Properties

Label 6008.2.a.b.1.30
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 1.30
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.09745 q^{3} -0.0446663 q^{5} +4.14700 q^{7} -1.79560 q^{9} +O(q^{10})\) \(q+1.09745 q^{3} -0.0446663 q^{5} +4.14700 q^{7} -1.79560 q^{9} -6.33765 q^{11} +2.84157 q^{13} -0.0490192 q^{15} +3.68590 q^{17} -2.76271 q^{19} +4.55115 q^{21} -6.82373 q^{23} -4.99800 q^{25} -5.26294 q^{27} +9.76715 q^{29} -9.04708 q^{31} -6.95528 q^{33} -0.185232 q^{35} -7.68047 q^{37} +3.11850 q^{39} +4.70273 q^{41} -0.928314 q^{43} +0.0802027 q^{45} -1.75621 q^{47} +10.1976 q^{49} +4.04511 q^{51} -6.88021 q^{53} +0.283080 q^{55} -3.03195 q^{57} +5.45578 q^{59} -1.13711 q^{61} -7.44634 q^{63} -0.126923 q^{65} -10.4060 q^{67} -7.48873 q^{69} -9.49858 q^{71} -12.8208 q^{73} -5.48508 q^{75} -26.2823 q^{77} +6.76255 q^{79} -0.389050 q^{81} +10.3424 q^{83} -0.164636 q^{85} +10.7190 q^{87} +4.86666 q^{89} +11.7840 q^{91} -9.92875 q^{93} +0.123400 q^{95} -7.30869 q^{97} +11.3799 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) 1.09745 0.633615 0.316808 0.948490i \(-0.397389\pi\)
0.316808 + 0.948490i \(0.397389\pi\)
\(4\) 0 0
\(5\) −0.0446663 −0.0199754 −0.00998770 0.999950i \(-0.503179\pi\)
−0.00998770 + 0.999950i \(0.503179\pi\)
\(6\) 0 0
\(7\) 4.14700 1.56742 0.783710 0.621127i \(-0.213325\pi\)
0.783710 + 0.621127i \(0.213325\pi\)
\(8\) 0 0
\(9\) −1.79560 −0.598532
\(10\) 0 0
\(11\) −6.33765 −1.91087 −0.955437 0.295194i \(-0.904616\pi\)
−0.955437 + 0.295194i \(0.904616\pi\)
\(12\) 0 0
\(13\) 2.84157 0.788111 0.394055 0.919087i \(-0.371072\pi\)
0.394055 + 0.919087i \(0.371072\pi\)
\(14\) 0 0
\(15\) −0.0490192 −0.0126567
\(16\) 0 0
\(17\) 3.68590 0.893962 0.446981 0.894543i \(-0.352499\pi\)
0.446981 + 0.894543i \(0.352499\pi\)
\(18\) 0 0
\(19\) −2.76271 −0.633810 −0.316905 0.948457i \(-0.602644\pi\)
−0.316905 + 0.948457i \(0.602644\pi\)
\(20\) 0 0
\(21\) 4.55115 0.993141
\(22\) 0 0
\(23\) −6.82373 −1.42285 −0.711423 0.702764i \(-0.751949\pi\)
−0.711423 + 0.702764i \(0.751949\pi\)
\(24\) 0 0
\(25\) −4.99800 −0.999601
\(26\) 0 0
\(27\) −5.26294 −1.01285
\(28\) 0 0
\(29\) 9.76715 1.81371 0.906857 0.421439i \(-0.138475\pi\)
0.906857 + 0.421439i \(0.138475\pi\)
\(30\) 0 0
\(31\) −9.04708 −1.62490 −0.812452 0.583028i \(-0.801868\pi\)
−0.812452 + 0.583028i \(0.801868\pi\)
\(32\) 0 0
\(33\) −6.95528 −1.21076
\(34\) 0 0
\(35\) −0.185232 −0.0313098
\(36\) 0 0
\(37\) −7.68047 −1.26266 −0.631331 0.775513i \(-0.717491\pi\)
−0.631331 + 0.775513i \(0.717491\pi\)
\(38\) 0 0
\(39\) 3.11850 0.499359
\(40\) 0 0
\(41\) 4.70273 0.734443 0.367222 0.930133i \(-0.380309\pi\)
0.367222 + 0.930133i \(0.380309\pi\)
\(42\) 0 0
\(43\) −0.928314 −0.141566 −0.0707832 0.997492i \(-0.522550\pi\)
−0.0707832 + 0.997492i \(0.522550\pi\)
\(44\) 0 0
\(45\) 0.0802027 0.0119559
\(46\) 0 0
\(47\) −1.75621 −0.256170 −0.128085 0.991763i \(-0.540883\pi\)
−0.128085 + 0.991763i \(0.540883\pi\)
\(48\) 0 0
\(49\) 10.1976 1.45681
\(50\) 0 0
\(51\) 4.04511 0.566428
\(52\) 0 0
\(53\) −6.88021 −0.945070 −0.472535 0.881312i \(-0.656661\pi\)
−0.472535 + 0.881312i \(0.656661\pi\)
\(54\) 0 0
\(55\) 0.283080 0.0381705
\(56\) 0 0
\(57\) −3.03195 −0.401592
\(58\) 0 0
\(59\) 5.45578 0.710282 0.355141 0.934813i \(-0.384433\pi\)
0.355141 + 0.934813i \(0.384433\pi\)
\(60\) 0 0
\(61\) −1.13711 −0.145592 −0.0727961 0.997347i \(-0.523192\pi\)
−0.0727961 + 0.997347i \(0.523192\pi\)
\(62\) 0 0
\(63\) −7.44634 −0.938151
\(64\) 0 0
\(65\) −0.126923 −0.0157428
\(66\) 0 0
\(67\) −10.4060 −1.27130 −0.635648 0.771979i \(-0.719267\pi\)
−0.635648 + 0.771979i \(0.719267\pi\)
\(68\) 0 0
\(69\) −7.48873 −0.901537
\(70\) 0 0
\(71\) −9.49858 −1.12727 −0.563637 0.826022i \(-0.690598\pi\)
−0.563637 + 0.826022i \(0.690598\pi\)
\(72\) 0 0
\(73\) −12.8208 −1.50057 −0.750283 0.661117i \(-0.770083\pi\)
−0.750283 + 0.661117i \(0.770083\pi\)
\(74\) 0 0
\(75\) −5.48508 −0.633362
\(76\) 0 0
\(77\) −26.2823 −2.99514
\(78\) 0 0
\(79\) 6.76255 0.760847 0.380423 0.924812i \(-0.375778\pi\)
0.380423 + 0.924812i \(0.375778\pi\)
\(80\) 0 0
\(81\) −0.389050 −0.0432278
\(82\) 0 0
\(83\) 10.3424 1.13522 0.567611 0.823297i \(-0.307868\pi\)
0.567611 + 0.823297i \(0.307868\pi\)
\(84\) 0 0
\(85\) −0.164636 −0.0178572
\(86\) 0 0
\(87\) 10.7190 1.14920
\(88\) 0 0
\(89\) 4.86666 0.515865 0.257933 0.966163i \(-0.416959\pi\)
0.257933 + 0.966163i \(0.416959\pi\)
\(90\) 0 0
\(91\) 11.7840 1.23530
\(92\) 0 0
\(93\) −9.92875 −1.02956
\(94\) 0 0
\(95\) 0.123400 0.0126606
\(96\) 0 0
\(97\) −7.30869 −0.742085 −0.371043 0.928616i \(-0.621000\pi\)
−0.371043 + 0.928616i \(0.621000\pi\)
\(98\) 0 0
\(99\) 11.3799 1.14372
\(100\) 0 0
\(101\) −14.3674 −1.42961 −0.714803 0.699325i \(-0.753484\pi\)
−0.714803 + 0.699325i \(0.753484\pi\)
\(102\) 0 0
\(103\) −14.3615 −1.41508 −0.707542 0.706671i \(-0.750196\pi\)
−0.707542 + 0.706671i \(0.750196\pi\)
\(104\) 0 0
\(105\) −0.203283 −0.0198384
\(106\) 0 0
\(107\) 6.61529 0.639525 0.319762 0.947498i \(-0.396397\pi\)
0.319762 + 0.947498i \(0.396397\pi\)
\(108\) 0 0
\(109\) 15.6887 1.50270 0.751351 0.659903i \(-0.229403\pi\)
0.751351 + 0.659903i \(0.229403\pi\)
\(110\) 0 0
\(111\) −8.42896 −0.800042
\(112\) 0 0
\(113\) −1.45766 −0.137125 −0.0685627 0.997647i \(-0.521841\pi\)
−0.0685627 + 0.997647i \(0.521841\pi\)
\(114\) 0 0
\(115\) 0.304791 0.0284219
\(116\) 0 0
\(117\) −5.10232 −0.471709
\(118\) 0 0
\(119\) 15.2854 1.40121
\(120\) 0 0
\(121\) 29.1659 2.65144
\(122\) 0 0
\(123\) 5.16103 0.465354
\(124\) 0 0
\(125\) 0.446574 0.0399428
\(126\) 0 0
\(127\) 0.340971 0.0302563 0.0151281 0.999886i \(-0.495184\pi\)
0.0151281 + 0.999886i \(0.495184\pi\)
\(128\) 0 0
\(129\) −1.01878 −0.0896987
\(130\) 0 0
\(131\) −0.930386 −0.0812882 −0.0406441 0.999174i \(-0.512941\pi\)
−0.0406441 + 0.999174i \(0.512941\pi\)
\(132\) 0 0
\(133\) −11.4570 −0.993447
\(134\) 0 0
\(135\) 0.235076 0.0202322
\(136\) 0 0
\(137\) 5.82807 0.497925 0.248963 0.968513i \(-0.419910\pi\)
0.248963 + 0.968513i \(0.419910\pi\)
\(138\) 0 0
\(139\) −8.12159 −0.688865 −0.344432 0.938811i \(-0.611929\pi\)
−0.344432 + 0.938811i \(0.611929\pi\)
\(140\) 0 0
\(141\) −1.92736 −0.162313
\(142\) 0 0
\(143\) −18.0089 −1.50598
\(144\) 0 0
\(145\) −0.436263 −0.0362297
\(146\) 0 0
\(147\) 11.1914 0.923055
\(148\) 0 0
\(149\) 0.144482 0.0118364 0.00591821 0.999982i \(-0.498116\pi\)
0.00591821 + 0.999982i \(0.498116\pi\)
\(150\) 0 0
\(151\) −2.52023 −0.205094 −0.102547 0.994728i \(-0.532699\pi\)
−0.102547 + 0.994728i \(0.532699\pi\)
\(152\) 0 0
\(153\) −6.61839 −0.535065
\(154\) 0 0
\(155\) 0.404100 0.0324581
\(156\) 0 0
\(157\) −9.89356 −0.789592 −0.394796 0.918769i \(-0.629185\pi\)
−0.394796 + 0.918769i \(0.629185\pi\)
\(158\) 0 0
\(159\) −7.55071 −0.598810
\(160\) 0 0
\(161\) −28.2980 −2.23020
\(162\) 0 0
\(163\) −3.02561 −0.236984 −0.118492 0.992955i \(-0.537806\pi\)
−0.118492 + 0.992955i \(0.537806\pi\)
\(164\) 0 0
\(165\) 0.310667 0.0241854
\(166\) 0 0
\(167\) −2.58138 −0.199753 −0.0998765 0.995000i \(-0.531845\pi\)
−0.0998765 + 0.995000i \(0.531845\pi\)
\(168\) 0 0
\(169\) −4.92546 −0.378881
\(170\) 0 0
\(171\) 4.96072 0.379355
\(172\) 0 0
\(173\) 2.26721 0.172373 0.0861864 0.996279i \(-0.472532\pi\)
0.0861864 + 0.996279i \(0.472532\pi\)
\(174\) 0 0
\(175\) −20.7268 −1.56680
\(176\) 0 0
\(177\) 5.98746 0.450045
\(178\) 0 0
\(179\) 1.23146 0.0920433 0.0460217 0.998940i \(-0.485346\pi\)
0.0460217 + 0.998940i \(0.485346\pi\)
\(180\) 0 0
\(181\) −4.51384 −0.335511 −0.167756 0.985829i \(-0.553652\pi\)
−0.167756 + 0.985829i \(0.553652\pi\)
\(182\) 0 0
\(183\) −1.24793 −0.0922494
\(184\) 0 0
\(185\) 0.343059 0.0252222
\(186\) 0 0
\(187\) −23.3600 −1.70825
\(188\) 0 0
\(189\) −21.8255 −1.58757
\(190\) 0 0
\(191\) 9.98607 0.722567 0.361283 0.932456i \(-0.382339\pi\)
0.361283 + 0.932456i \(0.382339\pi\)
\(192\) 0 0
\(193\) 5.39231 0.388147 0.194074 0.980987i \(-0.437830\pi\)
0.194074 + 0.980987i \(0.437830\pi\)
\(194\) 0 0
\(195\) −0.139292 −0.00997489
\(196\) 0 0
\(197\) −20.8726 −1.48711 −0.743556 0.668674i \(-0.766862\pi\)
−0.743556 + 0.668674i \(0.766862\pi\)
\(198\) 0 0
\(199\) 10.7561 0.762478 0.381239 0.924476i \(-0.375497\pi\)
0.381239 + 0.924476i \(0.375497\pi\)
\(200\) 0 0
\(201\) −11.4201 −0.805512
\(202\) 0 0
\(203\) 40.5044 2.84285
\(204\) 0 0
\(205\) −0.210054 −0.0146708
\(206\) 0 0
\(207\) 12.2527 0.851618
\(208\) 0 0
\(209\) 17.5091 1.21113
\(210\) 0 0
\(211\) −11.1041 −0.764438 −0.382219 0.924072i \(-0.624840\pi\)
−0.382219 + 0.924072i \(0.624840\pi\)
\(212\) 0 0
\(213\) −10.4243 −0.714258
\(214\) 0 0
\(215\) 0.0414644 0.00282785
\(216\) 0 0
\(217\) −37.5183 −2.54691
\(218\) 0 0
\(219\) −14.0703 −0.950781
\(220\) 0 0
\(221\) 10.4738 0.704541
\(222\) 0 0
\(223\) −16.3917 −1.09767 −0.548836 0.835930i \(-0.684929\pi\)
−0.548836 + 0.835930i \(0.684929\pi\)
\(224\) 0 0
\(225\) 8.97440 0.598293
\(226\) 0 0
\(227\) −7.66340 −0.508637 −0.254319 0.967120i \(-0.581851\pi\)
−0.254319 + 0.967120i \(0.581851\pi\)
\(228\) 0 0
\(229\) 16.8035 1.11040 0.555202 0.831715i \(-0.312641\pi\)
0.555202 + 0.831715i \(0.312641\pi\)
\(230\) 0 0
\(231\) −28.8436 −1.89777
\(232\) 0 0
\(233\) 8.43463 0.552571 0.276285 0.961076i \(-0.410897\pi\)
0.276285 + 0.961076i \(0.410897\pi\)
\(234\) 0 0
\(235\) 0.0784437 0.00511710
\(236\) 0 0
\(237\) 7.42159 0.482084
\(238\) 0 0
\(239\) −6.66677 −0.431237 −0.215619 0.976478i \(-0.569177\pi\)
−0.215619 + 0.976478i \(0.569177\pi\)
\(240\) 0 0
\(241\) −4.64555 −0.299246 −0.149623 0.988743i \(-0.547806\pi\)
−0.149623 + 0.988743i \(0.547806\pi\)
\(242\) 0 0
\(243\) 15.3619 0.985464
\(244\) 0 0
\(245\) −0.455492 −0.0291003
\(246\) 0 0
\(247\) −7.85046 −0.499513
\(248\) 0 0
\(249\) 11.3503 0.719294
\(250\) 0 0
\(251\) 26.8129 1.69242 0.846208 0.532853i \(-0.178880\pi\)
0.846208 + 0.532853i \(0.178880\pi\)
\(252\) 0 0
\(253\) 43.2464 2.71888
\(254\) 0 0
\(255\) −0.180680 −0.0113146
\(256\) 0 0
\(257\) 8.30438 0.518013 0.259006 0.965876i \(-0.416605\pi\)
0.259006 + 0.965876i \(0.416605\pi\)
\(258\) 0 0
\(259\) −31.8510 −1.97912
\(260\) 0 0
\(261\) −17.5378 −1.08557
\(262\) 0 0
\(263\) 7.37953 0.455041 0.227521 0.973773i \(-0.426938\pi\)
0.227521 + 0.973773i \(0.426938\pi\)
\(264\) 0 0
\(265\) 0.307314 0.0188781
\(266\) 0 0
\(267\) 5.34094 0.326860
\(268\) 0 0
\(269\) 19.9288 1.21508 0.607539 0.794290i \(-0.292157\pi\)
0.607539 + 0.794290i \(0.292157\pi\)
\(270\) 0 0
\(271\) −3.17593 −0.192924 −0.0964619 0.995337i \(-0.530753\pi\)
−0.0964619 + 0.995337i \(0.530753\pi\)
\(272\) 0 0
\(273\) 12.9324 0.782706
\(274\) 0 0
\(275\) 31.6756 1.91011
\(276\) 0 0
\(277\) 24.1463 1.45081 0.725405 0.688322i \(-0.241652\pi\)
0.725405 + 0.688322i \(0.241652\pi\)
\(278\) 0 0
\(279\) 16.2449 0.972557
\(280\) 0 0
\(281\) 6.22309 0.371239 0.185619 0.982622i \(-0.440571\pi\)
0.185619 + 0.982622i \(0.440571\pi\)
\(282\) 0 0
\(283\) −28.8669 −1.71596 −0.857981 0.513682i \(-0.828281\pi\)
−0.857981 + 0.513682i \(0.828281\pi\)
\(284\) 0 0
\(285\) 0.135426 0.00802195
\(286\) 0 0
\(287\) 19.5023 1.15118
\(288\) 0 0
\(289\) −3.41414 −0.200832
\(290\) 0 0
\(291\) −8.02095 −0.470197
\(292\) 0 0
\(293\) 27.6136 1.61321 0.806603 0.591093i \(-0.201304\pi\)
0.806603 + 0.591093i \(0.201304\pi\)
\(294\) 0 0
\(295\) −0.243690 −0.0141882
\(296\) 0 0
\(297\) 33.3547 1.93544
\(298\) 0 0
\(299\) −19.3901 −1.12136
\(300\) 0 0
\(301\) −3.84972 −0.221894
\(302\) 0 0
\(303\) −15.7675 −0.905821
\(304\) 0 0
\(305\) 0.0507906 0.00290826
\(306\) 0 0
\(307\) 31.3405 1.78869 0.894347 0.447373i \(-0.147641\pi\)
0.894347 + 0.447373i \(0.147641\pi\)
\(308\) 0 0
\(309\) −15.7611 −0.896619
\(310\) 0 0
\(311\) −23.4732 −1.33104 −0.665521 0.746379i \(-0.731791\pi\)
−0.665521 + 0.746379i \(0.731791\pi\)
\(312\) 0 0
\(313\) −6.27594 −0.354737 −0.177368 0.984145i \(-0.556758\pi\)
−0.177368 + 0.984145i \(0.556758\pi\)
\(314\) 0 0
\(315\) 0.332601 0.0187399
\(316\) 0 0
\(317\) −12.0524 −0.676929 −0.338464 0.940979i \(-0.609907\pi\)
−0.338464 + 0.940979i \(0.609907\pi\)
\(318\) 0 0
\(319\) −61.9008 −3.46578
\(320\) 0 0
\(321\) 7.25998 0.405212
\(322\) 0 0
\(323\) −10.1831 −0.566602
\(324\) 0 0
\(325\) −14.2022 −0.787796
\(326\) 0 0
\(327\) 17.2176 0.952135
\(328\) 0 0
\(329\) −7.28303 −0.401526
\(330\) 0 0
\(331\) −15.1868 −0.834745 −0.417372 0.908736i \(-0.637049\pi\)
−0.417372 + 0.908736i \(0.637049\pi\)
\(332\) 0 0
\(333\) 13.7910 0.755743
\(334\) 0 0
\(335\) 0.464798 0.0253946
\(336\) 0 0
\(337\) −29.2744 −1.59468 −0.797339 0.603531i \(-0.793760\pi\)
−0.797339 + 0.603531i \(0.793760\pi\)
\(338\) 0 0
\(339\) −1.59972 −0.0868847
\(340\) 0 0
\(341\) 57.3373 3.10499
\(342\) 0 0
\(343\) 13.2607 0.716008
\(344\) 0 0
\(345\) 0.334494 0.0180086
\(346\) 0 0
\(347\) −1.13669 −0.0610208 −0.0305104 0.999534i \(-0.509713\pi\)
−0.0305104 + 0.999534i \(0.509713\pi\)
\(348\) 0 0
\(349\) 30.4800 1.63156 0.815779 0.578364i \(-0.196309\pi\)
0.815779 + 0.578364i \(0.196309\pi\)
\(350\) 0 0
\(351\) −14.9550 −0.798241
\(352\) 0 0
\(353\) −16.1432 −0.859218 −0.429609 0.903015i \(-0.641349\pi\)
−0.429609 + 0.903015i \(0.641349\pi\)
\(354\) 0 0
\(355\) 0.424267 0.0225178
\(356\) 0 0
\(357\) 16.7751 0.887831
\(358\) 0 0
\(359\) −24.0899 −1.27142 −0.635708 0.771929i \(-0.719292\pi\)
−0.635708 + 0.771929i \(0.719292\pi\)
\(360\) 0 0
\(361\) −11.3674 −0.598285
\(362\) 0 0
\(363\) 32.0082 1.67999
\(364\) 0 0
\(365\) 0.572660 0.0299744
\(366\) 0 0
\(367\) −20.3603 −1.06280 −0.531399 0.847122i \(-0.678334\pi\)
−0.531399 + 0.847122i \(0.678334\pi\)
\(368\) 0 0
\(369\) −8.44421 −0.439588
\(370\) 0 0
\(371\) −28.5323 −1.48132
\(372\) 0 0
\(373\) −37.4220 −1.93764 −0.968818 0.247772i \(-0.920302\pi\)
−0.968818 + 0.247772i \(0.920302\pi\)
\(374\) 0 0
\(375\) 0.490095 0.0253084
\(376\) 0 0
\(377\) 27.7541 1.42941
\(378\) 0 0
\(379\) 11.4790 0.589635 0.294817 0.955554i \(-0.404741\pi\)
0.294817 + 0.955554i \(0.404741\pi\)
\(380\) 0 0
\(381\) 0.374200 0.0191709
\(382\) 0 0
\(383\) −6.17583 −0.315570 −0.157785 0.987473i \(-0.550435\pi\)
−0.157785 + 0.987473i \(0.550435\pi\)
\(384\) 0 0
\(385\) 1.17393 0.0598292
\(386\) 0 0
\(387\) 1.66688 0.0847320
\(388\) 0 0
\(389\) −28.8214 −1.46130 −0.730650 0.682752i \(-0.760783\pi\)
−0.730650 + 0.682752i \(0.760783\pi\)
\(390\) 0 0
\(391\) −25.1516 −1.27197
\(392\) 0 0
\(393\) −1.02106 −0.0515054
\(394\) 0 0
\(395\) −0.302058 −0.0151982
\(396\) 0 0
\(397\) 10.1865 0.511248 0.255624 0.966776i \(-0.417719\pi\)
0.255624 + 0.966776i \(0.417719\pi\)
\(398\) 0 0
\(399\) −12.5735 −0.629463
\(400\) 0 0
\(401\) −28.1703 −1.40676 −0.703378 0.710816i \(-0.748326\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(402\) 0 0
\(403\) −25.7080 −1.28060
\(404\) 0 0
\(405\) 0.0173775 0.000863493 0
\(406\) 0 0
\(407\) 48.6762 2.41279
\(408\) 0 0
\(409\) 35.7516 1.76780 0.883900 0.467675i \(-0.154908\pi\)
0.883900 + 0.467675i \(0.154908\pi\)
\(410\) 0 0
\(411\) 6.39603 0.315493
\(412\) 0 0
\(413\) 22.6251 1.11331
\(414\) 0 0
\(415\) −0.461956 −0.0226765
\(416\) 0 0
\(417\) −8.91307 −0.436475
\(418\) 0 0
\(419\) 18.5723 0.907317 0.453658 0.891176i \(-0.350119\pi\)
0.453658 + 0.891176i \(0.350119\pi\)
\(420\) 0 0
\(421\) 29.5659 1.44095 0.720476 0.693480i \(-0.243923\pi\)
0.720476 + 0.693480i \(0.243923\pi\)
\(422\) 0 0
\(423\) 3.15345 0.153326
\(424\) 0 0
\(425\) −18.4221 −0.893606
\(426\) 0 0
\(427\) −4.71561 −0.228204
\(428\) 0 0
\(429\) −19.7640 −0.954213
\(430\) 0 0
\(431\) 36.9474 1.77969 0.889846 0.456261i \(-0.150811\pi\)
0.889846 + 0.456261i \(0.150811\pi\)
\(432\) 0 0
\(433\) 10.6218 0.510452 0.255226 0.966881i \(-0.417850\pi\)
0.255226 + 0.966881i \(0.417850\pi\)
\(434\) 0 0
\(435\) −0.478778 −0.0229557
\(436\) 0 0
\(437\) 18.8520 0.901814
\(438\) 0 0
\(439\) 22.8405 1.09012 0.545058 0.838398i \(-0.316507\pi\)
0.545058 + 0.838398i \(0.316507\pi\)
\(440\) 0 0
\(441\) −18.3109 −0.871945
\(442\) 0 0
\(443\) 11.6837 0.555109 0.277554 0.960710i \(-0.410476\pi\)
0.277554 + 0.960710i \(0.410476\pi\)
\(444\) 0 0
\(445\) −0.217376 −0.0103046
\(446\) 0 0
\(447\) 0.158562 0.00749973
\(448\) 0 0
\(449\) 13.5886 0.641287 0.320644 0.947200i \(-0.396101\pi\)
0.320644 + 0.947200i \(0.396101\pi\)
\(450\) 0 0
\(451\) −29.8043 −1.40343
\(452\) 0 0
\(453\) −2.76584 −0.129950
\(454\) 0 0
\(455\) −0.526349 −0.0246756
\(456\) 0 0
\(457\) −34.8883 −1.63201 −0.816004 0.578046i \(-0.803815\pi\)
−0.816004 + 0.578046i \(0.803815\pi\)
\(458\) 0 0
\(459\) −19.3987 −0.905453
\(460\) 0 0
\(461\) 31.9313 1.48719 0.743595 0.668630i \(-0.233119\pi\)
0.743595 + 0.668630i \(0.233119\pi\)
\(462\) 0 0
\(463\) −32.0806 −1.49091 −0.745456 0.666555i \(-0.767768\pi\)
−0.745456 + 0.666555i \(0.767768\pi\)
\(464\) 0 0
\(465\) 0.443481 0.0205659
\(466\) 0 0
\(467\) 7.22053 0.334126 0.167063 0.985946i \(-0.446572\pi\)
0.167063 + 0.985946i \(0.446572\pi\)
\(468\) 0 0
\(469\) −43.1538 −1.99266
\(470\) 0 0
\(471\) −10.8577 −0.500297
\(472\) 0 0
\(473\) 5.88333 0.270516
\(474\) 0 0
\(475\) 13.8081 0.633557
\(476\) 0 0
\(477\) 12.3541 0.565654
\(478\) 0 0
\(479\) −37.2220 −1.70072 −0.850358 0.526205i \(-0.823614\pi\)
−0.850358 + 0.526205i \(0.823614\pi\)
\(480\) 0 0
\(481\) −21.8246 −0.995118
\(482\) 0 0
\(483\) −31.0558 −1.41309
\(484\) 0 0
\(485\) 0.326453 0.0148234
\(486\) 0 0
\(487\) −14.6015 −0.661657 −0.330829 0.943691i \(-0.607328\pi\)
−0.330829 + 0.943691i \(0.607328\pi\)
\(488\) 0 0
\(489\) −3.32047 −0.150157
\(490\) 0 0
\(491\) 22.7655 1.02739 0.513696 0.857972i \(-0.328276\pi\)
0.513696 + 0.857972i \(0.328276\pi\)
\(492\) 0 0
\(493\) 36.0007 1.62139
\(494\) 0 0
\(495\) −0.508297 −0.0228462
\(496\) 0 0
\(497\) −39.3907 −1.76691
\(498\) 0 0
\(499\) −13.5960 −0.608642 −0.304321 0.952570i \(-0.598430\pi\)
−0.304321 + 0.952570i \(0.598430\pi\)
\(500\) 0 0
\(501\) −2.83294 −0.126567
\(502\) 0 0
\(503\) 20.8709 0.930586 0.465293 0.885157i \(-0.345949\pi\)
0.465293 + 0.885157i \(0.345949\pi\)
\(504\) 0 0
\(505\) 0.641738 0.0285570
\(506\) 0 0
\(507\) −5.40546 −0.240065
\(508\) 0 0
\(509\) 11.8806 0.526598 0.263299 0.964714i \(-0.415189\pi\)
0.263299 + 0.964714i \(0.415189\pi\)
\(510\) 0 0
\(511\) −53.1681 −2.35202
\(512\) 0 0
\(513\) 14.5400 0.641957
\(514\) 0 0
\(515\) 0.641477 0.0282669
\(516\) 0 0
\(517\) 11.1303 0.489509
\(518\) 0 0
\(519\) 2.48816 0.109218
\(520\) 0 0
\(521\) −1.23770 −0.0542247 −0.0271123 0.999632i \(-0.508631\pi\)
−0.0271123 + 0.999632i \(0.508631\pi\)
\(522\) 0 0
\(523\) −17.2331 −0.753553 −0.376776 0.926304i \(-0.622967\pi\)
−0.376776 + 0.926304i \(0.622967\pi\)
\(524\) 0 0
\(525\) −22.7466 −0.992745
\(526\) 0 0
\(527\) −33.3466 −1.45260
\(528\) 0 0
\(529\) 23.5633 1.02449
\(530\) 0 0
\(531\) −9.79637 −0.425126
\(532\) 0 0
\(533\) 13.3632 0.578823
\(534\) 0 0
\(535\) −0.295481 −0.0127748
\(536\) 0 0
\(537\) 1.35147 0.0583200
\(538\) 0 0
\(539\) −64.6292 −2.78378
\(540\) 0 0
\(541\) −42.9788 −1.84780 −0.923901 0.382631i \(-0.875018\pi\)
−0.923901 + 0.382631i \(0.875018\pi\)
\(542\) 0 0
\(543\) −4.95373 −0.212585
\(544\) 0 0
\(545\) −0.700755 −0.0300171
\(546\) 0 0
\(547\) −44.2130 −1.89041 −0.945206 0.326475i \(-0.894139\pi\)
−0.945206 + 0.326475i \(0.894139\pi\)
\(548\) 0 0
\(549\) 2.04179 0.0871416
\(550\) 0 0
\(551\) −26.9838 −1.14955
\(552\) 0 0
\(553\) 28.0443 1.19257
\(554\) 0 0
\(555\) 0.376491 0.0159811
\(556\) 0 0
\(557\) −13.7776 −0.583777 −0.291888 0.956452i \(-0.594284\pi\)
−0.291888 + 0.956452i \(0.594284\pi\)
\(558\) 0 0
\(559\) −2.63787 −0.111570
\(560\) 0 0
\(561\) −25.6365 −1.08237
\(562\) 0 0
\(563\) 32.2279 1.35824 0.679121 0.734026i \(-0.262361\pi\)
0.679121 + 0.734026i \(0.262361\pi\)
\(564\) 0 0
\(565\) 0.0651085 0.00273913
\(566\) 0 0
\(567\) −1.61339 −0.0677562
\(568\) 0 0
\(569\) −0.774502 −0.0324688 −0.0162344 0.999868i \(-0.505168\pi\)
−0.0162344 + 0.999868i \(0.505168\pi\)
\(570\) 0 0
\(571\) 12.2585 0.513001 0.256500 0.966544i \(-0.417431\pi\)
0.256500 + 0.966544i \(0.417431\pi\)
\(572\) 0 0
\(573\) 10.9593 0.457829
\(574\) 0 0
\(575\) 34.1050 1.42228
\(576\) 0 0
\(577\) −33.1886 −1.38166 −0.690830 0.723017i \(-0.742755\pi\)
−0.690830 + 0.723017i \(0.742755\pi\)
\(578\) 0 0
\(579\) 5.91781 0.245936
\(580\) 0 0
\(581\) 42.8899 1.77937
\(582\) 0 0
\(583\) 43.6044 1.80591
\(584\) 0 0
\(585\) 0.227902 0.00942258
\(586\) 0 0
\(587\) −14.6862 −0.606163 −0.303082 0.952965i \(-0.598015\pi\)
−0.303082 + 0.952965i \(0.598015\pi\)
\(588\) 0 0
\(589\) 24.9945 1.02988
\(590\) 0 0
\(591\) −22.9067 −0.942256
\(592\) 0 0
\(593\) 10.4206 0.427922 0.213961 0.976842i \(-0.431364\pi\)
0.213961 + 0.976842i \(0.431364\pi\)
\(594\) 0 0
\(595\) −0.682745 −0.0279898
\(596\) 0 0
\(597\) 11.8043 0.483118
\(598\) 0 0
\(599\) −36.7275 −1.50064 −0.750322 0.661073i \(-0.770101\pi\)
−0.750322 + 0.661073i \(0.770101\pi\)
\(600\) 0 0
\(601\) 4.09296 0.166955 0.0834777 0.996510i \(-0.473397\pi\)
0.0834777 + 0.996510i \(0.473397\pi\)
\(602\) 0 0
\(603\) 18.6850 0.760911
\(604\) 0 0
\(605\) −1.30273 −0.0529636
\(606\) 0 0
\(607\) 42.9951 1.74512 0.872559 0.488509i \(-0.162459\pi\)
0.872559 + 0.488509i \(0.162459\pi\)
\(608\) 0 0
\(609\) 44.4517 1.80127
\(610\) 0 0
\(611\) −4.99041 −0.201890
\(612\) 0 0
\(613\) −19.4209 −0.784404 −0.392202 0.919879i \(-0.628287\pi\)
−0.392202 + 0.919879i \(0.628287\pi\)
\(614\) 0 0
\(615\) −0.230524 −0.00929564
\(616\) 0 0
\(617\) −39.8522 −1.60439 −0.802195 0.597062i \(-0.796335\pi\)
−0.802195 + 0.597062i \(0.796335\pi\)
\(618\) 0 0
\(619\) 26.8560 1.07943 0.539716 0.841847i \(-0.318532\pi\)
0.539716 + 0.841847i \(0.318532\pi\)
\(620\) 0 0
\(621\) 35.9129 1.44114
\(622\) 0 0
\(623\) 20.1821 0.808578
\(624\) 0 0
\(625\) 24.9701 0.998803
\(626\) 0 0
\(627\) 19.2155 0.767391
\(628\) 0 0
\(629\) −28.3095 −1.12877
\(630\) 0 0
\(631\) −9.92711 −0.395192 −0.197596 0.980284i \(-0.563313\pi\)
−0.197596 + 0.980284i \(0.563313\pi\)
\(632\) 0 0
\(633\) −12.1862 −0.484359
\(634\) 0 0
\(635\) −0.0152299 −0.000604382 0
\(636\) 0 0
\(637\) 28.9774 1.14813
\(638\) 0 0
\(639\) 17.0556 0.674710
\(640\) 0 0
\(641\) 1.94948 0.0769998 0.0384999 0.999259i \(-0.487742\pi\)
0.0384999 + 0.999259i \(0.487742\pi\)
\(642\) 0 0
\(643\) 9.35437 0.368900 0.184450 0.982842i \(-0.440950\pi\)
0.184450 + 0.982842i \(0.440950\pi\)
\(644\) 0 0
\(645\) 0.0455052 0.00179177
\(646\) 0 0
\(647\) 28.7731 1.13119 0.565594 0.824684i \(-0.308647\pi\)
0.565594 + 0.824684i \(0.308647\pi\)
\(648\) 0 0
\(649\) −34.5768 −1.35726
\(650\) 0 0
\(651\) −41.1746 −1.61376
\(652\) 0 0
\(653\) 38.7694 1.51717 0.758583 0.651577i \(-0.225892\pi\)
0.758583 + 0.651577i \(0.225892\pi\)
\(654\) 0 0
\(655\) 0.0415569 0.00162376
\(656\) 0 0
\(657\) 23.0210 0.898136
\(658\) 0 0
\(659\) −38.9003 −1.51534 −0.757671 0.652637i \(-0.773663\pi\)
−0.757671 + 0.652637i \(0.773663\pi\)
\(660\) 0 0
\(661\) −47.4785 −1.84670 −0.923349 0.383961i \(-0.874560\pi\)
−0.923349 + 0.383961i \(0.874560\pi\)
\(662\) 0 0
\(663\) 11.4945 0.446408
\(664\) 0 0
\(665\) 0.511742 0.0198445
\(666\) 0 0
\(667\) −66.6484 −2.58064
\(668\) 0 0
\(669\) −17.9892 −0.695502
\(670\) 0 0
\(671\) 7.20662 0.278209
\(672\) 0 0
\(673\) −32.4504 −1.25087 −0.625436 0.780275i \(-0.715079\pi\)
−0.625436 + 0.780275i \(0.715079\pi\)
\(674\) 0 0
\(675\) 26.3042 1.01245
\(676\) 0 0
\(677\) −9.73894 −0.374298 −0.187149 0.982332i \(-0.559925\pi\)
−0.187149 + 0.982332i \(0.559925\pi\)
\(678\) 0 0
\(679\) −30.3092 −1.16316
\(680\) 0 0
\(681\) −8.41022 −0.322280
\(682\) 0 0
\(683\) −6.64784 −0.254373 −0.127186 0.991879i \(-0.540595\pi\)
−0.127186 + 0.991879i \(0.540595\pi\)
\(684\) 0 0
\(685\) −0.260318 −0.00994625
\(686\) 0 0
\(687\) 18.4410 0.703569
\(688\) 0 0
\(689\) −19.5506 −0.744820
\(690\) 0 0
\(691\) 5.08544 0.193459 0.0967296 0.995311i \(-0.469162\pi\)
0.0967296 + 0.995311i \(0.469162\pi\)
\(692\) 0 0
\(693\) 47.1924 1.79269
\(694\) 0 0
\(695\) 0.362762 0.0137603
\(696\) 0 0
\(697\) 17.3338 0.656565
\(698\) 0 0
\(699\) 9.25661 0.350117
\(700\) 0 0
\(701\) 35.2295 1.33060 0.665299 0.746577i \(-0.268304\pi\)
0.665299 + 0.746577i \(0.268304\pi\)
\(702\) 0 0
\(703\) 21.2189 0.800288
\(704\) 0 0
\(705\) 0.0860883 0.00324227
\(706\) 0 0
\(707\) −59.5816 −2.24080
\(708\) 0 0
\(709\) −0.699610 −0.0262744 −0.0131372 0.999914i \(-0.504182\pi\)
−0.0131372 + 0.999914i \(0.504182\pi\)
\(710\) 0 0
\(711\) −12.1428 −0.455391
\(712\) 0 0
\(713\) 61.7348 2.31199
\(714\) 0 0
\(715\) 0.804392 0.0300826
\(716\) 0 0
\(717\) −7.31647 −0.273238
\(718\) 0 0
\(719\) 17.7467 0.661840 0.330920 0.943659i \(-0.392641\pi\)
0.330920 + 0.943659i \(0.392641\pi\)
\(720\) 0 0
\(721\) −59.5574 −2.21803
\(722\) 0 0
\(723\) −5.09827 −0.189607
\(724\) 0 0
\(725\) −48.8163 −1.81299
\(726\) 0 0
\(727\) 11.5641 0.428889 0.214444 0.976736i \(-0.431206\pi\)
0.214444 + 0.976736i \(0.431206\pi\)
\(728\) 0 0
\(729\) 18.0261 0.667633
\(730\) 0 0
\(731\) −3.42167 −0.126555
\(732\) 0 0
\(733\) −4.43798 −0.163920 −0.0819602 0.996636i \(-0.526118\pi\)
−0.0819602 + 0.996636i \(0.526118\pi\)
\(734\) 0 0
\(735\) −0.499881 −0.0184384
\(736\) 0 0
\(737\) 65.9497 2.42929
\(738\) 0 0
\(739\) −3.07315 −0.113048 −0.0565238 0.998401i \(-0.518002\pi\)
−0.0565238 + 0.998401i \(0.518002\pi\)
\(740\) 0 0
\(741\) −8.61551 −0.316499
\(742\) 0 0
\(743\) −40.4436 −1.48373 −0.741867 0.670547i \(-0.766059\pi\)
−0.741867 + 0.670547i \(0.766059\pi\)
\(744\) 0 0
\(745\) −0.00645348 −0.000236437 0
\(746\) 0 0
\(747\) −18.5707 −0.679467
\(748\) 0 0
\(749\) 27.4337 1.00240
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 29.4259 1.07234
\(754\) 0 0
\(755\) 0.112570 0.00409682
\(756\) 0 0
\(757\) 43.4929 1.58078 0.790388 0.612606i \(-0.209879\pi\)
0.790388 + 0.612606i \(0.209879\pi\)
\(758\) 0 0
\(759\) 47.4610 1.72272
\(760\) 0 0
\(761\) −27.5143 −0.997393 −0.498697 0.866777i \(-0.666188\pi\)
−0.498697 + 0.866777i \(0.666188\pi\)
\(762\) 0 0
\(763\) 65.0610 2.35537
\(764\) 0 0
\(765\) 0.295619 0.0106881
\(766\) 0 0
\(767\) 15.5030 0.559781
\(768\) 0 0
\(769\) 30.5849 1.10292 0.551459 0.834202i \(-0.314071\pi\)
0.551459 + 0.834202i \(0.314071\pi\)
\(770\) 0 0
\(771\) 9.11367 0.328221
\(772\) 0 0
\(773\) −25.4624 −0.915818 −0.457909 0.888999i \(-0.651402\pi\)
−0.457909 + 0.888999i \(0.651402\pi\)
\(774\) 0 0
\(775\) 45.2174 1.62426
\(776\) 0 0
\(777\) −34.9549 −1.25400
\(778\) 0 0
\(779\) −12.9923 −0.465498
\(780\) 0 0
\(781\) 60.1987 2.15408
\(782\) 0 0
\(783\) −51.4040 −1.83703
\(784\) 0 0
\(785\) 0.441909 0.0157724
\(786\) 0 0
\(787\) 11.1056 0.395873 0.197937 0.980215i \(-0.436576\pi\)
0.197937 + 0.980215i \(0.436576\pi\)
\(788\) 0 0
\(789\) 8.09870 0.288321
\(790\) 0 0
\(791\) −6.04493 −0.214933
\(792\) 0 0
\(793\) −3.23119 −0.114743
\(794\) 0 0
\(795\) 0.337263 0.0119615
\(796\) 0 0
\(797\) −29.8227 −1.05637 −0.528187 0.849128i \(-0.677128\pi\)
−0.528187 + 0.849128i \(0.677128\pi\)
\(798\) 0 0
\(799\) −6.47323 −0.229006
\(800\) 0 0
\(801\) −8.73856 −0.308762
\(802\) 0 0
\(803\) 81.2540 2.86739
\(804\) 0 0
\(805\) 1.26397 0.0445491
\(806\) 0 0
\(807\) 21.8709 0.769892
\(808\) 0 0
\(809\) −21.6261 −0.760334 −0.380167 0.924918i \(-0.624133\pi\)
−0.380167 + 0.924918i \(0.624133\pi\)
\(810\) 0 0
\(811\) 10.6998 0.375720 0.187860 0.982196i \(-0.439845\pi\)
0.187860 + 0.982196i \(0.439845\pi\)
\(812\) 0 0
\(813\) −3.48543 −0.122239
\(814\) 0 0
\(815\) 0.135143 0.00473385
\(816\) 0 0
\(817\) 2.56466 0.0897262
\(818\) 0 0
\(819\) −21.1593 −0.739367
\(820\) 0 0
\(821\) −23.9459 −0.835718 −0.417859 0.908512i \(-0.637219\pi\)
−0.417859 + 0.908512i \(0.637219\pi\)
\(822\) 0 0
\(823\) −7.12071 −0.248212 −0.124106 0.992269i \(-0.539606\pi\)
−0.124106 + 0.992269i \(0.539606\pi\)
\(824\) 0 0
\(825\) 34.7625 1.21028
\(826\) 0 0
\(827\) −28.7219 −0.998758 −0.499379 0.866384i \(-0.666438\pi\)
−0.499379 + 0.866384i \(0.666438\pi\)
\(828\) 0 0
\(829\) −32.9632 −1.14486 −0.572430 0.819954i \(-0.693999\pi\)
−0.572430 + 0.819954i \(0.693999\pi\)
\(830\) 0 0
\(831\) 26.4994 0.919255
\(832\) 0 0
\(833\) 37.5875 1.30233
\(834\) 0 0
\(835\) 0.115301 0.00399015
\(836\) 0 0
\(837\) 47.6143 1.64579
\(838\) 0 0
\(839\) 39.1866 1.35287 0.676437 0.736501i \(-0.263523\pi\)
0.676437 + 0.736501i \(0.263523\pi\)
\(840\) 0 0
\(841\) 66.3972 2.28956
\(842\) 0 0
\(843\) 6.82956 0.235222
\(844\) 0 0
\(845\) 0.220002 0.00756830
\(846\) 0 0
\(847\) 120.951 4.15593
\(848\) 0 0
\(849\) −31.6801 −1.08726
\(850\) 0 0
\(851\) 52.4095 1.79657
\(852\) 0 0
\(853\) 49.7163 1.70226 0.851128 0.524959i \(-0.175919\pi\)
0.851128 + 0.524959i \(0.175919\pi\)
\(854\) 0 0
\(855\) −0.221577 −0.00757777
\(856\) 0 0
\(857\) 27.0587 0.924309 0.462154 0.886799i \(-0.347077\pi\)
0.462154 + 0.886799i \(0.347077\pi\)
\(858\) 0 0
\(859\) −9.56499 −0.326353 −0.163177 0.986597i \(-0.552174\pi\)
−0.163177 + 0.986597i \(0.552174\pi\)
\(860\) 0 0
\(861\) 21.4028 0.729406
\(862\) 0 0
\(863\) −6.13783 −0.208934 −0.104467 0.994528i \(-0.533314\pi\)
−0.104467 + 0.994528i \(0.533314\pi\)
\(864\) 0 0
\(865\) −0.101268 −0.00344322
\(866\) 0 0
\(867\) −3.74686 −0.127250
\(868\) 0 0
\(869\) −42.8587 −1.45388
\(870\) 0 0
\(871\) −29.5694 −1.00192
\(872\) 0 0
\(873\) 13.1235 0.444162
\(874\) 0 0
\(875\) 1.85195 0.0626072
\(876\) 0 0
\(877\) 57.8520 1.95352 0.976762 0.214327i \(-0.0687558\pi\)
0.976762 + 0.214327i \(0.0687558\pi\)
\(878\) 0 0
\(879\) 30.3047 1.02215
\(880\) 0 0
\(881\) −3.36736 −0.113449 −0.0567246 0.998390i \(-0.518066\pi\)
−0.0567246 + 0.998390i \(0.518066\pi\)
\(882\) 0 0
\(883\) 22.7789 0.766572 0.383286 0.923630i \(-0.374792\pi\)
0.383286 + 0.923630i \(0.374792\pi\)
\(884\) 0 0
\(885\) −0.267438 −0.00898983
\(886\) 0 0
\(887\) −5.41195 −0.181715 −0.0908577 0.995864i \(-0.528961\pi\)
−0.0908577 + 0.995864i \(0.528961\pi\)
\(888\) 0 0
\(889\) 1.41401 0.0474243
\(890\) 0 0
\(891\) 2.46567 0.0826030
\(892\) 0 0
\(893\) 4.85192 0.162363
\(894\) 0 0
\(895\) −0.0550046 −0.00183860
\(896\) 0 0
\(897\) −21.2798 −0.710511
\(898\) 0 0
\(899\) −88.3642 −2.94711
\(900\) 0 0
\(901\) −25.3598 −0.844857
\(902\) 0 0
\(903\) −4.22489 −0.140596
\(904\) 0 0
\(905\) 0.201617 0.00670197
\(906\) 0 0
\(907\) 12.1356 0.402957 0.201479 0.979493i \(-0.435425\pi\)
0.201479 + 0.979493i \(0.435425\pi\)
\(908\) 0 0
\(909\) 25.7980 0.855665
\(910\) 0 0
\(911\) −16.8848 −0.559418 −0.279709 0.960085i \(-0.590238\pi\)
−0.279709 + 0.960085i \(0.590238\pi\)
\(912\) 0 0
\(913\) −65.5464 −2.16927
\(914\) 0 0
\(915\) 0.0557403 0.00184272
\(916\) 0 0
\(917\) −3.85831 −0.127413
\(918\) 0 0
\(919\) 30.3203 1.00017 0.500087 0.865975i \(-0.333301\pi\)
0.500087 + 0.865975i \(0.333301\pi\)
\(920\) 0 0
\(921\) 34.3947 1.13334
\(922\) 0 0
\(923\) −26.9909 −0.888417
\(924\) 0 0
\(925\) 38.3870 1.26216
\(926\) 0 0
\(927\) 25.7875 0.846973
\(928\) 0 0
\(929\) −4.34012 −0.142395 −0.0711974 0.997462i \(-0.522682\pi\)
−0.0711974 + 0.997462i \(0.522682\pi\)
\(930\) 0 0
\(931\) −28.1732 −0.923339
\(932\) 0 0
\(933\) −25.7607 −0.843368
\(934\) 0 0
\(935\) 1.04340 0.0341230
\(936\) 0 0
\(937\) −18.1328 −0.592372 −0.296186 0.955130i \(-0.595715\pi\)
−0.296186 + 0.955130i \(0.595715\pi\)
\(938\) 0 0
\(939\) −6.88755 −0.224767
\(940\) 0 0
\(941\) 8.34741 0.272118 0.136059 0.990701i \(-0.456556\pi\)
0.136059 + 0.990701i \(0.456556\pi\)
\(942\) 0 0
\(943\) −32.0902 −1.04500
\(944\) 0 0
\(945\) 0.974863 0.0317123
\(946\) 0 0
\(947\) 50.1004 1.62804 0.814022 0.580833i \(-0.197273\pi\)
0.814022 + 0.580833i \(0.197273\pi\)
\(948\) 0 0
\(949\) −36.4314 −1.18261
\(950\) 0 0
\(951\) −13.2269 −0.428912
\(952\) 0 0
\(953\) 31.2503 1.01230 0.506148 0.862446i \(-0.331069\pi\)
0.506148 + 0.862446i \(0.331069\pi\)
\(954\) 0 0
\(955\) −0.446041 −0.0144336
\(956\) 0 0
\(957\) −67.9333 −2.19597
\(958\) 0 0
\(959\) 24.1690 0.780458
\(960\) 0 0
\(961\) 50.8497 1.64031
\(962\) 0 0
\(963\) −11.8784 −0.382776
\(964\) 0 0
\(965\) −0.240855 −0.00775339
\(966\) 0 0
\(967\) −25.6787 −0.825771 −0.412886 0.910783i \(-0.635479\pi\)
−0.412886 + 0.910783i \(0.635479\pi\)
\(968\) 0 0
\(969\) −11.1755 −0.359008
\(970\) 0 0
\(971\) 8.83558 0.283547 0.141774 0.989899i \(-0.454720\pi\)
0.141774 + 0.989899i \(0.454720\pi\)
\(972\) 0 0
\(973\) −33.6803 −1.07974
\(974\) 0 0
\(975\) −15.5863 −0.499160
\(976\) 0 0
\(977\) −1.63013 −0.0521525 −0.0260763 0.999660i \(-0.508301\pi\)
−0.0260763 + 0.999660i \(0.508301\pi\)
\(978\) 0 0
\(979\) −30.8432 −0.985754
\(980\) 0 0
\(981\) −28.1705 −0.899415
\(982\) 0 0
\(983\) −15.8500 −0.505537 −0.252768 0.967527i \(-0.581341\pi\)
−0.252768 + 0.967527i \(0.581341\pi\)
\(984\) 0 0
\(985\) 0.932303 0.0297056
\(986\) 0 0
\(987\) −7.99279 −0.254413
\(988\) 0 0
\(989\) 6.33456 0.201427
\(990\) 0 0
\(991\) 25.5922 0.812962 0.406481 0.913659i \(-0.366756\pi\)
0.406481 + 0.913659i \(0.366756\pi\)
\(992\) 0 0
\(993\) −16.6669 −0.528907
\(994\) 0 0
\(995\) −0.480435 −0.0152308
\(996\) 0 0
\(997\) −4.34006 −0.137451 −0.0687256 0.997636i \(-0.521893\pi\)
−0.0687256 + 0.997636i \(0.521893\pi\)
\(998\) 0 0
\(999\) 40.4219 1.27889
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.1.30 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.30 44 1.1 even 1 trivial