Properties

Label 441.4.a.k.1.1
Level $441$
Weight $4$
Character 441.1
Self dual yes
Analytic conductor $26.020$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 441.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -21.0000 q^{8} +O(q^{10})\) \(q+3.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} -21.0000 q^{8} -9.00000 q^{10} +15.0000 q^{11} +64.0000 q^{13} -71.0000 q^{16} +84.0000 q^{17} +16.0000 q^{19} -3.00000 q^{20} +45.0000 q^{22} +84.0000 q^{23} -116.000 q^{25} +192.000 q^{26} +297.000 q^{29} +253.000 q^{31} -45.0000 q^{32} +252.000 q^{34} -316.000 q^{37} +48.0000 q^{38} +63.0000 q^{40} +360.000 q^{41} +26.0000 q^{43} +15.0000 q^{44} +252.000 q^{46} -30.0000 q^{47} -348.000 q^{50} +64.0000 q^{52} -363.000 q^{53} -45.0000 q^{55} +891.000 q^{58} -15.0000 q^{59} +118.000 q^{61} +759.000 q^{62} +433.000 q^{64} -192.000 q^{65} -370.000 q^{67} +84.0000 q^{68} +342.000 q^{71} -362.000 q^{73} -948.000 q^{74} +16.0000 q^{76} +467.000 q^{79} +213.000 q^{80} +1080.00 q^{82} +477.000 q^{83} -252.000 q^{85} +78.0000 q^{86} -315.000 q^{88} +906.000 q^{89} +84.0000 q^{92} -90.0000 q^{94} -48.0000 q^{95} -503.000 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 1.06066 0.530330 0.847791i \(-0.322068\pi\)
0.530330 + 0.847791i \(0.322068\pi\)
\(3\) 0 0
\(4\) 1.00000 0.125000
\(5\) −3.00000 −0.268328 −0.134164 0.990959i \(-0.542835\pi\)
−0.134164 + 0.990959i \(0.542835\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) −9.00000 −0.284605
\(11\) 15.0000 0.411152 0.205576 0.978641i \(-0.434093\pi\)
0.205576 + 0.978641i \(0.434093\pi\)
\(12\) 0 0
\(13\) 64.0000 1.36542 0.682708 0.730691i \(-0.260802\pi\)
0.682708 + 0.730691i \(0.260802\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −71.0000 −1.10938
\(17\) 84.0000 1.19841 0.599206 0.800595i \(-0.295483\pi\)
0.599206 + 0.800595i \(0.295483\pi\)
\(18\) 0 0
\(19\) 16.0000 0.193192 0.0965961 0.995324i \(-0.469204\pi\)
0.0965961 + 0.995324i \(0.469204\pi\)
\(20\) −3.00000 −0.0335410
\(21\) 0 0
\(22\) 45.0000 0.436092
\(23\) 84.0000 0.761531 0.380765 0.924672i \(-0.375661\pi\)
0.380765 + 0.924672i \(0.375661\pi\)
\(24\) 0 0
\(25\) −116.000 −0.928000
\(26\) 192.000 1.44824
\(27\) 0 0
\(28\) 0 0
\(29\) 297.000 1.90178 0.950888 0.309535i \(-0.100173\pi\)
0.950888 + 0.309535i \(0.100173\pi\)
\(30\) 0 0
\(31\) 253.000 1.46581 0.732906 0.680330i \(-0.238164\pi\)
0.732906 + 0.680330i \(0.238164\pi\)
\(32\) −45.0000 −0.248592
\(33\) 0 0
\(34\) 252.000 1.27111
\(35\) 0 0
\(36\) 0 0
\(37\) −316.000 −1.40406 −0.702028 0.712149i \(-0.747722\pi\)
−0.702028 + 0.712149i \(0.747722\pi\)
\(38\) 48.0000 0.204911
\(39\) 0 0
\(40\) 63.0000 0.249029
\(41\) 360.000 1.37128 0.685641 0.727940i \(-0.259522\pi\)
0.685641 + 0.727940i \(0.259522\pi\)
\(42\) 0 0
\(43\) 26.0000 0.0922084 0.0461042 0.998937i \(-0.485319\pi\)
0.0461042 + 0.998937i \(0.485319\pi\)
\(44\) 15.0000 0.0513940
\(45\) 0 0
\(46\) 252.000 0.807725
\(47\) −30.0000 −0.0931053 −0.0465527 0.998916i \(-0.514824\pi\)
−0.0465527 + 0.998916i \(0.514824\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −348.000 −0.984293
\(51\) 0 0
\(52\) 64.0000 0.170677
\(53\) −363.000 −0.940790 −0.470395 0.882456i \(-0.655889\pi\)
−0.470395 + 0.882456i \(0.655889\pi\)
\(54\) 0 0
\(55\) −45.0000 −0.110324
\(56\) 0 0
\(57\) 0 0
\(58\) 891.000 2.01714
\(59\) −15.0000 −0.0330989 −0.0165494 0.999863i \(-0.505268\pi\)
−0.0165494 + 0.999863i \(0.505268\pi\)
\(60\) 0 0
\(61\) 118.000 0.247678 0.123839 0.992302i \(-0.460479\pi\)
0.123839 + 0.992302i \(0.460479\pi\)
\(62\) 759.000 1.55473
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) −192.000 −0.366380
\(66\) 0 0
\(67\) −370.000 −0.674667 −0.337334 0.941385i \(-0.609525\pi\)
−0.337334 + 0.941385i \(0.609525\pi\)
\(68\) 84.0000 0.149801
\(69\) 0 0
\(70\) 0 0
\(71\) 342.000 0.571661 0.285831 0.958280i \(-0.407731\pi\)
0.285831 + 0.958280i \(0.407731\pi\)
\(72\) 0 0
\(73\) −362.000 −0.580396 −0.290198 0.956967i \(-0.593721\pi\)
−0.290198 + 0.956967i \(0.593721\pi\)
\(74\) −948.000 −1.48923
\(75\) 0 0
\(76\) 16.0000 0.0241490
\(77\) 0 0
\(78\) 0 0
\(79\) 467.000 0.665084 0.332542 0.943089i \(-0.392094\pi\)
0.332542 + 0.943089i \(0.392094\pi\)
\(80\) 213.000 0.297677
\(81\) 0 0
\(82\) 1080.00 1.45446
\(83\) 477.000 0.630814 0.315407 0.948957i \(-0.397859\pi\)
0.315407 + 0.948957i \(0.397859\pi\)
\(84\) 0 0
\(85\) −252.000 −0.321568
\(86\) 78.0000 0.0978018
\(87\) 0 0
\(88\) −315.000 −0.381581
\(89\) 906.000 1.07905 0.539527 0.841968i \(-0.318603\pi\)
0.539527 + 0.841968i \(0.318603\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 84.0000 0.0951914
\(93\) 0 0
\(94\) −90.0000 −0.0987531
\(95\) −48.0000 −0.0518389
\(96\) 0 0
\(97\) −503.000 −0.526515 −0.263257 0.964726i \(-0.584797\pi\)
−0.263257 + 0.964726i \(0.584797\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −116.000 −0.116000
\(101\) −1086.00 −1.06991 −0.534956 0.844880i \(-0.679672\pi\)
−0.534956 + 0.844880i \(0.679672\pi\)
\(102\) 0 0
\(103\) −1736.00 −1.66071 −0.830355 0.557235i \(-0.811862\pi\)
−0.830355 + 0.557235i \(0.811862\pi\)
\(104\) −1344.00 −1.26721
\(105\) 0 0
\(106\) −1089.00 −0.997859
\(107\) 1353.00 1.22242 0.611212 0.791467i \(-0.290682\pi\)
0.611212 + 0.791467i \(0.290682\pi\)
\(108\) 0 0
\(109\) −370.000 −0.325134 −0.162567 0.986698i \(-0.551977\pi\)
−0.162567 + 0.986698i \(0.551977\pi\)
\(110\) −135.000 −0.117016
\(111\) 0 0
\(112\) 0 0
\(113\) 648.000 0.539458 0.269729 0.962936i \(-0.413066\pi\)
0.269729 + 0.962936i \(0.413066\pi\)
\(114\) 0 0
\(115\) −252.000 −0.204340
\(116\) 297.000 0.237722
\(117\) 0 0
\(118\) −45.0000 −0.0351067
\(119\) 0 0
\(120\) 0 0
\(121\) −1106.00 −0.830954
\(122\) 354.000 0.262702
\(123\) 0 0
\(124\) 253.000 0.183226
\(125\) 723.000 0.517337
\(126\) 0 0
\(127\) 377.000 0.263412 0.131706 0.991289i \(-0.457954\pi\)
0.131706 + 0.991289i \(0.457954\pi\)
\(128\) 1659.00 1.14560
\(129\) 0 0
\(130\) −576.000 −0.388604
\(131\) −651.000 −0.434184 −0.217092 0.976151i \(-0.569657\pi\)
−0.217092 + 0.976151i \(0.569657\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1110.00 −0.715593
\(135\) 0 0
\(136\) −1764.00 −1.11222
\(137\) 1770.00 1.10381 0.551903 0.833909i \(-0.313902\pi\)
0.551903 + 0.833909i \(0.313902\pi\)
\(138\) 0 0
\(139\) 1558.00 0.950704 0.475352 0.879796i \(-0.342321\pi\)
0.475352 + 0.879796i \(0.342321\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1026.00 0.606338
\(143\) 960.000 0.561393
\(144\) 0 0
\(145\) −891.000 −0.510300
\(146\) −1086.00 −0.615603
\(147\) 0 0
\(148\) −316.000 −0.175507
\(149\) −2454.00 −1.34926 −0.674629 0.738157i \(-0.735696\pi\)
−0.674629 + 0.738157i \(0.735696\pi\)
\(150\) 0 0
\(151\) 1259.00 0.678516 0.339258 0.940693i \(-0.389824\pi\)
0.339258 + 0.940693i \(0.389824\pi\)
\(152\) −336.000 −0.179297
\(153\) 0 0
\(154\) 0 0
\(155\) −759.000 −0.393318
\(156\) 0 0
\(157\) 196.000 0.0996338 0.0498169 0.998758i \(-0.484136\pi\)
0.0498169 + 0.998758i \(0.484136\pi\)
\(158\) 1401.00 0.705428
\(159\) 0 0
\(160\) 135.000 0.0667043
\(161\) 0 0
\(162\) 0 0
\(163\) −1252.00 −0.601621 −0.300810 0.953684i \(-0.597257\pi\)
−0.300810 + 0.953684i \(0.597257\pi\)
\(164\) 360.000 0.171410
\(165\) 0 0
\(166\) 1431.00 0.669079
\(167\) −2646.00 −1.22607 −0.613035 0.790056i \(-0.710051\pi\)
−0.613035 + 0.790056i \(0.710051\pi\)
\(168\) 0 0
\(169\) 1899.00 0.864360
\(170\) −756.000 −0.341074
\(171\) 0 0
\(172\) 26.0000 0.0115261
\(173\) −786.000 −0.345425 −0.172712 0.984972i \(-0.555253\pi\)
−0.172712 + 0.984972i \(0.555253\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1065.00 −0.456122
\(177\) 0 0
\(178\) 2718.00 1.14451
\(179\) −2892.00 −1.20759 −0.603794 0.797140i \(-0.706345\pi\)
−0.603794 + 0.797140i \(0.706345\pi\)
\(180\) 0 0
\(181\) −1352.00 −0.555212 −0.277606 0.960695i \(-0.589541\pi\)
−0.277606 + 0.960695i \(0.589541\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1764.00 −0.706760
\(185\) 948.000 0.376748
\(186\) 0 0
\(187\) 1260.00 0.492729
\(188\) −30.0000 −0.0116382
\(189\) 0 0
\(190\) −144.000 −0.0549835
\(191\) −3912.00 −1.48200 −0.741001 0.671504i \(-0.765649\pi\)
−0.741001 + 0.671504i \(0.765649\pi\)
\(192\) 0 0
\(193\) 1493.00 0.556832 0.278416 0.960461i \(-0.410191\pi\)
0.278416 + 0.960461i \(0.410191\pi\)
\(194\) −1509.00 −0.558453
\(195\) 0 0
\(196\) 0 0
\(197\) 4086.00 1.47774 0.738872 0.673846i \(-0.235359\pi\)
0.738872 + 0.673846i \(0.235359\pi\)
\(198\) 0 0
\(199\) 3556.00 1.26672 0.633362 0.773855i \(-0.281674\pi\)
0.633362 + 0.773855i \(0.281674\pi\)
\(200\) 2436.00 0.861256
\(201\) 0 0
\(202\) −3258.00 −1.13481
\(203\) 0 0
\(204\) 0 0
\(205\) −1080.00 −0.367954
\(206\) −5208.00 −1.76145
\(207\) 0 0
\(208\) −4544.00 −1.51476
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 1250.00 0.407837 0.203918 0.978988i \(-0.434632\pi\)
0.203918 + 0.978988i \(0.434632\pi\)
\(212\) −363.000 −0.117599
\(213\) 0 0
\(214\) 4059.00 1.29658
\(215\) −78.0000 −0.0247421
\(216\) 0 0
\(217\) 0 0
\(218\) −1110.00 −0.344856
\(219\) 0 0
\(220\) −45.0000 −0.0137905
\(221\) 5376.00 1.63633
\(222\) 0 0
\(223\) −425.000 −0.127624 −0.0638119 0.997962i \(-0.520326\pi\)
−0.0638119 + 0.997962i \(0.520326\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1944.00 0.572181
\(227\) 3855.00 1.12716 0.563580 0.826061i \(-0.309424\pi\)
0.563580 + 0.826061i \(0.309424\pi\)
\(228\) 0 0
\(229\) 2188.00 0.631385 0.315692 0.948862i \(-0.397763\pi\)
0.315692 + 0.948862i \(0.397763\pi\)
\(230\) −756.000 −0.216735
\(231\) 0 0
\(232\) −6237.00 −1.76500
\(233\) −852.000 −0.239555 −0.119778 0.992801i \(-0.538218\pi\)
−0.119778 + 0.992801i \(0.538218\pi\)
\(234\) 0 0
\(235\) 90.0000 0.0249828
\(236\) −15.0000 −0.00413736
\(237\) 0 0
\(238\) 0 0
\(239\) −5508.00 −1.49072 −0.745362 0.666660i \(-0.767723\pi\)
−0.745362 + 0.666660i \(0.767723\pi\)
\(240\) 0 0
\(241\) −791.000 −0.211422 −0.105711 0.994397i \(-0.533712\pi\)
−0.105711 + 0.994397i \(0.533712\pi\)
\(242\) −3318.00 −0.881360
\(243\) 0 0
\(244\) 118.000 0.0309597
\(245\) 0 0
\(246\) 0 0
\(247\) 1024.00 0.263788
\(248\) −5313.00 −1.36039
\(249\) 0 0
\(250\) 2169.00 0.548718
\(251\) 5265.00 1.32400 0.662000 0.749504i \(-0.269708\pi\)
0.662000 + 0.749504i \(0.269708\pi\)
\(252\) 0 0
\(253\) 1260.00 0.313105
\(254\) 1131.00 0.279391
\(255\) 0 0
\(256\) 1513.00 0.369385
\(257\) −6870.00 −1.66747 −0.833733 0.552168i \(-0.813801\pi\)
−0.833733 + 0.552168i \(0.813801\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −192.000 −0.0457974
\(261\) 0 0
\(262\) −1953.00 −0.460522
\(263\) 222.000 0.0520498 0.0260249 0.999661i \(-0.491715\pi\)
0.0260249 + 0.999661i \(0.491715\pi\)
\(264\) 0 0
\(265\) 1089.00 0.252441
\(266\) 0 0
\(267\) 0 0
\(268\) −370.000 −0.0843334
\(269\) 7851.00 1.77949 0.889747 0.456454i \(-0.150881\pi\)
0.889747 + 0.456454i \(0.150881\pi\)
\(270\) 0 0
\(271\) −5183.00 −1.16179 −0.580895 0.813979i \(-0.697297\pi\)
−0.580895 + 0.813979i \(0.697297\pi\)
\(272\) −5964.00 −1.32949
\(273\) 0 0
\(274\) 5310.00 1.17076
\(275\) −1740.00 −0.381549
\(276\) 0 0
\(277\) −4960.00 −1.07588 −0.537938 0.842985i \(-0.680796\pi\)
−0.537938 + 0.842985i \(0.680796\pi\)
\(278\) 4674.00 1.00837
\(279\) 0 0
\(280\) 0 0
\(281\) 774.000 0.164317 0.0821583 0.996619i \(-0.473819\pi\)
0.0821583 + 0.996619i \(0.473819\pi\)
\(282\) 0 0
\(283\) −3698.00 −0.776761 −0.388380 0.921499i \(-0.626965\pi\)
−0.388380 + 0.921499i \(0.626965\pi\)
\(284\) 342.000 0.0714576
\(285\) 0 0
\(286\) 2880.00 0.595447
\(287\) 0 0
\(288\) 0 0
\(289\) 2143.00 0.436190
\(290\) −2673.00 −0.541255
\(291\) 0 0
\(292\) −362.000 −0.0725495
\(293\) −6273.00 −1.25076 −0.625380 0.780321i \(-0.715056\pi\)
−0.625380 + 0.780321i \(0.715056\pi\)
\(294\) 0 0
\(295\) 45.0000 0.00888136
\(296\) 6636.00 1.30307
\(297\) 0 0
\(298\) −7362.00 −1.43110
\(299\) 5376.00 1.03981
\(300\) 0 0
\(301\) 0 0
\(302\) 3777.00 0.719675
\(303\) 0 0
\(304\) −1136.00 −0.214323
\(305\) −354.000 −0.0664590
\(306\) 0 0
\(307\) 1684.00 0.313065 0.156533 0.987673i \(-0.449968\pi\)
0.156533 + 0.987673i \(0.449968\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2277.00 −0.417177
\(311\) −1320.00 −0.240676 −0.120338 0.992733i \(-0.538398\pi\)
−0.120338 + 0.992733i \(0.538398\pi\)
\(312\) 0 0
\(313\) 8503.00 1.53552 0.767760 0.640737i \(-0.221371\pi\)
0.767760 + 0.640737i \(0.221371\pi\)
\(314\) 588.000 0.105678
\(315\) 0 0
\(316\) 467.000 0.0831355
\(317\) 2577.00 0.456589 0.228295 0.973592i \(-0.426685\pi\)
0.228295 + 0.973592i \(0.426685\pi\)
\(318\) 0 0
\(319\) 4455.00 0.781919
\(320\) −1299.00 −0.226926
\(321\) 0 0
\(322\) 0 0
\(323\) 1344.00 0.231524
\(324\) 0 0
\(325\) −7424.00 −1.26711
\(326\) −3756.00 −0.638115
\(327\) 0 0
\(328\) −7560.00 −1.27266
\(329\) 0 0
\(330\) 0 0
\(331\) −484.000 −0.0803717 −0.0401859 0.999192i \(-0.512795\pi\)
−0.0401859 + 0.999192i \(0.512795\pi\)
\(332\) 477.000 0.0788517
\(333\) 0 0
\(334\) −7938.00 −1.30044
\(335\) 1110.00 0.181032
\(336\) 0 0
\(337\) −8359.00 −1.35117 −0.675584 0.737283i \(-0.736109\pi\)
−0.675584 + 0.737283i \(0.736109\pi\)
\(338\) 5697.00 0.916793
\(339\) 0 0
\(340\) −252.000 −0.0401959
\(341\) 3795.00 0.602671
\(342\) 0 0
\(343\) 0 0
\(344\) −546.000 −0.0855766
\(345\) 0 0
\(346\) −2358.00 −0.366378
\(347\) 1860.00 0.287752 0.143876 0.989596i \(-0.454043\pi\)
0.143876 + 0.989596i \(0.454043\pi\)
\(348\) 0 0
\(349\) 1918.00 0.294178 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −675.000 −0.102209
\(353\) −3048.00 −0.459571 −0.229786 0.973241i \(-0.573803\pi\)
−0.229786 + 0.973241i \(0.573803\pi\)
\(354\) 0 0
\(355\) −1026.00 −0.153393
\(356\) 906.000 0.134882
\(357\) 0 0
\(358\) −8676.00 −1.28084
\(359\) 30.0000 0.00441042 0.00220521 0.999998i \(-0.499298\pi\)
0.00220521 + 0.999998i \(0.499298\pi\)
\(360\) 0 0
\(361\) −6603.00 −0.962677
\(362\) −4056.00 −0.588891
\(363\) 0 0
\(364\) 0 0
\(365\) 1086.00 0.155737
\(366\) 0 0
\(367\) 11311.0 1.60880 0.804400 0.594088i \(-0.202487\pi\)
0.804400 + 0.594088i \(0.202487\pi\)
\(368\) −5964.00 −0.844823
\(369\) 0 0
\(370\) 2844.00 0.399601
\(371\) 0 0
\(372\) 0 0
\(373\) 1208.00 0.167689 0.0838443 0.996479i \(-0.473280\pi\)
0.0838443 + 0.996479i \(0.473280\pi\)
\(374\) 3780.00 0.522618
\(375\) 0 0
\(376\) 630.000 0.0864090
\(377\) 19008.0 2.59672
\(378\) 0 0
\(379\) 7640.00 1.03546 0.517731 0.855543i \(-0.326777\pi\)
0.517731 + 0.855543i \(0.326777\pi\)
\(380\) −48.0000 −0.00647986
\(381\) 0 0
\(382\) −11736.0 −1.57190
\(383\) 12750.0 1.70103 0.850515 0.525951i \(-0.176290\pi\)
0.850515 + 0.525951i \(0.176290\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4479.00 0.590609
\(387\) 0 0
\(388\) −503.000 −0.0658143
\(389\) −3126.00 −0.407441 −0.203720 0.979029i \(-0.565303\pi\)
−0.203720 + 0.979029i \(0.565303\pi\)
\(390\) 0 0
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) 0 0
\(394\) 12258.0 1.56738
\(395\) −1401.00 −0.178461
\(396\) 0 0
\(397\) 5932.00 0.749921 0.374960 0.927041i \(-0.377656\pi\)
0.374960 + 0.927041i \(0.377656\pi\)
\(398\) 10668.0 1.34356
\(399\) 0 0
\(400\) 8236.00 1.02950
\(401\) −1608.00 −0.200249 −0.100124 0.994975i \(-0.531924\pi\)
−0.100124 + 0.994975i \(0.531924\pi\)
\(402\) 0 0
\(403\) 16192.0 2.00144
\(404\) −1086.00 −0.133739
\(405\) 0 0
\(406\) 0 0
\(407\) −4740.00 −0.577280
\(408\) 0 0
\(409\) 4465.00 0.539805 0.269902 0.962888i \(-0.413009\pi\)
0.269902 + 0.962888i \(0.413009\pi\)
\(410\) −3240.00 −0.390274
\(411\) 0 0
\(412\) −1736.00 −0.207589
\(413\) 0 0
\(414\) 0 0
\(415\) −1431.00 −0.169265
\(416\) −2880.00 −0.339432
\(417\) 0 0
\(418\) 720.000 0.0842496
\(419\) −1584.00 −0.184686 −0.0923430 0.995727i \(-0.529436\pi\)
−0.0923430 + 0.995727i \(0.529436\pi\)
\(420\) 0 0
\(421\) −1330.00 −0.153967 −0.0769837 0.997032i \(-0.524529\pi\)
−0.0769837 + 0.997032i \(0.524529\pi\)
\(422\) 3750.00 0.432576
\(423\) 0 0
\(424\) 7623.00 0.873126
\(425\) −9744.00 −1.11213
\(426\) 0 0
\(427\) 0 0
\(428\) 1353.00 0.152803
\(429\) 0 0
\(430\) −234.000 −0.0262430
\(431\) −9588.00 −1.07155 −0.535775 0.844361i \(-0.679980\pi\)
−0.535775 + 0.844361i \(0.679980\pi\)
\(432\) 0 0
\(433\) −494.000 −0.0548271 −0.0274135 0.999624i \(-0.508727\pi\)
−0.0274135 + 0.999624i \(0.508727\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −370.000 −0.0406417
\(437\) 1344.00 0.147122
\(438\) 0 0
\(439\) 16009.0 1.74047 0.870237 0.492634i \(-0.163966\pi\)
0.870237 + 0.492634i \(0.163966\pi\)
\(440\) 945.000 0.102389
\(441\) 0 0
\(442\) 16128.0 1.73559
\(443\) −7773.00 −0.833649 −0.416824 0.908987i \(-0.636857\pi\)
−0.416824 + 0.908987i \(0.636857\pi\)
\(444\) 0 0
\(445\) −2718.00 −0.289541
\(446\) −1275.00 −0.135365
\(447\) 0 0
\(448\) 0 0
\(449\) −864.000 −0.0908122 −0.0454061 0.998969i \(-0.514458\pi\)
−0.0454061 + 0.998969i \(0.514458\pi\)
\(450\) 0 0
\(451\) 5400.00 0.563805
\(452\) 648.000 0.0674322
\(453\) 0 0
\(454\) 11565.0 1.19553
\(455\) 0 0
\(456\) 0 0
\(457\) 2519.00 0.257842 0.128921 0.991655i \(-0.458849\pi\)
0.128921 + 0.991655i \(0.458849\pi\)
\(458\) 6564.00 0.669685
\(459\) 0 0
\(460\) −252.000 −0.0255425
\(461\) −342.000 −0.0345521 −0.0172761 0.999851i \(-0.505499\pi\)
−0.0172761 + 0.999851i \(0.505499\pi\)
\(462\) 0 0
\(463\) −4336.00 −0.435229 −0.217614 0.976035i \(-0.569828\pi\)
−0.217614 + 0.976035i \(0.569828\pi\)
\(464\) −21087.0 −2.10978
\(465\) 0 0
\(466\) −2556.00 −0.254087
\(467\) 18636.0 1.84662 0.923310 0.384056i \(-0.125473\pi\)
0.923310 + 0.384056i \(0.125473\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 270.000 0.0264982
\(471\) 0 0
\(472\) 315.000 0.0307183
\(473\) 390.000 0.0379117
\(474\) 0 0
\(475\) −1856.00 −0.179282
\(476\) 0 0
\(477\) 0 0
\(478\) −16524.0 −1.58115
\(479\) 15078.0 1.43827 0.719135 0.694870i \(-0.244538\pi\)
0.719135 + 0.694870i \(0.244538\pi\)
\(480\) 0 0
\(481\) −20224.0 −1.91712
\(482\) −2373.00 −0.224247
\(483\) 0 0
\(484\) −1106.00 −0.103869
\(485\) 1509.00 0.141279
\(486\) 0 0
\(487\) 6221.00 0.578851 0.289425 0.957201i \(-0.406536\pi\)
0.289425 + 0.957201i \(0.406536\pi\)
\(488\) −2478.00 −0.229864
\(489\) 0 0
\(490\) 0 0
\(491\) 7371.00 0.677492 0.338746 0.940878i \(-0.389997\pi\)
0.338746 + 0.940878i \(0.389997\pi\)
\(492\) 0 0
\(493\) 24948.0 2.27911
\(494\) 3072.00 0.279789
\(495\) 0 0
\(496\) −17963.0 −1.62613
\(497\) 0 0
\(498\) 0 0
\(499\) 4274.00 0.383428 0.191714 0.981451i \(-0.438595\pi\)
0.191714 + 0.981451i \(0.438595\pi\)
\(500\) 723.000 0.0646671
\(501\) 0 0
\(502\) 15795.0 1.40431
\(503\) −2520.00 −0.223382 −0.111691 0.993743i \(-0.535627\pi\)
−0.111691 + 0.993743i \(0.535627\pi\)
\(504\) 0 0
\(505\) 3258.00 0.287087
\(506\) 3780.00 0.332098
\(507\) 0 0
\(508\) 377.000 0.0329265
\(509\) −14277.0 −1.24326 −0.621628 0.783313i \(-0.713528\pi\)
−0.621628 + 0.783313i \(0.713528\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) −20610.0 −1.76862
\(515\) 5208.00 0.445615
\(516\) 0 0
\(517\) −450.000 −0.0382804
\(518\) 0 0
\(519\) 0 0
\(520\) 4032.00 0.340029
\(521\) −6306.00 −0.530270 −0.265135 0.964211i \(-0.585417\pi\)
−0.265135 + 0.964211i \(0.585417\pi\)
\(522\) 0 0
\(523\) −8072.00 −0.674883 −0.337442 0.941346i \(-0.609562\pi\)
−0.337442 + 0.941346i \(0.609562\pi\)
\(524\) −651.000 −0.0542730
\(525\) 0 0
\(526\) 666.000 0.0552072
\(527\) 21252.0 1.75664
\(528\) 0 0
\(529\) −5111.00 −0.420071
\(530\) 3267.00 0.267754
\(531\) 0 0
\(532\) 0 0
\(533\) 23040.0 1.87237
\(534\) 0 0
\(535\) −4059.00 −0.328011
\(536\) 7770.00 0.626143
\(537\) 0 0
\(538\) 23553.0 1.88744
\(539\) 0 0
\(540\) 0 0
\(541\) −22858.0 −1.81653 −0.908264 0.418396i \(-0.862592\pi\)
−0.908264 + 0.418396i \(0.862592\pi\)
\(542\) −15549.0 −1.23226
\(543\) 0 0
\(544\) −3780.00 −0.297916
\(545\) 1110.00 0.0872425
\(546\) 0 0
\(547\) −24724.0 −1.93258 −0.966291 0.257454i \(-0.917116\pi\)
−0.966291 + 0.257454i \(0.917116\pi\)
\(548\) 1770.00 0.137976
\(549\) 0 0
\(550\) −5220.00 −0.404694
\(551\) 4752.00 0.367408
\(552\) 0 0
\(553\) 0 0
\(554\) −14880.0 −1.14114
\(555\) 0 0
\(556\) 1558.00 0.118838
\(557\) 9843.00 0.748764 0.374382 0.927275i \(-0.377855\pi\)
0.374382 + 0.927275i \(0.377855\pi\)
\(558\) 0 0
\(559\) 1664.00 0.125903
\(560\) 0 0
\(561\) 0 0
\(562\) 2322.00 0.174284
\(563\) −13371.0 −1.00092 −0.500462 0.865758i \(-0.666837\pi\)
−0.500462 + 0.865758i \(0.666837\pi\)
\(564\) 0 0
\(565\) −1944.00 −0.144752
\(566\) −11094.0 −0.823879
\(567\) 0 0
\(568\) −7182.00 −0.530546
\(569\) 5232.00 0.385478 0.192739 0.981250i \(-0.438263\pi\)
0.192739 + 0.981250i \(0.438263\pi\)
\(570\) 0 0
\(571\) −14398.0 −1.05523 −0.527616 0.849483i \(-0.676914\pi\)
−0.527616 + 0.849483i \(0.676914\pi\)
\(572\) 960.000 0.0701742
\(573\) 0 0
\(574\) 0 0
\(575\) −9744.00 −0.706701
\(576\) 0 0
\(577\) −19871.0 −1.43369 −0.716846 0.697231i \(-0.754415\pi\)
−0.716846 + 0.697231i \(0.754415\pi\)
\(578\) 6429.00 0.462649
\(579\) 0 0
\(580\) −891.000 −0.0637875
\(581\) 0 0
\(582\) 0 0
\(583\) −5445.00 −0.386808
\(584\) 7602.00 0.538652
\(585\) 0 0
\(586\) −18819.0 −1.32663
\(587\) −16137.0 −1.13466 −0.567330 0.823491i \(-0.692024\pi\)
−0.567330 + 0.823491i \(0.692024\pi\)
\(588\) 0 0
\(589\) 4048.00 0.283183
\(590\) 135.000 0.00942011
\(591\) 0 0
\(592\) 22436.0 1.55762
\(593\) −21324.0 −1.47668 −0.738340 0.674428i \(-0.764390\pi\)
−0.738340 + 0.674428i \(0.764390\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2454.00 −0.168657
\(597\) 0 0
\(598\) 16128.0 1.10288
\(599\) 8646.00 0.589760 0.294880 0.955534i \(-0.404720\pi\)
0.294880 + 0.955534i \(0.404720\pi\)
\(600\) 0 0
\(601\) −11195.0 −0.759823 −0.379911 0.925023i \(-0.624046\pi\)
−0.379911 + 0.925023i \(0.624046\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1259.00 0.0848145
\(605\) 3318.00 0.222968
\(606\) 0 0
\(607\) 8971.00 0.599871 0.299935 0.953959i \(-0.403035\pi\)
0.299935 + 0.953959i \(0.403035\pi\)
\(608\) −720.000 −0.0480261
\(609\) 0 0
\(610\) −1062.00 −0.0704904
\(611\) −1920.00 −0.127127
\(612\) 0 0
\(613\) −12772.0 −0.841527 −0.420764 0.907170i \(-0.638238\pi\)
−0.420764 + 0.907170i \(0.638238\pi\)
\(614\) 5052.00 0.332056
\(615\) 0 0
\(616\) 0 0
\(617\) −12762.0 −0.832705 −0.416352 0.909203i \(-0.636692\pi\)
−0.416352 + 0.909203i \(0.636692\pi\)
\(618\) 0 0
\(619\) −12842.0 −0.833867 −0.416933 0.908937i \(-0.636895\pi\)
−0.416933 + 0.908937i \(0.636895\pi\)
\(620\) −759.000 −0.0491648
\(621\) 0 0
\(622\) −3960.00 −0.255276
\(623\) 0 0
\(624\) 0 0
\(625\) 12331.0 0.789184
\(626\) 25509.0 1.62867
\(627\) 0 0
\(628\) 196.000 0.0124542
\(629\) −26544.0 −1.68264
\(630\) 0 0
\(631\) 21365.0 1.34790 0.673952 0.738775i \(-0.264596\pi\)
0.673952 + 0.738775i \(0.264596\pi\)
\(632\) −9807.00 −0.617249
\(633\) 0 0
\(634\) 7731.00 0.484286
\(635\) −1131.00 −0.0706809
\(636\) 0 0
\(637\) 0 0
\(638\) 13365.0 0.829350
\(639\) 0 0
\(640\) −4977.00 −0.307396
\(641\) −8274.00 −0.509834 −0.254917 0.966963i \(-0.582048\pi\)
−0.254917 + 0.966963i \(0.582048\pi\)
\(642\) 0 0
\(643\) −27998.0 −1.71716 −0.858580 0.512680i \(-0.828653\pi\)
−0.858580 + 0.512680i \(0.828653\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4032.00 0.245568
\(647\) −17466.0 −1.06130 −0.530649 0.847592i \(-0.678052\pi\)
−0.530649 + 0.847592i \(0.678052\pi\)
\(648\) 0 0
\(649\) −225.000 −0.0136087
\(650\) −22272.0 −1.34397
\(651\) 0 0
\(652\) −1252.00 −0.0752026
\(653\) −2157.00 −0.129265 −0.0646324 0.997909i \(-0.520587\pi\)
−0.0646324 + 0.997909i \(0.520587\pi\)
\(654\) 0 0
\(655\) 1953.00 0.116504
\(656\) −25560.0 −1.52127
\(657\) 0 0
\(658\) 0 0
\(659\) −19944.0 −1.17892 −0.589460 0.807798i \(-0.700659\pi\)
−0.589460 + 0.807798i \(0.700659\pi\)
\(660\) 0 0
\(661\) −27506.0 −1.61855 −0.809273 0.587432i \(-0.800139\pi\)
−0.809273 + 0.587432i \(0.800139\pi\)
\(662\) −1452.00 −0.0852471
\(663\) 0 0
\(664\) −10017.0 −0.585444
\(665\) 0 0
\(666\) 0 0
\(667\) 24948.0 1.44826
\(668\) −2646.00 −0.153259
\(669\) 0 0
\(670\) 3330.00 0.192014
\(671\) 1770.00 0.101833
\(672\) 0 0
\(673\) −19123.0 −1.09530 −0.547650 0.836707i \(-0.684478\pi\)
−0.547650 + 0.836707i \(0.684478\pi\)
\(674\) −25077.0 −1.43313
\(675\) 0 0
\(676\) 1899.00 0.108045
\(677\) 13857.0 0.786658 0.393329 0.919398i \(-0.371323\pi\)
0.393329 + 0.919398i \(0.371323\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 5292.00 0.298440
\(681\) 0 0
\(682\) 11385.0 0.639229
\(683\) 22245.0 1.24624 0.623120 0.782127i \(-0.285865\pi\)
0.623120 + 0.782127i \(0.285865\pi\)
\(684\) 0 0
\(685\) −5310.00 −0.296182
\(686\) 0 0
\(687\) 0 0
\(688\) −1846.00 −0.102294
\(689\) −23232.0 −1.28457
\(690\) 0 0
\(691\) 640.000 0.0352341 0.0176170 0.999845i \(-0.494392\pi\)
0.0176170 + 0.999845i \(0.494392\pi\)
\(692\) −786.000 −0.0431781
\(693\) 0 0
\(694\) 5580.00 0.305207
\(695\) −4674.00 −0.255101
\(696\) 0 0
\(697\) 30240.0 1.64336
\(698\) 5754.00 0.312023
\(699\) 0 0
\(700\) 0 0
\(701\) 15561.0 0.838418 0.419209 0.907890i \(-0.362307\pi\)
0.419209 + 0.907890i \(0.362307\pi\)
\(702\) 0 0
\(703\) −5056.00 −0.271253
\(704\) 6495.00 0.347712
\(705\) 0 0
\(706\) −9144.00 −0.487449
\(707\) 0 0
\(708\) 0 0
\(709\) 5534.00 0.293136 0.146568 0.989201i \(-0.453177\pi\)
0.146568 + 0.989201i \(0.453177\pi\)
\(710\) −3078.00 −0.162698
\(711\) 0 0
\(712\) −19026.0 −1.00145
\(713\) 21252.0 1.11626
\(714\) 0 0
\(715\) −2880.00 −0.150638
\(716\) −2892.00 −0.150948
\(717\) 0 0
\(718\) 90.0000 0.00467795
\(719\) −21846.0 −1.13313 −0.566564 0.824018i \(-0.691727\pi\)
−0.566564 + 0.824018i \(0.691727\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −19809.0 −1.02107
\(723\) 0 0
\(724\) −1352.00 −0.0694015
\(725\) −34452.0 −1.76485
\(726\) 0 0
\(727\) 11089.0 0.565706 0.282853 0.959163i \(-0.408719\pi\)
0.282853 + 0.959163i \(0.408719\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3258.00 0.165184
\(731\) 2184.00 0.110504
\(732\) 0 0
\(733\) −11762.0 −0.592687 −0.296343 0.955081i \(-0.595767\pi\)
−0.296343 + 0.955081i \(0.595767\pi\)
\(734\) 33933.0 1.70639
\(735\) 0 0
\(736\) −3780.00 −0.189311
\(737\) −5550.00 −0.277391
\(738\) 0 0
\(739\) −22726.0 −1.13124 −0.565622 0.824665i \(-0.691364\pi\)
−0.565622 + 0.824665i \(0.691364\pi\)
\(740\) 948.000 0.0470935
\(741\) 0 0
\(742\) 0 0
\(743\) −6678.00 −0.329734 −0.164867 0.986316i \(-0.552719\pi\)
−0.164867 + 0.986316i \(0.552719\pi\)
\(744\) 0 0
\(745\) 7362.00 0.362044
\(746\) 3624.00 0.177861
\(747\) 0 0
\(748\) 1260.00 0.0615911
\(749\) 0 0
\(750\) 0 0
\(751\) −19987.0 −0.971153 −0.485577 0.874194i \(-0.661390\pi\)
−0.485577 + 0.874194i \(0.661390\pi\)
\(752\) 2130.00 0.103289
\(753\) 0 0
\(754\) 57024.0 2.75423
\(755\) −3777.00 −0.182065
\(756\) 0 0
\(757\) 314.000 0.0150760 0.00753799 0.999972i \(-0.497601\pi\)
0.00753799 + 0.999972i \(0.497601\pi\)
\(758\) 22920.0 1.09827
\(759\) 0 0
\(760\) 1008.00 0.0481105
\(761\) −11496.0 −0.547608 −0.273804 0.961786i \(-0.588282\pi\)
−0.273804 + 0.961786i \(0.588282\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3912.00 −0.185250
\(765\) 0 0
\(766\) 38250.0 1.80421
\(767\) −960.000 −0.0451937
\(768\) 0 0
\(769\) −2765.00 −0.129660 −0.0648299 0.997896i \(-0.520650\pi\)
−0.0648299 + 0.997896i \(0.520650\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1493.00 0.0696039
\(773\) −14046.0 −0.653557 −0.326778 0.945101i \(-0.605963\pi\)
−0.326778 + 0.945101i \(0.605963\pi\)
\(774\) 0 0
\(775\) −29348.0 −1.36027
\(776\) 10563.0 0.488646
\(777\) 0 0
\(778\) −9378.00 −0.432156
\(779\) 5760.00 0.264921
\(780\) 0 0
\(781\) 5130.00 0.235039
\(782\) 21168.0 0.967987
\(783\) 0 0
\(784\) 0 0
\(785\) −588.000 −0.0267345
\(786\) 0 0
\(787\) 18514.0 0.838568 0.419284 0.907855i \(-0.362281\pi\)
0.419284 + 0.907855i \(0.362281\pi\)
\(788\) 4086.00 0.184718
\(789\) 0 0
\(790\) −4203.00 −0.189286
\(791\) 0 0
\(792\) 0 0
\(793\) 7552.00 0.338183
\(794\) 17796.0 0.795411
\(795\) 0 0
\(796\) 3556.00 0.158341
\(797\) −27495.0 −1.22199 −0.610993 0.791636i \(-0.709230\pi\)
−0.610993 + 0.791636i \(0.709230\pi\)
\(798\) 0 0
\(799\) −2520.00 −0.111578
\(800\) 5220.00 0.230694
\(801\) 0 0
\(802\) −4824.00 −0.212396
\(803\) −5430.00 −0.238631
\(804\) 0 0
\(805\) 0 0
\(806\) 48576.0 2.12285
\(807\) 0 0
\(808\) 22806.0 0.992961
\(809\) 7944.00 0.345236 0.172618 0.984989i \(-0.444777\pi\)
0.172618 + 0.984989i \(0.444777\pi\)
\(810\) 0 0
\(811\) 28942.0 1.25313 0.626567 0.779368i \(-0.284460\pi\)
0.626567 + 0.779368i \(0.284460\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −14220.0 −0.612298
\(815\) 3756.00 0.161432
\(816\) 0 0
\(817\) 416.000 0.0178140
\(818\) 13395.0 0.572549
\(819\) 0 0
\(820\) −1080.00 −0.0459942
\(821\) −8187.00 −0.348025 −0.174012 0.984743i \(-0.555673\pi\)
−0.174012 + 0.984743i \(0.555673\pi\)
\(822\) 0 0
\(823\) −280.000 −0.0118593 −0.00592964 0.999982i \(-0.501887\pi\)
−0.00592964 + 0.999982i \(0.501887\pi\)
\(824\) 36456.0 1.54127
\(825\) 0 0
\(826\) 0 0
\(827\) −25317.0 −1.06452 −0.532260 0.846581i \(-0.678657\pi\)
−0.532260 + 0.846581i \(0.678657\pi\)
\(828\) 0 0
\(829\) −15320.0 −0.641840 −0.320920 0.947106i \(-0.603992\pi\)
−0.320920 + 0.947106i \(0.603992\pi\)
\(830\) −4293.00 −0.179533
\(831\) 0 0
\(832\) 27712.0 1.15474
\(833\) 0 0
\(834\) 0 0
\(835\) 7938.00 0.328989
\(836\) 240.000 0.00992892
\(837\) 0 0
\(838\) −4752.00 −0.195889
\(839\) 34092.0 1.40284 0.701422 0.712746i \(-0.252549\pi\)
0.701422 + 0.712746i \(0.252549\pi\)
\(840\) 0 0
\(841\) 63820.0 2.61675
\(842\) −3990.00 −0.163307
\(843\) 0 0
\(844\) 1250.00 0.0509796
\(845\) −5697.00 −0.231932
\(846\) 0 0
\(847\) 0 0
\(848\) 25773.0 1.04369
\(849\) 0 0
\(850\) −29232.0 −1.17959
\(851\) −26544.0 −1.06923
\(852\) 0 0
\(853\) 7378.00 0.296152 0.148076 0.988976i \(-0.452692\pi\)
0.148076 + 0.988976i \(0.452692\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −28413.0 −1.13451
\(857\) −15594.0 −0.621565 −0.310782 0.950481i \(-0.600591\pi\)
−0.310782 + 0.950481i \(0.600591\pi\)
\(858\) 0 0
\(859\) 30538.0 1.21297 0.606486 0.795094i \(-0.292579\pi\)
0.606486 + 0.795094i \(0.292579\pi\)
\(860\) −78.0000 −0.00309277
\(861\) 0 0
\(862\) −28764.0 −1.13655
\(863\) 822.000 0.0324232 0.0162116 0.999869i \(-0.494839\pi\)
0.0162116 + 0.999869i \(0.494839\pi\)
\(864\) 0 0
\(865\) 2358.00 0.0926872
\(866\) −1482.00 −0.0581529
\(867\) 0 0
\(868\) 0 0
\(869\) 7005.00 0.273450
\(870\) 0 0
\(871\) −23680.0 −0.921201
\(872\) 7770.00 0.301749
\(873\) 0 0
\(874\) 4032.00 0.156046
\(875\) 0 0
\(876\) 0 0
\(877\) −41824.0 −1.61037 −0.805186 0.593022i \(-0.797935\pi\)
−0.805186 + 0.593022i \(0.797935\pi\)
\(878\) 48027.0 1.84605
\(879\) 0 0
\(880\) 3195.00 0.122390
\(881\) −46098.0 −1.76286 −0.881431 0.472313i \(-0.843419\pi\)
−0.881431 + 0.472313i \(0.843419\pi\)
\(882\) 0 0
\(883\) 21008.0 0.800652 0.400326 0.916373i \(-0.368897\pi\)
0.400326 + 0.916373i \(0.368897\pi\)
\(884\) 5376.00 0.204541
\(885\) 0 0
\(886\) −23319.0 −0.884218
\(887\) 24036.0 0.909865 0.454932 0.890526i \(-0.349663\pi\)
0.454932 + 0.890526i \(0.349663\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −8154.00 −0.307104
\(891\) 0 0
\(892\) −425.000 −0.0159530
\(893\) −480.000 −0.0179872
\(894\) 0 0
\(895\) 8676.00 0.324030
\(896\) 0 0
\(897\) 0 0
\(898\) −2592.00 −0.0963209
\(899\) 75141.0 2.78764
\(900\) 0 0
\(901\) −30492.0 −1.12745
\(902\) 16200.0 0.598006
\(903\) 0 0
\(904\) −13608.0 −0.500659
\(905\) 4056.00 0.148979
\(906\) 0 0
\(907\) 13292.0 0.486608 0.243304 0.969950i \(-0.421769\pi\)
0.243304 + 0.969950i \(0.421769\pi\)
\(908\) 3855.00 0.140895
\(909\) 0 0
\(910\) 0 0
\(911\) 9306.00 0.338443 0.169221 0.985578i \(-0.445875\pi\)
0.169221 + 0.985578i \(0.445875\pi\)
\(912\) 0 0
\(913\) 7155.00 0.259360
\(914\) 7557.00 0.273483
\(915\) 0 0
\(916\) 2188.00 0.0789231
\(917\) 0 0
\(918\) 0 0
\(919\) 16496.0 0.592114 0.296057 0.955170i \(-0.404328\pi\)
0.296057 + 0.955170i \(0.404328\pi\)
\(920\) 5292.00 0.189644
\(921\) 0 0
\(922\) −1026.00 −0.0366481
\(923\) 21888.0 0.780555
\(924\) 0 0
\(925\) 36656.0 1.30296
\(926\) −13008.0 −0.461630
\(927\) 0 0
\(928\) −13365.0 −0.472767
\(929\) 14154.0 0.499868 0.249934 0.968263i \(-0.419591\pi\)
0.249934 + 0.968263i \(0.419591\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −852.000 −0.0299444
\(933\) 0 0
\(934\) 55908.0 1.95864
\(935\) −3780.00 −0.132213
\(936\) 0 0
\(937\) 3781.00 0.131825 0.0659124 0.997825i \(-0.479004\pi\)
0.0659124 + 0.997825i \(0.479004\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 90.0000 0.00312285
\(941\) −25863.0 −0.895972 −0.447986 0.894041i \(-0.647859\pi\)
−0.447986 + 0.894041i \(0.647859\pi\)
\(942\) 0 0
\(943\) 30240.0 1.04427
\(944\) 1065.00 0.0367191
\(945\) 0 0
\(946\) 1170.00 0.0402114
\(947\) 42384.0 1.45438 0.727188 0.686438i \(-0.240827\pi\)
0.727188 + 0.686438i \(0.240827\pi\)
\(948\) 0 0
\(949\) −23168.0 −0.792482
\(950\) −5568.00 −0.190158
\(951\) 0 0
\(952\) 0 0
\(953\) −10530.0 −0.357923 −0.178961 0.983856i \(-0.557274\pi\)
−0.178961 + 0.983856i \(0.557274\pi\)
\(954\) 0 0
\(955\) 11736.0 0.397663
\(956\) −5508.00 −0.186340
\(957\) 0 0
\(958\) 45234.0 1.52552
\(959\) 0 0
\(960\) 0 0
\(961\) 34218.0 1.14860
\(962\) −60672.0 −2.03341
\(963\) 0 0
\(964\) −791.000 −0.0264278
\(965\) −4479.00 −0.149414
\(966\) 0 0
\(967\) −38341.0 −1.27504 −0.637520 0.770434i \(-0.720040\pi\)
−0.637520 + 0.770434i \(0.720040\pi\)
\(968\) 23226.0 0.771190
\(969\) 0 0
\(970\) 4527.00 0.149849
\(971\) 1923.00 0.0635551 0.0317776 0.999495i \(-0.489883\pi\)
0.0317776 + 0.999495i \(0.489883\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 18663.0 0.613964
\(975\) 0 0
\(976\) −8378.00 −0.274768
\(977\) −57090.0 −1.86947 −0.934734 0.355347i \(-0.884363\pi\)
−0.934734 + 0.355347i \(0.884363\pi\)
\(978\) 0 0
\(979\) 13590.0 0.443655
\(980\) 0 0
\(981\) 0 0
\(982\) 22113.0 0.718589
\(983\) 5484.00 0.177937 0.0889687 0.996034i \(-0.471643\pi\)
0.0889687 + 0.996034i \(0.471643\pi\)
\(984\) 0 0
\(985\) −12258.0 −0.396520
\(986\) 74844.0 2.41736
\(987\) 0 0
\(988\) 1024.00 0.0329735
\(989\) 2184.00 0.0702196
\(990\) 0 0
\(991\) −22465.0 −0.720105 −0.360053 0.932932i \(-0.617241\pi\)
−0.360053 + 0.932932i \(0.617241\pi\)
\(992\) −11385.0 −0.364389
\(993\) 0 0
\(994\) 0 0
\(995\) −10668.0 −0.339898
\(996\) 0 0
\(997\) −29366.0 −0.932829 −0.466415 0.884566i \(-0.654454\pi\)
−0.466415 + 0.884566i \(0.654454\pi\)
\(998\) 12822.0 0.406687
\(999\) 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 441.4.a.k.1.1 1
3.2 odd 2 147.4.a.a.1.1 1
7.2 even 3 441.4.e.c.361.1 2
7.3 odd 6 63.4.e.a.37.1 2
7.4 even 3 441.4.e.c.226.1 2
7.5 odd 6 63.4.e.a.46.1 2
7.6 odd 2 441.4.a.l.1.1 1
12.11 even 2 2352.4.a.bd.1.1 1
21.2 odd 6 147.4.e.h.67.1 2
21.5 even 6 21.4.e.a.4.1 2
21.11 odd 6 147.4.e.h.79.1 2
21.17 even 6 21.4.e.a.16.1 yes 2
21.20 even 2 147.4.a.b.1.1 1
84.47 odd 6 336.4.q.e.193.1 2
84.59 odd 6 336.4.q.e.289.1 2
84.83 odd 2 2352.4.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.e.a.4.1 2 21.5 even 6
21.4.e.a.16.1 yes 2 21.17 even 6
63.4.e.a.37.1 2 7.3 odd 6
63.4.e.a.46.1 2 7.5 odd 6
147.4.a.a.1.1 1 3.2 odd 2
147.4.a.b.1.1 1 21.20 even 2
147.4.e.h.67.1 2 21.2 odd 6
147.4.e.h.79.1 2 21.11 odd 6
336.4.q.e.193.1 2 84.47 odd 6
336.4.q.e.289.1 2 84.59 odd 6
441.4.a.k.1.1 1 1.1 even 1 trivial
441.4.a.l.1.1 1 7.6 odd 2
441.4.e.c.226.1 2 7.4 even 3
441.4.e.c.361.1 2 7.2 even 3
2352.4.a.i.1.1 1 84.83 odd 2
2352.4.a.bd.1.1 1 12.11 even 2