
\(230\) −0.0670352 −0.00442017
\(231\) −5.83852 −0.384147
\(232\) −0.734006 −0.0481899
\(233\) 19.1228 1.25278 0.626389 0.779510i \(-0.284532\pi\)
0.626389 + 0.779510i \(0.284532\pi\)
\(234\) 5.53396 0.361766
\(235\) −1.18048 −0.0770060
\(236\) 3.63628 0.236702
\(237\) 1.24872 0.0811128
\(238\) −48.2944 −3.13046
\(239\) 4.68204 0.302856 0.151428 0.988468i \(-0.451613\pi\)
0.151428 + 0.988468i \(0.451613\pi\)
\(240\) 0.190938 0.0123250
\(241\) −8.01668 −0.516400 −0.258200 0.966092i \(-0.583129\pi\)
−0.258200 + 0.966092i \(0.583129\pi\)
\(242\) 13.2577 0.852237
\(243\) −14.2392 −0.913442
\(244\) 5.59405 0.358123
\(245\) 1.21057 0.0773407
\(246\) 11.9585 0.762447
\(247\) −4.50627 −0.286727
\(248\) −4.37734 −0.277961
\(249\) 7.15055 0.453148
\(250\) 2.48987 0.157473
\(251\) −5.42543 −0.342450 −0.171225 0.985232i \(-0.554772\pi\)
−0.171225 + 0.985232i \(0.554772\pi\)
\(252\) 27.6751 1.74337
\(253\) −0.588661 −0.0370088
\(254\) −17.4953 −1.09776
\(255\) 0.405078 0.0253670
\(256\) 3.64396 0.227747
\(257\) −26.2750 −1.63899 −0.819494 0.573088i \(-0.805745\pi\)
−0.819494 + 0.573088i \(0.805745\pi\)
\(258\) 8.15133 0.507479
\(259\) −20.6056 −1.28037
\(260\) 0.299158 0.0185530
\(261\) −1.58095 −0.0978586
\(262\) 5.36383 0.331378
\(263\) 4.34782 0.268098 0.134049 0.990975i \(-0.457202\pi\)
0.134049 + 0.990975i \(0.457202\pi\)
\(264\) −1.68488 −0.103697
\(265\) 1.11624 0.0685699
\(266\) −40.1206 −2.45995
\(267\) −2.06484 −0.126366
\(268\) 27.1471 1.65827
\(269\) −27.7793 −1.69373 −0.846867 0.531804i \(-0.821514\pi\)
−0.846867 + 0.531804i \(0.821514\pi\)
\(270\) −0.891829 −0.0542750
\(271\) 2.34602 0.142511 0.0712553 0.997458i \(-0.477300\pi\)
0.0712553 + 0.997458i \(0.477300\pi\)
\(272\) 13.8691 0.840937
\(273\) 2.66669 0.161395
\(274\) 38.1311 2.30359
\(275\) 10.9173 0.658339
\(276\) −0.440905 −0.0265393
\(277\) −5.79566 −0.348227 −0.174114 0.984726i \(-0.555706\pi\)
−0.174114 + 0.984726i \(0.555706\pi\)
\(278\) −11.9777 −0.718374
\(279\) −9.42822 −0.564453
\(280\) 0.585127 0.0349680
\(281\) 12.6136 0.752462 0.376231 0.926526i \(-0.377220\pi\)
0.376231 + 0.926526i \(0.377220\pi\)
\(282\) −13.8228 −0.823138
\(283\) 5.76424 0.342648 0.171324 0.985215i \(-0.445195\pi\)
0.171324 + 0.985215i \(0.445195\pi\)
\(284\) 12.0977 0.717869
\(285\) 0.336518 0.0199336
\(286\) 4.67691 0.276552
\(287\) −36.4686 −2.15267
\(288\) −20.3813 −1.20098
\(289\) 12.4235 0.730796
\(290\) −0.152153 −0.00893473
\(291\) −4.84773 −0.284179
\(292\) 2.16081 0.126452
\(293\) 17.2908 1.01014 0.505071 0.863078i \(-0.331466\pi\)
0.505071 + 0.863078i \(0.331466\pi\)
\(294\) 14.1752 0.826715
\(295\) 0.165592 0.00964111
\(296\) −5.94637 −0.345626
\(297\) −7.83147 −0.454428
\(298\) −8.53027 −0.494145
\(299\) 0.268865 0.0155489
\(300\) 8.17703 0.472101
\(301\) −24.8583 −1.43281
\(302\) 33.3024 1.91634
\(303\) −6.29969 −0.361908
\(304\) 11.5217 0.660818
\(305\) 0.254746 0.0145867
\(306\) −30.0181 −1.71602
\(307\) 16.1681 0.922761 0.461380 0.887202i \(-0.347354\pi\)
0.461380 + 0.887202i \(0.347354\pi\)
\(308\) 23.3890 1.33271
\(309\) −4.36981 −0.248590
\(310\) −0.907384 −0.0515359
\(311\) −20.3183 −1.15215 −0.576073 0.817398i \(-0.695416\pi\)
−0.576073 + 0.817398i \(0.695416\pi\)
\(312\) 0.769553 0.0435674
\(313\) −16.7036 −0.944141 −0.472070 0.881561i \(-0.656493\pi\)
−0.472070 + 0.881561i \(0.656493\pi\)
\(314\) 15.3254 0.864865
\(315\) 1.26029 0.0710091
\(316\) −5.00233 −0.281403
\(317\) 18.4561 1.03660 0.518298 0.855200i \(-0.326566\pi\)
0.518298 + 0.855200i \(0.326566\pi\)
\(318\) 13.0706 0.732962
\(319\) −1.33611 −0.0748078
\(320\) −1.36467 −0.0762872
\(321\) 10.0035 0.558339
\(322\) 2.39378 0.133400
\(323\) 24.4436 1.36008
\(324\) 14.0542 0.780791
\(325\) −4.98638 −0.276594
\(326\) 34.6453 1.91883
\(327\) −1.52789 −0.0844924
\(328\) −10.5241 −0.581098
\(329\) 42.1540 2.32403
\(330\) −0.349261 −0.0192262
\(331\) 11.1424 0.612442 0.306221 0.951961i \(-0.400935\pi\)
0.306221 + 0.951961i \(0.400935\pi\)
\(332\) −28.6450 −1.57210
\(333\) −12.8077 −0.701858
\(334\) −45.7582 −2.50378
\(335\) 1.23624 0.0675432
\(336\) −6.81825 −0.371966
\(337\) −10.3952 −0.566263 −0.283131 0.959081i \(-0.591373\pi\)
−0.283131 + 0.959081i \(0.591373\pi\)
\(338\) −2.13613 −0.116190
\(339\) −12.1610 −0.660497
\(340\) −1.62274 −0.0880052
\(341\) −7.96807 −0.431495
\(342\) −24.9375 −1.34847
\(343\) −14.0531 −0.758797
\(344\) −7.17360 −0.386775
\(345\) −0.0200782 −0.00108098
\(346\) 8.03776 0.432113
\(347\) 31.7670 1.70534 0.852670 0.522450i \(-0.174982\pi\)
0.852670 + 0.522450i \(0.174982\pi\)
\(348\) −1.00074 −0.0536454
\(349\) 2.04418 0.109422 0.0547111 0.998502i \(-0.482576\pi\)
0.0547111 + 0.998502i \(0.482576\pi\)
\(350\) −44.3951 −2.37302
\(351\) 3.57695 0.190923
\(352\) −17.2249 −0.918089
\(353\) 3.96675 0.211129 0.105564 0.994412i \(-0.466335\pi\)
0.105564 + 0.994412i \(0.466335\pi\)
\(354\) 1.93899 0.103056
\(355\) 0.550915 0.0292396
\(356\) 8.27170 0.438399
\(357\) −14.4650 −0.765571
\(358\) 1.85225 0.0978947
\(359\) −2.48877 −0.131352 −0.0656761 0.997841i \(-0.520920\pi\)
−0.0656761 + 0.997841i \(0.520920\pi\)
\(360\) 0.363694 0.0191684
\(361\) 1.30651 0.0687638
\(362\) −11.4651 −0.602592
\(363\) 3.97091 0.208419
\(364\) −10.6827 −0.559926
\(365\) 0.0984006 0.00515052
\(366\) 2.98295 0.155921
\(367\) −18.0200 −0.940634 −0.470317 0.882498i \(-0.655860\pi\)
−0.470317 + 0.882498i \(0.655860\pi\)
\(368\) −0.687440 −0.0358353
\(369\) −22.6676 −1.18003
\(370\) −1.23263 −0.0640814
\(371\) −39.8600 −2.06943
\(372\) −5.96805 −0.309429
\(373\) 21.7523 1.12629 0.563146 0.826357i \(-0.309591\pi\)
0.563146 + 0.826357i \(0.309591\pi\)
\(374\) −25.3692 −1.31181
\(375\) 0.745760 0.0385109
\(376\) 12.1648 0.627353
\(377\) 0.610255 0.0314297
\(378\) 31.8465 1.63801
\(379\) 17.8322 0.915977 0.457989 0.888958i \(-0.348570\pi\)
0.457989 + 0.888958i \(0.348570\pi\)
\(380\) −1.34809 −0.0691554
\(381\) −5.24016 −0.268462
\(382\) 48.6911 2.49125
\(383\) 2.96331 0.151418 0.0757091 0.997130i \(-0.475878\pi\)
0.0757091 + 0.997130i \(0.475878\pi\)
\(384\) −5.91245 −0.301718
\(385\) 1.06511 0.0542828
\(386\) 21.3259 1.08546
\(387\) −15.4510 −0.785419
\(388\) 19.4199 0.985898
\(389\) −17.3684 −0.880611 −0.440305 0.897848i \(-0.645130\pi\)
−0.440305 + 0.897848i \(0.645130\pi\)
\(390\) 0.159522 0.00807769
\(391\) −1.45842 −0.0737553
\(392\) −12.4749 −0.630080
\(393\) 1.60656 0.0810403
\(394\) 18.3439 0.924150
\(395\) −0.227800 −0.0114619
\(396\) 14.5378 0.730552
\(397\) −10.9000 −0.547058 −0.273529 0.961864i \(-0.588191\pi\)
−0.273529 + 0.961864i \(0.588191\pi\)
\(398\) 45.1329 2.26231
\(399\) −12.0168 −0.601594
\(400\) 12.7493 0.637464
\(401\) 3.41055 0.170315 0.0851574 0.996368i \(-0.472861\pi\)
0.0851574 + 0.996368i \(0.472861\pi\)
\(402\) 14.4758 0.721988
\(403\) 3.63934 0.181288
\(404\) 25.2364 1.25556
\(405\) 0.640012 0.0318024
\(406\) 5.43327 0.269649
\(407\) −10.8242 −0.536535
\(408\) −4.17432 −0.206660
\(409\) 9.93654 0.491330 0.245665 0.969355i \(-0.420994\pi\)
0.245665 + 0.969355i \(0.420994\pi\)
\(410\) −2.18156 −0.107739
\(411\) 11.4209 0.563354
\(412\) 17.5054 0.862428
\(413\) −5.91315 −0.290967
\(414\) 1.48789 0.0731257
\(415\) −1.30446 −0.0640332
\(416\) 7.86729 0.385725
\(417\) −3.58753 −0.175682
\(418\) −21.0755 −1.03083
\(419\) 31.7402 1.55061 0.775306 0.631585i \(-0.217595\pi\)
0.775306 + 0.631585i \(0.217595\pi\)
\(420\) 0.797760 0.0389267
\(421\) 8.80466 0.429113 0.214556 0.976712i \(-0.431169\pi\)
0.214556 + 0.976712i \(0.431169\pi\)
\(422\) −6.20655 −0.302130
\(423\) 26.2015 1.27396
\(424\) −11.5028 −0.558626
\(425\) 27.0478 1.31201
\(426\) 6.45095 0.312549
\(427\) −9.09679 −0.440224
\(428\) −40.0737 −1.93704
\(429\) 1.40082 0.0676321
\(430\) −1.48702 −0.0717107
\(431\) 1.28633 0.0619603 0.0309801 0.999520i \(-0.490137\pi\)
0.0309801 + 0.999520i \(0.490137\pi\)
\(432\) −9.14562 −0.440019
\(433\) −24.1438 −1.16028 −0.580138 0.814518i \(-0.697001\pi\)
−0.580138 + 0.814518i \(0.697001\pi\)
\(434\) 32.4020 1.55535
\(435\) −0.0455725 −0.00218503
\(436\) 6.12069 0.293128
\(437\) −1.21158 −0.0579577
\(438\) 1.15222 0.0550553
\(439\) −23.8971 −1.14055 −0.570274 0.821454i \(-0.693163\pi\)
−0.570274 + 0.821454i \(0.693163\pi\)
\(440\) 0.307369 0.0146532
\(441\) −26.8694 −1.27950
\(442\) 11.5871 0.551143
\(443\) 16.5480 0.786222 0.393111 0.919491i \(-0.371399\pi\)
0.393111 + 0.919491i \(0.371399\pi\)
\(444\) −8.10727 −0.384754
\(445\) 0.376683 0.0178565
\(446\) 17.3774 0.822845
\(447\) −2.55497 −0.120846
\(448\) 48.7312 2.30233
\(449\) −3.08214 −0.145455 −0.0727275 0.997352i \(-0.523170\pi\)
−0.0727275 + 0.997352i \(0.523170\pi\)
\(450\) −27.5944 −1.30081
\(451\) −19.1571 −0.902071
\(452\) 48.7169 2.29145
\(453\) 9.97465 0.468650
\(454\) −55.4223 −2.60110
\(455\) −0.486476 −0.0228064
\(456\) −3.46782 −0.162396
\(457\) 34.6157 1.61925 0.809626 0.586946i \(-0.199670\pi\)
0.809626 + 0.586946i \(0.199670\pi\)
\(458\) −8.82176 −0.412214
\(459\) −19.4026 −0.905636
\(460\) 0.0804331 0.00375021
\(461\) −0.579141 −0.0269733 −0.0134866 0.999909i \(-0.504293\pi\)
−0.0134866 + 0.999909i \(0.504293\pi\)
\(462\) 12.4719 0.580244
\(463\) −7.93824 −0.368921 −0.184461 0.982840i \(-0.559054\pi\)
−0.184461 + 0.982840i \(0.559054\pi\)
\(464\) −1.56031 −0.0724358
\(465\) −0.271777 −0.0126034
\(466\) −40.8489 −1.89229
\(467\) 27.9849 1.29499 0.647493 0.762072i \(-0.275818\pi\)
0.647493 + 0.762072i \(0.275818\pi\)
\(468\) −6.63999 −0.306934
\(469\) −44.1454 −2.03844
\(470\) 2.52166 0.116316
\(471\) 4.59024 0.211507
\(472\) −1.70642 −0.0785443
\(473\) −13.0581 −0.600412
\(474\) −2.66742 −0.122519
\(475\) 22.4700 1.03099
\(476\) 57.9467 2.65598
\(477\) −24.7756 −1.13439
\(478\) −10.0015 −0.457456
\(479\) 32.5816 1.48869 0.744347 0.667794i \(-0.232761\pi\)
0.744347 + 0.667794i \(0.232761\pi\)
\(480\) −0.587511 −0.0268161
\(481\) 4.94383 0.225419
\(482\) 17.1247 0.780009
\(483\) 0.716979 0.0326237
\(484\) −15.9074 −0.723064
\(485\) 0.884359 0.0401567
\(486\) 30.4167 1.37973
\(487\) 17.5645 0.795921 0.397961 0.917402i \(-0.369718\pi\)
0.397961 + 0.917402i \(0.369718\pi\)
\(488\) −2.62515 −0.118835
\(489\) 10.3769 0.469259
\(490\) −2.58595 −0.116821
\(491\) −38.3563 −1.73100 −0.865498 0.500912i \(-0.832998\pi\)
−0.865498 + 0.500912i \(0.832998\pi\)
\(492\) −14.3486 −0.646883
\(493\) −3.31024 −0.149086
\(494\) 9.62600 0.433094
\(495\) 0.662032 0.0297561
\(496\) −9.30514 −0.417813
\(497\) −19.6728 −0.882445
\(498\) −15.2745 −0.684468
\(499\) −4.38411 −0.196259 −0.0981297 0.995174i \(-0.531286\pi\)
−0.0981297 + 0.995174i \(0.531286\pi\)
\(500\) −2.98750 −0.133605
\(501\) −13.7054 −0.612311
\(502\) 11.5894 0.517262
\(503\) 22.8439 1.01856 0.509280 0.860601i \(-0.329912\pi\)
0.509280 + 0.860601i \(0.329912\pi\)
\(504\) −12.9872 −0.578498
\(505\) 1.14923 0.0511403
\(506\) 1.25746 0.0559008
\(507\) −0.639809 −0.0284149
\(508\) 20.9920 0.931369
\(509\) 6.47904 0.287178 0.143589 0.989637i \(-0.454136\pi\)
0.143589 + 0.989637i \(0.454136\pi\)
\(510\) −0.865300 −0.0383161
\(511\) −3.51381 −0.155442
\(512\) −26.2659 −1.16080
\(513\) −16.1187 −0.711658
\(514\) 56.1268 2.47565
\(515\) 0.797172 0.0351276
\(516\) −9.78047 −0.430561
\(517\) 22.1436 0.973876
\(518\) 44.0163 1.93397
\(519\) 2.40745 0.105675
\(520\) −0.140388 −0.00615640
\(521\) 20.8086 0.911642 0.455821 0.890072i \(-0.349346\pi\)
0.455821 + 0.890072i \(0.349346\pi\)
\(522\) 3.37713 0.147813
\(523\) 24.7318 1.08144 0.540722 0.841201i \(-0.318151\pi\)
0.540722 + 0.841201i \(0.318151\pi\)
\(524\) −6.43586 −0.281152
\(525\) −13.2971 −0.580333
\(526\) −9.28753 −0.404955
\(527\) −19.7410 −0.859932
\(528\) −3.58164 −0.155871
\(529\) −22.9277 −0.996857
\(530\) −2.38443 −0.103573
\(531\) −3.67541 −0.159499
\(532\) 48.1392 2.08710
\(533\) 8.74980 0.378996
\(534\) 4.41077 0.190873
\(535\) −1.82491 −0.0788976
\(536\) −12.7395 −0.550262
\(537\) 0.554783 0.0239406
\(538\) 59.3403 2.55834
\(539\) −22.7081 −0.978109
\(540\) 1.07007 0.0460486
\(541\) 27.9528 1.20178 0.600891 0.799331i \(-0.294812\pi\)
0.600891 + 0.799331i \(0.294812\pi\)
\(542\) −5.01141 −0.215259
\(543\) −3.43400 −0.147367
\(544\) −42.6749 −1.82967
\(545\) 0.278728 0.0119394
\(546\) −5.69640 −0.243783
\(547\) −21.2347 −0.907929 −0.453965 0.891020i \(-0.649991\pi\)
−0.453965 + 0.891020i \(0.649991\pi\)
\(548\) −45.7521 −1.95443
\(549\) −5.65424 −0.241317
\(550\) −23.3209 −0.994405
\(551\) −2.74998 −0.117153
\(552\) 0.206906 0.00880650
\(553\) 8.13456 0.345917
\(554\) 12.3803 0.525988
\(555\) −0.369194 −0.0156714
\(556\) 14.3716 0.609491
\(557\) 15.2969 0.648149 0.324075 0.946031i \(-0.394947\pi\)
0.324075 + 0.946031i \(0.394947\pi\)
\(558\) 20.1399 0.852592
\(559\) 5.96416 0.252257
\(560\) 1.24383 0.0525616
\(561\) −7.59852 −0.320810
\(562\) −26.9442 −1.13657
\(563\) 22.0134 0.927756 0.463878 0.885899i \(-0.346458\pi\)
0.463878 + 0.885899i \(0.346458\pi\)
\(564\) 16.5855 0.698375
\(565\) 2.21850 0.0933332
\(566\) −12.3132 −0.517561
\(567\) −22.8543 −0.959792
\(568\) −5.67718 −0.238209
\(569\) 29.0560 1.21809 0.609045 0.793136i \(-0.291553\pi\)
0.609045 + 0.793136i \(0.291553\pi\)
\(570\) −0.718848 −0.0301092
\(571\) −8.09495 −0.338763 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(572\) −5.61165 −0.234635
\(573\) 14.5838 0.609249
\(574\) 77.9018 3.25156
\(575\) −1.34066 −0.0559095
\(576\) 30.2896 1.26207
\(577\) −0.235606 −0.00980841 −0.00490420 0.999988i \(-0.501561\pi\)
−0.00490420 + 0.999988i \(0.501561\pi\)
\(578\) −26.5383 −1.10385
\(579\) 6.38747 0.265454
\(580\) 0.182563 0.00758050
\(581\) 46.5811 1.93251
\(582\) 10.3554 0.429245
\(583\) −20.9386 −0.867186
\(584\) −1.01402 −0.0419603
\(585\) −0.302377 −0.0125017
\(586\) −36.9355 −1.52579
\(587\) 0.453552 0.0187201 0.00936004 0.999956i \(-0.497021\pi\)
0.00936004 + 0.999956i \(0.497021\pi\)
\(588\) −17.0083 −0.701411
\(589\) −16.3998 −0.675744
\(590\) −0.353726 −0.0145627
\(591\) 5.49431 0.226006
\(592\) −12.6405 −0.519522
\(593\) 20.8015 0.854214 0.427107 0.904201i \(-0.359533\pi\)
0.427107 + 0.904201i \(0.359533\pi\)
\(594\) 16.7291 0.686402
\(595\) 2.63882 0.108181
\(596\) 10.2352 0.419248
\(597\) 13.5181 0.553259
\(598\) −0.574332 −0.0234862
\(599\) 1.30736 0.0534173 0.0267086 0.999643i \(-0.491497\pi\)
0.0267086 + 0.999643i \(0.491497\pi\)
\(600\) −3.83728 −0.156656
\(601\) −14.5430 −0.593221 −0.296610 0.954999i \(-0.595856\pi\)
−0.296610 + 0.954999i \(0.595856\pi\)
\(602\) 53.1005 2.16422
\(603\) −27.4392 −1.11741
\(604\) −39.9583 −1.62588
\(605\) −0.724403 −0.0294512
\(606\) 13.4570 0.546652
\(607\) −15.1901 −0.616546 −0.308273 0.951298i \(-0.599751\pi\)
−0.308273 + 0.951298i \(0.599751\pi\)
\(608\) −35.4522 −1.43777
\(609\) 1.62736 0.0659439
\(610\) −0.544171 −0.0220328
\(611\) −10.1139 −0.409164
\(612\) 36.0176 1.45593
\(613\) 28.3113 1.14348 0.571740 0.820435i \(-0.306268\pi\)
0.571740 + 0.820435i \(0.306268\pi\)
\(614\) −34.5372 −1.39381
\(615\) −0.653415 −0.0263482
\(616\) −10.9759 −0.442232
\(617\) 1.00000 0.0402585
\(618\) 9.33449 0.375488
\(619\) 2.69966 0.108508 0.0542542 0.998527i \(-0.482722\pi\)
0.0542542 + 0.998527i \(0.482722\pi\)
\(620\) 1.08874 0.0437247
\(621\) 0.961716 0.0385923
\(622\) 43.4026 1.74029
\(623\) −13.4511 −0.538905
\(624\) 1.63588 0.0654876
\(625\) 24.7958 0.991833
\(626\) 35.6810 1.42610
\(627\) −6.31247 −0.252096
\(628\) −18.3884 −0.733778
\(629\) −26.8171 −1.06927
\(630\) −2.69214 −0.107258
\(631\) −38.1054 −1.51695 −0.758477 0.651700i \(-0.774056\pi\)
−0.758477 + 0.651700i \(0.774056\pi\)
\(632\) 2.34747 0.0933775
\(633\) −1.85897 −0.0738875
\(634\) −39.4246 −1.56575
\(635\) 0.955948 0.0379357
\(636\) −15.6829 −0.621867
\(637\) 10.3717 0.410942
\(638\) 2.85411 0.112995
\(639\) −12.2279 −0.483728
\(640\) 1.07859 0.0426351
\(641\) −35.5314 −1.40341 −0.701703 0.712469i \(-0.747577\pi\)
−0.701703 + 0.712469i \(0.747577\pi\)
\(642\) −21.3688 −0.843357
\(643\) −18.8499 −0.743369 −0.371684 0.928359i \(-0.621220\pi\)
−0.371684 + 0.928359i \(0.621220\pi\)
\(644\) −2.87221 −0.113181
\(645\) −0.445390 −0.0175372
\(646\) −52.2148 −2.05436
\(647\) 22.2327 0.874058 0.437029 0.899447i \(-0.356031\pi\)
0.437029 + 0.899447i \(0.356031\pi\)
\(648\) −6.59531 −0.259088
\(649\) −3.10619 −0.121929
\(650\) 10.6516 0.417789
\(651\) 9.70497 0.380368
\(652\) −41.5696 −1.62799
\(653\) 23.6639 0.926039 0.463019 0.886348i \(-0.346766\pi\)
0.463019 + 0.886348i \(0.346766\pi\)
\(654\) 3.26377 0.127624
\(655\) −0.293081 −0.0114516
\(656\) −22.3717 −0.873467
\(657\) −2.18406 −0.0852084
\(658\) −90.0467 −3.51038
\(659\) −47.8858 −1.86536 −0.932682 0.360699i \(-0.882538\pi\)
−0.932682 + 0.360699i \(0.882538\pi\)
\(660\) 0.419066 0.0163121
\(661\) −3.56827 −0.138790 −0.0693949 0.997589i \(-0.522107\pi\)
−0.0693949 + 0.997589i \(0.522107\pi\)
\(662\) −23.8017 −0.925078
\(663\) 3.47055 0.134785
\(664\) 13.4424 0.521666
\(665\) 2.19220 0.0850097
\(666\) 27.3590 1.06014
\(667\) 0.164076 0.00635306
\(668\) 54.9035 2.12428
\(669\) 5.20484 0.201231
\(670\) −2.64078 −0.102022
\(671\) −4.77857 −0.184475
\(672\) 20.9796 0.809305
\(673\) −33.4765 −1.29042 −0.645212 0.764004i \(-0.723231\pi\)
−0.645212 + 0.764004i \(0.723231\pi\)
\(674\) 22.2055 0.855326
\(675\) −17.8360 −0.686508
\(676\) 2.56307 0.0985795
\(677\) −36.3932 −1.39870 −0.699351 0.714778i \(-0.746528\pi\)
−0.699351 + 0.714778i \(0.746528\pi\)
\(678\) 25.9776 0.997664
\(679\) −31.5798 −1.21192
\(680\) 0.761511 0.0292026
\(681\) −16.5999 −0.636111
\(682\) 17.0209 0.651762
\(683\) −17.5353 −0.670969 −0.335484 0.942046i \(-0.608900\pi\)
−0.335484 + 0.942046i \(0.608900\pi\)
\(684\) 29.9216 1.14408
\(685\) −2.08349 −0.0796061
\(686\) 30.0193 1.14614
\(687\) −2.64227 −0.100809
\(688\) −15.2493 −0.581374
\(689\) 9.56348 0.364339
\(690\) 0.0428898 0.00163279
\(691\) −11.8126 −0.449371 −0.224686 0.974431i \(-0.572136\pi\)
−0.224686 + 0.974431i \(0.572136\pi\)
\(692\) −9.64420 −0.366618
\(693\) −23.6407 −0.898035
\(694\) −67.8585 −2.57587
\(695\) 0.654463 0.0248252
\(696\) 0.469624 0.0178011
\(697\) −47.4619 −1.79775
\(698\) −4.36663 −0.165280
\(699\) −12.2350 −0.462769
\(700\) 53.2680 2.01334
\(701\) −28.9909 −1.09497 −0.547486 0.836815i \(-0.684415\pi\)
−0.547486 + 0.836815i \(0.684415\pi\)
\(702\) −7.64084 −0.288385
\(703\) −22.2783 −0.840241
\(704\) 25.5987 0.964785
\(705\) 0.755282 0.0284456
\(706\) −8.47350 −0.318904
\(707\) −41.0383 −1.54341
\(708\) −2.32653 −0.0874363
\(709\) −15.7816 −0.592690 −0.296345 0.955081i \(-0.595768\pi\)
−0.296345 + 0.955081i \(0.595768\pi\)
\(710\) −1.17683 −0.0441656
\(711\) 5.05616 0.189621
\(712\) −3.88171 −0.145473
\(713\) 0.978490 0.0366447
\(714\) 30.8992 1.15638
\(715\) −0.255547 −0.00955693
\(716\) −2.22245 −0.0830569
\(717\) −2.99561 −0.111873
\(718\) 5.31634 0.198404
\(719\) −21.0178 −0.783831 −0.391915 0.920001i \(-0.628187\pi\)
−0.391915 + 0.920001i \(0.628187\pi\)
\(720\) 0.773123 0.0288126
\(721\) −28.4664 −1.06015
\(722\) −2.79088 −0.103866
\(723\) 5.12915 0.190755
\(724\) 13.7565 0.511258
\(725\) −3.04296 −0.113013
\(726\) −8.48240 −0.314811
\(727\) −41.2107 −1.52842 −0.764210 0.644967i \(-0.776871\pi\)
−0.764210 + 0.644967i \(0.776871\pi\)
\(728\) 5.01314 0.185799
\(729\) −7.33976 −0.271843
\(730\) −0.210197 −0.00777974
\(731\) −32.3517 −1.19657
\(732\) −3.57913 −0.132288
\(733\) −21.0344 −0.776922 −0.388461 0.921465i \(-0.626993\pi\)
−0.388461 + 0.921465i \(0.626993\pi\)
\(734\) 38.4930 1.42080
\(735\) −0.774536 −0.0285692
\(736\) 2.11524 0.0779687
\(737\) −23.1897 −0.854203
\(738\) 48.4210 1.78240
\(739\) 15.6149 0.574404 0.287202 0.957870i \(-0.407275\pi\)
0.287202 + 0.957870i \(0.407275\pi\)
\(740\) 1.47899 0.0543686
\(741\) 2.88316 0.105915
\(742\) 85.1462 3.12582
\(743\) 42.3014 1.55189 0.775945 0.630801i \(-0.217274\pi\)
0.775945 + 0.630801i \(0.217274\pi\)
\(744\) 2.80066 0.102677
\(745\) 0.466096 0.0170764
\(746\) −46.4659 −1.70124
\(747\) 28.9532 1.05934
\(748\) 30.4395 1.11298
\(749\) 65.1661 2.38112
\(750\) −1.59304 −0.0581697
\(751\) −7.50795 −0.273969 −0.136984 0.990573i \(-0.543741\pi\)
−0.136984 + 0.990573i \(0.543741\pi\)
\(752\) 25.8594 0.942995
\(753\) 3.47124 0.126499
\(754\) −1.30359 −0.0474738
\(755\) −1.81965 −0.0662238
\(756\) −38.2115 −1.38974
\(757\) −11.8844 −0.431947 −0.215973 0.976399i \(-0.569292\pi\)
−0.215973 + 0.976399i \(0.569292\pi\)
\(758\) −38.0919 −1.38356
\(759\) 0.376631 0.0136708
\(760\) 0.632625 0.0229477
\(761\) 7.90540 0.286571 0.143285 0.989681i \(-0.454233\pi\)
0.143285 + 0.989681i \(0.454233\pi\)
\(762\) 11.1937 0.405504
\(763\) −9.95318 −0.360329
\(764\) −58.4226 −2.11366
\(765\) 1.64020 0.0593014
\(766\) −6.33003 −0.228713
\(767\) 1.41872 0.0512271
\(768\) −2.33144 −0.0841286
\(769\) −51.4742 −1.85621 −0.928103 0.372324i \(-0.878561\pi\)
−0.928103 + 0.372324i \(0.878561\pi\)
\(770\) −2.27521 −0.0819928
\(771\) 16.8110 0.605432
\(772\) −25.5881 −0.920936
\(773\) 13.5595 0.487700 0.243850 0.969813i \(-0.421590\pi\)
0.243850 + 0.969813i \(0.421590\pi\)
\(774\) 33.0054 1.18636
\(775\) −18.1471 −0.651863
\(776\) −9.11331 −0.327149
\(777\) 13.1837 0.472961
\(778\) 37.1011 1.33014
\(779\) −39.4290 −1.41269
\(780\) −0.191404 −0.00685336
\(781\) −10.3342 −0.369785
\(782\) 3.11537 0.111406
\(783\) 2.18285 0.0780087
\(784\) −26.5186 −0.947094
\(785\) −0.837385 −0.0298875
\(786\) −3.43183 −0.122409
\(787\) −9.35235 −0.333375 −0.166688 0.986010i \(-0.553307\pi\)
−0.166688 + 0.986010i \(0.553307\pi\)
\(788\) −22.0101 −0.784078
\(789\) −2.78178 −0.0990339
\(790\) 0.486611 0.0173128
\(791\) −79.2212 −2.81678
\(792\) −6.82224 −0.242418
\(793\) 2.18256 0.0775051
\(794\) 23.2840 0.826316
\(795\) −0.714179 −0.0253293
\(796\) −54.1533 −1.91941
\(797\) 14.2050 0.503167 0.251584 0.967836i \(-0.419049\pi\)
0.251584 + 0.967836i \(0.419049\pi\)
\(798\) 25.6695 0.908692
\(799\) 54.8612 1.94085
\(800\) −39.2293 −1.38696
\(801\) −8.36070 −0.295411
\(802\) −7.28539 −0.257256
\(803\) −1.84582 −0.0651374
\(804\) −17.3690 −0.612557
\(805\) −0.130797 −0.00460997
\(806\) −7.77411 −0.273831
\(807\) 17.7735 0.625656
\(808\) −11.8429 −0.416630
\(809\) 25.7399 0.904966 0.452483 0.891773i \(-0.350538\pi\)
0.452483 + 0.891773i \(0.350538\pi\)
\(810\) −1.36715 −0.0480368
\(811\) −21.7318 −0.763108 −0.381554 0.924347i \(-0.624611\pi\)
−0.381554 + 0.924347i \(0.624611\pi\)
\(812\) −6.51918 −0.228778
\(813\) −1.50101 −0.0526426
\(814\) 23.1219 0.810422
\(815\) −1.89303 −0.0663098
\(816\) −8.87358 −0.310637
\(817\) −26.8761 −0.940277
\(818\) −21.2258 −0.742142
\(819\) 10.7976 0.377300
\(820\) 2.61757 0.0914095
\(821\) −47.0410 −1.64174 −0.820871 0.571114i \(-0.806511\pi\)
−0.820871 + 0.571114i \(0.806511\pi\)
\(822\) −24.3967 −0.850931
\(823\) −14.9180 −0.520007 −0.260004 0.965608i \(-0.583724\pi\)
−0.260004 + 0.965608i \(0.583724\pi\)
\(824\) −8.21485 −0.286178
\(825\) −6.98500 −0.243187
\(826\) 12.6313 0.439498
\(827\) 13.0808 0.454865 0.227432 0.973794i \(-0.426967\pi\)
0.227432 + 0.973794i \(0.426967\pi\)
\(828\) −1.78526 −0.0620421
\(829\) 33.5136 1.16398 0.581988 0.813197i \(-0.302275\pi\)
0.581988 + 0.813197i \(0.302275\pi\)
\(830\) 2.78649 0.0967205
\(831\) 3.70812 0.128633
\(832\) −11.6919 −0.405345
\(833\) −56.2598 −1.94929
\(834\) 7.66344 0.265363
\(835\) 2.50023 0.0865242
\(836\) 25.2877 0.874592
\(837\) 13.0177 0.449958
\(838\) −67.8014 −2.34216
\(839\) 27.8328 0.960896 0.480448 0.877023i \(-0.340474\pi\)
0.480448 + 0.877023i \(0.340474\pi\)
\(840\) −0.374370 −0.0129170
\(841\) −28.6276 −0.987158
\(842\) −18.8079 −0.648164
\(843\) −8.07027 −0.277955
\(844\) 7.44701 0.256337
\(845\) 0.116719 0.00401525
\(846\) −55.9698 −1.92428
\(847\) 25.8679 0.888831
\(848\) −24.4521 −0.839689
\(849\) −3.68801 −0.126572
\(850\) −57.7778 −1.98176
\(851\) 1.32922 0.0455652
\(852\) −7.74025 −0.265177
\(853\) 43.8400 1.50105 0.750527 0.660840i \(-0.229800\pi\)
0.750527 + 0.660840i \(0.229800\pi\)
\(854\) 19.4320 0.664948
\(855\) 1.36259 0.0465997
\(856\) 18.8056 0.642764
\(857\) 3.01314 0.102927 0.0514634 0.998675i \(-0.483611\pi\)
0.0514634 + 0.998675i \(0.483611\pi\)
\(858\) −2.99233 −0.102157
\(859\) 34.2581 1.16887 0.584435 0.811441i \(-0.301316\pi\)
0.584435 + 0.811441i \(0.301316\pi\)
\(860\) 1.78422 0.0608416
\(861\) 23.3330 0.795185
\(862\) −2.74777 −0.0935894
\(863\) −34.0234 −1.15817 −0.579085 0.815267i \(-0.696590\pi\)
−0.579085 + 0.815267i \(0.696590\pi\)
\(864\) 28.1409 0.957372
\(865\) −0.439184 −0.0149327
\(866\) 51.5743 1.75257
\(867\) −7.94869 −0.269952
\(868\) −38.8780 −1.31960
\(869\) 4.27311 0.144955
\(870\) 0.0973489 0.00330044
\(871\) 10.5917 0.358884
\(872\) −2.87229 −0.0972681
\(873\) −19.6289 −0.664337
\(874\) 2.58810 0.0875436
\(875\) 4.85814 0.164235
\(876\) −1.38251 −0.0467106
\(877\) 49.5190 1.67214 0.836069 0.548625i \(-0.184848\pi\)
0.836069 + 0.548625i \(0.184848\pi\)
\(878\) 51.0475 1.72277
\(879\) −11.0628 −0.373140
\(880\) 0.653389 0.0220258
\(881\) 16.8787 0.568659 0.284330 0.958727i \(-0.408229\pi\)
0.284330 + 0.958727i \(0.408229\pi\)
\(882\) 57.3967 1.93265
\(883\) −3.91223 −0.131657 −0.0658284 0.997831i \(-0.520969\pi\)
−0.0658284 + 0.997831i \(0.520969\pi\)
\(884\) −13.9030 −0.467607
\(885\) −0.105947 −0.00356137
\(886\) −35.3488 −1.18757
\(887\) −23.6495 −0.794073 −0.397037 0.917803i \(-0.629961\pi\)
−0.397037 + 0.917803i \(0.629961\pi\)
\(888\) 3.80454 0.127672
\(889\) −34.1362 −1.14489
\(890\) −0.804644 −0.0269717
\(891\) −12.0054 −0.402198
\(892\) −20.8505 −0.698127
\(893\) 45.5759 1.52514
\(894\) 5.45775 0.182534
\(895\) −0.101207 −0.00338299
\(896\) −38.5157 −1.28672
\(897\) −0.172022 −0.00574366
\(898\) 6.58385 0.219706
\(899\) 2.22092 0.0740720
\(900\) 33.1095 1.10365
\(901\) −51.8756 −1.72823
\(902\) 40.9220 1.36255
\(903\) 15.9045 0.529270
\(904\) −22.8617 −0.760368
\(905\) 0.626455 0.0208241
\(906\) −21.3072 −0.707884
\(907\) 11.2345 0.373034 0.186517 0.982452i \(-0.440280\pi\)
0.186517 + 0.982452i \(0.440280\pi\)
\(908\) 66.4991 2.20685
\(909\) −25.5080 −0.846046
\(910\) 1.03918 0.0344484
\(911\) −52.5667 −1.74161 −0.870806 0.491627i \(-0.836402\pi\)
−0.870806 + 0.491627i \(0.836402\pi\)
\(912\) −7.37172 −0.244102
\(913\) 24.4692 0.809812
\(914\) −73.9437 −2.44584
\(915\) −0.162989 −0.00538824
\(916\) 10.5849 0.349735
\(917\) 10.4657 0.345607
\(918\) 41.4465 1.36794
\(919\) −55.0573 −1.81617 −0.908086 0.418784i \(-0.862457\pi\)
−0.908086 + 0.418784i \(0.862457\pi\)
\(920\) −0.0377453 −0.00124443
\(921\) −10.3445 −0.340863
\(922\) 1.23712 0.0407425
\(923\) 4.72003 0.155362
\(924\) −14.9645 −0.492297
\(925\) −24.6518 −0.810547
\(926\) 16.9571 0.557246
\(927\) −17.6937 −0.581138
\(928\) 4.80105 0.157602
\(929\) 31.5090 1.03378 0.516888 0.856053i \(-0.327090\pi\)
0.516888 + 0.856053i \(0.327090\pi\)
\(930\) 0.580553 0.0190371
\(931\) −46.7378 −1.53177
\(932\) 49.0131 1.60548
\(933\) 12.9999 0.425596
\(934\) −59.7794 −1.95604
\(935\) 1.38618 0.0453329
\(936\) 3.11599 0.101849
\(937\) 3.93637 0.128595 0.0642977 0.997931i \(-0.479519\pi\)
0.0642977 + 0.997931i \(0.479519\pi\)
\(938\) 94.3004 3.07902
\(939\) 10.6871 0.348760
\(940\) −3.02565 −0.0986857
\(941\) −6.99845 −0.228143 −0.114071 0.993473i \(-0.536389\pi\)
−0.114071 + 0.993473i \(0.536389\pi\)
\(942\) −9.80536 −0.319476
\(943\) 2.35251 0.0766084
\(944\) −3.62742 −0.118063
\(945\) −1.74010 −0.0566055
\(946\) 27.8939 0.906908
\(947\) 29.8232 0.969122 0.484561 0.874757i \(-0.338979\pi\)
0.484561 + 0.874757i \(0.338979\pi\)
\(948\) 3.20054 0.103949
\(949\) 0.843058 0.0273668
\(950\) −47.9989 −1.55729
\(951\) −11.8084 −0.382913
\(952\) −27.1930 −0.881330
\(953\) 50.5632 1.63790 0.818951 0.573864i \(-0.194556\pi\)
0.818951 + 0.573864i \(0.194556\pi\)
\(954\) 52.9239 1.71347
\(955\) −2.66049 −0.0860915
\(956\) 12.0004 0.388120
\(957\) 0.854856 0.0276336
\(958\) −69.5987 −2.24863
\(959\) 74.3999 2.40250
\(960\) 0.873127 0.0281800
\(961\) −17.7552 −0.572749
\(962\) −10.5607 −0.340490
\(963\) 40.5049 1.30525
\(964\) −20.5473 −0.661783
\(965\) −1.16525 −0.0375107
\(966\) −1.53156 −0.0492772
\(967\) −60.2452 −1.93735 −0.968677 0.248324i \(-0.920120\pi\)
−0.968677 + 0.248324i \(0.920120\pi\)
\(968\) 7.46497 0.239933
\(969\) −15.6392 −0.502405
\(970\) −1.88911 −0.0606556
\(971\) 3.94780 0.126691 0.0633455 0.997992i \(-0.479823\pi\)
0.0633455 + 0.997992i \(0.479823\pi\)
\(972\) −36.4959 −1.17061
\(973\) −23.3704 −0.749221
\(974\) −37.5200 −1.20222
\(975\) 3.19033 0.102172
\(976\) −5.58043 −0.178625
\(977\) −48.1318 −1.53987 −0.769936 0.638122i \(-0.779712\pi\)
−0.769936 + 0.638122i \(0.779712\pi\)
\(978\) −22.1664 −0.708803
\(979\) −7.06588 −0.225826
\(980\) 3.10278 0.0991147
\(981\) −6.18655 −0.197521
\(982\) 81.9342 2.61463
\(983\) 31.6163 1.00840 0.504202 0.863586i \(-0.331787\pi\)
0.504202 + 0.863586i \(0.331787\pi\)
\(984\) 6.73343 0.214654
\(985\) −1.00231 −0.0319363
\(986\) 7.07111 0.225190
\(987\) −26.9706 −0.858482
\(988\) −11.5499 −0.367451
\(989\) 1.60355 0.0509900
\(990\) −1.41419 −0.0449459
\(991\) −15.1824 −0.482285 −0.241142 0.970490i \(-0.577522\pi\)
−0.241142 + 0.970490i \(0.577522\pi\)
\(992\) 28.6317 0.909057
\(993\) −7.12901 −0.226232
\(994\) 42.0237 1.33291
\(995\) −2.46607 −0.0781797
\(996\) 18.3273 0.580724
\(997\) −32.3155 −1.02344 −0.511721 0.859152i \(-0.670992\pi\)
−0.511721 + 0.859152i \(0.670992\pi\)
\(998\) 9.36503 0.296445
\(999\) 17.6838 0.559492
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 \(a_p\))