Properties

Label 1521.4.a.bf.1.3
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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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: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 13^{2} \)
Twist minimal: no (minimal twist has level 507)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-4.83218\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.03025 q^{2} +8.24289 q^{4} -8.08864 q^{5} +5.95078 q^{7} -0.978887 q^{8} +O(q^{10})\) \(q-4.03025 q^{2} +8.24289 q^{4} -8.08864 q^{5} +5.95078 q^{7} -0.978887 q^{8} +32.5992 q^{10} -17.2359 q^{11} -23.9831 q^{14} -61.9979 q^{16} -92.9299 q^{17} +13.3832 q^{19} -66.6738 q^{20} +69.4648 q^{22} -219.710 q^{23} -59.5738 q^{25} +49.0516 q^{28} +199.485 q^{29} +307.777 q^{31} +257.698 q^{32} +374.531 q^{34} -48.1337 q^{35} -333.777 q^{37} -53.9376 q^{38} +7.91787 q^{40} +200.689 q^{41} +116.806 q^{43} -142.073 q^{44} +885.487 q^{46} -338.610 q^{47} -307.588 q^{49} +240.097 q^{50} +26.6215 q^{53} +139.415 q^{55} -5.82514 q^{56} -803.976 q^{58} +280.058 q^{59} -207.084 q^{61} -1240.42 q^{62} -542.603 q^{64} -285.981 q^{67} -766.011 q^{68} +193.991 q^{70} +317.673 q^{71} -63.0668 q^{73} +1345.20 q^{74} +110.316 q^{76} -102.567 q^{77} -623.835 q^{79} +501.479 q^{80} -808.824 q^{82} -659.874 q^{83} +751.677 q^{85} -470.755 q^{86} +16.8720 q^{88} -1273.19 q^{89} -1811.05 q^{92} +1364.68 q^{94} -108.252 q^{95} +603.746 q^{97} +1239.66 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} + 44 q^{4} - 33 q^{5} + 83 q^{7} - 87 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 6 q^{2} + 44 q^{4} - 33 q^{5} + 83 q^{7} - 87 q^{8} - 54 q^{10} - 85 q^{11} - 158 q^{14} + 216 q^{16} - 178 q^{17} + 352 q^{19} - 402 q^{20} - 630 q^{22} - 150 q^{23} - 20 q^{25} + 940 q^{28} + 97 q^{29} + 717 q^{31} - 707 q^{32} + 632 q^{34} + 418 q^{35} + 1108 q^{37} + 660 q^{38} - 1506 q^{40} - 334 q^{41} + 242 q^{43} + 307 q^{44} + 979 q^{46} + 184 q^{47} - 38 q^{49} + 2031 q^{50} + 151 q^{53} + 2064 q^{55} - 2276 q^{56} + 1161 q^{58} - 537 q^{59} - 1340 q^{61} - 347 q^{62} + 893 q^{64} + 2308 q^{67} - 2785 q^{68} - 1420 q^{70} - 96 q^{71} + 2505 q^{73} + 1191 q^{74} + 2409 q^{76} + 2142 q^{77} - 1591 q^{79} + 2671 q^{80} + 1517 q^{82} - 1539 q^{83} + 4296 q^{85} + 3763 q^{86} - 3716 q^{88} + 592 q^{89} - 515 q^{92} - 692 q^{94} - 4158 q^{95} + 1445 q^{97} - 1457 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.03025 −1.42491 −0.712454 0.701719i \(-0.752416\pi\)
−0.712454 + 0.701719i \(0.752416\pi\)
\(3\) 0 0
\(4\) 8.24289 1.03036
\(5\) −8.08864 −0.723470 −0.361735 0.932281i \(-0.617816\pi\)
−0.361735 + 0.932281i \(0.617816\pi\)
\(6\) 0 0
\(7\) 5.95078 0.321312 0.160656 0.987010i \(-0.448639\pi\)
0.160656 + 0.987010i \(0.448639\pi\)
\(8\) −0.978887 −0.0432611
\(9\) 0 0
\(10\) 32.5992 1.03088
\(11\) −17.2359 −0.472437 −0.236219 0.971700i \(-0.575908\pi\)
−0.236219 + 0.971700i \(0.575908\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −23.9831 −0.457840
\(15\) 0 0
\(16\) −61.9979 −0.968718
\(17\) −92.9299 −1.32581 −0.662907 0.748702i \(-0.730677\pi\)
−0.662907 + 0.748702i \(0.730677\pi\)
\(18\) 0 0
\(19\) 13.3832 0.161596 0.0807979 0.996731i \(-0.474253\pi\)
0.0807979 + 0.996731i \(0.474253\pi\)
\(20\) −66.6738 −0.745435
\(21\) 0 0
\(22\) 69.4648 0.673179
\(23\) −219.710 −1.99186 −0.995930 0.0901293i \(-0.971272\pi\)
−0.995930 + 0.0901293i \(0.971272\pi\)
\(24\) 0 0
\(25\) −59.5738 −0.476591
\(26\) 0 0
\(27\) 0 0
\(28\) 49.0516 0.331067
\(29\) 199.485 1.27736 0.638681 0.769471i \(-0.279480\pi\)
0.638681 + 0.769471i \(0.279480\pi\)
\(30\) 0 0
\(31\) 307.777 1.78317 0.891586 0.452851i \(-0.149593\pi\)
0.891586 + 0.452851i \(0.149593\pi\)
\(32\) 257.698 1.42359
\(33\) 0 0
\(34\) 374.531 1.88916
\(35\) −48.1337 −0.232460
\(36\) 0 0
\(37\) −333.777 −1.48304 −0.741521 0.670930i \(-0.765895\pi\)
−0.741521 + 0.670930i \(0.765895\pi\)
\(38\) −53.9376 −0.230259
\(39\) 0 0
\(40\) 7.91787 0.0312981
\(41\) 200.689 0.764446 0.382223 0.924070i \(-0.375159\pi\)
0.382223 + 0.924070i \(0.375159\pi\)
\(42\) 0 0
\(43\) 116.806 0.414248 0.207124 0.978315i \(-0.433590\pi\)
0.207124 + 0.978315i \(0.433590\pi\)
\(44\) −142.073 −0.486781
\(45\) 0 0
\(46\) 885.487 2.83822
\(47\) −338.610 −1.05088 −0.525440 0.850831i \(-0.676099\pi\)
−0.525440 + 0.850831i \(0.676099\pi\)
\(48\) 0 0
\(49\) −307.588 −0.896759
\(50\) 240.097 0.679097
\(51\) 0 0
\(52\) 0 0
\(53\) 26.6215 0.0689951 0.0344975 0.999405i \(-0.489017\pi\)
0.0344975 + 0.999405i \(0.489017\pi\)
\(54\) 0 0
\(55\) 139.415 0.341794
\(56\) −5.82514 −0.0139003
\(57\) 0 0
\(58\) −803.976 −1.82012
\(59\) 280.058 0.617973 0.308987 0.951066i \(-0.400010\pi\)
0.308987 + 0.951066i \(0.400010\pi\)
\(60\) 0 0
\(61\) −207.084 −0.434663 −0.217332 0.976098i \(-0.569735\pi\)
−0.217332 + 0.976098i \(0.569735\pi\)
\(62\) −1240.42 −2.54086
\(63\) 0 0
\(64\) −542.603 −1.05977
\(65\) 0 0
\(66\) 0 0
\(67\) −285.981 −0.521465 −0.260732 0.965411i \(-0.583964\pi\)
−0.260732 + 0.965411i \(0.583964\pi\)
\(68\) −766.011 −1.36607
\(69\) 0 0
\(70\) 193.991 0.331233
\(71\) 317.673 0.530998 0.265499 0.964111i \(-0.414463\pi\)
0.265499 + 0.964111i \(0.414463\pi\)
\(72\) 0 0
\(73\) −63.0668 −0.101115 −0.0505576 0.998721i \(-0.516100\pi\)
−0.0505576 + 0.998721i \(0.516100\pi\)
\(74\) 1345.20 2.11320
\(75\) 0 0
\(76\) 110.316 0.166502
\(77\) −102.567 −0.151800
\(78\) 0 0
\(79\) −623.835 −0.888443 −0.444221 0.895917i \(-0.646520\pi\)
−0.444221 + 0.895917i \(0.646520\pi\)
\(80\) 501.479 0.700838
\(81\) 0 0
\(82\) −808.824 −1.08926
\(83\) −659.874 −0.872658 −0.436329 0.899787i \(-0.643722\pi\)
−0.436329 + 0.899787i \(0.643722\pi\)
\(84\) 0 0
\(85\) 751.677 0.959186
\(86\) −470.755 −0.590265
\(87\) 0 0
\(88\) 16.8720 0.0204382
\(89\) −1273.19 −1.51638 −0.758191 0.652032i \(-0.773917\pi\)
−0.758191 + 0.652032i \(0.773917\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1811.05 −2.05233
\(93\) 0 0
\(94\) 1364.68 1.49741
\(95\) −108.252 −0.116910
\(96\) 0 0
\(97\) 603.746 0.631970 0.315985 0.948764i \(-0.397665\pi\)
0.315985 + 0.948764i \(0.397665\pi\)
\(98\) 1239.66 1.27780
\(99\) 0 0
\(100\) −491.060 −0.491060
\(101\) 740.588 0.729616 0.364808 0.931083i \(-0.381135\pi\)
0.364808 + 0.931083i \(0.381135\pi\)
\(102\) 0 0
\(103\) −1888.57 −1.80666 −0.903332 0.428942i \(-0.858887\pi\)
−0.903332 + 0.428942i \(0.858887\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −107.291 −0.0983116
\(107\) 919.463 0.830728 0.415364 0.909655i \(-0.363654\pi\)
0.415364 + 0.909655i \(0.363654\pi\)
\(108\) 0 0
\(109\) 1570.40 1.37998 0.689988 0.723821i \(-0.257616\pi\)
0.689988 + 0.723821i \(0.257616\pi\)
\(110\) −561.876 −0.487025
\(111\) 0 0
\(112\) −368.936 −0.311260
\(113\) 1324.66 1.10277 0.551386 0.834250i \(-0.314099\pi\)
0.551386 + 0.834250i \(0.314099\pi\)
\(114\) 0 0
\(115\) 1777.16 1.44105
\(116\) 1644.34 1.31614
\(117\) 0 0
\(118\) −1128.70 −0.880555
\(119\) −553.006 −0.426000
\(120\) 0 0
\(121\) −1033.92 −0.776803
\(122\) 834.601 0.619354
\(123\) 0 0
\(124\) 2536.97 1.83731
\(125\) 1492.95 1.06827
\(126\) 0 0
\(127\) −2350.39 −1.64223 −0.821115 0.570763i \(-0.806648\pi\)
−0.821115 + 0.570763i \(0.806648\pi\)
\(128\) 125.240 0.0864824
\(129\) 0 0
\(130\) 0 0
\(131\) −2308.69 −1.53978 −0.769890 0.638177i \(-0.779689\pi\)
−0.769890 + 0.638177i \(0.779689\pi\)
\(132\) 0 0
\(133\) 79.6405 0.0519226
\(134\) 1152.57 0.743039
\(135\) 0 0
\(136\) 90.9680 0.0573562
\(137\) 374.912 0.233802 0.116901 0.993144i \(-0.462704\pi\)
0.116901 + 0.993144i \(0.462704\pi\)
\(138\) 0 0
\(139\) 487.711 0.297605 0.148802 0.988867i \(-0.452458\pi\)
0.148802 + 0.988867i \(0.452458\pi\)
\(140\) −396.761 −0.239517
\(141\) 0 0
\(142\) −1280.30 −0.756623
\(143\) 0 0
\(144\) 0 0
\(145\) −1613.57 −0.924134
\(146\) 254.175 0.144080
\(147\) 0 0
\(148\) −2751.28 −1.52807
\(149\) −1055.91 −0.580558 −0.290279 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(150\) 0 0
\(151\) −888.560 −0.478874 −0.239437 0.970912i \(-0.576963\pi\)
−0.239437 + 0.970912i \(0.576963\pi\)
\(152\) −13.1007 −0.00699081
\(153\) 0 0
\(154\) 413.370 0.216301
\(155\) −2489.50 −1.29007
\(156\) 0 0
\(157\) −3648.56 −1.85469 −0.927346 0.374206i \(-0.877915\pi\)
−0.927346 + 0.374206i \(0.877915\pi\)
\(158\) 2514.21 1.26595
\(159\) 0 0
\(160\) −2084.43 −1.02993
\(161\) −1307.45 −0.640008
\(162\) 0 0
\(163\) 1386.49 0.666249 0.333125 0.942883i \(-0.391897\pi\)
0.333125 + 0.942883i \(0.391897\pi\)
\(164\) 1654.25 0.787655
\(165\) 0 0
\(166\) 2659.46 1.24346
\(167\) 3376.19 1.56442 0.782209 0.623017i \(-0.214093\pi\)
0.782209 + 0.623017i \(0.214093\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −3029.44 −1.36675
\(171\) 0 0
\(172\) 962.815 0.426825
\(173\) −341.817 −0.150219 −0.0751095 0.997175i \(-0.523931\pi\)
−0.0751095 + 0.997175i \(0.523931\pi\)
\(174\) 0 0
\(175\) −354.511 −0.153134
\(176\) 1068.59 0.457658
\(177\) 0 0
\(178\) 5131.28 2.16070
\(179\) 2885.55 1.20489 0.602446 0.798159i \(-0.294193\pi\)
0.602446 + 0.798159i \(0.294193\pi\)
\(180\) 0 0
\(181\) 3795.62 1.55871 0.779354 0.626584i \(-0.215547\pi\)
0.779354 + 0.626584i \(0.215547\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 215.072 0.0861701
\(185\) 2699.80 1.07294
\(186\) 0 0
\(187\) 1601.73 0.626363
\(188\) −2791.12 −1.08278
\(189\) 0 0
\(190\) 436.282 0.166586
\(191\) 2805.90 1.06297 0.531486 0.847067i \(-0.321634\pi\)
0.531486 + 0.847067i \(0.321634\pi\)
\(192\) 0 0
\(193\) −2485.64 −0.927048 −0.463524 0.886084i \(-0.653415\pi\)
−0.463524 + 0.886084i \(0.653415\pi\)
\(194\) −2433.24 −0.900499
\(195\) 0 0
\(196\) −2535.41 −0.923985
\(197\) −2750.70 −0.994818 −0.497409 0.867516i \(-0.665715\pi\)
−0.497409 + 0.867516i \(0.665715\pi\)
\(198\) 0 0
\(199\) 3998.53 1.42436 0.712182 0.701994i \(-0.247707\pi\)
0.712182 + 0.701994i \(0.247707\pi\)
\(200\) 58.3161 0.0206178
\(201\) 0 0
\(202\) −2984.75 −1.03964
\(203\) 1187.09 0.410432
\(204\) 0 0
\(205\) −1623.30 −0.553054
\(206\) 7611.41 2.57433
\(207\) 0 0
\(208\) 0 0
\(209\) −230.671 −0.0763438
\(210\) 0 0
\(211\) −1375.80 −0.448882 −0.224441 0.974488i \(-0.572056\pi\)
−0.224441 + 0.974488i \(0.572056\pi\)
\(212\) 219.438 0.0710898
\(213\) 0 0
\(214\) −3705.66 −1.18371
\(215\) −944.799 −0.299696
\(216\) 0 0
\(217\) 1831.51 0.572955
\(218\) −6329.12 −1.96634
\(219\) 0 0
\(220\) 1149.18 0.352171
\(221\) 0 0
\(222\) 0 0
\(223\) 1694.37 0.508805 0.254403 0.967098i \(-0.418121\pi\)
0.254403 + 0.967098i \(0.418121\pi\)
\(224\) 1533.50 0.457418
\(225\) 0 0
\(226\) −5338.70 −1.57135
\(227\) 405.400 0.118534 0.0592672 0.998242i \(-0.481124\pi\)
0.0592672 + 0.998242i \(0.481124\pi\)
\(228\) 0 0
\(229\) 2359.54 0.680884 0.340442 0.940265i \(-0.389423\pi\)
0.340442 + 0.940265i \(0.389423\pi\)
\(230\) −7162.39 −2.05337
\(231\) 0 0
\(232\) −195.274 −0.0552601
\(233\) −938.507 −0.263878 −0.131939 0.991258i \(-0.542120\pi\)
−0.131939 + 0.991258i \(0.542120\pi\)
\(234\) 0 0
\(235\) 2738.90 0.760280
\(236\) 2308.49 0.636736
\(237\) 0 0
\(238\) 2228.75 0.607010
\(239\) −4664.25 −1.26237 −0.631183 0.775634i \(-0.717430\pi\)
−0.631183 + 0.775634i \(0.717430\pi\)
\(240\) 0 0
\(241\) −3774.94 −1.00898 −0.504492 0.863416i \(-0.668320\pi\)
−0.504492 + 0.863416i \(0.668320\pi\)
\(242\) 4166.97 1.10687
\(243\) 0 0
\(244\) −1706.97 −0.447860
\(245\) 2487.97 0.648778
\(246\) 0 0
\(247\) 0 0
\(248\) −301.279 −0.0771421
\(249\) 0 0
\(250\) −6016.96 −1.52219
\(251\) 960.695 0.241588 0.120794 0.992678i \(-0.461456\pi\)
0.120794 + 0.992678i \(0.461456\pi\)
\(252\) 0 0
\(253\) 3786.90 0.941029
\(254\) 9472.64 2.34003
\(255\) 0 0
\(256\) 3836.08 0.936542
\(257\) 16.7302 0.00406070 0.00203035 0.999998i \(-0.499354\pi\)
0.00203035 + 0.999998i \(0.499354\pi\)
\(258\) 0 0
\(259\) −1986.23 −0.476519
\(260\) 0 0
\(261\) 0 0
\(262\) 9304.58 2.19404
\(263\) 400.736 0.0939560 0.0469780 0.998896i \(-0.485041\pi\)
0.0469780 + 0.998896i \(0.485041\pi\)
\(264\) 0 0
\(265\) −215.332 −0.0499159
\(266\) −320.971 −0.0739849
\(267\) 0 0
\(268\) −2357.31 −0.537297
\(269\) −2236.97 −0.507027 −0.253514 0.967332i \(-0.581586\pi\)
−0.253514 + 0.967332i \(0.581586\pi\)
\(270\) 0 0
\(271\) −4018.89 −0.900850 −0.450425 0.892814i \(-0.648727\pi\)
−0.450425 + 0.892814i \(0.648727\pi\)
\(272\) 5761.46 1.28434
\(273\) 0 0
\(274\) −1510.99 −0.333147
\(275\) 1026.81 0.225159
\(276\) 0 0
\(277\) 6792.95 1.47346 0.736731 0.676186i \(-0.236368\pi\)
0.736731 + 0.676186i \(0.236368\pi\)
\(278\) −1965.59 −0.424059
\(279\) 0 0
\(280\) 47.1175 0.0100565
\(281\) 7286.80 1.54695 0.773477 0.633824i \(-0.218516\pi\)
0.773477 + 0.633824i \(0.218516\pi\)
\(282\) 0 0
\(283\) −2429.77 −0.510369 −0.255185 0.966892i \(-0.582136\pi\)
−0.255185 + 0.966892i \(0.582136\pi\)
\(284\) 2618.54 0.547120
\(285\) 0 0
\(286\) 0 0
\(287\) 1194.25 0.245626
\(288\) 0 0
\(289\) 3722.97 0.757780
\(290\) 6503.07 1.31681
\(291\) 0 0
\(292\) −519.853 −0.104185
\(293\) −4211.25 −0.839672 −0.419836 0.907600i \(-0.637912\pi\)
−0.419836 + 0.907600i \(0.637912\pi\)
\(294\) 0 0
\(295\) −2265.29 −0.447085
\(296\) 326.730 0.0641580
\(297\) 0 0
\(298\) 4255.56 0.827242
\(299\) 0 0
\(300\) 0 0
\(301\) 695.084 0.133103
\(302\) 3581.12 0.682351
\(303\) 0 0
\(304\) −829.731 −0.156541
\(305\) 1675.03 0.314466
\(306\) 0 0
\(307\) 8212.27 1.52671 0.763353 0.645982i \(-0.223552\pi\)
0.763353 + 0.645982i \(0.223552\pi\)
\(308\) −845.447 −0.156408
\(309\) 0 0
\(310\) 10033.3 1.83823
\(311\) 4238.55 0.772818 0.386409 0.922328i \(-0.373715\pi\)
0.386409 + 0.922328i \(0.373715\pi\)
\(312\) 0 0
\(313\) 3807.82 0.687638 0.343819 0.939036i \(-0.388279\pi\)
0.343819 + 0.939036i \(0.388279\pi\)
\(314\) 14704.6 2.64276
\(315\) 0 0
\(316\) −5142.20 −0.915416
\(317\) 10497.7 1.85996 0.929981 0.367608i \(-0.119823\pi\)
0.929981 + 0.367608i \(0.119823\pi\)
\(318\) 0 0
\(319\) −3438.31 −0.603474
\(320\) 4388.92 0.766713
\(321\) 0 0
\(322\) 5269.34 0.911953
\(323\) −1243.70 −0.214246
\(324\) 0 0
\(325\) 0 0
\(326\) −5587.91 −0.949343
\(327\) 0 0
\(328\) −196.452 −0.0330708
\(329\) −2014.99 −0.337660
\(330\) 0 0
\(331\) 11905.2 1.97695 0.988474 0.151389i \(-0.0483746\pi\)
0.988474 + 0.151389i \(0.0483746\pi\)
\(332\) −5439.27 −0.899152
\(333\) 0 0
\(334\) −13606.9 −2.22915
\(335\) 2313.20 0.377264
\(336\) 0 0
\(337\) 8981.18 1.45174 0.725869 0.687833i \(-0.241438\pi\)
0.725869 + 0.687833i \(0.241438\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 6195.99 0.988308
\(341\) −5304.80 −0.842437
\(342\) 0 0
\(343\) −3871.51 −0.609451
\(344\) −114.339 −0.0179208
\(345\) 0 0
\(346\) 1377.61 0.214048
\(347\) 5712.87 0.883813 0.441906 0.897061i \(-0.354302\pi\)
0.441906 + 0.897061i \(0.354302\pi\)
\(348\) 0 0
\(349\) 9507.28 1.45820 0.729102 0.684406i \(-0.239938\pi\)
0.729102 + 0.684406i \(0.239938\pi\)
\(350\) 1428.77 0.218202
\(351\) 0 0
\(352\) −4441.65 −0.672559
\(353\) 3972.96 0.599035 0.299518 0.954091i \(-0.403174\pi\)
0.299518 + 0.954091i \(0.403174\pi\)
\(354\) 0 0
\(355\) −2569.55 −0.384162
\(356\) −10494.8 −1.56242
\(357\) 0 0
\(358\) −11629.5 −1.71686
\(359\) 109.866 0.0161519 0.00807594 0.999967i \(-0.497429\pi\)
0.00807594 + 0.999967i \(0.497429\pi\)
\(360\) 0 0
\(361\) −6679.89 −0.973887
\(362\) −15297.3 −2.22101
\(363\) 0 0
\(364\) 0 0
\(365\) 510.125 0.0731539
\(366\) 0 0
\(367\) 7020.02 0.998480 0.499240 0.866464i \(-0.333613\pi\)
0.499240 + 0.866464i \(0.333613\pi\)
\(368\) 13621.6 1.92955
\(369\) 0 0
\(370\) −10880.9 −1.52884
\(371\) 158.418 0.0221689
\(372\) 0 0
\(373\) 2227.18 0.309166 0.154583 0.987980i \(-0.450597\pi\)
0.154583 + 0.987980i \(0.450597\pi\)
\(374\) −6455.36 −0.892510
\(375\) 0 0
\(376\) 331.461 0.0454622
\(377\) 0 0
\(378\) 0 0
\(379\) −11004.6 −1.49147 −0.745734 0.666244i \(-0.767901\pi\)
−0.745734 + 0.666244i \(0.767901\pi\)
\(380\) −892.309 −0.120459
\(381\) 0 0
\(382\) −11308.5 −1.51464
\(383\) 4436.85 0.591938 0.295969 0.955198i \(-0.404357\pi\)
0.295969 + 0.955198i \(0.404357\pi\)
\(384\) 0 0
\(385\) 829.627 0.109823
\(386\) 10017.7 1.32096
\(387\) 0 0
\(388\) 4976.61 0.651157
\(389\) 2561.58 0.333874 0.166937 0.985968i \(-0.446612\pi\)
0.166937 + 0.985968i \(0.446612\pi\)
\(390\) 0 0
\(391\) 20417.7 2.64083
\(392\) 301.094 0.0387948
\(393\) 0 0
\(394\) 11086.0 1.41752
\(395\) 5045.98 0.642762
\(396\) 0 0
\(397\) 2206.90 0.278996 0.139498 0.990222i \(-0.455451\pi\)
0.139498 + 0.990222i \(0.455451\pi\)
\(398\) −16115.1 −2.02959
\(399\) 0 0
\(400\) 3693.45 0.461682
\(401\) 8071.02 1.00511 0.502553 0.864546i \(-0.332394\pi\)
0.502553 + 0.864546i \(0.332394\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 6104.58 0.751768
\(405\) 0 0
\(406\) −4784.28 −0.584827
\(407\) 5752.93 0.700644
\(408\) 0 0
\(409\) 6298.36 0.761452 0.380726 0.924688i \(-0.375674\pi\)
0.380726 + 0.924688i \(0.375674\pi\)
\(410\) 6542.29 0.788051
\(411\) 0 0
\(412\) −15567.3 −1.86152
\(413\) 1666.56 0.198562
\(414\) 0 0
\(415\) 5337.49 0.631342
\(416\) 0 0
\(417\) 0 0
\(418\) 929.662 0.108783
\(419\) 1432.01 0.166965 0.0834824 0.996509i \(-0.473396\pi\)
0.0834824 + 0.996509i \(0.473396\pi\)
\(420\) 0 0
\(421\) 9641.43 1.11614 0.558069 0.829794i \(-0.311542\pi\)
0.558069 + 0.829794i \(0.311542\pi\)
\(422\) 5544.82 0.639615
\(423\) 0 0
\(424\) −26.0594 −0.00298480
\(425\) 5536.19 0.631870
\(426\) 0 0
\(427\) −1232.31 −0.139662
\(428\) 7579.03 0.855949
\(429\) 0 0
\(430\) 3807.77 0.427040
\(431\) −3370.61 −0.376698 −0.188349 0.982102i \(-0.560314\pi\)
−0.188349 + 0.982102i \(0.560314\pi\)
\(432\) 0 0
\(433\) 6248.91 0.693541 0.346770 0.937950i \(-0.387278\pi\)
0.346770 + 0.937950i \(0.387278\pi\)
\(434\) −7381.45 −0.816407
\(435\) 0 0
\(436\) 12944.7 1.42187
\(437\) −2940.43 −0.321876
\(438\) 0 0
\(439\) 2866.16 0.311604 0.155802 0.987788i \(-0.450204\pi\)
0.155802 + 0.987788i \(0.450204\pi\)
\(440\) −136.471 −0.0147864
\(441\) 0 0
\(442\) 0 0
\(443\) −10776.3 −1.15575 −0.577877 0.816124i \(-0.696119\pi\)
−0.577877 + 0.816124i \(0.696119\pi\)
\(444\) 0 0
\(445\) 10298.4 1.09706
\(446\) −6828.74 −0.725000
\(447\) 0 0
\(448\) −3228.91 −0.340517
\(449\) −13834.9 −1.45414 −0.727069 0.686564i \(-0.759118\pi\)
−0.727069 + 0.686564i \(0.759118\pi\)
\(450\) 0 0
\(451\) −3459.04 −0.361153
\(452\) 10919.0 1.13625
\(453\) 0 0
\(454\) −1633.86 −0.168901
\(455\) 0 0
\(456\) 0 0
\(457\) 17233.0 1.76395 0.881976 0.471295i \(-0.156213\pi\)
0.881976 + 0.471295i \(0.156213\pi\)
\(458\) −9509.51 −0.970197
\(459\) 0 0
\(460\) 14648.9 1.48480
\(461\) −11485.0 −1.16033 −0.580164 0.814500i \(-0.697012\pi\)
−0.580164 + 0.814500i \(0.697012\pi\)
\(462\) 0 0
\(463\) 1613.61 0.161967 0.0809837 0.996715i \(-0.474194\pi\)
0.0809837 + 0.996715i \(0.474194\pi\)
\(464\) −12367.7 −1.23740
\(465\) 0 0
\(466\) 3782.41 0.376002
\(467\) 8149.20 0.807495 0.403747 0.914871i \(-0.367707\pi\)
0.403747 + 0.914871i \(0.367707\pi\)
\(468\) 0 0
\(469\) −1701.81 −0.167553
\(470\) −11038.4 −1.08333
\(471\) 0 0
\(472\) −274.145 −0.0267342
\(473\) −2013.24 −0.195706
\(474\) 0 0
\(475\) −797.289 −0.0770150
\(476\) −4558.36 −0.438933
\(477\) 0 0
\(478\) 18798.1 1.79875
\(479\) −1827.62 −0.174334 −0.0871670 0.996194i \(-0.527781\pi\)
−0.0871670 + 0.996194i \(0.527781\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 15213.9 1.43771
\(483\) 0 0
\(484\) −8522.52 −0.800387
\(485\) −4883.49 −0.457212
\(486\) 0 0
\(487\) −7838.95 −0.729398 −0.364699 0.931125i \(-0.618828\pi\)
−0.364699 + 0.931125i \(0.618828\pi\)
\(488\) 202.712 0.0188040
\(489\) 0 0
\(490\) −10027.1 −0.924449
\(491\) −17196.1 −1.58055 −0.790273 0.612755i \(-0.790061\pi\)
−0.790273 + 0.612755i \(0.790061\pi\)
\(492\) 0 0
\(493\) −18538.2 −1.69354
\(494\) 0 0
\(495\) 0 0
\(496\) −19081.5 −1.72739
\(497\) 1890.40 0.170616
\(498\) 0 0
\(499\) 5355.28 0.480431 0.240216 0.970720i \(-0.422782\pi\)
0.240216 + 0.970720i \(0.422782\pi\)
\(500\) 12306.2 1.10070
\(501\) 0 0
\(502\) −3871.84 −0.344240
\(503\) −2979.80 −0.264141 −0.132071 0.991240i \(-0.542163\pi\)
−0.132071 + 0.991240i \(0.542163\pi\)
\(504\) 0 0
\(505\) −5990.35 −0.527856
\(506\) −15262.1 −1.34088
\(507\) 0 0
\(508\) −19374.0 −1.69209
\(509\) −15353.7 −1.33701 −0.668507 0.743706i \(-0.733066\pi\)
−0.668507 + 0.743706i \(0.733066\pi\)
\(510\) 0 0
\(511\) −375.297 −0.0324895
\(512\) −16462.3 −1.42097
\(513\) 0 0
\(514\) −67.4267 −0.00578611
\(515\) 15276.0 1.30707
\(516\) 0 0
\(517\) 5836.24 0.496475
\(518\) 8005.00 0.678995
\(519\) 0 0
\(520\) 0 0
\(521\) −433.801 −0.0364783 −0.0182391 0.999834i \(-0.505806\pi\)
−0.0182391 + 0.999834i \(0.505806\pi\)
\(522\) 0 0
\(523\) 18900.3 1.58021 0.790106 0.612970i \(-0.210026\pi\)
0.790106 + 0.612970i \(0.210026\pi\)
\(524\) −19030.3 −1.58653
\(525\) 0 0
\(526\) −1615.06 −0.133879
\(527\) −28601.7 −2.36415
\(528\) 0 0
\(529\) 36105.7 2.96751
\(530\) 867.839 0.0711255
\(531\) 0 0
\(532\) 656.468 0.0534990
\(533\) 0 0
\(534\) 0 0
\(535\) −7437.21 −0.601007
\(536\) 279.943 0.0225592
\(537\) 0 0
\(538\) 9015.53 0.722467
\(539\) 5301.55 0.423662
\(540\) 0 0
\(541\) 13247.5 1.05278 0.526391 0.850243i \(-0.323545\pi\)
0.526391 + 0.850243i \(0.323545\pi\)
\(542\) 16197.1 1.28363
\(543\) 0 0
\(544\) −23947.9 −1.88742
\(545\) −12702.4 −0.998372
\(546\) 0 0
\(547\) −5543.52 −0.433316 −0.216658 0.976248i \(-0.569516\pi\)
−0.216658 + 0.976248i \(0.569516\pi\)
\(548\) 3090.36 0.240901
\(549\) 0 0
\(550\) −4138.28 −0.320831
\(551\) 2669.76 0.206416
\(552\) 0 0
\(553\) −3712.31 −0.285467
\(554\) −27377.3 −2.09955
\(555\) 0 0
\(556\) 4020.14 0.306640
\(557\) −6733.19 −0.512198 −0.256099 0.966651i \(-0.582437\pi\)
−0.256099 + 0.966651i \(0.582437\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2984.19 0.225188
\(561\) 0 0
\(562\) −29367.6 −2.20427
\(563\) −24282.4 −1.81773 −0.908863 0.417096i \(-0.863048\pi\)
−0.908863 + 0.417096i \(0.863048\pi\)
\(564\) 0 0
\(565\) −10714.7 −0.797823
\(566\) 9792.55 0.727229
\(567\) 0 0
\(568\) −310.966 −0.0229716
\(569\) 19876.2 1.46441 0.732207 0.681082i \(-0.238490\pi\)
0.732207 + 0.681082i \(0.238490\pi\)
\(570\) 0 0
\(571\) 225.014 0.0164913 0.00824567 0.999966i \(-0.497375\pi\)
0.00824567 + 0.999966i \(0.497375\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −4813.14 −0.349994
\(575\) 13089.0 0.949302
\(576\) 0 0
\(577\) −12258.1 −0.884424 −0.442212 0.896910i \(-0.645806\pi\)
−0.442212 + 0.896910i \(0.645806\pi\)
\(578\) −15004.5 −1.07977
\(579\) 0 0
\(580\) −13300.4 −0.952191
\(581\) −3926.77 −0.280395
\(582\) 0 0
\(583\) −458.844 −0.0325958
\(584\) 61.7353 0.00437436
\(585\) 0 0
\(586\) 16972.4 1.19645
\(587\) −10282.3 −0.722992 −0.361496 0.932374i \(-0.617734\pi\)
−0.361496 + 0.932374i \(0.617734\pi\)
\(588\) 0 0
\(589\) 4119.04 0.288153
\(590\) 9129.67 0.637055
\(591\) 0 0
\(592\) 20693.5 1.43665
\(593\) −12355.1 −0.855586 −0.427793 0.903877i \(-0.640709\pi\)
−0.427793 + 0.903877i \(0.640709\pi\)
\(594\) 0 0
\(595\) 4473.07 0.308198
\(596\) −8703.71 −0.598184
\(597\) 0 0
\(598\) 0 0
\(599\) −13035.2 −0.889157 −0.444578 0.895740i \(-0.646646\pi\)
−0.444578 + 0.895740i \(0.646646\pi\)
\(600\) 0 0
\(601\) −5153.36 −0.349767 −0.174884 0.984589i \(-0.555955\pi\)
−0.174884 + 0.984589i \(0.555955\pi\)
\(602\) −2801.36 −0.189659
\(603\) 0 0
\(604\) −7324.30 −0.493413
\(605\) 8363.05 0.561994
\(606\) 0 0
\(607\) −1406.55 −0.0940530 −0.0470265 0.998894i \(-0.514975\pi\)
−0.0470265 + 0.998894i \(0.514975\pi\)
\(608\) 3448.83 0.230047
\(609\) 0 0
\(610\) −6750.79 −0.448085
\(611\) 0 0
\(612\) 0 0
\(613\) −15984.3 −1.05318 −0.526590 0.850120i \(-0.676530\pi\)
−0.526590 + 0.850120i \(0.676530\pi\)
\(614\) −33097.5 −2.17541
\(615\) 0 0
\(616\) 100.401 0.00656703
\(617\) 10324.4 0.673652 0.336826 0.941567i \(-0.390647\pi\)
0.336826 + 0.941567i \(0.390647\pi\)
\(618\) 0 0
\(619\) −7423.00 −0.481996 −0.240998 0.970526i \(-0.577475\pi\)
−0.240998 + 0.970526i \(0.577475\pi\)
\(620\) −20520.6 −1.32924
\(621\) 0 0
\(622\) −17082.4 −1.10119
\(623\) −7576.48 −0.487232
\(624\) 0 0
\(625\) −4629.23 −0.296271
\(626\) −15346.4 −0.979820
\(627\) 0 0
\(628\) −30074.6 −1.91100
\(629\) 31017.8 1.96624
\(630\) 0 0
\(631\) 1190.30 0.0750954 0.0375477 0.999295i \(-0.488045\pi\)
0.0375477 + 0.999295i \(0.488045\pi\)
\(632\) 610.665 0.0384350
\(633\) 0 0
\(634\) −42308.2 −2.65027
\(635\) 19011.5 1.18810
\(636\) 0 0
\(637\) 0 0
\(638\) 13857.2 0.859894
\(639\) 0 0
\(640\) −1013.02 −0.0625674
\(641\) −705.064 −0.0434451 −0.0217226 0.999764i \(-0.506915\pi\)
−0.0217226 + 0.999764i \(0.506915\pi\)
\(642\) 0 0
\(643\) 14641.4 0.897976 0.448988 0.893538i \(-0.351785\pi\)
0.448988 + 0.893538i \(0.351785\pi\)
\(644\) −10777.1 −0.659439
\(645\) 0 0
\(646\) 5012.42 0.305280
\(647\) −1520.83 −0.0924111 −0.0462056 0.998932i \(-0.514713\pi\)
−0.0462056 + 0.998932i \(0.514713\pi\)
\(648\) 0 0
\(649\) −4827.04 −0.291954
\(650\) 0 0
\(651\) 0 0
\(652\) 11428.7 0.686477
\(653\) 22054.4 1.32168 0.660838 0.750529i \(-0.270201\pi\)
0.660838 + 0.750529i \(0.270201\pi\)
\(654\) 0 0
\(655\) 18674.2 1.11398
\(656\) −12442.3 −0.740532
\(657\) 0 0
\(658\) 8120.92 0.481134
\(659\) 12652.3 0.747895 0.373947 0.927450i \(-0.378004\pi\)
0.373947 + 0.927450i \(0.378004\pi\)
\(660\) 0 0
\(661\) −10893.2 −0.640994 −0.320497 0.947250i \(-0.603850\pi\)
−0.320497 + 0.947250i \(0.603850\pi\)
\(662\) −47981.0 −2.81697
\(663\) 0 0
\(664\) 645.942 0.0377522
\(665\) −644.184 −0.0375645
\(666\) 0 0
\(667\) −43829.0 −2.54433
\(668\) 27829.6 1.61191
\(669\) 0 0
\(670\) −9322.76 −0.537567
\(671\) 3569.28 0.205351
\(672\) 0 0
\(673\) −9019.75 −0.516621 −0.258310 0.966062i \(-0.583166\pi\)
−0.258310 + 0.966062i \(0.583166\pi\)
\(674\) −36196.4 −2.06859
\(675\) 0 0
\(676\) 0 0
\(677\) 24923.6 1.41491 0.707454 0.706760i \(-0.249844\pi\)
0.707454 + 0.706760i \(0.249844\pi\)
\(678\) 0 0
\(679\) 3592.76 0.203060
\(680\) −735.807 −0.0414955
\(681\) 0 0
\(682\) 21379.7 1.20039
\(683\) 24634.2 1.38009 0.690044 0.723767i \(-0.257591\pi\)
0.690044 + 0.723767i \(0.257591\pi\)
\(684\) 0 0
\(685\) −3032.53 −0.169149
\(686\) 15603.1 0.868411
\(687\) 0 0
\(688\) −7241.70 −0.401290
\(689\) 0 0
\(690\) 0 0
\(691\) −10340.2 −0.569264 −0.284632 0.958637i \(-0.591871\pi\)
−0.284632 + 0.958637i \(0.591871\pi\)
\(692\) −2817.56 −0.154780
\(693\) 0 0
\(694\) −23024.3 −1.25935
\(695\) −3944.92 −0.215308
\(696\) 0 0
\(697\) −18650.0 −1.01351
\(698\) −38316.7 −2.07780
\(699\) 0 0
\(700\) −2922.19 −0.157784
\(701\) 20833.9 1.12252 0.561258 0.827641i \(-0.310317\pi\)
0.561258 + 0.827641i \(0.310317\pi\)
\(702\) 0 0
\(703\) −4467.00 −0.239653
\(704\) 9352.23 0.500676
\(705\) 0 0
\(706\) −16012.0 −0.853569
\(707\) 4407.07 0.234434
\(708\) 0 0
\(709\) 9189.56 0.486772 0.243386 0.969930i \(-0.421742\pi\)
0.243386 + 0.969930i \(0.421742\pi\)
\(710\) 10355.9 0.547395
\(711\) 0 0
\(712\) 1246.31 0.0656004
\(713\) −67621.8 −3.55183
\(714\) 0 0
\(715\) 0 0
\(716\) 23785.2 1.24147
\(717\) 0 0
\(718\) −442.788 −0.0230149
\(719\) −7503.22 −0.389183 −0.194592 0.980884i \(-0.562338\pi\)
−0.194592 + 0.980884i \(0.562338\pi\)
\(720\) 0 0
\(721\) −11238.5 −0.580503
\(722\) 26921.6 1.38770
\(723\) 0 0
\(724\) 31286.8 1.60603
\(725\) −11884.1 −0.608779
\(726\) 0 0
\(727\) −20727.2 −1.05740 −0.528700 0.848809i \(-0.677320\pi\)
−0.528700 + 0.848809i \(0.677320\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2055.93 −0.104237
\(731\) −10854.7 −0.549216
\(732\) 0 0
\(733\) 17361.3 0.874836 0.437418 0.899258i \(-0.355893\pi\)
0.437418 + 0.899258i \(0.355893\pi\)
\(734\) −28292.4 −1.42274
\(735\) 0 0
\(736\) −56618.9 −2.83560
\(737\) 4929.13 0.246359
\(738\) 0 0
\(739\) 18093.8 0.900663 0.450331 0.892861i \(-0.351306\pi\)
0.450331 + 0.892861i \(0.351306\pi\)
\(740\) 22254.1 1.10551
\(741\) 0 0
\(742\) −638.466 −0.0315887
\(743\) 14875.3 0.734482 0.367241 0.930126i \(-0.380302\pi\)
0.367241 + 0.930126i \(0.380302\pi\)
\(744\) 0 0
\(745\) 8540.85 0.420017
\(746\) −8976.07 −0.440533
\(747\) 0 0
\(748\) 13202.9 0.645380
\(749\) 5471.52 0.266923
\(750\) 0 0
\(751\) −17750.9 −0.862502 −0.431251 0.902232i \(-0.641928\pi\)
−0.431251 + 0.902232i \(0.641928\pi\)
\(752\) 20993.1 1.01801
\(753\) 0 0
\(754\) 0 0
\(755\) 7187.25 0.346451
\(756\) 0 0
\(757\) −10220.3 −0.490702 −0.245351 0.969434i \(-0.578903\pi\)
−0.245351 + 0.969434i \(0.578903\pi\)
\(758\) 44351.1 2.12520
\(759\) 0 0
\(760\) 105.967 0.00505765
\(761\) 14112.0 0.672221 0.336110 0.941823i \(-0.390888\pi\)
0.336110 + 0.941823i \(0.390888\pi\)
\(762\) 0 0
\(763\) 9345.13 0.443403
\(764\) 23128.7 1.09525
\(765\) 0 0
\(766\) −17881.6 −0.843457
\(767\) 0 0
\(768\) 0 0
\(769\) −22736.7 −1.06620 −0.533100 0.846052i \(-0.678973\pi\)
−0.533100 + 0.846052i \(0.678973\pi\)
\(770\) −3343.60 −0.156487
\(771\) 0 0
\(772\) −20488.8 −0.955194
\(773\) 343.173 0.0159678 0.00798388 0.999968i \(-0.497459\pi\)
0.00798388 + 0.999968i \(0.497459\pi\)
\(774\) 0 0
\(775\) −18335.4 −0.849844
\(776\) −590.999 −0.0273397
\(777\) 0 0
\(778\) −10323.8 −0.475740
\(779\) 2685.86 0.123531
\(780\) 0 0
\(781\) −5475.37 −0.250863
\(782\) −82288.3 −3.76294
\(783\) 0 0
\(784\) 19069.8 0.868706
\(785\) 29511.9 1.34181
\(786\) 0 0
\(787\) −19086.4 −0.864496 −0.432248 0.901755i \(-0.642279\pi\)
−0.432248 + 0.901755i \(0.642279\pi\)
\(788\) −22673.7 −1.02502
\(789\) 0 0
\(790\) −20336.6 −0.915876
\(791\) 7882.74 0.354334
\(792\) 0 0
\(793\) 0 0
\(794\) −8894.36 −0.397543
\(795\) 0 0
\(796\) 32959.5 1.46761
\(797\) −12031.1 −0.534709 −0.267354 0.963598i \(-0.586149\pi\)
−0.267354 + 0.963598i \(0.586149\pi\)
\(798\) 0 0
\(799\) 31467.0 1.39327
\(800\) −15352.1 −0.678471
\(801\) 0 0
\(802\) −32528.2 −1.43218
\(803\) 1087.01 0.0477706
\(804\) 0 0
\(805\) 10575.5 0.463027
\(806\) 0 0
\(807\) 0 0
\(808\) −724.952 −0.0315640
\(809\) −10175.4 −0.442210 −0.221105 0.975250i \(-0.570966\pi\)
−0.221105 + 0.975250i \(0.570966\pi\)
\(810\) 0 0
\(811\) 26754.1 1.15840 0.579201 0.815185i \(-0.303365\pi\)
0.579201 + 0.815185i \(0.303365\pi\)
\(812\) 9785.08 0.422893
\(813\) 0 0
\(814\) −23185.7 −0.998353
\(815\) −11214.9 −0.482011
\(816\) 0 0
\(817\) 1563.23 0.0669408
\(818\) −25383.9 −1.08500
\(819\) 0 0
\(820\) −13380.7 −0.569845
\(821\) 15777.5 0.670693 0.335347 0.942095i \(-0.391147\pi\)
0.335347 + 0.942095i \(0.391147\pi\)
\(822\) 0 0
\(823\) −13863.9 −0.587197 −0.293599 0.955929i \(-0.594853\pi\)
−0.293599 + 0.955929i \(0.594853\pi\)
\(824\) 1848.70 0.0781583
\(825\) 0 0
\(826\) −6716.66 −0.282933
\(827\) 26835.0 1.12835 0.564175 0.825655i \(-0.309194\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(828\) 0 0
\(829\) 625.251 0.0261953 0.0130976 0.999914i \(-0.495831\pi\)
0.0130976 + 0.999914i \(0.495831\pi\)
\(830\) −21511.4 −0.899604
\(831\) 0 0
\(832\) 0 0
\(833\) 28584.2 1.18893
\(834\) 0 0
\(835\) −27308.8 −1.13181
\(836\) −1901.40 −0.0786617
\(837\) 0 0
\(838\) −5771.35 −0.237909
\(839\) 27307.4 1.12367 0.561833 0.827251i \(-0.310096\pi\)
0.561833 + 0.827251i \(0.310096\pi\)
\(840\) 0 0
\(841\) 15405.4 0.631656
\(842\) −38857.3 −1.59039
\(843\) 0 0
\(844\) −11340.6 −0.462510
\(845\) 0 0
\(846\) 0 0
\(847\) −6152.66 −0.249596
\(848\) −1650.48 −0.0668368
\(849\) 0 0
\(850\) −22312.2 −0.900356
\(851\) 73334.2 2.95401
\(852\) 0 0
\(853\) 44801.9 1.79834 0.899172 0.437595i \(-0.144170\pi\)
0.899172 + 0.437595i \(0.144170\pi\)
\(854\) 4966.53 0.199006
\(855\) 0 0
\(856\) −900.051 −0.0359382
\(857\) 25167.1 1.00314 0.501571 0.865116i \(-0.332756\pi\)
0.501571 + 0.865116i \(0.332756\pi\)
\(858\) 0 0
\(859\) 4059.10 0.161228 0.0806138 0.996745i \(-0.474312\pi\)
0.0806138 + 0.996745i \(0.474312\pi\)
\(860\) −7787.87 −0.308795
\(861\) 0 0
\(862\) 13584.4 0.536759
\(863\) −818.924 −0.0323019 −0.0161509 0.999870i \(-0.505141\pi\)
−0.0161509 + 0.999870i \(0.505141\pi\)
\(864\) 0 0
\(865\) 2764.84 0.108679
\(866\) −25184.6 −0.988231
\(867\) 0 0
\(868\) 15096.9 0.590350
\(869\) 10752.3 0.419733
\(870\) 0 0
\(871\) 0 0
\(872\) −1537.25 −0.0596993
\(873\) 0 0
\(874\) 11850.7 0.458644
\(875\) 8884.23 0.343248
\(876\) 0 0
\(877\) 190.251 0.00732533 0.00366267 0.999993i \(-0.498834\pi\)
0.00366267 + 0.999993i \(0.498834\pi\)
\(878\) −11551.3 −0.444007
\(879\) 0 0
\(880\) −8643.43 −0.331102
\(881\) 19803.4 0.757315 0.378657 0.925537i \(-0.376386\pi\)
0.378657 + 0.925537i \(0.376386\pi\)
\(882\) 0 0
\(883\) 19652.1 0.748974 0.374487 0.927232i \(-0.377819\pi\)
0.374487 + 0.927232i \(0.377819\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 43431.2 1.64684
\(887\) 26295.0 0.995379 0.497689 0.867355i \(-0.334182\pi\)
0.497689 + 0.867355i \(0.334182\pi\)
\(888\) 0 0
\(889\) −13986.6 −0.527668
\(890\) −41505.1 −1.56321
\(891\) 0 0
\(892\) 13966.5 0.524253
\(893\) −4531.69 −0.169818
\(894\) 0 0
\(895\) −23340.2 −0.871704
\(896\) 745.275 0.0277878
\(897\) 0 0
\(898\) 55758.0 2.07201
\(899\) 61397.0 2.27776
\(900\) 0 0
\(901\) −2473.93 −0.0914746
\(902\) 13940.8 0.514609
\(903\) 0 0
\(904\) −1296.69 −0.0477072
\(905\) −30701.4 −1.12768
\(906\) 0 0
\(907\) 42417.3 1.55286 0.776429 0.630204i \(-0.217029\pi\)
0.776429 + 0.630204i \(0.217029\pi\)
\(908\) 3341.66 0.122133
\(909\) 0 0
\(910\) 0 0
\(911\) 872.245 0.0317220 0.0158610 0.999874i \(-0.494951\pi\)
0.0158610 + 0.999874i \(0.494951\pi\)
\(912\) 0 0
\(913\) 11373.5 0.412276
\(914\) −69453.2 −2.51347
\(915\) 0 0
\(916\) 19449.4 0.701557
\(917\) −13738.5 −0.494749
\(918\) 0 0
\(919\) −17181.4 −0.616716 −0.308358 0.951270i \(-0.599779\pi\)
−0.308358 + 0.951270i \(0.599779\pi\)
\(920\) −1739.64 −0.0623415
\(921\) 0 0
\(922\) 46287.5 1.65336
\(923\) 0 0
\(924\) 0 0
\(925\) 19884.4 0.706804
\(926\) −6503.25 −0.230788
\(927\) 0 0
\(928\) 51407.0 1.81845
\(929\) 56042.9 1.97923 0.989617 0.143728i \(-0.0459091\pi\)
0.989617 + 0.143728i \(0.0459091\pi\)
\(930\) 0 0
\(931\) −4116.52 −0.144912
\(932\) −7736.00 −0.271890
\(933\) 0 0
\(934\) −32843.3 −1.15060
\(935\) −12955.8 −0.453155
\(936\) 0 0
\(937\) −36672.5 −1.27859 −0.639295 0.768961i \(-0.720774\pi\)
−0.639295 + 0.768961i \(0.720774\pi\)
\(938\) 6858.71 0.238747
\(939\) 0 0
\(940\) 22576.4 0.783363
\(941\) −21069.0 −0.729895 −0.364947 0.931028i \(-0.618913\pi\)
−0.364947 + 0.931028i \(0.618913\pi\)
\(942\) 0 0
\(943\) −44093.4 −1.52267
\(944\) −17363.0 −0.598642
\(945\) 0 0
\(946\) 8113.87 0.278863
\(947\) −1838.70 −0.0630938 −0.0315469 0.999502i \(-0.510043\pi\)
−0.0315469 + 0.999502i \(0.510043\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 3213.27 0.109739
\(951\) 0 0
\(952\) 541.330 0.0184292
\(953\) −13599.8 −0.462266 −0.231133 0.972922i \(-0.574243\pi\)
−0.231133 + 0.972922i \(0.574243\pi\)
\(954\) 0 0
\(955\) −22695.9 −0.769029
\(956\) −38446.9 −1.30069
\(957\) 0 0
\(958\) 7365.75 0.248410
\(959\) 2231.02 0.0751235
\(960\) 0 0
\(961\) 64935.6 2.17971
\(962\) 0 0
\(963\) 0 0
\(964\) −31116.4 −1.03962
\(965\) 20105.5 0.670692
\(966\) 0 0
\(967\) −2081.30 −0.0692141 −0.0346070 0.999401i \(-0.511018\pi\)
−0.0346070 + 0.999401i \(0.511018\pi\)
\(968\) 1012.10 0.0336054
\(969\) 0 0
\(970\) 19681.6 0.651484
\(971\) −1636.62 −0.0540904 −0.0270452 0.999634i \(-0.508610\pi\)
−0.0270452 + 0.999634i \(0.508610\pi\)
\(972\) 0 0
\(973\) 2902.26 0.0956240
\(974\) 31592.9 1.03932
\(975\) 0 0
\(976\) 12838.8 0.421066
\(977\) −29387.1 −0.962311 −0.481156 0.876635i \(-0.659783\pi\)
−0.481156 + 0.876635i \(0.659783\pi\)
\(978\) 0 0
\(979\) 21944.6 0.716396
\(980\) 20508.1 0.668476
\(981\) 0 0
\(982\) 69304.4 2.25213
\(983\) 24084.4 0.781457 0.390728 0.920506i \(-0.372223\pi\)
0.390728 + 0.920506i \(0.372223\pi\)
\(984\) 0 0
\(985\) 22249.4 0.719722
\(986\) 74713.4 2.41314
\(987\) 0 0
\(988\) 0 0
\(989\) −25663.4 −0.825125
\(990\) 0 0
\(991\) 1413.43 0.0453068 0.0226534 0.999743i \(-0.492789\pi\)
0.0226534 + 0.999743i \(0.492789\pi\)
\(992\) 79313.5 2.53851
\(993\) 0 0
\(994\) −7618.79 −0.243112
\(995\) −32342.7 −1.03049
\(996\) 0 0
\(997\) −33357.4 −1.05962 −0.529809 0.848117i \(-0.677737\pi\)
−0.529809 + 0.848117i \(0.677737\pi\)
\(998\) −21583.1 −0.684570
\(999\) 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.bf.1.3 9
3.2 odd 2 507.4.a.p.1.7 yes 9
13.12 even 2 1521.4.a.bi.1.7 9
39.5 even 4 507.4.b.k.337.4 18
39.8 even 4 507.4.b.k.337.15 18
39.38 odd 2 507.4.a.o.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.3 9 39.38 odd 2
507.4.a.p.1.7 yes 9 3.2 odd 2
507.4.b.k.337.4 18 39.5 even 4
507.4.b.k.337.15 18 39.8 even 4
1521.4.a.bf.1.3 9 1.1 even 1 trivial
1521.4.a.bi.1.7 9 13.12 even 2