Properties

Label 8015.2.a.l.1.7
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.28892 q^{2}\) \(-1.23476 q^{3}\) \(+3.23914 q^{4}\) \(-1.00000 q^{5}\) \(+2.82625 q^{6}\) \(-1.00000 q^{7}\) \(-2.83628 q^{8}\) \(-1.47538 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.28892 q^{2}\) \(-1.23476 q^{3}\) \(+3.23914 q^{4}\) \(-1.00000 q^{5}\) \(+2.82625 q^{6}\) \(-1.00000 q^{7}\) \(-2.83628 q^{8}\) \(-1.47538 q^{9}\) \(+2.28892 q^{10}\) \(-4.24991 q^{11}\) \(-3.99954 q^{12}\) \(-5.17662 q^{13}\) \(+2.28892 q^{14}\) \(+1.23476 q^{15}\) \(+0.0137336 q^{16}\) \(+5.50025 q^{17}\) \(+3.37702 q^{18}\) \(+2.06636 q^{19}\) \(-3.23914 q^{20}\) \(+1.23476 q^{21}\) \(+9.72768 q^{22}\) \(-3.42535 q^{23}\) \(+3.50211 q^{24}\) \(+1.00000 q^{25}\) \(+11.8489 q^{26}\) \(+5.52600 q^{27}\) \(-3.23914 q^{28}\) \(+10.7573 q^{29}\) \(-2.82625 q^{30}\) \(-2.23815 q^{31}\) \(+5.64113 q^{32}\) \(+5.24760 q^{33}\) \(-12.5896 q^{34}\) \(+1.00000 q^{35}\) \(-4.77895 q^{36}\) \(+7.31231 q^{37}\) \(-4.72974 q^{38}\) \(+6.39187 q^{39}\) \(+2.83628 q^{40}\) \(-9.61223 q^{41}\) \(-2.82625 q^{42}\) \(-7.31457 q^{43}\) \(-13.7660 q^{44}\) \(+1.47538 q^{45}\) \(+7.84033 q^{46}\) \(+12.8166 q^{47}\) \(-0.0169576 q^{48}\) \(+1.00000 q^{49}\) \(-2.28892 q^{50}\) \(-6.79147 q^{51}\) \(-16.7678 q^{52}\) \(-3.37750 q^{53}\) \(-12.6485 q^{54}\) \(+4.24991 q^{55}\) \(+2.83628 q^{56}\) \(-2.55146 q^{57}\) \(-24.6226 q^{58}\) \(-12.1196 q^{59}\) \(+3.99954 q^{60}\) \(-0.787009 q^{61}\) \(+5.12293 q^{62}\) \(+1.47538 q^{63}\) \(-12.9395 q^{64}\) \(+5.17662 q^{65}\) \(-12.0113 q^{66}\) \(-10.2824 q^{67}\) \(+17.8161 q^{68}\) \(+4.22947 q^{69}\) \(-2.28892 q^{70}\) \(-3.37445 q^{71}\) \(+4.18458 q^{72}\) \(-9.34915 q^{73}\) \(-16.7373 q^{74}\) \(-1.23476 q^{75}\) \(+6.69324 q^{76}\) \(+4.24991 q^{77}\) \(-14.6304 q^{78}\) \(-5.57508 q^{79}\) \(-0.0137336 q^{80}\) \(-2.39713 q^{81}\) \(+22.0016 q^{82}\) \(-7.49068 q^{83}\) \(+3.99954 q^{84}\) \(-5.50025 q^{85}\) \(+16.7424 q^{86}\) \(-13.2826 q^{87}\) \(+12.0539 q^{88}\) \(-4.70327 q^{89}\) \(-3.37702 q^{90}\) \(+5.17662 q^{91}\) \(-11.0952 q^{92}\) \(+2.76357 q^{93}\) \(-29.3361 q^{94}\) \(-2.06636 q^{95}\) \(-6.96541 q^{96}\) \(+8.93925 q^{97}\) \(-2.28892 q^{98}\) \(+6.27022 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.28892 −1.61851 −0.809254 0.587459i \(-0.800128\pi\)
−0.809254 + 0.587459i \(0.800128\pi\)
\(3\) −1.23476 −0.712887 −0.356443 0.934317i \(-0.616011\pi\)
−0.356443 + 0.934317i \(0.616011\pi\)
\(4\) 3.23914 1.61957
\(5\) −1.00000 −0.447214
\(6\) 2.82625 1.15381
\(7\) −1.00000 −0.377964
\(8\) −2.83628 −1.00278
\(9\) −1.47538 −0.491792
\(10\) 2.28892 0.723819
\(11\) −4.24991 −1.28139 −0.640697 0.767793i \(-0.721355\pi\)
−0.640697 + 0.767793i \(0.721355\pi\)
\(12\) −3.99954 −1.15457
\(13\) −5.17662 −1.43574 −0.717868 0.696179i \(-0.754882\pi\)
−0.717868 + 0.696179i \(0.754882\pi\)
\(14\) 2.28892 0.611739
\(15\) 1.23476 0.318813
\(16\) 0.0137336 0.00343339
\(17\) 5.50025 1.33401 0.667004 0.745054i \(-0.267576\pi\)
0.667004 + 0.745054i \(0.267576\pi\)
\(18\) 3.37702 0.795970
\(19\) 2.06636 0.474057 0.237028 0.971503i \(-0.423827\pi\)
0.237028 + 0.971503i \(0.423827\pi\)
\(20\) −3.23914 −0.724293
\(21\) 1.23476 0.269446
\(22\) 9.72768 2.07395
\(23\) −3.42535 −0.714234 −0.357117 0.934060i \(-0.616240\pi\)
−0.357117 + 0.934060i \(0.616240\pi\)
\(24\) 3.50211 0.714866
\(25\) 1.00000 0.200000
\(26\) 11.8489 2.32375
\(27\) 5.52600 1.06348
\(28\) −3.23914 −0.612139
\(29\) 10.7573 1.99758 0.998790 0.0491731i \(-0.0156586\pi\)
0.998790 + 0.0491731i \(0.0156586\pi\)
\(30\) −2.82625 −0.516001
\(31\) −2.23815 −0.401983 −0.200992 0.979593i \(-0.564416\pi\)
−0.200992 + 0.979593i \(0.564416\pi\)
\(32\) 5.64113 0.997219
\(33\) 5.24760 0.913490
\(34\) −12.5896 −2.15910
\(35\) 1.00000 0.169031
\(36\) −4.77895 −0.796492
\(37\) 7.31231 1.20214 0.601068 0.799198i \(-0.294742\pi\)
0.601068 + 0.799198i \(0.294742\pi\)
\(38\) −4.72974 −0.767264
\(39\) 6.39187 1.02352
\(40\) 2.83628 0.448455
\(41\) −9.61223 −1.50118 −0.750589 0.660769i \(-0.770230\pi\)
−0.750589 + 0.660769i \(0.770230\pi\)
\(42\) −2.82625 −0.436100
\(43\) −7.31457 −1.11546 −0.557731 0.830022i \(-0.688328\pi\)
−0.557731 + 0.830022i \(0.688328\pi\)
\(44\) −13.7660 −2.07531
\(45\) 1.47538 0.219936
\(46\) 7.84033 1.15599
\(47\) 12.8166 1.86949 0.934745 0.355320i \(-0.115628\pi\)
0.934745 + 0.355320i \(0.115628\pi\)
\(48\) −0.0169576 −0.00244762
\(49\) 1.00000 0.142857
\(50\) −2.28892 −0.323702
\(51\) −6.79147 −0.950996
\(52\) −16.7678 −2.32527
\(53\) −3.37750 −0.463935 −0.231968 0.972723i \(-0.574516\pi\)
−0.231968 + 0.972723i \(0.574516\pi\)
\(54\) −12.6485 −1.72125
\(55\) 4.24991 0.573057
\(56\) 2.83628 0.379014
\(57\) −2.55146 −0.337949
\(58\) −24.6226 −3.23310
\(59\) −12.1196 −1.57784 −0.788920 0.614495i \(-0.789360\pi\)
−0.788920 + 0.614495i \(0.789360\pi\)
\(60\) 3.99954 0.516339
\(61\) −0.787009 −0.100766 −0.0503831 0.998730i \(-0.516044\pi\)
−0.0503831 + 0.998730i \(0.516044\pi\)
\(62\) 5.12293 0.650613
\(63\) 1.47538 0.185880
\(64\) −12.9395 −1.61744
\(65\) 5.17662 0.642081
\(66\) −12.0113 −1.47849
\(67\) −10.2824 −1.25620 −0.628099 0.778133i \(-0.716167\pi\)
−0.628099 + 0.778133i \(0.716167\pi\)
\(68\) 17.8161 2.16052
\(69\) 4.22947 0.509168
\(70\) −2.28892 −0.273578
\(71\) −3.37445 −0.400473 −0.200237 0.979748i \(-0.564171\pi\)
−0.200237 + 0.979748i \(0.564171\pi\)
\(72\) 4.18458 0.493158
\(73\) −9.34915 −1.09424 −0.547118 0.837056i \(-0.684275\pi\)
−0.547118 + 0.837056i \(0.684275\pi\)
\(74\) −16.7373 −1.94567
\(75\) −1.23476 −0.142577
\(76\) 6.69324 0.767767
\(77\) 4.24991 0.484322
\(78\) −14.6304 −1.65657
\(79\) −5.57508 −0.627245 −0.313623 0.949548i \(-0.601543\pi\)
−0.313623 + 0.949548i \(0.601543\pi\)
\(80\) −0.0137336 −0.00153546
\(81\) −2.39713 −0.266348
\(82\) 22.0016 2.42967
\(83\) −7.49068 −0.822208 −0.411104 0.911588i \(-0.634857\pi\)
−0.411104 + 0.911588i \(0.634857\pi\)
\(84\) 3.99954 0.436386
\(85\) −5.50025 −0.596586
\(86\) 16.7424 1.80538
\(87\) −13.2826 −1.42405
\(88\) 12.0539 1.28495
\(89\) −4.70327 −0.498546 −0.249273 0.968433i \(-0.580192\pi\)
−0.249273 + 0.968433i \(0.580192\pi\)
\(90\) −3.37702 −0.355969
\(91\) 5.17662 0.542657
\(92\) −11.0952 −1.15675
\(93\) 2.76357 0.286568
\(94\) −29.3361 −3.02578
\(95\) −2.06636 −0.212005
\(96\) −6.96541 −0.710905
\(97\) 8.93925 0.907643 0.453821 0.891093i \(-0.350060\pi\)
0.453821 + 0.891093i \(0.350060\pi\)
\(98\) −2.28892 −0.231215
\(99\) 6.27022 0.630180
\(100\) 3.23914 0.323914
\(101\) −19.9434 −1.98445 −0.992223 0.124472i \(-0.960276\pi\)
−0.992223 + 0.124472i \(0.960276\pi\)
\(102\) 15.5451 1.53920
\(103\) −6.89669 −0.679551 −0.339776 0.940507i \(-0.610351\pi\)
−0.339776 + 0.940507i \(0.610351\pi\)
\(104\) 14.6824 1.43972
\(105\) −1.23476 −0.120500
\(106\) 7.73082 0.750883
\(107\) −10.9224 −1.05591 −0.527953 0.849274i \(-0.677040\pi\)
−0.527953 + 0.849274i \(0.677040\pi\)
\(108\) 17.8995 1.72238
\(109\) −2.35087 −0.225172 −0.112586 0.993642i \(-0.535913\pi\)
−0.112586 + 0.993642i \(0.535913\pi\)
\(110\) −9.72768 −0.927498
\(111\) −9.02892 −0.856987
\(112\) −0.0137336 −0.00129770
\(113\) −3.12664 −0.294130 −0.147065 0.989127i \(-0.546983\pi\)
−0.147065 + 0.989127i \(0.546983\pi\)
\(114\) 5.84007 0.546973
\(115\) 3.42535 0.319415
\(116\) 34.8444 3.23522
\(117\) 7.63747 0.706085
\(118\) 27.7408 2.55375
\(119\) −5.50025 −0.504208
\(120\) −3.50211 −0.319698
\(121\) 7.06170 0.641973
\(122\) 1.80140 0.163091
\(123\) 11.8688 1.07017
\(124\) −7.24967 −0.651039
\(125\) −1.00000 −0.0894427
\(126\) −3.37702 −0.300848
\(127\) 10.0699 0.893560 0.446780 0.894644i \(-0.352571\pi\)
0.446780 + 0.894644i \(0.352571\pi\)
\(128\) 18.3352 1.62062
\(129\) 9.03171 0.795198
\(130\) −11.8489 −1.03921
\(131\) −19.7491 −1.72548 −0.862742 0.505645i \(-0.831255\pi\)
−0.862742 + 0.505645i \(0.831255\pi\)
\(132\) 16.9977 1.47946
\(133\) −2.06636 −0.179177
\(134\) 23.5356 2.03317
\(135\) −5.52600 −0.475602
\(136\) −15.6003 −1.33771
\(137\) −4.91543 −0.419953 −0.209977 0.977706i \(-0.567339\pi\)
−0.209977 + 0.977706i \(0.567339\pi\)
\(138\) −9.68090 −0.824093
\(139\) 3.50610 0.297384 0.148692 0.988884i \(-0.452494\pi\)
0.148692 + 0.988884i \(0.452494\pi\)
\(140\) 3.23914 0.273757
\(141\) −15.8253 −1.33273
\(142\) 7.72382 0.648169
\(143\) 22.0002 1.83975
\(144\) −0.0202622 −0.00168851
\(145\) −10.7573 −0.893345
\(146\) 21.3994 1.77103
\(147\) −1.23476 −0.101841
\(148\) 23.6856 1.94694
\(149\) −12.9909 −1.06425 −0.532127 0.846665i \(-0.678607\pi\)
−0.532127 + 0.846665i \(0.678607\pi\)
\(150\) 2.82625 0.230763
\(151\) −9.83820 −0.800621 −0.400310 0.916380i \(-0.631098\pi\)
−0.400310 + 0.916380i \(0.631098\pi\)
\(152\) −5.86079 −0.475373
\(153\) −8.11495 −0.656055
\(154\) −9.72768 −0.783879
\(155\) 2.23815 0.179772
\(156\) 20.7041 1.65766
\(157\) 11.6402 0.928991 0.464496 0.885575i \(-0.346236\pi\)
0.464496 + 0.885575i \(0.346236\pi\)
\(158\) 12.7609 1.01520
\(159\) 4.17039 0.330733
\(160\) −5.64113 −0.445970
\(161\) 3.42535 0.269955
\(162\) 5.48683 0.431086
\(163\) 12.7824 1.00120 0.500598 0.865680i \(-0.333113\pi\)
0.500598 + 0.865680i \(0.333113\pi\)
\(164\) −31.1353 −2.43126
\(165\) −5.24760 −0.408525
\(166\) 17.1455 1.33075
\(167\) −7.41059 −0.573449 −0.286724 0.958013i \(-0.592566\pi\)
−0.286724 + 0.958013i \(0.592566\pi\)
\(168\) −3.50211 −0.270194
\(169\) 13.7974 1.06134
\(170\) 12.5896 0.965580
\(171\) −3.04867 −0.233137
\(172\) −23.6929 −1.80657
\(173\) 8.94627 0.680172 0.340086 0.940394i \(-0.389544\pi\)
0.340086 + 0.940394i \(0.389544\pi\)
\(174\) 30.4029 2.30483
\(175\) −1.00000 −0.0755929
\(176\) −0.0583663 −0.00439953
\(177\) 14.9648 1.12482
\(178\) 10.7654 0.806900
\(179\) −16.4716 −1.23114 −0.615571 0.788081i \(-0.711075\pi\)
−0.615571 + 0.788081i \(0.711075\pi\)
\(180\) 4.77895 0.356202
\(181\) 16.8450 1.25208 0.626038 0.779792i \(-0.284675\pi\)
0.626038 + 0.779792i \(0.284675\pi\)
\(182\) −11.8489 −0.878296
\(183\) 0.971764 0.0718349
\(184\) 9.71524 0.716217
\(185\) −7.31231 −0.537612
\(186\) −6.32557 −0.463813
\(187\) −23.3756 −1.70939
\(188\) 41.5146 3.02777
\(189\) −5.52600 −0.401957
\(190\) 4.72974 0.343131
\(191\) −20.2823 −1.46757 −0.733787 0.679380i \(-0.762249\pi\)
−0.733787 + 0.679380i \(0.762249\pi\)
\(192\) 15.9772 1.15305
\(193\) −6.35064 −0.457129 −0.228565 0.973529i \(-0.573403\pi\)
−0.228565 + 0.973529i \(0.573403\pi\)
\(194\) −20.4612 −1.46903
\(195\) −6.39187 −0.457731
\(196\) 3.23914 0.231367
\(197\) 3.71252 0.264506 0.132253 0.991216i \(-0.457779\pi\)
0.132253 + 0.991216i \(0.457779\pi\)
\(198\) −14.3520 −1.01995
\(199\) 13.2835 0.941646 0.470823 0.882228i \(-0.343957\pi\)
0.470823 + 0.882228i \(0.343957\pi\)
\(200\) −2.83628 −0.200555
\(201\) 12.6963 0.895527
\(202\) 45.6489 3.21184
\(203\) −10.7573 −0.755014
\(204\) −21.9985 −1.54020
\(205\) 9.61223 0.671347
\(206\) 15.7860 1.09986
\(207\) 5.05368 0.351255
\(208\) −0.0710934 −0.00492944
\(209\) −8.78186 −0.607454
\(210\) 2.82625 0.195030
\(211\) 14.1290 0.972677 0.486339 0.873770i \(-0.338332\pi\)
0.486339 + 0.873770i \(0.338332\pi\)
\(212\) −10.9402 −0.751375
\(213\) 4.16662 0.285492
\(214\) 25.0004 1.70899
\(215\) 7.31457 0.498849
\(216\) −15.6733 −1.06643
\(217\) 2.23815 0.151935
\(218\) 5.38094 0.364443
\(219\) 11.5439 0.780066
\(220\) 13.7660 0.928105
\(221\) −28.4727 −1.91528
\(222\) 20.6664 1.38704
\(223\) 25.0249 1.67579 0.837895 0.545832i \(-0.183786\pi\)
0.837895 + 0.545832i \(0.183786\pi\)
\(224\) −5.64113 −0.376914
\(225\) −1.47538 −0.0983585
\(226\) 7.15663 0.476052
\(227\) −14.9275 −0.990774 −0.495387 0.868672i \(-0.664974\pi\)
−0.495387 + 0.868672i \(0.664974\pi\)
\(228\) −8.26452 −0.547331
\(229\) 1.00000 0.0660819
\(230\) −7.84033 −0.516976
\(231\) −5.24760 −0.345267
\(232\) −30.5107 −2.00313
\(233\) −20.9874 −1.37493 −0.687465 0.726217i \(-0.741277\pi\)
−0.687465 + 0.726217i \(0.741277\pi\)
\(234\) −17.4815 −1.14280
\(235\) −12.8166 −0.836061
\(236\) −39.2571 −2.55542
\(237\) 6.88386 0.447155
\(238\) 12.5896 0.816064
\(239\) 2.12440 0.137416 0.0687081 0.997637i \(-0.478112\pi\)
0.0687081 + 0.997637i \(0.478112\pi\)
\(240\) 0.0169576 0.00109461
\(241\) 20.3646 1.31180 0.655899 0.754849i \(-0.272290\pi\)
0.655899 + 0.754849i \(0.272290\pi\)
\(242\) −16.1636 −1.03904
\(243\) −13.6181 −0.873603
\(244\) −2.54923 −0.163198
\(245\) −1.00000 −0.0638877
\(246\) −27.1666 −1.73208
\(247\) −10.6968 −0.680620
\(248\) 6.34801 0.403099
\(249\) 9.24916 0.586141
\(250\) 2.28892 0.144764
\(251\) −6.12192 −0.386412 −0.193206 0.981158i \(-0.561889\pi\)
−0.193206 + 0.981158i \(0.561889\pi\)
\(252\) 4.77895 0.301046
\(253\) 14.5574 0.915216
\(254\) −23.0492 −1.44623
\(255\) 6.79147 0.425299
\(256\) −16.0888 −1.00555
\(257\) −8.88979 −0.554530 −0.277265 0.960793i \(-0.589428\pi\)
−0.277265 + 0.960793i \(0.589428\pi\)
\(258\) −20.6728 −1.28703
\(259\) −7.31231 −0.454365
\(260\) 16.7678 1.03989
\(261\) −15.8711 −0.982395
\(262\) 45.2040 2.79271
\(263\) 23.1737 1.42895 0.714474 0.699662i \(-0.246666\pi\)
0.714474 + 0.699662i \(0.246666\pi\)
\(264\) −14.8837 −0.916026
\(265\) 3.37750 0.207478
\(266\) 4.72974 0.289999
\(267\) 5.80739 0.355406
\(268\) −33.3062 −2.03450
\(269\) −27.0061 −1.64659 −0.823296 0.567613i \(-0.807867\pi\)
−0.823296 + 0.567613i \(0.807867\pi\)
\(270\) 12.6485 0.769766
\(271\) −4.32393 −0.262660 −0.131330 0.991339i \(-0.541925\pi\)
−0.131330 + 0.991339i \(0.541925\pi\)
\(272\) 0.0755380 0.00458017
\(273\) −6.39187 −0.386853
\(274\) 11.2510 0.679698
\(275\) −4.24991 −0.256279
\(276\) 13.6998 0.824633
\(277\) −2.14336 −0.128782 −0.0643909 0.997925i \(-0.520510\pi\)
−0.0643909 + 0.997925i \(0.520510\pi\)
\(278\) −8.02517 −0.481318
\(279\) 3.30211 0.197692
\(280\) −2.83628 −0.169500
\(281\) −12.0655 −0.719770 −0.359885 0.932997i \(-0.617184\pi\)
−0.359885 + 0.932997i \(0.617184\pi\)
\(282\) 36.2229 2.15704
\(283\) −28.3417 −1.68474 −0.842371 0.538898i \(-0.818841\pi\)
−0.842371 + 0.538898i \(0.818841\pi\)
\(284\) −10.9303 −0.648594
\(285\) 2.55146 0.151135
\(286\) −50.3565 −2.97764
\(287\) 9.61223 0.567392
\(288\) −8.32279 −0.490425
\(289\) 13.2528 0.779577
\(290\) 24.6226 1.44589
\(291\) −11.0378 −0.647047
\(292\) −30.2832 −1.77219
\(293\) 13.6939 0.800009 0.400004 0.916513i \(-0.369009\pi\)
0.400004 + 0.916513i \(0.369009\pi\)
\(294\) 2.82625 0.164830
\(295\) 12.1196 0.705632
\(296\) −20.7398 −1.20547
\(297\) −23.4850 −1.36274
\(298\) 29.7350 1.72250
\(299\) 17.7317 1.02545
\(300\) −3.99954 −0.230914
\(301\) 7.31457 0.421605
\(302\) 22.5188 1.29581
\(303\) 24.6253 1.41469
\(304\) 0.0283785 0.00162762
\(305\) 0.787009 0.0450640
\(306\) 18.5744 1.06183
\(307\) −16.6186 −0.948473 −0.474237 0.880397i \(-0.657276\pi\)
−0.474237 + 0.880397i \(0.657276\pi\)
\(308\) 13.7660 0.784392
\(309\) 8.51573 0.484443
\(310\) −5.12293 −0.290963
\(311\) −8.06307 −0.457215 −0.228607 0.973519i \(-0.573417\pi\)
−0.228607 + 0.973519i \(0.573417\pi\)
\(312\) −18.1291 −1.02636
\(313\) 28.0551 1.58577 0.792883 0.609374i \(-0.208579\pi\)
0.792883 + 0.609374i \(0.208579\pi\)
\(314\) −26.6435 −1.50358
\(315\) −1.47538 −0.0831281
\(316\) −18.0584 −1.01587
\(317\) 29.3418 1.64800 0.823999 0.566591i \(-0.191738\pi\)
0.823999 + 0.566591i \(0.191738\pi\)
\(318\) −9.54567 −0.535295
\(319\) −45.7175 −2.55969
\(320\) 12.9395 0.723342
\(321\) 13.4865 0.752741
\(322\) −7.84033 −0.436925
\(323\) 11.3655 0.632395
\(324\) −7.76463 −0.431368
\(325\) −5.17662 −0.287147
\(326\) −29.2579 −1.62044
\(327\) 2.90275 0.160522
\(328\) 27.2630 1.50535
\(329\) −12.8166 −0.706601
\(330\) 12.0113 0.661201
\(331\) −24.2101 −1.33071 −0.665354 0.746528i \(-0.731719\pi\)
−0.665354 + 0.746528i \(0.731719\pi\)
\(332\) −24.2633 −1.33162
\(333\) −10.7884 −0.591202
\(334\) 16.9622 0.928131
\(335\) 10.2824 0.561789
\(336\) 0.0169576 0.000925112 0
\(337\) 8.57543 0.467134 0.233567 0.972341i \(-0.424960\pi\)
0.233567 + 0.972341i \(0.424960\pi\)
\(338\) −31.5811 −1.71779
\(339\) 3.86064 0.209681
\(340\) −17.8161 −0.966212
\(341\) 9.51192 0.515099
\(342\) 6.97815 0.377335
\(343\) −1.00000 −0.0539949
\(344\) 20.7462 1.11856
\(345\) −4.22947 −0.227707
\(346\) −20.4773 −1.10086
\(347\) 30.5449 1.63973 0.819867 0.572554i \(-0.194047\pi\)
0.819867 + 0.572554i \(0.194047\pi\)
\(348\) −43.0243 −2.30634
\(349\) 1.50682 0.0806585 0.0403292 0.999186i \(-0.487159\pi\)
0.0403292 + 0.999186i \(0.487159\pi\)
\(350\) 2.28892 0.122348
\(351\) −28.6060 −1.52688
\(352\) −23.9743 −1.27783
\(353\) 4.33349 0.230648 0.115324 0.993328i \(-0.463209\pi\)
0.115324 + 0.993328i \(0.463209\pi\)
\(354\) −34.2531 −1.82053
\(355\) 3.37445 0.179097
\(356\) −15.2345 −0.807429
\(357\) 6.79147 0.359443
\(358\) 37.7020 1.99261
\(359\) 32.0004 1.68892 0.844459 0.535619i \(-0.179922\pi\)
0.844459 + 0.535619i \(0.179922\pi\)
\(360\) −4.18458 −0.220547
\(361\) −14.7301 −0.775270
\(362\) −38.5567 −2.02650
\(363\) −8.71948 −0.457654
\(364\) 16.7678 0.878871
\(365\) 9.34915 0.489357
\(366\) −2.22429 −0.116265
\(367\) −13.0534 −0.681380 −0.340690 0.940176i \(-0.610661\pi\)
−0.340690 + 0.940176i \(0.610661\pi\)
\(368\) −0.0470422 −0.00245224
\(369\) 14.1817 0.738268
\(370\) 16.7373 0.870129
\(371\) 3.37750 0.175351
\(372\) 8.95157 0.464117
\(373\) −25.1430 −1.30186 −0.650928 0.759139i \(-0.725620\pi\)
−0.650928 + 0.759139i \(0.725620\pi\)
\(374\) 53.5047 2.76666
\(375\) 1.23476 0.0637625
\(376\) −36.3514 −1.87468
\(377\) −55.6865 −2.86800
\(378\) 12.6485 0.650571
\(379\) 1.88304 0.0967254 0.0483627 0.998830i \(-0.484600\pi\)
0.0483627 + 0.998830i \(0.484600\pi\)
\(380\) −6.69324 −0.343356
\(381\) −12.4339 −0.637007
\(382\) 46.4244 2.37528
\(383\) 33.1675 1.69478 0.847389 0.530972i \(-0.178173\pi\)
0.847389 + 0.530972i \(0.178173\pi\)
\(384\) −22.6396 −1.15532
\(385\) −4.24991 −0.216595
\(386\) 14.5361 0.739867
\(387\) 10.7917 0.548575
\(388\) 28.9554 1.46999
\(389\) −15.2910 −0.775285 −0.387643 0.921810i \(-0.626711\pi\)
−0.387643 + 0.921810i \(0.626711\pi\)
\(390\) 14.6304 0.740841
\(391\) −18.8403 −0.952794
\(392\) −2.83628 −0.143254
\(393\) 24.3853 1.23007
\(394\) −8.49766 −0.428106
\(395\) 5.57508 0.280513
\(396\) 20.3101 1.02062
\(397\) 23.2690 1.16784 0.583918 0.811813i \(-0.301519\pi\)
0.583918 + 0.811813i \(0.301519\pi\)
\(398\) −30.4049 −1.52406
\(399\) 2.55146 0.127733
\(400\) 0.0137336 0.000686678 0
\(401\) 19.5247 0.975018 0.487509 0.873118i \(-0.337906\pi\)
0.487509 + 0.873118i \(0.337906\pi\)
\(402\) −29.0607 −1.44942
\(403\) 11.5860 0.577142
\(404\) −64.5995 −3.21395
\(405\) 2.39713 0.119114
\(406\) 24.6226 1.22200
\(407\) −31.0766 −1.54041
\(408\) 19.2625 0.953637
\(409\) 13.2205 0.653712 0.326856 0.945074i \(-0.394011\pi\)
0.326856 + 0.945074i \(0.394011\pi\)
\(410\) −22.0016 −1.08658
\(411\) 6.06935 0.299379
\(412\) −22.3393 −1.10058
\(413\) 12.1196 0.596368
\(414\) −11.5674 −0.568509
\(415\) 7.49068 0.367703
\(416\) −29.2020 −1.43174
\(417\) −4.32918 −0.212001
\(418\) 20.1009 0.983169
\(419\) −21.9974 −1.07464 −0.537321 0.843378i \(-0.680564\pi\)
−0.537321 + 0.843378i \(0.680564\pi\)
\(420\) −3.99954 −0.195158
\(421\) −7.43644 −0.362430 −0.181215 0.983444i \(-0.558003\pi\)
−0.181215 + 0.983444i \(0.558003\pi\)
\(422\) −32.3400 −1.57429
\(423\) −18.9093 −0.919401
\(424\) 9.57954 0.465224
\(425\) 5.50025 0.266802
\(426\) −9.53704 −0.462071
\(427\) 0.787009 0.0380860
\(428\) −35.3791 −1.71011
\(429\) −27.1648 −1.31153
\(430\) −16.7424 −0.807392
\(431\) 25.4620 1.22646 0.613230 0.789904i \(-0.289870\pi\)
0.613230 + 0.789904i \(0.289870\pi\)
\(432\) 0.0758916 0.00365134
\(433\) −30.3596 −1.45899 −0.729494 0.683987i \(-0.760245\pi\)
−0.729494 + 0.683987i \(0.760245\pi\)
\(434\) −5.12293 −0.245909
\(435\) 13.2826 0.636854
\(436\) −7.61478 −0.364682
\(437\) −7.07802 −0.338587
\(438\) −26.4231 −1.26254
\(439\) −23.8409 −1.13786 −0.568932 0.822385i \(-0.692643\pi\)
−0.568932 + 0.822385i \(0.692643\pi\)
\(440\) −12.0539 −0.574648
\(441\) −1.47538 −0.0702561
\(442\) 65.1717 3.09990
\(443\) −33.5119 −1.59220 −0.796100 0.605165i \(-0.793107\pi\)
−0.796100 + 0.605165i \(0.793107\pi\)
\(444\) −29.2459 −1.38795
\(445\) 4.70327 0.222956
\(446\) −57.2798 −2.71228
\(447\) 16.0406 0.758693
\(448\) 12.9395 0.611335
\(449\) 27.9818 1.32054 0.660270 0.751028i \(-0.270442\pi\)
0.660270 + 0.751028i \(0.270442\pi\)
\(450\) 3.37702 0.159194
\(451\) 40.8511 1.92360
\(452\) −10.1276 −0.476364
\(453\) 12.1478 0.570752
\(454\) 34.1678 1.60358
\(455\) −5.17662 −0.242684
\(456\) 7.23665 0.338887
\(457\) 13.7035 0.641024 0.320512 0.947244i \(-0.396145\pi\)
0.320512 + 0.947244i \(0.396145\pi\)
\(458\) −2.28892 −0.106954
\(459\) 30.3944 1.41869
\(460\) 11.0952 0.517315
\(461\) −2.60658 −0.121401 −0.0607003 0.998156i \(-0.519333\pi\)
−0.0607003 + 0.998156i \(0.519333\pi\)
\(462\) 12.0113 0.558817
\(463\) −3.79212 −0.176235 −0.0881174 0.996110i \(-0.528085\pi\)
−0.0881174 + 0.996110i \(0.528085\pi\)
\(464\) 0.147736 0.00685847
\(465\) −2.76357 −0.128157
\(466\) 48.0384 2.22534
\(467\) 5.97820 0.276638 0.138319 0.990388i \(-0.455830\pi\)
0.138319 + 0.990388i \(0.455830\pi\)
\(468\) 24.7388 1.14355
\(469\) 10.2824 0.474798
\(470\) 29.3361 1.35317
\(471\) −14.3728 −0.662266
\(472\) 34.3747 1.58222
\(473\) 31.0862 1.42935
\(474\) −15.7566 −0.723724
\(475\) 2.06636 0.0948113
\(476\) −17.8161 −0.816599
\(477\) 4.98309 0.228160
\(478\) −4.86258 −0.222409
\(479\) 8.01970 0.366429 0.183215 0.983073i \(-0.441350\pi\)
0.183215 + 0.983073i \(0.441350\pi\)
\(480\) 6.96541 0.317926
\(481\) −37.8531 −1.72595
\(482\) −46.6128 −2.12316
\(483\) −4.22947 −0.192447
\(484\) 22.8738 1.03972
\(485\) −8.93925 −0.405910
\(486\) 31.1708 1.41393
\(487\) −28.5490 −1.29368 −0.646839 0.762627i \(-0.723909\pi\)
−0.646839 + 0.762627i \(0.723909\pi\)
\(488\) 2.23218 0.101046
\(489\) −15.7832 −0.713739
\(490\) 2.28892 0.103403
\(491\) −10.0342 −0.452837 −0.226418 0.974030i \(-0.572702\pi\)
−0.226418 + 0.974030i \(0.572702\pi\)
\(492\) 38.4445 1.73321
\(493\) 59.1679 2.66479
\(494\) 24.4841 1.10159
\(495\) −6.27022 −0.281825
\(496\) −0.0307377 −0.00138016
\(497\) 3.37445 0.151365
\(498\) −21.1705 −0.948675
\(499\) 27.5309 1.23245 0.616226 0.787570i \(-0.288661\pi\)
0.616226 + 0.787570i \(0.288661\pi\)
\(500\) −3.23914 −0.144859
\(501\) 9.15027 0.408804
\(502\) 14.0126 0.625412
\(503\) 26.5894 1.18556 0.592781 0.805364i \(-0.298030\pi\)
0.592781 + 0.805364i \(0.298030\pi\)
\(504\) −4.18458 −0.186396
\(505\) 19.9434 0.887471
\(506\) −33.3207 −1.48128
\(507\) −17.0365 −0.756615
\(508\) 32.6178 1.44718
\(509\) 0.673363 0.0298463 0.0149231 0.999889i \(-0.495250\pi\)
0.0149231 + 0.999889i \(0.495250\pi\)
\(510\) −15.5451 −0.688349
\(511\) 9.34915 0.413582
\(512\) 0.155377 0.00686676
\(513\) 11.4187 0.504149
\(514\) 20.3480 0.897511
\(515\) 6.89669 0.303905
\(516\) 29.2549 1.28788
\(517\) −54.4692 −2.39555
\(518\) 16.7373 0.735393
\(519\) −11.0465 −0.484886
\(520\) −14.6824 −0.643864
\(521\) −24.3699 −1.06767 −0.533833 0.845590i \(-0.679249\pi\)
−0.533833 + 0.845590i \(0.679249\pi\)
\(522\) 36.3276 1.59001
\(523\) −6.08298 −0.265990 −0.132995 0.991117i \(-0.542459\pi\)
−0.132995 + 0.991117i \(0.542459\pi\)
\(524\) −63.9699 −2.79454
\(525\) 1.23476 0.0538892
\(526\) −53.0426 −2.31277
\(527\) −12.3104 −0.536249
\(528\) 0.0720682 0.00313636
\(529\) −11.2670 −0.489869
\(530\) −7.73082 −0.335805
\(531\) 17.8810 0.775970
\(532\) −6.69324 −0.290189
\(533\) 49.7589 2.15530
\(534\) −13.2926 −0.575228
\(535\) 10.9224 0.472215
\(536\) 29.1638 1.25969
\(537\) 20.3384 0.877665
\(538\) 61.8147 2.66502
\(539\) −4.24991 −0.183056
\(540\) −17.8995 −0.770270
\(541\) 15.1637 0.651938 0.325969 0.945380i \(-0.394309\pi\)
0.325969 + 0.945380i \(0.394309\pi\)
\(542\) 9.89711 0.425117
\(543\) −20.7994 −0.892589
\(544\) 31.0276 1.33030
\(545\) 2.35087 0.100700
\(546\) 14.6304 0.626125
\(547\) 26.8278 1.14707 0.573537 0.819180i \(-0.305571\pi\)
0.573537 + 0.819180i \(0.305571\pi\)
\(548\) −15.9217 −0.680143
\(549\) 1.16114 0.0495561
\(550\) 9.72768 0.414790
\(551\) 22.2285 0.946966
\(552\) −11.9960 −0.510582
\(553\) 5.57508 0.237076
\(554\) 4.90596 0.208434
\(555\) 9.02892 0.383256
\(556\) 11.3567 0.481633
\(557\) 16.6723 0.706429 0.353214 0.935542i \(-0.385089\pi\)
0.353214 + 0.935542i \(0.385089\pi\)
\(558\) −7.55826 −0.319967
\(559\) 37.8648 1.60151
\(560\) 0.0137336 0.000580348 0
\(561\) 28.8631 1.21860
\(562\) 27.6170 1.16495
\(563\) −6.38946 −0.269284 −0.134642 0.990894i \(-0.542988\pi\)
−0.134642 + 0.990894i \(0.542988\pi\)
\(564\) −51.2605 −2.15845
\(565\) 3.12664 0.131539
\(566\) 64.8719 2.72677
\(567\) 2.39713 0.100670
\(568\) 9.57087 0.401585
\(569\) −13.6707 −0.573106 −0.286553 0.958064i \(-0.592510\pi\)
−0.286553 + 0.958064i \(0.592510\pi\)
\(570\) −5.84007 −0.244614
\(571\) 42.9758 1.79848 0.899240 0.437456i \(-0.144120\pi\)
0.899240 + 0.437456i \(0.144120\pi\)
\(572\) 71.2615 2.97959
\(573\) 25.0437 1.04621
\(574\) −22.0016 −0.918329
\(575\) −3.42535 −0.142847
\(576\) 19.0907 0.795445
\(577\) −29.2570 −1.21798 −0.608992 0.793177i \(-0.708426\pi\)
−0.608992 + 0.793177i \(0.708426\pi\)
\(578\) −30.3346 −1.26175
\(579\) 7.84150 0.325881
\(580\) −34.8444 −1.44683
\(581\) 7.49068 0.310766
\(582\) 25.2646 1.04725
\(583\) 14.3541 0.594485
\(584\) 26.5168 1.09727
\(585\) −7.63747 −0.315771
\(586\) −31.3443 −1.29482
\(587\) −40.0257 −1.65204 −0.826020 0.563641i \(-0.809400\pi\)
−0.826020 + 0.563641i \(0.809400\pi\)
\(588\) −3.99954 −0.164938
\(589\) −4.62483 −0.190563
\(590\) −27.7408 −1.14207
\(591\) −4.58406 −0.188563
\(592\) 0.100424 0.00412740
\(593\) −41.4179 −1.70083 −0.850414 0.526114i \(-0.823649\pi\)
−0.850414 + 0.526114i \(0.823649\pi\)
\(594\) 53.7551 2.20560
\(595\) 5.50025 0.225488
\(596\) −42.0792 −1.72363
\(597\) −16.4019 −0.671287
\(598\) −40.5864 −1.65970
\(599\) −38.2839 −1.56424 −0.782118 0.623130i \(-0.785861\pi\)
−0.782118 + 0.623130i \(0.785861\pi\)
\(600\) 3.50211 0.142973
\(601\) 4.09602 0.167080 0.0835401 0.996504i \(-0.473377\pi\)
0.0835401 + 0.996504i \(0.473377\pi\)
\(602\) −16.7424 −0.682371
\(603\) 15.1705 0.617789
\(604\) −31.8673 −1.29666
\(605\) −7.06170 −0.287099
\(606\) −56.3652 −2.28968
\(607\) 25.4079 1.03128 0.515638 0.856807i \(-0.327555\pi\)
0.515638 + 0.856807i \(0.327555\pi\)
\(608\) 11.6566 0.472738
\(609\) 13.2826 0.538240
\(610\) −1.80140 −0.0729365
\(611\) −66.3466 −2.68410
\(612\) −26.2854 −1.06253
\(613\) −16.6802 −0.673708 −0.336854 0.941557i \(-0.609363\pi\)
−0.336854 + 0.941557i \(0.609363\pi\)
\(614\) 38.0386 1.53511
\(615\) −11.8688 −0.478595
\(616\) −12.0539 −0.485666
\(617\) 19.7477 0.795011 0.397505 0.917600i \(-0.369876\pi\)
0.397505 + 0.917600i \(0.369876\pi\)
\(618\) −19.4918 −0.784075
\(619\) 30.1313 1.21108 0.605540 0.795815i \(-0.292957\pi\)
0.605540 + 0.795815i \(0.292957\pi\)
\(620\) 7.24967 0.291154
\(621\) −18.9285 −0.759573
\(622\) 18.4557 0.740006
\(623\) 4.70327 0.188432
\(624\) 0.0877830 0.00351413
\(625\) 1.00000 0.0400000
\(626\) −64.2157 −2.56658
\(627\) 10.8435 0.433046
\(628\) 37.7043 1.50457
\(629\) 40.2196 1.60366
\(630\) 3.37702 0.134544
\(631\) −6.00301 −0.238976 −0.119488 0.992836i \(-0.538125\pi\)
−0.119488 + 0.992836i \(0.538125\pi\)
\(632\) 15.8125 0.628987
\(633\) −17.4458 −0.693409
\(634\) −67.1609 −2.66730
\(635\) −10.0699 −0.399612
\(636\) 13.5085 0.535645
\(637\) −5.17662 −0.205105
\(638\) 104.644 4.14288
\(639\) 4.97858 0.196950
\(640\) −18.3352 −0.724764
\(641\) −10.4335 −0.412100 −0.206050 0.978541i \(-0.566061\pi\)
−0.206050 + 0.978541i \(0.566061\pi\)
\(642\) −30.8694 −1.21832
\(643\) 42.9244 1.69277 0.846386 0.532570i \(-0.178774\pi\)
0.846386 + 0.532570i \(0.178774\pi\)
\(644\) 11.0952 0.437211
\(645\) −9.03171 −0.355623
\(646\) −26.0148 −1.02354
\(647\) 12.1895 0.479218 0.239609 0.970869i \(-0.422981\pi\)
0.239609 + 0.970869i \(0.422981\pi\)
\(648\) 6.79893 0.267087
\(649\) 51.5073 2.02184
\(650\) 11.8489 0.464750
\(651\) −2.76357 −0.108313
\(652\) 41.4040 1.62151
\(653\) 14.8871 0.582578 0.291289 0.956635i \(-0.405916\pi\)
0.291289 + 0.956635i \(0.405916\pi\)
\(654\) −6.64414 −0.259807
\(655\) 19.7491 0.771660
\(656\) −0.132010 −0.00515413
\(657\) 13.7935 0.538137
\(658\) 29.3361 1.14364
\(659\) 15.5012 0.603840 0.301920 0.953333i \(-0.402372\pi\)
0.301920 + 0.953333i \(0.402372\pi\)
\(660\) −16.9977 −0.661634
\(661\) 27.9806 1.08832 0.544159 0.838982i \(-0.316849\pi\)
0.544159 + 0.838982i \(0.316849\pi\)
\(662\) 55.4149 2.15376
\(663\) 35.1569 1.36538
\(664\) 21.2457 0.824491
\(665\) 2.06636 0.0801302
\(666\) 24.6938 0.956865
\(667\) −36.8475 −1.42674
\(668\) −24.0039 −0.928739
\(669\) −30.8996 −1.19465
\(670\) −23.5356 −0.909260
\(671\) 3.34472 0.129121
\(672\) 6.96541 0.268697
\(673\) −11.0603 −0.426344 −0.213172 0.977015i \(-0.568379\pi\)
−0.213172 + 0.977015i \(0.568379\pi\)
\(674\) −19.6284 −0.756059
\(675\) 5.52600 0.212696
\(676\) 44.6917 1.71891
\(677\) −13.0447 −0.501347 −0.250673 0.968072i \(-0.580652\pi\)
−0.250673 + 0.968072i \(0.580652\pi\)
\(678\) −8.83669 −0.339371
\(679\) −8.93925 −0.343057
\(680\) 15.6003 0.598243
\(681\) 18.4318 0.706310
\(682\) −21.7720 −0.833692
\(683\) −35.3192 −1.35145 −0.675726 0.737153i \(-0.736170\pi\)
−0.675726 + 0.737153i \(0.736170\pi\)
\(684\) −9.87505 −0.377582
\(685\) 4.91543 0.187809
\(686\) 2.28892 0.0873912
\(687\) −1.23476 −0.0471089
\(688\) −0.100455 −0.00382981
\(689\) 17.4840 0.666089
\(690\) 9.68090 0.368545
\(691\) 34.4836 1.31182 0.655910 0.754839i \(-0.272285\pi\)
0.655910 + 0.754839i \(0.272285\pi\)
\(692\) 28.9782 1.10159
\(693\) −6.27022 −0.238186
\(694\) −69.9146 −2.65392
\(695\) −3.50610 −0.132994
\(696\) 37.6733 1.42800
\(697\) −52.8697 −2.00258
\(698\) −3.44899 −0.130546
\(699\) 25.9143 0.980170
\(700\) −3.23914 −0.122428
\(701\) 42.9267 1.62132 0.810660 0.585518i \(-0.199109\pi\)
0.810660 + 0.585518i \(0.199109\pi\)
\(702\) 65.4768 2.47126
\(703\) 15.1099 0.569881
\(704\) 54.9918 2.07258
\(705\) 15.8253 0.596017
\(706\) −9.91899 −0.373306
\(707\) 19.9434 0.750050
\(708\) 48.4730 1.82173
\(709\) −3.85826 −0.144900 −0.0724499 0.997372i \(-0.523082\pi\)
−0.0724499 + 0.997372i \(0.523082\pi\)
\(710\) −7.72382 −0.289870
\(711\) 8.22534 0.308474
\(712\) 13.3398 0.499930
\(713\) 7.66643 0.287110
\(714\) −15.5451 −0.581761
\(715\) −22.0002 −0.822759
\(716\) −53.3537 −1.99392
\(717\) −2.62312 −0.0979622
\(718\) −73.2463 −2.73353
\(719\) −24.5534 −0.915688 −0.457844 0.889033i \(-0.651378\pi\)
−0.457844 + 0.889033i \(0.651378\pi\)
\(720\) 0.0202622 0.000755127 0
\(721\) 6.89669 0.256846
\(722\) 33.7160 1.25478
\(723\) −25.1453 −0.935163
\(724\) 54.5632 2.02782
\(725\) 10.7573 0.399516
\(726\) 19.9582 0.740717
\(727\) −5.40848 −0.200590 −0.100295 0.994958i \(-0.531979\pi\)
−0.100295 + 0.994958i \(0.531979\pi\)
\(728\) −14.6824 −0.544164
\(729\) 24.0065 0.889128
\(730\) −21.3994 −0.792028
\(731\) −40.2320 −1.48803
\(732\) 3.14768 0.116342
\(733\) 14.3497 0.530018 0.265009 0.964246i \(-0.414625\pi\)
0.265009 + 0.964246i \(0.414625\pi\)
\(734\) 29.8780 1.10282
\(735\) 1.23476 0.0455447
\(736\) −19.3228 −0.712248
\(737\) 43.6993 1.60969
\(738\) −32.4606 −1.19489
\(739\) 0.357320 0.0131442 0.00657212 0.999978i \(-0.497908\pi\)
0.00657212 + 0.999978i \(0.497908\pi\)
\(740\) −23.6856 −0.870699
\(741\) 13.2079 0.485205
\(742\) −7.73082 −0.283807
\(743\) 17.4493 0.640153 0.320076 0.947392i \(-0.396291\pi\)
0.320076 + 0.947392i \(0.396291\pi\)
\(744\) −7.83825 −0.287364
\(745\) 12.9909 0.475949
\(746\) 57.5503 2.10706
\(747\) 11.0516 0.404356
\(748\) −75.7167 −2.76848
\(749\) 10.9224 0.399095
\(750\) −2.82625 −0.103200
\(751\) −34.7459 −1.26790 −0.633949 0.773375i \(-0.718567\pi\)
−0.633949 + 0.773375i \(0.718567\pi\)
\(752\) 0.176017 0.00641868
\(753\) 7.55908 0.275468
\(754\) 127.462 4.64188
\(755\) 9.83820 0.358049
\(756\) −17.8995 −0.650997
\(757\) 11.6872 0.424777 0.212389 0.977185i \(-0.431876\pi\)
0.212389 + 0.977185i \(0.431876\pi\)
\(758\) −4.31013 −0.156551
\(759\) −17.9748 −0.652446
\(760\) 5.86079 0.212593
\(761\) −18.1052 −0.656311 −0.328156 0.944624i \(-0.606427\pi\)
−0.328156 + 0.944624i \(0.606427\pi\)
\(762\) 28.4601 1.03100
\(763\) 2.35087 0.0851071
\(764\) −65.6971 −2.37684
\(765\) 8.11495 0.293397
\(766\) −75.9176 −2.74301
\(767\) 62.7387 2.26536
\(768\) 19.8657 0.716842
\(769\) −40.6786 −1.46691 −0.733455 0.679738i \(-0.762093\pi\)
−0.733455 + 0.679738i \(0.762093\pi\)
\(770\) 9.72768 0.350561
\(771\) 10.9767 0.395317
\(772\) −20.5706 −0.740352
\(773\) 46.0140 1.65501 0.827505 0.561459i \(-0.189760\pi\)
0.827505 + 0.561459i \(0.189760\pi\)
\(774\) −24.7014 −0.887874
\(775\) −2.23815 −0.0803966
\(776\) −25.3542 −0.910163
\(777\) 9.02892 0.323911
\(778\) 34.9998 1.25481
\(779\) −19.8624 −0.711643
\(780\) −20.7041 −0.741327
\(781\) 14.3411 0.513164
\(782\) 43.1238 1.54210
\(783\) 59.4448 2.12439
\(784\) 0.0137336 0.000490484 0
\(785\) −11.6402 −0.415458
\(786\) −55.8159 −1.99089
\(787\) 21.5149 0.766923 0.383462 0.923557i \(-0.374732\pi\)
0.383462 + 0.923557i \(0.374732\pi\)
\(788\) 12.0254 0.428386
\(789\) −28.6138 −1.01868
\(790\) −12.7609 −0.454012
\(791\) 3.12664 0.111171
\(792\) −17.7841 −0.631930
\(793\) 4.07405 0.144674
\(794\) −53.2607 −1.89015
\(795\) −4.17039 −0.147909
\(796\) 43.0272 1.52506
\(797\) −13.6599 −0.483859 −0.241929 0.970294i \(-0.577780\pi\)
−0.241929 + 0.970294i \(0.577780\pi\)
\(798\) −5.84007 −0.206736
\(799\) 70.4944 2.49391
\(800\) 5.64113 0.199444
\(801\) 6.93910 0.245181
\(802\) −44.6904 −1.57807
\(803\) 39.7330 1.40215
\(804\) 41.1250 1.45037
\(805\) −3.42535 −0.120728
\(806\) −26.5195 −0.934109
\(807\) 33.3460 1.17383
\(808\) 56.5652 1.98996
\(809\) 22.5169 0.791651 0.395825 0.918326i \(-0.370459\pi\)
0.395825 + 0.918326i \(0.370459\pi\)
\(810\) −5.48683 −0.192787
\(811\) −9.89975 −0.347627 −0.173814 0.984779i \(-0.555609\pi\)
−0.173814 + 0.984779i \(0.555609\pi\)
\(812\) −34.8444 −1.22280
\(813\) 5.33900 0.187247
\(814\) 71.1318 2.49317
\(815\) −12.7824 −0.447748
\(816\) −0.0932710 −0.00326514
\(817\) −15.1146 −0.528792
\(818\) −30.2606 −1.05804
\(819\) −7.63747 −0.266875
\(820\) 31.1353 1.08729
\(821\) −29.0409 −1.01353 −0.506767 0.862083i \(-0.669160\pi\)
−0.506767 + 0.862083i \(0.669160\pi\)
\(822\) −13.8922 −0.484547
\(823\) −49.8840 −1.73885 −0.869423 0.494069i \(-0.835509\pi\)
−0.869423 + 0.494069i \(0.835509\pi\)
\(824\) 19.5610 0.681438
\(825\) 5.24760 0.182698
\(826\) −27.7408 −0.965226
\(827\) 1.91499 0.0665907 0.0332954 0.999446i \(-0.489400\pi\)
0.0332954 + 0.999446i \(0.489400\pi\)
\(828\) 16.3696 0.568882
\(829\) −9.93682 −0.345120 −0.172560 0.984999i \(-0.555204\pi\)
−0.172560 + 0.984999i \(0.555204\pi\)
\(830\) −17.1455 −0.595130
\(831\) 2.64652 0.0918068
\(832\) 66.9831 2.32222
\(833\) 5.50025 0.190573
\(834\) 9.90913 0.343125
\(835\) 7.41059 0.256454
\(836\) −28.4456 −0.983813
\(837\) −12.3680 −0.427501
\(838\) 50.3501 1.73932
\(839\) −49.2984 −1.70197 −0.850986 0.525189i \(-0.823995\pi\)
−0.850986 + 0.525189i \(0.823995\pi\)
\(840\) 3.50211 0.120834
\(841\) 86.7195 2.99033
\(842\) 17.0214 0.586596
\(843\) 14.8980 0.513115
\(844\) 45.7656 1.57532
\(845\) −13.7974 −0.474646
\(846\) 43.2818 1.48806
\(847\) −7.06170 −0.242643
\(848\) −0.0463851 −0.00159287
\(849\) 34.9951 1.20103
\(850\) −12.5896 −0.431820
\(851\) −25.0472 −0.858607
\(852\) 13.4962 0.462374
\(853\) −10.8776 −0.372441 −0.186220 0.982508i \(-0.559624\pi\)
−0.186220 + 0.982508i \(0.559624\pi\)
\(854\) −1.80140 −0.0616426
\(855\) 3.04867 0.104262
\(856\) 30.9789 1.05884
\(857\) −50.3237 −1.71903 −0.859513 0.511115i \(-0.829233\pi\)
−0.859513 + 0.511115i \(0.829233\pi\)
\(858\) 62.1780 2.12272
\(859\) −50.2860 −1.71574 −0.857868 0.513870i \(-0.828211\pi\)
−0.857868 + 0.513870i \(0.828211\pi\)
\(860\) 23.6929 0.807921
\(861\) −11.8688 −0.404486
\(862\) −58.2804 −1.98504
\(863\) −34.0057 −1.15757 −0.578784 0.815481i \(-0.696472\pi\)
−0.578784 + 0.815481i \(0.696472\pi\)
\(864\) 31.1729 1.06052
\(865\) −8.94627 −0.304182
\(866\) 69.4905 2.36138
\(867\) −16.3640 −0.555750
\(868\) 7.24967 0.246070
\(869\) 23.6936 0.803749
\(870\) −30.4029 −1.03075
\(871\) 53.2282 1.80357
\(872\) 6.66772 0.225797
\(873\) −13.1888 −0.446372
\(874\) 16.2010 0.548007
\(875\) 1.00000 0.0338062
\(876\) 37.3923 1.26337
\(877\) 0.837955 0.0282957 0.0141479 0.999900i \(-0.495496\pi\)
0.0141479 + 0.999900i \(0.495496\pi\)
\(878\) 54.5698 1.84164
\(879\) −16.9087 −0.570316
\(880\) 0.0583663 0.00196753
\(881\) 39.6615 1.33623 0.668114 0.744059i \(-0.267102\pi\)
0.668114 + 0.744059i \(0.267102\pi\)
\(882\) 3.37702 0.113710
\(883\) −6.93084 −0.233241 −0.116621 0.993177i \(-0.537206\pi\)
−0.116621 + 0.993177i \(0.537206\pi\)
\(884\) −92.2271 −3.10193
\(885\) −14.9648 −0.503036
\(886\) 76.7060 2.57699
\(887\) 41.7929 1.40327 0.701634 0.712537i \(-0.252454\pi\)
0.701634 + 0.712537i \(0.252454\pi\)
\(888\) 25.6085 0.859367
\(889\) −10.0699 −0.337734
\(890\) −10.7654 −0.360857
\(891\) 10.1876 0.341297
\(892\) 81.0590 2.71406
\(893\) 26.4837 0.886244
\(894\) −36.7155 −1.22795
\(895\) 16.4716 0.550584
\(896\) −18.3352 −0.612538
\(897\) −21.8944 −0.731031
\(898\) −64.0479 −2.13731
\(899\) −24.0764 −0.802994
\(900\) −4.77895 −0.159298
\(901\) −18.5771 −0.618894
\(902\) −93.5047 −3.11337
\(903\) −9.03171 −0.300556
\(904\) 8.86804 0.294947
\(905\) −16.8450 −0.559946
\(906\) −27.8052 −0.923767
\(907\) 52.2909 1.73629 0.868146 0.496309i \(-0.165312\pi\)
0.868146 + 0.496309i \(0.165312\pi\)
\(908\) −48.3523 −1.60463
\(909\) 29.4241 0.975936
\(910\) 11.8489 0.392786
\(911\) 24.0791 0.797775 0.398887 0.917000i \(-0.369396\pi\)
0.398887 + 0.917000i \(0.369396\pi\)
\(912\) −0.0350406 −0.00116031
\(913\) 31.8347 1.05357
\(914\) −31.3662 −1.03750
\(915\) −0.971764 −0.0321255
\(916\) 3.23914 0.107024
\(917\) 19.7491 0.652172
\(918\) −69.5702 −2.29616
\(919\) 2.37397 0.0783101 0.0391550 0.999233i \(-0.487533\pi\)
0.0391550 + 0.999233i \(0.487533\pi\)
\(920\) −9.71524 −0.320302
\(921\) 20.5199 0.676154
\(922\) 5.96625 0.196488
\(923\) 17.4682 0.574974
\(924\) −16.9977 −0.559183
\(925\) 7.31231 0.240427
\(926\) 8.67984 0.285237
\(927\) 10.1752 0.334198
\(928\) 60.6833 1.99203
\(929\) −11.6053 −0.380758 −0.190379 0.981711i \(-0.560972\pi\)
−0.190379 + 0.981711i \(0.560972\pi\)
\(930\) 6.32557 0.207424
\(931\) 2.06636 0.0677224
\(932\) −67.9811 −2.22679
\(933\) 9.95592 0.325942
\(934\) −13.6836 −0.447741
\(935\) 23.3756 0.764463
\(936\) −21.6620 −0.708045
\(937\) −3.52771 −0.115245 −0.0576226 0.998338i \(-0.518352\pi\)
−0.0576226 + 0.998338i \(0.518352\pi\)
\(938\) −23.5356 −0.768465
\(939\) −34.6412 −1.13047
\(940\) −41.5146 −1.35406
\(941\) 21.9597 0.715865 0.357932 0.933748i \(-0.383482\pi\)
0.357932 + 0.933748i \(0.383482\pi\)
\(942\) 32.8982 1.07188
\(943\) 32.9252 1.07219
\(944\) −0.166445 −0.00541734
\(945\) 5.52600 0.179761
\(946\) −71.1538 −2.31341
\(947\) −14.2735 −0.463826 −0.231913 0.972737i \(-0.574498\pi\)
−0.231913 + 0.972737i \(0.574498\pi\)
\(948\) 22.2978 0.724198
\(949\) 48.3970 1.57103
\(950\) −4.72974 −0.153453
\(951\) −36.2299 −1.17484
\(952\) 15.6003 0.505607
\(953\) 45.6186 1.47773 0.738866 0.673852i \(-0.235362\pi\)
0.738866 + 0.673852i \(0.235362\pi\)
\(954\) −11.4059 −0.369279
\(955\) 20.2823 0.656319
\(956\) 6.88123 0.222555
\(957\) 56.4500 1.82477
\(958\) −18.3564 −0.593069
\(959\) 4.91543 0.158727
\(960\) −15.9772 −0.515661
\(961\) −25.9907 −0.838410
\(962\) 86.6425 2.79347
\(963\) 16.1146 0.519286
\(964\) 65.9637 2.12455
\(965\) 6.35064 0.204434
\(966\) 9.68090 0.311478
\(967\) −16.1597 −0.519660 −0.259830 0.965654i \(-0.583667\pi\)
−0.259830 + 0.965654i \(0.583667\pi\)
\(968\) −20.0290 −0.643756
\(969\) −14.0337 −0.450826
\(970\) 20.4612 0.656969
\(971\) 39.6113 1.27119 0.635593 0.772024i \(-0.280756\pi\)
0.635593 + 0.772024i \(0.280756\pi\)
\(972\) −44.1110 −1.41486
\(973\) −3.50610 −0.112400
\(974\) 65.3462 2.09383
\(975\) 6.39187 0.204704
\(976\) −0.0108084 −0.000345969 0
\(977\) −10.8739 −0.347888 −0.173944 0.984756i \(-0.555651\pi\)
−0.173944 + 0.984756i \(0.555651\pi\)
\(978\) 36.1263 1.15519
\(979\) 19.9885 0.638834
\(980\) −3.23914 −0.103470
\(981\) 3.46842 0.110738
\(982\) 22.9674 0.732920
\(983\) −18.7160 −0.596947 −0.298473 0.954418i \(-0.596477\pi\)
−0.298473 + 0.954418i \(0.596477\pi\)
\(984\) −33.6631 −1.07314
\(985\) −3.71252 −0.118291
\(986\) −135.430 −4.31298
\(987\) 15.8253 0.503726
\(988\) −34.6484 −1.10231
\(989\) 25.0549 0.796701
\(990\) 14.3520 0.456136
\(991\) 44.1775 1.40335 0.701673 0.712499i \(-0.252437\pi\)
0.701673 + 0.712499i \(0.252437\pi\)
\(992\) −12.6257 −0.400865
\(993\) 29.8936 0.948644
\(994\) −7.72382 −0.244985
\(995\) −13.2835 −0.421117
\(996\) 29.9593 0.949296
\(997\) 20.2237 0.640492 0.320246 0.947334i \(-0.396234\pi\)
0.320246 + 0.947334i \(0.396234\pi\)
\(998\) −63.0159 −1.99473
\(999\) 40.4078 1.27845
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 \(a_p\))