Properties

Label 798.4.a.b.1.1
Level $798$
Weight $4$
Character 798.1
Self dual yes
Analytic conductor $47.084$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 798.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.0835241846\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 798.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.0000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.0000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -20.0000 q^{10} +8.00000 q^{11} -12.0000 q^{12} -50.0000 q^{13} +14.0000 q^{14} +30.0000 q^{15} +16.0000 q^{16} +114.000 q^{17} +18.0000 q^{18} +19.0000 q^{19} -40.0000 q^{20} -21.0000 q^{21} +16.0000 q^{22} -148.000 q^{23} -24.0000 q^{24} -25.0000 q^{25} -100.000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -30.0000 q^{29} +60.0000 q^{30} +304.000 q^{31} +32.0000 q^{32} -24.0000 q^{33} +228.000 q^{34} -70.0000 q^{35} +36.0000 q^{36} -274.000 q^{37} +38.0000 q^{38} +150.000 q^{39} -80.0000 q^{40} -202.000 q^{41} -42.0000 q^{42} -116.000 q^{43} +32.0000 q^{44} -90.0000 q^{45} -296.000 q^{46} -324.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -342.000 q^{51} -200.000 q^{52} -550.000 q^{53} -54.0000 q^{54} -80.0000 q^{55} +56.0000 q^{56} -57.0000 q^{57} -60.0000 q^{58} +628.000 q^{59} +120.000 q^{60} -58.0000 q^{61} +608.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} +500.000 q^{65} -48.0000 q^{66} -756.000 q^{67} +456.000 q^{68} +444.000 q^{69} -140.000 q^{70} -216.000 q^{71} +72.0000 q^{72} -278.000 q^{73} -548.000 q^{74} +75.0000 q^{75} +76.0000 q^{76} +56.0000 q^{77} +300.000 q^{78} -952.000 q^{79} -160.000 q^{80} +81.0000 q^{81} -404.000 q^{82} -1184.00 q^{83} -84.0000 q^{84} -1140.00 q^{85} -232.000 q^{86} +90.0000 q^{87} +64.0000 q^{88} +1542.00 q^{89} -180.000 q^{90} -350.000 q^{91} -592.000 q^{92} -912.000 q^{93} -648.000 q^{94} -190.000 q^{95} -96.0000 q^{96} -870.000 q^{97} +98.0000 q^{98} +72.0000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) −10.0000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) −6.00000 −0.408248
\(7\) 7.00000 0.377964
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) −20.0000 −0.632456
\(11\) 8.00000 0.219281 0.109640 0.993971i \(-0.465030\pi\)
0.109640 + 0.993971i \(0.465030\pi\)
\(12\) −12.0000 −0.288675
\(13\) −50.0000 −1.06673 −0.533366 0.845885i \(-0.679073\pi\)
−0.533366 + 0.845885i \(0.679073\pi\)
\(14\) 14.0000 0.267261
\(15\) 30.0000 0.516398
\(16\) 16.0000 0.250000
\(17\) 114.000 1.62642 0.813208 0.581974i \(-0.197719\pi\)
0.813208 + 0.581974i \(0.197719\pi\)
\(18\) 18.0000 0.235702
\(19\) 19.0000 0.229416
\(20\) −40.0000 −0.447214
\(21\) −21.0000 −0.218218
\(22\) 16.0000 0.155055
\(23\) −148.000 −1.34174 −0.670872 0.741573i \(-0.734080\pi\)
−0.670872 + 0.741573i \(0.734080\pi\)
\(24\) −24.0000 −0.204124
\(25\) −25.0000 −0.200000
\(26\) −100.000 −0.754293
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) −30.0000 −0.192099 −0.0960493 0.995377i \(-0.530621\pi\)
−0.0960493 + 0.995377i \(0.530621\pi\)
\(30\) 60.0000 0.365148
\(31\) 304.000 1.76129 0.880645 0.473776i \(-0.157109\pi\)
0.880645 + 0.473776i \(0.157109\pi\)
\(32\) 32.0000 0.176777
\(33\) −24.0000 −0.126602
\(34\) 228.000 1.15005
\(35\) −70.0000 −0.338062
\(36\) 36.0000 0.166667
\(37\) −274.000 −1.21744 −0.608721 0.793385i \(-0.708317\pi\)
−0.608721 + 0.793385i \(0.708317\pi\)
\(38\) 38.0000 0.162221
\(39\) 150.000 0.615878
\(40\) −80.0000 −0.316228
\(41\) −202.000 −0.769441 −0.384721 0.923033i \(-0.625702\pi\)
−0.384721 + 0.923033i \(0.625702\pi\)
\(42\) −42.0000 −0.154303
\(43\) −116.000 −0.411391 −0.205696 0.978616i \(-0.565946\pi\)
−0.205696 + 0.978616i \(0.565946\pi\)
\(44\) 32.0000 0.109640
\(45\) −90.0000 −0.298142
\(46\) −296.000 −0.948757
\(47\) −324.000 −1.00554 −0.502769 0.864421i \(-0.667685\pi\)
−0.502769 + 0.864421i \(0.667685\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) −50.0000 −0.141421
\(51\) −342.000 −0.939011
\(52\) −200.000 −0.533366
\(53\) −550.000 −1.42544 −0.712720 0.701449i \(-0.752537\pi\)
−0.712720 + 0.701449i \(0.752537\pi\)
\(54\) −54.0000 −0.136083
\(55\) −80.0000 −0.196131
\(56\) 56.0000 0.133631
\(57\) −57.0000 −0.132453
\(58\) −60.0000 −0.135834
\(59\) 628.000 1.38574 0.692870 0.721063i \(-0.256346\pi\)
0.692870 + 0.721063i \(0.256346\pi\)
\(60\) 120.000 0.258199
\(61\) −58.0000 −0.121740 −0.0608700 0.998146i \(-0.519388\pi\)
−0.0608700 + 0.998146i \(0.519388\pi\)
\(62\) 608.000 1.24542
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 500.000 0.954113
\(66\) −48.0000 −0.0895211
\(67\) −756.000 −1.37851 −0.689254 0.724519i \(-0.742062\pi\)
−0.689254 + 0.724519i \(0.742062\pi\)
\(68\) 456.000 0.813208
\(69\) 444.000 0.774657
\(70\) −140.000 −0.239046
\(71\) −216.000 −0.361049 −0.180525 0.983570i \(-0.557780\pi\)
−0.180525 + 0.983570i \(0.557780\pi\)
\(72\) 72.0000 0.117851
\(73\) −278.000 −0.445718 −0.222859 0.974851i \(-0.571539\pi\)
−0.222859 + 0.974851i \(0.571539\pi\)
\(74\) −548.000 −0.860861
\(75\) 75.0000 0.115470
\(76\) 76.0000 0.114708
\(77\) 56.0000 0.0828804
\(78\) 300.000 0.435491
\(79\) −952.000 −1.35580 −0.677901 0.735153i \(-0.737110\pi\)
−0.677901 + 0.735153i \(0.737110\pi\)
\(80\) −160.000 −0.223607
\(81\) 81.0000 0.111111
\(82\) −404.000 −0.544077
\(83\) −1184.00 −1.56579 −0.782897 0.622151i \(-0.786259\pi\)
−0.782897 + 0.622151i \(0.786259\pi\)
\(84\) −84.0000 −0.109109
\(85\) −1140.00 −1.45471
\(86\) −232.000 −0.290898
\(87\) 90.0000 0.110908
\(88\) 64.0000 0.0775275
\(89\) 1542.00 1.83654 0.918268 0.395960i \(-0.129588\pi\)
0.918268 + 0.395960i \(0.129588\pi\)
\(90\) −180.000 −0.210819
\(91\) −350.000 −0.403186
\(92\) −592.000 −0.670872
\(93\) −912.000 −1.01688
\(94\) −648.000 −0.711022
\(95\) −190.000 −0.205196
\(96\) −96.0000 −0.102062
\(97\) −870.000 −0.910671 −0.455336 0.890320i \(-0.650481\pi\)
−0.455336 + 0.890320i \(0.650481\pi\)
\(98\) 98.0000 0.101015
\(99\) 72.0000 0.0730937
\(100\) −100.000 −0.100000
\(101\) −594.000 −0.585200 −0.292600 0.956235i \(-0.594520\pi\)
−0.292600 + 0.956235i \(0.594520\pi\)
\(102\) −684.000 −0.663981
\(103\) −288.000 −0.275510 −0.137755 0.990466i \(-0.543989\pi\)
−0.137755 + 0.990466i \(0.543989\pi\)
\(104\) −400.000 −0.377146
\(105\) 210.000 0.195180
\(106\) −1100.00 −1.00794
\(107\) −276.000 −0.249364 −0.124682 0.992197i \(-0.539791\pi\)
−0.124682 + 0.992197i \(0.539791\pi\)
\(108\) −108.000 −0.0962250
\(109\) −1714.00 −1.50616 −0.753080 0.657929i \(-0.771433\pi\)
−0.753080 + 0.657929i \(0.771433\pi\)
\(110\) −160.000 −0.138685
\(111\) 822.000 0.702890
\(112\) 112.000 0.0944911
\(113\) −730.000 −0.607722 −0.303861 0.952716i \(-0.598276\pi\)
−0.303861 + 0.952716i \(0.598276\pi\)
\(114\) −114.000 −0.0936586
\(115\) 1480.00 1.20009
\(116\) −120.000 −0.0960493
\(117\) −450.000 −0.355577
\(118\) 1256.00 0.979866
\(119\) 798.000 0.614727
\(120\) 240.000 0.182574
\(121\) −1267.00 −0.951916
\(122\) −116.000 −0.0860832
\(123\) 606.000 0.444237
\(124\) 1216.00 0.880645
\(125\) 1500.00 1.07331
\(126\) 126.000 0.0890871
\(127\) 784.000 0.547785 0.273893 0.961760i \(-0.411689\pi\)
0.273893 + 0.961760i \(0.411689\pi\)
\(128\) 128.000 0.0883883
\(129\) 348.000 0.237517
\(130\) 1000.00 0.674660
\(131\) −120.000 −0.0800340 −0.0400170 0.999199i \(-0.512741\pi\)
−0.0400170 + 0.999199i \(0.512741\pi\)
\(132\) −96.0000 −0.0633010
\(133\) 133.000 0.0867110
\(134\) −1512.00 −0.974753
\(135\) 270.000 0.172133
\(136\) 912.000 0.575025
\(137\) −30.0000 −0.0187086 −0.00935428 0.999956i \(-0.502978\pi\)
−0.00935428 + 0.999956i \(0.502978\pi\)
\(138\) 888.000 0.547765
\(139\) 1140.00 0.695637 0.347818 0.937562i \(-0.386923\pi\)
0.347818 + 0.937562i \(0.386923\pi\)
\(140\) −280.000 −0.169031
\(141\) 972.000 0.580547
\(142\) −432.000 −0.255300
\(143\) −400.000 −0.233914
\(144\) 144.000 0.0833333
\(145\) 300.000 0.171818
\(146\) −556.000 −0.315170
\(147\) −147.000 −0.0824786
\(148\) −1096.00 −0.608721
\(149\) 406.000 0.223227 0.111613 0.993752i \(-0.464398\pi\)
0.111613 + 0.993752i \(0.464398\pi\)
\(150\) 150.000 0.0816497
\(151\) 2320.00 1.25032 0.625162 0.780495i \(-0.285033\pi\)
0.625162 + 0.780495i \(0.285033\pi\)
\(152\) 152.000 0.0811107
\(153\) 1026.00 0.542138
\(154\) 112.000 0.0586053
\(155\) −3040.00 −1.57535
\(156\) 600.000 0.307939
\(157\) −3194.00 −1.62362 −0.811812 0.583919i \(-0.801519\pi\)
−0.811812 + 0.583919i \(0.801519\pi\)
\(158\) −1904.00 −0.958697
\(159\) 1650.00 0.822978
\(160\) −320.000 −0.158114
\(161\) −1036.00 −0.507132
\(162\) 162.000 0.0785674
\(163\) −4.00000 −0.00192211 −0.000961056 1.00000i \(-0.500306\pi\)
−0.000961056 1.00000i \(0.500306\pi\)
\(164\) −808.000 −0.384721
\(165\) 240.000 0.113236
\(166\) −2368.00 −1.10718
\(167\) −632.000 −0.292848 −0.146424 0.989222i \(-0.546776\pi\)
−0.146424 + 0.989222i \(0.546776\pi\)
\(168\) −168.000 −0.0771517
\(169\) 303.000 0.137915
\(170\) −2280.00 −1.02864
\(171\) 171.000 0.0764719
\(172\) −464.000 −0.205696
\(173\) 3682.00 1.61813 0.809067 0.587716i \(-0.199973\pi\)
0.809067 + 0.587716i \(0.199973\pi\)
\(174\) 180.000 0.0784239
\(175\) −175.000 −0.0755929
\(176\) 128.000 0.0548202
\(177\) −1884.00 −0.800057
\(178\) 3084.00 1.29863
\(179\) 2196.00 0.916965 0.458483 0.888703i \(-0.348393\pi\)
0.458483 + 0.888703i \(0.348393\pi\)
\(180\) −360.000 −0.149071
\(181\) −3802.00 −1.56133 −0.780664 0.624951i \(-0.785119\pi\)
−0.780664 + 0.624951i \(0.785119\pi\)
\(182\) −700.000 −0.285096
\(183\) 174.000 0.0702866
\(184\) −1184.00 −0.474378
\(185\) 2740.00 1.08891
\(186\) −1824.00 −0.719044
\(187\) 912.000 0.356642
\(188\) −1296.00 −0.502769
\(189\) −189.000 −0.0727393
\(190\) −380.000 −0.145095
\(191\) 1852.00 0.701602 0.350801 0.936450i \(-0.385909\pi\)
0.350801 + 0.936450i \(0.385909\pi\)
\(192\) −192.000 −0.0721688
\(193\) 4242.00 1.58210 0.791051 0.611750i \(-0.209534\pi\)
0.791051 + 0.611750i \(0.209534\pi\)
\(194\) −1740.00 −0.643942
\(195\) −1500.00 −0.550858
\(196\) 196.000 0.0714286
\(197\) 670.000 0.242312 0.121156 0.992633i \(-0.461340\pi\)
0.121156 + 0.992633i \(0.461340\pi\)
\(198\) 144.000 0.0516850
\(199\) −4672.00 −1.66427 −0.832134 0.554575i \(-0.812881\pi\)
−0.832134 + 0.554575i \(0.812881\pi\)
\(200\) −200.000 −0.0707107
\(201\) 2268.00 0.795883
\(202\) −1188.00 −0.413799
\(203\) −210.000 −0.0726065
\(204\) −1368.00 −0.469506
\(205\) 2020.00 0.688209
\(206\) −576.000 −0.194815
\(207\) −1332.00 −0.447248
\(208\) −800.000 −0.266683
\(209\) 152.000 0.0503065
\(210\) 420.000 0.138013
\(211\) 1852.00 0.604251 0.302125 0.953268i \(-0.402304\pi\)
0.302125 + 0.953268i \(0.402304\pi\)
\(212\) −2200.00 −0.712720
\(213\) 648.000 0.208452
\(214\) −552.000 −0.176327
\(215\) 1160.00 0.367960
\(216\) −216.000 −0.0680414
\(217\) 2128.00 0.665705
\(218\) −3428.00 −1.06502
\(219\) 834.000 0.257336
\(220\) −320.000 −0.0980654
\(221\) −5700.00 −1.73495
\(222\) 1644.00 0.497018
\(223\) 4312.00 1.29486 0.647428 0.762127i \(-0.275845\pi\)
0.647428 + 0.762127i \(0.275845\pi\)
\(224\) 224.000 0.0668153
\(225\) −225.000 −0.0666667
\(226\) −1460.00 −0.429725
\(227\) 1476.00 0.431566 0.215783 0.976441i \(-0.430770\pi\)
0.215783 + 0.976441i \(0.430770\pi\)
\(228\) −228.000 −0.0662266
\(229\) −3042.00 −0.877821 −0.438911 0.898531i \(-0.644635\pi\)
−0.438911 + 0.898531i \(0.644635\pi\)
\(230\) 2960.00 0.848594
\(231\) −168.000 −0.0478510
\(232\) −240.000 −0.0679171
\(233\) 938.000 0.263736 0.131868 0.991267i \(-0.457903\pi\)
0.131868 + 0.991267i \(0.457903\pi\)
\(234\) −900.000 −0.251431
\(235\) 3240.00 0.899380
\(236\) 2512.00 0.692870
\(237\) 2856.00 0.782773
\(238\) 1596.00 0.434678
\(239\) 812.000 0.219765 0.109883 0.993945i \(-0.464952\pi\)
0.109883 + 0.993945i \(0.464952\pi\)
\(240\) 480.000 0.129099
\(241\) 842.000 0.225054 0.112527 0.993649i \(-0.464106\pi\)
0.112527 + 0.993649i \(0.464106\pi\)
\(242\) −2534.00 −0.673106
\(243\) −243.000 −0.0641500
\(244\) −232.000 −0.0608700
\(245\) −490.000 −0.127775
\(246\) 1212.00 0.314123
\(247\) −950.000 −0.244725
\(248\) 2432.00 0.622710
\(249\) 3552.00 0.904011
\(250\) 3000.00 0.758947
\(251\) −3288.00 −0.826840 −0.413420 0.910541i \(-0.635666\pi\)
−0.413420 + 0.910541i \(0.635666\pi\)
\(252\) 252.000 0.0629941
\(253\) −1184.00 −0.294219
\(254\) 1568.00 0.387343
\(255\) 3420.00 0.839877
\(256\) 256.000 0.0625000
\(257\) −2522.00 −0.612132 −0.306066 0.952010i \(-0.599013\pi\)
−0.306066 + 0.952010i \(0.599013\pi\)
\(258\) 696.000 0.167950
\(259\) −1918.00 −0.460150
\(260\) 2000.00 0.477057
\(261\) −270.000 −0.0640329
\(262\) −240.000 −0.0565926
\(263\) −3228.00 −0.756833 −0.378416 0.925635i \(-0.623531\pi\)
−0.378416 + 0.925635i \(0.623531\pi\)
\(264\) −192.000 −0.0447605
\(265\) 5500.00 1.27495
\(266\) 266.000 0.0613139
\(267\) −4626.00 −1.06032
\(268\) −3024.00 −0.689254
\(269\) 8434.00 1.91164 0.955818 0.293959i \(-0.0949730\pi\)
0.955818 + 0.293959i \(0.0949730\pi\)
\(270\) 540.000 0.121716
\(271\) −7400.00 −1.65874 −0.829369 0.558701i \(-0.811300\pi\)
−0.829369 + 0.558701i \(0.811300\pi\)
\(272\) 1824.00 0.406604
\(273\) 1050.00 0.232780
\(274\) −60.0000 −0.0132290
\(275\) −200.000 −0.0438562
\(276\) 1776.00 0.387328
\(277\) −1442.00 −0.312785 −0.156392 0.987695i \(-0.549986\pi\)
−0.156392 + 0.987695i \(0.549986\pi\)
\(278\) 2280.00 0.491890
\(279\) 2736.00 0.587097
\(280\) −560.000 −0.119523
\(281\) 6262.00 1.32939 0.664697 0.747113i \(-0.268561\pi\)
0.664697 + 0.747113i \(0.268561\pi\)
\(282\) 1944.00 0.410509
\(283\) −3796.00 −0.797346 −0.398673 0.917093i \(-0.630529\pi\)
−0.398673 + 0.917093i \(0.630529\pi\)
\(284\) −864.000 −0.180525
\(285\) 570.000 0.118470
\(286\) −800.000 −0.165402
\(287\) −1414.00 −0.290822
\(288\) 288.000 0.0589256
\(289\) 8083.00 1.64523
\(290\) 600.000 0.121494
\(291\) 2610.00 0.525776
\(292\) −1112.00 −0.222859
\(293\) −5046.00 −1.00611 −0.503055 0.864254i \(-0.667791\pi\)
−0.503055 + 0.864254i \(0.667791\pi\)
\(294\) −294.000 −0.0583212
\(295\) −6280.00 −1.23944
\(296\) −2192.00 −0.430430
\(297\) −216.000 −0.0422006
\(298\) 812.000 0.157845
\(299\) 7400.00 1.43128
\(300\) 300.000 0.0577350
\(301\) −812.000 −0.155491
\(302\) 4640.00 0.884113
\(303\) 1782.00 0.337865
\(304\) 304.000 0.0573539
\(305\) 580.000 0.108888
\(306\) 2052.00 0.383350
\(307\) 244.000 0.0453610 0.0226805 0.999743i \(-0.492780\pi\)
0.0226805 + 0.999743i \(0.492780\pi\)
\(308\) 224.000 0.0414402
\(309\) 864.000 0.159066
\(310\) −6080.00 −1.11394
\(311\) −8028.00 −1.46375 −0.731875 0.681439i \(-0.761354\pi\)
−0.731875 + 0.681439i \(0.761354\pi\)
\(312\) 1200.00 0.217746
\(313\) 9178.00 1.65742 0.828708 0.559681i \(-0.189076\pi\)
0.828708 + 0.559681i \(0.189076\pi\)
\(314\) −6388.00 −1.14808
\(315\) −630.000 −0.112687
\(316\) −3808.00 −0.677901
\(317\) 1514.00 0.268248 0.134124 0.990965i \(-0.457178\pi\)
0.134124 + 0.990965i \(0.457178\pi\)
\(318\) 3300.00 0.581933
\(319\) −240.000 −0.0421236
\(320\) −640.000 −0.111803
\(321\) 828.000 0.143970
\(322\) −2072.00 −0.358596
\(323\) 2166.00 0.373125
\(324\) 324.000 0.0555556
\(325\) 1250.00 0.213346
\(326\) −8.00000 −0.00135914
\(327\) 5142.00 0.869582
\(328\) −1616.00 −0.272039
\(329\) −2268.00 −0.380057
\(330\) 480.000 0.0800701
\(331\) −2196.00 −0.364662 −0.182331 0.983237i \(-0.558364\pi\)
−0.182331 + 0.983237i \(0.558364\pi\)
\(332\) −4736.00 −0.782897
\(333\) −2466.00 −0.405814
\(334\) −1264.00 −0.207075
\(335\) 7560.00 1.23298
\(336\) −336.000 −0.0545545
\(337\) 7594.00 1.22751 0.613756 0.789496i \(-0.289658\pi\)
0.613756 + 0.789496i \(0.289658\pi\)
\(338\) 606.000 0.0975209
\(339\) 2190.00 0.350869
\(340\) −4560.00 −0.727355
\(341\) 2432.00 0.386218
\(342\) 342.000 0.0540738
\(343\) 343.000 0.0539949
\(344\) −928.000 −0.145449
\(345\) −4440.00 −0.692874
\(346\) 7364.00 1.14419
\(347\) 4632.00 0.716596 0.358298 0.933607i \(-0.383357\pi\)
0.358298 + 0.933607i \(0.383357\pi\)
\(348\) 360.000 0.0554541
\(349\) 1798.00 0.275773 0.137886 0.990448i \(-0.455969\pi\)
0.137886 + 0.990448i \(0.455969\pi\)
\(350\) −350.000 −0.0534522
\(351\) 1350.00 0.205293
\(352\) 256.000 0.0387638
\(353\) 3666.00 0.552752 0.276376 0.961050i \(-0.410866\pi\)
0.276376 + 0.961050i \(0.410866\pi\)
\(354\) −3768.00 −0.565726
\(355\) 2160.00 0.322932
\(356\) 6168.00 0.918268
\(357\) −2394.00 −0.354913
\(358\) 4392.00 0.648392
\(359\) 12004.0 1.76475 0.882377 0.470543i \(-0.155942\pi\)
0.882377 + 0.470543i \(0.155942\pi\)
\(360\) −720.000 −0.105409
\(361\) 361.000 0.0526316
\(362\) −7604.00 −1.10403
\(363\) 3801.00 0.549589
\(364\) −1400.00 −0.201593
\(365\) 2780.00 0.398663
\(366\) 348.000 0.0497001
\(367\) 120.000 0.0170680 0.00853399 0.999964i \(-0.497284\pi\)
0.00853399 + 0.999964i \(0.497284\pi\)
\(368\) −2368.00 −0.335436
\(369\) −1818.00 −0.256480
\(370\) 5480.00 0.769977
\(371\) −3850.00 −0.538766
\(372\) −3648.00 −0.508441
\(373\) −7954.00 −1.10414 −0.552068 0.833799i \(-0.686161\pi\)
−0.552068 + 0.833799i \(0.686161\pi\)
\(374\) 1824.00 0.252184
\(375\) −4500.00 −0.619677
\(376\) −2592.00 −0.355511
\(377\) 1500.00 0.204918
\(378\) −378.000 −0.0514344
\(379\) −11268.0 −1.52717 −0.763586 0.645706i \(-0.776563\pi\)
−0.763586 + 0.645706i \(0.776563\pi\)
\(380\) −760.000 −0.102598
\(381\) −2352.00 −0.316264
\(382\) 3704.00 0.496108
\(383\) 1224.00 0.163299 0.0816494 0.996661i \(-0.473981\pi\)
0.0816494 + 0.996661i \(0.473981\pi\)
\(384\) −384.000 −0.0510310
\(385\) −560.000 −0.0741305
\(386\) 8484.00 1.11872
\(387\) −1044.00 −0.137130
\(388\) −3480.00 −0.455336
\(389\) 7038.00 0.917328 0.458664 0.888610i \(-0.348328\pi\)
0.458664 + 0.888610i \(0.348328\pi\)
\(390\) −3000.00 −0.389515
\(391\) −16872.0 −2.18223
\(392\) 392.000 0.0505076
\(393\) 360.000 0.0462076
\(394\) 1340.00 0.171341
\(395\) 9520.00 1.21267
\(396\) 288.000 0.0365468
\(397\) 13110.0 1.65736 0.828680 0.559722i \(-0.189092\pi\)
0.828680 + 0.559722i \(0.189092\pi\)
\(398\) −9344.00 −1.17682
\(399\) −399.000 −0.0500626
\(400\) −400.000 −0.0500000
\(401\) −4346.00 −0.541219 −0.270610 0.962689i \(-0.587225\pi\)
−0.270610 + 0.962689i \(0.587225\pi\)
\(402\) 4536.00 0.562774
\(403\) −15200.0 −1.87882
\(404\) −2376.00 −0.292600
\(405\) −810.000 −0.0993808
\(406\) −420.000 −0.0513405
\(407\) −2192.00 −0.266962
\(408\) −2736.00 −0.331991
\(409\) −14734.0 −1.78129 −0.890647 0.454695i \(-0.849748\pi\)
−0.890647 + 0.454695i \(0.849748\pi\)
\(410\) 4040.00 0.486638
\(411\) 90.0000 0.0108014
\(412\) −1152.00 −0.137755
\(413\) 4396.00 0.523760
\(414\) −2664.00 −0.316252
\(415\) 11840.0 1.40049
\(416\) −1600.00 −0.188573
\(417\) −3420.00 −0.401626
\(418\) 304.000 0.0355721
\(419\) 7528.00 0.877725 0.438863 0.898554i \(-0.355381\pi\)
0.438863 + 0.898554i \(0.355381\pi\)
\(420\) 840.000 0.0975900
\(421\) −11018.0 −1.27550 −0.637749 0.770244i \(-0.720134\pi\)
−0.637749 + 0.770244i \(0.720134\pi\)
\(422\) 3704.00 0.427270
\(423\) −2916.00 −0.335179
\(424\) −4400.00 −0.503969
\(425\) −2850.00 −0.325283
\(426\) 1296.00 0.147398
\(427\) −406.000 −0.0460134
\(428\) −1104.00 −0.124682
\(429\) 1200.00 0.135050
\(430\) 2320.00 0.260187
\(431\) −2448.00 −0.273587 −0.136794 0.990600i \(-0.543680\pi\)
−0.136794 + 0.990600i \(0.543680\pi\)
\(432\) −432.000 −0.0481125
\(433\) −46.0000 −0.00510536 −0.00255268 0.999997i \(-0.500813\pi\)
−0.00255268 + 0.999997i \(0.500813\pi\)
\(434\) 4256.00 0.470725
\(435\) −900.000 −0.0991993
\(436\) −6856.00 −0.753080
\(437\) −2812.00 −0.307817
\(438\) 1668.00 0.181964
\(439\) 16672.0 1.81255 0.906277 0.422684i \(-0.138912\pi\)
0.906277 + 0.422684i \(0.138912\pi\)
\(440\) −640.000 −0.0693427
\(441\) 441.000 0.0476190
\(442\) −11400.0 −1.22679
\(443\) −4232.00 −0.453879 −0.226939 0.973909i \(-0.572872\pi\)
−0.226939 + 0.973909i \(0.572872\pi\)
\(444\) 3288.00 0.351445
\(445\) −15420.0 −1.64265
\(446\) 8624.00 0.915601
\(447\) −1218.00 −0.128880
\(448\) 448.000 0.0472456
\(449\) 11150.0 1.17194 0.585970 0.810333i \(-0.300714\pi\)
0.585970 + 0.810333i \(0.300714\pi\)
\(450\) −450.000 −0.0471405
\(451\) −1616.00 −0.168724
\(452\) −2920.00 −0.303861
\(453\) −6960.00 −0.721875
\(454\) 2952.00 0.305163
\(455\) 3500.00 0.360621
\(456\) −456.000 −0.0468293
\(457\) 2538.00 0.259787 0.129893 0.991528i \(-0.458536\pi\)
0.129893 + 0.991528i \(0.458536\pi\)
\(458\) −6084.00 −0.620713
\(459\) −3078.00 −0.313004
\(460\) 5920.00 0.600047
\(461\) 7078.00 0.715087 0.357544 0.933896i \(-0.383614\pi\)
0.357544 + 0.933896i \(0.383614\pi\)
\(462\) −336.000 −0.0338358
\(463\) −11432.0 −1.14749 −0.573747 0.819032i \(-0.694511\pi\)
−0.573747 + 0.819032i \(0.694511\pi\)
\(464\) −480.000 −0.0480247
\(465\) 9120.00 0.909527
\(466\) 1876.00 0.186489
\(467\) 9984.00 0.989303 0.494651 0.869091i \(-0.335296\pi\)
0.494651 + 0.869091i \(0.335296\pi\)
\(468\) −1800.00 −0.177789
\(469\) −5292.00 −0.521027
\(470\) 6480.00 0.635958
\(471\) 9582.00 0.937400
\(472\) 5024.00 0.489933
\(473\) −928.000 −0.0902103
\(474\) 5712.00 0.553504
\(475\) −475.000 −0.0458831
\(476\) 3192.00 0.307364
\(477\) −4950.00 −0.475147
\(478\) 1624.00 0.155398
\(479\) −9276.00 −0.884825 −0.442413 0.896812i \(-0.645877\pi\)
−0.442413 + 0.896812i \(0.645877\pi\)
\(480\) 960.000 0.0912871
\(481\) 13700.0 1.29868
\(482\) 1684.00 0.159137
\(483\) 3108.00 0.292793
\(484\) −5068.00 −0.475958
\(485\) 8700.00 0.814529
\(486\) −486.000 −0.0453609
\(487\) −19240.0 −1.79024 −0.895121 0.445824i \(-0.852911\pi\)
−0.895121 + 0.445824i \(0.852911\pi\)
\(488\) −464.000 −0.0430416
\(489\) 12.0000 0.00110973
\(490\) −980.000 −0.0903508
\(491\) −11384.0 −1.04634 −0.523170 0.852228i \(-0.675251\pi\)
−0.523170 + 0.852228i \(0.675251\pi\)
\(492\) 2424.00 0.222119
\(493\) −3420.00 −0.312432
\(494\) −1900.00 −0.173047
\(495\) −720.000 −0.0653770
\(496\) 4864.00 0.440323
\(497\) −1512.00 −0.136464
\(498\) 7104.00 0.639233
\(499\) 6204.00 0.556572 0.278286 0.960498i \(-0.410234\pi\)
0.278286 + 0.960498i \(0.410234\pi\)
\(500\) 6000.00 0.536656
\(501\) 1896.00 0.169076
\(502\) −6576.00 −0.584664
\(503\) −17332.0 −1.53637 −0.768187 0.640226i \(-0.778841\pi\)
−0.768187 + 0.640226i \(0.778841\pi\)
\(504\) 504.000 0.0445435
\(505\) 5940.00 0.523419
\(506\) −2368.00 −0.208044
\(507\) −909.000 −0.0796255
\(508\) 3136.00 0.273893
\(509\) 4930.00 0.429309 0.214655 0.976690i \(-0.431137\pi\)
0.214655 + 0.976690i \(0.431137\pi\)
\(510\) 6840.00 0.593883
\(511\) −1946.00 −0.168466
\(512\) 512.000 0.0441942
\(513\) −513.000 −0.0441511
\(514\) −5044.00 −0.432843
\(515\) 2880.00 0.246423
\(516\) 1392.00 0.118758
\(517\) −2592.00 −0.220495
\(518\) −3836.00 −0.325375
\(519\) −11046.0 −0.934230
\(520\) 4000.00 0.337330
\(521\) 21014.0 1.76706 0.883532 0.468371i \(-0.155159\pi\)
0.883532 + 0.468371i \(0.155159\pi\)
\(522\) −540.000 −0.0452781
\(523\) −4828.00 −0.403659 −0.201830 0.979421i \(-0.564689\pi\)
−0.201830 + 0.979421i \(0.564689\pi\)
\(524\) −480.000 −0.0400170
\(525\) 525.000 0.0436436
\(526\) −6456.00 −0.535162
\(527\) 34656.0 2.86459
\(528\) −384.000 −0.0316505
\(529\) 9737.00 0.800279
\(530\) 11000.0 0.901527
\(531\) 5652.00 0.461913
\(532\) 532.000 0.0433555
\(533\) 10100.0 0.820787
\(534\) −9252.00 −0.749763
\(535\) 2760.00 0.223038
\(536\) −6048.00 −0.487377
\(537\) −6588.00 −0.529410
\(538\) 16868.0 1.35173
\(539\) 392.000 0.0313259
\(540\) 1080.00 0.0860663
\(541\) 16038.0 1.27454 0.637271 0.770640i \(-0.280063\pi\)
0.637271 + 0.770640i \(0.280063\pi\)
\(542\) −14800.0 −1.17290
\(543\) 11406.0 0.901433
\(544\) 3648.00 0.287512
\(545\) 17140.0 1.34715
\(546\) 2100.00 0.164600
\(547\) −14524.0 −1.13529 −0.567643 0.823275i \(-0.692145\pi\)
−0.567643 + 0.823275i \(0.692145\pi\)
\(548\) −120.000 −0.00935428
\(549\) −522.000 −0.0405800
\(550\) −400.000 −0.0310110
\(551\) −570.000 −0.0440704
\(552\) 3552.00 0.273883
\(553\) −6664.00 −0.512445
\(554\) −2884.00 −0.221172
\(555\) −8220.00 −0.628684
\(556\) 4560.00 0.347818
\(557\) −12322.0 −0.937343 −0.468671 0.883373i \(-0.655267\pi\)
−0.468671 + 0.883373i \(0.655267\pi\)
\(558\) 5472.00 0.415140
\(559\) 5800.00 0.438844
\(560\) −1120.00 −0.0845154
\(561\) −2736.00 −0.205907
\(562\) 12524.0 0.940023
\(563\) −11100.0 −0.830922 −0.415461 0.909611i \(-0.636380\pi\)
−0.415461 + 0.909611i \(0.636380\pi\)
\(564\) 3888.00 0.290274
\(565\) 7300.00 0.543563
\(566\) −7592.00 −0.563808
\(567\) 567.000 0.0419961
\(568\) −1728.00 −0.127650
\(569\) −9418.00 −0.693889 −0.346945 0.937886i \(-0.612781\pi\)
−0.346945 + 0.937886i \(0.612781\pi\)
\(570\) 1140.00 0.0837708
\(571\) −16452.0 −1.20577 −0.602885 0.797828i \(-0.705982\pi\)
−0.602885 + 0.797828i \(0.705982\pi\)
\(572\) −1600.00 −0.116957
\(573\) −5556.00 −0.405070
\(574\) −2828.00 −0.205642
\(575\) 3700.00 0.268349
\(576\) 576.000 0.0416667
\(577\) 16658.0 1.20187 0.600937 0.799296i \(-0.294794\pi\)
0.600937 + 0.799296i \(0.294794\pi\)
\(578\) 16166.0 1.16335
\(579\) −12726.0 −0.913427
\(580\) 1200.00 0.0859091
\(581\) −8288.00 −0.591814
\(582\) 5220.00 0.371780
\(583\) −4400.00 −0.312572
\(584\) −2224.00 −0.157585
\(585\) 4500.00 0.318038
\(586\) −10092.0 −0.711428
\(587\) −5544.00 −0.389822 −0.194911 0.980821i \(-0.562442\pi\)
−0.194911 + 0.980821i \(0.562442\pi\)
\(588\) −588.000 −0.0412393
\(589\) 5776.00 0.404068
\(590\) −12560.0 −0.876419
\(591\) −2010.00 −0.139899
\(592\) −4384.00 −0.304360
\(593\) 14058.0 0.973512 0.486756 0.873538i \(-0.338180\pi\)
0.486756 + 0.873538i \(0.338180\pi\)
\(594\) −432.000 −0.0298404
\(595\) −7980.00 −0.549829
\(596\) 1624.00 0.111613
\(597\) 14016.0 0.960865
\(598\) 14800.0 1.01207
\(599\) 4720.00 0.321960 0.160980 0.986958i \(-0.448535\pi\)
0.160980 + 0.986958i \(0.448535\pi\)
\(600\) 600.000 0.0408248
\(601\) −3558.00 −0.241487 −0.120744 0.992684i \(-0.538528\pi\)
−0.120744 + 0.992684i \(0.538528\pi\)
\(602\) −1624.00 −0.109949
\(603\) −6804.00 −0.459503
\(604\) 9280.00 0.625162
\(605\) 12670.0 0.851419
\(606\) 3564.00 0.238907
\(607\) −23744.0 −1.58771 −0.793854 0.608108i \(-0.791929\pi\)
−0.793854 + 0.608108i \(0.791929\pi\)
\(608\) 608.000 0.0405554
\(609\) 630.000 0.0419194
\(610\) 1160.00 0.0769951
\(611\) 16200.0 1.07264
\(612\) 4104.00 0.271069
\(613\) 16062.0 1.05830 0.529150 0.848528i \(-0.322511\pi\)
0.529150 + 0.848528i \(0.322511\pi\)
\(614\) 488.000 0.0320750
\(615\) −6060.00 −0.397338
\(616\) 448.000 0.0293027
\(617\) 14498.0 0.945977 0.472988 0.881069i \(-0.343175\pi\)
0.472988 + 0.881069i \(0.343175\pi\)
\(618\) 1728.00 0.112476
\(619\) −6764.00 −0.439205 −0.219603 0.975589i \(-0.570476\pi\)
−0.219603 + 0.975589i \(0.570476\pi\)
\(620\) −12160.0 −0.787673
\(621\) 3996.00 0.258219
\(622\) −16056.0 −1.03503
\(623\) 10794.0 0.694145
\(624\) 2400.00 0.153969
\(625\) −11875.0 −0.760000
\(626\) 18356.0 1.17197
\(627\) −456.000 −0.0290445
\(628\) −12776.0 −0.811812
\(629\) −31236.0 −1.98006
\(630\) −1260.00 −0.0796819
\(631\) 15016.0 0.947349 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(632\) −7616.00 −0.479348
\(633\) −5556.00 −0.348864
\(634\) 3028.00 0.189680
\(635\) −7840.00 −0.489954
\(636\) 6600.00 0.411489
\(637\) −2450.00 −0.152390
\(638\) −480.000 −0.0297859
\(639\) −1944.00 −0.120350
\(640\) −1280.00 −0.0790569
\(641\) −18906.0 −1.16496 −0.582482 0.812844i \(-0.697918\pi\)
−0.582482 + 0.812844i \(0.697918\pi\)
\(642\) 1656.00 0.101802
\(643\) −29532.0 −1.81124 −0.905621 0.424088i \(-0.860595\pi\)
−0.905621 + 0.424088i \(0.860595\pi\)
\(644\) −4144.00 −0.253566
\(645\) −3480.00 −0.212442
\(646\) 4332.00 0.263839
\(647\) 3636.00 0.220936 0.110468 0.993880i \(-0.464765\pi\)
0.110468 + 0.993880i \(0.464765\pi\)
\(648\) 648.000 0.0392837
\(649\) 5024.00 0.303866
\(650\) 2500.00 0.150859
\(651\) −6384.00 −0.384345
\(652\) −16.0000 −0.000961056 0
\(653\) 12126.0 0.726688 0.363344 0.931655i \(-0.381635\pi\)
0.363344 + 0.931655i \(0.381635\pi\)
\(654\) 10284.0 0.614887
\(655\) 1200.00 0.0715845
\(656\) −3232.00 −0.192360
\(657\) −2502.00 −0.148573
\(658\) −4536.00 −0.268741
\(659\) −4580.00 −0.270731 −0.135365 0.990796i \(-0.543221\pi\)
−0.135365 + 0.990796i \(0.543221\pi\)
\(660\) 960.000 0.0566181
\(661\) −18178.0 −1.06966 −0.534828 0.844961i \(-0.679623\pi\)
−0.534828 + 0.844961i \(0.679623\pi\)
\(662\) −4392.00 −0.257855
\(663\) 17100.0 1.00167
\(664\) −9472.00 −0.553592
\(665\) −1330.00 −0.0775567
\(666\) −4932.00 −0.286954
\(667\) 4440.00 0.257747
\(668\) −2528.00 −0.146424
\(669\) −12936.0 −0.747585
\(670\) 15120.0 0.871846
\(671\) −464.000 −0.0266953
\(672\) −672.000 −0.0385758
\(673\) 10802.0 0.618702 0.309351 0.950948i \(-0.399888\pi\)
0.309351 + 0.950948i \(0.399888\pi\)
\(674\) 15188.0 0.867982
\(675\) 675.000 0.0384900
\(676\) 1212.00 0.0689577
\(677\) 11186.0 0.635026 0.317513 0.948254i \(-0.397152\pi\)
0.317513 + 0.948254i \(0.397152\pi\)
\(678\) 4380.00 0.248102
\(679\) −6090.00 −0.344201
\(680\) −9120.00 −0.514318
\(681\) −4428.00 −0.249165
\(682\) 4864.00 0.273097
\(683\) −29940.0 −1.67734 −0.838669 0.544641i \(-0.816666\pi\)
−0.838669 + 0.544641i \(0.816666\pi\)
\(684\) 684.000 0.0382360
\(685\) 300.000 0.0167334
\(686\) 686.000 0.0381802
\(687\) 9126.00 0.506810
\(688\) −1856.00 −0.102848
\(689\) 27500.0 1.52056
\(690\) −8880.00 −0.489936
\(691\) −17036.0 −0.937887 −0.468944 0.883228i \(-0.655365\pi\)
−0.468944 + 0.883228i \(0.655365\pi\)
\(692\) 14728.0 0.809067
\(693\) 504.000 0.0276268
\(694\) 9264.00 0.506710
\(695\) −11400.0 −0.622197
\(696\) 720.000 0.0392120
\(697\) −23028.0 −1.25143
\(698\) 3596.00 0.195001
\(699\) −2814.00 −0.152268
\(700\) −700.000 −0.0377964
\(701\) −15762.0 −0.849248 −0.424624 0.905370i \(-0.639594\pi\)
−0.424624 + 0.905370i \(0.639594\pi\)
\(702\) 2700.00 0.145164
\(703\) −5206.00 −0.279300
\(704\) 512.000 0.0274101
\(705\) −9720.00 −0.519257
\(706\) 7332.00 0.390855
\(707\) −4158.00 −0.221185
\(708\) −7536.00 −0.400029
\(709\) −16210.0 −0.858645 −0.429323 0.903151i \(-0.641248\pi\)
−0.429323 + 0.903151i \(0.641248\pi\)
\(710\) 4320.00 0.228347
\(711\) −8568.00 −0.451934
\(712\) 12336.0 0.649313
\(713\) −44992.0 −2.36320
\(714\) −4788.00 −0.250961
\(715\) 4000.00 0.209219
\(716\) 8784.00 0.458483
\(717\) −2436.00 −0.126882
\(718\) 24008.0 1.24787
\(719\) 3916.00 0.203118 0.101559 0.994829i \(-0.467617\pi\)
0.101559 + 0.994829i \(0.467617\pi\)
\(720\) −1440.00 −0.0745356
\(721\) −2016.00 −0.104133
\(722\) 722.000 0.0372161
\(723\) −2526.00 −0.129935
\(724\) −15208.0 −0.780664
\(725\) 750.000 0.0384197
\(726\) 7602.00 0.388618
\(727\) −25520.0 −1.30190 −0.650952 0.759119i \(-0.725630\pi\)
−0.650952 + 0.759119i \(0.725630\pi\)
\(728\) −2800.00 −0.142548
\(729\) 729.000 0.0370370
\(730\) 5560.00 0.281897
\(731\) −13224.0 −0.669093
\(732\) 696.000 0.0351433
\(733\) 16726.0 0.842823 0.421411 0.906870i \(-0.361535\pi\)
0.421411 + 0.906870i \(0.361535\pi\)
\(734\) 240.000 0.0120689
\(735\) 1470.00 0.0737711
\(736\) −4736.00 −0.237189
\(737\) −6048.00 −0.302281
\(738\) −3636.00 −0.181359
\(739\) 3436.00 0.171036 0.0855178 0.996337i \(-0.472746\pi\)
0.0855178 + 0.996337i \(0.472746\pi\)
\(740\) 10960.0 0.544456
\(741\) 2850.00 0.141292
\(742\) −7700.00 −0.380965
\(743\) 24664.0 1.21781 0.608906 0.793242i \(-0.291609\pi\)
0.608906 + 0.793242i \(0.291609\pi\)
\(744\) −7296.00 −0.359522
\(745\) −4060.00 −0.199660
\(746\) −15908.0 −0.780742
\(747\) −10656.0 −0.521931
\(748\) 3648.00 0.178321
\(749\) −1932.00 −0.0942507
\(750\) −9000.00 −0.438178
\(751\) −29208.0 −1.41919 −0.709597 0.704608i \(-0.751123\pi\)
−0.709597 + 0.704608i \(0.751123\pi\)
\(752\) −5184.00 −0.251384
\(753\) 9864.00 0.477376
\(754\) 3000.00 0.144899
\(755\) −23200.0 −1.11832
\(756\) −756.000 −0.0363696
\(757\) 20686.0 0.993191 0.496595 0.867982i \(-0.334583\pi\)
0.496595 + 0.867982i \(0.334583\pi\)
\(758\) −22536.0 −1.07987
\(759\) 3552.00 0.169867
\(760\) −1520.00 −0.0725476
\(761\) −40182.0 −1.91406 −0.957028 0.289996i \(-0.906346\pi\)
−0.957028 + 0.289996i \(0.906346\pi\)
\(762\) −4704.00 −0.223632
\(763\) −11998.0 −0.569275
\(764\) 7408.00 0.350801
\(765\) −10260.0 −0.484903
\(766\) 2448.00 0.115470
\(767\) −31400.0 −1.47821
\(768\) −768.000 −0.0360844
\(769\) −4686.00 −0.219742 −0.109871 0.993946i \(-0.535044\pi\)
−0.109871 + 0.993946i \(0.535044\pi\)
\(770\) −1120.00 −0.0524182
\(771\) 7566.00 0.353415
\(772\) 16968.0 0.791051
\(773\) 31114.0 1.44773 0.723863 0.689943i \(-0.242365\pi\)
0.723863 + 0.689943i \(0.242365\pi\)
\(774\) −2088.00 −0.0969659
\(775\) −7600.00 −0.352258
\(776\) −6960.00 −0.321971
\(777\) 5754.00 0.265667
\(778\) 14076.0 0.648649
\(779\) −3838.00 −0.176522
\(780\) −6000.00 −0.275429
\(781\) −1728.00 −0.0791712
\(782\) −33744.0 −1.54307
\(783\) 810.000 0.0369694
\(784\) 784.000 0.0357143
\(785\) 31940.0 1.45221
\(786\) 720.000 0.0326737
\(787\) 25708.0 1.16441 0.582205 0.813042i \(-0.302190\pi\)
0.582205 + 0.813042i \(0.302190\pi\)
\(788\) 2680.00 0.121156
\(789\) 9684.00 0.436958
\(790\) 19040.0 0.857485
\(791\) −5110.00 −0.229697
\(792\) 576.000 0.0258425
\(793\) 2900.00 0.129864
\(794\) 26220.0 1.17193
\(795\) −16500.0 −0.736094
\(796\) −18688.0 −0.832134
\(797\) −41326.0 −1.83669 −0.918345 0.395781i \(-0.870474\pi\)
−0.918345 + 0.395781i \(0.870474\pi\)
\(798\) −798.000 −0.0353996
\(799\) −36936.0 −1.63542
\(800\) −800.000 −0.0353553
\(801\) 13878.0 0.612179
\(802\) −8692.00 −0.382700
\(803\) −2224.00 −0.0977376
\(804\) 9072.00 0.397941
\(805\) 10360.0 0.453593
\(806\) −30400.0 −1.32853
\(807\) −25302.0 −1.10368
\(808\) −4752.00 −0.206899
\(809\) −34086.0 −1.48133 −0.740667 0.671872i \(-0.765491\pi\)
−0.740667 + 0.671872i \(0.765491\pi\)
\(810\) −1620.00 −0.0702728
\(811\) 15564.0 0.673891 0.336946 0.941524i \(-0.390606\pi\)
0.336946 + 0.941524i \(0.390606\pi\)
\(812\) −840.000 −0.0363032
\(813\) 22200.0 0.957673
\(814\) −4384.00 −0.188770
\(815\) 40.0000 0.00171919
\(816\) −5472.00 −0.234753
\(817\) −2204.00 −0.0943797
\(818\) −29468.0 −1.25957
\(819\) −3150.00 −0.134395
\(820\) 8080.00 0.344105
\(821\) −16074.0 −0.683297 −0.341648 0.939828i \(-0.610985\pi\)
−0.341648 + 0.939828i \(0.610985\pi\)
\(822\) 180.000 0.00763774
\(823\) −22840.0 −0.967378 −0.483689 0.875240i \(-0.660703\pi\)
−0.483689 + 0.875240i \(0.660703\pi\)
\(824\) −2304.00 −0.0974073
\(825\) 600.000 0.0253204
\(826\) 8792.00 0.370354
\(827\) −32628.0 −1.37193 −0.685965 0.727634i \(-0.740620\pi\)
−0.685965 + 0.727634i \(0.740620\pi\)
\(828\) −5328.00 −0.223624
\(829\) 27326.0 1.14484 0.572419 0.819961i \(-0.306005\pi\)
0.572419 + 0.819961i \(0.306005\pi\)
\(830\) 23680.0 0.990295
\(831\) 4326.00 0.180586
\(832\) −3200.00 −0.133341
\(833\) 5586.00 0.232345
\(834\) −6840.00 −0.283993
\(835\) 6320.00 0.261931
\(836\) 608.000 0.0251533
\(837\) −8208.00 −0.338961
\(838\) 15056.0 0.620645
\(839\) 26400.0 1.08633 0.543164 0.839627i \(-0.317226\pi\)
0.543164 + 0.839627i \(0.317226\pi\)
\(840\) 1680.00 0.0690066
\(841\) −23489.0 −0.963098
\(842\) −22036.0 −0.901913
\(843\) −18786.0 −0.767526
\(844\) 7408.00 0.302125
\(845\) −3030.00 −0.123355
\(846\) −5832.00 −0.237007
\(847\) −8869.00 −0.359790
\(848\) −8800.00 −0.356360
\(849\) 11388.0 0.460348
\(850\) −5700.00 −0.230010
\(851\) 40552.0 1.63350
\(852\) 2592.00 0.104226
\(853\) 20078.0 0.805929 0.402965 0.915216i \(-0.367980\pi\)
0.402965 + 0.915216i \(0.367980\pi\)
\(854\) −812.000 −0.0325364
\(855\) −1710.00 −0.0683986
\(856\) −2208.00 −0.0881634
\(857\) 24214.0 0.965151 0.482576 0.875854i \(-0.339701\pi\)
0.482576 + 0.875854i \(0.339701\pi\)
\(858\) 2400.00 0.0954949
\(859\) 34708.0 1.37860 0.689302 0.724474i \(-0.257917\pi\)
0.689302 + 0.724474i \(0.257917\pi\)
\(860\) 4640.00 0.183980
\(861\) 4242.00 0.167906
\(862\) −4896.00 −0.193455
\(863\) 11072.0 0.436727 0.218363 0.975868i \(-0.429928\pi\)
0.218363 + 0.975868i \(0.429928\pi\)
\(864\) −864.000 −0.0340207
\(865\) −36820.0 −1.44730
\(866\) −92.0000 −0.00361003
\(867\) −24249.0 −0.949872
\(868\) 8512.00 0.332853
\(869\) −7616.00 −0.297302
\(870\) −1800.00 −0.0701445
\(871\) 37800.0 1.47050
\(872\) −13712.0 −0.532508
\(873\) −7830.00 −0.303557
\(874\) −5624.00 −0.217660
\(875\) 10500.0 0.405674
\(876\) 3336.00 0.128668
\(877\) −8314.00 −0.320118 −0.160059 0.987107i \(-0.551169\pi\)
−0.160059 + 0.987107i \(0.551169\pi\)
\(878\) 33344.0 1.28167
\(879\) 15138.0 0.580878
\(880\) −1280.00 −0.0490327
\(881\) −7710.00 −0.294843 −0.147421 0.989074i \(-0.547097\pi\)
−0.147421 + 0.989074i \(0.547097\pi\)
\(882\) 882.000 0.0336718
\(883\) −37748.0 −1.43864 −0.719321 0.694678i \(-0.755547\pi\)
−0.719321 + 0.694678i \(0.755547\pi\)
\(884\) −22800.0 −0.867474
\(885\) 18840.0 0.715593
\(886\) −8464.00 −0.320941
\(887\) −45624.0 −1.72706 −0.863531 0.504296i \(-0.831752\pi\)
−0.863531 + 0.504296i \(0.831752\pi\)
\(888\) 6576.00 0.248509
\(889\) 5488.00 0.207043
\(890\) −30840.0 −1.16153
\(891\) 648.000 0.0243646
\(892\) 17248.0 0.647428
\(893\) −6156.00 −0.230686
\(894\) −2436.00 −0.0911320
\(895\) −21960.0 −0.820158
\(896\) 896.000 0.0334077
\(897\) −22200.0 −0.826351
\(898\) 22300.0 0.828687
\(899\) −9120.00 −0.338342
\(900\) −900.000 −0.0333333
\(901\) −62700.0 −2.31836
\(902\) −3232.00 −0.119306
\(903\) 2436.00 0.0897730
\(904\) −5840.00 −0.214862
\(905\) 38020.0 1.39649
\(906\) −13920.0 −0.510443
\(907\) 11732.0 0.429498 0.214749 0.976669i \(-0.431107\pi\)
0.214749 + 0.976669i \(0.431107\pi\)
\(908\) 5904.00 0.215783
\(909\) −5346.00 −0.195067
\(910\) 7000.00 0.254998
\(911\) 18696.0 0.679941 0.339970 0.940436i \(-0.389583\pi\)
0.339970 + 0.940436i \(0.389583\pi\)
\(912\) −912.000 −0.0331133
\(913\) −9472.00 −0.343349
\(914\) 5076.00 0.183697
\(915\) −1740.00 −0.0628663
\(916\) −12168.0 −0.438911
\(917\) −840.000 −0.0302500
\(918\) −6156.00 −0.221327
\(919\) 37512.0 1.34647 0.673235 0.739428i \(-0.264904\pi\)
0.673235 + 0.739428i \(0.264904\pi\)
\(920\) 11840.0 0.424297
\(921\) −732.000 −0.0261892
\(922\) 14156.0 0.505643
\(923\) 10800.0 0.385142
\(924\) −672.000 −0.0239255
\(925\) 6850.00 0.243488
\(926\) −22864.0 −0.811401
\(927\) −2592.00 −0.0918365
\(928\) −960.000 −0.0339586
\(929\) −14838.0 −0.524025 −0.262012 0.965065i \(-0.584386\pi\)
−0.262012 + 0.965065i \(0.584386\pi\)
\(930\) 18240.0 0.643132
\(931\) 931.000 0.0327737
\(932\) 3752.00 0.131868
\(933\) 24084.0 0.845096
\(934\) 19968.0 0.699543
\(935\) −9120.00 −0.318990
\(936\) −3600.00 −0.125715
\(937\) 45754.0 1.59522 0.797608 0.603176i \(-0.206098\pi\)
0.797608 + 0.603176i \(0.206098\pi\)
\(938\) −10584.0 −0.368422
\(939\) −27534.0 −0.956910
\(940\) 12960.0 0.449690
\(941\) 28018.0 0.970628 0.485314 0.874340i \(-0.338705\pi\)
0.485314 + 0.874340i \(0.338705\pi\)
\(942\) 19164.0 0.662842
\(943\) 29896.0 1.03239
\(944\) 10048.0 0.346435
\(945\) 1890.00 0.0650600
\(946\) −1856.00 −0.0637883
\(947\) 14064.0 0.482596 0.241298 0.970451i \(-0.422427\pi\)
0.241298 + 0.970451i \(0.422427\pi\)
\(948\) 11424.0 0.391386
\(949\) 13900.0 0.475462
\(950\) −950.000 −0.0324443
\(951\) −4542.00 −0.154873
\(952\) 6384.00 0.217339
\(953\) −12218.0 −0.415299 −0.207649 0.978203i \(-0.566581\pi\)
−0.207649 + 0.978203i \(0.566581\pi\)
\(954\) −9900.00 −0.335979
\(955\) −18520.0 −0.627532
\(956\) 3248.00 0.109883
\(957\) 720.000 0.0243201
\(958\) −18552.0 −0.625666
\(959\) −210.000 −0.00707117
\(960\) 1920.00 0.0645497
\(961\) 62625.0 2.10214
\(962\) 27400.0 0.918307
\(963\) −2484.00 −0.0831213
\(964\) 3368.00 0.112527
\(965\) −42420.0 −1.41508
\(966\) 6216.00 0.207036
\(967\) 23256.0 0.773384 0.386692 0.922209i \(-0.373618\pi\)
0.386692 + 0.922209i \(0.373618\pi\)
\(968\) −10136.0 −0.336553
\(969\) −6498.00 −0.215424
\(970\) 17400.0 0.575959
\(971\) 15836.0 0.523379 0.261690 0.965152i \(-0.415720\pi\)
0.261690 + 0.965152i \(0.415720\pi\)
\(972\) −972.000 −0.0320750
\(973\) 7980.00 0.262926
\(974\) −38480.0 −1.26589
\(975\) −3750.00 −0.123176
\(976\) −928.000 −0.0304350
\(977\) 33718.0 1.10413 0.552065 0.833801i \(-0.313840\pi\)
0.552065 + 0.833801i \(0.313840\pi\)
\(978\) 24.0000 0.000784699 0
\(979\) 12336.0 0.402717
\(980\) −1960.00 −0.0638877
\(981\) −15426.0 −0.502053
\(982\) −22768.0 −0.739874
\(983\) 59832.0 1.94135 0.970674 0.240401i \(-0.0772789\pi\)
0.970674 + 0.240401i \(0.0772789\pi\)
\(984\) 4848.00 0.157062
\(985\) −6700.00 −0.216731
\(986\) −6840.00 −0.220923
\(987\) 6804.00 0.219426
\(988\) −3800.00 −0.122362
\(989\) 17168.0 0.551982
\(990\) −1440.00 −0.0462285
\(991\) −6304.00 −0.202072 −0.101036 0.994883i \(-0.532216\pi\)
−0.101036 + 0.994883i \(0.532216\pi\)
\(992\) 9728.00 0.311355
\(993\) 6588.00 0.210538
\(994\) −3024.00 −0.0964944
\(995\) 46720.0 1.48857
\(996\) 14208.0 0.452006
\(997\) −23266.0 −0.739059 −0.369529 0.929219i \(-0.620481\pi\)
−0.369529 + 0.929219i \(0.620481\pi\)
\(998\) 12408.0 0.393555
\(999\) 7398.00 0.234297
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 798.4.a.b.1.1 1
3.2 odd 2 2394.4.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
798.4.a.b.1.1 1 1.1 even 1 trivial
2394.4.a.c.1.1 1 3.2 odd 2