Properties

Label 1859.2.a.e.1.1
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.1
Root \(-2.26180\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.26180 q^{3} -1.00000 q^{4} -2.11575 q^{5} +2.26180 q^{6} -3.37755 q^{7} +3.00000 q^{8} +2.11575 q^{9} +2.11575 q^{10} -1.00000 q^{11} +2.26180 q^{12} +3.37755 q^{14} +4.78541 q^{15} -1.00000 q^{16} -2.14605 q^{17} -2.11575 q^{18} -3.14605 q^{19} +2.11575 q^{20} +7.63935 q^{21} +1.00000 q^{22} +4.52360 q^{23} -6.78541 q^{24} -0.523604 q^{25} +2.00000 q^{27} +3.37755 q^{28} +3.49330 q^{29} -4.78541 q^{30} +9.27871 q^{31} -5.00000 q^{32} +2.26180 q^{33} +2.14605 q^{34} +7.14605 q^{35} -2.11575 q^{36} +9.16296 q^{37} +3.14605 q^{38} -6.34725 q^{40} -10.0169 q^{41} -7.63935 q^{42} +2.52360 q^{43} +1.00000 q^{44} -4.47640 q^{45} -4.52360 q^{46} +1.96970 q^{47} +2.26180 q^{48} +4.40786 q^{49} +0.523604 q^{50} +4.85395 q^{51} +7.75510 q^{53} -2.00000 q^{54} +2.11575 q^{55} -10.1327 q^{56} +7.11575 q^{57} -3.49330 q^{58} +6.03030 q^{59} -4.78541 q^{60} +9.78541 q^{61} -9.27871 q^{62} -7.14605 q^{63} +7.00000 q^{64} -2.26180 q^{66} -4.03030 q^{67} +2.14605 q^{68} -10.2315 q^{69} -7.14605 q^{70} -6.00000 q^{71} +6.34725 q^{72} -10.8405 q^{73} -9.16296 q^{74} +1.18429 q^{75} +3.14605 q^{76} +3.37755 q^{77} +1.66966 q^{79} +2.11575 q^{80} -10.8709 q^{81} +10.0169 q^{82} -5.66966 q^{83} -7.63935 q^{84} +4.54051 q^{85} -2.52360 q^{86} -7.90116 q^{87} -3.00000 q^{88} -9.34725 q^{89} +4.47640 q^{90} -4.52360 q^{92} -20.9866 q^{93} -1.96970 q^{94} +6.65626 q^{95} +11.3090 q^{96} -11.6394 q^{97} -4.40786 q^{98} -2.11575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} - 3 q^{4} - 3 q^{5} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 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 \(0.615027\pi\)
\(3\) −2.26180 −1.30585 −0.652926 0.757422i \(-0.726459\pi\)
−0.652926 + 0.757422i \(0.726459\pi\)
\(4\) −1.00000 −0.500000
\(5\) −2.11575 −0.946192 −0.473096 0.881011i \(-0.656864\pi\)
−0.473096 + 0.881011i \(0.656864\pi\)
\(6\) 2.26180 0.923377
\(7\) −3.37755 −1.27659 −0.638297 0.769790i \(-0.720361\pi\)
−0.638297 + 0.769790i \(0.720361\pi\)
\(8\) 3.00000 1.06066
\(9\) 2.11575 0.705250
\(10\) 2.11575 0.669059
\(11\) −1.00000 −0.301511
\(12\) 2.26180 0.652926
\(13\) 0 0
\(14\) 3.37755 0.902689
\(15\) 4.78541 1.23559
\(16\) −1.00000 −0.250000
\(17\) −2.14605 −0.520494 −0.260247 0.965542i \(-0.583804\pi\)
−0.260247 + 0.965542i \(0.583804\pi\)
\(18\) −2.11575 −0.498687
\(19\) −3.14605 −0.721754 −0.360877 0.932613i \(-0.617523\pi\)
−0.360877 + 0.932613i \(0.617523\pi\)
\(20\) 2.11575 0.473096
\(21\) 7.63935 1.66704
\(22\) 1.00000 0.213201
\(23\) 4.52360 0.943237 0.471618 0.881803i \(-0.343670\pi\)
0.471618 + 0.881803i \(0.343670\pi\)
\(24\) −6.78541 −1.38507
\(25\) −0.523604 −0.104721
\(26\) 0 0
\(27\) 2.00000 0.384900
\(28\) 3.37755 0.638297
\(29\) 3.49330 0.648690 0.324345 0.945939i \(-0.394856\pi\)
0.324345 + 0.945939i \(0.394856\pi\)
\(30\) −4.78541 −0.873692
\(31\) 9.27871 1.66651 0.833253 0.552893i \(-0.186476\pi\)
0.833253 + 0.552893i \(0.186476\pi\)
\(32\) −5.00000 −0.883883
\(33\) 2.26180 0.393729
\(34\) 2.14605 0.368045
\(35\) 7.14605 1.20790
\(36\) −2.11575 −0.352625
\(37\) 9.16296 1.50638 0.753191 0.657802i \(-0.228514\pi\)
0.753191 + 0.657802i \(0.228514\pi\)
\(38\) 3.14605 0.510357
\(39\) 0 0
\(40\) −6.34725 −1.00359
\(41\) −10.0169 −1.56438 −0.782189 0.623041i \(-0.785897\pi\)
−0.782189 + 0.623041i \(0.785897\pi\)
\(42\) −7.63935 −1.17878
\(43\) 2.52360 0.384846 0.192423 0.981312i \(-0.438365\pi\)
0.192423 + 0.981312i \(0.438365\pi\)
\(44\) 1.00000 0.150756
\(45\) −4.47640 −0.667302
\(46\) −4.52360 −0.666969
\(47\) 1.96970 0.287310 0.143655 0.989628i \(-0.454114\pi\)
0.143655 + 0.989628i \(0.454114\pi\)
\(48\) 2.26180 0.326463
\(49\) 4.40786 0.629694
\(50\) 0.523604 0.0740489
\(51\) 4.85395 0.679689
\(52\) 0 0
\(53\) 7.75510 1.06525 0.532623 0.846353i \(-0.321206\pi\)
0.532623 + 0.846353i \(0.321206\pi\)
\(54\) −2.00000 −0.272166
\(55\) 2.11575 0.285288
\(56\) −10.1327 −1.35403
\(57\) 7.11575 0.942504
\(58\) −3.49330 −0.458693
\(59\) 6.03030 0.785079 0.392539 0.919735i \(-0.371597\pi\)
0.392539 + 0.919735i \(0.371597\pi\)
\(60\) −4.78541 −0.617793
\(61\) 9.78541 1.25289 0.626446 0.779464i \(-0.284509\pi\)
0.626446 + 0.779464i \(0.284509\pi\)
\(62\) −9.27871 −1.17840
\(63\) −7.14605 −0.900318
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) −2.26180 −0.278409
\(67\) −4.03030 −0.492380 −0.246190 0.969222i \(-0.579179\pi\)
−0.246190 + 0.969222i \(0.579179\pi\)
\(68\) 2.14605 0.260247
\(69\) −10.2315 −1.23173
\(70\) −7.14605 −0.854117
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 6.34725 0.748030
\(73\) −10.8405 −1.26879 −0.634395 0.773009i \(-0.718751\pi\)
−0.634395 + 0.773009i \(0.718751\pi\)
\(74\) −9.16296 −1.06517
\(75\) 1.18429 0.136750
\(76\) 3.14605 0.360877
\(77\) 3.37755 0.384908
\(78\) 0 0
\(79\) 1.66966 0.187851 0.0939256 0.995579i \(-0.470058\pi\)
0.0939256 + 0.995579i \(0.470058\pi\)
\(80\) 2.11575 0.236548
\(81\) −10.8709 −1.20787
\(82\) 10.0169 1.10618
\(83\) −5.66966 −0.622326 −0.311163 0.950357i \(-0.600718\pi\)
−0.311163 + 0.950357i \(0.600718\pi\)
\(84\) −7.63935 −0.833522
\(85\) 4.54051 0.492487
\(86\) −2.52360 −0.272127
\(87\) −7.90116 −0.847093
\(88\) −3.00000 −0.319801
\(89\) −9.34725 −0.990806 −0.495403 0.868663i \(-0.664980\pi\)
−0.495403 + 0.868663i \(0.664980\pi\)
\(90\) 4.47640 0.471854
\(91\) 0 0
\(92\) −4.52360 −0.471618
\(93\) −20.9866 −2.17621
\(94\) −1.96970 −0.203159
\(95\) 6.65626 0.682918
\(96\) 11.3090 1.15422
\(97\) −11.6394 −1.18180 −0.590899 0.806746i \(-0.701227\pi\)
−0.590899 + 0.806746i \(0.701227\pi\)
\(98\) −4.40786 −0.445261
\(99\) −2.11575 −0.212641
\(100\) 0.523604 0.0523604
\(101\) 0.901156 0.0896684 0.0448342 0.998994i \(-0.485724\pi\)
0.0448342 + 0.998994i \(0.485724\pi\)
\(102\) −4.85395 −0.480612
\(103\) 13.0472 1.28558 0.642790 0.766043i \(-0.277777\pi\)
0.642790 + 0.766043i \(0.277777\pi\)
\(104\) 0 0
\(105\) −16.1630 −1.57734
\(106\) −7.75510 −0.753242
\(107\) −13.6091 −1.31564 −0.657818 0.753177i \(-0.728521\pi\)
−0.657818 + 0.753177i \(0.728521\pi\)
\(108\) −2.00000 −0.192450
\(109\) −18.6866 −1.78985 −0.894924 0.446218i \(-0.852770\pi\)
−0.894924 + 0.446218i \(0.852770\pi\)
\(110\) −2.11575 −0.201729
\(111\) −20.7248 −1.96711
\(112\) 3.37755 0.319149
\(113\) 12.6394 1.18901 0.594505 0.804092i \(-0.297348\pi\)
0.594505 + 0.804092i \(0.297348\pi\)
\(114\) −7.11575 −0.666451
\(115\) −9.57081 −0.892483
\(116\) −3.49330 −0.324345
\(117\) 0 0
\(118\) −6.03030 −0.555134
\(119\) 7.24840 0.664460
\(120\) 14.3562 1.31054
\(121\) 1.00000 0.0909091
\(122\) −9.78541 −0.885929
\(123\) 22.6563 2.04285
\(124\) −9.27871 −0.833253
\(125\) 11.6866 1.04528
\(126\) 7.14605 0.636621
\(127\) 11.5102 1.02137 0.510683 0.859769i \(-0.329393\pi\)
0.510683 + 0.859769i \(0.329393\pi\)
\(128\) 3.00000 0.265165
\(129\) −5.70789 −0.502552
\(130\) 0 0
\(131\) 13.6091 1.18903 0.594514 0.804085i \(-0.297344\pi\)
0.594514 + 0.804085i \(0.297344\pi\)
\(132\) −2.26180 −0.196865
\(133\) 10.6260 0.921387
\(134\) 4.03030 0.348165
\(135\) −4.23150 −0.364189
\(136\) −6.43816 −0.552068
\(137\) 15.1024 1.29028 0.645140 0.764064i \(-0.276799\pi\)
0.645140 + 0.764064i \(0.276799\pi\)
\(138\) 10.2315 0.870963
\(139\) −15.2787 −1.29592 −0.647962 0.761673i \(-0.724378\pi\)
−0.647962 + 0.761673i \(0.724378\pi\)
\(140\) −7.14605 −0.603952
\(141\) −4.45506 −0.375184
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −2.11575 −0.176312
\(145\) −7.39095 −0.613785
\(146\) 10.8405 0.897170
\(147\) −9.96970 −0.822287
\(148\) −9.16296 −0.753191
\(149\) −4.37755 −0.358623 −0.179312 0.983792i \(-0.557387\pi\)
−0.179312 + 0.983792i \(0.557387\pi\)
\(150\) −1.18429 −0.0966969
\(151\) −2.29211 −0.186529 −0.0932645 0.995641i \(-0.529730\pi\)
−0.0932645 + 0.995641i \(0.529730\pi\)
\(152\) −9.43816 −0.765536
\(153\) −4.54051 −0.367078
\(154\) −3.37755 −0.272171
\(155\) −19.6314 −1.57683
\(156\) 0 0
\(157\) −24.0472 −1.91918 −0.959588 0.281408i \(-0.909198\pi\)
−0.959588 + 0.281408i \(0.909198\pi\)
\(158\) −1.66966 −0.132831
\(159\) −17.5405 −1.39105
\(160\) 10.5787 0.836323
\(161\) −15.2787 −1.20413
\(162\) 10.8709 0.854095
\(163\) 6.55391 0.513342 0.256671 0.966499i \(-0.417374\pi\)
0.256671 + 0.966499i \(0.417374\pi\)
\(164\) 10.0169 0.782189
\(165\) −4.78541 −0.372543
\(166\) 5.66966 0.440051
\(167\) 18.3259 1.41810 0.709051 0.705157i \(-0.249124\pi\)
0.709051 + 0.705157i \(0.249124\pi\)
\(168\) 22.9181 1.76817
\(169\) 0 0
\(170\) −4.54051 −0.348241
\(171\) −6.65626 −0.509017
\(172\) −2.52360 −0.192423
\(173\) 14.6866 1.11660 0.558299 0.829640i \(-0.311454\pi\)
0.558299 + 0.829640i \(0.311454\pi\)
\(174\) 7.90116 0.598985
\(175\) 1.76850 0.133686
\(176\) 1.00000 0.0753778
\(177\) −13.6394 −1.02520
\(178\) 9.34725 0.700606
\(179\) −6.49330 −0.485332 −0.242666 0.970110i \(-0.578022\pi\)
−0.242666 + 0.970110i \(0.578022\pi\)
\(180\) 4.47640 0.333651
\(181\) −17.1630 −1.27571 −0.637856 0.770155i \(-0.720179\pi\)
−0.637856 + 0.770155i \(0.720179\pi\)
\(182\) 0 0
\(183\) −22.1327 −1.63609
\(184\) 13.5708 1.00045
\(185\) −19.3865 −1.42533
\(186\) 20.9866 1.53881
\(187\) 2.14605 0.156935
\(188\) −1.96970 −0.143655
\(189\) −6.75510 −0.491361
\(190\) −6.65626 −0.482896
\(191\) 17.9697 1.30024 0.650121 0.759831i \(-0.274718\pi\)
0.650121 + 0.759831i \(0.274718\pi\)
\(192\) −15.8326 −1.14262
\(193\) 2.96970 0.213763 0.106882 0.994272i \(-0.465913\pi\)
0.106882 + 0.994272i \(0.465913\pi\)
\(194\) 11.6394 0.835657
\(195\) 0 0
\(196\) −4.40786 −0.314847
\(197\) −12.2315 −0.871458 −0.435729 0.900078i \(-0.643509\pi\)
−0.435729 + 0.900078i \(0.643509\pi\)
\(198\) 2.11575 0.150360
\(199\) −0.201195 −0.0142624 −0.00713118 0.999975i \(-0.502270\pi\)
−0.00713118 + 0.999975i \(0.502270\pi\)
\(200\) −1.57081 −0.111073
\(201\) 9.11575 0.642975
\(202\) −0.901156 −0.0634051
\(203\) −11.7988 −0.828114
\(204\) −4.85395 −0.339844
\(205\) 21.1933 1.48020
\(206\) −13.0472 −0.909042
\(207\) 9.57081 0.665218
\(208\) 0 0
\(209\) 3.14605 0.217617
\(210\) 16.1630 1.11535
\(211\) 11.6697 0.803372 0.401686 0.915777i \(-0.368424\pi\)
0.401686 + 0.915777i \(0.368424\pi\)
\(212\) −7.75510 −0.532623
\(213\) 13.5708 0.929857
\(214\) 13.6091 0.930296
\(215\) −5.33931 −0.364138
\(216\) 6.00000 0.408248
\(217\) −31.3393 −2.12745
\(218\) 18.6866 1.26561
\(219\) 24.5192 1.65685
\(220\) −2.11575 −0.142644
\(221\) 0 0
\(222\) 20.7248 1.39096
\(223\) 7.50670 0.502686 0.251343 0.967898i \(-0.419128\pi\)
0.251343 + 0.967898i \(0.419128\pi\)
\(224\) 16.8878 1.12836
\(225\) −1.10782 −0.0738544
\(226\) −12.6394 −0.840757
\(227\) 3.47640 0.230736 0.115368 0.993323i \(-0.463195\pi\)
0.115368 + 0.993323i \(0.463195\pi\)
\(228\) −7.11575 −0.471252
\(229\) −13.4079 −0.886016 −0.443008 0.896518i \(-0.646089\pi\)
−0.443008 + 0.896518i \(0.646089\pi\)
\(230\) 9.57081 0.631081
\(231\) −7.63935 −0.502633
\(232\) 10.4799 0.688039
\(233\) 0.292106 0.0191365 0.00956824 0.999954i \(-0.496954\pi\)
0.00956824 + 0.999954i \(0.496954\pi\)
\(234\) 0 0
\(235\) −4.16738 −0.271850
\(236\) −6.03030 −0.392539
\(237\) −3.77643 −0.245306
\(238\) −7.24840 −0.469844
\(239\) 21.8023 1.41027 0.705137 0.709071i \(-0.250885\pi\)
0.705137 + 0.709071i \(0.250885\pi\)
\(240\) −4.78541 −0.308897
\(241\) 2.54844 0.164160 0.0820798 0.996626i \(-0.473844\pi\)
0.0820798 + 0.996626i \(0.473844\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 18.5877 1.19240
\(244\) −9.78541 −0.626446
\(245\) −9.32592 −0.595811
\(246\) −22.6563 −1.44451
\(247\) 0 0
\(248\) 27.8361 1.76760
\(249\) 12.8236 0.812665
\(250\) −11.6866 −0.739123
\(251\) −26.8192 −1.69281 −0.846407 0.532537i \(-0.821239\pi\)
−0.846407 + 0.532537i \(0.821239\pi\)
\(252\) 7.14605 0.450159
\(253\) −4.52360 −0.284397
\(254\) −11.5102 −0.722215
\(255\) −10.2697 −0.643116
\(256\) −17.0000 −1.06250
\(257\) 3.06854 0.191410 0.0957051 0.995410i \(-0.469489\pi\)
0.0957051 + 0.995410i \(0.469489\pi\)
\(258\) 5.70789 0.355358
\(259\) −30.9484 −1.92304
\(260\) 0 0
\(261\) 7.39095 0.457488
\(262\) −13.6091 −0.840770
\(263\) 2.29211 0.141337 0.0706686 0.997500i \(-0.477487\pi\)
0.0706686 + 0.997500i \(0.477487\pi\)
\(264\) 6.78541 0.417613
\(265\) −16.4079 −1.00793
\(266\) −10.6260 −0.651519
\(267\) 21.1416 1.29385
\(268\) 4.03030 0.246190
\(269\) 11.2449 0.685613 0.342807 0.939406i \(-0.388622\pi\)
0.342807 + 0.939406i \(0.388622\pi\)
\(270\) 4.23150 0.257521
\(271\) 4.29211 0.260727 0.130363 0.991466i \(-0.458386\pi\)
0.130363 + 0.991466i \(0.458386\pi\)
\(272\) 2.14605 0.130124
\(273\) 0 0
\(274\) −15.1024 −0.912366
\(275\) 0.523604 0.0315745
\(276\) 10.2315 0.615864
\(277\) −4.83262 −0.290364 −0.145182 0.989405i \(-0.546377\pi\)
−0.145182 + 0.989405i \(0.546377\pi\)
\(278\) 15.2787 0.916356
\(279\) 19.6314 1.17530
\(280\) 21.4382 1.28118
\(281\) −3.78541 −0.225818 −0.112909 0.993605i \(-0.536017\pi\)
−0.112909 + 0.993605i \(0.536017\pi\)
\(282\) 4.45506 0.265295
\(283\) −12.4248 −0.738575 −0.369288 0.929315i \(-0.620398\pi\)
−0.369288 + 0.929315i \(0.620398\pi\)
\(284\) 6.00000 0.356034
\(285\) −15.0551 −0.891790
\(286\) 0 0
\(287\) 33.8326 1.99708
\(288\) −10.5787 −0.623359
\(289\) −12.3945 −0.729086
\(290\) 7.39095 0.434012
\(291\) 26.3259 1.54325
\(292\) 10.8405 0.634395
\(293\) −16.9012 −0.987376 −0.493688 0.869639i \(-0.664352\pi\)
−0.493688 + 0.869639i \(0.664352\pi\)
\(294\) 9.96970 0.581445
\(295\) −12.7586 −0.742835
\(296\) 27.4889 1.59776
\(297\) −2.00000 −0.116052
\(298\) 4.37755 0.253585
\(299\) 0 0
\(300\) −1.18429 −0.0683750
\(301\) −8.52360 −0.491292
\(302\) 2.29211 0.131896
\(303\) −2.03824 −0.117094
\(304\) 3.14605 0.180439
\(305\) −20.7035 −1.18548
\(306\) 4.54051 0.259564
\(307\) 8.42476 0.480826 0.240413 0.970671i \(-0.422717\pi\)
0.240413 + 0.970671i \(0.422717\pi\)
\(308\) −3.37755 −0.192454
\(309\) −29.5102 −1.67878
\(310\) 19.6314 1.11499
\(311\) −28.5877 −1.62106 −0.810530 0.585697i \(-0.800821\pi\)
−0.810530 + 0.585697i \(0.800821\pi\)
\(312\) 0 0
\(313\) 22.3945 1.26581 0.632905 0.774230i \(-0.281862\pi\)
0.632905 + 0.774230i \(0.281862\pi\)
\(314\) 24.0472 1.35706
\(315\) 15.1193 0.851874
\(316\) −1.66966 −0.0939256
\(317\) 26.2708 1.47551 0.737757 0.675067i \(-0.235885\pi\)
0.737757 + 0.675067i \(0.235885\pi\)
\(318\) 17.5405 0.983623
\(319\) −3.49330 −0.195587
\(320\) −14.8102 −0.827918
\(321\) 30.7810 1.71803
\(322\) 15.2787 0.851449
\(323\) 6.75160 0.375669
\(324\) 10.8709 0.603936
\(325\) 0 0
\(326\) −6.55391 −0.362987
\(327\) 42.2653 2.33728
\(328\) −30.0507 −1.65927
\(329\) −6.65275 −0.366778
\(330\) 4.78541 0.263428
\(331\) 8.29211 0.455775 0.227888 0.973687i \(-0.426818\pi\)
0.227888 + 0.973687i \(0.426818\pi\)
\(332\) 5.66966 0.311163
\(333\) 19.3865 1.06237
\(334\) −18.3259 −1.00275
\(335\) 8.52711 0.465886
\(336\) −7.63935 −0.416761
\(337\) −0.0516349 −0.00281273 −0.00140637 0.999999i \(-0.500448\pi\)
−0.00140637 + 0.999999i \(0.500448\pi\)
\(338\) 0 0
\(339\) −28.5877 −1.55267
\(340\) −4.54051 −0.246244
\(341\) −9.27871 −0.502470
\(342\) 6.65626 0.359929
\(343\) 8.75510 0.472731
\(344\) 7.57081 0.408191
\(345\) 21.6473 1.16545
\(346\) −14.6866 −0.789555
\(347\) −8.62245 −0.462877 −0.231439 0.972850i \(-0.574343\pi\)
−0.231439 + 0.972850i \(0.574343\pi\)
\(348\) 7.90116 0.423546
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) −1.76850 −0.0945304
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) 0.476396 0.0253560 0.0126780 0.999920i \(-0.495964\pi\)
0.0126780 + 0.999920i \(0.495964\pi\)
\(354\) 13.6394 0.724923
\(355\) 12.6945 0.673754
\(356\) 9.34725 0.495403
\(357\) −16.3945 −0.867687
\(358\) 6.49330 0.343182
\(359\) 10.2315 0.539998 0.269999 0.962861i \(-0.412977\pi\)
0.269999 + 0.962861i \(0.412977\pi\)
\(360\) −13.4292 −0.707780
\(361\) −9.10235 −0.479071
\(362\) 17.1630 0.902065
\(363\) −2.26180 −0.118714
\(364\) 0 0
\(365\) 22.9359 1.20052
\(366\) 22.1327 1.15689
\(367\) 21.3393 1.11390 0.556952 0.830545i \(-0.311971\pi\)
0.556952 + 0.830545i \(0.311971\pi\)
\(368\) −4.52360 −0.235809
\(369\) −21.1933 −1.10328
\(370\) 19.3865 1.00786
\(371\) −26.1933 −1.35989
\(372\) 20.9866 1.08810
\(373\) 21.2271 1.09910 0.549548 0.835462i \(-0.314800\pi\)
0.549548 + 0.835462i \(0.314800\pi\)
\(374\) −2.14605 −0.110970
\(375\) −26.4327 −1.36498
\(376\) 5.90909 0.304738
\(377\) 0 0
\(378\) 6.75510 0.347445
\(379\) 1.04721 0.0537915 0.0268958 0.999638i \(-0.491438\pi\)
0.0268958 + 0.999638i \(0.491438\pi\)
\(380\) −6.65626 −0.341459
\(381\) −26.0338 −1.33375
\(382\) −17.9697 −0.919410
\(383\) 28.9866 1.48115 0.740573 0.671976i \(-0.234554\pi\)
0.740573 + 0.671976i \(0.234554\pi\)
\(384\) −6.78541 −0.346266
\(385\) −7.14605 −0.364197
\(386\) −2.96970 −0.151154
\(387\) 5.33931 0.271413
\(388\) 11.6394 0.590899
\(389\) 15.5653 0.789195 0.394597 0.918854i \(-0.370884\pi\)
0.394597 + 0.918854i \(0.370884\pi\)
\(390\) 0 0
\(391\) −9.70789 −0.490949
\(392\) 13.2236 0.667891
\(393\) −30.7810 −1.55270
\(394\) 12.2315 0.616214
\(395\) −3.53258 −0.177743
\(396\) 2.11575 0.106320
\(397\) −18.9787 −0.952512 −0.476256 0.879307i \(-0.658006\pi\)
−0.476256 + 0.879307i \(0.658006\pi\)
\(398\) 0.201195 0.0100850
\(399\) −24.0338 −1.20320
\(400\) 0.523604 0.0261802
\(401\) 9.52360 0.475586 0.237793 0.971316i \(-0.423576\pi\)
0.237793 + 0.971316i \(0.423576\pi\)
\(402\) −9.11575 −0.454652
\(403\) 0 0
\(404\) −0.901156 −0.0448342
\(405\) 23.0000 1.14288
\(406\) 11.7988 0.585565
\(407\) −9.16296 −0.454191
\(408\) 14.5618 0.720919
\(409\) −9.91455 −0.490243 −0.245122 0.969492i \(-0.578828\pi\)
−0.245122 + 0.969492i \(0.578828\pi\)
\(410\) −21.1933 −1.04666
\(411\) −34.1585 −1.68492
\(412\) −13.0472 −0.642790
\(413\) −20.3677 −1.00223
\(414\) −9.57081 −0.470380
\(415\) 11.9956 0.588840
\(416\) 0 0
\(417\) 34.5574 1.69228
\(418\) −3.14605 −0.153878
\(419\) 7.01340 0.342627 0.171313 0.985217i \(-0.445199\pi\)
0.171313 + 0.985217i \(0.445199\pi\)
\(420\) 16.1630 0.788672
\(421\) −33.9787 −1.65602 −0.828009 0.560714i \(-0.810527\pi\)
−0.828009 + 0.560714i \(0.810527\pi\)
\(422\) −11.6697 −0.568070
\(423\) 4.16738 0.202625
\(424\) 23.2653 1.12986
\(425\) 1.12368 0.0545066
\(426\) −13.5708 −0.657508
\(427\) −33.0507 −1.59944
\(428\) 13.6091 0.657818
\(429\) 0 0
\(430\) 5.33931 0.257485
\(431\) −7.86735 −0.378957 −0.189478 0.981885i \(-0.560680\pi\)
−0.189478 + 0.981885i \(0.560680\pi\)
\(432\) −2.00000 −0.0962250
\(433\) −13.6528 −0.656109 −0.328055 0.944659i \(-0.606393\pi\)
−0.328055 + 0.944659i \(0.606393\pi\)
\(434\) 31.3393 1.50434
\(435\) 16.7169 0.801512
\(436\) 18.6866 0.894924
\(437\) −14.2315 −0.680785
\(438\) −24.5192 −1.17157
\(439\) −8.33034 −0.397586 −0.198793 0.980042i \(-0.563702\pi\)
−0.198793 + 0.980042i \(0.563702\pi\)
\(440\) 6.34725 0.302593
\(441\) 9.32592 0.444091
\(442\) 0 0
\(443\) −25.2484 −1.19959 −0.599794 0.800154i \(-0.704751\pi\)
−0.599794 + 0.800154i \(0.704751\pi\)
\(444\) 20.7248 0.983555
\(445\) 19.7764 0.937493
\(446\) −7.50670 −0.355452
\(447\) 9.90116 0.468309
\(448\) −23.6429 −1.11702
\(449\) 37.2708 1.75892 0.879458 0.475976i \(-0.157905\pi\)
0.879458 + 0.475976i \(0.157905\pi\)
\(450\) 1.10782 0.0522229
\(451\) 10.0169 0.471678
\(452\) −12.6394 −0.594505
\(453\) 5.18429 0.243579
\(454\) −3.47640 −0.163155
\(455\) 0 0
\(456\) 21.3472 0.999676
\(457\) 3.09091 0.144587 0.0722933 0.997383i \(-0.476968\pi\)
0.0722933 + 0.997383i \(0.476968\pi\)
\(458\) 13.4079 0.626508
\(459\) −4.29211 −0.200338
\(460\) 9.57081 0.446241
\(461\) 22.4799 1.04699 0.523497 0.852028i \(-0.324627\pi\)
0.523497 + 0.852028i \(0.324627\pi\)
\(462\) 7.63935 0.355415
\(463\) 29.0507 1.35010 0.675051 0.737771i \(-0.264122\pi\)
0.675051 + 0.737771i \(0.264122\pi\)
\(464\) −3.49330 −0.162172
\(465\) 44.4024 2.05911
\(466\) −0.292106 −0.0135315
\(467\) −7.47990 −0.346129 −0.173064 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(468\) 0 0
\(469\) 13.6126 0.628570
\(470\) 4.16738 0.192227
\(471\) 54.3900 2.50616
\(472\) 18.0909 0.832702
\(473\) −2.52360 −0.116035
\(474\) 3.77643 0.173457
\(475\) 1.64729 0.0755827
\(476\) −7.24840 −0.332230
\(477\) 16.4079 0.751264
\(478\) −21.8023 −0.997215
\(479\) −8.62245 −0.393970 −0.196985 0.980407i \(-0.563115\pi\)
−0.196985 + 0.980407i \(0.563115\pi\)
\(480\) −23.9270 −1.09211
\(481\) 0 0
\(482\) −2.54844 −0.116078
\(483\) 34.5574 1.57242
\(484\) −1.00000 −0.0454545
\(485\) 24.6260 1.11821
\(486\) −18.5877 −0.843156
\(487\) −8.09091 −0.366634 −0.183317 0.983054i \(-0.558683\pi\)
−0.183317 + 0.983054i \(0.558683\pi\)
\(488\) 29.3562 1.32889
\(489\) −14.8236 −0.670348
\(490\) 9.32592 0.421302
\(491\) 4.62245 0.208608 0.104304 0.994545i \(-0.466738\pi\)
0.104304 + 0.994545i \(0.466738\pi\)
\(492\) −22.6563 −1.02142
\(493\) −7.49681 −0.337639
\(494\) 0 0
\(495\) 4.47640 0.201199
\(496\) −9.27871 −0.416626
\(497\) 20.2653 0.909023
\(498\) −12.8236 −0.574641
\(499\) −39.5137 −1.76888 −0.884438 0.466657i \(-0.845458\pi\)
−0.884438 + 0.466657i \(0.845458\pi\)
\(500\) −11.6866 −0.522639
\(501\) −41.4496 −1.85183
\(502\) 26.8192 1.19700
\(503\) −37.7035 −1.68111 −0.840557 0.541723i \(-0.817772\pi\)
−0.840557 + 0.541723i \(0.817772\pi\)
\(504\) −21.4382 −0.954931
\(505\) −1.90662 −0.0848435
\(506\) 4.52360 0.201099
\(507\) 0 0
\(508\) −11.5102 −0.510683
\(509\) 7.72129 0.342240 0.171120 0.985250i \(-0.445261\pi\)
0.171120 + 0.985250i \(0.445261\pi\)
\(510\) 10.2697 0.454752
\(511\) 36.6145 1.61973
\(512\) 11.0000 0.486136
\(513\) −6.29211 −0.277803
\(514\) −3.06854 −0.135348
\(515\) −27.6046 −1.21641
\(516\) 5.70789 0.251276
\(517\) −1.96970 −0.0866272
\(518\) 30.9484 1.35979
\(519\) −33.2181 −1.45811
\(520\) 0 0
\(521\) 5.48979 0.240512 0.120256 0.992743i \(-0.461628\pi\)
0.120256 + 0.992743i \(0.461628\pi\)
\(522\) −7.39095 −0.323493
\(523\) 41.2137 1.80215 0.901074 0.433665i \(-0.142780\pi\)
0.901074 + 0.433665i \(0.142780\pi\)
\(524\) −13.6091 −0.594514
\(525\) −4.00000 −0.174574
\(526\) −2.29211 −0.0999406
\(527\) −19.9126 −0.867406
\(528\) −2.26180 −0.0984323
\(529\) −2.53700 −0.110304
\(530\) 16.4079 0.712712
\(531\) 12.7586 0.553677
\(532\) −10.6260 −0.460694
\(533\) 0 0
\(534\) −21.1416 −0.914888
\(535\) 28.7933 1.24484
\(536\) −12.0909 −0.522248
\(537\) 14.6866 0.633772
\(538\) −11.2449 −0.484802
\(539\) −4.40786 −0.189860
\(540\) 4.23150 0.182095
\(541\) −31.2539 −1.34371 −0.671854 0.740683i \(-0.734502\pi\)
−0.671854 + 0.740683i \(0.734502\pi\)
\(542\) −4.29211 −0.184362
\(543\) 38.8192 1.66589
\(544\) 10.7303 0.460056
\(545\) 39.5361 1.69354
\(546\) 0 0
\(547\) 2.40239 0.102719 0.0513594 0.998680i \(-0.483645\pi\)
0.0513594 + 0.998680i \(0.483645\pi\)
\(548\) −15.1024 −0.645140
\(549\) 20.7035 0.883602
\(550\) −0.523604 −0.0223266
\(551\) −10.9901 −0.468194
\(552\) −30.6945 −1.30644
\(553\) −5.63935 −0.239810
\(554\) 4.83262 0.205318
\(555\) 43.8485 1.86126
\(556\) 15.2787 0.647962
\(557\) −2.44609 −0.103644 −0.0518221 0.998656i \(-0.516503\pi\)
−0.0518221 + 0.998656i \(0.516503\pi\)
\(558\) −19.6314 −0.831064
\(559\) 0 0
\(560\) −7.14605 −0.301976
\(561\) −4.85395 −0.204934
\(562\) 3.78541 0.159678
\(563\) 38.4586 1.62084 0.810418 0.585852i \(-0.199240\pi\)
0.810418 + 0.585852i \(0.199240\pi\)
\(564\) 4.45506 0.187592
\(565\) −26.7417 −1.12503
\(566\) 12.4248 0.522252
\(567\) 36.7169 1.54196
\(568\) −18.0000 −0.755263
\(569\) 39.2519 1.64553 0.822763 0.568385i \(-0.192431\pi\)
0.822763 + 0.568385i \(0.192431\pi\)
\(570\) 15.0551 0.630591
\(571\) −39.3349 −1.64611 −0.823057 0.567959i \(-0.807733\pi\)
−0.823057 + 0.567959i \(0.807733\pi\)
\(572\) 0 0
\(573\) −40.6439 −1.69792
\(574\) −33.8326 −1.41215
\(575\) −2.36858 −0.0987766
\(576\) 14.8102 0.617094
\(577\) 24.0890 1.00284 0.501418 0.865205i \(-0.332812\pi\)
0.501418 + 0.865205i \(0.332812\pi\)
\(578\) 12.3945 0.515541
\(579\) −6.71687 −0.279143
\(580\) 7.39095 0.306892
\(581\) 19.1496 0.794458
\(582\) −26.3259 −1.09124
\(583\) −7.75510 −0.321184
\(584\) −32.5216 −1.34576
\(585\) 0 0
\(586\) 16.9012 0.698180
\(587\) −24.4665 −1.00984 −0.504920 0.863166i \(-0.668478\pi\)
−0.504920 + 0.863166i \(0.668478\pi\)
\(588\) 9.96970 0.411143
\(589\) −29.1913 −1.20281
\(590\) 12.7586 0.525264
\(591\) 27.6652 1.13800
\(592\) −9.16296 −0.376595
\(593\) −33.6215 −1.38067 −0.690335 0.723490i \(-0.742537\pi\)
−0.690335 + 0.723490i \(0.742537\pi\)
\(594\) 2.00000 0.0820610
\(595\) −15.3358 −0.628707
\(596\) 4.37755 0.179312
\(597\) 0.455064 0.0186245
\(598\) 0 0
\(599\) 3.01340 0.123124 0.0615621 0.998103i \(-0.480392\pi\)
0.0615621 + 0.998103i \(0.480392\pi\)
\(600\) 3.55287 0.145045
\(601\) −18.5743 −0.757662 −0.378831 0.925466i \(-0.623674\pi\)
−0.378831 + 0.925466i \(0.623674\pi\)
\(602\) 8.52360 0.347396
\(603\) −8.52711 −0.347251
\(604\) 2.29211 0.0932645
\(605\) −2.11575 −0.0860174
\(606\) 2.03824 0.0827977
\(607\) −19.2137 −0.779859 −0.389930 0.920845i \(-0.627501\pi\)
−0.389930 + 0.920845i \(0.627501\pi\)
\(608\) 15.7303 0.637946
\(609\) 26.6866 1.08139
\(610\) 20.7035 0.838259
\(611\) 0 0
\(612\) 4.54051 0.183539
\(613\) −18.9350 −0.764776 −0.382388 0.924002i \(-0.624898\pi\)
−0.382388 + 0.924002i \(0.624898\pi\)
\(614\) −8.42476 −0.339996
\(615\) −47.9350 −1.93292
\(616\) 10.1327 0.408256
\(617\) 1.72129 0.0692966 0.0346483 0.999400i \(-0.488969\pi\)
0.0346483 + 0.999400i \(0.488969\pi\)
\(618\) 29.5102 1.18707
\(619\) −16.3562 −0.657412 −0.328706 0.944432i \(-0.606613\pi\)
−0.328706 + 0.944432i \(0.606613\pi\)
\(620\) 19.6314 0.788417
\(621\) 9.04721 0.363052
\(622\) 28.5877 1.14626
\(623\) 31.5708 1.26486
\(624\) 0 0
\(625\) −22.1078 −0.884313
\(626\) −22.3945 −0.895063
\(627\) −7.11575 −0.284176
\(628\) 24.0472 0.959588
\(629\) −19.6642 −0.784063
\(630\) −15.1193 −0.602366
\(631\) 21.0775 0.839083 0.419541 0.907736i \(-0.362191\pi\)
0.419541 + 0.907736i \(0.362191\pi\)
\(632\) 5.00897 0.199246
\(633\) −26.3945 −1.04909
\(634\) −26.2708 −1.04335
\(635\) −24.3527 −0.966408
\(636\) 17.5405 0.695526
\(637\) 0 0
\(638\) 3.49330 0.138301
\(639\) −12.6945 −0.502187
\(640\) −6.34725 −0.250897
\(641\) −4.53700 −0.179201 −0.0896004 0.995978i \(-0.528559\pi\)
−0.0896004 + 0.995978i \(0.528559\pi\)
\(642\) −30.7810 −1.21483
\(643\) 0.983094 0.0387695 0.0193847 0.999812i \(-0.493829\pi\)
0.0193847 + 0.999812i \(0.493829\pi\)
\(644\) 15.2787 0.602065
\(645\) 12.0765 0.475511
\(646\) −6.75160 −0.265638
\(647\) −46.6856 −1.83540 −0.917701 0.397272i \(-0.869957\pi\)
−0.917701 + 0.397272i \(0.869957\pi\)
\(648\) −32.6126 −1.28114
\(649\) −6.03030 −0.236710
\(650\) 0 0
\(651\) 70.8833 2.77814
\(652\) −6.55391 −0.256671
\(653\) −25.8709 −1.01240 −0.506202 0.862415i \(-0.668951\pi\)
−0.506202 + 0.862415i \(0.668951\pi\)
\(654\) −42.2653 −1.65270
\(655\) −28.7933 −1.12505
\(656\) 10.0169 0.391094
\(657\) −22.9359 −0.894814
\(658\) 6.65275 0.259351
\(659\) 17.4988 0.681655 0.340828 0.940126i \(-0.389293\pi\)
0.340828 + 0.940126i \(0.389293\pi\)
\(660\) 4.78541 0.186272
\(661\) −21.6528 −0.842194 −0.421097 0.907016i \(-0.638355\pi\)
−0.421097 + 0.907016i \(0.638355\pi\)
\(662\) −8.29211 −0.322282
\(663\) 0 0
\(664\) −17.0090 −0.660076
\(665\) −22.4819 −0.871809
\(666\) −19.3865 −0.751213
\(667\) 15.8023 0.611868
\(668\) −18.3259 −0.709051
\(669\) −16.9787 −0.656433
\(670\) −8.52711 −0.329431
\(671\) −9.78541 −0.377761
\(672\) −38.1968 −1.47347
\(673\) −23.8798 −0.920500 −0.460250 0.887789i \(-0.652240\pi\)
−0.460250 + 0.887789i \(0.652240\pi\)
\(674\) 0.0516349 0.00198890
\(675\) −1.04721 −0.0403071
\(676\) 0 0
\(677\) −12.6945 −0.487889 −0.243945 0.969789i \(-0.578441\pi\)
−0.243945 + 0.969789i \(0.578441\pi\)
\(678\) 28.5877 1.09790
\(679\) 39.3125 1.50868
\(680\) 13.6215 0.522362
\(681\) −7.86292 −0.301308
\(682\) 9.27871 0.355300
\(683\) 37.8699 1.44905 0.724526 0.689247i \(-0.242059\pi\)
0.724526 + 0.689247i \(0.242059\pi\)
\(684\) 6.65626 0.254508
\(685\) −31.9528 −1.22085
\(686\) −8.75510 −0.334271
\(687\) 30.3259 1.15701
\(688\) −2.52360 −0.0962115
\(689\) 0 0
\(690\) −21.6473 −0.824098
\(691\) −25.7417 −0.979261 −0.489630 0.871930i \(-0.662868\pi\)
−0.489630 + 0.871930i \(0.662868\pi\)
\(692\) −14.6866 −0.558299
\(693\) 7.14605 0.271456
\(694\) 8.62245 0.327304
\(695\) 32.3259 1.22619
\(696\) −23.7035 −0.898478
\(697\) 21.4968 0.814250
\(698\) 30.0000 1.13552
\(699\) −0.660685 −0.0249894
\(700\) −1.76850 −0.0668431
\(701\) −33.5023 −1.26536 −0.632682 0.774412i \(-0.718046\pi\)
−0.632682 + 0.774412i \(0.718046\pi\)
\(702\) 0 0
\(703\) −28.8272 −1.08724
\(704\) −7.00000 −0.263822
\(705\) 9.42580 0.354996
\(706\) −0.476396 −0.0179294
\(707\) −3.04370 −0.114470
\(708\) 13.6394 0.512598
\(709\) 30.9235 1.16136 0.580679 0.814133i \(-0.302787\pi\)
0.580679 + 0.814133i \(0.302787\pi\)
\(710\) −12.6945 −0.476416
\(711\) 3.53258 0.132482
\(712\) −28.0417 −1.05091
\(713\) 41.9732 1.57191
\(714\) 16.3945 0.613547
\(715\) 0 0
\(716\) 6.49330 0.242666
\(717\) −49.3125 −1.84161
\(718\) −10.2315 −0.381836
\(719\) 9.21810 0.343777 0.171889 0.985116i \(-0.445013\pi\)
0.171889 + 0.985116i \(0.445013\pi\)
\(720\) 4.47640 0.166825
\(721\) −44.0676 −1.64116
\(722\) 9.10235 0.338754
\(723\) −5.76408 −0.214368
\(724\) 17.1630 0.637856
\(725\) −1.82911 −0.0679314
\(726\) 2.26180 0.0839434
\(727\) 33.5102 1.24282 0.621412 0.783484i \(-0.286559\pi\)
0.621412 + 0.783484i \(0.286559\pi\)
\(728\) 0 0
\(729\) −9.42919 −0.349229
\(730\) −22.9359 −0.848895
\(731\) −5.41579 −0.200310
\(732\) 22.1327 0.818046
\(733\) 1.29561 0.0478546 0.0239273 0.999714i \(-0.492383\pi\)
0.0239273 + 0.999714i \(0.492383\pi\)
\(734\) −21.3393 −0.787648
\(735\) 21.0934 0.778041
\(736\) −22.6180 −0.833711
\(737\) 4.03030 0.148458
\(738\) 21.1933 0.780135
\(739\) −28.8495 −1.06125 −0.530623 0.847608i \(-0.678042\pi\)
−0.530623 + 0.847608i \(0.678042\pi\)
\(740\) 19.3865 0.712663
\(741\) 0 0
\(742\) 26.1933 0.961585
\(743\) 31.7373 1.16433 0.582164 0.813071i \(-0.302206\pi\)
0.582164 + 0.813071i \(0.302206\pi\)
\(744\) −62.9598 −2.30822
\(745\) 9.26180 0.339326
\(746\) −21.2271 −0.777178
\(747\) −11.9956 −0.438895
\(748\) −2.14605 −0.0784675
\(749\) 45.9653 1.67953
\(750\) 26.4327 0.965186
\(751\) −36.1282 −1.31834 −0.659169 0.751995i \(-0.729092\pi\)
−0.659169 + 0.751995i \(0.729092\pi\)
\(752\) −1.96970 −0.0718274
\(753\) 60.6598 2.21056
\(754\) 0 0
\(755\) 4.84952 0.176492
\(756\) 6.75510 0.245681
\(757\) −22.0527 −0.801518 −0.400759 0.916183i \(-0.631254\pi\)
−0.400759 + 0.916183i \(0.631254\pi\)
\(758\) −1.04721 −0.0380363
\(759\) 10.2315 0.371380
\(760\) 19.9688 0.724344
\(761\) −40.1620 −1.45587 −0.727936 0.685645i \(-0.759520\pi\)
−0.727936 + 0.685645i \(0.759520\pi\)
\(762\) 26.0338 0.943105
\(763\) 63.1148 2.28491
\(764\) −17.9697 −0.650121
\(765\) 9.60658 0.347327
\(766\) −28.9866 −1.04733
\(767\) 0 0
\(768\) 38.4506 1.38747
\(769\) 24.9598 0.900074 0.450037 0.893010i \(-0.351411\pi\)
0.450037 + 0.893010i \(0.351411\pi\)
\(770\) 7.14605 0.257526
\(771\) −6.94043 −0.249954
\(772\) −2.96970 −0.106882
\(773\) −5.46846 −0.196687 −0.0983435 0.995153i \(-0.531354\pi\)
−0.0983435 + 0.995153i \(0.531354\pi\)
\(774\) −5.33931 −0.191918
\(775\) −4.85837 −0.174518
\(776\) −34.9181 −1.25349
\(777\) 69.9991 2.51120
\(778\) −15.5653 −0.558045
\(779\) 31.5137 1.12910
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 9.70789 0.347154
\(783\) 6.98660 0.249681
\(784\) −4.40786 −0.157423
\(785\) 50.8779 1.81591
\(786\) 30.7810 1.09792
\(787\) −37.5484 −1.33846 −0.669229 0.743056i \(-0.733375\pi\)
−0.669229 + 0.743056i \(0.733375\pi\)
\(788\) 12.2315 0.435729
\(789\) −5.18429 −0.184566
\(790\) 3.53258 0.125683
\(791\) −42.6901 −1.51788
\(792\) −6.34725 −0.225540
\(793\) 0 0
\(794\) 18.9787 0.673528
\(795\) 37.1113 1.31620
\(796\) 0.201195 0.00713118
\(797\) 7.76057 0.274893 0.137447 0.990509i \(-0.456110\pi\)
0.137447 + 0.990509i \(0.456110\pi\)
\(798\) 24.0338 0.850788
\(799\) −4.22707 −0.149543
\(800\) 2.61802 0.0925611
\(801\) −19.7764 −0.698766
\(802\) −9.52360 −0.336290
\(803\) 10.8405 0.382555
\(804\) −9.11575 −0.321488
\(805\) 32.3259 1.13934
\(806\) 0 0
\(807\) −25.4337 −0.895310
\(808\) 2.70347 0.0951077
\(809\) −6.80674 −0.239312 −0.119656 0.992815i \(-0.538179\pi\)
−0.119656 + 0.992815i \(0.538179\pi\)
\(810\) −23.0000 −0.808138
\(811\) 37.0810 1.30209 0.651045 0.759039i \(-0.274331\pi\)
0.651045 + 0.759039i \(0.274331\pi\)
\(812\) 11.7988 0.414057
\(813\) −9.70789 −0.340471
\(814\) 9.16296 0.321162
\(815\) −13.8664 −0.485720
\(816\) −4.85395 −0.169922
\(817\) −7.93939 −0.277764
\(818\) 9.91455 0.346654
\(819\) 0 0
\(820\) −21.1933 −0.740101
\(821\) 0.170892 0.00596417 0.00298208 0.999996i \(-0.499051\pi\)
0.00298208 + 0.999996i \(0.499051\pi\)
\(822\) 34.1585 1.19142
\(823\) 14.9260 0.520287 0.260144 0.965570i \(-0.416230\pi\)
0.260144 + 0.965570i \(0.416230\pi\)
\(824\) 39.1416 1.36356
\(825\) −1.18429 −0.0412317
\(826\) 20.3677 0.708682
\(827\) −10.0114 −0.348132 −0.174066 0.984734i \(-0.555691\pi\)
−0.174066 + 0.984734i \(0.555691\pi\)
\(828\) −9.57081 −0.332609
\(829\) −3.59214 −0.124760 −0.0623802 0.998052i \(-0.519869\pi\)
−0.0623802 + 0.998052i \(0.519869\pi\)
\(830\) −11.9956 −0.416372
\(831\) 10.9304 0.379172
\(832\) 0 0
\(833\) −9.45949 −0.327752
\(834\) −34.5574 −1.19663
\(835\) −38.7730 −1.34180
\(836\) −3.14605 −0.108809
\(837\) 18.5574 0.641438
\(838\) −7.01340 −0.242274
\(839\) 27.2216 0.939794 0.469897 0.882721i \(-0.344291\pi\)
0.469897 + 0.882721i \(0.344291\pi\)
\(840\) −48.4889 −1.67303
\(841\) −16.7968 −0.579202
\(842\) 33.9787 1.17098
\(843\) 8.56184 0.294885
\(844\) −11.6697 −0.401686
\(845\) 0 0
\(846\) −4.16738 −0.143278
\(847\) −3.37755 −0.116054
\(848\) −7.75510 −0.266311
\(849\) 28.1024 0.964470
\(850\) −1.12368 −0.0385420
\(851\) 41.4496 1.42087
\(852\) −13.5708 −0.464928
\(853\) −26.7114 −0.914581 −0.457290 0.889317i \(-0.651180\pi\)
−0.457290 + 0.889317i \(0.651180\pi\)
\(854\) 33.0507 1.13097
\(855\) 14.0830 0.481628
\(856\) −40.8272 −1.39544
\(857\) −26.6955 −0.911902 −0.455951 0.890005i \(-0.650701\pi\)
−0.455951 + 0.890005i \(0.650701\pi\)
\(858\) 0 0
\(859\) −21.3855 −0.729663 −0.364832 0.931073i \(-0.618873\pi\)
−0.364832 + 0.931073i \(0.618873\pi\)
\(860\) 5.33931 0.182069
\(861\) −76.5227 −2.60789
\(862\) 7.86735 0.267963
\(863\) −0.694496 −0.0236409 −0.0118205 0.999930i \(-0.503763\pi\)
−0.0118205 + 0.999930i \(0.503763\pi\)
\(864\) −10.0000 −0.340207
\(865\) −31.0731 −1.05652
\(866\) 13.6528 0.463939
\(867\) 28.0338 0.952078
\(868\) 31.3393 1.06373
\(869\) −1.66966 −0.0566392
\(870\) −16.7169 −0.566755
\(871\) 0 0
\(872\) −56.0597 −1.89842
\(873\) −24.6260 −0.833462
\(874\) 14.2315 0.481388
\(875\) −39.4720 −1.33440
\(876\) −24.5192 −0.828426
\(877\) 17.2609 0.582859 0.291429 0.956592i \(-0.405869\pi\)
0.291429 + 0.956592i \(0.405869\pi\)
\(878\) 8.33034 0.281135
\(879\) 38.2271 1.28937
\(880\) −2.11575 −0.0713219
\(881\) 27.7889 0.936232 0.468116 0.883667i \(-0.344933\pi\)
0.468116 + 0.883667i \(0.344933\pi\)
\(882\) −9.32592 −0.314020
\(883\) 13.1505 0.442549 0.221274 0.975212i \(-0.428978\pi\)
0.221274 + 0.975212i \(0.428978\pi\)
\(884\) 0 0
\(885\) 28.8575 0.970033
\(886\) 25.2484 0.848237
\(887\) −53.0204 −1.78025 −0.890126 0.455715i \(-0.849384\pi\)
−0.890126 + 0.455715i \(0.849384\pi\)
\(888\) −62.1744 −2.08644
\(889\) −38.8763 −1.30387
\(890\) −19.7764 −0.662908
\(891\) 10.8709 0.364187
\(892\) −7.50670 −0.251343
\(893\) −6.19677 −0.207367
\(894\) −9.90116 −0.331144
\(895\) 13.7382 0.459217
\(896\) −10.1327 −0.338508
\(897\) 0 0
\(898\) −37.2708 −1.24374
\(899\) 32.4133 1.08104
\(900\) 1.10782 0.0369272
\(901\) −16.6429 −0.554454
\(902\) −10.0169 −0.333526
\(903\) 19.2787 0.641555
\(904\) 37.9181 1.26114
\(905\) 36.3125 1.20707
\(906\) −5.18429 −0.172236
\(907\) −54.8192 −1.82024 −0.910121 0.414342i \(-0.864012\pi\)
−0.910121 + 0.414342i \(0.864012\pi\)
\(908\) −3.47640 −0.115368
\(909\) 1.90662 0.0632386
\(910\) 0 0
\(911\) −25.4799 −0.844187 −0.422093 0.906552i \(-0.638705\pi\)
−0.422093 + 0.906552i \(0.638705\pi\)
\(912\) −7.11575 −0.235626
\(913\) 5.66966 0.187638
\(914\) −3.09091 −0.102238
\(915\) 46.8272 1.54806
\(916\) 13.4079 0.443008
\(917\) −45.9653 −1.51791
\(918\) 4.29211 0.141661
\(919\) −14.2156 −0.468930 −0.234465 0.972125i \(-0.575334\pi\)
−0.234465 + 0.972125i \(0.575334\pi\)
\(920\) −28.7124 −0.946621
\(921\) −19.0551 −0.627888
\(922\) −22.4799 −0.740336
\(923\) 0 0
\(924\) 7.63935 0.251316
\(925\) −4.79777 −0.157750
\(926\) −29.0507 −0.954666
\(927\) 27.6046 0.906655
\(928\) −17.4665 −0.573366
\(929\) 4.60462 0.151073 0.0755364 0.997143i \(-0.475933\pi\)
0.0755364 + 0.997143i \(0.475933\pi\)
\(930\) −44.4024 −1.45601
\(931\) −13.8673 −0.454484
\(932\) −0.292106 −0.00956824
\(933\) 64.6598 2.11687
\(934\) 7.47990 0.244750
\(935\) −4.54051 −0.148491
\(936\) 0 0
\(937\) −54.9002 −1.79351 −0.896756 0.442525i \(-0.854083\pi\)
−0.896756 + 0.442525i \(0.854083\pi\)
\(938\) −13.6126 −0.444466
\(939\) −50.6518 −1.65296
\(940\) 4.16738 0.135925
\(941\) 0.292106 0.00952237 0.00476119 0.999989i \(-0.498484\pi\)
0.00476119 + 0.999989i \(0.498484\pi\)
\(942\) −54.3900 −1.77212
\(943\) −45.3125 −1.47558
\(944\) −6.03030 −0.196270
\(945\) 14.2921 0.464922
\(946\) 2.52360 0.0820495
\(947\) 4.46300 0.145028 0.0725140 0.997367i \(-0.476898\pi\)
0.0725140 + 0.997367i \(0.476898\pi\)
\(948\) 3.77643 0.122653
\(949\) 0 0
\(950\) −1.64729 −0.0534451
\(951\) −59.4193 −1.92680
\(952\) 21.7452 0.704766
\(953\) −40.4809 −1.31131 −0.655653 0.755062i \(-0.727607\pi\)
−0.655653 + 0.755062i \(0.727607\pi\)
\(954\) −16.4079 −0.531224
\(955\) −38.0194 −1.23028
\(956\) −21.8023 −0.705137
\(957\) 7.90116 0.255408
\(958\) 8.62245 0.278579
\(959\) −51.0090 −1.64717
\(960\) 33.4978 1.08114
\(961\) 55.0944 1.77724
\(962\) 0 0
\(963\) −28.7933 −0.927852
\(964\) −2.54844 −0.0820798
\(965\) −6.28313 −0.202261
\(966\) −34.5574 −1.11187
\(967\) 1.00897 0.0324464 0.0162232 0.999868i \(-0.494836\pi\)
0.0162232 + 0.999868i \(0.494836\pi\)
\(968\) 3.00000 0.0964237
\(969\) −15.2708 −0.490568
\(970\) −24.6260 −0.790692
\(971\) 25.8664 0.830093 0.415047 0.909800i \(-0.363765\pi\)
0.415047 + 0.909800i \(0.363765\pi\)
\(972\) −18.5877 −0.596201
\(973\) 51.6046 1.65437
\(974\) 8.09091 0.259249
\(975\) 0 0
\(976\) −9.78541 −0.313223
\(977\) 43.3677 1.38745 0.693727 0.720238i \(-0.255967\pi\)
0.693727 + 0.720238i \(0.255967\pi\)
\(978\) 14.8236 0.474008
\(979\) 9.34725 0.298739
\(980\) 9.32592 0.297905
\(981\) −39.5361 −1.26229
\(982\) −4.62245 −0.147508
\(983\) 17.0472 0.543722 0.271861 0.962337i \(-0.412361\pi\)
0.271861 + 0.962337i \(0.412361\pi\)
\(984\) 67.9688 2.16677
\(985\) 25.8788 0.824567
\(986\) 7.49681 0.238747
\(987\) 15.0472 0.478958
\(988\) 0 0
\(989\) 11.4158 0.363001
\(990\) −4.47640 −0.142269
\(991\) −40.0979 −1.27375 −0.636876 0.770966i \(-0.719774\pi\)
−0.636876 + 0.770966i \(0.719774\pi\)
\(992\) −46.3935 −1.47300
\(993\) −18.7551 −0.595175
\(994\) −20.2653 −0.642777
\(995\) 0.425679 0.0134949
\(996\) −12.8236 −0.406333
\(997\) −54.0428 −1.71155 −0.855776 0.517346i \(-0.826920\pi\)
−0.855776 + 0.517346i \(0.826920\pi\)
\(998\) 39.5137 1.25078
\(999\) 18.3259 0.579806
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.1.1 3
13.4 even 6 143.2.e.a.133.3 yes 6
13.10 even 6 143.2.e.a.100.3 6
13.12 even 2 1859.2.a.h.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.2.e.a.100.3 6 13.10 even 6
143.2.e.a.133.3 yes 6 13.4 even 6
1859.2.a.e.1.1 3 1.1 even 1 trivial
1859.2.a.h.1.1 3 13.12 even 2