Properties

Label 7600.2.a.bk.1.3
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 1.3
Root \(2.77339\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.77339 q^{3} +2.69168 q^{7} +0.144903 q^{9} +O(q^{10})\) \(q+1.77339 q^{3} +2.69168 q^{7} +0.144903 q^{9} -5.54677 q^{11} -2.91829 q^{13} +4.91829 q^{17} -1.00000 q^{19} +4.77339 q^{21} -3.60997 q^{23} -5.06319 q^{27} +1.08171 q^{29} -7.54677 q^{31} -9.83658 q^{33} +4.54677 q^{37} -5.17526 q^{39} +9.54677 q^{43} +0.836581 q^{47} +0.245129 q^{49} +8.72203 q^{51} +9.78523 q^{53} -1.77339 q^{57} -12.9933 q^{59} -7.38336 q^{61} +0.390032 q^{63} -2.85510 q^{67} -6.40187 q^{69} -14.4769 q^{71} +5.15674 q^{73} -14.9301 q^{77} +3.09355 q^{79} -9.41371 q^{81} -1.71019 q^{83} +1.91829 q^{87} -5.09355 q^{89} -7.85510 q^{91} -13.3834 q^{93} -17.2570 q^{97} -0.803744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} + O(q^{10}) \) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} - 2q^{11} - 6q^{13} + 12q^{17} - 3q^{19} + 7q^{21} + 2q^{23} - 17q^{27} + 6q^{29} - 8q^{31} - 24q^{33} - q^{37} + 11q^{39} + 14q^{43} - 3q^{47} + 9q^{49} - 15q^{51} - 10q^{53} + 2q^{57} - 6q^{59} - 2q^{61} + 14q^{63} - 4q^{67} + 6q^{71} - 12q^{73} - 10q^{77} - 20q^{79} + 23q^{81} + 4q^{83} + 3q^{87} + 14q^{89} - 19q^{91} - 20q^{93} - 28q^{97} + 36q^{99} + O(q^{100}) \)

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
\(3\) 1.77339 1.02387 0.511933 0.859025i \(-0.328930\pi\)
0.511933 + 0.859025i \(0.328930\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.69168 1.01736 0.508679 0.860956i \(-0.330134\pi\)
0.508679 + 0.860956i \(0.330134\pi\)
\(8\) 0 0
\(9\) 0.144903 0.0483010
\(10\) 0 0
\(11\) −5.54677 −1.67242 −0.836208 0.548413i \(-0.815232\pi\)
−0.836208 + 0.548413i \(0.815232\pi\)
\(12\) 0 0
\(13\) −2.91829 −0.809388 −0.404694 0.914452i \(-0.632622\pi\)
−0.404694 + 0.914452i \(0.632622\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.91829 1.19286 0.596430 0.802665i \(-0.296585\pi\)
0.596430 + 0.802665i \(0.296585\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 4.77339 1.04164
\(22\) 0 0
\(23\) −3.60997 −0.752730 −0.376365 0.926471i \(-0.622826\pi\)
−0.376365 + 0.926471i \(0.622826\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.06319 −0.974412
\(28\) 0 0
\(29\) 1.08171 0.200868 0.100434 0.994944i \(-0.467977\pi\)
0.100434 + 0.994944i \(0.467977\pi\)
\(30\) 0 0
\(31\) −7.54677 −1.35544 −0.677720 0.735320i \(-0.737032\pi\)
−0.677720 + 0.735320i \(0.737032\pi\)
\(32\) 0 0
\(33\) −9.83658 −1.71233
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.54677 0.747485 0.373743 0.927532i \(-0.378074\pi\)
0.373743 + 0.927532i \(0.378074\pi\)
\(38\) 0 0
\(39\) −5.17526 −0.828705
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 9.54677 1.45587 0.727935 0.685646i \(-0.240480\pi\)
0.727935 + 0.685646i \(0.240480\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.836581 0.122028 0.0610139 0.998137i \(-0.480567\pi\)
0.0610139 + 0.998137i \(0.480567\pi\)
\(48\) 0 0
\(49\) 0.245129 0.0350184
\(50\) 0 0
\(51\) 8.72203 1.22133
\(52\) 0 0
\(53\) 9.78523 1.34410 0.672052 0.740504i \(-0.265413\pi\)
0.672052 + 0.740504i \(0.265413\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.77339 −0.234891
\(58\) 0 0
\(59\) −12.9933 −1.69159 −0.845793 0.533511i \(-0.820872\pi\)
−0.845793 + 0.533511i \(0.820872\pi\)
\(60\) 0 0
\(61\) −7.38336 −0.945342 −0.472671 0.881239i \(-0.656710\pi\)
−0.472671 + 0.881239i \(0.656710\pi\)
\(62\) 0 0
\(63\) 0.390032 0.0491394
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.85510 −0.348806 −0.174403 0.984674i \(-0.555799\pi\)
−0.174403 + 0.984674i \(0.555799\pi\)
\(68\) 0 0
\(69\) −6.40187 −0.770695
\(70\) 0 0
\(71\) −14.4769 −1.71809 −0.859046 0.511898i \(-0.828943\pi\)
−0.859046 + 0.511898i \(0.828943\pi\)
\(72\) 0 0
\(73\) 5.15674 0.603551 0.301776 0.953379i \(-0.402421\pi\)
0.301776 + 0.953379i \(0.402421\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −14.9301 −1.70145
\(78\) 0 0
\(79\) 3.09355 0.348052 0.174026 0.984741i \(-0.444322\pi\)
0.174026 + 0.984741i \(0.444322\pi\)
\(80\) 0 0
\(81\) −9.41371 −1.04597
\(82\) 0 0
\(83\) −1.71019 −0.187718 −0.0938591 0.995585i \(-0.529920\pi\)
−0.0938591 + 0.995585i \(0.529920\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.91829 0.205662
\(88\) 0 0
\(89\) −5.09355 −0.539915 −0.269958 0.962872i \(-0.587010\pi\)
−0.269958 + 0.962872i \(0.587010\pi\)
\(90\) 0 0
\(91\) −7.85510 −0.823438
\(92\) 0 0
\(93\) −13.3834 −1.38779
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −17.2570 −1.75218 −0.876090 0.482148i \(-0.839857\pi\)
−0.876090 + 0.482148i \(0.839857\pi\)
\(98\) 0 0
\(99\) −0.803744 −0.0807793
\(100\) 0 0
\(101\) −9.38336 −0.933679 −0.466839 0.884342i \(-0.654607\pi\)
−0.466839 + 0.884342i \(0.654607\pi\)
\(102\) 0 0
\(103\) 12.9301 1.27404 0.637022 0.770846i \(-0.280166\pi\)
0.637022 + 0.770846i \(0.280166\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −18.9420 −1.83119 −0.915595 0.402102i \(-0.868280\pi\)
−0.915595 + 0.402102i \(0.868280\pi\)
\(108\) 0 0
\(109\) −2.69168 −0.257816 −0.128908 0.991657i \(-0.541147\pi\)
−0.128908 + 0.991657i \(0.541147\pi\)
\(110\) 0 0
\(111\) 8.06319 0.765324
\(112\) 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
\(117\) −0.422869 −0.0390942
\(118\) 0 0
\(119\) 13.2385 1.21357
\(120\) 0 0
\(121\) 19.7667 1.79697
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.87361 0.166256 0.0831282 0.996539i \(-0.473509\pi\)
0.0831282 + 0.996539i \(0.473509\pi\)
\(128\) 0 0
\(129\) 16.9301 1.49061
\(130\) 0 0
\(131\) 11.5468 1.00885 0.504423 0.863457i \(-0.331705\pi\)
0.504423 + 0.863457i \(0.331705\pi\)
\(132\) 0 0
\(133\) −2.69168 −0.233398
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.23845 0.362115 0.181058 0.983472i \(-0.442048\pi\)
0.181058 + 0.983472i \(0.442048\pi\)
\(138\) 0 0
\(139\) −9.21994 −0.782025 −0.391012 0.920385i \(-0.627875\pi\)
−0.391012 + 0.920385i \(0.627875\pi\)
\(140\) 0 0
\(141\) 1.48358 0.124940
\(142\) 0 0
\(143\) 16.1871 1.35363
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.434709 0.0358542
\(148\) 0 0
\(149\) −7.25697 −0.594514 −0.297257 0.954797i \(-0.596072\pi\)
−0.297257 + 0.954797i \(0.596072\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 0.712675 0.0576163
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −9.54677 −0.761916 −0.380958 0.924592i \(-0.624406\pi\)
−0.380958 + 0.924592i \(0.624406\pi\)
\(158\) 0 0
\(159\) 17.3530 1.37618
\(160\) 0 0
\(161\) −9.71687 −0.765797
\(162\) 0 0
\(163\) −15.7102 −1.23052 −0.615259 0.788325i \(-0.710948\pi\)
−0.615259 + 0.788325i \(0.710948\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.45323 −0.499366 −0.249683 0.968328i \(-0.580326\pi\)
−0.249683 + 0.968328i \(0.580326\pi\)
\(168\) 0 0
\(169\) −4.48358 −0.344891
\(170\) 0 0
\(171\) −0.144903 −0.0110810
\(172\) 0 0
\(173\) −0.873614 −0.0664196 −0.0332098 0.999448i \(-0.510573\pi\)
−0.0332098 + 0.999448i \(0.510573\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −23.0422 −1.73196
\(178\) 0 0
\(179\) 12.3834 0.925575 0.462788 0.886469i \(-0.346849\pi\)
0.462788 + 0.886469i \(0.346849\pi\)
\(180\) 0 0
\(181\) −17.6403 −1.31119 −0.655597 0.755111i \(-0.727583\pi\)
−0.655597 + 0.755111i \(0.727583\pi\)
\(182\) 0 0
\(183\) −13.0935 −0.967903
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −27.2806 −1.99496
\(188\) 0 0
\(189\) −13.6285 −0.991326
\(190\) 0 0
\(191\) 15.1567 1.09670 0.548352 0.836248i \(-0.315256\pi\)
0.548352 + 0.836248i \(0.315256\pi\)
\(192\) 0 0
\(193\) 23.3834 1.68317 0.841585 0.540124i \(-0.181623\pi\)
0.841585 + 0.540124i \(0.181623\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.0935 −1.64535 −0.822674 0.568514i \(-0.807519\pi\)
−0.822674 + 0.568514i \(0.807519\pi\)
\(198\) 0 0
\(199\) 25.7852 1.82787 0.913933 0.405865i \(-0.133030\pi\)
0.913933 + 0.405865i \(0.133030\pi\)
\(200\) 0 0
\(201\) −5.06319 −0.357130
\(202\) 0 0
\(203\) 2.91161 0.204355
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.523095 −0.0363576
\(208\) 0 0
\(209\) 5.54677 0.383678
\(210\) 0 0
\(211\) −14.2266 −0.979400 −0.489700 0.871891i \(-0.662894\pi\)
−0.489700 + 0.871891i \(0.662894\pi\)
\(212\) 0 0
\(213\) −25.6732 −1.75910
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −20.3135 −1.37897
\(218\) 0 0
\(219\) 9.14490 0.617955
\(220\) 0 0
\(221\) −14.3530 −0.965487
\(222\) 0 0
\(223\) 4.45323 0.298210 0.149105 0.988821i \(-0.452361\pi\)
0.149105 + 0.988821i \(0.452361\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.94865 −0.394826 −0.197413 0.980320i \(-0.563254\pi\)
−0.197413 + 0.980320i \(0.563254\pi\)
\(228\) 0 0
\(229\) 1.09355 0.0722638 0.0361319 0.999347i \(-0.488496\pi\)
0.0361319 + 0.999347i \(0.488496\pi\)
\(230\) 0 0
\(231\) −26.4769 −1.74205
\(232\) 0 0
\(233\) 14.0935 0.923299 0.461650 0.887062i \(-0.347258\pi\)
0.461650 + 0.887062i \(0.347258\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 5.48606 0.356358
\(238\) 0 0
\(239\) −15.6100 −1.00972 −0.504862 0.863200i \(-0.668457\pi\)
−0.504862 + 0.863200i \(0.668457\pi\)
\(240\) 0 0
\(241\) −5.21994 −0.336246 −0.168123 0.985766i \(-0.553771\pi\)
−0.168123 + 0.985766i \(0.553771\pi\)
\(242\) 0 0
\(243\) −1.50458 −0.0965188
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.91829 0.185686
\(248\) 0 0
\(249\) −3.03284 −0.192198
\(250\) 0 0
\(251\) 28.6403 1.80776 0.903881 0.427785i \(-0.140706\pi\)
0.903881 + 0.427785i \(0.140706\pi\)
\(252\) 0 0
\(253\) 20.0237 1.25888
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.45323 0.402541 0.201271 0.979536i \(-0.435493\pi\)
0.201271 + 0.979536i \(0.435493\pi\)
\(258\) 0 0
\(259\) 12.2385 0.760460
\(260\) 0 0
\(261\) 0.156743 0.00970214
\(262\) 0 0
\(263\) −22.1871 −1.36812 −0.684058 0.729428i \(-0.739786\pi\)
−0.684058 + 0.729428i \(0.739786\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −9.03284 −0.552801
\(268\) 0 0
\(269\) −20.4070 −1.24424 −0.622119 0.782922i \(-0.713728\pi\)
−0.622119 + 0.782922i \(0.713728\pi\)
\(270\) 0 0
\(271\) −15.9368 −0.968092 −0.484046 0.875043i \(-0.660833\pi\)
−0.484046 + 0.875043i \(0.660833\pi\)
\(272\) 0 0
\(273\) −13.9301 −0.843090
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.02368 0.241759 0.120880 0.992667i \(-0.461428\pi\)
0.120880 + 0.992667i \(0.461428\pi\)
\(278\) 0 0
\(279\) −1.09355 −0.0654691
\(280\) 0 0
\(281\) 1.67316 0.0998124 0.0499062 0.998754i \(-0.484108\pi\)
0.0499062 + 0.998754i \(0.484108\pi\)
\(282\) 0 0
\(283\) −16.8931 −1.00419 −0.502095 0.864812i \(-0.667437\pi\)
−0.502095 + 0.864812i \(0.667437\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.18958 0.422916
\(290\) 0 0
\(291\) −30.6033 −1.79400
\(292\) 0 0
\(293\) −1.08171 −0.0631942 −0.0315971 0.999501i \(-0.510059\pi\)
−0.0315971 + 0.999501i \(0.510059\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 28.0844 1.62962
\(298\) 0 0
\(299\) 10.5349 0.609251
\(300\) 0 0
\(301\) 25.6968 1.48114
\(302\) 0 0
\(303\) −16.6403 −0.955962
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2.38336 −0.136025 −0.0680126 0.997684i \(-0.521666\pi\)
−0.0680126 + 0.997684i \(0.521666\pi\)
\(308\) 0 0
\(309\) 22.9301 1.30445
\(310\) 0 0
\(311\) 29.4584 1.67043 0.835216 0.549922i \(-0.185343\pi\)
0.835216 + 0.549922i \(0.185343\pi\)
\(312\) 0 0
\(313\) 32.0355 1.81075 0.905377 0.424608i \(-0.139588\pi\)
0.905377 + 0.424608i \(0.139588\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.6665 −1.49774 −0.748870 0.662717i \(-0.769403\pi\)
−0.748870 + 0.662717i \(0.769403\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −33.5915 −1.87489
\(322\) 0 0
\(323\) −4.91829 −0.273661
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −4.77339 −0.263969
\(328\) 0 0
\(329\) 2.25181 0.124146
\(330\) 0 0
\(331\) 19.8721 1.09227 0.546135 0.837697i \(-0.316099\pi\)
0.546135 + 0.837697i \(0.316099\pi\)
\(332\) 0 0
\(333\) 0.658841 0.0361043
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 27.5705 1.50186 0.750929 0.660383i \(-0.229606\pi\)
0.750929 + 0.660383i \(0.229606\pi\)
\(338\) 0 0
\(339\) −10.6403 −0.577903
\(340\) 0 0
\(341\) 41.8603 2.26686
\(342\) 0 0
\(343\) −18.1819 −0.981732
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 27.2806 1.46450 0.732251 0.681035i \(-0.238470\pi\)
0.732251 + 0.681035i \(0.238470\pi\)
\(348\) 0 0
\(349\) 30.9538 1.65692 0.828460 0.560049i \(-0.189218\pi\)
0.828460 + 0.560049i \(0.189218\pi\)
\(350\) 0 0
\(351\) 14.7759 0.788677
\(352\) 0 0
\(353\) 11.1819 0.595154 0.297577 0.954698i \(-0.403821\pi\)
0.297577 + 0.954698i \(0.403821\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 23.4769 1.24253
\(358\) 0 0
\(359\) −20.3387 −1.07343 −0.536717 0.843762i \(-0.680336\pi\)
−0.536717 + 0.843762i \(0.680336\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 35.0540 1.83986
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 32.9538 1.72017 0.860087 0.510147i \(-0.170409\pi\)
0.860087 + 0.510147i \(0.170409\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 26.3387 1.36744
\(372\) 0 0
\(373\) −10.0869 −0.522278 −0.261139 0.965301i \(-0.584098\pi\)
−0.261139 + 0.965301i \(0.584098\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.15674 −0.162581
\(378\) 0 0
\(379\) 18.4256 0.946457 0.473229 0.880940i \(-0.343088\pi\)
0.473229 + 0.880940i \(0.343088\pi\)
\(380\) 0 0
\(381\) 3.32264 0.170224
\(382\) 0 0
\(383\) −28.1871 −1.44029 −0.720147 0.693822i \(-0.755926\pi\)
−0.720147 + 0.693822i \(0.755926\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.38336 0.0703199
\(388\) 0 0
\(389\) 20.0237 1.01524 0.507620 0.861581i \(-0.330525\pi\)
0.507620 + 0.861581i \(0.330525\pi\)
\(390\) 0 0
\(391\) −17.7549 −0.897902
\(392\) 0 0
\(393\) 20.4769 1.03292
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −8.32684 −0.417912 −0.208956 0.977925i \(-0.567007\pi\)
−0.208956 + 0.977925i \(0.567007\pi\)
\(398\) 0 0
\(399\) −4.77339 −0.238968
\(400\) 0 0
\(401\) −22.1501 −1.10612 −0.553061 0.833141i \(-0.686540\pi\)
−0.553061 + 0.833141i \(0.686540\pi\)
\(402\) 0 0
\(403\) 22.0237 1.09708
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −25.2199 −1.25011
\(408\) 0 0
\(409\) 34.0237 1.68236 0.841181 0.540753i \(-0.181861\pi\)
0.841181 + 0.540753i \(0.181861\pi\)
\(410\) 0 0
\(411\) 7.51642 0.370758
\(412\) 0 0
\(413\) −34.9738 −1.72095
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −16.3505 −0.800688
\(418\) 0 0
\(419\) −37.5334 −1.83363 −0.916814 0.399315i \(-0.869248\pi\)
−0.916814 + 0.399315i \(0.869248\pi\)
\(420\) 0 0
\(421\) 33.8341 1.64897 0.824487 0.565882i \(-0.191464\pi\)
0.824487 + 0.565882i \(0.191464\pi\)
\(422\) 0 0
\(423\) 0.121223 0.00589406
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −19.8736 −0.961752
\(428\) 0 0
\(429\) 28.7060 1.38594
\(430\) 0 0
\(431\) −24.8037 −1.19475 −0.597377 0.801960i \(-0.703790\pi\)
−0.597377 + 0.801960i \(0.703790\pi\)
\(432\) 0 0
\(433\) 1.68651 0.0810487 0.0405244 0.999179i \(-0.487097\pi\)
0.0405244 + 0.999179i \(0.487097\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.60997 0.172688
\(438\) 0 0
\(439\) −0.326839 −0.0155992 −0.00779958 0.999970i \(-0.502483\pi\)
−0.00779958 + 0.999970i \(0.502483\pi\)
\(440\) 0 0
\(441\) 0.0355199 0.00169142
\(442\) 0 0
\(443\) −0.490258 −0.0232929 −0.0116464 0.999932i \(-0.503707\pi\)
−0.0116464 + 0.999932i \(0.503707\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −12.8694 −0.608703
\(448\) 0 0
\(449\) 23.5468 1.11124 0.555621 0.831436i \(-0.312481\pi\)
0.555621 + 0.831436i \(0.312481\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −35.4677 −1.66642
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.01184 −0.374778 −0.187389 0.982286i \(-0.560003\pi\)
−0.187389 + 0.982286i \(0.560003\pi\)
\(458\) 0 0
\(459\) −24.9023 −1.16234
\(460\) 0 0
\(461\) 3.83658 0.178687 0.0893437 0.996001i \(-0.471523\pi\)
0.0893437 + 0.996001i \(0.471523\pi\)
\(462\) 0 0
\(463\) 6.58381 0.305975 0.152988 0.988228i \(-0.451110\pi\)
0.152988 + 0.988228i \(0.451110\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −22.6033 −1.04596 −0.522978 0.852346i \(-0.675179\pi\)
−0.522978 + 0.852346i \(0.675179\pi\)
\(468\) 0 0
\(469\) −7.68500 −0.354860
\(470\) 0 0
\(471\) −16.9301 −0.780099
\(472\) 0 0
\(473\) −52.9538 −2.43482
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 1.41791 0.0649215
\(478\) 0 0
\(479\) 35.7904 1.63530 0.817652 0.575712i \(-0.195275\pi\)
0.817652 + 0.575712i \(0.195275\pi\)
\(480\) 0 0
\(481\) −13.2688 −0.605006
\(482\) 0 0
\(483\) −17.2318 −0.784073
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 21.4070 0.970045 0.485023 0.874502i \(-0.338811\pi\)
0.485023 + 0.874502i \(0.338811\pi\)
\(488\) 0 0
\(489\) −27.8603 −1.25988
\(490\) 0 0
\(491\) 4.32684 0.195267 0.0976337 0.995222i \(-0.468873\pi\)
0.0976337 + 0.995222i \(0.468873\pi\)
\(492\) 0 0
\(493\) 5.32016 0.239608
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −38.9672 −1.74792
\(498\) 0 0
\(499\) 37.6968 1.68754 0.843771 0.536703i \(-0.180330\pi\)
0.843771 + 0.536703i \(0.180330\pi\)
\(500\) 0 0
\(501\) −11.4441 −0.511283
\(502\) 0 0
\(503\) 16.9183 0.754349 0.377175 0.926142i \(-0.376896\pi\)
0.377175 + 0.926142i \(0.376896\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −7.95113 −0.353122
\(508\) 0 0
\(509\) −6.79955 −0.301385 −0.150692 0.988581i \(-0.548150\pi\)
−0.150692 + 0.988581i \(0.548150\pi\)
\(510\) 0 0
\(511\) 13.8803 0.614028
\(512\) 0 0
\(513\) 5.06319 0.223545
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −4.64032 −0.204081
\(518\) 0 0
\(519\) −1.54926 −0.0680048
\(520\) 0 0
\(521\) −1.35968 −0.0595685 −0.0297842 0.999556i \(-0.509482\pi\)
−0.0297842 + 0.999556i \(0.509482\pi\)
\(522\) 0 0
\(523\) 21.9486 0.959747 0.479874 0.877338i \(-0.340682\pi\)
0.479874 + 0.877338i \(0.340682\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −37.1172 −1.61685
\(528\) 0 0
\(529\) −9.96813 −0.433397
\(530\) 0 0
\(531\) −1.88277 −0.0817053
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 21.9605 0.947665
\(538\) 0 0
\(539\) −1.35968 −0.0585654
\(540\) 0 0
\(541\) −39.8973 −1.71532 −0.857659 0.514218i \(-0.828082\pi\)
−0.857659 + 0.514218i \(0.828082\pi\)
\(542\) 0 0
\(543\) −31.2831 −1.34249
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.34632 0.314106 0.157053 0.987590i \(-0.449801\pi\)
0.157053 + 0.987590i \(0.449801\pi\)
\(548\) 0 0
\(549\) −1.06987 −0.0456609
\(550\) 0 0
\(551\) −1.08171 −0.0460824
\(552\) 0 0
\(553\) 8.32684 0.354093
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −26.9672 −1.14264 −0.571318 0.820729i \(-0.693568\pi\)
−0.571318 + 0.820729i \(0.693568\pi\)
\(558\) 0 0
\(559\) −27.8603 −1.17836
\(560\) 0 0
\(561\) −48.3792 −2.04257
\(562\) 0 0
\(563\) 44.8973 1.89220 0.946098 0.323881i \(-0.104988\pi\)
0.946098 + 0.323881i \(0.104988\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −25.3387 −1.06412
\(568\) 0 0
\(569\) 31.1172 1.30450 0.652251 0.758003i \(-0.273825\pi\)
0.652251 + 0.758003i \(0.273825\pi\)
\(570\) 0 0
\(571\) −33.2570 −1.39176 −0.695880 0.718158i \(-0.744986\pi\)
−0.695880 + 0.718158i \(0.744986\pi\)
\(572\) 0 0
\(573\) 26.8788 1.12288
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 23.4702 0.977078 0.488539 0.872542i \(-0.337530\pi\)
0.488539 + 0.872542i \(0.337530\pi\)
\(578\) 0 0
\(579\) 41.4677 1.72334
\(580\) 0 0
\(581\) −4.60329 −0.190977
\(582\) 0 0
\(583\) −54.2765 −2.24790
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.1501 0.418938 0.209469 0.977815i \(-0.432826\pi\)
0.209469 + 0.977815i \(0.432826\pi\)
\(588\) 0 0
\(589\) 7.54677 0.310959
\(590\) 0 0
\(591\) −40.9538 −1.68461
\(592\) 0 0
\(593\) −16.6732 −0.684685 −0.342342 0.939575i \(-0.611220\pi\)
−0.342342 + 0.939575i \(0.611220\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 45.7272 1.87149
\(598\) 0 0
\(599\) −18.2765 −0.746756 −0.373378 0.927679i \(-0.621800\pi\)
−0.373378 + 0.927679i \(0.621800\pi\)
\(600\) 0 0
\(601\) 7.96297 0.324816 0.162408 0.986724i \(-0.448074\pi\)
0.162408 + 0.986724i \(0.448074\pi\)
\(602\) 0 0
\(603\) −0.413712 −0.0168477
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.93013 0.281285 0.140643 0.990060i \(-0.455083\pi\)
0.140643 + 0.990060i \(0.455083\pi\)
\(608\) 0 0
\(609\) 5.16342 0.209232
\(610\) 0 0
\(611\) −2.44139 −0.0987679
\(612\) 0 0
\(613\) −34.2765 −1.38441 −0.692206 0.721700i \(-0.743361\pi\)
−0.692206 + 0.721700i \(0.743361\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 35.5139 1.42974 0.714869 0.699259i \(-0.246486\pi\)
0.714869 + 0.699259i \(0.246486\pi\)
\(618\) 0 0
\(619\) 29.5334 1.18705 0.593524 0.804816i \(-0.297736\pi\)
0.593524 + 0.804816i \(0.297736\pi\)
\(620\) 0 0
\(621\) 18.2780 0.733470
\(622\) 0 0
\(623\) −13.7102 −0.549287
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 9.83658 0.392835
\(628\) 0 0
\(629\) 22.3624 0.891646
\(630\) 0 0
\(631\) 15.1634 0.603646 0.301823 0.953364i \(-0.402405\pi\)
0.301823 + 0.953364i \(0.402405\pi\)
\(632\) 0 0
\(633\) −25.2293 −1.00277
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −0.715358 −0.0283435
\(638\) 0 0
\(639\) −2.09775 −0.0829855
\(640\) 0 0
\(641\) −25.0802 −0.990608 −0.495304 0.868720i \(-0.664943\pi\)
−0.495304 + 0.868720i \(0.664943\pi\)
\(642\) 0 0
\(643\) −19.1306 −0.754437 −0.377218 0.926124i \(-0.623119\pi\)
−0.377218 + 0.926124i \(0.623119\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −12.4019 −0.487568 −0.243784 0.969830i \(-0.578389\pi\)
−0.243784 + 0.969830i \(0.578389\pi\)
\(648\) 0 0
\(649\) 72.0710 2.82904
\(650\) 0 0
\(651\) −36.0237 −1.41188
\(652\) 0 0
\(653\) −10.7801 −0.421856 −0.210928 0.977502i \(-0.567649\pi\)
−0.210928 + 0.977502i \(0.567649\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.747227 0.0291521
\(658\) 0 0
\(659\) −8.56529 −0.333656 −0.166828 0.985986i \(-0.553353\pi\)
−0.166828 + 0.985986i \(0.553353\pi\)
\(660\) 0 0
\(661\) −26.2883 −1.02250 −0.511248 0.859433i \(-0.670817\pi\)
−0.511248 + 0.859433i \(0.670817\pi\)
\(662\) 0 0
\(663\) −25.4534 −0.988529
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.90494 −0.151200
\(668\) 0 0
\(669\) 7.89729 0.305327
\(670\) 0 0
\(671\) 40.9538 1.58100
\(672\) 0 0
\(673\) −12.9301 −0.498420 −0.249210 0.968449i \(-0.580171\pi\)
−0.249210 + 0.968449i \(0.580171\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −15.9250 −0.612046 −0.306023 0.952024i \(-0.598998\pi\)
−0.306023 + 0.952024i \(0.598998\pi\)
\(678\) 0 0
\(679\) −46.4502 −1.78260
\(680\) 0 0
\(681\) −10.5493 −0.404248
\(682\) 0 0
\(683\) −13.2898 −0.508520 −0.254260 0.967136i \(-0.581832\pi\)
−0.254260 + 0.967136i \(0.581832\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.93929 0.0739884
\(688\) 0 0
\(689\) −28.5561 −1.08790
\(690\) 0 0
\(691\) −27.2570 −1.03690 −0.518452 0.855107i \(-0.673492\pi\)
−0.518452 + 0.855107i \(0.673492\pi\)
\(692\) 0 0
\(693\) −2.16342 −0.0821815
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 24.9933 0.945334
\(700\) 0 0
\(701\) −41.4441 −1.56532 −0.782660 0.622449i \(-0.786138\pi\)
−0.782660 + 0.622449i \(0.786138\pi\)
\(702\) 0 0
\(703\) −4.54677 −0.171485
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −25.2570 −0.949886
\(708\) 0 0
\(709\) −36.7904 −1.38169 −0.690846 0.723002i \(-0.742762\pi\)
−0.690846 + 0.723002i \(0.742762\pi\)
\(710\) 0 0
\(711\) 0.448264 0.0168112
\(712\) 0 0
\(713\) 27.2436 1.02028
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −27.6825 −1.03382
\(718\) 0 0
\(719\) 4.13726 0.154294 0.0771469 0.997020i \(-0.475419\pi\)
0.0771469 + 0.997020i \(0.475419\pi\)
\(720\) 0 0
\(721\) 34.8037 1.29616
\(722\) 0 0
\(723\) −9.25697 −0.344270
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 40.4374 1.49974 0.749870 0.661585i \(-0.230116\pi\)
0.749870 + 0.661585i \(0.230116\pi\)
\(728\) 0 0
\(729\) 25.5729 0.947146
\(730\) 0 0
\(731\) 46.9538 1.73665
\(732\) 0 0
\(733\) 28.1264 1.03887 0.519436 0.854509i \(-0.326142\pi\)
0.519436 + 0.854509i \(0.326142\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.8366 0.583348
\(738\) 0 0
\(739\) 38.1501 1.40337 0.701686 0.712486i \(-0.252431\pi\)
0.701686 + 0.712486i \(0.252431\pi\)
\(740\) 0 0
\(741\) 5.17526 0.190118
\(742\) 0 0
\(743\) 17.8232 0.653871 0.326935 0.945047i \(-0.393984\pi\)
0.326935 + 0.945047i \(0.393984\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −0.247812 −0.00906697
\(748\) 0 0
\(749\) −50.9857 −1.86298
\(750\) 0 0
\(751\) −23.6968 −0.864710 −0.432355 0.901703i \(-0.642317\pi\)
−0.432355 + 0.901703i \(0.642317\pi\)
\(752\) 0 0
\(753\) 50.7904 1.85090
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −6.51394 −0.236753 −0.118377 0.992969i \(-0.537769\pi\)
−0.118377 + 0.992969i \(0.537769\pi\)
\(758\) 0 0
\(759\) 35.5097 1.28892
\(760\) 0 0
\(761\) 34.7786 1.26072 0.630361 0.776302i \(-0.282907\pi\)
0.630361 + 0.776302i \(0.282907\pi\)
\(762\) 0 0
\(763\) −7.24513 −0.262291
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 37.9183 1.36915
\(768\) 0 0
\(769\) −27.6850 −0.998347 −0.499173 0.866502i \(-0.666363\pi\)
−0.499173 + 0.866502i \(0.666363\pi\)
\(770\) 0 0
\(771\) 11.4441 0.412148
\(772\) 0 0
\(773\) −19.9738 −0.718409 −0.359205 0.933259i \(-0.616952\pi\)
−0.359205 + 0.933259i \(0.616952\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 21.7035 0.778609
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 80.3001 2.87336
\(782\) 0 0
\(783\) −5.47691 −0.195729
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −42.0118 −1.49756 −0.748780 0.662818i \(-0.769360\pi\)
−0.748780 + 0.662818i \(0.769360\pi\)
\(788\) 0 0
\(789\) −39.3463 −1.40077
\(790\) 0 0
\(791\) −16.1501 −0.574230
\(792\) 0 0
\(793\) 21.5468 0.765148
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −45.1054 −1.59771 −0.798857 0.601520i \(-0.794562\pi\)
−0.798857 + 0.601520i \(0.794562\pi\)
\(798\) 0 0
\(799\) 4.11455 0.145562
\(800\) 0 0
\(801\) −0.738070 −0.0260784
\(802\) 0 0
\(803\) −28.6033 −1.00939
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −36.1896 −1.27393
\(808\) 0 0
\(809\) 6.85510 0.241012 0.120506 0.992713i \(-0.461548\pi\)
0.120506 + 0.992713i \(0.461548\pi\)
\(810\) 0 0
\(811\) 15.1819 0.533110 0.266555 0.963820i \(-0.414115\pi\)
0.266555 + 0.963820i \(0.414115\pi\)
\(812\) 0 0
\(813\) −28.2621 −0.991196
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9.54677 −0.333999
\(818\) 0 0
\(819\) −1.13823 −0.0397729
\(820\) 0 0
\(821\) 22.5006 0.785276 0.392638 0.919693i \(-0.371563\pi\)
0.392638 + 0.919693i \(0.371563\pi\)
\(822\) 0 0
\(823\) 16.1896 0.564333 0.282167 0.959365i \(-0.408947\pi\)
0.282167 + 0.959365i \(0.408947\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.0817 0.872177 0.436088 0.899904i \(-0.356364\pi\)
0.436088 + 0.899904i \(0.356364\pi\)
\(828\) 0 0
\(829\) 21.3068 0.740016 0.370008 0.929029i \(-0.379355\pi\)
0.370008 + 0.929029i \(0.379355\pi\)
\(830\) 0 0
\(831\) 7.13554 0.247529
\(832\) 0 0
\(833\) 1.20562 0.0417721
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 38.2108 1.32076
\(838\) 0 0
\(839\) 11.4727 0.396082 0.198041 0.980194i \(-0.436542\pi\)
0.198041 + 0.980194i \(0.436542\pi\)
\(840\) 0 0
\(841\) −27.8299 −0.959652
\(842\) 0 0
\(843\) 2.96716 0.102195
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 53.2056 1.82817
\(848\) 0 0
\(849\) −29.9580 −1.02816
\(850\) 0 0
\(851\) −16.4137 −0.562655
\(852\) 0 0
\(853\) −38.9908 −1.33502 −0.667511 0.744600i \(-0.732640\pi\)
−0.667511 + 0.744600i \(0.732640\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −29.8973 −1.02127 −0.510636 0.859797i \(-0.670590\pi\)
−0.510636 + 0.859797i \(0.670590\pi\)
\(858\) 0 0
\(859\) 6.47691 0.220989 0.110495 0.993877i \(-0.464757\pi\)
0.110495 + 0.993877i \(0.464757\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 5.09355 0.173386 0.0866932 0.996235i \(-0.472370\pi\)
0.0866932 + 0.996235i \(0.472370\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 12.7499 0.433010
\(868\) 0 0
\(869\) −17.1592 −0.582087
\(870\) 0 0
\(871\) 8.33200 0.282319
\(872\) 0 0
\(873\) −2.50059 −0.0846320
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −29.8341 −1.00743 −0.503713 0.863871i \(-0.668033\pi\)
−0.503713 + 0.863871i \(0.668033\pi\)
\(878\) 0 0
\(879\) −1.91829 −0.0647023
\(880\) 0 0
\(881\) −11.5796 −0.390127 −0.195064 0.980791i \(-0.562491\pi\)
−0.195064 + 0.980791i \(0.562491\pi\)
\(882\) 0 0
\(883\) 48.0237 1.61613 0.808063 0.589096i \(-0.200516\pi\)
0.808063 + 0.589096i \(0.200516\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −9.38336 −0.315062 −0.157531 0.987514i \(-0.550353\pi\)
−0.157531 + 0.987514i \(0.550353\pi\)
\(888\) 0 0
\(889\) 5.04316 0.169142
\(890\) 0 0
\(891\) 52.2157 1.74929
\(892\) 0 0
\(893\) −0.836581 −0.0279951
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 18.6825 0.623791
\(898\) 0 0
\(899\) −8.16342 −0.272265
\(900\) 0 0
\(901\) 48.1266 1.60333
\(902\) 0 0
\(903\) 45.5705 1.51649
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 19.4347 0.645319 0.322659 0.946515i \(-0.395423\pi\)
0.322659 + 0.946515i \(0.395423\pi\)
\(908\) 0 0
\(909\) −1.35968 −0.0450976
\(910\) 0 0
\(911\) 19.9866 0.662187 0.331094 0.943598i \(-0.392582\pi\)
0.331094 + 0.943598i \(0.392582\pi\)
\(912\) 0 0
\(913\) 9.48606 0.313943
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 31.0802 1.02636
\(918\) 0 0
\(919\) −6.15158 −0.202922 −0.101461 0.994840i \(-0.532352\pi\)
−0.101461 + 0.994840i \(0.532352\pi\)
\(920\) 0 0
\(921\) −4.22661 −0.139272
\(922\) 0 0
\(923\) 42.2478 1.39060
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 1.87361 0.0615375
\(928\) 0 0
\(929\) −7.17010 −0.235243 −0.117622 0.993058i \(-0.537527\pi\)
−0.117622 + 0.993058i \(0.537527\pi\)
\(930\) 0 0
\(931\) −0.245129 −0.00803378
\(932\) 0 0
\(933\) 52.2411 1.71030
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −24.2646 −0.792690 −0.396345 0.918102i \(-0.629722\pi\)
−0.396345 + 0.918102i \(0.629722\pi\)
\(938\) 0 0
\(939\) 56.8114 1.85397
\(940\) 0 0
\(941\) −7.44806 −0.242800 −0.121400 0.992604i \(-0.538738\pi\)
−0.121400 + 0.992604i \(0.538738\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 52.9538 1.72077 0.860384 0.509647i \(-0.170224\pi\)
0.860384 + 0.509647i \(0.170224\pi\)
\(948\) 0 0
\(949\) −15.0489 −0.488507
\(950\) 0 0
\(951\) −47.2900 −1.53348
\(952\) 0 0
\(953\) −12.8694 −0.416881 −0.208441 0.978035i \(-0.566839\pi\)
−0.208441 + 0.978035i \(0.566839\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −10.6403 −0.343953
\(958\) 0 0
\(959\) 11.4085 0.368401
\(960\) 0 0
\(961\) 25.9538 0.837220
\(962\) 0 0
\(963\) −2.74475 −0.0884482
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −25.8603 −0.831610 −0.415805 0.909454i \(-0.636500\pi\)
−0.415805 + 0.909454i \(0.636500\pi\)
\(968\) 0 0
\(969\) −8.72203 −0.280192
\(970\) 0 0
\(971\) −35.0935 −1.12621 −0.563103 0.826387i \(-0.690392\pi\)
−0.563103 + 0.826387i \(0.690392\pi\)
\(972\) 0 0
\(973\) −24.8171 −0.795600
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −42.1737 −1.34926 −0.674629 0.738157i \(-0.735696\pi\)
−0.674629 + 0.738157i \(0.735696\pi\)
\(978\) 0 0
\(979\) 28.2528 0.902963
\(980\) 0 0
\(981\) −0.390032 −0.0124528
\(982\) 0 0
\(983\) 42.6270 1.35959 0.679795 0.733403i \(-0.262069\pi\)
0.679795 + 0.733403i \(0.262069\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3.99332 0.127109
\(988\) 0 0
\(989\) −34.4636 −1.09588
\(990\) 0 0
\(991\) 34.1737 1.08556 0.542782 0.839873i \(-0.317371\pi\)
0.542782 + 0.839873i \(0.317371\pi\)
\(992\) 0 0
\(993\) 35.2409 1.11834
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 29.3834 0.930580 0.465290 0.885158i \(-0.345950\pi\)
0.465290 + 0.885158i \(0.345950\pi\)
\(998\) 0 0
\(999\) −23.0212 −0.728359
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.1.3 3
4.3 odd 2 950.2.a.l.1.1 yes 3
5.4 even 2 7600.2.a.bz.1.1 3
12.11 even 2 8550.2.a.ci.1.1 3
20.3 even 4 950.2.b.h.799.1 6
20.7 even 4 950.2.b.h.799.6 6
20.19 odd 2 950.2.a.j.1.3 3
60.59 even 2 8550.2.a.cp.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.3 3 20.19 odd 2
950.2.a.l.1.1 yes 3 4.3 odd 2
950.2.b.h.799.1 6 20.3 even 4
950.2.b.h.799.6 6 20.7 even 4
7600.2.a.bk.1.3 3 1.1 even 1 trivial
7600.2.a.bz.1.1 3 5.4 even 2
8550.2.a.ci.1.1 3 12.11 even 2
8550.2.a.cp.1.3 3 60.59 even 2