Properties

Label 570.2.a.d.1.1
Level $570$
Weight $2$
Character 570.1
Self dual yes
Analytic conductor $4.551$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +2.00000 q^{13} -4.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -1.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +4.00000 q^{28} +10.0000 q^{29} +1.00000 q^{30} -1.00000 q^{32} +2.00000 q^{34} -4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +1.00000 q^{38} +2.00000 q^{39} +1.00000 q^{40} +2.00000 q^{41} -4.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} +1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} -1.00000 q^{54} -4.00000 q^{56} -1.00000 q^{57} -10.0000 q^{58} +8.00000 q^{59} -1.00000 q^{60} +6.00000 q^{61} +4.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} +12.0000 q^{67} -2.00000 q^{68} +4.00000 q^{70} -1.00000 q^{72} -14.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -2.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -12.0000 q^{83} +4.00000 q^{84} +2.00000 q^{85} +4.00000 q^{86} +10.0000 q^{87} +10.0000 q^{89} +1.00000 q^{90} +8.00000 q^{91} +1.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -9.00000 q^{98} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.00000 −0.408248
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −4.00000 −1.06904
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.00000 −0.229416
\(20\) −1.00000 −0.223607
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) 1.00000 0.192450
\(28\) 4.00000 0.755929
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 1.00000 0.182574
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −4.00000 −0.676123
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 1.00000 0.162221
\(39\) 2.00000 0.320256
\(40\) 1.00000 0.158114
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −4.00000 −0.617213
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) −1.00000 −0.141421
\(51\) −2.00000 −0.280056
\(52\) 2.00000 0.277350
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) −1.00000 −0.132453
\(58\) −10.0000 −1.31306
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) −1.00000 −0.129099
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 0 0
\(63\) 4.00000 0.503953
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 4.00000 0.436436
\(85\) 2.00000 0.216930
\(86\) 4.00000 0.431331
\(87\) 10.0000 1.07211
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 1.00000 0.105409
\(91\) 8.00000 0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −14.0000 −1.39305 −0.696526 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 2.00000 0.198030
\(103\) −20.0000 −1.97066 −0.985329 0.170664i \(-0.945409\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) −2.00000 −0.196116
\(105\) −4.00000 −0.390360
\(106\) 6.00000 0.582772
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 4.00000 0.377964
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 1.00000 0.0936586
\(115\) 0 0
\(116\) 10.0000 0.928477
\(117\) 2.00000 0.184900
\(118\) −8.00000 −0.736460
\(119\) −8.00000 −0.733359
\(120\) 1.00000 0.0912871
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) 2.00000 0.180334
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) −4.00000 −0.356348
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.00000 −0.352180
\(130\) 2.00000 0.175412
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −4.00000 −0.346844
\(134\) −12.0000 −1.03664
\(135\) −1.00000 −0.0860663
\(136\) 2.00000 0.171499
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) −4.00000 −0.338062
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −10.0000 −0.830455
\(146\) 14.0000 1.15865
\(147\) 9.00000 0.742307
\(148\) 2.00000 0.164399
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 1.00000 0.0811107
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) −4.00000 −0.308607
\(169\) −9.00000 −0.692308
\(170\) −2.00000 −0.153393
\(171\) −1.00000 −0.0764719
\(172\) −4.00000 −0.304997
\(173\) −14.0000 −1.06440 −0.532200 0.846619i \(-0.678635\pi\)
−0.532200 + 0.846619i \(0.678635\pi\)
\(174\) −10.0000 −0.758098
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) 8.00000 0.601317
\(178\) −10.0000 −0.749532
\(179\) −16.0000 −1.19590 −0.597948 0.801535i \(-0.704017\pi\)
−0.597948 + 0.801535i \(0.704017\pi\)
\(180\) −1.00000 −0.0745356
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −8.00000 −0.592999
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 4.00000 0.290957
\(190\) −1.00000 −0.0725476
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.0000 −1.58359 −0.791797 0.610784i \(-0.790854\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) −2.00000 −0.143592
\(195\) −2.00000 −0.143223
\(196\) 9.00000 0.642857
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) −8.00000 −0.567105 −0.283552 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.0000 0.846415
\(202\) 14.0000 0.985037
\(203\) 40.0000 2.80745
\(204\) −2.00000 −0.140028
\(205\) −2.00000 −0.139686
\(206\) 20.0000 1.39347
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 4.00000 0.276026
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) −4.00000 −0.273434
\(215\) 4.00000 0.272798
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −14.0000 −0.946032
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) −2.00000 −0.134231
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −4.00000 −0.267261
\(225\) 1.00000 0.0666667
\(226\) 2.00000 0.133038
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) −1.00000 −0.0662266
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −10.0000 −0.656532
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 8.00000 0.520756
\(237\) 0 0
\(238\) 8.00000 0.518563
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 11.0000 0.707107
\(243\) 1.00000 0.0641500
\(244\) 6.00000 0.384111
\(245\) −9.00000 −0.574989
\(246\) −2.00000 −0.127515
\(247\) −2.00000 −0.127257
\(248\) 0 0
\(249\) −12.0000 −0.760469
\(250\) 1.00000 0.0632456
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 4.00000 0.251976
\(253\) 0 0
\(254\) −4.00000 −0.250982
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 4.00000 0.249029
\(259\) 8.00000 0.497096
\(260\) −2.00000 −0.124035
\(261\) 10.0000 0.618984
\(262\) 0 0
\(263\) 32.0000 1.97320 0.986602 0.163144i \(-0.0521635\pi\)
0.986602 + 0.163144i \(0.0521635\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 4.00000 0.245256
\(267\) 10.0000 0.611990
\(268\) 12.0000 0.733017
\(269\) 10.0000 0.609711 0.304855 0.952399i \(-0.401392\pi\)
0.304855 + 0.952399i \(0.401392\pi\)
\(270\) 1.00000 0.0608581
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −2.00000 −0.121268
\(273\) 8.00000 0.484182
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −12.0000 −0.719712
\(279\) 0 0
\(280\) 4.00000 0.239046
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) 1.00000 0.0592349
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 10.0000 0.587220
\(291\) 2.00000 0.117242
\(292\) −14.0000 −0.819288
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) −9.00000 −0.524891
\(295\) −8.00000 −0.465778
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) −16.0000 −0.922225
\(302\) 16.0000 0.920697
\(303\) −14.0000 −0.804279
\(304\) −1.00000 −0.0573539
\(305\) −6.00000 −0.343559
\(306\) 2.00000 0.114332
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) −20.0000 −1.13776
\(310\) 0 0
\(311\) −32.0000 −1.81455 −0.907277 0.420534i \(-0.861843\pi\)
−0.907277 + 0.420534i \(0.861843\pi\)
\(312\) −2.00000 −0.113228
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 22.0000 1.24153
\(315\) −4.00000 −0.225374
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 2.00000 0.111283
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −12.0000 −0.664619
\(327\) −2.00000 −0.110600
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) −12.0000 −0.658586
\(333\) 2.00000 0.109599
\(334\) 16.0000 0.875481
\(335\) −12.0000 −0.655630
\(336\) 4.00000 0.218218
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) 9.00000 0.489535
\(339\) −2.00000 −0.108625
\(340\) 2.00000 0.108465
\(341\) 0 0
\(342\) 1.00000 0.0540738
\(343\) 8.00000 0.431959
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) −28.0000 −1.50312 −0.751559 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) 10.0000 0.536056
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −4.00000 −0.213809
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) −8.00000 −0.425195
\(355\) 0 0
\(356\) 10.0000 0.529999
\(357\) −8.00000 −0.423405
\(358\) 16.0000 0.845626
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) 1.00000 0.0527046
\(361\) 1.00000 0.0526316
\(362\) 10.0000 0.525588
\(363\) −11.0000 −0.577350
\(364\) 8.00000 0.419314
\(365\) 14.0000 0.732793
\(366\) −6.00000 −0.313625
\(367\) 28.0000 1.46159 0.730794 0.682598i \(-0.239150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) 0 0
\(369\) 2.00000 0.104116
\(370\) 2.00000 0.103975
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 20.0000 1.03005
\(378\) −4.00000 −0.205738
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 1.00000 0.0512989
\(381\) 4.00000 0.204926
\(382\) −8.00000 −0.409316
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) −4.00000 −0.203331
\(388\) 2.00000 0.101535
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 2.00000 0.101274
\(391\) 0 0
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) −10.0000 −0.503793
\(395\) 0 0
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 8.00000 0.401004
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −12.0000 −0.598506
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) −1.00000 −0.0496904
\(406\) −40.0000 −1.98517
\(407\) 0 0
\(408\) 2.00000 0.0990148
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 2.00000 0.0987730
\(411\) −18.0000 −0.887875
\(412\) −20.0000 −0.985329
\(413\) 32.0000 1.57462
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) −2.00000 −0.0980581
\(417\) 12.0000 0.587643
\(418\) 0 0
\(419\) −16.0000 −0.781651 −0.390826 0.920465i \(-0.627810\pi\)
−0.390826 + 0.920465i \(0.627810\pi\)
\(420\) −4.00000 −0.195180
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 24.0000 1.16144
\(428\) 4.00000 0.193347
\(429\) 0 0
\(430\) −4.00000 −0.192897
\(431\) 32.0000 1.54139 0.770693 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) 1.00000 0.0481125
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 0 0
\(435\) −10.0000 −0.479463
\(436\) −2.00000 −0.0957826
\(437\) 0 0
\(438\) 14.0000 0.668946
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 4.00000 0.190261
\(443\) 4.00000 0.190046 0.0950229 0.995475i \(-0.469708\pi\)
0.0950229 + 0.995475i \(0.469708\pi\)
\(444\) 2.00000 0.0949158
\(445\) −10.0000 −0.474045
\(446\) 12.0000 0.568216
\(447\) −6.00000 −0.283790
\(448\) 4.00000 0.188982
\(449\) 34.0000 1.60456 0.802280 0.596948i \(-0.203620\pi\)
0.802280 + 0.596948i \(0.203620\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 0 0
\(452\) −2.00000 −0.0940721
\(453\) −16.0000 −0.751746
\(454\) −20.0000 −0.938647
\(455\) −8.00000 −0.375046
\(456\) 1.00000 0.0468293
\(457\) −6.00000 −0.280668 −0.140334 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) −22.0000 −1.02799
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) 0 0
\(463\) 36.0000 1.67306 0.836531 0.547920i \(-0.184580\pi\)
0.836531 + 0.547920i \(0.184580\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 2.00000 0.0924500
\(469\) 48.0000 2.21643
\(470\) 0 0
\(471\) −22.0000 −1.01371
\(472\) −8.00000 −0.368230
\(473\) 0 0
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) −8.00000 −0.366679
\(477\) −6.00000 −0.274721
\(478\) −8.00000 −0.365911
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 1.00000 0.0456435
\(481\) 4.00000 0.182384
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) −2.00000 −0.0908153
\(486\) −1.00000 −0.0453609
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −6.00000 −0.271607
\(489\) 12.0000 0.542659
\(490\) 9.00000 0.406579
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 2.00000 0.0901670
\(493\) −20.0000 −0.900755
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) 12.0000 0.537194 0.268597 0.963253i \(-0.413440\pi\)
0.268597 + 0.963253i \(0.413440\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −16.0000 −0.714827
\(502\) −24.0000 −1.07117
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) −4.00000 −0.178174
\(505\) 14.0000 0.622992
\(506\) 0 0
\(507\) −9.00000 −0.399704
\(508\) 4.00000 0.177471
\(509\) −22.0000 −0.975133 −0.487566 0.873086i \(-0.662115\pi\)
−0.487566 + 0.873086i \(0.662115\pi\)
\(510\) −2.00000 −0.0885615
\(511\) −56.0000 −2.47729
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 −0.0441511
\(514\) −14.0000 −0.617514
\(515\) 20.0000 0.881305
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) −8.00000 −0.351500
\(519\) −14.0000 −0.614532
\(520\) 2.00000 0.0877058
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) −10.0000 −0.437688
\(523\) 36.0000 1.57417 0.787085 0.616844i \(-0.211589\pi\)
0.787085 + 0.616844i \(0.211589\pi\)
\(524\) 0 0
\(525\) 4.00000 0.174574
\(526\) −32.0000 −1.39527
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) 8.00000 0.347170
\(532\) −4.00000 −0.173422
\(533\) 4.00000 0.173259
\(534\) −10.0000 −0.432742
\(535\) −4.00000 −0.172935
\(536\) −12.0000 −0.518321
\(537\) −16.0000 −0.690451
\(538\) −10.0000 −0.431131
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) −10.0000 −0.429141
\(544\) 2.00000 0.0857493
\(545\) 2.00000 0.0856706
\(546\) −8.00000 −0.342368
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −18.0000 −0.768922
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) −10.0000 −0.426014
\(552\) 0 0
\(553\) 0 0
\(554\) 22.0000 0.934690
\(555\) −2.00000 −0.0848953
\(556\) 12.0000 0.508913
\(557\) 18.0000 0.762684 0.381342 0.924434i \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) −4.00000 −0.168133
\(567\) 4.00000 0.167984
\(568\) 0 0
\(569\) −38.0000 −1.59304 −0.796521 0.604610i \(-0.793329\pi\)
−0.796521 + 0.604610i \(0.793329\pi\)
\(570\) −1.00000 −0.0418854
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) −8.00000 −0.333914
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 34.0000 1.41544 0.707719 0.706494i \(-0.249724\pi\)
0.707719 + 0.706494i \(0.249724\pi\)
\(578\) 13.0000 0.540729
\(579\) −22.0000 −0.914289
\(580\) −10.0000 −0.415227
\(581\) −48.0000 −1.99138
\(582\) −2.00000 −0.0829027
\(583\) 0 0
\(584\) 14.0000 0.579324
\(585\) −2.00000 −0.0826898
\(586\) −26.0000 −1.07405
\(587\) −20.0000 −0.825488 −0.412744 0.910847i \(-0.635430\pi\)
−0.412744 + 0.910847i \(0.635430\pi\)
\(588\) 9.00000 0.371154
\(589\) 0 0
\(590\) 8.00000 0.329355
\(591\) 10.0000 0.411345
\(592\) 2.00000 0.0821995
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) 8.00000 0.327968
\(596\) −6.00000 −0.245770
\(597\) −8.00000 −0.327418
\(598\) 0 0
\(599\) −40.0000 −1.63436 −0.817178 0.576386i \(-0.804463\pi\)
−0.817178 + 0.576386i \(0.804463\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 16.0000 0.652111
\(603\) 12.0000 0.488678
\(604\) −16.0000 −0.651031
\(605\) 11.0000 0.447214
\(606\) 14.0000 0.568711
\(607\) 12.0000 0.487065 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) 1.00000 0.0405554
\(609\) 40.0000 1.62088
\(610\) 6.00000 0.242933
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) −6.00000 −0.242338 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(614\) −4.00000 −0.161427
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) 38.0000 1.52982 0.764911 0.644136i \(-0.222783\pi\)
0.764911 + 0.644136i \(0.222783\pi\)
\(618\) 20.0000 0.804518
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 32.0000 1.28308
\(623\) 40.0000 1.60257
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) 14.0000 0.559553
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −4.00000 −0.159490
\(630\) 4.00000 0.159364
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 20.0000 0.794929
\(634\) −18.0000 −0.714871
\(635\) −4.00000 −0.158735
\(636\) −6.00000 −0.237915
\(637\) 18.0000 0.713186
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) −22.0000 −0.868948 −0.434474 0.900684i \(-0.643066\pi\)
−0.434474 + 0.900684i \(0.643066\pi\)
\(642\) −4.00000 −0.157867
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) −2.00000 −0.0786889
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 12.0000 0.466393
\(663\) −4.00000 −0.155347
\(664\) 12.0000 0.465690
\(665\) 4.00000 0.155113
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) −16.0000 −0.619059
\(669\) −12.0000 −0.463947
\(670\) 12.0000 0.463600
\(671\) 0 0
\(672\) −4.00000 −0.154303
\(673\) −38.0000 −1.46479 −0.732396 0.680879i \(-0.761598\pi\)
−0.732396 + 0.680879i \(0.761598\pi\)
\(674\) −26.0000 −1.00148
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 2.00000 0.0768095
\(679\) 8.00000 0.307012
\(680\) −2.00000 −0.0766965
\(681\) 20.0000 0.766402
\(682\) 0 0
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) −1.00000 −0.0382360
\(685\) 18.0000 0.687745
\(686\) −8.00000 −0.305441
\(687\) 22.0000 0.839352
\(688\) −4.00000 −0.152499
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) −12.0000 −0.455186
\(696\) −10.0000 −0.379049
\(697\) −4.00000 −0.151511
\(698\) 10.0000 0.378506
\(699\) 6.00000 0.226941
\(700\) 4.00000 0.151186
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) −2.00000 −0.0754851
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) −56.0000 −2.10610
\(708\) 8.00000 0.300658
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.0000 −0.374766
\(713\) 0 0
\(714\) 8.00000 0.299392
\(715\) 0 0
\(716\) −16.0000 −0.597948
\(717\) 8.00000 0.298765
\(718\) 8.00000 0.298557
\(719\) −16.0000 −0.596699 −0.298350 0.954457i \(-0.596436\pi\)
−0.298350 + 0.954457i \(0.596436\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −80.0000 −2.97936
\(722\) −1.00000 −0.0372161
\(723\) 2.00000 0.0743808
\(724\) −10.0000 −0.371647
\(725\) 10.0000 0.371391
\(726\) 11.0000 0.408248
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) −8.00000 −0.296500
\(729\) 1.00000 0.0370370
\(730\) −14.0000 −0.518163
\(731\) 8.00000 0.295891
\(732\) 6.00000 0.221766
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −28.0000 −1.03350
\(735\) −9.00000 −0.331970
\(736\) 0 0
\(737\) 0 0
\(738\) −2.00000 −0.0736210
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −2.00000 −0.0734718
\(742\) 24.0000 0.881068
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) 22.0000 0.805477
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 16.0000 0.584627
\(750\) 1.00000 0.0365148
\(751\) 16.0000 0.583848 0.291924 0.956441i \(-0.405705\pi\)
0.291924 + 0.956441i \(0.405705\pi\)
\(752\) 0 0
\(753\) 24.0000 0.874609
\(754\) −20.0000 −0.728357
\(755\) 16.0000 0.582300
\(756\) 4.00000 0.145479
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) −28.0000 −1.01701
\(759\) 0 0
\(760\) −1.00000 −0.0362738
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) −4.00000 −0.144905
\(763\) −8.00000 −0.289619
\(764\) 8.00000 0.289430
\(765\) 2.00000 0.0723102
\(766\) 0 0
\(767\) 16.0000 0.577727
\(768\) 1.00000 0.0360844
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) −22.0000 −0.791797
\(773\) 10.0000 0.359675 0.179838 0.983696i \(-0.442443\pi\)
0.179838 + 0.983696i \(0.442443\pi\)
\(774\) 4.00000 0.143777
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) 8.00000 0.286998
\(778\) 6.00000 0.215110
\(779\) −2.00000 −0.0716574
\(780\) −2.00000 −0.0716115
\(781\) 0 0
\(782\) 0 0
\(783\) 10.0000 0.357371
\(784\) 9.00000 0.321429
\(785\) 22.0000 0.785214
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 10.0000 0.356235
\(789\) 32.0000 1.13923
\(790\) 0 0
\(791\) −8.00000 −0.284447
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) 30.0000 1.06466
\(795\) 6.00000 0.212798
\(796\) −8.00000 −0.283552
\(797\) −30.0000 −1.06265 −0.531327 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 4.00000 0.141598
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 10.0000 0.353333
\(802\) −18.0000 −0.635602
\(803\) 0 0
\(804\) 12.0000 0.423207
\(805\) 0 0
\(806\) 0 0
\(807\) 10.0000 0.352017
\(808\) 14.0000 0.492518
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 1.00000 0.0351364
\(811\) −4.00000 −0.140459 −0.0702295 0.997531i \(-0.522373\pi\)
−0.0702295 + 0.997531i \(0.522373\pi\)
\(812\) 40.0000 1.40372
\(813\) 0 0
\(814\) 0 0
\(815\) −12.0000 −0.420342
\(816\) −2.00000 −0.0700140
\(817\) 4.00000 0.139942
\(818\) −26.0000 −0.909069
\(819\) 8.00000 0.279543
\(820\) −2.00000 −0.0698430
\(821\) −46.0000 −1.60541 −0.802706 0.596376i \(-0.796607\pi\)
−0.802706 + 0.596376i \(0.796607\pi\)
\(822\) 18.0000 0.627822
\(823\) −36.0000 −1.25488 −0.627441 0.778664i \(-0.715897\pi\)
−0.627441 + 0.778664i \(0.715897\pi\)
\(824\) 20.0000 0.696733
\(825\) 0 0
\(826\) −32.0000 −1.11342
\(827\) −4.00000 −0.139094 −0.0695468 0.997579i \(-0.522155\pi\)
−0.0695468 + 0.997579i \(0.522155\pi\)
\(828\) 0 0
\(829\) 14.0000 0.486240 0.243120 0.969996i \(-0.421829\pi\)
0.243120 + 0.969996i \(0.421829\pi\)
\(830\) −12.0000 −0.416526
\(831\) −22.0000 −0.763172
\(832\) 2.00000 0.0693375
\(833\) −18.0000 −0.623663
\(834\) −12.0000 −0.415526
\(835\) 16.0000 0.553703
\(836\) 0 0
\(837\) 0 0
\(838\) 16.0000 0.552711
\(839\) −8.00000 −0.276191 −0.138095 0.990419i \(-0.544098\pi\)
−0.138095 + 0.990419i \(0.544098\pi\)
\(840\) 4.00000 0.138013
\(841\) 71.0000 2.44828
\(842\) 34.0000 1.17172
\(843\) −6.00000 −0.206651
\(844\) 20.0000 0.688428
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) −44.0000 −1.51186
\(848\) −6.00000 −0.206041
\(849\) 4.00000 0.137280
\(850\) 2.00000 0.0685994
\(851\) 0 0
\(852\) 0 0
\(853\) −6.00000 −0.205436 −0.102718 0.994711i \(-0.532754\pi\)
−0.102718 + 0.994711i \(0.532754\pi\)
\(854\) −24.0000 −0.821263
\(855\) 1.00000 0.0341993
\(856\) −4.00000 −0.136717
\(857\) 14.0000 0.478231 0.239115 0.970991i \(-0.423143\pi\)
0.239115 + 0.970991i \(0.423143\pi\)
\(858\) 0 0
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 4.00000 0.136399
\(861\) 8.00000 0.272639
\(862\) −32.0000 −1.08992
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 14.0000 0.476014
\(866\) 38.0000 1.29129
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 0 0
\(870\) 10.0000 0.339032
\(871\) 24.0000 0.813209
\(872\) 2.00000 0.0677285
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) −4.00000 −0.135225
\(876\) −14.0000 −0.473016
\(877\) 50.0000 1.68838 0.844190 0.536044i \(-0.180082\pi\)
0.844190 + 0.536044i \(0.180082\pi\)
\(878\) 0 0
\(879\) 26.0000 0.876958
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) −9.00000 −0.303046
\(883\) −4.00000 −0.134611 −0.0673054 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) −4.00000 −0.134535
\(885\) −8.00000 −0.268917
\(886\) −4.00000 −0.134383
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 16.0000 0.536623
\(890\) 10.0000 0.335201
\(891\) 0 0
\(892\) −12.0000 −0.401790
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) 16.0000 0.534821
\(896\) −4.00000 −0.133631
\(897\) 0 0
\(898\) −34.0000 −1.13459
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 12.0000 0.399778
\(902\) 0 0
\(903\) −16.0000 −0.532447
\(904\) 2.00000 0.0665190
\(905\) 10.0000 0.332411
\(906\) 16.0000 0.531564
\(907\) −20.0000 −0.664089 −0.332045 0.943264i \(-0.607738\pi\)
−0.332045 + 0.943264i \(0.607738\pi\)
\(908\) 20.0000 0.663723
\(909\) −14.0000 −0.464351
\(910\) 8.00000 0.265197
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 6.00000 0.198462
\(915\) −6.00000 −0.198354
\(916\) 22.0000 0.726900
\(917\) 0 0
\(918\) 2.00000 0.0660098
\(919\) 16.0000 0.527791 0.263896 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 0 0
\(921\) 4.00000 0.131804
\(922\) 30.0000 0.987997
\(923\) 0 0
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) −36.0000 −1.18303
\(927\) −20.0000 −0.656886
\(928\) −10.0000 −0.328266
\(929\) 26.0000 0.853032 0.426516 0.904480i \(-0.359741\pi\)
0.426516 + 0.904480i \(0.359741\pi\)
\(930\) 0 0
\(931\) −9.00000 −0.294963
\(932\) 6.00000 0.196537
\(933\) −32.0000 −1.04763
\(934\) 28.0000 0.916188
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) −48.0000 −1.56726
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 22.0000 0.716799
\(943\) 0 0
\(944\) 8.00000 0.260378
\(945\) −4.00000 −0.130120
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) −28.0000 −0.908918
\(950\) 1.00000 0.0324443
\(951\) 18.0000 0.583690
\(952\) 8.00000 0.259281
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 6.00000 0.194257
\(955\) −8.00000 −0.258874
\(956\) 8.00000 0.258738
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) −72.0000 −2.32500
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) −4.00000 −0.128965
\(963\) 4.00000 0.128898
\(964\) 2.00000 0.0644157
\(965\) 22.0000 0.708205
\(966\) 0 0
\(967\) −28.0000 −0.900419 −0.450210 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(968\) 11.0000 0.353553
\(969\) 2.00000 0.0642493
\(970\) 2.00000 0.0642161
\(971\) 16.0000 0.513464 0.256732 0.966483i \(-0.417354\pi\)
0.256732 + 0.966483i \(0.417354\pi\)
\(972\) 1.00000 0.0320750
\(973\) 48.0000 1.53881
\(974\) 12.0000 0.384505
\(975\) 2.00000 0.0640513
\(976\) 6.00000 0.192055
\(977\) 22.0000 0.703842 0.351921 0.936030i \(-0.385529\pi\)
0.351921 + 0.936030i \(0.385529\pi\)
\(978\) −12.0000 −0.383718
\(979\) 0 0
\(980\) −9.00000 −0.287494
\(981\) −2.00000 −0.0638551
\(982\) −24.0000 −0.765871
\(983\) −8.00000 −0.255160 −0.127580 0.991828i \(-0.540721\pi\)
−0.127580 + 0.991828i \(0.540721\pi\)
\(984\) −2.00000 −0.0637577
\(985\) −10.0000 −0.318626
\(986\) 20.0000 0.636930
\(987\) 0 0
\(988\) −2.00000 −0.0636285
\(989\) 0 0
\(990\) 0 0
\(991\) 24.0000 0.762385 0.381193 0.924496i \(-0.375513\pi\)
0.381193 + 0.924496i \(0.375513\pi\)
\(992\) 0 0
\(993\) −12.0000 −0.380808
\(994\) 0 0
\(995\) 8.00000 0.253617
\(996\) −12.0000 −0.380235
\(997\) 34.0000 1.07679 0.538395 0.842692i \(-0.319031\pi\)
0.538395 + 0.842692i \(0.319031\pi\)
\(998\) −12.0000 −0.379853
\(999\) 2.00000 0.0632772
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 570.2.a.d.1.1 1
3.2 odd 2 1710.2.a.t.1.1 1
4.3 odd 2 4560.2.a.a.1.1 1
5.2 odd 4 2850.2.d.f.799.1 2
5.3 odd 4 2850.2.d.f.799.2 2
5.4 even 2 2850.2.a.p.1.1 1
15.14 odd 2 8550.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.d.1.1 1 1.1 even 1 trivial
1710.2.a.t.1.1 1 3.2 odd 2
2850.2.a.p.1.1 1 5.4 even 2
2850.2.d.f.799.1 2 5.2 odd 4
2850.2.d.f.799.2 2 5.3 odd 4
4560.2.a.a.1.1 1 4.3 odd 2
8550.2.a.b.1.1 1 15.14 odd 2