Properties

Label 1521.4.a.bk.1.2
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(89.7419051187\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-5.04537\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.04537 q^{2} +17.4557 q^{4} -20.1174 q^{5} -15.4279 q^{7} -47.7076 q^{8} +O(q^{10})\) \(q-5.04537 q^{2} +17.4557 q^{4} -20.1174 q^{5} -15.4279 q^{7} -47.7076 q^{8} +101.500 q^{10} +26.9372 q^{11} +77.8394 q^{14} +101.057 q^{16} -23.2334 q^{17} +45.0794 q^{19} -351.164 q^{20} -135.908 q^{22} +142.010 q^{23} +279.710 q^{25} -269.305 q^{28} -2.29068 q^{29} +37.7740 q^{31} -128.207 q^{32} +117.221 q^{34} +310.369 q^{35} -313.840 q^{37} -227.442 q^{38} +959.753 q^{40} -5.86820 q^{41} -360.898 q^{43} +470.209 q^{44} -716.493 q^{46} -209.748 q^{47} -104.980 q^{49} -1411.24 q^{50} -276.886 q^{53} -541.906 q^{55} +736.028 q^{56} +11.5573 q^{58} -543.189 q^{59} +205.788 q^{61} -190.583 q^{62} -161.602 q^{64} -492.578 q^{67} -405.557 q^{68} -1565.93 q^{70} +826.859 q^{71} -66.1205 q^{73} +1583.44 q^{74} +786.894 q^{76} -415.584 q^{77} +317.642 q^{79} -2033.00 q^{80} +29.6072 q^{82} +141.450 q^{83} +467.396 q^{85} +1820.86 q^{86} -1285.11 q^{88} +641.320 q^{89} +2478.89 q^{92} +1058.26 q^{94} -906.880 q^{95} +1114.92 q^{97} +529.663 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 60 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 60 q^{4} + 80 q^{10} + 60 q^{14} + 500 q^{16} - 210 q^{17} + 580 q^{22} + 120 q^{23} + 960 q^{25} - 990 q^{29} + 120 q^{35} - 1380 q^{38} + 2000 q^{40} - 740 q^{43} + 1550 q^{49} - 330 q^{53} + 520 q^{55} + 5340 q^{56} + 2750 q^{61} + 1560 q^{62} + 3140 q^{64} - 1200 q^{68} + 4380 q^{74} - 4320 q^{77} + 1100 q^{79} - 4780 q^{82} + 6340 q^{88} + 1740 q^{92} + 6460 q^{94} + 2760 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.04537 −1.78381 −0.891903 0.452226i \(-0.850630\pi\)
−0.891903 + 0.452226i \(0.850630\pi\)
\(3\) 0 0
\(4\) 17.4557 2.18197
\(5\) −20.1174 −1.79935 −0.899677 0.436556i \(-0.856198\pi\)
−0.899677 + 0.436556i \(0.856198\pi\)
\(6\) 0 0
\(7\) −15.4279 −0.833028 −0.416514 0.909129i \(-0.636748\pi\)
−0.416514 + 0.909129i \(0.636748\pi\)
\(8\) −47.7076 −2.10840
\(9\) 0 0
\(10\) 101.500 3.20970
\(11\) 26.9372 0.738352 0.369176 0.929359i \(-0.379640\pi\)
0.369176 + 0.929359i \(0.379640\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 77.8394 1.48596
\(15\) 0 0
\(16\) 101.057 1.57901
\(17\) −23.2334 −0.331467 −0.165733 0.986171i \(-0.552999\pi\)
−0.165733 + 0.986171i \(0.552999\pi\)
\(18\) 0 0
\(19\) 45.0794 0.544312 0.272156 0.962253i \(-0.412263\pi\)
0.272156 + 0.962253i \(0.412263\pi\)
\(20\) −351.164 −3.92613
\(21\) 0 0
\(22\) −135.908 −1.31708
\(23\) 142.010 1.28744 0.643720 0.765261i \(-0.277390\pi\)
0.643720 + 0.765261i \(0.277390\pi\)
\(24\) 0 0
\(25\) 279.710 2.23768
\(26\) 0 0
\(27\) 0 0
\(28\) −269.305 −1.81764
\(29\) −2.29068 −0.0146679 −0.00733394 0.999973i \(-0.502334\pi\)
−0.00733394 + 0.999973i \(0.502334\pi\)
\(30\) 0 0
\(31\) 37.7740 0.218852 0.109426 0.993995i \(-0.465099\pi\)
0.109426 + 0.993995i \(0.465099\pi\)
\(32\) −128.207 −0.708251
\(33\) 0 0
\(34\) 117.221 0.591273
\(35\) 310.369 1.49891
\(36\) 0 0
\(37\) −313.840 −1.39446 −0.697228 0.716849i \(-0.745584\pi\)
−0.697228 + 0.716849i \(0.745584\pi\)
\(38\) −227.442 −0.970947
\(39\) 0 0
\(40\) 959.753 3.79376
\(41\) −5.86820 −0.0223527 −0.0111763 0.999938i \(-0.503558\pi\)
−0.0111763 + 0.999938i \(0.503558\pi\)
\(42\) 0 0
\(43\) −360.898 −1.27992 −0.639958 0.768410i \(-0.721048\pi\)
−0.639958 + 0.768410i \(0.721048\pi\)
\(44\) 470.209 1.61106
\(45\) 0 0
\(46\) −716.493 −2.29655
\(47\) −209.748 −0.650956 −0.325478 0.945550i \(-0.605525\pi\)
−0.325478 + 0.945550i \(0.605525\pi\)
\(48\) 0 0
\(49\) −104.980 −0.306064
\(50\) −1411.24 −3.99158
\(51\) 0 0
\(52\) 0 0
\(53\) −276.886 −0.717609 −0.358804 0.933413i \(-0.616815\pi\)
−0.358804 + 0.933413i \(0.616815\pi\)
\(54\) 0 0
\(55\) −541.906 −1.32856
\(56\) 736.028 1.75636
\(57\) 0 0
\(58\) 11.5573 0.0261647
\(59\) −543.189 −1.19860 −0.599298 0.800526i \(-0.704553\pi\)
−0.599298 + 0.800526i \(0.704553\pi\)
\(60\) 0 0
\(61\) 205.788 0.431942 0.215971 0.976400i \(-0.430708\pi\)
0.215971 + 0.976400i \(0.430708\pi\)
\(62\) −190.583 −0.390389
\(63\) 0 0
\(64\) −161.602 −0.315629
\(65\) 0 0
\(66\) 0 0
\(67\) −492.578 −0.898179 −0.449090 0.893487i \(-0.648252\pi\)
−0.449090 + 0.893487i \(0.648252\pi\)
\(68\) −405.557 −0.723249
\(69\) 0 0
\(70\) −1565.93 −2.67377
\(71\) 826.859 1.38211 0.691057 0.722800i \(-0.257145\pi\)
0.691057 + 0.722800i \(0.257145\pi\)
\(72\) 0 0
\(73\) −66.1205 −0.106011 −0.0530056 0.998594i \(-0.516880\pi\)
−0.0530056 + 0.998594i \(0.516880\pi\)
\(74\) 1583.44 2.48744
\(75\) 0 0
\(76\) 786.894 1.18767
\(77\) −415.584 −0.615068
\(78\) 0 0
\(79\) 317.642 0.452374 0.226187 0.974084i \(-0.427374\pi\)
0.226187 + 0.974084i \(0.427374\pi\)
\(80\) −2033.00 −2.84120
\(81\) 0 0
\(82\) 29.6072 0.0398728
\(83\) 141.450 0.187063 0.0935313 0.995616i \(-0.470184\pi\)
0.0935313 + 0.995616i \(0.470184\pi\)
\(84\) 0 0
\(85\) 467.396 0.596426
\(86\) 1820.86 2.28312
\(87\) 0 0
\(88\) −1285.11 −1.55674
\(89\) 641.320 0.763818 0.381909 0.924200i \(-0.375267\pi\)
0.381909 + 0.924200i \(0.375267\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2478.89 2.80915
\(93\) 0 0
\(94\) 1058.26 1.16118
\(95\) −906.880 −0.979410
\(96\) 0 0
\(97\) 1114.92 1.16704 0.583522 0.812097i \(-0.301674\pi\)
0.583522 + 0.812097i \(0.301674\pi\)
\(98\) 529.663 0.545960
\(99\) 0 0
\(100\) 4882.53 4.88253
\(101\) −1589.91 −1.56635 −0.783177 0.621799i \(-0.786402\pi\)
−0.783177 + 0.621799i \(0.786402\pi\)
\(102\) 0 0
\(103\) 527.502 0.504625 0.252312 0.967646i \(-0.418809\pi\)
0.252312 + 0.967646i \(0.418809\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1396.99 1.28008
\(107\) −1751.96 −1.58289 −0.791443 0.611243i \(-0.790670\pi\)
−0.791443 + 0.611243i \(0.790670\pi\)
\(108\) 0 0
\(109\) −967.122 −0.849848 −0.424924 0.905229i \(-0.639699\pi\)
−0.424924 + 0.905229i \(0.639699\pi\)
\(110\) 2734.12 2.36989
\(111\) 0 0
\(112\) −1559.09 −1.31536
\(113\) −1910.97 −1.59088 −0.795439 0.606033i \(-0.792760\pi\)
−0.795439 + 0.606033i \(0.792760\pi\)
\(114\) 0 0
\(115\) −2856.87 −2.31656
\(116\) −39.9855 −0.0320048
\(117\) 0 0
\(118\) 2740.59 2.13806
\(119\) 358.443 0.276121
\(120\) 0 0
\(121\) −605.387 −0.454836
\(122\) −1038.28 −0.770501
\(123\) 0 0
\(124\) 659.372 0.477527
\(125\) −3112.35 −2.22702
\(126\) 0 0
\(127\) 1233.11 0.861584 0.430792 0.902451i \(-0.358234\pi\)
0.430792 + 0.902451i \(0.358234\pi\)
\(128\) 1841.00 1.27127
\(129\) 0 0
\(130\) 0 0
\(131\) 1274.90 0.850292 0.425146 0.905125i \(-0.360223\pi\)
0.425146 + 0.905125i \(0.360223\pi\)
\(132\) 0 0
\(133\) −695.480 −0.453427
\(134\) 2485.24 1.60218
\(135\) 0 0
\(136\) 1108.41 0.698864
\(137\) 2031.32 1.26677 0.633385 0.773837i \(-0.281665\pi\)
0.633385 + 0.773837i \(0.281665\pi\)
\(138\) 0 0
\(139\) −1445.66 −0.882156 −0.441078 0.897469i \(-0.645404\pi\)
−0.441078 + 0.897469i \(0.645404\pi\)
\(140\) 5417.72 3.27058
\(141\) 0 0
\(142\) −4171.81 −2.46542
\(143\) 0 0
\(144\) 0 0
\(145\) 46.0825 0.0263927
\(146\) 333.602 0.189103
\(147\) 0 0
\(148\) −5478.30 −3.04266
\(149\) 966.318 0.531301 0.265650 0.964069i \(-0.414413\pi\)
0.265650 + 0.964069i \(0.414413\pi\)
\(150\) 0 0
\(151\) −1463.09 −0.788505 −0.394252 0.919002i \(-0.628996\pi\)
−0.394252 + 0.919002i \(0.628996\pi\)
\(152\) −2150.63 −1.14763
\(153\) 0 0
\(154\) 2096.78 1.09716
\(155\) −759.914 −0.393792
\(156\) 0 0
\(157\) −66.0424 −0.0335717 −0.0167859 0.999859i \(-0.505343\pi\)
−0.0167859 + 0.999859i \(0.505343\pi\)
\(158\) −1602.62 −0.806948
\(159\) 0 0
\(160\) 2579.19 1.27439
\(161\) −2190.92 −1.07247
\(162\) 0 0
\(163\) −3525.24 −1.69398 −0.846988 0.531612i \(-0.821587\pi\)
−0.846988 + 0.531612i \(0.821587\pi\)
\(164\) −102.434 −0.0487728
\(165\) 0 0
\(166\) −713.669 −0.333683
\(167\) 260.652 0.120777 0.0603887 0.998175i \(-0.480766\pi\)
0.0603887 + 0.998175i \(0.480766\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −2358.19 −1.06391
\(171\) 0 0
\(172\) −6299.74 −2.79273
\(173\) −911.753 −0.400689 −0.200345 0.979725i \(-0.564206\pi\)
−0.200345 + 0.979725i \(0.564206\pi\)
\(174\) 0 0
\(175\) −4315.33 −1.86405
\(176\) 2722.18 1.16587
\(177\) 0 0
\(178\) −3235.70 −1.36250
\(179\) −2690.48 −1.12344 −0.561721 0.827327i \(-0.689861\pi\)
−0.561721 + 0.827327i \(0.689861\pi\)
\(180\) 0 0
\(181\) 4773.85 1.96043 0.980213 0.197944i \(-0.0634265\pi\)
0.980213 + 0.197944i \(0.0634265\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6774.96 −2.71444
\(185\) 6313.63 2.50912
\(186\) 0 0
\(187\) −625.844 −0.244739
\(188\) −3661.31 −1.42036
\(189\) 0 0
\(190\) 4575.54 1.74708
\(191\) 2057.47 0.779443 0.389721 0.920933i \(-0.372571\pi\)
0.389721 + 0.920933i \(0.372571\pi\)
\(192\) 0 0
\(193\) −729.873 −0.272215 −0.136107 0.990694i \(-0.543459\pi\)
−0.136107 + 0.990694i \(0.543459\pi\)
\(194\) −5625.20 −2.08178
\(195\) 0 0
\(196\) −1832.50 −0.667822
\(197\) −1701.11 −0.615225 −0.307613 0.951512i \(-0.599530\pi\)
−0.307613 + 0.951512i \(0.599530\pi\)
\(198\) 0 0
\(199\) −1840.88 −0.655761 −0.327881 0.944719i \(-0.606334\pi\)
−0.327881 + 0.944719i \(0.606334\pi\)
\(200\) −13344.3 −4.71792
\(201\) 0 0
\(202\) 8021.66 2.79407
\(203\) 35.3404 0.0122188
\(204\) 0 0
\(205\) 118.053 0.0402204
\(206\) −2661.44 −0.900153
\(207\) 0 0
\(208\) 0 0
\(209\) 1214.31 0.401894
\(210\) 0 0
\(211\) 142.970 0.0466467 0.0233234 0.999728i \(-0.492575\pi\)
0.0233234 + 0.999728i \(0.492575\pi\)
\(212\) −4833.25 −1.56580
\(213\) 0 0
\(214\) 8839.31 2.82356
\(215\) 7260.32 2.30302
\(216\) 0 0
\(217\) −582.773 −0.182310
\(218\) 4879.48 1.51597
\(219\) 0 0
\(220\) −9459.37 −2.89887
\(221\) 0 0
\(222\) 0 0
\(223\) −2338.71 −0.702295 −0.351148 0.936320i \(-0.614208\pi\)
−0.351148 + 0.936320i \(0.614208\pi\)
\(224\) 1977.96 0.589993
\(225\) 0 0
\(226\) 9641.57 2.83782
\(227\) −3279.36 −0.958850 −0.479425 0.877583i \(-0.659155\pi\)
−0.479425 + 0.877583i \(0.659155\pi\)
\(228\) 0 0
\(229\) 1143.72 0.330041 0.165021 0.986290i \(-0.447231\pi\)
0.165021 + 0.986290i \(0.447231\pi\)
\(230\) 14414.0 4.13230
\(231\) 0 0
\(232\) 109.283 0.0309258
\(233\) 4238.17 1.19164 0.595819 0.803118i \(-0.296827\pi\)
0.595819 + 0.803118i \(0.296827\pi\)
\(234\) 0 0
\(235\) 4219.59 1.17130
\(236\) −9481.75 −2.61529
\(237\) 0 0
\(238\) −1808.48 −0.492547
\(239\) 3310.03 0.895849 0.447924 0.894072i \(-0.352163\pi\)
0.447924 + 0.894072i \(0.352163\pi\)
\(240\) 0 0
\(241\) 5702.86 1.52429 0.762145 0.647407i \(-0.224146\pi\)
0.762145 + 0.647407i \(0.224146\pi\)
\(242\) 3054.40 0.811340
\(243\) 0 0
\(244\) 3592.18 0.942483
\(245\) 2111.93 0.550718
\(246\) 0 0
\(247\) 0 0
\(248\) −1802.11 −0.461427
\(249\) 0 0
\(250\) 15703.0 3.97257
\(251\) 3910.23 0.983313 0.491657 0.870789i \(-0.336392\pi\)
0.491657 + 0.870789i \(0.336392\pi\)
\(252\) 0 0
\(253\) 3825.35 0.950585
\(254\) −6221.51 −1.53690
\(255\) 0 0
\(256\) −7995.69 −1.95207
\(257\) −6972.80 −1.69242 −0.846209 0.532851i \(-0.821121\pi\)
−0.846209 + 0.532851i \(0.821121\pi\)
\(258\) 0 0
\(259\) 4841.88 1.16162
\(260\) 0 0
\(261\) 0 0
\(262\) −6432.32 −1.51676
\(263\) −281.691 −0.0660449 −0.0330224 0.999455i \(-0.510513\pi\)
−0.0330224 + 0.999455i \(0.510513\pi\)
\(264\) 0 0
\(265\) 5570.23 1.29123
\(266\) 3508.95 0.808826
\(267\) 0 0
\(268\) −8598.31 −1.95980
\(269\) −4333.13 −0.982139 −0.491070 0.871120i \(-0.663394\pi\)
−0.491070 + 0.871120i \(0.663394\pi\)
\(270\) 0 0
\(271\) −428.596 −0.0960715 −0.0480357 0.998846i \(-0.515296\pi\)
−0.0480357 + 0.998846i \(0.515296\pi\)
\(272\) −2347.89 −0.523390
\(273\) 0 0
\(274\) −10248.8 −2.25967
\(275\) 7534.59 1.65219
\(276\) 0 0
\(277\) 8938.75 1.93891 0.969454 0.245274i \(-0.0788779\pi\)
0.969454 + 0.245274i \(0.0788779\pi\)
\(278\) 7293.91 1.57360
\(279\) 0 0
\(280\) −14807.0 −3.16031
\(281\) 775.819 0.164703 0.0823514 0.996603i \(-0.473757\pi\)
0.0823514 + 0.996603i \(0.473757\pi\)
\(282\) 0 0
\(283\) −4014.53 −0.843248 −0.421624 0.906771i \(-0.638540\pi\)
−0.421624 + 0.906771i \(0.638540\pi\)
\(284\) 14433.4 3.01573
\(285\) 0 0
\(286\) 0 0
\(287\) 90.5340 0.0186204
\(288\) 0 0
\(289\) −4373.21 −0.890130
\(290\) −232.503 −0.0470795
\(291\) 0 0
\(292\) −1154.18 −0.231313
\(293\) −4956.21 −0.988208 −0.494104 0.869403i \(-0.664504\pi\)
−0.494104 + 0.869403i \(0.664504\pi\)
\(294\) 0 0
\(295\) 10927.5 2.15670
\(296\) 14972.5 2.94007
\(297\) 0 0
\(298\) −4875.43 −0.947738
\(299\) 0 0
\(300\) 0 0
\(301\) 5567.89 1.06621
\(302\) 7381.80 1.40654
\(303\) 0 0
\(304\) 4555.58 0.859474
\(305\) −4139.92 −0.777217
\(306\) 0 0
\(307\) 3894.90 0.724084 0.362042 0.932162i \(-0.382080\pi\)
0.362042 + 0.932162i \(0.382080\pi\)
\(308\) −7254.33 −1.34206
\(309\) 0 0
\(310\) 3834.04 0.702448
\(311\) −3097.44 −0.564758 −0.282379 0.959303i \(-0.591124\pi\)
−0.282379 + 0.959303i \(0.591124\pi\)
\(312\) 0 0
\(313\) 4487.36 0.810353 0.405177 0.914238i \(-0.367210\pi\)
0.405177 + 0.914238i \(0.367210\pi\)
\(314\) 333.208 0.0598854
\(315\) 0 0
\(316\) 5544.68 0.987065
\(317\) 6820.62 1.20847 0.604233 0.796807i \(-0.293479\pi\)
0.604233 + 0.796807i \(0.293479\pi\)
\(318\) 0 0
\(319\) −61.7045 −0.0108301
\(320\) 3251.01 0.567928
\(321\) 0 0
\(322\) 11054.0 1.91309
\(323\) −1047.35 −0.180421
\(324\) 0 0
\(325\) 0 0
\(326\) 17786.1 3.02173
\(327\) 0 0
\(328\) 279.958 0.0471283
\(329\) 3235.98 0.542265
\(330\) 0 0
\(331\) −5012.96 −0.832438 −0.416219 0.909264i \(-0.636645\pi\)
−0.416219 + 0.909264i \(0.636645\pi\)
\(332\) 2469.12 0.408164
\(333\) 0 0
\(334\) −1315.08 −0.215444
\(335\) 9909.39 1.61614
\(336\) 0 0
\(337\) 3220.79 0.520616 0.260308 0.965526i \(-0.416176\pi\)
0.260308 + 0.965526i \(0.416176\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 8158.74 1.30138
\(341\) 1017.52 0.161590
\(342\) 0 0
\(343\) 6911.39 1.08799
\(344\) 17217.6 2.69858
\(345\) 0 0
\(346\) 4600.13 0.714753
\(347\) 3360.71 0.519921 0.259960 0.965619i \(-0.416290\pi\)
0.259960 + 0.965619i \(0.416290\pi\)
\(348\) 0 0
\(349\) −4591.32 −0.704205 −0.352102 0.935961i \(-0.614533\pi\)
−0.352102 + 0.935961i \(0.614533\pi\)
\(350\) 21772.4 3.32510
\(351\) 0 0
\(352\) −3453.54 −0.522938
\(353\) −1740.09 −0.262367 −0.131183 0.991358i \(-0.541878\pi\)
−0.131183 + 0.991358i \(0.541878\pi\)
\(354\) 0 0
\(355\) −16634.2 −2.48691
\(356\) 11194.7 1.66662
\(357\) 0 0
\(358\) 13574.5 2.00400
\(359\) −1425.49 −0.209567 −0.104784 0.994495i \(-0.533415\pi\)
−0.104784 + 0.994495i \(0.533415\pi\)
\(360\) 0 0
\(361\) −4826.85 −0.703725
\(362\) −24085.8 −3.49702
\(363\) 0 0
\(364\) 0 0
\(365\) 1330.17 0.190752
\(366\) 0 0
\(367\) 10849.2 1.54312 0.771559 0.636158i \(-0.219477\pi\)
0.771559 + 0.636158i \(0.219477\pi\)
\(368\) 14351.1 2.03288
\(369\) 0 0
\(370\) −31854.6 −4.47579
\(371\) 4271.77 0.597788
\(372\) 0 0
\(373\) −494.749 −0.0686786 −0.0343393 0.999410i \(-0.510933\pi\)
−0.0343393 + 0.999410i \(0.510933\pi\)
\(374\) 3157.61 0.436567
\(375\) 0 0
\(376\) 10006.6 1.37248
\(377\) 0 0
\(378\) 0 0
\(379\) 12643.3 1.71357 0.856786 0.515671i \(-0.172457\pi\)
0.856786 + 0.515671i \(0.172457\pi\)
\(380\) −15830.3 −2.13704
\(381\) 0 0
\(382\) −10380.7 −1.39037
\(383\) 2321.51 0.309722 0.154861 0.987936i \(-0.450507\pi\)
0.154861 + 0.987936i \(0.450507\pi\)
\(384\) 0 0
\(385\) 8360.47 1.10673
\(386\) 3682.48 0.485578
\(387\) 0 0
\(388\) 19461.8 2.54645
\(389\) 10477.6 1.36564 0.682821 0.730586i \(-0.260753\pi\)
0.682821 + 0.730586i \(0.260753\pi\)
\(390\) 0 0
\(391\) −3299.38 −0.426744
\(392\) 5008.35 0.645306
\(393\) 0 0
\(394\) 8582.75 1.09744
\(395\) −6390.14 −0.813982
\(396\) 0 0
\(397\) 1766.85 0.223364 0.111682 0.993744i \(-0.464376\pi\)
0.111682 + 0.993744i \(0.464376\pi\)
\(398\) 9287.91 1.16975
\(399\) 0 0
\(400\) 28266.5 3.53332
\(401\) −5001.65 −0.622869 −0.311434 0.950268i \(-0.600809\pi\)
−0.311434 + 0.950268i \(0.600809\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −27753.0 −3.41773
\(405\) 0 0
\(406\) −178.305 −0.0217959
\(407\) −8453.96 −1.02960
\(408\) 0 0
\(409\) 11208.6 1.35508 0.677541 0.735485i \(-0.263046\pi\)
0.677541 + 0.735485i \(0.263046\pi\)
\(410\) −595.620 −0.0717453
\(411\) 0 0
\(412\) 9207.94 1.10107
\(413\) 8380.26 0.998464
\(414\) 0 0
\(415\) −2845.61 −0.336592
\(416\) 0 0
\(417\) 0 0
\(418\) −6126.66 −0.716901
\(419\) −3285.19 −0.383036 −0.191518 0.981489i \(-0.561341\pi\)
−0.191518 + 0.981489i \(0.561341\pi\)
\(420\) 0 0
\(421\) 13289.9 1.53850 0.769250 0.638948i \(-0.220630\pi\)
0.769250 + 0.638948i \(0.220630\pi\)
\(422\) −721.336 −0.0832087
\(423\) 0 0
\(424\) 13209.6 1.51301
\(425\) −6498.61 −0.741715
\(426\) 0 0
\(427\) −3174.88 −0.359820
\(428\) −30581.8 −3.45380
\(429\) 0 0
\(430\) −36631.0 −4.10815
\(431\) −13692.3 −1.53024 −0.765119 0.643889i \(-0.777320\pi\)
−0.765119 + 0.643889i \(0.777320\pi\)
\(432\) 0 0
\(433\) −10002.5 −1.11014 −0.555070 0.831804i \(-0.687308\pi\)
−0.555070 + 0.831804i \(0.687308\pi\)
\(434\) 2940.30 0.325205
\(435\) 0 0
\(436\) −16881.8 −1.85434
\(437\) 6401.73 0.700769
\(438\) 0 0
\(439\) 4487.21 0.487842 0.243921 0.969795i \(-0.421566\pi\)
0.243921 + 0.969795i \(0.421566\pi\)
\(440\) 25853.1 2.80113
\(441\) 0 0
\(442\) 0 0
\(443\) −2035.35 −0.218290 −0.109145 0.994026i \(-0.534811\pi\)
−0.109145 + 0.994026i \(0.534811\pi\)
\(444\) 0 0
\(445\) −12901.7 −1.37438
\(446\) 11799.7 1.25276
\(447\) 0 0
\(448\) 2493.18 0.262928
\(449\) 3575.58 0.375818 0.187909 0.982186i \(-0.439829\pi\)
0.187909 + 0.982186i \(0.439829\pi\)
\(450\) 0 0
\(451\) −158.073 −0.0165041
\(452\) −33357.4 −3.47124
\(453\) 0 0
\(454\) 16545.6 1.71040
\(455\) 0 0
\(456\) 0 0
\(457\) −8058.60 −0.824869 −0.412435 0.910987i \(-0.635321\pi\)
−0.412435 + 0.910987i \(0.635321\pi\)
\(458\) −5770.51 −0.588730
\(459\) 0 0
\(460\) −49868.8 −5.05466
\(461\) 11692.1 1.18125 0.590626 0.806945i \(-0.298881\pi\)
0.590626 + 0.806945i \(0.298881\pi\)
\(462\) 0 0
\(463\) −1732.40 −0.173891 −0.0869455 0.996213i \(-0.527711\pi\)
−0.0869455 + 0.996213i \(0.527711\pi\)
\(464\) −231.489 −0.0231607
\(465\) 0 0
\(466\) −21383.1 −2.12565
\(467\) −10769.9 −1.06718 −0.533588 0.845745i \(-0.679157\pi\)
−0.533588 + 0.845745i \(0.679157\pi\)
\(468\) 0 0
\(469\) 7599.44 0.748208
\(470\) −21289.4 −2.08937
\(471\) 0 0
\(472\) 25914.2 2.52712
\(473\) −9721.58 −0.945029
\(474\) 0 0
\(475\) 12609.1 1.21799
\(476\) 6256.88 0.602487
\(477\) 0 0
\(478\) −16700.3 −1.59802
\(479\) 7911.64 0.754680 0.377340 0.926075i \(-0.376839\pi\)
0.377340 + 0.926075i \(0.376839\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −28773.0 −2.71904
\(483\) 0 0
\(484\) −10567.5 −0.992438
\(485\) −22429.3 −2.09993
\(486\) 0 0
\(487\) 10964.8 1.02025 0.510125 0.860100i \(-0.329599\pi\)
0.510125 + 0.860100i \(0.329599\pi\)
\(488\) −9817.66 −0.910707
\(489\) 0 0
\(490\) −10655.4 −0.982375
\(491\) 9139.37 0.840029 0.420014 0.907518i \(-0.362025\pi\)
0.420014 + 0.907518i \(0.362025\pi\)
\(492\) 0 0
\(493\) 53.2204 0.00486192
\(494\) 0 0
\(495\) 0 0
\(496\) 3817.31 0.345569
\(497\) −12756.7 −1.15134
\(498\) 0 0
\(499\) 12577.5 1.12835 0.564175 0.825655i \(-0.309194\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(500\) −54328.4 −4.85928
\(501\) 0 0
\(502\) −19728.6 −1.75404
\(503\) −13214.6 −1.17139 −0.585696 0.810531i \(-0.699179\pi\)
−0.585696 + 0.810531i \(0.699179\pi\)
\(504\) 0 0
\(505\) 31984.8 2.81842
\(506\) −19300.3 −1.69566
\(507\) 0 0
\(508\) 21524.9 1.87995
\(509\) 21719.8 1.89138 0.945689 0.325073i \(-0.105389\pi\)
0.945689 + 0.325073i \(0.105389\pi\)
\(510\) 0 0
\(511\) 1020.10 0.0883103
\(512\) 25613.2 2.21085
\(513\) 0 0
\(514\) 35180.4 3.01895
\(515\) −10612.0 −0.907999
\(516\) 0 0
\(517\) −5650.03 −0.480635
\(518\) −24429.1 −2.07211
\(519\) 0 0
\(520\) 0 0
\(521\) 4627.05 0.389088 0.194544 0.980894i \(-0.437677\pi\)
0.194544 + 0.980894i \(0.437677\pi\)
\(522\) 0 0
\(523\) 13784.0 1.15245 0.576224 0.817292i \(-0.304526\pi\)
0.576224 + 0.817292i \(0.304526\pi\)
\(524\) 22254.3 1.85531
\(525\) 0 0
\(526\) 1421.23 0.117811
\(527\) −877.619 −0.0725421
\(528\) 0 0
\(529\) 7999.85 0.657504
\(530\) −28103.9 −2.30331
\(531\) 0 0
\(532\) −12140.1 −0.989362
\(533\) 0 0
\(534\) 0 0
\(535\) 35245.0 2.84817
\(536\) 23499.7 1.89372
\(537\) 0 0
\(538\) 21862.2 1.75195
\(539\) −2827.87 −0.225983
\(540\) 0 0
\(541\) −454.638 −0.0361302 −0.0180651 0.999837i \(-0.505751\pi\)
−0.0180651 + 0.999837i \(0.505751\pi\)
\(542\) 2162.43 0.171373
\(543\) 0 0
\(544\) 2978.69 0.234762
\(545\) 19456.0 1.52918
\(546\) 0 0
\(547\) 11611.4 0.907621 0.453810 0.891098i \(-0.350064\pi\)
0.453810 + 0.891098i \(0.350064\pi\)
\(548\) 35458.2 2.76405
\(549\) 0 0
\(550\) −38014.8 −2.94719
\(551\) −103.263 −0.00798390
\(552\) 0 0
\(553\) −4900.55 −0.376840
\(554\) −45099.3 −3.45864
\(555\) 0 0
\(556\) −25235.1 −1.92483
\(557\) 4883.93 0.371524 0.185762 0.982595i \(-0.440525\pi\)
0.185762 + 0.982595i \(0.440525\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 31364.9 2.36680
\(561\) 0 0
\(562\) −3914.29 −0.293798
\(563\) −19617.3 −1.46851 −0.734256 0.678873i \(-0.762469\pi\)
−0.734256 + 0.678873i \(0.762469\pi\)
\(564\) 0 0
\(565\) 38443.8 2.86256
\(566\) 20254.8 1.50419
\(567\) 0 0
\(568\) −39447.5 −2.91405
\(569\) −7475.19 −0.550749 −0.275374 0.961337i \(-0.588802\pi\)
−0.275374 + 0.961337i \(0.588802\pi\)
\(570\) 0 0
\(571\) −7799.56 −0.571631 −0.285816 0.958285i \(-0.592265\pi\)
−0.285816 + 0.958285i \(0.592265\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −456.777 −0.0332152
\(575\) 39721.6 2.88088
\(576\) 0 0
\(577\) −13136.1 −0.947771 −0.473885 0.880587i \(-0.657149\pi\)
−0.473885 + 0.880587i \(0.657149\pi\)
\(578\) 22064.4 1.58782
\(579\) 0 0
\(580\) 804.404 0.0575880
\(581\) −2182.28 −0.155828
\(582\) 0 0
\(583\) −7458.54 −0.529848
\(584\) 3154.45 0.223514
\(585\) 0 0
\(586\) 25005.9 1.76277
\(587\) 22150.7 1.55751 0.778754 0.627330i \(-0.215852\pi\)
0.778754 + 0.627330i \(0.215852\pi\)
\(588\) 0 0
\(589\) 1702.83 0.119124
\(590\) −55133.4 −3.84713
\(591\) 0 0
\(592\) −31715.6 −2.20186
\(593\) −22770.3 −1.57684 −0.788419 0.615138i \(-0.789100\pi\)
−0.788419 + 0.615138i \(0.789100\pi\)
\(594\) 0 0
\(595\) −7210.94 −0.496840
\(596\) 16867.8 1.15928
\(597\) 0 0
\(598\) 0 0
\(599\) 7214.11 0.492088 0.246044 0.969259i \(-0.420869\pi\)
0.246044 + 0.969259i \(0.420869\pi\)
\(600\) 0 0
\(601\) 27276.7 1.85132 0.925658 0.378360i \(-0.123512\pi\)
0.925658 + 0.378360i \(0.123512\pi\)
\(602\) −28092.1 −1.90191
\(603\) 0 0
\(604\) −25539.2 −1.72049
\(605\) 12178.8 0.818412
\(606\) 0 0
\(607\) 11566.2 0.773403 0.386701 0.922205i \(-0.373614\pi\)
0.386701 + 0.922205i \(0.373614\pi\)
\(608\) −5779.50 −0.385509
\(609\) 0 0
\(610\) 20887.4 1.38640
\(611\) 0 0
\(612\) 0 0
\(613\) −24476.6 −1.61272 −0.806362 0.591422i \(-0.798567\pi\)
−0.806362 + 0.591422i \(0.798567\pi\)
\(614\) −19651.2 −1.29163
\(615\) 0 0
\(616\) 19826.5 1.29681
\(617\) 2423.28 0.158116 0.0790581 0.996870i \(-0.474809\pi\)
0.0790581 + 0.996870i \(0.474809\pi\)
\(618\) 0 0
\(619\) −17223.4 −1.11836 −0.559182 0.829045i \(-0.688885\pi\)
−0.559182 + 0.829045i \(0.688885\pi\)
\(620\) −13264.8 −0.859240
\(621\) 0 0
\(622\) 15627.7 1.00742
\(623\) −9894.22 −0.636282
\(624\) 0 0
\(625\) 27648.7 1.76952
\(626\) −22640.4 −1.44551
\(627\) 0 0
\(628\) −1152.82 −0.0732523
\(629\) 7291.57 0.462216
\(630\) 0 0
\(631\) −9242.58 −0.583108 −0.291554 0.956554i \(-0.594172\pi\)
−0.291554 + 0.956554i \(0.594172\pi\)
\(632\) −15154.0 −0.953786
\(633\) 0 0
\(634\) −34412.5 −2.15567
\(635\) −24807.0 −1.55029
\(636\) 0 0
\(637\) 0 0
\(638\) 311.322 0.0193187
\(639\) 0 0
\(640\) −37036.1 −2.28747
\(641\) 11598.8 0.714706 0.357353 0.933969i \(-0.383679\pi\)
0.357353 + 0.933969i \(0.383679\pi\)
\(642\) 0 0
\(643\) −25363.9 −1.55561 −0.777804 0.628507i \(-0.783666\pi\)
−0.777804 + 0.628507i \(0.783666\pi\)
\(644\) −38244.0 −2.34010
\(645\) 0 0
\(646\) 5284.26 0.321837
\(647\) 6590.09 0.400438 0.200219 0.979751i \(-0.435835\pi\)
0.200219 + 0.979751i \(0.435835\pi\)
\(648\) 0 0
\(649\) −14632.0 −0.884985
\(650\) 0 0
\(651\) 0 0
\(652\) −61535.6 −3.69620
\(653\) −15698.2 −0.940765 −0.470382 0.882463i \(-0.655884\pi\)
−0.470382 + 0.882463i \(0.655884\pi\)
\(654\) 0 0
\(655\) −25647.6 −1.52998
\(656\) −593.021 −0.0352951
\(657\) 0 0
\(658\) −16326.7 −0.967295
\(659\) −2840.81 −0.167925 −0.0839624 0.996469i \(-0.526758\pi\)
−0.0839624 + 0.996469i \(0.526758\pi\)
\(660\) 0 0
\(661\) −20819.1 −1.22507 −0.612533 0.790445i \(-0.709849\pi\)
−0.612533 + 0.790445i \(0.709849\pi\)
\(662\) 25292.2 1.48491
\(663\) 0 0
\(664\) −6748.26 −0.394403
\(665\) 13991.3 0.815876
\(666\) 0 0
\(667\) −325.300 −0.0188840
\(668\) 4549.87 0.263532
\(669\) 0 0
\(670\) −49996.5 −2.88289
\(671\) 5543.36 0.318925
\(672\) 0 0
\(673\) 31264.5 1.79073 0.895364 0.445335i \(-0.146916\pi\)
0.895364 + 0.445335i \(0.146916\pi\)
\(674\) −16250.1 −0.928679
\(675\) 0 0
\(676\) 0 0
\(677\) 27953.2 1.58689 0.793447 0.608639i \(-0.208284\pi\)
0.793447 + 0.608639i \(0.208284\pi\)
\(678\) 0 0
\(679\) −17200.9 −0.972180
\(680\) −22298.4 −1.25750
\(681\) 0 0
\(682\) −5133.79 −0.288245
\(683\) −34709.9 −1.94456 −0.972282 0.233811i \(-0.924880\pi\)
−0.972282 + 0.233811i \(0.924880\pi\)
\(684\) 0 0
\(685\) −40864.9 −2.27937
\(686\) −34870.5 −1.94076
\(687\) 0 0
\(688\) −36471.1 −2.02100
\(689\) 0 0
\(690\) 0 0
\(691\) 11860.8 0.652974 0.326487 0.945202i \(-0.394135\pi\)
0.326487 + 0.945202i \(0.394135\pi\)
\(692\) −15915.3 −0.874291
\(693\) 0 0
\(694\) −16956.0 −0.927438
\(695\) 29083.0 1.58731
\(696\) 0 0
\(697\) 136.338 0.00740916
\(698\) 23164.9 1.25617
\(699\) 0 0
\(700\) −75327.2 −4.06729
\(701\) −16100.5 −0.867486 −0.433743 0.901037i \(-0.642807\pi\)
−0.433743 + 0.901037i \(0.642807\pi\)
\(702\) 0 0
\(703\) −14147.7 −0.759019
\(704\) −4353.10 −0.233045
\(705\) 0 0
\(706\) 8779.38 0.468012
\(707\) 24528.9 1.30482
\(708\) 0 0
\(709\) 28465.5 1.50782 0.753910 0.656978i \(-0.228166\pi\)
0.753910 + 0.656978i \(0.228166\pi\)
\(710\) 83925.9 4.43617
\(711\) 0 0
\(712\) −30595.9 −1.61043
\(713\) 5364.28 0.281759
\(714\) 0 0
\(715\) 0 0
\(716\) −46964.4 −2.45131
\(717\) 0 0
\(718\) 7192.14 0.373828
\(719\) 27822.1 1.44310 0.721550 0.692362i \(-0.243430\pi\)
0.721550 + 0.692362i \(0.243430\pi\)
\(720\) 0 0
\(721\) −8138.25 −0.420367
\(722\) 24353.2 1.25531
\(723\) 0 0
\(724\) 83331.0 4.27758
\(725\) −640.725 −0.0328220
\(726\) 0 0
\(727\) 866.153 0.0441869 0.0220934 0.999756i \(-0.492967\pi\)
0.0220934 + 0.999756i \(0.492967\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −6711.20 −0.340264
\(731\) 8384.90 0.424250
\(732\) 0 0
\(733\) 23120.1 1.16502 0.582511 0.812823i \(-0.302070\pi\)
0.582511 + 0.812823i \(0.302070\pi\)
\(734\) −54738.3 −2.75262
\(735\) 0 0
\(736\) −18206.7 −0.911831
\(737\) −13268.7 −0.663172
\(738\) 0 0
\(739\) −20765.1 −1.03364 −0.516819 0.856095i \(-0.672884\pi\)
−0.516819 + 0.856095i \(0.672884\pi\)
\(740\) 110209. 5.47482
\(741\) 0 0
\(742\) −21552.7 −1.06634
\(743\) −36995.8 −1.82671 −0.913354 0.407166i \(-0.866517\pi\)
−0.913354 + 0.407166i \(0.866517\pi\)
\(744\) 0 0
\(745\) −19439.8 −0.955999
\(746\) 2496.19 0.122509
\(747\) 0 0
\(748\) −10924.6 −0.534013
\(749\) 27029.1 1.31859
\(750\) 0 0
\(751\) −34429.1 −1.67289 −0.836443 0.548055i \(-0.815369\pi\)
−0.836443 + 0.548055i \(0.815369\pi\)
\(752\) −21196.5 −1.02787
\(753\) 0 0
\(754\) 0 0
\(755\) 29433.5 1.41880
\(756\) 0 0
\(757\) 4268.88 0.204960 0.102480 0.994735i \(-0.467322\pi\)
0.102480 + 0.994735i \(0.467322\pi\)
\(758\) −63790.2 −3.05668
\(759\) 0 0
\(760\) 43265.1 2.06499
\(761\) −7342.11 −0.349739 −0.174869 0.984592i \(-0.555950\pi\)
−0.174869 + 0.984592i \(0.555950\pi\)
\(762\) 0 0
\(763\) 14920.7 0.707947
\(764\) 35914.7 1.70072
\(765\) 0 0
\(766\) −11712.9 −0.552484
\(767\) 0 0
\(768\) 0 0
\(769\) 14728.5 0.690666 0.345333 0.938480i \(-0.387766\pi\)
0.345333 + 0.938480i \(0.387766\pi\)
\(770\) −42181.7 −1.97418
\(771\) 0 0
\(772\) −12740.5 −0.593963
\(773\) 9937.41 0.462385 0.231193 0.972908i \(-0.425737\pi\)
0.231193 + 0.972908i \(0.425737\pi\)
\(774\) 0 0
\(775\) 10565.7 0.489719
\(776\) −53190.3 −2.46059
\(777\) 0 0
\(778\) −52863.3 −2.43604
\(779\) −264.535 −0.0121668
\(780\) 0 0
\(781\) 22273.3 1.02049
\(782\) 16646.6 0.761229
\(783\) 0 0
\(784\) −10608.9 −0.483279
\(785\) 1328.60 0.0604074
\(786\) 0 0
\(787\) −36305.0 −1.64439 −0.822194 0.569207i \(-0.807250\pi\)
−0.822194 + 0.569207i \(0.807250\pi\)
\(788\) −29694.2 −1.34240
\(789\) 0 0
\(790\) 32240.6 1.45199
\(791\) 29482.3 1.32525
\(792\) 0 0
\(793\) 0 0
\(794\) −8914.40 −0.398439
\(795\) 0 0
\(796\) −32133.9 −1.43085
\(797\) 9150.73 0.406694 0.203347 0.979107i \(-0.434818\pi\)
0.203347 + 0.979107i \(0.434818\pi\)
\(798\) 0 0
\(799\) 4873.17 0.215770
\(800\) −35860.7 −1.58484
\(801\) 0 0
\(802\) 25235.1 1.11108
\(803\) −1781.10 −0.0782736
\(804\) 0 0
\(805\) 44075.5 1.92976
\(806\) 0 0
\(807\) 0 0
\(808\) 75850.7 3.30250
\(809\) −30349.9 −1.31897 −0.659484 0.751719i \(-0.729225\pi\)
−0.659484 + 0.751719i \(0.729225\pi\)
\(810\) 0 0
\(811\) 4238.72 0.183529 0.0917643 0.995781i \(-0.470749\pi\)
0.0917643 + 0.995781i \(0.470749\pi\)
\(812\) 616.892 0.0266609
\(813\) 0 0
\(814\) 42653.3 1.83661
\(815\) 70918.6 3.04806
\(816\) 0 0
\(817\) −16269.1 −0.696674
\(818\) −56551.4 −2.41721
\(819\) 0 0
\(820\) 2060.70 0.0877595
\(821\) 5934.48 0.252271 0.126136 0.992013i \(-0.459743\pi\)
0.126136 + 0.992013i \(0.459743\pi\)
\(822\) 0 0
\(823\) −22459.6 −0.951265 −0.475633 0.879644i \(-0.657781\pi\)
−0.475633 + 0.879644i \(0.657781\pi\)
\(824\) −25165.9 −1.06395
\(825\) 0 0
\(826\) −42281.5 −1.78107
\(827\) 20138.4 0.846772 0.423386 0.905949i \(-0.360841\pi\)
0.423386 + 0.905949i \(0.360841\pi\)
\(828\) 0 0
\(829\) 5845.70 0.244909 0.122455 0.992474i \(-0.460923\pi\)
0.122455 + 0.992474i \(0.460923\pi\)
\(830\) 14357.2 0.600415
\(831\) 0 0
\(832\) 0 0
\(833\) 2439.05 0.101450
\(834\) 0 0
\(835\) −5243.63 −0.217322
\(836\) 21196.7 0.876919
\(837\) 0 0
\(838\) 16575.0 0.683261
\(839\) −27779.9 −1.14311 −0.571554 0.820564i \(-0.693659\pi\)
−0.571554 + 0.820564i \(0.693659\pi\)
\(840\) 0 0
\(841\) −24383.8 −0.999785
\(842\) −67052.3 −2.74439
\(843\) 0 0
\(844\) 2495.65 0.101782
\(845\) 0 0
\(846\) 0 0
\(847\) 9339.85 0.378891
\(848\) −27981.2 −1.13311
\(849\) 0 0
\(850\) 32787.9 1.32308
\(851\) −44568.4 −1.79528
\(852\) 0 0
\(853\) −16480.5 −0.661526 −0.330763 0.943714i \(-0.607306\pi\)
−0.330763 + 0.943714i \(0.607306\pi\)
\(854\) 16018.4 0.641849
\(855\) 0 0
\(856\) 83582.1 3.33736
\(857\) 45445.2 1.81141 0.905704 0.423910i \(-0.139343\pi\)
0.905704 + 0.423910i \(0.139343\pi\)
\(858\) 0 0
\(859\) −28243.1 −1.12182 −0.560909 0.827877i \(-0.689548\pi\)
−0.560909 + 0.827877i \(0.689548\pi\)
\(860\) 126734. 5.02512
\(861\) 0 0
\(862\) 69082.5 2.72965
\(863\) −328.319 −0.0129503 −0.00647514 0.999979i \(-0.502061\pi\)
−0.00647514 + 0.999979i \(0.502061\pi\)
\(864\) 0 0
\(865\) 18342.1 0.720982
\(866\) 50466.4 1.98027
\(867\) 0 0
\(868\) −10172.7 −0.397793
\(869\) 8556.40 0.334011
\(870\) 0 0
\(871\) 0 0
\(872\) 46139.1 1.79182
\(873\) 0 0
\(874\) −32299.1 −1.25004
\(875\) 48017.0 1.85517
\(876\) 0 0
\(877\) −42480.0 −1.63563 −0.817815 0.575482i \(-0.804815\pi\)
−0.817815 + 0.575482i \(0.804815\pi\)
\(878\) −22639.6 −0.870216
\(879\) 0 0
\(880\) −54763.3 −2.09781
\(881\) 5220.95 0.199657 0.0998287 0.995005i \(-0.468171\pi\)
0.0998287 + 0.995005i \(0.468171\pi\)
\(882\) 0 0
\(883\) 11790.3 0.449349 0.224674 0.974434i \(-0.427868\pi\)
0.224674 + 0.974434i \(0.427868\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 10269.1 0.389387
\(887\) 49352.3 1.86819 0.934097 0.357019i \(-0.116207\pi\)
0.934097 + 0.357019i \(0.116207\pi\)
\(888\) 0 0
\(889\) −19024.4 −0.717724
\(890\) 65093.8 2.45163
\(891\) 0 0
\(892\) −40823.9 −1.53238
\(893\) −9455.33 −0.354323
\(894\) 0 0
\(895\) 54125.5 2.02147
\(896\) −28402.7 −1.05900
\(897\) 0 0
\(898\) −18040.1 −0.670386
\(899\) −86.5281 −0.00321009
\(900\) 0 0
\(901\) 6433.02 0.237863
\(902\) 797.536 0.0294402
\(903\) 0 0
\(904\) 91168.1 3.35421
\(905\) −96037.3 −3.52750
\(906\) 0 0
\(907\) 6088.94 0.222910 0.111455 0.993769i \(-0.464449\pi\)
0.111455 + 0.993769i \(0.464449\pi\)
\(908\) −57243.7 −2.09218
\(909\) 0 0
\(910\) 0 0
\(911\) 30301.7 1.10202 0.551010 0.834499i \(-0.314243\pi\)
0.551010 + 0.834499i \(0.314243\pi\)
\(912\) 0 0
\(913\) 3810.28 0.138118
\(914\) 40658.6 1.47141
\(915\) 0 0
\(916\) 19964.5 0.720139
\(917\) −19669.0 −0.708317
\(918\) 0 0
\(919\) 34695.8 1.24538 0.622692 0.782467i \(-0.286039\pi\)
0.622692 + 0.782467i \(0.286039\pi\)
\(920\) 136295. 4.88424
\(921\) 0 0
\(922\) −58991.2 −2.10713
\(923\) 0 0
\(924\) 0 0
\(925\) −87783.9 −3.12034
\(926\) 8740.61 0.310188
\(927\) 0 0
\(928\) 293.681 0.0103885
\(929\) −16990.8 −0.600054 −0.300027 0.953931i \(-0.596996\pi\)
−0.300027 + 0.953931i \(0.596996\pi\)
\(930\) 0 0
\(931\) −4732.44 −0.166594
\(932\) 73980.4 2.60012
\(933\) 0 0
\(934\) 54338.0 1.90363
\(935\) 12590.3 0.440372
\(936\) 0 0
\(937\) 9307.86 0.324519 0.162260 0.986748i \(-0.448122\pi\)
0.162260 + 0.986748i \(0.448122\pi\)
\(938\) −38342.0 −1.33466
\(939\) 0 0
\(940\) 73656.0 2.55574
\(941\) 52285.3 1.81132 0.905659 0.424006i \(-0.139377\pi\)
0.905659 + 0.424006i \(0.139377\pi\)
\(942\) 0 0
\(943\) −833.344 −0.0287777
\(944\) −54892.8 −1.89260
\(945\) 0 0
\(946\) 49048.9 1.68575
\(947\) 12348.5 0.423731 0.211865 0.977299i \(-0.432046\pi\)
0.211865 + 0.977299i \(0.432046\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −63617.7 −2.17267
\(951\) 0 0
\(952\) −17100.5 −0.582174
\(953\) 25631.0 0.871218 0.435609 0.900136i \(-0.356533\pi\)
0.435609 + 0.900136i \(0.356533\pi\)
\(954\) 0 0
\(955\) −41391.0 −1.40249
\(956\) 57778.9 1.95471
\(957\) 0 0
\(958\) −39917.1 −1.34620
\(959\) −31339.0 −1.05525
\(960\) 0 0
\(961\) −28364.1 −0.952104
\(962\) 0 0
\(963\) 0 0
\(964\) 99547.7 3.32595
\(965\) 14683.1 0.489811
\(966\) 0 0
\(967\) 11185.6 0.371981 0.185991 0.982552i \(-0.440451\pi\)
0.185991 + 0.982552i \(0.440451\pi\)
\(968\) 28881.6 0.958977
\(969\) 0 0
\(970\) 113164. 3.74586
\(971\) 23541.3 0.778039 0.389019 0.921230i \(-0.372814\pi\)
0.389019 + 0.921230i \(0.372814\pi\)
\(972\) 0 0
\(973\) 22303.6 0.734860
\(974\) −55321.3 −1.81993
\(975\) 0 0
\(976\) 20796.3 0.682041
\(977\) 24198.8 0.792415 0.396207 0.918161i \(-0.370326\pi\)
0.396207 + 0.918161i \(0.370326\pi\)
\(978\) 0 0
\(979\) 17275.4 0.563966
\(980\) 36865.2 1.20165
\(981\) 0 0
\(982\) −46111.5 −1.49845
\(983\) −33757.4 −1.09532 −0.547658 0.836702i \(-0.684480\pi\)
−0.547658 + 0.836702i \(0.684480\pi\)
\(984\) 0 0
\(985\) 34222.0 1.10701
\(986\) −268.516 −0.00867272
\(987\) 0 0
\(988\) 0 0
\(989\) −51251.1 −1.64782
\(990\) 0 0
\(991\) 25298.5 0.810933 0.405466 0.914110i \(-0.367109\pi\)
0.405466 + 0.914110i \(0.367109\pi\)
\(992\) −4842.89 −0.155002
\(993\) 0 0
\(994\) 64362.2 2.05377
\(995\) 37033.7 1.17995
\(996\) 0 0
\(997\) −28766.1 −0.913773 −0.456886 0.889525i \(-0.651035\pi\)
−0.456886 + 0.889525i \(0.651035\pi\)
\(998\) −63458.2 −2.01276
\(999\) 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 1521.4.a.bk.1.2 10
3.2 odd 2 507.4.a.r.1.9 10
13.2 odd 12 117.4.q.e.82.1 10
13.7 odd 12 117.4.q.e.10.1 10
13.12 even 2 inner 1521.4.a.bk.1.9 10
39.2 even 12 39.4.j.c.4.5 10
39.5 even 4 507.4.b.i.337.2 10
39.8 even 4 507.4.b.i.337.9 10
39.20 even 12 39.4.j.c.10.5 yes 10
39.38 odd 2 507.4.a.r.1.2 10
156.59 odd 12 624.4.bv.h.49.5 10
156.119 odd 12 624.4.bv.h.433.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.5 10 39.2 even 12
39.4.j.c.10.5 yes 10 39.20 even 12
117.4.q.e.10.1 10 13.7 odd 12
117.4.q.e.82.1 10 13.2 odd 12
507.4.a.r.1.2 10 39.38 odd 2
507.4.a.r.1.9 10 3.2 odd 2
507.4.b.i.337.2 10 39.5 even 4
507.4.b.i.337.9 10 39.8 even 4
624.4.bv.h.49.5 10 156.59 odd 12
624.4.bv.h.433.1 10 156.119 odd 12
1521.4.a.bk.1.2 10 1.1 even 1 trivial
1521.4.a.bk.1.9 10 13.12 even 2 inner