Properties

Label 6012.2.a.d.1.1
Level $6012$
Weight $2$
Character 6012.1
Self dual yes
Analytic conductor $48.006$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.826865.1
Defining polynomial: \(x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 668)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.873948\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{5} -1.42676 q^{7} +O(q^{10})\) \(q-2.00000 q^{5} -1.42676 q^{7} -2.19055 q^{11} +1.74790 q^{13} -3.26510 q^{17} +5.89213 q^{19} -6.12900 q^{23} -1.00000 q^{25} +0.321133 q^{29} +1.75308 q^{31} +2.85353 q^{35} -2.47243 q^{37} +5.98963 q^{41} -3.49579 q^{43} -2.39634 q^{47} -4.96434 q^{49} +1.51720 q^{53} +4.38110 q^{55} -5.65526 q^{59} -4.51463 q^{61} -3.49579 q^{65} -9.61442 q^{67} +6.66956 q^{71} +2.86390 q^{73} +3.12540 q^{77} +10.4997 q^{79} +7.24369 q^{83} +6.53020 q^{85} +0.256634 q^{89} -2.49384 q^{91} -11.7843 q^{95} +5.83544 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 10q^{5} + 9q^{7} + O(q^{10}) \) \( 5q - 10q^{5} + 9q^{7} - 5q^{11} - 4q^{13} + 2q^{17} + 5q^{19} - 6q^{23} - 5q^{25} + 5q^{29} + 9q^{31} - 18q^{35} + 8q^{37} + 4q^{41} + 8q^{43} - 13q^{47} + 14q^{49} + 2q^{53} + 10q^{55} - 4q^{59} + 11q^{61} + 8q^{65} + 28q^{67} - 2q^{71} + 8q^{73} + 12q^{77} - 10q^{79} - 2q^{83} - 4q^{85} + 17q^{89} - 12q^{91} - 10q^{95} - 27q^{97} + O(q^{100}) \)

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 0
\(4\) 0 0
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 0 0
\(7\) −1.42676 −0.539266 −0.269633 0.962963i \(-0.586902\pi\)
−0.269633 + 0.962963i \(0.586902\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.19055 −0.660476 −0.330238 0.943898i \(-0.607129\pi\)
−0.330238 + 0.943898i \(0.607129\pi\)
\(12\) 0 0
\(13\) 1.74790 0.484779 0.242390 0.970179i \(-0.422069\pi\)
0.242390 + 0.970179i \(0.422069\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.26510 −0.791903 −0.395951 0.918271i \(-0.629585\pi\)
−0.395951 + 0.918271i \(0.629585\pi\)
\(18\) 0 0
\(19\) 5.89213 1.35175 0.675874 0.737018i \(-0.263767\pi\)
0.675874 + 0.737018i \(0.263767\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.12900 −1.27798 −0.638992 0.769213i \(-0.720648\pi\)
−0.638992 + 0.769213i \(0.720648\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.321133 0.0596329 0.0298164 0.999555i \(-0.490508\pi\)
0.0298164 + 0.999555i \(0.490508\pi\)
\(30\) 0 0
\(31\) 1.75308 0.314863 0.157431 0.987530i \(-0.449679\pi\)
0.157431 + 0.987530i \(0.449679\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.85353 0.482334
\(36\) 0 0
\(37\) −2.47243 −0.406465 −0.203232 0.979131i \(-0.565145\pi\)
−0.203232 + 0.979131i \(0.565145\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.98963 0.935423 0.467712 0.883881i \(-0.345079\pi\)
0.467712 + 0.883881i \(0.345079\pi\)
\(42\) 0 0
\(43\) −3.49579 −0.533104 −0.266552 0.963821i \(-0.585884\pi\)
−0.266552 + 0.963821i \(0.585884\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.39634 −0.349541 −0.174771 0.984609i \(-0.555918\pi\)
−0.174771 + 0.984609i \(0.555918\pi\)
\(48\) 0 0
\(49\) −4.96434 −0.709192
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.51720 0.208404 0.104202 0.994556i \(-0.466771\pi\)
0.104202 + 0.994556i \(0.466771\pi\)
\(54\) 0 0
\(55\) 4.38110 0.590747
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.65526 −0.736252 −0.368126 0.929776i \(-0.620001\pi\)
−0.368126 + 0.929776i \(0.620001\pi\)
\(60\) 0 0
\(61\) −4.51463 −0.578039 −0.289019 0.957323i \(-0.593329\pi\)
−0.289019 + 0.957323i \(0.593329\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.49579 −0.433600
\(66\) 0 0
\(67\) −9.61442 −1.17459 −0.587294 0.809374i \(-0.699807\pi\)
−0.587294 + 0.809374i \(0.699807\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.66956 0.791532 0.395766 0.918351i \(-0.370479\pi\)
0.395766 + 0.918351i \(0.370479\pi\)
\(72\) 0 0
\(73\) 2.86390 0.335194 0.167597 0.985856i \(-0.446399\pi\)
0.167597 + 0.985856i \(0.446399\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.12540 0.356172
\(78\) 0 0
\(79\) 10.4997 1.18131 0.590656 0.806924i \(-0.298869\pi\)
0.590656 + 0.806924i \(0.298869\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.24369 0.795098 0.397549 0.917581i \(-0.369861\pi\)
0.397549 + 0.917581i \(0.369861\pi\)
\(84\) 0 0
\(85\) 6.53020 0.708299
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.256634 0.0272032 0.0136016 0.999907i \(-0.495670\pi\)
0.0136016 + 0.999907i \(0.495670\pi\)
\(90\) 0 0
\(91\) −2.49384 −0.261425
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −11.7843 −1.20904
\(96\) 0 0
\(97\) 5.83544 0.592499 0.296250 0.955111i \(-0.404264\pi\)
0.296250 + 0.955111i \(0.404264\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.58843 0.556069 0.278035 0.960571i \(-0.410317\pi\)
0.278035 + 0.960571i \(0.410317\pi\)
\(102\) 0 0
\(103\) 6.17359 0.608302 0.304151 0.952624i \(-0.401627\pi\)
0.304151 + 0.952624i \(0.401627\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.9570 1.15592 0.577962 0.816064i \(-0.303848\pi\)
0.577962 + 0.816064i \(0.303848\pi\)
\(108\) 0 0
\(109\) −15.1784 −1.45382 −0.726911 0.686731i \(-0.759045\pi\)
−0.726911 + 0.686731i \(0.759045\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.710405 0.0668293 0.0334146 0.999442i \(-0.489362\pi\)
0.0334146 + 0.999442i \(0.489362\pi\)
\(114\) 0 0
\(115\) 12.2580 1.14306
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.65853 0.427046
\(120\) 0 0
\(121\) −6.20149 −0.563772
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) 11.5165 1.02192 0.510962 0.859603i \(-0.329289\pi\)
0.510962 + 0.859603i \(0.329289\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −8.02599 −0.701234 −0.350617 0.936519i \(-0.614028\pi\)
−0.350617 + 0.936519i \(0.614028\pi\)
\(132\) 0 0
\(133\) −8.40668 −0.728951
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.6656 1.33840 0.669201 0.743081i \(-0.266636\pi\)
0.669201 + 0.743081i \(0.266636\pi\)
\(138\) 0 0
\(139\) −2.22163 −0.188436 −0.0942182 0.995552i \(-0.530035\pi\)
−0.0942182 + 0.995552i \(0.530035\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.82886 −0.320185
\(144\) 0 0
\(145\) −0.642266 −0.0533373
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.02599 −0.493668 −0.246834 0.969058i \(-0.579390\pi\)
−0.246834 + 0.969058i \(0.579390\pi\)
\(150\) 0 0
\(151\) −10.9684 −0.892596 −0.446298 0.894884i \(-0.647258\pi\)
−0.446298 + 0.894884i \(0.647258\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.50616 −0.281622
\(156\) 0 0
\(157\) 20.0474 1.59996 0.799980 0.600027i \(-0.204843\pi\)
0.799980 + 0.600027i \(0.204843\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 8.74463 0.689174
\(162\) 0 0
\(163\) 5.21770 0.408682 0.204341 0.978900i \(-0.434495\pi\)
0.204341 + 0.978900i \(0.434495\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −9.94486 −0.764989
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 21.5165 1.63587 0.817935 0.575311i \(-0.195119\pi\)
0.817935 + 0.575311i \(0.195119\pi\)
\(174\) 0 0
\(175\) 1.42676 0.107853
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −10.1501 −0.758656 −0.379328 0.925262i \(-0.623845\pi\)
−0.379328 + 0.925262i \(0.623845\pi\)
\(180\) 0 0
\(181\) −3.64003 −0.270561 −0.135281 0.990807i \(-0.543194\pi\)
−0.135281 + 0.990807i \(0.543194\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.94486 0.363553
\(186\) 0 0
\(187\) 7.15236 0.523033
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 17.4861 1.26525 0.632626 0.774457i \(-0.281977\pi\)
0.632626 + 0.774457i \(0.281977\pi\)
\(192\) 0 0
\(193\) 4.75052 0.341950 0.170975 0.985275i \(-0.445308\pi\)
0.170975 + 0.985275i \(0.445308\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.67780 0.190785 0.0953927 0.995440i \(-0.469589\pi\)
0.0953927 + 0.995440i \(0.469589\pi\)
\(198\) 0 0
\(199\) 25.6656 1.81939 0.909693 0.415281i \(-0.136317\pi\)
0.909693 + 0.415281i \(0.136317\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.458181 −0.0321580
\(204\) 0 0
\(205\) −11.9793 −0.836668
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −12.9070 −0.892796
\(210\) 0 0
\(211\) 9.73234 0.670002 0.335001 0.942218i \(-0.391263\pi\)
0.335001 + 0.942218i \(0.391263\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.99159 0.476822
\(216\) 0 0
\(217\) −2.50123 −0.169795
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −5.70706 −0.383898
\(222\) 0 0
\(223\) 21.5995 1.44641 0.723205 0.690633i \(-0.242668\pi\)
0.723205 + 0.690633i \(0.242668\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.0401 0.931875 0.465938 0.884818i \(-0.345717\pi\)
0.465938 + 0.884818i \(0.345717\pi\)
\(228\) 0 0
\(229\) 5.77020 0.381305 0.190653 0.981658i \(-0.438940\pi\)
0.190653 + 0.981658i \(0.438940\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.4705 1.27556 0.637778 0.770221i \(-0.279854\pi\)
0.637778 + 0.770221i \(0.279854\pi\)
\(234\) 0 0
\(235\) 4.79267 0.312639
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.7014 0.950954 0.475477 0.879728i \(-0.342275\pi\)
0.475477 + 0.879728i \(0.342275\pi\)
\(240\) 0 0
\(241\) −21.6813 −1.39661 −0.698306 0.715799i \(-0.746063\pi\)
−0.698306 + 0.715799i \(0.746063\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9.92869 0.634321
\(246\) 0 0
\(247\) 10.2988 0.655299
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.71130 0.423613 0.211807 0.977312i \(-0.432065\pi\)
0.211807 + 0.977312i \(0.432065\pi\)
\(252\) 0 0
\(253\) 13.4259 0.844077
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 26.1000 1.62807 0.814037 0.580813i \(-0.197265\pi\)
0.814037 + 0.580813i \(0.197265\pi\)
\(258\) 0 0
\(259\) 3.52757 0.219193
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −16.1595 −0.996439 −0.498219 0.867051i \(-0.666013\pi\)
−0.498219 + 0.867051i \(0.666013\pi\)
\(264\) 0 0
\(265\) −3.03440 −0.186402
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.9418 −0.667131 −0.333566 0.942727i \(-0.608252\pi\)
−0.333566 + 0.942727i \(0.608252\pi\)
\(270\) 0 0
\(271\) 9.49579 0.576828 0.288414 0.957506i \(-0.406872\pi\)
0.288414 + 0.957506i \(0.406872\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.19055 0.132095
\(276\) 0 0
\(277\) 1.86063 0.111795 0.0558973 0.998437i \(-0.482198\pi\)
0.0558973 + 0.998437i \(0.482198\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.01042 −0.239242 −0.119621 0.992820i \(-0.538168\pi\)
−0.119621 + 0.992820i \(0.538168\pi\)
\(282\) 0 0
\(283\) −7.71234 −0.458451 −0.229225 0.973373i \(-0.573619\pi\)
−0.229225 + 0.973373i \(0.573619\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.54579 −0.504442
\(288\) 0 0
\(289\) −6.33913 −0.372890
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.05585 −0.529048 −0.264524 0.964379i \(-0.585215\pi\)
−0.264524 + 0.964379i \(0.585215\pi\)
\(294\) 0 0
\(295\) 11.3105 0.658524
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.7129 −0.619540
\(300\) 0 0
\(301\) 4.98767 0.287485
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.02926 0.517014
\(306\) 0 0
\(307\) 12.1632 0.694192 0.347096 0.937830i \(-0.387168\pi\)
0.347096 + 0.937830i \(0.387168\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.4952 −1.38900 −0.694499 0.719494i \(-0.744374\pi\)
−0.694499 + 0.719494i \(0.744374\pi\)
\(312\) 0 0
\(313\) 22.5593 1.27513 0.637563 0.770398i \(-0.279943\pi\)
0.637563 + 0.770398i \(0.279943\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.9546 −0.783770 −0.391885 0.920014i \(-0.628177\pi\)
−0.391885 + 0.920014i \(0.628177\pi\)
\(318\) 0 0
\(319\) −0.703457 −0.0393861
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −19.2384 −1.07045
\(324\) 0 0
\(325\) −1.74790 −0.0969559
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 3.41901 0.188496
\(330\) 0 0
\(331\) −21.5826 −1.18629 −0.593145 0.805096i \(-0.702114\pi\)
−0.593145 + 0.805096i \(0.702114\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 19.2288 1.05058
\(336\) 0 0
\(337\) 16.7494 0.912399 0.456199 0.889878i \(-0.349210\pi\)
0.456199 + 0.889878i \(0.349210\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.84021 −0.207959
\(342\) 0 0
\(343\) 17.0703 0.921709
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 12.7273 0.683239 0.341620 0.939838i \(-0.389025\pi\)
0.341620 + 0.939838i \(0.389025\pi\)
\(348\) 0 0
\(349\) 21.8665 1.17049 0.585244 0.810857i \(-0.300999\pi\)
0.585244 + 0.810857i \(0.300999\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −27.7352 −1.47620 −0.738099 0.674692i \(-0.764276\pi\)
−0.738099 + 0.674692i \(0.764276\pi\)
\(354\) 0 0
\(355\) −13.3391 −0.707967
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.30402 0.438269 0.219135 0.975695i \(-0.429677\pi\)
0.219135 + 0.975695i \(0.429677\pi\)
\(360\) 0 0
\(361\) 15.7172 0.827220
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −5.72780 −0.299807
\(366\) 0 0
\(367\) 12.4528 0.650031 0.325015 0.945709i \(-0.394631\pi\)
0.325015 + 0.945709i \(0.394631\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.16469 −0.112385
\(372\) 0 0
\(373\) 17.6189 0.912272 0.456136 0.889910i \(-0.349233\pi\)
0.456136 + 0.889910i \(0.349233\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.561307 0.0289088
\(378\) 0 0
\(379\) 12.1749 0.625383 0.312691 0.949855i \(-0.398769\pi\)
0.312691 + 0.949855i \(0.398769\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.9672 −0.866981 −0.433491 0.901158i \(-0.642718\pi\)
−0.433491 + 0.901158i \(0.642718\pi\)
\(384\) 0 0
\(385\) −6.25080 −0.318570
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −14.9358 −0.757275 −0.378637 0.925545i \(-0.623607\pi\)
−0.378637 + 0.925545i \(0.623607\pi\)
\(390\) 0 0
\(391\) 20.0118 1.01204
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −20.9995 −1.05660
\(396\) 0 0
\(397\) 27.3638 1.37335 0.686674 0.726966i \(-0.259070\pi\)
0.686674 + 0.726966i \(0.259070\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −16.3411 −0.816035 −0.408017 0.912974i \(-0.633780\pi\)
−0.408017 + 0.912974i \(0.633780\pi\)
\(402\) 0 0
\(403\) 3.06421 0.152639
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.41598 0.268460
\(408\) 0 0
\(409\) −19.2236 −0.950544 −0.475272 0.879839i \(-0.657650\pi\)
−0.475272 + 0.879839i \(0.657650\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.06872 0.397036
\(414\) 0 0
\(415\) −14.4874 −0.711158
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.15541 −0.0564456 −0.0282228 0.999602i \(-0.508985\pi\)
−0.0282228 + 0.999602i \(0.508985\pi\)
\(420\) 0 0
\(421\) 4.80899 0.234376 0.117188 0.993110i \(-0.462612\pi\)
0.117188 + 0.993110i \(0.462612\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.26510 0.158381
\(426\) 0 0
\(427\) 6.44131 0.311717
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 34.3708 1.65558 0.827791 0.561036i \(-0.189597\pi\)
0.827791 + 0.561036i \(0.189597\pi\)
\(432\) 0 0
\(433\) −20.0626 −0.964145 −0.482072 0.876131i \(-0.660116\pi\)
−0.482072 + 0.876131i \(0.660116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −36.1128 −1.72751
\(438\) 0 0
\(439\) 1.90270 0.0908108 0.0454054 0.998969i \(-0.485542\pi\)
0.0454054 + 0.998969i \(0.485542\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.8782 0.659373 0.329687 0.944090i \(-0.393057\pi\)
0.329687 + 0.944090i \(0.393057\pi\)
\(444\) 0 0
\(445\) −0.513269 −0.0243313
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −14.6316 −0.690509 −0.345254 0.938509i \(-0.612207\pi\)
−0.345254 + 0.938509i \(0.612207\pi\)
\(450\) 0 0
\(451\) −13.1206 −0.617824
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.98767 0.233826
\(456\) 0 0
\(457\) −15.1270 −0.707613 −0.353807 0.935319i \(-0.615113\pi\)
−0.353807 + 0.935319i \(0.615113\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.617968 0.0287816 0.0143908 0.999896i \(-0.495419\pi\)
0.0143908 + 0.999896i \(0.495419\pi\)
\(462\) 0 0
\(463\) −6.12321 −0.284570 −0.142285 0.989826i \(-0.545445\pi\)
−0.142285 + 0.989826i \(0.545445\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 22.0319 1.01952 0.509758 0.860318i \(-0.329735\pi\)
0.509758 + 0.860318i \(0.329735\pi\)
\(468\) 0 0
\(469\) 13.7175 0.633416
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.65771 0.352102
\(474\) 0 0
\(475\) −5.89213 −0.270349
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.88989 0.314807 0.157404 0.987534i \(-0.449688\pi\)
0.157404 + 0.987534i \(0.449688\pi\)
\(480\) 0 0
\(481\) −4.32155 −0.197046
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −11.6709 −0.529948
\(486\) 0 0
\(487\) −20.9486 −0.949272 −0.474636 0.880182i \(-0.657420\pi\)
−0.474636 + 0.880182i \(0.657420\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −13.3184 −0.601051 −0.300525 0.953774i \(-0.597162\pi\)
−0.300525 + 0.953774i \(0.597162\pi\)
\(492\) 0 0
\(493\) −1.04853 −0.0472234
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.51589 −0.426846
\(498\) 0 0
\(499\) 15.2496 0.682665 0.341333 0.939943i \(-0.389122\pi\)
0.341333 + 0.939943i \(0.389122\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 26.7387 1.19222 0.596110 0.802903i \(-0.296712\pi\)
0.596110 + 0.802903i \(0.296712\pi\)
\(504\) 0 0
\(505\) −11.1769 −0.497364
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.156638 −0.00694286 −0.00347143 0.999994i \(-0.501105\pi\)
−0.00347143 + 0.999994i \(0.501105\pi\)
\(510\) 0 0
\(511\) −4.08611 −0.180759
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.3472 −0.544082
\(516\) 0 0
\(517\) 5.24929 0.230864
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 32.1200 1.40720 0.703602 0.710594i \(-0.251574\pi\)
0.703602 + 0.710594i \(0.251574\pi\)
\(522\) 0 0
\(523\) 4.73691 0.207131 0.103565 0.994623i \(-0.466975\pi\)
0.103565 + 0.994623i \(0.466975\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.72399 −0.249341
\(528\) 0 0
\(529\) 14.5646 0.633244
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.4693 0.453474
\(534\) 0 0
\(535\) −23.9139 −1.03389
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.8746 0.468404
\(540\) 0 0
\(541\) 15.3824 0.661342 0.330671 0.943746i \(-0.392725\pi\)
0.330671 + 0.943746i \(0.392725\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 30.3567 1.30034
\(546\) 0 0
\(547\) 19.2682 0.823848 0.411924 0.911218i \(-0.364857\pi\)
0.411924 + 0.911218i \(0.364857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.89216 0.0806086
\(552\) 0 0
\(553\) −14.9806 −0.637041
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 10.0313 0.425039 0.212519 0.977157i \(-0.431833\pi\)
0.212519 + 0.977157i \(0.431833\pi\)
\(558\) 0 0
\(559\) −6.11029 −0.258438
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8.61733 0.363177 0.181589 0.983375i \(-0.441876\pi\)
0.181589 + 0.983375i \(0.441876\pi\)
\(564\) 0 0
\(565\) −1.42081 −0.0597739
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22.8782 0.959105 0.479552 0.877513i \(-0.340799\pi\)
0.479552 + 0.877513i \(0.340799\pi\)
\(570\) 0 0
\(571\) −36.9981 −1.54832 −0.774162 0.632987i \(-0.781829\pi\)
−0.774162 + 0.632987i \(0.781829\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.12900 0.255597
\(576\) 0 0
\(577\) 9.42378 0.392317 0.196158 0.980572i \(-0.437153\pi\)
0.196158 + 0.980572i \(0.437153\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −10.3350 −0.428770
\(582\) 0 0
\(583\) −3.32351 −0.137646
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.06497 0.250328 0.125164 0.992136i \(-0.460054\pi\)
0.125164 + 0.992136i \(0.460054\pi\)
\(588\) 0 0
\(589\) 10.3294 0.425615
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −30.0669 −1.23470 −0.617351 0.786688i \(-0.711794\pi\)
−0.617351 + 0.786688i \(0.711794\pi\)
\(594\) 0 0
\(595\) −9.31705 −0.381962
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.74168 0.357175 0.178588 0.983924i \(-0.442847\pi\)
0.178588 + 0.983924i \(0.442847\pi\)
\(600\) 0 0
\(601\) −5.47200 −0.223208 −0.111604 0.993753i \(-0.535599\pi\)
−0.111604 + 0.993753i \(0.535599\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 12.4030 0.504253
\(606\) 0 0
\(607\) 8.28118 0.336123 0.168061 0.985777i \(-0.446249\pi\)
0.168061 + 0.985777i \(0.446249\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.18855 −0.169450
\(612\) 0 0
\(613\) 46.5063 1.87837 0.939186 0.343408i \(-0.111581\pi\)
0.939186 + 0.343408i \(0.111581\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −34.1883 −1.37637 −0.688185 0.725535i \(-0.741592\pi\)
−0.688185 + 0.725535i \(0.741592\pi\)
\(618\) 0 0
\(619\) −23.3216 −0.937373 −0.468686 0.883365i \(-0.655273\pi\)
−0.468686 + 0.883365i \(0.655273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.366157 −0.0146698
\(624\) 0 0
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8.07272 0.321881
\(630\) 0 0
\(631\) −29.0863 −1.15791 −0.578953 0.815361i \(-0.696538\pi\)
−0.578953 + 0.815361i \(0.696538\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −23.0330 −0.914037
\(636\) 0 0
\(637\) −8.67716 −0.343802
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −31.0603 −1.22681 −0.613404 0.789769i \(-0.710200\pi\)
−0.613404 + 0.789769i \(0.710200\pi\)
\(642\) 0 0
\(643\) 14.9145 0.588169 0.294085 0.955779i \(-0.404985\pi\)
0.294085 + 0.955779i \(0.404985\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28.9951 −1.13991 −0.569957 0.821675i \(-0.693040\pi\)
−0.569957 + 0.821675i \(0.693040\pi\)
\(648\) 0 0
\(649\) 12.3881 0.486277
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.42152 −0.290426 −0.145213 0.989400i \(-0.546387\pi\)
−0.145213 + 0.989400i \(0.546387\pi\)
\(654\) 0 0
\(655\) 16.0520 0.627203
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.40447 0.0547102 0.0273551 0.999626i \(-0.491292\pi\)
0.0273551 + 0.999626i \(0.491292\pi\)
\(660\) 0 0
\(661\) 13.1593 0.511837 0.255919 0.966698i \(-0.417622\pi\)
0.255919 + 0.966698i \(0.417622\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 16.8134 0.651994
\(666\) 0 0
\(667\) −1.96822 −0.0762099
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.88952 0.381781
\(672\) 0 0
\(673\) −24.1775 −0.931974 −0.465987 0.884791i \(-0.654301\pi\)
−0.465987 + 0.884791i \(0.654301\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.6811 −0.525806 −0.262903 0.964822i \(-0.584680\pi\)
−0.262903 + 0.964822i \(0.584680\pi\)
\(678\) 0 0
\(679\) −8.32580 −0.319515
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 14.3047 0.547355 0.273678 0.961822i \(-0.411760\pi\)
0.273678 + 0.961822i \(0.411760\pi\)
\(684\) 0 0
\(685\) −31.3312 −1.19710
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.65191 0.101030
\(690\) 0 0
\(691\) 27.8109 1.05798 0.528989 0.848629i \(-0.322571\pi\)
0.528989 + 0.848629i \(0.322571\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.44326 0.168543
\(696\) 0 0
\(697\) −19.5567 −0.740764
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10.7440 −0.405796 −0.202898 0.979200i \(-0.565036\pi\)
−0.202898 + 0.979200i \(0.565036\pi\)
\(702\) 0 0
\(703\) −14.5679 −0.549437
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.97337 −0.299869
\(708\) 0 0
\(709\) −39.8043 −1.49488 −0.747440 0.664329i \(-0.768717\pi\)
−0.747440 + 0.664329i \(0.768717\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.7446 −0.402390
\(714\) 0 0
\(715\) 7.65771 0.286382
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −23.3327 −0.870162 −0.435081 0.900391i \(-0.643280\pi\)
−0.435081 + 0.900391i \(0.643280\pi\)
\(720\) 0 0
\(721\) −8.80826 −0.328037
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.321133 −0.0119266
\(726\) 0 0
\(727\) −21.2593 −0.788464 −0.394232 0.919011i \(-0.628989\pi\)
−0.394232 + 0.919011i \(0.628989\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 11.4141 0.422166
\(732\) 0 0
\(733\) −40.8733 −1.50969 −0.754846 0.655902i \(-0.772288\pi\)
−0.754846 + 0.655902i \(0.772288\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.0609 0.775787
\(738\) 0 0
\(739\) 38.5912 1.41960 0.709799 0.704404i \(-0.248786\pi\)
0.709799 + 0.704404i \(0.248786\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.3330 −0.672572 −0.336286 0.941760i \(-0.609171\pi\)
−0.336286 + 0.941760i \(0.609171\pi\)
\(744\) 0 0
\(745\) 12.0520 0.441551
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −17.0598 −0.623350
\(750\) 0 0
\(751\) −41.3572 −1.50915 −0.754573 0.656216i \(-0.772156\pi\)
−0.754573 + 0.656216i \(0.772156\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 21.9368 0.798362
\(756\) 0 0
\(757\) 14.2655 0.518490 0.259245 0.965812i \(-0.416526\pi\)
0.259245 + 0.965812i \(0.416526\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 41.8123 1.51569 0.757847 0.652432i \(-0.226251\pi\)
0.757847 + 0.652432i \(0.226251\pi\)
\(762\) 0 0
\(763\) 21.6559 0.783997
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.88481 −0.356920
\(768\) 0 0
\(769\) 3.27230 0.118002 0.0590010 0.998258i \(-0.481208\pi\)
0.0590010 + 0.998258i \(0.481208\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −23.3460 −0.839696 −0.419848 0.907594i \(-0.637917\pi\)
−0.419848 + 0.907594i \(0.637917\pi\)
\(774\) 0 0
\(775\) −1.75308 −0.0629726
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 35.2917 1.26446
\(780\) 0 0
\(781\) −14.6100 −0.522787
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −40.0949 −1.43105
\(786\) 0 0
\(787\) 44.5309 1.58736 0.793678 0.608338i \(-0.208163\pi\)
0.793678 + 0.608338i \(0.208163\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.01358 −0.0360388
\(792\) 0 0
\(793\) −7.89110 −0.280221
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.60786 −0.269484 −0.134742 0.990881i \(-0.543021\pi\)
−0.134742 + 0.990881i \(0.543021\pi\)
\(798\) 0 0
\(799\) 7.82427 0.276803
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −6.27351 −0.221387
\(804\) 0 0
\(805\) −17.4893 −0.616416
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.40132 −0.260217 −0.130108 0.991500i \(-0.541532\pi\)
−0.130108 + 0.991500i \(0.541532\pi\)
\(810\) 0 0
\(811\) −5.69610 −0.200017 −0.100009 0.994987i \(-0.531887\pi\)
−0.100009 + 0.994987i \(0.531887\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −10.4354 −0.365536
\(816\) 0 0
\(817\) −20.5977 −0.720621
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 45.1962 1.57736 0.788680 0.614804i \(-0.210765\pi\)
0.788680 + 0.614804i \(0.210765\pi\)
\(822\) 0 0
\(823\) 13.9450 0.486093 0.243047 0.970015i \(-0.421853\pi\)
0.243047 + 0.970015i \(0.421853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.90541 −0.101031 −0.0505155 0.998723i \(-0.516086\pi\)
−0.0505155 + 0.998723i \(0.516086\pi\)
\(828\) 0 0
\(829\) 31.2634 1.08582 0.542912 0.839790i \(-0.317322\pi\)
0.542912 + 0.839790i \(0.317322\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 16.2091 0.561611
\(834\) 0 0
\(835\) −2.00000 −0.0692129
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 44.4886 1.53592 0.767958 0.640500i \(-0.221273\pi\)
0.767958 + 0.640500i \(0.221273\pi\)
\(840\) 0 0
\(841\) −28.8969 −0.996444
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 19.8897 0.684227
\(846\) 0 0
\(847\) 8.84806 0.304023
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 15.1535 0.519455
\(852\) 0 0
\(853\) −17.2717 −0.591371 −0.295686 0.955285i \(-0.595548\pi\)
−0.295686 + 0.955285i \(0.595548\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 35.0334 1.19672 0.598359 0.801228i \(-0.295820\pi\)
0.598359 + 0.801228i \(0.295820\pi\)
\(858\) 0 0
\(859\) 38.9649 1.32947 0.664733 0.747081i \(-0.268546\pi\)
0.664733 + 0.747081i \(0.268546\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32.0638 −1.09146 −0.545732 0.837960i \(-0.683748\pi\)
−0.545732 + 0.837960i \(0.683748\pi\)
\(864\) 0 0
\(865\) −43.0330 −1.46317
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −23.0002 −0.780228
\(870\) 0 0
\(871\) −16.8050 −0.569416
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −17.1212 −0.578801
\(876\) 0 0
\(877\) 53.9033 1.82018 0.910092 0.414406i \(-0.136011\pi\)
0.910092 + 0.414406i \(0.136011\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −49.8614 −1.67987 −0.839937 0.542684i \(-0.817408\pi\)
−0.839937 + 0.542684i \(0.817408\pi\)
\(882\) 0 0
\(883\) 12.9835 0.436930 0.218465 0.975845i \(-0.429895\pi\)
0.218465 + 0.975845i \(0.429895\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −11.8245 −0.397027 −0.198513 0.980098i \(-0.563611\pi\)
−0.198513 + 0.980098i \(0.563611\pi\)
\(888\) 0 0
\(889\) −16.4313 −0.551089
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −14.1195 −0.472492
\(894\) 0 0
\(895\) 20.3002 0.678562
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0.562972 0.0187762
\(900\) 0 0
\(901\) −4.95381 −0.165036
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.28005 0.241997
\(906\) 0 0
\(907\) 1.08780 0.0361198 0.0180599 0.999837i \(-0.494251\pi\)
0.0180599 + 0.999837i \(0.494251\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 9.16245 0.303566 0.151783 0.988414i \(-0.451499\pi\)
0.151783 + 0.988414i \(0.451499\pi\)
\(912\) 0 0
\(913\) −15.8677 −0.525143
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.4512 0.378152
\(918\) 0 0
\(919\) −23.2997 −0.768587 −0.384293 0.923211i \(-0.625555\pi\)
−0.384293 + 0.923211i \(0.625555\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 11.6577 0.383718
\(924\) 0 0
\(925\) 2.47243 0.0812929
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −48.9106 −1.60471 −0.802353 0.596850i \(-0.796419\pi\)
−0.802353 + 0.596850i \(0.796419\pi\)
\(930\) 0 0
\(931\) −29.2506 −0.958648
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −14.3047 −0.467815
\(936\) 0 0
\(937\) 29.3682 0.959418 0.479709 0.877428i \(-0.340742\pi\)
0.479709 + 0.877428i \(0.340742\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 33.9716 1.10744 0.553721 0.832702i \(-0.313207\pi\)
0.553721 + 0.832702i \(0.313207\pi\)
\(942\) 0 0
\(943\) −36.7104 −1.19546
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −36.7945 −1.19566 −0.597830 0.801623i \(-0.703970\pi\)
−0.597830 + 0.801623i \(0.703970\pi\)
\(948\) 0 0
\(949\) 5.00580 0.162495
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.19613 0.168319 0.0841596 0.996452i \(-0.473179\pi\)
0.0841596 + 0.996452i \(0.473179\pi\)
\(954\) 0 0
\(955\) −34.9723 −1.13168
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −22.3511 −0.721755
\(960\) 0 0
\(961\) −27.9267 −0.900861
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −9.50105 −0.305849
\(966\) 0 0
\(967\) 49.3421 1.58673 0.793367 0.608743i \(-0.208326\pi\)
0.793367 + 0.608743i \(0.208326\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 43.3773 1.39204 0.696021 0.718021i \(-0.254952\pi\)
0.696021 + 0.718021i \(0.254952\pi\)
\(972\) 0 0
\(973\) 3.16975 0.101617
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −55.2452 −1.76745 −0.883725 0.468006i \(-0.844972\pi\)
−0.883725 + 0.468006i \(0.844972\pi\)
\(978\) 0 0
\(979\) −0.562170 −0.0179670
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 12.0299 0.383694 0.191847 0.981425i \(-0.438552\pi\)
0.191847 + 0.981425i \(0.438552\pi\)
\(984\) 0 0
\(985\) −5.35560 −0.170644
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 21.4257 0.681298
\(990\) 0 0
\(991\) 44.9737 1.42864 0.714318 0.699822i \(-0.246737\pi\)
0.714318 + 0.699822i \(0.246737\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −51.3312 −1.62731
\(996\) 0 0
\(997\) 44.0823 1.39610 0.698050 0.716049i \(-0.254051\pi\)
0.698050 + 0.716049i \(0.254051\pi\)
\(998\) 0 0
\(999\) 0 0
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 6012.2.a.d.1.1 5
3.2 odd 2 668.2.a.b.1.3 5
12.11 even 2 2672.2.a.j.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
668.2.a.b.1.3 5 3.2 odd 2
2672.2.a.j.1.3 5 12.11 even 2
6012.2.a.d.1.1 5 1.1 even 1 trivial