Properties

Label 6008.2.a.b.1.9
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.25093 q^{3} +3.53241 q^{5} +1.19008 q^{7} +2.06668 q^{9} +O(q^{10})\) \(q-2.25093 q^{3} +3.53241 q^{5} +1.19008 q^{7} +2.06668 q^{9} -4.93741 q^{11} -4.24028 q^{13} -7.95119 q^{15} -0.933955 q^{17} +5.44476 q^{19} -2.67878 q^{21} -8.71920 q^{23} +7.47789 q^{25} +2.10084 q^{27} +8.13482 q^{29} +5.52324 q^{31} +11.1138 q^{33} +4.20384 q^{35} +3.19527 q^{37} +9.54456 q^{39} +11.8689 q^{41} -9.73774 q^{43} +7.30035 q^{45} -10.8322 q^{47} -5.58371 q^{49} +2.10227 q^{51} -3.26943 q^{53} -17.4409 q^{55} -12.2558 q^{57} +1.18004 q^{59} -1.59464 q^{61} +2.45951 q^{63} -14.9784 q^{65} -2.80301 q^{67} +19.6263 q^{69} +10.4959 q^{71} -3.66483 q^{73} -16.8322 q^{75} -5.87590 q^{77} +7.27723 q^{79} -10.9289 q^{81} -10.1008 q^{83} -3.29911 q^{85} -18.3109 q^{87} +2.87868 q^{89} -5.04626 q^{91} -12.4324 q^{93} +19.2331 q^{95} -4.60723 q^{97} -10.2041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.25093 −1.29957 −0.649787 0.760116i \(-0.725142\pi\)
−0.649787 + 0.760116i \(0.725142\pi\)
\(4\) 0 0
\(5\) 3.53241 1.57974 0.789870 0.613274i \(-0.210148\pi\)
0.789870 + 0.613274i \(0.210148\pi\)
\(6\) 0 0
\(7\) 1.19008 0.449807 0.224904 0.974381i \(-0.427793\pi\)
0.224904 + 0.974381i \(0.427793\pi\)
\(8\) 0 0
\(9\) 2.06668 0.688893
\(10\) 0 0
\(11\) −4.93741 −1.48869 −0.744343 0.667798i \(-0.767237\pi\)
−0.744343 + 0.667798i \(0.767237\pi\)
\(12\) 0 0
\(13\) −4.24028 −1.17604 −0.588020 0.808846i \(-0.700093\pi\)
−0.588020 + 0.808846i \(0.700093\pi\)
\(14\) 0 0
\(15\) −7.95119 −2.05299
\(16\) 0 0
\(17\) −0.933955 −0.226517 −0.113259 0.993566i \(-0.536129\pi\)
−0.113259 + 0.993566i \(0.536129\pi\)
\(18\) 0 0
\(19\) 5.44476 1.24911 0.624557 0.780979i \(-0.285280\pi\)
0.624557 + 0.780979i \(0.285280\pi\)
\(20\) 0 0
\(21\) −2.67878 −0.584558
\(22\) 0 0
\(23\) −8.71920 −1.81808 −0.909039 0.416711i \(-0.863183\pi\)
−0.909039 + 0.416711i \(0.863183\pi\)
\(24\) 0 0
\(25\) 7.47789 1.49558
\(26\) 0 0
\(27\) 2.10084 0.404306
\(28\) 0 0
\(29\) 8.13482 1.51060 0.755299 0.655380i \(-0.227491\pi\)
0.755299 + 0.655380i \(0.227491\pi\)
\(30\) 0 0
\(31\) 5.52324 0.992003 0.496002 0.868322i \(-0.334801\pi\)
0.496002 + 0.868322i \(0.334801\pi\)
\(32\) 0 0
\(33\) 11.1138 1.93466
\(34\) 0 0
\(35\) 4.20384 0.710578
\(36\) 0 0
\(37\) 3.19527 0.525299 0.262650 0.964891i \(-0.415404\pi\)
0.262650 + 0.964891i \(0.415404\pi\)
\(38\) 0 0
\(39\) 9.54456 1.52835
\(40\) 0 0
\(41\) 11.8689 1.85361 0.926806 0.375540i \(-0.122543\pi\)
0.926806 + 0.375540i \(0.122543\pi\)
\(42\) 0 0
\(43\) −9.73774 −1.48499 −0.742495 0.669851i \(-0.766358\pi\)
−0.742495 + 0.669851i \(0.766358\pi\)
\(44\) 0 0
\(45\) 7.30035 1.08827
\(46\) 0 0
\(47\) −10.8322 −1.58003 −0.790017 0.613085i \(-0.789928\pi\)
−0.790017 + 0.613085i \(0.789928\pi\)
\(48\) 0 0
\(49\) −5.58371 −0.797674
\(50\) 0 0
\(51\) 2.10227 0.294376
\(52\) 0 0
\(53\) −3.26943 −0.449091 −0.224546 0.974464i \(-0.572090\pi\)
−0.224546 + 0.974464i \(0.572090\pi\)
\(54\) 0 0
\(55\) −17.4409 −2.35174
\(56\) 0 0
\(57\) −12.2558 −1.62332
\(58\) 0 0
\(59\) 1.18004 0.153628 0.0768140 0.997045i \(-0.475525\pi\)
0.0768140 + 0.997045i \(0.475525\pi\)
\(60\) 0 0
\(61\) −1.59464 −0.204173 −0.102087 0.994776i \(-0.532552\pi\)
−0.102087 + 0.994776i \(0.532552\pi\)
\(62\) 0 0
\(63\) 2.45951 0.309869
\(64\) 0 0
\(65\) −14.9784 −1.85784
\(66\) 0 0
\(67\) −2.80301 −0.342443 −0.171221 0.985233i \(-0.554771\pi\)
−0.171221 + 0.985233i \(0.554771\pi\)
\(68\) 0 0
\(69\) 19.6263 2.36273
\(70\) 0 0
\(71\) 10.4959 1.24563 0.622815 0.782369i \(-0.285989\pi\)
0.622815 + 0.782369i \(0.285989\pi\)
\(72\) 0 0
\(73\) −3.66483 −0.428936 −0.214468 0.976731i \(-0.568802\pi\)
−0.214468 + 0.976731i \(0.568802\pi\)
\(74\) 0 0
\(75\) −16.8322 −1.94361
\(76\) 0 0
\(77\) −5.87590 −0.669622
\(78\) 0 0
\(79\) 7.27723 0.818753 0.409376 0.912366i \(-0.365746\pi\)
0.409376 + 0.912366i \(0.365746\pi\)
\(80\) 0 0
\(81\) −10.9289 −1.21432
\(82\) 0 0
\(83\) −10.1008 −1.10870 −0.554352 0.832282i \(-0.687034\pi\)
−0.554352 + 0.832282i \(0.687034\pi\)
\(84\) 0 0
\(85\) −3.29911 −0.357838
\(86\) 0 0
\(87\) −18.3109 −1.96314
\(88\) 0 0
\(89\) 2.87868 0.305139 0.152570 0.988293i \(-0.451245\pi\)
0.152570 + 0.988293i \(0.451245\pi\)
\(90\) 0 0
\(91\) −5.04626 −0.528992
\(92\) 0 0
\(93\) −12.4324 −1.28918
\(94\) 0 0
\(95\) 19.2331 1.97328
\(96\) 0 0
\(97\) −4.60723 −0.467793 −0.233896 0.972262i \(-0.575148\pi\)
−0.233896 + 0.972262i \(0.575148\pi\)
\(98\) 0 0
\(99\) −10.2041 −1.02555
\(100\) 0 0
\(101\) −1.80928 −0.180030 −0.0900150 0.995940i \(-0.528691\pi\)
−0.0900150 + 0.995940i \(0.528691\pi\)
\(102\) 0 0
\(103\) 1.82726 0.180045 0.0900227 0.995940i \(-0.471306\pi\)
0.0900227 + 0.995940i \(0.471306\pi\)
\(104\) 0 0
\(105\) −9.46254 −0.923449
\(106\) 0 0
\(107\) 1.18976 0.115018 0.0575092 0.998345i \(-0.481684\pi\)
0.0575092 + 0.998345i \(0.481684\pi\)
\(108\) 0 0
\(109\) −4.85334 −0.464866 −0.232433 0.972612i \(-0.574669\pi\)
−0.232433 + 0.972612i \(0.574669\pi\)
\(110\) 0 0
\(111\) −7.19232 −0.682665
\(112\) 0 0
\(113\) −19.9551 −1.87721 −0.938607 0.344989i \(-0.887883\pi\)
−0.938607 + 0.344989i \(0.887883\pi\)
\(114\) 0 0
\(115\) −30.7997 −2.87209
\(116\) 0 0
\(117\) −8.76329 −0.810167
\(118\) 0 0
\(119\) −1.11148 −0.101889
\(120\) 0 0
\(121\) 13.3780 1.21619
\(122\) 0 0
\(123\) −26.7161 −2.40891
\(124\) 0 0
\(125\) 8.75291 0.782884
\(126\) 0 0
\(127\) −17.2642 −1.53195 −0.765976 0.642870i \(-0.777744\pi\)
−0.765976 + 0.642870i \(0.777744\pi\)
\(128\) 0 0
\(129\) 21.9189 1.92986
\(130\) 0 0
\(131\) −17.4217 −1.52214 −0.761070 0.648670i \(-0.775326\pi\)
−0.761070 + 0.648670i \(0.775326\pi\)
\(132\) 0 0
\(133\) 6.47969 0.561861
\(134\) 0 0
\(135\) 7.42100 0.638698
\(136\) 0 0
\(137\) 4.05458 0.346406 0.173203 0.984886i \(-0.444588\pi\)
0.173203 + 0.984886i \(0.444588\pi\)
\(138\) 0 0
\(139\) 6.87804 0.583388 0.291694 0.956512i \(-0.405781\pi\)
0.291694 + 0.956512i \(0.405781\pi\)
\(140\) 0 0
\(141\) 24.3824 2.05337
\(142\) 0 0
\(143\) 20.9360 1.75076
\(144\) 0 0
\(145\) 28.7355 2.38635
\(146\) 0 0
\(147\) 12.5685 1.03664
\(148\) 0 0
\(149\) 13.4939 1.10546 0.552732 0.833359i \(-0.313585\pi\)
0.552732 + 0.833359i \(0.313585\pi\)
\(150\) 0 0
\(151\) −17.2737 −1.40571 −0.702856 0.711332i \(-0.748092\pi\)
−0.702856 + 0.711332i \(0.748092\pi\)
\(152\) 0 0
\(153\) −1.93019 −0.156046
\(154\) 0 0
\(155\) 19.5103 1.56711
\(156\) 0 0
\(157\) 6.35462 0.507154 0.253577 0.967315i \(-0.418393\pi\)
0.253577 + 0.967315i \(0.418393\pi\)
\(158\) 0 0
\(159\) 7.35926 0.583628
\(160\) 0 0
\(161\) −10.3765 −0.817785
\(162\) 0 0
\(163\) −14.8835 −1.16577 −0.582884 0.812555i \(-0.698076\pi\)
−0.582884 + 0.812555i \(0.698076\pi\)
\(164\) 0 0
\(165\) 39.2583 3.05626
\(166\) 0 0
\(167\) −2.91665 −0.225697 −0.112848 0.993612i \(-0.535997\pi\)
−0.112848 + 0.993612i \(0.535997\pi\)
\(168\) 0 0
\(169\) 4.97994 0.383072
\(170\) 0 0
\(171\) 11.2526 0.860507
\(172\) 0 0
\(173\) 11.0386 0.839252 0.419626 0.907697i \(-0.362161\pi\)
0.419626 + 0.907697i \(0.362161\pi\)
\(174\) 0 0
\(175\) 8.89927 0.672722
\(176\) 0 0
\(177\) −2.65618 −0.199651
\(178\) 0 0
\(179\) 12.7589 0.953645 0.476823 0.878999i \(-0.341788\pi\)
0.476823 + 0.878999i \(0.341788\pi\)
\(180\) 0 0
\(181\) −19.6760 −1.46251 −0.731254 0.682105i \(-0.761065\pi\)
−0.731254 + 0.682105i \(0.761065\pi\)
\(182\) 0 0
\(183\) 3.58943 0.265338
\(184\) 0 0
\(185\) 11.2870 0.829836
\(186\) 0 0
\(187\) 4.61132 0.337213
\(188\) 0 0
\(189\) 2.50016 0.181860
\(190\) 0 0
\(191\) 8.69296 0.629000 0.314500 0.949257i \(-0.398163\pi\)
0.314500 + 0.949257i \(0.398163\pi\)
\(192\) 0 0
\(193\) −13.5177 −0.973028 −0.486514 0.873673i \(-0.661732\pi\)
−0.486514 + 0.873673i \(0.661732\pi\)
\(194\) 0 0
\(195\) 33.7153 2.41440
\(196\) 0 0
\(197\) 2.12411 0.151337 0.0756684 0.997133i \(-0.475891\pi\)
0.0756684 + 0.997133i \(0.475891\pi\)
\(198\) 0 0
\(199\) −13.3621 −0.947213 −0.473606 0.880737i \(-0.657048\pi\)
−0.473606 + 0.880737i \(0.657048\pi\)
\(200\) 0 0
\(201\) 6.30938 0.445030
\(202\) 0 0
\(203\) 9.68107 0.679478
\(204\) 0 0
\(205\) 41.9258 2.92822
\(206\) 0 0
\(207\) −18.0198 −1.25246
\(208\) 0 0
\(209\) −26.8830 −1.85954
\(210\) 0 0
\(211\) 5.47272 0.376758 0.188379 0.982096i \(-0.439677\pi\)
0.188379 + 0.982096i \(0.439677\pi\)
\(212\) 0 0
\(213\) −23.6255 −1.61879
\(214\) 0 0
\(215\) −34.3976 −2.34590
\(216\) 0 0
\(217\) 6.57309 0.446210
\(218\) 0 0
\(219\) 8.24928 0.557435
\(220\) 0 0
\(221\) 3.96022 0.266394
\(222\) 0 0
\(223\) −13.7689 −0.922034 −0.461017 0.887391i \(-0.652515\pi\)
−0.461017 + 0.887391i \(0.652515\pi\)
\(224\) 0 0
\(225\) 15.4544 1.03029
\(226\) 0 0
\(227\) 25.8486 1.71564 0.857818 0.513954i \(-0.171820\pi\)
0.857818 + 0.513954i \(0.171820\pi\)
\(228\) 0 0
\(229\) −7.83005 −0.517424 −0.258712 0.965954i \(-0.583298\pi\)
−0.258712 + 0.965954i \(0.583298\pi\)
\(230\) 0 0
\(231\) 13.2262 0.870223
\(232\) 0 0
\(233\) −23.8290 −1.56109 −0.780545 0.625099i \(-0.785059\pi\)
−0.780545 + 0.625099i \(0.785059\pi\)
\(234\) 0 0
\(235\) −38.2636 −2.49604
\(236\) 0 0
\(237\) −16.3805 −1.06403
\(238\) 0 0
\(239\) −7.72161 −0.499469 −0.249735 0.968314i \(-0.580343\pi\)
−0.249735 + 0.968314i \(0.580343\pi\)
\(240\) 0 0
\(241\) 13.0169 0.838494 0.419247 0.907872i \(-0.362294\pi\)
0.419247 + 0.907872i \(0.362294\pi\)
\(242\) 0 0
\(243\) 18.2976 1.17379
\(244\) 0 0
\(245\) −19.7239 −1.26012
\(246\) 0 0
\(247\) −23.0873 −1.46901
\(248\) 0 0
\(249\) 22.7361 1.44084
\(250\) 0 0
\(251\) −9.12953 −0.576251 −0.288125 0.957593i \(-0.593032\pi\)
−0.288125 + 0.957593i \(0.593032\pi\)
\(252\) 0 0
\(253\) 43.0503 2.70655
\(254\) 0 0
\(255\) 7.42605 0.465037
\(256\) 0 0
\(257\) 25.4545 1.58781 0.793903 0.608044i \(-0.208046\pi\)
0.793903 + 0.608044i \(0.208046\pi\)
\(258\) 0 0
\(259\) 3.80262 0.236283
\(260\) 0 0
\(261\) 16.8121 1.04064
\(262\) 0 0
\(263\) −27.0610 −1.66866 −0.834328 0.551269i \(-0.814144\pi\)
−0.834328 + 0.551269i \(0.814144\pi\)
\(264\) 0 0
\(265\) −11.5490 −0.709448
\(266\) 0 0
\(267\) −6.47970 −0.396551
\(268\) 0 0
\(269\) 3.73731 0.227868 0.113934 0.993488i \(-0.463655\pi\)
0.113934 + 0.993488i \(0.463655\pi\)
\(270\) 0 0
\(271\) −27.6698 −1.68082 −0.840412 0.541949i \(-0.817687\pi\)
−0.840412 + 0.541949i \(0.817687\pi\)
\(272\) 0 0
\(273\) 11.3588 0.687464
\(274\) 0 0
\(275\) −36.9214 −2.22645
\(276\) 0 0
\(277\) −13.1090 −0.787642 −0.393821 0.919187i \(-0.628847\pi\)
−0.393821 + 0.919187i \(0.628847\pi\)
\(278\) 0 0
\(279\) 11.4148 0.683385
\(280\) 0 0
\(281\) −26.1373 −1.55922 −0.779612 0.626263i \(-0.784584\pi\)
−0.779612 + 0.626263i \(0.784584\pi\)
\(282\) 0 0
\(283\) 17.0584 1.01402 0.507009 0.861941i \(-0.330751\pi\)
0.507009 + 0.861941i \(0.330751\pi\)
\(284\) 0 0
\(285\) −43.2924 −2.56442
\(286\) 0 0
\(287\) 14.1249 0.833768
\(288\) 0 0
\(289\) −16.1277 −0.948690
\(290\) 0 0
\(291\) 10.3705 0.607932
\(292\) 0 0
\(293\) 17.9400 1.04806 0.524032 0.851699i \(-0.324427\pi\)
0.524032 + 0.851699i \(0.324427\pi\)
\(294\) 0 0
\(295\) 4.16838 0.242692
\(296\) 0 0
\(297\) −10.3727 −0.601885
\(298\) 0 0
\(299\) 36.9718 2.13813
\(300\) 0 0
\(301\) −11.5887 −0.667959
\(302\) 0 0
\(303\) 4.07256 0.233962
\(304\) 0 0
\(305\) −5.63292 −0.322540
\(306\) 0 0
\(307\) −25.5218 −1.45660 −0.728302 0.685256i \(-0.759690\pi\)
−0.728302 + 0.685256i \(0.759690\pi\)
\(308\) 0 0
\(309\) −4.11304 −0.233982
\(310\) 0 0
\(311\) 1.05784 0.0599847 0.0299924 0.999550i \(-0.490452\pi\)
0.0299924 + 0.999550i \(0.490452\pi\)
\(312\) 0 0
\(313\) −0.516552 −0.0291972 −0.0145986 0.999893i \(-0.504647\pi\)
−0.0145986 + 0.999893i \(0.504647\pi\)
\(314\) 0 0
\(315\) 8.68799 0.489513
\(316\) 0 0
\(317\) 2.38840 0.134146 0.0670730 0.997748i \(-0.478634\pi\)
0.0670730 + 0.997748i \(0.478634\pi\)
\(318\) 0 0
\(319\) −40.1650 −2.24881
\(320\) 0 0
\(321\) −2.67807 −0.149475
\(322\) 0 0
\(323\) −5.08516 −0.282946
\(324\) 0 0
\(325\) −31.7083 −1.75886
\(326\) 0 0
\(327\) 10.9245 0.604128
\(328\) 0 0
\(329\) −12.8911 −0.710711
\(330\) 0 0
\(331\) −15.1964 −0.835270 −0.417635 0.908615i \(-0.637141\pi\)
−0.417635 + 0.908615i \(0.637141\pi\)
\(332\) 0 0
\(333\) 6.60360 0.361875
\(334\) 0 0
\(335\) −9.90138 −0.540970
\(336\) 0 0
\(337\) 5.99184 0.326396 0.163198 0.986593i \(-0.447819\pi\)
0.163198 + 0.986593i \(0.447819\pi\)
\(338\) 0 0
\(339\) 44.9174 2.43958
\(340\) 0 0
\(341\) −27.2705 −1.47678
\(342\) 0 0
\(343\) −14.9756 −0.808606
\(344\) 0 0
\(345\) 69.3280 3.73249
\(346\) 0 0
\(347\) −23.6805 −1.27124 −0.635618 0.772004i \(-0.719255\pi\)
−0.635618 + 0.772004i \(0.719255\pi\)
\(348\) 0 0
\(349\) −8.86011 −0.474271 −0.237135 0.971477i \(-0.576209\pi\)
−0.237135 + 0.971477i \(0.576209\pi\)
\(350\) 0 0
\(351\) −8.90812 −0.475480
\(352\) 0 0
\(353\) 16.3451 0.869959 0.434980 0.900440i \(-0.356756\pi\)
0.434980 + 0.900440i \(0.356756\pi\)
\(354\) 0 0
\(355\) 37.0757 1.96777
\(356\) 0 0
\(357\) 2.50186 0.132412
\(358\) 0 0
\(359\) 4.62338 0.244013 0.122006 0.992529i \(-0.461067\pi\)
0.122006 + 0.992529i \(0.461067\pi\)
\(360\) 0 0
\(361\) 10.6454 0.560286
\(362\) 0 0
\(363\) −30.1130 −1.58052
\(364\) 0 0
\(365\) −12.9457 −0.677608
\(366\) 0 0
\(367\) 34.0996 1.77999 0.889993 0.455973i \(-0.150709\pi\)
0.889993 + 0.455973i \(0.150709\pi\)
\(368\) 0 0
\(369\) 24.5292 1.27694
\(370\) 0 0
\(371\) −3.89088 −0.202005
\(372\) 0 0
\(373\) −22.6097 −1.17068 −0.585342 0.810787i \(-0.699040\pi\)
−0.585342 + 0.810787i \(0.699040\pi\)
\(374\) 0 0
\(375\) −19.7022 −1.01742
\(376\) 0 0
\(377\) −34.4939 −1.77653
\(378\) 0 0
\(379\) 14.1122 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(380\) 0 0
\(381\) 38.8605 1.99088
\(382\) 0 0
\(383\) 38.3368 1.95892 0.979461 0.201635i \(-0.0646254\pi\)
0.979461 + 0.201635i \(0.0646254\pi\)
\(384\) 0 0
\(385\) −20.7561 −1.05783
\(386\) 0 0
\(387\) −20.1248 −1.02300
\(388\) 0 0
\(389\) −19.3562 −0.981398 −0.490699 0.871329i \(-0.663259\pi\)
−0.490699 + 0.871329i \(0.663259\pi\)
\(390\) 0 0
\(391\) 8.14333 0.411826
\(392\) 0 0
\(393\) 39.2150 1.97813
\(394\) 0 0
\(395\) 25.7061 1.29342
\(396\) 0 0
\(397\) 10.1580 0.509813 0.254907 0.966966i \(-0.417955\pi\)
0.254907 + 0.966966i \(0.417955\pi\)
\(398\) 0 0
\(399\) −14.5853 −0.730180
\(400\) 0 0
\(401\) −23.3331 −1.16520 −0.582599 0.812760i \(-0.697964\pi\)
−0.582599 + 0.812760i \(0.697964\pi\)
\(402\) 0 0
\(403\) −23.4201 −1.16664
\(404\) 0 0
\(405\) −38.6052 −1.91831
\(406\) 0 0
\(407\) −15.7764 −0.782005
\(408\) 0 0
\(409\) 29.6766 1.46741 0.733707 0.679466i \(-0.237788\pi\)
0.733707 + 0.679466i \(0.237788\pi\)
\(410\) 0 0
\(411\) −9.12656 −0.450180
\(412\) 0 0
\(413\) 1.40434 0.0691030
\(414\) 0 0
\(415\) −35.6800 −1.75146
\(416\) 0 0
\(417\) −15.4820 −0.758156
\(418\) 0 0
\(419\) 11.5767 0.565560 0.282780 0.959185i \(-0.408743\pi\)
0.282780 + 0.959185i \(0.408743\pi\)
\(420\) 0 0
\(421\) −21.5270 −1.04916 −0.524580 0.851361i \(-0.675778\pi\)
−0.524580 + 0.851361i \(0.675778\pi\)
\(422\) 0 0
\(423\) −22.3866 −1.08847
\(424\) 0 0
\(425\) −6.98401 −0.338774
\(426\) 0 0
\(427\) −1.89775 −0.0918385
\(428\) 0 0
\(429\) −47.1254 −2.27524
\(430\) 0 0
\(431\) −30.2392 −1.45657 −0.728285 0.685275i \(-0.759682\pi\)
−0.728285 + 0.685275i \(0.759682\pi\)
\(432\) 0 0
\(433\) 13.0660 0.627914 0.313957 0.949437i \(-0.398345\pi\)
0.313957 + 0.949437i \(0.398345\pi\)
\(434\) 0 0
\(435\) −64.6816 −3.10124
\(436\) 0 0
\(437\) −47.4740 −2.27099
\(438\) 0 0
\(439\) 30.7871 1.46939 0.734695 0.678398i \(-0.237325\pi\)
0.734695 + 0.678398i \(0.237325\pi\)
\(440\) 0 0
\(441\) −11.5398 −0.549512
\(442\) 0 0
\(443\) −3.85147 −0.182989 −0.0914944 0.995806i \(-0.529164\pi\)
−0.0914944 + 0.995806i \(0.529164\pi\)
\(444\) 0 0
\(445\) 10.1687 0.482041
\(446\) 0 0
\(447\) −30.3738 −1.43663
\(448\) 0 0
\(449\) −28.3363 −1.33727 −0.668636 0.743590i \(-0.733122\pi\)
−0.668636 + 0.743590i \(0.733122\pi\)
\(450\) 0 0
\(451\) −58.6017 −2.75945
\(452\) 0 0
\(453\) 38.8818 1.82683
\(454\) 0 0
\(455\) −17.8254 −0.835669
\(456\) 0 0
\(457\) −24.7636 −1.15839 −0.579196 0.815189i \(-0.696633\pi\)
−0.579196 + 0.815189i \(0.696633\pi\)
\(458\) 0 0
\(459\) −1.96209 −0.0915823
\(460\) 0 0
\(461\) 16.0171 0.745990 0.372995 0.927833i \(-0.378331\pi\)
0.372995 + 0.927833i \(0.378331\pi\)
\(462\) 0 0
\(463\) −25.8891 −1.20317 −0.601585 0.798809i \(-0.705464\pi\)
−0.601585 + 0.798809i \(0.705464\pi\)
\(464\) 0 0
\(465\) −43.9163 −2.03657
\(466\) 0 0
\(467\) 21.2722 0.984362 0.492181 0.870493i \(-0.336200\pi\)
0.492181 + 0.870493i \(0.336200\pi\)
\(468\) 0 0
\(469\) −3.33580 −0.154033
\(470\) 0 0
\(471\) −14.3038 −0.659084
\(472\) 0 0
\(473\) 48.0792 2.21068
\(474\) 0 0
\(475\) 40.7153 1.86815
\(476\) 0 0
\(477\) −6.75688 −0.309376
\(478\) 0 0
\(479\) −32.4888 −1.48445 −0.742226 0.670150i \(-0.766230\pi\)
−0.742226 + 0.670150i \(0.766230\pi\)
\(480\) 0 0
\(481\) −13.5488 −0.617773
\(482\) 0 0
\(483\) 23.3568 1.06277
\(484\) 0 0
\(485\) −16.2746 −0.738991
\(486\) 0 0
\(487\) 13.8104 0.625807 0.312903 0.949785i \(-0.398698\pi\)
0.312903 + 0.949785i \(0.398698\pi\)
\(488\) 0 0
\(489\) 33.5018 1.51500
\(490\) 0 0
\(491\) −6.46238 −0.291643 −0.145822 0.989311i \(-0.546583\pi\)
−0.145822 + 0.989311i \(0.546583\pi\)
\(492\) 0 0
\(493\) −7.59756 −0.342177
\(494\) 0 0
\(495\) −36.0449 −1.62010
\(496\) 0 0
\(497\) 12.4909 0.560293
\(498\) 0 0
\(499\) −4.48661 −0.200848 −0.100424 0.994945i \(-0.532020\pi\)
−0.100424 + 0.994945i \(0.532020\pi\)
\(500\) 0 0
\(501\) 6.56516 0.293310
\(502\) 0 0
\(503\) −22.4536 −1.00116 −0.500578 0.865692i \(-0.666879\pi\)
−0.500578 + 0.865692i \(0.666879\pi\)
\(504\) 0 0
\(505\) −6.39111 −0.284400
\(506\) 0 0
\(507\) −11.2095 −0.497831
\(508\) 0 0
\(509\) −24.7392 −1.09655 −0.548274 0.836299i \(-0.684715\pi\)
−0.548274 + 0.836299i \(0.684715\pi\)
\(510\) 0 0
\(511\) −4.36144 −0.192939
\(512\) 0 0
\(513\) 11.4386 0.505024
\(514\) 0 0
\(515\) 6.45463 0.284425
\(516\) 0 0
\(517\) 53.4829 2.35217
\(518\) 0 0
\(519\) −24.8472 −1.09067
\(520\) 0 0
\(521\) 3.89577 0.170677 0.0853384 0.996352i \(-0.472803\pi\)
0.0853384 + 0.996352i \(0.472803\pi\)
\(522\) 0 0
\(523\) 19.9254 0.871278 0.435639 0.900122i \(-0.356522\pi\)
0.435639 + 0.900122i \(0.356522\pi\)
\(524\) 0 0
\(525\) −20.0316 −0.874252
\(526\) 0 0
\(527\) −5.15846 −0.224706
\(528\) 0 0
\(529\) 53.0244 2.30541
\(530\) 0 0
\(531\) 2.43876 0.105833
\(532\) 0 0
\(533\) −50.3274 −2.17992
\(534\) 0 0
\(535\) 4.20272 0.181699
\(536\) 0 0
\(537\) −28.7194 −1.23933
\(538\) 0 0
\(539\) 27.5691 1.18749
\(540\) 0 0
\(541\) 14.9395 0.642301 0.321150 0.947028i \(-0.395931\pi\)
0.321150 + 0.947028i \(0.395931\pi\)
\(542\) 0 0
\(543\) 44.2894 1.90064
\(544\) 0 0
\(545\) −17.1440 −0.734367
\(546\) 0 0
\(547\) 33.5067 1.43264 0.716320 0.697771i \(-0.245825\pi\)
0.716320 + 0.697771i \(0.245825\pi\)
\(548\) 0 0
\(549\) −3.29562 −0.140653
\(550\) 0 0
\(551\) 44.2922 1.88691
\(552\) 0 0
\(553\) 8.66048 0.368281
\(554\) 0 0
\(555\) −25.4062 −1.07843
\(556\) 0 0
\(557\) −1.15742 −0.0490414 −0.0245207 0.999699i \(-0.507806\pi\)
−0.0245207 + 0.999699i \(0.507806\pi\)
\(558\) 0 0
\(559\) 41.2907 1.74641
\(560\) 0 0
\(561\) −10.3797 −0.438233
\(562\) 0 0
\(563\) −27.5565 −1.16137 −0.580685 0.814129i \(-0.697215\pi\)
−0.580685 + 0.814129i \(0.697215\pi\)
\(564\) 0 0
\(565\) −70.4893 −2.96551
\(566\) 0 0
\(567\) −13.0062 −0.546210
\(568\) 0 0
\(569\) −35.1655 −1.47421 −0.737107 0.675776i \(-0.763809\pi\)
−0.737107 + 0.675776i \(0.763809\pi\)
\(570\) 0 0
\(571\) 3.72807 0.156015 0.0780074 0.996953i \(-0.475144\pi\)
0.0780074 + 0.996953i \(0.475144\pi\)
\(572\) 0 0
\(573\) −19.5672 −0.817433
\(574\) 0 0
\(575\) −65.2012 −2.71908
\(576\) 0 0
\(577\) −3.79664 −0.158056 −0.0790281 0.996872i \(-0.525182\pi\)
−0.0790281 + 0.996872i \(0.525182\pi\)
\(578\) 0 0
\(579\) 30.4275 1.26452
\(580\) 0 0
\(581\) −12.0207 −0.498703
\(582\) 0 0
\(583\) 16.1425 0.668556
\(584\) 0 0
\(585\) −30.9555 −1.27985
\(586\) 0 0
\(587\) 16.9850 0.701048 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(588\) 0 0
\(589\) 30.0727 1.23913
\(590\) 0 0
\(591\) −4.78123 −0.196673
\(592\) 0 0
\(593\) 24.9726 1.02550 0.512751 0.858537i \(-0.328626\pi\)
0.512751 + 0.858537i \(0.328626\pi\)
\(594\) 0 0
\(595\) −3.92619 −0.160958
\(596\) 0 0
\(597\) 30.0771 1.23097
\(598\) 0 0
\(599\) 13.6270 0.556785 0.278392 0.960467i \(-0.410198\pi\)
0.278392 + 0.960467i \(0.410198\pi\)
\(600\) 0 0
\(601\) −24.3804 −0.994497 −0.497248 0.867608i \(-0.665656\pi\)
−0.497248 + 0.867608i \(0.665656\pi\)
\(602\) 0 0
\(603\) −5.79293 −0.235906
\(604\) 0 0
\(605\) 47.2566 1.92126
\(606\) 0 0
\(607\) 11.2600 0.457028 0.228514 0.973541i \(-0.426613\pi\)
0.228514 + 0.973541i \(0.426613\pi\)
\(608\) 0 0
\(609\) −21.7914 −0.883032
\(610\) 0 0
\(611\) 45.9314 1.85818
\(612\) 0 0
\(613\) 18.7593 0.757681 0.378840 0.925462i \(-0.376323\pi\)
0.378840 + 0.925462i \(0.376323\pi\)
\(614\) 0 0
\(615\) −94.3720 −3.80545
\(616\) 0 0
\(617\) −30.0002 −1.20776 −0.603881 0.797074i \(-0.706380\pi\)
−0.603881 + 0.797074i \(0.706380\pi\)
\(618\) 0 0
\(619\) 19.2450 0.773522 0.386761 0.922180i \(-0.373594\pi\)
0.386761 + 0.922180i \(0.373594\pi\)
\(620\) 0 0
\(621\) −18.3176 −0.735060
\(622\) 0 0
\(623\) 3.42585 0.137254
\(624\) 0 0
\(625\) −6.47062 −0.258825
\(626\) 0 0
\(627\) 60.5118 2.41661
\(628\) 0 0
\(629\) −2.98424 −0.118989
\(630\) 0 0
\(631\) −27.6021 −1.09882 −0.549411 0.835552i \(-0.685148\pi\)
−0.549411 + 0.835552i \(0.685148\pi\)
\(632\) 0 0
\(633\) −12.3187 −0.489625
\(634\) 0 0
\(635\) −60.9842 −2.42008
\(636\) 0 0
\(637\) 23.6765 0.938097
\(638\) 0 0
\(639\) 21.6916 0.858107
\(640\) 0 0
\(641\) −17.2443 −0.681110 −0.340555 0.940225i \(-0.610615\pi\)
−0.340555 + 0.940225i \(0.610615\pi\)
\(642\) 0 0
\(643\) 7.14378 0.281723 0.140862 0.990029i \(-0.455013\pi\)
0.140862 + 0.990029i \(0.455013\pi\)
\(644\) 0 0
\(645\) 77.4266 3.04867
\(646\) 0 0
\(647\) −25.6846 −1.00976 −0.504882 0.863188i \(-0.668464\pi\)
−0.504882 + 0.863188i \(0.668464\pi\)
\(648\) 0 0
\(649\) −5.82634 −0.228704
\(650\) 0 0
\(651\) −14.7955 −0.579883
\(652\) 0 0
\(653\) −14.3382 −0.561096 −0.280548 0.959840i \(-0.590516\pi\)
−0.280548 + 0.959840i \(0.590516\pi\)
\(654\) 0 0
\(655\) −61.5404 −2.40458
\(656\) 0 0
\(657\) −7.57404 −0.295492
\(658\) 0 0
\(659\) 32.3569 1.26045 0.630223 0.776414i \(-0.282963\pi\)
0.630223 + 0.776414i \(0.282963\pi\)
\(660\) 0 0
\(661\) −25.9681 −1.01004 −0.505022 0.863107i \(-0.668515\pi\)
−0.505022 + 0.863107i \(0.668515\pi\)
\(662\) 0 0
\(663\) −8.91418 −0.346198
\(664\) 0 0
\(665\) 22.8889 0.887593
\(666\) 0 0
\(667\) −70.9291 −2.74639
\(668\) 0 0
\(669\) 30.9928 1.19825
\(670\) 0 0
\(671\) 7.87341 0.303950
\(672\) 0 0
\(673\) 46.8034 1.80414 0.902069 0.431592i \(-0.142048\pi\)
0.902069 + 0.431592i \(0.142048\pi\)
\(674\) 0 0
\(675\) 15.7098 0.604671
\(676\) 0 0
\(677\) 4.13878 0.159066 0.0795331 0.996832i \(-0.474657\pi\)
0.0795331 + 0.996832i \(0.474657\pi\)
\(678\) 0 0
\(679\) −5.48296 −0.210417
\(680\) 0 0
\(681\) −58.1835 −2.22960
\(682\) 0 0
\(683\) −8.59259 −0.328786 −0.164393 0.986395i \(-0.552567\pi\)
−0.164393 + 0.986395i \(0.552567\pi\)
\(684\) 0 0
\(685\) 14.3224 0.547231
\(686\) 0 0
\(687\) 17.6249 0.672431
\(688\) 0 0
\(689\) 13.8633 0.528150
\(690\) 0 0
\(691\) 10.0833 0.383588 0.191794 0.981435i \(-0.438569\pi\)
0.191794 + 0.981435i \(0.438569\pi\)
\(692\) 0 0
\(693\) −12.1436 −0.461298
\(694\) 0 0
\(695\) 24.2960 0.921601
\(696\) 0 0
\(697\) −11.0850 −0.419875
\(698\) 0 0
\(699\) 53.6374 2.02875
\(700\) 0 0
\(701\) −12.7822 −0.482775 −0.241388 0.970429i \(-0.577603\pi\)
−0.241388 + 0.970429i \(0.577603\pi\)
\(702\) 0 0
\(703\) 17.3975 0.656158
\(704\) 0 0
\(705\) 86.1286 3.24379
\(706\) 0 0
\(707\) −2.15318 −0.0809788
\(708\) 0 0
\(709\) 24.8184 0.932074 0.466037 0.884765i \(-0.345681\pi\)
0.466037 + 0.884765i \(0.345681\pi\)
\(710\) 0 0
\(711\) 15.0397 0.564033
\(712\) 0 0
\(713\) −48.1582 −1.80354
\(714\) 0 0
\(715\) 73.9544 2.76574
\(716\) 0 0
\(717\) 17.3808 0.649097
\(718\) 0 0
\(719\) 30.3511 1.13191 0.565953 0.824437i \(-0.308508\pi\)
0.565953 + 0.824437i \(0.308508\pi\)
\(720\) 0 0
\(721\) 2.17458 0.0809857
\(722\) 0 0
\(723\) −29.3002 −1.08969
\(724\) 0 0
\(725\) 60.8313 2.25922
\(726\) 0 0
\(727\) −18.2849 −0.678151 −0.339076 0.940759i \(-0.610114\pi\)
−0.339076 + 0.940759i \(0.610114\pi\)
\(728\) 0 0
\(729\) −8.39999 −0.311111
\(730\) 0 0
\(731\) 9.09460 0.336376
\(732\) 0 0
\(733\) −22.4056 −0.827568 −0.413784 0.910375i \(-0.635793\pi\)
−0.413784 + 0.910375i \(0.635793\pi\)
\(734\) 0 0
\(735\) 44.3972 1.63762
\(736\) 0 0
\(737\) 13.8396 0.509789
\(738\) 0 0
\(739\) −1.82051 −0.0669687 −0.0334844 0.999439i \(-0.510660\pi\)
−0.0334844 + 0.999439i \(0.510660\pi\)
\(740\) 0 0
\(741\) 51.9679 1.90909
\(742\) 0 0
\(743\) 28.0989 1.03085 0.515424 0.856936i \(-0.327635\pi\)
0.515424 + 0.856936i \(0.327635\pi\)
\(744\) 0 0
\(745\) 47.6659 1.74634
\(746\) 0 0
\(747\) −20.8751 −0.763779
\(748\) 0 0
\(749\) 1.41591 0.0517361
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 20.5499 0.748881
\(754\) 0 0
\(755\) −61.0177 −2.22066
\(756\) 0 0
\(757\) −8.03911 −0.292187 −0.146093 0.989271i \(-0.546670\pi\)
−0.146093 + 0.989271i \(0.546670\pi\)
\(758\) 0 0
\(759\) −96.9031 −3.51736
\(760\) 0 0
\(761\) −3.57818 −0.129709 −0.0648544 0.997895i \(-0.520658\pi\)
−0.0648544 + 0.997895i \(0.520658\pi\)
\(762\) 0 0
\(763\) −5.77585 −0.209100
\(764\) 0 0
\(765\) −6.81820 −0.246512
\(766\) 0 0
\(767\) −5.00369 −0.180673
\(768\) 0 0
\(769\) −2.99846 −0.108127 −0.0540636 0.998537i \(-0.517217\pi\)
−0.0540636 + 0.998537i \(0.517217\pi\)
\(770\) 0 0
\(771\) −57.2962 −2.06347
\(772\) 0 0
\(773\) 18.8092 0.676519 0.338259 0.941053i \(-0.390162\pi\)
0.338259 + 0.941053i \(0.390162\pi\)
\(774\) 0 0
\(775\) 41.3022 1.48362
\(776\) 0 0
\(777\) −8.55943 −0.307068
\(778\) 0 0
\(779\) 64.6234 2.31537
\(780\) 0 0
\(781\) −51.8224 −1.85435
\(782\) 0 0
\(783\) 17.0899 0.610744
\(784\) 0 0
\(785\) 22.4471 0.801171
\(786\) 0 0
\(787\) 25.4340 0.906625 0.453313 0.891352i \(-0.350242\pi\)
0.453313 + 0.891352i \(0.350242\pi\)
\(788\) 0 0
\(789\) 60.9125 2.16854
\(790\) 0 0
\(791\) −23.7481 −0.844384
\(792\) 0 0
\(793\) 6.76172 0.240116
\(794\) 0 0
\(795\) 25.9959 0.921980
\(796\) 0 0
\(797\) −30.8058 −1.09120 −0.545599 0.838046i \(-0.683698\pi\)
−0.545599 + 0.838046i \(0.683698\pi\)
\(798\) 0 0
\(799\) 10.1168 0.357905
\(800\) 0 0
\(801\) 5.94931 0.210209
\(802\) 0 0
\(803\) 18.0948 0.638552
\(804\) 0 0
\(805\) −36.6541 −1.29189
\(806\) 0 0
\(807\) −8.41241 −0.296131
\(808\) 0 0
\(809\) −0.831446 −0.0292321 −0.0146160 0.999893i \(-0.504653\pi\)
−0.0146160 + 0.999893i \(0.504653\pi\)
\(810\) 0 0
\(811\) 20.8900 0.733547 0.366773 0.930310i \(-0.380462\pi\)
0.366773 + 0.930310i \(0.380462\pi\)
\(812\) 0 0
\(813\) 62.2828 2.18435
\(814\) 0 0
\(815\) −52.5747 −1.84161
\(816\) 0 0
\(817\) −53.0197 −1.85492
\(818\) 0 0
\(819\) −10.4290 −0.364419
\(820\) 0 0
\(821\) 24.0976 0.841011 0.420506 0.907290i \(-0.361853\pi\)
0.420506 + 0.907290i \(0.361853\pi\)
\(822\) 0 0
\(823\) 24.2839 0.846482 0.423241 0.906017i \(-0.360892\pi\)
0.423241 + 0.906017i \(0.360892\pi\)
\(824\) 0 0
\(825\) 83.1075 2.89343
\(826\) 0 0
\(827\) 9.51253 0.330783 0.165391 0.986228i \(-0.447111\pi\)
0.165391 + 0.986228i \(0.447111\pi\)
\(828\) 0 0
\(829\) −15.8158 −0.549306 −0.274653 0.961543i \(-0.588563\pi\)
−0.274653 + 0.961543i \(0.588563\pi\)
\(830\) 0 0
\(831\) 29.5074 1.02360
\(832\) 0 0
\(833\) 5.21494 0.180687
\(834\) 0 0
\(835\) −10.3028 −0.356542
\(836\) 0 0
\(837\) 11.6034 0.401073
\(838\) 0 0
\(839\) −50.1793 −1.73238 −0.866191 0.499712i \(-0.833439\pi\)
−0.866191 + 0.499712i \(0.833439\pi\)
\(840\) 0 0
\(841\) 37.1754 1.28191
\(842\) 0 0
\(843\) 58.8333 2.02633
\(844\) 0 0
\(845\) 17.5912 0.605154
\(846\) 0 0
\(847\) 15.9209 0.547049
\(848\) 0 0
\(849\) −38.3973 −1.31779
\(850\) 0 0
\(851\) −27.8602 −0.955035
\(852\) 0 0
\(853\) −24.7996 −0.849123 −0.424562 0.905399i \(-0.639572\pi\)
−0.424562 + 0.905399i \(0.639572\pi\)
\(854\) 0 0
\(855\) 39.7487 1.35938
\(856\) 0 0
\(857\) 29.2281 0.998413 0.499206 0.866483i \(-0.333625\pi\)
0.499206 + 0.866483i \(0.333625\pi\)
\(858\) 0 0
\(859\) 1.04234 0.0355640 0.0177820 0.999842i \(-0.494340\pi\)
0.0177820 + 0.999842i \(0.494340\pi\)
\(860\) 0 0
\(861\) −31.7942 −1.08354
\(862\) 0 0
\(863\) 4.84799 0.165027 0.0825137 0.996590i \(-0.473705\pi\)
0.0825137 + 0.996590i \(0.473705\pi\)
\(864\) 0 0
\(865\) 38.9929 1.32580
\(866\) 0 0
\(867\) 36.3024 1.23289
\(868\) 0 0
\(869\) −35.9307 −1.21887
\(870\) 0 0
\(871\) 11.8855 0.402726
\(872\) 0 0
\(873\) −9.52166 −0.322260
\(874\) 0 0
\(875\) 10.4166 0.352147
\(876\) 0 0
\(877\) −23.7251 −0.801140 −0.400570 0.916266i \(-0.631188\pi\)
−0.400570 + 0.916266i \(0.631188\pi\)
\(878\) 0 0
\(879\) −40.3816 −1.36204
\(880\) 0 0
\(881\) −12.2267 −0.411929 −0.205965 0.978559i \(-0.566033\pi\)
−0.205965 + 0.978559i \(0.566033\pi\)
\(882\) 0 0
\(883\) −25.4653 −0.856977 −0.428489 0.903547i \(-0.640954\pi\)
−0.428489 + 0.903547i \(0.640954\pi\)
\(884\) 0 0
\(885\) −9.38272 −0.315397
\(886\) 0 0
\(887\) −0.757954 −0.0254496 −0.0127248 0.999919i \(-0.504051\pi\)
−0.0127248 + 0.999919i \(0.504051\pi\)
\(888\) 0 0
\(889\) −20.5458 −0.689083
\(890\) 0 0
\(891\) 53.9603 1.80774
\(892\) 0 0
\(893\) −58.9786 −1.97364
\(894\) 0 0
\(895\) 45.0696 1.50651
\(896\) 0 0
\(897\) −83.2209 −2.77866
\(898\) 0 0
\(899\) 44.9306 1.49852
\(900\) 0 0
\(901\) 3.05350 0.101727
\(902\) 0 0
\(903\) 26.0853 0.868063
\(904\) 0 0
\(905\) −69.5037 −2.31038
\(906\) 0 0
\(907\) 54.9506 1.82461 0.912303 0.409516i \(-0.134303\pi\)
0.912303 + 0.409516i \(0.134303\pi\)
\(908\) 0 0
\(909\) −3.73920 −0.124021
\(910\) 0 0
\(911\) 8.67904 0.287549 0.143775 0.989610i \(-0.454076\pi\)
0.143775 + 0.989610i \(0.454076\pi\)
\(912\) 0 0
\(913\) 49.8717 1.65051
\(914\) 0 0
\(915\) 12.6793 0.419165
\(916\) 0 0
\(917\) −20.7332 −0.684669
\(918\) 0 0
\(919\) −23.1237 −0.762781 −0.381390 0.924414i \(-0.624555\pi\)
−0.381390 + 0.924414i \(0.624555\pi\)
\(920\) 0 0
\(921\) 57.4477 1.89297
\(922\) 0 0
\(923\) −44.5054 −1.46491
\(924\) 0 0
\(925\) 23.8939 0.785626
\(926\) 0 0
\(927\) 3.77637 0.124032
\(928\) 0 0
\(929\) −17.8344 −0.585129 −0.292564 0.956246i \(-0.594509\pi\)
−0.292564 + 0.956246i \(0.594509\pi\)
\(930\) 0 0
\(931\) −30.4020 −0.996385
\(932\) 0 0
\(933\) −2.38113 −0.0779546
\(934\) 0 0
\(935\) 16.2890 0.532709
\(936\) 0 0
\(937\) −54.6764 −1.78620 −0.893101 0.449857i \(-0.851475\pi\)
−0.893101 + 0.449857i \(0.851475\pi\)
\(938\) 0 0
\(939\) 1.16272 0.0379440
\(940\) 0 0
\(941\) 8.54393 0.278524 0.139262 0.990256i \(-0.455527\pi\)
0.139262 + 0.990256i \(0.455527\pi\)
\(942\) 0 0
\(943\) −103.487 −3.37001
\(944\) 0 0
\(945\) 8.83157 0.287291
\(946\) 0 0
\(947\) 34.9613 1.13609 0.568044 0.822998i \(-0.307700\pi\)
0.568044 + 0.822998i \(0.307700\pi\)
\(948\) 0 0
\(949\) 15.5399 0.504447
\(950\) 0 0
\(951\) −5.37612 −0.174333
\(952\) 0 0
\(953\) −58.0334 −1.87989 −0.939944 0.341330i \(-0.889123\pi\)
−0.939944 + 0.341330i \(0.889123\pi\)
\(954\) 0 0
\(955\) 30.7071 0.993657
\(956\) 0 0
\(957\) 90.4085 2.92249
\(958\) 0 0
\(959\) 4.82526 0.155816
\(960\) 0 0
\(961\) −0.493821 −0.0159297
\(962\) 0 0
\(963\) 2.45885 0.0792355
\(964\) 0 0
\(965\) −47.7501 −1.53713
\(966\) 0 0
\(967\) −7.15038 −0.229941 −0.114970 0.993369i \(-0.536677\pi\)
−0.114970 + 0.993369i \(0.536677\pi\)
\(968\) 0 0
\(969\) 11.4463 0.367709
\(970\) 0 0
\(971\) 1.83517 0.0588933 0.0294466 0.999566i \(-0.490625\pi\)
0.0294466 + 0.999566i \(0.490625\pi\)
\(972\) 0 0
\(973\) 8.18541 0.262412
\(974\) 0 0
\(975\) 71.3731 2.28577
\(976\) 0 0
\(977\) −35.6590 −1.14083 −0.570416 0.821356i \(-0.693218\pi\)
−0.570416 + 0.821356i \(0.693218\pi\)
\(978\) 0 0
\(979\) −14.2132 −0.454257
\(980\) 0 0
\(981\) −10.0303 −0.320243
\(982\) 0 0
\(983\) 46.9647 1.49794 0.748970 0.662603i \(-0.230548\pi\)
0.748970 + 0.662603i \(0.230548\pi\)
\(984\) 0 0
\(985\) 7.50323 0.239073
\(986\) 0 0
\(987\) 29.0170 0.923621
\(988\) 0 0
\(989\) 84.9052 2.69983
\(990\) 0 0
\(991\) 6.27640 0.199376 0.0996882 0.995019i \(-0.468215\pi\)
0.0996882 + 0.995019i \(0.468215\pi\)
\(992\) 0 0
\(993\) 34.2060 1.08550
\(994\) 0 0
\(995\) −47.2003 −1.49635
\(996\) 0 0
\(997\) 3.78831 0.119977 0.0599885 0.998199i \(-0.480894\pi\)
0.0599885 + 0.998199i \(0.480894\pi\)
\(998\) 0 0
\(999\) 6.71274 0.212382
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 6008.2.a.b.1.9 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.9 44 1.1 even 1 trivial