Properties

Label 507.4.a.o.1.9
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 1.9
Root \(5.39246\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.83750 q^{2} +3.00000 q^{3} +15.4014 q^{4} -21.1983 q^{5} +14.5125 q^{6} -16.2806 q^{7} +35.8043 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.83750 q^{2} +3.00000 q^{3} +15.4014 q^{4} -21.1983 q^{5} +14.5125 q^{6} -16.2806 q^{7} +35.8043 q^{8} +9.00000 q^{9} -102.547 q^{10} -30.7532 q^{11} +46.2042 q^{12} -78.7575 q^{14} -63.5948 q^{15} +49.9922 q^{16} +46.2371 q^{17} +43.5375 q^{18} -144.865 q^{19} -326.483 q^{20} -48.8418 q^{21} -148.769 q^{22} +8.38045 q^{23} +107.413 q^{24} +324.366 q^{25} +27.0000 q^{27} -250.744 q^{28} -242.958 q^{29} -307.640 q^{30} -87.9353 q^{31} -44.5973 q^{32} -92.2597 q^{33} +223.672 q^{34} +345.121 q^{35} +138.613 q^{36} +49.6950 q^{37} -700.783 q^{38} -758.990 q^{40} +107.947 q^{41} -236.272 q^{42} -35.4166 q^{43} -473.643 q^{44} -190.784 q^{45} +40.5404 q^{46} +374.815 q^{47} +149.977 q^{48} -77.9418 q^{49} +1569.12 q^{50} +138.711 q^{51} -348.583 q^{53} +130.613 q^{54} +651.915 q^{55} -582.916 q^{56} -434.594 q^{57} -1175.31 q^{58} +679.430 q^{59} -979.450 q^{60} -230.403 q^{61} -425.387 q^{62} -146.525 q^{63} -615.677 q^{64} -446.306 q^{66} -295.642 q^{67} +712.117 q^{68} +25.1413 q^{69} +1669.52 q^{70} +329.215 q^{71} +322.239 q^{72} +48.9973 q^{73} +240.399 q^{74} +973.099 q^{75} -2231.12 q^{76} +500.681 q^{77} -107.942 q^{79} -1059.75 q^{80} +81.0000 q^{81} +522.192 q^{82} +515.654 q^{83} -752.233 q^{84} -980.147 q^{85} -171.328 q^{86} -728.874 q^{87} -1101.10 q^{88} +984.453 q^{89} -922.919 q^{90} +129.071 q^{92} -263.806 q^{93} +1813.17 q^{94} +3070.88 q^{95} -133.792 q^{96} +487.072 q^{97} -377.043 q^{98} -276.779 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 6 q^{2} + 27 q^{3} + 44 q^{4} - 33 q^{5} - 18 q^{6} - 83 q^{7} - 87 q^{8} + 81 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.83750 1.71031 0.855157 0.518368i \(-0.173460\pi\)
0.855157 + 0.518368i \(0.173460\pi\)
\(3\) 3.00000 0.577350
\(4\) 15.4014 1.92518
\(5\) −21.1983 −1.89603 −0.948015 0.318225i \(-0.896913\pi\)
−0.948015 + 0.318225i \(0.896913\pi\)
\(6\) 14.5125 0.987451
\(7\) −16.2806 −0.879070 −0.439535 0.898225i \(-0.644857\pi\)
−0.439535 + 0.898225i \(0.644857\pi\)
\(8\) 35.8043 1.58234
\(9\) 9.00000 0.333333
\(10\) −102.547 −3.24281
\(11\) −30.7532 −0.842950 −0.421475 0.906840i \(-0.638487\pi\)
−0.421475 + 0.906840i \(0.638487\pi\)
\(12\) 46.2042 1.11150
\(13\) 0 0
\(14\) −78.7575 −1.50349
\(15\) −63.5948 −1.09467
\(16\) 49.9922 0.781128
\(17\) 46.2371 0.659656 0.329828 0.944041i \(-0.393009\pi\)
0.329828 + 0.944041i \(0.393009\pi\)
\(18\) 43.5375 0.570105
\(19\) −144.865 −1.74917 −0.874585 0.484873i \(-0.838866\pi\)
−0.874585 + 0.484873i \(0.838866\pi\)
\(20\) −326.483 −3.65019
\(21\) −48.8418 −0.507531
\(22\) −148.769 −1.44171
\(23\) 8.38045 0.0759758 0.0379879 0.999278i \(-0.487905\pi\)
0.0379879 + 0.999278i \(0.487905\pi\)
\(24\) 107.413 0.913566
\(25\) 324.366 2.59493
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) −250.744 −1.69237
\(29\) −242.958 −1.55573 −0.777865 0.628431i \(-0.783697\pi\)
−0.777865 + 0.628431i \(0.783697\pi\)
\(30\) −307.640 −1.87224
\(31\) −87.9353 −0.509472 −0.254736 0.967011i \(-0.581989\pi\)
−0.254736 + 0.967011i \(0.581989\pi\)
\(32\) −44.5973 −0.246368
\(33\) −92.2597 −0.486677
\(34\) 223.672 1.12822
\(35\) 345.121 1.66674
\(36\) 138.613 0.641726
\(37\) 49.6950 0.220806 0.110403 0.993887i \(-0.464786\pi\)
0.110403 + 0.993887i \(0.464786\pi\)
\(38\) −700.783 −2.99163
\(39\) 0 0
\(40\) −758.990 −3.00017
\(41\) 107.947 0.411181 0.205591 0.978638i \(-0.434088\pi\)
0.205591 + 0.978638i \(0.434088\pi\)
\(42\) −236.272 −0.868039
\(43\) −35.4166 −0.125604 −0.0628021 0.998026i \(-0.520004\pi\)
−0.0628021 + 0.998026i \(0.520004\pi\)
\(44\) −473.643 −1.62283
\(45\) −190.784 −0.632010
\(46\) 40.5404 0.129943
\(47\) 374.815 1.16324 0.581621 0.813460i \(-0.302419\pi\)
0.581621 + 0.813460i \(0.302419\pi\)
\(48\) 149.977 0.450985
\(49\) −77.9418 −0.227236
\(50\) 1569.12 4.43815
\(51\) 138.711 0.380853
\(52\) 0 0
\(53\) −348.583 −0.903426 −0.451713 0.892163i \(-0.649187\pi\)
−0.451713 + 0.892163i \(0.649187\pi\)
\(54\) 130.613 0.329150
\(55\) 651.915 1.59826
\(56\) −582.916 −1.39099
\(57\) −434.594 −1.00988
\(58\) −1175.31 −2.66079
\(59\) 679.430 1.49923 0.749613 0.661877i \(-0.230240\pi\)
0.749613 + 0.661877i \(0.230240\pi\)
\(60\) −979.450 −2.10744
\(61\) −230.403 −0.483608 −0.241804 0.970325i \(-0.577739\pi\)
−0.241804 + 0.970325i \(0.577739\pi\)
\(62\) −425.387 −0.871358
\(63\) −146.525 −0.293023
\(64\) −615.677 −1.20249
\(65\) 0 0
\(66\) −446.306 −0.832372
\(67\) −295.642 −0.539082 −0.269541 0.962989i \(-0.586872\pi\)
−0.269541 + 0.962989i \(0.586872\pi\)
\(68\) 712.117 1.26995
\(69\) 25.1413 0.0438647
\(70\) 1669.52 2.85066
\(71\) 329.215 0.550290 0.275145 0.961403i \(-0.411274\pi\)
0.275145 + 0.961403i \(0.411274\pi\)
\(72\) 322.239 0.527448
\(73\) 48.9973 0.0785575 0.0392787 0.999228i \(-0.487494\pi\)
0.0392787 + 0.999228i \(0.487494\pi\)
\(74\) 240.399 0.377647
\(75\) 973.099 1.49818
\(76\) −2231.12 −3.36746
\(77\) 500.681 0.741012
\(78\) 0 0
\(79\) −107.942 −0.153727 −0.0768636 0.997042i \(-0.524491\pi\)
−0.0768636 + 0.997042i \(0.524491\pi\)
\(80\) −1059.75 −1.48104
\(81\) 81.0000 0.111111
\(82\) 522.192 0.703250
\(83\) 515.654 0.681932 0.340966 0.940076i \(-0.389246\pi\)
0.340966 + 0.940076i \(0.389246\pi\)
\(84\) −752.233 −0.977088
\(85\) −980.147 −1.25073
\(86\) −171.328 −0.214823
\(87\) −728.874 −0.898201
\(88\) −1101.10 −1.33384
\(89\) 984.453 1.17249 0.586246 0.810133i \(-0.300605\pi\)
0.586246 + 0.810133i \(0.300605\pi\)
\(90\) −922.919 −1.08094
\(91\) 0 0
\(92\) 129.071 0.146267
\(93\) −263.806 −0.294144
\(94\) 1813.17 1.98951
\(95\) 3070.88 3.31648
\(96\) −133.792 −0.142241
\(97\) 487.072 0.509842 0.254921 0.966962i \(-0.417951\pi\)
0.254921 + 0.966962i \(0.417951\pi\)
\(98\) −377.043 −0.388644
\(99\) −276.779 −0.280983
\(100\) 4995.70 4.99570
\(101\) 766.375 0.755021 0.377511 0.926005i \(-0.376780\pi\)
0.377511 + 0.926005i \(0.376780\pi\)
\(102\) 671.016 0.651378
\(103\) 1229.87 1.17653 0.588266 0.808668i \(-0.299811\pi\)
0.588266 + 0.808668i \(0.299811\pi\)
\(104\) 0 0
\(105\) 1035.36 0.962295
\(106\) −1686.27 −1.54514
\(107\) 76.8261 0.0694117 0.0347059 0.999398i \(-0.488951\pi\)
0.0347059 + 0.999398i \(0.488951\pi\)
\(108\) 415.838 0.370500
\(109\) −626.001 −0.550092 −0.275046 0.961431i \(-0.588693\pi\)
−0.275046 + 0.961431i \(0.588693\pi\)
\(110\) 3153.64 2.73353
\(111\) 149.085 0.127482
\(112\) −813.904 −0.686667
\(113\) −1343.21 −1.11822 −0.559108 0.829095i \(-0.688856\pi\)
−0.559108 + 0.829095i \(0.688856\pi\)
\(114\) −2102.35 −1.72722
\(115\) −177.651 −0.144052
\(116\) −3741.90 −2.99506
\(117\) 0 0
\(118\) 3286.74 2.56415
\(119\) −752.769 −0.579884
\(120\) −2276.97 −1.73215
\(121\) −385.238 −0.289435
\(122\) −1114.58 −0.827122
\(123\) 323.840 0.237396
\(124\) −1354.33 −0.980824
\(125\) −4226.22 −3.02404
\(126\) −708.817 −0.501162
\(127\) −2146.69 −1.49990 −0.749952 0.661492i \(-0.769923\pi\)
−0.749952 + 0.661492i \(0.769923\pi\)
\(128\) −2621.56 −1.81028
\(129\) −106.250 −0.0725177
\(130\) 0 0
\(131\) −798.626 −0.532644 −0.266322 0.963884i \(-0.585808\pi\)
−0.266322 + 0.963884i \(0.585808\pi\)
\(132\) −1420.93 −0.936940
\(133\) 2358.48 1.53764
\(134\) −1430.17 −0.921999
\(135\) −572.353 −0.364891
\(136\) 1655.49 1.04380
\(137\) 601.153 0.374891 0.187445 0.982275i \(-0.439979\pi\)
0.187445 + 0.982275i \(0.439979\pi\)
\(138\) 121.621 0.0750224
\(139\) −2134.18 −1.30229 −0.651146 0.758953i \(-0.725711\pi\)
−0.651146 + 0.758953i \(0.725711\pi\)
\(140\) 5315.35 3.20878
\(141\) 1124.44 0.671598
\(142\) 1592.58 0.941169
\(143\) 0 0
\(144\) 449.930 0.260376
\(145\) 5150.29 2.94971
\(146\) 237.024 0.134358
\(147\) −233.825 −0.131194
\(148\) 765.373 0.425090
\(149\) −3439.93 −1.89134 −0.945670 0.325127i \(-0.894593\pi\)
−0.945670 + 0.325127i \(0.894593\pi\)
\(150\) 4707.37 2.56237
\(151\) −2224.04 −1.19861 −0.599305 0.800521i \(-0.704556\pi\)
−0.599305 + 0.800521i \(0.704556\pi\)
\(152\) −5186.78 −2.76779
\(153\) 416.134 0.219885
\(154\) 2422.05 1.26736
\(155\) 1864.07 0.965975
\(156\) 0 0
\(157\) 2465.32 1.25321 0.626604 0.779338i \(-0.284444\pi\)
0.626604 + 0.779338i \(0.284444\pi\)
\(158\) −522.171 −0.262922
\(159\) −1045.75 −0.521593
\(160\) 945.386 0.467121
\(161\) −136.439 −0.0667881
\(162\) 391.838 0.190035
\(163\) 243.565 0.117040 0.0585199 0.998286i \(-0.481362\pi\)
0.0585199 + 0.998286i \(0.481362\pi\)
\(164\) 1662.53 0.791597
\(165\) 1955.75 0.922755
\(166\) 2494.47 1.16632
\(167\) −409.099 −0.189563 −0.0947814 0.995498i \(-0.530215\pi\)
−0.0947814 + 0.995498i \(0.530215\pi\)
\(168\) −1748.75 −0.803089
\(169\) 0 0
\(170\) −4741.46 −2.13914
\(171\) −1303.78 −0.583056
\(172\) −545.466 −0.241810
\(173\) −2618.97 −1.15096 −0.575481 0.817815i \(-0.695185\pi\)
−0.575481 + 0.817815i \(0.695185\pi\)
\(174\) −3525.93 −1.53621
\(175\) −5280.88 −2.28113
\(176\) −1537.42 −0.658452
\(177\) 2038.29 0.865578
\(178\) 4762.29 2.00533
\(179\) 163.311 0.0681925 0.0340963 0.999419i \(-0.489145\pi\)
0.0340963 + 0.999419i \(0.489145\pi\)
\(180\) −2938.35 −1.21673
\(181\) −3313.07 −1.36054 −0.680272 0.732960i \(-0.738138\pi\)
−0.680272 + 0.732960i \(0.738138\pi\)
\(182\) 0 0
\(183\) −691.209 −0.279211
\(184\) 300.056 0.120220
\(185\) −1053.45 −0.418654
\(186\) −1276.16 −0.503079
\(187\) −1421.94 −0.556057
\(188\) 5772.68 2.23945
\(189\) −439.576 −0.169177
\(190\) 14855.4 5.67222
\(191\) −4281.90 −1.62213 −0.811066 0.584954i \(-0.801112\pi\)
−0.811066 + 0.584954i \(0.801112\pi\)
\(192\) −1847.03 −0.694261
\(193\) −1877.33 −0.700171 −0.350086 0.936718i \(-0.613848\pi\)
−0.350086 + 0.936718i \(0.613848\pi\)
\(194\) 2356.21 0.871990
\(195\) 0 0
\(196\) −1200.41 −0.437468
\(197\) 1991.26 0.720158 0.360079 0.932922i \(-0.382750\pi\)
0.360079 + 0.932922i \(0.382750\pi\)
\(198\) −1338.92 −0.480570
\(199\) 1345.05 0.479137 0.239568 0.970879i \(-0.422994\pi\)
0.239568 + 0.970879i \(0.422994\pi\)
\(200\) 11613.7 4.10607
\(201\) −886.927 −0.311239
\(202\) 3707.34 1.29132
\(203\) 3955.51 1.36760
\(204\) 2136.35 0.733208
\(205\) −2288.28 −0.779612
\(206\) 5949.50 2.01224
\(207\) 75.4240 0.0253253
\(208\) 0 0
\(209\) 4455.05 1.47446
\(210\) 5008.56 1.64583
\(211\) −288.763 −0.0942147 −0.0471073 0.998890i \(-0.515000\pi\)
−0.0471073 + 0.998890i \(0.515000\pi\)
\(212\) −5368.67 −1.73925
\(213\) 987.644 0.317710
\(214\) 371.646 0.118716
\(215\) 750.771 0.238150
\(216\) 966.717 0.304522
\(217\) 1431.64 0.447862
\(218\) −3028.28 −0.940830
\(219\) 146.992 0.0453552
\(220\) 10040.4 3.07693
\(221\) 0 0
\(222\) 721.198 0.218035
\(223\) 1798.41 0.540046 0.270023 0.962854i \(-0.412969\pi\)
0.270023 + 0.962854i \(0.412969\pi\)
\(224\) 726.072 0.216575
\(225\) 2919.30 0.864977
\(226\) −6497.77 −1.91250
\(227\) −2486.10 −0.726909 −0.363454 0.931612i \(-0.618403\pi\)
−0.363454 + 0.931612i \(0.618403\pi\)
\(228\) −6693.36 −1.94420
\(229\) −6074.71 −1.75296 −0.876480 0.481438i \(-0.840115\pi\)
−0.876480 + 0.481438i \(0.840115\pi\)
\(230\) −859.386 −0.246375
\(231\) 1502.04 0.427824
\(232\) −8698.95 −2.46170
\(233\) 6367.16 1.79024 0.895121 0.445822i \(-0.147089\pi\)
0.895121 + 0.445822i \(0.147089\pi\)
\(234\) 0 0
\(235\) −7945.42 −2.20554
\(236\) 10464.2 2.88627
\(237\) −323.827 −0.0887544
\(238\) −3641.52 −0.991784
\(239\) 1886.43 0.510556 0.255278 0.966868i \(-0.417833\pi\)
0.255278 + 0.966868i \(0.417833\pi\)
\(240\) −3179.24 −0.855081
\(241\) −5847.91 −1.56306 −0.781529 0.623869i \(-0.785560\pi\)
−0.781529 + 0.623869i \(0.785560\pi\)
\(242\) −1863.59 −0.495025
\(243\) 243.000 0.0641500
\(244\) −3548.53 −0.931031
\(245\) 1652.23 0.430845
\(246\) 1566.58 0.406021
\(247\) 0 0
\(248\) −3148.46 −0.806160
\(249\) 1546.96 0.393713
\(250\) −20444.3 −5.17205
\(251\) −2388.65 −0.600678 −0.300339 0.953832i \(-0.597100\pi\)
−0.300339 + 0.953832i \(0.597100\pi\)
\(252\) −2256.70 −0.564122
\(253\) −257.726 −0.0640438
\(254\) −10384.6 −2.56531
\(255\) −2940.44 −0.722108
\(256\) −7756.38 −1.89365
\(257\) 4447.21 1.07941 0.539707 0.841853i \(-0.318535\pi\)
0.539707 + 0.841853i \(0.318535\pi\)
\(258\) −513.984 −0.124028
\(259\) −809.064 −0.194104
\(260\) 0 0
\(261\) −2186.62 −0.518577
\(262\) −3863.36 −0.910988
\(263\) 7590.87 1.77975 0.889873 0.456208i \(-0.150793\pi\)
0.889873 + 0.456208i \(0.150793\pi\)
\(264\) −3303.30 −0.770091
\(265\) 7389.36 1.71292
\(266\) 11409.2 2.62985
\(267\) 2953.36 0.676939
\(268\) −4553.31 −1.03783
\(269\) −557.911 −0.126455 −0.0632275 0.997999i \(-0.520139\pi\)
−0.0632275 + 0.997999i \(0.520139\pi\)
\(270\) −2768.76 −0.624079
\(271\) 2707.41 0.606877 0.303439 0.952851i \(-0.401865\pi\)
0.303439 + 0.952851i \(0.401865\pi\)
\(272\) 2311.50 0.515276
\(273\) 0 0
\(274\) 2908.08 0.641181
\(275\) −9975.31 −2.18740
\(276\) 387.212 0.0844472
\(277\) −1231.35 −0.267092 −0.133546 0.991043i \(-0.542636\pi\)
−0.133546 + 0.991043i \(0.542636\pi\)
\(278\) −10324.1 −2.22733
\(279\) −791.417 −0.169824
\(280\) 12356.8 2.63736
\(281\) 4601.44 0.976864 0.488432 0.872602i \(-0.337569\pi\)
0.488432 + 0.872602i \(0.337569\pi\)
\(282\) 5439.50 1.14864
\(283\) −54.5677 −0.0114619 −0.00573094 0.999984i \(-0.501824\pi\)
−0.00573094 + 0.999984i \(0.501824\pi\)
\(284\) 5070.37 1.05941
\(285\) 9212.63 1.91477
\(286\) 0 0
\(287\) −1757.44 −0.361457
\(288\) −401.376 −0.0821226
\(289\) −2775.13 −0.564854
\(290\) 24914.5 5.04494
\(291\) 1461.22 0.294357
\(292\) 754.627 0.151237
\(293\) −4745.24 −0.946144 −0.473072 0.881024i \(-0.656855\pi\)
−0.473072 + 0.881024i \(0.656855\pi\)
\(294\) −1131.13 −0.224384
\(295\) −14402.7 −2.84258
\(296\) 1779.30 0.349390
\(297\) −830.337 −0.162226
\(298\) −16640.6 −3.23479
\(299\) 0 0
\(300\) 14987.1 2.88427
\(301\) 576.604 0.110415
\(302\) −10758.8 −2.05000
\(303\) 2299.13 0.435912
\(304\) −7242.10 −1.36633
\(305\) 4884.15 0.916936
\(306\) 2013.05 0.376073
\(307\) −1028.82 −0.191264 −0.0956320 0.995417i \(-0.530487\pi\)
−0.0956320 + 0.995417i \(0.530487\pi\)
\(308\) 7711.20 1.42658
\(309\) 3689.61 0.679271
\(310\) 9017.46 1.65212
\(311\) −2437.84 −0.444492 −0.222246 0.974991i \(-0.571339\pi\)
−0.222246 + 0.974991i \(0.571339\pi\)
\(312\) 0 0
\(313\) 7934.20 1.43280 0.716402 0.697688i \(-0.245788\pi\)
0.716402 + 0.697688i \(0.245788\pi\)
\(314\) 11926.0 2.14338
\(315\) 3106.09 0.555581
\(316\) −1662.46 −0.295952
\(317\) −6942.72 −1.23010 −0.615050 0.788488i \(-0.710864\pi\)
−0.615050 + 0.788488i \(0.710864\pi\)
\(318\) −5058.81 −0.892089
\(319\) 7471.75 1.31140
\(320\) 13051.3 2.27997
\(321\) 230.478 0.0400749
\(322\) −660.023 −0.114229
\(323\) −6698.12 −1.15385
\(324\) 1247.51 0.213909
\(325\) 0 0
\(326\) 1178.25 0.200175
\(327\) −1878.00 −0.317596
\(328\) 3864.96 0.650630
\(329\) −6102.21 −1.02257
\(330\) 9460.92 1.57820
\(331\) 5439.27 0.903230 0.451615 0.892213i \(-0.350848\pi\)
0.451615 + 0.892213i \(0.350848\pi\)
\(332\) 7941.79 1.31284
\(333\) 447.255 0.0736018
\(334\) −1979.01 −0.324212
\(335\) 6267.10 1.02211
\(336\) −2441.71 −0.396447
\(337\) −1663.87 −0.268952 −0.134476 0.990917i \(-0.542935\pi\)
−0.134476 + 0.990917i \(0.542935\pi\)
\(338\) 0 0
\(339\) −4029.63 −0.645602
\(340\) −15095.6 −2.40787
\(341\) 2704.29 0.429460
\(342\) −6307.04 −0.997210
\(343\) 6853.19 1.07883
\(344\) −1268.07 −0.198749
\(345\) −532.953 −0.0831687
\(346\) −12669.3 −1.96851
\(347\) 9268.10 1.43383 0.716913 0.697163i \(-0.245554\pi\)
0.716913 + 0.697163i \(0.245554\pi\)
\(348\) −11225.7 −1.72920
\(349\) −5239.45 −0.803614 −0.401807 0.915724i \(-0.631618\pi\)
−0.401807 + 0.915724i \(0.631618\pi\)
\(350\) −25546.3 −3.90144
\(351\) 0 0
\(352\) 1371.51 0.207676
\(353\) −1218.01 −0.183649 −0.0918244 0.995775i \(-0.529270\pi\)
−0.0918244 + 0.995775i \(0.529270\pi\)
\(354\) 9860.23 1.48041
\(355\) −6978.78 −1.04337
\(356\) 15162.0 2.25726
\(357\) −2258.31 −0.334796
\(358\) 790.018 0.116631
\(359\) −5316.06 −0.781534 −0.390767 0.920490i \(-0.627790\pi\)
−0.390767 + 0.920490i \(0.627790\pi\)
\(360\) −6830.91 −1.00006
\(361\) 14126.7 2.05959
\(362\) −16027.0 −2.32696
\(363\) −1155.72 −0.167106
\(364\) 0 0
\(365\) −1038.66 −0.148947
\(366\) −3343.73 −0.477539
\(367\) −289.101 −0.0411197 −0.0205599 0.999789i \(-0.506545\pi\)
−0.0205599 + 0.999789i \(0.506545\pi\)
\(368\) 418.957 0.0593469
\(369\) 971.520 0.137060
\(370\) −5096.05 −0.716030
\(371\) 5675.15 0.794175
\(372\) −4062.98 −0.566279
\(373\) 6163.98 0.855654 0.427827 0.903861i \(-0.359279\pi\)
0.427827 + 0.903861i \(0.359279\pi\)
\(374\) −6878.64 −0.951032
\(375\) −12678.7 −1.74593
\(376\) 13420.0 1.84065
\(377\) 0 0
\(378\) −2126.45 −0.289346
\(379\) 2440.03 0.330702 0.165351 0.986235i \(-0.447124\pi\)
0.165351 + 0.986235i \(0.447124\pi\)
\(380\) 47295.9 6.38481
\(381\) −6440.06 −0.865970
\(382\) −20713.7 −2.77436
\(383\) 6577.28 0.877502 0.438751 0.898609i \(-0.355421\pi\)
0.438751 + 0.898609i \(0.355421\pi\)
\(384\) −7864.68 −1.04516
\(385\) −10613.6 −1.40498
\(386\) −9081.58 −1.19751
\(387\) −318.750 −0.0418681
\(388\) 7501.59 0.981535
\(389\) 4964.94 0.647127 0.323563 0.946206i \(-0.395119\pi\)
0.323563 + 0.946206i \(0.395119\pi\)
\(390\) 0 0
\(391\) 387.488 0.0501179
\(392\) −2790.65 −0.359565
\(393\) −2395.88 −0.307522
\(394\) 9632.70 1.23170
\(395\) 2288.19 0.291471
\(396\) −4262.79 −0.540943
\(397\) 12073.9 1.52637 0.763187 0.646178i \(-0.223634\pi\)
0.763187 + 0.646178i \(0.223634\pi\)
\(398\) 6506.69 0.819475
\(399\) 7075.45 0.887758
\(400\) 16215.8 2.02697
\(401\) 4916.90 0.612315 0.306158 0.951981i \(-0.400957\pi\)
0.306158 + 0.951981i \(0.400957\pi\)
\(402\) −4290.51 −0.532316
\(403\) 0 0
\(404\) 11803.3 1.45355
\(405\) −1717.06 −0.210670
\(406\) 19134.8 2.33902
\(407\) −1528.28 −0.186128
\(408\) 4966.47 0.602639
\(409\) −15350.9 −1.85588 −0.927939 0.372733i \(-0.878421\pi\)
−0.927939 + 0.372733i \(0.878421\pi\)
\(410\) −11069.6 −1.33338
\(411\) 1803.46 0.216443
\(412\) 18941.7 2.26503
\(413\) −11061.5 −1.31792
\(414\) 364.864 0.0433142
\(415\) −10931.0 −1.29296
\(416\) 0 0
\(417\) −6402.53 −0.751878
\(418\) 21551.3 2.52179
\(419\) −5488.58 −0.639939 −0.319970 0.947428i \(-0.603673\pi\)
−0.319970 + 0.947428i \(0.603673\pi\)
\(420\) 15946.0 1.85259
\(421\) 927.681 0.107393 0.0536964 0.998557i \(-0.482900\pi\)
0.0536964 + 0.998557i \(0.482900\pi\)
\(422\) −1396.89 −0.161137
\(423\) 3373.33 0.387747
\(424\) −12480.8 −1.42953
\(425\) 14997.8 1.71176
\(426\) 4777.73 0.543384
\(427\) 3751.10 0.425126
\(428\) 1183.23 0.133630
\(429\) 0 0
\(430\) 3631.85 0.407311
\(431\) −11002.3 −1.22961 −0.614806 0.788678i \(-0.710766\pi\)
−0.614806 + 0.788678i \(0.710766\pi\)
\(432\) 1349.79 0.150328
\(433\) −9596.76 −1.06511 −0.532553 0.846397i \(-0.678767\pi\)
−0.532553 + 0.846397i \(0.678767\pi\)
\(434\) 6925.56 0.765985
\(435\) 15450.9 1.70302
\(436\) −9641.30 −1.05902
\(437\) −1214.03 −0.132895
\(438\) 711.073 0.0775716
\(439\) −10346.3 −1.12483 −0.562416 0.826854i \(-0.690128\pi\)
−0.562416 + 0.826854i \(0.690128\pi\)
\(440\) 23341.4 2.52899
\(441\) −701.476 −0.0757452
\(442\) 0 0
\(443\) 5650.38 0.606000 0.303000 0.952991i \(-0.402012\pi\)
0.303000 + 0.952991i \(0.402012\pi\)
\(444\) 2296.12 0.245426
\(445\) −20868.7 −2.22308
\(446\) 8699.80 0.923649
\(447\) −10319.8 −1.09197
\(448\) 10023.6 1.05708
\(449\) 11987.8 1.25999 0.629997 0.776597i \(-0.283056\pi\)
0.629997 + 0.776597i \(0.283056\pi\)
\(450\) 14122.1 1.47938
\(451\) −3319.71 −0.346605
\(452\) −20687.3 −2.15276
\(453\) −6672.13 −0.692018
\(454\) −12026.5 −1.24324
\(455\) 0 0
\(456\) −15560.3 −1.59798
\(457\) −16437.6 −1.68253 −0.841265 0.540623i \(-0.818189\pi\)
−0.841265 + 0.540623i \(0.818189\pi\)
\(458\) −29386.4 −2.99811
\(459\) 1248.40 0.126951
\(460\) −2736.08 −0.277326
\(461\) 8847.70 0.893880 0.446940 0.894564i \(-0.352514\pi\)
0.446940 + 0.894564i \(0.352514\pi\)
\(462\) 7266.14 0.731713
\(463\) 10269.6 1.03081 0.515407 0.856945i \(-0.327641\pi\)
0.515407 + 0.856945i \(0.327641\pi\)
\(464\) −12146.0 −1.21523
\(465\) 5592.22 0.557706
\(466\) 30801.1 3.06188
\(467\) 14730.4 1.45962 0.729811 0.683649i \(-0.239608\pi\)
0.729811 + 0.683649i \(0.239608\pi\)
\(468\) 0 0
\(469\) 4813.24 0.473891
\(470\) −38436.0 −3.77217
\(471\) 7395.95 0.723540
\(472\) 24326.6 2.37229
\(473\) 1089.18 0.105878
\(474\) −1566.51 −0.151798
\(475\) −46989.2 −4.53897
\(476\) −11593.7 −1.11638
\(477\) −3137.25 −0.301142
\(478\) 9125.59 0.873211
\(479\) 635.077 0.0605792 0.0302896 0.999541i \(-0.490357\pi\)
0.0302896 + 0.999541i \(0.490357\pi\)
\(480\) 2836.16 0.269692
\(481\) 0 0
\(482\) −28289.3 −2.67332
\(483\) −409.316 −0.0385601
\(484\) −5933.22 −0.557214
\(485\) −10325.1 −0.966675
\(486\) 1175.51 0.109717
\(487\) −16611.1 −1.54563 −0.772815 0.634632i \(-0.781152\pi\)
−0.772815 + 0.634632i \(0.781152\pi\)
\(488\) −8249.43 −0.765234
\(489\) 730.696 0.0675730
\(490\) 7992.66 0.736881
\(491\) −2584.14 −0.237516 −0.118758 0.992923i \(-0.537891\pi\)
−0.118758 + 0.992923i \(0.537891\pi\)
\(492\) 4987.59 0.457029
\(493\) −11233.7 −1.02625
\(494\) 0 0
\(495\) 5867.24 0.532753
\(496\) −4396.08 −0.397963
\(497\) −5359.82 −0.483744
\(498\) 7483.42 0.673374
\(499\) 2183.88 0.195919 0.0979597 0.995190i \(-0.468768\pi\)
0.0979597 + 0.995190i \(0.468768\pi\)
\(500\) −65089.8 −5.82180
\(501\) −1227.30 −0.109444
\(502\) −11555.1 −1.02735
\(503\) −17214.9 −1.52600 −0.762998 0.646401i \(-0.776273\pi\)
−0.762998 + 0.646401i \(0.776273\pi\)
\(504\) −5246.25 −0.463664
\(505\) −16245.8 −1.43154
\(506\) −1246.75 −0.109535
\(507\) 0 0
\(508\) −33062.0 −2.88758
\(509\) 20260.6 1.76431 0.882157 0.470955i \(-0.156091\pi\)
0.882157 + 0.470955i \(0.156091\pi\)
\(510\) −14224.4 −1.23503
\(511\) −797.705 −0.0690575
\(512\) −16549.0 −1.42846
\(513\) −3911.34 −0.336628
\(514\) 21513.4 1.84614
\(515\) −26071.1 −2.23074
\(516\) −1636.40 −0.139609
\(517\) −11526.8 −0.980554
\(518\) −3913.85 −0.331978
\(519\) −7856.90 −0.664508
\(520\) 0 0
\(521\) −20731.5 −1.74331 −0.871653 0.490124i \(-0.836952\pi\)
−0.871653 + 0.490124i \(0.836952\pi\)
\(522\) −10577.8 −0.886930
\(523\) −944.353 −0.0789554 −0.0394777 0.999220i \(-0.512569\pi\)
−0.0394777 + 0.999220i \(0.512569\pi\)
\(524\) −12300.0 −1.02543
\(525\) −15842.6 −1.31701
\(526\) 36720.9 3.04393
\(527\) −4065.87 −0.336076
\(528\) −4612.27 −0.380158
\(529\) −12096.8 −0.994228
\(530\) 35746.0 2.92964
\(531\) 6114.87 0.499742
\(532\) 36324.0 2.96023
\(533\) 0 0
\(534\) 14286.9 1.15778
\(535\) −1628.58 −0.131607
\(536\) −10585.3 −0.853012
\(537\) 489.934 0.0393710
\(538\) −2698.89 −0.216278
\(539\) 2396.96 0.191548
\(540\) −8815.05 −0.702480
\(541\) 4883.06 0.388058 0.194029 0.980996i \(-0.437844\pi\)
0.194029 + 0.980996i \(0.437844\pi\)
\(542\) 13097.1 1.03795
\(543\) −9939.21 −0.785511
\(544\) −2062.05 −0.162518
\(545\) 13270.1 1.04299
\(546\) 0 0
\(547\) −16269.1 −1.27169 −0.635847 0.771815i \(-0.719349\pi\)
−0.635847 + 0.771815i \(0.719349\pi\)
\(548\) 9258.61 0.721730
\(549\) −2073.63 −0.161203
\(550\) −48255.6 −3.74114
\(551\) 35196.0 2.72124
\(552\) 900.169 0.0694090
\(553\) 1757.37 0.135137
\(554\) −5956.63 −0.456811
\(555\) −3160.34 −0.241710
\(556\) −32869.3 −2.50714
\(557\) −15661.0 −1.19134 −0.595670 0.803229i \(-0.703113\pi\)
−0.595670 + 0.803229i \(0.703113\pi\)
\(558\) −3828.48 −0.290453
\(559\) 0 0
\(560\) 17253.3 1.30194
\(561\) −4265.82 −0.321040
\(562\) 22259.5 1.67074
\(563\) −9915.18 −0.742230 −0.371115 0.928587i \(-0.621024\pi\)
−0.371115 + 0.928587i \(0.621024\pi\)
\(564\) 17318.0 1.29294
\(565\) 28473.7 2.12017
\(566\) −263.971 −0.0196034
\(567\) −1318.73 −0.0976745
\(568\) 11787.3 0.870748
\(569\) −11299.1 −0.832482 −0.416241 0.909254i \(-0.636653\pi\)
−0.416241 + 0.909254i \(0.636653\pi\)
\(570\) 44566.1 3.27486
\(571\) −17619.6 −1.29134 −0.645672 0.763615i \(-0.723423\pi\)
−0.645672 + 0.763615i \(0.723423\pi\)
\(572\) 0 0
\(573\) −12845.7 −0.936539
\(574\) −8501.61 −0.618206
\(575\) 2718.33 0.197152
\(576\) −5541.10 −0.400832
\(577\) 22153.5 1.59837 0.799186 0.601083i \(-0.205264\pi\)
0.799186 + 0.601083i \(0.205264\pi\)
\(578\) −13424.7 −0.966078
\(579\) −5631.99 −0.404244
\(580\) 79321.7 5.67872
\(581\) −8395.15 −0.599466
\(582\) 7068.63 0.503444
\(583\) 10720.1 0.761543
\(584\) 1754.31 0.124305
\(585\) 0 0
\(586\) −22955.1 −1.61820
\(587\) 9891.28 0.695497 0.347748 0.937588i \(-0.386946\pi\)
0.347748 + 0.937588i \(0.386946\pi\)
\(588\) −3601.24 −0.252573
\(589\) 12738.7 0.891153
\(590\) −69673.3 −4.86170
\(591\) 5973.77 0.415783
\(592\) 2484.36 0.172477
\(593\) 9746.23 0.674924 0.337462 0.941339i \(-0.390432\pi\)
0.337462 + 0.941339i \(0.390432\pi\)
\(594\) −4016.76 −0.277457
\(595\) 15957.4 1.09948
\(596\) −52979.7 −3.64116
\(597\) 4035.16 0.276630
\(598\) 0 0
\(599\) −8460.53 −0.577109 −0.288554 0.957464i \(-0.593175\pi\)
−0.288554 + 0.957464i \(0.593175\pi\)
\(600\) 34841.2 2.37064
\(601\) 6792.99 0.461052 0.230526 0.973066i \(-0.425955\pi\)
0.230526 + 0.973066i \(0.425955\pi\)
\(602\) 2789.32 0.188844
\(603\) −2660.78 −0.179694
\(604\) −34253.4 −2.30754
\(605\) 8166.38 0.548778
\(606\) 11122.0 0.745546
\(607\) 19073.4 1.27539 0.637697 0.770287i \(-0.279887\pi\)
0.637697 + 0.770287i \(0.279887\pi\)
\(608\) 6460.58 0.430939
\(609\) 11866.5 0.789582
\(610\) 23627.1 1.56825
\(611\) 0 0
\(612\) 6409.05 0.423318
\(613\) 14465.2 0.953091 0.476545 0.879150i \(-0.341889\pi\)
0.476545 + 0.879150i \(0.341889\pi\)
\(614\) −4976.93 −0.327122
\(615\) −6864.85 −0.450109
\(616\) 17926.6 1.17254
\(617\) −12897.3 −0.841536 −0.420768 0.907168i \(-0.638239\pi\)
−0.420768 + 0.907168i \(0.638239\pi\)
\(618\) 17848.5 1.16177
\(619\) 27735.8 1.80096 0.900481 0.434895i \(-0.143214\pi\)
0.900481 + 0.434895i \(0.143214\pi\)
\(620\) 28709.4 1.85967
\(621\) 226.272 0.0146216
\(622\) −11793.0 −0.760222
\(623\) −16027.5 −1.03070
\(624\) 0 0
\(625\) 49042.7 3.13873
\(626\) 38381.7 2.45055
\(627\) 13365.2 0.851281
\(628\) 37969.3 2.41265
\(629\) 2297.75 0.145656
\(630\) 15025.7 0.950219
\(631\) −28560.1 −1.80184 −0.900918 0.433990i \(-0.857105\pi\)
−0.900918 + 0.433990i \(0.857105\pi\)
\(632\) −3864.80 −0.243249
\(633\) −866.290 −0.0543949
\(634\) −33585.4 −2.10386
\(635\) 45506.1 2.84386
\(636\) −16106.0 −1.00416
\(637\) 0 0
\(638\) 36144.6 2.24291
\(639\) 2962.93 0.183430
\(640\) 55572.5 3.43234
\(641\) 1862.53 0.114767 0.0573833 0.998352i \(-0.481724\pi\)
0.0573833 + 0.998352i \(0.481724\pi\)
\(642\) 1114.94 0.0685407
\(643\) −29495.2 −1.80899 −0.904494 0.426487i \(-0.859751\pi\)
−0.904494 + 0.426487i \(0.859751\pi\)
\(644\) −2101.35 −0.128579
\(645\) 2252.31 0.137496
\(646\) −32402.2 −1.97345
\(647\) 27780.7 1.68805 0.844027 0.536301i \(-0.180179\pi\)
0.844027 + 0.536301i \(0.180179\pi\)
\(648\) 2900.15 0.175816
\(649\) −20894.7 −1.26377
\(650\) 0 0
\(651\) 4294.92 0.258573
\(652\) 3751.25 0.225322
\(653\) 276.678 0.0165808 0.00829039 0.999966i \(-0.497361\pi\)
0.00829039 + 0.999966i \(0.497361\pi\)
\(654\) −9084.84 −0.543188
\(655\) 16929.5 1.00991
\(656\) 5396.49 0.321185
\(657\) 440.975 0.0261858
\(658\) −29519.5 −1.74892
\(659\) 18114.9 1.07080 0.535398 0.844600i \(-0.320162\pi\)
0.535398 + 0.844600i \(0.320162\pi\)
\(660\) 30121.2 1.77647
\(661\) −27094.4 −1.59433 −0.797163 0.603764i \(-0.793667\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(662\) 26312.5 1.54481
\(663\) 0 0
\(664\) 18462.6 1.07905
\(665\) −49995.8 −2.91542
\(666\) 2163.60 0.125882
\(667\) −2036.10 −0.118198
\(668\) −6300.70 −0.364942
\(669\) 5395.23 0.311796
\(670\) 30317.1 1.74814
\(671\) 7085.64 0.407657
\(672\) 2178.22 0.125039
\(673\) 2410.31 0.138054 0.0690272 0.997615i \(-0.478010\pi\)
0.0690272 + 0.997615i \(0.478010\pi\)
\(674\) −8048.99 −0.459993
\(675\) 8757.89 0.499395
\(676\) 0 0
\(677\) 12508.3 0.710091 0.355046 0.934849i \(-0.384465\pi\)
0.355046 + 0.934849i \(0.384465\pi\)
\(678\) −19493.3 −1.10418
\(679\) −7929.83 −0.448187
\(680\) −35093.5 −1.97908
\(681\) −7458.30 −0.419681
\(682\) 13082.0 0.734511
\(683\) 16793.8 0.940844 0.470422 0.882442i \(-0.344102\pi\)
0.470422 + 0.882442i \(0.344102\pi\)
\(684\) −20080.1 −1.12249
\(685\) −12743.4 −0.710804
\(686\) 33152.3 1.84513
\(687\) −18224.1 −1.01207
\(688\) −1770.56 −0.0981131
\(689\) 0 0
\(690\) −2578.16 −0.142245
\(691\) 26026.9 1.43286 0.716432 0.697657i \(-0.245774\pi\)
0.716432 + 0.697657i \(0.245774\pi\)
\(692\) −40335.8 −2.21580
\(693\) 4506.13 0.247004
\(694\) 44834.4 2.45229
\(695\) 45240.8 2.46918
\(696\) −26096.9 −1.42126
\(697\) 4991.14 0.271238
\(698\) −25345.8 −1.37443
\(699\) 19101.5 1.03360
\(700\) −81333.0 −4.39157
\(701\) 5079.08 0.273658 0.136829 0.990595i \(-0.456309\pi\)
0.136829 + 0.990595i \(0.456309\pi\)
\(702\) 0 0
\(703\) −7199.04 −0.386226
\(704\) 18934.1 1.01364
\(705\) −23836.3 −1.27337
\(706\) −5892.11 −0.314097
\(707\) −12477.1 −0.663717
\(708\) 31392.6 1.66639
\(709\) 2530.72 0.134052 0.0670262 0.997751i \(-0.478649\pi\)
0.0670262 + 0.997751i \(0.478649\pi\)
\(710\) −33759.9 −1.78449
\(711\) −971.480 −0.0512424
\(712\) 35247.7 1.85529
\(713\) −736.937 −0.0387076
\(714\) −10924.6 −0.572607
\(715\) 0 0
\(716\) 2515.22 0.131283
\(717\) 5659.28 0.294770
\(718\) −25716.4 −1.33667
\(719\) 9503.67 0.492944 0.246472 0.969150i \(-0.420729\pi\)
0.246472 + 0.969150i \(0.420729\pi\)
\(720\) −9537.73 −0.493681
\(721\) −20023.0 −1.03425
\(722\) 68338.2 3.52255
\(723\) −17543.7 −0.902432
\(724\) −51026.0 −2.61929
\(725\) −78807.4 −4.03701
\(726\) −5590.77 −0.285803
\(727\) 33343.1 1.70100 0.850500 0.525975i \(-0.176300\pi\)
0.850500 + 0.525975i \(0.176300\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −5024.50 −0.254747
\(731\) −1637.56 −0.0828556
\(732\) −10645.6 −0.537531
\(733\) −32288.1 −1.62699 −0.813497 0.581569i \(-0.802439\pi\)
−0.813497 + 0.581569i \(0.802439\pi\)
\(734\) −1398.53 −0.0703277
\(735\) 4956.69 0.248749
\(736\) −373.746 −0.0187180
\(737\) 9091.96 0.454419
\(738\) 4699.73 0.234417
\(739\) 14168.8 0.705288 0.352644 0.935758i \(-0.385283\pi\)
0.352644 + 0.935758i \(0.385283\pi\)
\(740\) −16224.6 −0.805983
\(741\) 0 0
\(742\) 27453.5 1.35829
\(743\) −13248.6 −0.654165 −0.327083 0.944996i \(-0.606066\pi\)
−0.327083 + 0.944996i \(0.606066\pi\)
\(744\) −9445.39 −0.465437
\(745\) 72920.5 3.58604
\(746\) 29818.3 1.46344
\(747\) 4640.88 0.227311
\(748\) −21899.9 −1.07051
\(749\) −1250.78 −0.0610178
\(750\) −61333.0 −2.98609
\(751\) 5113.98 0.248484 0.124242 0.992252i \(-0.460350\pi\)
0.124242 + 0.992252i \(0.460350\pi\)
\(752\) 18737.8 0.908641
\(753\) −7165.95 −0.346802
\(754\) 0 0
\(755\) 47145.9 2.27260
\(756\) −6770.10 −0.325696
\(757\) 27380.4 1.31461 0.657303 0.753626i \(-0.271697\pi\)
0.657303 + 0.753626i \(0.271697\pi\)
\(758\) 11803.6 0.565604
\(759\) −773.178 −0.0369757
\(760\) 109951. 5.24781
\(761\) 10613.8 0.505586 0.252793 0.967520i \(-0.418651\pi\)
0.252793 + 0.967520i \(0.418651\pi\)
\(762\) −31153.8 −1.48108
\(763\) 10191.7 0.483569
\(764\) −65947.3 −3.12289
\(765\) −8821.32 −0.416909
\(766\) 31817.6 1.50080
\(767\) 0 0
\(768\) −23269.2 −1.09330
\(769\) −9172.22 −0.430115 −0.215058 0.976601i \(-0.568994\pi\)
−0.215058 + 0.976601i \(0.568994\pi\)
\(770\) −51343.2 −2.40296
\(771\) 13341.6 0.623200
\(772\) −28913.5 −1.34795
\(773\) −14952.1 −0.695718 −0.347859 0.937547i \(-0.613091\pi\)
−0.347859 + 0.937547i \(0.613091\pi\)
\(774\) −1541.95 −0.0716076
\(775\) −28523.2 −1.32205
\(776\) 17439.3 0.806745
\(777\) −2427.19 −0.112066
\(778\) 24017.9 1.10679
\(779\) −15637.7 −0.719226
\(780\) 0 0
\(781\) −10124.4 −0.463867
\(782\) 1874.47 0.0857174
\(783\) −6559.87 −0.299400
\(784\) −3896.48 −0.177500
\(785\) −52260.4 −2.37612
\(786\) −11590.1 −0.525959
\(787\) 2671.52 0.121003 0.0605015 0.998168i \(-0.480730\pi\)
0.0605015 + 0.998168i \(0.480730\pi\)
\(788\) 30668.1 1.38643
\(789\) 22772.6 1.02754
\(790\) 11069.1 0.498508
\(791\) 21868.3 0.982991
\(792\) −9909.89 −0.444612
\(793\) 0 0
\(794\) 58407.4 2.61058
\(795\) 22168.1 0.988957
\(796\) 20715.7 0.922423
\(797\) −12949.7 −0.575536 −0.287768 0.957700i \(-0.592913\pi\)
−0.287768 + 0.957700i \(0.592913\pi\)
\(798\) 34227.5 1.51835
\(799\) 17330.4 0.767339
\(800\) −14465.9 −0.639307
\(801\) 8860.08 0.390831
\(802\) 23785.5 1.04725
\(803\) −1506.82 −0.0662200
\(804\) −13659.9 −0.599190
\(805\) 2892.27 0.126632
\(806\) 0 0
\(807\) −1673.73 −0.0730089
\(808\) 27439.6 1.19470
\(809\) −11640.4 −0.505876 −0.252938 0.967482i \(-0.581397\pi\)
−0.252938 + 0.967482i \(0.581397\pi\)
\(810\) −8306.28 −0.360312
\(811\) −18135.3 −0.785225 −0.392613 0.919704i \(-0.628429\pi\)
−0.392613 + 0.919704i \(0.628429\pi\)
\(812\) 60920.4 2.63286
\(813\) 8122.24 0.350381
\(814\) −7393.06 −0.318337
\(815\) −5163.16 −0.221911
\(816\) 6934.49 0.297495
\(817\) 5130.61 0.219703
\(818\) −74260.0 −3.17413
\(819\) 0 0
\(820\) −35242.8 −1.50089
\(821\) 10789.1 0.458640 0.229320 0.973351i \(-0.426350\pi\)
0.229320 + 0.973351i \(0.426350\pi\)
\(822\) 8724.24 0.370186
\(823\) −12284.7 −0.520312 −0.260156 0.965567i \(-0.583774\pi\)
−0.260156 + 0.965567i \(0.583774\pi\)
\(824\) 44034.7 1.86168
\(825\) −29925.9 −1.26289
\(826\) −53510.2 −2.25407
\(827\) 36077.2 1.51696 0.758480 0.651696i \(-0.225942\pi\)
0.758480 + 0.651696i \(0.225942\pi\)
\(828\) 1161.64 0.0487556
\(829\) −8861.83 −0.371271 −0.185636 0.982619i \(-0.559434\pi\)
−0.185636 + 0.982619i \(0.559434\pi\)
\(830\) −52878.5 −2.21137
\(831\) −3694.04 −0.154205
\(832\) 0 0
\(833\) −3603.80 −0.149897
\(834\) −30972.2 −1.28595
\(835\) 8672.18 0.359417
\(836\) 68614.1 2.83860
\(837\) −2374.25 −0.0980480
\(838\) −26551.0 −1.09450
\(839\) 5833.37 0.240036 0.120018 0.992772i \(-0.461705\pi\)
0.120018 + 0.992772i \(0.461705\pi\)
\(840\) 37070.4 1.52268
\(841\) 34639.6 1.42030
\(842\) 4487.66 0.183676
\(843\) 13804.3 0.563993
\(844\) −4447.37 −0.181380
\(845\) 0 0
\(846\) 16318.5 0.663170
\(847\) 6271.92 0.254434
\(848\) −17426.4 −0.705692
\(849\) −163.703 −0.00661752
\(850\) 72551.7 2.92765
\(851\) 416.466 0.0167759
\(852\) 15211.1 0.611648
\(853\) −28649.5 −1.14999 −0.574995 0.818157i \(-0.694996\pi\)
−0.574995 + 0.818157i \(0.694996\pi\)
\(854\) 18146.0 0.727098
\(855\) 27637.9 1.10549
\(856\) 2750.71 0.109833
\(857\) 32336.1 1.28889 0.644445 0.764651i \(-0.277089\pi\)
0.644445 + 0.764651i \(0.277089\pi\)
\(858\) 0 0
\(859\) −13878.5 −0.551254 −0.275627 0.961265i \(-0.588885\pi\)
−0.275627 + 0.961265i \(0.588885\pi\)
\(860\) 11562.9 0.458480
\(861\) −5272.31 −0.208688
\(862\) −53223.7 −2.10302
\(863\) −32934.7 −1.29908 −0.649542 0.760326i \(-0.725039\pi\)
−0.649542 + 0.760326i \(0.725039\pi\)
\(864\) −1204.13 −0.0474135
\(865\) 55517.5 2.18226
\(866\) −46424.3 −1.82167
\(867\) −8325.38 −0.326119
\(868\) 22049.3 0.862213
\(869\) 3319.57 0.129584
\(870\) 74743.6 2.91270
\(871\) 0 0
\(872\) −22413.5 −0.870434
\(873\) 4383.65 0.169947
\(874\) −5872.87 −0.227292
\(875\) 68805.4 2.65834
\(876\) 2263.88 0.0873167
\(877\) −18375.7 −0.707531 −0.353765 0.935334i \(-0.615099\pi\)
−0.353765 + 0.935334i \(0.615099\pi\)
\(878\) −50050.2 −1.92382
\(879\) −14235.7 −0.546256
\(880\) 32590.7 1.24845
\(881\) 46883.4 1.79290 0.896448 0.443150i \(-0.146139\pi\)
0.896448 + 0.443150i \(0.146139\pi\)
\(882\) −3393.39 −0.129548
\(883\) 1050.05 0.0400194 0.0200097 0.999800i \(-0.493630\pi\)
0.0200097 + 0.999800i \(0.493630\pi\)
\(884\) 0 0
\(885\) −43208.2 −1.64116
\(886\) 27333.7 1.03645
\(887\) 27916.8 1.05677 0.528385 0.849005i \(-0.322798\pi\)
0.528385 + 0.849005i \(0.322798\pi\)
\(888\) 5337.89 0.201720
\(889\) 34949.4 1.31852
\(890\) −100952. −3.80217
\(891\) −2491.01 −0.0936611
\(892\) 27698.0 1.03968
\(893\) −54297.4 −2.03471
\(894\) −49921.9 −1.86761
\(895\) −3461.92 −0.129295
\(896\) 42680.6 1.59136
\(897\) 0 0
\(898\) 57990.8 2.15499
\(899\) 21364.6 0.792601
\(900\) 44961.3 1.66523
\(901\) −16117.5 −0.595950
\(902\) −16059.1 −0.592804
\(903\) 1729.81 0.0637481
\(904\) −48092.7 −1.76940
\(905\) 70231.3 2.57963
\(906\) −32276.4 −1.18357
\(907\) 23220.1 0.850066 0.425033 0.905178i \(-0.360263\pi\)
0.425033 + 0.905178i \(0.360263\pi\)
\(908\) −38289.5 −1.39943
\(909\) 6897.38 0.251674
\(910\) 0 0
\(911\) 16344.9 0.594435 0.297217 0.954810i \(-0.403941\pi\)
0.297217 + 0.954810i \(0.403941\pi\)
\(912\) −21726.3 −0.788848
\(913\) −15858.0 −0.574834
\(914\) −79516.7 −2.87766
\(915\) 14652.4 0.529393
\(916\) −93559.0 −3.37476
\(917\) 13002.1 0.468231
\(918\) 6039.15 0.217126
\(919\) −32931.7 −1.18206 −0.591032 0.806648i \(-0.701279\pi\)
−0.591032 + 0.806648i \(0.701279\pi\)
\(920\) −6360.67 −0.227940
\(921\) −3086.47 −0.110426
\(922\) 42800.8 1.52882
\(923\) 0 0
\(924\) 23133.6 0.823636
\(925\) 16119.4 0.572975
\(926\) 49679.0 1.76302
\(927\) 11068.8 0.392177
\(928\) 10835.3 0.383282
\(929\) −56305.5 −1.98851 −0.994253 0.107056i \(-0.965858\pi\)
−0.994253 + 0.107056i \(0.965858\pi\)
\(930\) 27052.4 0.953852
\(931\) 11291.0 0.397473
\(932\) 98063.3 3.44653
\(933\) −7313.51 −0.256628
\(934\) 71258.5 2.49641
\(935\) 30142.7 1.05430
\(936\) 0 0
\(937\) 7095.61 0.247389 0.123695 0.992320i \(-0.460526\pi\)
0.123695 + 0.992320i \(0.460526\pi\)
\(938\) 23284.0 0.810502
\(939\) 23802.6 0.827230
\(940\) −122371. −4.24606
\(941\) −5185.17 −0.179630 −0.0898150 0.995958i \(-0.528628\pi\)
−0.0898150 + 0.995958i \(0.528628\pi\)
\(942\) 35777.9 1.23748
\(943\) 904.641 0.0312398
\(944\) 33966.2 1.17109
\(945\) 9318.26 0.320765
\(946\) 5268.89 0.181085
\(947\) 38451.7 1.31944 0.659722 0.751510i \(-0.270674\pi\)
0.659722 + 0.751510i \(0.270674\pi\)
\(948\) −4987.39 −0.170868
\(949\) 0 0
\(950\) −227310. −7.76307
\(951\) −20828.2 −0.710199
\(952\) −26952.4 −0.917575
\(953\) −20930.5 −0.711445 −0.355722 0.934592i \(-0.615765\pi\)
−0.355722 + 0.934592i \(0.615765\pi\)
\(954\) −15176.4 −0.515048
\(955\) 90768.8 3.07561
\(956\) 29053.7 0.982910
\(957\) 22415.2 0.757139
\(958\) 3072.19 0.103609
\(959\) −9787.14 −0.329555
\(960\) 39153.9 1.31634
\(961\) −22058.4 −0.740438
\(962\) 0 0
\(963\) 691.435 0.0231372
\(964\) −90066.1 −3.00916
\(965\) 39796.1 1.32755
\(966\) −1980.07 −0.0659499
\(967\) −50788.1 −1.68897 −0.844486 0.535578i \(-0.820094\pi\)
−0.844486 + 0.535578i \(0.820094\pi\)
\(968\) −13793.2 −0.457986
\(969\) −20094.4 −0.666175
\(970\) −49947.6 −1.65332
\(971\) 15277.5 0.504922 0.252461 0.967607i \(-0.418760\pi\)
0.252461 + 0.967607i \(0.418760\pi\)
\(972\) 3742.54 0.123500
\(973\) 34745.7 1.14481
\(974\) −80356.3 −2.64351
\(975\) 0 0
\(976\) −11518.4 −0.377760
\(977\) 1293.19 0.0423469 0.0211734 0.999776i \(-0.493260\pi\)
0.0211734 + 0.999776i \(0.493260\pi\)
\(978\) 3534.74 0.115571
\(979\) −30275.1 −0.988353
\(980\) 25446.7 0.829453
\(981\) −5634.01 −0.183364
\(982\) −12500.8 −0.406227
\(983\) 8474.63 0.274973 0.137487 0.990504i \(-0.456098\pi\)
0.137487 + 0.990504i \(0.456098\pi\)
\(984\) 11594.9 0.375641
\(985\) −42211.1 −1.36544
\(986\) −54343.0 −1.75521
\(987\) −18306.6 −0.590382
\(988\) 0 0
\(989\) −296.807 −0.00954289
\(990\) 28382.8 0.911175
\(991\) −7080.71 −0.226969 −0.113484 0.993540i \(-0.536201\pi\)
−0.113484 + 0.993540i \(0.536201\pi\)
\(992\) 3921.68 0.125518
\(993\) 16317.8 0.521480
\(994\) −25928.1 −0.827354
\(995\) −28512.8 −0.908458
\(996\) 23825.4 0.757968
\(997\) 19423.1 0.616985 0.308493 0.951227i \(-0.400175\pi\)
0.308493 + 0.951227i \(0.400175\pi\)
\(998\) 10564.5 0.335084
\(999\) 1341.76 0.0424940
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.1.9 9
3.2 odd 2 1521.4.a.bi.1.1 9
13.5 odd 4 507.4.b.k.337.2 18
13.8 odd 4 507.4.b.k.337.17 18
13.12 even 2 507.4.a.p.1.1 yes 9
39.38 odd 2 1521.4.a.bf.1.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.9 9 1.1 even 1 trivial
507.4.a.p.1.1 yes 9 13.12 even 2
507.4.b.k.337.2 18 13.5 odd 4
507.4.b.k.337.17 18 13.8 odd 4
1521.4.a.bf.1.9 9 39.38 odd 2
1521.4.a.bi.1.1 9 3.2 odd 2