Properties

Label 8043.2.a.t.1.8
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 1.8
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.95494 q^{2}\) \(-1.00000 q^{3}\) \(+1.82179 q^{4}\) \(-1.46647 q^{5}\) \(+1.95494 q^{6}\) \(+1.00000 q^{7}\) \(+0.348396 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.95494 q^{2}\) \(-1.00000 q^{3}\) \(+1.82179 q^{4}\) \(-1.46647 q^{5}\) \(+1.95494 q^{6}\) \(+1.00000 q^{7}\) \(+0.348396 q^{8}\) \(+1.00000 q^{9}\) \(+2.86686 q^{10}\) \(+0.940724 q^{11}\) \(-1.82179 q^{12}\) \(-5.06092 q^{13}\) \(-1.95494 q^{14}\) \(+1.46647 q^{15}\) \(-4.32467 q^{16}\) \(-2.26100 q^{17}\) \(-1.95494 q^{18}\) \(+0.999722 q^{19}\) \(-2.67160 q^{20}\) \(-1.00000 q^{21}\) \(-1.83906 q^{22}\) \(-6.50961 q^{23}\) \(-0.348396 q^{24}\) \(-2.84946 q^{25}\) \(+9.89378 q^{26}\) \(-1.00000 q^{27}\) \(+1.82179 q^{28}\) \(-3.46685 q^{29}\) \(-2.86686 q^{30}\) \(-6.78497 q^{31}\) \(+7.75767 q^{32}\) \(-0.940724 q^{33}\) \(+4.42012 q^{34}\) \(-1.46647 q^{35}\) \(+1.82179 q^{36}\) \(-2.02507 q^{37}\) \(-1.95440 q^{38}\) \(+5.06092 q^{39}\) \(-0.510913 q^{40}\) \(-11.1501 q^{41}\) \(+1.95494 q^{42}\) \(-3.65442 q^{43}\) \(+1.71380 q^{44}\) \(-1.46647 q^{45}\) \(+12.7259 q^{46}\) \(+3.37434 q^{47}\) \(+4.32467 q^{48}\) \(+1.00000 q^{49}\) \(+5.57053 q^{50}\) \(+2.26100 q^{51}\) \(-9.21991 q^{52}\) \(-4.27583 q^{53}\) \(+1.95494 q^{54}\) \(-1.37954 q^{55}\) \(+0.348396 q^{56}\) \(-0.999722 q^{57}\) \(+6.77749 q^{58}\) \(-12.2811 q^{59}\) \(+2.67160 q^{60}\) \(+1.16065 q^{61}\) \(+13.2642 q^{62}\) \(+1.00000 q^{63}\) \(-6.51643 q^{64}\) \(+7.42169 q^{65}\) \(+1.83906 q^{66}\) \(+10.2723 q^{67}\) \(-4.11906 q^{68}\) \(+6.50961 q^{69}\) \(+2.86686 q^{70}\) \(+2.38139 q^{71}\) \(+0.348396 q^{72}\) \(-13.8312 q^{73}\) \(+3.95889 q^{74}\) \(+2.84946 q^{75}\) \(+1.82128 q^{76}\) \(+0.940724 q^{77}\) \(-9.89378 q^{78}\) \(+8.72222 q^{79}\) \(+6.34200 q^{80}\) \(+1.00000 q^{81}\) \(+21.7977 q^{82}\) \(-2.92312 q^{83}\) \(-1.82179 q^{84}\) \(+3.31569 q^{85}\) \(+7.14416 q^{86}\) \(+3.46685 q^{87}\) \(+0.327745 q^{88}\) \(-14.5404 q^{89}\) \(+2.86686 q^{90}\) \(-5.06092 q^{91}\) \(-11.8591 q^{92}\) \(+6.78497 q^{93}\) \(-6.59663 q^{94}\) \(-1.46606 q^{95}\) \(-7.75767 q^{96}\) \(+11.4502 q^{97}\) \(-1.95494 q^{98}\) \(+0.940724 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95494 −1.38235 −0.691175 0.722687i \(-0.742907\pi\)
−0.691175 + 0.722687i \(0.742907\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.82179 0.910893
\(5\) −1.46647 −0.655826 −0.327913 0.944708i \(-0.606345\pi\)
−0.327913 + 0.944708i \(0.606345\pi\)
\(6\) 1.95494 0.798101
\(7\) 1.00000 0.377964
\(8\) 0.348396 0.123177
\(9\) 1.00000 0.333333
\(10\) 2.86686 0.906581
\(11\) 0.940724 0.283639 0.141819 0.989893i \(-0.454705\pi\)
0.141819 + 0.989893i \(0.454705\pi\)
\(12\) −1.82179 −0.525904
\(13\) −5.06092 −1.40365 −0.701823 0.712351i \(-0.747630\pi\)
−0.701823 + 0.712351i \(0.747630\pi\)
\(14\) −1.95494 −0.522479
\(15\) 1.46647 0.378641
\(16\) −4.32467 −1.08117
\(17\) −2.26100 −0.548373 −0.274187 0.961677i \(-0.588409\pi\)
−0.274187 + 0.961677i \(0.588409\pi\)
\(18\) −1.95494 −0.460784
\(19\) 0.999722 0.229352 0.114676 0.993403i \(-0.463417\pi\)
0.114676 + 0.993403i \(0.463417\pi\)
\(20\) −2.67160 −0.597387
\(21\) −1.00000 −0.218218
\(22\) −1.83906 −0.392088
\(23\) −6.50961 −1.35735 −0.678674 0.734440i \(-0.737445\pi\)
−0.678674 + 0.734440i \(0.737445\pi\)
\(24\) −0.348396 −0.0711161
\(25\) −2.84946 −0.569892
\(26\) 9.89378 1.94033
\(27\) −1.00000 −0.192450
\(28\) 1.82179 0.344285
\(29\) −3.46685 −0.643779 −0.321889 0.946777i \(-0.604318\pi\)
−0.321889 + 0.946777i \(0.604318\pi\)
\(30\) −2.86686 −0.523415
\(31\) −6.78497 −1.21862 −0.609308 0.792934i \(-0.708553\pi\)
−0.609308 + 0.792934i \(0.708553\pi\)
\(32\) 7.75767 1.37137
\(33\) −0.940724 −0.163759
\(34\) 4.42012 0.758044
\(35\) −1.46647 −0.247879
\(36\) 1.82179 0.303631
\(37\) −2.02507 −0.332920 −0.166460 0.986048i \(-0.553234\pi\)
−0.166460 + 0.986048i \(0.553234\pi\)
\(38\) −1.95440 −0.317045
\(39\) 5.06092 0.810395
\(40\) −0.510913 −0.0807825
\(41\) −11.1501 −1.74135 −0.870673 0.491862i \(-0.836316\pi\)
−0.870673 + 0.491862i \(0.836316\pi\)
\(42\) 1.95494 0.301654
\(43\) −3.65442 −0.557293 −0.278647 0.960394i \(-0.589886\pi\)
−0.278647 + 0.960394i \(0.589886\pi\)
\(44\) 1.71380 0.258365
\(45\) −1.46647 −0.218609
\(46\) 12.7259 1.87633
\(47\) 3.37434 0.492198 0.246099 0.969245i \(-0.420851\pi\)
0.246099 + 0.969245i \(0.420851\pi\)
\(48\) 4.32467 0.624212
\(49\) 1.00000 0.142857
\(50\) 5.57053 0.787791
\(51\) 2.26100 0.316603
\(52\) −9.21991 −1.27857
\(53\) −4.27583 −0.587331 −0.293665 0.955908i \(-0.594875\pi\)
−0.293665 + 0.955908i \(0.594875\pi\)
\(54\) 1.95494 0.266034
\(55\) −1.37954 −0.186018
\(56\) 0.348396 0.0465564
\(57\) −0.999722 −0.132416
\(58\) 6.77749 0.889928
\(59\) −12.2811 −1.59887 −0.799434 0.600754i \(-0.794867\pi\)
−0.799434 + 0.600754i \(0.794867\pi\)
\(60\) 2.67160 0.344902
\(61\) 1.16065 0.148607 0.0743033 0.997236i \(-0.476327\pi\)
0.0743033 + 0.997236i \(0.476327\pi\)
\(62\) 13.2642 1.68456
\(63\) 1.00000 0.125988
\(64\) −6.51643 −0.814554
\(65\) 7.42169 0.920547
\(66\) 1.83906 0.226372
\(67\) 10.2723 1.25496 0.627481 0.778632i \(-0.284086\pi\)
0.627481 + 0.778632i \(0.284086\pi\)
\(68\) −4.11906 −0.499509
\(69\) 6.50961 0.783665
\(70\) 2.86686 0.342656
\(71\) 2.38139 0.282619 0.141309 0.989965i \(-0.454869\pi\)
0.141309 + 0.989965i \(0.454869\pi\)
\(72\) 0.348396 0.0410589
\(73\) −13.8312 −1.61882 −0.809410 0.587244i \(-0.800213\pi\)
−0.809410 + 0.587244i \(0.800213\pi\)
\(74\) 3.95889 0.460212
\(75\) 2.84946 0.329028
\(76\) 1.82128 0.208915
\(77\) 0.940724 0.107205
\(78\) −9.89378 −1.12025
\(79\) 8.72222 0.981326 0.490663 0.871349i \(-0.336755\pi\)
0.490663 + 0.871349i \(0.336755\pi\)
\(80\) 6.34200 0.709057
\(81\) 1.00000 0.111111
\(82\) 21.7977 2.40715
\(83\) −2.92312 −0.320854 −0.160427 0.987048i \(-0.551287\pi\)
−0.160427 + 0.987048i \(0.551287\pi\)
\(84\) −1.82179 −0.198773
\(85\) 3.31569 0.359637
\(86\) 7.14416 0.770375
\(87\) 3.46685 0.371686
\(88\) 0.327745 0.0349377
\(89\) −14.5404 −1.54127 −0.770637 0.637274i \(-0.780062\pi\)
−0.770637 + 0.637274i \(0.780062\pi\)
\(90\) 2.86686 0.302194
\(91\) −5.06092 −0.530528
\(92\) −11.8591 −1.23640
\(93\) 6.78497 0.703568
\(94\) −6.59663 −0.680391
\(95\) −1.46606 −0.150415
\(96\) −7.75767 −0.791764
\(97\) 11.4502 1.16260 0.581298 0.813691i \(-0.302545\pi\)
0.581298 + 0.813691i \(0.302545\pi\)
\(98\) −1.95494 −0.197479
\(99\) 0.940724 0.0945463
\(100\) −5.19111 −0.519111
\(101\) −1.17288 −0.116706 −0.0583530 0.998296i \(-0.518585\pi\)
−0.0583530 + 0.998296i \(0.518585\pi\)
\(102\) −4.42012 −0.437657
\(103\) −4.96745 −0.489457 −0.244729 0.969592i \(-0.578699\pi\)
−0.244729 + 0.969592i \(0.578699\pi\)
\(104\) −1.76321 −0.172897
\(105\) 1.46647 0.143113
\(106\) 8.35899 0.811897
\(107\) −2.93347 −0.283589 −0.141795 0.989896i \(-0.545287\pi\)
−0.141795 + 0.989896i \(0.545287\pi\)
\(108\) −1.82179 −0.175301
\(109\) 12.0323 1.15248 0.576242 0.817279i \(-0.304519\pi\)
0.576242 + 0.817279i \(0.304519\pi\)
\(110\) 2.69692 0.257142
\(111\) 2.02507 0.192211
\(112\) −4.32467 −0.408643
\(113\) 6.24653 0.587624 0.293812 0.955863i \(-0.405076\pi\)
0.293812 + 0.955863i \(0.405076\pi\)
\(114\) 1.95440 0.183046
\(115\) 9.54615 0.890183
\(116\) −6.31587 −0.586414
\(117\) −5.06092 −0.467882
\(118\) 24.0089 2.21020
\(119\) −2.26100 −0.207266
\(120\) 0.510913 0.0466398
\(121\) −10.1150 −0.919549
\(122\) −2.26901 −0.205426
\(123\) 11.1501 1.00537
\(124\) −12.3608 −1.11003
\(125\) 11.5110 1.02958
\(126\) −1.95494 −0.174160
\(127\) 18.1860 1.61375 0.806875 0.590723i \(-0.201157\pi\)
0.806875 + 0.590723i \(0.201157\pi\)
\(128\) −2.77611 −0.245375
\(129\) 3.65442 0.321754
\(130\) −14.5089 −1.27252
\(131\) −16.4153 −1.43421 −0.717104 0.696966i \(-0.754533\pi\)
−0.717104 + 0.696966i \(0.754533\pi\)
\(132\) −1.71380 −0.149167
\(133\) 0.999722 0.0866869
\(134\) −20.0817 −1.73480
\(135\) 1.46647 0.126214
\(136\) −0.787724 −0.0675468
\(137\) 8.89871 0.760268 0.380134 0.924931i \(-0.375878\pi\)
0.380134 + 0.924931i \(0.375878\pi\)
\(138\) −12.7259 −1.08330
\(139\) 12.1427 1.02993 0.514964 0.857212i \(-0.327805\pi\)
0.514964 + 0.857212i \(0.327805\pi\)
\(140\) −2.67160 −0.225791
\(141\) −3.37434 −0.284171
\(142\) −4.65546 −0.390678
\(143\) −4.76092 −0.398128
\(144\) −4.32467 −0.360389
\(145\) 5.08404 0.422207
\(146\) 27.0392 2.23778
\(147\) −1.00000 −0.0824786
\(148\) −3.68925 −0.303254
\(149\) −8.52571 −0.698453 −0.349227 0.937038i \(-0.613556\pi\)
−0.349227 + 0.937038i \(0.613556\pi\)
\(150\) −5.57053 −0.454831
\(151\) −0.344333 −0.0280214 −0.0140107 0.999902i \(-0.504460\pi\)
−0.0140107 + 0.999902i \(0.504460\pi\)
\(152\) 0.348300 0.0282508
\(153\) −2.26100 −0.182791
\(154\) −1.83906 −0.148195
\(155\) 9.94996 0.799200
\(156\) 9.21991 0.738184
\(157\) 11.2990 0.901756 0.450878 0.892586i \(-0.351111\pi\)
0.450878 + 0.892586i \(0.351111\pi\)
\(158\) −17.0514 −1.35654
\(159\) 4.27583 0.339095
\(160\) −11.3764 −0.899383
\(161\) −6.50961 −0.513029
\(162\) −1.95494 −0.153595
\(163\) −11.9852 −0.938753 −0.469377 0.882998i \(-0.655521\pi\)
−0.469377 + 0.882998i \(0.655521\pi\)
\(164\) −20.3130 −1.58618
\(165\) 1.37954 0.107397
\(166\) 5.71452 0.443533
\(167\) 5.74616 0.444651 0.222326 0.974972i \(-0.428635\pi\)
0.222326 + 0.974972i \(0.428635\pi\)
\(168\) −0.348396 −0.0268794
\(169\) 12.6129 0.970222
\(170\) −6.48197 −0.497145
\(171\) 0.999722 0.0764507
\(172\) −6.65757 −0.507635
\(173\) −8.70102 −0.661526 −0.330763 0.943714i \(-0.607306\pi\)
−0.330763 + 0.943714i \(0.607306\pi\)
\(174\) −6.77749 −0.513800
\(175\) −2.84946 −0.215399
\(176\) −4.06832 −0.306661
\(177\) 12.2811 0.923106
\(178\) 28.4255 2.13058
\(179\) −4.99206 −0.373124 −0.186562 0.982443i \(-0.559735\pi\)
−0.186562 + 0.982443i \(0.559735\pi\)
\(180\) −2.67160 −0.199129
\(181\) −16.3303 −1.21382 −0.606910 0.794771i \(-0.707591\pi\)
−0.606910 + 0.794771i \(0.707591\pi\)
\(182\) 9.89378 0.733376
\(183\) −1.16065 −0.0857980
\(184\) −2.26792 −0.167194
\(185\) 2.96971 0.218337
\(186\) −13.2642 −0.972578
\(187\) −2.12698 −0.155540
\(188\) 6.14733 0.448340
\(189\) −1.00000 −0.0727393
\(190\) 2.86607 0.207926
\(191\) 6.47927 0.468823 0.234412 0.972137i \(-0.424684\pi\)
0.234412 + 0.972137i \(0.424684\pi\)
\(192\) 6.51643 0.470283
\(193\) 1.34244 0.0966310 0.0483155 0.998832i \(-0.484615\pi\)
0.0483155 + 0.998832i \(0.484615\pi\)
\(194\) −22.3845 −1.60712
\(195\) −7.42169 −0.531478
\(196\) 1.82179 0.130128
\(197\) −24.8526 −1.77067 −0.885336 0.464952i \(-0.846071\pi\)
−0.885336 + 0.464952i \(0.846071\pi\)
\(198\) −1.83906 −0.130696
\(199\) 13.5146 0.958025 0.479013 0.877808i \(-0.340995\pi\)
0.479013 + 0.877808i \(0.340995\pi\)
\(200\) −0.992743 −0.0701975
\(201\) −10.2723 −0.724553
\(202\) 2.29291 0.161329
\(203\) −3.46685 −0.243325
\(204\) 4.11906 0.288392
\(205\) 16.3512 1.14202
\(206\) 9.71106 0.676601
\(207\) −6.50961 −0.452449
\(208\) 21.8868 1.51758
\(209\) 0.940462 0.0650532
\(210\) −2.86686 −0.197832
\(211\) −11.3459 −0.781085 −0.390543 0.920585i \(-0.627713\pi\)
−0.390543 + 0.920585i \(0.627713\pi\)
\(212\) −7.78965 −0.534996
\(213\) −2.38139 −0.163170
\(214\) 5.73476 0.392020
\(215\) 5.35910 0.365487
\(216\) −0.348396 −0.0237054
\(217\) −6.78497 −0.460594
\(218\) −23.5224 −1.59314
\(219\) 13.8312 0.934626
\(220\) −2.51323 −0.169442
\(221\) 11.4427 0.769722
\(222\) −3.95889 −0.265703
\(223\) −3.47833 −0.232926 −0.116463 0.993195i \(-0.537156\pi\)
−0.116463 + 0.993195i \(0.537156\pi\)
\(224\) 7.75767 0.518331
\(225\) −2.84946 −0.189964
\(226\) −12.2116 −0.812303
\(227\) 17.5596 1.16547 0.582737 0.812661i \(-0.301982\pi\)
0.582737 + 0.812661i \(0.301982\pi\)
\(228\) −1.82128 −0.120617
\(229\) −9.29845 −0.614459 −0.307230 0.951635i \(-0.599402\pi\)
−0.307230 + 0.951635i \(0.599402\pi\)
\(230\) −18.6621 −1.23055
\(231\) −0.940724 −0.0618951
\(232\) −1.20784 −0.0792986
\(233\) −22.8398 −1.49629 −0.748143 0.663538i \(-0.769054\pi\)
−0.748143 + 0.663538i \(0.769054\pi\)
\(234\) 9.89378 0.646777
\(235\) −4.94837 −0.322796
\(236\) −22.3736 −1.45640
\(237\) −8.72222 −0.566569
\(238\) 4.42012 0.286514
\(239\) 0.882131 0.0570603 0.0285302 0.999593i \(-0.490917\pi\)
0.0285302 + 0.999593i \(0.490917\pi\)
\(240\) −6.34200 −0.409374
\(241\) −12.1698 −0.783928 −0.391964 0.919981i \(-0.628204\pi\)
−0.391964 + 0.919981i \(0.628204\pi\)
\(242\) 19.7743 1.27114
\(243\) −1.00000 −0.0641500
\(244\) 2.11446 0.135365
\(245\) −1.46647 −0.0936894
\(246\) −21.7977 −1.38977
\(247\) −5.05951 −0.321929
\(248\) −2.36386 −0.150105
\(249\) 2.92312 0.185245
\(250\) −22.5033 −1.42324
\(251\) 11.5041 0.726133 0.363067 0.931763i \(-0.381730\pi\)
0.363067 + 0.931763i \(0.381730\pi\)
\(252\) 1.82179 0.114762
\(253\) −6.12374 −0.384996
\(254\) −35.5526 −2.23077
\(255\) −3.31569 −0.207637
\(256\) 18.4600 1.15375
\(257\) −13.9902 −0.872682 −0.436341 0.899781i \(-0.643726\pi\)
−0.436341 + 0.899781i \(0.643726\pi\)
\(258\) −7.14416 −0.444776
\(259\) −2.02507 −0.125832
\(260\) 13.5207 0.838520
\(261\) −3.46685 −0.214593
\(262\) 32.0908 1.98258
\(263\) −3.47715 −0.214410 −0.107205 0.994237i \(-0.534190\pi\)
−0.107205 + 0.994237i \(0.534190\pi\)
\(264\) −0.327745 −0.0201713
\(265\) 6.27038 0.385187
\(266\) −1.95440 −0.119832
\(267\) 14.5404 0.889855
\(268\) 18.7139 1.14314
\(269\) −20.4025 −1.24396 −0.621980 0.783033i \(-0.713671\pi\)
−0.621980 + 0.783033i \(0.713671\pi\)
\(270\) −2.86686 −0.174472
\(271\) −28.2484 −1.71597 −0.857983 0.513679i \(-0.828282\pi\)
−0.857983 + 0.513679i \(0.828282\pi\)
\(272\) 9.77807 0.592883
\(273\) 5.06092 0.306301
\(274\) −17.3964 −1.05096
\(275\) −2.68056 −0.161644
\(276\) 11.8591 0.713835
\(277\) −8.01304 −0.481457 −0.240728 0.970593i \(-0.577386\pi\)
−0.240728 + 0.970593i \(0.577386\pi\)
\(278\) −23.7382 −1.42372
\(279\) −6.78497 −0.406205
\(280\) −0.510913 −0.0305329
\(281\) 4.18120 0.249430 0.124715 0.992193i \(-0.460198\pi\)
0.124715 + 0.992193i \(0.460198\pi\)
\(282\) 6.59663 0.392824
\(283\) 23.6767 1.40743 0.703716 0.710481i \(-0.251523\pi\)
0.703716 + 0.710481i \(0.251523\pi\)
\(284\) 4.33838 0.257435
\(285\) 1.46606 0.0868421
\(286\) 9.30732 0.550353
\(287\) −11.1501 −0.658167
\(288\) 7.75767 0.457125
\(289\) −11.8879 −0.699287
\(290\) −9.93899 −0.583638
\(291\) −11.4502 −0.671225
\(292\) −25.1975 −1.47457
\(293\) −4.96299 −0.289941 −0.144971 0.989436i \(-0.546309\pi\)
−0.144971 + 0.989436i \(0.546309\pi\)
\(294\) 1.95494 0.114014
\(295\) 18.0099 1.04858
\(296\) −0.705528 −0.0410080
\(297\) −0.940724 −0.0545863
\(298\) 16.6672 0.965507
\(299\) 32.9446 1.90523
\(300\) 5.19111 0.299709
\(301\) −3.65442 −0.210637
\(302\) 0.673151 0.0387355
\(303\) 1.17288 0.0673803
\(304\) −4.32347 −0.247968
\(305\) −1.70207 −0.0974600
\(306\) 4.42012 0.252681
\(307\) 20.5415 1.17236 0.586181 0.810180i \(-0.300631\pi\)
0.586181 + 0.810180i \(0.300631\pi\)
\(308\) 1.71380 0.0976527
\(309\) 4.96745 0.282588
\(310\) −19.4516 −1.10477
\(311\) −14.1106 −0.800136 −0.400068 0.916485i \(-0.631013\pi\)
−0.400068 + 0.916485i \(0.631013\pi\)
\(312\) 1.76321 0.0998219
\(313\) 33.3060 1.88257 0.941283 0.337618i \(-0.109621\pi\)
0.941283 + 0.337618i \(0.109621\pi\)
\(314\) −22.0888 −1.24654
\(315\) −1.46647 −0.0826263
\(316\) 15.8900 0.893884
\(317\) −21.8091 −1.22492 −0.612459 0.790502i \(-0.709820\pi\)
−0.612459 + 0.790502i \(0.709820\pi\)
\(318\) −8.35899 −0.468749
\(319\) −3.26135 −0.182601
\(320\) 9.55616 0.534206
\(321\) 2.93347 0.163730
\(322\) 12.7259 0.709186
\(323\) −2.26037 −0.125770
\(324\) 1.82179 0.101210
\(325\) 14.4209 0.799927
\(326\) 23.4303 1.29769
\(327\) −12.0323 −0.665387
\(328\) −3.88464 −0.214493
\(329\) 3.37434 0.186033
\(330\) −2.69692 −0.148461
\(331\) 13.4444 0.738973 0.369486 0.929236i \(-0.379534\pi\)
0.369486 + 0.929236i \(0.379534\pi\)
\(332\) −5.32530 −0.292264
\(333\) −2.02507 −0.110973
\(334\) −11.2334 −0.614664
\(335\) −15.0640 −0.823036
\(336\) 4.32467 0.235930
\(337\) 19.6861 1.07237 0.536186 0.844100i \(-0.319864\pi\)
0.536186 + 0.844100i \(0.319864\pi\)
\(338\) −24.6574 −1.34119
\(339\) −6.24653 −0.339265
\(340\) 6.04048 0.327591
\(341\) −6.38278 −0.345647
\(342\) −1.95440 −0.105682
\(343\) 1.00000 0.0539949
\(344\) −1.27319 −0.0686456
\(345\) −9.54615 −0.513948
\(346\) 17.0100 0.914461
\(347\) 12.8226 0.688354 0.344177 0.938905i \(-0.388158\pi\)
0.344177 + 0.938905i \(0.388158\pi\)
\(348\) 6.31587 0.338566
\(349\) 5.75324 0.307964 0.153982 0.988074i \(-0.450790\pi\)
0.153982 + 0.988074i \(0.450790\pi\)
\(350\) 5.57053 0.297757
\(351\) 5.06092 0.270132
\(352\) 7.29782 0.388975
\(353\) 16.0578 0.854669 0.427335 0.904093i \(-0.359453\pi\)
0.427335 + 0.904093i \(0.359453\pi\)
\(354\) −24.0089 −1.27606
\(355\) −3.49223 −0.185349
\(356\) −26.4894 −1.40394
\(357\) 2.26100 0.119665
\(358\) 9.75917 0.515788
\(359\) 3.14721 0.166103 0.0830517 0.996545i \(-0.473533\pi\)
0.0830517 + 0.996545i \(0.473533\pi\)
\(360\) −0.510913 −0.0269275
\(361\) −18.0006 −0.947398
\(362\) 31.9247 1.67792
\(363\) 10.1150 0.530902
\(364\) −9.21991 −0.483255
\(365\) 20.2831 1.06166
\(366\) 2.26901 0.118603
\(367\) −8.21567 −0.428855 −0.214427 0.976740i \(-0.568788\pi\)
−0.214427 + 0.976740i \(0.568788\pi\)
\(368\) 28.1519 1.46752
\(369\) −11.1501 −0.580449
\(370\) −5.80560 −0.301819
\(371\) −4.27583 −0.221990
\(372\) 12.3608 0.640876
\(373\) −13.0096 −0.673612 −0.336806 0.941574i \(-0.609347\pi\)
−0.336806 + 0.941574i \(0.609347\pi\)
\(374\) 4.15811 0.215011
\(375\) −11.5110 −0.594426
\(376\) 1.17561 0.0606274
\(377\) 17.5455 0.903637
\(378\) 1.95494 0.100551
\(379\) 12.1158 0.622347 0.311173 0.950353i \(-0.399278\pi\)
0.311173 + 0.950353i \(0.399278\pi\)
\(380\) −2.67086 −0.137012
\(381\) −18.1860 −0.931699
\(382\) −12.6666 −0.648078
\(383\) −1.00000 −0.0510976
\(384\) 2.77611 0.141668
\(385\) −1.37954 −0.0703081
\(386\) −2.62439 −0.133578
\(387\) −3.65442 −0.185764
\(388\) 20.8599 1.05900
\(389\) −15.4354 −0.782604 −0.391302 0.920262i \(-0.627975\pi\)
−0.391302 + 0.920262i \(0.627975\pi\)
\(390\) 14.5089 0.734689
\(391\) 14.7182 0.744333
\(392\) 0.348396 0.0175967
\(393\) 16.4153 0.828040
\(394\) 48.5852 2.44769
\(395\) −12.7909 −0.643579
\(396\) 1.71380 0.0861216
\(397\) 14.5802 0.731759 0.365880 0.930662i \(-0.380768\pi\)
0.365880 + 0.930662i \(0.380768\pi\)
\(398\) −26.4202 −1.32433
\(399\) −0.999722 −0.0500487
\(400\) 12.3230 0.616149
\(401\) −8.42292 −0.420621 −0.210310 0.977635i \(-0.567447\pi\)
−0.210310 + 0.977635i \(0.567447\pi\)
\(402\) 20.0817 1.00159
\(403\) 34.3382 1.71051
\(404\) −2.13674 −0.106307
\(405\) −1.46647 −0.0728695
\(406\) 6.77749 0.336361
\(407\) −1.90503 −0.0944290
\(408\) 0.787724 0.0389982
\(409\) 2.32799 0.115112 0.0575559 0.998342i \(-0.481669\pi\)
0.0575559 + 0.998342i \(0.481669\pi\)
\(410\) −31.9657 −1.57867
\(411\) −8.89871 −0.438941
\(412\) −9.04963 −0.445843
\(413\) −12.2811 −0.604315
\(414\) 12.7259 0.625443
\(415\) 4.28667 0.210424
\(416\) −39.2609 −1.92492
\(417\) −12.1427 −0.594629
\(418\) −1.83855 −0.0899263
\(419\) −24.7529 −1.20926 −0.604630 0.796507i \(-0.706679\pi\)
−0.604630 + 0.796507i \(0.706679\pi\)
\(420\) 2.67160 0.130361
\(421\) 18.9269 0.922442 0.461221 0.887285i \(-0.347412\pi\)
0.461221 + 0.887285i \(0.347412\pi\)
\(422\) 22.1806 1.07973
\(423\) 3.37434 0.164066
\(424\) −1.48968 −0.0723455
\(425\) 6.44263 0.312514
\(426\) 4.65546 0.225558
\(427\) 1.16065 0.0561680
\(428\) −5.34416 −0.258320
\(429\) 4.76092 0.229860
\(430\) −10.4767 −0.505232
\(431\) −0.733052 −0.0353099 −0.0176549 0.999844i \(-0.505620\pi\)
−0.0176549 + 0.999844i \(0.505620\pi\)
\(432\) 4.32467 0.208071
\(433\) −1.90369 −0.0914856 −0.0457428 0.998953i \(-0.514565\pi\)
−0.0457428 + 0.998953i \(0.514565\pi\)
\(434\) 13.2642 0.636702
\(435\) −5.08404 −0.243761
\(436\) 21.9202 1.04979
\(437\) −6.50780 −0.311310
\(438\) −27.0392 −1.29198
\(439\) −15.0644 −0.718985 −0.359492 0.933148i \(-0.617050\pi\)
−0.359492 + 0.933148i \(0.617050\pi\)
\(440\) −0.480628 −0.0229131
\(441\) 1.00000 0.0476190
\(442\) −22.3698 −1.06403
\(443\) 28.4508 1.35174 0.675869 0.737021i \(-0.263768\pi\)
0.675869 + 0.737021i \(0.263768\pi\)
\(444\) 3.68925 0.175084
\(445\) 21.3230 1.01081
\(446\) 6.79992 0.321986
\(447\) 8.52571 0.403252
\(448\) −6.51643 −0.307872
\(449\) 7.79538 0.367887 0.183943 0.982937i \(-0.441114\pi\)
0.183943 + 0.982937i \(0.441114\pi\)
\(450\) 5.57053 0.262597
\(451\) −10.4891 −0.493913
\(452\) 11.3798 0.535263
\(453\) 0.344333 0.0161782
\(454\) −34.3280 −1.61109
\(455\) 7.42169 0.347934
\(456\) −0.348300 −0.0163106
\(457\) 9.99146 0.467381 0.233691 0.972311i \(-0.424920\pi\)
0.233691 + 0.972311i \(0.424920\pi\)
\(458\) 18.1779 0.849398
\(459\) 2.26100 0.105534
\(460\) 17.3911 0.810862
\(461\) 13.2834 0.618670 0.309335 0.950953i \(-0.399894\pi\)
0.309335 + 0.950953i \(0.399894\pi\)
\(462\) 1.83906 0.0855607
\(463\) −24.4910 −1.13819 −0.569097 0.822270i \(-0.692707\pi\)
−0.569097 + 0.822270i \(0.692707\pi\)
\(464\) 14.9930 0.696032
\(465\) −9.94996 −0.461418
\(466\) 44.6504 2.06839
\(467\) −0.0512726 −0.00237261 −0.00118631 0.999999i \(-0.500378\pi\)
−0.00118631 + 0.999999i \(0.500378\pi\)
\(468\) −9.21991 −0.426191
\(469\) 10.2723 0.474331
\(470\) 9.67377 0.446218
\(471\) −11.2990 −0.520629
\(472\) −4.27870 −0.196943
\(473\) −3.43780 −0.158070
\(474\) 17.0514 0.783197
\(475\) −2.84867 −0.130706
\(476\) −4.11906 −0.188797
\(477\) −4.27583 −0.195777
\(478\) −1.72451 −0.0788774
\(479\) 3.22870 0.147523 0.0737615 0.997276i \(-0.476500\pi\)
0.0737615 + 0.997276i \(0.476500\pi\)
\(480\) 11.3764 0.519259
\(481\) 10.2487 0.467301
\(482\) 23.7913 1.08366
\(483\) 6.50961 0.296197
\(484\) −18.4274 −0.837611
\(485\) −16.7914 −0.762460
\(486\) 1.95494 0.0886778
\(487\) 3.28653 0.148927 0.0744636 0.997224i \(-0.476276\pi\)
0.0744636 + 0.997224i \(0.476276\pi\)
\(488\) 0.404368 0.0183049
\(489\) 11.9852 0.541990
\(490\) 2.86686 0.129512
\(491\) 6.63849 0.299591 0.149796 0.988717i \(-0.452138\pi\)
0.149796 + 0.988717i \(0.452138\pi\)
\(492\) 20.3130 0.915782
\(493\) 7.83856 0.353031
\(494\) 9.89104 0.445019
\(495\) −1.37954 −0.0620059
\(496\) 29.3427 1.31753
\(497\) 2.38139 0.106820
\(498\) −5.71452 −0.256074
\(499\) −9.04986 −0.405127 −0.202564 0.979269i \(-0.564927\pi\)
−0.202564 + 0.979269i \(0.564927\pi\)
\(500\) 20.9706 0.937834
\(501\) −5.74616 −0.256719
\(502\) −22.4898 −1.00377
\(503\) 18.9139 0.843331 0.421665 0.906751i \(-0.361446\pi\)
0.421665 + 0.906751i \(0.361446\pi\)
\(504\) 0.348396 0.0155188
\(505\) 1.72000 0.0765388
\(506\) 11.9715 0.532200
\(507\) −12.6129 −0.560158
\(508\) 33.1311 1.46995
\(509\) 7.79853 0.345664 0.172832 0.984951i \(-0.444708\pi\)
0.172832 + 0.984951i \(0.444708\pi\)
\(510\) 6.48197 0.287027
\(511\) −13.8312 −0.611857
\(512\) −30.5359 −1.34951
\(513\) −0.999722 −0.0441388
\(514\) 27.3499 1.20635
\(515\) 7.28462 0.320999
\(516\) 6.65757 0.293083
\(517\) 3.17432 0.139607
\(518\) 3.95889 0.173944
\(519\) 8.70102 0.381932
\(520\) 2.58569 0.113390
\(521\) −27.1107 −1.18774 −0.593871 0.804560i \(-0.702401\pi\)
−0.593871 + 0.804560i \(0.702401\pi\)
\(522\) 6.77749 0.296643
\(523\) −6.00622 −0.262634 −0.131317 0.991340i \(-0.541921\pi\)
−0.131317 + 0.991340i \(0.541921\pi\)
\(524\) −29.9051 −1.30641
\(525\) 2.84946 0.124361
\(526\) 6.79762 0.296390
\(527\) 15.3408 0.668256
\(528\) 4.06832 0.177051
\(529\) 19.3750 0.842391
\(530\) −12.2582 −0.532463
\(531\) −12.2811 −0.532956
\(532\) 1.82128 0.0789625
\(533\) 56.4295 2.44423
\(534\) −28.4255 −1.23009
\(535\) 4.30185 0.185985
\(536\) 3.57883 0.154582
\(537\) 4.99206 0.215423
\(538\) 39.8856 1.71959
\(539\) 0.940724 0.0405198
\(540\) 2.67160 0.114967
\(541\) −12.8455 −0.552273 −0.276136 0.961118i \(-0.589054\pi\)
−0.276136 + 0.961118i \(0.589054\pi\)
\(542\) 55.2238 2.37207
\(543\) 16.3303 0.700799
\(544\) −17.5401 −0.752025
\(545\) −17.6450 −0.755828
\(546\) −9.89378 −0.423415
\(547\) −20.6363 −0.882345 −0.441172 0.897422i \(-0.645437\pi\)
−0.441172 + 0.897422i \(0.645437\pi\)
\(548\) 16.2116 0.692523
\(549\) 1.16065 0.0495355
\(550\) 5.24032 0.223448
\(551\) −3.46589 −0.147652
\(552\) 2.26792 0.0965293
\(553\) 8.72222 0.370906
\(554\) 15.6650 0.665542
\(555\) −2.96971 −0.126057
\(556\) 22.1214 0.938154
\(557\) 30.6316 1.29790 0.648951 0.760830i \(-0.275208\pi\)
0.648951 + 0.760830i \(0.275208\pi\)
\(558\) 13.2642 0.561518
\(559\) 18.4947 0.782243
\(560\) 6.34200 0.267998
\(561\) 2.12698 0.0898010
\(562\) −8.17400 −0.344799
\(563\) 7.88912 0.332487 0.166243 0.986085i \(-0.446836\pi\)
0.166243 + 0.986085i \(0.446836\pi\)
\(564\) −6.14733 −0.258849
\(565\) −9.16036 −0.385379
\(566\) −46.2864 −1.94556
\(567\) 1.00000 0.0419961
\(568\) 0.829667 0.0348120
\(569\) −27.1127 −1.13662 −0.568312 0.822813i \(-0.692403\pi\)
−0.568312 + 0.822813i \(0.692403\pi\)
\(570\) −2.86607 −0.120046
\(571\) 43.5057 1.82066 0.910329 0.413885i \(-0.135829\pi\)
0.910329 + 0.413885i \(0.135829\pi\)
\(572\) −8.67339 −0.362653
\(573\) −6.47927 −0.270675
\(574\) 21.7977 0.909817
\(575\) 18.5489 0.773542
\(576\) −6.51643 −0.271518
\(577\) −6.44412 −0.268272 −0.134136 0.990963i \(-0.542826\pi\)
−0.134136 + 0.990963i \(0.542826\pi\)
\(578\) 23.2401 0.966660
\(579\) −1.34244 −0.0557900
\(580\) 9.26204 0.384585
\(581\) −2.92312 −0.121271
\(582\) 22.3845 0.927868
\(583\) −4.02238 −0.166590
\(584\) −4.81874 −0.199401
\(585\) 7.42169 0.306849
\(586\) 9.70234 0.400800
\(587\) −21.3449 −0.881000 −0.440500 0.897753i \(-0.645199\pi\)
−0.440500 + 0.897753i \(0.645199\pi\)
\(588\) −1.82179 −0.0751292
\(589\) −6.78309 −0.279492
\(590\) −35.2083 −1.44950
\(591\) 24.8526 1.02230
\(592\) 8.75776 0.359942
\(593\) 30.0206 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(594\) 1.83906 0.0754574
\(595\) 3.31569 0.135930
\(596\) −15.5320 −0.636216
\(597\) −13.5146 −0.553116
\(598\) −64.4047 −2.63370
\(599\) −9.35266 −0.382139 −0.191070 0.981576i \(-0.561196\pi\)
−0.191070 + 0.981576i \(0.561196\pi\)
\(600\) 0.992743 0.0405285
\(601\) −34.8271 −1.42063 −0.710314 0.703885i \(-0.751447\pi\)
−0.710314 + 0.703885i \(0.751447\pi\)
\(602\) 7.14416 0.291174
\(603\) 10.2723 0.418321
\(604\) −0.627302 −0.0255245
\(605\) 14.8334 0.603064
\(606\) −2.29291 −0.0931432
\(607\) −11.0556 −0.448735 −0.224367 0.974505i \(-0.572032\pi\)
−0.224367 + 0.974505i \(0.572032\pi\)
\(608\) 7.75551 0.314528
\(609\) 3.46685 0.140484
\(610\) 3.32744 0.134724
\(611\) −17.0773 −0.690872
\(612\) −4.11906 −0.166503
\(613\) −21.4290 −0.865509 −0.432755 0.901512i \(-0.642458\pi\)
−0.432755 + 0.901512i \(0.642458\pi\)
\(614\) −40.1573 −1.62062
\(615\) −16.3512 −0.659345
\(616\) 0.327745 0.0132052
\(617\) 31.1684 1.25479 0.627396 0.778700i \(-0.284121\pi\)
0.627396 + 0.778700i \(0.284121\pi\)
\(618\) −9.71106 −0.390636
\(619\) 0.395176 0.0158835 0.00794173 0.999968i \(-0.497472\pi\)
0.00794173 + 0.999968i \(0.497472\pi\)
\(620\) 18.1267 0.727986
\(621\) 6.50961 0.261222
\(622\) 27.5853 1.10607
\(623\) −14.5404 −0.582547
\(624\) −21.8868 −0.876172
\(625\) −2.63325 −0.105330
\(626\) −65.1112 −2.60237
\(627\) −0.940462 −0.0375585
\(628\) 20.5843 0.821404
\(629\) 4.57869 0.182564
\(630\) 2.86686 0.114219
\(631\) 15.7391 0.626565 0.313282 0.949660i \(-0.398571\pi\)
0.313282 + 0.949660i \(0.398571\pi\)
\(632\) 3.03879 0.120877
\(633\) 11.3459 0.450960
\(634\) 42.6354 1.69327
\(635\) −26.6693 −1.05834
\(636\) 7.78965 0.308880
\(637\) −5.06092 −0.200521
\(638\) 6.37574 0.252418
\(639\) 2.38139 0.0942062
\(640\) 4.07108 0.160924
\(641\) 26.6973 1.05448 0.527240 0.849716i \(-0.323227\pi\)
0.527240 + 0.849716i \(0.323227\pi\)
\(642\) −5.73476 −0.226333
\(643\) 0.959406 0.0378353 0.0189176 0.999821i \(-0.493978\pi\)
0.0189176 + 0.999821i \(0.493978\pi\)
\(644\) −11.8591 −0.467315
\(645\) −5.35910 −0.211014
\(646\) 4.41889 0.173859
\(647\) −25.0747 −0.985790 −0.492895 0.870089i \(-0.664061\pi\)
−0.492895 + 0.870089i \(0.664061\pi\)
\(648\) 0.348396 0.0136863
\(649\) −11.5532 −0.453501
\(650\) −28.1920 −1.10578
\(651\) 6.78497 0.265924
\(652\) −21.8345 −0.855104
\(653\) −1.12924 −0.0441907 −0.0220953 0.999756i \(-0.507034\pi\)
−0.0220953 + 0.999756i \(0.507034\pi\)
\(654\) 23.5224 0.919798
\(655\) 24.0725 0.940591
\(656\) 48.2203 1.88269
\(657\) −13.8312 −0.539607
\(658\) −6.59663 −0.257164
\(659\) −22.1447 −0.862636 −0.431318 0.902200i \(-0.641951\pi\)
−0.431318 + 0.902200i \(0.641951\pi\)
\(660\) 2.51323 0.0978275
\(661\) 16.1186 0.626941 0.313470 0.949598i \(-0.398508\pi\)
0.313470 + 0.949598i \(0.398508\pi\)
\(662\) −26.2830 −1.02152
\(663\) −11.4427 −0.444399
\(664\) −1.01840 −0.0395217
\(665\) −1.46606 −0.0568515
\(666\) 3.95889 0.153404
\(667\) 22.5679 0.873831
\(668\) 10.4683 0.405030
\(669\) 3.47833 0.134480
\(670\) 29.4493 1.13772
\(671\) 1.09185 0.0421506
\(672\) −7.75767 −0.299259
\(673\) 13.1733 0.507792 0.253896 0.967231i \(-0.418288\pi\)
0.253896 + 0.967231i \(0.418288\pi\)
\(674\) −38.4852 −1.48239
\(675\) 2.84946 0.109676
\(676\) 22.9780 0.883768
\(677\) −6.89888 −0.265145 −0.132573 0.991173i \(-0.542324\pi\)
−0.132573 + 0.991173i \(0.542324\pi\)
\(678\) 12.2116 0.468983
\(679\) 11.4502 0.439420
\(680\) 1.15518 0.0442989
\(681\) −17.5596 −0.672887
\(682\) 12.4779 0.477805
\(683\) 17.7170 0.677924 0.338962 0.940800i \(-0.389924\pi\)
0.338962 + 0.940800i \(0.389924\pi\)
\(684\) 1.82128 0.0696384
\(685\) −13.0497 −0.498603
\(686\) −1.95494 −0.0746399
\(687\) 9.29845 0.354758
\(688\) 15.8041 0.602527
\(689\) 21.6396 0.824404
\(690\) 18.6621 0.710456
\(691\) −42.7887 −1.62776 −0.813879 0.581034i \(-0.802648\pi\)
−0.813879 + 0.581034i \(0.802648\pi\)
\(692\) −15.8514 −0.602580
\(693\) 0.940724 0.0357351
\(694\) −25.0674 −0.951547
\(695\) −17.8069 −0.675453
\(696\) 1.20784 0.0457830
\(697\) 25.2103 0.954907
\(698\) −11.2472 −0.425714
\(699\) 22.8398 0.863881
\(700\) −5.19111 −0.196206
\(701\) −1.75483 −0.0662789 −0.0331394 0.999451i \(-0.510551\pi\)
−0.0331394 + 0.999451i \(0.510551\pi\)
\(702\) −9.89378 −0.373417
\(703\) −2.02451 −0.0763558
\(704\) −6.13016 −0.231039
\(705\) 4.94837 0.186367
\(706\) −31.3920 −1.18145
\(707\) −1.17288 −0.0441107
\(708\) 22.3736 0.840851
\(709\) 41.5674 1.56110 0.780548 0.625095i \(-0.214940\pi\)
0.780548 + 0.625095i \(0.214940\pi\)
\(710\) 6.82710 0.256217
\(711\) 8.72222 0.327109
\(712\) −5.06581 −0.189849
\(713\) 44.1675 1.65409
\(714\) −4.42012 −0.165419
\(715\) 6.98176 0.261103
\(716\) −9.09446 −0.339876
\(717\) −0.882131 −0.0329438
\(718\) −6.15261 −0.229613
\(719\) 11.3608 0.423685 0.211842 0.977304i \(-0.432054\pi\)
0.211842 + 0.977304i \(0.432054\pi\)
\(720\) 6.34200 0.236352
\(721\) −4.96745 −0.184997
\(722\) 35.1900 1.30964
\(723\) 12.1698 0.452601
\(724\) −29.7503 −1.10566
\(725\) 9.87867 0.366885
\(726\) −19.7743 −0.733893
\(727\) 36.6164 1.35803 0.679014 0.734125i \(-0.262407\pi\)
0.679014 + 0.734125i \(0.262407\pi\)
\(728\) −1.76321 −0.0653487
\(729\) 1.00000 0.0370370
\(730\) −39.6522 −1.46759
\(731\) 8.26264 0.305605
\(732\) −2.11446 −0.0781529
\(733\) −43.2343 −1.59690 −0.798448 0.602063i \(-0.794345\pi\)
−0.798448 + 0.602063i \(0.794345\pi\)
\(734\) 16.0611 0.592827
\(735\) 1.46647 0.0540916
\(736\) −50.4994 −1.86143
\(737\) 9.66340 0.355956
\(738\) 21.7977 0.802383
\(739\) 4.29526 0.158004 0.0790018 0.996874i \(-0.474827\pi\)
0.0790018 + 0.996874i \(0.474827\pi\)
\(740\) 5.41018 0.198882
\(741\) 5.05951 0.185866
\(742\) 8.35899 0.306868
\(743\) 10.9100 0.400248 0.200124 0.979771i \(-0.435866\pi\)
0.200124 + 0.979771i \(0.435866\pi\)
\(744\) 2.36386 0.0866633
\(745\) 12.5027 0.458064
\(746\) 25.4330 0.931167
\(747\) −2.92312 −0.106951
\(748\) −3.87490 −0.141680
\(749\) −2.93347 −0.107187
\(750\) 22.5033 0.821705
\(751\) 4.57642 0.166996 0.0834980 0.996508i \(-0.473391\pi\)
0.0834980 + 0.996508i \(0.473391\pi\)
\(752\) −14.5929 −0.532148
\(753\) −11.5041 −0.419233
\(754\) −34.3003 −1.24914
\(755\) 0.504955 0.0183772
\(756\) −1.82179 −0.0662577
\(757\) −3.68657 −0.133991 −0.0669953 0.997753i \(-0.521341\pi\)
−0.0669953 + 0.997753i \(0.521341\pi\)
\(758\) −23.6857 −0.860302
\(759\) 6.12374 0.222278
\(760\) −0.510772 −0.0185276
\(761\) −16.0754 −0.582734 −0.291367 0.956611i \(-0.594110\pi\)
−0.291367 + 0.956611i \(0.594110\pi\)
\(762\) 35.5526 1.28793
\(763\) 12.0323 0.435598
\(764\) 11.8038 0.427048
\(765\) 3.31569 0.119879
\(766\) 1.95494 0.0706348
\(767\) 62.1538 2.24424
\(768\) −18.4600 −0.666117
\(769\) 25.5334 0.920758 0.460379 0.887722i \(-0.347714\pi\)
0.460379 + 0.887722i \(0.347714\pi\)
\(770\) 2.69692 0.0971904
\(771\) 13.9902 0.503843
\(772\) 2.44564 0.0880206
\(773\) 6.45187 0.232057 0.116029 0.993246i \(-0.462984\pi\)
0.116029 + 0.993246i \(0.462984\pi\)
\(774\) 7.14416 0.256792
\(775\) 19.3335 0.694480
\(776\) 3.98922 0.143205
\(777\) 2.02507 0.0726491
\(778\) 30.1752 1.08183
\(779\) −11.1470 −0.399381
\(780\) −13.5207 −0.484120
\(781\) 2.24023 0.0801616
\(782\) −28.7732 −1.02893
\(783\) 3.46685 0.123895
\(784\) −4.32467 −0.154452
\(785\) −16.5696 −0.591395
\(786\) −32.0908 −1.14464
\(787\) 4.02494 0.143474 0.0717368 0.997424i \(-0.477146\pi\)
0.0717368 + 0.997424i \(0.477146\pi\)
\(788\) −45.2761 −1.61289
\(789\) 3.47715 0.123790
\(790\) 25.0054 0.889652
\(791\) 6.24653 0.222101
\(792\) 0.327745 0.0116459
\(793\) −5.87398 −0.208591
\(794\) −28.5034 −1.01155
\(795\) −6.27038 −0.222388
\(796\) 24.6207 0.872659
\(797\) −25.8606 −0.916028 −0.458014 0.888945i \(-0.651439\pi\)
−0.458014 + 0.888945i \(0.651439\pi\)
\(798\) 1.95440 0.0691849
\(799\) −7.62939 −0.269908
\(800\) −22.1052 −0.781536
\(801\) −14.5404 −0.513758
\(802\) 16.4663 0.581445
\(803\) −13.0113 −0.459160
\(804\) −18.7139 −0.659990
\(805\) 9.54615 0.336458
\(806\) −67.1290 −2.36452
\(807\) 20.4025 0.718200
\(808\) −0.408628 −0.0143755
\(809\) 11.0174 0.387353 0.193676 0.981065i \(-0.437959\pi\)
0.193676 + 0.981065i \(0.437959\pi\)
\(810\) 2.86686 0.100731
\(811\) 46.7015 1.63991 0.819956 0.572426i \(-0.193998\pi\)
0.819956 + 0.572426i \(0.193998\pi\)
\(812\) −6.31587 −0.221644
\(813\) 28.2484 0.990713
\(814\) 3.72422 0.130534
\(815\) 17.5760 0.615659
\(816\) −9.77807 −0.342301
\(817\) −3.65340 −0.127816
\(818\) −4.55108 −0.159125
\(819\) −5.06092 −0.176843
\(820\) 29.7885 1.04026
\(821\) 34.6546 1.20945 0.604727 0.796433i \(-0.293282\pi\)
0.604727 + 0.796433i \(0.293282\pi\)
\(822\) 17.3964 0.606770
\(823\) 5.59300 0.194960 0.0974798 0.995238i \(-0.468922\pi\)
0.0974798 + 0.995238i \(0.468922\pi\)
\(824\) −1.73064 −0.0602897
\(825\) 2.68056 0.0933250
\(826\) 24.0089 0.835375
\(827\) −24.8420 −0.863842 −0.431921 0.901911i \(-0.642164\pi\)
−0.431921 + 0.901911i \(0.642164\pi\)
\(828\) −11.8591 −0.412133
\(829\) 41.6683 1.44720 0.723600 0.690220i \(-0.242486\pi\)
0.723600 + 0.690220i \(0.242486\pi\)
\(830\) −8.38018 −0.290880
\(831\) 8.01304 0.277969
\(832\) 32.9791 1.14335
\(833\) −2.26100 −0.0783390
\(834\) 23.7382 0.821986
\(835\) −8.42657 −0.291614
\(836\) 1.71332 0.0592565
\(837\) 6.78497 0.234523
\(838\) 48.3905 1.67162
\(839\) −15.4387 −0.533002 −0.266501 0.963835i \(-0.585868\pi\)
−0.266501 + 0.963835i \(0.585868\pi\)
\(840\) 0.510913 0.0176282
\(841\) −16.9809 −0.585549
\(842\) −37.0010 −1.27514
\(843\) −4.18120 −0.144008
\(844\) −20.6698 −0.711485
\(845\) −18.4964 −0.636296
\(846\) −6.59663 −0.226797
\(847\) −10.1150 −0.347557
\(848\) 18.4915 0.635002
\(849\) −23.6767 −0.812581
\(850\) −12.5950 −0.432004
\(851\) 13.1824 0.451888
\(852\) −4.33838 −0.148630
\(853\) −53.1353 −1.81932 −0.909659 0.415357i \(-0.863657\pi\)
−0.909659 + 0.415357i \(0.863657\pi\)
\(854\) −2.26901 −0.0776439
\(855\) −1.46606 −0.0501383
\(856\) −1.02201 −0.0349316
\(857\) −54.1981 −1.85137 −0.925685 0.378295i \(-0.876511\pi\)
−0.925685 + 0.378295i \(0.876511\pi\)
\(858\) −9.30732 −0.317747
\(859\) −4.42347 −0.150927 −0.0754633 0.997149i \(-0.524044\pi\)
−0.0754633 + 0.997149i \(0.524044\pi\)
\(860\) 9.76313 0.332920
\(861\) 11.1501 0.379993
\(862\) 1.43307 0.0488106
\(863\) −3.73404 −0.127108 −0.0635541 0.997978i \(-0.520244\pi\)
−0.0635541 + 0.997978i \(0.520244\pi\)
\(864\) −7.75767 −0.263921
\(865\) 12.7598 0.433846
\(866\) 3.72160 0.126465
\(867\) 11.8879 0.403734
\(868\) −12.3608 −0.419552
\(869\) 8.20520 0.278342
\(870\) 9.93899 0.336963
\(871\) −51.9873 −1.76152
\(872\) 4.19200 0.141959
\(873\) 11.4502 0.387532
\(874\) 12.7224 0.430340
\(875\) 11.5110 0.389143
\(876\) 25.1975 0.851345
\(877\) 34.0569 1.15002 0.575010 0.818147i \(-0.304998\pi\)
0.575010 + 0.818147i \(0.304998\pi\)
\(878\) 29.4500 0.993889
\(879\) 4.96299 0.167398
\(880\) 5.96607 0.201116
\(881\) 31.5757 1.06381 0.531906 0.846803i \(-0.321476\pi\)
0.531906 + 0.846803i \(0.321476\pi\)
\(882\) −1.95494 −0.0658262
\(883\) −37.6272 −1.26626 −0.633128 0.774047i \(-0.718229\pi\)
−0.633128 + 0.774047i \(0.718229\pi\)
\(884\) 20.8462 0.701134
\(885\) −18.0099 −0.605397
\(886\) −55.6196 −1.86858
\(887\) 29.9572 1.00587 0.502933 0.864325i \(-0.332254\pi\)
0.502933 + 0.864325i \(0.332254\pi\)
\(888\) 0.705528 0.0236760
\(889\) 18.1860 0.609940
\(890\) −41.6852 −1.39729
\(891\) 0.940724 0.0315154
\(892\) −6.33678 −0.212171
\(893\) 3.37341 0.112887
\(894\) −16.6672 −0.557436
\(895\) 7.32071 0.244704
\(896\) −2.77611 −0.0927432
\(897\) −32.9446 −1.09999
\(898\) −15.2395 −0.508549
\(899\) 23.5225 0.784519
\(900\) −5.19111 −0.173037
\(901\) 9.66766 0.322076
\(902\) 20.5056 0.682761
\(903\) 3.65442 0.121611
\(904\) 2.17627 0.0723817
\(905\) 23.9479 0.796054
\(906\) −0.673151 −0.0223639
\(907\) −1.89647 −0.0629711 −0.0314856 0.999504i \(-0.510024\pi\)
−0.0314856 + 0.999504i \(0.510024\pi\)
\(908\) 31.9899 1.06162
\(909\) −1.17288 −0.0389020
\(910\) −14.5089 −0.480967
\(911\) −13.5165 −0.447820 −0.223910 0.974610i \(-0.571882\pi\)
−0.223910 + 0.974610i \(0.571882\pi\)
\(912\) 4.32347 0.143164
\(913\) −2.74985 −0.0910066
\(914\) −19.5327 −0.646084
\(915\) 1.70207 0.0562686
\(916\) −16.9398 −0.559707
\(917\) −16.4153 −0.542080
\(918\) −4.42012 −0.145886
\(919\) −11.4446 −0.377523 −0.188762 0.982023i \(-0.560447\pi\)
−0.188762 + 0.982023i \(0.560447\pi\)
\(920\) 3.32585 0.109650
\(921\) −20.5415 −0.676864
\(922\) −25.9683 −0.855219
\(923\) −12.0520 −0.396696
\(924\) −1.71380 −0.0563798
\(925\) 5.77037 0.189728
\(926\) 47.8784 1.57338
\(927\) −4.96745 −0.163152
\(928\) −26.8947 −0.882862
\(929\) −5.49232 −0.180197 −0.0900986 0.995933i \(-0.528718\pi\)
−0.0900986 + 0.995933i \(0.528718\pi\)
\(930\) 19.4516 0.637842
\(931\) 0.999722 0.0327646
\(932\) −41.6093 −1.36296
\(933\) 14.1106 0.461959
\(934\) 0.100235 0.00327978
\(935\) 3.11915 0.102007
\(936\) −1.76321 −0.0576322
\(937\) −17.5025 −0.571780 −0.285890 0.958262i \(-0.592289\pi\)
−0.285890 + 0.958262i \(0.592289\pi\)
\(938\) −20.0817 −0.655692
\(939\) −33.3060 −1.08690
\(940\) −9.01488 −0.294033
\(941\) 0.517014 0.0168542 0.00842709 0.999964i \(-0.497318\pi\)
0.00842709 + 0.999964i \(0.497318\pi\)
\(942\) 22.0888 0.719692
\(943\) 72.5825 2.36361
\(944\) 53.1118 1.72864
\(945\) 1.46647 0.0477043
\(946\) 6.72068 0.218508
\(947\) 26.0157 0.845396 0.422698 0.906271i \(-0.361083\pi\)
0.422698 + 0.906271i \(0.361083\pi\)
\(948\) −15.8900 −0.516084
\(949\) 69.9986 2.27225
\(950\) 5.56898 0.180682
\(951\) 21.8091 0.707207
\(952\) −0.787724 −0.0255303
\(953\) 11.7992 0.382215 0.191108 0.981569i \(-0.438792\pi\)
0.191108 + 0.981569i \(0.438792\pi\)
\(954\) 8.35899 0.270632
\(955\) −9.50166 −0.307466
\(956\) 1.60706 0.0519759
\(957\) 3.26135 0.105425
\(958\) −6.31191 −0.203929
\(959\) 8.89871 0.287354
\(960\) −9.55616 −0.308424
\(961\) 15.0358 0.485026
\(962\) −20.0356 −0.645974
\(963\) −2.93347 −0.0945298
\(964\) −22.1708 −0.714074
\(965\) −1.96865 −0.0633731
\(966\) −12.7259 −0.409449
\(967\) −15.9799 −0.513877 −0.256939 0.966428i \(-0.582714\pi\)
−0.256939 + 0.966428i \(0.582714\pi\)
\(968\) −3.52404 −0.113267
\(969\) 2.26037 0.0726136
\(970\) 32.8263 1.05399
\(971\) −7.48091 −0.240074 −0.120037 0.992769i \(-0.538301\pi\)
−0.120037 + 0.992769i \(0.538301\pi\)
\(972\) −1.82179 −0.0584338
\(973\) 12.1427 0.389276
\(974\) −6.42498 −0.205869
\(975\) −14.4209 −0.461838
\(976\) −5.01944 −0.160668
\(977\) −22.1403 −0.708330 −0.354165 0.935183i \(-0.615235\pi\)
−0.354165 + 0.935183i \(0.615235\pi\)
\(978\) −23.4303 −0.749220
\(979\) −13.6785 −0.437165
\(980\) −2.67160 −0.0853410
\(981\) 12.0323 0.384161
\(982\) −12.9779 −0.414140
\(983\) 9.42302 0.300548 0.150274 0.988644i \(-0.451984\pi\)
0.150274 + 0.988644i \(0.451984\pi\)
\(984\) 3.88464 0.123838
\(985\) 36.4456 1.16125
\(986\) −15.3239 −0.488012
\(987\) −3.37434 −0.107406
\(988\) −9.21735 −0.293243
\(989\) 23.7888 0.756441
\(990\) 2.69692 0.0857139
\(991\) 55.5757 1.76542 0.882710 0.469917i \(-0.155716\pi\)
0.882710 + 0.469917i \(0.155716\pi\)
\(992\) −52.6355 −1.67118
\(993\) −13.4444 −0.426646
\(994\) −4.65546 −0.147662
\(995\) −19.8188 −0.628298
\(996\) 5.32530 0.168739
\(997\) 33.9626 1.07561 0.537804 0.843070i \(-0.319254\pi\)
0.537804 + 0.843070i \(0.319254\pi\)
\(998\) 17.6919 0.560028
\(999\) 2.02507 0.0640704
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 \(a_p\))