Properties

Label 294.6.a.m.1.1
Level $294$
Weight $6$
Character 294.1
Self dual yes
Analytic conductor $47.153$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.1528430250\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 294.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +66.0000 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +66.0000 q^{5} +36.0000 q^{6} +64.0000 q^{8} +81.0000 q^{9} +264.000 q^{10} -60.0000 q^{11} +144.000 q^{12} +658.000 q^{13} +594.000 q^{15} +256.000 q^{16} +414.000 q^{17} +324.000 q^{18} -956.000 q^{19} +1056.00 q^{20} -240.000 q^{22} +600.000 q^{23} +576.000 q^{24} +1231.00 q^{25} +2632.00 q^{26} +729.000 q^{27} +5574.00 q^{29} +2376.00 q^{30} +3592.00 q^{31} +1024.00 q^{32} -540.000 q^{33} +1656.00 q^{34} +1296.00 q^{36} -8458.00 q^{37} -3824.00 q^{38} +5922.00 q^{39} +4224.00 q^{40} -19194.0 q^{41} +13316.0 q^{43} -960.000 q^{44} +5346.00 q^{45} +2400.00 q^{46} +19680.0 q^{47} +2304.00 q^{48} +4924.00 q^{50} +3726.00 q^{51} +10528.0 q^{52} -31266.0 q^{53} +2916.00 q^{54} -3960.00 q^{55} -8604.00 q^{57} +22296.0 q^{58} -26340.0 q^{59} +9504.00 q^{60} +31090.0 q^{61} +14368.0 q^{62} +4096.00 q^{64} +43428.0 q^{65} -2160.00 q^{66} -16804.0 q^{67} +6624.00 q^{68} +5400.00 q^{69} +6120.00 q^{71} +5184.00 q^{72} +25558.0 q^{73} -33832.0 q^{74} +11079.0 q^{75} -15296.0 q^{76} +23688.0 q^{78} +74408.0 q^{79} +16896.0 q^{80} +6561.00 q^{81} -76776.0 q^{82} +6468.00 q^{83} +27324.0 q^{85} +53264.0 q^{86} +50166.0 q^{87} -3840.00 q^{88} +32742.0 q^{89} +21384.0 q^{90} +9600.00 q^{92} +32328.0 q^{93} +78720.0 q^{94} -63096.0 q^{95} +9216.00 q^{96} -166082. q^{97} -4860.00 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 0.707107
\(3\) 9.00000 0.577350
\(4\) 16.0000 0.500000
\(5\) 66.0000 1.18064 0.590322 0.807168i \(-0.299001\pi\)
0.590322 + 0.807168i \(0.299001\pi\)
\(6\) 36.0000 0.408248
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) 81.0000 0.333333
\(10\) 264.000 0.834841
\(11\) −60.0000 −0.149510 −0.0747549 0.997202i \(-0.523817\pi\)
−0.0747549 + 0.997202i \(0.523817\pi\)
\(12\) 144.000 0.288675
\(13\) 658.000 1.07986 0.539930 0.841710i \(-0.318451\pi\)
0.539930 + 0.841710i \(0.318451\pi\)
\(14\) 0 0
\(15\) 594.000 0.681645
\(16\) 256.000 0.250000
\(17\) 414.000 0.347439 0.173719 0.984795i \(-0.444421\pi\)
0.173719 + 0.984795i \(0.444421\pi\)
\(18\) 324.000 0.235702
\(19\) −956.000 −0.607539 −0.303769 0.952746i \(-0.598245\pi\)
−0.303769 + 0.952746i \(0.598245\pi\)
\(20\) 1056.00 0.590322
\(21\) 0 0
\(22\) −240.000 −0.105719
\(23\) 600.000 0.236500 0.118250 0.992984i \(-0.462272\pi\)
0.118250 + 0.992984i \(0.462272\pi\)
\(24\) 576.000 0.204124
\(25\) 1231.00 0.393920
\(26\) 2632.00 0.763576
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 5574.00 1.23076 0.615378 0.788232i \(-0.289003\pi\)
0.615378 + 0.788232i \(0.289003\pi\)
\(30\) 2376.00 0.481996
\(31\) 3592.00 0.671324 0.335662 0.941983i \(-0.391040\pi\)
0.335662 + 0.941983i \(0.391040\pi\)
\(32\) 1024.00 0.176777
\(33\) −540.000 −0.0863195
\(34\) 1656.00 0.245676
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) −8458.00 −1.01570 −0.507848 0.861447i \(-0.669559\pi\)
−0.507848 + 0.861447i \(0.669559\pi\)
\(38\) −3824.00 −0.429595
\(39\) 5922.00 0.623458
\(40\) 4224.00 0.417421
\(41\) −19194.0 −1.78322 −0.891612 0.452800i \(-0.850425\pi\)
−0.891612 + 0.452800i \(0.850425\pi\)
\(42\) 0 0
\(43\) 13316.0 1.09825 0.549127 0.835739i \(-0.314960\pi\)
0.549127 + 0.835739i \(0.314960\pi\)
\(44\) −960.000 −0.0747549
\(45\) 5346.00 0.393548
\(46\) 2400.00 0.167231
\(47\) 19680.0 1.29951 0.649756 0.760143i \(-0.274871\pi\)
0.649756 + 0.760143i \(0.274871\pi\)
\(48\) 2304.00 0.144338
\(49\) 0 0
\(50\) 4924.00 0.278544
\(51\) 3726.00 0.200594
\(52\) 10528.0 0.539930
\(53\) −31266.0 −1.52891 −0.764456 0.644676i \(-0.776992\pi\)
−0.764456 + 0.644676i \(0.776992\pi\)
\(54\) 2916.00 0.136083
\(55\) −3960.00 −0.176518
\(56\) 0 0
\(57\) −8604.00 −0.350763
\(58\) 22296.0 0.870276
\(59\) −26340.0 −0.985112 −0.492556 0.870281i \(-0.663937\pi\)
−0.492556 + 0.870281i \(0.663937\pi\)
\(60\) 9504.00 0.340823
\(61\) 31090.0 1.06978 0.534892 0.844920i \(-0.320352\pi\)
0.534892 + 0.844920i \(0.320352\pi\)
\(62\) 14368.0 0.474698
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 43428.0 1.27493
\(66\) −2160.00 −0.0610371
\(67\) −16804.0 −0.457326 −0.228663 0.973506i \(-0.573435\pi\)
−0.228663 + 0.973506i \(0.573435\pi\)
\(68\) 6624.00 0.173719
\(69\) 5400.00 0.136544
\(70\) 0 0
\(71\) 6120.00 0.144081 0.0720403 0.997402i \(-0.477049\pi\)
0.0720403 + 0.997402i \(0.477049\pi\)
\(72\) 5184.00 0.117851
\(73\) 25558.0 0.561332 0.280666 0.959806i \(-0.409445\pi\)
0.280666 + 0.959806i \(0.409445\pi\)
\(74\) −33832.0 −0.718205
\(75\) 11079.0 0.227430
\(76\) −15296.0 −0.303769
\(77\) 0 0
\(78\) 23688.0 0.440851
\(79\) 74408.0 1.34138 0.670690 0.741738i \(-0.265998\pi\)
0.670690 + 0.741738i \(0.265998\pi\)
\(80\) 16896.0 0.295161
\(81\) 6561.00 0.111111
\(82\) −76776.0 −1.26093
\(83\) 6468.00 0.103056 0.0515282 0.998672i \(-0.483591\pi\)
0.0515282 + 0.998672i \(0.483591\pi\)
\(84\) 0 0
\(85\) 27324.0 0.410201
\(86\) 53264.0 0.776583
\(87\) 50166.0 0.710577
\(88\) −3840.00 −0.0528597
\(89\) 32742.0 0.438157 0.219079 0.975707i \(-0.429695\pi\)
0.219079 + 0.975707i \(0.429695\pi\)
\(90\) 21384.0 0.278280
\(91\) 0 0
\(92\) 9600.00 0.118250
\(93\) 32328.0 0.387589
\(94\) 78720.0 0.918894
\(95\) −63096.0 −0.717287
\(96\) 9216.00 0.102062
\(97\) −166082. −1.79223 −0.896114 0.443824i \(-0.853622\pi\)
−0.896114 + 0.443824i \(0.853622\pi\)
\(98\) 0 0
\(99\) −4860.00 −0.0498366
\(100\) 19696.0 0.196960
\(101\) 22002.0 0.214614 0.107307 0.994226i \(-0.465777\pi\)
0.107307 + 0.994226i \(0.465777\pi\)
\(102\) 14904.0 0.141841
\(103\) 79264.0 0.736178 0.368089 0.929791i \(-0.380012\pi\)
0.368089 + 0.929791i \(0.380012\pi\)
\(104\) 42112.0 0.381788
\(105\) 0 0
\(106\) −125064. −1.08110
\(107\) 227988. 1.92510 0.962548 0.271110i \(-0.0873908\pi\)
0.962548 + 0.271110i \(0.0873908\pi\)
\(108\) 11664.0 0.0962250
\(109\) −8530.00 −0.0687674 −0.0343837 0.999409i \(-0.510947\pi\)
−0.0343837 + 0.999409i \(0.510947\pi\)
\(110\) −15840.0 −0.124817
\(111\) −76122.0 −0.586412
\(112\) 0 0
\(113\) −195438. −1.43984 −0.719918 0.694059i \(-0.755821\pi\)
−0.719918 + 0.694059i \(0.755821\pi\)
\(114\) −34416.0 −0.248027
\(115\) 39600.0 0.279223
\(116\) 89184.0 0.615378
\(117\) 53298.0 0.359953
\(118\) −105360. −0.696580
\(119\) 0 0
\(120\) 38016.0 0.240998
\(121\) −157451. −0.977647
\(122\) 124360. 0.756452
\(123\) −172746. −1.02954
\(124\) 57472.0 0.335662
\(125\) −125004. −0.715565
\(126\) 0 0
\(127\) 173000. 0.951780 0.475890 0.879505i \(-0.342126\pi\)
0.475890 + 0.879505i \(0.342126\pi\)
\(128\) 16384.0 0.0883883
\(129\) 119844. 0.634077
\(130\) 173712. 0.901512
\(131\) −151260. −0.770098 −0.385049 0.922896i \(-0.625815\pi\)
−0.385049 + 0.922896i \(0.625815\pi\)
\(132\) −8640.00 −0.0431597
\(133\) 0 0
\(134\) −67216.0 −0.323378
\(135\) 48114.0 0.227215
\(136\) 26496.0 0.122838
\(137\) −128454. −0.584718 −0.292359 0.956309i \(-0.594440\pi\)
−0.292359 + 0.956309i \(0.594440\pi\)
\(138\) 21600.0 0.0965508
\(139\) −154196. −0.676918 −0.338459 0.940981i \(-0.609906\pi\)
−0.338459 + 0.940981i \(0.609906\pi\)
\(140\) 0 0
\(141\) 177120. 0.750274
\(142\) 24480.0 0.101880
\(143\) −39480.0 −0.161450
\(144\) 20736.0 0.0833333
\(145\) 367884. 1.45308
\(146\) 102232. 0.396922
\(147\) 0 0
\(148\) −135328. −0.507848
\(149\) 29454.0 0.108687 0.0543436 0.998522i \(-0.482693\pi\)
0.0543436 + 0.998522i \(0.482693\pi\)
\(150\) 44316.0 0.160817
\(151\) −203872. −0.727638 −0.363819 0.931470i \(-0.618527\pi\)
−0.363819 + 0.931470i \(0.618527\pi\)
\(152\) −61184.0 −0.214797
\(153\) 33534.0 0.115813
\(154\) 0 0
\(155\) 237072. 0.792594
\(156\) 94752.0 0.311729
\(157\) −136142. −0.440801 −0.220401 0.975409i \(-0.570737\pi\)
−0.220401 + 0.975409i \(0.570737\pi\)
\(158\) 297632. 0.948499
\(159\) −281394. −0.882718
\(160\) 67584.0 0.208710
\(161\) 0 0
\(162\) 26244.0 0.0785674
\(163\) −171124. −0.504478 −0.252239 0.967665i \(-0.581167\pi\)
−0.252239 + 0.967665i \(0.581167\pi\)
\(164\) −307104. −0.891612
\(165\) −35640.0 −0.101913
\(166\) 25872.0 0.0728718
\(167\) 676200. 1.87622 0.938110 0.346336i \(-0.112574\pi\)
0.938110 + 0.346336i \(0.112574\pi\)
\(168\) 0 0
\(169\) 61671.0 0.166098
\(170\) 109296. 0.290056
\(171\) −77436.0 −0.202513
\(172\) 213056. 0.549127
\(173\) −133158. −0.338261 −0.169131 0.985594i \(-0.554096\pi\)
−0.169131 + 0.985594i \(0.554096\pi\)
\(174\) 200664. 0.502454
\(175\) 0 0
\(176\) −15360.0 −0.0373774
\(177\) −237060. −0.568755
\(178\) 130968. 0.309824
\(179\) −693396. −1.61752 −0.808758 0.588141i \(-0.799860\pi\)
−0.808758 + 0.588141i \(0.799860\pi\)
\(180\) 85536.0 0.196774
\(181\) −377174. −0.855747 −0.427873 0.903839i \(-0.640737\pi\)
−0.427873 + 0.903839i \(0.640737\pi\)
\(182\) 0 0
\(183\) 279810. 0.617640
\(184\) 38400.0 0.0836155
\(185\) −558228. −1.19917
\(186\) 129312. 0.274067
\(187\) −24840.0 −0.0519455
\(188\) 314880. 0.649756
\(189\) 0 0
\(190\) −252384. −0.507198
\(191\) −265344. −0.526291 −0.263145 0.964756i \(-0.584760\pi\)
−0.263145 + 0.964756i \(0.584760\pi\)
\(192\) 36864.0 0.0721688
\(193\) 295298. 0.570647 0.285323 0.958431i \(-0.407899\pi\)
0.285323 + 0.958431i \(0.407899\pi\)
\(194\) −664328. −1.26730
\(195\) 390852. 0.736081
\(196\) 0 0
\(197\) 201294. 0.369543 0.184772 0.982781i \(-0.440845\pi\)
0.184772 + 0.982781i \(0.440845\pi\)
\(198\) −19440.0 −0.0352398
\(199\) −652448. −1.16792 −0.583960 0.811782i \(-0.698498\pi\)
−0.583960 + 0.811782i \(0.698498\pi\)
\(200\) 78784.0 0.139272
\(201\) −151236. −0.264037
\(202\) 88008.0 0.151755
\(203\) 0 0
\(204\) 59616.0 0.100297
\(205\) −1.26680e6 −2.10535
\(206\) 317056. 0.520557
\(207\) 48600.0 0.0788334
\(208\) 168448. 0.269965
\(209\) 57360.0 0.0908330
\(210\) 0 0
\(211\) −1.14706e6 −1.77370 −0.886850 0.462058i \(-0.847111\pi\)
−0.886850 + 0.462058i \(0.847111\pi\)
\(212\) −500256. −0.764456
\(213\) 55080.0 0.0831850
\(214\) 911952. 1.36125
\(215\) 878856. 1.29665
\(216\) 46656.0 0.0680414
\(217\) 0 0
\(218\) −34120.0 −0.0486259
\(219\) 230022. 0.324085
\(220\) −63360.0 −0.0882589
\(221\) 272412. 0.375185
\(222\) −304488. −0.414656
\(223\) −701960. −0.945258 −0.472629 0.881262i \(-0.656695\pi\)
−0.472629 + 0.881262i \(0.656695\pi\)
\(224\) 0 0
\(225\) 99711.0 0.131307
\(226\) −781752. −1.01812
\(227\) −1.23611e6 −1.59218 −0.796089 0.605179i \(-0.793101\pi\)
−0.796089 + 0.605179i \(0.793101\pi\)
\(228\) −137664. −0.175381
\(229\) −105830. −0.133358 −0.0666792 0.997774i \(-0.521240\pi\)
−0.0666792 + 0.997774i \(0.521240\pi\)
\(230\) 158400. 0.197440
\(231\) 0 0
\(232\) 356736. 0.435138
\(233\) −438678. −0.529366 −0.264683 0.964335i \(-0.585267\pi\)
−0.264683 + 0.964335i \(0.585267\pi\)
\(234\) 213192. 0.254525
\(235\) 1.29888e6 1.53426
\(236\) −421440. −0.492556
\(237\) 669672. 0.774446
\(238\) 0 0
\(239\) 28464.0 0.0322330 0.0161165 0.999870i \(-0.494870\pi\)
0.0161165 + 0.999870i \(0.494870\pi\)
\(240\) 152064. 0.170411
\(241\) −892562. −0.989910 −0.494955 0.868919i \(-0.664815\pi\)
−0.494955 + 0.868919i \(0.664815\pi\)
\(242\) −629804. −0.691301
\(243\) 59049.0 0.0641500
\(244\) 497440. 0.534892
\(245\) 0 0
\(246\) −690984. −0.727998
\(247\) −629048. −0.656057
\(248\) 229888. 0.237349
\(249\) 58212.0 0.0594996
\(250\) −500016. −0.505981
\(251\) 110124. 0.110331 0.0551655 0.998477i \(-0.482431\pi\)
0.0551655 + 0.998477i \(0.482431\pi\)
\(252\) 0 0
\(253\) −36000.0 −0.0353591
\(254\) 692000. 0.673010
\(255\) 245916. 0.236830
\(256\) 65536.0 0.0625000
\(257\) −140802. −0.132977 −0.0664884 0.997787i \(-0.521180\pi\)
−0.0664884 + 0.997787i \(0.521180\pi\)
\(258\) 479376. 0.448360
\(259\) 0 0
\(260\) 694848. 0.637465
\(261\) 451494. 0.410252
\(262\) −605040. −0.544541
\(263\) −938760. −0.836884 −0.418442 0.908244i \(-0.637424\pi\)
−0.418442 + 0.908244i \(0.637424\pi\)
\(264\) −34560.0 −0.0305186
\(265\) −2.06356e6 −1.80510
\(266\) 0 0
\(267\) 294678. 0.252970
\(268\) −268864. −0.228663
\(269\) 1.11451e6 0.939078 0.469539 0.882912i \(-0.344420\pi\)
0.469539 + 0.882912i \(0.344420\pi\)
\(270\) 192456. 0.160665
\(271\) −567704. −0.469568 −0.234784 0.972048i \(-0.575438\pi\)
−0.234784 + 0.972048i \(0.575438\pi\)
\(272\) 105984. 0.0868596
\(273\) 0 0
\(274\) −513816. −0.413458
\(275\) −73860.0 −0.0588949
\(276\) 86400.0 0.0682718
\(277\) −1.21326e6 −0.950066 −0.475033 0.879968i \(-0.657564\pi\)
−0.475033 + 0.879968i \(0.657564\pi\)
\(278\) −616784. −0.478653
\(279\) 290952. 0.223775
\(280\) 0 0
\(281\) 687738. 0.519586 0.259793 0.965664i \(-0.416346\pi\)
0.259793 + 0.965664i \(0.416346\pi\)
\(282\) 708480. 0.530524
\(283\) 830908. 0.616718 0.308359 0.951270i \(-0.400220\pi\)
0.308359 + 0.951270i \(0.400220\pi\)
\(284\) 97920.0 0.0720403
\(285\) −567864. −0.414126
\(286\) −157920. −0.114162
\(287\) 0 0
\(288\) 82944.0 0.0589256
\(289\) −1.24846e6 −0.879286
\(290\) 1.47154e6 1.02749
\(291\) −1.49474e6 −1.03474
\(292\) 408928. 0.280666
\(293\) 1.31263e6 0.893248 0.446624 0.894722i \(-0.352626\pi\)
0.446624 + 0.894722i \(0.352626\pi\)
\(294\) 0 0
\(295\) −1.73844e6 −1.16307
\(296\) −541312. −0.359102
\(297\) −43740.0 −0.0287732
\(298\) 117816. 0.0768535
\(299\) 394800. 0.255387
\(300\) 177264. 0.113715
\(301\) 0 0
\(302\) −815488. −0.514518
\(303\) 198018. 0.123908
\(304\) −244736. −0.151885
\(305\) 2.05194e6 1.26303
\(306\) 134136. 0.0818921
\(307\) −1.69022e6 −1.02352 −0.511761 0.859128i \(-0.671007\pi\)
−0.511761 + 0.859128i \(0.671007\pi\)
\(308\) 0 0
\(309\) 713376. 0.425033
\(310\) 948288. 0.560449
\(311\) 1.50204e6 0.880604 0.440302 0.897850i \(-0.354871\pi\)
0.440302 + 0.897850i \(0.354871\pi\)
\(312\) 379008. 0.220426
\(313\) −810842. −0.467816 −0.233908 0.972259i \(-0.575152\pi\)
−0.233908 + 0.972259i \(0.575152\pi\)
\(314\) −544568. −0.311694
\(315\) 0 0
\(316\) 1.19053e6 0.670690
\(317\) 903558. 0.505019 0.252510 0.967594i \(-0.418744\pi\)
0.252510 + 0.967594i \(0.418744\pi\)
\(318\) −1.12558e6 −0.624176
\(319\) −334440. −0.184010
\(320\) 270336. 0.147580
\(321\) 2.05189e6 1.11146
\(322\) 0 0
\(323\) −395784. −0.211082
\(324\) 104976. 0.0555556
\(325\) 809998. 0.425379
\(326\) −684496. −0.356720
\(327\) −76770.0 −0.0397029
\(328\) −1.22842e6 −0.630465
\(329\) 0 0
\(330\) −142560. −0.0720631
\(331\) 1.12197e6 0.562875 0.281438 0.959580i \(-0.409189\pi\)
0.281438 + 0.959580i \(0.409189\pi\)
\(332\) 103488. 0.0515282
\(333\) −685098. −0.338565
\(334\) 2.70480e6 1.32669
\(335\) −1.10906e6 −0.539939
\(336\) 0 0
\(337\) −2.75217e6 −1.32008 −0.660041 0.751229i \(-0.729461\pi\)
−0.660041 + 0.751229i \(0.729461\pi\)
\(338\) 246684. 0.117449
\(339\) −1.75894e6 −0.831289
\(340\) 437184. 0.205101
\(341\) −215520. −0.100369
\(342\) −309744. −0.143198
\(343\) 0 0
\(344\) 852224. 0.388291
\(345\) 356400. 0.161209
\(346\) −532632. −0.239187
\(347\) 1.91749e6 0.854889 0.427445 0.904042i \(-0.359414\pi\)
0.427445 + 0.904042i \(0.359414\pi\)
\(348\) 802656. 0.355289
\(349\) −1.83659e6 −0.807140 −0.403570 0.914949i \(-0.632231\pi\)
−0.403570 + 0.914949i \(0.632231\pi\)
\(350\) 0 0
\(351\) 479682. 0.207819
\(352\) −61440.0 −0.0264298
\(353\) 622014. 0.265683 0.132841 0.991137i \(-0.457590\pi\)
0.132841 + 0.991137i \(0.457590\pi\)
\(354\) −948240. −0.402170
\(355\) 403920. 0.170108
\(356\) 523872. 0.219079
\(357\) 0 0
\(358\) −2.77358e6 −1.14376
\(359\) 3.74062e6 1.53182 0.765909 0.642949i \(-0.222289\pi\)
0.765909 + 0.642949i \(0.222289\pi\)
\(360\) 342144. 0.139140
\(361\) −1.56216e6 −0.630897
\(362\) −1.50870e6 −0.605104
\(363\) −1.41706e6 −0.564445
\(364\) 0 0
\(365\) 1.68683e6 0.662733
\(366\) 1.11924e6 0.436738
\(367\) −16232.0 −0.00629081 −0.00314541 0.999995i \(-0.501001\pi\)
−0.00314541 + 0.999995i \(0.501001\pi\)
\(368\) 153600. 0.0591251
\(369\) −1.55471e6 −0.594408
\(370\) −2.23291e6 −0.847944
\(371\) 0 0
\(372\) 517248. 0.193795
\(373\) 293606. 0.109268 0.0546340 0.998506i \(-0.482601\pi\)
0.0546340 + 0.998506i \(0.482601\pi\)
\(374\) −99360.0 −0.0367310
\(375\) −1.12504e6 −0.413131
\(376\) 1.25952e6 0.459447
\(377\) 3.66769e6 1.32904
\(378\) 0 0
\(379\) 3.18012e6 1.13722 0.568611 0.822607i \(-0.307481\pi\)
0.568611 + 0.822607i \(0.307481\pi\)
\(380\) −1.00954e6 −0.358643
\(381\) 1.55700e6 0.549511
\(382\) −1.06138e6 −0.372144
\(383\) 2.97984e6 1.03800 0.518998 0.854775i \(-0.326305\pi\)
0.518998 + 0.854775i \(0.326305\pi\)
\(384\) 147456. 0.0510310
\(385\) 0 0
\(386\) 1.18119e6 0.403508
\(387\) 1.07860e6 0.366085
\(388\) −2.65731e6 −0.896114
\(389\) 3.45977e6 1.15924 0.579620 0.814887i \(-0.303201\pi\)
0.579620 + 0.814887i \(0.303201\pi\)
\(390\) 1.56341e6 0.520488
\(391\) 248400. 0.0821693
\(392\) 0 0
\(393\) −1.36134e6 −0.444616
\(394\) 805176. 0.261307
\(395\) 4.91093e6 1.58369
\(396\) −77760.0 −0.0249183
\(397\) 3.90416e6 1.24323 0.621615 0.783323i \(-0.286477\pi\)
0.621615 + 0.783323i \(0.286477\pi\)
\(398\) −2.60979e6 −0.825844
\(399\) 0 0
\(400\) 315136. 0.0984800
\(401\) 5.44115e6 1.68978 0.844890 0.534940i \(-0.179666\pi\)
0.844890 + 0.534940i \(0.179666\pi\)
\(402\) −604944. −0.186702
\(403\) 2.36354e6 0.724936
\(404\) 352032. 0.107307
\(405\) 433026. 0.131183
\(406\) 0 0
\(407\) 507480. 0.151856
\(408\) 238464. 0.0709206
\(409\) −1.96995e6 −0.582299 −0.291150 0.956678i \(-0.594038\pi\)
−0.291150 + 0.956678i \(0.594038\pi\)
\(410\) −5.06722e6 −1.48871
\(411\) −1.15609e6 −0.337587
\(412\) 1.26822e6 0.368089
\(413\) 0 0
\(414\) 194400. 0.0557437
\(415\) 426888. 0.121673
\(416\) 673792. 0.190894
\(417\) −1.38776e6 −0.390819
\(418\) 229440. 0.0642286
\(419\) −139020. −0.0386850 −0.0193425 0.999813i \(-0.506157\pi\)
−0.0193425 + 0.999813i \(0.506157\pi\)
\(420\) 0 0
\(421\) 4.32743e6 1.18994 0.594970 0.803748i \(-0.297164\pi\)
0.594970 + 0.803748i \(0.297164\pi\)
\(422\) −4.58824e6 −1.25419
\(423\) 1.59408e6 0.433171
\(424\) −2.00102e6 −0.540552
\(425\) 509634. 0.136863
\(426\) 220320. 0.0588207
\(427\) 0 0
\(428\) 3.64781e6 0.962548
\(429\) −355320. −0.0932130
\(430\) 3.51542e6 0.916867
\(431\) −2.79936e6 −0.725881 −0.362941 0.931812i \(-0.618227\pi\)
−0.362941 + 0.931812i \(0.618227\pi\)
\(432\) 186624. 0.0481125
\(433\) 5.90241e6 1.51290 0.756449 0.654052i \(-0.226932\pi\)
0.756449 + 0.654052i \(0.226932\pi\)
\(434\) 0 0
\(435\) 3.31096e6 0.838939
\(436\) −136480. −0.0343837
\(437\) −573600. −0.143683
\(438\) 920088. 0.229163
\(439\) 446512. 0.110579 0.0552894 0.998470i \(-0.482392\pi\)
0.0552894 + 0.998470i \(0.482392\pi\)
\(440\) −253440. −0.0624085
\(441\) 0 0
\(442\) 1.08965e6 0.265296
\(443\) 3.49525e6 0.846193 0.423096 0.906085i \(-0.360943\pi\)
0.423096 + 0.906085i \(0.360943\pi\)
\(444\) −1.21795e6 −0.293206
\(445\) 2.16097e6 0.517308
\(446\) −2.80784e6 −0.668398
\(447\) 265086. 0.0627506
\(448\) 0 0
\(449\) −1.20613e6 −0.282343 −0.141171 0.989985i \(-0.545087\pi\)
−0.141171 + 0.989985i \(0.545087\pi\)
\(450\) 398844. 0.0928478
\(451\) 1.15164e6 0.266609
\(452\) −3.12701e6 −0.719918
\(453\) −1.83485e6 −0.420102
\(454\) −4.94443e6 −1.12584
\(455\) 0 0
\(456\) −550656. −0.124013
\(457\) 233546. 0.0523097 0.0261548 0.999658i \(-0.491674\pi\)
0.0261548 + 0.999658i \(0.491674\pi\)
\(458\) −423320. −0.0942986
\(459\) 301806. 0.0668646
\(460\) 633600. 0.139611
\(461\) 1.74489e6 0.382398 0.191199 0.981551i \(-0.438762\pi\)
0.191199 + 0.981551i \(0.438762\pi\)
\(462\) 0 0
\(463\) −2.91786e6 −0.632576 −0.316288 0.948663i \(-0.602437\pi\)
−0.316288 + 0.948663i \(0.602437\pi\)
\(464\) 1.42694e6 0.307689
\(465\) 2.13365e6 0.457605
\(466\) −1.75471e6 −0.374318
\(467\) 5.31076e6 1.12684 0.563422 0.826169i \(-0.309484\pi\)
0.563422 + 0.826169i \(0.309484\pi\)
\(468\) 852768. 0.179977
\(469\) 0 0
\(470\) 5.19552e6 1.08489
\(471\) −1.22528e6 −0.254497
\(472\) −1.68576e6 −0.348290
\(473\) −798960. −0.164200
\(474\) 2.67869e6 0.547616
\(475\) −1.17684e6 −0.239322
\(476\) 0 0
\(477\) −2.53255e6 −0.509638
\(478\) 113856. 0.0227922
\(479\) −2.34466e6 −0.466918 −0.233459 0.972367i \(-0.575004\pi\)
−0.233459 + 0.972367i \(0.575004\pi\)
\(480\) 608256. 0.120499
\(481\) −5.56536e6 −1.09681
\(482\) −3.57025e6 −0.699972
\(483\) 0 0
\(484\) −2.51922e6 −0.488823
\(485\) −1.09614e7 −2.11598
\(486\) 236196. 0.0453609
\(487\) 9.81531e6 1.87535 0.937674 0.347517i \(-0.112975\pi\)
0.937674 + 0.347517i \(0.112975\pi\)
\(488\) 1.98976e6 0.378226
\(489\) −1.54012e6 −0.291260
\(490\) 0 0
\(491\) −5.94520e6 −1.11292 −0.556458 0.830876i \(-0.687840\pi\)
−0.556458 + 0.830876i \(0.687840\pi\)
\(492\) −2.76394e6 −0.514772
\(493\) 2.30764e6 0.427612
\(494\) −2.51619e6 −0.463902
\(495\) −320760. −0.0588393
\(496\) 919552. 0.167831
\(497\) 0 0
\(498\) 232848. 0.0420726
\(499\) 6.47832e6 1.16469 0.582346 0.812941i \(-0.302135\pi\)
0.582346 + 0.812941i \(0.302135\pi\)
\(500\) −2.00006e6 −0.357782
\(501\) 6.08580e6 1.08324
\(502\) 440496. 0.0780158
\(503\) −4.71794e6 −0.831444 −0.415722 0.909492i \(-0.636471\pi\)
−0.415722 + 0.909492i \(0.636471\pi\)
\(504\) 0 0
\(505\) 1.45213e6 0.253383
\(506\) −144000. −0.0250027
\(507\) 555039. 0.0958967
\(508\) 2.76800e6 0.475890
\(509\) 1.90771e6 0.326375 0.163188 0.986595i \(-0.447822\pi\)
0.163188 + 0.986595i \(0.447822\pi\)
\(510\) 983664. 0.167464
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) −696924. −0.116921
\(514\) −563208. −0.0940288
\(515\) 5.23142e6 0.869164
\(516\) 1.91750e6 0.317039
\(517\) −1.18080e6 −0.194290
\(518\) 0 0
\(519\) −1.19842e6 −0.195295
\(520\) 2.77939e6 0.450756
\(521\) −8.01974e6 −1.29439 −0.647196 0.762324i \(-0.724059\pi\)
−0.647196 + 0.762324i \(0.724059\pi\)
\(522\) 1.80598e6 0.290092
\(523\) −1.91162e6 −0.305596 −0.152798 0.988257i \(-0.548828\pi\)
−0.152798 + 0.988257i \(0.548828\pi\)
\(524\) −2.42016e6 −0.385049
\(525\) 0 0
\(526\) −3.75504e6 −0.591766
\(527\) 1.48709e6 0.233244
\(528\) −138240. −0.0215799
\(529\) −6.07634e6 −0.944068
\(530\) −8.25422e6 −1.27640
\(531\) −2.13354e6 −0.328371
\(532\) 0 0
\(533\) −1.26297e7 −1.92563
\(534\) 1.17871e6 0.178877
\(535\) 1.50472e7 2.27285
\(536\) −1.07546e6 −0.161689
\(537\) −6.24056e6 −0.933874
\(538\) 4.45802e6 0.664028
\(539\) 0 0
\(540\) 769824. 0.113608
\(541\) −1.19900e7 −1.76128 −0.880639 0.473788i \(-0.842886\pi\)
−0.880639 + 0.473788i \(0.842886\pi\)
\(542\) −2.27082e6 −0.332035
\(543\) −3.39457e6 −0.494066
\(544\) 423936. 0.0614190
\(545\) −562980. −0.0811898
\(546\) 0 0
\(547\) 4.45809e6 0.637061 0.318530 0.947913i \(-0.396811\pi\)
0.318530 + 0.947913i \(0.396811\pi\)
\(548\) −2.05526e6 −0.292359
\(549\) 2.51829e6 0.356595
\(550\) −295440. −0.0416450
\(551\) −5.32874e6 −0.747732
\(552\) 345600. 0.0482754
\(553\) 0 0
\(554\) −4.85303e6 −0.671798
\(555\) −5.02405e6 −0.692344
\(556\) −2.46714e6 −0.338459
\(557\) 9.02612e6 1.23272 0.616358 0.787466i \(-0.288607\pi\)
0.616358 + 0.787466i \(0.288607\pi\)
\(558\) 1.16381e6 0.158233
\(559\) 8.76193e6 1.18596
\(560\) 0 0
\(561\) −223560. −0.0299907
\(562\) 2.75095e6 0.367403
\(563\) −6.84899e6 −0.910658 −0.455329 0.890323i \(-0.650478\pi\)
−0.455329 + 0.890323i \(0.650478\pi\)
\(564\) 2.83392e6 0.375137
\(565\) −1.28989e7 −1.69993
\(566\) 3.32363e6 0.436086
\(567\) 0 0
\(568\) 391680. 0.0509402
\(569\) −5.46322e6 −0.707405 −0.353703 0.935358i \(-0.615077\pi\)
−0.353703 + 0.935358i \(0.615077\pi\)
\(570\) −2.27146e6 −0.292831
\(571\) −1.02324e7 −1.31337 −0.656684 0.754166i \(-0.728041\pi\)
−0.656684 + 0.754166i \(0.728041\pi\)
\(572\) −631680. −0.0807248
\(573\) −2.38810e6 −0.303854
\(574\) 0 0
\(575\) 738600. 0.0931622
\(576\) 331776. 0.0416667
\(577\) −1.59437e7 −1.99365 −0.996825 0.0796186i \(-0.974630\pi\)
−0.996825 + 0.0796186i \(0.974630\pi\)
\(578\) −4.99384e6 −0.621749
\(579\) 2.65768e6 0.329463
\(580\) 5.88614e6 0.726542
\(581\) 0 0
\(582\) −5.97895e6 −0.731674
\(583\) 1.87596e6 0.228587
\(584\) 1.63571e6 0.198461
\(585\) 3.51767e6 0.424977
\(586\) 5.25050e6 0.631622
\(587\) 9.47713e6 1.13522 0.567612 0.823296i \(-0.307867\pi\)
0.567612 + 0.823296i \(0.307867\pi\)
\(588\) 0 0
\(589\) −3.43395e6 −0.407855
\(590\) −6.95376e6 −0.822412
\(591\) 1.81165e6 0.213356
\(592\) −2.16525e6 −0.253924
\(593\) −2.45349e6 −0.286515 −0.143258 0.989685i \(-0.545758\pi\)
−0.143258 + 0.989685i \(0.545758\pi\)
\(594\) −174960. −0.0203457
\(595\) 0 0
\(596\) 471264. 0.0543436
\(597\) −5.87203e6 −0.674299
\(598\) 1.57920e6 0.180586
\(599\) −9.29978e6 −1.05902 −0.529512 0.848302i \(-0.677625\pi\)
−0.529512 + 0.848302i \(0.677625\pi\)
\(600\) 709056. 0.0804086
\(601\) 1.14617e7 1.29438 0.647192 0.762327i \(-0.275943\pi\)
0.647192 + 0.762327i \(0.275943\pi\)
\(602\) 0 0
\(603\) −1.36112e6 −0.152442
\(604\) −3.26195e6 −0.363819
\(605\) −1.03918e7 −1.15425
\(606\) 792072. 0.0876159
\(607\) −1.12784e7 −1.24244 −0.621219 0.783637i \(-0.713362\pi\)
−0.621219 + 0.783637i \(0.713362\pi\)
\(608\) −978944. −0.107399
\(609\) 0 0
\(610\) 8.20776e6 0.893100
\(611\) 1.29494e7 1.40329
\(612\) 536544. 0.0579064
\(613\) 93782.0 0.0100802 0.00504009 0.999987i \(-0.498396\pi\)
0.00504009 + 0.999987i \(0.498396\pi\)
\(614\) −6.76088e6 −0.723740
\(615\) −1.14012e7 −1.21553
\(616\) 0 0
\(617\) −1.49642e7 −1.58248 −0.791242 0.611504i \(-0.790565\pi\)
−0.791242 + 0.611504i \(0.790565\pi\)
\(618\) 2.85350e6 0.300543
\(619\) 5.06888e6 0.531723 0.265861 0.964011i \(-0.414344\pi\)
0.265861 + 0.964011i \(0.414344\pi\)
\(620\) 3.79315e6 0.396297
\(621\) 437400. 0.0455145
\(622\) 6.00816e6 0.622681
\(623\) 0 0
\(624\) 1.51603e6 0.155864
\(625\) −1.20971e7 −1.23875
\(626\) −3.24337e6 −0.330796
\(627\) 516240. 0.0524424
\(628\) −2.17827e6 −0.220401
\(629\) −3.50161e6 −0.352892
\(630\) 0 0
\(631\) 1.55919e7 1.55892 0.779462 0.626450i \(-0.215493\pi\)
0.779462 + 0.626450i \(0.215493\pi\)
\(632\) 4.76211e6 0.474250
\(633\) −1.03235e7 −1.02405
\(634\) 3.61423e6 0.357102
\(635\) 1.14180e7 1.12371
\(636\) −4.50230e6 −0.441359
\(637\) 0 0
\(638\) −1.33776e6 −0.130115
\(639\) 495720. 0.0480269
\(640\) 1.08134e6 0.104355
\(641\) 1.09701e7 1.05455 0.527274 0.849695i \(-0.323214\pi\)
0.527274 + 0.849695i \(0.323214\pi\)
\(642\) 8.20757e6 0.785917
\(643\) 2.83704e6 0.270607 0.135303 0.990804i \(-0.456799\pi\)
0.135303 + 0.990804i \(0.456799\pi\)
\(644\) 0 0
\(645\) 7.90970e6 0.748619
\(646\) −1.58314e6 −0.149258
\(647\) 6.05686e6 0.568835 0.284418 0.958700i \(-0.408200\pi\)
0.284418 + 0.958700i \(0.408200\pi\)
\(648\) 419904. 0.0392837
\(649\) 1.58040e6 0.147284
\(650\) 3.23999e6 0.300788
\(651\) 0 0
\(652\) −2.73798e6 −0.252239
\(653\) −1.08892e6 −0.0999341 −0.0499671 0.998751i \(-0.515912\pi\)
−0.0499671 + 0.998751i \(0.515912\pi\)
\(654\) −307080. −0.0280742
\(655\) −9.98316e6 −0.909211
\(656\) −4.91366e6 −0.445806
\(657\) 2.07020e6 0.187111
\(658\) 0 0
\(659\) 7.41803e6 0.665388 0.332694 0.943035i \(-0.392042\pi\)
0.332694 + 0.943035i \(0.392042\pi\)
\(660\) −570240. −0.0509563
\(661\) −767654. −0.0683379 −0.0341690 0.999416i \(-0.510878\pi\)
−0.0341690 + 0.999416i \(0.510878\pi\)
\(662\) 4.48789e6 0.398013
\(663\) 2.45171e6 0.216613
\(664\) 413952. 0.0364359
\(665\) 0 0
\(666\) −2.74039e6 −0.239402
\(667\) 3.34440e6 0.291074
\(668\) 1.08192e7 0.938110
\(669\) −6.31764e6 −0.545745
\(670\) −4.43626e6 −0.381794
\(671\) −1.86540e6 −0.159943
\(672\) 0 0
\(673\) 1.42263e6 0.121075 0.0605373 0.998166i \(-0.480719\pi\)
0.0605373 + 0.998166i \(0.480719\pi\)
\(674\) −1.10087e7 −0.933439
\(675\) 897399. 0.0758099
\(676\) 986736. 0.0830490
\(677\) 6.16231e6 0.516739 0.258370 0.966046i \(-0.416815\pi\)
0.258370 + 0.966046i \(0.416815\pi\)
\(678\) −7.03577e6 −0.587810
\(679\) 0 0
\(680\) 1.74874e6 0.145028
\(681\) −1.11250e7 −0.919245
\(682\) −862080. −0.0709719
\(683\) 1.50621e7 1.23548 0.617739 0.786383i \(-0.288049\pi\)
0.617739 + 0.786383i \(0.288049\pi\)
\(684\) −1.23898e6 −0.101256
\(685\) −8.47796e6 −0.690343
\(686\) 0 0
\(687\) −952470. −0.0769945
\(688\) 3.40890e6 0.274563
\(689\) −2.05730e7 −1.65101
\(690\) 1.42560e6 0.113992
\(691\) 5.87636e6 0.468180 0.234090 0.972215i \(-0.424789\pi\)
0.234090 + 0.972215i \(0.424789\pi\)
\(692\) −2.13053e6 −0.169131
\(693\) 0 0
\(694\) 7.66997e6 0.604498
\(695\) −1.01769e7 −0.799199
\(696\) 3.21062e6 0.251227
\(697\) −7.94632e6 −0.619561
\(698\) −7.34636e6 −0.570734
\(699\) −3.94810e6 −0.305630
\(700\) 0 0
\(701\) 3.60077e6 0.276758 0.138379 0.990379i \(-0.455811\pi\)
0.138379 + 0.990379i \(0.455811\pi\)
\(702\) 1.91873e6 0.146950
\(703\) 8.08585e6 0.617074
\(704\) −245760. −0.0186887
\(705\) 1.16899e7 0.885806
\(706\) 2.48806e6 0.187866
\(707\) 0 0
\(708\) −3.79296e6 −0.284377
\(709\) 9.22516e6 0.689221 0.344610 0.938746i \(-0.388011\pi\)
0.344610 + 0.938746i \(0.388011\pi\)
\(710\) 1.61568e6 0.120284
\(711\) 6.02705e6 0.447127
\(712\) 2.09549e6 0.154912
\(713\) 2.15520e6 0.158768
\(714\) 0 0
\(715\) −2.60568e6 −0.190615
\(716\) −1.10943e7 −0.808758
\(717\) 256176. 0.0186098
\(718\) 1.49625e7 1.08316
\(719\) 2.63923e7 1.90395 0.951975 0.306177i \(-0.0990500\pi\)
0.951975 + 0.306177i \(0.0990500\pi\)
\(720\) 1.36858e6 0.0983870
\(721\) 0 0
\(722\) −6.24865e6 −0.446111
\(723\) −8.03306e6 −0.571525
\(724\) −6.03478e6 −0.427873
\(725\) 6.86159e6 0.484819
\(726\) −5.66824e6 −0.399123
\(727\) 9.79485e6 0.687324 0.343662 0.939093i \(-0.388333\pi\)
0.343662 + 0.939093i \(0.388333\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 6.74731e6 0.468623
\(731\) 5.51282e6 0.381576
\(732\) 4.47696e6 0.308820
\(733\) −4.07584e6 −0.280193 −0.140096 0.990138i \(-0.544741\pi\)
−0.140096 + 0.990138i \(0.544741\pi\)
\(734\) −64928.0 −0.00444828
\(735\) 0 0
\(736\) 614400. 0.0418077
\(737\) 1.00824e6 0.0683747
\(738\) −6.21886e6 −0.420310
\(739\) −1.65709e7 −1.11618 −0.558089 0.829781i \(-0.688465\pi\)
−0.558089 + 0.829781i \(0.688465\pi\)
\(740\) −8.93165e6 −0.599587
\(741\) −5.66143e6 −0.378775
\(742\) 0 0
\(743\) 1.44141e7 0.957892 0.478946 0.877844i \(-0.341019\pi\)
0.478946 + 0.877844i \(0.341019\pi\)
\(744\) 2.06899e6 0.137033
\(745\) 1.94396e6 0.128321
\(746\) 1.17442e6 0.0772641
\(747\) 523908. 0.0343521
\(748\) −397440. −0.0259727
\(749\) 0 0
\(750\) −4.50014e6 −0.292128
\(751\) 1.67944e7 1.08659 0.543295 0.839542i \(-0.317177\pi\)
0.543295 + 0.839542i \(0.317177\pi\)
\(752\) 5.03808e6 0.324878
\(753\) 991116. 0.0636997
\(754\) 1.46708e7 0.939776
\(755\) −1.34556e7 −0.859081
\(756\) 0 0
\(757\) 1.32943e7 0.843188 0.421594 0.906785i \(-0.361471\pi\)
0.421594 + 0.906785i \(0.361471\pi\)
\(758\) 1.27205e7 0.804137
\(759\) −324000. −0.0204146
\(760\) −4.03814e6 −0.253599
\(761\) 2.14786e6 0.134445 0.0672225 0.997738i \(-0.478586\pi\)
0.0672225 + 0.997738i \(0.478586\pi\)
\(762\) 6.22800e6 0.388563
\(763\) 0 0
\(764\) −4.24550e6 −0.263145
\(765\) 2.21324e6 0.136734
\(766\) 1.19194e7 0.733975
\(767\) −1.73317e7 −1.06378
\(768\) 589824. 0.0360844
\(769\) 1.31059e7 0.799193 0.399596 0.916691i \(-0.369150\pi\)
0.399596 + 0.916691i \(0.369150\pi\)
\(770\) 0 0
\(771\) −1.26722e6 −0.0767742
\(772\) 4.72477e6 0.285323
\(773\) 2.37154e7 1.42752 0.713759 0.700392i \(-0.246991\pi\)
0.713759 + 0.700392i \(0.246991\pi\)
\(774\) 4.31438e6 0.258861
\(775\) 4.42175e6 0.264448
\(776\) −1.06292e7 −0.633648
\(777\) 0 0
\(778\) 1.38391e7 0.819707
\(779\) 1.83495e7 1.08338
\(780\) 6.25363e6 0.368041
\(781\) −367200. −0.0215415
\(782\) 993600. 0.0581025
\(783\) 4.06345e6 0.236859
\(784\) 0 0
\(785\) −8.98537e6 −0.520430
\(786\) −5.44536e6 −0.314391
\(787\) 8.40048e6 0.483468 0.241734 0.970343i \(-0.422284\pi\)
0.241734 + 0.970343i \(0.422284\pi\)
\(788\) 3.22070e6 0.184772
\(789\) −8.44884e6 −0.483175
\(790\) 1.96437e7 1.11984
\(791\) 0 0
\(792\) −311040. −0.0176199
\(793\) 2.04572e7 1.15522
\(794\) 1.56166e7 0.879097
\(795\) −1.85720e7 −1.04218
\(796\) −1.04392e7 −0.583960
\(797\) −5.41023e6 −0.301696 −0.150848 0.988557i \(-0.548200\pi\)
−0.150848 + 0.988557i \(0.548200\pi\)
\(798\) 0 0
\(799\) 8.14752e6 0.451501
\(800\) 1.26054e6 0.0696359
\(801\) 2.65210e6 0.146052
\(802\) 2.17646e7 1.19485
\(803\) −1.53348e6 −0.0839246
\(804\) −2.41978e6 −0.132019
\(805\) 0 0
\(806\) 9.45414e6 0.512607
\(807\) 1.00306e7 0.542177
\(808\) 1.40813e6 0.0758776
\(809\) −2.60777e7 −1.40087 −0.700436 0.713715i \(-0.747011\pi\)
−0.700436 + 0.713715i \(0.747011\pi\)
\(810\) 1.73210e6 0.0927601
\(811\) −1.90021e7 −1.01449 −0.507247 0.861800i \(-0.669337\pi\)
−0.507247 + 0.861800i \(0.669337\pi\)
\(812\) 0 0
\(813\) −5.10934e6 −0.271105
\(814\) 2.02992e6 0.107379
\(815\) −1.12942e7 −0.595608
\(816\) 953856. 0.0501484
\(817\) −1.27301e7 −0.667231
\(818\) −7.87978e6 −0.411748
\(819\) 0 0
\(820\) −2.02689e7 −1.05268
\(821\) −3.10173e7 −1.60600 −0.803001 0.595978i \(-0.796764\pi\)
−0.803001 + 0.595978i \(0.796764\pi\)
\(822\) −4.62434e6 −0.238710
\(823\) −1.56290e7 −0.804323 −0.402162 0.915569i \(-0.631741\pi\)
−0.402162 + 0.915569i \(0.631741\pi\)
\(824\) 5.07290e6 0.260278
\(825\) −664740. −0.0340030
\(826\) 0 0
\(827\) 1.58421e7 0.805467 0.402733 0.915317i \(-0.368060\pi\)
0.402733 + 0.915317i \(0.368060\pi\)
\(828\) 777600. 0.0394167
\(829\) −2.06176e6 −0.104196 −0.0520980 0.998642i \(-0.516591\pi\)
−0.0520980 + 0.998642i \(0.516591\pi\)
\(830\) 1.70755e6 0.0860357
\(831\) −1.09193e7 −0.548521
\(832\) 2.69517e6 0.134983
\(833\) 0 0
\(834\) −5.55106e6 −0.276351
\(835\) 4.46292e7 2.21515
\(836\) 917760. 0.0454165
\(837\) 2.61857e6 0.129196
\(838\) −556080. −0.0273544
\(839\) −3.03900e7 −1.49048 −0.745240 0.666796i \(-0.767665\pi\)
−0.745240 + 0.666796i \(0.767665\pi\)
\(840\) 0 0
\(841\) 1.05583e7 0.514760
\(842\) 1.73097e7 0.841414
\(843\) 6.18964e6 0.299983
\(844\) −1.83530e7 −0.886850
\(845\) 4.07029e6 0.196103
\(846\) 6.37632e6 0.306298
\(847\) 0 0
\(848\) −8.00410e6 −0.382228
\(849\) 7.47817e6 0.356062
\(850\) 2.03854e6 0.0967768
\(851\) −5.07480e6 −0.240212
\(852\) 881280. 0.0415925
\(853\) 2.97738e7 1.40108 0.700538 0.713615i \(-0.252944\pi\)
0.700538 + 0.713615i \(0.252944\pi\)
\(854\) 0 0
\(855\) −5.11078e6 −0.239096
\(856\) 1.45912e7 0.680624
\(857\) −8.64100e6 −0.401894 −0.200947 0.979602i \(-0.564402\pi\)
−0.200947 + 0.979602i \(0.564402\pi\)
\(858\) −1.42128e6 −0.0659115
\(859\) 3.35663e7 1.55210 0.776051 0.630670i \(-0.217220\pi\)
0.776051 + 0.630670i \(0.217220\pi\)
\(860\) 1.40617e7 0.648323
\(861\) 0 0
\(862\) −1.11974e7 −0.513276
\(863\) 3.90191e7 1.78341 0.891703 0.452621i \(-0.149511\pi\)
0.891703 + 0.452621i \(0.149511\pi\)
\(864\) 746496. 0.0340207
\(865\) −8.78843e6 −0.399366
\(866\) 2.36097e7 1.06978
\(867\) −1.12361e7 −0.507656
\(868\) 0 0
\(869\) −4.46448e6 −0.200549
\(870\) 1.32438e7 0.593219
\(871\) −1.10570e7 −0.493848
\(872\) −545920. −0.0243130
\(873\) −1.34526e7 −0.597409
\(874\) −2.29440e6 −0.101599
\(875\) 0 0
\(876\) 3.68035e6 0.162043
\(877\) −1.81382e7 −0.796333 −0.398166 0.917313i \(-0.630353\pi\)
−0.398166 + 0.917313i \(0.630353\pi\)
\(878\) 1.78605e6 0.0781910
\(879\) 1.18136e7 0.515717
\(880\) −1.01376e6 −0.0441294
\(881\) −3.05312e7 −1.32527 −0.662634 0.748943i \(-0.730562\pi\)
−0.662634 + 0.748943i \(0.730562\pi\)
\(882\) 0 0
\(883\) −4.35533e7 −1.87983 −0.939916 0.341405i \(-0.889097\pi\)
−0.939916 + 0.341405i \(0.889097\pi\)
\(884\) 4.35859e6 0.187593
\(885\) −1.56460e7 −0.671497
\(886\) 1.39810e7 0.598348
\(887\) 1.34152e7 0.572515 0.286257 0.958153i \(-0.407589\pi\)
0.286257 + 0.958153i \(0.407589\pi\)
\(888\) −4.87181e6 −0.207328
\(889\) 0 0
\(890\) 8.64389e6 0.365792
\(891\) −393660. −0.0166122
\(892\) −1.12314e7 −0.472629
\(893\) −1.88141e7 −0.789504
\(894\) 1.06034e6 0.0443714
\(895\) −4.57641e7 −1.90971
\(896\) 0 0
\(897\) 3.55320e6 0.147448
\(898\) −4.82450e6 −0.199647
\(899\) 2.00218e7 0.826236
\(900\) 1.59538e6 0.0656533
\(901\) −1.29441e7 −0.531203
\(902\) 4.60656e6 0.188521
\(903\) 0 0
\(904\) −1.25080e7 −0.509059
\(905\) −2.48935e7 −1.01033
\(906\) −7.33939e6 −0.297057
\(907\) 3.10816e6 0.125454 0.0627272 0.998031i \(-0.480020\pi\)
0.0627272 + 0.998031i \(0.480020\pi\)
\(908\) −1.97777e7 −0.796089
\(909\) 1.78216e6 0.0715381
\(910\) 0 0
\(911\) 1.19035e6 0.0475203 0.0237602 0.999718i \(-0.492436\pi\)
0.0237602 + 0.999718i \(0.492436\pi\)
\(912\) −2.20262e6 −0.0876906
\(913\) −388080. −0.0154079
\(914\) 934184. 0.0369885
\(915\) 1.84675e7 0.729213
\(916\) −1.69328e6 −0.0666792
\(917\) 0 0
\(918\) 1.20722e6 0.0472804
\(919\) −4.71996e7 −1.84353 −0.921764 0.387752i \(-0.873252\pi\)
−0.921764 + 0.387752i \(0.873252\pi\)
\(920\) 2.53440e6 0.0987201
\(921\) −1.52120e7 −0.590931
\(922\) 6.97956e6 0.270396
\(923\) 4.02696e6 0.155587
\(924\) 0 0
\(925\) −1.04118e7 −0.400103
\(926\) −1.16715e7 −0.447299
\(927\) 6.42038e6 0.245393
\(928\) 5.70778e6 0.217569
\(929\) −1.33595e6 −0.0507870 −0.0253935 0.999678i \(-0.508084\pi\)
−0.0253935 + 0.999678i \(0.508084\pi\)
\(930\) 8.53459e6 0.323575
\(931\) 0 0
\(932\) −7.01885e6 −0.264683
\(933\) 1.35184e7 0.508417
\(934\) 2.12430e7 0.796800
\(935\) −1.63944e6 −0.0613291
\(936\) 3.41107e6 0.127263
\(937\) −1.47238e7 −0.547861 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(938\) 0 0
\(939\) −7.29758e6 −0.270094
\(940\) 2.07821e7 0.767131
\(941\) 2.69196e7 0.991049 0.495525 0.868594i \(-0.334976\pi\)
0.495525 + 0.868594i \(0.334976\pi\)
\(942\) −4.90111e6 −0.179956
\(943\) −1.15164e7 −0.421733
\(944\) −6.74304e6 −0.246278
\(945\) 0 0
\(946\) −3.19584e6 −0.116107
\(947\) −3.73160e6 −0.135214 −0.0676068 0.997712i \(-0.521536\pi\)
−0.0676068 + 0.997712i \(0.521536\pi\)
\(948\) 1.07148e7 0.387223
\(949\) 1.68172e7 0.606160
\(950\) −4.70734e6 −0.169226
\(951\) 8.13202e6 0.291573
\(952\) 0 0
\(953\) 2.18735e7 0.780166 0.390083 0.920780i \(-0.372446\pi\)
0.390083 + 0.920780i \(0.372446\pi\)
\(954\) −1.01302e7 −0.360368
\(955\) −1.75127e7 −0.621362
\(956\) 455424. 0.0161165
\(957\) −3.00996e6 −0.106238
\(958\) −9.37862e6 −0.330161
\(959\) 0 0
\(960\) 2.43302e6 0.0852056
\(961\) −1.57267e7 −0.549324
\(962\) −2.22615e7 −0.775561
\(963\) 1.84670e7 0.641699
\(964\) −1.42810e7 −0.494955
\(965\) 1.94897e7 0.673730
\(966\) 0 0
\(967\) 1.76025e7 0.605352 0.302676 0.953093i \(-0.402120\pi\)
0.302676 + 0.953093i \(0.402120\pi\)
\(968\) −1.00769e7 −0.345650
\(969\) −3.56206e6 −0.121868
\(970\) −4.38456e7 −1.49623
\(971\) −1.67317e7 −0.569497 −0.284749 0.958602i \(-0.591910\pi\)
−0.284749 + 0.958602i \(0.591910\pi\)
\(972\) 944784. 0.0320750
\(973\) 0 0
\(974\) 3.92612e7 1.32607
\(975\) 7.28998e6 0.245592
\(976\) 7.95904e6 0.267446
\(977\) 5.55382e7 1.86147 0.930733 0.365699i \(-0.119170\pi\)
0.930733 + 0.365699i \(0.119170\pi\)
\(978\) −6.16046e6 −0.205952
\(979\) −1.96452e6 −0.0655088
\(980\) 0 0
\(981\) −690930. −0.0229225
\(982\) −2.37808e7 −0.786951
\(983\) 3.86784e7 1.27669 0.638344 0.769751i \(-0.279620\pi\)
0.638344 + 0.769751i \(0.279620\pi\)
\(984\) −1.10557e7 −0.363999
\(985\) 1.32854e7 0.436299
\(986\) 9.23054e6 0.302367
\(987\) 0 0
\(988\) −1.00648e7 −0.328028
\(989\) 7.98960e6 0.259737
\(990\) −1.28304e6 −0.0416056
\(991\) 9.58498e6 0.310033 0.155016 0.987912i \(-0.450457\pi\)
0.155016 + 0.987912i \(0.450457\pi\)
\(992\) 3.67821e6 0.118674
\(993\) 1.00977e7 0.324976
\(994\) 0 0
\(995\) −4.30616e7 −1.37890
\(996\) 931392. 0.0297498
\(997\) 1.03650e7 0.330242 0.165121 0.986273i \(-0.447198\pi\)
0.165121 + 0.986273i \(0.447198\pi\)
\(998\) 2.59133e7 0.823561
\(999\) −6.16588e6 −0.195471
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 294.6.a.m.1.1 1
3.2 odd 2 882.6.a.a.1.1 1
7.2 even 3 294.6.e.a.67.1 2
7.3 odd 6 294.6.e.g.79.1 2
7.4 even 3 294.6.e.a.79.1 2
7.5 odd 6 294.6.e.g.67.1 2
7.6 odd 2 6.6.a.a.1.1 1
21.20 even 2 18.6.a.b.1.1 1
28.27 even 2 48.6.a.c.1.1 1
35.13 even 4 150.6.c.b.49.1 2
35.27 even 4 150.6.c.b.49.2 2
35.34 odd 2 150.6.a.d.1.1 1
56.13 odd 2 192.6.a.o.1.1 1
56.27 even 2 192.6.a.g.1.1 1
63.13 odd 6 162.6.c.e.55.1 2
63.20 even 6 162.6.c.h.109.1 2
63.34 odd 6 162.6.c.e.109.1 2
63.41 even 6 162.6.c.h.55.1 2
77.76 even 2 726.6.a.a.1.1 1
84.83 odd 2 144.6.a.j.1.1 1
91.90 odd 2 1014.6.a.c.1.1 1
105.62 odd 4 450.6.c.j.199.1 2
105.83 odd 4 450.6.c.j.199.2 2
105.104 even 2 450.6.a.m.1.1 1
112.13 odd 4 768.6.d.c.385.1 2
112.27 even 4 768.6.d.p.385.1 2
112.69 odd 4 768.6.d.c.385.2 2
112.83 even 4 768.6.d.p.385.2 2
168.83 odd 2 576.6.a.i.1.1 1
168.125 even 2 576.6.a.j.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.6.a.a.1.1 1 7.6 odd 2
18.6.a.b.1.1 1 21.20 even 2
48.6.a.c.1.1 1 28.27 even 2
144.6.a.j.1.1 1 84.83 odd 2
150.6.a.d.1.1 1 35.34 odd 2
150.6.c.b.49.1 2 35.13 even 4
150.6.c.b.49.2 2 35.27 even 4
162.6.c.e.55.1 2 63.13 odd 6
162.6.c.e.109.1 2 63.34 odd 6
162.6.c.h.55.1 2 63.41 even 6
162.6.c.h.109.1 2 63.20 even 6
192.6.a.g.1.1 1 56.27 even 2
192.6.a.o.1.1 1 56.13 odd 2
294.6.a.m.1.1 1 1.1 even 1 trivial
294.6.e.a.67.1 2 7.2 even 3
294.6.e.a.79.1 2 7.4 even 3
294.6.e.g.67.1 2 7.5 odd 6
294.6.e.g.79.1 2 7.3 odd 6
450.6.a.m.1.1 1 105.104 even 2
450.6.c.j.199.1 2 105.62 odd 4
450.6.c.j.199.2 2 105.83 odd 4
576.6.a.i.1.1 1 168.83 odd 2
576.6.a.j.1.1 1 168.125 even 2
726.6.a.a.1.1 1 77.76 even 2
768.6.d.c.385.1 2 112.13 odd 4
768.6.d.c.385.2 2 112.69 odd 4
768.6.d.p.385.1 2 112.27 even 4
768.6.d.p.385.2 2 112.83 even 4
882.6.a.a.1.1 1 3.2 odd 2
1014.6.a.c.1.1 1 91.90 odd 2