Properties

Label 7800.2.a.bh.1.1
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.3732.1
Defining polynomial: \(x^{3} - x^{2} - 13 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.20633\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -4.48688 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -4.48688 q^{7} +1.00000 q^{9} -1.20633 q^{11} +1.00000 q^{13} -3.00000 q^{17} -7.69321 q^{19} +4.48688 q^{21} -5.69321 q^{23} -1.00000 q^{27} -7.41266 q^{29} -1.20633 q^{31} +1.20633 q^{33} +0.719448 q^{37} -1.00000 q^{39} +1.28055 q^{41} -1.28055 q^{43} -5.92578 q^{47} +13.1321 q^{49} +3.00000 q^{51} -6.69321 q^{53} +7.69321 q^{57} +5.92578 q^{59} +9.41266 q^{61} -4.48688 q^{63} -11.2063 q^{67} +5.69321 q^{69} +5.13211 q^{71} -5.13211 q^{73} +5.41266 q^{77} +2.71945 q^{79} +1.00000 q^{81} -4.89954 q^{83} +7.41266 q^{87} -0.412660 q^{89} -4.48688 q^{91} +1.20633 q^{93} -12.9738 q^{97} -1.20633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q - 3 q^{3} - q^{7} + 3 q^{9} + 5 q^{11} + 3 q^{13} - 9 q^{17} - 2 q^{19} + q^{21} + 4 q^{23} - 3 q^{27} - 5 q^{29} + 5 q^{31} - 5 q^{33} + 6 q^{37} - 3 q^{39} - 13 q^{47} + 26 q^{49} + 9 q^{51} + q^{53} + 2 q^{57} + 13 q^{59} + 11 q^{61} - q^{63} - 25 q^{67} - 4 q^{69} + 2 q^{71} - 2 q^{73} - q^{77} + 12 q^{79} + 3 q^{81} + 15 q^{83} + 5 q^{87} + 16 q^{89} - q^{91} - 5 q^{93} - 14 q^{97} + 5 q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.48688 −1.69588 −0.847941 0.530091i \(-0.822158\pi\)
−0.847941 + 0.530091i \(0.822158\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.20633 −0.363722 −0.181861 0.983324i \(-0.558212\pi\)
−0.181861 + 0.983324i \(0.558212\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) −7.69321 −1.76494 −0.882472 0.470365i \(-0.844122\pi\)
−0.882472 + 0.470365i \(0.844122\pi\)
\(20\) 0 0
\(21\) 4.48688 0.979118
\(22\) 0 0
\(23\) −5.69321 −1.18712 −0.593558 0.804791i \(-0.702277\pi\)
−0.593558 + 0.804791i \(0.702277\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −7.41266 −1.37650 −0.688248 0.725475i \(-0.741620\pi\)
−0.688248 + 0.725475i \(0.741620\pi\)
\(30\) 0 0
\(31\) −1.20633 −0.216663 −0.108332 0.994115i \(-0.534551\pi\)
−0.108332 + 0.994115i \(0.534551\pi\)
\(32\) 0 0
\(33\) 1.20633 0.209995
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.719448 0.118277 0.0591383 0.998250i \(-0.481165\pi\)
0.0591383 + 0.998250i \(0.481165\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 1.28055 0.199989 0.0999943 0.994988i \(-0.468118\pi\)
0.0999943 + 0.994988i \(0.468118\pi\)
\(42\) 0 0
\(43\) −1.28055 −0.195282 −0.0976412 0.995222i \(-0.531130\pi\)
−0.0976412 + 0.995222i \(0.531130\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.92578 −0.864364 −0.432182 0.901787i \(-0.642256\pi\)
−0.432182 + 0.901787i \(0.642256\pi\)
\(48\) 0 0
\(49\) 13.1321 1.87602
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) −6.69321 −0.919383 −0.459692 0.888079i \(-0.652040\pi\)
−0.459692 + 0.888079i \(0.652040\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.69321 1.01899
\(58\) 0 0
\(59\) 5.92578 0.771471 0.385735 0.922609i \(-0.373948\pi\)
0.385735 + 0.922609i \(0.373948\pi\)
\(60\) 0 0
\(61\) 9.41266 1.20517 0.602584 0.798056i \(-0.294138\pi\)
0.602584 + 0.798056i \(0.294138\pi\)
\(62\) 0 0
\(63\) −4.48688 −0.565294
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.2063 −1.36907 −0.684536 0.728979i \(-0.739995\pi\)
−0.684536 + 0.728979i \(0.739995\pi\)
\(68\) 0 0
\(69\) 5.69321 0.685382
\(70\) 0 0
\(71\) 5.13211 0.609069 0.304535 0.952501i \(-0.401499\pi\)
0.304535 + 0.952501i \(0.401499\pi\)
\(72\) 0 0
\(73\) −5.13211 −0.600668 −0.300334 0.953834i \(-0.597098\pi\)
−0.300334 + 0.953834i \(0.597098\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.41266 0.616830
\(78\) 0 0
\(79\) 2.71945 0.305962 0.152981 0.988229i \(-0.451113\pi\)
0.152981 + 0.988229i \(0.451113\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.89954 −0.537795 −0.268897 0.963169i \(-0.586659\pi\)
−0.268897 + 0.963169i \(0.586659\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 7.41266 0.794721
\(88\) 0 0
\(89\) −0.412660 −0.0437419 −0.0218709 0.999761i \(-0.506962\pi\)
−0.0218709 + 0.999761i \(0.506962\pi\)
\(90\) 0 0
\(91\) −4.48688 −0.470353
\(92\) 0 0
\(93\) 1.20633 0.125091
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.9738 −1.31729 −0.658643 0.752456i \(-0.728869\pi\)
−0.658643 + 0.752456i \(0.728869\pi\)
\(98\) 0 0
\(99\) −1.20633 −0.121241
\(100\) 0 0
\(101\) 13.6670 1.35991 0.679957 0.733252i \(-0.261998\pi\)
0.679957 + 0.733252i \(0.261998\pi\)
\(102\) 0 0
\(103\) 0.719448 0.0708893 0.0354447 0.999372i \(-0.488715\pi\)
0.0354447 + 0.999372i \(0.488715\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 13.7991 1.33401 0.667004 0.745054i \(-0.267576\pi\)
0.667004 + 0.745054i \(0.267576\pi\)
\(108\) 0 0
\(109\) 0.867892 0.0831290 0.0415645 0.999136i \(-0.486766\pi\)
0.0415645 + 0.999136i \(0.486766\pi\)
\(110\) 0 0
\(111\) −0.719448 −0.0682870
\(112\) 0 0
\(113\) 6.41266 0.603252 0.301626 0.953426i \(-0.402471\pi\)
0.301626 + 0.953426i \(0.402471\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 13.4606 1.23394
\(120\) 0 0
\(121\) −9.54477 −0.867706
\(122\) 0 0
\(123\) −1.28055 −0.115463
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −15.1321 −1.34276 −0.671379 0.741114i \(-0.734298\pi\)
−0.671379 + 0.741114i \(0.734298\pi\)
\(128\) 0 0
\(129\) 1.28055 0.112746
\(130\) 0 0
\(131\) −7.69321 −0.672159 −0.336080 0.941834i \(-0.609101\pi\)
−0.336080 + 0.941834i \(0.609101\pi\)
\(132\) 0 0
\(133\) 34.5185 2.99314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −19.7991 −1.69155 −0.845775 0.533540i \(-0.820861\pi\)
−0.845775 + 0.533540i \(0.820861\pi\)
\(138\) 0 0
\(139\) −19.9475 −1.69193 −0.845964 0.533241i \(-0.820974\pi\)
−0.845964 + 0.533241i \(0.820974\pi\)
\(140\) 0 0
\(141\) 5.92578 0.499041
\(142\) 0 0
\(143\) −1.20633 −0.100878
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −13.1321 −1.08312
\(148\) 0 0
\(149\) 3.85156 0.315532 0.157766 0.987477i \(-0.449571\pi\)
0.157766 + 0.987477i \(0.449571\pi\)
\(150\) 0 0
\(151\) −12.0742 −0.982586 −0.491293 0.870994i \(-0.663476\pi\)
−0.491293 + 0.870994i \(0.663476\pi\)
\(152\) 0 0
\(153\) −3.00000 −0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.69321 −0.534176 −0.267088 0.963672i \(-0.586062\pi\)
−0.267088 + 0.963672i \(0.586062\pi\)
\(158\) 0 0
\(159\) 6.69321 0.530806
\(160\) 0 0
\(161\) 25.5448 2.01321
\(162\) 0 0
\(163\) 10.2543 0.803180 0.401590 0.915820i \(-0.368458\pi\)
0.401590 + 0.915820i \(0.368458\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.71945 −0.365202 −0.182601 0.983187i \(-0.558452\pi\)
−0.182601 + 0.983187i \(0.558452\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −7.69321 −0.588315
\(172\) 0 0
\(173\) −0.280552 −0.0213300 −0.0106650 0.999943i \(-0.503395\pi\)
−0.0106650 + 0.999943i \(0.503395\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.92578 −0.445409
\(178\) 0 0
\(179\) −2.15834 −0.161322 −0.0806611 0.996742i \(-0.525703\pi\)
−0.0806611 + 0.996742i \(0.525703\pi\)
\(180\) 0 0
\(181\) −5.10587 −0.379516 −0.189758 0.981831i \(-0.560770\pi\)
−0.189758 + 0.981831i \(0.560770\pi\)
\(182\) 0 0
\(183\) −9.41266 −0.695804
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.61899 0.264647
\(188\) 0 0
\(189\) 4.48688 0.326373
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 20.2543 1.45794 0.728969 0.684547i \(-0.240000\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.1059 −1.00500 −0.502501 0.864577i \(-0.667587\pi\)
−0.502501 + 0.864577i \(0.667587\pi\)
\(198\) 0 0
\(199\) 13.3864 0.948938 0.474469 0.880272i \(-0.342640\pi\)
0.474469 + 0.880272i \(0.342640\pi\)
\(200\) 0 0
\(201\) 11.2063 0.790434
\(202\) 0 0
\(203\) 33.2597 2.33438
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.69321 −0.395706
\(208\) 0 0
\(209\) 9.28055 0.641949
\(210\) 0 0
\(211\) 15.1321 1.04174 0.520869 0.853637i \(-0.325608\pi\)
0.520869 + 0.853637i \(0.325608\pi\)
\(212\) 0 0
\(213\) −5.13211 −0.351646
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 5.41266 0.367435
\(218\) 0 0
\(219\) 5.13211 0.346796
\(220\) 0 0
\(221\) −3.00000 −0.201802
\(222\) 0 0
\(223\) 19.0796 1.27767 0.638833 0.769345i \(-0.279417\pi\)
0.638833 + 0.769345i \(0.279417\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.7674 −1.17927 −0.589633 0.807671i \(-0.700728\pi\)
−0.589633 + 0.807671i \(0.700728\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) −5.41266 −0.356127
\(232\) 0 0
\(233\) −14.4127 −0.944205 −0.472102 0.881544i \(-0.656505\pi\)
−0.472102 + 0.881544i \(0.656505\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2.71945 −0.176647
\(238\) 0 0
\(239\) 26.0217 1.68321 0.841604 0.540096i \(-0.181612\pi\)
0.841604 + 0.540096i \(0.181612\pi\)
\(240\) 0 0
\(241\) 3.74568 0.241281 0.120640 0.992696i \(-0.461505\pi\)
0.120640 + 0.992696i \(0.461505\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.69321 −0.489507
\(248\) 0 0
\(249\) 4.89954 0.310496
\(250\) 0 0
\(251\) −6.66698 −0.420816 −0.210408 0.977614i \(-0.567479\pi\)
−0.210408 + 0.977614i \(0.567479\pi\)
\(252\) 0 0
\(253\) 6.86789 0.431781
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.1321 1.13105 0.565525 0.824731i \(-0.308674\pi\)
0.565525 + 0.824731i \(0.308674\pi\)
\(258\) 0 0
\(259\) −3.22808 −0.200583
\(260\) 0 0
\(261\) −7.41266 −0.458832
\(262\) 0 0
\(263\) 3.28055 0.202287 0.101144 0.994872i \(-0.467750\pi\)
0.101144 + 0.994872i \(0.467750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0.412660 0.0252544
\(268\) 0 0
\(269\) −24.9475 −1.52108 −0.760539 0.649293i \(-0.775065\pi\)
−0.760539 + 0.649293i \(0.775065\pi\)
\(270\) 0 0
\(271\) 7.31220 0.444185 0.222092 0.975026i \(-0.428711\pi\)
0.222092 + 0.975026i \(0.428711\pi\)
\(272\) 0 0
\(273\) 4.48688 0.271558
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 12.9738 0.779518 0.389759 0.920917i \(-0.372558\pi\)
0.389759 + 0.920917i \(0.372558\pi\)
\(278\) 0 0
\(279\) −1.20633 −0.0722211
\(280\) 0 0
\(281\) 33.3864 1.99167 0.995834 0.0911899i \(-0.0290670\pi\)
0.995834 + 0.0911899i \(0.0290670\pi\)
\(282\) 0 0
\(283\) 29.3864 1.74684 0.873421 0.486966i \(-0.161897\pi\)
0.873421 + 0.486966i \(0.161897\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.74568 −0.339157
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 12.9738 0.760535
\(292\) 0 0
\(293\) −10.8253 −0.632422 −0.316211 0.948689i \(-0.602411\pi\)
−0.316211 + 0.948689i \(0.602411\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.20633 0.0699984
\(298\) 0 0
\(299\) −5.69321 −0.329247
\(300\) 0 0
\(301\) 5.74568 0.331176
\(302\) 0 0
\(303\) −13.6670 −0.785147
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 13.5448 0.773041 0.386520 0.922281i \(-0.373677\pi\)
0.386520 + 0.922281i \(0.373677\pi\)
\(308\) 0 0
\(309\) −0.719448 −0.0409280
\(310\) 0 0
\(311\) −8.26422 −0.468621 −0.234310 0.972162i \(-0.575283\pi\)
−0.234310 + 0.972162i \(0.575283\pi\)
\(312\) 0 0
\(313\) 11.3068 0.639097 0.319549 0.947570i \(-0.396469\pi\)
0.319549 + 0.947570i \(0.396469\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.6407 1.21546 0.607732 0.794142i \(-0.292079\pi\)
0.607732 + 0.794142i \(0.292079\pi\)
\(318\) 0 0
\(319\) 8.94211 0.500662
\(320\) 0 0
\(321\) −13.7991 −0.770190
\(322\) 0 0
\(323\) 23.0796 1.28419
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.867892 −0.0479945
\(328\) 0 0
\(329\) 26.5883 1.46586
\(330\) 0 0
\(331\) −28.5185 −1.56752 −0.783760 0.621064i \(-0.786701\pi\)
−0.783760 + 0.621064i \(0.786701\pi\)
\(332\) 0 0
\(333\) 0.719448 0.0394255
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 33.6145 1.83110 0.915549 0.402206i \(-0.131756\pi\)
0.915549 + 0.402206i \(0.131756\pi\)
\(338\) 0 0
\(339\) −6.41266 −0.348288
\(340\) 0 0
\(341\) 1.45523 0.0788052
\(342\) 0 0
\(343\) −27.5140 −1.48562
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −34.8253 −1.86952 −0.934761 0.355278i \(-0.884386\pi\)
−0.934761 + 0.355278i \(0.884386\pi\)
\(348\) 0 0
\(349\) −2.66698 −0.142760 −0.0713800 0.997449i \(-0.522740\pi\)
−0.0713800 + 0.997449i \(0.522740\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −4.45523 −0.237128 −0.118564 0.992946i \(-0.537829\pi\)
−0.118564 + 0.992946i \(0.537829\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −13.4606 −0.712413
\(358\) 0 0
\(359\) 7.92578 0.418307 0.209153 0.977883i \(-0.432929\pi\)
0.209153 + 0.977883i \(0.432929\pi\)
\(360\) 0 0
\(361\) 40.1855 2.11503
\(362\) 0 0
\(363\) 9.54477 0.500970
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 18.7728 0.979935 0.489967 0.871741i \(-0.337009\pi\)
0.489967 + 0.871741i \(0.337009\pi\)
\(368\) 0 0
\(369\) 1.28055 0.0666629
\(370\) 0 0
\(371\) 30.0316 1.55917
\(372\) 0 0
\(373\) 30.2281 1.56515 0.782575 0.622556i \(-0.213906\pi\)
0.782575 + 0.622556i \(0.213906\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.41266 −0.381771
\(378\) 0 0
\(379\) 11.0579 0.568005 0.284003 0.958823i \(-0.408338\pi\)
0.284003 + 0.958823i \(0.408338\pi\)
\(380\) 0 0
\(381\) 15.1321 0.775241
\(382\) 0 0
\(383\) 22.2543 1.13714 0.568571 0.822634i \(-0.307496\pi\)
0.568571 + 0.822634i \(0.307496\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.28055 −0.0650941
\(388\) 0 0
\(389\) 23.2380 1.17821 0.589106 0.808056i \(-0.299480\pi\)
0.589106 + 0.808056i \(0.299480\pi\)
\(390\) 0 0
\(391\) 17.0796 0.863754
\(392\) 0 0
\(393\) 7.69321 0.388071
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.36019 −0.218832 −0.109416 0.993996i \(-0.534898\pi\)
−0.109416 + 0.993996i \(0.534898\pi\)
\(398\) 0 0
\(399\) −34.5185 −1.72809
\(400\) 0 0
\(401\) −30.8787 −1.54201 −0.771005 0.636829i \(-0.780246\pi\)
−0.771005 + 0.636829i \(0.780246\pi\)
\(402\) 0 0
\(403\) −1.20633 −0.0600916
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.867892 −0.0430198
\(408\) 0 0
\(409\) −32.8787 −1.62575 −0.812874 0.582440i \(-0.802098\pi\)
−0.812874 + 0.582440i \(0.802098\pi\)
\(410\) 0 0
\(411\) 19.7991 0.976617
\(412\) 0 0
\(413\) −26.5883 −1.30832
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 19.9475 0.976835
\(418\) 0 0
\(419\) 20.7194 1.01221 0.506106 0.862471i \(-0.331085\pi\)
0.506106 + 0.862471i \(0.331085\pi\)
\(420\) 0 0
\(421\) −24.2117 −1.18001 −0.590004 0.807400i \(-0.700874\pi\)
−0.590004 + 0.807400i \(0.700874\pi\)
\(422\) 0 0
\(423\) −5.92578 −0.288121
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −42.2335 −2.04382
\(428\) 0 0
\(429\) 1.20633 0.0582422
\(430\) 0 0
\(431\) 0.920365 0.0443324 0.0221662 0.999754i \(-0.492944\pi\)
0.0221662 + 0.999754i \(0.492944\pi\)
\(432\) 0 0
\(433\) −13.7991 −0.663142 −0.331571 0.943430i \(-0.607579\pi\)
−0.331571 + 0.943430i \(0.607579\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 43.7991 2.09519
\(438\) 0 0
\(439\) 21.3765 1.02025 0.510123 0.860102i \(-0.329600\pi\)
0.510123 + 0.860102i \(0.329600\pi\)
\(440\) 0 0
\(441\) 13.1321 0.625338
\(442\) 0 0
\(443\) −10.1059 −0.480144 −0.240072 0.970755i \(-0.577171\pi\)
−0.240072 + 0.970755i \(0.577171\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.85156 −0.182172
\(448\) 0 0
\(449\) −28.5086 −1.34541 −0.672703 0.739913i \(-0.734867\pi\)
−0.672703 + 0.739913i \(0.734867\pi\)
\(450\) 0 0
\(451\) −1.54477 −0.0727403
\(452\) 0 0
\(453\) 12.0742 0.567296
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 29.4923 1.37959 0.689796 0.724004i \(-0.257700\pi\)
0.689796 + 0.724004i \(0.257700\pi\)
\(458\) 0 0
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) 3.73578 0.173993 0.0869964 0.996209i \(-0.472273\pi\)
0.0869964 + 0.996209i \(0.472273\pi\)
\(462\) 0 0
\(463\) −7.00541 −0.325569 −0.162785 0.986662i \(-0.552048\pi\)
−0.162785 + 0.986662i \(0.552048\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −25.5349 −1.18161 −0.590806 0.806813i \(-0.701190\pi\)
−0.590806 + 0.806813i \(0.701190\pi\)
\(468\) 0 0
\(469\) 50.2815 2.32178
\(470\) 0 0
\(471\) 6.69321 0.308407
\(472\) 0 0
\(473\) 1.54477 0.0710285
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.69321 −0.306461
\(478\) 0 0
\(479\) 2.23257 0.102009 0.0510043 0.998698i \(-0.483758\pi\)
0.0510043 + 0.998698i \(0.483758\pi\)
\(480\) 0 0
\(481\) 0.719448 0.0328040
\(482\) 0 0
\(483\) −25.5448 −1.16233
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −26.4443 −1.19831 −0.599153 0.800635i \(-0.704496\pi\)
−0.599153 + 0.800635i \(0.704496\pi\)
\(488\) 0 0
\(489\) −10.2543 −0.463716
\(490\) 0 0
\(491\) 22.0000 0.992846 0.496423 0.868081i \(-0.334646\pi\)
0.496423 + 0.868081i \(0.334646\pi\)
\(492\) 0 0
\(493\) 22.2380 1.00155
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −23.0272 −1.03291
\(498\) 0 0
\(499\) 41.2597 1.84704 0.923520 0.383551i \(-0.125299\pi\)
0.923520 + 0.383551i \(0.125299\pi\)
\(500\) 0 0
\(501\) 4.71945 0.210849
\(502\) 0 0
\(503\) −25.1321 −1.12059 −0.560293 0.828295i \(-0.689311\pi\)
−0.560293 + 0.828295i \(0.689311\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −34.2018 −1.51597 −0.757985 0.652272i \(-0.773816\pi\)
−0.757985 + 0.652272i \(0.773816\pi\)
\(510\) 0 0
\(511\) 23.0272 1.01866
\(512\) 0 0
\(513\) 7.69321 0.339664
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 7.14844 0.314388
\(518\) 0 0
\(519\) 0.280552 0.0123149
\(520\) 0 0
\(521\) −1.17468 −0.0514637 −0.0257318 0.999669i \(-0.508192\pi\)
−0.0257318 + 0.999669i \(0.508192\pi\)
\(522\) 0 0
\(523\) 2.20092 0.0962394 0.0481197 0.998842i \(-0.484677\pi\)
0.0481197 + 0.998842i \(0.484677\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.61899 0.157646
\(528\) 0 0
\(529\) 9.41266 0.409246
\(530\) 0 0
\(531\) 5.92578 0.257157
\(532\) 0 0
\(533\) 1.28055 0.0554669
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.15834 0.0931394
\(538\) 0 0
\(539\) −15.8417 −0.682348
\(540\) 0 0
\(541\) −9.13211 −0.392620 −0.196310 0.980542i \(-0.562896\pi\)
−0.196310 + 0.980542i \(0.562896\pi\)
\(542\) 0 0
\(543\) 5.10587 0.219114
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −38.0534 −1.62705 −0.813523 0.581533i \(-0.802453\pi\)
−0.813523 + 0.581533i \(0.802453\pi\)
\(548\) 0 0
\(549\) 9.41266 0.401723
\(550\) 0 0
\(551\) 57.0272 2.42944
\(552\) 0 0
\(553\) −12.2018 −0.518875
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.2543 0.688717 0.344359 0.938838i \(-0.388096\pi\)
0.344359 + 0.938838i \(0.388096\pi\)
\(558\) 0 0
\(559\) −1.28055 −0.0541616
\(560\) 0 0
\(561\) −3.61899 −0.152794
\(562\) 0 0
\(563\) 7.95743 0.335366 0.167683 0.985841i \(-0.446372\pi\)
0.167683 + 0.985841i \(0.446372\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −4.48688 −0.188431
\(568\) 0 0
\(569\) −30.2806 −1.26943 −0.634713 0.772748i \(-0.718882\pi\)
−0.634713 + 0.772748i \(0.718882\pi\)
\(570\) 0 0
\(571\) 15.6407 0.654545 0.327272 0.944930i \(-0.393871\pi\)
0.327272 + 0.944930i \(0.393871\pi\)
\(572\) 0 0
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −8.67688 −0.361223 −0.180612 0.983555i \(-0.557808\pi\)
−0.180612 + 0.983555i \(0.557808\pi\)
\(578\) 0 0
\(579\) −20.2543 −0.841741
\(580\) 0 0
\(581\) 21.9837 0.912036
\(582\) 0 0
\(583\) 8.07422 0.334400
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −35.7150 −1.47411 −0.737057 0.675830i \(-0.763785\pi\)
−0.737057 + 0.675830i \(0.763785\pi\)
\(588\) 0 0
\(589\) 9.28055 0.382398
\(590\) 0 0
\(591\) 14.1059 0.580238
\(592\) 0 0
\(593\) −26.5086 −1.08858 −0.544289 0.838897i \(-0.683201\pi\)
−0.544289 + 0.838897i \(0.683201\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −13.3864 −0.547870
\(598\) 0 0
\(599\) −35.9050 −1.46704 −0.733518 0.679670i \(-0.762123\pi\)
−0.733518 + 0.679670i \(0.762123\pi\)
\(600\) 0 0
\(601\) 27.5185 1.12250 0.561252 0.827645i \(-0.310320\pi\)
0.561252 + 0.827645i \(0.310320\pi\)
\(602\) 0 0
\(603\) −11.2063 −0.456357
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −7.53487 −0.305831 −0.152915 0.988239i \(-0.548866\pi\)
−0.152915 + 0.988239i \(0.548866\pi\)
\(608\) 0 0
\(609\) −33.2597 −1.34775
\(610\) 0 0
\(611\) −5.92578 −0.239731
\(612\) 0 0
\(613\) 22.8253 0.921906 0.460953 0.887425i \(-0.347508\pi\)
0.460953 + 0.887425i \(0.347508\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −39.5349 −1.59161 −0.795807 0.605550i \(-0.792953\pi\)
−0.795807 + 0.605550i \(0.792953\pi\)
\(618\) 0 0
\(619\) −10.9837 −0.441471 −0.220735 0.975334i \(-0.570846\pi\)
−0.220735 + 0.975334i \(0.570846\pi\)
\(620\) 0 0
\(621\) 5.69321 0.228461
\(622\) 0 0
\(623\) 1.85156 0.0741810
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −9.28055 −0.370630
\(628\) 0 0
\(629\) −2.15834 −0.0860588
\(630\) 0 0
\(631\) −34.6670 −1.38007 −0.690035 0.723776i \(-0.742405\pi\)
−0.690035 + 0.723776i \(0.742405\pi\)
\(632\) 0 0
\(633\) −15.1321 −0.601447
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 13.1321 0.520313
\(638\) 0 0
\(639\) 5.13211 0.203023
\(640\) 0 0
\(641\) 10.1222 0.399803 0.199902 0.979816i \(-0.435938\pi\)
0.199902 + 0.979816i \(0.435938\pi\)
\(642\) 0 0
\(643\) 14.5710 0.574624 0.287312 0.957837i \(-0.407238\pi\)
0.287312 + 0.957837i \(0.407238\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 43.1855 1.69780 0.848899 0.528556i \(-0.177266\pi\)
0.848899 + 0.528556i \(0.177266\pi\)
\(648\) 0 0
\(649\) −7.14844 −0.280601
\(650\) 0 0
\(651\) −5.41266 −0.212139
\(652\) 0 0
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5.13211 −0.200223
\(658\) 0 0
\(659\) −25.7892 −1.00460 −0.502302 0.864692i \(-0.667513\pi\)
−0.502302 + 0.864692i \(0.667513\pi\)
\(660\) 0 0
\(661\) 28.6670 1.11502 0.557508 0.830172i \(-0.311758\pi\)
0.557508 + 0.830172i \(0.311758\pi\)
\(662\) 0 0
\(663\) 3.00000 0.116510
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 42.2018 1.63406
\(668\) 0 0
\(669\) −19.0796 −0.737661
\(670\) 0 0
\(671\) −11.3548 −0.438346
\(672\) 0 0
\(673\) −7.40276 −0.285355 −0.142678 0.989769i \(-0.545571\pi\)
−0.142678 + 0.989769i \(0.545571\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 45.3864 1.74434 0.872171 0.489201i \(-0.162712\pi\)
0.872171 + 0.489201i \(0.162712\pi\)
\(678\) 0 0
\(679\) 58.2117 2.23396
\(680\) 0 0
\(681\) 17.7674 0.680850
\(682\) 0 0
\(683\) 48.5403 1.85734 0.928671 0.370904i \(-0.120952\pi\)
0.928671 + 0.370904i \(0.120952\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −2.00000 −0.0763048
\(688\) 0 0
\(689\) −6.69321 −0.254991
\(690\) 0 0
\(691\) −0.803571 −0.0305693 −0.0152846 0.999883i \(-0.504865\pi\)
−0.0152846 + 0.999883i \(0.504865\pi\)
\(692\) 0 0
\(693\) 5.41266 0.205610
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.84166 −0.145513
\(698\) 0 0
\(699\) 14.4127 0.545137
\(700\) 0 0
\(701\) −31.6571 −1.19567 −0.597836 0.801619i \(-0.703972\pi\)
−0.597836 + 0.801619i \(0.703972\pi\)
\(702\) 0 0
\(703\) −5.53487 −0.208751
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −61.3221 −2.30626
\(708\) 0 0
\(709\) −8.66698 −0.325495 −0.162748 0.986668i \(-0.552036\pi\)
−0.162748 + 0.986668i \(0.552036\pi\)
\(710\) 0 0
\(711\) 2.71945 0.101987
\(712\) 0 0
\(713\) 6.86789 0.257205
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −26.0217 −0.971800
\(718\) 0 0
\(719\) 20.9312 0.780602 0.390301 0.920687i \(-0.372371\pi\)
0.390301 + 0.920687i \(0.372371\pi\)
\(720\) 0 0
\(721\) −3.22808 −0.120220
\(722\) 0 0
\(723\) −3.74568 −0.139304
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 42.6670 1.58243 0.791215 0.611538i \(-0.209449\pi\)
0.791215 + 0.611538i \(0.209449\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 3.84166 0.142089
\(732\) 0 0
\(733\) −20.2117 −0.746538 −0.373269 0.927723i \(-0.621763\pi\)
−0.373269 + 0.927723i \(0.621763\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.5185 0.497962
\(738\) 0 0
\(739\) 39.0054 1.43484 0.717419 0.696642i \(-0.245324\pi\)
0.717419 + 0.696642i \(0.245324\pi\)
\(740\) 0 0
\(741\) 7.69321 0.282617
\(742\) 0 0
\(743\) −35.3548 −1.29704 −0.648520 0.761197i \(-0.724612\pi\)
−0.648520 + 0.761197i \(0.724612\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −4.89954 −0.179265
\(748\) 0 0
\(749\) −61.9149 −2.26232
\(750\) 0 0
\(751\) −36.4661 −1.33067 −0.665333 0.746547i \(-0.731710\pi\)
−0.665333 + 0.746547i \(0.731710\pi\)
\(752\) 0 0
\(753\) 6.66698 0.242958
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.82532 −0.139034 −0.0695168 0.997581i \(-0.522146\pi\)
−0.0695168 + 0.997581i \(0.522146\pi\)
\(758\) 0 0
\(759\) −6.86789 −0.249289
\(760\) 0 0
\(761\) 30.2543 1.09672 0.548359 0.836243i \(-0.315253\pi\)
0.548359 + 0.836243i \(0.315253\pi\)
\(762\) 0 0
\(763\) −3.89413 −0.140977
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.92578 0.213967
\(768\) 0 0
\(769\) −38.9738 −1.40543 −0.702715 0.711472i \(-0.748029\pi\)
−0.702715 + 0.711472i \(0.748029\pi\)
\(770\) 0 0
\(771\) −18.1321 −0.653012
\(772\) 0 0
\(773\) 26.9213 0.968292 0.484146 0.874987i \(-0.339130\pi\)
0.484146 + 0.874987i \(0.339130\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3.22808 0.115807
\(778\) 0 0
\(779\) −9.85156 −0.352969
\(780\) 0 0
\(781\) −6.19102 −0.221532
\(782\) 0 0
\(783\) 7.41266 0.264907
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0316 −0.785344 −0.392672 0.919679i \(-0.628449\pi\)
−0.392672 + 0.919679i \(0.628449\pi\)
\(788\) 0 0
\(789\) −3.28055 −0.116791
\(790\) 0 0
\(791\) −28.7728 −1.02304
\(792\) 0 0
\(793\) 9.41266 0.334253
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.7466 1.72669 0.863347 0.504611i \(-0.168364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(798\) 0 0
\(799\) 17.7773 0.628917
\(800\) 0 0
\(801\) −0.412660 −0.0145806
\(802\) 0 0
\(803\) 6.19102 0.218476
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.9475 0.878195
\(808\) 0 0
\(809\) −25.7991 −0.907047 −0.453524 0.891244i \(-0.649833\pi\)
−0.453524 + 0.891244i \(0.649833\pi\)
\(810\) 0 0
\(811\) 40.1375 1.40942 0.704710 0.709496i \(-0.251077\pi\)
0.704710 + 0.709496i \(0.251077\pi\)
\(812\) 0 0
\(813\) −7.31220 −0.256450
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.85156 0.344662
\(818\) 0 0
\(819\) −4.48688 −0.156784
\(820\) 0 0
\(821\) 48.3176 1.68630 0.843148 0.537681i \(-0.180700\pi\)
0.843148 + 0.537681i \(0.180700\pi\)
\(822\) 0 0
\(823\) 18.0633 0.629647 0.314824 0.949150i \(-0.398055\pi\)
0.314824 + 0.949150i \(0.398055\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −39.2696 −1.36554 −0.682769 0.730634i \(-0.739225\pi\)
−0.682769 + 0.730634i \(0.739225\pi\)
\(828\) 0 0
\(829\) 55.9213 1.94223 0.971113 0.238619i \(-0.0766946\pi\)
0.971113 + 0.238619i \(0.0766946\pi\)
\(830\) 0 0
\(831\) −12.9738 −0.450055
\(832\) 0 0
\(833\) −39.3963 −1.36500
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1.20633 0.0416969
\(838\) 0 0
\(839\) −45.9574 −1.58663 −0.793313 0.608814i \(-0.791646\pi\)
−0.793313 + 0.608814i \(0.791646\pi\)
\(840\) 0 0
\(841\) 25.9475 0.894742
\(842\) 0 0
\(843\) −33.3864 −1.14989
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 42.8262 1.47153
\(848\) 0 0
\(849\) −29.3864 −1.00854
\(850\) 0 0
\(851\) −4.09597 −0.140408
\(852\) 0 0
\(853\) −32.7204 −1.12032 −0.560162 0.828383i \(-0.689261\pi\)
−0.560162 + 0.828383i \(0.689261\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.8951 −0.884558 −0.442279 0.896877i \(-0.645830\pi\)
−0.442279 + 0.896877i \(0.645830\pi\)
\(858\) 0 0
\(859\) 1.57744 0.0538215 0.0269108 0.999638i \(-0.491433\pi\)
0.0269108 + 0.999638i \(0.491433\pi\)
\(860\) 0 0
\(861\) 5.74568 0.195812
\(862\) 0 0
\(863\) −32.2761 −1.09869 −0.549345 0.835596i \(-0.685123\pi\)
−0.549345 + 0.835596i \(0.685123\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.00000 0.271694
\(868\) 0 0
\(869\) −3.28055 −0.111285
\(870\) 0 0
\(871\) −11.2063 −0.379712
\(872\) 0 0
\(873\) −12.9738 −0.439095
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 11.7991 0.398427 0.199213 0.979956i \(-0.436161\pi\)
0.199213 + 0.979956i \(0.436161\pi\)
\(878\) 0 0
\(879\) 10.8253 0.365129
\(880\) 0 0
\(881\) −46.0796 −1.55246 −0.776231 0.630448i \(-0.782871\pi\)
−0.776231 + 0.630448i \(0.782871\pi\)
\(882\) 0 0
\(883\) 9.32312 0.313748 0.156874 0.987619i \(-0.449858\pi\)
0.156874 + 0.987619i \(0.449858\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −53.1954 −1.78613 −0.893063 0.449931i \(-0.851449\pi\)
−0.893063 + 0.449931i \(0.851449\pi\)
\(888\) 0 0
\(889\) 67.8960 2.27716
\(890\) 0 0
\(891\) −1.20633 −0.0404136
\(892\) 0 0
\(893\) 45.5883 1.52555
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 5.69321 0.190091
\(898\) 0 0
\(899\) 8.94211 0.298236
\(900\) 0 0
\(901\) 20.0796 0.668950
\(902\) 0 0
\(903\) −5.74568 −0.191204
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 56.7204 1.88337 0.941685 0.336497i \(-0.109242\pi\)
0.941685 + 0.336497i \(0.109242\pi\)
\(908\) 0 0
\(909\) 13.6670 0.453305
\(910\) 0 0
\(911\) 33.5883 1.11283 0.556414 0.830905i \(-0.312177\pi\)
0.556414 + 0.830905i \(0.312177\pi\)
\(912\) 0 0
\(913\) 5.91046 0.195608
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 34.5185 1.13990
\(918\) 0 0
\(919\) −5.58734 −0.184309 −0.0921547 0.995745i \(-0.529375\pi\)
−0.0921547 + 0.995745i \(0.529375\pi\)
\(920\) 0 0
\(921\) −13.5448 −0.446315
\(922\) 0 0
\(923\) 5.13211 0.168925
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0.719448 0.0236298
\(928\) 0 0
\(929\) 22.2117 0.728744 0.364372 0.931254i \(-0.381284\pi\)
0.364372 + 0.931254i \(0.381284\pi\)
\(930\) 0 0
\(931\) −101.028 −3.31106
\(932\) 0 0
\(933\) 8.26422 0.270558
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −6.23798 −0.203786 −0.101893 0.994795i \(-0.532490\pi\)
−0.101893 + 0.994795i \(0.532490\pi\)
\(938\) 0 0
\(939\) −11.3068 −0.368983
\(940\) 0 0
\(941\) −11.1846 −0.364607 −0.182303 0.983242i \(-0.558355\pi\)
−0.182303 + 0.983242i \(0.558355\pi\)
\(942\) 0 0
\(943\) −7.29045 −0.237410
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10.9094 0.354509 0.177255 0.984165i \(-0.443278\pi\)
0.177255 + 0.984165i \(0.443278\pi\)
\(948\) 0 0
\(949\) −5.13211 −0.166595
\(950\) 0 0
\(951\) −21.6407 −0.701749
\(952\) 0 0
\(953\) −26.2806 −0.851311 −0.425655 0.904885i \(-0.639956\pi\)
−0.425655 + 0.904885i \(0.639956\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −8.94211 −0.289057
\(958\) 0 0
\(959\) 88.8361 2.86867
\(960\) 0 0
\(961\) −29.5448 −0.953057
\(962\) 0 0
\(963\) 13.7991 0.444669
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 13.4705 0.433184 0.216592 0.976262i \(-0.430506\pi\)
0.216592 + 0.976262i \(0.430506\pi\)
\(968\) 0 0
\(969\) −23.0796 −0.741425
\(970\) 0 0
\(971\) −11.5349 −0.370172 −0.185086 0.982722i \(-0.559256\pi\)
−0.185086 + 0.982722i \(0.559256\pi\)
\(972\) 0 0
\(973\) 89.5022 2.86931
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −16.2117 −0.518660 −0.259330 0.965789i \(-0.583502\pi\)
−0.259330 + 0.965789i \(0.583502\pi\)
\(978\) 0 0
\(979\) 0.497804 0.0159099
\(980\) 0 0
\(981\) 0.867892 0.0277097
\(982\) 0 0
\(983\) 17.1014 0.545449 0.272725 0.962092i \(-0.412075\pi\)
0.272725 + 0.962092i \(0.412075\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −26.5883 −0.846314
\(988\) 0 0
\(989\) 7.29045 0.231823
\(990\) 0 0
\(991\) −59.0470 −1.87569 −0.937844 0.347056i \(-0.887181\pi\)
−0.937844 + 0.347056i \(0.887181\pi\)
\(992\) 0 0
\(993\) 28.5185 0.905008
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −47.5195 −1.50496 −0.752478 0.658617i \(-0.771142\pi\)
−0.752478 + 0.658617i \(0.771142\pi\)
\(998\) 0 0
\(999\) −0.719448 −0.0227623
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 7800.2.a.bh.1.1 3
5.4 even 2 7800.2.a.bs.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bh.1.1 3 1.1 even 1 trivial
7800.2.a.bs.1.3 yes 3 5.4 even 2