Properties

Label 1856.4.a.d.1.1
Level $1856$
Weight $4$
Character 1856.1
Self dual yes
Analytic conductor $109.508$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1856 = 2^{6} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1856.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.507544971\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 58)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1856.1

$q$-expansion

\(f(q)\) \(=\) \(q+7.00000 q^{3} -5.00000 q^{5} +2.00000 q^{7} +22.0000 q^{9} +O(q^{10})\) \(q+7.00000 q^{3} -5.00000 q^{5} +2.00000 q^{7} +22.0000 q^{9} +37.0000 q^{11} -27.0000 q^{13} -35.0000 q^{15} +24.0000 q^{17} -88.0000 q^{19} +14.0000 q^{21} +28.0000 q^{23} -100.000 q^{25} -35.0000 q^{27} +29.0000 q^{29} +143.000 q^{31} +259.000 q^{33} -10.0000 q^{35} +360.000 q^{37} -189.000 q^{39} +386.000 q^{41} +381.000 q^{43} -110.000 q^{45} +103.000 q^{47} -339.000 q^{49} +168.000 q^{51} +431.000 q^{53} -185.000 q^{55} -616.000 q^{57} +288.000 q^{59} +840.000 q^{61} +44.0000 q^{63} +135.000 q^{65} -180.000 q^{67} +196.000 q^{69} -706.000 q^{71} +716.000 q^{73} -700.000 q^{75} +74.0000 q^{77} -931.000 q^{79} -839.000 q^{81} +1188.00 q^{83} -120.000 q^{85} +203.000 q^{87} -642.000 q^{89} -54.0000 q^{91} +1001.00 q^{93} +440.000 q^{95} +486.000 q^{97} +814.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 7.00000 1.34715 0.673575 0.739119i \(-0.264758\pi\)
0.673575 + 0.739119i \(0.264758\pi\)
\(4\) 0 0
\(5\) −5.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 2.00000 0.107990 0.0539949 0.998541i \(-0.482805\pi\)
0.0539949 + 0.998541i \(0.482805\pi\)
\(8\) 0 0
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) 37.0000 1.01417 0.507087 0.861895i \(-0.330722\pi\)
0.507087 + 0.861895i \(0.330722\pi\)
\(12\) 0 0
\(13\) −27.0000 −0.576035 −0.288017 0.957625i \(-0.592996\pi\)
−0.288017 + 0.957625i \(0.592996\pi\)
\(14\) 0 0
\(15\) −35.0000 −0.602464
\(16\) 0 0
\(17\) 24.0000 0.342403 0.171202 0.985236i \(-0.445235\pi\)
0.171202 + 0.985236i \(0.445235\pi\)
\(18\) 0 0
\(19\) −88.0000 −1.06256 −0.531279 0.847197i \(-0.678288\pi\)
−0.531279 + 0.847197i \(0.678288\pi\)
\(20\) 0 0
\(21\) 14.0000 0.145479
\(22\) 0 0
\(23\) 28.0000 0.253844 0.126922 0.991913i \(-0.459490\pi\)
0.126922 + 0.991913i \(0.459490\pi\)
\(24\) 0 0
\(25\) −100.000 −0.800000
\(26\) 0 0
\(27\) −35.0000 −0.249472
\(28\) 0 0
\(29\) 29.0000 0.185695
\(30\) 0 0
\(31\) 143.000 0.828502 0.414251 0.910163i \(-0.364044\pi\)
0.414251 + 0.910163i \(0.364044\pi\)
\(32\) 0 0
\(33\) 259.000 1.36625
\(34\) 0 0
\(35\) −10.0000 −0.0482945
\(36\) 0 0
\(37\) 360.000 1.59956 0.799779 0.600295i \(-0.204950\pi\)
0.799779 + 0.600295i \(0.204950\pi\)
\(38\) 0 0
\(39\) −189.000 −0.776006
\(40\) 0 0
\(41\) 386.000 1.47032 0.735159 0.677894i \(-0.237107\pi\)
0.735159 + 0.677894i \(0.237107\pi\)
\(42\) 0 0
\(43\) 381.000 1.35121 0.675604 0.737265i \(-0.263883\pi\)
0.675604 + 0.737265i \(0.263883\pi\)
\(44\) 0 0
\(45\) −110.000 −0.364396
\(46\) 0 0
\(47\) 103.000 0.319662 0.159831 0.987144i \(-0.448905\pi\)
0.159831 + 0.987144i \(0.448905\pi\)
\(48\) 0 0
\(49\) −339.000 −0.988338
\(50\) 0 0
\(51\) 168.000 0.461269
\(52\) 0 0
\(53\) 431.000 1.11703 0.558513 0.829496i \(-0.311372\pi\)
0.558513 + 0.829496i \(0.311372\pi\)
\(54\) 0 0
\(55\) −185.000 −0.453553
\(56\) 0 0
\(57\) −616.000 −1.43142
\(58\) 0 0
\(59\) 288.000 0.635498 0.317749 0.948175i \(-0.397073\pi\)
0.317749 + 0.948175i \(0.397073\pi\)
\(60\) 0 0
\(61\) 840.000 1.76313 0.881565 0.472062i \(-0.156490\pi\)
0.881565 + 0.472062i \(0.156490\pi\)
\(62\) 0 0
\(63\) 44.0000 0.0879917
\(64\) 0 0
\(65\) 135.000 0.257611
\(66\) 0 0
\(67\) −180.000 −0.328216 −0.164108 0.986442i \(-0.552475\pi\)
−0.164108 + 0.986442i \(0.552475\pi\)
\(68\) 0 0
\(69\) 196.000 0.341966
\(70\) 0 0
\(71\) −706.000 −1.18010 −0.590048 0.807368i \(-0.700891\pi\)
−0.590048 + 0.807368i \(0.700891\pi\)
\(72\) 0 0
\(73\) 716.000 1.14797 0.573983 0.818867i \(-0.305398\pi\)
0.573983 + 0.818867i \(0.305398\pi\)
\(74\) 0 0
\(75\) −700.000 −1.07772
\(76\) 0 0
\(77\) 74.0000 0.109521
\(78\) 0 0
\(79\) −931.000 −1.32589 −0.662947 0.748666i \(-0.730695\pi\)
−0.662947 + 0.748666i \(0.730695\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 0 0
\(83\) 1188.00 1.57108 0.785542 0.618809i \(-0.212384\pi\)
0.785542 + 0.618809i \(0.212384\pi\)
\(84\) 0 0
\(85\) −120.000 −0.153127
\(86\) 0 0
\(87\) 203.000 0.250160
\(88\) 0 0
\(89\) −642.000 −0.764628 −0.382314 0.924033i \(-0.624873\pi\)
−0.382314 + 0.924033i \(0.624873\pi\)
\(90\) 0 0
\(91\) −54.0000 −0.0622059
\(92\) 0 0
\(93\) 1001.00 1.11612
\(94\) 0 0
\(95\) 440.000 0.475190
\(96\) 0 0
\(97\) 486.000 0.508720 0.254360 0.967110i \(-0.418135\pi\)
0.254360 + 0.967110i \(0.418135\pi\)
\(98\) 0 0
\(99\) 814.000 0.826364
\(100\) 0 0
\(101\) −240.000 −0.236444 −0.118222 0.992987i \(-0.537720\pi\)
−0.118222 + 0.992987i \(0.537720\pi\)
\(102\) 0 0
\(103\) −542.000 −0.518494 −0.259247 0.965811i \(-0.583474\pi\)
−0.259247 + 0.965811i \(0.583474\pi\)
\(104\) 0 0
\(105\) −70.0000 −0.0650600
\(106\) 0 0
\(107\) 374.000 0.337906 0.168953 0.985624i \(-0.445961\pi\)
0.168953 + 0.985624i \(0.445961\pi\)
\(108\) 0 0
\(109\) −449.000 −0.394554 −0.197277 0.980348i \(-0.563210\pi\)
−0.197277 + 0.980348i \(0.563210\pi\)
\(110\) 0 0
\(111\) 2520.00 2.15485
\(112\) 0 0
\(113\) 898.000 0.747582 0.373791 0.927513i \(-0.378058\pi\)
0.373791 + 0.927513i \(0.378058\pi\)
\(114\) 0 0
\(115\) −140.000 −0.113522
\(116\) 0 0
\(117\) −594.000 −0.469362
\(118\) 0 0
\(119\) 48.0000 0.0369761
\(120\) 0 0
\(121\) 38.0000 0.0285500
\(122\) 0 0
\(123\) 2702.00 1.98074
\(124\) 0 0
\(125\) 1125.00 0.804984
\(126\) 0 0
\(127\) −1280.00 −0.894344 −0.447172 0.894448i \(-0.647569\pi\)
−0.447172 + 0.894448i \(0.647569\pi\)
\(128\) 0 0
\(129\) 2667.00 1.82028
\(130\) 0 0
\(131\) −1292.00 −0.861699 −0.430849 0.902424i \(-0.641786\pi\)
−0.430849 + 0.902424i \(0.641786\pi\)
\(132\) 0 0
\(133\) −176.000 −0.114745
\(134\) 0 0
\(135\) 175.000 0.111567
\(136\) 0 0
\(137\) 1852.00 1.15494 0.577471 0.816411i \(-0.304040\pi\)
0.577471 + 0.816411i \(0.304040\pi\)
\(138\) 0 0
\(139\) −1532.00 −0.934838 −0.467419 0.884036i \(-0.654816\pi\)
−0.467419 + 0.884036i \(0.654816\pi\)
\(140\) 0 0
\(141\) 721.000 0.430632
\(142\) 0 0
\(143\) −999.000 −0.584200
\(144\) 0 0
\(145\) −145.000 −0.0830455
\(146\) 0 0
\(147\) −2373.00 −1.33144
\(148\) 0 0
\(149\) 1357.00 0.746106 0.373053 0.927810i \(-0.378311\pi\)
0.373053 + 0.927810i \(0.378311\pi\)
\(150\) 0 0
\(151\) 2134.00 1.15008 0.575041 0.818124i \(-0.304986\pi\)
0.575041 + 0.818124i \(0.304986\pi\)
\(152\) 0 0
\(153\) 528.000 0.278995
\(154\) 0 0
\(155\) −715.000 −0.370517
\(156\) 0 0
\(157\) −2386.00 −1.21289 −0.606444 0.795126i \(-0.707405\pi\)
−0.606444 + 0.795126i \(0.707405\pi\)
\(158\) 0 0
\(159\) 3017.00 1.50480
\(160\) 0 0
\(161\) 56.0000 0.0274125
\(162\) 0 0
\(163\) 3937.00 1.89184 0.945919 0.324403i \(-0.105163\pi\)
0.945919 + 0.324403i \(0.105163\pi\)
\(164\) 0 0
\(165\) −1295.00 −0.611004
\(166\) 0 0
\(167\) 2762.00 1.27982 0.639910 0.768450i \(-0.278972\pi\)
0.639910 + 0.768450i \(0.278972\pi\)
\(168\) 0 0
\(169\) −1468.00 −0.668184
\(170\) 0 0
\(171\) −1936.00 −0.865787
\(172\) 0 0
\(173\) 3822.00 1.67966 0.839830 0.542849i \(-0.182654\pi\)
0.839830 + 0.542849i \(0.182654\pi\)
\(174\) 0 0
\(175\) −200.000 −0.0863919
\(176\) 0 0
\(177\) 2016.00 0.856112
\(178\) 0 0
\(179\) 1430.00 0.597113 0.298556 0.954392i \(-0.403495\pi\)
0.298556 + 0.954392i \(0.403495\pi\)
\(180\) 0 0
\(181\) 525.000 0.215596 0.107798 0.994173i \(-0.465620\pi\)
0.107798 + 0.994173i \(0.465620\pi\)
\(182\) 0 0
\(183\) 5880.00 2.37520
\(184\) 0 0
\(185\) −1800.00 −0.715344
\(186\) 0 0
\(187\) 888.000 0.347257
\(188\) 0 0
\(189\) −70.0000 −0.0269405
\(190\) 0 0
\(191\) −224.000 −0.0848590 −0.0424295 0.999099i \(-0.513510\pi\)
−0.0424295 + 0.999099i \(0.513510\pi\)
\(192\) 0 0
\(193\) −490.000 −0.182751 −0.0913756 0.995817i \(-0.529126\pi\)
−0.0913756 + 0.995817i \(0.529126\pi\)
\(194\) 0 0
\(195\) 945.000 0.347040
\(196\) 0 0
\(197\) −106.000 −0.0383360 −0.0191680 0.999816i \(-0.506102\pi\)
−0.0191680 + 0.999816i \(0.506102\pi\)
\(198\) 0 0
\(199\) 2034.00 0.724555 0.362277 0.932070i \(-0.381999\pi\)
0.362277 + 0.932070i \(0.381999\pi\)
\(200\) 0 0
\(201\) −1260.00 −0.442157
\(202\) 0 0
\(203\) 58.0000 0.0200532
\(204\) 0 0
\(205\) −1930.00 −0.657547
\(206\) 0 0
\(207\) 616.000 0.206836
\(208\) 0 0
\(209\) −3256.00 −1.07762
\(210\) 0 0
\(211\) 5717.00 1.86528 0.932641 0.360806i \(-0.117498\pi\)
0.932641 + 0.360806i \(0.117498\pi\)
\(212\) 0 0
\(213\) −4942.00 −1.58977
\(214\) 0 0
\(215\) −1905.00 −0.604279
\(216\) 0 0
\(217\) 286.000 0.0894698
\(218\) 0 0
\(219\) 5012.00 1.54648
\(220\) 0 0
\(221\) −648.000 −0.197236
\(222\) 0 0
\(223\) −3438.00 −1.03240 −0.516201 0.856468i \(-0.672654\pi\)
−0.516201 + 0.856468i \(0.672654\pi\)
\(224\) 0 0
\(225\) −2200.00 −0.651852
\(226\) 0 0
\(227\) 5754.00 1.68241 0.841204 0.540719i \(-0.181848\pi\)
0.841204 + 0.540719i \(0.181848\pi\)
\(228\) 0 0
\(229\) −2074.00 −0.598488 −0.299244 0.954177i \(-0.596734\pi\)
−0.299244 + 0.954177i \(0.596734\pi\)
\(230\) 0 0
\(231\) 518.000 0.147541
\(232\) 0 0
\(233\) 5063.00 1.42355 0.711777 0.702405i \(-0.247891\pi\)
0.711777 + 0.702405i \(0.247891\pi\)
\(234\) 0 0
\(235\) −515.000 −0.142957
\(236\) 0 0
\(237\) −6517.00 −1.78618
\(238\) 0 0
\(239\) 1624.00 0.439531 0.219765 0.975553i \(-0.429471\pi\)
0.219765 + 0.975553i \(0.429471\pi\)
\(240\) 0 0
\(241\) −4463.00 −1.19289 −0.596446 0.802653i \(-0.703421\pi\)
−0.596446 + 0.802653i \(0.703421\pi\)
\(242\) 0 0
\(243\) −4928.00 −1.30095
\(244\) 0 0
\(245\) 1695.00 0.441998
\(246\) 0 0
\(247\) 2376.00 0.612070
\(248\) 0 0
\(249\) 8316.00 2.11649
\(250\) 0 0
\(251\) −2229.00 −0.560531 −0.280265 0.959923i \(-0.590422\pi\)
−0.280265 + 0.959923i \(0.590422\pi\)
\(252\) 0 0
\(253\) 1036.00 0.257442
\(254\) 0 0
\(255\) −840.000 −0.206286
\(256\) 0 0
\(257\) −4187.00 −1.01626 −0.508128 0.861281i \(-0.669662\pi\)
−0.508128 + 0.861281i \(0.669662\pi\)
\(258\) 0 0
\(259\) 720.000 0.172736
\(260\) 0 0
\(261\) 638.000 0.151307
\(262\) 0 0
\(263\) 7611.00 1.78447 0.892233 0.451576i \(-0.149138\pi\)
0.892233 + 0.451576i \(0.149138\pi\)
\(264\) 0 0
\(265\) −2155.00 −0.499549
\(266\) 0 0
\(267\) −4494.00 −1.03007
\(268\) 0 0
\(269\) −5136.00 −1.16412 −0.582058 0.813147i \(-0.697753\pi\)
−0.582058 + 0.813147i \(0.697753\pi\)
\(270\) 0 0
\(271\) −4015.00 −0.899977 −0.449989 0.893034i \(-0.648572\pi\)
−0.449989 + 0.893034i \(0.648572\pi\)
\(272\) 0 0
\(273\) −378.000 −0.0838007
\(274\) 0 0
\(275\) −3700.00 −0.811340
\(276\) 0 0
\(277\) −2150.00 −0.466357 −0.233179 0.972434i \(-0.574913\pi\)
−0.233179 + 0.972434i \(0.574913\pi\)
\(278\) 0 0
\(279\) 3146.00 0.675076
\(280\) 0 0
\(281\) −1965.00 −0.417160 −0.208580 0.978005i \(-0.566884\pi\)
−0.208580 + 0.978005i \(0.566884\pi\)
\(282\) 0 0
\(283\) −2452.00 −0.515040 −0.257520 0.966273i \(-0.582905\pi\)
−0.257520 + 0.966273i \(0.582905\pi\)
\(284\) 0 0
\(285\) 3080.00 0.640152
\(286\) 0 0
\(287\) 772.000 0.158780
\(288\) 0 0
\(289\) −4337.00 −0.882760
\(290\) 0 0
\(291\) 3402.00 0.685322
\(292\) 0 0
\(293\) −142.000 −0.0283131 −0.0141565 0.999900i \(-0.504506\pi\)
−0.0141565 + 0.999900i \(0.504506\pi\)
\(294\) 0 0
\(295\) −1440.00 −0.284204
\(296\) 0 0
\(297\) −1295.00 −0.253008
\(298\) 0 0
\(299\) −756.000 −0.146223
\(300\) 0 0
\(301\) 762.000 0.145917
\(302\) 0 0
\(303\) −1680.00 −0.318526
\(304\) 0 0
\(305\) −4200.00 −0.788496
\(306\) 0 0
\(307\) 9097.00 1.69118 0.845592 0.533830i \(-0.179248\pi\)
0.845592 + 0.533830i \(0.179248\pi\)
\(308\) 0 0
\(309\) −3794.00 −0.698489
\(310\) 0 0
\(311\) 4592.00 0.837262 0.418631 0.908156i \(-0.362510\pi\)
0.418631 + 0.908156i \(0.362510\pi\)
\(312\) 0 0
\(313\) 1225.00 0.221218 0.110609 0.993864i \(-0.464720\pi\)
0.110609 + 0.993864i \(0.464720\pi\)
\(314\) 0 0
\(315\) −220.000 −0.0393511
\(316\) 0 0
\(317\) −9852.00 −1.74556 −0.872781 0.488111i \(-0.837686\pi\)
−0.872781 + 0.488111i \(0.837686\pi\)
\(318\) 0 0
\(319\) 1073.00 0.188327
\(320\) 0 0
\(321\) 2618.00 0.455210
\(322\) 0 0
\(323\) −2112.00 −0.363823
\(324\) 0 0
\(325\) 2700.00 0.460828
\(326\) 0 0
\(327\) −3143.00 −0.531524
\(328\) 0 0
\(329\) 206.000 0.0345202
\(330\) 0 0
\(331\) −4183.00 −0.694618 −0.347309 0.937751i \(-0.612904\pi\)
−0.347309 + 0.937751i \(0.612904\pi\)
\(332\) 0 0
\(333\) 7920.00 1.30334
\(334\) 0 0
\(335\) 900.000 0.146783
\(336\) 0 0
\(337\) −4480.00 −0.724158 −0.362079 0.932147i \(-0.617933\pi\)
−0.362079 + 0.932147i \(0.617933\pi\)
\(338\) 0 0
\(339\) 6286.00 1.00711
\(340\) 0 0
\(341\) 5291.00 0.840245
\(342\) 0 0
\(343\) −1364.00 −0.214720
\(344\) 0 0
\(345\) −980.000 −0.152932
\(346\) 0 0
\(347\) −5002.00 −0.773837 −0.386918 0.922114i \(-0.626461\pi\)
−0.386918 + 0.922114i \(0.626461\pi\)
\(348\) 0 0
\(349\) 6427.00 0.985758 0.492879 0.870098i \(-0.335945\pi\)
0.492879 + 0.870098i \(0.335945\pi\)
\(350\) 0 0
\(351\) 945.000 0.143705
\(352\) 0 0
\(353\) 9734.00 1.46767 0.733836 0.679326i \(-0.237728\pi\)
0.733836 + 0.679326i \(0.237728\pi\)
\(354\) 0 0
\(355\) 3530.00 0.527755
\(356\) 0 0
\(357\) 336.000 0.0498123
\(358\) 0 0
\(359\) −5379.00 −0.790788 −0.395394 0.918512i \(-0.629392\pi\)
−0.395394 + 0.918512i \(0.629392\pi\)
\(360\) 0 0
\(361\) 885.000 0.129028
\(362\) 0 0
\(363\) 266.000 0.0384611
\(364\) 0 0
\(365\) −3580.00 −0.513386
\(366\) 0 0
\(367\) 9640.00 1.37113 0.685564 0.728012i \(-0.259556\pi\)
0.685564 + 0.728012i \(0.259556\pi\)
\(368\) 0 0
\(369\) 8492.00 1.19804
\(370\) 0 0
\(371\) 862.000 0.120628
\(372\) 0 0
\(373\) −7543.00 −1.04708 −0.523541 0.852000i \(-0.675389\pi\)
−0.523541 + 0.852000i \(0.675389\pi\)
\(374\) 0 0
\(375\) 7875.00 1.08444
\(376\) 0 0
\(377\) −783.000 −0.106967
\(378\) 0 0
\(379\) 3804.00 0.515563 0.257781 0.966203i \(-0.417009\pi\)
0.257781 + 0.966203i \(0.417009\pi\)
\(380\) 0 0
\(381\) −8960.00 −1.20482
\(382\) 0 0
\(383\) −9174.00 −1.22394 −0.611971 0.790880i \(-0.709623\pi\)
−0.611971 + 0.790880i \(0.709623\pi\)
\(384\) 0 0
\(385\) −370.000 −0.0489791
\(386\) 0 0
\(387\) 8382.00 1.10098
\(388\) 0 0
\(389\) 4536.00 0.591219 0.295610 0.955309i \(-0.404477\pi\)
0.295610 + 0.955309i \(0.404477\pi\)
\(390\) 0 0
\(391\) 672.000 0.0869169
\(392\) 0 0
\(393\) −9044.00 −1.16084
\(394\) 0 0
\(395\) 4655.00 0.592958
\(396\) 0 0
\(397\) 9853.00 1.24561 0.622806 0.782376i \(-0.285993\pi\)
0.622806 + 0.782376i \(0.285993\pi\)
\(398\) 0 0
\(399\) −1232.00 −0.154579
\(400\) 0 0
\(401\) −11429.0 −1.42328 −0.711642 0.702542i \(-0.752048\pi\)
−0.711642 + 0.702542i \(0.752048\pi\)
\(402\) 0 0
\(403\) −3861.00 −0.477246
\(404\) 0 0
\(405\) 4195.00 0.514694
\(406\) 0 0
\(407\) 13320.0 1.62223
\(408\) 0 0
\(409\) 2662.00 0.321827 0.160914 0.986968i \(-0.448556\pi\)
0.160914 + 0.986968i \(0.448556\pi\)
\(410\) 0 0
\(411\) 12964.0 1.55588
\(412\) 0 0
\(413\) 576.000 0.0686274
\(414\) 0 0
\(415\) −5940.00 −0.702610
\(416\) 0 0
\(417\) −10724.0 −1.25937
\(418\) 0 0
\(419\) 5126.00 0.597665 0.298832 0.954306i \(-0.403403\pi\)
0.298832 + 0.954306i \(0.403403\pi\)
\(420\) 0 0
\(421\) 16200.0 1.87539 0.937696 0.347458i \(-0.112955\pi\)
0.937696 + 0.347458i \(0.112955\pi\)
\(422\) 0 0
\(423\) 2266.00 0.260465
\(424\) 0 0
\(425\) −2400.00 −0.273923
\(426\) 0 0
\(427\) 1680.00 0.190400
\(428\) 0 0
\(429\) −6993.00 −0.787005
\(430\) 0 0
\(431\) −12000.0 −1.34111 −0.670556 0.741859i \(-0.733945\pi\)
−0.670556 + 0.741859i \(0.733945\pi\)
\(432\) 0 0
\(433\) −3736.00 −0.414644 −0.207322 0.978273i \(-0.566475\pi\)
−0.207322 + 0.978273i \(0.566475\pi\)
\(434\) 0 0
\(435\) −1015.00 −0.111875
\(436\) 0 0
\(437\) −2464.00 −0.269723
\(438\) 0 0
\(439\) −3172.00 −0.344855 −0.172427 0.985022i \(-0.555161\pi\)
−0.172427 + 0.985022i \(0.555161\pi\)
\(440\) 0 0
\(441\) −7458.00 −0.805313
\(442\) 0 0
\(443\) −1540.00 −0.165164 −0.0825820 0.996584i \(-0.526317\pi\)
−0.0825820 + 0.996584i \(0.526317\pi\)
\(444\) 0 0
\(445\) 3210.00 0.341952
\(446\) 0 0
\(447\) 9499.00 1.00512
\(448\) 0 0
\(449\) 8358.00 0.878482 0.439241 0.898369i \(-0.355247\pi\)
0.439241 + 0.898369i \(0.355247\pi\)
\(450\) 0 0
\(451\) 14282.0 1.49116
\(452\) 0 0
\(453\) 14938.0 1.54933
\(454\) 0 0
\(455\) 270.000 0.0278193
\(456\) 0 0
\(457\) 798.000 0.0816824 0.0408412 0.999166i \(-0.486996\pi\)
0.0408412 + 0.999166i \(0.486996\pi\)
\(458\) 0 0
\(459\) −840.000 −0.0854201
\(460\) 0 0
\(461\) −15330.0 −1.54878 −0.774392 0.632706i \(-0.781944\pi\)
−0.774392 + 0.632706i \(0.781944\pi\)
\(462\) 0 0
\(463\) 6020.00 0.604262 0.302131 0.953266i \(-0.402302\pi\)
0.302131 + 0.953266i \(0.402302\pi\)
\(464\) 0 0
\(465\) −5005.00 −0.499143
\(466\) 0 0
\(467\) −3275.00 −0.324516 −0.162258 0.986748i \(-0.551878\pi\)
−0.162258 + 0.986748i \(0.551878\pi\)
\(468\) 0 0
\(469\) −360.000 −0.0354440
\(470\) 0 0
\(471\) −16702.0 −1.63394
\(472\) 0 0
\(473\) 14097.0 1.37036
\(474\) 0 0
\(475\) 8800.00 0.850046
\(476\) 0 0
\(477\) 9482.00 0.910170
\(478\) 0 0
\(479\) −13463.0 −1.28422 −0.642109 0.766614i \(-0.721940\pi\)
−0.642109 + 0.766614i \(0.721940\pi\)
\(480\) 0 0
\(481\) −9720.00 −0.921401
\(482\) 0 0
\(483\) 392.000 0.0369288
\(484\) 0 0
\(485\) −2430.00 −0.227506
\(486\) 0 0
\(487\) 12358.0 1.14989 0.574943 0.818194i \(-0.305024\pi\)
0.574943 + 0.818194i \(0.305024\pi\)
\(488\) 0 0
\(489\) 27559.0 2.54859
\(490\) 0 0
\(491\) 407.000 0.0374087 0.0187043 0.999825i \(-0.494046\pi\)
0.0187043 + 0.999825i \(0.494046\pi\)
\(492\) 0 0
\(493\) 696.000 0.0635827
\(494\) 0 0
\(495\) −4070.00 −0.369561
\(496\) 0 0
\(497\) −1412.00 −0.127438
\(498\) 0 0
\(499\) 14084.0 1.26350 0.631750 0.775172i \(-0.282337\pi\)
0.631750 + 0.775172i \(0.282337\pi\)
\(500\) 0 0
\(501\) 19334.0 1.72411
\(502\) 0 0
\(503\) −13767.0 −1.22036 −0.610179 0.792263i \(-0.708903\pi\)
−0.610179 + 0.792263i \(0.708903\pi\)
\(504\) 0 0
\(505\) 1200.00 0.105741
\(506\) 0 0
\(507\) −10276.0 −0.900144
\(508\) 0 0
\(509\) −21381.0 −1.86188 −0.930939 0.365174i \(-0.881009\pi\)
−0.930939 + 0.365174i \(0.881009\pi\)
\(510\) 0 0
\(511\) 1432.00 0.123969
\(512\) 0 0
\(513\) 3080.00 0.265079
\(514\) 0 0
\(515\) 2710.00 0.231877
\(516\) 0 0
\(517\) 3811.00 0.324193
\(518\) 0 0
\(519\) 26754.0 2.26276
\(520\) 0 0
\(521\) 10243.0 0.861332 0.430666 0.902511i \(-0.358279\pi\)
0.430666 + 0.902511i \(0.358279\pi\)
\(522\) 0 0
\(523\) −10568.0 −0.883569 −0.441784 0.897121i \(-0.645654\pi\)
−0.441784 + 0.897121i \(0.645654\pi\)
\(524\) 0 0
\(525\) −1400.00 −0.116383
\(526\) 0 0
\(527\) 3432.00 0.283682
\(528\) 0 0
\(529\) −11383.0 −0.935563
\(530\) 0 0
\(531\) 6336.00 0.517814
\(532\) 0 0
\(533\) −10422.0 −0.846955
\(534\) 0 0
\(535\) −1870.00 −0.151116
\(536\) 0 0
\(537\) 10010.0 0.804401
\(538\) 0 0
\(539\) −12543.0 −1.00235
\(540\) 0 0
\(541\) 15720.0 1.24927 0.624635 0.780916i \(-0.285248\pi\)
0.624635 + 0.780916i \(0.285248\pi\)
\(542\) 0 0
\(543\) 3675.00 0.290441
\(544\) 0 0
\(545\) 2245.00 0.176450
\(546\) 0 0
\(547\) −18106.0 −1.41528 −0.707639 0.706575i \(-0.750240\pi\)
−0.707639 + 0.706575i \(0.750240\pi\)
\(548\) 0 0
\(549\) 18480.0 1.43663
\(550\) 0 0
\(551\) −2552.00 −0.197312
\(552\) 0 0
\(553\) −1862.00 −0.143183
\(554\) 0 0
\(555\) −12600.0 −0.963676
\(556\) 0 0
\(557\) 2346.00 0.178462 0.0892309 0.996011i \(-0.471559\pi\)
0.0892309 + 0.996011i \(0.471559\pi\)
\(558\) 0 0
\(559\) −10287.0 −0.778343
\(560\) 0 0
\(561\) 6216.00 0.467807
\(562\) 0 0
\(563\) −691.000 −0.0517268 −0.0258634 0.999665i \(-0.508233\pi\)
−0.0258634 + 0.999665i \(0.508233\pi\)
\(564\) 0 0
\(565\) −4490.00 −0.334329
\(566\) 0 0
\(567\) −1678.00 −0.124285
\(568\) 0 0
\(569\) −15542.0 −1.14509 −0.572544 0.819874i \(-0.694043\pi\)
−0.572544 + 0.819874i \(0.694043\pi\)
\(570\) 0 0
\(571\) 12124.0 0.888570 0.444285 0.895885i \(-0.353458\pi\)
0.444285 + 0.895885i \(0.353458\pi\)
\(572\) 0 0
\(573\) −1568.00 −0.114318
\(574\) 0 0
\(575\) −2800.00 −0.203075
\(576\) 0 0
\(577\) 15808.0 1.14055 0.570274 0.821455i \(-0.306837\pi\)
0.570274 + 0.821455i \(0.306837\pi\)
\(578\) 0 0
\(579\) −3430.00 −0.246193
\(580\) 0 0
\(581\) 2376.00 0.169661
\(582\) 0 0
\(583\) 15947.0 1.13286
\(584\) 0 0
\(585\) 2970.00 0.209905
\(586\) 0 0
\(587\) −6516.00 −0.458167 −0.229084 0.973407i \(-0.573573\pi\)
−0.229084 + 0.973407i \(0.573573\pi\)
\(588\) 0 0
\(589\) −12584.0 −0.880331
\(590\) 0 0
\(591\) −742.000 −0.0516443
\(592\) 0 0
\(593\) 14751.0 1.02150 0.510751 0.859729i \(-0.329367\pi\)
0.510751 + 0.859729i \(0.329367\pi\)
\(594\) 0 0
\(595\) −240.000 −0.0165362
\(596\) 0 0
\(597\) 14238.0 0.976085
\(598\) 0 0
\(599\) 18681.0 1.27427 0.637133 0.770754i \(-0.280120\pi\)
0.637133 + 0.770754i \(0.280120\pi\)
\(600\) 0 0
\(601\) −22526.0 −1.52888 −0.764438 0.644697i \(-0.776984\pi\)
−0.764438 + 0.644697i \(0.776984\pi\)
\(602\) 0 0
\(603\) −3960.00 −0.267436
\(604\) 0 0
\(605\) −190.000 −0.0127679
\(606\) 0 0
\(607\) 9329.00 0.623810 0.311905 0.950113i \(-0.399033\pi\)
0.311905 + 0.950113i \(0.399033\pi\)
\(608\) 0 0
\(609\) 406.000 0.0270147
\(610\) 0 0
\(611\) −2781.00 −0.184136
\(612\) 0 0
\(613\) −19525.0 −1.28647 −0.643236 0.765668i \(-0.722409\pi\)
−0.643236 + 0.765668i \(0.722409\pi\)
\(614\) 0 0
\(615\) −13510.0 −0.885814
\(616\) 0 0
\(617\) −25332.0 −1.65288 −0.826441 0.563024i \(-0.809638\pi\)
−0.826441 + 0.563024i \(0.809638\pi\)
\(618\) 0 0
\(619\) −21091.0 −1.36950 −0.684749 0.728779i \(-0.740088\pi\)
−0.684749 + 0.728779i \(0.740088\pi\)
\(620\) 0 0
\(621\) −980.000 −0.0633270
\(622\) 0 0
\(623\) −1284.00 −0.0825720
\(624\) 0 0
\(625\) 6875.00 0.440000
\(626\) 0 0
\(627\) −22792.0 −1.45171
\(628\) 0 0
\(629\) 8640.00 0.547694
\(630\) 0 0
\(631\) −6242.00 −0.393804 −0.196902 0.980423i \(-0.563088\pi\)
−0.196902 + 0.980423i \(0.563088\pi\)
\(632\) 0 0
\(633\) 40019.0 2.51282
\(634\) 0 0
\(635\) 6400.00 0.399963
\(636\) 0 0
\(637\) 9153.00 0.569317
\(638\) 0 0
\(639\) −15532.0 −0.961559
\(640\) 0 0
\(641\) 15392.0 0.948436 0.474218 0.880407i \(-0.342731\pi\)
0.474218 + 0.880407i \(0.342731\pi\)
\(642\) 0 0
\(643\) −14870.0 −0.911999 −0.456000 0.889980i \(-0.650718\pi\)
−0.456000 + 0.889980i \(0.650718\pi\)
\(644\) 0 0
\(645\) −13335.0 −0.814054
\(646\) 0 0
\(647\) −17016.0 −1.03395 −0.516977 0.855999i \(-0.672943\pi\)
−0.516977 + 0.855999i \(0.672943\pi\)
\(648\) 0 0
\(649\) 10656.0 0.644506
\(650\) 0 0
\(651\) 2002.00 0.120529
\(652\) 0 0
\(653\) 24122.0 1.44558 0.722792 0.691065i \(-0.242858\pi\)
0.722792 + 0.691065i \(0.242858\pi\)
\(654\) 0 0
\(655\) 6460.00 0.385363
\(656\) 0 0
\(657\) 15752.0 0.935379
\(658\) 0 0
\(659\) −20217.0 −1.19506 −0.597528 0.801848i \(-0.703851\pi\)
−0.597528 + 0.801848i \(0.703851\pi\)
\(660\) 0 0
\(661\) −3942.00 −0.231961 −0.115980 0.993252i \(-0.537001\pi\)
−0.115980 + 0.993252i \(0.537001\pi\)
\(662\) 0 0
\(663\) −4536.00 −0.265707
\(664\) 0 0
\(665\) 880.000 0.0513157
\(666\) 0 0
\(667\) 812.000 0.0471376
\(668\) 0 0
\(669\) −24066.0 −1.39080
\(670\) 0 0
\(671\) 31080.0 1.78812
\(672\) 0 0
\(673\) −6551.00 −0.375219 −0.187610 0.982244i \(-0.560074\pi\)
−0.187610 + 0.982244i \(0.560074\pi\)
\(674\) 0 0
\(675\) 3500.00 0.199578
\(676\) 0 0
\(677\) −14958.0 −0.849162 −0.424581 0.905390i \(-0.639579\pi\)
−0.424581 + 0.905390i \(0.639579\pi\)
\(678\) 0 0
\(679\) 972.000 0.0549366
\(680\) 0 0
\(681\) 40278.0 2.26646
\(682\) 0 0
\(683\) −27584.0 −1.54535 −0.772674 0.634803i \(-0.781081\pi\)
−0.772674 + 0.634803i \(0.781081\pi\)
\(684\) 0 0
\(685\) −9260.00 −0.516506
\(686\) 0 0
\(687\) −14518.0 −0.806254
\(688\) 0 0
\(689\) −11637.0 −0.643446
\(690\) 0 0
\(691\) 24244.0 1.33471 0.667355 0.744739i \(-0.267426\pi\)
0.667355 + 0.744739i \(0.267426\pi\)
\(692\) 0 0
\(693\) 1628.00 0.0892390
\(694\) 0 0
\(695\) 7660.00 0.418072
\(696\) 0 0
\(697\) 9264.00 0.503442
\(698\) 0 0
\(699\) 35441.0 1.91774
\(700\) 0 0
\(701\) −7431.00 −0.400378 −0.200189 0.979757i \(-0.564156\pi\)
−0.200189 + 0.979757i \(0.564156\pi\)
\(702\) 0 0
\(703\) −31680.0 −1.69962
\(704\) 0 0
\(705\) −3605.00 −0.192585
\(706\) 0 0
\(707\) −480.000 −0.0255336
\(708\) 0 0
\(709\) 28429.0 1.50589 0.752943 0.658085i \(-0.228633\pi\)
0.752943 + 0.658085i \(0.228633\pi\)
\(710\) 0 0
\(711\) −20482.0 −1.08036
\(712\) 0 0
\(713\) 4004.00 0.210310
\(714\) 0 0
\(715\) 4995.00 0.261262
\(716\) 0 0
\(717\) 11368.0 0.592114
\(718\) 0 0
\(719\) 29890.0 1.55036 0.775180 0.631740i \(-0.217659\pi\)
0.775180 + 0.631740i \(0.217659\pi\)
\(720\) 0 0
\(721\) −1084.00 −0.0559921
\(722\) 0 0
\(723\) −31241.0 −1.60701
\(724\) 0 0
\(725\) −2900.00 −0.148556
\(726\) 0 0
\(727\) −13072.0 −0.666869 −0.333434 0.942773i \(-0.608208\pi\)
−0.333434 + 0.942773i \(0.608208\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) 9144.00 0.462658
\(732\) 0 0
\(733\) −13456.0 −0.678047 −0.339024 0.940778i \(-0.610097\pi\)
−0.339024 + 0.940778i \(0.610097\pi\)
\(734\) 0 0
\(735\) 11865.0 0.595438
\(736\) 0 0
\(737\) −6660.00 −0.332869
\(738\) 0 0
\(739\) 16915.0 0.841987 0.420993 0.907064i \(-0.361682\pi\)
0.420993 + 0.907064i \(0.361682\pi\)
\(740\) 0 0
\(741\) 16632.0 0.824550
\(742\) 0 0
\(743\) −10164.0 −0.501859 −0.250929 0.968005i \(-0.580736\pi\)
−0.250929 + 0.968005i \(0.580736\pi\)
\(744\) 0 0
\(745\) −6785.00 −0.333669
\(746\) 0 0
\(747\) 26136.0 1.28014
\(748\) 0 0
\(749\) 748.000 0.0364904
\(750\) 0 0
\(751\) −5816.00 −0.282595 −0.141298 0.989967i \(-0.545127\pi\)
−0.141298 + 0.989967i \(0.545127\pi\)
\(752\) 0 0
\(753\) −15603.0 −0.755119
\(754\) 0 0
\(755\) −10670.0 −0.514333
\(756\) 0 0
\(757\) −30496.0 −1.46420 −0.732098 0.681200i \(-0.761459\pi\)
−0.732098 + 0.681200i \(0.761459\pi\)
\(758\) 0 0
\(759\) 7252.00 0.346813
\(760\) 0 0
\(761\) −25654.0 −1.22202 −0.611010 0.791623i \(-0.709236\pi\)
−0.611010 + 0.791623i \(0.709236\pi\)
\(762\) 0 0
\(763\) −898.000 −0.0426078
\(764\) 0 0
\(765\) −2640.00 −0.124770
\(766\) 0 0
\(767\) −7776.00 −0.366069
\(768\) 0 0
\(769\) −15348.0 −0.719718 −0.359859 0.933007i \(-0.617175\pi\)
−0.359859 + 0.933007i \(0.617175\pi\)
\(770\) 0 0
\(771\) −29309.0 −1.36905
\(772\) 0 0
\(773\) −22062.0 −1.02654 −0.513270 0.858227i \(-0.671566\pi\)
−0.513270 + 0.858227i \(0.671566\pi\)
\(774\) 0 0
\(775\) −14300.0 −0.662802
\(776\) 0 0
\(777\) 5040.00 0.232701
\(778\) 0 0
\(779\) −33968.0 −1.56230
\(780\) 0 0
\(781\) −26122.0 −1.19682
\(782\) 0 0
\(783\) −1015.00 −0.0463259
\(784\) 0 0
\(785\) 11930.0 0.542420
\(786\) 0 0
\(787\) −14942.0 −0.676779 −0.338389 0.941006i \(-0.609882\pi\)
−0.338389 + 0.941006i \(0.609882\pi\)
\(788\) 0 0
\(789\) 53277.0 2.40394
\(790\) 0 0
\(791\) 1796.00 0.0807312
\(792\) 0 0
\(793\) −22680.0 −1.01562
\(794\) 0 0
\(795\) −15085.0 −0.672968
\(796\) 0 0
\(797\) −13744.0 −0.610837 −0.305419 0.952218i \(-0.598796\pi\)
−0.305419 + 0.952218i \(0.598796\pi\)
\(798\) 0 0
\(799\) 2472.00 0.109453
\(800\) 0 0
\(801\) −14124.0 −0.623030
\(802\) 0 0
\(803\) 26492.0 1.16424
\(804\) 0 0
\(805\) −280.000 −0.0122593
\(806\) 0 0
\(807\) −35952.0 −1.56824
\(808\) 0 0
\(809\) 19376.0 0.842057 0.421028 0.907047i \(-0.361669\pi\)
0.421028 + 0.907047i \(0.361669\pi\)
\(810\) 0 0
\(811\) 38174.0 1.65286 0.826431 0.563039i \(-0.190368\pi\)
0.826431 + 0.563039i \(0.190368\pi\)
\(812\) 0 0
\(813\) −28105.0 −1.21241
\(814\) 0 0
\(815\) −19685.0 −0.846056
\(816\) 0 0
\(817\) −33528.0 −1.43574
\(818\) 0 0
\(819\) −1188.00 −0.0506863
\(820\) 0 0
\(821\) 15533.0 0.660299 0.330149 0.943929i \(-0.392901\pi\)
0.330149 + 0.943929i \(0.392901\pi\)
\(822\) 0 0
\(823\) −13624.0 −0.577039 −0.288519 0.957474i \(-0.593163\pi\)
−0.288519 + 0.957474i \(0.593163\pi\)
\(824\) 0 0
\(825\) −25900.0 −1.09300
\(826\) 0 0
\(827\) −37475.0 −1.57574 −0.787868 0.615844i \(-0.788815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(828\) 0 0
\(829\) −11600.0 −0.485989 −0.242994 0.970028i \(-0.578130\pi\)
−0.242994 + 0.970028i \(0.578130\pi\)
\(830\) 0 0
\(831\) −15050.0 −0.628254
\(832\) 0 0
\(833\) −8136.00 −0.338410
\(834\) 0 0
\(835\) −13810.0 −0.572353
\(836\) 0 0
\(837\) −5005.00 −0.206688
\(838\) 0 0
\(839\) 10783.0 0.443707 0.221854 0.975080i \(-0.428789\pi\)
0.221854 + 0.975080i \(0.428789\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) 0 0
\(843\) −13755.0 −0.561978
\(844\) 0 0
\(845\) 7340.00 0.298821
\(846\) 0 0
\(847\) 76.0000 0.00308311
\(848\) 0 0
\(849\) −17164.0 −0.693836
\(850\) 0 0
\(851\) 10080.0 0.406038
\(852\) 0 0
\(853\) 20026.0 0.803842 0.401921 0.915674i \(-0.368343\pi\)
0.401921 + 0.915674i \(0.368343\pi\)
\(854\) 0 0
\(855\) 9680.00 0.387192
\(856\) 0 0
\(857\) −37259.0 −1.48511 −0.742557 0.669783i \(-0.766387\pi\)
−0.742557 + 0.669783i \(0.766387\pi\)
\(858\) 0 0
\(859\) −19681.0 −0.781731 −0.390866 0.920448i \(-0.627824\pi\)
−0.390866 + 0.920448i \(0.627824\pi\)
\(860\) 0 0
\(861\) 5404.00 0.213900
\(862\) 0 0
\(863\) 12422.0 0.489977 0.244988 0.969526i \(-0.421216\pi\)
0.244988 + 0.969526i \(0.421216\pi\)
\(864\) 0 0
\(865\) −19110.0 −0.751167
\(866\) 0 0
\(867\) −30359.0 −1.18921
\(868\) 0 0
\(869\) −34447.0 −1.34469
\(870\) 0 0
\(871\) 4860.00 0.189064
\(872\) 0 0
\(873\) 10692.0 0.414512
\(874\) 0 0
\(875\) 2250.00 0.0869302
\(876\) 0 0
\(877\) 6111.00 0.235295 0.117648 0.993055i \(-0.462465\pi\)
0.117648 + 0.993055i \(0.462465\pi\)
\(878\) 0 0
\(879\) −994.000 −0.0381420
\(880\) 0 0
\(881\) −33998.0 −1.30014 −0.650069 0.759875i \(-0.725260\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(882\) 0 0
\(883\) 5214.00 0.198715 0.0993573 0.995052i \(-0.468321\pi\)
0.0993573 + 0.995052i \(0.468321\pi\)
\(884\) 0 0
\(885\) −10080.0 −0.382865
\(886\) 0 0
\(887\) 27507.0 1.04126 0.520628 0.853783i \(-0.325698\pi\)
0.520628 + 0.853783i \(0.325698\pi\)
\(888\) 0 0
\(889\) −2560.00 −0.0965800
\(890\) 0 0
\(891\) −31043.0 −1.16720
\(892\) 0 0
\(893\) −9064.00 −0.339659
\(894\) 0 0
\(895\) −7150.00 −0.267037
\(896\) 0 0
\(897\) −5292.00 −0.196984
\(898\) 0 0
\(899\) 4147.00 0.153849
\(900\) 0 0
\(901\) 10344.0 0.382473
\(902\) 0 0
\(903\) 5334.00 0.196572
\(904\) 0 0
\(905\) −2625.00 −0.0964176
\(906\) 0 0
\(907\) 49012.0 1.79429 0.897143 0.441741i \(-0.145639\pi\)
0.897143 + 0.441741i \(0.145639\pi\)
\(908\) 0 0
\(909\) −5280.00 −0.192658
\(910\) 0 0
\(911\) −38047.0 −1.38370 −0.691851 0.722040i \(-0.743205\pi\)
−0.691851 + 0.722040i \(0.743205\pi\)
\(912\) 0 0
\(913\) 43956.0 1.59335
\(914\) 0 0
\(915\) −29400.0 −1.06222
\(916\) 0 0
\(917\) −2584.00 −0.0930547
\(918\) 0 0
\(919\) −23214.0 −0.833253 −0.416626 0.909078i \(-0.636788\pi\)
−0.416626 + 0.909078i \(0.636788\pi\)
\(920\) 0 0
\(921\) 63679.0 2.27828
\(922\) 0 0
\(923\) 19062.0 0.679776
\(924\) 0 0
\(925\) −36000.0 −1.27965
\(926\) 0 0
\(927\) −11924.0 −0.422476
\(928\) 0 0
\(929\) 13890.0 0.490545 0.245272 0.969454i \(-0.421123\pi\)
0.245272 + 0.969454i \(0.421123\pi\)
\(930\) 0 0
\(931\) 29832.0 1.05017
\(932\) 0 0
\(933\) 32144.0 1.12792
\(934\) 0 0
\(935\) −4440.00 −0.155298
\(936\) 0 0
\(937\) 20830.0 0.726240 0.363120 0.931742i \(-0.381712\pi\)
0.363120 + 0.931742i \(0.381712\pi\)
\(938\) 0 0
\(939\) 8575.00 0.298013
\(940\) 0 0
\(941\) −32305.0 −1.11914 −0.559571 0.828782i \(-0.689034\pi\)
−0.559571 + 0.828782i \(0.689034\pi\)
\(942\) 0 0
\(943\) 10808.0 0.373231
\(944\) 0 0
\(945\) 350.000 0.0120481
\(946\) 0 0
\(947\) −35759.0 −1.22704 −0.613522 0.789677i \(-0.710248\pi\)
−0.613522 + 0.789677i \(0.710248\pi\)
\(948\) 0 0
\(949\) −19332.0 −0.661268
\(950\) 0 0
\(951\) −68964.0 −2.35154
\(952\) 0 0
\(953\) 21847.0 0.742596 0.371298 0.928514i \(-0.378913\pi\)
0.371298 + 0.928514i \(0.378913\pi\)
\(954\) 0 0
\(955\) 1120.00 0.0379501
\(956\) 0 0
\(957\) 7511.00 0.253705
\(958\) 0 0
\(959\) 3704.00 0.124722
\(960\) 0 0
\(961\) −9342.00 −0.313585
\(962\) 0 0
\(963\) 8228.00 0.275331
\(964\) 0 0
\(965\) 2450.00 0.0817288
\(966\) 0 0
\(967\) 9151.00 0.304319 0.152159 0.988356i \(-0.451377\pi\)
0.152159 + 0.988356i \(0.451377\pi\)
\(968\) 0 0
\(969\) −14784.0 −0.490124
\(970\) 0 0
\(971\) −26980.0 −0.891688 −0.445844 0.895111i \(-0.647096\pi\)
−0.445844 + 0.895111i \(0.647096\pi\)
\(972\) 0 0
\(973\) −3064.00 −0.100953
\(974\) 0 0
\(975\) 18900.0 0.620805
\(976\) 0 0
\(977\) −25659.0 −0.840229 −0.420115 0.907471i \(-0.638010\pi\)
−0.420115 + 0.907471i \(0.638010\pi\)
\(978\) 0 0
\(979\) −23754.0 −0.775466
\(980\) 0 0
\(981\) −9878.00 −0.321489
\(982\) 0 0
\(983\) −48693.0 −1.57992 −0.789962 0.613156i \(-0.789900\pi\)
−0.789962 + 0.613156i \(0.789900\pi\)
\(984\) 0 0
\(985\) 530.000 0.0171444
\(986\) 0 0
\(987\) 1442.00 0.0465039
\(988\) 0 0
\(989\) 10668.0 0.342996
\(990\) 0 0
\(991\) 10898.0 0.349330 0.174665 0.984628i \(-0.444116\pi\)
0.174665 + 0.984628i \(0.444116\pi\)
\(992\) 0 0
\(993\) −29281.0 −0.935755
\(994\) 0 0
\(995\) −10170.0 −0.324031
\(996\) 0 0
\(997\) 41216.0 1.30925 0.654626 0.755953i \(-0.272826\pi\)
0.654626 + 0.755953i \(0.272826\pi\)
\(998\) 0 0
\(999\) −12600.0 −0.399045
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 1856.4.a.d.1.1 1
4.3 odd 2 1856.4.a.a.1.1 1
8.3 odd 2 58.4.a.a.1.1 1
8.5 even 2 464.4.a.a.1.1 1
24.11 even 2 522.4.a.e.1.1 1
40.19 odd 2 1450.4.a.e.1.1 1
232.115 odd 2 1682.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
58.4.a.a.1.1 1 8.3 odd 2
464.4.a.a.1.1 1 8.5 even 2
522.4.a.e.1.1 1 24.11 even 2
1450.4.a.e.1.1 1 40.19 odd 2
1682.4.a.b.1.1 1 232.115 odd 2
1856.4.a.a.1.1 1 4.3 odd 2
1856.4.a.d.1.1 1 1.1 even 1 trivial