Properties

Label 507.4.a.a.1.1
Level $507$
Weight $4$
Character 507.1
Self dual yes
Analytic conductor $29.914$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 507.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.9139683729\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 507.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{5} -9.00000 q^{6} -2.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{2} +3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{5} -9.00000 q^{6} -2.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} -27.0000 q^{10} -30.0000 q^{11} +3.00000 q^{12} +6.00000 q^{14} +27.0000 q^{15} -71.0000 q^{16} -111.000 q^{17} -27.0000 q^{18} +46.0000 q^{19} +9.00000 q^{20} -6.00000 q^{21} +90.0000 q^{22} -6.00000 q^{23} +63.0000 q^{24} -44.0000 q^{25} +27.0000 q^{27} -2.00000 q^{28} -105.000 q^{29} -81.0000 q^{30} +100.000 q^{31} +45.0000 q^{32} -90.0000 q^{33} +333.000 q^{34} -18.0000 q^{35} +9.00000 q^{36} -17.0000 q^{37} -138.000 q^{38} +189.000 q^{40} +231.000 q^{41} +18.0000 q^{42} -514.000 q^{43} -30.0000 q^{44} +81.0000 q^{45} +18.0000 q^{46} +162.000 q^{47} -213.000 q^{48} -339.000 q^{49} +132.000 q^{50} -333.000 q^{51} +639.000 q^{53} -81.0000 q^{54} -270.000 q^{55} -42.0000 q^{56} +138.000 q^{57} +315.000 q^{58} -600.000 q^{59} +27.0000 q^{60} +233.000 q^{61} -300.000 q^{62} -18.0000 q^{63} +433.000 q^{64} +270.000 q^{66} -926.000 q^{67} -111.000 q^{68} -18.0000 q^{69} +54.0000 q^{70} +930.000 q^{71} +189.000 q^{72} +253.000 q^{73} +51.0000 q^{74} -132.000 q^{75} +46.0000 q^{76} +60.0000 q^{77} -1324.00 q^{79} -639.000 q^{80} +81.0000 q^{81} -693.000 q^{82} -810.000 q^{83} -6.00000 q^{84} -999.000 q^{85} +1542.00 q^{86} -315.000 q^{87} -630.000 q^{88} -498.000 q^{89} -243.000 q^{90} -6.00000 q^{92} +300.000 q^{93} -486.000 q^{94} +414.000 q^{95} +135.000 q^{96} -1358.00 q^{97} +1017.00 q^{98} -270.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.00000 −1.06066 −0.530330 0.847791i \(-0.677932\pi\)
−0.530330 + 0.847791i \(0.677932\pi\)
\(3\) 3.00000 0.577350
\(4\) 1.00000 0.125000
\(5\) 9.00000 0.804984 0.402492 0.915423i \(-0.368144\pi\)
0.402492 + 0.915423i \(0.368144\pi\)
\(6\) −9.00000 −0.612372
\(7\) −2.00000 −0.107990 −0.0539949 0.998541i \(-0.517195\pi\)
−0.0539949 + 0.998541i \(0.517195\pi\)
\(8\) 21.0000 0.928078
\(9\) 9.00000 0.333333
\(10\) −27.0000 −0.853815
\(11\) −30.0000 −0.822304 −0.411152 0.911567i \(-0.634873\pi\)
−0.411152 + 0.911567i \(0.634873\pi\)
\(12\) 3.00000 0.0721688
\(13\) 0 0
\(14\) 6.00000 0.114541
\(15\) 27.0000 0.464758
\(16\) −71.0000 −1.10938
\(17\) −111.000 −1.58361 −0.791807 0.610771i \(-0.790860\pi\)
−0.791807 + 0.610771i \(0.790860\pi\)
\(18\) −27.0000 −0.353553
\(19\) 46.0000 0.555428 0.277714 0.960664i \(-0.410423\pi\)
0.277714 + 0.960664i \(0.410423\pi\)
\(20\) 9.00000 0.100623
\(21\) −6.00000 −0.0623480
\(22\) 90.0000 0.872185
\(23\) −6.00000 −0.0543951 −0.0271975 0.999630i \(-0.508658\pi\)
−0.0271975 + 0.999630i \(0.508658\pi\)
\(24\) 63.0000 0.535826
\(25\) −44.0000 −0.352000
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) −2.00000 −0.0134987
\(29\) −105.000 −0.672345 −0.336173 0.941800i \(-0.609133\pi\)
−0.336173 + 0.941800i \(0.609133\pi\)
\(30\) −81.0000 −0.492950
\(31\) 100.000 0.579372 0.289686 0.957122i \(-0.406449\pi\)
0.289686 + 0.957122i \(0.406449\pi\)
\(32\) 45.0000 0.248592
\(33\) −90.0000 −0.474757
\(34\) 333.000 1.67968
\(35\) −18.0000 −0.0869302
\(36\) 9.00000 0.0416667
\(37\) −17.0000 −0.0755347 −0.0377673 0.999287i \(-0.512025\pi\)
−0.0377673 + 0.999287i \(0.512025\pi\)
\(38\) −138.000 −0.589120
\(39\) 0 0
\(40\) 189.000 0.747088
\(41\) 231.000 0.879906 0.439953 0.898021i \(-0.354995\pi\)
0.439953 + 0.898021i \(0.354995\pi\)
\(42\) 18.0000 0.0661300
\(43\) −514.000 −1.82289 −0.911445 0.411422i \(-0.865032\pi\)
−0.911445 + 0.411422i \(0.865032\pi\)
\(44\) −30.0000 −0.102788
\(45\) 81.0000 0.268328
\(46\) 18.0000 0.0576947
\(47\) 162.000 0.502769 0.251384 0.967887i \(-0.419114\pi\)
0.251384 + 0.967887i \(0.419114\pi\)
\(48\) −213.000 −0.640498
\(49\) −339.000 −0.988338
\(50\) 132.000 0.373352
\(51\) −333.000 −0.914301
\(52\) 0 0
\(53\) 639.000 1.65610 0.828051 0.560653i \(-0.189450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(54\) −81.0000 −0.204124
\(55\) −270.000 −0.661942
\(56\) −42.0000 −0.100223
\(57\) 138.000 0.320676
\(58\) 315.000 0.713130
\(59\) −600.000 −1.32396 −0.661978 0.749524i \(-0.730283\pi\)
−0.661978 + 0.749524i \(0.730283\pi\)
\(60\) 27.0000 0.0580948
\(61\) 233.000 0.489059 0.244529 0.969642i \(-0.421367\pi\)
0.244529 + 0.969642i \(0.421367\pi\)
\(62\) −300.000 −0.614517
\(63\) −18.0000 −0.0359966
\(64\) 433.000 0.845703
\(65\) 0 0
\(66\) 270.000 0.503556
\(67\) −926.000 −1.68849 −0.844246 0.535957i \(-0.819951\pi\)
−0.844246 + 0.535957i \(0.819951\pi\)
\(68\) −111.000 −0.197952
\(69\) −18.0000 −0.0314050
\(70\) 54.0000 0.0922033
\(71\) 930.000 1.55452 0.777258 0.629182i \(-0.216610\pi\)
0.777258 + 0.629182i \(0.216610\pi\)
\(72\) 189.000 0.309359
\(73\) 253.000 0.405636 0.202818 0.979216i \(-0.434990\pi\)
0.202818 + 0.979216i \(0.434990\pi\)
\(74\) 51.0000 0.0801166
\(75\) −132.000 −0.203227
\(76\) 46.0000 0.0694284
\(77\) 60.0000 0.0888004
\(78\) 0 0
\(79\) −1324.00 −1.88559 −0.942795 0.333373i \(-0.891813\pi\)
−0.942795 + 0.333373i \(0.891813\pi\)
\(80\) −639.000 −0.893030
\(81\) 81.0000 0.111111
\(82\) −693.000 −0.933281
\(83\) −810.000 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(84\) −6.00000 −0.00779350
\(85\) −999.000 −1.27479
\(86\) 1542.00 1.93347
\(87\) −315.000 −0.388179
\(88\) −630.000 −0.763162
\(89\) −498.000 −0.593122 −0.296561 0.955014i \(-0.595840\pi\)
−0.296561 + 0.955014i \(0.595840\pi\)
\(90\) −243.000 −0.284605
\(91\) 0 0
\(92\) −6.00000 −0.00679938
\(93\) 300.000 0.334501
\(94\) −486.000 −0.533267
\(95\) 414.000 0.447111
\(96\) 135.000 0.143525
\(97\) −1358.00 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 1017.00 1.04829
\(99\) −270.000 −0.274101
\(100\) −44.0000 −0.0440000
\(101\) −357.000 −0.351711 −0.175856 0.984416i \(-0.556269\pi\)
−0.175856 + 0.984416i \(0.556269\pi\)
\(102\) 999.000 0.969762
\(103\) 1118.00 1.06951 0.534756 0.845006i \(-0.320403\pi\)
0.534756 + 0.845006i \(0.320403\pi\)
\(104\) 0 0
\(105\) −54.0000 −0.0501891
\(106\) −1917.00 −1.75656
\(107\) 714.000 0.645093 0.322547 0.946554i \(-0.395461\pi\)
0.322547 + 0.946554i \(0.395461\pi\)
\(108\) 27.0000 0.0240563
\(109\) −2006.00 −1.76275 −0.881376 0.472416i \(-0.843382\pi\)
−0.881376 + 0.472416i \(0.843382\pi\)
\(110\) 810.000 0.702095
\(111\) −51.0000 −0.0436100
\(112\) 142.000 0.119801
\(113\) −1119.00 −0.931563 −0.465782 0.884900i \(-0.654227\pi\)
−0.465782 + 0.884900i \(0.654227\pi\)
\(114\) −414.000 −0.340129
\(115\) −54.0000 −0.0437872
\(116\) −105.000 −0.0840431
\(117\) 0 0
\(118\) 1800.00 1.40427
\(119\) 222.000 0.171014
\(120\) 567.000 0.431332
\(121\) −431.000 −0.323817
\(122\) −699.000 −0.518725
\(123\) 693.000 0.508014
\(124\) 100.000 0.0724215
\(125\) −1521.00 −1.08834
\(126\) 54.0000 0.0381802
\(127\) −604.000 −0.422018 −0.211009 0.977484i \(-0.567675\pi\)
−0.211009 + 0.977484i \(0.567675\pi\)
\(128\) −1659.00 −1.14560
\(129\) −1542.00 −1.05245
\(130\) 0 0
\(131\) −1584.00 −1.05645 −0.528224 0.849105i \(-0.677142\pi\)
−0.528224 + 0.849105i \(0.677142\pi\)
\(132\) −90.0000 −0.0593447
\(133\) −92.0000 −0.0599805
\(134\) 2778.00 1.79092
\(135\) 243.000 0.154919
\(136\) −2331.00 −1.46972
\(137\) −717.000 −0.447135 −0.223567 0.974688i \(-0.571770\pi\)
−0.223567 + 0.974688i \(0.571770\pi\)
\(138\) 54.0000 0.0333100
\(139\) −820.000 −0.500370 −0.250185 0.968198i \(-0.580492\pi\)
−0.250185 + 0.968198i \(0.580492\pi\)
\(140\) −18.0000 −0.0108663
\(141\) 486.000 0.290274
\(142\) −2790.00 −1.64881
\(143\) 0 0
\(144\) −639.000 −0.369792
\(145\) −945.000 −0.541227
\(146\) −759.000 −0.430242
\(147\) −1017.00 −0.570617
\(148\) −17.0000 −0.00944183
\(149\) 1749.00 0.961635 0.480818 0.876821i \(-0.340340\pi\)
0.480818 + 0.876821i \(0.340340\pi\)
\(150\) 396.000 0.215555
\(151\) 370.000 0.199405 0.0997026 0.995017i \(-0.468211\pi\)
0.0997026 + 0.995017i \(0.468211\pi\)
\(152\) 966.000 0.515480
\(153\) −999.000 −0.527872
\(154\) −180.000 −0.0941871
\(155\) 900.000 0.466385
\(156\) 0 0
\(157\) −2611.00 −1.32726 −0.663632 0.748059i \(-0.730986\pi\)
−0.663632 + 0.748059i \(0.730986\pi\)
\(158\) 3972.00 1.99997
\(159\) 1917.00 0.956151
\(160\) 405.000 0.200113
\(161\) 12.0000 0.00587411
\(162\) −243.000 −0.117851
\(163\) 1636.00 0.786144 0.393072 0.919508i \(-0.371412\pi\)
0.393072 + 0.919508i \(0.371412\pi\)
\(164\) 231.000 0.109988
\(165\) −810.000 −0.382172
\(166\) 2430.00 1.13617
\(167\) −264.000 −0.122329 −0.0611645 0.998128i \(-0.519481\pi\)
−0.0611645 + 0.998128i \(0.519481\pi\)
\(168\) −126.000 −0.0578638
\(169\) 0 0
\(170\) 2997.00 1.35211
\(171\) 414.000 0.185143
\(172\) −514.000 −0.227861
\(173\) 1410.00 0.619655 0.309827 0.950793i \(-0.399729\pi\)
0.309827 + 0.950793i \(0.399729\pi\)
\(174\) 945.000 0.411726
\(175\) 88.0000 0.0380124
\(176\) 2130.00 0.912243
\(177\) −1800.00 −0.764386
\(178\) 1494.00 0.629101
\(179\) −474.000 −0.197924 −0.0989621 0.995091i \(-0.531552\pi\)
−0.0989621 + 0.995091i \(0.531552\pi\)
\(180\) 81.0000 0.0335410
\(181\) 2249.00 0.923574 0.461787 0.886991i \(-0.347208\pi\)
0.461787 + 0.886991i \(0.347208\pi\)
\(182\) 0 0
\(183\) 699.000 0.282358
\(184\) −126.000 −0.0504828
\(185\) −153.000 −0.0608042
\(186\) −900.000 −0.354791
\(187\) 3330.00 1.30221
\(188\) 162.000 0.0628461
\(189\) −54.0000 −0.0207827
\(190\) −1242.00 −0.474232
\(191\) 3444.00 1.30471 0.652354 0.757915i \(-0.273782\pi\)
0.652354 + 0.757915i \(0.273782\pi\)
\(192\) 1299.00 0.488267
\(193\) 4273.00 1.59366 0.796832 0.604201i \(-0.206507\pi\)
0.796832 + 0.604201i \(0.206507\pi\)
\(194\) 4074.00 1.50771
\(195\) 0 0
\(196\) −339.000 −0.123542
\(197\) 1986.00 0.718257 0.359129 0.933288i \(-0.383074\pi\)
0.359129 + 0.933288i \(0.383074\pi\)
\(198\) 810.000 0.290728
\(199\) −2386.00 −0.849945 −0.424973 0.905206i \(-0.639716\pi\)
−0.424973 + 0.905206i \(0.639716\pi\)
\(200\) −924.000 −0.326683
\(201\) −2778.00 −0.974851
\(202\) 1071.00 0.373046
\(203\) 210.000 0.0726065
\(204\) −333.000 −0.114288
\(205\) 2079.00 0.708311
\(206\) −3354.00 −1.13439
\(207\) −54.0000 −0.0181317
\(208\) 0 0
\(209\) −1380.00 −0.456730
\(210\) 162.000 0.0532336
\(211\) −1600.00 −0.522031 −0.261016 0.965335i \(-0.584057\pi\)
−0.261016 + 0.965335i \(0.584057\pi\)
\(212\) 639.000 0.207013
\(213\) 2790.00 0.897501
\(214\) −2142.00 −0.684225
\(215\) −4626.00 −1.46740
\(216\) 567.000 0.178609
\(217\) −200.000 −0.0625663
\(218\) 6018.00 1.86968
\(219\) 759.000 0.234194
\(220\) −270.000 −0.0827427
\(221\) 0 0
\(222\) 153.000 0.0462553
\(223\) 3832.00 1.15072 0.575358 0.817902i \(-0.304863\pi\)
0.575358 + 0.817902i \(0.304863\pi\)
\(224\) −90.0000 −0.0268454
\(225\) −396.000 −0.117333
\(226\) 3357.00 0.988072
\(227\) 1398.00 0.408760 0.204380 0.978892i \(-0.434482\pi\)
0.204380 + 0.978892i \(0.434482\pi\)
\(228\) 138.000 0.0400845
\(229\) −4466.00 −1.28874 −0.644370 0.764714i \(-0.722880\pi\)
−0.644370 + 0.764714i \(0.722880\pi\)
\(230\) 162.000 0.0464433
\(231\) 180.000 0.0512690
\(232\) −2205.00 −0.623989
\(233\) −1638.00 −0.460553 −0.230277 0.973125i \(-0.573963\pi\)
−0.230277 + 0.973125i \(0.573963\pi\)
\(234\) 0 0
\(235\) 1458.00 0.404721
\(236\) −600.000 −0.165494
\(237\) −3972.00 −1.08865
\(238\) −666.000 −0.181388
\(239\) 594.000 0.160764 0.0803821 0.996764i \(-0.474386\pi\)
0.0803821 + 0.996764i \(0.474386\pi\)
\(240\) −1917.00 −0.515591
\(241\) −2303.00 −0.615557 −0.307779 0.951458i \(-0.599586\pi\)
−0.307779 + 0.951458i \(0.599586\pi\)
\(242\) 1293.00 0.343459
\(243\) 243.000 0.0641500
\(244\) 233.000 0.0611324
\(245\) −3051.00 −0.795597
\(246\) −2079.00 −0.538830
\(247\) 0 0
\(248\) 2100.00 0.537702
\(249\) −2430.00 −0.618454
\(250\) 4563.00 1.15436
\(251\) 6324.00 1.59031 0.795154 0.606407i \(-0.207390\pi\)
0.795154 + 0.606407i \(0.207390\pi\)
\(252\) −18.0000 −0.00449958
\(253\) 180.000 0.0447293
\(254\) 1812.00 0.447618
\(255\) −2997.00 −0.735998
\(256\) 1513.00 0.369385
\(257\) 7833.00 1.90120 0.950601 0.310414i \(-0.100468\pi\)
0.950601 + 0.310414i \(0.100468\pi\)
\(258\) 4626.00 1.11629
\(259\) 34.0000 0.00815698
\(260\) 0 0
\(261\) −945.000 −0.224115
\(262\) 4752.00 1.12053
\(263\) −3030.00 −0.710410 −0.355205 0.934788i \(-0.615589\pi\)
−0.355205 + 0.934788i \(0.615589\pi\)
\(264\) −1890.00 −0.440612
\(265\) 5751.00 1.33314
\(266\) 276.000 0.0636190
\(267\) −1494.00 −0.342439
\(268\) −926.000 −0.211061
\(269\) −534.000 −0.121036 −0.0605178 0.998167i \(-0.519275\pi\)
−0.0605178 + 0.998167i \(0.519275\pi\)
\(270\) −729.000 −0.164317
\(271\) 3688.00 0.826679 0.413340 0.910577i \(-0.364362\pi\)
0.413340 + 0.910577i \(0.364362\pi\)
\(272\) 7881.00 1.75682
\(273\) 0 0
\(274\) 2151.00 0.474258
\(275\) 1320.00 0.289451
\(276\) −18.0000 −0.00392563
\(277\) 1865.00 0.404538 0.202269 0.979330i \(-0.435168\pi\)
0.202269 + 0.979330i \(0.435168\pi\)
\(278\) 2460.00 0.530723
\(279\) 900.000 0.193124
\(280\) −378.000 −0.0806779
\(281\) −2997.00 −0.636249 −0.318125 0.948049i \(-0.603053\pi\)
−0.318125 + 0.948049i \(0.603053\pi\)
\(282\) −1458.00 −0.307882
\(283\) −4114.00 −0.864141 −0.432071 0.901840i \(-0.642217\pi\)
−0.432071 + 0.901840i \(0.642217\pi\)
\(284\) 930.000 0.194315
\(285\) 1242.00 0.258139
\(286\) 0 0
\(287\) −462.000 −0.0950209
\(288\) 405.000 0.0828641
\(289\) 7408.00 1.50784
\(290\) 2835.00 0.574058
\(291\) −4074.00 −0.820695
\(292\) 253.000 0.0507045
\(293\) 4665.00 0.930144 0.465072 0.885273i \(-0.346028\pi\)
0.465072 + 0.885273i \(0.346028\pi\)
\(294\) 3051.00 0.605231
\(295\) −5400.00 −1.06576
\(296\) −357.000 −0.0701020
\(297\) −810.000 −0.158252
\(298\) −5247.00 −1.01997
\(299\) 0 0
\(300\) −132.000 −0.0254034
\(301\) 1028.00 0.196854
\(302\) −1110.00 −0.211501
\(303\) −1071.00 −0.203061
\(304\) −3266.00 −0.616177
\(305\) 2097.00 0.393685
\(306\) 2997.00 0.559892
\(307\) −1502.00 −0.279230 −0.139615 0.990206i \(-0.544587\pi\)
−0.139615 + 0.990206i \(0.544587\pi\)
\(308\) 60.0000 0.0111001
\(309\) 3354.00 0.617483
\(310\) −2700.00 −0.494676
\(311\) 2106.00 0.383988 0.191994 0.981396i \(-0.438505\pi\)
0.191994 + 0.981396i \(0.438505\pi\)
\(312\) 0 0
\(313\) −3898.00 −0.703923 −0.351962 0.936014i \(-0.614485\pi\)
−0.351962 + 0.936014i \(0.614485\pi\)
\(314\) 7833.00 1.40778
\(315\) −162.000 −0.0289767
\(316\) −1324.00 −0.235699
\(317\) −9351.00 −1.65680 −0.828398 0.560140i \(-0.810747\pi\)
−0.828398 + 0.560140i \(0.810747\pi\)
\(318\) −5751.00 −1.01415
\(319\) 3150.00 0.552872
\(320\) 3897.00 0.680778
\(321\) 2142.00 0.372445
\(322\) −36.0000 −0.00623044
\(323\) −5106.00 −0.879583
\(324\) 81.0000 0.0138889
\(325\) 0 0
\(326\) −4908.00 −0.833831
\(327\) −6018.00 −1.01773
\(328\) 4851.00 0.816621
\(329\) −324.000 −0.0542939
\(330\) 2430.00 0.405355
\(331\) 9172.00 1.52308 0.761539 0.648119i \(-0.224444\pi\)
0.761539 + 0.648119i \(0.224444\pi\)
\(332\) −810.000 −0.133899
\(333\) −153.000 −0.0251782
\(334\) 792.000 0.129749
\(335\) −8334.00 −1.35921
\(336\) 426.000 0.0691673
\(337\) −11089.0 −1.79245 −0.896226 0.443598i \(-0.853702\pi\)
−0.896226 + 0.443598i \(0.853702\pi\)
\(338\) 0 0
\(339\) −3357.00 −0.537838
\(340\) −999.000 −0.159348
\(341\) −3000.00 −0.476420
\(342\) −1242.00 −0.196373
\(343\) 1364.00 0.214720
\(344\) −10794.0 −1.69178
\(345\) −162.000 −0.0252805
\(346\) −4230.00 −0.657243
\(347\) 9762.00 1.51024 0.755118 0.655589i \(-0.227580\pi\)
0.755118 + 0.655589i \(0.227580\pi\)
\(348\) −315.000 −0.0485223
\(349\) 8290.00 1.27150 0.635750 0.771895i \(-0.280691\pi\)
0.635750 + 0.771895i \(0.280691\pi\)
\(350\) −264.000 −0.0403183
\(351\) 0 0
\(352\) −1350.00 −0.204418
\(353\) −12405.0 −1.87040 −0.935200 0.354119i \(-0.884781\pi\)
−0.935200 + 0.354119i \(0.884781\pi\)
\(354\) 5400.00 0.810754
\(355\) 8370.00 1.25136
\(356\) −498.000 −0.0741403
\(357\) 666.000 0.0987352
\(358\) 1422.00 0.209930
\(359\) 1098.00 0.161421 0.0807106 0.996738i \(-0.474281\pi\)
0.0807106 + 0.996738i \(0.474281\pi\)
\(360\) 1701.00 0.249029
\(361\) −4743.00 −0.691500
\(362\) −6747.00 −0.979598
\(363\) −1293.00 −0.186956
\(364\) 0 0
\(365\) 2277.00 0.326530
\(366\) −2097.00 −0.299486
\(367\) −5734.00 −0.815565 −0.407783 0.913079i \(-0.633698\pi\)
−0.407783 + 0.913079i \(0.633698\pi\)
\(368\) 426.000 0.0603445
\(369\) 2079.00 0.293302
\(370\) 459.000 0.0644926
\(371\) −1278.00 −0.178842
\(372\) 300.000 0.0418126
\(373\) −8971.00 −1.24531 −0.622655 0.782496i \(-0.713946\pi\)
−0.622655 + 0.782496i \(0.713946\pi\)
\(374\) −9990.00 −1.38120
\(375\) −4563.00 −0.628353
\(376\) 3402.00 0.466608
\(377\) 0 0
\(378\) 162.000 0.0220433
\(379\) −7244.00 −0.981792 −0.490896 0.871218i \(-0.663331\pi\)
−0.490896 + 0.871218i \(0.663331\pi\)
\(380\) 414.000 0.0558888
\(381\) −1812.00 −0.243652
\(382\) −10332.0 −1.38385
\(383\) 6312.00 0.842110 0.421055 0.907035i \(-0.361660\pi\)
0.421055 + 0.907035i \(0.361660\pi\)
\(384\) −4977.00 −0.661410
\(385\) 540.000 0.0714830
\(386\) −12819.0 −1.69034
\(387\) −4626.00 −0.607630
\(388\) −1358.00 −0.177686
\(389\) 3627.00 0.472741 0.236370 0.971663i \(-0.424042\pi\)
0.236370 + 0.971663i \(0.424042\pi\)
\(390\) 0 0
\(391\) 666.000 0.0861408
\(392\) −7119.00 −0.917255
\(393\) −4752.00 −0.609941
\(394\) −5958.00 −0.761827
\(395\) −11916.0 −1.51787
\(396\) −270.000 −0.0342627
\(397\) 3898.00 0.492783 0.246392 0.969170i \(-0.420755\pi\)
0.246392 + 0.969170i \(0.420755\pi\)
\(398\) 7158.00 0.901503
\(399\) −276.000 −0.0346298
\(400\) 3124.00 0.390500
\(401\) 5703.00 0.710210 0.355105 0.934826i \(-0.384445\pi\)
0.355105 + 0.934826i \(0.384445\pi\)
\(402\) 8334.00 1.03399
\(403\) 0 0
\(404\) −357.000 −0.0439639
\(405\) 729.000 0.0894427
\(406\) −630.000 −0.0770108
\(407\) 510.000 0.0621124
\(408\) −6993.00 −0.848542
\(409\) −6311.00 −0.762980 −0.381490 0.924373i \(-0.624589\pi\)
−0.381490 + 0.924373i \(0.624589\pi\)
\(410\) −6237.00 −0.751277
\(411\) −2151.00 −0.258153
\(412\) 1118.00 0.133689
\(413\) 1200.00 0.142974
\(414\) 162.000 0.0192316
\(415\) −7290.00 −0.862294
\(416\) 0 0
\(417\) −2460.00 −0.288889
\(418\) 4140.00 0.484435
\(419\) −2328.00 −0.271433 −0.135716 0.990748i \(-0.543334\pi\)
−0.135716 + 0.990748i \(0.543334\pi\)
\(420\) −54.0000 −0.00627364
\(421\) −2045.00 −0.236739 −0.118370 0.992970i \(-0.537767\pi\)
−0.118370 + 0.992970i \(0.537767\pi\)
\(422\) 4800.00 0.553697
\(423\) 1458.00 0.167590
\(424\) 13419.0 1.53699
\(425\) 4884.00 0.557432
\(426\) −8370.00 −0.951943
\(427\) −466.000 −0.0528134
\(428\) 714.000 0.0806367
\(429\) 0 0
\(430\) 13878.0 1.55641
\(431\) −5034.00 −0.562597 −0.281298 0.959620i \(-0.590765\pi\)
−0.281298 + 0.959620i \(0.590765\pi\)
\(432\) −1917.00 −0.213499
\(433\) 4283.00 0.475353 0.237676 0.971344i \(-0.423614\pi\)
0.237676 + 0.971344i \(0.423614\pi\)
\(434\) 600.000 0.0663616
\(435\) −2835.00 −0.312478
\(436\) −2006.00 −0.220344
\(437\) −276.000 −0.0302125
\(438\) −2277.00 −0.248400
\(439\) −1306.00 −0.141986 −0.0709931 0.997477i \(-0.522617\pi\)
−0.0709931 + 0.997477i \(0.522617\pi\)
\(440\) −5670.00 −0.614333
\(441\) −3051.00 −0.329446
\(442\) 0 0
\(443\) −5796.00 −0.621617 −0.310808 0.950473i \(-0.600600\pi\)
−0.310808 + 0.950473i \(0.600600\pi\)
\(444\) −51.0000 −0.00545125
\(445\) −4482.00 −0.477454
\(446\) −11496.0 −1.22052
\(447\) 5247.00 0.555200
\(448\) −866.000 −0.0913274
\(449\) −2706.00 −0.284419 −0.142209 0.989837i \(-0.545421\pi\)
−0.142209 + 0.989837i \(0.545421\pi\)
\(450\) 1188.00 0.124451
\(451\) −6930.00 −0.723550
\(452\) −1119.00 −0.116445
\(453\) 1110.00 0.115127
\(454\) −4194.00 −0.433555
\(455\) 0 0
\(456\) 2898.00 0.297612
\(457\) 829.000 0.0848555 0.0424278 0.999100i \(-0.486491\pi\)
0.0424278 + 0.999100i \(0.486491\pi\)
\(458\) 13398.0 1.36692
\(459\) −2997.00 −0.304767
\(460\) −54.0000 −0.00547340
\(461\) 5493.00 0.554956 0.277478 0.960732i \(-0.410502\pi\)
0.277478 + 0.960732i \(0.410502\pi\)
\(462\) −540.000 −0.0543789
\(463\) 15346.0 1.54037 0.770183 0.637823i \(-0.220165\pi\)
0.770183 + 0.637823i \(0.220165\pi\)
\(464\) 7455.00 0.745883
\(465\) 2700.00 0.269268
\(466\) 4914.00 0.488491
\(467\) −9594.00 −0.950658 −0.475329 0.879808i \(-0.657671\pi\)
−0.475329 + 0.879808i \(0.657671\pi\)
\(468\) 0 0
\(469\) 1852.00 0.182340
\(470\) −4374.00 −0.429271
\(471\) −7833.00 −0.766296
\(472\) −12600.0 −1.22873
\(473\) 15420.0 1.49897
\(474\) 11916.0 1.15468
\(475\) −2024.00 −0.195511
\(476\) 222.000 0.0213768
\(477\) 5751.00 0.552034
\(478\) −1782.00 −0.170516
\(479\) 12840.0 1.22479 0.612395 0.790552i \(-0.290206\pi\)
0.612395 + 0.790552i \(0.290206\pi\)
\(480\) 1215.00 0.115535
\(481\) 0 0
\(482\) 6909.00 0.652897
\(483\) 36.0000 0.00339142
\(484\) −431.000 −0.0404771
\(485\) −12222.0 −1.14427
\(486\) −729.000 −0.0680414
\(487\) 14086.0 1.31067 0.655336 0.755337i \(-0.272527\pi\)
0.655336 + 0.755337i \(0.272527\pi\)
\(488\) 4893.00 0.453885
\(489\) 4908.00 0.453880
\(490\) 9153.00 0.843858
\(491\) 11694.0 1.07483 0.537416 0.843317i \(-0.319400\pi\)
0.537416 + 0.843317i \(0.319400\pi\)
\(492\) 693.000 0.0635017
\(493\) 11655.0 1.06474
\(494\) 0 0
\(495\) −2430.00 −0.220647
\(496\) −7100.00 −0.642741
\(497\) −1860.00 −0.167872
\(498\) 7290.00 0.655969
\(499\) 3688.00 0.330857 0.165428 0.986222i \(-0.447099\pi\)
0.165428 + 0.986222i \(0.447099\pi\)
\(500\) −1521.00 −0.136042
\(501\) −792.000 −0.0706266
\(502\) −18972.0 −1.68678
\(503\) −4746.00 −0.420703 −0.210352 0.977626i \(-0.567461\pi\)
−0.210352 + 0.977626i \(0.567461\pi\)
\(504\) −378.000 −0.0334077
\(505\) −3213.00 −0.283122
\(506\) −540.000 −0.0474425
\(507\) 0 0
\(508\) −604.000 −0.0527523
\(509\) 14505.0 1.26311 0.631555 0.775331i \(-0.282417\pi\)
0.631555 + 0.775331i \(0.282417\pi\)
\(510\) 8991.00 0.780643
\(511\) −506.000 −0.0438045
\(512\) 8733.00 0.753804
\(513\) 1242.00 0.106892
\(514\) −23499.0 −2.01653
\(515\) 10062.0 0.860941
\(516\) −1542.00 −0.131556
\(517\) −4860.00 −0.413429
\(518\) −102.000 −0.00865178
\(519\) 4230.00 0.357758
\(520\) 0 0
\(521\) 5085.00 0.427597 0.213798 0.976878i \(-0.431416\pi\)
0.213798 + 0.976878i \(0.431416\pi\)
\(522\) 2835.00 0.237710
\(523\) −10882.0 −0.909821 −0.454911 0.890537i \(-0.650329\pi\)
−0.454911 + 0.890537i \(0.650329\pi\)
\(524\) −1584.00 −0.132056
\(525\) 264.000 0.0219465
\(526\) 9090.00 0.753503
\(527\) −11100.0 −0.917502
\(528\) 6390.00 0.526684
\(529\) −12131.0 −0.997041
\(530\) −17253.0 −1.41400
\(531\) −5400.00 −0.441318
\(532\) −92.0000 −0.00749757
\(533\) 0 0
\(534\) 4482.00 0.363212
\(535\) 6426.00 0.519290
\(536\) −19446.0 −1.56705
\(537\) −1422.00 −0.114272
\(538\) 1602.00 0.128378
\(539\) 10170.0 0.812714
\(540\) 243.000 0.0193649
\(541\) 4699.00 0.373430 0.186715 0.982414i \(-0.440216\pi\)
0.186715 + 0.982414i \(0.440216\pi\)
\(542\) −11064.0 −0.876826
\(543\) 6747.00 0.533226
\(544\) −4995.00 −0.393674
\(545\) −18054.0 −1.41899
\(546\) 0 0
\(547\) 8270.00 0.646434 0.323217 0.946325i \(-0.395236\pi\)
0.323217 + 0.946325i \(0.395236\pi\)
\(548\) −717.000 −0.0558918
\(549\) 2097.00 0.163020
\(550\) −3960.00 −0.307009
\(551\) −4830.00 −0.373439
\(552\) −378.000 −0.0291463
\(553\) 2648.00 0.203625
\(554\) −5595.00 −0.429077
\(555\) −459.000 −0.0351053
\(556\) −820.000 −0.0625463
\(557\) 22785.0 1.73327 0.866635 0.498943i \(-0.166278\pi\)
0.866635 + 0.498943i \(0.166278\pi\)
\(558\) −2700.00 −0.204839
\(559\) 0 0
\(560\) 1278.00 0.0964381
\(561\) 9990.00 0.751833
\(562\) 8991.00 0.674844
\(563\) −11928.0 −0.892905 −0.446452 0.894807i \(-0.647313\pi\)
−0.446452 + 0.894807i \(0.647313\pi\)
\(564\) 486.000 0.0362842
\(565\) −10071.0 −0.749894
\(566\) 12342.0 0.916560
\(567\) −162.000 −0.0119989
\(568\) 19530.0 1.44271
\(569\) −7962.00 −0.586616 −0.293308 0.956018i \(-0.594756\pi\)
−0.293308 + 0.956018i \(0.594756\pi\)
\(570\) −3726.00 −0.273798
\(571\) 20618.0 1.51110 0.755549 0.655093i \(-0.227370\pi\)
0.755549 + 0.655093i \(0.227370\pi\)
\(572\) 0 0
\(573\) 10332.0 0.753273
\(574\) 1386.00 0.100785
\(575\) 264.000 0.0191471
\(576\) 3897.00 0.281901
\(577\) 3493.00 0.252020 0.126010 0.992029i \(-0.459783\pi\)
0.126010 + 0.992029i \(0.459783\pi\)
\(578\) −22224.0 −1.59930
\(579\) 12819.0 0.920103
\(580\) −945.000 −0.0676534
\(581\) 1620.00 0.115678
\(582\) 12222.0 0.870478
\(583\) −19170.0 −1.36182
\(584\) 5313.00 0.376461
\(585\) 0 0
\(586\) −13995.0 −0.986567
\(587\) −10416.0 −0.732392 −0.366196 0.930538i \(-0.619340\pi\)
−0.366196 + 0.930538i \(0.619340\pi\)
\(588\) −1017.00 −0.0713272
\(589\) 4600.00 0.321799
\(590\) 16200.0 1.13041
\(591\) 5958.00 0.414686
\(592\) 1207.00 0.0837963
\(593\) −2061.00 −0.142724 −0.0713618 0.997450i \(-0.522734\pi\)
−0.0713618 + 0.997450i \(0.522734\pi\)
\(594\) 2430.00 0.167852
\(595\) 1998.00 0.137664
\(596\) 1749.00 0.120204
\(597\) −7158.00 −0.490716
\(598\) 0 0
\(599\) 12456.0 0.849647 0.424823 0.905276i \(-0.360336\pi\)
0.424823 + 0.905276i \(0.360336\pi\)
\(600\) −2772.00 −0.188611
\(601\) −781.000 −0.0530077 −0.0265039 0.999649i \(-0.508437\pi\)
−0.0265039 + 0.999649i \(0.508437\pi\)
\(602\) −3084.00 −0.208795
\(603\) −8334.00 −0.562830
\(604\) 370.000 0.0249256
\(605\) −3879.00 −0.260667
\(606\) 3213.00 0.215378
\(607\) 19304.0 1.29082 0.645408 0.763838i \(-0.276687\pi\)
0.645408 + 0.763838i \(0.276687\pi\)
\(608\) 2070.00 0.138075
\(609\) 630.000 0.0419194
\(610\) −6291.00 −0.417566
\(611\) 0 0
\(612\) −999.000 −0.0659840
\(613\) −12041.0 −0.793363 −0.396681 0.917956i \(-0.629838\pi\)
−0.396681 + 0.917956i \(0.629838\pi\)
\(614\) 4506.00 0.296168
\(615\) 6237.00 0.408943
\(616\) 1260.00 0.0824137
\(617\) −9717.00 −0.634022 −0.317011 0.948422i \(-0.602679\pi\)
−0.317011 + 0.948422i \(0.602679\pi\)
\(618\) −10062.0 −0.654940
\(619\) 21040.0 1.36619 0.683093 0.730332i \(-0.260634\pi\)
0.683093 + 0.730332i \(0.260634\pi\)
\(620\) 900.000 0.0582982
\(621\) −162.000 −0.0104683
\(622\) −6318.00 −0.407281
\(623\) 996.000 0.0640512
\(624\) 0 0
\(625\) −8189.00 −0.524096
\(626\) 11694.0 0.746623
\(627\) −4140.00 −0.263693
\(628\) −2611.00 −0.165908
\(629\) 1887.00 0.119618
\(630\) 486.000 0.0307344
\(631\) 5068.00 0.319737 0.159868 0.987138i \(-0.448893\pi\)
0.159868 + 0.987138i \(0.448893\pi\)
\(632\) −27804.0 −1.74997
\(633\) −4800.00 −0.301395
\(634\) 28053.0 1.75730
\(635\) −5436.00 −0.339718
\(636\) 1917.00 0.119519
\(637\) 0 0
\(638\) −9450.00 −0.586409
\(639\) 8370.00 0.518172
\(640\) −14931.0 −0.922187
\(641\) 10185.0 0.627587 0.313794 0.949491i \(-0.398400\pi\)
0.313794 + 0.949491i \(0.398400\pi\)
\(642\) −6426.00 −0.395037
\(643\) −25928.0 −1.59020 −0.795101 0.606476i \(-0.792582\pi\)
−0.795101 + 0.606476i \(0.792582\pi\)
\(644\) 12.0000 0.000734264 0
\(645\) −13878.0 −0.847203
\(646\) 15318.0 0.932939
\(647\) 23160.0 1.40729 0.703643 0.710554i \(-0.251556\pi\)
0.703643 + 0.710554i \(0.251556\pi\)
\(648\) 1701.00 0.103120
\(649\) 18000.0 1.08869
\(650\) 0 0
\(651\) −600.000 −0.0361227
\(652\) 1636.00 0.0982680
\(653\) 16626.0 0.996364 0.498182 0.867073i \(-0.334001\pi\)
0.498182 + 0.867073i \(0.334001\pi\)
\(654\) 18054.0 1.07946
\(655\) −14256.0 −0.850424
\(656\) −16401.0 −0.976146
\(657\) 2277.00 0.135212
\(658\) 972.000 0.0575874
\(659\) −14808.0 −0.875323 −0.437661 0.899140i \(-0.644193\pi\)
−0.437661 + 0.899140i \(0.644193\pi\)
\(660\) −810.000 −0.0477715
\(661\) −4853.00 −0.285567 −0.142784 0.989754i \(-0.545605\pi\)
−0.142784 + 0.989754i \(0.545605\pi\)
\(662\) −27516.0 −1.61547
\(663\) 0 0
\(664\) −17010.0 −0.994151
\(665\) −828.000 −0.0482834
\(666\) 459.000 0.0267055
\(667\) 630.000 0.0365723
\(668\) −264.000 −0.0152911
\(669\) 11496.0 0.664366
\(670\) 25002.0 1.44166
\(671\) −6990.00 −0.402155
\(672\) −270.000 −0.0154992
\(673\) −16165.0 −0.925877 −0.462938 0.886391i \(-0.653205\pi\)
−0.462938 + 0.886391i \(0.653205\pi\)
\(674\) 33267.0 1.90118
\(675\) −1188.00 −0.0677424
\(676\) 0 0
\(677\) −25686.0 −1.45819 −0.729094 0.684414i \(-0.760058\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(678\) 10071.0 0.570464
\(679\) 2716.00 0.153506
\(680\) −20979.0 −1.18310
\(681\) 4194.00 0.235998
\(682\) 9000.00 0.505319
\(683\) 19056.0 1.06758 0.533790 0.845617i \(-0.320767\pi\)
0.533790 + 0.845617i \(0.320767\pi\)
\(684\) 414.000 0.0231428
\(685\) −6453.00 −0.359936
\(686\) −4092.00 −0.227745
\(687\) −13398.0 −0.744055
\(688\) 36494.0 2.02227
\(689\) 0 0
\(690\) 486.000 0.0268141
\(691\) 16390.0 0.902323 0.451161 0.892442i \(-0.351010\pi\)
0.451161 + 0.892442i \(0.351010\pi\)
\(692\) 1410.00 0.0774569
\(693\) 540.000 0.0296001
\(694\) −29286.0 −1.60185
\(695\) −7380.00 −0.402790
\(696\) −6615.00 −0.360260
\(697\) −25641.0 −1.39343
\(698\) −24870.0 −1.34863
\(699\) −4914.00 −0.265901
\(700\) 88.0000 0.00475155
\(701\) −27846.0 −1.50033 −0.750163 0.661253i \(-0.770025\pi\)
−0.750163 + 0.661253i \(0.770025\pi\)
\(702\) 0 0
\(703\) −782.000 −0.0419540
\(704\) −12990.0 −0.695425
\(705\) 4374.00 0.233666
\(706\) 37215.0 1.98386
\(707\) 714.000 0.0379812
\(708\) −1800.00 −0.0955482
\(709\) 12283.0 0.650632 0.325316 0.945605i \(-0.394529\pi\)
0.325316 + 0.945605i \(0.394529\pi\)
\(710\) −25110.0 −1.32727
\(711\) −11916.0 −0.628530
\(712\) −10458.0 −0.550464
\(713\) −600.000 −0.0315150
\(714\) −1998.00 −0.104724
\(715\) 0 0
\(716\) −474.000 −0.0247405
\(717\) 1782.00 0.0928173
\(718\) −3294.00 −0.171213
\(719\) 25512.0 1.32328 0.661639 0.749822i \(-0.269861\pi\)
0.661639 + 0.749822i \(0.269861\pi\)
\(720\) −5751.00 −0.297677
\(721\) −2236.00 −0.115497
\(722\) 14229.0 0.733447
\(723\) −6909.00 −0.355392
\(724\) 2249.00 0.115447
\(725\) 4620.00 0.236666
\(726\) 3879.00 0.198296
\(727\) 6110.00 0.311702 0.155851 0.987781i \(-0.450188\pi\)
0.155851 + 0.987781i \(0.450188\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −6831.00 −0.346338
\(731\) 57054.0 2.88676
\(732\) 699.000 0.0352948
\(733\) 27127.0 1.36693 0.683464 0.729984i \(-0.260473\pi\)
0.683464 + 0.729984i \(0.260473\pi\)
\(734\) 17202.0 0.865037
\(735\) −9153.00 −0.459338
\(736\) −270.000 −0.0135222
\(737\) 27780.0 1.38845
\(738\) −6237.00 −0.311094
\(739\) 880.000 0.0438042 0.0219021 0.999760i \(-0.493028\pi\)
0.0219021 + 0.999760i \(0.493028\pi\)
\(740\) −153.000 −0.00760053
\(741\) 0 0
\(742\) 3834.00 0.189691
\(743\) 21876.0 1.08015 0.540076 0.841616i \(-0.318396\pi\)
0.540076 + 0.841616i \(0.318396\pi\)
\(744\) 6300.00 0.310442
\(745\) 15741.0 0.774102
\(746\) 26913.0 1.32085
\(747\) −7290.00 −0.357064
\(748\) 3330.00 0.162777
\(749\) −1428.00 −0.0696635
\(750\) 13689.0 0.666469
\(751\) 11798.0 0.573256 0.286628 0.958042i \(-0.407466\pi\)
0.286628 + 0.958042i \(0.407466\pi\)
\(752\) −11502.0 −0.557759
\(753\) 18972.0 0.918165
\(754\) 0 0
\(755\) 3330.00 0.160518
\(756\) −54.0000 −0.00259783
\(757\) −8074.00 −0.387655 −0.193827 0.981036i \(-0.562090\pi\)
−0.193827 + 0.981036i \(0.562090\pi\)
\(758\) 21732.0 1.04135
\(759\) 540.000 0.0258245
\(760\) 8694.00 0.414953
\(761\) −19554.0 −0.931448 −0.465724 0.884930i \(-0.654206\pi\)
−0.465724 + 0.884930i \(0.654206\pi\)
\(762\) 5436.00 0.258432
\(763\) 4012.00 0.190359
\(764\) 3444.00 0.163088
\(765\) −8991.00 −0.424928
\(766\) −18936.0 −0.893193
\(767\) 0 0
\(768\) 4539.00 0.213264
\(769\) −14030.0 −0.657913 −0.328956 0.944345i \(-0.606697\pi\)
−0.328956 + 0.944345i \(0.606697\pi\)
\(770\) −1620.00 −0.0758192
\(771\) 23499.0 1.09766
\(772\) 4273.00 0.199208
\(773\) −36042.0 −1.67703 −0.838513 0.544882i \(-0.816574\pi\)
−0.838513 + 0.544882i \(0.816574\pi\)
\(774\) 13878.0 0.644489
\(775\) −4400.00 −0.203939
\(776\) −28518.0 −1.31925
\(777\) 102.000 0.00470943
\(778\) −10881.0 −0.501417
\(779\) 10626.0 0.488724
\(780\) 0 0
\(781\) −27900.0 −1.27828
\(782\) −1998.00 −0.0913662
\(783\) −2835.00 −0.129393
\(784\) 24069.0 1.09644
\(785\) −23499.0 −1.06843
\(786\) 14256.0 0.646940
\(787\) −28628.0 −1.29667 −0.648334 0.761356i \(-0.724534\pi\)
−0.648334 + 0.761356i \(0.724534\pi\)
\(788\) 1986.00 0.0897821
\(789\) −9090.00 −0.410155
\(790\) 35748.0 1.60995
\(791\) 2238.00 0.100599
\(792\) −5670.00 −0.254387
\(793\) 0 0
\(794\) −11694.0 −0.522676
\(795\) 17253.0 0.769687
\(796\) −2386.00 −0.106243
\(797\) −37434.0 −1.66371 −0.831857 0.554990i \(-0.812722\pi\)
−0.831857 + 0.554990i \(0.812722\pi\)
\(798\) 828.000 0.0367304
\(799\) −17982.0 −0.796192
\(800\) −1980.00 −0.0875045
\(801\) −4482.00 −0.197707
\(802\) −17109.0 −0.753292
\(803\) −7590.00 −0.333556
\(804\) −2778.00 −0.121856
\(805\) 108.000 0.00472857
\(806\) 0 0
\(807\) −1602.00 −0.0698799
\(808\) −7497.00 −0.326415
\(809\) 37569.0 1.63270 0.816351 0.577556i \(-0.195994\pi\)
0.816351 + 0.577556i \(0.195994\pi\)
\(810\) −2187.00 −0.0948683
\(811\) −5516.00 −0.238832 −0.119416 0.992844i \(-0.538102\pi\)
−0.119416 + 0.992844i \(0.538102\pi\)
\(812\) 210.000 0.00907581
\(813\) 11064.0 0.477283
\(814\) −1530.00 −0.0658802
\(815\) 14724.0 0.632833
\(816\) 23643.0 1.01430
\(817\) −23644.0 −1.01248
\(818\) 18933.0 0.809263
\(819\) 0 0
\(820\) 2079.00 0.0885388
\(821\) −8778.00 −0.373148 −0.186574 0.982441i \(-0.559738\pi\)
−0.186574 + 0.982441i \(0.559738\pi\)
\(822\) 6453.00 0.273813
\(823\) −3088.00 −0.130791 −0.0653955 0.997859i \(-0.520831\pi\)
−0.0653955 + 0.997859i \(0.520831\pi\)
\(824\) 23478.0 0.992591
\(825\) 3960.00 0.167115
\(826\) −3600.00 −0.151647
\(827\) −13176.0 −0.554020 −0.277010 0.960867i \(-0.589343\pi\)
−0.277010 + 0.960867i \(0.589343\pi\)
\(828\) −54.0000 −0.00226646
\(829\) −2359.00 −0.0988317 −0.0494158 0.998778i \(-0.515736\pi\)
−0.0494158 + 0.998778i \(0.515736\pi\)
\(830\) 21870.0 0.914601
\(831\) 5595.00 0.233560
\(832\) 0 0
\(833\) 37629.0 1.56515
\(834\) 7380.00 0.306413
\(835\) −2376.00 −0.0984729
\(836\) −1380.00 −0.0570913
\(837\) 2700.00 0.111500
\(838\) 6984.00 0.287898
\(839\) 2676.00 0.110114 0.0550571 0.998483i \(-0.482466\pi\)
0.0550571 + 0.998483i \(0.482466\pi\)
\(840\) −1134.00 −0.0465794
\(841\) −13364.0 −0.547952
\(842\) 6135.00 0.251100
\(843\) −8991.00 −0.367339
\(844\) −1600.00 −0.0652539
\(845\) 0 0
\(846\) −4374.00 −0.177756
\(847\) 862.000 0.0349689
\(848\) −45369.0 −1.83724
\(849\) −12342.0 −0.498912
\(850\) −14652.0 −0.591246
\(851\) 102.000 0.00410871
\(852\) 2790.00 0.112188
\(853\) −2477.00 −0.0994266 −0.0497133 0.998764i \(-0.515831\pi\)
−0.0497133 + 0.998764i \(0.515831\pi\)
\(854\) 1398.00 0.0560171
\(855\) 3726.00 0.149037
\(856\) 14994.0 0.598697
\(857\) −17199.0 −0.685539 −0.342769 0.939420i \(-0.611365\pi\)
−0.342769 + 0.939420i \(0.611365\pi\)
\(858\) 0 0
\(859\) 24338.0 0.966708 0.483354 0.875425i \(-0.339418\pi\)
0.483354 + 0.875425i \(0.339418\pi\)
\(860\) −4626.00 −0.183425
\(861\) −1386.00 −0.0548603
\(862\) 15102.0 0.596724
\(863\) −25146.0 −0.991865 −0.495933 0.868361i \(-0.665174\pi\)
−0.495933 + 0.868361i \(0.665174\pi\)
\(864\) 1215.00 0.0478416
\(865\) 12690.0 0.498813
\(866\) −12849.0 −0.504188
\(867\) 22224.0 0.870550
\(868\) −200.000 −0.00782079
\(869\) 39720.0 1.55053
\(870\) 8505.00 0.331433
\(871\) 0 0
\(872\) −42126.0 −1.63597
\(873\) −12222.0 −0.473828
\(874\) 828.000 0.0320452
\(875\) 3042.00 0.117530
\(876\) 759.000 0.0292742
\(877\) −18089.0 −0.696490 −0.348245 0.937403i \(-0.613222\pi\)
−0.348245 + 0.937403i \(0.613222\pi\)
\(878\) 3918.00 0.150599
\(879\) 13995.0 0.537019
\(880\) 19170.0 0.734342
\(881\) −15099.0 −0.577410 −0.288705 0.957418i \(-0.593225\pi\)
−0.288705 + 0.957418i \(0.593225\pi\)
\(882\) 9153.00 0.349430
\(883\) 33488.0 1.27629 0.638143 0.769918i \(-0.279703\pi\)
0.638143 + 0.769918i \(0.279703\pi\)
\(884\) 0 0
\(885\) −16200.0 −0.615319
\(886\) 17388.0 0.659324
\(887\) −39768.0 −1.50539 −0.752694 0.658371i \(-0.771246\pi\)
−0.752694 + 0.658371i \(0.771246\pi\)
\(888\) −1071.00 −0.0404734
\(889\) 1208.00 0.0455737
\(890\) 13446.0 0.506417
\(891\) −2430.00 −0.0913671
\(892\) 3832.00 0.143840
\(893\) 7452.00 0.279252
\(894\) −15741.0 −0.588879
\(895\) −4266.00 −0.159326
\(896\) 3318.00 0.123713
\(897\) 0 0
\(898\) 8118.00 0.301672
\(899\) −10500.0 −0.389538
\(900\) −396.000 −0.0146667
\(901\) −70929.0 −2.62263
\(902\) 20790.0 0.767440
\(903\) 3084.00 0.113653
\(904\) −23499.0 −0.864563
\(905\) 20241.0 0.743463
\(906\) −3330.00 −0.122110
\(907\) 32156.0 1.17720 0.588601 0.808424i \(-0.299679\pi\)
0.588601 + 0.808424i \(0.299679\pi\)
\(908\) 1398.00 0.0510950
\(909\) −3213.00 −0.117237
\(910\) 0 0
\(911\) 11520.0 0.418962 0.209481 0.977813i \(-0.432823\pi\)
0.209481 + 0.977813i \(0.432823\pi\)
\(912\) −9798.00 −0.355750
\(913\) 24300.0 0.880846
\(914\) −2487.00 −0.0900029
\(915\) 6291.00 0.227294
\(916\) −4466.00 −0.161093
\(917\) 3168.00 0.114086
\(918\) 8991.00 0.323254
\(919\) 4952.00 0.177749 0.0888745 0.996043i \(-0.471673\pi\)
0.0888745 + 0.996043i \(0.471673\pi\)
\(920\) −1134.00 −0.0406379
\(921\) −4506.00 −0.161214
\(922\) −16479.0 −0.588619
\(923\) 0 0
\(924\) 180.000 0.00640862
\(925\) 748.000 0.0265882
\(926\) −46038.0 −1.63380
\(927\) 10062.0 0.356504
\(928\) −4725.00 −0.167140
\(929\) −8781.00 −0.310113 −0.155057 0.987906i \(-0.549556\pi\)
−0.155057 + 0.987906i \(0.549556\pi\)
\(930\) −8100.00 −0.285602
\(931\) −15594.0 −0.548950
\(932\) −1638.00 −0.0575692
\(933\) 6318.00 0.221696
\(934\) 28782.0 1.00833
\(935\) 29970.0 1.04826
\(936\) 0 0
\(937\) 50039.0 1.74461 0.872307 0.488959i \(-0.162623\pi\)
0.872307 + 0.488959i \(0.162623\pi\)
\(938\) −5556.00 −0.193401
\(939\) −11694.0 −0.406410
\(940\) 1458.00 0.0505901
\(941\) 50670.0 1.75536 0.877681 0.479246i \(-0.159090\pi\)
0.877681 + 0.479246i \(0.159090\pi\)
\(942\) 23499.0 0.812780
\(943\) −1386.00 −0.0478625
\(944\) 42600.0 1.46876
\(945\) −486.000 −0.0167297
\(946\) −46260.0 −1.58990
\(947\) −42384.0 −1.45438 −0.727188 0.686438i \(-0.759173\pi\)
−0.727188 + 0.686438i \(0.759173\pi\)
\(948\) −3972.00 −0.136081
\(949\) 0 0
\(950\) 6072.00 0.207370
\(951\) −28053.0 −0.956552
\(952\) 4662.00 0.158715
\(953\) −50538.0 −1.71782 −0.858912 0.512123i \(-0.828859\pi\)
−0.858912 + 0.512123i \(0.828859\pi\)
\(954\) −17253.0 −0.585520
\(955\) 30996.0 1.05027
\(956\) 594.000 0.0200955
\(957\) 9450.00 0.319201
\(958\) −38520.0 −1.29909
\(959\) 1434.00 0.0482860
\(960\) 11691.0 0.393047
\(961\) −19791.0 −0.664328
\(962\) 0 0
\(963\) 6426.00 0.215031
\(964\) −2303.00 −0.0769446
\(965\) 38457.0 1.28288
\(966\) −108.000 −0.00359715
\(967\) 6886.00 0.228996 0.114498 0.993423i \(-0.463474\pi\)
0.114498 + 0.993423i \(0.463474\pi\)
\(968\) −9051.00 −0.300527
\(969\) −15318.0 −0.507828
\(970\) 36666.0 1.21368
\(971\) 9060.00 0.299433 0.149716 0.988729i \(-0.452164\pi\)
0.149716 + 0.988729i \(0.452164\pi\)
\(972\) 243.000 0.00801875
\(973\) 1640.00 0.0540349
\(974\) −42258.0 −1.39018
\(975\) 0 0
\(976\) −16543.0 −0.542550
\(977\) 28311.0 0.927072 0.463536 0.886078i \(-0.346581\pi\)
0.463536 + 0.886078i \(0.346581\pi\)
\(978\) −14724.0 −0.481413
\(979\) 14940.0 0.487727
\(980\) −3051.00 −0.0994496
\(981\) −18054.0 −0.587584
\(982\) −35082.0 −1.14003
\(983\) −4284.00 −0.139001 −0.0695007 0.997582i \(-0.522141\pi\)
−0.0695007 + 0.997582i \(0.522141\pi\)
\(984\) 14553.0 0.471476
\(985\) 17874.0 0.578186
\(986\) −34965.0 −1.12932
\(987\) −972.000 −0.0313466
\(988\) 0 0
\(989\) 3084.00 0.0991562
\(990\) 7290.00 0.234032
\(991\) −2458.00 −0.0787901 −0.0393950 0.999224i \(-0.512543\pi\)
−0.0393950 + 0.999224i \(0.512543\pi\)
\(992\) 4500.00 0.144027
\(993\) 27516.0 0.879349
\(994\) 5580.00 0.178055
\(995\) −21474.0 −0.684193
\(996\) −2430.00 −0.0773067
\(997\) 24101.0 0.765583 0.382792 0.923835i \(-0.374963\pi\)
0.382792 + 0.923835i \(0.374963\pi\)
\(998\) −11064.0 −0.350927
\(999\) −459.000 −0.0145367
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.a.1.1 1
3.2 odd 2 1521.4.a.j.1.1 1
13.4 even 6 39.4.e.a.16.1 2
13.5 odd 4 507.4.b.c.337.2 2
13.8 odd 4 507.4.b.c.337.1 2
13.10 even 6 39.4.e.a.22.1 yes 2
13.12 even 2 507.4.a.e.1.1 1
39.17 odd 6 117.4.g.b.55.1 2
39.23 odd 6 117.4.g.b.100.1 2
39.38 odd 2 1521.4.a.c.1.1 1
52.23 odd 6 624.4.q.b.529.1 2
52.43 odd 6 624.4.q.b.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.a.16.1 2 13.4 even 6
39.4.e.a.22.1 yes 2 13.10 even 6
117.4.g.b.55.1 2 39.17 odd 6
117.4.g.b.100.1 2 39.23 odd 6
507.4.a.a.1.1 1 1.1 even 1 trivial
507.4.a.e.1.1 1 13.12 even 2
507.4.b.c.337.1 2 13.8 odd 4
507.4.b.c.337.2 2 13.5 odd 4
624.4.q.b.289.1 2 52.43 odd 6
624.4.q.b.529.1 2 52.23 odd 6
1521.4.a.c.1.1 1 39.38 odd 2
1521.4.a.j.1.1 1 3.2 odd 2