Properties

Label 1859.2.a.e.1.2
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $1$
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: \(1\)
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 \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) −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 \(-0.276861\pi\)
0.644990 + 0.764191i \(0.276861\pi\)
\(6\) 0.339877 0.138754
\(7\) 3.54461 1.33974 0.669868 0.742480i \(-0.266351\pi\)
0.669868 + 0.742480i \(0.266351\pi\)
\(8\) 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 \(-0.753111\pi\)
−0.713983 + 0.700163i \(0.753111\pi\)
\(20\) −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 \(-0.772456\pi\)
−0.755192 + 0.655504i \(0.772456\pi\)
\(32\) −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 \(-0.593573\pi\)
−0.289751 + 0.957102i \(0.593573\pi\)
\(38\) 6.22436 1.00972
\(39\) 0 0
\(40\) 8.65345 1.36823
\(41\) 5.74934 0.897896 0.448948 0.893558i \(-0.351799\pi\)
0.448948 + 0.893558i \(0.351799\pi\)
\(42\) 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 \(-0.646986\pi\)
−0.445533 + 0.895265i \(0.646986\pi\)
\(48\) 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 \(-0.129476\pi\)
0.918408 + 0.395636i \(0.129476\pi\)
\(60\) 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 \(-0.765016\pi\)
−0.739665 + 0.672975i \(0.765016\pi\)
\(68\) 5.22436 0.633547
\(69\) −0.231033 −0.0278131
\(70\) −10.2244 −1.22204
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) −8.65345 −1.01982
\(73\) 16.0825 1.88232 0.941160 0.337963i \(-0.109738\pi\)
0.941160 + 0.337963i \(0.109738\pi\)
\(74\) 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 \(-0.586742\pi\)
−0.269148 + 0.963099i \(0.586742\pi\)
\(84\) 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 \(-0.403136\pi\)
0.299632 + 0.954055i \(0.403136\pi\)
\(90\) 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 \(-0.545324\pi\)
−0.141908 + 0.989880i \(0.545324\pi\)
\(98\) −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 \(-0.532907\pi\)
−0.103195 + 0.994661i \(0.532907\pi\)
\(110\) 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 \(-0.699714\pi\)
−0.587058 + 0.809545i \(0.699714\pi\)
\(138\) 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 \(-0.466762\pi\)
0.104231 + 0.994553i \(0.466762\pi\)
\(150\) 1.12847 0.0921396
\(151\) −8.44872 −0.687547 −0.343774 0.939053i \(-0.611705\pi\)
−0.343774 + 0.939053i \(0.611705\pi\)
\(152\) −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 \(-0.361148\pi\)
0.422514 + 0.906356i \(0.361148\pi\)
\(164\) −5.74934 −0.448948
\(165\) 0.980369 0.0763216
\(166\) 4.90411 0.380633
\(167\) −7.04995 −0.545542 −0.272771 0.962079i \(-0.587940\pi\)
−0.272771 + 0.962079i \(0.587940\pi\)
\(168\) −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 \(-0.558863\pi\)
−0.183871 + 0.982950i \(0.558863\pi\)
\(194\) 2.79527 0.200689
\(195\) 0 0
\(196\) −5.56424 −0.397446
\(197\) −2.23103 −0.158954 −0.0794772 0.996837i \(-0.525325\pi\)
−0.0794772 + 0.996837i \(0.525325\pi\)
\(198\) −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 \(-0.274545\pi\)
0.650534 + 0.759477i \(0.274545\pi\)
\(224\) −17.7230 −1.18417
\(225\) −9.57720 −0.638480
\(226\) −3.79527 −0.252458
\(227\) 7.32025 0.485862 0.242931 0.970044i \(-0.421891\pi\)
0.242931 + 0.970044i \(0.421891\pi\)
\(228\) −2.11552 −0.140103
\(229\) −14.5642 −0.962432 −0.481216 0.876602i \(-0.659805\pi\)
−0.481216 + 0.876602i \(0.659805\pi\)
\(230\) −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 \(-0.497217\pi\)
0.00874193 + 0.999962i \(0.497217\pi\)
\(240\) 0.980369 0.0632826
\(241\) −30.5313 −1.96669 −0.983346 0.181745i \(-0.941826\pi\)
−0.983346 + 0.181745i \(0.941826\pi\)
\(242\) −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 \(-0.397205\pi\)
0.317357 + 0.948306i \(0.397205\pi\)
\(272\) 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 \(-0.481187\pi\)
0.0590695 + 0.998254i \(0.481187\pi\)
\(282\) −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 \(-0.557354\pi\)
−0.179210 + 0.983811i \(0.557354\pi\)
\(294\) 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 \(-0.556478\pi\)
−0.176501 + 0.984300i \(0.556478\pi\)
\(308\) 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 \(-0.287421\pi\)
0.619288 + 0.785164i \(0.287421\pi\)
\(318\) −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 \(-0.370021\pi\)
0.397087 + 0.917781i \(0.370021\pi\)
\(332\) 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 \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) −11.7690 −0.629078
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) 4.32025 0.229944 0.114972 0.993369i \(-0.463322\pi\)
0.114972 + 0.993369i \(0.463322\pi\)
\(354\) 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 \(-0.498059\pi\)
0.00609672 + 0.999981i \(0.498059\pi\)
\(360\) −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 \(-0.554554\pi\)
−0.170550 + 0.985349i \(0.554554\pi\)
\(380\) 17.9541 0.921024
\(381\) 5.49867 0.281706
\(382\) −9.89116 −0.506076
\(383\) 5.14182 0.262735 0.131367 0.991334i \(-0.458063\pi\)
0.131367 + 0.991334i \(0.458063\pi\)
\(384\) −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 \(-0.569268\pi\)
−0.215899 + 0.976416i \(0.569268\pi\)
\(398\) −17.8778 −0.896134
\(399\) 7.49867 0.375403
\(400\) −3.32025 −0.166012
\(401\) 5.67975 0.283633 0.141817 0.989893i \(-0.454706\pi\)
0.141817 + 0.989893i \(0.454706\pi\)
\(402\) −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 \(-0.692466\pi\)
−0.568473 + 0.822702i \(0.692466\pi\)
\(410\) −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 \(-0.695069\pi\)
−0.575182 + 0.818025i \(0.695069\pi\)
\(422\) −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 \(-0.742223\pi\)
−0.689621 + 0.724170i \(0.742223\pi\)
\(432\) −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 \(-0.215262\pi\)
0.779915 + 0.625885i \(0.215262\pi\)
\(450\) 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 \(-0.279290\pi\)
0.639141 + 0.769090i \(0.279290\pi\)
\(458\) 14.5642 0.680542
\(459\) −10.4487 −0.487705
\(460\) −1.96074 −0.0914199
\(461\) −13.2873 −0.618850 −0.309425 0.950924i \(-0.600137\pi\)
−0.309425 + 0.950924i \(0.600137\pi\)
\(462\) −1.20473 −0.0560491
\(463\) −18.2480 −0.848057 −0.424028 0.905649i \(-0.639384\pi\)
−0.424028 + 0.905649i \(0.639384\pi\)
\(464\) 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 \(-0.615562\pi\)
−0.355126 + 0.934819i \(0.615562\pi\)
\(480\) 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 \(-0.761613\pi\)
−0.732428 + 0.680845i \(0.761613\pi\)
\(488\) 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 \(-0.286347\pi\)
0.621935 + 0.783069i \(0.286347\pi\)
\(500\) 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 \(-0.309598\pi\)
0.563127 + 0.826370i \(0.309598\pi\)
\(510\) −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 \(-0.871886\pi\)
−0.920091 + 0.391704i \(0.871886\pi\)
\(542\) −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 \(-0.487936\pi\)
0.0378927 + 0.999282i \(0.487936\pi\)
\(558\) −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 \(-0.702980\pi\)
−0.595334 + 0.803478i \(0.702980\pi\)
\(578\) −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 \(-0.241699\pi\)
0.725304 + 0.688429i \(0.241699\pi\)
\(588\) 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 \(-0.326826\pi\)
0.517600 + 0.855623i \(0.326826\pi\)
\(594\) 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 \(-0.343597\pi\)
0.471822 + 0.881694i \(0.343597\pi\)
\(614\) 6.18510 0.249610
\(615\) −5.63647 −0.227285
\(616\) −10.6338 −0.428449
\(617\) 19.4095 0.781395 0.390698 0.920519i \(-0.372234\pi\)
0.390698 + 0.920519i \(0.372234\pi\)
\(618\) 1.82157 0.0732744
\(619\) 0.941108 0.0378263 0.0189132 0.999821i \(-0.493979\pi\)
0.0189132 + 0.999821i \(0.493979\pi\)
\(620\) 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 \(-0.359457\pi\)
0.427321 + 0.904100i \(0.359457\pi\)
\(632\) 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 \(-0.392862\pi\)
0.330265 + 0.943888i \(0.392862\pi\)
\(644\) −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 \(-0.752586\pi\)
−0.712827 + 0.701340i \(0.752586\pi\)
\(662\) −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 \(-0.852099\pi\)
−0.893980 + 0.448106i \(0.852099\pi\)
\(684\) −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 \(-0.427026\pi\)
0.227250 + 0.973836i \(0.427026\pi\)
\(692\) 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 \(-0.213614\pi\)
0.783145 + 0.621840i \(0.213614\pi\)
\(710\) 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 \(-0.702415\pi\)
−0.593906 + 0.804534i \(0.702415\pi\)
\(734\) −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 \(-0.497833\pi\)
0.00680899 + 0.999977i \(0.497833\pi\)
\(740\) 10.1677 0.373773
\(741\) 0 0
\(742\) 21.5839 0.792369
\(743\) −32.0932 −1.17739 −0.588693 0.808357i \(-0.700357\pi\)
−0.588693 + 0.808357i \(0.700357\pi\)
\(744\) 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 \(-0.255938\pi\)
0.693794 + 0.720173i \(0.255938\pi\)
\(762\) −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 \(-0.817305\pi\)
−0.839760 + 0.542957i \(0.817305\pi\)
\(770\) 10.2244 0.368460
\(771\) −1.95633 −0.0704557
\(772\) 5.10884 0.183871
\(773\) −22.7819 −0.819409 −0.409704 0.912218i \(-0.634368\pi\)
−0.409704 + 0.912218i \(0.634368\pi\)
\(774\) −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 \(-0.525379\pi\)
−0.0796466 + 0.996823i \(0.525379\pi\)
\(788\) 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 \(-0.511958\pi\)
−0.0375581 + 0.999294i \(0.511958\pi\)
\(812\) 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 \(-0.649814\pi\)
−0.453470 + 0.891271i \(0.649814\pi\)
\(822\) −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 \(-0.230615\pi\)
0.748831 + 0.662761i \(0.230615\pi\)
\(828\) 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 \(-0.794161\pi\)
−0.798099 + 0.602526i \(0.794161\pi\)
\(840\) −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 \(-0.394219\pi\)
0.326237 + 0.945288i \(0.394219\pi\)
\(854\) −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 \(-0.333771\pi\)
0.498809 + 0.866712i \(0.333771\pi\)
\(864\) −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 \(-0.824107\pi\)
−0.851171 + 0.524888i \(0.824107\pi\)
\(878\) 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 \(-0.717317\pi\)
−0.630906 + 0.775859i \(0.717317\pi\)
\(930\) −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 \(-0.466480\pi\)
0.105111 + 0.994460i \(0.466480\pi\)
\(942\) −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 \(-0.581239\pi\)
−0.252458 + 0.967608i \(0.581239\pi\)
\(948\) 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 \(-0.506591\pi\)
−0.0207041 + 0.999786i \(0.506591\pi\)
\(968\) 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 \(-0.642216\pi\)
−0.432068 + 0.901841i \(0.642216\pi\)
\(978\) 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 \(-0.452311\pi\)
0.149261 + 0.988798i \(0.452311\pi\)
\(984\) −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.e.1.2 3
13.4 even 6 143.2.e.a.133.2 yes 6
13.10 even 6 143.2.e.a.100.2 6
13.12 even 2 1859.2.a.h.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.a.100.2 6 13.10 even 6
143.2.e.a.133.2 yes 6 13.4 even 6
1859.2.a.e.1.2 3 1.1 even 1 trivial
1859.2.a.h.1.2 3 13.12 even 2