Properties

Label 644.2.a.d.1.3
Level $644$
Weight $2$
Character 644.1
Self dual yes
Analytic conductor $5.142$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 644.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.14236589017\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.6963152.1
Defining polynomial: \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.435854\) of defining polynomial
Character \(\chi\) \(=\) 644.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.43585 q^{3} +2.34236 q^{5} -1.00000 q^{7} -0.938323 q^{9} +O(q^{10})\) \(q+1.43585 q^{3} +2.34236 q^{5} -1.00000 q^{7} -0.938323 q^{9} +5.38507 q^{11} -5.32339 q^{13} +3.36328 q^{15} +7.88754 q^{17} +6.06364 q^{19} -1.43585 q^{21} -1.00000 q^{23} +0.486637 q^{25} -5.65486 q^{27} +1.87468 q^{29} -5.83096 q^{31} +7.73218 q^{33} -2.34236 q^{35} +1.19193 q^{37} -7.64362 q^{39} +6.45169 q^{41} -6.93535 q^{43} -2.19789 q^{45} -10.8577 q^{47} +1.00000 q^{49} +11.3254 q^{51} +7.94029 q^{53} +12.6138 q^{55} +8.70650 q^{57} -2.69561 q^{59} -3.27771 q^{61} +0.938323 q^{63} -12.4693 q^{65} -1.82865 q^{67} -1.43585 q^{69} +7.30161 q^{71} -7.51039 q^{73} +0.698740 q^{75} -5.38507 q^{77} -2.49158 q^{79} -5.30458 q^{81} -16.8120 q^{83} +18.4754 q^{85} +2.69177 q^{87} +13.2665 q^{89} +5.32339 q^{91} -8.37240 q^{93} +14.2032 q^{95} +11.9624 q^{97} -5.05294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 3 q^{3} + 2 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 3 q^{3} + 2 q^{5} - 5 q^{7} + 10 q^{9} + 2 q^{11} + 13 q^{13} + 4 q^{15} + 4 q^{17} + 12 q^{19} - 3 q^{21} - 5 q^{23} + 19 q^{25} + 15 q^{27} + 13 q^{29} - 3 q^{31} + 24 q^{33} - 2 q^{35} - 4 q^{37} + 3 q^{39} + q^{41} - 8 q^{43} - 16 q^{45} + 5 q^{47} + 5 q^{49} - 16 q^{51} - 8 q^{53} - 2 q^{55} + 12 q^{57} + 12 q^{59} + 20 q^{61} - 10 q^{63} - 12 q^{65} - 12 q^{67} - 3 q^{69} + 9 q^{71} - 9 q^{73} + 35 q^{75} - 2 q^{77} - 8 q^{79} - 11 q^{81} - 28 q^{83} + 16 q^{85} - 15 q^{87} + 32 q^{89} - 13 q^{91} - 15 q^{93} - 36 q^{95} + 4 q^{97} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.43585 0.828991 0.414495 0.910051i \(-0.363958\pi\)
0.414495 + 0.910051i \(0.363958\pi\)
\(4\) 0 0
\(5\) 2.34236 1.04753 0.523767 0.851862i \(-0.324526\pi\)
0.523767 + 0.851862i \(0.324526\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −0.938323 −0.312774
\(10\) 0 0
\(11\) 5.38507 1.62366 0.811830 0.583894i \(-0.198472\pi\)
0.811830 + 0.583894i \(0.198472\pi\)
\(12\) 0 0
\(13\) −5.32339 −1.47644 −0.738222 0.674558i \(-0.764334\pi\)
−0.738222 + 0.674558i \(0.764334\pi\)
\(14\) 0 0
\(15\) 3.36328 0.868396
\(16\) 0 0
\(17\) 7.88754 1.91301 0.956505 0.291717i \(-0.0942265\pi\)
0.956505 + 0.291717i \(0.0942265\pi\)
\(18\) 0 0
\(19\) 6.06364 1.39109 0.695547 0.718480i \(-0.255162\pi\)
0.695547 + 0.718480i \(0.255162\pi\)
\(20\) 0 0
\(21\) −1.43585 −0.313329
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0.486637 0.0973275
\(26\) 0 0
\(27\) −5.65486 −1.08828
\(28\) 0 0
\(29\) 1.87468 0.348120 0.174060 0.984735i \(-0.444311\pi\)
0.174060 + 0.984735i \(0.444311\pi\)
\(30\) 0 0
\(31\) −5.83096 −1.04727 −0.523635 0.851942i \(-0.675425\pi\)
−0.523635 + 0.851942i \(0.675425\pi\)
\(32\) 0 0
\(33\) 7.73218 1.34600
\(34\) 0 0
\(35\) −2.34236 −0.395931
\(36\) 0 0
\(37\) 1.19193 0.195952 0.0979762 0.995189i \(-0.468763\pi\)
0.0979762 + 0.995189i \(0.468763\pi\)
\(38\) 0 0
\(39\) −7.64362 −1.22396
\(40\) 0 0
\(41\) 6.45169 1.00758 0.503792 0.863825i \(-0.331938\pi\)
0.503792 + 0.863825i \(0.331938\pi\)
\(42\) 0 0
\(43\) −6.93535 −1.05763 −0.528815 0.848737i \(-0.677364\pi\)
−0.528815 + 0.848737i \(0.677364\pi\)
\(44\) 0 0
\(45\) −2.19789 −0.327642
\(46\) 0 0
\(47\) −10.8577 −1.58376 −0.791878 0.610679i \(-0.790896\pi\)
−0.791878 + 0.610679i \(0.790896\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 11.3254 1.58587
\(52\) 0 0
\(53\) 7.94029 1.09068 0.545341 0.838214i \(-0.316400\pi\)
0.545341 + 0.838214i \(0.316400\pi\)
\(54\) 0 0
\(55\) 12.6138 1.70084
\(56\) 0 0
\(57\) 8.70650 1.15320
\(58\) 0 0
\(59\) −2.69561 −0.350938 −0.175469 0.984485i \(-0.556144\pi\)
−0.175469 + 0.984485i \(0.556144\pi\)
\(60\) 0 0
\(61\) −3.27771 −0.419667 −0.209834 0.977737i \(-0.567292\pi\)
−0.209834 + 0.977737i \(0.567292\pi\)
\(62\) 0 0
\(63\) 0.938323 0.118218
\(64\) 0 0
\(65\) −12.4693 −1.54663
\(66\) 0 0
\(67\) −1.82865 −0.223405 −0.111702 0.993742i \(-0.535630\pi\)
−0.111702 + 0.993742i \(0.535630\pi\)
\(68\) 0 0
\(69\) −1.43585 −0.172857
\(70\) 0 0
\(71\) 7.30161 0.866541 0.433271 0.901264i \(-0.357359\pi\)
0.433271 + 0.901264i \(0.357359\pi\)
\(72\) 0 0
\(73\) −7.51039 −0.879024 −0.439512 0.898237i \(-0.644849\pi\)
−0.439512 + 0.898237i \(0.644849\pi\)
\(74\) 0 0
\(75\) 0.698740 0.0806836
\(76\) 0 0
\(77\) −5.38507 −0.613686
\(78\) 0 0
\(79\) −2.49158 −0.280324 −0.140162 0.990129i \(-0.544762\pi\)
−0.140162 + 0.990129i \(0.544762\pi\)
\(80\) 0 0
\(81\) −5.30458 −0.589398
\(82\) 0 0
\(83\) −16.8120 −1.84536 −0.922678 0.385571i \(-0.874004\pi\)
−0.922678 + 0.385571i \(0.874004\pi\)
\(84\) 0 0
\(85\) 18.4754 2.00394
\(86\) 0 0
\(87\) 2.69177 0.288588
\(88\) 0 0
\(89\) 13.2665 1.40624 0.703121 0.711070i \(-0.251789\pi\)
0.703121 + 0.711070i \(0.251789\pi\)
\(90\) 0 0
\(91\) 5.32339 0.558043
\(92\) 0 0
\(93\) −8.37240 −0.868178
\(94\) 0 0
\(95\) 14.2032 1.45722
\(96\) 0 0
\(97\) 11.9624 1.21460 0.607300 0.794473i \(-0.292253\pi\)
0.607300 + 0.794473i \(0.292253\pi\)
\(98\) 0 0
\(99\) −5.05294 −0.507839
\(100\) 0 0
\(101\) −14.4918 −1.44199 −0.720993 0.692943i \(-0.756314\pi\)
−0.720993 + 0.692943i \(0.756314\pi\)
\(102\) 0 0
\(103\) 7.55642 0.744556 0.372278 0.928121i \(-0.378577\pi\)
0.372278 + 0.928121i \(0.378577\pi\)
\(104\) 0 0
\(105\) −3.36328 −0.328223
\(106\) 0 0
\(107\) −10.9353 −1.05716 −0.528580 0.848883i \(-0.677275\pi\)
−0.528580 + 0.848883i \(0.677275\pi\)
\(108\) 0 0
\(109\) −12.6250 −1.20926 −0.604628 0.796508i \(-0.706678\pi\)
−0.604628 + 0.796508i \(0.706678\pi\)
\(110\) 0 0
\(111\) 1.71144 0.162443
\(112\) 0 0
\(113\) −3.15008 −0.296335 −0.148167 0.988962i \(-0.547337\pi\)
−0.148167 + 0.988962i \(0.547337\pi\)
\(114\) 0 0
\(115\) −2.34236 −0.218426
\(116\) 0 0
\(117\) 4.99506 0.461794
\(118\) 0 0
\(119\) −7.88754 −0.723050
\(120\) 0 0
\(121\) 17.9990 1.63627
\(122\) 0 0
\(123\) 9.26368 0.835278
\(124\) 0 0
\(125\) −10.5719 −0.945580
\(126\) 0 0
\(127\) −9.25975 −0.821670 −0.410835 0.911710i \(-0.634763\pi\)
−0.410835 + 0.911710i \(0.634763\pi\)
\(128\) 0 0
\(129\) −9.95815 −0.876766
\(130\) 0 0
\(131\) 5.02289 0.438852 0.219426 0.975629i \(-0.429582\pi\)
0.219426 + 0.975629i \(0.429582\pi\)
\(132\) 0 0
\(133\) −6.06364 −0.525784
\(134\) 0 0
\(135\) −13.2457 −1.14001
\(136\) 0 0
\(137\) −15.7114 −1.34232 −0.671159 0.741313i \(-0.734203\pi\)
−0.671159 + 0.741313i \(0.734203\pi\)
\(138\) 0 0
\(139\) −0.0569290 −0.00482865 −0.00241433 0.999997i \(-0.500769\pi\)
−0.00241433 + 0.999997i \(0.500769\pi\)
\(140\) 0 0
\(141\) −15.5900 −1.31292
\(142\) 0 0
\(143\) −28.6669 −2.39724
\(144\) 0 0
\(145\) 4.39118 0.364667
\(146\) 0 0
\(147\) 1.43585 0.118427
\(148\) 0 0
\(149\) 1.55642 0.127507 0.0637536 0.997966i \(-0.479693\pi\)
0.0637536 + 0.997966i \(0.479693\pi\)
\(150\) 0 0
\(151\) −3.44675 −0.280492 −0.140246 0.990117i \(-0.544789\pi\)
−0.140246 + 0.990117i \(0.544789\pi\)
\(152\) 0 0
\(153\) −7.40106 −0.598340
\(154\) 0 0
\(155\) −13.6582 −1.09705
\(156\) 0 0
\(157\) 20.0366 1.59910 0.799548 0.600603i \(-0.205073\pi\)
0.799548 + 0.600603i \(0.205073\pi\)
\(158\) 0 0
\(159\) 11.4011 0.904165
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −20.4556 −1.60221 −0.801104 0.598526i \(-0.795753\pi\)
−0.801104 + 0.598526i \(0.795753\pi\)
\(164\) 0 0
\(165\) 18.1115 1.40998
\(166\) 0 0
\(167\) 18.3044 1.41644 0.708220 0.705992i \(-0.249499\pi\)
0.708220 + 0.705992i \(0.249499\pi\)
\(168\) 0 0
\(169\) 15.3385 1.17989
\(170\) 0 0
\(171\) −5.68965 −0.435099
\(172\) 0 0
\(173\) 0.0636396 0.00483843 0.00241922 0.999997i \(-0.499230\pi\)
0.00241922 + 0.999997i \(0.499230\pi\)
\(174\) 0 0
\(175\) −0.486637 −0.0367863
\(176\) 0 0
\(177\) −3.87050 −0.290925
\(178\) 0 0
\(179\) −10.0500 −0.751169 −0.375585 0.926788i \(-0.622558\pi\)
−0.375585 + 0.926788i \(0.622558\pi\)
\(180\) 0 0
\(181\) −0.138173 −0.0102703 −0.00513516 0.999987i \(-0.501635\pi\)
−0.00513516 + 0.999987i \(0.501635\pi\)
\(182\) 0 0
\(183\) −4.70631 −0.347900
\(184\) 0 0
\(185\) 2.79193 0.205267
\(186\) 0 0
\(187\) 42.4750 3.10608
\(188\) 0 0
\(189\) 5.65486 0.411330
\(190\) 0 0
\(191\) −8.55149 −0.618764 −0.309382 0.950938i \(-0.600122\pi\)
−0.309382 + 0.950938i \(0.600122\pi\)
\(192\) 0 0
\(193\) −24.3765 −1.75466 −0.877330 0.479887i \(-0.840678\pi\)
−0.877330 + 0.479887i \(0.840678\pi\)
\(194\) 0 0
\(195\) −17.9041 −1.28214
\(196\) 0 0
\(197\) 21.5421 1.53481 0.767404 0.641164i \(-0.221548\pi\)
0.767404 + 0.641164i \(0.221548\pi\)
\(198\) 0 0
\(199\) 6.51951 0.462156 0.231078 0.972935i \(-0.425775\pi\)
0.231078 + 0.972935i \(0.425775\pi\)
\(200\) 0 0
\(201\) −2.62567 −0.185201
\(202\) 0 0
\(203\) −1.87468 −0.131577
\(204\) 0 0
\(205\) 15.1122 1.05548
\(206\) 0 0
\(207\) 0.938323 0.0652180
\(208\) 0 0
\(209\) 32.6531 2.25866
\(210\) 0 0
\(211\) −18.2352 −1.25536 −0.627681 0.778471i \(-0.715996\pi\)
−0.627681 + 0.778471i \(0.715996\pi\)
\(212\) 0 0
\(213\) 10.4840 0.718355
\(214\) 0 0
\(215\) −16.2451 −1.10790
\(216\) 0 0
\(217\) 5.83096 0.395831
\(218\) 0 0
\(219\) −10.7838 −0.728703
\(220\) 0 0
\(221\) −41.9885 −2.82445
\(222\) 0 0
\(223\) −19.8496 −1.32923 −0.664614 0.747187i \(-0.731404\pi\)
−0.664614 + 0.747187i \(0.731404\pi\)
\(224\) 0 0
\(225\) −0.456623 −0.0304415
\(226\) 0 0
\(227\) −0.579223 −0.0384444 −0.0192222 0.999815i \(-0.506119\pi\)
−0.0192222 + 0.999815i \(0.506119\pi\)
\(228\) 0 0
\(229\) 14.6538 0.968347 0.484174 0.874972i \(-0.339120\pi\)
0.484174 + 0.874972i \(0.339120\pi\)
\(230\) 0 0
\(231\) −7.73218 −0.508740
\(232\) 0 0
\(233\) 14.5953 0.956170 0.478085 0.878314i \(-0.341331\pi\)
0.478085 + 0.878314i \(0.341331\pi\)
\(234\) 0 0
\(235\) −25.4326 −1.65904
\(236\) 0 0
\(237\) −3.57754 −0.232386
\(238\) 0 0
\(239\) −12.9435 −0.837243 −0.418621 0.908161i \(-0.637487\pi\)
−0.418621 + 0.908161i \(0.637487\pi\)
\(240\) 0 0
\(241\) 1.24075 0.0799239 0.0399619 0.999201i \(-0.487276\pi\)
0.0399619 + 0.999201i \(0.487276\pi\)
\(242\) 0 0
\(243\) 9.34797 0.599672
\(244\) 0 0
\(245\) 2.34236 0.149648
\(246\) 0 0
\(247\) −32.2791 −2.05387
\(248\) 0 0
\(249\) −24.1396 −1.52978
\(250\) 0 0
\(251\) 19.8766 1.25460 0.627301 0.778777i \(-0.284159\pi\)
0.627301 + 0.778777i \(0.284159\pi\)
\(252\) 0 0
\(253\) −5.38507 −0.338557
\(254\) 0 0
\(255\) 26.5280 1.66125
\(256\) 0 0
\(257\) 4.85803 0.303036 0.151518 0.988455i \(-0.451584\pi\)
0.151518 + 0.988455i \(0.451584\pi\)
\(258\) 0 0
\(259\) −1.19193 −0.0740630
\(260\) 0 0
\(261\) −1.75906 −0.108883
\(262\) 0 0
\(263\) 11.5760 0.713806 0.356903 0.934141i \(-0.383833\pi\)
0.356903 + 0.934141i \(0.383833\pi\)
\(264\) 0 0
\(265\) 18.5990 1.14253
\(266\) 0 0
\(267\) 19.0487 1.16576
\(268\) 0 0
\(269\) −4.38805 −0.267544 −0.133772 0.991012i \(-0.542709\pi\)
−0.133772 + 0.991012i \(0.542709\pi\)
\(270\) 0 0
\(271\) −1.44396 −0.0877145 −0.0438572 0.999038i \(-0.513965\pi\)
−0.0438572 + 0.999038i \(0.513965\pi\)
\(272\) 0 0
\(273\) 7.64362 0.462613
\(274\) 0 0
\(275\) 2.62058 0.158027
\(276\) 0 0
\(277\) 0.281027 0.0168853 0.00844263 0.999964i \(-0.497313\pi\)
0.00844263 + 0.999964i \(0.497313\pi\)
\(278\) 0 0
\(279\) 5.47132 0.327559
\(280\) 0 0
\(281\) −19.5185 −1.16438 −0.582188 0.813054i \(-0.697803\pi\)
−0.582188 + 0.813054i \(0.697803\pi\)
\(282\) 0 0
\(283\) 27.3097 1.62339 0.811697 0.584079i \(-0.198544\pi\)
0.811697 + 0.584079i \(0.198544\pi\)
\(284\) 0 0
\(285\) 20.3937 1.20802
\(286\) 0 0
\(287\) −6.45169 −0.380831
\(288\) 0 0
\(289\) 45.2133 2.65960
\(290\) 0 0
\(291\) 17.1763 1.00689
\(292\) 0 0
\(293\) 20.8180 1.21620 0.608100 0.793860i \(-0.291932\pi\)
0.608100 + 0.793860i \(0.291932\pi\)
\(294\) 0 0
\(295\) −6.31408 −0.367620
\(296\) 0 0
\(297\) −30.4518 −1.76699
\(298\) 0 0
\(299\) 5.32339 0.307860
\(300\) 0 0
\(301\) 6.93535 0.399747
\(302\) 0 0
\(303\) −20.8081 −1.19539
\(304\) 0 0
\(305\) −7.67756 −0.439616
\(306\) 0 0
\(307\) 18.1772 1.03742 0.518712 0.854949i \(-0.326412\pi\)
0.518712 + 0.854949i \(0.326412\pi\)
\(308\) 0 0
\(309\) 10.8499 0.617230
\(310\) 0 0
\(311\) −12.6176 −0.715478 −0.357739 0.933822i \(-0.616452\pi\)
−0.357739 + 0.933822i \(0.616452\pi\)
\(312\) 0 0
\(313\) −19.2510 −1.08813 −0.544066 0.839042i \(-0.683116\pi\)
−0.544066 + 0.839042i \(0.683116\pi\)
\(314\) 0 0
\(315\) 2.19789 0.123837
\(316\) 0 0
\(317\) 10.9197 0.613312 0.306656 0.951820i \(-0.400790\pi\)
0.306656 + 0.951820i \(0.400790\pi\)
\(318\) 0 0
\(319\) 10.0953 0.565228
\(320\) 0 0
\(321\) −15.7016 −0.876376
\(322\) 0 0
\(323\) 47.8272 2.66118
\(324\) 0 0
\(325\) −2.59056 −0.143699
\(326\) 0 0
\(327\) −18.1277 −1.00246
\(328\) 0 0
\(329\) 10.8577 0.598603
\(330\) 0 0
\(331\) 33.1364 1.82134 0.910671 0.413133i \(-0.135566\pi\)
0.910671 + 0.413133i \(0.135566\pi\)
\(332\) 0 0
\(333\) −1.11842 −0.0612888
\(334\) 0 0
\(335\) −4.28335 −0.234024
\(336\) 0 0
\(337\) 35.6458 1.94175 0.970875 0.239588i \(-0.0770125\pi\)
0.970875 + 0.239588i \(0.0770125\pi\)
\(338\) 0 0
\(339\) −4.52305 −0.245659
\(340\) 0 0
\(341\) −31.4001 −1.70041
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −3.36328 −0.181073
\(346\) 0 0
\(347\) −0.117783 −0.00632293 −0.00316146 0.999995i \(-0.501006\pi\)
−0.00316146 + 0.999995i \(0.501006\pi\)
\(348\) 0 0
\(349\) −12.7083 −0.680258 −0.340129 0.940379i \(-0.610471\pi\)
−0.340129 + 0.940379i \(0.610471\pi\)
\(350\) 0 0
\(351\) 30.1030 1.60678
\(352\) 0 0
\(353\) −15.4791 −0.823870 −0.411935 0.911213i \(-0.635147\pi\)
−0.411935 + 0.911213i \(0.635147\pi\)
\(354\) 0 0
\(355\) 17.1030 0.907731
\(356\) 0 0
\(357\) −11.3254 −0.599401
\(358\) 0 0
\(359\) 7.66806 0.404705 0.202352 0.979313i \(-0.435141\pi\)
0.202352 + 0.979313i \(0.435141\pi\)
\(360\) 0 0
\(361\) 17.7677 0.935143
\(362\) 0 0
\(363\) 25.8439 1.35645
\(364\) 0 0
\(365\) −17.5920 −0.920808
\(366\) 0 0
\(367\) 10.1079 0.527628 0.263814 0.964574i \(-0.415019\pi\)
0.263814 + 0.964574i \(0.415019\pi\)
\(368\) 0 0
\(369\) −6.05376 −0.315146
\(370\) 0 0
\(371\) −7.94029 −0.412239
\(372\) 0 0
\(373\) −28.8437 −1.49347 −0.746734 0.665123i \(-0.768379\pi\)
−0.746734 + 0.665123i \(0.768379\pi\)
\(374\) 0 0
\(375\) −15.1797 −0.783877
\(376\) 0 0
\(377\) −9.97968 −0.513980
\(378\) 0 0
\(379\) 27.2020 1.39727 0.698636 0.715477i \(-0.253790\pi\)
0.698636 + 0.715477i \(0.253790\pi\)
\(380\) 0 0
\(381\) −13.2957 −0.681157
\(382\) 0 0
\(383\) 19.6517 1.00416 0.502078 0.864822i \(-0.332569\pi\)
0.502078 + 0.864822i \(0.332569\pi\)
\(384\) 0 0
\(385\) −12.6138 −0.642857
\(386\) 0 0
\(387\) 6.50760 0.330800
\(388\) 0 0
\(389\) 12.9990 0.659075 0.329537 0.944143i \(-0.393107\pi\)
0.329537 + 0.944143i \(0.393107\pi\)
\(390\) 0 0
\(391\) −7.88754 −0.398890
\(392\) 0 0
\(393\) 7.21214 0.363804
\(394\) 0 0
\(395\) −5.83616 −0.293649
\(396\) 0 0
\(397\) 27.2637 1.36832 0.684162 0.729330i \(-0.260168\pi\)
0.684162 + 0.729330i \(0.260168\pi\)
\(398\) 0 0
\(399\) −8.70650 −0.435870
\(400\) 0 0
\(401\) 10.3543 0.517069 0.258535 0.966002i \(-0.416760\pi\)
0.258535 + 0.966002i \(0.416760\pi\)
\(402\) 0 0
\(403\) 31.0405 1.54624
\(404\) 0 0
\(405\) −12.4252 −0.617414
\(406\) 0 0
\(407\) 6.41863 0.318160
\(408\) 0 0
\(409\) 14.4338 0.713707 0.356853 0.934160i \(-0.383850\pi\)
0.356853 + 0.934160i \(0.383850\pi\)
\(410\) 0 0
\(411\) −22.5593 −1.11277
\(412\) 0 0
\(413\) 2.69561 0.132642
\(414\) 0 0
\(415\) −39.3797 −1.93307
\(416\) 0 0
\(417\) −0.0817417 −0.00400291
\(418\) 0 0
\(419\) 38.7780 1.89443 0.947214 0.320601i \(-0.103885\pi\)
0.947214 + 0.320601i \(0.103885\pi\)
\(420\) 0 0
\(421\) 33.3097 1.62342 0.811708 0.584063i \(-0.198538\pi\)
0.811708 + 0.584063i \(0.198538\pi\)
\(422\) 0 0
\(423\) 10.1880 0.495358
\(424\) 0 0
\(425\) 3.83837 0.186188
\(426\) 0 0
\(427\) 3.27771 0.158619
\(428\) 0 0
\(429\) −41.1614 −1.98729
\(430\) 0 0
\(431\) −0.967325 −0.0465944 −0.0232972 0.999729i \(-0.507416\pi\)
−0.0232972 + 0.999729i \(0.507416\pi\)
\(432\) 0 0
\(433\) 11.4173 0.548679 0.274340 0.961633i \(-0.411541\pi\)
0.274340 + 0.961633i \(0.411541\pi\)
\(434\) 0 0
\(435\) 6.30509 0.302306
\(436\) 0 0
\(437\) −6.06364 −0.290063
\(438\) 0 0
\(439\) −10.3789 −0.495357 −0.247678 0.968842i \(-0.579668\pi\)
−0.247678 + 0.968842i \(0.579668\pi\)
\(440\) 0 0
\(441\) −0.938323 −0.0446820
\(442\) 0 0
\(443\) −23.2218 −1.10330 −0.551651 0.834075i \(-0.686002\pi\)
−0.551651 + 0.834075i \(0.686002\pi\)
\(444\) 0 0
\(445\) 31.0748 1.47309
\(446\) 0 0
\(447\) 2.23480 0.105702
\(448\) 0 0
\(449\) −10.6505 −0.502629 −0.251314 0.967905i \(-0.580863\pi\)
−0.251314 + 0.967905i \(0.580863\pi\)
\(450\) 0 0
\(451\) 34.7428 1.63597
\(452\) 0 0
\(453\) −4.94903 −0.232526
\(454\) 0 0
\(455\) 12.4693 0.584569
\(456\) 0 0
\(457\) 0.379938 0.0177727 0.00888637 0.999961i \(-0.497171\pi\)
0.00888637 + 0.999961i \(0.497171\pi\)
\(458\) 0 0
\(459\) −44.6029 −2.08189
\(460\) 0 0
\(461\) −16.3880 −0.763267 −0.381634 0.924314i \(-0.624638\pi\)
−0.381634 + 0.924314i \(0.624638\pi\)
\(462\) 0 0
\(463\) −36.2349 −1.68398 −0.841989 0.539495i \(-0.818615\pi\)
−0.841989 + 0.539495i \(0.818615\pi\)
\(464\) 0 0
\(465\) −19.6112 −0.909446
\(466\) 0 0
\(467\) 17.1603 0.794083 0.397041 0.917801i \(-0.370037\pi\)
0.397041 + 0.917801i \(0.370037\pi\)
\(468\) 0 0
\(469\) 1.82865 0.0844391
\(470\) 0 0
\(471\) 28.7696 1.32564
\(472\) 0 0
\(473\) −37.3473 −1.71723
\(474\) 0 0
\(475\) 2.95079 0.135392
\(476\) 0 0
\(477\) −7.45055 −0.341137
\(478\) 0 0
\(479\) −16.8299 −0.768976 −0.384488 0.923130i \(-0.625622\pi\)
−0.384488 + 0.923130i \(0.625622\pi\)
\(480\) 0 0
\(481\) −6.34512 −0.289313
\(482\) 0 0
\(483\) 1.43585 0.0653336
\(484\) 0 0
\(485\) 28.0203 1.27233
\(486\) 0 0
\(487\) −26.9276 −1.22021 −0.610103 0.792322i \(-0.708872\pi\)
−0.610103 + 0.792322i \(0.708872\pi\)
\(488\) 0 0
\(489\) −29.3713 −1.32821
\(490\) 0 0
\(491\) −21.3432 −0.963203 −0.481602 0.876390i \(-0.659945\pi\)
−0.481602 + 0.876390i \(0.659945\pi\)
\(492\) 0 0
\(493\) 14.7866 0.665957
\(494\) 0 0
\(495\) −11.8358 −0.531979
\(496\) 0 0
\(497\) −7.30161 −0.327522
\(498\) 0 0
\(499\) −19.5203 −0.873847 −0.436923 0.899499i \(-0.643932\pi\)
−0.436923 + 0.899499i \(0.643932\pi\)
\(500\) 0 0
\(501\) 26.2825 1.17422
\(502\) 0 0
\(503\) 5.02673 0.224131 0.112065 0.993701i \(-0.464253\pi\)
0.112065 + 0.993701i \(0.464253\pi\)
\(504\) 0 0
\(505\) −33.9449 −1.51053
\(506\) 0 0
\(507\) 22.0239 0.978115
\(508\) 0 0
\(509\) −10.5354 −0.466973 −0.233486 0.972360i \(-0.575013\pi\)
−0.233486 + 0.972360i \(0.575013\pi\)
\(510\) 0 0
\(511\) 7.51039 0.332240
\(512\) 0 0
\(513\) −34.2890 −1.51390
\(514\) 0 0
\(515\) 17.6998 0.779948
\(516\) 0 0
\(517\) −58.4694 −2.57148
\(518\) 0 0
\(519\) 0.0913772 0.00401101
\(520\) 0 0
\(521\) 10.8559 0.475606 0.237803 0.971313i \(-0.423573\pi\)
0.237803 + 0.971313i \(0.423573\pi\)
\(522\) 0 0
\(523\) 16.5175 0.722259 0.361130 0.932516i \(-0.382391\pi\)
0.361130 + 0.932516i \(0.382391\pi\)
\(524\) 0 0
\(525\) −0.698740 −0.0304955
\(526\) 0 0
\(527\) −45.9919 −2.00344
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 2.52935 0.109764
\(532\) 0 0
\(533\) −34.3449 −1.48764
\(534\) 0 0
\(535\) −25.6145 −1.10741
\(536\) 0 0
\(537\) −14.4303 −0.622712
\(538\) 0 0
\(539\) 5.38507 0.231951
\(540\) 0 0
\(541\) −11.0983 −0.477152 −0.238576 0.971124i \(-0.576681\pi\)
−0.238576 + 0.971124i \(0.576681\pi\)
\(542\) 0 0
\(543\) −0.198396 −0.00851400
\(544\) 0 0
\(545\) −29.5723 −1.26674
\(546\) 0 0
\(547\) −3.70757 −0.158524 −0.0792621 0.996854i \(-0.525256\pi\)
−0.0792621 + 0.996854i \(0.525256\pi\)
\(548\) 0 0
\(549\) 3.07555 0.131261
\(550\) 0 0
\(551\) 11.3674 0.484268
\(552\) 0 0
\(553\) 2.49158 0.105953
\(554\) 0 0
\(555\) 4.00880 0.170164
\(556\) 0 0
\(557\) −14.5792 −0.617741 −0.308871 0.951104i \(-0.599951\pi\)
−0.308871 + 0.951104i \(0.599951\pi\)
\(558\) 0 0
\(559\) 36.9196 1.56153
\(560\) 0 0
\(561\) 60.9878 2.57491
\(562\) 0 0
\(563\) −15.2872 −0.644280 −0.322140 0.946692i \(-0.604402\pi\)
−0.322140 + 0.946692i \(0.604402\pi\)
\(564\) 0 0
\(565\) −7.37861 −0.310420
\(566\) 0 0
\(567\) 5.30458 0.222771
\(568\) 0 0
\(569\) 17.3853 0.728828 0.364414 0.931237i \(-0.381269\pi\)
0.364414 + 0.931237i \(0.381269\pi\)
\(570\) 0 0
\(571\) −5.96802 −0.249754 −0.124877 0.992172i \(-0.539854\pi\)
−0.124877 + 0.992172i \(0.539854\pi\)
\(572\) 0 0
\(573\) −12.2787 −0.512949
\(574\) 0 0
\(575\) −0.486637 −0.0202942
\(576\) 0 0
\(577\) −22.1611 −0.922579 −0.461289 0.887250i \(-0.652613\pi\)
−0.461289 + 0.887250i \(0.652613\pi\)
\(578\) 0 0
\(579\) −35.0011 −1.45460
\(580\) 0 0
\(581\) 16.8120 0.697479
\(582\) 0 0
\(583\) 42.7590 1.77090
\(584\) 0 0
\(585\) 11.7002 0.483745
\(586\) 0 0
\(587\) 9.96131 0.411147 0.205574 0.978642i \(-0.434094\pi\)
0.205574 + 0.978642i \(0.434094\pi\)
\(588\) 0 0
\(589\) −35.3568 −1.45685
\(590\) 0 0
\(591\) 30.9312 1.27234
\(592\) 0 0
\(593\) 8.77014 0.360147 0.180073 0.983653i \(-0.442367\pi\)
0.180073 + 0.983653i \(0.442367\pi\)
\(594\) 0 0
\(595\) −18.4754 −0.757419
\(596\) 0 0
\(597\) 9.36106 0.383123
\(598\) 0 0
\(599\) 11.3276 0.462832 0.231416 0.972855i \(-0.425664\pi\)
0.231416 + 0.972855i \(0.425664\pi\)
\(600\) 0 0
\(601\) 5.77090 0.235400 0.117700 0.993049i \(-0.462448\pi\)
0.117700 + 0.993049i \(0.462448\pi\)
\(602\) 0 0
\(603\) 1.71586 0.0698753
\(604\) 0 0
\(605\) 42.1601 1.71405
\(606\) 0 0
\(607\) 1.19400 0.0484630 0.0242315 0.999706i \(-0.492286\pi\)
0.0242315 + 0.999706i \(0.492286\pi\)
\(608\) 0 0
\(609\) −2.69177 −0.109076
\(610\) 0 0
\(611\) 57.7997 2.33833
\(612\) 0 0
\(613\) −42.3622 −1.71099 −0.855496 0.517810i \(-0.826747\pi\)
−0.855496 + 0.517810i \(0.826747\pi\)
\(614\) 0 0
\(615\) 21.6988 0.874982
\(616\) 0 0
\(617\) 33.9063 1.36502 0.682508 0.730878i \(-0.260889\pi\)
0.682508 + 0.730878i \(0.260889\pi\)
\(618\) 0 0
\(619\) 27.6830 1.11267 0.556337 0.830957i \(-0.312206\pi\)
0.556337 + 0.830957i \(0.312206\pi\)
\(620\) 0 0
\(621\) 5.65486 0.226922
\(622\) 0 0
\(623\) −13.2665 −0.531510
\(624\) 0 0
\(625\) −27.1964 −1.08785
\(626\) 0 0
\(627\) 46.8851 1.87241
\(628\) 0 0
\(629\) 9.40141 0.374859
\(630\) 0 0
\(631\) −0.801923 −0.0319240 −0.0159620 0.999873i \(-0.505081\pi\)
−0.0159620 + 0.999873i \(0.505081\pi\)
\(632\) 0 0
\(633\) −26.1831 −1.04068
\(634\) 0 0
\(635\) −21.6897 −0.860728
\(636\) 0 0
\(637\) −5.32339 −0.210921
\(638\) 0 0
\(639\) −6.85126 −0.271032
\(640\) 0 0
\(641\) 19.1287 0.755538 0.377769 0.925900i \(-0.376691\pi\)
0.377769 + 0.925900i \(0.376691\pi\)
\(642\) 0 0
\(643\) −43.8827 −1.73056 −0.865282 0.501286i \(-0.832861\pi\)
−0.865282 + 0.501286i \(0.832861\pi\)
\(644\) 0 0
\(645\) −23.3255 −0.918442
\(646\) 0 0
\(647\) 41.0032 1.61200 0.806001 0.591914i \(-0.201627\pi\)
0.806001 + 0.591914i \(0.201627\pi\)
\(648\) 0 0
\(649\) −14.5160 −0.569804
\(650\) 0 0
\(651\) 8.37240 0.328140
\(652\) 0 0
\(653\) 35.1744 1.37648 0.688240 0.725483i \(-0.258383\pi\)
0.688240 + 0.725483i \(0.258383\pi\)
\(654\) 0 0
\(655\) 11.7654 0.459712
\(656\) 0 0
\(657\) 7.04717 0.274936
\(658\) 0 0
\(659\) −24.7839 −0.965445 −0.482723 0.875773i \(-0.660352\pi\)
−0.482723 + 0.875773i \(0.660352\pi\)
\(660\) 0 0
\(661\) 41.4545 1.61239 0.806197 0.591648i \(-0.201522\pi\)
0.806197 + 0.591648i \(0.201522\pi\)
\(662\) 0 0
\(663\) −60.2893 −2.34144
\(664\) 0 0
\(665\) −14.2032 −0.550777
\(666\) 0 0
\(667\) −1.87468 −0.0725880
\(668\) 0 0
\(669\) −28.5011 −1.10192
\(670\) 0 0
\(671\) −17.6507 −0.681397
\(672\) 0 0
\(673\) −36.0660 −1.39024 −0.695121 0.718893i \(-0.744649\pi\)
−0.695121 + 0.718893i \(0.744649\pi\)
\(674\) 0 0
\(675\) −2.75187 −0.105919
\(676\) 0 0
\(677\) 3.41266 0.131159 0.0655795 0.997847i \(-0.479110\pi\)
0.0655795 + 0.997847i \(0.479110\pi\)
\(678\) 0 0
\(679\) −11.9624 −0.459076
\(680\) 0 0
\(681\) −0.831679 −0.0318700
\(682\) 0 0
\(683\) −24.2314 −0.927188 −0.463594 0.886048i \(-0.653440\pi\)
−0.463594 + 0.886048i \(0.653440\pi\)
\(684\) 0 0
\(685\) −36.8018 −1.40612
\(686\) 0 0
\(687\) 21.0407 0.802751
\(688\) 0 0
\(689\) −42.2693 −1.61033
\(690\) 0 0
\(691\) 7.37573 0.280586 0.140293 0.990110i \(-0.455196\pi\)
0.140293 + 0.990110i \(0.455196\pi\)
\(692\) 0 0
\(693\) 5.05294 0.191945
\(694\) 0 0
\(695\) −0.133348 −0.00505818
\(696\) 0 0
\(697\) 50.8879 1.92752
\(698\) 0 0
\(699\) 20.9567 0.792656
\(700\) 0 0
\(701\) 3.25950 0.123109 0.0615547 0.998104i \(-0.480394\pi\)
0.0615547 + 0.998104i \(0.480394\pi\)
\(702\) 0 0
\(703\) 7.22744 0.272588
\(704\) 0 0
\(705\) −36.5175 −1.37533
\(706\) 0 0
\(707\) 14.4918 0.545019
\(708\) 0 0
\(709\) 43.0749 1.61771 0.808856 0.588006i \(-0.200087\pi\)
0.808856 + 0.588006i \(0.200087\pi\)
\(710\) 0 0
\(711\) 2.33790 0.0876782
\(712\) 0 0
\(713\) 5.83096 0.218371
\(714\) 0 0
\(715\) −67.1480 −2.51119
\(716\) 0 0
\(717\) −18.5849 −0.694066
\(718\) 0 0
\(719\) 0.219003 0.00816744 0.00408372 0.999992i \(-0.498700\pi\)
0.00408372 + 0.999992i \(0.498700\pi\)
\(720\) 0 0
\(721\) −7.55642 −0.281416
\(722\) 0 0
\(723\) 1.78154 0.0662562
\(724\) 0 0
\(725\) 0.912291 0.0338816
\(726\) 0 0
\(727\) −22.7045 −0.842062 −0.421031 0.907046i \(-0.638332\pi\)
−0.421031 + 0.907046i \(0.638332\pi\)
\(728\) 0 0
\(729\) 29.3361 1.08652
\(730\) 0 0
\(731\) −54.7028 −2.02326
\(732\) 0 0
\(733\) 17.9129 0.661628 0.330814 0.943696i \(-0.392677\pi\)
0.330814 + 0.943696i \(0.392677\pi\)
\(734\) 0 0
\(735\) 3.36328 0.124057
\(736\) 0 0
\(737\) −9.84740 −0.362734
\(738\) 0 0
\(739\) −11.3452 −0.417339 −0.208670 0.977986i \(-0.566913\pi\)
−0.208670 + 0.977986i \(0.566913\pi\)
\(740\) 0 0
\(741\) −46.3481 −1.70264
\(742\) 0 0
\(743\) 9.31548 0.341752 0.170876 0.985293i \(-0.445340\pi\)
0.170876 + 0.985293i \(0.445340\pi\)
\(744\) 0 0
\(745\) 3.64570 0.133568
\(746\) 0 0
\(747\) 15.7751 0.577180
\(748\) 0 0
\(749\) 10.9353 0.399569
\(750\) 0 0
\(751\) 5.43047 0.198161 0.0990803 0.995079i \(-0.468410\pi\)
0.0990803 + 0.995079i \(0.468410\pi\)
\(752\) 0 0
\(753\) 28.5400 1.04005
\(754\) 0 0
\(755\) −8.07351 −0.293825
\(756\) 0 0
\(757\) −9.50823 −0.345582 −0.172791 0.984958i \(-0.555279\pi\)
−0.172791 + 0.984958i \(0.555279\pi\)
\(758\) 0 0
\(759\) −7.73218 −0.280660
\(760\) 0 0
\(761\) 21.6974 0.786529 0.393265 0.919425i \(-0.371346\pi\)
0.393265 + 0.919425i \(0.371346\pi\)
\(762\) 0 0
\(763\) 12.6250 0.457056
\(764\) 0 0
\(765\) −17.3359 −0.626782
\(766\) 0 0
\(767\) 14.3498 0.518141
\(768\) 0 0
\(769\) −10.7850 −0.388916 −0.194458 0.980911i \(-0.562295\pi\)
−0.194458 + 0.980911i \(0.562295\pi\)
\(770\) 0 0
\(771\) 6.97542 0.251214
\(772\) 0 0
\(773\) −25.1118 −0.903210 −0.451605 0.892218i \(-0.649148\pi\)
−0.451605 + 0.892218i \(0.649148\pi\)
\(774\) 0 0
\(775\) −2.83756 −0.101928
\(776\) 0 0
\(777\) −1.71144 −0.0613976
\(778\) 0 0
\(779\) 39.1207 1.40164
\(780\) 0 0
\(781\) 39.3197 1.40697
\(782\) 0 0
\(783\) −10.6011 −0.378851
\(784\) 0 0
\(785\) 46.9329 1.67511
\(786\) 0 0
\(787\) 1.64538 0.0586516 0.0293258 0.999570i \(-0.490664\pi\)
0.0293258 + 0.999570i \(0.490664\pi\)
\(788\) 0 0
\(789\) 16.6214 0.591739
\(790\) 0 0
\(791\) 3.15008 0.112004
\(792\) 0 0
\(793\) 17.4485 0.619615
\(794\) 0 0
\(795\) 26.7054 0.947144
\(796\) 0 0
\(797\) 12.0243 0.425923 0.212962 0.977061i \(-0.431689\pi\)
0.212962 + 0.977061i \(0.431689\pi\)
\(798\) 0 0
\(799\) −85.6404 −3.02974
\(800\) 0 0
\(801\) −12.4482 −0.439837
\(802\) 0 0
\(803\) −40.4440 −1.42724
\(804\) 0 0
\(805\) 2.34236 0.0825572
\(806\) 0 0
\(807\) −6.30059 −0.221791
\(808\) 0 0
\(809\) 11.4285 0.401803 0.200901 0.979611i \(-0.435613\pi\)
0.200901 + 0.979611i \(0.435613\pi\)
\(810\) 0 0
\(811\) 24.2552 0.851714 0.425857 0.904790i \(-0.359973\pi\)
0.425857 + 0.904790i \(0.359973\pi\)
\(812\) 0 0
\(813\) −2.07332 −0.0727145
\(814\) 0 0
\(815\) −47.9143 −1.67837
\(816\) 0 0
\(817\) −42.0535 −1.47126
\(818\) 0 0
\(819\) −4.99506 −0.174542
\(820\) 0 0
\(821\) 16.1394 0.563268 0.281634 0.959522i \(-0.409124\pi\)
0.281634 + 0.959522i \(0.409124\pi\)
\(822\) 0 0
\(823\) −5.72512 −0.199565 −0.0997825 0.995009i \(-0.531815\pi\)
−0.0997825 + 0.995009i \(0.531815\pi\)
\(824\) 0 0
\(825\) 3.76277 0.131003
\(826\) 0 0
\(827\) −27.6141 −0.960237 −0.480118 0.877204i \(-0.659406\pi\)
−0.480118 + 0.877204i \(0.659406\pi\)
\(828\) 0 0
\(829\) 27.3694 0.950580 0.475290 0.879829i \(-0.342343\pi\)
0.475290 + 0.879829i \(0.342343\pi\)
\(830\) 0 0
\(831\) 0.403514 0.0139977
\(832\) 0 0
\(833\) 7.88754 0.273287
\(834\) 0 0
\(835\) 42.8755 1.48377
\(836\) 0 0
\(837\) 32.9732 1.13972
\(838\) 0 0
\(839\) 9.24538 0.319186 0.159593 0.987183i \(-0.448982\pi\)
0.159593 + 0.987183i \(0.448982\pi\)
\(840\) 0 0
\(841\) −25.4856 −0.878813
\(842\) 0 0
\(843\) −28.0257 −0.965257
\(844\) 0 0
\(845\) 35.9283 1.23597
\(846\) 0 0
\(847\) −17.9990 −0.618453
\(848\) 0 0
\(849\) 39.2128 1.34578
\(850\) 0 0
\(851\) −1.19193 −0.0408589
\(852\) 0 0
\(853\) 48.3601 1.65582 0.827910 0.560862i \(-0.189530\pi\)
0.827910 + 0.560862i \(0.189530\pi\)
\(854\) 0 0
\(855\) −13.3272 −0.455781
\(856\) 0 0
\(857\) −1.42104 −0.0485416 −0.0242708 0.999705i \(-0.507726\pi\)
−0.0242708 + 0.999705i \(0.507726\pi\)
\(858\) 0 0
\(859\) −7.68890 −0.262342 −0.131171 0.991360i \(-0.541874\pi\)
−0.131171 + 0.991360i \(0.541874\pi\)
\(860\) 0 0
\(861\) −9.26368 −0.315705
\(862\) 0 0
\(863\) 1.91806 0.0652916 0.0326458 0.999467i \(-0.489607\pi\)
0.0326458 + 0.999467i \(0.489607\pi\)
\(864\) 0 0
\(865\) 0.149067 0.00506842
\(866\) 0 0
\(867\) 64.9197 2.20479
\(868\) 0 0
\(869\) −13.4173 −0.455151
\(870\) 0 0
\(871\) 9.73461 0.329845
\(872\) 0 0
\(873\) −11.2246 −0.379896
\(874\) 0 0
\(875\) 10.5719 0.357396
\(876\) 0 0
\(877\) −18.2136 −0.615029 −0.307515 0.951543i \(-0.599497\pi\)
−0.307515 + 0.951543i \(0.599497\pi\)
\(878\) 0 0
\(879\) 29.8916 1.00822
\(880\) 0 0
\(881\) −42.2662 −1.42399 −0.711993 0.702187i \(-0.752207\pi\)
−0.711993 + 0.702187i \(0.752207\pi\)
\(882\) 0 0
\(883\) 17.1758 0.578011 0.289006 0.957327i \(-0.406675\pi\)
0.289006 + 0.957327i \(0.406675\pi\)
\(884\) 0 0
\(885\) −9.06609 −0.304753
\(886\) 0 0
\(887\) 11.8742 0.398696 0.199348 0.979929i \(-0.436118\pi\)
0.199348 + 0.979929i \(0.436118\pi\)
\(888\) 0 0
\(889\) 9.25975 0.310562
\(890\) 0 0
\(891\) −28.5655 −0.956982
\(892\) 0 0
\(893\) −65.8371 −2.20315
\(894\) 0 0
\(895\) −23.5406 −0.786875
\(896\) 0 0
\(897\) 7.64362 0.255213
\(898\) 0 0
\(899\) −10.9312 −0.364576
\(900\) 0 0
\(901\) 62.6293 2.08649
\(902\) 0 0
\(903\) 9.95815 0.331386
\(904\) 0 0
\(905\) −0.323651 −0.0107585
\(906\) 0 0
\(907\) 16.7923 0.557579 0.278790 0.960352i \(-0.410067\pi\)
0.278790 + 0.960352i \(0.410067\pi\)
\(908\) 0 0
\(909\) 13.5980 0.451016
\(910\) 0 0
\(911\) 42.6355 1.41258 0.706288 0.707925i \(-0.250368\pi\)
0.706288 + 0.707925i \(0.250368\pi\)
\(912\) 0 0
\(913\) −90.5338 −2.99623
\(914\) 0 0
\(915\) −11.0239 −0.364437
\(916\) 0 0
\(917\) −5.02289 −0.165870
\(918\) 0 0
\(919\) −19.9742 −0.658887 −0.329444 0.944175i \(-0.606861\pi\)
−0.329444 + 0.944175i \(0.606861\pi\)
\(920\) 0 0
\(921\) 26.0997 0.860016
\(922\) 0 0
\(923\) −38.8693 −1.27940
\(924\) 0 0
\(925\) 0.580038 0.0190715
\(926\) 0 0
\(927\) −7.09036 −0.232878
\(928\) 0 0
\(929\) 6.02222 0.197583 0.0987914 0.995108i \(-0.468502\pi\)
0.0987914 + 0.995108i \(0.468502\pi\)
\(930\) 0 0
\(931\) 6.06364 0.198728
\(932\) 0 0
\(933\) −18.1170 −0.593125
\(934\) 0 0
\(935\) 99.4915 3.25372
\(936\) 0 0
\(937\) −24.6553 −0.805452 −0.402726 0.915320i \(-0.631937\pi\)
−0.402726 + 0.915320i \(0.631937\pi\)
\(938\) 0 0
\(939\) −27.6417 −0.902051
\(940\) 0 0
\(941\) 50.1049 1.63337 0.816686 0.577082i \(-0.195809\pi\)
0.816686 + 0.577082i \(0.195809\pi\)
\(942\) 0 0
\(943\) −6.45169 −0.210096
\(944\) 0 0
\(945\) 13.2457 0.430883
\(946\) 0 0
\(947\) 19.9519 0.648351 0.324175 0.945997i \(-0.394913\pi\)
0.324175 + 0.945997i \(0.394913\pi\)
\(948\) 0 0
\(949\) 39.9807 1.29783
\(950\) 0 0
\(951\) 15.6791 0.508430
\(952\) 0 0
\(953\) −40.2873 −1.30503 −0.652517 0.757774i \(-0.726287\pi\)
−0.652517 + 0.757774i \(0.726287\pi\)
\(954\) 0 0
\(955\) −20.0306 −0.648176
\(956\) 0 0
\(957\) 14.4954 0.468569
\(958\) 0 0
\(959\) 15.7114 0.507349
\(960\) 0 0
\(961\) 3.00006 0.0967762
\(962\) 0 0
\(963\) 10.2609 0.330652
\(964\) 0 0
\(965\) −57.0985 −1.83807
\(966\) 0 0
\(967\) −31.2689 −1.00554 −0.502771 0.864420i \(-0.667686\pi\)
−0.502771 + 0.864420i \(0.667686\pi\)
\(968\) 0 0
\(969\) 68.6729 2.20609
\(970\) 0 0
\(971\) −42.5037 −1.36401 −0.682005 0.731347i \(-0.738892\pi\)
−0.682005 + 0.731347i \(0.738892\pi\)
\(972\) 0 0
\(973\) 0.0569290 0.00182506
\(974\) 0 0
\(975\) −3.71967 −0.119125
\(976\) 0 0
\(977\) −33.2556 −1.06394 −0.531971 0.846762i \(-0.678549\pi\)
−0.531971 + 0.846762i \(0.678549\pi\)
\(978\) 0 0
\(979\) 71.4409 2.28326
\(980\) 0 0
\(981\) 11.8463 0.378224
\(982\) 0 0
\(983\) 46.5016 1.48317 0.741586 0.670858i \(-0.234074\pi\)
0.741586 + 0.670858i \(0.234074\pi\)
\(984\) 0 0
\(985\) 50.4592 1.60776
\(986\) 0 0
\(987\) 15.5900 0.496237
\(988\) 0 0
\(989\) 6.93535 0.220531
\(990\) 0 0
\(991\) −31.1965 −0.990991 −0.495496 0.868610i \(-0.665014\pi\)
−0.495496 + 0.868610i \(0.665014\pi\)
\(992\) 0 0
\(993\) 47.5790 1.50988
\(994\) 0 0
\(995\) 15.2710 0.484124
\(996\) 0 0
\(997\) 7.37962 0.233715 0.116857 0.993149i \(-0.462718\pi\)
0.116857 + 0.993149i \(0.462718\pi\)
\(998\) 0 0
\(999\) −6.74020 −0.213251
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 644.2.a.d.1.3 5
3.2 odd 2 5796.2.a.t.1.2 5
4.3 odd 2 2576.2.a.bb.1.3 5
7.6 odd 2 4508.2.a.f.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.a.d.1.3 5 1.1 even 1 trivial
2576.2.a.bb.1.3 5 4.3 odd 2
4508.2.a.f.1.3 5 7.6 odd 2
5796.2.a.t.1.2 5 3.2 odd 2