Properties

Label 4600.2.a.bg.1.5
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.791953.1
Defining polynomial: \(x^{5} - 2 x^{4} - 7 x^{3} + 7 x^{2} + 9 x + 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.08344\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.08344 q^{3} -0.555022 q^{7} +6.50759 q^{9} +O(q^{10})\) \(q+3.08344 q^{3} -0.555022 q^{7} +6.50759 q^{9} +4.65190 q^{11} +5.02256 q^{13} +1.32867 q^{17} -0.196402 q^{19} -1.71138 q^{21} +1.00000 q^{23} +10.8154 q^{27} -0.812298 q^{29} -2.11145 q^{31} +14.3439 q^{33} -5.64564 q^{37} +15.4868 q^{39} -4.89714 q^{41} +1.66507 q^{43} -9.89310 q^{47} -6.69195 q^{49} +4.09688 q^{51} +2.23261 q^{53} -0.605593 q^{57} +2.43488 q^{59} -5.71138 q^{61} -3.61185 q^{63} +6.91830 q^{67} +3.08344 q^{69} +0.0120411 q^{71} +15.2989 q^{73} -2.58191 q^{77} +10.6351 q^{79} +13.8260 q^{81} -5.64020 q^{83} -2.50467 q^{87} +9.06693 q^{89} -2.78763 q^{91} -6.51051 q^{93} -14.0720 q^{97} +30.2727 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q + 3q^{3} - q^{7} + 4q^{9} + O(q^{10}) \) \( 5q + 3q^{3} - q^{7} + 4q^{9} - 4q^{11} - q^{13} + 5q^{17} + 4q^{19} - 6q^{21} + 5q^{23} + 6q^{27} - 11q^{29} + 4q^{31} + 13q^{33} + 6q^{37} + 31q^{39} - 8q^{41} + 3q^{43} + 2q^{47} - 2q^{49} - 5q^{51} + 18q^{53} + 27q^{57} + 23q^{59} - 26q^{61} + 5q^{63} + 3q^{67} + 3q^{69} - 2q^{71} + 4q^{73} + 15q^{77} + 43q^{79} - 3q^{81} + 30q^{83} + 27q^{87} + 15q^{89} - 19q^{91} - 15q^{93} + 8q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 3.08344 1.78022 0.890112 0.455742i \(-0.150626\pi\)
0.890112 + 0.455742i \(0.150626\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.555022 −0.209779 −0.104889 0.994484i \(-0.533449\pi\)
−0.104889 + 0.994484i \(0.533449\pi\)
\(8\) 0 0
\(9\) 6.50759 2.16920
\(10\) 0 0
\(11\) 4.65190 1.40260 0.701301 0.712866i \(-0.252603\pi\)
0.701301 + 0.712866i \(0.252603\pi\)
\(12\) 0 0
\(13\) 5.02256 1.39301 0.696504 0.717553i \(-0.254738\pi\)
0.696504 + 0.717553i \(0.254738\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.32867 0.322251 0.161125 0.986934i \(-0.448488\pi\)
0.161125 + 0.986934i \(0.448488\pi\)
\(18\) 0 0
\(19\) −0.196402 −0.0450577 −0.0225288 0.999746i \(-0.507172\pi\)
−0.0225288 + 0.999746i \(0.507172\pi\)
\(20\) 0 0
\(21\) −1.71138 −0.373453
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 10.8154 2.08143
\(28\) 0 0
\(29\) −0.812298 −0.150840 −0.0754200 0.997152i \(-0.524030\pi\)
−0.0754200 + 0.997152i \(0.524030\pi\)
\(30\) 0 0
\(31\) −2.11145 −0.379227 −0.189613 0.981859i \(-0.560723\pi\)
−0.189613 + 0.981859i \(0.560723\pi\)
\(32\) 0 0
\(33\) 14.3439 2.49694
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.64564 −0.928138 −0.464069 0.885799i \(-0.653611\pi\)
−0.464069 + 0.885799i \(0.653611\pi\)
\(38\) 0 0
\(39\) 15.4868 2.47987
\(40\) 0 0
\(41\) −4.89714 −0.764804 −0.382402 0.923996i \(-0.624903\pi\)
−0.382402 + 0.923996i \(0.624903\pi\)
\(42\) 0 0
\(43\) 1.66507 0.253920 0.126960 0.991908i \(-0.459478\pi\)
0.126960 + 0.991908i \(0.459478\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.89310 −1.44306 −0.721528 0.692385i \(-0.756560\pi\)
−0.721528 + 0.692385i \(0.756560\pi\)
\(48\) 0 0
\(49\) −6.69195 −0.955993
\(50\) 0 0
\(51\) 4.09688 0.573678
\(52\) 0 0
\(53\) 2.23261 0.306673 0.153336 0.988174i \(-0.450998\pi\)
0.153336 + 0.988174i \(0.450998\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.605593 −0.0802127
\(58\) 0 0
\(59\) 2.43488 0.316994 0.158497 0.987359i \(-0.449335\pi\)
0.158497 + 0.987359i \(0.449335\pi\)
\(60\) 0 0
\(61\) −5.71138 −0.731267 −0.365633 0.930759i \(-0.619148\pi\)
−0.365633 + 0.930759i \(0.619148\pi\)
\(62\) 0 0
\(63\) −3.61185 −0.455051
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 6.91830 0.845205 0.422602 0.906315i \(-0.361117\pi\)
0.422602 + 0.906315i \(0.361117\pi\)
\(68\) 0 0
\(69\) 3.08344 0.371202
\(70\) 0 0
\(71\) 0.0120411 0.00142902 0.000714510 1.00000i \(-0.499773\pi\)
0.000714510 1.00000i \(0.499773\pi\)
\(72\) 0 0
\(73\) 15.2989 1.79061 0.895303 0.445458i \(-0.146959\pi\)
0.895303 + 0.445458i \(0.146959\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.58191 −0.294236
\(78\) 0 0
\(79\) 10.6351 1.19654 0.598272 0.801293i \(-0.295854\pi\)
0.598272 + 0.801293i \(0.295854\pi\)
\(80\) 0 0
\(81\) 13.8260 1.53622
\(82\) 0 0
\(83\) −5.64020 −0.619092 −0.309546 0.950884i \(-0.600177\pi\)
−0.309546 + 0.950884i \(0.600177\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.50467 −0.268529
\(88\) 0 0
\(89\) 9.06693 0.961093 0.480547 0.876969i \(-0.340438\pi\)
0.480547 + 0.876969i \(0.340438\pi\)
\(90\) 0 0
\(91\) −2.78763 −0.292223
\(92\) 0 0
\(93\) −6.51051 −0.675108
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0720 −1.42880 −0.714398 0.699739i \(-0.753299\pi\)
−0.714398 + 0.699739i \(0.753299\pi\)
\(98\) 0 0
\(99\) 30.2727 3.04252
\(100\) 0 0
\(101\) 7.53015 0.749278 0.374639 0.927171i \(-0.377767\pi\)
0.374639 + 0.927171i \(0.377767\pi\)
\(102\) 0 0
\(103\) −14.4476 −1.42357 −0.711784 0.702399i \(-0.752112\pi\)
−0.711784 + 0.702399i \(0.752112\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.35862 0.228016 0.114008 0.993480i \(-0.463631\pi\)
0.114008 + 0.993480i \(0.463631\pi\)
\(108\) 0 0
\(109\) −10.3578 −0.992101 −0.496050 0.868294i \(-0.665217\pi\)
−0.496050 + 0.868294i \(0.665217\pi\)
\(110\) 0 0
\(111\) −17.4080 −1.65229
\(112\) 0 0
\(113\) −19.2723 −1.81298 −0.906491 0.422226i \(-0.861249\pi\)
−0.906491 + 0.422226i \(0.861249\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 32.6848 3.02171
\(118\) 0 0
\(119\) −0.737442 −0.0676012
\(120\) 0 0
\(121\) 10.6402 0.967291
\(122\) 0 0
\(123\) −15.1000 −1.36152
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −18.4934 −1.64102 −0.820510 0.571632i \(-0.806311\pi\)
−0.820510 + 0.571632i \(0.806311\pi\)
\(128\) 0 0
\(129\) 5.13413 0.452035
\(130\) 0 0
\(131\) −14.7727 −1.29070 −0.645351 0.763887i \(-0.723289\pi\)
−0.645351 + 0.763887i \(0.723289\pi\)
\(132\) 0 0
\(133\) 0.109007 0.00945213
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 11.6173 0.992533 0.496266 0.868170i \(-0.334704\pi\)
0.496266 + 0.868170i \(0.334704\pi\)
\(138\) 0 0
\(139\) 11.1389 0.944787 0.472393 0.881388i \(-0.343390\pi\)
0.472393 + 0.881388i \(0.343390\pi\)
\(140\) 0 0
\(141\) −30.5047 −2.56896
\(142\) 0 0
\(143\) 23.3645 1.95384
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −20.6342 −1.70188
\(148\) 0 0
\(149\) −12.4796 −1.02237 −0.511184 0.859472i \(-0.670793\pi\)
−0.511184 + 0.859472i \(0.670793\pi\)
\(150\) 0 0
\(151\) 1.32673 0.107968 0.0539840 0.998542i \(-0.482808\pi\)
0.0539840 + 0.998542i \(0.482808\pi\)
\(152\) 0 0
\(153\) 8.64646 0.699025
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 23.1754 1.84960 0.924798 0.380458i \(-0.124234\pi\)
0.924798 + 0.380458i \(0.124234\pi\)
\(158\) 0 0
\(159\) 6.88412 0.545946
\(160\) 0 0
\(161\) −0.555022 −0.0437418
\(162\) 0 0
\(163\) 25.0682 1.96349 0.981746 0.190196i \(-0.0609125\pi\)
0.981746 + 0.190196i \(0.0609125\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.39603 −0.340175 −0.170087 0.985429i \(-0.554405\pi\)
−0.170087 + 0.985429i \(0.554405\pi\)
\(168\) 0 0
\(169\) 12.2261 0.940473
\(170\) 0 0
\(171\) −1.27810 −0.0977389
\(172\) 0 0
\(173\) 19.4211 1.47656 0.738281 0.674493i \(-0.235638\pi\)
0.738281 + 0.674493i \(0.235638\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 7.50779 0.564320
\(178\) 0 0
\(179\) 10.4169 0.778592 0.389296 0.921113i \(-0.372718\pi\)
0.389296 + 0.921113i \(0.372718\pi\)
\(180\) 0 0
\(181\) −9.13693 −0.679143 −0.339571 0.940580i \(-0.610282\pi\)
−0.339571 + 0.940580i \(0.610282\pi\)
\(182\) 0 0
\(183\) −17.6107 −1.30182
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.18086 0.451989
\(188\) 0 0
\(189\) −6.00280 −0.436640
\(190\) 0 0
\(191\) −1.49819 −0.108405 −0.0542026 0.998530i \(-0.517262\pi\)
−0.0542026 + 0.998530i \(0.517262\pi\)
\(192\) 0 0
\(193\) 14.4113 1.03735 0.518675 0.854972i \(-0.326425\pi\)
0.518675 + 0.854972i \(0.326425\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 24.4686 1.74331 0.871657 0.490116i \(-0.163046\pi\)
0.871657 + 0.490116i \(0.163046\pi\)
\(198\) 0 0
\(199\) −1.61185 −0.114261 −0.0571307 0.998367i \(-0.518195\pi\)
−0.0571307 + 0.998367i \(0.518195\pi\)
\(200\) 0 0
\(201\) 21.3321 1.50465
\(202\) 0 0
\(203\) 0.450843 0.0316430
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.50759 0.452309
\(208\) 0 0
\(209\) −0.913642 −0.0631979
\(210\) 0 0
\(211\) 6.25081 0.430324 0.215162 0.976578i \(-0.430972\pi\)
0.215162 + 0.976578i \(0.430972\pi\)
\(212\) 0 0
\(213\) 0.0371281 0.00254398
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.17190 0.0795536
\(218\) 0 0
\(219\) 47.1733 3.18768
\(220\) 0 0
\(221\) 6.67334 0.448898
\(222\) 0 0
\(223\) 21.2953 1.42604 0.713019 0.701144i \(-0.247327\pi\)
0.713019 + 0.701144i \(0.247327\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.5174 0.698061 0.349031 0.937111i \(-0.386511\pi\)
0.349031 + 0.937111i \(0.386511\pi\)
\(228\) 0 0
\(229\) −24.0063 −1.58638 −0.793190 0.608975i \(-0.791581\pi\)
−0.793190 + 0.608975i \(0.791581\pi\)
\(230\) 0 0
\(231\) −7.96115 −0.523805
\(232\) 0 0
\(233\) −11.3112 −0.741021 −0.370510 0.928828i \(-0.620817\pi\)
−0.370510 + 0.928828i \(0.620817\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 32.7927 2.13012
\(238\) 0 0
\(239\) −25.5592 −1.65329 −0.826644 0.562726i \(-0.809753\pi\)
−0.826644 + 0.562726i \(0.809753\pi\)
\(240\) 0 0
\(241\) −16.1617 −1.04106 −0.520532 0.853842i \(-0.674266\pi\)
−0.520532 + 0.853842i \(0.674266\pi\)
\(242\) 0 0
\(243\) 10.1852 0.653380
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −0.986440 −0.0627657
\(248\) 0 0
\(249\) −17.3912 −1.10212
\(250\) 0 0
\(251\) −13.3497 −0.842627 −0.421313 0.906915i \(-0.638431\pi\)
−0.421313 + 0.906915i \(0.638431\pi\)
\(252\) 0 0
\(253\) 4.65190 0.292463
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.1834 0.635222 0.317611 0.948221i \(-0.397119\pi\)
0.317611 + 0.948221i \(0.397119\pi\)
\(258\) 0 0
\(259\) 3.13345 0.194703
\(260\) 0 0
\(261\) −5.28610 −0.327201
\(262\) 0 0
\(263\) −23.3073 −1.43719 −0.718594 0.695430i \(-0.755214\pi\)
−0.718594 + 0.695430i \(0.755214\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 27.9573 1.71096
\(268\) 0 0
\(269\) 9.80817 0.598015 0.299007 0.954251i \(-0.403344\pi\)
0.299007 + 0.954251i \(0.403344\pi\)
\(270\) 0 0
\(271\) −6.08332 −0.369535 −0.184768 0.982782i \(-0.559153\pi\)
−0.184768 + 0.982782i \(0.559153\pi\)
\(272\) 0 0
\(273\) −8.59549 −0.520223
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.0445722 0.00267809 0.00133904 0.999999i \(-0.499574\pi\)
0.00133904 + 0.999999i \(0.499574\pi\)
\(278\) 0 0
\(279\) −13.7404 −0.822617
\(280\) 0 0
\(281\) 27.9996 1.67032 0.835158 0.550010i \(-0.185376\pi\)
0.835158 + 0.550010i \(0.185376\pi\)
\(282\) 0 0
\(283\) −12.1798 −0.724013 −0.362006 0.932176i \(-0.617908\pi\)
−0.362006 + 0.932176i \(0.617908\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.71802 0.160440
\(288\) 0 0
\(289\) −15.2346 −0.896155
\(290\) 0 0
\(291\) −43.3902 −2.54358
\(292\) 0 0
\(293\) 2.71056 0.158352 0.0791762 0.996861i \(-0.474771\pi\)
0.0791762 + 0.996861i \(0.474771\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 50.3124 2.91942
\(298\) 0 0
\(299\) 5.02256 0.290462
\(300\) 0 0
\(301\) −0.924148 −0.0532670
\(302\) 0 0
\(303\) 23.2188 1.33388
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 32.1631 1.83564 0.917821 0.396994i \(-0.129947\pi\)
0.917821 + 0.396994i \(0.129947\pi\)
\(308\) 0 0
\(309\) −44.5484 −2.53427
\(310\) 0 0
\(311\) −4.07951 −0.231328 −0.115664 0.993288i \(-0.536900\pi\)
−0.115664 + 0.993288i \(0.536900\pi\)
\(312\) 0 0
\(313\) −13.7806 −0.778925 −0.389462 0.921042i \(-0.627339\pi\)
−0.389462 + 0.921042i \(0.627339\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.4630 −0.587658 −0.293829 0.955858i \(-0.594930\pi\)
−0.293829 + 0.955858i \(0.594930\pi\)
\(318\) 0 0
\(319\) −3.77873 −0.211568
\(320\) 0 0
\(321\) 7.27266 0.405920
\(322\) 0 0
\(323\) −0.260954 −0.0145199
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −31.9377 −1.76616
\(328\) 0 0
\(329\) 5.49088 0.302722
\(330\) 0 0
\(331\) −12.6451 −0.695038 −0.347519 0.937673i \(-0.612976\pi\)
−0.347519 + 0.937673i \(0.612976\pi\)
\(332\) 0 0
\(333\) −36.7395 −2.01331
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −24.5733 −1.33859 −0.669295 0.742997i \(-0.733404\pi\)
−0.669295 + 0.742997i \(0.733404\pi\)
\(338\) 0 0
\(339\) −59.4248 −3.22751
\(340\) 0 0
\(341\) −9.82224 −0.531904
\(342\) 0 0
\(343\) 7.59933 0.410325
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.50569 0.188195 0.0940977 0.995563i \(-0.470003\pi\)
0.0940977 + 0.995563i \(0.470003\pi\)
\(348\) 0 0
\(349\) −18.1085 −0.969327 −0.484664 0.874701i \(-0.661058\pi\)
−0.484664 + 0.874701i \(0.661058\pi\)
\(350\) 0 0
\(351\) 54.3212 2.89945
\(352\) 0 0
\(353\) 20.1915 1.07469 0.537343 0.843364i \(-0.319428\pi\)
0.537343 + 0.843364i \(0.319428\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.27386 −0.120345
\(358\) 0 0
\(359\) −9.43409 −0.497912 −0.248956 0.968515i \(-0.580088\pi\)
−0.248956 + 0.968515i \(0.580088\pi\)
\(360\) 0 0
\(361\) −18.9614 −0.997970
\(362\) 0 0
\(363\) 32.8084 1.72199
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 30.3412 1.58380 0.791899 0.610652i \(-0.209092\pi\)
0.791899 + 0.610652i \(0.209092\pi\)
\(368\) 0 0
\(369\) −31.8686 −1.65901
\(370\) 0 0
\(371\) −1.23915 −0.0643333
\(372\) 0 0
\(373\) −14.7893 −0.765758 −0.382879 0.923798i \(-0.625067\pi\)
−0.382879 + 0.923798i \(0.625067\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.07982 −0.210121
\(378\) 0 0
\(379\) −11.2405 −0.577385 −0.288693 0.957422i \(-0.593221\pi\)
−0.288693 + 0.957422i \(0.593221\pi\)
\(380\) 0 0
\(381\) −57.0231 −2.92138
\(382\) 0 0
\(383\) 30.4602 1.55644 0.778221 0.627991i \(-0.216122\pi\)
0.778221 + 0.627991i \(0.216122\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 10.8356 0.550803
\(388\) 0 0
\(389\) 1.94011 0.0983673 0.0491836 0.998790i \(-0.484338\pi\)
0.0491836 + 0.998790i \(0.484338\pi\)
\(390\) 0 0
\(391\) 1.32867 0.0671939
\(392\) 0 0
\(393\) −45.5509 −2.29774
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −18.3206 −0.919487 −0.459743 0.888052i \(-0.652059\pi\)
−0.459743 + 0.888052i \(0.652059\pi\)
\(398\) 0 0
\(399\) 0.336117 0.0168269
\(400\) 0 0
\(401\) −1.32199 −0.0660170 −0.0330085 0.999455i \(-0.510509\pi\)
−0.0330085 + 0.999455i \(0.510509\pi\)
\(402\) 0 0
\(403\) −10.6049 −0.528266
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −26.2630 −1.30181
\(408\) 0 0
\(409\) 21.9963 1.08765 0.543823 0.839200i \(-0.316976\pi\)
0.543823 + 0.839200i \(0.316976\pi\)
\(410\) 0 0
\(411\) 35.8212 1.76693
\(412\) 0 0
\(413\) −1.35141 −0.0664985
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 34.3460 1.68193
\(418\) 0 0
\(419\) 28.3194 1.38349 0.691746 0.722141i \(-0.256842\pi\)
0.691746 + 0.722141i \(0.256842\pi\)
\(420\) 0 0
\(421\) 14.7650 0.719602 0.359801 0.933029i \(-0.382845\pi\)
0.359801 + 0.933029i \(0.382845\pi\)
\(422\) 0 0
\(423\) −64.3802 −3.13027
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 3.16994 0.153404
\(428\) 0 0
\(429\) 72.0429 3.47826
\(430\) 0 0
\(431\) −27.0514 −1.30302 −0.651510 0.758640i \(-0.725864\pi\)
−0.651510 + 0.758640i \(0.725864\pi\)
\(432\) 0 0
\(433\) −38.2700 −1.83914 −0.919570 0.392926i \(-0.871463\pi\)
−0.919570 + 0.392926i \(0.871463\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.196402 −0.00939517
\(438\) 0 0
\(439\) −2.39959 −0.114526 −0.0572630 0.998359i \(-0.518237\pi\)
−0.0572630 + 0.998359i \(0.518237\pi\)
\(440\) 0 0
\(441\) −43.5485 −2.07374
\(442\) 0 0
\(443\) 10.6542 0.506198 0.253099 0.967440i \(-0.418550\pi\)
0.253099 + 0.967440i \(0.418550\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −38.4800 −1.82004
\(448\) 0 0
\(449\) −28.9533 −1.36639 −0.683195 0.730236i \(-0.739410\pi\)
−0.683195 + 0.730236i \(0.739410\pi\)
\(450\) 0 0
\(451\) −22.7810 −1.07272
\(452\) 0 0
\(453\) 4.09090 0.192207
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −38.5855 −1.80496 −0.902478 0.430736i \(-0.858254\pi\)
−0.902478 + 0.430736i \(0.858254\pi\)
\(458\) 0 0
\(459\) 14.3702 0.670743
\(460\) 0 0
\(461\) −8.07659 −0.376164 −0.188082 0.982153i \(-0.560227\pi\)
−0.188082 + 0.982153i \(0.560227\pi\)
\(462\) 0 0
\(463\) 6.07771 0.282455 0.141228 0.989977i \(-0.454895\pi\)
0.141228 + 0.989977i \(0.454895\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.2961 −0.476446 −0.238223 0.971210i \(-0.576565\pi\)
−0.238223 + 0.971210i \(0.576565\pi\)
\(468\) 0 0
\(469\) −3.83981 −0.177306
\(470\) 0 0
\(471\) 71.4598 3.29270
\(472\) 0 0
\(473\) 7.74572 0.356149
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 14.5289 0.665233
\(478\) 0 0
\(479\) −33.9760 −1.55240 −0.776201 0.630486i \(-0.782856\pi\)
−0.776201 + 0.630486i \(0.782856\pi\)
\(480\) 0 0
\(481\) −28.3556 −1.29290
\(482\) 0 0
\(483\) −1.71138 −0.0778703
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.4951 0.747464 0.373732 0.927537i \(-0.378078\pi\)
0.373732 + 0.927537i \(0.378078\pi\)
\(488\) 0 0
\(489\) 77.2962 3.49546
\(490\) 0 0
\(491\) 27.4876 1.24050 0.620249 0.784405i \(-0.287032\pi\)
0.620249 + 0.784405i \(0.287032\pi\)
\(492\) 0 0
\(493\) −1.07928 −0.0486082
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.00668310 −0.000299778 0
\(498\) 0 0
\(499\) 18.2961 0.819045 0.409523 0.912300i \(-0.365695\pi\)
0.409523 + 0.912300i \(0.365695\pi\)
\(500\) 0 0
\(501\) −13.5549 −0.605587
\(502\) 0 0
\(503\) −1.97389 −0.0880115 −0.0440058 0.999031i \(-0.514012\pi\)
−0.0440058 + 0.999031i \(0.514012\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 37.6986 1.67425
\(508\) 0 0
\(509\) −38.3441 −1.69957 −0.849787 0.527126i \(-0.823269\pi\)
−0.849787 + 0.527126i \(0.823269\pi\)
\(510\) 0 0
\(511\) −8.49125 −0.375631
\(512\) 0 0
\(513\) −2.12417 −0.0937844
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −46.0217 −2.02403
\(518\) 0 0
\(519\) 59.8839 2.62861
\(520\) 0 0
\(521\) −23.1814 −1.01560 −0.507799 0.861476i \(-0.669541\pi\)
−0.507799 + 0.861476i \(0.669541\pi\)
\(522\) 0 0
\(523\) −43.5123 −1.90266 −0.951331 0.308172i \(-0.900283\pi\)
−0.951331 + 0.308172i \(0.900283\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.80542 −0.122206
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 15.8452 0.687622
\(532\) 0 0
\(533\) −24.5962 −1.06538
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 32.1197 1.38607
\(538\) 0 0
\(539\) −31.1303 −1.34088
\(540\) 0 0
\(541\) 18.6112 0.800158 0.400079 0.916481i \(-0.368983\pi\)
0.400079 + 0.916481i \(0.368983\pi\)
\(542\) 0 0
\(543\) −28.1732 −1.20903
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 6.78956 0.290300 0.145150 0.989410i \(-0.453633\pi\)
0.145150 + 0.989410i \(0.453633\pi\)
\(548\) 0 0
\(549\) −37.1673 −1.58626
\(550\) 0 0
\(551\) 0.159537 0.00679649
\(552\) 0 0
\(553\) −5.90272 −0.251009
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.9869 −1.05873 −0.529364 0.848395i \(-0.677570\pi\)
−0.529364 + 0.848395i \(0.677570\pi\)
\(558\) 0 0
\(559\) 8.36290 0.353713
\(560\) 0 0
\(561\) 19.0583 0.804642
\(562\) 0 0
\(563\) 44.7551 1.88620 0.943100 0.332508i \(-0.107895\pi\)
0.943100 + 0.332508i \(0.107895\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −7.67371 −0.322265
\(568\) 0 0
\(569\) −27.4895 −1.15242 −0.576211 0.817301i \(-0.695469\pi\)
−0.576211 + 0.817301i \(0.695469\pi\)
\(570\) 0 0
\(571\) −1.40495 −0.0587952 −0.0293976 0.999568i \(-0.509359\pi\)
−0.0293976 + 0.999568i \(0.509359\pi\)
\(572\) 0 0
\(573\) −4.61957 −0.192985
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 19.1987 0.799253 0.399627 0.916678i \(-0.369140\pi\)
0.399627 + 0.916678i \(0.369140\pi\)
\(578\) 0 0
\(579\) 44.4364 1.84671
\(580\) 0 0
\(581\) 3.13043 0.129872
\(582\) 0 0
\(583\) 10.3859 0.430139
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.8565 0.943390 0.471695 0.881762i \(-0.343642\pi\)
0.471695 + 0.881762i \(0.343642\pi\)
\(588\) 0 0
\(589\) 0.414692 0.0170871
\(590\) 0 0
\(591\) 75.4473 3.10349
\(592\) 0 0
\(593\) 26.5387 1.08981 0.544906 0.838497i \(-0.316565\pi\)
0.544906 + 0.838497i \(0.316565\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −4.97005 −0.203411
\(598\) 0 0
\(599\) −8.82768 −0.360689 −0.180345 0.983603i \(-0.557721\pi\)
−0.180345 + 0.983603i \(0.557721\pi\)
\(600\) 0 0
\(601\) −30.3072 −1.23626 −0.618129 0.786077i \(-0.712109\pi\)
−0.618129 + 0.786077i \(0.712109\pi\)
\(602\) 0 0
\(603\) 45.0215 1.83342
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −38.0102 −1.54278 −0.771392 0.636360i \(-0.780439\pi\)
−0.771392 + 0.636360i \(0.780439\pi\)
\(608\) 0 0
\(609\) 1.39015 0.0563316
\(610\) 0 0
\(611\) −49.6887 −2.01019
\(612\) 0 0
\(613\) 31.7417 1.28204 0.641018 0.767526i \(-0.278512\pi\)
0.641018 + 0.767526i \(0.278512\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −46.6699 −1.87886 −0.939430 0.342741i \(-0.888645\pi\)
−0.939430 + 0.342741i \(0.888645\pi\)
\(618\) 0 0
\(619\) 23.2223 0.933383 0.466692 0.884420i \(-0.345446\pi\)
0.466692 + 0.884420i \(0.345446\pi\)
\(620\) 0 0
\(621\) 10.8154 0.434009
\(622\) 0 0
\(623\) −5.03235 −0.201617
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.81716 −0.112506
\(628\) 0 0
\(629\) −7.50121 −0.299093
\(630\) 0 0
\(631\) −13.0906 −0.521129 −0.260565 0.965456i \(-0.583909\pi\)
−0.260565 + 0.965456i \(0.583909\pi\)
\(632\) 0 0
\(633\) 19.2740 0.766072
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −33.6107 −1.33171
\(638\) 0 0
\(639\) 0.0783588 0.00309983
\(640\) 0 0
\(641\) 22.8746 0.903494 0.451747 0.892146i \(-0.350801\pi\)
0.451747 + 0.892146i \(0.350801\pi\)
\(642\) 0 0
\(643\) 30.6333 1.20806 0.604030 0.796962i \(-0.293561\pi\)
0.604030 + 0.796962i \(0.293561\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.74454 0.343783 0.171892 0.985116i \(-0.445012\pi\)
0.171892 + 0.985116i \(0.445012\pi\)
\(648\) 0 0
\(649\) 11.3268 0.444616
\(650\) 0 0
\(651\) 3.61348 0.141623
\(652\) 0 0
\(653\) 24.7443 0.968320 0.484160 0.874979i \(-0.339125\pi\)
0.484160 + 0.874979i \(0.339125\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 99.5593 3.88418
\(658\) 0 0
\(659\) 8.30726 0.323605 0.161803 0.986823i \(-0.448269\pi\)
0.161803 + 0.986823i \(0.448269\pi\)
\(660\) 0 0
\(661\) −14.1755 −0.551364 −0.275682 0.961249i \(-0.588904\pi\)
−0.275682 + 0.961249i \(0.588904\pi\)
\(662\) 0 0
\(663\) 20.5768 0.799138
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.812298 −0.0314523
\(668\) 0 0
\(669\) 65.6627 2.53867
\(670\) 0 0
\(671\) −26.5688 −1.02568
\(672\) 0 0
\(673\) −7.30229 −0.281482 −0.140741 0.990046i \(-0.544949\pi\)
−0.140741 + 0.990046i \(0.544949\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −39.7090 −1.52614 −0.763071 0.646315i \(-0.776309\pi\)
−0.763071 + 0.646315i \(0.776309\pi\)
\(678\) 0 0
\(679\) 7.81027 0.299731
\(680\) 0 0
\(681\) 32.4296 1.24271
\(682\) 0 0
\(683\) 38.5993 1.47696 0.738481 0.674274i \(-0.235543\pi\)
0.738481 + 0.674274i \(0.235543\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −74.0219 −2.82411
\(688\) 0 0
\(689\) 11.2134 0.427198
\(690\) 0 0
\(691\) −21.4163 −0.814713 −0.407357 0.913269i \(-0.633549\pi\)
−0.407357 + 0.913269i \(0.633549\pi\)
\(692\) 0 0
\(693\) −16.8020 −0.638255
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.50669 −0.246459
\(698\) 0 0
\(699\) −34.8773 −1.31918
\(700\) 0 0
\(701\) −5.40147 −0.204011 −0.102005 0.994784i \(-0.532526\pi\)
−0.102005 + 0.994784i \(0.532526\pi\)
\(702\) 0 0
\(703\) 1.10881 0.0418197
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.17940 −0.157182
\(708\) 0 0
\(709\) −15.3161 −0.575208 −0.287604 0.957749i \(-0.592859\pi\)
−0.287604 + 0.957749i \(0.592859\pi\)
\(710\) 0 0
\(711\) 69.2090 2.59554
\(712\) 0 0
\(713\) −2.11145 −0.0790742
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −78.8102 −2.94322
\(718\) 0 0
\(719\) 11.6505 0.434491 0.217245 0.976117i \(-0.430293\pi\)
0.217245 + 0.976117i \(0.430293\pi\)
\(720\) 0 0
\(721\) 8.01875 0.298634
\(722\) 0 0
\(723\) −49.8334 −1.85333
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 28.8188 1.06883 0.534415 0.845223i \(-0.320532\pi\)
0.534415 + 0.845223i \(0.320532\pi\)
\(728\) 0 0
\(729\) −10.0725 −0.373056
\(730\) 0 0
\(731\) 2.21233 0.0818259
\(732\) 0 0
\(733\) −25.2304 −0.931906 −0.465953 0.884810i \(-0.654288\pi\)
−0.465953 + 0.884810i \(0.654288\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 32.1833 1.18549
\(738\) 0 0
\(739\) −1.22800 −0.0451728 −0.0225864 0.999745i \(-0.507190\pi\)
−0.0225864 + 0.999745i \(0.507190\pi\)
\(740\) 0 0
\(741\) −3.04163 −0.111737
\(742\) 0 0
\(743\) 35.1117 1.28812 0.644061 0.764974i \(-0.277248\pi\)
0.644061 + 0.764974i \(0.277248\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −36.7041 −1.34293
\(748\) 0 0
\(749\) −1.30909 −0.0478329
\(750\) 0 0
\(751\) 31.7367 1.15809 0.579044 0.815296i \(-0.303426\pi\)
0.579044 + 0.815296i \(0.303426\pi\)
\(752\) 0 0
\(753\) −41.1630 −1.50006
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.22287 −0.117137 −0.0585685 0.998283i \(-0.518654\pi\)
−0.0585685 + 0.998283i \(0.518654\pi\)
\(758\) 0 0
\(759\) 14.3439 0.520649
\(760\) 0 0
\(761\) −9.60077 −0.348027 −0.174014 0.984743i \(-0.555674\pi\)
−0.174014 + 0.984743i \(0.555674\pi\)
\(762\) 0 0
\(763\) 5.74882 0.208121
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.2293 0.441575
\(768\) 0 0
\(769\) 14.9778 0.540113 0.270056 0.962844i \(-0.412958\pi\)
0.270056 + 0.962844i \(0.412958\pi\)
\(770\) 0 0
\(771\) 31.3998 1.13084
\(772\) 0 0
\(773\) 28.7430 1.03381 0.516906 0.856042i \(-0.327084\pi\)
0.516906 + 0.856042i \(0.327084\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 9.66181 0.346616
\(778\) 0 0
\(779\) 0.961806 0.0344603
\(780\) 0 0
\(781\) 0.0560142 0.00200435
\(782\) 0 0
\(783\) −8.78536 −0.313963
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −34.1965 −1.21897 −0.609486 0.792797i \(-0.708624\pi\)
−0.609486 + 0.792797i \(0.708624\pi\)
\(788\) 0 0
\(789\) −71.8666 −2.55852
\(790\) 0 0
\(791\) 10.6965 0.380324
\(792\) 0 0
\(793\) −28.6857 −1.01866
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −0.303391 −0.0107467 −0.00537334 0.999986i \(-0.501710\pi\)
−0.00537334 + 0.999986i \(0.501710\pi\)
\(798\) 0 0
\(799\) −13.1447 −0.465026
\(800\) 0 0
\(801\) 59.0039 2.08480
\(802\) 0 0
\(803\) 71.1692 2.51151
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 30.2429 1.06460
\(808\) 0 0
\(809\) −13.1865 −0.463611 −0.231806 0.972762i \(-0.574463\pi\)
−0.231806 + 0.972762i \(0.574463\pi\)
\(810\) 0 0
\(811\) 14.7284 0.517185 0.258593 0.965986i \(-0.416741\pi\)
0.258593 + 0.965986i \(0.416741\pi\)
\(812\) 0 0
\(813\) −18.7575 −0.657856
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.327022 −0.0114410
\(818\) 0 0
\(819\) −18.1408 −0.633890
\(820\) 0 0
\(821\) 36.6177 1.27797 0.638984 0.769220i \(-0.279355\pi\)
0.638984 + 0.769220i \(0.279355\pi\)
\(822\) 0 0
\(823\) 0.420867 0.0146705 0.00733525 0.999973i \(-0.497665\pi\)
0.00733525 + 0.999973i \(0.497665\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 35.1118 1.22096 0.610479 0.792032i \(-0.290977\pi\)
0.610479 + 0.792032i \(0.290977\pi\)
\(828\) 0 0
\(829\) −35.6234 −1.23725 −0.618626 0.785685i \(-0.712311\pi\)
−0.618626 + 0.785685i \(0.712311\pi\)
\(830\) 0 0
\(831\) 0.137436 0.00476759
\(832\) 0 0
\(833\) −8.89141 −0.308069
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −22.8362 −0.789335
\(838\) 0 0
\(839\) −19.9998 −0.690469 −0.345235 0.938516i \(-0.612201\pi\)
−0.345235 + 0.938516i \(0.612201\pi\)
\(840\) 0 0
\(841\) −28.3402 −0.977247
\(842\) 0 0
\(843\) 86.3350 2.97354
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −5.90554 −0.202917
\(848\) 0 0
\(849\) −37.5556 −1.28890
\(850\) 0 0
\(851\) −5.64564 −0.193530
\(852\) 0 0
\(853\) 42.4994 1.45515 0.727577 0.686026i \(-0.240647\pi\)
0.727577 + 0.686026i \(0.240647\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −18.0100 −0.615208 −0.307604 0.951514i \(-0.599527\pi\)
−0.307604 + 0.951514i \(0.599527\pi\)
\(858\) 0 0
\(859\) 22.3869 0.763832 0.381916 0.924197i \(-0.375264\pi\)
0.381916 + 0.924197i \(0.375264\pi\)
\(860\) 0 0
\(861\) 8.38084 0.285618
\(862\) 0 0
\(863\) 18.7613 0.638642 0.319321 0.947647i \(-0.396545\pi\)
0.319321 + 0.947647i \(0.396545\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −46.9750 −1.59536
\(868\) 0 0
\(869\) 49.4735 1.67827
\(870\) 0 0
\(871\) 34.7476 1.17738
\(872\) 0 0
\(873\) −91.5749 −3.09934
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −31.6345 −1.06822 −0.534111 0.845415i \(-0.679353\pi\)
−0.534111 + 0.845415i \(0.679353\pi\)
\(878\) 0 0
\(879\) 8.35783 0.281903
\(880\) 0 0
\(881\) 39.6850 1.33702 0.668512 0.743702i \(-0.266932\pi\)
0.668512 + 0.743702i \(0.266932\pi\)
\(882\) 0 0
\(883\) −10.3778 −0.349242 −0.174621 0.984636i \(-0.555870\pi\)
−0.174621 + 0.984636i \(0.555870\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.0199 0.806508 0.403254 0.915088i \(-0.367879\pi\)
0.403254 + 0.915088i \(0.367879\pi\)
\(888\) 0 0
\(889\) 10.2642 0.344251
\(890\) 0 0
\(891\) 64.3170 2.15470
\(892\) 0 0
\(893\) 1.94302 0.0650207
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 15.4868 0.517088
\(898\) 0 0
\(899\) 1.71512 0.0572025
\(900\) 0 0
\(901\) 2.96641 0.0988254
\(902\) 0 0
\(903\) −2.84955 −0.0948271
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −18.5181 −0.614885 −0.307442 0.951567i \(-0.599473\pi\)
−0.307442 + 0.951567i \(0.599473\pi\)
\(908\) 0 0
\(909\) 49.0032 1.62533
\(910\) 0 0
\(911\) −3.34956 −0.110976 −0.0554879 0.998459i \(-0.517671\pi\)
−0.0554879 + 0.998459i \(0.517671\pi\)
\(912\) 0 0
\(913\) −26.2376 −0.868339
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.19920 0.270761
\(918\) 0 0
\(919\) −32.9754 −1.08776 −0.543878 0.839164i \(-0.683045\pi\)
−0.543878 + 0.839164i \(0.683045\pi\)
\(920\) 0 0
\(921\) 99.1728 3.26785
\(922\) 0 0
\(923\) 0.0604774 0.00199064
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −94.0193 −3.08800
\(928\) 0 0
\(929\) −36.5008 −1.19755 −0.598777 0.800916i \(-0.704346\pi\)
−0.598777 + 0.800916i \(0.704346\pi\)
\(930\) 0 0
\(931\) 1.31431 0.0430748
\(932\) 0 0
\(933\) −12.5789 −0.411816
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −12.4598 −0.407043 −0.203521 0.979071i \(-0.565239\pi\)
−0.203521 + 0.979071i \(0.565239\pi\)
\(938\) 0 0
\(939\) −42.4916 −1.38666
\(940\) 0 0
\(941\) −45.2938 −1.47653 −0.738267 0.674508i \(-0.764356\pi\)
−0.738267 + 0.674508i \(0.764356\pi\)
\(942\) 0 0
\(943\) −4.89714 −0.159473
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −41.4016 −1.34537 −0.672685 0.739929i \(-0.734859\pi\)
−0.672685 + 0.739929i \(0.734859\pi\)
\(948\) 0 0
\(949\) 76.8399 2.49433
\(950\) 0 0
\(951\) −32.2619 −1.04616
\(952\) 0 0
\(953\) 15.3738 0.498006 0.249003 0.968503i \(-0.419897\pi\)
0.249003 + 0.968503i \(0.419897\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −11.6515 −0.376639
\(958\) 0 0
\(959\) −6.44785 −0.208212
\(960\) 0 0
\(961\) −26.5418 −0.856187
\(962\) 0 0
\(963\) 15.3489 0.494612
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −53.4925 −1.72020 −0.860101 0.510124i \(-0.829600\pi\)
−0.860101 + 0.510124i \(0.829600\pi\)
\(968\) 0 0
\(969\) −0.804635 −0.0258486
\(970\) 0 0
\(971\) 19.8881 0.638241 0.319120 0.947714i \(-0.396613\pi\)
0.319120 + 0.947714i \(0.396613\pi\)
\(972\) 0 0
\(973\) −6.18231 −0.198196
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 14.8758 0.475919 0.237960 0.971275i \(-0.423521\pi\)
0.237960 + 0.971275i \(0.423521\pi\)
\(978\) 0 0
\(979\) 42.1785 1.34803
\(980\) 0 0
\(981\) −67.4045 −2.15206
\(982\) 0 0
\(983\) 1.16403 0.0371269 0.0185634 0.999828i \(-0.494091\pi\)
0.0185634 + 0.999828i \(0.494091\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 16.9308 0.538913
\(988\) 0 0
\(989\) 1.66507 0.0529460
\(990\) 0 0
\(991\) −47.8693 −1.52062 −0.760310 0.649561i \(-0.774953\pi\)
−0.760310 + 0.649561i \(0.774953\pi\)
\(992\) 0 0
\(993\) −38.9904 −1.23732
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 11.4353 0.362159 0.181079 0.983468i \(-0.442041\pi\)
0.181079 + 0.983468i \(0.442041\pi\)
\(998\) 0 0
\(999\) −61.0601 −1.93186
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 4600.2.a.bg.1.5 yes 5
4.3 odd 2 9200.2.a.cs.1.1 5
5.2 odd 4 4600.2.e.v.4049.1 10
5.3 odd 4 4600.2.e.v.4049.10 10
5.4 even 2 4600.2.a.bc.1.1 5
20.19 odd 2 9200.2.a.cw.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.bc.1.1 5 5.4 even 2
4600.2.a.bg.1.5 yes 5 1.1 even 1 trivial
4600.2.e.v.4049.1 10 5.2 odd 4
4600.2.e.v.4049.10 10 5.3 odd 4
9200.2.a.cs.1.1 5 4.3 odd 2
9200.2.a.cw.1.5 5 20.19 odd 2