Properties

Label 507.4.a.p.1.1
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $0$
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: \(0\)
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: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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 \(-0.826540\pi\)
−0.855157 + 0.518368i \(0.826540\pi\)
\(3\) 3.00000 0.577350
\(4\) 15.4014 1.92518
\(5\) 21.1983 1.89603 0.948015 0.318225i \(-0.103087\pi\)
0.948015 + 0.318225i \(0.103087\pi\)
\(6\) −14.5125 −0.987451
\(7\) 16.2806 0.879070 0.439535 0.898225i \(-0.355143\pi\)
0.439535 + 0.898225i \(0.355143\pi\)
\(8\) −35.8043 −1.58234
\(9\) 9.00000 0.333333
\(10\) −102.547 −3.24281
\(11\) 30.7532 0.842950 0.421475 0.906840i \(-0.361513\pi\)
0.421475 + 0.906840i \(0.361513\pi\)
\(12\) 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 \(-0.161134\pi\)
0.874585 + 0.484873i \(0.161134\pi\)
\(20\) 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 \(-0.418011\pi\)
0.254736 + 0.967011i \(0.418011\pi\)
\(32\) 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 \(-0.535214\pi\)
−0.110403 + 0.993887i \(0.535214\pi\)
\(38\) −700.783 −2.99163
\(39\) 0 0
\(40\) −758.990 −3.00017
\(41\) −107.947 −0.411181 −0.205591 0.978638i \(-0.565912\pi\)
−0.205591 + 0.978638i \(0.565912\pi\)
\(42\) −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 \(-0.697581\pi\)
−0.581621 + 0.813460i \(0.697581\pi\)
\(48\) 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 \(-0.769760\pi\)
−0.749613 + 0.661877i \(0.769760\pi\)
\(60\) 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 \(-0.413128\pi\)
0.269541 + 0.962989i \(0.413128\pi\)
\(68\) 712.117 1.26995
\(69\) 25.1413 0.0438647
\(70\) −1669.52 −2.85066
\(71\) −329.215 −0.550290 −0.275145 0.961403i \(-0.588726\pi\)
−0.275145 + 0.961403i \(0.588726\pi\)
\(72\) −322.239 −0.527448
\(73\) −48.9973 −0.0785575 −0.0392787 0.999228i \(-0.512506\pi\)
−0.0392787 + 0.999228i \(0.512506\pi\)
\(74\) 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 \(-0.610754\pi\)
−0.340966 + 0.940076i \(0.610754\pi\)
\(84\) 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 \(-0.699395\pi\)
−0.586246 + 0.810133i \(0.699395\pi\)
\(90\) −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 \(-0.582049\pi\)
−0.254921 + 0.966962i \(0.582049\pi\)
\(98\) 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 \(-0.411307\pi\)
0.275046 + 0.961431i \(0.411307\pi\)
\(110\) −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 \(-0.560021\pi\)
−0.187445 + 0.982275i \(0.560021\pi\)
\(138\) −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 \(-0.105407\pi\)
0.945670 + 0.325127i \(0.105407\pi\)
\(150\) −4707.37 −2.56237
\(151\) 2224.04 1.19861 0.599305 0.800521i \(-0.295444\pi\)
0.599305 + 0.800521i \(0.295444\pi\)
\(152\) −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 \(-0.518638\pi\)
−0.0585199 + 0.998286i \(0.518638\pi\)
\(164\) −1662.53 −0.791597
\(165\) 1955.75 0.922755
\(166\) 2494.47 1.16632
\(167\) 409.099 0.189563 0.0947814 0.995498i \(-0.469785\pi\)
0.0947814 + 0.995498i \(0.469785\pi\)
\(168\) −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 \(-0.386152\pi\)
0.350086 + 0.936718i \(0.386152\pi\)
\(194\) 2356.21 0.871990
\(195\) 0 0
\(196\) −1200.41 −0.437468
\(197\) −1991.26 −0.720158 −0.360079 0.932922i \(-0.617250\pi\)
−0.360079 + 0.932922i \(0.617250\pi\)
\(198\) −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 \(-0.587031\pi\)
−0.270023 + 0.962854i \(0.587031\pi\)
\(224\) 726.072 0.216575
\(225\) 2919.30 0.864977
\(226\) 6497.77 1.91250
\(227\) 2486.10 0.726909 0.363454 0.931612i \(-0.381597\pi\)
0.363454 + 0.931612i \(0.381597\pi\)
\(228\) 6693.36 1.94420
\(229\) 6074.71 1.75296 0.876480 0.481438i \(-0.159885\pi\)
0.876480 + 0.481438i \(0.159885\pi\)
\(230\) −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 \(-0.582167\pi\)
−0.255278 + 0.966868i \(0.582167\pi\)
\(240\) 3179.24 0.855081
\(241\) 5847.91 1.56306 0.781529 0.623869i \(-0.214440\pi\)
0.781529 + 0.623869i \(0.214440\pi\)
\(242\) 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 \(-0.598135\pi\)
−0.303439 + 0.952851i \(0.598135\pi\)
\(272\) 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 \(-0.662431\pi\)
−0.488432 + 0.872602i \(0.662431\pi\)
\(282\) 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 \(-0.343145\pi\)
0.473072 + 0.881024i \(0.343145\pi\)
\(294\) 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 \(-0.469513\pi\)
0.0956320 + 0.995417i \(0.469513\pi\)
\(308\) 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 \(-0.289136\pi\)
0.615050 + 0.788488i \(0.289136\pi\)
\(318\) 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 \(-0.649152\pi\)
−0.451615 + 0.892213i \(0.649152\pi\)
\(332\) −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 \(-0.368382\pi\)
0.401807 + 0.915724i \(0.368382\pi\)
\(350\) −25546.3 −3.90144
\(351\) 0 0
\(352\) 1371.51 0.207676
\(353\) 1218.01 0.183649 0.0918244 0.995775i \(-0.470730\pi\)
0.0918244 + 0.995775i \(0.470730\pi\)
\(354\) 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 \(-0.372210\pi\)
0.390767 + 0.920490i \(0.372210\pi\)
\(360\) −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 \(-0.552876\pi\)
−0.165351 + 0.986235i \(0.552876\pi\)
\(380\) 47295.9 6.38481
\(381\) −6440.06 −0.865970
\(382\) 20713.7 2.77436
\(383\) −6577.28 −0.877502 −0.438751 0.898609i \(-0.644579\pi\)
−0.438751 + 0.898609i \(0.644579\pi\)
\(384\) 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 \(-0.776366\pi\)
−0.763187 + 0.646178i \(0.776366\pi\)
\(398\) −6506.69 −0.819475
\(399\) 7075.45 0.887758
\(400\) 16215.8 2.02697
\(401\) −4916.90 −0.612315 −0.306158 0.951981i \(-0.599043\pi\)
−0.306158 + 0.951981i \(0.599043\pi\)
\(402\) −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 \(-0.121579\pi\)
0.927939 + 0.372733i \(0.121579\pi\)
\(410\) 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 \(-0.517100\pi\)
−0.0536964 + 0.998557i \(0.517100\pi\)
\(422\) 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 \(-0.289234\pi\)
0.614806 + 0.788678i \(0.289234\pi\)
\(432\) 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 \(-0.716944\pi\)
−0.629997 + 0.776597i \(0.716944\pi\)
\(450\) −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 \(-0.181811\pi\)
0.841265 + 0.540623i \(0.181811\pi\)
\(458\) −29386.4 −2.99811
\(459\) 1248.40 0.126951
\(460\) 2736.08 0.277326
\(461\) −8847.70 −0.893880 −0.446940 0.894564i \(-0.647486\pi\)
−0.446940 + 0.894564i \(0.647486\pi\)
\(462\) −7266.14 −0.731713
\(463\) −10269.6 −1.03081 −0.515407 0.856945i \(-0.672359\pi\)
−0.515407 + 0.856945i \(0.672359\pi\)
\(464\) −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 \(-0.509643\pi\)
−0.0302896 + 0.999541i \(0.509643\pi\)
\(480\) 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 \(-0.218848\pi\)
0.772815 + 0.634632i \(0.218848\pi\)
\(488\) 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 \(-0.531232\pi\)
−0.0979597 + 0.995190i \(0.531232\pi\)
\(500\) 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 \(-0.843909\pi\)
−0.882157 + 0.470955i \(0.843909\pi\)
\(510\) −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 \(-0.562156\pi\)
−0.194029 + 0.980996i \(0.562156\pi\)
\(542\) 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 \(-0.296887\pi\)
0.595670 + 0.803229i \(0.296887\pi\)
\(558\) −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 \(-0.794736\pi\)
−0.799186 + 0.601083i \(0.794736\pi\)
\(578\) 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 \(-0.613054\pi\)
−0.347748 + 0.937588i \(0.613054\pi\)
\(588\) −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 \(-0.609568\pi\)
−0.337462 + 0.941339i \(0.609568\pi\)
\(594\) −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 \(-0.658111\pi\)
−0.476545 + 0.879150i \(0.658111\pi\)
\(614\) −4976.93 −0.327122
\(615\) −6864.85 −0.450109
\(616\) −17926.6 −1.17254
\(617\) 12897.3 0.841536 0.420768 0.907168i \(-0.361761\pi\)
0.420768 + 0.907168i \(0.361761\pi\)
\(618\) −17848.5 −1.16177
\(619\) −27735.8 −1.80096 −0.900481 0.434895i \(-0.856786\pi\)
−0.900481 + 0.434895i \(0.856786\pi\)
\(620\) 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 \(-0.142895\pi\)
0.900918 + 0.433990i \(0.142895\pi\)
\(632\) 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 \(-0.140249\pi\)
0.904494 + 0.426487i \(0.140249\pi\)
\(644\) 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 \(-0.206333\pi\)
0.797163 + 0.603764i \(0.206333\pi\)
\(662\) 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 \(-0.655898\pi\)
−0.470422 + 0.882442i \(0.655898\pi\)
\(684\) 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 \(-0.754226\pi\)
−0.716432 + 0.697657i \(0.754226\pi\)
\(692\) −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 \(-0.521351\pi\)
−0.0670262 + 0.997751i \(0.521351\pi\)
\(710\) 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 \(-0.197561\pi\)
0.813497 + 0.581569i \(0.197561\pi\)
\(734\) 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 \(-0.614717\pi\)
−0.352644 + 0.935758i \(0.614717\pi\)
\(740\) −16224.6 −0.805983
\(741\) 0 0
\(742\) 27453.5 1.35829
\(743\) 13248.6 0.654165 0.327083 0.944996i \(-0.393934\pi\)
0.327083 + 0.944996i \(0.393934\pi\)
\(744\) −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 \(-0.581349\pi\)
−0.252793 + 0.967520i \(0.581349\pi\)
\(762\) 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 \(-0.431006\pi\)
0.215058 + 0.976601i \(0.431006\pi\)
\(770\) −51343.2 −2.40296
\(771\) 13341.6 0.623200
\(772\) 28913.5 1.34795
\(773\) 14952.1 0.695718 0.347859 0.937547i \(-0.386909\pi\)
0.347859 + 0.937547i \(0.386909\pi\)
\(774\) 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 \(-0.519270\pi\)
−0.0605015 + 0.998168i \(0.519270\pi\)
\(788\) −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 \(-0.371571\pi\)
0.392613 + 0.919704i \(0.371571\pi\)
\(812\) −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 \(-0.573650\pi\)
−0.229320 + 0.973351i \(0.573650\pi\)
\(822\) 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 \(-0.774058\pi\)
−0.758480 + 0.651696i \(0.774058\pi\)
\(828\) 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 \(-0.538295\pi\)
−0.120018 + 0.992772i \(0.538295\pi\)
\(840\) −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 \(-0.305004\pi\)
0.574995 + 0.818157i \(0.305004\pi\)
\(854\) 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 \(-0.274961\pi\)
0.649542 + 0.760326i \(0.274961\pi\)
\(864\) 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 \(-0.384901\pi\)
0.353765 + 0.935334i \(0.384901\pi\)
\(878\) 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 \(-0.0341424\pi\)
0.994253 + 0.107056i \(0.0341424\pi\)
\(930\) −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 \(-0.471372\pi\)
0.0898150 + 0.995958i \(0.471372\pi\)
\(942\) −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 \(-0.729326\pi\)
−0.659722 + 0.751510i \(0.729326\pi\)
\(948\) −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 \(-0.179906\pi\)
0.844486 + 0.535578i \(0.179906\pi\)
\(968\) 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 \(-0.506740\pi\)
−0.0211734 + 0.999776i \(0.506740\pi\)
\(978\) 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 \(-0.543902\pi\)
−0.137487 + 0.990504i \(0.543902\pi\)
\(984\) 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.p.1.1 yes 9
3.2 odd 2 1521.4.a.bf.1.9 9
13.5 odd 4 507.4.b.k.337.17 18
13.8 odd 4 507.4.b.k.337.2 18
13.12 even 2 507.4.a.o.1.9 9
39.38 odd 2 1521.4.a.bi.1.1 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.9 9 13.12 even 2
507.4.a.p.1.1 yes 9 1.1 even 1 trivial
507.4.b.k.337.2 18 13.8 odd 4
507.4.b.k.337.17 18 13.5 odd 4
1521.4.a.bf.1.9 9 3.2 odd 2
1521.4.a.bi.1.1 9 39.38 odd 2