Properties

Label 507.4.b.i.337.10
Level $507$
Weight $4$
Character 507.337
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.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
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: \( 2^{5}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.10
Root \(5.36472i\) of defining polynomial
Character \(\chi\) \(=\) 507.337
Dual form 507.4.b.i.337.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.36472i q^{2} +3.00000 q^{3} -20.7803 q^{4} -2.69631i q^{5} +16.0942i q^{6} +15.2025i q^{7} -68.5626i q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.36472i q^{2} +3.00000 q^{3} -20.7803 q^{4} -2.69631i q^{5} +16.0942i q^{6} +15.2025i q^{7} -68.5626i q^{8} +9.00000 q^{9} +14.4650 q^{10} -66.8848i q^{11} -62.3408 q^{12} -81.5570 q^{14} -8.08894i q^{15} +201.577 q^{16} -4.16354 q^{17} +48.2825i q^{18} -26.0850i q^{19} +56.0301i q^{20} +45.6074i q^{21} +358.819 q^{22} -47.3242 q^{23} -205.688i q^{24} +117.730 q^{25} +27.0000 q^{27} -315.911i q^{28} +257.007 q^{29} +43.3949 q^{30} -206.242i q^{31} +532.906i q^{32} -200.655i q^{33} -22.3362i q^{34} +40.9906 q^{35} -187.022 q^{36} +175.686i q^{37} +139.939 q^{38} -184.866 q^{40} -156.463i q^{41} -244.671 q^{42} -51.9845 q^{43} +1389.88i q^{44} -24.2668i q^{45} -253.881i q^{46} -354.222i q^{47} +604.732 q^{48} +111.885 q^{49} +631.588i q^{50} -12.4906 q^{51} -10.4723 q^{53} +144.848i q^{54} -180.342 q^{55} +1042.32 q^{56} -78.2550i q^{57} +1378.77i q^{58} +445.114i q^{59} +168.090i q^{60} +119.696 q^{61} +1106.43 q^{62} +136.822i q^{63} -1246.28 q^{64} +1076.46 q^{66} +22.4078i q^{67} +86.5195 q^{68} -141.973 q^{69} +219.903i q^{70} -285.207i q^{71} -617.064i q^{72} +740.989i q^{73} -942.507 q^{74} +353.190 q^{75} +542.053i q^{76} +1016.81 q^{77} -547.679 q^{79} -543.516i q^{80} +81.0000 q^{81} +839.378 q^{82} -603.056i q^{83} -947.734i q^{84} +11.2262i q^{85} -278.882i q^{86} +771.021 q^{87} -4585.80 q^{88} +215.668i q^{89} +130.185 q^{90} +983.409 q^{92} -618.726i q^{93} +1900.31 q^{94} -70.3333 q^{95} +1598.72i q^{96} -1447.50i q^{97} +600.233i q^{98} -601.964i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 30 q^{3} - 60 q^{4} + 90 q^{9}+O(q^{10}) \) 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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.36472i 1.89672i 0.317201 + 0.948358i \(0.397257\pi\)
−0.317201 + 0.948358i \(0.602743\pi\)
\(3\) 3.00000 0.577350
\(4\) −20.7803 −2.59753
\(5\) − 2.69631i − 0.241165i −0.992703 0.120583i \(-0.961524\pi\)
0.992703 0.120583i \(-0.0384763\pi\)
\(6\) 16.0942i 1.09507i
\(7\) 15.2025i 0.820856i 0.911893 + 0.410428i \(0.134621\pi\)
−0.911893 + 0.410428i \(0.865379\pi\)
\(8\) − 68.5626i − 3.03007i
\(9\) 9.00000 0.333333
\(10\) 14.4650 0.457423
\(11\) − 66.8848i − 1.83332i −0.399666 0.916661i \(-0.630874\pi\)
0.399666 0.916661i \(-0.369126\pi\)
\(12\) −62.3408 −1.49969
\(13\) 0 0
\(14\) −81.5570 −1.55693
\(15\) − 8.08894i − 0.139237i
\(16\) 201.577 3.14965
\(17\) −4.16354 −0.0594004 −0.0297002 0.999559i \(-0.509455\pi\)
−0.0297002 + 0.999559i \(0.509455\pi\)
\(18\) 48.2825i 0.632239i
\(19\) − 26.0850i − 0.314963i −0.987522 0.157482i \(-0.949662\pi\)
0.987522 0.157482i \(-0.0503375\pi\)
\(20\) 56.0301i 0.626436i
\(21\) 45.6074i 0.473921i
\(22\) 358.819 3.47729
\(23\) −47.3242 −0.429034 −0.214517 0.976720i \(-0.568818\pi\)
−0.214517 + 0.976720i \(0.568818\pi\)
\(24\) − 205.688i − 1.74941i
\(25\) 117.730 0.941839
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) − 315.911i − 2.13220i
\(29\) 257.007 1.64569 0.822845 0.568266i \(-0.192386\pi\)
0.822845 + 0.568266i \(0.192386\pi\)
\(30\) 43.3949 0.264093
\(31\) − 206.242i − 1.19491i −0.801903 0.597455i \(-0.796179\pi\)
0.801903 0.597455i \(-0.203821\pi\)
\(32\) 532.906i 2.94392i
\(33\) − 200.655i − 1.05847i
\(34\) − 22.3362i − 0.112666i
\(35\) 40.9906 0.197962
\(36\) −187.022 −0.865845
\(37\) 175.686i 0.780611i 0.920685 + 0.390305i \(0.127631\pi\)
−0.920685 + 0.390305i \(0.872369\pi\)
\(38\) 139.939 0.597396
\(39\) 0 0
\(40\) −184.866 −0.730748
\(41\) − 156.463i − 0.595984i −0.954568 0.297992i \(-0.903683\pi\)
0.954568 0.297992i \(-0.0963169\pi\)
\(42\) −244.671 −0.898895
\(43\) −51.9845 −0.184362 −0.0921809 0.995742i \(-0.529384\pi\)
−0.0921809 + 0.995742i \(0.529384\pi\)
\(44\) 1389.88i 4.76211i
\(45\) − 24.2668i − 0.0803885i
\(46\) − 253.881i − 0.813755i
\(47\) − 354.222i − 1.09933i −0.835384 0.549666i \(-0.814755\pi\)
0.835384 0.549666i \(-0.185245\pi\)
\(48\) 604.732 1.81845
\(49\) 111.885 0.326196
\(50\) 631.588i 1.78640i
\(51\) −12.4906 −0.0342948
\(52\) 0 0
\(53\) −10.4723 −0.0271412 −0.0135706 0.999908i \(-0.504320\pi\)
−0.0135706 + 0.999908i \(0.504320\pi\)
\(54\) 144.848i 0.365023i
\(55\) −180.342 −0.442134
\(56\) 1042.32 2.48725
\(57\) − 78.2550i − 0.181844i
\(58\) 1378.77i 3.12141i
\(59\) 445.114i 0.982185i 0.871107 + 0.491092i \(0.163402\pi\)
−0.871107 + 0.491092i \(0.836598\pi\)
\(60\) 168.090i 0.361673i
\(61\) 119.696 0.251238 0.125619 0.992079i \(-0.459908\pi\)
0.125619 + 0.992079i \(0.459908\pi\)
\(62\) 1106.43 2.26640
\(63\) 136.822i 0.273619i
\(64\) −1246.28 −2.43413
\(65\) 0 0
\(66\) 1076.46 2.00761
\(67\) 22.4078i 0.0408589i 0.999791 + 0.0204294i \(0.00650334\pi\)
−0.999791 + 0.0204294i \(0.993497\pi\)
\(68\) 86.5195 0.154295
\(69\) −141.973 −0.247703
\(70\) 219.903i 0.375478i
\(71\) − 285.207i − 0.476731i −0.971176 0.238365i \(-0.923388\pi\)
0.971176 0.238365i \(-0.0766116\pi\)
\(72\) − 617.064i − 1.01002i
\(73\) 740.989i 1.18803i 0.804454 + 0.594015i \(0.202458\pi\)
−0.804454 + 0.594015i \(0.797542\pi\)
\(74\) −942.507 −1.48060
\(75\) 353.190 0.543771
\(76\) 542.053i 0.818128i
\(77\) 1016.81 1.50489
\(78\) 0 0
\(79\) −547.679 −0.779983 −0.389992 0.920818i \(-0.627522\pi\)
−0.389992 + 0.920818i \(0.627522\pi\)
\(80\) − 543.516i − 0.759586i
\(81\) 81.0000 0.111111
\(82\) 839.378 1.13041
\(83\) − 603.056i − 0.797518i −0.917056 0.398759i \(-0.869441\pi\)
0.917056 0.398759i \(-0.130559\pi\)
\(84\) − 947.734i − 1.23103i
\(85\) 11.2262i 0.0143253i
\(86\) − 278.882i − 0.349682i
\(87\) 771.021 0.950139
\(88\) −4585.80 −5.55509
\(89\) 215.668i 0.256863i 0.991718 + 0.128431i \(0.0409942\pi\)
−0.991718 + 0.128431i \(0.959006\pi\)
\(90\) 130.185 0.152474
\(91\) 0 0
\(92\) 983.409 1.11443
\(93\) − 618.726i − 0.689881i
\(94\) 1900.31 2.08512
\(95\) −70.3333 −0.0759583
\(96\) 1598.72i 1.69967i
\(97\) − 1447.50i − 1.51517i −0.652735 0.757586i \(-0.726378\pi\)
0.652735 0.757586i \(-0.273622\pi\)
\(98\) 600.233i 0.618700i
\(99\) − 601.964i − 0.611107i
\(100\) −2446.46 −2.44646
\(101\) 883.450 0.870362 0.435181 0.900343i \(-0.356684\pi\)
0.435181 + 0.900343i \(0.356684\pi\)
\(102\) − 67.0087i − 0.0650476i
\(103\) −1251.74 −1.19745 −0.598726 0.800954i \(-0.704326\pi\)
−0.598726 + 0.800954i \(0.704326\pi\)
\(104\) 0 0
\(105\) 122.972 0.114293
\(106\) − 56.1812i − 0.0514792i
\(107\) −341.614 −0.308645 −0.154323 0.988021i \(-0.549319\pi\)
−0.154323 + 0.988021i \(0.549319\pi\)
\(108\) −561.067 −0.499896
\(109\) − 775.177i − 0.681179i −0.940212 0.340589i \(-0.889373\pi\)
0.940212 0.340589i \(-0.110627\pi\)
\(110\) − 967.487i − 0.838603i
\(111\) 527.058i 0.450686i
\(112\) 3064.47i 2.58541i
\(113\) 1279.05 1.06480 0.532402 0.846492i \(-0.321290\pi\)
0.532402 + 0.846492i \(0.321290\pi\)
\(114\) 419.816 0.344907
\(115\) 127.601i 0.103468i
\(116\) −5340.67 −4.27473
\(117\) 0 0
\(118\) −2387.91 −1.86293
\(119\) − 63.2961i − 0.0487592i
\(120\) −554.599 −0.421898
\(121\) −3142.58 −2.36107
\(122\) 642.137i 0.476528i
\(123\) − 469.388i − 0.344091i
\(124\) 4285.77i 3.10382i
\(125\) − 654.476i − 0.468305i
\(126\) −734.013 −0.518977
\(127\) 1113.82 0.778233 0.389117 0.921188i \(-0.372780\pi\)
0.389117 + 0.921188i \(0.372780\pi\)
\(128\) − 2422.68i − 1.67294i
\(129\) −155.953 −0.106441
\(130\) 0 0
\(131\) 2100.12 1.40068 0.700339 0.713811i \(-0.253032\pi\)
0.700339 + 0.713811i \(0.253032\pi\)
\(132\) 4169.65i 2.74941i
\(133\) 396.556 0.258540
\(134\) −120.211 −0.0774977
\(135\) − 72.8004i − 0.0464123i
\(136\) 285.463i 0.179987i
\(137\) − 1205.02i − 0.751471i −0.926727 0.375736i \(-0.877390\pi\)
0.926727 0.375736i \(-0.122610\pi\)
\(138\) − 761.643i − 0.469822i
\(139\) 322.890 0.197030 0.0985149 0.995136i \(-0.468591\pi\)
0.0985149 + 0.995136i \(0.468591\pi\)
\(140\) −851.796 −0.514213
\(141\) − 1062.67i − 0.634700i
\(142\) 1530.06 0.904223
\(143\) 0 0
\(144\) 1814.20 1.04988
\(145\) − 692.971i − 0.396884i
\(146\) −3975.20 −2.25336
\(147\) 335.655 0.188329
\(148\) − 3650.80i − 2.02766i
\(149\) − 1128.86i − 0.620669i −0.950627 0.310335i \(-0.899559\pi\)
0.950627 0.310335i \(-0.100441\pi\)
\(150\) 1894.77i 1.03138i
\(151\) − 2940.44i − 1.58470i −0.610066 0.792350i \(-0.708857\pi\)
0.610066 0.792350i \(-0.291143\pi\)
\(152\) −1788.46 −0.954361
\(153\) −37.4719 −0.0198001
\(154\) 5454.93i 2.85436i
\(155\) −556.093 −0.288171
\(156\) 0 0
\(157\) 629.388 0.319940 0.159970 0.987122i \(-0.448860\pi\)
0.159970 + 0.987122i \(0.448860\pi\)
\(158\) − 2938.15i − 1.47941i
\(159\) −31.4170 −0.0156700
\(160\) 1436.88 0.709972
\(161\) − 719.444i − 0.352175i
\(162\) 434.543i 0.210746i
\(163\) − 394.912i − 0.189766i −0.995488 0.0948832i \(-0.969752\pi\)
0.995488 0.0948832i \(-0.0302478\pi\)
\(164\) 3251.33i 1.54809i
\(165\) −541.027 −0.255266
\(166\) 3235.23 1.51267
\(167\) − 151.860i − 0.0703669i −0.999381 0.0351834i \(-0.988798\pi\)
0.999381 0.0351834i \(-0.0112015\pi\)
\(168\) 3126.96 1.43601
\(169\) 0 0
\(170\) −60.2255 −0.0271711
\(171\) − 234.765i − 0.104988i
\(172\) 1080.25 0.478886
\(173\) −538.813 −0.236793 −0.118397 0.992966i \(-0.537775\pi\)
−0.118397 + 0.992966i \(0.537775\pi\)
\(174\) 4136.31i 1.80214i
\(175\) 1789.78i 0.773114i
\(176\) − 13482.5i − 5.77432i
\(177\) 1335.34i 0.567065i
\(178\) −1157.00 −0.487196
\(179\) 2220.80 0.927319 0.463659 0.886014i \(-0.346536\pi\)
0.463659 + 0.886014i \(0.346536\pi\)
\(180\) 504.271i 0.208812i
\(181\) 3822.78 1.56986 0.784932 0.619582i \(-0.212698\pi\)
0.784932 + 0.619582i \(0.212698\pi\)
\(182\) 0 0
\(183\) 359.089 0.145052
\(184\) 3244.67i 1.30000i
\(185\) 473.704 0.188256
\(186\) 3319.30 1.30851
\(187\) 278.478i 0.108900i
\(188\) 7360.84i 2.85555i
\(189\) 410.467i 0.157974i
\(190\) − 377.319i − 0.144071i
\(191\) 3464.19 1.31236 0.656178 0.754606i \(-0.272172\pi\)
0.656178 + 0.754606i \(0.272172\pi\)
\(192\) −3738.83 −1.40535
\(193\) 4697.40i 1.75195i 0.482357 + 0.875975i \(0.339781\pi\)
−0.482357 + 0.875975i \(0.660219\pi\)
\(194\) 7765.46 2.87385
\(195\) 0 0
\(196\) −2325.00 −0.847304
\(197\) 2887.89i 1.04443i 0.852813 + 0.522217i \(0.174895\pi\)
−0.852813 + 0.522217i \(0.825105\pi\)
\(198\) 3229.37 1.15910
\(199\) −63.0092 −0.0224453 −0.0112226 0.999937i \(-0.503572\pi\)
−0.0112226 + 0.999937i \(0.503572\pi\)
\(200\) − 8071.87i − 2.85384i
\(201\) 67.2233i 0.0235899i
\(202\) 4739.47i 1.65083i
\(203\) 3907.14i 1.35087i
\(204\) 259.558 0.0890820
\(205\) −421.872 −0.143731
\(206\) − 6715.24i − 2.27123i
\(207\) −425.918 −0.143011
\(208\) 0 0
\(209\) −1744.69 −0.577429
\(210\) 659.710i 0.216782i
\(211\) −1049.70 −0.342484 −0.171242 0.985229i \(-0.554778\pi\)
−0.171242 + 0.985229i \(0.554778\pi\)
\(212\) 217.618 0.0705002
\(213\) − 855.622i − 0.275241i
\(214\) − 1832.66i − 0.585412i
\(215\) 140.166i 0.0444617i
\(216\) − 1851.19i − 0.583137i
\(217\) 3135.39 0.980848
\(218\) 4158.61 1.29200
\(219\) 2222.97i 0.685909i
\(220\) 3747.56 1.14846
\(221\) 0 0
\(222\) −2827.52 −0.854823
\(223\) − 2313.49i − 0.694722i −0.937732 0.347361i \(-0.887078\pi\)
0.937732 0.347361i \(-0.112922\pi\)
\(224\) −8101.49 −2.41653
\(225\) 1059.57 0.313946
\(226\) 6861.74i 2.01963i
\(227\) − 3799.46i − 1.11092i −0.831543 0.555460i \(-0.812542\pi\)
0.831543 0.555460i \(-0.187458\pi\)
\(228\) 1626.16i 0.472347i
\(229\) − 4321.07i − 1.24692i −0.781856 0.623459i \(-0.785727\pi\)
0.781856 0.623459i \(-0.214273\pi\)
\(230\) −684.543 −0.196250
\(231\) 3050.44 0.868850
\(232\) − 17621.1i − 4.98655i
\(233\) −5279.77 −1.48450 −0.742251 0.670122i \(-0.766242\pi\)
−0.742251 + 0.670122i \(0.766242\pi\)
\(234\) 0 0
\(235\) −955.094 −0.265121
\(236\) − 9249.59i − 2.55126i
\(237\) −1643.04 −0.450323
\(238\) 339.566 0.0924823
\(239\) − 1547.92i − 0.418939i −0.977815 0.209469i \(-0.932826\pi\)
0.977815 0.209469i \(-0.0671737\pi\)
\(240\) − 1630.55i − 0.438547i
\(241\) − 4918.01i − 1.31451i −0.753669 0.657255i \(-0.771718\pi\)
0.753669 0.657255i \(-0.228282\pi\)
\(242\) − 16859.1i − 4.47828i
\(243\) 243.000 0.0641500
\(244\) −2487.32 −0.652600
\(245\) − 301.677i − 0.0786671i
\(246\) 2518.14 0.652644
\(247\) 0 0
\(248\) −14140.5 −3.62066
\(249\) − 1809.17i − 0.460447i
\(250\) 3511.08 0.888241
\(251\) −1155.78 −0.290646 −0.145323 0.989384i \(-0.546422\pi\)
−0.145323 + 0.989384i \(0.546422\pi\)
\(252\) − 2843.20i − 0.710734i
\(253\) 3165.27i 0.786556i
\(254\) 5975.34i 1.47609i
\(255\) 33.6786i 0.00827073i
\(256\) 3026.80 0.738965
\(257\) −2351.95 −0.570859 −0.285429 0.958400i \(-0.592136\pi\)
−0.285429 + 0.958400i \(0.592136\pi\)
\(258\) − 836.647i − 0.201889i
\(259\) −2670.86 −0.640769
\(260\) 0 0
\(261\) 2313.06 0.548563
\(262\) 11266.6i 2.65669i
\(263\) 5521.88 1.29465 0.647326 0.762213i \(-0.275887\pi\)
0.647326 + 0.762213i \(0.275887\pi\)
\(264\) −13757.4 −3.20723
\(265\) 28.2367i 0.00654553i
\(266\) 2127.41i 0.490376i
\(267\) 647.004i 0.148300i
\(268\) − 465.639i − 0.106132i
\(269\) 3916.95 0.887810 0.443905 0.896074i \(-0.353593\pi\)
0.443905 + 0.896074i \(0.353593\pi\)
\(270\) 390.554 0.0880310
\(271\) − 2777.53i − 0.622593i −0.950313 0.311297i \(-0.899237\pi\)
0.950313 0.311297i \(-0.100763\pi\)
\(272\) −839.276 −0.187090
\(273\) 0 0
\(274\) 6464.58 1.42533
\(275\) − 7874.34i − 1.72669i
\(276\) 2950.23 0.643416
\(277\) −6583.08 −1.42794 −0.713969 0.700177i \(-0.753104\pi\)
−0.713969 + 0.700177i \(0.753104\pi\)
\(278\) 1732.21i 0.373710i
\(279\) − 1856.18i − 0.398303i
\(280\) − 2810.42i − 0.599839i
\(281\) 2871.66i 0.609640i 0.952410 + 0.304820i \(0.0985963\pi\)
−0.952410 + 0.304820i \(0.901404\pi\)
\(282\) 5700.92 1.20385
\(283\) −7518.04 −1.57916 −0.789578 0.613651i \(-0.789700\pi\)
−0.789578 + 0.613651i \(0.789700\pi\)
\(284\) 5926.69i 1.23832i
\(285\) −211.000 −0.0438546
\(286\) 0 0
\(287\) 2378.62 0.489217
\(288\) 4796.16i 0.981307i
\(289\) −4895.66 −0.996472
\(290\) 3717.60 0.752776
\(291\) − 4342.51i − 0.874785i
\(292\) − 15397.9i − 3.08595i
\(293\) 4506.57i 0.898555i 0.893392 + 0.449278i \(0.148319\pi\)
−0.893392 + 0.449278i \(0.851681\pi\)
\(294\) 1800.70i 0.357207i
\(295\) 1200.17 0.236869
\(296\) 12045.5 2.36530
\(297\) − 1805.89i − 0.352823i
\(298\) 6056.02 1.17723
\(299\) 0 0
\(300\) −7339.38 −1.41246
\(301\) − 790.292i − 0.151335i
\(302\) 15774.7 3.00573
\(303\) 2650.35 0.502504
\(304\) − 5258.15i − 0.992024i
\(305\) − 322.738i − 0.0605900i
\(306\) − 201.026i − 0.0375552i
\(307\) 9538.89i 1.77333i 0.462409 + 0.886667i \(0.346985\pi\)
−0.462409 + 0.886667i \(0.653015\pi\)
\(308\) −21129.7 −3.90901
\(309\) −3755.22 −0.691350
\(310\) − 2983.29i − 0.546578i
\(311\) 7466.28 1.36133 0.680666 0.732594i \(-0.261691\pi\)
0.680666 + 0.732594i \(0.261691\pi\)
\(312\) 0 0
\(313\) −1821.65 −0.328964 −0.164482 0.986380i \(-0.552595\pi\)
−0.164482 + 0.986380i \(0.552595\pi\)
\(314\) 3376.49i 0.606836i
\(315\) 368.915 0.0659874
\(316\) 11380.9 2.02603
\(317\) − 3125.14i − 0.553708i −0.960912 0.276854i \(-0.910708\pi\)
0.960912 0.276854i \(-0.0892918\pi\)
\(318\) − 168.543i − 0.0297215i
\(319\) − 17189.9i − 3.01708i
\(320\) 3360.35i 0.587029i
\(321\) −1024.84 −0.178196
\(322\) 3859.62 0.667976
\(323\) 108.606i 0.0187090i
\(324\) −1683.20 −0.288615
\(325\) 0 0
\(326\) 2118.60 0.359933
\(327\) − 2325.53i − 0.393279i
\(328\) −10727.5 −1.80587
\(329\) 5385.05 0.902394
\(330\) − 2902.46i − 0.484167i
\(331\) 1553.67i 0.257999i 0.991645 + 0.128999i \(0.0411765\pi\)
−0.991645 + 0.128999i \(0.958823\pi\)
\(332\) 12531.7i 2.07158i
\(333\) 1581.17i 0.260204i
\(334\) 814.686 0.133466
\(335\) 60.4183 0.00985375
\(336\) 9193.42i 1.49269i
\(337\) 3190.43 0.515709 0.257855 0.966184i \(-0.416984\pi\)
0.257855 + 0.966184i \(0.416984\pi\)
\(338\) 0 0
\(339\) 3837.15 0.614764
\(340\) − 233.283i − 0.0372105i
\(341\) −13794.5 −2.19065
\(342\) 1259.45 0.199132
\(343\) 6915.37i 1.08862i
\(344\) 3564.19i 0.558629i
\(345\) 382.802i 0.0597373i
\(346\) − 2890.59i − 0.449130i
\(347\) −5718.68 −0.884712 −0.442356 0.896840i \(-0.645857\pi\)
−0.442356 + 0.896840i \(0.645857\pi\)
\(348\) −16022.0 −2.46802
\(349\) − 3328.46i − 0.510511i −0.966874 0.255256i \(-0.917840\pi\)
0.966874 0.255256i \(-0.0821596\pi\)
\(350\) −9601.70 −1.46638
\(351\) 0 0
\(352\) 35643.4 5.39715
\(353\) 12306.5i 1.85555i 0.373142 + 0.927774i \(0.378281\pi\)
−0.373142 + 0.927774i \(0.621719\pi\)
\(354\) −7163.74 −1.07556
\(355\) −769.008 −0.114971
\(356\) − 4481.64i − 0.667210i
\(357\) − 189.888i − 0.0281511i
\(358\) 11914.0i 1.75886i
\(359\) 8539.97i 1.25549i 0.778418 + 0.627747i \(0.216023\pi\)
−0.778418 + 0.627747i \(0.783977\pi\)
\(360\) −1663.80 −0.243583
\(361\) 6178.57 0.900798
\(362\) 20508.2i 2.97759i
\(363\) −9427.74 −1.36316
\(364\) 0 0
\(365\) 1997.94 0.286512
\(366\) 1926.41i 0.275123i
\(367\) 2496.65 0.355107 0.177553 0.984111i \(-0.443182\pi\)
0.177553 + 0.984111i \(0.443182\pi\)
\(368\) −9539.49 −1.35130
\(369\) − 1408.16i − 0.198661i
\(370\) 2541.29i 0.357069i
\(371\) − 159.205i − 0.0222790i
\(372\) 12857.3i 1.79199i
\(373\) −1142.91 −0.158653 −0.0793264 0.996849i \(-0.525277\pi\)
−0.0793264 + 0.996849i \(0.525277\pi\)
\(374\) −1493.96 −0.206552
\(375\) − 1963.43i − 0.270376i
\(376\) −24286.4 −3.33105
\(377\) 0 0
\(378\) −2202.04 −0.299632
\(379\) 12181.8i 1.65102i 0.564384 + 0.825512i \(0.309114\pi\)
−0.564384 + 0.825512i \(0.690886\pi\)
\(380\) 1461.54 0.197304
\(381\) 3341.46 0.449313
\(382\) 18584.4i 2.48917i
\(383\) 10180.6i 1.35824i 0.734029 + 0.679118i \(0.237638\pi\)
−0.734029 + 0.679118i \(0.762362\pi\)
\(384\) − 7268.04i − 0.965874i
\(385\) − 2741.65i − 0.362928i
\(386\) −25200.3 −3.32295
\(387\) −467.860 −0.0614539
\(388\) 30079.5i 3.93571i
\(389\) −5845.83 −0.761941 −0.380971 0.924587i \(-0.624410\pi\)
−0.380971 + 0.924587i \(0.624410\pi\)
\(390\) 0 0
\(391\) 197.036 0.0254848
\(392\) − 7671.13i − 0.988395i
\(393\) 6300.37 0.808681
\(394\) −15492.7 −1.98100
\(395\) 1476.71i 0.188105i
\(396\) 12509.0i 1.58737i
\(397\) − 2500.92i − 0.316166i −0.987426 0.158083i \(-0.949469\pi\)
0.987426 0.158083i \(-0.0505313\pi\)
\(398\) − 338.027i − 0.0425723i
\(399\) 1189.67 0.149268
\(400\) 23731.7 2.96646
\(401\) − 9189.25i − 1.14436i −0.820127 0.572181i \(-0.806098\pi\)
0.820127 0.572181i \(-0.193902\pi\)
\(402\) −360.634 −0.0447433
\(403\) 0 0
\(404\) −18358.3 −2.26080
\(405\) − 218.401i − 0.0267962i
\(406\) −20960.7 −2.56223
\(407\) 11750.7 1.43111
\(408\) 856.390i 0.103916i
\(409\) − 9214.38i − 1.11399i −0.830516 0.556995i \(-0.811954\pi\)
0.830516 0.556995i \(-0.188046\pi\)
\(410\) − 2263.23i − 0.272617i
\(411\) − 3615.05i − 0.433862i
\(412\) 26011.5 3.11042
\(413\) −6766.83 −0.806232
\(414\) − 2284.93i − 0.271252i
\(415\) −1626.03 −0.192334
\(416\) 0 0
\(417\) 968.669 0.113755
\(418\) − 9359.78i − 1.09522i
\(419\) −6494.41 −0.757214 −0.378607 0.925558i \(-0.623597\pi\)
−0.378607 + 0.925558i \(0.623597\pi\)
\(420\) −2555.39 −0.296881
\(421\) − 3059.56i − 0.354190i −0.984194 0.177095i \(-0.943330\pi\)
0.984194 0.177095i \(-0.0566699\pi\)
\(422\) − 5631.33i − 0.649595i
\(423\) − 3188.00i − 0.366444i
\(424\) 718.010i 0.0822398i
\(425\) −490.173 −0.0559456
\(426\) 4590.18 0.522054
\(427\) 1819.68i 0.206230i
\(428\) 7098.82 0.801716
\(429\) 0 0
\(430\) −751.954 −0.0843313
\(431\) − 7937.05i − 0.887040i −0.896264 0.443520i \(-0.853729\pi\)
0.896264 0.443520i \(-0.146271\pi\)
\(432\) 5442.59 0.606150
\(433\) −7294.37 −0.809573 −0.404786 0.914411i \(-0.632654\pi\)
−0.404786 + 0.914411i \(0.632654\pi\)
\(434\) 16820.5i 1.86039i
\(435\) − 2078.91i − 0.229141i
\(436\) 16108.4i 1.76938i
\(437\) 1234.45i 0.135130i
\(438\) −11925.6 −1.30098
\(439\) −15214.7 −1.65412 −0.827059 0.562115i \(-0.809988\pi\)
−0.827059 + 0.562115i \(0.809988\pi\)
\(440\) 12364.7i 1.33970i
\(441\) 1006.97 0.108732
\(442\) 0 0
\(443\) 1517.05 0.162703 0.0813515 0.996685i \(-0.474076\pi\)
0.0813515 + 0.996685i \(0.474076\pi\)
\(444\) − 10952.4i − 1.17067i
\(445\) 581.509 0.0619464
\(446\) 12411.3 1.31769
\(447\) − 3386.58i − 0.358343i
\(448\) − 18946.5i − 1.99807i
\(449\) − 705.247i − 0.0741262i −0.999313 0.0370631i \(-0.988200\pi\)
0.999313 0.0370631i \(-0.0118002\pi\)
\(450\) 5684.30i 0.595467i
\(451\) −10465.0 −1.09263
\(452\) −26579.0 −2.76586
\(453\) − 8821.33i − 0.914927i
\(454\) 20383.1 2.10710
\(455\) 0 0
\(456\) −5365.37 −0.551001
\(457\) 7277.73i 0.744940i 0.928044 + 0.372470i \(0.121489\pi\)
−0.928044 + 0.372470i \(0.878511\pi\)
\(458\) 23181.4 2.36505
\(459\) −112.416 −0.0114316
\(460\) − 2651.58i − 0.268762i
\(461\) − 1961.88i − 0.198208i −0.995077 0.0991041i \(-0.968402\pi\)
0.995077 0.0991041i \(-0.0315977\pi\)
\(462\) 16364.8i 1.64796i
\(463\) − 10374.1i − 1.04131i −0.853768 0.520653i \(-0.825689\pi\)
0.853768 0.520653i \(-0.174311\pi\)
\(464\) 51806.8 5.18334
\(465\) −1668.28 −0.166376
\(466\) − 28324.5i − 2.81568i
\(467\) −8788.92 −0.870883 −0.435442 0.900217i \(-0.643408\pi\)
−0.435442 + 0.900217i \(0.643408\pi\)
\(468\) 0 0
\(469\) −340.653 −0.0335392
\(470\) − 5123.82i − 0.502860i
\(471\) 1888.16 0.184718
\(472\) 30518.2 2.97609
\(473\) 3476.97i 0.337995i
\(474\) − 8814.44i − 0.854136i
\(475\) − 3070.98i − 0.296645i
\(476\) 1315.31i 0.126654i
\(477\) −94.2510 −0.00904707
\(478\) 8304.14 0.794608
\(479\) − 11141.7i − 1.06279i −0.847125 0.531394i \(-0.821668\pi\)
0.847125 0.531394i \(-0.178332\pi\)
\(480\) 4310.65 0.409903
\(481\) 0 0
\(482\) 26383.8 2.49325
\(483\) − 2158.33i − 0.203328i
\(484\) 65303.7 6.13295
\(485\) −3902.92 −0.365407
\(486\) 1303.63i 0.121674i
\(487\) 19640.5i 1.82750i 0.406273 + 0.913752i \(0.366828\pi\)
−0.406273 + 0.913752i \(0.633172\pi\)
\(488\) − 8206.69i − 0.761269i
\(489\) − 1184.74i − 0.109562i
\(490\) 1618.41 0.149209
\(491\) 3410.31 0.313453 0.156726 0.987642i \(-0.449906\pi\)
0.156726 + 0.987642i \(0.449906\pi\)
\(492\) 9754.00i 0.893789i
\(493\) −1070.06 −0.0977546
\(494\) 0 0
\(495\) −1623.08 −0.147378
\(496\) − 41573.8i − 3.76354i
\(497\) 4335.86 0.391327
\(498\) 9705.68 0.873338
\(499\) 5032.44i 0.451469i 0.974189 + 0.225735i \(0.0724782\pi\)
−0.974189 + 0.225735i \(0.927522\pi\)
\(500\) 13600.2i 1.21644i
\(501\) − 455.580i − 0.0406263i
\(502\) − 6200.44i − 0.551274i
\(503\) 17189.4 1.52373 0.761866 0.647735i \(-0.224284\pi\)
0.761866 + 0.647735i \(0.224284\pi\)
\(504\) 9380.89 0.829083
\(505\) − 2382.06i − 0.209901i
\(506\) −16980.8 −1.49187
\(507\) 0 0
\(508\) −23145.5 −2.02149
\(509\) 930.560i 0.0810341i 0.999179 + 0.0405170i \(0.0129005\pi\)
−0.999179 + 0.0405170i \(0.987099\pi\)
\(510\) −180.676 −0.0156872
\(511\) −11264.9 −0.975201
\(512\) − 3143.50i − 0.271337i
\(513\) − 704.295i − 0.0606148i
\(514\) − 12617.6i − 1.08276i
\(515\) 3375.08i 0.288784i
\(516\) 3240.75 0.276485
\(517\) −23692.1 −2.01543
\(518\) − 14328.4i − 1.21536i
\(519\) −1616.44 −0.136713
\(520\) 0 0
\(521\) −9869.60 −0.829933 −0.414966 0.909837i \(-0.636207\pi\)
−0.414966 + 0.909837i \(0.636207\pi\)
\(522\) 12408.9i 1.04047i
\(523\) −21420.6 −1.79093 −0.895466 0.445129i \(-0.853158\pi\)
−0.895466 + 0.445129i \(0.853158\pi\)
\(524\) −43641.1 −3.63831
\(525\) 5369.35i 0.446358i
\(526\) 29623.4i 2.45559i
\(527\) 858.697i 0.0709781i
\(528\) − 40447.4i − 3.33380i
\(529\) −9927.42 −0.815930
\(530\) −151.482 −0.0124150
\(531\) 4006.03i 0.327395i
\(532\) −8240.54 −0.671565
\(533\) 0 0
\(534\) −3471.00 −0.281283
\(535\) 921.097i 0.0744345i
\(536\) 1536.34 0.123805
\(537\) 6662.39 0.535388
\(538\) 21013.4i 1.68392i
\(539\) − 7483.41i − 0.598021i
\(540\) 1512.81i 0.120558i
\(541\) 7771.50i 0.617602i 0.951127 + 0.308801i \(0.0999277\pi\)
−0.951127 + 0.308801i \(0.900072\pi\)
\(542\) 14900.7 1.18088
\(543\) 11468.3 0.906361
\(544\) − 2218.78i − 0.174870i
\(545\) −2090.12 −0.164277
\(546\) 0 0
\(547\) −15577.5 −1.21763 −0.608817 0.793310i \(-0.708356\pi\)
−0.608817 + 0.793310i \(0.708356\pi\)
\(548\) 25040.6i 1.95197i
\(549\) 1077.27 0.0837461
\(550\) 42243.7 3.27505
\(551\) − 6704.02i − 0.518332i
\(552\) 9734.01i 0.750556i
\(553\) − 8326.07i − 0.640254i
\(554\) − 35316.4i − 2.70840i
\(555\) 1421.11 0.108690
\(556\) −6709.74 −0.511792
\(557\) − 22804.5i − 1.73475i −0.497652 0.867377i \(-0.665804\pi\)
0.497652 0.867377i \(-0.334196\pi\)
\(558\) 9957.89 0.755468
\(559\) 0 0
\(560\) 8262.78 0.623511
\(561\) 835.433i 0.0628734i
\(562\) −15405.7 −1.15631
\(563\) 3517.41 0.263306 0.131653 0.991296i \(-0.457972\pi\)
0.131653 + 0.991296i \(0.457972\pi\)
\(564\) 22082.5i 1.64865i
\(565\) − 3448.71i − 0.256794i
\(566\) − 40332.2i − 2.99521i
\(567\) 1231.40i 0.0912062i
\(568\) −19554.6 −1.44453
\(569\) 6093.44 0.448946 0.224473 0.974480i \(-0.427934\pi\)
0.224473 + 0.974480i \(0.427934\pi\)
\(570\) − 1131.96i − 0.0831797i
\(571\) −10460.2 −0.766630 −0.383315 0.923618i \(-0.625218\pi\)
−0.383315 + 0.923618i \(0.625218\pi\)
\(572\) 0 0
\(573\) 10392.6 0.757689
\(574\) 12760.6i 0.927906i
\(575\) −5571.47 −0.404081
\(576\) −11216.5 −0.811378
\(577\) 9648.19i 0.696117i 0.937473 + 0.348058i \(0.113159\pi\)
−0.937473 + 0.348058i \(0.886841\pi\)
\(578\) − 26263.9i − 1.89002i
\(579\) 14092.2i 1.01149i
\(580\) 14400.1i 1.03092i
\(581\) 9167.93 0.654647
\(582\) 23296.4 1.65922
\(583\) 700.440i 0.0497586i
\(584\) 50804.1 3.59981
\(585\) 0 0
\(586\) −24176.5 −1.70430
\(587\) − 2170.73i − 0.152633i −0.997084 0.0763166i \(-0.975684\pi\)
0.997084 0.0763166i \(-0.0243160\pi\)
\(588\) −6975.01 −0.489191
\(589\) −5379.82 −0.376353
\(590\) 6438.56i 0.449274i
\(591\) 8663.66i 0.603004i
\(592\) 35414.3i 2.45865i
\(593\) 22885.9i 1.58484i 0.609975 + 0.792421i \(0.291180\pi\)
−0.609975 + 0.792421i \(0.708820\pi\)
\(594\) 9688.11 0.669205
\(595\) −170.666 −0.0117590
\(596\) 23458.0i 1.61221i
\(597\) −189.028 −0.0129588
\(598\) 0 0
\(599\) −23978.7 −1.63563 −0.817815 0.575482i \(-0.804815\pi\)
−0.817815 + 0.575482i \(0.804815\pi\)
\(600\) − 24215.6i − 1.64766i
\(601\) 12873.2 0.873728 0.436864 0.899528i \(-0.356089\pi\)
0.436864 + 0.899528i \(0.356089\pi\)
\(602\) 4239.70 0.287039
\(603\) 201.670i 0.0136196i
\(604\) 61103.2i 4.11631i
\(605\) 8473.38i 0.569408i
\(606\) 14218.4i 0.953107i
\(607\) −7117.15 −0.475908 −0.237954 0.971276i \(-0.576477\pi\)
−0.237954 + 0.971276i \(0.576477\pi\)
\(608\) 13900.9 0.927227
\(609\) 11721.4i 0.779927i
\(610\) 1731.40 0.114922
\(611\) 0 0
\(612\) 778.675 0.0514315
\(613\) − 173.297i − 0.0114183i −0.999984 0.00570913i \(-0.998183\pi\)
0.999984 0.00570913i \(-0.00181728\pi\)
\(614\) −51173.5 −3.36351
\(615\) −1265.62 −0.0829830
\(616\) − 69715.5i − 4.55993i
\(617\) 6102.75i 0.398197i 0.979979 + 0.199099i \(0.0638014\pi\)
−0.979979 + 0.199099i \(0.936199\pi\)
\(618\) − 20145.7i − 1.31129i
\(619\) − 14867.8i − 0.965409i −0.875783 0.482705i \(-0.839654\pi\)
0.875783 0.482705i \(-0.160346\pi\)
\(620\) 11555.8 0.748534
\(621\) −1277.75 −0.0825676
\(622\) 40054.6i 2.58206i
\(623\) −3278.69 −0.210847
\(624\) 0 0
\(625\) 12951.6 0.828900
\(626\) − 9772.64i − 0.623951i
\(627\) −5234.07 −0.333379
\(628\) −13078.9 −0.831056
\(629\) − 731.475i − 0.0463686i
\(630\) 1979.13i 0.125159i
\(631\) − 17210.6i − 1.08580i −0.839796 0.542902i \(-0.817325\pi\)
0.839796 0.542902i \(-0.182675\pi\)
\(632\) 37550.3i 2.36340i
\(633\) −3149.09 −0.197733
\(634\) 16765.5 1.05023
\(635\) − 3003.21i − 0.187683i
\(636\) 652.853 0.0407033
\(637\) 0 0
\(638\) 92218.9 5.72254
\(639\) − 2566.87i − 0.158910i
\(640\) −6532.30 −0.403456
\(641\) 12636.0 0.778616 0.389308 0.921108i \(-0.372714\pi\)
0.389308 + 0.921108i \(0.372714\pi\)
\(642\) − 5497.99i − 0.337988i
\(643\) 9586.37i 0.587947i 0.955814 + 0.293973i \(0.0949777\pi\)
−0.955814 + 0.293973i \(0.905022\pi\)
\(644\) 14950.2i 0.914786i
\(645\) 420.499i 0.0256700i
\(646\) −582.641 −0.0354856
\(647\) −5244.32 −0.318664 −0.159332 0.987225i \(-0.550934\pi\)
−0.159332 + 0.987225i \(0.550934\pi\)
\(648\) − 5553.57i − 0.336674i
\(649\) 29771.4 1.80066
\(650\) 0 0
\(651\) 9406.17 0.566293
\(652\) 8206.39i 0.492925i
\(653\) 18869.0 1.13078 0.565392 0.824822i \(-0.308725\pi\)
0.565392 + 0.824822i \(0.308725\pi\)
\(654\) 12475.8 0.745938
\(655\) − 5662.59i − 0.337795i
\(656\) − 31539.3i − 1.87714i
\(657\) 6668.90i 0.396010i
\(658\) 28889.3i 1.71159i
\(659\) −24299.8 −1.43639 −0.718197 0.695839i \(-0.755033\pi\)
−0.718197 + 0.695839i \(0.755033\pi\)
\(660\) 11242.7 0.663062
\(661\) 29915.0i 1.76030i 0.474694 + 0.880151i \(0.342559\pi\)
−0.474694 + 0.880151i \(0.657441\pi\)
\(662\) −8335.03 −0.489350
\(663\) 0 0
\(664\) −41347.1 −2.41653
\(665\) − 1069.24i − 0.0623508i
\(666\) −8482.56 −0.493532
\(667\) −12162.6 −0.706056
\(668\) 3155.69i 0.182780i
\(669\) − 6940.48i − 0.401098i
\(670\) 324.128i 0.0186898i
\(671\) − 8005.86i − 0.460600i
\(672\) −24304.5 −1.39519
\(673\) −15493.7 −0.887426 −0.443713 0.896169i \(-0.646339\pi\)
−0.443713 + 0.896169i \(0.646339\pi\)
\(674\) 17115.8i 0.978154i
\(675\) 3178.71 0.181257
\(676\) 0 0
\(677\) 11729.7 0.665891 0.332945 0.942946i \(-0.391958\pi\)
0.332945 + 0.942946i \(0.391958\pi\)
\(678\) 20585.2i 1.16603i
\(679\) 22005.6 1.24374
\(680\) 769.698 0.0434067
\(681\) − 11398.4i − 0.641390i
\(682\) − 74003.5i − 4.15505i
\(683\) − 1168.42i − 0.0654587i −0.999464 0.0327294i \(-0.989580\pi\)
0.999464 0.0327294i \(-0.0104199\pi\)
\(684\) 4878.48i 0.272709i
\(685\) −3249.10 −0.181229
\(686\) −37099.1 −2.06480
\(687\) − 12963.2i − 0.719909i
\(688\) −10478.9 −0.580675
\(689\) 0 0
\(690\) −2053.63 −0.113305
\(691\) − 32992.9i − 1.81637i −0.418574 0.908183i \(-0.637470\pi\)
0.418574 0.908183i \(-0.362530\pi\)
\(692\) 11196.7 0.615078
\(693\) 9151.33 0.501631
\(694\) − 30679.2i − 1.67805i
\(695\) − 870.612i − 0.0475168i
\(696\) − 52863.2i − 2.87899i
\(697\) 651.438i 0.0354017i
\(698\) 17856.3 0.968295
\(699\) −15839.3 −0.857078
\(700\) − 37192.2i − 2.00819i
\(701\) 14785.8 0.796651 0.398326 0.917244i \(-0.369591\pi\)
0.398326 + 0.917244i \(0.369591\pi\)
\(702\) 0 0
\(703\) 4582.77 0.245864
\(704\) 83357.0i 4.46255i
\(705\) −2865.28 −0.153068
\(706\) −66021.0 −3.51945
\(707\) 13430.6i 0.714442i
\(708\) − 27748.8i − 1.47297i
\(709\) 12634.0i 0.669225i 0.942356 + 0.334612i \(0.108605\pi\)
−0.942356 + 0.334612i \(0.891395\pi\)
\(710\) − 4125.52i − 0.218067i
\(711\) −4929.11 −0.259994
\(712\) 14786.8 0.778312
\(713\) 9760.24i 0.512656i
\(714\) 1018.70 0.0533947
\(715\) 0 0
\(716\) −46148.7 −2.40874
\(717\) − 4643.75i − 0.241874i
\(718\) −45814.6 −2.38132
\(719\) 27296.5 1.41584 0.707920 0.706292i \(-0.249634\pi\)
0.707920 + 0.706292i \(0.249634\pi\)
\(720\) − 4891.64i − 0.253195i
\(721\) − 19029.5i − 0.982936i
\(722\) 33146.3i 1.70856i
\(723\) − 14754.0i − 0.758932i
\(724\) −79438.5 −4.07777
\(725\) 30257.4 1.54997
\(726\) − 50577.2i − 2.58553i
\(727\) −4658.21 −0.237639 −0.118819 0.992916i \(-0.537911\pi\)
−0.118819 + 0.992916i \(0.537911\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 10718.4i 0.543432i
\(731\) 216.439 0.0109512
\(732\) −7461.96 −0.376779
\(733\) 166.474i 0.00838864i 0.999991 + 0.00419432i \(0.00133510\pi\)
−0.999991 + 0.00419432i \(0.998665\pi\)
\(734\) 13393.9i 0.673537i
\(735\) − 905.031i − 0.0454185i
\(736\) − 25219.4i − 1.26304i
\(737\) 1498.74 0.0749074
\(738\) 7554.41 0.376804
\(739\) 12738.1i 0.634069i 0.948414 + 0.317035i \(0.102687\pi\)
−0.948414 + 0.317035i \(0.897313\pi\)
\(740\) −9843.70 −0.489002
\(741\) 0 0
\(742\) 854.092 0.0422570
\(743\) 30724.5i 1.51705i 0.651641 + 0.758527i \(0.274081\pi\)
−0.651641 + 0.758527i \(0.725919\pi\)
\(744\) −42421.5 −2.09039
\(745\) −3043.76 −0.149684
\(746\) − 6131.38i − 0.300919i
\(747\) − 5427.50i − 0.265839i
\(748\) − 5786.84i − 0.282871i
\(749\) − 5193.37i − 0.253353i
\(750\) 10533.2 0.512826
\(751\) 39538.6 1.92115 0.960575 0.278021i \(-0.0896785\pi\)
0.960575 + 0.278021i \(0.0896785\pi\)
\(752\) − 71403.2i − 3.46251i
\(753\) −3467.34 −0.167805
\(754\) 0 0
\(755\) −7928.35 −0.382175
\(756\) − 8529.61i − 0.410342i
\(757\) 23035.1 1.10598 0.552990 0.833188i \(-0.313487\pi\)
0.552990 + 0.833188i \(0.313487\pi\)
\(758\) −65352.1 −3.13153
\(759\) 9495.81i 0.454119i
\(760\) 4822.23i 0.230159i
\(761\) 32454.0i 1.54594i 0.634445 + 0.772968i \(0.281229\pi\)
−0.634445 + 0.772968i \(0.718771\pi\)
\(762\) 17926.0i 0.852220i
\(763\) 11784.6 0.559150
\(764\) −71986.8 −3.40889
\(765\) 101.036i 0.00477511i
\(766\) −54616.1 −2.57619
\(767\) 0 0
\(768\) 9080.40 0.426641
\(769\) 32216.2i 1.51072i 0.655307 + 0.755362i \(0.272539\pi\)
−0.655307 + 0.755362i \(0.727461\pi\)
\(770\) 14708.2 0.688372
\(771\) −7055.86 −0.329586
\(772\) − 97613.2i − 4.55075i
\(773\) − 2924.60i − 0.136081i −0.997683 0.0680404i \(-0.978325\pi\)
0.997683 0.0680404i \(-0.0216747\pi\)
\(774\) − 2509.94i − 0.116561i
\(775\) − 24280.9i − 1.12541i
\(776\) −99244.7 −4.59108
\(777\) −8012.58 −0.369948
\(778\) − 31361.2i − 1.44519i
\(779\) −4081.32 −0.187713
\(780\) 0 0
\(781\) −19076.1 −0.874001
\(782\) 1057.04i 0.0483374i
\(783\) 6939.19 0.316713
\(784\) 22553.5 1.02740
\(785\) − 1697.03i − 0.0771586i
\(786\) 33799.8i 1.53384i
\(787\) 25507.1i 1.15531i 0.816280 + 0.577656i \(0.196033\pi\)
−0.816280 + 0.577656i \(0.803967\pi\)
\(788\) − 60011.1i − 2.71295i
\(789\) 16565.6 0.747468
\(790\) −7922.16 −0.356782
\(791\) 19444.7i 0.874050i
\(792\) −41272.2 −1.85170
\(793\) 0 0
\(794\) 13416.8 0.599677
\(795\) 84.7100i 0.00377906i
\(796\) 1309.35 0.0583023
\(797\) −5448.98 −0.242174 −0.121087 0.992642i \(-0.538638\pi\)
−0.121087 + 0.992642i \(0.538638\pi\)
\(798\) 6382.24i 0.283119i
\(799\) 1474.82i 0.0653008i
\(800\) 62739.0i 2.77270i
\(801\) 1941.01i 0.0856209i
\(802\) 49297.8 2.17053
\(803\) 49560.9 2.17804
\(804\) − 1396.92i − 0.0612755i
\(805\) −1939.85 −0.0849324
\(806\) 0 0
\(807\) 11750.9 0.512577
\(808\) − 60571.7i − 2.63726i
\(809\) −2453.12 −0.106610 −0.0533048 0.998578i \(-0.516975\pi\)
−0.0533048 + 0.998578i \(0.516975\pi\)
\(810\) 1171.66 0.0508247
\(811\) 5133.85i 0.222286i 0.993804 + 0.111143i \(0.0354512\pi\)
−0.993804 + 0.111143i \(0.964549\pi\)
\(812\) − 81191.4i − 3.50894i
\(813\) − 8332.58i − 0.359454i
\(814\) 63039.4i 2.71441i
\(815\) −1064.81 −0.0457651
\(816\) −2517.83 −0.108017
\(817\) 1356.01i 0.0580673i
\(818\) 49432.6 2.11292
\(819\) 0 0
\(820\) 8766.61 0.373345
\(821\) 23854.0i 1.01402i 0.861941 + 0.507009i \(0.169249\pi\)
−0.861941 + 0.507009i \(0.830751\pi\)
\(822\) 19393.8 0.822913
\(823\) −757.156 −0.0320690 −0.0160345 0.999871i \(-0.505104\pi\)
−0.0160345 + 0.999871i \(0.505104\pi\)
\(824\) 85822.6i 3.62836i
\(825\) − 23623.0i − 0.996907i
\(826\) − 36302.2i − 1.52919i
\(827\) 28621.2i 1.20345i 0.798702 + 0.601726i \(0.205520\pi\)
−0.798702 + 0.601726i \(0.794480\pi\)
\(828\) 8850.68 0.371476
\(829\) −27429.2 −1.14916 −0.574582 0.818447i \(-0.694835\pi\)
−0.574582 + 0.818447i \(0.694835\pi\)
\(830\) − 8723.19i − 0.364803i
\(831\) −19749.2 −0.824421
\(832\) 0 0
\(833\) −465.838 −0.0193761
\(834\) 5196.64i 0.215761i
\(835\) −409.462 −0.0169701
\(836\) 36255.1 1.49989
\(837\) − 5568.54i − 0.229960i
\(838\) − 34840.7i − 1.43622i
\(839\) − 4633.62i − 0.190668i −0.995445 0.0953339i \(-0.969608\pi\)
0.995445 0.0953339i \(-0.0303919\pi\)
\(840\) − 8431.27i − 0.346317i
\(841\) 41663.6 1.70829
\(842\) 16413.7 0.671798
\(843\) 8614.98i 0.351976i
\(844\) 21813.0 0.889614
\(845\) 0 0
\(846\) 17102.7 0.695041
\(847\) − 47775.0i − 1.93810i
\(848\) −2110.99 −0.0854853
\(849\) −22554.1 −0.911726
\(850\) − 2629.64i − 0.106113i
\(851\) − 8314.19i − 0.334908i
\(852\) 17780.1i 0.714947i
\(853\) − 14854.6i − 0.596261i −0.954525 0.298131i \(-0.903637\pi\)
0.954525 0.298131i \(-0.0963631\pi\)
\(854\) −9762.07 −0.391161
\(855\) −632.999 −0.0253194
\(856\) 23421.9i 0.935216i
\(857\) 42799.5 1.70595 0.852977 0.521948i \(-0.174794\pi\)
0.852977 + 0.521948i \(0.174794\pi\)
\(858\) 0 0
\(859\) −8246.47 −0.327551 −0.163775 0.986498i \(-0.552367\pi\)
−0.163775 + 0.986498i \(0.552367\pi\)
\(860\) − 2912.70i − 0.115491i
\(861\) 7135.85 0.282450
\(862\) 42580.1 1.68246
\(863\) − 17695.4i − 0.697983i −0.937126 0.348991i \(-0.886524\pi\)
0.937126 0.348991i \(-0.113476\pi\)
\(864\) 14388.5i 0.566558i
\(865\) 1452.81i 0.0571064i
\(866\) − 39132.3i − 1.53553i
\(867\) −14687.0 −0.575313
\(868\) −65154.2 −2.54779
\(869\) 36631.4i 1.42996i
\(870\) 11152.8 0.434615
\(871\) 0 0
\(872\) −53148.2 −2.06402
\(873\) − 13027.5i − 0.505058i
\(874\) −6622.49 −0.256303
\(875\) 9949.64 0.384411
\(876\) − 46193.8i − 1.78167i
\(877\) 14346.8i 0.552401i 0.961100 + 0.276200i \(0.0890754\pi\)
−0.961100 + 0.276200i \(0.910925\pi\)
\(878\) − 81622.7i − 3.13739i
\(879\) 13519.7i 0.518781i
\(880\) −36353.0 −1.39257
\(881\) 2063.51 0.0789121 0.0394560 0.999221i \(-0.487437\pi\)
0.0394560 + 0.999221i \(0.487437\pi\)
\(882\) 5402.09i 0.206233i
\(883\) 34137.1 1.30103 0.650513 0.759495i \(-0.274554\pi\)
0.650513 + 0.759495i \(0.274554\pi\)
\(884\) 0 0
\(885\) 3600.50 0.136756
\(886\) 8138.58i 0.308602i
\(887\) −22238.5 −0.841821 −0.420910 0.907102i \(-0.638289\pi\)
−0.420910 + 0.907102i \(0.638289\pi\)
\(888\) 36136.5 1.36561
\(889\) 16932.8i 0.638817i
\(890\) 3119.63i 0.117495i
\(891\) − 5417.67i − 0.203702i
\(892\) 48075.0i 1.80456i
\(893\) −9239.89 −0.346250
\(894\) 18168.0 0.679676
\(895\) − 5987.96i − 0.223637i
\(896\) 36830.7 1.37325
\(897\) 0 0
\(898\) 3783.45 0.140596
\(899\) − 53005.7i − 1.96645i
\(900\) −22018.1 −0.815486
\(901\) 43.6019 0.00161220
\(902\) − 56141.7i − 2.07241i
\(903\) − 2370.88i − 0.0873730i
\(904\) − 87694.9i − 3.22643i
\(905\) − 10307.4i − 0.378597i
\(906\) 47324.0 1.73536
\(907\) 44160.3 1.61667 0.808335 0.588723i \(-0.200369\pi\)
0.808335 + 0.588723i \(0.200369\pi\)
\(908\) 78953.8i 2.88565i
\(909\) 7951.05 0.290121
\(910\) 0 0
\(911\) 11916.3 0.433376 0.216688 0.976241i \(-0.430475\pi\)
0.216688 + 0.976241i \(0.430475\pi\)
\(912\) − 15774.4i − 0.572745i
\(913\) −40335.3 −1.46211
\(914\) −39043.0 −1.41294
\(915\) − 968.215i − 0.0349816i
\(916\) 89793.0i 3.23891i
\(917\) 31927.1i 1.14975i
\(918\) − 603.078i − 0.0216825i
\(919\) −20128.9 −0.722516 −0.361258 0.932466i \(-0.617653\pi\)
−0.361258 + 0.932466i \(0.617653\pi\)
\(920\) 8748.64 0.313515
\(921\) 28616.7i 1.02383i
\(922\) 10525.0 0.375945
\(923\) 0 0
\(924\) −63389.0 −2.25687
\(925\) 20683.5i 0.735210i
\(926\) 55654.1 1.97506
\(927\) −11265.7 −0.399151
\(928\) 136961.i 4.84478i
\(929\) 31428.4i 1.10994i 0.831871 + 0.554969i \(0.187270\pi\)
−0.831871 + 0.554969i \(0.812730\pi\)
\(930\) − 8949.86i − 0.315567i
\(931\) − 2918.52i − 0.102740i
\(932\) 109715. 3.85605
\(933\) 22398.9 0.785965
\(934\) − 47150.1i − 1.65182i
\(935\) 750.863 0.0262629
\(936\) 0 0
\(937\) 42473.2 1.48083 0.740416 0.672149i \(-0.234629\pi\)
0.740416 + 0.672149i \(0.234629\pi\)
\(938\) − 1827.51i − 0.0636144i
\(939\) −5464.94 −0.189927
\(940\) 19847.1 0.688661
\(941\) 42644.0i 1.47732i 0.674079 + 0.738659i \(0.264541\pi\)
−0.674079 + 0.738659i \(0.735459\pi\)
\(942\) 10129.5i 0.350357i
\(943\) 7404.46i 0.255697i
\(944\) 89725.0i 3.09354i
\(945\) 1106.75 0.0380978
\(946\) −18653.0 −0.641080
\(947\) 4282.95i 0.146966i 0.997296 + 0.0734831i \(0.0234115\pi\)
−0.997296 + 0.0734831i \(0.976588\pi\)
\(948\) 34142.7 1.16973
\(949\) 0 0
\(950\) 16475.0 0.562651
\(951\) − 9375.42i − 0.319683i
\(952\) −4339.74 −0.147744
\(953\) −40593.9 −1.37982 −0.689908 0.723897i \(-0.742349\pi\)
−0.689908 + 0.723897i \(0.742349\pi\)
\(954\) − 505.630i − 0.0171597i
\(955\) − 9340.54i − 0.316495i
\(956\) 32166.1i 1.08821i
\(957\) − 51569.6i − 1.74191i
\(958\) 59771.9 2.01581
\(959\) 18319.2 0.616850
\(960\) 10081.1i 0.338922i
\(961\) −12744.8 −0.427808
\(962\) 0 0
\(963\) −3074.52 −0.102882
\(964\) 102198.i 3.41448i
\(965\) 12665.7 0.422510
\(966\) 11578.9 0.385656
\(967\) − 17709.4i − 0.588931i −0.955662 0.294466i \(-0.904858\pi\)
0.955662 0.294466i \(-0.0951416\pi\)
\(968\) 215464.i 7.15420i
\(969\) 325.818i 0.0108016i
\(970\) − 20938.1i − 0.693074i
\(971\) 4038.97 0.133488 0.0667440 0.997770i \(-0.478739\pi\)
0.0667440 + 0.997770i \(0.478739\pi\)
\(972\) −5049.61 −0.166632
\(973\) 4908.72i 0.161733i
\(974\) −105366. −3.46626
\(975\) 0 0
\(976\) 24128.1 0.791312
\(977\) 2764.30i 0.0905197i 0.998975 + 0.0452598i \(0.0144116\pi\)
−0.998975 + 0.0452598i \(0.985588\pi\)
\(978\) 6355.79 0.207807
\(979\) 14424.9 0.470912
\(980\) 6268.93i 0.204340i
\(981\) − 6976.59i − 0.227060i
\(982\) 18295.4i 0.594531i
\(983\) − 17804.5i − 0.577695i −0.957375 0.288848i \(-0.906728\pi\)
0.957375 0.288848i \(-0.0932721\pi\)
\(984\) −32182.4 −1.04262
\(985\) 7786.65 0.251881
\(986\) − 5740.57i − 0.185413i
\(987\) 16155.2 0.520997
\(988\) 0 0
\(989\) 2460.12 0.0790974
\(990\) − 8707.39i − 0.279534i
\(991\) −8129.69 −0.260593 −0.130297 0.991475i \(-0.541593\pi\)
−0.130297 + 0.991475i \(0.541593\pi\)
\(992\) 109908. 3.51772
\(993\) 4661.02i 0.148956i
\(994\) 23260.7i 0.742237i
\(995\) 169.893i 0.00541302i
\(996\) 37595.0i 1.19603i
\(997\) −29452.9 −0.935589 −0.467795 0.883837i \(-0.654951\pi\)
−0.467795 + 0.883837i \(0.654951\pi\)
\(998\) −26997.7 −0.856309
\(999\) 4743.52i 0.150229i
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.b.i.337.10 10
13.3 even 3 39.4.j.c.4.1 10
13.4 even 6 39.4.j.c.10.1 yes 10
13.5 odd 4 507.4.a.r.1.10 10
13.8 odd 4 507.4.a.r.1.1 10
13.12 even 2 inner 507.4.b.i.337.1 10
39.5 even 4 1521.4.a.bk.1.1 10
39.8 even 4 1521.4.a.bk.1.10 10
39.17 odd 6 117.4.q.e.10.5 10
39.29 odd 6 117.4.q.e.82.5 10
52.3 odd 6 624.4.bv.h.433.3 10
52.43 odd 6 624.4.bv.h.49.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.1 10 13.3 even 3
39.4.j.c.10.1 yes 10 13.4 even 6
117.4.q.e.10.5 10 39.17 odd 6
117.4.q.e.82.5 10 39.29 odd 6
507.4.a.r.1.1 10 13.8 odd 4
507.4.a.r.1.10 10 13.5 odd 4
507.4.b.i.337.1 10 13.12 even 2 inner
507.4.b.i.337.10 10 1.1 even 1 trivial
624.4.bv.h.49.3 10 52.43 odd 6
624.4.bv.h.433.3 10 52.3 odd 6
1521.4.a.bk.1.1 10 39.5 even 4
1521.4.a.bk.1.10 10 39.8 even 4