Properties

Label 441.4.a.t.1.1
Level $441$
Weight $4$
Character 441.1
Self dual yes
Analytic conductor $26.020$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.57516.1
Defining polynomial: \(x^{3} - x^{2} - 24 x + 6\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(5.30829\) of defining polynomial
Character \(\chi\) \(=\) 441.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.30829 q^{2} +20.1780 q^{4} +5.56140 q^{5} -64.6443 q^{8} +O(q^{10})\) \(q-5.30829 q^{2} +20.1780 q^{4} +5.56140 q^{5} -64.6443 q^{8} -29.5215 q^{10} +13.9174 q^{11} -38.6718 q^{13} +181.727 q^{16} +43.4788 q^{17} +109.028 q^{19} +112.218 q^{20} -73.8775 q^{22} +74.8778 q^{23} -94.0708 q^{25} +205.281 q^{26} +72.3589 q^{29} -64.0431 q^{31} -447.507 q^{32} -230.798 q^{34} +188.727 q^{37} -578.751 q^{38} -359.513 q^{40} -24.7923 q^{41} -243.881 q^{43} +280.825 q^{44} -397.474 q^{46} -620.549 q^{47} +499.356 q^{50} -780.319 q^{52} +287.839 q^{53} +77.4001 q^{55} -384.102 q^{58} +525.051 q^{59} +383.436 q^{61} +339.960 q^{62} +921.681 q^{64} -215.069 q^{65} +198.117 q^{67} +877.314 q^{68} -785.432 q^{71} +331.141 q^{73} -1001.82 q^{74} +2199.96 q^{76} +437.647 q^{79} +1010.66 q^{80} +131.605 q^{82} +241.241 q^{83} +241.803 q^{85} +1294.59 q^{86} -899.680 q^{88} +1585.54 q^{89} +1510.88 q^{92} +3294.05 q^{94} +606.347 q^{95} -79.2754 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 25q^{4} + 11q^{5} - 39q^{8} + O(q^{10}) \) \( 3q - q^{2} + 25q^{4} + 11q^{5} - 39q^{8} + 55q^{10} - 35q^{11} - 62q^{13} + 241q^{16} + 48q^{17} + 202q^{19} + 439q^{20} - 7q^{22} - 216q^{23} + 130q^{25} + 274q^{26} - 53q^{29} + 95q^{31} - 683q^{32} + 24q^{34} + 262q^{37} - 398q^{38} - 21q^{40} + 244q^{41} + 360q^{43} + 905q^{44} - 1056q^{46} - 210q^{47} + 1378q^{50} - 324q^{52} - 393q^{53} + 1031q^{55} - 1249q^{58} + 1143q^{59} + 70q^{61} + 1059q^{62} - 399q^{64} + 472q^{65} - 628q^{67} + 1944q^{68} - 318q^{71} - 988q^{73} - 1002q^{74} + 2340q^{76} + 861q^{79} + 175q^{80} - 124q^{82} + 519q^{83} + 1800q^{85} + 3208q^{86} - 891q^{88} + 1766q^{89} + 672q^{92} + 3294q^{94} + 736q^{95} - 19q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.30829 −1.87677 −0.938383 0.345598i \(-0.887676\pi\)
−0.938383 + 0.345598i \(0.887676\pi\)
\(3\) 0 0
\(4\) 20.1780 2.52225
\(5\) 5.56140 0.497427 0.248713 0.968577i \(-0.419992\pi\)
0.248713 + 0.968577i \(0.419992\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −64.6443 −2.85690
\(9\) 0 0
\(10\) −29.5215 −0.933553
\(11\) 13.9174 0.381477 0.190738 0.981641i \(-0.438912\pi\)
0.190738 + 0.981641i \(0.438912\pi\)
\(12\) 0 0
\(13\) −38.6718 −0.825048 −0.412524 0.910947i \(-0.635353\pi\)
−0.412524 + 0.910947i \(0.635353\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 181.727 2.83949
\(17\) 43.4788 0.620303 0.310152 0.950687i \(-0.399620\pi\)
0.310152 + 0.950687i \(0.399620\pi\)
\(18\) 0 0
\(19\) 109.028 1.31646 0.658228 0.752818i \(-0.271306\pi\)
0.658228 + 0.752818i \(0.271306\pi\)
\(20\) 112.218 1.25463
\(21\) 0 0
\(22\) −73.8775 −0.715943
\(23\) 74.8778 0.678831 0.339415 0.940637i \(-0.389771\pi\)
0.339415 + 0.940637i \(0.389771\pi\)
\(24\) 0 0
\(25\) −94.0708 −0.752567
\(26\) 205.281 1.54842
\(27\) 0 0
\(28\) 0 0
\(29\) 72.3589 0.463335 0.231667 0.972795i \(-0.425582\pi\)
0.231667 + 0.972795i \(0.425582\pi\)
\(30\) 0 0
\(31\) −64.0431 −0.371048 −0.185524 0.982640i \(-0.559398\pi\)
−0.185524 + 0.982640i \(0.559398\pi\)
\(32\) −447.507 −2.47215
\(33\) 0 0
\(34\) −230.798 −1.16416
\(35\) 0 0
\(36\) 0 0
\(37\) 188.727 0.838556 0.419278 0.907858i \(-0.362283\pi\)
0.419278 + 0.907858i \(0.362283\pi\)
\(38\) −578.751 −2.47068
\(39\) 0 0
\(40\) −359.513 −1.42110
\(41\) −24.7923 −0.0944367 −0.0472184 0.998885i \(-0.515036\pi\)
−0.0472184 + 0.998885i \(0.515036\pi\)
\(42\) 0 0
\(43\) −243.881 −0.864920 −0.432460 0.901653i \(-0.642354\pi\)
−0.432460 + 0.901653i \(0.642354\pi\)
\(44\) 280.825 0.962180
\(45\) 0 0
\(46\) −397.474 −1.27401
\(47\) −620.549 −1.92588 −0.962940 0.269717i \(-0.913070\pi\)
−0.962940 + 0.269717i \(0.913070\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 499.356 1.41239
\(51\) 0 0
\(52\) −780.319 −2.08098
\(53\) 287.839 0.745995 0.372997 0.927832i \(-0.378330\pi\)
0.372997 + 0.927832i \(0.378330\pi\)
\(54\) 0 0
\(55\) 77.4001 0.189757
\(56\) 0 0
\(57\) 0 0
\(58\) −384.102 −0.869571
\(59\) 525.051 1.15857 0.579287 0.815124i \(-0.303331\pi\)
0.579287 + 0.815124i \(0.303331\pi\)
\(60\) 0 0
\(61\) 383.436 0.804818 0.402409 0.915460i \(-0.368173\pi\)
0.402409 + 0.915460i \(0.368173\pi\)
\(62\) 339.960 0.696369
\(63\) 0 0
\(64\) 921.681 1.80016
\(65\) −215.069 −0.410401
\(66\) 0 0
\(67\) 198.117 0.361251 0.180625 0.983552i \(-0.442188\pi\)
0.180625 + 0.983552i \(0.442188\pi\)
\(68\) 877.314 1.56456
\(69\) 0 0
\(70\) 0 0
\(71\) −785.432 −1.31287 −0.656434 0.754384i \(-0.727936\pi\)
−0.656434 + 0.754384i \(0.727936\pi\)
\(72\) 0 0
\(73\) 331.141 0.530919 0.265459 0.964122i \(-0.414476\pi\)
0.265459 + 0.964122i \(0.414476\pi\)
\(74\) −1001.82 −1.57377
\(75\) 0 0
\(76\) 2199.96 3.32043
\(77\) 0 0
\(78\) 0 0
\(79\) 437.647 0.623280 0.311640 0.950200i \(-0.399122\pi\)
0.311640 + 0.950200i \(0.399122\pi\)
\(80\) 1010.66 1.41244
\(81\) 0 0
\(82\) 131.605 0.177236
\(83\) 241.241 0.319032 0.159516 0.987195i \(-0.449007\pi\)
0.159516 + 0.987195i \(0.449007\pi\)
\(84\) 0 0
\(85\) 241.803 0.308555
\(86\) 1294.59 1.62325
\(87\) 0 0
\(88\) −899.680 −1.08984
\(89\) 1585.54 1.88840 0.944198 0.329378i \(-0.106839\pi\)
0.944198 + 0.329378i \(0.106839\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1510.88 1.71218
\(93\) 0 0
\(94\) 3294.05 3.61442
\(95\) 606.347 0.654841
\(96\) 0 0
\(97\) −79.2754 −0.0829814 −0.0414907 0.999139i \(-0.513211\pi\)
−0.0414907 + 0.999139i \(0.513211\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1898.16 −1.89816
\(101\) 1154.97 1.13786 0.568931 0.822385i \(-0.307357\pi\)
0.568931 + 0.822385i \(0.307357\pi\)
\(102\) 0 0
\(103\) 1444.86 1.38220 0.691098 0.722761i \(-0.257127\pi\)
0.691098 + 0.722761i \(0.257127\pi\)
\(104\) 2499.91 2.35708
\(105\) 0 0
\(106\) −1527.93 −1.40006
\(107\) −990.960 −0.895325 −0.447662 0.894203i \(-0.647743\pi\)
−0.447662 + 0.894203i \(0.647743\pi\)
\(108\) 0 0
\(109\) 1953.17 1.71633 0.858164 0.513376i \(-0.171605\pi\)
0.858164 + 0.513376i \(0.171605\pi\)
\(110\) −410.862 −0.356129
\(111\) 0 0
\(112\) 0 0
\(113\) −672.882 −0.560172 −0.280086 0.959975i \(-0.590363\pi\)
−0.280086 + 0.959975i \(0.590363\pi\)
\(114\) 0 0
\(115\) 416.426 0.337669
\(116\) 1460.06 1.16865
\(117\) 0 0
\(118\) −2787.13 −2.17437
\(119\) 0 0
\(120\) 0 0
\(121\) −1137.31 −0.854475
\(122\) −2035.39 −1.51045
\(123\) 0 0
\(124\) −1292.26 −0.935874
\(125\) −1218.34 −0.871773
\(126\) 0 0
\(127\) 175.815 0.122843 0.0614216 0.998112i \(-0.480437\pi\)
0.0614216 + 0.998112i \(0.480437\pi\)
\(128\) −1312.50 −0.906325
\(129\) 0 0
\(130\) 1141.65 0.770226
\(131\) 1125.93 0.750939 0.375470 0.926835i \(-0.377481\pi\)
0.375470 + 0.926835i \(0.377481\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1051.66 −0.677983
\(135\) 0 0
\(136\) −2810.66 −1.77215
\(137\) −1868.70 −1.16536 −0.582678 0.812703i \(-0.697995\pi\)
−0.582678 + 0.812703i \(0.697995\pi\)
\(138\) 0 0
\(139\) 2817.19 1.71907 0.859537 0.511074i \(-0.170752\pi\)
0.859537 + 0.511074i \(0.170752\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4169.30 2.46394
\(143\) −538.210 −0.314737
\(144\) 0 0
\(145\) 402.417 0.230475
\(146\) −1757.79 −0.996410
\(147\) 0 0
\(148\) 3808.14 2.11505
\(149\) −1800.33 −0.989855 −0.494928 0.868934i \(-0.664805\pi\)
−0.494928 + 0.868934i \(0.664805\pi\)
\(150\) 0 0
\(151\) −452.984 −0.244128 −0.122064 0.992522i \(-0.538951\pi\)
−0.122064 + 0.992522i \(0.538951\pi\)
\(152\) −7048.03 −3.76099
\(153\) 0 0
\(154\) 0 0
\(155\) −356.169 −0.184569
\(156\) 0 0
\(157\) 1863.66 0.947364 0.473682 0.880696i \(-0.342925\pi\)
0.473682 + 0.880696i \(0.342925\pi\)
\(158\) −2323.16 −1.16975
\(159\) 0 0
\(160\) −2488.77 −1.22971
\(161\) 0 0
\(162\) 0 0
\(163\) 2321.14 1.11537 0.557686 0.830052i \(-0.311689\pi\)
0.557686 + 0.830052i \(0.311689\pi\)
\(164\) −500.259 −0.238193
\(165\) 0 0
\(166\) −1280.58 −0.598749
\(167\) 3211.62 1.48816 0.744079 0.668092i \(-0.232889\pi\)
0.744079 + 0.668092i \(0.232889\pi\)
\(168\) 0 0
\(169\) −701.494 −0.319296
\(170\) −1283.56 −0.579086
\(171\) 0 0
\(172\) −4921.04 −2.18154
\(173\) 214.277 0.0941687 0.0470844 0.998891i \(-0.485007\pi\)
0.0470844 + 0.998891i \(0.485007\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2529.17 1.08320
\(177\) 0 0
\(178\) −8416.53 −3.54408
\(179\) 2437.22 1.01769 0.508845 0.860858i \(-0.330073\pi\)
0.508845 + 0.860858i \(0.330073\pi\)
\(180\) 0 0
\(181\) 248.631 0.102103 0.0510514 0.998696i \(-0.483743\pi\)
0.0510514 + 0.998696i \(0.483743\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4840.43 −1.93935
\(185\) 1049.59 0.417120
\(186\) 0 0
\(187\) 605.110 0.236631
\(188\) −12521.4 −4.85755
\(189\) 0 0
\(190\) −3218.67 −1.22898
\(191\) 4313.08 1.63394 0.816972 0.576677i \(-0.195651\pi\)
0.816972 + 0.576677i \(0.195651\pi\)
\(192\) 0 0
\(193\) 2060.85 0.768618 0.384309 0.923205i \(-0.374440\pi\)
0.384309 + 0.923205i \(0.374440\pi\)
\(194\) 420.817 0.155737
\(195\) 0 0
\(196\) 0 0
\(197\) 1666.09 0.602557 0.301279 0.953536i \(-0.402587\pi\)
0.301279 + 0.953536i \(0.402587\pi\)
\(198\) 0 0
\(199\) 1087.53 0.387403 0.193702 0.981061i \(-0.437951\pi\)
0.193702 + 0.981061i \(0.437951\pi\)
\(200\) 6081.15 2.15001
\(201\) 0 0
\(202\) −6130.94 −2.13550
\(203\) 0 0
\(204\) 0 0
\(205\) −137.880 −0.0469754
\(206\) −7669.74 −2.59406
\(207\) 0 0
\(208\) −7027.72 −2.34271
\(209\) 1517.38 0.502198
\(210\) 0 0
\(211\) −4676.47 −1.52579 −0.762895 0.646522i \(-0.776223\pi\)
−0.762895 + 0.646522i \(0.776223\pi\)
\(212\) 5808.01 1.88158
\(213\) 0 0
\(214\) 5260.31 1.68031
\(215\) −1356.32 −0.430234
\(216\) 0 0
\(217\) 0 0
\(218\) −10368.0 −3.22114
\(219\) 0 0
\(220\) 1561.78 0.478614
\(221\) −1681.40 −0.511780
\(222\) 0 0
\(223\) −3246.03 −0.974754 −0.487377 0.873192i \(-0.662046\pi\)
−0.487377 + 0.873192i \(0.662046\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 3571.86 1.05131
\(227\) 5138.16 1.50234 0.751171 0.660108i \(-0.229490\pi\)
0.751171 + 0.660108i \(0.229490\pi\)
\(228\) 0 0
\(229\) −614.806 −0.177413 −0.0887064 0.996058i \(-0.528273\pi\)
−0.0887064 + 0.996058i \(0.528273\pi\)
\(230\) −2210.51 −0.633725
\(231\) 0 0
\(232\) −4677.59 −1.32370
\(233\) −2827.42 −0.794979 −0.397490 0.917607i \(-0.630119\pi\)
−0.397490 + 0.917607i \(0.630119\pi\)
\(234\) 0 0
\(235\) −3451.12 −0.957984
\(236\) 10594.5 2.92221
\(237\) 0 0
\(238\) 0 0
\(239\) 3432.45 0.928983 0.464491 0.885578i \(-0.346237\pi\)
0.464491 + 0.885578i \(0.346237\pi\)
\(240\) 0 0
\(241\) 2636.11 0.704593 0.352296 0.935888i \(-0.385401\pi\)
0.352296 + 0.935888i \(0.385401\pi\)
\(242\) 6037.16 1.60365
\(243\) 0 0
\(244\) 7736.96 2.02995
\(245\) 0 0
\(246\) 0 0
\(247\) −4216.30 −1.08614
\(248\) 4140.02 1.06005
\(249\) 0 0
\(250\) 6467.31 1.63611
\(251\) 2057.57 0.517422 0.258711 0.965955i \(-0.416702\pi\)
0.258711 + 0.965955i \(0.416702\pi\)
\(252\) 0 0
\(253\) 1042.10 0.258958
\(254\) −933.279 −0.230548
\(255\) 0 0
\(256\) −406.321 −0.0991996
\(257\) 2150.21 0.521892 0.260946 0.965353i \(-0.415966\pi\)
0.260946 + 0.965353i \(0.415966\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4339.66 −1.03513
\(261\) 0 0
\(262\) −5976.77 −1.40934
\(263\) 4590.15 1.07620 0.538100 0.842881i \(-0.319142\pi\)
0.538100 + 0.842881i \(0.319142\pi\)
\(264\) 0 0
\(265\) 1600.79 0.371078
\(266\) 0 0
\(267\) 0 0
\(268\) 3997.59 0.911164
\(269\) −379.378 −0.0859891 −0.0429945 0.999075i \(-0.513690\pi\)
−0.0429945 + 0.999075i \(0.513690\pi\)
\(270\) 0 0
\(271\) 5368.84 1.20345 0.601723 0.798705i \(-0.294481\pi\)
0.601723 + 0.798705i \(0.294481\pi\)
\(272\) 7901.28 1.76134
\(273\) 0 0
\(274\) 9919.61 2.18710
\(275\) −1309.22 −0.287087
\(276\) 0 0
\(277\) −4781.60 −1.03718 −0.518590 0.855023i \(-0.673543\pi\)
−0.518590 + 0.855023i \(0.673543\pi\)
\(278\) −14954.5 −3.22630
\(279\) 0 0
\(280\) 0 0
\(281\) 2076.57 0.440845 0.220423 0.975404i \(-0.429256\pi\)
0.220423 + 0.975404i \(0.429256\pi\)
\(282\) 0 0
\(283\) −2557.62 −0.537224 −0.268612 0.963248i \(-0.586565\pi\)
−0.268612 + 0.963248i \(0.586565\pi\)
\(284\) −15848.4 −3.31138
\(285\) 0 0
\(286\) 2856.97 0.590687
\(287\) 0 0
\(288\) 0 0
\(289\) −3022.60 −0.615224
\(290\) −2136.15 −0.432548
\(291\) 0 0
\(292\) 6681.75 1.33911
\(293\) 560.049 0.111667 0.0558335 0.998440i \(-0.482218\pi\)
0.0558335 + 0.998440i \(0.482218\pi\)
\(294\) 0 0
\(295\) 2920.02 0.576305
\(296\) −12200.2 −2.39567
\(297\) 0 0
\(298\) 9556.66 1.85773
\(299\) −2895.66 −0.560068
\(300\) 0 0
\(301\) 0 0
\(302\) 2404.57 0.458171
\(303\) 0 0
\(304\) 19813.3 3.73806
\(305\) 2132.44 0.400338
\(306\) 0 0
\(307\) −3653.02 −0.679117 −0.339558 0.940585i \(-0.610278\pi\)
−0.339558 + 0.940585i \(0.610278\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1890.65 0.346393
\(311\) 3492.27 0.636747 0.318374 0.947965i \(-0.396863\pi\)
0.318374 + 0.947965i \(0.396863\pi\)
\(312\) 0 0
\(313\) −8712.09 −1.57328 −0.786640 0.617412i \(-0.788181\pi\)
−0.786640 + 0.617412i \(0.788181\pi\)
\(314\) −9892.85 −1.77798
\(315\) 0 0
\(316\) 8830.83 1.57207
\(317\) −1940.33 −0.343785 −0.171892 0.985116i \(-0.554988\pi\)
−0.171892 + 0.985116i \(0.554988\pi\)
\(318\) 0 0
\(319\) 1007.05 0.176752
\(320\) 5125.84 0.895447
\(321\) 0 0
\(322\) 0 0
\(323\) 4740.39 0.816602
\(324\) 0 0
\(325\) 3637.89 0.620904
\(326\) −12321.3 −2.09329
\(327\) 0 0
\(328\) 1602.68 0.269797
\(329\) 0 0
\(330\) 0 0
\(331\) −5731.51 −0.951759 −0.475879 0.879510i \(-0.657870\pi\)
−0.475879 + 0.879510i \(0.657870\pi\)
\(332\) 4867.76 0.804678
\(333\) 0 0
\(334\) −17048.2 −2.79292
\(335\) 1101.81 0.179696
\(336\) 0 0
\(337\) 2403.74 0.388547 0.194273 0.980947i \(-0.437765\pi\)
0.194273 + 0.980947i \(0.437765\pi\)
\(338\) 3723.73 0.599244
\(339\) 0 0
\(340\) 4879.09 0.778253
\(341\) −891.312 −0.141546
\(342\) 0 0
\(343\) 0 0
\(344\) 15765.6 2.47099
\(345\) 0 0
\(346\) −1137.45 −0.176733
\(347\) 3336.44 0.516166 0.258083 0.966123i \(-0.416909\pi\)
0.258083 + 0.966123i \(0.416909\pi\)
\(348\) 0 0
\(349\) 2424.54 0.371870 0.185935 0.982562i \(-0.440469\pi\)
0.185935 + 0.982562i \(0.440469\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6228.12 −0.943069
\(353\) −12403.1 −1.87012 −0.935059 0.354491i \(-0.884654\pi\)
−0.935059 + 0.354491i \(0.884654\pi\)
\(354\) 0 0
\(355\) −4368.10 −0.653055
\(356\) 31993.1 4.76300
\(357\) 0 0
\(358\) −12937.5 −1.90997
\(359\) −1353.84 −0.199034 −0.0995168 0.995036i \(-0.531730\pi\)
−0.0995168 + 0.995036i \(0.531730\pi\)
\(360\) 0 0
\(361\) 5028.05 0.733059
\(362\) −1319.81 −0.191623
\(363\) 0 0
\(364\) 0 0
\(365\) 1841.61 0.264093
\(366\) 0 0
\(367\) 1378.06 0.196006 0.0980031 0.995186i \(-0.468754\pi\)
0.0980031 + 0.995186i \(0.468754\pi\)
\(368\) 13607.3 1.92753
\(369\) 0 0
\(370\) −5571.52 −0.782837
\(371\) 0 0
\(372\) 0 0
\(373\) 5456.92 0.757503 0.378752 0.925498i \(-0.376353\pi\)
0.378752 + 0.925498i \(0.376353\pi\)
\(374\) −3212.10 −0.444101
\(375\) 0 0
\(376\) 40115.0 5.50205
\(377\) −2798.25 −0.382273
\(378\) 0 0
\(379\) 554.675 0.0751761 0.0375881 0.999293i \(-0.488033\pi\)
0.0375881 + 0.999293i \(0.488033\pi\)
\(380\) 12234.9 1.65167
\(381\) 0 0
\(382\) −22895.1 −3.06653
\(383\) 5860.66 0.781895 0.390948 0.920413i \(-0.372147\pi\)
0.390948 + 0.920413i \(0.372147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10939.6 −1.44252
\(387\) 0 0
\(388\) −1599.62 −0.209300
\(389\) −7778.86 −1.01389 −0.506946 0.861978i \(-0.669226\pi\)
−0.506946 + 0.861978i \(0.669226\pi\)
\(390\) 0 0
\(391\) 3255.60 0.421081
\(392\) 0 0
\(393\) 0 0
\(394\) −8844.08 −1.13086
\(395\) 2433.93 0.310036
\(396\) 0 0
\(397\) −8027.88 −1.01488 −0.507440 0.861687i \(-0.669408\pi\)
−0.507440 + 0.861687i \(0.669408\pi\)
\(398\) −5772.95 −0.727065
\(399\) 0 0
\(400\) −17095.2 −2.13690
\(401\) −779.980 −0.0971330 −0.0485665 0.998820i \(-0.515465\pi\)
−0.0485665 + 0.998820i \(0.515465\pi\)
\(402\) 0 0
\(403\) 2476.66 0.306132
\(404\) 23305.0 2.86997
\(405\) 0 0
\(406\) 0 0
\(407\) 2626.59 0.319890
\(408\) 0 0
\(409\) −14692.5 −1.77628 −0.888139 0.459575i \(-0.848002\pi\)
−0.888139 + 0.459575i \(0.848002\pi\)
\(410\) 731.907 0.0881617
\(411\) 0 0
\(412\) 29154.4 3.48624
\(413\) 0 0
\(414\) 0 0
\(415\) 1341.64 0.158695
\(416\) 17305.9 2.03964
\(417\) 0 0
\(418\) −8054.70 −0.942508
\(419\) 3370.31 0.392960 0.196480 0.980508i \(-0.437049\pi\)
0.196480 + 0.980508i \(0.437049\pi\)
\(420\) 0 0
\(421\) 15651.0 1.81184 0.905919 0.423450i \(-0.139181\pi\)
0.905919 + 0.423450i \(0.139181\pi\)
\(422\) 24824.1 2.86355
\(423\) 0 0
\(424\) −18607.2 −2.13123
\(425\) −4090.08 −0.466819
\(426\) 0 0
\(427\) 0 0
\(428\) −19995.6 −2.25823
\(429\) 0 0
\(430\) 7199.75 0.807449
\(431\) −4888.12 −0.546294 −0.273147 0.961972i \(-0.588064\pi\)
−0.273147 + 0.961972i \(0.588064\pi\)
\(432\) 0 0
\(433\) 5255.73 0.583313 0.291656 0.956523i \(-0.405794\pi\)
0.291656 + 0.956523i \(0.405794\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 39411.0 4.32901
\(437\) 8163.76 0.893651
\(438\) 0 0
\(439\) 824.977 0.0896902 0.0448451 0.998994i \(-0.485721\pi\)
0.0448451 + 0.998994i \(0.485721\pi\)
\(440\) −5003.48 −0.542117
\(441\) 0 0
\(442\) 8925.37 0.960490
\(443\) −13027.3 −1.39717 −0.698583 0.715529i \(-0.746186\pi\)
−0.698583 + 0.715529i \(0.746186\pi\)
\(444\) 0 0
\(445\) 8817.84 0.939339
\(446\) 17230.9 1.82939
\(447\) 0 0
\(448\) 0 0
\(449\) −16526.1 −1.73700 −0.868500 0.495689i \(-0.834916\pi\)
−0.868500 + 0.495689i \(0.834916\pi\)
\(450\) 0 0
\(451\) −345.044 −0.0360254
\(452\) −13577.4 −1.41289
\(453\) 0 0
\(454\) −27274.9 −2.81954
\(455\) 0 0
\(456\) 0 0
\(457\) −3710.82 −0.379836 −0.189918 0.981800i \(-0.560822\pi\)
−0.189918 + 0.981800i \(0.560822\pi\)
\(458\) 3263.57 0.332962
\(459\) 0 0
\(460\) 8402.63 0.851684
\(461\) −9714.00 −0.981401 −0.490701 0.871328i \(-0.663259\pi\)
−0.490701 + 0.871328i \(0.663259\pi\)
\(462\) 0 0
\(463\) −43.2780 −0.00434406 −0.00217203 0.999998i \(-0.500691\pi\)
−0.00217203 + 0.999998i \(0.500691\pi\)
\(464\) 13149.6 1.31563
\(465\) 0 0
\(466\) 15008.8 1.49199
\(467\) −1533.24 −0.151927 −0.0759633 0.997111i \(-0.524203\pi\)
−0.0759633 + 0.997111i \(0.524203\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 18319.6 1.79791
\(471\) 0 0
\(472\) −33941.6 −3.30993
\(473\) −3394.19 −0.329947
\(474\) 0 0
\(475\) −10256.3 −0.990722
\(476\) 0 0
\(477\) 0 0
\(478\) −18220.5 −1.74348
\(479\) −7035.37 −0.671095 −0.335547 0.942023i \(-0.608921\pi\)
−0.335547 + 0.942023i \(0.608921\pi\)
\(480\) 0 0
\(481\) −7298.42 −0.691849
\(482\) −13993.3 −1.32236
\(483\) 0 0
\(484\) −22948.6 −2.15520
\(485\) −440.882 −0.0412772
\(486\) 0 0
\(487\) −15371.3 −1.43026 −0.715132 0.698989i \(-0.753634\pi\)
−0.715132 + 0.698989i \(0.753634\pi\)
\(488\) −24786.9 −2.29929
\(489\) 0 0
\(490\) 0 0
\(491\) 2393.35 0.219980 0.109990 0.993933i \(-0.464918\pi\)
0.109990 + 0.993933i \(0.464918\pi\)
\(492\) 0 0
\(493\) 3146.08 0.287408
\(494\) 22381.3 2.03843
\(495\) 0 0
\(496\) −11638.4 −1.05359
\(497\) 0 0
\(498\) 0 0
\(499\) 693.520 0.0622169 0.0311084 0.999516i \(-0.490096\pi\)
0.0311084 + 0.999516i \(0.490096\pi\)
\(500\) −24583.7 −2.19883
\(501\) 0 0
\(502\) −10922.2 −0.971079
\(503\) −8646.95 −0.766498 −0.383249 0.923645i \(-0.625195\pi\)
−0.383249 + 0.923645i \(0.625195\pi\)
\(504\) 0 0
\(505\) 6423.27 0.566003
\(506\) −5531.79 −0.486004
\(507\) 0 0
\(508\) 3547.60 0.309841
\(509\) −15500.9 −1.34983 −0.674916 0.737895i \(-0.735820\pi\)
−0.674916 + 0.737895i \(0.735820\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 12656.9 1.09250
\(513\) 0 0
\(514\) −11413.9 −0.979469
\(515\) 8035.44 0.687541
\(516\) 0 0
\(517\) −8636.41 −0.734678
\(518\) 0 0
\(519\) 0 0
\(520\) 13903.0 1.17248
\(521\) 864.707 0.0727131 0.0363565 0.999339i \(-0.488425\pi\)
0.0363565 + 0.999339i \(0.488425\pi\)
\(522\) 0 0
\(523\) 6255.61 0.523019 0.261509 0.965201i \(-0.415780\pi\)
0.261509 + 0.965201i \(0.415780\pi\)
\(524\) 22719.0 1.89406
\(525\) 0 0
\(526\) −24365.9 −2.01978
\(527\) −2784.51 −0.230162
\(528\) 0 0
\(529\) −6560.31 −0.539189
\(530\) −8497.45 −0.696426
\(531\) 0 0
\(532\) 0 0
\(533\) 958.762 0.0779148
\(534\) 0 0
\(535\) −5511.13 −0.445358
\(536\) −12807.1 −1.03206
\(537\) 0 0
\(538\) 2013.85 0.161381
\(539\) 0 0
\(540\) 0 0
\(541\) 143.871 0.0114334 0.00571671 0.999984i \(-0.498180\pi\)
0.00571671 + 0.999984i \(0.498180\pi\)
\(542\) −28499.4 −2.25858
\(543\) 0 0
\(544\) −19457.1 −1.53348
\(545\) 10862.4 0.853747
\(546\) 0 0
\(547\) 5455.65 0.426448 0.213224 0.977003i \(-0.431604\pi\)
0.213224 + 0.977003i \(0.431604\pi\)
\(548\) −37706.6 −2.93932
\(549\) 0 0
\(550\) 6949.72 0.538795
\(551\) 7889.13 0.609960
\(552\) 0 0
\(553\) 0 0
\(554\) 25382.2 1.94654
\(555\) 0 0
\(556\) 56845.3 4.33593
\(557\) −24809.9 −1.88730 −0.943652 0.330940i \(-0.892634\pi\)
−0.943652 + 0.330940i \(0.892634\pi\)
\(558\) 0 0
\(559\) 9431.33 0.713600
\(560\) 0 0
\(561\) 0 0
\(562\) −11023.0 −0.827363
\(563\) 16369.8 1.22541 0.612705 0.790312i \(-0.290081\pi\)
0.612705 + 0.790312i \(0.290081\pi\)
\(564\) 0 0
\(565\) −3742.17 −0.278645
\(566\) 13576.6 1.00824
\(567\) 0 0
\(568\) 50773.7 3.75074
\(569\) 18450.6 1.35938 0.679691 0.733498i \(-0.262114\pi\)
0.679691 + 0.733498i \(0.262114\pi\)
\(570\) 0 0
\(571\) −7108.69 −0.520997 −0.260499 0.965474i \(-0.583887\pi\)
−0.260499 + 0.965474i \(0.583887\pi\)
\(572\) −10860.0 −0.793844
\(573\) 0 0
\(574\) 0 0
\(575\) −7043.82 −0.510865
\(576\) 0 0
\(577\) −7594.17 −0.547919 −0.273960 0.961741i \(-0.588333\pi\)
−0.273960 + 0.961741i \(0.588333\pi\)
\(578\) 16044.8 1.15463
\(579\) 0 0
\(580\) 8119.96 0.581315
\(581\) 0 0
\(582\) 0 0
\(583\) 4005.96 0.284580
\(584\) −21406.4 −1.51678
\(585\) 0 0
\(586\) −2972.91 −0.209573
\(587\) −1763.34 −0.123988 −0.0619939 0.998077i \(-0.519746\pi\)
−0.0619939 + 0.998077i \(0.519746\pi\)
\(588\) 0 0
\(589\) −6982.47 −0.488468
\(590\) −15500.3 −1.08159
\(591\) 0 0
\(592\) 34296.9 2.38107
\(593\) −12316.1 −0.852889 −0.426445 0.904514i \(-0.640234\pi\)
−0.426445 + 0.904514i \(0.640234\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −36327.0 −2.49666
\(597\) 0 0
\(598\) 15371.0 1.05112
\(599\) 8903.40 0.607317 0.303659 0.952781i \(-0.401792\pi\)
0.303659 + 0.952781i \(0.401792\pi\)
\(600\) 0 0
\(601\) 19157.1 1.30022 0.650112 0.759838i \(-0.274722\pi\)
0.650112 + 0.759838i \(0.274722\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −9140.31 −0.615751
\(605\) −6325.02 −0.425039
\(606\) 0 0
\(607\) 7569.93 0.506184 0.253092 0.967442i \(-0.418552\pi\)
0.253092 + 0.967442i \(0.418552\pi\)
\(608\) −48790.7 −3.25448
\(609\) 0 0
\(610\) −11319.6 −0.751340
\(611\) 23997.7 1.58894
\(612\) 0 0
\(613\) 2907.13 0.191546 0.0957730 0.995403i \(-0.469468\pi\)
0.0957730 + 0.995403i \(0.469468\pi\)
\(614\) 19391.3 1.27454
\(615\) 0 0
\(616\) 0 0
\(617\) 12510.9 0.816320 0.408160 0.912910i \(-0.366171\pi\)
0.408160 + 0.912910i \(0.366171\pi\)
\(618\) 0 0
\(619\) −10065.6 −0.653585 −0.326792 0.945096i \(-0.605968\pi\)
−0.326792 + 0.945096i \(0.605968\pi\)
\(620\) −7186.78 −0.465529
\(621\) 0 0
\(622\) −18538.0 −1.19503
\(623\) 0 0
\(624\) 0 0
\(625\) 4983.18 0.318923
\(626\) 46246.4 2.95268
\(627\) 0 0
\(628\) 37604.9 2.38949
\(629\) 8205.63 0.520159
\(630\) 0 0
\(631\) −25146.6 −1.58648 −0.793242 0.608907i \(-0.791608\pi\)
−0.793242 + 0.608907i \(0.791608\pi\)
\(632\) −28291.4 −1.78065
\(633\) 0 0
\(634\) 10299.8 0.645203
\(635\) 977.779 0.0611055
\(636\) 0 0
\(637\) 0 0
\(638\) −5345.70 −0.331721
\(639\) 0 0
\(640\) −7299.33 −0.450830
\(641\) 28958.9 1.78441 0.892206 0.451629i \(-0.149157\pi\)
0.892206 + 0.451629i \(0.149157\pi\)
\(642\) 0 0
\(643\) −7341.90 −0.450290 −0.225145 0.974325i \(-0.572286\pi\)
−0.225145 + 0.974325i \(0.572286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −25163.4 −1.53257
\(647\) 6071.98 0.368955 0.184478 0.982837i \(-0.440941\pi\)
0.184478 + 0.982837i \(0.440941\pi\)
\(648\) 0 0
\(649\) 7307.33 0.441969
\(650\) −19311.0 −1.16529
\(651\) 0 0
\(652\) 46835.9 2.81324
\(653\) −26262.1 −1.57384 −0.786920 0.617056i \(-0.788325\pi\)
−0.786920 + 0.617056i \(0.788325\pi\)
\(654\) 0 0
\(655\) 6261.75 0.373537
\(656\) −4505.44 −0.268152
\(657\) 0 0
\(658\) 0 0
\(659\) −26130.1 −1.54459 −0.772296 0.635263i \(-0.780892\pi\)
−0.772296 + 0.635263i \(0.780892\pi\)
\(660\) 0 0
\(661\) 11925.5 0.701737 0.350868 0.936425i \(-0.385886\pi\)
0.350868 + 0.936425i \(0.385886\pi\)
\(662\) 30424.5 1.78623
\(663\) 0 0
\(664\) −15594.9 −0.911444
\(665\) 0 0
\(666\) 0 0
\(667\) 5418.08 0.314526
\(668\) 64804.0 3.75350
\(669\) 0 0
\(670\) −5848.71 −0.337247
\(671\) 5336.42 0.307019
\(672\) 0 0
\(673\) −6359.85 −0.364271 −0.182135 0.983273i \(-0.558301\pi\)
−0.182135 + 0.983273i \(0.558301\pi\)
\(674\) −12759.8 −0.729211
\(675\) 0 0
\(676\) −14154.7 −0.805344
\(677\) 8561.61 0.486041 0.243020 0.970021i \(-0.421862\pi\)
0.243020 + 0.970021i \(0.421862\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −15631.2 −0.881513
\(681\) 0 0
\(682\) 4731.34 0.265649
\(683\) 6705.88 0.375686 0.187843 0.982199i \(-0.439850\pi\)
0.187843 + 0.982199i \(0.439850\pi\)
\(684\) 0 0
\(685\) −10392.6 −0.579679
\(686\) 0 0
\(687\) 0 0
\(688\) −44319.9 −2.45593
\(689\) −11131.2 −0.615481
\(690\) 0 0
\(691\) 25330.6 1.39453 0.697267 0.716811i \(-0.254399\pi\)
0.697267 + 0.716811i \(0.254399\pi\)
\(692\) 4323.68 0.237517
\(693\) 0 0
\(694\) −17710.8 −0.968723
\(695\) 15667.5 0.855113
\(696\) 0 0
\(697\) −1077.94 −0.0585794
\(698\) −12870.2 −0.697912
\(699\) 0 0
\(700\) 0 0
\(701\) 27184.1 1.46467 0.732333 0.680947i \(-0.238432\pi\)
0.732333 + 0.680947i \(0.238432\pi\)
\(702\) 0 0
\(703\) 20576.5 1.10392
\(704\) 12827.4 0.686719
\(705\) 0 0
\(706\) 65839.5 3.50977
\(707\) 0 0
\(708\) 0 0
\(709\) 16145.5 0.855228 0.427614 0.903961i \(-0.359354\pi\)
0.427614 + 0.903961i \(0.359354\pi\)
\(710\) 23187.2 1.22563
\(711\) 0 0
\(712\) −102496. −5.39496
\(713\) −4795.41 −0.251879
\(714\) 0 0
\(715\) −2993.20 −0.156558
\(716\) 49178.2 2.56687
\(717\) 0 0
\(718\) 7186.59 0.373539
\(719\) 17297.5 0.897200 0.448600 0.893733i \(-0.351923\pi\)
0.448600 + 0.893733i \(0.351923\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −26690.4 −1.37578
\(723\) 0 0
\(724\) 5016.87 0.257528
\(725\) −6806.86 −0.348690
\(726\) 0 0
\(727\) −3514.71 −0.179303 −0.0896516 0.995973i \(-0.528575\pi\)
−0.0896516 + 0.995973i \(0.528575\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −9775.78 −0.495641
\(731\) −10603.7 −0.536513
\(732\) 0 0
\(733\) 27511.2 1.38629 0.693144 0.720799i \(-0.256225\pi\)
0.693144 + 0.720799i \(0.256225\pi\)
\(734\) −7315.16 −0.367858
\(735\) 0 0
\(736\) −33508.4 −1.67817
\(737\) 2757.26 0.137809
\(738\) 0 0
\(739\) 16101.6 0.801497 0.400749 0.916188i \(-0.368750\pi\)
0.400749 + 0.916188i \(0.368750\pi\)
\(740\) 21178.6 1.05208
\(741\) 0 0
\(742\) 0 0
\(743\) −14682.4 −0.724961 −0.362480 0.931991i \(-0.618070\pi\)
−0.362480 + 0.931991i \(0.618070\pi\)
\(744\) 0 0
\(745\) −10012.3 −0.492380
\(746\) −28966.9 −1.42166
\(747\) 0 0
\(748\) 12209.9 0.596843
\(749\) 0 0
\(750\) 0 0
\(751\) −7273.06 −0.353393 −0.176696 0.984265i \(-0.556541\pi\)
−0.176696 + 0.984265i \(0.556541\pi\)
\(752\) −112771. −5.46851
\(753\) 0 0
\(754\) 14853.9 0.717437
\(755\) −2519.23 −0.121436
\(756\) 0 0
\(757\) 8505.93 0.408393 0.204196 0.978930i \(-0.434542\pi\)
0.204196 + 0.978930i \(0.434542\pi\)
\(758\) −2944.38 −0.141088
\(759\) 0 0
\(760\) −39196.9 −1.87082
\(761\) 14217.7 0.677256 0.338628 0.940920i \(-0.390037\pi\)
0.338628 + 0.940920i \(0.390037\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 87029.3 4.12121
\(765\) 0 0
\(766\) −31110.1 −1.46743
\(767\) −20304.7 −0.955879
\(768\) 0 0
\(769\) −16379.1 −0.768068 −0.384034 0.923319i \(-0.625466\pi\)
−0.384034 + 0.923319i \(0.625466\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 41583.8 1.93865
\(773\) −39896.7 −1.85638 −0.928192 0.372102i \(-0.878637\pi\)
−0.928192 + 0.372102i \(0.878637\pi\)
\(774\) 0 0
\(775\) 6024.59 0.279238
\(776\) 5124.70 0.237070
\(777\) 0 0
\(778\) 41292.5 1.90284
\(779\) −2703.05 −0.124322
\(780\) 0 0
\(781\) −10931.1 −0.500829
\(782\) −17281.7 −0.790270
\(783\) 0 0
\(784\) 0 0
\(785\) 10364.5 0.471244
\(786\) 0 0
\(787\) 33128.5 1.50051 0.750257 0.661146i \(-0.229930\pi\)
0.750257 + 0.661146i \(0.229930\pi\)
\(788\) 33618.3 1.51980
\(789\) 0 0
\(790\) −12920.0 −0.581865
\(791\) 0 0
\(792\) 0 0
\(793\) −14828.1 −0.664013
\(794\) 42614.3 1.90469
\(795\) 0 0
\(796\) 21944.2 0.977127
\(797\) −17851.5 −0.793390 −0.396695 0.917951i \(-0.629843\pi\)
−0.396695 + 0.917951i \(0.629843\pi\)
\(798\) 0 0
\(799\) −26980.7 −1.19463
\(800\) 42097.4 1.86046
\(801\) 0 0
\(802\) 4140.36 0.182296
\(803\) 4608.61 0.202533
\(804\) 0 0
\(805\) 0 0
\(806\) −13146.8 −0.574538
\(807\) 0 0
\(808\) −74662.5 −3.25076
\(809\) 5057.03 0.219772 0.109886 0.993944i \(-0.464951\pi\)
0.109886 + 0.993944i \(0.464951\pi\)
\(810\) 0 0
\(811\) 17535.4 0.759251 0.379626 0.925140i \(-0.376053\pi\)
0.379626 + 0.925140i \(0.376053\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −13942.7 −0.600358
\(815\) 12908.8 0.554815
\(816\) 0 0
\(817\) −26589.8 −1.13863
\(818\) 77992.1 3.33366
\(819\) 0 0
\(820\) −2782.14 −0.118484
\(821\) 18700.8 0.794959 0.397480 0.917611i \(-0.369885\pi\)
0.397480 + 0.917611i \(0.369885\pi\)
\(822\) 0 0
\(823\) 22222.6 0.941230 0.470615 0.882339i \(-0.344032\pi\)
0.470615 + 0.882339i \(0.344032\pi\)
\(824\) −93402.0 −3.94880
\(825\) 0 0
\(826\) 0 0
\(827\) −25178.9 −1.05872 −0.529358 0.848399i \(-0.677567\pi\)
−0.529358 + 0.848399i \(0.677567\pi\)
\(828\) 0 0
\(829\) −12278.9 −0.514432 −0.257216 0.966354i \(-0.582805\pi\)
−0.257216 + 0.966354i \(0.582805\pi\)
\(830\) −7121.81 −0.297834
\(831\) 0 0
\(832\) −35643.1 −1.48522
\(833\) 0 0
\(834\) 0 0
\(835\) 17861.1 0.740249
\(836\) 30617.7 1.26667
\(837\) 0 0
\(838\) −17890.6 −0.737494
\(839\) −25765.0 −1.06020 −0.530098 0.847936i \(-0.677845\pi\)
−0.530098 + 0.847936i \(0.677845\pi\)
\(840\) 0 0
\(841\) −19153.2 −0.785321
\(842\) −83080.2 −3.40040
\(843\) 0 0
\(844\) −94361.8 −3.84842
\(845\) −3901.29 −0.158826
\(846\) 0 0
\(847\) 0 0
\(848\) 52308.2 2.11824
\(849\) 0 0
\(850\) 21711.4 0.876111
\(851\) 14131.5 0.569238
\(852\) 0 0
\(853\) −37864.5 −1.51988 −0.759939 0.649995i \(-0.774771\pi\)
−0.759939 + 0.649995i \(0.774771\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 64060.0 2.55786
\(857\) −29208.7 −1.16424 −0.582118 0.813104i \(-0.697776\pi\)
−0.582118 + 0.813104i \(0.697776\pi\)
\(858\) 0 0
\(859\) −34902.9 −1.38635 −0.693173 0.720771i \(-0.743788\pi\)
−0.693173 + 0.720771i \(0.743788\pi\)
\(860\) −27367.8 −1.08516
\(861\) 0 0
\(862\) 25947.6 1.02527
\(863\) 13589.3 0.536021 0.268011 0.963416i \(-0.413634\pi\)
0.268011 + 0.963416i \(0.413634\pi\)
\(864\) 0 0
\(865\) 1191.68 0.0468420
\(866\) −27899.0 −1.09474
\(867\) 0 0
\(868\) 0 0
\(869\) 6090.89 0.237767
\(870\) 0 0
\(871\) −7661.52 −0.298049
\(872\) −126261. −4.90338
\(873\) 0 0
\(874\) −43335.7 −1.67717
\(875\) 0 0
\(876\) 0 0
\(877\) −2379.75 −0.0916288 −0.0458144 0.998950i \(-0.514588\pi\)
−0.0458144 + 0.998950i \(0.514588\pi\)
\(878\) −4379.22 −0.168327
\(879\) 0 0
\(880\) 14065.7 0.538812
\(881\) −24235.5 −0.926803 −0.463401 0.886148i \(-0.653371\pi\)
−0.463401 + 0.886148i \(0.653371\pi\)
\(882\) 0 0
\(883\) −9844.13 −0.375177 −0.187589 0.982248i \(-0.560067\pi\)
−0.187589 + 0.982248i \(0.560067\pi\)
\(884\) −33927.3 −1.29084
\(885\) 0 0
\(886\) 69152.6 2.62215
\(887\) 28609.9 1.08300 0.541502 0.840699i \(-0.317856\pi\)
0.541502 + 0.840699i \(0.317856\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −46807.7 −1.76292
\(891\) 0 0
\(892\) −65498.4 −2.45857
\(893\) −67657.0 −2.53534
\(894\) 0 0
\(895\) 13554.4 0.506226
\(896\) 0 0
\(897\) 0 0
\(898\) 87725.2 3.25994
\(899\) −4634.09 −0.171919
\(900\) 0 0
\(901\) 12514.9 0.462743
\(902\) 1831.59 0.0676113
\(903\) 0 0
\(904\) 43498.0 1.60036
\(905\) 1382.74 0.0507886
\(906\) 0 0
\(907\) 44578.3 1.63197 0.815986 0.578071i \(-0.196194\pi\)
0.815986 + 0.578071i \(0.196194\pi\)
\(908\) 103678. 3.78928
\(909\) 0 0
\(910\) 0 0
\(911\) −45870.6 −1.66823 −0.834116 0.551589i \(-0.814022\pi\)
−0.834116 + 0.551589i \(0.814022\pi\)
\(912\) 0 0
\(913\) 3357.45 0.121703
\(914\) 19698.1 0.712863
\(915\) 0 0
\(916\) −12405.6 −0.447479
\(917\) 0 0
\(918\) 0 0
\(919\) 31088.3 1.11590 0.557948 0.829876i \(-0.311589\pi\)
0.557948 + 0.829876i \(0.311589\pi\)
\(920\) −26919.6 −0.964686
\(921\) 0 0
\(922\) 51564.8 1.84186
\(923\) 30374.0 1.08318
\(924\) 0 0
\(925\) −17753.7 −0.631069
\(926\) 229.732 0.00815278
\(927\) 0 0
\(928\) −32381.1 −1.14543
\(929\) −42094.5 −1.48663 −0.743313 0.668943i \(-0.766747\pi\)
−0.743313 + 0.668943i \(0.766747\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −57051.5 −2.00513
\(933\) 0 0
\(934\) 8138.87 0.285130
\(935\) 3365.26 0.117707
\(936\) 0 0
\(937\) 44385.1 1.54749 0.773745 0.633497i \(-0.218381\pi\)
0.773745 + 0.633497i \(0.218381\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −69636.6 −2.41627
\(941\) 40991.6 1.42007 0.710036 0.704165i \(-0.248679\pi\)
0.710036 + 0.704165i \(0.248679\pi\)
\(942\) 0 0
\(943\) −1856.39 −0.0641066
\(944\) 95416.1 3.28976
\(945\) 0 0
\(946\) 18017.4 0.619233
\(947\) 52622.4 1.80570 0.902851 0.429955i \(-0.141470\pi\)
0.902851 + 0.429955i \(0.141470\pi\)
\(948\) 0 0
\(949\) −12805.8 −0.438034
\(950\) 54443.6 1.85935
\(951\) 0 0
\(952\) 0 0
\(953\) 10798.1 0.367035 0.183517 0.983016i \(-0.441252\pi\)
0.183517 + 0.983016i \(0.441252\pi\)
\(954\) 0 0
\(955\) 23986.8 0.812768
\(956\) 69260.0 2.34313
\(957\) 0 0
\(958\) 37345.8 1.25949
\(959\) 0 0
\(960\) 0 0
\(961\) −25689.5 −0.862324
\(962\) 38742.2 1.29844
\(963\) 0 0
\(964\) 53191.4 1.77716
\(965\) 11461.2 0.382331
\(966\) 0 0
\(967\) 15648.9 0.520408 0.260204 0.965554i \(-0.416210\pi\)
0.260204 + 0.965554i \(0.416210\pi\)
\(968\) 73520.4 2.44115
\(969\) 0 0
\(970\) 2340.33 0.0774675
\(971\) 47259.8 1.56194 0.780968 0.624571i \(-0.214726\pi\)
0.780968 + 0.624571i \(0.214726\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 81595.2 2.68427
\(975\) 0 0
\(976\) 69680.7 2.28527
\(977\) 48966.5 1.60346 0.801728 0.597689i \(-0.203914\pi\)
0.801728 + 0.597689i \(0.203914\pi\)
\(978\) 0 0
\(979\) 22066.6 0.720380
\(980\) 0 0
\(981\) 0 0
\(982\) −12704.6 −0.412851
\(983\) −19111.3 −0.620097 −0.310049 0.950721i \(-0.600345\pi\)
−0.310049 + 0.950721i \(0.600345\pi\)
\(984\) 0 0
\(985\) 9265.77 0.299728
\(986\) −16700.3 −0.539397
\(987\) 0 0
\(988\) −85076.4 −2.73951
\(989\) −18261.3 −0.587134
\(990\) 0 0
\(991\) −54102.5 −1.73423 −0.867115 0.498107i \(-0.834029\pi\)
−0.867115 + 0.498107i \(0.834029\pi\)
\(992\) 28659.7 0.917286
\(993\) 0 0
\(994\) 0 0
\(995\) 6048.21 0.192705
\(996\) 0 0
\(997\) −9192.80 −0.292015 −0.146008 0.989283i \(-0.546642\pi\)
−0.146008 + 0.989283i \(0.546642\pi\)
\(998\) −3681.41 −0.116766
\(999\) 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 441.4.a.t.1.1 3
3.2 odd 2 147.4.a.m.1.3 3
7.2 even 3 441.4.e.w.361.3 6
7.3 odd 6 63.4.e.c.37.3 6
7.4 even 3 441.4.e.w.226.3 6
7.5 odd 6 63.4.e.c.46.3 6
7.6 odd 2 441.4.a.s.1.1 3
12.11 even 2 2352.4.a.cg.1.2 3
21.2 odd 6 147.4.e.n.67.1 6
21.5 even 6 21.4.e.b.4.1 6
21.11 odd 6 147.4.e.n.79.1 6
21.17 even 6 21.4.e.b.16.1 yes 6
21.20 even 2 147.4.a.l.1.3 3
84.47 odd 6 336.4.q.k.193.2 6
84.59 odd 6 336.4.q.k.289.2 6
84.83 odd 2 2352.4.a.ci.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.e.b.4.1 6 21.5 even 6
21.4.e.b.16.1 yes 6 21.17 even 6
63.4.e.c.37.3 6 7.3 odd 6
63.4.e.c.46.3 6 7.5 odd 6
147.4.a.l.1.3 3 21.20 even 2
147.4.a.m.1.3 3 3.2 odd 2
147.4.e.n.67.1 6 21.2 odd 6
147.4.e.n.79.1 6 21.11 odd 6
336.4.q.k.193.2 6 84.47 odd 6
336.4.q.k.289.2 6 84.59 odd 6
441.4.a.s.1.1 3 7.6 odd 2
441.4.a.t.1.1 3 1.1 even 1 trivial
441.4.e.w.226.3 6 7.4 even 3
441.4.e.w.361.3 6 7.2 even 3
2352.4.a.cg.1.2 3 12.11 even 2
2352.4.a.ci.1.2 3 84.83 odd 2