Properties

Label 370.4.a.c.1.1
Level $370$
Weight $4$
Character 370.1
Self dual yes
Analytic conductor $21.831$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 370.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.8307067021\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 370.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +6.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +12.0000 q^{6} +3.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +6.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +12.0000 q^{6} +3.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} +5.00000 q^{11} +24.0000 q^{12} -16.0000 q^{13} +6.00000 q^{14} +30.0000 q^{15} +16.0000 q^{16} +115.000 q^{17} +18.0000 q^{18} +110.000 q^{19} +20.0000 q^{20} +18.0000 q^{21} +10.0000 q^{22} +6.00000 q^{23} +48.0000 q^{24} +25.0000 q^{25} -32.0000 q^{26} -108.000 q^{27} +12.0000 q^{28} -111.000 q^{29} +60.0000 q^{30} -79.0000 q^{31} +32.0000 q^{32} +30.0000 q^{33} +230.000 q^{34} +15.0000 q^{35} +36.0000 q^{36} -37.0000 q^{37} +220.000 q^{38} -96.0000 q^{39} +40.0000 q^{40} +171.000 q^{41} +36.0000 q^{42} +361.000 q^{43} +20.0000 q^{44} +45.0000 q^{45} +12.0000 q^{46} -428.000 q^{47} +96.0000 q^{48} -334.000 q^{49} +50.0000 q^{50} +690.000 q^{51} -64.0000 q^{52} -527.000 q^{53} -216.000 q^{54} +25.0000 q^{55} +24.0000 q^{56} +660.000 q^{57} -222.000 q^{58} +112.000 q^{59} +120.000 q^{60} -323.000 q^{61} -158.000 q^{62} +27.0000 q^{63} +64.0000 q^{64} -80.0000 q^{65} +60.0000 q^{66} -464.000 q^{67} +460.000 q^{68} +36.0000 q^{69} +30.0000 q^{70} -366.000 q^{71} +72.0000 q^{72} +712.000 q^{73} -74.0000 q^{74} +150.000 q^{75} +440.000 q^{76} +15.0000 q^{77} -192.000 q^{78} +176.000 q^{79} +80.0000 q^{80} -891.000 q^{81} +342.000 q^{82} -180.000 q^{83} +72.0000 q^{84} +575.000 q^{85} +722.000 q^{86} -666.000 q^{87} +40.0000 q^{88} +446.000 q^{89} +90.0000 q^{90} -48.0000 q^{91} +24.0000 q^{92} -474.000 q^{93} -856.000 q^{94} +550.000 q^{95} +192.000 q^{96} -1407.00 q^{97} -668.000 q^{98} +45.0000 q^{99} +O(q^{100})\)

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
\(3\) 6.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 12.0000 0.816497
\(7\) 3.00000 0.161985 0.0809924 0.996715i \(-0.474191\pi\)
0.0809924 + 0.996715i \(0.474191\pi\)
\(8\) 8.00000 0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) 5.00000 0.137051 0.0685253 0.997649i \(-0.478171\pi\)
0.0685253 + 0.997649i \(0.478171\pi\)
\(12\) 24.0000 0.577350
\(13\) −16.0000 −0.341354 −0.170677 0.985327i \(-0.554595\pi\)
−0.170677 + 0.985327i \(0.554595\pi\)
\(14\) 6.00000 0.114541
\(15\) 30.0000 0.516398
\(16\) 16.0000 0.250000
\(17\) 115.000 1.64068 0.820341 0.571875i \(-0.193784\pi\)
0.820341 + 0.571875i \(0.193784\pi\)
\(18\) 18.0000 0.235702
\(19\) 110.000 1.32820 0.664098 0.747645i \(-0.268816\pi\)
0.664098 + 0.747645i \(0.268816\pi\)
\(20\) 20.0000 0.223607
\(21\) 18.0000 0.187044
\(22\) 10.0000 0.0969094
\(23\) 6.00000 0.0543951 0.0271975 0.999630i \(-0.491342\pi\)
0.0271975 + 0.999630i \(0.491342\pi\)
\(24\) 48.0000 0.408248
\(25\) 25.0000 0.200000
\(26\) −32.0000 −0.241374
\(27\) −108.000 −0.769800
\(28\) 12.0000 0.0809924
\(29\) −111.000 −0.710765 −0.355382 0.934721i \(-0.615649\pi\)
−0.355382 + 0.934721i \(0.615649\pi\)
\(30\) 60.0000 0.365148
\(31\) −79.0000 −0.457704 −0.228852 0.973461i \(-0.573497\pi\)
−0.228852 + 0.973461i \(0.573497\pi\)
\(32\) 32.0000 0.176777
\(33\) 30.0000 0.158252
\(34\) 230.000 1.16014
\(35\) 15.0000 0.0724418
\(36\) 36.0000 0.166667
\(37\) −37.0000 −0.164399
\(38\) 220.000 0.939177
\(39\) −96.0000 −0.394162
\(40\) 40.0000 0.158114
\(41\) 171.000 0.651359 0.325679 0.945480i \(-0.394407\pi\)
0.325679 + 0.945480i \(0.394407\pi\)
\(42\) 36.0000 0.132260
\(43\) 361.000 1.28028 0.640139 0.768259i \(-0.278877\pi\)
0.640139 + 0.768259i \(0.278877\pi\)
\(44\) 20.0000 0.0685253
\(45\) 45.0000 0.149071
\(46\) 12.0000 0.0384631
\(47\) −428.000 −1.32830 −0.664151 0.747598i \(-0.731207\pi\)
−0.664151 + 0.747598i \(0.731207\pi\)
\(48\) 96.0000 0.288675
\(49\) −334.000 −0.973761
\(50\) 50.0000 0.141421
\(51\) 690.000 1.89450
\(52\) −64.0000 −0.170677
\(53\) −527.000 −1.36583 −0.682915 0.730498i \(-0.739288\pi\)
−0.682915 + 0.730498i \(0.739288\pi\)
\(54\) −216.000 −0.544331
\(55\) 25.0000 0.0612909
\(56\) 24.0000 0.0572703
\(57\) 660.000 1.53367
\(58\) −222.000 −0.502587
\(59\) 112.000 0.247138 0.123569 0.992336i \(-0.460566\pi\)
0.123569 + 0.992336i \(0.460566\pi\)
\(60\) 120.000 0.258199
\(61\) −323.000 −0.677966 −0.338983 0.940793i \(-0.610083\pi\)
−0.338983 + 0.940793i \(0.610083\pi\)
\(62\) −158.000 −0.323645
\(63\) 27.0000 0.0539949
\(64\) 64.0000 0.125000
\(65\) −80.0000 −0.152658
\(66\) 60.0000 0.111901
\(67\) −464.000 −0.846069 −0.423034 0.906114i \(-0.639035\pi\)
−0.423034 + 0.906114i \(0.639035\pi\)
\(68\) 460.000 0.820341
\(69\) 36.0000 0.0628100
\(70\) 30.0000 0.0512241
\(71\) −366.000 −0.611778 −0.305889 0.952067i \(-0.598954\pi\)
−0.305889 + 0.952067i \(0.598954\pi\)
\(72\) 72.0000 0.117851
\(73\) 712.000 1.14155 0.570776 0.821106i \(-0.306642\pi\)
0.570776 + 0.821106i \(0.306642\pi\)
\(74\) −74.0000 −0.116248
\(75\) 150.000 0.230940
\(76\) 440.000 0.664098
\(77\) 15.0000 0.0222001
\(78\) −192.000 −0.278714
\(79\) 176.000 0.250652 0.125326 0.992116i \(-0.460002\pi\)
0.125326 + 0.992116i \(0.460002\pi\)
\(80\) 80.0000 0.111803
\(81\) −891.000 −1.22222
\(82\) 342.000 0.460580
\(83\) −180.000 −0.238043 −0.119021 0.992892i \(-0.537976\pi\)
−0.119021 + 0.992892i \(0.537976\pi\)
\(84\) 72.0000 0.0935220
\(85\) 575.000 0.733735
\(86\) 722.000 0.905294
\(87\) −666.000 −0.820721
\(88\) 40.0000 0.0484547
\(89\) 446.000 0.531190 0.265595 0.964085i \(-0.414432\pi\)
0.265595 + 0.964085i \(0.414432\pi\)
\(90\) 90.0000 0.105409
\(91\) −48.0000 −0.0552941
\(92\) 24.0000 0.0271975
\(93\) −474.000 −0.528511
\(94\) −856.000 −0.939252
\(95\) 550.000 0.593987
\(96\) 192.000 0.204124
\(97\) −1407.00 −1.47278 −0.736388 0.676560i \(-0.763470\pi\)
−0.736388 + 0.676560i \(0.763470\pi\)
\(98\) −668.000 −0.688553
\(99\) 45.0000 0.0456835
\(100\) 100.000 0.100000
\(101\) 1758.00 1.73196 0.865978 0.500082i \(-0.166697\pi\)
0.865978 + 0.500082i \(0.166697\pi\)
\(102\) 1380.00 1.33961
\(103\) 384.000 0.367346 0.183673 0.982987i \(-0.441201\pi\)
0.183673 + 0.982987i \(0.441201\pi\)
\(104\) −128.000 −0.120687
\(105\) 90.0000 0.0836486
\(106\) −1054.00 −0.965788
\(107\) −794.000 −0.717373 −0.358686 0.933458i \(-0.616775\pi\)
−0.358686 + 0.933458i \(0.616775\pi\)
\(108\) −432.000 −0.384900
\(109\) 201.000 0.176627 0.0883133 0.996093i \(-0.471852\pi\)
0.0883133 + 0.996093i \(0.471852\pi\)
\(110\) 50.0000 0.0433392
\(111\) −222.000 −0.189832
\(112\) 48.0000 0.0404962
\(113\) −1759.00 −1.46436 −0.732181 0.681111i \(-0.761497\pi\)
−0.732181 + 0.681111i \(0.761497\pi\)
\(114\) 1320.00 1.08447
\(115\) 30.0000 0.0243262
\(116\) −444.000 −0.355382
\(117\) −144.000 −0.113785
\(118\) 224.000 0.174753
\(119\) 345.000 0.265766
\(120\) 240.000 0.182574
\(121\) −1306.00 −0.981217
\(122\) −646.000 −0.479394
\(123\) 1026.00 0.752124
\(124\) −316.000 −0.228852
\(125\) 125.000 0.0894427
\(126\) 54.0000 0.0381802
\(127\) 1052.00 0.735039 0.367519 0.930016i \(-0.380207\pi\)
0.367519 + 0.930016i \(0.380207\pi\)
\(128\) 128.000 0.0883883
\(129\) 2166.00 1.47834
\(130\) −160.000 −0.107946
\(131\) 468.000 0.312132 0.156066 0.987747i \(-0.450119\pi\)
0.156066 + 0.987747i \(0.450119\pi\)
\(132\) 120.000 0.0791262
\(133\) 330.000 0.215148
\(134\) −928.000 −0.598261
\(135\) −540.000 −0.344265
\(136\) 920.000 0.580069
\(137\) 48.0000 0.0299337 0.0149668 0.999888i \(-0.495236\pi\)
0.0149668 + 0.999888i \(0.495236\pi\)
\(138\) 72.0000 0.0444134
\(139\) 941.000 0.574206 0.287103 0.957900i \(-0.407308\pi\)
0.287103 + 0.957900i \(0.407308\pi\)
\(140\) 60.0000 0.0362209
\(141\) −2568.00 −1.53379
\(142\) −732.000 −0.432592
\(143\) −80.0000 −0.0467828
\(144\) 144.000 0.0833333
\(145\) −555.000 −0.317864
\(146\) 1424.00 0.807199
\(147\) −2004.00 −1.12440
\(148\) −148.000 −0.0821995
\(149\) −790.000 −0.434358 −0.217179 0.976132i \(-0.569686\pi\)
−0.217179 + 0.976132i \(0.569686\pi\)
\(150\) 300.000 0.163299
\(151\) −504.000 −0.271622 −0.135811 0.990735i \(-0.543364\pi\)
−0.135811 + 0.990735i \(0.543364\pi\)
\(152\) 880.000 0.469588
\(153\) 1035.00 0.546894
\(154\) 30.0000 0.0156978
\(155\) −395.000 −0.204691
\(156\) −384.000 −0.197081
\(157\) −2199.00 −1.11783 −0.558915 0.829225i \(-0.688782\pi\)
−0.558915 + 0.829225i \(0.688782\pi\)
\(158\) 352.000 0.177238
\(159\) −3162.00 −1.57713
\(160\) 160.000 0.0790569
\(161\) 18.0000 0.00881117
\(162\) −1782.00 −0.864242
\(163\) −379.000 −0.182120 −0.0910600 0.995845i \(-0.529026\pi\)
−0.0910600 + 0.995845i \(0.529026\pi\)
\(164\) 684.000 0.325679
\(165\) 150.000 0.0707726
\(166\) −360.000 −0.168322
\(167\) −2644.00 −1.22514 −0.612571 0.790415i \(-0.709865\pi\)
−0.612571 + 0.790415i \(0.709865\pi\)
\(168\) 144.000 0.0661300
\(169\) −1941.00 −0.883477
\(170\) 1150.00 0.518829
\(171\) 990.000 0.442732
\(172\) 1444.00 0.640139
\(173\) 517.000 0.227207 0.113603 0.993526i \(-0.463761\pi\)
0.113603 + 0.993526i \(0.463761\pi\)
\(174\) −1332.00 −0.580337
\(175\) 75.0000 0.0323970
\(176\) 80.0000 0.0342627
\(177\) 672.000 0.285371
\(178\) 892.000 0.375608
\(179\) 2872.00 1.19924 0.599618 0.800286i \(-0.295319\pi\)
0.599618 + 0.800286i \(0.295319\pi\)
\(180\) 180.000 0.0745356
\(181\) −110.000 −0.0451726 −0.0225863 0.999745i \(-0.507190\pi\)
−0.0225863 + 0.999745i \(0.507190\pi\)
\(182\) −96.0000 −0.0390989
\(183\) −1938.00 −0.782847
\(184\) 48.0000 0.0192316
\(185\) −185.000 −0.0735215
\(186\) −948.000 −0.373714
\(187\) 575.000 0.224856
\(188\) −1712.00 −0.664151
\(189\) −324.000 −0.124696
\(190\) 1100.00 0.420013
\(191\) −3609.00 −1.36722 −0.683608 0.729850i \(-0.739590\pi\)
−0.683608 + 0.729850i \(0.739590\pi\)
\(192\) 384.000 0.144338
\(193\) −58.0000 −0.0216318 −0.0108159 0.999942i \(-0.503443\pi\)
−0.0108159 + 0.999942i \(0.503443\pi\)
\(194\) −2814.00 −1.04141
\(195\) −480.000 −0.176274
\(196\) −1336.00 −0.486880
\(197\) −1354.00 −0.489688 −0.244844 0.969563i \(-0.578737\pi\)
−0.244844 + 0.969563i \(0.578737\pi\)
\(198\) 90.0000 0.0323031
\(199\) 1888.00 0.672547 0.336273 0.941764i \(-0.390833\pi\)
0.336273 + 0.941764i \(0.390833\pi\)
\(200\) 200.000 0.0707107
\(201\) −2784.00 −0.976956
\(202\) 3516.00 1.22468
\(203\) −333.000 −0.115133
\(204\) 2760.00 0.947248
\(205\) 855.000 0.291297
\(206\) 768.000 0.259753
\(207\) 54.0000 0.0181317
\(208\) −256.000 −0.0853385
\(209\) 550.000 0.182030
\(210\) 180.000 0.0591485
\(211\) −3893.00 −1.27017 −0.635083 0.772444i \(-0.719034\pi\)
−0.635083 + 0.772444i \(0.719034\pi\)
\(212\) −2108.00 −0.682915
\(213\) −2196.00 −0.706420
\(214\) −1588.00 −0.507259
\(215\) 1805.00 0.572558
\(216\) −864.000 −0.272166
\(217\) −237.000 −0.0741411
\(218\) 402.000 0.124894
\(219\) 4272.00 1.31815
\(220\) 100.000 0.0306454
\(221\) −1840.00 −0.560053
\(222\) −444.000 −0.134231
\(223\) 5909.00 1.77442 0.887211 0.461365i \(-0.152640\pi\)
0.887211 + 0.461365i \(0.152640\pi\)
\(224\) 96.0000 0.0286351
\(225\) 225.000 0.0666667
\(226\) −3518.00 −1.03546
\(227\) −2917.00 −0.852899 −0.426450 0.904511i \(-0.640236\pi\)
−0.426450 + 0.904511i \(0.640236\pi\)
\(228\) 2640.00 0.766835
\(229\) −2142.00 −0.618111 −0.309055 0.951044i \(-0.600013\pi\)
−0.309055 + 0.951044i \(0.600013\pi\)
\(230\) 60.0000 0.0172012
\(231\) 90.0000 0.0256345
\(232\) −888.000 −0.251293
\(233\) 5588.00 1.57117 0.785584 0.618755i \(-0.212363\pi\)
0.785584 + 0.618755i \(0.212363\pi\)
\(234\) −288.000 −0.0804579
\(235\) −2140.00 −0.594035
\(236\) 448.000 0.123569
\(237\) 1056.00 0.289429
\(238\) 690.000 0.187925
\(239\) 1371.00 0.371057 0.185528 0.982639i \(-0.440600\pi\)
0.185528 + 0.982639i \(0.440600\pi\)
\(240\) 480.000 0.129099
\(241\) 4184.00 1.11832 0.559160 0.829060i \(-0.311124\pi\)
0.559160 + 0.829060i \(0.311124\pi\)
\(242\) −2612.00 −0.693825
\(243\) −2430.00 −0.641500
\(244\) −1292.00 −0.338983
\(245\) −1670.00 −0.435479
\(246\) 2052.00 0.531832
\(247\) −1760.00 −0.453385
\(248\) −632.000 −0.161823
\(249\) −1080.00 −0.274868
\(250\) 250.000 0.0632456
\(251\) −5062.00 −1.27295 −0.636475 0.771297i \(-0.719608\pi\)
−0.636475 + 0.771297i \(0.719608\pi\)
\(252\) 108.000 0.0269975
\(253\) 30.0000 0.00745488
\(254\) 2104.00 0.519751
\(255\) 3450.00 0.847245
\(256\) 256.000 0.0625000
\(257\) 5450.00 1.32281 0.661404 0.750030i \(-0.269961\pi\)
0.661404 + 0.750030i \(0.269961\pi\)
\(258\) 4332.00 1.04534
\(259\) −111.000 −0.0266301
\(260\) −320.000 −0.0763291
\(261\) −999.000 −0.236922
\(262\) 936.000 0.220711
\(263\) 6517.00 1.52797 0.763984 0.645236i \(-0.223241\pi\)
0.763984 + 0.645236i \(0.223241\pi\)
\(264\) 240.000 0.0559507
\(265\) −2635.00 −0.610818
\(266\) 660.000 0.152132
\(267\) 2676.00 0.613365
\(268\) −1856.00 −0.423034
\(269\) 6686.00 1.51544 0.757719 0.652581i \(-0.226314\pi\)
0.757719 + 0.652581i \(0.226314\pi\)
\(270\) −1080.00 −0.243432
\(271\) −7046.00 −1.57939 −0.789694 0.613501i \(-0.789761\pi\)
−0.789694 + 0.613501i \(0.789761\pi\)
\(272\) 1840.00 0.410171
\(273\) −288.000 −0.0638482
\(274\) 96.0000 0.0211663
\(275\) 125.000 0.0274101
\(276\) 144.000 0.0314050
\(277\) −5116.00 −1.10971 −0.554857 0.831946i \(-0.687227\pi\)
−0.554857 + 0.831946i \(0.687227\pi\)
\(278\) 1882.00 0.406025
\(279\) −711.000 −0.152568
\(280\) 120.000 0.0256120
\(281\) −808.000 −0.171535 −0.0857673 0.996315i \(-0.527334\pi\)
−0.0857673 + 0.996315i \(0.527334\pi\)
\(282\) −5136.00 −1.08455
\(283\) 2092.00 0.439422 0.219711 0.975565i \(-0.429489\pi\)
0.219711 + 0.975565i \(0.429489\pi\)
\(284\) −1464.00 −0.305889
\(285\) 3300.00 0.685878
\(286\) −160.000 −0.0330804
\(287\) 513.000 0.105510
\(288\) 288.000 0.0589256
\(289\) 8312.00 1.69184
\(290\) −1110.00 −0.224764
\(291\) −8442.00 −1.70061
\(292\) 2848.00 0.570776
\(293\) 2199.00 0.438454 0.219227 0.975674i \(-0.429647\pi\)
0.219227 + 0.975674i \(0.429647\pi\)
\(294\) −4008.00 −0.795072
\(295\) 560.000 0.110524
\(296\) −296.000 −0.0581238
\(297\) −540.000 −0.105502
\(298\) −1580.00 −0.307137
\(299\) −96.0000 −0.0185680
\(300\) 600.000 0.115470
\(301\) 1083.00 0.207386
\(302\) −1008.00 −0.192066
\(303\) 10548.0 1.99989
\(304\) 1760.00 0.332049
\(305\) −1615.00 −0.303196
\(306\) 2070.00 0.386712
\(307\) 3166.00 0.588577 0.294289 0.955717i \(-0.404917\pi\)
0.294289 + 0.955717i \(0.404917\pi\)
\(308\) 60.0000 0.0111001
\(309\) 2304.00 0.424175
\(310\) −790.000 −0.144739
\(311\) −9045.00 −1.64918 −0.824590 0.565731i \(-0.808594\pi\)
−0.824590 + 0.565731i \(0.808594\pi\)
\(312\) −768.000 −0.139357
\(313\) 8906.00 1.60830 0.804148 0.594429i \(-0.202622\pi\)
0.804148 + 0.594429i \(0.202622\pi\)
\(314\) −4398.00 −0.790425
\(315\) 135.000 0.0241473
\(316\) 704.000 0.125326
\(317\) 9689.00 1.71668 0.858341 0.513079i \(-0.171495\pi\)
0.858341 + 0.513079i \(0.171495\pi\)
\(318\) −6324.00 −1.11520
\(319\) −555.000 −0.0974108
\(320\) 320.000 0.0559017
\(321\) −4764.00 −0.828351
\(322\) 36.0000 0.00623044
\(323\) 12650.0 2.17915
\(324\) −3564.00 −0.611111
\(325\) −400.000 −0.0682708
\(326\) −758.000 −0.128778
\(327\) 1206.00 0.203951
\(328\) 1368.00 0.230290
\(329\) −1284.00 −0.215165
\(330\) 300.000 0.0500438
\(331\) 98.0000 0.0162736 0.00813681 0.999967i \(-0.497410\pi\)
0.00813681 + 0.999967i \(0.497410\pi\)
\(332\) −720.000 −0.119021
\(333\) −333.000 −0.0547997
\(334\) −5288.00 −0.866307
\(335\) −2320.00 −0.378374
\(336\) 288.000 0.0467610
\(337\) −6020.00 −0.973087 −0.486543 0.873656i \(-0.661742\pi\)
−0.486543 + 0.873656i \(0.661742\pi\)
\(338\) −3882.00 −0.624713
\(339\) −10554.0 −1.69090
\(340\) 2300.00 0.366868
\(341\) −395.000 −0.0627286
\(342\) 1980.00 0.313059
\(343\) −2031.00 −0.319719
\(344\) 2888.00 0.452647
\(345\) 180.000 0.0280895
\(346\) 1034.00 0.160659
\(347\) 9700.00 1.50064 0.750322 0.661073i \(-0.229899\pi\)
0.750322 + 0.661073i \(0.229899\pi\)
\(348\) −2664.00 −0.410360
\(349\) 6234.00 0.956156 0.478078 0.878317i \(-0.341334\pi\)
0.478078 + 0.878317i \(0.341334\pi\)
\(350\) 150.000 0.0229081
\(351\) 1728.00 0.262774
\(352\) 160.000 0.0242274
\(353\) 9939.00 1.49858 0.749291 0.662241i \(-0.230394\pi\)
0.749291 + 0.662241i \(0.230394\pi\)
\(354\) 1344.00 0.201788
\(355\) −1830.00 −0.273595
\(356\) 1784.00 0.265595
\(357\) 2070.00 0.306880
\(358\) 5744.00 0.847988
\(359\) −1920.00 −0.282267 −0.141133 0.989991i \(-0.545075\pi\)
−0.141133 + 0.989991i \(0.545075\pi\)
\(360\) 360.000 0.0527046
\(361\) 5241.00 0.764106
\(362\) −220.000 −0.0319418
\(363\) −7836.00 −1.13301
\(364\) −192.000 −0.0276471
\(365\) 3560.00 0.510518
\(366\) −3876.00 −0.553557
\(367\) 7031.00 1.00004 0.500021 0.866013i \(-0.333326\pi\)
0.500021 + 0.866013i \(0.333326\pi\)
\(368\) 96.0000 0.0135988
\(369\) 1539.00 0.217120
\(370\) −370.000 −0.0519875
\(371\) −1581.00 −0.221244
\(372\) −1896.00 −0.264255
\(373\) 2158.00 0.299563 0.149782 0.988719i \(-0.452143\pi\)
0.149782 + 0.988719i \(0.452143\pi\)
\(374\) 1150.00 0.158998
\(375\) 750.000 0.103280
\(376\) −3424.00 −0.469626
\(377\) 1776.00 0.242622
\(378\) −648.000 −0.0881733
\(379\) −2440.00 −0.330698 −0.165349 0.986235i \(-0.552875\pi\)
−0.165349 + 0.986235i \(0.552875\pi\)
\(380\) 2200.00 0.296994
\(381\) 6312.00 0.848749
\(382\) −7218.00 −0.966767
\(383\) −1860.00 −0.248150 −0.124075 0.992273i \(-0.539596\pi\)
−0.124075 + 0.992273i \(0.539596\pi\)
\(384\) 768.000 0.102062
\(385\) 75.0000 0.00992819
\(386\) −116.000 −0.0152960
\(387\) 3249.00 0.426760
\(388\) −5628.00 −0.736388
\(389\) 2011.00 0.262112 0.131056 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(390\) −960.000 −0.124645
\(391\) 690.000 0.0892450
\(392\) −2672.00 −0.344276
\(393\) 2808.00 0.360419
\(394\) −2708.00 −0.346262
\(395\) 880.000 0.112095
\(396\) 180.000 0.0228418
\(397\) 6010.00 0.759781 0.379891 0.925031i \(-0.375962\pi\)
0.379891 + 0.925031i \(0.375962\pi\)
\(398\) 3776.00 0.475562
\(399\) 1980.00 0.248431
\(400\) 400.000 0.0500000
\(401\) 9338.00 1.16289 0.581443 0.813587i \(-0.302488\pi\)
0.581443 + 0.813587i \(0.302488\pi\)
\(402\) −5568.00 −0.690812
\(403\) 1264.00 0.156239
\(404\) 7032.00 0.865978
\(405\) −4455.00 −0.546594
\(406\) −666.000 −0.0814114
\(407\) −185.000 −0.0225310
\(408\) 5520.00 0.669806
\(409\) −760.000 −0.0918816 −0.0459408 0.998944i \(-0.514629\pi\)
−0.0459408 + 0.998944i \(0.514629\pi\)
\(410\) 1710.00 0.205978
\(411\) 288.000 0.0345645
\(412\) 1536.00 0.183673
\(413\) 336.000 0.0400326
\(414\) 108.000 0.0128210
\(415\) −900.000 −0.106456
\(416\) −512.000 −0.0603434
\(417\) 5646.00 0.663036
\(418\) 1100.00 0.128715
\(419\) −10772.0 −1.25596 −0.627979 0.778230i \(-0.716118\pi\)
−0.627979 + 0.778230i \(0.716118\pi\)
\(420\) 360.000 0.0418243
\(421\) −1014.00 −0.117386 −0.0586928 0.998276i \(-0.518693\pi\)
−0.0586928 + 0.998276i \(0.518693\pi\)
\(422\) −7786.00 −0.898143
\(423\) −3852.00 −0.442767
\(424\) −4216.00 −0.482894
\(425\) 2875.00 0.328136
\(426\) −4392.00 −0.499514
\(427\) −969.000 −0.109820
\(428\) −3176.00 −0.358686
\(429\) −480.000 −0.0540201
\(430\) 3610.00 0.404860
\(431\) −4445.00 −0.496771 −0.248385 0.968661i \(-0.579900\pi\)
−0.248385 + 0.968661i \(0.579900\pi\)
\(432\) −1728.00 −0.192450
\(433\) 8482.00 0.941383 0.470692 0.882298i \(-0.344004\pi\)
0.470692 + 0.882298i \(0.344004\pi\)
\(434\) −474.000 −0.0524256
\(435\) −3330.00 −0.367037
\(436\) 804.000 0.0883133
\(437\) 660.000 0.0722473
\(438\) 8544.00 0.932073
\(439\) −7433.00 −0.808104 −0.404052 0.914736i \(-0.632399\pi\)
−0.404052 + 0.914736i \(0.632399\pi\)
\(440\) 200.000 0.0216696
\(441\) −3006.00 −0.324587
\(442\) −3680.00 −0.396018
\(443\) −5382.00 −0.577216 −0.288608 0.957447i \(-0.593192\pi\)
−0.288608 + 0.957447i \(0.593192\pi\)
\(444\) −888.000 −0.0949158
\(445\) 2230.00 0.237555
\(446\) 11818.0 1.25471
\(447\) −4740.00 −0.501553
\(448\) 192.000 0.0202481
\(449\) 4974.00 0.522801 0.261400 0.965230i \(-0.415816\pi\)
0.261400 + 0.965230i \(0.415816\pi\)
\(450\) 450.000 0.0471405
\(451\) 855.000 0.0892691
\(452\) −7036.00 −0.732181
\(453\) −3024.00 −0.313642
\(454\) −5834.00 −0.603091
\(455\) −240.000 −0.0247283
\(456\) 5280.00 0.542234
\(457\) 2721.00 0.278519 0.139259 0.990256i \(-0.455528\pi\)
0.139259 + 0.990256i \(0.455528\pi\)
\(458\) −4284.00 −0.437070
\(459\) −12420.0 −1.26300
\(460\) 120.000 0.0121631
\(461\) 13075.0 1.32096 0.660481 0.750843i \(-0.270352\pi\)
0.660481 + 0.750843i \(0.270352\pi\)
\(462\) 180.000 0.0181263
\(463\) 5084.00 0.510310 0.255155 0.966900i \(-0.417874\pi\)
0.255155 + 0.966900i \(0.417874\pi\)
\(464\) −1776.00 −0.177691
\(465\) −2370.00 −0.236357
\(466\) 11176.0 1.11098
\(467\) 11941.0 1.18322 0.591610 0.806224i \(-0.298493\pi\)
0.591610 + 0.806224i \(0.298493\pi\)
\(468\) −576.000 −0.0568923
\(469\) −1392.00 −0.137050
\(470\) −4280.00 −0.420046
\(471\) −13194.0 −1.29076
\(472\) 896.000 0.0873766
\(473\) 1805.00 0.175463
\(474\) 2112.00 0.204657
\(475\) 2750.00 0.265639
\(476\) 1380.00 0.132883
\(477\) −4743.00 −0.455277
\(478\) 2742.00 0.262377
\(479\) 1216.00 0.115993 0.0579963 0.998317i \(-0.481529\pi\)
0.0579963 + 0.998317i \(0.481529\pi\)
\(480\) 960.000 0.0912871
\(481\) 592.000 0.0561182
\(482\) 8368.00 0.790772
\(483\) 108.000 0.0101743
\(484\) −5224.00 −0.490609
\(485\) −7035.00 −0.658645
\(486\) −4860.00 −0.453609
\(487\) −1618.00 −0.150551 −0.0752757 0.997163i \(-0.523984\pi\)
−0.0752757 + 0.997163i \(0.523984\pi\)
\(488\) −2584.00 −0.239697
\(489\) −2274.00 −0.210294
\(490\) −3340.00 −0.307930
\(491\) 11132.0 1.02318 0.511589 0.859230i \(-0.329057\pi\)
0.511589 + 0.859230i \(0.329057\pi\)
\(492\) 4104.00 0.376062
\(493\) −12765.0 −1.16614
\(494\) −3520.00 −0.320592
\(495\) 225.000 0.0204303
\(496\) −1264.00 −0.114426
\(497\) −1098.00 −0.0990987
\(498\) −2160.00 −0.194361
\(499\) −16562.0 −1.48581 −0.742903 0.669399i \(-0.766552\pi\)
−0.742903 + 0.669399i \(0.766552\pi\)
\(500\) 500.000 0.0447214
\(501\) −15864.0 −1.41467
\(502\) −10124.0 −0.900112
\(503\) −11232.0 −0.995646 −0.497823 0.867279i \(-0.665867\pi\)
−0.497823 + 0.867279i \(0.665867\pi\)
\(504\) 216.000 0.0190901
\(505\) 8790.00 0.774554
\(506\) 60.0000 0.00527139
\(507\) −11646.0 −1.02015
\(508\) 4208.00 0.367519
\(509\) 3036.00 0.264378 0.132189 0.991225i \(-0.457799\pi\)
0.132189 + 0.991225i \(0.457799\pi\)
\(510\) 6900.00 0.599092
\(511\) 2136.00 0.184914
\(512\) 512.000 0.0441942
\(513\) −11880.0 −1.02245
\(514\) 10900.0 0.935367
\(515\) 1920.00 0.164282
\(516\) 8664.00 0.739169
\(517\) −2140.00 −0.182045
\(518\) −222.000 −0.0188303
\(519\) 3102.00 0.262356
\(520\) −640.000 −0.0539728
\(521\) 19417.0 1.63277 0.816386 0.577507i \(-0.195974\pi\)
0.816386 + 0.577507i \(0.195974\pi\)
\(522\) −1998.00 −0.167529
\(523\) −156.000 −0.0130428 −0.00652142 0.999979i \(-0.502076\pi\)
−0.00652142 + 0.999979i \(0.502076\pi\)
\(524\) 1872.00 0.156066
\(525\) 450.000 0.0374088
\(526\) 13034.0 1.08044
\(527\) −9085.00 −0.750947
\(528\) 480.000 0.0395631
\(529\) −12131.0 −0.997041
\(530\) −5270.00 −0.431914
\(531\) 1008.00 0.0823794
\(532\) 1320.00 0.107574
\(533\) −2736.00 −0.222344
\(534\) 5352.00 0.433715
\(535\) −3970.00 −0.320819
\(536\) −3712.00 −0.299131
\(537\) 17232.0 1.38476
\(538\) 13372.0 1.07158
\(539\) −1670.00 −0.133455
\(540\) −2160.00 −0.172133
\(541\) −19290.0 −1.53298 −0.766490 0.642257i \(-0.777998\pi\)
−0.766490 + 0.642257i \(0.777998\pi\)
\(542\) −14092.0 −1.11680
\(543\) −660.000 −0.0521608
\(544\) 3680.00 0.290034
\(545\) 1005.00 0.0789899
\(546\) −576.000 −0.0451475
\(547\) −24479.0 −1.91343 −0.956715 0.291026i \(-0.906003\pi\)
−0.956715 + 0.291026i \(0.906003\pi\)
\(548\) 192.000 0.0149668
\(549\) −2907.00 −0.225989
\(550\) 250.000 0.0193819
\(551\) −12210.0 −0.944035
\(552\) 288.000 0.0222067
\(553\) 528.000 0.0406019
\(554\) −10232.0 −0.784686
\(555\) −1110.00 −0.0848953
\(556\) 3764.00 0.287103
\(557\) −3496.00 −0.265943 −0.132972 0.991120i \(-0.542452\pi\)
−0.132972 + 0.991120i \(0.542452\pi\)
\(558\) −1422.00 −0.107882
\(559\) −5776.00 −0.437028
\(560\) 240.000 0.0181104
\(561\) 3450.00 0.259642
\(562\) −1616.00 −0.121293
\(563\) 8475.00 0.634420 0.317210 0.948355i \(-0.397254\pi\)
0.317210 + 0.948355i \(0.397254\pi\)
\(564\) −10272.0 −0.766896
\(565\) −8795.00 −0.654882
\(566\) 4184.00 0.310718
\(567\) −2673.00 −0.197981
\(568\) −2928.00 −0.216296
\(569\) 12594.0 0.927887 0.463944 0.885865i \(-0.346434\pi\)
0.463944 + 0.885865i \(0.346434\pi\)
\(570\) 6600.00 0.484989
\(571\) −9993.00 −0.732389 −0.366194 0.930538i \(-0.619339\pi\)
−0.366194 + 0.930538i \(0.619339\pi\)
\(572\) −320.000 −0.0233914
\(573\) −21654.0 −1.57872
\(574\) 1026.00 0.0746070
\(575\) 150.000 0.0108790
\(576\) 576.000 0.0416667
\(577\) 8830.00 0.637084 0.318542 0.947909i \(-0.396807\pi\)
0.318542 + 0.947909i \(0.396807\pi\)
\(578\) 16624.0 1.19631
\(579\) −348.000 −0.0249782
\(580\) −2220.00 −0.158932
\(581\) −540.000 −0.0385593
\(582\) −16884.0 −1.20252
\(583\) −2635.00 −0.187188
\(584\) 5696.00 0.403600
\(585\) −720.000 −0.0508860
\(586\) 4398.00 0.310034
\(587\) −18699.0 −1.31480 −0.657402 0.753540i \(-0.728345\pi\)
−0.657402 + 0.753540i \(0.728345\pi\)
\(588\) −8016.00 −0.562201
\(589\) −8690.00 −0.607921
\(590\) 1120.00 0.0781520
\(591\) −8124.00 −0.565443
\(592\) −592.000 −0.0410997
\(593\) 9700.00 0.671722 0.335861 0.941912i \(-0.390973\pi\)
0.335861 + 0.941912i \(0.390973\pi\)
\(594\) −1080.00 −0.0746009
\(595\) 1725.00 0.118854
\(596\) −3160.00 −0.217179
\(597\) 11328.0 0.776590
\(598\) −192.000 −0.0131295
\(599\) −7896.00 −0.538601 −0.269300 0.963056i \(-0.586792\pi\)
−0.269300 + 0.963056i \(0.586792\pi\)
\(600\) 1200.00 0.0816497
\(601\) −8867.00 −0.601818 −0.300909 0.953653i \(-0.597290\pi\)
−0.300909 + 0.953653i \(0.597290\pi\)
\(602\) 2166.00 0.146644
\(603\) −4176.00 −0.282023
\(604\) −2016.00 −0.135811
\(605\) −6530.00 −0.438814
\(606\) 21096.0 1.41414
\(607\) −3174.00 −0.212238 −0.106119 0.994353i \(-0.533843\pi\)
−0.106119 + 0.994353i \(0.533843\pi\)
\(608\) 3520.00 0.234794
\(609\) −1998.00 −0.132944
\(610\) −3230.00 −0.214392
\(611\) 6848.00 0.453421
\(612\) 4140.00 0.273447
\(613\) −16185.0 −1.06640 −0.533202 0.845988i \(-0.679012\pi\)
−0.533202 + 0.845988i \(0.679012\pi\)
\(614\) 6332.00 0.416187
\(615\) 5130.00 0.336360
\(616\) 120.000 0.00784892
\(617\) 204.000 0.0133107 0.00665537 0.999978i \(-0.497882\pi\)
0.00665537 + 0.999978i \(0.497882\pi\)
\(618\) 4608.00 0.299937
\(619\) −2699.00 −0.175254 −0.0876268 0.996153i \(-0.527928\pi\)
−0.0876268 + 0.996153i \(0.527928\pi\)
\(620\) −1580.00 −0.102346
\(621\) −648.000 −0.0418733
\(622\) −18090.0 −1.16615
\(623\) 1338.00 0.0860447
\(624\) −1536.00 −0.0985404
\(625\) 625.000 0.0400000
\(626\) 17812.0 1.13724
\(627\) 3300.00 0.210190
\(628\) −8796.00 −0.558915
\(629\) −4255.00 −0.269726
\(630\) 270.000 0.0170747
\(631\) −23523.0 −1.48405 −0.742025 0.670372i \(-0.766135\pi\)
−0.742025 + 0.670372i \(0.766135\pi\)
\(632\) 1408.00 0.0886190
\(633\) −23358.0 −1.46666
\(634\) 19378.0 1.21388
\(635\) 5260.00 0.328719
\(636\) −12648.0 −0.788563
\(637\) 5344.00 0.332397
\(638\) −1110.00 −0.0688798
\(639\) −3294.00 −0.203926
\(640\) 640.000 0.0395285
\(641\) 16319.0 1.00556 0.502778 0.864415i \(-0.332311\pi\)
0.502778 + 0.864415i \(0.332311\pi\)
\(642\) −9528.00 −0.585732
\(643\) −7403.00 −0.454037 −0.227019 0.973890i \(-0.572898\pi\)
−0.227019 + 0.973890i \(0.572898\pi\)
\(644\) 72.0000 0.00440559
\(645\) 10830.0 0.661133
\(646\) 25300.0 1.54089
\(647\) 15344.0 0.932357 0.466178 0.884691i \(-0.345630\pi\)
0.466178 + 0.884691i \(0.345630\pi\)
\(648\) −7128.00 −0.432121
\(649\) 560.000 0.0338705
\(650\) −800.000 −0.0482747
\(651\) −1422.00 −0.0856107
\(652\) −1516.00 −0.0910600
\(653\) 6118.00 0.366640 0.183320 0.983053i \(-0.441316\pi\)
0.183320 + 0.983053i \(0.441316\pi\)
\(654\) 2412.00 0.144215
\(655\) 2340.00 0.139590
\(656\) 2736.00 0.162840
\(657\) 6408.00 0.380517
\(658\) −2568.00 −0.152144
\(659\) 5540.00 0.327478 0.163739 0.986504i \(-0.447645\pi\)
0.163739 + 0.986504i \(0.447645\pi\)
\(660\) 600.000 0.0353863
\(661\) 1247.00 0.0733777 0.0366889 0.999327i \(-0.488319\pi\)
0.0366889 + 0.999327i \(0.488319\pi\)
\(662\) 196.000 0.0115072
\(663\) −11040.0 −0.646694
\(664\) −1440.00 −0.0841609
\(665\) 1650.00 0.0962169
\(666\) −666.000 −0.0387492
\(667\) −666.000 −0.0386621
\(668\) −10576.0 −0.612571
\(669\) 35454.0 2.04893
\(670\) −4640.00 −0.267551
\(671\) −1615.00 −0.0929156
\(672\) 576.000 0.0330650
\(673\) 19006.0 1.08860 0.544300 0.838891i \(-0.316795\pi\)
0.544300 + 0.838891i \(0.316795\pi\)
\(674\) −12040.0 −0.688076
\(675\) −2700.00 −0.153960
\(676\) −7764.00 −0.441739
\(677\) 6938.00 0.393869 0.196934 0.980417i \(-0.436901\pi\)
0.196934 + 0.980417i \(0.436901\pi\)
\(678\) −21108.0 −1.19565
\(679\) −4221.00 −0.238567
\(680\) 4600.00 0.259415
\(681\) −17502.0 −0.984843
\(682\) −790.000 −0.0443558
\(683\) 4719.00 0.264374 0.132187 0.991225i \(-0.457800\pi\)
0.132187 + 0.991225i \(0.457800\pi\)
\(684\) 3960.00 0.221366
\(685\) 240.000 0.0133868
\(686\) −4062.00 −0.226076
\(687\) −12852.0 −0.713733
\(688\) 5776.00 0.320070
\(689\) 8432.00 0.466232
\(690\) 360.000 0.0198623
\(691\) −22805.0 −1.25549 −0.627745 0.778419i \(-0.716022\pi\)
−0.627745 + 0.778419i \(0.716022\pi\)
\(692\) 2068.00 0.113603
\(693\) 135.000 0.00740004
\(694\) 19400.0 1.06112
\(695\) 4705.00 0.256793
\(696\) −5328.00 −0.290169
\(697\) 19665.0 1.06867
\(698\) 12468.0 0.676104
\(699\) 33528.0 1.81423
\(700\) 300.000 0.0161985
\(701\) 17378.0 0.936317 0.468158 0.883645i \(-0.344918\pi\)
0.468158 + 0.883645i \(0.344918\pi\)
\(702\) 3456.00 0.185810
\(703\) −4070.00 −0.218354
\(704\) 320.000 0.0171313
\(705\) −12840.0 −0.685932
\(706\) 19878.0 1.05966
\(707\) 5274.00 0.280550
\(708\) 2688.00 0.142685
\(709\) −15015.0 −0.795346 −0.397673 0.917527i \(-0.630182\pi\)
−0.397673 + 0.917527i \(0.630182\pi\)
\(710\) −3660.00 −0.193461
\(711\) 1584.00 0.0835508
\(712\) 3568.00 0.187804
\(713\) −474.000 −0.0248968
\(714\) 4140.00 0.216997
\(715\) −400.000 −0.0209219
\(716\) 11488.0 0.599618
\(717\) 8226.00 0.428460
\(718\) −3840.00 −0.199593
\(719\) 14306.0 0.742036 0.371018 0.928626i \(-0.379009\pi\)
0.371018 + 0.928626i \(0.379009\pi\)
\(720\) 720.000 0.0372678
\(721\) 1152.00 0.0595045
\(722\) 10482.0 0.540304
\(723\) 25104.0 1.29132
\(724\) −440.000 −0.0225863
\(725\) −2775.00 −0.142153
\(726\) −15672.0 −0.801160
\(727\) −16988.0 −0.866644 −0.433322 0.901239i \(-0.642659\pi\)
−0.433322 + 0.901239i \(0.642659\pi\)
\(728\) −384.000 −0.0195494
\(729\) 9477.00 0.481481
\(730\) 7120.00 0.360990
\(731\) 41515.0 2.10053
\(732\) −7752.00 −0.391424
\(733\) −2909.00 −0.146584 −0.0732922 0.997311i \(-0.523351\pi\)
−0.0732922 + 0.997311i \(0.523351\pi\)
\(734\) 14062.0 0.707136
\(735\) −10020.0 −0.502848
\(736\) 192.000 0.00961578
\(737\) −2320.00 −0.115954
\(738\) 3078.00 0.153527
\(739\) 10149.0 0.505192 0.252596 0.967572i \(-0.418716\pi\)
0.252596 + 0.967572i \(0.418716\pi\)
\(740\) −740.000 −0.0367607
\(741\) −10560.0 −0.523524
\(742\) −3162.00 −0.156443
\(743\) 37473.0 1.85027 0.925135 0.379638i \(-0.123951\pi\)
0.925135 + 0.379638i \(0.123951\pi\)
\(744\) −3792.00 −0.186857
\(745\) −3950.00 −0.194251
\(746\) 4316.00 0.211823
\(747\) −1620.00 −0.0793477
\(748\) 2300.00 0.112428
\(749\) −2382.00 −0.116203
\(750\) 1500.00 0.0730297
\(751\) 9950.00 0.483463 0.241731 0.970343i \(-0.422285\pi\)
0.241731 + 0.970343i \(0.422285\pi\)
\(752\) −6848.00 −0.332076
\(753\) −30372.0 −1.46988
\(754\) 3552.00 0.171560
\(755\) −2520.00 −0.121473
\(756\) −1296.00 −0.0623480
\(757\) 20830.0 1.00010 0.500052 0.865995i \(-0.333314\pi\)
0.500052 + 0.865995i \(0.333314\pi\)
\(758\) −4880.00 −0.233838
\(759\) 180.000 0.00860815
\(760\) 4400.00 0.210006
\(761\) 22515.0 1.07249 0.536247 0.844061i \(-0.319842\pi\)
0.536247 + 0.844061i \(0.319842\pi\)
\(762\) 12624.0 0.600157
\(763\) 603.000 0.0286108
\(764\) −14436.0 −0.683608
\(765\) 5175.00 0.244578
\(766\) −3720.00 −0.175469
\(767\) −1792.00 −0.0843616
\(768\) 1536.00 0.0721688
\(769\) 29064.0 1.36291 0.681453 0.731862i \(-0.261348\pi\)
0.681453 + 0.731862i \(0.261348\pi\)
\(770\) 150.000 0.00702029
\(771\) 32700.0 1.52745
\(772\) −232.000 −0.0108159
\(773\) 8843.00 0.411463 0.205731 0.978609i \(-0.434043\pi\)
0.205731 + 0.978609i \(0.434043\pi\)
\(774\) 6498.00 0.301765
\(775\) −1975.00 −0.0915408
\(776\) −11256.0 −0.520705
\(777\) −666.000 −0.0307498
\(778\) 4022.00 0.185341
\(779\) 18810.0 0.865132
\(780\) −1920.00 −0.0881372
\(781\) −1830.00 −0.0838445
\(782\) 1380.00 0.0631058
\(783\) 11988.0 0.547147
\(784\) −5344.00 −0.243440
\(785\) −10995.0 −0.499909
\(786\) 5616.00 0.254855
\(787\) 33450.0 1.51507 0.757537 0.652792i \(-0.226402\pi\)
0.757537 + 0.652792i \(0.226402\pi\)
\(788\) −5416.00 −0.244844
\(789\) 39102.0 1.76434
\(790\) 1760.00 0.0792633
\(791\) −5277.00 −0.237204
\(792\) 360.000 0.0161516
\(793\) 5168.00 0.231426
\(794\) 12020.0 0.537247
\(795\) −15810.0 −0.705312
\(796\) 7552.00 0.336273
\(797\) −10866.0 −0.482928 −0.241464 0.970410i \(-0.577628\pi\)
−0.241464 + 0.970410i \(0.577628\pi\)
\(798\) 3960.00 0.175667
\(799\) −49220.0 −2.17932
\(800\) 800.000 0.0353553
\(801\) 4014.00 0.177063
\(802\) 18676.0 0.822285
\(803\) 3560.00 0.156450
\(804\) −11136.0 −0.488478
\(805\) 90.0000 0.00394048
\(806\) 2528.00 0.110478
\(807\) 40116.0 1.74988
\(808\) 14064.0 0.612339
\(809\) −22342.0 −0.970955 −0.485478 0.874249i \(-0.661354\pi\)
−0.485478 + 0.874249i \(0.661354\pi\)
\(810\) −8910.00 −0.386501
\(811\) 7432.00 0.321791 0.160896 0.986971i \(-0.448562\pi\)
0.160896 + 0.986971i \(0.448562\pi\)
\(812\) −1332.00 −0.0575665
\(813\) −42276.0 −1.82372
\(814\) −370.000 −0.0159318
\(815\) −1895.00 −0.0814466
\(816\) 11040.0 0.473624
\(817\) 39710.0 1.70046
\(818\) −1520.00 −0.0649701
\(819\) −432.000 −0.0184314
\(820\) 3420.00 0.145648
\(821\) 20208.0 0.859031 0.429515 0.903060i \(-0.358684\pi\)
0.429515 + 0.903060i \(0.358684\pi\)
\(822\) 576.000 0.0244408
\(823\) −36448.0 −1.54374 −0.771870 0.635781i \(-0.780678\pi\)
−0.771870 + 0.635781i \(0.780678\pi\)
\(824\) 3072.00 0.129876
\(825\) 750.000 0.0316505
\(826\) 672.000 0.0283073
\(827\) 12819.0 0.539009 0.269504 0.962999i \(-0.413140\pi\)
0.269504 + 0.962999i \(0.413140\pi\)
\(828\) 216.000 0.00906584
\(829\) −18851.0 −0.789774 −0.394887 0.918730i \(-0.629216\pi\)
−0.394887 + 0.918730i \(0.629216\pi\)
\(830\) −1800.00 −0.0752758
\(831\) −30696.0 −1.28139
\(832\) −1024.00 −0.0426692
\(833\) −38410.0 −1.59763
\(834\) 11292.0 0.468837
\(835\) −13220.0 −0.547901
\(836\) 2200.00 0.0910151
\(837\) 8532.00 0.352341
\(838\) −21544.0 −0.888097
\(839\) −5844.00 −0.240474 −0.120237 0.992745i \(-0.538365\pi\)
−0.120237 + 0.992745i \(0.538365\pi\)
\(840\) 720.000 0.0295742
\(841\) −12068.0 −0.494813
\(842\) −2028.00 −0.0830042
\(843\) −4848.00 −0.198071
\(844\) −15572.0 −0.635083
\(845\) −9705.00 −0.395103
\(846\) −7704.00 −0.313084
\(847\) −3918.00 −0.158942
\(848\) −8432.00 −0.341458
\(849\) 12552.0 0.507401
\(850\) 5750.00 0.232027
\(851\) −222.000 −0.00894249
\(852\) −8784.00 −0.353210
\(853\) −27602.0 −1.10794 −0.553971 0.832536i \(-0.686888\pi\)
−0.553971 + 0.832536i \(0.686888\pi\)
\(854\) −1938.00 −0.0776546
\(855\) 4950.00 0.197996
\(856\) −6352.00 −0.253630
\(857\) 2889.00 0.115153 0.0575766 0.998341i \(-0.481663\pi\)
0.0575766 + 0.998341i \(0.481663\pi\)
\(858\) −960.000 −0.0381980
\(859\) −2260.00 −0.0897674 −0.0448837 0.998992i \(-0.514292\pi\)
−0.0448837 + 0.998992i \(0.514292\pi\)
\(860\) 7220.00 0.286279
\(861\) 3078.00 0.121833
\(862\) −8890.00 −0.351270
\(863\) 49323.0 1.94551 0.972755 0.231837i \(-0.0744737\pi\)
0.972755 + 0.231837i \(0.0744737\pi\)
\(864\) −3456.00 −0.136083
\(865\) 2585.00 0.101610
\(866\) 16964.0 0.665658
\(867\) 49872.0 1.95357
\(868\) −948.000 −0.0370705
\(869\) 880.000 0.0343521
\(870\) −6660.00 −0.259535
\(871\) 7424.00 0.288809
\(872\) 1608.00 0.0624470
\(873\) −12663.0 −0.490925
\(874\) 1320.00 0.0510866
\(875\) 375.000 0.0144884
\(876\) 17088.0 0.659075
\(877\) −24255.0 −0.933903 −0.466952 0.884283i \(-0.654648\pi\)
−0.466952 + 0.884283i \(0.654648\pi\)
\(878\) −14866.0 −0.571416
\(879\) 13194.0 0.506283
\(880\) 400.000 0.0153227
\(881\) −42849.0 −1.63861 −0.819307 0.573355i \(-0.805642\pi\)
−0.819307 + 0.573355i \(0.805642\pi\)
\(882\) −6012.00 −0.229518
\(883\) −22021.0 −0.839259 −0.419629 0.907695i \(-0.637840\pi\)
−0.419629 + 0.907695i \(0.637840\pi\)
\(884\) −7360.00 −0.280027
\(885\) 3360.00 0.127622
\(886\) −10764.0 −0.408153
\(887\) −9955.00 −0.376839 −0.188419 0.982089i \(-0.560336\pi\)
−0.188419 + 0.982089i \(0.560336\pi\)
\(888\) −1776.00 −0.0671156
\(889\) 3156.00 0.119065
\(890\) 4460.00 0.167977
\(891\) −4455.00 −0.167506
\(892\) 23636.0 0.887211
\(893\) −47080.0 −1.76425
\(894\) −9480.00 −0.354652
\(895\) 14360.0 0.536315
\(896\) 384.000 0.0143176
\(897\) −576.000 −0.0214404
\(898\) 9948.00 0.369676
\(899\) 8769.00 0.325320
\(900\) 900.000 0.0333333
\(901\) −60605.0 −2.24089
\(902\) 1710.00 0.0631228
\(903\) 6498.00 0.239468
\(904\) −14072.0 −0.517730
\(905\) −550.000 −0.0202018
\(906\) −6048.00 −0.221779
\(907\) 26644.0 0.975413 0.487706 0.873008i \(-0.337834\pi\)
0.487706 + 0.873008i \(0.337834\pi\)
\(908\) −11668.0 −0.426450
\(909\) 15822.0 0.577319
\(910\) −480.000 −0.0174855
\(911\) 12696.0 0.461731 0.230866 0.972986i \(-0.425844\pi\)
0.230866 + 0.972986i \(0.425844\pi\)
\(912\) 10560.0 0.383417
\(913\) −900.000 −0.0326239
\(914\) 5442.00 0.196942
\(915\) −9690.00 −0.350100
\(916\) −8568.00 −0.309055
\(917\) 1404.00 0.0505607
\(918\) −24840.0 −0.893074
\(919\) 1448.00 0.0519751 0.0259875 0.999662i \(-0.491727\pi\)
0.0259875 + 0.999662i \(0.491727\pi\)
\(920\) 240.000 0.00860061
\(921\) 18996.0 0.679630
\(922\) 26150.0 0.934061
\(923\) 5856.00 0.208833
\(924\) 360.000 0.0128172
\(925\) −925.000 −0.0328798
\(926\) 10168.0 0.360844
\(927\) 3456.00 0.122449
\(928\) −3552.00 −0.125647
\(929\) −20283.0 −0.716323 −0.358161 0.933660i \(-0.616596\pi\)
−0.358161 + 0.933660i \(0.616596\pi\)
\(930\) −4740.00 −0.167130
\(931\) −36740.0 −1.29335
\(932\) 22352.0 0.785584
\(933\) −54270.0 −1.90431
\(934\) 23882.0 0.836663
\(935\) 2875.00 0.100559
\(936\) −1152.00 −0.0402290
\(937\) −54206.0 −1.88990 −0.944948 0.327220i \(-0.893888\pi\)
−0.944948 + 0.327220i \(0.893888\pi\)
\(938\) −2784.00 −0.0969092
\(939\) 53436.0 1.85710
\(940\) −8560.00 −0.297017
\(941\) 29370.0 1.01747 0.508733 0.860925i \(-0.330114\pi\)
0.508733 + 0.860925i \(0.330114\pi\)
\(942\) −26388.0 −0.912704
\(943\) 1026.00 0.0354307
\(944\) 1792.00 0.0617846
\(945\) −1620.00 −0.0557657
\(946\) 3610.00 0.124071
\(947\) −18721.0 −0.642398 −0.321199 0.947012i \(-0.604086\pi\)
−0.321199 + 0.947012i \(0.604086\pi\)
\(948\) 4224.00 0.144714
\(949\) −11392.0 −0.389673
\(950\) 5500.00 0.187835
\(951\) 58134.0 1.98225
\(952\) 2760.00 0.0939623
\(953\) −53772.0 −1.82775 −0.913875 0.405995i \(-0.866925\pi\)
−0.913875 + 0.405995i \(0.866925\pi\)
\(954\) −9486.00 −0.321929
\(955\) −18045.0 −0.611437
\(956\) 5484.00 0.185528
\(957\) −3330.00 −0.112480
\(958\) 2432.00 0.0820192
\(959\) 144.000 0.00484880
\(960\) 1920.00 0.0645497
\(961\) −23550.0 −0.790507
\(962\) 1184.00 0.0396816
\(963\) −7146.00 −0.239124
\(964\) 16736.0 0.559160
\(965\) −290.000 −0.00967402
\(966\) 216.000 0.00719429
\(967\) −25448.0 −0.846280 −0.423140 0.906064i \(-0.639072\pi\)
−0.423140 + 0.906064i \(0.639072\pi\)
\(968\) −10448.0 −0.346913
\(969\) 75900.0 2.51626
\(970\) −14070.0 −0.465732
\(971\) 31407.0 1.03800 0.519000 0.854774i \(-0.326304\pi\)
0.519000 + 0.854774i \(0.326304\pi\)
\(972\) −9720.00 −0.320750
\(973\) 2823.00 0.0930126
\(974\) −3236.00 −0.106456
\(975\) −2400.00 −0.0788323
\(976\) −5168.00 −0.169491
\(977\) −7589.00 −0.248509 −0.124255 0.992250i \(-0.539654\pi\)
−0.124255 + 0.992250i \(0.539654\pi\)
\(978\) −4548.00 −0.148700
\(979\) 2230.00 0.0727999
\(980\) −6680.00 −0.217740
\(981\) 1809.00 0.0588756
\(982\) 22264.0 0.723496
\(983\) −48513.0 −1.57408 −0.787042 0.616900i \(-0.788388\pi\)
−0.787042 + 0.616900i \(0.788388\pi\)
\(984\) 8208.00 0.265916
\(985\) −6770.00 −0.218995
\(986\) −25530.0 −0.824585
\(987\) −7704.00 −0.248451
\(988\) −7040.00 −0.226693
\(989\) 2166.00 0.0696408
\(990\) 450.000 0.0144464
\(991\) −13213.0 −0.423537 −0.211768 0.977320i \(-0.567922\pi\)
−0.211768 + 0.977320i \(0.567922\pi\)
\(992\) −2528.00 −0.0809114
\(993\) 588.000 0.0187912
\(994\) −2196.00 −0.0700733
\(995\) 9440.00 0.300772
\(996\) −4320.00 −0.137434
\(997\) 50596.0 1.60721 0.803607 0.595161i \(-0.202912\pi\)
0.803607 + 0.595161i \(0.202912\pi\)
\(998\) −33124.0 −1.05062
\(999\) 3996.00 0.126554
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 370.4.a.c.1.1 1
5.4 even 2 1850.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.4.a.c.1.1 1 1.1 even 1 trivial
1850.4.a.a.1.1 1 5.4 even 2