Properties

Label 2160.4.a.o.1.1
Level $2160$
Weight $4$
Character 2160.1
Self dual yes
Analytic conductor $127.444$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2160.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(127.444125612\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2160.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.00000 q^{5} +4.00000 q^{7} +O(q^{10})\) \(q+5.00000 q^{5} +4.00000 q^{7} +42.0000 q^{11} +20.0000 q^{13} -93.0000 q^{17} -59.0000 q^{19} +9.00000 q^{23} +25.0000 q^{25} -120.000 q^{29} -47.0000 q^{31} +20.0000 q^{35} -262.000 q^{37} -126.000 q^{41} +178.000 q^{43} +144.000 q^{47} -327.000 q^{49} -741.000 q^{53} +210.000 q^{55} -444.000 q^{59} +221.000 q^{61} +100.000 q^{65} +538.000 q^{67} +690.000 q^{71} -1126.00 q^{73} +168.000 q^{77} -665.000 q^{79} +75.0000 q^{83} -465.000 q^{85} +1086.00 q^{89} +80.0000 q^{91} -295.000 q^{95} +1544.00 q^{97} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 4.00000 0.215980 0.107990 0.994152i \(-0.465559\pi\)
0.107990 + 0.994152i \(0.465559\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 42.0000 1.15123 0.575613 0.817723i \(-0.304764\pi\)
0.575613 + 0.817723i \(0.304764\pi\)
\(12\) 0 0
\(13\) 20.0000 0.426692 0.213346 0.976977i \(-0.431564\pi\)
0.213346 + 0.976977i \(0.431564\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −93.0000 −1.32681 −0.663406 0.748259i \(-0.730890\pi\)
−0.663406 + 0.748259i \(0.730890\pi\)
\(18\) 0 0
\(19\) −59.0000 −0.712396 −0.356198 0.934410i \(-0.615927\pi\)
−0.356198 + 0.934410i \(0.615927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 9.00000 0.0815926 0.0407963 0.999167i \(-0.487011\pi\)
0.0407963 + 0.999167i \(0.487011\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −120.000 −0.768395 −0.384197 0.923251i \(-0.625522\pi\)
−0.384197 + 0.923251i \(0.625522\pi\)
\(30\) 0 0
\(31\) −47.0000 −0.272305 −0.136152 0.990688i \(-0.543474\pi\)
−0.136152 + 0.990688i \(0.543474\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 20.0000 0.0965891
\(36\) 0 0
\(37\) −262.000 −1.16412 −0.582061 0.813145i \(-0.697754\pi\)
−0.582061 + 0.813145i \(0.697754\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −126.000 −0.479949 −0.239974 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(42\) 0 0
\(43\) 178.000 0.631273 0.315637 0.948880i \(-0.397782\pi\)
0.315637 + 0.948880i \(0.397782\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 144.000 0.446906 0.223453 0.974715i \(-0.428267\pi\)
0.223453 + 0.974715i \(0.428267\pi\)
\(48\) 0 0
\(49\) −327.000 −0.953353
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −741.000 −1.92046 −0.960228 0.279217i \(-0.909925\pi\)
−0.960228 + 0.279217i \(0.909925\pi\)
\(54\) 0 0
\(55\) 210.000 0.514844
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −444.000 −0.979727 −0.489863 0.871799i \(-0.662953\pi\)
−0.489863 + 0.871799i \(0.662953\pi\)
\(60\) 0 0
\(61\) 221.000 0.463871 0.231936 0.972731i \(-0.425494\pi\)
0.231936 + 0.972731i \(0.425494\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 100.000 0.190823
\(66\) 0 0
\(67\) 538.000 0.981002 0.490501 0.871441i \(-0.336814\pi\)
0.490501 + 0.871441i \(0.336814\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 690.000 1.15335 0.576676 0.816973i \(-0.304350\pi\)
0.576676 + 0.816973i \(0.304350\pi\)
\(72\) 0 0
\(73\) −1126.00 −1.80532 −0.902660 0.430355i \(-0.858388\pi\)
−0.902660 + 0.430355i \(0.858388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 168.000 0.248641
\(78\) 0 0
\(79\) −665.000 −0.947068 −0.473534 0.880776i \(-0.657022\pi\)
−0.473534 + 0.880776i \(0.657022\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 75.0000 0.0991846 0.0495923 0.998770i \(-0.484208\pi\)
0.0495923 + 0.998770i \(0.484208\pi\)
\(84\) 0 0
\(85\) −465.000 −0.593369
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1086.00 1.29344 0.646718 0.762729i \(-0.276141\pi\)
0.646718 + 0.762729i \(0.276141\pi\)
\(90\) 0 0
\(91\) 80.0000 0.0921569
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −295.000 −0.318593
\(96\) 0 0
\(97\) 1544.00 1.61618 0.808090 0.589059i \(-0.200501\pi\)
0.808090 + 0.589059i \(0.200501\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 132.000 0.130044 0.0650222 0.997884i \(-0.479288\pi\)
0.0650222 + 0.997884i \(0.479288\pi\)
\(102\) 0 0
\(103\) 892.000 0.853314 0.426657 0.904413i \(-0.359691\pi\)
0.426657 + 0.904413i \(0.359691\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1140.00 −1.02998 −0.514990 0.857196i \(-0.672205\pi\)
−0.514990 + 0.857196i \(0.672205\pi\)
\(108\) 0 0
\(109\) −1735.00 −1.52461 −0.762307 0.647216i \(-0.775933\pi\)
−0.762307 + 0.647216i \(0.775933\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1434.00 1.19380 0.596900 0.802316i \(-0.296399\pi\)
0.596900 + 0.802316i \(0.296399\pi\)
\(114\) 0 0
\(115\) 45.0000 0.0364893
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −372.000 −0.286565
\(120\) 0 0
\(121\) 433.000 0.325319
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −686.000 −0.479312 −0.239656 0.970858i \(-0.577035\pi\)
−0.239656 + 0.970858i \(0.577035\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −114.000 −0.0760323 −0.0380161 0.999277i \(-0.512104\pi\)
−0.0380161 + 0.999277i \(0.512104\pi\)
\(132\) 0 0
\(133\) −236.000 −0.153863
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −159.000 −0.0991554 −0.0495777 0.998770i \(-0.515788\pi\)
−0.0495777 + 0.998770i \(0.515788\pi\)
\(138\) 0 0
\(139\) −2276.00 −1.38883 −0.694417 0.719573i \(-0.744337\pi\)
−0.694417 + 0.719573i \(0.744337\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 840.000 0.491219
\(144\) 0 0
\(145\) −600.000 −0.343636
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1398.00 0.768648 0.384324 0.923198i \(-0.374434\pi\)
0.384324 + 0.923198i \(0.374434\pi\)
\(150\) 0 0
\(151\) −2624.00 −1.41416 −0.707080 0.707134i \(-0.749988\pi\)
−0.707080 + 0.707134i \(0.749988\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −235.000 −0.121778
\(156\) 0 0
\(157\) −394.000 −0.200284 −0.100142 0.994973i \(-0.531930\pi\)
−0.100142 + 0.994973i \(0.531930\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 36.0000 0.0176223
\(162\) 0 0
\(163\) 3346.00 1.60785 0.803923 0.594733i \(-0.202742\pi\)
0.803923 + 0.594733i \(0.202742\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1491.00 −0.690881 −0.345440 0.938441i \(-0.612270\pi\)
−0.345440 + 0.938441i \(0.612270\pi\)
\(168\) 0 0
\(169\) −1797.00 −0.817934
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2403.00 −1.05605 −0.528025 0.849229i \(-0.677067\pi\)
−0.528025 + 0.849229i \(0.677067\pi\)
\(174\) 0 0
\(175\) 100.000 0.0431959
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2640.00 −1.10236 −0.551181 0.834386i \(-0.685823\pi\)
−0.551181 + 0.834386i \(0.685823\pi\)
\(180\) 0 0
\(181\) 1073.00 0.440638 0.220319 0.975428i \(-0.429290\pi\)
0.220319 + 0.975428i \(0.429290\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1310.00 −0.520611
\(186\) 0 0
\(187\) −3906.00 −1.52746
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1470.00 0.556887 0.278444 0.960453i \(-0.410181\pi\)
0.278444 + 0.960453i \(0.410181\pi\)
\(192\) 0 0
\(193\) −4720.00 −1.76038 −0.880189 0.474623i \(-0.842584\pi\)
−0.880189 + 0.474623i \(0.842584\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 765.000 0.276670 0.138335 0.990385i \(-0.455825\pi\)
0.138335 + 0.990385i \(0.455825\pi\)
\(198\) 0 0
\(199\) −668.000 −0.237956 −0.118978 0.992897i \(-0.537962\pi\)
−0.118978 + 0.992897i \(0.537962\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −480.000 −0.165958
\(204\) 0 0
\(205\) −630.000 −0.214640
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2478.00 −0.820128
\(210\) 0 0
\(211\) −4601.00 −1.50117 −0.750583 0.660777i \(-0.770227\pi\)
−0.750583 + 0.660777i \(0.770227\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 890.000 0.282314
\(216\) 0 0
\(217\) −188.000 −0.0588123
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1860.00 −0.566141
\(222\) 0 0
\(223\) 2158.00 0.648029 0.324014 0.946052i \(-0.394967\pi\)
0.324014 + 0.946052i \(0.394967\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3123.00 0.913131 0.456566 0.889690i \(-0.349079\pi\)
0.456566 + 0.889690i \(0.349079\pi\)
\(228\) 0 0
\(229\) 2027.00 0.584925 0.292463 0.956277i \(-0.405525\pi\)
0.292463 + 0.956277i \(0.405525\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 438.000 0.123152 0.0615758 0.998102i \(-0.480387\pi\)
0.0615758 + 0.998102i \(0.480387\pi\)
\(234\) 0 0
\(235\) 720.000 0.199862
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6414.00 1.73593 0.867965 0.496626i \(-0.165428\pi\)
0.867965 + 0.496626i \(0.165428\pi\)
\(240\) 0 0
\(241\) 3431.00 0.917055 0.458527 0.888680i \(-0.348377\pi\)
0.458527 + 0.888680i \(0.348377\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1635.00 −0.426352
\(246\) 0 0
\(247\) −1180.00 −0.303974
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7308.00 1.83776 0.918878 0.394541i \(-0.129096\pi\)
0.918878 + 0.394541i \(0.129096\pi\)
\(252\) 0 0
\(253\) 378.000 0.0939314
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3729.00 0.905092 0.452546 0.891741i \(-0.350516\pi\)
0.452546 + 0.891741i \(0.350516\pi\)
\(258\) 0 0
\(259\) −1048.00 −0.251427
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1956.00 −0.458601 −0.229301 0.973356i \(-0.573644\pi\)
−0.229301 + 0.973356i \(0.573644\pi\)
\(264\) 0 0
\(265\) −3705.00 −0.858854
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −990.000 −0.224392 −0.112196 0.993686i \(-0.535788\pi\)
−0.112196 + 0.993686i \(0.535788\pi\)
\(270\) 0 0
\(271\) −8495.00 −1.90419 −0.952093 0.305808i \(-0.901073\pi\)
−0.952093 + 0.305808i \(0.901073\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1050.00 0.230245
\(276\) 0 0
\(277\) −1366.00 −0.296300 −0.148150 0.988965i \(-0.547332\pi\)
−0.148150 + 0.988965i \(0.547332\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5520.00 −1.17187 −0.585935 0.810358i \(-0.699273\pi\)
−0.585935 + 0.810358i \(0.699273\pi\)
\(282\) 0 0
\(283\) −5438.00 −1.14225 −0.571123 0.820865i \(-0.693492\pi\)
−0.571123 + 0.820865i \(0.693492\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −504.000 −0.103659
\(288\) 0 0
\(289\) 3736.00 0.760432
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8253.00 1.64555 0.822774 0.568369i \(-0.192425\pi\)
0.822774 + 0.568369i \(0.192425\pi\)
\(294\) 0 0
\(295\) −2220.00 −0.438147
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 180.000 0.0348149
\(300\) 0 0
\(301\) 712.000 0.136342
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1105.00 0.207450
\(306\) 0 0
\(307\) −9290.00 −1.72706 −0.863531 0.504295i \(-0.831752\pi\)
−0.863531 + 0.504295i \(0.831752\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8112.00 −1.47907 −0.739533 0.673121i \(-0.764953\pi\)
−0.739533 + 0.673121i \(0.764953\pi\)
\(312\) 0 0
\(313\) −7900.00 −1.42663 −0.713314 0.700845i \(-0.752807\pi\)
−0.713314 + 0.700845i \(0.752807\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4419.00 0.782952 0.391476 0.920188i \(-0.371965\pi\)
0.391476 + 0.920188i \(0.371965\pi\)
\(318\) 0 0
\(319\) −5040.00 −0.884595
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5487.00 0.945216
\(324\) 0 0
\(325\) 500.000 0.0853385
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 576.000 0.0965225
\(330\) 0 0
\(331\) 8200.00 1.36167 0.680835 0.732437i \(-0.261617\pi\)
0.680835 + 0.732437i \(0.261617\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2690.00 0.438718
\(336\) 0 0
\(337\) −9556.00 −1.54465 −0.772327 0.635225i \(-0.780907\pi\)
−0.772327 + 0.635225i \(0.780907\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1974.00 −0.313484
\(342\) 0 0
\(343\) −2680.00 −0.421885
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10116.0 −1.56500 −0.782500 0.622650i \(-0.786056\pi\)
−0.782500 + 0.622650i \(0.786056\pi\)
\(348\) 0 0
\(349\) −6751.00 −1.03545 −0.517726 0.855546i \(-0.673221\pi\)
−0.517726 + 0.855546i \(0.673221\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4062.00 0.612460 0.306230 0.951958i \(-0.400932\pi\)
0.306230 + 0.951958i \(0.400932\pi\)
\(354\) 0 0
\(355\) 3450.00 0.515794
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8778.00 −1.29049 −0.645244 0.763977i \(-0.723244\pi\)
−0.645244 + 0.763977i \(0.723244\pi\)
\(360\) 0 0
\(361\) −3378.00 −0.492492
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5630.00 −0.807363
\(366\) 0 0
\(367\) −956.000 −0.135975 −0.0679875 0.997686i \(-0.521658\pi\)
−0.0679875 + 0.997686i \(0.521658\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2964.00 −0.414780
\(372\) 0 0
\(373\) 2300.00 0.319275 0.159637 0.987176i \(-0.448968\pi\)
0.159637 + 0.987176i \(0.448968\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2400.00 −0.327868
\(378\) 0 0
\(379\) −29.0000 −0.00393042 −0.00196521 0.999998i \(-0.500626\pi\)
−0.00196521 + 0.999998i \(0.500626\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8127.00 −1.08426 −0.542128 0.840296i \(-0.682381\pi\)
−0.542128 + 0.840296i \(0.682381\pi\)
\(384\) 0 0
\(385\) 840.000 0.111196
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7938.00 −1.03463 −0.517317 0.855794i \(-0.673069\pi\)
−0.517317 + 0.855794i \(0.673069\pi\)
\(390\) 0 0
\(391\) −837.000 −0.108258
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3325.00 −0.423542
\(396\) 0 0
\(397\) 272.000 0.0343861 0.0171931 0.999852i \(-0.494527\pi\)
0.0171931 + 0.999852i \(0.494527\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 4554.00 0.567122 0.283561 0.958954i \(-0.408484\pi\)
0.283561 + 0.958954i \(0.408484\pi\)
\(402\) 0 0
\(403\) −940.000 −0.116190
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11004.0 −1.34017
\(408\) 0 0
\(409\) 1001.00 0.121018 0.0605089 0.998168i \(-0.480728\pi\)
0.0605089 + 0.998168i \(0.480728\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1776.00 −0.211601
\(414\) 0 0
\(415\) 375.000 0.0443567
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1794.00 0.209171 0.104585 0.994516i \(-0.466648\pi\)
0.104585 + 0.994516i \(0.466648\pi\)
\(420\) 0 0
\(421\) −16129.0 −1.86717 −0.933586 0.358354i \(-0.883338\pi\)
−0.933586 + 0.358354i \(0.883338\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2325.00 −0.265363
\(426\) 0 0
\(427\) 884.000 0.100187
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13356.0 1.49266 0.746329 0.665577i \(-0.231814\pi\)
0.746329 + 0.665577i \(0.231814\pi\)
\(432\) 0 0
\(433\) −11500.0 −1.27634 −0.638169 0.769896i \(-0.720308\pi\)
−0.638169 + 0.769896i \(0.720308\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −531.000 −0.0581263
\(438\) 0 0
\(439\) 11149.0 1.21210 0.606051 0.795426i \(-0.292753\pi\)
0.606051 + 0.795426i \(0.292753\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3849.00 −0.412803 −0.206401 0.978467i \(-0.566175\pi\)
−0.206401 + 0.978467i \(0.566175\pi\)
\(444\) 0 0
\(445\) 5430.00 0.578442
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18048.0 1.89697 0.948483 0.316828i \(-0.102618\pi\)
0.948483 + 0.316828i \(0.102618\pi\)
\(450\) 0 0
\(451\) −5292.00 −0.552529
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 400.000 0.0412138
\(456\) 0 0
\(457\) −4264.00 −0.436458 −0.218229 0.975898i \(-0.570028\pi\)
−0.218229 + 0.975898i \(0.570028\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10242.0 −1.03475 −0.517373 0.855760i \(-0.673090\pi\)
−0.517373 + 0.855760i \(0.673090\pi\)
\(462\) 0 0
\(463\) −3302.00 −0.331441 −0.165720 0.986173i \(-0.552995\pi\)
−0.165720 + 0.986173i \(0.552995\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1923.00 0.190548 0.0952739 0.995451i \(-0.469627\pi\)
0.0952739 + 0.995451i \(0.469627\pi\)
\(468\) 0 0
\(469\) 2152.00 0.211877
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7476.00 0.726738
\(474\) 0 0
\(475\) −1475.00 −0.142479
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15246.0 −1.45430 −0.727148 0.686481i \(-0.759154\pi\)
−0.727148 + 0.686481i \(0.759154\pi\)
\(480\) 0 0
\(481\) −5240.00 −0.496722
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7720.00 0.722778
\(486\) 0 0
\(487\) 8206.00 0.763551 0.381776 0.924255i \(-0.375313\pi\)
0.381776 + 0.924255i \(0.375313\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16806.0 1.54469 0.772346 0.635202i \(-0.219083\pi\)
0.772346 + 0.635202i \(0.219083\pi\)
\(492\) 0 0
\(493\) 11160.0 1.01952
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2760.00 0.249100
\(498\) 0 0
\(499\) 5425.00 0.486686 0.243343 0.969940i \(-0.421756\pi\)
0.243343 + 0.969940i \(0.421756\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 19665.0 1.74318 0.871589 0.490236i \(-0.163090\pi\)
0.871589 + 0.490236i \(0.163090\pi\)
\(504\) 0 0
\(505\) 660.000 0.0581577
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −14724.0 −1.28218 −0.641090 0.767466i \(-0.721518\pi\)
−0.641090 + 0.767466i \(0.721518\pi\)
\(510\) 0 0
\(511\) −4504.00 −0.389912
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4460.00 0.381614
\(516\) 0 0
\(517\) 6048.00 0.514489
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2058.00 0.173057 0.0865284 0.996249i \(-0.472423\pi\)
0.0865284 + 0.996249i \(0.472423\pi\)
\(522\) 0 0
\(523\) −11912.0 −0.995938 −0.497969 0.867195i \(-0.665921\pi\)
−0.497969 + 0.867195i \(0.665921\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4371.00 0.361297
\(528\) 0 0
\(529\) −12086.0 −0.993343
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2520.00 −0.204790
\(534\) 0 0
\(535\) −5700.00 −0.460621
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −13734.0 −1.09752
\(540\) 0 0
\(541\) −5170.00 −0.410861 −0.205430 0.978672i \(-0.565859\pi\)
−0.205430 + 0.978672i \(0.565859\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8675.00 −0.681828
\(546\) 0 0
\(547\) 4186.00 0.327204 0.163602 0.986526i \(-0.447689\pi\)
0.163602 + 0.986526i \(0.447689\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7080.00 0.547401
\(552\) 0 0
\(553\) −2660.00 −0.204547
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 13026.0 0.990896 0.495448 0.868637i \(-0.335004\pi\)
0.495448 + 0.868637i \(0.335004\pi\)
\(558\) 0 0
\(559\) 3560.00 0.269359
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10668.0 0.798584 0.399292 0.916824i \(-0.369256\pi\)
0.399292 + 0.916824i \(0.369256\pi\)
\(564\) 0 0
\(565\) 7170.00 0.533883
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15372.0 −1.13256 −0.566281 0.824212i \(-0.691618\pi\)
−0.566281 + 0.824212i \(0.691618\pi\)
\(570\) 0 0
\(571\) 14989.0 1.09855 0.549273 0.835643i \(-0.314905\pi\)
0.549273 + 0.835643i \(0.314905\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 225.000 0.0163185
\(576\) 0 0
\(577\) −1066.00 −0.0769119 −0.0384559 0.999260i \(-0.512244\pi\)
−0.0384559 + 0.999260i \(0.512244\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 300.000 0.0214219
\(582\) 0 0
\(583\) −31122.0 −2.21088
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 621.000 0.0436651 0.0218325 0.999762i \(-0.493050\pi\)
0.0218325 + 0.999762i \(0.493050\pi\)
\(588\) 0 0
\(589\) 2773.00 0.193989
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20187.0 −1.39794 −0.698972 0.715149i \(-0.746359\pi\)
−0.698972 + 0.715149i \(0.746359\pi\)
\(594\) 0 0
\(595\) −1860.00 −0.128156
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18228.0 1.24337 0.621683 0.783269i \(-0.286449\pi\)
0.621683 + 0.783269i \(0.286449\pi\)
\(600\) 0 0
\(601\) −11743.0 −0.797017 −0.398508 0.917165i \(-0.630472\pi\)
−0.398508 + 0.917165i \(0.630472\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2165.00 0.145487
\(606\) 0 0
\(607\) 24418.0 1.63278 0.816389 0.577503i \(-0.195973\pi\)
0.816389 + 0.577503i \(0.195973\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2880.00 0.190691
\(612\) 0 0
\(613\) 2672.00 0.176054 0.0880270 0.996118i \(-0.471944\pi\)
0.0880270 + 0.996118i \(0.471944\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −8601.00 −0.561205 −0.280602 0.959824i \(-0.590534\pi\)
−0.280602 + 0.959824i \(0.590534\pi\)
\(618\) 0 0
\(619\) −21308.0 −1.38359 −0.691794 0.722095i \(-0.743179\pi\)
−0.691794 + 0.722095i \(0.743179\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4344.00 0.279356
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 24366.0 1.54457
\(630\) 0 0
\(631\) 19015.0 1.19964 0.599822 0.800134i \(-0.295238\pi\)
0.599822 + 0.800134i \(0.295238\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −3430.00 −0.214355
\(636\) 0 0
\(637\) −6540.00 −0.406788
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4416.00 −0.272108 −0.136054 0.990701i \(-0.543442\pi\)
−0.136054 + 0.990701i \(0.543442\pi\)
\(642\) 0 0
\(643\) −7580.00 −0.464893 −0.232446 0.972609i \(-0.574673\pi\)
−0.232446 + 0.972609i \(0.574673\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14901.0 0.905439 0.452719 0.891653i \(-0.350454\pi\)
0.452719 + 0.891653i \(0.350454\pi\)
\(648\) 0 0
\(649\) −18648.0 −1.12789
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 12915.0 0.773971 0.386985 0.922086i \(-0.373516\pi\)
0.386985 + 0.922086i \(0.373516\pi\)
\(654\) 0 0
\(655\) −570.000 −0.0340027
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −28128.0 −1.66269 −0.831344 0.555758i \(-0.812428\pi\)
−0.831344 + 0.555758i \(0.812428\pi\)
\(660\) 0 0
\(661\) −8362.00 −0.492049 −0.246024 0.969264i \(-0.579124\pi\)
−0.246024 + 0.969264i \(0.579124\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1180.00 −0.0688097
\(666\) 0 0
\(667\) −1080.00 −0.0626953
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9282.00 0.534020
\(672\) 0 0
\(673\) 29708.0 1.70157 0.850787 0.525511i \(-0.176126\pi\)
0.850787 + 0.525511i \(0.176126\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6762.00 0.383877 0.191939 0.981407i \(-0.438523\pi\)
0.191939 + 0.981407i \(0.438523\pi\)
\(678\) 0 0
\(679\) 6176.00 0.349062
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 19155.0 1.07313 0.536563 0.843860i \(-0.319722\pi\)
0.536563 + 0.843860i \(0.319722\pi\)
\(684\) 0 0
\(685\) −795.000 −0.0443436
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −14820.0 −0.819444
\(690\) 0 0
\(691\) 22975.0 1.26485 0.632424 0.774622i \(-0.282060\pi\)
0.632424 + 0.774622i \(0.282060\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11380.0 −0.621105
\(696\) 0 0
\(697\) 11718.0 0.636802
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6450.00 −0.347522 −0.173761 0.984788i \(-0.555592\pi\)
−0.173761 + 0.984788i \(0.555592\pi\)
\(702\) 0 0
\(703\) 15458.0 0.829317
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 528.000 0.0280870
\(708\) 0 0
\(709\) 34538.0 1.82948 0.914740 0.404042i \(-0.132395\pi\)
0.914740 + 0.404042i \(0.132395\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −423.000 −0.0222181
\(714\) 0 0
\(715\) 4200.00 0.219680
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −27114.0 −1.40637 −0.703186 0.711006i \(-0.748240\pi\)
−0.703186 + 0.711006i \(0.748240\pi\)
\(720\) 0 0
\(721\) 3568.00 0.184299
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3000.00 −0.153679
\(726\) 0 0
\(727\) −236.000 −0.0120396 −0.00601978 0.999982i \(-0.501916\pi\)
−0.00601978 + 0.999982i \(0.501916\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −16554.0 −0.837581
\(732\) 0 0
\(733\) 27128.0 1.36698 0.683489 0.729960i \(-0.260462\pi\)
0.683489 + 0.729960i \(0.260462\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 22596.0 1.12935
\(738\) 0 0
\(739\) −5249.00 −0.261282 −0.130641 0.991430i \(-0.541704\pi\)
−0.130641 + 0.991430i \(0.541704\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −13896.0 −0.686130 −0.343065 0.939312i \(-0.611465\pi\)
−0.343065 + 0.939312i \(0.611465\pi\)
\(744\) 0 0
\(745\) 6990.00 0.343750
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4560.00 −0.222455
\(750\) 0 0
\(751\) −27665.0 −1.34422 −0.672111 0.740451i \(-0.734612\pi\)
−0.672111 + 0.740451i \(0.734612\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −13120.0 −0.632431
\(756\) 0 0
\(757\) −8122.00 −0.389959 −0.194980 0.980807i \(-0.562464\pi\)
−0.194980 + 0.980807i \(0.562464\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 10584.0 0.504165 0.252083 0.967706i \(-0.418885\pi\)
0.252083 + 0.967706i \(0.418885\pi\)
\(762\) 0 0
\(763\) −6940.00 −0.329286
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8880.00 −0.418042
\(768\) 0 0
\(769\) −18619.0 −0.873106 −0.436553 0.899679i \(-0.643801\pi\)
−0.436553 + 0.899679i \(0.643801\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22251.0 1.03533 0.517667 0.855582i \(-0.326801\pi\)
0.517667 + 0.855582i \(0.326801\pi\)
\(774\) 0 0
\(775\) −1175.00 −0.0544610
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7434.00 0.341914
\(780\) 0 0
\(781\) 28980.0 1.32777
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1970.00 −0.0895698
\(786\) 0 0
\(787\) −24854.0 −1.12573 −0.562865 0.826549i \(-0.690301\pi\)
−0.562865 + 0.826549i \(0.690301\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5736.00 0.257837
\(792\) 0 0
\(793\) 4420.00 0.197930
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3681.00 0.163598 0.0817991 0.996649i \(-0.473933\pi\)
0.0817991 + 0.996649i \(0.473933\pi\)
\(798\) 0 0
\(799\) −13392.0 −0.592960
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −47292.0 −2.07833
\(804\) 0 0
\(805\) 180.000 0.00788095
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −5142.00 −0.223465 −0.111732 0.993738i \(-0.535640\pi\)
−0.111732 + 0.993738i \(0.535640\pi\)
\(810\) 0 0
\(811\) 18484.0 0.800322 0.400161 0.916445i \(-0.368954\pi\)
0.400161 + 0.916445i \(0.368954\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 16730.0 0.719051
\(816\) 0 0
\(817\) −10502.0 −0.449717
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 25014.0 1.06333 0.531665 0.846954i \(-0.321566\pi\)
0.531665 + 0.846954i \(0.321566\pi\)
\(822\) 0 0
\(823\) 32146.0 1.36153 0.680765 0.732502i \(-0.261648\pi\)
0.680765 + 0.732502i \(0.261648\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 10977.0 0.461557 0.230779 0.973006i \(-0.425873\pi\)
0.230779 + 0.973006i \(0.425873\pi\)
\(828\) 0 0
\(829\) 36602.0 1.53346 0.766731 0.641969i \(-0.221882\pi\)
0.766731 + 0.641969i \(0.221882\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 30411.0 1.26492
\(834\) 0 0
\(835\) −7455.00 −0.308971
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −11076.0 −0.455764 −0.227882 0.973689i \(-0.573180\pi\)
−0.227882 + 0.973689i \(0.573180\pi\)
\(840\) 0 0
\(841\) −9989.00 −0.409570
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −8985.00 −0.365791
\(846\) 0 0
\(847\) 1732.00 0.0702624
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2358.00 −0.0949838
\(852\) 0 0
\(853\) 36848.0 1.47908 0.739538 0.673115i \(-0.235044\pi\)
0.739538 + 0.673115i \(0.235044\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −26961.0 −1.07464 −0.537322 0.843377i \(-0.680564\pi\)
−0.537322 + 0.843377i \(0.680564\pi\)
\(858\) 0 0
\(859\) 415.000 0.0164838 0.00824192 0.999966i \(-0.497376\pi\)
0.00824192 + 0.999966i \(0.497376\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 45501.0 1.79475 0.897377 0.441265i \(-0.145470\pi\)
0.897377 + 0.441265i \(0.145470\pi\)
\(864\) 0 0
\(865\) −12015.0 −0.472280
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −27930.0 −1.09029
\(870\) 0 0
\(871\) 10760.0 0.418586
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 500.000 0.0193178
\(876\) 0 0
\(877\) 35042.0 1.34924 0.674620 0.738165i \(-0.264307\pi\)
0.674620 + 0.738165i \(0.264307\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1080.00 0.0413009 0.0206505 0.999787i \(-0.493426\pi\)
0.0206505 + 0.999787i \(0.493426\pi\)
\(882\) 0 0
\(883\) 20164.0 0.768485 0.384243 0.923232i \(-0.374463\pi\)
0.384243 + 0.923232i \(0.374463\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −20067.0 −0.759621 −0.379811 0.925064i \(-0.624011\pi\)
−0.379811 + 0.925064i \(0.624011\pi\)
\(888\) 0 0
\(889\) −2744.00 −0.103522
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −8496.00 −0.318374
\(894\) 0 0
\(895\) −13200.0 −0.492991
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5640.00 0.209238
\(900\) 0 0
\(901\) 68913.0 2.54809
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5365.00 0.197059
\(906\) 0 0
\(907\) 26524.0 0.971020 0.485510 0.874231i \(-0.338634\pi\)
0.485510 + 0.874231i \(0.338634\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −35568.0 −1.29355 −0.646773 0.762683i \(-0.723882\pi\)
−0.646773 + 0.762683i \(0.723882\pi\)
\(912\) 0 0
\(913\) 3150.00 0.114184
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −456.000 −0.0164214
\(918\) 0 0
\(919\) 23704.0 0.850841 0.425420 0.904996i \(-0.360126\pi\)
0.425420 + 0.904996i \(0.360126\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 13800.0 0.492126
\(924\) 0 0
\(925\) −6550.00 −0.232825
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −40590.0 −1.43349 −0.716746 0.697334i \(-0.754369\pi\)
−0.716746 + 0.697334i \(0.754369\pi\)
\(930\) 0 0
\(931\) 19293.0 0.679165
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −19530.0 −0.683101
\(936\) 0 0
\(937\) −12964.0 −0.451991 −0.225995 0.974128i \(-0.572563\pi\)
−0.225995 + 0.974128i \(0.572563\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 29922.0 1.03659 0.518294 0.855203i \(-0.326567\pi\)
0.518294 + 0.855203i \(0.326567\pi\)
\(942\) 0 0
\(943\) −1134.00 −0.0391603
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5241.00 −0.179841 −0.0899206 0.995949i \(-0.528661\pi\)
−0.0899206 + 0.995949i \(0.528661\pi\)
\(948\) 0 0
\(949\) −22520.0 −0.770316
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 26214.0 0.891033 0.445517 0.895274i \(-0.353020\pi\)
0.445517 + 0.895274i \(0.353020\pi\)
\(954\) 0 0
\(955\) 7350.00 0.249048
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −636.000 −0.0214155
\(960\) 0 0
\(961\) −27582.0 −0.925850
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23600.0 −0.787265
\(966\) 0 0
\(967\) −18278.0 −0.607840 −0.303920 0.952698i \(-0.598295\pi\)
−0.303920 + 0.952698i \(0.598295\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 24942.0 0.824333 0.412166 0.911109i \(-0.364772\pi\)
0.412166 + 0.911109i \(0.364772\pi\)
\(972\) 0 0
\(973\) −9104.00 −0.299960
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −11226.0 −0.367607 −0.183803 0.982963i \(-0.558841\pi\)
−0.183803 + 0.982963i \(0.558841\pi\)
\(978\) 0 0
\(979\) 45612.0 1.48904
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 23073.0 0.748641 0.374321 0.927299i \(-0.377876\pi\)
0.374321 + 0.927299i \(0.377876\pi\)
\(984\) 0 0
\(985\) 3825.00 0.123731
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1602.00 0.0515072
\(990\) 0 0
\(991\) −22037.0 −0.706386 −0.353193 0.935551i \(-0.614904\pi\)
−0.353193 + 0.935551i \(0.614904\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3340.00 −0.106417
\(996\) 0 0
\(997\) 19082.0 0.606151 0.303076 0.952966i \(-0.401986\pi\)
0.303076 + 0.952966i \(0.401986\pi\)
\(998\) 0 0
\(999\) 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 2160.4.a.o.1.1 1
3.2 odd 2 2160.4.a.e.1.1 1
4.3 odd 2 270.4.a.e.1.1 1
12.11 even 2 270.4.a.i.1.1 yes 1
20.3 even 4 1350.4.c.d.649.2 2
20.7 even 4 1350.4.c.d.649.1 2
20.19 odd 2 1350.4.a.u.1.1 1
36.7 odd 6 810.4.e.q.271.1 2
36.11 even 6 810.4.e.h.271.1 2
36.23 even 6 810.4.e.h.541.1 2
36.31 odd 6 810.4.e.q.541.1 2
60.23 odd 4 1350.4.c.q.649.1 2
60.47 odd 4 1350.4.c.q.649.2 2
60.59 even 2 1350.4.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.4.a.e.1.1 1 4.3 odd 2
270.4.a.i.1.1 yes 1 12.11 even 2
810.4.e.h.271.1 2 36.11 even 6
810.4.e.h.541.1 2 36.23 even 6
810.4.e.q.271.1 2 36.7 odd 6
810.4.e.q.541.1 2 36.31 odd 6
1350.4.a.g.1.1 1 60.59 even 2
1350.4.a.u.1.1 1 20.19 odd 2
1350.4.c.d.649.1 2 20.7 even 4
1350.4.c.d.649.2 2 20.3 even 4
1350.4.c.q.649.1 2 60.23 odd 4
1350.4.c.q.649.2 2 60.47 odd 4
2160.4.a.e.1.1 1 3.2 odd 2
2160.4.a.o.1.1 1 1.1 even 1 trivial