Properties

Label 1521.4.a.bc.1.6
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(89.7419051187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 52x^{6} + 805x^{4} - 4210x^{2} + 4992 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 117)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.75628\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.75628 q^{2} -0.402937 q^{4} +0.313209 q^{5} +28.5660 q^{7} -23.1608 q^{8} +O(q^{10})\) \(q+2.75628 q^{2} -0.402937 q^{4} +0.313209 q^{5} +28.5660 q^{7} -23.1608 q^{8} +0.863291 q^{10} +63.2173 q^{11} +78.7357 q^{14} -60.6141 q^{16} +98.8270 q^{17} -14.4897 q^{19} -0.126204 q^{20} +174.244 q^{22} -14.3900 q^{23} -124.902 q^{25} -11.5103 q^{28} -196.283 q^{29} +118.691 q^{31} +18.2172 q^{32} +272.395 q^{34} +8.94712 q^{35} +319.114 q^{37} -39.9377 q^{38} -7.25418 q^{40} +346.106 q^{41} -69.4854 q^{43} -25.4726 q^{44} -39.6628 q^{46} -101.875 q^{47} +473.014 q^{49} -344.264 q^{50} -594.823 q^{53} +19.8002 q^{55} -661.611 q^{56} -541.010 q^{58} -204.473 q^{59} -215.978 q^{61} +327.144 q^{62} +535.125 q^{64} +68.6049 q^{67} -39.8211 q^{68} +24.6607 q^{70} +946.241 q^{71} -779.872 q^{73} +879.567 q^{74} +5.83844 q^{76} +1805.86 q^{77} +240.022 q^{79} -18.9849 q^{80} +953.965 q^{82} +855.576 q^{83} +30.9535 q^{85} -191.521 q^{86} -1464.16 q^{88} +1264.06 q^{89} +5.79825 q^{92} -280.795 q^{94} -4.53831 q^{95} +662.290 q^{97} +1303.76 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 40 q^{4} - 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 40 q^{4} - 22 q^{7} + 36 q^{10} + 204 q^{16} + 244 q^{19} + 136 q^{22} + 354 q^{25} - 452 q^{28} + 242 q^{31} - 1292 q^{34} + 1018 q^{37} + 1700 q^{40} + 74 q^{43} - 896 q^{46} + 298 q^{49} + 1300 q^{55} + 812 q^{58} + 1148 q^{61} + 3636 q^{64} - 2198 q^{67} + 2200 q^{70} - 2176 q^{73} + 6936 q^{76} + 1862 q^{79} + 5436 q^{82} - 890 q^{85} + 3528 q^{88} - 3104 q^{94} - 4370 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.75628 0.974491 0.487246 0.873265i \(-0.338002\pi\)
0.487246 + 0.873265i \(0.338002\pi\)
\(3\) 0 0
\(4\) −0.402937 −0.0503671
\(5\) 0.313209 0.0280143 0.0140071 0.999902i \(-0.495541\pi\)
0.0140071 + 0.999902i \(0.495541\pi\)
\(6\) 0 0
\(7\) 28.5660 1.54242 0.771208 0.636583i \(-0.219653\pi\)
0.771208 + 0.636583i \(0.219653\pi\)
\(8\) −23.1608 −1.02357
\(9\) 0 0
\(10\) 0.863291 0.0272997
\(11\) 63.2173 1.73279 0.866397 0.499356i \(-0.166430\pi\)
0.866397 + 0.499356i \(0.166430\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 78.7357 1.50307
\(15\) 0 0
\(16\) −60.6141 −0.947096
\(17\) 98.8270 1.40995 0.704973 0.709234i \(-0.250959\pi\)
0.704973 + 0.709234i \(0.250959\pi\)
\(18\) 0 0
\(19\) −14.4897 −0.174956 −0.0874782 0.996166i \(-0.527881\pi\)
−0.0874782 + 0.996166i \(0.527881\pi\)
\(20\) −0.126204 −0.00141100
\(21\) 0 0
\(22\) 174.244 1.68859
\(23\) −14.3900 −0.130457 −0.0652286 0.997870i \(-0.520778\pi\)
−0.0652286 + 0.997870i \(0.520778\pi\)
\(24\) 0 0
\(25\) −124.902 −0.999215
\(26\) 0 0
\(27\) 0 0
\(28\) −11.5103 −0.0776871
\(29\) −196.283 −1.25686 −0.628428 0.777868i \(-0.716301\pi\)
−0.628428 + 0.777868i \(0.716301\pi\)
\(30\) 0 0
\(31\) 118.691 0.687661 0.343830 0.939032i \(-0.388276\pi\)
0.343830 + 0.939032i \(0.388276\pi\)
\(32\) 18.2172 0.100637
\(33\) 0 0
\(34\) 272.395 1.37398
\(35\) 8.94712 0.0432097
\(36\) 0 0
\(37\) 319.114 1.41789 0.708947 0.705262i \(-0.249171\pi\)
0.708947 + 0.705262i \(0.249171\pi\)
\(38\) −39.9377 −0.170493
\(39\) 0 0
\(40\) −7.25418 −0.0286747
\(41\) 346.106 1.31836 0.659180 0.751986i \(-0.270904\pi\)
0.659180 + 0.751986i \(0.270904\pi\)
\(42\) 0 0
\(43\) −69.4854 −0.246428 −0.123214 0.992380i \(-0.539320\pi\)
−0.123214 + 0.992380i \(0.539320\pi\)
\(44\) −25.4726 −0.0872758
\(45\) 0 0
\(46\) −39.6628 −0.127129
\(47\) −101.875 −0.316170 −0.158085 0.987426i \(-0.550532\pi\)
−0.158085 + 0.987426i \(0.550532\pi\)
\(48\) 0 0
\(49\) 473.014 1.37905
\(50\) −344.264 −0.973726
\(51\) 0 0
\(52\) 0 0
\(53\) −594.823 −1.54161 −0.770804 0.637072i \(-0.780145\pi\)
−0.770804 + 0.637072i \(0.780145\pi\)
\(54\) 0 0
\(55\) 19.8002 0.0485430
\(56\) −661.611 −1.57878
\(57\) 0 0
\(58\) −541.010 −1.22480
\(59\) −204.473 −0.451189 −0.225595 0.974221i \(-0.572432\pi\)
−0.225595 + 0.974221i \(0.572432\pi\)
\(60\) 0 0
\(61\) −215.978 −0.453331 −0.226666 0.973973i \(-0.572782\pi\)
−0.226666 + 0.973973i \(0.572782\pi\)
\(62\) 327.144 0.670119
\(63\) 0 0
\(64\) 535.125 1.04517
\(65\) 0 0
\(66\) 0 0
\(67\) 68.6049 0.125096 0.0625480 0.998042i \(-0.480077\pi\)
0.0625480 + 0.998042i \(0.480077\pi\)
\(68\) −39.8211 −0.0710149
\(69\) 0 0
\(70\) 24.6607 0.0421075
\(71\) 946.241 1.58166 0.790832 0.612033i \(-0.209648\pi\)
0.790832 + 0.612033i \(0.209648\pi\)
\(72\) 0 0
\(73\) −779.872 −1.25037 −0.625185 0.780476i \(-0.714977\pi\)
−0.625185 + 0.780476i \(0.714977\pi\)
\(74\) 879.567 1.38172
\(75\) 0 0
\(76\) 5.83844 0.00881204
\(77\) 1805.86 2.67269
\(78\) 0 0
\(79\) 240.022 0.341831 0.170915 0.985286i \(-0.445328\pi\)
0.170915 + 0.985286i \(0.445328\pi\)
\(80\) −18.9849 −0.0265322
\(81\) 0 0
\(82\) 953.965 1.28473
\(83\) 855.576 1.13147 0.565733 0.824588i \(-0.308593\pi\)
0.565733 + 0.824588i \(0.308593\pi\)
\(84\) 0 0
\(85\) 30.9535 0.0394986
\(86\) −191.521 −0.240142
\(87\) 0 0
\(88\) −1464.16 −1.77364
\(89\) 1264.06 1.50551 0.752753 0.658303i \(-0.228726\pi\)
0.752753 + 0.658303i \(0.228726\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.79825 0.00657075
\(93\) 0 0
\(94\) −280.795 −0.308105
\(95\) −4.53831 −0.00490128
\(96\) 0 0
\(97\) 662.290 0.693251 0.346625 0.938004i \(-0.387328\pi\)
0.346625 + 0.938004i \(0.387328\pi\)
\(98\) 1303.76 1.34387
\(99\) 0 0
\(100\) 50.3276 0.0503276
\(101\) −793.571 −0.781814 −0.390907 0.920430i \(-0.627839\pi\)
−0.390907 + 0.920430i \(0.627839\pi\)
\(102\) 0 0
\(103\) 980.791 0.938254 0.469127 0.883131i \(-0.344569\pi\)
0.469127 + 0.883131i \(0.344569\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1639.50 −1.50228
\(107\) −805.944 −0.728164 −0.364082 0.931367i \(-0.618617\pi\)
−0.364082 + 0.931367i \(0.618617\pi\)
\(108\) 0 0
\(109\) 845.184 0.742697 0.371348 0.928494i \(-0.378896\pi\)
0.371348 + 0.928494i \(0.378896\pi\)
\(110\) 54.5749 0.0473047
\(111\) 0 0
\(112\) −1731.50 −1.46082
\(113\) 56.3774 0.0469340 0.0234670 0.999725i \(-0.492530\pi\)
0.0234670 + 0.999725i \(0.492530\pi\)
\(114\) 0 0
\(115\) −4.50707 −0.00365467
\(116\) 79.0896 0.0633042
\(117\) 0 0
\(118\) −563.585 −0.439680
\(119\) 2823.09 2.17472
\(120\) 0 0
\(121\) 2665.43 2.00257
\(122\) −595.296 −0.441767
\(123\) 0 0
\(124\) −47.8249 −0.0346355
\(125\) −78.2716 −0.0560066
\(126\) 0 0
\(127\) 1666.65 1.16450 0.582248 0.813011i \(-0.302173\pi\)
0.582248 + 0.813011i \(0.302173\pi\)
\(128\) 1329.21 0.917868
\(129\) 0 0
\(130\) 0 0
\(131\) −602.630 −0.401924 −0.200962 0.979599i \(-0.564407\pi\)
−0.200962 + 0.979599i \(0.564407\pi\)
\(132\) 0 0
\(133\) −413.913 −0.269856
\(134\) 189.094 0.121905
\(135\) 0 0
\(136\) −2288.92 −1.44318
\(137\) 421.654 0.262951 0.131476 0.991319i \(-0.458029\pi\)
0.131476 + 0.991319i \(0.458029\pi\)
\(138\) 0 0
\(139\) 29.1702 0.0177999 0.00889995 0.999960i \(-0.497167\pi\)
0.00889995 + 0.999960i \(0.497167\pi\)
\(140\) −3.60512 −0.00217635
\(141\) 0 0
\(142\) 2608.10 1.54132
\(143\) 0 0
\(144\) 0 0
\(145\) −61.4776 −0.0352099
\(146\) −2149.54 −1.21848
\(147\) 0 0
\(148\) −128.583 −0.0714152
\(149\) 2141.80 1.17760 0.588802 0.808278i \(-0.299600\pi\)
0.588802 + 0.808278i \(0.299600\pi\)
\(150\) 0 0
\(151\) 1459.30 0.786462 0.393231 0.919440i \(-0.371357\pi\)
0.393231 + 0.919440i \(0.371357\pi\)
\(152\) 335.594 0.179081
\(153\) 0 0
\(154\) 4977.46 2.60451
\(155\) 37.1750 0.0192643
\(156\) 0 0
\(157\) 2008.20 1.02084 0.510419 0.859926i \(-0.329490\pi\)
0.510419 + 0.859926i \(0.329490\pi\)
\(158\) 661.568 0.333111
\(159\) 0 0
\(160\) 5.70579 0.00281927
\(161\) −411.063 −0.201219
\(162\) 0 0
\(163\) 548.495 0.263567 0.131784 0.991279i \(-0.457930\pi\)
0.131784 + 0.991279i \(0.457930\pi\)
\(164\) −139.459 −0.0664019
\(165\) 0 0
\(166\) 2358.21 1.10260
\(167\) −3962.58 −1.83613 −0.918064 0.396432i \(-0.870248\pi\)
−0.918064 + 0.396432i \(0.870248\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 85.3165 0.0384910
\(171\) 0 0
\(172\) 27.9982 0.0124119
\(173\) −1729.54 −0.760084 −0.380042 0.924969i \(-0.624091\pi\)
−0.380042 + 0.924969i \(0.624091\pi\)
\(174\) 0 0
\(175\) −3567.94 −1.54121
\(176\) −3831.86 −1.64112
\(177\) 0 0
\(178\) 3484.10 1.46710
\(179\) 1452.91 0.606680 0.303340 0.952882i \(-0.401898\pi\)
0.303340 + 0.952882i \(0.401898\pi\)
\(180\) 0 0
\(181\) −550.329 −0.225998 −0.112999 0.993595i \(-0.536046\pi\)
−0.112999 + 0.993595i \(0.536046\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 333.284 0.133533
\(185\) 99.9495 0.0397213
\(186\) 0 0
\(187\) 6247.58 2.44314
\(188\) 41.0491 0.0159246
\(189\) 0 0
\(190\) −12.5089 −0.00477625
\(191\) 1868.68 0.707921 0.353960 0.935260i \(-0.384835\pi\)
0.353960 + 0.935260i \(0.384835\pi\)
\(192\) 0 0
\(193\) 4156.52 1.55022 0.775112 0.631824i \(-0.217694\pi\)
0.775112 + 0.631824i \(0.217694\pi\)
\(194\) 1825.45 0.675567
\(195\) 0 0
\(196\) −190.595 −0.0694587
\(197\) −1522.18 −0.550513 −0.275257 0.961371i \(-0.588763\pi\)
−0.275257 + 0.961371i \(0.588763\pi\)
\(198\) 0 0
\(199\) 808.130 0.287873 0.143937 0.989587i \(-0.454024\pi\)
0.143937 + 0.989587i \(0.454024\pi\)
\(200\) 2892.83 1.02277
\(201\) 0 0
\(202\) −2187.30 −0.761871
\(203\) −5607.01 −1.93860
\(204\) 0 0
\(205\) 108.404 0.0369329
\(206\) 2703.33 0.914320
\(207\) 0 0
\(208\) 0 0
\(209\) −916.001 −0.303163
\(210\) 0 0
\(211\) −5260.03 −1.71619 −0.858094 0.513493i \(-0.828351\pi\)
−0.858094 + 0.513493i \(0.828351\pi\)
\(212\) 239.676 0.0776464
\(213\) 0 0
\(214\) −2221.41 −0.709590
\(215\) −21.7635 −0.00690351
\(216\) 0 0
\(217\) 3390.51 1.06066
\(218\) 2329.56 0.723751
\(219\) 0 0
\(220\) −7.97824 −0.00244497
\(221\) 0 0
\(222\) 0 0
\(223\) −4690.71 −1.40858 −0.704290 0.709912i \(-0.748734\pi\)
−0.704290 + 0.709912i \(0.748734\pi\)
\(224\) 520.392 0.155224
\(225\) 0 0
\(226\) 155.392 0.0457368
\(227\) −3560.61 −1.04108 −0.520542 0.853836i \(-0.674270\pi\)
−0.520542 + 0.853836i \(0.674270\pi\)
\(228\) 0 0
\(229\) −3144.82 −0.907490 −0.453745 0.891131i \(-0.649912\pi\)
−0.453745 + 0.891131i \(0.649912\pi\)
\(230\) −12.4227 −0.00356144
\(231\) 0 0
\(232\) 4546.07 1.28648
\(233\) 852.543 0.239708 0.119854 0.992792i \(-0.461757\pi\)
0.119854 + 0.992792i \(0.461757\pi\)
\(234\) 0 0
\(235\) −31.9081 −0.00885727
\(236\) 82.3898 0.0227251
\(237\) 0 0
\(238\) 7781.22 2.11925
\(239\) −2189.33 −0.592534 −0.296267 0.955105i \(-0.595742\pi\)
−0.296267 + 0.955105i \(0.595742\pi\)
\(240\) 0 0
\(241\) 6329.98 1.69191 0.845954 0.533257i \(-0.179032\pi\)
0.845954 + 0.533257i \(0.179032\pi\)
\(242\) 7346.65 1.95149
\(243\) 0 0
\(244\) 87.0257 0.0228330
\(245\) 148.152 0.0386331
\(246\) 0 0
\(247\) 0 0
\(248\) −2748.97 −0.703871
\(249\) 0 0
\(250\) −215.738 −0.0545779
\(251\) 3602.97 0.906046 0.453023 0.891499i \(-0.350346\pi\)
0.453023 + 0.891499i \(0.350346\pi\)
\(252\) 0 0
\(253\) −909.695 −0.226055
\(254\) 4593.74 1.13479
\(255\) 0 0
\(256\) −617.315 −0.150712
\(257\) −3072.64 −0.745781 −0.372891 0.927875i \(-0.621633\pi\)
−0.372891 + 0.927875i \(0.621633\pi\)
\(258\) 0 0
\(259\) 9115.80 2.18698
\(260\) 0 0
\(261\) 0 0
\(262\) −1661.01 −0.391671
\(263\) 3543.20 0.830734 0.415367 0.909654i \(-0.363653\pi\)
0.415367 + 0.909654i \(0.363653\pi\)
\(264\) 0 0
\(265\) −186.304 −0.0431871
\(266\) −1140.86 −0.262972
\(267\) 0 0
\(268\) −27.6435 −0.00630072
\(269\) −5899.97 −1.33728 −0.668638 0.743588i \(-0.733122\pi\)
−0.668638 + 0.743588i \(0.733122\pi\)
\(270\) 0 0
\(271\) −2109.52 −0.472858 −0.236429 0.971649i \(-0.575977\pi\)
−0.236429 + 0.971649i \(0.575977\pi\)
\(272\) −5990.32 −1.33535
\(273\) 0 0
\(274\) 1162.19 0.256244
\(275\) −7895.96 −1.73143
\(276\) 0 0
\(277\) 7265.00 1.57585 0.787927 0.615769i \(-0.211155\pi\)
0.787927 + 0.615769i \(0.211155\pi\)
\(278\) 80.4012 0.0173458
\(279\) 0 0
\(280\) −207.223 −0.0442283
\(281\) 4771.36 1.01294 0.506469 0.862258i \(-0.330951\pi\)
0.506469 + 0.862258i \(0.330951\pi\)
\(282\) 0 0
\(283\) 2036.26 0.427714 0.213857 0.976865i \(-0.431397\pi\)
0.213857 + 0.976865i \(0.431397\pi\)
\(284\) −381.275 −0.0796639
\(285\) 0 0
\(286\) 0 0
\(287\) 9886.86 2.03346
\(288\) 0 0
\(289\) 4853.78 0.987947
\(290\) −169.449 −0.0343118
\(291\) 0 0
\(292\) 314.239 0.0629776
\(293\) 3719.02 0.741527 0.370764 0.928727i \(-0.379096\pi\)
0.370764 + 0.928727i \(0.379096\pi\)
\(294\) 0 0
\(295\) −64.0429 −0.0126397
\(296\) −7390.95 −1.45132
\(297\) 0 0
\(298\) 5903.39 1.14756
\(299\) 0 0
\(300\) 0 0
\(301\) −1984.92 −0.380095
\(302\) 4022.22 0.766400
\(303\) 0 0
\(304\) 878.282 0.165700
\(305\) −67.6464 −0.0126997
\(306\) 0 0
\(307\) −7282.24 −1.35381 −0.676905 0.736070i \(-0.736679\pi\)
−0.676905 + 0.736070i \(0.736679\pi\)
\(308\) −727.649 −0.134616
\(309\) 0 0
\(310\) 102.465 0.0187729
\(311\) −4569.28 −0.833120 −0.416560 0.909108i \(-0.636764\pi\)
−0.416560 + 0.909108i \(0.636764\pi\)
\(312\) 0 0
\(313\) 21.0294 0.00379761 0.00189880 0.999998i \(-0.499396\pi\)
0.00189880 + 0.999998i \(0.499396\pi\)
\(314\) 5535.15 0.994797
\(315\) 0 0
\(316\) −96.7138 −0.0172170
\(317\) −5159.17 −0.914095 −0.457047 0.889442i \(-0.651093\pi\)
−0.457047 + 0.889442i \(0.651093\pi\)
\(318\) 0 0
\(319\) −12408.5 −2.17787
\(320\) 167.606 0.0292796
\(321\) 0 0
\(322\) −1133.00 −0.196087
\(323\) −1431.98 −0.246679
\(324\) 0 0
\(325\) 0 0
\(326\) 1511.80 0.256844
\(327\) 0 0
\(328\) −8016.11 −1.34944
\(329\) −2910.15 −0.487666
\(330\) 0 0
\(331\) −7577.53 −1.25830 −0.629152 0.777282i \(-0.716598\pi\)
−0.629152 + 0.777282i \(0.716598\pi\)
\(332\) −344.743 −0.0569887
\(333\) 0 0
\(334\) −10922.0 −1.78929
\(335\) 21.4877 0.00350447
\(336\) 0 0
\(337\) −2109.79 −0.341032 −0.170516 0.985355i \(-0.554543\pi\)
−0.170516 + 0.985355i \(0.554543\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −12.4723 −0.00198943
\(341\) 7503.30 1.19157
\(342\) 0 0
\(343\) 3713.98 0.584653
\(344\) 1609.34 0.252237
\(345\) 0 0
\(346\) −4767.09 −0.740695
\(347\) −8107.91 −1.25434 −0.627169 0.778883i \(-0.715786\pi\)
−0.627169 + 0.778883i \(0.715786\pi\)
\(348\) 0 0
\(349\) 8686.38 1.33230 0.666148 0.745820i \(-0.267942\pi\)
0.666148 + 0.745820i \(0.267942\pi\)
\(350\) −9834.24 −1.50189
\(351\) 0 0
\(352\) 1151.64 0.174383
\(353\) −9050.23 −1.36458 −0.682288 0.731083i \(-0.739015\pi\)
−0.682288 + 0.731083i \(0.739015\pi\)
\(354\) 0 0
\(355\) 296.371 0.0443092
\(356\) −509.336 −0.0758279
\(357\) 0 0
\(358\) 4004.63 0.591204
\(359\) −7043.80 −1.03554 −0.517768 0.855521i \(-0.673237\pi\)
−0.517768 + 0.855521i \(0.673237\pi\)
\(360\) 0 0
\(361\) −6649.05 −0.969390
\(362\) −1516.86 −0.220233
\(363\) 0 0
\(364\) 0 0
\(365\) −244.263 −0.0350282
\(366\) 0 0
\(367\) 13825.1 1.96639 0.983194 0.182565i \(-0.0584401\pi\)
0.983194 + 0.182565i \(0.0584401\pi\)
\(368\) 872.236 0.123556
\(369\) 0 0
\(370\) 275.488 0.0387080
\(371\) −16991.7 −2.37780
\(372\) 0 0
\(373\) 6368.19 0.884001 0.442000 0.897015i \(-0.354269\pi\)
0.442000 + 0.897015i \(0.354269\pi\)
\(374\) 17220.1 2.38082
\(375\) 0 0
\(376\) 2359.51 0.323623
\(377\) 0 0
\(378\) 0 0
\(379\) 2451.66 0.332278 0.166139 0.986102i \(-0.446870\pi\)
0.166139 + 0.986102i \(0.446870\pi\)
\(380\) 1.82865 0.000246863 0
\(381\) 0 0
\(382\) 5150.60 0.689863
\(383\) −10830.9 −1.44500 −0.722500 0.691371i \(-0.757007\pi\)
−0.722500 + 0.691371i \(0.757007\pi\)
\(384\) 0 0
\(385\) 565.613 0.0748735
\(386\) 11456.5 1.51068
\(387\) 0 0
\(388\) −266.861 −0.0349170
\(389\) 4978.07 0.648838 0.324419 0.945914i \(-0.394831\pi\)
0.324419 + 0.945914i \(0.394831\pi\)
\(390\) 0 0
\(391\) −1422.12 −0.183938
\(392\) −10955.4 −1.41156
\(393\) 0 0
\(394\) −4195.56 −0.536470
\(395\) 75.1772 0.00957614
\(396\) 0 0
\(397\) 9450.67 1.19475 0.597375 0.801962i \(-0.296210\pi\)
0.597375 + 0.801962i \(0.296210\pi\)
\(398\) 2227.43 0.280530
\(399\) 0 0
\(400\) 7570.82 0.946353
\(401\) −8776.77 −1.09300 −0.546498 0.837461i \(-0.684039\pi\)
−0.546498 + 0.837461i \(0.684039\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 319.759 0.0393777
\(405\) 0 0
\(406\) −15454.5 −1.88914
\(407\) 20173.5 2.45692
\(408\) 0 0
\(409\) −4520.19 −0.546477 −0.273238 0.961946i \(-0.588095\pi\)
−0.273238 + 0.961946i \(0.588095\pi\)
\(410\) 298.791 0.0359908
\(411\) 0 0
\(412\) −395.197 −0.0472571
\(413\) −5840.98 −0.695922
\(414\) 0 0
\(415\) 267.974 0.0316972
\(416\) 0 0
\(417\) 0 0
\(418\) −2524.75 −0.295430
\(419\) −12006.4 −1.39989 −0.699944 0.714198i \(-0.746792\pi\)
−0.699944 + 0.714198i \(0.746792\pi\)
\(420\) 0 0
\(421\) −9731.52 −1.12657 −0.563284 0.826263i \(-0.690462\pi\)
−0.563284 + 0.826263i \(0.690462\pi\)
\(422\) −14498.1 −1.67241
\(423\) 0 0
\(424\) 13776.6 1.57795
\(425\) −12343.7 −1.40884
\(426\) 0 0
\(427\) −6169.63 −0.699226
\(428\) 324.745 0.0366755
\(429\) 0 0
\(430\) −59.9861 −0.00672741
\(431\) 4111.03 0.459446 0.229723 0.973256i \(-0.426218\pi\)
0.229723 + 0.973256i \(0.426218\pi\)
\(432\) 0 0
\(433\) 2906.06 0.322532 0.161266 0.986911i \(-0.448442\pi\)
0.161266 + 0.986911i \(0.448442\pi\)
\(434\) 9345.19 1.03360
\(435\) 0 0
\(436\) −340.556 −0.0374075
\(437\) 208.507 0.0228243
\(438\) 0 0
\(439\) 8874.72 0.964846 0.482423 0.875938i \(-0.339757\pi\)
0.482423 + 0.875938i \(0.339757\pi\)
\(440\) −458.590 −0.0496873
\(441\) 0 0
\(442\) 0 0
\(443\) −12640.5 −1.35569 −0.677843 0.735207i \(-0.737085\pi\)
−0.677843 + 0.735207i \(0.737085\pi\)
\(444\) 0 0
\(445\) 395.915 0.0421756
\(446\) −12928.9 −1.37265
\(447\) 0 0
\(448\) 15286.4 1.61208
\(449\) 1774.29 0.186490 0.0932451 0.995643i \(-0.470276\pi\)
0.0932451 + 0.995643i \(0.470276\pi\)
\(450\) 0 0
\(451\) 21879.9 2.28444
\(452\) −22.7165 −0.00236393
\(453\) 0 0
\(454\) −9814.04 −1.01453
\(455\) 0 0
\(456\) 0 0
\(457\) 6168.82 0.631433 0.315717 0.948854i \(-0.397755\pi\)
0.315717 + 0.948854i \(0.397755\pi\)
\(458\) −8667.98 −0.884341
\(459\) 0 0
\(460\) 1.81607 0.000184075 0
\(461\) 7455.38 0.753214 0.376607 0.926373i \(-0.377091\pi\)
0.376607 + 0.926373i \(0.377091\pi\)
\(462\) 0 0
\(463\) 5399.78 0.542006 0.271003 0.962578i \(-0.412645\pi\)
0.271003 + 0.962578i \(0.412645\pi\)
\(464\) 11897.5 1.19036
\(465\) 0 0
\(466\) 2349.85 0.233593
\(467\) −3992.01 −0.395564 −0.197782 0.980246i \(-0.563374\pi\)
−0.197782 + 0.980246i \(0.563374\pi\)
\(468\) 0 0
\(469\) 1959.77 0.192950
\(470\) −87.9477 −0.00863133
\(471\) 0 0
\(472\) 4735.77 0.461825
\(473\) −4392.68 −0.427009
\(474\) 0 0
\(475\) 1809.79 0.174819
\(476\) −1137.53 −0.109535
\(477\) 0 0
\(478\) −6034.39 −0.577419
\(479\) −3151.62 −0.300629 −0.150315 0.988638i \(-0.548029\pi\)
−0.150315 + 0.988638i \(0.548029\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 17447.2 1.64875
\(483\) 0 0
\(484\) −1074.00 −0.100864
\(485\) 207.435 0.0194209
\(486\) 0 0
\(487\) −3909.18 −0.363741 −0.181870 0.983323i \(-0.558215\pi\)
−0.181870 + 0.983323i \(0.558215\pi\)
\(488\) 5002.24 0.464018
\(489\) 0 0
\(490\) 408.349 0.0376476
\(491\) −6645.13 −0.610775 −0.305388 0.952228i \(-0.598786\pi\)
−0.305388 + 0.952228i \(0.598786\pi\)
\(492\) 0 0
\(493\) −19398.1 −1.77210
\(494\) 0 0
\(495\) 0 0
\(496\) −7194.33 −0.651281
\(497\) 27030.3 2.43959
\(498\) 0 0
\(499\) 6111.83 0.548303 0.274151 0.961687i \(-0.411603\pi\)
0.274151 + 0.961687i \(0.411603\pi\)
\(500\) 31.5385 0.00282089
\(501\) 0 0
\(502\) 9930.79 0.882934
\(503\) −10954.1 −0.971010 −0.485505 0.874234i \(-0.661364\pi\)
−0.485505 + 0.874234i \(0.661364\pi\)
\(504\) 0 0
\(505\) −248.554 −0.0219020
\(506\) −2507.37 −0.220289
\(507\) 0 0
\(508\) −671.553 −0.0586523
\(509\) 11121.1 0.968439 0.484220 0.874947i \(-0.339104\pi\)
0.484220 + 0.874947i \(0.339104\pi\)
\(510\) 0 0
\(511\) −22277.8 −1.92859
\(512\) −12335.2 −1.06473
\(513\) 0 0
\(514\) −8469.04 −0.726757
\(515\) 307.193 0.0262845
\(516\) 0 0
\(517\) −6440.25 −0.547857
\(518\) 25125.7 2.13119
\(519\) 0 0
\(520\) 0 0
\(521\) −2403.33 −0.202096 −0.101048 0.994882i \(-0.532220\pi\)
−0.101048 + 0.994882i \(0.532220\pi\)
\(522\) 0 0
\(523\) 4251.72 0.355477 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(524\) 242.822 0.0202437
\(525\) 0 0
\(526\) 9766.04 0.809543
\(527\) 11729.8 0.969564
\(528\) 0 0
\(529\) −11959.9 −0.982981
\(530\) −513.506 −0.0420854
\(531\) 0 0
\(532\) 166.781 0.0135918
\(533\) 0 0
\(534\) 0 0
\(535\) −252.429 −0.0203990
\(536\) −1588.95 −0.128045
\(537\) 0 0
\(538\) −16261.9 −1.30316
\(539\) 29902.7 2.38961
\(540\) 0 0
\(541\) −8924.44 −0.709227 −0.354613 0.935013i \(-0.615388\pi\)
−0.354613 + 0.935013i \(0.615388\pi\)
\(542\) −5814.43 −0.460796
\(543\) 0 0
\(544\) 1800.35 0.141892
\(545\) 264.719 0.0208061
\(546\) 0 0
\(547\) −14696.0 −1.14873 −0.574367 0.818598i \(-0.694752\pi\)
−0.574367 + 0.818598i \(0.694752\pi\)
\(548\) −169.900 −0.0132441
\(549\) 0 0
\(550\) −21763.5 −1.68727
\(551\) 2844.09 0.219895
\(552\) 0 0
\(553\) 6856.47 0.527245
\(554\) 20024.3 1.53566
\(555\) 0 0
\(556\) −11.7538 −0.000896530 0
\(557\) −2464.03 −0.187440 −0.0937202 0.995599i \(-0.529876\pi\)
−0.0937202 + 0.995599i \(0.529876\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −542.322 −0.0409237
\(561\) 0 0
\(562\) 13151.2 0.987098
\(563\) −18029.2 −1.34963 −0.674815 0.737987i \(-0.735776\pi\)
−0.674815 + 0.737987i \(0.735776\pi\)
\(564\) 0 0
\(565\) 17.6579 0.00131482
\(566\) 5612.50 0.416804
\(567\) 0 0
\(568\) −21915.7 −1.61895
\(569\) −11924.6 −0.878572 −0.439286 0.898347i \(-0.644768\pi\)
−0.439286 + 0.898347i \(0.644768\pi\)
\(570\) 0 0
\(571\) 5834.77 0.427632 0.213816 0.976874i \(-0.431411\pi\)
0.213816 + 0.976874i \(0.431411\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 27250.9 1.98159
\(575\) 1797.33 0.130355
\(576\) 0 0
\(577\) 15927.5 1.14917 0.574586 0.818444i \(-0.305163\pi\)
0.574586 + 0.818444i \(0.305163\pi\)
\(578\) 13378.4 0.962745
\(579\) 0 0
\(580\) 24.7716 0.00177342
\(581\) 24440.4 1.74519
\(582\) 0 0
\(583\) −37603.1 −2.67129
\(584\) 18062.5 1.27985
\(585\) 0 0
\(586\) 10250.7 0.722612
\(587\) 13511.1 0.950022 0.475011 0.879980i \(-0.342444\pi\)
0.475011 + 0.879980i \(0.342444\pi\)
\(588\) 0 0
\(589\) −1719.80 −0.120311
\(590\) −176.520 −0.0123173
\(591\) 0 0
\(592\) −19342.8 −1.34288
\(593\) −15830.4 −1.09625 −0.548126 0.836396i \(-0.684659\pi\)
−0.548126 + 0.836396i \(0.684659\pi\)
\(594\) 0 0
\(595\) 884.217 0.0609233
\(596\) −863.009 −0.0593125
\(597\) 0 0
\(598\) 0 0
\(599\) 5914.12 0.403413 0.201706 0.979446i \(-0.435351\pi\)
0.201706 + 0.979446i \(0.435351\pi\)
\(600\) 0 0
\(601\) 9892.19 0.671399 0.335700 0.941969i \(-0.391027\pi\)
0.335700 + 0.941969i \(0.391027\pi\)
\(602\) −5470.98 −0.370399
\(603\) 0 0
\(604\) −588.004 −0.0396118
\(605\) 834.836 0.0561007
\(606\) 0 0
\(607\) −16782.3 −1.12220 −0.561098 0.827749i \(-0.689621\pi\)
−0.561098 + 0.827749i \(0.689621\pi\)
\(608\) −263.962 −0.0176070
\(609\) 0 0
\(610\) −186.452 −0.0123758
\(611\) 0 0
\(612\) 0 0
\(613\) 12245.7 0.806847 0.403424 0.915013i \(-0.367820\pi\)
0.403424 + 0.915013i \(0.367820\pi\)
\(614\) −20071.9 −1.31928
\(615\) 0 0
\(616\) −41825.3 −2.73569
\(617\) −10043.7 −0.655341 −0.327670 0.944792i \(-0.606264\pi\)
−0.327670 + 0.944792i \(0.606264\pi\)
\(618\) 0 0
\(619\) −9942.69 −0.645607 −0.322803 0.946466i \(-0.604625\pi\)
−0.322803 + 0.946466i \(0.604625\pi\)
\(620\) −14.9792 −0.000970288 0
\(621\) 0 0
\(622\) −12594.2 −0.811868
\(623\) 36109.1 2.32212
\(624\) 0 0
\(625\) 15588.2 0.997646
\(626\) 57.9628 0.00370074
\(627\) 0 0
\(628\) −809.176 −0.0514166
\(629\) 31537.1 1.99915
\(630\) 0 0
\(631\) 10268.6 0.647841 0.323920 0.946084i \(-0.394999\pi\)
0.323920 + 0.946084i \(0.394999\pi\)
\(632\) −5559.11 −0.349889
\(633\) 0 0
\(634\) −14220.1 −0.890777
\(635\) 522.009 0.0326225
\(636\) 0 0
\(637\) 0 0
\(638\) −34201.2 −2.12232
\(639\) 0 0
\(640\) 416.322 0.0257134
\(641\) 13657.4 0.841555 0.420777 0.907164i \(-0.361757\pi\)
0.420777 + 0.907164i \(0.361757\pi\)
\(642\) 0 0
\(643\) 24671.6 1.51314 0.756572 0.653910i \(-0.226873\pi\)
0.756572 + 0.653910i \(0.226873\pi\)
\(644\) 165.633 0.0101348
\(645\) 0 0
\(646\) −3946.92 −0.240386
\(647\) 16512.3 1.00334 0.501672 0.865058i \(-0.332718\pi\)
0.501672 + 0.865058i \(0.332718\pi\)
\(648\) 0 0
\(649\) −12926.3 −0.781818
\(650\) 0 0
\(651\) 0 0
\(652\) −221.009 −0.0132751
\(653\) −30594.8 −1.83348 −0.916742 0.399479i \(-0.869191\pi\)
−0.916742 + 0.399479i \(0.869191\pi\)
\(654\) 0 0
\(655\) −188.749 −0.0112596
\(656\) −20978.9 −1.24861
\(657\) 0 0
\(658\) −8021.19 −0.475226
\(659\) 2307.79 0.136417 0.0682084 0.997671i \(-0.478272\pi\)
0.0682084 + 0.997671i \(0.478272\pi\)
\(660\) 0 0
\(661\) −27622.5 −1.62540 −0.812700 0.582683i \(-0.802003\pi\)
−0.812700 + 0.582683i \(0.802003\pi\)
\(662\) −20885.8 −1.22621
\(663\) 0 0
\(664\) −19815.9 −1.15814
\(665\) −129.641 −0.00755981
\(666\) 0 0
\(667\) 2824.51 0.163966
\(668\) 1596.67 0.0924805
\(669\) 0 0
\(670\) 59.2260 0.00341508
\(671\) −13653.6 −0.785530
\(672\) 0 0
\(673\) −11305.9 −0.647562 −0.323781 0.946132i \(-0.604954\pi\)
−0.323781 + 0.946132i \(0.604954\pi\)
\(674\) −5815.17 −0.332332
\(675\) 0 0
\(676\) 0 0
\(677\) −15455.8 −0.877419 −0.438710 0.898629i \(-0.644564\pi\)
−0.438710 + 0.898629i \(0.644564\pi\)
\(678\) 0 0
\(679\) 18918.9 1.06928
\(680\) −716.909 −0.0404297
\(681\) 0 0
\(682\) 20681.2 1.16118
\(683\) −16841.9 −0.943540 −0.471770 0.881722i \(-0.656385\pi\)
−0.471770 + 0.881722i \(0.656385\pi\)
\(684\) 0 0
\(685\) 132.066 0.00736639
\(686\) 10236.7 0.569739
\(687\) 0 0
\(688\) 4211.80 0.233391
\(689\) 0 0
\(690\) 0 0
\(691\) −25041.6 −1.37862 −0.689310 0.724467i \(-0.742086\pi\)
−0.689310 + 0.724467i \(0.742086\pi\)
\(692\) 696.896 0.0382832
\(693\) 0 0
\(694\) −22347.6 −1.22234
\(695\) 9.13638 0.000498652 0
\(696\) 0 0
\(697\) 34204.7 1.85881
\(698\) 23942.1 1.29831
\(699\) 0 0
\(700\) 1437.66 0.0776261
\(701\) 28309.0 1.52527 0.762635 0.646829i \(-0.223905\pi\)
0.762635 + 0.646829i \(0.223905\pi\)
\(702\) 0 0
\(703\) −4623.88 −0.248069
\(704\) 33829.1 1.81106
\(705\) 0 0
\(706\) −24945.0 −1.32977
\(707\) −22669.1 −1.20588
\(708\) 0 0
\(709\) −5041.17 −0.267031 −0.133516 0.991047i \(-0.542627\pi\)
−0.133516 + 0.991047i \(0.542627\pi\)
\(710\) 816.882 0.0431789
\(711\) 0 0
\(712\) −29276.6 −1.54100
\(713\) −1707.96 −0.0897103
\(714\) 0 0
\(715\) 0 0
\(716\) −585.431 −0.0305567
\(717\) 0 0
\(718\) −19414.7 −1.00912
\(719\) −11839.2 −0.614088 −0.307044 0.951695i \(-0.599340\pi\)
−0.307044 + 0.951695i \(0.599340\pi\)
\(720\) 0 0
\(721\) 28017.2 1.44718
\(722\) −18326.6 −0.944662
\(723\) 0 0
\(724\) 221.748 0.0113829
\(725\) 24516.1 1.25587
\(726\) 0 0
\(727\) −31004.9 −1.58172 −0.790858 0.611999i \(-0.790365\pi\)
−0.790858 + 0.611999i \(0.790365\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −673.256 −0.0341347
\(731\) −6867.03 −0.347451
\(732\) 0 0
\(733\) 15666.0 0.789411 0.394706 0.918808i \(-0.370847\pi\)
0.394706 + 0.918808i \(0.370847\pi\)
\(734\) 38105.8 1.91623
\(735\) 0 0
\(736\) −262.145 −0.0131288
\(737\) 4337.02 0.216765
\(738\) 0 0
\(739\) −33339.4 −1.65955 −0.829777 0.558095i \(-0.811533\pi\)
−0.829777 + 0.558095i \(0.811533\pi\)
\(740\) −40.2733 −0.00200064
\(741\) 0 0
\(742\) −46833.8 −2.31715
\(743\) −2026.14 −0.100043 −0.0500215 0.998748i \(-0.515929\pi\)
−0.0500215 + 0.998748i \(0.515929\pi\)
\(744\) 0 0
\(745\) 670.831 0.0329897
\(746\) 17552.5 0.861451
\(747\) 0 0
\(748\) −2517.38 −0.123054
\(749\) −23022.6 −1.12313
\(750\) 0 0
\(751\) 35474.8 1.72369 0.861846 0.507170i \(-0.169309\pi\)
0.861846 + 0.507170i \(0.169309\pi\)
\(752\) 6175.06 0.299443
\(753\) 0 0
\(754\) 0 0
\(755\) 457.065 0.0220322
\(756\) 0 0
\(757\) 2398.58 0.115162 0.0575811 0.998341i \(-0.481661\pi\)
0.0575811 + 0.998341i \(0.481661\pi\)
\(758\) 6757.46 0.323802
\(759\) 0 0
\(760\) 105.111 0.00501682
\(761\) 5005.07 0.238415 0.119207 0.992869i \(-0.461965\pi\)
0.119207 + 0.992869i \(0.461965\pi\)
\(762\) 0 0
\(763\) 24143.5 1.14555
\(764\) −752.960 −0.0356559
\(765\) 0 0
\(766\) −29853.1 −1.40814
\(767\) 0 0
\(768\) 0 0
\(769\) 14109.6 0.661644 0.330822 0.943693i \(-0.392674\pi\)
0.330822 + 0.943693i \(0.392674\pi\)
\(770\) 1558.99 0.0729635
\(771\) 0 0
\(772\) −1674.82 −0.0780803
\(773\) 12733.7 0.592496 0.296248 0.955111i \(-0.404265\pi\)
0.296248 + 0.955111i \(0.404265\pi\)
\(774\) 0 0
\(775\) −14824.7 −0.687121
\(776\) −15339.2 −0.709593
\(777\) 0 0
\(778\) 13720.9 0.632287
\(779\) −5014.98 −0.230655
\(780\) 0 0
\(781\) 59818.8 2.74070
\(782\) −3919.75 −0.179246
\(783\) 0 0
\(784\) −28671.3 −1.30609
\(785\) 628.986 0.0285980
\(786\) 0 0
\(787\) 28429.3 1.28767 0.643834 0.765165i \(-0.277343\pi\)
0.643834 + 0.765165i \(0.277343\pi\)
\(788\) 613.344 0.0277278
\(789\) 0 0
\(790\) 207.209 0.00933186
\(791\) 1610.48 0.0723918
\(792\) 0 0
\(793\) 0 0
\(794\) 26048.7 1.16427
\(795\) 0 0
\(796\) −325.625 −0.0144993
\(797\) −11926.7 −0.530070 −0.265035 0.964239i \(-0.585384\pi\)
−0.265035 + 0.964239i \(0.585384\pi\)
\(798\) 0 0
\(799\) −10068.0 −0.445782
\(800\) −2275.36 −0.100558
\(801\) 0 0
\(802\) −24191.2 −1.06511
\(803\) −49301.4 −2.16663
\(804\) 0 0
\(805\) −128.749 −0.00563702
\(806\) 0 0
\(807\) 0 0
\(808\) 18379.7 0.800244
\(809\) −20005.7 −0.869421 −0.434710 0.900570i \(-0.643149\pi\)
−0.434710 + 0.900570i \(0.643149\pi\)
\(810\) 0 0
\(811\) −5933.84 −0.256924 −0.128462 0.991714i \(-0.541004\pi\)
−0.128462 + 0.991714i \(0.541004\pi\)
\(812\) 2259.27 0.0976415
\(813\) 0 0
\(814\) 55603.8 2.39424
\(815\) 171.794 0.00738364
\(816\) 0 0
\(817\) 1006.82 0.0431142
\(818\) −12458.9 −0.532537
\(819\) 0 0
\(820\) −43.6798 −0.00186020
\(821\) 18457.0 0.784597 0.392299 0.919838i \(-0.371680\pi\)
0.392299 + 0.919838i \(0.371680\pi\)
\(822\) 0 0
\(823\) −26520.3 −1.12325 −0.561627 0.827390i \(-0.689825\pi\)
−0.561627 + 0.827390i \(0.689825\pi\)
\(824\) −22715.9 −0.960372
\(825\) 0 0
\(826\) −16099.4 −0.678170
\(827\) 25664.8 1.07915 0.539573 0.841939i \(-0.318586\pi\)
0.539573 + 0.841939i \(0.318586\pi\)
\(828\) 0 0
\(829\) 4362.69 0.182777 0.0913887 0.995815i \(-0.470869\pi\)
0.0913887 + 0.995815i \(0.470869\pi\)
\(830\) 738.612 0.0308887
\(831\) 0 0
\(832\) 0 0
\(833\) 46746.6 1.94439
\(834\) 0 0
\(835\) −1241.12 −0.0514378
\(836\) 369.091 0.0152695
\(837\) 0 0
\(838\) −33093.1 −1.36418
\(839\) 35020.2 1.44104 0.720520 0.693435i \(-0.243903\pi\)
0.720520 + 0.693435i \(0.243903\pi\)
\(840\) 0 0
\(841\) 14138.0 0.579687
\(842\) −26822.8 −1.09783
\(843\) 0 0
\(844\) 2119.46 0.0864394
\(845\) 0 0
\(846\) 0 0
\(847\) 76140.4 3.08880
\(848\) 36054.7 1.46005
\(849\) 0 0
\(850\) −34022.6 −1.37290
\(851\) −4592.04 −0.184974
\(852\) 0 0
\(853\) 8318.36 0.333898 0.166949 0.985966i \(-0.446608\pi\)
0.166949 + 0.985966i \(0.446608\pi\)
\(854\) −17005.2 −0.681389
\(855\) 0 0
\(856\) 18666.3 0.745330
\(857\) −34832.3 −1.38839 −0.694193 0.719789i \(-0.744239\pi\)
−0.694193 + 0.719789i \(0.744239\pi\)
\(858\) 0 0
\(859\) −12571.8 −0.499353 −0.249676 0.968329i \(-0.580324\pi\)
−0.249676 + 0.968329i \(0.580324\pi\)
\(860\) 8.76930 0.000347710 0
\(861\) 0 0
\(862\) 11331.1 0.447726
\(863\) −22474.2 −0.886480 −0.443240 0.896403i \(-0.646171\pi\)
−0.443240 + 0.896403i \(0.646171\pi\)
\(864\) 0 0
\(865\) −541.708 −0.0212932
\(866\) 8009.90 0.314304
\(867\) 0 0
\(868\) −1366.16 −0.0534223
\(869\) 15173.6 0.592322
\(870\) 0 0
\(871\) 0 0
\(872\) −19575.2 −0.760205
\(873\) 0 0
\(874\) 574.702 0.0222421
\(875\) −2235.90 −0.0863855
\(876\) 0 0
\(877\) 5385.19 0.207349 0.103675 0.994611i \(-0.466940\pi\)
0.103675 + 0.994611i \(0.466940\pi\)
\(878\) 24461.2 0.940233
\(879\) 0 0
\(880\) −1200.17 −0.0459749
\(881\) 29772.7 1.13856 0.569278 0.822145i \(-0.307223\pi\)
0.569278 + 0.822145i \(0.307223\pi\)
\(882\) 0 0
\(883\) −27309.6 −1.04082 −0.520409 0.853917i \(-0.674220\pi\)
−0.520409 + 0.853917i \(0.674220\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −34840.7 −1.32110
\(887\) 6529.97 0.247187 0.123594 0.992333i \(-0.460558\pi\)
0.123594 + 0.992333i \(0.460558\pi\)
\(888\) 0 0
\(889\) 47609.3 1.79614
\(890\) 1091.25 0.0410998
\(891\) 0 0
\(892\) 1890.06 0.0709461
\(893\) 1476.14 0.0553159
\(894\) 0 0
\(895\) 455.065 0.0169957
\(896\) 37970.3 1.41573
\(897\) 0 0
\(898\) 4890.45 0.181733
\(899\) −23297.0 −0.864290
\(900\) 0 0
\(901\) −58784.6 −2.17358
\(902\) 60307.1 2.22617
\(903\) 0 0
\(904\) −1305.75 −0.0480404
\(905\) −172.368 −0.00633116
\(906\) 0 0
\(907\) 19437.4 0.711586 0.355793 0.934565i \(-0.384211\pi\)
0.355793 + 0.934565i \(0.384211\pi\)
\(908\) 1434.70 0.0524364
\(909\) 0 0
\(910\) 0 0
\(911\) −50234.6 −1.82694 −0.913472 0.406901i \(-0.866609\pi\)
−0.913472 + 0.406901i \(0.866609\pi\)
\(912\) 0 0
\(913\) 54087.2 1.96060
\(914\) 17003.0 0.615326
\(915\) 0 0
\(916\) 1267.16 0.0457077
\(917\) −17214.7 −0.619934
\(918\) 0 0
\(919\) 12285.2 0.440971 0.220486 0.975390i \(-0.429236\pi\)
0.220486 + 0.975390i \(0.429236\pi\)
\(920\) 104.387 0.00374082
\(921\) 0 0
\(922\) 20549.1 0.734000
\(923\) 0 0
\(924\) 0 0
\(925\) −39858.0 −1.41678
\(926\) 14883.3 0.528180
\(927\) 0 0
\(928\) −3575.72 −0.126486
\(929\) −25610.0 −0.904454 −0.452227 0.891903i \(-0.649370\pi\)
−0.452227 + 0.891903i \(0.649370\pi\)
\(930\) 0 0
\(931\) −6853.84 −0.241273
\(932\) −343.521 −0.0120734
\(933\) 0 0
\(934\) −11003.1 −0.385474
\(935\) 1956.80 0.0684429
\(936\) 0 0
\(937\) −29893.2 −1.04223 −0.521114 0.853487i \(-0.674483\pi\)
−0.521114 + 0.853487i \(0.674483\pi\)
\(938\) 5401.66 0.188028
\(939\) 0 0
\(940\) 12.8570 0.000446115 0
\(941\) −44960.3 −1.55756 −0.778780 0.627297i \(-0.784161\pi\)
−0.778780 + 0.627297i \(0.784161\pi\)
\(942\) 0 0
\(943\) −4980.46 −0.171989
\(944\) 12394.0 0.427320
\(945\) 0 0
\(946\) −12107.4 −0.416117
\(947\) 33597.6 1.15288 0.576439 0.817140i \(-0.304442\pi\)
0.576439 + 0.817140i \(0.304442\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 4988.29 0.170360
\(951\) 0 0
\(952\) −65385.1 −2.22599
\(953\) 25850.3 0.878670 0.439335 0.898323i \(-0.355214\pi\)
0.439335 + 0.898323i \(0.355214\pi\)
\(954\) 0 0
\(955\) 585.288 0.0198319
\(956\) 882.160 0.0298442
\(957\) 0 0
\(958\) −8686.75 −0.292960
\(959\) 12044.9 0.405580
\(960\) 0 0
\(961\) −15703.5 −0.527123
\(962\) 0 0
\(963\) 0 0
\(964\) −2550.58 −0.0852165
\(965\) 1301.86 0.0434284
\(966\) 0 0
\(967\) 6296.49 0.209392 0.104696 0.994504i \(-0.466613\pi\)
0.104696 + 0.994504i \(0.466613\pi\)
\(968\) −61733.5 −2.04978
\(969\) 0 0
\(970\) 571.749 0.0189255
\(971\) 7806.43 0.258002 0.129001 0.991644i \(-0.458823\pi\)
0.129001 + 0.991644i \(0.458823\pi\)
\(972\) 0 0
\(973\) 833.276 0.0274549
\(974\) −10774.8 −0.354462
\(975\) 0 0
\(976\) 13091.3 0.429348
\(977\) −55692.8 −1.82372 −0.911858 0.410507i \(-0.865352\pi\)
−0.911858 + 0.410507i \(0.865352\pi\)
\(978\) 0 0
\(979\) 79910.4 2.60873
\(980\) −59.6960 −0.00194584
\(981\) 0 0
\(982\) −18315.8 −0.595195
\(983\) 44635.5 1.44827 0.724135 0.689658i \(-0.242239\pi\)
0.724135 + 0.689658i \(0.242239\pi\)
\(984\) 0 0
\(985\) −476.762 −0.0154222
\(986\) −53466.4 −1.72689
\(987\) 0 0
\(988\) 0 0
\(989\) 999.892 0.0321484
\(990\) 0 0
\(991\) 3884.32 0.124510 0.0622551 0.998060i \(-0.480171\pi\)
0.0622551 + 0.998060i \(0.480171\pi\)
\(992\) 2162.21 0.0692039
\(993\) 0 0
\(994\) 74503.0 2.37735
\(995\) 253.114 0.00806456
\(996\) 0 0
\(997\) −18021.4 −0.572462 −0.286231 0.958161i \(-0.592402\pi\)
−0.286231 + 0.958161i \(0.592402\pi\)
\(998\) 16845.9 0.534316
\(999\) 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 1521.4.a.bc.1.6 8
3.2 odd 2 inner 1521.4.a.bc.1.3 8
13.3 even 3 117.4.g.f.100.3 yes 16
13.9 even 3 117.4.g.f.55.3 16
13.12 even 2 1521.4.a.bd.1.3 8
39.29 odd 6 117.4.g.f.100.6 yes 16
39.35 odd 6 117.4.g.f.55.6 yes 16
39.38 odd 2 1521.4.a.bd.1.6 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.g.f.55.3 16 13.9 even 3
117.4.g.f.55.6 yes 16 39.35 odd 6
117.4.g.f.100.3 yes 16 13.3 even 3
117.4.g.f.100.6 yes 16 39.29 odd 6
1521.4.a.bc.1.3 8 3.2 odd 2 inner
1521.4.a.bc.1.6 8 1.1 even 1 trivial
1521.4.a.bd.1.3 8 13.12 even 2
1521.4.a.bd.1.6 8 39.38 odd 2