Properties

Label 5733.2.a.bu.1.6
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.4507648.1
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 637)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.66745\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.44785 q^{2} +3.99195 q^{4} +0.910286 q^{5} +4.87599 q^{8} +O(q^{10})\) \(q+2.44785 q^{2} +3.99195 q^{4} +0.910286 q^{5} +4.87599 q^{8} +2.22824 q^{10} -3.67837 q^{11} -1.00000 q^{13} +3.95177 q^{16} +7.18531 q^{17} +1.97802 q^{19} +3.63382 q^{20} -9.00407 q^{22} +0.596700 q^{23} -4.17138 q^{25} -2.44785 q^{26} +3.64900 q^{29} +7.08833 q^{31} -0.0786478 q^{32} +17.5885 q^{34} +0.710851 q^{37} +4.84189 q^{38} +4.43855 q^{40} +5.27529 q^{41} +11.0790 q^{43} -14.6839 q^{44} +1.46063 q^{46} +12.1135 q^{47} -10.2109 q^{50} -3.99195 q^{52} +11.4484 q^{53} -3.34837 q^{55} +8.93219 q^{58} +9.58986 q^{59} -6.98536 q^{61} +17.3511 q^{62} -8.09606 q^{64} -0.910286 q^{65} +1.22839 q^{67} +28.6834 q^{68} -11.3635 q^{71} -6.53419 q^{73} +1.74005 q^{74} +7.89616 q^{76} -11.5204 q^{79} +3.59725 q^{80} +12.9131 q^{82} +7.16403 q^{83} +6.54069 q^{85} +27.1198 q^{86} -17.9357 q^{88} +12.8490 q^{89} +2.38200 q^{92} +29.6520 q^{94} +1.80056 q^{95} -9.09062 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 4 q^{4} + 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 4 q^{4} + 6 q^{5} - 4 q^{10} - 4 q^{11} - 6 q^{13} + 16 q^{17} - 2 q^{19} + 16 q^{20} - 12 q^{22} + 6 q^{23} - 4 q^{25} + 6 q^{29} - 6 q^{31} + 20 q^{32} + 8 q^{38} - 4 q^{40} - 8 q^{41} + 2 q^{43} + 4 q^{44} + 8 q^{46} + 30 q^{47} - 8 q^{50} - 4 q^{52} + 14 q^{53} + 8 q^{55} - 8 q^{58} + 24 q^{59} + 28 q^{62} - 20 q^{64} - 6 q^{65} + 16 q^{67} + 28 q^{68} - 8 q^{71} + 6 q^{73} + 12 q^{74} + 16 q^{76} - 22 q^{79} - 28 q^{80} + 40 q^{82} + 50 q^{83} - 8 q^{85} + 16 q^{86} - 44 q^{88} + 26 q^{89} - 20 q^{92} + 32 q^{94} + 6 q^{95} + 14 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.44785 1.73089 0.865444 0.501005i \(-0.167036\pi\)
0.865444 + 0.501005i \(0.167036\pi\)
\(3\) 0 0
\(4\) 3.99195 1.99598
\(5\) 0.910286 0.407092 0.203546 0.979065i \(-0.434753\pi\)
0.203546 + 0.979065i \(0.434753\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 4.87599 1.72392
\(9\) 0 0
\(10\) 2.22824 0.704632
\(11\) −3.67837 −1.10907 −0.554534 0.832161i \(-0.687104\pi\)
−0.554534 + 0.832161i \(0.687104\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 3.95177 0.987943
\(17\) 7.18531 1.74269 0.871347 0.490668i \(-0.163247\pi\)
0.871347 + 0.490668i \(0.163247\pi\)
\(18\) 0 0
\(19\) 1.97802 0.453789 0.226894 0.973919i \(-0.427143\pi\)
0.226894 + 0.973919i \(0.427143\pi\)
\(20\) 3.63382 0.812547
\(21\) 0 0
\(22\) −9.00407 −1.91967
\(23\) 0.596700 0.124421 0.0622103 0.998063i \(-0.480185\pi\)
0.0622103 + 0.998063i \(0.480185\pi\)
\(24\) 0 0
\(25\) −4.17138 −0.834276
\(26\) −2.44785 −0.480062
\(27\) 0 0
\(28\) 0 0
\(29\) 3.64900 0.677602 0.338801 0.940858i \(-0.389979\pi\)
0.338801 + 0.940858i \(0.389979\pi\)
\(30\) 0 0
\(31\) 7.08833 1.27310 0.636551 0.771235i \(-0.280361\pi\)
0.636551 + 0.771235i \(0.280361\pi\)
\(32\) −0.0786478 −0.0139031
\(33\) 0 0
\(34\) 17.5885 3.01641
\(35\) 0 0
\(36\) 0 0
\(37\) 0.710851 0.116863 0.0584316 0.998291i \(-0.481390\pi\)
0.0584316 + 0.998291i \(0.481390\pi\)
\(38\) 4.84189 0.785458
\(39\) 0 0
\(40\) 4.43855 0.701796
\(41\) 5.27529 0.823863 0.411931 0.911215i \(-0.364854\pi\)
0.411931 + 0.911215i \(0.364854\pi\)
\(42\) 0 0
\(43\) 11.0790 1.68954 0.844768 0.535132i \(-0.179738\pi\)
0.844768 + 0.535132i \(0.179738\pi\)
\(44\) −14.6839 −2.21367
\(45\) 0 0
\(46\) 1.46063 0.215358
\(47\) 12.1135 1.76693 0.883467 0.468494i \(-0.155203\pi\)
0.883467 + 0.468494i \(0.155203\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −10.2109 −1.44404
\(51\) 0 0
\(52\) −3.99195 −0.553584
\(53\) 11.4484 1.57256 0.786282 0.617868i \(-0.212003\pi\)
0.786282 + 0.617868i \(0.212003\pi\)
\(54\) 0 0
\(55\) −3.34837 −0.451494
\(56\) 0 0
\(57\) 0 0
\(58\) 8.93219 1.17285
\(59\) 9.58986 1.24849 0.624247 0.781227i \(-0.285406\pi\)
0.624247 + 0.781227i \(0.285406\pi\)
\(60\) 0 0
\(61\) −6.98536 −0.894384 −0.447192 0.894438i \(-0.647576\pi\)
−0.447192 + 0.894438i \(0.647576\pi\)
\(62\) 17.3511 2.20360
\(63\) 0 0
\(64\) −8.09606 −1.01201
\(65\) −0.910286 −0.112907
\(66\) 0 0
\(67\) 1.22839 0.150072 0.0750360 0.997181i \(-0.476093\pi\)
0.0750360 + 0.997181i \(0.476093\pi\)
\(68\) 28.6834 3.47837
\(69\) 0 0
\(70\) 0 0
\(71\) −11.3635 −1.34859 −0.674297 0.738460i \(-0.735553\pi\)
−0.674297 + 0.738460i \(0.735553\pi\)
\(72\) 0 0
\(73\) −6.53419 −0.764769 −0.382384 0.924003i \(-0.624897\pi\)
−0.382384 + 0.924003i \(0.624897\pi\)
\(74\) 1.74005 0.202277
\(75\) 0 0
\(76\) 7.89616 0.905752
\(77\) 0 0
\(78\) 0 0
\(79\) −11.5204 −1.29615 −0.648074 0.761577i \(-0.724425\pi\)
−0.648074 + 0.761577i \(0.724425\pi\)
\(80\) 3.59725 0.402184
\(81\) 0 0
\(82\) 12.9131 1.42601
\(83\) 7.16403 0.786355 0.393177 0.919463i \(-0.371376\pi\)
0.393177 + 0.919463i \(0.371376\pi\)
\(84\) 0 0
\(85\) 6.54069 0.709437
\(86\) 27.1198 2.92440
\(87\) 0 0
\(88\) −17.9357 −1.91195
\(89\) 12.8490 1.36199 0.680997 0.732286i \(-0.261547\pi\)
0.680997 + 0.732286i \(0.261547\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.38200 0.248341
\(93\) 0 0
\(94\) 29.6520 3.05837
\(95\) 1.80056 0.184734
\(96\) 0 0
\(97\) −9.09062 −0.923012 −0.461506 0.887137i \(-0.652691\pi\)
−0.461506 + 0.887137i \(0.652691\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −16.6519 −1.66519
\(101\) −5.80645 −0.577763 −0.288882 0.957365i \(-0.593283\pi\)
−0.288882 + 0.957365i \(0.593283\pi\)
\(102\) 0 0
\(103\) −12.8682 −1.26794 −0.633971 0.773357i \(-0.718576\pi\)
−0.633971 + 0.773357i \(0.718576\pi\)
\(104\) −4.87599 −0.478130
\(105\) 0 0
\(106\) 28.0240 2.72193
\(107\) −4.45747 −0.430920 −0.215460 0.976513i \(-0.569125\pi\)
−0.215460 + 0.976513i \(0.569125\pi\)
\(108\) 0 0
\(109\) 0.878896 0.0841830 0.0420915 0.999114i \(-0.486598\pi\)
0.0420915 + 0.999114i \(0.486598\pi\)
\(110\) −8.19628 −0.781485
\(111\) 0 0
\(112\) 0 0
\(113\) 5.36723 0.504906 0.252453 0.967609i \(-0.418763\pi\)
0.252453 + 0.967609i \(0.418763\pi\)
\(114\) 0 0
\(115\) 0.543168 0.0506507
\(116\) 14.5666 1.35248
\(117\) 0 0
\(118\) 23.4745 2.16100
\(119\) 0 0
\(120\) 0 0
\(121\) 2.53037 0.230034
\(122\) −17.0991 −1.54808
\(123\) 0 0
\(124\) 28.2963 2.54108
\(125\) −8.34858 −0.746720
\(126\) 0 0
\(127\) 6.61029 0.586568 0.293284 0.956025i \(-0.405252\pi\)
0.293284 + 0.956025i \(0.405252\pi\)
\(128\) −19.6606 −1.73777
\(129\) 0 0
\(130\) −2.22824 −0.195430
\(131\) −19.9665 −1.74448 −0.872240 0.489079i \(-0.837333\pi\)
−0.872240 + 0.489079i \(0.837333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00692 0.259758
\(135\) 0 0
\(136\) 35.0355 3.00427
\(137\) −5.75451 −0.491641 −0.245821 0.969315i \(-0.579057\pi\)
−0.245821 + 0.969315i \(0.579057\pi\)
\(138\) 0 0
\(139\) 1.55138 0.131586 0.0657931 0.997833i \(-0.479042\pi\)
0.0657931 + 0.997833i \(0.479042\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −27.8160 −2.33427
\(143\) 3.67837 0.307600
\(144\) 0 0
\(145\) 3.32163 0.275847
\(146\) −15.9947 −1.32373
\(147\) 0 0
\(148\) 2.83768 0.233256
\(149\) −14.9337 −1.22341 −0.611707 0.791084i \(-0.709517\pi\)
−0.611707 + 0.791084i \(0.709517\pi\)
\(150\) 0 0
\(151\) −7.90102 −0.642976 −0.321488 0.946914i \(-0.604183\pi\)
−0.321488 + 0.946914i \(0.604183\pi\)
\(152\) 9.64481 0.782297
\(153\) 0 0
\(154\) 0 0
\(155\) 6.45241 0.518270
\(156\) 0 0
\(157\) −12.4948 −0.997194 −0.498597 0.866834i \(-0.666151\pi\)
−0.498597 + 0.866834i \(0.666151\pi\)
\(158\) −28.2002 −2.24349
\(159\) 0 0
\(160\) −0.0715920 −0.00565985
\(161\) 0 0
\(162\) 0 0
\(163\) 7.01427 0.549400 0.274700 0.961530i \(-0.411421\pi\)
0.274700 + 0.961530i \(0.411421\pi\)
\(164\) 21.0587 1.64441
\(165\) 0 0
\(166\) 17.5365 1.36109
\(167\) 4.82764 0.373574 0.186787 0.982400i \(-0.440193\pi\)
0.186787 + 0.982400i \(0.440193\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 16.0106 1.22796
\(171\) 0 0
\(172\) 44.2270 3.37227
\(173\) −22.2124 −1.68878 −0.844388 0.535732i \(-0.820036\pi\)
−0.844388 + 0.535732i \(0.820036\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −14.5361 −1.09570
\(177\) 0 0
\(178\) 31.4524 2.35746
\(179\) −4.57505 −0.341956 −0.170978 0.985275i \(-0.554693\pi\)
−0.170978 + 0.985275i \(0.554693\pi\)
\(180\) 0 0
\(181\) 7.23332 0.537649 0.268824 0.963189i \(-0.413365\pi\)
0.268824 + 0.963189i \(0.413365\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.90951 0.214492
\(185\) 0.647078 0.0475741
\(186\) 0 0
\(187\) −26.4302 −1.93277
\(188\) 48.3565 3.52676
\(189\) 0 0
\(190\) 4.40751 0.319754
\(191\) −1.97242 −0.142719 −0.0713596 0.997451i \(-0.522734\pi\)
−0.0713596 + 0.997451i \(0.522734\pi\)
\(192\) 0 0
\(193\) −25.2073 −1.81446 −0.907230 0.420635i \(-0.861807\pi\)
−0.907230 + 0.420635i \(0.861807\pi\)
\(194\) −22.2524 −1.59763
\(195\) 0 0
\(196\) 0 0
\(197\) 3.04497 0.216945 0.108473 0.994099i \(-0.465404\pi\)
0.108473 + 0.994099i \(0.465404\pi\)
\(198\) 0 0
\(199\) −4.05691 −0.287587 −0.143794 0.989608i \(-0.545930\pi\)
−0.143794 + 0.989608i \(0.545930\pi\)
\(200\) −20.3396 −1.43823
\(201\) 0 0
\(202\) −14.2133 −1.00004
\(203\) 0 0
\(204\) 0 0
\(205\) 4.80203 0.335388
\(206\) −31.4994 −2.19467
\(207\) 0 0
\(208\) −3.95177 −0.274006
\(209\) −7.27588 −0.503283
\(210\) 0 0
\(211\) 16.4116 1.12982 0.564910 0.825152i \(-0.308911\pi\)
0.564910 + 0.825152i \(0.308911\pi\)
\(212\) 45.7016 3.13880
\(213\) 0 0
\(214\) −10.9112 −0.745875
\(215\) 10.0851 0.687797
\(216\) 0 0
\(217\) 0 0
\(218\) 2.15140 0.145711
\(219\) 0 0
\(220\) −13.3665 −0.901170
\(221\) −7.18531 −0.483336
\(222\) 0 0
\(223\) 16.1205 1.07951 0.539755 0.841822i \(-0.318517\pi\)
0.539755 + 0.841822i \(0.318517\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 13.1381 0.873936
\(227\) −8.67804 −0.575982 −0.287991 0.957633i \(-0.592987\pi\)
−0.287991 + 0.957633i \(0.592987\pi\)
\(228\) 0 0
\(229\) 20.7592 1.37180 0.685902 0.727694i \(-0.259408\pi\)
0.685902 + 0.727694i \(0.259408\pi\)
\(230\) 1.32959 0.0876707
\(231\) 0 0
\(232\) 17.7925 1.16813
\(233\) 9.84468 0.644946 0.322473 0.946579i \(-0.395486\pi\)
0.322473 + 0.946579i \(0.395486\pi\)
\(234\) 0 0
\(235\) 11.0267 0.719305
\(236\) 38.2823 2.49196
\(237\) 0 0
\(238\) 0 0
\(239\) −1.13539 −0.0734424 −0.0367212 0.999326i \(-0.511691\pi\)
−0.0367212 + 0.999326i \(0.511691\pi\)
\(240\) 0 0
\(241\) 21.8208 1.40560 0.702802 0.711386i \(-0.251932\pi\)
0.702802 + 0.711386i \(0.251932\pi\)
\(242\) 6.19396 0.398163
\(243\) 0 0
\(244\) −27.8852 −1.78517
\(245\) 0 0
\(246\) 0 0
\(247\) −1.97802 −0.125858
\(248\) 34.5626 2.19473
\(249\) 0 0
\(250\) −20.4360 −1.29249
\(251\) 9.44377 0.596086 0.298043 0.954552i \(-0.403666\pi\)
0.298043 + 0.954552i \(0.403666\pi\)
\(252\) 0 0
\(253\) −2.19488 −0.137991
\(254\) 16.1810 1.01528
\(255\) 0 0
\(256\) −31.9341 −1.99588
\(257\) −3.62752 −0.226279 −0.113139 0.993579i \(-0.536091\pi\)
−0.113139 + 0.993579i \(0.536091\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −3.63382 −0.225360
\(261\) 0 0
\(262\) −48.8749 −3.01950
\(263\) −6.59584 −0.406717 −0.203359 0.979104i \(-0.565186\pi\)
−0.203359 + 0.979104i \(0.565186\pi\)
\(264\) 0 0
\(265\) 10.4214 0.640179
\(266\) 0 0
\(267\) 0 0
\(268\) 4.90369 0.299540
\(269\) 23.5313 1.43473 0.717365 0.696698i \(-0.245348\pi\)
0.717365 + 0.696698i \(0.245348\pi\)
\(270\) 0 0
\(271\) −2.69767 −0.163872 −0.0819358 0.996638i \(-0.526110\pi\)
−0.0819358 + 0.996638i \(0.526110\pi\)
\(272\) 28.3947 1.72168
\(273\) 0 0
\(274\) −14.0862 −0.850976
\(275\) 15.3439 0.925269
\(276\) 0 0
\(277\) −24.7549 −1.48738 −0.743690 0.668525i \(-0.766926\pi\)
−0.743690 + 0.668525i \(0.766926\pi\)
\(278\) 3.79754 0.227761
\(279\) 0 0
\(280\) 0 0
\(281\) 4.05377 0.241828 0.120914 0.992663i \(-0.461418\pi\)
0.120914 + 0.992663i \(0.461418\pi\)
\(282\) 0 0
\(283\) −12.9237 −0.768235 −0.384118 0.923284i \(-0.625494\pi\)
−0.384118 + 0.923284i \(0.625494\pi\)
\(284\) −45.3624 −2.69176
\(285\) 0 0
\(286\) 9.00407 0.532422
\(287\) 0 0
\(288\) 0 0
\(289\) 34.6287 2.03698
\(290\) 8.13085 0.477460
\(291\) 0 0
\(292\) −26.0842 −1.52646
\(293\) −23.5553 −1.37611 −0.688057 0.725656i \(-0.741536\pi\)
−0.688057 + 0.725656i \(0.741536\pi\)
\(294\) 0 0
\(295\) 8.72952 0.508252
\(296\) 3.46610 0.201463
\(297\) 0 0
\(298\) −36.5553 −2.11759
\(299\) −0.596700 −0.0345081
\(300\) 0 0
\(301\) 0 0
\(302\) −19.3405 −1.11292
\(303\) 0 0
\(304\) 7.81669 0.448318
\(305\) −6.35868 −0.364097
\(306\) 0 0
\(307\) −19.9551 −1.13890 −0.569450 0.822026i \(-0.692844\pi\)
−0.569450 + 0.822026i \(0.692844\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 15.7945 0.897068
\(311\) 6.48069 0.367486 0.183743 0.982974i \(-0.441179\pi\)
0.183743 + 0.982974i \(0.441179\pi\)
\(312\) 0 0
\(313\) −16.1154 −0.910897 −0.455449 0.890262i \(-0.650521\pi\)
−0.455449 + 0.890262i \(0.650521\pi\)
\(314\) −30.5854 −1.72603
\(315\) 0 0
\(316\) −45.9889 −2.58708
\(317\) −14.5303 −0.816106 −0.408053 0.912958i \(-0.633792\pi\)
−0.408053 + 0.912958i \(0.633792\pi\)
\(318\) 0 0
\(319\) −13.4224 −0.751508
\(320\) −7.36974 −0.411981
\(321\) 0 0
\(322\) 0 0
\(323\) 14.2127 0.790815
\(324\) 0 0
\(325\) 4.17138 0.231386
\(326\) 17.1699 0.950951
\(327\) 0 0
\(328\) 25.7223 1.42028
\(329\) 0 0
\(330\) 0 0
\(331\) 21.0945 1.15946 0.579730 0.814809i \(-0.303158\pi\)
0.579730 + 0.814809i \(0.303158\pi\)
\(332\) 28.5985 1.56955
\(333\) 0 0
\(334\) 11.8173 0.646615
\(335\) 1.11819 0.0610932
\(336\) 0 0
\(337\) −32.8693 −1.79050 −0.895251 0.445562i \(-0.853004\pi\)
−0.895251 + 0.445562i \(0.853004\pi\)
\(338\) 2.44785 0.133145
\(339\) 0 0
\(340\) 26.1101 1.41602
\(341\) −26.0735 −1.41196
\(342\) 0 0
\(343\) 0 0
\(344\) 54.0213 2.91263
\(345\) 0 0
\(346\) −54.3725 −2.92308
\(347\) −15.9160 −0.854418 −0.427209 0.904153i \(-0.640503\pi\)
−0.427209 + 0.904153i \(0.640503\pi\)
\(348\) 0 0
\(349\) 29.6245 1.58576 0.792882 0.609375i \(-0.208580\pi\)
0.792882 + 0.609375i \(0.208580\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.289295 0.0154195
\(353\) −28.7078 −1.52796 −0.763980 0.645240i \(-0.776757\pi\)
−0.763980 + 0.645240i \(0.776757\pi\)
\(354\) 0 0
\(355\) −10.3440 −0.549002
\(356\) 51.2927 2.71851
\(357\) 0 0
\(358\) −11.1990 −0.591887
\(359\) −27.2931 −1.44048 −0.720238 0.693727i \(-0.755968\pi\)
−0.720238 + 0.693727i \(0.755968\pi\)
\(360\) 0 0
\(361\) −15.0874 −0.794076
\(362\) 17.7061 0.930610
\(363\) 0 0
\(364\) 0 0
\(365\) −5.94798 −0.311332
\(366\) 0 0
\(367\) 9.98326 0.521122 0.260561 0.965457i \(-0.416093\pi\)
0.260561 + 0.965457i \(0.416093\pi\)
\(368\) 2.35802 0.122921
\(369\) 0 0
\(370\) 1.58395 0.0823455
\(371\) 0 0
\(372\) 0 0
\(373\) 4.68608 0.242636 0.121318 0.992614i \(-0.461288\pi\)
0.121318 + 0.992614i \(0.461288\pi\)
\(374\) −64.6971 −3.34541
\(375\) 0 0
\(376\) 59.0653 3.04606
\(377\) −3.64900 −0.187933
\(378\) 0 0
\(379\) −2.45019 −0.125858 −0.0629288 0.998018i \(-0.520044\pi\)
−0.0629288 + 0.998018i \(0.520044\pi\)
\(380\) 7.18777 0.368725
\(381\) 0 0
\(382\) −4.82818 −0.247031
\(383\) −10.7671 −0.550175 −0.275087 0.961419i \(-0.588707\pi\)
−0.275087 + 0.961419i \(0.588707\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −61.7035 −3.14063
\(387\) 0 0
\(388\) −36.2893 −1.84231
\(389\) −14.0372 −0.711714 −0.355857 0.934540i \(-0.615811\pi\)
−0.355857 + 0.934540i \(0.615811\pi\)
\(390\) 0 0
\(391\) 4.28748 0.216827
\(392\) 0 0
\(393\) 0 0
\(394\) 7.45363 0.375508
\(395\) −10.4869 −0.527652
\(396\) 0 0
\(397\) −26.4605 −1.32801 −0.664007 0.747726i \(-0.731146\pi\)
−0.664007 + 0.747726i \(0.731146\pi\)
\(398\) −9.93070 −0.497781
\(399\) 0 0
\(400\) −16.4843 −0.824217
\(401\) 19.0156 0.949593 0.474796 0.880096i \(-0.342522\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(402\) 0 0
\(403\) −7.08833 −0.353095
\(404\) −23.1791 −1.15320
\(405\) 0 0
\(406\) 0 0
\(407\) −2.61477 −0.129609
\(408\) 0 0
\(409\) −12.7759 −0.631728 −0.315864 0.948804i \(-0.602294\pi\)
−0.315864 + 0.948804i \(0.602294\pi\)
\(410\) 11.7546 0.580520
\(411\) 0 0
\(412\) −51.3693 −2.53078
\(413\) 0 0
\(414\) 0 0
\(415\) 6.52132 0.320119
\(416\) 0.0786478 0.00385603
\(417\) 0 0
\(418\) −17.8102 −0.871127
\(419\) 12.9811 0.634170 0.317085 0.948397i \(-0.397296\pi\)
0.317085 + 0.948397i \(0.397296\pi\)
\(420\) 0 0
\(421\) −11.6737 −0.568943 −0.284472 0.958684i \(-0.591818\pi\)
−0.284472 + 0.958684i \(0.591818\pi\)
\(422\) 40.1731 1.95559
\(423\) 0 0
\(424\) 55.8225 2.71098
\(425\) −29.9726 −1.45389
\(426\) 0 0
\(427\) 0 0
\(428\) −17.7940 −0.860107
\(429\) 0 0
\(430\) 24.6868 1.19050
\(431\) 0.467684 0.0225275 0.0112638 0.999937i \(-0.496415\pi\)
0.0112638 + 0.999937i \(0.496415\pi\)
\(432\) 0 0
\(433\) 9.27593 0.445773 0.222886 0.974844i \(-0.428452\pi\)
0.222886 + 0.974844i \(0.428452\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 3.50851 0.168027
\(437\) 1.18029 0.0564607
\(438\) 0 0
\(439\) 35.7077 1.70424 0.852119 0.523348i \(-0.175317\pi\)
0.852119 + 0.523348i \(0.175317\pi\)
\(440\) −16.3266 −0.778340
\(441\) 0 0
\(442\) −17.5885 −0.836601
\(443\) 36.3458 1.72684 0.863421 0.504484i \(-0.168317\pi\)
0.863421 + 0.504484i \(0.168317\pi\)
\(444\) 0 0
\(445\) 11.6963 0.554457
\(446\) 39.4605 1.86851
\(447\) 0 0
\(448\) 0 0
\(449\) 40.4910 1.91089 0.955444 0.295171i \(-0.0953767\pi\)
0.955444 + 0.295171i \(0.0953767\pi\)
\(450\) 0 0
\(451\) −19.4045 −0.913720
\(452\) 21.4257 1.00778
\(453\) 0 0
\(454\) −21.2425 −0.996960
\(455\) 0 0
\(456\) 0 0
\(457\) 5.01988 0.234820 0.117410 0.993084i \(-0.462541\pi\)
0.117410 + 0.993084i \(0.462541\pi\)
\(458\) 50.8153 2.37444
\(459\) 0 0
\(460\) 2.16830 0.101098
\(461\) −17.3627 −0.808661 −0.404331 0.914613i \(-0.632495\pi\)
−0.404331 + 0.914613i \(0.632495\pi\)
\(462\) 0 0
\(463\) 35.4306 1.64660 0.823301 0.567606i \(-0.192130\pi\)
0.823301 + 0.567606i \(0.192130\pi\)
\(464\) 14.4200 0.669433
\(465\) 0 0
\(466\) 24.0983 1.11633
\(467\) 35.4958 1.64255 0.821275 0.570533i \(-0.193263\pi\)
0.821275 + 0.570533i \(0.193263\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 26.9918 1.24504
\(471\) 0 0
\(472\) 46.7601 2.15231
\(473\) −40.7527 −1.87381
\(474\) 0 0
\(475\) −8.25107 −0.378585
\(476\) 0 0
\(477\) 0 0
\(478\) −2.77926 −0.127121
\(479\) −24.0270 −1.09782 −0.548911 0.835881i \(-0.684958\pi\)
−0.548911 + 0.835881i \(0.684958\pi\)
\(480\) 0 0
\(481\) −0.710851 −0.0324120
\(482\) 53.4140 2.43294
\(483\) 0 0
\(484\) 10.1011 0.459142
\(485\) −8.27506 −0.375751
\(486\) 0 0
\(487\) 20.8076 0.942880 0.471440 0.881898i \(-0.343734\pi\)
0.471440 + 0.881898i \(0.343734\pi\)
\(488\) −34.0606 −1.54185
\(489\) 0 0
\(490\) 0 0
\(491\) 36.2195 1.63456 0.817281 0.576240i \(-0.195481\pi\)
0.817281 + 0.576240i \(0.195481\pi\)
\(492\) 0 0
\(493\) 26.2192 1.18085
\(494\) −4.84189 −0.217847
\(495\) 0 0
\(496\) 28.0115 1.25775
\(497\) 0 0
\(498\) 0 0
\(499\) −40.1828 −1.79883 −0.899416 0.437094i \(-0.856008\pi\)
−0.899416 + 0.437094i \(0.856008\pi\)
\(500\) −33.3271 −1.49043
\(501\) 0 0
\(502\) 23.1169 1.03176
\(503\) 38.5636 1.71946 0.859732 0.510745i \(-0.170630\pi\)
0.859732 + 0.510745i \(0.170630\pi\)
\(504\) 0 0
\(505\) −5.28553 −0.235203
\(506\) −5.37273 −0.238847
\(507\) 0 0
\(508\) 26.3879 1.17078
\(509\) 4.33977 0.192357 0.0961785 0.995364i \(-0.469338\pi\)
0.0961785 + 0.995364i \(0.469338\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −38.8484 −1.71687
\(513\) 0 0
\(514\) −8.87962 −0.391663
\(515\) −11.7138 −0.516170
\(516\) 0 0
\(517\) −44.5578 −1.95965
\(518\) 0 0
\(519\) 0 0
\(520\) −4.43855 −0.194643
\(521\) 13.7844 0.603905 0.301952 0.953323i \(-0.402362\pi\)
0.301952 + 0.953323i \(0.402362\pi\)
\(522\) 0 0
\(523\) 29.4834 1.28922 0.644609 0.764512i \(-0.277020\pi\)
0.644609 + 0.764512i \(0.277020\pi\)
\(524\) −79.7052 −3.48194
\(525\) 0 0
\(526\) −16.1456 −0.703982
\(527\) 50.9318 2.21863
\(528\) 0 0
\(529\) −22.6439 −0.984520
\(530\) 25.5099 1.10808
\(531\) 0 0
\(532\) 0 0
\(533\) −5.27529 −0.228498
\(534\) 0 0
\(535\) −4.05758 −0.175424
\(536\) 5.98963 0.258713
\(537\) 0 0
\(538\) 57.6011 2.48336
\(539\) 0 0
\(540\) 0 0
\(541\) 23.2519 0.999679 0.499840 0.866118i \(-0.333392\pi\)
0.499840 + 0.866118i \(0.333392\pi\)
\(542\) −6.60348 −0.283644
\(543\) 0 0
\(544\) −0.565109 −0.0242288
\(545\) 0.800047 0.0342703
\(546\) 0 0
\(547\) 1.18365 0.0506093 0.0253046 0.999680i \(-0.491944\pi\)
0.0253046 + 0.999680i \(0.491944\pi\)
\(548\) −22.9717 −0.981304
\(549\) 0 0
\(550\) 37.5594 1.60154
\(551\) 7.21780 0.307488
\(552\) 0 0
\(553\) 0 0
\(554\) −60.5962 −2.57449
\(555\) 0 0
\(556\) 6.19303 0.262643
\(557\) 6.42824 0.272373 0.136187 0.990683i \(-0.456515\pi\)
0.136187 + 0.990683i \(0.456515\pi\)
\(558\) 0 0
\(559\) −11.0790 −0.468593
\(560\) 0 0
\(561\) 0 0
\(562\) 9.92300 0.418577
\(563\) 11.4563 0.482824 0.241412 0.970423i \(-0.422390\pi\)
0.241412 + 0.970423i \(0.422390\pi\)
\(564\) 0 0
\(565\) 4.88571 0.205543
\(566\) −31.6353 −1.32973
\(567\) 0 0
\(568\) −55.4081 −2.32487
\(569\) −38.3335 −1.60702 −0.803512 0.595288i \(-0.797038\pi\)
−0.803512 + 0.595288i \(0.797038\pi\)
\(570\) 0 0
\(571\) 6.25857 0.261913 0.130956 0.991388i \(-0.458195\pi\)
0.130956 + 0.991388i \(0.458195\pi\)
\(572\) 14.6839 0.613963
\(573\) 0 0
\(574\) 0 0
\(575\) −2.48906 −0.103801
\(576\) 0 0
\(577\) −0.0451932 −0.00188142 −0.000940708 1.00000i \(-0.500299\pi\)
−0.000940708 1.00000i \(0.500299\pi\)
\(578\) 84.7657 3.52579
\(579\) 0 0
\(580\) 13.2598 0.550583
\(581\) 0 0
\(582\) 0 0
\(583\) −42.1115 −1.74408
\(584\) −31.8606 −1.31840
\(585\) 0 0
\(586\) −57.6597 −2.38190
\(587\) 2.71409 0.112023 0.0560113 0.998430i \(-0.482162\pi\)
0.0560113 + 0.998430i \(0.482162\pi\)
\(588\) 0 0
\(589\) 14.0209 0.577719
\(590\) 21.3685 0.879728
\(591\) 0 0
\(592\) 2.80912 0.115454
\(593\) 6.78615 0.278674 0.139337 0.990245i \(-0.455503\pi\)
0.139337 + 0.990245i \(0.455503\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −59.6145 −2.44190
\(597\) 0 0
\(598\) −1.46063 −0.0597296
\(599\) 26.8337 1.09640 0.548198 0.836348i \(-0.315314\pi\)
0.548198 + 0.836348i \(0.315314\pi\)
\(600\) 0 0
\(601\) −12.3356 −0.503178 −0.251589 0.967834i \(-0.580953\pi\)
−0.251589 + 0.967834i \(0.580953\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −31.5405 −1.28336
\(605\) 2.30336 0.0936450
\(606\) 0 0
\(607\) 17.4596 0.708665 0.354332 0.935120i \(-0.384708\pi\)
0.354332 + 0.935120i \(0.384708\pi\)
\(608\) −0.155567 −0.00630907
\(609\) 0 0
\(610\) −15.5651 −0.630211
\(611\) −12.1135 −0.490059
\(612\) 0 0
\(613\) 1.05026 0.0424198 0.0212099 0.999775i \(-0.493248\pi\)
0.0212099 + 0.999775i \(0.493248\pi\)
\(614\) −48.8471 −1.97131
\(615\) 0 0
\(616\) 0 0
\(617\) −10.5872 −0.426223 −0.213111 0.977028i \(-0.568360\pi\)
−0.213111 + 0.977028i \(0.568360\pi\)
\(618\) 0 0
\(619\) −1.23805 −0.0497616 −0.0248808 0.999690i \(-0.507921\pi\)
−0.0248808 + 0.999690i \(0.507921\pi\)
\(620\) 25.7577 1.03445
\(621\) 0 0
\(622\) 15.8637 0.636078
\(623\) 0 0
\(624\) 0 0
\(625\) 13.2573 0.530292
\(626\) −39.4481 −1.57666
\(627\) 0 0
\(628\) −49.8786 −1.99037
\(629\) 5.10769 0.203657
\(630\) 0 0
\(631\) −21.2658 −0.846577 −0.423289 0.905995i \(-0.639124\pi\)
−0.423289 + 0.905995i \(0.639124\pi\)
\(632\) −56.1735 −2.23446
\(633\) 0 0
\(634\) −35.5681 −1.41259
\(635\) 6.01725 0.238787
\(636\) 0 0
\(637\) 0 0
\(638\) −32.8559 −1.30078
\(639\) 0 0
\(640\) −17.8968 −0.707433
\(641\) −11.0506 −0.436474 −0.218237 0.975896i \(-0.570031\pi\)
−0.218237 + 0.975896i \(0.570031\pi\)
\(642\) 0 0
\(643\) −6.50321 −0.256461 −0.128231 0.991744i \(-0.540930\pi\)
−0.128231 + 0.991744i \(0.540930\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 34.7905 1.36881
\(647\) −0.893941 −0.0351444 −0.0175722 0.999846i \(-0.505594\pi\)
−0.0175722 + 0.999846i \(0.505594\pi\)
\(648\) 0 0
\(649\) −35.2750 −1.38467
\(650\) 10.2109 0.400504
\(651\) 0 0
\(652\) 28.0006 1.09659
\(653\) 38.5477 1.50849 0.754244 0.656594i \(-0.228003\pi\)
0.754244 + 0.656594i \(0.228003\pi\)
\(654\) 0 0
\(655\) −18.1752 −0.710164
\(656\) 20.8468 0.813930
\(657\) 0 0
\(658\) 0 0
\(659\) 10.8013 0.420759 0.210380 0.977620i \(-0.432530\pi\)
0.210380 + 0.977620i \(0.432530\pi\)
\(660\) 0 0
\(661\) −40.6339 −1.58047 −0.790237 0.612801i \(-0.790043\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(662\) 51.6361 2.00690
\(663\) 0 0
\(664\) 34.9318 1.35562
\(665\) 0 0
\(666\) 0 0
\(667\) 2.17736 0.0843077
\(668\) 19.2717 0.745645
\(669\) 0 0
\(670\) 2.73716 0.105746
\(671\) 25.6947 0.991934
\(672\) 0 0
\(673\) 32.3136 1.24560 0.622799 0.782382i \(-0.285995\pi\)
0.622799 + 0.782382i \(0.285995\pi\)
\(674\) −80.4589 −3.09916
\(675\) 0 0
\(676\) 3.99195 0.153537
\(677\) −25.2158 −0.969123 −0.484562 0.874757i \(-0.661021\pi\)
−0.484562 + 0.874757i \(0.661021\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 31.8923 1.22302
\(681\) 0 0
\(682\) −63.8238 −2.44394
\(683\) 6.28731 0.240577 0.120289 0.992739i \(-0.461618\pi\)
0.120289 + 0.992739i \(0.461618\pi\)
\(684\) 0 0
\(685\) −5.23826 −0.200143
\(686\) 0 0
\(687\) 0 0
\(688\) 43.7818 1.66917
\(689\) −11.4484 −0.436151
\(690\) 0 0
\(691\) −17.1531 −0.652533 −0.326267 0.945278i \(-0.605791\pi\)
−0.326267 + 0.945278i \(0.605791\pi\)
\(692\) −88.6707 −3.37076
\(693\) 0 0
\(694\) −38.9600 −1.47890
\(695\) 1.41220 0.0535678
\(696\) 0 0
\(697\) 37.9046 1.43574
\(698\) 72.5162 2.74478
\(699\) 0 0
\(700\) 0 0
\(701\) 23.6620 0.893702 0.446851 0.894609i \(-0.352545\pi\)
0.446851 + 0.894609i \(0.352545\pi\)
\(702\) 0 0
\(703\) 1.40608 0.0530312
\(704\) 29.7803 1.12239
\(705\) 0 0
\(706\) −70.2722 −2.64473
\(707\) 0 0
\(708\) 0 0
\(709\) −21.5030 −0.807563 −0.403782 0.914855i \(-0.632304\pi\)
−0.403782 + 0.914855i \(0.632304\pi\)
\(710\) −25.3205 −0.950262
\(711\) 0 0
\(712\) 62.6517 2.34797
\(713\) 4.22961 0.158400
\(714\) 0 0
\(715\) 3.34837 0.125222
\(716\) −18.2634 −0.682535
\(717\) 0 0
\(718\) −66.8094 −2.49330
\(719\) −12.8693 −0.479943 −0.239971 0.970780i \(-0.577138\pi\)
−0.239971 + 0.970780i \(0.577138\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −36.9317 −1.37446
\(723\) 0 0
\(724\) 28.8751 1.07313
\(725\) −15.2214 −0.565307
\(726\) 0 0
\(727\) 16.4329 0.609463 0.304732 0.952438i \(-0.401433\pi\)
0.304732 + 0.952438i \(0.401433\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −14.5597 −0.538880
\(731\) 79.6063 2.94434
\(732\) 0 0
\(733\) −21.7222 −0.802328 −0.401164 0.916006i \(-0.631394\pi\)
−0.401164 + 0.916006i \(0.631394\pi\)
\(734\) 24.4375 0.902004
\(735\) 0 0
\(736\) −0.0469292 −0.00172983
\(737\) −4.51848 −0.166440
\(738\) 0 0
\(739\) 1.58001 0.0581218 0.0290609 0.999578i \(-0.490748\pi\)
0.0290609 + 0.999578i \(0.490748\pi\)
\(740\) 2.58310 0.0949568
\(741\) 0 0
\(742\) 0 0
\(743\) −45.9718 −1.68654 −0.843271 0.537489i \(-0.819373\pi\)
−0.843271 + 0.537489i \(0.819373\pi\)
\(744\) 0 0
\(745\) −13.5939 −0.498043
\(746\) 11.4708 0.419976
\(747\) 0 0
\(748\) −105.508 −3.85776
\(749\) 0 0
\(750\) 0 0
\(751\) −6.42286 −0.234373 −0.117187 0.993110i \(-0.537388\pi\)
−0.117187 + 0.993110i \(0.537388\pi\)
\(752\) 47.8698 1.74563
\(753\) 0 0
\(754\) −8.93219 −0.325291
\(755\) −7.19219 −0.261750
\(756\) 0 0
\(757\) −6.10016 −0.221714 −0.110857 0.993836i \(-0.535360\pi\)
−0.110857 + 0.993836i \(0.535360\pi\)
\(758\) −5.99768 −0.217846
\(759\) 0 0
\(760\) 8.77954 0.318467
\(761\) 18.3948 0.666812 0.333406 0.942783i \(-0.391802\pi\)
0.333406 + 0.942783i \(0.391802\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −7.87380 −0.284864
\(765\) 0 0
\(766\) −26.3563 −0.952291
\(767\) −9.58986 −0.346270
\(768\) 0 0
\(769\) 24.1850 0.872133 0.436066 0.899914i \(-0.356371\pi\)
0.436066 + 0.899914i \(0.356371\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −100.626 −3.62162
\(773\) −10.7601 −0.387014 −0.193507 0.981099i \(-0.561986\pi\)
−0.193507 + 0.981099i \(0.561986\pi\)
\(774\) 0 0
\(775\) −29.5681 −1.06212
\(776\) −44.3258 −1.59120
\(777\) 0 0
\(778\) −34.3609 −1.23190
\(779\) 10.4346 0.373860
\(780\) 0 0
\(781\) 41.7989 1.49568
\(782\) 10.4951 0.375303
\(783\) 0 0
\(784\) 0 0
\(785\) −11.3738 −0.405950
\(786\) 0 0
\(787\) 14.7348 0.525238 0.262619 0.964900i \(-0.415414\pi\)
0.262619 + 0.964900i \(0.415414\pi\)
\(788\) 12.1554 0.433018
\(789\) 0 0
\(790\) −25.6703 −0.913307
\(791\) 0 0
\(792\) 0 0
\(793\) 6.98536 0.248058
\(794\) −64.7713 −2.29865
\(795\) 0 0
\(796\) −16.1950 −0.574017
\(797\) 32.5732 1.15380 0.576901 0.816814i \(-0.304262\pi\)
0.576901 + 0.816814i \(0.304262\pi\)
\(798\) 0 0
\(799\) 87.0392 3.07922
\(800\) 0.328070 0.0115990
\(801\) 0 0
\(802\) 46.5472 1.64364
\(803\) 24.0351 0.848181
\(804\) 0 0
\(805\) 0 0
\(806\) −17.3511 −0.611168
\(807\) 0 0
\(808\) −28.3122 −0.996019
\(809\) 23.6926 0.832987 0.416493 0.909139i \(-0.363259\pi\)
0.416493 + 0.909139i \(0.363259\pi\)
\(810\) 0 0
\(811\) −45.8568 −1.61025 −0.805125 0.593105i \(-0.797902\pi\)
−0.805125 + 0.593105i \(0.797902\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −6.40056 −0.224339
\(815\) 6.38500 0.223657
\(816\) 0 0
\(817\) 21.9145 0.766693
\(818\) −31.2735 −1.09345
\(819\) 0 0
\(820\) 19.1695 0.669427
\(821\) −13.2923 −0.463905 −0.231953 0.972727i \(-0.574511\pi\)
−0.231953 + 0.972727i \(0.574511\pi\)
\(822\) 0 0
\(823\) −4.13033 −0.143974 −0.0719871 0.997406i \(-0.522934\pi\)
−0.0719871 + 0.997406i \(0.522934\pi\)
\(824\) −62.7453 −2.18584
\(825\) 0 0
\(826\) 0 0
\(827\) 4.67317 0.162502 0.0812510 0.996694i \(-0.474108\pi\)
0.0812510 + 0.996694i \(0.474108\pi\)
\(828\) 0 0
\(829\) −1.74971 −0.0607700 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(830\) 15.9632 0.554091
\(831\) 0 0
\(832\) 8.09606 0.280681
\(833\) 0 0
\(834\) 0 0
\(835\) 4.39454 0.152079
\(836\) −29.0450 −1.00454
\(837\) 0 0
\(838\) 31.7758 1.09768
\(839\) −15.4495 −0.533374 −0.266687 0.963783i \(-0.585929\pi\)
−0.266687 + 0.963783i \(0.585929\pi\)
\(840\) 0 0
\(841\) −15.6848 −0.540855
\(842\) −28.5755 −0.984777
\(843\) 0 0
\(844\) 65.5143 2.25510
\(845\) 0.910286 0.0313148
\(846\) 0 0
\(847\) 0 0
\(848\) 45.2416 1.55360
\(849\) 0 0
\(850\) −73.3684 −2.51652
\(851\) 0.424165 0.0145402
\(852\) 0 0
\(853\) 0.602575 0.0206318 0.0103159 0.999947i \(-0.496716\pi\)
0.0103159 + 0.999947i \(0.496716\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −21.7346 −0.742874
\(857\) −43.1639 −1.47445 −0.737226 0.675647i \(-0.763865\pi\)
−0.737226 + 0.675647i \(0.763865\pi\)
\(858\) 0 0
\(859\) −37.9408 −1.29452 −0.647261 0.762269i \(-0.724086\pi\)
−0.647261 + 0.762269i \(0.724086\pi\)
\(860\) 40.2592 1.37283
\(861\) 0 0
\(862\) 1.14482 0.0389927
\(863\) −33.9067 −1.15420 −0.577098 0.816675i \(-0.695815\pi\)
−0.577098 + 0.816675i \(0.695815\pi\)
\(864\) 0 0
\(865\) −20.2196 −0.687488
\(866\) 22.7061 0.771583
\(867\) 0 0
\(868\) 0 0
\(869\) 42.3763 1.43752
\(870\) 0 0
\(871\) −1.22839 −0.0416225
\(872\) 4.28549 0.145125
\(873\) 0 0
\(874\) 2.88916 0.0977272
\(875\) 0 0
\(876\) 0 0
\(877\) 6.51036 0.219839 0.109920 0.993940i \(-0.464941\pi\)
0.109920 + 0.993940i \(0.464941\pi\)
\(878\) 87.4071 2.94985
\(879\) 0 0
\(880\) −13.2320 −0.446050
\(881\) −24.5160 −0.825966 −0.412983 0.910739i \(-0.635513\pi\)
−0.412983 + 0.910739i \(0.635513\pi\)
\(882\) 0 0
\(883\) −28.7175 −0.966419 −0.483210 0.875505i \(-0.660529\pi\)
−0.483210 + 0.875505i \(0.660529\pi\)
\(884\) −28.6834 −0.964727
\(885\) 0 0
\(886\) 88.9690 2.98897
\(887\) 6.94442 0.233171 0.116585 0.993181i \(-0.462805\pi\)
0.116585 + 0.993181i \(0.462805\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 28.6307 0.959704
\(891\) 0 0
\(892\) 64.3523 2.15467
\(893\) 23.9607 0.801815
\(894\) 0 0
\(895\) −4.16461 −0.139208
\(896\) 0 0
\(897\) 0 0
\(898\) 99.1158 3.30754
\(899\) 25.8653 0.862656
\(900\) 0 0
\(901\) 82.2605 2.74050
\(902\) −47.4991 −1.58155
\(903\) 0 0
\(904\) 26.1705 0.870419
\(905\) 6.58439 0.218873
\(906\) 0 0
\(907\) 0.229549 0.00762204 0.00381102 0.999993i \(-0.498787\pi\)
0.00381102 + 0.999993i \(0.498787\pi\)
\(908\) −34.6423 −1.14965
\(909\) 0 0
\(910\) 0 0
\(911\) 26.6727 0.883706 0.441853 0.897087i \(-0.354321\pi\)
0.441853 + 0.897087i \(0.354321\pi\)
\(912\) 0 0
\(913\) −26.3519 −0.872122
\(914\) 12.2879 0.406447
\(915\) 0 0
\(916\) 82.8696 2.73809
\(917\) 0 0
\(918\) 0 0
\(919\) −43.2331 −1.42613 −0.713064 0.701099i \(-0.752693\pi\)
−0.713064 + 0.701099i \(0.752693\pi\)
\(920\) 2.64848 0.0873179
\(921\) 0 0
\(922\) −42.5012 −1.39970
\(923\) 11.3635 0.374033
\(924\) 0 0
\(925\) −2.96523 −0.0974961
\(926\) 86.7287 2.85008
\(927\) 0 0
\(928\) −0.286986 −0.00942077
\(929\) −23.8491 −0.782465 −0.391233 0.920292i \(-0.627951\pi\)
−0.391233 + 0.920292i \(0.627951\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 39.2995 1.28730
\(933\) 0 0
\(934\) 86.8883 2.84307
\(935\) −24.0590 −0.786815
\(936\) 0 0
\(937\) 27.2033 0.888694 0.444347 0.895855i \(-0.353436\pi\)
0.444347 + 0.895855i \(0.353436\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 44.0182 1.43572
\(941\) 13.4515 0.438505 0.219253 0.975668i \(-0.429638\pi\)
0.219253 + 0.975668i \(0.429638\pi\)
\(942\) 0 0
\(943\) 3.14777 0.102505
\(944\) 37.8970 1.23344
\(945\) 0 0
\(946\) −99.7564 −3.24336
\(947\) −15.0341 −0.488543 −0.244271 0.969707i \(-0.578549\pi\)
−0.244271 + 0.969707i \(0.578549\pi\)
\(948\) 0 0
\(949\) 6.53419 0.212109
\(950\) −20.1974 −0.655289
\(951\) 0 0
\(952\) 0 0
\(953\) −28.3775 −0.919237 −0.459618 0.888116i \(-0.652014\pi\)
−0.459618 + 0.888116i \(0.652014\pi\)
\(954\) 0 0
\(955\) −1.79546 −0.0580999
\(956\) −4.53243 −0.146589
\(957\) 0 0
\(958\) −58.8144 −1.90021
\(959\) 0 0
\(960\) 0 0
\(961\) 19.2444 0.620787
\(962\) −1.74005 −0.0561016
\(963\) 0 0
\(964\) 87.1077 2.80555
\(965\) −22.9458 −0.738653
\(966\) 0 0
\(967\) −52.0994 −1.67540 −0.837701 0.546129i \(-0.816101\pi\)
−0.837701 + 0.546129i \(0.816101\pi\)
\(968\) 12.3381 0.396561
\(969\) 0 0
\(970\) −20.2561 −0.650384
\(971\) −20.8418 −0.668845 −0.334423 0.942423i \(-0.608541\pi\)
−0.334423 + 0.942423i \(0.608541\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 50.9337 1.63202
\(975\) 0 0
\(976\) −27.6046 −0.883601
\(977\) −34.6302 −1.10792 −0.553960 0.832544i \(-0.686884\pi\)
−0.553960 + 0.832544i \(0.686884\pi\)
\(978\) 0 0
\(979\) −47.2634 −1.51054
\(980\) 0 0
\(981\) 0 0
\(982\) 88.6597 2.82924
\(983\) −58.8628 −1.87743 −0.938717 0.344690i \(-0.887984\pi\)
−0.938717 + 0.344690i \(0.887984\pi\)
\(984\) 0 0
\(985\) 2.77180 0.0883168
\(986\) 64.1806 2.04393
\(987\) 0 0
\(988\) −7.89616 −0.251210
\(989\) 6.61086 0.210213
\(990\) 0 0
\(991\) −29.3747 −0.933118 −0.466559 0.884490i \(-0.654507\pi\)
−0.466559 + 0.884490i \(0.654507\pi\)
\(992\) −0.557482 −0.0177001
\(993\) 0 0
\(994\) 0 0
\(995\) −3.69295 −0.117075
\(996\) 0 0
\(997\) 7.50606 0.237719 0.118860 0.992911i \(-0.462076\pi\)
0.118860 + 0.992911i \(0.462076\pi\)
\(998\) −98.3614 −3.11358
\(999\) 0 0
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 5733.2.a.bu.1.6 6
3.2 odd 2 637.2.a.m.1.1 6
7.6 odd 2 5733.2.a.br.1.6 6
21.2 odd 6 637.2.e.o.508.6 12
21.5 even 6 637.2.e.n.508.6 12
21.11 odd 6 637.2.e.o.79.6 12
21.17 even 6 637.2.e.n.79.6 12
21.20 even 2 637.2.a.n.1.1 yes 6
39.38 odd 2 8281.2.a.cc.1.6 6
273.272 even 2 8281.2.a.cd.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.m.1.1 6 3.2 odd 2
637.2.a.n.1.1 yes 6 21.20 even 2
637.2.e.n.79.6 12 21.17 even 6
637.2.e.n.508.6 12 21.5 even 6
637.2.e.o.79.6 12 21.11 odd 6
637.2.e.o.508.6 12 21.2 odd 6
5733.2.a.br.1.6 6 7.6 odd 2
5733.2.a.bu.1.6 6 1.1 even 1 trivial
8281.2.a.cc.1.6 6 39.38 odd 2
8281.2.a.cd.1.6 6 273.272 even 2