Properties

Label 4600.2.a.bd.1.4
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.521397.1
Defining polynomial: \(x^{5} - 9 x^{3} - 3 x^{2} + 18 x + 12\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.36629\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36629 q^{3} -3.28093 q^{7} -1.13327 q^{9} +O(q^{10})\) \(q+1.36629 q^{3} -3.28093 q^{7} -1.13327 q^{9} +3.49709 q^{11} +3.41420 q^{13} -7.46023 q^{17} +3.49709 q^{19} -4.48269 q^{21} +1.00000 q^{23} -5.64722 q^{27} -3.46268 q^{29} +2.01105 q^{31} +4.77803 q^{33} +0.511497 q^{37} +4.66477 q^{39} -7.07954 q^{41} -2.76452 q^{43} -0.889198 q^{47} +3.76452 q^{49} -10.1928 q^{51} -14.2383 q^{53} +4.77803 q^{57} -4.71325 q^{59} +13.4769 q^{61} +3.71817 q^{63} -2.30025 q^{67} +1.36629 q^{69} -10.6214 q^{71} +3.70765 q^{73} -11.4737 q^{77} -7.97978 q^{79} -4.31592 q^{81} +9.42336 q^{83} -4.73101 q^{87} +0.801390 q^{89} -11.2018 q^{91} +2.74766 q^{93} +11.7722 q^{97} -3.96313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 4 q^{7} + 3 q^{9} + O(q^{10}) \) \( 5 q - 4 q^{7} + 3 q^{9} - 4 q^{13} - 6 q^{17} + 5 q^{23} - 9 q^{27} + 12 q^{29} - 18 q^{31} - 6 q^{33} - 10 q^{37} + 9 q^{39} - 6 q^{41} - 10 q^{43} - 22 q^{47} + 15 q^{49} - 6 q^{51} - 10 q^{53} - 6 q^{57} - q^{59} + 10 q^{61} - 8 q^{67} + 8 q^{71} - 6 q^{73} - 27 q^{81} + 2 q^{83} - 39 q^{87} + 14 q^{89} - 46 q^{91} + 3 q^{93} - 6 q^{97} - 6 q^{99} + O(q^{100}) \)

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
\(3\) 1.36629 0.788825 0.394413 0.918933i \(-0.370948\pi\)
0.394413 + 0.918933i \(0.370948\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −3.28093 −1.24008 −0.620038 0.784572i \(-0.712883\pi\)
−0.620038 + 0.784572i \(0.712883\pi\)
\(8\) 0 0
\(9\) −1.13327 −0.377755
\(10\) 0 0
\(11\) 3.49709 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(12\) 0 0
\(13\) 3.41420 0.946928 0.473464 0.880813i \(-0.343003\pi\)
0.473464 + 0.880813i \(0.343003\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.46023 −1.80937 −0.904685 0.426080i \(-0.859894\pi\)
−0.904685 + 0.426080i \(0.859894\pi\)
\(18\) 0 0
\(19\) 3.49709 0.802288 0.401144 0.916015i \(-0.368613\pi\)
0.401144 + 0.916015i \(0.368613\pi\)
\(20\) 0 0
\(21\) −4.48269 −0.978203
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.64722 −1.08681
\(28\) 0 0
\(29\) −3.46268 −0.643004 −0.321502 0.946909i \(-0.604188\pi\)
−0.321502 + 0.946909i \(0.604188\pi\)
\(30\) 0 0
\(31\) 2.01105 0.361195 0.180597 0.983557i \(-0.442197\pi\)
0.180597 + 0.983557i \(0.442197\pi\)
\(32\) 0 0
\(33\) 4.77803 0.831748
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.511497 0.0840896 0.0420448 0.999116i \(-0.486613\pi\)
0.0420448 + 0.999116i \(0.486613\pi\)
\(38\) 0 0
\(39\) 4.66477 0.746961
\(40\) 0 0
\(41\) −7.07954 −1.10564 −0.552819 0.833301i \(-0.686448\pi\)
−0.552819 + 0.833301i \(0.686448\pi\)
\(42\) 0 0
\(43\) −2.76452 −0.421586 −0.210793 0.977531i \(-0.567605\pi\)
−0.210793 + 0.977531i \(0.567605\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.889198 −0.129703 −0.0648514 0.997895i \(-0.520657\pi\)
−0.0648514 + 0.997895i \(0.520657\pi\)
\(48\) 0 0
\(49\) 3.76452 0.537789
\(50\) 0 0
\(51\) −10.1928 −1.42728
\(52\) 0 0
\(53\) −14.2383 −1.95577 −0.977887 0.209132i \(-0.932936\pi\)
−0.977887 + 0.209132i \(0.932936\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.77803 0.632865
\(58\) 0 0
\(59\) −4.71325 −0.613613 −0.306807 0.951772i \(-0.599261\pi\)
−0.306807 + 0.951772i \(0.599261\pi\)
\(60\) 0 0
\(61\) 13.4769 1.72554 0.862769 0.505599i \(-0.168728\pi\)
0.862769 + 0.505599i \(0.168728\pi\)
\(62\) 0 0
\(63\) 3.71817 0.468445
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.30025 −0.281020 −0.140510 0.990079i \(-0.544874\pi\)
−0.140510 + 0.990079i \(0.544874\pi\)
\(68\) 0 0
\(69\) 1.36629 0.164481
\(70\) 0 0
\(71\) −10.6214 −1.26053 −0.630264 0.776381i \(-0.717053\pi\)
−0.630264 + 0.776381i \(0.717053\pi\)
\(72\) 0 0
\(73\) 3.70765 0.433948 0.216974 0.976177i \(-0.430381\pi\)
0.216974 + 0.976177i \(0.430381\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.4737 −1.30755
\(78\) 0 0
\(79\) −7.97978 −0.897796 −0.448898 0.893583i \(-0.648183\pi\)
−0.448898 + 0.893583i \(0.648183\pi\)
\(80\) 0 0
\(81\) −4.31592 −0.479546
\(82\) 0 0
\(83\) 9.42336 1.03435 0.517174 0.855880i \(-0.326984\pi\)
0.517174 + 0.855880i \(0.326984\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.73101 −0.507218
\(88\) 0 0
\(89\) 0.801390 0.0849471 0.0424736 0.999098i \(-0.486476\pi\)
0.0424736 + 0.999098i \(0.486476\pi\)
\(90\) 0 0
\(91\) −11.2018 −1.17426
\(92\) 0 0
\(93\) 2.74766 0.284919
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 11.7722 1.19529 0.597644 0.801762i \(-0.296104\pi\)
0.597644 + 0.801762i \(0.296104\pi\)
\(98\) 0 0
\(99\) −3.96313 −0.398310
\(100\) 0 0
\(101\) 11.1559 1.11006 0.555028 0.831831i \(-0.312707\pi\)
0.555028 + 0.831831i \(0.312707\pi\)
\(102\) 0 0
\(103\) 1.28585 0.126698 0.0633491 0.997991i \(-0.479822\pi\)
0.0633491 + 0.997991i \(0.479822\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −13.8975 −1.34352 −0.671759 0.740770i \(-0.734461\pi\)
−0.671759 + 0.740770i \(0.734461\pi\)
\(108\) 0 0
\(109\) −3.77713 −0.361783 −0.180892 0.983503i \(-0.557898\pi\)
−0.180892 + 0.983503i \(0.557898\pi\)
\(110\) 0 0
\(111\) 0.698851 0.0663320
\(112\) 0 0
\(113\) −19.3111 −1.81663 −0.908317 0.418282i \(-0.862632\pi\)
−0.908317 + 0.418282i \(0.862632\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −3.86919 −0.357707
\(118\) 0 0
\(119\) 24.4765 2.24376
\(120\) 0 0
\(121\) 1.22966 0.111788
\(122\) 0 0
\(123\) −9.67267 −0.872155
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −13.7612 −1.22111 −0.610553 0.791975i \(-0.709053\pi\)
−0.610553 + 0.791975i \(0.709053\pi\)
\(128\) 0 0
\(129\) −3.77713 −0.332558
\(130\) 0 0
\(131\) −7.41665 −0.647996 −0.323998 0.946058i \(-0.605027\pi\)
−0.323998 + 0.946058i \(0.605027\pi\)
\(132\) 0 0
\(133\) −11.4737 −0.994899
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.5502 1.75573 0.877863 0.478912i \(-0.158969\pi\)
0.877863 + 0.478912i \(0.158969\pi\)
\(138\) 0 0
\(139\) −5.49652 −0.466209 −0.233104 0.972452i \(-0.574888\pi\)
−0.233104 + 0.972452i \(0.574888\pi\)
\(140\) 0 0
\(141\) −1.21490 −0.102313
\(142\) 0 0
\(143\) 11.9398 0.998454
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.14341 0.424221
\(148\) 0 0
\(149\) 4.80139 0.393345 0.196673 0.980469i \(-0.436986\pi\)
0.196673 + 0.980469i \(0.436986\pi\)
\(150\) 0 0
\(151\) −3.26862 −0.265997 −0.132998 0.991116i \(-0.542461\pi\)
−0.132998 + 0.991116i \(0.542461\pi\)
\(152\) 0 0
\(153\) 8.45441 0.683499
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −21.8392 −1.74296 −0.871480 0.490430i \(-0.836840\pi\)
−0.871480 + 0.490430i \(0.836840\pi\)
\(158\) 0 0
\(159\) −19.4535 −1.54276
\(160\) 0 0
\(161\) −3.28093 −0.258574
\(162\) 0 0
\(163\) −23.2435 −1.82057 −0.910285 0.413982i \(-0.864138\pi\)
−0.910285 + 0.413982i \(0.864138\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.13179 0.319728 0.159864 0.987139i \(-0.448894\pi\)
0.159864 + 0.987139i \(0.448894\pi\)
\(168\) 0 0
\(169\) −1.34325 −0.103327
\(170\) 0 0
\(171\) −3.96313 −0.303068
\(172\) 0 0
\(173\) −5.88548 −0.447465 −0.223732 0.974651i \(-0.571824\pi\)
−0.223732 + 0.974651i \(0.571824\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.43965 −0.484034
\(178\) 0 0
\(179\) −6.85789 −0.512583 −0.256292 0.966600i \(-0.582501\pi\)
−0.256292 + 0.966600i \(0.582501\pi\)
\(180\) 0 0
\(181\) −2.29042 −0.170246 −0.0851229 0.996370i \(-0.527128\pi\)
−0.0851229 + 0.996370i \(0.527128\pi\)
\(182\) 0 0
\(183\) 18.4133 1.36115
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −26.0891 −1.90782
\(188\) 0 0
\(189\) 18.5281 1.34772
\(190\) 0 0
\(191\) −9.58748 −0.693725 −0.346863 0.937916i \(-0.612753\pi\)
−0.346863 + 0.937916i \(0.612753\pi\)
\(192\) 0 0
\(193\) −13.9410 −1.00350 −0.501749 0.865013i \(-0.667310\pi\)
−0.501749 + 0.865013i \(0.667310\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.1011 −1.07591 −0.537954 0.842974i \(-0.680803\pi\)
−0.537954 + 0.842974i \(0.680803\pi\)
\(198\) 0 0
\(199\) 14.5128 1.02879 0.514394 0.857554i \(-0.328017\pi\)
0.514394 + 0.857554i \(0.328017\pi\)
\(200\) 0 0
\(201\) −3.14280 −0.221676
\(202\) 0 0
\(203\) 11.3608 0.797374
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.13327 −0.0787674
\(208\) 0 0
\(209\) 12.2297 0.845944
\(210\) 0 0
\(211\) −23.4846 −1.61674 −0.808372 0.588672i \(-0.799651\pi\)
−0.808372 + 0.588672i \(0.799651\pi\)
\(212\) 0 0
\(213\) −14.5119 −0.994336
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −6.59811 −0.447909
\(218\) 0 0
\(219\) 5.06571 0.342309
\(220\) 0 0
\(221\) −25.4707 −1.71334
\(222\) 0 0
\(223\) 8.20720 0.549595 0.274797 0.961502i \(-0.411389\pi\)
0.274797 + 0.961502i \(0.411389\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.9942 −1.12794 −0.563972 0.825794i \(-0.690727\pi\)
−0.563972 + 0.825794i \(0.690727\pi\)
\(228\) 0 0
\(229\) 19.6818 1.30061 0.650306 0.759672i \(-0.274641\pi\)
0.650306 + 0.759672i \(0.274641\pi\)
\(230\) 0 0
\(231\) −15.6764 −1.03143
\(232\) 0 0
\(233\) −24.8799 −1.62993 −0.814967 0.579507i \(-0.803245\pi\)
−0.814967 + 0.579507i \(0.803245\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −10.9027 −0.708204
\(238\) 0 0
\(239\) −0.0718483 −0.00464748 −0.00232374 0.999997i \(-0.500740\pi\)
−0.00232374 + 0.999997i \(0.500740\pi\)
\(240\) 0 0
\(241\) −8.50658 −0.547957 −0.273979 0.961736i \(-0.588340\pi\)
−0.273979 + 0.961736i \(0.588340\pi\)
\(242\) 0 0
\(243\) 11.0449 0.708530
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 11.9398 0.759709
\(248\) 0 0
\(249\) 12.8750 0.815920
\(250\) 0 0
\(251\) −19.8858 −1.25518 −0.627591 0.778543i \(-0.715959\pi\)
−0.627591 + 0.778543i \(0.715959\pi\)
\(252\) 0 0
\(253\) 3.49709 0.219860
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.4062 0.711498 0.355749 0.934582i \(-0.384226\pi\)
0.355749 + 0.934582i \(0.384226\pi\)
\(258\) 0 0
\(259\) −1.67819 −0.104277
\(260\) 0 0
\(261\) 3.92414 0.242898
\(262\) 0 0
\(263\) 13.3903 0.825679 0.412840 0.910804i \(-0.364537\pi\)
0.412840 + 0.910804i \(0.364537\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.09493 0.0670084
\(268\) 0 0
\(269\) 13.8103 0.842027 0.421014 0.907054i \(-0.361674\pi\)
0.421014 + 0.907054i \(0.361674\pi\)
\(270\) 0 0
\(271\) 26.7574 1.62540 0.812699 0.582683i \(-0.197997\pi\)
0.812699 + 0.582683i \(0.197997\pi\)
\(272\) 0 0
\(273\) −15.3048 −0.926288
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.80667 0.108552 0.0542760 0.998526i \(-0.482715\pi\)
0.0542760 + 0.998526i \(0.482715\pi\)
\(278\) 0 0
\(279\) −2.27905 −0.136443
\(280\) 0 0
\(281\) 27.1348 1.61873 0.809364 0.587308i \(-0.199812\pi\)
0.809364 + 0.587308i \(0.199812\pi\)
\(282\) 0 0
\(283\) −20.9875 −1.24758 −0.623788 0.781594i \(-0.714407\pi\)
−0.623788 + 0.781594i \(0.714407\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.2275 1.37108
\(288\) 0 0
\(289\) 38.6550 2.27382
\(290\) 0 0
\(291\) 16.0842 0.942873
\(292\) 0 0
\(293\) −0.00671252 −0.000392149 0 −0.000196075 1.00000i \(-0.500062\pi\)
−0.000196075 1.00000i \(0.500062\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −19.7489 −1.14594
\(298\) 0 0
\(299\) 3.41420 0.197448
\(300\) 0 0
\(301\) 9.07022 0.522799
\(302\) 0 0
\(303\) 15.2422 0.875641
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 19.9767 1.14013 0.570067 0.821598i \(-0.306917\pi\)
0.570067 + 0.821598i \(0.306917\pi\)
\(308\) 0 0
\(309\) 1.75683 0.0999427
\(310\) 0 0
\(311\) 23.8601 1.35298 0.676491 0.736451i \(-0.263500\pi\)
0.676491 + 0.736451i \(0.263500\pi\)
\(312\) 0 0
\(313\) 17.4406 0.985803 0.492901 0.870085i \(-0.335936\pi\)
0.492901 + 0.870085i \(0.335936\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.35581 −0.0761499 −0.0380750 0.999275i \(-0.512123\pi\)
−0.0380750 + 0.999275i \(0.512123\pi\)
\(318\) 0 0
\(319\) −12.1093 −0.677992
\(320\) 0 0
\(321\) −18.9879 −1.05980
\(322\) 0 0
\(323\) −26.0891 −1.45164
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −5.16063 −0.285384
\(328\) 0 0
\(329\) 2.91740 0.160841
\(330\) 0 0
\(331\) 17.4050 0.956667 0.478333 0.878178i \(-0.341241\pi\)
0.478333 + 0.878178i \(0.341241\pi\)
\(332\) 0 0
\(333\) −0.579662 −0.0317653
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −22.4648 −1.22373 −0.611867 0.790961i \(-0.709581\pi\)
−0.611867 + 0.790961i \(0.709581\pi\)
\(338\) 0 0
\(339\) −26.3845 −1.43301
\(340\) 0 0
\(341\) 7.03282 0.380849
\(342\) 0 0
\(343\) 10.6154 0.573177
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.97296 −0.159597 −0.0797984 0.996811i \(-0.525428\pi\)
−0.0797984 + 0.996811i \(0.525428\pi\)
\(348\) 0 0
\(349\) −4.36975 −0.233908 −0.116954 0.993137i \(-0.537313\pi\)
−0.116954 + 0.993137i \(0.537313\pi\)
\(350\) 0 0
\(351\) −19.2807 −1.02913
\(352\) 0 0
\(353\) −31.4419 −1.67348 −0.836742 0.547598i \(-0.815542\pi\)
−0.836742 + 0.547598i \(0.815542\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 33.4419 1.76993
\(358\) 0 0
\(359\) 27.7912 1.46676 0.733381 0.679818i \(-0.237941\pi\)
0.733381 + 0.679818i \(0.237941\pi\)
\(360\) 0 0
\(361\) −6.77034 −0.356333
\(362\) 0 0
\(363\) 1.68007 0.0881809
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −13.9061 −0.725890 −0.362945 0.931811i \(-0.618229\pi\)
−0.362945 + 0.931811i \(0.618229\pi\)
\(368\) 0 0
\(369\) 8.02299 0.417660
\(370\) 0 0
\(371\) 46.7148 2.42531
\(372\) 0 0
\(373\) 26.2799 1.36072 0.680362 0.732876i \(-0.261823\pi\)
0.680362 + 0.732876i \(0.261823\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −11.8223 −0.608879
\(378\) 0 0
\(379\) −3.06792 −0.157588 −0.0787942 0.996891i \(-0.525107\pi\)
−0.0787942 + 0.996891i \(0.525107\pi\)
\(380\) 0 0
\(381\) −18.8017 −0.963239
\(382\) 0 0
\(383\) −28.8872 −1.47607 −0.738034 0.674763i \(-0.764246\pi\)
−0.738034 + 0.674763i \(0.764246\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.13294 0.159256
\(388\) 0 0
\(389\) 24.4697 1.24066 0.620331 0.784340i \(-0.286998\pi\)
0.620331 + 0.784340i \(0.286998\pi\)
\(390\) 0 0
\(391\) −7.46023 −0.377280
\(392\) 0 0
\(393\) −10.1333 −0.511156
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.44828 0.424007 0.212004 0.977269i \(-0.432001\pi\)
0.212004 + 0.977269i \(0.432001\pi\)
\(398\) 0 0
\(399\) −15.6764 −0.784801
\(400\) 0 0
\(401\) 20.3352 1.01549 0.507746 0.861507i \(-0.330479\pi\)
0.507746 + 0.861507i \(0.330479\pi\)
\(402\) 0 0
\(403\) 6.86611 0.342025
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.78875 0.0886652
\(408\) 0 0
\(409\) 6.05655 0.299477 0.149738 0.988726i \(-0.452157\pi\)
0.149738 + 0.988726i \(0.452157\pi\)
\(410\) 0 0
\(411\) 28.0775 1.38496
\(412\) 0 0
\(413\) 15.4639 0.760927
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.50982 −0.367757
\(418\) 0 0
\(419\) 7.02434 0.343162 0.171581 0.985170i \(-0.445113\pi\)
0.171581 + 0.985170i \(0.445113\pi\)
\(420\) 0 0
\(421\) 7.17652 0.349762 0.174881 0.984590i \(-0.444046\pi\)
0.174881 + 0.984590i \(0.444046\pi\)
\(422\) 0 0
\(423\) 1.00770 0.0489959
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −44.2167 −2.13980
\(428\) 0 0
\(429\) 16.3131 0.787605
\(430\) 0 0
\(431\) 11.2944 0.544034 0.272017 0.962292i \(-0.412309\pi\)
0.272017 + 0.962292i \(0.412309\pi\)
\(432\) 0 0
\(433\) 22.2266 1.06814 0.534072 0.845439i \(-0.320661\pi\)
0.534072 + 0.845439i \(0.320661\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.49709 0.167289
\(438\) 0 0
\(439\) −30.2573 −1.44410 −0.722052 0.691839i \(-0.756801\pi\)
−0.722052 + 0.691839i \(0.756801\pi\)
\(440\) 0 0
\(441\) −4.26620 −0.203153
\(442\) 0 0
\(443\) −14.0307 −0.666620 −0.333310 0.942817i \(-0.608166\pi\)
−0.333310 + 0.942817i \(0.608166\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 6.56007 0.310281
\(448\) 0 0
\(449\) 8.70110 0.410630 0.205315 0.978696i \(-0.434178\pi\)
0.205315 + 0.978696i \(0.434178\pi\)
\(450\) 0 0
\(451\) −24.7578 −1.16580
\(452\) 0 0
\(453\) −4.46587 −0.209825
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 33.8379 1.58287 0.791434 0.611255i \(-0.209335\pi\)
0.791434 + 0.611255i \(0.209335\pi\)
\(458\) 0 0
\(459\) 42.1295 1.96644
\(460\) 0 0
\(461\) 39.6512 1.84674 0.923370 0.383912i \(-0.125423\pi\)
0.923370 + 0.383912i \(0.125423\pi\)
\(462\) 0 0
\(463\) 34.8490 1.61957 0.809784 0.586727i \(-0.199584\pi\)
0.809784 + 0.586727i \(0.199584\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.9442 −0.645258 −0.322629 0.946525i \(-0.604567\pi\)
−0.322629 + 0.946525i \(0.604567\pi\)
\(468\) 0 0
\(469\) 7.54697 0.348486
\(470\) 0 0
\(471\) −29.8386 −1.37489
\(472\) 0 0
\(473\) −9.66780 −0.444526
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 16.1357 0.738804
\(478\) 0 0
\(479\) −32.4103 −1.48086 −0.740432 0.672131i \(-0.765379\pi\)
−0.740432 + 0.672131i \(0.765379\pi\)
\(480\) 0 0
\(481\) 1.74635 0.0796268
\(482\) 0 0
\(483\) −4.48269 −0.203969
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −25.1999 −1.14192 −0.570959 0.820979i \(-0.693428\pi\)
−0.570959 + 0.820979i \(0.693428\pi\)
\(488\) 0 0
\(489\) −31.7572 −1.43611
\(490\) 0 0
\(491\) −32.9247 −1.48587 −0.742936 0.669363i \(-0.766567\pi\)
−0.742936 + 0.669363i \(0.766567\pi\)
\(492\) 0 0
\(493\) 25.8324 1.16343
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 34.8481 1.56315
\(498\) 0 0
\(499\) 12.4047 0.555309 0.277654 0.960681i \(-0.410443\pi\)
0.277654 + 0.960681i \(0.410443\pi\)
\(500\) 0 0
\(501\) 5.64521 0.252209
\(502\) 0 0
\(503\) 3.74517 0.166989 0.0834945 0.996508i \(-0.473392\pi\)
0.0834945 + 0.996508i \(0.473392\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.83526 −0.0815069
\(508\) 0 0
\(509\) −5.84783 −0.259201 −0.129600 0.991566i \(-0.541369\pi\)
−0.129600 + 0.991566i \(0.541369\pi\)
\(510\) 0 0
\(511\) −12.1646 −0.538128
\(512\) 0 0
\(513\) −19.7489 −0.871933
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −3.10961 −0.136760
\(518\) 0 0
\(519\) −8.04124 −0.352971
\(520\) 0 0
\(521\) 18.3808 0.805278 0.402639 0.915359i \(-0.368093\pi\)
0.402639 + 0.915359i \(0.368093\pi\)
\(522\) 0 0
\(523\) −23.4541 −1.02558 −0.512789 0.858515i \(-0.671388\pi\)
−0.512789 + 0.858515i \(0.671388\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −15.0029 −0.653535
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 5.34137 0.231796
\(532\) 0 0
\(533\) −24.1710 −1.04696
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −9.36984 −0.404338
\(538\) 0 0
\(539\) 13.1649 0.567052
\(540\) 0 0
\(541\) 3.03474 0.130474 0.0652368 0.997870i \(-0.479220\pi\)
0.0652368 + 0.997870i \(0.479220\pi\)
\(542\) 0 0
\(543\) −3.12937 −0.134294
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16.4383 −0.702851 −0.351426 0.936216i \(-0.614303\pi\)
−0.351426 + 0.936216i \(0.614303\pi\)
\(548\) 0 0
\(549\) −15.2729 −0.651830
\(550\) 0 0
\(551\) −12.1093 −0.515875
\(552\) 0 0
\(553\) 26.1811 1.11334
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.72395 0.284903 0.142451 0.989802i \(-0.454502\pi\)
0.142451 + 0.989802i \(0.454502\pi\)
\(558\) 0 0
\(559\) −9.43863 −0.399212
\(560\) 0 0
\(561\) −35.6452 −1.50494
\(562\) 0 0
\(563\) 42.0044 1.77027 0.885137 0.465331i \(-0.154065\pi\)
0.885137 + 0.465331i \(0.154065\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 14.1602 0.594674
\(568\) 0 0
\(569\) −39.1152 −1.63980 −0.819898 0.572510i \(-0.805970\pi\)
−0.819898 + 0.572510i \(0.805970\pi\)
\(570\) 0 0
\(571\) −13.2607 −0.554944 −0.277472 0.960734i \(-0.589497\pi\)
−0.277472 + 0.960734i \(0.589497\pi\)
\(572\) 0 0
\(573\) −13.0992 −0.547228
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −9.31588 −0.387825 −0.193913 0.981019i \(-0.562118\pi\)
−0.193913 + 0.981019i \(0.562118\pi\)
\(578\) 0 0
\(579\) −19.0474 −0.791584
\(580\) 0 0
\(581\) −30.9174 −1.28267
\(582\) 0 0
\(583\) −49.7925 −2.06220
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −7.80336 −0.322079 −0.161040 0.986948i \(-0.551485\pi\)
−0.161040 + 0.986948i \(0.551485\pi\)
\(588\) 0 0
\(589\) 7.03282 0.289782
\(590\) 0 0
\(591\) −20.6324 −0.848704
\(592\) 0 0
\(593\) −12.8383 −0.527204 −0.263602 0.964632i \(-0.584911\pi\)
−0.263602 + 0.964632i \(0.584911\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 19.8287 0.811534
\(598\) 0 0
\(599\) −10.4957 −0.428843 −0.214422 0.976741i \(-0.568787\pi\)
−0.214422 + 0.976741i \(0.568787\pi\)
\(600\) 0 0
\(601\) −28.1978 −1.15021 −0.575106 0.818079i \(-0.695039\pi\)
−0.575106 + 0.818079i \(0.695039\pi\)
\(602\) 0 0
\(603\) 2.60679 0.106157
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 46.5662 1.89007 0.945033 0.326976i \(-0.106030\pi\)
0.945033 + 0.326976i \(0.106030\pi\)
\(608\) 0 0
\(609\) 15.5221 0.628989
\(610\) 0 0
\(611\) −3.03590 −0.122819
\(612\) 0 0
\(613\) 30.3120 1.22429 0.612145 0.790746i \(-0.290307\pi\)
0.612145 + 0.790746i \(0.290307\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.1879 0.973768 0.486884 0.873467i \(-0.338134\pi\)
0.486884 + 0.873467i \(0.338134\pi\)
\(618\) 0 0
\(619\) −4.29534 −0.172644 −0.0863221 0.996267i \(-0.527511\pi\)
−0.0863221 + 0.996267i \(0.527511\pi\)
\(620\) 0 0
\(621\) −5.64722 −0.226615
\(622\) 0 0
\(623\) −2.62931 −0.105341
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 16.7092 0.667301
\(628\) 0 0
\(629\) −3.81588 −0.152149
\(630\) 0 0
\(631\) 12.3857 0.493066 0.246533 0.969134i \(-0.420709\pi\)
0.246533 + 0.969134i \(0.420709\pi\)
\(632\) 0 0
\(633\) −32.0866 −1.27533
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 12.8528 0.509248
\(638\) 0 0
\(639\) 12.0369 0.476171
\(640\) 0 0
\(641\) −5.21653 −0.206041 −0.103020 0.994679i \(-0.532851\pi\)
−0.103020 + 0.994679i \(0.532851\pi\)
\(642\) 0 0
\(643\) 12.5639 0.495471 0.247735 0.968828i \(-0.420314\pi\)
0.247735 + 0.968828i \(0.420314\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.7423 −0.894094 −0.447047 0.894510i \(-0.647524\pi\)
−0.447047 + 0.894510i \(0.647524\pi\)
\(648\) 0 0
\(649\) −16.4827 −0.647002
\(650\) 0 0
\(651\) −9.01490 −0.353322
\(652\) 0 0
\(653\) 9.36997 0.366675 0.183338 0.983050i \(-0.441310\pi\)
0.183338 + 0.983050i \(0.441310\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −4.20175 −0.163926
\(658\) 0 0
\(659\) −15.4086 −0.600235 −0.300117 0.953902i \(-0.597026\pi\)
−0.300117 + 0.953902i \(0.597026\pi\)
\(660\) 0 0
\(661\) 43.1386 1.67790 0.838948 0.544211i \(-0.183171\pi\)
0.838948 + 0.544211i \(0.183171\pi\)
\(662\) 0 0
\(663\) −34.8002 −1.35153
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −3.46268 −0.134076
\(668\) 0 0
\(669\) 11.2134 0.433534
\(670\) 0 0
\(671\) 47.1299 1.81943
\(672\) 0 0
\(673\) −12.6356 −0.487066 −0.243533 0.969893i \(-0.578306\pi\)
−0.243533 + 0.969893i \(0.578306\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.9139 0.419454 0.209727 0.977760i \(-0.432742\pi\)
0.209727 + 0.977760i \(0.432742\pi\)
\(678\) 0 0
\(679\) −38.6238 −1.48225
\(680\) 0 0
\(681\) −23.2189 −0.889750
\(682\) 0 0
\(683\) 17.5334 0.670896 0.335448 0.942059i \(-0.391112\pi\)
0.335448 + 0.942059i \(0.391112\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 26.8910 1.02596
\(688\) 0 0
\(689\) −48.6122 −1.85198
\(690\) 0 0
\(691\) −52.2318 −1.98699 −0.993496 0.113871i \(-0.963675\pi\)
−0.993496 + 0.113871i \(0.963675\pi\)
\(692\) 0 0
\(693\) 13.0028 0.493935
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 52.8150 2.00051
\(698\) 0 0
\(699\) −33.9930 −1.28573
\(700\) 0 0
\(701\) 26.0270 0.983026 0.491513 0.870870i \(-0.336444\pi\)
0.491513 + 0.870870i \(0.336444\pi\)
\(702\) 0 0
\(703\) 1.78875 0.0674641
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −36.6019 −1.37655
\(708\) 0 0
\(709\) −34.7971 −1.30683 −0.653415 0.757000i \(-0.726664\pi\)
−0.653415 + 0.757000i \(0.726664\pi\)
\(710\) 0 0
\(711\) 9.04321 0.339147
\(712\) 0 0
\(713\) 2.01105 0.0753143
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.0981652 −0.00366605
\(718\) 0 0
\(719\) 4.40110 0.164133 0.0820667 0.996627i \(-0.473848\pi\)
0.0820667 + 0.996627i \(0.473848\pi\)
\(720\) 0 0
\(721\) −4.21878 −0.157115
\(722\) 0 0
\(723\) −11.6224 −0.432242
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −0.744921 −0.0276276 −0.0138138 0.999905i \(-0.504397\pi\)
−0.0138138 + 0.999905i \(0.504397\pi\)
\(728\) 0 0
\(729\) 28.0382 1.03845
\(730\) 0 0
\(731\) 20.6240 0.762805
\(732\) 0 0
\(733\) 7.35631 0.271711 0.135856 0.990729i \(-0.456622\pi\)
0.135856 + 0.990729i \(0.456622\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.04419 −0.296311
\(738\) 0 0
\(739\) 13.2496 0.487394 0.243697 0.969851i \(-0.421640\pi\)
0.243697 + 0.969851i \(0.421640\pi\)
\(740\) 0 0
\(741\) 16.3131 0.599278
\(742\) 0 0
\(743\) 28.8314 1.05772 0.528861 0.848708i \(-0.322619\pi\)
0.528861 + 0.848708i \(0.322619\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −10.6792 −0.390730
\(748\) 0 0
\(749\) 45.5966 1.66607
\(750\) 0 0
\(751\) −24.3962 −0.890228 −0.445114 0.895474i \(-0.646837\pi\)
−0.445114 + 0.895474i \(0.646837\pi\)
\(752\) 0 0
\(753\) −27.1697 −0.990120
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 9.49825 0.345220 0.172610 0.984990i \(-0.444780\pi\)
0.172610 + 0.984990i \(0.444780\pi\)
\(758\) 0 0
\(759\) 4.77803 0.173431
\(760\) 0 0
\(761\) −8.43957 −0.305934 −0.152967 0.988231i \(-0.548883\pi\)
−0.152967 + 0.988231i \(0.548883\pi\)
\(762\) 0 0
\(763\) 12.3925 0.448639
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.0920 −0.581048
\(768\) 0 0
\(769\) 8.85911 0.319468 0.159734 0.987160i \(-0.448936\pi\)
0.159734 + 0.987160i \(0.448936\pi\)
\(770\) 0 0
\(771\) 15.5841 0.561247
\(772\) 0 0
\(773\) 32.7351 1.17740 0.588699 0.808352i \(-0.299640\pi\)
0.588699 + 0.808352i \(0.299640\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −2.29288 −0.0822567
\(778\) 0 0
\(779\) −24.7578 −0.887041
\(780\) 0 0
\(781\) −37.1440 −1.32912
\(782\) 0 0
\(783\) 19.5545 0.698822
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.736862 0.0262663 0.0131331 0.999914i \(-0.495819\pi\)
0.0131331 + 0.999914i \(0.495819\pi\)
\(788\) 0 0
\(789\) 18.2949 0.651316
\(790\) 0 0
\(791\) 63.3584 2.25276
\(792\) 0 0
\(793\) 46.0127 1.63396
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −41.7353 −1.47834 −0.739170 0.673519i \(-0.764782\pi\)
−0.739170 + 0.673519i \(0.764782\pi\)
\(798\) 0 0
\(799\) 6.63362 0.234681
\(800\) 0 0
\(801\) −0.908187 −0.0320892
\(802\) 0 0
\(803\) 12.9660 0.457560
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 18.8688 0.664212
\(808\) 0 0
\(809\) 21.3182 0.749506 0.374753 0.927125i \(-0.377727\pi\)
0.374753 + 0.927125i \(0.377727\pi\)
\(810\) 0 0
\(811\) 24.3126 0.853732 0.426866 0.904315i \(-0.359618\pi\)
0.426866 + 0.904315i \(0.359618\pi\)
\(812\) 0 0
\(813\) 36.5583 1.28216
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9.66780 −0.338233
\(818\) 0 0
\(819\) 12.6946 0.443584
\(820\) 0 0
\(821\) 49.3157 1.72113 0.860566 0.509340i \(-0.170110\pi\)
0.860566 + 0.509340i \(0.170110\pi\)
\(822\) 0 0
\(823\) 41.5427 1.44809 0.724043 0.689755i \(-0.242282\pi\)
0.724043 + 0.689755i \(0.242282\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.306510 −0.0106584 −0.00532919 0.999986i \(-0.501696\pi\)
−0.00532919 + 0.999986i \(0.501696\pi\)
\(828\) 0 0
\(829\) 17.5423 0.609268 0.304634 0.952469i \(-0.401466\pi\)
0.304634 + 0.952469i \(0.401466\pi\)
\(830\) 0 0
\(831\) 2.46842 0.0856285
\(832\) 0 0
\(833\) −28.0842 −0.973060
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −11.3568 −0.392549
\(838\) 0 0
\(839\) −44.1480 −1.52416 −0.762078 0.647485i \(-0.775821\pi\)
−0.762078 + 0.647485i \(0.775821\pi\)
\(840\) 0 0
\(841\) −17.0098 −0.586546
\(842\) 0 0
\(843\) 37.0739 1.27689
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −4.03445 −0.138625
\(848\) 0 0
\(849\) −28.6749 −0.984119
\(850\) 0 0
\(851\) 0.511497 0.0175339
\(852\) 0 0
\(853\) −41.2098 −1.41100 −0.705499 0.708711i \(-0.749277\pi\)
−0.705499 + 0.708711i \(0.749277\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 19.3245 0.660114 0.330057 0.943961i \(-0.392932\pi\)
0.330057 + 0.943961i \(0.392932\pi\)
\(858\) 0 0
\(859\) −16.2174 −0.553330 −0.276665 0.960966i \(-0.589229\pi\)
−0.276665 + 0.960966i \(0.589229\pi\)
\(860\) 0 0
\(861\) 31.7354 1.08154
\(862\) 0 0
\(863\) −56.9036 −1.93702 −0.968510 0.248974i \(-0.919907\pi\)
−0.968510 + 0.248974i \(0.919907\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 52.8137 1.79365
\(868\) 0 0
\(869\) −27.9061 −0.946648
\(870\) 0 0
\(871\) −7.85351 −0.266106
\(872\) 0 0
\(873\) −13.3410 −0.451526
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 33.4569 1.12976 0.564880 0.825173i \(-0.308923\pi\)
0.564880 + 0.825173i \(0.308923\pi\)
\(878\) 0 0
\(879\) −0.00917121 −0.000309337 0
\(880\) 0 0
\(881\) −5.99700 −0.202044 −0.101022 0.994884i \(-0.532211\pi\)
−0.101022 + 0.994884i \(0.532211\pi\)
\(882\) 0 0
\(883\) 51.3210 1.72709 0.863544 0.504273i \(-0.168239\pi\)
0.863544 + 0.504273i \(0.168239\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 27.1121 0.910336 0.455168 0.890405i \(-0.349579\pi\)
0.455168 + 0.890405i \(0.349579\pi\)
\(888\) 0 0
\(889\) 45.1495 1.51426
\(890\) 0 0
\(891\) −15.0932 −0.505640
\(892\) 0 0
\(893\) −3.10961 −0.104059
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.66477 0.155752
\(898\) 0 0
\(899\) −6.96362 −0.232250
\(900\) 0 0
\(901\) 106.221 3.53872
\(902\) 0 0
\(903\) 12.3925 0.412397
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 40.6194 1.34875 0.674373 0.738391i \(-0.264414\pi\)
0.674373 + 0.738391i \(0.264414\pi\)
\(908\) 0 0
\(909\) −12.6426 −0.419329
\(910\) 0 0
\(911\) 32.2475 1.06841 0.534203 0.845356i \(-0.320612\pi\)
0.534203 + 0.845356i \(0.320612\pi\)
\(912\) 0 0
\(913\) 32.9544 1.09063
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 24.3335 0.803565
\(918\) 0 0
\(919\) −30.4042 −1.00294 −0.501470 0.865175i \(-0.667207\pi\)
−0.501470 + 0.865175i \(0.667207\pi\)
\(920\) 0 0
\(921\) 27.2939 0.899366
\(922\) 0 0
\(923\) −36.2636 −1.19363
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.45720 −0.0478609
\(928\) 0 0
\(929\) −25.2834 −0.829520 −0.414760 0.909931i \(-0.636134\pi\)
−0.414760 + 0.909931i \(0.636134\pi\)
\(930\) 0 0
\(931\) 13.1649 0.431462
\(932\) 0 0
\(933\) 32.5997 1.06727
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 22.1769 0.724487 0.362243 0.932084i \(-0.382011\pi\)
0.362243 + 0.932084i \(0.382011\pi\)
\(938\) 0 0
\(939\) 23.8289 0.777626
\(940\) 0 0
\(941\) 4.23228 0.137968 0.0689842 0.997618i \(-0.478024\pi\)
0.0689842 + 0.997618i \(0.478024\pi\)
\(942\) 0 0
\(943\) −7.07954 −0.230542
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −45.2374 −1.47002 −0.735009 0.678058i \(-0.762822\pi\)
−0.735009 + 0.678058i \(0.762822\pi\)
\(948\) 0 0
\(949\) 12.6587 0.410917
\(950\) 0 0
\(951\) −1.85242 −0.0600690
\(952\) 0 0
\(953\) 43.7170 1.41613 0.708066 0.706146i \(-0.249568\pi\)
0.708066 + 0.706146i \(0.249568\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −16.5448 −0.534817
\(958\) 0 0
\(959\) −67.4240 −2.17723
\(960\) 0 0
\(961\) −26.9557 −0.869538
\(962\) 0 0
\(963\) 15.7495 0.507521
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 5.58482 0.179596 0.0897979 0.995960i \(-0.471378\pi\)
0.0897979 + 0.995960i \(0.471378\pi\)
\(968\) 0 0
\(969\) −35.6452 −1.14509
\(970\) 0 0
\(971\) 39.1206 1.25544 0.627720 0.778439i \(-0.283988\pi\)
0.627720 + 0.778439i \(0.283988\pi\)
\(972\) 0 0
\(973\) 18.0337 0.578135
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 52.3050 1.67339 0.836693 0.547672i \(-0.184486\pi\)
0.836693 + 0.547672i \(0.184486\pi\)
\(978\) 0 0
\(979\) 2.80253 0.0895694
\(980\) 0 0
\(981\) 4.28049 0.136665
\(982\) 0 0
\(983\) −22.4395 −0.715710 −0.357855 0.933777i \(-0.616492\pi\)
−0.357855 + 0.933777i \(0.616492\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3.98600 0.126876
\(988\) 0 0
\(989\) −2.76452 −0.0879067
\(990\) 0 0
\(991\) −0.851383 −0.0270451 −0.0135225 0.999909i \(-0.504304\pi\)
−0.0135225 + 0.999909i \(0.504304\pi\)
\(992\) 0 0
\(993\) 23.7802 0.754643
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −12.1784 −0.385693 −0.192846 0.981229i \(-0.561772\pi\)
−0.192846 + 0.981229i \(0.561772\pi\)
\(998\) 0 0
\(999\) −2.88853 −0.0913892
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 4600.2.a.bd.1.4 5
4.3 odd 2 9200.2.a.cv.1.2 5
5.2 odd 4 4600.2.e.w.4049.4 10
5.3 odd 4 4600.2.e.w.4049.7 10
5.4 even 2 4600.2.a.bf.1.2 yes 5
20.19 odd 2 9200.2.a.ct.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bd.1.4 5 1.1 even 1 trivial
4600.2.a.bf.1.2 yes 5 5.4 even 2
4600.2.e.w.4049.4 10 5.2 odd 4
4600.2.e.w.4049.7 10 5.3 odd 4
9200.2.a.ct.1.4 5 20.19 odd 2
9200.2.a.cv.1.2 5 4.3 odd 2