Properties

Label 507.4.a.o.1.3
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $1$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.9139683729\)
Analytic rank: \(1\)
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: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-4.83218\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} -8.08864 q^{5} -12.0907 q^{6} -5.95078 q^{7} -0.978887 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.03025 q^{2} +3.00000 q^{3} +8.24289 q^{4} -8.08864 q^{5} -12.0907 q^{6} -5.95078 q^{7} -0.978887 q^{8} +9.00000 q^{9} +32.5992 q^{10} -17.2359 q^{11} +24.7287 q^{12} +23.9831 q^{14} -24.2659 q^{15} -61.9979 q^{16} +92.9299 q^{17} -36.2722 q^{18} -13.3832 q^{19} -66.6738 q^{20} -17.8523 q^{21} +69.4648 q^{22} +219.710 q^{23} -2.93666 q^{24} -59.5738 q^{25} +27.0000 q^{27} -49.0516 q^{28} -199.485 q^{29} +97.7977 q^{30} -307.777 q^{31} +257.698 q^{32} -51.7076 q^{33} -374.531 q^{34} +48.1337 q^{35} +74.1860 q^{36} +333.777 q^{37} +53.9376 q^{38} +7.91787 q^{40} +200.689 q^{41} +71.9493 q^{42} +116.806 q^{43} -142.073 q^{44} -72.7978 q^{45} -885.487 q^{46} -338.610 q^{47} -185.994 q^{48} -307.588 q^{49} +240.097 q^{50} +278.790 q^{51} -26.6215 q^{53} -108.817 q^{54} +139.415 q^{55} +5.82514 q^{56} -40.1496 q^{57} +803.976 q^{58} +280.058 q^{59} -200.021 q^{60} -207.084 q^{61} +1240.42 q^{62} -53.5570 q^{63} -542.603 q^{64} +208.394 q^{66} +285.981 q^{67} +766.011 q^{68} +659.131 q^{69} -193.991 q^{70} +317.673 q^{71} -8.80999 q^{72} +63.0668 q^{73} -1345.20 q^{74} -178.721 q^{75} -110.316 q^{76} +102.567 q^{77} -623.835 q^{79} +501.479 q^{80} +81.0000 q^{81} -808.824 q^{82} -659.874 q^{83} -147.155 q^{84} -751.677 q^{85} -470.755 q^{86} -598.456 q^{87} +16.8720 q^{88} -1273.19 q^{89} +293.393 q^{90} +1811.05 q^{92} -923.331 q^{93} +1364.68 q^{94} +108.252 q^{95} +773.094 q^{96} -603.746 q^{97} +1239.66 q^{98} -155.123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9} - 54 q^{10} - 85 q^{11} + 132 q^{12} + 158 q^{14} - 99 q^{15} + 216 q^{16} + 178 q^{17} - 54 q^{18} - 352 q^{19} - 402 q^{20} - 249 q^{21} - 630 q^{22} + 150 q^{23} - 261 q^{24} - 20 q^{25} + 243 q^{27} - 940 q^{28} - 97 q^{29} - 162 q^{30} - 717 q^{31} - 707 q^{32} - 255 q^{33} - 632 q^{34} - 418 q^{35} + 396 q^{36} - 1108 q^{37} - 660 q^{38} - 1506 q^{40} - 334 q^{41} + 474 q^{42} + 242 q^{43} + 307 q^{44} - 297 q^{45} - 979 q^{46} + 184 q^{47} + 648 q^{48} - 38 q^{49} + 2031 q^{50} + 534 q^{51} - 151 q^{53} - 162 q^{54} + 2064 q^{55} + 2276 q^{56} - 1056 q^{57} - 1161 q^{58} - 537 q^{59} - 1206 q^{60} - 1340 q^{61} + 347 q^{62} - 747 q^{63} + 893 q^{64} - 1890 q^{66} - 2308 q^{67} + 2785 q^{68} + 450 q^{69} + 1420 q^{70} - 96 q^{71} - 783 q^{72} - 2505 q^{73} - 1191 q^{74} - 60 q^{75} - 2409 q^{76} - 2142 q^{77} - 1591 q^{79} + 2671 q^{80} + 729 q^{81} + 1517 q^{82} - 1539 q^{83} - 2820 q^{84} - 4296 q^{85} + 3763 q^{86} - 291 q^{87} - 3716 q^{88} + 592 q^{89} - 486 q^{90} + 515 q^{92} - 2151 q^{93} - 692 q^{94} + 4158 q^{95} - 2121 q^{96} - 1445 q^{97} - 1457 q^{98} - 765 q^{99}+O(q^{100}) \) 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 \(0.752416\pi\)
\(3\) 3.00000 0.577350
\(4\) 8.24289 1.03036
\(5\) −8.08864 −0.723470 −0.361735 0.932281i \(-0.617816\pi\)
−0.361735 + 0.932281i \(0.617816\pi\)
\(6\) −12.0907 −0.822671
\(7\) −5.95078 −0.321312 −0.160656 0.987010i \(-0.551361\pi\)
−0.160656 + 0.987010i \(0.551361\pi\)
\(8\) −0.978887 −0.0432611
\(9\) 9.00000 0.333333
\(10\) 32.5992 1.03088
\(11\) −17.2359 −0.472437 −0.236219 0.971700i \(-0.575908\pi\)
−0.236219 + 0.971700i \(0.575908\pi\)
\(12\) 24.7287 0.594879
\(13\) 0 0
\(14\) 23.9831 0.457840
\(15\) −24.2659 −0.417696
\(16\) −61.9979 −0.968718
\(17\) 92.9299 1.32581 0.662907 0.748702i \(-0.269323\pi\)
0.662907 + 0.748702i \(0.269323\pi\)
\(18\) −36.2722 −0.474969
\(19\) −13.3832 −0.161596 −0.0807979 0.996731i \(-0.525747\pi\)
−0.0807979 + 0.996731i \(0.525747\pi\)
\(20\) −66.6738 −0.745435
\(21\) −17.8523 −0.185510
\(22\) 69.4648 0.673179
\(23\) 219.710 1.99186 0.995930 0.0901293i \(-0.0287280\pi\)
0.995930 + 0.0901293i \(0.0287280\pi\)
\(24\) −2.93666 −0.0249768
\(25\) −59.5738 −0.476591
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) −49.0516 −0.331067
\(29\) −199.485 −1.27736 −0.638681 0.769471i \(-0.720520\pi\)
−0.638681 + 0.769471i \(0.720520\pi\)
\(30\) 97.7977 0.595178
\(31\) −307.777 −1.78317 −0.891586 0.452851i \(-0.850407\pi\)
−0.891586 + 0.452851i \(0.850407\pi\)
\(32\) 257.698 1.42359
\(33\) −51.7076 −0.272762
\(34\) −374.531 −1.88916
\(35\) 48.1337 0.232460
\(36\) 74.1860 0.343454
\(37\) 333.777 1.48304 0.741521 0.670930i \(-0.234105\pi\)
0.741521 + 0.670930i \(0.234105\pi\)
\(38\) 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 \(0.375159\pi\)
\(42\) 71.9493 0.264334
\(43\) 116.806 0.414248 0.207124 0.978315i \(-0.433590\pi\)
0.207124 + 0.978315i \(0.433590\pi\)
\(44\) −142.073 −0.486781
\(45\) −72.7978 −0.241157
\(46\) −885.487 −2.83822
\(47\) −338.610 −1.05088 −0.525440 0.850831i \(-0.676099\pi\)
−0.525440 + 0.850831i \(0.676099\pi\)
\(48\) −185.994 −0.559289
\(49\) −307.588 −0.896759
\(50\) 240.097 0.679097
\(51\) 278.790 0.765459
\(52\) 0 0
\(53\) −26.6215 −0.0689951 −0.0344975 0.999405i \(-0.510983\pi\)
−0.0344975 + 0.999405i \(0.510983\pi\)
\(54\) −108.817 −0.274224
\(55\) 139.415 0.341794
\(56\) 5.82514 0.0139003
\(57\) −40.1496 −0.0932973
\(58\) 803.976 1.82012
\(59\) 280.058 0.617973 0.308987 0.951066i \(-0.400010\pi\)
0.308987 + 0.951066i \(0.400010\pi\)
\(60\) −200.021 −0.430377
\(61\) −207.084 −0.434663 −0.217332 0.976098i \(-0.569735\pi\)
−0.217332 + 0.976098i \(0.569735\pi\)
\(62\) 1240.42 2.54086
\(63\) −53.5570 −0.107104
\(64\) −542.603 −1.05977
\(65\) 0 0
\(66\) 208.394 0.388660
\(67\) 285.981 0.521465 0.260732 0.965411i \(-0.416036\pi\)
0.260732 + 0.965411i \(0.416036\pi\)
\(68\) 766.011 1.36607
\(69\) 659.131 1.15000
\(70\) −193.991 −0.331233
\(71\) 317.673 0.530998 0.265499 0.964111i \(-0.414463\pi\)
0.265499 + 0.964111i \(0.414463\pi\)
\(72\) −8.80999 −0.0144204
\(73\) 63.0668 0.101115 0.0505576 0.998721i \(-0.483900\pi\)
0.0505576 + 0.998721i \(0.483900\pi\)
\(74\) −1345.20 −2.11320
\(75\) −178.721 −0.275160
\(76\) −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
\(81\) 81.0000 0.111111
\(82\) −808.824 −1.08926
\(83\) −659.874 −0.872658 −0.436329 0.899787i \(-0.643722\pi\)
−0.436329 + 0.899787i \(0.643722\pi\)
\(84\) −147.155 −0.191142
\(85\) −751.677 −0.959186
\(86\) −470.755 −0.590265
\(87\) −598.456 −0.737486
\(88\) 16.8720 0.0204382
\(89\) −1273.19 −1.51638 −0.758191 0.652032i \(-0.773917\pi\)
−0.758191 + 0.652032i \(0.773917\pi\)
\(90\) 293.393 0.343626
\(91\) 0 0
\(92\) 1811.05 2.05233
\(93\) −923.331 −1.02952
\(94\) 1364.68 1.49741
\(95\) 108.252 0.116910
\(96\) 773.094 0.821912
\(97\) −603.746 −0.631970 −0.315985 0.948764i \(-0.602335\pi\)
−0.315985 + 0.948764i \(0.602335\pi\)
\(98\) 1239.66 1.27780
\(99\) −155.123 −0.157479
\(100\) −491.060 −0.491060
\(101\) −740.588 −0.729616 −0.364808 0.931083i \(-0.618865\pi\)
−0.364808 + 0.931083i \(0.618865\pi\)
\(102\) −1123.59 −1.09071
\(103\) −1888.57 −1.80666 −0.903332 0.428942i \(-0.858887\pi\)
−0.903332 + 0.428942i \(0.858887\pi\)
\(104\) 0 0
\(105\) 144.401 0.134211
\(106\) 107.291 0.0983116
\(107\) −919.463 −0.830728 −0.415364 0.909655i \(-0.636346\pi\)
−0.415364 + 0.909655i \(0.636346\pi\)
\(108\) 222.558 0.198293
\(109\) −1570.40 −1.37998 −0.689988 0.723821i \(-0.742384\pi\)
−0.689988 + 0.723821i \(0.742384\pi\)
\(110\) −561.876 −0.487025
\(111\) 1001.33 0.856234
\(112\) 368.936 0.311260
\(113\) −1324.66 −1.10277 −0.551386 0.834250i \(-0.685901\pi\)
−0.551386 + 0.834250i \(0.685901\pi\)
\(114\) 161.813 0.132940
\(115\) −1777.16 −1.44105
\(116\) −1644.34 −1.31614
\(117\) 0 0
\(118\) −1128.70 −0.880555
\(119\) −553.006 −0.426000
\(120\) 23.7536 0.0180700
\(121\) −1033.92 −0.776803
\(122\) 834.601 0.619354
\(123\) 602.066 0.441353
\(124\) −2536.97 −1.83731
\(125\) 1492.95 1.06827
\(126\) 215.848 0.152613
\(127\) −2350.39 −1.64223 −0.821115 0.570763i \(-0.806648\pi\)
−0.821115 + 0.570763i \(0.806648\pi\)
\(128\) 125.240 0.0864824
\(129\) 350.417 0.239166
\(130\) 0 0
\(131\) 2308.69 1.53978 0.769890 0.638177i \(-0.220311\pi\)
0.769890 + 0.638177i \(0.220311\pi\)
\(132\) −426.220 −0.281043
\(133\) 79.6405 0.0519226
\(134\) −1152.57 −0.743039
\(135\) −218.393 −0.139232
\(136\) −90.9680 −0.0573562
\(137\) 374.912 0.233802 0.116901 0.993144i \(-0.462704\pi\)
0.116901 + 0.993144i \(0.462704\pi\)
\(138\) −2656.46 −1.63864
\(139\) 487.711 0.297605 0.148802 0.988867i \(-0.452458\pi\)
0.148802 + 0.988867i \(0.452458\pi\)
\(140\) 396.761 0.239517
\(141\) −1015.83 −0.606726
\(142\) −1280.30 −0.756623
\(143\) 0 0
\(144\) −557.981 −0.322906
\(145\) 1613.57 0.924134
\(146\) −254.175 −0.144080
\(147\) −922.765 −0.517744
\(148\) 2751.28 1.52807
\(149\) −1055.91 −0.580558 −0.290279 0.956942i \(-0.593748\pi\)
−0.290279 + 0.956942i \(0.593748\pi\)
\(150\) 720.292 0.392077
\(151\) 888.560 0.478874 0.239437 0.970912i \(-0.423037\pi\)
0.239437 + 0.970912i \(0.423037\pi\)
\(152\) 13.1007 0.00699081
\(153\) 836.369 0.441938
\(154\) −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
\(159\) −79.8644 −0.0398343
\(160\) −2084.43 −1.02993
\(161\) −1307.45 −0.640008
\(162\) −326.450 −0.158323
\(163\) −1386.49 −0.666249 −0.333125 0.942883i \(-0.608103\pi\)
−0.333125 + 0.942883i \(0.608103\pi\)
\(164\) 1654.25 0.787655
\(165\) 418.244 0.197335
\(166\) 2659.46 1.24346
\(167\) 3376.19 1.56442 0.782209 0.623017i \(-0.214093\pi\)
0.782209 + 0.623017i \(0.214093\pi\)
\(168\) 17.4754 0.00802535
\(169\) 0 0
\(170\) 3029.44 1.36675
\(171\) −120.449 −0.0538652
\(172\) 962.815 0.426825
\(173\) 341.817 0.150219 0.0751095 0.997175i \(-0.476069\pi\)
0.0751095 + 0.997175i \(0.476069\pi\)
\(174\) 2411.93 1.05085
\(175\) 354.511 0.153134
\(176\) 1068.59 0.457658
\(177\) 840.174 0.356787
\(178\) 5131.28 2.16070
\(179\) −2885.55 −1.20489 −0.602446 0.798159i \(-0.705807\pi\)
−0.602446 + 0.798159i \(0.705807\pi\)
\(180\) −600.064 −0.248478
\(181\) 3795.62 1.55871 0.779354 0.626584i \(-0.215547\pi\)
0.779354 + 0.626584i \(0.215547\pi\)
\(182\) 0 0
\(183\) −621.253 −0.250953
\(184\) −215.072 −0.0861701
\(185\) −2699.80 −1.07294
\(186\) 3721.25 1.46696
\(187\) −1601.73 −0.626363
\(188\) −2791.12 −1.08278
\(189\) −160.671 −0.0618365
\(190\) −436.282 −0.166586
\(191\) −2805.90 −1.06297 −0.531486 0.847067i \(-0.678366\pi\)
−0.531486 + 0.847067i \(0.678366\pi\)
\(192\) −1627.81 −0.611859
\(193\) 2485.64 0.927048 0.463524 0.886084i \(-0.346585\pi\)
0.463524 + 0.886084i \(0.346585\pi\)
\(194\) 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 \(0.665715\pi\)
\(198\) 625.183 0.224393
\(199\) 3998.53 1.42436 0.712182 0.701994i \(-0.247707\pi\)
0.712182 + 0.701994i \(0.247707\pi\)
\(200\) 58.3161 0.0206178
\(201\) 857.943 0.301068
\(202\) 2984.75 1.03964
\(203\) 1187.09 0.410432
\(204\) 2298.03 0.788698
\(205\) −1623.30 −0.553054
\(206\) 7611.41 2.57433
\(207\) 1977.39 0.663953
\(208\) 0 0
\(209\) 230.671 0.0763438
\(210\) −581.973 −0.191238
\(211\) −1375.80 −0.448882 −0.224441 0.974488i \(-0.572056\pi\)
−0.224441 + 0.974488i \(0.572056\pi\)
\(212\) −219.438 −0.0710898
\(213\) 953.020 0.306572
\(214\) 3705.66 1.18371
\(215\) −944.799 −0.299696
\(216\) −26.4300 −0.00832561
\(217\) 1831.51 0.572955
\(218\) 6329.12 1.96634
\(219\) 189.200 0.0583789
\(220\) 1149.18 0.352171
\(221\) 0 0
\(222\) −4035.61 −1.22005
\(223\) −1694.37 −0.508805 −0.254403 0.967098i \(-0.581879\pi\)
−0.254403 + 0.967098i \(0.581879\pi\)
\(224\) −1533.50 −0.457418
\(225\) −536.164 −0.158864
\(226\) 5338.70 1.57135
\(227\) 405.400 0.118534 0.0592672 0.998242i \(-0.481124\pi\)
0.0592672 + 0.998242i \(0.481124\pi\)
\(228\) −330.949 −0.0961299
\(229\) −2359.54 −0.680884 −0.340442 0.940265i \(-0.610577\pi\)
−0.340442 + 0.940265i \(0.610577\pi\)
\(230\) 7162.39 2.05337
\(231\) 307.701 0.0876416
\(232\) 195.274 0.0552601
\(233\) 938.507 0.263878 0.131939 0.991258i \(-0.457880\pi\)
0.131939 + 0.991258i \(0.457880\pi\)
\(234\) 0 0
\(235\) 2738.90 0.760280
\(236\) 2308.49 0.636736
\(237\) −1871.51 −0.512943
\(238\) 2228.75 0.607010
\(239\) −4664.25 −1.26237 −0.631183 0.775634i \(-0.717430\pi\)
−0.631183 + 0.775634i \(0.717430\pi\)
\(240\) 1504.44 0.404629
\(241\) 3774.94 1.00898 0.504492 0.863416i \(-0.331680\pi\)
0.504492 + 0.863416i \(0.331680\pi\)
\(242\) 4166.97 1.10687
\(243\) 243.000 0.0641500
\(244\) −1706.97 −0.447860
\(245\) 2487.97 0.648778
\(246\) −2426.47 −0.628887
\(247\) 0 0
\(248\) 301.279 0.0771421
\(249\) −1979.62 −0.503829
\(250\) −6016.96 −1.52219
\(251\) −960.695 −0.241588 −0.120794 0.992678i \(-0.538544\pi\)
−0.120794 + 0.992678i \(0.538544\pi\)
\(252\) −441.464 −0.110356
\(253\) −3786.90 −0.941029
\(254\) 9472.64 2.34003
\(255\) −2255.03 −0.553787
\(256\) 3836.08 0.936542
\(257\) −16.7302 −0.00406070 −0.00203035 0.999998i \(-0.500646\pi\)
−0.00203035 + 0.999998i \(0.500646\pi\)
\(258\) −1412.27 −0.340790
\(259\) −1986.23 −0.476519
\(260\) 0 0
\(261\) −1795.37 −0.425788
\(262\) −9304.58 −2.19404
\(263\) −400.736 −0.0939560 −0.0469780 0.998896i \(-0.514959\pi\)
−0.0469780 + 0.998896i \(0.514959\pi\)
\(264\) 50.6159 0.0118000
\(265\) 215.332 0.0499159
\(266\) −320.971 −0.0739849
\(267\) −3819.57 −0.875484
\(268\) 2357.31 0.537297
\(269\) 2236.97 0.507027 0.253514 0.967332i \(-0.418414\pi\)
0.253514 + 0.967332i \(0.418414\pi\)
\(270\) 880.179 0.198393
\(271\) 4018.89 0.900850 0.450425 0.892814i \(-0.351273\pi\)
0.450425 + 0.892814i \(0.351273\pi\)
\(272\) −5761.46 −1.28434
\(273\) 0 0
\(274\) −1510.99 −0.333147
\(275\) 1026.81 0.225159
\(276\) 5433.14 1.18492
\(277\) 6792.95 1.47346 0.736731 0.676186i \(-0.236368\pi\)
0.736731 + 0.676186i \(0.236368\pi\)
\(278\) −1965.59 −0.424059
\(279\) −2769.99 −0.594391
\(280\) −47.1175 −0.0100565
\(281\) 7286.80 1.54695 0.773477 0.633824i \(-0.218516\pi\)
0.773477 + 0.633824i \(0.218516\pi\)
\(282\) 4094.04 0.864528
\(283\) −2429.77 −0.510369 −0.255185 0.966892i \(-0.582136\pi\)
−0.255185 + 0.966892i \(0.582136\pi\)
\(284\) 2618.54 0.547120
\(285\) 324.756 0.0674979
\(286\) 0 0
\(287\) −1194.25 −0.245626
\(288\) 2319.28 0.474531
\(289\) 3722.97 0.757780
\(290\) −6503.07 −1.31681
\(291\) −1811.24 −0.364868
\(292\) 519.853 0.104185
\(293\) −4211.25 −0.839672 −0.419836 0.907600i \(-0.637912\pi\)
−0.419836 + 0.907600i \(0.637912\pi\)
\(294\) 3718.97 0.737737
\(295\) −2265.29 −0.447085
\(296\) −326.730 −0.0641580
\(297\) −465.368 −0.0909206
\(298\) 4255.56 0.827242
\(299\) 0 0
\(300\) −1473.18 −0.283514
\(301\) −695.084 −0.133103
\(302\) −3581.12 −0.682351
\(303\) −2221.76 −0.421244
\(304\) 829.731 0.156541
\(305\) 1675.03 0.314466
\(306\) −3370.78 −0.629720
\(307\) −8212.27 −1.52671 −0.763353 0.645982i \(-0.776448\pi\)
−0.763353 + 0.645982i \(0.776448\pi\)
\(308\) 845.447 0.156408
\(309\) −5665.71 −1.04308
\(310\) −10033.3 −1.83823
\(311\) −4238.55 −0.772818 −0.386409 0.922328i \(-0.626285\pi\)
−0.386409 + 0.922328i \(0.626285\pi\)
\(312\) 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
\(315\) 433.204 0.0774865
\(316\) −5142.20 −0.915416
\(317\) 10497.7 1.85996 0.929981 0.367608i \(-0.119823\pi\)
0.929981 + 0.367608i \(0.119823\pi\)
\(318\) 321.873 0.0567602
\(319\) 3438.31 0.603474
\(320\) 4388.92 0.766713
\(321\) −2758.39 −0.479621
\(322\) 5269.34 0.911953
\(323\) −1243.70 −0.214246
\(324\) 667.674 0.114485
\(325\) 0 0
\(326\) 5587.91 0.949343
\(327\) −4711.21 −0.796730
\(328\) −196.452 −0.0330708
\(329\) 2014.99 0.337660
\(330\) −1685.63 −0.281184
\(331\) −11905.2 −1.97695 −0.988474 0.151389i \(-0.951625\pi\)
−0.988474 + 0.151389i \(0.951625\pi\)
\(332\) −5439.27 −0.899152
\(333\) 3003.99 0.494347
\(334\) −13606.9 −2.22915
\(335\) −2313.20 −0.377264
\(336\) 1106.81 0.179706
\(337\) 8981.18 1.45174 0.725869 0.687833i \(-0.241438\pi\)
0.725869 + 0.687833i \(0.241438\pi\)
\(338\) 0 0
\(339\) −3973.97 −0.636686
\(340\) −6195.99 −0.988308
\(341\) 5304.80 0.842437
\(342\) 485.439 0.0767530
\(343\) 3871.51 0.609451
\(344\) −114.339 −0.0179208
\(345\) −5331.48 −0.831992
\(346\) −1377.61 −0.214048
\(347\) −5712.87 −0.883813 −0.441906 0.897061i \(-0.645698\pi\)
−0.441906 + 0.897061i \(0.645698\pi\)
\(348\) −4933.01 −0.759876
\(349\) −9507.28 −1.45820 −0.729102 0.684406i \(-0.760062\pi\)
−0.729102 + 0.684406i \(0.760062\pi\)
\(350\) −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 \(0.403174\pi\)
\(354\) −3386.11 −0.508389
\(355\) −2569.55 −0.384162
\(356\) −10494.8 −1.56242
\(357\) −1659.02 −0.245951
\(358\) 11629.5 1.71686
\(359\) 109.866 0.0161519 0.00807594 0.999967i \(-0.497429\pi\)
0.00807594 + 0.999967i \(0.497429\pi\)
\(360\) 71.2609 0.0104327
\(361\) −6679.89 −0.973887
\(362\) −15297.3 −2.22101
\(363\) −3101.77 −0.448487
\(364\) 0 0
\(365\) −510.125 −0.0731539
\(366\) 2503.80 0.357584
\(367\) 7020.02 0.998480 0.499240 0.866464i \(-0.333613\pi\)
0.499240 + 0.866464i \(0.333613\pi\)
\(368\) −13621.6 −1.92955
\(369\) 1806.20 0.254815
\(370\) 10880.9 1.52884
\(371\) 158.418 0.0221689
\(372\) −7610.91 −1.06077
\(373\) 2227.18 0.309166 0.154583 0.987980i \(-0.450597\pi\)
0.154583 + 0.987980i \(0.450597\pi\)
\(374\) 6455.36 0.892510
\(375\) 4478.86 0.616766
\(376\) 331.461 0.0454622
\(377\) 0 0
\(378\) 647.544 0.0881113
\(379\) 11004.6 1.49147 0.745734 0.666244i \(-0.232099\pi\)
0.745734 + 0.666244i \(0.232099\pi\)
\(380\) 892.309 0.120459
\(381\) −7051.16 −0.948142
\(382\) 11308.5 1.51464
\(383\) 4436.85 0.591938 0.295969 0.955198i \(-0.404357\pi\)
0.295969 + 0.955198i \(0.404357\pi\)
\(384\) 375.720 0.0499306
\(385\) −829.627 −0.109823
\(386\) −10017.7 −1.32096
\(387\) 1051.25 0.138083
\(388\) −4976.61 −0.651157
\(389\) −2561.58 −0.333874 −0.166937 0.985968i \(-0.553388\pi\)
−0.166937 + 0.985968i \(0.553388\pi\)
\(390\) 0 0
\(391\) 20417.7 2.64083
\(392\) 301.094 0.0387948
\(393\) 6926.07 0.888992
\(394\) 11086.0 1.41752
\(395\) 5045.98 0.642762
\(396\) −1278.66 −0.162260
\(397\) −2206.90 −0.278996 −0.139498 0.990222i \(-0.544549\pi\)
−0.139498 + 0.990222i \(0.544549\pi\)
\(398\) −16115.1 −2.02959
\(399\) 238.922 0.0299775
\(400\) 3693.45 0.461682
\(401\) 8071.02 1.00511 0.502553 0.864546i \(-0.332394\pi\)
0.502553 + 0.864546i \(0.332394\pi\)
\(402\) −3457.72 −0.428994
\(403\) 0 0
\(404\) −6104.58 −0.751768
\(405\) −655.180 −0.0803856
\(406\) −4784.28 −0.584827
\(407\) −5752.93 −0.700644
\(408\) −272.904 −0.0331146
\(409\) −6298.36 −0.761452 −0.380726 0.924688i \(-0.624326\pi\)
−0.380726 + 0.924688i \(0.624326\pi\)
\(410\) 6542.29 0.788051
\(411\) 1124.74 0.134986
\(412\) −15567.3 −1.86152
\(413\) −1666.56 −0.198562
\(414\) −7969.38 −0.946072
\(415\) 5337.49 0.631342
\(416\) 0 0
\(417\) 1463.13 0.171822
\(418\) −929.662 −0.108783
\(419\) −1432.01 −0.166965 −0.0834824 0.996509i \(-0.526604\pi\)
−0.0834824 + 0.996509i \(0.526604\pi\)
\(420\) 1190.28 0.138285
\(421\) −9641.43 −1.11614 −0.558069 0.829794i \(-0.688458\pi\)
−0.558069 + 0.829794i \(0.688458\pi\)
\(422\) 5544.82 0.639615
\(423\) −3047.49 −0.350293
\(424\) 26.0594 0.00298480
\(425\) −5536.19 −0.631870
\(426\) −3840.90 −0.436837
\(427\) 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 \(0.560314\pi\)
\(432\) −1673.94 −0.186430
\(433\) 6248.91 0.693541 0.346770 0.937950i \(-0.387278\pi\)
0.346770 + 0.937950i \(0.387278\pi\)
\(434\) −7381.45 −0.816407
\(435\) 4840.70 0.533549
\(436\) −12944.7 −1.42187
\(437\) −2940.43 −0.321876
\(438\) −762.524 −0.0831845
\(439\) 2866.16 0.311604 0.155802 0.987788i \(-0.450204\pi\)
0.155802 + 0.987788i \(0.450204\pi\)
\(440\) −136.471 −0.0147864
\(441\) −2768.29 −0.298920
\(442\) 0 0
\(443\) 10776.3 1.15575 0.577877 0.816124i \(-0.303881\pi\)
0.577877 + 0.816124i \(0.303881\pi\)
\(444\) 8253.85 0.882230
\(445\) 10298.4 1.09706
\(446\) 6828.74 0.725000
\(447\) −3167.72 −0.335185
\(448\) 3228.91 0.340517
\(449\) −13834.9 −1.45414 −0.727069 0.686564i \(-0.759118\pi\)
−0.727069 + 0.686564i \(0.759118\pi\)
\(450\) 2160.87 0.226366
\(451\) −3459.04 −0.361153
\(452\) −10919.0 −1.13625
\(453\) 2665.68 0.276478
\(454\) −1633.86 −0.168901
\(455\) 0 0
\(456\) 39.3020 0.00403615
\(457\) −17233.0 −1.76395 −0.881976 0.471295i \(-0.843787\pi\)
−0.881976 + 0.471295i \(0.843787\pi\)
\(458\) 9509.51 0.970197
\(459\) 2509.11 0.255153
\(460\) −14648.9 −1.48480
\(461\) −11485.0 −1.16033 −0.580164 0.814500i \(-0.697012\pi\)
−0.580164 + 0.814500i \(0.697012\pi\)
\(462\) −1240.11 −0.124881
\(463\) −1613.61 −0.161967 −0.0809837 0.996715i \(-0.525806\pi\)
−0.0809837 + 0.996715i \(0.525806\pi\)
\(464\) 12367.7 1.23740
\(465\) 7468.49 0.744824
\(466\) −3782.41 −0.376002
\(467\) −8149.20 −0.807495 −0.403747 0.914871i \(-0.632293\pi\)
−0.403747 + 0.914871i \(0.632293\pi\)
\(468\) 0 0
\(469\) −1701.81 −0.167553
\(470\) −11038.4 −1.08333
\(471\) −10945.7 −1.07081
\(472\) −274.145 −0.0267342
\(473\) −2013.24 −0.195706
\(474\) 7542.63 0.730896
\(475\) 797.289 0.0770150
\(476\) −4558.36 −0.438933
\(477\) −239.593 −0.0229984
\(478\) 18798.1 1.79875
\(479\) −1827.62 −0.174334 −0.0871670 0.996194i \(-0.527781\pi\)
−0.0871670 + 0.996194i \(0.527781\pi\)
\(480\) −6253.28 −0.594629
\(481\) 0 0
\(482\) −15213.9 −1.43771
\(483\) −3922.34 −0.369509
\(484\) −8522.52 −0.800387
\(485\) 4883.49 0.457212
\(486\) −979.350 −0.0914078
\(487\) 7838.95 0.729398 0.364699 0.931125i \(-0.381172\pi\)
0.364699 + 0.931125i \(0.381172\pi\)
\(488\) 202.712 0.0188040
\(489\) −4159.48 −0.384659
\(490\) −10027.1 −0.924449
\(491\) 17196.1 1.58055 0.790273 0.612755i \(-0.209939\pi\)
0.790273 + 0.612755i \(0.209939\pi\)
\(492\) 4962.76 0.454753
\(493\) −18538.2 −1.69354
\(494\) 0 0
\(495\) 1254.73 0.113931
\(496\) 19081.5 1.72739
\(497\) −1890.40 −0.170616
\(498\) 7978.37 0.717910
\(499\) −5355.28 −0.480431 −0.240216 0.970720i \(-0.577218\pi\)
−0.240216 + 0.970720i \(0.577218\pi\)
\(500\) 12306.2 1.10070
\(501\) 10128.6 0.903217
\(502\) 3871.84 0.344240
\(503\) 2979.80 0.264141 0.132071 0.991240i \(-0.457837\pi\)
0.132071 + 0.991240i \(0.457837\pi\)
\(504\) 52.4263 0.00463344
\(505\) 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 \(0.733066\pi\)
\(510\) 9088.33 0.789094
\(511\) −375.297 −0.0324895
\(512\) −16462.3 −1.42097
\(513\) −361.347 −0.0310991
\(514\) 67.4267 0.00578611
\(515\) 15276.0 1.30707
\(516\) 2888.44 0.246428
\(517\) 5836.24 0.496475
\(518\) 8005.00 0.678995
\(519\) 1025.45 0.0867289
\(520\) 0 0
\(521\) 433.801 0.0364783 0.0182391 0.999834i \(-0.494194\pi\)
0.0182391 + 0.999834i \(0.494194\pi\)
\(522\) 7235.78 0.606708
\(523\) 18900.3 1.58021 0.790106 0.612970i \(-0.210026\pi\)
0.790106 + 0.612970i \(0.210026\pi\)
\(524\) 19030.3 1.58653
\(525\) 1063.53 0.0884121
\(526\) 1615.06 0.133879
\(527\) −28601.7 −2.36415
\(528\) 3205.76 0.264229
\(529\) 36105.7 2.96751
\(530\) −867.839 −0.0711255
\(531\) 2520.52 0.205991
\(532\) 656.468 0.0534990
\(533\) 0 0
\(534\) 15393.8 1.24748
\(535\) 7437.21 0.601007
\(536\) −279.943 −0.0225592
\(537\) −8656.64 −0.695645
\(538\) −9015.53 −0.722467
\(539\) 5301.55 0.423662
\(540\) −1800.19 −0.143459
\(541\) −13247.5 −1.05278 −0.526391 0.850243i \(-0.676455\pi\)
−0.526391 + 0.850243i \(0.676455\pi\)
\(542\) −16197.1 −1.28363
\(543\) 11386.9 0.899920
\(544\) 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
\(549\) −1863.76 −0.144888
\(550\) −4138.28 −0.320831
\(551\) 2669.76 0.206416
\(552\) −645.215 −0.0497503
\(553\) 3712.31 0.285467
\(554\) −27377.3 −2.09955
\(555\) −8099.40 −0.619460
\(556\) 4020.14 0.306640
\(557\) −6733.19 −0.512198 −0.256099 0.966651i \(-0.582437\pi\)
−0.256099 + 0.966651i \(0.582437\pi\)
\(558\) 11163.7 0.846952
\(559\) 0 0
\(560\) −2984.19 −0.225188
\(561\) −4805.18 −0.361631
\(562\) −29367.6 −2.20427
\(563\) 24282.4 1.81773 0.908863 0.417096i \(-0.136952\pi\)
0.908863 + 0.417096i \(0.136952\pi\)
\(564\) −8373.37 −0.625146
\(565\) 10714.7 0.797823
\(566\) 9792.55 0.727229
\(567\) −482.013 −0.0357013
\(568\) −310.966 −0.0229716
\(569\) −19876.2 −1.46441 −0.732207 0.681082i \(-0.761510\pi\)
−0.732207 + 0.681082i \(0.761510\pi\)
\(570\) −1308.85 −0.0961782
\(571\) 225.014 0.0164913 0.00824567 0.999966i \(-0.497375\pi\)
0.00824567 + 0.999966i \(0.497375\pi\)
\(572\) 0 0
\(573\) −8417.70 −0.613707
\(574\) 4813.14 0.349994
\(575\) −13089.0 −0.949302
\(576\) −4883.43 −0.353257
\(577\) 12258.1 0.884424 0.442212 0.896910i \(-0.354194\pi\)
0.442212 + 0.896910i \(0.354194\pi\)
\(578\) −15004.5 −1.07977
\(579\) 7456.92 0.535231
\(580\) 13300.4 0.952191
\(581\) 3926.77 0.280395
\(582\) 7299.73 0.519903
\(583\) 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 \(0.617734\pi\)
\(588\) −7606.24 −0.533463
\(589\) 4119.04 0.288153
\(590\) 9129.67 0.637055
\(591\) −8252.10 −0.574359
\(592\) −20693.5 −1.43665
\(593\) −12355.1 −0.855586 −0.427793 0.903877i \(-0.640709\pi\)
−0.427793 + 0.903877i \(0.640709\pi\)
\(594\) 1875.55 0.129553
\(595\) 4473.07 0.308198
\(596\) −8703.71 −0.598184
\(597\) 11995.6 0.822357
\(598\) 0 0
\(599\) 13035.2 0.889157 0.444578 0.895740i \(-0.353354\pi\)
0.444578 + 0.895740i \(0.353354\pi\)
\(600\) 174.948 0.0119037
\(601\) −5153.36 −0.349767 −0.174884 0.984589i \(-0.555955\pi\)
−0.174884 + 0.984589i \(0.555955\pi\)
\(602\) 2801.36 0.189659
\(603\) 2573.83 0.173822
\(604\) 7324.30 0.493413
\(605\) 8363.05 0.561994
\(606\) 8954.25 0.600234
\(607\) −1406.55 −0.0940530 −0.0470265 0.998894i \(-0.514975\pi\)
−0.0470265 + 0.998894i \(0.514975\pi\)
\(608\) −3448.83 −0.230047
\(609\) 3561.28 0.236963
\(610\) −6750.79 −0.448085
\(611\) 0 0
\(612\) 6894.10 0.455355
\(613\) 15984.3 1.05318 0.526590 0.850120i \(-0.323470\pi\)
0.526590 + 0.850120i \(0.323470\pi\)
\(614\) 33097.5 2.17541
\(615\) −4869.90 −0.319306
\(616\) −100.401 −0.00656703
\(617\) 10324.4 0.673652 0.336826 0.941567i \(-0.390647\pi\)
0.336826 + 0.941567i \(0.390647\pi\)
\(618\) 22834.2 1.48629
\(619\) 7423.00 0.481996 0.240998 0.970526i \(-0.422525\pi\)
0.240998 + 0.970526i \(0.422525\pi\)
\(620\) 20520.6 1.32924
\(621\) 5932.18 0.383334
\(622\) 17082.4 1.10119
\(623\) 7576.48 0.487232
\(624\) 0 0
\(625\) −4629.23 −0.296271
\(626\) −15346.4 −0.979820
\(627\) 692.014 0.0440771
\(628\) −30074.6 −1.91100
\(629\) 31017.8 1.96624
\(630\) −1745.92 −0.110411
\(631\) −1190.30 −0.0750954 −0.0375477 0.999295i \(-0.511955\pi\)
−0.0375477 + 0.999295i \(0.511955\pi\)
\(632\) 610.665 0.0384350
\(633\) −4127.41 −0.259162
\(634\) −42308.2 −2.65027
\(635\) 19011.5 1.18810
\(636\) −658.313 −0.0410437
\(637\) 0 0
\(638\) −13857.2 −0.859894
\(639\) 2859.06 0.176999
\(640\) −1013.02 −0.0625674
\(641\) 705.064 0.0434451 0.0217226 0.999764i \(-0.493085\pi\)
0.0217226 + 0.999764i \(0.493085\pi\)
\(642\) 11117.0 0.683415
\(643\) −14641.4 −0.897976 −0.448988 0.893538i \(-0.648215\pi\)
−0.448988 + 0.893538i \(0.648215\pi\)
\(644\) −10777.1 −0.659439
\(645\) −2834.40 −0.173030
\(646\) 5012.42 0.305280
\(647\) 1520.83 0.0924111 0.0462056 0.998932i \(-0.485287\pi\)
0.0462056 + 0.998932i \(0.485287\pi\)
\(648\) −79.2899 −0.00480679
\(649\) −4827.04 −0.291954
\(650\) 0 0
\(651\) 5494.54 0.330796
\(652\) −11428.7 −0.686477
\(653\) −22054.4 −1.32168 −0.660838 0.750529i \(-0.729799\pi\)
−0.660838 + 0.750529i \(0.729799\pi\)
\(654\) 18987.3 1.13527
\(655\) −18674.2 −1.11398
\(656\) −12442.3 −0.740532
\(657\) 567.601 0.0337051
\(658\) −8120.92 −0.481134
\(659\) −12652.3 −0.747895 −0.373947 0.927450i \(-0.621996\pi\)
−0.373947 + 0.927450i \(0.621996\pi\)
\(660\) 3447.54 0.203326
\(661\) 10893.2 0.640994 0.320497 0.947250i \(-0.396150\pi\)
0.320497 + 0.947250i \(0.396150\pi\)
\(662\) 47981.0 2.81697
\(663\) 0 0
\(664\) 645.942 0.0377522
\(665\) −644.184 −0.0375645
\(666\) −12106.8 −0.704399
\(667\) −43829.0 −2.54433
\(668\) 27829.6 1.61191
\(669\) −5083.12 −0.293759
\(670\) 9322.76 0.537567
\(671\) 3569.28 0.205351
\(672\) −4600.51 −0.264090
\(673\) −9019.75 −0.516621 −0.258310 0.966062i \(-0.583166\pi\)
−0.258310 + 0.966062i \(0.583166\pi\)
\(674\) −36196.4 −2.06859
\(675\) −1608.49 −0.0917199
\(676\) 0 0
\(677\) −24923.6 −1.41491 −0.707454 0.706760i \(-0.750156\pi\)
−0.707454 + 0.706760i \(0.750156\pi\)
\(678\) 16016.1 0.907218
\(679\) 3592.76 0.203060
\(680\) 735.807 0.0414955
\(681\) 1216.20 0.0684359
\(682\) −21379.7 −1.20039
\(683\) 24634.2 1.38009 0.690044 0.723767i \(-0.257591\pi\)
0.690044 + 0.723767i \(0.257591\pi\)
\(684\) −992.846 −0.0555006
\(685\) −3032.53 −0.169149
\(686\) −15603.1 −0.868411
\(687\) −7078.61 −0.393109
\(688\) −7241.70 −0.401290
\(689\) 0 0
\(690\) 21487.2 1.18551
\(691\) 10340.2 0.569264 0.284632 0.958637i \(-0.408129\pi\)
0.284632 + 0.958637i \(0.408129\pi\)
\(692\) 2817.56 0.154780
\(693\) 923.102 0.0505999
\(694\) 23024.3 1.25935
\(695\) −3944.92 −0.215308
\(696\) 585.821 0.0319045
\(697\) 18650.0 1.01351
\(698\) 38316.7 2.07780
\(699\) 2815.52 0.152350
\(700\) 2922.19 0.157784
\(701\) −20833.9 −1.12252 −0.561258 0.827641i \(-0.689683\pi\)
−0.561258 + 0.827641i \(0.689683\pi\)
\(702\) 0 0
\(703\) −4467.00 −0.239653
\(704\) 9352.23 0.500676
\(705\) 8216.69 0.438948
\(706\) −16012.0 −0.853569
\(707\) 4407.07 0.234434
\(708\) 6925.46 0.367619
\(709\) −9189.56 −0.486772 −0.243386 0.969930i \(-0.578258\pi\)
−0.243386 + 0.969930i \(0.578258\pi\)
\(710\) 10355.9 0.547395
\(711\) −5614.52 −0.296148
\(712\) 1246.31 0.0656004
\(713\) −67621.8 −3.55183
\(714\) 6686.25 0.350457
\(715\) 0 0
\(716\) −23785.2 −1.24147
\(717\) −13992.8 −0.728827
\(718\) −442.788 −0.0230149
\(719\) 7503.22 0.389183 0.194592 0.980884i \(-0.437662\pi\)
0.194592 + 0.980884i \(0.437662\pi\)
\(720\) 4513.31 0.233613
\(721\) 11238.5 0.580503
\(722\) 26921.6 1.38770
\(723\) 11324.8 0.582537
\(724\) 31286.8 1.60603
\(725\) 11884.1 0.608779
\(726\) 12500.9 0.639053
\(727\) −20727.2 −1.05740 −0.528700 0.848809i \(-0.677320\pi\)
−0.528700 + 0.848809i \(0.677320\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 2055.93 0.104237
\(731\) 10854.7 0.549216
\(732\) −5120.92 −0.258572
\(733\) −17361.3 −0.874836 −0.437418 0.899258i \(-0.644107\pi\)
−0.437418 + 0.899258i \(0.644107\pi\)
\(734\) −28292.4 −1.42274
\(735\) 7463.92 0.374572
\(736\) 56618.9 2.83560
\(737\) −4929.13 −0.246359
\(738\) −7279.42 −0.363088
\(739\) −18093.8 −0.900663 −0.450331 0.892861i \(-0.648694\pi\)
−0.450331 + 0.892861i \(0.648694\pi\)
\(740\) −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 \(0.380302\pi\)
\(744\) 903.837 0.0445380
\(745\) 8540.85 0.420017
\(746\) −8976.07 −0.440533
\(747\) −5938.87 −0.290886
\(748\) −13202.9 −0.645380
\(749\) 5471.52 0.266923
\(750\) −18050.9 −0.878834
\(751\) −17750.9 −0.862502 −0.431251 0.902232i \(-0.641928\pi\)
−0.431251 + 0.902232i \(0.641928\pi\)
\(752\) 20993.1 1.01801
\(753\) −2882.09 −0.139481
\(754\) 0 0
\(755\) −7187.25 −0.346451
\(756\) −1324.39 −0.0637139
\(757\) −10220.3 −0.490702 −0.245351 0.969434i \(-0.578903\pi\)
−0.245351 + 0.969434i \(0.578903\pi\)
\(758\) −44351.1 −2.12520
\(759\) −11360.7 −0.543303
\(760\) −105.967 −0.00505765
\(761\) 14112.0 0.672221 0.336110 0.941823i \(-0.390888\pi\)
0.336110 + 0.941823i \(0.390888\pi\)
\(762\) 28417.9 1.35101
\(763\) 9345.13 0.443403
\(764\) −23128.7 −1.09525
\(765\) −6765.10 −0.319729
\(766\) −17881.6 −0.843457
\(767\) 0 0
\(768\) 11508.2 0.540713
\(769\) 22736.7 1.06620 0.533100 0.846052i \(-0.321027\pi\)
0.533100 + 0.846052i \(0.321027\pi\)
\(770\) 3343.60 0.156487
\(771\) −50.1905 −0.00234444
\(772\) 20488.8 0.955194
\(773\) 343.173 0.0159678 0.00798388 0.999968i \(-0.497459\pi\)
0.00798388 + 0.999968i \(0.497459\pi\)
\(774\) −4236.80 −0.196755
\(775\) 18335.4 0.849844
\(776\) 590.999 0.0273397
\(777\) −5958.69 −0.275118
\(778\) 10323.8 0.475740
\(779\) −2685.86 −0.123531
\(780\) 0 0
\(781\) −5475.37 −0.250863
\(782\) −82288.3 −3.76294
\(783\) −5386.11 −0.245829
\(784\) 19069.8 0.868706
\(785\) 29511.9 1.34181
\(786\) −27913.8 −1.26673
\(787\) 19086.4 0.864496 0.432248 0.901755i \(-0.357721\pi\)
0.432248 + 0.901755i \(0.357721\pi\)
\(788\) −22673.7 −1.02502
\(789\) −1202.21 −0.0542455
\(790\) −20336.6 −0.915876
\(791\) 7882.74 0.354334
\(792\) 151.848 0.00681272
\(793\) 0 0
\(794\) 8894.36 0.397543
\(795\) 645.995 0.0288190
\(796\) 32959.5 1.46761
\(797\) 12031.1 0.534709 0.267354 0.963598i \(-0.413851\pi\)
0.267354 + 0.963598i \(0.413851\pi\)
\(798\) −962.913 −0.0427152
\(799\) −31467.0 −1.39327
\(800\) −15352.1 −0.678471
\(801\) −11458.7 −0.505461
\(802\) −32528.2 −1.43218
\(803\) −1087.01 −0.0477706
\(804\) 7071.93 0.310208
\(805\) 10575.5 0.463027
\(806\) 0 0
\(807\) 6710.91 0.292732
\(808\) 724.952 0.0315640
\(809\) 10175.4 0.442210 0.221105 0.975250i \(-0.429034\pi\)
0.221105 + 0.975250i \(0.429034\pi\)
\(810\) 2640.54 0.114542
\(811\) −26754.1 −1.15840 −0.579201 0.815185i \(-0.696635\pi\)
−0.579201 + 0.815185i \(0.696635\pi\)
\(812\) 9785.08 0.422893
\(813\) 12056.7 0.520106
\(814\) 23185.7 0.998353
\(815\) 11214.9 0.482011
\(816\) −17284.4 −0.741513
\(817\) −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 \(0.391147\pi\)
\(822\) −4532.97 −0.192342
\(823\) −13863.9 −0.587197 −0.293599 0.955929i \(-0.594853\pi\)
−0.293599 + 0.955929i \(0.594853\pi\)
\(824\) 1848.70 0.0781583
\(825\) 3080.42 0.129996
\(826\) 6716.66 0.282933
\(827\) 26835.0 1.12835 0.564175 0.825655i \(-0.309194\pi\)
0.564175 + 0.825655i \(0.309194\pi\)
\(828\) 16299.4 0.684111
\(829\) 625.251 0.0261953 0.0130976 0.999914i \(-0.495831\pi\)
0.0130976 + 0.999914i \(0.495831\pi\)
\(830\) −21511.4 −0.899604
\(831\) 20378.9 0.850704
\(832\) 0 0
\(833\) −28584.2 −1.18893
\(834\) −5896.78 −0.244831
\(835\) −27308.8 −1.13181
\(836\) 1901.40 0.0786617
\(837\) −8309.98 −0.343172
\(838\) 5771.35 0.237909
\(839\) 27307.4 1.12367 0.561833 0.827251i \(-0.310096\pi\)
0.561833 + 0.827251i \(0.310096\pi\)
\(840\) −141.353 −0.00580610
\(841\) 15405.4 0.631656
\(842\) 38857.3 1.59039
\(843\) 21860.4 0.893135
\(844\) −11340.6 −0.462510
\(845\) 0 0
\(846\) 12282.1 0.499135
\(847\) 6152.66 0.249596
\(848\) 1650.48 0.0668368
\(849\) −7289.30 −0.294662
\(850\) 22312.2 0.900356
\(851\) 73334.2 2.95401
\(852\) 7855.63 0.315880
\(853\) −44801.9 −1.79834 −0.899172 0.437595i \(-0.855830\pi\)
−0.899172 + 0.437595i \(0.855830\pi\)
\(854\) −4966.53 −0.199006
\(855\) 974.268 0.0389699
\(856\) 900.051 0.0359382
\(857\) −25167.1 −1.00314 −0.501571 0.865116i \(-0.667244\pi\)
−0.501571 + 0.865116i \(0.667244\pi\)
\(858\) 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
\(861\) −3582.76 −0.141812
\(862\) 13584.4 0.536759
\(863\) −818.924 −0.0323019 −0.0161509 0.999870i \(-0.505141\pi\)
−0.0161509 + 0.999870i \(0.505141\pi\)
\(864\) 6957.85 0.273971
\(865\) −2764.84 −0.108679
\(866\) −25184.6 −0.988231
\(867\) 11168.9 0.437505
\(868\) 15096.9 0.590350
\(869\) 10752.3 0.419733
\(870\) −19509.2 −0.760258
\(871\) 0 0
\(872\) 1537.25 0.0596993
\(873\) −5433.71 −0.210657
\(874\) 11850.7 0.458644
\(875\) −8884.23 −0.343248
\(876\) 1559.56 0.0601513
\(877\) −190.251 −0.00732533 −0.00366267 0.999993i \(-0.501166\pi\)
−0.00366267 + 0.999993i \(0.501166\pi\)
\(878\) −11551.3 −0.444007
\(879\) −12633.8 −0.484785
\(880\) −8643.43 −0.331102
\(881\) −19803.4 −0.757315 −0.378657 0.925537i \(-0.623614\pi\)
−0.378657 + 0.925537i \(0.623614\pi\)
\(882\) 11156.9 0.425933
\(883\) 19652.1 0.748974 0.374487 0.927232i \(-0.377819\pi\)
0.374487 + 0.927232i \(0.377819\pi\)
\(884\) 0 0
\(885\) −6795.87 −0.258125
\(886\) −43431.2 −1.64684
\(887\) −26295.0 −0.995379 −0.497689 0.867355i \(-0.665818\pi\)
−0.497689 + 0.867355i \(0.665818\pi\)
\(888\) −980.189 −0.0370417
\(889\) 13986.6 0.527668
\(890\) −41505.1 −1.56321
\(891\) −1396.11 −0.0524930
\(892\) −13966.5 −0.524253
\(893\) 4531.69 0.169818
\(894\) 12766.7 0.477608
\(895\) 23340.2 0.871704
\(896\) −745.275 −0.0277878
\(897\) 0 0
\(898\) 55758.0 2.07201
\(899\) 61397.0 2.27776
\(900\) −4419.54 −0.163687
\(901\) −2473.93 −0.0914746
\(902\) 13940.8 0.514609
\(903\) −2085.25 −0.0768470
\(904\) 1296.69 0.0477072
\(905\) −30701.4 −1.12768
\(906\) −10743.3 −0.393956
\(907\) 42417.3 1.55286 0.776429 0.630204i \(-0.217029\pi\)
0.776429 + 0.630204i \(0.217029\pi\)
\(908\) 3341.66 0.122133
\(909\) −6665.29 −0.243205
\(910\) 0 0
\(911\) −872.245 −0.0317220 −0.0158610 0.999874i \(-0.505049\pi\)
−0.0158610 + 0.999874i \(0.505049\pi\)
\(912\) 2489.19 0.0903788
\(913\) 11373.5 0.412276
\(914\) 69453.2 2.51347
\(915\) 5025.10 0.181557
\(916\) −19449.4 −0.701557
\(917\) −13738.5 −0.494749
\(918\) −10112.3 −0.363569
\(919\) −17181.4 −0.616716 −0.308358 0.951270i \(-0.599779\pi\)
−0.308358 + 0.951270i \(0.599779\pi\)
\(920\) 1739.64 0.0623415
\(921\) −24636.8 −0.881444
\(922\) 46287.5 1.65336
\(923\) 0 0
\(924\) 2536.34 0.0903025
\(925\) −19884.4 −0.706804
\(926\) 6503.25 0.230788
\(927\) −16997.1 −0.602221
\(928\) −51407.0 −1.81845
\(929\) 56042.9 1.97923 0.989617 0.143728i \(-0.0459091\pi\)
0.989617 + 0.143728i \(0.0459091\pi\)
\(930\) −30099.9 −1.06130
\(931\) 4116.52 0.144912
\(932\) 7736.00 0.271890
\(933\) −12715.7 −0.446187
\(934\) 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
\(939\) 11423.5 0.397008
\(940\) 22576.4 0.783363
\(941\) −21069.0 −0.729895 −0.364947 0.931028i \(-0.618913\pi\)
−0.364947 + 0.931028i \(0.618913\pi\)
\(942\) 44113.7 1.52580
\(943\) 44093.4 1.52267
\(944\) −17363.0 −0.598642
\(945\) 1299.61 0.0447369
\(946\) 8113.87 0.278863
\(947\) −1838.70 −0.0630938 −0.0315469 0.999502i \(-0.510043\pi\)
−0.0315469 + 0.999502i \(0.510043\pi\)
\(948\) −15426.6 −0.528516
\(949\) 0 0
\(950\) −3213.27 −0.109739
\(951\) 31493.0 1.07385
\(952\) 541.330 0.0184292
\(953\) 13599.8 0.462266 0.231133 0.972922i \(-0.425757\pi\)
0.231133 + 0.972922i \(0.425757\pi\)
\(954\) 965.620 0.0327705
\(955\) 22695.9 0.769029
\(956\) −38446.9 −1.30069
\(957\) 10314.9 0.348416
\(958\) 7365.75 0.248410
\(959\) −2231.02 −0.0751235
\(960\) 13166.8 0.442662
\(961\) 64935.6 2.17971
\(962\) 0 0
\(963\) −8275.17 −0.276909
\(964\) 31116.4 1.03962
\(965\) −20105.5 −0.670692
\(966\) 15808.0 0.526516
\(967\) 2081.30 0.0692141 0.0346070 0.999401i \(-0.488982\pi\)
0.0346070 + 0.999401i \(0.488982\pi\)
\(968\) 1012.10 0.0336054
\(969\) −3731.10 −0.123695
\(970\) −19681.6 −0.651484
\(971\) 1636.62 0.0540904 0.0270452 0.999634i \(-0.491390\pi\)
0.0270452 + 0.999634i \(0.491390\pi\)
\(972\) 2003.02 0.0660977
\(973\) −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 \(0.659783\pi\)
\(978\) 16763.7 0.548104
\(979\) 21944.6 0.716396
\(980\) 20508.1 0.668476
\(981\) −14133.6 −0.459992
\(982\) −69304.4 −2.25213
\(983\) 24084.4 0.781457 0.390728 0.920506i \(-0.372223\pi\)
0.390728 + 0.920506i \(0.372223\pi\)
\(984\) −589.355 −0.0190934
\(985\) 22249.4 0.719722
\(986\) 74713.4 2.41314
\(987\) 6044.98 0.194948
\(988\) 0 0
\(989\) 25663.4 0.825125
\(990\) −5056.88 −0.162342
\(991\) 1413.43 0.0453068 0.0226534 0.999743i \(-0.492789\pi\)
0.0226534 + 0.999743i \(0.492789\pi\)
\(992\) −79313.5 −2.53851
\(993\) −35715.7 −1.14139
\(994\) 7618.79 0.243112
\(995\) −32342.7 −1.03049
\(996\) −16317.8 −0.519126
\(997\) −33357.4 −1.05962 −0.529809 0.848117i \(-0.677737\pi\)
−0.529809 + 0.848117i \(0.677737\pi\)
\(998\) 21583.1 0.684570
\(999\) 9011.97 0.285411
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 507.4.a.o.1.3 9
3.2 odd 2 1521.4.a.bi.1.7 9
13.5 odd 4 507.4.b.k.337.15 18
13.8 odd 4 507.4.b.k.337.4 18
13.12 even 2 507.4.a.p.1.7 yes 9
39.38 odd 2 1521.4.a.bf.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.3 9 1.1 even 1 trivial
507.4.a.p.1.7 yes 9 13.12 even 2
507.4.b.k.337.4 18 13.8 odd 4
507.4.b.k.337.15 18 13.5 odd 4
1521.4.a.bf.1.3 9 39.38 odd 2
1521.4.a.bi.1.7 9 3.2 odd 2