Properties

Label 2070.4.a.e.1.1
Level $2070$
Weight $4$
Character 2070.1
Self dual yes
Analytic conductor $122.134$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2070.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(122.133953712\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2070.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.0000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -18.0000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +32.0000 q^{11} -47.0000 q^{13} +36.0000 q^{14} +16.0000 q^{16} -20.0000 q^{17} +36.0000 q^{19} +20.0000 q^{20} -64.0000 q^{22} +23.0000 q^{23} +25.0000 q^{25} +94.0000 q^{26} -72.0000 q^{28} +27.0000 q^{29} -33.0000 q^{31} -32.0000 q^{32} +40.0000 q^{34} -90.0000 q^{35} +56.0000 q^{37} -72.0000 q^{38} -40.0000 q^{40} +157.000 q^{41} +18.0000 q^{43} +128.000 q^{44} -46.0000 q^{46} -65.0000 q^{47} -19.0000 q^{49} -50.0000 q^{50} -188.000 q^{52} +14.0000 q^{53} +160.000 q^{55} +144.000 q^{56} -54.0000 q^{58} +744.000 q^{59} +552.000 q^{61} +66.0000 q^{62} +64.0000 q^{64} -235.000 q^{65} -156.000 q^{67} -80.0000 q^{68} +180.000 q^{70} -699.000 q^{71} -609.000 q^{73} -112.000 q^{74} +144.000 q^{76} -576.000 q^{77} -644.000 q^{79} +80.0000 q^{80} -314.000 q^{82} -512.000 q^{83} -100.000 q^{85} -36.0000 q^{86} -256.000 q^{88} +102.000 q^{89} +846.000 q^{91} +92.0000 q^{92} +130.000 q^{94} +180.000 q^{95} +578.000 q^{97} +38.0000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) −18.0000 −0.971909 −0.485954 0.873984i \(-0.661528\pi\)
−0.485954 + 0.873984i \(0.661528\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −10.0000 −0.316228
\(11\) 32.0000 0.877124 0.438562 0.898701i \(-0.355488\pi\)
0.438562 + 0.898701i \(0.355488\pi\)
\(12\) 0 0
\(13\) −47.0000 −1.00273 −0.501364 0.865237i \(-0.667168\pi\)
−0.501364 + 0.865237i \(0.667168\pi\)
\(14\) 36.0000 0.687243
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −20.0000 −0.285336 −0.142668 0.989771i \(-0.545568\pi\)
−0.142668 + 0.989771i \(0.545568\pi\)
\(18\) 0 0
\(19\) 36.0000 0.434682 0.217341 0.976096i \(-0.430262\pi\)
0.217341 + 0.976096i \(0.430262\pi\)
\(20\) 20.0000 0.223607
\(21\) 0 0
\(22\) −64.0000 −0.620220
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 94.0000 0.709035
\(27\) 0 0
\(28\) −72.0000 −0.485954
\(29\) 27.0000 0.172889 0.0864444 0.996257i \(-0.472450\pi\)
0.0864444 + 0.996257i \(0.472450\pi\)
\(30\) 0 0
\(31\) −33.0000 −0.191193 −0.0955964 0.995420i \(-0.530476\pi\)
−0.0955964 + 0.995420i \(0.530476\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 40.0000 0.201763
\(35\) −90.0000 −0.434651
\(36\) 0 0
\(37\) 56.0000 0.248820 0.124410 0.992231i \(-0.460296\pi\)
0.124410 + 0.992231i \(0.460296\pi\)
\(38\) −72.0000 −0.307367
\(39\) 0 0
\(40\) −40.0000 −0.158114
\(41\) 157.000 0.598031 0.299016 0.954248i \(-0.403342\pi\)
0.299016 + 0.954248i \(0.403342\pi\)
\(42\) 0 0
\(43\) 18.0000 0.0638366 0.0319183 0.999490i \(-0.489838\pi\)
0.0319183 + 0.999490i \(0.489838\pi\)
\(44\) 128.000 0.438562
\(45\) 0 0
\(46\) −46.0000 −0.147442
\(47\) −65.0000 −0.201728 −0.100864 0.994900i \(-0.532161\pi\)
−0.100864 + 0.994900i \(0.532161\pi\)
\(48\) 0 0
\(49\) −19.0000 −0.0553936
\(50\) −50.0000 −0.141421
\(51\) 0 0
\(52\) −188.000 −0.501364
\(53\) 14.0000 0.0362839 0.0181420 0.999835i \(-0.494225\pi\)
0.0181420 + 0.999835i \(0.494225\pi\)
\(54\) 0 0
\(55\) 160.000 0.392262
\(56\) 144.000 0.343622
\(57\) 0 0
\(58\) −54.0000 −0.122251
\(59\) 744.000 1.64170 0.820852 0.571141i \(-0.193499\pi\)
0.820852 + 0.571141i \(0.193499\pi\)
\(60\) 0 0
\(61\) 552.000 1.15863 0.579314 0.815104i \(-0.303320\pi\)
0.579314 + 0.815104i \(0.303320\pi\)
\(62\) 66.0000 0.135194
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −235.000 −0.448433
\(66\) 0 0
\(67\) −156.000 −0.284454 −0.142227 0.989834i \(-0.545426\pi\)
−0.142227 + 0.989834i \(0.545426\pi\)
\(68\) −80.0000 −0.142668
\(69\) 0 0
\(70\) 180.000 0.307344
\(71\) −699.000 −1.16839 −0.584197 0.811612i \(-0.698591\pi\)
−0.584197 + 0.811612i \(0.698591\pi\)
\(72\) 0 0
\(73\) −609.000 −0.976412 −0.488206 0.872728i \(-0.662348\pi\)
−0.488206 + 0.872728i \(0.662348\pi\)
\(74\) −112.000 −0.175942
\(75\) 0 0
\(76\) 144.000 0.217341
\(77\) −576.000 −0.852484
\(78\) 0 0
\(79\) −644.000 −0.917160 −0.458580 0.888653i \(-0.651642\pi\)
−0.458580 + 0.888653i \(0.651642\pi\)
\(80\) 80.0000 0.111803
\(81\) 0 0
\(82\) −314.000 −0.422872
\(83\) −512.000 −0.677100 −0.338550 0.940948i \(-0.609936\pi\)
−0.338550 + 0.940948i \(0.609936\pi\)
\(84\) 0 0
\(85\) −100.000 −0.127606
\(86\) −36.0000 −0.0451393
\(87\) 0 0
\(88\) −256.000 −0.310110
\(89\) 102.000 0.121483 0.0607415 0.998154i \(-0.480653\pi\)
0.0607415 + 0.998154i \(0.480653\pi\)
\(90\) 0 0
\(91\) 846.000 0.974559
\(92\) 92.0000 0.104257
\(93\) 0 0
\(94\) 130.000 0.142643
\(95\) 180.000 0.194396
\(96\) 0 0
\(97\) 578.000 0.605021 0.302510 0.953146i \(-0.402175\pi\)
0.302510 + 0.953146i \(0.402175\pi\)
\(98\) 38.0000 0.0391692
\(99\) 0 0
\(100\) 100.000 0.100000
\(101\) 6.00000 0.00591111 0.00295556 0.999996i \(-0.499059\pi\)
0.00295556 + 0.999996i \(0.499059\pi\)
\(102\) 0 0
\(103\) −160.000 −0.153061 −0.0765304 0.997067i \(-0.524384\pi\)
−0.0765304 + 0.997067i \(0.524384\pi\)
\(104\) 376.000 0.354518
\(105\) 0 0
\(106\) −28.0000 −0.0256566
\(107\) −380.000 −0.343327 −0.171663 0.985156i \(-0.554914\pi\)
−0.171663 + 0.985156i \(0.554914\pi\)
\(108\) 0 0
\(109\) 250.000 0.219685 0.109842 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(110\) −320.000 −0.277371
\(111\) 0 0
\(112\) −288.000 −0.242977
\(113\) 390.000 0.324674 0.162337 0.986735i \(-0.448097\pi\)
0.162337 + 0.986735i \(0.448097\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) 108.000 0.0864444
\(117\) 0 0
\(118\) −1488.00 −1.16086
\(119\) 360.000 0.277321
\(120\) 0 0
\(121\) −307.000 −0.230654
\(122\) −1104.00 −0.819274
\(123\) 0 0
\(124\) −132.000 −0.0955964
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −769.000 −0.537305 −0.268652 0.963237i \(-0.586578\pi\)
−0.268652 + 0.963237i \(0.586578\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) 470.000 0.317090
\(131\) 213.000 0.142060 0.0710301 0.997474i \(-0.477371\pi\)
0.0710301 + 0.997474i \(0.477371\pi\)
\(132\) 0 0
\(133\) −648.000 −0.422472
\(134\) 312.000 0.201140
\(135\) 0 0
\(136\) 160.000 0.100882
\(137\) −2836.00 −1.76858 −0.884291 0.466936i \(-0.845358\pi\)
−0.884291 + 0.466936i \(0.845358\pi\)
\(138\) 0 0
\(139\) −1631.00 −0.995249 −0.497625 0.867393i \(-0.665794\pi\)
−0.497625 + 0.867393i \(0.665794\pi\)
\(140\) −360.000 −0.217325
\(141\) 0 0
\(142\) 1398.00 0.826180
\(143\) −1504.00 −0.879516
\(144\) 0 0
\(145\) 135.000 0.0773182
\(146\) 1218.00 0.690427
\(147\) 0 0
\(148\) 224.000 0.124410
\(149\) 1966.00 1.08095 0.540473 0.841361i \(-0.318245\pi\)
0.540473 + 0.841361i \(0.318245\pi\)
\(150\) 0 0
\(151\) 35.0000 0.0188626 0.00943132 0.999956i \(-0.496998\pi\)
0.00943132 + 0.999956i \(0.496998\pi\)
\(152\) −288.000 −0.153683
\(153\) 0 0
\(154\) 1152.00 0.602797
\(155\) −165.000 −0.0855040
\(156\) 0 0
\(157\) 1702.00 0.865187 0.432594 0.901589i \(-0.357599\pi\)
0.432594 + 0.901589i \(0.357599\pi\)
\(158\) 1288.00 0.648530
\(159\) 0 0
\(160\) −160.000 −0.0790569
\(161\) −414.000 −0.202657
\(162\) 0 0
\(163\) −2045.00 −0.982680 −0.491340 0.870968i \(-0.663493\pi\)
−0.491340 + 0.870968i \(0.663493\pi\)
\(164\) 628.000 0.299016
\(165\) 0 0
\(166\) 1024.00 0.478782
\(167\) −1016.00 −0.470781 −0.235391 0.971901i \(-0.575637\pi\)
−0.235391 + 0.971901i \(0.575637\pi\)
\(168\) 0 0
\(169\) 12.0000 0.00546199
\(170\) 200.000 0.0902312
\(171\) 0 0
\(172\) 72.0000 0.0319183
\(173\) −598.000 −0.262804 −0.131402 0.991329i \(-0.541948\pi\)
−0.131402 + 0.991329i \(0.541948\pi\)
\(174\) 0 0
\(175\) −450.000 −0.194382
\(176\) 512.000 0.219281
\(177\) 0 0
\(178\) −204.000 −0.0859014
\(179\) 4607.00 1.92371 0.961853 0.273567i \(-0.0882036\pi\)
0.961853 + 0.273567i \(0.0882036\pi\)
\(180\) 0 0
\(181\) −1212.00 −0.497720 −0.248860 0.968540i \(-0.580056\pi\)
−0.248860 + 0.968540i \(0.580056\pi\)
\(182\) −1692.00 −0.689117
\(183\) 0 0
\(184\) −184.000 −0.0737210
\(185\) 280.000 0.111276
\(186\) 0 0
\(187\) −640.000 −0.250275
\(188\) −260.000 −0.100864
\(189\) 0 0
\(190\) −360.000 −0.137459
\(191\) 1058.00 0.400807 0.200404 0.979713i \(-0.435775\pi\)
0.200404 + 0.979713i \(0.435775\pi\)
\(192\) 0 0
\(193\) 1047.00 0.390491 0.195245 0.980754i \(-0.437450\pi\)
0.195245 + 0.980754i \(0.437450\pi\)
\(194\) −1156.00 −0.427814
\(195\) 0 0
\(196\) −76.0000 −0.0276968
\(197\) −251.000 −0.0907767 −0.0453883 0.998969i \(-0.514453\pi\)
−0.0453883 + 0.998969i \(0.514453\pi\)
\(198\) 0 0
\(199\) −3508.00 −1.24963 −0.624813 0.780775i \(-0.714825\pi\)
−0.624813 + 0.780775i \(0.714825\pi\)
\(200\) −200.000 −0.0707107
\(201\) 0 0
\(202\) −12.0000 −0.00417979
\(203\) −486.000 −0.168032
\(204\) 0 0
\(205\) 785.000 0.267448
\(206\) 320.000 0.108230
\(207\) 0 0
\(208\) −752.000 −0.250682
\(209\) 1152.00 0.381270
\(210\) 0 0
\(211\) −3296.00 −1.07538 −0.537692 0.843141i \(-0.680704\pi\)
−0.537692 + 0.843141i \(0.680704\pi\)
\(212\) 56.0000 0.0181420
\(213\) 0 0
\(214\) 760.000 0.242769
\(215\) 90.0000 0.0285486
\(216\) 0 0
\(217\) 594.000 0.185822
\(218\) −500.000 −0.155341
\(219\) 0 0
\(220\) 640.000 0.196131
\(221\) 940.000 0.286114
\(222\) 0 0
\(223\) −2720.00 −0.816792 −0.408396 0.912805i \(-0.633912\pi\)
−0.408396 + 0.912805i \(0.633912\pi\)
\(224\) 576.000 0.171811
\(225\) 0 0
\(226\) −780.000 −0.229579
\(227\) 4134.00 1.20874 0.604368 0.796705i \(-0.293426\pi\)
0.604368 + 0.796705i \(0.293426\pi\)
\(228\) 0 0
\(229\) −4510.00 −1.30144 −0.650719 0.759319i \(-0.725532\pi\)
−0.650719 + 0.759319i \(0.725532\pi\)
\(230\) −230.000 −0.0659380
\(231\) 0 0
\(232\) −216.000 −0.0611254
\(233\) 5003.00 1.40668 0.703342 0.710852i \(-0.251690\pi\)
0.703342 + 0.710852i \(0.251690\pi\)
\(234\) 0 0
\(235\) −325.000 −0.0902156
\(236\) 2976.00 0.820852
\(237\) 0 0
\(238\) −720.000 −0.196095
\(239\) 6309.00 1.70751 0.853756 0.520674i \(-0.174319\pi\)
0.853756 + 0.520674i \(0.174319\pi\)
\(240\) 0 0
\(241\) 3038.00 0.812012 0.406006 0.913871i \(-0.366921\pi\)
0.406006 + 0.913871i \(0.366921\pi\)
\(242\) 614.000 0.163097
\(243\) 0 0
\(244\) 2208.00 0.579314
\(245\) −95.0000 −0.0247728
\(246\) 0 0
\(247\) −1692.00 −0.435868
\(248\) 264.000 0.0675968
\(249\) 0 0
\(250\) −250.000 −0.0632456
\(251\) 1332.00 0.334961 0.167480 0.985875i \(-0.446437\pi\)
0.167480 + 0.985875i \(0.446437\pi\)
\(252\) 0 0
\(253\) 736.000 0.182893
\(254\) 1538.00 0.379932
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) −3301.00 −0.801209 −0.400605 0.916251i \(-0.631200\pi\)
−0.400605 + 0.916251i \(0.631200\pi\)
\(258\) 0 0
\(259\) −1008.00 −0.241830
\(260\) −940.000 −0.224217
\(261\) 0 0
\(262\) −426.000 −0.100452
\(263\) −2072.00 −0.485798 −0.242899 0.970052i \(-0.578098\pi\)
−0.242899 + 0.970052i \(0.578098\pi\)
\(264\) 0 0
\(265\) 70.0000 0.0162267
\(266\) 1296.00 0.298733
\(267\) 0 0
\(268\) −624.000 −0.142227
\(269\) −5721.00 −1.29671 −0.648356 0.761337i \(-0.724543\pi\)
−0.648356 + 0.761337i \(0.724543\pi\)
\(270\) 0 0
\(271\) −5900.00 −1.32251 −0.661254 0.750162i \(-0.729975\pi\)
−0.661254 + 0.750162i \(0.729975\pi\)
\(272\) −320.000 −0.0713340
\(273\) 0 0
\(274\) 5672.00 1.25058
\(275\) 800.000 0.175425
\(276\) 0 0
\(277\) 6371.00 1.38194 0.690968 0.722885i \(-0.257185\pi\)
0.690968 + 0.722885i \(0.257185\pi\)
\(278\) 3262.00 0.703747
\(279\) 0 0
\(280\) 720.000 0.153672
\(281\) −3190.00 −0.677222 −0.338611 0.940926i \(-0.609957\pi\)
−0.338611 + 0.940926i \(0.609957\pi\)
\(282\) 0 0
\(283\) −4226.00 −0.887667 −0.443833 0.896109i \(-0.646382\pi\)
−0.443833 + 0.896109i \(0.646382\pi\)
\(284\) −2796.00 −0.584197
\(285\) 0 0
\(286\) 3008.00 0.621912
\(287\) −2826.00 −0.581232
\(288\) 0 0
\(289\) −4513.00 −0.918583
\(290\) −270.000 −0.0546722
\(291\) 0 0
\(292\) −2436.00 −0.488206
\(293\) −6048.00 −1.20590 −0.602949 0.797780i \(-0.706008\pi\)
−0.602949 + 0.797780i \(0.706008\pi\)
\(294\) 0 0
\(295\) 3720.00 0.734192
\(296\) −448.000 −0.0879712
\(297\) 0 0
\(298\) −3932.00 −0.764344
\(299\) −1081.00 −0.209083
\(300\) 0 0
\(301\) −324.000 −0.0620434
\(302\) −70.0000 −0.0133379
\(303\) 0 0
\(304\) 576.000 0.108671
\(305\) 2760.00 0.518155
\(306\) 0 0
\(307\) 8628.00 1.60399 0.801997 0.597328i \(-0.203771\pi\)
0.801997 + 0.597328i \(0.203771\pi\)
\(308\) −2304.00 −0.426242
\(309\) 0 0
\(310\) 330.000 0.0604605
\(311\) −8247.00 −1.50368 −0.751840 0.659346i \(-0.770833\pi\)
−0.751840 + 0.659346i \(0.770833\pi\)
\(312\) 0 0
\(313\) 2620.00 0.473135 0.236567 0.971615i \(-0.423978\pi\)
0.236567 + 0.971615i \(0.423978\pi\)
\(314\) −3404.00 −0.611780
\(315\) 0 0
\(316\) −2576.00 −0.458580
\(317\) −9906.00 −1.75513 −0.877565 0.479457i \(-0.840834\pi\)
−0.877565 + 0.479457i \(0.840834\pi\)
\(318\) 0 0
\(319\) 864.000 0.151645
\(320\) 320.000 0.0559017
\(321\) 0 0
\(322\) 828.000 0.143300
\(323\) −720.000 −0.124031
\(324\) 0 0
\(325\) −1175.00 −0.200545
\(326\) 4090.00 0.694859
\(327\) 0 0
\(328\) −1256.00 −0.211436
\(329\) 1170.00 0.196061
\(330\) 0 0
\(331\) −8115.00 −1.34756 −0.673778 0.738934i \(-0.735329\pi\)
−0.673778 + 0.738934i \(0.735329\pi\)
\(332\) −2048.00 −0.338550
\(333\) 0 0
\(334\) 2032.00 0.332892
\(335\) −780.000 −0.127212
\(336\) 0 0
\(337\) −7586.00 −1.22622 −0.613109 0.789998i \(-0.710082\pi\)
−0.613109 + 0.789998i \(0.710082\pi\)
\(338\) −24.0000 −0.00386221
\(339\) 0 0
\(340\) −400.000 −0.0638031
\(341\) −1056.00 −0.167700
\(342\) 0 0
\(343\) 6516.00 1.02575
\(344\) −144.000 −0.0225697
\(345\) 0 0
\(346\) 1196.00 0.185831
\(347\) −1356.00 −0.209781 −0.104890 0.994484i \(-0.533449\pi\)
−0.104890 + 0.994484i \(0.533449\pi\)
\(348\) 0 0
\(349\) 6649.00 1.01981 0.509904 0.860231i \(-0.329681\pi\)
0.509904 + 0.860231i \(0.329681\pi\)
\(350\) 900.000 0.137449
\(351\) 0 0
\(352\) −1024.00 −0.155055
\(353\) −10691.0 −1.61197 −0.805984 0.591938i \(-0.798363\pi\)
−0.805984 + 0.591938i \(0.798363\pi\)
\(354\) 0 0
\(355\) −3495.00 −0.522522
\(356\) 408.000 0.0607415
\(357\) 0 0
\(358\) −9214.00 −1.36027
\(359\) 6420.00 0.943829 0.471915 0.881644i \(-0.343563\pi\)
0.471915 + 0.881644i \(0.343563\pi\)
\(360\) 0 0
\(361\) −5563.00 −0.811051
\(362\) 2424.00 0.351941
\(363\) 0 0
\(364\) 3384.00 0.487280
\(365\) −3045.00 −0.436665
\(366\) 0 0
\(367\) −524.000 −0.0745302 −0.0372651 0.999305i \(-0.511865\pi\)
−0.0372651 + 0.999305i \(0.511865\pi\)
\(368\) 368.000 0.0521286
\(369\) 0 0
\(370\) −560.000 −0.0786838
\(371\) −252.000 −0.0352647
\(372\) 0 0
\(373\) 5566.00 0.772645 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(374\) 1280.00 0.176971
\(375\) 0 0
\(376\) 520.000 0.0713217
\(377\) −1269.00 −0.173360
\(378\) 0 0
\(379\) 2240.00 0.303591 0.151796 0.988412i \(-0.451494\pi\)
0.151796 + 0.988412i \(0.451494\pi\)
\(380\) 720.000 0.0971979
\(381\) 0 0
\(382\) −2116.00 −0.283414
\(383\) −8778.00 −1.17111 −0.585555 0.810633i \(-0.699123\pi\)
−0.585555 + 0.810633i \(0.699123\pi\)
\(384\) 0 0
\(385\) −2880.00 −0.381243
\(386\) −2094.00 −0.276119
\(387\) 0 0
\(388\) 2312.00 0.302510
\(389\) −4056.00 −0.528656 −0.264328 0.964433i \(-0.585150\pi\)
−0.264328 + 0.964433i \(0.585150\pi\)
\(390\) 0 0
\(391\) −460.000 −0.0594967
\(392\) 152.000 0.0195846
\(393\) 0 0
\(394\) 502.000 0.0641888
\(395\) −3220.00 −0.410167
\(396\) 0 0
\(397\) −9151.00 −1.15687 −0.578433 0.815730i \(-0.696335\pi\)
−0.578433 + 0.815730i \(0.696335\pi\)
\(398\) 7016.00 0.883619
\(399\) 0 0
\(400\) 400.000 0.0500000
\(401\) −15930.0 −1.98381 −0.991903 0.126997i \(-0.959466\pi\)
−0.991903 + 0.126997i \(0.959466\pi\)
\(402\) 0 0
\(403\) 1551.00 0.191714
\(404\) 24.0000 0.00295556
\(405\) 0 0
\(406\) 972.000 0.118817
\(407\) 1792.00 0.218246
\(408\) 0 0
\(409\) −5891.00 −0.712203 −0.356102 0.934447i \(-0.615894\pi\)
−0.356102 + 0.934447i \(0.615894\pi\)
\(410\) −1570.00 −0.189114
\(411\) 0 0
\(412\) −640.000 −0.0765304
\(413\) −13392.0 −1.59559
\(414\) 0 0
\(415\) −2560.00 −0.302808
\(416\) 1504.00 0.177259
\(417\) 0 0
\(418\) −2304.00 −0.269599
\(419\) −15282.0 −1.78180 −0.890900 0.454199i \(-0.849926\pi\)
−0.890900 + 0.454199i \(0.849926\pi\)
\(420\) 0 0
\(421\) −10934.0 −1.26577 −0.632887 0.774244i \(-0.718130\pi\)
−0.632887 + 0.774244i \(0.718130\pi\)
\(422\) 6592.00 0.760411
\(423\) 0 0
\(424\) −112.000 −0.0128283
\(425\) −500.000 −0.0570672
\(426\) 0 0
\(427\) −9936.00 −1.12608
\(428\) −1520.00 −0.171663
\(429\) 0 0
\(430\) −180.000 −0.0201869
\(431\) 2794.00 0.312256 0.156128 0.987737i \(-0.450099\pi\)
0.156128 + 0.987737i \(0.450099\pi\)
\(432\) 0 0
\(433\) −15062.0 −1.67167 −0.835835 0.548980i \(-0.815016\pi\)
−0.835835 + 0.548980i \(0.815016\pi\)
\(434\) −1188.00 −0.131396
\(435\) 0 0
\(436\) 1000.00 0.109842
\(437\) 828.000 0.0906376
\(438\) 0 0
\(439\) 261.000 0.0283755 0.0141878 0.999899i \(-0.495484\pi\)
0.0141878 + 0.999899i \(0.495484\pi\)
\(440\) −1280.00 −0.138685
\(441\) 0 0
\(442\) −1880.00 −0.202313
\(443\) 7083.00 0.759647 0.379823 0.925059i \(-0.375985\pi\)
0.379823 + 0.925059i \(0.375985\pi\)
\(444\) 0 0
\(445\) 510.000 0.0543288
\(446\) 5440.00 0.577559
\(447\) 0 0
\(448\) −1152.00 −0.121489
\(449\) 10370.0 1.08996 0.544978 0.838450i \(-0.316538\pi\)
0.544978 + 0.838450i \(0.316538\pi\)
\(450\) 0 0
\(451\) 5024.00 0.524547
\(452\) 1560.00 0.162337
\(453\) 0 0
\(454\) −8268.00 −0.854706
\(455\) 4230.00 0.435836
\(456\) 0 0
\(457\) −10496.0 −1.07436 −0.537180 0.843468i \(-0.680510\pi\)
−0.537180 + 0.843468i \(0.680510\pi\)
\(458\) 9020.00 0.920255
\(459\) 0 0
\(460\) 460.000 0.0466252
\(461\) −18021.0 −1.82065 −0.910327 0.413889i \(-0.864170\pi\)
−0.910327 + 0.413889i \(0.864170\pi\)
\(462\) 0 0
\(463\) −17188.0 −1.72526 −0.862629 0.505838i \(-0.831183\pi\)
−0.862629 + 0.505838i \(0.831183\pi\)
\(464\) 432.000 0.0432222
\(465\) 0 0
\(466\) −10006.0 −0.994676
\(467\) 15246.0 1.51071 0.755354 0.655317i \(-0.227465\pi\)
0.755354 + 0.655317i \(0.227465\pi\)
\(468\) 0 0
\(469\) 2808.00 0.276464
\(470\) 650.000 0.0637921
\(471\) 0 0
\(472\) −5952.00 −0.580430
\(473\) 576.000 0.0559926
\(474\) 0 0
\(475\) 900.000 0.0869365
\(476\) 1440.00 0.138660
\(477\) 0 0
\(478\) −12618.0 −1.20739
\(479\) 8556.00 0.816145 0.408073 0.912949i \(-0.366201\pi\)
0.408073 + 0.912949i \(0.366201\pi\)
\(480\) 0 0
\(481\) −2632.00 −0.249499
\(482\) −6076.00 −0.574179
\(483\) 0 0
\(484\) −1228.00 −0.115327
\(485\) 2890.00 0.270573
\(486\) 0 0
\(487\) −1805.00 −0.167951 −0.0839757 0.996468i \(-0.526762\pi\)
−0.0839757 + 0.996468i \(0.526762\pi\)
\(488\) −4416.00 −0.409637
\(489\) 0 0
\(490\) 190.000 0.0175170
\(491\) −5245.00 −0.482085 −0.241042 0.970515i \(-0.577489\pi\)
−0.241042 + 0.970515i \(0.577489\pi\)
\(492\) 0 0
\(493\) −540.000 −0.0493314
\(494\) 3384.00 0.308205
\(495\) 0 0
\(496\) −528.000 −0.0477982
\(497\) 12582.0 1.13557
\(498\) 0 0
\(499\) 9027.00 0.809828 0.404914 0.914355i \(-0.367302\pi\)
0.404914 + 0.914355i \(0.367302\pi\)
\(500\) 500.000 0.0447214
\(501\) 0 0
\(502\) −2664.00 −0.236853
\(503\) −3522.00 −0.312203 −0.156102 0.987741i \(-0.549893\pi\)
−0.156102 + 0.987741i \(0.549893\pi\)
\(504\) 0 0
\(505\) 30.0000 0.00264353
\(506\) −1472.00 −0.129325
\(507\) 0 0
\(508\) −3076.00 −0.268652
\(509\) −3949.00 −0.343883 −0.171941 0.985107i \(-0.555004\pi\)
−0.171941 + 0.985107i \(0.555004\pi\)
\(510\) 0 0
\(511\) 10962.0 0.948983
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 6602.00 0.566540
\(515\) −800.000 −0.0684509
\(516\) 0 0
\(517\) −2080.00 −0.176941
\(518\) 2016.00 0.171000
\(519\) 0 0
\(520\) 1880.00 0.158545
\(521\) −3236.00 −0.272115 −0.136057 0.990701i \(-0.543443\pi\)
−0.136057 + 0.990701i \(0.543443\pi\)
\(522\) 0 0
\(523\) 12394.0 1.03624 0.518118 0.855309i \(-0.326633\pi\)
0.518118 + 0.855309i \(0.326633\pi\)
\(524\) 852.000 0.0710301
\(525\) 0 0
\(526\) 4144.00 0.343511
\(527\) 660.000 0.0545542
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) −140.000 −0.0114740
\(531\) 0 0
\(532\) −2592.00 −0.211236
\(533\) −7379.00 −0.599662
\(534\) 0 0
\(535\) −1900.00 −0.153540
\(536\) 1248.00 0.100570
\(537\) 0 0
\(538\) 11442.0 0.916914
\(539\) −608.000 −0.0485870
\(540\) 0 0
\(541\) −7159.00 −0.568927 −0.284463 0.958687i \(-0.591815\pi\)
−0.284463 + 0.958687i \(0.591815\pi\)
\(542\) 11800.0 0.935154
\(543\) 0 0
\(544\) 640.000 0.0504408
\(545\) 1250.00 0.0982461
\(546\) 0 0
\(547\) −19761.0 −1.54464 −0.772321 0.635232i \(-0.780904\pi\)
−0.772321 + 0.635232i \(0.780904\pi\)
\(548\) −11344.0 −0.884291
\(549\) 0 0
\(550\) −1600.00 −0.124044
\(551\) 972.000 0.0751517
\(552\) 0 0
\(553\) 11592.0 0.891396
\(554\) −12742.0 −0.977176
\(555\) 0 0
\(556\) −6524.00 −0.497625
\(557\) −18010.0 −1.37003 −0.685016 0.728528i \(-0.740205\pi\)
−0.685016 + 0.728528i \(0.740205\pi\)
\(558\) 0 0
\(559\) −846.000 −0.0640107
\(560\) −1440.00 −0.108663
\(561\) 0 0
\(562\) 6380.00 0.478868
\(563\) 2648.00 0.198224 0.0991118 0.995076i \(-0.468400\pi\)
0.0991118 + 0.995076i \(0.468400\pi\)
\(564\) 0 0
\(565\) 1950.00 0.145198
\(566\) 8452.00 0.627675
\(567\) 0 0
\(568\) 5592.00 0.413090
\(569\) 1566.00 0.115378 0.0576890 0.998335i \(-0.481627\pi\)
0.0576890 + 0.998335i \(0.481627\pi\)
\(570\) 0 0
\(571\) 2864.00 0.209903 0.104952 0.994477i \(-0.466531\pi\)
0.104952 + 0.994477i \(0.466531\pi\)
\(572\) −6016.00 −0.439758
\(573\) 0 0
\(574\) 5652.00 0.410993
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −929.000 −0.0670273 −0.0335137 0.999438i \(-0.510670\pi\)
−0.0335137 + 0.999438i \(0.510670\pi\)
\(578\) 9026.00 0.649537
\(579\) 0 0
\(580\) 540.000 0.0386591
\(581\) 9216.00 0.658079
\(582\) 0 0
\(583\) 448.000 0.0318255
\(584\) 4872.00 0.345214
\(585\) 0 0
\(586\) 12096.0 0.852698
\(587\) 19499.0 1.37106 0.685528 0.728046i \(-0.259571\pi\)
0.685528 + 0.728046i \(0.259571\pi\)
\(588\) 0 0
\(589\) −1188.00 −0.0831081
\(590\) −7440.00 −0.519152
\(591\) 0 0
\(592\) 896.000 0.0622050
\(593\) −6570.00 −0.454971 −0.227485 0.973782i \(-0.573050\pi\)
−0.227485 + 0.973782i \(0.573050\pi\)
\(594\) 0 0
\(595\) 1800.00 0.124022
\(596\) 7864.00 0.540473
\(597\) 0 0
\(598\) 2162.00 0.147844
\(599\) −1880.00 −0.128238 −0.0641191 0.997942i \(-0.520424\pi\)
−0.0641191 + 0.997942i \(0.520424\pi\)
\(600\) 0 0
\(601\) 3701.00 0.251193 0.125596 0.992081i \(-0.459916\pi\)
0.125596 + 0.992081i \(0.459916\pi\)
\(602\) 648.000 0.0438713
\(603\) 0 0
\(604\) 140.000 0.00943132
\(605\) −1535.00 −0.103151
\(606\) 0 0
\(607\) −3080.00 −0.205953 −0.102976 0.994684i \(-0.532837\pi\)
−0.102976 + 0.994684i \(0.532837\pi\)
\(608\) −1152.00 −0.0768417
\(609\) 0 0
\(610\) −5520.00 −0.366391
\(611\) 3055.00 0.202278
\(612\) 0 0
\(613\) 24004.0 1.58159 0.790793 0.612083i \(-0.209668\pi\)
0.790793 + 0.612083i \(0.209668\pi\)
\(614\) −17256.0 −1.13419
\(615\) 0 0
\(616\) 4608.00 0.301399
\(617\) −780.000 −0.0508940 −0.0254470 0.999676i \(-0.508101\pi\)
−0.0254470 + 0.999676i \(0.508101\pi\)
\(618\) 0 0
\(619\) 21892.0 1.42151 0.710754 0.703440i \(-0.248354\pi\)
0.710754 + 0.703440i \(0.248354\pi\)
\(620\) −660.000 −0.0427520
\(621\) 0 0
\(622\) 16494.0 1.06326
\(623\) −1836.00 −0.118070
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) −5240.00 −0.334557
\(627\) 0 0
\(628\) 6808.00 0.432594
\(629\) −1120.00 −0.0709973
\(630\) 0 0
\(631\) 8050.00 0.507869 0.253935 0.967221i \(-0.418275\pi\)
0.253935 + 0.967221i \(0.418275\pi\)
\(632\) 5152.00 0.324265
\(633\) 0 0
\(634\) 19812.0 1.24106
\(635\) −3845.00 −0.240290
\(636\) 0 0
\(637\) 893.000 0.0555447
\(638\) −1728.00 −0.107229
\(639\) 0 0
\(640\) −640.000 −0.0395285
\(641\) 25890.0 1.59531 0.797655 0.603114i \(-0.206074\pi\)
0.797655 + 0.603114i \(0.206074\pi\)
\(642\) 0 0
\(643\) 4774.00 0.292797 0.146398 0.989226i \(-0.453232\pi\)
0.146398 + 0.989226i \(0.453232\pi\)
\(644\) −1656.00 −0.101328
\(645\) 0 0
\(646\) 1440.00 0.0877029
\(647\) −3349.00 −0.203497 −0.101749 0.994810i \(-0.532444\pi\)
−0.101749 + 0.994810i \(0.532444\pi\)
\(648\) 0 0
\(649\) 23808.0 1.43998
\(650\) 2350.00 0.141807
\(651\) 0 0
\(652\) −8180.00 −0.491340
\(653\) −24813.0 −1.48699 −0.743497 0.668739i \(-0.766834\pi\)
−0.743497 + 0.668739i \(0.766834\pi\)
\(654\) 0 0
\(655\) 1065.00 0.0635313
\(656\) 2512.00 0.149508
\(657\) 0 0
\(658\) −2340.00 −0.138636
\(659\) −18180.0 −1.07465 −0.537323 0.843376i \(-0.680565\pi\)
−0.537323 + 0.843376i \(0.680565\pi\)
\(660\) 0 0
\(661\) −29250.0 −1.72117 −0.860585 0.509307i \(-0.829902\pi\)
−0.860585 + 0.509307i \(0.829902\pi\)
\(662\) 16230.0 0.952865
\(663\) 0 0
\(664\) 4096.00 0.239391
\(665\) −3240.00 −0.188935
\(666\) 0 0
\(667\) 621.000 0.0360498
\(668\) −4064.00 −0.235391
\(669\) 0 0
\(670\) 1560.00 0.0899523
\(671\) 17664.0 1.01626
\(672\) 0 0
\(673\) −23027.0 −1.31891 −0.659454 0.751745i \(-0.729213\pi\)
−0.659454 + 0.751745i \(0.729213\pi\)
\(674\) 15172.0 0.867068
\(675\) 0 0
\(676\) 48.0000 0.00273100
\(677\) −20106.0 −1.14141 −0.570706 0.821154i \(-0.693331\pi\)
−0.570706 + 0.821154i \(0.693331\pi\)
\(678\) 0 0
\(679\) −10404.0 −0.588025
\(680\) 800.000 0.0451156
\(681\) 0 0
\(682\) 2112.00 0.118582
\(683\) 18745.0 1.05016 0.525079 0.851054i \(-0.324036\pi\)
0.525079 + 0.851054i \(0.324036\pi\)
\(684\) 0 0
\(685\) −14180.0 −0.790934
\(686\) −13032.0 −0.725312
\(687\) 0 0
\(688\) 288.000 0.0159592
\(689\) −658.000 −0.0363829
\(690\) 0 0
\(691\) 24424.0 1.34462 0.672310 0.740270i \(-0.265302\pi\)
0.672310 + 0.740270i \(0.265302\pi\)
\(692\) −2392.00 −0.131402
\(693\) 0 0
\(694\) 2712.00 0.148337
\(695\) −8155.00 −0.445089
\(696\) 0 0
\(697\) −3140.00 −0.170640
\(698\) −13298.0 −0.721113
\(699\) 0 0
\(700\) −1800.00 −0.0971909
\(701\) 27278.0 1.46972 0.734862 0.678217i \(-0.237247\pi\)
0.734862 + 0.678217i \(0.237247\pi\)
\(702\) 0 0
\(703\) 2016.00 0.108158
\(704\) 2048.00 0.109640
\(705\) 0 0
\(706\) 21382.0 1.13983
\(707\) −108.000 −0.00574506
\(708\) 0 0
\(709\) 12214.0 0.646977 0.323488 0.946232i \(-0.395144\pi\)
0.323488 + 0.946232i \(0.395144\pi\)
\(710\) 6990.00 0.369479
\(711\) 0 0
\(712\) −816.000 −0.0429507
\(713\) −759.000 −0.0398664
\(714\) 0 0
\(715\) −7520.00 −0.393332
\(716\) 18428.0 0.961853
\(717\) 0 0
\(718\) −12840.0 −0.667388
\(719\) −12932.0 −0.670768 −0.335384 0.942082i \(-0.608866\pi\)
−0.335384 + 0.942082i \(0.608866\pi\)
\(720\) 0 0
\(721\) 2880.00 0.148761
\(722\) 11126.0 0.573500
\(723\) 0 0
\(724\) −4848.00 −0.248860
\(725\) 675.000 0.0345778
\(726\) 0 0
\(727\) 10046.0 0.512497 0.256249 0.966611i \(-0.417513\pi\)
0.256249 + 0.966611i \(0.417513\pi\)
\(728\) −6768.00 −0.344559
\(729\) 0 0
\(730\) 6090.00 0.308769
\(731\) −360.000 −0.0182149
\(732\) 0 0
\(733\) −5924.00 −0.298510 −0.149255 0.988799i \(-0.547688\pi\)
−0.149255 + 0.988799i \(0.547688\pi\)
\(734\) 1048.00 0.0527008
\(735\) 0 0
\(736\) −736.000 −0.0368605
\(737\) −4992.00 −0.249502
\(738\) 0 0
\(739\) 829.000 0.0412656 0.0206328 0.999787i \(-0.493432\pi\)
0.0206328 + 0.999787i \(0.493432\pi\)
\(740\) 1120.00 0.0556379
\(741\) 0 0
\(742\) 504.000 0.0249359
\(743\) −7072.00 −0.349188 −0.174594 0.984641i \(-0.555861\pi\)
−0.174594 + 0.984641i \(0.555861\pi\)
\(744\) 0 0
\(745\) 9830.00 0.483414
\(746\) −11132.0 −0.546342
\(747\) 0 0
\(748\) −2560.00 −0.125138
\(749\) 6840.00 0.333682
\(750\) 0 0
\(751\) 16234.0 0.788798 0.394399 0.918939i \(-0.370953\pi\)
0.394399 + 0.918939i \(0.370953\pi\)
\(752\) −1040.00 −0.0504320
\(753\) 0 0
\(754\) 2538.00 0.122584
\(755\) 175.000 0.00843563
\(756\) 0 0
\(757\) 9128.00 0.438260 0.219130 0.975696i \(-0.429678\pi\)
0.219130 + 0.975696i \(0.429678\pi\)
\(758\) −4480.00 −0.214671
\(759\) 0 0
\(760\) −1440.00 −0.0687293
\(761\) −165.000 −0.00785972 −0.00392986 0.999992i \(-0.501251\pi\)
−0.00392986 + 0.999992i \(0.501251\pi\)
\(762\) 0 0
\(763\) −4500.00 −0.213514
\(764\) 4232.00 0.200404
\(765\) 0 0
\(766\) 17556.0 0.828099
\(767\) −34968.0 −1.64618
\(768\) 0 0
\(769\) −20834.0 −0.976974 −0.488487 0.872571i \(-0.662451\pi\)
−0.488487 + 0.872571i \(0.662451\pi\)
\(770\) 5760.00 0.269579
\(771\) 0 0
\(772\) 4188.00 0.195245
\(773\) 31782.0 1.47881 0.739404 0.673262i \(-0.235107\pi\)
0.739404 + 0.673262i \(0.235107\pi\)
\(774\) 0 0
\(775\) −825.000 −0.0382385
\(776\) −4624.00 −0.213907
\(777\) 0 0
\(778\) 8112.00 0.373817
\(779\) 5652.00 0.259954
\(780\) 0 0
\(781\) −22368.0 −1.02483
\(782\) 920.000 0.0420705
\(783\) 0 0
\(784\) −304.000 −0.0138484
\(785\) 8510.00 0.386923
\(786\) 0 0
\(787\) 33104.0 1.49940 0.749701 0.661776i \(-0.230197\pi\)
0.749701 + 0.661776i \(0.230197\pi\)
\(788\) −1004.00 −0.0453883
\(789\) 0 0
\(790\) 6440.00 0.290032
\(791\) −7020.00 −0.315553
\(792\) 0 0
\(793\) −25944.0 −1.16179
\(794\) 18302.0 0.818027
\(795\) 0 0
\(796\) −14032.0 −0.624813
\(797\) −4736.00 −0.210486 −0.105243 0.994447i \(-0.533562\pi\)
−0.105243 + 0.994447i \(0.533562\pi\)
\(798\) 0 0
\(799\) 1300.00 0.0575603
\(800\) −800.000 −0.0353553
\(801\) 0 0
\(802\) 31860.0 1.40276
\(803\) −19488.0 −0.856434
\(804\) 0 0
\(805\) −2070.00 −0.0906309
\(806\) −3102.00 −0.135562
\(807\) 0 0
\(808\) −48.0000 −0.00208989
\(809\) 7470.00 0.324637 0.162318 0.986738i \(-0.448103\pi\)
0.162318 + 0.986738i \(0.448103\pi\)
\(810\) 0 0
\(811\) 19919.0 0.862455 0.431227 0.902243i \(-0.358081\pi\)
0.431227 + 0.902243i \(0.358081\pi\)
\(812\) −1944.00 −0.0840160
\(813\) 0 0
\(814\) −3584.00 −0.154323
\(815\) −10225.0 −0.439468
\(816\) 0 0
\(817\) 648.000 0.0277487
\(818\) 11782.0 0.503604
\(819\) 0 0
\(820\) 3140.00 0.133724
\(821\) 22694.0 0.964709 0.482354 0.875976i \(-0.339782\pi\)
0.482354 + 0.875976i \(0.339782\pi\)
\(822\) 0 0
\(823\) −31907.0 −1.35141 −0.675704 0.737173i \(-0.736160\pi\)
−0.675704 + 0.737173i \(0.736160\pi\)
\(824\) 1280.00 0.0541152
\(825\) 0 0
\(826\) 26784.0 1.12825
\(827\) 15236.0 0.640638 0.320319 0.947310i \(-0.396210\pi\)
0.320319 + 0.947310i \(0.396210\pi\)
\(828\) 0 0
\(829\) 27286.0 1.14316 0.571581 0.820545i \(-0.306330\pi\)
0.571581 + 0.820545i \(0.306330\pi\)
\(830\) 5120.00 0.214118
\(831\) 0 0
\(832\) −3008.00 −0.125341
\(833\) 380.000 0.0158058
\(834\) 0 0
\(835\) −5080.00 −0.210540
\(836\) 4608.00 0.190635
\(837\) 0 0
\(838\) 30564.0 1.25992
\(839\) −23054.0 −0.948644 −0.474322 0.880351i \(-0.657307\pi\)
−0.474322 + 0.880351i \(0.657307\pi\)
\(840\) 0 0
\(841\) −23660.0 −0.970109
\(842\) 21868.0 0.895037
\(843\) 0 0
\(844\) −13184.0 −0.537692
\(845\) 60.0000 0.00244268
\(846\) 0 0
\(847\) 5526.00 0.224174
\(848\) 224.000 0.00907098
\(849\) 0 0
\(850\) 1000.00 0.0403526
\(851\) 1288.00 0.0518826
\(852\) 0 0
\(853\) −34506.0 −1.38507 −0.692534 0.721385i \(-0.743506\pi\)
−0.692534 + 0.721385i \(0.743506\pi\)
\(854\) 19872.0 0.796260
\(855\) 0 0
\(856\) 3040.00 0.121384
\(857\) 22263.0 0.887386 0.443693 0.896179i \(-0.353668\pi\)
0.443693 + 0.896179i \(0.353668\pi\)
\(858\) 0 0
\(859\) 12851.0 0.510443 0.255221 0.966883i \(-0.417852\pi\)
0.255221 + 0.966883i \(0.417852\pi\)
\(860\) 360.000 0.0142743
\(861\) 0 0
\(862\) −5588.00 −0.220798
\(863\) −15723.0 −0.620182 −0.310091 0.950707i \(-0.600360\pi\)
−0.310091 + 0.950707i \(0.600360\pi\)
\(864\) 0 0
\(865\) −2990.00 −0.117530
\(866\) 30124.0 1.18205
\(867\) 0 0
\(868\) 2376.00 0.0929109
\(869\) −20608.0 −0.804463
\(870\) 0 0
\(871\) 7332.00 0.285230
\(872\) −2000.00 −0.0776704
\(873\) 0 0
\(874\) −1656.00 −0.0640904
\(875\) −2250.00 −0.0869302
\(876\) 0 0
\(877\) −886.000 −0.0341141 −0.0170571 0.999855i \(-0.505430\pi\)
−0.0170571 + 0.999855i \(0.505430\pi\)
\(878\) −522.000 −0.0200645
\(879\) 0 0
\(880\) 2560.00 0.0980654
\(881\) 37120.0 1.41953 0.709764 0.704439i \(-0.248801\pi\)
0.709764 + 0.704439i \(0.248801\pi\)
\(882\) 0 0
\(883\) −7524.00 −0.286753 −0.143376 0.989668i \(-0.545796\pi\)
−0.143376 + 0.989668i \(0.545796\pi\)
\(884\) 3760.00 0.143057
\(885\) 0 0
\(886\) −14166.0 −0.537151
\(887\) −9221.00 −0.349054 −0.174527 0.984652i \(-0.555840\pi\)
−0.174527 + 0.984652i \(0.555840\pi\)
\(888\) 0 0
\(889\) 13842.0 0.522211
\(890\) −1020.00 −0.0384163
\(891\) 0 0
\(892\) −10880.0 −0.408396
\(893\) −2340.00 −0.0876877
\(894\) 0 0
\(895\) 23035.0 0.860307
\(896\) 2304.00 0.0859054
\(897\) 0 0
\(898\) −20740.0 −0.770716
\(899\) −891.000 −0.0330551
\(900\) 0 0
\(901\) −280.000 −0.0103531
\(902\) −10048.0 −0.370911
\(903\) 0 0
\(904\) −3120.00 −0.114789
\(905\) −6060.00 −0.222587
\(906\) 0 0
\(907\) 29116.0 1.06591 0.532955 0.846143i \(-0.321081\pi\)
0.532955 + 0.846143i \(0.321081\pi\)
\(908\) 16536.0 0.604368
\(909\) 0 0
\(910\) −8460.00 −0.308183
\(911\) −11440.0 −0.416053 −0.208026 0.978123i \(-0.566704\pi\)
−0.208026 + 0.978123i \(0.566704\pi\)
\(912\) 0 0
\(913\) −16384.0 −0.593901
\(914\) 20992.0 0.759687
\(915\) 0 0
\(916\) −18040.0 −0.650719
\(917\) −3834.00 −0.138070
\(918\) 0 0
\(919\) 2958.00 0.106176 0.0530878 0.998590i \(-0.483094\pi\)
0.0530878 + 0.998590i \(0.483094\pi\)
\(920\) −920.000 −0.0329690
\(921\) 0 0
\(922\) 36042.0 1.28740
\(923\) 32853.0 1.17158
\(924\) 0 0
\(925\) 1400.00 0.0497640
\(926\) 34376.0 1.21994
\(927\) 0 0
\(928\) −864.000 −0.0305627
\(929\) −20907.0 −0.738360 −0.369180 0.929358i \(-0.620361\pi\)
−0.369180 + 0.929358i \(0.620361\pi\)
\(930\) 0 0
\(931\) −684.000 −0.0240786
\(932\) 20012.0 0.703342
\(933\) 0 0
\(934\) −30492.0 −1.06823
\(935\) −3200.00 −0.111926
\(936\) 0 0
\(937\) 9748.00 0.339865 0.169932 0.985456i \(-0.445645\pi\)
0.169932 + 0.985456i \(0.445645\pi\)
\(938\) −5616.00 −0.195489
\(939\) 0 0
\(940\) −1300.00 −0.0451078
\(941\) −19624.0 −0.679834 −0.339917 0.940455i \(-0.610399\pi\)
−0.339917 + 0.940455i \(0.610399\pi\)
\(942\) 0 0
\(943\) 3611.00 0.124698
\(944\) 11904.0 0.410426
\(945\) 0 0
\(946\) −1152.00 −0.0395928
\(947\) 41859.0 1.43636 0.718181 0.695856i \(-0.244975\pi\)
0.718181 + 0.695856i \(0.244975\pi\)
\(948\) 0 0
\(949\) 28623.0 0.979075
\(950\) −1800.00 −0.0614734
\(951\) 0 0
\(952\) −2880.00 −0.0980476
\(953\) −29226.0 −0.993413 −0.496707 0.867918i \(-0.665458\pi\)
−0.496707 + 0.867918i \(0.665458\pi\)
\(954\) 0 0
\(955\) 5290.00 0.179246
\(956\) 25236.0 0.853756
\(957\) 0 0
\(958\) −17112.0 −0.577102
\(959\) 51048.0 1.71890
\(960\) 0 0
\(961\) −28702.0 −0.963445
\(962\) 5264.00 0.176422
\(963\) 0 0
\(964\) 12152.0 0.406006
\(965\) 5235.00 0.174633
\(966\) 0 0
\(967\) −29849.0 −0.992636 −0.496318 0.868141i \(-0.665315\pi\)
−0.496318 + 0.868141i \(0.665315\pi\)
\(968\) 2456.00 0.0815484
\(969\) 0 0
\(970\) −5780.00 −0.191324
\(971\) 9390.00 0.310339 0.155170 0.987888i \(-0.450408\pi\)
0.155170 + 0.987888i \(0.450408\pi\)
\(972\) 0 0
\(973\) 29358.0 0.967291
\(974\) 3610.00 0.118760
\(975\) 0 0
\(976\) 8832.00 0.289657
\(977\) −33536.0 −1.09817 −0.549085 0.835767i \(-0.685024\pi\)
−0.549085 + 0.835767i \(0.685024\pi\)
\(978\) 0 0
\(979\) 3264.00 0.106556
\(980\) −380.000 −0.0123864
\(981\) 0 0
\(982\) 10490.0 0.340885
\(983\) −28994.0 −0.940758 −0.470379 0.882465i \(-0.655883\pi\)
−0.470379 + 0.882465i \(0.655883\pi\)
\(984\) 0 0
\(985\) −1255.00 −0.0405966
\(986\) 1080.00 0.0348826
\(987\) 0 0
\(988\) −6768.00 −0.217934
\(989\) 414.000 0.0133109
\(990\) 0 0
\(991\) 11272.0 0.361319 0.180659 0.983546i \(-0.442177\pi\)
0.180659 + 0.983546i \(0.442177\pi\)
\(992\) 1056.00 0.0337984
\(993\) 0 0
\(994\) −25164.0 −0.802971
\(995\) −17540.0 −0.558850
\(996\) 0 0
\(997\) 61186.0 1.94361 0.971805 0.235784i \(-0.0757658\pi\)
0.971805 + 0.235784i \(0.0757658\pi\)
\(998\) −18054.0 −0.572635
\(999\) 0 0
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 2070.4.a.e.1.1 1
3.2 odd 2 230.4.a.e.1.1 1
12.11 even 2 1840.4.a.d.1.1 1
15.2 even 4 1150.4.b.f.599.2 2
15.8 even 4 1150.4.b.f.599.1 2
15.14 odd 2 1150.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.e.1.1 1 3.2 odd 2
1150.4.a.b.1.1 1 15.14 odd 2
1150.4.b.f.599.1 2 15.8 even 4
1150.4.b.f.599.2 2 15.2 even 4
1840.4.a.d.1.1 1 12.11 even 2
2070.4.a.e.1.1 1 1.1 even 1 trivial