Properties

Label 2151.4.a.h.1.8
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.45149 q^{2} +11.8157 q^{4} +14.0297 q^{5} +23.7055 q^{7} -16.9858 q^{8} +O(q^{10})\) \(q-4.45149 q^{2} +11.8157 q^{4} +14.0297 q^{5} +23.7055 q^{7} -16.9858 q^{8} -62.4530 q^{10} +36.5037 q^{11} +56.5575 q^{13} -105.525 q^{14} -18.9141 q^{16} -7.01736 q^{17} -45.1390 q^{19} +165.771 q^{20} -162.496 q^{22} +174.255 q^{23} +71.8322 q^{25} -251.765 q^{26} +280.099 q^{28} -226.036 q^{29} +97.8926 q^{31} +220.082 q^{32} +31.2377 q^{34} +332.581 q^{35} -338.487 q^{37} +200.936 q^{38} -238.305 q^{40} -481.138 q^{41} -58.7919 q^{43} +431.318 q^{44} -775.695 q^{46} +407.573 q^{47} +218.952 q^{49} -319.760 q^{50} +668.269 q^{52} +302.026 q^{53} +512.135 q^{55} -402.656 q^{56} +1006.20 q^{58} +785.873 q^{59} -81.0979 q^{61} -435.768 q^{62} -828.379 q^{64} +793.484 q^{65} +813.974 q^{67} -82.9154 q^{68} -1480.48 q^{70} +437.780 q^{71} -631.448 q^{73} +1506.77 q^{74} -533.351 q^{76} +865.339 q^{77} -757.443 q^{79} -265.359 q^{80} +2141.78 q^{82} +650.447 q^{83} -98.4514 q^{85} +261.712 q^{86} -620.043 q^{88} +806.535 q^{89} +1340.73 q^{91} +2058.95 q^{92} -1814.31 q^{94} -633.286 q^{95} +1218.57 q^{97} -974.663 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45149 −1.57384 −0.786919 0.617056i \(-0.788325\pi\)
−0.786919 + 0.617056i \(0.788325\pi\)
\(3\) 0 0
\(4\) 11.8157 1.47697
\(5\) 14.0297 1.25485 0.627427 0.778676i \(-0.284108\pi\)
0.627427 + 0.778676i \(0.284108\pi\)
\(6\) 0 0
\(7\) 23.7055 1.27998 0.639989 0.768384i \(-0.278939\pi\)
0.639989 + 0.768384i \(0.278939\pi\)
\(8\) −16.9858 −0.750672
\(9\) 0 0
\(10\) −62.4530 −1.97494
\(11\) 36.5037 1.00057 0.500285 0.865861i \(-0.333229\pi\)
0.500285 + 0.865861i \(0.333229\pi\)
\(12\) 0 0
\(13\) 56.5575 1.20663 0.603316 0.797502i \(-0.293846\pi\)
0.603316 + 0.797502i \(0.293846\pi\)
\(14\) −105.525 −2.01448
\(15\) 0 0
\(16\) −18.9141 −0.295532
\(17\) −7.01736 −0.100115 −0.0500577 0.998746i \(-0.515941\pi\)
−0.0500577 + 0.998746i \(0.515941\pi\)
\(18\) 0 0
\(19\) −45.1390 −0.545031 −0.272516 0.962151i \(-0.587856\pi\)
−0.272516 + 0.962151i \(0.587856\pi\)
\(20\) 165.771 1.85338
\(21\) 0 0
\(22\) −162.496 −1.57474
\(23\) 174.255 1.57977 0.789885 0.613255i \(-0.210140\pi\)
0.789885 + 0.613255i \(0.210140\pi\)
\(24\) 0 0
\(25\) 71.8322 0.574657
\(26\) −251.765 −1.89905
\(27\) 0 0
\(28\) 280.099 1.89049
\(29\) −226.036 −1.44737 −0.723686 0.690130i \(-0.757554\pi\)
−0.723686 + 0.690130i \(0.757554\pi\)
\(30\) 0 0
\(31\) 97.8926 0.567162 0.283581 0.958948i \(-0.408477\pi\)
0.283581 + 0.958948i \(0.408477\pi\)
\(32\) 220.082 1.21579
\(33\) 0 0
\(34\) 31.2377 0.157565
\(35\) 332.581 1.60619
\(36\) 0 0
\(37\) −338.487 −1.50397 −0.751984 0.659181i \(-0.770903\pi\)
−0.751984 + 0.659181i \(0.770903\pi\)
\(38\) 200.936 0.857791
\(39\) 0 0
\(40\) −238.305 −0.941983
\(41\) −481.138 −1.83271 −0.916356 0.400365i \(-0.868883\pi\)
−0.916356 + 0.400365i \(0.868883\pi\)
\(42\) 0 0
\(43\) −58.7919 −0.208504 −0.104252 0.994551i \(-0.533245\pi\)
−0.104252 + 0.994551i \(0.533245\pi\)
\(44\) 431.318 1.47781
\(45\) 0 0
\(46\) −775.695 −2.48630
\(47\) 407.573 1.26491 0.632454 0.774598i \(-0.282048\pi\)
0.632454 + 0.774598i \(0.282048\pi\)
\(48\) 0 0
\(49\) 218.952 0.638344
\(50\) −319.760 −0.904418
\(51\) 0 0
\(52\) 668.269 1.78216
\(53\) 302.026 0.782762 0.391381 0.920229i \(-0.371997\pi\)
0.391381 + 0.920229i \(0.371997\pi\)
\(54\) 0 0
\(55\) 512.135 1.25557
\(56\) −402.656 −0.960844
\(57\) 0 0
\(58\) 1006.20 2.27793
\(59\) 785.873 1.73410 0.867050 0.498221i \(-0.166013\pi\)
0.867050 + 0.498221i \(0.166013\pi\)
\(60\) 0 0
\(61\) −81.0979 −0.170222 −0.0851108 0.996371i \(-0.527124\pi\)
−0.0851108 + 0.996371i \(0.527124\pi\)
\(62\) −435.768 −0.892622
\(63\) 0 0
\(64\) −828.379 −1.61793
\(65\) 793.484 1.51415
\(66\) 0 0
\(67\) 813.974 1.48422 0.742110 0.670278i \(-0.233825\pi\)
0.742110 + 0.670278i \(0.233825\pi\)
\(68\) −82.9154 −0.147867
\(69\) 0 0
\(70\) −1480.48 −2.52788
\(71\) 437.780 0.731760 0.365880 0.930662i \(-0.380768\pi\)
0.365880 + 0.930662i \(0.380768\pi\)
\(72\) 0 0
\(73\) −631.448 −1.01240 −0.506201 0.862415i \(-0.668951\pi\)
−0.506201 + 0.862415i \(0.668951\pi\)
\(74\) 1506.77 2.36700
\(75\) 0 0
\(76\) −533.351 −0.804994
\(77\) 865.339 1.28071
\(78\) 0 0
\(79\) −757.443 −1.07872 −0.539361 0.842075i \(-0.681334\pi\)
−0.539361 + 0.842075i \(0.681334\pi\)
\(80\) −265.359 −0.370850
\(81\) 0 0
\(82\) 2141.78 2.88439
\(83\) 650.447 0.860191 0.430096 0.902783i \(-0.358480\pi\)
0.430096 + 0.902783i \(0.358480\pi\)
\(84\) 0 0
\(85\) −98.4514 −0.125630
\(86\) 261.712 0.328152
\(87\) 0 0
\(88\) −620.043 −0.751100
\(89\) 806.535 0.960590 0.480295 0.877107i \(-0.340530\pi\)
0.480295 + 0.877107i \(0.340530\pi\)
\(90\) 0 0
\(91\) 1340.73 1.54446
\(92\) 2058.95 2.33327
\(93\) 0 0
\(94\) −1814.31 −1.99076
\(95\) −633.286 −0.683934
\(96\) 0 0
\(97\) 1218.57 1.27554 0.637768 0.770228i \(-0.279858\pi\)
0.637768 + 0.770228i \(0.279858\pi\)
\(98\) −974.663 −1.00465
\(99\) 0 0
\(100\) 848.751 0.848751
\(101\) −1266.55 −1.24779 −0.623895 0.781508i \(-0.714451\pi\)
−0.623895 + 0.781508i \(0.714451\pi\)
\(102\) 0 0
\(103\) 1515.00 1.44930 0.724650 0.689117i \(-0.242002\pi\)
0.724650 + 0.689117i \(0.242002\pi\)
\(104\) −960.672 −0.905785
\(105\) 0 0
\(106\) −1344.46 −1.23194
\(107\) 111.078 0.100358 0.0501789 0.998740i \(-0.484021\pi\)
0.0501789 + 0.998740i \(0.484021\pi\)
\(108\) 0 0
\(109\) −1871.22 −1.64431 −0.822157 0.569260i \(-0.807230\pi\)
−0.822157 + 0.569260i \(0.807230\pi\)
\(110\) −2279.76 −1.97606
\(111\) 0 0
\(112\) −448.368 −0.378275
\(113\) 2092.28 1.74182 0.870908 0.491446i \(-0.163532\pi\)
0.870908 + 0.491446i \(0.163532\pi\)
\(114\) 0 0
\(115\) 2444.74 1.98238
\(116\) −2670.78 −2.13772
\(117\) 0 0
\(118\) −3498.30 −2.72919
\(119\) −166.350 −0.128145
\(120\) 0 0
\(121\) 1.51748 0.00114011
\(122\) 361.006 0.267901
\(123\) 0 0
\(124\) 1156.67 0.837681
\(125\) −745.928 −0.533743
\(126\) 0 0
\(127\) 384.445 0.268614 0.134307 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(128\) 1926.87 1.33057
\(129\) 0 0
\(130\) −3532.19 −2.38302
\(131\) 2035.31 1.35745 0.678724 0.734393i \(-0.262533\pi\)
0.678724 + 0.734393i \(0.262533\pi\)
\(132\) 0 0
\(133\) −1070.04 −0.697628
\(134\) −3623.40 −2.33592
\(135\) 0 0
\(136\) 119.195 0.0751537
\(137\) 2884.67 1.79894 0.899468 0.436987i \(-0.143954\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(138\) 0 0
\(139\) 1709.80 1.04333 0.521666 0.853150i \(-0.325311\pi\)
0.521666 + 0.853150i \(0.325311\pi\)
\(140\) 3929.70 2.37229
\(141\) 0 0
\(142\) −1948.77 −1.15167
\(143\) 2064.56 1.20732
\(144\) 0 0
\(145\) −3171.21 −1.81624
\(146\) 2810.88 1.59336
\(147\) 0 0
\(148\) −3999.47 −2.22131
\(149\) −414.246 −0.227761 −0.113880 0.993494i \(-0.536328\pi\)
−0.113880 + 0.993494i \(0.536328\pi\)
\(150\) 0 0
\(151\) 1120.72 0.603991 0.301995 0.953309i \(-0.402347\pi\)
0.301995 + 0.953309i \(0.402347\pi\)
\(152\) 766.720 0.409140
\(153\) 0 0
\(154\) −3852.05 −2.01563
\(155\) 1373.40 0.711706
\(156\) 0 0
\(157\) −346.520 −0.176149 −0.0880743 0.996114i \(-0.528071\pi\)
−0.0880743 + 0.996114i \(0.528071\pi\)
\(158\) 3371.75 1.69773
\(159\) 0 0
\(160\) 3087.68 1.52564
\(161\) 4130.81 2.02207
\(162\) 0 0
\(163\) −3269.21 −1.57095 −0.785473 0.618896i \(-0.787580\pi\)
−0.785473 + 0.618896i \(0.787580\pi\)
\(164\) −5685.01 −2.70686
\(165\) 0 0
\(166\) −2895.46 −1.35380
\(167\) −281.159 −0.130280 −0.0651399 0.997876i \(-0.520749\pi\)
−0.0651399 + 0.997876i \(0.520749\pi\)
\(168\) 0 0
\(169\) 1001.75 0.455963
\(170\) 438.255 0.197721
\(171\) 0 0
\(172\) −694.671 −0.307954
\(173\) −1132.71 −0.497794 −0.248897 0.968530i \(-0.580068\pi\)
−0.248897 + 0.968530i \(0.580068\pi\)
\(174\) 0 0
\(175\) 1702.82 0.735549
\(176\) −690.433 −0.295701
\(177\) 0 0
\(178\) −3590.28 −1.51181
\(179\) −2743.00 −1.14537 −0.572685 0.819775i \(-0.694098\pi\)
−0.572685 + 0.819775i \(0.694098\pi\)
\(180\) 0 0
\(181\) −3516.42 −1.44405 −0.722025 0.691867i \(-0.756789\pi\)
−0.722025 + 0.691867i \(0.756789\pi\)
\(182\) −5968.22 −2.43074
\(183\) 0 0
\(184\) −2959.86 −1.18589
\(185\) −4748.86 −1.88726
\(186\) 0 0
\(187\) −256.159 −0.100172
\(188\) 4815.78 1.86823
\(189\) 0 0
\(190\) 2819.07 1.07640
\(191\) −817.974 −0.309877 −0.154939 0.987924i \(-0.549518\pi\)
−0.154939 + 0.987924i \(0.549518\pi\)
\(192\) 0 0
\(193\) −1107.75 −0.413148 −0.206574 0.978431i \(-0.566231\pi\)
−0.206574 + 0.978431i \(0.566231\pi\)
\(194\) −5424.45 −2.00749
\(195\) 0 0
\(196\) 2587.08 0.942815
\(197\) 3084.42 1.11551 0.557756 0.830005i \(-0.311662\pi\)
0.557756 + 0.830005i \(0.311662\pi\)
\(198\) 0 0
\(199\) −1855.10 −0.660828 −0.330414 0.943836i \(-0.607188\pi\)
−0.330414 + 0.943836i \(0.607188\pi\)
\(200\) −1220.12 −0.431379
\(201\) 0 0
\(202\) 5638.05 1.96382
\(203\) −5358.30 −1.85260
\(204\) 0 0
\(205\) −6750.22 −2.29978
\(206\) −6744.03 −2.28096
\(207\) 0 0
\(208\) −1069.73 −0.356599
\(209\) −1647.74 −0.545342
\(210\) 0 0
\(211\) 5350.57 1.74573 0.872864 0.487964i \(-0.162260\pi\)
0.872864 + 0.487964i \(0.162260\pi\)
\(212\) 3568.66 1.15612
\(213\) 0 0
\(214\) −494.461 −0.157947
\(215\) −824.833 −0.261642
\(216\) 0 0
\(217\) 2320.60 0.725955
\(218\) 8329.71 2.58789
\(219\) 0 0
\(220\) 6051.26 1.85444
\(221\) −396.885 −0.120802
\(222\) 0 0
\(223\) 2047.76 0.614923 0.307462 0.951560i \(-0.400520\pi\)
0.307462 + 0.951560i \(0.400520\pi\)
\(224\) 5217.16 1.55619
\(225\) 0 0
\(226\) −9313.76 −2.74134
\(227\) −1577.39 −0.461211 −0.230605 0.973047i \(-0.574071\pi\)
−0.230605 + 0.973047i \(0.574071\pi\)
\(228\) 0 0
\(229\) −3083.95 −0.889926 −0.444963 0.895549i \(-0.646783\pi\)
−0.444963 + 0.895549i \(0.646783\pi\)
\(230\) −10882.8 −3.11995
\(231\) 0 0
\(232\) 3839.39 1.08650
\(233\) −6317.07 −1.77616 −0.888080 0.459689i \(-0.847961\pi\)
−0.888080 + 0.459689i \(0.847961\pi\)
\(234\) 0 0
\(235\) 5718.13 1.58727
\(236\) 9285.68 2.56121
\(237\) 0 0
\(238\) 740.507 0.201680
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −3832.63 −1.02440 −0.512202 0.858865i \(-0.671170\pi\)
−0.512202 + 0.858865i \(0.671170\pi\)
\(242\) −6.75506 −0.00179434
\(243\) 0 0
\(244\) −958.232 −0.251412
\(245\) 3071.83 0.801029
\(246\) 0 0
\(247\) −2552.95 −0.657653
\(248\) −1662.78 −0.425753
\(249\) 0 0
\(250\) 3320.49 0.840025
\(251\) 5227.23 1.31450 0.657251 0.753672i \(-0.271719\pi\)
0.657251 + 0.753672i \(0.271719\pi\)
\(252\) 0 0
\(253\) 6360.95 1.58067
\(254\) −1711.35 −0.422755
\(255\) 0 0
\(256\) −1950.39 −0.476169
\(257\) 7083.43 1.71927 0.859635 0.510909i \(-0.170691\pi\)
0.859635 + 0.510909i \(0.170691\pi\)
\(258\) 0 0
\(259\) −8024.00 −1.92505
\(260\) 9375.61 2.23635
\(261\) 0 0
\(262\) −9060.16 −2.13641
\(263\) −1996.26 −0.468040 −0.234020 0.972232i \(-0.575188\pi\)
−0.234020 + 0.972232i \(0.575188\pi\)
\(264\) 0 0
\(265\) 4237.33 0.982252
\(266\) 4763.29 1.09795
\(267\) 0 0
\(268\) 9617.71 2.19215
\(269\) −7347.36 −1.66534 −0.832670 0.553770i \(-0.813189\pi\)
−0.832670 + 0.553770i \(0.813189\pi\)
\(270\) 0 0
\(271\) −289.105 −0.0648041 −0.0324020 0.999475i \(-0.510316\pi\)
−0.0324020 + 0.999475i \(0.510316\pi\)
\(272\) 132.727 0.0295873
\(273\) 0 0
\(274\) −12841.1 −2.83123
\(275\) 2622.14 0.574985
\(276\) 0 0
\(277\) −74.8453 −0.0162347 −0.00811736 0.999967i \(-0.502584\pi\)
−0.00811736 + 0.999967i \(0.502584\pi\)
\(278\) −7611.15 −1.64204
\(279\) 0 0
\(280\) −5649.15 −1.20572
\(281\) 5156.24 1.09464 0.547322 0.836922i \(-0.315647\pi\)
0.547322 + 0.836922i \(0.315647\pi\)
\(282\) 0 0
\(283\) 5977.40 1.25555 0.627773 0.778397i \(-0.283967\pi\)
0.627773 + 0.778397i \(0.283967\pi\)
\(284\) 5172.70 1.08079
\(285\) 0 0
\(286\) −9190.35 −1.90013
\(287\) −11405.6 −2.34583
\(288\) 0 0
\(289\) −4863.76 −0.989977
\(290\) 14116.6 2.85847
\(291\) 0 0
\(292\) −7461.03 −1.49529
\(293\) −507.037 −0.101097 −0.0505485 0.998722i \(-0.516097\pi\)
−0.0505485 + 0.998722i \(0.516097\pi\)
\(294\) 0 0
\(295\) 11025.6 2.17604
\(296\) 5749.45 1.12899
\(297\) 0 0
\(298\) 1844.01 0.358459
\(299\) 9855.43 1.90620
\(300\) 0 0
\(301\) −1393.69 −0.266881
\(302\) −4988.85 −0.950584
\(303\) 0 0
\(304\) 853.762 0.161074
\(305\) −1137.78 −0.213603
\(306\) 0 0
\(307\) −6594.14 −1.22589 −0.612944 0.790126i \(-0.710015\pi\)
−0.612944 + 0.790126i \(0.710015\pi\)
\(308\) 10224.6 1.89157
\(309\) 0 0
\(310\) −6113.69 −1.12011
\(311\) 2390.42 0.435847 0.217924 0.975966i \(-0.430072\pi\)
0.217924 + 0.975966i \(0.430072\pi\)
\(312\) 0 0
\(313\) 3916.45 0.707256 0.353628 0.935386i \(-0.384948\pi\)
0.353628 + 0.935386i \(0.384948\pi\)
\(314\) 1542.53 0.277229
\(315\) 0 0
\(316\) −8949.76 −1.59324
\(317\) 8075.22 1.43076 0.715378 0.698738i \(-0.246255\pi\)
0.715378 + 0.698738i \(0.246255\pi\)
\(318\) 0 0
\(319\) −8251.13 −1.44820
\(320\) −11621.9 −2.03026
\(321\) 0 0
\(322\) −18388.3 −3.18241
\(323\) 316.757 0.0545660
\(324\) 0 0
\(325\) 4062.65 0.693400
\(326\) 14552.8 2.47242
\(327\) 0 0
\(328\) 8172.50 1.37576
\(329\) 9661.74 1.61905
\(330\) 0 0
\(331\) 68.3404 0.0113484 0.00567421 0.999984i \(-0.498194\pi\)
0.00567421 + 0.999984i \(0.498194\pi\)
\(332\) 7685.52 1.27048
\(333\) 0 0
\(334\) 1251.57 0.205039
\(335\) 11419.8 1.86248
\(336\) 0 0
\(337\) 10721.2 1.73300 0.866500 0.499177i \(-0.166364\pi\)
0.866500 + 0.499177i \(0.166364\pi\)
\(338\) −4459.28 −0.717612
\(339\) 0 0
\(340\) −1163.28 −0.185552
\(341\) 3573.44 0.567485
\(342\) 0 0
\(343\) −2940.62 −0.462911
\(344\) 998.626 0.156518
\(345\) 0 0
\(346\) 5042.25 0.783448
\(347\) −11225.7 −1.73668 −0.868338 0.495973i \(-0.834811\pi\)
−0.868338 + 0.495973i \(0.834811\pi\)
\(348\) 0 0
\(349\) 2207.14 0.338526 0.169263 0.985571i \(-0.445861\pi\)
0.169263 + 0.985571i \(0.445861\pi\)
\(350\) −7580.08 −1.15764
\(351\) 0 0
\(352\) 8033.79 1.21648
\(353\) −1614.73 −0.243466 −0.121733 0.992563i \(-0.538845\pi\)
−0.121733 + 0.992563i \(0.538845\pi\)
\(354\) 0 0
\(355\) 6141.92 0.918252
\(356\) 9529.81 1.41876
\(357\) 0 0
\(358\) 12210.4 1.80263
\(359\) −6709.88 −0.986445 −0.493223 0.869903i \(-0.664181\pi\)
−0.493223 + 0.869903i \(0.664181\pi\)
\(360\) 0 0
\(361\) −4821.47 −0.702941
\(362\) 15653.3 2.27270
\(363\) 0 0
\(364\) 15841.7 2.28112
\(365\) −8859.02 −1.27042
\(366\) 0 0
\(367\) −4429.43 −0.630012 −0.315006 0.949090i \(-0.602006\pi\)
−0.315006 + 0.949090i \(0.602006\pi\)
\(368\) −3295.87 −0.466873
\(369\) 0 0
\(370\) 21139.5 2.97024
\(371\) 7159.68 1.00192
\(372\) 0 0
\(373\) 7732.75 1.07342 0.536711 0.843766i \(-0.319667\pi\)
0.536711 + 0.843766i \(0.319667\pi\)
\(374\) 1140.29 0.157655
\(375\) 0 0
\(376\) −6922.94 −0.949531
\(377\) −12784.0 −1.74645
\(378\) 0 0
\(379\) 13844.7 1.87640 0.938198 0.346100i \(-0.112494\pi\)
0.938198 + 0.346100i \(0.112494\pi\)
\(380\) −7482.75 −1.01015
\(381\) 0 0
\(382\) 3641.20 0.487697
\(383\) 4062.56 0.542004 0.271002 0.962579i \(-0.412645\pi\)
0.271002 + 0.962579i \(0.412645\pi\)
\(384\) 0 0
\(385\) 12140.4 1.60710
\(386\) 4931.14 0.650229
\(387\) 0 0
\(388\) 14398.3 1.88393
\(389\) −5590.09 −0.728609 −0.364305 0.931280i \(-0.618693\pi\)
−0.364305 + 0.931280i \(0.618693\pi\)
\(390\) 0 0
\(391\) −1222.81 −0.158159
\(392\) −3719.07 −0.479187
\(393\) 0 0
\(394\) −13730.3 −1.75564
\(395\) −10626.7 −1.35364
\(396\) 0 0
\(397\) 12532.4 1.58434 0.792170 0.610301i \(-0.208951\pi\)
0.792170 + 0.610301i \(0.208951\pi\)
\(398\) 8257.97 1.04004
\(399\) 0 0
\(400\) −1358.64 −0.169830
\(401\) 6998.95 0.871598 0.435799 0.900044i \(-0.356466\pi\)
0.435799 + 0.900044i \(0.356466\pi\)
\(402\) 0 0
\(403\) 5536.56 0.684357
\(404\) −14965.3 −1.84295
\(405\) 0 0
\(406\) 23852.4 2.91570
\(407\) −12356.0 −1.50483
\(408\) 0 0
\(409\) 7220.74 0.872964 0.436482 0.899713i \(-0.356224\pi\)
0.436482 + 0.899713i \(0.356224\pi\)
\(410\) 30048.5 3.61949
\(411\) 0 0
\(412\) 17900.9 2.14057
\(413\) 18629.5 2.21961
\(414\) 0 0
\(415\) 9125.58 1.07941
\(416\) 12447.3 1.46701
\(417\) 0 0
\(418\) 7334.89 0.858280
\(419\) −12911.8 −1.50545 −0.752724 0.658336i \(-0.771260\pi\)
−0.752724 + 0.658336i \(0.771260\pi\)
\(420\) 0 0
\(421\) 650.097 0.0752584 0.0376292 0.999292i \(-0.488019\pi\)
0.0376292 + 0.999292i \(0.488019\pi\)
\(422\) −23818.0 −2.74749
\(423\) 0 0
\(424\) −5130.14 −0.587598
\(425\) −504.072 −0.0575320
\(426\) 0 0
\(427\) −1922.47 −0.217880
\(428\) 1312.46 0.148225
\(429\) 0 0
\(430\) 3671.73 0.411783
\(431\) 6911.08 0.772378 0.386189 0.922420i \(-0.373791\pi\)
0.386189 + 0.922420i \(0.373791\pi\)
\(432\) 0 0
\(433\) 6163.77 0.684092 0.342046 0.939683i \(-0.388880\pi\)
0.342046 + 0.939683i \(0.388880\pi\)
\(434\) −10330.1 −1.14254
\(435\) 0 0
\(436\) −22109.9 −2.42860
\(437\) −7865.70 −0.861024
\(438\) 0 0
\(439\) −2441.71 −0.265458 −0.132729 0.991152i \(-0.542374\pi\)
−0.132729 + 0.991152i \(0.542374\pi\)
\(440\) −8699.00 −0.942520
\(441\) 0 0
\(442\) 1766.73 0.190124
\(443\) −1068.49 −0.114594 −0.0572972 0.998357i \(-0.518248\pi\)
−0.0572972 + 0.998357i \(0.518248\pi\)
\(444\) 0 0
\(445\) 11315.4 1.20540
\(446\) −9115.56 −0.967790
\(447\) 0 0
\(448\) −19637.2 −2.07091
\(449\) 15299.1 1.60804 0.804018 0.594605i \(-0.202691\pi\)
0.804018 + 0.594605i \(0.202691\pi\)
\(450\) 0 0
\(451\) −17563.3 −1.83376
\(452\) 24721.9 2.57261
\(453\) 0 0
\(454\) 7021.72 0.725871
\(455\) 18810.0 1.93808
\(456\) 0 0
\(457\) −1516.60 −0.155237 −0.0776186 0.996983i \(-0.524732\pi\)
−0.0776186 + 0.996983i \(0.524732\pi\)
\(458\) 13728.2 1.40060
\(459\) 0 0
\(460\) 28886.5 2.92791
\(461\) −17802.2 −1.79855 −0.899275 0.437384i \(-0.855905\pi\)
−0.899275 + 0.437384i \(0.855905\pi\)
\(462\) 0 0
\(463\) −4493.23 −0.451011 −0.225506 0.974242i \(-0.572403\pi\)
−0.225506 + 0.974242i \(0.572403\pi\)
\(464\) 4275.26 0.427745
\(465\) 0 0
\(466\) 28120.4 2.79539
\(467\) −1115.34 −0.110518 −0.0552590 0.998472i \(-0.517598\pi\)
−0.0552590 + 0.998472i \(0.517598\pi\)
\(468\) 0 0
\(469\) 19295.7 1.89977
\(470\) −25454.2 −2.49811
\(471\) 0 0
\(472\) −13348.6 −1.30174
\(473\) −2146.12 −0.208623
\(474\) 0 0
\(475\) −3242.43 −0.313206
\(476\) −1965.55 −0.189267
\(477\) 0 0
\(478\) 1063.91 0.101803
\(479\) −850.433 −0.0811217 −0.0405608 0.999177i \(-0.512914\pi\)
−0.0405608 + 0.999177i \(0.512914\pi\)
\(480\) 0 0
\(481\) −19144.0 −1.81474
\(482\) 17060.9 1.61225
\(483\) 0 0
\(484\) 17.9302 0.00168390
\(485\) 17096.2 1.60061
\(486\) 0 0
\(487\) 3249.57 0.302366 0.151183 0.988506i \(-0.451692\pi\)
0.151183 + 0.988506i \(0.451692\pi\)
\(488\) 1377.51 0.127781
\(489\) 0 0
\(490\) −13674.2 −1.26069
\(491\) −21221.2 −1.95051 −0.975256 0.221080i \(-0.929042\pi\)
−0.975256 + 0.221080i \(0.929042\pi\)
\(492\) 0 0
\(493\) 1586.17 0.144904
\(494\) 11364.4 1.03504
\(495\) 0 0
\(496\) −1851.55 −0.167615
\(497\) 10377.8 0.936637
\(498\) 0 0
\(499\) 1277.06 0.114567 0.0572836 0.998358i \(-0.481756\pi\)
0.0572836 + 0.998358i \(0.481756\pi\)
\(500\) −8813.70 −0.788321
\(501\) 0 0
\(502\) −23268.9 −2.06881
\(503\) −7789.84 −0.690521 −0.345260 0.938507i \(-0.612209\pi\)
−0.345260 + 0.938507i \(0.612209\pi\)
\(504\) 0 0
\(505\) −17769.4 −1.56579
\(506\) −28315.7 −2.48772
\(507\) 0 0
\(508\) 4542.51 0.396735
\(509\) 714.739 0.0622401 0.0311201 0.999516i \(-0.490093\pi\)
0.0311201 + 0.999516i \(0.490093\pi\)
\(510\) 0 0
\(511\) −14968.8 −1.29585
\(512\) −6732.80 −0.581154
\(513\) 0 0
\(514\) −31531.8 −2.70585
\(515\) 21255.0 1.81866
\(516\) 0 0
\(517\) 14877.9 1.26563
\(518\) 35718.8 3.02971
\(519\) 0 0
\(520\) −13477.9 −1.13663
\(521\) 16998.2 1.42938 0.714688 0.699443i \(-0.246569\pi\)
0.714688 + 0.699443i \(0.246569\pi\)
\(522\) 0 0
\(523\) 20805.5 1.73951 0.869754 0.493485i \(-0.164277\pi\)
0.869754 + 0.493485i \(0.164277\pi\)
\(524\) 24048.7 2.00491
\(525\) 0 0
\(526\) 8886.32 0.736620
\(527\) −686.948 −0.0567816
\(528\) 0 0
\(529\) 18197.8 1.49567
\(530\) −18862.4 −1.54591
\(531\) 0 0
\(532\) −12643.4 −1.03038
\(533\) −27212.0 −2.21141
\(534\) 0 0
\(535\) 1558.38 0.125934
\(536\) −13826.0 −1.11416
\(537\) 0 0
\(538\) 32706.7 2.62098
\(539\) 7992.56 0.638708
\(540\) 0 0
\(541\) −10482.0 −0.833010 −0.416505 0.909133i \(-0.636745\pi\)
−0.416505 + 0.909133i \(0.636745\pi\)
\(542\) 1286.95 0.101991
\(543\) 0 0
\(544\) −1544.39 −0.121719
\(545\) −26252.6 −2.06337
\(546\) 0 0
\(547\) 4223.09 0.330103 0.165051 0.986285i \(-0.447221\pi\)
0.165051 + 0.986285i \(0.447221\pi\)
\(548\) 34084.6 2.65697
\(549\) 0 0
\(550\) −11672.4 −0.904933
\(551\) 10203.0 0.788863
\(552\) 0 0
\(553\) −17955.6 −1.38074
\(554\) 333.173 0.0255508
\(555\) 0 0
\(556\) 20202.6 1.54097
\(557\) 6773.17 0.515240 0.257620 0.966246i \(-0.417062\pi\)
0.257620 + 0.966246i \(0.417062\pi\)
\(558\) 0 0
\(559\) −3325.13 −0.251588
\(560\) −6290.46 −0.474680
\(561\) 0 0
\(562\) −22952.9 −1.72279
\(563\) −3722.21 −0.278637 −0.139318 0.990248i \(-0.544491\pi\)
−0.139318 + 0.990248i \(0.544491\pi\)
\(564\) 0 0
\(565\) 29354.0 2.18572
\(566\) −26608.3 −1.97603
\(567\) 0 0
\(568\) −7436.03 −0.549312
\(569\) −18264.4 −1.34566 −0.672831 0.739796i \(-0.734922\pi\)
−0.672831 + 0.739796i \(0.734922\pi\)
\(570\) 0 0
\(571\) 14134.6 1.03593 0.517963 0.855403i \(-0.326690\pi\)
0.517963 + 0.855403i \(0.326690\pi\)
\(572\) 24394.3 1.78317
\(573\) 0 0
\(574\) 50772.1 3.69196
\(575\) 12517.1 0.907826
\(576\) 0 0
\(577\) 9177.26 0.662139 0.331069 0.943606i \(-0.392591\pi\)
0.331069 + 0.943606i \(0.392591\pi\)
\(578\) 21651.0 1.55806
\(579\) 0 0
\(580\) −37470.2 −2.68253
\(581\) 15419.2 1.10103
\(582\) 0 0
\(583\) 11025.0 0.783209
\(584\) 10725.6 0.759982
\(585\) 0 0
\(586\) 2257.07 0.159110
\(587\) −9434.81 −0.663401 −0.331701 0.943385i \(-0.607622\pi\)
−0.331701 + 0.943385i \(0.607622\pi\)
\(588\) 0 0
\(589\) −4418.77 −0.309121
\(590\) −49080.1 −3.42474
\(591\) 0 0
\(592\) 6402.16 0.444471
\(593\) −20277.0 −1.40418 −0.702090 0.712089i \(-0.747749\pi\)
−0.702090 + 0.712089i \(0.747749\pi\)
\(594\) 0 0
\(595\) −2333.84 −0.160804
\(596\) −4894.63 −0.336396
\(597\) 0 0
\(598\) −43871.3 −3.00005
\(599\) −2802.75 −0.191181 −0.0955904 0.995421i \(-0.530474\pi\)
−0.0955904 + 0.995421i \(0.530474\pi\)
\(600\) 0 0
\(601\) −4087.51 −0.277426 −0.138713 0.990333i \(-0.544297\pi\)
−0.138713 + 0.990333i \(0.544297\pi\)
\(602\) 6204.01 0.420028
\(603\) 0 0
\(604\) 13242.1 0.892075
\(605\) 21.2898 0.00143067
\(606\) 0 0
\(607\) −4522.40 −0.302403 −0.151201 0.988503i \(-0.548314\pi\)
−0.151201 + 0.988503i \(0.548314\pi\)
\(608\) −9934.27 −0.662645
\(609\) 0 0
\(610\) 5064.81 0.336177
\(611\) 23051.3 1.52628
\(612\) 0 0
\(613\) 22808.1 1.50279 0.751397 0.659851i \(-0.229381\pi\)
0.751397 + 0.659851i \(0.229381\pi\)
\(614\) 29353.7 1.92935
\(615\) 0 0
\(616\) −14698.4 −0.961391
\(617\) 22347.1 1.45812 0.729062 0.684448i \(-0.239957\pi\)
0.729062 + 0.684448i \(0.239957\pi\)
\(618\) 0 0
\(619\) −13531.6 −0.878644 −0.439322 0.898330i \(-0.644781\pi\)
−0.439322 + 0.898330i \(0.644781\pi\)
\(620\) 16227.8 1.05117
\(621\) 0 0
\(622\) −10640.9 −0.685954
\(623\) 19119.3 1.22953
\(624\) 0 0
\(625\) −19444.2 −1.24443
\(626\) −17434.0 −1.11311
\(627\) 0 0
\(628\) −4094.40 −0.260166
\(629\) 2375.28 0.150570
\(630\) 0 0
\(631\) 19524.9 1.23182 0.615908 0.787818i \(-0.288789\pi\)
0.615908 + 0.787818i \(0.288789\pi\)
\(632\) 12865.8 0.809766
\(633\) 0 0
\(634\) −35946.8 −2.25178
\(635\) 5393.65 0.337071
\(636\) 0 0
\(637\) 12383.4 0.770248
\(638\) 36729.8 2.27923
\(639\) 0 0
\(640\) 27033.3 1.66967
\(641\) −4541.75 −0.279857 −0.139929 0.990162i \(-0.544687\pi\)
−0.139929 + 0.990162i \(0.544687\pi\)
\(642\) 0 0
\(643\) −27511.4 −1.68732 −0.843658 0.536880i \(-0.819603\pi\)
−0.843658 + 0.536880i \(0.819603\pi\)
\(644\) 48808.6 2.98654
\(645\) 0 0
\(646\) −1410.04 −0.0858781
\(647\) 22096.3 1.34265 0.671327 0.741162i \(-0.265725\pi\)
0.671327 + 0.741162i \(0.265725\pi\)
\(648\) 0 0
\(649\) 28687.2 1.73509
\(650\) −18084.8 −1.09130
\(651\) 0 0
\(652\) −38628.1 −2.32024
\(653\) 10058.9 0.602812 0.301406 0.953496i \(-0.402544\pi\)
0.301406 + 0.953496i \(0.402544\pi\)
\(654\) 0 0
\(655\) 28554.8 1.70340
\(656\) 9100.28 0.541626
\(657\) 0 0
\(658\) −43009.1 −2.54813
\(659\) −377.712 −0.0223271 −0.0111636 0.999938i \(-0.503554\pi\)
−0.0111636 + 0.999938i \(0.503554\pi\)
\(660\) 0 0
\(661\) −31831.9 −1.87310 −0.936549 0.350536i \(-0.885999\pi\)
−0.936549 + 0.350536i \(0.885999\pi\)
\(662\) −304.217 −0.0178606
\(663\) 0 0
\(664\) −11048.3 −0.645721
\(665\) −15012.4 −0.875421
\(666\) 0 0
\(667\) −39387.9 −2.28651
\(668\) −3322.10 −0.192419
\(669\) 0 0
\(670\) −50835.1 −2.93124
\(671\) −2960.37 −0.170319
\(672\) 0 0
\(673\) 4977.25 0.285080 0.142540 0.989789i \(-0.454473\pi\)
0.142540 + 0.989789i \(0.454473\pi\)
\(674\) −47725.3 −2.72746
\(675\) 0 0
\(676\) 11836.4 0.673443
\(677\) −17528.8 −0.995106 −0.497553 0.867433i \(-0.665768\pi\)
−0.497553 + 0.867433i \(0.665768\pi\)
\(678\) 0 0
\(679\) 28886.9 1.63266
\(680\) 1672.27 0.0943069
\(681\) 0 0
\(682\) −15907.1 −0.893131
\(683\) −4754.01 −0.266335 −0.133168 0.991094i \(-0.542515\pi\)
−0.133168 + 0.991094i \(0.542515\pi\)
\(684\) 0 0
\(685\) 40471.1 2.25740
\(686\) 13090.1 0.728548
\(687\) 0 0
\(688\) 1111.99 0.0616198
\(689\) 17081.8 0.944507
\(690\) 0 0
\(691\) −7006.36 −0.385723 −0.192861 0.981226i \(-0.561777\pi\)
−0.192861 + 0.981226i \(0.561777\pi\)
\(692\) −13383.8 −0.735226
\(693\) 0 0
\(694\) 49971.0 2.73325
\(695\) 23987.9 1.30923
\(696\) 0 0
\(697\) 3376.32 0.183483
\(698\) −9825.06 −0.532785
\(699\) 0 0
\(700\) 20120.1 1.08638
\(701\) −11572.3 −0.623511 −0.311756 0.950162i \(-0.600917\pi\)
−0.311756 + 0.950162i \(0.600917\pi\)
\(702\) 0 0
\(703\) 15278.9 0.819710
\(704\) −30238.9 −1.61885
\(705\) 0 0
\(706\) 7187.97 0.383177
\(707\) −30024.3 −1.59715
\(708\) 0 0
\(709\) −25780.5 −1.36559 −0.682796 0.730609i \(-0.739236\pi\)
−0.682796 + 0.730609i \(0.739236\pi\)
\(710\) −27340.7 −1.44518
\(711\) 0 0
\(712\) −13699.6 −0.721088
\(713\) 17058.3 0.895986
\(714\) 0 0
\(715\) 28965.1 1.51501
\(716\) −32410.6 −1.69168
\(717\) 0 0
\(718\) 29868.9 1.55251
\(719\) 5465.62 0.283495 0.141748 0.989903i \(-0.454728\pi\)
0.141748 + 0.989903i \(0.454728\pi\)
\(720\) 0 0
\(721\) 35914.0 1.85507
\(722\) 21462.7 1.10632
\(723\) 0 0
\(724\) −41549.1 −2.13282
\(725\) −16236.6 −0.831743
\(726\) 0 0
\(727\) −18761.8 −0.957134 −0.478567 0.878051i \(-0.658844\pi\)
−0.478567 + 0.878051i \(0.658844\pi\)
\(728\) −22773.2 −1.15939
\(729\) 0 0
\(730\) 39435.8 1.99943
\(731\) 412.564 0.0208745
\(732\) 0 0
\(733\) 17761.5 0.895000 0.447500 0.894284i \(-0.352314\pi\)
0.447500 + 0.894284i \(0.352314\pi\)
\(734\) 19717.5 0.991537
\(735\) 0 0
\(736\) 38350.4 1.92067
\(737\) 29713.0 1.48507
\(738\) 0 0
\(739\) 14899.8 0.741676 0.370838 0.928698i \(-0.379071\pi\)
0.370838 + 0.928698i \(0.379071\pi\)
\(740\) −56111.3 −2.78742
\(741\) 0 0
\(742\) −31871.2 −1.57686
\(743\) −1841.01 −0.0909019 −0.0454509 0.998967i \(-0.514472\pi\)
−0.0454509 + 0.998967i \(0.514472\pi\)
\(744\) 0 0
\(745\) −5811.74 −0.285806
\(746\) −34422.2 −1.68939
\(747\) 0 0
\(748\) −3026.72 −0.147951
\(749\) 2633.15 0.128456
\(750\) 0 0
\(751\) −401.276 −0.0194977 −0.00974885 0.999952i \(-0.503103\pi\)
−0.00974885 + 0.999952i \(0.503103\pi\)
\(752\) −7708.87 −0.373821
\(753\) 0 0
\(754\) 56907.9 2.74863
\(755\) 15723.3 0.757920
\(756\) 0 0
\(757\) −40970.6 −1.96711 −0.983554 0.180612i \(-0.942192\pi\)
−0.983554 + 0.180612i \(0.942192\pi\)
\(758\) −61629.5 −2.95314
\(759\) 0 0
\(760\) 10756.8 0.513410
\(761\) 26698.7 1.27178 0.635892 0.771778i \(-0.280632\pi\)
0.635892 + 0.771778i \(0.280632\pi\)
\(762\) 0 0
\(763\) −44358.2 −2.10469
\(764\) −9664.98 −0.457679
\(765\) 0 0
\(766\) −18084.5 −0.853026
\(767\) 44447.0 2.09242
\(768\) 0 0
\(769\) −32725.1 −1.53459 −0.767294 0.641296i \(-0.778397\pi\)
−0.767294 + 0.641296i \(0.778397\pi\)
\(770\) −54043.0 −2.52932
\(771\) 0 0
\(772\) −13088.9 −0.610207
\(773\) −21560.3 −1.00319 −0.501597 0.865101i \(-0.667254\pi\)
−0.501597 + 0.865101i \(0.667254\pi\)
\(774\) 0 0
\(775\) 7031.84 0.325924
\(776\) −20698.3 −0.957509
\(777\) 0 0
\(778\) 24884.2 1.14671
\(779\) 21718.1 0.998885
\(780\) 0 0
\(781\) 15980.6 0.732177
\(782\) 5443.33 0.248917
\(783\) 0 0
\(784\) −4141.28 −0.188651
\(785\) −4861.57 −0.221041
\(786\) 0 0
\(787\) −4776.67 −0.216353 −0.108177 0.994132i \(-0.534501\pi\)
−0.108177 + 0.994132i \(0.534501\pi\)
\(788\) 36444.8 1.64758
\(789\) 0 0
\(790\) 47304.6 2.13041
\(791\) 49598.6 2.22949
\(792\) 0 0
\(793\) −4586.69 −0.205395
\(794\) −55787.8 −2.49349
\(795\) 0 0
\(796\) −21919.4 −0.976022
\(797\) 39883.7 1.77259 0.886294 0.463123i \(-0.153271\pi\)
0.886294 + 0.463123i \(0.153271\pi\)
\(798\) 0 0
\(799\) −2860.09 −0.126637
\(800\) 15809.0 0.698664
\(801\) 0 0
\(802\) −31155.7 −1.37175
\(803\) −23050.2 −1.01298
\(804\) 0 0
\(805\) 57954.0 2.53740
\(806\) −24645.9 −1.07707
\(807\) 0 0
\(808\) 21513.4 0.936681
\(809\) −19395.9 −0.842921 −0.421460 0.906847i \(-0.638482\pi\)
−0.421460 + 0.906847i \(0.638482\pi\)
\(810\) 0 0
\(811\) 34882.1 1.51033 0.755163 0.655537i \(-0.227558\pi\)
0.755163 + 0.655537i \(0.227558\pi\)
\(812\) −63312.3 −2.73624
\(813\) 0 0
\(814\) 55002.6 2.36835
\(815\) −45866.0 −1.97131
\(816\) 0 0
\(817\) 2653.81 0.113641
\(818\) −32143.0 −1.37390
\(819\) 0 0
\(820\) −79758.9 −3.39671
\(821\) −15825.4 −0.672729 −0.336365 0.941732i \(-0.609197\pi\)
−0.336365 + 0.941732i \(0.609197\pi\)
\(822\) 0 0
\(823\) −24669.0 −1.04485 −0.522423 0.852687i \(-0.674972\pi\)
−0.522423 + 0.852687i \(0.674972\pi\)
\(824\) −25733.5 −1.08795
\(825\) 0 0
\(826\) −82929.2 −3.49331
\(827\) −22234.8 −0.934921 −0.467461 0.884014i \(-0.654831\pi\)
−0.467461 + 0.884014i \(0.654831\pi\)
\(828\) 0 0
\(829\) −14531.7 −0.608813 −0.304407 0.952542i \(-0.598458\pi\)
−0.304407 + 0.952542i \(0.598458\pi\)
\(830\) −40622.4 −1.69882
\(831\) 0 0
\(832\) −46851.1 −1.95225
\(833\) −1536.47 −0.0639081
\(834\) 0 0
\(835\) −3944.57 −0.163482
\(836\) −19469.3 −0.805453
\(837\) 0 0
\(838\) 57476.7 2.36933
\(839\) 10721.4 0.441171 0.220586 0.975368i \(-0.429203\pi\)
0.220586 + 0.975368i \(0.429203\pi\)
\(840\) 0 0
\(841\) 26703.1 1.09488
\(842\) −2893.90 −0.118445
\(843\) 0 0
\(844\) 63221.0 2.57838
\(845\) 14054.3 0.572167
\(846\) 0 0
\(847\) 35.9727 0.00145931
\(848\) −5712.53 −0.231332
\(849\) 0 0
\(850\) 2243.87 0.0905461
\(851\) −58983.0 −2.37592
\(852\) 0 0
\(853\) −42748.0 −1.71590 −0.857951 0.513731i \(-0.828263\pi\)
−0.857951 + 0.513731i \(0.828263\pi\)
\(854\) 8557.84 0.342908
\(855\) 0 0
\(856\) −1886.74 −0.0753357
\(857\) −29280.0 −1.16708 −0.583539 0.812085i \(-0.698332\pi\)
−0.583539 + 0.812085i \(0.698332\pi\)
\(858\) 0 0
\(859\) −21086.2 −0.837545 −0.418773 0.908091i \(-0.637540\pi\)
−0.418773 + 0.908091i \(0.637540\pi\)
\(860\) −9746.02 −0.386438
\(861\) 0 0
\(862\) −30764.6 −1.21560
\(863\) −10275.9 −0.405326 −0.202663 0.979249i \(-0.564960\pi\)
−0.202663 + 0.979249i \(0.564960\pi\)
\(864\) 0 0
\(865\) −15891.6 −0.624659
\(866\) −27438.0 −1.07665
\(867\) 0 0
\(868\) 27419.6 1.07221
\(869\) −27649.5 −1.07934
\(870\) 0 0
\(871\) 46036.3 1.79091
\(872\) 31784.1 1.23434
\(873\) 0 0
\(874\) 35014.1 1.35511
\(875\) −17682.6 −0.683179
\(876\) 0 0
\(877\) −42597.5 −1.64015 −0.820077 0.572253i \(-0.806070\pi\)
−0.820077 + 0.572253i \(0.806070\pi\)
\(878\) 10869.2 0.417789
\(879\) 0 0
\(880\) −9686.56 −0.371061
\(881\) 5871.79 0.224547 0.112273 0.993677i \(-0.464187\pi\)
0.112273 + 0.993677i \(0.464187\pi\)
\(882\) 0 0
\(883\) 16601.8 0.632725 0.316362 0.948638i \(-0.397538\pi\)
0.316362 + 0.948638i \(0.397538\pi\)
\(884\) −4689.49 −0.178421
\(885\) 0 0
\(886\) 4756.36 0.180353
\(887\) 7463.42 0.282522 0.141261 0.989972i \(-0.454884\pi\)
0.141261 + 0.989972i \(0.454884\pi\)
\(888\) 0 0
\(889\) 9113.48 0.343820
\(890\) −50370.5 −1.89710
\(891\) 0 0
\(892\) 24195.8 0.908222
\(893\) −18397.4 −0.689415
\(894\) 0 0
\(895\) −38483.4 −1.43727
\(896\) 45677.4 1.70310
\(897\) 0 0
\(898\) −68103.7 −2.53079
\(899\) −22127.2 −0.820895
\(900\) 0 0
\(901\) −2119.42 −0.0783665
\(902\) 78182.9 2.88604
\(903\) 0 0
\(904\) −35539.0 −1.30753
\(905\) −49334.2 −1.81207
\(906\) 0 0
\(907\) 14908.7 0.545795 0.272897 0.962043i \(-0.412018\pi\)
0.272897 + 0.962043i \(0.412018\pi\)
\(908\) −18638.0 −0.681194
\(909\) 0 0
\(910\) −83732.3 −3.05022
\(911\) −17426.7 −0.633778 −0.316889 0.948463i \(-0.602638\pi\)
−0.316889 + 0.948463i \(0.602638\pi\)
\(912\) 0 0
\(913\) 23743.7 0.860682
\(914\) 6751.11 0.244318
\(915\) 0 0
\(916\) −36439.1 −1.31439
\(917\) 48248.1 1.73751
\(918\) 0 0
\(919\) 4025.33 0.144487 0.0722434 0.997387i \(-0.476984\pi\)
0.0722434 + 0.997387i \(0.476984\pi\)
\(920\) −41525.9 −1.48812
\(921\) 0 0
\(922\) 79246.3 2.83063
\(923\) 24759.8 0.882966
\(924\) 0 0
\(925\) −24314.2 −0.864267
\(926\) 20001.6 0.709819
\(927\) 0 0
\(928\) −49746.4 −1.75970
\(929\) −14049.4 −0.496173 −0.248086 0.968738i \(-0.579802\pi\)
−0.248086 + 0.968738i \(0.579802\pi\)
\(930\) 0 0
\(931\) −9883.28 −0.347918
\(932\) −74641.0 −2.62333
\(933\) 0 0
\(934\) 4964.94 0.173938
\(935\) −3593.84 −0.125702
\(936\) 0 0
\(937\) 10784.7 0.376010 0.188005 0.982168i \(-0.439798\pi\)
0.188005 + 0.982168i \(0.439798\pi\)
\(938\) −85894.5 −2.98993
\(939\) 0 0
\(940\) 67563.9 2.34435
\(941\) −807.886 −0.0279876 −0.0139938 0.999902i \(-0.504455\pi\)
−0.0139938 + 0.999902i \(0.504455\pi\)
\(942\) 0 0
\(943\) −83840.8 −2.89526
\(944\) −14864.1 −0.512483
\(945\) 0 0
\(946\) 9553.43 0.328339
\(947\) 40932.1 1.40456 0.702278 0.711902i \(-0.252166\pi\)
0.702278 + 0.711902i \(0.252166\pi\)
\(948\) 0 0
\(949\) −35713.1 −1.22160
\(950\) 14433.6 0.492936
\(951\) 0 0
\(952\) 2825.59 0.0961952
\(953\) −1797.29 −0.0610912 −0.0305456 0.999533i \(-0.509724\pi\)
−0.0305456 + 0.999533i \(0.509724\pi\)
\(954\) 0 0
\(955\) −11475.9 −0.388850
\(956\) −2823.96 −0.0955372
\(957\) 0 0
\(958\) 3785.69 0.127672
\(959\) 68382.7 2.30260
\(960\) 0 0
\(961\) −20208.0 −0.678327
\(962\) 85219.1 2.85611
\(963\) 0 0
\(964\) −45285.4 −1.51301
\(965\) −15541.4 −0.518440
\(966\) 0 0
\(967\) −12648.8 −0.420640 −0.210320 0.977633i \(-0.567451\pi\)
−0.210320 + 0.977633i \(0.567451\pi\)
\(968\) −25.7756 −0.000855846 0
\(969\) 0 0
\(970\) −76103.4 −2.51910
\(971\) 54297.9 1.79454 0.897272 0.441477i \(-0.145545\pi\)
0.897272 + 0.441477i \(0.145545\pi\)
\(972\) 0 0
\(973\) 40531.7 1.33544
\(974\) −14465.4 −0.475875
\(975\) 0 0
\(976\) 1533.89 0.0503060
\(977\) −38106.3 −1.24783 −0.623914 0.781493i \(-0.714458\pi\)
−0.623914 + 0.781493i \(0.714458\pi\)
\(978\) 0 0
\(979\) 29441.5 0.961137
\(980\) 36296.0 1.18309
\(981\) 0 0
\(982\) 94466.1 3.06979
\(983\) −35577.7 −1.15438 −0.577189 0.816611i \(-0.695850\pi\)
−0.577189 + 0.816611i \(0.695850\pi\)
\(984\) 0 0
\(985\) 43273.5 1.39981
\(986\) −7060.84 −0.228056
\(987\) 0 0
\(988\) −30165.0 −0.971332
\(989\) −10244.8 −0.329389
\(990\) 0 0
\(991\) 26708.2 0.856120 0.428060 0.903750i \(-0.359197\pi\)
0.428060 + 0.903750i \(0.359197\pi\)
\(992\) 21544.4 0.689551
\(993\) 0 0
\(994\) −46196.7 −1.47412
\(995\) −26026.5 −0.829242
\(996\) 0 0
\(997\) 18318.2 0.581888 0.290944 0.956740i \(-0.406031\pi\)
0.290944 + 0.956740i \(0.406031\pi\)
\(998\) −5684.81 −0.180310
\(999\) 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 2151.4.a.h.1.8 yes 59
3.2 odd 2 2151.4.a.g.1.52 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.52 59 3.2 odd 2
2151.4.a.h.1.8 yes 59 1.1 even 1 trivial