Properties

Label 4033.2.a.d.1.16
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.06826 q^{2}\) \(+0.566483 q^{3}\) \(+2.27770 q^{4}\) \(+0.827262 q^{5}\) \(-1.17163 q^{6}\) \(+0.908209 q^{7}\) \(-0.574346 q^{8}\) \(-2.67910 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.06826 q^{2}\) \(+0.566483 q^{3}\) \(+2.27770 q^{4}\) \(+0.827262 q^{5}\) \(-1.17163 q^{6}\) \(+0.908209 q^{7}\) \(-0.574346 q^{8}\) \(-2.67910 q^{9}\) \(-1.71099 q^{10}\) \(+3.66274 q^{11}\) \(+1.29028 q^{12}\) \(-3.44386 q^{13}\) \(-1.87841 q^{14}\) \(+0.468630 q^{15}\) \(-3.36749 q^{16}\) \(+5.13833 q^{17}\) \(+5.54107 q^{18}\) \(-1.92001 q^{19}\) \(+1.88425 q^{20}\) \(+0.514485 q^{21}\) \(-7.57550 q^{22}\) \(+4.20861 q^{23}\) \(-0.325357 q^{24}\) \(-4.31564 q^{25}\) \(+7.12280 q^{26}\) \(-3.21711 q^{27}\) \(+2.06862 q^{28}\) \(-6.65775 q^{29}\) \(-0.969249 q^{30}\) \(-4.64372 q^{31}\) \(+8.11354 q^{32}\) \(+2.07488 q^{33}\) \(-10.6274 q^{34}\) \(+0.751327 q^{35}\) \(-6.10217 q^{36}\) \(-1.00000 q^{37}\) \(+3.97108 q^{38}\) \(-1.95089 q^{39}\) \(-0.475134 q^{40}\) \(-1.85570 q^{41}\) \(-1.06409 q^{42}\) \(+3.74176 q^{43}\) \(+8.34261 q^{44}\) \(-2.21632 q^{45}\) \(-8.70450 q^{46}\) \(+8.96463 q^{47}\) \(-1.90763 q^{48}\) \(-6.17516 q^{49}\) \(+8.92586 q^{50}\) \(+2.91078 q^{51}\) \(-7.84407 q^{52}\) \(-8.79679 q^{53}\) \(+6.65383 q^{54}\) \(+3.03005 q^{55}\) \(-0.521626 q^{56}\) \(-1.08765 q^{57}\) \(+13.7700 q^{58}\) \(-3.28335 q^{59}\) \(+1.06740 q^{60}\) \(-3.51226 q^{61}\) \(+9.60442 q^{62}\) \(-2.43318 q^{63}\) \(-10.0459 q^{64}\) \(-2.84898 q^{65}\) \(-4.29140 q^{66}\) \(+4.69107 q^{67}\) \(+11.7035 q^{68}\) \(+2.38411 q^{69}\) \(-1.55394 q^{70}\) \(-4.16845 q^{71}\) \(+1.53873 q^{72}\) \(-7.60926 q^{73}\) \(+2.06826 q^{74}\) \(-2.44474 q^{75}\) \(-4.37320 q^{76}\) \(+3.32654 q^{77}\) \(+4.03495 q^{78}\) \(+4.34396 q^{79}\) \(-2.78580 q^{80}\) \(+6.21485 q^{81}\) \(+3.83807 q^{82}\) \(-3.77274 q^{83}\) \(+1.17184 q^{84}\) \(+4.25074 q^{85}\) \(-7.73892 q^{86}\) \(-3.77151 q^{87}\) \(-2.10368 q^{88}\) \(-8.21640 q^{89}\) \(+4.58391 q^{90}\) \(-3.12775 q^{91}\) \(+9.58594 q^{92}\) \(-2.63059 q^{93}\) \(-18.5412 q^{94}\) \(-1.58835 q^{95}\) \(+4.59619 q^{96}\) \(-11.2358 q^{97}\) \(+12.7718 q^{98}\) \(-9.81284 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.06826 −1.46248 −0.731240 0.682120i \(-0.761058\pi\)
−0.731240 + 0.682120i \(0.761058\pi\)
\(3\) 0.566483 0.327059 0.163530 0.986538i \(-0.447712\pi\)
0.163530 + 0.986538i \(0.447712\pi\)
\(4\) 2.27770 1.13885
\(5\) 0.827262 0.369963 0.184981 0.982742i \(-0.440777\pi\)
0.184981 + 0.982742i \(0.440777\pi\)
\(6\) −1.17163 −0.478318
\(7\) 0.908209 0.343271 0.171635 0.985161i \(-0.445095\pi\)
0.171635 + 0.985161i \(0.445095\pi\)
\(8\) −0.574346 −0.203062
\(9\) −2.67910 −0.893032
\(10\) −1.71099 −0.541063
\(11\) 3.66274 1.10436 0.552179 0.833725i \(-0.313796\pi\)
0.552179 + 0.833725i \(0.313796\pi\)
\(12\) 1.29028 0.372471
\(13\) −3.44386 −0.955156 −0.477578 0.878589i \(-0.658485\pi\)
−0.477578 + 0.878589i \(0.658485\pi\)
\(14\) −1.87841 −0.502027
\(15\) 0.468630 0.121000
\(16\) −3.36749 −0.841874
\(17\) 5.13833 1.24623 0.623114 0.782131i \(-0.285867\pi\)
0.623114 + 0.782131i \(0.285867\pi\)
\(18\) 5.54107 1.30604
\(19\) −1.92001 −0.440481 −0.220240 0.975446i \(-0.570684\pi\)
−0.220240 + 0.975446i \(0.570684\pi\)
\(20\) 1.88425 0.421331
\(21\) 0.514485 0.112270
\(22\) −7.57550 −1.61510
\(23\) 4.20861 0.877556 0.438778 0.898595i \(-0.355411\pi\)
0.438778 + 0.898595i \(0.355411\pi\)
\(24\) −0.325357 −0.0664133
\(25\) −4.31564 −0.863127
\(26\) 7.12280 1.39690
\(27\) −3.21711 −0.619134
\(28\) 2.06862 0.390933
\(29\) −6.65775 −1.23631 −0.618157 0.786055i \(-0.712120\pi\)
−0.618157 + 0.786055i \(0.712120\pi\)
\(30\) −0.969249 −0.176960
\(31\) −4.64372 −0.834037 −0.417019 0.908898i \(-0.636925\pi\)
−0.417019 + 0.908898i \(0.636925\pi\)
\(32\) 8.11354 1.43429
\(33\) 2.07488 0.361191
\(34\) −10.6274 −1.82258
\(35\) 0.751327 0.126997
\(36\) −6.10217 −1.01703
\(37\) −1.00000 −0.164399
\(38\) 3.97108 0.644194
\(39\) −1.95089 −0.312393
\(40\) −0.475134 −0.0751253
\(41\) −1.85570 −0.289812 −0.144906 0.989445i \(-0.546288\pi\)
−0.144906 + 0.989445i \(0.546288\pi\)
\(42\) −1.06409 −0.164193
\(43\) 3.74176 0.570612 0.285306 0.958436i \(-0.407905\pi\)
0.285306 + 0.958436i \(0.407905\pi\)
\(44\) 8.34261 1.25770
\(45\) −2.21632 −0.330389
\(46\) −8.70450 −1.28341
\(47\) 8.96463 1.30763 0.653813 0.756656i \(-0.273168\pi\)
0.653813 + 0.756656i \(0.273168\pi\)
\(48\) −1.90763 −0.275343
\(49\) −6.17516 −0.882165
\(50\) 8.92586 1.26231
\(51\) 2.91078 0.407590
\(52\) −7.84407 −1.08778
\(53\) −8.79679 −1.20833 −0.604166 0.796859i \(-0.706494\pi\)
−0.604166 + 0.796859i \(0.706494\pi\)
\(54\) 6.65383 0.905471
\(55\) 3.03005 0.408572
\(56\) −0.521626 −0.0697052
\(57\) −1.08765 −0.144063
\(58\) 13.7700 1.80808
\(59\) −3.28335 −0.427456 −0.213728 0.976893i \(-0.568561\pi\)
−0.213728 + 0.976893i \(0.568561\pi\)
\(60\) 1.06740 0.137800
\(61\) −3.51226 −0.449699 −0.224850 0.974393i \(-0.572189\pi\)
−0.224850 + 0.974393i \(0.572189\pi\)
\(62\) 9.60442 1.21976
\(63\) −2.43318 −0.306552
\(64\) −10.0459 −1.25574
\(65\) −2.84898 −0.353372
\(66\) −4.29140 −0.528234
\(67\) 4.69107 0.573106 0.286553 0.958064i \(-0.407491\pi\)
0.286553 + 0.958064i \(0.407491\pi\)
\(68\) 11.7035 1.41926
\(69\) 2.38411 0.287013
\(70\) −1.55394 −0.185731
\(71\) −4.16845 −0.494704 −0.247352 0.968926i \(-0.579560\pi\)
−0.247352 + 0.968926i \(0.579560\pi\)
\(72\) 1.53873 0.181341
\(73\) −7.60926 −0.890596 −0.445298 0.895382i \(-0.646902\pi\)
−0.445298 + 0.895382i \(0.646902\pi\)
\(74\) 2.06826 0.240430
\(75\) −2.44474 −0.282294
\(76\) −4.37320 −0.501640
\(77\) 3.32654 0.379094
\(78\) 4.03495 0.456868
\(79\) 4.34396 0.488734 0.244367 0.969683i \(-0.421420\pi\)
0.244367 + 0.969683i \(0.421420\pi\)
\(80\) −2.78580 −0.311462
\(81\) 6.21485 0.690539
\(82\) 3.83807 0.423844
\(83\) −3.77274 −0.414112 −0.207056 0.978329i \(-0.566388\pi\)
−0.207056 + 0.978329i \(0.566388\pi\)
\(84\) 1.17184 0.127858
\(85\) 4.25074 0.461058
\(86\) −7.73892 −0.834509
\(87\) −3.77151 −0.404348
\(88\) −2.10368 −0.224253
\(89\) −8.21640 −0.870937 −0.435468 0.900204i \(-0.643417\pi\)
−0.435468 + 0.900204i \(0.643417\pi\)
\(90\) 4.58391 0.483187
\(91\) −3.12775 −0.327877
\(92\) 9.58594 0.999403
\(93\) −2.63059 −0.272780
\(94\) −18.5412 −1.91238
\(95\) −1.58835 −0.162962
\(96\) 4.59619 0.469096
\(97\) −11.2358 −1.14083 −0.570413 0.821358i \(-0.693217\pi\)
−0.570413 + 0.821358i \(0.693217\pi\)
\(98\) 12.7718 1.29015
\(99\) −9.81284 −0.986228
\(100\) −9.82971 −0.982971
\(101\) −11.9020 −1.18429 −0.592145 0.805832i \(-0.701719\pi\)
−0.592145 + 0.805832i \(0.701719\pi\)
\(102\) −6.02024 −0.596093
\(103\) 10.6958 1.05389 0.526945 0.849900i \(-0.323338\pi\)
0.526945 + 0.849900i \(0.323338\pi\)
\(104\) 1.97797 0.193956
\(105\) 0.425614 0.0415357
\(106\) 18.1940 1.76716
\(107\) 2.00346 0.193682 0.0968408 0.995300i \(-0.469126\pi\)
0.0968408 + 0.995300i \(0.469126\pi\)
\(108\) −7.32761 −0.705099
\(109\) −1.00000 −0.0957826
\(110\) −6.26693 −0.597528
\(111\) −0.566483 −0.0537682
\(112\) −3.05839 −0.288991
\(113\) −11.6445 −1.09542 −0.547712 0.836667i \(-0.684501\pi\)
−0.547712 + 0.836667i \(0.684501\pi\)
\(114\) 2.24955 0.210690
\(115\) 3.48163 0.324663
\(116\) −15.1643 −1.40797
\(117\) 9.22644 0.852985
\(118\) 6.79082 0.625146
\(119\) 4.66668 0.427794
\(120\) −0.269156 −0.0245704
\(121\) 2.41569 0.219608
\(122\) 7.26427 0.657676
\(123\) −1.05122 −0.0947857
\(124\) −10.5770 −0.949842
\(125\) −7.70647 −0.689288
\(126\) 5.03245 0.448326
\(127\) 5.98802 0.531351 0.265675 0.964063i \(-0.414405\pi\)
0.265675 + 0.964063i \(0.414405\pi\)
\(128\) 4.55047 0.402209
\(129\) 2.11964 0.186624
\(130\) 5.89242 0.516800
\(131\) −8.91813 −0.779181 −0.389590 0.920988i \(-0.627383\pi\)
−0.389590 + 0.920988i \(0.627383\pi\)
\(132\) 4.72595 0.411341
\(133\) −1.74377 −0.151204
\(134\) −9.70236 −0.838156
\(135\) −2.66140 −0.229057
\(136\) −2.95118 −0.253061
\(137\) 21.6555 1.85015 0.925075 0.379784i \(-0.124002\pi\)
0.925075 + 0.379784i \(0.124002\pi\)
\(138\) −4.93096 −0.419751
\(139\) 1.87524 0.159056 0.0795279 0.996833i \(-0.474659\pi\)
0.0795279 + 0.996833i \(0.474659\pi\)
\(140\) 1.71129 0.144631
\(141\) 5.07832 0.427671
\(142\) 8.62144 0.723495
\(143\) −12.6140 −1.05483
\(144\) 9.02184 0.751820
\(145\) −5.50771 −0.457390
\(146\) 15.7379 1.30248
\(147\) −3.49812 −0.288520
\(148\) −2.27770 −0.187225
\(149\) 2.68685 0.220116 0.110058 0.993925i \(-0.464896\pi\)
0.110058 + 0.993925i \(0.464896\pi\)
\(150\) 5.05635 0.412849
\(151\) −4.50649 −0.366733 −0.183367 0.983045i \(-0.558700\pi\)
−0.183367 + 0.983045i \(0.558700\pi\)
\(152\) 1.10275 0.0894448
\(153\) −13.7661 −1.11292
\(154\) −6.88014 −0.554418
\(155\) −3.84158 −0.308563
\(156\) −4.44354 −0.355768
\(157\) −0.685829 −0.0547351 −0.0273676 0.999625i \(-0.508712\pi\)
−0.0273676 + 0.999625i \(0.508712\pi\)
\(158\) −8.98444 −0.714764
\(159\) −4.98323 −0.395196
\(160\) 6.71203 0.530632
\(161\) 3.82230 0.301240
\(162\) −12.8539 −1.00990
\(163\) 14.1208 1.10603 0.553014 0.833172i \(-0.313478\pi\)
0.553014 + 0.833172i \(0.313478\pi\)
\(164\) −4.22672 −0.330052
\(165\) 1.71647 0.133627
\(166\) 7.80300 0.605630
\(167\) −11.2878 −0.873473 −0.436736 0.899590i \(-0.643866\pi\)
−0.436736 + 0.899590i \(0.643866\pi\)
\(168\) −0.295492 −0.0227977
\(169\) −1.13981 −0.0876778
\(170\) −8.79164 −0.674288
\(171\) 5.14389 0.393363
\(172\) 8.52258 0.649841
\(173\) −19.2251 −1.46166 −0.730828 0.682561i \(-0.760866\pi\)
−0.730828 + 0.682561i \(0.760866\pi\)
\(174\) 7.80045 0.591351
\(175\) −3.91950 −0.296286
\(176\) −12.3343 −0.929731
\(177\) −1.85996 −0.139803
\(178\) 16.9936 1.27373
\(179\) 12.7294 0.951444 0.475722 0.879596i \(-0.342187\pi\)
0.475722 + 0.879596i \(0.342187\pi\)
\(180\) −5.04809 −0.376262
\(181\) 23.5062 1.74720 0.873599 0.486646i \(-0.161780\pi\)
0.873599 + 0.486646i \(0.161780\pi\)
\(182\) 6.46899 0.479514
\(183\) −1.98964 −0.147078
\(184\) −2.41720 −0.178198
\(185\) −0.827262 −0.0608215
\(186\) 5.44075 0.398935
\(187\) 18.8204 1.37628
\(188\) 20.4187 1.48919
\(189\) −2.92181 −0.212531
\(190\) 3.28512 0.238328
\(191\) 20.7342 1.50027 0.750137 0.661282i \(-0.229988\pi\)
0.750137 + 0.661282i \(0.229988\pi\)
\(192\) −5.69085 −0.410701
\(193\) −2.48917 −0.179175 −0.0895873 0.995979i \(-0.528555\pi\)
−0.0895873 + 0.995979i \(0.528555\pi\)
\(194\) 23.2386 1.66844
\(195\) −1.61390 −0.115574
\(196\) −14.0651 −1.00465
\(197\) 1.81073 0.129009 0.0645044 0.997917i \(-0.479453\pi\)
0.0645044 + 0.997917i \(0.479453\pi\)
\(198\) 20.2955 1.44234
\(199\) −21.5718 −1.52919 −0.764593 0.644514i \(-0.777060\pi\)
−0.764593 + 0.644514i \(0.777060\pi\)
\(200\) 2.47867 0.175268
\(201\) 2.65742 0.187440
\(202\) 24.6163 1.73200
\(203\) −6.04663 −0.424390
\(204\) 6.62986 0.464183
\(205\) −1.53515 −0.107220
\(206\) −22.1217 −1.54129
\(207\) −11.2753 −0.783686
\(208\) 11.5972 0.804120
\(209\) −7.03251 −0.486449
\(210\) −0.880281 −0.0607451
\(211\) 10.2421 0.705093 0.352546 0.935794i \(-0.385316\pi\)
0.352546 + 0.935794i \(0.385316\pi\)
\(212\) −20.0364 −1.37611
\(213\) −2.36136 −0.161798
\(214\) −4.14367 −0.283255
\(215\) 3.09541 0.211105
\(216\) 1.84774 0.125722
\(217\) −4.21747 −0.286301
\(218\) 2.06826 0.140080
\(219\) −4.31052 −0.291278
\(220\) 6.90153 0.465301
\(221\) −17.6957 −1.19034
\(222\) 1.17163 0.0786350
\(223\) −3.85467 −0.258128 −0.129064 0.991636i \(-0.541197\pi\)
−0.129064 + 0.991636i \(0.541197\pi\)
\(224\) 7.36879 0.492348
\(225\) 11.5620 0.770801
\(226\) 24.0839 1.60204
\(227\) −25.9936 −1.72526 −0.862629 0.505837i \(-0.831184\pi\)
−0.862629 + 0.505837i \(0.831184\pi\)
\(228\) −2.47735 −0.164066
\(229\) −4.19456 −0.277184 −0.138592 0.990350i \(-0.544258\pi\)
−0.138592 + 0.990350i \(0.544258\pi\)
\(230\) −7.20090 −0.474814
\(231\) 1.88443 0.123986
\(232\) 3.82385 0.251048
\(233\) −17.3657 −1.13766 −0.568832 0.822454i \(-0.692605\pi\)
−0.568832 + 0.822454i \(0.692605\pi\)
\(234\) −19.0827 −1.24747
\(235\) 7.41610 0.483773
\(236\) −7.47847 −0.486807
\(237\) 2.46078 0.159845
\(238\) −9.65190 −0.625640
\(239\) 13.5667 0.877558 0.438779 0.898595i \(-0.355411\pi\)
0.438779 + 0.898595i \(0.355411\pi\)
\(240\) −1.57811 −0.101867
\(241\) 1.00763 0.0649071 0.0324535 0.999473i \(-0.489668\pi\)
0.0324535 + 0.999473i \(0.489668\pi\)
\(242\) −4.99628 −0.321173
\(243\) 13.1720 0.844981
\(244\) −7.99987 −0.512139
\(245\) −5.10847 −0.326368
\(246\) 2.17420 0.138622
\(247\) 6.61225 0.420728
\(248\) 2.66710 0.169361
\(249\) −2.13719 −0.135439
\(250\) 15.9390 1.00807
\(251\) 11.2271 0.708648 0.354324 0.935123i \(-0.384711\pi\)
0.354324 + 0.935123i \(0.384711\pi\)
\(252\) −5.54204 −0.349116
\(253\) 15.4151 0.969137
\(254\) −12.3848 −0.777090
\(255\) 2.40798 0.150793
\(256\) 10.6803 0.667517
\(257\) 4.44146 0.277051 0.138525 0.990359i \(-0.455764\pi\)
0.138525 + 0.990359i \(0.455764\pi\)
\(258\) −4.38397 −0.272934
\(259\) −0.908209 −0.0564334
\(260\) −6.48910 −0.402437
\(261\) 17.8368 1.10407
\(262\) 18.4450 1.13954
\(263\) −10.9128 −0.672913 −0.336456 0.941699i \(-0.609228\pi\)
−0.336456 + 0.941699i \(0.609228\pi\)
\(264\) −1.19170 −0.0733441
\(265\) −7.27725 −0.447038
\(266\) 3.60657 0.221133
\(267\) −4.65445 −0.284848
\(268\) 10.6848 0.652680
\(269\) 16.0528 0.978757 0.489378 0.872072i \(-0.337224\pi\)
0.489378 + 0.872072i \(0.337224\pi\)
\(270\) 5.50446 0.334991
\(271\) −3.96112 −0.240621 −0.120310 0.992736i \(-0.538389\pi\)
−0.120310 + 0.992736i \(0.538389\pi\)
\(272\) −17.3033 −1.04917
\(273\) −1.77182 −0.107235
\(274\) −44.7891 −2.70581
\(275\) −15.8071 −0.953202
\(276\) 5.43027 0.326864
\(277\) 2.73817 0.164521 0.0822603 0.996611i \(-0.473786\pi\)
0.0822603 + 0.996611i \(0.473786\pi\)
\(278\) −3.87848 −0.232616
\(279\) 12.4410 0.744822
\(280\) −0.431521 −0.0257883
\(281\) −6.28063 −0.374671 −0.187336 0.982296i \(-0.559985\pi\)
−0.187336 + 0.982296i \(0.559985\pi\)
\(282\) −10.5033 −0.625461
\(283\) −20.5295 −1.22035 −0.610177 0.792265i \(-0.708902\pi\)
−0.610177 + 0.792265i \(0.708902\pi\)
\(284\) −9.49446 −0.563393
\(285\) −0.899775 −0.0532981
\(286\) 26.0890 1.54267
\(287\) −1.68537 −0.0994840
\(288\) −21.7370 −1.28086
\(289\) 9.40242 0.553083
\(290\) 11.3914 0.668924
\(291\) −6.36491 −0.373118
\(292\) −17.3316 −1.01425
\(293\) −12.7213 −0.743184 −0.371592 0.928396i \(-0.621188\pi\)
−0.371592 + 0.928396i \(0.621188\pi\)
\(294\) 7.23503 0.421955
\(295\) −2.71619 −0.158143
\(296\) 0.574346 0.0333832
\(297\) −11.7835 −0.683746
\(298\) −5.55711 −0.321915
\(299\) −14.4939 −0.838203
\(300\) −5.56837 −0.321490
\(301\) 3.39830 0.195875
\(302\) 9.32059 0.536340
\(303\) −6.74227 −0.387333
\(304\) 6.46563 0.370829
\(305\) −2.90556 −0.166372
\(306\) 28.4718 1.62763
\(307\) 24.5729 1.40245 0.701224 0.712941i \(-0.252637\pi\)
0.701224 + 0.712941i \(0.252637\pi\)
\(308\) 7.57684 0.431730
\(309\) 6.05900 0.344684
\(310\) 7.94538 0.451267
\(311\) −27.0646 −1.53469 −0.767347 0.641232i \(-0.778424\pi\)
−0.767347 + 0.641232i \(0.778424\pi\)
\(312\) 1.12049 0.0634350
\(313\) 3.08938 0.174622 0.0873109 0.996181i \(-0.472173\pi\)
0.0873109 + 0.996181i \(0.472173\pi\)
\(314\) 1.41847 0.0800490
\(315\) −2.01288 −0.113413
\(316\) 9.89422 0.556594
\(317\) −17.3550 −0.974757 −0.487378 0.873191i \(-0.662047\pi\)
−0.487378 + 0.873191i \(0.662047\pi\)
\(318\) 10.3066 0.577967
\(319\) −24.3856 −1.36533
\(320\) −8.31061 −0.464577
\(321\) 1.13493 0.0633454
\(322\) −7.90551 −0.440557
\(323\) −9.86565 −0.548939
\(324\) 14.1555 0.786418
\(325\) 14.8625 0.824421
\(326\) −29.2055 −1.61754
\(327\) −0.566483 −0.0313266
\(328\) 1.06581 0.0588497
\(329\) 8.14176 0.448870
\(330\) −3.55011 −0.195427
\(331\) −23.2287 −1.27677 −0.638383 0.769719i \(-0.720396\pi\)
−0.638383 + 0.769719i \(0.720396\pi\)
\(332\) −8.59314 −0.471610
\(333\) 2.67910 0.146814
\(334\) 23.3460 1.27744
\(335\) 3.88075 0.212028
\(336\) −1.73253 −0.0945171
\(337\) −2.48202 −0.135204 −0.0676021 0.997712i \(-0.521535\pi\)
−0.0676021 + 0.997712i \(0.521535\pi\)
\(338\) 2.35742 0.128227
\(339\) −6.59643 −0.358269
\(340\) 9.68190 0.525075
\(341\) −17.0088 −0.921077
\(342\) −10.6389 −0.575286
\(343\) −11.9658 −0.646092
\(344\) −2.14906 −0.115870
\(345\) 1.97228 0.106184
\(346\) 39.7625 2.13764
\(347\) 26.6694 1.43169 0.715845 0.698259i \(-0.246041\pi\)
0.715845 + 0.698259i \(0.246041\pi\)
\(348\) −8.59034 −0.460491
\(349\) −11.2802 −0.603817 −0.301909 0.953337i \(-0.597624\pi\)
−0.301909 + 0.953337i \(0.597624\pi\)
\(350\) 8.10654 0.433313
\(351\) 11.0793 0.591369
\(352\) 29.7178 1.58397
\(353\) 15.5913 0.829839 0.414920 0.909858i \(-0.363810\pi\)
0.414920 + 0.909858i \(0.363810\pi\)
\(354\) 3.84689 0.204460
\(355\) −3.44840 −0.183022
\(356\) −18.7145 −0.991864
\(357\) 2.64360 0.139914
\(358\) −26.3278 −1.39147
\(359\) 19.9836 1.05470 0.527348 0.849650i \(-0.323187\pi\)
0.527348 + 0.849650i \(0.323187\pi\)
\(360\) 1.27293 0.0670893
\(361\) −15.3136 −0.805977
\(362\) −48.6168 −2.55524
\(363\) 1.36845 0.0718250
\(364\) −7.12406 −0.373402
\(365\) −6.29485 −0.329488
\(366\) 4.11509 0.215099
\(367\) −20.4708 −1.06856 −0.534282 0.845306i \(-0.679418\pi\)
−0.534282 + 0.845306i \(0.679418\pi\)
\(368\) −14.1725 −0.738792
\(369\) 4.97160 0.258811
\(370\) 1.71099 0.0889503
\(371\) −7.98932 −0.414785
\(372\) −5.99169 −0.310655
\(373\) −0.516857 −0.0267618 −0.0133809 0.999910i \(-0.504259\pi\)
−0.0133809 + 0.999910i \(0.504259\pi\)
\(374\) −38.9254 −2.01279
\(375\) −4.36559 −0.225438
\(376\) −5.14880 −0.265529
\(377\) 22.9284 1.18087
\(378\) 6.04307 0.310822
\(379\) 13.5502 0.696025 0.348013 0.937490i \(-0.386857\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(380\) −3.61778 −0.185588
\(381\) 3.39211 0.173783
\(382\) −42.8837 −2.19412
\(383\) 6.13999 0.313739 0.156869 0.987619i \(-0.449860\pi\)
0.156869 + 0.987619i \(0.449860\pi\)
\(384\) 2.57777 0.131546
\(385\) 2.75192 0.140251
\(386\) 5.14826 0.262039
\(387\) −10.0245 −0.509575
\(388\) −25.5918 −1.29923
\(389\) −21.7974 −1.10517 −0.552586 0.833456i \(-0.686359\pi\)
−0.552586 + 0.833456i \(0.686359\pi\)
\(390\) 3.33796 0.169024
\(391\) 21.6252 1.09364
\(392\) 3.54667 0.179134
\(393\) −5.05197 −0.254838
\(394\) −3.74505 −0.188673
\(395\) 3.59360 0.180813
\(396\) −22.3507 −1.12316
\(397\) −1.29433 −0.0649607 −0.0324804 0.999472i \(-0.510341\pi\)
−0.0324804 + 0.999472i \(0.510341\pi\)
\(398\) 44.6161 2.23640
\(399\) −0.987818 −0.0494527
\(400\) 14.5329 0.726644
\(401\) −26.3691 −1.31681 −0.658404 0.752665i \(-0.728768\pi\)
−0.658404 + 0.752665i \(0.728768\pi\)
\(402\) −5.49622 −0.274127
\(403\) 15.9923 0.796636
\(404\) −27.1090 −1.34873
\(405\) 5.14131 0.255474
\(406\) 12.5060 0.620662
\(407\) −3.66274 −0.181555
\(408\) −1.67179 −0.0827661
\(409\) −5.89273 −0.291377 −0.145688 0.989331i \(-0.546540\pi\)
−0.145688 + 0.989331i \(0.546540\pi\)
\(410\) 3.17509 0.156807
\(411\) 12.2675 0.605109
\(412\) 24.3618 1.20022
\(413\) −2.98197 −0.146733
\(414\) 23.3202 1.14613
\(415\) −3.12104 −0.153206
\(416\) −27.9419 −1.36997
\(417\) 1.06229 0.0520207
\(418\) 14.5450 0.711422
\(419\) −10.6981 −0.522638 −0.261319 0.965253i \(-0.584157\pi\)
−0.261319 + 0.965253i \(0.584157\pi\)
\(420\) 0.969420 0.0473028
\(421\) 21.9973 1.07209 0.536043 0.844191i \(-0.319919\pi\)
0.536043 + 0.844191i \(0.319919\pi\)
\(422\) −21.1832 −1.03118
\(423\) −24.0171 −1.16775
\(424\) 5.05240 0.245366
\(425\) −22.1752 −1.07565
\(426\) 4.88390 0.236626
\(427\) −3.18987 −0.154369
\(428\) 4.56327 0.220574
\(429\) −7.14561 −0.344993
\(430\) −6.40212 −0.308737
\(431\) −15.2122 −0.732747 −0.366373 0.930468i \(-0.619401\pi\)
−0.366373 + 0.930468i \(0.619401\pi\)
\(432\) 10.8336 0.521233
\(433\) −30.9661 −1.48813 −0.744067 0.668105i \(-0.767106\pi\)
−0.744067 + 0.668105i \(0.767106\pi\)
\(434\) 8.72283 0.418709
\(435\) −3.12002 −0.149594
\(436\) −2.27770 −0.109082
\(437\) −8.08058 −0.386547
\(438\) 8.91527 0.425988
\(439\) 12.5976 0.601250 0.300625 0.953742i \(-0.402805\pi\)
0.300625 + 0.953742i \(0.402805\pi\)
\(440\) −1.74030 −0.0829653
\(441\) 16.5438 0.787802
\(442\) 36.5993 1.74085
\(443\) 21.1345 1.00413 0.502065 0.864830i \(-0.332574\pi\)
0.502065 + 0.864830i \(0.332574\pi\)
\(444\) −1.29028 −0.0612338
\(445\) −6.79712 −0.322214
\(446\) 7.97246 0.377507
\(447\) 1.52206 0.0719908
\(448\) −9.12380 −0.431059
\(449\) −33.2923 −1.57116 −0.785580 0.618760i \(-0.787635\pi\)
−0.785580 + 0.618760i \(0.787635\pi\)
\(450\) −23.9132 −1.12728
\(451\) −6.79696 −0.320056
\(452\) −26.5227 −1.24752
\(453\) −2.55285 −0.119944
\(454\) 53.7616 2.52315
\(455\) −2.58747 −0.121302
\(456\) 0.624690 0.0292538
\(457\) −21.1726 −0.990411 −0.495205 0.868776i \(-0.664907\pi\)
−0.495205 + 0.868776i \(0.664907\pi\)
\(458\) 8.67543 0.405376
\(459\) −16.5306 −0.771582
\(460\) 7.93008 0.369742
\(461\) −34.6730 −1.61488 −0.807440 0.589949i \(-0.799148\pi\)
−0.807440 + 0.589949i \(0.799148\pi\)
\(462\) −3.89749 −0.181327
\(463\) −30.7884 −1.43086 −0.715428 0.698686i \(-0.753768\pi\)
−0.715428 + 0.698686i \(0.753768\pi\)
\(464\) 22.4199 1.04082
\(465\) −2.17619 −0.100918
\(466\) 35.9167 1.66381
\(467\) −18.8646 −0.872951 −0.436476 0.899716i \(-0.643773\pi\)
−0.436476 + 0.899716i \(0.643773\pi\)
\(468\) 21.0150 0.971420
\(469\) 4.26048 0.196731
\(470\) −15.3384 −0.707509
\(471\) −0.388511 −0.0179016
\(472\) 1.88578 0.0868000
\(473\) 13.7051 0.630161
\(474\) −5.08954 −0.233770
\(475\) 8.28607 0.380191
\(476\) 10.6293 0.487192
\(477\) 23.5674 1.07908
\(478\) −28.0595 −1.28341
\(479\) 15.4620 0.706476 0.353238 0.935533i \(-0.385081\pi\)
0.353238 + 0.935533i \(0.385081\pi\)
\(480\) 3.80225 0.173548
\(481\) 3.44386 0.157027
\(482\) −2.08404 −0.0949253
\(483\) 2.16527 0.0985232
\(484\) 5.50221 0.250100
\(485\) −9.29498 −0.422063
\(486\) −27.2430 −1.23577
\(487\) −38.3096 −1.73597 −0.867987 0.496586i \(-0.834587\pi\)
−0.867987 + 0.496586i \(0.834587\pi\)
\(488\) 2.01725 0.0913168
\(489\) 7.99921 0.361737
\(490\) 10.5656 0.477307
\(491\) 14.2844 0.644645 0.322323 0.946630i \(-0.395536\pi\)
0.322323 + 0.946630i \(0.395536\pi\)
\(492\) −2.39437 −0.107946
\(493\) −34.2097 −1.54073
\(494\) −13.6759 −0.615306
\(495\) −8.11779 −0.364868
\(496\) 15.6377 0.702154
\(497\) −3.78583 −0.169818
\(498\) 4.42027 0.198077
\(499\) 20.8113 0.931642 0.465821 0.884879i \(-0.345759\pi\)
0.465821 + 0.884879i \(0.345759\pi\)
\(500\) −17.5530 −0.784994
\(501\) −6.39433 −0.285677
\(502\) −23.2206 −1.03638
\(503\) 39.5125 1.76178 0.880888 0.473325i \(-0.156946\pi\)
0.880888 + 0.473325i \(0.156946\pi\)
\(504\) 1.39749 0.0622490
\(505\) −9.84605 −0.438143
\(506\) −31.8824 −1.41734
\(507\) −0.645684 −0.0286758
\(508\) 13.6389 0.605128
\(509\) −23.0736 −1.02272 −0.511361 0.859366i \(-0.670858\pi\)
−0.511361 + 0.859366i \(0.670858\pi\)
\(510\) −4.98032 −0.220532
\(511\) −6.91080 −0.305716
\(512\) −31.1905 −1.37844
\(513\) 6.17689 0.272717
\(514\) −9.18609 −0.405181
\(515\) 8.84824 0.389900
\(516\) 4.82790 0.212536
\(517\) 32.8352 1.44409
\(518\) 1.87841 0.0825327
\(519\) −10.8907 −0.478049
\(520\) 1.63630 0.0717564
\(521\) −6.98837 −0.306166 −0.153083 0.988213i \(-0.548920\pi\)
−0.153083 + 0.988213i \(0.548920\pi\)
\(522\) −36.8910 −1.61468
\(523\) −9.60392 −0.419950 −0.209975 0.977707i \(-0.567338\pi\)
−0.209975 + 0.977707i \(0.567338\pi\)
\(524\) −20.3128 −0.887368
\(525\) −2.22033 −0.0969033
\(526\) 22.5705 0.984121
\(527\) −23.8610 −1.03940
\(528\) −6.98716 −0.304077
\(529\) −5.28758 −0.229895
\(530\) 15.0512 0.653784
\(531\) 8.79642 0.381732
\(532\) −3.97178 −0.172199
\(533\) 6.39078 0.276815
\(534\) 9.62662 0.416584
\(535\) 1.65738 0.0716550
\(536\) −2.69430 −0.116376
\(537\) 7.21102 0.311179
\(538\) −33.2014 −1.43141
\(539\) −22.6180 −0.974227
\(540\) −6.06185 −0.260861
\(541\) −35.3986 −1.52191 −0.760953 0.648807i \(-0.775268\pi\)
−0.760953 + 0.648807i \(0.775268\pi\)
\(542\) 8.19263 0.351903
\(543\) 13.3158 0.571438
\(544\) 41.6900 1.78745
\(545\) −0.827262 −0.0354360
\(546\) 3.66458 0.156829
\(547\) −1.38663 −0.0592880 −0.0296440 0.999561i \(-0.509437\pi\)
−0.0296440 + 0.999561i \(0.509437\pi\)
\(548\) 49.3245 2.10704
\(549\) 9.40970 0.401596
\(550\) 32.6931 1.39404
\(551\) 12.7830 0.544572
\(552\) −1.36930 −0.0582814
\(553\) 3.94523 0.167768
\(554\) −5.66324 −0.240608
\(555\) −0.468630 −0.0198922
\(556\) 4.27122 0.181140
\(557\) 35.6545 1.51073 0.755366 0.655303i \(-0.227459\pi\)
0.755366 + 0.655303i \(0.227459\pi\)
\(558\) −25.7312 −1.08929
\(559\) −12.8861 −0.545024
\(560\) −2.53009 −0.106916
\(561\) 10.6614 0.450126
\(562\) 12.9900 0.547949
\(563\) −17.9662 −0.757184 −0.378592 0.925564i \(-0.623592\pi\)
−0.378592 + 0.925564i \(0.623592\pi\)
\(564\) 11.5669 0.487053
\(565\) −9.63308 −0.405267
\(566\) 42.4604 1.78474
\(567\) 5.64438 0.237042
\(568\) 2.39413 0.100456
\(569\) −42.4547 −1.77979 −0.889897 0.456161i \(-0.849224\pi\)
−0.889897 + 0.456161i \(0.849224\pi\)
\(570\) 1.86097 0.0779474
\(571\) 23.1152 0.967340 0.483670 0.875251i \(-0.339304\pi\)
0.483670 + 0.875251i \(0.339304\pi\)
\(572\) −28.7308 −1.20130
\(573\) 11.7456 0.490679
\(574\) 3.48577 0.145493
\(575\) −18.1628 −0.757443
\(576\) 26.9140 1.12142
\(577\) −21.5015 −0.895120 −0.447560 0.894254i \(-0.647707\pi\)
−0.447560 + 0.894254i \(0.647707\pi\)
\(578\) −19.4466 −0.808873
\(579\) −1.41008 −0.0586007
\(580\) −12.5449 −0.520898
\(581\) −3.42643 −0.142152
\(582\) 13.1643 0.545677
\(583\) −32.2204 −1.33443
\(584\) 4.37034 0.180846
\(585\) 7.63268 0.315573
\(586\) 26.3109 1.08689
\(587\) −19.1595 −0.790796 −0.395398 0.918510i \(-0.629393\pi\)
−0.395398 + 0.918510i \(0.629393\pi\)
\(588\) −7.96766 −0.328581
\(589\) 8.91600 0.367377
\(590\) 5.61779 0.231281
\(591\) 1.02575 0.0421935
\(592\) 3.36749 0.138403
\(593\) −20.7519 −0.852179 −0.426089 0.904681i \(-0.640109\pi\)
−0.426089 + 0.904681i \(0.640109\pi\)
\(594\) 24.3713 0.999965
\(595\) 3.86057 0.158268
\(596\) 6.11983 0.250678
\(597\) −12.2201 −0.500134
\(598\) 29.9771 1.22585
\(599\) 30.5677 1.24896 0.624480 0.781041i \(-0.285311\pi\)
0.624480 + 0.781041i \(0.285311\pi\)
\(600\) 1.40412 0.0573231
\(601\) −0.554696 −0.0226265 −0.0113133 0.999936i \(-0.503601\pi\)
−0.0113133 + 0.999936i \(0.503601\pi\)
\(602\) −7.02856 −0.286463
\(603\) −12.5678 −0.511802
\(604\) −10.2644 −0.417653
\(605\) 1.99841 0.0812469
\(606\) 13.9448 0.566467
\(607\) 0.103356 0.00419510 0.00209755 0.999998i \(-0.499332\pi\)
0.00209755 + 0.999998i \(0.499332\pi\)
\(608\) −15.5781 −0.631775
\(609\) −3.42532 −0.138801
\(610\) 6.00946 0.243316
\(611\) −30.8730 −1.24899
\(612\) −31.3549 −1.26745
\(613\) −36.2794 −1.46531 −0.732656 0.680599i \(-0.761720\pi\)
−0.732656 + 0.680599i \(0.761720\pi\)
\(614\) −50.8231 −2.05105
\(615\) −0.869638 −0.0350672
\(616\) −1.91058 −0.0769796
\(617\) 32.8406 1.32211 0.661056 0.750336i \(-0.270108\pi\)
0.661056 + 0.750336i \(0.270108\pi\)
\(618\) −12.5316 −0.504094
\(619\) −1.58179 −0.0635776 −0.0317888 0.999495i \(-0.510120\pi\)
−0.0317888 + 0.999495i \(0.510120\pi\)
\(620\) −8.74994 −0.351406
\(621\) −13.5396 −0.543325
\(622\) 55.9767 2.24446
\(623\) −7.46221 −0.298967
\(624\) 6.56962 0.262995
\(625\) 15.2029 0.608116
\(626\) −6.38963 −0.255381
\(627\) −3.98380 −0.159098
\(628\) −1.56211 −0.0623349
\(629\) −5.13833 −0.204879
\(630\) 4.16315 0.165864
\(631\) −23.0889 −0.919156 −0.459578 0.888137i \(-0.651999\pi\)
−0.459578 + 0.888137i \(0.651999\pi\)
\(632\) −2.49494 −0.0992432
\(633\) 5.80196 0.230607
\(634\) 35.8947 1.42556
\(635\) 4.95366 0.196580
\(636\) −11.3503 −0.450068
\(637\) 21.2664 0.842605
\(638\) 50.4358 1.99677
\(639\) 11.1677 0.441787
\(640\) 3.76444 0.148802
\(641\) 23.0963 0.912249 0.456124 0.889916i \(-0.349237\pi\)
0.456124 + 0.889916i \(0.349237\pi\)
\(642\) −2.34732 −0.0926413
\(643\) 10.9299 0.431032 0.215516 0.976500i \(-0.430857\pi\)
0.215516 + 0.976500i \(0.430857\pi\)
\(644\) 8.70604 0.343066
\(645\) 1.75350 0.0690440
\(646\) 20.4047 0.802813
\(647\) −36.9697 −1.45343 −0.726714 0.686940i \(-0.758954\pi\)
−0.726714 + 0.686940i \(0.758954\pi\)
\(648\) −3.56947 −0.140222
\(649\) −12.0261 −0.472065
\(650\) −30.7394 −1.20570
\(651\) −2.38913 −0.0936373
\(652\) 32.1629 1.25960
\(653\) −10.1742 −0.398146 −0.199073 0.979985i \(-0.563793\pi\)
−0.199073 + 0.979985i \(0.563793\pi\)
\(654\) 1.17163 0.0458145
\(655\) −7.37763 −0.288268
\(656\) 6.24907 0.243985
\(657\) 20.3859 0.795331
\(658\) −16.8393 −0.656463
\(659\) 4.76037 0.185438 0.0927188 0.995692i \(-0.470444\pi\)
0.0927188 + 0.995692i \(0.470444\pi\)
\(660\) 3.90960 0.152181
\(661\) −24.3994 −0.949028 −0.474514 0.880248i \(-0.657376\pi\)
−0.474514 + 0.880248i \(0.657376\pi\)
\(662\) 48.0430 1.86724
\(663\) −10.0243 −0.389312
\(664\) 2.16685 0.0840903
\(665\) −1.44256 −0.0559399
\(666\) −5.54107 −0.214712
\(667\) −28.0199 −1.08493
\(668\) −25.7101 −0.994752
\(669\) −2.18361 −0.0844231
\(670\) −8.02639 −0.310087
\(671\) −12.8645 −0.496630
\(672\) 4.17430 0.161027
\(673\) 13.9063 0.536048 0.268024 0.963412i \(-0.413629\pi\)
0.268024 + 0.963412i \(0.413629\pi\)
\(674\) 5.13346 0.197733
\(675\) 13.8839 0.534391
\(676\) −2.59614 −0.0998516
\(677\) −23.2190 −0.892377 −0.446189 0.894939i \(-0.647219\pi\)
−0.446189 + 0.894939i \(0.647219\pi\)
\(678\) 13.6431 0.523961
\(679\) −10.2045 −0.391612
\(680\) −2.44140 −0.0936233
\(681\) −14.7250 −0.564262
\(682\) 35.1785 1.34706
\(683\) −6.20677 −0.237495 −0.118748 0.992924i \(-0.537888\pi\)
−0.118748 + 0.992924i \(0.537888\pi\)
\(684\) 11.7162 0.447981
\(685\) 17.9147 0.684487
\(686\) 24.7484 0.944897
\(687\) −2.37615 −0.0906556
\(688\) −12.6003 −0.480384
\(689\) 30.2949 1.15414
\(690\) −4.07919 −0.155292
\(691\) 38.4674 1.46337 0.731685 0.681643i \(-0.238734\pi\)
0.731685 + 0.681643i \(0.238734\pi\)
\(692\) −43.7889 −1.66460
\(693\) −8.91212 −0.338543
\(694\) −55.1593 −2.09382
\(695\) 1.55131 0.0588447
\(696\) 2.16615 0.0821076
\(697\) −9.53520 −0.361172
\(698\) 23.3305 0.883071
\(699\) −9.83737 −0.372084
\(700\) −8.92743 −0.337425
\(701\) −40.5402 −1.53118 −0.765591 0.643328i \(-0.777553\pi\)
−0.765591 + 0.643328i \(0.777553\pi\)
\(702\) −22.9149 −0.864866
\(703\) 1.92001 0.0724146
\(704\) −36.7956 −1.38679
\(705\) 4.20110 0.158223
\(706\) −32.2468 −1.21362
\(707\) −10.8095 −0.406532
\(708\) −4.23643 −0.159215
\(709\) −39.5545 −1.48550 −0.742751 0.669568i \(-0.766479\pi\)
−0.742751 + 0.669568i \(0.766479\pi\)
\(710\) 7.13219 0.267666
\(711\) −11.6379 −0.436455
\(712\) 4.71905 0.176854
\(713\) −19.5436 −0.731915
\(714\) −5.46764 −0.204621
\(715\) −10.4351 −0.390250
\(716\) 28.9938 1.08355
\(717\) 7.68532 0.287014
\(718\) −41.3313 −1.54247
\(719\) 20.2663 0.755806 0.377903 0.925845i \(-0.376645\pi\)
0.377903 + 0.925845i \(0.376645\pi\)
\(720\) 7.46343 0.278146
\(721\) 9.71403 0.361769
\(722\) 31.6724 1.17872
\(723\) 0.570805 0.0212285
\(724\) 53.5399 1.98979
\(725\) 28.7324 1.06710
\(726\) −2.83031 −0.105043
\(727\) 47.5678 1.76419 0.882095 0.471071i \(-0.156132\pi\)
0.882095 + 0.471071i \(0.156132\pi\)
\(728\) 1.79641 0.0665793
\(729\) −11.1829 −0.414180
\(730\) 13.0194 0.481869
\(731\) 19.2264 0.711113
\(732\) −4.53179 −0.167500
\(733\) −7.55288 −0.278972 −0.139486 0.990224i \(-0.544545\pi\)
−0.139486 + 0.990224i \(0.544545\pi\)
\(734\) 42.3388 1.56275
\(735\) −2.89387 −0.106742
\(736\) 34.1468 1.25867
\(737\) 17.1822 0.632914
\(738\) −10.2826 −0.378506
\(739\) 40.8664 1.50330 0.751648 0.659565i \(-0.229259\pi\)
0.751648 + 0.659565i \(0.229259\pi\)
\(740\) −1.88425 −0.0692664
\(741\) 3.74573 0.137603
\(742\) 16.5240 0.606615
\(743\) −22.5862 −0.828607 −0.414304 0.910139i \(-0.635975\pi\)
−0.414304 + 0.910139i \(0.635975\pi\)
\(744\) 1.51087 0.0553912
\(745\) 2.22273 0.0814346
\(746\) 1.06899 0.0391386
\(747\) 10.1075 0.369815
\(748\) 42.8671 1.56738
\(749\) 1.81956 0.0664852
\(750\) 9.02917 0.329699
\(751\) −23.7528 −0.866752 −0.433376 0.901213i \(-0.642678\pi\)
−0.433376 + 0.901213i \(0.642678\pi\)
\(752\) −30.1884 −1.10086
\(753\) 6.35997 0.231770
\(754\) −47.4218 −1.72700
\(755\) −3.72805 −0.135678
\(756\) −6.65500 −0.242040
\(757\) −6.05143 −0.219943 −0.109972 0.993935i \(-0.535076\pi\)
−0.109972 + 0.993935i \(0.535076\pi\)
\(758\) −28.0252 −1.01792
\(759\) 8.73238 0.316965
\(760\) 0.912263 0.0330913
\(761\) 22.3581 0.810480 0.405240 0.914210i \(-0.367188\pi\)
0.405240 + 0.914210i \(0.367188\pi\)
\(762\) −7.01577 −0.254155
\(763\) −0.908209 −0.0328794
\(764\) 47.2262 1.70858
\(765\) −11.3882 −0.411740
\(766\) −12.6991 −0.458837
\(767\) 11.3074 0.408287
\(768\) 6.05020 0.218318
\(769\) 5.19037 0.187169 0.0935847 0.995611i \(-0.470167\pi\)
0.0935847 + 0.995611i \(0.470167\pi\)
\(770\) −5.69168 −0.205114
\(771\) 2.51601 0.0906120
\(772\) −5.66958 −0.204053
\(773\) 35.8599 1.28979 0.644895 0.764271i \(-0.276901\pi\)
0.644895 + 0.764271i \(0.276901\pi\)
\(774\) 20.7333 0.745244
\(775\) 20.0406 0.719881
\(776\) 6.45325 0.231658
\(777\) −0.514485 −0.0184571
\(778\) 45.0827 1.61629
\(779\) 3.56297 0.127657
\(780\) −3.67597 −0.131621
\(781\) −15.2680 −0.546331
\(782\) −44.7266 −1.59942
\(783\) 21.4187 0.765444
\(784\) 20.7948 0.742672
\(785\) −0.567360 −0.0202500
\(786\) 10.4488 0.372696
\(787\) 29.5628 1.05380 0.526900 0.849927i \(-0.323354\pi\)
0.526900 + 0.849927i \(0.323354\pi\)
\(788\) 4.12428 0.146921
\(789\) −6.18193 −0.220082
\(790\) −7.43249 −0.264436
\(791\) −10.5757 −0.376027
\(792\) 5.63596 0.200265
\(793\) 12.0958 0.429533
\(794\) 2.67702 0.0950037
\(795\) −4.12244 −0.146208
\(796\) −49.1340 −1.74151
\(797\) 26.7360 0.947036 0.473518 0.880784i \(-0.342984\pi\)
0.473518 + 0.880784i \(0.342984\pi\)
\(798\) 2.04306 0.0723236
\(799\) 46.0632 1.62960
\(800\) −35.0151 −1.23797
\(801\) 22.0125 0.777774
\(802\) 54.5380 1.92581
\(803\) −27.8708 −0.983538
\(804\) 6.05278 0.213465
\(805\) 3.16204 0.111447
\(806\) −33.0763 −1.16506
\(807\) 9.09365 0.320112
\(808\) 6.83584 0.240484
\(809\) 54.7136 1.92363 0.961814 0.273705i \(-0.0882493\pi\)
0.961814 + 0.273705i \(0.0882493\pi\)
\(810\) −10.6336 −0.373625
\(811\) 33.9340 1.19159 0.595793 0.803138i \(-0.296838\pi\)
0.595793 + 0.803138i \(0.296838\pi\)
\(812\) −13.7724 −0.483316
\(813\) −2.24391 −0.0786973
\(814\) 7.57550 0.265521
\(815\) 11.6816 0.409189
\(816\) −9.80203 −0.343140
\(817\) −7.18421 −0.251344
\(818\) 12.1877 0.426133
\(819\) 8.37954 0.292805
\(820\) −3.49661 −0.122107
\(821\) 54.2457 1.89319 0.946594 0.322429i \(-0.104499\pi\)
0.946594 + 0.322429i \(0.104499\pi\)
\(822\) −25.3723 −0.884960
\(823\) −2.57690 −0.0898249 −0.0449125 0.998991i \(-0.514301\pi\)
−0.0449125 + 0.998991i \(0.514301\pi\)
\(824\) −6.14309 −0.214005
\(825\) −8.95445 −0.311754
\(826\) 6.16749 0.214594
\(827\) 16.2438 0.564852 0.282426 0.959289i \(-0.408861\pi\)
0.282426 + 0.959289i \(0.408861\pi\)
\(828\) −25.6817 −0.892499
\(829\) 20.6824 0.718331 0.359166 0.933274i \(-0.383061\pi\)
0.359166 + 0.933274i \(0.383061\pi\)
\(830\) 6.45512 0.224061
\(831\) 1.55113 0.0538080
\(832\) 34.5968 1.19943
\(833\) −31.7300 −1.09938
\(834\) −2.19709 −0.0760792
\(835\) −9.33793 −0.323153
\(836\) −16.0179 −0.553991
\(837\) 14.9394 0.516381
\(838\) 22.1265 0.764347
\(839\) 6.46322 0.223135 0.111568 0.993757i \(-0.464413\pi\)
0.111568 + 0.993757i \(0.464413\pi\)
\(840\) −0.244450 −0.00843432
\(841\) 15.3257 0.528471
\(842\) −45.4962 −1.56790
\(843\) −3.55787 −0.122540
\(844\) 23.3283 0.802993
\(845\) −0.942923 −0.0324375
\(846\) 49.6736 1.70781
\(847\) 2.19395 0.0753851
\(848\) 29.6231 1.01726
\(849\) −11.6296 −0.399128
\(850\) 45.8640 1.57312
\(851\) −4.20861 −0.144269
\(852\) −5.37846 −0.184263
\(853\) 35.1204 1.20250 0.601250 0.799061i \(-0.294670\pi\)
0.601250 + 0.799061i \(0.294670\pi\)
\(854\) 6.59748 0.225761
\(855\) 4.25535 0.145530
\(856\) −1.15068 −0.0393293
\(857\) 7.26892 0.248302 0.124151 0.992263i \(-0.460379\pi\)
0.124151 + 0.992263i \(0.460379\pi\)
\(858\) 14.7790 0.504546
\(859\) 9.27986 0.316625 0.158312 0.987389i \(-0.449395\pi\)
0.158312 + 0.987389i \(0.449395\pi\)
\(860\) 7.05041 0.240417
\(861\) −0.954732 −0.0325372
\(862\) 31.4628 1.07163
\(863\) −3.01742 −0.102714 −0.0513571 0.998680i \(-0.516355\pi\)
−0.0513571 + 0.998680i \(0.516355\pi\)
\(864\) −26.1022 −0.888015
\(865\) −15.9042 −0.540759
\(866\) 64.0459 2.17637
\(867\) 5.32631 0.180891
\(868\) −9.60612 −0.326053
\(869\) 15.9108 0.539738
\(870\) 6.45302 0.218778
\(871\) −16.1554 −0.547405
\(872\) 0.574346 0.0194498
\(873\) 30.1019 1.01879
\(874\) 16.7127 0.565317
\(875\) −6.99909 −0.236612
\(876\) −9.81805 −0.331721
\(877\) −4.78980 −0.161740 −0.0808700 0.996725i \(-0.525770\pi\)
−0.0808700 + 0.996725i \(0.525770\pi\)
\(878\) −26.0551 −0.879316
\(879\) −7.20638 −0.243065
\(880\) −10.2037 −0.343966
\(881\) 23.3558 0.786876 0.393438 0.919351i \(-0.371286\pi\)
0.393438 + 0.919351i \(0.371286\pi\)
\(882\) −34.2169 −1.15214
\(883\) 24.7528 0.832999 0.416500 0.909136i \(-0.363257\pi\)
0.416500 + 0.909136i \(0.363257\pi\)
\(884\) −40.3054 −1.35562
\(885\) −1.53868 −0.0517221
\(886\) −43.7116 −1.46852
\(887\) 14.9511 0.502010 0.251005 0.967986i \(-0.419239\pi\)
0.251005 + 0.967986i \(0.419239\pi\)
\(888\) 0.325357 0.0109183
\(889\) 5.43837 0.182397
\(890\) 14.0582 0.471232
\(891\) 22.7634 0.762602
\(892\) −8.77976 −0.293968
\(893\) −17.2122 −0.575984
\(894\) −3.14801 −0.105285
\(895\) 10.5306 0.351999
\(896\) 4.13278 0.138067
\(897\) −8.21054 −0.274142
\(898\) 68.8570 2.29779
\(899\) 30.9168 1.03113
\(900\) 26.3347 0.877824
\(901\) −45.2008 −1.50586
\(902\) 14.0579 0.468076
\(903\) 1.92508 0.0640626
\(904\) 6.68798 0.222439
\(905\) 19.4458 0.646399
\(906\) 5.27996 0.175415
\(907\) −17.9615 −0.596401 −0.298201 0.954503i \(-0.596386\pi\)
−0.298201 + 0.954503i \(0.596386\pi\)
\(908\) −59.2056 −1.96481
\(909\) 31.8865 1.05761
\(910\) 5.35155 0.177402
\(911\) 13.2807 0.440009 0.220004 0.975499i \(-0.429393\pi\)
0.220004 + 0.975499i \(0.429393\pi\)
\(912\) 3.66267 0.121283
\(913\) −13.8186 −0.457328
\(914\) 43.7904 1.44846
\(915\) −1.64595 −0.0544135
\(916\) −9.55392 −0.315670
\(917\) −8.09953 −0.267470
\(918\) 34.1895 1.12842
\(919\) 10.9126 0.359974 0.179987 0.983669i \(-0.442394\pi\)
0.179987 + 0.983669i \(0.442394\pi\)
\(920\) −1.99966 −0.0659267
\(921\) 13.9201 0.458684
\(922\) 71.7126 2.36173
\(923\) 14.3556 0.472520
\(924\) 4.29215 0.141201
\(925\) 4.31564 0.141897
\(926\) 63.6783 2.09260
\(927\) −28.6551 −0.941157
\(928\) −54.0180 −1.77323
\(929\) −13.2692 −0.435347 −0.217674 0.976022i \(-0.569847\pi\)
−0.217674 + 0.976022i \(0.569847\pi\)
\(930\) 4.50092 0.147591
\(931\) 11.8564 0.388577
\(932\) −39.5537 −1.29563
\(933\) −15.3317 −0.501936
\(934\) 39.0170 1.27667
\(935\) 15.5694 0.509173
\(936\) −5.29917 −0.173209
\(937\) 10.4383 0.341005 0.170502 0.985357i \(-0.445461\pi\)
0.170502 + 0.985357i \(0.445461\pi\)
\(938\) −8.81177 −0.287714
\(939\) 1.75008 0.0571117
\(940\) 16.8916 0.550944
\(941\) −28.5359 −0.930244 −0.465122 0.885247i \(-0.653990\pi\)
−0.465122 + 0.885247i \(0.653990\pi\)
\(942\) 0.803541 0.0261808
\(943\) −7.80993 −0.254326
\(944\) 11.0567 0.359864
\(945\) −2.41710 −0.0786284
\(946\) −28.3457 −0.921598
\(947\) 5.82379 0.189248 0.0946238 0.995513i \(-0.469835\pi\)
0.0946238 + 0.995513i \(0.469835\pi\)
\(948\) 5.60491 0.182039
\(949\) 26.2052 0.850658
\(950\) −17.1377 −0.556022
\(951\) −9.83135 −0.318803
\(952\) −2.68029 −0.0868685
\(953\) −10.2662 −0.332556 −0.166278 0.986079i \(-0.553175\pi\)
−0.166278 + 0.986079i \(0.553175\pi\)
\(954\) −48.7436 −1.57813
\(955\) 17.1526 0.555046
\(956\) 30.9009 0.999405
\(957\) −13.8141 −0.446545
\(958\) −31.9794 −1.03321
\(959\) 19.6677 0.635103
\(960\) −4.70782 −0.151944
\(961\) −9.43583 −0.304382
\(962\) −7.12280 −0.229648
\(963\) −5.36746 −0.172964
\(964\) 2.29507 0.0739193
\(965\) −2.05920 −0.0662880
\(966\) −4.47834 −0.144088
\(967\) 24.3180 0.782013 0.391006 0.920388i \(-0.372127\pi\)
0.391006 + 0.920388i \(0.372127\pi\)
\(968\) −1.38744 −0.0445941
\(969\) −5.58873 −0.179536
\(970\) 19.2244 0.617259
\(971\) 3.96068 0.127104 0.0635521 0.997979i \(-0.479757\pi\)
0.0635521 + 0.997979i \(0.479757\pi\)
\(972\) 30.0017 0.962305
\(973\) 1.70311 0.0545992
\(974\) 79.2342 2.53883
\(975\) 8.41934 0.269635
\(976\) 11.8275 0.378590
\(977\) −15.4809 −0.495279 −0.247639 0.968852i \(-0.579655\pi\)
−0.247639 + 0.968852i \(0.579655\pi\)
\(978\) −16.5444 −0.529033
\(979\) −30.0946 −0.961827
\(980\) −11.6355 −0.371684
\(981\) 2.67910 0.0855370
\(982\) −29.5438 −0.942781
\(983\) −53.6476 −1.71109 −0.855546 0.517727i \(-0.826778\pi\)
−0.855546 + 0.517727i \(0.826778\pi\)
\(984\) 0.603766 0.0192474
\(985\) 1.49794 0.0477285
\(986\) 70.7545 2.25328
\(987\) 4.61217 0.146807
\(988\) 15.0607 0.479145
\(989\) 15.7476 0.500745
\(990\) 16.7897 0.533612
\(991\) 44.8371 1.42430 0.712149 0.702029i \(-0.247722\pi\)
0.712149 + 0.702029i \(0.247722\pi\)
\(992\) −37.6771 −1.19625
\(993\) −13.1587 −0.417578
\(994\) 7.83007 0.248355
\(995\) −17.8455 −0.565742
\(996\) −4.86787 −0.154244
\(997\) 27.6398 0.875360 0.437680 0.899131i \(-0.355800\pi\)
0.437680 + 0.899131i \(0.355800\pi\)
\(998\) −43.0432 −1.36251
\(999\) 3.21711 0.101785
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 \(a_p\))