Properties

Label 4598.2.a.l.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -3.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +2.00000 q^{10} -1.00000 q^{12} +2.00000 q^{13} -3.00000 q^{14} -2.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} +2.00000 q^{20} +3.00000 q^{21} -1.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} +2.00000 q^{26} +5.00000 q^{27} -3.00000 q^{28} -5.00000 q^{29} -2.00000 q^{30} -8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} -6.00000 q^{35} -2.00000 q^{36} +3.00000 q^{37} -1.00000 q^{38} -2.00000 q^{39} +2.00000 q^{40} +6.00000 q^{41} +3.00000 q^{42} -2.00000 q^{43} -4.00000 q^{45} -1.00000 q^{46} -3.00000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} +1.00000 q^{53} +5.00000 q^{54} -3.00000 q^{56} +1.00000 q^{57} -5.00000 q^{58} -3.00000 q^{59} -2.00000 q^{60} +6.00000 q^{61} -8.00000 q^{62} +6.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -12.0000 q^{67} +2.00000 q^{68} +1.00000 q^{69} -6.00000 q^{70} -14.0000 q^{71} -2.00000 q^{72} -6.00000 q^{73} +3.00000 q^{74} +1.00000 q^{75} -1.00000 q^{76} -2.00000 q^{78} +4.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +2.00000 q^{83} +3.00000 q^{84} +4.00000 q^{85} -2.00000 q^{86} +5.00000 q^{87} -4.00000 q^{89} -4.00000 q^{90} -6.00000 q^{91} -1.00000 q^{92} +8.00000 q^{93} -3.00000 q^{94} -2.00000 q^{95} -1.00000 q^{96} -4.00000 q^{97} +2.00000 q^{98} +O(q^{100})\)

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 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00000 0.894427 0.447214 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −1.00000 −0.408248
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 2.00000 0.632456
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −3.00000 −0.801784
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416
\(20\) 2.00000 0.447214
\(21\) 3.00000 0.654654
\(22\) 0 0
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.00000 −0.200000
\(26\) 2.00000 0.392232
\(27\) 5.00000 0.962250
\(28\) −3.00000 −0.566947
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −2.00000 −0.365148
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) −6.00000 −1.01419
\(36\) −2.00000 −0.333333
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −1.00000 −0.162221
\(39\) −2.00000 −0.320256
\(40\) 2.00000 0.316228
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 3.00000 0.462910
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −4.00000 −0.596285
\(46\) −1.00000 −0.147442
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) −2.00000 −0.280056
\(52\) 2.00000 0.277350
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) 1.00000 0.132453
\(58\) −5.00000 −0.656532
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −2.00000 −0.258199
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) −8.00000 −1.01600
\(63\) 6.00000 0.755929
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 2.00000 0.242536
\(69\) 1.00000 0.120386
\(70\) −6.00000 −0.717137
\(71\) −14.0000 −1.66149 −0.830747 0.556650i \(-0.812086\pi\)
−0.830747 + 0.556650i \(0.812086\pi\)
\(72\) −2.00000 −0.235702
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 3.00000 0.348743
\(75\) 1.00000 0.115470
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 2.00000 0.223607
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 3.00000 0.327327
\(85\) 4.00000 0.433861
\(86\) −2.00000 −0.215666
\(87\) 5.00000 0.536056
\(88\) 0 0
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) −4.00000 −0.421637
\(91\) −6.00000 −0.628971
\(92\) −1.00000 −0.104257
\(93\) 8.00000 0.829561
\(94\) −3.00000 −0.309426
\(95\) −2.00000 −0.205196
\(96\) −1.00000 −0.102062
\(97\) −4.00000 −0.406138 −0.203069 0.979164i \(-0.565092\pi\)
−0.203069 + 0.979164i \(0.565092\pi\)
\(98\) 2.00000 0.202031
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) −2.00000 −0.198030
\(103\) −12.0000 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(104\) 2.00000 0.196116
\(105\) 6.00000 0.585540
\(106\) 1.00000 0.0971286
\(107\) −7.00000 −0.676716 −0.338358 0.941018i \(-0.609871\pi\)
−0.338358 + 0.941018i \(0.609871\pi\)
\(108\) 5.00000 0.481125
\(109\) 1.00000 0.0957826 0.0478913 0.998853i \(-0.484750\pi\)
0.0478913 + 0.998853i \(0.484750\pi\)
\(110\) 0 0
\(111\) −3.00000 −0.284747
\(112\) −3.00000 −0.283473
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 1.00000 0.0936586
\(115\) −2.00000 −0.186501
\(116\) −5.00000 −0.464238
\(117\) −4.00000 −0.369800
\(118\) −3.00000 −0.276172
\(119\) −6.00000 −0.550019
\(120\) −2.00000 −0.182574
\(121\) 0 0
\(122\) 6.00000 0.543214
\(123\) −6.00000 −0.541002
\(124\) −8.00000 −0.718421
\(125\) −12.0000 −1.07331
\(126\) 6.00000 0.534522
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 0.176090
\(130\) 4.00000 0.350823
\(131\) 2.00000 0.174741 0.0873704 0.996176i \(-0.472154\pi\)
0.0873704 + 0.996176i \(0.472154\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) −12.0000 −1.03664
\(135\) 10.0000 0.860663
\(136\) 2.00000 0.171499
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 1.00000 0.0851257
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) −6.00000 −0.507093
\(141\) 3.00000 0.252646
\(142\) −14.0000 −1.17485
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) −10.0000 −0.830455
\(146\) −6.00000 −0.496564
\(147\) −2.00000 −0.164957
\(148\) 3.00000 0.246598
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 1.00000 0.0816497
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −16.0000 −1.28515
\(156\) −2.00000 −0.160128
\(157\) −4.00000 −0.319235 −0.159617 0.987179i \(-0.551026\pi\)
−0.159617 + 0.987179i \(0.551026\pi\)
\(158\) 4.00000 0.318223
\(159\) −1.00000 −0.0793052
\(160\) 2.00000 0.158114
\(161\) 3.00000 0.236433
\(162\) 1.00000 0.0785674
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) −22.0000 −1.70241 −0.851206 0.524832i \(-0.824128\pi\)
−0.851206 + 0.524832i \(0.824128\pi\)
\(168\) 3.00000 0.231455
\(169\) −9.00000 −0.692308
\(170\) 4.00000 0.306786
\(171\) 2.00000 0.152944
\(172\) −2.00000 −0.152499
\(173\) 11.0000 0.836315 0.418157 0.908375i \(-0.362676\pi\)
0.418157 + 0.908375i \(0.362676\pi\)
\(174\) 5.00000 0.379049
\(175\) 3.00000 0.226779
\(176\) 0 0
\(177\) 3.00000 0.225494
\(178\) −4.00000 −0.299813
\(179\) 17.0000 1.27064 0.635320 0.772249i \(-0.280868\pi\)
0.635320 + 0.772249i \(0.280868\pi\)
\(180\) −4.00000 −0.298142
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −6.00000 −0.444750
\(183\) −6.00000 −0.443533
\(184\) −1.00000 −0.0737210
\(185\) 6.00000 0.441129
\(186\) 8.00000 0.586588
\(187\) 0 0
\(188\) −3.00000 −0.218797
\(189\) −15.0000 −1.09109
\(190\) −2.00000 −0.145095
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −4.00000 −0.287183
\(195\) −4.00000 −0.286446
\(196\) 2.00000 0.142857
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 12.0000 0.846415
\(202\) −18.0000 −1.26648
\(203\) 15.0000 1.05279
\(204\) −2.00000 −0.140028
\(205\) 12.0000 0.838116
\(206\) −12.0000 −0.836080
\(207\) 2.00000 0.139010
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 6.00000 0.414039
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 1.00000 0.0686803
\(213\) 14.0000 0.959264
\(214\) −7.00000 −0.478510
\(215\) −4.00000 −0.272798
\(216\) 5.00000 0.340207
\(217\) 24.0000 1.62923
\(218\) 1.00000 0.0677285
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) −3.00000 −0.201347
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) −3.00000 −0.200446
\(225\) 2.00000 0.133333
\(226\) 6.00000 0.399114
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 1.00000 0.0662266
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) 17.0000 1.11371 0.556854 0.830611i \(-0.312008\pi\)
0.556854 + 0.830611i \(0.312008\pi\)
\(234\) −4.00000 −0.261488
\(235\) −6.00000 −0.391397
\(236\) −3.00000 −0.195283
\(237\) −4.00000 −0.259828
\(238\) −6.00000 −0.388922
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) −2.00000 −0.129099
\(241\) 28.0000 1.80364 0.901819 0.432113i \(-0.142232\pi\)
0.901819 + 0.432113i \(0.142232\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 6.00000 0.384111
\(245\) 4.00000 0.255551
\(246\) −6.00000 −0.382546
\(247\) −2.00000 −0.127257
\(248\) −8.00000 −0.508001
\(249\) −2.00000 −0.126745
\(250\) −12.0000 −0.758947
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) 20.0000 1.25491
\(255\) −4.00000 −0.250490
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 2.00000 0.124515
\(259\) −9.00000 −0.559233
\(260\) 4.00000 0.248069
\(261\) 10.0000 0.618984
\(262\) 2.00000 0.123560
\(263\) 16.0000 0.986602 0.493301 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 3.00000 0.183942
\(267\) 4.00000 0.244796
\(268\) −12.0000 −0.733017
\(269\) −21.0000 −1.28039 −0.640196 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 10.0000 0.608581
\(271\) −12.0000 −0.728948 −0.364474 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 2.00000 0.121268
\(273\) 6.00000 0.363137
\(274\) −10.0000 −0.604122
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −16.0000 −0.959616
\(279\) 16.0000 0.957895
\(280\) −6.00000 −0.358569
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 3.00000 0.178647
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −14.0000 −0.830747
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) −18.0000 −1.06251
\(288\) −2.00000 −0.117851
\(289\) −13.0000 −0.764706
\(290\) −10.0000 −0.587220
\(291\) 4.00000 0.234484
\(292\) −6.00000 −0.351123
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −2.00000 −0.116642
\(295\) −6.00000 −0.349334
\(296\) 3.00000 0.174371
\(297\) 0 0
\(298\) 0 0
\(299\) −2.00000 −0.115663
\(300\) 1.00000 0.0577350
\(301\) 6.00000 0.345834
\(302\) 0 0
\(303\) 18.0000 1.03407
\(304\) −1.00000 −0.0573539
\(305\) 12.0000 0.687118
\(306\) −4.00000 −0.228665
\(307\) 1.00000 0.0570730 0.0285365 0.999593i \(-0.490915\pi\)
0.0285365 + 0.999593i \(0.490915\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) −16.0000 −0.908739
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) −2.00000 −0.113228
\(313\) −27.0000 −1.52613 −0.763065 0.646322i \(-0.776306\pi\)
−0.763065 + 0.646322i \(0.776306\pi\)
\(314\) −4.00000 −0.225733
\(315\) 12.0000 0.676123
\(316\) 4.00000 0.225018
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) −1.00000 −0.0560772
\(319\) 0 0
\(320\) 2.00000 0.111803
\(321\) 7.00000 0.390702
\(322\) 3.00000 0.167183
\(323\) −2.00000 −0.111283
\(324\) 1.00000 0.0555556
\(325\) −2.00000 −0.110940
\(326\) 10.0000 0.553849
\(327\) −1.00000 −0.0553001
\(328\) 6.00000 0.331295
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 11.0000 0.604615 0.302307 0.953211i \(-0.402243\pi\)
0.302307 + 0.953211i \(0.402243\pi\)
\(332\) 2.00000 0.109764
\(333\) −6.00000 −0.328798
\(334\) −22.0000 −1.20379
\(335\) −24.0000 −1.31126
\(336\) 3.00000 0.163663
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) −9.00000 −0.489535
\(339\) −6.00000 −0.325875
\(340\) 4.00000 0.216930
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) 15.0000 0.809924
\(344\) −2.00000 −0.107833
\(345\) 2.00000 0.107676
\(346\) 11.0000 0.591364
\(347\) −14.0000 −0.751559 −0.375780 0.926709i \(-0.622625\pi\)
−0.375780 + 0.926709i \(0.622625\pi\)
\(348\) 5.00000 0.268028
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 3.00000 0.160357
\(351\) 10.0000 0.533761
\(352\) 0 0
\(353\) 29.0000 1.54351 0.771757 0.635917i \(-0.219378\pi\)
0.771757 + 0.635917i \(0.219378\pi\)
\(354\) 3.00000 0.159448
\(355\) −28.0000 −1.48609
\(356\) −4.00000 −0.212000
\(357\) 6.00000 0.317554
\(358\) 17.0000 0.898478
\(359\) −8.00000 −0.422224 −0.211112 0.977462i \(-0.567708\pi\)
−0.211112 + 0.977462i \(0.567708\pi\)
\(360\) −4.00000 −0.210819
\(361\) 1.00000 0.0526316
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) −6.00000 −0.314485
\(365\) −12.0000 −0.628109
\(366\) −6.00000 −0.313625
\(367\) 7.00000 0.365397 0.182699 0.983169i \(-0.441517\pi\)
0.182699 + 0.983169i \(0.441517\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −12.0000 −0.624695
\(370\) 6.00000 0.311925
\(371\) −3.00000 −0.155752
\(372\) 8.00000 0.414781
\(373\) 1.00000 0.0517780 0.0258890 0.999665i \(-0.491758\pi\)
0.0258890 + 0.999665i \(0.491758\pi\)
\(374\) 0 0
\(375\) 12.0000 0.619677
\(376\) −3.00000 −0.154713
\(377\) −10.0000 −0.515026
\(378\) −15.0000 −0.771517
\(379\) −35.0000 −1.79783 −0.898915 0.438124i \(-0.855643\pi\)
−0.898915 + 0.438124i \(0.855643\pi\)
\(380\) −2.00000 −0.102598
\(381\) −20.0000 −1.02463
\(382\) 3.00000 0.153493
\(383\) 4.00000 0.204390 0.102195 0.994764i \(-0.467413\pi\)
0.102195 + 0.994764i \(0.467413\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 4.00000 0.203331
\(388\) −4.00000 −0.203069
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) −4.00000 −0.202548
\(391\) −2.00000 −0.101144
\(392\) 2.00000 0.101015
\(393\) −2.00000 −0.100887
\(394\) 12.0000 0.604551
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 8.00000 0.401004
\(399\) −3.00000 −0.150188
\(400\) −1.00000 −0.0500000
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 12.0000 0.598506
\(403\) −16.0000 −0.797017
\(404\) −18.0000 −0.895533
\(405\) 2.00000 0.0993808
\(406\) 15.0000 0.744438
\(407\) 0 0
\(408\) −2.00000 −0.0990148
\(409\) 20.0000 0.988936 0.494468 0.869196i \(-0.335363\pi\)
0.494468 + 0.869196i \(0.335363\pi\)
\(410\) 12.0000 0.592638
\(411\) 10.0000 0.493264
\(412\) −12.0000 −0.591198
\(413\) 9.00000 0.442861
\(414\) 2.00000 0.0982946
\(415\) 4.00000 0.196352
\(416\) 2.00000 0.0980581
\(417\) 16.0000 0.783523
\(418\) 0 0
\(419\) −22.0000 −1.07477 −0.537385 0.843337i \(-0.680588\pi\)
−0.537385 + 0.843337i \(0.680588\pi\)
\(420\) 6.00000 0.292770
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 5.00000 0.243396
\(423\) 6.00000 0.291730
\(424\) 1.00000 0.0485643
\(425\) −2.00000 −0.0970143
\(426\) 14.0000 0.678302
\(427\) −18.0000 −0.871081
\(428\) −7.00000 −0.338358
\(429\) 0 0
\(430\) −4.00000 −0.192897
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 5.00000 0.240563
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) 24.0000 1.15204
\(435\) 10.0000 0.479463
\(436\) 1.00000 0.0478913
\(437\) 1.00000 0.0478365
\(438\) 6.00000 0.286691
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) −4.00000 −0.190476
\(442\) 4.00000 0.190261
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −3.00000 −0.142374
\(445\) −8.00000 −0.379236
\(446\) −2.00000 −0.0947027
\(447\) 0 0
\(448\) −3.00000 −0.141737
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 2.00000 0.0942809
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 0 0
\(454\) −24.0000 −1.12638
\(455\) −12.0000 −0.562569
\(456\) 1.00000 0.0468293
\(457\) 31.0000 1.45012 0.725059 0.688686i \(-0.241812\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 20.0000 0.934539
\(459\) 10.0000 0.466760
\(460\) −2.00000 −0.0932505
\(461\) 22.0000 1.02464 0.512321 0.858794i \(-0.328786\pi\)
0.512321 + 0.858794i \(0.328786\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −5.00000 −0.232119
\(465\) 16.0000 0.741982
\(466\) 17.0000 0.787510
\(467\) −14.0000 −0.647843 −0.323921 0.946084i \(-0.605001\pi\)
−0.323921 + 0.946084i \(0.605001\pi\)
\(468\) −4.00000 −0.184900
\(469\) 36.0000 1.66233
\(470\) −6.00000 −0.276759
\(471\) 4.00000 0.184310
\(472\) −3.00000 −0.138086
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 1.00000 0.0458831
\(476\) −6.00000 −0.275010
\(477\) −2.00000 −0.0915737
\(478\) −5.00000 −0.228695
\(479\) −15.0000 −0.685367 −0.342684 0.939451i \(-0.611336\pi\)
−0.342684 + 0.939451i \(0.611336\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 6.00000 0.273576
\(482\) 28.0000 1.27537
\(483\) −3.00000 −0.136505
\(484\) 0 0
\(485\) −8.00000 −0.363261
\(486\) −16.0000 −0.725775
\(487\) −30.0000 −1.35943 −0.679715 0.733476i \(-0.737896\pi\)
−0.679715 + 0.733476i \(0.737896\pi\)
\(488\) 6.00000 0.271607
\(489\) −10.0000 −0.452216
\(490\) 4.00000 0.180702
\(491\) −32.0000 −1.44414 −0.722070 0.691820i \(-0.756809\pi\)
−0.722070 + 0.691820i \(0.756809\pi\)
\(492\) −6.00000 −0.270501
\(493\) −10.0000 −0.450377
\(494\) −2.00000 −0.0899843
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 42.0000 1.88396
\(498\) −2.00000 −0.0896221
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) −12.0000 −0.536656
\(501\) 22.0000 0.982888
\(502\) −18.0000 −0.803379
\(503\) −7.00000 −0.312115 −0.156057 0.987748i \(-0.549878\pi\)
−0.156057 + 0.987748i \(0.549878\pi\)
\(504\) 6.00000 0.267261
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) 20.0000 0.887357
\(509\) 19.0000 0.842160 0.421080 0.907023i \(-0.361651\pi\)
0.421080 + 0.907023i \(0.361651\pi\)
\(510\) −4.00000 −0.177123
\(511\) 18.0000 0.796273
\(512\) 1.00000 0.0441942
\(513\) −5.00000 −0.220755
\(514\) −8.00000 −0.352865
\(515\) −24.0000 −1.05757
\(516\) 2.00000 0.0880451
\(517\) 0 0
\(518\) −9.00000 −0.395437
\(519\) −11.0000 −0.482846
\(520\) 4.00000 0.175412
\(521\) 38.0000 1.66481 0.832405 0.554168i \(-0.186963\pi\)
0.832405 + 0.554168i \(0.186963\pi\)
\(522\) 10.0000 0.437688
\(523\) 21.0000 0.918266 0.459133 0.888368i \(-0.348160\pi\)
0.459133 + 0.888368i \(0.348160\pi\)
\(524\) 2.00000 0.0873704
\(525\) −3.00000 −0.130931
\(526\) 16.0000 0.697633
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 2.00000 0.0868744
\(531\) 6.00000 0.260378
\(532\) 3.00000 0.130066
\(533\) 12.0000 0.519778
\(534\) 4.00000 0.173097
\(535\) −14.0000 −0.605273
\(536\) −12.0000 −0.518321
\(537\) −17.0000 −0.733604
\(538\) −21.0000 −0.905374
\(539\) 0 0
\(540\) 10.0000 0.430331
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −12.0000 −0.515444
\(543\) 14.0000 0.600798
\(544\) 2.00000 0.0857493
\(545\) 2.00000 0.0856706
\(546\) 6.00000 0.256776
\(547\) 19.0000 0.812381 0.406191 0.913788i \(-0.366857\pi\)
0.406191 + 0.913788i \(0.366857\pi\)
\(548\) −10.0000 −0.427179
\(549\) −12.0000 −0.512148
\(550\) 0 0
\(551\) 5.00000 0.213007
\(552\) 1.00000 0.0425628
\(553\) −12.0000 −0.510292
\(554\) −2.00000 −0.0849719
\(555\) −6.00000 −0.254686
\(556\) −16.0000 −0.678551
\(557\) 30.0000 1.27114 0.635570 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 16.0000 0.677334
\(559\) −4.00000 −0.169182
\(560\) −6.00000 −0.253546
\(561\) 0 0
\(562\) −20.0000 −0.843649
\(563\) 9.00000 0.379305 0.189652 0.981851i \(-0.439264\pi\)
0.189652 + 0.981851i \(0.439264\pi\)
\(564\) 3.00000 0.126323
\(565\) 12.0000 0.504844
\(566\) −4.00000 −0.168133
\(567\) −3.00000 −0.125988
\(568\) −14.0000 −0.587427
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 2.00000 0.0837708
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) −3.00000 −0.125327
\(574\) −18.0000 −0.751305
\(575\) 1.00000 0.0417029
\(576\) −2.00000 −0.0833333
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −13.0000 −0.540729
\(579\) 14.0000 0.581820
\(580\) −10.0000 −0.415227
\(581\) −6.00000 −0.248922
\(582\) 4.00000 0.165805
\(583\) 0 0
\(584\) −6.00000 −0.248282
\(585\) −8.00000 −0.330759
\(586\) 9.00000 0.371787
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) −2.00000 −0.0824786
\(589\) 8.00000 0.329634
\(590\) −6.00000 −0.247016
\(591\) −12.0000 −0.493614
\(592\) 3.00000 0.123299
\(593\) −27.0000 −1.10876 −0.554379 0.832265i \(-0.687044\pi\)
−0.554379 + 0.832265i \(0.687044\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 0 0
\(597\) −8.00000 −0.327418
\(598\) −2.00000 −0.0817861
\(599\) −44.0000 −1.79779 −0.898896 0.438163i \(-0.855629\pi\)
−0.898896 + 0.438163i \(0.855629\pi\)
\(600\) 1.00000 0.0408248
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 6.00000 0.244542
\(603\) 24.0000 0.977356
\(604\) 0 0
\(605\) 0 0
\(606\) 18.0000 0.731200
\(607\) 16.0000 0.649420 0.324710 0.945814i \(-0.394733\pi\)
0.324710 + 0.945814i \(0.394733\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −15.0000 −0.607831
\(610\) 12.0000 0.485866
\(611\) −6.00000 −0.242734
\(612\) −4.00000 −0.161690
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) 1.00000 0.0403567
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) −3.00000 −0.120775 −0.0603877 0.998175i \(-0.519234\pi\)
−0.0603877 + 0.998175i \(0.519234\pi\)
\(618\) 12.0000 0.482711
\(619\) 46.0000 1.84890 0.924448 0.381308i \(-0.124526\pi\)
0.924448 + 0.381308i \(0.124526\pi\)
\(620\) −16.0000 −0.642575
\(621\) −5.00000 −0.200643
\(622\) 24.0000 0.962312
\(623\) 12.0000 0.480770
\(624\) −2.00000 −0.0800641
\(625\) −19.0000 −0.760000
\(626\) −27.0000 −1.07914
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 6.00000 0.239236
\(630\) 12.0000 0.478091
\(631\) 31.0000 1.23409 0.617045 0.786928i \(-0.288330\pi\)
0.617045 + 0.786928i \(0.288330\pi\)
\(632\) 4.00000 0.159111
\(633\) −5.00000 −0.198732
\(634\) −6.00000 −0.238290
\(635\) 40.0000 1.58735
\(636\) −1.00000 −0.0396526
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) 28.0000 1.10766
\(640\) 2.00000 0.0790569
\(641\) 2.00000 0.0789953 0.0394976 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) 7.00000 0.276268
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 3.00000 0.118217
\(645\) 4.00000 0.157500
\(646\) −2.00000 −0.0786889
\(647\) 21.0000 0.825595 0.412798 0.910823i \(-0.364552\pi\)
0.412798 + 0.910823i \(0.364552\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) −24.0000 −0.940634
\(652\) 10.0000 0.391630
\(653\) −46.0000 −1.80012 −0.900060 0.435767i \(-0.856477\pi\)
−0.900060 + 0.435767i \(0.856477\pi\)
\(654\) −1.00000 −0.0391031
\(655\) 4.00000 0.156293
\(656\) 6.00000 0.234261
\(657\) 12.0000 0.468165
\(658\) 9.00000 0.350857
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 23.0000 0.894596 0.447298 0.894385i \(-0.352386\pi\)
0.447298 + 0.894385i \(0.352386\pi\)
\(662\) 11.0000 0.427527
\(663\) −4.00000 −0.155347
\(664\) 2.00000 0.0776151
\(665\) 6.00000 0.232670
\(666\) −6.00000 −0.232495
\(667\) 5.00000 0.193601
\(668\) −22.0000 −0.851206
\(669\) 2.00000 0.0773245
\(670\) −24.0000 −0.927201
\(671\) 0 0
\(672\) 3.00000 0.115728
\(673\) 48.0000 1.85026 0.925132 0.379646i \(-0.123954\pi\)
0.925132 + 0.379646i \(0.123954\pi\)
\(674\) 26.0000 1.00148
\(675\) −5.00000 −0.192450
\(676\) −9.00000 −0.346154
\(677\) −35.0000 −1.34516 −0.672580 0.740025i \(-0.734814\pi\)
−0.672580 + 0.740025i \(0.734814\pi\)
\(678\) −6.00000 −0.230429
\(679\) 12.0000 0.460518
\(680\) 4.00000 0.153393
\(681\) 24.0000 0.919682
\(682\) 0 0
\(683\) −4.00000 −0.153056 −0.0765279 0.997067i \(-0.524383\pi\)
−0.0765279 + 0.997067i \(0.524383\pi\)
\(684\) 2.00000 0.0764719
\(685\) −20.0000 −0.764161
\(686\) 15.0000 0.572703
\(687\) −20.0000 −0.763048
\(688\) −2.00000 −0.0762493
\(689\) 2.00000 0.0761939
\(690\) 2.00000 0.0761387
\(691\) −2.00000 −0.0760836 −0.0380418 0.999276i \(-0.512112\pi\)
−0.0380418 + 0.999276i \(0.512112\pi\)
\(692\) 11.0000 0.418157
\(693\) 0 0
\(694\) −14.0000 −0.531433
\(695\) −32.0000 −1.21383
\(696\) 5.00000 0.189525
\(697\) 12.0000 0.454532
\(698\) 26.0000 0.984115
\(699\) −17.0000 −0.642999
\(700\) 3.00000 0.113389
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 10.0000 0.377426
\(703\) −3.00000 −0.113147
\(704\) 0 0
\(705\) 6.00000 0.225973
\(706\) 29.0000 1.09143
\(707\) 54.0000 2.03088
\(708\) 3.00000 0.112747
\(709\) 40.0000 1.50223 0.751116 0.660171i \(-0.229516\pi\)
0.751116 + 0.660171i \(0.229516\pi\)
\(710\) −28.0000 −1.05082
\(711\) −8.00000 −0.300023
\(712\) −4.00000 −0.149906
\(713\) 8.00000 0.299602
\(714\) 6.00000 0.224544
\(715\) 0 0
\(716\) 17.0000 0.635320
\(717\) 5.00000 0.186728
\(718\) −8.00000 −0.298557
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) −4.00000 −0.149071
\(721\) 36.0000 1.34071
\(722\) 1.00000 0.0372161
\(723\) −28.0000 −1.04133
\(724\) −14.0000 −0.520306
\(725\) 5.00000 0.185695
\(726\) 0 0
\(727\) −7.00000 −0.259616 −0.129808 0.991539i \(-0.541436\pi\)
−0.129808 + 0.991539i \(0.541436\pi\)
\(728\) −6.00000 −0.222375
\(729\) 13.0000 0.481481
\(730\) −12.0000 −0.444140
\(731\) −4.00000 −0.147945
\(732\) −6.00000 −0.221766
\(733\) 32.0000 1.18195 0.590973 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) 7.00000 0.258375
\(735\) −4.00000 −0.147542
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) −12.0000 −0.441726
\(739\) 40.0000 1.47142 0.735712 0.677295i \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) 6.00000 0.220564
\(741\) 2.00000 0.0734718
\(742\) −3.00000 −0.110133
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 8.00000 0.293294
\(745\) 0 0
\(746\) 1.00000 0.0366126
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 21.0000 0.767323
\(750\) 12.0000 0.438178
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) −3.00000 −0.109399
\(753\) 18.0000 0.655956
\(754\) −10.0000 −0.364179
\(755\) 0 0
\(756\) −15.0000 −0.545545
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) −35.0000 −1.27126
\(759\) 0 0
\(760\) −2.00000 −0.0725476
\(761\) 1.00000 0.0362500 0.0181250 0.999836i \(-0.494230\pi\)
0.0181250 + 0.999836i \(0.494230\pi\)
\(762\) −20.0000 −0.724524
\(763\) −3.00000 −0.108607
\(764\) 3.00000 0.108536
\(765\) −8.00000 −0.289241
\(766\) 4.00000 0.144526
\(767\) −6.00000 −0.216647
\(768\) −1.00000 −0.0360844
\(769\) 31.0000 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) −14.0000 −0.503871
\(773\) −49.0000 −1.76241 −0.881204 0.472737i \(-0.843266\pi\)
−0.881204 + 0.472737i \(0.843266\pi\)
\(774\) 4.00000 0.143777
\(775\) 8.00000 0.287368
\(776\) −4.00000 −0.143592
\(777\) 9.00000 0.322873
\(778\) −24.0000 −0.860442
\(779\) −6.00000 −0.214972
\(780\) −4.00000 −0.143223
\(781\) 0 0
\(782\) −2.00000 −0.0715199
\(783\) −25.0000 −0.893427
\(784\) 2.00000 0.0714286
\(785\) −8.00000 −0.285532
\(786\) −2.00000 −0.0713376
\(787\) −19.0000 −0.677277 −0.338638 0.940917i \(-0.609966\pi\)
−0.338638 + 0.940917i \(0.609966\pi\)
\(788\) 12.0000 0.427482
\(789\) −16.0000 −0.569615
\(790\) 8.00000 0.284627
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) −2.00000 −0.0709773
\(795\) −2.00000 −0.0709327
\(796\) 8.00000 0.283552
\(797\) 38.0000 1.34603 0.673015 0.739629i \(-0.264999\pi\)
0.673015 + 0.739629i \(0.264999\pi\)
\(798\) −3.00000 −0.106199
\(799\) −6.00000 −0.212265
\(800\) −1.00000 −0.0353553
\(801\) 8.00000 0.282666
\(802\) 14.0000 0.494357
\(803\) 0 0
\(804\) 12.0000 0.423207
\(805\) 6.00000 0.211472
\(806\) −16.0000 −0.563576
\(807\) 21.0000 0.739235
\(808\) −18.0000 −0.633238
\(809\) 23.0000 0.808637 0.404318 0.914618i \(-0.367509\pi\)
0.404318 + 0.914618i \(0.367509\pi\)
\(810\) 2.00000 0.0702728
\(811\) 19.0000 0.667180 0.333590 0.942718i \(-0.391740\pi\)
0.333590 + 0.942718i \(0.391740\pi\)
\(812\) 15.0000 0.526397
\(813\) 12.0000 0.420858
\(814\) 0 0
\(815\) 20.0000 0.700569
\(816\) −2.00000 −0.0700140
\(817\) 2.00000 0.0699711
\(818\) 20.0000 0.699284
\(819\) 12.0000 0.419314
\(820\) 12.0000 0.419058
\(821\) −22.0000 −0.767805 −0.383903 0.923374i \(-0.625420\pi\)
−0.383903 + 0.923374i \(0.625420\pi\)
\(822\) 10.0000 0.348790
\(823\) 11.0000 0.383436 0.191718 0.981450i \(-0.438594\pi\)
0.191718 + 0.981450i \(0.438594\pi\)
\(824\) −12.0000 −0.418040
\(825\) 0 0
\(826\) 9.00000 0.313150
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) 2.00000 0.0695048
\(829\) 34.0000 1.18087 0.590434 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 4.00000 0.138842
\(831\) 2.00000 0.0693792
\(832\) 2.00000 0.0693375
\(833\) 4.00000 0.138592
\(834\) 16.0000 0.554035
\(835\) −44.0000 −1.52268
\(836\) 0 0
\(837\) −40.0000 −1.38260
\(838\) −22.0000 −0.759977
\(839\) 14.0000 0.483334 0.241667 0.970359i \(-0.422306\pi\)
0.241667 + 0.970359i \(0.422306\pi\)
\(840\) 6.00000 0.207020
\(841\) −4.00000 −0.137931
\(842\) −27.0000 −0.930481
\(843\) 20.0000 0.688837
\(844\) 5.00000 0.172107
\(845\) −18.0000 −0.619219
\(846\) 6.00000 0.206284
\(847\) 0 0
\(848\) 1.00000 0.0343401
\(849\) 4.00000 0.137280
\(850\) −2.00000 −0.0685994
\(851\) −3.00000 −0.102839
\(852\) 14.0000 0.479632
\(853\) −18.0000 −0.616308 −0.308154 0.951336i \(-0.599711\pi\)
−0.308154 + 0.951336i \(0.599711\pi\)
\(854\) −18.0000 −0.615947
\(855\) 4.00000 0.136797
\(856\) −7.00000 −0.239255
\(857\) 42.0000 1.43469 0.717346 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) −30.0000 −1.02359 −0.511793 0.859109i \(-0.671019\pi\)
−0.511793 + 0.859109i \(0.671019\pi\)
\(860\) −4.00000 −0.136399
\(861\) 18.0000 0.613438
\(862\) 16.0000 0.544962
\(863\) 36.0000 1.22545 0.612727 0.790295i \(-0.290072\pi\)
0.612727 + 0.790295i \(0.290072\pi\)
\(864\) 5.00000 0.170103
\(865\) 22.0000 0.748022
\(866\) 6.00000 0.203888
\(867\) 13.0000 0.441503
\(868\) 24.0000 0.814613
\(869\) 0 0
\(870\) 10.0000 0.339032
\(871\) −24.0000 −0.813209
\(872\) 1.00000 0.0338643
\(873\) 8.00000 0.270759
\(874\) 1.00000 0.0338255
\(875\) 36.0000 1.21702
\(876\) 6.00000 0.202721
\(877\) 6.00000 0.202606 0.101303 0.994856i \(-0.467699\pi\)
0.101303 + 0.994856i \(0.467699\pi\)
\(878\) 8.00000 0.269987
\(879\) −9.00000 −0.303562
\(880\) 0 0
\(881\) 57.0000 1.92038 0.960189 0.279350i \(-0.0901189\pi\)
0.960189 + 0.279350i \(0.0901189\pi\)
\(882\) −4.00000 −0.134687
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 4.00000 0.134535
\(885\) 6.00000 0.201688
\(886\) 18.0000 0.604722
\(887\) 14.0000 0.470074 0.235037 0.971986i \(-0.424479\pi\)
0.235037 + 0.971986i \(0.424479\pi\)
\(888\) −3.00000 −0.100673
\(889\) −60.0000 −2.01234
\(890\) −8.00000 −0.268161
\(891\) 0 0
\(892\) −2.00000 −0.0669650
\(893\) 3.00000 0.100391
\(894\) 0 0
\(895\) 34.0000 1.13649
\(896\) −3.00000 −0.100223
\(897\) 2.00000 0.0667781
\(898\) −6.00000 −0.200223
\(899\) 40.0000 1.33407
\(900\) 2.00000 0.0666667
\(901\) 2.00000 0.0666297
\(902\) 0 0
\(903\) −6.00000 −0.199667
\(904\) 6.00000 0.199557
\(905\) −28.0000 −0.930751
\(906\) 0 0
\(907\) −17.0000 −0.564476 −0.282238 0.959344i \(-0.591077\pi\)
−0.282238 + 0.959344i \(0.591077\pi\)
\(908\) −24.0000 −0.796468
\(909\) 36.0000 1.19404
\(910\) −12.0000 −0.397796
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 1.00000 0.0331133
\(913\) 0 0
\(914\) 31.0000 1.02539
\(915\) −12.0000 −0.396708
\(916\) 20.0000 0.660819
\(917\) −6.00000 −0.198137
\(918\) 10.0000 0.330049
\(919\) −24.0000 −0.791687 −0.395843 0.918318i \(-0.629548\pi\)
−0.395843 + 0.918318i \(0.629548\pi\)
\(920\) −2.00000 −0.0659380
\(921\) −1.00000 −0.0329511
\(922\) 22.0000 0.724531
\(923\) −28.0000 −0.921631
\(924\) 0 0
\(925\) −3.00000 −0.0986394
\(926\) 16.0000 0.525793
\(927\) 24.0000 0.788263
\(928\) −5.00000 −0.164133
\(929\) 25.0000 0.820223 0.410112 0.912035i \(-0.365490\pi\)
0.410112 + 0.912035i \(0.365490\pi\)
\(930\) 16.0000 0.524661
\(931\) −2.00000 −0.0655474
\(932\) 17.0000 0.556854
\(933\) −24.0000 −0.785725
\(934\) −14.0000 −0.458094
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −25.0000 −0.816714 −0.408357 0.912822i \(-0.633898\pi\)
−0.408357 + 0.912822i \(0.633898\pi\)
\(938\) 36.0000 1.17544
\(939\) 27.0000 0.881112
\(940\) −6.00000 −0.195698
\(941\) 18.0000 0.586783 0.293392 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 4.00000 0.130327
\(943\) −6.00000 −0.195387
\(944\) −3.00000 −0.0976417
\(945\) −30.0000 −0.975900
\(946\) 0 0
\(947\) 24.0000 0.779895 0.389948 0.920837i \(-0.372493\pi\)
0.389948 + 0.920837i \(0.372493\pi\)
\(948\) −4.00000 −0.129914
\(949\) −12.0000 −0.389536
\(950\) 1.00000 0.0324443
\(951\) 6.00000 0.194563
\(952\) −6.00000 −0.194461
\(953\) −24.0000 −0.777436 −0.388718 0.921357i \(-0.627082\pi\)
−0.388718 + 0.921357i \(0.627082\pi\)
\(954\) −2.00000 −0.0647524
\(955\) 6.00000 0.194155
\(956\) −5.00000 −0.161712
\(957\) 0 0
\(958\) −15.0000 −0.484628
\(959\) 30.0000 0.968751
\(960\) −2.00000 −0.0645497
\(961\) 33.0000 1.06452
\(962\) 6.00000 0.193448
\(963\) 14.0000 0.451144
\(964\) 28.0000 0.901819
\(965\) −28.0000 −0.901352
\(966\) −3.00000 −0.0965234
\(967\) 1.00000 0.0321578 0.0160789 0.999871i \(-0.494882\pi\)
0.0160789 + 0.999871i \(0.494882\pi\)
\(968\) 0 0
\(969\) 2.00000 0.0642493
\(970\) −8.00000 −0.256865
\(971\) 29.0000 0.930654 0.465327 0.885139i \(-0.345937\pi\)
0.465327 + 0.885139i \(0.345937\pi\)
\(972\) −16.0000 −0.513200
\(973\) 48.0000 1.53881
\(974\) −30.0000 −0.961262
\(975\) 2.00000 0.0640513
\(976\) 6.00000 0.192055
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −10.0000 −0.319765
\(979\) 0 0
\(980\) 4.00000 0.127775
\(981\) −2.00000 −0.0638551
\(982\) −32.0000 −1.02116
\(983\) −26.0000 −0.829271 −0.414636 0.909988i \(-0.636091\pi\)
−0.414636 + 0.909988i \(0.636091\pi\)
\(984\) −6.00000 −0.191273
\(985\) 24.0000 0.764704
\(986\) −10.0000 −0.318465
\(987\) −9.00000 −0.286473
\(988\) −2.00000 −0.0636285
\(989\) 2.00000 0.0635963
\(990\) 0 0
\(991\) 14.0000 0.444725 0.222362 0.974964i \(-0.428623\pi\)
0.222362 + 0.974964i \(0.428623\pi\)
\(992\) −8.00000 −0.254000
\(993\) −11.0000 −0.349074
\(994\) 42.0000 1.33216
\(995\) 16.0000 0.507234
\(996\) −2.00000 −0.0633724
\(997\) −2.00000 −0.0633406 −0.0316703 0.999498i \(-0.510083\pi\)
−0.0316703 + 0.999498i \(0.510083\pi\)
\(998\) 8.00000 0.253236
\(999\) 15.0000 0.474579
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 4598.2.a.l.1.1 yes 1
11.10 odd 2 4598.2.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.c.1.1 1 11.10 odd 2
4598.2.a.l.1.1 yes 1 1.1 even 1 trivial