Properties

Label 4598.2.a.c.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 \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −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 \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −3.00000 −0.801784
\(15\) −2.00000 −0.516398
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 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 \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 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 \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 3.00000 0.462910
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 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 \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 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 \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −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 \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 2.00000 0.223607
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) −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 \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) −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 \(-0.390129\pi\)
0.338358 + 0.941018i \(0.390129\pi\)
\(108\) 5.00000 0.481125
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) 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 \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.00000 −0.176090
\(130\) 4.00000 0.350823
\(131\) −2.00000 −0.174741 −0.0873704 0.996176i \(-0.527846\pi\)
−0.0873704 + 0.996176i \(0.527846\pi\)
\(132\) 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 \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 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 \(-0.175872\pi\)
0.851206 + 0.524832i \(0.175872\pi\)
\(168\) 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 \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(174\) 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 \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 4.00000 0.287183
\(195\) 4.00000 0.286446
\(196\) 2.00000 0.142857
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 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 \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 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 \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) −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 \(-0.687992\pi\)
−0.556854 + 0.830611i \(0.687992\pi\)
\(234\) −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 \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) −2.00000 −0.129099
\(241\) −28.0000 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) 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 \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 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 \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) −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 \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −16.0000 −0.959616
\(279\) 16.0000 0.957895
\(280\) −6.00000 −0.358569
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) −3.00000 −0.178647
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) −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 \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 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 \(-0.509085\pi\)
−0.0285365 + 0.999593i \(0.509085\pi\)
\(308\) 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 \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 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 \(-0.377375\pi\)
0.375780 + 0.926709i \(0.377375\pi\)
\(348\) −5.00000 −0.268028
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 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 \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 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 \(-0.508242\pi\)
−0.0258890 + 0.999665i \(0.508242\pi\)
\(374\) 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 \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 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 \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) 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 \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 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 \(-0.758188\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −20.0000 −0.934539
\(459\) −10.0000 −0.466760
\(460\) −2.00000 −0.0932505
\(461\) −22.0000 −1.02464 −0.512321 0.858794i \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 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 \(-0.388664\pi\)
0.342684 + 0.939451i \(0.388664\pi\)
\(480\) 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 \(-0.243191\pi\)
0.722070 + 0.691820i \(0.243191\pi\)
\(492\) 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 \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(504\) 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 \(-0.651840\pi\)
−0.459133 + 0.888368i \(0.651840\pi\)
\(524\) −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 \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) −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 \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) −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 \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) −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 \(-0.560736\pi\)
−0.189652 + 0.981851i \(0.560736\pi\)
\(564\) 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 \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 2.00000 0.0837708
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 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 \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) 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 \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −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 \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) −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 \(-0.151698\pi\)
0.888572 + 0.458738i \(0.151698\pi\)
\(614\) 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 \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 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 \(-0.876046\pi\)
−0.925132 + 0.379646i \(0.876046\pi\)
\(674\) 26.0000 1.00148
\(675\) −5.00000 −0.192450
\(676\) −9.00000 −0.346154
\(677\) 35.0000 1.34516 0.672580 0.740025i \(-0.265186\pi\)
0.672580 + 0.740025i \(0.265186\pi\)
\(678\) 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 \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 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 \(-0.701256\pi\)
−0.590973 + 0.806691i \(0.701256\pi\)
\(734\) −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 \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 6.00000 0.220564
\(741\) 2.00000 0.0734718
\(742\) −3.00000 −0.110133
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) −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 \(-0.505770\pi\)
−0.0181250 + 0.999836i \(0.505770\pi\)
\(762\) −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 \(-0.688793\pi\)
−0.558944 + 0.829205i \(0.688793\pi\)
\(770\) 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 \(-0.390034\pi\)
0.338638 + 0.940917i \(0.390034\pi\)
\(788\) −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 \(-0.632491\pi\)
−0.404318 + 0.914618i \(0.632491\pi\)
\(810\) −2.00000 −0.0702728
\(811\) −19.0000 −0.667180 −0.333590 0.942718i \(-0.608260\pi\)
−0.333590 + 0.942718i \(0.608260\pi\)
\(812\) 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 \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −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 \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 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 \(-0.400289\pi\)
0.308154 + 0.951336i \(0.400289\pi\)
\(854\) 18.0000 0.615947
\(855\) −4.00000 −0.136797
\(856\) −7.00000 −0.239255
\(857\) −42.0000 −1.43469 −0.717346 0.696717i \(-0.754643\pi\)
−0.717346 + 0.696717i \(0.754643\pi\)
\(858\) 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 \(-0.532301\pi\)
−0.101303 + 0.994856i \(0.532301\pi\)
\(878\) 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 \(-0.575521\pi\)
−0.235037 + 0.971986i \(0.575521\pi\)
\(888\) 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 \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 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 \(-0.366102\pi\)
0.408357 + 0.912822i \(0.366102\pi\)
\(938\) 36.0000 1.17544
\(939\) 27.0000 0.881112
\(940\) −6.00000 −0.195698
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −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 \(-0.372918\pi\)
0.388718 + 0.921357i \(0.372918\pi\)
\(954\) 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 \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) 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 \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) −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.c.1.1 1
11.10 odd 2 4598.2.a.l.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.c.1.1 1 1.1 even 1 trivial
4598.2.a.l.1.1 yes 1 11.10 odd 2