Properties

Label 7360.2.a.ca.1.2
Level $7360$
Weight $2$
Character 7360.1
Self dual yes
Analytic conductor $58.770$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7360 = 2^{6} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7360.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(58.7698958877\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.621.1
Defining polynomial: \(x^{3} - 6 x - 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.523976\) of defining polynomial
Character \(\chi\) \(=\) 7360.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.523976 q^{3} +1.00000 q^{5} -0.476024 q^{7} -2.72545 q^{9} +O(q^{10})\) \(q-0.523976 q^{3} +1.00000 q^{5} -0.476024 q^{7} -2.72545 q^{9} -1.67750 q^{11} -2.67750 q^{13} -0.523976 q^{15} +1.67750 q^{17} +7.92692 q^{19} +0.249425 q^{21} -1.00000 q^{23} +1.00000 q^{25} +3.00000 q^{27} +2.20147 q^{29} -6.77340 q^{31} +0.878968 q^{33} -0.476024 q^{35} -4.00000 q^{37} +1.40294 q^{39} +5.97487 q^{41} -0.402945 q^{43} -2.72545 q^{45} -1.79853 q^{47} -6.77340 q^{49} -0.878968 q^{51} +10.8059 q^{53} -1.67750 q^{55} -4.15352 q^{57} +9.45090 q^{59} -6.32250 q^{61} +1.29738 q^{63} -2.67750 q^{65} +14.7100 q^{67} +0.523976 q^{69} -9.97487 q^{71} -6.10557 q^{73} -0.523976 q^{75} +0.798528 q^{77} +6.60442 q^{81} +4.49885 q^{83} +1.67750 q^{85} -1.15352 q^{87} -3.59706 q^{89} +1.27455 q^{91} +3.54910 q^{93} +7.92692 q^{95} -6.08044 q^{97} +4.57193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{5} - 3 q^{7} + 3 q^{9} + O(q^{10}) \) \( 3 q + 3 q^{5} - 3 q^{7} + 3 q^{9} + 3 q^{11} - 3 q^{17} + 3 q^{19} - 12 q^{21} - 3 q^{23} + 3 q^{25} + 9 q^{27} - 3 q^{29} - 6 q^{31} - 15 q^{33} - 3 q^{35} - 12 q^{37} - 15 q^{39} - 6 q^{41} + 18 q^{43} + 3 q^{45} - 15 q^{47} - 6 q^{49} + 15 q^{51} - 6 q^{53} + 3 q^{55} - 6 q^{57} + 6 q^{59} - 27 q^{61} - 12 q^{63} + 12 q^{67} - 6 q^{71} - 15 q^{73} + 12 q^{77} - 9 q^{81} - 12 q^{83} - 3 q^{85} + 3 q^{87} - 30 q^{89} + 15 q^{91} + 33 q^{93} + 3 q^{95} + 9 q^{97} + 9 q^{99} + O(q^{100}) \)

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
\(3\) −0.523976 −0.302518 −0.151259 0.988494i \(-0.548333\pi\)
−0.151259 + 0.988494i \(0.548333\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −0.476024 −0.179920 −0.0899600 0.995945i \(-0.528674\pi\)
−0.0899600 + 0.995945i \(0.528674\pi\)
\(8\) 0 0
\(9\) −2.72545 −0.908483
\(10\) 0 0
\(11\) −1.67750 −0.505784 −0.252892 0.967495i \(-0.581382\pi\)
−0.252892 + 0.967495i \(0.581382\pi\)
\(12\) 0 0
\(13\) −2.67750 −0.742604 −0.371302 0.928512i \(-0.621089\pi\)
−0.371302 + 0.928512i \(0.621089\pi\)
\(14\) 0 0
\(15\) −0.523976 −0.135290
\(16\) 0 0
\(17\) 1.67750 0.406853 0.203426 0.979090i \(-0.434792\pi\)
0.203426 + 0.979090i \(0.434792\pi\)
\(18\) 0 0
\(19\) 7.92692 1.81856 0.909280 0.416184i \(-0.136633\pi\)
0.909280 + 0.416184i \(0.136633\pi\)
\(20\) 0 0
\(21\) 0.249425 0.0544290
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 3.00000 0.577350
\(28\) 0 0
\(29\) 2.20147 0.408803 0.204402 0.978887i \(-0.434475\pi\)
0.204402 + 0.978887i \(0.434475\pi\)
\(30\) 0 0
\(31\) −6.77340 −1.21654 −0.608269 0.793731i \(-0.708136\pi\)
−0.608269 + 0.793731i \(0.708136\pi\)
\(32\) 0 0
\(33\) 0.878968 0.153009
\(34\) 0 0
\(35\) −0.476024 −0.0804627
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 1.40294 0.224651
\(40\) 0 0
\(41\) 5.97487 0.933119 0.466559 0.884490i \(-0.345493\pi\)
0.466559 + 0.884490i \(0.345493\pi\)
\(42\) 0 0
\(43\) −0.402945 −0.0614485 −0.0307242 0.999528i \(-0.509781\pi\)
−0.0307242 + 0.999528i \(0.509781\pi\)
\(44\) 0 0
\(45\) −2.72545 −0.406286
\(46\) 0 0
\(47\) −1.79853 −0.262342 −0.131171 0.991360i \(-0.541874\pi\)
−0.131171 + 0.991360i \(0.541874\pi\)
\(48\) 0 0
\(49\) −6.77340 −0.967629
\(50\) 0 0
\(51\) −0.878968 −0.123080
\(52\) 0 0
\(53\) 10.8059 1.48430 0.742152 0.670232i \(-0.233805\pi\)
0.742152 + 0.670232i \(0.233805\pi\)
\(54\) 0 0
\(55\) −1.67750 −0.226194
\(56\) 0 0
\(57\) −4.15352 −0.550147
\(58\) 0 0
\(59\) 9.45090 1.23040 0.615201 0.788370i \(-0.289075\pi\)
0.615201 + 0.788370i \(0.289075\pi\)
\(60\) 0 0
\(61\) −6.32250 −0.809514 −0.404757 0.914424i \(-0.632644\pi\)
−0.404757 + 0.914424i \(0.632644\pi\)
\(62\) 0 0
\(63\) 1.29738 0.163454
\(64\) 0 0
\(65\) −2.67750 −0.332102
\(66\) 0 0
\(67\) 14.7100 1.79711 0.898555 0.438860i \(-0.144618\pi\)
0.898555 + 0.438860i \(0.144618\pi\)
\(68\) 0 0
\(69\) 0.523976 0.0630793
\(70\) 0 0
\(71\) −9.97487 −1.18380 −0.591900 0.806012i \(-0.701622\pi\)
−0.591900 + 0.806012i \(0.701622\pi\)
\(72\) 0 0
\(73\) −6.10557 −0.714603 −0.357301 0.933989i \(-0.616303\pi\)
−0.357301 + 0.933989i \(0.616303\pi\)
\(74\) 0 0
\(75\) −0.523976 −0.0605036
\(76\) 0 0
\(77\) 0.798528 0.0910007
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 6.60442 0.733824
\(82\) 0 0
\(83\) 4.49885 0.493813 0.246906 0.969039i \(-0.420586\pi\)
0.246906 + 0.969039i \(0.420586\pi\)
\(84\) 0 0
\(85\) 1.67750 0.181950
\(86\) 0 0
\(87\) −1.15352 −0.123670
\(88\) 0 0
\(89\) −3.59706 −0.381287 −0.190644 0.981659i \(-0.561057\pi\)
−0.190644 + 0.981659i \(0.561057\pi\)
\(90\) 0 0
\(91\) 1.27455 0.133609
\(92\) 0 0
\(93\) 3.54910 0.368025
\(94\) 0 0
\(95\) 7.92692 0.813285
\(96\) 0 0
\(97\) −6.08044 −0.617375 −0.308688 0.951163i \(-0.599890\pi\)
−0.308688 + 0.951163i \(0.599890\pi\)
\(98\) 0 0
\(99\) 4.57193 0.459496
\(100\) 0 0
\(101\) −11.4509 −1.13941 −0.569703 0.821850i \(-0.692942\pi\)
−0.569703 + 0.821850i \(0.692942\pi\)
\(102\) 0 0
\(103\) 2.32250 0.228843 0.114422 0.993432i \(-0.463499\pi\)
0.114422 + 0.993432i \(0.463499\pi\)
\(104\) 0 0
\(105\) 0.249425 0.0243414
\(106\) 0 0
\(107\) −7.85384 −0.759260 −0.379630 0.925138i \(-0.623949\pi\)
−0.379630 + 0.925138i \(0.623949\pi\)
\(108\) 0 0
\(109\) −13.9269 −1.33396 −0.666979 0.745077i \(-0.732413\pi\)
−0.666979 + 0.745077i \(0.732413\pi\)
\(110\) 0 0
\(111\) 2.09591 0.198935
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 7.29738 0.674643
\(118\) 0 0
\(119\) −0.798528 −0.0732009
\(120\) 0 0
\(121\) −8.18601 −0.744182
\(122\) 0 0
\(123\) −3.13069 −0.282285
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 11.1033 0.985256 0.492628 0.870240i \(-0.336036\pi\)
0.492628 + 0.870240i \(0.336036\pi\)
\(128\) 0 0
\(129\) 0.211133 0.0185893
\(130\) 0 0
\(131\) 7.65237 0.668591 0.334295 0.942468i \(-0.391502\pi\)
0.334295 + 0.942468i \(0.391502\pi\)
\(132\) 0 0
\(133\) −3.77340 −0.327195
\(134\) 0 0
\(135\) 3.00000 0.258199
\(136\) 0 0
\(137\) −21.3778 −1.82643 −0.913215 0.407478i \(-0.866408\pi\)
−0.913215 + 0.407478i \(0.866408\pi\)
\(138\) 0 0
\(139\) −8.60442 −0.729817 −0.364909 0.931043i \(-0.618900\pi\)
−0.364909 + 0.931043i \(0.618900\pi\)
\(140\) 0 0
\(141\) 0.942386 0.0793632
\(142\) 0 0
\(143\) 4.49149 0.375597
\(144\) 0 0
\(145\) 2.20147 0.182822
\(146\) 0 0
\(147\) 3.54910 0.292725
\(148\) 0 0
\(149\) −4.97487 −0.407558 −0.203779 0.979017i \(-0.565322\pi\)
−0.203779 + 0.979017i \(0.565322\pi\)
\(150\) 0 0
\(151\) 0.926921 0.0754318 0.0377159 0.999289i \(-0.487992\pi\)
0.0377159 + 0.999289i \(0.487992\pi\)
\(152\) 0 0
\(153\) −4.57193 −0.369619
\(154\) 0 0
\(155\) −6.77340 −0.544053
\(156\) 0 0
\(157\) −22.3527 −1.78394 −0.891970 0.452096i \(-0.850677\pi\)
−0.891970 + 0.452096i \(0.850677\pi\)
\(158\) 0 0
\(159\) −5.66203 −0.449028
\(160\) 0 0
\(161\) 0.476024 0.0375159
\(162\) 0 0
\(163\) −7.93658 −0.621641 −0.310821 0.950469i \(-0.600604\pi\)
−0.310821 + 0.950469i \(0.600604\pi\)
\(164\) 0 0
\(165\) 0.878968 0.0684276
\(166\) 0 0
\(167\) −12.8059 −0.990949 −0.495475 0.868622i \(-0.665006\pi\)
−0.495475 + 0.868622i \(0.665006\pi\)
\(168\) 0 0
\(169\) −5.83102 −0.448540
\(170\) 0 0
\(171\) −21.6044 −1.65213
\(172\) 0 0
\(173\) 24.6752 1.87602 0.938010 0.346608i \(-0.112666\pi\)
0.938010 + 0.346608i \(0.112666\pi\)
\(174\) 0 0
\(175\) −0.476024 −0.0359840
\(176\) 0 0
\(177\) −4.95205 −0.372219
\(178\) 0 0
\(179\) −13.1033 −0.979384 −0.489692 0.871895i \(-0.662891\pi\)
−0.489692 + 0.871895i \(0.662891\pi\)
\(180\) 0 0
\(181\) −9.52398 −0.707912 −0.353956 0.935262i \(-0.615164\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(182\) 0 0
\(183\) 3.31284 0.244892
\(184\) 0 0
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) −2.81399 −0.205780
\(188\) 0 0
\(189\) −1.42807 −0.103877
\(190\) 0 0
\(191\) −5.85384 −0.423569 −0.211785 0.977316i \(-0.567928\pi\)
−0.211785 + 0.977316i \(0.567928\pi\)
\(192\) 0 0
\(193\) 4.41261 0.317626 0.158813 0.987309i \(-0.449233\pi\)
0.158813 + 0.987309i \(0.449233\pi\)
\(194\) 0 0
\(195\) 1.40294 0.100467
\(196\) 0 0
\(197\) −11.4258 −0.814053 −0.407026 0.913416i \(-0.633434\pi\)
−0.407026 + 0.913416i \(0.633434\pi\)
\(198\) 0 0
\(199\) 0.307039 0.0217654 0.0108827 0.999941i \(-0.496536\pi\)
0.0108827 + 0.999941i \(0.496536\pi\)
\(200\) 0 0
\(201\) −7.70768 −0.543658
\(202\) 0 0
\(203\) −1.04795 −0.0735519
\(204\) 0 0
\(205\) 5.97487 0.417303
\(206\) 0 0
\(207\) 2.72545 0.189432
\(208\) 0 0
\(209\) −13.2974 −0.919799
\(210\) 0 0
\(211\) 17.3047 1.19131 0.595654 0.803241i \(-0.296893\pi\)
0.595654 + 0.803241i \(0.296893\pi\)
\(212\) 0 0
\(213\) 5.22660 0.358121
\(214\) 0 0
\(215\) −0.402945 −0.0274806
\(216\) 0 0
\(217\) 3.22430 0.218880
\(218\) 0 0
\(219\) 3.19917 0.216180
\(220\) 0 0
\(221\) −4.49149 −0.302130
\(222\) 0 0
\(223\) 1.90409 0.127508 0.0637538 0.997966i \(-0.479693\pi\)
0.0637538 + 0.997966i \(0.479693\pi\)
\(224\) 0 0
\(225\) −2.72545 −0.181697
\(226\) 0 0
\(227\) 17.3550 1.15189 0.575946 0.817488i \(-0.304634\pi\)
0.575946 + 0.817488i \(0.304634\pi\)
\(228\) 0 0
\(229\) 6.19181 0.409166 0.204583 0.978849i \(-0.434416\pi\)
0.204583 + 0.978849i \(0.434416\pi\)
\(230\) 0 0
\(231\) −0.418410 −0.0275293
\(232\) 0 0
\(233\) −15.7985 −1.03500 −0.517498 0.855684i \(-0.673137\pi\)
−0.517498 + 0.855684i \(0.673137\pi\)
\(234\) 0 0
\(235\) −1.79853 −0.117323
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.34763 −0.410594 −0.205297 0.978700i \(-0.565816\pi\)
−0.205297 + 0.978700i \(0.565816\pi\)
\(240\) 0 0
\(241\) 5.69296 0.366716 0.183358 0.983046i \(-0.441303\pi\)
0.183358 + 0.983046i \(0.441303\pi\)
\(242\) 0 0
\(243\) −12.4606 −0.799345
\(244\) 0 0
\(245\) −6.77340 −0.432737
\(246\) 0 0
\(247\) −21.2243 −1.35047
\(248\) 0 0
\(249\) −2.35729 −0.149387
\(250\) 0 0
\(251\) −28.9246 −1.82571 −0.912853 0.408288i \(-0.866126\pi\)
−0.912853 + 0.408288i \(0.866126\pi\)
\(252\) 0 0
\(253\) 1.67750 0.105463
\(254\) 0 0
\(255\) −0.878968 −0.0550431
\(256\) 0 0
\(257\) −14.5085 −0.905016 −0.452508 0.891760i \(-0.649471\pi\)
−0.452508 + 0.891760i \(0.649471\pi\)
\(258\) 0 0
\(259\) 1.90409 0.118315
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 15.7734 0.972630 0.486315 0.873784i \(-0.338341\pi\)
0.486315 + 0.873784i \(0.338341\pi\)
\(264\) 0 0
\(265\) 10.8059 0.663801
\(266\) 0 0
\(267\) 1.88477 0.115346
\(268\) 0 0
\(269\) 6.20147 0.378110 0.189055 0.981966i \(-0.439457\pi\)
0.189055 + 0.981966i \(0.439457\pi\)
\(270\) 0 0
\(271\) 25.5696 1.55324 0.776622 0.629967i \(-0.216931\pi\)
0.776622 + 0.629967i \(0.216931\pi\)
\(272\) 0 0
\(273\) −0.667835 −0.0404192
\(274\) 0 0
\(275\) −1.67750 −0.101157
\(276\) 0 0
\(277\) −7.03829 −0.422890 −0.211445 0.977390i \(-0.567817\pi\)
−0.211445 + 0.977390i \(0.567817\pi\)
\(278\) 0 0
\(279\) 18.4606 1.10520
\(280\) 0 0
\(281\) 29.0627 1.73373 0.866867 0.498540i \(-0.166130\pi\)
0.866867 + 0.498540i \(0.166130\pi\)
\(282\) 0 0
\(283\) −18.6141 −1.10649 −0.553246 0.833018i \(-0.686611\pi\)
−0.553246 + 0.833018i \(0.686611\pi\)
\(284\) 0 0
\(285\) −4.15352 −0.246033
\(286\) 0 0
\(287\) −2.84418 −0.167887
\(288\) 0 0
\(289\) −14.1860 −0.834471
\(290\) 0 0
\(291\) 3.18601 0.186767
\(292\) 0 0
\(293\) −23.4006 −1.36708 −0.683540 0.729913i \(-0.739561\pi\)
−0.683540 + 0.729913i \(0.739561\pi\)
\(294\) 0 0
\(295\) 9.45090 0.550253
\(296\) 0 0
\(297\) −5.03249 −0.292015
\(298\) 0 0
\(299\) 2.67750 0.154844
\(300\) 0 0
\(301\) 0.191811 0.0110558
\(302\) 0 0
\(303\) 6.00000 0.344691
\(304\) 0 0
\(305\) −6.32250 −0.362026
\(306\) 0 0
\(307\) −1.53134 −0.0873981 −0.0436990 0.999045i \(-0.513914\pi\)
−0.0436990 + 0.999045i \(0.513914\pi\)
\(308\) 0 0
\(309\) −1.21694 −0.0692291
\(310\) 0 0
\(311\) 7.55646 0.428488 0.214244 0.976780i \(-0.431271\pi\)
0.214244 + 0.976780i \(0.431271\pi\)
\(312\) 0 0
\(313\) −2.32987 −0.131692 −0.0658459 0.997830i \(-0.520975\pi\)
−0.0658459 + 0.997830i \(0.520975\pi\)
\(314\) 0 0
\(315\) 1.29738 0.0730990
\(316\) 0 0
\(317\) 15.3778 0.863704 0.431852 0.901944i \(-0.357860\pi\)
0.431852 + 0.901944i \(0.357860\pi\)
\(318\) 0 0
\(319\) −3.69296 −0.206766
\(320\) 0 0
\(321\) 4.11523 0.229690
\(322\) 0 0
\(323\) 13.2974 0.739886
\(324\) 0 0
\(325\) −2.67750 −0.148521
\(326\) 0 0
\(327\) 7.29738 0.403546
\(328\) 0 0
\(329\) 0.856142 0.0472006
\(330\) 0 0
\(331\) 22.9115 1.25933 0.629664 0.776868i \(-0.283193\pi\)
0.629664 + 0.776868i \(0.283193\pi\)
\(332\) 0 0
\(333\) 10.9018 0.597415
\(334\) 0 0
\(335\) 14.7100 0.803692
\(336\) 0 0
\(337\) 26.5410 1.44578 0.722890 0.690963i \(-0.242813\pi\)
0.722890 + 0.690963i \(0.242813\pi\)
\(338\) 0 0
\(339\) 5.23976 0.284585
\(340\) 0 0
\(341\) 11.3624 0.615306
\(342\) 0 0
\(343\) 6.55646 0.354016
\(344\) 0 0
\(345\) 0.523976 0.0282099
\(346\) 0 0
\(347\) −3.27455 −0.175787 −0.0878936 0.996130i \(-0.528014\pi\)
−0.0878936 + 0.996130i \(0.528014\pi\)
\(348\) 0 0
\(349\) −32.0553 −1.71588 −0.857941 0.513749i \(-0.828256\pi\)
−0.857941 + 0.513749i \(0.828256\pi\)
\(350\) 0 0
\(351\) −8.03249 −0.428742
\(352\) 0 0
\(353\) 11.1535 0.593642 0.296821 0.954933i \(-0.404074\pi\)
0.296821 + 0.954933i \(0.404074\pi\)
\(354\) 0 0
\(355\) −9.97487 −0.529411
\(356\) 0 0
\(357\) 0.418410 0.0221446
\(358\) 0 0
\(359\) −22.4029 −1.18238 −0.591191 0.806532i \(-0.701342\pi\)
−0.591191 + 0.806532i \(0.701342\pi\)
\(360\) 0 0
\(361\) 43.8361 2.30716
\(362\) 0 0
\(363\) 4.28927 0.225129
\(364\) 0 0
\(365\) −6.10557 −0.319580
\(366\) 0 0
\(367\) −14.2877 −0.745813 −0.372906 0.927869i \(-0.621639\pi\)
−0.372906 + 0.927869i \(0.621639\pi\)
\(368\) 0 0
\(369\) −16.2842 −0.847722
\(370\) 0 0
\(371\) −5.14386 −0.267056
\(372\) 0 0
\(373\) 1.23976 0.0641925 0.0320963 0.999485i \(-0.489782\pi\)
0.0320963 + 0.999485i \(0.489782\pi\)
\(374\) 0 0
\(375\) −0.523976 −0.0270580
\(376\) 0 0
\(377\) −5.89443 −0.303579
\(378\) 0 0
\(379\) 4.38748 0.225370 0.112685 0.993631i \(-0.464055\pi\)
0.112685 + 0.993631i \(0.464055\pi\)
\(380\) 0 0
\(381\) −5.81785 −0.298057
\(382\) 0 0
\(383\) −18.4989 −0.945247 −0.472624 0.881264i \(-0.656693\pi\)
−0.472624 + 0.881264i \(0.656693\pi\)
\(384\) 0 0
\(385\) 0.798528 0.0406967
\(386\) 0 0
\(387\) 1.09821 0.0558249
\(388\) 0 0
\(389\) −21.6775 −1.09909 −0.549546 0.835463i \(-0.685199\pi\)
−0.549546 + 0.835463i \(0.685199\pi\)
\(390\) 0 0
\(391\) −1.67750 −0.0848346
\(392\) 0 0
\(393\) −4.00966 −0.202261
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 20.6849 1.03814 0.519072 0.854731i \(-0.326278\pi\)
0.519072 + 0.854731i \(0.326278\pi\)
\(398\) 0 0
\(399\) 1.97717 0.0989825
\(400\) 0 0
\(401\) −28.5638 −1.42641 −0.713205 0.700956i \(-0.752757\pi\)
−0.713205 + 0.700956i \(0.752757\pi\)
\(402\) 0 0
\(403\) 18.1358 0.903406
\(404\) 0 0
\(405\) 6.60442 0.328176
\(406\) 0 0
\(407\) 6.70998 0.332602
\(408\) 0 0
\(409\) 16.7734 0.829391 0.414696 0.909960i \(-0.363888\pi\)
0.414696 + 0.909960i \(0.363888\pi\)
\(410\) 0 0
\(411\) 11.2015 0.552528
\(412\) 0 0
\(413\) −4.49885 −0.221374
\(414\) 0 0
\(415\) 4.49885 0.220840
\(416\) 0 0
\(417\) 4.50851 0.220783
\(418\) 0 0
\(419\) −4.59476 −0.224469 −0.112234 0.993682i \(-0.535801\pi\)
−0.112234 + 0.993682i \(0.535801\pi\)
\(420\) 0 0
\(421\) −31.8310 −1.55135 −0.775674 0.631133i \(-0.782590\pi\)
−0.775674 + 0.631133i \(0.782590\pi\)
\(422\) 0 0
\(423\) 4.90179 0.238333
\(424\) 0 0
\(425\) 1.67750 0.0813705
\(426\) 0 0
\(427\) 3.00966 0.145648
\(428\) 0 0
\(429\) −2.35343 −0.113625
\(430\) 0 0
\(431\) 16.0650 0.773823 0.386911 0.922117i \(-0.373542\pi\)
0.386911 + 0.922117i \(0.373542\pi\)
\(432\) 0 0
\(433\) −7.68486 −0.369311 −0.184655 0.982803i \(-0.559117\pi\)
−0.184655 + 0.982803i \(0.559117\pi\)
\(434\) 0 0
\(435\) −1.15352 −0.0553070
\(436\) 0 0
\(437\) −7.92692 −0.379196
\(438\) 0 0
\(439\) −15.9822 −0.762790 −0.381395 0.924412i \(-0.624556\pi\)
−0.381395 + 0.924412i \(0.624556\pi\)
\(440\) 0 0
\(441\) 18.4606 0.879074
\(442\) 0 0
\(443\) −3.57929 −0.170057 −0.0850286 0.996379i \(-0.527098\pi\)
−0.0850286 + 0.996379i \(0.527098\pi\)
\(444\) 0 0
\(445\) −3.59706 −0.170517
\(446\) 0 0
\(447\) 2.60672 0.123293
\(448\) 0 0
\(449\) −28.5217 −1.34602 −0.673011 0.739633i \(-0.734999\pi\)
−0.673011 + 0.739633i \(0.734999\pi\)
\(450\) 0 0
\(451\) −10.0228 −0.471956
\(452\) 0 0
\(453\) −0.485685 −0.0228195
\(454\) 0 0
\(455\) 1.27455 0.0597519
\(456\) 0 0
\(457\) −4.49885 −0.210447 −0.105224 0.994449i \(-0.533556\pi\)
−0.105224 + 0.994449i \(0.533556\pi\)
\(458\) 0 0
\(459\) 5.03249 0.234896
\(460\) 0 0
\(461\) −2.29738 −0.107000 −0.0534998 0.998568i \(-0.517038\pi\)
−0.0534998 + 0.998568i \(0.517038\pi\)
\(462\) 0 0
\(463\) 33.4966 1.55672 0.778358 0.627820i \(-0.216053\pi\)
0.778358 + 0.627820i \(0.216053\pi\)
\(464\) 0 0
\(465\) 3.54910 0.164586
\(466\) 0 0
\(467\) −5.23976 −0.242467 −0.121234 0.992624i \(-0.538685\pi\)
−0.121234 + 0.992624i \(0.538685\pi\)
\(468\) 0 0
\(469\) −7.00230 −0.323336
\(470\) 0 0
\(471\) 11.7123 0.539674
\(472\) 0 0
\(473\) 0.675938 0.0310797
\(474\) 0 0
\(475\) 7.92692 0.363712
\(476\) 0 0
\(477\) −29.4509 −1.34846
\(478\) 0 0
\(479\) 2.40294 0.109793 0.0548967 0.998492i \(-0.482517\pi\)
0.0548967 + 0.998492i \(0.482517\pi\)
\(480\) 0 0
\(481\) 10.7100 0.488333
\(482\) 0 0
\(483\) −0.249425 −0.0113492
\(484\) 0 0
\(485\) −6.08044 −0.276099
\(486\) 0 0
\(487\) −25.8944 −1.17339 −0.586694 0.809808i \(-0.699571\pi\)
−0.586694 + 0.809808i \(0.699571\pi\)
\(488\) 0 0
\(489\) 4.15858 0.188058
\(490\) 0 0
\(491\) −0.489189 −0.0220768 −0.0110384 0.999939i \(-0.503514\pi\)
−0.0110384 + 0.999939i \(0.503514\pi\)
\(492\) 0 0
\(493\) 3.69296 0.166323
\(494\) 0 0
\(495\) 4.57193 0.205493
\(496\) 0 0
\(497\) 4.74828 0.212989
\(498\) 0 0
\(499\) −38.4583 −1.72163 −0.860814 0.508920i \(-0.830045\pi\)
−0.860814 + 0.508920i \(0.830045\pi\)
\(500\) 0 0
\(501\) 6.70998 0.299780
\(502\) 0 0
\(503\) −37.8960 −1.68970 −0.844849 0.535004i \(-0.820310\pi\)
−0.844849 + 0.535004i \(0.820310\pi\)
\(504\) 0 0
\(505\) −11.4509 −0.509558
\(506\) 0 0
\(507\) 3.05531 0.135691
\(508\) 0 0
\(509\) −8.70032 −0.385635 −0.192818 0.981235i \(-0.561763\pi\)
−0.192818 + 0.981235i \(0.561763\pi\)
\(510\) 0 0
\(511\) 2.90639 0.128571
\(512\) 0 0
\(513\) 23.7808 1.04995
\(514\) 0 0
\(515\) 2.32250 0.102342
\(516\) 0 0
\(517\) 3.01702 0.132689
\(518\) 0 0
\(519\) −12.9292 −0.567530
\(520\) 0 0
\(521\) 25.1129 1.10022 0.550109 0.835093i \(-0.314586\pi\)
0.550109 + 0.835093i \(0.314586\pi\)
\(522\) 0 0
\(523\) 12.7100 0.555769 0.277884 0.960615i \(-0.410367\pi\)
0.277884 + 0.960615i \(0.410367\pi\)
\(524\) 0 0
\(525\) 0.249425 0.0108858
\(526\) 0 0
\(527\) −11.3624 −0.494952
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −25.7579 −1.11780
\(532\) 0 0
\(533\) −15.9977 −0.692937
\(534\) 0 0
\(535\) −7.85384 −0.339551
\(536\) 0 0
\(537\) 6.86580 0.296281
\(538\) 0 0
\(539\) 11.3624 0.489411
\(540\) 0 0
\(541\) 0.251725 0.0108225 0.00541124 0.999985i \(-0.498278\pi\)
0.00541124 + 0.999985i \(0.498278\pi\)
\(542\) 0 0
\(543\) 4.99034 0.214156
\(544\) 0 0
\(545\) −13.9269 −0.596564
\(546\) 0 0
\(547\) 24.3395 1.04068 0.520342 0.853958i \(-0.325805\pi\)
0.520342 + 0.853958i \(0.325805\pi\)
\(548\) 0 0
\(549\) 17.2317 0.735429
\(550\) 0 0
\(551\) 17.4509 0.743433
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 2.09591 0.0889662
\(556\) 0 0
\(557\) 23.4966 0.995581 0.497790 0.867297i \(-0.334145\pi\)
0.497790 + 0.867297i \(0.334145\pi\)
\(558\) 0 0
\(559\) 1.07888 0.0456319
\(560\) 0 0
\(561\) 1.47447 0.0622520
\(562\) 0 0
\(563\) −19.5159 −0.822496 −0.411248 0.911523i \(-0.634907\pi\)
−0.411248 + 0.911523i \(0.634907\pi\)
\(564\) 0 0
\(565\) −10.0000 −0.420703
\(566\) 0 0
\(567\) −3.14386 −0.132030
\(568\) 0 0
\(569\) −8.51817 −0.357100 −0.178550 0.983931i \(-0.557141\pi\)
−0.178550 + 0.983931i \(0.557141\pi\)
\(570\) 0 0
\(571\) −27.4811 −1.15005 −0.575024 0.818137i \(-0.695007\pi\)
−0.575024 + 0.818137i \(0.695007\pi\)
\(572\) 0 0
\(573\) 3.06728 0.128137
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −26.1512 −1.08869 −0.544345 0.838862i \(-0.683222\pi\)
−0.544345 + 0.838862i \(0.683222\pi\)
\(578\) 0 0
\(579\) −2.31210 −0.0960877
\(580\) 0 0
\(581\) −2.14156 −0.0888468
\(582\) 0 0
\(583\) −18.1268 −0.750737
\(584\) 0 0
\(585\) 7.29738 0.301709
\(586\) 0 0
\(587\) −34.3276 −1.41685 −0.708425 0.705786i \(-0.750594\pi\)
−0.708425 + 0.705786i \(0.750594\pi\)
\(588\) 0 0
\(589\) −53.6922 −2.21235
\(590\) 0 0
\(591\) 5.98683 0.246265
\(592\) 0 0
\(593\) 15.9497 0.654978 0.327489 0.944855i \(-0.393798\pi\)
0.327489 + 0.944855i \(0.393798\pi\)
\(594\) 0 0
\(595\) −0.798528 −0.0327364
\(596\) 0 0
\(597\) −0.160881 −0.00658443
\(598\) 0 0
\(599\) −40.5940 −1.65863 −0.829313 0.558784i \(-0.811268\pi\)
−0.829313 + 0.558784i \(0.811268\pi\)
\(600\) 0 0
\(601\) −29.0302 −1.18417 −0.592083 0.805877i \(-0.701694\pi\)
−0.592083 + 0.805877i \(0.701694\pi\)
\(602\) 0 0
\(603\) −40.0913 −1.63264
\(604\) 0 0
\(605\) −8.18601 −0.332809
\(606\) 0 0
\(607\) −16.9977 −0.689915 −0.344958 0.938618i \(-0.612107\pi\)
−0.344958 + 0.938618i \(0.612107\pi\)
\(608\) 0 0
\(609\) 0.549103 0.0222508
\(610\) 0 0
\(611\) 4.81555 0.194816
\(612\) 0 0
\(613\) −30.3024 −1.22390 −0.611952 0.790895i \(-0.709615\pi\)
−0.611952 + 0.790895i \(0.709615\pi\)
\(614\) 0 0
\(615\) −3.13069 −0.126242
\(616\) 0 0
\(617\) −6.13069 −0.246812 −0.123406 0.992356i \(-0.539382\pi\)
−0.123406 + 0.992356i \(0.539382\pi\)
\(618\) 0 0
\(619\) −33.7305 −1.35574 −0.677872 0.735180i \(-0.737098\pi\)
−0.677872 + 0.735180i \(0.737098\pi\)
\(620\) 0 0
\(621\) −3.00000 −0.120386
\(622\) 0 0
\(623\) 1.71228 0.0686012
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 6.96751 0.278256
\(628\) 0 0
\(629\) −6.70998 −0.267545
\(630\) 0 0
\(631\) −4.85614 −0.193320 −0.0966600 0.995317i \(-0.530816\pi\)
−0.0966600 + 0.995317i \(0.530816\pi\)
\(632\) 0 0
\(633\) −9.06728 −0.360392
\(634\) 0 0
\(635\) 11.1033 0.440620
\(636\) 0 0
\(637\) 18.1358 0.718565
\(638\) 0 0
\(639\) 27.1860 1.07546
\(640\) 0 0
\(641\) 7.78887 0.307642 0.153821 0.988099i \(-0.450842\pi\)
0.153821 + 0.988099i \(0.450842\pi\)
\(642\) 0 0
\(643\) 43.6427 1.72110 0.860550 0.509366i \(-0.170120\pi\)
0.860550 + 0.509366i \(0.170120\pi\)
\(644\) 0 0
\(645\) 0.211133 0.00831337
\(646\) 0 0
\(647\) 15.4606 0.607817 0.303909 0.952701i \(-0.401708\pi\)
0.303909 + 0.952701i \(0.401708\pi\)
\(648\) 0 0
\(649\) −15.8538 −0.622318
\(650\) 0 0
\(651\) −1.68946 −0.0662150
\(652\) 0 0
\(653\) 9.70613 0.379830 0.189915 0.981801i \(-0.439179\pi\)
0.189915 + 0.981801i \(0.439179\pi\)
\(654\) 0 0
\(655\) 7.65237 0.299003
\(656\) 0 0
\(657\) 16.6404 0.649204
\(658\) 0 0
\(659\) 50.7100 1.97538 0.987690 0.156422i \(-0.0499961\pi\)
0.987690 + 0.156422i \(0.0499961\pi\)
\(660\) 0 0
\(661\) −33.0132 −1.28406 −0.642032 0.766678i \(-0.721908\pi\)
−0.642032 + 0.766678i \(0.721908\pi\)
\(662\) 0 0
\(663\) 2.35343 0.0913998
\(664\) 0 0
\(665\) −3.77340 −0.146326
\(666\) 0 0
\(667\) −2.20147 −0.0852413
\(668\) 0 0
\(669\) −0.997701 −0.0385733
\(670\) 0 0
\(671\) 10.6060 0.409439
\(672\) 0 0
\(673\) 19.2494 0.742011 0.371005 0.928631i \(-0.379013\pi\)
0.371005 + 0.928631i \(0.379013\pi\)
\(674\) 0 0
\(675\) 3.00000 0.115470
\(676\) 0 0
\(677\) 25.1941 0.968288 0.484144 0.874988i \(-0.339131\pi\)
0.484144 + 0.874988i \(0.339131\pi\)
\(678\) 0 0
\(679\) 2.89443 0.111078
\(680\) 0 0
\(681\) −9.09361 −0.348468
\(682\) 0 0
\(683\) 9.48339 0.362872 0.181436 0.983403i \(-0.441926\pi\)
0.181436 + 0.983403i \(0.441926\pi\)
\(684\) 0 0
\(685\) −21.3778 −0.816804
\(686\) 0 0
\(687\) −3.24436 −0.123780
\(688\) 0 0
\(689\) −28.9327 −1.10225
\(690\) 0 0
\(691\) −23.8538 −0.907443 −0.453721 0.891144i \(-0.649904\pi\)
−0.453721 + 0.891144i \(0.649904\pi\)
\(692\) 0 0
\(693\) −2.17635 −0.0826726
\(694\) 0 0
\(695\) −8.60442 −0.326384
\(696\) 0 0
\(697\) 10.0228 0.379642
\(698\) 0 0
\(699\) 8.27806 0.313105
\(700\) 0 0
\(701\) −19.8767 −0.750731 −0.375366 0.926877i \(-0.622483\pi\)
−0.375366 + 0.926877i \(0.622483\pi\)
\(702\) 0 0
\(703\) −31.7077 −1.19588
\(704\) 0 0
\(705\) 0.942386 0.0354923
\(706\) 0 0
\(707\) 5.45090 0.205002
\(708\) 0 0
\(709\) 6.72545 0.252580 0.126290 0.991993i \(-0.459693\pi\)
0.126290 + 0.991993i \(0.459693\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.77340 0.253666
\(714\) 0 0
\(715\) 4.49149 0.167972
\(716\) 0 0
\(717\) 3.32601 0.124212
\(718\) 0 0
\(719\) 38.2294 1.42571 0.712857 0.701309i \(-0.247401\pi\)
0.712857 + 0.701309i \(0.247401\pi\)
\(720\) 0 0
\(721\) −1.10557 −0.0411735
\(722\) 0 0
\(723\) −2.98298 −0.110938
\(724\) 0 0
\(725\) 2.20147 0.0817606
\(726\) 0 0
\(727\) 3.72315 0.138084 0.0690420 0.997614i \(-0.478006\pi\)
0.0690420 + 0.997614i \(0.478006\pi\)
\(728\) 0 0
\(729\) −13.2842 −0.492008
\(730\) 0 0
\(731\) −0.675938 −0.0250005
\(732\) 0 0
\(733\) 8.49885 0.313912 0.156956 0.987606i \(-0.449832\pi\)
0.156956 + 0.987606i \(0.449832\pi\)
\(734\) 0 0
\(735\) 3.54910 0.130911
\(736\) 0 0
\(737\) −24.6759 −0.908950
\(738\) 0 0
\(739\) −0.251725 −0.00925984 −0.00462992 0.999989i \(-0.501474\pi\)
−0.00462992 + 0.999989i \(0.501474\pi\)
\(740\) 0 0
\(741\) 11.1210 0.408541
\(742\) 0 0
\(743\) 29.7305 1.09071 0.545353 0.838206i \(-0.316395\pi\)
0.545353 + 0.838206i \(0.316395\pi\)
\(744\) 0 0
\(745\) −4.97487 −0.182265
\(746\) 0 0
\(747\) −12.2614 −0.448621
\(748\) 0 0
\(749\) 3.73861 0.136606
\(750\) 0 0
\(751\) −10.6597 −0.388979 −0.194490 0.980905i \(-0.562305\pi\)
−0.194490 + 0.980905i \(0.562305\pi\)
\(752\) 0 0
\(753\) 15.1558 0.552309
\(754\) 0 0
\(755\) 0.926921 0.0337341
\(756\) 0 0
\(757\) 16.1918 0.588501 0.294251 0.955728i \(-0.404930\pi\)
0.294251 + 0.955728i \(0.404930\pi\)
\(758\) 0 0
\(759\) −0.878968 −0.0319045
\(760\) 0 0
\(761\) −46.9343 −1.70137 −0.850683 0.525679i \(-0.823811\pi\)
−0.850683 + 0.525679i \(0.823811\pi\)
\(762\) 0 0
\(763\) 6.62954 0.240006
\(764\) 0 0
\(765\) −4.57193 −0.165298
\(766\) 0 0
\(767\) −25.3047 −0.913701
\(768\) 0 0
\(769\) −35.9954 −1.29803 −0.649014 0.760777i \(-0.724818\pi\)
−0.649014 + 0.760777i \(0.724818\pi\)
\(770\) 0 0
\(771\) 7.60212 0.273784
\(772\) 0 0
\(773\) 21.8229 0.784916 0.392458 0.919770i \(-0.371625\pi\)
0.392458 + 0.919770i \(0.371625\pi\)
\(774\) 0 0
\(775\) −6.77340 −0.243308
\(776\) 0 0
\(777\) −0.997701 −0.0357923
\(778\) 0 0
\(779\) 47.3624 1.69693
\(780\) 0 0
\(781\) 16.7328 0.598747
\(782\) 0 0
\(783\) 6.60442 0.236023
\(784\) 0 0
\(785\) −22.3527 −0.797802
\(786\) 0 0
\(787\) −7.16318 −0.255340 −0.127670 0.991817i \(-0.540750\pi\)
−0.127670 + 0.991817i \(0.540750\pi\)
\(788\) 0 0
\(789\) −8.26489 −0.294238
\(790\) 0 0
\(791\) 4.76024 0.169255
\(792\) 0 0
\(793\) 16.9285 0.601148
\(794\) 0 0
\(795\) −5.66203 −0.200812
\(796\) 0 0
\(797\) 48.0604 1.70239 0.851193 0.524853i \(-0.175880\pi\)
0.851193 + 0.524853i \(0.175880\pi\)
\(798\) 0 0
\(799\) −3.01702 −0.106735
\(800\) 0 0
\(801\) 9.80359 0.346393
\(802\) 0 0
\(803\) 10.2421 0.361435
\(804\) 0 0
\(805\) 0.476024 0.0167776
\(806\) 0 0
\(807\) −3.24943 −0.114385
\(808\) 0 0
\(809\) 0.0611183 0.00214880 0.00107440 0.999999i \(-0.499658\pi\)
0.00107440 + 0.999999i \(0.499658\pi\)
\(810\) 0 0
\(811\) 25.9092 0.909794 0.454897 0.890544i \(-0.349676\pi\)
0.454897 + 0.890544i \(0.349676\pi\)
\(812\) 0 0
\(813\) −13.3979 −0.469884
\(814\) 0 0
\(815\) −7.93658 −0.278006
\(816\) 0 0
\(817\) −3.19411 −0.111748
\(818\) 0 0
\(819\) −3.47372 −0.121382
\(820\) 0 0
\(821\) 21.0936 0.736172 0.368086 0.929792i \(-0.380013\pi\)
0.368086 + 0.929792i \(0.380013\pi\)
\(822\) 0 0
\(823\) 37.2641 1.29895 0.649473 0.760384i \(-0.274989\pi\)
0.649473 + 0.760384i \(0.274989\pi\)
\(824\) 0 0
\(825\) 0.878968 0.0306017
\(826\) 0 0
\(827\) −4.45320 −0.154853 −0.0774264 0.996998i \(-0.524670\pi\)
−0.0774264 + 0.996998i \(0.524670\pi\)
\(828\) 0 0
\(829\) 38.1300 1.32431 0.662154 0.749368i \(-0.269642\pi\)
0.662154 + 0.749368i \(0.269642\pi\)
\(830\) 0 0
\(831\) 3.68790 0.127932
\(832\) 0 0
\(833\) −11.3624 −0.393682
\(834\) 0 0
\(835\) −12.8059 −0.443166
\(836\) 0 0
\(837\) −20.3202 −0.702369
\(838\) 0 0
\(839\) 7.15858 0.247142 0.123571 0.992336i \(-0.460565\pi\)
0.123571 + 0.992336i \(0.460565\pi\)
\(840\) 0 0
\(841\) −24.1535 −0.832880
\(842\) 0 0
\(843\) −15.2282 −0.524486
\(844\) 0 0
\(845\) −5.83102 −0.200593
\(846\) 0 0
\(847\) 3.89673 0.133893
\(848\) 0 0
\(849\) 9.75334 0.334734
\(850\) 0 0
\(851\) 4.00000 0.137118
\(852\) 0 0
\(853\) 49.6199 1.69895 0.849476 0.527627i \(-0.176918\pi\)
0.849476 + 0.527627i \(0.176918\pi\)
\(854\) 0 0
\(855\) −21.6044 −0.738855
\(856\) 0 0
\(857\) −44.0360 −1.50424 −0.752120 0.659026i \(-0.770969\pi\)
−0.752120 + 0.659026i \(0.770969\pi\)
\(858\) 0 0
\(859\) −49.5062 −1.68913 −0.844565 0.535453i \(-0.820141\pi\)
−0.844565 + 0.535453i \(0.820141\pi\)
\(860\) 0 0
\(861\) 1.49028 0.0507887
\(862\) 0 0
\(863\) −20.7962 −0.707912 −0.353956 0.935262i \(-0.615164\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(864\) 0 0
\(865\) 24.6752 0.838982
\(866\) 0 0
\(867\) 7.43313 0.252442
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −39.3859 −1.33454
\(872\) 0 0
\(873\) 16.5719 0.560875
\(874\) 0 0
\(875\) −0.476024 −0.0160925
\(876\) 0 0
\(877\) 5.42071 0.183044 0.0915222 0.995803i \(-0.470827\pi\)
0.0915222 + 0.995803i \(0.470827\pi\)
\(878\) 0 0
\(879\) 12.2614 0.413566
\(880\) 0 0
\(881\) −45.8036 −1.54316 −0.771581 0.636131i \(-0.780534\pi\)
−0.771581 + 0.636131i \(0.780534\pi\)
\(882\) 0 0
\(883\) 57.1860 1.92446 0.962231 0.272234i \(-0.0877624\pi\)
0.962231 + 0.272234i \(0.0877624\pi\)
\(884\) 0 0
\(885\) −4.95205 −0.166461
\(886\) 0 0
\(887\) 15.5371 0.521686 0.260843 0.965381i \(-0.415999\pi\)
0.260843 + 0.965381i \(0.415999\pi\)
\(888\) 0 0
\(889\) −5.28542 −0.177267
\(890\) 0 0
\(891\) −11.0789 −0.371157
\(892\) 0 0
\(893\) −14.2568 −0.477085
\(894\) 0 0
\(895\) −13.1033 −0.437994
\(896\) 0 0
\(897\) −1.40294 −0.0468430
\(898\) 0 0
\(899\) −14.9115 −0.497325
\(900\) 0 0
\(901\) 18.1268 0.603892
\(902\) 0 0
\(903\) −0.100505 −0.00334458
\(904\) 0 0
\(905\) −9.52398 −0.316588
\(906\) 0 0
\(907\) −32.8515 −1.09082 −0.545409 0.838170i \(-0.683626\pi\)
−0.545409 + 0.838170i \(0.683626\pi\)
\(908\) 0 0
\(909\) 31.2088 1.03513
\(910\) 0 0
\(911\) −8.95205 −0.296595 −0.148297 0.988943i \(-0.547379\pi\)
−0.148297 + 0.988943i \(0.547379\pi\)
\(912\) 0 0
\(913\) −7.54680 −0.249763
\(914\) 0 0
\(915\) 3.31284 0.109519
\(916\) 0 0
\(917\) −3.64271 −0.120293
\(918\) 0 0
\(919\) 49.8229 1.64351 0.821753 0.569844i \(-0.192996\pi\)
0.821753 + 0.569844i \(0.192996\pi\)
\(920\) 0 0
\(921\) 0.802385 0.0264395
\(922\) 0 0
\(923\) 26.7077 0.879094
\(924\) 0 0
\(925\) −4.00000 −0.131519
\(926\) 0 0
\(927\) −6.32987 −0.207900
\(928\) 0 0
\(929\) 25.0723 0.822597 0.411298 0.911501i \(-0.365075\pi\)
0.411298 + 0.911501i \(0.365075\pi\)
\(930\) 0 0
\(931\) −53.6922 −1.75969
\(932\) 0 0
\(933\) −3.95941 −0.129625
\(934\) 0 0
\(935\) −2.81399 −0.0920274
\(936\) 0 0
\(937\) 21.3322 0.696891 0.348446 0.937329i \(-0.386710\pi\)
0.348446 + 0.937329i \(0.386710\pi\)
\(938\) 0 0
\(939\) 1.22079 0.0398391
\(940\) 0 0
\(941\) −3.93428 −0.128254 −0.0641270 0.997942i \(-0.520426\pi\)
−0.0641270 + 0.997942i \(0.520426\pi\)
\(942\) 0 0
\(943\) −5.97487 −0.194569
\(944\) 0 0
\(945\) −1.42807 −0.0464551
\(946\) 0 0
\(947\) 48.6420 1.58065 0.790326 0.612687i \(-0.209911\pi\)
0.790326 + 0.612687i \(0.209911\pi\)
\(948\) 0 0
\(949\) 16.3476 0.530667
\(950\) 0 0
\(951\) −8.05761 −0.261286
\(952\) 0 0
\(953\) −15.5623 −0.504111 −0.252056 0.967713i \(-0.581107\pi\)
−0.252056 + 0.967713i \(0.581107\pi\)
\(954\) 0 0
\(955\) −5.85384 −0.189426
\(956\) 0 0
\(957\) 1.93502 0.0625505
\(958\) 0 0
\(959\) 10.1763 0.328611
\(960\) 0 0
\(961\) 14.8790 0.479967
\(962\) 0 0
\(963\) 21.4052 0.689774
\(964\) 0 0
\(965\) 4.41261 0.142047
\(966\) 0 0
\(967\) −6.80083 −0.218700 −0.109350 0.994003i \(-0.534877\pi\)
−0.109350 + 0.994003i \(0.534877\pi\)
\(968\) 0 0
\(969\) −6.96751 −0.223829
\(970\) 0 0
\(971\) 6.46406 0.207442 0.103721 0.994606i \(-0.466925\pi\)
0.103721 + 0.994606i \(0.466925\pi\)
\(972\) 0 0
\(973\) 4.09591 0.131309
\(974\) 0 0
\(975\) 1.40294 0.0449302
\(976\) 0 0
\(977\) 9.18601 0.293886 0.146943 0.989145i \(-0.453057\pi\)
0.146943 + 0.989145i \(0.453057\pi\)
\(978\) 0 0
\(979\) 6.03405 0.192849
\(980\) 0 0
\(981\) 37.9571 1.21188
\(982\) 0 0
\(983\) −15.3705 −0.490241 −0.245121 0.969493i \(-0.578828\pi\)
−0.245121 + 0.969493i \(0.578828\pi\)
\(984\) 0 0
\(985\) −11.4258 −0.364055
\(986\) 0 0
\(987\) −0.448598 −0.0142790
\(988\) 0 0
\(989\) 0.402945 0.0128129
\(990\) 0 0
\(991\) 52.0109 1.65218 0.826090 0.563538i \(-0.190560\pi\)
0.826090 + 0.563538i \(0.190560\pi\)
\(992\) 0 0
\(993\) −12.0051 −0.380969
\(994\) 0 0
\(995\) 0.307039 0.00973379
\(996\) 0 0
\(997\) −15.7123 −0.497613 −0.248807 0.968553i \(-0.580038\pi\)
−0.248807 + 0.968553i \(0.580038\pi\)
\(998\) 0 0
\(999\) −12.0000 −0.379663
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 7360.2.a.ca.1.2 3
4.3 odd 2 7360.2.a.cb.1.2 3
8.3 odd 2 920.2.a.g.1.2 3
8.5 even 2 1840.2.a.t.1.2 3
24.11 even 2 8280.2.a.bo.1.2 3
40.3 even 4 4600.2.e.r.4049.3 6
40.19 odd 2 4600.2.a.y.1.2 3
40.27 even 4 4600.2.e.r.4049.4 6
40.29 even 2 9200.2.a.cd.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.a.g.1.2 3 8.3 odd 2
1840.2.a.t.1.2 3 8.5 even 2
4600.2.a.y.1.2 3 40.19 odd 2
4600.2.e.r.4049.3 6 40.3 even 4
4600.2.e.r.4049.4 6 40.27 even 4
7360.2.a.ca.1.2 3 1.1 even 1 trivial
7360.2.a.cb.1.2 3 4.3 odd 2
8280.2.a.bo.1.2 3 24.11 even 2
9200.2.a.cd.1.2 3 40.29 even 2