Properties

Label 8007.2.a.j.1.18
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 1.18
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.55552 q^{2}\) \(-1.00000 q^{3}\) \(+0.419651 q^{4}\) \(-2.03554 q^{5}\) \(+1.55552 q^{6}\) \(-4.57317 q^{7}\) \(+2.45827 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.55552 q^{2}\) \(-1.00000 q^{3}\) \(+0.419651 q^{4}\) \(-2.03554 q^{5}\) \(+1.55552 q^{6}\) \(-4.57317 q^{7}\) \(+2.45827 q^{8}\) \(+1.00000 q^{9}\) \(+3.16632 q^{10}\) \(+3.90117 q^{11}\) \(-0.419651 q^{12}\) \(-2.99785 q^{13}\) \(+7.11366 q^{14}\) \(+2.03554 q^{15}\) \(-4.66320 q^{16}\) \(+1.00000 q^{17}\) \(-1.55552 q^{18}\) \(+7.30910 q^{19}\) \(-0.854216 q^{20}\) \(+4.57317 q^{21}\) \(-6.06836 q^{22}\) \(+3.66963 q^{23}\) \(-2.45827 q^{24}\) \(-0.856587 q^{25}\) \(+4.66322 q^{26}\) \(-1.00000 q^{27}\) \(-1.91913 q^{28}\) \(+0.0200199 q^{29}\) \(-3.16632 q^{30}\) \(-8.38816 q^{31}\) \(+2.33717 q^{32}\) \(-3.90117 q^{33}\) \(-1.55552 q^{34}\) \(+9.30885 q^{35}\) \(+0.419651 q^{36}\) \(-0.292369 q^{37}\) \(-11.3695 q^{38}\) \(+2.99785 q^{39}\) \(-5.00390 q^{40}\) \(-5.24937 q^{41}\) \(-7.11366 q^{42}\) \(+9.50720 q^{43}\) \(+1.63713 q^{44}\) \(-2.03554 q^{45}\) \(-5.70819 q^{46}\) \(+10.0553 q^{47}\) \(+4.66320 q^{48}\) \(+13.9138 q^{49}\) \(+1.33244 q^{50}\) \(-1.00000 q^{51}\) \(-1.25805 q^{52}\) \(+12.8571 q^{53}\) \(+1.55552 q^{54}\) \(-7.94099 q^{55}\) \(-11.2421 q^{56}\) \(-7.30910 q^{57}\) \(-0.0311414 q^{58}\) \(+8.07056 q^{59}\) \(+0.854216 q^{60}\) \(-12.6110 q^{61}\) \(+13.0480 q^{62}\) \(-4.57317 q^{63}\) \(+5.69087 q^{64}\) \(+6.10223 q^{65}\) \(+6.06836 q^{66}\) \(+10.2107 q^{67}\) \(+0.419651 q^{68}\) \(-3.66963 q^{69}\) \(-14.4801 q^{70}\) \(-0.437604 q^{71}\) \(+2.45827 q^{72}\) \(-7.02387 q^{73}\) \(+0.454787 q^{74}\) \(+0.856587 q^{75}\) \(+3.06727 q^{76}\) \(-17.8407 q^{77}\) \(-4.66322 q^{78}\) \(+8.59159 q^{79}\) \(+9.49211 q^{80}\) \(+1.00000 q^{81}\) \(+8.16551 q^{82}\) \(+2.89402 q^{83}\) \(+1.91913 q^{84}\) \(-2.03554 q^{85}\) \(-14.7887 q^{86}\) \(-0.0200199 q^{87}\) \(+9.59013 q^{88}\) \(-9.08276 q^{89}\) \(+3.16632 q^{90}\) \(+13.7096 q^{91}\) \(+1.53996 q^{92}\) \(+8.38816 q^{93}\) \(-15.6413 q^{94}\) \(-14.8779 q^{95}\) \(-2.33717 q^{96}\) \(-15.4111 q^{97}\) \(-21.6433 q^{98}\) \(+3.90117 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55552 −1.09992 −0.549960 0.835191i \(-0.685357\pi\)
−0.549960 + 0.835191i \(0.685357\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.419651 0.209826
\(5\) −2.03554 −0.910320 −0.455160 0.890410i \(-0.650418\pi\)
−0.455160 + 0.890410i \(0.650418\pi\)
\(6\) 1.55552 0.635040
\(7\) −4.57317 −1.72849 −0.864247 0.503068i \(-0.832205\pi\)
−0.864247 + 0.503068i \(0.832205\pi\)
\(8\) 2.45827 0.869129
\(9\) 1.00000 0.333333
\(10\) 3.16632 1.00128
\(11\) 3.90117 1.17625 0.588124 0.808771i \(-0.299867\pi\)
0.588124 + 0.808771i \(0.299867\pi\)
\(12\) −0.419651 −0.121143
\(13\) −2.99785 −0.831453 −0.415726 0.909490i \(-0.636473\pi\)
−0.415726 + 0.909490i \(0.636473\pi\)
\(14\) 7.11366 1.90121
\(15\) 2.03554 0.525574
\(16\) −4.66320 −1.16580
\(17\) 1.00000 0.242536
\(18\) −1.55552 −0.366640
\(19\) 7.30910 1.67682 0.838411 0.545038i \(-0.183485\pi\)
0.838411 + 0.545038i \(0.183485\pi\)
\(20\) −0.854216 −0.191008
\(21\) 4.57317 0.997946
\(22\) −6.06836 −1.29378
\(23\) 3.66963 0.765171 0.382585 0.923920i \(-0.375034\pi\)
0.382585 + 0.923920i \(0.375034\pi\)
\(24\) −2.45827 −0.501792
\(25\) −0.856587 −0.171317
\(26\) 4.66322 0.914532
\(27\) −1.00000 −0.192450
\(28\) −1.91913 −0.362682
\(29\) 0.0200199 0.00371761 0.00185880 0.999998i \(-0.499408\pi\)
0.00185880 + 0.999998i \(0.499408\pi\)
\(30\) −3.16632 −0.578089
\(31\) −8.38816 −1.50656 −0.753279 0.657701i \(-0.771529\pi\)
−0.753279 + 0.657701i \(0.771529\pi\)
\(32\) 2.33717 0.413157
\(33\) −3.90117 −0.679107
\(34\) −1.55552 −0.266770
\(35\) 9.30885 1.57348
\(36\) 0.419651 0.0699419
\(37\) −0.292369 −0.0480652 −0.0240326 0.999711i \(-0.507651\pi\)
−0.0240326 + 0.999711i \(0.507651\pi\)
\(38\) −11.3695 −1.84437
\(39\) 2.99785 0.480040
\(40\) −5.00390 −0.791186
\(41\) −5.24937 −0.819814 −0.409907 0.912127i \(-0.634439\pi\)
−0.409907 + 0.912127i \(0.634439\pi\)
\(42\) −7.11366 −1.09766
\(43\) 9.50720 1.44983 0.724917 0.688836i \(-0.241878\pi\)
0.724917 + 0.688836i \(0.241878\pi\)
\(44\) 1.63713 0.246807
\(45\) −2.03554 −0.303440
\(46\) −5.70819 −0.841627
\(47\) 10.0553 1.46672 0.733361 0.679839i \(-0.237950\pi\)
0.733361 + 0.679839i \(0.237950\pi\)
\(48\) 4.66320 0.673074
\(49\) 13.9138 1.98769
\(50\) 1.33244 0.188436
\(51\) −1.00000 −0.140028
\(52\) −1.25805 −0.174460
\(53\) 12.8571 1.76606 0.883031 0.469314i \(-0.155499\pi\)
0.883031 + 0.469314i \(0.155499\pi\)
\(54\) 1.55552 0.211680
\(55\) −7.94099 −1.07076
\(56\) −11.2421 −1.50228
\(57\) −7.30910 −0.968114
\(58\) −0.0311414 −0.00408907
\(59\) 8.07056 1.05070 0.525349 0.850887i \(-0.323935\pi\)
0.525349 + 0.850887i \(0.323935\pi\)
\(60\) 0.854216 0.110279
\(61\) −12.6110 −1.61467 −0.807335 0.590094i \(-0.799091\pi\)
−0.807335 + 0.590094i \(0.799091\pi\)
\(62\) 13.0480 1.65709
\(63\) −4.57317 −0.576165
\(64\) 5.69087 0.711359
\(65\) 6.10223 0.756888
\(66\) 6.06836 0.746964
\(67\) 10.2107 1.24744 0.623720 0.781648i \(-0.285621\pi\)
0.623720 + 0.781648i \(0.285621\pi\)
\(68\) 0.419651 0.0508902
\(69\) −3.66963 −0.441771
\(70\) −14.4801 −1.73071
\(71\) −0.437604 −0.0519340 −0.0259670 0.999663i \(-0.508266\pi\)
−0.0259670 + 0.999663i \(0.508266\pi\)
\(72\) 2.45827 0.289710
\(73\) −7.02387 −0.822082 −0.411041 0.911617i \(-0.634835\pi\)
−0.411041 + 0.911617i \(0.634835\pi\)
\(74\) 0.454787 0.0528679
\(75\) 0.856587 0.0989102
\(76\) 3.06727 0.351840
\(77\) −17.8407 −2.03314
\(78\) −4.66322 −0.528005
\(79\) 8.59159 0.966629 0.483314 0.875447i \(-0.339433\pi\)
0.483314 + 0.875447i \(0.339433\pi\)
\(80\) 9.49211 1.06125
\(81\) 1.00000 0.111111
\(82\) 8.16551 0.901730
\(83\) 2.89402 0.317660 0.158830 0.987306i \(-0.449228\pi\)
0.158830 + 0.987306i \(0.449228\pi\)
\(84\) 1.91913 0.209395
\(85\) −2.03554 −0.220785
\(86\) −14.7887 −1.59470
\(87\) −0.0200199 −0.00214636
\(88\) 9.59013 1.02231
\(89\) −9.08276 −0.962771 −0.481385 0.876509i \(-0.659866\pi\)
−0.481385 + 0.876509i \(0.659866\pi\)
\(90\) 3.16632 0.333760
\(91\) 13.7096 1.43716
\(92\) 1.53996 0.160552
\(93\) 8.38816 0.869812
\(94\) −15.6413 −1.61328
\(95\) −14.8779 −1.52645
\(96\) −2.33717 −0.238536
\(97\) −15.4111 −1.56476 −0.782382 0.622799i \(-0.785995\pi\)
−0.782382 + 0.622799i \(0.785995\pi\)
\(98\) −21.6433 −2.18630
\(99\) 3.90117 0.392083
\(100\) −0.359468 −0.0359468
\(101\) −12.8823 −1.28184 −0.640919 0.767609i \(-0.721447\pi\)
−0.640919 + 0.767609i \(0.721447\pi\)
\(102\) 1.55552 0.154020
\(103\) −6.60272 −0.650585 −0.325293 0.945613i \(-0.605463\pi\)
−0.325293 + 0.945613i \(0.605463\pi\)
\(104\) −7.36951 −0.722640
\(105\) −9.30885 −0.908451
\(106\) −19.9996 −1.94253
\(107\) 11.9939 1.15950 0.579748 0.814796i \(-0.303151\pi\)
0.579748 + 0.814796i \(0.303151\pi\)
\(108\) −0.419651 −0.0403810
\(109\) −18.4739 −1.76948 −0.884739 0.466087i \(-0.845663\pi\)
−0.884739 + 0.466087i \(0.845663\pi\)
\(110\) 12.3524 1.17775
\(111\) 0.292369 0.0277504
\(112\) 21.3256 2.01508
\(113\) 16.2992 1.53330 0.766650 0.642065i \(-0.221922\pi\)
0.766650 + 0.642065i \(0.221922\pi\)
\(114\) 11.3695 1.06485
\(115\) −7.46967 −0.696550
\(116\) 0.00840138 0.000780049 0
\(117\) −2.99785 −0.277151
\(118\) −12.5539 −1.15568
\(119\) −4.57317 −0.419221
\(120\) 5.00390 0.456791
\(121\) 4.21915 0.383560
\(122\) 19.6167 1.77601
\(123\) 5.24937 0.473320
\(124\) −3.52010 −0.316114
\(125\) 11.9213 1.06627
\(126\) 7.11366 0.633735
\(127\) −0.143771 −0.0127576 −0.00637882 0.999980i \(-0.502030\pi\)
−0.00637882 + 0.999980i \(0.502030\pi\)
\(128\) −13.5266 −1.19560
\(129\) −9.50720 −0.837063
\(130\) −9.49216 −0.832517
\(131\) −19.5325 −1.70656 −0.853280 0.521453i \(-0.825390\pi\)
−0.853280 + 0.521453i \(0.825390\pi\)
\(132\) −1.63713 −0.142494
\(133\) −33.4257 −2.89838
\(134\) −15.8830 −1.37208
\(135\) 2.03554 0.175191
\(136\) 2.45827 0.210795
\(137\) −12.6038 −1.07681 −0.538406 0.842686i \(-0.680973\pi\)
−0.538406 + 0.842686i \(0.680973\pi\)
\(138\) 5.70819 0.485914
\(139\) 7.63118 0.647268 0.323634 0.946182i \(-0.395095\pi\)
0.323634 + 0.946182i \(0.395095\pi\)
\(140\) 3.90647 0.330157
\(141\) −10.0553 −0.846813
\(142\) 0.680703 0.0571233
\(143\) −11.6951 −0.977995
\(144\) −4.66320 −0.388600
\(145\) −0.0407513 −0.00338421
\(146\) 10.9258 0.904225
\(147\) −13.9138 −1.14759
\(148\) −0.122693 −0.0100853
\(149\) −11.3207 −0.927429 −0.463714 0.885985i \(-0.653484\pi\)
−0.463714 + 0.885985i \(0.653484\pi\)
\(150\) −1.33244 −0.108793
\(151\) 4.35225 0.354181 0.177091 0.984195i \(-0.443331\pi\)
0.177091 + 0.984195i \(0.443331\pi\)
\(152\) 17.9677 1.45738
\(153\) 1.00000 0.0808452
\(154\) 27.7516 2.23629
\(155\) 17.0744 1.37145
\(156\) 1.25805 0.100725
\(157\) −1.00000 −0.0798087
\(158\) −13.3644 −1.06322
\(159\) −12.8571 −1.01964
\(160\) −4.75740 −0.376105
\(161\) −16.7818 −1.32259
\(162\) −1.55552 −0.122213
\(163\) −6.81731 −0.533973 −0.266987 0.963700i \(-0.586028\pi\)
−0.266987 + 0.963700i \(0.586028\pi\)
\(164\) −2.20290 −0.172018
\(165\) 7.94099 0.618205
\(166\) −4.50172 −0.349401
\(167\) −21.0854 −1.63164 −0.815819 0.578307i \(-0.803713\pi\)
−0.815819 + 0.578307i \(0.803713\pi\)
\(168\) 11.2421 0.867344
\(169\) −4.01292 −0.308686
\(170\) 3.16632 0.242846
\(171\) 7.30910 0.558941
\(172\) 3.98971 0.304212
\(173\) −22.7687 −1.73107 −0.865536 0.500847i \(-0.833022\pi\)
−0.865536 + 0.500847i \(0.833022\pi\)
\(174\) 0.0311414 0.00236083
\(175\) 3.91731 0.296121
\(176\) −18.1919 −1.37127
\(177\) −8.07056 −0.606621
\(178\) 14.1284 1.05897
\(179\) 10.9699 0.819929 0.409965 0.912101i \(-0.365541\pi\)
0.409965 + 0.912101i \(0.365541\pi\)
\(180\) −0.854216 −0.0636695
\(181\) 10.5405 0.783467 0.391733 0.920079i \(-0.371876\pi\)
0.391733 + 0.920079i \(0.371876\pi\)
\(182\) −21.3257 −1.58076
\(183\) 12.6110 0.932230
\(184\) 9.02094 0.665032
\(185\) 0.595128 0.0437547
\(186\) −13.0480 −0.956724
\(187\) 3.90117 0.285282
\(188\) 4.21974 0.307756
\(189\) 4.57317 0.332649
\(190\) 23.1430 1.67897
\(191\) −12.2544 −0.886696 −0.443348 0.896350i \(-0.646209\pi\)
−0.443348 + 0.896350i \(0.646209\pi\)
\(192\) −5.69087 −0.410703
\(193\) 2.36320 0.170107 0.0850533 0.996376i \(-0.472894\pi\)
0.0850533 + 0.996376i \(0.472894\pi\)
\(194\) 23.9724 1.72112
\(195\) −6.10223 −0.436990
\(196\) 5.83896 0.417068
\(197\) 14.7699 1.05231 0.526156 0.850388i \(-0.323633\pi\)
0.526156 + 0.850388i \(0.323633\pi\)
\(198\) −6.06836 −0.431260
\(199\) 2.29742 0.162860 0.0814299 0.996679i \(-0.474051\pi\)
0.0814299 + 0.996679i \(0.474051\pi\)
\(200\) −2.10572 −0.148897
\(201\) −10.2107 −0.720209
\(202\) 20.0387 1.40992
\(203\) −0.0915544 −0.00642586
\(204\) −0.419651 −0.0293815
\(205\) 10.6853 0.746293
\(206\) 10.2707 0.715592
\(207\) 3.66963 0.255057
\(208\) 13.9795 0.969307
\(209\) 28.5141 1.97236
\(210\) 14.4801 0.999224
\(211\) −9.90698 −0.682024 −0.341012 0.940059i \(-0.610770\pi\)
−0.341012 + 0.940059i \(0.610770\pi\)
\(212\) 5.39551 0.370565
\(213\) 0.437604 0.0299841
\(214\) −18.6568 −1.27535
\(215\) −19.3523 −1.31981
\(216\) −2.45827 −0.167264
\(217\) 38.3604 2.60408
\(218\) 28.7366 1.94629
\(219\) 7.02387 0.474629
\(220\) −3.33244 −0.224673
\(221\) −2.99785 −0.201657
\(222\) −0.454787 −0.0305233
\(223\) 1.74311 0.116727 0.0583637 0.998295i \(-0.481412\pi\)
0.0583637 + 0.998295i \(0.481412\pi\)
\(224\) −10.6883 −0.714139
\(225\) −0.856587 −0.0571058
\(226\) −25.3538 −1.68651
\(227\) −15.4763 −1.02720 −0.513599 0.858031i \(-0.671688\pi\)
−0.513599 + 0.858031i \(0.671688\pi\)
\(228\) −3.06727 −0.203135
\(229\) 22.2233 1.46855 0.734277 0.678850i \(-0.237521\pi\)
0.734277 + 0.678850i \(0.237521\pi\)
\(230\) 11.6192 0.766150
\(231\) 17.8407 1.17383
\(232\) 0.0492144 0.00323108
\(233\) −1.48059 −0.0969966 −0.0484983 0.998823i \(-0.515444\pi\)
−0.0484983 + 0.998823i \(0.515444\pi\)
\(234\) 4.66322 0.304844
\(235\) −20.4680 −1.33519
\(236\) 3.38682 0.220463
\(237\) −8.59159 −0.558083
\(238\) 7.11366 0.461110
\(239\) −28.7088 −1.85702 −0.928510 0.371308i \(-0.878909\pi\)
−0.928510 + 0.371308i \(0.878909\pi\)
\(240\) −9.49211 −0.612713
\(241\) 18.9584 1.22122 0.610610 0.791931i \(-0.290924\pi\)
0.610610 + 0.791931i \(0.290924\pi\)
\(242\) −6.56299 −0.421885
\(243\) −1.00000 −0.0641500
\(244\) −5.29221 −0.338799
\(245\) −28.3221 −1.80944
\(246\) −8.16551 −0.520614
\(247\) −21.9116 −1.39420
\(248\) −20.6204 −1.30939
\(249\) −2.89402 −0.183401
\(250\) −18.5439 −1.17282
\(251\) −9.85301 −0.621916 −0.310958 0.950424i \(-0.600650\pi\)
−0.310958 + 0.950424i \(0.600650\pi\)
\(252\) −1.91913 −0.120894
\(253\) 14.3159 0.900031
\(254\) 0.223639 0.0140324
\(255\) 2.03554 0.127470
\(256\) 9.65922 0.603701
\(257\) 22.6093 1.41033 0.705164 0.709045i \(-0.250874\pi\)
0.705164 + 0.709045i \(0.250874\pi\)
\(258\) 14.7887 0.920702
\(259\) 1.33705 0.0830804
\(260\) 2.56081 0.158815
\(261\) 0.0200199 0.00123920
\(262\) 30.3832 1.87708
\(263\) 24.3146 1.49930 0.749652 0.661832i \(-0.230221\pi\)
0.749652 + 0.661832i \(0.230221\pi\)
\(264\) −9.59013 −0.590232
\(265\) −26.1712 −1.60768
\(266\) 51.9945 3.18799
\(267\) 9.08276 0.555856
\(268\) 4.28494 0.261745
\(269\) 8.21607 0.500943 0.250471 0.968124i \(-0.419414\pi\)
0.250471 + 0.968124i \(0.419414\pi\)
\(270\) −3.16632 −0.192696
\(271\) −22.6957 −1.37867 −0.689333 0.724445i \(-0.742096\pi\)
−0.689333 + 0.724445i \(0.742096\pi\)
\(272\) −4.66320 −0.282748
\(273\) −13.7096 −0.829746
\(274\) 19.6054 1.18441
\(275\) −3.34169 −0.201512
\(276\) −1.53996 −0.0926950
\(277\) 16.4110 0.986041 0.493020 0.870018i \(-0.335893\pi\)
0.493020 + 0.870018i \(0.335893\pi\)
\(278\) −11.8705 −0.711944
\(279\) −8.38816 −0.502186
\(280\) 22.8837 1.36756
\(281\) −31.3631 −1.87096 −0.935482 0.353375i \(-0.885034\pi\)
−0.935482 + 0.353375i \(0.885034\pi\)
\(282\) 15.6413 0.931427
\(283\) −7.24052 −0.430404 −0.215202 0.976570i \(-0.569041\pi\)
−0.215202 + 0.976570i \(0.569041\pi\)
\(284\) −0.183641 −0.0108971
\(285\) 14.8779 0.881294
\(286\) 18.1920 1.07572
\(287\) 24.0062 1.41704
\(288\) 2.33717 0.137719
\(289\) 1.00000 0.0588235
\(290\) 0.0633896 0.00372236
\(291\) 15.4111 0.903417
\(292\) −2.94758 −0.172494
\(293\) 27.1349 1.58524 0.792620 0.609716i \(-0.208716\pi\)
0.792620 + 0.609716i \(0.208716\pi\)
\(294\) 21.6433 1.26226
\(295\) −16.4279 −0.956471
\(296\) −0.718722 −0.0417748
\(297\) −3.90117 −0.226369
\(298\) 17.6096 1.02010
\(299\) −11.0010 −0.636203
\(300\) 0.359468 0.0207539
\(301\) −43.4780 −2.50603
\(302\) −6.77002 −0.389571
\(303\) 12.8823 0.740069
\(304\) −34.0838 −1.95484
\(305\) 25.6701 1.46987
\(306\) −1.55552 −0.0889233
\(307\) 23.6325 1.34878 0.674388 0.738377i \(-0.264408\pi\)
0.674388 + 0.738377i \(0.264408\pi\)
\(308\) −7.48687 −0.426604
\(309\) 6.60272 0.375615
\(310\) −26.5596 −1.50849
\(311\) 3.33390 0.189048 0.0945240 0.995523i \(-0.469867\pi\)
0.0945240 + 0.995523i \(0.469867\pi\)
\(312\) 7.36951 0.417216
\(313\) 23.0077 1.30047 0.650236 0.759732i \(-0.274670\pi\)
0.650236 + 0.759732i \(0.274670\pi\)
\(314\) 1.55552 0.0877832
\(315\) 9.30885 0.524494
\(316\) 3.60547 0.202823
\(317\) −8.74775 −0.491323 −0.245661 0.969356i \(-0.579005\pi\)
−0.245661 + 0.969356i \(0.579005\pi\)
\(318\) 19.9996 1.12152
\(319\) 0.0781012 0.00437283
\(320\) −11.5840 −0.647564
\(321\) −11.9939 −0.669436
\(322\) 26.1045 1.45475
\(323\) 7.30910 0.406689
\(324\) 0.419651 0.0233140
\(325\) 2.56792 0.142442
\(326\) 10.6045 0.587328
\(327\) 18.4739 1.02161
\(328\) −12.9044 −0.712524
\(329\) −45.9848 −2.53522
\(330\) −12.3524 −0.679976
\(331\) 27.0704 1.48792 0.743962 0.668222i \(-0.232944\pi\)
0.743962 + 0.668222i \(0.232944\pi\)
\(332\) 1.21448 0.0666532
\(333\) −0.292369 −0.0160217
\(334\) 32.7988 1.79467
\(335\) −20.7843 −1.13557
\(336\) −21.3256 −1.16340
\(337\) −0.0116226 −0.000633126 0 −0.000316563 1.00000i \(-0.500101\pi\)
−0.000316563 1.00000i \(0.500101\pi\)
\(338\) 6.24218 0.339530
\(339\) −16.2992 −0.885251
\(340\) −0.854216 −0.0463263
\(341\) −32.7237 −1.77209
\(342\) −11.3695 −0.614791
\(343\) −31.6181 −1.70722
\(344\) 23.3713 1.26009
\(345\) 7.46967 0.402153
\(346\) 35.4172 1.90404
\(347\) 29.9886 1.60987 0.804936 0.593362i \(-0.202200\pi\)
0.804936 + 0.593362i \(0.202200\pi\)
\(348\) −0.00840138 −0.000450361 0
\(349\) 17.8530 0.955651 0.477826 0.878455i \(-0.341425\pi\)
0.477826 + 0.878455i \(0.341425\pi\)
\(350\) −6.09347 −0.325710
\(351\) 2.99785 0.160013
\(352\) 9.11770 0.485975
\(353\) 8.74485 0.465442 0.232721 0.972544i \(-0.425237\pi\)
0.232721 + 0.972544i \(0.425237\pi\)
\(354\) 12.5539 0.667235
\(355\) 0.890759 0.0472766
\(356\) −3.81159 −0.202014
\(357\) 4.57317 0.242038
\(358\) −17.0639 −0.901857
\(359\) −9.22375 −0.486811 −0.243405 0.969925i \(-0.578265\pi\)
−0.243405 + 0.969925i \(0.578265\pi\)
\(360\) −5.00390 −0.263729
\(361\) 34.4229 1.81173
\(362\) −16.3959 −0.861751
\(363\) −4.21915 −0.221448
\(364\) 5.75327 0.301553
\(365\) 14.2974 0.748358
\(366\) −19.6167 −1.02538
\(367\) −24.6412 −1.28626 −0.643131 0.765756i \(-0.722365\pi\)
−0.643131 + 0.765756i \(0.722365\pi\)
\(368\) −17.1122 −0.892035
\(369\) −5.24937 −0.273271
\(370\) −0.925735 −0.0481267
\(371\) −58.7978 −3.05263
\(372\) 3.52010 0.182509
\(373\) 17.3678 0.899268 0.449634 0.893213i \(-0.351554\pi\)
0.449634 + 0.893213i \(0.351554\pi\)
\(374\) −6.06836 −0.313788
\(375\) −11.9213 −0.615613
\(376\) 24.7187 1.27477
\(377\) −0.0600167 −0.00309102
\(378\) −7.11366 −0.365887
\(379\) 2.10251 0.107999 0.0539994 0.998541i \(-0.482803\pi\)
0.0539994 + 0.998541i \(0.482803\pi\)
\(380\) −6.24355 −0.320287
\(381\) 0.143771 0.00736562
\(382\) 19.0620 0.975295
\(383\) −17.7158 −0.905237 −0.452619 0.891704i \(-0.649510\pi\)
−0.452619 + 0.891704i \(0.649510\pi\)
\(384\) 13.5266 0.690277
\(385\) 36.3154 1.85081
\(386\) −3.67601 −0.187104
\(387\) 9.50720 0.483278
\(388\) −6.46730 −0.328327
\(389\) −7.01741 −0.355797 −0.177898 0.984049i \(-0.556930\pi\)
−0.177898 + 0.984049i \(0.556930\pi\)
\(390\) 9.49216 0.480654
\(391\) 3.66963 0.185581
\(392\) 34.2040 1.72756
\(393\) 19.5325 0.985283
\(394\) −22.9749 −1.15746
\(395\) −17.4885 −0.879942
\(396\) 1.63713 0.0822690
\(397\) −6.33329 −0.317859 −0.158929 0.987290i \(-0.550804\pi\)
−0.158929 + 0.987290i \(0.550804\pi\)
\(398\) −3.57369 −0.179133
\(399\) 33.4257 1.67338
\(400\) 3.99443 0.199722
\(401\) 22.9700 1.14707 0.573533 0.819182i \(-0.305572\pi\)
0.573533 + 0.819182i \(0.305572\pi\)
\(402\) 15.8830 0.792173
\(403\) 25.1464 1.25263
\(404\) −5.40608 −0.268962
\(405\) −2.03554 −0.101147
\(406\) 0.142415 0.00706794
\(407\) −1.14058 −0.0565366
\(408\) −2.45827 −0.121702
\(409\) −26.3680 −1.30381 −0.651907 0.758299i \(-0.726031\pi\)
−0.651907 + 0.758299i \(0.726031\pi\)
\(410\) −16.6212 −0.820863
\(411\) 12.6038 0.621697
\(412\) −2.77084 −0.136509
\(413\) −36.9080 −1.81613
\(414\) −5.70819 −0.280542
\(415\) −5.89089 −0.289172
\(416\) −7.00647 −0.343521
\(417\) −7.63118 −0.373701
\(418\) −44.3543 −2.16944
\(419\) −3.87461 −0.189287 −0.0946436 0.995511i \(-0.530171\pi\)
−0.0946436 + 0.995511i \(0.530171\pi\)
\(420\) −3.90647 −0.190616
\(421\) 18.7232 0.912515 0.456258 0.889848i \(-0.349190\pi\)
0.456258 + 0.889848i \(0.349190\pi\)
\(422\) 15.4105 0.750173
\(423\) 10.0553 0.488908
\(424\) 31.6063 1.53494
\(425\) −0.856587 −0.0415506
\(426\) −0.680703 −0.0329801
\(427\) 57.6721 2.79095
\(428\) 5.03327 0.243292
\(429\) 11.6951 0.564646
\(430\) 30.1029 1.45169
\(431\) 10.1227 0.487592 0.243796 0.969827i \(-0.421607\pi\)
0.243796 + 0.969827i \(0.421607\pi\)
\(432\) 4.66320 0.224358
\(433\) 14.5325 0.698386 0.349193 0.937051i \(-0.386456\pi\)
0.349193 + 0.937051i \(0.386456\pi\)
\(434\) −59.6706 −2.86428
\(435\) 0.0407513 0.00195388
\(436\) −7.75259 −0.371282
\(437\) 26.8217 1.28306
\(438\) −10.9258 −0.522055
\(439\) 7.05792 0.336856 0.168428 0.985714i \(-0.446131\pi\)
0.168428 + 0.985714i \(0.446131\pi\)
\(440\) −19.5211 −0.930631
\(441\) 13.9138 0.662564
\(442\) 4.66322 0.221807
\(443\) 18.0831 0.859155 0.429577 0.903030i \(-0.358663\pi\)
0.429577 + 0.903030i \(0.358663\pi\)
\(444\) 0.122693 0.00582275
\(445\) 18.4883 0.876429
\(446\) −2.71145 −0.128391
\(447\) 11.3207 0.535451
\(448\) −26.0253 −1.22958
\(449\) 29.8017 1.40643 0.703214 0.710978i \(-0.251748\pi\)
0.703214 + 0.710978i \(0.251748\pi\)
\(450\) 1.33244 0.0628119
\(451\) −20.4787 −0.964304
\(452\) 6.83998 0.321725
\(453\) −4.35225 −0.204487
\(454\) 24.0737 1.12984
\(455\) −27.9065 −1.30828
\(456\) −17.9677 −0.841416
\(457\) −8.18031 −0.382659 −0.191329 0.981526i \(-0.561280\pi\)
−0.191329 + 0.981526i \(0.561280\pi\)
\(458\) −34.5688 −1.61529
\(459\) −1.00000 −0.0466760
\(460\) −3.13466 −0.146154
\(461\) −37.4805 −1.74564 −0.872821 0.488040i \(-0.837712\pi\)
−0.872821 + 0.488040i \(0.837712\pi\)
\(462\) −27.7516 −1.29112
\(463\) −18.9114 −0.878889 −0.439444 0.898270i \(-0.644825\pi\)
−0.439444 + 0.898270i \(0.644825\pi\)
\(464\) −0.0933568 −0.00433398
\(465\) −17.0744 −0.791807
\(466\) 2.30309 0.106689
\(467\) 16.1399 0.746867 0.373434 0.927657i \(-0.378180\pi\)
0.373434 + 0.927657i \(0.378180\pi\)
\(468\) −1.25805 −0.0581534
\(469\) −46.6954 −2.15619
\(470\) 31.8385 1.46860
\(471\) 1.00000 0.0460776
\(472\) 19.8396 0.913192
\(473\) 37.0892 1.70537
\(474\) 13.3644 0.613848
\(475\) −6.26088 −0.287269
\(476\) −1.91913 −0.0879634
\(477\) 12.8571 0.588688
\(478\) 44.6572 2.04257
\(479\) −36.8349 −1.68303 −0.841514 0.540235i \(-0.818335\pi\)
−0.841514 + 0.540235i \(0.818335\pi\)
\(480\) 4.75740 0.217144
\(481\) 0.876477 0.0399639
\(482\) −29.4903 −1.34325
\(483\) 16.7818 0.763599
\(484\) 1.77057 0.0804806
\(485\) 31.3699 1.42444
\(486\) 1.55552 0.0705599
\(487\) 33.6704 1.52575 0.762876 0.646545i \(-0.223787\pi\)
0.762876 + 0.646545i \(0.223787\pi\)
\(488\) −31.0012 −1.40336
\(489\) 6.81731 0.308290
\(490\) 44.0557 1.99024
\(491\) −4.69357 −0.211818 −0.105909 0.994376i \(-0.533775\pi\)
−0.105909 + 0.994376i \(0.533775\pi\)
\(492\) 2.20290 0.0993146
\(493\) 0.0200199 0.000901652 0
\(494\) 34.0839 1.53351
\(495\) −7.94099 −0.356921
\(496\) 39.1156 1.75634
\(497\) 2.00123 0.0897676
\(498\) 4.50172 0.201727
\(499\) 0.881169 0.0394465 0.0197233 0.999805i \(-0.493721\pi\)
0.0197233 + 0.999805i \(0.493721\pi\)
\(500\) 5.00279 0.223732
\(501\) 21.0854 0.942027
\(502\) 15.3266 0.684059
\(503\) −25.8710 −1.15353 −0.576767 0.816909i \(-0.695686\pi\)
−0.576767 + 0.816909i \(0.695686\pi\)
\(504\) −11.2421 −0.500762
\(505\) 26.2224 1.16688
\(506\) −22.2686 −0.989962
\(507\) 4.01292 0.178220
\(508\) −0.0603338 −0.00267688
\(509\) 23.4381 1.03887 0.519437 0.854509i \(-0.326142\pi\)
0.519437 + 0.854509i \(0.326142\pi\)
\(510\) −3.16632 −0.140207
\(511\) 32.1213 1.42096
\(512\) 12.0281 0.531572
\(513\) −7.30910 −0.322705
\(514\) −35.1692 −1.55125
\(515\) 13.4401 0.592241
\(516\) −3.98971 −0.175637
\(517\) 39.2276 1.72523
\(518\) −2.07981 −0.0913818
\(519\) 22.7687 0.999435
\(520\) 15.0009 0.657834
\(521\) −17.2047 −0.753752 −0.376876 0.926264i \(-0.623002\pi\)
−0.376876 + 0.926264i \(0.623002\pi\)
\(522\) −0.0311414 −0.00136302
\(523\) 43.1495 1.88680 0.943398 0.331663i \(-0.107610\pi\)
0.943398 + 0.331663i \(0.107610\pi\)
\(524\) −8.19683 −0.358080
\(525\) −3.91731 −0.170966
\(526\) −37.8220 −1.64912
\(527\) −8.38816 −0.365394
\(528\) 18.1919 0.791702
\(529\) −9.53382 −0.414514
\(530\) 40.7099 1.76832
\(531\) 8.07056 0.350233
\(532\) −14.0271 −0.608154
\(533\) 15.7368 0.681636
\(534\) −14.1284 −0.611397
\(535\) −24.4141 −1.05551
\(536\) 25.1007 1.08419
\(537\) −10.9699 −0.473386
\(538\) −12.7803 −0.550997
\(539\) 54.2803 2.33802
\(540\) 0.854216 0.0367596
\(541\) 39.7907 1.71074 0.855369 0.518020i \(-0.173331\pi\)
0.855369 + 0.518020i \(0.173331\pi\)
\(542\) 35.3037 1.51642
\(543\) −10.5405 −0.452335
\(544\) 2.33717 0.100205
\(545\) 37.6043 1.61079
\(546\) 21.3257 0.912654
\(547\) 24.3389 1.04066 0.520328 0.853966i \(-0.325810\pi\)
0.520328 + 0.853966i \(0.325810\pi\)
\(548\) −5.28918 −0.225943
\(549\) −12.6110 −0.538223
\(550\) 5.19808 0.221647
\(551\) 0.146328 0.00623377
\(552\) −9.02094 −0.383957
\(553\) −39.2907 −1.67081
\(554\) −25.5277 −1.08457
\(555\) −0.595128 −0.0252618
\(556\) 3.20243 0.135813
\(557\) 20.6363 0.874386 0.437193 0.899368i \(-0.355973\pi\)
0.437193 + 0.899368i \(0.355973\pi\)
\(558\) 13.0480 0.552365
\(559\) −28.5011 −1.20547
\(560\) −43.4090 −1.83436
\(561\) −3.90117 −0.164708
\(562\) 48.7860 2.05791
\(563\) 30.1633 1.27123 0.635615 0.772006i \(-0.280747\pi\)
0.635615 + 0.772006i \(0.280747\pi\)
\(564\) −4.21974 −0.177683
\(565\) −33.1776 −1.39579
\(566\) 11.2628 0.473410
\(567\) −4.57317 −0.192055
\(568\) −1.07575 −0.0451374
\(569\) −27.6164 −1.15774 −0.578870 0.815420i \(-0.696506\pi\)
−0.578870 + 0.815420i \(0.696506\pi\)
\(570\) −23.1430 −0.969353
\(571\) 0.901806 0.0377394 0.0188697 0.999822i \(-0.493993\pi\)
0.0188697 + 0.999822i \(0.493993\pi\)
\(572\) −4.90787 −0.205208
\(573\) 12.2544 0.511934
\(574\) −37.3422 −1.55863
\(575\) −3.14336 −0.131087
\(576\) 5.69087 0.237120
\(577\) −30.3879 −1.26506 −0.632531 0.774535i \(-0.717984\pi\)
−0.632531 + 0.774535i \(0.717984\pi\)
\(578\) −1.55552 −0.0647012
\(579\) −2.36320 −0.0982111
\(580\) −0.0171013 −0.000710094 0
\(581\) −13.2348 −0.549074
\(582\) −23.9724 −0.993687
\(583\) 50.1579 2.07733
\(584\) −17.2666 −0.714496
\(585\) 6.10223 0.252296
\(586\) −42.2090 −1.74364
\(587\) 1.30714 0.0539513 0.0269756 0.999636i \(-0.491412\pi\)
0.0269756 + 0.999636i \(0.491412\pi\)
\(588\) −5.83896 −0.240795
\(589\) −61.3099 −2.52623
\(590\) 25.5540 1.05204
\(591\) −14.7699 −0.607552
\(592\) 1.36337 0.0560343
\(593\) −9.28720 −0.381380 −0.190690 0.981650i \(-0.561072\pi\)
−0.190690 + 0.981650i \(0.561072\pi\)
\(594\) 6.06836 0.248988
\(595\) 9.30885 0.381626
\(596\) −4.75075 −0.194598
\(597\) −2.29742 −0.0940271
\(598\) 17.1123 0.699773
\(599\) −1.51023 −0.0617065 −0.0308533 0.999524i \(-0.509822\pi\)
−0.0308533 + 0.999524i \(0.509822\pi\)
\(600\) 2.10572 0.0859657
\(601\) −17.2911 −0.705319 −0.352660 0.935752i \(-0.614723\pi\)
−0.352660 + 0.935752i \(0.614723\pi\)
\(602\) 67.6310 2.75644
\(603\) 10.2107 0.415813
\(604\) 1.82643 0.0743163
\(605\) −8.58825 −0.349162
\(606\) −20.0387 −0.814018
\(607\) −32.5581 −1.32149 −0.660747 0.750609i \(-0.729760\pi\)
−0.660747 + 0.750609i \(0.729760\pi\)
\(608\) 17.0826 0.692791
\(609\) 0.0915544 0.00370997
\(610\) −39.9304 −1.61674
\(611\) −30.1444 −1.21951
\(612\) 0.419651 0.0169634
\(613\) −26.5098 −1.07072 −0.535361 0.844623i \(-0.679824\pi\)
−0.535361 + 0.844623i \(0.679824\pi\)
\(614\) −36.7608 −1.48355
\(615\) −10.6853 −0.430872
\(616\) −43.8573 −1.76706
\(617\) −5.76815 −0.232217 −0.116108 0.993237i \(-0.537042\pi\)
−0.116108 + 0.993237i \(0.537042\pi\)
\(618\) −10.2707 −0.413147
\(619\) 7.31853 0.294157 0.147078 0.989125i \(-0.453013\pi\)
0.147078 + 0.989125i \(0.453013\pi\)
\(620\) 7.16530 0.287765
\(621\) −3.66963 −0.147257
\(622\) −5.18595 −0.207938
\(623\) 41.5370 1.66414
\(624\) −13.9795 −0.559630
\(625\) −19.9833 −0.799333
\(626\) −35.7890 −1.43042
\(627\) −28.5141 −1.13874
\(628\) −0.419651 −0.0167459
\(629\) −0.292369 −0.0116575
\(630\) −14.4801 −0.576902
\(631\) 3.29006 0.130975 0.0654875 0.997853i \(-0.479140\pi\)
0.0654875 + 0.997853i \(0.479140\pi\)
\(632\) 21.1204 0.840125
\(633\) 9.90698 0.393767
\(634\) 13.6073 0.540416
\(635\) 0.292652 0.0116135
\(636\) −5.39551 −0.213946
\(637\) −41.7115 −1.65267
\(638\) −0.121488 −0.00480976
\(639\) −0.437604 −0.0173113
\(640\) 27.5339 1.08837
\(641\) −0.187578 −0.00740889 −0.00370444 0.999993i \(-0.501179\pi\)
−0.00370444 + 0.999993i \(0.501179\pi\)
\(642\) 18.6568 0.736326
\(643\) 31.9532 1.26011 0.630056 0.776550i \(-0.283032\pi\)
0.630056 + 0.776550i \(0.283032\pi\)
\(644\) −7.04251 −0.277514
\(645\) 19.3523 0.761995
\(646\) −11.3695 −0.447326
\(647\) −30.0127 −1.17992 −0.589961 0.807432i \(-0.700857\pi\)
−0.589961 + 0.807432i \(0.700857\pi\)
\(648\) 2.45827 0.0965699
\(649\) 31.4847 1.23588
\(650\) −3.99445 −0.156675
\(651\) −38.3604 −1.50346
\(652\) −2.86089 −0.112041
\(653\) 1.78674 0.0699207 0.0349604 0.999389i \(-0.488870\pi\)
0.0349604 + 0.999389i \(0.488870\pi\)
\(654\) −28.7366 −1.12369
\(655\) 39.7591 1.55352
\(656\) 24.4788 0.955738
\(657\) −7.02387 −0.274027
\(658\) 71.5303 2.78854
\(659\) −26.4067 −1.02866 −0.514329 0.857593i \(-0.671959\pi\)
−0.514329 + 0.857593i \(0.671959\pi\)
\(660\) 3.33244 0.129715
\(661\) 12.5774 0.489203 0.244602 0.969624i \(-0.421343\pi\)
0.244602 + 0.969624i \(0.421343\pi\)
\(662\) −42.1086 −1.63660
\(663\) 2.99785 0.116427
\(664\) 7.11429 0.276088
\(665\) 68.0393 2.63845
\(666\) 0.454787 0.0176226
\(667\) 0.0734657 0.00284460
\(668\) −8.84852 −0.342359
\(669\) −1.74311 −0.0673926
\(670\) 32.3305 1.24904
\(671\) −49.1976 −1.89925
\(672\) 10.6883 0.412309
\(673\) −24.0994 −0.928963 −0.464481 0.885583i \(-0.653759\pi\)
−0.464481 + 0.885583i \(0.653759\pi\)
\(674\) 0.0180793 0.000696388 0
\(675\) 0.856587 0.0329701
\(676\) −1.68403 −0.0647702
\(677\) 14.9500 0.574576 0.287288 0.957844i \(-0.407246\pi\)
0.287288 + 0.957844i \(0.407246\pi\)
\(678\) 25.3538 0.973706
\(679\) 70.4777 2.70468
\(680\) −5.00390 −0.191891
\(681\) 15.4763 0.593053
\(682\) 50.9024 1.94915
\(683\) −25.5419 −0.977332 −0.488666 0.872471i \(-0.662516\pi\)
−0.488666 + 0.872471i \(0.662516\pi\)
\(684\) 3.06727 0.117280
\(685\) 25.6554 0.980243
\(686\) 49.1827 1.87780
\(687\) −22.2233 −0.847870
\(688\) −44.3339 −1.69022
\(689\) −38.5437 −1.46840
\(690\) −11.6192 −0.442337
\(691\) 17.3517 0.660090 0.330045 0.943965i \(-0.392936\pi\)
0.330045 + 0.943965i \(0.392936\pi\)
\(692\) −9.55491 −0.363223
\(693\) −17.8407 −0.677713
\(694\) −46.6479 −1.77073
\(695\) −15.5336 −0.589221
\(696\) −0.0492144 −0.00186547
\(697\) −5.24937 −0.198834
\(698\) −27.7708 −1.05114
\(699\) 1.48059 0.0560010
\(700\) 1.64391 0.0621338
\(701\) 1.33976 0.0506021 0.0253010 0.999680i \(-0.491946\pi\)
0.0253010 + 0.999680i \(0.491946\pi\)
\(702\) −4.66322 −0.176002
\(703\) −2.13695 −0.0805968
\(704\) 22.2011 0.836734
\(705\) 20.4680 0.770871
\(706\) −13.6028 −0.511949
\(707\) 58.9129 2.21565
\(708\) −3.38682 −0.127285
\(709\) −39.3559 −1.47804 −0.739021 0.673683i \(-0.764712\pi\)
−0.739021 + 0.673683i \(0.764712\pi\)
\(710\) −1.38560 −0.0520005
\(711\) 8.59159 0.322210
\(712\) −22.3279 −0.836772
\(713\) −30.7814 −1.15277
\(714\) −7.11366 −0.266222
\(715\) 23.8059 0.890288
\(716\) 4.60353 0.172042
\(717\) 28.7088 1.07215
\(718\) 14.3478 0.535453
\(719\) 5.94444 0.221690 0.110845 0.993838i \(-0.464644\pi\)
0.110845 + 0.993838i \(0.464644\pi\)
\(720\) 9.49211 0.353750
\(721\) 30.1953 1.12453
\(722\) −53.5457 −1.99276
\(723\) −18.9584 −0.705072
\(724\) 4.42332 0.164391
\(725\) −0.0171488 −0.000636891 0
\(726\) 6.56299 0.243575
\(727\) 20.6021 0.764090 0.382045 0.924144i \(-0.375220\pi\)
0.382045 + 0.924144i \(0.375220\pi\)
\(728\) 33.7020 1.24908
\(729\) 1.00000 0.0370370
\(730\) −22.2399 −0.823134
\(731\) 9.50720 0.351637
\(732\) 5.29221 0.195606
\(733\) 14.8374 0.548031 0.274015 0.961725i \(-0.411648\pi\)
0.274015 + 0.961725i \(0.411648\pi\)
\(734\) 38.3300 1.41479
\(735\) 28.3221 1.04468
\(736\) 8.57655 0.316136
\(737\) 39.8338 1.46730
\(738\) 8.16551 0.300577
\(739\) 12.3645 0.454835 0.227418 0.973797i \(-0.426972\pi\)
0.227418 + 0.973797i \(0.426972\pi\)
\(740\) 0.249746 0.00918085
\(741\) 21.9116 0.804941
\(742\) 91.4613 3.35765
\(743\) 33.1650 1.21670 0.608352 0.793667i \(-0.291831\pi\)
0.608352 + 0.793667i \(0.291831\pi\)
\(744\) 20.6204 0.755979
\(745\) 23.0437 0.844257
\(746\) −27.0159 −0.989124
\(747\) 2.89402 0.105887
\(748\) 1.63713 0.0598595
\(749\) −54.8502 −2.00418
\(750\) 18.5439 0.677126
\(751\) −7.12050 −0.259831 −0.129915 0.991525i \(-0.541471\pi\)
−0.129915 + 0.991525i \(0.541471\pi\)
\(752\) −46.8900 −1.70990
\(753\) 9.85301 0.359064
\(754\) 0.0933573 0.00339987
\(755\) −8.85917 −0.322418
\(756\) 1.91913 0.0697982
\(757\) −19.1231 −0.695040 −0.347520 0.937673i \(-0.612976\pi\)
−0.347520 + 0.937673i \(0.612976\pi\)
\(758\) −3.27050 −0.118790
\(759\) −14.3159 −0.519633
\(760\) −36.5740 −1.32668
\(761\) 0.227241 0.00823748 0.00411874 0.999992i \(-0.498689\pi\)
0.00411874 + 0.999992i \(0.498689\pi\)
\(762\) −0.223639 −0.00810160
\(763\) 84.4842 3.05853
\(764\) −5.14256 −0.186051
\(765\) −2.03554 −0.0735950
\(766\) 27.5574 0.995689
\(767\) −24.1943 −0.873606
\(768\) −9.65922 −0.348547
\(769\) −50.3546 −1.81583 −0.907917 0.419150i \(-0.862328\pi\)
−0.907917 + 0.419150i \(0.862328\pi\)
\(770\) −56.4895 −2.03574
\(771\) −22.6093 −0.814253
\(772\) 0.991718 0.0356927
\(773\) 40.3326 1.45066 0.725331 0.688400i \(-0.241687\pi\)
0.725331 + 0.688400i \(0.241687\pi\)
\(774\) −14.7887 −0.531568
\(775\) 7.18519 0.258100
\(776\) −37.8847 −1.35998
\(777\) −1.33705 −0.0479665
\(778\) 10.9157 0.391348
\(779\) −38.3682 −1.37468
\(780\) −2.56081 −0.0916916
\(781\) −1.70717 −0.0610873
\(782\) −5.70819 −0.204125
\(783\) −0.0200199 −0.000715454 0
\(784\) −64.8829 −2.31725
\(785\) 2.03554 0.0726514
\(786\) −30.3832 −1.08373
\(787\) −50.3999 −1.79656 −0.898282 0.439420i \(-0.855184\pi\)
−0.898282 + 0.439420i \(0.855184\pi\)
\(788\) 6.19820 0.220802
\(789\) −24.3146 −0.865624
\(790\) 27.2038 0.967866
\(791\) −74.5389 −2.65030
\(792\) 9.59013 0.340771
\(793\) 37.8058 1.34252
\(794\) 9.85158 0.349619
\(795\) 26.1712 0.928196
\(796\) 0.964115 0.0341722
\(797\) 4.47487 0.158508 0.0792540 0.996854i \(-0.474746\pi\)
0.0792540 + 0.996854i \(0.474746\pi\)
\(798\) −51.9945 −1.84058
\(799\) 10.0553 0.355733
\(800\) −2.00199 −0.0707810
\(801\) −9.08276 −0.320924
\(802\) −35.7303 −1.26168
\(803\) −27.4014 −0.966973
\(804\) −4.28494 −0.151118
\(805\) 34.1600 1.20398
\(806\) −39.1158 −1.37780
\(807\) −8.21607 −0.289219
\(808\) −31.6682 −1.11408
\(809\) 53.5951 1.88430 0.942152 0.335185i \(-0.108799\pi\)
0.942152 + 0.335185i \(0.108799\pi\)
\(810\) 3.16632 0.111253
\(811\) 17.6500 0.619777 0.309888 0.950773i \(-0.399708\pi\)
0.309888 + 0.950773i \(0.399708\pi\)
\(812\) −0.0384209 −0.00134831
\(813\) 22.6957 0.795973
\(814\) 1.77420 0.0621857
\(815\) 13.8769 0.486087
\(816\) 4.66320 0.163244
\(817\) 69.4891 2.43112
\(818\) 41.0161 1.43409
\(819\) 13.7096 0.479054
\(820\) 4.48409 0.156591
\(821\) 8.85028 0.308877 0.154438 0.988002i \(-0.450643\pi\)
0.154438 + 0.988002i \(0.450643\pi\)
\(822\) −19.6054 −0.683818
\(823\) −32.6985 −1.13980 −0.569899 0.821715i \(-0.693018\pi\)
−0.569899 + 0.821715i \(0.693018\pi\)
\(824\) −16.2313 −0.565443
\(825\) 3.34169 0.116343
\(826\) 57.4113 1.99759
\(827\) 4.70982 0.163777 0.0818883 0.996642i \(-0.473905\pi\)
0.0818883 + 0.996642i \(0.473905\pi\)
\(828\) 1.53996 0.0535175
\(829\) 14.3182 0.497292 0.248646 0.968594i \(-0.420014\pi\)
0.248646 + 0.968594i \(0.420014\pi\)
\(830\) 9.16342 0.318067
\(831\) −16.4110 −0.569291
\(832\) −17.0604 −0.591461
\(833\) 13.9138 0.482086
\(834\) 11.8705 0.411041
\(835\) 42.9201 1.48531
\(836\) 11.9660 0.413851
\(837\) 8.38816 0.289937
\(838\) 6.02705 0.208201
\(839\) 16.1658 0.558106 0.279053 0.960276i \(-0.409980\pi\)
0.279053 + 0.960276i \(0.409980\pi\)
\(840\) −22.8837 −0.789561
\(841\) −28.9996 −0.999986
\(842\) −29.1244 −1.00369
\(843\) 31.3631 1.08020
\(844\) −4.15747 −0.143106
\(845\) 8.16844 0.281003
\(846\) −15.6413 −0.537760
\(847\) −19.2949 −0.662980
\(848\) −59.9553 −2.05887
\(849\) 7.24052 0.248494
\(850\) 1.33244 0.0457023
\(851\) −1.07289 −0.0367781
\(852\) 0.183641 0.00629143
\(853\) 29.2751 1.00236 0.501180 0.865343i \(-0.332899\pi\)
0.501180 + 0.865343i \(0.332899\pi\)
\(854\) −89.7102 −3.06982
\(855\) −14.8779 −0.508815
\(856\) 29.4843 1.00775
\(857\) −25.2945 −0.864044 −0.432022 0.901863i \(-0.642200\pi\)
−0.432022 + 0.901863i \(0.642200\pi\)
\(858\) −18.1920 −0.621065
\(859\) −18.6871 −0.637597 −0.318798 0.947823i \(-0.603279\pi\)
−0.318798 + 0.947823i \(0.603279\pi\)
\(860\) −8.12120 −0.276931
\(861\) −24.0062 −0.818130
\(862\) −15.7460 −0.536312
\(863\) 20.3477 0.692642 0.346321 0.938116i \(-0.387431\pi\)
0.346321 + 0.938116i \(0.387431\pi\)
\(864\) −2.33717 −0.0795121
\(865\) 46.3465 1.57583
\(866\) −22.6056 −0.768169
\(867\) −1.00000 −0.0339618
\(868\) 16.0980 0.546402
\(869\) 33.5173 1.13700
\(870\) −0.0633896 −0.00214911
\(871\) −30.6102 −1.03719
\(872\) −45.4138 −1.53790
\(873\) −15.4111 −0.521588
\(874\) −41.7217 −1.41126
\(875\) −54.5181 −1.84305
\(876\) 2.94758 0.0995894
\(877\) 13.6123 0.459656 0.229828 0.973231i \(-0.426184\pi\)
0.229828 + 0.973231i \(0.426184\pi\)
\(878\) −10.9788 −0.370515
\(879\) −27.1349 −0.915239
\(880\) 37.0304 1.24829
\(881\) 11.0251 0.371443 0.185722 0.982602i \(-0.440538\pi\)
0.185722 + 0.982602i \(0.440538\pi\)
\(882\) −21.6433 −0.728768
\(883\) −53.5863 −1.80332 −0.901661 0.432444i \(-0.857651\pi\)
−0.901661 + 0.432444i \(0.857651\pi\)
\(884\) −1.25805 −0.0423128
\(885\) 16.4279 0.552219
\(886\) −28.1287 −0.945002
\(887\) 9.04956 0.303854 0.151927 0.988392i \(-0.451452\pi\)
0.151927 + 0.988392i \(0.451452\pi\)
\(888\) 0.718722 0.0241187
\(889\) 0.657490 0.0220515
\(890\) −28.7590 −0.964003
\(891\) 3.90117 0.130694
\(892\) 0.731499 0.0244924
\(893\) 73.4955 2.45943
\(894\) −17.6096 −0.588954
\(895\) −22.3297 −0.746398
\(896\) 61.8595 2.06658
\(897\) 11.0010 0.367312
\(898\) −46.3572 −1.54696
\(899\) −0.167930 −0.00560079
\(900\) −0.359468 −0.0119823
\(901\) 12.8571 0.428333
\(902\) 31.8551 1.06066
\(903\) 43.4780 1.44686
\(904\) 40.0678 1.33264
\(905\) −21.4555 −0.713205
\(906\) 6.77002 0.224919
\(907\) −24.3664 −0.809073 −0.404536 0.914522i \(-0.632567\pi\)
−0.404536 + 0.914522i \(0.632567\pi\)
\(908\) −6.49464 −0.215532
\(909\) −12.8823 −0.427279
\(910\) 43.4092 1.43900
\(911\) 29.3668 0.972964 0.486482 0.873691i \(-0.338280\pi\)
0.486482 + 0.873691i \(0.338280\pi\)
\(912\) 34.0838 1.12863
\(913\) 11.2901 0.373647
\(914\) 12.7247 0.420894
\(915\) −25.6701 −0.848627
\(916\) 9.32601 0.308140
\(917\) 89.3252 2.94978
\(918\) 1.55552 0.0513399
\(919\) 31.8257 1.04983 0.524916 0.851154i \(-0.324097\pi\)
0.524916 + 0.851154i \(0.324097\pi\)
\(920\) −18.3625 −0.605392
\(921\) −23.6325 −0.778716
\(922\) 58.3018 1.92007
\(923\) 1.31187 0.0431807
\(924\) 7.48687 0.246300
\(925\) 0.250440 0.00823440
\(926\) 29.4172 0.966708
\(927\) −6.60272 −0.216862
\(928\) 0.0467900 0.00153596
\(929\) 4.19586 0.137662 0.0688308 0.997628i \(-0.478073\pi\)
0.0688308 + 0.997628i \(0.478073\pi\)
\(930\) 26.5596 0.870925
\(931\) 101.698 3.33301
\(932\) −0.621331 −0.0203524
\(933\) −3.33390 −0.109147
\(934\) −25.1060 −0.821495
\(935\) −7.94099 −0.259698
\(936\) −7.36951 −0.240880
\(937\) 7.21006 0.235542 0.117771 0.993041i \(-0.462425\pi\)
0.117771 + 0.993041i \(0.462425\pi\)
\(938\) 72.6357 2.37164
\(939\) −23.0077 −0.750828
\(940\) −8.58943 −0.280156
\(941\) −13.4599 −0.438780 −0.219390 0.975637i \(-0.570407\pi\)
−0.219390 + 0.975637i \(0.570407\pi\)
\(942\) −1.55552 −0.0506817
\(943\) −19.2632 −0.627297
\(944\) −37.6346 −1.22490
\(945\) −9.30885 −0.302817
\(946\) −57.6932 −1.87577
\(947\) −34.3024 −1.11468 −0.557340 0.830285i \(-0.688178\pi\)
−0.557340 + 0.830285i \(0.688178\pi\)
\(948\) −3.60547 −0.117100
\(949\) 21.0565 0.683523
\(950\) 9.73894 0.315973
\(951\) 8.74775 0.283665
\(952\) −11.2421 −0.364358
\(953\) −17.8045 −0.576744 −0.288372 0.957518i \(-0.593114\pi\)
−0.288372 + 0.957518i \(0.593114\pi\)
\(954\) −19.9996 −0.647510
\(955\) 24.9443 0.807177
\(956\) −12.0477 −0.389650
\(957\) −0.0781012 −0.00252465
\(958\) 57.2975 1.85120
\(959\) 57.6391 1.86126
\(960\) 11.5840 0.373871
\(961\) 39.3613 1.26972
\(962\) −1.36338 −0.0439572
\(963\) 11.9939 0.386499
\(964\) 7.95593 0.256243
\(965\) −4.81038 −0.154851
\(966\) −26.1045 −0.839899
\(967\) 43.4496 1.39724 0.698622 0.715491i \(-0.253797\pi\)
0.698622 + 0.715491i \(0.253797\pi\)
\(968\) 10.3718 0.333363
\(969\) −7.30910 −0.234802
\(970\) −48.7967 −1.56677
\(971\) 51.7609 1.66108 0.830542 0.556955i \(-0.188031\pi\)
0.830542 + 0.556955i \(0.188031\pi\)
\(972\) −0.419651 −0.0134603
\(973\) −34.8987 −1.11880
\(974\) −52.3751 −1.67821
\(975\) −2.56792 −0.0822391
\(976\) 58.8074 1.88238
\(977\) −22.4290 −0.717568 −0.358784 0.933421i \(-0.616809\pi\)
−0.358784 + 0.933421i \(0.616809\pi\)
\(978\) −10.6045 −0.339094
\(979\) −35.4334 −1.13246
\(980\) −11.8854 −0.379666
\(981\) −18.4739 −0.589826
\(982\) 7.30095 0.232983
\(983\) 15.4291 0.492113 0.246057 0.969255i \(-0.420865\pi\)
0.246057 + 0.969255i \(0.420865\pi\)
\(984\) 12.9044 0.411376
\(985\) −30.0647 −0.957940
\(986\) −0.0311414 −0.000991746 0
\(987\) 45.9848 1.46371
\(988\) −9.19521 −0.292539
\(989\) 34.8879 1.10937
\(990\) 12.3524 0.392585
\(991\) 26.9603 0.856424 0.428212 0.903678i \(-0.359144\pi\)
0.428212 + 0.903678i \(0.359144\pi\)
\(992\) −19.6046 −0.622445
\(993\) −27.0704 −0.859053
\(994\) −3.11296 −0.0987373
\(995\) −4.67648 −0.148255
\(996\) −1.21448 −0.0384823
\(997\) −2.52224 −0.0798802 −0.0399401 0.999202i \(-0.512717\pi\)
−0.0399401 + 0.999202i \(0.512717\pi\)
\(998\) −1.37068 −0.0433880
\(999\) 0.292369 0.00925015
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 \(a_p\))