Properties

Label 1521.4.a.bk.1.9
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 1.9
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 \(-0.149370\pi\)
0.891903 + 0.452226i \(0.149370\pi\)
\(3\) 0 0
\(4\) 17.4557 2.18197
\(5\) 20.1174 1.79935 0.899677 0.436556i \(-0.143802\pi\)
0.899677 + 0.436556i \(0.143802\pi\)
\(6\) 0 0
\(7\) 15.4279 0.833028 0.416514 0.909129i \(-0.363252\pi\)
0.416514 + 0.909129i \(0.363252\pi\)
\(8\) 47.7076 2.10840
\(9\) 0 0
\(10\) 101.500 3.20970
\(11\) −26.9372 −0.738352 −0.369176 0.929359i \(-0.620360\pi\)
−0.369176 + 0.929359i \(0.620360\pi\)
\(12\) 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 \(-0.587737\pi\)
−0.272156 + 0.962253i \(0.587737\pi\)
\(20\) 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 \(-0.534901\pi\)
−0.109426 + 0.993995i \(0.534901\pi\)
\(32\) 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 \(-0.254416\pi\)
0.697228 + 0.716849i \(0.254416\pi\)
\(38\) −227.442 −0.970947
\(39\) 0 0
\(40\) 959.753 3.79376
\(41\) 5.86820 0.0223527 0.0111763 0.999938i \(-0.496442\pi\)
0.0111763 + 0.999938i \(0.496442\pi\)
\(42\) 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 \(-0.394475\pi\)
0.325478 + 0.945550i \(0.394475\pi\)
\(48\) 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 \(-0.295447\pi\)
0.599298 + 0.800526i \(0.295447\pi\)
\(60\) 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 \(-0.351748\pi\)
0.449090 + 0.893487i \(0.351748\pi\)
\(68\) −405.557 −0.723249
\(69\) 0 0
\(70\) 1565.93 2.67377
\(71\) −826.859 −1.38211 −0.691057 0.722800i \(-0.742855\pi\)
−0.691057 + 0.722800i \(0.742855\pi\)
\(72\) 0 0
\(73\) 66.1205 0.106011 0.0530056 0.998594i \(-0.483120\pi\)
0.0530056 + 0.998594i \(0.483120\pi\)
\(74\) 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 \(-0.529816\pi\)
−0.0935313 + 0.995616i \(0.529816\pi\)
\(84\) 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 \(-0.624733\pi\)
−0.381909 + 0.924200i \(0.624733\pi\)
\(90\) 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 \(-0.698326\pi\)
−0.583522 + 0.812097i \(0.698326\pi\)
\(98\) −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 \(-0.360301\pi\)
0.424924 + 0.905229i \(0.360301\pi\)
\(110\) −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 \(-0.718335\pi\)
−0.633385 + 0.773837i \(0.718335\pi\)
\(138\) 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 \(-0.585587\pi\)
−0.265650 + 0.964069i \(0.585587\pi\)
\(150\) 0 0
\(151\) 1463.09 0.788505 0.394252 0.919002i \(-0.371004\pi\)
0.394252 + 0.919002i \(0.371004\pi\)
\(152\) −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 \(-0.178413\pi\)
0.846988 + 0.531612i \(0.178413\pi\)
\(164\) 102.434 0.0487728
\(165\) 0 0
\(166\) −713.669 −0.333683
\(167\) −260.652 −0.120777 −0.0603887 0.998175i \(-0.519234\pi\)
−0.0603887 + 0.998175i \(0.519234\pi\)
\(168\) 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 \(-0.456541\pi\)
0.136107 + 0.990694i \(0.456541\pi\)
\(194\) −5625.20 −2.08178
\(195\) 0 0
\(196\) −1832.50 −0.667822
\(197\) 1701.11 0.615225 0.307613 0.951512i \(-0.400470\pi\)
0.307613 + 0.951512i \(0.400470\pi\)
\(198\) 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 \(-0.385792\pi\)
0.351148 + 0.936320i \(0.385792\pi\)
\(224\) 1977.96 0.589993
\(225\) 0 0
\(226\) −9641.57 −2.83782
\(227\) 3279.36 0.958850 0.479425 0.877583i \(-0.340845\pi\)
0.479425 + 0.877583i \(0.340845\pi\)
\(228\) 0 0
\(229\) −1143.72 −0.330041 −0.165021 0.986290i \(-0.552769\pi\)
−0.165021 + 0.986290i \(0.552769\pi\)
\(230\) 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 \(-0.647837\pi\)
−0.447924 + 0.894072i \(0.647837\pi\)
\(240\) 0 0
\(241\) −5702.86 −1.52429 −0.762145 0.647407i \(-0.775854\pi\)
−0.762145 + 0.647407i \(0.775854\pi\)
\(242\) −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 \(-0.484704\pi\)
0.0480357 + 0.998846i \(0.484704\pi\)
\(272\) −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 \(-0.526243\pi\)
−0.0823514 + 0.996603i \(0.526243\pi\)
\(282\) 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 \(-0.335496\pi\)
0.494104 + 0.869403i \(0.335496\pi\)
\(294\) 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 \(-0.617920\pi\)
−0.362042 + 0.932162i \(0.617920\pi\)
\(308\) −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 \(-0.706521\pi\)
−0.604233 + 0.796807i \(0.706521\pi\)
\(318\) 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 \(-0.363355\pi\)
0.416219 + 0.909264i \(0.363355\pi\)
\(332\) −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 \(-0.385467\pi\)
0.352102 + 0.935961i \(0.385467\pi\)
\(350\) 21772.4 3.32510
\(351\) 0 0
\(352\) −3453.54 −0.522938
\(353\) 1740.09 0.262367 0.131183 0.991358i \(-0.458122\pi\)
0.131183 + 0.991358i \(0.458122\pi\)
\(354\) 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 \(-0.466585\pi\)
0.104784 + 0.994495i \(0.466585\pi\)
\(360\) 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 \(-0.827543\pi\)
−0.856786 + 0.515671i \(0.827543\pi\)
\(380\) −15830.3 −2.13704
\(381\) 0 0
\(382\) 10380.7 1.39037
\(383\) −2321.51 −0.309722 −0.154861 0.987936i \(-0.549493\pi\)
−0.154861 + 0.987936i \(0.549493\pi\)
\(384\) 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 \(-0.535624\pi\)
−0.111682 + 0.993744i \(0.535624\pi\)
\(398\) −9287.91 −1.16975
\(399\) 0 0
\(400\) 28266.5 3.53332
\(401\) 5001.65 0.622869 0.311434 0.950268i \(-0.399191\pi\)
0.311434 + 0.950268i \(0.399191\pi\)
\(402\) 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 \(-0.736954\pi\)
−0.677541 + 0.735485i \(0.736954\pi\)
\(410\) 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 \(-0.779370\pi\)
−0.769250 + 0.638948i \(0.779370\pi\)
\(422\) 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 \(-0.222680\pi\)
0.765119 + 0.643889i \(0.222680\pi\)
\(432\) 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 \(-0.560171\pi\)
−0.187909 + 0.982186i \(0.560171\pi\)
\(450\) 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 \(-0.364679\pi\)
0.412435 + 0.910987i \(0.364679\pi\)
\(458\) −5770.51 −0.588730
\(459\) 0 0
\(460\) 49868.8 5.05466
\(461\) −11692.1 −1.18125 −0.590626 0.806945i \(-0.701119\pi\)
−0.590626 + 0.806945i \(0.701119\pi\)
\(462\) 0 0
\(463\) 1732.40 0.173891 0.0869455 0.996213i \(-0.472289\pi\)
0.0869455 + 0.996213i \(0.472289\pi\)
\(464\) −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 \(-0.623161\pi\)
−0.377340 + 0.926075i \(0.623161\pi\)
\(480\) 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 \(-0.670401\pi\)
−0.510125 + 0.860100i \(0.670401\pi\)
\(488\) 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 \(-0.690806\pi\)
−0.564175 + 0.825655i \(0.690806\pi\)
\(500\) 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 \(-0.894611\pi\)
−0.945689 + 0.325073i \(0.894611\pi\)
\(510\) 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 \(-0.494249\pi\)
0.0180651 + 0.999837i \(0.494249\pi\)
\(542\) 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 \(-0.559475\pi\)
−0.185762 + 0.982595i \(0.559475\pi\)
\(558\) 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 \(-0.342851\pi\)
0.473885 + 0.880587i \(0.342851\pi\)
\(578\) −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 \(-0.784148\pi\)
−0.778754 + 0.627330i \(0.784148\pi\)
\(588\) 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 \(-0.210900\pi\)
0.788419 + 0.615138i \(0.210900\pi\)
\(594\) 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 \(-0.201433\pi\)
0.806362 + 0.591422i \(0.201433\pi\)
\(614\) −19651.2 −1.29163
\(615\) 0 0
\(616\) −19826.5 −1.29681
\(617\) −2423.28 −0.158116 −0.0790581 0.996870i \(-0.525191\pi\)
−0.0790581 + 0.996870i \(0.525191\pi\)
\(618\) 0 0
\(619\) 17223.4 1.11836 0.559182 0.829045i \(-0.311115\pi\)
0.559182 + 0.829045i \(0.311115\pi\)
\(620\) −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 \(-0.405828\pi\)
0.291554 + 0.956554i \(0.405828\pi\)
\(632\) 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 \(-0.216334\pi\)
0.777804 + 0.628507i \(0.216334\pi\)
\(644\) 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 \(-0.290151\pi\)
0.612533 + 0.790445i \(0.290151\pi\)
\(662\) 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 \(-0.0751196\pi\)
0.972282 + 0.233811i \(0.0751196\pi\)
\(684\) 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 \(-0.605865\pi\)
−0.326487 + 0.945202i \(0.605865\pi\)
\(692\) −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 \(-0.771834\pi\)
−0.753910 + 0.656978i \(0.771834\pi\)
\(710\) −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 \(-0.697930\pi\)
−0.582511 + 0.812823i \(0.697930\pi\)
\(734\) 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 \(-0.327116\pi\)
0.516819 + 0.856095i \(0.327116\pi\)
\(740\) 110209. 5.47482
\(741\) 0 0
\(742\) −21552.7 −1.06634
\(743\) 36995.8 1.82671 0.913354 0.407166i \(-0.133483\pi\)
0.913354 + 0.407166i \(0.133483\pi\)
\(744\) 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 \(-0.444050\pi\)
0.174869 + 0.984592i \(0.444050\pi\)
\(762\) 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 \(-0.612234\pi\)
−0.345333 + 0.938480i \(0.612234\pi\)
\(770\) −42181.7 −1.97418
\(771\) 0 0
\(772\) 12740.5 0.593963
\(773\) −9937.41 −0.462385 −0.231193 0.972908i \(-0.574263\pi\)
−0.231193 + 0.972908i \(0.574263\pi\)
\(774\) 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 \(-0.192750\pi\)
0.822194 + 0.569207i \(0.192750\pi\)
\(788\) 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 \(-0.529251\pi\)
−0.0917643 + 0.995781i \(0.529251\pi\)
\(812\) −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 \(-0.540257\pi\)
−0.126136 + 0.992013i \(0.540257\pi\)
\(822\) 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 \(-0.639159\pi\)
−0.423386 + 0.905949i \(0.639159\pi\)
\(828\) 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 \(-0.306341\pi\)
0.571554 + 0.820564i \(0.306341\pi\)
\(840\) 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 \(-0.392694\pi\)
0.330763 + 0.943714i \(0.392694\pi\)
\(854\) 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 \(-0.497939\pi\)
0.00647514 + 0.999979i \(0.497939\pi\)
\(864\) 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 \(-0.195185\pi\)
0.817815 + 0.575482i \(0.195185\pi\)
\(878\) 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 \(-0.403004\pi\)
0.300027 + 0.953931i \(0.403004\pi\)
\(930\) 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 \(-0.860623\pi\)
−0.905659 + 0.424006i \(0.860623\pi\)
\(942\) 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 \(-0.567954\pi\)
−0.211865 + 0.977299i \(0.567954\pi\)
\(948\) 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 \(-0.559549\pi\)
−0.185991 + 0.982552i \(0.559549\pi\)
\(968\) −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 \(-0.629674\pi\)
−0.396207 + 0.918161i \(0.629674\pi\)
\(978\) 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 \(-0.315520\pi\)
0.547658 + 0.836702i \(0.315520\pi\)
\(984\) 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.1.9 10
3.2 odd 2 507.4.a.r.1.2 10
13.6 odd 12 117.4.q.e.10.1 10
13.11 odd 12 117.4.q.e.82.1 10
13.12 even 2 inner 1521.4.a.bk.1.2 10
39.5 even 4 507.4.b.i.337.9 10
39.8 even 4 507.4.b.i.337.2 10
39.11 even 12 39.4.j.c.4.5 10
39.32 even 12 39.4.j.c.10.5 yes 10
39.38 odd 2 507.4.a.r.1.9 10
156.11 odd 12 624.4.bv.h.433.1 10
156.71 odd 12 624.4.bv.h.49.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.5 10 39.11 even 12
39.4.j.c.10.5 yes 10 39.32 even 12
117.4.q.e.10.1 10 13.6 odd 12
117.4.q.e.82.1 10 13.11 odd 12
507.4.a.r.1.2 10 3.2 odd 2
507.4.a.r.1.9 10 39.38 odd 2
507.4.b.i.337.2 10 39.8 even 4
507.4.b.i.337.9 10 39.5 even 4
624.4.bv.h.49.5 10 156.71 odd 12
624.4.bv.h.433.1 10 156.11 odd 12
1521.4.a.bk.1.2 10 13.12 even 2 inner
1521.4.a.bk.1.9 10 1.1 even 1 trivial