Properties

Label 1859.2.a.h.1.2
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.756.1
Defining polynomial: \( x^{3} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.339877\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.339877 q^{3} -1.00000 q^{4} -2.88448 q^{5} -0.339877 q^{6} -3.54461 q^{7} -3.00000 q^{8} -2.88448 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.339877 q^{3} -1.00000 q^{4} -2.88448 q^{5} -0.339877 q^{6} -3.54461 q^{7} -3.00000 q^{8} -2.88448 q^{9} -2.88448 q^{10} +1.00000 q^{11} +0.339877 q^{12} -3.54461 q^{14} +0.980369 q^{15} -1.00000 q^{16} -5.22436 q^{17} -2.88448 q^{18} +6.22436 q^{19} +2.88448 q^{20} +1.20473 q^{21} +1.00000 q^{22} +0.679754 q^{23} +1.01963 q^{24} +3.32025 q^{25} +2.00000 q^{27} +3.54461 q^{28} -8.42909 q^{29} +0.980369 q^{30} +8.40946 q^{31} +5.00000 q^{32} -0.339877 q^{33} -5.22436 q^{34} +10.2244 q^{35} +2.88448 q^{36} +3.52498 q^{37} +6.22436 q^{38} +8.65345 q^{40} -5.74934 q^{41} +1.20473 q^{42} -1.32025 q^{43} -1.00000 q^{44} +8.32025 q^{45} +0.679754 q^{46} +6.10884 q^{47} +0.339877 q^{48} +5.56424 q^{49} +3.32025 q^{50} +1.77564 q^{51} -6.08921 q^{53} +2.00000 q^{54} -2.88448 q^{55} +10.6338 q^{56} -2.11552 q^{57} -8.42909 q^{58} -14.1088 q^{59} -0.980369 q^{60} +4.01963 q^{61} +8.40946 q^{62} +10.2244 q^{63} +7.00000 q^{64} -0.339877 q^{66} +12.1088 q^{67} +5.22436 q^{68} -0.231033 q^{69} +10.2244 q^{70} +6.00000 q^{71} +8.65345 q^{72} -16.0825 q^{73} +3.52498 q^{74} -1.12847 q^{75} -6.22436 q^{76} -3.54461 q^{77} +0.904114 q^{79} +2.88448 q^{80} +7.97370 q^{81} -5.74934 q^{82} +4.90411 q^{83} -1.20473 q^{84} +15.0696 q^{85} -1.32025 q^{86} +2.86485 q^{87} -3.00000 q^{88} -5.65345 q^{89} +8.32025 q^{90} -0.679754 q^{92} -2.85818 q^{93} +6.10884 q^{94} -17.9541 q^{95} -1.69938 q^{96} +2.79527 q^{97} +5.56424 q^{98} -2.88448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 9 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} + 6 q^{19} - 3 q^{20} - 6 q^{21} + 3 q^{22} + 12 q^{25} + 6 q^{27} - 3 q^{29} + 6 q^{30} + 6 q^{31} + 15 q^{32} - 3 q^{34} + 18 q^{35} - 3 q^{36} + 3 q^{37} + 6 q^{38} - 9 q^{40} + 3 q^{41} - 6 q^{42} - 6 q^{43} - 3 q^{44} + 27 q^{45} - 6 q^{47} + 3 q^{49} + 12 q^{50} + 18 q^{51} + 3 q^{53} + 6 q^{54} + 3 q^{55} - 18 q^{57} - 3 q^{58} - 18 q^{59} - 6 q^{60} + 9 q^{61} + 6 q^{62} + 18 q^{63} + 21 q^{64} + 12 q^{67} + 3 q^{68} - 24 q^{69} + 18 q^{70} + 18 q^{71} - 9 q^{72} + 9 q^{73} + 3 q^{74} + 24 q^{75} - 6 q^{76} - 12 q^{79} - 3 q^{80} - 9 q^{81} + 3 q^{82} + 6 q^{84} + 27 q^{85} - 6 q^{86} - 9 q^{88} + 18 q^{89} + 27 q^{90} + 36 q^{93} - 6 q^{94} - 24 q^{95} + 18 q^{97} + 3 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) −0.339877 −0.196228 −0.0981140 0.995175i \(-0.531281\pi\)
−0.0981140 + 0.995175i \(0.531281\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.88448 −1.28998 −0.644990 0.764191i \(-0.723139\pi\)
−0.644990 + 0.764191i \(0.723139\pi\)
\(6\) −0.339877 −0.138754
\(7\) −3.54461 −1.33974 −0.669868 0.742480i \(-0.733649\pi\)
−0.669868 + 0.742480i \(0.733649\pi\)
\(8\) −3.00000 −1.06066
\(9\) −2.88448 −0.961495
\(10\) −2.88448 −0.912154
\(11\) 1.00000 0.301511
\(12\) 0.339877 0.0981140
\(13\) 0 0
\(14\) −3.54461 −0.947336
\(15\) 0.980369 0.253130
\(16\) −1.00000 −0.250000
\(17\) −5.22436 −1.26709 −0.633547 0.773704i \(-0.718402\pi\)
−0.633547 + 0.773704i \(0.718402\pi\)
\(18\) −2.88448 −0.679879
\(19\) 6.22436 1.42797 0.713983 0.700163i \(-0.246889\pi\)
0.713983 + 0.700163i \(0.246889\pi\)
\(20\) 2.88448 0.644990
\(21\) 1.20473 0.262894
\(22\) 1.00000 0.213201
\(23\) 0.679754 0.141738 0.0708692 0.997486i \(-0.477423\pi\)
0.0708692 + 0.997486i \(0.477423\pi\)
\(24\) 1.01963 0.208131
\(25\) 3.32025 0.664049
\(26\) 0 0
\(27\) 2.00000 0.384900
\(28\) 3.54461 0.669868
\(29\) −8.42909 −1.56524 −0.782621 0.622498i \(-0.786118\pi\)
−0.782621 + 0.622498i \(0.786118\pi\)
\(30\) 0.980369 0.178990
\(31\) 8.40946 1.51038 0.755192 0.655504i \(-0.227544\pi\)
0.755192 + 0.655504i \(0.227544\pi\)
\(32\) 5.00000 0.883883
\(33\) −0.339877 −0.0591650
\(34\) −5.22436 −0.895970
\(35\) 10.2244 1.72823
\(36\) 2.88448 0.480747
\(37\) 3.52498 0.579503 0.289751 0.957102i \(-0.406427\pi\)
0.289751 + 0.957102i \(0.406427\pi\)
\(38\) 6.22436 1.00972
\(39\) 0 0
\(40\) 8.65345 1.36823
\(41\) −5.74934 −0.897896 −0.448948 0.893558i \(-0.648201\pi\)
−0.448948 + 0.893558i \(0.648201\pi\)
\(42\) 1.20473 0.185894
\(43\) −1.32025 −0.201336 −0.100668 0.994920i \(-0.532098\pi\)
−0.100668 + 0.994920i \(0.532098\pi\)
\(44\) −1.00000 −0.150756
\(45\) 8.32025 1.24031
\(46\) 0.679754 0.100224
\(47\) 6.10884 0.891067 0.445533 0.895265i \(-0.353014\pi\)
0.445533 + 0.895265i \(0.353014\pi\)
\(48\) 0.339877 0.0490570
\(49\) 5.56424 0.794891
\(50\) 3.32025 0.469554
\(51\) 1.77564 0.248639
\(52\) 0 0
\(53\) −6.08921 −0.836418 −0.418209 0.908351i \(-0.637342\pi\)
−0.418209 + 0.908351i \(0.637342\pi\)
\(54\) 2.00000 0.272166
\(55\) −2.88448 −0.388944
\(56\) 10.6338 1.42100
\(57\) −2.11552 −0.280207
\(58\) −8.42909 −1.10679
\(59\) −14.1088 −1.83682 −0.918408 0.395636i \(-0.870524\pi\)
−0.918408 + 0.395636i \(0.870524\pi\)
\(60\) −0.980369 −0.126565
\(61\) 4.01963 0.514661 0.257330 0.966323i \(-0.417157\pi\)
0.257330 + 0.966323i \(0.417157\pi\)
\(62\) 8.40946 1.06800
\(63\) 10.2244 1.28815
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −0.339877 −0.0418360
\(67\) 12.1088 1.47933 0.739665 0.672975i \(-0.234984\pi\)
0.739665 + 0.672975i \(0.234984\pi\)
\(68\) 5.22436 0.633547
\(69\) −0.231033 −0.0278131
\(70\) 10.2244 1.22204
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 8.65345 1.01982
\(73\) −16.0825 −1.88232 −0.941160 0.337963i \(-0.890262\pi\)
−0.941160 + 0.337963i \(0.890262\pi\)
\(74\) 3.52498 0.409770
\(75\) −1.12847 −0.130305
\(76\) −6.22436 −0.713983
\(77\) −3.54461 −0.403945
\(78\) 0 0
\(79\) 0.904114 0.101721 0.0508604 0.998706i \(-0.483804\pi\)
0.0508604 + 0.998706i \(0.483804\pi\)
\(80\) 2.88448 0.322495
\(81\) 7.97370 0.885966
\(82\) −5.74934 −0.634908
\(83\) 4.90411 0.538296 0.269148 0.963099i \(-0.413258\pi\)
0.269148 + 0.963099i \(0.413258\pi\)
\(84\) −1.20473 −0.131447
\(85\) 15.0696 1.63453
\(86\) −1.32025 −0.142366
\(87\) 2.86485 0.307144
\(88\) −3.00000 −0.319801
\(89\) −5.65345 −0.599265 −0.299632 0.954055i \(-0.596864\pi\)
−0.299632 + 0.954055i \(0.596864\pi\)
\(90\) 8.32025 0.877031
\(91\) 0 0
\(92\) −0.679754 −0.0708692
\(93\) −2.85818 −0.296380
\(94\) 6.10884 0.630079
\(95\) −17.9541 −1.84205
\(96\) −1.69938 −0.173443
\(97\) 2.79527 0.283817 0.141908 0.989880i \(-0.454676\pi\)
0.141908 + 0.989880i \(0.454676\pi\)
\(98\) 5.56424 0.562073
\(99\) −2.88448 −0.289902
\(100\) −3.32025 −0.332025
\(101\) −9.86485 −0.981590 −0.490795 0.871275i \(-0.663294\pi\)
−0.490795 + 0.871275i \(0.663294\pi\)
\(102\) 1.77564 0.175815
\(103\) 5.35951 0.528088 0.264044 0.964511i \(-0.414944\pi\)
0.264044 + 0.964511i \(0.414944\pi\)
\(104\) 0 0
\(105\) −3.47502 −0.339128
\(106\) −6.08921 −0.591437
\(107\) 3.31357 0.320335 0.160168 0.987090i \(-0.448797\pi\)
0.160168 + 0.987090i \(0.448797\pi\)
\(108\) −2.00000 −0.192450
\(109\) 2.15478 0.206390 0.103195 0.994661i \(-0.467093\pi\)
0.103195 + 0.994661i \(0.467093\pi\)
\(110\) −2.88448 −0.275025
\(111\) −1.19806 −0.113715
\(112\) 3.54461 0.334934
\(113\) 3.79527 0.357029 0.178514 0.983937i \(-0.442871\pi\)
0.178514 + 0.983937i \(0.442871\pi\)
\(114\) −2.11552 −0.198136
\(115\) −1.96074 −0.182840
\(116\) 8.42909 0.782621
\(117\) 0 0
\(118\) −14.1088 −1.29882
\(119\) 18.5183 1.69757
\(120\) −2.94111 −0.268485
\(121\) 1.00000 0.0909091
\(122\) 4.01963 0.363920
\(123\) 1.95407 0.176192
\(124\) −8.40946 −0.755192
\(125\) 4.84522 0.433370
\(126\) 10.2244 0.910858
\(127\) −16.1784 −1.43560 −0.717802 0.696248i \(-0.754852\pi\)
−0.717802 + 0.696248i \(0.754852\pi\)
\(128\) −3.00000 −0.265165
\(129\) 0.448721 0.0395077
\(130\) 0 0
\(131\) −3.31357 −0.289508 −0.144754 0.989468i \(-0.546239\pi\)
−0.144754 + 0.989468i \(0.546239\pi\)
\(132\) 0.339877 0.0295825
\(133\) −22.0629 −1.91310
\(134\) 12.1088 1.04604
\(135\) −5.76897 −0.496514
\(136\) 15.6731 1.34396
\(137\) 13.7427 1.17412 0.587058 0.809545i \(-0.300286\pi\)
0.587058 + 0.809545i \(0.300286\pi\)
\(138\) −0.231033 −0.0196668
\(139\) 2.40946 0.204368 0.102184 0.994766i \(-0.467417\pi\)
0.102184 + 0.994766i \(0.467417\pi\)
\(140\) −10.2244 −0.864116
\(141\) −2.07625 −0.174852
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) 2.88448 0.240374
\(145\) 24.3136 2.01913
\(146\) −16.0825 −1.33100
\(147\) −1.89116 −0.155980
\(148\) −3.52498 −0.289751
\(149\) −2.54461 −0.208462 −0.104231 0.994553i \(-0.533238\pi\)
−0.104231 + 0.994553i \(0.533238\pi\)
\(150\) −1.12847 −0.0921396
\(151\) 8.44872 0.687547 0.343774 0.939053i \(-0.388295\pi\)
0.343774 + 0.939053i \(0.388295\pi\)
\(152\) −18.6731 −1.51459
\(153\) 15.0696 1.21830
\(154\) −3.54461 −0.285633
\(155\) −24.2569 −1.94837
\(156\) 0 0
\(157\) −16.3595 −1.30563 −0.652815 0.757517i \(-0.726412\pi\)
−0.652815 + 0.757517i \(0.726412\pi\)
\(158\) 0.904114 0.0719275
\(159\) 2.06958 0.164129
\(160\) −14.4224 −1.14019
\(161\) −2.40946 −0.189892
\(162\) 7.97370 0.626473
\(163\) −10.7886 −0.845028 −0.422514 0.906356i \(-0.638852\pi\)
−0.422514 + 0.906356i \(0.638852\pi\)
\(164\) 5.74934 0.448948
\(165\) 0.980369 0.0763216
\(166\) 4.90411 0.380633
\(167\) 7.04995 0.545542 0.272771 0.962079i \(-0.412060\pi\)
0.272771 + 0.962079i \(0.412060\pi\)
\(168\) −3.61419 −0.278841
\(169\) 0 0
\(170\) 15.0696 1.15578
\(171\) −17.9541 −1.37298
\(172\) 1.32025 0.100668
\(173\) −1.84522 −0.140290 −0.0701448 0.997537i \(-0.522346\pi\)
−0.0701448 + 0.997537i \(0.522346\pi\)
\(174\) 2.86485 0.217184
\(175\) −11.7690 −0.889650
\(176\) −1.00000 −0.0753778
\(177\) 4.79527 0.360435
\(178\) −5.65345 −0.423744
\(179\) 5.42909 0.405789 0.202895 0.979201i \(-0.434965\pi\)
0.202895 + 0.979201i \(0.434965\pi\)
\(180\) −8.32025 −0.620155
\(181\) −4.47502 −0.332626 −0.166313 0.986073i \(-0.553186\pi\)
−0.166313 + 0.986073i \(0.553186\pi\)
\(182\) 0 0
\(183\) −1.36618 −0.100991
\(184\) −2.03926 −0.150336
\(185\) −10.1677 −0.747547
\(186\) −2.85818 −0.209572
\(187\) −5.22436 −0.382043
\(188\) −6.10884 −0.445533
\(189\) −7.08921 −0.515664
\(190\) −17.9541 −1.30252
\(191\) 9.89116 0.715699 0.357849 0.933779i \(-0.383510\pi\)
0.357849 + 0.933779i \(0.383510\pi\)
\(192\) −2.37914 −0.171700
\(193\) 5.10884 0.367743 0.183871 0.982950i \(-0.441137\pi\)
0.183871 + 0.982950i \(0.441137\pi\)
\(194\) 2.79527 0.200689
\(195\) 0 0
\(196\) −5.56424 −0.397446
\(197\) 2.23103 0.158954 0.0794772 0.996837i \(-0.474675\pi\)
0.0794772 + 0.996837i \(0.474675\pi\)
\(198\) −2.88448 −0.204991
\(199\) 17.8778 1.26732 0.633662 0.773610i \(-0.281551\pi\)
0.633662 + 0.773610i \(0.281551\pi\)
\(200\) −9.96074 −0.704331
\(201\) −4.11552 −0.290286
\(202\) −9.86485 −0.694089
\(203\) 29.8778 2.09701
\(204\) −1.77564 −0.124320
\(205\) 16.5839 1.15827
\(206\) 5.35951 0.373415
\(207\) −1.96074 −0.136281
\(208\) 0 0
\(209\) 6.22436 0.430548
\(210\) −3.47502 −0.239799
\(211\) 10.9041 0.750670 0.375335 0.926889i \(-0.377528\pi\)
0.375335 + 0.926889i \(0.377528\pi\)
\(212\) 6.08921 0.418209
\(213\) −2.03926 −0.139728
\(214\) 3.31357 0.226511
\(215\) 3.80823 0.259719
\(216\) −6.00000 −0.408248
\(217\) −29.8082 −2.02351
\(218\) 2.15478 0.145940
\(219\) 5.46608 0.369364
\(220\) 2.88448 0.194472
\(221\) 0 0
\(222\) −1.19806 −0.0804084
\(223\) −19.4291 −1.30107 −0.650534 0.759477i \(-0.725455\pi\)
−0.650534 + 0.759477i \(0.725455\pi\)
\(224\) −17.7230 −1.18417
\(225\) −9.57720 −0.638480
\(226\) 3.79527 0.252458
\(227\) −7.32025 −0.485862 −0.242931 0.970044i \(-0.578109\pi\)
−0.242931 + 0.970044i \(0.578109\pi\)
\(228\) 2.11552 0.140103
\(229\) 14.5642 0.962432 0.481216 0.876602i \(-0.340195\pi\)
0.481216 + 0.876602i \(0.340195\pi\)
\(230\) −1.96074 −0.129287
\(231\) 1.20473 0.0792654
\(232\) 25.2873 1.66019
\(233\) 6.44872 0.422470 0.211235 0.977435i \(-0.432252\pi\)
0.211235 + 0.977435i \(0.432252\pi\)
\(234\) 0 0
\(235\) −17.6209 −1.14946
\(236\) 14.1088 0.918408
\(237\) −0.307288 −0.0199605
\(238\) 18.5183 1.20036
\(239\) −0.270294 −0.0174839 −0.00874193 0.999962i \(-0.502783\pi\)
−0.00874193 + 0.999962i \(0.502783\pi\)
\(240\) −0.980369 −0.0632826
\(241\) 30.5313 1.96669 0.983346 0.181745i \(-0.0581744\pi\)
0.983346 + 0.181745i \(0.0581744\pi\)
\(242\) 1.00000 0.0642824
\(243\) −8.71008 −0.558752
\(244\) −4.01963 −0.257330
\(245\) −16.0500 −1.02539
\(246\) 1.95407 0.124587
\(247\) 0 0
\(248\) −25.2284 −1.60200
\(249\) −1.66680 −0.105629
\(250\) 4.84522 0.306439
\(251\) 10.4790 0.661431 0.330716 0.943730i \(-0.392710\pi\)
0.330716 + 0.943730i \(0.392710\pi\)
\(252\) −10.2244 −0.644074
\(253\) 0.679754 0.0427358
\(254\) −16.1784 −1.01512
\(255\) −5.12180 −0.320740
\(256\) −17.0000 −1.06250
\(257\) 5.75601 0.359050 0.179525 0.983753i \(-0.442544\pi\)
0.179525 + 0.983753i \(0.442544\pi\)
\(258\) 0.448721 0.0279362
\(259\) −12.4947 −0.776380
\(260\) 0 0
\(261\) 24.3136 1.50497
\(262\) −3.31357 −0.204713
\(263\) 8.44872 0.520970 0.260485 0.965478i \(-0.416117\pi\)
0.260485 + 0.965478i \(0.416117\pi\)
\(264\) 1.01963 0.0627539
\(265\) 17.5642 1.07896
\(266\) −22.0629 −1.35276
\(267\) 1.92148 0.117593
\(268\) −12.1088 −0.739665
\(269\) 25.0892 1.52972 0.764858 0.644199i \(-0.222809\pi\)
0.764858 + 0.644199i \(0.222809\pi\)
\(270\) −5.76897 −0.351088
\(271\) −10.4487 −0.634715 −0.317357 0.948306i \(-0.602795\pi\)
−0.317357 + 0.948306i \(0.602795\pi\)
\(272\) 5.22436 0.316773
\(273\) 0 0
\(274\) 13.7427 0.830225
\(275\) 3.32025 0.200218
\(276\) 0.231033 0.0139065
\(277\) 8.62086 0.517977 0.258989 0.965880i \(-0.416611\pi\)
0.258989 + 0.965880i \(0.416611\pi\)
\(278\) 2.40946 0.144510
\(279\) −24.2569 −1.45223
\(280\) −30.6731 −1.83307
\(281\) −1.98037 −0.118139 −0.0590695 0.998254i \(-0.518813\pi\)
−0.0590695 + 0.998254i \(0.518813\pi\)
\(282\) −2.07625 −0.123639
\(283\) 2.18510 0.129891 0.0649453 0.997889i \(-0.479313\pi\)
0.0649453 + 0.997889i \(0.479313\pi\)
\(284\) −6.00000 −0.356034
\(285\) 6.10217 0.361461
\(286\) 0 0
\(287\) 20.3791 1.20294
\(288\) −14.4224 −0.849849
\(289\) 10.2939 0.605526
\(290\) 24.3136 1.42774
\(291\) −0.950048 −0.0556928
\(292\) 16.0825 0.941160
\(293\) 6.13515 0.358419 0.179210 0.983811i \(-0.442646\pi\)
0.179210 + 0.983811i \(0.442646\pi\)
\(294\) −1.89116 −0.110294
\(295\) 40.6967 2.36946
\(296\) −10.5749 −0.614655
\(297\) 2.00000 0.116052
\(298\) −2.54461 −0.147405
\(299\) 0 0
\(300\) 1.12847 0.0651525
\(301\) 4.67975 0.269737
\(302\) 8.44872 0.486169
\(303\) 3.35284 0.192615
\(304\) −6.22436 −0.356992
\(305\) −11.5946 −0.663903
\(306\) 15.0696 0.861471
\(307\) 6.18510 0.353002 0.176501 0.984300i \(-0.443522\pi\)
0.176501 + 0.984300i \(0.443522\pi\)
\(308\) 3.54461 0.201973
\(309\) −1.82157 −0.103626
\(310\) −24.2569 −1.37770
\(311\) −1.28992 −0.0731449 −0.0365725 0.999331i \(-0.511644\pi\)
−0.0365725 + 0.999331i \(0.511644\pi\)
\(312\) 0 0
\(313\) −0.293944 −0.0166147 −0.00830734 0.999965i \(-0.502644\pi\)
−0.00830734 + 0.999965i \(0.502644\pi\)
\(314\) −16.3595 −0.923220
\(315\) −29.4920 −1.66169
\(316\) −0.904114 −0.0508604
\(317\) −22.0522 −1.23858 −0.619288 0.785164i \(-0.712579\pi\)
−0.619288 + 0.785164i \(0.712579\pi\)
\(318\) 2.06958 0.116056
\(319\) −8.42909 −0.471938
\(320\) −20.1914 −1.12873
\(321\) −1.12621 −0.0628588
\(322\) −2.40946 −0.134274
\(323\) −32.5183 −1.80937
\(324\) −7.97370 −0.442983
\(325\) 0 0
\(326\) −10.7886 −0.597525
\(327\) −0.732359 −0.0404996
\(328\) 17.2480 0.952362
\(329\) −21.6535 −1.19379
\(330\) 0.980369 0.0539676
\(331\) −14.4487 −0.794174 −0.397087 0.917781i \(-0.629979\pi\)
−0.397087 + 0.917781i \(0.629979\pi\)
\(332\) −4.90411 −0.269148
\(333\) −10.1677 −0.557189
\(334\) 7.04995 0.385756
\(335\) −34.9278 −1.90831
\(336\) −1.20473 −0.0657234
\(337\) −18.5053 −1.00805 −0.504025 0.863689i \(-0.668148\pi\)
−0.504025 + 0.863689i \(0.668148\pi\)
\(338\) 0 0
\(339\) −1.28992 −0.0700591
\(340\) −15.0696 −0.817263
\(341\) 8.40946 0.455398
\(342\) −17.9541 −0.970845
\(343\) 5.08921 0.274792
\(344\) 3.96074 0.213549
\(345\) 0.666410 0.0358783
\(346\) −1.84522 −0.0991998
\(347\) −15.5446 −0.834478 −0.417239 0.908797i \(-0.637002\pi\)
−0.417239 + 0.908797i \(0.637002\pi\)
\(348\) −2.86485 −0.153572
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) −11.7690 −0.629078
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) −4.32025 −0.229944 −0.114972 0.993369i \(-0.536678\pi\)
−0.114972 + 0.993369i \(0.536678\pi\)
\(354\) 4.79527 0.254866
\(355\) −17.3069 −0.918555
\(356\) 5.65345 0.299632
\(357\) −6.29394 −0.333111
\(358\) 5.42909 0.286936
\(359\) −0.231033 −0.0121934 −0.00609672 0.999981i \(-0.501941\pi\)
−0.00609672 + 0.999981i \(0.501941\pi\)
\(360\) −24.9607 −1.31555
\(361\) 19.7427 1.03909
\(362\) −4.47502 −0.235202
\(363\) −0.339877 −0.0178389
\(364\) 0 0
\(365\) 46.3898 2.42815
\(366\) −1.36618 −0.0714113
\(367\) 19.8082 1.03398 0.516991 0.855991i \(-0.327052\pi\)
0.516991 + 0.855991i \(0.327052\pi\)
\(368\) −0.679754 −0.0354346
\(369\) 16.5839 0.863322
\(370\) −10.1677 −0.528595
\(371\) 21.5839 1.12058
\(372\) 2.85818 0.148190
\(373\) −14.9148 −0.772259 −0.386130 0.922445i \(-0.626188\pi\)
−0.386130 + 0.922445i \(0.626188\pi\)
\(374\) −5.22436 −0.270145
\(375\) −1.64678 −0.0850393
\(376\) −18.3265 −0.945119
\(377\) 0 0
\(378\) −7.08921 −0.364630
\(379\) 6.64049 0.341099 0.170550 0.985349i \(-0.445446\pi\)
0.170550 + 0.985349i \(0.445446\pi\)
\(380\) 17.9541 0.921024
\(381\) 5.49867 0.281706
\(382\) 9.89116 0.506076
\(383\) −5.14182 −0.262735 −0.131367 0.991334i \(-0.541937\pi\)
−0.131367 + 0.991334i \(0.541937\pi\)
\(384\) 1.01963 0.0520328
\(385\) 10.2244 0.521082
\(386\) 5.10884 0.260033
\(387\) 3.80823 0.193583
\(388\) −2.79527 −0.141908
\(389\) −33.2806 −1.68739 −0.843697 0.536820i \(-0.819625\pi\)
−0.843697 + 0.536820i \(0.819625\pi\)
\(390\) 0 0
\(391\) −3.55128 −0.179596
\(392\) −16.6927 −0.843109
\(393\) 1.12621 0.0568096
\(394\) 2.23103 0.112398
\(395\) −2.60790 −0.131218
\(396\) 2.88448 0.144951
\(397\) 8.60350 0.431797 0.215899 0.976416i \(-0.430732\pi\)
0.215899 + 0.976416i \(0.430732\pi\)
\(398\) 17.8778 0.896134
\(399\) 7.49867 0.375403
\(400\) −3.32025 −0.166012
\(401\) −5.67975 −0.283633 −0.141817 0.989893i \(-0.545294\pi\)
−0.141817 + 0.989893i \(0.545294\pi\)
\(402\) −4.11552 −0.205263
\(403\) 0 0
\(404\) 9.86485 0.490795
\(405\) −23.0000 −1.14288
\(406\) 29.8778 1.48281
\(407\) 3.52498 0.174727
\(408\) −5.32692 −0.263722
\(409\) 22.9933 1.13695 0.568473 0.822702i \(-0.307534\pi\)
0.568473 + 0.822702i \(0.307534\pi\)
\(410\) 16.5839 0.819019
\(411\) −4.67081 −0.230394
\(412\) −5.35951 −0.264044
\(413\) 50.0103 2.46085
\(414\) −1.96074 −0.0963650
\(415\) −14.1458 −0.694392
\(416\) 0 0
\(417\) −0.818920 −0.0401027
\(418\) 6.22436 0.304443
\(419\) 30.8582 1.50752 0.753760 0.657149i \(-0.228238\pi\)
0.753760 + 0.657149i \(0.228238\pi\)
\(420\) 3.47502 0.169564
\(421\) 23.6035 1.15036 0.575182 0.818025i \(-0.304931\pi\)
0.575182 + 0.818025i \(0.304931\pi\)
\(422\) 10.9041 0.530804
\(423\) −17.6209 −0.856756
\(424\) 18.2676 0.887155
\(425\) −17.3462 −0.841413
\(426\) −2.03926 −0.0988025
\(427\) −14.2480 −0.689510
\(428\) −3.31357 −0.160168
\(429\) 0 0
\(430\) 3.80823 0.183649
\(431\) 28.6338 1.37924 0.689621 0.724170i \(-0.257777\pi\)
0.689621 + 0.724170i \(0.257777\pi\)
\(432\) −2.00000 −0.0962250
\(433\) −28.6535 −1.37700 −0.688498 0.725238i \(-0.741730\pi\)
−0.688498 + 0.725238i \(0.741730\pi\)
\(434\) −29.8082 −1.43084
\(435\) −8.26362 −0.396210
\(436\) −2.15478 −0.103195
\(437\) 4.23103 0.202398
\(438\) 5.46608 0.261180
\(439\) −9.09589 −0.434123 −0.217061 0.976158i \(-0.569647\pi\)
−0.217061 + 0.976158i \(0.569647\pi\)
\(440\) 8.65345 0.412537
\(441\) −16.0500 −0.764283
\(442\) 0 0
\(443\) 0.518304 0.0246254 0.0123127 0.999924i \(-0.496081\pi\)
0.0123127 + 0.999924i \(0.496081\pi\)
\(444\) 1.19806 0.0568573
\(445\) 16.3073 0.773040
\(446\) −19.4291 −0.919994
\(447\) 0.864853 0.0409061
\(448\) −24.8122 −1.17227
\(449\) −33.0522 −1.55983 −0.779915 0.625885i \(-0.784738\pi\)
−0.779915 + 0.625885i \(0.784738\pi\)
\(450\) −9.57720 −0.451473
\(451\) −5.74934 −0.270726
\(452\) −3.79527 −0.178514
\(453\) −2.87153 −0.134916
\(454\) −7.32025 −0.343556
\(455\) 0 0
\(456\) 6.34655 0.297204
\(457\) −27.3265 −1.27828 −0.639141 0.769090i \(-0.720710\pi\)
−0.639141 + 0.769090i \(0.720710\pi\)
\(458\) 14.5642 0.680542
\(459\) −10.4487 −0.487705
\(460\) 1.96074 0.0914199
\(461\) 13.2873 0.618850 0.309425 0.950924i \(-0.399863\pi\)
0.309425 + 0.950924i \(0.399863\pi\)
\(462\) 1.20473 0.0560491
\(463\) 18.2480 0.848057 0.424028 0.905649i \(-0.360616\pi\)
0.424028 + 0.905649i \(0.360616\pi\)
\(464\) 8.42909 0.391311
\(465\) 8.24438 0.382324
\(466\) 6.44872 0.298731
\(467\) 28.2873 1.30898 0.654489 0.756071i \(-0.272884\pi\)
0.654489 + 0.756071i \(0.272884\pi\)
\(468\) 0 0
\(469\) −42.9211 −1.98191
\(470\) −17.6209 −0.812790
\(471\) 5.56022 0.256201
\(472\) 42.3265 1.94824
\(473\) −1.32025 −0.0607050
\(474\) −0.307288 −0.0141142
\(475\) 20.6664 0.948240
\(476\) −18.5183 −0.848785
\(477\) 17.5642 0.804211
\(478\) −0.270294 −0.0123630
\(479\) 15.5446 0.710251 0.355126 0.934819i \(-0.384438\pi\)
0.355126 + 0.934819i \(0.384438\pi\)
\(480\) 4.90185 0.223738
\(481\) 0 0
\(482\) 30.5313 1.39066
\(483\) 0.818920 0.0372621
\(484\) −1.00000 −0.0454545
\(485\) −8.06291 −0.366118
\(486\) −8.71008 −0.395097
\(487\) 32.3265 1.46486 0.732428 0.680845i \(-0.238387\pi\)
0.732428 + 0.680845i \(0.238387\pi\)
\(488\) −12.0589 −0.545880
\(489\) 3.66680 0.165818
\(490\) −16.0500 −0.725063
\(491\) 11.5446 0.521001 0.260500 0.965474i \(-0.416112\pi\)
0.260500 + 0.965474i \(0.416112\pi\)
\(492\) −1.95407 −0.0880961
\(493\) 44.0366 1.98331
\(494\) 0 0
\(495\) 8.32025 0.373967
\(496\) −8.40946 −0.377596
\(497\) −21.2676 −0.953984
\(498\) −1.66680 −0.0746909
\(499\) −27.7859 −1.24387 −0.621935 0.783069i \(-0.713653\pi\)
−0.621935 + 0.783069i \(0.713653\pi\)
\(500\) −4.84522 −0.216685
\(501\) −2.39612 −0.107051
\(502\) 10.4790 0.467703
\(503\) −5.40544 −0.241017 −0.120508 0.992712i \(-0.538452\pi\)
−0.120508 + 0.992712i \(0.538452\pi\)
\(504\) −30.6731 −1.36629
\(505\) 28.4550 1.26623
\(506\) 0.679754 0.0302187
\(507\) 0 0
\(508\) 16.1784 0.717802
\(509\) −25.4095 −1.12625 −0.563127 0.826370i \(-0.690402\pi\)
−0.563127 + 0.826370i \(0.690402\pi\)
\(510\) −5.12180 −0.226797
\(511\) 57.0063 2.52181
\(512\) −11.0000 −0.486136
\(513\) 12.4487 0.549624
\(514\) 5.75601 0.253887
\(515\) −15.4594 −0.681223
\(516\) −0.448721 −0.0197538
\(517\) 6.10884 0.268667
\(518\) −12.4947 −0.548984
\(519\) 0.627148 0.0275288
\(520\) 0 0
\(521\) 33.1784 1.45357 0.726787 0.686863i \(-0.241013\pi\)
0.726787 + 0.686863i \(0.241013\pi\)
\(522\) 24.3136 1.06418
\(523\) −18.7730 −0.820885 −0.410443 0.911886i \(-0.634626\pi\)
−0.410443 + 0.911886i \(0.634626\pi\)
\(524\) 3.31357 0.144754
\(525\) 4.00000 0.174574
\(526\) 8.44872 0.368382
\(527\) −43.9341 −1.91380
\(528\) 0.339877 0.0147912
\(529\) −22.5379 −0.979910
\(530\) 17.5642 0.762942
\(531\) 40.6967 1.76609
\(532\) 22.0629 0.956549
\(533\) 0 0
\(534\) 1.92148 0.0831505
\(535\) −9.55795 −0.413226
\(536\) −36.3265 −1.56907
\(537\) −1.84522 −0.0796272
\(538\) 25.0892 1.08167
\(539\) 5.56424 0.239669
\(540\) 5.76897 0.248257
\(541\) 42.8016 1.84018 0.920091 0.391704i \(-0.128114\pi\)
0.920091 + 0.391704i \(0.128114\pi\)
\(542\) −10.4487 −0.448811
\(543\) 1.52096 0.0652705
\(544\) −26.1218 −1.11996
\(545\) −6.21542 −0.266239
\(546\) 0 0
\(547\) −33.7556 −1.44329 −0.721643 0.692265i \(-0.756613\pi\)
−0.721643 + 0.692265i \(0.756613\pi\)
\(548\) −13.7427 −0.587058
\(549\) −11.5946 −0.494844
\(550\) 3.32025 0.141576
\(551\) −52.4657 −2.23511
\(552\) 0.693098 0.0295002
\(553\) −3.20473 −0.136279
\(554\) 8.62086 0.366265
\(555\) 3.45578 0.146690
\(556\) −2.40946 −0.102184
\(557\) −1.78860 −0.0757853 −0.0378927 0.999282i \(-0.512064\pi\)
−0.0378927 + 0.999282i \(0.512064\pi\)
\(558\) −24.2569 −1.02688
\(559\) 0 0
\(560\) −10.2244 −0.432058
\(561\) 1.77564 0.0749676
\(562\) −1.98037 −0.0835368
\(563\) −7.68377 −0.323832 −0.161916 0.986805i \(-0.551767\pi\)
−0.161916 + 0.986805i \(0.551767\pi\)
\(564\) 2.07625 0.0874261
\(565\) −10.9474 −0.460560
\(566\) 2.18510 0.0918466
\(567\) −28.2636 −1.18696
\(568\) −18.0000 −0.755263
\(569\) −26.1258 −1.09525 −0.547626 0.836723i \(-0.684468\pi\)
−0.547626 + 0.836723i \(0.684468\pi\)
\(570\) 6.10217 0.255592
\(571\) −11.6624 −0.488056 −0.244028 0.969768i \(-0.578469\pi\)
−0.244028 + 0.969768i \(0.578469\pi\)
\(572\) 0 0
\(573\) −3.36178 −0.140440
\(574\) 20.3791 0.850609
\(575\) 2.25695 0.0941213
\(576\) −20.1914 −0.841308
\(577\) 28.6008 1.19067 0.595334 0.803478i \(-0.297020\pi\)
0.595334 + 0.803478i \(0.297020\pi\)
\(578\) 10.2939 0.428172
\(579\) −1.73638 −0.0721614
\(580\) −24.3136 −1.00957
\(581\) −17.3832 −0.721175
\(582\) −0.950048 −0.0393807
\(583\) −6.08921 −0.252189
\(584\) 48.2476 1.99650
\(585\) 0 0
\(586\) 6.13515 0.253441
\(587\) −35.1455 −1.45061 −0.725304 0.688429i \(-0.758301\pi\)
−0.725304 + 0.688429i \(0.758301\pi\)
\(588\) 1.89116 0.0779899
\(589\) 52.3435 2.15678
\(590\) 40.6967 1.67546
\(591\) −0.758276 −0.0311913
\(592\) −3.52498 −0.144876
\(593\) −25.2087 −1.03520 −0.517600 0.855623i \(-0.673174\pi\)
−0.517600 + 0.855623i \(0.673174\pi\)
\(594\) 2.00000 0.0820610
\(595\) −53.4157 −2.18983
\(596\) 2.54461 0.104231
\(597\) −6.07625 −0.248685
\(598\) 0 0
\(599\) 26.8582 1.09740 0.548698 0.836021i \(-0.315124\pi\)
0.548698 + 0.836021i \(0.315124\pi\)
\(600\) 3.38542 0.138209
\(601\) 32.5683 1.32849 0.664243 0.747516i \(-0.268754\pi\)
0.664243 + 0.747516i \(0.268754\pi\)
\(602\) 4.67975 0.190733
\(603\) −34.9278 −1.42237
\(604\) −8.44872 −0.343774
\(605\) −2.88448 −0.117271
\(606\) 3.35284 0.136200
\(607\) 40.7730 1.65492 0.827462 0.561521i \(-0.189784\pi\)
0.827462 + 0.561521i \(0.189784\pi\)
\(608\) 31.1218 1.26216
\(609\) −10.1548 −0.411492
\(610\) −11.5946 −0.469450
\(611\) 0 0
\(612\) −15.0696 −0.609152
\(613\) −23.3635 −0.943644 −0.471822 0.881694i \(-0.656403\pi\)
−0.471822 + 0.881694i \(0.656403\pi\)
\(614\) 6.18510 0.249610
\(615\) −5.63647 −0.227285
\(616\) 10.6338 0.428449
\(617\) −19.4095 −0.781395 −0.390698 0.920519i \(-0.627766\pi\)
−0.390698 + 0.920519i \(0.627766\pi\)
\(618\) −1.82157 −0.0732744
\(619\) −0.941108 −0.0378263 −0.0189132 0.999821i \(-0.506021\pi\)
−0.0189132 + 0.999821i \(0.506021\pi\)
\(620\) 24.2569 0.974183
\(621\) 1.35951 0.0545552
\(622\) −1.28992 −0.0517213
\(623\) 20.0393 0.802856
\(624\) 0 0
\(625\) −30.5772 −1.22309
\(626\) −0.293944 −0.0117483
\(627\) −2.11552 −0.0844856
\(628\) 16.3595 0.652815
\(629\) −18.4157 −0.734284
\(630\) −29.4920 −1.17499
\(631\) −21.4684 −0.854642 −0.427321 0.904100i \(-0.640543\pi\)
−0.427321 + 0.904100i \(0.640543\pi\)
\(632\) −2.71234 −0.107891
\(633\) −3.70606 −0.147303
\(634\) −22.0522 −0.875806
\(635\) 46.6664 1.85190
\(636\) −2.06958 −0.0820643
\(637\) 0 0
\(638\) −8.42909 −0.333711
\(639\) −17.3069 −0.684650
\(640\) 8.65345 0.342058
\(641\) −24.5379 −0.969190 −0.484595 0.874739i \(-0.661033\pi\)
−0.484595 + 0.874739i \(0.661033\pi\)
\(642\) −1.12621 −0.0444479
\(643\) −16.7493 −0.660529 −0.330265 0.943888i \(-0.607138\pi\)
−0.330265 + 0.943888i \(0.607138\pi\)
\(644\) 2.40946 0.0949460
\(645\) −1.29433 −0.0509642
\(646\) −32.5183 −1.27942
\(647\) 35.5986 1.39952 0.699762 0.714376i \(-0.253289\pi\)
0.699762 + 0.714376i \(0.253289\pi\)
\(648\) −23.9211 −0.939709
\(649\) −14.1088 −0.553821
\(650\) 0 0
\(651\) 10.1311 0.397070
\(652\) 10.7886 0.422514
\(653\) −7.02630 −0.274960 −0.137480 0.990505i \(-0.543900\pi\)
−0.137480 + 0.990505i \(0.543900\pi\)
\(654\) −0.732359 −0.0286375
\(655\) 9.55795 0.373460
\(656\) 5.74934 0.224474
\(657\) 46.3898 1.80984
\(658\) −21.6535 −0.844139
\(659\) 42.8908 1.67079 0.835394 0.549652i \(-0.185240\pi\)
0.835394 + 0.549652i \(0.185240\pi\)
\(660\) −0.980369 −0.0381608
\(661\) 36.6535 1.42565 0.712827 0.701340i \(-0.247414\pi\)
0.712827 + 0.701340i \(0.247414\pi\)
\(662\) −14.4487 −0.561565
\(663\) 0 0
\(664\) −14.7123 −0.570950
\(665\) 63.6401 2.46786
\(666\) −10.1677 −0.393992
\(667\) −5.72971 −0.221855
\(668\) −7.04995 −0.272771
\(669\) 6.60350 0.255306
\(670\) −34.9278 −1.34938
\(671\) 4.01963 0.155176
\(672\) 6.02365 0.232367
\(673\) −2.73865 −0.105567 −0.0527835 0.998606i \(-0.516809\pi\)
−0.0527835 + 0.998606i \(0.516809\pi\)
\(674\) −18.5053 −0.712799
\(675\) 6.64049 0.255593
\(676\) 0 0
\(677\) 17.3069 0.665158 0.332579 0.943075i \(-0.392081\pi\)
0.332579 + 0.943075i \(0.392081\pi\)
\(678\) −1.28992 −0.0495393
\(679\) −9.90813 −0.380239
\(680\) −45.2087 −1.73368
\(681\) 2.48798 0.0953397
\(682\) 8.40946 0.322015
\(683\) 46.7271 1.78796 0.893980 0.448106i \(-0.147901\pi\)
0.893980 + 0.448106i \(0.147901\pi\)
\(684\) 17.9541 0.686491
\(685\) −39.6405 −1.51459
\(686\) 5.08921 0.194307
\(687\) −4.95005 −0.188856
\(688\) 1.32025 0.0503339
\(689\) 0 0
\(690\) 0.666410 0.0253698
\(691\) −11.9474 −0.454500 −0.227250 0.973836i \(-0.572974\pi\)
−0.227250 + 0.973836i \(0.572974\pi\)
\(692\) 1.84522 0.0701448
\(693\) 10.2244 0.388391
\(694\) −15.5446 −0.590065
\(695\) −6.95005 −0.263630
\(696\) −8.59456 −0.325776
\(697\) 30.0366 1.13772
\(698\) 30.0000 1.13552
\(699\) −2.19177 −0.0829004
\(700\) 11.7690 0.444825
\(701\) −19.2833 −0.728318 −0.364159 0.931337i \(-0.618644\pi\)
−0.364159 + 0.931337i \(0.618644\pi\)
\(702\) 0 0
\(703\) 21.9407 0.827510
\(704\) 7.00000 0.263822
\(705\) 5.98892 0.225556
\(706\) −4.32025 −0.162595
\(707\) 34.9670 1.31507
\(708\) −4.79527 −0.180217
\(709\) −41.7057 −1.56629 −0.783145 0.621840i \(-0.786386\pi\)
−0.783145 + 0.621840i \(0.786386\pi\)
\(710\) −17.3069 −0.649516
\(711\) −2.60790 −0.0978040
\(712\) 16.9604 0.635616
\(713\) 5.71636 0.214079
\(714\) −6.29394 −0.235545
\(715\) 0 0
\(716\) −5.42909 −0.202895
\(717\) 0.0918667 0.00343082
\(718\) −0.231033 −0.00862206
\(719\) −24.6271 −0.918438 −0.459219 0.888323i \(-0.651871\pi\)
−0.459219 + 0.888323i \(0.651871\pi\)
\(720\) −8.32025 −0.310077
\(721\) −18.9973 −0.707498
\(722\) 19.7427 0.734746
\(723\) −10.3769 −0.385920
\(724\) 4.47502 0.166313
\(725\) −27.9867 −1.03940
\(726\) −0.339877 −0.0126140
\(727\) 5.82157 0.215910 0.107955 0.994156i \(-0.465570\pi\)
0.107955 + 0.994156i \(0.465570\pi\)
\(728\) 0 0
\(729\) −20.9607 −0.776324
\(730\) 46.3898 1.71696
\(731\) 6.89744 0.255111
\(732\) 1.36618 0.0504954
\(733\) 32.1588 1.18781 0.593906 0.804534i \(-0.297585\pi\)
0.593906 + 0.804534i \(0.297585\pi\)
\(734\) 19.8082 0.731135
\(735\) 5.45501 0.201211
\(736\) 3.39877 0.125280
\(737\) 12.1088 0.446035
\(738\) 16.5839 0.610461
\(739\) −0.370199 −0.0136180 −0.00680899 0.999977i \(-0.502167\pi\)
−0.00680899 + 0.999977i \(0.502167\pi\)
\(740\) 10.1677 0.373773
\(741\) 0 0
\(742\) 21.5839 0.792369
\(743\) 32.0932 1.17739 0.588693 0.808357i \(-0.299643\pi\)
0.588693 + 0.808357i \(0.299643\pi\)
\(744\) 8.57454 0.314358
\(745\) 7.33988 0.268912
\(746\) −14.9148 −0.546070
\(747\) −14.1458 −0.517569
\(748\) 5.22436 0.191022
\(749\) −11.7453 −0.429165
\(750\) −1.64678 −0.0601319
\(751\) 10.7797 0.393355 0.196678 0.980468i \(-0.436985\pi\)
0.196678 + 0.980468i \(0.436985\pi\)
\(752\) −6.10884 −0.222767
\(753\) −3.56158 −0.129791
\(754\) 0 0
\(755\) −24.3702 −0.886922
\(756\) 7.08921 0.257832
\(757\) −51.6794 −1.87832 −0.939159 0.343482i \(-0.888394\pi\)
−0.939159 + 0.343482i \(0.888394\pi\)
\(758\) 6.64049 0.241194
\(759\) −0.231033 −0.00838595
\(760\) 53.8622 1.95379
\(761\) −38.2783 −1.38759 −0.693794 0.720173i \(-0.744062\pi\)
−0.693794 + 0.720173i \(0.744062\pi\)
\(762\) 5.49867 0.199196
\(763\) −7.63784 −0.276508
\(764\) −9.89116 −0.357849
\(765\) −43.4680 −1.57159
\(766\) −5.14182 −0.185781
\(767\) 0 0
\(768\) 5.77791 0.208492
\(769\) 46.5745 1.67952 0.839760 0.542957i \(-0.182695\pi\)
0.839760 + 0.542957i \(0.182695\pi\)
\(770\) 10.2244 0.368460
\(771\) −1.95633 −0.0704557
\(772\) −5.10884 −0.183871
\(773\) 22.7819 0.819409 0.409704 0.912218i \(-0.365632\pi\)
0.409704 + 0.912218i \(0.365632\pi\)
\(774\) 3.80823 0.136884
\(775\) 27.9215 1.00297
\(776\) −8.38581 −0.301033
\(777\) 4.24664 0.152348
\(778\) −33.2806 −1.19317
\(779\) −35.7859 −1.28216
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −3.55128 −0.126993
\(783\) −16.8582 −0.602462
\(784\) −5.56424 −0.198723
\(785\) 47.1887 1.68424
\(786\) 1.12621 0.0401705
\(787\) 4.46874 0.159293 0.0796466 0.996823i \(-0.474621\pi\)
0.0796466 + 0.996823i \(0.474621\pi\)
\(788\) −2.23103 −0.0794772
\(789\) −2.87153 −0.102229
\(790\) −2.60790 −0.0927850
\(791\) −13.4527 −0.478324
\(792\) 8.65345 0.307487
\(793\) 0 0
\(794\) 8.60350 0.305327
\(795\) −5.96968 −0.211723
\(796\) −17.8778 −0.633662
\(797\) 31.2306 1.10625 0.553123 0.833100i \(-0.313436\pi\)
0.553123 + 0.833100i \(0.313436\pi\)
\(798\) 7.49867 0.265450
\(799\) −31.9148 −1.12906
\(800\) 16.6012 0.586942
\(801\) 16.3073 0.576190
\(802\) −5.67975 −0.200559
\(803\) −16.0825 −0.567541
\(804\) 4.11552 0.145143
\(805\) 6.95005 0.244957
\(806\) 0 0
\(807\) −8.52724 −0.300173
\(808\) 29.5946 1.04113
\(809\) −11.4161 −0.401370 −0.200685 0.979656i \(-0.564317\pi\)
−0.200685 + 0.979656i \(0.564317\pi\)
\(810\) −23.0000 −0.808138
\(811\) 2.13917 0.0751163 0.0375581 0.999294i \(-0.488042\pi\)
0.0375581 + 0.999294i \(0.488042\pi\)
\(812\) −29.8778 −1.04851
\(813\) 3.55128 0.124549
\(814\) 3.52498 0.123550
\(815\) 31.1195 1.09007
\(816\) −1.77564 −0.0621598
\(817\) −8.21769 −0.287501
\(818\) 22.9933 0.803943
\(819\) 0 0
\(820\) −16.5839 −0.579134
\(821\) 25.9867 0.906941 0.453470 0.891271i \(-0.350186\pi\)
0.453470 + 0.891271i \(0.350186\pi\)
\(822\) −4.67081 −0.162913
\(823\) −25.0759 −0.874090 −0.437045 0.899440i \(-0.643975\pi\)
−0.437045 + 0.899440i \(0.643975\pi\)
\(824\) −16.0785 −0.560122
\(825\) −1.12847 −0.0392885
\(826\) 50.0103 1.74008
\(827\) −43.0692 −1.49766 −0.748831 0.662761i \(-0.769385\pi\)
−0.748831 + 0.662761i \(0.769385\pi\)
\(828\) 1.96074 0.0681404
\(829\) −2.43576 −0.0845975 −0.0422988 0.999105i \(-0.513468\pi\)
−0.0422988 + 0.999105i \(0.513468\pi\)
\(830\) −14.1458 −0.491009
\(831\) −2.93003 −0.101642
\(832\) 0 0
\(833\) −29.0696 −1.00720
\(834\) −0.818920 −0.0283569
\(835\) −20.3355 −0.703738
\(836\) −6.22436 −0.215274
\(837\) 16.8189 0.581347
\(838\) 30.8582 1.06598
\(839\) 46.2347 1.59620 0.798099 0.602526i \(-0.205839\pi\)
0.798099 + 0.602526i \(0.205839\pi\)
\(840\) 10.4251 0.359699
\(841\) 42.0496 1.44999
\(842\) 23.6035 0.813430
\(843\) 0.673082 0.0231822
\(844\) −10.9041 −0.375335
\(845\) 0 0
\(846\) −17.6209 −0.605818
\(847\) −3.54461 −0.121794
\(848\) 6.08921 0.209104
\(849\) −0.742665 −0.0254882
\(850\) −17.3462 −0.594969
\(851\) 2.39612 0.0821378
\(852\) 2.03926 0.0698639
\(853\) −19.0562 −0.652473 −0.326237 0.945288i \(-0.605781\pi\)
−0.326237 + 0.945288i \(0.605781\pi\)
\(854\) −14.2480 −0.487557
\(855\) 51.7882 1.77112
\(856\) −9.94072 −0.339767
\(857\) −7.86712 −0.268736 −0.134368 0.990932i \(-0.542900\pi\)
−0.134368 + 0.990932i \(0.542900\pi\)
\(858\) 0 0
\(859\) −0.993713 −0.0339051 −0.0169525 0.999856i \(-0.505396\pi\)
−0.0169525 + 0.999856i \(0.505396\pi\)
\(860\) −3.80823 −0.129860
\(861\) −6.92640 −0.236051
\(862\) 28.6338 0.975272
\(863\) −29.3069 −0.997619 −0.498809 0.866712i \(-0.666229\pi\)
−0.498809 + 0.866712i \(0.666229\pi\)
\(864\) 10.0000 0.340207
\(865\) 5.32251 0.180971
\(866\) −28.6535 −0.973684
\(867\) −3.49867 −0.118821
\(868\) 29.8082 1.01176
\(869\) 0.904114 0.0306700
\(870\) −8.26362 −0.280163
\(871\) 0 0
\(872\) −6.46433 −0.218910
\(873\) −8.06291 −0.272888
\(874\) 4.23103 0.143117
\(875\) −17.1744 −0.580601
\(876\) −5.46608 −0.184682
\(877\) 50.4135 1.70234 0.851171 0.524888i \(-0.175893\pi\)
0.851171 + 0.524888i \(0.175893\pi\)
\(878\) −9.09589 −0.306971
\(879\) −2.08519 −0.0703319
\(880\) 2.88448 0.0972359
\(881\) −17.5879 −0.592551 −0.296275 0.955103i \(-0.595745\pi\)
−0.296275 + 0.955103i \(0.595745\pi\)
\(882\) −16.0500 −0.540430
\(883\) 42.3702 1.42587 0.712935 0.701230i \(-0.247365\pi\)
0.712935 + 0.701230i \(0.247365\pi\)
\(884\) 0 0
\(885\) −13.8319 −0.464954
\(886\) 0.518304 0.0174128
\(887\) 2.35685 0.0791354 0.0395677 0.999217i \(-0.487402\pi\)
0.0395677 + 0.999217i \(0.487402\pi\)
\(888\) 3.59417 0.120613
\(889\) 57.3462 1.92333
\(890\) 16.3073 0.546622
\(891\) 7.97370 0.267129
\(892\) 19.4291 0.650534
\(893\) 38.0236 1.27241
\(894\) 0.864853 0.0289250
\(895\) −15.6601 −0.523460
\(896\) 10.6338 0.355251
\(897\) 0 0
\(898\) −33.0522 −1.10297
\(899\) −70.8841 −2.36412
\(900\) 9.57720 0.319240
\(901\) 31.8122 1.05982
\(902\) −5.74934 −0.191432
\(903\) −1.59054 −0.0529299
\(904\) −11.3858 −0.378686
\(905\) 12.9081 0.429081
\(906\) −2.87153 −0.0954000
\(907\) −17.5210 −0.581774 −0.290887 0.956757i \(-0.593950\pi\)
−0.290887 + 0.956757i \(0.593950\pi\)
\(908\) 7.32025 0.242931
\(909\) 28.4550 0.943793
\(910\) 0 0
\(911\) 10.2873 0.340833 0.170416 0.985372i \(-0.445489\pi\)
0.170416 + 0.985372i \(0.445489\pi\)
\(912\) 2.11552 0.0700517
\(913\) 4.90411 0.162302
\(914\) −27.3265 −0.903881
\(915\) 3.94072 0.130276
\(916\) −14.5642 −0.481216
\(917\) 11.7453 0.387865
\(918\) −10.4487 −0.344859
\(919\) −31.1544 −1.02769 −0.513844 0.857883i \(-0.671779\pi\)
−0.513844 + 0.857883i \(0.671779\pi\)
\(920\) 5.88222 0.193931
\(921\) −2.10217 −0.0692689
\(922\) 13.2873 0.437593
\(923\) 0 0
\(924\) −1.20473 −0.0396327
\(925\) 11.7038 0.384818
\(926\) 18.2480 0.599667
\(927\) −15.4594 −0.507754
\(928\) −42.1455 −1.38349
\(929\) 38.4594 1.26181 0.630906 0.775859i \(-0.282683\pi\)
0.630906 + 0.775859i \(0.282683\pi\)
\(930\) 8.24438 0.270344
\(931\) 34.6338 1.13508
\(932\) −6.44872 −0.211235
\(933\) 0.438416 0.0143531
\(934\) 28.2873 0.925588
\(935\) 15.0696 0.492828
\(936\) 0 0
\(937\) 21.6182 0.706236 0.353118 0.935579i \(-0.385121\pi\)
0.353118 + 0.935579i \(0.385121\pi\)
\(938\) −42.9211 −1.40142
\(939\) 0.0999046 0.00326026
\(940\) 17.6209 0.574729
\(941\) −6.44872 −0.210222 −0.105111 0.994460i \(-0.533520\pi\)
−0.105111 + 0.994460i \(0.533520\pi\)
\(942\) 5.56022 0.181162
\(943\) −3.90813 −0.127266
\(944\) 14.1088 0.459204
\(945\) 20.4487 0.665197
\(946\) −1.32025 −0.0429249
\(947\) 15.5379 0.504915 0.252458 0.967608i \(-0.418761\pi\)
0.252458 + 0.967608i \(0.418761\pi\)
\(948\) 0.307288 0.00998024
\(949\) 0 0
\(950\) 20.6664 0.670507
\(951\) 7.49504 0.243043
\(952\) −55.5549 −1.80055
\(953\) −15.8868 −0.514622 −0.257311 0.966329i \(-0.582837\pi\)
−0.257311 + 0.966329i \(0.582837\pi\)
\(954\) 17.5642 0.568663
\(955\) −28.5309 −0.923238
\(956\) 0.270294 0.00874193
\(957\) 2.86485 0.0926075
\(958\) 15.5446 0.502223
\(959\) −48.7123 −1.57300
\(960\) 6.86259 0.221489
\(961\) 39.7190 1.28126
\(962\) 0 0
\(963\) −9.55795 −0.308001
\(964\) −30.5313 −0.983346
\(965\) −14.7364 −0.474381
\(966\) 0.818920 0.0263483
\(967\) 1.28766 0.0414083 0.0207041 0.999786i \(-0.493409\pi\)
0.0207041 + 0.999786i \(0.493409\pi\)
\(968\) −3.00000 −0.0964237
\(969\) 11.0522 0.355048
\(970\) −8.06291 −0.258884
\(971\) −19.1195 −0.613575 −0.306788 0.951778i \(-0.599254\pi\)
−0.306788 + 0.951778i \(0.599254\pi\)
\(972\) 8.71008 0.279376
\(973\) −8.54059 −0.273799
\(974\) 32.3265 1.03581
\(975\) 0 0
\(976\) −4.01963 −0.128665
\(977\) 27.0103 0.864136 0.432068 0.901841i \(-0.357784\pi\)
0.432068 + 0.901841i \(0.357784\pi\)
\(978\) 3.66680 0.117251
\(979\) −5.65345 −0.180685
\(980\) 16.0500 0.512697
\(981\) −6.21542 −0.198443
\(982\) 11.5446 0.368403
\(983\) −9.35951 −0.298522 −0.149261 0.988798i \(-0.547689\pi\)
−0.149261 + 0.988798i \(0.547689\pi\)
\(984\) −5.86220 −0.186880
\(985\) −6.43538 −0.205048
\(986\) 44.0366 1.40241
\(987\) 7.35951 0.234256
\(988\) 0 0
\(989\) −0.897442 −0.0285370
\(990\) 8.32025 0.264435
\(991\) 14.8885 0.472949 0.236474 0.971638i \(-0.424008\pi\)
0.236474 + 0.971638i \(0.424008\pi\)
\(992\) 42.0473 1.33500
\(993\) 4.91079 0.155839
\(994\) −21.2676 −0.674569
\(995\) −51.5683 −1.63482
\(996\) 1.66680 0.0528144
\(997\) −20.2137 −0.640173 −0.320087 0.947388i \(-0.603712\pi\)
−0.320087 + 0.947388i \(0.603712\pi\)
\(998\) −27.7859 −0.879549
\(999\) 7.04995 0.223051
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1859.2.a.h.1.2 3
13.3 even 3 143.2.e.a.100.2 6
13.9 even 3 143.2.e.a.133.2 yes 6
13.12 even 2 1859.2.a.e.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.a.100.2 6 13.3 even 3
143.2.e.a.133.2 yes 6 13.9 even 3
1859.2.a.e.1.2 3 13.12 even 2
1859.2.a.h.1.2 3 1.1 even 1 trivial