Properties

Label 1386.4.a.g.1.1
Level $1386$
Weight $4$
Character 1386.1
Self dual yes
Analytic conductor $81.777$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(81.7766472680\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1386.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +14.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +14.0000 q^{5} +7.00000 q^{7} -8.00000 q^{8} -28.0000 q^{10} +11.0000 q^{11} -16.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -108.000 q^{17} +116.000 q^{19} +56.0000 q^{20} -22.0000 q^{22} -68.0000 q^{23} +71.0000 q^{25} +32.0000 q^{26} +28.0000 q^{28} -122.000 q^{29} -262.000 q^{31} -32.0000 q^{32} +216.000 q^{34} +98.0000 q^{35} +130.000 q^{37} -232.000 q^{38} -112.000 q^{40} -204.000 q^{41} -396.000 q^{43} +44.0000 q^{44} +136.000 q^{46} -166.000 q^{47} +49.0000 q^{49} -142.000 q^{50} -64.0000 q^{52} -442.000 q^{53} +154.000 q^{55} -56.0000 q^{56} +244.000 q^{58} -702.000 q^{59} +196.000 q^{61} +524.000 q^{62} +64.0000 q^{64} -224.000 q^{65} -416.000 q^{67} -432.000 q^{68} -196.000 q^{70} -492.000 q^{71} +408.000 q^{73} -260.000 q^{74} +464.000 q^{76} +77.0000 q^{77} +600.000 q^{79} +224.000 q^{80} +408.000 q^{82} +1212.00 q^{83} -1512.00 q^{85} +792.000 q^{86} -88.0000 q^{88} -1146.00 q^{89} -112.000 q^{91} -272.000 q^{92} +332.000 q^{94} +1624.00 q^{95} -482.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) 14.0000 1.25220 0.626099 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(6\) 0 0
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −28.0000 −0.885438
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −16.0000 −0.341354 −0.170677 0.985327i \(-0.554595\pi\)
−0.170677 + 0.985327i \(0.554595\pi\)
\(14\) −14.0000 −0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −108.000 −1.54081 −0.770407 0.637552i \(-0.779947\pi\)
−0.770407 + 0.637552i \(0.779947\pi\)
\(18\) 0 0
\(19\) 116.000 1.40064 0.700322 0.713827i \(-0.253040\pi\)
0.700322 + 0.713827i \(0.253040\pi\)
\(20\) 56.0000 0.626099
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) −68.0000 −0.616477 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(24\) 0 0
\(25\) 71.0000 0.568000
\(26\) 32.0000 0.241374
\(27\) 0 0
\(28\) 28.0000 0.188982
\(29\) −122.000 −0.781201 −0.390601 0.920560i \(-0.627733\pi\)
−0.390601 + 0.920560i \(0.627733\pi\)
\(30\) 0 0
\(31\) −262.000 −1.51795 −0.758977 0.651117i \(-0.774301\pi\)
−0.758977 + 0.651117i \(0.774301\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 216.000 1.08952
\(35\) 98.0000 0.473286
\(36\) 0 0
\(37\) 130.000 0.577618 0.288809 0.957387i \(-0.406741\pi\)
0.288809 + 0.957387i \(0.406741\pi\)
\(38\) −232.000 −0.990404
\(39\) 0 0
\(40\) −112.000 −0.442719
\(41\) −204.000 −0.777060 −0.388530 0.921436i \(-0.627017\pi\)
−0.388530 + 0.921436i \(0.627017\pi\)
\(42\) 0 0
\(43\) −396.000 −1.40441 −0.702203 0.711977i \(-0.747800\pi\)
−0.702203 + 0.711977i \(0.747800\pi\)
\(44\) 44.0000 0.150756
\(45\) 0 0
\(46\) 136.000 0.435915
\(47\) −166.000 −0.515183 −0.257591 0.966254i \(-0.582929\pi\)
−0.257591 + 0.966254i \(0.582929\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) −142.000 −0.401637
\(51\) 0 0
\(52\) −64.0000 −0.170677
\(53\) −442.000 −1.14554 −0.572768 0.819718i \(-0.694130\pi\)
−0.572768 + 0.819718i \(0.694130\pi\)
\(54\) 0 0
\(55\) 154.000 0.377552
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) 244.000 0.552393
\(59\) −702.000 −1.54903 −0.774514 0.632557i \(-0.782005\pi\)
−0.774514 + 0.632557i \(0.782005\pi\)
\(60\) 0 0
\(61\) 196.000 0.411397 0.205699 0.978615i \(-0.434053\pi\)
0.205699 + 0.978615i \(0.434053\pi\)
\(62\) 524.000 1.07336
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −224.000 −0.427443
\(66\) 0 0
\(67\) −416.000 −0.758545 −0.379272 0.925285i \(-0.623826\pi\)
−0.379272 + 0.925285i \(0.623826\pi\)
\(68\) −432.000 −0.770407
\(69\) 0 0
\(70\) −196.000 −0.334664
\(71\) −492.000 −0.822390 −0.411195 0.911548i \(-0.634888\pi\)
−0.411195 + 0.911548i \(0.634888\pi\)
\(72\) 0 0
\(73\) 408.000 0.654148 0.327074 0.944999i \(-0.393937\pi\)
0.327074 + 0.944999i \(0.393937\pi\)
\(74\) −260.000 −0.408438
\(75\) 0 0
\(76\) 464.000 0.700322
\(77\) 77.0000 0.113961
\(78\) 0 0
\(79\) 600.000 0.854497 0.427249 0.904134i \(-0.359483\pi\)
0.427249 + 0.904134i \(0.359483\pi\)
\(80\) 224.000 0.313050
\(81\) 0 0
\(82\) 408.000 0.549464
\(83\) 1212.00 1.60282 0.801411 0.598114i \(-0.204083\pi\)
0.801411 + 0.598114i \(0.204083\pi\)
\(84\) 0 0
\(85\) −1512.00 −1.92941
\(86\) 792.000 0.993065
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) −1146.00 −1.36490 −0.682448 0.730934i \(-0.739085\pi\)
−0.682448 + 0.730934i \(0.739085\pi\)
\(90\) 0 0
\(91\) −112.000 −0.129020
\(92\) −272.000 −0.308239
\(93\) 0 0
\(94\) 332.000 0.364289
\(95\) 1624.00 1.75388
\(96\) 0 0
\(97\) −482.000 −0.504533 −0.252266 0.967658i \(-0.581176\pi\)
−0.252266 + 0.967658i \(0.581176\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) 284.000 0.284000
\(101\) −1216.00 −1.19799 −0.598993 0.800754i \(-0.704432\pi\)
−0.598993 + 0.800754i \(0.704432\pi\)
\(102\) 0 0
\(103\) 1406.00 1.34502 0.672511 0.740087i \(-0.265216\pi\)
0.672511 + 0.740087i \(0.265216\pi\)
\(104\) 128.000 0.120687
\(105\) 0 0
\(106\) 884.000 0.810016
\(107\) 588.000 0.531253 0.265627 0.964076i \(-0.414421\pi\)
0.265627 + 0.964076i \(0.414421\pi\)
\(108\) 0 0
\(109\) 154.000 0.135326 0.0676630 0.997708i \(-0.478446\pi\)
0.0676630 + 0.997708i \(0.478446\pi\)
\(110\) −308.000 −0.266970
\(111\) 0 0
\(112\) 112.000 0.0944911
\(113\) 1902.00 1.58341 0.791704 0.610905i \(-0.209194\pi\)
0.791704 + 0.610905i \(0.209194\pi\)
\(114\) 0 0
\(115\) −952.000 −0.771952
\(116\) −488.000 −0.390601
\(117\) 0 0
\(118\) 1404.00 1.09533
\(119\) −756.000 −0.582373
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) −392.000 −0.290902
\(123\) 0 0
\(124\) −1048.00 −0.758977
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) 64.0000 0.0447172 0.0223586 0.999750i \(-0.492882\pi\)
0.0223586 + 0.999750i \(0.492882\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 448.000 0.302248
\(131\) 1584.00 1.05645 0.528224 0.849105i \(-0.322858\pi\)
0.528224 + 0.849105i \(0.322858\pi\)
\(132\) 0 0
\(133\) 812.000 0.529393
\(134\) 832.000 0.536372
\(135\) 0 0
\(136\) 864.000 0.544760
\(137\) −998.000 −0.622371 −0.311186 0.950349i \(-0.600726\pi\)
−0.311186 + 0.950349i \(0.600726\pi\)
\(138\) 0 0
\(139\) 276.000 0.168417 0.0842087 0.996448i \(-0.473164\pi\)
0.0842087 + 0.996448i \(0.473164\pi\)
\(140\) 392.000 0.236643
\(141\) 0 0
\(142\) 984.000 0.581517
\(143\) −176.000 −0.102922
\(144\) 0 0
\(145\) −1708.00 −0.978218
\(146\) −816.000 −0.462552
\(147\) 0 0
\(148\) 520.000 0.288809
\(149\) −1318.00 −0.724663 −0.362331 0.932049i \(-0.618019\pi\)
−0.362331 + 0.932049i \(0.618019\pi\)
\(150\) 0 0
\(151\) −984.000 −0.530310 −0.265155 0.964206i \(-0.585423\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(152\) −928.000 −0.495202
\(153\) 0 0
\(154\) −154.000 −0.0805823
\(155\) −3668.00 −1.90078
\(156\) 0 0
\(157\) 1706.00 0.867221 0.433610 0.901101i \(-0.357239\pi\)
0.433610 + 0.901101i \(0.357239\pi\)
\(158\) −1200.00 −0.604221
\(159\) 0 0
\(160\) −448.000 −0.221359
\(161\) −476.000 −0.233007
\(162\) 0 0
\(163\) 1168.00 0.561257 0.280628 0.959817i \(-0.409457\pi\)
0.280628 + 0.959817i \(0.409457\pi\)
\(164\) −816.000 −0.388530
\(165\) 0 0
\(166\) −2424.00 −1.13337
\(167\) −72.0000 −0.0333624 −0.0166812 0.999861i \(-0.505310\pi\)
−0.0166812 + 0.999861i \(0.505310\pi\)
\(168\) 0 0
\(169\) −1941.00 −0.883477
\(170\) 3024.00 1.36430
\(171\) 0 0
\(172\) −1584.00 −0.702203
\(173\) 4328.00 1.90203 0.951017 0.309140i \(-0.100041\pi\)
0.951017 + 0.309140i \(0.100041\pi\)
\(174\) 0 0
\(175\) 497.000 0.214684
\(176\) 176.000 0.0753778
\(177\) 0 0
\(178\) 2292.00 0.965127
\(179\) 1924.00 0.803388 0.401694 0.915774i \(-0.368421\pi\)
0.401694 + 0.915774i \(0.368421\pi\)
\(180\) 0 0
\(181\) 2230.00 0.915771 0.457886 0.889011i \(-0.348607\pi\)
0.457886 + 0.889011i \(0.348607\pi\)
\(182\) 224.000 0.0912307
\(183\) 0 0
\(184\) 544.000 0.217958
\(185\) 1820.00 0.723292
\(186\) 0 0
\(187\) −1188.00 −0.464573
\(188\) −664.000 −0.257591
\(189\) 0 0
\(190\) −3248.00 −1.24018
\(191\) −2176.00 −0.824345 −0.412172 0.911106i \(-0.635230\pi\)
−0.412172 + 0.911106i \(0.635230\pi\)
\(192\) 0 0
\(193\) −3126.00 −1.16588 −0.582939 0.812516i \(-0.698097\pi\)
−0.582939 + 0.812516i \(0.698097\pi\)
\(194\) 964.000 0.356759
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 1122.00 0.405783 0.202891 0.979201i \(-0.434966\pi\)
0.202891 + 0.979201i \(0.434966\pi\)
\(198\) 0 0
\(199\) −5586.00 −1.98985 −0.994927 0.100597i \(-0.967925\pi\)
−0.994927 + 0.100597i \(0.967925\pi\)
\(200\) −568.000 −0.200818
\(201\) 0 0
\(202\) 2432.00 0.847104
\(203\) −854.000 −0.295266
\(204\) 0 0
\(205\) −2856.00 −0.973033
\(206\) −2812.00 −0.951074
\(207\) 0 0
\(208\) −256.000 −0.0853385
\(209\) 1276.00 0.422310
\(210\) 0 0
\(211\) 3372.00 1.10018 0.550090 0.835105i \(-0.314593\pi\)
0.550090 + 0.835105i \(0.314593\pi\)
\(212\) −1768.00 −0.572768
\(213\) 0 0
\(214\) −1176.00 −0.375653
\(215\) −5544.00 −1.75859
\(216\) 0 0
\(217\) −1834.00 −0.573733
\(218\) −308.000 −0.0956899
\(219\) 0 0
\(220\) 616.000 0.188776
\(221\) 1728.00 0.525963
\(222\) 0 0
\(223\) 606.000 0.181977 0.0909883 0.995852i \(-0.470997\pi\)
0.0909883 + 0.995852i \(0.470997\pi\)
\(224\) −224.000 −0.0668153
\(225\) 0 0
\(226\) −3804.00 −1.11964
\(227\) −144.000 −0.0421040 −0.0210520 0.999778i \(-0.506702\pi\)
−0.0210520 + 0.999778i \(0.506702\pi\)
\(228\) 0 0
\(229\) −1010.00 −0.291453 −0.145726 0.989325i \(-0.546552\pi\)
−0.145726 + 0.989325i \(0.546552\pi\)
\(230\) 1904.00 0.545852
\(231\) 0 0
\(232\) 976.000 0.276196
\(233\) −3790.00 −1.06563 −0.532814 0.846233i \(-0.678865\pi\)
−0.532814 + 0.846233i \(0.678865\pi\)
\(234\) 0 0
\(235\) −2324.00 −0.645111
\(236\) −2808.00 −0.774514
\(237\) 0 0
\(238\) 1512.00 0.411800
\(239\) −2184.00 −0.591093 −0.295546 0.955328i \(-0.595502\pi\)
−0.295546 + 0.955328i \(0.595502\pi\)
\(240\) 0 0
\(241\) −4268.00 −1.14077 −0.570386 0.821377i \(-0.693206\pi\)
−0.570386 + 0.821377i \(0.693206\pi\)
\(242\) −242.000 −0.0642824
\(243\) 0 0
\(244\) 784.000 0.205699
\(245\) 686.000 0.178885
\(246\) 0 0
\(247\) −1856.00 −0.478115
\(248\) 2096.00 0.536678
\(249\) 0 0
\(250\) 1512.00 0.382509
\(251\) −7922.00 −1.99216 −0.996080 0.0884559i \(-0.971807\pi\)
−0.996080 + 0.0884559i \(0.971807\pi\)
\(252\) 0 0
\(253\) −748.000 −0.185875
\(254\) −128.000 −0.0316198
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −4002.00 −0.971354 −0.485677 0.874138i \(-0.661427\pi\)
−0.485677 + 0.874138i \(0.661427\pi\)
\(258\) 0 0
\(259\) 910.000 0.218319
\(260\) −896.000 −0.213721
\(261\) 0 0
\(262\) −3168.00 −0.747022
\(263\) 3960.00 0.928457 0.464228 0.885716i \(-0.346332\pi\)
0.464228 + 0.885716i \(0.346332\pi\)
\(264\) 0 0
\(265\) −6188.00 −1.43444
\(266\) −1624.00 −0.374338
\(267\) 0 0
\(268\) −1664.00 −0.379272
\(269\) −1878.00 −0.425664 −0.212832 0.977089i \(-0.568269\pi\)
−0.212832 + 0.977089i \(0.568269\pi\)
\(270\) 0 0
\(271\) −4740.00 −1.06249 −0.531244 0.847219i \(-0.678275\pi\)
−0.531244 + 0.847219i \(0.678275\pi\)
\(272\) −1728.00 −0.385204
\(273\) 0 0
\(274\) 1996.00 0.440083
\(275\) 781.000 0.171258
\(276\) 0 0
\(277\) 710.000 0.154006 0.0770032 0.997031i \(-0.475465\pi\)
0.0770032 + 0.997031i \(0.475465\pi\)
\(278\) −552.000 −0.119089
\(279\) 0 0
\(280\) −784.000 −0.167332
\(281\) 90.0000 0.0191066 0.00955329 0.999954i \(-0.496959\pi\)
0.00955329 + 0.999954i \(0.496959\pi\)
\(282\) 0 0
\(283\) −3448.00 −0.724248 −0.362124 0.932130i \(-0.617948\pi\)
−0.362124 + 0.932130i \(0.617948\pi\)
\(284\) −1968.00 −0.411195
\(285\) 0 0
\(286\) 352.000 0.0727769
\(287\) −1428.00 −0.293701
\(288\) 0 0
\(289\) 6751.00 1.37411
\(290\) 3416.00 0.691705
\(291\) 0 0
\(292\) 1632.00 0.327074
\(293\) 2804.00 0.559083 0.279542 0.960134i \(-0.409817\pi\)
0.279542 + 0.960134i \(0.409817\pi\)
\(294\) 0 0
\(295\) −9828.00 −1.93969
\(296\) −1040.00 −0.204219
\(297\) 0 0
\(298\) 2636.00 0.512414
\(299\) 1088.00 0.210437
\(300\) 0 0
\(301\) −2772.00 −0.530815
\(302\) 1968.00 0.374986
\(303\) 0 0
\(304\) 1856.00 0.350161
\(305\) 2744.00 0.515151
\(306\) 0 0
\(307\) 1320.00 0.245395 0.122698 0.992444i \(-0.460845\pi\)
0.122698 + 0.992444i \(0.460845\pi\)
\(308\) 308.000 0.0569803
\(309\) 0 0
\(310\) 7336.00 1.34405
\(311\) 1066.00 0.194364 0.0971822 0.995267i \(-0.469017\pi\)
0.0971822 + 0.995267i \(0.469017\pi\)
\(312\) 0 0
\(313\) −9254.00 −1.67114 −0.835570 0.549384i \(-0.814863\pi\)
−0.835570 + 0.549384i \(0.814863\pi\)
\(314\) −3412.00 −0.613218
\(315\) 0 0
\(316\) 2400.00 0.427249
\(317\) 9722.00 1.72253 0.861265 0.508156i \(-0.169673\pi\)
0.861265 + 0.508156i \(0.169673\pi\)
\(318\) 0 0
\(319\) −1342.00 −0.235541
\(320\) 896.000 0.156525
\(321\) 0 0
\(322\) 952.000 0.164761
\(323\) −12528.0 −2.15813
\(324\) 0 0
\(325\) −1136.00 −0.193889
\(326\) −2336.00 −0.396868
\(327\) 0 0
\(328\) 1632.00 0.274732
\(329\) −1162.00 −0.194721
\(330\) 0 0
\(331\) 2620.00 0.435070 0.217535 0.976053i \(-0.430198\pi\)
0.217535 + 0.976053i \(0.430198\pi\)
\(332\) 4848.00 0.801411
\(333\) 0 0
\(334\) 144.000 0.0235908
\(335\) −5824.00 −0.949848
\(336\) 0 0
\(337\) 2806.00 0.453568 0.226784 0.973945i \(-0.427179\pi\)
0.226784 + 0.973945i \(0.427179\pi\)
\(338\) 3882.00 0.624713
\(339\) 0 0
\(340\) −6048.00 −0.964703
\(341\) −2882.00 −0.457680
\(342\) 0 0
\(343\) 343.000 0.0539949
\(344\) 3168.00 0.496532
\(345\) 0 0
\(346\) −8656.00 −1.34494
\(347\) −5564.00 −0.860781 −0.430391 0.902643i \(-0.641624\pi\)
−0.430391 + 0.902643i \(0.641624\pi\)
\(348\) 0 0
\(349\) 10060.0 1.54298 0.771489 0.636242i \(-0.219512\pi\)
0.771489 + 0.636242i \(0.219512\pi\)
\(350\) −994.000 −0.151804
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) 5102.00 0.769269 0.384635 0.923069i \(-0.374327\pi\)
0.384635 + 0.923069i \(0.374327\pi\)
\(354\) 0 0
\(355\) −6888.00 −1.02979
\(356\) −4584.00 −0.682448
\(357\) 0 0
\(358\) −3848.00 −0.568081
\(359\) −7976.00 −1.17258 −0.586291 0.810100i \(-0.699413\pi\)
−0.586291 + 0.810100i \(0.699413\pi\)
\(360\) 0 0
\(361\) 6597.00 0.961802
\(362\) −4460.00 −0.647548
\(363\) 0 0
\(364\) −448.000 −0.0645098
\(365\) 5712.00 0.819123
\(366\) 0 0
\(367\) −1234.00 −0.175516 −0.0877579 0.996142i \(-0.527970\pi\)
−0.0877579 + 0.996142i \(0.527970\pi\)
\(368\) −1088.00 −0.154119
\(369\) 0 0
\(370\) −3640.00 −0.511445
\(371\) −3094.00 −0.432972
\(372\) 0 0
\(373\) 8030.00 1.11469 0.557343 0.830283i \(-0.311821\pi\)
0.557343 + 0.830283i \(0.311821\pi\)
\(374\) 2376.00 0.328503
\(375\) 0 0
\(376\) 1328.00 0.182145
\(377\) 1952.00 0.266666
\(378\) 0 0
\(379\) −5184.00 −0.702597 −0.351298 0.936264i \(-0.614260\pi\)
−0.351298 + 0.936264i \(0.614260\pi\)
\(380\) 6496.00 0.876941
\(381\) 0 0
\(382\) 4352.00 0.582900
\(383\) −7570.00 −1.00994 −0.504972 0.863135i \(-0.668497\pi\)
−0.504972 + 0.863135i \(0.668497\pi\)
\(384\) 0 0
\(385\) 1078.00 0.142701
\(386\) 6252.00 0.824400
\(387\) 0 0
\(388\) −1928.00 −0.252266
\(389\) 5370.00 0.699922 0.349961 0.936764i \(-0.386195\pi\)
0.349961 + 0.936764i \(0.386195\pi\)
\(390\) 0 0
\(391\) 7344.00 0.949877
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) −2244.00 −0.286932
\(395\) 8400.00 1.07000
\(396\) 0 0
\(397\) 11442.0 1.44649 0.723246 0.690590i \(-0.242649\pi\)
0.723246 + 0.690590i \(0.242649\pi\)
\(398\) 11172.0 1.40704
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) −2362.00 −0.294146 −0.147073 0.989126i \(-0.546985\pi\)
−0.147073 + 0.989126i \(0.546985\pi\)
\(402\) 0 0
\(403\) 4192.00 0.518160
\(404\) −4864.00 −0.598993
\(405\) 0 0
\(406\) 1708.00 0.208785
\(407\) 1430.00 0.174158
\(408\) 0 0
\(409\) −16.0000 −0.00193435 −0.000967175 1.00000i \(-0.500308\pi\)
−0.000967175 1.00000i \(0.500308\pi\)
\(410\) 5712.00 0.688038
\(411\) 0 0
\(412\) 5624.00 0.672511
\(413\) −4914.00 −0.585477
\(414\) 0 0
\(415\) 16968.0 2.00705
\(416\) 512.000 0.0603434
\(417\) 0 0
\(418\) −2552.00 −0.298618
\(419\) −9462.00 −1.10322 −0.551610 0.834102i \(-0.685986\pi\)
−0.551610 + 0.834102i \(0.685986\pi\)
\(420\) 0 0
\(421\) −6302.00 −0.729550 −0.364775 0.931096i \(-0.618854\pi\)
−0.364775 + 0.931096i \(0.618854\pi\)
\(422\) −6744.00 −0.777945
\(423\) 0 0
\(424\) 3536.00 0.405008
\(425\) −7668.00 −0.875183
\(426\) 0 0
\(427\) 1372.00 0.155494
\(428\) 2352.00 0.265627
\(429\) 0 0
\(430\) 11088.0 1.24351
\(431\) −7816.00 −0.873512 −0.436756 0.899580i \(-0.643873\pi\)
−0.436756 + 0.899580i \(0.643873\pi\)
\(432\) 0 0
\(433\) −9506.00 −1.05503 −0.527516 0.849545i \(-0.676877\pi\)
−0.527516 + 0.849545i \(0.676877\pi\)
\(434\) 3668.00 0.405690
\(435\) 0 0
\(436\) 616.000 0.0676630
\(437\) −7888.00 −0.863465
\(438\) 0 0
\(439\) −8228.00 −0.894535 −0.447268 0.894400i \(-0.647603\pi\)
−0.447268 + 0.894400i \(0.647603\pi\)
\(440\) −1232.00 −0.133485
\(441\) 0 0
\(442\) −3456.00 −0.371912
\(443\) −7668.00 −0.822388 −0.411194 0.911548i \(-0.634888\pi\)
−0.411194 + 0.911548i \(0.634888\pi\)
\(444\) 0 0
\(445\) −16044.0 −1.70912
\(446\) −1212.00 −0.128677
\(447\) 0 0
\(448\) 448.000 0.0472456
\(449\) 922.000 0.0969084 0.0484542 0.998825i \(-0.484571\pi\)
0.0484542 + 0.998825i \(0.484571\pi\)
\(450\) 0 0
\(451\) −2244.00 −0.234292
\(452\) 7608.00 0.791704
\(453\) 0 0
\(454\) 288.000 0.0297720
\(455\) −1568.00 −0.161558
\(456\) 0 0
\(457\) 3386.00 0.346587 0.173294 0.984870i \(-0.444559\pi\)
0.173294 + 0.984870i \(0.444559\pi\)
\(458\) 2020.00 0.206088
\(459\) 0 0
\(460\) −3808.00 −0.385976
\(461\) 3300.00 0.333398 0.166699 0.986008i \(-0.446689\pi\)
0.166699 + 0.986008i \(0.446689\pi\)
\(462\) 0 0
\(463\) 14236.0 1.42895 0.714474 0.699662i \(-0.246666\pi\)
0.714474 + 0.699662i \(0.246666\pi\)
\(464\) −1952.00 −0.195300
\(465\) 0 0
\(466\) 7580.00 0.753512
\(467\) −3770.00 −0.373565 −0.186782 0.982401i \(-0.559806\pi\)
−0.186782 + 0.982401i \(0.559806\pi\)
\(468\) 0 0
\(469\) −2912.00 −0.286703
\(470\) 4648.00 0.456162
\(471\) 0 0
\(472\) 5616.00 0.547664
\(473\) −4356.00 −0.423444
\(474\) 0 0
\(475\) 8236.00 0.795565
\(476\) −3024.00 −0.291187
\(477\) 0 0
\(478\) 4368.00 0.417966
\(479\) −17796.0 −1.69754 −0.848768 0.528765i \(-0.822655\pi\)
−0.848768 + 0.528765i \(0.822655\pi\)
\(480\) 0 0
\(481\) −2080.00 −0.197172
\(482\) 8536.00 0.806648
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −6748.00 −0.631775
\(486\) 0 0
\(487\) −3684.00 −0.342788 −0.171394 0.985203i \(-0.554827\pi\)
−0.171394 + 0.985203i \(0.554827\pi\)
\(488\) −1568.00 −0.145451
\(489\) 0 0
\(490\) −1372.00 −0.126491
\(491\) 17236.0 1.58422 0.792108 0.610381i \(-0.208984\pi\)
0.792108 + 0.610381i \(0.208984\pi\)
\(492\) 0 0
\(493\) 13176.0 1.20369
\(494\) 3712.00 0.338078
\(495\) 0 0
\(496\) −4192.00 −0.379489
\(497\) −3444.00 −0.310834
\(498\) 0 0
\(499\) 13176.0 1.18204 0.591021 0.806656i \(-0.298725\pi\)
0.591021 + 0.806656i \(0.298725\pi\)
\(500\) −3024.00 −0.270475
\(501\) 0 0
\(502\) 15844.0 1.40867
\(503\) −15428.0 −1.36760 −0.683798 0.729672i \(-0.739673\pi\)
−0.683798 + 0.729672i \(0.739673\pi\)
\(504\) 0 0
\(505\) −17024.0 −1.50011
\(506\) 1496.00 0.131433
\(507\) 0 0
\(508\) 256.000 0.0223586
\(509\) 7842.00 0.682889 0.341445 0.939902i \(-0.389084\pi\)
0.341445 + 0.939902i \(0.389084\pi\)
\(510\) 0 0
\(511\) 2856.00 0.247245
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 8004.00 0.686851
\(515\) 19684.0 1.68423
\(516\) 0 0
\(517\) −1826.00 −0.155333
\(518\) −1820.00 −0.154375
\(519\) 0 0
\(520\) 1792.00 0.151124
\(521\) 17250.0 1.45055 0.725275 0.688460i \(-0.241713\pi\)
0.725275 + 0.688460i \(0.241713\pi\)
\(522\) 0 0
\(523\) 1032.00 0.0862834 0.0431417 0.999069i \(-0.486263\pi\)
0.0431417 + 0.999069i \(0.486263\pi\)
\(524\) 6336.00 0.528224
\(525\) 0 0
\(526\) −7920.00 −0.656518
\(527\) 28296.0 2.33889
\(528\) 0 0
\(529\) −7543.00 −0.619956
\(530\) 12376.0 1.01430
\(531\) 0 0
\(532\) 3248.00 0.264697
\(533\) 3264.00 0.265252
\(534\) 0 0
\(535\) 8232.00 0.665234
\(536\) 3328.00 0.268186
\(537\) 0 0
\(538\) 3756.00 0.300990
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 94.0000 0.00747020 0.00373510 0.999993i \(-0.498811\pi\)
0.00373510 + 0.999993i \(0.498811\pi\)
\(542\) 9480.00 0.751293
\(543\) 0 0
\(544\) 3456.00 0.272380
\(545\) 2156.00 0.169455
\(546\) 0 0
\(547\) −11676.0 −0.912669 −0.456334 0.889808i \(-0.650838\pi\)
−0.456334 + 0.889808i \(0.650838\pi\)
\(548\) −3992.00 −0.311186
\(549\) 0 0
\(550\) −1562.00 −0.121098
\(551\) −14152.0 −1.09418
\(552\) 0 0
\(553\) 4200.00 0.322970
\(554\) −1420.00 −0.108899
\(555\) 0 0
\(556\) 1104.00 0.0842087
\(557\) 1858.00 0.141339 0.0706696 0.997500i \(-0.477486\pi\)
0.0706696 + 0.997500i \(0.477486\pi\)
\(558\) 0 0
\(559\) 6336.00 0.479399
\(560\) 1568.00 0.118322
\(561\) 0 0
\(562\) −180.000 −0.0135104
\(563\) 23028.0 1.72383 0.861913 0.507056i \(-0.169266\pi\)
0.861913 + 0.507056i \(0.169266\pi\)
\(564\) 0 0
\(565\) 26628.0 1.98274
\(566\) 6896.00 0.512121
\(567\) 0 0
\(568\) 3936.00 0.290759
\(569\) 17066.0 1.25737 0.628685 0.777660i \(-0.283593\pi\)
0.628685 + 0.777660i \(0.283593\pi\)
\(570\) 0 0
\(571\) −10252.0 −0.751371 −0.375686 0.926747i \(-0.622593\pi\)
−0.375686 + 0.926747i \(0.622593\pi\)
\(572\) −704.000 −0.0514610
\(573\) 0 0
\(574\) 2856.00 0.207678
\(575\) −4828.00 −0.350159
\(576\) 0 0
\(577\) 2142.00 0.154545 0.0772726 0.997010i \(-0.475379\pi\)
0.0772726 + 0.997010i \(0.475379\pi\)
\(578\) −13502.0 −0.971642
\(579\) 0 0
\(580\) −6832.00 −0.489109
\(581\) 8484.00 0.605810
\(582\) 0 0
\(583\) −4862.00 −0.345392
\(584\) −3264.00 −0.231276
\(585\) 0 0
\(586\) −5608.00 −0.395332
\(587\) −3474.00 −0.244271 −0.122136 0.992513i \(-0.538974\pi\)
−0.122136 + 0.992513i \(0.538974\pi\)
\(588\) 0 0
\(589\) −30392.0 −2.12611
\(590\) 19656.0 1.37157
\(591\) 0 0
\(592\) 2080.00 0.144405
\(593\) 17424.0 1.20661 0.603303 0.797512i \(-0.293851\pi\)
0.603303 + 0.797512i \(0.293851\pi\)
\(594\) 0 0
\(595\) −10584.0 −0.729247
\(596\) −5272.00 −0.362331
\(597\) 0 0
\(598\) −2176.00 −0.148801
\(599\) −6916.00 −0.471753 −0.235877 0.971783i \(-0.575796\pi\)
−0.235877 + 0.971783i \(0.575796\pi\)
\(600\) 0 0
\(601\) 16468.0 1.11771 0.558855 0.829265i \(-0.311241\pi\)
0.558855 + 0.829265i \(0.311241\pi\)
\(602\) 5544.00 0.375343
\(603\) 0 0
\(604\) −3936.00 −0.265155
\(605\) 1694.00 0.113836
\(606\) 0 0
\(607\) −17176.0 −1.14852 −0.574261 0.818673i \(-0.694710\pi\)
−0.574261 + 0.818673i \(0.694710\pi\)
\(608\) −3712.00 −0.247601
\(609\) 0 0
\(610\) −5488.00 −0.364267
\(611\) 2656.00 0.175860
\(612\) 0 0
\(613\) 11402.0 0.751260 0.375630 0.926770i \(-0.377426\pi\)
0.375630 + 0.926770i \(0.377426\pi\)
\(614\) −2640.00 −0.173521
\(615\) 0 0
\(616\) −616.000 −0.0402911
\(617\) −3654.00 −0.238419 −0.119209 0.992869i \(-0.538036\pi\)
−0.119209 + 0.992869i \(0.538036\pi\)
\(618\) 0 0
\(619\) −11318.0 −0.734909 −0.367455 0.930041i \(-0.619771\pi\)
−0.367455 + 0.930041i \(0.619771\pi\)
\(620\) −14672.0 −0.950390
\(621\) 0 0
\(622\) −2132.00 −0.137436
\(623\) −8022.00 −0.515882
\(624\) 0 0
\(625\) −19459.0 −1.24538
\(626\) 18508.0 1.18167
\(627\) 0 0
\(628\) 6824.00 0.433610
\(629\) −14040.0 −0.890002
\(630\) 0 0
\(631\) −23872.0 −1.50607 −0.753034 0.657981i \(-0.771411\pi\)
−0.753034 + 0.657981i \(0.771411\pi\)
\(632\) −4800.00 −0.302110
\(633\) 0 0
\(634\) −19444.0 −1.21801
\(635\) 896.000 0.0559948
\(636\) 0 0
\(637\) −784.000 −0.0487649
\(638\) 2684.00 0.166553
\(639\) 0 0
\(640\) −1792.00 −0.110680
\(641\) 27026.0 1.66531 0.832654 0.553793i \(-0.186820\pi\)
0.832654 + 0.553793i \(0.186820\pi\)
\(642\) 0 0
\(643\) 6498.00 0.398532 0.199266 0.979945i \(-0.436144\pi\)
0.199266 + 0.979945i \(0.436144\pi\)
\(644\) −1904.00 −0.116503
\(645\) 0 0
\(646\) 25056.0 1.52603
\(647\) 6422.00 0.390224 0.195112 0.980781i \(-0.437493\pi\)
0.195112 + 0.980781i \(0.437493\pi\)
\(648\) 0 0
\(649\) −7722.00 −0.467049
\(650\) 2272.00 0.137100
\(651\) 0 0
\(652\) 4672.00 0.280628
\(653\) −23670.0 −1.41850 −0.709249 0.704958i \(-0.750966\pi\)
−0.709249 + 0.704958i \(0.750966\pi\)
\(654\) 0 0
\(655\) 22176.0 1.32288
\(656\) −3264.00 −0.194265
\(657\) 0 0
\(658\) 2324.00 0.137688
\(659\) 9812.00 0.580002 0.290001 0.957026i \(-0.406344\pi\)
0.290001 + 0.957026i \(0.406344\pi\)
\(660\) 0 0
\(661\) −5190.00 −0.305397 −0.152699 0.988273i \(-0.548796\pi\)
−0.152699 + 0.988273i \(0.548796\pi\)
\(662\) −5240.00 −0.307641
\(663\) 0 0
\(664\) −9696.00 −0.566683
\(665\) 11368.0 0.662905
\(666\) 0 0
\(667\) 8296.00 0.481593
\(668\) −288.000 −0.0166812
\(669\) 0 0
\(670\) 11648.0 0.671644
\(671\) 2156.00 0.124041
\(672\) 0 0
\(673\) 94.0000 0.00538400 0.00269200 0.999996i \(-0.499143\pi\)
0.00269200 + 0.999996i \(0.499143\pi\)
\(674\) −5612.00 −0.320721
\(675\) 0 0
\(676\) −7764.00 −0.441739
\(677\) 12432.0 0.705762 0.352881 0.935668i \(-0.385202\pi\)
0.352881 + 0.935668i \(0.385202\pi\)
\(678\) 0 0
\(679\) −3374.00 −0.190695
\(680\) 12096.0 0.682148
\(681\) 0 0
\(682\) 5764.00 0.323629
\(683\) 2308.00 0.129302 0.0646509 0.997908i \(-0.479407\pi\)
0.0646509 + 0.997908i \(0.479407\pi\)
\(684\) 0 0
\(685\) −13972.0 −0.779332
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) −6336.00 −0.351101
\(689\) 7072.00 0.391033
\(690\) 0 0
\(691\) 26446.0 1.45594 0.727969 0.685610i \(-0.240464\pi\)
0.727969 + 0.685610i \(0.240464\pi\)
\(692\) 17312.0 0.951017
\(693\) 0 0
\(694\) 11128.0 0.608664
\(695\) 3864.00 0.210892
\(696\) 0 0
\(697\) 22032.0 1.19730
\(698\) −20120.0 −1.09105
\(699\) 0 0
\(700\) 1988.00 0.107342
\(701\) −26450.0 −1.42511 −0.712555 0.701616i \(-0.752462\pi\)
−0.712555 + 0.701616i \(0.752462\pi\)
\(702\) 0 0
\(703\) 15080.0 0.809037
\(704\) 704.000 0.0376889
\(705\) 0 0
\(706\) −10204.0 −0.543956
\(707\) −8512.00 −0.452796
\(708\) 0 0
\(709\) 17102.0 0.905894 0.452947 0.891537i \(-0.350373\pi\)
0.452947 + 0.891537i \(0.350373\pi\)
\(710\) 13776.0 0.728175
\(711\) 0 0
\(712\) 9168.00 0.482564
\(713\) 17816.0 0.935785
\(714\) 0 0
\(715\) −2464.00 −0.128879
\(716\) 7696.00 0.401694
\(717\) 0 0
\(718\) 15952.0 0.829141
\(719\) 16854.0 0.874198 0.437099 0.899413i \(-0.356006\pi\)
0.437099 + 0.899413i \(0.356006\pi\)
\(720\) 0 0
\(721\) 9842.00 0.508371
\(722\) −13194.0 −0.680097
\(723\) 0 0
\(724\) 8920.00 0.457886
\(725\) −8662.00 −0.443722
\(726\) 0 0
\(727\) −34670.0 −1.76869 −0.884346 0.466832i \(-0.845395\pi\)
−0.884346 + 0.466832i \(0.845395\pi\)
\(728\) 896.000 0.0456153
\(729\) 0 0
\(730\) −11424.0 −0.579207
\(731\) 42768.0 2.16393
\(732\) 0 0
\(733\) 11716.0 0.590369 0.295184 0.955440i \(-0.404619\pi\)
0.295184 + 0.955440i \(0.404619\pi\)
\(734\) 2468.00 0.124108
\(735\) 0 0
\(736\) 2176.00 0.108979
\(737\) −4576.00 −0.228710
\(738\) 0 0
\(739\) 29772.0 1.48198 0.740988 0.671518i \(-0.234357\pi\)
0.740988 + 0.671518i \(0.234357\pi\)
\(740\) 7280.00 0.361646
\(741\) 0 0
\(742\) 6188.00 0.306157
\(743\) 24928.0 1.23085 0.615424 0.788196i \(-0.288985\pi\)
0.615424 + 0.788196i \(0.288985\pi\)
\(744\) 0 0
\(745\) −18452.0 −0.907421
\(746\) −16060.0 −0.788202
\(747\) 0 0
\(748\) −4752.00 −0.232287
\(749\) 4116.00 0.200795
\(750\) 0 0
\(751\) −4652.00 −0.226037 −0.113019 0.993593i \(-0.536052\pi\)
−0.113019 + 0.993593i \(0.536052\pi\)
\(752\) −2656.00 −0.128796
\(753\) 0 0
\(754\) −3904.00 −0.188561
\(755\) −13776.0 −0.664053
\(756\) 0 0
\(757\) −1802.00 −0.0865189 −0.0432594 0.999064i \(-0.513774\pi\)
−0.0432594 + 0.999064i \(0.513774\pi\)
\(758\) 10368.0 0.496811
\(759\) 0 0
\(760\) −12992.0 −0.620091
\(761\) 808.000 0.0384888 0.0192444 0.999815i \(-0.493874\pi\)
0.0192444 + 0.999815i \(0.493874\pi\)
\(762\) 0 0
\(763\) 1078.00 0.0511484
\(764\) −8704.00 −0.412172
\(765\) 0 0
\(766\) 15140.0 0.714139
\(767\) 11232.0 0.528767
\(768\) 0 0
\(769\) 23144.0 1.08530 0.542649 0.839960i \(-0.317421\pi\)
0.542649 + 0.839960i \(0.317421\pi\)
\(770\) −2156.00 −0.100905
\(771\) 0 0
\(772\) −12504.0 −0.582939
\(773\) 27466.0 1.27799 0.638993 0.769212i \(-0.279351\pi\)
0.638993 + 0.769212i \(0.279351\pi\)
\(774\) 0 0
\(775\) −18602.0 −0.862198
\(776\) 3856.00 0.178379
\(777\) 0 0
\(778\) −10740.0 −0.494920
\(779\) −23664.0 −1.08838
\(780\) 0 0
\(781\) −5412.00 −0.247960
\(782\) −14688.0 −0.671665
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) 23884.0 1.08593
\(786\) 0 0
\(787\) 23604.0 1.06911 0.534556 0.845133i \(-0.320479\pi\)
0.534556 + 0.845133i \(0.320479\pi\)
\(788\) 4488.00 0.202891
\(789\) 0 0
\(790\) −16800.0 −0.756604
\(791\) 13314.0 0.598472
\(792\) 0 0
\(793\) −3136.00 −0.140432
\(794\) −22884.0 −1.02282
\(795\) 0 0
\(796\) −22344.0 −0.994927
\(797\) −4122.00 −0.183198 −0.0915990 0.995796i \(-0.529198\pi\)
−0.0915990 + 0.995796i \(0.529198\pi\)
\(798\) 0 0
\(799\) 17928.0 0.793801
\(800\) −2272.00 −0.100409
\(801\) 0 0
\(802\) 4724.00 0.207993
\(803\) 4488.00 0.197233
\(804\) 0 0
\(805\) −6664.00 −0.291770
\(806\) −8384.00 −0.366394
\(807\) 0 0
\(808\) 9728.00 0.423552
\(809\) 9110.00 0.395909 0.197955 0.980211i \(-0.436570\pi\)
0.197955 + 0.980211i \(0.436570\pi\)
\(810\) 0 0
\(811\) −28352.0 −1.22759 −0.613794 0.789466i \(-0.710357\pi\)
−0.613794 + 0.789466i \(0.710357\pi\)
\(812\) −3416.00 −0.147633
\(813\) 0 0
\(814\) −2860.00 −0.123149
\(815\) 16352.0 0.702804
\(816\) 0 0
\(817\) −45936.0 −1.96707
\(818\) 32.0000 0.00136779
\(819\) 0 0
\(820\) −11424.0 −0.486516
\(821\) 14002.0 0.595217 0.297609 0.954688i \(-0.403811\pi\)
0.297609 + 0.954688i \(0.403811\pi\)
\(822\) 0 0
\(823\) −14848.0 −0.628881 −0.314440 0.949277i \(-0.601817\pi\)
−0.314440 + 0.949277i \(0.601817\pi\)
\(824\) −11248.0 −0.475537
\(825\) 0 0
\(826\) 9828.00 0.413995
\(827\) −10500.0 −0.441500 −0.220750 0.975330i \(-0.570851\pi\)
−0.220750 + 0.975330i \(0.570851\pi\)
\(828\) 0 0
\(829\) 23890.0 1.00089 0.500443 0.865770i \(-0.333171\pi\)
0.500443 + 0.865770i \(0.333171\pi\)
\(830\) −33936.0 −1.41920
\(831\) 0 0
\(832\) −1024.00 −0.0426692
\(833\) −5292.00 −0.220116
\(834\) 0 0
\(835\) −1008.00 −0.0417764
\(836\) 5104.00 0.211155
\(837\) 0 0
\(838\) 18924.0 0.780094
\(839\) 670.000 0.0275697 0.0137848 0.999905i \(-0.495612\pi\)
0.0137848 + 0.999905i \(0.495612\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) 12604.0 0.515870
\(843\) 0 0
\(844\) 13488.0 0.550090
\(845\) −27174.0 −1.10629
\(846\) 0 0
\(847\) 847.000 0.0343604
\(848\) −7072.00 −0.286384
\(849\) 0 0
\(850\) 15336.0 0.618848
\(851\) −8840.00 −0.356088
\(852\) 0 0
\(853\) −4776.00 −0.191708 −0.0958541 0.995395i \(-0.530558\pi\)
−0.0958541 + 0.995395i \(0.530558\pi\)
\(854\) −2744.00 −0.109951
\(855\) 0 0
\(856\) −4704.00 −0.187826
\(857\) 13024.0 0.519126 0.259563 0.965726i \(-0.416421\pi\)
0.259563 + 0.965726i \(0.416421\pi\)
\(858\) 0 0
\(859\) −32998.0 −1.31068 −0.655342 0.755332i \(-0.727475\pi\)
−0.655342 + 0.755332i \(0.727475\pi\)
\(860\) −22176.0 −0.879297
\(861\) 0 0
\(862\) 15632.0 0.617666
\(863\) −22272.0 −0.878503 −0.439251 0.898364i \(-0.644756\pi\)
−0.439251 + 0.898364i \(0.644756\pi\)
\(864\) 0 0
\(865\) 60592.0 2.38172
\(866\) 19012.0 0.746021
\(867\) 0 0
\(868\) −7336.00 −0.286866
\(869\) 6600.00 0.257641
\(870\) 0 0
\(871\) 6656.00 0.258932
\(872\) −1232.00 −0.0478449
\(873\) 0 0
\(874\) 15776.0 0.610562
\(875\) −5292.00 −0.204460
\(876\) 0 0
\(877\) −30398.0 −1.17043 −0.585215 0.810878i \(-0.698990\pi\)
−0.585215 + 0.810878i \(0.698990\pi\)
\(878\) 16456.0 0.632532
\(879\) 0 0
\(880\) 2464.00 0.0943880
\(881\) −1630.00 −0.0623338 −0.0311669 0.999514i \(-0.509922\pi\)
−0.0311669 + 0.999514i \(0.509922\pi\)
\(882\) 0 0
\(883\) −20228.0 −0.770925 −0.385462 0.922724i \(-0.625958\pi\)
−0.385462 + 0.922724i \(0.625958\pi\)
\(884\) 6912.00 0.262982
\(885\) 0 0
\(886\) 15336.0 0.581516
\(887\) −38908.0 −1.47283 −0.736416 0.676528i \(-0.763484\pi\)
−0.736416 + 0.676528i \(0.763484\pi\)
\(888\) 0 0
\(889\) 448.000 0.0169015
\(890\) 32088.0 1.20853
\(891\) 0 0
\(892\) 2424.00 0.0909883
\(893\) −19256.0 −0.721587
\(894\) 0 0
\(895\) 26936.0 1.00600
\(896\) −896.000 −0.0334077
\(897\) 0 0
\(898\) −1844.00 −0.0685246
\(899\) 31964.0 1.18583
\(900\) 0 0
\(901\) 47736.0 1.76506
\(902\) 4488.00 0.165670
\(903\) 0 0
\(904\) −15216.0 −0.559819
\(905\) 31220.0 1.14673
\(906\) 0 0
\(907\) −20936.0 −0.766448 −0.383224 0.923655i \(-0.625186\pi\)
−0.383224 + 0.923655i \(0.625186\pi\)
\(908\) −576.000 −0.0210520
\(909\) 0 0
\(910\) 3136.00 0.114239
\(911\) −48204.0 −1.75310 −0.876548 0.481315i \(-0.840159\pi\)
−0.876548 + 0.481315i \(0.840159\pi\)
\(912\) 0 0
\(913\) 13332.0 0.483269
\(914\) −6772.00 −0.245074
\(915\) 0 0
\(916\) −4040.00 −0.145726
\(917\) 11088.0 0.399300
\(918\) 0 0
\(919\) −27304.0 −0.980061 −0.490030 0.871705i \(-0.663014\pi\)
−0.490030 + 0.871705i \(0.663014\pi\)
\(920\) 7616.00 0.272926
\(921\) 0 0
\(922\) −6600.00 −0.235748
\(923\) 7872.00 0.280726
\(924\) 0 0
\(925\) 9230.00 0.328087
\(926\) −28472.0 −1.01042
\(927\) 0 0
\(928\) 3904.00 0.138098
\(929\) −30.0000 −0.00105949 −0.000529746 1.00000i \(-0.500169\pi\)
−0.000529746 1.00000i \(0.500169\pi\)
\(930\) 0 0
\(931\) 5684.00 0.200092
\(932\) −15160.0 −0.532814
\(933\) 0 0
\(934\) 7540.00 0.264150
\(935\) −16632.0 −0.581737
\(936\) 0 0
\(937\) 4736.00 0.165121 0.0825605 0.996586i \(-0.473690\pi\)
0.0825605 + 0.996586i \(0.473690\pi\)
\(938\) 5824.00 0.202730
\(939\) 0 0
\(940\) −9296.00 −0.322555
\(941\) −19996.0 −0.692722 −0.346361 0.938101i \(-0.612583\pi\)
−0.346361 + 0.938101i \(0.612583\pi\)
\(942\) 0 0
\(943\) 13872.0 0.479040
\(944\) −11232.0 −0.387257
\(945\) 0 0
\(946\) 8712.00 0.299420
\(947\) 1252.00 0.0429615 0.0214807 0.999769i \(-0.493162\pi\)
0.0214807 + 0.999769i \(0.493162\pi\)
\(948\) 0 0
\(949\) −6528.00 −0.223296
\(950\) −16472.0 −0.562550
\(951\) 0 0
\(952\) 6048.00 0.205900
\(953\) −17986.0 −0.611357 −0.305679 0.952135i \(-0.598883\pi\)
−0.305679 + 0.952135i \(0.598883\pi\)
\(954\) 0 0
\(955\) −30464.0 −1.03224
\(956\) −8736.00 −0.295546
\(957\) 0 0
\(958\) 35592.0 1.20034
\(959\) −6986.00 −0.235234
\(960\) 0 0
\(961\) 38853.0 1.30419
\(962\) 4160.00 0.139422
\(963\) 0 0
\(964\) −17072.0 −0.570386
\(965\) −43764.0 −1.45991
\(966\) 0 0
\(967\) 14256.0 0.474087 0.237043 0.971499i \(-0.423822\pi\)
0.237043 + 0.971499i \(0.423822\pi\)
\(968\) −968.000 −0.0321412
\(969\) 0 0
\(970\) 13496.0 0.446732
\(971\) 50214.0 1.65957 0.829786 0.558082i \(-0.188463\pi\)
0.829786 + 0.558082i \(0.188463\pi\)
\(972\) 0 0
\(973\) 1932.00 0.0636558
\(974\) 7368.00 0.242388
\(975\) 0 0
\(976\) 3136.00 0.102849
\(977\) 35814.0 1.17276 0.586382 0.810034i \(-0.300552\pi\)
0.586382 + 0.810034i \(0.300552\pi\)
\(978\) 0 0
\(979\) −12606.0 −0.411532
\(980\) 2744.00 0.0894427
\(981\) 0 0
\(982\) −34472.0 −1.12021
\(983\) 19274.0 0.625377 0.312688 0.949856i \(-0.398770\pi\)
0.312688 + 0.949856i \(0.398770\pi\)
\(984\) 0 0
\(985\) 15708.0 0.508120
\(986\) −26352.0 −0.851135
\(987\) 0 0
\(988\) −7424.00 −0.239058
\(989\) 26928.0 0.865784
\(990\) 0 0
\(991\) 59996.0 1.92314 0.961572 0.274553i \(-0.0885298\pi\)
0.961572 + 0.274553i \(0.0885298\pi\)
\(992\) 8384.00 0.268339
\(993\) 0 0
\(994\) 6888.00 0.219793
\(995\) −78204.0 −2.49169
\(996\) 0 0
\(997\) 24344.0 0.773302 0.386651 0.922226i \(-0.373632\pi\)
0.386651 + 0.922226i \(0.373632\pi\)
\(998\) −26352.0 −0.835830
\(999\) 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 1386.4.a.g.1.1 1
3.2 odd 2 154.4.a.c.1.1 1
12.11 even 2 1232.4.a.i.1.1 1
21.20 even 2 1078.4.a.h.1.1 1
33.32 even 2 1694.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.c.1.1 1 3.2 odd 2
1078.4.a.h.1.1 1 21.20 even 2
1232.4.a.i.1.1 1 12.11 even 2
1386.4.a.g.1.1 1 1.1 even 1 trivial
1694.4.a.a.1.1 1 33.32 even 2