Properties

Label 4332.2.a.o.1.1
Level $4332$
Weight $2$
Character 4332.1
Self dual yes
Analytic conductor $34.591$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.1
Root \(1.87939\) of defining polynomial
Character \(\chi\) \(=\) 4332.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -0.879385 q^{5} -2.18479 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -0.879385 q^{5} -2.18479 q^{7} +1.00000 q^{9} -0.162504 q^{11} +0.758770 q^{13} -0.879385 q^{15} +3.10607 q^{17} -2.18479 q^{21} +1.29086 q^{23} -4.22668 q^{25} +1.00000 q^{27} -6.51754 q^{29} +0.958111 q^{31} -0.162504 q^{33} +1.92127 q^{35} -1.16250 q^{37} +0.758770 q^{39} -10.5963 q^{41} -0.177052 q^{43} -0.879385 q^{45} -3.46791 q^{47} -2.22668 q^{49} +3.10607 q^{51} +8.33275 q^{53} +0.142903 q^{55} -2.78106 q^{59} +7.22668 q^{61} -2.18479 q^{63} -0.667252 q^{65} +1.06418 q^{67} +1.29086 q^{69} +5.08378 q^{71} +2.24897 q^{73} -4.22668 q^{75} +0.355037 q^{77} -5.24123 q^{79} +1.00000 q^{81} -17.1138 q^{83} -2.73143 q^{85} -6.51754 q^{87} +15.6236 q^{89} -1.65776 q^{91} +0.958111 q^{93} -9.41921 q^{97} -0.162504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{3} + 3 q^{5} - 3 q^{7} + 3 q^{9} - 3 q^{11} - 9 q^{13} + 3 q^{15} - 3 q^{17} - 3 q^{21} - 12 q^{23} - 6 q^{25} + 3 q^{27} + 3 q^{29} + 6 q^{31} - 3 q^{33} - 3 q^{35} - 6 q^{37} - 9 q^{39} - 18 q^{41} - 21 q^{43} + 3 q^{45} - 15 q^{47} - 3 q^{51} + 6 q^{53} + 9 q^{59} + 15 q^{61} - 3 q^{63} - 21 q^{65} - 6 q^{67} - 12 q^{69} + 9 q^{71} - 6 q^{73} - 6 q^{75} - 24 q^{77} - 27 q^{79} + 3 q^{81} - 15 q^{83} - 18 q^{85} + 3 q^{87} + 12 q^{89} + 9 q^{91} + 6 q^{93} + 6 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −0.879385 −0.393273 −0.196637 0.980476i \(-0.563002\pi\)
−0.196637 + 0.980476i \(0.563002\pi\)
\(6\) 0 0
\(7\) −2.18479 −0.825774 −0.412887 0.910782i \(-0.635480\pi\)
−0.412887 + 0.910782i \(0.635480\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.162504 −0.0489967 −0.0244984 0.999700i \(-0.507799\pi\)
−0.0244984 + 0.999700i \(0.507799\pi\)
\(12\) 0 0
\(13\) 0.758770 0.210445 0.105223 0.994449i \(-0.466445\pi\)
0.105223 + 0.994449i \(0.466445\pi\)
\(14\) 0 0
\(15\) −0.879385 −0.227056
\(16\) 0 0
\(17\) 3.10607 0.753332 0.376666 0.926349i \(-0.377070\pi\)
0.376666 + 0.926349i \(0.377070\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) 0 0
\(21\) −2.18479 −0.476761
\(22\) 0 0
\(23\) 1.29086 0.269163 0.134581 0.990903i \(-0.457031\pi\)
0.134581 + 0.990903i \(0.457031\pi\)
\(24\) 0 0
\(25\) −4.22668 −0.845336
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.51754 −1.21028 −0.605138 0.796120i \(-0.706882\pi\)
−0.605138 + 0.796120i \(0.706882\pi\)
\(30\) 0 0
\(31\) 0.958111 0.172082 0.0860409 0.996292i \(-0.472578\pi\)
0.0860409 + 0.996292i \(0.472578\pi\)
\(32\) 0 0
\(33\) −0.162504 −0.0282883
\(34\) 0 0
\(35\) 1.92127 0.324755
\(36\) 0 0
\(37\) −1.16250 −0.191114 −0.0955572 0.995424i \(-0.530463\pi\)
−0.0955572 + 0.995424i \(0.530463\pi\)
\(38\) 0 0
\(39\) 0.758770 0.121501
\(40\) 0 0
\(41\) −10.5963 −1.65486 −0.827429 0.561570i \(-0.810198\pi\)
−0.827429 + 0.561570i \(0.810198\pi\)
\(42\) 0 0
\(43\) −0.177052 −0.0270001 −0.0135001 0.999909i \(-0.504297\pi\)
−0.0135001 + 0.999909i \(0.504297\pi\)
\(44\) 0 0
\(45\) −0.879385 −0.131091
\(46\) 0 0
\(47\) −3.46791 −0.505847 −0.252923 0.967486i \(-0.581392\pi\)
−0.252923 + 0.967486i \(0.581392\pi\)
\(48\) 0 0
\(49\) −2.22668 −0.318097
\(50\) 0 0
\(51\) 3.10607 0.434936
\(52\) 0 0
\(53\) 8.33275 1.14459 0.572296 0.820047i \(-0.306053\pi\)
0.572296 + 0.820047i \(0.306053\pi\)
\(54\) 0 0
\(55\) 0.142903 0.0192691
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.78106 −0.362063 −0.181032 0.983477i \(-0.557944\pi\)
−0.181032 + 0.983477i \(0.557944\pi\)
\(60\) 0 0
\(61\) 7.22668 0.925282 0.462641 0.886546i \(-0.346902\pi\)
0.462641 + 0.886546i \(0.346902\pi\)
\(62\) 0 0
\(63\) −2.18479 −0.275258
\(64\) 0 0
\(65\) −0.667252 −0.0827624
\(66\) 0 0
\(67\) 1.06418 0.130010 0.0650050 0.997885i \(-0.479294\pi\)
0.0650050 + 0.997885i \(0.479294\pi\)
\(68\) 0 0
\(69\) 1.29086 0.155401
\(70\) 0 0
\(71\) 5.08378 0.603333 0.301667 0.953413i \(-0.402457\pi\)
0.301667 + 0.953413i \(0.402457\pi\)
\(72\) 0 0
\(73\) 2.24897 0.263222 0.131611 0.991301i \(-0.457985\pi\)
0.131611 + 0.991301i \(0.457985\pi\)
\(74\) 0 0
\(75\) −4.22668 −0.488055
\(76\) 0 0
\(77\) 0.355037 0.0404602
\(78\) 0 0
\(79\) −5.24123 −0.589684 −0.294842 0.955546i \(-0.595267\pi\)
−0.294842 + 0.955546i \(0.595267\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −17.1138 −1.87848 −0.939242 0.343255i \(-0.888470\pi\)
−0.939242 + 0.343255i \(0.888470\pi\)
\(84\) 0 0
\(85\) −2.73143 −0.296265
\(86\) 0 0
\(87\) −6.51754 −0.698754
\(88\) 0 0
\(89\) 15.6236 1.65610 0.828050 0.560655i \(-0.189451\pi\)
0.828050 + 0.560655i \(0.189451\pi\)
\(90\) 0 0
\(91\) −1.65776 −0.173780
\(92\) 0 0
\(93\) 0.958111 0.0993515
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −9.41921 −0.956376 −0.478188 0.878257i \(-0.658706\pi\)
−0.478188 + 0.878257i \(0.658706\pi\)
\(98\) 0 0
\(99\) −0.162504 −0.0163322
\(100\) 0 0
\(101\) −6.30541 −0.627411 −0.313706 0.949520i \(-0.601571\pi\)
−0.313706 + 0.949520i \(0.601571\pi\)
\(102\) 0 0
\(103\) −8.61587 −0.848947 −0.424473 0.905440i \(-0.639541\pi\)
−0.424473 + 0.905440i \(0.639541\pi\)
\(104\) 0 0
\(105\) 1.92127 0.187497
\(106\) 0 0
\(107\) −13.1480 −1.27106 −0.635530 0.772076i \(-0.719219\pi\)
−0.635530 + 0.772076i \(0.719219\pi\)
\(108\) 0 0
\(109\) −10.0496 −0.962580 −0.481290 0.876561i \(-0.659832\pi\)
−0.481290 + 0.876561i \(0.659832\pi\)
\(110\) 0 0
\(111\) −1.16250 −0.110340
\(112\) 0 0
\(113\) 8.04458 0.756770 0.378385 0.925648i \(-0.376480\pi\)
0.378385 + 0.925648i \(0.376480\pi\)
\(114\) 0 0
\(115\) −1.13516 −0.105854
\(116\) 0 0
\(117\) 0.758770 0.0701484
\(118\) 0 0
\(119\) −6.78611 −0.622082
\(120\) 0 0
\(121\) −10.9736 −0.997599
\(122\) 0 0
\(123\) −10.5963 −0.955433
\(124\) 0 0
\(125\) 8.11381 0.725721
\(126\) 0 0
\(127\) 20.0496 1.77912 0.889558 0.456821i \(-0.151012\pi\)
0.889558 + 0.456821i \(0.151012\pi\)
\(128\) 0 0
\(129\) −0.177052 −0.0155885
\(130\) 0 0
\(131\) −15.9094 −1.39001 −0.695006 0.719004i \(-0.744598\pi\)
−0.695006 + 0.719004i \(0.744598\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.879385 −0.0756854
\(136\) 0 0
\(137\) −5.04458 −0.430987 −0.215494 0.976505i \(-0.569136\pi\)
−0.215494 + 0.976505i \(0.569136\pi\)
\(138\) 0 0
\(139\) −10.5544 −0.895211 −0.447605 0.894231i \(-0.647723\pi\)
−0.447605 + 0.894231i \(0.647723\pi\)
\(140\) 0 0
\(141\) −3.46791 −0.292051
\(142\) 0 0
\(143\) −0.123303 −0.0103111
\(144\) 0 0
\(145\) 5.73143 0.475969
\(146\) 0 0
\(147\) −2.22668 −0.183654
\(148\) 0 0
\(149\) 13.7956 1.13018 0.565090 0.825029i \(-0.308841\pi\)
0.565090 + 0.825029i \(0.308841\pi\)
\(150\) 0 0
\(151\) −20.2841 −1.65069 −0.825346 0.564627i \(-0.809020\pi\)
−0.825346 + 0.564627i \(0.809020\pi\)
\(152\) 0 0
\(153\) 3.10607 0.251111
\(154\) 0 0
\(155\) −0.842549 −0.0676751
\(156\) 0 0
\(157\) −13.1753 −1.05150 −0.525752 0.850638i \(-0.676216\pi\)
−0.525752 + 0.850638i \(0.676216\pi\)
\(158\) 0 0
\(159\) 8.33275 0.660830
\(160\) 0 0
\(161\) −2.82026 −0.222268
\(162\) 0 0
\(163\) −17.4902 −1.36994 −0.684969 0.728572i \(-0.740184\pi\)
−0.684969 + 0.728572i \(0.740184\pi\)
\(164\) 0 0
\(165\) 0.142903 0.0111250
\(166\) 0 0
\(167\) 14.9067 1.15352 0.576759 0.816915i \(-0.304317\pi\)
0.576759 + 0.816915i \(0.304317\pi\)
\(168\) 0 0
\(169\) −12.4243 −0.955713
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.79561 0.136517 0.0682587 0.997668i \(-0.478256\pi\)
0.0682587 + 0.997668i \(0.478256\pi\)
\(174\) 0 0
\(175\) 9.23442 0.698057
\(176\) 0 0
\(177\) −2.78106 −0.209037
\(178\) 0 0
\(179\) 7.83481 0.585601 0.292801 0.956174i \(-0.405413\pi\)
0.292801 + 0.956174i \(0.405413\pi\)
\(180\) 0 0
\(181\) −0.419215 −0.0311600 −0.0155800 0.999879i \(-0.504959\pi\)
−0.0155800 + 0.999879i \(0.504959\pi\)
\(182\) 0 0
\(183\) 7.22668 0.534212
\(184\) 0 0
\(185\) 1.02229 0.0751602
\(186\) 0 0
\(187\) −0.504748 −0.0369108
\(188\) 0 0
\(189\) −2.18479 −0.158920
\(190\) 0 0
\(191\) −19.5398 −1.41385 −0.706926 0.707287i \(-0.749919\pi\)
−0.706926 + 0.707287i \(0.749919\pi\)
\(192\) 0 0
\(193\) −16.6408 −1.19783 −0.598917 0.800811i \(-0.704402\pi\)
−0.598917 + 0.800811i \(0.704402\pi\)
\(194\) 0 0
\(195\) −0.667252 −0.0477829
\(196\) 0 0
\(197\) −21.9959 −1.56714 −0.783571 0.621302i \(-0.786604\pi\)
−0.783571 + 0.621302i \(0.786604\pi\)
\(198\) 0 0
\(199\) −21.7442 −1.54141 −0.770704 0.637194i \(-0.780095\pi\)
−0.770704 + 0.637194i \(0.780095\pi\)
\(200\) 0 0
\(201\) 1.06418 0.0750613
\(202\) 0 0
\(203\) 14.2395 0.999415
\(204\) 0 0
\(205\) 9.31820 0.650811
\(206\) 0 0
\(207\) 1.29086 0.0897209
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −8.62630 −0.593859 −0.296929 0.954899i \(-0.595963\pi\)
−0.296929 + 0.954899i \(0.595963\pi\)
\(212\) 0 0
\(213\) 5.08378 0.348335
\(214\) 0 0
\(215\) 0.155697 0.0106184
\(216\) 0 0
\(217\) −2.09327 −0.142101
\(218\) 0 0
\(219\) 2.24897 0.151971
\(220\) 0 0
\(221\) 2.35679 0.158535
\(222\) 0 0
\(223\) 15.1584 1.01508 0.507540 0.861628i \(-0.330555\pi\)
0.507540 + 0.861628i \(0.330555\pi\)
\(224\) 0 0
\(225\) −4.22668 −0.281779
\(226\) 0 0
\(227\) −5.71419 −0.379264 −0.189632 0.981855i \(-0.560730\pi\)
−0.189632 + 0.981855i \(0.560730\pi\)
\(228\) 0 0
\(229\) 22.1634 1.46460 0.732301 0.680982i \(-0.238447\pi\)
0.732301 + 0.680982i \(0.238447\pi\)
\(230\) 0 0
\(231\) 0.355037 0.0233597
\(232\) 0 0
\(233\) −10.8280 −0.709366 −0.354683 0.934987i \(-0.615411\pi\)
−0.354683 + 0.934987i \(0.615411\pi\)
\(234\) 0 0
\(235\) 3.04963 0.198936
\(236\) 0 0
\(237\) −5.24123 −0.340454
\(238\) 0 0
\(239\) −9.86215 −0.637929 −0.318965 0.947767i \(-0.603335\pi\)
−0.318965 + 0.947767i \(0.603335\pi\)
\(240\) 0 0
\(241\) −6.90673 −0.444901 −0.222451 0.974944i \(-0.571406\pi\)
−0.222451 + 0.974944i \(0.571406\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 1.95811 0.125099
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −17.1138 −1.08454
\(250\) 0 0
\(251\) 24.8922 1.57118 0.785590 0.618747i \(-0.212359\pi\)
0.785590 + 0.618747i \(0.212359\pi\)
\(252\) 0 0
\(253\) −0.209770 −0.0131881
\(254\) 0 0
\(255\) −2.73143 −0.171049
\(256\) 0 0
\(257\) −14.2567 −0.889309 −0.444655 0.895702i \(-0.646674\pi\)
−0.444655 + 0.895702i \(0.646674\pi\)
\(258\) 0 0
\(259\) 2.53983 0.157817
\(260\) 0 0
\(261\) −6.51754 −0.403426
\(262\) 0 0
\(263\) 21.6168 1.33295 0.666475 0.745528i \(-0.267803\pi\)
0.666475 + 0.745528i \(0.267803\pi\)
\(264\) 0 0
\(265\) −7.32770 −0.450137
\(266\) 0 0
\(267\) 15.6236 0.956149
\(268\) 0 0
\(269\) −10.6263 −0.647897 −0.323948 0.946075i \(-0.605010\pi\)
−0.323948 + 0.946075i \(0.605010\pi\)
\(270\) 0 0
\(271\) −12.1506 −0.738099 −0.369050 0.929410i \(-0.620317\pi\)
−0.369050 + 0.929410i \(0.620317\pi\)
\(272\) 0 0
\(273\) −1.65776 −0.100332
\(274\) 0 0
\(275\) 0.686852 0.0414187
\(276\) 0 0
\(277\) 9.81521 0.589739 0.294869 0.955538i \(-0.404724\pi\)
0.294869 + 0.955538i \(0.404724\pi\)
\(278\) 0 0
\(279\) 0.958111 0.0573606
\(280\) 0 0
\(281\) 28.2148 1.68316 0.841578 0.540136i \(-0.181627\pi\)
0.841578 + 0.540136i \(0.181627\pi\)
\(282\) 0 0
\(283\) −15.4192 −0.916577 −0.458289 0.888803i \(-0.651537\pi\)
−0.458289 + 0.888803i \(0.651537\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.1506 1.36654
\(288\) 0 0
\(289\) −7.35235 −0.432491
\(290\) 0 0
\(291\) −9.41921 −0.552164
\(292\) 0 0
\(293\) 27.7769 1.62275 0.811373 0.584529i \(-0.198721\pi\)
0.811373 + 0.584529i \(0.198721\pi\)
\(294\) 0 0
\(295\) 2.44562 0.142390
\(296\) 0 0
\(297\) −0.162504 −0.00942943
\(298\) 0 0
\(299\) 0.979466 0.0566440
\(300\) 0 0
\(301\) 0.386821 0.0222960
\(302\) 0 0
\(303\) −6.30541 −0.362236
\(304\) 0 0
\(305\) −6.35504 −0.363888
\(306\) 0 0
\(307\) 27.1908 1.55186 0.775930 0.630819i \(-0.217281\pi\)
0.775930 + 0.630819i \(0.217281\pi\)
\(308\) 0 0
\(309\) −8.61587 −0.490140
\(310\) 0 0
\(311\) −5.94356 −0.337029 −0.168514 0.985699i \(-0.553897\pi\)
−0.168514 + 0.985699i \(0.553897\pi\)
\(312\) 0 0
\(313\) 7.15064 0.404178 0.202089 0.979367i \(-0.435227\pi\)
0.202089 + 0.979367i \(0.435227\pi\)
\(314\) 0 0
\(315\) 1.92127 0.108252
\(316\) 0 0
\(317\) 22.2909 1.25198 0.625990 0.779831i \(-0.284695\pi\)
0.625990 + 0.779831i \(0.284695\pi\)
\(318\) 0 0
\(319\) 1.05913 0.0592996
\(320\) 0 0
\(321\) −13.1480 −0.733847
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −3.20708 −0.177897
\(326\) 0 0
\(327\) −10.0496 −0.555746
\(328\) 0 0
\(329\) 7.57667 0.417715
\(330\) 0 0
\(331\) 6.30365 0.346480 0.173240 0.984880i \(-0.444576\pi\)
0.173240 + 0.984880i \(0.444576\pi\)
\(332\) 0 0
\(333\) −1.16250 −0.0637048
\(334\) 0 0
\(335\) −0.935822 −0.0511294
\(336\) 0 0
\(337\) −25.8726 −1.40937 −0.704685 0.709521i \(-0.748911\pi\)
−0.704685 + 0.709521i \(0.748911\pi\)
\(338\) 0 0
\(339\) 8.04458 0.436921
\(340\) 0 0
\(341\) −0.155697 −0.00843145
\(342\) 0 0
\(343\) 20.1584 1.08845
\(344\) 0 0
\(345\) −1.13516 −0.0611151
\(346\) 0 0
\(347\) −18.6040 −0.998715 −0.499358 0.866396i \(-0.666431\pi\)
−0.499358 + 0.866396i \(0.666431\pi\)
\(348\) 0 0
\(349\) −1.74329 −0.0933161 −0.0466581 0.998911i \(-0.514857\pi\)
−0.0466581 + 0.998911i \(0.514857\pi\)
\(350\) 0 0
\(351\) 0.758770 0.0405002
\(352\) 0 0
\(353\) −10.6723 −0.568029 −0.284015 0.958820i \(-0.591666\pi\)
−0.284015 + 0.958820i \(0.591666\pi\)
\(354\) 0 0
\(355\) −4.47060 −0.237275
\(356\) 0 0
\(357\) −6.78611 −0.359159
\(358\) 0 0
\(359\) −6.81252 −0.359551 −0.179776 0.983708i \(-0.557537\pi\)
−0.179776 + 0.983708i \(0.557537\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) −10.9736 −0.575964
\(364\) 0 0
\(365\) −1.97771 −0.103518
\(366\) 0 0
\(367\) −17.9905 −0.939097 −0.469548 0.882907i \(-0.655583\pi\)
−0.469548 + 0.882907i \(0.655583\pi\)
\(368\) 0 0
\(369\) −10.5963 −0.551620
\(370\) 0 0
\(371\) −18.2053 −0.945173
\(372\) 0 0
\(373\) 3.36009 0.173979 0.0869894 0.996209i \(-0.472275\pi\)
0.0869894 + 0.996209i \(0.472275\pi\)
\(374\) 0 0
\(375\) 8.11381 0.418995
\(376\) 0 0
\(377\) −4.94532 −0.254697
\(378\) 0 0
\(379\) 15.1584 0.778634 0.389317 0.921104i \(-0.372711\pi\)
0.389317 + 0.921104i \(0.372711\pi\)
\(380\) 0 0
\(381\) 20.0496 1.02717
\(382\) 0 0
\(383\) 7.13516 0.364590 0.182295 0.983244i \(-0.441647\pi\)
0.182295 + 0.983244i \(0.441647\pi\)
\(384\) 0 0
\(385\) −0.312214 −0.0159119
\(386\) 0 0
\(387\) −0.177052 −0.00900005
\(388\) 0 0
\(389\) 24.9358 1.26430 0.632148 0.774848i \(-0.282173\pi\)
0.632148 + 0.774848i \(0.282173\pi\)
\(390\) 0 0
\(391\) 4.00950 0.202769
\(392\) 0 0
\(393\) −15.9094 −0.802524
\(394\) 0 0
\(395\) 4.60906 0.231907
\(396\) 0 0
\(397\) 20.6536 1.03658 0.518288 0.855206i \(-0.326569\pi\)
0.518288 + 0.855206i \(0.326569\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 36.3218 1.81383 0.906913 0.421319i \(-0.138433\pi\)
0.906913 + 0.421319i \(0.138433\pi\)
\(402\) 0 0
\(403\) 0.726986 0.0362138
\(404\) 0 0
\(405\) −0.879385 −0.0436970
\(406\) 0 0
\(407\) 0.188911 0.00936399
\(408\) 0 0
\(409\) 4.95636 0.245076 0.122538 0.992464i \(-0.460897\pi\)
0.122538 + 0.992464i \(0.460897\pi\)
\(410\) 0 0
\(411\) −5.04458 −0.248831
\(412\) 0 0
\(413\) 6.07604 0.298982
\(414\) 0 0
\(415\) 15.0496 0.738757
\(416\) 0 0
\(417\) −10.5544 −0.516850
\(418\) 0 0
\(419\) −35.0966 −1.71458 −0.857290 0.514834i \(-0.827854\pi\)
−0.857290 + 0.514834i \(0.827854\pi\)
\(420\) 0 0
\(421\) −18.4020 −0.896858 −0.448429 0.893819i \(-0.648016\pi\)
−0.448429 + 0.893819i \(0.648016\pi\)
\(422\) 0 0
\(423\) −3.46791 −0.168616
\(424\) 0 0
\(425\) −13.1284 −0.636819
\(426\) 0 0
\(427\) −15.7888 −0.764074
\(428\) 0 0
\(429\) −0.123303 −0.00595313
\(430\) 0 0
\(431\) 8.79385 0.423585 0.211792 0.977315i \(-0.432070\pi\)
0.211792 + 0.977315i \(0.432070\pi\)
\(432\) 0 0
\(433\) 17.4115 0.836742 0.418371 0.908276i \(-0.362601\pi\)
0.418371 + 0.908276i \(0.362601\pi\)
\(434\) 0 0
\(435\) 5.73143 0.274801
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −28.4911 −1.35981 −0.679904 0.733301i \(-0.737978\pi\)
−0.679904 + 0.733301i \(0.737978\pi\)
\(440\) 0 0
\(441\) −2.22668 −0.106032
\(442\) 0 0
\(443\) 18.0428 0.857240 0.428620 0.903485i \(-0.359000\pi\)
0.428620 + 0.903485i \(0.359000\pi\)
\(444\) 0 0
\(445\) −13.7392 −0.651299
\(446\) 0 0
\(447\) 13.7956 0.652510
\(448\) 0 0
\(449\) 9.53478 0.449974 0.224987 0.974362i \(-0.427766\pi\)
0.224987 + 0.974362i \(0.427766\pi\)
\(450\) 0 0
\(451\) 1.72193 0.0810827
\(452\) 0 0
\(453\) −20.2841 −0.953028
\(454\) 0 0
\(455\) 1.45781 0.0683430
\(456\) 0 0
\(457\) 10.4584 0.489224 0.244612 0.969621i \(-0.421339\pi\)
0.244612 + 0.969621i \(0.421339\pi\)
\(458\) 0 0
\(459\) 3.10607 0.144979
\(460\) 0 0
\(461\) 41.6614 1.94036 0.970182 0.242378i \(-0.0779274\pi\)
0.970182 + 0.242378i \(0.0779274\pi\)
\(462\) 0 0
\(463\) 13.8179 0.642172 0.321086 0.947050i \(-0.395952\pi\)
0.321086 + 0.947050i \(0.395952\pi\)
\(464\) 0 0
\(465\) −0.842549 −0.0390723
\(466\) 0 0
\(467\) −7.45336 −0.344901 −0.172450 0.985018i \(-0.555168\pi\)
−0.172450 + 0.985018i \(0.555168\pi\)
\(468\) 0 0
\(469\) −2.32501 −0.107359
\(470\) 0 0
\(471\) −13.1753 −0.607086
\(472\) 0 0
\(473\) 0.0287716 0.00132292
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.33275 0.381530
\(478\) 0 0
\(479\) 23.7870 1.08686 0.543429 0.839455i \(-0.317126\pi\)
0.543429 + 0.839455i \(0.317126\pi\)
\(480\) 0 0
\(481\) −0.882074 −0.0402191
\(482\) 0 0
\(483\) −2.82026 −0.128326
\(484\) 0 0
\(485\) 8.28312 0.376117
\(486\) 0 0
\(487\) 4.85710 0.220096 0.110048 0.993926i \(-0.464900\pi\)
0.110048 + 0.993926i \(0.464900\pi\)
\(488\) 0 0
\(489\) −17.4902 −0.790934
\(490\) 0 0
\(491\) −2.99764 −0.135281 −0.0676407 0.997710i \(-0.521547\pi\)
−0.0676407 + 0.997710i \(0.521547\pi\)
\(492\) 0 0
\(493\) −20.2439 −0.911740
\(494\) 0 0
\(495\) 0.142903 0.00642303
\(496\) 0 0
\(497\) −11.1070 −0.498217
\(498\) 0 0
\(499\) 2.52435 0.113005 0.0565027 0.998402i \(-0.482005\pi\)
0.0565027 + 0.998402i \(0.482005\pi\)
\(500\) 0 0
\(501\) 14.9067 0.665983
\(502\) 0 0
\(503\) 18.3482 0.818107 0.409054 0.912510i \(-0.365859\pi\)
0.409054 + 0.912510i \(0.365859\pi\)
\(504\) 0 0
\(505\) 5.54488 0.246744
\(506\) 0 0
\(507\) −12.4243 −0.551781
\(508\) 0 0
\(509\) 16.2736 0.721316 0.360658 0.932698i \(-0.382552\pi\)
0.360658 + 0.932698i \(0.382552\pi\)
\(510\) 0 0
\(511\) −4.91353 −0.217362
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.57667 0.333868
\(516\) 0 0
\(517\) 0.563549 0.0247848
\(518\) 0 0
\(519\) 1.79561 0.0788184
\(520\) 0 0
\(521\) 28.2909 1.23945 0.619723 0.784821i \(-0.287245\pi\)
0.619723 + 0.784821i \(0.287245\pi\)
\(522\) 0 0
\(523\) 4.84793 0.211985 0.105992 0.994367i \(-0.466198\pi\)
0.105992 + 0.994367i \(0.466198\pi\)
\(524\) 0 0
\(525\) 9.23442 0.403023
\(526\) 0 0
\(527\) 2.97596 0.129635
\(528\) 0 0
\(529\) −21.3337 −0.927551
\(530\) 0 0
\(531\) −2.78106 −0.120688
\(532\) 0 0
\(533\) −8.04013 −0.348257
\(534\) 0 0
\(535\) 11.5621 0.499874
\(536\) 0 0
\(537\) 7.83481 0.338097
\(538\) 0 0
\(539\) 0.361844 0.0155857
\(540\) 0 0
\(541\) −24.3131 −1.04530 −0.522652 0.852546i \(-0.675057\pi\)
−0.522652 + 0.852546i \(0.675057\pi\)
\(542\) 0 0
\(543\) −0.419215 −0.0179902
\(544\) 0 0
\(545\) 8.83750 0.378557
\(546\) 0 0
\(547\) −22.7733 −0.973717 −0.486858 0.873481i \(-0.661857\pi\)
−0.486858 + 0.873481i \(0.661857\pi\)
\(548\) 0 0
\(549\) 7.22668 0.308427
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 11.4510 0.486946
\(554\) 0 0
\(555\) 1.02229 0.0433937
\(556\) 0 0
\(557\) 19.1343 0.810748 0.405374 0.914151i \(-0.367141\pi\)
0.405374 + 0.914151i \(0.367141\pi\)
\(558\) 0 0
\(559\) −0.134342 −0.00568205
\(560\) 0 0
\(561\) −0.504748 −0.0213105
\(562\) 0 0
\(563\) −21.3482 −0.899721 −0.449860 0.893099i \(-0.648526\pi\)
−0.449860 + 0.893099i \(0.648526\pi\)
\(564\) 0 0
\(565\) −7.07428 −0.297617
\(566\) 0 0
\(567\) −2.18479 −0.0917527
\(568\) 0 0
\(569\) 39.2121 1.64386 0.821929 0.569590i \(-0.192898\pi\)
0.821929 + 0.569590i \(0.192898\pi\)
\(570\) 0 0
\(571\) −7.27900 −0.304617 −0.152308 0.988333i \(-0.548671\pi\)
−0.152308 + 0.988333i \(0.548671\pi\)
\(572\) 0 0
\(573\) −19.5398 −0.816288
\(574\) 0 0
\(575\) −5.45605 −0.227533
\(576\) 0 0
\(577\) 14.9923 0.624136 0.312068 0.950060i \(-0.398978\pi\)
0.312068 + 0.950060i \(0.398978\pi\)
\(578\) 0 0
\(579\) −16.6408 −0.691570
\(580\) 0 0
\(581\) 37.3901 1.55120
\(582\) 0 0
\(583\) −1.35410 −0.0560812
\(584\) 0 0
\(585\) −0.667252 −0.0275875
\(586\) 0 0
\(587\) −12.0104 −0.495723 −0.247862 0.968795i \(-0.579728\pi\)
−0.247862 + 0.968795i \(0.579728\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −21.9959 −0.904790
\(592\) 0 0
\(593\) −36.3806 −1.49397 −0.746987 0.664839i \(-0.768500\pi\)
−0.746987 + 0.664839i \(0.768500\pi\)
\(594\) 0 0
\(595\) 5.96761 0.244648
\(596\) 0 0
\(597\) −21.7442 −0.889932
\(598\) 0 0
\(599\) 13.8060 0.564099 0.282050 0.959400i \(-0.408986\pi\)
0.282050 + 0.959400i \(0.408986\pi\)
\(600\) 0 0
\(601\) −0.967606 −0.0394695 −0.0197347 0.999805i \(-0.506282\pi\)
−0.0197347 + 0.999805i \(0.506282\pi\)
\(602\) 0 0
\(603\) 1.06418 0.0433367
\(604\) 0 0
\(605\) 9.65002 0.392329
\(606\) 0 0
\(607\) 1.53890 0.0624619 0.0312309 0.999512i \(-0.490057\pi\)
0.0312309 + 0.999512i \(0.490057\pi\)
\(608\) 0 0
\(609\) 14.2395 0.577013
\(610\) 0 0
\(611\) −2.63135 −0.106453
\(612\) 0 0
\(613\) 41.1753 1.66305 0.831527 0.555484i \(-0.187467\pi\)
0.831527 + 0.555484i \(0.187467\pi\)
\(614\) 0 0
\(615\) 9.31820 0.375746
\(616\) 0 0
\(617\) 30.6860 1.23537 0.617687 0.786424i \(-0.288070\pi\)
0.617687 + 0.786424i \(0.288070\pi\)
\(618\) 0 0
\(619\) −11.9581 −0.480637 −0.240319 0.970694i \(-0.577252\pi\)
−0.240319 + 0.970694i \(0.577252\pi\)
\(620\) 0 0
\(621\) 1.29086 0.0518004
\(622\) 0 0
\(623\) −34.1343 −1.36756
\(624\) 0 0
\(625\) 13.9982 0.559930
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.61081 −0.143973
\(630\) 0 0
\(631\) −48.1762 −1.91787 −0.958933 0.283634i \(-0.908460\pi\)
−0.958933 + 0.283634i \(0.908460\pi\)
\(632\) 0 0
\(633\) −8.62630 −0.342864
\(634\) 0 0
\(635\) −17.6313 −0.699679
\(636\) 0 0
\(637\) −1.68954 −0.0669420
\(638\) 0 0
\(639\) 5.08378 0.201111
\(640\) 0 0
\(641\) 6.72967 0.265806 0.132903 0.991129i \(-0.457570\pi\)
0.132903 + 0.991129i \(0.457570\pi\)
\(642\) 0 0
\(643\) −25.6928 −1.01323 −0.506613 0.862173i \(-0.669103\pi\)
−0.506613 + 0.862173i \(0.669103\pi\)
\(644\) 0 0
\(645\) 0.155697 0.00613055
\(646\) 0 0
\(647\) −50.4380 −1.98292 −0.991461 0.130403i \(-0.958373\pi\)
−0.991461 + 0.130403i \(0.958373\pi\)
\(648\) 0 0
\(649\) 0.451933 0.0177399
\(650\) 0 0
\(651\) −2.09327 −0.0820419
\(652\) 0 0
\(653\) −35.8607 −1.40334 −0.701669 0.712503i \(-0.747562\pi\)
−0.701669 + 0.712503i \(0.747562\pi\)
\(654\) 0 0
\(655\) 13.9905 0.546654
\(656\) 0 0
\(657\) 2.24897 0.0877407
\(658\) 0 0
\(659\) −12.6108 −0.491248 −0.245624 0.969365i \(-0.578993\pi\)
−0.245624 + 0.969365i \(0.578993\pi\)
\(660\) 0 0
\(661\) −44.5699 −1.73357 −0.866783 0.498685i \(-0.833816\pi\)
−0.866783 + 0.498685i \(0.833816\pi\)
\(662\) 0 0
\(663\) 2.35679 0.0915302
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.41323 −0.325762
\(668\) 0 0
\(669\) 15.1584 0.586057
\(670\) 0 0
\(671\) −1.17436 −0.0453358
\(672\) 0 0
\(673\) −12.8203 −0.494185 −0.247092 0.968992i \(-0.579475\pi\)
−0.247092 + 0.968992i \(0.579475\pi\)
\(674\) 0 0
\(675\) −4.22668 −0.162685
\(676\) 0 0
\(677\) −29.3688 −1.12873 −0.564367 0.825524i \(-0.690880\pi\)
−0.564367 + 0.825524i \(0.690880\pi\)
\(678\) 0 0
\(679\) 20.5790 0.789751
\(680\) 0 0
\(681\) −5.71419 −0.218968
\(682\) 0 0
\(683\) 38.0033 1.45416 0.727078 0.686555i \(-0.240878\pi\)
0.727078 + 0.686555i \(0.240878\pi\)
\(684\) 0 0
\(685\) 4.43613 0.169496
\(686\) 0 0
\(687\) 22.1634 0.845588
\(688\) 0 0
\(689\) 6.32264 0.240874
\(690\) 0 0
\(691\) 32.2918 1.22844 0.614219 0.789136i \(-0.289471\pi\)
0.614219 + 0.789136i \(0.289471\pi\)
\(692\) 0 0
\(693\) 0.355037 0.0134867
\(694\) 0 0
\(695\) 9.28136 0.352062
\(696\) 0 0
\(697\) −32.9127 −1.24666
\(698\) 0 0
\(699\) −10.8280 −0.409553
\(700\) 0 0
\(701\) 23.1138 0.872996 0.436498 0.899705i \(-0.356219\pi\)
0.436498 + 0.899705i \(0.356219\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 3.04963 0.114856
\(706\) 0 0
\(707\) 13.7760 0.518100
\(708\) 0 0
\(709\) 36.7588 1.38050 0.690252 0.723569i \(-0.257500\pi\)
0.690252 + 0.723569i \(0.257500\pi\)
\(710\) 0 0
\(711\) −5.24123 −0.196561
\(712\) 0 0
\(713\) 1.23679 0.0463180
\(714\) 0 0
\(715\) 0.108431 0.00405509
\(716\) 0 0
\(717\) −9.86215 −0.368309
\(718\) 0 0
\(719\) 32.9504 1.22884 0.614421 0.788979i \(-0.289390\pi\)
0.614421 + 0.788979i \(0.289390\pi\)
\(720\) 0 0
\(721\) 18.8239 0.701038
\(722\) 0 0
\(723\) −6.90673 −0.256864
\(724\) 0 0
\(725\) 27.5476 1.02309
\(726\) 0 0
\(727\) −7.92303 −0.293849 −0.146924 0.989148i \(-0.546937\pi\)
−0.146924 + 0.989148i \(0.546937\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.549935 −0.0203401
\(732\) 0 0
\(733\) −7.43470 −0.274607 −0.137303 0.990529i \(-0.543844\pi\)
−0.137303 + 0.990529i \(0.543844\pi\)
\(734\) 0 0
\(735\) 1.95811 0.0722260
\(736\) 0 0
\(737\) −0.172933 −0.00637007
\(738\) 0 0
\(739\) 19.3500 0.711801 0.355900 0.934524i \(-0.384174\pi\)
0.355900 + 0.934524i \(0.384174\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 31.3833 1.15134 0.575671 0.817681i \(-0.304741\pi\)
0.575671 + 0.817681i \(0.304741\pi\)
\(744\) 0 0
\(745\) −12.1317 −0.444469
\(746\) 0 0
\(747\) −17.1138 −0.626161
\(748\) 0 0
\(749\) 28.7256 1.04961
\(750\) 0 0
\(751\) 5.22256 0.190574 0.0952870 0.995450i \(-0.469623\pi\)
0.0952870 + 0.995450i \(0.469623\pi\)
\(752\) 0 0
\(753\) 24.8922 0.907121
\(754\) 0 0
\(755\) 17.8375 0.649173
\(756\) 0 0
\(757\) −29.7716 −1.08207 −0.541033 0.841001i \(-0.681967\pi\)
−0.541033 + 0.841001i \(0.681967\pi\)
\(758\) 0 0
\(759\) −0.209770 −0.00761415
\(760\) 0 0
\(761\) −9.35267 −0.339034 −0.169517 0.985527i \(-0.554221\pi\)
−0.169517 + 0.985527i \(0.554221\pi\)
\(762\) 0 0
\(763\) 21.9564 0.794873
\(764\) 0 0
\(765\) −2.73143 −0.0987550
\(766\) 0 0
\(767\) −2.11019 −0.0761944
\(768\) 0 0
\(769\) 38.8334 1.40037 0.700184 0.713963i \(-0.253101\pi\)
0.700184 + 0.713963i \(0.253101\pi\)
\(770\) 0 0
\(771\) −14.2567 −0.513443
\(772\) 0 0
\(773\) −23.7674 −0.854856 −0.427428 0.904049i \(-0.640580\pi\)
−0.427428 + 0.904049i \(0.640580\pi\)
\(774\) 0 0
\(775\) −4.04963 −0.145467
\(776\) 0 0
\(777\) 2.53983 0.0911159
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −0.826133 −0.0295614
\(782\) 0 0
\(783\) −6.51754 −0.232918
\(784\) 0 0
\(785\) 11.5862 0.413528
\(786\) 0 0
\(787\) −13.7561 −0.490351 −0.245176 0.969479i \(-0.578846\pi\)
−0.245176 + 0.969479i \(0.578846\pi\)
\(788\) 0 0
\(789\) 21.6168 0.769578
\(790\) 0 0
\(791\) −17.5757 −0.624921
\(792\) 0 0
\(793\) 5.48339 0.194721
\(794\) 0 0
\(795\) −7.32770 −0.259887
\(796\) 0 0
\(797\) −7.77238 −0.275312 −0.137656 0.990480i \(-0.543957\pi\)
−0.137656 + 0.990480i \(0.543957\pi\)
\(798\) 0 0
\(799\) −10.7716 −0.381071
\(800\) 0 0
\(801\) 15.6236 0.552033
\(802\) 0 0
\(803\) −0.365466 −0.0128970
\(804\) 0 0
\(805\) 2.48009 0.0874119
\(806\) 0 0
\(807\) −10.6263 −0.374063
\(808\) 0 0
\(809\) 13.6919 0.481382 0.240691 0.970602i \(-0.422626\pi\)
0.240691 + 0.970602i \(0.422626\pi\)
\(810\) 0 0
\(811\) −22.1084 −0.776332 −0.388166 0.921589i \(-0.626891\pi\)
−0.388166 + 0.921589i \(0.626891\pi\)
\(812\) 0 0
\(813\) −12.1506 −0.426142
\(814\) 0 0
\(815\) 15.3806 0.538760
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −1.65776 −0.0579267
\(820\) 0 0
\(821\) −21.5776 −0.753063 −0.376532 0.926404i \(-0.622883\pi\)
−0.376532 + 0.926404i \(0.622883\pi\)
\(822\) 0 0
\(823\) −9.35235 −0.326002 −0.163001 0.986626i \(-0.552117\pi\)
−0.163001 + 0.986626i \(0.552117\pi\)
\(824\) 0 0
\(825\) 0.686852 0.0239131
\(826\) 0 0
\(827\) −33.5800 −1.16769 −0.583845 0.811865i \(-0.698452\pi\)
−0.583845 + 0.811865i \(0.698452\pi\)
\(828\) 0 0
\(829\) 0.650340 0.0225872 0.0112936 0.999936i \(-0.496405\pi\)
0.0112936 + 0.999936i \(0.496405\pi\)
\(830\) 0 0
\(831\) 9.81521 0.340486
\(832\) 0 0
\(833\) −6.91622 −0.239633
\(834\) 0 0
\(835\) −13.1088 −0.453647
\(836\) 0 0
\(837\) 0.958111 0.0331172
\(838\) 0 0
\(839\) −22.9077 −0.790860 −0.395430 0.918496i \(-0.629404\pi\)
−0.395430 + 0.918496i \(0.629404\pi\)
\(840\) 0 0
\(841\) 13.4783 0.464770
\(842\) 0 0
\(843\) 28.2148 0.971770
\(844\) 0 0
\(845\) 10.9257 0.375856
\(846\) 0 0
\(847\) 23.9750 0.823792
\(848\) 0 0
\(849\) −15.4192 −0.529186
\(850\) 0 0
\(851\) −1.50063 −0.0514409
\(852\) 0 0
\(853\) 30.5158 1.04484 0.522420 0.852688i \(-0.325029\pi\)
0.522420 + 0.852688i \(0.325029\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0473 0.616483 0.308241 0.951308i \(-0.400260\pi\)
0.308241 + 0.951308i \(0.400260\pi\)
\(858\) 0 0
\(859\) 36.8857 1.25852 0.629262 0.777193i \(-0.283357\pi\)
0.629262 + 0.777193i \(0.283357\pi\)
\(860\) 0 0
\(861\) 23.1506 0.788972
\(862\) 0 0
\(863\) −28.1712 −0.958958 −0.479479 0.877553i \(-0.659174\pi\)
−0.479479 + 0.877553i \(0.659174\pi\)
\(864\) 0 0
\(865\) −1.57903 −0.0536886
\(866\) 0 0
\(867\) −7.35235 −0.249699
\(868\) 0 0
\(869\) 0.851720 0.0288926
\(870\) 0 0
\(871\) 0.807467 0.0273600
\(872\) 0 0
\(873\) −9.41921 −0.318792
\(874\) 0 0
\(875\) −17.7270 −0.599282
\(876\) 0 0
\(877\) 12.7115 0.429237 0.214619 0.976698i \(-0.431149\pi\)
0.214619 + 0.976698i \(0.431149\pi\)
\(878\) 0 0
\(879\) 27.7769 0.936893
\(880\) 0 0
\(881\) 36.8530 1.24161 0.620804 0.783966i \(-0.286806\pi\)
0.620804 + 0.783966i \(0.286806\pi\)
\(882\) 0 0
\(883\) −39.6245 −1.33347 −0.666736 0.745294i \(-0.732309\pi\)
−0.666736 + 0.745294i \(0.732309\pi\)
\(884\) 0 0
\(885\) 2.44562 0.0822087
\(886\) 0 0
\(887\) −47.5057 −1.59508 −0.797542 0.603263i \(-0.793867\pi\)
−0.797542 + 0.603263i \(0.793867\pi\)
\(888\) 0 0
\(889\) −43.8043 −1.46915
\(890\) 0 0
\(891\) −0.162504 −0.00544408
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) −6.88981 −0.230301
\(896\) 0 0
\(897\) 0.979466 0.0327034
\(898\) 0 0
\(899\) −6.24453 −0.208267
\(900\) 0 0
\(901\) 25.8821 0.862257
\(902\) 0 0
\(903\) 0.386821 0.0128726
\(904\) 0 0
\(905\) 0.368651 0.0122544
\(906\) 0 0
\(907\) 23.0060 0.763901 0.381951 0.924183i \(-0.375252\pi\)
0.381951 + 0.924183i \(0.375252\pi\)
\(908\) 0 0
\(909\) −6.30541 −0.209137
\(910\) 0 0
\(911\) 13.7888 0.456843 0.228422 0.973562i \(-0.426644\pi\)
0.228422 + 0.973562i \(0.426644\pi\)
\(912\) 0 0
\(913\) 2.78106 0.0920396
\(914\) 0 0
\(915\) −6.35504 −0.210091
\(916\) 0 0
\(917\) 34.7588 1.14784
\(918\) 0 0
\(919\) 54.6623 1.80314 0.901572 0.432630i \(-0.142414\pi\)
0.901572 + 0.432630i \(0.142414\pi\)
\(920\) 0 0
\(921\) 27.1908 0.895967
\(922\) 0 0
\(923\) 3.85742 0.126969
\(924\) 0 0
\(925\) 4.91353 0.161556
\(926\) 0 0
\(927\) −8.61587 −0.282982
\(928\) 0 0
\(929\) 46.8084 1.53573 0.767867 0.640609i \(-0.221318\pi\)
0.767867 + 0.640609i \(0.221318\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −5.94356 −0.194584
\(934\) 0 0
\(935\) 0.443868 0.0145160
\(936\) 0 0
\(937\) −38.3209 −1.25189 −0.625944 0.779868i \(-0.715286\pi\)
−0.625944 + 0.779868i \(0.715286\pi\)
\(938\) 0 0
\(939\) 7.15064 0.233352
\(940\) 0 0
\(941\) −29.4584 −0.960317 −0.480158 0.877182i \(-0.659421\pi\)
−0.480158 + 0.877182i \(0.659421\pi\)
\(942\) 0 0
\(943\) −13.6783 −0.445426
\(944\) 0 0
\(945\) 1.92127 0.0624991
\(946\) 0 0
\(947\) −37.9273 −1.23247 −0.616235 0.787562i \(-0.711343\pi\)
−0.616235 + 0.787562i \(0.711343\pi\)
\(948\) 0 0
\(949\) 1.70645 0.0553938
\(950\) 0 0
\(951\) 22.2909 0.722831
\(952\) 0 0
\(953\) −8.23267 −0.266682 −0.133341 0.991070i \(-0.542571\pi\)
−0.133341 + 0.991070i \(0.542571\pi\)
\(954\) 0 0
\(955\) 17.1830 0.556030
\(956\) 0 0
\(957\) 1.05913 0.0342367
\(958\) 0 0
\(959\) 11.0214 0.355898
\(960\) 0 0
\(961\) −30.0820 −0.970388
\(962\) 0 0
\(963\) −13.1480 −0.423687
\(964\) 0 0
\(965\) 14.6337 0.471076
\(966\) 0 0
\(967\) −16.2294 −0.521901 −0.260951 0.965352i \(-0.584036\pi\)
−0.260951 + 0.965352i \(0.584036\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 33.1962 1.06532 0.532658 0.846331i \(-0.321193\pi\)
0.532658 + 0.846331i \(0.321193\pi\)
\(972\) 0 0
\(973\) 23.0591 0.739242
\(974\) 0 0
\(975\) −3.20708 −0.102709
\(976\) 0 0
\(977\) 23.9932 0.767610 0.383805 0.923414i \(-0.374613\pi\)
0.383805 + 0.923414i \(0.374613\pi\)
\(978\) 0 0
\(979\) −2.53890 −0.0811435
\(980\) 0 0
\(981\) −10.0496 −0.320860
\(982\) 0 0
\(983\) 46.4962 1.48300 0.741499 0.670954i \(-0.234115\pi\)
0.741499 + 0.670954i \(0.234115\pi\)
\(984\) 0 0
\(985\) 19.3429 0.616315
\(986\) 0 0
\(987\) 7.57667 0.241168
\(988\) 0 0
\(989\) −0.228549 −0.00726743
\(990\) 0 0
\(991\) 35.2513 1.11980 0.559898 0.828562i \(-0.310840\pi\)
0.559898 + 0.828562i \(0.310840\pi\)
\(992\) 0 0
\(993\) 6.30365 0.200040
\(994\) 0 0
\(995\) 19.1215 0.606194
\(996\) 0 0
\(997\) 55.5877 1.76048 0.880240 0.474529i \(-0.157381\pi\)
0.880240 + 0.474529i \(0.157381\pi\)
\(998\) 0 0
\(999\) −1.16250 −0.0367800
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4332.2.a.o.1.1 3
19.6 even 9 228.2.q.a.169.1 yes 6
19.16 even 9 228.2.q.a.85.1 6
19.18 odd 2 4332.2.a.n.1.1 3
57.35 odd 18 684.2.bo.a.541.1 6
57.44 odd 18 684.2.bo.a.397.1 6
76.35 odd 18 912.2.bo.e.769.1 6
76.63 odd 18 912.2.bo.e.625.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
228.2.q.a.85.1 6 19.16 even 9
228.2.q.a.169.1 yes 6 19.6 even 9
684.2.bo.a.397.1 6 57.44 odd 18
684.2.bo.a.541.1 6 57.35 odd 18
912.2.bo.e.625.1 6 76.63 odd 18
912.2.bo.e.769.1 6 76.35 odd 18
4332.2.a.n.1.1 3 19.18 odd 2
4332.2.a.o.1.1 3 1.1 even 1 trivial