Properties

Label 912.4.a.b.1.1
Level $912$
Weight $4$
Character 912.1
Self dual yes
Analytic conductor $53.810$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 912.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.8097419252\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 912.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{3} -7.00000 q^{5} +15.0000 q^{7} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -7.00000 q^{5} +15.0000 q^{7} +9.00000 q^{9} +49.0000 q^{11} +14.0000 q^{13} +21.0000 q^{15} -33.0000 q^{17} +19.0000 q^{19} -45.0000 q^{21} +148.000 q^{23} -76.0000 q^{25} -27.0000 q^{27} -278.000 q^{29} -94.0000 q^{31} -147.000 q^{33} -105.000 q^{35} +160.000 q^{37} -42.0000 q^{39} +400.000 q^{41} -73.0000 q^{43} -63.0000 q^{45} -173.000 q^{47} -118.000 q^{49} +99.0000 q^{51} +170.000 q^{53} -343.000 q^{55} -57.0000 q^{57} +12.0000 q^{59} +419.000 q^{61} +135.000 q^{63} -98.0000 q^{65} -444.000 q^{67} -444.000 q^{69} +952.000 q^{71} -27.0000 q^{73} +228.000 q^{75} +735.000 q^{77} +556.000 q^{79} +81.0000 q^{81} +276.000 q^{83} +231.000 q^{85} +834.000 q^{87} +1386.00 q^{89} +210.000 q^{91} +282.000 q^{93} -133.000 q^{95} +130.000 q^{97} +441.000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −0.577350
\(4\) 0 0
\(5\) −7.00000 −0.626099 −0.313050 0.949737i \(-0.601351\pi\)
−0.313050 + 0.949737i \(0.601351\pi\)
\(6\) 0 0
\(7\) 15.0000 0.809924 0.404962 0.914334i \(-0.367285\pi\)
0.404962 + 0.914334i \(0.367285\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 49.0000 1.34310 0.671548 0.740961i \(-0.265630\pi\)
0.671548 + 0.740961i \(0.265630\pi\)
\(12\) 0 0
\(13\) 14.0000 0.298685 0.149342 0.988786i \(-0.452284\pi\)
0.149342 + 0.988786i \(0.452284\pi\)
\(14\) 0 0
\(15\) 21.0000 0.361478
\(16\) 0 0
\(17\) −33.0000 −0.470804 −0.235402 0.971898i \(-0.575641\pi\)
−0.235402 + 0.971898i \(0.575641\pi\)
\(18\) 0 0
\(19\) 19.0000 0.229416
\(20\) 0 0
\(21\) −45.0000 −0.467610
\(22\) 0 0
\(23\) 148.000 1.34174 0.670872 0.741573i \(-0.265920\pi\)
0.670872 + 0.741573i \(0.265920\pi\)
\(24\) 0 0
\(25\) −76.0000 −0.608000
\(26\) 0 0
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −278.000 −1.78011 −0.890057 0.455849i \(-0.849336\pi\)
−0.890057 + 0.455849i \(0.849336\pi\)
\(30\) 0 0
\(31\) −94.0000 −0.544610 −0.272305 0.962211i \(-0.587786\pi\)
−0.272305 + 0.962211i \(0.587786\pi\)
\(32\) 0 0
\(33\) −147.000 −0.775437
\(34\) 0 0
\(35\) −105.000 −0.507093
\(36\) 0 0
\(37\) 160.000 0.710915 0.355457 0.934693i \(-0.384325\pi\)
0.355457 + 0.934693i \(0.384325\pi\)
\(38\) 0 0
\(39\) −42.0000 −0.172446
\(40\) 0 0
\(41\) 400.000 1.52365 0.761823 0.647785i \(-0.224304\pi\)
0.761823 + 0.647785i \(0.224304\pi\)
\(42\) 0 0
\(43\) −73.0000 −0.258893 −0.129446 0.991586i \(-0.541320\pi\)
−0.129446 + 0.991586i \(0.541320\pi\)
\(44\) 0 0
\(45\) −63.0000 −0.208700
\(46\) 0 0
\(47\) −173.000 −0.536907 −0.268454 0.963293i \(-0.586513\pi\)
−0.268454 + 0.963293i \(0.586513\pi\)
\(48\) 0 0
\(49\) −118.000 −0.344023
\(50\) 0 0
\(51\) 99.0000 0.271819
\(52\) 0 0
\(53\) 170.000 0.440590 0.220295 0.975433i \(-0.429298\pi\)
0.220295 + 0.975433i \(0.429298\pi\)
\(54\) 0 0
\(55\) −343.000 −0.840911
\(56\) 0 0
\(57\) −57.0000 −0.132453
\(58\) 0 0
\(59\) 12.0000 0.0264791 0.0132396 0.999912i \(-0.495786\pi\)
0.0132396 + 0.999912i \(0.495786\pi\)
\(60\) 0 0
\(61\) 419.000 0.879466 0.439733 0.898128i \(-0.355073\pi\)
0.439733 + 0.898128i \(0.355073\pi\)
\(62\) 0 0
\(63\) 135.000 0.269975
\(64\) 0 0
\(65\) −98.0000 −0.187006
\(66\) 0 0
\(67\) −444.000 −0.809600 −0.404800 0.914405i \(-0.632659\pi\)
−0.404800 + 0.914405i \(0.632659\pi\)
\(68\) 0 0
\(69\) −444.000 −0.774657
\(70\) 0 0
\(71\) 952.000 1.59129 0.795645 0.605763i \(-0.207132\pi\)
0.795645 + 0.605763i \(0.207132\pi\)
\(72\) 0 0
\(73\) −27.0000 −0.0432892 −0.0216446 0.999766i \(-0.506890\pi\)
−0.0216446 + 0.999766i \(0.506890\pi\)
\(74\) 0 0
\(75\) 228.000 0.351029
\(76\) 0 0
\(77\) 735.000 1.08781
\(78\) 0 0
\(79\) 556.000 0.791834 0.395917 0.918286i \(-0.370427\pi\)
0.395917 + 0.918286i \(0.370427\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 276.000 0.364999 0.182500 0.983206i \(-0.441581\pi\)
0.182500 + 0.983206i \(0.441581\pi\)
\(84\) 0 0
\(85\) 231.000 0.294770
\(86\) 0 0
\(87\) 834.000 1.02775
\(88\) 0 0
\(89\) 1386.00 1.65074 0.825369 0.564593i \(-0.190967\pi\)
0.825369 + 0.564593i \(0.190967\pi\)
\(90\) 0 0
\(91\) 210.000 0.241912
\(92\) 0 0
\(93\) 282.000 0.314431
\(94\) 0 0
\(95\) −133.000 −0.143637
\(96\) 0 0
\(97\) 130.000 0.136077 0.0680387 0.997683i \(-0.478326\pi\)
0.0680387 + 0.997683i \(0.478326\pi\)
\(98\) 0 0
\(99\) 441.000 0.447699
\(100\) 0 0
\(101\) −238.000 −0.234474 −0.117237 0.993104i \(-0.537404\pi\)
−0.117237 + 0.993104i \(0.537404\pi\)
\(102\) 0 0
\(103\) 1374.00 1.31441 0.657205 0.753712i \(-0.271739\pi\)
0.657205 + 0.753712i \(0.271739\pi\)
\(104\) 0 0
\(105\) 315.000 0.292770
\(106\) 0 0
\(107\) −218.000 −0.196961 −0.0984806 0.995139i \(-0.531398\pi\)
−0.0984806 + 0.995139i \(0.531398\pi\)
\(108\) 0 0
\(109\) −2184.00 −1.91917 −0.959584 0.281423i \(-0.909194\pi\)
−0.959584 + 0.281423i \(0.909194\pi\)
\(110\) 0 0
\(111\) −480.000 −0.410447
\(112\) 0 0
\(113\) 1334.00 1.11055 0.555275 0.831667i \(-0.312613\pi\)
0.555275 + 0.831667i \(0.312613\pi\)
\(114\) 0 0
\(115\) −1036.00 −0.840065
\(116\) 0 0
\(117\) 126.000 0.0995616
\(118\) 0 0
\(119\) −495.000 −0.381316
\(120\) 0 0
\(121\) 1070.00 0.803907
\(122\) 0 0
\(123\) −1200.00 −0.879678
\(124\) 0 0
\(125\) 1407.00 1.00677
\(126\) 0 0
\(127\) 666.000 0.465338 0.232669 0.972556i \(-0.425254\pi\)
0.232669 + 0.972556i \(0.425254\pi\)
\(128\) 0 0
\(129\) 219.000 0.149472
\(130\) 0 0
\(131\) 303.000 0.202086 0.101043 0.994882i \(-0.467782\pi\)
0.101043 + 0.994882i \(0.467782\pi\)
\(132\) 0 0
\(133\) 285.000 0.185809
\(134\) 0 0
\(135\) 189.000 0.120493
\(136\) 0 0
\(137\) 583.000 0.363570 0.181785 0.983338i \(-0.441813\pi\)
0.181785 + 0.983338i \(0.441813\pi\)
\(138\) 0 0
\(139\) 1467.00 0.895175 0.447587 0.894240i \(-0.352283\pi\)
0.447587 + 0.894240i \(0.352283\pi\)
\(140\) 0 0
\(141\) 519.000 0.309984
\(142\) 0 0
\(143\) 686.000 0.401162
\(144\) 0 0
\(145\) 1946.00 1.11453
\(146\) 0 0
\(147\) 354.000 0.198622
\(148\) 0 0
\(149\) 351.000 0.192987 0.0964934 0.995334i \(-0.469237\pi\)
0.0964934 + 0.995334i \(0.469237\pi\)
\(150\) 0 0
\(151\) 3100.00 1.67069 0.835346 0.549725i \(-0.185267\pi\)
0.835346 + 0.549725i \(0.185267\pi\)
\(152\) 0 0
\(153\) −297.000 −0.156935
\(154\) 0 0
\(155\) 658.000 0.340980
\(156\) 0 0
\(157\) −2474.00 −1.25762 −0.628811 0.777558i \(-0.716458\pi\)
−0.628811 + 0.777558i \(0.716458\pi\)
\(158\) 0 0
\(159\) −510.000 −0.254375
\(160\) 0 0
\(161\) 2220.00 1.08671
\(162\) 0 0
\(163\) −2360.00 −1.13405 −0.567023 0.823702i \(-0.691905\pi\)
−0.567023 + 0.823702i \(0.691905\pi\)
\(164\) 0 0
\(165\) 1029.00 0.485500
\(166\) 0 0
\(167\) 1110.00 0.514338 0.257169 0.966366i \(-0.417210\pi\)
0.257169 + 0.966366i \(0.417210\pi\)
\(168\) 0 0
\(169\) −2001.00 −0.910787
\(170\) 0 0
\(171\) 171.000 0.0764719
\(172\) 0 0
\(173\) −258.000 −0.113384 −0.0566918 0.998392i \(-0.518055\pi\)
−0.0566918 + 0.998392i \(0.518055\pi\)
\(174\) 0 0
\(175\) −1140.00 −0.492434
\(176\) 0 0
\(177\) −36.0000 −0.0152877
\(178\) 0 0
\(179\) 3762.00 1.57087 0.785433 0.618946i \(-0.212440\pi\)
0.785433 + 0.618946i \(0.212440\pi\)
\(180\) 0 0
\(181\) 706.000 0.289926 0.144963 0.989437i \(-0.453694\pi\)
0.144963 + 0.989437i \(0.453694\pi\)
\(182\) 0 0
\(183\) −1257.00 −0.507760
\(184\) 0 0
\(185\) −1120.00 −0.445103
\(186\) 0 0
\(187\) −1617.00 −0.632336
\(188\) 0 0
\(189\) −405.000 −0.155870
\(190\) 0 0
\(191\) −2659.00 −1.00732 −0.503661 0.863901i \(-0.668014\pi\)
−0.503661 + 0.863901i \(0.668014\pi\)
\(192\) 0 0
\(193\) 3648.00 1.36056 0.680282 0.732951i \(-0.261857\pi\)
0.680282 + 0.732951i \(0.261857\pi\)
\(194\) 0 0
\(195\) 294.000 0.107968
\(196\) 0 0
\(197\) 494.000 0.178660 0.0893301 0.996002i \(-0.471527\pi\)
0.0893301 + 0.996002i \(0.471527\pi\)
\(198\) 0 0
\(199\) 3679.00 1.31054 0.655270 0.755395i \(-0.272555\pi\)
0.655270 + 0.755395i \(0.272555\pi\)
\(200\) 0 0
\(201\) 1332.00 0.467423
\(202\) 0 0
\(203\) −4170.00 −1.44176
\(204\) 0 0
\(205\) −2800.00 −0.953954
\(206\) 0 0
\(207\) 1332.00 0.447248
\(208\) 0 0
\(209\) 931.000 0.308127
\(210\) 0 0
\(211\) −792.000 −0.258405 −0.129203 0.991618i \(-0.541242\pi\)
−0.129203 + 0.991618i \(0.541242\pi\)
\(212\) 0 0
\(213\) −2856.00 −0.918732
\(214\) 0 0
\(215\) 511.000 0.162093
\(216\) 0 0
\(217\) −1410.00 −0.441092
\(218\) 0 0
\(219\) 81.0000 0.0249930
\(220\) 0 0
\(221\) −462.000 −0.140622
\(222\) 0 0
\(223\) 4636.00 1.39215 0.696075 0.717969i \(-0.254928\pi\)
0.696075 + 0.717969i \(0.254928\pi\)
\(224\) 0 0
\(225\) −684.000 −0.202667
\(226\) 0 0
\(227\) 6446.00 1.88474 0.942370 0.334572i \(-0.108592\pi\)
0.942370 + 0.334572i \(0.108592\pi\)
\(228\) 0 0
\(229\) 5765.00 1.66359 0.831795 0.555084i \(-0.187314\pi\)
0.831795 + 0.555084i \(0.187314\pi\)
\(230\) 0 0
\(231\) −2205.00 −0.628045
\(232\) 0 0
\(233\) −5847.00 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(234\) 0 0
\(235\) 1211.00 0.336157
\(236\) 0 0
\(237\) −1668.00 −0.457166
\(238\) 0 0
\(239\) −2823.00 −0.764036 −0.382018 0.924155i \(-0.624771\pi\)
−0.382018 + 0.924155i \(0.624771\pi\)
\(240\) 0 0
\(241\) −6140.00 −1.64113 −0.820565 0.571554i \(-0.806341\pi\)
−0.820565 + 0.571554i \(0.806341\pi\)
\(242\) 0 0
\(243\) −243.000 −0.0641500
\(244\) 0 0
\(245\) 826.000 0.215393
\(246\) 0 0
\(247\) 266.000 0.0685230
\(248\) 0 0
\(249\) −828.000 −0.210732
\(250\) 0 0
\(251\) 3103.00 0.780317 0.390159 0.920748i \(-0.372420\pi\)
0.390159 + 0.920748i \(0.372420\pi\)
\(252\) 0 0
\(253\) 7252.00 1.80209
\(254\) 0 0
\(255\) −693.000 −0.170186
\(256\) 0 0
\(257\) 2336.00 0.566987 0.283494 0.958974i \(-0.408507\pi\)
0.283494 + 0.958974i \(0.408507\pi\)
\(258\) 0 0
\(259\) 2400.00 0.575787
\(260\) 0 0
\(261\) −2502.00 −0.593371
\(262\) 0 0
\(263\) 2739.00 0.642182 0.321091 0.947048i \(-0.395950\pi\)
0.321091 + 0.947048i \(0.395950\pi\)
\(264\) 0 0
\(265\) −1190.00 −0.275853
\(266\) 0 0
\(267\) −4158.00 −0.953054
\(268\) 0 0
\(269\) −6486.00 −1.47011 −0.735053 0.678010i \(-0.762843\pi\)
−0.735053 + 0.678010i \(0.762843\pi\)
\(270\) 0 0
\(271\) 308.000 0.0690394 0.0345197 0.999404i \(-0.489010\pi\)
0.0345197 + 0.999404i \(0.489010\pi\)
\(272\) 0 0
\(273\) −630.000 −0.139668
\(274\) 0 0
\(275\) −3724.00 −0.816602
\(276\) 0 0
\(277\) 2977.00 0.645742 0.322871 0.946443i \(-0.395352\pi\)
0.322871 + 0.946443i \(0.395352\pi\)
\(278\) 0 0
\(279\) −846.000 −0.181537
\(280\) 0 0
\(281\) 4570.00 0.970190 0.485095 0.874462i \(-0.338785\pi\)
0.485095 + 0.874462i \(0.338785\pi\)
\(282\) 0 0
\(283\) −6429.00 −1.35040 −0.675202 0.737633i \(-0.735944\pi\)
−0.675202 + 0.737633i \(0.735944\pi\)
\(284\) 0 0
\(285\) 399.000 0.0829288
\(286\) 0 0
\(287\) 6000.00 1.23404
\(288\) 0 0
\(289\) −3824.00 −0.778343
\(290\) 0 0
\(291\) −390.000 −0.0785643
\(292\) 0 0
\(293\) 5724.00 1.14130 0.570648 0.821195i \(-0.306692\pi\)
0.570648 + 0.821195i \(0.306692\pi\)
\(294\) 0 0
\(295\) −84.0000 −0.0165785
\(296\) 0 0
\(297\) −1323.00 −0.258479
\(298\) 0 0
\(299\) 2072.00 0.400759
\(300\) 0 0
\(301\) −1095.00 −0.209684
\(302\) 0 0
\(303\) 714.000 0.135374
\(304\) 0 0
\(305\) −2933.00 −0.550633
\(306\) 0 0
\(307\) −8304.00 −1.54376 −0.771880 0.635768i \(-0.780683\pi\)
−0.771880 + 0.635768i \(0.780683\pi\)
\(308\) 0 0
\(309\) −4122.00 −0.758875
\(310\) 0 0
\(311\) 791.000 0.144223 0.0721117 0.997397i \(-0.477026\pi\)
0.0721117 + 0.997397i \(0.477026\pi\)
\(312\) 0 0
\(313\) 10166.0 1.83583 0.917917 0.396772i \(-0.129869\pi\)
0.917917 + 0.396772i \(0.129869\pi\)
\(314\) 0 0
\(315\) −945.000 −0.169031
\(316\) 0 0
\(317\) 6408.00 1.13536 0.567680 0.823249i \(-0.307841\pi\)
0.567680 + 0.823249i \(0.307841\pi\)
\(318\) 0 0
\(319\) −13622.0 −2.39086
\(320\) 0 0
\(321\) 654.000 0.113716
\(322\) 0 0
\(323\) −627.000 −0.108010
\(324\) 0 0
\(325\) −1064.00 −0.181600
\(326\) 0 0
\(327\) 6552.00 1.10803
\(328\) 0 0
\(329\) −2595.00 −0.434854
\(330\) 0 0
\(331\) −2576.00 −0.427764 −0.213882 0.976860i \(-0.568611\pi\)
−0.213882 + 0.976860i \(0.568611\pi\)
\(332\) 0 0
\(333\) 1440.00 0.236972
\(334\) 0 0
\(335\) 3108.00 0.506890
\(336\) 0 0
\(337\) −7922.00 −1.28053 −0.640265 0.768154i \(-0.721176\pi\)
−0.640265 + 0.768154i \(0.721176\pi\)
\(338\) 0 0
\(339\) −4002.00 −0.641176
\(340\) 0 0
\(341\) −4606.00 −0.731463
\(342\) 0 0
\(343\) −6915.00 −1.08856
\(344\) 0 0
\(345\) 3108.00 0.485012
\(346\) 0 0
\(347\) −2305.00 −0.356596 −0.178298 0.983977i \(-0.557059\pi\)
−0.178298 + 0.983977i \(0.557059\pi\)
\(348\) 0 0
\(349\) −4619.00 −0.708451 −0.354226 0.935160i \(-0.615255\pi\)
−0.354226 + 0.935160i \(0.615255\pi\)
\(350\) 0 0
\(351\) −378.000 −0.0574819
\(352\) 0 0
\(353\) 12366.0 1.86452 0.932260 0.361788i \(-0.117834\pi\)
0.932260 + 0.361788i \(0.117834\pi\)
\(354\) 0 0
\(355\) −6664.00 −0.996305
\(356\) 0 0
\(357\) 1485.00 0.220153
\(358\) 0 0
\(359\) 12417.0 1.82547 0.912736 0.408551i \(-0.133966\pi\)
0.912736 + 0.408551i \(0.133966\pi\)
\(360\) 0 0
\(361\) 361.000 0.0526316
\(362\) 0 0
\(363\) −3210.00 −0.464136
\(364\) 0 0
\(365\) 189.000 0.0271033
\(366\) 0 0
\(367\) −5776.00 −0.821539 −0.410769 0.911739i \(-0.634740\pi\)
−0.410769 + 0.911739i \(0.634740\pi\)
\(368\) 0 0
\(369\) 3600.00 0.507882
\(370\) 0 0
\(371\) 2550.00 0.356845
\(372\) 0 0
\(373\) 3392.00 0.470861 0.235430 0.971891i \(-0.424350\pi\)
0.235430 + 0.971891i \(0.424350\pi\)
\(374\) 0 0
\(375\) −4221.00 −0.581257
\(376\) 0 0
\(377\) −3892.00 −0.531693
\(378\) 0 0
\(379\) −5766.00 −0.781476 −0.390738 0.920502i \(-0.627780\pi\)
−0.390738 + 0.920502i \(0.627780\pi\)
\(380\) 0 0
\(381\) −1998.00 −0.268663
\(382\) 0 0
\(383\) −8482.00 −1.13162 −0.565809 0.824536i \(-0.691436\pi\)
−0.565809 + 0.824536i \(0.691436\pi\)
\(384\) 0 0
\(385\) −5145.00 −0.681074
\(386\) 0 0
\(387\) −657.000 −0.0862976
\(388\) 0 0
\(389\) −1983.00 −0.258463 −0.129231 0.991614i \(-0.541251\pi\)
−0.129231 + 0.991614i \(0.541251\pi\)
\(390\) 0 0
\(391\) −4884.00 −0.631699
\(392\) 0 0
\(393\) −909.000 −0.116674
\(394\) 0 0
\(395\) −3892.00 −0.495767
\(396\) 0 0
\(397\) −4555.00 −0.575841 −0.287921 0.957654i \(-0.592964\pi\)
−0.287921 + 0.957654i \(0.592964\pi\)
\(398\) 0 0
\(399\) −855.000 −0.107277
\(400\) 0 0
\(401\) −11624.0 −1.44757 −0.723784 0.690026i \(-0.757599\pi\)
−0.723784 + 0.690026i \(0.757599\pi\)
\(402\) 0 0
\(403\) −1316.00 −0.162667
\(404\) 0 0
\(405\) −567.000 −0.0695666
\(406\) 0 0
\(407\) 7840.00 0.954826
\(408\) 0 0
\(409\) −12446.0 −1.50468 −0.752341 0.658774i \(-0.771075\pi\)
−0.752341 + 0.658774i \(0.771075\pi\)
\(410\) 0 0
\(411\) −1749.00 −0.209907
\(412\) 0 0
\(413\) 180.000 0.0214461
\(414\) 0 0
\(415\) −1932.00 −0.228526
\(416\) 0 0
\(417\) −4401.00 −0.516829
\(418\) 0 0
\(419\) 468.000 0.0545663 0.0272832 0.999628i \(-0.491314\pi\)
0.0272832 + 0.999628i \(0.491314\pi\)
\(420\) 0 0
\(421\) −7894.00 −0.913848 −0.456924 0.889506i \(-0.651049\pi\)
−0.456924 + 0.889506i \(0.651049\pi\)
\(422\) 0 0
\(423\) −1557.00 −0.178969
\(424\) 0 0
\(425\) 2508.00 0.286249
\(426\) 0 0
\(427\) 6285.00 0.712301
\(428\) 0 0
\(429\) −2058.00 −0.231611
\(430\) 0 0
\(431\) 9234.00 1.03199 0.515993 0.856593i \(-0.327423\pi\)
0.515993 + 0.856593i \(0.327423\pi\)
\(432\) 0 0
\(433\) 9842.00 1.09232 0.546162 0.837680i \(-0.316088\pi\)
0.546162 + 0.837680i \(0.316088\pi\)
\(434\) 0 0
\(435\) −5838.00 −0.643473
\(436\) 0 0
\(437\) 2812.00 0.307817
\(438\) 0 0
\(439\) 10966.0 1.19221 0.596103 0.802908i \(-0.296715\pi\)
0.596103 + 0.802908i \(0.296715\pi\)
\(440\) 0 0
\(441\) −1062.00 −0.114674
\(442\) 0 0
\(443\) 8795.00 0.943257 0.471629 0.881797i \(-0.343666\pi\)
0.471629 + 0.881797i \(0.343666\pi\)
\(444\) 0 0
\(445\) −9702.00 −1.03353
\(446\) 0 0
\(447\) −1053.00 −0.111421
\(448\) 0 0
\(449\) 2476.00 0.260244 0.130122 0.991498i \(-0.458463\pi\)
0.130122 + 0.991498i \(0.458463\pi\)
\(450\) 0 0
\(451\) 19600.0 2.04640
\(452\) 0 0
\(453\) −9300.00 −0.964574
\(454\) 0 0
\(455\) −1470.00 −0.151461
\(456\) 0 0
\(457\) −13837.0 −1.41634 −0.708170 0.706042i \(-0.750479\pi\)
−0.708170 + 0.706042i \(0.750479\pi\)
\(458\) 0 0
\(459\) 891.000 0.0906064
\(460\) 0 0
\(461\) 407.000 0.0411190 0.0205595 0.999789i \(-0.493455\pi\)
0.0205595 + 0.999789i \(0.493455\pi\)
\(462\) 0 0
\(463\) 17741.0 1.78076 0.890382 0.455213i \(-0.150437\pi\)
0.890382 + 0.455213i \(0.150437\pi\)
\(464\) 0 0
\(465\) −1974.00 −0.196865
\(466\) 0 0
\(467\) −16765.0 −1.66122 −0.830612 0.556851i \(-0.812009\pi\)
−0.830612 + 0.556851i \(0.812009\pi\)
\(468\) 0 0
\(469\) −6660.00 −0.655715
\(470\) 0 0
\(471\) 7422.00 0.726089
\(472\) 0 0
\(473\) −3577.00 −0.347718
\(474\) 0 0
\(475\) −1444.00 −0.139485
\(476\) 0 0
\(477\) 1530.00 0.146863
\(478\) 0 0
\(479\) 824.000 0.0786003 0.0393001 0.999227i \(-0.487487\pi\)
0.0393001 + 0.999227i \(0.487487\pi\)
\(480\) 0 0
\(481\) 2240.00 0.212339
\(482\) 0 0
\(483\) −6660.00 −0.627413
\(484\) 0 0
\(485\) −910.000 −0.0851979
\(486\) 0 0
\(487\) 668.000 0.0621560 0.0310780 0.999517i \(-0.490106\pi\)
0.0310780 + 0.999517i \(0.490106\pi\)
\(488\) 0 0
\(489\) 7080.00 0.654742
\(490\) 0 0
\(491\) −15080.0 −1.38605 −0.693025 0.720913i \(-0.743723\pi\)
−0.693025 + 0.720913i \(0.743723\pi\)
\(492\) 0 0
\(493\) 9174.00 0.838086
\(494\) 0 0
\(495\) −3087.00 −0.280304
\(496\) 0 0
\(497\) 14280.0 1.28882
\(498\) 0 0
\(499\) −10915.0 −0.979203 −0.489602 0.871946i \(-0.662858\pi\)
−0.489602 + 0.871946i \(0.662858\pi\)
\(500\) 0 0
\(501\) −3330.00 −0.296953
\(502\) 0 0
\(503\) 16728.0 1.48283 0.741416 0.671046i \(-0.234154\pi\)
0.741416 + 0.671046i \(0.234154\pi\)
\(504\) 0 0
\(505\) 1666.00 0.146804
\(506\) 0 0
\(507\) 6003.00 0.525843
\(508\) 0 0
\(509\) 17754.0 1.54604 0.773018 0.634384i \(-0.218746\pi\)
0.773018 + 0.634384i \(0.218746\pi\)
\(510\) 0 0
\(511\) −405.000 −0.0350609
\(512\) 0 0
\(513\) −513.000 −0.0441511
\(514\) 0 0
\(515\) −9618.00 −0.822951
\(516\) 0 0
\(517\) −8477.00 −0.721118
\(518\) 0 0
\(519\) 774.000 0.0654621
\(520\) 0 0
\(521\) −2584.00 −0.217288 −0.108644 0.994081i \(-0.534651\pi\)
−0.108644 + 0.994081i \(0.534651\pi\)
\(522\) 0 0
\(523\) 2158.00 0.180426 0.0902130 0.995922i \(-0.471245\pi\)
0.0902130 + 0.995922i \(0.471245\pi\)
\(524\) 0 0
\(525\) 3420.00 0.284307
\(526\) 0 0
\(527\) 3102.00 0.256405
\(528\) 0 0
\(529\) 9737.00 0.800279
\(530\) 0 0
\(531\) 108.000 0.00882637
\(532\) 0 0
\(533\) 5600.00 0.455090
\(534\) 0 0
\(535\) 1526.00 0.123317
\(536\) 0 0
\(537\) −11286.0 −0.906940
\(538\) 0 0
\(539\) −5782.00 −0.462056
\(540\) 0 0
\(541\) −14137.0 −1.12347 −0.561735 0.827317i \(-0.689866\pi\)
−0.561735 + 0.827317i \(0.689866\pi\)
\(542\) 0 0
\(543\) −2118.00 −0.167389
\(544\) 0 0
\(545\) 15288.0 1.20159
\(546\) 0 0
\(547\) −10222.0 −0.799015 −0.399507 0.916730i \(-0.630819\pi\)
−0.399507 + 0.916730i \(0.630819\pi\)
\(548\) 0 0
\(549\) 3771.00 0.293155
\(550\) 0 0
\(551\) −5282.00 −0.408386
\(552\) 0 0
\(553\) 8340.00 0.641325
\(554\) 0 0
\(555\) 3360.00 0.256980
\(556\) 0 0
\(557\) 10387.0 0.790146 0.395073 0.918650i \(-0.370719\pi\)
0.395073 + 0.918650i \(0.370719\pi\)
\(558\) 0 0
\(559\) −1022.00 −0.0773274
\(560\) 0 0
\(561\) 4851.00 0.365079
\(562\) 0 0
\(563\) 10404.0 0.778821 0.389411 0.921064i \(-0.372679\pi\)
0.389411 + 0.921064i \(0.372679\pi\)
\(564\) 0 0
\(565\) −9338.00 −0.695314
\(566\) 0 0
\(567\) 1215.00 0.0899915
\(568\) 0 0
\(569\) 4258.00 0.313716 0.156858 0.987621i \(-0.449863\pi\)
0.156858 + 0.987621i \(0.449863\pi\)
\(570\) 0 0
\(571\) −6440.00 −0.471989 −0.235994 0.971754i \(-0.575835\pi\)
−0.235994 + 0.971754i \(0.575835\pi\)
\(572\) 0 0
\(573\) 7977.00 0.581578
\(574\) 0 0
\(575\) −11248.0 −0.815781
\(576\) 0 0
\(577\) −14869.0 −1.07280 −0.536399 0.843964i \(-0.680216\pi\)
−0.536399 + 0.843964i \(0.680216\pi\)
\(578\) 0 0
\(579\) −10944.0 −0.785522
\(580\) 0 0
\(581\) 4140.00 0.295622
\(582\) 0 0
\(583\) 8330.00 0.591755
\(584\) 0 0
\(585\) −882.000 −0.0623354
\(586\) 0 0
\(587\) −1041.00 −0.0731970 −0.0365985 0.999330i \(-0.511652\pi\)
−0.0365985 + 0.999330i \(0.511652\pi\)
\(588\) 0 0
\(589\) −1786.00 −0.124942
\(590\) 0 0
\(591\) −1482.00 −0.103149
\(592\) 0 0
\(593\) −15662.0 −1.08459 −0.542294 0.840188i \(-0.682444\pi\)
−0.542294 + 0.840188i \(0.682444\pi\)
\(594\) 0 0
\(595\) 3465.00 0.238741
\(596\) 0 0
\(597\) −11037.0 −0.756640
\(598\) 0 0
\(599\) −18900.0 −1.28920 −0.644602 0.764518i \(-0.722977\pi\)
−0.644602 + 0.764518i \(0.722977\pi\)
\(600\) 0 0
\(601\) 6100.00 0.414017 0.207008 0.978339i \(-0.433627\pi\)
0.207008 + 0.978339i \(0.433627\pi\)
\(602\) 0 0
\(603\) −3996.00 −0.269867
\(604\) 0 0
\(605\) −7490.00 −0.503325
\(606\) 0 0
\(607\) 5902.00 0.394654 0.197327 0.980338i \(-0.436774\pi\)
0.197327 + 0.980338i \(0.436774\pi\)
\(608\) 0 0
\(609\) 12510.0 0.832399
\(610\) 0 0
\(611\) −2422.00 −0.160366
\(612\) 0 0
\(613\) 15901.0 1.04769 0.523846 0.851813i \(-0.324497\pi\)
0.523846 + 0.851813i \(0.324497\pi\)
\(614\) 0 0
\(615\) 8400.00 0.550765
\(616\) 0 0
\(617\) −30429.0 −1.98545 −0.992727 0.120385i \(-0.961587\pi\)
−0.992727 + 0.120385i \(0.961587\pi\)
\(618\) 0 0
\(619\) 22484.0 1.45995 0.729974 0.683475i \(-0.239532\pi\)
0.729974 + 0.683475i \(0.239532\pi\)
\(620\) 0 0
\(621\) −3996.00 −0.258219
\(622\) 0 0
\(623\) 20790.0 1.33697
\(624\) 0 0
\(625\) −349.000 −0.0223360
\(626\) 0 0
\(627\) −2793.00 −0.177897
\(628\) 0 0
\(629\) −5280.00 −0.334702
\(630\) 0 0
\(631\) −29885.0 −1.88542 −0.942712 0.333607i \(-0.891734\pi\)
−0.942712 + 0.333607i \(0.891734\pi\)
\(632\) 0 0
\(633\) 2376.00 0.149190
\(634\) 0 0
\(635\) −4662.00 −0.291348
\(636\) 0 0
\(637\) −1652.00 −0.102755
\(638\) 0 0
\(639\) 8568.00 0.530430
\(640\) 0 0
\(641\) 4038.00 0.248817 0.124408 0.992231i \(-0.460297\pi\)
0.124408 + 0.992231i \(0.460297\pi\)
\(642\) 0 0
\(643\) −19993.0 −1.22620 −0.613100 0.790005i \(-0.710078\pi\)
−0.613100 + 0.790005i \(0.710078\pi\)
\(644\) 0 0
\(645\) −1533.00 −0.0935842
\(646\) 0 0
\(647\) 17077.0 1.03766 0.518830 0.854877i \(-0.326368\pi\)
0.518830 + 0.854877i \(0.326368\pi\)
\(648\) 0 0
\(649\) 588.000 0.0355640
\(650\) 0 0
\(651\) 4230.00 0.254665
\(652\) 0 0
\(653\) 17631.0 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) 0 0
\(655\) −2121.00 −0.126526
\(656\) 0 0
\(657\) −243.000 −0.0144297
\(658\) 0 0
\(659\) −12014.0 −0.710165 −0.355083 0.934835i \(-0.615547\pi\)
−0.355083 + 0.934835i \(0.615547\pi\)
\(660\) 0 0
\(661\) 10852.0 0.638569 0.319284 0.947659i \(-0.396558\pi\)
0.319284 + 0.947659i \(0.396558\pi\)
\(662\) 0 0
\(663\) 1386.00 0.0811882
\(664\) 0 0
\(665\) −1995.00 −0.116335
\(666\) 0 0
\(667\) −41144.0 −2.38846
\(668\) 0 0
\(669\) −13908.0 −0.803758
\(670\) 0 0
\(671\) 20531.0 1.18121
\(672\) 0 0
\(673\) −1708.00 −0.0978285 −0.0489142 0.998803i \(-0.515576\pi\)
−0.0489142 + 0.998803i \(0.515576\pi\)
\(674\) 0 0
\(675\) 2052.00 0.117010
\(676\) 0 0
\(677\) 17902.0 1.01629 0.508146 0.861271i \(-0.330331\pi\)
0.508146 + 0.861271i \(0.330331\pi\)
\(678\) 0 0
\(679\) 1950.00 0.110212
\(680\) 0 0
\(681\) −19338.0 −1.08816
\(682\) 0 0
\(683\) −2938.00 −0.164597 −0.0822983 0.996608i \(-0.526226\pi\)
−0.0822983 + 0.996608i \(0.526226\pi\)
\(684\) 0 0
\(685\) −4081.00 −0.227631
\(686\) 0 0
\(687\) −17295.0 −0.960474
\(688\) 0 0
\(689\) 2380.00 0.131598
\(690\) 0 0
\(691\) −519.000 −0.0285726 −0.0142863 0.999898i \(-0.504548\pi\)
−0.0142863 + 0.999898i \(0.504548\pi\)
\(692\) 0 0
\(693\) 6615.00 0.362602
\(694\) 0 0
\(695\) −10269.0 −0.560468
\(696\) 0 0
\(697\) −13200.0 −0.717340
\(698\) 0 0
\(699\) 17541.0 0.949158
\(700\) 0 0
\(701\) −4942.00 −0.266272 −0.133136 0.991098i \(-0.542505\pi\)
−0.133136 + 0.991098i \(0.542505\pi\)
\(702\) 0 0
\(703\) 3040.00 0.163095
\(704\) 0 0
\(705\) −3633.00 −0.194080
\(706\) 0 0
\(707\) −3570.00 −0.189906
\(708\) 0 0
\(709\) 19302.0 1.02243 0.511214 0.859453i \(-0.329196\pi\)
0.511214 + 0.859453i \(0.329196\pi\)
\(710\) 0 0
\(711\) 5004.00 0.263945
\(712\) 0 0
\(713\) −13912.0 −0.730727
\(714\) 0 0
\(715\) −4802.00 −0.251167
\(716\) 0 0
\(717\) 8469.00 0.441117
\(718\) 0 0
\(719\) 22973.0 1.19158 0.595792 0.803139i \(-0.296838\pi\)
0.595792 + 0.803139i \(0.296838\pi\)
\(720\) 0 0
\(721\) 20610.0 1.06457
\(722\) 0 0
\(723\) 18420.0 0.947506
\(724\) 0 0
\(725\) 21128.0 1.08231
\(726\) 0 0
\(727\) 32429.0 1.65437 0.827184 0.561932i \(-0.189942\pi\)
0.827184 + 0.561932i \(0.189942\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 2409.00 0.121888
\(732\) 0 0
\(733\) 2682.00 0.135146 0.0675729 0.997714i \(-0.478474\pi\)
0.0675729 + 0.997714i \(0.478474\pi\)
\(734\) 0 0
\(735\) −2478.00 −0.124357
\(736\) 0 0
\(737\) −21756.0 −1.08737
\(738\) 0 0
\(739\) 15835.0 0.788227 0.394114 0.919062i \(-0.371052\pi\)
0.394114 + 0.919062i \(0.371052\pi\)
\(740\) 0 0
\(741\) −798.000 −0.0395618
\(742\) 0 0
\(743\) 16876.0 0.833271 0.416636 0.909074i \(-0.363209\pi\)
0.416636 + 0.909074i \(0.363209\pi\)
\(744\) 0 0
\(745\) −2457.00 −0.120829
\(746\) 0 0
\(747\) 2484.00 0.121666
\(748\) 0 0
\(749\) −3270.00 −0.159524
\(750\) 0 0
\(751\) 35296.0 1.71501 0.857503 0.514479i \(-0.172015\pi\)
0.857503 + 0.514479i \(0.172015\pi\)
\(752\) 0 0
\(753\) −9309.00 −0.450516
\(754\) 0 0
\(755\) −21700.0 −1.04602
\(756\) 0 0
\(757\) 18259.0 0.876664 0.438332 0.898813i \(-0.355569\pi\)
0.438332 + 0.898813i \(0.355569\pi\)
\(758\) 0 0
\(759\) −21756.0 −1.04044
\(760\) 0 0
\(761\) 13455.0 0.640924 0.320462 0.947261i \(-0.396162\pi\)
0.320462 + 0.947261i \(0.396162\pi\)
\(762\) 0 0
\(763\) −32760.0 −1.55438
\(764\) 0 0
\(765\) 2079.00 0.0982567
\(766\) 0 0
\(767\) 168.000 0.00790890
\(768\) 0 0
\(769\) −16061.0 −0.753153 −0.376576 0.926386i \(-0.622899\pi\)
−0.376576 + 0.926386i \(0.622899\pi\)
\(770\) 0 0
\(771\) −7008.00 −0.327350
\(772\) 0 0
\(773\) 4680.00 0.217759 0.108880 0.994055i \(-0.465274\pi\)
0.108880 + 0.994055i \(0.465274\pi\)
\(774\) 0 0
\(775\) 7144.00 0.331123
\(776\) 0 0
\(777\) −7200.00 −0.332431
\(778\) 0 0
\(779\) 7600.00 0.349548
\(780\) 0 0
\(781\) 46648.0 2.13726
\(782\) 0 0
\(783\) 7506.00 0.342583
\(784\) 0 0
\(785\) 17318.0 0.787396
\(786\) 0 0
\(787\) 37760.0 1.71029 0.855145 0.518388i \(-0.173468\pi\)
0.855145 + 0.518388i \(0.173468\pi\)
\(788\) 0 0
\(789\) −8217.00 −0.370764
\(790\) 0 0
\(791\) 20010.0 0.899461
\(792\) 0 0
\(793\) 5866.00 0.262683
\(794\) 0 0
\(795\) 3570.00 0.159264
\(796\) 0 0
\(797\) 22008.0 0.978122 0.489061 0.872250i \(-0.337340\pi\)
0.489061 + 0.872250i \(0.337340\pi\)
\(798\) 0 0
\(799\) 5709.00 0.252778
\(800\) 0 0
\(801\) 12474.0 0.550246
\(802\) 0 0
\(803\) −1323.00 −0.0581415
\(804\) 0 0
\(805\) −15540.0 −0.680389
\(806\) 0 0
\(807\) 19458.0 0.848766
\(808\) 0 0
\(809\) −12615.0 −0.548232 −0.274116 0.961697i \(-0.588385\pi\)
−0.274116 + 0.961697i \(0.588385\pi\)
\(810\) 0 0
\(811\) −45402.0 −1.96582 −0.982910 0.184087i \(-0.941067\pi\)
−0.982910 + 0.184087i \(0.941067\pi\)
\(812\) 0 0
\(813\) −924.000 −0.0398599
\(814\) 0 0
\(815\) 16520.0 0.710025
\(816\) 0 0
\(817\) −1387.00 −0.0593941
\(818\) 0 0
\(819\) 1890.00 0.0806373
\(820\) 0 0
\(821\) 1335.00 0.0567501 0.0283750 0.999597i \(-0.490967\pi\)
0.0283750 + 0.999597i \(0.490967\pi\)
\(822\) 0 0
\(823\) 559.000 0.0236762 0.0118381 0.999930i \(-0.496232\pi\)
0.0118381 + 0.999930i \(0.496232\pi\)
\(824\) 0 0
\(825\) 11172.0 0.471466
\(826\) 0 0
\(827\) −13856.0 −0.582612 −0.291306 0.956630i \(-0.594090\pi\)
−0.291306 + 0.956630i \(0.594090\pi\)
\(828\) 0 0
\(829\) 18228.0 0.763673 0.381836 0.924230i \(-0.375292\pi\)
0.381836 + 0.924230i \(0.375292\pi\)
\(830\) 0 0
\(831\) −8931.00 −0.372819
\(832\) 0 0
\(833\) 3894.00 0.161968
\(834\) 0 0
\(835\) −7770.00 −0.322026
\(836\) 0 0
\(837\) 2538.00 0.104810
\(838\) 0 0
\(839\) 13414.0 0.551970 0.275985 0.961162i \(-0.410996\pi\)
0.275985 + 0.961162i \(0.410996\pi\)
\(840\) 0 0
\(841\) 52895.0 2.16881
\(842\) 0 0
\(843\) −13710.0 −0.560139
\(844\) 0 0
\(845\) 14007.0 0.570243
\(846\) 0 0
\(847\) 16050.0 0.651103
\(848\) 0 0
\(849\) 19287.0 0.779656
\(850\) 0 0
\(851\) 23680.0 0.953866
\(852\) 0 0
\(853\) −44718.0 −1.79498 −0.897488 0.441038i \(-0.854610\pi\)
−0.897488 + 0.441038i \(0.854610\pi\)
\(854\) 0 0
\(855\) −1197.00 −0.0478790
\(856\) 0 0
\(857\) −33924.0 −1.35218 −0.676092 0.736817i \(-0.736328\pi\)
−0.676092 + 0.736817i \(0.736328\pi\)
\(858\) 0 0
\(859\) 16427.0 0.652482 0.326241 0.945287i \(-0.394218\pi\)
0.326241 + 0.945287i \(0.394218\pi\)
\(860\) 0 0
\(861\) −18000.0 −0.712472
\(862\) 0 0
\(863\) −23292.0 −0.918736 −0.459368 0.888246i \(-0.651924\pi\)
−0.459368 + 0.888246i \(0.651924\pi\)
\(864\) 0 0
\(865\) 1806.00 0.0709894
\(866\) 0 0
\(867\) 11472.0 0.449377
\(868\) 0 0
\(869\) 27244.0 1.06351
\(870\) 0 0
\(871\) −6216.00 −0.241815
\(872\) 0 0
\(873\) 1170.00 0.0453591
\(874\) 0 0
\(875\) 21105.0 0.815405
\(876\) 0 0
\(877\) −43598.0 −1.67868 −0.839339 0.543609i \(-0.817057\pi\)
−0.839339 + 0.543609i \(0.817057\pi\)
\(878\) 0 0
\(879\) −17172.0 −0.658927
\(880\) 0 0
\(881\) 39123.0 1.49613 0.748063 0.663627i \(-0.230984\pi\)
0.748063 + 0.663627i \(0.230984\pi\)
\(882\) 0 0
\(883\) 4115.00 0.156830 0.0784149 0.996921i \(-0.475014\pi\)
0.0784149 + 0.996921i \(0.475014\pi\)
\(884\) 0 0
\(885\) 252.000 0.00957162
\(886\) 0 0
\(887\) −13384.0 −0.506641 −0.253321 0.967382i \(-0.581523\pi\)
−0.253321 + 0.967382i \(0.581523\pi\)
\(888\) 0 0
\(889\) 9990.00 0.376888
\(890\) 0 0
\(891\) 3969.00 0.149233
\(892\) 0 0
\(893\) −3287.00 −0.123175
\(894\) 0 0
\(895\) −26334.0 −0.983518
\(896\) 0 0
\(897\) −6216.00 −0.231378
\(898\) 0 0
\(899\) 26132.0 0.969467
\(900\) 0 0
\(901\) −5610.00 −0.207432
\(902\) 0 0
\(903\) 3285.00 0.121061
\(904\) 0 0
\(905\) −4942.00 −0.181522
\(906\) 0 0
\(907\) 36718.0 1.34421 0.672106 0.740454i \(-0.265390\pi\)
0.672106 + 0.740454i \(0.265390\pi\)
\(908\) 0 0
\(909\) −2142.00 −0.0781580
\(910\) 0 0
\(911\) −46614.0 −1.69527 −0.847635 0.530580i \(-0.821974\pi\)
−0.847635 + 0.530580i \(0.821974\pi\)
\(912\) 0 0
\(913\) 13524.0 0.490229
\(914\) 0 0
\(915\) 8799.00 0.317908
\(916\) 0 0
\(917\) 4545.00 0.163674
\(918\) 0 0
\(919\) −11192.0 −0.401730 −0.200865 0.979619i \(-0.564375\pi\)
−0.200865 + 0.979619i \(0.564375\pi\)
\(920\) 0 0
\(921\) 24912.0 0.891290
\(922\) 0 0
\(923\) 13328.0 0.475294
\(924\) 0 0
\(925\) −12160.0 −0.432236
\(926\) 0 0
\(927\) 12366.0 0.438137
\(928\) 0 0
\(929\) 542.000 0.0191415 0.00957074 0.999954i \(-0.496953\pi\)
0.00957074 + 0.999954i \(0.496953\pi\)
\(930\) 0 0
\(931\) −2242.00 −0.0789244
\(932\) 0 0
\(933\) −2373.00 −0.0832675
\(934\) 0 0
\(935\) 11319.0 0.395905
\(936\) 0 0
\(937\) 39053.0 1.36159 0.680793 0.732476i \(-0.261635\pi\)
0.680793 + 0.732476i \(0.261635\pi\)
\(938\) 0 0
\(939\) −30498.0 −1.05992
\(940\) 0 0
\(941\) −33398.0 −1.15701 −0.578504 0.815680i \(-0.696363\pi\)
−0.578504 + 0.815680i \(0.696363\pi\)
\(942\) 0 0
\(943\) 59200.0 2.04434
\(944\) 0 0
\(945\) 2835.00 0.0975900
\(946\) 0 0
\(947\) 54084.0 1.85585 0.927927 0.372762i \(-0.121589\pi\)
0.927927 + 0.372762i \(0.121589\pi\)
\(948\) 0 0
\(949\) −378.000 −0.0129298
\(950\) 0 0
\(951\) −19224.0 −0.655500
\(952\) 0 0
\(953\) −30484.0 −1.03617 −0.518087 0.855328i \(-0.673356\pi\)
−0.518087 + 0.855328i \(0.673356\pi\)
\(954\) 0 0
\(955\) 18613.0 0.630683
\(956\) 0 0
\(957\) 40866.0 1.38037
\(958\) 0 0
\(959\) 8745.00 0.294464
\(960\) 0 0
\(961\) −20955.0 −0.703400
\(962\) 0 0
\(963\) −1962.00 −0.0656538
\(964\) 0 0
\(965\) −25536.0 −0.851848
\(966\) 0 0
\(967\) −13584.0 −0.451739 −0.225870 0.974158i \(-0.572522\pi\)
−0.225870 + 0.974158i \(0.572522\pi\)
\(968\) 0 0
\(969\) 1881.00 0.0623596
\(970\) 0 0
\(971\) −43892.0 −1.45063 −0.725315 0.688417i \(-0.758306\pi\)
−0.725315 + 0.688417i \(0.758306\pi\)
\(972\) 0 0
\(973\) 22005.0 0.725024
\(974\) 0 0
\(975\) 3192.00 0.104847
\(976\) 0 0
\(977\) 30542.0 1.00013 0.500064 0.865988i \(-0.333310\pi\)
0.500064 + 0.865988i \(0.333310\pi\)
\(978\) 0 0
\(979\) 67914.0 2.21710
\(980\) 0 0
\(981\) −19656.0 −0.639723
\(982\) 0 0
\(983\) 2868.00 0.0930570 0.0465285 0.998917i \(-0.485184\pi\)
0.0465285 + 0.998917i \(0.485184\pi\)
\(984\) 0 0
\(985\) −3458.00 −0.111859
\(986\) 0 0
\(987\) 7785.00 0.251063
\(988\) 0 0
\(989\) −10804.0 −0.347368
\(990\) 0 0
\(991\) 23696.0 0.759564 0.379782 0.925076i \(-0.375999\pi\)
0.379782 + 0.925076i \(0.375999\pi\)
\(992\) 0 0
\(993\) 7728.00 0.246969
\(994\) 0 0
\(995\) −25753.0 −0.820528
\(996\) 0 0
\(997\) −46811.0 −1.48698 −0.743490 0.668747i \(-0.766831\pi\)
−0.743490 + 0.668747i \(0.766831\pi\)
\(998\) 0 0
\(999\) −4320.00 −0.136816
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 912.4.a.b.1.1 1
4.3 odd 2 114.4.a.b.1.1 1
12.11 even 2 342.4.a.c.1.1 1
76.75 even 2 2166.4.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.4.a.b.1.1 1 4.3 odd 2
342.4.a.c.1.1 1 12.11 even 2
912.4.a.b.1.1 1 1.1 even 1 trivial
2166.4.a.d.1.1 1 76.75 even 2