Properties

Label 1521.4.a.u.1.1
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(89.7419051187\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.3144.1
Defining polynomial: \( x^{3} - x^{2} - 16x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.73549\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.73549 q^{2} +5.95388 q^{4} -3.90776 q^{5} -36.4129 q^{7} +7.64325 q^{8} +O(q^{10})\) \(q-3.73549 q^{2} +5.95388 q^{4} -3.90776 q^{5} -36.4129 q^{7} +7.64325 q^{8} +14.5974 q^{10} +19.1943 q^{11} +136.020 q^{14} -76.1823 q^{16} +83.8839 q^{17} -46.8492 q^{19} -23.2664 q^{20} -71.7000 q^{22} -103.905 q^{23} -109.729 q^{25} -216.798 q^{28} -108.341 q^{29} +147.532 q^{31} +223.432 q^{32} -313.347 q^{34} +142.293 q^{35} +160.012 q^{37} +175.005 q^{38} -29.8680 q^{40} +231.490 q^{41} -340.314 q^{43} +114.280 q^{44} +388.135 q^{46} +119.653 q^{47} +982.902 q^{49} +409.893 q^{50} +732.879 q^{53} -75.0067 q^{55} -278.313 q^{56} +404.706 q^{58} -229.782 q^{59} +108.943 q^{61} -551.104 q^{62} -225.170 q^{64} -10.3955 q^{67} +499.435 q^{68} -531.535 q^{70} -869.201 q^{71} +1099.07 q^{73} -597.724 q^{74} -278.934 q^{76} -698.920 q^{77} +140.410 q^{79} +297.703 q^{80} -864.729 q^{82} -159.474 q^{83} -327.799 q^{85} +1271.24 q^{86} +146.707 q^{88} +1067.93 q^{89} -618.636 q^{92} -446.964 q^{94} +183.075 q^{95} -858.881 q^{97} -3671.62 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + 10 q^{4} + 4 q^{5} - 30 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{2} + 10 q^{4} + 4 q^{5} - 30 q^{7} - 6 q^{8} - 4 q^{10} - 16 q^{11} + 176 q^{14} - 110 q^{16} + 146 q^{17} - 94 q^{19} - 244 q^{20} - 56 q^{22} + 48 q^{23} + 145 q^{25} - 80 q^{28} + 2 q^{29} - 302 q^{31} + 154 q^{32} - 164 q^{34} - 80 q^{35} - 374 q^{37} - 312 q^{38} - 516 q^{40} + 480 q^{41} - 260 q^{43} + 712 q^{44} + 1104 q^{46} - 24 q^{47} + 447 q^{49} + 814 q^{50} + 678 q^{53} - 1552 q^{55} - 96 q^{56} + 628 q^{58} - 1788 q^{59} + 230 q^{61} - 1952 q^{62} - 750 q^{64} - 74 q^{67} + 460 q^{68} - 1216 q^{70} - 948 q^{71} + 222 q^{73} - 1724 q^{74} - 2392 q^{76} - 112 q^{77} - 24 q^{79} + 1100 q^{80} + 564 q^{82} - 796 q^{83} + 248 q^{85} + 1800 q^{86} + 1608 q^{88} + 1436 q^{89} + 1296 q^{92} - 1920 q^{94} + 4032 q^{95} - 3242 q^{97} - 5070 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.73549 −1.32069 −0.660347 0.750960i \(-0.729591\pi\)
−0.660347 + 0.750960i \(0.729591\pi\)
\(3\) 0 0
\(4\) 5.95388 0.744235
\(5\) −3.90776 −0.349521 −0.174761 0.984611i \(-0.555915\pi\)
−0.174761 + 0.984611i \(0.555915\pi\)
\(6\) 0 0
\(7\) −36.4129 −1.96611 −0.983057 0.183301i \(-0.941322\pi\)
−0.983057 + 0.183301i \(0.941322\pi\)
\(8\) 7.64325 0.337787
\(9\) 0 0
\(10\) 14.5974 0.461611
\(11\) 19.1943 0.526117 0.263059 0.964780i \(-0.415269\pi\)
0.263059 + 0.964780i \(0.415269\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 136.020 2.59664
\(15\) 0 0
\(16\) −76.1823 −1.19035
\(17\) 83.8839 1.19676 0.598378 0.801214i \(-0.295812\pi\)
0.598378 + 0.801214i \(0.295812\pi\)
\(18\) 0 0
\(19\) −46.8492 −0.565681 −0.282840 0.959167i \(-0.591277\pi\)
−0.282840 + 0.959167i \(0.591277\pi\)
\(20\) −23.2664 −0.260126
\(21\) 0 0
\(22\) −71.7000 −0.694840
\(23\) −103.905 −0.941983 −0.470991 0.882138i \(-0.656104\pi\)
−0.470991 + 0.882138i \(0.656104\pi\)
\(24\) 0 0
\(25\) −109.729 −0.877835
\(26\) 0 0
\(27\) 0 0
\(28\) −216.798 −1.46325
\(29\) −108.341 −0.693738 −0.346869 0.937914i \(-0.612755\pi\)
−0.346869 + 0.937914i \(0.612755\pi\)
\(30\) 0 0
\(31\) 147.532 0.854759 0.427379 0.904072i \(-0.359437\pi\)
0.427379 + 0.904072i \(0.359437\pi\)
\(32\) 223.432 1.23430
\(33\) 0 0
\(34\) −313.347 −1.58055
\(35\) 142.293 0.687198
\(36\) 0 0
\(37\) 160.012 0.710969 0.355484 0.934682i \(-0.384316\pi\)
0.355484 + 0.934682i \(0.384316\pi\)
\(38\) 175.005 0.747092
\(39\) 0 0
\(40\) −29.8680 −0.118064
\(41\) 231.490 0.881772 0.440886 0.897563i \(-0.354664\pi\)
0.440886 + 0.897563i \(0.354664\pi\)
\(42\) 0 0
\(43\) −340.314 −1.20692 −0.603458 0.797395i \(-0.706211\pi\)
−0.603458 + 0.797395i \(0.706211\pi\)
\(44\) 114.280 0.391555
\(45\) 0 0
\(46\) 388.135 1.24407
\(47\) 119.653 0.371346 0.185673 0.982612i \(-0.440554\pi\)
0.185673 + 0.982612i \(0.440554\pi\)
\(48\) 0 0
\(49\) 982.902 2.86560
\(50\) 409.893 1.15935
\(51\) 0 0
\(52\) 0 0
\(53\) 732.879 1.89941 0.949705 0.313146i \(-0.101383\pi\)
0.949705 + 0.313146i \(0.101383\pi\)
\(54\) 0 0
\(55\) −75.0067 −0.183889
\(56\) −278.313 −0.664128
\(57\) 0 0
\(58\) 404.706 0.916216
\(59\) −229.782 −0.507035 −0.253518 0.967331i \(-0.581588\pi\)
−0.253518 + 0.967331i \(0.581588\pi\)
\(60\) 0 0
\(61\) 108.943 0.228668 0.114334 0.993442i \(-0.463527\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(62\) −551.104 −1.12888
\(63\) 0 0
\(64\) −225.170 −0.439786
\(65\) 0 0
\(66\) 0 0
\(67\) −10.3955 −0.0189555 −0.00947774 0.999955i \(-0.503017\pi\)
−0.00947774 + 0.999955i \(0.503017\pi\)
\(68\) 499.435 0.890667
\(69\) 0 0
\(70\) −531.535 −0.907579
\(71\) −869.201 −1.45289 −0.726445 0.687224i \(-0.758829\pi\)
−0.726445 + 0.687224i \(0.758829\pi\)
\(72\) 0 0
\(73\) 1099.07 1.76214 0.881072 0.472982i \(-0.156822\pi\)
0.881072 + 0.472982i \(0.156822\pi\)
\(74\) −597.724 −0.938973
\(75\) 0 0
\(76\) −278.934 −0.421000
\(77\) −698.920 −1.03441
\(78\) 0 0
\(79\) 140.410 0.199967 0.0999835 0.994989i \(-0.468121\pi\)
0.0999835 + 0.994989i \(0.468121\pi\)
\(80\) 297.703 0.416052
\(81\) 0 0
\(82\) −864.729 −1.16455
\(83\) −159.474 −0.210898 −0.105449 0.994425i \(-0.533628\pi\)
−0.105449 + 0.994425i \(0.533628\pi\)
\(84\) 0 0
\(85\) −327.799 −0.418291
\(86\) 1271.24 1.59397
\(87\) 0 0
\(88\) 146.707 0.177716
\(89\) 1067.93 1.27192 0.635959 0.771723i \(-0.280605\pi\)
0.635959 + 0.771723i \(0.280605\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −618.636 −0.701057
\(93\) 0 0
\(94\) −446.964 −0.490434
\(95\) 183.075 0.197717
\(96\) 0 0
\(97\) −858.881 −0.899032 −0.449516 0.893272i \(-0.648404\pi\)
−0.449516 + 0.893272i \(0.648404\pi\)
\(98\) −3671.62 −3.78459
\(99\) 0 0
\(100\) −653.316 −0.653316
\(101\) 1574.16 1.55084 0.775421 0.631444i \(-0.217538\pi\)
0.775421 + 0.631444i \(0.217538\pi\)
\(102\) 0 0
\(103\) −129.724 −0.124098 −0.0620489 0.998073i \(-0.519763\pi\)
−0.0620489 + 0.998073i \(0.519763\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2737.66 −2.50854
\(107\) 1957.43 1.76853 0.884263 0.466990i \(-0.154661\pi\)
0.884263 + 0.466990i \(0.154661\pi\)
\(108\) 0 0
\(109\) −1228.77 −1.07977 −0.539886 0.841738i \(-0.681533\pi\)
−0.539886 + 0.841738i \(0.681533\pi\)
\(110\) 280.187 0.242861
\(111\) 0 0
\(112\) 2774.02 2.34036
\(113\) −1629.50 −1.35655 −0.678275 0.734808i \(-0.737272\pi\)
−0.678275 + 0.734808i \(0.737272\pi\)
\(114\) 0 0
\(115\) 406.035 0.329243
\(116\) −645.049 −0.516304
\(117\) 0 0
\(118\) 858.349 0.669639
\(119\) −3054.46 −2.35296
\(120\) 0 0
\(121\) −962.580 −0.723201
\(122\) −406.956 −0.302000
\(123\) 0 0
\(124\) 878.388 0.636142
\(125\) 917.267 0.656343
\(126\) 0 0
\(127\) 276.112 0.192921 0.0964607 0.995337i \(-0.469248\pi\)
0.0964607 + 0.995337i \(0.469248\pi\)
\(128\) −946.337 −0.653478
\(129\) 0 0
\(130\) 0 0
\(131\) 96.2240 0.0641765 0.0320883 0.999485i \(-0.489784\pi\)
0.0320883 + 0.999485i \(0.489784\pi\)
\(132\) 0 0
\(133\) 1705.92 1.11219
\(134\) 38.8324 0.0250344
\(135\) 0 0
\(136\) 641.146 0.404249
\(137\) 2618.38 1.63287 0.816435 0.577438i \(-0.195947\pi\)
0.816435 + 0.577438i \(0.195947\pi\)
\(138\) 0 0
\(139\) 1963.34 1.19805 0.599023 0.800732i \(-0.295556\pi\)
0.599023 + 0.800732i \(0.295556\pi\)
\(140\) 847.197 0.511437
\(141\) 0 0
\(142\) 3246.89 1.91882
\(143\) 0 0
\(144\) 0 0
\(145\) 423.370 0.242476
\(146\) −4105.57 −2.32725
\(147\) 0 0
\(148\) 952.694 0.529128
\(149\) −301.111 −0.165557 −0.0827784 0.996568i \(-0.526379\pi\)
−0.0827784 + 0.996568i \(0.526379\pi\)
\(150\) 0 0
\(151\) −342.973 −0.184839 −0.0924197 0.995720i \(-0.529460\pi\)
−0.0924197 + 0.995720i \(0.529460\pi\)
\(152\) −358.080 −0.191080
\(153\) 0 0
\(154\) 2610.81 1.36614
\(155\) −576.520 −0.298756
\(156\) 0 0
\(157\) −1286.97 −0.654211 −0.327106 0.944988i \(-0.606073\pi\)
−0.327106 + 0.944988i \(0.606073\pi\)
\(158\) −524.501 −0.264095
\(159\) 0 0
\(160\) −873.121 −0.431414
\(161\) 3783.47 1.85205
\(162\) 0 0
\(163\) −532.561 −0.255910 −0.127955 0.991780i \(-0.540841\pi\)
−0.127955 + 0.991780i \(0.540841\pi\)
\(164\) 1378.26 0.656246
\(165\) 0 0
\(166\) 595.714 0.278532
\(167\) 41.9542 0.0194402 0.00972011 0.999953i \(-0.496906\pi\)
0.00972011 + 0.999953i \(0.496906\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 1224.49 0.552435
\(171\) 0 0
\(172\) −2026.19 −0.898229
\(173\) 1066.50 0.468694 0.234347 0.972153i \(-0.424705\pi\)
0.234347 + 0.972153i \(0.424705\pi\)
\(174\) 0 0
\(175\) 3995.57 1.72592
\(176\) −1462.26 −0.626263
\(177\) 0 0
\(178\) −3989.25 −1.67982
\(179\) −3174.61 −1.32559 −0.662797 0.748799i \(-0.730631\pi\)
−0.662797 + 0.748799i \(0.730631\pi\)
\(180\) 0 0
\(181\) −2725.43 −1.11923 −0.559613 0.828754i \(-0.689050\pi\)
−0.559613 + 0.828754i \(0.689050\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −794.169 −0.318190
\(185\) −625.290 −0.248498
\(186\) 0 0
\(187\) 1610.09 0.629634
\(188\) 712.402 0.276368
\(189\) 0 0
\(190\) −683.877 −0.261124
\(191\) −784.888 −0.297343 −0.148672 0.988887i \(-0.547500\pi\)
−0.148672 + 0.988887i \(0.547500\pi\)
\(192\) 0 0
\(193\) 1255.87 0.468391 0.234195 0.972190i \(-0.424754\pi\)
0.234195 + 0.972190i \(0.424754\pi\)
\(194\) 3208.34 1.18735
\(195\) 0 0
\(196\) 5852.08 2.13268
\(197\) −2777.35 −1.00446 −0.502229 0.864734i \(-0.667487\pi\)
−0.502229 + 0.864734i \(0.667487\pi\)
\(198\) 0 0
\(199\) 1490.43 0.530924 0.265462 0.964121i \(-0.414476\pi\)
0.265462 + 0.964121i \(0.414476\pi\)
\(200\) −838.689 −0.296521
\(201\) 0 0
\(202\) −5880.27 −2.04819
\(203\) 3945.01 1.36397
\(204\) 0 0
\(205\) −904.608 −0.308198
\(206\) 484.582 0.163895
\(207\) 0 0
\(208\) 0 0
\(209\) −899.236 −0.297614
\(210\) 0 0
\(211\) 2305.63 0.752255 0.376127 0.926568i \(-0.377255\pi\)
0.376127 + 0.926568i \(0.377255\pi\)
\(212\) 4363.48 1.41361
\(213\) 0 0
\(214\) −7311.97 −2.33568
\(215\) 1329.87 0.421842
\(216\) 0 0
\(217\) −5372.07 −1.68055
\(218\) 4590.07 1.42605
\(219\) 0 0
\(220\) −446.581 −0.136857
\(221\) 0 0
\(222\) 0 0
\(223\) −1241.98 −0.372956 −0.186478 0.982459i \(-0.559707\pi\)
−0.186478 + 0.982459i \(0.559707\pi\)
\(224\) −8135.83 −2.42678
\(225\) 0 0
\(226\) 6086.97 1.79159
\(227\) −1724.76 −0.504300 −0.252150 0.967688i \(-0.581138\pi\)
−0.252150 + 0.967688i \(0.581138\pi\)
\(228\) 0 0
\(229\) 3273.72 0.944688 0.472344 0.881414i \(-0.343408\pi\)
0.472344 + 0.881414i \(0.343408\pi\)
\(230\) −1516.74 −0.434829
\(231\) 0 0
\(232\) −828.076 −0.234336
\(233\) 2129.52 0.598752 0.299376 0.954135i \(-0.403222\pi\)
0.299376 + 0.954135i \(0.403222\pi\)
\(234\) 0 0
\(235\) −467.577 −0.129793
\(236\) −1368.10 −0.377354
\(237\) 0 0
\(238\) 11409.9 3.10754
\(239\) −5082.38 −1.37553 −0.687765 0.725933i \(-0.741408\pi\)
−0.687765 + 0.725933i \(0.741408\pi\)
\(240\) 0 0
\(241\) −4765.65 −1.27379 −0.636893 0.770953i \(-0.719781\pi\)
−0.636893 + 0.770953i \(0.719781\pi\)
\(242\) 3595.71 0.955127
\(243\) 0 0
\(244\) 648.634 0.170183
\(245\) −3840.95 −1.00159
\(246\) 0 0
\(247\) 0 0
\(248\) 1127.62 0.288727
\(249\) 0 0
\(250\) −3426.44 −0.866829
\(251\) 4339.96 1.09138 0.545689 0.837988i \(-0.316268\pi\)
0.545689 + 0.837988i \(0.316268\pi\)
\(252\) 0 0
\(253\) −1994.37 −0.495594
\(254\) −1031.41 −0.254790
\(255\) 0 0
\(256\) 5336.40 1.30283
\(257\) −4359.49 −1.05812 −0.529062 0.848583i \(-0.677456\pi\)
−0.529062 + 0.848583i \(0.677456\pi\)
\(258\) 0 0
\(259\) −5826.51 −1.39785
\(260\) 0 0
\(261\) 0 0
\(262\) −359.444 −0.0847576
\(263\) −608.077 −0.142569 −0.0712844 0.997456i \(-0.522710\pi\)
−0.0712844 + 0.997456i \(0.522710\pi\)
\(264\) 0 0
\(265\) −2863.92 −0.663884
\(266\) −6372.43 −1.46887
\(267\) 0 0
\(268\) −61.8938 −0.0141073
\(269\) −3454.29 −0.782942 −0.391471 0.920190i \(-0.628034\pi\)
−0.391471 + 0.920190i \(0.628034\pi\)
\(270\) 0 0
\(271\) −3703.72 −0.830204 −0.415102 0.909775i \(-0.636254\pi\)
−0.415102 + 0.909775i \(0.636254\pi\)
\(272\) −6390.47 −1.42456
\(273\) 0 0
\(274\) −9780.92 −2.15652
\(275\) −2106.18 −0.461844
\(276\) 0 0
\(277\) −3566.89 −0.773696 −0.386848 0.922144i \(-0.626436\pi\)
−0.386848 + 0.922144i \(0.626436\pi\)
\(278\) −7334.04 −1.58225
\(279\) 0 0
\(280\) 1087.58 0.232127
\(281\) −117.474 −0.0249392 −0.0124696 0.999922i \(-0.503969\pi\)
−0.0124696 + 0.999922i \(0.503969\pi\)
\(282\) 0 0
\(283\) −1737.62 −0.364984 −0.182492 0.983207i \(-0.558416\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(284\) −5175.12 −1.08129
\(285\) 0 0
\(286\) 0 0
\(287\) −8429.23 −1.73366
\(288\) 0 0
\(289\) 2123.51 0.432223
\(290\) −1581.50 −0.320237
\(291\) 0 0
\(292\) 6543.74 1.31145
\(293\) 1904.05 0.379643 0.189822 0.981819i \(-0.439209\pi\)
0.189822 + 0.981819i \(0.439209\pi\)
\(294\) 0 0
\(295\) 897.934 0.177219
\(296\) 1223.01 0.240156
\(297\) 0 0
\(298\) 1124.80 0.218650
\(299\) 0 0
\(300\) 0 0
\(301\) 12391.8 2.37293
\(302\) 1281.17 0.244117
\(303\) 0 0
\(304\) 3569.08 0.673358
\(305\) −425.724 −0.0799242
\(306\) 0 0
\(307\) −2862.39 −0.532134 −0.266067 0.963955i \(-0.585724\pi\)
−0.266067 + 0.963955i \(0.585724\pi\)
\(308\) −4161.29 −0.769842
\(309\) 0 0
\(310\) 2153.58 0.394566
\(311\) −4201.55 −0.766071 −0.383036 0.923734i \(-0.625121\pi\)
−0.383036 + 0.923734i \(0.625121\pi\)
\(312\) 0 0
\(313\) 3427.74 0.619002 0.309501 0.950899i \(-0.399838\pi\)
0.309501 + 0.950899i \(0.399838\pi\)
\(314\) 4807.45 0.864014
\(315\) 0 0
\(316\) 835.987 0.148823
\(317\) 1676.09 0.296966 0.148483 0.988915i \(-0.452561\pi\)
0.148483 + 0.988915i \(0.452561\pi\)
\(318\) 0 0
\(319\) −2079.52 −0.364987
\(320\) 879.912 0.153714
\(321\) 0 0
\(322\) −14133.1 −2.44599
\(323\) −3929.89 −0.676982
\(324\) 0 0
\(325\) 0 0
\(326\) 1989.37 0.337979
\(327\) 0 0
\(328\) 1769.34 0.297851
\(329\) −4356.93 −0.730108
\(330\) 0 0
\(331\) −11156.6 −1.85264 −0.926319 0.376740i \(-0.877045\pi\)
−0.926319 + 0.376740i \(0.877045\pi\)
\(332\) −949.490 −0.156958
\(333\) 0 0
\(334\) −156.720 −0.0256746
\(335\) 40.6233 0.00662534
\(336\) 0 0
\(337\) 1636.44 0.264517 0.132259 0.991215i \(-0.457777\pi\)
0.132259 + 0.991215i \(0.457777\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −1951.67 −0.311307
\(341\) 2831.77 0.449703
\(342\) 0 0
\(343\) −23300.7 −3.66799
\(344\) −2601.10 −0.407681
\(345\) 0 0
\(346\) −3983.88 −0.619002
\(347\) 2977.87 0.460693 0.230347 0.973109i \(-0.426014\pi\)
0.230347 + 0.973109i \(0.426014\pi\)
\(348\) 0 0
\(349\) −9847.29 −1.51035 −0.755177 0.655521i \(-0.772449\pi\)
−0.755177 + 0.655521i \(0.772449\pi\)
\(350\) −14925.4 −2.27942
\(351\) 0 0
\(352\) 4288.62 0.649387
\(353\) 4687.34 0.706747 0.353374 0.935482i \(-0.385034\pi\)
0.353374 + 0.935482i \(0.385034\pi\)
\(354\) 0 0
\(355\) 3396.63 0.507816
\(356\) 6358.35 0.946606
\(357\) 0 0
\(358\) 11858.7 1.75070
\(359\) −2069.88 −0.304301 −0.152151 0.988357i \(-0.548620\pi\)
−0.152151 + 0.988357i \(0.548620\pi\)
\(360\) 0 0
\(361\) −4664.16 −0.680005
\(362\) 10180.8 1.47816
\(363\) 0 0
\(364\) 0 0
\(365\) −4294.91 −0.615906
\(366\) 0 0
\(367\) −7299.16 −1.03818 −0.519092 0.854719i \(-0.673730\pi\)
−0.519092 + 0.854719i \(0.673730\pi\)
\(368\) 7915.70 1.12129
\(369\) 0 0
\(370\) 2335.76 0.328191
\(371\) −26686.3 −3.73446
\(372\) 0 0
\(373\) −8964.32 −1.24438 −0.622192 0.782865i \(-0.713758\pi\)
−0.622192 + 0.782865i \(0.713758\pi\)
\(374\) −6014.48 −0.831554
\(375\) 0 0
\(376\) 914.541 0.125436
\(377\) 0 0
\(378\) 0 0
\(379\) 4399.26 0.596239 0.298120 0.954529i \(-0.403641\pi\)
0.298120 + 0.954529i \(0.403641\pi\)
\(380\) 1090.01 0.147148
\(381\) 0 0
\(382\) 2931.94 0.392700
\(383\) 3529.74 0.470917 0.235459 0.971884i \(-0.424341\pi\)
0.235459 + 0.971884i \(0.424341\pi\)
\(384\) 0 0
\(385\) 2731.21 0.361547
\(386\) −4691.28 −0.618601
\(387\) 0 0
\(388\) −5113.68 −0.669092
\(389\) 3034.77 0.395549 0.197775 0.980248i \(-0.436629\pi\)
0.197775 + 0.980248i \(0.436629\pi\)
\(390\) 0 0
\(391\) −8715.93 −1.12732
\(392\) 7512.57 0.967964
\(393\) 0 0
\(394\) 10374.8 1.32658
\(395\) −548.690 −0.0698927
\(396\) 0 0
\(397\) 3997.36 0.505344 0.252672 0.967552i \(-0.418691\pi\)
0.252672 + 0.967552i \(0.418691\pi\)
\(398\) −5567.49 −0.701188
\(399\) 0 0
\(400\) 8359.44 1.04493
\(401\) −9092.88 −1.13236 −0.566181 0.824281i \(-0.691580\pi\)
−0.566181 + 0.824281i \(0.691580\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 9372.38 1.15419
\(405\) 0 0
\(406\) −14736.5 −1.80138
\(407\) 3071.32 0.374053
\(408\) 0 0
\(409\) −7143.54 −0.863631 −0.431816 0.901962i \(-0.642127\pi\)
−0.431816 + 0.901962i \(0.642127\pi\)
\(410\) 3379.15 0.407036
\(411\) 0 0
\(412\) −772.361 −0.0923579
\(413\) 8367.04 0.996889
\(414\) 0 0
\(415\) 623.187 0.0737134
\(416\) 0 0
\(417\) 0 0
\(418\) 3359.09 0.393058
\(419\) −8213.84 −0.957691 −0.478845 0.877899i \(-0.658945\pi\)
−0.478845 + 0.877899i \(0.658945\pi\)
\(420\) 0 0
\(421\) 7997.40 0.925818 0.462909 0.886406i \(-0.346806\pi\)
0.462909 + 0.886406i \(0.346806\pi\)
\(422\) −8612.64 −0.993499
\(423\) 0 0
\(424\) 5601.58 0.641597
\(425\) −9204.53 −1.05055
\(426\) 0 0
\(427\) −3966.94 −0.449587
\(428\) 11654.3 1.31620
\(429\) 0 0
\(430\) −4967.70 −0.557125
\(431\) −13694.8 −1.53053 −0.765263 0.643718i \(-0.777391\pi\)
−0.765263 + 0.643718i \(0.777391\pi\)
\(432\) 0 0
\(433\) 6716.57 0.745445 0.372722 0.927943i \(-0.378424\pi\)
0.372722 + 0.927943i \(0.378424\pi\)
\(434\) 20067.3 2.21950
\(435\) 0 0
\(436\) −7315.97 −0.803604
\(437\) 4867.84 0.532862
\(438\) 0 0
\(439\) −5933.32 −0.645061 −0.322531 0.946559i \(-0.604534\pi\)
−0.322531 + 0.946559i \(0.604534\pi\)
\(440\) −573.295 −0.0621154
\(441\) 0 0
\(442\) 0 0
\(443\) 6923.40 0.742530 0.371265 0.928527i \(-0.378924\pi\)
0.371265 + 0.928527i \(0.378924\pi\)
\(444\) 0 0
\(445\) −4173.23 −0.444562
\(446\) 4639.41 0.492561
\(447\) 0 0
\(448\) 8199.11 0.864669
\(449\) 8886.78 0.934061 0.467030 0.884241i \(-0.345324\pi\)
0.467030 + 0.884241i \(0.345324\pi\)
\(450\) 0 0
\(451\) 4443.28 0.463916
\(452\) −9701.84 −1.00959
\(453\) 0 0
\(454\) 6442.81 0.666026
\(455\) 0 0
\(456\) 0 0
\(457\) −10965.0 −1.12237 −0.561184 0.827691i \(-0.689654\pi\)
−0.561184 + 0.827691i \(0.689654\pi\)
\(458\) −12228.9 −1.24764
\(459\) 0 0
\(460\) 2417.48 0.245034
\(461\) 10069.2 1.01729 0.508644 0.860977i \(-0.330147\pi\)
0.508644 + 0.860977i \(0.330147\pi\)
\(462\) 0 0
\(463\) −5599.72 −0.562076 −0.281038 0.959697i \(-0.590679\pi\)
−0.281038 + 0.959697i \(0.590679\pi\)
\(464\) 8253.66 0.825790
\(465\) 0 0
\(466\) −7954.78 −0.790769
\(467\) 13247.8 1.31271 0.656355 0.754452i \(-0.272097\pi\)
0.656355 + 0.754452i \(0.272097\pi\)
\(468\) 0 0
\(469\) 378.532 0.0372686
\(470\) 1746.63 0.171417
\(471\) 0 0
\(472\) −1756.28 −0.171270
\(473\) −6532.08 −0.634979
\(474\) 0 0
\(475\) 5140.73 0.496575
\(476\) −18185.9 −1.75115
\(477\) 0 0
\(478\) 18985.2 1.81666
\(479\) 16725.4 1.59541 0.797707 0.603045i \(-0.206046\pi\)
0.797707 + 0.603045i \(0.206046\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 17802.0 1.68228
\(483\) 0 0
\(484\) −5731.09 −0.538231
\(485\) 3356.30 0.314231
\(486\) 0 0
\(487\) 5305.86 0.493699 0.246850 0.969054i \(-0.420605\pi\)
0.246850 + 0.969054i \(0.420605\pi\)
\(488\) 832.679 0.0772410
\(489\) 0 0
\(490\) 14347.8 1.32279
\(491\) −16200.2 −1.48901 −0.744506 0.667616i \(-0.767315\pi\)
−0.744506 + 0.667616i \(0.767315\pi\)
\(492\) 0 0
\(493\) −9088.05 −0.830234
\(494\) 0 0
\(495\) 0 0
\(496\) −11239.3 −1.01746
\(497\) 31650.2 2.85655
\(498\) 0 0
\(499\) −4392.70 −0.394076 −0.197038 0.980396i \(-0.563132\pi\)
−0.197038 + 0.980396i \(0.563132\pi\)
\(500\) 5461.30 0.488473
\(501\) 0 0
\(502\) −16211.9 −1.44138
\(503\) 14955.2 1.32568 0.662841 0.748760i \(-0.269350\pi\)
0.662841 + 0.748760i \(0.269350\pi\)
\(504\) 0 0
\(505\) −6151.46 −0.542052
\(506\) 7449.96 0.654528
\(507\) 0 0
\(508\) 1643.94 0.143579
\(509\) 13403.4 1.16719 0.583593 0.812047i \(-0.301647\pi\)
0.583593 + 0.812047i \(0.301647\pi\)
\(510\) 0 0
\(511\) −40020.4 −3.46458
\(512\) −12363.4 −1.06716
\(513\) 0 0
\(514\) 16284.8 1.39746
\(515\) 506.930 0.0433748
\(516\) 0 0
\(517\) 2296.66 0.195371
\(518\) 21764.9 1.84613
\(519\) 0 0
\(520\) 0 0
\(521\) −19643.0 −1.65178 −0.825888 0.563834i \(-0.809326\pi\)
−0.825888 + 0.563834i \(0.809326\pi\)
\(522\) 0 0
\(523\) 14657.4 1.22548 0.612738 0.790286i \(-0.290068\pi\)
0.612738 + 0.790286i \(0.290068\pi\)
\(524\) 572.906 0.0477624
\(525\) 0 0
\(526\) 2271.46 0.188290
\(527\) 12375.6 1.02294
\(528\) 0 0
\(529\) −1370.83 −0.112668
\(530\) 10698.1 0.876788
\(531\) 0 0
\(532\) 10156.8 0.827733
\(533\) 0 0
\(534\) 0 0
\(535\) −7649.19 −0.618137
\(536\) −79.4558 −0.00640292
\(537\) 0 0
\(538\) 12903.4 1.03403
\(539\) 18866.1 1.50764
\(540\) 0 0
\(541\) −13921.3 −1.10633 −0.553164 0.833072i \(-0.686580\pi\)
−0.553164 + 0.833072i \(0.686580\pi\)
\(542\) 13835.2 1.09645
\(543\) 0 0
\(544\) 18742.4 1.47716
\(545\) 4801.75 0.377403
\(546\) 0 0
\(547\) −2324.11 −0.181667 −0.0908335 0.995866i \(-0.528953\pi\)
−0.0908335 + 0.995866i \(0.528953\pi\)
\(548\) 15589.5 1.21524
\(549\) 0 0
\(550\) 7867.60 0.609955
\(551\) 5075.68 0.392434
\(552\) 0 0
\(553\) −5112.75 −0.393158
\(554\) 13324.1 1.02182
\(555\) 0 0
\(556\) 11689.5 0.891628
\(557\) −16962.8 −1.29037 −0.645185 0.764027i \(-0.723220\pi\)
−0.645185 + 0.764027i \(0.723220\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −10840.2 −0.818006
\(561\) 0 0
\(562\) 438.823 0.0329370
\(563\) 389.000 0.0291197 0.0145599 0.999894i \(-0.495365\pi\)
0.0145599 + 0.999894i \(0.495365\pi\)
\(564\) 0 0
\(565\) 6367.69 0.474143
\(566\) 6490.85 0.482033
\(567\) 0 0
\(568\) −6643.53 −0.490768
\(569\) −2217.56 −0.163383 −0.0816914 0.996658i \(-0.526032\pi\)
−0.0816914 + 0.996658i \(0.526032\pi\)
\(570\) 0 0
\(571\) −17087.3 −1.25233 −0.626167 0.779689i \(-0.715377\pi\)
−0.626167 + 0.779689i \(0.715377\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 31487.3 2.28964
\(575\) 11401.4 0.826906
\(576\) 0 0
\(577\) 3977.26 0.286959 0.143480 0.989653i \(-0.454171\pi\)
0.143480 + 0.989653i \(0.454171\pi\)
\(578\) −7932.35 −0.570835
\(579\) 0 0
\(580\) 2520.70 0.180459
\(581\) 5806.92 0.414650
\(582\) 0 0
\(583\) 14067.1 0.999312
\(584\) 8400.48 0.595230
\(585\) 0 0
\(586\) −7112.54 −0.501393
\(587\) −16880.3 −1.18693 −0.593463 0.804861i \(-0.702240\pi\)
−0.593463 + 0.804861i \(0.702240\pi\)
\(588\) 0 0
\(589\) −6911.75 −0.483521
\(590\) −3354.22 −0.234053
\(591\) 0 0
\(592\) −12190.1 −0.846301
\(593\) 2423.25 0.167810 0.0839048 0.996474i \(-0.473261\pi\)
0.0839048 + 0.996474i \(0.473261\pi\)
\(594\) 0 0
\(595\) 11936.1 0.822408
\(596\) −1792.78 −0.123213
\(597\) 0 0
\(598\) 0 0
\(599\) 3900.55 0.266064 0.133032 0.991112i \(-0.457529\pi\)
0.133032 + 0.991112i \(0.457529\pi\)
\(600\) 0 0
\(601\) 28653.4 1.94476 0.972378 0.233413i \(-0.0749893\pi\)
0.972378 + 0.233413i \(0.0749893\pi\)
\(602\) −46289.5 −3.13392
\(603\) 0 0
\(604\) −2042.02 −0.137564
\(605\) 3761.54 0.252774
\(606\) 0 0
\(607\) 214.736 0.0143589 0.00717946 0.999974i \(-0.497715\pi\)
0.00717946 + 0.999974i \(0.497715\pi\)
\(608\) −10467.6 −0.698220
\(609\) 0 0
\(610\) 1590.29 0.105555
\(611\) 0 0
\(612\) 0 0
\(613\) −26438.5 −1.74199 −0.870996 0.491290i \(-0.836525\pi\)
−0.870996 + 0.491290i \(0.836525\pi\)
\(614\) 10692.4 0.702787
\(615\) 0 0
\(616\) −5342.02 −0.349409
\(617\) 6700.96 0.437229 0.218615 0.975811i \(-0.429846\pi\)
0.218615 + 0.975811i \(0.429846\pi\)
\(618\) 0 0
\(619\) 27319.1 1.77391 0.886953 0.461860i \(-0.152818\pi\)
0.886953 + 0.461860i \(0.152818\pi\)
\(620\) −3432.53 −0.222345
\(621\) 0 0
\(622\) 15694.9 1.01175
\(623\) −38886.6 −2.50074
\(624\) 0 0
\(625\) 10131.7 0.648429
\(626\) −12804.3 −0.817513
\(627\) 0 0
\(628\) −7662.45 −0.486887
\(629\) 13422.4 0.850855
\(630\) 0 0
\(631\) 7126.87 0.449629 0.224815 0.974402i \(-0.427822\pi\)
0.224815 + 0.974402i \(0.427822\pi\)
\(632\) 1073.19 0.0675463
\(633\) 0 0
\(634\) −6261.00 −0.392202
\(635\) −1078.98 −0.0674301
\(636\) 0 0
\(637\) 0 0
\(638\) 7768.04 0.482037
\(639\) 0 0
\(640\) 3698.06 0.228404
\(641\) −23615.0 −1.45513 −0.727565 0.686039i \(-0.759348\pi\)
−0.727565 + 0.686039i \(0.759348\pi\)
\(642\) 0 0
\(643\) 8144.41 0.499509 0.249755 0.968309i \(-0.419650\pi\)
0.249755 + 0.968309i \(0.419650\pi\)
\(644\) 22526.3 1.37836
\(645\) 0 0
\(646\) 14680.1 0.894086
\(647\) −9682.00 −0.588313 −0.294157 0.955757i \(-0.595039\pi\)
−0.294157 + 0.955757i \(0.595039\pi\)
\(648\) 0 0
\(649\) −4410.50 −0.266760
\(650\) 0 0
\(651\) 0 0
\(652\) −3170.80 −0.190457
\(653\) 18193.6 1.09030 0.545152 0.838337i \(-0.316472\pi\)
0.545152 + 0.838337i \(0.316472\pi\)
\(654\) 0 0
\(655\) −376.020 −0.0224310
\(656\) −17635.5 −1.04962
\(657\) 0 0
\(658\) 16275.3 0.964250
\(659\) −9300.88 −0.549789 −0.274895 0.961474i \(-0.588643\pi\)
−0.274895 + 0.961474i \(0.588643\pi\)
\(660\) 0 0
\(661\) 5437.29 0.319949 0.159974 0.987121i \(-0.448859\pi\)
0.159974 + 0.987121i \(0.448859\pi\)
\(662\) 41675.4 2.44677
\(663\) 0 0
\(664\) −1218.90 −0.0712388
\(665\) −6666.32 −0.388735
\(666\) 0 0
\(667\) 11257.1 0.653489
\(668\) 249.791 0.0144681
\(669\) 0 0
\(670\) −151.748 −0.00875005
\(671\) 2091.08 0.120306
\(672\) 0 0
\(673\) −8682.75 −0.497319 −0.248659 0.968591i \(-0.579990\pi\)
−0.248659 + 0.968591i \(0.579990\pi\)
\(674\) −6112.89 −0.349347
\(675\) 0 0
\(676\) 0 0
\(677\) −13300.1 −0.755041 −0.377521 0.926001i \(-0.623223\pi\)
−0.377521 + 0.926001i \(0.623223\pi\)
\(678\) 0 0
\(679\) 31274.4 1.76760
\(680\) −2505.45 −0.141293
\(681\) 0 0
\(682\) −10578.0 −0.593921
\(683\) −504.175 −0.0282455 −0.0141228 0.999900i \(-0.504496\pi\)
−0.0141228 + 0.999900i \(0.504496\pi\)
\(684\) 0 0
\(685\) −10232.0 −0.570722
\(686\) 87039.6 4.84429
\(687\) 0 0
\(688\) 25925.9 1.43665
\(689\) 0 0
\(690\) 0 0
\(691\) −13443.8 −0.740124 −0.370062 0.929007i \(-0.620664\pi\)
−0.370062 + 0.929007i \(0.620664\pi\)
\(692\) 6349.79 0.348819
\(693\) 0 0
\(694\) −11123.8 −0.608435
\(695\) −7672.27 −0.418742
\(696\) 0 0
\(697\) 19418.3 1.05527
\(698\) 36784.4 1.99472
\(699\) 0 0
\(700\) 23789.1 1.28449
\(701\) −28735.6 −1.54826 −0.774128 0.633030i \(-0.781811\pi\)
−0.774128 + 0.633030i \(0.781811\pi\)
\(702\) 0 0
\(703\) −7496.44 −0.402181
\(704\) −4321.98 −0.231379
\(705\) 0 0
\(706\) −17509.5 −0.933398
\(707\) −57319.9 −3.04913
\(708\) 0 0
\(709\) −17610.2 −0.932812 −0.466406 0.884571i \(-0.654451\pi\)
−0.466406 + 0.884571i \(0.654451\pi\)
\(710\) −12688.1 −0.670670
\(711\) 0 0
\(712\) 8162.48 0.429638
\(713\) −15329.3 −0.805168
\(714\) 0 0
\(715\) 0 0
\(716\) −18901.2 −0.986553
\(717\) 0 0
\(718\) 7732.02 0.401889
\(719\) 9226.04 0.478544 0.239272 0.970953i \(-0.423091\pi\)
0.239272 + 0.970953i \(0.423091\pi\)
\(720\) 0 0
\(721\) 4723.63 0.243990
\(722\) 17422.9 0.898079
\(723\) 0 0
\(724\) −16226.9 −0.832967
\(725\) 11888.2 0.608987
\(726\) 0 0
\(727\) 33246.0 1.69604 0.848022 0.529961i \(-0.177793\pi\)
0.848022 + 0.529961i \(0.177793\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16043.6 0.813424
\(731\) −28546.9 −1.44438
\(732\) 0 0
\(733\) 4423.26 0.222888 0.111444 0.993771i \(-0.464452\pi\)
0.111444 + 0.993771i \(0.464452\pi\)
\(734\) 27266.0 1.37112
\(735\) 0 0
\(736\) −23215.6 −1.16269
\(737\) −199.535 −0.00997281
\(738\) 0 0
\(739\) 4529.56 0.225470 0.112735 0.993625i \(-0.464039\pi\)
0.112735 + 0.993625i \(0.464039\pi\)
\(740\) −3722.90 −0.184941
\(741\) 0 0
\(742\) 99686.4 4.93208
\(743\) 10851.5 0.535803 0.267901 0.963446i \(-0.413670\pi\)
0.267901 + 0.963446i \(0.413670\pi\)
\(744\) 0 0
\(745\) 1176.67 0.0578656
\(746\) 33486.1 1.64345
\(747\) 0 0
\(748\) 9586.29 0.468595
\(749\) −71275.9 −3.47712
\(750\) 0 0
\(751\) −33022.6 −1.60454 −0.802272 0.596958i \(-0.796376\pi\)
−0.802272 + 0.596958i \(0.796376\pi\)
\(752\) −9115.48 −0.442031
\(753\) 0 0
\(754\) 0 0
\(755\) 1340.26 0.0646053
\(756\) 0 0
\(757\) −3443.77 −0.165345 −0.0826724 0.996577i \(-0.526346\pi\)
−0.0826724 + 0.996577i \(0.526346\pi\)
\(758\) −16433.4 −0.787450
\(759\) 0 0
\(760\) 1399.29 0.0667864
\(761\) 19562.6 0.931858 0.465929 0.884822i \(-0.345720\pi\)
0.465929 + 0.884822i \(0.345720\pi\)
\(762\) 0 0
\(763\) 44743.2 2.12295
\(764\) −4673.13 −0.221293
\(765\) 0 0
\(766\) −13185.3 −0.621938
\(767\) 0 0
\(768\) 0 0
\(769\) 17061.1 0.800049 0.400025 0.916504i \(-0.369002\pi\)
0.400025 + 0.916504i \(0.369002\pi\)
\(770\) −10202.4 −0.477493
\(771\) 0 0
\(772\) 7477.29 0.348593
\(773\) 10798.4 0.502448 0.251224 0.967929i \(-0.419167\pi\)
0.251224 + 0.967929i \(0.419167\pi\)
\(774\) 0 0
\(775\) −16188.6 −0.750337
\(776\) −6564.64 −0.303682
\(777\) 0 0
\(778\) −11336.3 −0.522400
\(779\) −10845.1 −0.498802
\(780\) 0 0
\(781\) −16683.7 −0.764391
\(782\) 32558.2 1.48885
\(783\) 0 0
\(784\) −74879.8 −3.41107
\(785\) 5029.16 0.228661
\(786\) 0 0
\(787\) 35607.0 1.61277 0.806386 0.591390i \(-0.201420\pi\)
0.806386 + 0.591390i \(0.201420\pi\)
\(788\) −16536.0 −0.747553
\(789\) 0 0
\(790\) 2049.63 0.0923069
\(791\) 59334.8 2.66713
\(792\) 0 0
\(793\) 0 0
\(794\) −14932.1 −0.667405
\(795\) 0 0
\(796\) 8873.85 0.395132
\(797\) −22155.3 −0.984668 −0.492334 0.870406i \(-0.663856\pi\)
−0.492334 + 0.870406i \(0.663856\pi\)
\(798\) 0 0
\(799\) 10037.0 0.444410
\(800\) −24517.1 −1.08351
\(801\) 0 0
\(802\) 33966.4 1.49550
\(803\) 21095.9 0.927094
\(804\) 0 0
\(805\) −14784.9 −0.647329
\(806\) 0 0
\(807\) 0 0
\(808\) 12031.7 0.523855
\(809\) 22524.6 0.978889 0.489445 0.872034i \(-0.337200\pi\)
0.489445 + 0.872034i \(0.337200\pi\)
\(810\) 0 0
\(811\) −4452.39 −0.192780 −0.0963900 0.995344i \(-0.530730\pi\)
−0.0963900 + 0.995344i \(0.530730\pi\)
\(812\) 23488.1 1.01511
\(813\) 0 0
\(814\) −11472.9 −0.494010
\(815\) 2081.12 0.0894460
\(816\) 0 0
\(817\) 15943.4 0.682729
\(818\) 26684.6 1.14059
\(819\) 0 0
\(820\) −5385.93 −0.229372
\(821\) −7097.27 −0.301701 −0.150851 0.988557i \(-0.548201\pi\)
−0.150851 + 0.988557i \(0.548201\pi\)
\(822\) 0 0
\(823\) −12193.8 −0.516463 −0.258231 0.966083i \(-0.583140\pi\)
−0.258231 + 0.966083i \(0.583140\pi\)
\(824\) −991.512 −0.0419187
\(825\) 0 0
\(826\) −31255.0 −1.31659
\(827\) 7427.97 0.312329 0.156164 0.987731i \(-0.450087\pi\)
0.156164 + 0.987731i \(0.450087\pi\)
\(828\) 0 0
\(829\) 16966.2 0.710810 0.355405 0.934712i \(-0.384343\pi\)
0.355405 + 0.934712i \(0.384343\pi\)
\(830\) −2327.91 −0.0973529
\(831\) 0 0
\(832\) 0 0
\(833\) 82449.7 3.42943
\(834\) 0 0
\(835\) −163.947 −0.00679477
\(836\) −5353.94 −0.221495
\(837\) 0 0
\(838\) 30682.7 1.26482
\(839\) 12025.7 0.494844 0.247422 0.968908i \(-0.420417\pi\)
0.247422 + 0.968908i \(0.420417\pi\)
\(840\) 0 0
\(841\) −12651.3 −0.518728
\(842\) −29874.2 −1.22272
\(843\) 0 0
\(844\) 13727.4 0.559855
\(845\) 0 0
\(846\) 0 0
\(847\) 35050.4 1.42189
\(848\) −55832.5 −2.26096
\(849\) 0 0
\(850\) 34383.4 1.38746
\(851\) −16626.0 −0.669720
\(852\) 0 0
\(853\) 22187.2 0.890593 0.445297 0.895383i \(-0.353098\pi\)
0.445297 + 0.895383i \(0.353098\pi\)
\(854\) 14818.5 0.593767
\(855\) 0 0
\(856\) 14961.2 0.597385
\(857\) −5746.19 −0.229038 −0.114519 0.993421i \(-0.536533\pi\)
−0.114519 + 0.993421i \(0.536533\pi\)
\(858\) 0 0
\(859\) 8305.66 0.329902 0.164951 0.986302i \(-0.447253\pi\)
0.164951 + 0.986302i \(0.447253\pi\)
\(860\) 7917.87 0.313950
\(861\) 0 0
\(862\) 51156.9 2.02136
\(863\) 38086.4 1.50229 0.751146 0.660137i \(-0.229502\pi\)
0.751146 + 0.660137i \(0.229502\pi\)
\(864\) 0 0
\(865\) −4167.61 −0.163819
\(866\) −25089.7 −0.984505
\(867\) 0 0
\(868\) −31984.7 −1.25073
\(869\) 2695.07 0.105206
\(870\) 0 0
\(871\) 0 0
\(872\) −9391.82 −0.364733
\(873\) 0 0
\(874\) −18183.8 −0.703748
\(875\) −33400.4 −1.29044
\(876\) 0 0
\(877\) 2098.53 0.0808009 0.0404005 0.999184i \(-0.487137\pi\)
0.0404005 + 0.999184i \(0.487137\pi\)
\(878\) 22163.8 0.851929
\(879\) 0 0
\(880\) 5714.18 0.218892
\(881\) −14555.3 −0.556619 −0.278309 0.960491i \(-0.589774\pi\)
−0.278309 + 0.960491i \(0.589774\pi\)
\(882\) 0 0
\(883\) 2122.88 0.0809066 0.0404533 0.999181i \(-0.487120\pi\)
0.0404533 + 0.999181i \(0.487120\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −25862.3 −0.980656
\(887\) 12487.3 0.472696 0.236348 0.971668i \(-0.424049\pi\)
0.236348 + 0.971668i \(0.424049\pi\)
\(888\) 0 0
\(889\) −10054.1 −0.379305
\(890\) 15589.1 0.587131
\(891\) 0 0
\(892\) −7394.61 −0.277567
\(893\) −5605.66 −0.210063
\(894\) 0 0
\(895\) 12405.6 0.463323
\(896\) 34458.9 1.28481
\(897\) 0 0
\(898\) −33196.5 −1.23361
\(899\) −15983.7 −0.592978
\(900\) 0 0
\(901\) 61476.8 2.27313
\(902\) −16597.8 −0.612691
\(903\) 0 0
\(904\) −12454.7 −0.458226
\(905\) 10650.3 0.391193
\(906\) 0 0
\(907\) 29679.8 1.08655 0.543275 0.839555i \(-0.317184\pi\)
0.543275 + 0.839555i \(0.317184\pi\)
\(908\) −10269.0 −0.375318
\(909\) 0 0
\(910\) 0 0
\(911\) −24800.0 −0.901934 −0.450967 0.892541i \(-0.648921\pi\)
−0.450967 + 0.892541i \(0.648921\pi\)
\(912\) 0 0
\(913\) −3060.99 −0.110957
\(914\) 40959.7 1.48230
\(915\) 0 0
\(916\) 19491.3 0.703070
\(917\) −3503.80 −0.126178
\(918\) 0 0
\(919\) −6597.90 −0.236828 −0.118414 0.992964i \(-0.537781\pi\)
−0.118414 + 0.992964i \(0.537781\pi\)
\(920\) 3103.43 0.111214
\(921\) 0 0
\(922\) −37613.4 −1.34353
\(923\) 0 0
\(924\) 0 0
\(925\) −17558.0 −0.624113
\(926\) 20917.7 0.742331
\(927\) 0 0
\(928\) −24206.8 −0.856281
\(929\) 15056.0 0.531724 0.265862 0.964011i \(-0.414344\pi\)
0.265862 + 0.964011i \(0.414344\pi\)
\(930\) 0 0
\(931\) −46048.1 −1.62102
\(932\) 12678.9 0.445612
\(933\) 0 0
\(934\) −49487.1 −1.73369
\(935\) −6291.85 −0.220070
\(936\) 0 0
\(937\) −35777.0 −1.24737 −0.623683 0.781677i \(-0.714365\pi\)
−0.623683 + 0.781677i \(0.714365\pi\)
\(938\) −1414.00 −0.0492205
\(939\) 0 0
\(940\) −2783.90 −0.0965966
\(941\) −22973.6 −0.795873 −0.397937 0.917413i \(-0.630274\pi\)
−0.397937 + 0.917413i \(0.630274\pi\)
\(942\) 0 0
\(943\) −24052.9 −0.830615
\(944\) 17505.3 0.603549
\(945\) 0 0
\(946\) 24400.5 0.838614
\(947\) −51038.3 −1.75134 −0.875671 0.482908i \(-0.839580\pi\)
−0.875671 + 0.482908i \(0.839580\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −19203.1 −0.655823
\(951\) 0 0
\(952\) −23346.0 −0.794799
\(953\) 22586.5 0.767733 0.383866 0.923389i \(-0.374592\pi\)
0.383866 + 0.923389i \(0.374592\pi\)
\(954\) 0 0
\(955\) 3067.16 0.103928
\(956\) −30259.9 −1.02372
\(957\) 0 0
\(958\) −62477.6 −2.10706
\(959\) −95342.8 −3.21041
\(960\) 0 0
\(961\) −8025.32 −0.269387
\(962\) 0 0
\(963\) 0 0
\(964\) −28374.1 −0.947996
\(965\) −4907.64 −0.163712
\(966\) 0 0
\(967\) 36678.7 1.21976 0.609880 0.792494i \(-0.291218\pi\)
0.609880 + 0.792494i \(0.291218\pi\)
\(968\) −7357.24 −0.244288
\(969\) 0 0
\(970\) −12537.4 −0.415003
\(971\) −32635.2 −1.07859 −0.539296 0.842116i \(-0.681310\pi\)
−0.539296 + 0.842116i \(0.681310\pi\)
\(972\) 0 0
\(973\) −71491.0 −2.35549
\(974\) −19820.0 −0.652026
\(975\) 0 0
\(976\) −8299.54 −0.272194
\(977\) 44432.6 1.45499 0.727496 0.686112i \(-0.240684\pi\)
0.727496 + 0.686112i \(0.240684\pi\)
\(978\) 0 0
\(979\) 20498.2 0.669178
\(980\) −22868.6 −0.745418
\(981\) 0 0
\(982\) 60515.6 1.96653
\(983\) 484.485 0.0157199 0.00785996 0.999969i \(-0.497498\pi\)
0.00785996 + 0.999969i \(0.497498\pi\)
\(984\) 0 0
\(985\) 10853.2 0.351079
\(986\) 33948.3 1.09649
\(987\) 0 0
\(988\) 0 0
\(989\) 35360.2 1.13689
\(990\) 0 0
\(991\) −48017.1 −1.53917 −0.769583 0.638546i \(-0.779536\pi\)
−0.769583 + 0.638546i \(0.779536\pi\)
\(992\) 32963.4 1.05503
\(993\) 0 0
\(994\) −118229. −3.77263
\(995\) −5824.25 −0.185569
\(996\) 0 0
\(997\) −26561.9 −0.843755 −0.421877 0.906653i \(-0.638629\pi\)
−0.421877 + 0.906653i \(0.638629\pi\)
\(998\) 16408.9 0.520455
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1521.4.a.u.1.1 3
3.2 odd 2 507.4.a.h.1.3 3
13.12 even 2 117.4.a.f.1.3 3
39.5 even 4 507.4.b.g.337.2 6
39.8 even 4 507.4.b.g.337.5 6
39.38 odd 2 39.4.a.c.1.1 3
52.51 odd 2 1872.4.a.bk.1.2 3
156.155 even 2 624.4.a.t.1.2 3
195.194 odd 2 975.4.a.l.1.3 3
273.272 even 2 1911.4.a.k.1.1 3
312.77 odd 2 2496.4.a.bl.1.2 3
312.155 even 2 2496.4.a.bp.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.a.c.1.1 3 39.38 odd 2
117.4.a.f.1.3 3 13.12 even 2
507.4.a.h.1.3 3 3.2 odd 2
507.4.b.g.337.2 6 39.5 even 4
507.4.b.g.337.5 6 39.8 even 4
624.4.a.t.1.2 3 156.155 even 2
975.4.a.l.1.3 3 195.194 odd 2
1521.4.a.u.1.1 3 1.1 even 1 trivial
1872.4.a.bk.1.2 3 52.51 odd 2
1911.4.a.k.1.1 3 273.272 even 2
2496.4.a.bl.1.2 3 312.77 odd 2
2496.4.a.bp.1.2 3 312.155 even 2