Properties

Label 507.4.a.r.1.1
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{3}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-5.36472\) of defining polynomial
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.36472 q^{2} +3.00000 q^{3} +20.7803 q^{4} +2.69631 q^{5} -16.0942 q^{6} +15.2025 q^{7} -68.5626 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.36472 q^{2} +3.00000 q^{3} +20.7803 q^{4} +2.69631 q^{5} -16.0942 q^{6} +15.2025 q^{7} -68.5626 q^{8} +9.00000 q^{9} -14.4650 q^{10} -66.8848 q^{11} +62.3408 q^{12} -81.5570 q^{14} +8.08894 q^{15} +201.577 q^{16} +4.16354 q^{17} -48.2825 q^{18} +26.0850 q^{19} +56.0301 q^{20} +45.6074 q^{21} +358.819 q^{22} +47.3242 q^{23} -205.688 q^{24} -117.730 q^{25} +27.0000 q^{27} +315.911 q^{28} +257.007 q^{29} -43.3949 q^{30} +206.242 q^{31} -532.906 q^{32} -200.655 q^{33} -22.3362 q^{34} +40.9906 q^{35} +187.022 q^{36} +175.686 q^{37} -139.939 q^{38} -184.866 q^{40} +156.463 q^{41} -244.671 q^{42} +51.9845 q^{43} -1389.88 q^{44} +24.2668 q^{45} -253.881 q^{46} -354.222 q^{47} +604.732 q^{48} -111.885 q^{49} +631.588 q^{50} +12.4906 q^{51} -10.4723 q^{53} -144.848 q^{54} -180.342 q^{55} -1042.32 q^{56} +78.2550 q^{57} -1378.77 q^{58} +445.114 q^{59} +168.090 q^{60} +119.696 q^{61} -1106.43 q^{62} +136.822 q^{63} +1246.28 q^{64} +1076.46 q^{66} -22.4078 q^{67} +86.5195 q^{68} +141.973 q^{69} -219.903 q^{70} +285.207 q^{71} -617.064 q^{72} +740.989 q^{73} -942.507 q^{74} -353.190 q^{75} +542.053 q^{76} -1016.81 q^{77} -547.679 q^{79} +543.516 q^{80} +81.0000 q^{81} -839.378 q^{82} +603.056 q^{83} +947.734 q^{84} +11.2262 q^{85} -278.882 q^{86} +771.021 q^{87} +4585.80 q^{88} +215.668 q^{89} -130.185 q^{90} +983.409 q^{92} +618.726 q^{93} +1900.31 q^{94} +70.3333 q^{95} -1598.72 q^{96} +1447.50 q^{97} +600.233 q^{98} -601.964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 30 q^{3} + 60 q^{4} + 90 q^{9} + 80 q^{10} + 180 q^{12} - 60 q^{14} + 500 q^{16} + 210 q^{17} + 580 q^{22} - 120 q^{23} + 960 q^{25} + 270 q^{27} + 990 q^{29} + 240 q^{30} - 120 q^{35} + 540 q^{36} + 1380 q^{38} + 2000 q^{40} - 180 q^{42} - 740 q^{43} + 1500 q^{48} + 1550 q^{49} + 630 q^{51} + 330 q^{53} + 520 q^{55} - 5340 q^{56} + 2750 q^{61} - 1560 q^{62} + 3140 q^{64} + 1740 q^{66} + 1200 q^{68} - 360 q^{69} - 4380 q^{74} + 2880 q^{75} + 4320 q^{77} + 1100 q^{79} + 810 q^{81} - 4780 q^{82} + 2970 q^{87} + 6340 q^{88} + 720 q^{90} - 1740 q^{92} + 6460 q^{94} - 2760 q^{95}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.36472 −1.89672 −0.948358 0.317201i \(-0.897257\pi\)
−0.948358 + 0.317201i \(0.897257\pi\)
\(3\) 3.00000 0.577350
\(4\) 20.7803 2.59753
\(5\) 2.69631 0.241165 0.120583 0.992703i \(-0.461524\pi\)
0.120583 + 0.992703i \(0.461524\pi\)
\(6\) −16.0942 −1.09507
\(7\) 15.2025 0.820856 0.410428 0.911893i \(-0.365379\pi\)
0.410428 + 0.911893i \(0.365379\pi\)
\(8\) −68.5626 −3.03007
\(9\) 9.00000 0.333333
\(10\) −14.4650 −0.457423
\(11\) −66.8848 −1.83332 −0.916661 0.399666i \(-0.869126\pi\)
−0.916661 + 0.399666i \(0.869126\pi\)
\(12\) 62.3408 1.49969
\(13\) 0 0
\(14\) −81.5570 −1.55693
\(15\) 8.08894 0.139237
\(16\) 201.577 3.14965
\(17\) 4.16354 0.0594004 0.0297002 0.999559i \(-0.490545\pi\)
0.0297002 + 0.999559i \(0.490545\pi\)
\(18\) −48.2825 −0.632239
\(19\) 26.0850 0.314963 0.157482 0.987522i \(-0.449662\pi\)
0.157482 + 0.987522i \(0.449662\pi\)
\(20\) 56.0301 0.626436
\(21\) 45.6074 0.473921
\(22\) 358.819 3.47729
\(23\) 47.3242 0.429034 0.214517 0.976720i \(-0.431182\pi\)
0.214517 + 0.976720i \(0.431182\pi\)
\(24\) −205.688 −1.74941
\(25\) −117.730 −0.941839
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 315.911 2.13220
\(29\) 257.007 1.64569 0.822845 0.568266i \(-0.192386\pi\)
0.822845 + 0.568266i \(0.192386\pi\)
\(30\) −43.3949 −0.264093
\(31\) 206.242 1.19491 0.597455 0.801903i \(-0.296179\pi\)
0.597455 + 0.801903i \(0.296179\pi\)
\(32\) −532.906 −2.94392
\(33\) −200.655 −1.05847
\(34\) −22.3362 −0.112666
\(35\) 40.9906 0.197962
\(36\) 187.022 0.865845
\(37\) 175.686 0.780611 0.390305 0.920685i \(-0.372369\pi\)
0.390305 + 0.920685i \(0.372369\pi\)
\(38\) −139.939 −0.597396
\(39\) 0 0
\(40\) −184.866 −0.730748
\(41\) 156.463 0.595984 0.297992 0.954568i \(-0.403683\pi\)
0.297992 + 0.954568i \(0.403683\pi\)
\(42\) −244.671 −0.898895
\(43\) 51.9845 0.184362 0.0921809 0.995742i \(-0.470616\pi\)
0.0921809 + 0.995742i \(0.470616\pi\)
\(44\) −1389.88 −4.76211
\(45\) 24.2668 0.0803885
\(46\) −253.881 −0.813755
\(47\) −354.222 −1.09933 −0.549666 0.835384i \(-0.685245\pi\)
−0.549666 + 0.835384i \(0.685245\pi\)
\(48\) 604.732 1.81845
\(49\) −111.885 −0.326196
\(50\) 631.588 1.78640
\(51\) 12.4906 0.0342948
\(52\) 0 0
\(53\) −10.4723 −0.0271412 −0.0135706 0.999908i \(-0.504320\pi\)
−0.0135706 + 0.999908i \(0.504320\pi\)
\(54\) −144.848 −0.365023
\(55\) −180.342 −0.442134
\(56\) −1042.32 −2.48725
\(57\) 78.2550 0.181844
\(58\) −1378.77 −3.12141
\(59\) 445.114 0.982185 0.491092 0.871107i \(-0.336598\pi\)
0.491092 + 0.871107i \(0.336598\pi\)
\(60\) 168.090 0.361673
\(61\) 119.696 0.251238 0.125619 0.992079i \(-0.459908\pi\)
0.125619 + 0.992079i \(0.459908\pi\)
\(62\) −1106.43 −2.26640
\(63\) 136.822 0.273619
\(64\) 1246.28 2.43413
\(65\) 0 0
\(66\) 1076.46 2.00761
\(67\) −22.4078 −0.0408589 −0.0204294 0.999791i \(-0.506503\pi\)
−0.0204294 + 0.999791i \(0.506503\pi\)
\(68\) 86.5195 0.154295
\(69\) 141.973 0.247703
\(70\) −219.903 −0.375478
\(71\) 285.207 0.476731 0.238365 0.971176i \(-0.423388\pi\)
0.238365 + 0.971176i \(0.423388\pi\)
\(72\) −617.064 −1.01002
\(73\) 740.989 1.18803 0.594015 0.804454i \(-0.297542\pi\)
0.594015 + 0.804454i \(0.297542\pi\)
\(74\) −942.507 −1.48060
\(75\) −353.190 −0.543771
\(76\) 542.053 0.818128
\(77\) −1016.81 −1.50489
\(78\) 0 0
\(79\) −547.679 −0.779983 −0.389992 0.920818i \(-0.627522\pi\)
−0.389992 + 0.920818i \(0.627522\pi\)
\(80\) 543.516 0.759586
\(81\) 81.0000 0.111111
\(82\) −839.378 −1.13041
\(83\) 603.056 0.797518 0.398759 0.917056i \(-0.369441\pi\)
0.398759 + 0.917056i \(0.369441\pi\)
\(84\) 947.734 1.23103
\(85\) 11.2262 0.0143253
\(86\) −278.882 −0.349682
\(87\) 771.021 0.950139
\(88\) 4585.80 5.55509
\(89\) 215.668 0.256863 0.128431 0.991718i \(-0.459006\pi\)
0.128431 + 0.991718i \(0.459006\pi\)
\(90\) −130.185 −0.152474
\(91\) 0 0
\(92\) 983.409 1.11443
\(93\) 618.726 0.689881
\(94\) 1900.31 2.08512
\(95\) 70.3333 0.0759583
\(96\) −1598.72 −1.69967
\(97\) 1447.50 1.51517 0.757586 0.652735i \(-0.226378\pi\)
0.757586 + 0.652735i \(0.226378\pi\)
\(98\) 600.233 0.618700
\(99\) −601.964 −0.611107
\(100\) −2446.46 −2.44646
\(101\) −883.450 −0.870362 −0.435181 0.900343i \(-0.643316\pi\)
−0.435181 + 0.900343i \(0.643316\pi\)
\(102\) −67.0087 −0.0650476
\(103\) 1251.74 1.19745 0.598726 0.800954i \(-0.295674\pi\)
0.598726 + 0.800954i \(0.295674\pi\)
\(104\) 0 0
\(105\) 122.972 0.114293
\(106\) 56.1812 0.0514792
\(107\) −341.614 −0.308645 −0.154323 0.988021i \(-0.549319\pi\)
−0.154323 + 0.988021i \(0.549319\pi\)
\(108\) 561.067 0.499896
\(109\) 775.177 0.681179 0.340589 0.940212i \(-0.389373\pi\)
0.340589 + 0.940212i \(0.389373\pi\)
\(110\) 967.487 0.838603
\(111\) 527.058 0.450686
\(112\) 3064.47 2.58541
\(113\) 1279.05 1.06480 0.532402 0.846492i \(-0.321290\pi\)
0.532402 + 0.846492i \(0.321290\pi\)
\(114\) −419.816 −0.344907
\(115\) 127.601 0.103468
\(116\) 5340.67 4.27473
\(117\) 0 0
\(118\) −2387.91 −1.86293
\(119\) 63.2961 0.0487592
\(120\) −554.599 −0.421898
\(121\) 3142.58 2.36107
\(122\) −642.137 −0.476528
\(123\) 469.388 0.344091
\(124\) 4285.77 3.10382
\(125\) −654.476 −0.468305
\(126\) −734.013 −0.518977
\(127\) −1113.82 −0.778233 −0.389117 0.921188i \(-0.627220\pi\)
−0.389117 + 0.921188i \(0.627220\pi\)
\(128\) −2422.68 −1.67294
\(129\) 155.953 0.106441
\(130\) 0 0
\(131\) 2100.12 1.40068 0.700339 0.713811i \(-0.253032\pi\)
0.700339 + 0.713811i \(0.253032\pi\)
\(132\) −4169.65 −2.74941
\(133\) 396.556 0.258540
\(134\) 120.211 0.0774977
\(135\) 72.8004 0.0464123
\(136\) −285.463 −0.179987
\(137\) −1205.02 −0.751471 −0.375736 0.926727i \(-0.622610\pi\)
−0.375736 + 0.926727i \(0.622610\pi\)
\(138\) −761.643 −0.469822
\(139\) 322.890 0.197030 0.0985149 0.995136i \(-0.468591\pi\)
0.0985149 + 0.995136i \(0.468591\pi\)
\(140\) 851.796 0.514213
\(141\) −1062.67 −0.634700
\(142\) −1530.06 −0.904223
\(143\) 0 0
\(144\) 1814.20 1.04988
\(145\) 692.971 0.396884
\(146\) −3975.20 −2.25336
\(147\) −335.655 −0.188329
\(148\) 3650.80 2.02766
\(149\) 1128.86 0.620669 0.310335 0.950627i \(-0.399559\pi\)
0.310335 + 0.950627i \(0.399559\pi\)
\(150\) 1894.77 1.03138
\(151\) −2940.44 −1.58470 −0.792350 0.610066i \(-0.791143\pi\)
−0.792350 + 0.610066i \(0.791143\pi\)
\(152\) −1788.46 −0.954361
\(153\) 37.4719 0.0198001
\(154\) 5454.93 2.85436
\(155\) 556.093 0.288171
\(156\) 0 0
\(157\) 629.388 0.319940 0.159970 0.987122i \(-0.448860\pi\)
0.159970 + 0.987122i \(0.448860\pi\)
\(158\) 2938.15 1.47941
\(159\) −31.4170 −0.0156700
\(160\) −1436.88 −0.709972
\(161\) 719.444 0.352175
\(162\) −434.543 −0.210746
\(163\) −394.912 −0.189766 −0.0948832 0.995488i \(-0.530248\pi\)
−0.0948832 + 0.995488i \(0.530248\pi\)
\(164\) 3251.33 1.54809
\(165\) −541.027 −0.255266
\(166\) −3235.23 −1.51267
\(167\) −151.860 −0.0703669 −0.0351834 0.999381i \(-0.511202\pi\)
−0.0351834 + 0.999381i \(0.511202\pi\)
\(168\) −3126.96 −1.43601
\(169\) 0 0
\(170\) −60.2255 −0.0271711
\(171\) 234.765 0.104988
\(172\) 1080.25 0.478886
\(173\) 538.813 0.236793 0.118397 0.992966i \(-0.462225\pi\)
0.118397 + 0.992966i \(0.462225\pi\)
\(174\) −4136.31 −1.80214
\(175\) −1789.78 −0.773114
\(176\) −13482.5 −5.77432
\(177\) 1335.34 0.567065
\(178\) −1157.00 −0.487196
\(179\) −2220.80 −0.927319 −0.463659 0.886014i \(-0.653464\pi\)
−0.463659 + 0.886014i \(0.653464\pi\)
\(180\) 504.271 0.208812
\(181\) −3822.78 −1.56986 −0.784932 0.619582i \(-0.787302\pi\)
−0.784932 + 0.619582i \(0.787302\pi\)
\(182\) 0 0
\(183\) 359.089 0.145052
\(184\) −3244.67 −1.30000
\(185\) 473.704 0.188256
\(186\) −3319.30 −1.30851
\(187\) −278.478 −0.108900
\(188\) −7360.84 −2.85555
\(189\) 410.467 0.157974
\(190\) −377.319 −0.144071
\(191\) 3464.19 1.31236 0.656178 0.754606i \(-0.272172\pi\)
0.656178 + 0.754606i \(0.272172\pi\)
\(192\) 3738.83 1.40535
\(193\) 4697.40 1.75195 0.875975 0.482357i \(-0.160219\pi\)
0.875975 + 0.482357i \(0.160219\pi\)
\(194\) −7765.46 −2.87385
\(195\) 0 0
\(196\) −2325.00 −0.847304
\(197\) −2887.89 −1.04443 −0.522217 0.852813i \(-0.674895\pi\)
−0.522217 + 0.852813i \(0.674895\pi\)
\(198\) 3229.37 1.15910
\(199\) 63.0092 0.0224453 0.0112226 0.999937i \(-0.496428\pi\)
0.0112226 + 0.999937i \(0.496428\pi\)
\(200\) 8071.87 2.85384
\(201\) −67.2233 −0.0235899
\(202\) 4739.47 1.65083
\(203\) 3907.14 1.35087
\(204\) 259.558 0.0890820
\(205\) 421.872 0.143731
\(206\) −6715.24 −2.27123
\(207\) 425.918 0.143011
\(208\) 0 0
\(209\) −1744.69 −0.577429
\(210\) −659.710 −0.216782
\(211\) −1049.70 −0.342484 −0.171242 0.985229i \(-0.554778\pi\)
−0.171242 + 0.985229i \(0.554778\pi\)
\(212\) −217.618 −0.0705002
\(213\) 855.622 0.275241
\(214\) 1832.66 0.585412
\(215\) 140.166 0.0444617
\(216\) −1851.19 −0.583137
\(217\) 3135.39 0.980848
\(218\) −4158.61 −1.29200
\(219\) 2222.97 0.685909
\(220\) −3747.56 −1.14846
\(221\) 0 0
\(222\) −2827.52 −0.854823
\(223\) 2313.49 0.694722 0.347361 0.937732i \(-0.387078\pi\)
0.347361 + 0.937732i \(0.387078\pi\)
\(224\) −8101.49 −2.41653
\(225\) −1059.57 −0.313946
\(226\) −6861.74 −2.01963
\(227\) 3799.46 1.11092 0.555460 0.831543i \(-0.312542\pi\)
0.555460 + 0.831543i \(0.312542\pi\)
\(228\) 1626.16 0.472347
\(229\) −4321.07 −1.24692 −0.623459 0.781856i \(-0.714273\pi\)
−0.623459 + 0.781856i \(0.714273\pi\)
\(230\) −684.543 −0.196250
\(231\) −3050.44 −0.868850
\(232\) −17621.1 −4.98655
\(233\) 5279.77 1.48450 0.742251 0.670122i \(-0.233758\pi\)
0.742251 + 0.670122i \(0.233758\pi\)
\(234\) 0 0
\(235\) −955.094 −0.265121
\(236\) 9249.59 2.55126
\(237\) −1643.04 −0.450323
\(238\) −339.566 −0.0924823
\(239\) 1547.92 0.418939 0.209469 0.977815i \(-0.432826\pi\)
0.209469 + 0.977815i \(0.432826\pi\)
\(240\) 1630.55 0.438547
\(241\) −4918.01 −1.31451 −0.657255 0.753669i \(-0.728282\pi\)
−0.657255 + 0.753669i \(0.728282\pi\)
\(242\) −16859.1 −4.47828
\(243\) 243.000 0.0641500
\(244\) 2487.32 0.652600
\(245\) −301.677 −0.0786671
\(246\) −2518.14 −0.652644
\(247\) 0 0
\(248\) −14140.5 −3.62066
\(249\) 1809.17 0.460447
\(250\) 3511.08 0.888241
\(251\) 1155.78 0.290646 0.145323 0.989384i \(-0.453578\pi\)
0.145323 + 0.989384i \(0.453578\pi\)
\(252\) 2843.20 0.710734
\(253\) −3165.27 −0.786556
\(254\) 5975.34 1.47609
\(255\) 33.6786 0.00827073
\(256\) 3026.80 0.738965
\(257\) 2351.95 0.570859 0.285429 0.958400i \(-0.407864\pi\)
0.285429 + 0.958400i \(0.407864\pi\)
\(258\) −836.647 −0.201889
\(259\) 2670.86 0.640769
\(260\) 0 0
\(261\) 2313.06 0.548563
\(262\) −11266.6 −2.65669
\(263\) 5521.88 1.29465 0.647326 0.762213i \(-0.275887\pi\)
0.647326 + 0.762213i \(0.275887\pi\)
\(264\) 13757.4 3.20723
\(265\) −28.2367 −0.00654553
\(266\) −2127.41 −0.490376
\(267\) 647.004 0.148300
\(268\) −465.639 −0.106132
\(269\) 3916.95 0.887810 0.443905 0.896074i \(-0.353593\pi\)
0.443905 + 0.896074i \(0.353593\pi\)
\(270\) −390.554 −0.0880310
\(271\) −2777.53 −0.622593 −0.311297 0.950313i \(-0.600763\pi\)
−0.311297 + 0.950313i \(0.600763\pi\)
\(272\) 839.276 0.187090
\(273\) 0 0
\(274\) 6464.58 1.42533
\(275\) 7874.34 1.72669
\(276\) 2950.23 0.643416
\(277\) 6583.08 1.42794 0.713969 0.700177i \(-0.246896\pi\)
0.713969 + 0.700177i \(0.246896\pi\)
\(278\) −1732.21 −0.373710
\(279\) 1856.18 0.398303
\(280\) −2810.42 −0.599839
\(281\) 2871.66 0.609640 0.304820 0.952410i \(-0.401404\pi\)
0.304820 + 0.952410i \(0.401404\pi\)
\(282\) 5700.92 1.20385
\(283\) 7518.04 1.57916 0.789578 0.613651i \(-0.210300\pi\)
0.789578 + 0.613651i \(0.210300\pi\)
\(284\) 5926.69 1.23832
\(285\) 211.000 0.0438546
\(286\) 0 0
\(287\) 2378.62 0.489217
\(288\) −4796.16 −0.981307
\(289\) −4895.66 −0.996472
\(290\) −3717.60 −0.752776
\(291\) 4342.51 0.874785
\(292\) 15397.9 3.08595
\(293\) 4506.57 0.898555 0.449278 0.893392i \(-0.351681\pi\)
0.449278 + 0.893392i \(0.351681\pi\)
\(294\) 1800.70 0.357207
\(295\) 1200.17 0.236869
\(296\) −12045.5 −2.36530
\(297\) −1805.89 −0.352823
\(298\) −6056.02 −1.17723
\(299\) 0 0
\(300\) −7339.38 −1.41246
\(301\) 790.292 0.151335
\(302\) 15774.7 3.00573
\(303\) −2650.35 −0.502504
\(304\) 5258.15 0.992024
\(305\) 322.738 0.0605900
\(306\) −201.026 −0.0375552
\(307\) 9538.89 1.77333 0.886667 0.462409i \(-0.153015\pi\)
0.886667 + 0.462409i \(0.153015\pi\)
\(308\) −21129.7 −3.90901
\(309\) 3755.22 0.691350
\(310\) −2983.29 −0.546578
\(311\) −7466.28 −1.36133 −0.680666 0.732594i \(-0.738309\pi\)
−0.680666 + 0.732594i \(0.738309\pi\)
\(312\) 0 0
\(313\) −1821.65 −0.328964 −0.164482 0.986380i \(-0.552595\pi\)
−0.164482 + 0.986380i \(0.552595\pi\)
\(314\) −3376.49 −0.606836
\(315\) 368.915 0.0659874
\(316\) −11380.9 −2.02603
\(317\) 3125.14 0.553708 0.276854 0.960912i \(-0.410708\pi\)
0.276854 + 0.960912i \(0.410708\pi\)
\(318\) 168.543 0.0297215
\(319\) −17189.9 −3.01708
\(320\) 3360.35 0.587029
\(321\) −1024.84 −0.178196
\(322\) −3859.62 −0.667976
\(323\) 108.606 0.0187090
\(324\) 1683.20 0.288615
\(325\) 0 0
\(326\) 2118.60 0.359933
\(327\) 2325.53 0.393279
\(328\) −10727.5 −1.80587
\(329\) −5385.05 −0.902394
\(330\) 2902.46 0.484167
\(331\) −1553.67 −0.257999 −0.128999 0.991645i \(-0.541177\pi\)
−0.128999 + 0.991645i \(0.541177\pi\)
\(332\) 12531.7 2.07158
\(333\) 1581.17 0.260204
\(334\) 814.686 0.133466
\(335\) −60.4183 −0.00985375
\(336\) 9193.42 1.49269
\(337\) −3190.43 −0.515709 −0.257855 0.966184i \(-0.583016\pi\)
−0.257855 + 0.966184i \(0.583016\pi\)
\(338\) 0 0
\(339\) 3837.15 0.614764
\(340\) 233.283 0.0372105
\(341\) −13794.5 −2.19065
\(342\) −1259.45 −0.199132
\(343\) −6915.37 −1.08862
\(344\) −3564.19 −0.558629
\(345\) 382.802 0.0597373
\(346\) −2890.59 −0.449130
\(347\) −5718.68 −0.884712 −0.442356 0.896840i \(-0.645857\pi\)
−0.442356 + 0.896840i \(0.645857\pi\)
\(348\) 16022.0 2.46802
\(349\) −3328.46 −0.510511 −0.255256 0.966874i \(-0.582160\pi\)
−0.255256 + 0.966874i \(0.582160\pi\)
\(350\) 9601.70 1.46638
\(351\) 0 0
\(352\) 35643.4 5.39715
\(353\) −12306.5 −1.85555 −0.927774 0.373142i \(-0.878281\pi\)
−0.927774 + 0.373142i \(0.878281\pi\)
\(354\) −7163.74 −1.07556
\(355\) 769.008 0.114971
\(356\) 4481.64 0.667210
\(357\) 189.888 0.0281511
\(358\) 11914.0 1.75886
\(359\) 8539.97 1.25549 0.627747 0.778418i \(-0.283977\pi\)
0.627747 + 0.778418i \(0.283977\pi\)
\(360\) −1663.80 −0.243583
\(361\) −6178.57 −0.900798
\(362\) 20508.2 2.97759
\(363\) 9427.74 1.36316
\(364\) 0 0
\(365\) 1997.94 0.286512
\(366\) −1926.41 −0.275123
\(367\) 2496.65 0.355107 0.177553 0.984111i \(-0.443182\pi\)
0.177553 + 0.984111i \(0.443182\pi\)
\(368\) 9539.49 1.35130
\(369\) 1408.16 0.198661
\(370\) −2541.29 −0.357069
\(371\) −159.205 −0.0222790
\(372\) 12857.3 1.79199
\(373\) −1142.91 −0.158653 −0.0793264 0.996849i \(-0.525277\pi\)
−0.0793264 + 0.996849i \(0.525277\pi\)
\(374\) 1493.96 0.206552
\(375\) −1963.43 −0.270376
\(376\) 24286.4 3.33105
\(377\) 0 0
\(378\) −2202.04 −0.299632
\(379\) −12181.8 −1.65102 −0.825512 0.564384i \(-0.809114\pi\)
−0.825512 + 0.564384i \(0.809114\pi\)
\(380\) 1461.54 0.197304
\(381\) −3341.46 −0.449313
\(382\) −18584.4 −2.48917
\(383\) −10180.6 −1.35824 −0.679118 0.734029i \(-0.737638\pi\)
−0.679118 + 0.734029i \(0.737638\pi\)
\(384\) −7268.04 −0.965874
\(385\) −2741.65 −0.362928
\(386\) −25200.3 −3.32295
\(387\) 467.860 0.0614539
\(388\) 30079.5 3.93571
\(389\) 5845.83 0.761941 0.380971 0.924587i \(-0.375590\pi\)
0.380971 + 0.924587i \(0.375590\pi\)
\(390\) 0 0
\(391\) 197.036 0.0254848
\(392\) 7671.13 0.988395
\(393\) 6300.37 0.808681
\(394\) 15492.7 1.98100
\(395\) −1476.71 −0.188105
\(396\) −12509.0 −1.58737
\(397\) −2500.92 −0.316166 −0.158083 0.987426i \(-0.550531\pi\)
−0.158083 + 0.987426i \(0.550531\pi\)
\(398\) −338.027 −0.0425723
\(399\) 1189.67 0.149268
\(400\) −23731.7 −2.96646
\(401\) −9189.25 −1.14436 −0.572181 0.820127i \(-0.693902\pi\)
−0.572181 + 0.820127i \(0.693902\pi\)
\(402\) 360.634 0.0447433
\(403\) 0 0
\(404\) −18358.3 −2.26080
\(405\) 218.401 0.0267962
\(406\) −20960.7 −2.56223
\(407\) −11750.7 −1.43111
\(408\) −856.390 −0.103916
\(409\) 9214.38 1.11399 0.556995 0.830516i \(-0.311954\pi\)
0.556995 + 0.830516i \(0.311954\pi\)
\(410\) −2263.23 −0.272617
\(411\) −3615.05 −0.433862
\(412\) 26011.5 3.11042
\(413\) 6766.83 0.806232
\(414\) −2284.93 −0.271252
\(415\) 1626.03 0.192334
\(416\) 0 0
\(417\) 968.669 0.113755
\(418\) 9359.78 1.09522
\(419\) −6494.41 −0.757214 −0.378607 0.925558i \(-0.623597\pi\)
−0.378607 + 0.925558i \(0.623597\pi\)
\(420\) 2555.39 0.296881
\(421\) 3059.56 0.354190 0.177095 0.984194i \(-0.443330\pi\)
0.177095 + 0.984194i \(0.443330\pi\)
\(422\) 5631.33 0.649595
\(423\) −3188.00 −0.366444
\(424\) 718.010 0.0822398
\(425\) −490.173 −0.0559456
\(426\) −4590.18 −0.522054
\(427\) 1819.68 0.206230
\(428\) −7098.82 −0.801716
\(429\) 0 0
\(430\) −751.954 −0.0843313
\(431\) 7937.05 0.887040 0.443520 0.896264i \(-0.353729\pi\)
0.443520 + 0.896264i \(0.353729\pi\)
\(432\) 5442.59 0.606150
\(433\) 7294.37 0.809573 0.404786 0.914411i \(-0.367346\pi\)
0.404786 + 0.914411i \(0.367346\pi\)
\(434\) −16820.5 −1.86039
\(435\) 2078.91 0.229141
\(436\) 16108.4 1.76938
\(437\) 1234.45 0.135130
\(438\) −11925.6 −1.30098
\(439\) 15214.7 1.65412 0.827059 0.562115i \(-0.190012\pi\)
0.827059 + 0.562115i \(0.190012\pi\)
\(440\) 12364.7 1.33970
\(441\) −1006.97 −0.108732
\(442\) 0 0
\(443\) 1517.05 0.162703 0.0813515 0.996685i \(-0.474076\pi\)
0.0813515 + 0.996685i \(0.474076\pi\)
\(444\) 10952.4 1.17067
\(445\) 581.509 0.0619464
\(446\) −12411.3 −1.31769
\(447\) 3386.58 0.358343
\(448\) 18946.5 1.99807
\(449\) −705.247 −0.0741262 −0.0370631 0.999313i \(-0.511800\pi\)
−0.0370631 + 0.999313i \(0.511800\pi\)
\(450\) 5684.30 0.595467
\(451\) −10465.0 −1.09263
\(452\) 26579.0 2.76586
\(453\) −8821.33 −0.914927
\(454\) −20383.1 −2.10710
\(455\) 0 0
\(456\) −5365.37 −0.551001
\(457\) −7277.73 −0.744940 −0.372470 0.928044i \(-0.621489\pi\)
−0.372470 + 0.928044i \(0.621489\pi\)
\(458\) 23181.4 2.36505
\(459\) 112.416 0.0114316
\(460\) 2651.58 0.268762
\(461\) 1961.88 0.198208 0.0991041 0.995077i \(-0.468402\pi\)
0.0991041 + 0.995077i \(0.468402\pi\)
\(462\) 16364.8 1.64796
\(463\) −10374.1 −1.04131 −0.520653 0.853768i \(-0.674311\pi\)
−0.520653 + 0.853768i \(0.674311\pi\)
\(464\) 51806.8 5.18334
\(465\) 1668.28 0.166376
\(466\) −28324.5 −2.81568
\(467\) 8788.92 0.870883 0.435442 0.900217i \(-0.356592\pi\)
0.435442 + 0.900217i \(0.356592\pi\)
\(468\) 0 0
\(469\) −340.653 −0.0335392
\(470\) 5123.82 0.502860
\(471\) 1888.16 0.184718
\(472\) −30518.2 −2.97609
\(473\) −3476.97 −0.337995
\(474\) 8814.44 0.854136
\(475\) −3070.98 −0.296645
\(476\) 1315.31 0.126654
\(477\) −94.2510 −0.00904707
\(478\) −8304.14 −0.794608
\(479\) −11141.7 −1.06279 −0.531394 0.847125i \(-0.678332\pi\)
−0.531394 + 0.847125i \(0.678332\pi\)
\(480\) −4310.65 −0.409903
\(481\) 0 0
\(482\) 26383.8 2.49325
\(483\) 2158.33 0.203328
\(484\) 65303.7 6.13295
\(485\) 3902.92 0.365407
\(486\) −1303.63 −0.121674
\(487\) −19640.5 −1.82750 −0.913752 0.406273i \(-0.866828\pi\)
−0.913752 + 0.406273i \(0.866828\pi\)
\(488\) −8206.69 −0.761269
\(489\) −1184.74 −0.109562
\(490\) 1618.41 0.149209
\(491\) −3410.31 −0.313453 −0.156726 0.987642i \(-0.550094\pi\)
−0.156726 + 0.987642i \(0.550094\pi\)
\(492\) 9754.00 0.893789
\(493\) 1070.06 0.0977546
\(494\) 0 0
\(495\) −1623.08 −0.147378
\(496\) 41573.8 3.76354
\(497\) 4335.86 0.391327
\(498\) −9705.68 −0.873338
\(499\) −5032.44 −0.451469 −0.225735 0.974189i \(-0.572478\pi\)
−0.225735 + 0.974189i \(0.572478\pi\)
\(500\) −13600.2 −1.21644
\(501\) −455.580 −0.0406263
\(502\) −6200.44 −0.551274
\(503\) 17189.4 1.52373 0.761866 0.647735i \(-0.224284\pi\)
0.761866 + 0.647735i \(0.224284\pi\)
\(504\) −9380.89 −0.829083
\(505\) −2382.06 −0.209901
\(506\) 16980.8 1.49187
\(507\) 0 0
\(508\) −23145.5 −2.02149
\(509\) −930.560 −0.0810341 −0.0405170 0.999179i \(-0.512901\pi\)
−0.0405170 + 0.999179i \(0.512901\pi\)
\(510\) −180.676 −0.0156872
\(511\) 11264.9 0.975201
\(512\) 3143.50 0.271337
\(513\) 704.295 0.0606148
\(514\) −12617.6 −1.08276
\(515\) 3375.08 0.288784
\(516\) 3240.75 0.276485
\(517\) 23692.1 2.01543
\(518\) −14328.4 −1.21536
\(519\) 1616.44 0.136713
\(520\) 0 0
\(521\) −9869.60 −0.829933 −0.414966 0.909837i \(-0.636207\pi\)
−0.414966 + 0.909837i \(0.636207\pi\)
\(522\) −12408.9 −1.04047
\(523\) −21420.6 −1.79093 −0.895466 0.445129i \(-0.853158\pi\)
−0.895466 + 0.445129i \(0.853158\pi\)
\(524\) 43641.1 3.63831
\(525\) −5369.35 −0.446358
\(526\) −29623.4 −2.45559
\(527\) 858.697 0.0709781
\(528\) −40447.4 −3.33380
\(529\) −9927.42 −0.815930
\(530\) 151.482 0.0124150
\(531\) 4006.03 0.327395
\(532\) 8240.54 0.671565
\(533\) 0 0
\(534\) −3471.00 −0.281283
\(535\) −921.097 −0.0744345
\(536\) 1536.34 0.123805
\(537\) −6662.39 −0.535388
\(538\) −21013.4 −1.68392
\(539\) 7483.41 0.598021
\(540\) 1512.81 0.120558
\(541\) 7771.50 0.617602 0.308801 0.951127i \(-0.400072\pi\)
0.308801 + 0.951127i \(0.400072\pi\)
\(542\) 14900.7 1.18088
\(543\) −11468.3 −0.906361
\(544\) −2218.78 −0.174870
\(545\) 2090.12 0.164277
\(546\) 0 0
\(547\) −15577.5 −1.21763 −0.608817 0.793310i \(-0.708356\pi\)
−0.608817 + 0.793310i \(0.708356\pi\)
\(548\) −25040.6 −1.95197
\(549\) 1077.27 0.0837461
\(550\) −42243.7 −3.27505
\(551\) 6704.02 0.518332
\(552\) −9734.01 −0.750556
\(553\) −8326.07 −0.640254
\(554\) −35316.4 −2.70840
\(555\) 1421.11 0.108690
\(556\) 6709.74 0.511792
\(557\) −22804.5 −1.73475 −0.867377 0.497652i \(-0.834196\pi\)
−0.867377 + 0.497652i \(0.834196\pi\)
\(558\) −9957.89 −0.755468
\(559\) 0 0
\(560\) 8262.78 0.623511
\(561\) −835.433 −0.0628734
\(562\) −15405.7 −1.15631
\(563\) −3517.41 −0.263306 −0.131653 0.991296i \(-0.542028\pi\)
−0.131653 + 0.991296i \(0.542028\pi\)
\(564\) −22082.5 −1.64865
\(565\) 3448.71 0.256794
\(566\) −40332.2 −2.99521
\(567\) 1231.40 0.0912062
\(568\) −19554.6 −1.44453
\(569\) −6093.44 −0.448946 −0.224473 0.974480i \(-0.572066\pi\)
−0.224473 + 0.974480i \(0.572066\pi\)
\(570\) −1131.96 −0.0831797
\(571\) 10460.2 0.766630 0.383315 0.923618i \(-0.374782\pi\)
0.383315 + 0.923618i \(0.374782\pi\)
\(572\) 0 0
\(573\) 10392.6 0.757689
\(574\) −12760.6 −0.927906
\(575\) −5571.47 −0.404081
\(576\) 11216.5 0.811378
\(577\) −9648.19 −0.696117 −0.348058 0.937473i \(-0.613159\pi\)
−0.348058 + 0.937473i \(0.613159\pi\)
\(578\) 26263.9 1.89002
\(579\) 14092.2 1.01149
\(580\) 14400.1 1.03092
\(581\) 9167.93 0.654647
\(582\) −23296.4 −1.65922
\(583\) 700.440 0.0497586
\(584\) −50804.1 −3.59981
\(585\) 0 0
\(586\) −24176.5 −1.70430
\(587\) 2170.73 0.152633 0.0763166 0.997084i \(-0.475684\pi\)
0.0763166 + 0.997084i \(0.475684\pi\)
\(588\) −6975.01 −0.489191
\(589\) 5379.82 0.376353
\(590\) −6438.56 −0.449274
\(591\) −8663.66 −0.603004
\(592\) 35414.3 2.45865
\(593\) 22885.9 1.58484 0.792421 0.609975i \(-0.208820\pi\)
0.792421 + 0.609975i \(0.208820\pi\)
\(594\) 9688.11 0.669205
\(595\) 170.666 0.0117590
\(596\) 23458.0 1.61221
\(597\) 189.028 0.0129588
\(598\) 0 0
\(599\) −23978.7 −1.63563 −0.817815 0.575482i \(-0.804815\pi\)
−0.817815 + 0.575482i \(0.804815\pi\)
\(600\) 24215.6 1.64766
\(601\) 12873.2 0.873728 0.436864 0.899528i \(-0.356089\pi\)
0.436864 + 0.899528i \(0.356089\pi\)
\(602\) −4239.70 −0.287039
\(603\) −201.670 −0.0136196
\(604\) −61103.2 −4.11631
\(605\) 8473.38 0.569408
\(606\) 14218.4 0.953107
\(607\) −7117.15 −0.475908 −0.237954 0.971276i \(-0.576477\pi\)
−0.237954 + 0.971276i \(0.576477\pi\)
\(608\) −13900.9 −0.927227
\(609\) 11721.4 0.779927
\(610\) −1731.40 −0.114922
\(611\) 0 0
\(612\) 778.675 0.0514315
\(613\) 173.297 0.0114183 0.00570913 0.999984i \(-0.498183\pi\)
0.00570913 + 0.999984i \(0.498183\pi\)
\(614\) −51173.5 −3.36351
\(615\) 1265.62 0.0829830
\(616\) 69715.5 4.55993
\(617\) −6102.75 −0.398197 −0.199099 0.979979i \(-0.563801\pi\)
−0.199099 + 0.979979i \(0.563801\pi\)
\(618\) −20145.7 −1.31129
\(619\) −14867.8 −0.965409 −0.482705 0.875783i \(-0.660346\pi\)
−0.482705 + 0.875783i \(0.660346\pi\)
\(620\) 11555.8 0.748534
\(621\) 1277.75 0.0825676
\(622\) 40054.6 2.58206
\(623\) 3278.69 0.210847
\(624\) 0 0
\(625\) 12951.6 0.828900
\(626\) 9772.64 0.623951
\(627\) −5234.07 −0.333379
\(628\) 13078.9 0.831056
\(629\) 731.475 0.0463686
\(630\) −1979.13 −0.125159
\(631\) −17210.6 −1.08580 −0.542902 0.839796i \(-0.682675\pi\)
−0.542902 + 0.839796i \(0.682675\pi\)
\(632\) 37550.3 2.36340
\(633\) −3149.09 −0.197733
\(634\) −16765.5 −1.05023
\(635\) −3003.21 −0.187683
\(636\) −652.853 −0.0407033
\(637\) 0 0
\(638\) 92218.9 5.72254
\(639\) 2566.87 0.158910
\(640\) −6532.30 −0.403456
\(641\) −12636.0 −0.778616 −0.389308 0.921108i \(-0.627286\pi\)
−0.389308 + 0.921108i \(0.627286\pi\)
\(642\) 5497.99 0.337988
\(643\) −9586.37 −0.587947 −0.293973 0.955814i \(-0.594978\pi\)
−0.293973 + 0.955814i \(0.594978\pi\)
\(644\) 14950.2 0.914786
\(645\) 420.499 0.0256700
\(646\) −582.641 −0.0354856
\(647\) 5244.32 0.318664 0.159332 0.987225i \(-0.449066\pi\)
0.159332 + 0.987225i \(0.449066\pi\)
\(648\) −5553.57 −0.336674
\(649\) −29771.4 −1.80066
\(650\) 0 0
\(651\) 9406.17 0.566293
\(652\) −8206.39 −0.492925
\(653\) 18869.0 1.13078 0.565392 0.824822i \(-0.308725\pi\)
0.565392 + 0.824822i \(0.308725\pi\)
\(654\) −12475.8 −0.745938
\(655\) 5662.59 0.337795
\(656\) 31539.3 1.87714
\(657\) 6668.90 0.396010
\(658\) 28889.3 1.71159
\(659\) −24299.8 −1.43639 −0.718197 0.695839i \(-0.755033\pi\)
−0.718197 + 0.695839i \(0.755033\pi\)
\(660\) −11242.7 −0.663062
\(661\) 29915.0 1.76030 0.880151 0.474694i \(-0.157441\pi\)
0.880151 + 0.474694i \(0.157441\pi\)
\(662\) 8335.03 0.489350
\(663\) 0 0
\(664\) −41347.1 −2.41653
\(665\) 1069.24 0.0623508
\(666\) −8482.56 −0.493532
\(667\) 12162.6 0.706056
\(668\) −3155.69 −0.182780
\(669\) 6940.48 0.401098
\(670\) 324.128 0.0186898
\(671\) −8005.86 −0.460600
\(672\) −24304.5 −1.39519
\(673\) 15493.7 0.887426 0.443713 0.896169i \(-0.353661\pi\)
0.443713 + 0.896169i \(0.353661\pi\)
\(674\) 17115.8 0.978154
\(675\) −3178.71 −0.181257
\(676\) 0 0
\(677\) 11729.7 0.665891 0.332945 0.942946i \(-0.391958\pi\)
0.332945 + 0.942946i \(0.391958\pi\)
\(678\) −20585.2 −1.16603
\(679\) 22005.6 1.24374
\(680\) −769.698 −0.0434067
\(681\) 11398.4 0.641390
\(682\) 74003.5 4.15505
\(683\) −1168.42 −0.0654587 −0.0327294 0.999464i \(-0.510420\pi\)
−0.0327294 + 0.999464i \(0.510420\pi\)
\(684\) 4878.48 0.272709
\(685\) −3249.10 −0.181229
\(686\) 37099.1 2.06480
\(687\) −12963.2 −0.719909
\(688\) 10478.9 0.580675
\(689\) 0 0
\(690\) −2053.63 −0.113305
\(691\) 32992.9 1.81637 0.908183 0.418574i \(-0.137470\pi\)
0.908183 + 0.418574i \(0.137470\pi\)
\(692\) 11196.7 0.615078
\(693\) −9151.33 −0.501631
\(694\) 30679.2 1.67805
\(695\) 870.612 0.0475168
\(696\) −52863.2 −2.87899
\(697\) 651.438 0.0354017
\(698\) 17856.3 0.968295
\(699\) 15839.3 0.857078
\(700\) −37192.2 −2.00819
\(701\) −14785.8 −0.796651 −0.398326 0.917244i \(-0.630409\pi\)
−0.398326 + 0.917244i \(0.630409\pi\)
\(702\) 0 0
\(703\) 4582.77 0.245864
\(704\) −83357.0 −4.46255
\(705\) −2865.28 −0.153068
\(706\) 66021.0 3.51945
\(707\) −13430.6 −0.714442
\(708\) 27748.8 1.47297
\(709\) 12634.0 0.669225 0.334612 0.942356i \(-0.391395\pi\)
0.334612 + 0.942356i \(0.391395\pi\)
\(710\) −4125.52 −0.218067
\(711\) −4929.11 −0.259994
\(712\) −14786.8 −0.778312
\(713\) 9760.24 0.512656
\(714\) −1018.70 −0.0533947
\(715\) 0 0
\(716\) −46148.7 −2.40874
\(717\) 4643.75 0.241874
\(718\) −45814.6 −2.38132
\(719\) −27296.5 −1.41584 −0.707920 0.706292i \(-0.750366\pi\)
−0.707920 + 0.706292i \(0.750366\pi\)
\(720\) 4891.64 0.253195
\(721\) 19029.5 0.982936
\(722\) 33146.3 1.70856
\(723\) −14754.0 −0.758932
\(724\) −79438.5 −4.07777
\(725\) −30257.4 −1.54997
\(726\) −50577.2 −2.58553
\(727\) 4658.21 0.237639 0.118819 0.992916i \(-0.462089\pi\)
0.118819 + 0.992916i \(0.462089\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −10718.4 −0.543432
\(731\) 216.439 0.0109512
\(732\) 7461.96 0.376779
\(733\) −166.474 −0.00838864 −0.00419432 0.999991i \(-0.501335\pi\)
−0.00419432 + 0.999991i \(0.501335\pi\)
\(734\) −13393.9 −0.673537
\(735\) −905.031 −0.0454185
\(736\) −25219.4 −1.26304
\(737\) 1498.74 0.0749074
\(738\) −7554.41 −0.376804
\(739\) 12738.1 0.634069 0.317035 0.948414i \(-0.397313\pi\)
0.317035 + 0.948414i \(0.397313\pi\)
\(740\) 9843.70 0.489002
\(741\) 0 0
\(742\) 854.092 0.0422570
\(743\) −30724.5 −1.51705 −0.758527 0.651641i \(-0.774081\pi\)
−0.758527 + 0.651641i \(0.774081\pi\)
\(744\) −42421.5 −2.09039
\(745\) 3043.76 0.149684
\(746\) 6131.38 0.300919
\(747\) 5427.50 0.265839
\(748\) −5786.84 −0.282871
\(749\) −5193.37 −0.253353
\(750\) 10533.2 0.512826
\(751\) −39538.6 −1.92115 −0.960575 0.278021i \(-0.910322\pi\)
−0.960575 + 0.278021i \(0.910322\pi\)
\(752\) −71403.2 −3.46251
\(753\) 3467.34 0.167805
\(754\) 0 0
\(755\) −7928.35 −0.382175
\(756\) 8529.61 0.410342
\(757\) 23035.1 1.10598 0.552990 0.833188i \(-0.313487\pi\)
0.552990 + 0.833188i \(0.313487\pi\)
\(758\) 65352.1 3.13153
\(759\) −9495.81 −0.454119
\(760\) −4822.23 −0.230159
\(761\) 32454.0 1.54594 0.772968 0.634445i \(-0.218771\pi\)
0.772968 + 0.634445i \(0.218771\pi\)
\(762\) 17926.0 0.852220
\(763\) 11784.6 0.559150
\(764\) 71986.8 3.40889
\(765\) 101.036 0.00477511
\(766\) 54616.1 2.57619
\(767\) 0 0
\(768\) 9080.40 0.426641
\(769\) −32216.2 −1.51072 −0.755362 0.655307i \(-0.772539\pi\)
−0.755362 + 0.655307i \(0.772539\pi\)
\(770\) 14708.2 0.688372
\(771\) 7055.86 0.329586
\(772\) 97613.2 4.55075
\(773\) 2924.60 0.136081 0.0680404 0.997683i \(-0.478325\pi\)
0.0680404 + 0.997683i \(0.478325\pi\)
\(774\) −2509.94 −0.116561
\(775\) −24280.9 −1.12541
\(776\) −99244.7 −4.59108
\(777\) 8012.58 0.369948
\(778\) −31361.2 −1.44519
\(779\) 4081.32 0.187713
\(780\) 0 0
\(781\) −19076.1 −0.874001
\(782\) −1057.04 −0.0483374
\(783\) 6939.19 0.316713
\(784\) −22553.5 −1.02740
\(785\) 1697.03 0.0771586
\(786\) −33799.8 −1.53384
\(787\) 25507.1 1.15531 0.577656 0.816280i \(-0.303967\pi\)
0.577656 + 0.816280i \(0.303967\pi\)
\(788\) −60011.1 −2.71295
\(789\) 16565.6 0.747468
\(790\) 7922.16 0.356782
\(791\) 19444.7 0.874050
\(792\) 41272.2 1.85170
\(793\) 0 0
\(794\) 13416.8 0.599677
\(795\) −84.7100 −0.00377906
\(796\) 1309.35 0.0583023
\(797\) 5448.98 0.242174 0.121087 0.992642i \(-0.461362\pi\)
0.121087 + 0.992642i \(0.461362\pi\)
\(798\) −6382.24 −0.283119
\(799\) −1474.82 −0.0653008
\(800\) 62739.0 2.77270
\(801\) 1941.01 0.0856209
\(802\) 49297.8 2.17053
\(803\) −49560.9 −2.17804
\(804\) −1396.92 −0.0612755
\(805\) 1939.85 0.0849324
\(806\) 0 0
\(807\) 11750.9 0.512577
\(808\) 60571.7 2.63726
\(809\) −2453.12 −0.106610 −0.0533048 0.998578i \(-0.516975\pi\)
−0.0533048 + 0.998578i \(0.516975\pi\)
\(810\) −1171.66 −0.0508247
\(811\) −5133.85 −0.222286 −0.111143 0.993804i \(-0.535451\pi\)
−0.111143 + 0.993804i \(0.535451\pi\)
\(812\) 81191.4 3.50894
\(813\) −8332.58 −0.359454
\(814\) 63039.4 2.71441
\(815\) −1064.81 −0.0457651
\(816\) 2517.83 0.108017
\(817\) 1356.01 0.0580673
\(818\) −49432.6 −2.11292
\(819\) 0 0
\(820\) 8766.61 0.373345
\(821\) −23854.0 −1.01402 −0.507009 0.861941i \(-0.669249\pi\)
−0.507009 + 0.861941i \(0.669249\pi\)
\(822\) 19393.8 0.822913
\(823\) 757.156 0.0320690 0.0160345 0.999871i \(-0.494896\pi\)
0.0160345 + 0.999871i \(0.494896\pi\)
\(824\) −85822.6 −3.62836
\(825\) 23623.0 0.996907
\(826\) −36302.2 −1.52919
\(827\) 28621.2 1.20345 0.601726 0.798702i \(-0.294480\pi\)
0.601726 + 0.798702i \(0.294480\pi\)
\(828\) 8850.68 0.371476
\(829\) 27429.2 1.14916 0.574582 0.818447i \(-0.305165\pi\)
0.574582 + 0.818447i \(0.305165\pi\)
\(830\) −8723.19 −0.364803
\(831\) 19749.2 0.824421
\(832\) 0 0
\(833\) −465.838 −0.0193761
\(834\) −5196.64 −0.215761
\(835\) −409.462 −0.0169701
\(836\) −36255.1 −1.49989
\(837\) 5568.54 0.229960
\(838\) 34840.7 1.43622
\(839\) −4633.62 −0.190668 −0.0953339 0.995445i \(-0.530392\pi\)
−0.0953339 + 0.995445i \(0.530392\pi\)
\(840\) −8431.27 −0.346317
\(841\) 41663.6 1.70829
\(842\) −16413.7 −0.671798
\(843\) 8614.98 0.351976
\(844\) −21813.0 −0.889614
\(845\) 0 0
\(846\) 17102.7 0.695041
\(847\) 47775.0 1.93810
\(848\) −2110.99 −0.0854853
\(849\) 22554.1 0.911726
\(850\) 2629.64 0.106113
\(851\) 8314.19 0.334908
\(852\) 17780.1 0.714947
\(853\) −14854.6 −0.596261 −0.298131 0.954525i \(-0.596363\pi\)
−0.298131 + 0.954525i \(0.596363\pi\)
\(854\) −9762.07 −0.391161
\(855\) 632.999 0.0253194
\(856\) 23421.9 0.935216
\(857\) −42799.5 −1.70595 −0.852977 0.521948i \(-0.825206\pi\)
−0.852977 + 0.521948i \(0.825206\pi\)
\(858\) 0 0
\(859\) −8246.47 −0.327551 −0.163775 0.986498i \(-0.552367\pi\)
−0.163775 + 0.986498i \(0.552367\pi\)
\(860\) 2912.70 0.115491
\(861\) 7135.85 0.282450
\(862\) −42580.1 −1.68246
\(863\) 17695.4 0.697983 0.348991 0.937126i \(-0.386524\pi\)
0.348991 + 0.937126i \(0.386524\pi\)
\(864\) −14388.5 −0.566558
\(865\) 1452.81 0.0571064
\(866\) −39132.3 −1.53553
\(867\) −14687.0 −0.575313
\(868\) 65154.2 2.54779
\(869\) 36631.4 1.42996
\(870\) −11152.8 −0.434615
\(871\) 0 0
\(872\) −53148.2 −2.06402
\(873\) 13027.5 0.505058
\(874\) −6622.49 −0.256303
\(875\) −9949.64 −0.384411
\(876\) 46193.8 1.78167
\(877\) −14346.8 −0.552401 −0.276200 0.961100i \(-0.589075\pi\)
−0.276200 + 0.961100i \(0.589075\pi\)
\(878\) −81622.7 −3.13739
\(879\) 13519.7 0.518781
\(880\) −36353.0 −1.39257
\(881\) −2063.51 −0.0789121 −0.0394560 0.999221i \(-0.512563\pi\)
−0.0394560 + 0.999221i \(0.512563\pi\)
\(882\) 5402.09 0.206233
\(883\) −34137.1 −1.30103 −0.650513 0.759495i \(-0.725446\pi\)
−0.650513 + 0.759495i \(0.725446\pi\)
\(884\) 0 0
\(885\) 3600.50 0.136756
\(886\) −8138.58 −0.308602
\(887\) −22238.5 −0.841821 −0.420910 0.907102i \(-0.638289\pi\)
−0.420910 + 0.907102i \(0.638289\pi\)
\(888\) −36136.5 −1.36561
\(889\) −16932.8 −0.638817
\(890\) −3119.63 −0.117495
\(891\) −5417.67 −0.203702
\(892\) 48075.0 1.80456
\(893\) −9239.89 −0.346250
\(894\) −18168.0 −0.679676
\(895\) −5987.96 −0.223637
\(896\) −36830.7 −1.37325
\(897\) 0 0
\(898\) 3783.45 0.140596
\(899\) 53005.7 1.96645
\(900\) −22018.1 −0.815486
\(901\) −43.6019 −0.00161220
\(902\) 56141.7 2.07241
\(903\) 2370.88 0.0873730
\(904\) −87694.9 −3.22643
\(905\) −10307.4 −0.378597
\(906\) 47324.0 1.73536
\(907\) −44160.3 −1.61667 −0.808335 0.588723i \(-0.799631\pi\)
−0.808335 + 0.588723i \(0.799631\pi\)
\(908\) 78953.8 2.88565
\(909\) −7951.05 −0.290121
\(910\) 0 0
\(911\) 11916.3 0.433376 0.216688 0.976241i \(-0.430475\pi\)
0.216688 + 0.976241i \(0.430475\pi\)
\(912\) 15774.4 0.572745
\(913\) −40335.3 −1.46211
\(914\) 39043.0 1.41294
\(915\) 968.215 0.0349816
\(916\) −89793.0 −3.23891
\(917\) 31927.1 1.14975
\(918\) −603.078 −0.0216825
\(919\) −20128.9 −0.722516 −0.361258 0.932466i \(-0.617653\pi\)
−0.361258 + 0.932466i \(0.617653\pi\)
\(920\) −8748.64 −0.313515
\(921\) 28616.7 1.02383
\(922\) −10525.0 −0.375945
\(923\) 0 0
\(924\) −63389.0 −2.25687
\(925\) −20683.5 −0.735210
\(926\) 55654.1 1.97506
\(927\) 11265.7 0.399151
\(928\) −136961. −4.84478
\(929\) −31428.4 −1.10994 −0.554969 0.831871i \(-0.687270\pi\)
−0.554969 + 0.831871i \(0.687270\pi\)
\(930\) −8949.86 −0.315567
\(931\) −2918.52 −0.102740
\(932\) 109715. 3.85605
\(933\) −22398.9 −0.785965
\(934\) −47150.1 −1.65182
\(935\) −750.863 −0.0262629
\(936\) 0 0
\(937\) 42473.2 1.48083 0.740416 0.672149i \(-0.234629\pi\)
0.740416 + 0.672149i \(0.234629\pi\)
\(938\) 1827.51 0.0636144
\(939\) −5464.94 −0.189927
\(940\) −19847.1 −0.688661
\(941\) −42644.0 −1.47732 −0.738659 0.674079i \(-0.764541\pi\)
−0.738659 + 0.674079i \(0.764541\pi\)
\(942\) −10129.5 −0.350357
\(943\) 7404.46 0.255697
\(944\) 89725.0 3.09354
\(945\) 1106.75 0.0380978
\(946\) 18653.0 0.641080
\(947\) 4282.95 0.146966 0.0734831 0.997296i \(-0.476588\pi\)
0.0734831 + 0.997296i \(0.476588\pi\)
\(948\) −34142.7 −1.16973
\(949\) 0 0
\(950\) 16475.0 0.562651
\(951\) 9375.42 0.319683
\(952\) −4339.74 −0.147744
\(953\) 40593.9 1.37982 0.689908 0.723897i \(-0.257651\pi\)
0.689908 + 0.723897i \(0.257651\pi\)
\(954\) 505.630 0.0171597
\(955\) 9340.54 0.316495
\(956\) 32166.1 1.08821
\(957\) −51569.6 −1.74191
\(958\) 59771.9 2.01581
\(959\) −18319.2 −0.616850
\(960\) 10081.1 0.338922
\(961\) 12744.8 0.427808
\(962\) 0 0
\(963\) −3074.52 −0.102882
\(964\) −102198. −3.41448
\(965\) 12665.7 0.422510
\(966\) −11578.9 −0.385656
\(967\) 17709.4 0.588931 0.294466 0.955662i \(-0.404858\pi\)
0.294466 + 0.955662i \(0.404858\pi\)
\(968\) −215464. −7.15420
\(969\) 325.818 0.0108016
\(970\) −20938.1 −0.693074
\(971\) 4038.97 0.133488 0.0667440 0.997770i \(-0.478739\pi\)
0.0667440 + 0.997770i \(0.478739\pi\)
\(972\) 5049.61 0.166632
\(973\) 4908.72 0.161733
\(974\) 105366. 3.46626
\(975\) 0 0
\(976\) 24128.1 0.791312
\(977\) −2764.30 −0.0905197 −0.0452598 0.998975i \(-0.514412\pi\)
−0.0452598 + 0.998975i \(0.514412\pi\)
\(978\) 6355.79 0.207807
\(979\) −14424.9 −0.470912
\(980\) −6268.93 −0.204340
\(981\) 6976.59 0.227060
\(982\) 18295.4 0.594531
\(983\) −17804.5 −0.577695 −0.288848 0.957375i \(-0.593272\pi\)
−0.288848 + 0.957375i \(0.593272\pi\)
\(984\) −32182.4 −1.04262
\(985\) −7786.65 −0.251881
\(986\) −5740.57 −0.185413
\(987\) −16155.2 −0.520997
\(988\) 0 0
\(989\) 2460.12 0.0790974
\(990\) 8707.39 0.279534
\(991\) −8129.69 −0.260593 −0.130297 0.991475i \(-0.541593\pi\)
−0.130297 + 0.991475i \(0.541593\pi\)
\(992\) −109908. −3.51772
\(993\) −4661.02 −0.148956
\(994\) −23260.7 −0.742237
\(995\) 169.893 0.00541302
\(996\) 37595.0 1.19603
\(997\) −29452.9 −0.935589 −0.467795 0.883837i \(-0.654951\pi\)
−0.467795 + 0.883837i \(0.654951\pi\)
\(998\) 26997.7 0.856309
\(999\) 4743.52 0.150229
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.r.1.1 10
3.2 odd 2 1521.4.a.bk.1.10 10
13.2 odd 12 39.4.j.c.4.1 10
13.5 odd 4 507.4.b.i.337.10 10
13.7 odd 12 39.4.j.c.10.1 yes 10
13.8 odd 4 507.4.b.i.337.1 10
13.12 even 2 inner 507.4.a.r.1.10 10
39.2 even 12 117.4.q.e.82.5 10
39.20 even 12 117.4.q.e.10.5 10
39.38 odd 2 1521.4.a.bk.1.1 10
52.7 even 12 624.4.bv.h.49.3 10
52.15 even 12 624.4.bv.h.433.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.1 10 13.2 odd 12
39.4.j.c.10.1 yes 10 13.7 odd 12
117.4.q.e.10.5 10 39.20 even 12
117.4.q.e.82.5 10 39.2 even 12
507.4.a.r.1.1 10 1.1 even 1 trivial
507.4.a.r.1.10 10 13.12 even 2 inner
507.4.b.i.337.1 10 13.8 odd 4
507.4.b.i.337.10 10 13.5 odd 4
624.4.bv.h.49.3 10 52.7 even 12
624.4.bv.h.433.3 10 52.15 even 12
1521.4.a.bk.1.1 10 39.38 odd 2
1521.4.a.bk.1.10 10 3.2 odd 2