Properties

Label 1521.4.a.bm.1.12
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 7\cdot 13^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(1.32218\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.32218 q^{2} -6.25184 q^{4} -12.9610 q^{5} -5.54391 q^{7} -18.8435 q^{8} +O(q^{10})\) \(q+1.32218 q^{2} -6.25184 q^{4} -12.9610 q^{5} -5.54391 q^{7} -18.8435 q^{8} -17.1367 q^{10} +0.841909 q^{11} -7.33006 q^{14} +25.1002 q^{16} +10.1858 q^{17} +73.0894 q^{19} +81.0298 q^{20} +1.11316 q^{22} +139.073 q^{23} +42.9863 q^{25} +34.6596 q^{28} +250.377 q^{29} +161.445 q^{31} +183.935 q^{32} +13.4674 q^{34} +71.8544 q^{35} -195.826 q^{37} +96.6374 q^{38} +244.230 q^{40} -183.760 q^{41} +115.071 q^{43} -5.26348 q^{44} +183.880 q^{46} -551.780 q^{47} -312.265 q^{49} +56.8357 q^{50} -324.717 q^{53} -10.9119 q^{55} +104.467 q^{56} +331.043 q^{58} +521.559 q^{59} -444.586 q^{61} +213.459 q^{62} +42.3942 q^{64} -55.0046 q^{67} -63.6797 q^{68} +95.0045 q^{70} -279.871 q^{71} -908.097 q^{73} -258.918 q^{74} -456.943 q^{76} -4.66747 q^{77} +941.507 q^{79} -325.322 q^{80} -242.964 q^{82} +946.563 q^{83} -132.017 q^{85} +152.145 q^{86} -15.8645 q^{88} +32.9886 q^{89} -869.461 q^{92} -729.553 q^{94} -947.308 q^{95} +68.2675 q^{97} -412.871 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 56 q^{4} - 94 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 56 q^{4} - 94 q^{7} + 156 q^{10} + 88 q^{16} - 448 q^{19} - 256 q^{22} - 16 q^{25} - 1300 q^{28} - 818 q^{31} - 900 q^{34} - 524 q^{37} + 800 q^{40} + 752 q^{43} - 1650 q^{46} + 2948 q^{49} - 464 q^{55} - 1626 q^{58} - 1784 q^{61} - 4274 q^{64} - 2872 q^{67} - 5772 q^{70} - 3078 q^{73} - 5726 q^{76} + 3326 q^{79} - 1038 q^{82} - 2340 q^{85} + 780 q^{88} + 1220 q^{94} - 4630 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32218 0.467462 0.233731 0.972301i \(-0.424907\pi\)
0.233731 + 0.972301i \(0.424907\pi\)
\(3\) 0 0
\(4\) −6.25184 −0.781480
\(5\) −12.9610 −1.15926 −0.579631 0.814879i \(-0.696803\pi\)
−0.579631 + 0.814879i \(0.696803\pi\)
\(6\) 0 0
\(7\) −5.54391 −0.299343 −0.149672 0.988736i \(-0.547822\pi\)
−0.149672 + 0.988736i \(0.547822\pi\)
\(8\) −18.8435 −0.832773
\(9\) 0 0
\(10\) −17.1367 −0.541911
\(11\) 0.841909 0.0230768 0.0115384 0.999933i \(-0.496327\pi\)
0.0115384 + 0.999933i \(0.496327\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −7.33006 −0.139931
\(15\) 0 0
\(16\) 25.1002 0.392190
\(17\) 10.1858 0.145318 0.0726591 0.997357i \(-0.476851\pi\)
0.0726591 + 0.997357i \(0.476851\pi\)
\(18\) 0 0
\(19\) 73.0894 0.882519 0.441260 0.897380i \(-0.354532\pi\)
0.441260 + 0.897380i \(0.354532\pi\)
\(20\) 81.0298 0.905940
\(21\) 0 0
\(22\) 1.11316 0.0107875
\(23\) 139.073 1.26081 0.630407 0.776265i \(-0.282888\pi\)
0.630407 + 0.776265i \(0.282888\pi\)
\(24\) 0 0
\(25\) 42.9863 0.343890
\(26\) 0 0
\(27\) 0 0
\(28\) 34.6596 0.233931
\(29\) 250.377 1.60323 0.801617 0.597838i \(-0.203973\pi\)
0.801617 + 0.597838i \(0.203973\pi\)
\(30\) 0 0
\(31\) 161.445 0.935366 0.467683 0.883896i \(-0.345089\pi\)
0.467683 + 0.883896i \(0.345089\pi\)
\(32\) 183.935 1.01611
\(33\) 0 0
\(34\) 13.4674 0.0679307
\(35\) 71.8544 0.347017
\(36\) 0 0
\(37\) −195.826 −0.870099 −0.435049 0.900407i \(-0.643269\pi\)
−0.435049 + 0.900407i \(0.643269\pi\)
\(38\) 96.6374 0.412544
\(39\) 0 0
\(40\) 244.230 0.965403
\(41\) −183.760 −0.699962 −0.349981 0.936757i \(-0.613812\pi\)
−0.349981 + 0.936757i \(0.613812\pi\)
\(42\) 0 0
\(43\) 115.071 0.408097 0.204049 0.978961i \(-0.434590\pi\)
0.204049 + 0.978961i \(0.434590\pi\)
\(44\) −5.26348 −0.0180341
\(45\) 0 0
\(46\) 183.880 0.589382
\(47\) −551.780 −1.71245 −0.856227 0.516600i \(-0.827198\pi\)
−0.856227 + 0.516600i \(0.827198\pi\)
\(48\) 0 0
\(49\) −312.265 −0.910394
\(50\) 56.8357 0.160755
\(51\) 0 0
\(52\) 0 0
\(53\) −324.717 −0.841572 −0.420786 0.907160i \(-0.638246\pi\)
−0.420786 + 0.907160i \(0.638246\pi\)
\(54\) 0 0
\(55\) −10.9119 −0.0267521
\(56\) 104.467 0.249285
\(57\) 0 0
\(58\) 331.043 0.749450
\(59\) 521.559 1.15087 0.575434 0.817848i \(-0.304833\pi\)
0.575434 + 0.817848i \(0.304833\pi\)
\(60\) 0 0
\(61\) −444.586 −0.933170 −0.466585 0.884476i \(-0.654516\pi\)
−0.466585 + 0.884476i \(0.654516\pi\)
\(62\) 213.459 0.437248
\(63\) 0 0
\(64\) 42.3942 0.0828011
\(65\) 0 0
\(66\) 0 0
\(67\) −55.0046 −0.100297 −0.0501484 0.998742i \(-0.515969\pi\)
−0.0501484 + 0.998742i \(0.515969\pi\)
\(68\) −63.6797 −0.113563
\(69\) 0 0
\(70\) 95.0045 0.162217
\(71\) −279.871 −0.467811 −0.233906 0.972259i \(-0.575151\pi\)
−0.233906 + 0.972259i \(0.575151\pi\)
\(72\) 0 0
\(73\) −908.097 −1.45596 −0.727978 0.685601i \(-0.759540\pi\)
−0.727978 + 0.685601i \(0.759540\pi\)
\(74\) −258.918 −0.406738
\(75\) 0 0
\(76\) −456.943 −0.689671
\(77\) −4.66747 −0.00690789
\(78\) 0 0
\(79\) 941.507 1.34086 0.670429 0.741974i \(-0.266110\pi\)
0.670429 + 0.741974i \(0.266110\pi\)
\(80\) −325.322 −0.454651
\(81\) 0 0
\(82\) −242.964 −0.327206
\(83\) 946.563 1.25179 0.625896 0.779906i \(-0.284733\pi\)
0.625896 + 0.779906i \(0.284733\pi\)
\(84\) 0 0
\(85\) −132.017 −0.168462
\(86\) 152.145 0.190770
\(87\) 0 0
\(88\) −15.8645 −0.0192178
\(89\) 32.9886 0.0392897 0.0196448 0.999807i \(-0.493746\pi\)
0.0196448 + 0.999807i \(0.493746\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −869.461 −0.985300
\(93\) 0 0
\(94\) −729.553 −0.800507
\(95\) −947.308 −1.02307
\(96\) 0 0
\(97\) 68.2675 0.0714589 0.0357294 0.999361i \(-0.488625\pi\)
0.0357294 + 0.999361i \(0.488625\pi\)
\(98\) −412.871 −0.425574
\(99\) 0 0
\(100\) −268.743 −0.268743
\(101\) −1643.68 −1.61933 −0.809667 0.586890i \(-0.800352\pi\)
−0.809667 + 0.586890i \(0.800352\pi\)
\(102\) 0 0
\(103\) −166.289 −0.159078 −0.0795388 0.996832i \(-0.525345\pi\)
−0.0795388 + 0.996832i \(0.525345\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −429.335 −0.393403
\(107\) −445.544 −0.402546 −0.201273 0.979535i \(-0.564508\pi\)
−0.201273 + 0.979535i \(0.564508\pi\)
\(108\) 0 0
\(109\) 884.955 0.777645 0.388822 0.921313i \(-0.372882\pi\)
0.388822 + 0.921313i \(0.372882\pi\)
\(110\) −14.4276 −0.0125056
\(111\) 0 0
\(112\) −139.153 −0.117399
\(113\) 1513.58 1.26005 0.630023 0.776576i \(-0.283045\pi\)
0.630023 + 0.776576i \(0.283045\pi\)
\(114\) 0 0
\(115\) −1802.52 −1.46161
\(116\) −1565.31 −1.25289
\(117\) 0 0
\(118\) 689.596 0.537987
\(119\) −56.4690 −0.0435000
\(120\) 0 0
\(121\) −1330.29 −0.999467
\(122\) −587.823 −0.436221
\(123\) 0 0
\(124\) −1009.33 −0.730970
\(125\) 1062.98 0.760604
\(126\) 0 0
\(127\) 2584.41 1.80574 0.902871 0.429912i \(-0.141455\pi\)
0.902871 + 0.429912i \(0.141455\pi\)
\(128\) −1415.43 −0.977401
\(129\) 0 0
\(130\) 0 0
\(131\) 1486.33 0.991311 0.495655 0.868519i \(-0.334928\pi\)
0.495655 + 0.868519i \(0.334928\pi\)
\(132\) 0 0
\(133\) −405.201 −0.264176
\(134\) −72.7261 −0.0468849
\(135\) 0 0
\(136\) −191.935 −0.121017
\(137\) 1481.51 0.923895 0.461947 0.886907i \(-0.347151\pi\)
0.461947 + 0.886907i \(0.347151\pi\)
\(138\) 0 0
\(139\) −917.381 −0.559793 −0.279897 0.960030i \(-0.590300\pi\)
−0.279897 + 0.960030i \(0.590300\pi\)
\(140\) −449.222 −0.271187
\(141\) 0 0
\(142\) −370.040 −0.218684
\(143\) 0 0
\(144\) 0 0
\(145\) −3245.12 −1.85857
\(146\) −1200.67 −0.680603
\(147\) 0 0
\(148\) 1224.27 0.679965
\(149\) −2278.14 −1.25257 −0.626283 0.779596i \(-0.715424\pi\)
−0.626283 + 0.779596i \(0.715424\pi\)
\(150\) 0 0
\(151\) −2196.92 −1.18399 −0.591996 0.805941i \(-0.701660\pi\)
−0.591996 + 0.805941i \(0.701660\pi\)
\(152\) −1377.26 −0.734938
\(153\) 0 0
\(154\) −6.17124 −0.00322917
\(155\) −2092.48 −1.08434
\(156\) 0 0
\(157\) 3197.69 1.62550 0.812750 0.582612i \(-0.197969\pi\)
0.812750 + 0.582612i \(0.197969\pi\)
\(158\) 1244.84 0.626800
\(159\) 0 0
\(160\) −2383.97 −1.17794
\(161\) −771.008 −0.377416
\(162\) 0 0
\(163\) −3083.17 −1.48155 −0.740774 0.671754i \(-0.765541\pi\)
−0.740774 + 0.671754i \(0.765541\pi\)
\(164\) 1148.84 0.547006
\(165\) 0 0
\(166\) 1251.53 0.585165
\(167\) −524.082 −0.242842 −0.121421 0.992601i \(-0.538745\pi\)
−0.121421 + 0.992601i \(0.538745\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −174.551 −0.0787495
\(171\) 0 0
\(172\) −719.405 −0.318919
\(173\) −2981.68 −1.31036 −0.655182 0.755471i \(-0.727408\pi\)
−0.655182 + 0.755471i \(0.727408\pi\)
\(174\) 0 0
\(175\) −238.312 −0.102941
\(176\) 21.1321 0.00905050
\(177\) 0 0
\(178\) 43.6168 0.0183664
\(179\) 332.862 0.138990 0.0694952 0.997582i \(-0.477861\pi\)
0.0694952 + 0.997582i \(0.477861\pi\)
\(180\) 0 0
\(181\) −2546.13 −1.04559 −0.522796 0.852458i \(-0.675111\pi\)
−0.522796 + 0.852458i \(0.675111\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2620.62 −1.04997
\(185\) 2538.10 1.00867
\(186\) 0 0
\(187\) 8.57548 0.00335348
\(188\) 3449.64 1.33825
\(189\) 0 0
\(190\) −1252.51 −0.478247
\(191\) 3424.25 1.29723 0.648613 0.761118i \(-0.275349\pi\)
0.648613 + 0.761118i \(0.275349\pi\)
\(192\) 0 0
\(193\) −2912.13 −1.08611 −0.543055 0.839697i \(-0.682733\pi\)
−0.543055 + 0.839697i \(0.682733\pi\)
\(194\) 90.2620 0.0334043
\(195\) 0 0
\(196\) 1952.23 0.711454
\(197\) −80.9189 −0.0292651 −0.0146326 0.999893i \(-0.504658\pi\)
−0.0146326 + 0.999893i \(0.504658\pi\)
\(198\) 0 0
\(199\) −875.929 −0.312025 −0.156013 0.987755i \(-0.549864\pi\)
−0.156013 + 0.987755i \(0.549864\pi\)
\(200\) −810.012 −0.286383
\(201\) 0 0
\(202\) −2173.25 −0.756977
\(203\) −1388.07 −0.479917
\(204\) 0 0
\(205\) 2381.70 0.811440
\(206\) −219.865 −0.0743626
\(207\) 0 0
\(208\) 0 0
\(209\) 61.5347 0.0203657
\(210\) 0 0
\(211\) −3862.86 −1.26033 −0.630167 0.776460i \(-0.717014\pi\)
−0.630167 + 0.776460i \(0.717014\pi\)
\(212\) 2030.08 0.657672
\(213\) 0 0
\(214\) −589.090 −0.188175
\(215\) −1491.43 −0.473092
\(216\) 0 0
\(217\) −895.036 −0.279996
\(218\) 1170.07 0.363519
\(219\) 0 0
\(220\) 68.2197 0.0209062
\(221\) 0 0
\(222\) 0 0
\(223\) −6391.24 −1.91923 −0.959617 0.281311i \(-0.909231\pi\)
−0.959617 + 0.281311i \(0.909231\pi\)
\(224\) −1019.72 −0.304165
\(225\) 0 0
\(226\) 2001.22 0.589023
\(227\) −1271.34 −0.371727 −0.185864 0.982576i \(-0.559508\pi\)
−0.185864 + 0.982576i \(0.559508\pi\)
\(228\) 0 0
\(229\) −5964.71 −1.72122 −0.860610 0.509265i \(-0.829917\pi\)
−0.860610 + 0.509265i \(0.829917\pi\)
\(230\) −2383.25 −0.683249
\(231\) 0 0
\(232\) −4717.98 −1.33513
\(233\) 5160.98 1.45110 0.725551 0.688168i \(-0.241585\pi\)
0.725551 + 0.688168i \(0.241585\pi\)
\(234\) 0 0
\(235\) 7151.59 1.98518
\(236\) −3260.70 −0.899380
\(237\) 0 0
\(238\) −74.6622 −0.0203346
\(239\) 3799.33 1.02828 0.514139 0.857707i \(-0.328112\pi\)
0.514139 + 0.857707i \(0.328112\pi\)
\(240\) 0 0
\(241\) 120.502 0.0322083 0.0161042 0.999870i \(-0.494874\pi\)
0.0161042 + 0.999870i \(0.494874\pi\)
\(242\) −1758.89 −0.467213
\(243\) 0 0
\(244\) 2779.48 0.729253
\(245\) 4047.25 1.05539
\(246\) 0 0
\(247\) 0 0
\(248\) −3042.19 −0.778948
\(249\) 0 0
\(250\) 1405.45 0.355553
\(251\) 6961.35 1.75058 0.875292 0.483595i \(-0.160669\pi\)
0.875292 + 0.483595i \(0.160669\pi\)
\(252\) 0 0
\(253\) 117.087 0.0290956
\(254\) 3417.06 0.844115
\(255\) 0 0
\(256\) −2210.60 −0.539698
\(257\) 1154.03 0.280103 0.140052 0.990144i \(-0.455273\pi\)
0.140052 + 0.990144i \(0.455273\pi\)
\(258\) 0 0
\(259\) 1085.64 0.260458
\(260\) 0 0
\(261\) 0 0
\(262\) 1965.20 0.463400
\(263\) 2627.40 0.616018 0.308009 0.951383i \(-0.400337\pi\)
0.308009 + 0.951383i \(0.400337\pi\)
\(264\) 0 0
\(265\) 4208.64 0.975604
\(266\) −535.750 −0.123492
\(267\) 0 0
\(268\) 343.880 0.0783799
\(269\) −5162.02 −1.17001 −0.585007 0.811028i \(-0.698908\pi\)
−0.585007 + 0.811028i \(0.698908\pi\)
\(270\) 0 0
\(271\) −3053.24 −0.684394 −0.342197 0.939628i \(-0.611171\pi\)
−0.342197 + 0.939628i \(0.611171\pi\)
\(272\) 255.664 0.0569924
\(273\) 0 0
\(274\) 1958.82 0.431885
\(275\) 36.1905 0.00793590
\(276\) 0 0
\(277\) −3425.81 −0.743094 −0.371547 0.928414i \(-0.621173\pi\)
−0.371547 + 0.928414i \(0.621173\pi\)
\(278\) −1212.94 −0.261682
\(279\) 0 0
\(280\) −1353.99 −0.288987
\(281\) −5619.38 −1.19297 −0.596484 0.802625i \(-0.703436\pi\)
−0.596484 + 0.802625i \(0.703436\pi\)
\(282\) 0 0
\(283\) −2181.00 −0.458116 −0.229058 0.973413i \(-0.573565\pi\)
−0.229058 + 0.973413i \(0.573565\pi\)
\(284\) 1749.71 0.365585
\(285\) 0 0
\(286\) 0 0
\(287\) 1018.75 0.209529
\(288\) 0 0
\(289\) −4809.25 −0.978883
\(290\) −4290.64 −0.868810
\(291\) 0 0
\(292\) 5677.28 1.13780
\(293\) −4610.74 −0.919325 −0.459662 0.888094i \(-0.652030\pi\)
−0.459662 + 0.888094i \(0.652030\pi\)
\(294\) 0 0
\(295\) −6759.91 −1.33416
\(296\) 3690.06 0.724595
\(297\) 0 0
\(298\) −3012.11 −0.585526
\(299\) 0 0
\(300\) 0 0
\(301\) −637.944 −0.122161
\(302\) −2904.73 −0.553471
\(303\) 0 0
\(304\) 1834.56 0.346115
\(305\) 5762.25 1.08179
\(306\) 0 0
\(307\) −4432.85 −0.824091 −0.412045 0.911163i \(-0.635186\pi\)
−0.412045 + 0.911163i \(0.635186\pi\)
\(308\) 29.1803 0.00539838
\(309\) 0 0
\(310\) −2766.64 −0.506885
\(311\) 8942.00 1.63040 0.815200 0.579180i \(-0.196627\pi\)
0.815200 + 0.579180i \(0.196627\pi\)
\(312\) 0 0
\(313\) 7883.46 1.42364 0.711820 0.702362i \(-0.247871\pi\)
0.711820 + 0.702362i \(0.247871\pi\)
\(314\) 4227.93 0.759859
\(315\) 0 0
\(316\) −5886.15 −1.04785
\(317\) 670.707 0.118835 0.0594174 0.998233i \(-0.481076\pi\)
0.0594174 + 0.998233i \(0.481076\pi\)
\(318\) 0 0
\(319\) 210.794 0.0369976
\(320\) −549.469 −0.0959882
\(321\) 0 0
\(322\) −1019.41 −0.176427
\(323\) 744.471 0.128246
\(324\) 0 0
\(325\) 0 0
\(326\) −4076.51 −0.692567
\(327\) 0 0
\(328\) 3462.68 0.582910
\(329\) 3059.02 0.512611
\(330\) 0 0
\(331\) 2842.70 0.472051 0.236026 0.971747i \(-0.424155\pi\)
0.236026 + 0.971747i \(0.424155\pi\)
\(332\) −5917.76 −0.978251
\(333\) 0 0
\(334\) −692.931 −0.113520
\(335\) 712.912 0.116270
\(336\) 0 0
\(337\) 1886.14 0.304880 0.152440 0.988313i \(-0.451287\pi\)
0.152440 + 0.988313i \(0.451287\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 825.350 0.131650
\(341\) 135.922 0.0215853
\(342\) 0 0
\(343\) 3632.73 0.571863
\(344\) −2168.34 −0.339852
\(345\) 0 0
\(346\) −3942.32 −0.612545
\(347\) 4059.65 0.628050 0.314025 0.949415i \(-0.398322\pi\)
0.314025 + 0.949415i \(0.398322\pi\)
\(348\) 0 0
\(349\) −7316.53 −1.12219 −0.561096 0.827751i \(-0.689620\pi\)
−0.561096 + 0.827751i \(0.689620\pi\)
\(350\) −315.092 −0.0481211
\(351\) 0 0
\(352\) 154.857 0.0234485
\(353\) −3390.13 −0.511157 −0.255579 0.966788i \(-0.582266\pi\)
−0.255579 + 0.966788i \(0.582266\pi\)
\(354\) 0 0
\(355\) 3627.40 0.542316
\(356\) −206.239 −0.0307041
\(357\) 0 0
\(358\) 440.104 0.0649727
\(359\) 12580.6 1.84952 0.924759 0.380552i \(-0.124266\pi\)
0.924759 + 0.380552i \(0.124266\pi\)
\(360\) 0 0
\(361\) −1516.94 −0.221160
\(362\) −3366.44 −0.488774
\(363\) 0 0
\(364\) 0 0
\(365\) 11769.8 1.68783
\(366\) 0 0
\(367\) −1833.08 −0.260725 −0.130362 0.991466i \(-0.541614\pi\)
−0.130362 + 0.991466i \(0.541614\pi\)
\(368\) 3490.75 0.494478
\(369\) 0 0
\(370\) 3355.82 0.471516
\(371\) 1800.20 0.251919
\(372\) 0 0
\(373\) 1383.58 0.192062 0.0960312 0.995378i \(-0.469385\pi\)
0.0960312 + 0.995378i \(0.469385\pi\)
\(374\) 11.3383 0.00156763
\(375\) 0 0
\(376\) 10397.5 1.42609
\(377\) 0 0
\(378\) 0 0
\(379\) 1495.54 0.202693 0.101346 0.994851i \(-0.467685\pi\)
0.101346 + 0.994851i \(0.467685\pi\)
\(380\) 5922.42 0.799510
\(381\) 0 0
\(382\) 4527.48 0.606404
\(383\) −1454.92 −0.194107 −0.0970537 0.995279i \(-0.530942\pi\)
−0.0970537 + 0.995279i \(0.530942\pi\)
\(384\) 0 0
\(385\) 60.4949 0.00800806
\(386\) −3850.36 −0.507715
\(387\) 0 0
\(388\) −426.797 −0.0558437
\(389\) −14163.0 −1.84600 −0.922999 0.384801i \(-0.874270\pi\)
−0.922999 + 0.384801i \(0.874270\pi\)
\(390\) 0 0
\(391\) 1416.56 0.183219
\(392\) 5884.17 0.758152
\(393\) 0 0
\(394\) −106.989 −0.0136803
\(395\) −12202.8 −1.55441
\(396\) 0 0
\(397\) 4877.38 0.616596 0.308298 0.951290i \(-0.400241\pi\)
0.308298 + 0.951290i \(0.400241\pi\)
\(398\) −1158.14 −0.145860
\(399\) 0 0
\(400\) 1078.96 0.134870
\(401\) 1233.69 0.153635 0.0768176 0.997045i \(-0.475524\pi\)
0.0768176 + 0.997045i \(0.475524\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 10276.0 1.26548
\(405\) 0 0
\(406\) −1835.28 −0.224343
\(407\) −164.868 −0.0200791
\(408\) 0 0
\(409\) −5113.24 −0.618174 −0.309087 0.951034i \(-0.600023\pi\)
−0.309087 + 0.951034i \(0.600023\pi\)
\(410\) 3149.04 0.379317
\(411\) 0 0
\(412\) 1039.61 0.124316
\(413\) −2891.48 −0.344505
\(414\) 0 0
\(415\) −12268.4 −1.45116
\(416\) 0 0
\(417\) 0 0
\(418\) 81.3600 0.00952021
\(419\) −8630.26 −1.00624 −0.503121 0.864216i \(-0.667815\pi\)
−0.503121 + 0.864216i \(0.667815\pi\)
\(420\) 0 0
\(421\) −13265.8 −1.53571 −0.767854 0.640624i \(-0.778676\pi\)
−0.767854 + 0.640624i \(0.778676\pi\)
\(422\) −5107.40 −0.589158
\(423\) 0 0
\(424\) 6118.81 0.700839
\(425\) 437.848 0.0499735
\(426\) 0 0
\(427\) 2464.74 0.279338
\(428\) 2785.47 0.314581
\(429\) 0 0
\(430\) −1971.94 −0.221152
\(431\) 4617.20 0.516015 0.258008 0.966143i \(-0.416934\pi\)
0.258008 + 0.966143i \(0.416934\pi\)
\(432\) 0 0
\(433\) 12484.6 1.38561 0.692805 0.721125i \(-0.256374\pi\)
0.692805 + 0.721125i \(0.256374\pi\)
\(434\) −1183.40 −0.130887
\(435\) 0 0
\(436\) −5532.59 −0.607714
\(437\) 10164.8 1.11269
\(438\) 0 0
\(439\) −5668.93 −0.616317 −0.308159 0.951335i \(-0.599713\pi\)
−0.308159 + 0.951335i \(0.599713\pi\)
\(440\) 205.619 0.0222785
\(441\) 0 0
\(442\) 0 0
\(443\) −4801.47 −0.514954 −0.257477 0.966284i \(-0.582891\pi\)
−0.257477 + 0.966284i \(0.582891\pi\)
\(444\) 0 0
\(445\) −427.563 −0.0455470
\(446\) −8450.38 −0.897168
\(447\) 0 0
\(448\) −235.029 −0.0247859
\(449\) −16254.1 −1.70841 −0.854207 0.519934i \(-0.825957\pi\)
−0.854207 + 0.519934i \(0.825957\pi\)
\(450\) 0 0
\(451\) −154.709 −0.0161529
\(452\) −9462.63 −0.984700
\(453\) 0 0
\(454\) −1680.95 −0.173768
\(455\) 0 0
\(456\) 0 0
\(457\) −7646.07 −0.782643 −0.391322 0.920254i \(-0.627982\pi\)
−0.391322 + 0.920254i \(0.627982\pi\)
\(458\) −7886.43 −0.804604
\(459\) 0 0
\(460\) 11269.0 1.14222
\(461\) 5645.67 0.570380 0.285190 0.958471i \(-0.407943\pi\)
0.285190 + 0.958471i \(0.407943\pi\)
\(462\) 0 0
\(463\) −3141.05 −0.315285 −0.157642 0.987496i \(-0.550389\pi\)
−0.157642 + 0.987496i \(0.550389\pi\)
\(464\) 6284.49 0.628772
\(465\) 0 0
\(466\) 6823.75 0.678335
\(467\) 1234.77 0.122352 0.0611759 0.998127i \(-0.480515\pi\)
0.0611759 + 0.998127i \(0.480515\pi\)
\(468\) 0 0
\(469\) 304.941 0.0300231
\(470\) 9455.70 0.927998
\(471\) 0 0
\(472\) −9828.01 −0.958413
\(473\) 96.8794 0.00941759
\(474\) 0 0
\(475\) 3141.84 0.303490
\(476\) 353.035 0.0339944
\(477\) 0 0
\(478\) 5023.41 0.480680
\(479\) −11758.1 −1.12159 −0.560795 0.827955i \(-0.689505\pi\)
−0.560795 + 0.827955i \(0.689505\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 159.325 0.0150562
\(483\) 0 0
\(484\) 8316.76 0.781063
\(485\) −884.811 −0.0828396
\(486\) 0 0
\(487\) −8650.25 −0.804888 −0.402444 0.915445i \(-0.631839\pi\)
−0.402444 + 0.915445i \(0.631839\pi\)
\(488\) 8377.56 0.777119
\(489\) 0 0
\(490\) 5351.20 0.493352
\(491\) 3819.18 0.351033 0.175516 0.984476i \(-0.443840\pi\)
0.175516 + 0.984476i \(0.443840\pi\)
\(492\) 0 0
\(493\) 2550.28 0.232979
\(494\) 0 0
\(495\) 0 0
\(496\) 4052.29 0.366841
\(497\) 1551.58 0.140036
\(498\) 0 0
\(499\) −17077.9 −1.53208 −0.766042 0.642791i \(-0.777776\pi\)
−0.766042 + 0.642791i \(0.777776\pi\)
\(500\) −6645.55 −0.594396
\(501\) 0 0
\(502\) 9204.17 0.818331
\(503\) −2996.47 −0.265618 −0.132809 0.991142i \(-0.542400\pi\)
−0.132809 + 0.991142i \(0.542400\pi\)
\(504\) 0 0
\(505\) 21303.7 1.87723
\(506\) 154.810 0.0136011
\(507\) 0 0
\(508\) −16157.3 −1.41115
\(509\) −8256.37 −0.718973 −0.359486 0.933150i \(-0.617048\pi\)
−0.359486 + 0.933150i \(0.617048\pi\)
\(510\) 0 0
\(511\) 5034.41 0.435830
\(512\) 8400.60 0.725113
\(513\) 0 0
\(514\) 1525.84 0.130938
\(515\) 2155.27 0.184413
\(516\) 0 0
\(517\) −464.548 −0.0395180
\(518\) 1435.42 0.121754
\(519\) 0 0
\(520\) 0 0
\(521\) −6348.47 −0.533842 −0.266921 0.963718i \(-0.586006\pi\)
−0.266921 + 0.963718i \(0.586006\pi\)
\(522\) 0 0
\(523\) 7444.93 0.622455 0.311228 0.950335i \(-0.399260\pi\)
0.311228 + 0.950335i \(0.399260\pi\)
\(524\) −9292.32 −0.774689
\(525\) 0 0
\(526\) 3473.91 0.287965
\(527\) 1644.44 0.135926
\(528\) 0 0
\(529\) 7174.28 0.589651
\(530\) 5564.59 0.456057
\(531\) 0 0
\(532\) 2533.25 0.206448
\(533\) 0 0
\(534\) 0 0
\(535\) 5774.68 0.466656
\(536\) 1036.48 0.0835245
\(537\) 0 0
\(538\) −6825.12 −0.546937
\(539\) −262.899 −0.0210090
\(540\) 0 0
\(541\) 6247.50 0.496490 0.248245 0.968697i \(-0.420146\pi\)
0.248245 + 0.968697i \(0.420146\pi\)
\(542\) −4036.93 −0.319928
\(543\) 0 0
\(544\) 1873.52 0.147659
\(545\) −11469.9 −0.901495
\(546\) 0 0
\(547\) −23338.4 −1.82427 −0.912137 0.409884i \(-0.865569\pi\)
−0.912137 + 0.409884i \(0.865569\pi\)
\(548\) −9262.13 −0.722005
\(549\) 0 0
\(550\) 47.8505 0.00370973
\(551\) 18299.9 1.41488
\(552\) 0 0
\(553\) −5219.63 −0.401377
\(554\) −4529.54 −0.347368
\(555\) 0 0
\(556\) 5735.32 0.437467
\(557\) 14975.3 1.13918 0.569592 0.821927i \(-0.307101\pi\)
0.569592 + 0.821927i \(0.307101\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1803.56 0.136097
\(561\) 0 0
\(562\) −7429.84 −0.557667
\(563\) 23463.5 1.75642 0.878212 0.478271i \(-0.158736\pi\)
0.878212 + 0.478271i \(0.158736\pi\)
\(564\) 0 0
\(565\) −19617.4 −1.46072
\(566\) −2883.67 −0.214152
\(567\) 0 0
\(568\) 5273.75 0.389581
\(569\) −22359.6 −1.64739 −0.823694 0.567035i \(-0.808091\pi\)
−0.823694 + 0.567035i \(0.808091\pi\)
\(570\) 0 0
\(571\) −2998.13 −0.219733 −0.109867 0.993946i \(-0.535042\pi\)
−0.109867 + 0.993946i \(0.535042\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1346.97 0.0979467
\(575\) 5978.23 0.433581
\(576\) 0 0
\(577\) −3370.06 −0.243150 −0.121575 0.992582i \(-0.538795\pi\)
−0.121575 + 0.992582i \(0.538795\pi\)
\(578\) −6358.70 −0.457590
\(579\) 0 0
\(580\) 20288.0 1.45243
\(581\) −5247.66 −0.374716
\(582\) 0 0
\(583\) −273.382 −0.0194208
\(584\) 17111.7 1.21248
\(585\) 0 0
\(586\) −6096.23 −0.429749
\(587\) −21645.2 −1.52197 −0.760983 0.648772i \(-0.775283\pi\)
−0.760983 + 0.648772i \(0.775283\pi\)
\(588\) 0 0
\(589\) 11799.9 0.825479
\(590\) −8937.82 −0.623668
\(591\) 0 0
\(592\) −4915.27 −0.341244
\(593\) −22232.6 −1.53960 −0.769801 0.638284i \(-0.779645\pi\)
−0.769801 + 0.638284i \(0.779645\pi\)
\(594\) 0 0
\(595\) 731.891 0.0504279
\(596\) 14242.5 0.978854
\(597\) 0 0
\(598\) 0 0
\(599\) −21337.0 −1.45544 −0.727718 0.685877i \(-0.759419\pi\)
−0.727718 + 0.685877i \(0.759419\pi\)
\(600\) 0 0
\(601\) −1592.47 −0.108084 −0.0540419 0.998539i \(-0.517210\pi\)
−0.0540419 + 0.998539i \(0.517210\pi\)
\(602\) −843.477 −0.0571056
\(603\) 0 0
\(604\) 13734.8 0.925266
\(605\) 17241.8 1.15865
\(606\) 0 0
\(607\) 18462.3 1.23454 0.617268 0.786753i \(-0.288239\pi\)
0.617268 + 0.786753i \(0.288239\pi\)
\(608\) 13443.7 0.896734
\(609\) 0 0
\(610\) 7618.74 0.505695
\(611\) 0 0
\(612\) 0 0
\(613\) 20041.2 1.32048 0.660241 0.751054i \(-0.270454\pi\)
0.660241 + 0.751054i \(0.270454\pi\)
\(614\) −5861.03 −0.385231
\(615\) 0 0
\(616\) 87.9515 0.00575271
\(617\) 18752.7 1.22359 0.611796 0.791016i \(-0.290447\pi\)
0.611796 + 0.791016i \(0.290447\pi\)
\(618\) 0 0
\(619\) 7276.59 0.472489 0.236245 0.971694i \(-0.424083\pi\)
0.236245 + 0.971694i \(0.424083\pi\)
\(620\) 13081.8 0.847386
\(621\) 0 0
\(622\) 11822.9 0.762149
\(623\) −182.886 −0.0117611
\(624\) 0 0
\(625\) −19150.5 −1.22563
\(626\) 10423.4 0.665497
\(627\) 0 0
\(628\) −19991.5 −1.27030
\(629\) −1994.64 −0.126441
\(630\) 0 0
\(631\) 22411.5 1.41393 0.706963 0.707251i \(-0.250065\pi\)
0.706963 + 0.707251i \(0.250065\pi\)
\(632\) −17741.3 −1.11663
\(633\) 0 0
\(634\) 886.796 0.0555507
\(635\) −33496.4 −2.09333
\(636\) 0 0
\(637\) 0 0
\(638\) 278.708 0.0172949
\(639\) 0 0
\(640\) 18345.3 1.13306
\(641\) −18756.0 −1.15572 −0.577861 0.816135i \(-0.696113\pi\)
−0.577861 + 0.816135i \(0.696113\pi\)
\(642\) 0 0
\(643\) −14712.9 −0.902366 −0.451183 0.892431i \(-0.648998\pi\)
−0.451183 + 0.892431i \(0.648998\pi\)
\(644\) 4820.22 0.294943
\(645\) 0 0
\(646\) 984.326 0.0599501
\(647\) 17409.3 1.05785 0.528925 0.848668i \(-0.322595\pi\)
0.528925 + 0.848668i \(0.322595\pi\)
\(648\) 0 0
\(649\) 439.106 0.0265584
\(650\) 0 0
\(651\) 0 0
\(652\) 19275.5 1.15780
\(653\) 17232.4 1.03270 0.516351 0.856377i \(-0.327290\pi\)
0.516351 + 0.856377i \(0.327290\pi\)
\(654\) 0 0
\(655\) −19264.3 −1.14919
\(656\) −4612.40 −0.274518
\(657\) 0 0
\(658\) 4044.58 0.239626
\(659\) 7718.22 0.456236 0.228118 0.973634i \(-0.426743\pi\)
0.228118 + 0.973634i \(0.426743\pi\)
\(660\) 0 0
\(661\) 31375.2 1.84623 0.923113 0.384530i \(-0.125636\pi\)
0.923113 + 0.384530i \(0.125636\pi\)
\(662\) 3758.57 0.220666
\(663\) 0 0
\(664\) −17836.6 −1.04246
\(665\) 5251.79 0.306249
\(666\) 0 0
\(667\) 34820.6 2.02138
\(668\) 3276.48 0.189776
\(669\) 0 0
\(670\) 942.599 0.0543519
\(671\) −374.301 −0.0215346
\(672\) 0 0
\(673\) −24768.7 −1.41867 −0.709333 0.704873i \(-0.751004\pi\)
−0.709333 + 0.704873i \(0.751004\pi\)
\(674\) 2493.82 0.142520
\(675\) 0 0
\(676\) 0 0
\(677\) −17050.3 −0.967944 −0.483972 0.875084i \(-0.660806\pi\)
−0.483972 + 0.875084i \(0.660806\pi\)
\(678\) 0 0
\(679\) −378.469 −0.0213907
\(680\) 2487.67 0.140291
\(681\) 0 0
\(682\) 179.713 0.0100903
\(683\) 23209.9 1.30029 0.650147 0.759808i \(-0.274707\pi\)
0.650147 + 0.759808i \(0.274707\pi\)
\(684\) 0 0
\(685\) −19201.7 −1.07104
\(686\) 4803.13 0.267324
\(687\) 0 0
\(688\) 2888.30 0.160052
\(689\) 0 0
\(690\) 0 0
\(691\) −1501.07 −0.0826389 −0.0413195 0.999146i \(-0.513156\pi\)
−0.0413195 + 0.999146i \(0.513156\pi\)
\(692\) 18641.0 1.02402
\(693\) 0 0
\(694\) 5367.59 0.293589
\(695\) 11890.1 0.648948
\(696\) 0 0
\(697\) −1871.73 −0.101717
\(698\) −9673.78 −0.524581
\(699\) 0 0
\(700\) 1489.89 0.0804464
\(701\) −3944.82 −0.212544 −0.106272 0.994337i \(-0.533891\pi\)
−0.106272 + 0.994337i \(0.533891\pi\)
\(702\) 0 0
\(703\) −14312.8 −0.767879
\(704\) 35.6920 0.00191079
\(705\) 0 0
\(706\) −4482.37 −0.238946
\(707\) 9112.44 0.484736
\(708\) 0 0
\(709\) 24251.8 1.28462 0.642311 0.766444i \(-0.277976\pi\)
0.642311 + 0.766444i \(0.277976\pi\)
\(710\) 4796.07 0.253512
\(711\) 0 0
\(712\) −621.620 −0.0327194
\(713\) 22452.6 1.17932
\(714\) 0 0
\(715\) 0 0
\(716\) −2081.00 −0.108618
\(717\) 0 0
\(718\) 16633.8 0.864579
\(719\) −6941.00 −0.360022 −0.180011 0.983665i \(-0.557613\pi\)
−0.180011 + 0.983665i \(0.557613\pi\)
\(720\) 0 0
\(721\) 921.894 0.0476188
\(722\) −2005.67 −0.103384
\(723\) 0 0
\(724\) 15918.0 0.817108
\(725\) 10762.8 0.551336
\(726\) 0 0
\(727\) 3587.40 0.183011 0.0915056 0.995805i \(-0.470832\pi\)
0.0915056 + 0.995805i \(0.470832\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 15561.8 0.788998
\(731\) 1172.09 0.0593039
\(732\) 0 0
\(733\) −32867.4 −1.65619 −0.828093 0.560591i \(-0.810574\pi\)
−0.828093 + 0.560591i \(0.810574\pi\)
\(734\) −2423.66 −0.121879
\(735\) 0 0
\(736\) 25580.4 1.28112
\(737\) −46.3089 −0.00231453
\(738\) 0 0
\(739\) 19818.9 0.986534 0.493267 0.869878i \(-0.335803\pi\)
0.493267 + 0.869878i \(0.335803\pi\)
\(740\) −15867.8 −0.788258
\(741\) 0 0
\(742\) 2380.20 0.117762
\(743\) −13341.0 −0.658727 −0.329364 0.944203i \(-0.606834\pi\)
−0.329364 + 0.944203i \(0.606834\pi\)
\(744\) 0 0
\(745\) 29526.8 1.45205
\(746\) 1829.35 0.0897818
\(747\) 0 0
\(748\) −53.6125 −0.00262068
\(749\) 2470.06 0.120499
\(750\) 0 0
\(751\) −32392.8 −1.57394 −0.786971 0.616990i \(-0.788352\pi\)
−0.786971 + 0.616990i \(0.788352\pi\)
\(752\) −13849.8 −0.671607
\(753\) 0 0
\(754\) 0 0
\(755\) 28474.2 1.37256
\(756\) 0 0
\(757\) −6177.77 −0.296612 −0.148306 0.988942i \(-0.547382\pi\)
−0.148306 + 0.988942i \(0.547382\pi\)
\(758\) 1977.37 0.0947512
\(759\) 0 0
\(760\) 17850.6 0.851987
\(761\) 4215.28 0.200793 0.100397 0.994947i \(-0.467989\pi\)
0.100397 + 0.994947i \(0.467989\pi\)
\(762\) 0 0
\(763\) −4906.11 −0.232783
\(764\) −21407.9 −1.01376
\(765\) 0 0
\(766\) −1923.67 −0.0907378
\(767\) 0 0
\(768\) 0 0
\(769\) 6536.90 0.306536 0.153268 0.988185i \(-0.451020\pi\)
0.153268 + 0.988185i \(0.451020\pi\)
\(770\) 79.9852 0.00374346
\(771\) 0 0
\(772\) 18206.1 0.848773
\(773\) −9953.50 −0.463134 −0.231567 0.972819i \(-0.574385\pi\)
−0.231567 + 0.972819i \(0.574385\pi\)
\(774\) 0 0
\(775\) 6939.92 0.321663
\(776\) −1286.40 −0.0595091
\(777\) 0 0
\(778\) −18726.1 −0.862934
\(779\) −13430.9 −0.617730
\(780\) 0 0
\(781\) −235.626 −0.0107956
\(782\) 1872.95 0.0856479
\(783\) 0 0
\(784\) −7837.90 −0.357047
\(785\) −41445.1 −1.88438
\(786\) 0 0
\(787\) 17827.4 0.807467 0.403733 0.914877i \(-0.367712\pi\)
0.403733 + 0.914877i \(0.367712\pi\)
\(788\) 505.892 0.0228701
\(789\) 0 0
\(790\) −16134.3 −0.726626
\(791\) −8391.13 −0.377186
\(792\) 0 0
\(793\) 0 0
\(794\) 6448.78 0.288235
\(795\) 0 0
\(796\) 5476.17 0.243841
\(797\) 249.882 0.0111057 0.00555287 0.999985i \(-0.498232\pi\)
0.00555287 + 0.999985i \(0.498232\pi\)
\(798\) 0 0
\(799\) −5620.30 −0.248851
\(800\) 7906.68 0.349429
\(801\) 0 0
\(802\) 1631.17 0.0718185
\(803\) −764.535 −0.0335988
\(804\) 0 0
\(805\) 9993.00 0.437524
\(806\) 0 0
\(807\) 0 0
\(808\) 30972.8 1.34854
\(809\) −13019.9 −0.565829 −0.282914 0.959145i \(-0.591301\pi\)
−0.282914 + 0.959145i \(0.591301\pi\)
\(810\) 0 0
\(811\) 956.251 0.0414038 0.0207019 0.999786i \(-0.493410\pi\)
0.0207019 + 0.999786i \(0.493410\pi\)
\(812\) 8677.96 0.375045
\(813\) 0 0
\(814\) −217.985 −0.00938622
\(815\) 39960.8 1.71750
\(816\) 0 0
\(817\) 8410.48 0.360153
\(818\) −6760.62 −0.288973
\(819\) 0 0
\(820\) −14890.0 −0.634124
\(821\) −7853.26 −0.333837 −0.166919 0.985971i \(-0.553382\pi\)
−0.166919 + 0.985971i \(0.553382\pi\)
\(822\) 0 0
\(823\) 33820.9 1.43247 0.716236 0.697858i \(-0.245863\pi\)
0.716236 + 0.697858i \(0.245863\pi\)
\(824\) 3133.48 0.132476
\(825\) 0 0
\(826\) −3823.06 −0.161043
\(827\) 7297.39 0.306838 0.153419 0.988161i \(-0.450972\pi\)
0.153419 + 0.988161i \(0.450972\pi\)
\(828\) 0 0
\(829\) −8454.13 −0.354191 −0.177095 0.984194i \(-0.556670\pi\)
−0.177095 + 0.984194i \(0.556670\pi\)
\(830\) −16221.0 −0.678360
\(831\) 0 0
\(832\) 0 0
\(833\) −3180.66 −0.132297
\(834\) 0 0
\(835\) 6792.60 0.281518
\(836\) −384.705 −0.0159154
\(837\) 0 0
\(838\) −11410.8 −0.470380
\(839\) −32007.9 −1.31709 −0.658543 0.752543i \(-0.728827\pi\)
−0.658543 + 0.752543i \(0.728827\pi\)
\(840\) 0 0
\(841\) 38299.5 1.57036
\(842\) −17539.7 −0.717885
\(843\) 0 0
\(844\) 24150.0 0.984925
\(845\) 0 0
\(846\) 0 0
\(847\) 7375.02 0.299184
\(848\) −8150.45 −0.330056
\(849\) 0 0
\(850\) 578.914 0.0233607
\(851\) −27234.1 −1.09703
\(852\) 0 0
\(853\) −9986.02 −0.400838 −0.200419 0.979710i \(-0.564230\pi\)
−0.200419 + 0.979710i \(0.564230\pi\)
\(854\) 3258.84 0.130580
\(855\) 0 0
\(856\) 8395.62 0.335229
\(857\) −289.524 −0.0115402 −0.00577010 0.999983i \(-0.501837\pi\)
−0.00577010 + 0.999983i \(0.501837\pi\)
\(858\) 0 0
\(859\) −7833.85 −0.311161 −0.155581 0.987823i \(-0.549725\pi\)
−0.155581 + 0.987823i \(0.549725\pi\)
\(860\) 9324.18 0.369712
\(861\) 0 0
\(862\) 6104.77 0.241217
\(863\) 33370.8 1.31629 0.658143 0.752893i \(-0.271342\pi\)
0.658143 + 0.752893i \(0.271342\pi\)
\(864\) 0 0
\(865\) 38645.4 1.51906
\(866\) 16506.8 0.647720
\(867\) 0 0
\(868\) 5595.62 0.218811
\(869\) 792.663 0.0309428
\(870\) 0 0
\(871\) 0 0
\(872\) −16675.7 −0.647602
\(873\) 0 0
\(874\) 13439.7 0.520141
\(875\) −5893.04 −0.227681
\(876\) 0 0
\(877\) 25422.4 0.978852 0.489426 0.872045i \(-0.337206\pi\)
0.489426 + 0.872045i \(0.337206\pi\)
\(878\) −7495.35 −0.288105
\(879\) 0 0
\(880\) −273.892 −0.0104919
\(881\) −40373.6 −1.54395 −0.771976 0.635652i \(-0.780731\pi\)
−0.771976 + 0.635652i \(0.780731\pi\)
\(882\) 0 0
\(883\) −16898.9 −0.644045 −0.322023 0.946732i \(-0.604363\pi\)
−0.322023 + 0.946732i \(0.604363\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −6348.41 −0.240721
\(887\) −49889.1 −1.88851 −0.944257 0.329210i \(-0.893218\pi\)
−0.944257 + 0.329210i \(0.893218\pi\)
\(888\) 0 0
\(889\) −14327.7 −0.540536
\(890\) −565.316 −0.0212915
\(891\) 0 0
\(892\) 39957.0 1.49984
\(893\) −40329.3 −1.51127
\(894\) 0 0
\(895\) −4314.21 −0.161126
\(896\) 7847.01 0.292578
\(897\) 0 0
\(898\) −21490.8 −0.798618
\(899\) 40422.0 1.49961
\(900\) 0 0
\(901\) −3307.49 −0.122296
\(902\) −204.553 −0.00755087
\(903\) 0 0
\(904\) −28521.1 −1.04933
\(905\) 33000.2 1.21212
\(906\) 0 0
\(907\) −3061.06 −0.112063 −0.0560313 0.998429i \(-0.517845\pi\)
−0.0560313 + 0.998429i \(0.517845\pi\)
\(908\) 7948.24 0.290497
\(909\) 0 0
\(910\) 0 0
\(911\) 15247.2 0.554514 0.277257 0.960796i \(-0.410575\pi\)
0.277257 + 0.960796i \(0.410575\pi\)
\(912\) 0 0
\(913\) 796.920 0.0288874
\(914\) −10109.5 −0.365856
\(915\) 0 0
\(916\) 37290.4 1.34510
\(917\) −8240.11 −0.296742
\(918\) 0 0
\(919\) −29419.2 −1.05599 −0.527993 0.849249i \(-0.677055\pi\)
−0.527993 + 0.849249i \(0.677055\pi\)
\(920\) 33965.8 1.21719
\(921\) 0 0
\(922\) 7464.60 0.266631
\(923\) 0 0
\(924\) 0 0
\(925\) −8417.85 −0.299219
\(926\) −4153.03 −0.147383
\(927\) 0 0
\(928\) 46053.0 1.62906
\(929\) −16910.0 −0.597200 −0.298600 0.954378i \(-0.596520\pi\)
−0.298600 + 0.954378i \(0.596520\pi\)
\(930\) 0 0
\(931\) −22823.3 −0.803440
\(932\) −32265.6 −1.13401
\(933\) 0 0
\(934\) 1632.59 0.0571948
\(935\) −111.146 −0.00388757
\(936\) 0 0
\(937\) 32828.7 1.14457 0.572287 0.820053i \(-0.306056\pi\)
0.572287 + 0.820053i \(0.306056\pi\)
\(938\) 403.187 0.0140347
\(939\) 0 0
\(940\) −44710.6 −1.55138
\(941\) 22244.7 0.770623 0.385311 0.922787i \(-0.374094\pi\)
0.385311 + 0.922787i \(0.374094\pi\)
\(942\) 0 0
\(943\) −25556.0 −0.882522
\(944\) 13091.2 0.451359
\(945\) 0 0
\(946\) 128.092 0.00440236
\(947\) 17502.1 0.600573 0.300287 0.953849i \(-0.402918\pi\)
0.300287 + 0.953849i \(0.402918\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 4154.08 0.141870
\(951\) 0 0
\(952\) 1064.07 0.0362256
\(953\) −31522.6 −1.07148 −0.535739 0.844384i \(-0.679967\pi\)
−0.535739 + 0.844384i \(0.679967\pi\)
\(954\) 0 0
\(955\) −44381.6 −1.50383
\(956\) −23752.8 −0.803578
\(957\) 0 0
\(958\) −15546.4 −0.524301
\(959\) −8213.34 −0.276562
\(960\) 0 0
\(961\) −3726.54 −0.125090
\(962\) 0 0
\(963\) 0 0
\(964\) −753.358 −0.0251701
\(965\) 37743.9 1.25909
\(966\) 0 0
\(967\) −35433.0 −1.17833 −0.589167 0.808011i \(-0.700544\pi\)
−0.589167 + 0.808011i \(0.700544\pi\)
\(968\) 25067.4 0.832330
\(969\) 0 0
\(970\) −1169.88 −0.0387243
\(971\) 5907.77 0.195252 0.0976258 0.995223i \(-0.468875\pi\)
0.0976258 + 0.995223i \(0.468875\pi\)
\(972\) 0 0
\(973\) 5085.88 0.167570
\(974\) −11437.2 −0.376254
\(975\) 0 0
\(976\) −11159.2 −0.365980
\(977\) −231.490 −0.00758035 −0.00379018 0.999993i \(-0.501206\pi\)
−0.00379018 + 0.999993i \(0.501206\pi\)
\(978\) 0 0
\(979\) 27.7734 0.000906681 0
\(980\) −25302.8 −0.824762
\(981\) 0 0
\(982\) 5049.65 0.164094
\(983\) −7577.90 −0.245877 −0.122939 0.992414i \(-0.539232\pi\)
−0.122939 + 0.992414i \(0.539232\pi\)
\(984\) 0 0
\(985\) 1048.79 0.0339260
\(986\) 3371.93 0.108909
\(987\) 0 0
\(988\) 0 0
\(989\) 16003.3 0.514534
\(990\) 0 0
\(991\) −6578.71 −0.210878 −0.105439 0.994426i \(-0.533625\pi\)
−0.105439 + 0.994426i \(0.533625\pi\)
\(992\) 29695.4 0.950433
\(993\) 0 0
\(994\) 2051.47 0.0654615
\(995\) 11352.9 0.361719
\(996\) 0 0
\(997\) 14907.8 0.473556 0.236778 0.971564i \(-0.423909\pi\)
0.236778 + 0.971564i \(0.423909\pi\)
\(998\) −22580.0 −0.716190
\(999\) 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.bm.1.12 yes 18
3.2 odd 2 inner 1521.4.a.bm.1.7 18
13.12 even 2 1521.4.a.bn.1.7 yes 18
39.38 odd 2 1521.4.a.bn.1.12 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.4.a.bm.1.7 18 3.2 odd 2 inner
1521.4.a.bm.1.12 yes 18 1.1 even 1 trivial
1521.4.a.bn.1.7 yes 18 13.12 even 2
1521.4.a.bn.1.12 yes 18 39.38 odd 2