Properties

Label 6008.2.a.b.1.32
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 1.32
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.25524 q^{3} +4.39073 q^{5} -3.72993 q^{7} -1.42437 q^{9} +O(q^{10})\) \(q+1.25524 q^{3} +4.39073 q^{5} -3.72993 q^{7} -1.42437 q^{9} +0.335194 q^{11} -6.63601 q^{13} +5.51143 q^{15} +5.58436 q^{17} -3.46817 q^{19} -4.68197 q^{21} -2.62801 q^{23} +14.2785 q^{25} -5.55365 q^{27} +4.43185 q^{29} -10.1044 q^{31} +0.420749 q^{33} -16.3771 q^{35} -4.76934 q^{37} -8.32979 q^{39} -5.06307 q^{41} -4.97138 q^{43} -6.25402 q^{45} +0.633362 q^{47} +6.91240 q^{49} +7.00973 q^{51} +6.19399 q^{53} +1.47175 q^{55} -4.35339 q^{57} +3.08291 q^{59} +7.40841 q^{61} +5.31280 q^{63} -29.1369 q^{65} -11.5319 q^{67} -3.29878 q^{69} -0.566138 q^{71} -12.8813 q^{73} +17.9230 q^{75} -1.25025 q^{77} +16.1760 q^{79} -2.69807 q^{81} +12.8071 q^{83} +24.5194 q^{85} +5.56304 q^{87} -7.99806 q^{89} +24.7519 q^{91} -12.6834 q^{93} -15.2278 q^{95} -14.3787 q^{97} -0.477440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.25524 0.724714 0.362357 0.932039i \(-0.381972\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(4\) 0 0
\(5\) 4.39073 1.96359 0.981797 0.189932i \(-0.0608268\pi\)
0.981797 + 0.189932i \(0.0608268\pi\)
\(6\) 0 0
\(7\) −3.72993 −1.40978 −0.704891 0.709316i \(-0.749004\pi\)
−0.704891 + 0.709316i \(0.749004\pi\)
\(8\) 0 0
\(9\) −1.42437 −0.474790
\(10\) 0 0
\(11\) 0.335194 0.101065 0.0505324 0.998722i \(-0.483908\pi\)
0.0505324 + 0.998722i \(0.483908\pi\)
\(12\) 0 0
\(13\) −6.63601 −1.84050 −0.920248 0.391335i \(-0.872013\pi\)
−0.920248 + 0.391335i \(0.872013\pi\)
\(14\) 0 0
\(15\) 5.51143 1.42304
\(16\) 0 0
\(17\) 5.58436 1.35441 0.677204 0.735796i \(-0.263192\pi\)
0.677204 + 0.735796i \(0.263192\pi\)
\(18\) 0 0
\(19\) −3.46817 −0.795652 −0.397826 0.917461i \(-0.630235\pi\)
−0.397826 + 0.917461i \(0.630235\pi\)
\(20\) 0 0
\(21\) −4.68197 −1.02169
\(22\) 0 0
\(23\) −2.62801 −0.547977 −0.273989 0.961733i \(-0.588343\pi\)
−0.273989 + 0.961733i \(0.588343\pi\)
\(24\) 0 0
\(25\) 14.2785 2.85570
\(26\) 0 0
\(27\) −5.55365 −1.06880
\(28\) 0 0
\(29\) 4.43185 0.822974 0.411487 0.911416i \(-0.365010\pi\)
0.411487 + 0.911416i \(0.365010\pi\)
\(30\) 0 0
\(31\) −10.1044 −1.81480 −0.907398 0.420271i \(-0.861935\pi\)
−0.907398 + 0.420271i \(0.861935\pi\)
\(32\) 0 0
\(33\) 0.420749 0.0732430
\(34\) 0 0
\(35\) −16.3771 −2.76824
\(36\) 0 0
\(37\) −4.76934 −0.784075 −0.392037 0.919949i \(-0.628230\pi\)
−0.392037 + 0.919949i \(0.628230\pi\)
\(38\) 0 0
\(39\) −8.32979 −1.33383
\(40\) 0 0
\(41\) −5.06307 −0.790719 −0.395359 0.918527i \(-0.629380\pi\)
−0.395359 + 0.918527i \(0.629380\pi\)
\(42\) 0 0
\(43\) −4.97138 −0.758129 −0.379065 0.925370i \(-0.623754\pi\)
−0.379065 + 0.925370i \(0.623754\pi\)
\(44\) 0 0
\(45\) −6.25402 −0.932294
\(46\) 0 0
\(47\) 0.633362 0.0923854 0.0461927 0.998933i \(-0.485291\pi\)
0.0461927 + 0.998933i \(0.485291\pi\)
\(48\) 0 0
\(49\) 6.91240 0.987486
\(50\) 0 0
\(51\) 7.00973 0.981558
\(52\) 0 0
\(53\) 6.19399 0.850810 0.425405 0.905003i \(-0.360132\pi\)
0.425405 + 0.905003i \(0.360132\pi\)
\(54\) 0 0
\(55\) 1.47175 0.198450
\(56\) 0 0
\(57\) −4.35339 −0.576620
\(58\) 0 0
\(59\) 3.08291 0.401361 0.200680 0.979657i \(-0.435685\pi\)
0.200680 + 0.979657i \(0.435685\pi\)
\(60\) 0 0
\(61\) 7.40841 0.948549 0.474275 0.880377i \(-0.342710\pi\)
0.474275 + 0.880377i \(0.342710\pi\)
\(62\) 0 0
\(63\) 5.31280 0.669350
\(64\) 0 0
\(65\) −29.1369 −3.61399
\(66\) 0 0
\(67\) −11.5319 −1.40884 −0.704421 0.709783i \(-0.748793\pi\)
−0.704421 + 0.709783i \(0.748793\pi\)
\(68\) 0 0
\(69\) −3.29878 −0.397127
\(70\) 0 0
\(71\) −0.566138 −0.0671882 −0.0335941 0.999436i \(-0.510695\pi\)
−0.0335941 + 0.999436i \(0.510695\pi\)
\(72\) 0 0
\(73\) −12.8813 −1.50764 −0.753822 0.657078i \(-0.771792\pi\)
−0.753822 + 0.657078i \(0.771792\pi\)
\(74\) 0 0
\(75\) 17.9230 2.06957
\(76\) 0 0
\(77\) −1.25025 −0.142479
\(78\) 0 0
\(79\) 16.1760 1.81994 0.909970 0.414675i \(-0.136105\pi\)
0.909970 + 0.414675i \(0.136105\pi\)
\(80\) 0 0
\(81\) −2.69807 −0.299785
\(82\) 0 0
\(83\) 12.8071 1.40576 0.702881 0.711307i \(-0.251897\pi\)
0.702881 + 0.711307i \(0.251897\pi\)
\(84\) 0 0
\(85\) 24.5194 2.65951
\(86\) 0 0
\(87\) 5.56304 0.596421
\(88\) 0 0
\(89\) −7.99806 −0.847793 −0.423896 0.905711i \(-0.639338\pi\)
−0.423896 + 0.905711i \(0.639338\pi\)
\(90\) 0 0
\(91\) 24.7519 2.59470
\(92\) 0 0
\(93\) −12.6834 −1.31521
\(94\) 0 0
\(95\) −15.2278 −1.56234
\(96\) 0 0
\(97\) −14.3787 −1.45994 −0.729970 0.683480i \(-0.760466\pi\)
−0.729970 + 0.683480i \(0.760466\pi\)
\(98\) 0 0
\(99\) −0.477440 −0.0479845
\(100\) 0 0
\(101\) 12.0514 1.19916 0.599579 0.800316i \(-0.295335\pi\)
0.599579 + 0.800316i \(0.295335\pi\)
\(102\) 0 0
\(103\) −8.74140 −0.861316 −0.430658 0.902515i \(-0.641718\pi\)
−0.430658 + 0.902515i \(0.641718\pi\)
\(104\) 0 0
\(105\) −20.5573 −2.00618
\(106\) 0 0
\(107\) −15.2038 −1.46981 −0.734903 0.678172i \(-0.762772\pi\)
−0.734903 + 0.678172i \(0.762772\pi\)
\(108\) 0 0
\(109\) −10.3346 −0.989876 −0.494938 0.868928i \(-0.664809\pi\)
−0.494938 + 0.868928i \(0.664809\pi\)
\(110\) 0 0
\(111\) −5.98667 −0.568230
\(112\) 0 0
\(113\) −19.1314 −1.79973 −0.899867 0.436165i \(-0.856336\pi\)
−0.899867 + 0.436165i \(0.856336\pi\)
\(114\) 0 0
\(115\) −11.5389 −1.07600
\(116\) 0 0
\(117\) 9.45212 0.873849
\(118\) 0 0
\(119\) −20.8293 −1.90942
\(120\) 0 0
\(121\) −10.8876 −0.989786
\(122\) 0 0
\(123\) −6.35538 −0.573045
\(124\) 0 0
\(125\) 40.7395 3.64385
\(126\) 0 0
\(127\) −6.76390 −0.600200 −0.300100 0.953908i \(-0.597020\pi\)
−0.300100 + 0.953908i \(0.597020\pi\)
\(128\) 0 0
\(129\) −6.24029 −0.549427
\(130\) 0 0
\(131\) −18.0192 −1.57435 −0.787173 0.616732i \(-0.788456\pi\)
−0.787173 + 0.616732i \(0.788456\pi\)
\(132\) 0 0
\(133\) 12.9360 1.12170
\(134\) 0 0
\(135\) −24.3846 −2.09869
\(136\) 0 0
\(137\) 3.41751 0.291977 0.145989 0.989286i \(-0.453364\pi\)
0.145989 + 0.989286i \(0.453364\pi\)
\(138\) 0 0
\(139\) 1.26617 0.107395 0.0536977 0.998557i \(-0.482899\pi\)
0.0536977 + 0.998557i \(0.482899\pi\)
\(140\) 0 0
\(141\) 0.795023 0.0669530
\(142\) 0 0
\(143\) −2.22435 −0.186009
\(144\) 0 0
\(145\) 19.4591 1.61599
\(146\) 0 0
\(147\) 8.67673 0.715645
\(148\) 0 0
\(149\) −12.5806 −1.03065 −0.515323 0.856996i \(-0.672328\pi\)
−0.515323 + 0.856996i \(0.672328\pi\)
\(150\) 0 0
\(151\) 9.51437 0.774269 0.387134 0.922023i \(-0.373465\pi\)
0.387134 + 0.922023i \(0.373465\pi\)
\(152\) 0 0
\(153\) −7.95420 −0.643059
\(154\) 0 0
\(155\) −44.3655 −3.56353
\(156\) 0 0
\(157\) −16.8830 −1.34741 −0.673706 0.739000i \(-0.735298\pi\)
−0.673706 + 0.739000i \(0.735298\pi\)
\(158\) 0 0
\(159\) 7.77495 0.616594
\(160\) 0 0
\(161\) 9.80228 0.772528
\(162\) 0 0
\(163\) −4.38273 −0.343282 −0.171641 0.985160i \(-0.554907\pi\)
−0.171641 + 0.985160i \(0.554907\pi\)
\(164\) 0 0
\(165\) 1.84740 0.143820
\(166\) 0 0
\(167\) 2.79764 0.216488 0.108244 0.994124i \(-0.465477\pi\)
0.108244 + 0.994124i \(0.465477\pi\)
\(168\) 0 0
\(169\) 31.0366 2.38743
\(170\) 0 0
\(171\) 4.93995 0.377767
\(172\) 0 0
\(173\) −6.40593 −0.487034 −0.243517 0.969897i \(-0.578301\pi\)
−0.243517 + 0.969897i \(0.578301\pi\)
\(174\) 0 0
\(175\) −53.2579 −4.02592
\(176\) 0 0
\(177\) 3.86980 0.290872
\(178\) 0 0
\(179\) −14.3346 −1.07142 −0.535710 0.844402i \(-0.679956\pi\)
−0.535710 + 0.844402i \(0.679956\pi\)
\(180\) 0 0
\(181\) 3.98508 0.296209 0.148104 0.988972i \(-0.452683\pi\)
0.148104 + 0.988972i \(0.452683\pi\)
\(182\) 0 0
\(183\) 9.29934 0.687427
\(184\) 0 0
\(185\) −20.9409 −1.53961
\(186\) 0 0
\(187\) 1.87184 0.136883
\(188\) 0 0
\(189\) 20.7147 1.50678
\(190\) 0 0
\(191\) 13.5415 0.979829 0.489914 0.871771i \(-0.337028\pi\)
0.489914 + 0.871771i \(0.337028\pi\)
\(192\) 0 0
\(193\) 9.04622 0.651161 0.325581 0.945514i \(-0.394440\pi\)
0.325581 + 0.945514i \(0.394440\pi\)
\(194\) 0 0
\(195\) −36.5739 −2.61911
\(196\) 0 0
\(197\) 10.5277 0.750069 0.375035 0.927011i \(-0.377631\pi\)
0.375035 + 0.927011i \(0.377631\pi\)
\(198\) 0 0
\(199\) −3.35669 −0.237949 −0.118975 0.992897i \(-0.537961\pi\)
−0.118975 + 0.992897i \(0.537961\pi\)
\(200\) 0 0
\(201\) −14.4753 −1.02101
\(202\) 0 0
\(203\) −16.5305 −1.16021
\(204\) 0 0
\(205\) −22.2306 −1.55265
\(206\) 0 0
\(207\) 3.74325 0.260174
\(208\) 0 0
\(209\) −1.16251 −0.0804124
\(210\) 0 0
\(211\) 22.4356 1.54453 0.772267 0.635299i \(-0.219123\pi\)
0.772267 + 0.635299i \(0.219123\pi\)
\(212\) 0 0
\(213\) −0.710639 −0.0486922
\(214\) 0 0
\(215\) −21.8280 −1.48866
\(216\) 0 0
\(217\) 37.6886 2.55847
\(218\) 0 0
\(219\) −16.1692 −1.09261
\(220\) 0 0
\(221\) −37.0579 −2.49278
\(222\) 0 0
\(223\) 13.3050 0.890969 0.445485 0.895290i \(-0.353031\pi\)
0.445485 + 0.895290i \(0.353031\pi\)
\(224\) 0 0
\(225\) −20.3379 −1.35586
\(226\) 0 0
\(227\) 6.53166 0.433521 0.216761 0.976225i \(-0.430451\pi\)
0.216761 + 0.976225i \(0.430451\pi\)
\(228\) 0 0
\(229\) 23.0806 1.52521 0.762606 0.646863i \(-0.223920\pi\)
0.762606 + 0.646863i \(0.223920\pi\)
\(230\) 0 0
\(231\) −1.56937 −0.103257
\(232\) 0 0
\(233\) −1.30377 −0.0854126 −0.0427063 0.999088i \(-0.513598\pi\)
−0.0427063 + 0.999088i \(0.513598\pi\)
\(234\) 0 0
\(235\) 2.78092 0.181407
\(236\) 0 0
\(237\) 20.3048 1.31894
\(238\) 0 0
\(239\) 6.30117 0.407589 0.203794 0.979014i \(-0.434673\pi\)
0.203794 + 0.979014i \(0.434673\pi\)
\(240\) 0 0
\(241\) 9.47972 0.610643 0.305321 0.952249i \(-0.401236\pi\)
0.305321 + 0.952249i \(0.401236\pi\)
\(242\) 0 0
\(243\) 13.2742 0.851542
\(244\) 0 0
\(245\) 30.3505 1.93902
\(246\) 0 0
\(247\) 23.0148 1.46440
\(248\) 0 0
\(249\) 16.0760 1.01878
\(250\) 0 0
\(251\) −19.0411 −1.20186 −0.600931 0.799301i \(-0.705203\pi\)
−0.600931 + 0.799301i \(0.705203\pi\)
\(252\) 0 0
\(253\) −0.880891 −0.0553812
\(254\) 0 0
\(255\) 30.7778 1.92738
\(256\) 0 0
\(257\) 7.99855 0.498936 0.249468 0.968383i \(-0.419744\pi\)
0.249468 + 0.968383i \(0.419744\pi\)
\(258\) 0 0
\(259\) 17.7893 1.10537
\(260\) 0 0
\(261\) −6.31259 −0.390740
\(262\) 0 0
\(263\) −5.68627 −0.350630 −0.175315 0.984512i \(-0.556094\pi\)
−0.175315 + 0.984512i \(0.556094\pi\)
\(264\) 0 0
\(265\) 27.1961 1.67065
\(266\) 0 0
\(267\) −10.0395 −0.614407
\(268\) 0 0
\(269\) −5.42860 −0.330987 −0.165494 0.986211i \(-0.552922\pi\)
−0.165494 + 0.986211i \(0.552922\pi\)
\(270\) 0 0
\(271\) −4.45134 −0.270400 −0.135200 0.990818i \(-0.543168\pi\)
−0.135200 + 0.990818i \(0.543168\pi\)
\(272\) 0 0
\(273\) 31.0696 1.88042
\(274\) 0 0
\(275\) 4.78607 0.288611
\(276\) 0 0
\(277\) −0.594859 −0.0357416 −0.0178708 0.999840i \(-0.505689\pi\)
−0.0178708 + 0.999840i \(0.505689\pi\)
\(278\) 0 0
\(279\) 14.3923 0.861647
\(280\) 0 0
\(281\) 20.2008 1.20508 0.602539 0.798089i \(-0.294156\pi\)
0.602539 + 0.798089i \(0.294156\pi\)
\(282\) 0 0
\(283\) 8.98521 0.534115 0.267058 0.963681i \(-0.413949\pi\)
0.267058 + 0.963681i \(0.413949\pi\)
\(284\) 0 0
\(285\) −19.1146 −1.13225
\(286\) 0 0
\(287\) 18.8849 1.11474
\(288\) 0 0
\(289\) 14.1851 0.834419
\(290\) 0 0
\(291\) −18.0488 −1.05804
\(292\) 0 0
\(293\) −5.23411 −0.305780 −0.152890 0.988243i \(-0.548858\pi\)
−0.152890 + 0.988243i \(0.548858\pi\)
\(294\) 0 0
\(295\) 13.5362 0.788110
\(296\) 0 0
\(297\) −1.86155 −0.108018
\(298\) 0 0
\(299\) 17.4395 1.00855
\(300\) 0 0
\(301\) 18.5429 1.06880
\(302\) 0 0
\(303\) 15.1274 0.869046
\(304\) 0 0
\(305\) 32.5283 1.86257
\(306\) 0 0
\(307\) −31.7945 −1.81461 −0.907305 0.420473i \(-0.861864\pi\)
−0.907305 + 0.420473i \(0.861864\pi\)
\(308\) 0 0
\(309\) −10.9726 −0.624208
\(310\) 0 0
\(311\) 3.58229 0.203133 0.101566 0.994829i \(-0.467615\pi\)
0.101566 + 0.994829i \(0.467615\pi\)
\(312\) 0 0
\(313\) 19.2869 1.09016 0.545080 0.838384i \(-0.316499\pi\)
0.545080 + 0.838384i \(0.316499\pi\)
\(314\) 0 0
\(315\) 23.3271 1.31433
\(316\) 0 0
\(317\) −17.9167 −1.00630 −0.503151 0.864198i \(-0.667826\pi\)
−0.503151 + 0.864198i \(0.667826\pi\)
\(318\) 0 0
\(319\) 1.48553 0.0831737
\(320\) 0 0
\(321\) −19.0844 −1.06519
\(322\) 0 0
\(323\) −19.3675 −1.07764
\(324\) 0 0
\(325\) −94.7523 −5.25591
\(326\) 0 0
\(327\) −12.9724 −0.717377
\(328\) 0 0
\(329\) −2.36240 −0.130243
\(330\) 0 0
\(331\) −30.2449 −1.66241 −0.831204 0.555967i \(-0.812348\pi\)
−0.831204 + 0.555967i \(0.812348\pi\)
\(332\) 0 0
\(333\) 6.79330 0.372271
\(334\) 0 0
\(335\) −50.6333 −2.76639
\(336\) 0 0
\(337\) 25.3476 1.38077 0.690387 0.723440i \(-0.257440\pi\)
0.690387 + 0.723440i \(0.257440\pi\)
\(338\) 0 0
\(339\) −24.0146 −1.30429
\(340\) 0 0
\(341\) −3.38692 −0.183412
\(342\) 0 0
\(343\) 0.326736 0.0176421
\(344\) 0 0
\(345\) −14.4841 −0.779796
\(346\) 0 0
\(347\) 27.4348 1.47278 0.736389 0.676558i \(-0.236529\pi\)
0.736389 + 0.676558i \(0.236529\pi\)
\(348\) 0 0
\(349\) −12.4475 −0.666297 −0.333149 0.942874i \(-0.608111\pi\)
−0.333149 + 0.942874i \(0.608111\pi\)
\(350\) 0 0
\(351\) 36.8541 1.96712
\(352\) 0 0
\(353\) −28.5836 −1.52135 −0.760677 0.649131i \(-0.775133\pi\)
−0.760677 + 0.649131i \(0.775133\pi\)
\(354\) 0 0
\(355\) −2.48576 −0.131930
\(356\) 0 0
\(357\) −26.1458 −1.38378
\(358\) 0 0
\(359\) 3.34397 0.176488 0.0882439 0.996099i \(-0.471875\pi\)
0.0882439 + 0.996099i \(0.471875\pi\)
\(360\) 0 0
\(361\) −6.97181 −0.366937
\(362\) 0 0
\(363\) −13.6666 −0.717312
\(364\) 0 0
\(365\) −56.5584 −2.96040
\(366\) 0 0
\(367\) −12.5017 −0.652585 −0.326292 0.945269i \(-0.605799\pi\)
−0.326292 + 0.945269i \(0.605799\pi\)
\(368\) 0 0
\(369\) 7.21168 0.375425
\(370\) 0 0
\(371\) −23.1032 −1.19946
\(372\) 0 0
\(373\) 29.8112 1.54357 0.771784 0.635885i \(-0.219365\pi\)
0.771784 + 0.635885i \(0.219365\pi\)
\(374\) 0 0
\(375\) 51.1379 2.64075
\(376\) 0 0
\(377\) −29.4098 −1.51468
\(378\) 0 0
\(379\) −0.518401 −0.0266285 −0.0133142 0.999911i \(-0.504238\pi\)
−0.0133142 + 0.999911i \(0.504238\pi\)
\(380\) 0 0
\(381\) −8.49033 −0.434973
\(382\) 0 0
\(383\) −14.5407 −0.742993 −0.371496 0.928434i \(-0.621155\pi\)
−0.371496 + 0.928434i \(0.621155\pi\)
\(384\) 0 0
\(385\) −5.48951 −0.279772
\(386\) 0 0
\(387\) 7.08109 0.359952
\(388\) 0 0
\(389\) 34.3902 1.74365 0.871826 0.489816i \(-0.162936\pi\)
0.871826 + 0.489816i \(0.162936\pi\)
\(390\) 0 0
\(391\) −14.6757 −0.742184
\(392\) 0 0
\(393\) −22.6185 −1.14095
\(394\) 0 0
\(395\) 71.0244 3.57362
\(396\) 0 0
\(397\) 20.1567 1.01164 0.505818 0.862640i \(-0.331191\pi\)
0.505818 + 0.862640i \(0.331191\pi\)
\(398\) 0 0
\(399\) 16.2378 0.812909
\(400\) 0 0
\(401\) −22.3751 −1.11736 −0.558680 0.829383i \(-0.688692\pi\)
−0.558680 + 0.829383i \(0.688692\pi\)
\(402\) 0 0
\(403\) 67.0526 3.34013
\(404\) 0 0
\(405\) −11.8465 −0.588656
\(406\) 0 0
\(407\) −1.59865 −0.0792423
\(408\) 0 0
\(409\) 15.0462 0.743987 0.371994 0.928235i \(-0.378674\pi\)
0.371994 + 0.928235i \(0.378674\pi\)
\(410\) 0 0
\(411\) 4.28980 0.211600
\(412\) 0 0
\(413\) −11.4990 −0.565831
\(414\) 0 0
\(415\) 56.2326 2.76035
\(416\) 0 0
\(417\) 1.58935 0.0778309
\(418\) 0 0
\(419\) −21.6630 −1.05831 −0.529155 0.848525i \(-0.677491\pi\)
−0.529155 + 0.848525i \(0.677491\pi\)
\(420\) 0 0
\(421\) −8.06331 −0.392982 −0.196491 0.980506i \(-0.562955\pi\)
−0.196491 + 0.980506i \(0.562955\pi\)
\(422\) 0 0
\(423\) −0.902142 −0.0438636
\(424\) 0 0
\(425\) 79.7364 3.86779
\(426\) 0 0
\(427\) −27.6329 −1.33725
\(428\) 0 0
\(429\) −2.79209 −0.134804
\(430\) 0 0
\(431\) 24.3222 1.17156 0.585779 0.810471i \(-0.300789\pi\)
0.585779 + 0.810471i \(0.300789\pi\)
\(432\) 0 0
\(433\) 1.88103 0.0903966 0.0451983 0.998978i \(-0.485608\pi\)
0.0451983 + 0.998978i \(0.485608\pi\)
\(434\) 0 0
\(435\) 24.4258 1.17113
\(436\) 0 0
\(437\) 9.11436 0.435999
\(438\) 0 0
\(439\) −16.0473 −0.765898 −0.382949 0.923770i \(-0.625091\pi\)
−0.382949 + 0.923770i \(0.625091\pi\)
\(440\) 0 0
\(441\) −9.84581 −0.468848
\(442\) 0 0
\(443\) 26.6310 1.26528 0.632639 0.774447i \(-0.281972\pi\)
0.632639 + 0.774447i \(0.281972\pi\)
\(444\) 0 0
\(445\) −35.1173 −1.66472
\(446\) 0 0
\(447\) −15.7917 −0.746923
\(448\) 0 0
\(449\) −23.3422 −1.10159 −0.550794 0.834641i \(-0.685675\pi\)
−0.550794 + 0.834641i \(0.685675\pi\)
\(450\) 0 0
\(451\) −1.69711 −0.0799138
\(452\) 0 0
\(453\) 11.9428 0.561123
\(454\) 0 0
\(455\) 108.679 5.09494
\(456\) 0 0
\(457\) 35.4364 1.65765 0.828823 0.559511i \(-0.189011\pi\)
0.828823 + 0.559511i \(0.189011\pi\)
\(458\) 0 0
\(459\) −31.0136 −1.44759
\(460\) 0 0
\(461\) 25.4362 1.18468 0.592340 0.805688i \(-0.298204\pi\)
0.592340 + 0.805688i \(0.298204\pi\)
\(462\) 0 0
\(463\) −8.72845 −0.405646 −0.202823 0.979215i \(-0.565012\pi\)
−0.202823 + 0.979215i \(0.565012\pi\)
\(464\) 0 0
\(465\) −55.6895 −2.58254
\(466\) 0 0
\(467\) 42.7389 1.97772 0.988861 0.148843i \(-0.0475548\pi\)
0.988861 + 0.148843i \(0.0475548\pi\)
\(468\) 0 0
\(469\) 43.0131 1.98616
\(470\) 0 0
\(471\) −21.1923 −0.976488
\(472\) 0 0
\(473\) −1.66638 −0.0766201
\(474\) 0 0
\(475\) −49.5203 −2.27215
\(476\) 0 0
\(477\) −8.82252 −0.403956
\(478\) 0 0
\(479\) −8.78288 −0.401300 −0.200650 0.979663i \(-0.564305\pi\)
−0.200650 + 0.979663i \(0.564305\pi\)
\(480\) 0 0
\(481\) 31.6494 1.44309
\(482\) 0 0
\(483\) 12.3042 0.559862
\(484\) 0 0
\(485\) −63.1332 −2.86673
\(486\) 0 0
\(487\) 2.20490 0.0999133 0.0499567 0.998751i \(-0.484092\pi\)
0.0499567 + 0.998751i \(0.484092\pi\)
\(488\) 0 0
\(489\) −5.50138 −0.248781
\(490\) 0 0
\(491\) −19.3931 −0.875200 −0.437600 0.899170i \(-0.644171\pi\)
−0.437600 + 0.899170i \(0.644171\pi\)
\(492\) 0 0
\(493\) 24.7491 1.11464
\(494\) 0 0
\(495\) −2.09631 −0.0942221
\(496\) 0 0
\(497\) 2.11166 0.0947207
\(498\) 0 0
\(499\) 0.127065 0.00568823 0.00284412 0.999996i \(-0.499095\pi\)
0.00284412 + 0.999996i \(0.499095\pi\)
\(500\) 0 0
\(501\) 3.51171 0.156892
\(502\) 0 0
\(503\) −14.7666 −0.658412 −0.329206 0.944258i \(-0.606781\pi\)
−0.329206 + 0.944258i \(0.606781\pi\)
\(504\) 0 0
\(505\) 52.9144 2.35466
\(506\) 0 0
\(507\) 38.9584 1.73020
\(508\) 0 0
\(509\) −9.40117 −0.416700 −0.208350 0.978054i \(-0.566809\pi\)
−0.208350 + 0.978054i \(0.566809\pi\)
\(510\) 0 0
\(511\) 48.0465 2.12545
\(512\) 0 0
\(513\) 19.2610 0.850394
\(514\) 0 0
\(515\) −38.3811 −1.69128
\(516\) 0 0
\(517\) 0.212299 0.00933691
\(518\) 0 0
\(519\) −8.04099 −0.352960
\(520\) 0 0
\(521\) −31.7278 −1.39002 −0.695010 0.719000i \(-0.744600\pi\)
−0.695010 + 0.719000i \(0.744600\pi\)
\(522\) 0 0
\(523\) 15.9567 0.697736 0.348868 0.937172i \(-0.386566\pi\)
0.348868 + 0.937172i \(0.386566\pi\)
\(524\) 0 0
\(525\) −66.8515 −2.91764
\(526\) 0 0
\(527\) −56.4264 −2.45797
\(528\) 0 0
\(529\) −16.0936 −0.699721
\(530\) 0 0
\(531\) −4.39120 −0.190562
\(532\) 0 0
\(533\) 33.5986 1.45532
\(534\) 0 0
\(535\) −66.7558 −2.88610
\(536\) 0 0
\(537\) −17.9934 −0.776473
\(538\) 0 0
\(539\) 2.31699 0.0998000
\(540\) 0 0
\(541\) 31.9904 1.37538 0.687688 0.726007i \(-0.258626\pi\)
0.687688 + 0.726007i \(0.258626\pi\)
\(542\) 0 0
\(543\) 5.00224 0.214667
\(544\) 0 0
\(545\) −45.3765 −1.94372
\(546\) 0 0
\(547\) −29.3708 −1.25580 −0.627902 0.778292i \(-0.716086\pi\)
−0.627902 + 0.778292i \(0.716086\pi\)
\(548\) 0 0
\(549\) −10.5523 −0.450361
\(550\) 0 0
\(551\) −15.3704 −0.654801
\(552\) 0 0
\(553\) −60.3353 −2.56572
\(554\) 0 0
\(555\) −26.2859 −1.11577
\(556\) 0 0
\(557\) 20.3153 0.860785 0.430393 0.902642i \(-0.358375\pi\)
0.430393 + 0.902642i \(0.358375\pi\)
\(558\) 0 0
\(559\) 32.9901 1.39533
\(560\) 0 0
\(561\) 2.34962 0.0992009
\(562\) 0 0
\(563\) 22.8787 0.964223 0.482112 0.876110i \(-0.339870\pi\)
0.482112 + 0.876110i \(0.339870\pi\)
\(564\) 0 0
\(565\) −84.0010 −3.53395
\(566\) 0 0
\(567\) 10.0636 0.422632
\(568\) 0 0
\(569\) 7.34976 0.308118 0.154059 0.988062i \(-0.450765\pi\)
0.154059 + 0.988062i \(0.450765\pi\)
\(570\) 0 0
\(571\) 33.7168 1.41100 0.705502 0.708707i \(-0.250721\pi\)
0.705502 + 0.708707i \(0.250721\pi\)
\(572\) 0 0
\(573\) 16.9979 0.710095
\(574\) 0 0
\(575\) −37.5240 −1.56486
\(576\) 0 0
\(577\) −15.0193 −0.625263 −0.312631 0.949875i \(-0.601210\pi\)
−0.312631 + 0.949875i \(0.601210\pi\)
\(578\) 0 0
\(579\) 11.3552 0.471906
\(580\) 0 0
\(581\) −47.7696 −1.98182
\(582\) 0 0
\(583\) 2.07619 0.0859869
\(584\) 0 0
\(585\) 41.5017 1.71588
\(586\) 0 0
\(587\) −14.8722 −0.613843 −0.306922 0.951735i \(-0.599299\pi\)
−0.306922 + 0.951735i \(0.599299\pi\)
\(588\) 0 0
\(589\) 35.0436 1.44395
\(590\) 0 0
\(591\) 13.2148 0.543586
\(592\) 0 0
\(593\) −2.67847 −0.109992 −0.0549959 0.998487i \(-0.517515\pi\)
−0.0549959 + 0.998487i \(0.517515\pi\)
\(594\) 0 0
\(595\) −91.4559 −3.74933
\(596\) 0 0
\(597\) −4.21345 −0.172445
\(598\) 0 0
\(599\) 36.0046 1.47111 0.735554 0.677467i \(-0.236922\pi\)
0.735554 + 0.677467i \(0.236922\pi\)
\(600\) 0 0
\(601\) 28.4925 1.16223 0.581117 0.813820i \(-0.302616\pi\)
0.581117 + 0.813820i \(0.302616\pi\)
\(602\) 0 0
\(603\) 16.4256 0.668903
\(604\) 0 0
\(605\) −47.8047 −1.94354
\(606\) 0 0
\(607\) 4.01590 0.163000 0.0815002 0.996673i \(-0.474029\pi\)
0.0815002 + 0.996673i \(0.474029\pi\)
\(608\) 0 0
\(609\) −20.7498 −0.840823
\(610\) 0 0
\(611\) −4.20300 −0.170035
\(612\) 0 0
\(613\) −26.4257 −1.06732 −0.533662 0.845698i \(-0.679184\pi\)
−0.533662 + 0.845698i \(0.679184\pi\)
\(614\) 0 0
\(615\) −27.9047 −1.12523
\(616\) 0 0
\(617\) 16.9602 0.682792 0.341396 0.939920i \(-0.389100\pi\)
0.341396 + 0.939920i \(0.389100\pi\)
\(618\) 0 0
\(619\) −39.2046 −1.57577 −0.787883 0.615825i \(-0.788823\pi\)
−0.787883 + 0.615825i \(0.788823\pi\)
\(620\) 0 0
\(621\) 14.5950 0.585678
\(622\) 0 0
\(623\) 29.8322 1.19520
\(624\) 0 0
\(625\) 107.483 4.29934
\(626\) 0 0
\(627\) −1.45923 −0.0582760
\(628\) 0 0
\(629\) −26.6337 −1.06196
\(630\) 0 0
\(631\) 48.6081 1.93506 0.967529 0.252761i \(-0.0813387\pi\)
0.967529 + 0.252761i \(0.0813387\pi\)
\(632\) 0 0
\(633\) 28.1621 1.11934
\(634\) 0 0
\(635\) −29.6985 −1.17855
\(636\) 0 0
\(637\) −45.8707 −1.81746
\(638\) 0 0
\(639\) 0.806389 0.0319002
\(640\) 0 0
\(641\) −13.1633 −0.519920 −0.259960 0.965619i \(-0.583709\pi\)
−0.259960 + 0.965619i \(0.583709\pi\)
\(642\) 0 0
\(643\) −23.5489 −0.928677 −0.464339 0.885658i \(-0.653708\pi\)
−0.464339 + 0.885658i \(0.653708\pi\)
\(644\) 0 0
\(645\) −27.3994 −1.07885
\(646\) 0 0
\(647\) −8.32122 −0.327141 −0.163570 0.986532i \(-0.552301\pi\)
−0.163570 + 0.986532i \(0.552301\pi\)
\(648\) 0 0
\(649\) 1.03337 0.0405634
\(650\) 0 0
\(651\) 47.3083 1.85416
\(652\) 0 0
\(653\) 12.8063 0.501148 0.250574 0.968097i \(-0.419381\pi\)
0.250574 + 0.968097i \(0.419381\pi\)
\(654\) 0 0
\(655\) −79.1176 −3.09138
\(656\) 0 0
\(657\) 18.3478 0.715814
\(658\) 0 0
\(659\) −35.2512 −1.37319 −0.686595 0.727040i \(-0.740895\pi\)
−0.686595 + 0.727040i \(0.740895\pi\)
\(660\) 0 0
\(661\) −0.199310 −0.00775224 −0.00387612 0.999992i \(-0.501234\pi\)
−0.00387612 + 0.999992i \(0.501234\pi\)
\(662\) 0 0
\(663\) −46.5166 −1.80655
\(664\) 0 0
\(665\) 56.7986 2.20256
\(666\) 0 0
\(667\) −11.6469 −0.450971
\(668\) 0 0
\(669\) 16.7010 0.645698
\(670\) 0 0
\(671\) 2.48325 0.0958649
\(672\) 0 0
\(673\) −17.4544 −0.672819 −0.336410 0.941716i \(-0.609213\pi\)
−0.336410 + 0.941716i \(0.609213\pi\)
\(674\) 0 0
\(675\) −79.2979 −3.05218
\(676\) 0 0
\(677\) 21.8693 0.840505 0.420253 0.907407i \(-0.361941\pi\)
0.420253 + 0.907407i \(0.361941\pi\)
\(678\) 0 0
\(679\) 53.6317 2.05820
\(680\) 0 0
\(681\) 8.19881 0.314179
\(682\) 0 0
\(683\) 7.71128 0.295064 0.147532 0.989057i \(-0.452867\pi\)
0.147532 + 0.989057i \(0.452867\pi\)
\(684\) 0 0
\(685\) 15.0054 0.573325
\(686\) 0 0
\(687\) 28.9718 1.10534
\(688\) 0 0
\(689\) −41.1033 −1.56591
\(690\) 0 0
\(691\) −21.2904 −0.809926 −0.404963 0.914333i \(-0.632716\pi\)
−0.404963 + 0.914333i \(0.632716\pi\)
\(692\) 0 0
\(693\) 1.78082 0.0676477
\(694\) 0 0
\(695\) 5.55942 0.210881
\(696\) 0 0
\(697\) −28.2740 −1.07096
\(698\) 0 0
\(699\) −1.63654 −0.0618997
\(700\) 0 0
\(701\) 9.86278 0.372512 0.186256 0.982501i \(-0.440365\pi\)
0.186256 + 0.982501i \(0.440365\pi\)
\(702\) 0 0
\(703\) 16.5409 0.623851
\(704\) 0 0
\(705\) 3.49073 0.131469
\(706\) 0 0
\(707\) −44.9509 −1.69055
\(708\) 0 0
\(709\) −21.0510 −0.790586 −0.395293 0.918555i \(-0.629357\pi\)
−0.395293 + 0.918555i \(0.629357\pi\)
\(710\) 0 0
\(711\) −23.0406 −0.864088
\(712\) 0 0
\(713\) 26.5543 0.994467
\(714\) 0 0
\(715\) −9.76652 −0.365247
\(716\) 0 0
\(717\) 7.90948 0.295385
\(718\) 0 0
\(719\) 10.2812 0.383424 0.191712 0.981451i \(-0.438596\pi\)
0.191712 + 0.981451i \(0.438596\pi\)
\(720\) 0 0
\(721\) 32.6048 1.21427
\(722\) 0 0
\(723\) 11.8993 0.442541
\(724\) 0 0
\(725\) 63.2803 2.35017
\(726\) 0 0
\(727\) 10.9986 0.407915 0.203958 0.978980i \(-0.434620\pi\)
0.203958 + 0.978980i \(0.434620\pi\)
\(728\) 0 0
\(729\) 24.7566 0.916910
\(730\) 0 0
\(731\) −27.7620 −1.02682
\(732\) 0 0
\(733\) −49.8169 −1.84003 −0.920015 0.391882i \(-0.871824\pi\)
−0.920015 + 0.391882i \(0.871824\pi\)
\(734\) 0 0
\(735\) 38.0972 1.40524
\(736\) 0 0
\(737\) −3.86541 −0.142384
\(738\) 0 0
\(739\) −10.6389 −0.391357 −0.195678 0.980668i \(-0.562691\pi\)
−0.195678 + 0.980668i \(0.562691\pi\)
\(740\) 0 0
\(741\) 28.8891 1.06127
\(742\) 0 0
\(743\) −52.1630 −1.91367 −0.956837 0.290625i \(-0.906137\pi\)
−0.956837 + 0.290625i \(0.906137\pi\)
\(744\) 0 0
\(745\) −55.2382 −2.02377
\(746\) 0 0
\(747\) −18.2420 −0.667441
\(748\) 0 0
\(749\) 56.7091 2.07211
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −23.9011 −0.871006
\(754\) 0 0
\(755\) 41.7751 1.52035
\(756\) 0 0
\(757\) 38.4968 1.39919 0.699595 0.714540i \(-0.253364\pi\)
0.699595 + 0.714540i \(0.253364\pi\)
\(758\) 0 0
\(759\) −1.10573 −0.0401355
\(760\) 0 0
\(761\) 28.1326 1.01980 0.509902 0.860232i \(-0.329682\pi\)
0.509902 + 0.860232i \(0.329682\pi\)
\(762\) 0 0
\(763\) 38.5474 1.39551
\(764\) 0 0
\(765\) −34.9247 −1.26271
\(766\) 0 0
\(767\) −20.4582 −0.738703
\(768\) 0 0
\(769\) −8.58509 −0.309586 −0.154793 0.987947i \(-0.549471\pi\)
−0.154793 + 0.987947i \(0.549471\pi\)
\(770\) 0 0
\(771\) 10.0401 0.361586
\(772\) 0 0
\(773\) 22.0473 0.792986 0.396493 0.918038i \(-0.370227\pi\)
0.396493 + 0.918038i \(0.370227\pi\)
\(774\) 0 0
\(775\) −144.275 −5.18252
\(776\) 0 0
\(777\) 22.3299 0.801081
\(778\) 0 0
\(779\) 17.5596 0.629137
\(780\) 0 0
\(781\) −0.189766 −0.00679036
\(782\) 0 0
\(783\) −24.6130 −0.879595
\(784\) 0 0
\(785\) −74.1288 −2.64577
\(786\) 0 0
\(787\) −12.3972 −0.441911 −0.220955 0.975284i \(-0.570918\pi\)
−0.220955 + 0.975284i \(0.570918\pi\)
\(788\) 0 0
\(789\) −7.13764 −0.254107
\(790\) 0 0
\(791\) 71.3590 2.53723
\(792\) 0 0
\(793\) −49.1622 −1.74580
\(794\) 0 0
\(795\) 34.1377 1.21074
\(796\) 0 0
\(797\) −15.0503 −0.533109 −0.266554 0.963820i \(-0.585885\pi\)
−0.266554 + 0.963820i \(0.585885\pi\)
\(798\) 0 0
\(799\) 3.53693 0.125127
\(800\) 0 0
\(801\) 11.3922 0.402523
\(802\) 0 0
\(803\) −4.31774 −0.152370
\(804\) 0 0
\(805\) 43.0392 1.51693
\(806\) 0 0
\(807\) −6.81420 −0.239871
\(808\) 0 0
\(809\) −21.1326 −0.742984 −0.371492 0.928436i \(-0.621154\pi\)
−0.371492 + 0.928436i \(0.621154\pi\)
\(810\) 0 0
\(811\) 30.8794 1.08432 0.542162 0.840274i \(-0.317606\pi\)
0.542162 + 0.840274i \(0.317606\pi\)
\(812\) 0 0
\(813\) −5.58750 −0.195962
\(814\) 0 0
\(815\) −19.2434 −0.674066
\(816\) 0 0
\(817\) 17.2416 0.603207
\(818\) 0 0
\(819\) −35.2558 −1.23194
\(820\) 0 0
\(821\) −31.8193 −1.11050 −0.555251 0.831683i \(-0.687378\pi\)
−0.555251 + 0.831683i \(0.687378\pi\)
\(822\) 0 0
\(823\) 28.8273 1.00486 0.502428 0.864619i \(-0.332440\pi\)
0.502428 + 0.864619i \(0.332440\pi\)
\(824\) 0 0
\(825\) 6.00768 0.209160
\(826\) 0 0
\(827\) −24.5278 −0.852915 −0.426458 0.904508i \(-0.640239\pi\)
−0.426458 + 0.904508i \(0.640239\pi\)
\(828\) 0 0
\(829\) −35.4745 −1.23208 −0.616041 0.787714i \(-0.711264\pi\)
−0.616041 + 0.787714i \(0.711264\pi\)
\(830\) 0 0
\(831\) −0.746691 −0.0259024
\(832\) 0 0
\(833\) 38.6014 1.33746
\(834\) 0 0
\(835\) 12.2837 0.425094
\(836\) 0 0
\(837\) 56.1161 1.93966
\(838\) 0 0
\(839\) −9.39021 −0.324186 −0.162093 0.986775i \(-0.551824\pi\)
−0.162093 + 0.986775i \(0.551824\pi\)
\(840\) 0 0
\(841\) −9.35870 −0.322714
\(842\) 0 0
\(843\) 25.3569 0.873337
\(844\) 0 0
\(845\) 136.273 4.68794
\(846\) 0 0
\(847\) 40.6102 1.39538
\(848\) 0 0
\(849\) 11.2786 0.387081
\(850\) 0 0
\(851\) 12.5339 0.429655
\(852\) 0 0
\(853\) −17.4390 −0.597100 −0.298550 0.954394i \(-0.596503\pi\)
−0.298550 + 0.954394i \(0.596503\pi\)
\(854\) 0 0
\(855\) 21.6900 0.741782
\(856\) 0 0
\(857\) −32.4703 −1.10917 −0.554583 0.832129i \(-0.687122\pi\)
−0.554583 + 0.832129i \(0.687122\pi\)
\(858\) 0 0
\(859\) 23.8328 0.813165 0.406582 0.913614i \(-0.366720\pi\)
0.406582 + 0.913614i \(0.366720\pi\)
\(860\) 0 0
\(861\) 23.7051 0.807869
\(862\) 0 0
\(863\) 40.1305 1.36606 0.683029 0.730392i \(-0.260662\pi\)
0.683029 + 0.730392i \(0.260662\pi\)
\(864\) 0 0
\(865\) −28.1267 −0.956337
\(866\) 0 0
\(867\) 17.8058 0.604715
\(868\) 0 0
\(869\) 5.42209 0.183932
\(870\) 0 0
\(871\) 76.5255 2.59297
\(872\) 0 0
\(873\) 20.4806 0.693164
\(874\) 0 0
\(875\) −151.955 −5.13703
\(876\) 0 0
\(877\) −24.3447 −0.822060 −0.411030 0.911622i \(-0.634831\pi\)
−0.411030 + 0.911622i \(0.634831\pi\)
\(878\) 0 0
\(879\) −6.57007 −0.221603
\(880\) 0 0
\(881\) −27.2359 −0.917601 −0.458800 0.888539i \(-0.651721\pi\)
−0.458800 + 0.888539i \(0.651721\pi\)
\(882\) 0 0
\(883\) −5.21691 −0.175563 −0.0877815 0.996140i \(-0.527978\pi\)
−0.0877815 + 0.996140i \(0.527978\pi\)
\(884\) 0 0
\(885\) 16.9912 0.571154
\(886\) 0 0
\(887\) 41.7894 1.40315 0.701576 0.712595i \(-0.252480\pi\)
0.701576 + 0.712595i \(0.252480\pi\)
\(888\) 0 0
\(889\) 25.2289 0.846151
\(890\) 0 0
\(891\) −0.904375 −0.0302977
\(892\) 0 0
\(893\) −2.19661 −0.0735066
\(894\) 0 0
\(895\) −62.9394 −2.10383
\(896\) 0 0
\(897\) 21.8907 0.730910
\(898\) 0 0
\(899\) −44.7810 −1.49353
\(900\) 0 0
\(901\) 34.5895 1.15234
\(902\) 0 0
\(903\) 23.2759 0.774572
\(904\) 0 0
\(905\) 17.4974 0.581634
\(906\) 0 0
\(907\) 10.8587 0.360558 0.180279 0.983615i \(-0.442300\pi\)
0.180279 + 0.983615i \(0.442300\pi\)
\(908\) 0 0
\(909\) −17.1656 −0.569348
\(910\) 0 0
\(911\) −2.84690 −0.0943221 −0.0471611 0.998887i \(-0.515017\pi\)
−0.0471611 + 0.998887i \(0.515017\pi\)
\(912\) 0 0
\(913\) 4.29286 0.142073
\(914\) 0 0
\(915\) 40.8309 1.34983
\(916\) 0 0
\(917\) 67.2105 2.21949
\(918\) 0 0
\(919\) −29.7791 −0.982321 −0.491161 0.871069i \(-0.663427\pi\)
−0.491161 + 0.871069i \(0.663427\pi\)
\(920\) 0 0
\(921\) −39.9098 −1.31507
\(922\) 0 0
\(923\) 3.75689 0.123660
\(924\) 0 0
\(925\) −68.0991 −2.23909
\(926\) 0 0
\(927\) 12.4510 0.408944
\(928\) 0 0
\(929\) 36.5135 1.19797 0.598984 0.800761i \(-0.295571\pi\)
0.598984 + 0.800761i \(0.295571\pi\)
\(930\) 0 0
\(931\) −23.9734 −0.785696
\(932\) 0 0
\(933\) 4.49663 0.147213
\(934\) 0 0
\(935\) 8.21877 0.268782
\(936\) 0 0
\(937\) −36.3632 −1.18793 −0.593967 0.804489i \(-0.702439\pi\)
−0.593967 + 0.804489i \(0.702439\pi\)
\(938\) 0 0
\(939\) 24.2097 0.790054
\(940\) 0 0
\(941\) 10.3357 0.336935 0.168467 0.985707i \(-0.446118\pi\)
0.168467 + 0.985707i \(0.446118\pi\)
\(942\) 0 0
\(943\) 13.3058 0.433296
\(944\) 0 0
\(945\) 90.9529 2.95870
\(946\) 0 0
\(947\) −42.3939 −1.37762 −0.688808 0.724943i \(-0.741866\pi\)
−0.688808 + 0.724943i \(0.741866\pi\)
\(948\) 0 0
\(949\) 85.4805 2.77481
\(950\) 0 0
\(951\) −22.4898 −0.729281
\(952\) 0 0
\(953\) 28.2563 0.915310 0.457655 0.889130i \(-0.348689\pi\)
0.457655 + 0.889130i \(0.348689\pi\)
\(954\) 0 0
\(955\) 59.4571 1.92399
\(956\) 0 0
\(957\) 1.86470 0.0602771
\(958\) 0 0
\(959\) −12.7471 −0.411625
\(960\) 0 0
\(961\) 71.0981 2.29349
\(962\) 0 0
\(963\) 21.6558 0.697849
\(964\) 0 0
\(965\) 39.7195 1.27862
\(966\) 0 0
\(967\) −29.4948 −0.948488 −0.474244 0.880393i \(-0.657279\pi\)
−0.474244 + 0.880393i \(0.657279\pi\)
\(968\) 0 0
\(969\) −24.3109 −0.780979
\(970\) 0 0
\(971\) 24.5156 0.786743 0.393371 0.919380i \(-0.371309\pi\)
0.393371 + 0.919380i \(0.371309\pi\)
\(972\) 0 0
\(973\) −4.72274 −0.151404
\(974\) 0 0
\(975\) −118.937 −3.80903
\(976\) 0 0
\(977\) −3.71085 −0.118721 −0.0593603 0.998237i \(-0.518906\pi\)
−0.0593603 + 0.998237i \(0.518906\pi\)
\(978\) 0 0
\(979\) −2.68090 −0.0856820
\(980\) 0 0
\(981\) 14.7203 0.469983
\(982\) 0 0
\(983\) 18.8140 0.600072 0.300036 0.953928i \(-0.403001\pi\)
0.300036 + 0.953928i \(0.403001\pi\)
\(984\) 0 0
\(985\) 46.2244 1.47283
\(986\) 0 0
\(987\) −2.96538 −0.0943891
\(988\) 0 0
\(989\) 13.0648 0.415437
\(990\) 0 0
\(991\) −35.7069 −1.13427 −0.567133 0.823626i \(-0.691948\pi\)
−0.567133 + 0.823626i \(0.691948\pi\)
\(992\) 0 0
\(993\) −37.9646 −1.20477
\(994\) 0 0
\(995\) −14.7383 −0.467236
\(996\) 0 0
\(997\) −39.4721 −1.25010 −0.625048 0.780587i \(-0.714920\pi\)
−0.625048 + 0.780587i \(0.714920\pi\)
\(998\) 0 0
\(999\) 26.4873 0.838020
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.1.32 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.32 44 1.1 even 1 trivial