Properties

Label 8550.2.a.cp.1.1
Level $8550$
Weight $2$
Character 8550.1
Self dual yes
Analytic conductor $68.272$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8550.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(68.2720937282\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.993.1
Defining polynomial: \(x^{3} - x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.480031\) of defining polynomial
Character \(\chi\) \(=\) 8550.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.76957 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} -4.76957 q^{7} +1.00000 q^{8} -0.960061 q^{11} -2.24960 q^{13} -4.76957 q^{14} +1.00000 q^{16} -0.249601 q^{17} +1.00000 q^{19} -0.960061 q^{22} -9.01917 q^{23} -2.24960 q^{26} -4.76957 q^{28} -6.24960 q^{29} +2.96006 q^{31} +1.00000 q^{32} -0.249601 q^{34} +0.0399387 q^{37} +1.00000 q^{38} +4.96006 q^{43} -0.960061 q^{44} -9.01917 q^{46} +9.49920 q^{47} +15.7488 q^{49} -2.24960 q^{52} -6.84945 q^{53} -4.76957 q^{56} -6.24960 q^{58} +14.5583 q^{59} +7.53914 q^{61} +2.96006 q^{62} +1.00000 q^{64} -5.72963 q^{67} -0.249601 q^{68} +9.61902 q^{71} +12.0591 q^{73} +0.0399387 q^{74} +1.00000 q^{76} +4.57908 q^{77} +6.07988 q^{79} +7.45926 q^{83} +4.96006 q^{86} -0.960061 q^{88} -4.07988 q^{89} +10.7296 q^{91} -9.01917 q^{92} +9.49920 q^{94} +18.4193 q^{97} +15.7488 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + 3q^{4} - 2q^{7} + 3q^{8} + O(q^{10}) \) \( 3q + 3q^{2} + 3q^{4} - 2q^{7} + 3q^{8} - 2q^{11} + 6q^{13} - 2q^{14} + 3q^{16} + 12q^{17} + 3q^{19} - 2q^{22} - 2q^{23} + 6q^{26} - 2q^{28} - 6q^{29} + 8q^{31} + 3q^{32} + 12q^{34} + q^{37} + 3q^{38} + 14q^{43} - 2q^{44} - 2q^{46} + 3q^{47} + 9q^{49} + 6q^{52} - 10q^{53} - 2q^{56} - 6q^{58} - 6q^{59} - 2q^{61} + 8q^{62} + 3q^{64} - 4q^{67} + 12q^{68} + 6q^{71} + 12q^{73} + q^{74} + 3q^{76} - 10q^{77} + 20q^{79} - 4q^{83} + 14q^{86} - 2q^{88} - 14q^{89} + 19q^{91} - 2q^{92} + 3q^{94} + 28q^{97} + 9q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) −4.76957 −1.80273 −0.901364 0.433062i \(-0.857433\pi\)
−0.901364 + 0.433062i \(0.857433\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −0.960061 −0.289469 −0.144735 0.989471i \(-0.546233\pi\)
−0.144735 + 0.989471i \(0.546233\pi\)
\(12\) 0 0
\(13\) −2.24960 −0.623927 −0.311964 0.950094i \(-0.600987\pi\)
−0.311964 + 0.950094i \(0.600987\pi\)
\(14\) −4.76957 −1.27472
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.249601 −0.0605372 −0.0302686 0.999542i \(-0.509636\pi\)
−0.0302686 + 0.999542i \(0.509636\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) −0.960061 −0.204686
\(23\) −9.01917 −1.88063 −0.940314 0.340309i \(-0.889468\pi\)
−0.940314 + 0.340309i \(0.889468\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.24960 −0.441183
\(27\) 0 0
\(28\) −4.76957 −0.901364
\(29\) −6.24960 −1.16052 −0.580261 0.814431i \(-0.697049\pi\)
−0.580261 + 0.814431i \(0.697049\pi\)
\(30\) 0 0
\(31\) 2.96006 0.531643 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −0.249601 −0.0428063
\(35\) 0 0
\(36\) 0 0
\(37\) 0.0399387 0.00656589 0.00328294 0.999995i \(-0.498955\pi\)
0.00328294 + 0.999995i \(0.498955\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 4.96006 0.756402 0.378201 0.925723i \(-0.376543\pi\)
0.378201 + 0.925723i \(0.376543\pi\)
\(44\) −0.960061 −0.144735
\(45\) 0 0
\(46\) −9.01917 −1.32980
\(47\) 9.49920 1.38560 0.692801 0.721129i \(-0.256377\pi\)
0.692801 + 0.721129i \(0.256377\pi\)
\(48\) 0 0
\(49\) 15.7488 2.24983
\(50\) 0 0
\(51\) 0 0
\(52\) −2.24960 −0.311964
\(53\) −6.84945 −0.940844 −0.470422 0.882442i \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.76957 −0.637361
\(57\) 0 0
\(58\) −6.24960 −0.820613
\(59\) 14.5583 1.89533 0.947665 0.319265i \(-0.103436\pi\)
0.947665 + 0.319265i \(0.103436\pi\)
\(60\) 0 0
\(61\) 7.53914 0.965288 0.482644 0.875817i \(-0.339676\pi\)
0.482644 + 0.875817i \(0.339676\pi\)
\(62\) 2.96006 0.375928
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.72963 −0.699986 −0.349993 0.936752i \(-0.613816\pi\)
−0.349993 + 0.936752i \(0.613816\pi\)
\(68\) −0.249601 −0.0302686
\(69\) 0 0
\(70\) 0 0
\(71\) 9.61902 1.14157 0.570784 0.821100i \(-0.306639\pi\)
0.570784 + 0.821100i \(0.306639\pi\)
\(72\) 0 0
\(73\) 12.0591 1.41141 0.705706 0.708505i \(-0.250630\pi\)
0.705706 + 0.708505i \(0.250630\pi\)
\(74\) 0.0399387 0.00464278
\(75\) 0 0
\(76\) 1.00000 0.114708
\(77\) 4.57908 0.521835
\(78\) 0 0
\(79\) 6.07988 0.684040 0.342020 0.939693i \(-0.388889\pi\)
0.342020 + 0.939693i \(0.388889\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.45926 0.818761 0.409380 0.912364i \(-0.365745\pi\)
0.409380 + 0.912364i \(0.365745\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.96006 0.534857
\(87\) 0 0
\(88\) −0.960061 −0.102343
\(89\) −4.07988 −0.432466 −0.216233 0.976342i \(-0.569377\pi\)
−0.216233 + 0.976342i \(0.569377\pi\)
\(90\) 0 0
\(91\) 10.7296 1.12477
\(92\) −9.01917 −0.940314
\(93\) 0 0
\(94\) 9.49920 0.979768
\(95\) 0 0
\(96\) 0 0
\(97\) 18.4193 1.87020 0.935100 0.354385i \(-0.115310\pi\)
0.935100 + 0.354385i \(0.115310\pi\)
\(98\) 15.7488 1.59087
\(99\) 0 0
\(100\) 0 0
\(101\) −5.53914 −0.551165 −0.275583 0.961277i \(-0.588871\pi\)
−0.275583 + 0.961277i \(0.588871\pi\)
\(102\) 0 0
\(103\) −6.57908 −0.648256 −0.324128 0.946013i \(-0.605071\pi\)
−0.324128 + 0.946013i \(0.605071\pi\)
\(104\) −2.24960 −0.220592
\(105\) 0 0
\(106\) −6.84945 −0.665277
\(107\) −14.9086 −1.44126 −0.720632 0.693317i \(-0.756148\pi\)
−0.720632 + 0.693317i \(0.756148\pi\)
\(108\) 0 0
\(109\) 4.76957 0.456842 0.228421 0.973562i \(-0.426644\pi\)
0.228421 + 0.973562i \(0.426644\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.76957 −0.450682
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.24960 −0.580261
\(117\) 0 0
\(118\) 14.5583 1.34020
\(119\) 1.19049 0.109132
\(120\) 0 0
\(121\) −10.0783 −0.916207
\(122\) 7.53914 0.682562
\(123\) 0 0
\(124\) 2.96006 0.265821
\(125\) 0 0
\(126\) 0 0
\(127\) 17.9585 1.59356 0.796778 0.604272i \(-0.206536\pi\)
0.796778 + 0.604272i \(0.206536\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 6.96006 0.608103 0.304052 0.952656i \(-0.401660\pi\)
0.304052 + 0.952656i \(0.401660\pi\)
\(132\) 0 0
\(133\) −4.76957 −0.413574
\(134\) −5.72963 −0.494965
\(135\) 0 0
\(136\) −0.249601 −0.0214031
\(137\) −7.80951 −0.667211 −0.333606 0.942713i \(-0.608265\pi\)
−0.333606 + 0.942713i \(0.608265\pi\)
\(138\) 0 0
\(139\) −16.0383 −1.36035 −0.680177 0.733048i \(-0.738097\pi\)
−0.680177 + 0.733048i \(0.738097\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 9.61902 0.807210
\(143\) 2.15975 0.180608
\(144\) 0 0
\(145\) 0 0
\(146\) 12.0591 0.998019
\(147\) 0 0
\(148\) 0.0399387 0.00328294
\(149\) 8.41932 0.689738 0.344869 0.938651i \(-0.387923\pi\)
0.344869 + 0.938651i \(0.387923\pi\)
\(150\) 0 0
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 1.00000 0.0811107
\(153\) 0 0
\(154\) 4.57908 0.368993
\(155\) 0 0
\(156\) 0 0
\(157\) 4.96006 0.395856 0.197928 0.980217i \(-0.436579\pi\)
0.197928 + 0.980217i \(0.436579\pi\)
\(158\) 6.07988 0.483689
\(159\) 0 0
\(160\) 0 0
\(161\) 43.0176 3.39026
\(162\) 0 0
\(163\) −21.4593 −1.68082 −0.840410 0.541952i \(-0.817686\pi\)
−0.840410 + 0.541952i \(0.817686\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 7.45926 0.578951
\(167\) 11.0399 0.854296 0.427148 0.904182i \(-0.359518\pi\)
0.427148 + 0.904182i \(0.359518\pi\)
\(168\) 0 0
\(169\) −7.93929 −0.610715
\(170\) 0 0
\(171\) 0 0
\(172\) 4.96006 0.378201
\(173\) −16.9585 −1.28933 −0.644664 0.764466i \(-0.723003\pi\)
−0.644664 + 0.764466i \(0.723003\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.960061 −0.0723673
\(177\) 0 0
\(178\) −4.07988 −0.305800
\(179\) −2.53914 −0.189784 −0.0948922 0.995488i \(-0.530251\pi\)
−0.0948922 + 0.995488i \(0.530251\pi\)
\(180\) 0 0
\(181\) −3.88018 −0.288412 −0.144206 0.989548i \(-0.546063\pi\)
−0.144206 + 0.989548i \(0.546063\pi\)
\(182\) 10.7296 0.795333
\(183\) 0 0
\(184\) −9.01917 −0.664902
\(185\) 0 0
\(186\) 0 0
\(187\) 0.239632 0.0175237
\(188\) 9.49920 0.692801
\(189\) 0 0
\(190\) 0 0
\(191\) −2.05911 −0.148992 −0.0744960 0.997221i \(-0.523735\pi\)
−0.0744960 + 0.997221i \(0.523735\pi\)
\(192\) 0 0
\(193\) −8.46086 −0.609026 −0.304513 0.952508i \(-0.598494\pi\)
−0.304513 + 0.952508i \(0.598494\pi\)
\(194\) 18.4193 1.32243
\(195\) 0 0
\(196\) 15.7488 1.12491
\(197\) −13.9201 −0.991768 −0.495884 0.868389i \(-0.665156\pi\)
−0.495884 + 0.868389i \(0.665156\pi\)
\(198\) 0 0
\(199\) −9.15055 −0.648665 −0.324333 0.945943i \(-0.605140\pi\)
−0.324333 + 0.945943i \(0.605140\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −5.53914 −0.389733
\(203\) 29.8079 2.09211
\(204\) 0 0
\(205\) 0 0
\(206\) −6.57908 −0.458386
\(207\) 0 0
\(208\) −2.24960 −0.155982
\(209\) −0.960061 −0.0664088
\(210\) 0 0
\(211\) 16.5200 1.13728 0.568641 0.822586i \(-0.307469\pi\)
0.568641 + 0.822586i \(0.307469\pi\)
\(212\) −6.84945 −0.470422
\(213\) 0 0
\(214\) −14.9086 −1.01913
\(215\) 0 0
\(216\) 0 0
\(217\) −14.1182 −0.958407
\(218\) 4.76957 0.323036
\(219\) 0 0
\(220\) 0 0
\(221\) 0.561503 0.0377708
\(222\) 0 0
\(223\) 9.03994 0.605359 0.302680 0.953092i \(-0.402119\pi\)
0.302680 + 0.953092i \(0.402119\pi\)
\(224\) −4.76957 −0.318680
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) −0.350246 −0.0232466 −0.0116233 0.999932i \(-0.503700\pi\)
−0.0116233 + 0.999932i \(0.503700\pi\)
\(228\) 0 0
\(229\) −8.07988 −0.533933 −0.266967 0.963706i \(-0.586021\pi\)
−0.266967 + 0.963706i \(0.586021\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.24960 −0.410306
\(233\) 4.92012 0.322328 0.161164 0.986928i \(-0.448475\pi\)
0.161164 + 0.986928i \(0.448475\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 14.5583 0.947665
\(237\) 0 0
\(238\) 1.19049 0.0771680
\(239\) −2.98083 −0.192814 −0.0964069 0.995342i \(-0.530735\pi\)
−0.0964069 + 0.995342i \(0.530735\pi\)
\(240\) 0 0
\(241\) 20.0383 1.29078 0.645392 0.763852i \(-0.276694\pi\)
0.645392 + 0.763852i \(0.276694\pi\)
\(242\) −10.0783 −0.647857
\(243\) 0 0
\(244\) 7.53914 0.482644
\(245\) 0 0
\(246\) 0 0
\(247\) −2.24960 −0.143139
\(248\) 2.96006 0.187964
\(249\) 0 0
\(250\) 0 0
\(251\) 14.8802 0.939229 0.469614 0.882872i \(-0.344393\pi\)
0.469614 + 0.882872i \(0.344393\pi\)
\(252\) 0 0
\(253\) 8.65896 0.544384
\(254\) 17.9585 1.12681
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.0399 0.688652 0.344326 0.938850i \(-0.388107\pi\)
0.344326 + 0.938850i \(0.388107\pi\)
\(258\) 0 0
\(259\) −0.190491 −0.0118365
\(260\) 0 0
\(261\) 0 0
\(262\) 6.96006 0.429994
\(263\) 3.84025 0.236800 0.118400 0.992966i \(-0.462224\pi\)
0.118400 + 0.992966i \(0.462224\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.76957 −0.292441
\(267\) 0 0
\(268\) −5.72963 −0.349993
\(269\) −23.1981 −1.41441 −0.707207 0.707007i \(-0.750045\pi\)
−0.707207 + 0.707007i \(0.750045\pi\)
\(270\) 0 0
\(271\) 23.9792 1.45663 0.728317 0.685240i \(-0.240303\pi\)
0.728317 + 0.685240i \(0.240303\pi\)
\(272\) −0.249601 −0.0151343
\(273\) 0 0
\(274\) −7.80951 −0.471790
\(275\) 0 0
\(276\) 0 0
\(277\) 24.6590 1.48161 0.740807 0.671718i \(-0.234444\pi\)
0.740807 + 0.671718i \(0.234444\pi\)
\(278\) −16.0383 −0.961916
\(279\) 0 0
\(280\) 0 0
\(281\) 18.9984 1.13335 0.566675 0.823941i \(-0.308230\pi\)
0.566675 + 0.823941i \(0.308230\pi\)
\(282\) 0 0
\(283\) 29.0367 1.72606 0.863028 0.505156i \(-0.168565\pi\)
0.863028 + 0.505156i \(0.168565\pi\)
\(284\) 9.61902 0.570784
\(285\) 0 0
\(286\) 2.15975 0.127709
\(287\) 0 0
\(288\) 0 0
\(289\) −16.9377 −0.996335
\(290\) 0 0
\(291\) 0 0
\(292\) 12.0591 0.705706
\(293\) −6.24960 −0.365106 −0.182553 0.983196i \(-0.558436\pi\)
−0.182553 + 0.983196i \(0.558436\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.0399387 0.00232139
\(297\) 0 0
\(298\) 8.41932 0.487718
\(299\) 20.2895 1.17337
\(300\) 0 0
\(301\) −23.6574 −1.36359
\(302\) 20.0000 1.15087
\(303\) 0 0
\(304\) 1.00000 0.0573539
\(305\) 0 0
\(306\) 0 0
\(307\) 12.5391 0.715647 0.357823 0.933789i \(-0.383519\pi\)
0.357823 + 0.933789i \(0.383519\pi\)
\(308\) 4.57908 0.260917
\(309\) 0 0
\(310\) 0 0
\(311\) −7.84785 −0.445011 −0.222505 0.974931i \(-0.571424\pi\)
−0.222505 + 0.974931i \(0.571424\pi\)
\(312\) 0 0
\(313\) 10.9884 0.621103 0.310552 0.950557i \(-0.399486\pi\)
0.310552 + 0.950557i \(0.399486\pi\)
\(314\) 4.96006 0.279912
\(315\) 0 0
\(316\) 6.07988 0.342020
\(317\) 21.5567 1.21075 0.605373 0.795942i \(-0.293024\pi\)
0.605373 + 0.795942i \(0.293024\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) 0 0
\(322\) 43.0176 2.39728
\(323\) −0.249601 −0.0138882
\(324\) 0 0
\(325\) 0 0
\(326\) −21.4593 −1.18852
\(327\) 0 0
\(328\) 0 0
\(329\) −45.3071 −2.49786
\(330\) 0 0
\(331\) 33.4876 1.84065 0.920324 0.391158i \(-0.127925\pi\)
0.920324 + 0.391158i \(0.127925\pi\)
\(332\) 7.45926 0.409380
\(333\) 0 0
\(334\) 11.0399 0.604079
\(335\) 0 0
\(336\) 0 0
\(337\) 5.69890 0.310439 0.155219 0.987880i \(-0.450392\pi\)
0.155219 + 0.987880i \(0.450392\pi\)
\(338\) −7.93929 −0.431841
\(339\) 0 0
\(340\) 0 0
\(341\) −2.84184 −0.153894
\(342\) 0 0
\(343\) −41.7280 −2.25310
\(344\) 4.96006 0.267429
\(345\) 0 0
\(346\) −16.9585 −0.911693
\(347\) 0.239632 0.0128641 0.00643207 0.999979i \(-0.497953\pi\)
0.00643207 + 0.999979i \(0.497953\pi\)
\(348\) 0 0
\(349\) −17.2380 −0.922731 −0.461365 0.887210i \(-0.652640\pi\)
−0.461365 + 0.887210i \(0.652640\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.960061 −0.0511714
\(353\) 34.7280 1.84839 0.924193 0.381925i \(-0.124739\pi\)
0.924193 + 0.381925i \(0.124739\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −4.07988 −0.216233
\(357\) 0 0
\(358\) −2.53914 −0.134198
\(359\) −26.6689 −1.40753 −0.703766 0.710432i \(-0.748500\pi\)
−0.703766 + 0.710432i \(0.748500\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −3.88018 −0.203938
\(363\) 0 0
\(364\) 10.7296 0.562386
\(365\) 0 0
\(366\) 0 0
\(367\) −15.2380 −0.795419 −0.397710 0.917511i \(-0.630195\pi\)
−0.397710 + 0.917511i \(0.630195\pi\)
\(368\) −9.01917 −0.470157
\(369\) 0 0
\(370\) 0 0
\(371\) 32.6689 1.69609
\(372\) 0 0
\(373\) −26.6382 −1.37927 −0.689637 0.724156i \(-0.742230\pi\)
−0.689637 + 0.724156i \(0.742230\pi\)
\(374\) 0.239632 0.0123911
\(375\) 0 0
\(376\) 9.49920 0.489884
\(377\) 14.0591 0.724081
\(378\) 0 0
\(379\) 11.9693 0.614820 0.307410 0.951577i \(-0.400538\pi\)
0.307410 + 0.951577i \(0.400538\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −2.05911 −0.105353
\(383\) 9.84025 0.502813 0.251407 0.967882i \(-0.419107\pi\)
0.251407 + 0.967882i \(0.419107\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −8.46086 −0.430646
\(387\) 0 0
\(388\) 18.4193 0.935100
\(389\) 8.65896 0.439027 0.219513 0.975610i \(-0.429553\pi\)
0.219513 + 0.975610i \(0.429553\pi\)
\(390\) 0 0
\(391\) 2.25120 0.113848
\(392\) 15.7488 0.795435
\(393\) 0 0
\(394\) −13.9201 −0.701286
\(395\) 0 0
\(396\) 0 0
\(397\) 28.9984 1.45539 0.727694 0.685902i \(-0.240592\pi\)
0.727694 + 0.685902i \(0.240592\pi\)
\(398\) −9.15055 −0.458676
\(399\) 0 0
\(400\) 0 0
\(401\) −22.6174 −1.12946 −0.564730 0.825276i \(-0.691020\pi\)
−0.564730 + 0.825276i \(0.691020\pi\)
\(402\) 0 0
\(403\) −6.65896 −0.331706
\(404\) −5.53914 −0.275583
\(405\) 0 0
\(406\) 29.8079 1.47934
\(407\) −0.0383436 −0.00190062
\(408\) 0 0
\(409\) 5.34104 0.264098 0.132049 0.991243i \(-0.457844\pi\)
0.132049 + 0.991243i \(0.457844\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −6.57908 −0.324128
\(413\) −69.4369 −3.41677
\(414\) 0 0
\(415\) 0 0
\(416\) −2.24960 −0.110296
\(417\) 0 0
\(418\) −0.960061 −0.0469581
\(419\) 22.1566 1.08242 0.541210 0.840888i \(-0.317967\pi\)
0.541210 + 0.840888i \(0.317967\pi\)
\(420\) 0 0
\(421\) 29.2787 1.42696 0.713479 0.700676i \(-0.247118\pi\)
0.713479 + 0.700676i \(0.247118\pi\)
\(422\) 16.5200 0.804180
\(423\) 0 0
\(424\) −6.84945 −0.332639
\(425\) 0 0
\(426\) 0 0
\(427\) −35.9585 −1.74015
\(428\) −14.9086 −0.720632
\(429\) 0 0
\(430\) 0 0
\(431\) −21.3794 −1.02981 −0.514904 0.857248i \(-0.672173\pi\)
−0.514904 + 0.857248i \(0.672173\pi\)
\(432\) 0 0
\(433\) −36.1182 −1.73573 −0.867865 0.496799i \(-0.834509\pi\)
−0.867865 + 0.496799i \(0.834509\pi\)
\(434\) −14.1182 −0.677696
\(435\) 0 0
\(436\) 4.76957 0.228421
\(437\) −9.01917 −0.431445
\(438\) 0 0
\(439\) 20.9984 1.00220 0.501100 0.865390i \(-0.332929\pi\)
0.501100 + 0.865390i \(0.332929\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.561503 0.0267080
\(443\) 31.4976 1.49650 0.748248 0.663419i \(-0.230895\pi\)
0.748248 + 0.663419i \(0.230895\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 9.03994 0.428054
\(447\) 0 0
\(448\) −4.76957 −0.225341
\(449\) −18.9601 −0.894781 −0.447390 0.894339i \(-0.647647\pi\)
−0.447390 + 0.894339i \(0.647647\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 0 0
\(454\) −0.350246 −0.0164378
\(455\) 0 0
\(456\) 0 0
\(457\) −6.32948 −0.296081 −0.148040 0.988981i \(-0.547297\pi\)
−0.148040 + 0.988981i \(0.547297\pi\)
\(458\) −8.07988 −0.377548
\(459\) 0 0
\(460\) 0 0
\(461\) 6.49920 0.302698 0.151349 0.988480i \(-0.451638\pi\)
0.151349 + 0.988480i \(0.451638\pi\)
\(462\) 0 0
\(463\) 28.4177 1.32068 0.660342 0.750965i \(-0.270411\pi\)
0.660342 + 0.750965i \(0.270411\pi\)
\(464\) −6.24960 −0.290130
\(465\) 0 0
\(466\) 4.92012 0.227920
\(467\) −17.5775 −0.813389 −0.406694 0.913564i \(-0.633319\pi\)
−0.406694 + 0.913564i \(0.633319\pi\)
\(468\) 0 0
\(469\) 27.3279 1.26188
\(470\) 0 0
\(471\) 0 0
\(472\) 14.5583 0.670101
\(473\) −4.76196 −0.218955
\(474\) 0 0
\(475\) 0 0
\(476\) 1.19049 0.0545660
\(477\) 0 0
\(478\) −2.98083 −0.136340
\(479\) −22.7372 −1.03889 −0.519446 0.854504i \(-0.673861\pi\)
−0.519446 + 0.854504i \(0.673861\pi\)
\(480\) 0 0
\(481\) −0.0898462 −0.00409664
\(482\) 20.0383 0.912722
\(483\) 0 0
\(484\) −10.0783 −0.458104
\(485\) 0 0
\(486\) 0 0
\(487\) −22.1981 −1.00589 −0.502946 0.864318i \(-0.667751\pi\)
−0.502946 + 0.864318i \(0.667751\pi\)
\(488\) 7.53914 0.341281
\(489\) 0 0
\(490\) 0 0
\(491\) 24.9984 1.12816 0.564081 0.825719i \(-0.309231\pi\)
0.564081 + 0.825719i \(0.309231\pi\)
\(492\) 0 0
\(493\) 1.55991 0.0702547
\(494\) −2.24960 −0.101214
\(495\) 0 0
\(496\) 2.96006 0.132911
\(497\) −45.8786 −2.05794
\(498\) 0 0
\(499\) 11.6574 0.521855 0.260928 0.965358i \(-0.415972\pi\)
0.260928 + 0.965358i \(0.415972\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 14.8802 0.664135
\(503\) −11.7504 −0.523924 −0.261962 0.965078i \(-0.584370\pi\)
−0.261962 + 0.965078i \(0.584370\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8.65896 0.384938
\(507\) 0 0
\(508\) 17.9585 0.796778
\(509\) −29.9569 −1.32781 −0.663907 0.747815i \(-0.731103\pi\)
−0.663907 + 0.747815i \(0.731103\pi\)
\(510\) 0 0
\(511\) −57.5168 −2.54439
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 11.0399 0.486951
\(515\) 0 0
\(516\) 0 0
\(517\) −9.11982 −0.401089
\(518\) −0.190491 −0.00836968
\(519\) 0 0
\(520\) 0 0
\(521\) 15.1198 0.662411 0.331206 0.943559i \(-0.392545\pi\)
0.331206 + 0.943559i \(0.392545\pi\)
\(522\) 0 0
\(523\) 15.6498 0.684316 0.342158 0.939642i \(-0.388842\pi\)
0.342158 + 0.939642i \(0.388842\pi\)
\(524\) 6.96006 0.304052
\(525\) 0 0
\(526\) 3.84025 0.167443
\(527\) −0.738835 −0.0321842
\(528\) 0 0
\(529\) 58.3455 2.53676
\(530\) 0 0
\(531\) 0 0
\(532\) −4.76957 −0.206787
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −5.72963 −0.247482
\(537\) 0 0
\(538\) −23.1981 −1.00014
\(539\) −15.1198 −0.651257
\(540\) 0 0
\(541\) −27.2995 −1.17370 −0.586849 0.809697i \(-0.699632\pi\)
−0.586849 + 0.809697i \(0.699632\pi\)
\(542\) 23.9792 1.03000
\(543\) 0 0
\(544\) −0.249601 −0.0107016
\(545\) 0 0
\(546\) 0 0
\(547\) −33.9968 −1.45360 −0.726799 0.686850i \(-0.758993\pi\)
−0.726799 + 0.686850i \(0.758993\pi\)
\(548\) −7.80951 −0.333606
\(549\) 0 0
\(550\) 0 0
\(551\) −6.24960 −0.266242
\(552\) 0 0
\(553\) −28.9984 −1.23314
\(554\) 24.6590 1.04766
\(555\) 0 0
\(556\) −16.0383 −0.680177
\(557\) −33.8786 −1.43548 −0.717741 0.696310i \(-0.754824\pi\)
−0.717741 + 0.696310i \(0.754824\pi\)
\(558\) 0 0
\(559\) −11.1582 −0.471940
\(560\) 0 0
\(561\) 0 0
\(562\) 18.9984 0.801399
\(563\) −32.2995 −1.36126 −0.680631 0.732626i \(-0.738294\pi\)
−0.680631 + 0.732626i \(0.738294\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 29.0367 1.22051
\(567\) 0 0
\(568\) 9.61902 0.403605
\(569\) 6.73883 0.282507 0.141253 0.989973i \(-0.454887\pi\)
0.141253 + 0.989973i \(0.454887\pi\)
\(570\) 0 0
\(571\) 34.4193 1.44040 0.720202 0.693764i \(-0.244049\pi\)
0.720202 + 0.693764i \(0.244049\pi\)
\(572\) 2.15975 0.0903039
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 28.1773 1.17304 0.586519 0.809936i \(-0.300498\pi\)
0.586519 + 0.809936i \(0.300498\pi\)
\(578\) −16.9377 −0.704515
\(579\) 0 0
\(580\) 0 0
\(581\) −35.5775 −1.47600
\(582\) 0 0
\(583\) 6.57589 0.272346
\(584\) 12.0591 0.499010
\(585\) 0 0
\(586\) −6.24960 −0.258169
\(587\) 34.6174 1.42881 0.714407 0.699730i \(-0.246697\pi\)
0.714407 + 0.699730i \(0.246697\pi\)
\(588\) 0 0
\(589\) 2.96006 0.121967
\(590\) 0 0
\(591\) 0 0
\(592\) 0.0399387 0.00164147
\(593\) 3.99840 0.164195 0.0820974 0.996624i \(-0.473838\pi\)
0.0820974 + 0.996624i \(0.473838\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 8.41932 0.344869
\(597\) 0 0
\(598\) 20.2895 0.829701
\(599\) 42.5759 1.73960 0.869802 0.493401i \(-0.164247\pi\)
0.869802 + 0.493401i \(0.164247\pi\)
\(600\) 0 0
\(601\) −18.4577 −0.752904 −0.376452 0.926436i \(-0.622856\pi\)
−0.376452 + 0.926436i \(0.622856\pi\)
\(602\) −23.6574 −0.964202
\(603\) 0 0
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) 0 0
\(607\) −12.5791 −0.510569 −0.255285 0.966866i \(-0.582169\pi\)
−0.255285 + 0.966866i \(0.582169\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0 0
\(610\) 0 0
\(611\) −21.3694 −0.864514
\(612\) 0 0
\(613\) −26.5759 −1.07339 −0.536695 0.843776i \(-0.680327\pi\)
−0.536695 + 0.843776i \(0.680327\pi\)
\(614\) 12.5391 0.506039
\(615\) 0 0
\(616\) 4.57908 0.184496
\(617\) 37.8386 1.52333 0.761663 0.647973i \(-0.224383\pi\)
0.761663 + 0.647973i \(0.224383\pi\)
\(618\) 0 0
\(619\) 30.1566 1.21209 0.606047 0.795429i \(-0.292754\pi\)
0.606047 + 0.795429i \(0.292754\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −7.84785 −0.314670
\(623\) 19.4593 0.779619
\(624\) 0 0
\(625\) 0 0
\(626\) 10.9884 0.439186
\(627\) 0 0
\(628\) 4.96006 0.197928
\(629\) −0.00996876 −0.000397480 0
\(630\) 0 0
\(631\) −25.4992 −1.01511 −0.507554 0.861620i \(-0.669450\pi\)
−0.507554 + 0.861620i \(0.669450\pi\)
\(632\) 6.07988 0.241845
\(633\) 0 0
\(634\) 21.5567 0.856127
\(635\) 0 0
\(636\) 0 0
\(637\) −35.4285 −1.40373
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) −39.1965 −1.54817 −0.774084 0.633082i \(-0.781789\pi\)
−0.774084 + 0.633082i \(0.781789\pi\)
\(642\) 0 0
\(643\) −36.3778 −1.43460 −0.717300 0.696764i \(-0.754622\pi\)
−0.717300 + 0.696764i \(0.754622\pi\)
\(644\) 43.0176 1.69513
\(645\) 0 0
\(646\) −0.249601 −0.00982043
\(647\) 10.6897 0.420255 0.210128 0.977674i \(-0.432612\pi\)
0.210128 + 0.977674i \(0.432612\pi\)
\(648\) 0 0
\(649\) −13.9769 −0.548640
\(650\) 0 0
\(651\) 0 0
\(652\) −21.4593 −0.840410
\(653\) −36.0383 −1.41029 −0.705145 0.709063i \(-0.749118\pi\)
−0.705145 + 0.709063i \(0.749118\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −45.3071 −1.76626
\(659\) −17.1889 −0.669584 −0.334792 0.942292i \(-0.608666\pi\)
−0.334792 + 0.942292i \(0.608666\pi\)
\(660\) 0 0
\(661\) 48.9054 1.90220 0.951099 0.308886i \(-0.0999560\pi\)
0.951099 + 0.308886i \(0.0999560\pi\)
\(662\) 33.4876 1.30153
\(663\) 0 0
\(664\) 7.45926 0.289476
\(665\) 0 0
\(666\) 0 0
\(667\) 56.3662 2.18251
\(668\) 11.0399 0.427148
\(669\) 0 0
\(670\) 0 0
\(671\) −7.23804 −0.279421
\(672\) 0 0
\(673\) −6.57908 −0.253605 −0.126802 0.991928i \(-0.540471\pi\)
−0.126802 + 0.991928i \(0.540471\pi\)
\(674\) 5.69890 0.219513
\(675\) 0 0
\(676\) −7.93929 −0.305357
\(677\) −38.3087 −1.47232 −0.736162 0.676806i \(-0.763364\pi\)
−0.736162 + 0.676806i \(0.763364\pi\)
\(678\) 0 0
\(679\) −87.8523 −3.37146
\(680\) 0 0
\(681\) 0 0
\(682\) −2.84184 −0.108820
\(683\) 7.54074 0.288538 0.144269 0.989538i \(-0.453917\pi\)
0.144269 + 0.989538i \(0.453917\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −41.7280 −1.59318
\(687\) 0 0
\(688\) 4.96006 0.189101
\(689\) 15.4085 0.587018
\(690\) 0 0
\(691\) 28.4193 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(692\) −16.9585 −0.644664
\(693\) 0 0
\(694\) 0.239632 0.00909632
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −17.2380 −0.652469
\(699\) 0 0
\(700\) 0 0
\(701\) 24.2596 0.916271 0.458136 0.888882i \(-0.348517\pi\)
0.458136 + 0.888882i \(0.348517\pi\)
\(702\) 0 0
\(703\) 0.0399387 0.00150632
\(704\) −0.960061 −0.0361837
\(705\) 0 0
\(706\) 34.7280 1.30701
\(707\) 26.4193 0.993601
\(708\) 0 0
\(709\) 21.7372 0.816359 0.408180 0.912902i \(-0.366164\pi\)
0.408180 + 0.912902i \(0.366164\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −4.07988 −0.152900
\(713\) −26.6973 −0.999822
\(714\) 0 0
\(715\) 0 0
\(716\) −2.53914 −0.0948922
\(717\) 0 0
\(718\) −26.6689 −0.995275
\(719\) 48.9361 1.82501 0.912504 0.409067i \(-0.134146\pi\)
0.912504 + 0.409067i \(0.134146\pi\)
\(720\) 0 0
\(721\) 31.3794 1.16863
\(722\) 1.00000 0.0372161
\(723\) 0 0
\(724\) −3.88018 −0.144206
\(725\) 0 0
\(726\) 0 0
\(727\) −4.29874 −0.159432 −0.0797158 0.996818i \(-0.525401\pi\)
−0.0797158 + 0.996818i \(0.525401\pi\)
\(728\) 10.7296 0.397667
\(729\) 0 0
\(730\) 0 0
\(731\) −1.23804 −0.0457905
\(732\) 0 0
\(733\) −12.0415 −0.444764 −0.222382 0.974960i \(-0.571383\pi\)
−0.222382 + 0.974960i \(0.571383\pi\)
\(734\) −15.2380 −0.562446
\(735\) 0 0
\(736\) −9.01917 −0.332451
\(737\) 5.50080 0.202624
\(738\) 0 0
\(739\) 6.61742 0.243426 0.121713 0.992565i \(-0.461161\pi\)
0.121713 + 0.992565i \(0.461161\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 32.6689 1.19931
\(743\) 47.6158 1.74686 0.873428 0.486954i \(-0.161892\pi\)
0.873428 + 0.486954i \(0.161892\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −26.6382 −0.975293
\(747\) 0 0
\(748\) 0.239632 0.00876183
\(749\) 71.1074 2.59821
\(750\) 0 0
\(751\) −25.6574 −0.936250 −0.468125 0.883662i \(-0.655070\pi\)
−0.468125 + 0.883662i \(0.655070\pi\)
\(752\) 9.49920 0.346400
\(753\) 0 0
\(754\) 14.0591 0.512003
\(755\) 0 0
\(756\) 0 0
\(757\) 8.83865 0.321246 0.160623 0.987016i \(-0.448650\pi\)
0.160623 + 0.987016i \(0.448650\pi\)
\(758\) 11.9693 0.434743
\(759\) 0 0
\(760\) 0 0
\(761\) 9.40776 0.341031 0.170516 0.985355i \(-0.445457\pi\)
0.170516 + 0.985355i \(0.445457\pi\)
\(762\) 0 0
\(763\) −22.7488 −0.823562
\(764\) −2.05911 −0.0744960
\(765\) 0 0
\(766\) 9.84025 0.355543
\(767\) −32.7504 −1.18255
\(768\) 0 0
\(769\) 7.32788 0.264250 0.132125 0.991233i \(-0.457820\pi\)
0.132125 + 0.991233i \(0.457820\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −8.46086 −0.304513
\(773\) −54.4369 −1.95796 −0.978980 0.203958i \(-0.934619\pi\)
−0.978980 + 0.203958i \(0.934619\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 18.4193 0.661215
\(777\) 0 0
\(778\) 8.65896 0.310439
\(779\) 0 0
\(780\) 0 0
\(781\) −9.23485 −0.330449
\(782\) 2.25120 0.0805026
\(783\) 0 0
\(784\) 15.7488 0.562457
\(785\) 0 0
\(786\) 0 0
\(787\) −27.6705 −0.986348 −0.493174 0.869931i \(-0.664163\pi\)
−0.493174 + 0.869931i \(0.664163\pi\)
\(788\) −13.9201 −0.495884
\(789\) 0 0
\(790\) 0 0
\(791\) 28.6174 1.01752
\(792\) 0 0
\(793\) −16.9601 −0.602269
\(794\) 28.9984 1.02911
\(795\) 0 0
\(796\) −9.15055 −0.324333
\(797\) −21.5906 −0.764780 −0.382390 0.924001i \(-0.624899\pi\)
−0.382390 + 0.924001i \(0.624899\pi\)
\(798\) 0 0
\(799\) −2.37101 −0.0838804
\(800\) 0 0
\(801\) 0 0
\(802\) −22.6174 −0.798649
\(803\) −11.5775 −0.408561
\(804\) 0 0
\(805\) 0 0
\(806\) −6.65896 −0.234552
\(807\) 0 0
\(808\) −5.53914 −0.194866
\(809\) −9.72963 −0.342076 −0.171038 0.985264i \(-0.554712\pi\)
−0.171038 + 0.985264i \(0.554712\pi\)
\(810\) 0 0
\(811\) −38.7280 −1.35993 −0.679963 0.733247i \(-0.738004\pi\)
−0.679963 + 0.733247i \(0.738004\pi\)
\(812\) 29.8079 1.04605
\(813\) 0 0
\(814\) −0.0383436 −0.00134394
\(815\) 0 0
\(816\) 0 0
\(817\) 4.96006 0.173531
\(818\) 5.34104 0.186745
\(819\) 0 0
\(820\) 0 0
\(821\) 30.2780 1.05671 0.528354 0.849024i \(-0.322809\pi\)
0.528354 + 0.849024i \(0.322809\pi\)
\(822\) 0 0
\(823\) −7.93770 −0.276691 −0.138345 0.990384i \(-0.544178\pi\)
−0.138345 + 0.990384i \(0.544178\pi\)
\(824\) −6.57908 −0.229193
\(825\) 0 0
\(826\) −69.4369 −2.41602
\(827\) −30.2496 −1.05188 −0.525941 0.850521i \(-0.676287\pi\)
−0.525941 + 0.850521i \(0.676287\pi\)
\(828\) 0 0
\(829\) −40.6765 −1.41275 −0.706377 0.707836i \(-0.749672\pi\)
−0.706377 + 0.707836i \(0.749672\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −2.24960 −0.0779909
\(833\) −3.93092 −0.136198
\(834\) 0 0
\(835\) 0 0
\(836\) −0.960061 −0.0332044
\(837\) 0 0
\(838\) 22.1566 0.765386
\(839\) −45.9553 −1.58655 −0.793276 0.608862i \(-0.791626\pi\)
−0.793276 + 0.608862i \(0.791626\pi\)
\(840\) 0 0
\(841\) 10.0575 0.346811
\(842\) 29.2787 1.00901
\(843\) 0 0
\(844\) 16.5200 0.568641
\(845\) 0 0
\(846\) 0 0
\(847\) 48.0691 1.65167
\(848\) −6.84945 −0.235211
\(849\) 0 0
\(850\) 0 0
\(851\) −0.360214 −0.0123480
\(852\) 0 0
\(853\) 17.2196 0.589589 0.294794 0.955561i \(-0.404749\pi\)
0.294794 + 0.955561i \(0.404749\pi\)
\(854\) −35.9585 −1.23047
\(855\) 0 0
\(856\) −14.9086 −0.509564
\(857\) −17.2995 −0.590940 −0.295470 0.955352i \(-0.595476\pi\)
−0.295470 + 0.955352i \(0.595476\pi\)
\(858\) 0 0
\(859\) 17.6190 0.601153 0.300577 0.953758i \(-0.402821\pi\)
0.300577 + 0.953758i \(0.402821\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −21.3794 −0.728185
\(863\) 4.07988 0.138881 0.0694403 0.997586i \(-0.477879\pi\)
0.0694403 + 0.997586i \(0.477879\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −36.1182 −1.22735
\(867\) 0 0
\(868\) −14.1182 −0.479204
\(869\) −5.83705 −0.198009
\(870\) 0 0
\(871\) 12.8894 0.436740
\(872\) 4.76957 0.161518
\(873\) 0 0
\(874\) −9.01917 −0.305078
\(875\) 0 0
\(876\) 0 0
\(877\) 25.2787 0.853602 0.426801 0.904345i \(-0.359640\pi\)
0.426801 + 0.904345i \(0.359640\pi\)
\(878\) 20.9984 0.708662
\(879\) 0 0
\(880\) 0 0
\(881\) 0.0814726 0.00274488 0.00137244 0.999999i \(-0.499563\pi\)
0.00137244 + 0.999999i \(0.499563\pi\)
\(882\) 0 0
\(883\) 19.3410 0.650878 0.325439 0.945563i \(-0.394488\pi\)
0.325439 + 0.945563i \(0.394488\pi\)
\(884\) 0.561503 0.0188854
\(885\) 0 0
\(886\) 31.4976 1.05818
\(887\) −5.53914 −0.185986 −0.0929931 0.995667i \(-0.529643\pi\)
−0.0929931 + 0.995667i \(0.529643\pi\)
\(888\) 0 0
\(889\) −85.6542 −2.87275
\(890\) 0 0
\(891\) 0 0
\(892\) 9.03994 0.302680
\(893\) 9.49920 0.317879
\(894\) 0 0
\(895\) 0 0
\(896\) −4.76957 −0.159340
\(897\) 0 0
\(898\) −18.9601 −0.632705
\(899\) −18.4992 −0.616983
\(900\) 0 0
\(901\) 1.70963 0.0569561
\(902\) 0 0
\(903\) 0 0
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 0 0
\(907\) 10.8111 0.358977 0.179488 0.983760i \(-0.442556\pi\)
0.179488 + 0.983760i \(0.442556\pi\)
\(908\) −0.350246 −0.0116233
\(909\) 0 0
\(910\) 0 0
\(911\) −35.1166 −1.16347 −0.581733 0.813380i \(-0.697625\pi\)
−0.581733 + 0.813380i \(0.697625\pi\)
\(912\) 0 0
\(913\) −7.16135 −0.237006
\(914\) −6.32948 −0.209361
\(915\) 0 0
\(916\) −8.07988 −0.266967
\(917\) −33.1965 −1.09625
\(918\) 0 0
\(919\) 30.8287 1.01694 0.508472 0.861078i \(-0.330210\pi\)
0.508472 + 0.861078i \(0.330210\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 6.49920 0.214040
\(923\) −21.6390 −0.712255
\(924\) 0 0
\(925\) 0 0
\(926\) 28.4177 0.933865
\(927\) 0 0
\(928\) −6.24960 −0.205153
\(929\) 45.0575 1.47829 0.739145 0.673547i \(-0.235230\pi\)
0.739145 + 0.673547i \(0.235230\pi\)
\(930\) 0 0
\(931\) 15.7488 0.516146
\(932\) 4.92012 0.161164
\(933\) 0 0
\(934\) −17.5775 −0.575153
\(935\) 0 0
\(936\) 0 0
\(937\) −22.2464 −0.726759 −0.363379 0.931641i \(-0.618377\pi\)
−0.363379 + 0.931641i \(0.618377\pi\)
\(938\) 27.3279 0.892287
\(939\) 0 0
\(940\) 0 0
\(941\) 53.9277 1.75799 0.878997 0.476828i \(-0.158213\pi\)
0.878997 + 0.476828i \(0.158213\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 14.5583 0.473833
\(945\) 0 0
\(946\) −4.76196 −0.154825
\(947\) −4.76196 −0.154743 −0.0773715 0.997002i \(-0.524653\pi\)
−0.0773715 + 0.997002i \(0.524653\pi\)
\(948\) 0 0
\(949\) −27.1282 −0.880618
\(950\) 0 0
\(951\) 0 0
\(952\) 1.19049 0.0385840
\(953\) 4.37779 0.141811 0.0709053 0.997483i \(-0.477411\pi\)
0.0709053 + 0.997483i \(0.477411\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −2.98083 −0.0964069
\(957\) 0 0
\(958\) −22.7372 −0.734607
\(959\) 37.2480 1.20280
\(960\) 0 0
\(961\) −22.2380 −0.717356
\(962\) −0.0898462 −0.00289676
\(963\) 0 0
\(964\) 20.0383 0.645392
\(965\) 0 0
\(966\) 0 0
\(967\) 13.1582 0.423138 0.211569 0.977363i \(-0.432143\pi\)
0.211569 + 0.977363i \(0.432143\pi\)
\(968\) −10.0783 −0.323928
\(969\) 0 0
\(970\) 0 0
\(971\) −25.9201 −0.831816 −0.415908 0.909407i \(-0.636536\pi\)
−0.415908 + 0.909407i \(0.636536\pi\)
\(972\) 0 0
\(973\) 76.4960 2.45235
\(974\) −22.1981 −0.711273
\(975\) 0 0
\(976\) 7.53914 0.241322
\(977\) 31.2764 1.00062 0.500310 0.865846i \(-0.333219\pi\)
0.500310 + 0.865846i \(0.333219\pi\)
\(978\) 0 0
\(979\) 3.91693 0.125186
\(980\) 0 0
\(981\) 0 0
\(982\) 24.9984 0.797731
\(983\) 26.2364 0.836813 0.418406 0.908260i \(-0.362589\pi\)
0.418406 + 0.908260i \(0.362589\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 1.55991 0.0496776
\(987\) 0 0
\(988\) −2.24960 −0.0715693
\(989\) −44.7356 −1.42251
\(990\) 0 0
\(991\) 39.2764 1.24766 0.623828 0.781562i \(-0.285577\pi\)
0.623828 + 0.781562i \(0.285577\pi\)
\(992\) 2.96006 0.0939820
\(993\) 0 0
\(994\) −45.8786 −1.45518
\(995\) 0 0
\(996\) 0 0
\(997\) −14.4609 −0.457980 −0.228990 0.973429i \(-0.573542\pi\)
−0.228990 + 0.973429i \(0.573542\pi\)
\(998\) 11.6574 0.369007
\(999\) 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 8550.2.a.cp.1.1 3
3.2 odd 2 950.2.a.j.1.2 3
5.4 even 2 8550.2.a.ci.1.3 3
12.11 even 2 7600.2.a.bz.1.2 3
15.2 even 4 950.2.b.h.799.2 6
15.8 even 4 950.2.b.h.799.5 6
15.14 odd 2 950.2.a.l.1.2 yes 3
60.59 even 2 7600.2.a.bk.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.2 3 3.2 odd 2
950.2.a.l.1.2 yes 3 15.14 odd 2
950.2.b.h.799.2 6 15.2 even 4
950.2.b.h.799.5 6 15.8 even 4
7600.2.a.bk.1.2 3 60.59 even 2
7600.2.a.bz.1.2 3 12.11 even 2
8550.2.a.ci.1.3 3 5.4 even 2
8550.2.a.cp.1.1 3 1.1 even 1 trivial