Properties

Label 570.2.a.a.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

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.00000 q^{11} -1.00000 q^{12} -6.00000 q^{13} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} -4.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} -2.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} -6.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} +6.00000 q^{39} +1.00000 q^{40} +4.00000 q^{41} -2.00000 q^{42} +12.0000 q^{43} +4.00000 q^{44} -1.00000 q^{45} -4.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} -4.00000 q^{51} -6.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} -4.00000 q^{55} +2.00000 q^{56} -1.00000 q^{57} -6.00000 q^{58} +10.0000 q^{59} +1.00000 q^{60} +2.00000 q^{61} +6.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +6.00000 q^{65} +4.00000 q^{66} +12.0000 q^{67} +4.00000 q^{68} -4.00000 q^{69} -2.00000 q^{70} +8.00000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -10.0000 q^{74} -1.00000 q^{75} +1.00000 q^{76} -8.00000 q^{77} -6.00000 q^{78} +10.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -4.00000 q^{82} +2.00000 q^{83} +2.00000 q^{84} -4.00000 q^{85} -12.0000 q^{86} -6.00000 q^{87} -4.00000 q^{88} -8.00000 q^{89} +1.00000 q^{90} +12.0000 q^{91} +4.00000 q^{92} +6.00000 q^{93} -4.00000 q^{94} -1.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} +3.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)

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
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 4.00000 1.20605 0.603023 0.797724i \(-0.293963\pi\)
0.603023 + 0.797724i \(0.293963\pi\)
\(12\) −1.00000 −0.288675
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 0.534522
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 0.229416
\(20\) −1.00000 −0.223607
\(21\) 2.00000 0.436436
\(22\) −4.00000 −0.852803
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) −1.00000 −0.192450
\(28\) −2.00000 −0.377964
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 −0.182574
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.00000 −0.696311
\(34\) −4.00000 −0.685994
\(35\) 2.00000 0.338062
\(36\) 1.00000 0.166667
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −1.00000 −0.162221
\(39\) 6.00000 0.960769
\(40\) 1.00000 0.158114
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) −2.00000 −0.308607
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) 4.00000 0.603023
\(45\) −1.00000 −0.149071
\(46\) −4.00000 −0.589768
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) −1.00000 −0.144338
\(49\) −3.00000 −0.428571
\(50\) −1.00000 −0.141421
\(51\) −4.00000 −0.560112
\(52\) −6.00000 −0.832050
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) −4.00000 −0.539360
\(56\) 2.00000 0.267261
\(57\) −1.00000 −0.132453
\(58\) −6.00000 −0.787839
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 1.00000 0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 6.00000 0.762001
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 4.00000 0.492366
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 4.00000 0.485071
\(69\) −4.00000 −0.481543
\(70\) −2.00000 −0.239046
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −10.0000 −1.16248
\(75\) −1.00000 −0.115470
\(76\) 1.00000 0.114708
\(77\) −8.00000 −0.911685
\(78\) −6.00000 −0.679366
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 2.00000 0.218218
\(85\) −4.00000 −0.433861
\(86\) −12.0000 −1.29399
\(87\) −6.00000 −0.643268
\(88\) −4.00000 −0.426401
\(89\) −8.00000 −0.847998 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 1.00000 0.105409
\(91\) 12.0000 1.25794
\(92\) 4.00000 0.417029
\(93\) 6.00000 0.622171
\(94\) −4.00000 −0.412568
\(95\) −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 \(0.467625\pi\)
\(98\) 3.00000 0.303046
\(99\) 4.00000 0.402015
\(100\) 1.00000 0.100000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 4.00000 0.396059
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 6.00000 0.588348
\(105\) −2.00000 −0.195180
\(106\) 10.0000 0.971286
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 4.00000 0.381385
\(111\) −10.0000 −0.949158
\(112\) −2.00000 −0.188982
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 1.00000 0.0936586
\(115\) −4.00000 −0.373002
\(116\) 6.00000 0.557086
\(117\) −6.00000 −0.554700
\(118\) −10.0000 −0.920575
\(119\) −8.00000 −0.733359
\(120\) −1.00000 −0.0912871
\(121\) 5.00000 0.454545
\(122\) −2.00000 −0.181071
\(123\) −4.00000 −0.360668
\(124\) −6.00000 −0.538816
\(125\) −1.00000 −0.0894427
\(126\) 2.00000 0.178174
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.0000 −1.05654
\(130\) −6.00000 −0.526235
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −4.00000 −0.348155
\(133\) −2.00000 −0.173422
\(134\) −12.0000 −1.03664
\(135\) 1.00000 0.0860663
\(136\) −4.00000 −0.342997
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 4.00000 0.340503
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 0.169031
\(141\) −4.00000 −0.336861
\(142\) −8.00000 −0.671345
\(143\) −24.0000 −2.00698
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) 2.00000 0.165521
\(147\) 3.00000 0.247436
\(148\) 10.0000 0.821995
\(149\) 14.0000 1.14692 0.573462 0.819232i \(-0.305600\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 1.00000 0.0816497
\(151\) −2.00000 −0.162758 −0.0813788 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 4.00000 0.323381
\(154\) 8.00000 0.644658
\(155\) 6.00000 0.481932
\(156\) 6.00000 0.480384
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) −10.0000 −0.795557
\(159\) 10.0000 0.793052
\(160\) 1.00000 0.0790569
\(161\) −8.00000 −0.630488
\(162\) −1.00000 −0.0785674
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 4.00000 0.312348
\(165\) 4.00000 0.311400
\(166\) −2.00000 −0.155230
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) −2.00000 −0.154303
\(169\) 23.0000 1.76923
\(170\) 4.00000 0.306786
\(171\) 1.00000 0.0764719
\(172\) 12.0000 0.914991
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 6.00000 0.454859
\(175\) −2.00000 −0.151186
\(176\) 4.00000 0.301511
\(177\) −10.0000 −0.751646
\(178\) 8.00000 0.599625
\(179\) −2.00000 −0.149487 −0.0747435 0.997203i \(-0.523814\pi\)
−0.0747435 + 0.997203i \(0.523814\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −12.0000 −0.889499
\(183\) −2.00000 −0.147844
\(184\) −4.00000 −0.294884
\(185\) −10.0000 −0.735215
\(186\) −6.00000 −0.439941
\(187\) 16.0000 1.17004
\(188\) 4.00000 0.291730
\(189\) 2.00000 0.145479
\(190\) 1.00000 0.0725476
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −2.00000 −0.143592
\(195\) −6.00000 −0.429669
\(196\) −3.00000 −0.214286
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) −4.00000 −0.284268
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −12.0000 −0.846415
\(202\) 10.0000 0.703598
\(203\) −12.0000 −0.842235
\(204\) −4.00000 −0.280056
\(205\) −4.00000 −0.279372
\(206\) 12.0000 0.836080
\(207\) 4.00000 0.278019
\(208\) −6.00000 −0.416025
\(209\) 4.00000 0.276686
\(210\) 2.00000 0.138013
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) −10.0000 −0.686803
\(213\) −8.00000 −0.548151
\(214\) −8.00000 −0.546869
\(215\) −12.0000 −0.818393
\(216\) 1.00000 0.0680414
\(217\) 12.0000 0.814613
\(218\) 16.0000 1.08366
\(219\) 2.00000 0.135147
\(220\) −4.00000 −0.269680
\(221\) −24.0000 −1.61441
\(222\) 10.0000 0.671156
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 2.00000 0.133631
\(225\) 1.00000 0.0666667
\(226\) 14.0000 0.931266
\(227\) 20.0000 1.32745 0.663723 0.747978i \(-0.268975\pi\)
0.663723 + 0.747978i \(0.268975\pi\)
\(228\) −1.00000 −0.0662266
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 4.00000 0.263752
\(231\) 8.00000 0.526361
\(232\) −6.00000 −0.393919
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) 6.00000 0.392232
\(235\) −4.00000 −0.260931
\(236\) 10.0000 0.650945
\(237\) −10.0000 −0.649570
\(238\) 8.00000 0.518563
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 1.00000 0.0645497
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −5.00000 −0.321412
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) 3.00000 0.191663
\(246\) 4.00000 0.255031
\(247\) −6.00000 −0.381771
\(248\) 6.00000 0.381000
\(249\) −2.00000 −0.126745
\(250\) 1.00000 0.0632456
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −2.00000 −0.125988
\(253\) 16.0000 1.00591
\(254\) 20.0000 1.25491
\(255\) 4.00000 0.250490
\(256\) 1.00000 0.0625000
\(257\) −18.0000 −1.12281 −0.561405 0.827541i \(-0.689739\pi\)
−0.561405 + 0.827541i \(0.689739\pi\)
\(258\) 12.0000 0.747087
\(259\) −20.0000 −1.24274
\(260\) 6.00000 0.372104
\(261\) 6.00000 0.371391
\(262\) −12.0000 −0.741362
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 4.00000 0.246183
\(265\) 10.0000 0.614295
\(266\) 2.00000 0.122628
\(267\) 8.00000 0.489592
\(268\) 12.0000 0.733017
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 4.00000 0.242536
\(273\) −12.0000 −0.726273
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) −4.00000 −0.240772
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 4.00000 0.239904
\(279\) −6.00000 −0.359211
\(280\) −2.00000 −0.119523
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 4.00000 0.238197
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) 8.00000 0.474713
\(285\) 1.00000 0.0592349
\(286\) 24.0000 1.41915
\(287\) −8.00000 −0.472225
\(288\) −1.00000 −0.0589256
\(289\) −1.00000 −0.0588235
\(290\) 6.00000 0.352332
\(291\) −2.00000 −0.117242
\(292\) −2.00000 −0.117041
\(293\) 2.00000 0.116841 0.0584206 0.998292i \(-0.481394\pi\)
0.0584206 + 0.998292i \(0.481394\pi\)
\(294\) −3.00000 −0.174964
\(295\) −10.0000 −0.582223
\(296\) −10.0000 −0.581238
\(297\) −4.00000 −0.232104
\(298\) −14.0000 −0.810998
\(299\) −24.0000 −1.38796
\(300\) −1.00000 −0.0577350
\(301\) −24.0000 −1.38334
\(302\) 2.00000 0.115087
\(303\) 10.0000 0.574485
\(304\) 1.00000 0.0573539
\(305\) −2.00000 −0.114520
\(306\) −4.00000 −0.228665
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −8.00000 −0.455842
\(309\) 12.0000 0.682656
\(310\) −6.00000 −0.340777
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) −6.00000 −0.339683
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −12.0000 −0.677199
\(315\) 2.00000 0.112687
\(316\) 10.0000 0.562544
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) −10.0000 −0.560772
\(319\) 24.0000 1.34374
\(320\) −1.00000 −0.0559017
\(321\) −8.00000 −0.446516
\(322\) 8.00000 0.445823
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) −6.00000 −0.332820
\(326\) 16.0000 0.886158
\(327\) 16.0000 0.884802
\(328\) −4.00000 −0.220863
\(329\) −8.00000 −0.441054
\(330\) −4.00000 −0.220193
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 2.00000 0.109764
\(333\) 10.0000 0.547997
\(334\) −24.0000 −1.31322
\(335\) −12.0000 −0.655630
\(336\) 2.00000 0.109109
\(337\) −34.0000 −1.85210 −0.926049 0.377403i \(-0.876817\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) −23.0000 −1.25104
\(339\) 14.0000 0.760376
\(340\) −4.00000 −0.216930
\(341\) −24.0000 −1.29967
\(342\) −1.00000 −0.0540738
\(343\) 20.0000 1.07990
\(344\) −12.0000 −0.646997
\(345\) 4.00000 0.215353
\(346\) 18.0000 0.967686
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) −6.00000 −0.321634
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 2.00000 0.106904
\(351\) 6.00000 0.320256
\(352\) −4.00000 −0.213201
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 10.0000 0.531494
\(355\) −8.00000 −0.424596
\(356\) −8.00000 −0.423999
\(357\) 8.00000 0.423405
\(358\) 2.00000 0.105703
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 1.00000 0.0527046
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −5.00000 −0.262432
\(364\) 12.0000 0.628971
\(365\) 2.00000 0.104685
\(366\) 2.00000 0.104542
\(367\) −22.0000 −1.14839 −0.574195 0.818718i \(-0.694685\pi\)
−0.574195 + 0.818718i \(0.694685\pi\)
\(368\) 4.00000 0.208514
\(369\) 4.00000 0.208232
\(370\) 10.0000 0.519875
\(371\) 20.0000 1.03835
\(372\) 6.00000 0.311086
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) −16.0000 −0.827340
\(375\) 1.00000 0.0516398
\(376\) −4.00000 −0.206284
\(377\) −36.0000 −1.85409
\(378\) −2.00000 −0.102869
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 20.0000 1.02463
\(382\) 8.00000 0.409316
\(383\) −16.0000 −0.817562 −0.408781 0.912633i \(-0.634046\pi\)
−0.408781 + 0.912633i \(0.634046\pi\)
\(384\) 1.00000 0.0510310
\(385\) 8.00000 0.407718
\(386\) −14.0000 −0.712581
\(387\) 12.0000 0.609994
\(388\) 2.00000 0.101535
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 6.00000 0.303822
\(391\) 16.0000 0.809155
\(392\) 3.00000 0.151523
\(393\) −12.0000 −0.605320
\(394\) −22.0000 −1.10834
\(395\) −10.0000 −0.503155
\(396\) 4.00000 0.201008
\(397\) −24.0000 −1.20453 −0.602263 0.798298i \(-0.705734\pi\)
−0.602263 + 0.798298i \(0.705734\pi\)
\(398\) 4.00000 0.200502
\(399\) 2.00000 0.100125
\(400\) 1.00000 0.0500000
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 12.0000 0.598506
\(403\) 36.0000 1.79329
\(404\) −10.0000 −0.497519
\(405\) −1.00000 −0.0496904
\(406\) 12.0000 0.595550
\(407\) 40.0000 1.98273
\(408\) 4.00000 0.198030
\(409\) −6.00000 −0.296681 −0.148340 0.988936i \(-0.547393\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 4.00000 0.197546
\(411\) 0 0
\(412\) −12.0000 −0.591198
\(413\) −20.0000 −0.984136
\(414\) −4.00000 −0.196589
\(415\) −2.00000 −0.0981761
\(416\) 6.00000 0.294174
\(417\) 4.00000 0.195881
\(418\) −4.00000 −0.195646
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −2.00000 −0.0975900
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 8.00000 0.389434
\(423\) 4.00000 0.194487
\(424\) 10.0000 0.485643
\(425\) 4.00000 0.194029
\(426\) 8.00000 0.387601
\(427\) −4.00000 −0.193574
\(428\) 8.00000 0.386695
\(429\) 24.0000 1.15873
\(430\) 12.0000 0.578691
\(431\) −40.0000 −1.92673 −0.963366 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) −12.0000 −0.576018
\(435\) 6.00000 0.287678
\(436\) −16.0000 −0.766261
\(437\) 4.00000 0.191346
\(438\) −2.00000 −0.0955637
\(439\) −38.0000 −1.81364 −0.906821 0.421517i \(-0.861498\pi\)
−0.906821 + 0.421517i \(0.861498\pi\)
\(440\) 4.00000 0.190693
\(441\) −3.00000 −0.142857
\(442\) 24.0000 1.14156
\(443\) 6.00000 0.285069 0.142534 0.989790i \(-0.454475\pi\)
0.142534 + 0.989790i \(0.454475\pi\)
\(444\) −10.0000 −0.474579
\(445\) 8.00000 0.379236
\(446\) −24.0000 −1.13643
\(447\) −14.0000 −0.662177
\(448\) −2.00000 −0.0944911
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 16.0000 0.753411
\(452\) −14.0000 −0.658505
\(453\) 2.00000 0.0939682
\(454\) −20.0000 −0.938647
\(455\) −12.0000 −0.562569
\(456\) 1.00000 0.0468293
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 26.0000 1.21490
\(459\) −4.00000 −0.186704
\(460\) −4.00000 −0.186501
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) −8.00000 −0.372194
\(463\) −18.0000 −0.836531 −0.418265 0.908325i \(-0.637362\pi\)
−0.418265 + 0.908325i \(0.637362\pi\)
\(464\) 6.00000 0.278543
\(465\) −6.00000 −0.278243
\(466\) 12.0000 0.555889
\(467\) −22.0000 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) −6.00000 −0.277350
\(469\) −24.0000 −1.10822
\(470\) 4.00000 0.184506
\(471\) −12.0000 −0.552931
\(472\) −10.0000 −0.460287
\(473\) 48.0000 2.20704
\(474\) 10.0000 0.459315
\(475\) 1.00000 0.0458831
\(476\) −8.00000 −0.366679
\(477\) −10.0000 −0.457869
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −60.0000 −2.73576
\(482\) −10.0000 −0.455488
\(483\) 8.00000 0.364013
\(484\) 5.00000 0.227273
\(485\) −2.00000 −0.0908153
\(486\) 1.00000 0.0453609
\(487\) 20.0000 0.906287 0.453143 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 16.0000 0.723545
\(490\) −3.00000 −0.135526
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −4.00000 −0.180334
\(493\) 24.0000 1.08091
\(494\) 6.00000 0.269953
\(495\) −4.00000 −0.179787
\(496\) −6.00000 −0.269408
\(497\) −16.0000 −0.717698
\(498\) 2.00000 0.0896221
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −24.0000 −1.07224
\(502\) 0 0
\(503\) −8.00000 −0.356702 −0.178351 0.983967i \(-0.557076\pi\)
−0.178351 + 0.983967i \(0.557076\pi\)
\(504\) 2.00000 0.0890871
\(505\) 10.0000 0.444994
\(506\) −16.0000 −0.711287
\(507\) −23.0000 −1.02147
\(508\) −20.0000 −0.887357
\(509\) 38.0000 1.68432 0.842160 0.539227i \(-0.181284\pi\)
0.842160 + 0.539227i \(0.181284\pi\)
\(510\) −4.00000 −0.177123
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 −0.0441511
\(514\) 18.0000 0.793946
\(515\) 12.0000 0.528783
\(516\) −12.0000 −0.528271
\(517\) 16.0000 0.703679
\(518\) 20.0000 0.878750
\(519\) 18.0000 0.790112
\(520\) −6.00000 −0.263117
\(521\) 40.0000 1.75243 0.876216 0.481919i \(-0.160060\pi\)
0.876216 + 0.481919i \(0.160060\pi\)
\(522\) −6.00000 −0.262613
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 12.0000 0.524222
\(525\) 2.00000 0.0872872
\(526\) −12.0000 −0.523225
\(527\) −24.0000 −1.04546
\(528\) −4.00000 −0.174078
\(529\) −7.00000 −0.304348
\(530\) −10.0000 −0.434372
\(531\) 10.0000 0.433963
\(532\) −2.00000 −0.0867110
\(533\) −24.0000 −1.03956
\(534\) −8.00000 −0.346194
\(535\) −8.00000 −0.345870
\(536\) −12.0000 −0.518321
\(537\) 2.00000 0.0863064
\(538\) −14.0000 −0.603583
\(539\) −12.0000 −0.516877
\(540\) 1.00000 0.0430331
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) −20.0000 −0.859074
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) 16.0000 0.685365
\(546\) 12.0000 0.513553
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 0 0
\(549\) 2.00000 0.0853579
\(550\) −4.00000 −0.170561
\(551\) 6.00000 0.255609
\(552\) 4.00000 0.170251
\(553\) −20.0000 −0.850487
\(554\) −28.0000 −1.18961
\(555\) 10.0000 0.424476
\(556\) −4.00000 −0.169638
\(557\) 10.0000 0.423714 0.211857 0.977301i \(-0.432049\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(558\) 6.00000 0.254000
\(559\) −72.0000 −3.04528
\(560\) 2.00000 0.0845154
\(561\) −16.0000 −0.675521
\(562\) −4.00000 −0.168730
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −4.00000 −0.168430
\(565\) 14.0000 0.588984
\(566\) −28.0000 −1.17693
\(567\) −2.00000 −0.0839921
\(568\) −8.00000 −0.335673
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) −1.00000 −0.0418854
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −24.0000 −1.00349
\(573\) 8.00000 0.334205
\(574\) 8.00000 0.333914
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 10.0000 0.416305 0.208153 0.978096i \(-0.433255\pi\)
0.208153 + 0.978096i \(0.433255\pi\)
\(578\) 1.00000 0.0415945
\(579\) −14.0000 −0.581820
\(580\) −6.00000 −0.249136
\(581\) −4.00000 −0.165948
\(582\) 2.00000 0.0829027
\(583\) −40.0000 −1.65663
\(584\) 2.00000 0.0827606
\(585\) 6.00000 0.248069
\(586\) −2.00000 −0.0826192
\(587\) 22.0000 0.908037 0.454019 0.890992i \(-0.349990\pi\)
0.454019 + 0.890992i \(0.349990\pi\)
\(588\) 3.00000 0.123718
\(589\) −6.00000 −0.247226
\(590\) 10.0000 0.411693
\(591\) −22.0000 −0.904959
\(592\) 10.0000 0.410997
\(593\) −8.00000 −0.328521 −0.164260 0.986417i \(-0.552524\pi\)
−0.164260 + 0.986417i \(0.552524\pi\)
\(594\) 4.00000 0.164122
\(595\) 8.00000 0.327968
\(596\) 14.0000 0.573462
\(597\) 4.00000 0.163709
\(598\) 24.0000 0.981433
\(599\) −28.0000 −1.14405 −0.572024 0.820237i \(-0.693842\pi\)
−0.572024 + 0.820237i \(0.693842\pi\)
\(600\) 1.00000 0.0408248
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 24.0000 0.978167
\(603\) 12.0000 0.488678
\(604\) −2.00000 −0.0813788
\(605\) −5.00000 −0.203279
\(606\) −10.0000 −0.406222
\(607\) −28.0000 −1.13648 −0.568242 0.822861i \(-0.692376\pi\)
−0.568242 + 0.822861i \(0.692376\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 12.0000 0.486265
\(610\) 2.00000 0.0809776
\(611\) −24.0000 −0.970936
\(612\) 4.00000 0.161690
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 12.0000 0.484281
\(615\) 4.00000 0.161296
\(616\) 8.00000 0.322329
\(617\) −48.0000 −1.93241 −0.966204 0.257780i \(-0.917009\pi\)
−0.966204 + 0.257780i \(0.917009\pi\)
\(618\) −12.0000 −0.482711
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 6.00000 0.240966
\(621\) −4.00000 −0.160514
\(622\) −16.0000 −0.641542
\(623\) 16.0000 0.641026
\(624\) 6.00000 0.240192
\(625\) 1.00000 0.0400000
\(626\) −6.00000 −0.239808
\(627\) −4.00000 −0.159745
\(628\) 12.0000 0.478852
\(629\) 40.0000 1.59490
\(630\) −2.00000 −0.0796819
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) −10.0000 −0.397779
\(633\) 8.00000 0.317971
\(634\) −18.0000 −0.714871
\(635\) 20.0000 0.793676
\(636\) 10.0000 0.396526
\(637\) 18.0000 0.713186
\(638\) −24.0000 −0.950169
\(639\) 8.00000 0.316475
\(640\) 1.00000 0.0395285
\(641\) −20.0000 −0.789953 −0.394976 0.918691i \(-0.629247\pi\)
−0.394976 + 0.918691i \(0.629247\pi\)
\(642\) 8.00000 0.315735
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) −8.00000 −0.315244
\(645\) 12.0000 0.472500
\(646\) −4.00000 −0.157378
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 40.0000 1.57014
\(650\) 6.00000 0.235339
\(651\) −12.0000 −0.470317
\(652\) −16.0000 −0.626608
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) −16.0000 −0.625650
\(655\) −12.0000 −0.468879
\(656\) 4.00000 0.156174
\(657\) −2.00000 −0.0780274
\(658\) 8.00000 0.311872
\(659\) 22.0000 0.856998 0.428499 0.903542i \(-0.359042\pi\)
0.428499 + 0.903542i \(0.359042\pi\)
\(660\) 4.00000 0.155700
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) 12.0000 0.466393
\(663\) 24.0000 0.932083
\(664\) −2.00000 −0.0776151
\(665\) 2.00000 0.0775567
\(666\) −10.0000 −0.387492
\(667\) 24.0000 0.929284
\(668\) 24.0000 0.928588
\(669\) −24.0000 −0.927894
\(670\) 12.0000 0.463600
\(671\) 8.00000 0.308837
\(672\) −2.00000 −0.0771517
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 34.0000 1.30963
\(675\) −1.00000 −0.0384900
\(676\) 23.0000 0.884615
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −14.0000 −0.537667
\(679\) −4.00000 −0.153506
\(680\) 4.00000 0.153393
\(681\) −20.0000 −0.766402
\(682\) 24.0000 0.919007
\(683\) −12.0000 −0.459167 −0.229584 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 1.00000 0.0382360
\(685\) 0 0
\(686\) −20.0000 −0.763604
\(687\) 26.0000 0.991962
\(688\) 12.0000 0.457496
\(689\) 60.0000 2.28582
\(690\) −4.00000 −0.152277
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) −18.0000 −0.684257
\(693\) −8.00000 −0.303895
\(694\) 2.00000 0.0759190
\(695\) 4.00000 0.151729
\(696\) 6.00000 0.227429
\(697\) 16.0000 0.606043
\(698\) −22.0000 −0.832712
\(699\) 12.0000 0.453882
\(700\) −2.00000 −0.0755929
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) −6.00000 −0.226455
\(703\) 10.0000 0.377157
\(704\) 4.00000 0.150756
\(705\) 4.00000 0.150649
\(706\) 0 0
\(707\) 20.0000 0.752177
\(708\) −10.0000 −0.375823
\(709\) 14.0000 0.525781 0.262891 0.964826i \(-0.415324\pi\)
0.262891 + 0.964826i \(0.415324\pi\)
\(710\) 8.00000 0.300235
\(711\) 10.0000 0.375029
\(712\) 8.00000 0.299813
\(713\) −24.0000 −0.898807
\(714\) −8.00000 −0.299392
\(715\) 24.0000 0.897549
\(716\) −2.00000 −0.0747435
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0000 1.49175 0.745874 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 24.0000 0.893807
\(722\) −1.00000 −0.0372161
\(723\) −10.0000 −0.371904
\(724\) 0 0
\(725\) 6.00000 0.222834
\(726\) 5.00000 0.185567
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) −12.0000 −0.444750
\(729\) 1.00000 0.0370370
\(730\) −2.00000 −0.0740233
\(731\) 48.0000 1.77534
\(732\) −2.00000 −0.0739221
\(733\) −8.00000 −0.295487 −0.147743 0.989026i \(-0.547201\pi\)
−0.147743 + 0.989026i \(0.547201\pi\)
\(734\) 22.0000 0.812035
\(735\) −3.00000 −0.110657
\(736\) −4.00000 −0.147442
\(737\) 48.0000 1.76810
\(738\) −4.00000 −0.147242
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −10.0000 −0.367607
\(741\) 6.00000 0.220416
\(742\) −20.0000 −0.734223
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) −6.00000 −0.219971
\(745\) −14.0000 −0.512920
\(746\) −14.0000 −0.512576
\(747\) 2.00000 0.0731762
\(748\) 16.0000 0.585018
\(749\) −16.0000 −0.584627
\(750\) −1.00000 −0.0365148
\(751\) −38.0000 −1.38664 −0.693320 0.720630i \(-0.743853\pi\)
−0.693320 + 0.720630i \(0.743853\pi\)
\(752\) 4.00000 0.145865
\(753\) 0 0
\(754\) 36.0000 1.31104
\(755\) 2.00000 0.0727875
\(756\) 2.00000 0.0727393
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) −8.00000 −0.290573
\(759\) −16.0000 −0.580763
\(760\) 1.00000 0.0362738
\(761\) −34.0000 −1.23250 −0.616250 0.787551i \(-0.711349\pi\)
−0.616250 + 0.787551i \(0.711349\pi\)
\(762\) −20.0000 −0.724524
\(763\) 32.0000 1.15848
\(764\) −8.00000 −0.289430
\(765\) −4.00000 −0.144620
\(766\) 16.0000 0.578103
\(767\) −60.0000 −2.16647
\(768\) −1.00000 −0.0360844
\(769\) −18.0000 −0.649097 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(770\) −8.00000 −0.288300
\(771\) 18.0000 0.648254
\(772\) 14.0000 0.503871
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) −12.0000 −0.431331
\(775\) −6.00000 −0.215526
\(776\) −2.00000 −0.0717958
\(777\) 20.0000 0.717496
\(778\) 10.0000 0.358517
\(779\) 4.00000 0.143315
\(780\) −6.00000 −0.214834
\(781\) 32.0000 1.14505
\(782\) −16.0000 −0.572159
\(783\) −6.00000 −0.214423
\(784\) −3.00000 −0.107143
\(785\) −12.0000 −0.428298
\(786\) 12.0000 0.428026
\(787\) 4.00000 0.142585 0.0712923 0.997455i \(-0.477288\pi\)
0.0712923 + 0.997455i \(0.477288\pi\)
\(788\) 22.0000 0.783718
\(789\) −12.0000 −0.427211
\(790\) 10.0000 0.355784
\(791\) 28.0000 0.995565
\(792\) −4.00000 −0.142134
\(793\) −12.0000 −0.426132
\(794\) 24.0000 0.851728
\(795\) −10.0000 −0.354663
\(796\) −4.00000 −0.141776
\(797\) 2.00000 0.0708436 0.0354218 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 16.0000 0.566039
\(800\) −1.00000 −0.0353553
\(801\) −8.00000 −0.282666
\(802\) 24.0000 0.847469
\(803\) −8.00000 −0.282314
\(804\) −12.0000 −0.423207
\(805\) 8.00000 0.281963
\(806\) −36.0000 −1.26805
\(807\) −14.0000 −0.492823
\(808\) 10.0000 0.351799
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 1.00000 0.0351364
\(811\) −8.00000 −0.280918 −0.140459 0.990086i \(-0.544858\pi\)
−0.140459 + 0.990086i \(0.544858\pi\)
\(812\) −12.0000 −0.421117
\(813\) −20.0000 −0.701431
\(814\) −40.0000 −1.40200
\(815\) 16.0000 0.560456
\(816\) −4.00000 −0.140028
\(817\) 12.0000 0.419827
\(818\) 6.00000 0.209785
\(819\) 12.0000 0.419314
\(820\) −4.00000 −0.139686
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) −26.0000 −0.906303 −0.453152 0.891434i \(-0.649700\pi\)
−0.453152 + 0.891434i \(0.649700\pi\)
\(824\) 12.0000 0.418040
\(825\) −4.00000 −0.139262
\(826\) 20.0000 0.695889
\(827\) 48.0000 1.66912 0.834562 0.550914i \(-0.185721\pi\)
0.834562 + 0.550914i \(0.185721\pi\)
\(828\) 4.00000 0.139010
\(829\) −40.0000 −1.38926 −0.694629 0.719368i \(-0.744431\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(830\) 2.00000 0.0694210
\(831\) −28.0000 −0.971309
\(832\) −6.00000 −0.208013
\(833\) −12.0000 −0.415775
\(834\) −4.00000 −0.138509
\(835\) −24.0000 −0.830554
\(836\) 4.00000 0.138343
\(837\) 6.00000 0.207390
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 2.00000 0.0690066
\(841\) 7.00000 0.241379
\(842\) 8.00000 0.275698
\(843\) −4.00000 −0.137767
\(844\) −8.00000 −0.275371
\(845\) −23.0000 −0.791224
\(846\) −4.00000 −0.137523
\(847\) −10.0000 −0.343604
\(848\) −10.0000 −0.343401
\(849\) −28.0000 −0.960958
\(850\) −4.00000 −0.137199
\(851\) 40.0000 1.37118
\(852\) −8.00000 −0.274075
\(853\) −36.0000 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) 4.00000 0.136877
\(855\) −1.00000 −0.0341993
\(856\) −8.00000 −0.273434
\(857\) 30.0000 1.02478 0.512390 0.858753i \(-0.328760\pi\)
0.512390 + 0.858753i \(0.328760\pi\)
\(858\) −24.0000 −0.819346
\(859\) 4.00000 0.136478 0.0682391 0.997669i \(-0.478262\pi\)
0.0682391 + 0.997669i \(0.478262\pi\)
\(860\) −12.0000 −0.409197
\(861\) 8.00000 0.272639
\(862\) 40.0000 1.36241
\(863\) 32.0000 1.08929 0.544646 0.838666i \(-0.316664\pi\)
0.544646 + 0.838666i \(0.316664\pi\)
\(864\) 1.00000 0.0340207
\(865\) 18.0000 0.612018
\(866\) −30.0000 −1.01944
\(867\) 1.00000 0.0339618
\(868\) 12.0000 0.407307
\(869\) 40.0000 1.35691
\(870\) −6.00000 −0.203419
\(871\) −72.0000 −2.43963
\(872\) 16.0000 0.541828
\(873\) 2.00000 0.0676897
\(874\) −4.00000 −0.135302
\(875\) 2.00000 0.0676123
\(876\) 2.00000 0.0675737
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) 38.0000 1.28244
\(879\) −2.00000 −0.0674583
\(880\) −4.00000 −0.134840
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 3.00000 0.101015
\(883\) 36.0000 1.21150 0.605748 0.795656i \(-0.292874\pi\)
0.605748 + 0.795656i \(0.292874\pi\)
\(884\) −24.0000 −0.807207
\(885\) 10.0000 0.336146
\(886\) −6.00000 −0.201574
\(887\) 48.0000 1.61168 0.805841 0.592132i \(-0.201714\pi\)
0.805841 + 0.592132i \(0.201714\pi\)
\(888\) 10.0000 0.335578
\(889\) 40.0000 1.34156
\(890\) −8.00000 −0.268161
\(891\) 4.00000 0.134005
\(892\) 24.0000 0.803579
\(893\) 4.00000 0.133855
\(894\) 14.0000 0.468230
\(895\) 2.00000 0.0668526
\(896\) 2.00000 0.0668153
\(897\) 24.0000 0.801337
\(898\) −12.0000 −0.400445
\(899\) −36.0000 −1.20067
\(900\) 1.00000 0.0333333
\(901\) −40.0000 −1.33259
\(902\) −16.0000 −0.532742
\(903\) 24.0000 0.798670
\(904\) 14.0000 0.465633
\(905\) 0 0
\(906\) −2.00000 −0.0664455
\(907\) −20.0000 −0.664089 −0.332045 0.943264i \(-0.607738\pi\)
−0.332045 + 0.943264i \(0.607738\pi\)
\(908\) 20.0000 0.663723
\(909\) −10.0000 −0.331679
\(910\) 12.0000 0.397796
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 8.00000 0.264761
\(914\) 22.0000 0.727695
\(915\) 2.00000 0.0661180
\(916\) −26.0000 −0.859064
\(917\) −24.0000 −0.792550
\(918\) 4.00000 0.132020
\(919\) 16.0000 0.527791 0.263896 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 4.00000 0.131876
\(921\) 12.0000 0.395413
\(922\) −18.0000 −0.592798
\(923\) −48.0000 −1.57994
\(924\) 8.00000 0.263181
\(925\) 10.0000 0.328798
\(926\) 18.0000 0.591517
\(927\) −12.0000 −0.394132
\(928\) −6.00000 −0.196960
\(929\) 42.0000 1.37798 0.688988 0.724773i \(-0.258055\pi\)
0.688988 + 0.724773i \(0.258055\pi\)
\(930\) 6.00000 0.196748
\(931\) −3.00000 −0.0983210
\(932\) −12.0000 −0.393073
\(933\) −16.0000 −0.523816
\(934\) 22.0000 0.719862
\(935\) −16.0000 −0.523256
\(936\) 6.00000 0.196116
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 24.0000 0.783628
\(939\) −6.00000 −0.195803
\(940\) −4.00000 −0.130466
\(941\) 10.0000 0.325991 0.162995 0.986627i \(-0.447884\pi\)
0.162995 + 0.986627i \(0.447884\pi\)
\(942\) 12.0000 0.390981
\(943\) 16.0000 0.521032
\(944\) 10.0000 0.325472
\(945\) −2.00000 −0.0650600
\(946\) −48.0000 −1.56061
\(947\) −38.0000 −1.23483 −0.617417 0.786636i \(-0.711821\pi\)
−0.617417 + 0.786636i \(0.711821\pi\)
\(948\) −10.0000 −0.324785
\(949\) 12.0000 0.389536
\(950\) −1.00000 −0.0324443
\(951\) −18.0000 −0.583690
\(952\) 8.00000 0.259281
\(953\) 6.00000 0.194359 0.0971795 0.995267i \(-0.469018\pi\)
0.0971795 + 0.995267i \(0.469018\pi\)
\(954\) 10.0000 0.323762
\(955\) 8.00000 0.258874
\(956\) 0 0
\(957\) −24.0000 −0.775810
\(958\) 24.0000 0.775405
\(959\) 0 0
\(960\) 1.00000 0.0322749
\(961\) 5.00000 0.161290
\(962\) 60.0000 1.93448
\(963\) 8.00000 0.257796
\(964\) 10.0000 0.322078
\(965\) −14.0000 −0.450676
\(966\) −8.00000 −0.257396
\(967\) −18.0000 −0.578841 −0.289420 0.957202i \(-0.593463\pi\)
−0.289420 + 0.957202i \(0.593463\pi\)
\(968\) −5.00000 −0.160706
\(969\) −4.00000 −0.128499
\(970\) 2.00000 0.0642161
\(971\) −42.0000 −1.34784 −0.673922 0.738802i \(-0.735392\pi\)
−0.673922 + 0.738802i \(0.735392\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 8.00000 0.256468
\(974\) −20.0000 −0.640841
\(975\) 6.00000 0.192154
\(976\) 2.00000 0.0640184
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) −16.0000 −0.511624
\(979\) −32.0000 −1.02272
\(980\) 3.00000 0.0958315
\(981\) −16.0000 −0.510841
\(982\) −12.0000 −0.382935
\(983\) 24.0000 0.765481 0.382741 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 4.00000 0.127515
\(985\) −22.0000 −0.700978
\(986\) −24.0000 −0.764316
\(987\) 8.00000 0.254643
\(988\) −6.00000 −0.190885
\(989\) 48.0000 1.52631
\(990\) 4.00000 0.127128
\(991\) −2.00000 −0.0635321 −0.0317660 0.999495i \(-0.510113\pi\)
−0.0317660 + 0.999495i \(0.510113\pi\)
\(992\) 6.00000 0.190500
\(993\) 12.0000 0.380808
\(994\) 16.0000 0.507489
\(995\) 4.00000 0.126809
\(996\) −2.00000 −0.0633724
\(997\) −52.0000 −1.64686 −0.823428 0.567420i \(-0.807941\pi\)
−0.823428 + 0.567420i \(0.807941\pi\)
\(998\) 4.00000 0.126618
\(999\) −10.0000 −0.316386
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.a.1.1 1
3.2 odd 2 1710.2.a.q.1.1 1
4.3 odd 2 4560.2.a.t.1.1 1
5.2 odd 4 2850.2.d.r.799.1 2
5.3 odd 4 2850.2.d.r.799.2 2
5.4 even 2 2850.2.a.bb.1.1 1
15.14 odd 2 8550.2.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.2.a.a.1.1 1 1.1 even 1 trivial
1710.2.a.q.1.1 1 3.2 odd 2
2850.2.a.bb.1.1 1 5.4 even 2
2850.2.d.r.799.1 2 5.2 odd 4
2850.2.d.r.799.2 2 5.3 odd 4
4560.2.a.t.1.1 1 4.3 odd 2
8550.2.a.n.1.1 1 15.14 odd 2