Properties

Label 8043.2.a.t.1.14
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 1.14
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.61741 q^{2}\) \(-1.00000 q^{3}\) \(+0.616031 q^{4}\) \(-3.81830 q^{5}\) \(+1.61741 q^{6}\) \(+1.00000 q^{7}\) \(+2.23845 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.61741 q^{2}\) \(-1.00000 q^{3}\) \(+0.616031 q^{4}\) \(-3.81830 q^{5}\) \(+1.61741 q^{6}\) \(+1.00000 q^{7}\) \(+2.23845 q^{8}\) \(+1.00000 q^{9}\) \(+6.17577 q^{10}\) \(-5.83242 q^{11}\) \(-0.616031 q^{12}\) \(+2.66196 q^{13}\) \(-1.61741 q^{14}\) \(+3.81830 q^{15}\) \(-4.85257 q^{16}\) \(+1.83267 q^{17}\) \(-1.61741 q^{18}\) \(-1.69967 q^{19}\) \(-2.35219 q^{20}\) \(-1.00000 q^{21}\) \(+9.43344 q^{22}\) \(-8.47805 q^{23}\) \(-2.23845 q^{24}\) \(+9.57940 q^{25}\) \(-4.30549 q^{26}\) \(-1.00000 q^{27}\) \(+0.616031 q^{28}\) \(-1.07148 q^{29}\) \(-6.17577 q^{30}\) \(-2.20955 q^{31}\) \(+3.37171 q^{32}\) \(+5.83242 q^{33}\) \(-2.96419 q^{34}\) \(-3.81830 q^{35}\) \(+0.616031 q^{36}\) \(-8.02038 q^{37}\) \(+2.74907 q^{38}\) \(-2.66196 q^{39}\) \(-8.54708 q^{40}\) \(-3.22910 q^{41}\) \(+1.61741 q^{42}\) \(+3.13100 q^{43}\) \(-3.59295 q^{44}\) \(-3.81830 q^{45}\) \(+13.7125 q^{46}\) \(-0.289107 q^{47}\) \(+4.85257 q^{48}\) \(+1.00000 q^{49}\) \(-15.4939 q^{50}\) \(-1.83267 q^{51}\) \(+1.63985 q^{52}\) \(+6.72259 q^{53}\) \(+1.61741 q^{54}\) \(+22.2699 q^{55}\) \(+2.23845 q^{56}\) \(+1.69967 q^{57}\) \(+1.73303 q^{58}\) \(+7.98601 q^{59}\) \(+2.35219 q^{60}\) \(+6.92080 q^{61}\) \(+3.57376 q^{62}\) \(+1.00000 q^{63}\) \(+4.25168 q^{64}\) \(-10.1641 q^{65}\) \(-9.43344 q^{66}\) \(+2.40863 q^{67}\) \(+1.12898 q^{68}\) \(+8.47805 q^{69}\) \(+6.17577 q^{70}\) \(-11.3491 q^{71}\) \(+2.23845 q^{72}\) \(-4.36922 q^{73}\) \(+12.9723 q^{74}\) \(-9.57940 q^{75}\) \(-1.04705 q^{76}\) \(-5.83242 q^{77}\) \(+4.30549 q^{78}\) \(-4.87186 q^{79}\) \(+18.5286 q^{80}\) \(+1.00000 q^{81}\) \(+5.22280 q^{82}\) \(-5.97861 q^{83}\) \(-0.616031 q^{84}\) \(-6.99768 q^{85}\) \(-5.06413 q^{86}\) \(+1.07148 q^{87}\) \(-13.0556 q^{88}\) \(-14.2467 q^{89}\) \(+6.17577 q^{90}\) \(+2.66196 q^{91}\) \(-5.22274 q^{92}\) \(+2.20955 q^{93}\) \(+0.467605 q^{94}\) \(+6.48984 q^{95}\) \(-3.37171 q^{96}\) \(+8.87913 q^{97}\) \(-1.61741 q^{98}\) \(-5.83242 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61741 −1.14368 −0.571842 0.820363i \(-0.693771\pi\)
−0.571842 + 0.820363i \(0.693771\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.616031 0.308015
\(5\) −3.81830 −1.70759 −0.853797 0.520605i \(-0.825706\pi\)
−0.853797 + 0.520605i \(0.825706\pi\)
\(6\) 1.61741 0.660307
\(7\) 1.00000 0.377964
\(8\) 2.23845 0.791413
\(9\) 1.00000 0.333333
\(10\) 6.17577 1.95295
\(11\) −5.83242 −1.75854 −0.879270 0.476324i \(-0.841969\pi\)
−0.879270 + 0.476324i \(0.841969\pi\)
\(12\) −0.616031 −0.177833
\(13\) 2.66196 0.738294 0.369147 0.929371i \(-0.379650\pi\)
0.369147 + 0.929371i \(0.379650\pi\)
\(14\) −1.61741 −0.432272
\(15\) 3.81830 0.985880
\(16\) −4.85257 −1.21314
\(17\) 1.83267 0.444488 0.222244 0.974991i \(-0.428662\pi\)
0.222244 + 0.974991i \(0.428662\pi\)
\(18\) −1.61741 −0.381228
\(19\) −1.69967 −0.389930 −0.194965 0.980810i \(-0.562459\pi\)
−0.194965 + 0.980810i \(0.562459\pi\)
\(20\) −2.35219 −0.525965
\(21\) −1.00000 −0.218218
\(22\) 9.43344 2.01122
\(23\) −8.47805 −1.76779 −0.883897 0.467681i \(-0.845090\pi\)
−0.883897 + 0.467681i \(0.845090\pi\)
\(24\) −2.23845 −0.456922
\(25\) 9.57940 1.91588
\(26\) −4.30549 −0.844376
\(27\) −1.00000 −0.192450
\(28\) 0.616031 0.116419
\(29\) −1.07148 −0.198969 −0.0994844 0.995039i \(-0.531719\pi\)
−0.0994844 + 0.995039i \(0.531719\pi\)
\(30\) −6.17577 −1.12754
\(31\) −2.20955 −0.396847 −0.198424 0.980116i \(-0.563582\pi\)
−0.198424 + 0.980116i \(0.563582\pi\)
\(32\) 3.37171 0.596040
\(33\) 5.83242 1.01529
\(34\) −2.96419 −0.508354
\(35\) −3.81830 −0.645410
\(36\) 0.616031 0.102672
\(37\) −8.02038 −1.31854 −0.659271 0.751905i \(-0.729135\pi\)
−0.659271 + 0.751905i \(0.729135\pi\)
\(38\) 2.74907 0.445958
\(39\) −2.66196 −0.426254
\(40\) −8.54708 −1.35141
\(41\) −3.22910 −0.504301 −0.252151 0.967688i \(-0.581138\pi\)
−0.252151 + 0.967688i \(0.581138\pi\)
\(42\) 1.61741 0.249573
\(43\) 3.13100 0.477474 0.238737 0.971084i \(-0.423267\pi\)
0.238737 + 0.971084i \(0.423267\pi\)
\(44\) −3.59295 −0.541657
\(45\) −3.81830 −0.569198
\(46\) 13.7125 2.02180
\(47\) −0.289107 −0.0421705 −0.0210853 0.999778i \(-0.506712\pi\)
−0.0210853 + 0.999778i \(0.506712\pi\)
\(48\) 4.85257 0.700408
\(49\) 1.00000 0.142857
\(50\) −15.4939 −2.19116
\(51\) −1.83267 −0.256625
\(52\) 1.63985 0.227406
\(53\) 6.72259 0.923418 0.461709 0.887031i \(-0.347236\pi\)
0.461709 + 0.887031i \(0.347236\pi\)
\(54\) 1.61741 0.220102
\(55\) 22.2699 3.00287
\(56\) 2.23845 0.299126
\(57\) 1.69967 0.225126
\(58\) 1.73303 0.227558
\(59\) 7.98601 1.03969 0.519845 0.854260i \(-0.325990\pi\)
0.519845 + 0.854260i \(0.325990\pi\)
\(60\) 2.35219 0.303666
\(61\) 6.92080 0.886118 0.443059 0.896492i \(-0.353893\pi\)
0.443059 + 0.896492i \(0.353893\pi\)
\(62\) 3.57376 0.453868
\(63\) 1.00000 0.125988
\(64\) 4.25168 0.531460
\(65\) −10.1641 −1.26071
\(66\) −9.43344 −1.16118
\(67\) 2.40863 0.294261 0.147130 0.989117i \(-0.452996\pi\)
0.147130 + 0.989117i \(0.452996\pi\)
\(68\) 1.12898 0.136909
\(69\) 8.47805 1.02064
\(70\) 6.17577 0.738146
\(71\) −11.3491 −1.34689 −0.673443 0.739239i \(-0.735185\pi\)
−0.673443 + 0.739239i \(0.735185\pi\)
\(72\) 2.23845 0.263804
\(73\) −4.36922 −0.511378 −0.255689 0.966759i \(-0.582302\pi\)
−0.255689 + 0.966759i \(0.582302\pi\)
\(74\) 12.9723 1.50800
\(75\) −9.57940 −1.10613
\(76\) −1.04705 −0.120105
\(77\) −5.83242 −0.664666
\(78\) 4.30549 0.487501
\(79\) −4.87186 −0.548127 −0.274064 0.961712i \(-0.588368\pi\)
−0.274064 + 0.961712i \(0.588368\pi\)
\(80\) 18.5286 2.07155
\(81\) 1.00000 0.111111
\(82\) 5.22280 0.576762
\(83\) −5.97861 −0.656238 −0.328119 0.944636i \(-0.606415\pi\)
−0.328119 + 0.944636i \(0.606415\pi\)
\(84\) −0.616031 −0.0672144
\(85\) −6.99768 −0.759005
\(86\) −5.06413 −0.546080
\(87\) 1.07148 0.114875
\(88\) −13.0556 −1.39173
\(89\) −14.2467 −1.51015 −0.755073 0.655641i \(-0.772399\pi\)
−0.755073 + 0.655641i \(0.772399\pi\)
\(90\) 6.17577 0.650984
\(91\) 2.66196 0.279049
\(92\) −5.22274 −0.544508
\(93\) 2.20955 0.229120
\(94\) 0.467605 0.0482298
\(95\) 6.48984 0.665843
\(96\) −3.37171 −0.344124
\(97\) 8.87913 0.901539 0.450769 0.892640i \(-0.351150\pi\)
0.450769 + 0.892640i \(0.351150\pi\)
\(98\) −1.61741 −0.163384
\(99\) −5.83242 −0.586180
\(100\) 5.90120 0.590120
\(101\) −0.314415 −0.0312855 −0.0156427 0.999878i \(-0.504979\pi\)
−0.0156427 + 0.999878i \(0.504979\pi\)
\(102\) 2.96419 0.293498
\(103\) −12.9244 −1.27348 −0.636740 0.771079i \(-0.719717\pi\)
−0.636740 + 0.771079i \(0.719717\pi\)
\(104\) 5.95867 0.584295
\(105\) 3.81830 0.372628
\(106\) −10.8732 −1.05610
\(107\) 2.85690 0.276187 0.138093 0.990419i \(-0.455903\pi\)
0.138093 + 0.990419i \(0.455903\pi\)
\(108\) −0.616031 −0.0592776
\(109\) −6.91442 −0.662282 −0.331141 0.943581i \(-0.607434\pi\)
−0.331141 + 0.943581i \(0.607434\pi\)
\(110\) −36.0197 −3.43434
\(111\) 8.02038 0.761261
\(112\) −4.85257 −0.458525
\(113\) −15.9840 −1.50365 −0.751824 0.659363i \(-0.770826\pi\)
−0.751824 + 0.659363i \(0.770826\pi\)
\(114\) −2.74907 −0.257474
\(115\) 32.3717 3.01868
\(116\) −0.660064 −0.0612854
\(117\) 2.66196 0.246098
\(118\) −12.9167 −1.18908
\(119\) 1.83267 0.168001
\(120\) 8.54708 0.780238
\(121\) 23.0171 2.09246
\(122\) −11.1938 −1.01344
\(123\) 3.22910 0.291158
\(124\) −1.36115 −0.122235
\(125\) −17.4855 −1.56395
\(126\) −1.61741 −0.144091
\(127\) −18.0523 −1.60188 −0.800940 0.598745i \(-0.795666\pi\)
−0.800940 + 0.598745i \(0.795666\pi\)
\(128\) −13.6202 −1.20386
\(129\) −3.13100 −0.275670
\(130\) 16.4396 1.44185
\(131\) −22.4093 −1.95791 −0.978954 0.204083i \(-0.934579\pi\)
−0.978954 + 0.204083i \(0.934579\pi\)
\(132\) 3.59295 0.312726
\(133\) −1.69967 −0.147380
\(134\) −3.89575 −0.336542
\(135\) 3.81830 0.328627
\(136\) 4.10235 0.351773
\(137\) −6.03905 −0.515951 −0.257975 0.966152i \(-0.583055\pi\)
−0.257975 + 0.966152i \(0.583055\pi\)
\(138\) −13.7125 −1.16729
\(139\) −5.20717 −0.441666 −0.220833 0.975312i \(-0.570878\pi\)
−0.220833 + 0.975312i \(0.570878\pi\)
\(140\) −2.35219 −0.198796
\(141\) 0.289107 0.0243472
\(142\) 18.3561 1.54041
\(143\) −15.5256 −1.29832
\(144\) −4.85257 −0.404381
\(145\) 4.09123 0.339758
\(146\) 7.06684 0.584856
\(147\) −1.00000 −0.0824786
\(148\) −4.94080 −0.406131
\(149\) 1.54488 0.126562 0.0632808 0.997996i \(-0.479844\pi\)
0.0632808 + 0.997996i \(0.479844\pi\)
\(150\) 15.4939 1.26507
\(151\) 6.02046 0.489938 0.244969 0.969531i \(-0.421222\pi\)
0.244969 + 0.969531i \(0.421222\pi\)
\(152\) −3.80462 −0.308596
\(153\) 1.83267 0.148163
\(154\) 9.43344 0.760168
\(155\) 8.43673 0.677654
\(156\) −1.63985 −0.131293
\(157\) −17.5234 −1.39852 −0.699262 0.714866i \(-0.746488\pi\)
−0.699262 + 0.714866i \(0.746488\pi\)
\(158\) 7.87982 0.626885
\(159\) −6.72259 −0.533136
\(160\) −12.8742 −1.01779
\(161\) −8.47805 −0.668164
\(162\) −1.61741 −0.127076
\(163\) −22.0962 −1.73071 −0.865353 0.501163i \(-0.832906\pi\)
−0.865353 + 0.501163i \(0.832906\pi\)
\(164\) −1.98923 −0.155332
\(165\) −22.2699 −1.73371
\(166\) 9.66989 0.750529
\(167\) −9.14586 −0.707728 −0.353864 0.935297i \(-0.615132\pi\)
−0.353864 + 0.935297i \(0.615132\pi\)
\(168\) −2.23845 −0.172700
\(169\) −5.91398 −0.454922
\(170\) 11.3182 0.868063
\(171\) −1.69967 −0.129977
\(172\) 1.92879 0.147069
\(173\) −0.552490 −0.0420050 −0.0210025 0.999779i \(-0.506686\pi\)
−0.0210025 + 0.999779i \(0.506686\pi\)
\(174\) −1.73303 −0.131380
\(175\) 9.57940 0.724135
\(176\) 28.3022 2.13336
\(177\) −7.98601 −0.600266
\(178\) 23.0428 1.72713
\(179\) 6.60544 0.493714 0.246857 0.969052i \(-0.420602\pi\)
0.246857 + 0.969052i \(0.420602\pi\)
\(180\) −2.35219 −0.175322
\(181\) 14.3503 1.06665 0.533326 0.845909i \(-0.320942\pi\)
0.533326 + 0.845909i \(0.320942\pi\)
\(182\) −4.30549 −0.319144
\(183\) −6.92080 −0.511600
\(184\) −18.9777 −1.39906
\(185\) 30.6242 2.25154
\(186\) −3.57376 −0.262041
\(187\) −10.6889 −0.781649
\(188\) −0.178098 −0.0129892
\(189\) −1.00000 −0.0727393
\(190\) −10.4968 −0.761515
\(191\) 11.1348 0.805684 0.402842 0.915269i \(-0.368022\pi\)
0.402842 + 0.915269i \(0.368022\pi\)
\(192\) −4.25168 −0.306839
\(193\) −8.74547 −0.629513 −0.314757 0.949172i \(-0.601923\pi\)
−0.314757 + 0.949172i \(0.601923\pi\)
\(194\) −14.3612 −1.03108
\(195\) 10.1641 0.727870
\(196\) 0.616031 0.0440022
\(197\) 1.79970 0.128224 0.0641118 0.997943i \(-0.479579\pi\)
0.0641118 + 0.997943i \(0.479579\pi\)
\(198\) 9.43344 0.670405
\(199\) −9.09677 −0.644853 −0.322426 0.946595i \(-0.604498\pi\)
−0.322426 + 0.946595i \(0.604498\pi\)
\(200\) 21.4430 1.51625
\(201\) −2.40863 −0.169892
\(202\) 0.508540 0.0357807
\(203\) −1.07148 −0.0752031
\(204\) −1.12898 −0.0790445
\(205\) 12.3297 0.861142
\(206\) 20.9041 1.45646
\(207\) −8.47805 −0.589265
\(208\) −12.9173 −0.895656
\(209\) 9.91317 0.685708
\(210\) −6.17577 −0.426169
\(211\) 6.97807 0.480390 0.240195 0.970725i \(-0.422789\pi\)
0.240195 + 0.970725i \(0.422789\pi\)
\(212\) 4.14132 0.284427
\(213\) 11.3491 0.777625
\(214\) −4.62079 −0.315871
\(215\) −11.9551 −0.815332
\(216\) −2.23845 −0.152307
\(217\) −2.20955 −0.149994
\(218\) 11.1835 0.757442
\(219\) 4.36922 0.295244
\(220\) 13.7189 0.924931
\(221\) 4.87849 0.328163
\(222\) −12.9723 −0.870642
\(223\) −16.3296 −1.09351 −0.546757 0.837291i \(-0.684138\pi\)
−0.546757 + 0.837291i \(0.684138\pi\)
\(224\) 3.37171 0.225282
\(225\) 9.57940 0.638627
\(226\) 25.8528 1.71970
\(227\) −3.43480 −0.227976 −0.113988 0.993482i \(-0.536362\pi\)
−0.113988 + 0.993482i \(0.536362\pi\)
\(228\) 1.04705 0.0693424
\(229\) −1.08011 −0.0713757 −0.0356879 0.999363i \(-0.511362\pi\)
−0.0356879 + 0.999363i \(0.511362\pi\)
\(230\) −52.3585 −3.45242
\(231\) 5.83242 0.383745
\(232\) −2.39846 −0.157466
\(233\) 14.9222 0.977588 0.488794 0.872399i \(-0.337437\pi\)
0.488794 + 0.872399i \(0.337437\pi\)
\(234\) −4.30549 −0.281459
\(235\) 1.10389 0.0720102
\(236\) 4.91963 0.320241
\(237\) 4.87186 0.316462
\(238\) −2.96419 −0.192140
\(239\) −10.8737 −0.703361 −0.351680 0.936120i \(-0.614390\pi\)
−0.351680 + 0.936120i \(0.614390\pi\)
\(240\) −18.5286 −1.19601
\(241\) 12.7179 0.819233 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(242\) −37.2282 −2.39312
\(243\) −1.00000 −0.0641500
\(244\) 4.26343 0.272938
\(245\) −3.81830 −0.243942
\(246\) −5.22280 −0.332994
\(247\) −4.52444 −0.287883
\(248\) −4.94598 −0.314070
\(249\) 5.97861 0.378879
\(250\) 28.2813 1.78867
\(251\) −16.1665 −1.02042 −0.510209 0.860051i \(-0.670432\pi\)
−0.510209 + 0.860051i \(0.670432\pi\)
\(252\) 0.616031 0.0388063
\(253\) 49.4475 3.10874
\(254\) 29.1980 1.83205
\(255\) 6.99768 0.438212
\(256\) 13.5261 0.845379
\(257\) −21.9692 −1.37040 −0.685202 0.728353i \(-0.740286\pi\)
−0.685202 + 0.728353i \(0.740286\pi\)
\(258\) 5.06413 0.315279
\(259\) −8.02038 −0.498362
\(260\) −6.26143 −0.388317
\(261\) −1.07148 −0.0663229
\(262\) 36.2451 2.23923
\(263\) −16.8388 −1.03833 −0.519163 0.854675i \(-0.673756\pi\)
−0.519163 + 0.854675i \(0.673756\pi\)
\(264\) 13.0556 0.803516
\(265\) −25.6688 −1.57682
\(266\) 2.74907 0.168556
\(267\) 14.2467 0.871883
\(268\) 1.48379 0.0906368
\(269\) −0.655115 −0.0399430 −0.0199715 0.999801i \(-0.506358\pi\)
−0.0199715 + 0.999801i \(0.506358\pi\)
\(270\) −6.17577 −0.375846
\(271\) 4.32325 0.262619 0.131309 0.991341i \(-0.458082\pi\)
0.131309 + 0.991341i \(0.458082\pi\)
\(272\) −8.89315 −0.539227
\(273\) −2.66196 −0.161109
\(274\) 9.76764 0.590085
\(275\) −55.8711 −3.36915
\(276\) 5.22274 0.314372
\(277\) 19.2556 1.15696 0.578479 0.815698i \(-0.303647\pi\)
0.578479 + 0.815698i \(0.303647\pi\)
\(278\) 8.42215 0.505127
\(279\) −2.20955 −0.132282
\(280\) −8.54708 −0.510786
\(281\) −14.4857 −0.864142 −0.432071 0.901840i \(-0.642217\pi\)
−0.432071 + 0.901840i \(0.642217\pi\)
\(282\) −0.467605 −0.0278455
\(283\) −23.0964 −1.37294 −0.686469 0.727159i \(-0.740840\pi\)
−0.686469 + 0.727159i \(0.740840\pi\)
\(284\) −6.99137 −0.414861
\(285\) −6.48984 −0.384425
\(286\) 25.1114 1.48487
\(287\) −3.22910 −0.190608
\(288\) 3.37171 0.198680
\(289\) −13.6413 −0.802431
\(290\) −6.61721 −0.388576
\(291\) −8.87913 −0.520504
\(292\) −2.69157 −0.157512
\(293\) 28.0899 1.64103 0.820516 0.571624i \(-0.193686\pi\)
0.820516 + 0.571624i \(0.193686\pi\)
\(294\) 1.61741 0.0943295
\(295\) −30.4930 −1.77537
\(296\) −17.9532 −1.04351
\(297\) 5.83242 0.338431
\(298\) −2.49871 −0.144747
\(299\) −22.5682 −1.30515
\(300\) −5.90120 −0.340706
\(301\) 3.13100 0.180468
\(302\) −9.73758 −0.560335
\(303\) 0.314415 0.0180627
\(304\) 8.24775 0.473041
\(305\) −26.4257 −1.51313
\(306\) −2.96419 −0.169451
\(307\) −13.8386 −0.789809 −0.394905 0.918722i \(-0.629222\pi\)
−0.394905 + 0.918722i \(0.629222\pi\)
\(308\) −3.59295 −0.204727
\(309\) 12.9244 0.735244
\(310\) −13.6457 −0.775023
\(311\) 15.6609 0.888049 0.444024 0.896015i \(-0.353550\pi\)
0.444024 + 0.896015i \(0.353550\pi\)
\(312\) −5.95867 −0.337343
\(313\) −9.07104 −0.512725 −0.256363 0.966581i \(-0.582524\pi\)
−0.256363 + 0.966581i \(0.582524\pi\)
\(314\) 28.3427 1.59947
\(315\) −3.81830 −0.215137
\(316\) −3.00122 −0.168832
\(317\) 28.5237 1.60205 0.801026 0.598630i \(-0.204288\pi\)
0.801026 + 0.598630i \(0.204288\pi\)
\(318\) 10.8732 0.609739
\(319\) 6.24932 0.349895
\(320\) −16.2342 −0.907519
\(321\) −2.85690 −0.159457
\(322\) 13.7125 0.764169
\(323\) −3.11493 −0.173319
\(324\) 0.616031 0.0342239
\(325\) 25.5000 1.41448
\(326\) 35.7387 1.97938
\(327\) 6.91442 0.382369
\(328\) −7.22820 −0.399110
\(329\) −0.289107 −0.0159390
\(330\) 36.0197 1.98282
\(331\) 17.1939 0.945065 0.472532 0.881313i \(-0.343340\pi\)
0.472532 + 0.881313i \(0.343340\pi\)
\(332\) −3.68301 −0.202131
\(333\) −8.02038 −0.439514
\(334\) 14.7926 0.809418
\(335\) −9.19686 −0.502478
\(336\) 4.85257 0.264729
\(337\) −28.5883 −1.55730 −0.778651 0.627458i \(-0.784096\pi\)
−0.778651 + 0.627458i \(0.784096\pi\)
\(338\) 9.56536 0.520287
\(339\) 15.9840 0.868132
\(340\) −4.31079 −0.233785
\(341\) 12.8870 0.697872
\(342\) 2.74907 0.148653
\(343\) 1.00000 0.0539949
\(344\) 7.00861 0.377879
\(345\) −32.3717 −1.74283
\(346\) 0.893605 0.0480405
\(347\) −17.8369 −0.957534 −0.478767 0.877942i \(-0.658916\pi\)
−0.478767 + 0.877942i \(0.658916\pi\)
\(348\) 0.660064 0.0353832
\(349\) 6.53762 0.349951 0.174975 0.984573i \(-0.444015\pi\)
0.174975 + 0.984573i \(0.444015\pi\)
\(350\) −15.4939 −0.828182
\(351\) −2.66196 −0.142085
\(352\) −19.6652 −1.04816
\(353\) −2.52280 −0.134275 −0.0671375 0.997744i \(-0.521387\pi\)
−0.0671375 + 0.997744i \(0.521387\pi\)
\(354\) 12.9167 0.686515
\(355\) 43.3341 2.29994
\(356\) −8.77640 −0.465148
\(357\) −1.83267 −0.0969952
\(358\) −10.6837 −0.564653
\(359\) −4.77378 −0.251950 −0.125975 0.992033i \(-0.540206\pi\)
−0.125975 + 0.992033i \(0.540206\pi\)
\(360\) −8.54708 −0.450471
\(361\) −16.1111 −0.847954
\(362\) −23.2105 −1.21991
\(363\) −23.0171 −1.20808
\(364\) 1.63985 0.0859513
\(365\) 16.6830 0.873227
\(366\) 11.1938 0.585110
\(367\) 2.61693 0.136602 0.0683012 0.997665i \(-0.478242\pi\)
0.0683012 + 0.997665i \(0.478242\pi\)
\(368\) 41.1403 2.14459
\(369\) −3.22910 −0.168100
\(370\) −49.5320 −2.57505
\(371\) 6.72259 0.349019
\(372\) 1.36115 0.0705724
\(373\) 3.48855 0.180630 0.0903150 0.995913i \(-0.471213\pi\)
0.0903150 + 0.995913i \(0.471213\pi\)
\(374\) 17.2884 0.893961
\(375\) 17.4855 0.902949
\(376\) −0.647151 −0.0333743
\(377\) −2.85223 −0.146897
\(378\) 1.61741 0.0831908
\(379\) 3.43946 0.176673 0.0883367 0.996091i \(-0.471845\pi\)
0.0883367 + 0.996091i \(0.471845\pi\)
\(380\) 3.99794 0.205090
\(381\) 18.0523 0.924846
\(382\) −18.0096 −0.921449
\(383\) −1.00000 −0.0510976
\(384\) 13.6202 0.695051
\(385\) 22.2699 1.13498
\(386\) 14.1451 0.719965
\(387\) 3.13100 0.159158
\(388\) 5.46981 0.277688
\(389\) −0.775682 −0.0393286 −0.0196643 0.999807i \(-0.506260\pi\)
−0.0196643 + 0.999807i \(0.506260\pi\)
\(390\) −16.4396 −0.832454
\(391\) −15.5375 −0.785763
\(392\) 2.23845 0.113059
\(393\) 22.4093 1.13040
\(394\) −2.91087 −0.146647
\(395\) 18.6022 0.935980
\(396\) −3.59295 −0.180552
\(397\) 18.2597 0.916430 0.458215 0.888841i \(-0.348489\pi\)
0.458215 + 0.888841i \(0.348489\pi\)
\(398\) 14.7132 0.737509
\(399\) 1.69967 0.0850898
\(400\) −46.4847 −2.32423
\(401\) 37.2852 1.86193 0.930967 0.365104i \(-0.118967\pi\)
0.930967 + 0.365104i \(0.118967\pi\)
\(402\) 3.89575 0.194302
\(403\) −5.88173 −0.292990
\(404\) −0.193689 −0.00963641
\(405\) −3.81830 −0.189733
\(406\) 1.73303 0.0860087
\(407\) 46.7782 2.31871
\(408\) −4.10235 −0.203096
\(409\) 7.77100 0.384251 0.192125 0.981370i \(-0.438462\pi\)
0.192125 + 0.981370i \(0.438462\pi\)
\(410\) −19.9422 −0.984875
\(411\) 6.03905 0.297884
\(412\) −7.96183 −0.392251
\(413\) 7.98601 0.392966
\(414\) 13.7125 0.673933
\(415\) 22.8281 1.12059
\(416\) 8.97535 0.440053
\(417\) 5.20717 0.254996
\(418\) −16.0337 −0.784234
\(419\) 18.3597 0.896932 0.448466 0.893800i \(-0.351970\pi\)
0.448466 + 0.893800i \(0.351970\pi\)
\(420\) 2.35219 0.114775
\(421\) −15.4350 −0.752257 −0.376129 0.926567i \(-0.622745\pi\)
−0.376129 + 0.926567i \(0.622745\pi\)
\(422\) −11.2864 −0.549415
\(423\) −0.289107 −0.0140568
\(424\) 15.0482 0.730805
\(425\) 17.5559 0.851585
\(426\) −18.3561 −0.889358
\(427\) 6.92080 0.334921
\(428\) 1.75994 0.0850698
\(429\) 15.5256 0.749585
\(430\) 19.3364 0.932483
\(431\) −20.3818 −0.981755 −0.490878 0.871229i \(-0.663324\pi\)
−0.490878 + 0.871229i \(0.663324\pi\)
\(432\) 4.85257 0.233469
\(433\) 34.7468 1.66983 0.834913 0.550382i \(-0.185518\pi\)
0.834913 + 0.550382i \(0.185518\pi\)
\(434\) 3.57376 0.171546
\(435\) −4.09123 −0.196159
\(436\) −4.25950 −0.203993
\(437\) 14.4099 0.689317
\(438\) −7.06684 −0.337667
\(439\) 5.86283 0.279817 0.139909 0.990164i \(-0.455319\pi\)
0.139909 + 0.990164i \(0.455319\pi\)
\(440\) 49.8501 2.37651
\(441\) 1.00000 0.0476190
\(442\) −7.89054 −0.375315
\(443\) 40.3266 1.91597 0.957987 0.286812i \(-0.0925956\pi\)
0.957987 + 0.286812i \(0.0925956\pi\)
\(444\) 4.94080 0.234480
\(445\) 54.3981 2.57872
\(446\) 26.4118 1.25064
\(447\) −1.54488 −0.0730704
\(448\) 4.25168 0.200873
\(449\) −6.84391 −0.322984 −0.161492 0.986874i \(-0.551631\pi\)
−0.161492 + 0.986874i \(0.551631\pi\)
\(450\) −15.4939 −0.730388
\(451\) 18.8335 0.886834
\(452\) −9.84664 −0.463147
\(453\) −6.02046 −0.282866
\(454\) 5.55549 0.260732
\(455\) −10.1641 −0.476503
\(456\) 3.80462 0.178168
\(457\) −19.1964 −0.897971 −0.448985 0.893539i \(-0.648214\pi\)
−0.448985 + 0.893539i \(0.648214\pi\)
\(458\) 1.74699 0.0816313
\(459\) −1.83267 −0.0855417
\(460\) 19.9420 0.929799
\(461\) −9.48991 −0.441989 −0.220995 0.975275i \(-0.570930\pi\)
−0.220995 + 0.975275i \(0.570930\pi\)
\(462\) −9.43344 −0.438883
\(463\) 21.7366 1.01018 0.505092 0.863066i \(-0.331459\pi\)
0.505092 + 0.863066i \(0.331459\pi\)
\(464\) 5.19943 0.241377
\(465\) −8.43673 −0.391244
\(466\) −24.1354 −1.11805
\(467\) 10.3772 0.480202 0.240101 0.970748i \(-0.422819\pi\)
0.240101 + 0.970748i \(0.422819\pi\)
\(468\) 1.63985 0.0758020
\(469\) 2.40863 0.111220
\(470\) −1.78546 −0.0823569
\(471\) 17.5234 0.807438
\(472\) 17.8763 0.822824
\(473\) −18.2613 −0.839657
\(474\) −7.87982 −0.361932
\(475\) −16.2818 −0.747060
\(476\) 1.12898 0.0517467
\(477\) 6.72259 0.307806
\(478\) 17.5873 0.804423
\(479\) −26.4060 −1.20652 −0.603262 0.797543i \(-0.706132\pi\)
−0.603262 + 0.797543i \(0.706132\pi\)
\(480\) 12.8742 0.587624
\(481\) −21.3499 −0.973472
\(482\) −20.5701 −0.936944
\(483\) 8.47805 0.385764
\(484\) 14.1792 0.644510
\(485\) −33.9031 −1.53946
\(486\) 1.61741 0.0733674
\(487\) 37.9905 1.72151 0.860756 0.509018i \(-0.169991\pi\)
0.860756 + 0.509018i \(0.169991\pi\)
\(488\) 15.4919 0.701285
\(489\) 22.0962 0.999224
\(490\) 6.17577 0.278993
\(491\) −12.1865 −0.549968 −0.274984 0.961449i \(-0.588673\pi\)
−0.274984 + 0.961449i \(0.588673\pi\)
\(492\) 1.98923 0.0896812
\(493\) −1.96367 −0.0884392
\(494\) 7.31790 0.329248
\(495\) 22.2699 1.00096
\(496\) 10.7220 0.481432
\(497\) −11.3491 −0.509075
\(498\) −9.66989 −0.433318
\(499\) −20.6727 −0.925438 −0.462719 0.886505i \(-0.653126\pi\)
−0.462719 + 0.886505i \(0.653126\pi\)
\(500\) −10.7716 −0.481721
\(501\) 9.14586 0.408607
\(502\) 26.1479 1.16704
\(503\) −17.1737 −0.765739 −0.382870 0.923802i \(-0.625064\pi\)
−0.382870 + 0.923802i \(0.625064\pi\)
\(504\) 2.23845 0.0997086
\(505\) 1.20053 0.0534229
\(506\) −79.9771 −3.55542
\(507\) 5.91398 0.262649
\(508\) −11.1207 −0.493403
\(509\) −2.98112 −0.132136 −0.0660679 0.997815i \(-0.521045\pi\)
−0.0660679 + 0.997815i \(0.521045\pi\)
\(510\) −11.3182 −0.501176
\(511\) −4.36922 −0.193283
\(512\) 5.36304 0.237015
\(513\) 1.69967 0.0750421
\(514\) 35.5334 1.56731
\(515\) 49.3492 2.17459
\(516\) −1.92879 −0.0849104
\(517\) 1.68619 0.0741585
\(518\) 12.9723 0.569969
\(519\) 0.552490 0.0242516
\(520\) −22.7520 −0.997740
\(521\) −31.0279 −1.35936 −0.679678 0.733510i \(-0.737881\pi\)
−0.679678 + 0.733510i \(0.737881\pi\)
\(522\) 1.73303 0.0758525
\(523\) −8.67493 −0.379328 −0.189664 0.981849i \(-0.560740\pi\)
−0.189664 + 0.981849i \(0.560740\pi\)
\(524\) −13.8048 −0.603065
\(525\) −9.57940 −0.418079
\(526\) 27.2353 1.18752
\(527\) −4.04938 −0.176394
\(528\) −28.3022 −1.23169
\(529\) 48.8773 2.12510
\(530\) 41.5172 1.80339
\(531\) 7.98601 0.346563
\(532\) −1.04705 −0.0453952
\(533\) −8.59574 −0.372323
\(534\) −23.0428 −0.997160
\(535\) −10.9085 −0.471615
\(536\) 5.39160 0.232882
\(537\) −6.60544 −0.285046
\(538\) 1.05959 0.0456823
\(539\) −5.83242 −0.251220
\(540\) 2.35219 0.101222
\(541\) −2.47586 −0.106446 −0.0532228 0.998583i \(-0.516949\pi\)
−0.0532228 + 0.998583i \(0.516949\pi\)
\(542\) −6.99249 −0.300353
\(543\) −14.3503 −0.615832
\(544\) 6.17923 0.264932
\(545\) 26.4013 1.13091
\(546\) 4.30549 0.184258
\(547\) 3.95202 0.168976 0.0844881 0.996424i \(-0.473074\pi\)
0.0844881 + 0.996424i \(0.473074\pi\)
\(548\) −3.72024 −0.158921
\(549\) 6.92080 0.295373
\(550\) 90.3667 3.85325
\(551\) 1.82116 0.0775840
\(552\) 18.9777 0.807745
\(553\) −4.87186 −0.207173
\(554\) −31.1443 −1.32319
\(555\) −30.6242 −1.29993
\(556\) −3.20777 −0.136040
\(557\) −19.8735 −0.842066 −0.421033 0.907045i \(-0.638332\pi\)
−0.421033 + 0.907045i \(0.638332\pi\)
\(558\) 3.57376 0.151289
\(559\) 8.33460 0.352516
\(560\) 18.5286 0.782974
\(561\) 10.6889 0.451285
\(562\) 23.4293 0.988306
\(563\) 37.8407 1.59480 0.797399 0.603453i \(-0.206209\pi\)
0.797399 + 0.603453i \(0.206209\pi\)
\(564\) 0.178098 0.00749930
\(565\) 61.0317 2.56762
\(566\) 37.3564 1.57021
\(567\) 1.00000 0.0419961
\(568\) −25.4043 −1.06594
\(569\) 38.8416 1.62833 0.814163 0.580637i \(-0.197196\pi\)
0.814163 + 0.580637i \(0.197196\pi\)
\(570\) 10.4968 0.439661
\(571\) −0.300788 −0.0125876 −0.00629379 0.999980i \(-0.502003\pi\)
−0.00629379 + 0.999980i \(0.502003\pi\)
\(572\) −9.56427 −0.399902
\(573\) −11.1348 −0.465162
\(574\) 5.22280 0.217995
\(575\) −81.2146 −3.38688
\(576\) 4.25168 0.177153
\(577\) −20.5200 −0.854258 −0.427129 0.904191i \(-0.640475\pi\)
−0.427129 + 0.904191i \(0.640475\pi\)
\(578\) 22.0637 0.917728
\(579\) 8.74547 0.363450
\(580\) 2.52032 0.104651
\(581\) −5.97861 −0.248035
\(582\) 14.3612 0.595292
\(583\) −39.2089 −1.62387
\(584\) −9.78029 −0.404711
\(585\) −10.1641 −0.420236
\(586\) −45.4331 −1.87682
\(587\) 17.7252 0.731597 0.365798 0.930694i \(-0.380796\pi\)
0.365798 + 0.930694i \(0.380796\pi\)
\(588\) −0.616031 −0.0254047
\(589\) 3.75550 0.154743
\(590\) 49.3198 2.03046
\(591\) −1.79970 −0.0740300
\(592\) 38.9194 1.59958
\(593\) −19.5349 −0.802202 −0.401101 0.916034i \(-0.631372\pi\)
−0.401101 + 0.916034i \(0.631372\pi\)
\(594\) −9.43344 −0.387059
\(595\) −6.99768 −0.286877
\(596\) 0.951694 0.0389829
\(597\) 9.09677 0.372306
\(598\) 36.5021 1.49268
\(599\) −12.9827 −0.530459 −0.265230 0.964185i \(-0.585448\pi\)
−0.265230 + 0.964185i \(0.585448\pi\)
\(600\) −21.4430 −0.875408
\(601\) 21.3752 0.871911 0.435956 0.899968i \(-0.356410\pi\)
0.435956 + 0.899968i \(0.356410\pi\)
\(602\) −5.06413 −0.206399
\(603\) 2.40863 0.0980870
\(604\) 3.70879 0.150908
\(605\) −87.8861 −3.57308
\(606\) −0.508540 −0.0206580
\(607\) −22.5833 −0.916627 −0.458313 0.888791i \(-0.651546\pi\)
−0.458313 + 0.888791i \(0.651546\pi\)
\(608\) −5.73078 −0.232414
\(609\) 1.07148 0.0434185
\(610\) 42.7413 1.73054
\(611\) −0.769589 −0.0311342
\(612\) 1.12898 0.0456363
\(613\) −36.6141 −1.47883 −0.739414 0.673251i \(-0.764897\pi\)
−0.739414 + 0.673251i \(0.764897\pi\)
\(614\) 22.3827 0.903293
\(615\) −12.3297 −0.497181
\(616\) −13.0556 −0.526025
\(617\) −35.0818 −1.41234 −0.706170 0.708042i \(-0.749579\pi\)
−0.706170 + 0.708042i \(0.749579\pi\)
\(618\) −20.9041 −0.840887
\(619\) −39.3616 −1.58208 −0.791039 0.611766i \(-0.790460\pi\)
−0.791039 + 0.611766i \(0.790460\pi\)
\(620\) 5.19728 0.208728
\(621\) 8.47805 0.340212
\(622\) −25.3302 −1.01565
\(623\) −14.2467 −0.570782
\(624\) 12.9173 0.517107
\(625\) 18.8679 0.754718
\(626\) 14.6716 0.586396
\(627\) −9.91317 −0.395894
\(628\) −10.7950 −0.430767
\(629\) −14.6987 −0.586076
\(630\) 6.17577 0.246049
\(631\) 41.2313 1.64139 0.820695 0.571366i \(-0.193586\pi\)
0.820695 + 0.571366i \(0.193586\pi\)
\(632\) −10.9054 −0.433795
\(633\) −6.97807 −0.277353
\(634\) −46.1347 −1.83224
\(635\) 68.9289 2.73536
\(636\) −4.14132 −0.164214
\(637\) 2.66196 0.105471
\(638\) −10.1077 −0.400169
\(639\) −11.3491 −0.448962
\(640\) 52.0058 2.05571
\(641\) −23.8154 −0.940653 −0.470327 0.882492i \(-0.655864\pi\)
−0.470327 + 0.882492i \(0.655864\pi\)
\(642\) 4.62079 0.182368
\(643\) 17.1991 0.678268 0.339134 0.940738i \(-0.389866\pi\)
0.339134 + 0.940738i \(0.389866\pi\)
\(644\) −5.22274 −0.205805
\(645\) 11.9551 0.470732
\(646\) 5.03813 0.198223
\(647\) 36.9235 1.45161 0.725806 0.687899i \(-0.241467\pi\)
0.725806 + 0.687899i \(0.241467\pi\)
\(648\) 2.23845 0.0879347
\(649\) −46.5778 −1.82834
\(650\) −41.2440 −1.61772
\(651\) 2.20955 0.0865992
\(652\) −13.6119 −0.533084
\(653\) 21.7155 0.849795 0.424897 0.905242i \(-0.360310\pi\)
0.424897 + 0.905242i \(0.360310\pi\)
\(654\) −11.1835 −0.437309
\(655\) 85.5653 3.34331
\(656\) 15.6694 0.611789
\(657\) −4.36922 −0.170459
\(658\) 0.467605 0.0182291
\(659\) 24.6953 0.961994 0.480997 0.876722i \(-0.340275\pi\)
0.480997 + 0.876722i \(0.340275\pi\)
\(660\) −13.7189 −0.534009
\(661\) 7.53059 0.292906 0.146453 0.989218i \(-0.453214\pi\)
0.146453 + 0.989218i \(0.453214\pi\)
\(662\) −27.8097 −1.08086
\(663\) −4.87849 −0.189465
\(664\) −13.3828 −0.519355
\(665\) 6.48984 0.251665
\(666\) 12.9723 0.502666
\(667\) 9.08405 0.351736
\(668\) −5.63413 −0.217991
\(669\) 16.3296 0.631340
\(670\) 14.8751 0.574677
\(671\) −40.3650 −1.55827
\(672\) −3.37171 −0.130066
\(673\) 48.9265 1.88598 0.942989 0.332824i \(-0.108002\pi\)
0.942989 + 0.332824i \(0.108002\pi\)
\(674\) 46.2391 1.78106
\(675\) −9.57940 −0.368711
\(676\) −3.64319 −0.140123
\(677\) 41.4004 1.59115 0.795574 0.605857i \(-0.207170\pi\)
0.795574 + 0.605857i \(0.207170\pi\)
\(678\) −25.8528 −0.992870
\(679\) 8.87913 0.340750
\(680\) −15.6640 −0.600686
\(681\) 3.43480 0.131622
\(682\) −20.8437 −0.798145
\(683\) −42.0704 −1.60978 −0.804890 0.593423i \(-0.797776\pi\)
−0.804890 + 0.593423i \(0.797776\pi\)
\(684\) −1.04705 −0.0400348
\(685\) 23.0589 0.881035
\(686\) −1.61741 −0.0617532
\(687\) 1.08011 0.0412088
\(688\) −15.1934 −0.579243
\(689\) 17.8952 0.681754
\(690\) 52.3585 1.99325
\(691\) −39.7522 −1.51224 −0.756122 0.654431i \(-0.772908\pi\)
−0.756122 + 0.654431i \(0.772908\pi\)
\(692\) −0.340350 −0.0129382
\(693\) −5.83242 −0.221555
\(694\) 28.8496 1.09512
\(695\) 19.8825 0.754187
\(696\) 2.39846 0.0909133
\(697\) −5.91788 −0.224156
\(698\) −10.5740 −0.400233
\(699\) −14.9222 −0.564411
\(700\) 5.90120 0.223045
\(701\) 0.473823 0.0178961 0.00894803 0.999960i \(-0.497152\pi\)
0.00894803 + 0.999960i \(0.497152\pi\)
\(702\) 4.30549 0.162500
\(703\) 13.6320 0.514140
\(704\) −24.7976 −0.934594
\(705\) −1.10389 −0.0415751
\(706\) 4.08041 0.153568
\(707\) −0.314415 −0.0118248
\(708\) −4.91963 −0.184891
\(709\) 44.3251 1.66466 0.832332 0.554277i \(-0.187005\pi\)
0.832332 + 0.554277i \(0.187005\pi\)
\(710\) −70.0892 −2.63040
\(711\) −4.87186 −0.182709
\(712\) −31.8905 −1.19515
\(713\) 18.7327 0.701545
\(714\) 2.96419 0.110932
\(715\) 59.2815 2.21700
\(716\) 4.06915 0.152071
\(717\) 10.8737 0.406086
\(718\) 7.72118 0.288152
\(719\) −32.8297 −1.22434 −0.612171 0.790725i \(-0.709704\pi\)
−0.612171 + 0.790725i \(0.709704\pi\)
\(720\) 18.5286 0.690518
\(721\) −12.9244 −0.481330
\(722\) 26.0584 0.969793
\(723\) −12.7179 −0.472984
\(724\) 8.84025 0.328545
\(725\) −10.2641 −0.381200
\(726\) 37.2282 1.38167
\(727\) 24.9801 0.926461 0.463231 0.886238i \(-0.346690\pi\)
0.463231 + 0.886238i \(0.346690\pi\)
\(728\) 5.95867 0.220843
\(729\) 1.00000 0.0370370
\(730\) −26.9833 −0.998697
\(731\) 5.73810 0.212231
\(732\) −4.26343 −0.157581
\(733\) −8.97575 −0.331527 −0.165763 0.986166i \(-0.553009\pi\)
−0.165763 + 0.986166i \(0.553009\pi\)
\(734\) −4.23265 −0.156230
\(735\) 3.81830 0.140840
\(736\) −28.5855 −1.05368
\(737\) −14.0481 −0.517469
\(738\) 5.22280 0.192254
\(739\) 5.18372 0.190686 0.0953430 0.995444i \(-0.469605\pi\)
0.0953430 + 0.995444i \(0.469605\pi\)
\(740\) 18.8654 0.693508
\(741\) 4.52444 0.166210
\(742\) −10.8732 −0.399168
\(743\) 26.6816 0.978852 0.489426 0.872045i \(-0.337206\pi\)
0.489426 + 0.872045i \(0.337206\pi\)
\(744\) 4.94598 0.181328
\(745\) −5.89882 −0.216116
\(746\) −5.64243 −0.206584
\(747\) −5.97861 −0.218746
\(748\) −6.58469 −0.240760
\(749\) 2.85690 0.104389
\(750\) −28.2813 −1.03269
\(751\) 8.72133 0.318246 0.159123 0.987259i \(-0.449133\pi\)
0.159123 + 0.987259i \(0.449133\pi\)
\(752\) 1.40291 0.0511588
\(753\) 16.1665 0.589138
\(754\) 4.61324 0.168004
\(755\) −22.9879 −0.836615
\(756\) −0.616031 −0.0224048
\(757\) −4.40542 −0.160118 −0.0800589 0.996790i \(-0.525511\pi\)
−0.0800589 + 0.996790i \(0.525511\pi\)
\(758\) −5.56304 −0.202059
\(759\) −49.4475 −1.79483
\(760\) 14.5272 0.526957
\(761\) −20.1386 −0.730025 −0.365013 0.931003i \(-0.618935\pi\)
−0.365013 + 0.931003i \(0.618935\pi\)
\(762\) −29.1980 −1.05773
\(763\) −6.91442 −0.250319
\(764\) 6.85936 0.248163
\(765\) −6.99768 −0.253002
\(766\) 1.61741 0.0584396
\(767\) 21.2584 0.767597
\(768\) −13.5261 −0.488080
\(769\) 15.5277 0.559941 0.279971 0.960009i \(-0.409675\pi\)
0.279971 + 0.960009i \(0.409675\pi\)
\(770\) −36.0197 −1.29806
\(771\) 21.9692 0.791203
\(772\) −5.38748 −0.193900
\(773\) −45.9176 −1.65154 −0.825771 0.564006i \(-0.809260\pi\)
−0.825771 + 0.564006i \(0.809260\pi\)
\(774\) −5.06413 −0.182027
\(775\) −21.1662 −0.760312
\(776\) 19.8755 0.713489
\(777\) 8.02038 0.287730
\(778\) 1.25460 0.0449796
\(779\) 5.48840 0.196642
\(780\) 6.26143 0.224195
\(781\) 66.1925 2.36855
\(782\) 25.1305 0.898666
\(783\) 1.07148 0.0382916
\(784\) −4.85257 −0.173306
\(785\) 66.9097 2.38811
\(786\) −36.2451 −1.29282
\(787\) −47.2905 −1.68572 −0.842862 0.538130i \(-0.819131\pi\)
−0.842862 + 0.538130i \(0.819131\pi\)
\(788\) 1.10867 0.0394948
\(789\) 16.8388 0.599477
\(790\) −30.0875 −1.07047
\(791\) −15.9840 −0.568326
\(792\) −13.0556 −0.463910
\(793\) 18.4229 0.654216
\(794\) −29.5336 −1.04811
\(795\) 25.6688 0.910380
\(796\) −5.60389 −0.198625
\(797\) 35.1234 1.24413 0.622066 0.782964i \(-0.286293\pi\)
0.622066 + 0.782964i \(0.286293\pi\)
\(798\) −2.74907 −0.0973159
\(799\) −0.529837 −0.0187443
\(800\) 32.2990 1.14194
\(801\) −14.2467 −0.503382
\(802\) −60.3056 −2.12947
\(803\) 25.4831 0.899279
\(804\) −1.48379 −0.0523292
\(805\) 32.3717 1.14095
\(806\) 9.51320 0.335088
\(807\) 0.655115 0.0230611
\(808\) −0.703804 −0.0247597
\(809\) 19.1133 0.671987 0.335994 0.941864i \(-0.390928\pi\)
0.335994 + 0.941864i \(0.390928\pi\)
\(810\) 6.17577 0.216995
\(811\) 10.1460 0.356273 0.178136 0.984006i \(-0.442993\pi\)
0.178136 + 0.984006i \(0.442993\pi\)
\(812\) −0.660064 −0.0231637
\(813\) −4.32325 −0.151623
\(814\) −75.6597 −2.65187
\(815\) 84.3698 2.95534
\(816\) 8.89315 0.311323
\(817\) −5.32167 −0.186182
\(818\) −12.5689 −0.439462
\(819\) 2.66196 0.0930163
\(820\) 7.59546 0.265245
\(821\) −40.6747 −1.41956 −0.709779 0.704425i \(-0.751205\pi\)
−0.709779 + 0.704425i \(0.751205\pi\)
\(822\) −9.76764 −0.340686
\(823\) 31.2483 1.08925 0.544624 0.838681i \(-0.316673\pi\)
0.544624 + 0.838681i \(0.316673\pi\)
\(824\) −28.9307 −1.00785
\(825\) 55.8711 1.94518
\(826\) −12.9167 −0.449429
\(827\) 46.0537 1.60144 0.800721 0.599037i \(-0.204450\pi\)
0.800721 + 0.599037i \(0.204450\pi\)
\(828\) −5.22274 −0.181503
\(829\) −30.8646 −1.07197 −0.535986 0.844227i \(-0.680060\pi\)
−0.535986 + 0.844227i \(0.680060\pi\)
\(830\) −36.9225 −1.28160
\(831\) −19.2556 −0.667970
\(832\) 11.3178 0.392374
\(833\) 1.83267 0.0634983
\(834\) −8.42215 −0.291635
\(835\) 34.9216 1.20851
\(836\) 6.10681 0.211209
\(837\) 2.20955 0.0763733
\(838\) −29.6953 −1.02581
\(839\) −8.46162 −0.292128 −0.146064 0.989275i \(-0.546660\pi\)
−0.146064 + 0.989275i \(0.546660\pi\)
\(840\) 8.54708 0.294902
\(841\) −27.8519 −0.960411
\(842\) 24.9648 0.860345
\(843\) 14.4857 0.498912
\(844\) 4.29870 0.147968
\(845\) 22.5814 0.776822
\(846\) 0.467605 0.0160766
\(847\) 23.0171 0.790876
\(848\) −32.6218 −1.12024
\(849\) 23.0964 0.792666
\(850\) −28.3951 −0.973945
\(851\) 67.9971 2.33091
\(852\) 6.99137 0.239520
\(853\) 6.03293 0.206563 0.103282 0.994652i \(-0.467066\pi\)
0.103282 + 0.994652i \(0.467066\pi\)
\(854\) −11.1938 −0.383044
\(855\) 6.48984 0.221948
\(856\) 6.39503 0.218578
\(857\) 12.3878 0.423159 0.211579 0.977361i \(-0.432139\pi\)
0.211579 + 0.977361i \(0.432139\pi\)
\(858\) −25.1114 −0.857289
\(859\) −35.3322 −1.20552 −0.602760 0.797922i \(-0.705932\pi\)
−0.602760 + 0.797922i \(0.705932\pi\)
\(860\) −7.36471 −0.251135
\(861\) 3.22910 0.110048
\(862\) 32.9658 1.12282
\(863\) −18.1617 −0.618230 −0.309115 0.951025i \(-0.600033\pi\)
−0.309115 + 0.951025i \(0.600033\pi\)
\(864\) −3.37171 −0.114708
\(865\) 2.10957 0.0717275
\(866\) −56.2000 −1.90975
\(867\) 13.6413 0.463284
\(868\) −1.36115 −0.0462005
\(869\) 28.4147 0.963904
\(870\) 6.61721 0.224345
\(871\) 6.41167 0.217251
\(872\) −15.4776 −0.524138
\(873\) 8.87913 0.300513
\(874\) −23.3067 −0.788361
\(875\) −17.4855 −0.591119
\(876\) 2.69157 0.0909398
\(877\) −26.9720 −0.910780 −0.455390 0.890292i \(-0.650500\pi\)
−0.455390 + 0.890292i \(0.650500\pi\)
\(878\) −9.48262 −0.320023
\(879\) −28.0899 −0.947450
\(880\) −108.066 −3.64291
\(881\) 29.9656 1.00957 0.504783 0.863246i \(-0.331572\pi\)
0.504783 + 0.863246i \(0.331572\pi\)
\(882\) −1.61741 −0.0544612
\(883\) −11.7049 −0.393903 −0.196951 0.980413i \(-0.563104\pi\)
−0.196951 + 0.980413i \(0.563104\pi\)
\(884\) 3.00530 0.101079
\(885\) 30.4930 1.02501
\(886\) −65.2248 −2.19127
\(887\) −1.49587 −0.0502263 −0.0251132 0.999685i \(-0.507995\pi\)
−0.0251132 + 0.999685i \(0.507995\pi\)
\(888\) 17.9532 0.602471
\(889\) −18.0523 −0.605454
\(890\) −87.9843 −2.94924
\(891\) −5.83242 −0.195393
\(892\) −10.0596 −0.336819
\(893\) 0.491385 0.0164436
\(894\) 2.49871 0.0835695
\(895\) −25.2216 −0.843063
\(896\) −13.6202 −0.455017
\(897\) 22.5682 0.753530
\(898\) 11.0694 0.369392
\(899\) 2.36749 0.0789602
\(900\) 5.90120 0.196707
\(901\) 12.3203 0.410448
\(902\) −30.4615 −1.01426
\(903\) −3.13100 −0.104193
\(904\) −35.7794 −1.19001
\(905\) −54.7939 −1.82141
\(906\) 9.73758 0.323509
\(907\) 36.7886 1.22154 0.610772 0.791806i \(-0.290859\pi\)
0.610772 + 0.791806i \(0.290859\pi\)
\(908\) −2.11594 −0.0702200
\(909\) −0.314415 −0.0104285
\(910\) 16.4396 0.544969
\(911\) −4.99085 −0.165354 −0.0826771 0.996576i \(-0.526347\pi\)
−0.0826771 + 0.996576i \(0.526347\pi\)
\(912\) −8.24775 −0.273110
\(913\) 34.8697 1.15402
\(914\) 31.0486 1.02700
\(915\) 26.4257 0.873606
\(916\) −0.665381 −0.0219848
\(917\) −22.4093 −0.740019
\(918\) 2.96419 0.0978328
\(919\) −9.44433 −0.311540 −0.155770 0.987793i \(-0.549786\pi\)
−0.155770 + 0.987793i \(0.549786\pi\)
\(920\) 72.4625 2.38902
\(921\) 13.8386 0.455997
\(922\) 15.3491 0.505497
\(923\) −30.2107 −0.994398
\(924\) 3.59295 0.118199
\(925\) −76.8304 −2.52617
\(926\) −35.1570 −1.15533
\(927\) −12.9244 −0.424493
\(928\) −3.61272 −0.118593
\(929\) −46.1310 −1.51351 −0.756755 0.653699i \(-0.773216\pi\)
−0.756755 + 0.653699i \(0.773216\pi\)
\(930\) 13.6457 0.447460
\(931\) −1.69967 −0.0557043
\(932\) 9.19255 0.301112
\(933\) −15.6609 −0.512715
\(934\) −16.7843 −0.549199
\(935\) 40.8134 1.33474
\(936\) 5.95867 0.194765
\(937\) 19.8670 0.649026 0.324513 0.945881i \(-0.394800\pi\)
0.324513 + 0.945881i \(0.394800\pi\)
\(938\) −3.89575 −0.127201
\(939\) 9.07104 0.296022
\(940\) 0.680033 0.0221802
\(941\) −11.9238 −0.388703 −0.194352 0.980932i \(-0.562260\pi\)
−0.194352 + 0.980932i \(0.562260\pi\)
\(942\) −28.3427 −0.923454
\(943\) 27.3765 0.891501
\(944\) −38.7527 −1.26129
\(945\) 3.81830 0.124209
\(946\) 29.5361 0.960303
\(947\) 36.3155 1.18009 0.590047 0.807369i \(-0.299109\pi\)
0.590047 + 0.807369i \(0.299109\pi\)
\(948\) 3.00122 0.0974750
\(949\) −11.6307 −0.377548
\(950\) 26.3344 0.854401
\(951\) −28.5237 −0.924945
\(952\) 4.10235 0.132958
\(953\) 32.9455 1.06721 0.533605 0.845734i \(-0.320837\pi\)
0.533605 + 0.845734i \(0.320837\pi\)
\(954\) −10.8732 −0.352033
\(955\) −42.5159 −1.37578
\(956\) −6.69853 −0.216646
\(957\) −6.24932 −0.202012
\(958\) 42.7095 1.37988
\(959\) −6.03905 −0.195011
\(960\) 16.2342 0.523956
\(961\) −26.1179 −0.842512
\(962\) 34.5317 1.11335
\(963\) 2.85690 0.0920623
\(964\) 7.83462 0.252336
\(965\) 33.3928 1.07495
\(966\) −13.7125 −0.441193
\(967\) 20.0960 0.646245 0.323123 0.946357i \(-0.395267\pi\)
0.323123 + 0.946357i \(0.395267\pi\)
\(968\) 51.5226 1.65600
\(969\) 3.11493 0.100066
\(970\) 54.8355 1.76066
\(971\) 32.6097 1.04649 0.523247 0.852181i \(-0.324721\pi\)
0.523247 + 0.852181i \(0.324721\pi\)
\(972\) −0.616031 −0.0197592
\(973\) −5.20717 −0.166934
\(974\) −61.4463 −1.96887
\(975\) −25.5000 −0.816652
\(976\) −33.5837 −1.07499
\(977\) 44.6229 1.42761 0.713807 0.700342i \(-0.246969\pi\)
0.713807 + 0.700342i \(0.246969\pi\)
\(978\) −35.7387 −1.14280
\(979\) 83.0926 2.65565
\(980\) −2.35219 −0.0751379
\(981\) −6.91442 −0.220761
\(982\) 19.7106 0.628991
\(983\) −21.0947 −0.672815 −0.336408 0.941716i \(-0.609212\pi\)
−0.336408 + 0.941716i \(0.609212\pi\)
\(984\) 7.22820 0.230426
\(985\) −6.87181 −0.218954
\(986\) 3.17607 0.101147
\(987\) 0.289107 0.00920236
\(988\) −2.78719 −0.0886725
\(989\) −26.5448 −0.844076
\(990\) −36.0197 −1.14478
\(991\) 14.6930 0.466739 0.233369 0.972388i \(-0.425025\pi\)
0.233369 + 0.972388i \(0.425025\pi\)
\(992\) −7.44997 −0.236537
\(993\) −17.1939 −0.545633
\(994\) 18.3561 0.582221
\(995\) 34.7342 1.10115
\(996\) 3.68301 0.116701
\(997\) 22.1576 0.701740 0.350870 0.936424i \(-0.385886\pi\)
0.350870 + 0.936424i \(0.385886\pi\)
\(998\) 33.4364 1.05841
\(999\) 8.02038 0.253754
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 \(a_p\))