Properties

Label 4332.2.a.o.1.3
Level $4332$
Weight $2$
Character 4332.1
Self dual yes
Analytic conductor $34.591$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4332 = 2^{2} \cdot 3 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4332.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(34.5911941556\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{18})^+\)
Defining polynomial: \( x^{3} - 3x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 228)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.53209\) of defining polynomial
Character \(\chi\) \(=\) 4332.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +2.53209 q^{5} -3.22668 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +2.53209 q^{5} -3.22668 q^{7} +1.00000 q^{9} +3.10607 q^{11} -6.06418 q^{13} +2.53209 q^{15} -5.94356 q^{17} -3.22668 q^{21} -6.71688 q^{23} +1.41147 q^{25} +1.00000 q^{27} +7.12836 q^{29} +7.63816 q^{31} +3.10607 q^{33} -8.17024 q^{35} +2.10607 q^{37} -6.06418 q^{39} -7.04189 q^{41} -9.36959 q^{43} +2.53209 q^{45} -4.65270 q^{47} +3.41147 q^{49} -5.94356 q^{51} -6.35504 q^{53} +7.86484 q^{55} -0.268571 q^{59} +1.58853 q^{61} -3.22668 q^{63} -15.3550 q^{65} -1.30541 q^{67} -6.71688 q^{69} -8.27631 q^{71} +0.921274 q^{73} +1.41147 q^{75} -10.0223 q^{77} -12.0642 q^{79} +1.00000 q^{81} +0.0864665 q^{83} -15.0496 q^{85} +7.12836 q^{87} -7.07192 q^{89} +19.5672 q^{91} +7.63816 q^{93} +3.32770 q^{97} +3.10607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 3 q^{9} - 3 q^{11} - 9 q^{13} + 3 q^{15} - 3 q^{17} - 3 q^{21} - 12 q^{23} - 6 q^{25} + 3 q^{27} + 3 q^{29} + 6 q^{31} - 3 q^{33} - 3 q^{35} - 6 q^{37} - 9 q^{39} - 18 q^{41} - 21 q^{43} + 3 q^{45} - 15 q^{47} - 3 q^{51} + 6 q^{53} + 9 q^{59} + 15 q^{61} - 3 q^{63} - 21 q^{65} - 6 q^{67} - 12 q^{69} + 9 q^{71} - 6 q^{73} - 6 q^{75} - 24 q^{77} - 27 q^{79} + 3 q^{81} - 15 q^{83} - 18 q^{85} + 3 q^{87} + 12 q^{89} + 9 q^{91} + 6 q^{93} + 6 q^{97} - 3 q^{99}+O(q^{100}) \) 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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 2.53209 1.13238 0.566192 0.824273i \(-0.308416\pi\)
0.566192 + 0.824273i \(0.308416\pi\)
\(6\) 0 0
\(7\) −3.22668 −1.21957 −0.609786 0.792566i \(-0.708744\pi\)
−0.609786 + 0.792566i \(0.708744\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.10607 0.936514 0.468257 0.883592i \(-0.344882\pi\)
0.468257 + 0.883592i \(0.344882\pi\)
\(12\) 0 0
\(13\) −6.06418 −1.68190 −0.840950 0.541113i \(-0.818003\pi\)
−0.840950 + 0.541113i \(0.818003\pi\)
\(14\) 0 0
\(15\) 2.53209 0.653783
\(16\) 0 0
\(17\) −5.94356 −1.44153 −0.720763 0.693182i \(-0.756208\pi\)
−0.720763 + 0.693182i \(0.756208\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) −3.22668 −0.704120
\(22\) 0 0
\(23\) −6.71688 −1.40057 −0.700283 0.713865i \(-0.746943\pi\)
−0.700283 + 0.713865i \(0.746943\pi\)
\(24\) 0 0
\(25\) 1.41147 0.282295
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 7.12836 1.32370 0.661851 0.749635i \(-0.269771\pi\)
0.661851 + 0.749635i \(0.269771\pi\)
\(30\) 0 0
\(31\) 7.63816 1.37185 0.685927 0.727671i \(-0.259397\pi\)
0.685927 + 0.727671i \(0.259397\pi\)
\(32\) 0 0
\(33\) 3.10607 0.540697
\(34\) 0 0
\(35\) −8.17024 −1.38102
\(36\) 0 0
\(37\) 2.10607 0.346235 0.173118 0.984901i \(-0.444616\pi\)
0.173118 + 0.984901i \(0.444616\pi\)
\(38\) 0 0
\(39\) −6.06418 −0.971046
\(40\) 0 0
\(41\) −7.04189 −1.09976 −0.549879 0.835244i \(-0.685326\pi\)
−0.549879 + 0.835244i \(0.685326\pi\)
\(42\) 0 0
\(43\) −9.36959 −1.42885 −0.714424 0.699713i \(-0.753311\pi\)
−0.714424 + 0.699713i \(0.753311\pi\)
\(44\) 0 0
\(45\) 2.53209 0.377462
\(46\) 0 0
\(47\) −4.65270 −0.678667 −0.339333 0.940666i \(-0.610201\pi\)
−0.339333 + 0.940666i \(0.610201\pi\)
\(48\) 0 0
\(49\) 3.41147 0.487353
\(50\) 0 0
\(51\) −5.94356 −0.832265
\(52\) 0 0
\(53\) −6.35504 −0.872931 −0.436466 0.899721i \(-0.643770\pi\)
−0.436466 + 0.899721i \(0.643770\pi\)
\(54\) 0 0
\(55\) 7.86484 1.06049
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.268571 −0.0349649 −0.0174825 0.999847i \(-0.505565\pi\)
−0.0174825 + 0.999847i \(0.505565\pi\)
\(60\) 0 0
\(61\) 1.58853 0.203390 0.101695 0.994816i \(-0.467573\pi\)
0.101695 + 0.994816i \(0.467573\pi\)
\(62\) 0 0
\(63\) −3.22668 −0.406524
\(64\) 0 0
\(65\) −15.3550 −1.90456
\(66\) 0 0
\(67\) −1.30541 −0.159481 −0.0797404 0.996816i \(-0.525409\pi\)
−0.0797404 + 0.996816i \(0.525409\pi\)
\(68\) 0 0
\(69\) −6.71688 −0.808617
\(70\) 0 0
\(71\) −8.27631 −0.982217 −0.491109 0.871098i \(-0.663408\pi\)
−0.491109 + 0.871098i \(0.663408\pi\)
\(72\) 0 0
\(73\) 0.921274 0.107827 0.0539135 0.998546i \(-0.482830\pi\)
0.0539135 + 0.998546i \(0.482830\pi\)
\(74\) 0 0
\(75\) 1.41147 0.162983
\(76\) 0 0
\(77\) −10.0223 −1.14215
\(78\) 0 0
\(79\) −12.0642 −1.35733 −0.678663 0.734450i \(-0.737440\pi\)
−0.678663 + 0.734450i \(0.737440\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 0.0864665 0.00949093 0.00474546 0.999989i \(-0.498489\pi\)
0.00474546 + 0.999989i \(0.498489\pi\)
\(84\) 0 0
\(85\) −15.0496 −1.63236
\(86\) 0 0
\(87\) 7.12836 0.764240
\(88\) 0 0
\(89\) −7.07192 −0.749622 −0.374811 0.927101i \(-0.622292\pi\)
−0.374811 + 0.927101i \(0.622292\pi\)
\(90\) 0 0
\(91\) 19.5672 2.05120
\(92\) 0 0
\(93\) 7.63816 0.792040
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 3.32770 0.337876 0.168938 0.985627i \(-0.445966\pi\)
0.168938 + 0.985627i \(0.445966\pi\)
\(98\) 0 0
\(99\) 3.10607 0.312171
\(100\) 0 0
\(101\) −10.7588 −1.07054 −0.535269 0.844682i \(-0.679790\pi\)
−0.535269 + 0.844682i \(0.679790\pi\)
\(102\) 0 0
\(103\) 5.92902 0.584203 0.292102 0.956387i \(-0.405645\pi\)
0.292102 + 0.956387i \(0.405645\pi\)
\(104\) 0 0
\(105\) −8.17024 −0.797334
\(106\) 0 0
\(107\) 2.58172 0.249584 0.124792 0.992183i \(-0.460174\pi\)
0.124792 + 0.992183i \(0.460174\pi\)
\(108\) 0 0
\(109\) 4.78106 0.457942 0.228971 0.973433i \(-0.426464\pi\)
0.228971 + 0.973433i \(0.426464\pi\)
\(110\) 0 0
\(111\) 2.10607 0.199899
\(112\) 0 0
\(113\) 16.6655 1.56776 0.783879 0.620914i \(-0.213238\pi\)
0.783879 + 0.620914i \(0.213238\pi\)
\(114\) 0 0
\(115\) −17.0077 −1.58598
\(116\) 0 0
\(117\) −6.06418 −0.560633
\(118\) 0 0
\(119\) 19.1780 1.75804
\(120\) 0 0
\(121\) −1.35235 −0.122941
\(122\) 0 0
\(123\) −7.04189 −0.634946
\(124\) 0 0
\(125\) −9.08647 −0.812718
\(126\) 0 0
\(127\) 5.21894 0.463106 0.231553 0.972822i \(-0.425619\pi\)
0.231553 + 0.972822i \(0.425619\pi\)
\(128\) 0 0
\(129\) −9.36959 −0.824946
\(130\) 0 0
\(131\) −8.65776 −0.756432 −0.378216 0.925717i \(-0.623462\pi\)
−0.378216 + 0.925717i \(0.623462\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.53209 0.217928
\(136\) 0 0
\(137\) −13.6655 −1.16752 −0.583761 0.811925i \(-0.698420\pi\)
−0.583761 + 0.811925i \(0.698420\pi\)
\(138\) 0 0
\(139\) −13.6800 −1.16033 −0.580163 0.814500i \(-0.697011\pi\)
−0.580163 + 0.814500i \(0.697011\pi\)
\(140\) 0 0
\(141\) −4.65270 −0.391828
\(142\) 0 0
\(143\) −18.8357 −1.57512
\(144\) 0 0
\(145\) 18.0496 1.49894
\(146\) 0 0
\(147\) 3.41147 0.281374
\(148\) 0 0
\(149\) 23.7442 1.94520 0.972601 0.232480i \(-0.0746839\pi\)
0.972601 + 0.232480i \(0.0746839\pi\)
\(150\) 0 0
\(151\) 8.33544 0.678328 0.339164 0.940727i \(-0.389856\pi\)
0.339164 + 0.940727i \(0.389856\pi\)
\(152\) 0 0
\(153\) −5.94356 −0.480509
\(154\) 0 0
\(155\) 19.3405 1.55347
\(156\) 0 0
\(157\) 21.6955 1.73149 0.865746 0.500484i \(-0.166845\pi\)
0.865746 + 0.500484i \(0.166845\pi\)
\(158\) 0 0
\(159\) −6.35504 −0.503987
\(160\) 0 0
\(161\) 21.6732 1.70809
\(162\) 0 0
\(163\) −22.9855 −1.80036 −0.900180 0.435519i \(-0.856565\pi\)
−0.900180 + 0.435519i \(0.856565\pi\)
\(164\) 0 0
\(165\) 7.86484 0.612277
\(166\) 0 0
\(167\) −7.64590 −0.591657 −0.295829 0.955241i \(-0.595596\pi\)
−0.295829 + 0.955241i \(0.595596\pi\)
\(168\) 0 0
\(169\) 23.7743 1.82879
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.7442 0.892897 0.446448 0.894809i \(-0.352689\pi\)
0.446448 + 0.894809i \(0.352689\pi\)
\(174\) 0 0
\(175\) −4.55438 −0.344279
\(176\) 0 0
\(177\) −0.268571 −0.0201870
\(178\) 0 0
\(179\) −4.19759 −0.313742 −0.156871 0.987619i \(-0.550141\pi\)
−0.156871 + 0.987619i \(0.550141\pi\)
\(180\) 0 0
\(181\) 12.3277 0.916310 0.458155 0.888872i \(-0.348510\pi\)
0.458155 + 0.888872i \(0.348510\pi\)
\(182\) 0 0
\(183\) 1.58853 0.117427
\(184\) 0 0
\(185\) 5.33275 0.392071
\(186\) 0 0
\(187\) −18.4611 −1.35001
\(188\) 0 0
\(189\) −3.22668 −0.234707
\(190\) 0 0
\(191\) −10.2044 −0.738364 −0.369182 0.929357i \(-0.620362\pi\)
−0.369182 + 0.929357i \(0.620362\pi\)
\(192\) 0 0
\(193\) −21.7074 −1.56253 −0.781266 0.624198i \(-0.785426\pi\)
−0.781266 + 0.624198i \(0.785426\pi\)
\(194\) 0 0
\(195\) −15.3550 −1.09960
\(196\) 0 0
\(197\) −16.6851 −1.18876 −0.594382 0.804183i \(-0.702603\pi\)
−0.594382 + 0.804183i \(0.702603\pi\)
\(198\) 0 0
\(199\) −2.46017 −0.174397 −0.0871984 0.996191i \(-0.527791\pi\)
−0.0871984 + 0.996191i \(0.527791\pi\)
\(200\) 0 0
\(201\) −1.30541 −0.0920763
\(202\) 0 0
\(203\) −23.0009 −1.61435
\(204\) 0 0
\(205\) −17.8307 −1.24535
\(206\) 0 0
\(207\) −6.71688 −0.466856
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −1.23173 −0.0847961 −0.0423980 0.999101i \(-0.513500\pi\)
−0.0423980 + 0.999101i \(0.513500\pi\)
\(212\) 0 0
\(213\) −8.27631 −0.567084
\(214\) 0 0
\(215\) −23.7246 −1.61801
\(216\) 0 0
\(217\) −24.6459 −1.67307
\(218\) 0 0
\(219\) 0.921274 0.0622539
\(220\) 0 0
\(221\) 36.0428 2.42450
\(222\) 0 0
\(223\) 6.57903 0.440564 0.220282 0.975436i \(-0.429302\pi\)
0.220282 + 0.975436i \(0.429302\pi\)
\(224\) 0 0
\(225\) 1.41147 0.0940983
\(226\) 0 0
\(227\) 9.72967 0.645781 0.322891 0.946436i \(-0.395345\pi\)
0.322891 + 0.946436i \(0.395345\pi\)
\(228\) 0 0
\(229\) −9.86753 −0.652064 −0.326032 0.945359i \(-0.605712\pi\)
−0.326032 + 0.945359i \(0.605712\pi\)
\(230\) 0 0
\(231\) −10.0223 −0.659418
\(232\) 0 0
\(233\) 21.8161 1.42922 0.714611 0.699522i \(-0.246604\pi\)
0.714611 + 0.699522i \(0.246604\pi\)
\(234\) 0 0
\(235\) −11.7811 −0.768512
\(236\) 0 0
\(237\) −12.0642 −0.783653
\(238\) 0 0
\(239\) 21.3114 1.37852 0.689260 0.724514i \(-0.257936\pi\)
0.689260 + 0.724514i \(0.257936\pi\)
\(240\) 0 0
\(241\) 15.6459 1.00784 0.503920 0.863750i \(-0.331890\pi\)
0.503920 + 0.863750i \(0.331890\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 8.63816 0.551872
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.0864665 0.00547959
\(250\) 0 0
\(251\) −10.1215 −0.638866 −0.319433 0.947609i \(-0.603493\pi\)
−0.319433 + 0.947609i \(0.603493\pi\)
\(252\) 0 0
\(253\) −20.8631 −1.31165
\(254\) 0 0
\(255\) −15.0496 −0.942444
\(256\) 0 0
\(257\) −4.77837 −0.298067 −0.149033 0.988832i \(-0.547616\pi\)
−0.149033 + 0.988832i \(0.547616\pi\)
\(258\) 0 0
\(259\) −6.79561 −0.422258
\(260\) 0 0
\(261\) 7.12836 0.441234
\(262\) 0 0
\(263\) −21.6905 −1.33749 −0.668746 0.743491i \(-0.733169\pi\)
−0.668746 + 0.743491i \(0.733169\pi\)
\(264\) 0 0
\(265\) −16.0915 −0.988494
\(266\) 0 0
\(267\) −7.07192 −0.432794
\(268\) 0 0
\(269\) −3.23173 −0.197042 −0.0985212 0.995135i \(-0.531411\pi\)
−0.0985212 + 0.995135i \(0.531411\pi\)
\(270\) 0 0
\(271\) −11.7219 −0.712057 −0.356028 0.934475i \(-0.615869\pi\)
−0.356028 + 0.934475i \(0.615869\pi\)
\(272\) 0 0
\(273\) 19.5672 1.18426
\(274\) 0 0
\(275\) 4.38413 0.264373
\(276\) 0 0
\(277\) 8.77332 0.527138 0.263569 0.964641i \(-0.415100\pi\)
0.263569 + 0.964641i \(0.415100\pi\)
\(278\) 0 0
\(279\) 7.63816 0.457284
\(280\) 0 0
\(281\) 25.4165 1.51622 0.758111 0.652125i \(-0.226122\pi\)
0.758111 + 0.652125i \(0.226122\pi\)
\(282\) 0 0
\(283\) −2.67230 −0.158852 −0.0794260 0.996841i \(-0.525309\pi\)
−0.0794260 + 0.996841i \(0.525309\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 22.7219 1.34123
\(288\) 0 0
\(289\) 18.3259 1.07800
\(290\) 0 0
\(291\) 3.32770 0.195073
\(292\) 0 0
\(293\) 19.9537 1.16571 0.582853 0.812578i \(-0.301936\pi\)
0.582853 + 0.812578i \(0.301936\pi\)
\(294\) 0 0
\(295\) −0.680045 −0.0395937
\(296\) 0 0
\(297\) 3.10607 0.180232
\(298\) 0 0
\(299\) 40.7324 2.35561
\(300\) 0 0
\(301\) 30.2327 1.74258
\(302\) 0 0
\(303\) −10.7588 −0.618075
\(304\) 0 0
\(305\) 4.02229 0.230316
\(306\) 0 0
\(307\) −23.9813 −1.36869 −0.684343 0.729160i \(-0.739911\pi\)
−0.684343 + 0.729160i \(0.739911\pi\)
\(308\) 0 0
\(309\) 5.92902 0.337290
\(310\) 0 0
\(311\) −0.162504 −0.00921475 −0.00460737 0.999989i \(-0.501467\pi\)
−0.00460737 + 0.999989i \(0.501467\pi\)
\(312\) 0 0
\(313\) 6.72193 0.379946 0.189973 0.981789i \(-0.439160\pi\)
0.189973 + 0.981789i \(0.439160\pi\)
\(314\) 0 0
\(315\) −8.17024 −0.460341
\(316\) 0 0
\(317\) 14.2831 0.802220 0.401110 0.916030i \(-0.368625\pi\)
0.401110 + 0.916030i \(0.368625\pi\)
\(318\) 0 0
\(319\) 22.1411 1.23967
\(320\) 0 0
\(321\) 2.58172 0.144097
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −8.55943 −0.474792
\(326\) 0 0
\(327\) 4.78106 0.264393
\(328\) 0 0
\(329\) 15.0128 0.827682
\(330\) 0 0
\(331\) −33.3063 −1.83068 −0.915341 0.402680i \(-0.868079\pi\)
−0.915341 + 0.402680i \(0.868079\pi\)
\(332\) 0 0
\(333\) 2.10607 0.115412
\(334\) 0 0
\(335\) −3.30541 −0.180594
\(336\) 0 0
\(337\) −1.84936 −0.100741 −0.0503704 0.998731i \(-0.516040\pi\)
−0.0503704 + 0.998731i \(0.516040\pi\)
\(338\) 0 0
\(339\) 16.6655 0.905146
\(340\) 0 0
\(341\) 23.7246 1.28476
\(342\) 0 0
\(343\) 11.5790 0.625209
\(344\) 0 0
\(345\) −17.0077 −0.915666
\(346\) 0 0
\(347\) −6.89899 −0.370357 −0.185178 0.982705i \(-0.559286\pi\)
−0.185178 + 0.982705i \(0.559286\pi\)
\(348\) 0 0
\(349\) −11.2216 −0.600680 −0.300340 0.953832i \(-0.597100\pi\)
−0.300340 + 0.953832i \(0.597100\pi\)
\(350\) 0 0
\(351\) −6.06418 −0.323682
\(352\) 0 0
\(353\) −1.90848 −0.101578 −0.0507891 0.998709i \(-0.516174\pi\)
−0.0507891 + 0.998709i \(0.516174\pi\)
\(354\) 0 0
\(355\) −20.9564 −1.11225
\(356\) 0 0
\(357\) 19.1780 1.01501
\(358\) 0 0
\(359\) 9.53033 0.502992 0.251496 0.967858i \(-0.419078\pi\)
0.251496 + 0.967858i \(0.419078\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) −1.35235 −0.0709799
\(364\) 0 0
\(365\) 2.33275 0.122102
\(366\) 0 0
\(367\) 17.9222 0.935532 0.467766 0.883852i \(-0.345059\pi\)
0.467766 + 0.883852i \(0.345059\pi\)
\(368\) 0 0
\(369\) −7.04189 −0.366586
\(370\) 0 0
\(371\) 20.5057 1.06460
\(372\) 0 0
\(373\) −30.4688 −1.57762 −0.788808 0.614639i \(-0.789302\pi\)
−0.788808 + 0.614639i \(0.789302\pi\)
\(374\) 0 0
\(375\) −9.08647 −0.469223
\(376\) 0 0
\(377\) −43.2276 −2.22634
\(378\) 0 0
\(379\) 6.57903 0.337942 0.168971 0.985621i \(-0.445956\pi\)
0.168971 + 0.985621i \(0.445956\pi\)
\(380\) 0 0
\(381\) 5.21894 0.267374
\(382\) 0 0
\(383\) 23.0077 1.17564 0.587820 0.808992i \(-0.299986\pi\)
0.587820 + 0.808992i \(0.299986\pi\)
\(384\) 0 0
\(385\) −25.3773 −1.29335
\(386\) 0 0
\(387\) −9.36959 −0.476283
\(388\) 0 0
\(389\) 27.3054 1.38444 0.692220 0.721687i \(-0.256633\pi\)
0.692220 + 0.721687i \(0.256633\pi\)
\(390\) 0 0
\(391\) 39.9222 2.01895
\(392\) 0 0
\(393\) −8.65776 −0.436726
\(394\) 0 0
\(395\) −30.5476 −1.53702
\(396\) 0 0
\(397\) −5.88207 −0.295213 −0.147606 0.989046i \(-0.547157\pi\)
−0.147606 + 0.989046i \(0.547157\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.28850 −0.214157 −0.107079 0.994251i \(-0.534150\pi\)
−0.107079 + 0.994251i \(0.534150\pi\)
\(402\) 0 0
\(403\) −46.3191 −2.30732
\(404\) 0 0
\(405\) 2.53209 0.125821
\(406\) 0 0
\(407\) 6.54158 0.324254
\(408\) 0 0
\(409\) −32.4270 −1.60341 −0.801705 0.597720i \(-0.796073\pi\)
−0.801705 + 0.597720i \(0.796073\pi\)
\(410\) 0 0
\(411\) −13.6655 −0.674069
\(412\) 0 0
\(413\) 0.866592 0.0426422
\(414\) 0 0
\(415\) 0.218941 0.0107474
\(416\) 0 0
\(417\) −13.6800 −0.669915
\(418\) 0 0
\(419\) 9.86577 0.481974 0.240987 0.970528i \(-0.422529\pi\)
0.240987 + 0.970528i \(0.422529\pi\)
\(420\) 0 0
\(421\) 22.1070 1.07743 0.538715 0.842488i \(-0.318910\pi\)
0.538715 + 0.842488i \(0.318910\pi\)
\(422\) 0 0
\(423\) −4.65270 −0.226222
\(424\) 0 0
\(425\) −8.38919 −0.406935
\(426\) 0 0
\(427\) −5.12567 −0.248048
\(428\) 0 0
\(429\) −18.8357 −0.909398
\(430\) 0 0
\(431\) −25.3209 −1.21966 −0.609832 0.792531i \(-0.708763\pi\)
−0.609832 + 0.792531i \(0.708763\pi\)
\(432\) 0 0
\(433\) 12.8152 0.615860 0.307930 0.951409i \(-0.400364\pi\)
0.307930 + 0.951409i \(0.400364\pi\)
\(434\) 0 0
\(435\) 18.0496 0.865414
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −5.22399 −0.249328 −0.124664 0.992199i \(-0.539785\pi\)
−0.124664 + 0.992199i \(0.539785\pi\)
\(440\) 0 0
\(441\) 3.41147 0.162451
\(442\) 0 0
\(443\) −17.3996 −0.826681 −0.413340 0.910577i \(-0.635638\pi\)
−0.413340 + 0.910577i \(0.635638\pi\)
\(444\) 0 0
\(445\) −17.9067 −0.848860
\(446\) 0 0
\(447\) 23.7442 1.12306
\(448\) 0 0
\(449\) 23.6509 1.11616 0.558079 0.829788i \(-0.311539\pi\)
0.558079 + 0.829788i \(0.311539\pi\)
\(450\) 0 0
\(451\) −21.8726 −1.02994
\(452\) 0 0
\(453\) 8.33544 0.391633
\(454\) 0 0
\(455\) 49.5458 2.32274
\(456\) 0 0
\(457\) −24.2695 −1.13528 −0.567640 0.823277i \(-0.692143\pi\)
−0.567640 + 0.823277i \(0.692143\pi\)
\(458\) 0 0
\(459\) −5.94356 −0.277422
\(460\) 0 0
\(461\) 6.97502 0.324859 0.162430 0.986720i \(-0.448067\pi\)
0.162430 + 0.986720i \(0.448067\pi\)
\(462\) 0 0
\(463\) 28.0770 1.30485 0.652424 0.757854i \(-0.273752\pi\)
0.652424 + 0.757854i \(0.273752\pi\)
\(464\) 0 0
\(465\) 19.3405 0.896894
\(466\) 0 0
\(467\) 3.82295 0.176905 0.0884525 0.996080i \(-0.471808\pi\)
0.0884525 + 0.996080i \(0.471808\pi\)
\(468\) 0 0
\(469\) 4.21213 0.194498
\(470\) 0 0
\(471\) 21.6955 0.999677
\(472\) 0 0
\(473\) −29.1026 −1.33814
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.35504 −0.290977
\(478\) 0 0
\(479\) −30.9394 −1.41366 −0.706830 0.707384i \(-0.749875\pi\)
−0.706830 + 0.707384i \(0.749875\pi\)
\(480\) 0 0
\(481\) −12.7716 −0.582333
\(482\) 0 0
\(483\) 21.6732 0.986166
\(484\) 0 0
\(485\) 8.42602 0.382606
\(486\) 0 0
\(487\) −2.86484 −0.129818 −0.0649091 0.997891i \(-0.520676\pi\)
−0.0649091 + 0.997891i \(0.520676\pi\)
\(488\) 0 0
\(489\) −22.9855 −1.03944
\(490\) 0 0
\(491\) −41.7502 −1.88416 −0.942080 0.335387i \(-0.891133\pi\)
−0.942080 + 0.335387i \(0.891133\pi\)
\(492\) 0 0
\(493\) −42.3678 −1.90815
\(494\) 0 0
\(495\) 7.86484 0.353498
\(496\) 0 0
\(497\) 26.7050 1.19788
\(498\) 0 0
\(499\) 9.49020 0.424840 0.212420 0.977178i \(-0.431866\pi\)
0.212420 + 0.977178i \(0.431866\pi\)
\(500\) 0 0
\(501\) −7.64590 −0.341593
\(502\) 0 0
\(503\) −12.6408 −0.563627 −0.281814 0.959469i \(-0.590936\pi\)
−0.281814 + 0.959469i \(0.590936\pi\)
\(504\) 0 0
\(505\) −27.2422 −1.21226
\(506\) 0 0
\(507\) 23.7743 1.05585
\(508\) 0 0
\(509\) −19.4962 −0.864153 −0.432077 0.901837i \(-0.642219\pi\)
−0.432077 + 0.901837i \(0.642219\pi\)
\(510\) 0 0
\(511\) −2.97266 −0.131503
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15.0128 0.661543
\(516\) 0 0
\(517\) −14.4516 −0.635581
\(518\) 0 0
\(519\) 11.7442 0.515514
\(520\) 0 0
\(521\) 20.2831 0.888620 0.444310 0.895873i \(-0.353449\pi\)
0.444310 + 0.895873i \(0.353449\pi\)
\(522\) 0 0
\(523\) 15.2668 0.667571 0.333786 0.942649i \(-0.391674\pi\)
0.333786 + 0.942649i \(0.391674\pi\)
\(524\) 0 0
\(525\) −4.55438 −0.198769
\(526\) 0 0
\(527\) −45.3979 −1.97756
\(528\) 0 0
\(529\) 22.1165 0.961587
\(530\) 0 0
\(531\) −0.268571 −0.0116550
\(532\) 0 0
\(533\) 42.7033 1.84968
\(534\) 0 0
\(535\) 6.53714 0.282625
\(536\) 0 0
\(537\) −4.19759 −0.181139
\(538\) 0 0
\(539\) 10.5963 0.456414
\(540\) 0 0
\(541\) −20.6159 −0.886345 −0.443173 0.896436i \(-0.646147\pi\)
−0.443173 + 0.896436i \(0.646147\pi\)
\(542\) 0 0
\(543\) 12.3277 0.529032
\(544\) 0 0
\(545\) 12.1061 0.518567
\(546\) 0 0
\(547\) −28.4115 −1.21479 −0.607393 0.794401i \(-0.707785\pi\)
−0.607393 + 0.794401i \(0.707785\pi\)
\(548\) 0 0
\(549\) 1.58853 0.0677966
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 38.9273 1.65536
\(554\) 0 0
\(555\) 5.33275 0.226363
\(556\) 0 0
\(557\) −37.8188 −1.60244 −0.801218 0.598373i \(-0.795814\pi\)
−0.801218 + 0.598373i \(0.795814\pi\)
\(558\) 0 0
\(559\) 56.8188 2.40318
\(560\) 0 0
\(561\) −18.4611 −0.779428
\(562\) 0 0
\(563\) 9.64084 0.406313 0.203157 0.979146i \(-0.434880\pi\)
0.203157 + 0.979146i \(0.434880\pi\)
\(564\) 0 0
\(565\) 42.1985 1.77531
\(566\) 0 0
\(567\) −3.22668 −0.135508
\(568\) 0 0
\(569\) 21.1129 0.885098 0.442549 0.896744i \(-0.354074\pi\)
0.442549 + 0.896744i \(0.354074\pi\)
\(570\) 0 0
\(571\) −2.11112 −0.0883476 −0.0441738 0.999024i \(-0.514066\pi\)
−0.0441738 + 0.999024i \(0.514066\pi\)
\(572\) 0 0
\(573\) −10.2044 −0.426295
\(574\) 0 0
\(575\) −9.48070 −0.395373
\(576\) 0 0
\(577\) 23.1429 0.963452 0.481726 0.876322i \(-0.340010\pi\)
0.481726 + 0.876322i \(0.340010\pi\)
\(578\) 0 0
\(579\) −21.7074 −0.902128
\(580\) 0 0
\(581\) −0.279000 −0.0115749
\(582\) 0 0
\(583\) −19.7392 −0.817513
\(584\) 0 0
\(585\) −15.3550 −0.634853
\(586\) 0 0
\(587\) −19.1607 −0.790849 −0.395424 0.918499i \(-0.629402\pi\)
−0.395424 + 0.918499i \(0.629402\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −16.6851 −0.686333
\(592\) 0 0
\(593\) 37.2012 1.52767 0.763835 0.645411i \(-0.223314\pi\)
0.763835 + 0.645411i \(0.223314\pi\)
\(594\) 0 0
\(595\) 48.5604 1.99078
\(596\) 0 0
\(597\) −2.46017 −0.100688
\(598\) 0 0
\(599\) 30.9050 1.26274 0.631371 0.775481i \(-0.282492\pi\)
0.631371 + 0.775481i \(0.282492\pi\)
\(600\) 0 0
\(601\) −43.5604 −1.77686 −0.888432 0.459008i \(-0.848205\pi\)
−0.888432 + 0.459008i \(0.848205\pi\)
\(602\) 0 0
\(603\) −1.30541 −0.0531603
\(604\) 0 0
\(605\) −3.42427 −0.139216
\(606\) 0 0
\(607\) 20.9659 0.850978 0.425489 0.904964i \(-0.360102\pi\)
0.425489 + 0.904964i \(0.360102\pi\)
\(608\) 0 0
\(609\) −23.0009 −0.932045
\(610\) 0 0
\(611\) 28.2148 1.14145
\(612\) 0 0
\(613\) 6.30447 0.254635 0.127318 0.991862i \(-0.459363\pi\)
0.127318 + 0.991862i \(0.459363\pi\)
\(614\) 0 0
\(615\) −17.8307 −0.719003
\(616\) 0 0
\(617\) −38.4424 −1.54763 −0.773817 0.633409i \(-0.781655\pi\)
−0.773817 + 0.633409i \(0.781655\pi\)
\(618\) 0 0
\(619\) −18.6382 −0.749131 −0.374565 0.927201i \(-0.622208\pi\)
−0.374565 + 0.927201i \(0.622208\pi\)
\(620\) 0 0
\(621\) −6.71688 −0.269539
\(622\) 0 0
\(623\) 22.8188 0.914217
\(624\) 0 0
\(625\) −30.0651 −1.20260
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.5175 −0.499107
\(630\) 0 0
\(631\) 15.4570 0.615333 0.307666 0.951494i \(-0.400452\pi\)
0.307666 + 0.951494i \(0.400452\pi\)
\(632\) 0 0
\(633\) −1.23173 −0.0489570
\(634\) 0 0
\(635\) 13.2148 0.524414
\(636\) 0 0
\(637\) −20.6878 −0.819680
\(638\) 0 0
\(639\) −8.27631 −0.327406
\(640\) 0 0
\(641\) −25.0155 −0.988052 −0.494026 0.869447i \(-0.664475\pi\)
−0.494026 + 0.869447i \(0.664475\pi\)
\(642\) 0 0
\(643\) 22.8239 0.900086 0.450043 0.893007i \(-0.351409\pi\)
0.450043 + 0.893007i \(0.351409\pi\)
\(644\) 0 0
\(645\) −23.7246 −0.934156
\(646\) 0 0
\(647\) 46.1252 1.81337 0.906684 0.421811i \(-0.138605\pi\)
0.906684 + 0.421811i \(0.138605\pi\)
\(648\) 0 0
\(649\) −0.834198 −0.0327452
\(650\) 0 0
\(651\) −24.6459 −0.965949
\(652\) 0 0
\(653\) −14.6774 −0.574369 −0.287185 0.957875i \(-0.592719\pi\)
−0.287185 + 0.957875i \(0.592719\pi\)
\(654\) 0 0
\(655\) −21.9222 −0.856572
\(656\) 0 0
\(657\) 0.921274 0.0359423
\(658\) 0 0
\(659\) −21.5175 −0.838204 −0.419102 0.907939i \(-0.637655\pi\)
−0.419102 + 0.907939i \(0.637655\pi\)
\(660\) 0 0
\(661\) −31.3942 −1.22109 −0.610547 0.791980i \(-0.709050\pi\)
−0.610547 + 0.791980i \(0.709050\pi\)
\(662\) 0 0
\(663\) 36.0428 1.39979
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −47.8803 −1.85393
\(668\) 0 0
\(669\) 6.57903 0.254360
\(670\) 0 0
\(671\) 4.93407 0.190478
\(672\) 0 0
\(673\) 11.6732 0.449970 0.224985 0.974362i \(-0.427767\pi\)
0.224985 + 0.974362i \(0.427767\pi\)
\(674\) 0 0
\(675\) 1.41147 0.0543277
\(676\) 0 0
\(677\) 41.3732 1.59010 0.795051 0.606543i \(-0.207444\pi\)
0.795051 + 0.606543i \(0.207444\pi\)
\(678\) 0 0
\(679\) −10.7374 −0.412064
\(680\) 0 0
\(681\) 9.72967 0.372842
\(682\) 0 0
\(683\) −29.5117 −1.12923 −0.564616 0.825354i \(-0.690976\pi\)
−0.564616 + 0.825354i \(0.690976\pi\)
\(684\) 0 0
\(685\) −34.6023 −1.32208
\(686\) 0 0
\(687\) −9.86753 −0.376470
\(688\) 0 0
\(689\) 38.5381 1.46818
\(690\) 0 0
\(691\) −4.47834 −0.170364 −0.0851820 0.996365i \(-0.527147\pi\)
−0.0851820 + 0.996365i \(0.527147\pi\)
\(692\) 0 0
\(693\) −10.0223 −0.380715
\(694\) 0 0
\(695\) −34.6391 −1.31394
\(696\) 0 0
\(697\) 41.8539 1.58533
\(698\) 0 0
\(699\) 21.8161 0.825162
\(700\) 0 0
\(701\) 5.91353 0.223351 0.111676 0.993745i \(-0.464378\pi\)
0.111676 + 0.993745i \(0.464378\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −11.7811 −0.443700
\(706\) 0 0
\(707\) 34.7151 1.30560
\(708\) 0 0
\(709\) 29.9358 1.12426 0.562132 0.827048i \(-0.309981\pi\)
0.562132 + 0.827048i \(0.309981\pi\)
\(710\) 0 0
\(711\) −12.0642 −0.452442
\(712\) 0 0
\(713\) −51.3046 −1.92137
\(714\) 0 0
\(715\) −47.6938 −1.78365
\(716\) 0 0
\(717\) 21.3114 0.795889
\(718\) 0 0
\(719\) 47.7811 1.78193 0.890966 0.454069i \(-0.150028\pi\)
0.890966 + 0.454069i \(0.150028\pi\)
\(720\) 0 0
\(721\) −19.1310 −0.712477
\(722\) 0 0
\(723\) 15.6459 0.581877
\(724\) 0 0
\(725\) 10.0615 0.373674
\(726\) 0 0
\(727\) −41.8949 −1.55379 −0.776897 0.629627i \(-0.783208\pi\)
−0.776897 + 0.629627i \(0.783208\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 55.6887 2.05972
\(732\) 0 0
\(733\) 21.6135 0.798313 0.399156 0.916883i \(-0.369303\pi\)
0.399156 + 0.916883i \(0.369303\pi\)
\(734\) 0 0
\(735\) 8.63816 0.318623
\(736\) 0 0
\(737\) −4.05468 −0.149356
\(738\) 0 0
\(739\) 32.4243 1.19275 0.596373 0.802707i \(-0.296608\pi\)
0.596373 + 0.802707i \(0.296608\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −26.8976 −0.986776 −0.493388 0.869809i \(-0.664242\pi\)
−0.493388 + 0.869809i \(0.664242\pi\)
\(744\) 0 0
\(745\) 60.1225 2.20272
\(746\) 0 0
\(747\) 0.0864665 0.00316364
\(748\) 0 0
\(749\) −8.33038 −0.304386
\(750\) 0 0
\(751\) −5.72638 −0.208958 −0.104479 0.994527i \(-0.533318\pi\)
−0.104479 + 0.994527i \(0.533318\pi\)
\(752\) 0 0
\(753\) −10.1215 −0.368850
\(754\) 0 0
\(755\) 21.1061 0.768128
\(756\) 0 0
\(757\) 8.65364 0.314522 0.157261 0.987557i \(-0.449734\pi\)
0.157261 + 0.987557i \(0.449734\pi\)
\(758\) 0 0
\(759\) −20.8631 −0.757282
\(760\) 0 0
\(761\) −37.7279 −1.36764 −0.683818 0.729653i \(-0.739682\pi\)
−0.683818 + 0.729653i \(0.739682\pi\)
\(762\) 0 0
\(763\) −15.4270 −0.558493
\(764\) 0 0
\(765\) −15.0496 −0.544121
\(766\) 0 0
\(767\) 1.62866 0.0588075
\(768\) 0 0
\(769\) 36.7912 1.32672 0.663362 0.748299i \(-0.269129\pi\)
0.663362 + 0.748299i \(0.269129\pi\)
\(770\) 0 0
\(771\) −4.77837 −0.172089
\(772\) 0 0
\(773\) 19.9685 0.718218 0.359109 0.933296i \(-0.383081\pi\)
0.359109 + 0.933296i \(0.383081\pi\)
\(774\) 0 0
\(775\) 10.7811 0.387267
\(776\) 0 0
\(777\) −6.79561 −0.243791
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −25.7068 −0.919861
\(782\) 0 0
\(783\) 7.12836 0.254747
\(784\) 0 0
\(785\) 54.9350 1.96071
\(786\) 0 0
\(787\) 8.36783 0.298281 0.149140 0.988816i \(-0.452349\pi\)
0.149140 + 0.988816i \(0.452349\pi\)
\(788\) 0 0
\(789\) −21.6905 −0.772201
\(790\) 0 0
\(791\) −53.7743 −1.91199
\(792\) 0 0
\(793\) −9.63310 −0.342082
\(794\) 0 0
\(795\) −16.0915 −0.570707
\(796\) 0 0
\(797\) −42.1729 −1.49384 −0.746921 0.664913i \(-0.768469\pi\)
−0.746921 + 0.664913i \(0.768469\pi\)
\(798\) 0 0
\(799\) 27.6536 0.978315
\(800\) 0 0
\(801\) −7.07192 −0.249874
\(802\) 0 0
\(803\) 2.86154 0.100982
\(804\) 0 0
\(805\) 54.8786 1.93422
\(806\) 0 0
\(807\) −3.23173 −0.113762
\(808\) 0 0
\(809\) −6.06242 −0.213143 −0.106572 0.994305i \(-0.533987\pi\)
−0.106572 + 0.994305i \(0.533987\pi\)
\(810\) 0 0
\(811\) 25.6938 0.902230 0.451115 0.892466i \(-0.351026\pi\)
0.451115 + 0.892466i \(0.351026\pi\)
\(812\) 0 0
\(813\) −11.7219 −0.411106
\(814\) 0 0
\(815\) −58.2012 −2.03870
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 19.5672 0.683732
\(820\) 0 0
\(821\) −0.251334 −0.00877163 −0.00438582 0.999990i \(-0.501396\pi\)
−0.00438582 + 0.999990i \(0.501396\pi\)
\(822\) 0 0
\(823\) 16.3259 0.569087 0.284543 0.958663i \(-0.408158\pi\)
0.284543 + 0.958663i \(0.408158\pi\)
\(824\) 0 0
\(825\) 4.38413 0.152636
\(826\) 0 0
\(827\) 26.4989 0.921456 0.460728 0.887541i \(-0.347588\pi\)
0.460728 + 0.887541i \(0.347588\pi\)
\(828\) 0 0
\(829\) 41.6296 1.44586 0.722928 0.690924i \(-0.242796\pi\)
0.722928 + 0.690924i \(0.242796\pi\)
\(830\) 0 0
\(831\) 8.77332 0.304343
\(832\) 0 0
\(833\) −20.2763 −0.702533
\(834\) 0 0
\(835\) −19.3601 −0.669984
\(836\) 0 0
\(837\) 7.63816 0.264013
\(838\) 0 0
\(839\) 28.4074 0.980731 0.490365 0.871517i \(-0.336863\pi\)
0.490365 + 0.871517i \(0.336863\pi\)
\(840\) 0 0
\(841\) 21.8135 0.752188
\(842\) 0 0
\(843\) 25.4165 0.875392
\(844\) 0 0
\(845\) 60.1985 2.07089
\(846\) 0 0
\(847\) 4.36360 0.149935
\(848\) 0 0
\(849\) −2.67230 −0.0917132
\(850\) 0 0
\(851\) −14.1462 −0.484926
\(852\) 0 0
\(853\) −27.1935 −0.931087 −0.465543 0.885025i \(-0.654141\pi\)
−0.465543 + 0.885025i \(0.654141\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 41.9691 1.43364 0.716819 0.697259i \(-0.245597\pi\)
0.716819 + 0.697259i \(0.245597\pi\)
\(858\) 0 0
\(859\) 35.3138 1.20489 0.602445 0.798160i \(-0.294193\pi\)
0.602445 + 0.798160i \(0.294193\pi\)
\(860\) 0 0
\(861\) 22.7219 0.774361
\(862\) 0 0
\(863\) 12.0104 0.408840 0.204420 0.978883i \(-0.434469\pi\)
0.204420 + 0.978883i \(0.434469\pi\)
\(864\) 0 0
\(865\) 29.7374 1.01110
\(866\) 0 0
\(867\) 18.3259 0.622382
\(868\) 0 0
\(869\) −37.4721 −1.27116
\(870\) 0 0
\(871\) 7.91622 0.268231
\(872\) 0 0
\(873\) 3.32770 0.112625
\(874\) 0 0
\(875\) 29.3191 0.991168
\(876\) 0 0
\(877\) −18.0333 −0.608942 −0.304471 0.952522i \(-0.598480\pi\)
−0.304471 + 0.952522i \(0.598480\pi\)
\(878\) 0 0
\(879\) 19.9537 0.673021
\(880\) 0 0
\(881\) 23.8203 0.802525 0.401262 0.915963i \(-0.368572\pi\)
0.401262 + 0.915963i \(0.368572\pi\)
\(882\) 0 0
\(883\) 11.8334 0.398225 0.199112 0.979977i \(-0.436194\pi\)
0.199112 + 0.979977i \(0.436194\pi\)
\(884\) 0 0
\(885\) −0.680045 −0.0228595
\(886\) 0 0
\(887\) −36.6996 −1.23225 −0.616127 0.787647i \(-0.711299\pi\)
−0.616127 + 0.787647i \(0.711299\pi\)
\(888\) 0 0
\(889\) −16.8399 −0.564791
\(890\) 0 0
\(891\) 3.10607 0.104057
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −10.6287 −0.355277
\(896\) 0 0
\(897\) 40.7324 1.36001
\(898\) 0 0
\(899\) 54.4475 1.81593
\(900\) 0 0
\(901\) 37.7716 1.25835
\(902\) 0 0
\(903\) 30.2327 1.00608
\(904\) 0 0
\(905\) 31.2148 1.03762
\(906\) 0 0
\(907\) −29.2080 −0.969836 −0.484918 0.874560i \(-0.661151\pi\)
−0.484918 + 0.874560i \(0.661151\pi\)
\(908\) 0 0
\(909\) −10.7588 −0.356846
\(910\) 0 0
\(911\) 3.12567 0.103558 0.0517790 0.998659i \(-0.483511\pi\)
0.0517790 + 0.998659i \(0.483511\pi\)
\(912\) 0 0
\(913\) 0.268571 0.00888839
\(914\) 0 0
\(915\) 4.02229 0.132973
\(916\) 0 0
\(917\) 27.9358 0.922522
\(918\) 0 0
\(919\) −8.78644 −0.289838 −0.144919 0.989444i \(-0.546292\pi\)
−0.144919 + 0.989444i \(0.546292\pi\)
\(920\) 0 0
\(921\) −23.9813 −0.790212
\(922\) 0 0
\(923\) 50.1890 1.65199
\(924\) 0 0
\(925\) 2.97266 0.0977404
\(926\) 0 0
\(927\) 5.92902 0.194734
\(928\) 0 0
\(929\) 25.1548 0.825301 0.412651 0.910889i \(-0.364603\pi\)
0.412651 + 0.910889i \(0.364603\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.162504 −0.00532014
\(934\) 0 0
\(935\) −46.7452 −1.52873
\(936\) 0 0
\(937\) −26.4730 −0.864834 −0.432417 0.901674i \(-0.642339\pi\)
−0.432417 + 0.901674i \(0.642339\pi\)
\(938\) 0 0
\(939\) 6.72193 0.219362
\(940\) 0 0
\(941\) 5.26950 0.171781 0.0858905 0.996305i \(-0.472626\pi\)
0.0858905 + 0.996305i \(0.472626\pi\)
\(942\) 0 0
\(943\) 47.2995 1.54028
\(944\) 0 0
\(945\) −8.17024 −0.265778
\(946\) 0 0
\(947\) 24.3783 0.792187 0.396093 0.918210i \(-0.370366\pi\)
0.396093 + 0.918210i \(0.370366\pi\)
\(948\) 0 0
\(949\) −5.58677 −0.181354
\(950\) 0 0
\(951\) 14.2831 0.463162
\(952\) 0 0
\(953\) 49.6195 1.60733 0.803666 0.595080i \(-0.202880\pi\)
0.803666 + 0.595080i \(0.202880\pi\)
\(954\) 0 0
\(955\) −25.8384 −0.836112
\(956\) 0 0
\(957\) 22.1411 0.715722
\(958\) 0 0
\(959\) 44.0942 1.42388
\(960\) 0 0
\(961\) 27.3414 0.881981
\(962\) 0 0
\(963\) 2.58172 0.0831947
\(964\) 0 0
\(965\) −54.9650 −1.76939
\(966\) 0 0
\(967\) −25.8922 −0.832636 −0.416318 0.909219i \(-0.636680\pi\)
−0.416318 + 0.909219i \(0.636680\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.6260 0.405187 0.202593 0.979263i \(-0.435063\pi\)
0.202593 + 0.979263i \(0.435063\pi\)
\(972\) 0 0
\(973\) 44.1411 1.41510
\(974\) 0 0
\(975\) −8.55943 −0.274121
\(976\) 0 0
\(977\) 3.38144 0.108182 0.0540910 0.998536i \(-0.482774\pi\)
0.0540910 + 0.998536i \(0.482774\pi\)
\(978\) 0 0
\(979\) −21.9659 −0.702032
\(980\) 0 0
\(981\) 4.78106 0.152647
\(982\) 0 0
\(983\) −0.222563 −0.00709865 −0.00354933 0.999994i \(-0.501130\pi\)
−0.00354933 + 0.999994i \(0.501130\pi\)
\(984\) 0 0
\(985\) −42.2481 −1.34614
\(986\) 0 0
\(987\) 15.0128 0.477862
\(988\) 0 0
\(989\) 62.9344 2.00120
\(990\) 0 0
\(991\) −4.82893 −0.153396 −0.0766981 0.997054i \(-0.524438\pi\)
−0.0766981 + 0.997054i \(0.524438\pi\)
\(992\) 0 0
\(993\) −33.3063 −1.05694
\(994\) 0 0
\(995\) −6.22937 −0.197484
\(996\) 0 0
\(997\) −12.6418 −0.400369 −0.200185 0.979758i \(-0.564154\pi\)
−0.200185 + 0.979758i \(0.564154\pi\)
\(998\) 0 0
\(999\) 2.10607 0.0666330
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 4332.2.a.o.1.3 3
19.9 even 9 228.2.q.a.157.1 yes 6
19.17 even 9 228.2.q.a.61.1 6
19.18 odd 2 4332.2.a.n.1.3 3
57.17 odd 18 684.2.bo.a.289.1 6
57.47 odd 18 684.2.bo.a.613.1 6
76.47 odd 18 912.2.bo.e.385.1 6
76.55 odd 18 912.2.bo.e.289.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
228.2.q.a.61.1 6 19.17 even 9
228.2.q.a.157.1 yes 6 19.9 even 9
684.2.bo.a.289.1 6 57.17 odd 18
684.2.bo.a.613.1 6 57.47 odd 18
912.2.bo.e.289.1 6 76.55 odd 18
912.2.bo.e.385.1 6 76.47 odd 18
4332.2.a.n.1.3 3 19.18 odd 2
4332.2.a.o.1.3 3 1.1 even 1 trivial