Properties

Label 1110.4.a.a.1.1
Level $1110$
Weight $4$
Character 1110.1
Self dual yes
Analytic conductor $65.492$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1110.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(65.4921201064\)
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 \(\chi\) \(=\) 1110.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -47.0000 q^{11} +12.0000 q^{12} +35.0000 q^{13} -2.00000 q^{14} -15.0000 q^{15} +16.0000 q^{16} +55.0000 q^{17} -18.0000 q^{18} -125.000 q^{19} -20.0000 q^{20} +3.00000 q^{21} +94.0000 q^{22} +213.000 q^{23} -24.0000 q^{24} +25.0000 q^{25} -70.0000 q^{26} +27.0000 q^{27} +4.00000 q^{28} +6.00000 q^{29} +30.0000 q^{30} -98.0000 q^{31} -32.0000 q^{32} -141.000 q^{33} -110.000 q^{34} -5.00000 q^{35} +36.0000 q^{36} -37.0000 q^{37} +250.000 q^{38} +105.000 q^{39} +40.0000 q^{40} -40.0000 q^{41} -6.00000 q^{42} -188.000 q^{43} -188.000 q^{44} -45.0000 q^{45} -426.000 q^{46} +304.000 q^{47} +48.0000 q^{48} -342.000 q^{49} -50.0000 q^{50} +165.000 q^{51} +140.000 q^{52} +341.000 q^{53} -54.0000 q^{54} +235.000 q^{55} -8.00000 q^{56} -375.000 q^{57} -12.0000 q^{58} -518.000 q^{59} -60.0000 q^{60} -382.000 q^{61} +196.000 q^{62} +9.00000 q^{63} +64.0000 q^{64} -175.000 q^{65} +282.000 q^{66} -578.000 q^{67} +220.000 q^{68} +639.000 q^{69} +10.0000 q^{70} +882.000 q^{71} -72.0000 q^{72} -713.000 q^{73} +74.0000 q^{74} +75.0000 q^{75} -500.000 q^{76} -47.0000 q^{77} -210.000 q^{78} +288.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +80.0000 q^{82} -849.000 q^{83} +12.0000 q^{84} -275.000 q^{85} +376.000 q^{86} +18.0000 q^{87} +376.000 q^{88} -1263.00 q^{89} +90.0000 q^{90} +35.0000 q^{91} +852.000 q^{92} -294.000 q^{93} -608.000 q^{94} +625.000 q^{95} -96.0000 q^{96} -1756.00 q^{97} +684.000 q^{98} -423.000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 3.00000 0.577350
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) −6.00000 −0.408248
\(7\) 1.00000 0.0539949 0.0269975 0.999636i \(-0.491405\pi\)
0.0269975 + 0.999636i \(0.491405\pi\)
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) 10.0000 0.316228
\(11\) −47.0000 −1.28828 −0.644138 0.764909i \(-0.722784\pi\)
−0.644138 + 0.764909i \(0.722784\pi\)
\(12\) 12.0000 0.288675
\(13\) 35.0000 0.746712 0.373356 0.927688i \(-0.378207\pi\)
0.373356 + 0.927688i \(0.378207\pi\)
\(14\) −2.00000 −0.0381802
\(15\) −15.0000 −0.258199
\(16\) 16.0000 0.250000
\(17\) 55.0000 0.784674 0.392337 0.919822i \(-0.371667\pi\)
0.392337 + 0.919822i \(0.371667\pi\)
\(18\) −18.0000 −0.235702
\(19\) −125.000 −1.50931 −0.754657 0.656119i \(-0.772197\pi\)
−0.754657 + 0.656119i \(0.772197\pi\)
\(20\) −20.0000 −0.223607
\(21\) 3.00000 0.0311740
\(22\) 94.0000 0.910949
\(23\) 213.000 1.93102 0.965512 0.260357i \(-0.0838403\pi\)
0.965512 + 0.260357i \(0.0838403\pi\)
\(24\) −24.0000 −0.204124
\(25\) 25.0000 0.200000
\(26\) −70.0000 −0.528005
\(27\) 27.0000 0.192450
\(28\) 4.00000 0.0269975
\(29\) 6.00000 0.0384197 0.0192099 0.999815i \(-0.493885\pi\)
0.0192099 + 0.999815i \(0.493885\pi\)
\(30\) 30.0000 0.182574
\(31\) −98.0000 −0.567785 −0.283892 0.958856i \(-0.591626\pi\)
−0.283892 + 0.958856i \(0.591626\pi\)
\(32\) −32.0000 −0.176777
\(33\) −141.000 −0.743786
\(34\) −110.000 −0.554848
\(35\) −5.00000 −0.0241473
\(36\) 36.0000 0.166667
\(37\) −37.0000 −0.164399
\(38\) 250.000 1.06725
\(39\) 105.000 0.431114
\(40\) 40.0000 0.158114
\(41\) −40.0000 −0.152365 −0.0761823 0.997094i \(-0.524273\pi\)
−0.0761823 + 0.997094i \(0.524273\pi\)
\(42\) −6.00000 −0.0220433
\(43\) −188.000 −0.666738 −0.333369 0.942796i \(-0.608185\pi\)
−0.333369 + 0.942796i \(0.608185\pi\)
\(44\) −188.000 −0.644138
\(45\) −45.0000 −0.149071
\(46\) −426.000 −1.36544
\(47\) 304.000 0.943467 0.471734 0.881741i \(-0.343628\pi\)
0.471734 + 0.881741i \(0.343628\pi\)
\(48\) 48.0000 0.144338
\(49\) −342.000 −0.997085
\(50\) −50.0000 −0.141421
\(51\) 165.000 0.453032
\(52\) 140.000 0.373356
\(53\) 341.000 0.883773 0.441886 0.897071i \(-0.354309\pi\)
0.441886 + 0.897071i \(0.354309\pi\)
\(54\) −54.0000 −0.136083
\(55\) 235.000 0.576134
\(56\) −8.00000 −0.0190901
\(57\) −375.000 −0.871403
\(58\) −12.0000 −0.0271668
\(59\) −518.000 −1.14301 −0.571507 0.820597i \(-0.693641\pi\)
−0.571507 + 0.820597i \(0.693641\pi\)
\(60\) −60.0000 −0.129099
\(61\) −382.000 −0.801805 −0.400902 0.916121i \(-0.631303\pi\)
−0.400902 + 0.916121i \(0.631303\pi\)
\(62\) 196.000 0.401484
\(63\) 9.00000 0.0179983
\(64\) 64.0000 0.125000
\(65\) −175.000 −0.333940
\(66\) 282.000 0.525936
\(67\) −578.000 −1.05394 −0.526970 0.849884i \(-0.676672\pi\)
−0.526970 + 0.849884i \(0.676672\pi\)
\(68\) 220.000 0.392337
\(69\) 639.000 1.11488
\(70\) 10.0000 0.0170747
\(71\) 882.000 1.47428 0.737142 0.675738i \(-0.236175\pi\)
0.737142 + 0.675738i \(0.236175\pi\)
\(72\) −72.0000 −0.117851
\(73\) −713.000 −1.14316 −0.571578 0.820548i \(-0.693668\pi\)
−0.571578 + 0.820548i \(0.693668\pi\)
\(74\) 74.0000 0.116248
\(75\) 75.0000 0.115470
\(76\) −500.000 −0.754657
\(77\) −47.0000 −0.0695604
\(78\) −210.000 −0.304844
\(79\) 288.000 0.410159 0.205079 0.978745i \(-0.434255\pi\)
0.205079 + 0.978745i \(0.434255\pi\)
\(80\) −80.0000 −0.111803
\(81\) 81.0000 0.111111
\(82\) 80.0000 0.107738
\(83\) −849.000 −1.12277 −0.561385 0.827555i \(-0.689731\pi\)
−0.561385 + 0.827555i \(0.689731\pi\)
\(84\) 12.0000 0.0155870
\(85\) −275.000 −0.350917
\(86\) 376.000 0.471455
\(87\) 18.0000 0.0221816
\(88\) 376.000 0.455474
\(89\) −1263.00 −1.50424 −0.752122 0.659024i \(-0.770970\pi\)
−0.752122 + 0.659024i \(0.770970\pi\)
\(90\) 90.0000 0.105409
\(91\) 35.0000 0.0403186
\(92\) 852.000 0.965512
\(93\) −294.000 −0.327811
\(94\) −608.000 −0.667132
\(95\) 625.000 0.674986
\(96\) −96.0000 −0.102062
\(97\) −1756.00 −1.83809 −0.919045 0.394152i \(-0.871038\pi\)
−0.919045 + 0.394152i \(0.871038\pi\)
\(98\) 684.000 0.705045
\(99\) −423.000 −0.429425
\(100\) 100.000 0.100000
\(101\) 98.0000 0.0965482 0.0482741 0.998834i \(-0.484628\pi\)
0.0482741 + 0.998834i \(0.484628\pi\)
\(102\) −330.000 −0.320342
\(103\) 1464.00 1.40051 0.700253 0.713894i \(-0.253070\pi\)
0.700253 + 0.713894i \(0.253070\pi\)
\(104\) −280.000 −0.264002
\(105\) −15.0000 −0.0139414
\(106\) −682.000 −0.624922
\(107\) −603.000 −0.544806 −0.272403 0.962183i \(-0.587818\pi\)
−0.272403 + 0.962183i \(0.587818\pi\)
\(108\) 108.000 0.0962250
\(109\) −617.000 −0.542182 −0.271091 0.962554i \(-0.587384\pi\)
−0.271091 + 0.962554i \(0.587384\pi\)
\(110\) −470.000 −0.407389
\(111\) −111.000 −0.0949158
\(112\) 16.0000 0.0134987
\(113\) 70.0000 0.0582747 0.0291374 0.999575i \(-0.490724\pi\)
0.0291374 + 0.999575i \(0.490724\pi\)
\(114\) 750.000 0.616175
\(115\) −1065.00 −0.863581
\(116\) 24.0000 0.0192099
\(117\) 315.000 0.248904
\(118\) 1036.00 0.808233
\(119\) 55.0000 0.0423684
\(120\) 120.000 0.0912871
\(121\) 878.000 0.659654
\(122\) 764.000 0.566962
\(123\) −120.000 −0.0879678
\(124\) −392.000 −0.283892
\(125\) −125.000 −0.0894427
\(126\) −18.0000 −0.0127267
\(127\) 263.000 0.183760 0.0918798 0.995770i \(-0.470712\pi\)
0.0918798 + 0.995770i \(0.470712\pi\)
\(128\) −128.000 −0.0883883
\(129\) −564.000 −0.384941
\(130\) 350.000 0.236131
\(131\) 1308.00 0.872370 0.436185 0.899857i \(-0.356329\pi\)
0.436185 + 0.899857i \(0.356329\pi\)
\(132\) −564.000 −0.371893
\(133\) −125.000 −0.0814953
\(134\) 1156.00 0.745248
\(135\) −135.000 −0.0860663
\(136\) −440.000 −0.277424
\(137\) −522.000 −0.325529 −0.162764 0.986665i \(-0.552041\pi\)
−0.162764 + 0.986665i \(0.552041\pi\)
\(138\) −1278.00 −0.788338
\(139\) 2310.00 1.40958 0.704790 0.709416i \(-0.251041\pi\)
0.704790 + 0.709416i \(0.251041\pi\)
\(140\) −20.0000 −0.0120736
\(141\) 912.000 0.544711
\(142\) −1764.00 −1.04248
\(143\) −1645.00 −0.961971
\(144\) 144.000 0.0833333
\(145\) −30.0000 −0.0171818
\(146\) 1426.00 0.808333
\(147\) −1026.00 −0.575667
\(148\) −148.000 −0.0821995
\(149\) −1158.00 −0.636692 −0.318346 0.947975i \(-0.603127\pi\)
−0.318346 + 0.947975i \(0.603127\pi\)
\(150\) −150.000 −0.0816497
\(151\) 3045.00 1.64105 0.820525 0.571610i \(-0.193681\pi\)
0.820525 + 0.571610i \(0.193681\pi\)
\(152\) 1000.00 0.533623
\(153\) 495.000 0.261558
\(154\) 94.0000 0.0491866
\(155\) 490.000 0.253921
\(156\) 420.000 0.215557
\(157\) −1972.00 −1.00244 −0.501219 0.865321i \(-0.667115\pi\)
−0.501219 + 0.865321i \(0.667115\pi\)
\(158\) −576.000 −0.290026
\(159\) 1023.00 0.510246
\(160\) 160.000 0.0790569
\(161\) 213.000 0.104266
\(162\) −162.000 −0.0785674
\(163\) −1601.00 −0.769325 −0.384663 0.923057i \(-0.625682\pi\)
−0.384663 + 0.923057i \(0.625682\pi\)
\(164\) −160.000 −0.0761823
\(165\) 705.000 0.332631
\(166\) 1698.00 0.793918
\(167\) −2541.00 −1.17742 −0.588708 0.808346i \(-0.700363\pi\)
−0.588708 + 0.808346i \(0.700363\pi\)
\(168\) −24.0000 −0.0110217
\(169\) −972.000 −0.442421
\(170\) 550.000 0.248136
\(171\) −1125.00 −0.503105
\(172\) −752.000 −0.333369
\(173\) −1629.00 −0.715899 −0.357950 0.933741i \(-0.616524\pi\)
−0.357950 + 0.933741i \(0.616524\pi\)
\(174\) −36.0000 −0.0156848
\(175\) 25.0000 0.0107990
\(176\) −752.000 −0.322069
\(177\) −1554.00 −0.659920
\(178\) 2526.00 1.06366
\(179\) −2640.00 −1.10236 −0.551181 0.834386i \(-0.685823\pi\)
−0.551181 + 0.834386i \(0.685823\pi\)
\(180\) −180.000 −0.0745356
\(181\) −4202.00 −1.72559 −0.862796 0.505552i \(-0.831289\pi\)
−0.862796 + 0.505552i \(0.831289\pi\)
\(182\) −70.0000 −0.0285096
\(183\) −1146.00 −0.462922
\(184\) −1704.00 −0.682720
\(185\) 185.000 0.0735215
\(186\) 588.000 0.231797
\(187\) −2585.00 −1.01088
\(188\) 1216.00 0.471734
\(189\) 27.0000 0.0103913
\(190\) −1250.00 −0.477287
\(191\) −2185.00 −0.827754 −0.413877 0.910333i \(-0.635826\pi\)
−0.413877 + 0.910333i \(0.635826\pi\)
\(192\) 192.000 0.0721688
\(193\) 2654.00 0.989840 0.494920 0.868939i \(-0.335197\pi\)
0.494920 + 0.868939i \(0.335197\pi\)
\(194\) 3512.00 1.29973
\(195\) −525.000 −0.192800
\(196\) −1368.00 −0.498542
\(197\) −1329.00 −0.480646 −0.240323 0.970693i \(-0.577253\pi\)
−0.240323 + 0.970693i \(0.577253\pi\)
\(198\) 846.000 0.303650
\(199\) −1480.00 −0.527208 −0.263604 0.964631i \(-0.584911\pi\)
−0.263604 + 0.964631i \(0.584911\pi\)
\(200\) −200.000 −0.0707107
\(201\) −1734.00 −0.608492
\(202\) −196.000 −0.0682699
\(203\) 6.00000 0.00207447
\(204\) 660.000 0.226516
\(205\) 200.000 0.0681395
\(206\) −2928.00 −0.990308
\(207\) 1917.00 0.643675
\(208\) 560.000 0.186678
\(209\) 5875.00 1.94441
\(210\) 30.0000 0.00985808
\(211\) −278.000 −0.0907029 −0.0453514 0.998971i \(-0.514441\pi\)
−0.0453514 + 0.998971i \(0.514441\pi\)
\(212\) 1364.00 0.441886
\(213\) 2646.00 0.851178
\(214\) 1206.00 0.385236
\(215\) 940.000 0.298174
\(216\) −216.000 −0.0680414
\(217\) −98.0000 −0.0306575
\(218\) 1234.00 0.383381
\(219\) −2139.00 −0.660001
\(220\) 940.000 0.288067
\(221\) 1925.00 0.585925
\(222\) 222.000 0.0671156
\(223\) −4800.00 −1.44140 −0.720699 0.693248i \(-0.756179\pi\)
−0.720699 + 0.693248i \(0.756179\pi\)
\(224\) −32.0000 −0.00954504
\(225\) 225.000 0.0666667
\(226\) −140.000 −0.0412065
\(227\) 2840.00 0.830385 0.415193 0.909734i \(-0.363714\pi\)
0.415193 + 0.909734i \(0.363714\pi\)
\(228\) −1500.00 −0.435701
\(229\) 1070.00 0.308767 0.154383 0.988011i \(-0.450661\pi\)
0.154383 + 0.988011i \(0.450661\pi\)
\(230\) 2130.00 0.610644
\(231\) −141.000 −0.0401607
\(232\) −48.0000 −0.0135834
\(233\) 3294.00 0.926168 0.463084 0.886314i \(-0.346743\pi\)
0.463084 + 0.886314i \(0.346743\pi\)
\(234\) −630.000 −0.176002
\(235\) −1520.00 −0.421931
\(236\) −2072.00 −0.571507
\(237\) 864.000 0.236805
\(238\) −110.000 −0.0299590
\(239\) 3492.00 0.945099 0.472550 0.881304i \(-0.343334\pi\)
0.472550 + 0.881304i \(0.343334\pi\)
\(240\) −240.000 −0.0645497
\(241\) −6642.00 −1.77531 −0.887653 0.460513i \(-0.847666\pi\)
−0.887653 + 0.460513i \(0.847666\pi\)
\(242\) −1756.00 −0.466446
\(243\) 243.000 0.0641500
\(244\) −1528.00 −0.400902
\(245\) 1710.00 0.445910
\(246\) 240.000 0.0622026
\(247\) −4375.00 −1.12702
\(248\) 784.000 0.200742
\(249\) −2547.00 −0.648231
\(250\) 250.000 0.0632456
\(251\) −6518.00 −1.63909 −0.819547 0.573012i \(-0.805775\pi\)
−0.819547 + 0.573012i \(0.805775\pi\)
\(252\) 36.0000 0.00899915
\(253\) −10011.0 −2.48769
\(254\) −526.000 −0.129938
\(255\) −825.000 −0.202602
\(256\) 256.000 0.0625000
\(257\) 4627.00 1.12305 0.561526 0.827459i \(-0.310214\pi\)
0.561526 + 0.827459i \(0.310214\pi\)
\(258\) 1128.00 0.272195
\(259\) −37.0000 −0.00887671
\(260\) −700.000 −0.166970
\(261\) 54.0000 0.0128066
\(262\) −2616.00 −0.616859
\(263\) −1380.00 −0.323553 −0.161777 0.986827i \(-0.551722\pi\)
−0.161777 + 0.986827i \(0.551722\pi\)
\(264\) 1128.00 0.262968
\(265\) −1705.00 −0.395235
\(266\) 250.000 0.0576259
\(267\) −3789.00 −0.868476
\(268\) −2312.00 −0.526970
\(269\) −8631.00 −1.95629 −0.978144 0.207930i \(-0.933327\pi\)
−0.978144 + 0.207930i \(0.933327\pi\)
\(270\) 270.000 0.0608581
\(271\) −4060.00 −0.910064 −0.455032 0.890475i \(-0.650372\pi\)
−0.455032 + 0.890475i \(0.650372\pi\)
\(272\) 880.000 0.196169
\(273\) 105.000 0.0232780
\(274\) 1044.00 0.230184
\(275\) −1175.00 −0.257655
\(276\) 2556.00 0.557439
\(277\) 3437.00 0.745521 0.372760 0.927928i \(-0.378411\pi\)
0.372760 + 0.927928i \(0.378411\pi\)
\(278\) −4620.00 −0.996724
\(279\) −882.000 −0.189262
\(280\) 40.0000 0.00853735
\(281\) 1149.00 0.243927 0.121964 0.992535i \(-0.461081\pi\)
0.121964 + 0.992535i \(0.461081\pi\)
\(282\) −1824.00 −0.385169
\(283\) 219.000 0.0460007 0.0230004 0.999735i \(-0.492678\pi\)
0.0230004 + 0.999735i \(0.492678\pi\)
\(284\) 3528.00 0.737142
\(285\) 1875.00 0.389703
\(286\) 3290.00 0.680216
\(287\) −40.0000 −0.00822692
\(288\) −288.000 −0.0589256
\(289\) −1888.00 −0.384287
\(290\) 60.0000 0.0121494
\(291\) −5268.00 −1.06122
\(292\) −2852.00 −0.571578
\(293\) −2907.00 −0.579620 −0.289810 0.957084i \(-0.593592\pi\)
−0.289810 + 0.957084i \(0.593592\pi\)
\(294\) 2052.00 0.407058
\(295\) 2590.00 0.511172
\(296\) 296.000 0.0581238
\(297\) −1269.00 −0.247929
\(298\) 2316.00 0.450209
\(299\) 7455.00 1.44192
\(300\) 300.000 0.0577350
\(301\) −188.000 −0.0360005
\(302\) −6090.00 −1.16040
\(303\) 294.000 0.0557421
\(304\) −2000.00 −0.377329
\(305\) 1910.00 0.358578
\(306\) −990.000 −0.184949
\(307\) −7178.00 −1.33443 −0.667215 0.744865i \(-0.732514\pi\)
−0.667215 + 0.744865i \(0.732514\pi\)
\(308\) −188.000 −0.0347802
\(309\) 4392.00 0.808583
\(310\) −980.000 −0.179549
\(311\) −1320.00 −0.240676 −0.120338 0.992733i \(-0.538398\pi\)
−0.120338 + 0.992733i \(0.538398\pi\)
\(312\) −840.000 −0.152422
\(313\) 1152.00 0.208035 0.104017 0.994575i \(-0.466830\pi\)
0.104017 + 0.994575i \(0.466830\pi\)
\(314\) 3944.00 0.708831
\(315\) −45.0000 −0.00804909
\(316\) 1152.00 0.205079
\(317\) −1682.00 −0.298014 −0.149007 0.988836i \(-0.547608\pi\)
−0.149007 + 0.988836i \(0.547608\pi\)
\(318\) −2046.00 −0.360799
\(319\) −282.000 −0.0494952
\(320\) −320.000 −0.0559017
\(321\) −1809.00 −0.314544
\(322\) −426.000 −0.0737269
\(323\) −6875.00 −1.18432
\(324\) 324.000 0.0555556
\(325\) 875.000 0.149342
\(326\) 3202.00 0.543995
\(327\) −1851.00 −0.313029
\(328\) 320.000 0.0538690
\(329\) 304.000 0.0509424
\(330\) −1410.00 −0.235206
\(331\) −10076.0 −1.67319 −0.836597 0.547819i \(-0.815458\pi\)
−0.836597 + 0.547819i \(0.815458\pi\)
\(332\) −3396.00 −0.561385
\(333\) −333.000 −0.0547997
\(334\) 5082.00 0.832559
\(335\) 2890.00 0.471336
\(336\) 48.0000 0.00779350
\(337\) −1721.00 −0.278186 −0.139093 0.990279i \(-0.544419\pi\)
−0.139093 + 0.990279i \(0.544419\pi\)
\(338\) 1944.00 0.312839
\(339\) 210.000 0.0336449
\(340\) −1100.00 −0.175458
\(341\) 4606.00 0.731463
\(342\) 2250.00 0.355749
\(343\) −685.000 −0.107832
\(344\) 1504.00 0.235727
\(345\) −3195.00 −0.498588
\(346\) 3258.00 0.506217
\(347\) −4564.00 −0.706076 −0.353038 0.935609i \(-0.614851\pi\)
−0.353038 + 0.935609i \(0.614851\pi\)
\(348\) 72.0000 0.0110908
\(349\) −4160.00 −0.638051 −0.319025 0.947746i \(-0.603356\pi\)
−0.319025 + 0.947746i \(0.603356\pi\)
\(350\) −50.0000 −0.00763604
\(351\) 945.000 0.143705
\(352\) 1504.00 0.227737
\(353\) 10438.0 1.57382 0.786910 0.617067i \(-0.211679\pi\)
0.786910 + 0.617067i \(0.211679\pi\)
\(354\) 3108.00 0.466634
\(355\) −4410.00 −0.659320
\(356\) −5052.00 −0.752122
\(357\) 165.000 0.0244614
\(358\) 5280.00 0.779488
\(359\) 8572.00 1.26020 0.630101 0.776513i \(-0.283013\pi\)
0.630101 + 0.776513i \(0.283013\pi\)
\(360\) 360.000 0.0527046
\(361\) 8766.00 1.27803
\(362\) 8404.00 1.22018
\(363\) 2634.00 0.380852
\(364\) 140.000 0.0201593
\(365\) 3565.00 0.511235
\(366\) 2292.00 0.327335
\(367\) −10015.0 −1.42447 −0.712233 0.701944i \(-0.752316\pi\)
−0.712233 + 0.701944i \(0.752316\pi\)
\(368\) 3408.00 0.482756
\(369\) −360.000 −0.0507882
\(370\) −370.000 −0.0519875
\(371\) 341.000 0.0477192
\(372\) −1176.00 −0.163905
\(373\) 8718.00 1.21019 0.605095 0.796153i \(-0.293135\pi\)
0.605095 + 0.796153i \(0.293135\pi\)
\(374\) 5170.00 0.714798
\(375\) −375.000 −0.0516398
\(376\) −2432.00 −0.333566
\(377\) 210.000 0.0286885
\(378\) −54.0000 −0.00734778
\(379\) 12986.0 1.76002 0.880008 0.474959i \(-0.157537\pi\)
0.880008 + 0.474959i \(0.157537\pi\)
\(380\) 2500.00 0.337493
\(381\) 789.000 0.106094
\(382\) 4370.00 0.585311
\(383\) −1569.00 −0.209327 −0.104663 0.994508i \(-0.533377\pi\)
−0.104663 + 0.994508i \(0.533377\pi\)
\(384\) −384.000 −0.0510310
\(385\) 235.000 0.0311083
\(386\) −5308.00 −0.699923
\(387\) −1692.00 −0.222246
\(388\) −7024.00 −0.919045
\(389\) −2046.00 −0.266674 −0.133337 0.991071i \(-0.542569\pi\)
−0.133337 + 0.991071i \(0.542569\pi\)
\(390\) 1050.00 0.136330
\(391\) 11715.0 1.51523
\(392\) 2736.00 0.352523
\(393\) 3924.00 0.503663
\(394\) 2658.00 0.339868
\(395\) −1440.00 −0.183429
\(396\) −1692.00 −0.214713
\(397\) 10228.0 1.29302 0.646510 0.762906i \(-0.276228\pi\)
0.646510 + 0.762906i \(0.276228\pi\)
\(398\) 2960.00 0.372792
\(399\) −375.000 −0.0470513
\(400\) 400.000 0.0500000
\(401\) −6927.00 −0.862638 −0.431319 0.902199i \(-0.641952\pi\)
−0.431319 + 0.902199i \(0.641952\pi\)
\(402\) 3468.00 0.430269
\(403\) −3430.00 −0.423971
\(404\) 392.000 0.0482741
\(405\) −405.000 −0.0496904
\(406\) −12.0000 −0.00146687
\(407\) 1739.00 0.211791
\(408\) −1320.00 −0.160171
\(409\) 4008.00 0.484555 0.242277 0.970207i \(-0.422106\pi\)
0.242277 + 0.970207i \(0.422106\pi\)
\(410\) −400.000 −0.0481819
\(411\) −1566.00 −0.187944
\(412\) 5856.00 0.700253
\(413\) −518.000 −0.0617170
\(414\) −3834.00 −0.455147
\(415\) 4245.00 0.502118
\(416\) −1120.00 −0.132001
\(417\) 6930.00 0.813821
\(418\) −11750.0 −1.37491
\(419\) −9481.00 −1.10543 −0.552717 0.833369i \(-0.686409\pi\)
−0.552717 + 0.833369i \(0.686409\pi\)
\(420\) −60.0000 −0.00697071
\(421\) 10930.0 1.26531 0.632655 0.774434i \(-0.281965\pi\)
0.632655 + 0.774434i \(0.281965\pi\)
\(422\) 556.000 0.0641366
\(423\) 2736.00 0.314489
\(424\) −2728.00 −0.312461
\(425\) 1375.00 0.156935
\(426\) −5292.00 −0.601874
\(427\) −382.000 −0.0432934
\(428\) −2412.00 −0.272403
\(429\) −4935.00 −0.555394
\(430\) −1880.00 −0.210841
\(431\) 14185.0 1.58531 0.792654 0.609672i \(-0.208699\pi\)
0.792654 + 0.609672i \(0.208699\pi\)
\(432\) 432.000 0.0481125
\(433\) 6293.00 0.698435 0.349217 0.937042i \(-0.386447\pi\)
0.349217 + 0.937042i \(0.386447\pi\)
\(434\) 196.000 0.0216781
\(435\) −90.0000 −0.00991993
\(436\) −2468.00 −0.271091
\(437\) −26625.0 −2.91452
\(438\) 4278.00 0.466691
\(439\) 10996.0 1.19547 0.597734 0.801695i \(-0.296068\pi\)
0.597734 + 0.801695i \(0.296068\pi\)
\(440\) −1880.00 −0.203694
\(441\) −3078.00 −0.332362
\(442\) −3850.00 −0.414312
\(443\) 11820.0 1.26769 0.633843 0.773462i \(-0.281476\pi\)
0.633843 + 0.773462i \(0.281476\pi\)
\(444\) −444.000 −0.0474579
\(445\) 6315.00 0.672718
\(446\) 9600.00 1.01922
\(447\) −3474.00 −0.367594
\(448\) 64.0000 0.00674937
\(449\) 9022.00 0.948273 0.474136 0.880451i \(-0.342760\pi\)
0.474136 + 0.880451i \(0.342760\pi\)
\(450\) −450.000 −0.0471405
\(451\) 1880.00 0.196288
\(452\) 280.000 0.0291374
\(453\) 9135.00 0.947461
\(454\) −5680.00 −0.587171
\(455\) −175.000 −0.0180310
\(456\) 3000.00 0.308087
\(457\) −16724.0 −1.71185 −0.855925 0.517099i \(-0.827012\pi\)
−0.855925 + 0.517099i \(0.827012\pi\)
\(458\) −2140.00 −0.218331
\(459\) 1485.00 0.151011
\(460\) −4260.00 −0.431790
\(461\) −638.000 −0.0644569 −0.0322284 0.999481i \(-0.510260\pi\)
−0.0322284 + 0.999481i \(0.510260\pi\)
\(462\) 282.000 0.0283979
\(463\) 1868.00 0.187502 0.0937509 0.995596i \(-0.470114\pi\)
0.0937509 + 0.995596i \(0.470114\pi\)
\(464\) 96.0000 0.00960493
\(465\) 1470.00 0.146601
\(466\) −6588.00 −0.654900
\(467\) −2436.00 −0.241380 −0.120690 0.992690i \(-0.538511\pi\)
−0.120690 + 0.992690i \(0.538511\pi\)
\(468\) 1260.00 0.124452
\(469\) −578.000 −0.0569074
\(470\) 3040.00 0.298351
\(471\) −5916.00 −0.578758
\(472\) 4144.00 0.404117
\(473\) 8836.00 0.858942
\(474\) −1728.00 −0.167447
\(475\) −3125.00 −0.301863
\(476\) 220.000 0.0211842
\(477\) 3069.00 0.294591
\(478\) −6984.00 −0.668286
\(479\) 14589.0 1.39163 0.695813 0.718223i \(-0.255044\pi\)
0.695813 + 0.718223i \(0.255044\pi\)
\(480\) 480.000 0.0456435
\(481\) −1295.00 −0.122759
\(482\) 13284.0 1.25533
\(483\) 639.000 0.0601977
\(484\) 3512.00 0.329827
\(485\) 8780.00 0.822019
\(486\) −486.000 −0.0453609
\(487\) 10206.0 0.949647 0.474823 0.880081i \(-0.342512\pi\)
0.474823 + 0.880081i \(0.342512\pi\)
\(488\) 3056.00 0.283481
\(489\) −4803.00 −0.444170
\(490\) −3420.00 −0.315306
\(491\) 19221.0 1.76666 0.883332 0.468749i \(-0.155295\pi\)
0.883332 + 0.468749i \(0.155295\pi\)
\(492\) −480.000 −0.0439839
\(493\) 330.000 0.0301470
\(494\) 8750.00 0.796925
\(495\) 2115.00 0.192045
\(496\) −1568.00 −0.141946
\(497\) 882.000 0.0796038
\(498\) 5094.00 0.458369
\(499\) 10757.0 0.965029 0.482514 0.875888i \(-0.339724\pi\)
0.482514 + 0.875888i \(0.339724\pi\)
\(500\) −500.000 −0.0447214
\(501\) −7623.00 −0.679781
\(502\) 13036.0 1.15901
\(503\) 13428.0 1.19031 0.595154 0.803612i \(-0.297091\pi\)
0.595154 + 0.803612i \(0.297091\pi\)
\(504\) −72.0000 −0.00636336
\(505\) −490.000 −0.0431777
\(506\) 20022.0 1.75906
\(507\) −2916.00 −0.255432
\(508\) 1052.00 0.0918798
\(509\) 6207.00 0.540512 0.270256 0.962789i \(-0.412892\pi\)
0.270256 + 0.962789i \(0.412892\pi\)
\(510\) 1650.00 0.143261
\(511\) −713.000 −0.0617246
\(512\) −512.000 −0.0441942
\(513\) −3375.00 −0.290468
\(514\) −9254.00 −0.794118
\(515\) −7320.00 −0.626326
\(516\) −2256.00 −0.192471
\(517\) −14288.0 −1.21545
\(518\) 74.0000 0.00627678
\(519\) −4887.00 −0.413325
\(520\) 1400.00 0.118066
\(521\) −9660.00 −0.812308 −0.406154 0.913805i \(-0.633130\pi\)
−0.406154 + 0.913805i \(0.633130\pi\)
\(522\) −108.000 −0.00905562
\(523\) −3732.00 −0.312025 −0.156012 0.987755i \(-0.549864\pi\)
−0.156012 + 0.987755i \(0.549864\pi\)
\(524\) 5232.00 0.436185
\(525\) 75.0000 0.00623480
\(526\) 2760.00 0.228787
\(527\) −5390.00 −0.445526
\(528\) −2256.00 −0.185947
\(529\) 33202.0 2.72886
\(530\) 3410.00 0.279473
\(531\) −4662.00 −0.381005
\(532\) −500.000 −0.0407476
\(533\) −1400.00 −0.113772
\(534\) 7578.00 0.614105
\(535\) 3015.00 0.243645
\(536\) 4624.00 0.372624
\(537\) −7920.00 −0.636449
\(538\) 17262.0 1.38330
\(539\) 16074.0 1.28452
\(540\) −540.000 −0.0430331
\(541\) −12991.0 −1.03240 −0.516198 0.856469i \(-0.672653\pi\)
−0.516198 + 0.856469i \(0.672653\pi\)
\(542\) 8120.00 0.643513
\(543\) −12606.0 −0.996271
\(544\) −1760.00 −0.138712
\(545\) 3085.00 0.242471
\(546\) −210.000 −0.0164600
\(547\) 23635.0 1.84746 0.923729 0.383046i \(-0.125125\pi\)
0.923729 + 0.383046i \(0.125125\pi\)
\(548\) −2088.00 −0.162764
\(549\) −3438.00 −0.267268
\(550\) 2350.00 0.182190
\(551\) −750.000 −0.0579874
\(552\) −5112.00 −0.394169
\(553\) 288.000 0.0221465
\(554\) −6874.00 −0.527163
\(555\) 555.000 0.0424476
\(556\) 9240.00 0.704790
\(557\) 19024.0 1.44717 0.723584 0.690236i \(-0.242493\pi\)
0.723584 + 0.690236i \(0.242493\pi\)
\(558\) 1764.00 0.133828
\(559\) −6580.00 −0.497861
\(560\) −80.0000 −0.00603682
\(561\) −7755.00 −0.583630
\(562\) −2298.00 −0.172483
\(563\) 6218.00 0.465466 0.232733 0.972541i \(-0.425233\pi\)
0.232733 + 0.972541i \(0.425233\pi\)
\(564\) 3648.00 0.272356
\(565\) −350.000 −0.0260613
\(566\) −438.000 −0.0325274
\(567\) 81.0000 0.00599944
\(568\) −7056.00 −0.521238
\(569\) −19137.0 −1.40996 −0.704978 0.709229i \(-0.749043\pi\)
−0.704978 + 0.709229i \(0.749043\pi\)
\(570\) −3750.00 −0.275562
\(571\) −20662.0 −1.51432 −0.757161 0.653228i \(-0.773414\pi\)
−0.757161 + 0.653228i \(0.773414\pi\)
\(572\) −6580.00 −0.480985
\(573\) −6555.00 −0.477904
\(574\) 80.0000 0.00581731
\(575\) 5325.00 0.386205
\(576\) 576.000 0.0416667
\(577\) −4222.00 −0.304617 −0.152309 0.988333i \(-0.548671\pi\)
−0.152309 + 0.988333i \(0.548671\pi\)
\(578\) 3776.00 0.271732
\(579\) 7962.00 0.571484
\(580\) −120.000 −0.00859091
\(581\) −849.000 −0.0606238
\(582\) 10536.0 0.750397
\(583\) −16027.0 −1.13854
\(584\) 5704.00 0.404166
\(585\) −1575.00 −0.111313
\(586\) 5814.00 0.409853
\(587\) −19744.0 −1.38828 −0.694141 0.719839i \(-0.744216\pi\)
−0.694141 + 0.719839i \(0.744216\pi\)
\(588\) −4104.00 −0.287834
\(589\) 12250.0 0.856965
\(590\) −5180.00 −0.361453
\(591\) −3987.00 −0.277501
\(592\) −592.000 −0.0410997
\(593\) −4896.00 −0.339047 −0.169523 0.985526i \(-0.554223\pi\)
−0.169523 + 0.985526i \(0.554223\pi\)
\(594\) 2538.00 0.175312
\(595\) −275.000 −0.0189477
\(596\) −4632.00 −0.318346
\(597\) −4440.00 −0.304384
\(598\) −14910.0 −1.01959
\(599\) 5228.00 0.356612 0.178306 0.983975i \(-0.442938\pi\)
0.178306 + 0.983975i \(0.442938\pi\)
\(600\) −600.000 −0.0408248
\(601\) −12197.0 −0.827830 −0.413915 0.910315i \(-0.635839\pi\)
−0.413915 + 0.910315i \(0.635839\pi\)
\(602\) 376.000 0.0254562
\(603\) −5202.00 −0.351313
\(604\) 12180.0 0.820525
\(605\) −4390.00 −0.295006
\(606\) −588.000 −0.0394156
\(607\) 6842.00 0.457509 0.228755 0.973484i \(-0.426535\pi\)
0.228755 + 0.973484i \(0.426535\pi\)
\(608\) 4000.00 0.266812
\(609\) 18.0000 0.00119770
\(610\) −3820.00 −0.253553
\(611\) 10640.0 0.704498
\(612\) 1980.00 0.130779
\(613\) −13086.0 −0.862216 −0.431108 0.902300i \(-0.641877\pi\)
−0.431108 + 0.902300i \(0.641877\pi\)
\(614\) 14356.0 0.943585
\(615\) 600.000 0.0393404
\(616\) 376.000 0.0245933
\(617\) 974.000 0.0635523 0.0317761 0.999495i \(-0.489884\pi\)
0.0317761 + 0.999495i \(0.489884\pi\)
\(618\) −8784.00 −0.571755
\(619\) 2600.00 0.168825 0.0844126 0.996431i \(-0.473099\pi\)
0.0844126 + 0.996431i \(0.473099\pi\)
\(620\) 1960.00 0.126960
\(621\) 5751.00 0.371626
\(622\) 2640.00 0.170184
\(623\) −1263.00 −0.0812216
\(624\) 1680.00 0.107779
\(625\) 625.000 0.0400000
\(626\) −2304.00 −0.147103
\(627\) 17625.0 1.12261
\(628\) −7888.00 −0.501219
\(629\) −2035.00 −0.129000
\(630\) 90.0000 0.00569156
\(631\) −11644.0 −0.734612 −0.367306 0.930100i \(-0.619720\pi\)
−0.367306 + 0.930100i \(0.619720\pi\)
\(632\) −2304.00 −0.145013
\(633\) −834.000 −0.0523673
\(634\) 3364.00 0.210728
\(635\) −1315.00 −0.0821798
\(636\) 4092.00 0.255123
\(637\) −11970.0 −0.744535
\(638\) 564.000 0.0349984
\(639\) 7938.00 0.491428
\(640\) 640.000 0.0395285
\(641\) 6144.00 0.378586 0.189293 0.981921i \(-0.439380\pi\)
0.189293 + 0.981921i \(0.439380\pi\)
\(642\) 3618.00 0.222416
\(643\) 12161.0 0.745852 0.372926 0.927861i \(-0.378354\pi\)
0.372926 + 0.927861i \(0.378354\pi\)
\(644\) 852.000 0.0521328
\(645\) 2820.00 0.172151
\(646\) 13750.0 0.837440
\(647\) 8989.00 0.546204 0.273102 0.961985i \(-0.411950\pi\)
0.273102 + 0.961985i \(0.411950\pi\)
\(648\) −648.000 −0.0392837
\(649\) 24346.0 1.47252
\(650\) −1750.00 −0.105601
\(651\) −294.000 −0.0177001
\(652\) −6404.00 −0.384663
\(653\) −16216.0 −0.971793 −0.485897 0.874016i \(-0.661507\pi\)
−0.485897 + 0.874016i \(0.661507\pi\)
\(654\) 3702.00 0.221345
\(655\) −6540.00 −0.390136
\(656\) −640.000 −0.0380912
\(657\) −6417.00 −0.381052
\(658\) −608.000 −0.0360217
\(659\) 14484.0 0.856171 0.428085 0.903738i \(-0.359188\pi\)
0.428085 + 0.903738i \(0.359188\pi\)
\(660\) 2820.00 0.166316
\(661\) 11093.0 0.652750 0.326375 0.945240i \(-0.394173\pi\)
0.326375 + 0.945240i \(0.394173\pi\)
\(662\) 20152.0 1.18313
\(663\) 5775.00 0.338284
\(664\) 6792.00 0.396959
\(665\) 625.000 0.0364458
\(666\) 666.000 0.0387492
\(667\) 1278.00 0.0741894
\(668\) −10164.0 −0.588708
\(669\) −14400.0 −0.832192
\(670\) −5780.00 −0.333285
\(671\) 17954.0 1.03295
\(672\) −96.0000 −0.00551083
\(673\) −29045.0 −1.66360 −0.831800 0.555076i \(-0.812689\pi\)
−0.831800 + 0.555076i \(0.812689\pi\)
\(674\) 3442.00 0.196708
\(675\) 675.000 0.0384900
\(676\) −3888.00 −0.221211
\(677\) 4839.00 0.274709 0.137354 0.990522i \(-0.456140\pi\)
0.137354 + 0.990522i \(0.456140\pi\)
\(678\) −420.000 −0.0237906
\(679\) −1756.00 −0.0992476
\(680\) 2200.00 0.124068
\(681\) 8520.00 0.479423
\(682\) −9212.00 −0.517222
\(683\) 2712.00 0.151935 0.0759676 0.997110i \(-0.475795\pi\)
0.0759676 + 0.997110i \(0.475795\pi\)
\(684\) −4500.00 −0.251552
\(685\) 2610.00 0.145581
\(686\) 1370.00 0.0762490
\(687\) 3210.00 0.178267
\(688\) −3008.00 −0.166684
\(689\) 11935.0 0.659923
\(690\) 6390.00 0.352555
\(691\) −4818.00 −0.265247 −0.132623 0.991167i \(-0.542340\pi\)
−0.132623 + 0.991167i \(0.542340\pi\)
\(692\) −6516.00 −0.357950
\(693\) −423.000 −0.0231868
\(694\) 9128.00 0.499271
\(695\) −11550.0 −0.630383
\(696\) −144.000 −0.00784239
\(697\) −2200.00 −0.119557
\(698\) 8320.00 0.451170
\(699\) 9882.00 0.534723
\(700\) 100.000 0.00539949
\(701\) −2928.00 −0.157759 −0.0788795 0.996884i \(-0.525134\pi\)
−0.0788795 + 0.996884i \(0.525134\pi\)
\(702\) −1890.00 −0.101615
\(703\) 4625.00 0.248130
\(704\) −3008.00 −0.161034
\(705\) −4560.00 −0.243602
\(706\) −20876.0 −1.11286
\(707\) 98.0000 0.00521311
\(708\) −6216.00 −0.329960
\(709\) 31433.0 1.66501 0.832504 0.554019i \(-0.186906\pi\)
0.832504 + 0.554019i \(0.186906\pi\)
\(710\) 8820.00 0.466209
\(711\) 2592.00 0.136720
\(712\) 10104.0 0.531831
\(713\) −20874.0 −1.09641
\(714\) −330.000 −0.0172968
\(715\) 8225.00 0.430206
\(716\) −10560.0 −0.551181
\(717\) 10476.0 0.545653
\(718\) −17144.0 −0.891098
\(719\) −10958.0 −0.568379 −0.284189 0.958768i \(-0.591724\pi\)
−0.284189 + 0.958768i \(0.591724\pi\)
\(720\) −720.000 −0.0372678
\(721\) 1464.00 0.0756203
\(722\) −17532.0 −0.903703
\(723\) −19926.0 −1.02497
\(724\) −16808.0 −0.862796
\(725\) 150.000 0.00768395
\(726\) −5268.00 −0.269303
\(727\) 29582.0 1.50913 0.754564 0.656227i \(-0.227849\pi\)
0.754564 + 0.656227i \(0.227849\pi\)
\(728\) −280.000 −0.0142548
\(729\) 729.000 0.0370370
\(730\) −7130.00 −0.361497
\(731\) −10340.0 −0.523172
\(732\) −4584.00 −0.231461
\(733\) −17514.0 −0.882530 −0.441265 0.897377i \(-0.645470\pi\)
−0.441265 + 0.897377i \(0.645470\pi\)
\(734\) 20030.0 1.00725
\(735\) 5130.00 0.257446
\(736\) −6816.00 −0.341360
\(737\) 27166.0 1.35776
\(738\) 720.000 0.0359127
\(739\) −12826.0 −0.638447 −0.319223 0.947680i \(-0.603422\pi\)
−0.319223 + 0.947680i \(0.603422\pi\)
\(740\) 740.000 0.0367607
\(741\) −13125.0 −0.650687
\(742\) −682.000 −0.0337426
\(743\) −31962.0 −1.57816 −0.789079 0.614291i \(-0.789442\pi\)
−0.789079 + 0.614291i \(0.789442\pi\)
\(744\) 2352.00 0.115899
\(745\) 5790.00 0.284737
\(746\) −17436.0 −0.855734
\(747\) −7641.00 −0.374256
\(748\) −10340.0 −0.505438
\(749\) −603.000 −0.0294167
\(750\) 750.000 0.0365148
\(751\) 9308.00 0.452269 0.226134 0.974096i \(-0.427391\pi\)
0.226134 + 0.974096i \(0.427391\pi\)
\(752\) 4864.00 0.235867
\(753\) −19554.0 −0.946331
\(754\) −420.000 −0.0202858
\(755\) −15225.0 −0.733900
\(756\) 108.000 0.00519566
\(757\) −33487.0 −1.60780 −0.803901 0.594763i \(-0.797246\pi\)
−0.803901 + 0.594763i \(0.797246\pi\)
\(758\) −25972.0 −1.24452
\(759\) −30033.0 −1.43627
\(760\) −5000.00 −0.238644
\(761\) 1246.00 0.0593528 0.0296764 0.999560i \(-0.490552\pi\)
0.0296764 + 0.999560i \(0.490552\pi\)
\(762\) −1578.00 −0.0750196
\(763\) −617.000 −0.0292751
\(764\) −8740.00 −0.413877
\(765\) −2475.00 −0.116972
\(766\) 3138.00 0.148016
\(767\) −18130.0 −0.853502
\(768\) 768.000 0.0360844
\(769\) −4670.00 −0.218992 −0.109496 0.993987i \(-0.534924\pi\)
−0.109496 + 0.993987i \(0.534924\pi\)
\(770\) −470.000 −0.0219969
\(771\) 13881.0 0.648394
\(772\) 10616.0 0.494920
\(773\) 16347.0 0.760622 0.380311 0.924859i \(-0.375817\pi\)
0.380311 + 0.924859i \(0.375817\pi\)
\(774\) 3384.00 0.157152
\(775\) −2450.00 −0.113557
\(776\) 14048.0 0.649863
\(777\) −111.000 −0.00512497
\(778\) 4092.00 0.188567
\(779\) 5000.00 0.229966
\(780\) −2100.00 −0.0964001
\(781\) −41454.0 −1.89928
\(782\) −23430.0 −1.07143
\(783\) 162.000 0.00739388
\(784\) −5472.00 −0.249271
\(785\) 9860.00 0.448304
\(786\) −7848.00 −0.356144
\(787\) −16794.0 −0.760663 −0.380331 0.924850i \(-0.624190\pi\)
−0.380331 + 0.924850i \(0.624190\pi\)
\(788\) −5316.00 −0.240323
\(789\) −4140.00 −0.186803
\(790\) 2880.00 0.129704
\(791\) 70.0000 0.00314654
\(792\) 3384.00 0.151825
\(793\) −13370.0 −0.598717
\(794\) −20456.0 −0.914303
\(795\) −5115.00 −0.228189
\(796\) −5920.00 −0.263604
\(797\) 354.000 0.0157332 0.00786658 0.999969i \(-0.497496\pi\)
0.00786658 + 0.999969i \(0.497496\pi\)
\(798\) 750.000 0.0332703
\(799\) 16720.0 0.740314
\(800\) −800.000 −0.0353553
\(801\) −11367.0 −0.501415
\(802\) 13854.0 0.609977
\(803\) 33511.0 1.47270
\(804\) −6936.00 −0.304246
\(805\) −1065.00 −0.0466290
\(806\) 6860.00 0.299793
\(807\) −25893.0 −1.12946
\(808\) −784.000 −0.0341349
\(809\) 21309.0 0.926062 0.463031 0.886342i \(-0.346762\pi\)
0.463031 + 0.886342i \(0.346762\pi\)
\(810\) 810.000 0.0351364
\(811\) 38560.0 1.66957 0.834787 0.550573i \(-0.185591\pi\)
0.834787 + 0.550573i \(0.185591\pi\)
\(812\) 24.0000 0.00103724
\(813\) −12180.0 −0.525426
\(814\) −3478.00 −0.149759
\(815\) 8005.00 0.344053
\(816\) 2640.00 0.113258
\(817\) 23500.0 1.00632
\(818\) −8016.00 −0.342632
\(819\) 315.000 0.0134395
\(820\) 800.000 0.0340698
\(821\) 20327.0 0.864089 0.432045 0.901852i \(-0.357792\pi\)
0.432045 + 0.901852i \(0.357792\pi\)
\(822\) 3132.00 0.132897
\(823\) −23017.0 −0.974875 −0.487438 0.873158i \(-0.662068\pi\)
−0.487438 + 0.873158i \(0.662068\pi\)
\(824\) −11712.0 −0.495154
\(825\) −3525.00 −0.148757
\(826\) 1036.00 0.0436405
\(827\) −34212.0 −1.43853 −0.719267 0.694734i \(-0.755522\pi\)
−0.719267 + 0.694734i \(0.755522\pi\)
\(828\) 7668.00 0.321837
\(829\) −8357.00 −0.350121 −0.175061 0.984558i \(-0.556012\pi\)
−0.175061 + 0.984558i \(0.556012\pi\)
\(830\) −8490.00 −0.355051
\(831\) 10311.0 0.430427
\(832\) 2240.00 0.0933390
\(833\) −18810.0 −0.782386
\(834\) −13860.0 −0.575459
\(835\) 12705.0 0.526556
\(836\) 23500.0 0.972206
\(837\) −2646.00 −0.109270
\(838\) 18962.0 0.781660
\(839\) −6526.00 −0.268537 −0.134268 0.990945i \(-0.542868\pi\)
−0.134268 + 0.990945i \(0.542868\pi\)
\(840\) 120.000 0.00492904
\(841\) −24353.0 −0.998524
\(842\) −21860.0 −0.894709
\(843\) 3447.00 0.140832
\(844\) −1112.00 −0.0453514
\(845\) 4860.00 0.197857
\(846\) −5472.00 −0.222377
\(847\) 878.000 0.0356180
\(848\) 5456.00 0.220943
\(849\) 657.000 0.0265585
\(850\) −2750.00 −0.110970
\(851\) −7881.00 −0.317459
\(852\) 10584.0 0.425589
\(853\) 41095.0 1.64955 0.824775 0.565461i \(-0.191302\pi\)
0.824775 + 0.565461i \(0.191302\pi\)
\(854\) 764.000 0.0306130
\(855\) 5625.00 0.224995
\(856\) 4824.00 0.192618
\(857\) 11333.0 0.451725 0.225862 0.974159i \(-0.427480\pi\)
0.225862 + 0.974159i \(0.427480\pi\)
\(858\) 9870.00 0.392723
\(859\) 39969.0 1.58757 0.793786 0.608197i \(-0.208107\pi\)
0.793786 + 0.608197i \(0.208107\pi\)
\(860\) 3760.00 0.149087
\(861\) −120.000 −0.00474981
\(862\) −28370.0 −1.12098
\(863\) 26268.0 1.03612 0.518061 0.855344i \(-0.326654\pi\)
0.518061 + 0.855344i \(0.326654\pi\)
\(864\) −864.000 −0.0340207
\(865\) 8145.00 0.320160
\(866\) −12586.0 −0.493868
\(867\) −5664.00 −0.221868
\(868\) −392.000 −0.0153287
\(869\) −13536.0 −0.528397
\(870\) 180.000 0.00701445
\(871\) −20230.0 −0.786989
\(872\) 4936.00 0.191690
\(873\) −15804.0 −0.612697
\(874\) 53250.0 2.06088
\(875\) −125.000 −0.00482945
\(876\) −8556.00 −0.330001
\(877\) −11524.0 −0.443715 −0.221857 0.975079i \(-0.571212\pi\)
−0.221857 + 0.975079i \(0.571212\pi\)
\(878\) −21992.0 −0.845324
\(879\) −8721.00 −0.334644
\(880\) 3760.00 0.144034
\(881\) −39144.0 −1.49693 −0.748465 0.663175i \(-0.769209\pi\)
−0.748465 + 0.663175i \(0.769209\pi\)
\(882\) 6156.00 0.235015
\(883\) 25627.0 0.976690 0.488345 0.872651i \(-0.337601\pi\)
0.488345 + 0.872651i \(0.337601\pi\)
\(884\) 7700.00 0.292963
\(885\) 7770.00 0.295125
\(886\) −23640.0 −0.896390
\(887\) 1358.00 0.0514061 0.0257030 0.999670i \(-0.491818\pi\)
0.0257030 + 0.999670i \(0.491818\pi\)
\(888\) 888.000 0.0335578
\(889\) 263.000 0.00992209
\(890\) −12630.0 −0.475684
\(891\) −3807.00 −0.143142
\(892\) −19200.0 −0.720699
\(893\) −38000.0 −1.42399
\(894\) 6948.00 0.259928
\(895\) 13200.0 0.492991
\(896\) −128.000 −0.00477252
\(897\) 22365.0 0.832492
\(898\) −18044.0 −0.670530
\(899\) −588.000 −0.0218141
\(900\) 900.000 0.0333333
\(901\) 18755.0 0.693474
\(902\) −3760.00 −0.138796
\(903\) −564.000 −0.0207849
\(904\) −560.000 −0.0206032
\(905\) 21010.0 0.771708
\(906\) −18270.0 −0.669956
\(907\) 25507.0 0.933788 0.466894 0.884313i \(-0.345373\pi\)
0.466894 + 0.884313i \(0.345373\pi\)
\(908\) 11360.0 0.415193
\(909\) 882.000 0.0321827
\(910\) 350.000 0.0127499
\(911\) 17640.0 0.641536 0.320768 0.947158i \(-0.396059\pi\)
0.320768 + 0.947158i \(0.396059\pi\)
\(912\) −6000.00 −0.217851
\(913\) 39903.0 1.44644
\(914\) 33448.0 1.21046
\(915\) 5730.00 0.207025
\(916\) 4280.00 0.154383
\(917\) 1308.00 0.0471036
\(918\) −2970.00 −0.106781
\(919\) −15656.0 −0.561963 −0.280981 0.959713i \(-0.590660\pi\)
−0.280981 + 0.959713i \(0.590660\pi\)
\(920\) 8520.00 0.305322
\(921\) −21534.0 −0.770434
\(922\) 1276.00 0.0455779
\(923\) 30870.0 1.10087
\(924\) −564.000 −0.0200803
\(925\) −925.000 −0.0328798
\(926\) −3736.00 −0.132584
\(927\) 13176.0 0.466836
\(928\) −192.000 −0.00679171
\(929\) 30690.0 1.08386 0.541930 0.840424i \(-0.317694\pi\)
0.541930 + 0.840424i \(0.317694\pi\)
\(930\) −2940.00 −0.103663
\(931\) 42750.0 1.50491
\(932\) 13176.0 0.463084
\(933\) −3960.00 −0.138955
\(934\) 4872.00 0.170682
\(935\) 12925.0 0.452078
\(936\) −2520.00 −0.0880008
\(937\) −37474.0 −1.30653 −0.653267 0.757128i \(-0.726602\pi\)
−0.653267 + 0.757128i \(0.726602\pi\)
\(938\) 1156.00 0.0402396
\(939\) 3456.00 0.120109
\(940\) −6080.00 −0.210966
\(941\) −3830.00 −0.132683 −0.0663414 0.997797i \(-0.521133\pi\)
−0.0663414 + 0.997797i \(0.521133\pi\)
\(942\) 11832.0 0.409244
\(943\) −8520.00 −0.294220
\(944\) −8288.00 −0.285754
\(945\) −135.000 −0.00464714
\(946\) −17672.0 −0.607364
\(947\) −18916.0 −0.649089 −0.324545 0.945870i \(-0.605211\pi\)
−0.324545 + 0.945870i \(0.605211\pi\)
\(948\) 3456.00 0.118403
\(949\) −24955.0 −0.853608
\(950\) 6250.00 0.213449
\(951\) −5046.00 −0.172059
\(952\) −440.000 −0.0149795
\(953\) −24738.0 −0.840863 −0.420431 0.907324i \(-0.638121\pi\)
−0.420431 + 0.907324i \(0.638121\pi\)
\(954\) −6138.00 −0.208307
\(955\) 10925.0 0.370183
\(956\) 13968.0 0.472550
\(957\) −846.000 −0.0285761
\(958\) −29178.0 −0.984028
\(959\) −522.000 −0.0175769
\(960\) −960.000 −0.0322749
\(961\) −20187.0 −0.677621
\(962\) 2590.00 0.0868035
\(963\) −5427.00 −0.181602
\(964\) −26568.0 −0.887653
\(965\) −13270.0 −0.442670
\(966\) −1278.00 −0.0425662
\(967\) −6854.00 −0.227932 −0.113966 0.993485i \(-0.536355\pi\)
−0.113966 + 0.993485i \(0.536355\pi\)
\(968\) −7024.00 −0.233223
\(969\) −20625.0 −0.683767
\(970\) −17560.0 −0.581255
\(971\) −45916.0 −1.51752 −0.758761 0.651369i \(-0.774195\pi\)
−0.758761 + 0.651369i \(0.774195\pi\)
\(972\) 972.000 0.0320750
\(973\) 2310.00 0.0761102
\(974\) −20412.0 −0.671502
\(975\) 2625.00 0.0862229
\(976\) −6112.00 −0.200451
\(977\) 11443.0 0.374712 0.187356 0.982292i \(-0.440008\pi\)
0.187356 + 0.982292i \(0.440008\pi\)
\(978\) 9606.00 0.314076
\(979\) 59361.0 1.93788
\(980\) 6840.00 0.222955
\(981\) −5553.00 −0.180727
\(982\) −38442.0 −1.24922
\(983\) 30042.0 0.974762 0.487381 0.873189i \(-0.337952\pi\)
0.487381 + 0.873189i \(0.337952\pi\)
\(984\) 960.000 0.0311013
\(985\) 6645.00 0.214952
\(986\) −660.000 −0.0213171
\(987\) 912.000 0.0294116
\(988\) −17500.0 −0.563511
\(989\) −40044.0 −1.28749
\(990\) −4230.00 −0.135796
\(991\) −23648.0 −0.758026 −0.379013 0.925391i \(-0.623736\pi\)
−0.379013 + 0.925391i \(0.623736\pi\)
\(992\) 3136.00 0.100371
\(993\) −30228.0 −0.966019
\(994\) −1764.00 −0.0562884
\(995\) 7400.00 0.235775
\(996\) −10188.0 −0.324116
\(997\) 34605.0 1.09925 0.549625 0.835412i \(-0.314771\pi\)
0.549625 + 0.835412i \(0.314771\pi\)
\(998\) −21514.0 −0.682379
\(999\) −999.000 −0.0316386
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 1110.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1110.4.a.a.1.1 1 1.1 even 1 trivial