Properties

Label 7600.2.a.bk.1.2
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.993.1
Defining polynomial: \(x^{3} - x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
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 1.2
Root \(0.480031\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.519969 q^{3} -4.76957 q^{7} -2.72963 q^{9} +O(q^{10})\) \(q-0.519969 q^{3} -4.76957 q^{7} -2.72963 q^{9} -0.960061 q^{11} +2.24960 q^{13} -0.249601 q^{17} -1.00000 q^{19} +2.48003 q^{21} +9.01917 q^{23} +2.97923 q^{27} +6.24960 q^{29} -2.96006 q^{31} +0.499202 q^{33} -0.0399387 q^{37} -1.16972 q^{39} +4.96006 q^{43} -9.49920 q^{47} +15.7488 q^{49} +0.129785 q^{51} -6.84945 q^{53} +0.519969 q^{57} +14.5583 q^{59} +7.53914 q^{61} +13.0192 q^{63} -5.72963 q^{67} -4.68969 q^{69} +9.61902 q^{71} -12.0591 q^{73} +4.57908 q^{77} -6.07988 q^{79} +6.63979 q^{81} -7.45926 q^{83} -3.24960 q^{87} +4.07988 q^{89} -10.7296 q^{91} +1.53914 q^{93} -18.4193 q^{97} +2.62061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} + O(q^{10}) \) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} - 2q^{11} - 6q^{13} + 12q^{17} - 3q^{19} + 7q^{21} + 2q^{23} - 17q^{27} + 6q^{29} - 8q^{31} - 24q^{33} - q^{37} + 11q^{39} + 14q^{43} - 3q^{47} + 9q^{49} - 15q^{51} - 10q^{53} + 2q^{57} - 6q^{59} - 2q^{61} + 14q^{63} - 4q^{67} + 6q^{71} - 12q^{73} - 10q^{77} - 20q^{79} + 23q^{81} + 4q^{83} + 3q^{87} + 14q^{89} - 19q^{91} - 20q^{93} - 28q^{97} + 36q^{99} + O(q^{100}) \)

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
\(3\) −0.519969 −0.300204 −0.150102 0.988670i \(-0.547960\pi\)
−0.150102 + 0.988670i \(0.547960\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.76957 −1.80273 −0.901364 0.433062i \(-0.857433\pi\)
−0.901364 + 0.433062i \(0.857433\pi\)
\(8\) 0 0
\(9\) −2.72963 −0.909877
\(10\) 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 \(-0.399013\pi\)
0.311964 + 0.950094i \(0.399013\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −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
\(21\) 2.48003 0.541187
\(22\) 0 0
\(23\) 9.01917 1.88063 0.940314 0.340309i \(-0.110532\pi\)
0.940314 + 0.340309i \(0.110532\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2.97923 0.573354
\(28\) 0 0
\(29\) 6.24960 1.16052 0.580261 0.814431i \(-0.302951\pi\)
0.580261 + 0.814431i \(0.302951\pi\)
\(30\) 0 0
\(31\) −2.96006 −0.531643 −0.265821 0.964022i \(-0.585643\pi\)
−0.265821 + 0.964022i \(0.585643\pi\)
\(32\) 0 0
\(33\) 0.499202 0.0869000
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.0399387 −0.00656589 −0.00328294 0.999995i \(-0.501045\pi\)
−0.00328294 + 0.999995i \(0.501045\pi\)
\(38\) 0 0
\(39\) −1.16972 −0.187306
\(40\) 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 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.49920 −1.38560 −0.692801 0.721129i \(-0.743623\pi\)
−0.692801 + 0.721129i \(0.743623\pi\)
\(48\) 0 0
\(49\) 15.7488 2.24983
\(50\) 0 0
\(51\) 0.129785 0.0181735
\(52\) 0 0
\(53\) −6.84945 −0.940844 −0.470422 0.882442i \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0.519969 0.0688716
\(58\) 0 0
\(59\) 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 \(0.339676\pi\)
\(62\) 0 0
\(63\) 13.0192 1.64026
\(64\) 0 0
\(65\) 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 0
\(69\) −4.68969 −0.564573
\(70\) 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 \(-0.749370\pi\)
−0.705706 + 0.708505i \(0.749370\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.57908 0.521835
\(78\) 0 0
\(79\) −6.07988 −0.684040 −0.342020 0.939693i \(-0.611111\pi\)
−0.342020 + 0.939693i \(0.611111\pi\)
\(80\) 0 0
\(81\) 6.63979 0.737754
\(82\) 0 0
\(83\) −7.45926 −0.818761 −0.409380 0.912364i \(-0.634255\pi\)
−0.409380 + 0.912364i \(0.634255\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.24960 −0.348394
\(88\) 0 0
\(89\) 4.07988 0.432466 0.216233 0.976342i \(-0.430623\pi\)
0.216233 + 0.976342i \(0.430623\pi\)
\(90\) 0 0
\(91\) −10.7296 −1.12477
\(92\) 0 0
\(93\) 1.53914 0.159602
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −18.4193 −1.87020 −0.935100 0.354385i \(-0.884690\pi\)
−0.935100 + 0.354385i \(0.884690\pi\)
\(98\) 0 0
\(99\) 2.62061 0.263382
\(100\) 0 0
\(101\) 5.53914 0.551165 0.275583 0.961277i \(-0.411129\pi\)
0.275583 + 0.961277i \(0.411129\pi\)
\(102\) 0 0
\(103\) −6.57908 −0.648256 −0.324128 0.946013i \(-0.605071\pi\)
−0.324128 + 0.946013i \(0.605071\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.9086 1.44126 0.720632 0.693317i \(-0.243852\pi\)
0.720632 + 0.693317i \(0.243852\pi\)
\(108\) 0 0
\(109\) 4.76957 0.456842 0.228421 0.973562i \(-0.426644\pi\)
0.228421 + 0.973562i \(0.426644\pi\)
\(110\) 0 0
\(111\) 0.0207669 0.00197111
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.14058 −0.567697
\(118\) 0 0
\(119\) 1.19049 0.109132
\(120\) 0 0
\(121\) −10.0783 −0.916207
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 17.9585 1.59356 0.796778 0.604272i \(-0.206536\pi\)
0.796778 + 0.604272i \(0.206536\pi\)
\(128\) 0 0
\(129\) −2.57908 −0.227075
\(130\) 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
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −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 \(-0.261903\pi\)
0.680177 + 0.733048i \(0.261903\pi\)
\(140\) 0 0
\(141\) 4.93929 0.415964
\(142\) 0 0
\(143\) −2.15975 −0.180608
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −8.18890 −0.675409
\(148\) 0 0
\(149\) −8.41932 −0.689738 −0.344869 0.938651i \(-0.612077\pi\)
−0.344869 + 0.938651i \(0.612077\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 0.681319 0.0550814
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.96006 −0.395856 −0.197928 0.980217i \(-0.563421\pi\)
−0.197928 + 0.980217i \(0.563421\pi\)
\(158\) 0 0
\(159\) 3.56150 0.282446
\(160\) 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
\(166\) 0 0
\(167\) −11.0399 −0.854296 −0.427148 0.904182i \(-0.640482\pi\)
−0.427148 + 0.904182i \(0.640482\pi\)
\(168\) 0 0
\(169\) −7.93929 −0.610715
\(170\) 0 0
\(171\) 2.72963 0.208740
\(172\) 0 0
\(173\) −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 0
\(177\) −7.56988 −0.568987
\(178\) 0 0
\(179\) −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 \(0.546063\pi\)
\(182\) 0 0
\(183\) −3.92012 −0.289784
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.239632 0.0175237
\(188\) 0 0
\(189\) −14.2097 −1.03360
\(190\) 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 \(-0.401506\pi\)
0.304513 + 0.952508i \(0.401506\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −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 \(-0.394860\pi\)
0.324333 + 0.945943i \(0.394860\pi\)
\(200\) 0 0
\(201\) 2.97923 0.210139
\(202\) 0 0
\(203\) −29.8079 −2.09211
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −24.6190 −1.71114
\(208\) 0 0
\(209\) 0.960061 0.0664088
\(210\) 0 0
\(211\) −16.5200 −1.13728 −0.568641 0.822586i \(-0.692531\pi\)
−0.568641 + 0.822586i \(0.692531\pi\)
\(212\) 0 0
\(213\) −5.00160 −0.342704
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 14.1182 0.958407
\(218\) 0 0
\(219\) 6.27037 0.423712
\(220\) 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 \(0.402119\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.350246 0.0232466 0.0116233 0.999932i \(-0.496300\pi\)
0.0116233 + 0.999932i \(0.496300\pi\)
\(228\) 0 0
\(229\) −8.07988 −0.533933 −0.266967 0.963706i \(-0.586021\pi\)
−0.266967 + 0.963706i \(0.586021\pi\)
\(230\) 0 0
\(231\) −2.38098 −0.156657
\(232\) 0 0
\(233\) 4.92012 0.322328 0.161164 0.986928i \(-0.448475\pi\)
0.161164 + 0.986928i \(0.448475\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 3.16135 0.205352
\(238\) 0 0
\(239\) −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 \(0.276694\pi\)
\(242\) 0 0
\(243\) −12.3902 −0.794831
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.24960 −0.143139
\(248\) 0 0
\(249\) 3.87859 0.245796
\(250\) 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
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 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
\(261\) −17.0591 −1.05593
\(262\) 0 0
\(263\) −3.84025 −0.236800 −0.118400 0.992966i \(-0.537776\pi\)
−0.118400 + 0.992966i \(0.537776\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.12141 −0.129828
\(268\) 0 0
\(269\) 23.1981 1.41441 0.707207 0.707007i \(-0.249955\pi\)
0.707207 + 0.707007i \(0.249955\pi\)
\(270\) 0 0
\(271\) −23.9792 −1.45663 −0.728317 0.685240i \(-0.759697\pi\)
−0.728317 + 0.685240i \(0.759697\pi\)
\(272\) 0 0
\(273\) 5.57908 0.337661
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −24.6590 −1.48161 −0.740807 0.671718i \(-0.765556\pi\)
−0.740807 + 0.671718i \(0.765556\pi\)
\(278\) 0 0
\(279\) 8.07988 0.483730
\(280\) 0 0
\(281\) −18.9984 −1.13335 −0.566675 0.823941i \(-0.691770\pi\)
−0.566675 + 0.823941i \(0.691770\pi\)
\(282\) 0 0
\(283\) 29.0367 1.72606 0.863028 0.505156i \(-0.168565\pi\)
0.863028 + 0.505156i \(0.168565\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.9377 −0.996335
\(290\) 0 0
\(291\) 9.57748 0.561442
\(292\) 0 0
\(293\) −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 0
\(297\) −2.86025 −0.165968
\(298\) 0 0
\(299\) 20.2895 1.17337
\(300\) 0 0
\(301\) −23.6574 −1.36359
\(302\) 0 0
\(303\) −2.88018 −0.165462
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.5391 0.715647 0.357823 0.933789i \(-0.383519\pi\)
0.357823 + 0.933789i \(0.383519\pi\)
\(308\) 0 0
\(309\) 3.42092 0.194609
\(310\) 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 \(-0.600514\pi\)
−0.310552 + 0.950557i \(0.600514\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 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
\(321\) −7.75199 −0.432674
\(322\) 0 0
\(323\) 0.249601 0.0138882
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.48003 −0.137146
\(328\) 0 0
\(329\) 45.3071 2.49786
\(330\) 0 0
\(331\) −33.4876 −1.84065 −0.920324 0.391158i \(-0.872075\pi\)
−0.920324 + 0.391158i \(0.872075\pi\)
\(332\) 0 0
\(333\) 0.109018 0.00597415
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.69890 −0.310439 −0.155219 0.987880i \(-0.549608\pi\)
−0.155219 + 0.987880i \(0.549608\pi\)
\(338\) 0 0
\(339\) 3.11982 0.169445
\(340\) 0 0
\(341\) 2.84184 0.153894
\(342\) 0 0
\(343\) −41.7280 −2.25310
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.239632 −0.0128641 −0.00643207 0.999979i \(-0.502047\pi\)
−0.00643207 + 0.999979i \(0.502047\pi\)
\(348\) 0 0
\(349\) −17.2380 −0.922731 −0.461365 0.887210i \(-0.652640\pi\)
−0.461365 + 0.887210i \(0.652640\pi\)
\(350\) 0 0
\(351\) 6.70209 0.357731
\(352\) 0 0
\(353\) 34.7280 1.84839 0.924193 0.381925i \(-0.124739\pi\)
0.924193 + 0.381925i \(0.124739\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.619019 −0.0327619
\(358\) 0 0
\(359\) −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
\(362\) 0 0
\(363\) 5.24040 0.275050
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −15.2380 −0.795419 −0.397710 0.917511i \(-0.630195\pi\)
−0.397710 + 0.917511i \(0.630195\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 32.6689 1.69609
\(372\) 0 0
\(373\) 26.6382 1.37927 0.689637 0.724156i \(-0.257770\pi\)
0.689637 + 0.724156i \(0.257770\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.0591 0.724081
\(378\) 0 0
\(379\) −11.9693 −0.614820 −0.307410 0.951577i \(-0.599462\pi\)
−0.307410 + 0.951577i \(0.599462\pi\)
\(380\) 0 0
\(381\) −9.33785 −0.478393
\(382\) 0 0
\(383\) −9.84025 −0.502813 −0.251407 0.967882i \(-0.580893\pi\)
−0.251407 + 0.967882i \(0.580893\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.5391 −0.688233
\(388\) 0 0
\(389\) −8.65896 −0.439027 −0.219513 0.975610i \(-0.570447\pi\)
−0.219513 + 0.975610i \(0.570447\pi\)
\(390\) 0 0
\(391\) −2.25120 −0.113848
\(392\) 0 0
\(393\) −3.61902 −0.182555
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −28.9984 −1.45539 −0.727694 0.685902i \(-0.759408\pi\)
−0.727694 + 0.685902i \(0.759408\pi\)
\(398\) 0 0
\(399\) −2.48003 −0.124157
\(400\) 0 0
\(401\) 22.6174 1.12946 0.564730 0.825276i \(-0.308980\pi\)
0.564730 + 0.825276i \(0.308980\pi\)
\(402\) 0 0
\(403\) −6.65896 −0.331706
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 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
\(411\) 4.06071 0.200300
\(412\) 0 0
\(413\) −69.4369 −3.41677
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −8.33945 −0.408384
\(418\) 0 0
\(419\) 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 \(0.247118\pi\)
\(422\) 0 0
\(423\) 25.9293 1.26073
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −35.9585 −1.74015
\(428\) 0 0
\(429\) 1.12301 0.0542193
\(430\) 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 \(-0.165491\pi\)
0.867865 + 0.496799i \(0.165491\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.01917 −0.431445
\(438\) 0 0
\(439\) −20.9984 −1.00220 −0.501100 0.865390i \(-0.667071\pi\)
−0.501100 + 0.865390i \(0.667071\pi\)
\(440\) 0 0
\(441\) −42.9884 −2.04707
\(442\) 0 0
\(443\) −31.4976 −1.49650 −0.748248 0.663419i \(-0.769105\pi\)
−0.748248 + 0.663419i \(0.769105\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.37779 0.207062
\(448\) 0 0
\(449\) 18.9601 0.894781 0.447390 0.894339i \(-0.352353\pi\)
0.447390 + 0.894339i \(0.352353\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 10.3994 0.488606
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6.32948 0.296081 0.148040 0.988981i \(-0.452703\pi\)
0.148040 + 0.988981i \(0.452703\pi\)
\(458\) 0 0
\(459\) −0.743620 −0.0347092
\(460\) 0 0
\(461\) −6.49920 −0.302698 −0.151349 0.988480i \(-0.548362\pi\)
−0.151349 + 0.988480i \(0.548362\pi\)
\(462\) 0 0
\(463\) 28.4177 1.32068 0.660342 0.750965i \(-0.270411\pi\)
0.660342 + 0.750965i \(0.270411\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.5775 0.813389 0.406694 0.913564i \(-0.366681\pi\)
0.406694 + 0.913564i \(0.366681\pi\)
\(468\) 0 0
\(469\) 27.3279 1.26188
\(470\) 0 0
\(471\) 2.57908 0.118838
\(472\) 0 0
\(473\) −4.76196 −0.218955
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 18.6965 0.856053
\(478\) 0 0
\(479\) −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
\(482\) 0 0
\(483\) 22.3678 1.01777
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −22.1981 −1.00589 −0.502946 0.864318i \(-0.667751\pi\)
−0.502946 + 0.864318i \(0.667751\pi\)
\(488\) 0 0
\(489\) 11.1582 0.504589
\(490\) 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
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −45.8786 −2.05794
\(498\) 0 0
\(499\) −11.6574 −0.521855 −0.260928 0.965358i \(-0.584028\pi\)
−0.260928 + 0.965358i \(0.584028\pi\)
\(500\) 0 0
\(501\) 5.74043 0.256463
\(502\) 0 0
\(503\) 11.7504 0.523924 0.261962 0.965078i \(-0.415630\pi\)
0.261962 + 0.965078i \(0.415630\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.12819 0.183339
\(508\) 0 0
\(509\) 29.9569 1.32781 0.663907 0.747815i \(-0.268897\pi\)
0.663907 + 0.747815i \(0.268897\pi\)
\(510\) 0 0
\(511\) 57.5168 2.54439
\(512\) 0 0
\(513\) −2.97923 −0.131536
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 9.11982 0.401089
\(518\) 0 0
\(519\) 8.81788 0.387062
\(520\) 0 0
\(521\) −15.1198 −0.662411 −0.331206 0.943559i \(-0.607455\pi\)
−0.331206 + 0.943559i \(0.607455\pi\)
\(522\) 0 0
\(523\) 15.6498 0.684316 0.342158 0.939642i \(-0.388842\pi\)
0.342158 + 0.939642i \(0.388842\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.738835 0.0321842
\(528\) 0 0
\(529\) 58.3455 2.53676
\(530\) 0 0
\(531\) −39.7388 −1.72452
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 1.32028 0.0569741
\(538\) 0 0
\(539\) −15.1198 −0.651257
\(540\) 0 0
\(541\) −27.2995 −1.17370 −0.586849 0.809697i \(-0.699632\pi\)
−0.586849 + 0.809697i \(0.699632\pi\)
\(542\) 0 0
\(543\) 2.01758 0.0865825
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −33.9968 −1.45360 −0.726799 0.686850i \(-0.758993\pi\)
−0.726799 + 0.686850i \(0.758993\pi\)
\(548\) 0 0
\(549\) −20.5791 −0.878294
\(550\) 0 0
\(551\) −6.24960 −0.266242
\(552\) 0 0
\(553\) 28.9984 1.23314
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −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
\(561\) −0.124602 −0.00526068
\(562\) 0 0
\(563\) 32.2995 1.36126 0.680631 0.732626i \(-0.261706\pi\)
0.680631 + 0.732626i \(0.261706\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −31.6689 −1.32997
\(568\) 0 0
\(569\) −6.73883 −0.282507 −0.141253 0.989973i \(-0.545113\pi\)
−0.141253 + 0.989973i \(0.545113\pi\)
\(570\) 0 0
\(571\) −34.4193 −1.44040 −0.720202 0.693764i \(-0.755951\pi\)
−0.720202 + 0.693764i \(0.755951\pi\)
\(572\) 0 0
\(573\) 1.07067 0.0447281
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −28.1773 −1.17304 −0.586519 0.809936i \(-0.699502\pi\)
−0.586519 + 0.809936i \(0.699502\pi\)
\(578\) 0 0
\(579\) −4.39939 −0.182832
\(580\) 0 0
\(581\) 35.5775 1.47600
\(582\) 0 0
\(583\) 6.57589 0.272346
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.6174 −1.42881 −0.714407 0.699730i \(-0.753303\pi\)
−0.714407 + 0.699730i \(0.753303\pi\)
\(588\) 0 0
\(589\) 2.96006 0.121967
\(590\) 0 0
\(591\) 7.23804 0.297733
\(592\) 0 0
\(593\) 3.99840 0.164195 0.0820974 0.996624i \(-0.473838\pi\)
0.0820974 + 0.996624i \(0.473838\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.75801 −0.194732
\(598\) 0 0
\(599\) 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 \(0.622856\pi\)
\(602\) 0 0
\(603\) 15.6398 0.636901
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −12.5791 −0.510569 −0.255285 0.966866i \(-0.582169\pi\)
−0.255285 + 0.966866i \(0.582169\pi\)
\(608\) 0 0
\(609\) 15.4992 0.628059
\(610\) 0 0
\(611\) −21.3694 −0.864514
\(612\) 0 0
\(613\) 26.5759 1.07339 0.536695 0.843776i \(-0.319673\pi\)
0.536695 + 0.843776i \(0.319673\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 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 \(-0.707246\pi\)
−0.606047 + 0.795429i \(0.707246\pi\)
\(620\) 0 0
\(621\) 26.8702 1.07826
\(622\) 0 0
\(623\) −19.4593 −0.779619
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −0.499202 −0.0199362
\(628\) 0 0
\(629\) 0.00996876 0.000397480 0
\(630\) 0 0
\(631\) 25.4992 1.01511 0.507554 0.861620i \(-0.330550\pi\)
0.507554 + 0.861620i \(0.330550\pi\)
\(632\) 0 0
\(633\) 8.58988 0.341417
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 35.4285 1.40373
\(638\) 0 0
\(639\) −26.2564 −1.03869
\(640\) 0 0
\(641\) 39.1965 1.54817 0.774084 0.633082i \(-0.218211\pi\)
0.774084 + 0.633082i \(0.218211\pi\)
\(642\) 0 0
\(643\) −36.3778 −1.43460 −0.717300 0.696764i \(-0.754622\pi\)
−0.717300 + 0.696764i \(0.754622\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.6897 −0.420255 −0.210128 0.977674i \(-0.567388\pi\)
−0.210128 + 0.977674i \(0.567388\pi\)
\(648\) 0 0
\(649\) −13.9769 −0.548640
\(650\) 0 0
\(651\) −7.34104 −0.287718
\(652\) 0 0
\(653\) −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
\(657\) 32.9169 1.28421
\(658\) 0 0
\(659\) −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 \(0.0999560\pi\)
\(662\) 0 0
\(663\) 0.291964 0.0113390
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 56.3662 2.18251
\(668\) 0 0
\(669\) −4.70049 −0.181731
\(670\) 0 0
\(671\) −7.23804 −0.279421
\(672\) 0 0
\(673\) 6.57908 0.253605 0.126802 0.991928i \(-0.459529\pi\)
0.126802 + 0.991928i \(0.459529\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −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
\(681\) −0.182117 −0.00697874
\(682\) 0 0
\(683\) −7.54074 −0.288538 −0.144269 0.989538i \(-0.546083\pi\)
−0.144269 + 0.989538i \(0.546083\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 4.20129 0.160289
\(688\) 0 0
\(689\) −15.4085 −0.587018
\(690\) 0 0
\(691\) −28.4193 −1.08112 −0.540561 0.841305i \(-0.681788\pi\)
−0.540561 + 0.841305i \(0.681788\pi\)
\(692\) 0 0
\(693\) −12.4992 −0.474805
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −2.55831 −0.0967643
\(700\) 0 0
\(701\) −24.2596 −0.916271 −0.458136 0.888882i \(-0.651483\pi\)
−0.458136 + 0.888882i \(0.651483\pi\)
\(702\) 0 0
\(703\) 0.0399387 0.00150632
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −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
\(711\) 16.5958 0.622392
\(712\) 0 0
\(713\) −26.6973 −0.999822
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.54994 0.0578835
\(718\) 0 0
\(719\) 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
\(722\) 0 0
\(723\) −10.4193 −0.387499
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −4.29874 −0.159432 −0.0797158 0.996818i \(-0.525401\pi\)
−0.0797158 + 0.996818i \(0.525401\pi\)
\(728\) 0 0
\(729\) −13.4768 −0.499142
\(730\) 0 0
\(731\) −1.23804 −0.0457905
\(732\) 0 0
\(733\) 12.0415 0.444764 0.222382 0.974960i \(-0.428617\pi\)
0.222382 + 0.974960i \(0.428617\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.50080 0.202624
\(738\) 0 0
\(739\) −6.61742 −0.243426 −0.121713 0.992565i \(-0.538839\pi\)
−0.121713 + 0.992565i \(0.538839\pi\)
\(740\) 0 0
\(741\) 1.16972 0.0429709
\(742\) 0 0
\(743\) −47.6158 −1.74686 −0.873428 0.486954i \(-0.838108\pi\)
−0.873428 + 0.486954i \(0.838108\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 20.3610 0.744972
\(748\) 0 0
\(749\) −71.1074 −2.59821
\(750\) 0 0
\(751\) 25.6574 0.936250 0.468125 0.883662i \(-0.344930\pi\)
0.468125 + 0.883662i \(0.344930\pi\)
\(752\) 0 0
\(753\) −7.73724 −0.281961
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8.83865 −0.321246 −0.160623 0.987016i \(-0.551350\pi\)
−0.160623 + 0.987016i \(0.551350\pi\)
\(758\) 0 0
\(759\) 4.50239 0.163426
\(760\) 0 0
\(761\) −9.40776 −0.341031 −0.170516 0.985355i \(-0.554543\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(762\) 0 0
\(763\) −22.7488 −0.823562
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 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
\(771\) −5.74043 −0.206737
\(772\) 0 0
\(773\) −54.4369 −1.95796 −0.978980 0.203958i \(-0.934619\pi\)
−0.978980 + 0.203958i \(0.934619\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.0990493 −0.00355337
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −9.23485 −0.330449
\(782\) 0 0
\(783\) 18.6190 0.665389
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −27.6705 −0.986348 −0.493174 0.869931i \(-0.664163\pi\)
−0.493174 + 0.869931i \(0.664163\pi\)
\(788\) 0 0
\(789\) 1.99681 0.0710883
\(790\) 0 0
\(791\) 28.6174 1.01752
\(792\) 0 0
\(793\) 16.9601 0.602269
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −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
\(801\) −11.1366 −0.393491
\(802\) 0 0
\(803\) 11.5775 0.408561
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −12.0623 −0.424613
\(808\) 0 0
\(809\) 9.72963 0.342076 0.171038 0.985264i \(-0.445288\pi\)
0.171038 + 0.985264i \(0.445288\pi\)
\(810\) 0 0
\(811\) 38.7280 1.35993 0.679963 0.733247i \(-0.261996\pi\)
0.679963 + 0.733247i \(0.261996\pi\)
\(812\) 0 0
\(813\) 12.4685 0.437288
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −4.96006 −0.173531
\(818\) 0 0
\(819\) 29.2879 1.02340
\(820\) 0 0
\(821\) −30.2780 −1.05671 −0.528354 0.849024i \(-0.677191\pi\)
−0.528354 + 0.849024i \(0.677191\pi\)
\(822\) 0 0
\(823\) −7.93770 −0.276691 −0.138345 0.990384i \(-0.544178\pi\)
−0.138345 + 0.990384i \(0.544178\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 30.2496 1.05188 0.525941 0.850521i \(-0.323713\pi\)
0.525941 + 0.850521i \(0.323713\pi\)
\(828\) 0 0
\(829\) −40.6765 −1.41275 −0.706377 0.707836i \(-0.749672\pi\)
−0.706377 + 0.707836i \(0.749672\pi\)
\(830\) 0 0
\(831\) 12.8219 0.444787
\(832\) 0 0
\(833\) −3.93092 −0.136198
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −8.81871 −0.304819
\(838\) 0 0
\(839\) −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
\(842\) 0 0
\(843\) 9.87859 0.340237
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 48.0691 1.65167
\(848\) 0 0
\(849\) −15.0982 −0.518170
\(850\) 0 0
\(851\) −0.360214 −0.0123480
\(852\) 0 0
\(853\) −17.2196 −0.589589 −0.294794 0.955561i \(-0.595251\pi\)
−0.294794 + 0.955561i \(0.595251\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −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 \(-0.597179\pi\)
−0.300577 + 0.953758i \(0.597179\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.07988 −0.138881 −0.0694403 0.997586i \(-0.522121\pi\)
−0.0694403 + 0.997586i \(0.522121\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.80708 0.299104
\(868\) 0 0
\(869\) 5.83705 0.198009
\(870\) 0 0
\(871\) −12.8894 −0.436740
\(872\) 0 0
\(873\) 50.2780 1.70165
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −25.2787 −0.853602 −0.426801 0.904345i \(-0.640360\pi\)
−0.426801 + 0.904345i \(0.640360\pi\)
\(878\) 0 0
\(879\) 3.24960 0.109606
\(880\) 0 0
\(881\) −0.0814726 −0.00274488 −0.00137244 0.999999i \(-0.500437\pi\)
−0.00137244 + 0.999999i \(0.500437\pi\)
\(882\) 0 0
\(883\) 19.3410 0.650878 0.325439 0.945563i \(-0.394488\pi\)
0.325439 + 0.945563i \(0.394488\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 5.53914 0.185986 0.0929931 0.995667i \(-0.470357\pi\)
0.0929931 + 0.995667i \(0.470357\pi\)
\(888\) 0 0
\(889\) −85.6542 −2.87275
\(890\) 0 0
\(891\) −6.37460 −0.213557
\(892\) 0 0
\(893\) 9.49920 0.317879
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −10.5499 −0.352252
\(898\) 0 0
\(899\) −18.4992 −0.616983
\(900\) 0 0
\(901\) 1.70963 0.0569561
\(902\) 0 0
\(903\) 12.3011 0.409355
\(904\) 0 0
\(905\) 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 0
\(909\) −15.1198 −0.501493
\(910\) 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
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −33.1965 −1.09625
\(918\) 0 0
\(919\) −30.8287 −1.01694 −0.508472 0.861078i \(-0.669790\pi\)
−0.508472 + 0.861078i \(0.669790\pi\)
\(920\) 0 0
\(921\) −6.51997 −0.214840
\(922\) 0 0
\(923\) 21.6390 0.712255
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 17.9585 0.589833
\(928\) 0 0
\(929\) −45.0575 −1.47829 −0.739145 0.673547i \(-0.764770\pi\)
−0.739145 + 0.673547i \(0.764770\pi\)
\(930\) 0 0
\(931\) −15.7488 −0.516146
\(932\) 0 0
\(933\) 4.08064 0.133594
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 22.2464 0.726759 0.363379 0.931641i \(-0.381623\pi\)
0.363379 + 0.931641i \(0.381623\pi\)
\(938\) 0 0
\(939\) 5.71365 0.186458
\(940\) 0 0
\(941\) −53.9277 −1.75799 −0.878997 0.476828i \(-0.841787\pi\)
−0.878997 + 0.476828i \(0.841787\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.76196 0.154743 0.0773715 0.997002i \(-0.475347\pi\)
0.0773715 + 0.997002i \(0.475347\pi\)
\(948\) 0 0
\(949\) −27.1282 −0.880618
\(950\) 0 0
\(951\) −11.2088 −0.363471
\(952\) 0 0
\(953\) 4.37779 0.141811 0.0709053 0.997483i \(-0.477411\pi\)
0.0709053 + 0.997483i \(0.477411\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 3.11982 0.100849
\(958\) 0 0
\(959\) 37.2480 1.20280
\(960\) 0 0
\(961\) −22.2380 −0.717356
\(962\) 0 0
\(963\) −40.6949 −1.31137
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 13.1582 0.423138 0.211569 0.977363i \(-0.432143\pi\)
0.211569 + 0.977363i \(0.432143\pi\)
\(968\) 0 0
\(969\) −0.129785 −0.00416929
\(970\) 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
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 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
\(981\) −13.0192 −0.415670
\(982\) 0 0
\(983\) −26.2364 −0.836813 −0.418406 0.908260i \(-0.637411\pi\)
−0.418406 + 0.908260i \(0.637411\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −23.5583 −0.749869
\(988\) 0 0
\(989\) 44.7356 1.42251
\(990\) 0 0
\(991\) −39.2764 −1.24766 −0.623828 0.781562i \(-0.714423\pi\)
−0.623828 + 0.781562i \(0.714423\pi\)
\(992\) 0 0
\(993\) 17.4125 0.552570
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 14.4609 0.457980 0.228990 0.973429i \(-0.426458\pi\)
0.228990 + 0.973429i \(0.426458\pi\)
\(998\) 0 0
\(999\) −0.118987 −0.00376458
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 7600.2.a.bk.1.2 3
4.3 odd 2 950.2.a.l.1.2 yes 3
5.4 even 2 7600.2.a.bz.1.2 3
12.11 even 2 8550.2.a.ci.1.3 3
20.3 even 4 950.2.b.h.799.2 6
20.7 even 4 950.2.b.h.799.5 6
20.19 odd 2 950.2.a.j.1.2 3
60.59 even 2 8550.2.a.cp.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.2 3 20.19 odd 2
950.2.a.l.1.2 yes 3 4.3 odd 2
950.2.b.h.799.2 6 20.3 even 4
950.2.b.h.799.5 6 20.7 even 4
7600.2.a.bk.1.2 3 1.1 even 1 trivial
7600.2.a.bz.1.2 3 5.4 even 2
8550.2.a.ci.1.3 3 12.11 even 2
8550.2.a.cp.1.1 3 60.59 even 2