Properties

Label 8043.2.a.t.1.13
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.64173 q^{2}\) \(-1.00000 q^{3}\) \(+0.695293 q^{4}\) \(+0.237832 q^{5}\) \(+1.64173 q^{6}\) \(+1.00000 q^{7}\) \(+2.14198 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.64173 q^{2}\) \(-1.00000 q^{3}\) \(+0.695293 q^{4}\) \(+0.237832 q^{5}\) \(+1.64173 q^{6}\) \(+1.00000 q^{7}\) \(+2.14198 q^{8}\) \(+1.00000 q^{9}\) \(-0.390457 q^{10}\) \(+5.78104 q^{11}\) \(-0.695293 q^{12}\) \(-2.25763 q^{13}\) \(-1.64173 q^{14}\) \(-0.237832 q^{15}\) \(-4.90715 q^{16}\) \(+1.36602 q^{17}\) \(-1.64173 q^{18}\) \(-1.08935 q^{19}\) \(+0.165363 q^{20}\) \(-1.00000 q^{21}\) \(-9.49094 q^{22}\) \(+8.19746 q^{23}\) \(-2.14198 q^{24}\) \(-4.94344 q^{25}\) \(+3.70643 q^{26}\) \(-1.00000 q^{27}\) \(+0.695293 q^{28}\) \(+4.22185 q^{29}\) \(+0.390457 q^{30}\) \(-2.42770 q^{31}\) \(+3.77228 q^{32}\) \(-5.78104 q^{33}\) \(-2.24264 q^{34}\) \(+0.237832 q^{35}\) \(+0.695293 q^{36}\) \(-1.97831 q^{37}\) \(+1.78842 q^{38}\) \(+2.25763 q^{39}\) \(+0.509432 q^{40}\) \(+4.27690 q^{41}\) \(+1.64173 q^{42}\) \(+4.64096 q^{43}\) \(+4.01952 q^{44}\) \(+0.237832 q^{45}\) \(-13.4581 q^{46}\) \(-2.78914 q^{47}\) \(+4.90715 q^{48}\) \(+1.00000 q^{49}\) \(+8.11581 q^{50}\) \(-1.36602 q^{51}\) \(-1.56971 q^{52}\) \(+4.58089 q^{53}\) \(+1.64173 q^{54}\) \(+1.37492 q^{55}\) \(+2.14198 q^{56}\) \(+1.08935 q^{57}\) \(-6.93115 q^{58}\) \(+2.07593 q^{59}\) \(-0.165363 q^{60}\) \(-2.14607 q^{61}\) \(+3.98564 q^{62}\) \(+1.00000 q^{63}\) \(+3.62123 q^{64}\) \(-0.536937 q^{65}\) \(+9.49094 q^{66}\) \(+7.93805 q^{67}\) \(+0.949783 q^{68}\) \(-8.19746 q^{69}\) \(-0.390457 q^{70}\) \(-1.57991 q^{71}\) \(+2.14198 q^{72}\) \(+9.02206 q^{73}\) \(+3.24786 q^{74}\) \(+4.94344 q^{75}\) \(-0.757417 q^{76}\) \(+5.78104 q^{77}\) \(-3.70643 q^{78}\) \(+8.22828 q^{79}\) \(-1.16708 q^{80}\) \(+1.00000 q^{81}\) \(-7.02154 q^{82}\) \(+2.94888 q^{83}\) \(-0.695293 q^{84}\) \(+0.324883 q^{85}\) \(-7.61923 q^{86}\) \(-4.22185 q^{87}\) \(+12.3829 q^{88}\) \(-2.57906 q^{89}\) \(-0.390457 q^{90}\) \(-2.25763 q^{91}\) \(+5.69964 q^{92}\) \(+2.42770 q^{93}\) \(+4.57903 q^{94}\) \(-0.259082 q^{95}\) \(-3.77228 q^{96}\) \(-5.87142 q^{97}\) \(-1.64173 q^{98}\) \(+5.78104 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64173 −1.16088 −0.580441 0.814302i \(-0.697120\pi\)
−0.580441 + 0.814302i \(0.697120\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.695293 0.347646
\(5\) 0.237832 0.106362 0.0531808 0.998585i \(-0.483064\pi\)
0.0531808 + 0.998585i \(0.483064\pi\)
\(6\) 1.64173 0.670235
\(7\) 1.00000 0.377964
\(8\) 2.14198 0.757305
\(9\) 1.00000 0.333333
\(10\) −0.390457 −0.123473
\(11\) 5.78104 1.74305 0.871525 0.490352i \(-0.163132\pi\)
0.871525 + 0.490352i \(0.163132\pi\)
\(12\) −0.695293 −0.200714
\(13\) −2.25763 −0.626154 −0.313077 0.949728i \(-0.601360\pi\)
−0.313077 + 0.949728i \(0.601360\pi\)
\(14\) −1.64173 −0.438772
\(15\) −0.237832 −0.0614079
\(16\) −4.90715 −1.22679
\(17\) 1.36602 0.331308 0.165654 0.986184i \(-0.447026\pi\)
0.165654 + 0.986184i \(0.447026\pi\)
\(18\) −1.64173 −0.386961
\(19\) −1.08935 −0.249914 −0.124957 0.992162i \(-0.539879\pi\)
−0.124957 + 0.992162i \(0.539879\pi\)
\(20\) 0.165363 0.0369763
\(21\) −1.00000 −0.218218
\(22\) −9.49094 −2.02347
\(23\) 8.19746 1.70929 0.854644 0.519214i \(-0.173775\pi\)
0.854644 + 0.519214i \(0.173775\pi\)
\(24\) −2.14198 −0.437230
\(25\) −4.94344 −0.988687
\(26\) 3.70643 0.726891
\(27\) −1.00000 −0.192450
\(28\) 0.695293 0.131398
\(29\) 4.22185 0.783977 0.391989 0.919970i \(-0.371787\pi\)
0.391989 + 0.919970i \(0.371787\pi\)
\(30\) 0.390457 0.0712874
\(31\) −2.42770 −0.436028 −0.218014 0.975946i \(-0.569958\pi\)
−0.218014 + 0.975946i \(0.569958\pi\)
\(32\) 3.77228 0.666851
\(33\) −5.78104 −1.00635
\(34\) −2.24264 −0.384610
\(35\) 0.237832 0.0402009
\(36\) 0.695293 0.115882
\(37\) −1.97831 −0.325232 −0.162616 0.986689i \(-0.551993\pi\)
−0.162616 + 0.986689i \(0.551993\pi\)
\(38\) 1.78842 0.290121
\(39\) 2.25763 0.361510
\(40\) 0.509432 0.0805483
\(41\) 4.27690 0.667940 0.333970 0.942584i \(-0.391612\pi\)
0.333970 + 0.942584i \(0.391612\pi\)
\(42\) 1.64173 0.253325
\(43\) 4.64096 0.707740 0.353870 0.935295i \(-0.384865\pi\)
0.353870 + 0.935295i \(0.384865\pi\)
\(44\) 4.01952 0.605965
\(45\) 0.237832 0.0354539
\(46\) −13.4581 −1.98428
\(47\) −2.78914 −0.406838 −0.203419 0.979092i \(-0.565205\pi\)
−0.203419 + 0.979092i \(0.565205\pi\)
\(48\) 4.90715 0.708287
\(49\) 1.00000 0.142857
\(50\) 8.11581 1.14775
\(51\) −1.36602 −0.191281
\(52\) −1.56971 −0.217680
\(53\) 4.58089 0.629234 0.314617 0.949219i \(-0.398124\pi\)
0.314617 + 0.949219i \(0.398124\pi\)
\(54\) 1.64173 0.223412
\(55\) 1.37492 0.185394
\(56\) 2.14198 0.286235
\(57\) 1.08935 0.144288
\(58\) −6.93115 −0.910105
\(59\) 2.07593 0.270263 0.135131 0.990828i \(-0.456854\pi\)
0.135131 + 0.990828i \(0.456854\pi\)
\(60\) −0.165363 −0.0213483
\(61\) −2.14607 −0.274776 −0.137388 0.990517i \(-0.543871\pi\)
−0.137388 + 0.990517i \(0.543871\pi\)
\(62\) 3.98564 0.506177
\(63\) 1.00000 0.125988
\(64\) 3.62123 0.452653
\(65\) −0.536937 −0.0665988
\(66\) 9.49094 1.16825
\(67\) 7.93805 0.969787 0.484893 0.874573i \(-0.338858\pi\)
0.484893 + 0.874573i \(0.338858\pi\)
\(68\) 0.949783 0.115178
\(69\) −8.19746 −0.986858
\(70\) −0.390457 −0.0466685
\(71\) −1.57991 −0.187501 −0.0937503 0.995596i \(-0.529886\pi\)
−0.0937503 + 0.995596i \(0.529886\pi\)
\(72\) 2.14198 0.252435
\(73\) 9.02206 1.05595 0.527976 0.849259i \(-0.322951\pi\)
0.527976 + 0.849259i \(0.322951\pi\)
\(74\) 3.24786 0.377556
\(75\) 4.94344 0.570819
\(76\) −0.757417 −0.0868817
\(77\) 5.78104 0.658811
\(78\) −3.70643 −0.419671
\(79\) 8.22828 0.925753 0.462877 0.886423i \(-0.346817\pi\)
0.462877 + 0.886423i \(0.346817\pi\)
\(80\) −1.16708 −0.130483
\(81\) 1.00000 0.111111
\(82\) −7.02154 −0.775399
\(83\) 2.94888 0.323682 0.161841 0.986817i \(-0.448257\pi\)
0.161841 + 0.986817i \(0.448257\pi\)
\(84\) −0.695293 −0.0758627
\(85\) 0.324883 0.0352385
\(86\) −7.61923 −0.821603
\(87\) −4.22185 −0.452629
\(88\) 12.3829 1.32002
\(89\) −2.57906 −0.273379 −0.136690 0.990614i \(-0.543646\pi\)
−0.136690 + 0.990614i \(0.543646\pi\)
\(90\) −0.390457 −0.0411578
\(91\) −2.25763 −0.236664
\(92\) 5.69964 0.594228
\(93\) 2.42770 0.251741
\(94\) 4.57903 0.472291
\(95\) −0.259082 −0.0265813
\(96\) −3.77228 −0.385007
\(97\) −5.87142 −0.596152 −0.298076 0.954542i \(-0.596345\pi\)
−0.298076 + 0.954542i \(0.596345\pi\)
\(98\) −1.64173 −0.165840
\(99\) 5.78104 0.581016
\(100\) −3.43714 −0.343714
\(101\) −2.77484 −0.276107 −0.138053 0.990425i \(-0.544085\pi\)
−0.138053 + 0.990425i \(0.544085\pi\)
\(102\) 2.24264 0.222055
\(103\) −4.20839 −0.414665 −0.207333 0.978270i \(-0.566478\pi\)
−0.207333 + 0.978270i \(0.566478\pi\)
\(104\) −4.83581 −0.474190
\(105\) −0.237832 −0.0232100
\(106\) −7.52061 −0.730466
\(107\) 4.66666 0.451143 0.225572 0.974227i \(-0.427575\pi\)
0.225572 + 0.974227i \(0.427575\pi\)
\(108\) −0.695293 −0.0669046
\(109\) 4.78502 0.458322 0.229161 0.973389i \(-0.426402\pi\)
0.229161 + 0.973389i \(0.426402\pi\)
\(110\) −2.25725 −0.215220
\(111\) 1.97831 0.187773
\(112\) −4.90715 −0.463682
\(113\) −8.17744 −0.769268 −0.384634 0.923069i \(-0.625672\pi\)
−0.384634 + 0.923069i \(0.625672\pi\)
\(114\) −1.78842 −0.167501
\(115\) 1.94962 0.181803
\(116\) 2.93542 0.272547
\(117\) −2.25763 −0.208718
\(118\) −3.40812 −0.313743
\(119\) 1.36602 0.125223
\(120\) −0.509432 −0.0465046
\(121\) 22.4204 2.03822
\(122\) 3.52327 0.318982
\(123\) −4.27690 −0.385635
\(124\) −1.68796 −0.151584
\(125\) −2.36487 −0.211520
\(126\) −1.64173 −0.146257
\(127\) 17.2615 1.53171 0.765855 0.643014i \(-0.222316\pi\)
0.765855 + 0.643014i \(0.222316\pi\)
\(128\) −13.4897 −1.19233
\(129\) −4.64096 −0.408614
\(130\) 0.881508 0.0773134
\(131\) 11.4196 0.997733 0.498866 0.866679i \(-0.333750\pi\)
0.498866 + 0.866679i \(0.333750\pi\)
\(132\) −4.01952 −0.349854
\(133\) −1.08935 −0.0944586
\(134\) −13.0322 −1.12581
\(135\) −0.237832 −0.0204693
\(136\) 2.92599 0.250902
\(137\) −10.8164 −0.924108 −0.462054 0.886852i \(-0.652887\pi\)
−0.462054 + 0.886852i \(0.652887\pi\)
\(138\) 13.4581 1.14563
\(139\) 22.6325 1.91967 0.959833 0.280574i \(-0.0905247\pi\)
0.959833 + 0.280574i \(0.0905247\pi\)
\(140\) 0.165363 0.0139757
\(141\) 2.78914 0.234888
\(142\) 2.59379 0.217666
\(143\) −13.0515 −1.09142
\(144\) −4.90715 −0.408929
\(145\) 1.00409 0.0833851
\(146\) −14.8118 −1.22584
\(147\) −1.00000 −0.0824786
\(148\) −1.37550 −0.113066
\(149\) −22.8771 −1.87417 −0.937084 0.349105i \(-0.886486\pi\)
−0.937084 + 0.349105i \(0.886486\pi\)
\(150\) −8.11581 −0.662653
\(151\) 18.5290 1.50787 0.753935 0.656949i \(-0.228153\pi\)
0.753935 + 0.656949i \(0.228153\pi\)
\(152\) −2.33337 −0.189261
\(153\) 1.36602 0.110436
\(154\) −9.49094 −0.764801
\(155\) −0.577385 −0.0463767
\(156\) 1.56971 0.125678
\(157\) −18.4086 −1.46916 −0.734582 0.678520i \(-0.762622\pi\)
−0.734582 + 0.678520i \(0.762622\pi\)
\(158\) −13.5086 −1.07469
\(159\) −4.58089 −0.363288
\(160\) 0.897168 0.0709274
\(161\) 8.19746 0.646050
\(162\) −1.64173 −0.128987
\(163\) −10.7594 −0.842744 −0.421372 0.906888i \(-0.638451\pi\)
−0.421372 + 0.906888i \(0.638451\pi\)
\(164\) 2.97370 0.232207
\(165\) −1.37492 −0.107037
\(166\) −4.84129 −0.375757
\(167\) 6.47908 0.501366 0.250683 0.968069i \(-0.419345\pi\)
0.250683 + 0.968069i \(0.419345\pi\)
\(168\) −2.14198 −0.165258
\(169\) −7.90310 −0.607931
\(170\) −0.533372 −0.0409077
\(171\) −1.08935 −0.0833047
\(172\) 3.22683 0.246043
\(173\) 20.7885 1.58052 0.790259 0.612774i \(-0.209946\pi\)
0.790259 + 0.612774i \(0.209946\pi\)
\(174\) 6.93115 0.525449
\(175\) −4.94344 −0.373689
\(176\) −28.3685 −2.13835
\(177\) −2.07593 −0.156036
\(178\) 4.23413 0.317361
\(179\) 9.63053 0.719819 0.359910 0.932987i \(-0.382807\pi\)
0.359910 + 0.932987i \(0.382807\pi\)
\(180\) 0.165363 0.0123254
\(181\) −7.91612 −0.588401 −0.294200 0.955744i \(-0.595053\pi\)
−0.294200 + 0.955744i \(0.595053\pi\)
\(182\) 3.70643 0.274739
\(183\) 2.14607 0.158642
\(184\) 17.5588 1.29445
\(185\) −0.470505 −0.0345922
\(186\) −3.98564 −0.292242
\(187\) 7.89701 0.577487
\(188\) −1.93927 −0.141436
\(189\) −1.00000 −0.0727393
\(190\) 0.425344 0.0308577
\(191\) −2.05238 −0.148505 −0.0742526 0.997239i \(-0.523657\pi\)
−0.0742526 + 0.997239i \(0.523657\pi\)
\(192\) −3.62123 −0.261340
\(193\) 14.1555 1.01894 0.509469 0.860489i \(-0.329842\pi\)
0.509469 + 0.860489i \(0.329842\pi\)
\(194\) 9.63931 0.692062
\(195\) 0.536937 0.0384509
\(196\) 0.695293 0.0496638
\(197\) −1.36118 −0.0969803 −0.0484901 0.998824i \(-0.515441\pi\)
−0.0484901 + 0.998824i \(0.515441\pi\)
\(198\) −9.49094 −0.674491
\(199\) −23.4644 −1.66334 −0.831672 0.555267i \(-0.812616\pi\)
−0.831672 + 0.555267i \(0.812616\pi\)
\(200\) −10.5888 −0.748738
\(201\) −7.93805 −0.559907
\(202\) 4.55555 0.320528
\(203\) 4.22185 0.296316
\(204\) −0.949783 −0.0664981
\(205\) 1.01718 0.0710432
\(206\) 6.90907 0.481378
\(207\) 8.19746 0.569763
\(208\) 11.0785 0.768159
\(209\) −6.29758 −0.435612
\(210\) 0.390457 0.0269441
\(211\) −27.3996 −1.88626 −0.943132 0.332419i \(-0.892135\pi\)
−0.943132 + 0.332419i \(0.892135\pi\)
\(212\) 3.18506 0.218751
\(213\) 1.57991 0.108254
\(214\) −7.66142 −0.523724
\(215\) 1.10377 0.0752765
\(216\) −2.14198 −0.145743
\(217\) −2.42770 −0.164803
\(218\) −7.85573 −0.532057
\(219\) −9.02206 −0.609654
\(220\) 0.955969 0.0644514
\(221\) −3.08397 −0.207450
\(222\) −3.24786 −0.217982
\(223\) −2.53124 −0.169505 −0.0847523 0.996402i \(-0.527010\pi\)
−0.0847523 + 0.996402i \(0.527010\pi\)
\(224\) 3.77228 0.252046
\(225\) −4.94344 −0.329562
\(226\) 13.4252 0.893030
\(227\) −27.0352 −1.79439 −0.897195 0.441635i \(-0.854399\pi\)
−0.897195 + 0.441635i \(0.854399\pi\)
\(228\) 0.757417 0.0501612
\(229\) −6.76803 −0.447244 −0.223622 0.974676i \(-0.571788\pi\)
−0.223622 + 0.974676i \(0.571788\pi\)
\(230\) −3.20076 −0.211052
\(231\) −5.78104 −0.380365
\(232\) 9.04312 0.593710
\(233\) 1.85586 0.121581 0.0607907 0.998151i \(-0.480638\pi\)
0.0607907 + 0.998151i \(0.480638\pi\)
\(234\) 3.70643 0.242297
\(235\) −0.663346 −0.0432719
\(236\) 1.44338 0.0939558
\(237\) −8.22828 −0.534484
\(238\) −2.24264 −0.145369
\(239\) −9.15287 −0.592050 −0.296025 0.955180i \(-0.595661\pi\)
−0.296025 + 0.955180i \(0.595661\pi\)
\(240\) 1.16708 0.0753346
\(241\) 2.21622 0.142759 0.0713796 0.997449i \(-0.477260\pi\)
0.0713796 + 0.997449i \(0.477260\pi\)
\(242\) −36.8084 −2.36613
\(243\) −1.00000 −0.0641500
\(244\) −1.49215 −0.0955248
\(245\) 0.237832 0.0151945
\(246\) 7.02154 0.447677
\(247\) 2.45935 0.156485
\(248\) −5.20010 −0.330206
\(249\) −2.94888 −0.186878
\(250\) 3.88248 0.245550
\(251\) −2.11671 −0.133605 −0.0668027 0.997766i \(-0.521280\pi\)
−0.0668027 + 0.997766i \(0.521280\pi\)
\(252\) 0.695293 0.0437993
\(253\) 47.3899 2.97937
\(254\) −28.3388 −1.77813
\(255\) −0.324883 −0.0203450
\(256\) 14.9040 0.931498
\(257\) −19.8853 −1.24041 −0.620205 0.784440i \(-0.712951\pi\)
−0.620205 + 0.784440i \(0.712951\pi\)
\(258\) 7.61923 0.474353
\(259\) −1.97831 −0.122926
\(260\) −0.373328 −0.0231528
\(261\) 4.22185 0.261326
\(262\) −18.7479 −1.15825
\(263\) 9.06635 0.559055 0.279527 0.960138i \(-0.409822\pi\)
0.279527 + 0.960138i \(0.409822\pi\)
\(264\) −12.3829 −0.762114
\(265\) 1.08948 0.0669264
\(266\) 1.78842 0.109655
\(267\) 2.57906 0.157836
\(268\) 5.51927 0.337143
\(269\) −0.433491 −0.0264304 −0.0132152 0.999913i \(-0.504207\pi\)
−0.0132152 + 0.999913i \(0.504207\pi\)
\(270\) 0.390457 0.0237625
\(271\) −14.7685 −0.897124 −0.448562 0.893752i \(-0.648064\pi\)
−0.448562 + 0.893752i \(0.648064\pi\)
\(272\) −6.70327 −0.406445
\(273\) 2.25763 0.136638
\(274\) 17.7577 1.07278
\(275\) −28.5782 −1.72333
\(276\) −5.69964 −0.343078
\(277\) 9.88525 0.593947 0.296974 0.954886i \(-0.404023\pi\)
0.296974 + 0.954886i \(0.404023\pi\)
\(278\) −37.1566 −2.22850
\(279\) −2.42770 −0.145343
\(280\) 0.509432 0.0304444
\(281\) 17.6017 1.05003 0.525014 0.851094i \(-0.324060\pi\)
0.525014 + 0.851094i \(0.324060\pi\)
\(282\) −4.57903 −0.272677
\(283\) −16.9893 −1.00991 −0.504954 0.863146i \(-0.668491\pi\)
−0.504954 + 0.863146i \(0.668491\pi\)
\(284\) −1.09850 −0.0651839
\(285\) 0.259082 0.0153467
\(286\) 21.4270 1.26701
\(287\) 4.27690 0.252458
\(288\) 3.77228 0.222284
\(289\) −15.1340 −0.890235
\(290\) −1.64845 −0.0968003
\(291\) 5.87142 0.344189
\(292\) 6.27297 0.367098
\(293\) −2.27390 −0.132843 −0.0664214 0.997792i \(-0.521158\pi\)
−0.0664214 + 0.997792i \(0.521158\pi\)
\(294\) 1.64173 0.0957479
\(295\) 0.493722 0.0287456
\(296\) −4.23750 −0.246300
\(297\) −5.78104 −0.335450
\(298\) 37.5582 2.17569
\(299\) −18.5068 −1.07028
\(300\) 3.43714 0.198443
\(301\) 4.64096 0.267501
\(302\) −30.4197 −1.75046
\(303\) 2.77484 0.159410
\(304\) 5.34561 0.306592
\(305\) −0.510403 −0.0292256
\(306\) −2.24264 −0.128203
\(307\) 0.926766 0.0528933 0.0264467 0.999650i \(-0.491581\pi\)
0.0264467 + 0.999650i \(0.491581\pi\)
\(308\) 4.01952 0.229033
\(309\) 4.20839 0.239407
\(310\) 0.947913 0.0538379
\(311\) 28.9611 1.64223 0.821117 0.570760i \(-0.193351\pi\)
0.821117 + 0.570760i \(0.193351\pi\)
\(312\) 4.83581 0.273774
\(313\) −3.57283 −0.201948 −0.100974 0.994889i \(-0.532196\pi\)
−0.100974 + 0.994889i \(0.532196\pi\)
\(314\) 30.2220 1.70553
\(315\) 0.237832 0.0134003
\(316\) 5.72106 0.321835
\(317\) 3.05312 0.171481 0.0857403 0.996318i \(-0.472674\pi\)
0.0857403 + 0.996318i \(0.472674\pi\)
\(318\) 7.52061 0.421735
\(319\) 24.4067 1.36651
\(320\) 0.861244 0.0481450
\(321\) −4.66666 −0.260468
\(322\) −13.4581 −0.749988
\(323\) −1.48807 −0.0827986
\(324\) 0.695293 0.0386274
\(325\) 11.1605 0.619071
\(326\) 17.6641 0.978326
\(327\) −4.78502 −0.264612
\(328\) 9.16105 0.505834
\(329\) −2.78914 −0.153770
\(330\) 2.25725 0.124257
\(331\) −13.2567 −0.728655 −0.364327 0.931271i \(-0.618701\pi\)
−0.364327 + 0.931271i \(0.618701\pi\)
\(332\) 2.05034 0.112527
\(333\) −1.97831 −0.108411
\(334\) −10.6369 −0.582027
\(335\) 1.88792 0.103148
\(336\) 4.90715 0.267707
\(337\) 13.8112 0.752344 0.376172 0.926550i \(-0.377240\pi\)
0.376172 + 0.926550i \(0.377240\pi\)
\(338\) 12.9748 0.705736
\(339\) 8.17744 0.444137
\(340\) 0.225889 0.0122505
\(341\) −14.0346 −0.760019
\(342\) 1.78842 0.0967069
\(343\) 1.00000 0.0539949
\(344\) 9.94087 0.535976
\(345\) −1.94962 −0.104964
\(346\) −34.1291 −1.83479
\(347\) 27.0004 1.44946 0.724730 0.689033i \(-0.241965\pi\)
0.724730 + 0.689033i \(0.241965\pi\)
\(348\) −2.93542 −0.157355
\(349\) 8.00928 0.428727 0.214363 0.976754i \(-0.431232\pi\)
0.214363 + 0.976754i \(0.431232\pi\)
\(350\) 8.11581 0.433808
\(351\) 2.25763 0.120503
\(352\) 21.8077 1.16235
\(353\) 11.4012 0.606826 0.303413 0.952859i \(-0.401874\pi\)
0.303413 + 0.952859i \(0.401874\pi\)
\(354\) 3.40812 0.181140
\(355\) −0.375753 −0.0199429
\(356\) −1.79320 −0.0950394
\(357\) −1.36602 −0.0722974
\(358\) −15.8108 −0.835625
\(359\) 15.6374 0.825310 0.412655 0.910887i \(-0.364602\pi\)
0.412655 + 0.910887i \(0.364602\pi\)
\(360\) 0.509432 0.0268494
\(361\) −17.8133 −0.937543
\(362\) 12.9962 0.683064
\(363\) −22.4204 −1.17677
\(364\) −1.56971 −0.0822754
\(365\) 2.14573 0.112313
\(366\) −3.52327 −0.184164
\(367\) 25.4077 1.32627 0.663136 0.748499i \(-0.269225\pi\)
0.663136 + 0.748499i \(0.269225\pi\)
\(368\) −40.2262 −2.09694
\(369\) 4.27690 0.222647
\(370\) 0.772444 0.0401575
\(371\) 4.58089 0.237828
\(372\) 1.68796 0.0875168
\(373\) 8.30425 0.429978 0.214989 0.976617i \(-0.431028\pi\)
0.214989 + 0.976617i \(0.431028\pi\)
\(374\) −12.9648 −0.670394
\(375\) 2.36487 0.122121
\(376\) −5.97429 −0.308100
\(377\) −9.53137 −0.490891
\(378\) 1.64173 0.0844417
\(379\) −8.20219 −0.421318 −0.210659 0.977560i \(-0.567561\pi\)
−0.210659 + 0.977560i \(0.567561\pi\)
\(380\) −0.180138 −0.00924089
\(381\) −17.2615 −0.884333
\(382\) 3.36947 0.172397
\(383\) −1.00000 −0.0510976
\(384\) 13.4897 0.688391
\(385\) 1.37492 0.0700722
\(386\) −23.2396 −1.18287
\(387\) 4.64096 0.235913
\(388\) −4.08235 −0.207250
\(389\) 32.8469 1.66541 0.832703 0.553720i \(-0.186792\pi\)
0.832703 + 0.553720i \(0.186792\pi\)
\(390\) −0.881508 −0.0446369
\(391\) 11.1979 0.566302
\(392\) 2.14198 0.108186
\(393\) −11.4196 −0.576041
\(394\) 2.23470 0.112583
\(395\) 1.95695 0.0984647
\(396\) 4.01952 0.201988
\(397\) −6.05116 −0.303699 −0.151850 0.988404i \(-0.548523\pi\)
−0.151850 + 0.988404i \(0.548523\pi\)
\(398\) 38.5223 1.93095
\(399\) 1.08935 0.0545357
\(400\) 24.2582 1.21291
\(401\) −39.2333 −1.95922 −0.979608 0.200918i \(-0.935607\pi\)
−0.979608 + 0.200918i \(0.935607\pi\)
\(402\) 13.0322 0.649986
\(403\) 5.48086 0.273021
\(404\) −1.92933 −0.0959876
\(405\) 0.237832 0.0118180
\(406\) −6.93115 −0.343987
\(407\) −11.4367 −0.566895
\(408\) −2.92599 −0.144858
\(409\) 5.53149 0.273515 0.136757 0.990605i \(-0.456332\pi\)
0.136757 + 0.990605i \(0.456332\pi\)
\(410\) −1.66995 −0.0824728
\(411\) 10.8164 0.533534
\(412\) −2.92607 −0.144157
\(413\) 2.07593 0.102150
\(414\) −13.4581 −0.661427
\(415\) 0.701339 0.0344274
\(416\) −8.51641 −0.417552
\(417\) −22.6325 −1.10832
\(418\) 10.3390 0.505695
\(419\) −32.6458 −1.59485 −0.797425 0.603418i \(-0.793805\pi\)
−0.797425 + 0.603418i \(0.793805\pi\)
\(420\) −0.165363 −0.00806888
\(421\) −8.43878 −0.411281 −0.205641 0.978628i \(-0.565928\pi\)
−0.205641 + 0.978628i \(0.565928\pi\)
\(422\) 44.9828 2.18973
\(423\) −2.78914 −0.135613
\(424\) 9.81219 0.476522
\(425\) −6.75283 −0.327560
\(426\) −2.59379 −0.125670
\(427\) −2.14607 −0.103855
\(428\) 3.24470 0.156838
\(429\) 13.0515 0.630130
\(430\) −1.81210 −0.0873871
\(431\) 6.86425 0.330639 0.165320 0.986240i \(-0.447134\pi\)
0.165320 + 0.986240i \(0.447134\pi\)
\(432\) 4.90715 0.236096
\(433\) 26.5261 1.27476 0.637381 0.770549i \(-0.280018\pi\)
0.637381 + 0.770549i \(0.280018\pi\)
\(434\) 3.98564 0.191317
\(435\) −1.00409 −0.0481424
\(436\) 3.32699 0.159334
\(437\) −8.92991 −0.427175
\(438\) 14.8118 0.707736
\(439\) 39.6901 1.89431 0.947153 0.320784i \(-0.103946\pi\)
0.947153 + 0.320784i \(0.103946\pi\)
\(440\) 2.94505 0.140400
\(441\) 1.00000 0.0476190
\(442\) 5.06306 0.240825
\(443\) 6.52266 0.309901 0.154950 0.987922i \(-0.450478\pi\)
0.154950 + 0.987922i \(0.450478\pi\)
\(444\) 1.37550 0.0652785
\(445\) −0.613382 −0.0290771
\(446\) 4.15563 0.196775
\(447\) 22.8771 1.08205
\(448\) 3.62123 0.171087
\(449\) 24.5161 1.15698 0.578492 0.815688i \(-0.303641\pi\)
0.578492 + 0.815688i \(0.303641\pi\)
\(450\) 8.11581 0.382583
\(451\) 24.7249 1.16425
\(452\) −5.68571 −0.267433
\(453\) −18.5290 −0.870569
\(454\) 44.3846 2.08307
\(455\) −0.536937 −0.0251720
\(456\) 2.33337 0.109270
\(457\) −40.0070 −1.87145 −0.935723 0.352735i \(-0.885252\pi\)
−0.935723 + 0.352735i \(0.885252\pi\)
\(458\) 11.1113 0.519197
\(459\) −1.36602 −0.0637603
\(460\) 1.35556 0.0632031
\(461\) −28.2518 −1.31582 −0.657908 0.753098i \(-0.728558\pi\)
−0.657908 + 0.753098i \(0.728558\pi\)
\(462\) 9.49094 0.441558
\(463\) −0.0447845 −0.00208131 −0.00104066 0.999999i \(-0.500331\pi\)
−0.00104066 + 0.999999i \(0.500331\pi\)
\(464\) −20.7173 −0.961774
\(465\) 0.577385 0.0267756
\(466\) −3.04683 −0.141142
\(467\) 25.4153 1.17608 0.588040 0.808832i \(-0.299900\pi\)
0.588040 + 0.808832i \(0.299900\pi\)
\(468\) −1.56971 −0.0725601
\(469\) 7.93805 0.366545
\(470\) 1.08904 0.0502336
\(471\) 18.4086 0.848222
\(472\) 4.44660 0.204671
\(473\) 26.8296 1.23363
\(474\) 13.5086 0.620473
\(475\) 5.38513 0.247087
\(476\) 0.949783 0.0435332
\(477\) 4.58089 0.209745
\(478\) 15.0266 0.687300
\(479\) −34.4517 −1.57414 −0.787070 0.616864i \(-0.788403\pi\)
−0.787070 + 0.616864i \(0.788403\pi\)
\(480\) −0.897168 −0.0409499
\(481\) 4.46629 0.203645
\(482\) −3.63844 −0.165726
\(483\) −8.19746 −0.372997
\(484\) 15.5888 0.708580
\(485\) −1.39641 −0.0634077
\(486\) 1.64173 0.0744706
\(487\) 14.4934 0.656760 0.328380 0.944546i \(-0.393497\pi\)
0.328380 + 0.944546i \(0.393497\pi\)
\(488\) −4.59684 −0.208089
\(489\) 10.7594 0.486558
\(490\) −0.390457 −0.0176390
\(491\) 13.5744 0.612604 0.306302 0.951934i \(-0.400908\pi\)
0.306302 + 0.951934i \(0.400908\pi\)
\(492\) −2.97370 −0.134065
\(493\) 5.76712 0.259738
\(494\) −4.03760 −0.181660
\(495\) 1.37492 0.0617979
\(496\) 11.9131 0.534914
\(497\) −1.57991 −0.0708686
\(498\) 4.84129 0.216943
\(499\) 22.9928 1.02930 0.514649 0.857401i \(-0.327922\pi\)
0.514649 + 0.857401i \(0.327922\pi\)
\(500\) −1.64427 −0.0735342
\(501\) −6.47908 −0.289464
\(502\) 3.47507 0.155100
\(503\) 37.3508 1.66539 0.832694 0.553733i \(-0.186797\pi\)
0.832694 + 0.553733i \(0.186797\pi\)
\(504\) 2.14198 0.0954115
\(505\) −0.659946 −0.0293672
\(506\) −77.8016 −3.45870
\(507\) 7.90310 0.350989
\(508\) 12.0018 0.532493
\(509\) −29.8651 −1.32375 −0.661875 0.749614i \(-0.730239\pi\)
−0.661875 + 0.749614i \(0.730239\pi\)
\(510\) 0.533372 0.0236181
\(511\) 9.02206 0.399112
\(512\) 2.51093 0.110969
\(513\) 1.08935 0.0480960
\(514\) 32.6464 1.43997
\(515\) −1.00089 −0.0441045
\(516\) −3.22683 −0.142053
\(517\) −16.1241 −0.709138
\(518\) 3.24786 0.142703
\(519\) −20.7885 −0.912512
\(520\) −1.15011 −0.0504357
\(521\) −16.8500 −0.738214 −0.369107 0.929387i \(-0.620336\pi\)
−0.369107 + 0.929387i \(0.620336\pi\)
\(522\) −6.93115 −0.303368
\(523\) −29.5296 −1.29124 −0.645620 0.763659i \(-0.723401\pi\)
−0.645620 + 0.763659i \(0.723401\pi\)
\(524\) 7.93995 0.346858
\(525\) 4.94344 0.215749
\(526\) −14.8845 −0.648997
\(527\) −3.31629 −0.144460
\(528\) 28.3685 1.23458
\(529\) 44.1984 1.92167
\(530\) −1.78864 −0.0776936
\(531\) 2.07593 0.0900875
\(532\) −0.757417 −0.0328382
\(533\) −9.65567 −0.418233
\(534\) −4.23413 −0.183229
\(535\) 1.10988 0.0479844
\(536\) 17.0032 0.734425
\(537\) −9.63053 −0.415588
\(538\) 0.711677 0.0306826
\(539\) 5.78104 0.249007
\(540\) −0.165363 −0.00711608
\(541\) −13.5892 −0.584244 −0.292122 0.956381i \(-0.594361\pi\)
−0.292122 + 0.956381i \(0.594361\pi\)
\(542\) 24.2460 1.04146
\(543\) 7.91612 0.339713
\(544\) 5.15300 0.220933
\(545\) 1.13803 0.0487479
\(546\) −3.70643 −0.158621
\(547\) 10.0767 0.430847 0.215424 0.976521i \(-0.430887\pi\)
0.215424 + 0.976521i \(0.430887\pi\)
\(548\) −7.52057 −0.321263
\(549\) −2.14607 −0.0915919
\(550\) 46.9178 2.00058
\(551\) −4.59907 −0.195927
\(552\) −17.5588 −0.747353
\(553\) 8.22828 0.349902
\(554\) −16.2290 −0.689503
\(555\) 0.470505 0.0199718
\(556\) 15.7362 0.667365
\(557\) 39.7523 1.68436 0.842179 0.539198i \(-0.181273\pi\)
0.842179 + 0.539198i \(0.181273\pi\)
\(558\) 3.98564 0.168726
\(559\) −10.4776 −0.443155
\(560\) −1.16708 −0.0493180
\(561\) −7.89701 −0.333412
\(562\) −28.8973 −1.21896
\(563\) 24.7189 1.04178 0.520889 0.853625i \(-0.325601\pi\)
0.520889 + 0.853625i \(0.325601\pi\)
\(564\) 1.93927 0.0816579
\(565\) −1.94486 −0.0818207
\(566\) 27.8919 1.17238
\(567\) 1.00000 0.0419961
\(568\) −3.38414 −0.141995
\(569\) 3.43028 0.143805 0.0719024 0.997412i \(-0.477093\pi\)
0.0719024 + 0.997412i \(0.477093\pi\)
\(570\) −0.425344 −0.0178157
\(571\) −14.3960 −0.602452 −0.301226 0.953553i \(-0.597396\pi\)
−0.301226 + 0.953553i \(0.597396\pi\)
\(572\) −9.07459 −0.379428
\(573\) 2.05238 0.0857396
\(574\) −7.02154 −0.293073
\(575\) −40.5236 −1.68995
\(576\) 3.62123 0.150884
\(577\) −30.5189 −1.27052 −0.635260 0.772299i \(-0.719107\pi\)
−0.635260 + 0.772299i \(0.719107\pi\)
\(578\) 24.8460 1.03346
\(579\) −14.1555 −0.588284
\(580\) 0.698137 0.0289885
\(581\) 2.94888 0.122340
\(582\) −9.63931 −0.399562
\(583\) 26.4823 1.09679
\(584\) 19.3251 0.799678
\(585\) −0.536937 −0.0221996
\(586\) 3.73314 0.154215
\(587\) 42.0285 1.73470 0.867350 0.497698i \(-0.165821\pi\)
0.867350 + 0.497698i \(0.165821\pi\)
\(588\) −0.695293 −0.0286734
\(589\) 2.64462 0.108970
\(590\) −0.810560 −0.0333702
\(591\) 1.36118 0.0559916
\(592\) 9.70786 0.398991
\(593\) −9.97632 −0.409678 −0.204839 0.978796i \(-0.565667\pi\)
−0.204839 + 0.978796i \(0.565667\pi\)
\(594\) 9.49094 0.389418
\(595\) 0.324883 0.0133189
\(596\) −15.9063 −0.651548
\(597\) 23.4644 0.960333
\(598\) 30.3833 1.24247
\(599\) 36.0274 1.47204 0.736020 0.676960i \(-0.236703\pi\)
0.736020 + 0.676960i \(0.236703\pi\)
\(600\) 10.5888 0.432284
\(601\) 5.63556 0.229879 0.114940 0.993372i \(-0.463333\pi\)
0.114940 + 0.993372i \(0.463333\pi\)
\(602\) −7.61923 −0.310537
\(603\) 7.93805 0.323262
\(604\) 12.8831 0.524206
\(605\) 5.33230 0.216789
\(606\) −4.55555 −0.185057
\(607\) −39.4141 −1.59977 −0.799885 0.600153i \(-0.795106\pi\)
−0.799885 + 0.600153i \(0.795106\pi\)
\(608\) −4.10933 −0.166655
\(609\) −4.22185 −0.171078
\(610\) 0.837947 0.0339275
\(611\) 6.29685 0.254743
\(612\) 0.949783 0.0383927
\(613\) 16.4373 0.663897 0.331949 0.943297i \(-0.392294\pi\)
0.331949 + 0.943297i \(0.392294\pi\)
\(614\) −1.52150 −0.0614029
\(615\) −1.01718 −0.0410168
\(616\) 12.3829 0.498921
\(617\) −24.7027 −0.994492 −0.497246 0.867610i \(-0.665655\pi\)
−0.497246 + 0.867610i \(0.665655\pi\)
\(618\) −6.90907 −0.277923
\(619\) 23.2597 0.934885 0.467443 0.884023i \(-0.345175\pi\)
0.467443 + 0.884023i \(0.345175\pi\)
\(620\) −0.401452 −0.0161227
\(621\) −8.19746 −0.328953
\(622\) −47.5465 −1.90644
\(623\) −2.57906 −0.103328
\(624\) −11.0785 −0.443497
\(625\) 24.1547 0.966190
\(626\) 5.86564 0.234438
\(627\) 6.29758 0.251501
\(628\) −12.7994 −0.510750
\(629\) −2.70241 −0.107752
\(630\) −0.390457 −0.0155562
\(631\) −2.08624 −0.0830519 −0.0415260 0.999137i \(-0.513222\pi\)
−0.0415260 + 0.999137i \(0.513222\pi\)
\(632\) 17.6248 0.701078
\(633\) 27.3996 1.08903
\(634\) −5.01242 −0.199069
\(635\) 4.10533 0.162915
\(636\) −3.18506 −0.126296
\(637\) −2.25763 −0.0894506
\(638\) −40.0693 −1.58636
\(639\) −1.57991 −0.0625002
\(640\) −3.20827 −0.126818
\(641\) 26.0119 1.02741 0.513704 0.857968i \(-0.328273\pi\)
0.513704 + 0.857968i \(0.328273\pi\)
\(642\) 7.66142 0.302372
\(643\) −29.1598 −1.14995 −0.574975 0.818171i \(-0.694988\pi\)
−0.574975 + 0.818171i \(0.694988\pi\)
\(644\) 5.69964 0.224597
\(645\) −1.10377 −0.0434609
\(646\) 2.44302 0.0961194
\(647\) −9.26412 −0.364210 −0.182105 0.983279i \(-0.558291\pi\)
−0.182105 + 0.983279i \(0.558291\pi\)
\(648\) 2.14198 0.0841450
\(649\) 12.0010 0.471081
\(650\) −18.3225 −0.718668
\(651\) 2.42770 0.0951491
\(652\) −7.48095 −0.292977
\(653\) 5.52170 0.216081 0.108041 0.994146i \(-0.465542\pi\)
0.108041 + 0.994146i \(0.465542\pi\)
\(654\) 7.85573 0.307183
\(655\) 2.71594 0.106121
\(656\) −20.9874 −0.819421
\(657\) 9.02206 0.351984
\(658\) 4.57903 0.178509
\(659\) −13.8918 −0.541147 −0.270573 0.962699i \(-0.587213\pi\)
−0.270573 + 0.962699i \(0.587213\pi\)
\(660\) −0.955969 −0.0372111
\(661\) 18.1436 0.705703 0.352852 0.935679i \(-0.385212\pi\)
0.352852 + 0.935679i \(0.385212\pi\)
\(662\) 21.7640 0.845882
\(663\) 3.08397 0.119771
\(664\) 6.31646 0.245126
\(665\) −0.259082 −0.0100468
\(666\) 3.24786 0.125852
\(667\) 34.6084 1.34004
\(668\) 4.50486 0.174298
\(669\) 2.53124 0.0978635
\(670\) −3.09947 −0.119743
\(671\) −12.4065 −0.478948
\(672\) −3.77228 −0.145519
\(673\) 11.3744 0.438452 0.219226 0.975674i \(-0.429647\pi\)
0.219226 + 0.975674i \(0.429647\pi\)
\(674\) −22.6743 −0.873383
\(675\) 4.94344 0.190273
\(676\) −5.49497 −0.211345
\(677\) 24.4944 0.941397 0.470699 0.882294i \(-0.344002\pi\)
0.470699 + 0.882294i \(0.344002\pi\)
\(678\) −13.4252 −0.515591
\(679\) −5.87142 −0.225324
\(680\) 0.695894 0.0266863
\(681\) 27.0352 1.03599
\(682\) 23.0412 0.882292
\(683\) −9.63629 −0.368722 −0.184361 0.982859i \(-0.559022\pi\)
−0.184361 + 0.982859i \(0.559022\pi\)
\(684\) −0.757417 −0.0289606
\(685\) −2.57249 −0.0982896
\(686\) −1.64173 −0.0626817
\(687\) 6.76803 0.258216
\(688\) −22.7739 −0.868248
\(689\) −10.3420 −0.393998
\(690\) 3.20076 0.121851
\(691\) −15.0802 −0.573679 −0.286839 0.957979i \(-0.592605\pi\)
−0.286839 + 0.957979i \(0.592605\pi\)
\(692\) 14.4541 0.549461
\(693\) 5.78104 0.219604
\(694\) −44.3276 −1.68265
\(695\) 5.38274 0.204179
\(696\) −9.04312 −0.342779
\(697\) 5.84233 0.221294
\(698\) −13.1491 −0.497701
\(699\) −1.85586 −0.0701950
\(700\) −3.43714 −0.129912
\(701\) 26.2730 0.992317 0.496158 0.868232i \(-0.334744\pi\)
0.496158 + 0.868232i \(0.334744\pi\)
\(702\) −3.70643 −0.139890
\(703\) 2.15507 0.0812800
\(704\) 20.9345 0.788997
\(705\) 0.663346 0.0249831
\(706\) −18.7178 −0.704453
\(707\) −2.77484 −0.104359
\(708\) −1.44338 −0.0542454
\(709\) −14.4530 −0.542792 −0.271396 0.962468i \(-0.587485\pi\)
−0.271396 + 0.962468i \(0.587485\pi\)
\(710\) 0.616886 0.0231513
\(711\) 8.22828 0.308584
\(712\) −5.52429 −0.207032
\(713\) −19.9010 −0.745298
\(714\) 2.24264 0.0839287
\(715\) −3.10405 −0.116085
\(716\) 6.69604 0.250243
\(717\) 9.15287 0.341820
\(718\) −25.6725 −0.958087
\(719\) −12.6577 −0.472051 −0.236026 0.971747i \(-0.575845\pi\)
−0.236026 + 0.971747i \(0.575845\pi\)
\(720\) −1.16708 −0.0434944
\(721\) −4.20839 −0.156729
\(722\) 29.2447 1.08838
\(723\) −2.21622 −0.0824220
\(724\) −5.50402 −0.204555
\(725\) −20.8704 −0.775108
\(726\) 36.8084 1.36609
\(727\) 18.4504 0.684287 0.342143 0.939648i \(-0.388847\pi\)
0.342143 + 0.939648i \(0.388847\pi\)
\(728\) −4.83581 −0.179227
\(729\) 1.00000 0.0370370
\(730\) −3.52272 −0.130382
\(731\) 6.33964 0.234480
\(732\) 1.49215 0.0551513
\(733\) 0.491812 0.0181655 0.00908275 0.999959i \(-0.497109\pi\)
0.00908275 + 0.999959i \(0.497109\pi\)
\(734\) −41.7127 −1.53964
\(735\) −0.237832 −0.00877256
\(736\) 30.9231 1.13984
\(737\) 45.8902 1.69039
\(738\) −7.02154 −0.258466
\(739\) −10.5570 −0.388344 −0.194172 0.980967i \(-0.562202\pi\)
−0.194172 + 0.980967i \(0.562202\pi\)
\(740\) −0.327139 −0.0120259
\(741\) −2.45935 −0.0903465
\(742\) −7.52061 −0.276090
\(743\) 3.77989 0.138671 0.0693354 0.997593i \(-0.477912\pi\)
0.0693354 + 0.997593i \(0.477912\pi\)
\(744\) 5.20010 0.190645
\(745\) −5.44091 −0.199340
\(746\) −13.6334 −0.499153
\(747\) 2.94888 0.107894
\(748\) 5.49074 0.200761
\(749\) 4.66666 0.170516
\(750\) −3.88248 −0.141768
\(751\) −31.8886 −1.16363 −0.581815 0.813321i \(-0.697657\pi\)
−0.581815 + 0.813321i \(0.697657\pi\)
\(752\) 13.6867 0.499104
\(753\) 2.11671 0.0771371
\(754\) 15.6480 0.569866
\(755\) 4.40679 0.160380
\(756\) −0.695293 −0.0252876
\(757\) −29.7429 −1.08102 −0.540512 0.841336i \(-0.681769\pi\)
−0.540512 + 0.841336i \(0.681769\pi\)
\(758\) 13.4658 0.489101
\(759\) −47.3899 −1.72014
\(760\) −0.554950 −0.0201301
\(761\) −14.3994 −0.521978 −0.260989 0.965342i \(-0.584049\pi\)
−0.260989 + 0.965342i \(0.584049\pi\)
\(762\) 28.3388 1.02661
\(763\) 4.78502 0.173229
\(764\) −1.42701 −0.0516273
\(765\) 0.324883 0.0117462
\(766\) 1.64173 0.0593183
\(767\) −4.68668 −0.169226
\(768\) −14.9040 −0.537801
\(769\) 6.53624 0.235703 0.117851 0.993031i \(-0.462399\pi\)
0.117851 + 0.993031i \(0.462399\pi\)
\(770\) −2.25725 −0.0813456
\(771\) 19.8853 0.716151
\(772\) 9.84224 0.354230
\(773\) 0.894761 0.0321823 0.0160912 0.999871i \(-0.494878\pi\)
0.0160912 + 0.999871i \(0.494878\pi\)
\(774\) −7.61923 −0.273868
\(775\) 12.0012 0.431095
\(776\) −12.5765 −0.451469
\(777\) 1.97831 0.0709714
\(778\) −53.9260 −1.93334
\(779\) −4.65904 −0.166928
\(780\) 0.373328 0.0133673
\(781\) −9.13351 −0.326823
\(782\) −18.3840 −0.657409
\(783\) −4.22185 −0.150876
\(784\) −4.90715 −0.175255
\(785\) −4.37815 −0.156263
\(786\) 18.7479 0.668716
\(787\) 43.6054 1.55436 0.777182 0.629275i \(-0.216648\pi\)
0.777182 + 0.629275i \(0.216648\pi\)
\(788\) −0.946421 −0.0337148
\(789\) −9.06635 −0.322771
\(790\) −3.21279 −0.114306
\(791\) −8.17744 −0.290756
\(792\) 12.3829 0.440007
\(793\) 4.84503 0.172052
\(794\) 9.93441 0.352559
\(795\) −1.08948 −0.0386400
\(796\) −16.3146 −0.578256
\(797\) −21.8603 −0.774333 −0.387166 0.922010i \(-0.626546\pi\)
−0.387166 + 0.922010i \(0.626546\pi\)
\(798\) −1.78842 −0.0633095
\(799\) −3.81002 −0.134789
\(800\) −18.6480 −0.659307
\(801\) −2.57906 −0.0911265
\(802\) 64.4106 2.27442
\(803\) 52.1569 1.84058
\(804\) −5.51927 −0.194650
\(805\) 1.94962 0.0687150
\(806\) −8.99811 −0.316945
\(807\) 0.433491 0.0152596
\(808\) −5.94366 −0.209097
\(809\) 16.4303 0.577658 0.288829 0.957381i \(-0.406734\pi\)
0.288829 + 0.957381i \(0.406734\pi\)
\(810\) −0.390457 −0.0137193
\(811\) 9.27313 0.325623 0.162812 0.986657i \(-0.447944\pi\)
0.162812 + 0.986657i \(0.447944\pi\)
\(812\) 2.93542 0.103013
\(813\) 14.7685 0.517955
\(814\) 18.7760 0.658098
\(815\) −2.55894 −0.0896356
\(816\) 6.70327 0.234661
\(817\) −5.05563 −0.176874
\(818\) −9.08124 −0.317518
\(819\) −2.25763 −0.0788880
\(820\) 0.707241 0.0246979
\(821\) −11.1906 −0.390554 −0.195277 0.980748i \(-0.562561\pi\)
−0.195277 + 0.980748i \(0.562561\pi\)
\(822\) −17.7577 −0.619370
\(823\) 6.95247 0.242348 0.121174 0.992631i \(-0.461334\pi\)
0.121174 + 0.992631i \(0.461334\pi\)
\(824\) −9.01431 −0.314028
\(825\) 28.5782 0.994965
\(826\) −3.40812 −0.118584
\(827\) −25.9722 −0.903142 −0.451571 0.892235i \(-0.649136\pi\)
−0.451571 + 0.892235i \(0.649136\pi\)
\(828\) 5.69964 0.198076
\(829\) 44.4629 1.54426 0.772131 0.635464i \(-0.219191\pi\)
0.772131 + 0.635464i \(0.219191\pi\)
\(830\) −1.15141 −0.0399661
\(831\) −9.88525 −0.342916
\(832\) −8.17540 −0.283431
\(833\) 1.36602 0.0473298
\(834\) 37.1566 1.28663
\(835\) 1.54093 0.0533262
\(836\) −4.37866 −0.151439
\(837\) 2.42770 0.0839137
\(838\) 53.5957 1.85143
\(839\) −42.0751 −1.45259 −0.726296 0.687382i \(-0.758760\pi\)
−0.726296 + 0.687382i \(0.758760\pi\)
\(840\) −0.509432 −0.0175771
\(841\) −11.1760 −0.385380
\(842\) 13.8542 0.477449
\(843\) −17.6017 −0.606234
\(844\) −19.0507 −0.655753
\(845\) −1.87961 −0.0646605
\(846\) 4.57903 0.157430
\(847\) 22.4204 0.770375
\(848\) −22.4791 −0.771937
\(849\) 16.9893 0.583071
\(850\) 11.0864 0.380259
\(851\) −16.2171 −0.555915
\(852\) 1.09850 0.0376339
\(853\) 22.3841 0.766418 0.383209 0.923662i \(-0.374819\pi\)
0.383209 + 0.923662i \(0.374819\pi\)
\(854\) 3.52327 0.120564
\(855\) −0.259082 −0.00886043
\(856\) 9.99591 0.341653
\(857\) 49.7405 1.69910 0.849552 0.527505i \(-0.176872\pi\)
0.849552 + 0.527505i \(0.176872\pi\)
\(858\) −21.4270 −0.731507
\(859\) −6.12407 −0.208951 −0.104475 0.994527i \(-0.533316\pi\)
−0.104475 + 0.994527i \(0.533316\pi\)
\(860\) 0.767443 0.0261696
\(861\) −4.27690 −0.145756
\(862\) −11.2693 −0.383833
\(863\) −39.6564 −1.34992 −0.674959 0.737855i \(-0.735839\pi\)
−0.674959 + 0.737855i \(0.735839\pi\)
\(864\) −3.77228 −0.128336
\(865\) 4.94416 0.168106
\(866\) −43.5488 −1.47985
\(867\) 15.1340 0.513977
\(868\) −1.68796 −0.0572932
\(869\) 47.5680 1.61363
\(870\) 1.64845 0.0558877
\(871\) −17.9212 −0.607236
\(872\) 10.2494 0.347089
\(873\) −5.87142 −0.198717
\(874\) 14.6605 0.495900
\(875\) −2.36487 −0.0799471
\(876\) −6.27297 −0.211944
\(877\) 49.0629 1.65674 0.828369 0.560183i \(-0.189269\pi\)
0.828369 + 0.560183i \(0.189269\pi\)
\(878\) −65.1606 −2.19906
\(879\) 2.27390 0.0766968
\(880\) −6.74693 −0.227439
\(881\) 8.89268 0.299602 0.149801 0.988716i \(-0.452137\pi\)
0.149801 + 0.988716i \(0.452137\pi\)
\(882\) −1.64173 −0.0552801
\(883\) 55.8572 1.87974 0.939872 0.341528i \(-0.110944\pi\)
0.939872 + 0.341528i \(0.110944\pi\)
\(884\) −2.14426 −0.0721193
\(885\) −0.493722 −0.0165963
\(886\) −10.7085 −0.359758
\(887\) 16.3919 0.550387 0.275193 0.961389i \(-0.411258\pi\)
0.275193 + 0.961389i \(0.411258\pi\)
\(888\) 4.23750 0.142201
\(889\) 17.2615 0.578932
\(890\) 1.00701 0.0337551
\(891\) 5.78104 0.193672
\(892\) −1.75995 −0.0589276
\(893\) 3.03835 0.101674
\(894\) −37.5582 −1.25613
\(895\) 2.29045 0.0765612
\(896\) −13.4897 −0.450658
\(897\) 18.5068 0.617926
\(898\) −40.2489 −1.34312
\(899\) −10.2494 −0.341836
\(900\) −3.43714 −0.114571
\(901\) 6.25759 0.208470
\(902\) −40.5918 −1.35156
\(903\) −4.64096 −0.154442
\(904\) −17.5159 −0.582571
\(905\) −1.88271 −0.0625833
\(906\) 30.4197 1.01063
\(907\) 31.3764 1.04184 0.520918 0.853607i \(-0.325590\pi\)
0.520918 + 0.853607i \(0.325590\pi\)
\(908\) −18.7974 −0.623813
\(909\) −2.77484 −0.0920356
\(910\) 0.881508 0.0292217
\(911\) −4.11265 −0.136258 −0.0681292 0.997677i \(-0.521703\pi\)
−0.0681292 + 0.997677i \(0.521703\pi\)
\(912\) −5.34561 −0.177011
\(913\) 17.0476 0.564194
\(914\) 65.6808 2.17253
\(915\) 0.510403 0.0168734
\(916\) −4.70576 −0.155483
\(917\) 11.4196 0.377108
\(918\) 2.24264 0.0740182
\(919\) −7.62239 −0.251439 −0.125720 0.992066i \(-0.540124\pi\)
−0.125720 + 0.992066i \(0.540124\pi\)
\(920\) 4.17605 0.137680
\(921\) −0.926766 −0.0305380
\(922\) 46.3819 1.52751
\(923\) 3.56685 0.117404
\(924\) −4.01952 −0.132232
\(925\) 9.77964 0.321552
\(926\) 0.0735243 0.00241616
\(927\) −4.20839 −0.138222
\(928\) 15.9260 0.522796
\(929\) 52.6591 1.72769 0.863845 0.503758i \(-0.168050\pi\)
0.863845 + 0.503758i \(0.168050\pi\)
\(930\) −0.947913 −0.0310833
\(931\) −1.08935 −0.0357020
\(932\) 1.29037 0.0422673
\(933\) −28.9611 −0.948144
\(934\) −41.7252 −1.36529
\(935\) 1.87816 0.0614225
\(936\) −4.83581 −0.158063
\(937\) 25.4912 0.832760 0.416380 0.909191i \(-0.363299\pi\)
0.416380 + 0.909191i \(0.363299\pi\)
\(938\) −13.0322 −0.425515
\(939\) 3.57283 0.116595
\(940\) −0.461220 −0.0150433
\(941\) −45.8401 −1.49434 −0.747172 0.664631i \(-0.768589\pi\)
−0.747172 + 0.664631i \(0.768589\pi\)
\(942\) −30.2220 −0.984686
\(943\) 35.0597 1.14170
\(944\) −10.1869 −0.331555
\(945\) −0.237832 −0.00773667
\(946\) −44.0471 −1.43209
\(947\) −10.4076 −0.338202 −0.169101 0.985599i \(-0.554086\pi\)
−0.169101 + 0.985599i \(0.554086\pi\)
\(948\) −5.72106 −0.185811
\(949\) −20.3685 −0.661189
\(950\) −8.84096 −0.286839
\(951\) −3.05312 −0.0990043
\(952\) 2.92599 0.0948319
\(953\) −28.7135 −0.930120 −0.465060 0.885279i \(-0.653967\pi\)
−0.465060 + 0.885279i \(0.653967\pi\)
\(954\) −7.52061 −0.243489
\(955\) −0.488122 −0.0157953
\(956\) −6.36392 −0.205824
\(957\) −24.4067 −0.788956
\(958\) 56.5606 1.82739
\(959\) −10.8164 −0.349280
\(960\) −0.861244 −0.0277965
\(961\) −25.1063 −0.809879
\(962\) −7.33246 −0.236408
\(963\) 4.66666 0.150381
\(964\) 1.54092 0.0496297
\(965\) 3.36664 0.108376
\(966\) 13.4581 0.433006
\(967\) 43.2551 1.39099 0.695495 0.718530i \(-0.255185\pi\)
0.695495 + 0.718530i \(0.255185\pi\)
\(968\) 48.0242 1.54356
\(969\) 1.48807 0.0478038
\(970\) 2.29254 0.0736089
\(971\) 34.8729 1.11912 0.559562 0.828788i \(-0.310969\pi\)
0.559562 + 0.828788i \(0.310969\pi\)
\(972\) −0.695293 −0.0223015
\(973\) 22.6325 0.725565
\(974\) −23.7944 −0.762421
\(975\) −11.1605 −0.357421
\(976\) 10.5311 0.337092
\(977\) 19.6616 0.629031 0.314515 0.949252i \(-0.398158\pi\)
0.314515 + 0.949252i \(0.398158\pi\)
\(978\) −17.6641 −0.564837
\(979\) −14.9096 −0.476514
\(980\) 0.165363 0.00528232
\(981\) 4.78502 0.152774
\(982\) −22.2856 −0.711161
\(983\) 7.83129 0.249779 0.124890 0.992171i \(-0.460142\pi\)
0.124890 + 0.992171i \(0.460142\pi\)
\(984\) −9.16105 −0.292044
\(985\) −0.323733 −0.0103150
\(986\) −9.46809 −0.301525
\(987\) 2.78914 0.0887793
\(988\) 1.70997 0.0544014
\(989\) 38.0441 1.20973
\(990\) −2.25725 −0.0717400
\(991\) 2.12575 0.0675267 0.0337633 0.999430i \(-0.489251\pi\)
0.0337633 + 0.999430i \(0.489251\pi\)
\(992\) −9.15797 −0.290766
\(993\) 13.2567 0.420689
\(994\) 2.59379 0.0822700
\(995\) −5.58058 −0.176916
\(996\) −2.05034 −0.0649675
\(997\) 7.82010 0.247665 0.123832 0.992303i \(-0.460481\pi\)
0.123832 + 0.992303i \(0.460481\pi\)
\(998\) −37.7481 −1.19489
\(999\) 1.97831 0.0625909
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 \(a_p\))