Properties

Label 9904.2.a.n.1.18
Level 9904
Weight 2
Character 9904.1
Self dual yes
Analytic conductor 79.084
Analytic rank 0
Dimension 30
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9904 = 2^{4} \cdot 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9904.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(79.0838381619\)
Analytic rank: \(0\)
Dimension: \(30\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 619)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 9904.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.725873 q^{3} -0.225133 q^{5} -2.47282 q^{7} -2.47311 q^{9} +O(q^{10})\) \(q+0.725873 q^{3} -0.225133 q^{5} -2.47282 q^{7} -2.47311 q^{9} +4.06256 q^{11} +2.26536 q^{13} -0.163418 q^{15} +7.19086 q^{17} +7.47015 q^{19} -1.79495 q^{21} +0.178059 q^{23} -4.94931 q^{25} -3.97278 q^{27} +10.5609 q^{29} -1.27650 q^{31} +2.94891 q^{33} +0.556714 q^{35} +2.08508 q^{37} +1.64436 q^{39} +4.23367 q^{41} -8.52011 q^{43} +0.556779 q^{45} -9.96677 q^{47} -0.885174 q^{49} +5.21965 q^{51} +0.619984 q^{53} -0.914619 q^{55} +5.42238 q^{57} -11.8540 q^{59} +6.30300 q^{61} +6.11554 q^{63} -0.510008 q^{65} -12.5388 q^{67} +0.129248 q^{69} +9.50401 q^{71} +5.14906 q^{73} -3.59258 q^{75} -10.0460 q^{77} +16.3932 q^{79} +4.53559 q^{81} -4.79273 q^{83} -1.61890 q^{85} +7.66589 q^{87} -1.64933 q^{89} -5.60182 q^{91} -0.926577 q^{93} -1.68178 q^{95} +3.34400 q^{97} -10.0472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q - q^{3} + 21q^{5} - 2q^{7} + 43q^{9} + O(q^{10}) \) \( 30q - q^{3} + 21q^{5} - 2q^{7} + 43q^{9} - 23q^{11} + 9q^{13} + 2q^{15} + 4q^{17} + q^{19} + 30q^{21} - 4q^{23} + 35q^{25} + 5q^{27} + 90q^{29} - 2q^{31} - 6q^{33} - 9q^{35} + 19q^{37} - 32q^{39} + 59q^{41} + 4q^{43} + 30q^{45} - 4q^{47} + 30q^{49} + 34q^{53} + 17q^{55} - 8q^{57} - 13q^{59} + 16q^{61} + 40q^{63} + 31q^{65} + 11q^{67} + 6q^{69} - 42q^{71} - 4q^{73} + 52q^{75} + 29q^{77} - 3q^{79} + 30q^{81} + 11q^{83} + 19q^{85} + 20q^{87} + 58q^{89} + 39q^{91} - 15q^{93} - 23q^{95} - 9q^{97} + 8q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.725873 0.419083 0.209542 0.977800i \(-0.432803\pi\)
0.209542 + 0.977800i \(0.432803\pi\)
\(4\) 0 0
\(5\) −0.225133 −0.100683 −0.0503414 0.998732i \(-0.516031\pi\)
−0.0503414 + 0.998732i \(0.516031\pi\)
\(6\) 0 0
\(7\) −2.47282 −0.934637 −0.467319 0.884089i \(-0.654780\pi\)
−0.467319 + 0.884089i \(0.654780\pi\)
\(8\) 0 0
\(9\) −2.47311 −0.824369
\(10\) 0 0
\(11\) 4.06256 1.22491 0.612455 0.790506i \(-0.290182\pi\)
0.612455 + 0.790506i \(0.290182\pi\)
\(12\) 0 0
\(13\) 2.26536 0.628298 0.314149 0.949374i \(-0.398281\pi\)
0.314149 + 0.949374i \(0.398281\pi\)
\(14\) 0 0
\(15\) −0.163418 −0.0421944
\(16\) 0 0
\(17\) 7.19086 1.74404 0.872019 0.489471i \(-0.162810\pi\)
0.872019 + 0.489471i \(0.162810\pi\)
\(18\) 0 0
\(19\) 7.47015 1.71377 0.856885 0.515507i \(-0.172397\pi\)
0.856885 + 0.515507i \(0.172397\pi\)
\(20\) 0 0
\(21\) −1.79495 −0.391691
\(22\) 0 0
\(23\) 0.178059 0.0371279 0.0185639 0.999828i \(-0.494091\pi\)
0.0185639 + 0.999828i \(0.494091\pi\)
\(24\) 0 0
\(25\) −4.94931 −0.989863
\(26\) 0 0
\(27\) −3.97278 −0.764562
\(28\) 0 0
\(29\) 10.5609 1.96111 0.980557 0.196232i \(-0.0628707\pi\)
0.980557 + 0.196232i \(0.0628707\pi\)
\(30\) 0 0
\(31\) −1.27650 −0.229266 −0.114633 0.993408i \(-0.536569\pi\)
−0.114633 + 0.993408i \(0.536569\pi\)
\(32\) 0 0
\(33\) 2.94891 0.513339
\(34\) 0 0
\(35\) 0.556714 0.0941018
\(36\) 0 0
\(37\) 2.08508 0.342784 0.171392 0.985203i \(-0.445173\pi\)
0.171392 + 0.985203i \(0.445173\pi\)
\(38\) 0 0
\(39\) 1.64436 0.263309
\(40\) 0 0
\(41\) 4.23367 0.661188 0.330594 0.943773i \(-0.392751\pi\)
0.330594 + 0.943773i \(0.392751\pi\)
\(42\) 0 0
\(43\) −8.52011 −1.29930 −0.649652 0.760232i \(-0.725085\pi\)
−0.649652 + 0.760232i \(0.725085\pi\)
\(44\) 0 0
\(45\) 0.556779 0.0829997
\(46\) 0 0
\(47\) −9.96677 −1.45380 −0.726901 0.686742i \(-0.759040\pi\)
−0.726901 + 0.686742i \(0.759040\pi\)
\(48\) 0 0
\(49\) −0.885174 −0.126453
\(50\) 0 0
\(51\) 5.21965 0.730897
\(52\) 0 0
\(53\) 0.619984 0.0851614 0.0425807 0.999093i \(-0.486442\pi\)
0.0425807 + 0.999093i \(0.486442\pi\)
\(54\) 0 0
\(55\) −0.914619 −0.123327
\(56\) 0 0
\(57\) 5.42238 0.718212
\(58\) 0 0
\(59\) −11.8540 −1.54326 −0.771628 0.636074i \(-0.780557\pi\)
−0.771628 + 0.636074i \(0.780557\pi\)
\(60\) 0 0
\(61\) 6.30300 0.807017 0.403508 0.914976i \(-0.367791\pi\)
0.403508 + 0.914976i \(0.367791\pi\)
\(62\) 0 0
\(63\) 6.11554 0.770486
\(64\) 0 0
\(65\) −0.510008 −0.0632587
\(66\) 0 0
\(67\) −12.5388 −1.53186 −0.765928 0.642927i \(-0.777720\pi\)
−0.765928 + 0.642927i \(0.777720\pi\)
\(68\) 0 0
\(69\) 0.129248 0.0155597
\(70\) 0 0
\(71\) 9.50401 1.12792 0.563959 0.825803i \(-0.309277\pi\)
0.563959 + 0.825803i \(0.309277\pi\)
\(72\) 0 0
\(73\) 5.14906 0.602652 0.301326 0.953521i \(-0.402571\pi\)
0.301326 + 0.953521i \(0.402571\pi\)
\(74\) 0 0
\(75\) −3.59258 −0.414835
\(76\) 0 0
\(77\) −10.0460 −1.14485
\(78\) 0 0
\(79\) 16.3932 1.84438 0.922190 0.386737i \(-0.126398\pi\)
0.922190 + 0.386737i \(0.126398\pi\)
\(80\) 0 0
\(81\) 4.53559 0.503954
\(82\) 0 0
\(83\) −4.79273 −0.526071 −0.263035 0.964786i \(-0.584724\pi\)
−0.263035 + 0.964786i \(0.584724\pi\)
\(84\) 0 0
\(85\) −1.61890 −0.175595
\(86\) 0 0
\(87\) 7.66589 0.821870
\(88\) 0 0
\(89\) −1.64933 −0.174829 −0.0874143 0.996172i \(-0.527860\pi\)
−0.0874143 + 0.996172i \(0.527860\pi\)
\(90\) 0 0
\(91\) −5.60182 −0.587231
\(92\) 0 0
\(93\) −0.926577 −0.0960816
\(94\) 0 0
\(95\) −1.68178 −0.172547
\(96\) 0 0
\(97\) 3.34400 0.339531 0.169766 0.985484i \(-0.445699\pi\)
0.169766 + 0.985484i \(0.445699\pi\)
\(98\) 0 0
\(99\) −10.0472 −1.00978
\(100\) 0 0
\(101\) −12.6806 −1.26176 −0.630882 0.775878i \(-0.717307\pi\)
−0.630882 + 0.775878i \(0.717307\pi\)
\(102\) 0 0
\(103\) 4.47808 0.441238 0.220619 0.975360i \(-0.429192\pi\)
0.220619 + 0.975360i \(0.429192\pi\)
\(104\) 0 0
\(105\) 0.404104 0.0394365
\(106\) 0 0
\(107\) −15.0754 −1.45740 −0.728699 0.684834i \(-0.759875\pi\)
−0.728699 + 0.684834i \(0.759875\pi\)
\(108\) 0 0
\(109\) 3.66599 0.351138 0.175569 0.984467i \(-0.443823\pi\)
0.175569 + 0.984467i \(0.443823\pi\)
\(110\) 0 0
\(111\) 1.51350 0.143655
\(112\) 0 0
\(113\) 6.54316 0.615528 0.307764 0.951463i \(-0.400419\pi\)
0.307764 + 0.951463i \(0.400419\pi\)
\(114\) 0 0
\(115\) −0.0400870 −0.00373814
\(116\) 0 0
\(117\) −5.60248 −0.517949
\(118\) 0 0
\(119\) −17.7817 −1.63004
\(120\) 0 0
\(121\) 5.50443 0.500403
\(122\) 0 0
\(123\) 3.07311 0.277093
\(124\) 0 0
\(125\) 2.23992 0.200345
\(126\) 0 0
\(127\) 15.0494 1.33542 0.667711 0.744420i \(-0.267274\pi\)
0.667711 + 0.744420i \(0.267274\pi\)
\(128\) 0 0
\(129\) −6.18452 −0.544516
\(130\) 0 0
\(131\) −9.57374 −0.836462 −0.418231 0.908341i \(-0.637350\pi\)
−0.418231 + 0.908341i \(0.637350\pi\)
\(132\) 0 0
\(133\) −18.4723 −1.60175
\(134\) 0 0
\(135\) 0.894406 0.0769782
\(136\) 0 0
\(137\) 2.15272 0.183919 0.0919595 0.995763i \(-0.470687\pi\)
0.0919595 + 0.995763i \(0.470687\pi\)
\(138\) 0 0
\(139\) −5.62106 −0.476772 −0.238386 0.971171i \(-0.576618\pi\)
−0.238386 + 0.971171i \(0.576618\pi\)
\(140\) 0 0
\(141\) −7.23461 −0.609264
\(142\) 0 0
\(143\) 9.20317 0.769608
\(144\) 0 0
\(145\) −2.37762 −0.197450
\(146\) 0 0
\(147\) −0.642524 −0.0529945
\(148\) 0 0
\(149\) 15.1382 1.24017 0.620086 0.784534i \(-0.287098\pi\)
0.620086 + 0.784534i \(0.287098\pi\)
\(150\) 0 0
\(151\) 19.7193 1.60474 0.802369 0.596828i \(-0.203573\pi\)
0.802369 + 0.596828i \(0.203573\pi\)
\(152\) 0 0
\(153\) −17.7838 −1.43773
\(154\) 0 0
\(155\) 0.287383 0.0230831
\(156\) 0 0
\(157\) 15.7111 1.25389 0.626943 0.779065i \(-0.284306\pi\)
0.626943 + 0.779065i \(0.284306\pi\)
\(158\) 0 0
\(159\) 0.450030 0.0356897
\(160\) 0 0
\(161\) −0.440308 −0.0347011
\(162\) 0 0
\(163\) 11.8717 0.929864 0.464932 0.885346i \(-0.346079\pi\)
0.464932 + 0.885346i \(0.346079\pi\)
\(164\) 0 0
\(165\) −0.663897 −0.0516843
\(166\) 0 0
\(167\) 5.37936 0.416267 0.208134 0.978100i \(-0.433261\pi\)
0.208134 + 0.978100i \(0.433261\pi\)
\(168\) 0 0
\(169\) −7.86814 −0.605242
\(170\) 0 0
\(171\) −18.4745 −1.41278
\(172\) 0 0
\(173\) −18.6393 −1.41712 −0.708560 0.705651i \(-0.750655\pi\)
−0.708560 + 0.705651i \(0.750655\pi\)
\(174\) 0 0
\(175\) 12.2388 0.925163
\(176\) 0 0
\(177\) −8.60448 −0.646753
\(178\) 0 0
\(179\) 22.6264 1.69117 0.845587 0.533837i \(-0.179250\pi\)
0.845587 + 0.533837i \(0.179250\pi\)
\(180\) 0 0
\(181\) 12.1002 0.899398 0.449699 0.893180i \(-0.351531\pi\)
0.449699 + 0.893180i \(0.351531\pi\)
\(182\) 0 0
\(183\) 4.57518 0.338207
\(184\) 0 0
\(185\) −0.469420 −0.0345124
\(186\) 0 0
\(187\) 29.2133 2.13629
\(188\) 0 0
\(189\) 9.82397 0.714588
\(190\) 0 0
\(191\) 0.166765 0.0120667 0.00603336 0.999982i \(-0.498080\pi\)
0.00603336 + 0.999982i \(0.498080\pi\)
\(192\) 0 0
\(193\) −16.5260 −1.18956 −0.594782 0.803887i \(-0.702762\pi\)
−0.594782 + 0.803887i \(0.702762\pi\)
\(194\) 0 0
\(195\) −0.370201 −0.0265107
\(196\) 0 0
\(197\) 9.82274 0.699841 0.349921 0.936779i \(-0.386209\pi\)
0.349921 + 0.936779i \(0.386209\pi\)
\(198\) 0 0
\(199\) −11.5691 −0.820113 −0.410056 0.912060i \(-0.634491\pi\)
−0.410056 + 0.912060i \(0.634491\pi\)
\(200\) 0 0
\(201\) −9.10156 −0.641975
\(202\) 0 0
\(203\) −26.1152 −1.83293
\(204\) 0 0
\(205\) −0.953140 −0.0665702
\(206\) 0 0
\(207\) −0.440359 −0.0306071
\(208\) 0 0
\(209\) 30.3480 2.09921
\(210\) 0 0
\(211\) 19.2316 1.32396 0.661978 0.749523i \(-0.269717\pi\)
0.661978 + 0.749523i \(0.269717\pi\)
\(212\) 0 0
\(213\) 6.89871 0.472692
\(214\) 0 0
\(215\) 1.91816 0.130817
\(216\) 0 0
\(217\) 3.15655 0.214281
\(218\) 0 0
\(219\) 3.73757 0.252561
\(220\) 0 0
\(221\) 16.2899 1.09578
\(222\) 0 0
\(223\) 2.26463 0.151651 0.0758255 0.997121i \(-0.475841\pi\)
0.0758255 + 0.997121i \(0.475841\pi\)
\(224\) 0 0
\(225\) 12.2402 0.816013
\(226\) 0 0
\(227\) −12.6616 −0.840378 −0.420189 0.907437i \(-0.638036\pi\)
−0.420189 + 0.907437i \(0.638036\pi\)
\(228\) 0 0
\(229\) 27.7524 1.83393 0.916967 0.398964i \(-0.130630\pi\)
0.916967 + 0.398964i \(0.130630\pi\)
\(230\) 0 0
\(231\) −7.29211 −0.479786
\(232\) 0 0
\(233\) −10.9164 −0.715157 −0.357579 0.933883i \(-0.616398\pi\)
−0.357579 + 0.933883i \(0.616398\pi\)
\(234\) 0 0
\(235\) 2.24385 0.146373
\(236\) 0 0
\(237\) 11.8994 0.772949
\(238\) 0 0
\(239\) −6.41476 −0.414936 −0.207468 0.978242i \(-0.566522\pi\)
−0.207468 + 0.978242i \(0.566522\pi\)
\(240\) 0 0
\(241\) 9.85126 0.634576 0.317288 0.948329i \(-0.397228\pi\)
0.317288 + 0.948329i \(0.397228\pi\)
\(242\) 0 0
\(243\) 15.2106 0.975761
\(244\) 0 0
\(245\) 0.199282 0.0127317
\(246\) 0 0
\(247\) 16.9226 1.07676
\(248\) 0 0
\(249\) −3.47892 −0.220467
\(250\) 0 0
\(251\) −5.56947 −0.351542 −0.175771 0.984431i \(-0.556242\pi\)
−0.175771 + 0.984431i \(0.556242\pi\)
\(252\) 0 0
\(253\) 0.723376 0.0454783
\(254\) 0 0
\(255\) −1.17512 −0.0735887
\(256\) 0 0
\(257\) 24.0328 1.49913 0.749564 0.661932i \(-0.230263\pi\)
0.749564 + 0.661932i \(0.230263\pi\)
\(258\) 0 0
\(259\) −5.15601 −0.320379
\(260\) 0 0
\(261\) −26.1183 −1.61668
\(262\) 0 0
\(263\) −14.9598 −0.922463 −0.461232 0.887280i \(-0.652592\pi\)
−0.461232 + 0.887280i \(0.652592\pi\)
\(264\) 0 0
\(265\) −0.139579 −0.00857428
\(266\) 0 0
\(267\) −1.19720 −0.0732677
\(268\) 0 0
\(269\) 13.4385 0.819357 0.409679 0.912230i \(-0.365641\pi\)
0.409679 + 0.912230i \(0.365641\pi\)
\(270\) 0 0
\(271\) −5.72605 −0.347833 −0.173916 0.984760i \(-0.555642\pi\)
−0.173916 + 0.984760i \(0.555642\pi\)
\(272\) 0 0
\(273\) −4.06621 −0.246098
\(274\) 0 0
\(275\) −20.1069 −1.21249
\(276\) 0 0
\(277\) 12.0981 0.726905 0.363452 0.931613i \(-0.381598\pi\)
0.363452 + 0.931613i \(0.381598\pi\)
\(278\) 0 0
\(279\) 3.15692 0.189000
\(280\) 0 0
\(281\) −6.21778 −0.370921 −0.185461 0.982652i \(-0.559378\pi\)
−0.185461 + 0.982652i \(0.559378\pi\)
\(282\) 0 0
\(283\) −12.9505 −0.769826 −0.384913 0.922953i \(-0.625769\pi\)
−0.384913 + 0.922953i \(0.625769\pi\)
\(284\) 0 0
\(285\) −1.22076 −0.0723116
\(286\) 0 0
\(287\) −10.4691 −0.617971
\(288\) 0 0
\(289\) 34.7084 2.04167
\(290\) 0 0
\(291\) 2.42732 0.142292
\(292\) 0 0
\(293\) 14.3490 0.838279 0.419139 0.907922i \(-0.362332\pi\)
0.419139 + 0.907922i \(0.362332\pi\)
\(294\) 0 0
\(295\) 2.66873 0.155379
\(296\) 0 0
\(297\) −16.1397 −0.936520
\(298\) 0 0
\(299\) 0.403368 0.0233274
\(300\) 0 0
\(301\) 21.0687 1.21438
\(302\) 0 0
\(303\) −9.20450 −0.528784
\(304\) 0 0
\(305\) −1.41902 −0.0812526
\(306\) 0 0
\(307\) 28.7422 1.64040 0.820202 0.572075i \(-0.193861\pi\)
0.820202 + 0.572075i \(0.193861\pi\)
\(308\) 0 0
\(309\) 3.25052 0.184916
\(310\) 0 0
\(311\) 29.9677 1.69931 0.849655 0.527339i \(-0.176810\pi\)
0.849655 + 0.527339i \(0.176810\pi\)
\(312\) 0 0
\(313\) −13.6402 −0.770990 −0.385495 0.922710i \(-0.625969\pi\)
−0.385495 + 0.922710i \(0.625969\pi\)
\(314\) 0 0
\(315\) −1.37681 −0.0775746
\(316\) 0 0
\(317\) 12.9433 0.726967 0.363484 0.931601i \(-0.381587\pi\)
0.363484 + 0.931601i \(0.381587\pi\)
\(318\) 0 0
\(319\) 42.9044 2.40219
\(320\) 0 0
\(321\) −10.9429 −0.610771
\(322\) 0 0
\(323\) 53.7168 2.98888
\(324\) 0 0
\(325\) −11.2120 −0.621929
\(326\) 0 0
\(327\) 2.66104 0.147156
\(328\) 0 0
\(329\) 24.6460 1.35878
\(330\) 0 0
\(331\) −8.48346 −0.466293 −0.233147 0.972442i \(-0.574902\pi\)
−0.233147 + 0.972442i \(0.574902\pi\)
\(332\) 0 0
\(333\) −5.15662 −0.282581
\(334\) 0 0
\(335\) 2.82290 0.154231
\(336\) 0 0
\(337\) −28.4431 −1.54939 −0.774697 0.632332i \(-0.782098\pi\)
−0.774697 + 0.632332i \(0.782098\pi\)
\(338\) 0 0
\(339\) 4.74950 0.257958
\(340\) 0 0
\(341\) −5.18586 −0.280830
\(342\) 0 0
\(343\) 19.4986 1.05283
\(344\) 0 0
\(345\) −0.0290981 −0.00156659
\(346\) 0 0
\(347\) −6.37057 −0.341990 −0.170995 0.985272i \(-0.554698\pi\)
−0.170995 + 0.985272i \(0.554698\pi\)
\(348\) 0 0
\(349\) −12.7281 −0.681317 −0.340659 0.940187i \(-0.610650\pi\)
−0.340659 + 0.940187i \(0.610650\pi\)
\(350\) 0 0
\(351\) −8.99978 −0.480373
\(352\) 0 0
\(353\) 1.48049 0.0787984 0.0393992 0.999224i \(-0.487456\pi\)
0.0393992 + 0.999224i \(0.487456\pi\)
\(354\) 0 0
\(355\) −2.13967 −0.113562
\(356\) 0 0
\(357\) −12.9072 −0.683124
\(358\) 0 0
\(359\) 27.5753 1.45537 0.727685 0.685911i \(-0.240596\pi\)
0.727685 + 0.685911i \(0.240596\pi\)
\(360\) 0 0
\(361\) 36.8032 1.93701
\(362\) 0 0
\(363\) 3.99552 0.209710
\(364\) 0 0
\(365\) −1.15923 −0.0606766
\(366\) 0 0
\(367\) −6.08957 −0.317873 −0.158936 0.987289i \(-0.550807\pi\)
−0.158936 + 0.987289i \(0.550807\pi\)
\(368\) 0 0
\(369\) −10.4703 −0.545063
\(370\) 0 0
\(371\) −1.53311 −0.0795950
\(372\) 0 0
\(373\) 22.4949 1.16474 0.582371 0.812923i \(-0.302125\pi\)
0.582371 + 0.812923i \(0.302125\pi\)
\(374\) 0 0
\(375\) 1.62590 0.0839611
\(376\) 0 0
\(377\) 23.9243 1.23216
\(378\) 0 0
\(379\) 14.1157 0.725075 0.362538 0.931969i \(-0.381910\pi\)
0.362538 + 0.931969i \(0.381910\pi\)
\(380\) 0 0
\(381\) 10.9240 0.559653
\(382\) 0 0
\(383\) −24.3617 −1.24482 −0.622412 0.782690i \(-0.713847\pi\)
−0.622412 + 0.782690i \(0.713847\pi\)
\(384\) 0 0
\(385\) 2.26169 0.115266
\(386\) 0 0
\(387\) 21.0711 1.07111
\(388\) 0 0
\(389\) −16.7319 −0.848341 −0.424170 0.905582i \(-0.639434\pi\)
−0.424170 + 0.905582i \(0.639434\pi\)
\(390\) 0 0
\(391\) 1.28040 0.0647525
\(392\) 0 0
\(393\) −6.94932 −0.350547
\(394\) 0 0
\(395\) −3.69066 −0.185697
\(396\) 0 0
\(397\) −21.7689 −1.09255 −0.546274 0.837607i \(-0.683954\pi\)
−0.546274 + 0.837607i \(0.683954\pi\)
\(398\) 0 0
\(399\) −13.4086 −0.671268
\(400\) 0 0
\(401\) 20.2269 1.01008 0.505041 0.863095i \(-0.331477\pi\)
0.505041 + 0.863095i \(0.331477\pi\)
\(402\) 0 0
\(403\) −2.89173 −0.144047
\(404\) 0 0
\(405\) −1.02111 −0.0507395
\(406\) 0 0
\(407\) 8.47075 0.419880
\(408\) 0 0
\(409\) 28.5461 1.41151 0.705757 0.708454i \(-0.250607\pi\)
0.705757 + 0.708454i \(0.250607\pi\)
\(410\) 0 0
\(411\) 1.56260 0.0770773
\(412\) 0 0
\(413\) 29.3127 1.44238
\(414\) 0 0
\(415\) 1.07900 0.0529662
\(416\) 0 0
\(417\) −4.08018 −0.199807
\(418\) 0 0
\(419\) 36.3207 1.77438 0.887192 0.461400i \(-0.152653\pi\)
0.887192 + 0.461400i \(0.152653\pi\)
\(420\) 0 0
\(421\) −20.8986 −1.01853 −0.509267 0.860609i \(-0.670083\pi\)
−0.509267 + 0.860609i \(0.670083\pi\)
\(422\) 0 0
\(423\) 24.6489 1.19847
\(424\) 0 0
\(425\) −35.5898 −1.72636
\(426\) 0 0
\(427\) −15.5862 −0.754268
\(428\) 0 0
\(429\) 6.68034 0.322530
\(430\) 0 0
\(431\) −5.65795 −0.272534 −0.136267 0.990672i \(-0.543510\pi\)
−0.136267 + 0.990672i \(0.543510\pi\)
\(432\) 0 0
\(433\) −0.797593 −0.0383299 −0.0191649 0.999816i \(-0.506101\pi\)
−0.0191649 + 0.999816i \(0.506101\pi\)
\(434\) 0 0
\(435\) −1.72585 −0.0827481
\(436\) 0 0
\(437\) 1.33013 0.0636286
\(438\) 0 0
\(439\) 18.2826 0.872581 0.436290 0.899806i \(-0.356292\pi\)
0.436290 + 0.899806i \(0.356292\pi\)
\(440\) 0 0
\(441\) 2.18913 0.104244
\(442\) 0 0
\(443\) 18.4038 0.874391 0.437195 0.899367i \(-0.355972\pi\)
0.437195 + 0.899367i \(0.355972\pi\)
\(444\) 0 0
\(445\) 0.371319 0.0176022
\(446\) 0 0
\(447\) 10.9884 0.519735
\(448\) 0 0
\(449\) 2.95767 0.139581 0.0697905 0.997562i \(-0.477767\pi\)
0.0697905 + 0.997562i \(0.477767\pi\)
\(450\) 0 0
\(451\) 17.1996 0.809896
\(452\) 0 0
\(453\) 14.3138 0.672519
\(454\) 0 0
\(455\) 1.26116 0.0591240
\(456\) 0 0
\(457\) 18.1383 0.848472 0.424236 0.905552i \(-0.360543\pi\)
0.424236 + 0.905552i \(0.360543\pi\)
\(458\) 0 0
\(459\) −28.5677 −1.33343
\(460\) 0 0
\(461\) −16.5572 −0.771145 −0.385573 0.922677i \(-0.625996\pi\)
−0.385573 + 0.922677i \(0.625996\pi\)
\(462\) 0 0
\(463\) −4.01151 −0.186430 −0.0932152 0.995646i \(-0.529714\pi\)
−0.0932152 + 0.995646i \(0.529714\pi\)
\(464\) 0 0
\(465\) 0.208603 0.00967376
\(466\) 0 0
\(467\) 4.61263 0.213447 0.106724 0.994289i \(-0.465964\pi\)
0.106724 + 0.994289i \(0.465964\pi\)
\(468\) 0 0
\(469\) 31.0061 1.43173
\(470\) 0 0
\(471\) 11.4043 0.525482
\(472\) 0 0
\(473\) −34.6135 −1.59153
\(474\) 0 0
\(475\) −36.9721 −1.69640
\(476\) 0 0
\(477\) −1.53329 −0.0702044
\(478\) 0 0
\(479\) 37.2886 1.70376 0.851879 0.523739i \(-0.175463\pi\)
0.851879 + 0.523739i \(0.175463\pi\)
\(480\) 0 0
\(481\) 4.72345 0.215371
\(482\) 0 0
\(483\) −0.319607 −0.0145426
\(484\) 0 0
\(485\) −0.752845 −0.0341849
\(486\) 0 0
\(487\) −25.0176 −1.13366 −0.566828 0.823836i \(-0.691830\pi\)
−0.566828 + 0.823836i \(0.691830\pi\)
\(488\) 0 0
\(489\) 8.61736 0.389690
\(490\) 0 0
\(491\) 23.7021 1.06966 0.534830 0.844960i \(-0.320376\pi\)
0.534830 + 0.844960i \(0.320376\pi\)
\(492\) 0 0
\(493\) 75.9421 3.42026
\(494\) 0 0
\(495\) 2.26195 0.101667
\(496\) 0 0
\(497\) −23.5017 −1.05419
\(498\) 0 0
\(499\) −27.1748 −1.21651 −0.608255 0.793742i \(-0.708130\pi\)
−0.608255 + 0.793742i \(0.708130\pi\)
\(500\) 0 0
\(501\) 3.90473 0.174451
\(502\) 0 0
\(503\) −12.0746 −0.538381 −0.269191 0.963087i \(-0.586756\pi\)
−0.269191 + 0.963087i \(0.586756\pi\)
\(504\) 0 0
\(505\) 2.85482 0.127038
\(506\) 0 0
\(507\) −5.71128 −0.253647
\(508\) 0 0
\(509\) −43.7176 −1.93775 −0.968873 0.247557i \(-0.920372\pi\)
−0.968873 + 0.247557i \(0.920372\pi\)
\(510\) 0 0
\(511\) −12.7327 −0.563261
\(512\) 0 0
\(513\) −29.6773 −1.31028
\(514\) 0 0
\(515\) −1.00817 −0.0444251
\(516\) 0 0
\(517\) −40.4906 −1.78078
\(518\) 0 0
\(519\) −13.5298 −0.593891
\(520\) 0 0
\(521\) −35.3638 −1.54932 −0.774659 0.632379i \(-0.782078\pi\)
−0.774659 + 0.632379i \(0.782078\pi\)
\(522\) 0 0
\(523\) −19.8938 −0.869897 −0.434949 0.900455i \(-0.643233\pi\)
−0.434949 + 0.900455i \(0.643233\pi\)
\(524\) 0 0
\(525\) 8.88378 0.387720
\(526\) 0 0
\(527\) −9.17913 −0.399849
\(528\) 0 0
\(529\) −22.9683 −0.998622
\(530\) 0 0
\(531\) 29.3162 1.27221
\(532\) 0 0
\(533\) 9.59079 0.415423
\(534\) 0 0
\(535\) 3.39399 0.146735
\(536\) 0 0
\(537\) 16.4239 0.708743
\(538\) 0 0
\(539\) −3.59608 −0.154894
\(540\) 0 0
\(541\) −15.3119 −0.658311 −0.329156 0.944276i \(-0.606764\pi\)
−0.329156 + 0.944276i \(0.606764\pi\)
\(542\) 0 0
\(543\) 8.78319 0.376923
\(544\) 0 0
\(545\) −0.825337 −0.0353535
\(546\) 0 0
\(547\) −42.3037 −1.80878 −0.904388 0.426711i \(-0.859672\pi\)
−0.904388 + 0.426711i \(0.859672\pi\)
\(548\) 0 0
\(549\) −15.5880 −0.665280
\(550\) 0 0
\(551\) 78.8917 3.36090
\(552\) 0 0
\(553\) −40.5374 −1.72383
\(554\) 0 0
\(555\) −0.340739 −0.0144636
\(556\) 0 0
\(557\) 7.44351 0.315392 0.157696 0.987488i \(-0.449593\pi\)
0.157696 + 0.987488i \(0.449593\pi\)
\(558\) 0 0
\(559\) −19.3011 −0.816350
\(560\) 0 0
\(561\) 21.2052 0.895283
\(562\) 0 0
\(563\) 30.6551 1.29196 0.645978 0.763356i \(-0.276450\pi\)
0.645978 + 0.763356i \(0.276450\pi\)
\(564\) 0 0
\(565\) −1.47308 −0.0619731
\(566\) 0 0
\(567\) −11.2157 −0.471014
\(568\) 0 0
\(569\) 45.0445 1.88836 0.944182 0.329425i \(-0.106855\pi\)
0.944182 + 0.329425i \(0.106855\pi\)
\(570\) 0 0
\(571\) 20.5533 0.860127 0.430063 0.902799i \(-0.358491\pi\)
0.430063 + 0.902799i \(0.358491\pi\)
\(572\) 0 0
\(573\) 0.121051 0.00505696
\(574\) 0 0
\(575\) −0.881270 −0.0367515
\(576\) 0 0
\(577\) 2.43980 0.101570 0.0507851 0.998710i \(-0.483828\pi\)
0.0507851 + 0.998710i \(0.483828\pi\)
\(578\) 0 0
\(579\) −11.9957 −0.498526
\(580\) 0 0
\(581\) 11.8516 0.491685
\(582\) 0 0
\(583\) 2.51873 0.104315
\(584\) 0 0
\(585\) 1.26131 0.0521486
\(586\) 0 0
\(587\) −28.0624 −1.15826 −0.579129 0.815236i \(-0.696607\pi\)
−0.579129 + 0.815236i \(0.696607\pi\)
\(588\) 0 0
\(589\) −9.53565 −0.392910
\(590\) 0 0
\(591\) 7.13007 0.293292
\(592\) 0 0
\(593\) −20.1600 −0.827873 −0.413937 0.910306i \(-0.635847\pi\)
−0.413937 + 0.910306i \(0.635847\pi\)
\(594\) 0 0
\(595\) 4.00325 0.164117
\(596\) 0 0
\(597\) −8.39771 −0.343696
\(598\) 0 0
\(599\) −23.5060 −0.960427 −0.480214 0.877152i \(-0.659441\pi\)
−0.480214 + 0.877152i \(0.659441\pi\)
\(600\) 0 0
\(601\) −20.9839 −0.855952 −0.427976 0.903790i \(-0.640773\pi\)
−0.427976 + 0.903790i \(0.640773\pi\)
\(602\) 0 0
\(603\) 31.0097 1.26281
\(604\) 0 0
\(605\) −1.23923 −0.0503819
\(606\) 0 0
\(607\) −32.2511 −1.30903 −0.654516 0.756048i \(-0.727128\pi\)
−0.654516 + 0.756048i \(0.727128\pi\)
\(608\) 0 0
\(609\) −18.9564 −0.768150
\(610\) 0 0
\(611\) −22.5783 −0.913421
\(612\) 0 0
\(613\) −37.2120 −1.50298 −0.751489 0.659746i \(-0.770664\pi\)
−0.751489 + 0.659746i \(0.770664\pi\)
\(614\) 0 0
\(615\) −0.691859 −0.0278985
\(616\) 0 0
\(617\) 38.3479 1.54383 0.771915 0.635726i \(-0.219299\pi\)
0.771915 + 0.635726i \(0.219299\pi\)
\(618\) 0 0
\(619\) −1.00000 −0.0401934
\(620\) 0 0
\(621\) −0.707390 −0.0283866
\(622\) 0 0
\(623\) 4.07849 0.163401
\(624\) 0 0
\(625\) 24.2423 0.969692
\(626\) 0 0
\(627\) 22.0288 0.879745
\(628\) 0 0
\(629\) 14.9935 0.597829
\(630\) 0 0
\(631\) −38.9829 −1.55188 −0.775942 0.630804i \(-0.782725\pi\)
−0.775942 + 0.630804i \(0.782725\pi\)
\(632\) 0 0
\(633\) 13.9597 0.554848
\(634\) 0 0
\(635\) −3.38813 −0.134454
\(636\) 0 0
\(637\) −2.00524 −0.0794504
\(638\) 0 0
\(639\) −23.5044 −0.929822
\(640\) 0 0
\(641\) −0.319675 −0.0126264 −0.00631321 0.999980i \(-0.502010\pi\)
−0.00631321 + 0.999980i \(0.502010\pi\)
\(642\) 0 0
\(643\) −0.159017 −0.00627101 −0.00313550 0.999995i \(-0.500998\pi\)
−0.00313550 + 0.999995i \(0.500998\pi\)
\(644\) 0 0
\(645\) 1.39234 0.0548234
\(646\) 0 0
\(647\) −24.6688 −0.969829 −0.484915 0.874562i \(-0.661149\pi\)
−0.484915 + 0.874562i \(0.661149\pi\)
\(648\) 0 0
\(649\) −48.1575 −1.89035
\(650\) 0 0
\(651\) 2.29126 0.0898014
\(652\) 0 0
\(653\) −28.3461 −1.10927 −0.554635 0.832094i \(-0.687142\pi\)
−0.554635 + 0.832094i \(0.687142\pi\)
\(654\) 0 0
\(655\) 2.15537 0.0842172
\(656\) 0 0
\(657\) −12.7342 −0.496808
\(658\) 0 0
\(659\) −39.5061 −1.53894 −0.769470 0.638683i \(-0.779479\pi\)
−0.769470 + 0.638683i \(0.779479\pi\)
\(660\) 0 0
\(661\) −15.7041 −0.610818 −0.305409 0.952221i \(-0.598793\pi\)
−0.305409 + 0.952221i \(0.598793\pi\)
\(662\) 0 0
\(663\) 11.8244 0.459221
\(664\) 0 0
\(665\) 4.15874 0.161269
\(666\) 0 0
\(667\) 1.88047 0.0728120
\(668\) 0 0
\(669\) 1.64384 0.0635544
\(670\) 0 0
\(671\) 25.6064 0.988523
\(672\) 0 0
\(673\) −23.0243 −0.887522 −0.443761 0.896145i \(-0.646356\pi\)
−0.443761 + 0.896145i \(0.646356\pi\)
\(674\) 0 0
\(675\) 19.6626 0.756812
\(676\) 0 0
\(677\) 7.63096 0.293282 0.146641 0.989190i \(-0.453154\pi\)
0.146641 + 0.989190i \(0.453154\pi\)
\(678\) 0 0
\(679\) −8.26909 −0.317339
\(680\) 0 0
\(681\) −9.19070 −0.352188
\(682\) 0 0
\(683\) −0.644724 −0.0246697 −0.0123348 0.999924i \(-0.503926\pi\)
−0.0123348 + 0.999924i \(0.503926\pi\)
\(684\) 0 0
\(685\) −0.484648 −0.0185175
\(686\) 0 0
\(687\) 20.1448 0.768571
\(688\) 0 0
\(689\) 1.40449 0.0535067
\(690\) 0 0
\(691\) 29.5024 1.12232 0.561162 0.827706i \(-0.310354\pi\)
0.561162 + 0.827706i \(0.310354\pi\)
\(692\) 0 0
\(693\) 24.8448 0.943776
\(694\) 0 0
\(695\) 1.26549 0.0480027
\(696\) 0 0
\(697\) 30.4437 1.15314
\(698\) 0 0
\(699\) −7.92393 −0.299710
\(700\) 0 0
\(701\) −30.4332 −1.14944 −0.574722 0.818348i \(-0.694890\pi\)
−0.574722 + 0.818348i \(0.694890\pi\)
\(702\) 0 0
\(703\) 15.5758 0.587453
\(704\) 0 0
\(705\) 1.62875 0.0613424
\(706\) 0 0
\(707\) 31.3568 1.17929
\(708\) 0 0
\(709\) 10.4754 0.393413 0.196707 0.980462i \(-0.436975\pi\)
0.196707 + 0.980462i \(0.436975\pi\)
\(710\) 0 0
\(711\) −40.5422 −1.52045
\(712\) 0 0
\(713\) −0.227292 −0.00851217
\(714\) 0 0
\(715\) −2.07194 −0.0774862
\(716\) 0 0
\(717\) −4.65630 −0.173893
\(718\) 0 0
\(719\) −0.815327 −0.0304066 −0.0152033 0.999884i \(-0.504840\pi\)
−0.0152033 + 0.999884i \(0.504840\pi\)
\(720\) 0 0
\(721\) −11.0735 −0.412398
\(722\) 0 0
\(723\) 7.15077 0.265940
\(724\) 0 0
\(725\) −52.2694 −1.94123
\(726\) 0 0
\(727\) −5.58478 −0.207128 −0.103564 0.994623i \(-0.533025\pi\)
−0.103564 + 0.994623i \(0.533025\pi\)
\(728\) 0 0
\(729\) −2.56578 −0.0950290
\(730\) 0 0
\(731\) −61.2669 −2.26604
\(732\) 0 0
\(733\) 27.7414 1.02465 0.512327 0.858791i \(-0.328784\pi\)
0.512327 + 0.858791i \(0.328784\pi\)
\(734\) 0 0
\(735\) 0.144654 0.00533563
\(736\) 0 0
\(737\) −50.9396 −1.87638
\(738\) 0 0
\(739\) 10.9980 0.404569 0.202285 0.979327i \(-0.435163\pi\)
0.202285 + 0.979327i \(0.435163\pi\)
\(740\) 0 0
\(741\) 12.2837 0.451251
\(742\) 0 0
\(743\) −27.5706 −1.01147 −0.505733 0.862690i \(-0.668778\pi\)
−0.505733 + 0.862690i \(0.668778\pi\)
\(744\) 0 0
\(745\) −3.40812 −0.124864
\(746\) 0 0
\(747\) 11.8529 0.433677
\(748\) 0 0
\(749\) 37.2788 1.36214
\(750\) 0 0
\(751\) −2.39041 −0.0872274 −0.0436137 0.999048i \(-0.513887\pi\)
−0.0436137 + 0.999048i \(0.513887\pi\)
\(752\) 0 0
\(753\) −4.04273 −0.147325
\(754\) 0 0
\(755\) −4.43948 −0.161569
\(756\) 0 0
\(757\) 22.8502 0.830505 0.415253 0.909706i \(-0.363693\pi\)
0.415253 + 0.909706i \(0.363693\pi\)
\(758\) 0 0
\(759\) 0.525080 0.0190592
\(760\) 0 0
\(761\) 35.2537 1.27795 0.638974 0.769229i \(-0.279359\pi\)
0.638974 + 0.769229i \(0.279359\pi\)
\(762\) 0 0
\(763\) −9.06532 −0.328187
\(764\) 0 0
\(765\) 4.00372 0.144755
\(766\) 0 0
\(767\) −26.8535 −0.969625
\(768\) 0 0
\(769\) 14.0283 0.505875 0.252937 0.967483i \(-0.418603\pi\)
0.252937 + 0.967483i \(0.418603\pi\)
\(770\) 0 0
\(771\) 17.4448 0.628259
\(772\) 0 0
\(773\) 2.05297 0.0738401 0.0369200 0.999318i \(-0.488245\pi\)
0.0369200 + 0.999318i \(0.488245\pi\)
\(774\) 0 0
\(775\) 6.31780 0.226942
\(776\) 0 0
\(777\) −3.74261 −0.134265
\(778\) 0 0
\(779\) 31.6262 1.13312
\(780\) 0 0
\(781\) 38.6107 1.38160
\(782\) 0 0
\(783\) −41.9563 −1.49939
\(784\) 0 0
\(785\) −3.53710 −0.126245
\(786\) 0 0
\(787\) 7.63128 0.272026 0.136013 0.990707i \(-0.456571\pi\)
0.136013 + 0.990707i \(0.456571\pi\)
\(788\) 0 0
\(789\) −10.8589 −0.386589
\(790\) 0 0
\(791\) −16.1800 −0.575296
\(792\) 0 0
\(793\) 14.2786 0.507047
\(794\) 0 0
\(795\) −0.101317 −0.00359333
\(796\) 0 0
\(797\) 23.8432 0.844570 0.422285 0.906463i \(-0.361228\pi\)
0.422285 + 0.906463i \(0.361228\pi\)
\(798\) 0 0
\(799\) −71.6696 −2.53549
\(800\) 0 0
\(801\) 4.07897 0.144123
\(802\) 0 0
\(803\) 20.9184 0.738194
\(804\) 0 0
\(805\) 0.0991279 0.00349380
\(806\) 0 0
\(807\) 9.75462 0.343379
\(808\) 0 0
\(809\) 19.9428 0.701152 0.350576 0.936534i \(-0.385986\pi\)
0.350576 + 0.936534i \(0.385986\pi\)
\(810\) 0 0
\(811\) 24.3626 0.855488 0.427744 0.903900i \(-0.359308\pi\)
0.427744 + 0.903900i \(0.359308\pi\)
\(812\) 0 0
\(813\) −4.15639 −0.145771
\(814\) 0 0
\(815\) −2.67272 −0.0936212
\(816\) 0 0
\(817\) −63.6465 −2.22671
\(818\) 0 0
\(819\) 13.8539 0.484095
\(820\) 0 0
\(821\) −15.6976 −0.547850 −0.273925 0.961751i \(-0.588322\pi\)
−0.273925 + 0.961751i \(0.588322\pi\)
\(822\) 0 0
\(823\) 7.38747 0.257511 0.128755 0.991676i \(-0.458902\pi\)
0.128755 + 0.991676i \(0.458902\pi\)
\(824\) 0 0
\(825\) −14.5951 −0.508135
\(826\) 0 0
\(827\) −11.5262 −0.400806 −0.200403 0.979714i \(-0.564225\pi\)
−0.200403 + 0.979714i \(0.564225\pi\)
\(828\) 0 0
\(829\) −17.7336 −0.615914 −0.307957 0.951400i \(-0.599645\pi\)
−0.307957 + 0.951400i \(0.599645\pi\)
\(830\) 0 0
\(831\) 8.78169 0.304634
\(832\) 0 0
\(833\) −6.36516 −0.220540
\(834\) 0 0
\(835\) −1.21107 −0.0419109
\(836\) 0 0
\(837\) 5.07126 0.175288
\(838\) 0 0
\(839\) 28.6447 0.988924 0.494462 0.869199i \(-0.335365\pi\)
0.494462 + 0.869199i \(0.335365\pi\)
\(840\) 0 0
\(841\) 82.5332 2.84597
\(842\) 0 0
\(843\) −4.51332 −0.155447
\(844\) 0 0
\(845\) 1.77138 0.0609374
\(846\) 0 0
\(847\) −13.6115 −0.467695
\(848\) 0 0
\(849\) −9.40041 −0.322621
\(850\) 0 0
\(851\) 0.371266 0.0127269
\(852\) 0 0
\(853\) 41.6536 1.42619 0.713097 0.701066i \(-0.247292\pi\)
0.713097 + 0.701066i \(0.247292\pi\)
\(854\) 0 0
\(855\) 4.15922 0.142242
\(856\) 0 0
\(857\) −9.05282 −0.309238 −0.154619 0.987974i \(-0.549415\pi\)
−0.154619 + 0.987974i \(0.549415\pi\)
\(858\) 0 0
\(859\) −9.47579 −0.323310 −0.161655 0.986847i \(-0.551683\pi\)
−0.161655 + 0.986847i \(0.551683\pi\)
\(860\) 0 0
\(861\) −7.59924 −0.258981
\(862\) 0 0
\(863\) 34.6314 1.17887 0.589434 0.807817i \(-0.299351\pi\)
0.589434 + 0.807817i \(0.299351\pi\)
\(864\) 0 0
\(865\) 4.19633 0.142679
\(866\) 0 0
\(867\) 25.1939 0.855630
\(868\) 0 0
\(869\) 66.5985 2.25920
\(870\) 0 0
\(871\) −28.4048 −0.962461
\(872\) 0 0
\(873\) −8.27007 −0.279899
\(874\) 0 0
\(875\) −5.53892 −0.187250
\(876\) 0 0
\(877\) 15.5441 0.524886 0.262443 0.964947i \(-0.415472\pi\)
0.262443 + 0.964947i \(0.415472\pi\)
\(878\) 0 0
\(879\) 10.4156 0.351308
\(880\) 0 0
\(881\) 52.4905 1.76845 0.884224 0.467063i \(-0.154688\pi\)
0.884224 + 0.467063i \(0.154688\pi\)
\(882\) 0 0
\(883\) 32.8989 1.10713 0.553567 0.832804i \(-0.313266\pi\)
0.553567 + 0.832804i \(0.313266\pi\)
\(884\) 0 0
\(885\) 1.93716 0.0651168
\(886\) 0 0
\(887\) 40.9458 1.37483 0.687413 0.726267i \(-0.258746\pi\)
0.687413 + 0.726267i \(0.258746\pi\)
\(888\) 0 0
\(889\) −37.2145 −1.24814
\(890\) 0 0
\(891\) 18.4261 0.617298
\(892\) 0 0
\(893\) −74.4533 −2.49148
\(894\) 0 0
\(895\) −5.09395 −0.170272
\(896\) 0 0
\(897\) 0.292794 0.00977611
\(898\) 0 0
\(899\) −13.4810 −0.449617
\(900\) 0 0
\(901\) 4.45822 0.148525
\(902\) 0 0
\(903\) 15.2932 0.508925
\(904\) 0 0
\(905\) −2.72415 −0.0905539
\(906\) 0 0
\(907\) 22.3371 0.741692 0.370846 0.928694i \(-0.379068\pi\)
0.370846 + 0.928694i \(0.379068\pi\)
\(908\) 0 0
\(909\) 31.3604 1.04016
\(910\) 0 0
\(911\) −15.9284 −0.527732 −0.263866 0.964559i \(-0.584998\pi\)
−0.263866 + 0.964559i \(0.584998\pi\)
\(912\) 0 0
\(913\) −19.4708 −0.644389
\(914\) 0 0
\(915\) −1.03003 −0.0340516
\(916\) 0 0
\(917\) 23.6741 0.781788
\(918\) 0 0
\(919\) 40.6296 1.34025 0.670124 0.742249i \(-0.266241\pi\)
0.670124 + 0.742249i \(0.266241\pi\)
\(920\) 0 0
\(921\) 20.8632 0.687465
\(922\) 0 0
\(923\) 21.5300 0.708669
\(924\) 0 0
\(925\) −10.3197 −0.339309
\(926\) 0 0
\(927\) −11.0748 −0.363743
\(928\) 0 0
\(929\) −38.1089 −1.25031 −0.625155 0.780500i \(-0.714964\pi\)
−0.625155 + 0.780500i \(0.714964\pi\)
\(930\) 0 0
\(931\) −6.61238 −0.216712
\(932\) 0 0
\(933\) 21.7527 0.712152
\(934\) 0 0
\(935\) −6.57689 −0.215087
\(936\) 0 0
\(937\) 20.9882 0.685653 0.342827 0.939399i \(-0.388616\pi\)
0.342827 + 0.939399i \(0.388616\pi\)
\(938\) 0 0
\(939\) −9.90106 −0.323109
\(940\) 0 0
\(941\) 0.271913 0.00886412 0.00443206 0.999990i \(-0.498589\pi\)
0.00443206 + 0.999990i \(0.498589\pi\)
\(942\) 0 0
\(943\) 0.753843 0.0245485
\(944\) 0 0
\(945\) −2.21170 −0.0719467
\(946\) 0 0
\(947\) −18.9489 −0.615756 −0.307878 0.951426i \(-0.599619\pi\)
−0.307878 + 0.951426i \(0.599619\pi\)
\(948\) 0 0
\(949\) 11.6645 0.378645
\(950\) 0 0
\(951\) 9.39519 0.304660
\(952\) 0 0
\(953\) −2.67357 −0.0866055 −0.0433027 0.999062i \(-0.513788\pi\)
−0.0433027 + 0.999062i \(0.513788\pi\)
\(954\) 0 0
\(955\) −0.0375445 −0.00121491
\(956\) 0 0
\(957\) 31.1432 1.00672
\(958\) 0 0
\(959\) −5.32327 −0.171897
\(960\) 0 0
\(961\) −29.3705 −0.947437
\(962\) 0 0
\(963\) 37.2832 1.20143
\(964\) 0 0
\(965\) 3.72054 0.119769
\(966\) 0 0
\(967\) −20.1196 −0.647004 −0.323502 0.946227i \(-0.604860\pi\)
−0.323502 + 0.946227i \(0.604860\pi\)
\(968\) 0 0
\(969\) 38.9916 1.25259
\(970\) 0 0
\(971\) −15.9577 −0.512106 −0.256053 0.966663i \(-0.582422\pi\)
−0.256053 + 0.966663i \(0.582422\pi\)
\(972\) 0 0
\(973\) 13.8998 0.445609
\(974\) 0 0
\(975\) −8.13848 −0.260640
\(976\) 0 0
\(977\) 42.1759 1.34933 0.674663 0.738126i \(-0.264289\pi\)
0.674663 + 0.738126i \(0.264289\pi\)
\(978\) 0 0
\(979\) −6.70051 −0.214149
\(980\) 0 0
\(981\) −9.06639 −0.289467
\(982\) 0 0
\(983\) 31.8772 1.01673 0.508363 0.861143i \(-0.330251\pi\)
0.508363 + 0.861143i \(0.330251\pi\)
\(984\) 0 0
\(985\) −2.21143 −0.0704619
\(986\) 0 0
\(987\) 17.8899 0.569441
\(988\) 0 0
\(989\) −1.51708 −0.0482404
\(990\) 0 0
\(991\) −28.4135 −0.902584 −0.451292 0.892376i \(-0.649037\pi\)
−0.451292 + 0.892376i \(0.649037\pi\)
\(992\) 0 0
\(993\) −6.15792 −0.195416
\(994\) 0 0
\(995\) 2.60459 0.0825712
\(996\) 0 0
\(997\) −38.9058 −1.23216 −0.616079 0.787684i \(-0.711280\pi\)
−0.616079 + 0.787684i \(0.711280\pi\)
\(998\) 0 0
\(999\) −8.28355 −0.262080
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 9904.2.a.n.1.18 30
4.3 odd 2 619.2.a.b.1.8 30
12.11 even 2 5571.2.a.g.1.23 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
619.2.a.b.1.8 30 4.3 odd 2
5571.2.a.g.1.23 30 12.11 even 2
9904.2.a.n.1.18 30 1.1 even 1 trivial