Properties

Label 507.4.a.p.1.6
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 1.6
Root \(-0.100291\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.34727 q^{2} +3.00000 q^{3} -2.49032 q^{4} +15.3991 q^{5} +7.04181 q^{6} -10.1317 q^{7} -24.6236 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.34727 q^{2} +3.00000 q^{3} -2.49032 q^{4} +15.3991 q^{5} +7.04181 q^{6} -10.1317 q^{7} -24.6236 q^{8} +9.00000 q^{9} +36.1458 q^{10} +15.0669 q^{11} -7.47096 q^{12} -23.7819 q^{14} +46.1972 q^{15} -37.8757 q^{16} +90.8352 q^{17} +21.1254 q^{18} +114.640 q^{19} -38.3486 q^{20} -30.3952 q^{21} +35.3661 q^{22} +75.7635 q^{23} -73.8709 q^{24} +112.132 q^{25} +27.0000 q^{27} +25.2313 q^{28} +214.817 q^{29} +108.437 q^{30} -284.476 q^{31} +108.084 q^{32} +45.2007 q^{33} +213.215 q^{34} -156.019 q^{35} -22.4129 q^{36} +358.878 q^{37} +269.091 q^{38} -379.181 q^{40} +313.154 q^{41} -71.3458 q^{42} -296.702 q^{43} -37.5214 q^{44} +138.592 q^{45} +177.837 q^{46} -316.691 q^{47} -113.627 q^{48} -240.348 q^{49} +263.203 q^{50} +272.506 q^{51} +163.911 q^{53} +63.3763 q^{54} +232.016 q^{55} +249.480 q^{56} +343.920 q^{57} +504.233 q^{58} +254.149 q^{59} -115.046 q^{60} -935.247 q^{61} -667.742 q^{62} -91.1856 q^{63} +556.709 q^{64} +106.098 q^{66} -240.494 q^{67} -226.209 q^{68} +227.291 q^{69} -366.220 q^{70} +947.455 q^{71} -221.613 q^{72} -430.712 q^{73} +842.384 q^{74} +336.395 q^{75} -285.490 q^{76} -152.654 q^{77} -496.620 q^{79} -583.251 q^{80} +81.0000 q^{81} +735.058 q^{82} +392.527 q^{83} +75.6938 q^{84} +1398.78 q^{85} -696.439 q^{86} +644.451 q^{87} -371.002 q^{88} +979.895 q^{89} +325.312 q^{90} -188.675 q^{92} -853.428 q^{93} -743.360 q^{94} +1765.35 q^{95} +324.253 q^{96} -553.356 q^{97} -564.162 q^{98} +135.602 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 6 q^{2} + 27 q^{3} + 44 q^{4} + 33 q^{5} + 18 q^{6} + 83 q^{7} + 87 q^{8} + 81 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34727 0.829886 0.414943 0.909848i \(-0.363802\pi\)
0.414943 + 0.909848i \(0.363802\pi\)
\(3\) 3.00000 0.577350
\(4\) −2.49032 −0.311290
\(5\) 15.3991 1.37734 0.688668 0.725077i \(-0.258196\pi\)
0.688668 + 0.725077i \(0.258196\pi\)
\(6\) 7.04181 0.479135
\(7\) −10.1317 −0.547062 −0.273531 0.961863i \(-0.588192\pi\)
−0.273531 + 0.961863i \(0.588192\pi\)
\(8\) −24.6236 −1.08822
\(9\) 9.00000 0.333333
\(10\) 36.1458 1.14303
\(11\) 15.0669 0.412985 0.206493 0.978448i \(-0.433795\pi\)
0.206493 + 0.978448i \(0.433795\pi\)
\(12\) −7.47096 −0.179723
\(13\) 0 0
\(14\) −23.7819 −0.453999
\(15\) 46.1972 0.795205
\(16\) −37.8757 −0.591809
\(17\) 90.8352 1.29593 0.647964 0.761671i \(-0.275621\pi\)
0.647964 + 0.761671i \(0.275621\pi\)
\(18\) 21.1254 0.276629
\(19\) 114.640 1.38422 0.692110 0.721792i \(-0.256681\pi\)
0.692110 + 0.721792i \(0.256681\pi\)
\(20\) −38.3486 −0.428751
\(21\) −30.3952 −0.315847
\(22\) 35.3661 0.342731
\(23\) 75.7635 0.686860 0.343430 0.939178i \(-0.388411\pi\)
0.343430 + 0.939178i \(0.388411\pi\)
\(24\) −73.8709 −0.628284
\(25\) 112.132 0.897052
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 25.2313 0.170295
\(29\) 214.817 1.37553 0.687767 0.725931i \(-0.258591\pi\)
0.687767 + 0.725931i \(0.258591\pi\)
\(30\) 108.437 0.659929
\(31\) −284.476 −1.64817 −0.824087 0.566463i \(-0.808311\pi\)
−0.824087 + 0.566463i \(0.808311\pi\)
\(32\) 108.084 0.597087
\(33\) 45.2007 0.238437
\(34\) 213.215 1.07547
\(35\) −156.019 −0.753488
\(36\) −22.4129 −0.103763
\(37\) 358.878 1.59457 0.797286 0.603602i \(-0.206268\pi\)
0.797286 + 0.603602i \(0.206268\pi\)
\(38\) 269.091 1.14874
\(39\) 0 0
\(40\) −379.181 −1.49884
\(41\) 313.154 1.19284 0.596421 0.802672i \(-0.296589\pi\)
0.596421 + 0.802672i \(0.296589\pi\)
\(42\) −71.3458 −0.262116
\(43\) −296.702 −1.05225 −0.526123 0.850409i \(-0.676355\pi\)
−0.526123 + 0.850409i \(0.676355\pi\)
\(44\) −37.5214 −0.128558
\(45\) 138.592 0.459112
\(46\) 177.837 0.570015
\(47\) −316.691 −0.982854 −0.491427 0.870919i \(-0.663525\pi\)
−0.491427 + 0.870919i \(0.663525\pi\)
\(48\) −113.627 −0.341681
\(49\) −240.348 −0.700723
\(50\) 263.203 0.744451
\(51\) 272.506 0.748204
\(52\) 0 0
\(53\) 163.911 0.424810 0.212405 0.977182i \(-0.431870\pi\)
0.212405 + 0.977182i \(0.431870\pi\)
\(54\) 63.3763 0.159712
\(55\) 232.016 0.568819
\(56\) 249.480 0.595324
\(57\) 343.920 0.799180
\(58\) 504.233 1.14154
\(59\) 254.149 0.560803 0.280401 0.959883i \(-0.409532\pi\)
0.280401 + 0.959883i \(0.409532\pi\)
\(60\) −115.046 −0.247539
\(61\) −935.247 −1.96305 −0.981526 0.191330i \(-0.938720\pi\)
−0.981526 + 0.191330i \(0.938720\pi\)
\(62\) −667.742 −1.36780
\(63\) −91.1856 −0.182354
\(64\) 556.709 1.08732
\(65\) 0 0
\(66\) 106.098 0.197876
\(67\) −240.494 −0.438522 −0.219261 0.975666i \(-0.570365\pi\)
−0.219261 + 0.975666i \(0.570365\pi\)
\(68\) −226.209 −0.403409
\(69\) 227.291 0.396559
\(70\) −366.220 −0.625309
\(71\) 947.455 1.58369 0.791847 0.610720i \(-0.209120\pi\)
0.791847 + 0.610720i \(0.209120\pi\)
\(72\) −221.613 −0.362740
\(73\) −430.712 −0.690562 −0.345281 0.938499i \(-0.612216\pi\)
−0.345281 + 0.938499i \(0.612216\pi\)
\(74\) 842.384 1.32331
\(75\) 336.395 0.517913
\(76\) −285.490 −0.430894
\(77\) −152.654 −0.225929
\(78\) 0 0
\(79\) −496.620 −0.707268 −0.353634 0.935384i \(-0.615054\pi\)
−0.353634 + 0.935384i \(0.615054\pi\)
\(80\) −583.251 −0.815119
\(81\) 81.0000 0.111111
\(82\) 735.058 0.989922
\(83\) 392.527 0.519102 0.259551 0.965729i \(-0.416425\pi\)
0.259551 + 0.965729i \(0.416425\pi\)
\(84\) 75.6938 0.0983199
\(85\) 1398.78 1.78493
\(86\) −696.439 −0.873244
\(87\) 644.451 0.794165
\(88\) −371.002 −0.449419
\(89\) 979.895 1.16706 0.583532 0.812090i \(-0.301670\pi\)
0.583532 + 0.812090i \(0.301670\pi\)
\(90\) 325.312 0.381010
\(91\) 0 0
\(92\) −188.675 −0.213813
\(93\) −853.428 −0.951574
\(94\) −743.360 −0.815656
\(95\) 1765.35 1.90654
\(96\) 324.253 0.344729
\(97\) −553.356 −0.579225 −0.289613 0.957144i \(-0.593526\pi\)
−0.289613 + 0.957144i \(0.593526\pi\)
\(98\) −564.162 −0.581520
\(99\) 135.602 0.137662
\(100\) −279.243 −0.279243
\(101\) −763.951 −0.752633 −0.376317 0.926491i \(-0.622810\pi\)
−0.376317 + 0.926491i \(0.622810\pi\)
\(102\) 639.645 0.620924
\(103\) 182.518 0.174602 0.0873010 0.996182i \(-0.472176\pi\)
0.0873010 + 0.996182i \(0.472176\pi\)
\(104\) 0 0
\(105\) −468.058 −0.435027
\(106\) 384.744 0.352544
\(107\) 183.699 0.165971 0.0829855 0.996551i \(-0.473554\pi\)
0.0829855 + 0.996551i \(0.473554\pi\)
\(108\) −67.2386 −0.0599078
\(109\) 1774.42 1.55925 0.779627 0.626244i \(-0.215408\pi\)
0.779627 + 0.626244i \(0.215408\pi\)
\(110\) 544.605 0.472055
\(111\) 1076.63 0.920627
\(112\) 383.747 0.323756
\(113\) 417.288 0.347391 0.173695 0.984799i \(-0.444429\pi\)
0.173695 + 0.984799i \(0.444429\pi\)
\(114\) 807.273 0.663228
\(115\) 1166.69 0.946037
\(116\) −534.963 −0.428190
\(117\) 0 0
\(118\) 596.556 0.465402
\(119\) −920.318 −0.708953
\(120\) −1137.54 −0.865358
\(121\) −1103.99 −0.829443
\(122\) −2195.28 −1.62911
\(123\) 939.463 0.688687
\(124\) 708.436 0.513060
\(125\) −198.162 −0.141793
\(126\) −214.037 −0.151333
\(127\) −1951.69 −1.36366 −0.681828 0.731513i \(-0.738815\pi\)
−0.681828 + 0.731513i \(0.738815\pi\)
\(128\) 442.072 0.305266
\(129\) −890.105 −0.607514
\(130\) 0 0
\(131\) −1475.61 −0.984159 −0.492080 0.870550i \(-0.663763\pi\)
−0.492080 + 0.870550i \(0.663763\pi\)
\(132\) −112.564 −0.0742231
\(133\) −1161.50 −0.757255
\(134\) −564.503 −0.363923
\(135\) 415.775 0.265068
\(136\) −2236.69 −1.41026
\(137\) −1900.71 −1.18532 −0.592660 0.805453i \(-0.701922\pi\)
−0.592660 + 0.805453i \(0.701922\pi\)
\(138\) 533.512 0.329099
\(139\) −2326.76 −1.41981 −0.709903 0.704299i \(-0.751261\pi\)
−0.709903 + 0.704299i \(0.751261\pi\)
\(140\) 388.538 0.234553
\(141\) −950.073 −0.567451
\(142\) 2223.93 1.31428
\(143\) 0 0
\(144\) −340.882 −0.197270
\(145\) 3307.98 1.89457
\(146\) −1011.00 −0.573088
\(147\) −721.044 −0.404563
\(148\) −893.721 −0.496374
\(149\) −1370.92 −0.753761 −0.376881 0.926262i \(-0.623003\pi\)
−0.376881 + 0.926262i \(0.623003\pi\)
\(150\) 789.609 0.429809
\(151\) 1177.57 0.634628 0.317314 0.948320i \(-0.397219\pi\)
0.317314 + 0.948320i \(0.397219\pi\)
\(152\) −2822.85 −1.50634
\(153\) 817.517 0.431976
\(154\) −358.320 −0.187495
\(155\) −4380.67 −2.27009
\(156\) 0 0
\(157\) 1621.57 0.824302 0.412151 0.911116i \(-0.364778\pi\)
0.412151 + 0.911116i \(0.364778\pi\)
\(158\) −1165.70 −0.586951
\(159\) 491.734 0.245264
\(160\) 1664.40 0.822389
\(161\) −767.616 −0.375755
\(162\) 190.129 0.0922095
\(163\) −133.130 −0.0639727 −0.0319864 0.999488i \(-0.510183\pi\)
−0.0319864 + 0.999488i \(0.510183\pi\)
\(164\) −779.854 −0.371320
\(165\) 696.049 0.328408
\(166\) 921.368 0.430795
\(167\) −490.724 −0.227385 −0.113693 0.993516i \(-0.536268\pi\)
−0.113693 + 0.993516i \(0.536268\pi\)
\(168\) 748.440 0.343711
\(169\) 0 0
\(170\) 3283.31 1.48129
\(171\) 1031.76 0.461407
\(172\) 738.882 0.327554
\(173\) 2008.13 0.882518 0.441259 0.897380i \(-0.354532\pi\)
0.441259 + 0.897380i \(0.354532\pi\)
\(174\) 1512.70 0.659066
\(175\) −1136.09 −0.490743
\(176\) −570.670 −0.244408
\(177\) 762.446 0.323779
\(178\) 2300.08 0.968529
\(179\) −2152.60 −0.898843 −0.449421 0.893320i \(-0.648370\pi\)
−0.449421 + 0.893320i \(0.648370\pi\)
\(180\) −345.138 −0.142917
\(181\) 834.690 0.342774 0.171387 0.985204i \(-0.445175\pi\)
0.171387 + 0.985204i \(0.445175\pi\)
\(182\) 0 0
\(183\) −2805.74 −1.13337
\(184\) −1865.57 −0.747455
\(185\) 5526.39 2.19626
\(186\) −2003.23 −0.789697
\(187\) 1368.60 0.535200
\(188\) 788.662 0.305953
\(189\) −273.557 −0.105282
\(190\) 4143.75 1.58221
\(191\) 4464.71 1.69139 0.845695 0.533667i \(-0.179186\pi\)
0.845695 + 0.533667i \(0.179186\pi\)
\(192\) 1670.13 0.627766
\(193\) −3299.84 −1.23071 −0.615357 0.788248i \(-0.710988\pi\)
−0.615357 + 0.788248i \(0.710988\pi\)
\(194\) −1298.88 −0.480691
\(195\) 0 0
\(196\) 598.543 0.218128
\(197\) 2973.59 1.07543 0.537714 0.843127i \(-0.319288\pi\)
0.537714 + 0.843127i \(0.319288\pi\)
\(198\) 318.295 0.114244
\(199\) −5430.82 −1.93457 −0.967287 0.253684i \(-0.918358\pi\)
−0.967287 + 0.253684i \(0.918358\pi\)
\(200\) −2761.08 −0.976191
\(201\) −721.481 −0.253181
\(202\) −1793.20 −0.624600
\(203\) −2176.47 −0.752503
\(204\) −678.626 −0.232909
\(205\) 4822.29 1.64294
\(206\) 428.419 0.144900
\(207\) 681.872 0.228953
\(208\) 0 0
\(209\) 1727.27 0.571663
\(210\) −1098.66 −0.361022
\(211\) 1228.25 0.400742 0.200371 0.979720i \(-0.435785\pi\)
0.200371 + 0.979720i \(0.435785\pi\)
\(212\) −408.192 −0.132239
\(213\) 2842.37 0.914346
\(214\) 431.192 0.137737
\(215\) −4568.93 −1.44930
\(216\) −664.838 −0.209428
\(217\) 2882.24 0.901654
\(218\) 4165.05 1.29400
\(219\) −1292.14 −0.398696
\(220\) −577.795 −0.177068
\(221\) 0 0
\(222\) 2527.15 0.764015
\(223\) −685.256 −0.205776 −0.102888 0.994693i \(-0.532808\pi\)
−0.102888 + 0.994693i \(0.532808\pi\)
\(224\) −1095.08 −0.326644
\(225\) 1009.18 0.299017
\(226\) 979.487 0.288294
\(227\) 287.067 0.0839354 0.0419677 0.999119i \(-0.486637\pi\)
0.0419677 + 0.999119i \(0.486637\pi\)
\(228\) −856.470 −0.248777
\(229\) −2302.23 −0.664347 −0.332174 0.943218i \(-0.607782\pi\)
−0.332174 + 0.943218i \(0.607782\pi\)
\(230\) 2738.53 0.785102
\(231\) −457.961 −0.130440
\(232\) −5289.57 −1.49688
\(233\) −970.620 −0.272908 −0.136454 0.990646i \(-0.543571\pi\)
−0.136454 + 0.990646i \(0.543571\pi\)
\(234\) 0 0
\(235\) −4876.75 −1.35372
\(236\) −632.912 −0.174572
\(237\) −1489.86 −0.408341
\(238\) −2160.24 −0.588350
\(239\) −5007.40 −1.35524 −0.677619 0.735413i \(-0.736988\pi\)
−0.677619 + 0.735413i \(0.736988\pi\)
\(240\) −1749.75 −0.470609
\(241\) −540.092 −0.144358 −0.0721792 0.997392i \(-0.522995\pi\)
−0.0721792 + 0.997392i \(0.522995\pi\)
\(242\) −2591.36 −0.688343
\(243\) 243.000 0.0641500
\(244\) 2329.07 0.611078
\(245\) −3701.14 −0.965130
\(246\) 2205.17 0.571531
\(247\) 0 0
\(248\) 7004.83 1.79358
\(249\) 1177.58 0.299704
\(250\) −465.141 −0.117672
\(251\) −6087.80 −1.53091 −0.765455 0.643489i \(-0.777486\pi\)
−0.765455 + 0.643489i \(0.777486\pi\)
\(252\) 227.081 0.0567650
\(253\) 1141.52 0.283663
\(254\) −4581.14 −1.13168
\(255\) 4196.34 1.03053
\(256\) −3416.01 −0.833987
\(257\) −5096.34 −1.23697 −0.618484 0.785797i \(-0.712253\pi\)
−0.618484 + 0.785797i \(0.712253\pi\)
\(258\) −2089.32 −0.504167
\(259\) −3636.06 −0.872330
\(260\) 0 0
\(261\) 1933.35 0.458511
\(262\) −3463.66 −0.816739
\(263\) 3405.50 0.798450 0.399225 0.916853i \(-0.369279\pi\)
0.399225 + 0.916853i \(0.369279\pi\)
\(264\) −1113.00 −0.259472
\(265\) 2524.08 0.585106
\(266\) −2726.36 −0.628435
\(267\) 2939.68 0.673804
\(268\) 598.906 0.136507
\(269\) −2720.44 −0.616611 −0.308306 0.951287i \(-0.599762\pi\)
−0.308306 + 0.951287i \(0.599762\pi\)
\(270\) 975.937 0.219976
\(271\) 6954.27 1.55883 0.779413 0.626511i \(-0.215518\pi\)
0.779413 + 0.626511i \(0.215518\pi\)
\(272\) −3440.45 −0.766941
\(273\) 0 0
\(274\) −4461.49 −0.983680
\(275\) 1689.47 0.370470
\(276\) −566.026 −0.123445
\(277\) −6563.96 −1.42379 −0.711895 0.702286i \(-0.752163\pi\)
−0.711895 + 0.702286i \(0.752163\pi\)
\(278\) −5461.53 −1.17828
\(279\) −2560.28 −0.549392
\(280\) 3841.76 0.819961
\(281\) −652.800 −0.138586 −0.0692932 0.997596i \(-0.522074\pi\)
−0.0692932 + 0.997596i \(0.522074\pi\)
\(282\) −2230.08 −0.470919
\(283\) 6010.62 1.26252 0.631262 0.775570i \(-0.282537\pi\)
0.631262 + 0.775570i \(0.282537\pi\)
\(284\) −2359.47 −0.492988
\(285\) 5296.05 1.10074
\(286\) 0 0
\(287\) −3172.80 −0.652558
\(288\) 972.759 0.199029
\(289\) 3338.04 0.679430
\(290\) 7764.73 1.57228
\(291\) −1660.07 −0.334416
\(292\) 1072.61 0.214965
\(293\) −1912.72 −0.381372 −0.190686 0.981651i \(-0.561071\pi\)
−0.190686 + 0.981651i \(0.561071\pi\)
\(294\) −1692.49 −0.335741
\(295\) 3913.66 0.772413
\(296\) −8836.87 −1.73525
\(297\) 406.806 0.0794791
\(298\) −3217.93 −0.625535
\(299\) 0 0
\(300\) −837.730 −0.161221
\(301\) 3006.10 0.575644
\(302\) 2764.06 0.526669
\(303\) −2291.85 −0.434533
\(304\) −4342.07 −0.819194
\(305\) −14401.9 −2.70378
\(306\) 1918.93 0.358491
\(307\) −1983.07 −0.368665 −0.184332 0.982864i \(-0.559012\pi\)
−0.184332 + 0.982864i \(0.559012\pi\)
\(308\) 380.157 0.0703294
\(309\) 547.553 0.100807
\(310\) −10282.6 −1.88391
\(311\) 1893.76 0.345291 0.172645 0.984984i \(-0.444769\pi\)
0.172645 + 0.984984i \(0.444769\pi\)
\(312\) 0 0
\(313\) 4574.19 0.826034 0.413017 0.910723i \(-0.364475\pi\)
0.413017 + 0.910723i \(0.364475\pi\)
\(314\) 3806.26 0.684076
\(315\) −1404.17 −0.251163
\(316\) 1236.74 0.220165
\(317\) 7594.53 1.34559 0.672794 0.739830i \(-0.265094\pi\)
0.672794 + 0.739830i \(0.265094\pi\)
\(318\) 1154.23 0.203541
\(319\) 3236.62 0.568076
\(320\) 8572.81 1.49761
\(321\) 551.098 0.0958234
\(322\) −1801.80 −0.311834
\(323\) 10413.3 1.79385
\(324\) −201.716 −0.0345878
\(325\) 0 0
\(326\) −312.492 −0.0530901
\(327\) 5323.27 0.900236
\(328\) −7710.99 −1.29807
\(329\) 3208.63 0.537682
\(330\) 1633.82 0.272541
\(331\) −1738.58 −0.288705 −0.144352 0.989526i \(-0.546110\pi\)
−0.144352 + 0.989526i \(0.546110\pi\)
\(332\) −977.519 −0.161591
\(333\) 3229.90 0.531524
\(334\) −1151.86 −0.188704
\(335\) −3703.38 −0.603992
\(336\) 1151.24 0.186921
\(337\) −2710.61 −0.438149 −0.219074 0.975708i \(-0.570304\pi\)
−0.219074 + 0.975708i \(0.570304\pi\)
\(338\) 0 0
\(339\) 1251.86 0.200566
\(340\) −3483.41 −0.555630
\(341\) −4286.17 −0.680672
\(342\) 2421.82 0.382915
\(343\) 5910.33 0.930401
\(344\) 7305.87 1.14508
\(345\) 3500.06 0.546195
\(346\) 4713.63 0.732389
\(347\) −2506.81 −0.387817 −0.193908 0.981020i \(-0.562116\pi\)
−0.193908 + 0.981020i \(0.562116\pi\)
\(348\) −1604.89 −0.247216
\(349\) 7536.48 1.15593 0.577963 0.816063i \(-0.303848\pi\)
0.577963 + 0.816063i \(0.303848\pi\)
\(350\) −2666.70 −0.407261
\(351\) 0 0
\(352\) 1628.50 0.246588
\(353\) −8992.88 −1.35593 −0.677964 0.735095i \(-0.737138\pi\)
−0.677964 + 0.735095i \(0.737138\pi\)
\(354\) 1789.67 0.268700
\(355\) 14589.9 2.18128
\(356\) −2440.25 −0.363295
\(357\) −2760.96 −0.409314
\(358\) −5052.74 −0.745937
\(359\) −4566.64 −0.671359 −0.335679 0.941976i \(-0.608966\pi\)
−0.335679 + 0.941976i \(0.608966\pi\)
\(360\) −3412.63 −0.499615
\(361\) 6283.31 0.916068
\(362\) 1959.24 0.284463
\(363\) −3311.97 −0.478879
\(364\) 0 0
\(365\) −6632.57 −0.951136
\(366\) −6585.84 −0.940566
\(367\) −6449.50 −0.917332 −0.458666 0.888609i \(-0.651673\pi\)
−0.458666 + 0.888609i \(0.651673\pi\)
\(368\) −2869.60 −0.406490
\(369\) 2818.39 0.397614
\(370\) 12971.9 1.82264
\(371\) −1660.71 −0.232398
\(372\) 2125.31 0.296215
\(373\) 7648.89 1.06178 0.530891 0.847440i \(-0.321857\pi\)
0.530891 + 0.847440i \(0.321857\pi\)
\(374\) 3212.49 0.444154
\(375\) −594.487 −0.0818645
\(376\) 7798.08 1.06956
\(377\) 0 0
\(378\) −642.112 −0.0873722
\(379\) −10297.8 −1.39567 −0.697837 0.716256i \(-0.745854\pi\)
−0.697837 + 0.716256i \(0.745854\pi\)
\(380\) −4396.28 −0.593486
\(381\) −5855.06 −0.787307
\(382\) 10479.9 1.40366
\(383\) 10258.0 1.36856 0.684282 0.729217i \(-0.260116\pi\)
0.684282 + 0.729217i \(0.260116\pi\)
\(384\) 1326.22 0.176245
\(385\) −2350.73 −0.311180
\(386\) −7745.63 −1.02135
\(387\) −2670.31 −0.350749
\(388\) 1378.03 0.180307
\(389\) −4771.57 −0.621924 −0.310962 0.950422i \(-0.600651\pi\)
−0.310962 + 0.950422i \(0.600651\pi\)
\(390\) 0 0
\(391\) 6882.00 0.890122
\(392\) 5918.24 0.762541
\(393\) −4426.84 −0.568205
\(394\) 6979.82 0.892483
\(395\) −7647.50 −0.974145
\(396\) −337.693 −0.0428528
\(397\) 2291.22 0.289655 0.144827 0.989457i \(-0.453737\pi\)
0.144827 + 0.989457i \(0.453737\pi\)
\(398\) −12747.6 −1.60548
\(399\) −3484.50 −0.437201
\(400\) −4247.07 −0.530883
\(401\) 7534.63 0.938308 0.469154 0.883116i \(-0.344559\pi\)
0.469154 + 0.883116i \(0.344559\pi\)
\(402\) −1693.51 −0.210111
\(403\) 0 0
\(404\) 1902.48 0.234287
\(405\) 1247.33 0.153037
\(406\) −5108.76 −0.624491
\(407\) 5407.18 0.658535
\(408\) −6710.08 −0.814211
\(409\) −1517.97 −0.183517 −0.0917587 0.995781i \(-0.529249\pi\)
−0.0917587 + 0.995781i \(0.529249\pi\)
\(410\) 11319.2 1.36345
\(411\) −5702.14 −0.684345
\(412\) −454.528 −0.0543519
\(413\) −2574.97 −0.306794
\(414\) 1600.54 0.190005
\(415\) 6044.56 0.714978
\(416\) 0 0
\(417\) −6980.28 −0.819726
\(418\) 4054.36 0.474415
\(419\) 8080.97 0.942199 0.471100 0.882080i \(-0.343857\pi\)
0.471100 + 0.882080i \(0.343857\pi\)
\(420\) 1165.61 0.135419
\(421\) 8073.13 0.934585 0.467293 0.884103i \(-0.345229\pi\)
0.467293 + 0.884103i \(0.345229\pi\)
\(422\) 2883.05 0.332570
\(423\) −2850.22 −0.327618
\(424\) −4036.09 −0.462287
\(425\) 10185.5 1.16252
\(426\) 6671.80 0.758803
\(427\) 9475.68 1.07391
\(428\) −457.470 −0.0516651
\(429\) 0 0
\(430\) −10724.5 −1.20275
\(431\) 2241.39 0.250496 0.125248 0.992125i \(-0.460027\pi\)
0.125248 + 0.992125i \(0.460027\pi\)
\(432\) −1022.65 −0.113894
\(433\) 10237.9 1.13626 0.568130 0.822939i \(-0.307667\pi\)
0.568130 + 0.822939i \(0.307667\pi\)
\(434\) 6765.39 0.748270
\(435\) 9923.94 1.09383
\(436\) −4418.88 −0.485380
\(437\) 8685.52 0.950766
\(438\) −3033.00 −0.330872
\(439\) −5416.69 −0.588894 −0.294447 0.955668i \(-0.595135\pi\)
−0.294447 + 0.955668i \(0.595135\pi\)
\(440\) −5713.08 −0.619001
\(441\) −2163.13 −0.233574
\(442\) 0 0
\(443\) −2537.44 −0.272138 −0.136069 0.990699i \(-0.543447\pi\)
−0.136069 + 0.990699i \(0.543447\pi\)
\(444\) −2681.16 −0.286582
\(445\) 15089.5 1.60744
\(446\) −1608.48 −0.170771
\(447\) −4112.77 −0.435184
\(448\) −5640.43 −0.594833
\(449\) 7790.61 0.818846 0.409423 0.912345i \(-0.365730\pi\)
0.409423 + 0.912345i \(0.365730\pi\)
\(450\) 2368.83 0.248150
\(451\) 4718.26 0.492626
\(452\) −1039.18 −0.108139
\(453\) 3532.70 0.366403
\(454\) 673.825 0.0696568
\(455\) 0 0
\(456\) −8468.55 −0.869685
\(457\) 6599.71 0.675539 0.337770 0.941229i \(-0.390328\pi\)
0.337770 + 0.941229i \(0.390328\pi\)
\(458\) −5403.95 −0.551332
\(459\) 2452.55 0.249401
\(460\) −2905.43 −0.294492
\(461\) 4482.57 0.452872 0.226436 0.974026i \(-0.427293\pi\)
0.226436 + 0.974026i \(0.427293\pi\)
\(462\) −1074.96 −0.108250
\(463\) −3805.86 −0.382016 −0.191008 0.981589i \(-0.561176\pi\)
−0.191008 + 0.981589i \(0.561176\pi\)
\(464\) −8136.35 −0.814053
\(465\) −13142.0 −1.31064
\(466\) −2278.31 −0.226482
\(467\) 14778.8 1.46441 0.732207 0.681082i \(-0.238490\pi\)
0.732207 + 0.681082i \(0.238490\pi\)
\(468\) 0 0
\(469\) 2436.62 0.239899
\(470\) −11447.0 −1.12343
\(471\) 4864.71 0.475911
\(472\) −6258.06 −0.610277
\(473\) −4470.37 −0.434562
\(474\) −3497.11 −0.338877
\(475\) 12854.8 1.24172
\(476\) 2291.89 0.220690
\(477\) 1475.20 0.141603
\(478\) −11753.7 −1.12469
\(479\) 11171.2 1.06560 0.532801 0.846240i \(-0.321139\pi\)
0.532801 + 0.846240i \(0.321139\pi\)
\(480\) 4993.20 0.474807
\(481\) 0 0
\(482\) −1267.74 −0.119801
\(483\) −2302.85 −0.216942
\(484\) 2749.29 0.258197
\(485\) −8521.18 −0.797787
\(486\) 570.387 0.0532372
\(487\) 6046.57 0.562621 0.281310 0.959617i \(-0.409231\pi\)
0.281310 + 0.959617i \(0.409231\pi\)
\(488\) 23029.2 2.13623
\(489\) −399.390 −0.0369347
\(490\) −8687.57 −0.800948
\(491\) −1035.04 −0.0951338 −0.0475669 0.998868i \(-0.515147\pi\)
−0.0475669 + 0.998868i \(0.515147\pi\)
\(492\) −2339.56 −0.214381
\(493\) 19512.9 1.78259
\(494\) 0 0
\(495\) 2088.15 0.189606
\(496\) 10774.7 0.975404
\(497\) −9599.37 −0.866379
\(498\) 2764.10 0.248720
\(499\) −11698.3 −1.04947 −0.524736 0.851265i \(-0.675836\pi\)
−0.524736 + 0.851265i \(0.675836\pi\)
\(500\) 493.488 0.0441389
\(501\) −1472.17 −0.131281
\(502\) −14289.7 −1.27048
\(503\) −13552.0 −1.20130 −0.600651 0.799511i \(-0.705092\pi\)
−0.600651 + 0.799511i \(0.705092\pi\)
\(504\) 2245.32 0.198441
\(505\) −11764.1 −1.03663
\(506\) 2679.46 0.235408
\(507\) 0 0
\(508\) 4860.33 0.424492
\(509\) 5076.46 0.442064 0.221032 0.975267i \(-0.429058\pi\)
0.221032 + 0.975267i \(0.429058\pi\)
\(510\) 9849.94 0.855221
\(511\) 4363.86 0.377781
\(512\) −11554.9 −0.997380
\(513\) 3095.28 0.266393
\(514\) −11962.5 −1.02654
\(515\) 2810.60 0.240486
\(516\) 2216.65 0.189113
\(517\) −4771.55 −0.405904
\(518\) −8534.81 −0.723934
\(519\) 6024.40 0.509522
\(520\) 0 0
\(521\) −8493.73 −0.714236 −0.357118 0.934059i \(-0.616241\pi\)
−0.357118 + 0.934059i \(0.616241\pi\)
\(522\) 4538.10 0.380512
\(523\) −1384.53 −0.115758 −0.0578789 0.998324i \(-0.518434\pi\)
−0.0578789 + 0.998324i \(0.518434\pi\)
\(524\) 3674.75 0.306359
\(525\) −3408.26 −0.283331
\(526\) 7993.64 0.662622
\(527\) −25840.4 −2.13592
\(528\) −1712.01 −0.141109
\(529\) −6426.89 −0.528223
\(530\) 5924.71 0.485571
\(531\) 2287.34 0.186934
\(532\) 2892.51 0.235726
\(533\) 0 0
\(534\) 6900.24 0.559181
\(535\) 2828.80 0.228598
\(536\) 5921.82 0.477208
\(537\) −6457.80 −0.518947
\(538\) −6385.62 −0.511717
\(539\) −3621.30 −0.289388
\(540\) −1035.41 −0.0825131
\(541\) 5026.83 0.399483 0.199742 0.979849i \(-0.435990\pi\)
0.199742 + 0.979849i \(0.435990\pi\)
\(542\) 16323.6 1.29365
\(543\) 2504.07 0.197900
\(544\) 9817.87 0.773782
\(545\) 27324.5 2.14762
\(546\) 0 0
\(547\) 1540.36 0.120404 0.0602021 0.998186i \(-0.480825\pi\)
0.0602021 + 0.998186i \(0.480825\pi\)
\(548\) 4733.38 0.368978
\(549\) −8417.23 −0.654351
\(550\) 3965.65 0.307447
\(551\) 24626.6 1.90404
\(552\) −5596.72 −0.431544
\(553\) 5031.63 0.386920
\(554\) −15407.4 −1.18158
\(555\) 16579.2 1.26801
\(556\) 5794.38 0.441972
\(557\) −8550.51 −0.650443 −0.325221 0.945638i \(-0.605439\pi\)
−0.325221 + 0.945638i \(0.605439\pi\)
\(558\) −6009.68 −0.455932
\(559\) 0 0
\(560\) 5909.35 0.445921
\(561\) 4105.81 0.308998
\(562\) −1532.30 −0.115011
\(563\) −6569.35 −0.491768 −0.245884 0.969299i \(-0.579078\pi\)
−0.245884 + 0.969299i \(0.579078\pi\)
\(564\) 2365.99 0.176642
\(565\) 6425.85 0.478473
\(566\) 14108.5 1.04775
\(567\) −820.671 −0.0607847
\(568\) −23329.8 −1.72341
\(569\) 23766.1 1.75102 0.875508 0.483204i \(-0.160527\pi\)
0.875508 + 0.483204i \(0.160527\pi\)
\(570\) 12431.3 0.913488
\(571\) −24971.7 −1.83018 −0.915091 0.403248i \(-0.867881\pi\)
−0.915091 + 0.403248i \(0.867881\pi\)
\(572\) 0 0
\(573\) 13394.1 0.976524
\(574\) −7447.41 −0.541549
\(575\) 8495.48 0.616150
\(576\) 5010.38 0.362441
\(577\) −16643.4 −1.20082 −0.600409 0.799693i \(-0.704996\pi\)
−0.600409 + 0.799693i \(0.704996\pi\)
\(578\) 7835.28 0.563849
\(579\) −9899.53 −0.710553
\(580\) −8237.93 −0.589761
\(581\) −3976.98 −0.283981
\(582\) −3896.63 −0.277527
\(583\) 2469.64 0.175441
\(584\) 10605.7 0.751484
\(585\) 0 0
\(586\) −4489.66 −0.316495
\(587\) −6720.67 −0.472558 −0.236279 0.971685i \(-0.575928\pi\)
−0.236279 + 0.971685i \(0.575928\pi\)
\(588\) 1795.63 0.125936
\(589\) −32612.3 −2.28144
\(590\) 9186.41 0.641014
\(591\) 8920.77 0.620899
\(592\) −13592.8 −0.943681
\(593\) 26349.8 1.82471 0.912357 0.409395i \(-0.134260\pi\)
0.912357 + 0.409395i \(0.134260\pi\)
\(594\) 954.884 0.0659586
\(595\) −14172.1 −0.976466
\(596\) 3414.04 0.234638
\(597\) −16292.4 −1.11693
\(598\) 0 0
\(599\) −6136.81 −0.418603 −0.209302 0.977851i \(-0.567119\pi\)
−0.209302 + 0.977851i \(0.567119\pi\)
\(600\) −8283.25 −0.563604
\(601\) 12493.7 0.847966 0.423983 0.905670i \(-0.360632\pi\)
0.423983 + 0.905670i \(0.360632\pi\)
\(602\) 7056.14 0.477719
\(603\) −2164.44 −0.146174
\(604\) −2932.51 −0.197553
\(605\) −17000.4 −1.14242
\(606\) −5379.60 −0.360613
\(607\) 18696.6 1.25020 0.625099 0.780545i \(-0.285059\pi\)
0.625099 + 0.780545i \(0.285059\pi\)
\(608\) 12390.8 0.826501
\(609\) −6529.40 −0.434458
\(610\) −33805.3 −2.24383
\(611\) 0 0
\(612\) −2035.88 −0.134470
\(613\) 1238.64 0.0816123 0.0408062 0.999167i \(-0.487007\pi\)
0.0408062 + 0.999167i \(0.487007\pi\)
\(614\) −4654.81 −0.305949
\(615\) 14466.9 0.948553
\(616\) 3758.89 0.245860
\(617\) 16549.5 1.07983 0.539917 0.841718i \(-0.318456\pi\)
0.539917 + 0.841718i \(0.318456\pi\)
\(618\) 1285.26 0.0836579
\(619\) 13945.4 0.905513 0.452756 0.891634i \(-0.350441\pi\)
0.452756 + 0.891634i \(0.350441\pi\)
\(620\) 10909.3 0.706656
\(621\) 2045.62 0.132186
\(622\) 4445.17 0.286552
\(623\) −9928.03 −0.638456
\(624\) 0 0
\(625\) −17068.0 −1.09235
\(626\) 10736.9 0.685513
\(627\) 5181.80 0.330050
\(628\) −4038.23 −0.256597
\(629\) 32598.8 2.06645
\(630\) −3295.98 −0.208436
\(631\) 15343.1 0.967987 0.483994 0.875072i \(-0.339186\pi\)
0.483994 + 0.875072i \(0.339186\pi\)
\(632\) 12228.6 0.769663
\(633\) 3684.76 0.231368
\(634\) 17826.4 1.11668
\(635\) −30054.2 −1.87821
\(636\) −1224.58 −0.0763484
\(637\) 0 0
\(638\) 7597.23 0.471438
\(639\) 8527.10 0.527898
\(640\) 6807.51 0.420454
\(641\) 11067.7 0.681979 0.340989 0.940067i \(-0.389238\pi\)
0.340989 + 0.940067i \(0.389238\pi\)
\(642\) 1293.58 0.0795224
\(643\) −25118.7 −1.54057 −0.770284 0.637701i \(-0.779885\pi\)
−0.770284 + 0.637701i \(0.779885\pi\)
\(644\) 1911.61 0.116969
\(645\) −13706.8 −0.836751
\(646\) 24442.9 1.48869
\(647\) −4447.03 −0.270217 −0.135109 0.990831i \(-0.543138\pi\)
−0.135109 + 0.990831i \(0.543138\pi\)
\(648\) −1994.51 −0.120913
\(649\) 3829.23 0.231603
\(650\) 0 0
\(651\) 8646.71 0.520570
\(652\) 331.537 0.0199141
\(653\) −19426.2 −1.16418 −0.582088 0.813126i \(-0.697764\pi\)
−0.582088 + 0.813126i \(0.697764\pi\)
\(654\) 12495.1 0.747093
\(655\) −22723.1 −1.35552
\(656\) −11861.0 −0.705934
\(657\) −3876.41 −0.230187
\(658\) 7531.52 0.446215
\(659\) −14099.4 −0.833438 −0.416719 0.909035i \(-0.636820\pi\)
−0.416719 + 0.909035i \(0.636820\pi\)
\(660\) −1733.38 −0.102230
\(661\) 2754.25 0.162070 0.0810348 0.996711i \(-0.474177\pi\)
0.0810348 + 0.996711i \(0.474177\pi\)
\(662\) −4080.93 −0.239592
\(663\) 0 0
\(664\) −9665.44 −0.564898
\(665\) −17886.0 −1.04299
\(666\) 7581.45 0.441104
\(667\) 16275.3 0.944800
\(668\) 1222.06 0.0707828
\(669\) −2055.77 −0.118805
\(670\) −8692.83 −0.501244
\(671\) −14091.3 −0.810712
\(672\) −3285.25 −0.188588
\(673\) 11936.8 0.683700 0.341850 0.939754i \(-0.388946\pi\)
0.341850 + 0.939754i \(0.388946\pi\)
\(674\) −6362.53 −0.363613
\(675\) 3027.55 0.172638
\(676\) 0 0
\(677\) −10255.2 −0.582186 −0.291093 0.956695i \(-0.594019\pi\)
−0.291093 + 0.956695i \(0.594019\pi\)
\(678\) 2938.46 0.166447
\(679\) 5606.46 0.316872
\(680\) −34443.0 −1.94239
\(681\) 861.202 0.0484601
\(682\) −10060.8 −0.564880
\(683\) 10605.7 0.594169 0.297085 0.954851i \(-0.403986\pi\)
0.297085 + 0.954851i \(0.403986\pi\)
\(684\) −2569.41 −0.143631
\(685\) −29269.2 −1.63258
\(686\) 13873.1 0.772127
\(687\) −6906.69 −0.383561
\(688\) 11237.8 0.622728
\(689\) 0 0
\(690\) 8215.60 0.453279
\(691\) 4660.14 0.256556 0.128278 0.991738i \(-0.459055\pi\)
0.128278 + 0.991738i \(0.459055\pi\)
\(692\) −5000.90 −0.274719
\(693\) −1373.88 −0.0753096
\(694\) −5884.15 −0.321844
\(695\) −35829.9 −1.95555
\(696\) −15868.7 −0.864227
\(697\) 28445.4 1.54584
\(698\) 17690.2 0.959287
\(699\) −2911.86 −0.157563
\(700\) 2829.22 0.152764
\(701\) −24016.9 −1.29402 −0.647008 0.762483i \(-0.723980\pi\)
−0.647008 + 0.762483i \(0.723980\pi\)
\(702\) 0 0
\(703\) 41141.7 2.20724
\(704\) 8387.88 0.449048
\(705\) −14630.2 −0.781570
\(706\) −21108.7 −1.12527
\(707\) 7740.15 0.411737
\(708\) −1898.74 −0.100789
\(709\) −7252.56 −0.384169 −0.192084 0.981378i \(-0.561525\pi\)
−0.192084 + 0.981378i \(0.561525\pi\)
\(710\) 34246.5 1.81021
\(711\) −4469.58 −0.235756
\(712\) −24128.6 −1.27002
\(713\) −21552.9 −1.13207
\(714\) −6480.71 −0.339684
\(715\) 0 0
\(716\) 5360.66 0.279801
\(717\) −15022.2 −0.782447
\(718\) −10719.1 −0.557151
\(719\) 10951.7 0.568050 0.284025 0.958817i \(-0.408330\pi\)
0.284025 + 0.958817i \(0.408330\pi\)
\(720\) −5249.26 −0.271706
\(721\) −1849.22 −0.0955182
\(722\) 14748.6 0.760231
\(723\) −1620.28 −0.0833454
\(724\) −2078.65 −0.106702
\(725\) 24087.7 1.23393
\(726\) −7774.08 −0.397415
\(727\) −27856.0 −1.42108 −0.710538 0.703658i \(-0.751549\pi\)
−0.710538 + 0.703658i \(0.751549\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −15568.4 −0.789334
\(731\) −26951.0 −1.36364
\(732\) 6987.20 0.352806
\(733\) −31213.8 −1.57286 −0.786431 0.617678i \(-0.788073\pi\)
−0.786431 + 0.617678i \(0.788073\pi\)
\(734\) −15138.7 −0.761281
\(735\) −11103.4 −0.557218
\(736\) 8188.85 0.410116
\(737\) −3623.49 −0.181103
\(738\) 6615.52 0.329974
\(739\) 14423.1 0.717946 0.358973 0.933348i \(-0.383127\pi\)
0.358973 + 0.933348i \(0.383127\pi\)
\(740\) −13762.5 −0.683674
\(741\) 0 0
\(742\) −3898.13 −0.192864
\(743\) 13469.7 0.665079 0.332539 0.943089i \(-0.392095\pi\)
0.332539 + 0.943089i \(0.392095\pi\)
\(744\) 21014.5 1.03552
\(745\) −21111.0 −1.03818
\(746\) 17954.0 0.881158
\(747\) 3532.75 0.173034
\(748\) −3408.26 −0.166602
\(749\) −1861.19 −0.0907965
\(750\) −1395.42 −0.0679381
\(751\) −32033.6 −1.55649 −0.778245 0.627961i \(-0.783890\pi\)
−0.778245 + 0.627961i \(0.783890\pi\)
\(752\) 11994.9 0.581661
\(753\) −18263.4 −0.883871
\(754\) 0 0
\(755\) 18133.4 0.874096
\(756\) 681.244 0.0327733
\(757\) −26097.2 −1.25300 −0.626498 0.779423i \(-0.715512\pi\)
−0.626498 + 0.779423i \(0.715512\pi\)
\(758\) −24171.6 −1.15825
\(759\) 3424.56 0.163773
\(760\) −43469.3 −2.07473
\(761\) 18238.2 0.868772 0.434386 0.900727i \(-0.356965\pi\)
0.434386 + 0.900727i \(0.356965\pi\)
\(762\) −13743.4 −0.653375
\(763\) −17978.0 −0.853009
\(764\) −11118.6 −0.526513
\(765\) 12589.0 0.594976
\(766\) 24078.4 1.13575
\(767\) 0 0
\(768\) −10248.0 −0.481502
\(769\) −18817.0 −0.882390 −0.441195 0.897411i \(-0.645445\pi\)
−0.441195 + 0.897411i \(0.645445\pi\)
\(770\) −5517.79 −0.258243
\(771\) −15289.0 −0.714164
\(772\) 8217.67 0.383109
\(773\) −13795.6 −0.641904 −0.320952 0.947095i \(-0.604003\pi\)
−0.320952 + 0.947095i \(0.604003\pi\)
\(774\) −6267.95 −0.291081
\(775\) −31898.7 −1.47850
\(776\) 13625.6 0.630325
\(777\) −10908.2 −0.503640
\(778\) −11200.2 −0.516126
\(779\) 35900.0 1.65116
\(780\) 0 0
\(781\) 14275.2 0.654043
\(782\) 16153.9 0.738699
\(783\) 5800.05 0.264722
\(784\) 9103.36 0.414694
\(785\) 24970.7 1.13534
\(786\) −10391.0 −0.471545
\(787\) −40545.4 −1.83645 −0.918227 0.396055i \(-0.870379\pi\)
−0.918227 + 0.396055i \(0.870379\pi\)
\(788\) −7405.19 −0.334770
\(789\) 10216.5 0.460985
\(790\) −17950.7 −0.808429
\(791\) −4227.85 −0.190044
\(792\) −3339.01 −0.149806
\(793\) 0 0
\(794\) 5378.11 0.240380
\(795\) 7572.25 0.337811
\(796\) 13524.5 0.602214
\(797\) −31576.4 −1.40338 −0.701690 0.712482i \(-0.747571\pi\)
−0.701690 + 0.712482i \(0.747571\pi\)
\(798\) −8179.07 −0.362827
\(799\) −28766.7 −1.27371
\(800\) 12119.7 0.535619
\(801\) 8819.05 0.389021
\(802\) 17685.8 0.778688
\(803\) −6489.50 −0.285192
\(804\) 1796.72 0.0788126
\(805\) −11820.6 −0.517541
\(806\) 0 0
\(807\) −8161.33 −0.356001
\(808\) 18811.2 0.819031
\(809\) 31130.1 1.35287 0.676437 0.736501i \(-0.263523\pi\)
0.676437 + 0.736501i \(0.263523\pi\)
\(810\) 2927.81 0.127003
\(811\) −8733.71 −0.378153 −0.189076 0.981962i \(-0.560549\pi\)
−0.189076 + 0.981962i \(0.560549\pi\)
\(812\) 5420.10 0.234247
\(813\) 20862.8 0.899988
\(814\) 12692.1 0.546509
\(815\) −2050.08 −0.0881119
\(816\) −10321.4 −0.442794
\(817\) −34013.8 −1.45654
\(818\) −3563.08 −0.152298
\(819\) 0 0
\(820\) −12009.0 −0.511431
\(821\) −36960.1 −1.57115 −0.785576 0.618765i \(-0.787633\pi\)
−0.785576 + 0.618765i \(0.787633\pi\)
\(822\) −13384.5 −0.567928
\(823\) 20509.7 0.868679 0.434340 0.900749i \(-0.356982\pi\)
0.434340 + 0.900749i \(0.356982\pi\)
\(824\) −4494.25 −0.190006
\(825\) 5068.42 0.213891
\(826\) −6044.15 −0.254604
\(827\) −11533.4 −0.484952 −0.242476 0.970157i \(-0.577960\pi\)
−0.242476 + 0.970157i \(0.577960\pi\)
\(828\) −1698.08 −0.0712709
\(829\) 34096.4 1.42849 0.714244 0.699897i \(-0.246771\pi\)
0.714244 + 0.699897i \(0.246771\pi\)
\(830\) 14188.2 0.593350
\(831\) −19691.9 −0.822026
\(832\) 0 0
\(833\) −21832.1 −0.908087
\(834\) −16384.6 −0.680279
\(835\) −7556.69 −0.313186
\(836\) −4301.45 −0.177953
\(837\) −7680.85 −0.317191
\(838\) 18968.2 0.781917
\(839\) −1855.42 −0.0763484 −0.0381742 0.999271i \(-0.512154\pi\)
−0.0381742 + 0.999271i \(0.512154\pi\)
\(840\) 11525.3 0.473405
\(841\) 21757.3 0.892094
\(842\) 18949.8 0.775599
\(843\) −1958.40 −0.0800129
\(844\) −3058.75 −0.124747
\(845\) 0 0
\(846\) −6690.24 −0.271885
\(847\) 11185.3 0.453757
\(848\) −6208.26 −0.251406
\(849\) 18031.9 0.728918
\(850\) 23908.1 0.964755
\(851\) 27189.9 1.09525
\(852\) −7078.40 −0.284627
\(853\) −28668.7 −1.15076 −0.575380 0.817886i \(-0.695146\pi\)
−0.575380 + 0.817886i \(0.695146\pi\)
\(854\) 22242.0 0.891224
\(855\) 15888.1 0.635512
\(856\) −4523.35 −0.180613
\(857\) 449.310 0.0179091 0.00895457 0.999960i \(-0.497150\pi\)
0.00895457 + 0.999960i \(0.497150\pi\)
\(858\) 0 0
\(859\) 33466.9 1.32931 0.664654 0.747151i \(-0.268579\pi\)
0.664654 + 0.747151i \(0.268579\pi\)
\(860\) 11378.1 0.451151
\(861\) −9518.39 −0.376755
\(862\) 5261.14 0.207883
\(863\) −25097.5 −0.989953 −0.494976 0.868906i \(-0.664823\pi\)
−0.494976 + 0.868906i \(0.664823\pi\)
\(864\) 2918.28 0.114910
\(865\) 30923.4 1.21552
\(866\) 24031.0 0.942965
\(867\) 10014.1 0.392269
\(868\) −7177.69 −0.280676
\(869\) −7482.53 −0.292091
\(870\) 23294.2 0.907755
\(871\) 0 0
\(872\) −43692.7 −1.69681
\(873\) −4980.21 −0.193075
\(874\) 20387.3 0.789027
\(875\) 2007.73 0.0775698
\(876\) 3217.83 0.124110
\(877\) 27015.2 1.04018 0.520090 0.854112i \(-0.325899\pi\)
0.520090 + 0.854112i \(0.325899\pi\)
\(878\) −12714.4 −0.488715
\(879\) −5738.15 −0.220185
\(880\) −8787.79 −0.336632
\(881\) 48638.7 1.86002 0.930010 0.367534i \(-0.119798\pi\)
0.930010 + 0.367534i \(0.119798\pi\)
\(882\) −5077.46 −0.193840
\(883\) −25479.0 −0.971048 −0.485524 0.874223i \(-0.661371\pi\)
−0.485524 + 0.874223i \(0.661371\pi\)
\(884\) 0 0
\(885\) 11741.0 0.445953
\(886\) −5956.05 −0.225843
\(887\) 42359.7 1.60350 0.801748 0.597663i \(-0.203904\pi\)
0.801748 + 0.597663i \(0.203904\pi\)
\(888\) −26510.6 −1.00184
\(889\) 19774.0 0.746005
\(890\) 35419.1 1.33399
\(891\) 1220.42 0.0458873
\(892\) 1706.51 0.0640561
\(893\) −36305.4 −1.36049
\(894\) −9653.78 −0.361153
\(895\) −33148.1 −1.23801
\(896\) −4478.96 −0.167000
\(897\) 0 0
\(898\) 18286.7 0.679548
\(899\) −61110.3 −2.26712
\(900\) −2513.19 −0.0930811
\(901\) 14888.9 0.550524
\(902\) 11075.0 0.408823
\(903\) 9018.31 0.332348
\(904\) −10275.1 −0.378038
\(905\) 12853.5 0.472114
\(906\) 8292.19 0.304072
\(907\) −5314.91 −0.194574 −0.0972871 0.995256i \(-0.531016\pi\)
−0.0972871 + 0.995256i \(0.531016\pi\)
\(908\) −714.890 −0.0261283
\(909\) −6875.56 −0.250878
\(910\) 0 0
\(911\) 2471.71 0.0898919 0.0449459 0.998989i \(-0.485688\pi\)
0.0449459 + 0.998989i \(0.485688\pi\)
\(912\) −13026.2 −0.472962
\(913\) 5914.17 0.214382
\(914\) 15491.3 0.560620
\(915\) −43205.8 −1.56103
\(916\) 5733.29 0.206805
\(917\) 14950.5 0.538396
\(918\) 5756.80 0.206975
\(919\) −9636.13 −0.345883 −0.172942 0.984932i \(-0.555327\pi\)
−0.172942 + 0.984932i \(0.555327\pi\)
\(920\) −28728.1 −1.02950
\(921\) −5949.22 −0.212849
\(922\) 10521.8 0.375832
\(923\) 0 0
\(924\) 1140.47 0.0406047
\(925\) 40241.5 1.43041
\(926\) −8933.38 −0.317029
\(927\) 1642.66 0.0582007
\(928\) 23218.3 0.821314
\(929\) −53249.1 −1.88057 −0.940283 0.340394i \(-0.889439\pi\)
−0.940283 + 0.340394i \(0.889439\pi\)
\(930\) −30847.8 −1.08768
\(931\) −27553.5 −0.969955
\(932\) 2417.16 0.0849534
\(933\) 5681.28 0.199354
\(934\) 34689.8 1.21530
\(935\) 21075.3 0.737149
\(936\) 0 0
\(937\) −41122.6 −1.43374 −0.716871 0.697205i \(-0.754427\pi\)
−0.716871 + 0.697205i \(0.754427\pi\)
\(938\) 5719.40 0.199088
\(939\) 13722.6 0.476911
\(940\) 12144.7 0.421399
\(941\) −8005.71 −0.277342 −0.138671 0.990339i \(-0.544283\pi\)
−0.138671 + 0.990339i \(0.544283\pi\)
\(942\) 11418.8 0.394952
\(943\) 23725.7 0.819315
\(944\) −9626.07 −0.331888
\(945\) −4212.52 −0.145009
\(946\) −10493.2 −0.360637
\(947\) −17468.6 −0.599424 −0.299712 0.954030i \(-0.596891\pi\)
−0.299712 + 0.954030i \(0.596891\pi\)
\(948\) 3710.23 0.127113
\(949\) 0 0
\(950\) 30173.6 1.03048
\(951\) 22783.6 0.776875
\(952\) 22661.6 0.771498
\(953\) 30681.4 1.04288 0.521442 0.853287i \(-0.325394\pi\)
0.521442 + 0.853287i \(0.325394\pi\)
\(954\) 3462.70 0.117515
\(955\) 68752.5 2.32961
\(956\) 12470.0 0.421872
\(957\) 9709.87 0.327979
\(958\) 26221.8 0.884328
\(959\) 19257.5 0.648444
\(960\) 25718.4 0.864644
\(961\) 51135.6 1.71648
\(962\) 0 0
\(963\) 1653.29 0.0553237
\(964\) 1345.00 0.0449373
\(965\) −50814.5 −1.69511
\(966\) −5405.41 −0.180037
\(967\) 15616.0 0.519313 0.259656 0.965701i \(-0.416391\pi\)
0.259656 + 0.965701i \(0.416391\pi\)
\(968\) 27184.2 0.902617
\(969\) 31240.0 1.03568
\(970\) −20001.5 −0.662072
\(971\) 7185.98 0.237496 0.118748 0.992924i \(-0.462112\pi\)
0.118748 + 0.992924i \(0.462112\pi\)
\(972\) −605.148 −0.0199693
\(973\) 23574.1 0.776723
\(974\) 14192.9 0.466911
\(975\) 0 0
\(976\) 35423.2 1.16175
\(977\) 33165.3 1.08603 0.543015 0.839723i \(-0.317283\pi\)
0.543015 + 0.839723i \(0.317283\pi\)
\(978\) −937.477 −0.0306516
\(979\) 14764.0 0.481980
\(980\) 9217.01 0.300435
\(981\) 15969.8 0.519752
\(982\) −2429.52 −0.0789502
\(983\) −11658.7 −0.378287 −0.189143 0.981949i \(-0.560571\pi\)
−0.189143 + 0.981949i \(0.560571\pi\)
\(984\) −23133.0 −0.749444
\(985\) 45790.5 1.48123
\(986\) 45802.1 1.47935
\(987\) 9625.89 0.310431
\(988\) 0 0
\(989\) −22479.2 −0.722746
\(990\) 4901.45 0.157352
\(991\) −1957.32 −0.0627409 −0.0313704 0.999508i \(-0.509987\pi\)
−0.0313704 + 0.999508i \(0.509987\pi\)
\(992\) −30747.4 −0.984104
\(993\) −5215.75 −0.166684
\(994\) −22532.3 −0.718996
\(995\) −83629.5 −2.66456
\(996\) −2932.56 −0.0932948
\(997\) −11434.8 −0.363233 −0.181617 0.983369i \(-0.558133\pi\)
−0.181617 + 0.983369i \(0.558133\pi\)
\(998\) −27459.0 −0.870942
\(999\) 9689.70 0.306876
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.1.6 yes 9
3.2 odd 2 1521.4.a.bf.1.4 9
13.5 odd 4 507.4.b.k.337.7 18
13.8 odd 4 507.4.b.k.337.12 18
13.12 even 2 507.4.a.o.1.4 9
39.38 odd 2 1521.4.a.bi.1.6 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.4.a.o.1.4 9 13.12 even 2
507.4.a.p.1.6 yes 9 1.1 even 1 trivial
507.4.b.k.337.7 18 13.5 odd 4
507.4.b.k.337.12 18 13.8 odd 4
1521.4.a.bf.1.4 9 3.2 odd 2
1521.4.a.bi.1.6 9 39.38 odd 2