Properties

Label 8007.2.a.j.1.11
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.11517 q^{2}\) \(-1.00000 q^{3}\) \(+2.47395 q^{4}\) \(+2.21169 q^{5}\) \(+2.11517 q^{6}\) \(-2.99289 q^{7}\) \(-1.00248 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.11517 q^{2}\) \(-1.00000 q^{3}\) \(+2.47395 q^{4}\) \(+2.21169 q^{5}\) \(+2.11517 q^{6}\) \(-2.99289 q^{7}\) \(-1.00248 q^{8}\) \(+1.00000 q^{9}\) \(-4.67809 q^{10}\) \(-4.68964 q^{11}\) \(-2.47395 q^{12}\) \(-6.95442 q^{13}\) \(+6.33047 q^{14}\) \(-2.21169 q^{15}\) \(-2.82747 q^{16}\) \(+1.00000 q^{17}\) \(-2.11517 q^{18}\) \(-3.64474 q^{19}\) \(+5.47160 q^{20}\) \(+2.99289 q^{21}\) \(+9.91940 q^{22}\) \(+2.77589 q^{23}\) \(+1.00248 q^{24}\) \(-0.108448 q^{25}\) \(+14.7098 q^{26}\) \(-1.00000 q^{27}\) \(-7.40425 q^{28}\) \(-3.63506 q^{29}\) \(+4.67809 q^{30}\) \(+4.06933 q^{31}\) \(+7.98556 q^{32}\) \(+4.68964 q^{33}\) \(-2.11517 q^{34}\) \(-6.61933 q^{35}\) \(+2.47395 q^{36}\) \(-8.99989 q^{37}\) \(+7.70925 q^{38}\) \(+6.95442 q^{39}\) \(-2.21718 q^{40}\) \(-10.7319 q^{41}\) \(-6.33047 q^{42}\) \(-5.09670 q^{43}\) \(-11.6019 q^{44}\) \(+2.21169 q^{45}\) \(-5.87148 q^{46}\) \(+12.1496 q^{47}\) \(+2.82747 q^{48}\) \(+1.95738 q^{49}\) \(+0.229386 q^{50}\) \(-1.00000 q^{51}\) \(-17.2049 q^{52}\) \(+2.12525 q^{53}\) \(+2.11517 q^{54}\) \(-10.3720 q^{55}\) \(+3.00032 q^{56}\) \(+3.64474 q^{57}\) \(+7.68878 q^{58}\) \(-12.0228 q^{59}\) \(-5.47160 q^{60}\) \(+2.48960 q^{61}\) \(-8.60732 q^{62}\) \(-2.99289 q^{63}\) \(-11.2359 q^{64}\) \(-15.3810 q^{65}\) \(-9.91940 q^{66}\) \(-5.59912 q^{67}\) \(+2.47395 q^{68}\) \(-2.77589 q^{69}\) \(+14.0010 q^{70}\) \(-4.99860 q^{71}\) \(-1.00248 q^{72}\) \(-16.7937 q^{73}\) \(+19.0363 q^{74}\) \(+0.108448 q^{75}\) \(-9.01690 q^{76}\) \(+14.0356 q^{77}\) \(-14.7098 q^{78}\) \(-7.56114 q^{79}\) \(-6.25348 q^{80}\) \(+1.00000 q^{81}\) \(+22.6999 q^{82}\) \(-7.89794 q^{83}\) \(+7.40425 q^{84}\) \(+2.21169 q^{85}\) \(+10.7804 q^{86}\) \(+3.63506 q^{87}\) \(+4.70129 q^{88}\) \(-3.95383 q^{89}\) \(-4.67809 q^{90}\) \(+20.8138 q^{91}\) \(+6.86741 q^{92}\) \(-4.06933 q^{93}\) \(-25.6986 q^{94}\) \(-8.06102 q^{95}\) \(-7.98556 q^{96}\) \(+6.85456 q^{97}\) \(-4.14019 q^{98}\) \(-4.68964 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11517 −1.49565 −0.747826 0.663895i \(-0.768902\pi\)
−0.747826 + 0.663895i \(0.768902\pi\)
\(3\) −1.00000 −0.577350
\(4\) 2.47395 1.23697
\(5\) 2.21169 0.989096 0.494548 0.869150i \(-0.335334\pi\)
0.494548 + 0.869150i \(0.335334\pi\)
\(6\) 2.11517 0.863515
\(7\) −2.99289 −1.13121 −0.565603 0.824678i \(-0.691356\pi\)
−0.565603 + 0.824678i \(0.691356\pi\)
\(8\) −1.00248 −0.354431
\(9\) 1.00000 0.333333
\(10\) −4.67809 −1.47934
\(11\) −4.68964 −1.41398 −0.706990 0.707223i \(-0.749948\pi\)
−0.706990 + 0.707223i \(0.749948\pi\)
\(12\) −2.47395 −0.714168
\(13\) −6.95442 −1.92881 −0.964405 0.264431i \(-0.914816\pi\)
−0.964405 + 0.264431i \(0.914816\pi\)
\(14\) 6.33047 1.69189
\(15\) −2.21169 −0.571055
\(16\) −2.82747 −0.706869
\(17\) 1.00000 0.242536
\(18\) −2.11517 −0.498551
\(19\) −3.64474 −0.836160 −0.418080 0.908410i \(-0.637297\pi\)
−0.418080 + 0.908410i \(0.637297\pi\)
\(20\) 5.47160 1.22349
\(21\) 2.99289 0.653102
\(22\) 9.91940 2.11482
\(23\) 2.77589 0.578813 0.289407 0.957206i \(-0.406542\pi\)
0.289407 + 0.957206i \(0.406542\pi\)
\(24\) 1.00248 0.204631
\(25\) −0.108448 −0.0216896
\(26\) 14.7098 2.88483
\(27\) −1.00000 −0.192450
\(28\) −7.40425 −1.39927
\(29\) −3.63506 −0.675014 −0.337507 0.941323i \(-0.609584\pi\)
−0.337507 + 0.941323i \(0.609584\pi\)
\(30\) 4.67809 0.854099
\(31\) 4.06933 0.730873 0.365436 0.930836i \(-0.380920\pi\)
0.365436 + 0.930836i \(0.380920\pi\)
\(32\) 7.98556 1.41166
\(33\) 4.68964 0.816362
\(34\) −2.11517 −0.362749
\(35\) −6.61933 −1.11887
\(36\) 2.47395 0.412325
\(37\) −8.99989 −1.47957 −0.739787 0.672841i \(-0.765074\pi\)
−0.739787 + 0.672841i \(0.765074\pi\)
\(38\) 7.70925 1.25061
\(39\) 6.95442 1.11360
\(40\) −2.21718 −0.350567
\(41\) −10.7319 −1.67605 −0.838023 0.545635i \(-0.816289\pi\)
−0.838023 + 0.545635i \(0.816289\pi\)
\(42\) −6.33047 −0.976813
\(43\) −5.09670 −0.777240 −0.388620 0.921398i \(-0.627048\pi\)
−0.388620 + 0.921398i \(0.627048\pi\)
\(44\) −11.6019 −1.74906
\(45\) 2.21169 0.329699
\(46\) −5.87148 −0.865703
\(47\) 12.1496 1.77221 0.886103 0.463487i \(-0.153402\pi\)
0.886103 + 0.463487i \(0.153402\pi\)
\(48\) 2.82747 0.408111
\(49\) 1.95738 0.279626
\(50\) 0.229386 0.0324401
\(51\) −1.00000 −0.140028
\(52\) −17.2049 −2.38589
\(53\) 2.12525 0.291926 0.145963 0.989290i \(-0.453372\pi\)
0.145963 + 0.989290i \(0.453372\pi\)
\(54\) 2.11517 0.287838
\(55\) −10.3720 −1.39856
\(56\) 3.00032 0.400935
\(57\) 3.64474 0.482757
\(58\) 7.68878 1.00959
\(59\) −12.0228 −1.56524 −0.782619 0.622502i \(-0.786116\pi\)
−0.782619 + 0.622502i \(0.786116\pi\)
\(60\) −5.47160 −0.706380
\(61\) 2.48960 0.318761 0.159380 0.987217i \(-0.449050\pi\)
0.159380 + 0.987217i \(0.449050\pi\)
\(62\) −8.60732 −1.09313
\(63\) −2.99289 −0.377068
\(64\) −11.2359 −1.40448
\(65\) −15.3810 −1.90778
\(66\) −9.91940 −1.22099
\(67\) −5.59912 −0.684041 −0.342021 0.939692i \(-0.611111\pi\)
−0.342021 + 0.939692i \(0.611111\pi\)
\(68\) 2.47395 0.300010
\(69\) −2.77589 −0.334178
\(70\) 14.0010 1.67344
\(71\) −4.99860 −0.593224 −0.296612 0.954998i \(-0.595857\pi\)
−0.296612 + 0.954998i \(0.595857\pi\)
\(72\) −1.00248 −0.118144
\(73\) −16.7937 −1.96556 −0.982778 0.184790i \(-0.940839\pi\)
−0.982778 + 0.184790i \(0.940839\pi\)
\(74\) 19.0363 2.21293
\(75\) 0.108448 0.0125225
\(76\) −9.01690 −1.03431
\(77\) 14.0356 1.59950
\(78\) −14.7098 −1.66556
\(79\) −7.56114 −0.850695 −0.425347 0.905030i \(-0.639848\pi\)
−0.425347 + 0.905030i \(0.639848\pi\)
\(80\) −6.25348 −0.699161
\(81\) 1.00000 0.111111
\(82\) 22.6999 2.50678
\(83\) −7.89794 −0.866912 −0.433456 0.901175i \(-0.642706\pi\)
−0.433456 + 0.901175i \(0.642706\pi\)
\(84\) 7.40425 0.807870
\(85\) 2.21169 0.239891
\(86\) 10.7804 1.16248
\(87\) 3.63506 0.389720
\(88\) 4.70129 0.501159
\(89\) −3.95383 −0.419105 −0.209552 0.977797i \(-0.567201\pi\)
−0.209552 + 0.977797i \(0.567201\pi\)
\(90\) −4.67809 −0.493114
\(91\) 20.8138 2.18188
\(92\) 6.86741 0.715977
\(93\) −4.06933 −0.421969
\(94\) −25.6986 −2.65060
\(95\) −8.06102 −0.827043
\(96\) −7.98556 −0.815023
\(97\) 6.85456 0.695975 0.347988 0.937499i \(-0.386865\pi\)
0.347988 + 0.937499i \(0.386865\pi\)
\(98\) −4.14019 −0.418223
\(99\) −4.68964 −0.471327
\(100\) −0.268295 −0.0268295
\(101\) 10.2019 1.01512 0.507562 0.861615i \(-0.330547\pi\)
0.507562 + 0.861615i \(0.330547\pi\)
\(102\) 2.11517 0.209433
\(103\) −8.15582 −0.803617 −0.401808 0.915724i \(-0.631618\pi\)
−0.401808 + 0.915724i \(0.631618\pi\)
\(104\) 6.97169 0.683630
\(105\) 6.61933 0.645980
\(106\) −4.49527 −0.436619
\(107\) −15.2536 −1.47462 −0.737310 0.675555i \(-0.763904\pi\)
−0.737310 + 0.675555i \(0.763904\pi\)
\(108\) −2.47395 −0.238056
\(109\) 9.54476 0.914222 0.457111 0.889410i \(-0.348884\pi\)
0.457111 + 0.889410i \(0.348884\pi\)
\(110\) 21.9386 2.09176
\(111\) 8.99989 0.854232
\(112\) 8.46231 0.799614
\(113\) 16.2493 1.52860 0.764300 0.644860i \(-0.223084\pi\)
0.764300 + 0.644860i \(0.223084\pi\)
\(114\) −7.70925 −0.722037
\(115\) 6.13940 0.572502
\(116\) −8.99296 −0.834975
\(117\) −6.95442 −0.642936
\(118\) 25.4303 2.34105
\(119\) −2.99289 −0.274358
\(120\) 2.21718 0.202400
\(121\) 10.9928 0.999341
\(122\) −5.26593 −0.476755
\(123\) 10.7319 0.967666
\(124\) 10.0673 0.904071
\(125\) −11.2983 −1.01055
\(126\) 6.33047 0.563963
\(127\) −9.93243 −0.881361 −0.440680 0.897664i \(-0.645263\pi\)
−0.440680 + 0.897664i \(0.645263\pi\)
\(128\) 7.79468 0.688959
\(129\) 5.09670 0.448740
\(130\) 32.5334 2.85337
\(131\) −21.7380 −1.89926 −0.949629 0.313376i \(-0.898540\pi\)
−0.949629 + 0.313376i \(0.898540\pi\)
\(132\) 11.6019 1.00982
\(133\) 10.9083 0.945869
\(134\) 11.8431 1.02309
\(135\) −2.21169 −0.190352
\(136\) −1.00248 −0.0859622
\(137\) 1.01464 0.0866867 0.0433433 0.999060i \(-0.486199\pi\)
0.0433433 + 0.999060i \(0.486199\pi\)
\(138\) 5.87148 0.499814
\(139\) 9.47463 0.803628 0.401814 0.915721i \(-0.368380\pi\)
0.401814 + 0.915721i \(0.368380\pi\)
\(140\) −16.3759 −1.38401
\(141\) −12.1496 −1.02318
\(142\) 10.5729 0.887257
\(143\) 32.6137 2.72730
\(144\) −2.82747 −0.235623
\(145\) −8.03962 −0.667654
\(146\) 35.5216 2.93979
\(147\) −1.95738 −0.161442
\(148\) −22.2653 −1.83019
\(149\) −9.83733 −0.805905 −0.402953 0.915221i \(-0.632016\pi\)
−0.402953 + 0.915221i \(0.632016\pi\)
\(150\) −0.229386 −0.0187293
\(151\) 12.2730 0.998762 0.499381 0.866382i \(-0.333561\pi\)
0.499381 + 0.866382i \(0.333561\pi\)
\(152\) 3.65379 0.296362
\(153\) 1.00000 0.0808452
\(154\) −29.6876 −2.39230
\(155\) 9.00007 0.722903
\(156\) 17.2049 1.37749
\(157\) −1.00000 −0.0798087
\(158\) 15.9931 1.27234
\(159\) −2.12525 −0.168543
\(160\) 17.6615 1.39627
\(161\) −8.30793 −0.654757
\(162\) −2.11517 −0.166184
\(163\) −9.37235 −0.734099 −0.367050 0.930201i \(-0.619632\pi\)
−0.367050 + 0.930201i \(0.619632\pi\)
\(164\) −26.5503 −2.07323
\(165\) 10.3720 0.807460
\(166\) 16.7055 1.29660
\(167\) −24.8082 −1.91972 −0.959859 0.280484i \(-0.909505\pi\)
−0.959859 + 0.280484i \(0.909505\pi\)
\(168\) −3.00032 −0.231480
\(169\) 35.3640 2.72030
\(170\) −4.67809 −0.358793
\(171\) −3.64474 −0.278720
\(172\) −12.6090 −0.961426
\(173\) 11.7404 0.892603 0.446301 0.894883i \(-0.352741\pi\)
0.446301 + 0.894883i \(0.352741\pi\)
\(174\) −7.68878 −0.582885
\(175\) 0.324573 0.0245354
\(176\) 13.2598 0.999498
\(177\) 12.0228 0.903690
\(178\) 8.36302 0.626835
\(179\) 8.94912 0.668888 0.334444 0.942416i \(-0.391451\pi\)
0.334444 + 0.942416i \(0.391451\pi\)
\(180\) 5.47160 0.407829
\(181\) 13.0507 0.970052 0.485026 0.874500i \(-0.338810\pi\)
0.485026 + 0.874500i \(0.338810\pi\)
\(182\) −44.0247 −3.26333
\(183\) −2.48960 −0.184037
\(184\) −2.78278 −0.205150
\(185\) −19.9049 −1.46344
\(186\) 8.60732 0.631119
\(187\) −4.68964 −0.342941
\(188\) 30.0576 2.19217
\(189\) 2.99289 0.217701
\(190\) 17.0504 1.23697
\(191\) 19.3245 1.39827 0.699135 0.714990i \(-0.253569\pi\)
0.699135 + 0.714990i \(0.253569\pi\)
\(192\) 11.2359 0.810879
\(193\) 7.91560 0.569777 0.284889 0.958561i \(-0.408043\pi\)
0.284889 + 0.958561i \(0.408043\pi\)
\(194\) −14.4986 −1.04094
\(195\) 15.3810 1.10146
\(196\) 4.84246 0.345890
\(197\) 17.5967 1.25371 0.626855 0.779136i \(-0.284342\pi\)
0.626855 + 0.779136i \(0.284342\pi\)
\(198\) 9.91940 0.704941
\(199\) −19.0361 −1.34943 −0.674715 0.738078i \(-0.735734\pi\)
−0.674715 + 0.738078i \(0.735734\pi\)
\(200\) 0.108717 0.00768749
\(201\) 5.59912 0.394931
\(202\) −21.5787 −1.51827
\(203\) 10.8793 0.763580
\(204\) −2.47395 −0.173211
\(205\) −23.7357 −1.65777
\(206\) 17.2510 1.20193
\(207\) 2.77589 0.192938
\(208\) 19.6634 1.36341
\(209\) 17.0925 1.18231
\(210\) −14.0010 −0.966161
\(211\) −17.4733 −1.20291 −0.601457 0.798905i \(-0.705413\pi\)
−0.601457 + 0.798905i \(0.705413\pi\)
\(212\) 5.25776 0.361105
\(213\) 4.99860 0.342498
\(214\) 32.2639 2.20552
\(215\) −11.2723 −0.768765
\(216\) 1.00248 0.0682103
\(217\) −12.1790 −0.826767
\(218\) −20.1888 −1.36736
\(219\) 16.7937 1.13481
\(220\) −25.6598 −1.72999
\(221\) −6.95442 −0.467805
\(222\) −19.0363 −1.27763
\(223\) 25.5231 1.70915 0.854576 0.519326i \(-0.173817\pi\)
0.854576 + 0.519326i \(0.173817\pi\)
\(224\) −23.8999 −1.59688
\(225\) −0.108448 −0.00722988
\(226\) −34.3699 −2.28625
\(227\) −12.0584 −0.800343 −0.400172 0.916440i \(-0.631049\pi\)
−0.400172 + 0.916440i \(0.631049\pi\)
\(228\) 9.01690 0.597159
\(229\) −13.1585 −0.869536 −0.434768 0.900542i \(-0.643170\pi\)
−0.434768 + 0.900542i \(0.643170\pi\)
\(230\) −12.9859 −0.856263
\(231\) −14.0356 −0.923473
\(232\) 3.64409 0.239246
\(233\) −3.11835 −0.204290 −0.102145 0.994770i \(-0.532571\pi\)
−0.102145 + 0.994770i \(0.532571\pi\)
\(234\) 14.7098 0.961609
\(235\) 26.8712 1.75288
\(236\) −29.7438 −1.93616
\(237\) 7.56114 0.491149
\(238\) 6.33047 0.410343
\(239\) 0.545179 0.0352647 0.0176324 0.999845i \(-0.494387\pi\)
0.0176324 + 0.999845i \(0.494387\pi\)
\(240\) 6.25348 0.403661
\(241\) −23.4255 −1.50897 −0.754484 0.656319i \(-0.772113\pi\)
−0.754484 + 0.656319i \(0.772113\pi\)
\(242\) −23.2516 −1.49467
\(243\) −1.00000 −0.0641500
\(244\) 6.15915 0.394299
\(245\) 4.32911 0.276576
\(246\) −22.6999 −1.44729
\(247\) 25.3470 1.61279
\(248\) −4.07943 −0.259044
\(249\) 7.89794 0.500512
\(250\) 23.8978 1.51143
\(251\) 16.2359 1.02480 0.512402 0.858746i \(-0.328756\pi\)
0.512402 + 0.858746i \(0.328756\pi\)
\(252\) −7.40425 −0.466424
\(253\) −13.0179 −0.818431
\(254\) 21.0088 1.31821
\(255\) −2.21169 −0.138501
\(256\) 5.98467 0.374042
\(257\) −31.4934 −1.96450 −0.982251 0.187570i \(-0.939939\pi\)
−0.982251 + 0.187570i \(0.939939\pi\)
\(258\) −10.7804 −0.671158
\(259\) 26.9357 1.67370
\(260\) −38.0518 −2.35987
\(261\) −3.63506 −0.225005
\(262\) 45.9796 2.84063
\(263\) −12.5384 −0.773151 −0.386576 0.922258i \(-0.626342\pi\)
−0.386576 + 0.922258i \(0.626342\pi\)
\(264\) −4.70129 −0.289344
\(265\) 4.70039 0.288742
\(266\) −23.0729 −1.41469
\(267\) 3.95383 0.241970
\(268\) −13.8519 −0.846142
\(269\) −27.3995 −1.67058 −0.835290 0.549810i \(-0.814700\pi\)
−0.835290 + 0.549810i \(0.814700\pi\)
\(270\) 4.67809 0.284700
\(271\) −24.1438 −1.46663 −0.733317 0.679887i \(-0.762029\pi\)
−0.733317 + 0.679887i \(0.762029\pi\)
\(272\) −2.82747 −0.171441
\(273\) −20.8138 −1.25971
\(274\) −2.14614 −0.129653
\(275\) 0.508583 0.0306687
\(276\) −6.86741 −0.413370
\(277\) 17.7425 1.06604 0.533021 0.846102i \(-0.321057\pi\)
0.533021 + 0.846102i \(0.321057\pi\)
\(278\) −20.0405 −1.20195
\(279\) 4.06933 0.243624
\(280\) 6.63576 0.396563
\(281\) −15.2451 −0.909446 −0.454723 0.890633i \(-0.650262\pi\)
−0.454723 + 0.890633i \(0.650262\pi\)
\(282\) 25.6986 1.53033
\(283\) −0.603246 −0.0358593 −0.0179296 0.999839i \(-0.505707\pi\)
−0.0179296 + 0.999839i \(0.505707\pi\)
\(284\) −12.3663 −0.733803
\(285\) 8.06102 0.477493
\(286\) −68.9837 −4.07909
\(287\) 32.1195 1.89595
\(288\) 7.98556 0.470554
\(289\) 1.00000 0.0588235
\(290\) 17.0052 0.998578
\(291\) −6.85456 −0.401821
\(292\) −41.5468 −2.43134
\(293\) 12.3145 0.719419 0.359710 0.933064i \(-0.382876\pi\)
0.359710 + 0.933064i \(0.382876\pi\)
\(294\) 4.14019 0.241461
\(295\) −26.5907 −1.54817
\(296\) 9.02224 0.524407
\(297\) 4.68964 0.272121
\(298\) 20.8076 1.20535
\(299\) −19.3047 −1.11642
\(300\) 0.268295 0.0154900
\(301\) 15.2539 0.879218
\(302\) −25.9595 −1.49380
\(303\) −10.2019 −0.586083
\(304\) 10.3054 0.591056
\(305\) 5.50621 0.315285
\(306\) −2.11517 −0.120916
\(307\) 6.64694 0.379361 0.189680 0.981846i \(-0.439255\pi\)
0.189680 + 0.981846i \(0.439255\pi\)
\(308\) 34.7233 1.97854
\(309\) 8.15582 0.463968
\(310\) −19.0367 −1.08121
\(311\) 10.3816 0.588685 0.294343 0.955700i \(-0.404899\pi\)
0.294343 + 0.955700i \(0.404899\pi\)
\(312\) −6.97169 −0.394694
\(313\) 13.3531 0.754763 0.377382 0.926058i \(-0.376825\pi\)
0.377382 + 0.926058i \(0.376825\pi\)
\(314\) 2.11517 0.119366
\(315\) −6.61933 −0.372957
\(316\) −18.7059 −1.05229
\(317\) 9.25260 0.519678 0.259839 0.965652i \(-0.416331\pi\)
0.259839 + 0.965652i \(0.416331\pi\)
\(318\) 4.49527 0.252082
\(319\) 17.0471 0.954457
\(320\) −24.8502 −1.38917
\(321\) 15.2536 0.851372
\(322\) 17.5727 0.979288
\(323\) −3.64474 −0.202799
\(324\) 2.47395 0.137442
\(325\) 0.754194 0.0418352
\(326\) 19.8241 1.09796
\(327\) −9.54476 −0.527826
\(328\) 10.7586 0.594043
\(329\) −36.3625 −2.00473
\(330\) −21.9386 −1.20768
\(331\) −24.4559 −1.34422 −0.672109 0.740452i \(-0.734611\pi\)
−0.672109 + 0.740452i \(0.734611\pi\)
\(332\) −19.5391 −1.07235
\(333\) −8.99989 −0.493191
\(334\) 52.4736 2.87123
\(335\) −12.3835 −0.676582
\(336\) −8.46231 −0.461657
\(337\) 18.2007 0.991456 0.495728 0.868478i \(-0.334901\pi\)
0.495728 + 0.868478i \(0.334901\pi\)
\(338\) −74.8008 −4.06863
\(339\) −16.2493 −0.882538
\(340\) 5.47160 0.296739
\(341\) −19.0837 −1.03344
\(342\) 7.70925 0.416868
\(343\) 15.0920 0.814891
\(344\) 5.10936 0.275478
\(345\) −6.13940 −0.330534
\(346\) −24.8329 −1.33502
\(347\) 8.80901 0.472892 0.236446 0.971645i \(-0.424017\pi\)
0.236446 + 0.971645i \(0.424017\pi\)
\(348\) 8.99296 0.482073
\(349\) 4.21599 0.225677 0.112838 0.993613i \(-0.464006\pi\)
0.112838 + 0.993613i \(0.464006\pi\)
\(350\) −0.686528 −0.0366965
\(351\) 6.95442 0.371199
\(352\) −37.4494 −1.99606
\(353\) −5.00317 −0.266292 −0.133146 0.991096i \(-0.542508\pi\)
−0.133146 + 0.991096i \(0.542508\pi\)
\(354\) −25.4303 −1.35161
\(355\) −11.0553 −0.586755
\(356\) −9.78156 −0.518422
\(357\) 2.99289 0.158400
\(358\) −18.9289 −1.00042
\(359\) −10.5320 −0.555858 −0.277929 0.960602i \(-0.589648\pi\)
−0.277929 + 0.960602i \(0.589648\pi\)
\(360\) −2.21718 −0.116856
\(361\) −5.71588 −0.300836
\(362\) −27.6045 −1.45086
\(363\) −10.9928 −0.576970
\(364\) 51.4923 2.69893
\(365\) −37.1424 −1.94412
\(366\) 5.26593 0.275255
\(367\) 4.38556 0.228924 0.114462 0.993428i \(-0.463486\pi\)
0.114462 + 0.993428i \(0.463486\pi\)
\(368\) −7.84876 −0.409145
\(369\) −10.7319 −0.558682
\(370\) 42.1023 2.18880
\(371\) −6.36064 −0.330228
\(372\) −10.0673 −0.521965
\(373\) 10.4074 0.538875 0.269438 0.963018i \(-0.413162\pi\)
0.269438 + 0.963018i \(0.413162\pi\)
\(374\) 9.91940 0.512920
\(375\) 11.2983 0.583441
\(376\) −12.1798 −0.628126
\(377\) 25.2798 1.30197
\(378\) −6.33047 −0.325604
\(379\) −16.0605 −0.824972 −0.412486 0.910964i \(-0.635339\pi\)
−0.412486 + 0.910964i \(0.635339\pi\)
\(380\) −19.9425 −1.02303
\(381\) 9.93243 0.508854
\(382\) −40.8746 −2.09132
\(383\) −25.8834 −1.32258 −0.661290 0.750130i \(-0.729991\pi\)
−0.661290 + 0.750130i \(0.729991\pi\)
\(384\) −7.79468 −0.397771
\(385\) 31.0423 1.58206
\(386\) −16.7428 −0.852188
\(387\) −5.09670 −0.259080
\(388\) 16.9578 0.860904
\(389\) 17.8472 0.904889 0.452444 0.891793i \(-0.350552\pi\)
0.452444 + 0.891793i \(0.350552\pi\)
\(390\) −32.5334 −1.64739
\(391\) 2.77589 0.140383
\(392\) −1.96224 −0.0991081
\(393\) 21.7380 1.09654
\(394\) −37.2200 −1.87511
\(395\) −16.7229 −0.841419
\(396\) −11.6019 −0.583019
\(397\) 16.6494 0.835609 0.417805 0.908537i \(-0.362800\pi\)
0.417805 + 0.908537i \(0.362800\pi\)
\(398\) 40.2645 2.01828
\(399\) −10.9083 −0.546098
\(400\) 0.306634 0.0153317
\(401\) −4.02629 −0.201063 −0.100532 0.994934i \(-0.532054\pi\)
−0.100532 + 0.994934i \(0.532054\pi\)
\(402\) −11.8431 −0.590680
\(403\) −28.2998 −1.40971
\(404\) 25.2389 1.25568
\(405\) 2.21169 0.109900
\(406\) −23.0117 −1.14205
\(407\) 42.2063 2.09209
\(408\) 1.00248 0.0496303
\(409\) −12.2830 −0.607356 −0.303678 0.952775i \(-0.598215\pi\)
−0.303678 + 0.952775i \(0.598215\pi\)
\(410\) 50.2050 2.47945
\(411\) −1.01464 −0.0500486
\(412\) −20.1771 −0.994053
\(413\) 35.9829 1.77060
\(414\) −5.87148 −0.288568
\(415\) −17.4678 −0.857459
\(416\) −55.5349 −2.72282
\(417\) −9.47463 −0.463975
\(418\) −36.1536 −1.76833
\(419\) 4.96217 0.242418 0.121209 0.992627i \(-0.461323\pi\)
0.121209 + 0.992627i \(0.461323\pi\)
\(420\) 16.3759 0.799061
\(421\) 5.39691 0.263029 0.131515 0.991314i \(-0.458016\pi\)
0.131515 + 0.991314i \(0.458016\pi\)
\(422\) 36.9591 1.79914
\(423\) 12.1496 0.590736
\(424\) −2.13053 −0.103468
\(425\) −0.108448 −0.00526051
\(426\) −10.5729 −0.512258
\(427\) −7.45110 −0.360584
\(428\) −37.7366 −1.82407
\(429\) −32.6137 −1.57461
\(430\) 23.8428 1.14980
\(431\) −15.1582 −0.730145 −0.365072 0.930979i \(-0.618956\pi\)
−0.365072 + 0.930979i \(0.618956\pi\)
\(432\) 2.82747 0.136037
\(433\) 7.10789 0.341583 0.170792 0.985307i \(-0.445368\pi\)
0.170792 + 0.985307i \(0.445368\pi\)
\(434\) 25.7607 1.23656
\(435\) 8.03962 0.385470
\(436\) 23.6132 1.13087
\(437\) −10.1174 −0.483981
\(438\) −35.5216 −1.69729
\(439\) 13.1216 0.626260 0.313130 0.949710i \(-0.398622\pi\)
0.313130 + 0.949710i \(0.398622\pi\)
\(440\) 10.3978 0.495694
\(441\) 1.95738 0.0932085
\(442\) 14.7098 0.699673
\(443\) −25.8189 −1.22669 −0.613346 0.789814i \(-0.710177\pi\)
−0.613346 + 0.789814i \(0.710177\pi\)
\(444\) 22.2653 1.05666
\(445\) −8.74462 −0.414535
\(446\) −53.9857 −2.55630
\(447\) 9.83733 0.465290
\(448\) 33.6277 1.58876
\(449\) −12.1983 −0.575675 −0.287837 0.957679i \(-0.592936\pi\)
−0.287837 + 0.957679i \(0.592936\pi\)
\(450\) 0.229386 0.0108134
\(451\) 50.3289 2.36990
\(452\) 40.1998 1.89084
\(453\) −12.2730 −0.576636
\(454\) 25.5055 1.19703
\(455\) 46.0336 2.15809
\(456\) −3.65379 −0.171104
\(457\) 33.8724 1.58449 0.792243 0.610206i \(-0.208913\pi\)
0.792243 + 0.610206i \(0.208913\pi\)
\(458\) 27.8324 1.30052
\(459\) −1.00000 −0.0466760
\(460\) 15.1886 0.708170
\(461\) 29.5625 1.37686 0.688430 0.725302i \(-0.258300\pi\)
0.688430 + 0.725302i \(0.258300\pi\)
\(462\) 29.6876 1.38119
\(463\) 27.5942 1.28241 0.641207 0.767368i \(-0.278434\pi\)
0.641207 + 0.767368i \(0.278434\pi\)
\(464\) 10.2780 0.477146
\(465\) −9.00007 −0.417368
\(466\) 6.59584 0.305546
\(467\) −2.87292 −0.132943 −0.0664714 0.997788i \(-0.521174\pi\)
−0.0664714 + 0.997788i \(0.521174\pi\)
\(468\) −17.2049 −0.795296
\(469\) 16.7575 0.773791
\(470\) −56.8371 −2.62170
\(471\) 1.00000 0.0460776
\(472\) 12.0527 0.554769
\(473\) 23.9017 1.09900
\(474\) −15.9931 −0.734588
\(475\) 0.395265 0.0181360
\(476\) −7.40425 −0.339373
\(477\) 2.12525 0.0973086
\(478\) −1.15315 −0.0527437
\(479\) −18.6693 −0.853021 −0.426510 0.904483i \(-0.640257\pi\)
−0.426510 + 0.904483i \(0.640257\pi\)
\(480\) −17.6615 −0.806135
\(481\) 62.5890 2.85381
\(482\) 49.5489 2.25689
\(483\) 8.30793 0.378024
\(484\) 27.1955 1.23616
\(485\) 15.1601 0.688386
\(486\) 2.11517 0.0959461
\(487\) 19.4921 0.883273 0.441636 0.897194i \(-0.354398\pi\)
0.441636 + 0.897194i \(0.354398\pi\)
\(488\) −2.49578 −0.112979
\(489\) 9.37235 0.423832
\(490\) −9.15680 −0.413662
\(491\) −29.2036 −1.31794 −0.658970 0.752169i \(-0.729008\pi\)
−0.658970 + 0.752169i \(0.729008\pi\)
\(492\) 26.5503 1.19698
\(493\) −3.63506 −0.163715
\(494\) −53.6133 −2.41218
\(495\) −10.3720 −0.466187
\(496\) −11.5059 −0.516631
\(497\) 14.9602 0.671058
\(498\) −16.7055 −0.748591
\(499\) −39.9318 −1.78759 −0.893797 0.448473i \(-0.851968\pi\)
−0.893797 + 0.448473i \(0.851968\pi\)
\(500\) −27.9514 −1.25002
\(501\) 24.8082 1.10835
\(502\) −34.3418 −1.53275
\(503\) 24.3591 1.08612 0.543060 0.839694i \(-0.317266\pi\)
0.543060 + 0.839694i \(0.317266\pi\)
\(504\) 3.00032 0.133645
\(505\) 22.5633 1.00406
\(506\) 27.5352 1.22409
\(507\) −35.3640 −1.57057
\(508\) −24.5723 −1.09022
\(509\) −11.9945 −0.531645 −0.265823 0.964022i \(-0.585644\pi\)
−0.265823 + 0.964022i \(0.585644\pi\)
\(510\) 4.67809 0.207149
\(511\) 50.2617 2.22345
\(512\) −28.2480 −1.24839
\(513\) 3.64474 0.160919
\(514\) 66.6139 2.93821
\(515\) −18.0381 −0.794854
\(516\) 12.6090 0.555079
\(517\) −56.9775 −2.50587
\(518\) −56.9736 −2.50327
\(519\) −11.7404 −0.515344
\(520\) 15.4192 0.676176
\(521\) −16.2521 −0.712016 −0.356008 0.934483i \(-0.615862\pi\)
−0.356008 + 0.934483i \(0.615862\pi\)
\(522\) 7.68878 0.336529
\(523\) 10.7979 0.472157 0.236079 0.971734i \(-0.424138\pi\)
0.236079 + 0.971734i \(0.424138\pi\)
\(524\) −53.7787 −2.34933
\(525\) −0.324573 −0.0141655
\(526\) 26.5209 1.15637
\(527\) 4.06933 0.177263
\(528\) −13.2598 −0.577061
\(529\) −15.2944 −0.664975
\(530\) −9.94212 −0.431858
\(531\) −12.0228 −0.521746
\(532\) 26.9866 1.17002
\(533\) 74.6344 3.23277
\(534\) −8.36302 −0.361903
\(535\) −33.7361 −1.45854
\(536\) 5.61302 0.242446
\(537\) −8.94912 −0.386183
\(538\) 57.9547 2.49861
\(539\) −9.17941 −0.395385
\(540\) −5.47160 −0.235460
\(541\) 7.82090 0.336247 0.168123 0.985766i \(-0.446229\pi\)
0.168123 + 0.985766i \(0.446229\pi\)
\(542\) 51.0683 2.19357
\(543\) −13.0507 −0.560060
\(544\) 7.98556 0.342378
\(545\) 21.1100 0.904253
\(546\) 44.0247 1.88409
\(547\) −19.1823 −0.820175 −0.410087 0.912046i \(-0.634502\pi\)
−0.410087 + 0.912046i \(0.634502\pi\)
\(548\) 2.51017 0.107229
\(549\) 2.48960 0.106254
\(550\) −1.07574 −0.0458697
\(551\) 13.2489 0.564420
\(552\) 2.78278 0.118443
\(553\) 22.6296 0.962311
\(554\) −37.5284 −1.59443
\(555\) 19.9049 0.844917
\(556\) 23.4398 0.994067
\(557\) −13.3471 −0.565535 −0.282768 0.959188i \(-0.591252\pi\)
−0.282768 + 0.959188i \(0.591252\pi\)
\(558\) −8.60732 −0.364377
\(559\) 35.4446 1.49915
\(560\) 18.7160 0.790894
\(561\) 4.68964 0.197997
\(562\) 32.2460 1.36021
\(563\) −0.865035 −0.0364569 −0.0182284 0.999834i \(-0.505803\pi\)
−0.0182284 + 0.999834i \(0.505803\pi\)
\(564\) −30.0576 −1.26565
\(565\) 35.9382 1.51193
\(566\) 1.27597 0.0536330
\(567\) −2.99289 −0.125689
\(568\) 5.01101 0.210257
\(569\) 12.0048 0.503267 0.251634 0.967823i \(-0.419032\pi\)
0.251634 + 0.967823i \(0.419032\pi\)
\(570\) −17.0504 −0.714164
\(571\) −25.6057 −1.07156 −0.535782 0.844356i \(-0.679983\pi\)
−0.535782 + 0.844356i \(0.679983\pi\)
\(572\) 80.6848 3.37360
\(573\) −19.3245 −0.807291
\(574\) −67.9382 −2.83568
\(575\) −0.301040 −0.0125542
\(576\) −11.2359 −0.468161
\(577\) 11.8436 0.493056 0.246528 0.969136i \(-0.420710\pi\)
0.246528 + 0.969136i \(0.420710\pi\)
\(578\) −2.11517 −0.0879795
\(579\) −7.91560 −0.328961
\(580\) −19.8896 −0.825871
\(581\) 23.6377 0.980655
\(582\) 14.4986 0.600985
\(583\) −9.96667 −0.412777
\(584\) 16.8354 0.696655
\(585\) −15.3810 −0.635926
\(586\) −26.0472 −1.07600
\(587\) 14.5040 0.598643 0.299322 0.954152i \(-0.403240\pi\)
0.299322 + 0.954152i \(0.403240\pi\)
\(588\) −4.84246 −0.199700
\(589\) −14.8316 −0.611127
\(590\) 56.2438 2.31552
\(591\) −17.5967 −0.723830
\(592\) 25.4470 1.04586
\(593\) 1.28751 0.0528717 0.0264359 0.999651i \(-0.491584\pi\)
0.0264359 + 0.999651i \(0.491584\pi\)
\(594\) −9.91940 −0.406998
\(595\) −6.61933 −0.271366
\(596\) −24.3370 −0.996884
\(597\) 19.0361 0.779094
\(598\) 40.8328 1.66978
\(599\) 42.3012 1.72838 0.864190 0.503166i \(-0.167832\pi\)
0.864190 + 0.503166i \(0.167832\pi\)
\(600\) −0.108717 −0.00443837
\(601\) 9.10385 0.371354 0.185677 0.982611i \(-0.440552\pi\)
0.185677 + 0.982611i \(0.440552\pi\)
\(602\) −32.2645 −1.31500
\(603\) −5.59912 −0.228014
\(604\) 30.3628 1.23544
\(605\) 24.3125 0.988444
\(606\) 21.5787 0.876575
\(607\) 19.1639 0.777839 0.388920 0.921272i \(-0.372848\pi\)
0.388920 + 0.921272i \(0.372848\pi\)
\(608\) −29.1053 −1.18037
\(609\) −10.8793 −0.440853
\(610\) −11.6466 −0.471557
\(611\) −84.4937 −3.41825
\(612\) 2.47395 0.100003
\(613\) −1.50860 −0.0609319 −0.0304660 0.999536i \(-0.509699\pi\)
−0.0304660 + 0.999536i \(0.509699\pi\)
\(614\) −14.0594 −0.567392
\(615\) 23.7357 0.957114
\(616\) −14.0704 −0.566914
\(617\) 7.44653 0.299786 0.149893 0.988702i \(-0.452107\pi\)
0.149893 + 0.988702i \(0.452107\pi\)
\(618\) −17.2510 −0.693935
\(619\) −34.9998 −1.40676 −0.703380 0.710814i \(-0.748327\pi\)
−0.703380 + 0.710814i \(0.748327\pi\)
\(620\) 22.2657 0.894213
\(621\) −2.77589 −0.111393
\(622\) −21.9588 −0.880468
\(623\) 11.8334 0.474093
\(624\) −19.6634 −0.787168
\(625\) −24.4460 −0.977840
\(626\) −28.2441 −1.12886
\(627\) −17.0925 −0.682610
\(628\) −2.47395 −0.0987213
\(629\) −8.99989 −0.358849
\(630\) 14.0010 0.557814
\(631\) −4.55011 −0.181137 −0.0905686 0.995890i \(-0.528868\pi\)
−0.0905686 + 0.995890i \(0.528868\pi\)
\(632\) 7.57992 0.301513
\(633\) 17.4733 0.694502
\(634\) −19.5708 −0.777257
\(635\) −21.9674 −0.871750
\(636\) −5.25776 −0.208484
\(637\) −13.6124 −0.539344
\(638\) −36.0576 −1.42754
\(639\) −4.99860 −0.197741
\(640\) 17.2394 0.681446
\(641\) 15.7780 0.623193 0.311596 0.950215i \(-0.399136\pi\)
0.311596 + 0.950215i \(0.399136\pi\)
\(642\) −32.2639 −1.27336
\(643\) 13.7775 0.543331 0.271665 0.962392i \(-0.412426\pi\)
0.271665 + 0.962392i \(0.412426\pi\)
\(644\) −20.5534 −0.809917
\(645\) 11.2723 0.443846
\(646\) 7.70925 0.303316
\(647\) 17.9724 0.706568 0.353284 0.935516i \(-0.385065\pi\)
0.353284 + 0.935516i \(0.385065\pi\)
\(648\) −1.00248 −0.0393813
\(649\) 56.3827 2.21322
\(650\) −1.59525 −0.0625708
\(651\) 12.1790 0.477334
\(652\) −23.1867 −0.908062
\(653\) 22.5831 0.883745 0.441873 0.897078i \(-0.354314\pi\)
0.441873 + 0.897078i \(0.354314\pi\)
\(654\) 20.1888 0.789444
\(655\) −48.0776 −1.87855
\(656\) 30.3443 1.18474
\(657\) −16.7937 −0.655185
\(658\) 76.9129 2.99838
\(659\) −47.4653 −1.84899 −0.924493 0.381200i \(-0.875511\pi\)
−0.924493 + 0.381200i \(0.875511\pi\)
\(660\) 25.6598 0.998808
\(661\) −34.7572 −1.35190 −0.675950 0.736948i \(-0.736266\pi\)
−0.675950 + 0.736948i \(0.736266\pi\)
\(662\) 51.7284 2.01048
\(663\) 6.95442 0.270087
\(664\) 7.91755 0.307261
\(665\) 24.1257 0.935555
\(666\) 19.0363 0.737642
\(667\) −10.0905 −0.390707
\(668\) −61.3743 −2.37464
\(669\) −25.5231 −0.986779
\(670\) 26.1932 1.01193
\(671\) −11.6753 −0.450722
\(672\) 23.8999 0.921958
\(673\) 3.53855 0.136401 0.0682005 0.997672i \(-0.478274\pi\)
0.0682005 + 0.997672i \(0.478274\pi\)
\(674\) −38.4976 −1.48287
\(675\) 0.108448 0.00417417
\(676\) 87.4886 3.36495
\(677\) 37.6929 1.44866 0.724328 0.689456i \(-0.242150\pi\)
0.724328 + 0.689456i \(0.242150\pi\)
\(678\) 34.3699 1.31997
\(679\) −20.5149 −0.787291
\(680\) −2.21718 −0.0850249
\(681\) 12.0584 0.462078
\(682\) 40.3653 1.54567
\(683\) 12.0601 0.461465 0.230733 0.973017i \(-0.425888\pi\)
0.230733 + 0.973017i \(0.425888\pi\)
\(684\) −9.01690 −0.344770
\(685\) 2.24407 0.0857414
\(686\) −31.9222 −1.21879
\(687\) 13.1585 0.502027
\(688\) 14.4108 0.549406
\(689\) −14.7799 −0.563069
\(690\) 12.9859 0.494364
\(691\) 5.84913 0.222511 0.111256 0.993792i \(-0.464513\pi\)
0.111256 + 0.993792i \(0.464513\pi\)
\(692\) 29.0450 1.10413
\(693\) 14.0356 0.533167
\(694\) −18.6326 −0.707282
\(695\) 20.9549 0.794865
\(696\) −3.64409 −0.138129
\(697\) −10.7319 −0.406501
\(698\) −8.91754 −0.337534
\(699\) 3.11835 0.117947
\(700\) 0.802978 0.0303497
\(701\) −38.6454 −1.45962 −0.729808 0.683652i \(-0.760390\pi\)
−0.729808 + 0.683652i \(0.760390\pi\)
\(702\) −14.7098 −0.555185
\(703\) 32.8023 1.23716
\(704\) 52.6922 1.98591
\(705\) −26.8712 −1.01203
\(706\) 10.5826 0.398280
\(707\) −30.5331 −1.14831
\(708\) 29.7438 1.11784
\(709\) 43.4457 1.63164 0.815819 0.578308i \(-0.196287\pi\)
0.815819 + 0.578308i \(0.196287\pi\)
\(710\) 23.3839 0.877582
\(711\) −7.56114 −0.283565
\(712\) 3.96364 0.148544
\(713\) 11.2960 0.423039
\(714\) −6.33047 −0.236912
\(715\) 72.1313 2.69756
\(716\) 22.1397 0.827398
\(717\) −0.545179 −0.0203601
\(718\) 22.2770 0.831370
\(719\) −20.9423 −0.781015 −0.390507 0.920600i \(-0.627700\pi\)
−0.390507 + 0.920600i \(0.627700\pi\)
\(720\) −6.25348 −0.233054
\(721\) 24.4095 0.909056
\(722\) 12.0901 0.449945
\(723\) 23.4255 0.871203
\(724\) 32.2868 1.19993
\(725\) 0.394216 0.0146408
\(726\) 23.2516 0.862946
\(727\) −21.1461 −0.784264 −0.392132 0.919909i \(-0.628262\pi\)
−0.392132 + 0.919909i \(0.628262\pi\)
\(728\) −20.8655 −0.773326
\(729\) 1.00000 0.0370370
\(730\) 78.5626 2.90773
\(731\) −5.09670 −0.188508
\(732\) −6.15915 −0.227649
\(733\) 23.2197 0.857638 0.428819 0.903390i \(-0.358930\pi\)
0.428819 + 0.903390i \(0.358930\pi\)
\(734\) −9.27621 −0.342391
\(735\) −4.32911 −0.159681
\(736\) 22.1670 0.817088
\(737\) 26.2579 0.967221
\(738\) 22.6999 0.835594
\(739\) 1.84687 0.0679381 0.0339690 0.999423i \(-0.489185\pi\)
0.0339690 + 0.999423i \(0.489185\pi\)
\(740\) −49.2438 −1.81024
\(741\) −25.3470 −0.931147
\(742\) 13.4538 0.493906
\(743\) −2.62844 −0.0964282 −0.0482141 0.998837i \(-0.515353\pi\)
−0.0482141 + 0.998837i \(0.515353\pi\)
\(744\) 4.07943 0.149559
\(745\) −21.7571 −0.797118
\(746\) −22.0135 −0.805970
\(747\) −7.89794 −0.288971
\(748\) −11.6019 −0.424209
\(749\) 45.6523 1.66810
\(750\) −23.8978 −0.872624
\(751\) −0.923927 −0.0337146 −0.0168573 0.999858i \(-0.505366\pi\)
−0.0168573 + 0.999858i \(0.505366\pi\)
\(752\) −34.3528 −1.25272
\(753\) −16.2359 −0.591670
\(754\) −53.4710 −1.94730
\(755\) 27.1440 0.987871
\(756\) 7.40425 0.269290
\(757\) 18.1811 0.660804 0.330402 0.943840i \(-0.392816\pi\)
0.330402 + 0.943840i \(0.392816\pi\)
\(758\) 33.9707 1.23387
\(759\) 13.0179 0.472521
\(760\) 8.08103 0.293130
\(761\) 13.2886 0.481710 0.240855 0.970561i \(-0.422572\pi\)
0.240855 + 0.970561i \(0.422572\pi\)
\(762\) −21.0088 −0.761068
\(763\) −28.5664 −1.03417
\(764\) 47.8077 1.72962
\(765\) 2.21169 0.0799637
\(766\) 54.7478 1.97812
\(767\) 83.6117 3.01904
\(768\) −5.98467 −0.215953
\(769\) 15.6726 0.565168 0.282584 0.959243i \(-0.408808\pi\)
0.282584 + 0.959243i \(0.408808\pi\)
\(770\) −65.6597 −2.36621
\(771\) 31.4934 1.13421
\(772\) 19.5828 0.704800
\(773\) −20.3744 −0.732818 −0.366409 0.930454i \(-0.619413\pi\)
−0.366409 + 0.930454i \(0.619413\pi\)
\(774\) 10.7804 0.387493
\(775\) −0.441311 −0.0158524
\(776\) −6.87158 −0.246675
\(777\) −26.9357 −0.966312
\(778\) −37.7499 −1.35340
\(779\) 39.1151 1.40144
\(780\) 38.0518 1.36247
\(781\) 23.4416 0.838807
\(782\) −5.87148 −0.209964
\(783\) 3.63506 0.129907
\(784\) −5.53444 −0.197659
\(785\) −2.21169 −0.0789384
\(786\) −45.9796 −1.64004
\(787\) −6.38489 −0.227597 −0.113798 0.993504i \(-0.536302\pi\)
−0.113798 + 0.993504i \(0.536302\pi\)
\(788\) 43.5332 1.55081
\(789\) 12.5384 0.446379
\(790\) 35.3717 1.25847
\(791\) −48.6322 −1.72916
\(792\) 4.70129 0.167053
\(793\) −17.3137 −0.614829
\(794\) −35.2163 −1.24978
\(795\) −4.70039 −0.166706
\(796\) −47.0942 −1.66921
\(797\) −11.4414 −0.405276 −0.202638 0.979254i \(-0.564951\pi\)
−0.202638 + 0.979254i \(0.564951\pi\)
\(798\) 23.0729 0.816772
\(799\) 12.1496 0.429823
\(800\) −0.866019 −0.0306184
\(801\) −3.95383 −0.139702
\(802\) 8.51629 0.300721
\(803\) 78.7565 2.77926
\(804\) 13.8519 0.488520
\(805\) −18.3745 −0.647617
\(806\) 59.8589 2.10844
\(807\) 27.3995 0.964510
\(808\) −10.2272 −0.359792
\(809\) 3.89624 0.136985 0.0684923 0.997652i \(-0.478181\pi\)
0.0684923 + 0.997652i \(0.478181\pi\)
\(810\) −4.67809 −0.164371
\(811\) −19.7153 −0.692298 −0.346149 0.938179i \(-0.612511\pi\)
−0.346149 + 0.938179i \(0.612511\pi\)
\(812\) 26.9149 0.944529
\(813\) 24.1438 0.846761
\(814\) −89.2735 −3.12904
\(815\) −20.7287 −0.726094
\(816\) 2.82747 0.0989814
\(817\) 18.5762 0.649897
\(818\) 25.9807 0.908393
\(819\) 20.8138 0.727293
\(820\) −58.7208 −2.05062
\(821\) 2.43074 0.0848334 0.0424167 0.999100i \(-0.486494\pi\)
0.0424167 + 0.999100i \(0.486494\pi\)
\(822\) 2.14614 0.0748552
\(823\) −42.4943 −1.48126 −0.740630 0.671913i \(-0.765473\pi\)
−0.740630 + 0.671913i \(0.765473\pi\)
\(824\) 8.17607 0.284827
\(825\) −0.508583 −0.0177066
\(826\) −76.1101 −2.64821
\(827\) −18.0549 −0.627831 −0.313915 0.949451i \(-0.601641\pi\)
−0.313915 + 0.949451i \(0.601641\pi\)
\(828\) 6.86741 0.238659
\(829\) −22.3010 −0.774546 −0.387273 0.921965i \(-0.626583\pi\)
−0.387273 + 0.921965i \(0.626583\pi\)
\(830\) 36.9473 1.28246
\(831\) −17.7425 −0.615479
\(832\) 78.1390 2.70898
\(833\) 1.95738 0.0678192
\(834\) 20.0405 0.693945
\(835\) −54.8680 −1.89878
\(836\) 42.2860 1.46249
\(837\) −4.06933 −0.140656
\(838\) −10.4958 −0.362573
\(839\) −46.1079 −1.59182 −0.795910 0.605415i \(-0.793007\pi\)
−0.795910 + 0.605415i \(0.793007\pi\)
\(840\) −6.63576 −0.228956
\(841\) −15.7863 −0.544356
\(842\) −11.4154 −0.393400
\(843\) 15.2451 0.525069
\(844\) −43.2281 −1.48797
\(845\) 78.2139 2.69064
\(846\) −25.6986 −0.883535
\(847\) −32.9001 −1.13046
\(848\) −6.00909 −0.206353
\(849\) 0.603246 0.0207034
\(850\) 0.229386 0.00786789
\(851\) −24.9827 −0.856397
\(852\) 12.3663 0.423661
\(853\) −35.6243 −1.21975 −0.609876 0.792497i \(-0.708781\pi\)
−0.609876 + 0.792497i \(0.708781\pi\)
\(854\) 15.7603 0.539308
\(855\) −8.06102 −0.275681
\(856\) 15.2915 0.522651
\(857\) 13.0494 0.445758 0.222879 0.974846i \(-0.428454\pi\)
0.222879 + 0.974846i \(0.428454\pi\)
\(858\) 68.9837 2.35506
\(859\) 0.382639 0.0130555 0.00652773 0.999979i \(-0.497922\pi\)
0.00652773 + 0.999979i \(0.497922\pi\)
\(860\) −27.8871 −0.950942
\(861\) −32.1195 −1.09463
\(862\) 32.0622 1.09204
\(863\) 38.0383 1.29484 0.647419 0.762134i \(-0.275848\pi\)
0.647419 + 0.762134i \(0.275848\pi\)
\(864\) −7.98556 −0.271674
\(865\) 25.9660 0.882870
\(866\) −15.0344 −0.510890
\(867\) −1.00000 −0.0339618
\(868\) −30.1303 −1.02269
\(869\) 35.4591 1.20287
\(870\) −17.0052 −0.576529
\(871\) 38.9386 1.31938
\(872\) −9.56846 −0.324029
\(873\) 6.85456 0.231992
\(874\) 21.4000 0.723867
\(875\) 33.8145 1.14314
\(876\) 41.5468 1.40374
\(877\) −7.75974 −0.262028 −0.131014 0.991381i \(-0.541823\pi\)
−0.131014 + 0.991381i \(0.541823\pi\)
\(878\) −27.7544 −0.936667
\(879\) −12.3145 −0.415357
\(880\) 29.3266 0.988600
\(881\) −29.7293 −1.00161 −0.500803 0.865561i \(-0.666962\pi\)
−0.500803 + 0.865561i \(0.666962\pi\)
\(882\) −4.14019 −0.139408
\(883\) −46.3870 −1.56105 −0.780523 0.625127i \(-0.785047\pi\)
−0.780523 + 0.625127i \(0.785047\pi\)
\(884\) −17.2049 −0.578663
\(885\) 26.5907 0.893836
\(886\) 54.6114 1.83471
\(887\) 32.1160 1.07835 0.539175 0.842194i \(-0.318736\pi\)
0.539175 + 0.842194i \(0.318736\pi\)
\(888\) −9.02224 −0.302767
\(889\) 29.7267 0.997000
\(890\) 18.4964 0.620000
\(891\) −4.68964 −0.157109
\(892\) 63.1428 2.11418
\(893\) −44.2823 −1.48185
\(894\) −20.8076 −0.695911
\(895\) 19.7926 0.661595
\(896\) −23.3286 −0.779354
\(897\) 19.3047 0.644565
\(898\) 25.8016 0.861009
\(899\) −14.7923 −0.493349
\(900\) −0.268295 −0.00894318
\(901\) 2.12525 0.0708024
\(902\) −106.454 −3.54454
\(903\) −15.2539 −0.507617
\(904\) −16.2896 −0.541784
\(905\) 28.8641 0.959474
\(906\) 25.9595 0.862446
\(907\) 46.8974 1.55720 0.778601 0.627520i \(-0.215930\pi\)
0.778601 + 0.627520i \(0.215930\pi\)
\(908\) −29.8318 −0.990004
\(909\) 10.2019 0.338375
\(910\) −97.3689 −3.22775
\(911\) 40.6151 1.34564 0.672820 0.739806i \(-0.265083\pi\)
0.672820 + 0.739806i \(0.265083\pi\)
\(912\) −10.3054 −0.341246
\(913\) 37.0385 1.22580
\(914\) −71.6460 −2.36984
\(915\) −5.50621 −0.182030
\(916\) −32.5534 −1.07559
\(917\) 65.0594 2.14845
\(918\) 2.11517 0.0698111
\(919\) 52.3789 1.72782 0.863910 0.503647i \(-0.168009\pi\)
0.863910 + 0.503647i \(0.168009\pi\)
\(920\) −6.15464 −0.202913
\(921\) −6.64694 −0.219024
\(922\) −62.5296 −2.05930
\(923\) 34.7623 1.14422
\(924\) −34.7233 −1.14231
\(925\) 0.976022 0.0320914
\(926\) −58.3665 −1.91804
\(927\) −8.15582 −0.267872
\(928\) −29.0280 −0.952891
\(929\) 25.3934 0.833131 0.416566 0.909106i \(-0.363234\pi\)
0.416566 + 0.909106i \(0.363234\pi\)
\(930\) 19.0367 0.624238
\(931\) −7.13414 −0.233812
\(932\) −7.71463 −0.252701
\(933\) −10.3816 −0.339878
\(934\) 6.07671 0.198836
\(935\) −10.3720 −0.339201
\(936\) 6.97169 0.227877
\(937\) 34.9127 1.14055 0.570274 0.821454i \(-0.306837\pi\)
0.570274 + 0.821454i \(0.306837\pi\)
\(938\) −35.4451 −1.15732
\(939\) −13.3531 −0.435763
\(940\) 66.4779 2.16827
\(941\) 25.4958 0.831138 0.415569 0.909562i \(-0.363582\pi\)
0.415569 + 0.909562i \(0.363582\pi\)
\(942\) −2.11517 −0.0689160
\(943\) −29.7907 −0.970118
\(944\) 33.9942 1.10642
\(945\) 6.61933 0.215327
\(946\) −50.5562 −1.64372
\(947\) −5.90348 −0.191837 −0.0959187 0.995389i \(-0.530579\pi\)
−0.0959187 + 0.995389i \(0.530579\pi\)
\(948\) 18.7059 0.607539
\(949\) 116.791 3.79118
\(950\) −0.836054 −0.0271252
\(951\) −9.25260 −0.300036
\(952\) 3.00032 0.0972409
\(953\) 12.0090 0.389010 0.194505 0.980902i \(-0.437690\pi\)
0.194505 + 0.980902i \(0.437690\pi\)
\(954\) −4.49527 −0.145540
\(955\) 42.7396 1.38302
\(956\) 1.34875 0.0436215
\(957\) −17.0471 −0.551056
\(958\) 39.4887 1.27582
\(959\) −3.03671 −0.0980604
\(960\) 24.8502 0.802037
\(961\) −14.4406 −0.465825
\(962\) −132.387 −4.26831
\(963\) −15.2536 −0.491540
\(964\) −57.9534 −1.86655
\(965\) 17.5068 0.563564
\(966\) −17.5727 −0.565392
\(967\) 38.3175 1.23221 0.616104 0.787665i \(-0.288710\pi\)
0.616104 + 0.787665i \(0.288710\pi\)
\(968\) −11.0201 −0.354198
\(969\) 3.64474 0.117086
\(970\) −32.0663 −1.02959
\(971\) 2.10520 0.0675590 0.0337795 0.999429i \(-0.489246\pi\)
0.0337795 + 0.999429i \(0.489246\pi\)
\(972\) −2.47395 −0.0793520
\(973\) −28.3565 −0.909068
\(974\) −41.2292 −1.32107
\(975\) −0.754194 −0.0241535
\(976\) −7.03928 −0.225322
\(977\) 2.62543 0.0839948 0.0419974 0.999118i \(-0.486628\pi\)
0.0419974 + 0.999118i \(0.486628\pi\)
\(978\) −19.8241 −0.633906
\(979\) 18.5420 0.592606
\(980\) 10.7100 0.342118
\(981\) 9.54476 0.304741
\(982\) 61.7706 1.97118
\(983\) −32.0679 −1.02281 −0.511404 0.859340i \(-0.670874\pi\)
−0.511404 + 0.859340i \(0.670874\pi\)
\(984\) −10.7586 −0.342971
\(985\) 38.9183 1.24004
\(986\) 7.68878 0.244861
\(987\) 36.3625 1.15743
\(988\) 62.7073 1.99498
\(989\) −14.1479 −0.449877
\(990\) 21.9386 0.697254
\(991\) −25.0986 −0.797283 −0.398642 0.917107i \(-0.630518\pi\)
−0.398642 + 0.917107i \(0.630518\pi\)
\(992\) 32.4958 1.03174
\(993\) 24.4559 0.776084
\(994\) −31.6435 −1.00367
\(995\) −42.1018 −1.33472
\(996\) 19.5391 0.619120
\(997\) 36.6615 1.16108 0.580540 0.814231i \(-0.302841\pi\)
0.580540 + 0.814231i \(0.302841\pi\)
\(998\) 84.4626 2.67362
\(999\) 8.99989 0.284744
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 \(a_p\))