Properties

Label 230.4.a.e.1.1
Level $230$
Weight $4$
Character 230.1
Self dual yes
Analytic conductor $13.570$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.5704393013\)
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 \(\chi\) \(=\) 230.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.00000 q^{6} -18.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.00000 q^{6} -18.0000 q^{7} +8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -32.0000 q^{11} +4.00000 q^{12} -47.0000 q^{13} -36.0000 q^{14} -5.00000 q^{15} +16.0000 q^{16} +20.0000 q^{17} -52.0000 q^{18} +36.0000 q^{19} -20.0000 q^{20} -18.0000 q^{21} -64.0000 q^{22} -23.0000 q^{23} +8.00000 q^{24} +25.0000 q^{25} -94.0000 q^{26} -53.0000 q^{27} -72.0000 q^{28} -27.0000 q^{29} -10.0000 q^{30} -33.0000 q^{31} +32.0000 q^{32} -32.0000 q^{33} +40.0000 q^{34} +90.0000 q^{35} -104.000 q^{36} +56.0000 q^{37} +72.0000 q^{38} -47.0000 q^{39} -40.0000 q^{40} -157.000 q^{41} -36.0000 q^{42} +18.0000 q^{43} -128.000 q^{44} +130.000 q^{45} -46.0000 q^{46} +65.0000 q^{47} +16.0000 q^{48} -19.0000 q^{49} +50.0000 q^{50} +20.0000 q^{51} -188.000 q^{52} -14.0000 q^{53} -106.000 q^{54} +160.000 q^{55} -144.000 q^{56} +36.0000 q^{57} -54.0000 q^{58} -744.000 q^{59} -20.0000 q^{60} +552.000 q^{61} -66.0000 q^{62} +468.000 q^{63} +64.0000 q^{64} +235.000 q^{65} -64.0000 q^{66} -156.000 q^{67} +80.0000 q^{68} -23.0000 q^{69} +180.000 q^{70} +699.000 q^{71} -208.000 q^{72} -609.000 q^{73} +112.000 q^{74} +25.0000 q^{75} +144.000 q^{76} +576.000 q^{77} -94.0000 q^{78} -644.000 q^{79} -80.0000 q^{80} +649.000 q^{81} -314.000 q^{82} +512.000 q^{83} -72.0000 q^{84} -100.000 q^{85} +36.0000 q^{86} -27.0000 q^{87} -256.000 q^{88} -102.000 q^{89} +260.000 q^{90} +846.000 q^{91} -92.0000 q^{92} -33.0000 q^{93} +130.000 q^{94} -180.000 q^{95} +32.0000 q^{96} +578.000 q^{97} -38.0000 q^{98} +832.000 q^{99} +O(q^{100})\)

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
\(3\) 1.00000 0.192450 0.0962250 0.995360i \(-0.469323\pi\)
0.0962250 + 0.995360i \(0.469323\pi\)
\(4\) 4.00000 0.500000
\(5\) −5.00000 −0.447214
\(6\) 2.00000 0.136083
\(7\) −18.0000 −0.971909 −0.485954 0.873984i \(-0.661528\pi\)
−0.485954 + 0.873984i \(0.661528\pi\)
\(8\) 8.00000 0.353553
\(9\) −26.0000 −0.962963
\(10\) −10.0000 −0.316228
\(11\) −32.0000 −0.877124 −0.438562 0.898701i \(-0.644512\pi\)
−0.438562 + 0.898701i \(0.644512\pi\)
\(12\) 4.00000 0.0962250
\(13\) −47.0000 −1.00273 −0.501364 0.865237i \(-0.667168\pi\)
−0.501364 + 0.865237i \(0.667168\pi\)
\(14\) −36.0000 −0.687243
\(15\) −5.00000 −0.0860663
\(16\) 16.0000 0.250000
\(17\) 20.0000 0.285336 0.142668 0.989771i \(-0.454432\pi\)
0.142668 + 0.989771i \(0.454432\pi\)
\(18\) −52.0000 −0.680918
\(19\) 36.0000 0.434682 0.217341 0.976096i \(-0.430262\pi\)
0.217341 + 0.976096i \(0.430262\pi\)
\(20\) −20.0000 −0.223607
\(21\) −18.0000 −0.187044
\(22\) −64.0000 −0.620220
\(23\) −23.0000 −0.208514
\(24\) 8.00000 0.0680414
\(25\) 25.0000 0.200000
\(26\) −94.0000 −0.709035
\(27\) −53.0000 −0.377772
\(28\) −72.0000 −0.485954
\(29\) −27.0000 −0.172889 −0.0864444 0.996257i \(-0.527550\pi\)
−0.0864444 + 0.996257i \(0.527550\pi\)
\(30\) −10.0000 −0.0608581
\(31\) −33.0000 −0.191193 −0.0955964 0.995420i \(-0.530476\pi\)
−0.0955964 + 0.995420i \(0.530476\pi\)
\(32\) 32.0000 0.176777
\(33\) −32.0000 −0.168803
\(34\) 40.0000 0.201763
\(35\) 90.0000 0.434651
\(36\) −104.000 −0.481481
\(37\) 56.0000 0.248820 0.124410 0.992231i \(-0.460296\pi\)
0.124410 + 0.992231i \(0.460296\pi\)
\(38\) 72.0000 0.307367
\(39\) −47.0000 −0.192975
\(40\) −40.0000 −0.158114
\(41\) −157.000 −0.598031 −0.299016 0.954248i \(-0.596658\pi\)
−0.299016 + 0.954248i \(0.596658\pi\)
\(42\) −36.0000 −0.132260
\(43\) 18.0000 0.0638366 0.0319183 0.999490i \(-0.489838\pi\)
0.0319183 + 0.999490i \(0.489838\pi\)
\(44\) −128.000 −0.438562
\(45\) 130.000 0.430650
\(46\) −46.0000 −0.147442
\(47\) 65.0000 0.201728 0.100864 0.994900i \(-0.467839\pi\)
0.100864 + 0.994900i \(0.467839\pi\)
\(48\) 16.0000 0.0481125
\(49\) −19.0000 −0.0553936
\(50\) 50.0000 0.141421
\(51\) 20.0000 0.0549129
\(52\) −188.000 −0.501364
\(53\) −14.0000 −0.0362839 −0.0181420 0.999835i \(-0.505775\pi\)
−0.0181420 + 0.999835i \(0.505775\pi\)
\(54\) −106.000 −0.267125
\(55\) 160.000 0.392262
\(56\) −144.000 −0.343622
\(57\) 36.0000 0.0836547
\(58\) −54.0000 −0.122251
\(59\) −744.000 −1.64170 −0.820852 0.571141i \(-0.806501\pi\)
−0.820852 + 0.571141i \(0.806501\pi\)
\(60\) −20.0000 −0.0430331
\(61\) 552.000 1.15863 0.579314 0.815104i \(-0.303320\pi\)
0.579314 + 0.815104i \(0.303320\pi\)
\(62\) −66.0000 −0.135194
\(63\) 468.000 0.935912
\(64\) 64.0000 0.125000
\(65\) 235.000 0.448433
\(66\) −64.0000 −0.119361
\(67\) −156.000 −0.284454 −0.142227 0.989834i \(-0.545426\pi\)
−0.142227 + 0.989834i \(0.545426\pi\)
\(68\) 80.0000 0.142668
\(69\) −23.0000 −0.0401286
\(70\) 180.000 0.307344
\(71\) 699.000 1.16839 0.584197 0.811612i \(-0.301409\pi\)
0.584197 + 0.811612i \(0.301409\pi\)
\(72\) −208.000 −0.340459
\(73\) −609.000 −0.976412 −0.488206 0.872728i \(-0.662348\pi\)
−0.488206 + 0.872728i \(0.662348\pi\)
\(74\) 112.000 0.175942
\(75\) 25.0000 0.0384900
\(76\) 144.000 0.217341
\(77\) 576.000 0.852484
\(78\) −94.0000 −0.136454
\(79\) −644.000 −0.917160 −0.458580 0.888653i \(-0.651642\pi\)
−0.458580 + 0.888653i \(0.651642\pi\)
\(80\) −80.0000 −0.111803
\(81\) 649.000 0.890261
\(82\) −314.000 −0.422872
\(83\) 512.000 0.677100 0.338550 0.940948i \(-0.390064\pi\)
0.338550 + 0.940948i \(0.390064\pi\)
\(84\) −72.0000 −0.0935220
\(85\) −100.000 −0.127606
\(86\) 36.0000 0.0451393
\(87\) −27.0000 −0.0332725
\(88\) −256.000 −0.310110
\(89\) −102.000 −0.121483 −0.0607415 0.998154i \(-0.519347\pi\)
−0.0607415 + 0.998154i \(0.519347\pi\)
\(90\) 260.000 0.304516
\(91\) 846.000 0.974559
\(92\) −92.0000 −0.104257
\(93\) −33.0000 −0.0367951
\(94\) 130.000 0.142643
\(95\) −180.000 −0.194396
\(96\) 32.0000 0.0340207
\(97\) 578.000 0.605021 0.302510 0.953146i \(-0.402175\pi\)
0.302510 + 0.953146i \(0.402175\pi\)
\(98\) −38.0000 −0.0391692
\(99\) 832.000 0.844638
\(100\) 100.000 0.100000
\(101\) −6.00000 −0.00591111 −0.00295556 0.999996i \(-0.500941\pi\)
−0.00295556 + 0.999996i \(0.500941\pi\)
\(102\) 40.0000 0.0388293
\(103\) −160.000 −0.153061 −0.0765304 0.997067i \(-0.524384\pi\)
−0.0765304 + 0.997067i \(0.524384\pi\)
\(104\) −376.000 −0.354518
\(105\) 90.0000 0.0836486
\(106\) −28.0000 −0.0256566
\(107\) 380.000 0.343327 0.171663 0.985156i \(-0.445086\pi\)
0.171663 + 0.985156i \(0.445086\pi\)
\(108\) −212.000 −0.188886
\(109\) 250.000 0.219685 0.109842 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(110\) 320.000 0.277371
\(111\) 56.0000 0.0478854
\(112\) −288.000 −0.242977
\(113\) −390.000 −0.324674 −0.162337 0.986735i \(-0.551903\pi\)
−0.162337 + 0.986735i \(0.551903\pi\)
\(114\) 72.0000 0.0591528
\(115\) 115.000 0.0932505
\(116\) −108.000 −0.0864444
\(117\) 1222.00 0.965589
\(118\) −1488.00 −1.16086
\(119\) −360.000 −0.277321
\(120\) −40.0000 −0.0304290
\(121\) −307.000 −0.230654
\(122\) 1104.00 0.819274
\(123\) −157.000 −0.115091
\(124\) −132.000 −0.0955964
\(125\) −125.000 −0.0894427
\(126\) 936.000 0.661790
\(127\) −769.000 −0.537305 −0.268652 0.963237i \(-0.586578\pi\)
−0.268652 + 0.963237i \(0.586578\pi\)
\(128\) 128.000 0.0883883
\(129\) 18.0000 0.0122854
\(130\) 470.000 0.317090
\(131\) −213.000 −0.142060 −0.0710301 0.997474i \(-0.522629\pi\)
−0.0710301 + 0.997474i \(0.522629\pi\)
\(132\) −128.000 −0.0844013
\(133\) −648.000 −0.422472
\(134\) −312.000 −0.201140
\(135\) 265.000 0.168945
\(136\) 160.000 0.100882
\(137\) 2836.00 1.76858 0.884291 0.466936i \(-0.154642\pi\)
0.884291 + 0.466936i \(0.154642\pi\)
\(138\) −46.0000 −0.0283752
\(139\) −1631.00 −0.995249 −0.497625 0.867393i \(-0.665794\pi\)
−0.497625 + 0.867393i \(0.665794\pi\)
\(140\) 360.000 0.217325
\(141\) 65.0000 0.0388226
\(142\) 1398.00 0.826180
\(143\) 1504.00 0.879516
\(144\) −416.000 −0.240741
\(145\) 135.000 0.0773182
\(146\) −1218.00 −0.690427
\(147\) −19.0000 −0.0106605
\(148\) 224.000 0.124410
\(149\) −1966.00 −1.08095 −0.540473 0.841361i \(-0.681755\pi\)
−0.540473 + 0.841361i \(0.681755\pi\)
\(150\) 50.0000 0.0272166
\(151\) 35.0000 0.0188626 0.00943132 0.999956i \(-0.496998\pi\)
0.00943132 + 0.999956i \(0.496998\pi\)
\(152\) 288.000 0.153683
\(153\) −520.000 −0.274768
\(154\) 1152.00 0.602797
\(155\) 165.000 0.0855040
\(156\) −188.000 −0.0964875
\(157\) 1702.00 0.865187 0.432594 0.901589i \(-0.357599\pi\)
0.432594 + 0.901589i \(0.357599\pi\)
\(158\) −1288.00 −0.648530
\(159\) −14.0000 −0.00698284
\(160\) −160.000 −0.0790569
\(161\) 414.000 0.202657
\(162\) 1298.00 0.629509
\(163\) −2045.00 −0.982680 −0.491340 0.870968i \(-0.663493\pi\)
−0.491340 + 0.870968i \(0.663493\pi\)
\(164\) −628.000 −0.299016
\(165\) 160.000 0.0754908
\(166\) 1024.00 0.478782
\(167\) 1016.00 0.470781 0.235391 0.971901i \(-0.424363\pi\)
0.235391 + 0.971901i \(0.424363\pi\)
\(168\) −144.000 −0.0661300
\(169\) 12.0000 0.00546199
\(170\) −200.000 −0.0902312
\(171\) −936.000 −0.418583
\(172\) 72.0000 0.0319183
\(173\) 598.000 0.262804 0.131402 0.991329i \(-0.458052\pi\)
0.131402 + 0.991329i \(0.458052\pi\)
\(174\) −54.0000 −0.0235272
\(175\) −450.000 −0.194382
\(176\) −512.000 −0.219281
\(177\) −744.000 −0.315946
\(178\) −204.000 −0.0859014
\(179\) −4607.00 −1.92371 −0.961853 0.273567i \(-0.911796\pi\)
−0.961853 + 0.273567i \(0.911796\pi\)
\(180\) 520.000 0.215325
\(181\) −1212.00 −0.497720 −0.248860 0.968540i \(-0.580056\pi\)
−0.248860 + 0.968540i \(0.580056\pi\)
\(182\) 1692.00 0.689117
\(183\) 552.000 0.222978
\(184\) −184.000 −0.0737210
\(185\) −280.000 −0.111276
\(186\) −66.0000 −0.0260180
\(187\) −640.000 −0.250275
\(188\) 260.000 0.100864
\(189\) 954.000 0.367160
\(190\) −360.000 −0.137459
\(191\) −1058.00 −0.400807 −0.200404 0.979713i \(-0.564225\pi\)
−0.200404 + 0.979713i \(0.564225\pi\)
\(192\) 64.0000 0.0240563
\(193\) 1047.00 0.390491 0.195245 0.980754i \(-0.437450\pi\)
0.195245 + 0.980754i \(0.437450\pi\)
\(194\) 1156.00 0.427814
\(195\) 235.000 0.0863010
\(196\) −76.0000 −0.0276968
\(197\) 251.000 0.0907767 0.0453883 0.998969i \(-0.485547\pi\)
0.0453883 + 0.998969i \(0.485547\pi\)
\(198\) 1664.00 0.597249
\(199\) −3508.00 −1.24963 −0.624813 0.780775i \(-0.714825\pi\)
−0.624813 + 0.780775i \(0.714825\pi\)
\(200\) 200.000 0.0707107
\(201\) −156.000 −0.0547432
\(202\) −12.0000 −0.00417979
\(203\) 486.000 0.168032
\(204\) 80.0000 0.0274565
\(205\) 785.000 0.267448
\(206\) −320.000 −0.108230
\(207\) 598.000 0.200792
\(208\) −752.000 −0.250682
\(209\) −1152.00 −0.381270
\(210\) 180.000 0.0591485
\(211\) −3296.00 −1.07538 −0.537692 0.843141i \(-0.680704\pi\)
−0.537692 + 0.843141i \(0.680704\pi\)
\(212\) −56.0000 −0.0181420
\(213\) 699.000 0.224858
\(214\) 760.000 0.242769
\(215\) −90.0000 −0.0285486
\(216\) −424.000 −0.133563
\(217\) 594.000 0.185822
\(218\) 500.000 0.155341
\(219\) −609.000 −0.187911
\(220\) 640.000 0.196131
\(221\) −940.000 −0.286114
\(222\) 112.000 0.0338601
\(223\) −2720.00 −0.816792 −0.408396 0.912805i \(-0.633912\pi\)
−0.408396 + 0.912805i \(0.633912\pi\)
\(224\) −576.000 −0.171811
\(225\) −650.000 −0.192593
\(226\) −780.000 −0.229579
\(227\) −4134.00 −1.20874 −0.604368 0.796705i \(-0.706574\pi\)
−0.604368 + 0.796705i \(0.706574\pi\)
\(228\) 144.000 0.0418273
\(229\) −4510.00 −1.30144 −0.650719 0.759319i \(-0.725532\pi\)
−0.650719 + 0.759319i \(0.725532\pi\)
\(230\) 230.000 0.0659380
\(231\) 576.000 0.164061
\(232\) −216.000 −0.0611254
\(233\) −5003.00 −1.40668 −0.703342 0.710852i \(-0.748310\pi\)
−0.703342 + 0.710852i \(0.748310\pi\)
\(234\) 2444.00 0.682775
\(235\) −325.000 −0.0902156
\(236\) −2976.00 −0.820852
\(237\) −644.000 −0.176508
\(238\) −720.000 −0.196095
\(239\) −6309.00 −1.70751 −0.853756 0.520674i \(-0.825681\pi\)
−0.853756 + 0.520674i \(0.825681\pi\)
\(240\) −80.0000 −0.0215166
\(241\) 3038.00 0.812012 0.406006 0.913871i \(-0.366921\pi\)
0.406006 + 0.913871i \(0.366921\pi\)
\(242\) −614.000 −0.163097
\(243\) 2080.00 0.549103
\(244\) 2208.00 0.579314
\(245\) 95.0000 0.0247728
\(246\) −314.000 −0.0813817
\(247\) −1692.00 −0.435868
\(248\) −264.000 −0.0675968
\(249\) 512.000 0.130308
\(250\) −250.000 −0.0632456
\(251\) −1332.00 −0.334961 −0.167480 0.985875i \(-0.553563\pi\)
−0.167480 + 0.985875i \(0.553563\pi\)
\(252\) 1872.00 0.467956
\(253\) 736.000 0.182893
\(254\) −1538.00 −0.379932
\(255\) −100.000 −0.0245578
\(256\) 256.000 0.0625000
\(257\) 3301.00 0.801209 0.400605 0.916251i \(-0.368800\pi\)
0.400605 + 0.916251i \(0.368800\pi\)
\(258\) 36.0000 0.00868706
\(259\) −1008.00 −0.241830
\(260\) 940.000 0.224217
\(261\) 702.000 0.166485
\(262\) −426.000 −0.100452
\(263\) 2072.00 0.485798 0.242899 0.970052i \(-0.421902\pi\)
0.242899 + 0.970052i \(0.421902\pi\)
\(264\) −256.000 −0.0596807
\(265\) 70.0000 0.0162267
\(266\) −1296.00 −0.298733
\(267\) −102.000 −0.0233794
\(268\) −624.000 −0.142227
\(269\) 5721.00 1.29671 0.648356 0.761337i \(-0.275457\pi\)
0.648356 + 0.761337i \(0.275457\pi\)
\(270\) 530.000 0.119462
\(271\) −5900.00 −1.32251 −0.661254 0.750162i \(-0.729975\pi\)
−0.661254 + 0.750162i \(0.729975\pi\)
\(272\) 320.000 0.0713340
\(273\) 846.000 0.187554
\(274\) 5672.00 1.25058
\(275\) −800.000 −0.175425
\(276\) −92.0000 −0.0200643
\(277\) 6371.00 1.38194 0.690968 0.722885i \(-0.257185\pi\)
0.690968 + 0.722885i \(0.257185\pi\)
\(278\) −3262.00 −0.703747
\(279\) 858.000 0.184112
\(280\) 720.000 0.153672
\(281\) 3190.00 0.677222 0.338611 0.940926i \(-0.390043\pi\)
0.338611 + 0.940926i \(0.390043\pi\)
\(282\) 130.000 0.0274517
\(283\) −4226.00 −0.887667 −0.443833 0.896109i \(-0.646382\pi\)
−0.443833 + 0.896109i \(0.646382\pi\)
\(284\) 2796.00 0.584197
\(285\) −180.000 −0.0374115
\(286\) 3008.00 0.621912
\(287\) 2826.00 0.581232
\(288\) −832.000 −0.170229
\(289\) −4513.00 −0.918583
\(290\) 270.000 0.0546722
\(291\) 578.000 0.116436
\(292\) −2436.00 −0.488206
\(293\) 6048.00 1.20590 0.602949 0.797780i \(-0.293992\pi\)
0.602949 + 0.797780i \(0.293992\pi\)
\(294\) −38.0000 −0.00753811
\(295\) 3720.00 0.734192
\(296\) 448.000 0.0879712
\(297\) 1696.00 0.331353
\(298\) −3932.00 −0.764344
\(299\) 1081.00 0.209083
\(300\) 100.000 0.0192450
\(301\) −324.000 −0.0620434
\(302\) 70.0000 0.0133379
\(303\) −6.00000 −0.00113759
\(304\) 576.000 0.108671
\(305\) −2760.00 −0.518155
\(306\) −1040.00 −0.194290
\(307\) 8628.00 1.60399 0.801997 0.597328i \(-0.203771\pi\)
0.801997 + 0.597328i \(0.203771\pi\)
\(308\) 2304.00 0.426242
\(309\) −160.000 −0.0294566
\(310\) 330.000 0.0604605
\(311\) 8247.00 1.50368 0.751840 0.659346i \(-0.229167\pi\)
0.751840 + 0.659346i \(0.229167\pi\)
\(312\) −376.000 −0.0682269
\(313\) 2620.00 0.473135 0.236567 0.971615i \(-0.423978\pi\)
0.236567 + 0.971615i \(0.423978\pi\)
\(314\) 3404.00 0.611780
\(315\) −2340.00 −0.418553
\(316\) −2576.00 −0.458580
\(317\) 9906.00 1.75513 0.877565 0.479457i \(-0.159166\pi\)
0.877565 + 0.479457i \(0.159166\pi\)
\(318\) −28.0000 −0.00493762
\(319\) 864.000 0.151645
\(320\) −320.000 −0.0559017
\(321\) 380.000 0.0660733
\(322\) 828.000 0.143300
\(323\) 720.000 0.124031
\(324\) 2596.00 0.445130
\(325\) −1175.00 −0.200545
\(326\) −4090.00 −0.694859
\(327\) 250.000 0.0422784
\(328\) −1256.00 −0.211436
\(329\) −1170.00 −0.196061
\(330\) 320.000 0.0533801
\(331\) −8115.00 −1.34756 −0.673778 0.738934i \(-0.735329\pi\)
−0.673778 + 0.738934i \(0.735329\pi\)
\(332\) 2048.00 0.338550
\(333\) −1456.00 −0.239605
\(334\) 2032.00 0.332892
\(335\) 780.000 0.127212
\(336\) −288.000 −0.0467610
\(337\) −7586.00 −1.22622 −0.613109 0.789998i \(-0.710082\pi\)
−0.613109 + 0.789998i \(0.710082\pi\)
\(338\) 24.0000 0.00386221
\(339\) −390.000 −0.0624835
\(340\) −400.000 −0.0638031
\(341\) 1056.00 0.167700
\(342\) −1872.00 −0.295983
\(343\) 6516.00 1.02575
\(344\) 144.000 0.0225697
\(345\) 115.000 0.0179461
\(346\) 1196.00 0.185831
\(347\) 1356.00 0.209781 0.104890 0.994484i \(-0.466551\pi\)
0.104890 + 0.994484i \(0.466551\pi\)
\(348\) −108.000 −0.0166362
\(349\) 6649.00 1.01981 0.509904 0.860231i \(-0.329681\pi\)
0.509904 + 0.860231i \(0.329681\pi\)
\(350\) −900.000 −0.137449
\(351\) 2491.00 0.378803
\(352\) −1024.00 −0.155055
\(353\) 10691.0 1.61197 0.805984 0.591938i \(-0.201637\pi\)
0.805984 + 0.591938i \(0.201637\pi\)
\(354\) −1488.00 −0.223408
\(355\) −3495.00 −0.522522
\(356\) −408.000 −0.0607415
\(357\) −360.000 −0.0533704
\(358\) −9214.00 −1.36027
\(359\) −6420.00 −0.943829 −0.471915 0.881644i \(-0.656437\pi\)
−0.471915 + 0.881644i \(0.656437\pi\)
\(360\) 1040.00 0.152258
\(361\) −5563.00 −0.811051
\(362\) −2424.00 −0.351941
\(363\) −307.000 −0.0443893
\(364\) 3384.00 0.487280
\(365\) 3045.00 0.436665
\(366\) 1104.00 0.157669
\(367\) −524.000 −0.0745302 −0.0372651 0.999305i \(-0.511865\pi\)
−0.0372651 + 0.999305i \(0.511865\pi\)
\(368\) −368.000 −0.0521286
\(369\) 4082.00 0.575882
\(370\) −560.000 −0.0786838
\(371\) 252.000 0.0352647
\(372\) −132.000 −0.0183975
\(373\) 5566.00 0.772645 0.386322 0.922364i \(-0.373745\pi\)
0.386322 + 0.922364i \(0.373745\pi\)
\(374\) −1280.00 −0.176971
\(375\) −125.000 −0.0172133
\(376\) 520.000 0.0713217
\(377\) 1269.00 0.173360
\(378\) 1908.00 0.259622
\(379\) 2240.00 0.303591 0.151796 0.988412i \(-0.451494\pi\)
0.151796 + 0.988412i \(0.451494\pi\)
\(380\) −720.000 −0.0971979
\(381\) −769.000 −0.103404
\(382\) −2116.00 −0.283414
\(383\) 8778.00 1.17111 0.585555 0.810633i \(-0.300877\pi\)
0.585555 + 0.810633i \(0.300877\pi\)
\(384\) 128.000 0.0170103
\(385\) −2880.00 −0.381243
\(386\) 2094.00 0.276119
\(387\) −468.000 −0.0614723
\(388\) 2312.00 0.302510
\(389\) 4056.00 0.528656 0.264328 0.964433i \(-0.414850\pi\)
0.264328 + 0.964433i \(0.414850\pi\)
\(390\) 470.000 0.0610240
\(391\) −460.000 −0.0594967
\(392\) −152.000 −0.0195846
\(393\) −213.000 −0.0273395
\(394\) 502.000 0.0641888
\(395\) 3220.00 0.410167
\(396\) 3328.00 0.422319
\(397\) −9151.00 −1.15687 −0.578433 0.815730i \(-0.696335\pi\)
−0.578433 + 0.815730i \(0.696335\pi\)
\(398\) −7016.00 −0.883619
\(399\) −648.000 −0.0813047
\(400\) 400.000 0.0500000
\(401\) 15930.0 1.98381 0.991903 0.126997i \(-0.0405340\pi\)
0.991903 + 0.126997i \(0.0405340\pi\)
\(402\) −312.000 −0.0387093
\(403\) 1551.00 0.191714
\(404\) −24.0000 −0.00295556
\(405\) −3245.00 −0.398137
\(406\) 972.000 0.118817
\(407\) −1792.00 −0.218246
\(408\) 160.000 0.0194147
\(409\) −5891.00 −0.712203 −0.356102 0.934447i \(-0.615894\pi\)
−0.356102 + 0.934447i \(0.615894\pi\)
\(410\) 1570.00 0.189114
\(411\) 2836.00 0.340364
\(412\) −640.000 −0.0765304
\(413\) 13392.0 1.59559
\(414\) 1196.00 0.141981
\(415\) −2560.00 −0.302808
\(416\) −1504.00 −0.177259
\(417\) −1631.00 −0.191536
\(418\) −2304.00 −0.269599
\(419\) 15282.0 1.78180 0.890900 0.454199i \(-0.150074\pi\)
0.890900 + 0.454199i \(0.150074\pi\)
\(420\) 360.000 0.0418243
\(421\) −10934.0 −1.26577 −0.632887 0.774244i \(-0.718130\pi\)
−0.632887 + 0.774244i \(0.718130\pi\)
\(422\) −6592.00 −0.760411
\(423\) −1690.00 −0.194257
\(424\) −112.000 −0.0128283
\(425\) 500.000 0.0570672
\(426\) 1398.00 0.158998
\(427\) −9936.00 −1.12608
\(428\) 1520.00 0.171663
\(429\) 1504.00 0.169263
\(430\) −180.000 −0.0201869
\(431\) −2794.00 −0.312256 −0.156128 0.987737i \(-0.549901\pi\)
−0.156128 + 0.987737i \(0.549901\pi\)
\(432\) −848.000 −0.0944431
\(433\) −15062.0 −1.67167 −0.835835 0.548980i \(-0.815016\pi\)
−0.835835 + 0.548980i \(0.815016\pi\)
\(434\) 1188.00 0.131396
\(435\) 135.000 0.0148799
\(436\) 1000.00 0.109842
\(437\) −828.000 −0.0906376
\(438\) −1218.00 −0.132873
\(439\) 261.000 0.0283755 0.0141878 0.999899i \(-0.495484\pi\)
0.0141878 + 0.999899i \(0.495484\pi\)
\(440\) 1280.00 0.138685
\(441\) 494.000 0.0533420
\(442\) −1880.00 −0.202313
\(443\) −7083.00 −0.759647 −0.379823 0.925059i \(-0.624015\pi\)
−0.379823 + 0.925059i \(0.624015\pi\)
\(444\) 224.000 0.0239427
\(445\) 510.000 0.0543288
\(446\) −5440.00 −0.577559
\(447\) −1966.00 −0.208028
\(448\) −1152.00 −0.121489
\(449\) −10370.0 −1.08996 −0.544978 0.838450i \(-0.683462\pi\)
−0.544978 + 0.838450i \(0.683462\pi\)
\(450\) −1300.00 −0.136184
\(451\) 5024.00 0.524547
\(452\) −1560.00 −0.162337
\(453\) 35.0000 0.00363012
\(454\) −8268.00 −0.854706
\(455\) −4230.00 −0.435836
\(456\) 288.000 0.0295764
\(457\) −10496.0 −1.07436 −0.537180 0.843468i \(-0.680510\pi\)
−0.537180 + 0.843468i \(0.680510\pi\)
\(458\) −9020.00 −0.920255
\(459\) −1060.00 −0.107792
\(460\) 460.000 0.0466252
\(461\) 18021.0 1.82065 0.910327 0.413889i \(-0.135830\pi\)
0.910327 + 0.413889i \(0.135830\pi\)
\(462\) 1152.00 0.116008
\(463\) −17188.0 −1.72526 −0.862629 0.505838i \(-0.831183\pi\)
−0.862629 + 0.505838i \(0.831183\pi\)
\(464\) −432.000 −0.0432222
\(465\) 165.000 0.0164553
\(466\) −10006.0 −0.994676
\(467\) −15246.0 −1.51071 −0.755354 0.655317i \(-0.772535\pi\)
−0.755354 + 0.655317i \(0.772535\pi\)
\(468\) 4888.00 0.482795
\(469\) 2808.00 0.276464
\(470\) −650.000 −0.0637921
\(471\) 1702.00 0.166505
\(472\) −5952.00 −0.580430
\(473\) −576.000 −0.0559926
\(474\) −1288.00 −0.124810
\(475\) 900.000 0.0869365
\(476\) −1440.00 −0.138660
\(477\) 364.000 0.0349401
\(478\) −12618.0 −1.20739
\(479\) −8556.00 −0.816145 −0.408073 0.912949i \(-0.633799\pi\)
−0.408073 + 0.912949i \(0.633799\pi\)
\(480\) −160.000 −0.0152145
\(481\) −2632.00 −0.249499
\(482\) 6076.00 0.574179
\(483\) 414.000 0.0390014
\(484\) −1228.00 −0.115327
\(485\) −2890.00 −0.270573
\(486\) 4160.00 0.388275
\(487\) −1805.00 −0.167951 −0.0839757 0.996468i \(-0.526762\pi\)
−0.0839757 + 0.996468i \(0.526762\pi\)
\(488\) 4416.00 0.409637
\(489\) −2045.00 −0.189117
\(490\) 190.000 0.0175170
\(491\) 5245.00 0.482085 0.241042 0.970515i \(-0.422511\pi\)
0.241042 + 0.970515i \(0.422511\pi\)
\(492\) −628.000 −0.0575456
\(493\) −540.000 −0.0493314
\(494\) −3384.00 −0.308205
\(495\) −4160.00 −0.377734
\(496\) −528.000 −0.0477982
\(497\) −12582.0 −1.13557
\(498\) 1024.00 0.0921416
\(499\) 9027.00 0.809828 0.404914 0.914355i \(-0.367302\pi\)
0.404914 + 0.914355i \(0.367302\pi\)
\(500\) −500.000 −0.0447214
\(501\) 1016.00 0.0906019
\(502\) −2664.00 −0.236853
\(503\) 3522.00 0.312203 0.156102 0.987741i \(-0.450107\pi\)
0.156102 + 0.987741i \(0.450107\pi\)
\(504\) 3744.00 0.330895
\(505\) 30.0000 0.00264353
\(506\) 1472.00 0.129325
\(507\) 12.0000 0.00105116
\(508\) −3076.00 −0.268652
\(509\) 3949.00 0.343883 0.171941 0.985107i \(-0.444996\pi\)
0.171941 + 0.985107i \(0.444996\pi\)
\(510\) −200.000 −0.0173650
\(511\) 10962.0 0.948983
\(512\) 512.000 0.0441942
\(513\) −1908.00 −0.164211
\(514\) 6602.00 0.566540
\(515\) 800.000 0.0684509
\(516\) 72.0000 0.00614268
\(517\) −2080.00 −0.176941
\(518\) −2016.00 −0.171000
\(519\) 598.000 0.0505767
\(520\) 1880.00 0.158545
\(521\) 3236.00 0.272115 0.136057 0.990701i \(-0.456557\pi\)
0.136057 + 0.990701i \(0.456557\pi\)
\(522\) 1404.00 0.117723
\(523\) 12394.0 1.03624 0.518118 0.855309i \(-0.326633\pi\)
0.518118 + 0.855309i \(0.326633\pi\)
\(524\) −852.000 −0.0710301
\(525\) −450.000 −0.0374088
\(526\) 4144.00 0.343511
\(527\) −660.000 −0.0545542
\(528\) −512.000 −0.0422006
\(529\) 529.000 0.0434783
\(530\) 140.000 0.0114740
\(531\) 19344.0 1.58090
\(532\) −2592.00 −0.211236
\(533\) 7379.00 0.599662
\(534\) −204.000 −0.0165317
\(535\) −1900.00 −0.153540
\(536\) −1248.00 −0.100570
\(537\) −4607.00 −0.370217
\(538\) 11442.0 0.916914
\(539\) 608.000 0.0485870
\(540\) 1060.00 0.0844725
\(541\) −7159.00 −0.568927 −0.284463 0.958687i \(-0.591815\pi\)
−0.284463 + 0.958687i \(0.591815\pi\)
\(542\) −11800.0 −0.935154
\(543\) −1212.00 −0.0957862
\(544\) 640.000 0.0504408
\(545\) −1250.00 −0.0982461
\(546\) 1692.00 0.132621
\(547\) −19761.0 −1.54464 −0.772321 0.635232i \(-0.780904\pi\)
−0.772321 + 0.635232i \(0.780904\pi\)
\(548\) 11344.0 0.884291
\(549\) −14352.0 −1.11572
\(550\) −1600.00 −0.124044
\(551\) −972.000 −0.0751517
\(552\) −184.000 −0.0141876
\(553\) 11592.0 0.891396
\(554\) 12742.0 0.977176
\(555\) −280.000 −0.0214150
\(556\) −6524.00 −0.497625
\(557\) 18010.0 1.37003 0.685016 0.728528i \(-0.259795\pi\)
0.685016 + 0.728528i \(0.259795\pi\)
\(558\) 1716.00 0.130187
\(559\) −846.000 −0.0640107
\(560\) 1440.00 0.108663
\(561\) −640.000 −0.0481655
\(562\) 6380.00 0.478868
\(563\) −2648.00 −0.198224 −0.0991118 0.995076i \(-0.531600\pi\)
−0.0991118 + 0.995076i \(0.531600\pi\)
\(564\) 260.000 0.0194113
\(565\) 1950.00 0.145198
\(566\) −8452.00 −0.627675
\(567\) −11682.0 −0.865252
\(568\) 5592.00 0.413090
\(569\) −1566.00 −0.115378 −0.0576890 0.998335i \(-0.518373\pi\)
−0.0576890 + 0.998335i \(0.518373\pi\)
\(570\) −360.000 −0.0264539
\(571\) 2864.00 0.209903 0.104952 0.994477i \(-0.466531\pi\)
0.104952 + 0.994477i \(0.466531\pi\)
\(572\) 6016.00 0.439758
\(573\) −1058.00 −0.0771354
\(574\) 5652.00 0.410993
\(575\) −575.000 −0.0417029
\(576\) −1664.00 −0.120370
\(577\) −929.000 −0.0670273 −0.0335137 0.999438i \(-0.510670\pi\)
−0.0335137 + 0.999438i \(0.510670\pi\)
\(578\) −9026.00 −0.649537
\(579\) 1047.00 0.0751500
\(580\) 540.000 0.0386591
\(581\) −9216.00 −0.658079
\(582\) 1156.00 0.0823329
\(583\) 448.000 0.0318255
\(584\) −4872.00 −0.345214
\(585\) −6110.00 −0.431825
\(586\) 12096.0 0.852698
\(587\) −19499.0 −1.37106 −0.685528 0.728046i \(-0.740429\pi\)
−0.685528 + 0.728046i \(0.740429\pi\)
\(588\) −76.0000 −0.00533025
\(589\) −1188.00 −0.0831081
\(590\) 7440.00 0.519152
\(591\) 251.000 0.0174700
\(592\) 896.000 0.0622050
\(593\) 6570.00 0.454971 0.227485 0.973782i \(-0.426950\pi\)
0.227485 + 0.973782i \(0.426950\pi\)
\(594\) 3392.00 0.234302
\(595\) 1800.00 0.124022
\(596\) −7864.00 −0.540473
\(597\) −3508.00 −0.240491
\(598\) 2162.00 0.147844
\(599\) 1880.00 0.128238 0.0641191 0.997942i \(-0.479576\pi\)
0.0641191 + 0.997942i \(0.479576\pi\)
\(600\) 200.000 0.0136083
\(601\) 3701.00 0.251193 0.125596 0.992081i \(-0.459916\pi\)
0.125596 + 0.992081i \(0.459916\pi\)
\(602\) −648.000 −0.0438713
\(603\) 4056.00 0.273919
\(604\) 140.000 0.00943132
\(605\) 1535.00 0.103151
\(606\) −12.0000 −0.000804400 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
\(609\) 486.000 0.0323378
\(610\) −5520.00 −0.366391
\(611\) −3055.00 −0.202278
\(612\) −2080.00 −0.137384
\(613\) 24004.0 1.58159 0.790793 0.612083i \(-0.209668\pi\)
0.790793 + 0.612083i \(0.209668\pi\)
\(614\) 17256.0 1.13419
\(615\) 785.000 0.0514703
\(616\) 4608.00 0.301399
\(617\) 780.000 0.0508940 0.0254470 0.999676i \(-0.491899\pi\)
0.0254470 + 0.999676i \(0.491899\pi\)
\(618\) −320.000 −0.0208289
\(619\) 21892.0 1.42151 0.710754 0.703440i \(-0.248354\pi\)
0.710754 + 0.703440i \(0.248354\pi\)
\(620\) 660.000 0.0427520
\(621\) 1219.00 0.0787710
\(622\) 16494.0 1.06326
\(623\) 1836.00 0.118070
\(624\) −752.000 −0.0482437
\(625\) 625.000 0.0400000
\(626\) 5240.00 0.334557
\(627\) −1152.00 −0.0733755
\(628\) 6808.00 0.432594
\(629\) 1120.00 0.0709973
\(630\) −4680.00 −0.295961
\(631\) 8050.00 0.507869 0.253935 0.967221i \(-0.418275\pi\)
0.253935 + 0.967221i \(0.418275\pi\)
\(632\) −5152.00 −0.324265
\(633\) −3296.00 −0.206958
\(634\) 19812.0 1.24106
\(635\) 3845.00 0.240290
\(636\) −56.0000 −0.00349142
\(637\) 893.000 0.0555447
\(638\) 1728.00 0.107229
\(639\) −18174.0 −1.12512
\(640\) −640.000 −0.0395285
\(641\) −25890.0 −1.59531 −0.797655 0.603114i \(-0.793926\pi\)
−0.797655 + 0.603114i \(0.793926\pi\)
\(642\) 760.000 0.0467209
\(643\) 4774.00 0.292797 0.146398 0.989226i \(-0.453232\pi\)
0.146398 + 0.989226i \(0.453232\pi\)
\(644\) 1656.00 0.101328
\(645\) −90.0000 −0.00549418
\(646\) 1440.00 0.0877029
\(647\) 3349.00 0.203497 0.101749 0.994810i \(-0.467556\pi\)
0.101749 + 0.994810i \(0.467556\pi\)
\(648\) 5192.00 0.314755
\(649\) 23808.0 1.43998
\(650\) −2350.00 −0.141807
\(651\) 594.000 0.0357614
\(652\) −8180.00 −0.491340
\(653\) 24813.0 1.48699 0.743497 0.668739i \(-0.233166\pi\)
0.743497 + 0.668739i \(0.233166\pi\)
\(654\) 500.000 0.0298953
\(655\) 1065.00 0.0635313
\(656\) −2512.00 −0.149508
\(657\) 15834.0 0.940248
\(658\) −2340.00 −0.138636
\(659\) 18180.0 1.07465 0.537323 0.843376i \(-0.319435\pi\)
0.537323 + 0.843376i \(0.319435\pi\)
\(660\) 640.000 0.0377454
\(661\) −29250.0 −1.72117 −0.860585 0.509307i \(-0.829902\pi\)
−0.860585 + 0.509307i \(0.829902\pi\)
\(662\) −16230.0 −0.952865
\(663\) −940.000 −0.0550627
\(664\) 4096.00 0.239391
\(665\) 3240.00 0.188935
\(666\) −2912.00 −0.169426
\(667\) 621.000 0.0360498
\(668\) 4064.00 0.235391
\(669\) −2720.00 −0.157192
\(670\) 1560.00 0.0899523
\(671\) −17664.0 −1.01626
\(672\) −576.000 −0.0330650
\(673\) −23027.0 −1.31891 −0.659454 0.751745i \(-0.729213\pi\)
−0.659454 + 0.751745i \(0.729213\pi\)
\(674\) −15172.0 −0.867068
\(675\) −1325.00 −0.0755545
\(676\) 48.0000 0.00273100
\(677\) 20106.0 1.14141 0.570706 0.821154i \(-0.306669\pi\)
0.570706 + 0.821154i \(0.306669\pi\)
\(678\) −780.000 −0.0441825
\(679\) −10404.0 −0.588025
\(680\) −800.000 −0.0451156
\(681\) −4134.00 −0.232621
\(682\) 2112.00 0.118582
\(683\) −18745.0 −1.05016 −0.525079 0.851054i \(-0.675964\pi\)
−0.525079 + 0.851054i \(0.675964\pi\)
\(684\) −3744.00 −0.209292
\(685\) −14180.0 −0.790934
\(686\) 13032.0 0.725312
\(687\) −4510.00 −0.250462
\(688\) 288.000 0.0159592
\(689\) 658.000 0.0363829
\(690\) 230.000 0.0126898
\(691\) 24424.0 1.34462 0.672310 0.740270i \(-0.265302\pi\)
0.672310 + 0.740270i \(0.265302\pi\)
\(692\) 2392.00 0.131402
\(693\) −14976.0 −0.820911
\(694\) 2712.00 0.148337
\(695\) 8155.00 0.445089
\(696\) −216.000 −0.0117636
\(697\) −3140.00 −0.170640
\(698\) 13298.0 0.721113
\(699\) −5003.00 −0.270717
\(700\) −1800.00 −0.0971909
\(701\) −27278.0 −1.46972 −0.734862 0.678217i \(-0.762753\pi\)
−0.734862 + 0.678217i \(0.762753\pi\)
\(702\) 4982.00 0.267854
\(703\) 2016.00 0.108158
\(704\) −2048.00 −0.109640
\(705\) −325.000 −0.0173620
\(706\) 21382.0 1.13983
\(707\) 108.000 0.00574506
\(708\) −2976.00 −0.157973
\(709\) 12214.0 0.646977 0.323488 0.946232i \(-0.395144\pi\)
0.323488 + 0.946232i \(0.395144\pi\)
\(710\) −6990.00 −0.369479
\(711\) 16744.0 0.883191
\(712\) −816.000 −0.0429507
\(713\) 759.000 0.0398664
\(714\) −720.000 −0.0377385
\(715\) −7520.00 −0.393332
\(716\) −18428.0 −0.961853
\(717\) −6309.00 −0.328611
\(718\) −12840.0 −0.667388
\(719\) 12932.0 0.670768 0.335384 0.942082i \(-0.391134\pi\)
0.335384 + 0.942082i \(0.391134\pi\)
\(720\) 2080.00 0.107663
\(721\) 2880.00 0.148761
\(722\) −11126.0 −0.573500
\(723\) 3038.00 0.156272
\(724\) −4848.00 −0.248860
\(725\) −675.000 −0.0345778
\(726\) −614.000 −0.0313880
\(727\) 10046.0 0.512497 0.256249 0.966611i \(-0.417513\pi\)
0.256249 + 0.966611i \(0.417513\pi\)
\(728\) 6768.00 0.344559
\(729\) −15443.0 −0.784586
\(730\) 6090.00 0.308769
\(731\) 360.000 0.0182149
\(732\) 2208.00 0.111489
\(733\) −5924.00 −0.298510 −0.149255 0.988799i \(-0.547688\pi\)
−0.149255 + 0.988799i \(0.547688\pi\)
\(734\) −1048.00 −0.0527008
\(735\) 95.0000 0.00476752
\(736\) −736.000 −0.0368605
\(737\) 4992.00 0.249502
\(738\) 8164.00 0.407210
\(739\) 829.000 0.0412656 0.0206328 0.999787i \(-0.493432\pi\)
0.0206328 + 0.999787i \(0.493432\pi\)
\(740\) −1120.00 −0.0556379
\(741\) −1692.00 −0.0838828
\(742\) 504.000 0.0249359
\(743\) 7072.00 0.349188 0.174594 0.984641i \(-0.444139\pi\)
0.174594 + 0.984641i \(0.444139\pi\)
\(744\) −264.000 −0.0130090
\(745\) 9830.00 0.483414
\(746\) 11132.0 0.546342
\(747\) −13312.0 −0.652022
\(748\) −2560.00 −0.125138
\(749\) −6840.00 −0.333682
\(750\) −250.000 −0.0121716
\(751\) 16234.0 0.788798 0.394399 0.918939i \(-0.370953\pi\)
0.394399 + 0.918939i \(0.370953\pi\)
\(752\) 1040.00 0.0504320
\(753\) −1332.00 −0.0644632
\(754\) 2538.00 0.122584
\(755\) −175.000 −0.00843563
\(756\) 3816.00 0.183580
\(757\) 9128.00 0.438260 0.219130 0.975696i \(-0.429678\pi\)
0.219130 + 0.975696i \(0.429678\pi\)
\(758\) 4480.00 0.214671
\(759\) 736.000 0.0351978
\(760\) −1440.00 −0.0687293
\(761\) 165.000 0.00785972 0.00392986 0.999992i \(-0.498749\pi\)
0.00392986 + 0.999992i \(0.498749\pi\)
\(762\) −1538.00 −0.0731179
\(763\) −4500.00 −0.213514
\(764\) −4232.00 −0.200404
\(765\) 2600.00 0.122880
\(766\) 17556.0 0.828099
\(767\) 34968.0 1.64618
\(768\) 256.000 0.0120281
\(769\) −20834.0 −0.976974 −0.488487 0.872571i \(-0.662451\pi\)
−0.488487 + 0.872571i \(0.662451\pi\)
\(770\) −5760.00 −0.269579
\(771\) 3301.00 0.154193
\(772\) 4188.00 0.195245
\(773\) −31782.0 −1.47881 −0.739404 0.673262i \(-0.764893\pi\)
−0.739404 + 0.673262i \(0.764893\pi\)
\(774\) −936.000 −0.0434675
\(775\) −825.000 −0.0382385
\(776\) 4624.00 0.213907
\(777\) −1008.00 −0.0465403
\(778\) 8112.00 0.373817
\(779\) −5652.00 −0.259954
\(780\) 940.000 0.0431505
\(781\) −22368.0 −1.02483
\(782\) −920.000 −0.0420705
\(783\) 1431.00 0.0653126
\(784\) −304.000 −0.0138484
\(785\) −8510.00 −0.386923
\(786\) −426.000 −0.0193320
\(787\) 33104.0 1.49940 0.749701 0.661776i \(-0.230197\pi\)
0.749701 + 0.661776i \(0.230197\pi\)
\(788\) 1004.00 0.0453883
\(789\) 2072.00 0.0934920
\(790\) 6440.00 0.290032
\(791\) 7020.00 0.315553
\(792\) 6656.00 0.298625
\(793\) −25944.0 −1.16179
\(794\) −18302.0 −0.818027
\(795\) 70.0000 0.00312282
\(796\) −14032.0 −0.624813
\(797\) 4736.00 0.210486 0.105243 0.994447i \(-0.466438\pi\)
0.105243 + 0.994447i \(0.466438\pi\)
\(798\) −1296.00 −0.0574911
\(799\) 1300.00 0.0575603
\(800\) 800.000 0.0353553
\(801\) 2652.00 0.116984
\(802\) 31860.0 1.40276
\(803\) 19488.0 0.856434
\(804\) −624.000 −0.0273716
\(805\) −2070.00 −0.0906309
\(806\) 3102.00 0.135562
\(807\) 5721.00 0.249552
\(808\) −48.0000 −0.00208989
\(809\) −7470.00 −0.324637 −0.162318 0.986738i \(-0.551897\pi\)
−0.162318 + 0.986738i \(0.551897\pi\)
\(810\) −6490.00 −0.281525
\(811\) 19919.0 0.862455 0.431227 0.902243i \(-0.358081\pi\)
0.431227 + 0.902243i \(0.358081\pi\)
\(812\) 1944.00 0.0840160
\(813\) −5900.00 −0.254517
\(814\) −3584.00 −0.154323
\(815\) 10225.0 0.439468
\(816\) 320.000 0.0137282
\(817\) 648.000 0.0277487
\(818\) −11782.0 −0.503604
\(819\) −21996.0 −0.938465
\(820\) 3140.00 0.133724
\(821\) −22694.0 −0.964709 −0.482354 0.875976i \(-0.660218\pi\)
−0.482354 + 0.875976i \(0.660218\pi\)
\(822\) 5672.00 0.240674
\(823\) −31907.0 −1.35141 −0.675704 0.737173i \(-0.736160\pi\)
−0.675704 + 0.737173i \(0.736160\pi\)
\(824\) −1280.00 −0.0541152
\(825\) −800.000 −0.0337605
\(826\) 26784.0 1.12825
\(827\) −15236.0 −0.640638 −0.320319 0.947310i \(-0.603790\pi\)
−0.320319 + 0.947310i \(0.603790\pi\)
\(828\) 2392.00 0.100396
\(829\) 27286.0 1.14316 0.571581 0.820545i \(-0.306330\pi\)
0.571581 + 0.820545i \(0.306330\pi\)
\(830\) −5120.00 −0.214118
\(831\) 6371.00 0.265954
\(832\) −3008.00 −0.125341
\(833\) −380.000 −0.0158058
\(834\) −3262.00 −0.135436
\(835\) −5080.00 −0.210540
\(836\) −4608.00 −0.190635
\(837\) 1749.00 0.0722273
\(838\) 30564.0 1.25992
\(839\) 23054.0 0.948644 0.474322 0.880351i \(-0.342693\pi\)
0.474322 + 0.880351i \(0.342693\pi\)
\(840\) 720.000 0.0295742
\(841\) −23660.0 −0.970109
\(842\) −21868.0 −0.895037
\(843\) 3190.00 0.130331
\(844\) −13184.0 −0.537692
\(845\) −60.0000 −0.00244268
\(846\) −3380.00 −0.137360
\(847\) 5526.00 0.224174
\(848\) −224.000 −0.00907098
\(849\) −4226.00 −0.170832
\(850\) 1000.00 0.0403526
\(851\) −1288.00 −0.0518826
\(852\) 2796.00 0.112429
\(853\) −34506.0 −1.38507 −0.692534 0.721385i \(-0.743506\pi\)
−0.692534 + 0.721385i \(0.743506\pi\)
\(854\) −19872.0 −0.796260
\(855\) 4680.00 0.187196
\(856\) 3040.00 0.121384
\(857\) −22263.0 −0.887386 −0.443693 0.896179i \(-0.646332\pi\)
−0.443693 + 0.896179i \(0.646332\pi\)
\(858\) 3008.00 0.119687
\(859\) 12851.0 0.510443 0.255221 0.966883i \(-0.417852\pi\)
0.255221 + 0.966883i \(0.417852\pi\)
\(860\) −360.000 −0.0142743
\(861\) 2826.00 0.111858
\(862\) −5588.00 −0.220798
\(863\) 15723.0 0.620182 0.310091 0.950707i \(-0.399640\pi\)
0.310091 + 0.950707i \(0.399640\pi\)
\(864\) −1696.00 −0.0667814
\(865\) −2990.00 −0.117530
\(866\) −30124.0 −1.18205
\(867\) −4513.00 −0.176781
\(868\) 2376.00 0.0929109
\(869\) 20608.0 0.804463
\(870\) 270.000 0.0105217
\(871\) 7332.00 0.285230
\(872\) 2000.00 0.0776704
\(873\) −15028.0 −0.582613
\(874\) −1656.00 −0.0640904
\(875\) 2250.00 0.0869302
\(876\) −2436.00 −0.0939553
\(877\) −886.000 −0.0341141 −0.0170571 0.999855i \(-0.505430\pi\)
−0.0170571 + 0.999855i \(0.505430\pi\)
\(878\) 522.000 0.0200645
\(879\) 6048.00 0.232075
\(880\) 2560.00 0.0980654
\(881\) −37120.0 −1.41953 −0.709764 0.704439i \(-0.751199\pi\)
−0.709764 + 0.704439i \(0.751199\pi\)
\(882\) 988.000 0.0377185
\(883\) −7524.00 −0.286753 −0.143376 0.989668i \(-0.545796\pi\)
−0.143376 + 0.989668i \(0.545796\pi\)
\(884\) −3760.00 −0.143057
\(885\) 3720.00 0.141295
\(886\) −14166.0 −0.537151
\(887\) 9221.00 0.349054 0.174527 0.984652i \(-0.444160\pi\)
0.174527 + 0.984652i \(0.444160\pi\)
\(888\) 448.000 0.0169301
\(889\) 13842.0 0.522211
\(890\) 1020.00 0.0384163
\(891\) −20768.0 −0.780869
\(892\) −10880.0 −0.408396
\(893\) 2340.00 0.0876877
\(894\) −3932.00 −0.147098
\(895\) 23035.0 0.860307
\(896\) −2304.00 −0.0859054
\(897\) 1081.00 0.0402381
\(898\) −20740.0 −0.770716
\(899\) 891.000 0.0330551
\(900\) −2600.00 −0.0962963
\(901\) −280.000 −0.0103531
\(902\) 10048.0 0.370911
\(903\) −324.000 −0.0119402
\(904\) −3120.00 −0.114789
\(905\) 6060.00 0.222587
\(906\) 70.0000 0.00256688
\(907\) 29116.0 1.06591 0.532955 0.846143i \(-0.321081\pi\)
0.532955 + 0.846143i \(0.321081\pi\)
\(908\) −16536.0 −0.604368
\(909\) 156.000 0.00569218
\(910\) −8460.00 −0.308183
\(911\) 11440.0 0.416053 0.208026 0.978123i \(-0.433296\pi\)
0.208026 + 0.978123i \(0.433296\pi\)
\(912\) 576.000 0.0209137
\(913\) −16384.0 −0.593901
\(914\) −20992.0 −0.759687
\(915\) −2760.00 −0.0997189
\(916\) −18040.0 −0.650719
\(917\) 3834.00 0.138070
\(918\) −2120.00 −0.0762205
\(919\) 2958.00 0.106176 0.0530878 0.998590i \(-0.483094\pi\)
0.0530878 + 0.998590i \(0.483094\pi\)
\(920\) 920.000 0.0329690
\(921\) 8628.00 0.308689
\(922\) 36042.0 1.28740
\(923\) −32853.0 −1.17158
\(924\) 2304.00 0.0820303
\(925\) 1400.00 0.0497640
\(926\) −34376.0 −1.21994
\(927\) 4160.00 0.147392
\(928\) −864.000 −0.0305627
\(929\) 20907.0 0.738360 0.369180 0.929358i \(-0.379639\pi\)
0.369180 + 0.929358i \(0.379639\pi\)
\(930\) 330.000 0.0116356
\(931\) −684.000 −0.0240786
\(932\) −20012.0 −0.703342
\(933\) 8247.00 0.289383
\(934\) −30492.0 −1.06823
\(935\) 3200.00 0.111926
\(936\) 9776.00 0.341387
\(937\) 9748.00 0.339865 0.169932 0.985456i \(-0.445645\pi\)
0.169932 + 0.985456i \(0.445645\pi\)
\(938\) 5616.00 0.195489
\(939\) 2620.00 0.0910548
\(940\) −1300.00 −0.0451078
\(941\) 19624.0 0.679834 0.339917 0.940455i \(-0.389601\pi\)
0.339917 + 0.940455i \(0.389601\pi\)
\(942\) 3404.00 0.117737
\(943\) 3611.00 0.124698
\(944\) −11904.0 −0.410426
\(945\) −4770.00 −0.164199
\(946\) −1152.00 −0.0395928
\(947\) −41859.0 −1.43636 −0.718181 0.695856i \(-0.755025\pi\)
−0.718181 + 0.695856i \(0.755025\pi\)
\(948\) −2576.00 −0.0882538
\(949\) 28623.0 0.979075
\(950\) 1800.00 0.0614734
\(951\) 9906.00 0.337775
\(952\) −2880.00 −0.0980476
\(953\) 29226.0 0.993413 0.496707 0.867918i \(-0.334542\pi\)
0.496707 + 0.867918i \(0.334542\pi\)
\(954\) 728.000 0.0247064
\(955\) 5290.00 0.179246
\(956\) −25236.0 −0.853756
\(957\) 864.000 0.0291841
\(958\) −17112.0 −0.577102
\(959\) −51048.0 −1.71890
\(960\) −320.000 −0.0107583
\(961\) −28702.0 −0.963445
\(962\) −5264.00 −0.176422
\(963\) −9880.00 −0.330611
\(964\) 12152.0 0.406006
\(965\) −5235.00 −0.174633
\(966\) 828.000 0.0275781
\(967\) −29849.0 −0.992636 −0.496318 0.868141i \(-0.665315\pi\)
−0.496318 + 0.868141i \(0.665315\pi\)
\(968\) −2456.00 −0.0815484
\(969\) 720.000 0.0238697
\(970\) −5780.00 −0.191324
\(971\) −9390.00 −0.310339 −0.155170 0.987888i \(-0.549592\pi\)
−0.155170 + 0.987888i \(0.549592\pi\)
\(972\) 8320.00 0.274552
\(973\) 29358.0 0.967291
\(974\) −3610.00 −0.118760
\(975\) −1175.00 −0.0385950
\(976\) 8832.00 0.289657
\(977\) 33536.0 1.09817 0.549085 0.835767i \(-0.314976\pi\)
0.549085 + 0.835767i \(0.314976\pi\)
\(978\) −4090.00 −0.133726
\(979\) 3264.00 0.106556
\(980\) 380.000 0.0123864
\(981\) −6500.00 −0.211548
\(982\) 10490.0 0.340885
\(983\) 28994.0 0.940758 0.470379 0.882465i \(-0.344117\pi\)
0.470379 + 0.882465i \(0.344117\pi\)
\(984\) −1256.00 −0.0406909
\(985\) −1255.00 −0.0405966
\(986\) −1080.00 −0.0348826
\(987\) −1170.00 −0.0377320
\(988\) −6768.00 −0.217934
\(989\) −414.000 −0.0133109
\(990\) −8320.00 −0.267098
\(991\) 11272.0 0.361319 0.180659 0.983546i \(-0.442177\pi\)
0.180659 + 0.983546i \(0.442177\pi\)
\(992\) −1056.00 −0.0337984
\(993\) −8115.00 −0.259337
\(994\) −25164.0 −0.802971
\(995\) 17540.0 0.558850
\(996\) 2048.00 0.0651540
\(997\) 61186.0 1.94361 0.971805 0.235784i \(-0.0757658\pi\)
0.971805 + 0.235784i \(0.0757658\pi\)
\(998\) 18054.0 0.572635
\(999\) −2968.00 −0.0939974
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 230.4.a.e.1.1 1
3.2 odd 2 2070.4.a.e.1.1 1
4.3 odd 2 1840.4.a.d.1.1 1
5.2 odd 4 1150.4.b.f.599.2 2
5.3 odd 4 1150.4.b.f.599.1 2
5.4 even 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 1.1 even 1 trivial
1150.4.a.b.1.1 1 5.4 even 2
1150.4.b.f.599.1 2 5.3 odd 4
1150.4.b.f.599.2 2 5.2 odd 4
1840.4.a.d.1.1 1 4.3 odd 2
2070.4.a.e.1.1 1 3.2 odd 2