Properties

Label 5445.2.a.bx.1.6
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.4785439006\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.27433728.1
Defining polynomial: \(x^{6} - 9 x^{4} + 15 x^{2} - 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 605)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.62383\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.62383 q^{2} +4.88448 q^{4} -1.00000 q^{5} +2.62383 q^{7} +7.56839 q^{8} +O(q^{10})\) \(q+2.62383 q^{2} +4.88448 q^{4} -1.00000 q^{5} +2.62383 q^{7} +7.56839 q^{8} -2.62383 q^{10} +6.72812 q^{13} +6.88448 q^{14} +10.0892 q^{16} +1.78356 q^{17} +1.48046 q^{19} -4.88448 q^{20} -5.20473 q^{23} +1.00000 q^{25} +17.6535 q^{26} +12.8161 q^{28} +1.17737 q^{29} -4.56424 q^{31} +11.3356 q^{32} +4.67975 q^{34} -2.62383 q^{35} -0.679754 q^{37} +3.88448 q^{38} -7.56839 q^{40} +5.49925 q^{41} -3.80120 q^{43} -13.6563 q^{46} -6.66012 q^{47} -0.115516 q^{49} +2.62383 q^{50} +32.8634 q^{52} -14.2939 q^{53} +19.8582 q^{56} +3.08921 q^{58} +3.88448 q^{59} -3.21251 q^{61} -11.9758 q^{62} +9.56424 q^{64} -6.72812 q^{65} +4.66012 q^{67} +8.71176 q^{68} -6.88448 q^{70} -3.88448 q^{71} +3.56712 q^{73} -1.78356 q^{74} +7.23130 q^{76} +15.1368 q^{79} -10.0892 q^{80} +14.4291 q^{82} +7.33431 q^{83} -1.78356 q^{85} -9.97370 q^{86} -3.44872 q^{89} +17.6535 q^{91} -25.4224 q^{92} -17.4750 q^{94} -1.48046 q^{95} +1.47502 q^{97} -0.303095 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{4} - 6q^{5} + O(q^{10}) \) \( 6q + 6q^{4} - 6q^{5} + 18q^{14} + 18q^{16} - 6q^{20} - 12q^{23} + 6q^{25} + 36q^{26} + 24q^{34} - 42q^{47} - 24q^{49} - 24q^{53} + 30q^{56} - 24q^{58} + 30q^{64} + 30q^{67} - 18q^{70} - 18q^{80} + 42q^{82} + 6q^{86} + 30q^{89} + 36q^{91} - 36q^{92} + 24q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62383 1.85533 0.927664 0.373416i \(-0.121814\pi\)
0.927664 + 0.373416i \(0.121814\pi\)
\(3\) 0 0
\(4\) 4.88448 2.44224
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 2.62383 0.991715 0.495857 0.868404i \(-0.334854\pi\)
0.495857 + 0.868404i \(0.334854\pi\)
\(8\) 7.56839 2.67583
\(9\) 0 0
\(10\) −2.62383 −0.829728
\(11\) 0 0
\(12\) 0 0
\(13\) 6.72812 1.86605 0.933023 0.359817i \(-0.117161\pi\)
0.933023 + 0.359817i \(0.117161\pi\)
\(14\) 6.88448 1.83996
\(15\) 0 0
\(16\) 10.0892 2.52230
\(17\) 1.78356 0.432576 0.216288 0.976330i \(-0.430605\pi\)
0.216288 + 0.976330i \(0.430605\pi\)
\(18\) 0 0
\(19\) 1.48046 0.339642 0.169821 0.985475i \(-0.445681\pi\)
0.169821 + 0.985475i \(0.445681\pi\)
\(20\) −4.88448 −1.09220
\(21\) 0 0
\(22\) 0 0
\(23\) −5.20473 −1.08526 −0.542631 0.839971i \(-0.682572\pi\)
−0.542631 + 0.839971i \(0.682572\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 17.6535 3.46213
\(27\) 0 0
\(28\) 12.8161 2.42201
\(29\) 1.17737 0.218632 0.109316 0.994007i \(-0.465134\pi\)
0.109316 + 0.994007i \(0.465134\pi\)
\(30\) 0 0
\(31\) −4.56424 −0.819761 −0.409881 0.912139i \(-0.634430\pi\)
−0.409881 + 0.912139i \(0.634430\pi\)
\(32\) 11.3356 2.00387
\(33\) 0 0
\(34\) 4.67975 0.802571
\(35\) −2.62383 −0.443508
\(36\) 0 0
\(37\) −0.679754 −0.111751 −0.0558754 0.998438i \(-0.517795\pi\)
−0.0558754 + 0.998438i \(0.517795\pi\)
\(38\) 3.88448 0.630146
\(39\) 0 0
\(40\) −7.56839 −1.19667
\(41\) 5.49925 0.858838 0.429419 0.903105i \(-0.358718\pi\)
0.429419 + 0.903105i \(0.358718\pi\)
\(42\) 0 0
\(43\) −3.80120 −0.579677 −0.289839 0.957076i \(-0.593602\pi\)
−0.289839 + 0.957076i \(0.593602\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −13.6563 −2.01352
\(47\) −6.66012 −0.971479 −0.485739 0.874104i \(-0.661450\pi\)
−0.485739 + 0.874104i \(0.661450\pi\)
\(48\) 0 0
\(49\) −0.115516 −0.0165023
\(50\) 2.62383 0.371066
\(51\) 0 0
\(52\) 32.8634 4.55733
\(53\) −14.2939 −1.96342 −0.981712 0.190372i \(-0.939031\pi\)
−0.981712 + 0.190372i \(0.939031\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 19.8582 2.65366
\(57\) 0 0
\(58\) 3.08921 0.405634
\(59\) 3.88448 0.505717 0.252858 0.967503i \(-0.418629\pi\)
0.252858 + 0.967503i \(0.418629\pi\)
\(60\) 0 0
\(61\) −3.21251 −0.411320 −0.205660 0.978623i \(-0.565934\pi\)
−0.205660 + 0.978623i \(0.565934\pi\)
\(62\) −11.9758 −1.52093
\(63\) 0 0
\(64\) 9.56424 1.19553
\(65\) −6.72812 −0.834521
\(66\) 0 0
\(67\) 4.66012 0.569325 0.284662 0.958628i \(-0.408119\pi\)
0.284662 + 0.958628i \(0.408119\pi\)
\(68\) 8.71176 1.05646
\(69\) 0 0
\(70\) −6.88448 −0.822853
\(71\) −3.88448 −0.461003 −0.230502 0.973072i \(-0.574037\pi\)
−0.230502 + 0.973072i \(0.574037\pi\)
\(72\) 0 0
\(73\) 3.56712 0.417499 0.208750 0.977969i \(-0.433061\pi\)
0.208750 + 0.977969i \(0.433061\pi\)
\(74\) −1.78356 −0.207334
\(75\) 0 0
\(76\) 7.23130 0.829487
\(77\) 0 0
\(78\) 0 0
\(79\) 15.1368 1.70302 0.851511 0.524337i \(-0.175687\pi\)
0.851511 + 0.524337i \(0.175687\pi\)
\(80\) −10.0892 −1.12801
\(81\) 0 0
\(82\) 14.4291 1.59343
\(83\) 7.33431 0.805045 0.402523 0.915410i \(-0.368133\pi\)
0.402523 + 0.915410i \(0.368133\pi\)
\(84\) 0 0
\(85\) −1.78356 −0.193454
\(86\) −9.97370 −1.07549
\(87\) 0 0
\(88\) 0 0
\(89\) −3.44872 −0.365564 −0.182782 0.983153i \(-0.558510\pi\)
−0.182782 + 0.983153i \(0.558510\pi\)
\(90\) 0 0
\(91\) 17.6535 1.85058
\(92\) −25.4224 −2.65047
\(93\) 0 0
\(94\) −17.4750 −1.80241
\(95\) −1.48046 −0.151892
\(96\) 0 0
\(97\) 1.47502 0.149766 0.0748830 0.997192i \(-0.476142\pi\)
0.0748830 + 0.997192i \(0.476142\pi\)
\(98\) −0.303095 −0.0306172
\(99\) 0 0
\(100\) 4.88448 0.488448
\(101\) −3.41259 −0.339566 −0.169783 0.985481i \(-0.554307\pi\)
−0.169783 + 0.985481i \(0.554307\pi\)
\(102\) 0 0
\(103\) −4.97370 −0.490073 −0.245036 0.969514i \(-0.578800\pi\)
−0.245036 + 0.969514i \(0.578800\pi\)
\(104\) 50.9211 4.99322
\(105\) 0 0
\(106\) −37.5049 −3.64280
\(107\) 7.06522 0.683021 0.341510 0.939878i \(-0.389062\pi\)
0.341510 + 0.939878i \(0.389062\pi\)
\(108\) 0 0
\(109\) 10.6439 1.01950 0.509750 0.860323i \(-0.329738\pi\)
0.509750 + 0.860323i \(0.329738\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 26.4724 2.50140
\(113\) 13.7690 1.29528 0.647638 0.761948i \(-0.275757\pi\)
0.647638 + 0.761948i \(0.275757\pi\)
\(114\) 0 0
\(115\) 5.20473 0.485344
\(116\) 5.75084 0.533952
\(117\) 0 0
\(118\) 10.1922 0.938270
\(119\) 4.67975 0.428992
\(120\) 0 0
\(121\) 0 0
\(122\) −8.42909 −0.763134
\(123\) 0 0
\(124\) −22.2939 −2.00206
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 12.3129 1.09259 0.546296 0.837592i \(-0.316037\pi\)
0.546296 + 0.837592i \(0.316037\pi\)
\(128\) 2.42375 0.214231
\(129\) 0 0
\(130\) −17.6535 −1.54831
\(131\) 19.5102 1.70461 0.852306 0.523043i \(-0.175203\pi\)
0.852306 + 0.523043i \(0.175203\pi\)
\(132\) 0 0
\(133\) 3.88448 0.336827
\(134\) 12.2274 1.05628
\(135\) 0 0
\(136\) 13.4987 1.15750
\(137\) 8.56424 0.731692 0.365846 0.930675i \(-0.380780\pi\)
0.365846 + 0.930675i \(0.380780\pi\)
\(138\) 0 0
\(139\) −1.98364 −0.168250 −0.0841250 0.996455i \(-0.526810\pi\)
−0.0841250 + 0.996455i \(0.526810\pi\)
\(140\) −12.8161 −1.08315
\(141\) 0 0
\(142\) −10.1922 −0.855313
\(143\) 0 0
\(144\) 0 0
\(145\) −1.17737 −0.0977751
\(146\) 9.35951 0.774598
\(147\) 0 0
\(148\) −3.32025 −0.272923
\(149\) −18.3493 −1.50323 −0.751617 0.659600i \(-0.770726\pi\)
−0.751617 + 0.659600i \(0.770726\pi\)
\(150\) 0 0
\(151\) −17.2234 −1.40162 −0.700812 0.713346i \(-0.747179\pi\)
−0.700812 + 0.713346i \(0.747179\pi\)
\(152\) 11.2047 0.908824
\(153\) 0 0
\(154\) 0 0
\(155\) 4.56424 0.366608
\(156\) 0 0
\(157\) −20.8974 −1.66780 −0.833899 0.551917i \(-0.813896\pi\)
−0.833899 + 0.551917i \(0.813896\pi\)
\(158\) 39.7164 3.15966
\(159\) 0 0
\(160\) −11.3356 −0.896157
\(161\) −13.6563 −1.07627
\(162\) 0 0
\(163\) 9.45539 0.740604 0.370302 0.928912i \(-0.379254\pi\)
0.370302 + 0.928912i \(0.379254\pi\)
\(164\) 26.8610 2.09749
\(165\) 0 0
\(166\) 19.2440 1.49362
\(167\) −9.44902 −0.731187 −0.365593 0.930775i \(-0.619134\pi\)
−0.365593 + 0.930775i \(0.619134\pi\)
\(168\) 0 0
\(169\) 32.2676 2.48213
\(170\) −4.67975 −0.358921
\(171\) 0 0
\(172\) −18.5669 −1.41571
\(173\) −9.08286 −0.690557 −0.345279 0.938500i \(-0.612216\pi\)
−0.345279 + 0.938500i \(0.612216\pi\)
\(174\) 0 0
\(175\) 2.62383 0.198343
\(176\) 0 0
\(177\) 0 0
\(178\) −9.04886 −0.678241
\(179\) 13.7690 1.02914 0.514570 0.857448i \(-0.327951\pi\)
0.514570 + 0.857448i \(0.327951\pi\)
\(180\) 0 0
\(181\) −23.8582 −1.77336 −0.886682 0.462379i \(-0.846996\pi\)
−0.886682 + 0.462379i \(0.846996\pi\)
\(182\) 46.3197 3.43344
\(183\) 0 0
\(184\) −39.3915 −2.90398
\(185\) 0.679754 0.0499765
\(186\) 0 0
\(187\) 0 0
\(188\) −32.5313 −2.37259
\(189\) 0 0
\(190\) −3.88448 −0.281810
\(191\) −16.0629 −1.16227 −0.581136 0.813807i \(-0.697391\pi\)
−0.581136 + 0.813807i \(0.697391\pi\)
\(192\) 0 0
\(193\) −21.4588 −1.54464 −0.772319 0.635235i \(-0.780903\pi\)
−0.772319 + 0.635235i \(0.780903\pi\)
\(194\) 3.87021 0.277865
\(195\) 0 0
\(196\) −0.564237 −0.0403027
\(197\) 9.21494 0.656537 0.328269 0.944584i \(-0.393535\pi\)
0.328269 + 0.944584i \(0.393535\pi\)
\(198\) 0 0
\(199\) −16.4880 −1.16880 −0.584401 0.811465i \(-0.698670\pi\)
−0.584401 + 0.811465i \(0.698670\pi\)
\(200\) 7.56839 0.535166
\(201\) 0 0
\(202\) −8.95407 −0.630006
\(203\) 3.08921 0.216820
\(204\) 0 0
\(205\) −5.49925 −0.384084
\(206\) −13.0501 −0.909246
\(207\) 0 0
\(208\) 67.8815 4.70673
\(209\) 0 0
\(210\) 0 0
\(211\) −14.8337 −1.02119 −0.510597 0.859820i \(-0.670576\pi\)
−0.510597 + 0.859820i \(0.670576\pi\)
\(212\) −69.8185 −4.79516
\(213\) 0 0
\(214\) 18.5379 1.26723
\(215\) 3.80120 0.259240
\(216\) 0 0
\(217\) −11.9758 −0.812969
\(218\) 27.9278 1.89151
\(219\) 0 0
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 23.4028 1.56717 0.783583 0.621287i \(-0.213390\pi\)
0.783583 + 0.621287i \(0.213390\pi\)
\(224\) 29.7427 1.98727
\(225\) 0 0
\(226\) 36.1274 2.40316
\(227\) −2.62383 −0.174150 −0.0870749 0.996202i \(-0.527752\pi\)
−0.0870749 + 0.996202i \(0.527752\pi\)
\(228\) 0 0
\(229\) −22.0366 −1.45622 −0.728110 0.685460i \(-0.759601\pi\)
−0.728110 + 0.685460i \(0.759601\pi\)
\(230\) 13.6563 0.900471
\(231\) 0 0
\(232\) 8.91079 0.585022
\(233\) 5.34473 0.350145 0.175072 0.984556i \(-0.443984\pi\)
0.175072 + 0.984556i \(0.443984\pi\)
\(234\) 0 0
\(235\) 6.66012 0.434459
\(236\) 18.9737 1.23508
\(237\) 0 0
\(238\) 12.2789 0.795921
\(239\) −12.5820 −0.813860 −0.406930 0.913459i \(-0.633401\pi\)
−0.406930 + 0.913459i \(0.633401\pi\)
\(240\) 0 0
\(241\) 4.28687 0.276141 0.138071 0.990422i \(-0.455910\pi\)
0.138071 + 0.990422i \(0.455910\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −15.6915 −1.00454
\(245\) 0.115516 0.00738007
\(246\) 0 0
\(247\) 9.96074 0.633787
\(248\) −34.5440 −2.19354
\(249\) 0 0
\(250\) −2.62383 −0.165946
\(251\) −10.0629 −0.635165 −0.317583 0.948231i \(-0.602871\pi\)
−0.317583 + 0.948231i \(0.602871\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 32.3069 2.02712
\(255\) 0 0
\(256\) −12.7690 −0.798060
\(257\) 3.16547 0.197457 0.0987283 0.995114i \(-0.468523\pi\)
0.0987283 + 0.995114i \(0.468523\pi\)
\(258\) 0 0
\(259\) −1.78356 −0.110825
\(260\) −32.8634 −2.03810
\(261\) 0 0
\(262\) 51.1914 3.16261
\(263\) 22.3681 1.37928 0.689638 0.724155i \(-0.257770\pi\)
0.689638 + 0.724155i \(0.257770\pi\)
\(264\) 0 0
\(265\) 14.2939 0.878070
\(266\) 10.1922 0.624925
\(267\) 0 0
\(268\) 22.7623 1.39043
\(269\) −15.9737 −0.973934 −0.486967 0.873421i \(-0.661897\pi\)
−0.486967 + 0.873421i \(0.661897\pi\)
\(270\) 0 0
\(271\) 15.6400 0.950060 0.475030 0.879970i \(-0.342437\pi\)
0.475030 + 0.879970i \(0.342437\pi\)
\(272\) 17.9947 1.09109
\(273\) 0 0
\(274\) 22.4711 1.35753
\(275\) 0 0
\(276\) 0 0
\(277\) −23.8836 −1.43502 −0.717512 0.696546i \(-0.754719\pi\)
−0.717512 + 0.696546i \(0.754719\pi\)
\(278\) −5.20473 −0.312159
\(279\) 0 0
\(280\) −19.8582 −1.18675
\(281\) 12.2439 0.730408 0.365204 0.930928i \(-0.380999\pi\)
0.365204 + 0.930928i \(0.380999\pi\)
\(282\) 0 0
\(283\) 20.8536 1.23962 0.619810 0.784752i \(-0.287210\pi\)
0.619810 + 0.784752i \(0.287210\pi\)
\(284\) −18.9737 −1.12588
\(285\) 0 0
\(286\) 0 0
\(287\) 14.4291 0.851722
\(288\) 0 0
\(289\) −13.8189 −0.812878
\(290\) −3.08921 −0.181405
\(291\) 0 0
\(292\) 17.4235 1.01963
\(293\) 14.3305 0.837198 0.418599 0.908171i \(-0.362521\pi\)
0.418599 + 0.908171i \(0.362521\pi\)
\(294\) 0 0
\(295\) −3.88448 −0.226163
\(296\) −5.14464 −0.299026
\(297\) 0 0
\(298\) −48.1455 −2.78899
\(299\) −35.0181 −2.02515
\(300\) 0 0
\(301\) −9.97370 −0.574874
\(302\) −45.1914 −2.60047
\(303\) 0 0
\(304\) 14.9367 0.856679
\(305\) 3.21251 0.183948
\(306\) 0 0
\(307\) −10.2952 −0.587580 −0.293790 0.955870i \(-0.594917\pi\)
−0.293790 + 0.955870i \(0.594917\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 11.9758 0.680179
\(311\) 19.1521 1.08602 0.543009 0.839727i \(-0.317285\pi\)
0.543009 + 0.839727i \(0.317285\pi\)
\(312\) 0 0
\(313\) −14.9737 −0.846363 −0.423182 0.906045i \(-0.639087\pi\)
−0.423182 + 0.906045i \(0.639087\pi\)
\(314\) −54.8313 −3.09431
\(315\) 0 0
\(316\) 73.9354 4.15919
\(317\) −12.1784 −0.684009 −0.342004 0.939698i \(-0.611106\pi\)
−0.342004 + 0.939698i \(0.611106\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −9.56424 −0.534657
\(321\) 0 0
\(322\) −35.8319 −1.99683
\(323\) 2.64049 0.146921
\(324\) 0 0
\(325\) 6.72812 0.373209
\(326\) 24.8093 1.37406
\(327\) 0 0
\(328\) 41.6205 2.29811
\(329\) −17.4750 −0.963430
\(330\) 0 0
\(331\) −15.8319 −0.870199 −0.435099 0.900382i \(-0.643287\pi\)
−0.435099 + 0.900382i \(0.643287\pi\)
\(332\) 35.8243 1.96612
\(333\) 0 0
\(334\) −24.7926 −1.35659
\(335\) −4.66012 −0.254610
\(336\) 0 0
\(337\) −6.72812 −0.366504 −0.183252 0.983066i \(-0.558662\pi\)
−0.183252 + 0.983066i \(0.558662\pi\)
\(338\) 84.6648 4.60516
\(339\) 0 0
\(340\) −8.71176 −0.472462
\(341\) 0 0
\(342\) 0 0
\(343\) −18.6699 −1.00808
\(344\) −28.7690 −1.55112
\(345\) 0 0
\(346\) −23.8319 −1.28121
\(347\) 33.5036 1.79857 0.899284 0.437366i \(-0.144088\pi\)
0.899284 + 0.437366i \(0.144088\pi\)
\(348\) 0 0
\(349\) −22.7742 −1.21907 −0.609537 0.792757i \(-0.708645\pi\)
−0.609537 + 0.792757i \(0.708645\pi\)
\(350\) 6.88448 0.367991
\(351\) 0 0
\(352\) 0 0
\(353\) 15.4617 0.822942 0.411471 0.911423i \(-0.365015\pi\)
0.411471 + 0.911423i \(0.365015\pi\)
\(354\) 0 0
\(355\) 3.88448 0.206167
\(356\) −16.8452 −0.892795
\(357\) 0 0
\(358\) 36.1274 1.90939
\(359\) 9.58603 0.505932 0.252966 0.967475i \(-0.418594\pi\)
0.252966 + 0.967475i \(0.418594\pi\)
\(360\) 0 0
\(361\) −16.8082 −0.884644
\(362\) −62.5998 −3.29017
\(363\) 0 0
\(364\) 86.2280 4.51957
\(365\) −3.56712 −0.186711
\(366\) 0 0
\(367\) −10.8386 −0.565768 −0.282884 0.959154i \(-0.591291\pi\)
−0.282884 + 0.959154i \(0.591291\pi\)
\(368\) −52.5116 −2.73736
\(369\) 0 0
\(370\) 1.78356 0.0927228
\(371\) −37.5049 −1.94716
\(372\) 0 0
\(373\) 10.0212 0.518878 0.259439 0.965759i \(-0.416462\pi\)
0.259439 + 0.965759i \(0.416462\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −50.4064 −2.59951
\(377\) 7.92148 0.407977
\(378\) 0 0
\(379\) 4.19177 0.215317 0.107658 0.994188i \(-0.465665\pi\)
0.107658 + 0.994188i \(0.465665\pi\)
\(380\) −7.23130 −0.370958
\(381\) 0 0
\(382\) −42.1463 −2.15639
\(383\) −19.2440 −0.983322 −0.491661 0.870787i \(-0.663610\pi\)
−0.491661 + 0.870787i \(0.663610\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −56.3042 −2.86581
\(387\) 0 0
\(388\) 7.20473 0.365765
\(389\) 28.4224 1.44107 0.720537 0.693417i \(-0.243895\pi\)
0.720537 + 0.693417i \(0.243895\pi\)
\(390\) 0 0
\(391\) −9.28294 −0.469458
\(392\) −0.874273 −0.0441575
\(393\) 0 0
\(394\) 24.1784 1.21809
\(395\) −15.1368 −0.761615
\(396\) 0 0
\(397\) −22.1784 −1.11310 −0.556552 0.830813i \(-0.687876\pi\)
−0.556552 + 0.830813i \(0.687876\pi\)
\(398\) −43.2617 −2.16851
\(399\) 0 0
\(400\) 10.0892 0.504461
\(401\) −22.0759 −1.10242 −0.551208 0.834368i \(-0.685833\pi\)
−0.551208 + 0.834368i \(0.685833\pi\)
\(402\) 0 0
\(403\) −30.7088 −1.52971
\(404\) −16.6688 −0.829302
\(405\) 0 0
\(406\) 8.10557 0.402273
\(407\) 0 0
\(408\) 0 0
\(409\) −24.6713 −1.21992 −0.609959 0.792433i \(-0.708814\pi\)
−0.609959 + 0.792433i \(0.708814\pi\)
\(410\) −14.4291 −0.712602
\(411\) 0 0
\(412\) −24.2939 −1.19688
\(413\) 10.1922 0.501527
\(414\) 0 0
\(415\) −7.33431 −0.360027
\(416\) 76.2673 3.73931
\(417\) 0 0
\(418\) 0 0
\(419\) −17.6535 −0.862428 −0.431214 0.902250i \(-0.641915\pi\)
−0.431214 + 0.902250i \(0.641915\pi\)
\(420\) 0 0
\(421\) 1.52498 0.0743228 0.0371614 0.999309i \(-0.488168\pi\)
0.0371614 + 0.999309i \(0.488168\pi\)
\(422\) −38.9211 −1.89465
\(423\) 0 0
\(424\) −108.182 −5.25379
\(425\) 1.78356 0.0865153
\(426\) 0 0
\(427\) −8.42909 −0.407912
\(428\) 34.5099 1.66810
\(429\) 0 0
\(430\) 9.97370 0.480974
\(431\) −16.7493 −0.806787 −0.403393 0.915027i \(-0.632169\pi\)
−0.403393 + 0.915027i \(0.632169\pi\)
\(432\) 0 0
\(433\) 7.47502 0.359227 0.179613 0.983737i \(-0.442515\pi\)
0.179613 + 0.983737i \(0.442515\pi\)
\(434\) −31.4224 −1.50832
\(435\) 0 0
\(436\) 51.9899 2.48987
\(437\) −7.70541 −0.368600
\(438\) 0 0
\(439\) −17.4585 −0.833250 −0.416625 0.909078i \(-0.636787\pi\)
−0.416625 + 0.909078i \(0.636787\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 31.4860 1.49763
\(443\) 14.6838 0.697647 0.348824 0.937188i \(-0.386581\pi\)
0.348824 + 0.937188i \(0.386581\pi\)
\(444\) 0 0
\(445\) 3.44872 0.163485
\(446\) 61.4049 2.90761
\(447\) 0 0
\(448\) 25.0949 1.18562
\(449\) 1.30729 0.0616947 0.0308474 0.999524i \(-0.490179\pi\)
0.0308474 + 0.999524i \(0.490179\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 67.2543 3.16338
\(453\) 0 0
\(454\) −6.88448 −0.323105
\(455\) −17.6535 −0.827607
\(456\) 0 0
\(457\) −10.1922 −0.476772 −0.238386 0.971170i \(-0.576618\pi\)
−0.238386 + 0.971170i \(0.576618\pi\)
\(458\) −57.8203 −2.70177
\(459\) 0 0
\(460\) 25.4224 1.18533
\(461\) −4.12180 −0.191971 −0.0959857 0.995383i \(-0.530600\pi\)
−0.0959857 + 0.995383i \(0.530600\pi\)
\(462\) 0 0
\(463\) 32.7623 1.52259 0.761296 0.648404i \(-0.224563\pi\)
0.761296 + 0.648404i \(0.224563\pi\)
\(464\) 11.8787 0.551456
\(465\) 0 0
\(466\) 14.0236 0.649633
\(467\) −37.9144 −1.75447 −0.877235 0.480061i \(-0.840614\pi\)
−0.877235 + 0.480061i \(0.840614\pi\)
\(468\) 0 0
\(469\) 12.2274 0.564608
\(470\) 17.4750 0.806063
\(471\) 0 0
\(472\) 29.3993 1.35321
\(473\) 0 0
\(474\) 0 0
\(475\) 1.48046 0.0679283
\(476\) 22.8582 1.04770
\(477\) 0 0
\(478\) −33.0130 −1.50998
\(479\) −6.46004 −0.295167 −0.147583 0.989050i \(-0.547149\pi\)
−0.147583 + 0.989050i \(0.547149\pi\)
\(480\) 0 0
\(481\) −4.57347 −0.208532
\(482\) 11.2480 0.512333
\(483\) 0 0
\(484\) 0 0
\(485\) −1.47502 −0.0669774
\(486\) 0 0
\(487\) 43.4617 1.96944 0.984718 0.174154i \(-0.0557192\pi\)
0.984718 + 0.174154i \(0.0557192\pi\)
\(488\) −24.3136 −1.10062
\(489\) 0 0
\(490\) 0.303095 0.0136924
\(491\) −5.45369 −0.246122 −0.123061 0.992399i \(-0.539271\pi\)
−0.123061 + 0.992399i \(0.539271\pi\)
\(492\) 0 0
\(493\) 2.09990 0.0945749
\(494\) 26.1353 1.17588
\(495\) 0 0
\(496\) −46.0496 −2.06769
\(497\) −10.1922 −0.457184
\(498\) 0 0
\(499\) 12.4880 0.559039 0.279519 0.960140i \(-0.409825\pi\)
0.279519 + 0.960140i \(0.409825\pi\)
\(500\) −4.88448 −0.218441
\(501\) 0 0
\(502\) −26.4034 −1.17844
\(503\) −20.8536 −0.929817 −0.464909 0.885359i \(-0.653913\pi\)
−0.464909 + 0.885359i \(0.653913\pi\)
\(504\) 0 0
\(505\) 3.41259 0.151858
\(506\) 0 0
\(507\) 0 0
\(508\) 60.1421 2.66837
\(509\) 26.5772 1.17801 0.589007 0.808128i \(-0.299519\pi\)
0.589007 + 0.808128i \(0.299519\pi\)
\(510\) 0 0
\(511\) 9.35951 0.414040
\(512\) −38.3511 −1.69490
\(513\) 0 0
\(514\) 8.30565 0.366347
\(515\) 4.97370 0.219167
\(516\) 0 0
\(517\) 0 0
\(518\) −4.67975 −0.205617
\(519\) 0 0
\(520\) −50.9211 −2.23304
\(521\) 23.0393 1.00937 0.504684 0.863304i \(-0.331609\pi\)
0.504684 + 0.863304i \(0.331609\pi\)
\(522\) 0 0
\(523\) 1.18332 0.0517429 0.0258714 0.999665i \(-0.491764\pi\)
0.0258714 + 0.999665i \(0.491764\pi\)
\(524\) 95.2971 4.16307
\(525\) 0 0
\(526\) 58.6901 2.55901
\(527\) −8.14058 −0.354609
\(528\) 0 0
\(529\) 4.08921 0.177792
\(530\) 37.5049 1.62911
\(531\) 0 0
\(532\) 18.9737 0.822614
\(533\) 36.9996 1.60263
\(534\) 0 0
\(535\) −7.06522 −0.305456
\(536\) 35.2697 1.52342
\(537\) 0 0
\(538\) −41.9123 −1.80697
\(539\) 0 0
\(540\) 0 0
\(541\) 31.6055 1.35883 0.679413 0.733756i \(-0.262235\pi\)
0.679413 + 0.733756i \(0.262235\pi\)
\(542\) 41.0366 1.76267
\(543\) 0 0
\(544\) 20.2177 0.866826
\(545\) −10.6439 −0.455934
\(546\) 0 0
\(547\) 4.97958 0.212911 0.106456 0.994317i \(-0.466050\pi\)
0.106456 + 0.994317i \(0.466050\pi\)
\(548\) 41.8319 1.78697
\(549\) 0 0
\(550\) 0 0
\(551\) 1.74305 0.0742564
\(552\) 0 0
\(553\) 39.7164 1.68891
\(554\) −62.6664 −2.66244
\(555\) 0 0
\(556\) −9.68905 −0.410907
\(557\) −25.1289 −1.06475 −0.532374 0.846510i \(-0.678700\pi\)
−0.532374 + 0.846510i \(0.678700\pi\)
\(558\) 0 0
\(559\) −25.5749 −1.08170
\(560\) −26.4724 −1.11866
\(561\) 0 0
\(562\) 32.1258 1.35515
\(563\) −11.3356 −0.477738 −0.238869 0.971052i \(-0.576777\pi\)
−0.238869 + 0.971052i \(0.576777\pi\)
\(564\) 0 0
\(565\) −13.7690 −0.579265
\(566\) 54.7164 2.29990
\(567\) 0 0
\(568\) −29.3993 −1.23357
\(569\) −11.9593 −0.501359 −0.250680 0.968070i \(-0.580654\pi\)
−0.250680 + 0.968070i \(0.580654\pi\)
\(570\) 0 0
\(571\) 29.8054 1.24732 0.623659 0.781697i \(-0.285645\pi\)
0.623659 + 0.781697i \(0.285645\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 37.8595 1.58022
\(575\) −5.20473 −0.217052
\(576\) 0 0
\(577\) −18.4857 −0.769570 −0.384785 0.923006i \(-0.625724\pi\)
−0.384785 + 0.923006i \(0.625724\pi\)
\(578\) −36.2585 −1.50815
\(579\) 0 0
\(580\) −5.75084 −0.238790
\(581\) 19.2440 0.798375
\(582\) 0 0
\(583\) 0 0
\(584\) 26.9973 1.11716
\(585\) 0 0
\(586\) 37.6008 1.55328
\(587\) 2.68377 0.110771 0.0553856 0.998465i \(-0.482361\pi\)
0.0553856 + 0.998465i \(0.482361\pi\)
\(588\) 0 0
\(589\) −6.75719 −0.278425
\(590\) −10.1922 −0.419607
\(591\) 0 0
\(592\) −6.85818 −0.281870
\(593\) −28.7251 −1.17960 −0.589800 0.807550i \(-0.700793\pi\)
−0.589800 + 0.807550i \(0.700793\pi\)
\(594\) 0 0
\(595\) −4.67975 −0.191851
\(596\) −89.6269 −3.67126
\(597\) 0 0
\(598\) −91.8814 −3.75731
\(599\) 34.1807 1.39659 0.698293 0.715812i \(-0.253943\pi\)
0.698293 + 0.715812i \(0.253943\pi\)
\(600\) 0 0
\(601\) 32.4573 1.32396 0.661980 0.749521i \(-0.269716\pi\)
0.661980 + 0.749521i \(0.269716\pi\)
\(602\) −26.1693 −1.06658
\(603\) 0 0
\(604\) −84.1276 −3.42310
\(605\) 0 0
\(606\) 0 0
\(607\) −5.34473 −0.216936 −0.108468 0.994100i \(-0.534594\pi\)
−0.108468 + 0.994100i \(0.534594\pi\)
\(608\) 16.7819 0.680597
\(609\) 0 0
\(610\) 8.42909 0.341284
\(611\) −44.8101 −1.81282
\(612\) 0 0
\(613\) 30.2056 1.21999 0.609996 0.792405i \(-0.291171\pi\)
0.609996 + 0.792405i \(0.291171\pi\)
\(614\) −27.0130 −1.09015
\(615\) 0 0
\(616\) 0 0
\(617\) −0.973697 −0.0391996 −0.0195998 0.999808i \(-0.506239\pi\)
−0.0195998 + 0.999808i \(0.506239\pi\)
\(618\) 0 0
\(619\) 1.82157 0.0732152 0.0366076 0.999330i \(-0.488345\pi\)
0.0366076 + 0.999330i \(0.488345\pi\)
\(620\) 22.2939 0.895346
\(621\) 0 0
\(622\) 50.2519 2.01492
\(623\) −9.04886 −0.362535
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −39.2884 −1.57028
\(627\) 0 0
\(628\) −102.073 −4.07316
\(629\) −1.21238 −0.0483408
\(630\) 0 0
\(631\) −32.3569 −1.28811 −0.644053 0.764981i \(-0.722748\pi\)
−0.644053 + 0.764981i \(0.722748\pi\)
\(632\) 114.561 4.55700
\(633\) 0 0
\(634\) −31.9541 −1.26906
\(635\) −12.3129 −0.488622
\(636\) 0 0
\(637\) −0.777208 −0.0307941
\(638\) 0 0
\(639\) 0 0
\(640\) −2.42375 −0.0958071
\(641\) 13.7690 0.543842 0.271921 0.962320i \(-0.412341\pi\)
0.271921 + 0.962320i \(0.412341\pi\)
\(642\) 0 0
\(643\) 32.1611 1.26831 0.634154 0.773207i \(-0.281348\pi\)
0.634154 + 0.773207i \(0.281348\pi\)
\(644\) −66.7041 −2.62851
\(645\) 0 0
\(646\) 6.92820 0.272587
\(647\) −19.4813 −0.765889 −0.382945 0.923771i \(-0.625090\pi\)
−0.382945 + 0.923771i \(0.625090\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 17.6535 0.692425
\(651\) 0 0
\(652\) 46.1847 1.80873
\(653\) −0.779658 −0.0305104 −0.0152552 0.999884i \(-0.504856\pi\)
−0.0152552 + 0.999884i \(0.504856\pi\)
\(654\) 0 0
\(655\) −19.5102 −0.762326
\(656\) 55.4831 2.16625
\(657\) 0 0
\(658\) −45.8515 −1.78748
\(659\) −28.1929 −1.09824 −0.549119 0.835744i \(-0.685037\pi\)
−0.549119 + 0.835744i \(0.685037\pi\)
\(660\) 0 0
\(661\) 1.70340 0.0662547 0.0331274 0.999451i \(-0.489453\pi\)
0.0331274 + 0.999451i \(0.489453\pi\)
\(662\) −41.5402 −1.61450
\(663\) 0 0
\(664\) 55.5090 2.15417
\(665\) −3.88448 −0.150634
\(666\) 0 0
\(667\) −6.12788 −0.237273
\(668\) −46.1536 −1.78574
\(669\) 0 0
\(670\) −12.2274 −0.472385
\(671\) 0 0
\(672\) 0 0
\(673\) −11.0044 −0.424190 −0.212095 0.977249i \(-0.568029\pi\)
−0.212095 + 0.977249i \(0.568029\pi\)
\(674\) −17.6535 −0.679986
\(675\) 0 0
\(676\) 157.611 6.06195
\(677\) −21.3908 −0.822115 −0.411058 0.911609i \(-0.634840\pi\)
−0.411058 + 0.911609i \(0.634840\pi\)
\(678\) 0 0
\(679\) 3.87021 0.148525
\(680\) −13.4987 −0.517650
\(681\) 0 0
\(682\) 0 0
\(683\) −34.0959 −1.30464 −0.652321 0.757942i \(-0.726205\pi\)
−0.652321 + 0.757942i \(0.726205\pi\)
\(684\) 0 0
\(685\) −8.56424 −0.327223
\(686\) −48.9867 −1.87032
\(687\) 0 0
\(688\) −38.3511 −1.46212
\(689\) −96.1714 −3.66384
\(690\) 0 0
\(691\) 46.3199 1.76209 0.881045 0.473032i \(-0.156840\pi\)
0.881045 + 0.473032i \(0.156840\pi\)
\(692\) −44.3651 −1.68651
\(693\) 0 0
\(694\) 87.9077 3.33693
\(695\) 1.98364 0.0752437
\(696\) 0 0
\(697\) 9.80823 0.371513
\(698\) −59.7556 −2.26178
\(699\) 0 0
\(700\) 12.8161 0.484401
\(701\) 43.3647 1.63786 0.818931 0.573893i \(-0.194567\pi\)
0.818931 + 0.573893i \(0.194567\pi\)
\(702\) 0 0
\(703\) −1.00635 −0.0379552
\(704\) 0 0
\(705\) 0 0
\(706\) 40.5688 1.52683
\(707\) −8.95407 −0.336752
\(708\) 0 0
\(709\) 19.1784 0.720261 0.360130 0.932902i \(-0.382732\pi\)
0.360130 + 0.932902i \(0.382732\pi\)
\(710\) 10.1922 0.382507
\(711\) 0 0
\(712\) −26.1013 −0.978187
\(713\) 23.7556 0.889655
\(714\) 0 0
\(715\) 0 0
\(716\) 67.2543 2.51341
\(717\) 0 0
\(718\) 25.1521 0.938669
\(719\) 32.2939 1.20436 0.602180 0.798360i \(-0.294299\pi\)
0.602180 + 0.798360i \(0.294299\pi\)
\(720\) 0 0
\(721\) −13.0501 −0.486012
\(722\) −44.1019 −1.64130
\(723\) 0 0
\(724\) −116.535 −4.33099
\(725\) 1.17737 0.0437264
\(726\) 0 0
\(727\) −40.8622 −1.51550 −0.757748 0.652548i \(-0.773700\pi\)
−0.757748 + 0.652548i \(0.773700\pi\)
\(728\) 133.608 4.95185
\(729\) 0 0
\(730\) −9.35951 −0.346411
\(731\) −6.77966 −0.250755
\(732\) 0 0
\(733\) 9.92414 0.366557 0.183278 0.983061i \(-0.441329\pi\)
0.183278 + 0.983061i \(0.441329\pi\)
\(734\) −28.4385 −1.04968
\(735\) 0 0
\(736\) −58.9987 −2.17472
\(737\) 0 0
\(738\) 0 0
\(739\) −33.3725 −1.22763 −0.613814 0.789450i \(-0.710366\pi\)
−0.613814 + 0.789450i \(0.710366\pi\)
\(740\) 3.32025 0.122055
\(741\) 0 0
\(742\) −98.4064 −3.61261
\(743\) 3.80715 0.139671 0.0698354 0.997559i \(-0.477753\pi\)
0.0698354 + 0.997559i \(0.477753\pi\)
\(744\) 0 0
\(745\) 18.3493 0.672266
\(746\) 26.2939 0.962690
\(747\) 0 0
\(748\) 0 0
\(749\) 18.5379 0.677361
\(750\) 0 0
\(751\) 22.5094 0.821378 0.410689 0.911775i \(-0.365288\pi\)
0.410689 + 0.911775i \(0.365288\pi\)
\(752\) −67.1954 −2.45036
\(753\) 0 0
\(754\) 20.7846 0.756931
\(755\) 17.2234 0.626825
\(756\) 0 0
\(757\) −33.6927 −1.22458 −0.612291 0.790632i \(-0.709752\pi\)
−0.612291 + 0.790632i \(0.709752\pi\)
\(758\) 10.9985 0.399483
\(759\) 0 0
\(760\) −11.2047 −0.406438
\(761\) 18.7719 0.680481 0.340241 0.940338i \(-0.389491\pi\)
0.340241 + 0.940338i \(0.389491\pi\)
\(762\) 0 0
\(763\) 27.9278 1.01105
\(764\) −78.4590 −2.83855
\(765\) 0 0
\(766\) −50.4930 −1.82438
\(767\) 26.1353 0.943690
\(768\) 0 0
\(769\) 21.5618 0.777539 0.388770 0.921335i \(-0.372900\pi\)
0.388770 + 0.921335i \(0.372900\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −104.815 −3.77238
\(773\) 23.3832 0.841034 0.420517 0.907285i \(-0.361849\pi\)
0.420517 + 0.907285i \(0.361849\pi\)
\(774\) 0 0
\(775\) −4.56424 −0.163952
\(776\) 11.1636 0.400749
\(777\) 0 0
\(778\) 74.5756 2.67366
\(779\) 8.14143 0.291697
\(780\) 0 0
\(781\) 0 0
\(782\) −24.3569 −0.870999
\(783\) 0 0
\(784\) −1.16547 −0.0416239
\(785\) 20.8974 0.745862
\(786\) 0 0
\(787\) −25.0949 −0.894538 −0.447269 0.894400i \(-0.647603\pi\)
−0.447269 + 0.894400i \(0.647603\pi\)
\(788\) 45.0102 1.60342
\(789\) 0 0
\(790\) −39.7164 −1.41304
\(791\) 36.1274 1.28454
\(792\) 0 0
\(793\) −21.6142 −0.767542
\(794\) −58.1924 −2.06517
\(795\) 0 0
\(796\) −80.5353 −2.85450
\(797\) 12.0763 0.427763 0.213881 0.976860i \(-0.431389\pi\)
0.213881 + 0.976860i \(0.431389\pi\)
\(798\) 0 0
\(799\) −11.8787 −0.420239
\(800\) 11.3356 0.400774
\(801\) 0 0
\(802\) −57.9233 −2.04534
\(803\) 0 0
\(804\) 0 0
\(805\) 13.6563 0.481322
\(806\) −80.5745 −2.83812
\(807\) 0 0
\(808\) −25.8279 −0.908621
\(809\) 9.11192 0.320358 0.160179 0.987088i \(-0.448793\pi\)
0.160179 + 0.987088i \(0.448793\pi\)
\(810\) 0 0
\(811\) −2.98999 −0.104993 −0.0524964 0.998621i \(-0.516718\pi\)
−0.0524964 + 0.998621i \(0.516718\pi\)
\(812\) 15.0892 0.529528
\(813\) 0 0
\(814\) 0 0
\(815\) −9.45539 −0.331208
\(816\) 0 0
\(817\) −5.62753 −0.196882
\(818\) −64.7333 −2.26335
\(819\) 0 0
\(820\) −26.8610 −0.938026
\(821\) 35.2697 1.23092 0.615460 0.788168i \(-0.288970\pi\)
0.615460 + 0.788168i \(0.288970\pi\)
\(822\) 0 0
\(823\) 15.5576 0.542303 0.271151 0.962537i \(-0.412596\pi\)
0.271151 + 0.962537i \(0.412596\pi\)
\(824\) −37.6429 −1.31135
\(825\) 0 0
\(826\) 26.7427 0.930496
\(827\) −10.5293 −0.366140 −0.183070 0.983100i \(-0.558604\pi\)
−0.183070 + 0.983100i \(0.558604\pi\)
\(828\) 0 0
\(829\) 25.6249 0.889989 0.444994 0.895533i \(-0.353206\pi\)
0.444994 + 0.895533i \(0.353206\pi\)
\(830\) −19.2440 −0.667969
\(831\) 0 0
\(832\) 64.3494 2.23091
\(833\) −0.206030 −0.00713852
\(834\) 0 0
\(835\) 9.44902 0.326997
\(836\) 0 0
\(837\) 0 0
\(838\) −46.3197 −1.60009
\(839\) −26.1258 −0.901964 −0.450982 0.892533i \(-0.648926\pi\)
−0.450982 + 0.892533i \(0.648926\pi\)
\(840\) 0 0
\(841\) −27.6138 −0.952200
\(842\) 4.00128 0.137893
\(843\) 0 0
\(844\) −72.4549 −2.49400
\(845\) −32.2676 −1.11004
\(846\) 0 0
\(847\) 0 0
\(848\) −144.215 −4.95235
\(849\) 0 0
\(850\) 4.67975 0.160514
\(851\) 3.53793 0.121279
\(852\) 0 0
\(853\) −2.75490 −0.0943259 −0.0471629 0.998887i \(-0.515018\pi\)
−0.0471629 + 0.998887i \(0.515018\pi\)
\(854\) −22.1165 −0.756811
\(855\) 0 0
\(856\) 53.4724 1.82765
\(857\) 20.3164 0.693997 0.346998 0.937866i \(-0.387201\pi\)
0.346998 + 0.937866i \(0.387201\pi\)
\(858\) 0 0
\(859\) 22.6249 0.771951 0.385975 0.922509i \(-0.373865\pi\)
0.385975 + 0.922509i \(0.373865\pi\)
\(860\) 18.5669 0.633126
\(861\) 0 0
\(862\) −43.9474 −1.49685
\(863\) −43.1088 −1.46744 −0.733721 0.679451i \(-0.762218\pi\)
−0.733721 + 0.679451i \(0.762218\pi\)
\(864\) 0 0
\(865\) 9.08286 0.308826
\(866\) 19.6132 0.666483
\(867\) 0 0
\(868\) −58.4955 −1.98547
\(869\) 0 0
\(870\) 0 0
\(871\) 31.3539 1.06239
\(872\) 80.5572 2.72801
\(873\) 0 0
\(874\) −20.2177 −0.683874
\(875\) −2.62383 −0.0887016
\(876\) 0 0
\(877\) 16.6853 0.563421 0.281711 0.959499i \(-0.409098\pi\)
0.281711 + 0.959499i \(0.409098\pi\)
\(878\) −45.8082 −1.54595
\(879\) 0 0
\(880\) 0 0
\(881\) 43.5116 1.46594 0.732972 0.680259i \(-0.238133\pi\)
0.732972 + 0.680259i \(0.238133\pi\)
\(882\) 0 0
\(883\) −26.9996 −0.908609 −0.454305 0.890846i \(-0.650112\pi\)
−0.454305 + 0.890846i \(0.650112\pi\)
\(884\) 58.6138 1.97140
\(885\) 0 0
\(886\) 38.5277 1.29436
\(887\) −22.9403 −0.770259 −0.385130 0.922863i \(-0.625843\pi\)
−0.385130 + 0.922863i \(0.625843\pi\)
\(888\) 0 0
\(889\) 32.3069 1.08354
\(890\) 9.04886 0.303318
\(891\) 0 0
\(892\) 114.311 3.82740
\(893\) −9.86007 −0.329955
\(894\) 0 0
\(895\) −13.7690 −0.460246
\(896\) 6.35951 0.212456
\(897\) 0 0
\(898\) 3.43010 0.114464
\(899\) −5.37379 −0.179226
\(900\) 0 0
\(901\) −25.4941 −0.849331
\(902\) 0 0
\(903\) 0 0
\(904\) 104.209 3.46594
\(905\) 23.8582 0.793073
\(906\) 0 0
\(907\) 41.7337 1.38575 0.692873 0.721060i \(-0.256345\pi\)
0.692873 + 0.721060i \(0.256345\pi\)
\(908\) −12.8161 −0.425316
\(909\) 0 0
\(910\) −46.3197 −1.53548
\(911\) 38.7271 1.28308 0.641542 0.767088i \(-0.278295\pi\)
0.641542 + 0.767088i \(0.278295\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −26.7427 −0.884569
\(915\) 0 0
\(916\) −107.637 −3.55644
\(917\) 51.1914 1.69049
\(918\) 0 0
\(919\) 2.85196 0.0940775 0.0470388 0.998893i \(-0.485022\pi\)
0.0470388 + 0.998893i \(0.485022\pi\)
\(920\) 39.3915 1.29870
\(921\) 0 0
\(922\) −10.8149 −0.356170
\(923\) −26.1353 −0.860253
\(924\) 0 0
\(925\) −0.679754 −0.0223502
\(926\) 85.9627 2.82491
\(927\) 0 0
\(928\) 13.3462 0.438109
\(929\) 13.2284 0.434009 0.217005 0.976171i \(-0.430371\pi\)
0.217005 + 0.976171i \(0.430371\pi\)
\(930\) 0 0
\(931\) −0.171018 −0.00560488
\(932\) 26.1062 0.855138
\(933\) 0 0
\(934\) −99.4810 −3.25512
\(935\) 0 0
\(936\) 0 0
\(937\) −1.68054 −0.0549010 −0.0274505 0.999623i \(-0.508739\pi\)
−0.0274505 + 0.999623i \(0.508739\pi\)
\(938\) 32.0825 1.04753
\(939\) 0 0
\(940\) 32.5313 1.06105
\(941\) −14.6851 −0.478721 −0.239361 0.970931i \(-0.576938\pi\)
−0.239361 + 0.970931i \(0.576938\pi\)
\(942\) 0 0
\(943\) −28.6221 −0.932064
\(944\) 39.1914 1.27557
\(945\) 0 0
\(946\) 0 0
\(947\) −17.6535 −0.573660 −0.286830 0.957981i \(-0.592601\pi\)
−0.286830 + 0.957981i \(0.592601\pi\)
\(948\) 0 0
\(949\) 24.0000 0.779073
\(950\) 3.88448 0.126029
\(951\) 0 0
\(952\) 35.4182 1.14791
\(953\) 21.7678 0.705130 0.352565 0.935787i \(-0.385310\pi\)
0.352565 + 0.935787i \(0.385310\pi\)
\(954\) 0 0
\(955\) 16.0629 0.519784
\(956\) −61.4564 −1.98764
\(957\) 0 0
\(958\) −16.9500 −0.547631
\(959\) 22.4711 0.725630
\(960\) 0 0
\(961\) −10.1677 −0.327991
\(962\) −12.0000 −0.386896
\(963\) 0 0
\(964\) 20.9391 0.674404
\(965\) 21.4588 0.690783
\(966\) 0 0
\(967\) 14.0684 0.452409 0.226204 0.974080i \(-0.427368\pi\)
0.226204 + 0.974080i \(0.427368\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −3.87021 −0.124265
\(971\) 14.7324 0.472784 0.236392 0.971658i \(-0.424035\pi\)
0.236392 + 0.971658i \(0.424035\pi\)
\(972\) 0 0
\(973\) −5.20473 −0.166856
\(974\) 114.036 3.65395
\(975\) 0 0
\(976\) −32.4117 −1.03747
\(977\) −13.1418 −0.420444 −0.210222 0.977654i \(-0.567419\pi\)
−0.210222 + 0.977654i \(0.567419\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.564237 0.0180239
\(981\) 0 0
\(982\) −14.3096 −0.456636
\(983\) −18.4157 −0.587371 −0.293686 0.955902i \(-0.594882\pi\)
−0.293686 + 0.955902i \(0.594882\pi\)
\(984\) 0 0
\(985\) −9.21494 −0.293612
\(986\) 5.50979 0.175468
\(987\) 0 0
\(988\) 48.6531 1.54786
\(989\) 19.7842 0.629101
\(990\) 0 0
\(991\) 44.3591 1.40911 0.704557 0.709647i \(-0.251146\pi\)
0.704557 + 0.709647i \(0.251146\pi\)
\(992\) −51.7383 −1.64269
\(993\) 0 0
\(994\) −26.7427 −0.848226
\(995\) 16.4880 0.522704
\(996\) 0 0
\(997\) −50.4930 −1.59913 −0.799564 0.600581i \(-0.794936\pi\)
−0.799564 + 0.600581i \(0.794936\pi\)
\(998\) 32.7663 1.03720
\(999\) 0 0
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 5445.2.a.bx.1.6 6
3.2 odd 2 605.2.a.m.1.1 6
11.10 odd 2 inner 5445.2.a.bx.1.1 6
12.11 even 2 9680.2.a.cw.1.3 6
15.14 odd 2 3025.2.a.bg.1.6 6
33.2 even 10 605.2.g.q.81.1 24
33.5 odd 10 605.2.g.q.366.6 24
33.8 even 10 605.2.g.q.251.6 24
33.14 odd 10 605.2.g.q.251.1 24
33.17 even 10 605.2.g.q.366.1 24
33.20 odd 10 605.2.g.q.81.6 24
33.26 odd 10 605.2.g.q.511.1 24
33.29 even 10 605.2.g.q.511.6 24
33.32 even 2 605.2.a.m.1.6 yes 6
132.131 odd 2 9680.2.a.cw.1.4 6
165.164 even 2 3025.2.a.bg.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.m.1.1 6 3.2 odd 2
605.2.a.m.1.6 yes 6 33.32 even 2
605.2.g.q.81.1 24 33.2 even 10
605.2.g.q.81.6 24 33.20 odd 10
605.2.g.q.251.1 24 33.14 odd 10
605.2.g.q.251.6 24 33.8 even 10
605.2.g.q.366.1 24 33.17 even 10
605.2.g.q.366.6 24 33.5 odd 10
605.2.g.q.511.1 24 33.26 odd 10
605.2.g.q.511.6 24 33.29 even 10
3025.2.a.bg.1.1 6 165.164 even 2
3025.2.a.bg.1.6 6 15.14 odd 2
5445.2.a.bx.1.1 6 11.10 odd 2 inner
5445.2.a.bx.1.6 6 1.1 even 1 trivial
9680.2.a.cw.1.3 6 12.11 even 2
9680.2.a.cw.1.4 6 132.131 odd 2