Properties

Label 2151.4.a.h.1.17
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 1.17
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.95118 q^{2} +0.709472 q^{4} -16.6350 q^{5} -30.2397 q^{7} +21.5157 q^{8} +O(q^{10})\) \(q-2.95118 q^{2} +0.709472 q^{4} -16.6350 q^{5} -30.2397 q^{7} +21.5157 q^{8} +49.0928 q^{10} -7.82864 q^{11} +48.9031 q^{13} +89.2428 q^{14} -69.1724 q^{16} +47.2093 q^{17} +48.8394 q^{19} -11.8020 q^{20} +23.1037 q^{22} -130.630 q^{23} +151.722 q^{25} -144.322 q^{26} -21.4542 q^{28} +145.591 q^{29} -122.337 q^{31} +32.0150 q^{32} -139.323 q^{34} +503.036 q^{35} -31.4938 q^{37} -144.134 q^{38} -357.912 q^{40} -123.558 q^{41} -306.194 q^{43} -5.55420 q^{44} +385.514 q^{46} -143.310 q^{47} +571.438 q^{49} -447.758 q^{50} +34.6954 q^{52} +285.587 q^{53} +130.229 q^{55} -650.627 q^{56} -429.666 q^{58} -260.993 q^{59} -604.367 q^{61} +361.038 q^{62} +458.897 q^{64} -813.501 q^{65} -517.550 q^{67} +33.4937 q^{68} -1484.55 q^{70} -246.465 q^{71} -882.001 q^{73} +92.9438 q^{74} +34.6502 q^{76} +236.735 q^{77} -1165.14 q^{79} +1150.68 q^{80} +364.643 q^{82} -34.8380 q^{83} -785.324 q^{85} +903.633 q^{86} -168.438 q^{88} +810.810 q^{89} -1478.81 q^{91} -92.6786 q^{92} +422.934 q^{94} -812.440 q^{95} -192.023 q^{97} -1686.42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.95118 −1.04340 −0.521700 0.853129i \(-0.674702\pi\)
−0.521700 + 0.853129i \(0.674702\pi\)
\(3\) 0 0
\(4\) 0.709472 0.0886840
\(5\) −16.6350 −1.48788 −0.743938 0.668249i \(-0.767044\pi\)
−0.743938 + 0.668249i \(0.767044\pi\)
\(6\) 0 0
\(7\) −30.2397 −1.63279 −0.816395 0.577494i \(-0.804031\pi\)
−0.816395 + 0.577494i \(0.804031\pi\)
\(8\) 21.5157 0.950867
\(9\) 0 0
\(10\) 49.0928 1.55245
\(11\) −7.82864 −0.214584 −0.107292 0.994228i \(-0.534218\pi\)
−0.107292 + 0.994228i \(0.534218\pi\)
\(12\) 0 0
\(13\) 48.9031 1.04333 0.521665 0.853151i \(-0.325311\pi\)
0.521665 + 0.853151i \(0.325311\pi\)
\(14\) 89.2428 1.70365
\(15\) 0 0
\(16\) −69.1724 −1.08082
\(17\) 47.2093 0.673526 0.336763 0.941590i \(-0.390668\pi\)
0.336763 + 0.941590i \(0.390668\pi\)
\(18\) 0 0
\(19\) 48.8394 0.589711 0.294856 0.955542i \(-0.404728\pi\)
0.294856 + 0.955542i \(0.404728\pi\)
\(20\) −11.8020 −0.131951
\(21\) 0 0
\(22\) 23.1037 0.223897
\(23\) −130.630 −1.18427 −0.592137 0.805837i \(-0.701716\pi\)
−0.592137 + 0.805837i \(0.701716\pi\)
\(24\) 0 0
\(25\) 151.722 1.21377
\(26\) −144.322 −1.08861
\(27\) 0 0
\(28\) −21.4542 −0.144802
\(29\) 145.591 0.932263 0.466131 0.884715i \(-0.345647\pi\)
0.466131 + 0.884715i \(0.345647\pi\)
\(30\) 0 0
\(31\) −122.337 −0.708784 −0.354392 0.935097i \(-0.615312\pi\)
−0.354392 + 0.935097i \(0.615312\pi\)
\(32\) 32.0150 0.176860
\(33\) 0 0
\(34\) −139.323 −0.702757
\(35\) 503.036 2.42939
\(36\) 0 0
\(37\) −31.4938 −0.139934 −0.0699668 0.997549i \(-0.522289\pi\)
−0.0699668 + 0.997549i \(0.522289\pi\)
\(38\) −144.134 −0.615305
\(39\) 0 0
\(40\) −357.912 −1.41477
\(41\) −123.558 −0.470648 −0.235324 0.971917i \(-0.575615\pi\)
−0.235324 + 0.971917i \(0.575615\pi\)
\(42\) 0 0
\(43\) −306.194 −1.08591 −0.542955 0.839762i \(-0.682694\pi\)
−0.542955 + 0.839762i \(0.682694\pi\)
\(44\) −5.55420 −0.0190302
\(45\) 0 0
\(46\) 385.514 1.23567
\(47\) −143.310 −0.444764 −0.222382 0.974960i \(-0.571383\pi\)
−0.222382 + 0.974960i \(0.571383\pi\)
\(48\) 0 0
\(49\) 571.438 1.66600
\(50\) −447.758 −1.26645
\(51\) 0 0
\(52\) 34.6954 0.0925267
\(53\) 285.587 0.740160 0.370080 0.929000i \(-0.379330\pi\)
0.370080 + 0.929000i \(0.379330\pi\)
\(54\) 0 0
\(55\) 130.229 0.319274
\(56\) −650.627 −1.55257
\(57\) 0 0
\(58\) −429.666 −0.972723
\(59\) −260.993 −0.575905 −0.287952 0.957645i \(-0.592974\pi\)
−0.287952 + 0.957645i \(0.592974\pi\)
\(60\) 0 0
\(61\) −604.367 −1.26855 −0.634273 0.773109i \(-0.718700\pi\)
−0.634273 + 0.773109i \(0.718700\pi\)
\(62\) 361.038 0.739545
\(63\) 0 0
\(64\) 458.897 0.896284
\(65\) −813.501 −1.55234
\(66\) 0 0
\(67\) −517.550 −0.943713 −0.471857 0.881675i \(-0.656416\pi\)
−0.471857 + 0.881675i \(0.656416\pi\)
\(68\) 33.4937 0.0597310
\(69\) 0 0
\(70\) −1484.55 −2.53482
\(71\) −246.465 −0.411972 −0.205986 0.978555i \(-0.566040\pi\)
−0.205986 + 0.978555i \(0.566040\pi\)
\(72\) 0 0
\(73\) −882.001 −1.41412 −0.707058 0.707156i \(-0.749978\pi\)
−0.707058 + 0.707156i \(0.749978\pi\)
\(74\) 92.9438 0.146007
\(75\) 0 0
\(76\) 34.6502 0.0522980
\(77\) 236.735 0.350370
\(78\) 0 0
\(79\) −1165.14 −1.65935 −0.829676 0.558245i \(-0.811475\pi\)
−0.829676 + 0.558245i \(0.811475\pi\)
\(80\) 1150.68 1.60812
\(81\) 0 0
\(82\) 364.643 0.491075
\(83\) −34.8380 −0.0460719 −0.0230360 0.999735i \(-0.507333\pi\)
−0.0230360 + 0.999735i \(0.507333\pi\)
\(84\) 0 0
\(85\) −785.324 −1.00212
\(86\) 903.633 1.13304
\(87\) 0 0
\(88\) −168.438 −0.204041
\(89\) 810.810 0.965682 0.482841 0.875708i \(-0.339605\pi\)
0.482841 + 0.875708i \(0.339605\pi\)
\(90\) 0 0
\(91\) −1478.81 −1.70354
\(92\) −92.6786 −0.105026
\(93\) 0 0
\(94\) 422.934 0.464067
\(95\) −812.440 −0.877417
\(96\) 0 0
\(97\) −192.023 −0.200999 −0.100500 0.994937i \(-0.532044\pi\)
−0.100500 + 0.994937i \(0.532044\pi\)
\(98\) −1686.42 −1.73831
\(99\) 0 0
\(100\) 107.642 0.107642
\(101\) 1491.59 1.46949 0.734747 0.678341i \(-0.237301\pi\)
0.734747 + 0.678341i \(0.237301\pi\)
\(102\) 0 0
\(103\) −1282.36 −1.22675 −0.613373 0.789793i \(-0.710188\pi\)
−0.613373 + 0.789793i \(0.710188\pi\)
\(104\) 1052.18 0.992068
\(105\) 0 0
\(106\) −842.820 −0.772283
\(107\) −189.030 −0.170787 −0.0853933 0.996347i \(-0.527215\pi\)
−0.0853933 + 0.996347i \(0.527215\pi\)
\(108\) 0 0
\(109\) −1025.50 −0.901152 −0.450576 0.892738i \(-0.648781\pi\)
−0.450576 + 0.892738i \(0.648781\pi\)
\(110\) −384.329 −0.333131
\(111\) 0 0
\(112\) 2091.75 1.76475
\(113\) −529.570 −0.440865 −0.220433 0.975402i \(-0.570747\pi\)
−0.220433 + 0.975402i \(0.570747\pi\)
\(114\) 0 0
\(115\) 2173.03 1.76205
\(116\) 103.293 0.0826768
\(117\) 0 0
\(118\) 770.237 0.600899
\(119\) −1427.59 −1.09973
\(120\) 0 0
\(121\) −1269.71 −0.953954
\(122\) 1783.60 1.32360
\(123\) 0 0
\(124\) −86.7944 −0.0628578
\(125\) −444.514 −0.318069
\(126\) 0 0
\(127\) −231.452 −0.161717 −0.0808584 0.996726i \(-0.525766\pi\)
−0.0808584 + 0.996726i \(0.525766\pi\)
\(128\) −1610.41 −1.11204
\(129\) 0 0
\(130\) 2400.79 1.61972
\(131\) −2676.49 −1.78509 −0.892544 0.450961i \(-0.851081\pi\)
−0.892544 + 0.450961i \(0.851081\pi\)
\(132\) 0 0
\(133\) −1476.89 −0.962874
\(134\) 1527.38 0.984670
\(135\) 0 0
\(136\) 1015.74 0.640433
\(137\) 2459.96 1.53408 0.767038 0.641602i \(-0.221730\pi\)
0.767038 + 0.641602i \(0.221730\pi\)
\(138\) 0 0
\(139\) −450.639 −0.274984 −0.137492 0.990503i \(-0.543904\pi\)
−0.137492 + 0.990503i \(0.543904\pi\)
\(140\) 356.890 0.215448
\(141\) 0 0
\(142\) 727.362 0.429851
\(143\) −382.845 −0.223882
\(144\) 0 0
\(145\) −2421.90 −1.38709
\(146\) 2602.95 1.47549
\(147\) 0 0
\(148\) −22.3440 −0.0124099
\(149\) 430.148 0.236504 0.118252 0.992984i \(-0.462271\pi\)
0.118252 + 0.992984i \(0.462271\pi\)
\(150\) 0 0
\(151\) 3413.85 1.83983 0.919917 0.392113i \(-0.128256\pi\)
0.919917 + 0.392113i \(0.128256\pi\)
\(152\) 1050.81 0.560737
\(153\) 0 0
\(154\) −698.649 −0.365576
\(155\) 2035.06 1.05458
\(156\) 0 0
\(157\) 864.393 0.439402 0.219701 0.975567i \(-0.429492\pi\)
0.219701 + 0.975567i \(0.429492\pi\)
\(158\) 3438.55 1.73137
\(159\) 0 0
\(160\) −532.568 −0.263145
\(161\) 3950.22 1.93367
\(162\) 0 0
\(163\) 1065.54 0.512024 0.256012 0.966674i \(-0.417591\pi\)
0.256012 + 0.966674i \(0.417591\pi\)
\(164\) −87.6613 −0.0417390
\(165\) 0 0
\(166\) 102.813 0.0480715
\(167\) −330.435 −0.153113 −0.0765565 0.997065i \(-0.524393\pi\)
−0.0765565 + 0.997065i \(0.524393\pi\)
\(168\) 0 0
\(169\) 194.515 0.0885367
\(170\) 2317.63 1.04561
\(171\) 0 0
\(172\) −217.236 −0.0963028
\(173\) 885.439 0.389125 0.194563 0.980890i \(-0.437671\pi\)
0.194563 + 0.980890i \(0.437671\pi\)
\(174\) 0 0
\(175\) −4588.02 −1.98184
\(176\) 541.526 0.231926
\(177\) 0 0
\(178\) −2392.85 −1.00759
\(179\) 3123.34 1.30418 0.652092 0.758140i \(-0.273891\pi\)
0.652092 + 0.758140i \(0.273891\pi\)
\(180\) 0 0
\(181\) −612.109 −0.251368 −0.125684 0.992070i \(-0.540113\pi\)
−0.125684 + 0.992070i \(0.540113\pi\)
\(182\) 4364.25 1.77747
\(183\) 0 0
\(184\) −2810.60 −1.12609
\(185\) 523.897 0.208204
\(186\) 0 0
\(187\) −369.584 −0.144528
\(188\) −101.675 −0.0394435
\(189\) 0 0
\(190\) 2397.66 0.915497
\(191\) −3649.85 −1.38269 −0.691345 0.722525i \(-0.742982\pi\)
−0.691345 + 0.722525i \(0.742982\pi\)
\(192\) 0 0
\(193\) 76.0810 0.0283753 0.0141876 0.999899i \(-0.495484\pi\)
0.0141876 + 0.999899i \(0.495484\pi\)
\(194\) 566.694 0.209723
\(195\) 0 0
\(196\) 405.419 0.147748
\(197\) −3599.52 −1.30180 −0.650902 0.759162i \(-0.725609\pi\)
−0.650902 + 0.759162i \(0.725609\pi\)
\(198\) 0 0
\(199\) −3965.15 −1.41247 −0.706237 0.707976i \(-0.749608\pi\)
−0.706237 + 0.707976i \(0.749608\pi\)
\(200\) 3264.39 1.15414
\(201\) 0 0
\(202\) −4401.96 −1.53327
\(203\) −4402.63 −1.52219
\(204\) 0 0
\(205\) 2055.39 0.700266
\(206\) 3784.48 1.27999
\(207\) 0 0
\(208\) −3382.75 −1.12765
\(209\) −382.345 −0.126543
\(210\) 0 0
\(211\) 315.363 0.102893 0.0514466 0.998676i \(-0.483617\pi\)
0.0514466 + 0.998676i \(0.483617\pi\)
\(212\) 202.616 0.0656403
\(213\) 0 0
\(214\) 557.861 0.178199
\(215\) 5093.52 1.61570
\(216\) 0 0
\(217\) 3699.42 1.15729
\(218\) 3026.45 0.940262
\(219\) 0 0
\(220\) 92.3938 0.0283145
\(221\) 2308.68 0.702709
\(222\) 0 0
\(223\) −4273.57 −1.28332 −0.641658 0.766991i \(-0.721753\pi\)
−0.641658 + 0.766991i \(0.721753\pi\)
\(224\) −968.124 −0.288775
\(225\) 0 0
\(226\) 1562.86 0.459999
\(227\) −4235.90 −1.23853 −0.619265 0.785182i \(-0.712569\pi\)
−0.619265 + 0.785182i \(0.712569\pi\)
\(228\) 0 0
\(229\) 6473.11 1.86793 0.933963 0.357370i \(-0.116327\pi\)
0.933963 + 0.357370i \(0.116327\pi\)
\(230\) −6413.01 −1.83853
\(231\) 0 0
\(232\) 3132.49 0.886458
\(233\) 2644.21 0.743467 0.371733 0.928340i \(-0.378764\pi\)
0.371733 + 0.928340i \(0.378764\pi\)
\(234\) 0 0
\(235\) 2383.96 0.661754
\(236\) −185.167 −0.0510735
\(237\) 0 0
\(238\) 4213.09 1.14745
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −2159.55 −0.577214 −0.288607 0.957448i \(-0.593192\pi\)
−0.288607 + 0.957448i \(0.593192\pi\)
\(242\) 3747.15 0.995356
\(243\) 0 0
\(244\) −428.782 −0.112500
\(245\) −9505.85 −2.47880
\(246\) 0 0
\(247\) 2388.40 0.615263
\(248\) −2632.15 −0.673960
\(249\) 0 0
\(250\) 1311.84 0.331873
\(251\) 5514.44 1.38673 0.693364 0.720588i \(-0.256128\pi\)
0.693364 + 0.720588i \(0.256128\pi\)
\(252\) 0 0
\(253\) 1022.66 0.254126
\(254\) 683.057 0.168735
\(255\) 0 0
\(256\) 1081.43 0.264021
\(257\) −3422.74 −0.830758 −0.415379 0.909648i \(-0.636351\pi\)
−0.415379 + 0.909648i \(0.636351\pi\)
\(258\) 0 0
\(259\) 952.362 0.228482
\(260\) −577.156 −0.137668
\(261\) 0 0
\(262\) 7898.82 1.86256
\(263\) −4157.22 −0.974697 −0.487348 0.873208i \(-0.662036\pi\)
−0.487348 + 0.873208i \(0.662036\pi\)
\(264\) 0 0
\(265\) −4750.73 −1.10127
\(266\) 4358.56 1.00466
\(267\) 0 0
\(268\) −367.187 −0.0836923
\(269\) −74.1339 −0.0168031 −0.00840153 0.999965i \(-0.502674\pi\)
−0.00840153 + 0.999965i \(0.502674\pi\)
\(270\) 0 0
\(271\) −3124.03 −0.700263 −0.350131 0.936701i \(-0.613863\pi\)
−0.350131 + 0.936701i \(0.613863\pi\)
\(272\) −3265.58 −0.727959
\(273\) 0 0
\(274\) −7259.78 −1.60066
\(275\) −1187.77 −0.260456
\(276\) 0 0
\(277\) −3431.12 −0.744246 −0.372123 0.928184i \(-0.621370\pi\)
−0.372123 + 0.928184i \(0.621370\pi\)
\(278\) 1329.92 0.286918
\(279\) 0 0
\(280\) 10823.1 2.31002
\(281\) −1449.47 −0.307716 −0.153858 0.988093i \(-0.549170\pi\)
−0.153858 + 0.988093i \(0.549170\pi\)
\(282\) 0 0
\(283\) −3287.48 −0.690532 −0.345266 0.938505i \(-0.612211\pi\)
−0.345266 + 0.938505i \(0.612211\pi\)
\(284\) −174.860 −0.0365353
\(285\) 0 0
\(286\) 1129.84 0.233598
\(287\) 3736.37 0.768470
\(288\) 0 0
\(289\) −2684.28 −0.546363
\(290\) 7147.48 1.44729
\(291\) 0 0
\(292\) −625.755 −0.125409
\(293\) −2698.79 −0.538106 −0.269053 0.963125i \(-0.586711\pi\)
−0.269053 + 0.963125i \(0.586711\pi\)
\(294\) 0 0
\(295\) 4341.60 0.856874
\(296\) −677.610 −0.133058
\(297\) 0 0
\(298\) −1269.45 −0.246768
\(299\) −6388.23 −1.23559
\(300\) 0 0
\(301\) 9259.20 1.77306
\(302\) −10074.9 −1.91968
\(303\) 0 0
\(304\) −3378.34 −0.637371
\(305\) 10053.6 1.88744
\(306\) 0 0
\(307\) 10156.3 1.88811 0.944055 0.329787i \(-0.106977\pi\)
0.944055 + 0.329787i \(0.106977\pi\)
\(308\) 167.957 0.0310722
\(309\) 0 0
\(310\) −6005.84 −1.10035
\(311\) −5483.97 −0.999895 −0.499948 0.866056i \(-0.666647\pi\)
−0.499948 + 0.866056i \(0.666647\pi\)
\(312\) 0 0
\(313\) −2535.58 −0.457889 −0.228944 0.973439i \(-0.573527\pi\)
−0.228944 + 0.973439i \(0.573527\pi\)
\(314\) −2550.98 −0.458472
\(315\) 0 0
\(316\) −826.636 −0.147158
\(317\) 7331.70 1.29902 0.649510 0.760353i \(-0.274974\pi\)
0.649510 + 0.760353i \(0.274974\pi\)
\(318\) 0 0
\(319\) −1139.78 −0.200049
\(320\) −7633.74 −1.33356
\(321\) 0 0
\(322\) −11657.8 −2.01759
\(323\) 2305.67 0.397186
\(324\) 0 0
\(325\) 7419.66 1.26637
\(326\) −3144.61 −0.534245
\(327\) 0 0
\(328\) −2658.44 −0.447524
\(329\) 4333.65 0.726207
\(330\) 0 0
\(331\) −9699.52 −1.61068 −0.805338 0.592816i \(-0.798016\pi\)
−0.805338 + 0.592816i \(0.798016\pi\)
\(332\) −24.7166 −0.00408584
\(333\) 0 0
\(334\) 975.175 0.159758
\(335\) 8609.42 1.40413
\(336\) 0 0
\(337\) 2893.84 0.467767 0.233883 0.972265i \(-0.424857\pi\)
0.233883 + 0.972265i \(0.424857\pi\)
\(338\) −574.049 −0.0923792
\(339\) 0 0
\(340\) −557.166 −0.0888722
\(341\) 957.729 0.152094
\(342\) 0 0
\(343\) −6907.90 −1.08744
\(344\) −6587.96 −1.03256
\(345\) 0 0
\(346\) −2613.09 −0.406014
\(347\) −3600.31 −0.556987 −0.278494 0.960438i \(-0.589835\pi\)
−0.278494 + 0.960438i \(0.589835\pi\)
\(348\) 0 0
\(349\) 4910.29 0.753129 0.376565 0.926390i \(-0.377105\pi\)
0.376565 + 0.926390i \(0.377105\pi\)
\(350\) 13540.1 2.06785
\(351\) 0 0
\(352\) −250.634 −0.0379512
\(353\) 5905.36 0.890398 0.445199 0.895432i \(-0.353133\pi\)
0.445199 + 0.895432i \(0.353133\pi\)
\(354\) 0 0
\(355\) 4099.93 0.612962
\(356\) 575.247 0.0856406
\(357\) 0 0
\(358\) −9217.53 −1.36079
\(359\) −3567.83 −0.524520 −0.262260 0.964997i \(-0.584468\pi\)
−0.262260 + 0.964997i \(0.584468\pi\)
\(360\) 0 0
\(361\) −4473.72 −0.652240
\(362\) 1806.44 0.262278
\(363\) 0 0
\(364\) −1049.18 −0.151077
\(365\) 14672.1 2.10403
\(366\) 0 0
\(367\) 2879.49 0.409559 0.204779 0.978808i \(-0.434352\pi\)
0.204779 + 0.978808i \(0.434352\pi\)
\(368\) 9036.02 1.27999
\(369\) 0 0
\(370\) −1546.12 −0.217240
\(371\) −8636.07 −1.20852
\(372\) 0 0
\(373\) −766.449 −0.106395 −0.0531974 0.998584i \(-0.516941\pi\)
−0.0531974 + 0.998584i \(0.516941\pi\)
\(374\) 1090.71 0.150800
\(375\) 0 0
\(376\) −3083.41 −0.422912
\(377\) 7119.87 0.972658
\(378\) 0 0
\(379\) −5364.00 −0.726993 −0.363496 0.931596i \(-0.618417\pi\)
−0.363496 + 0.931596i \(0.618417\pi\)
\(380\) −576.404 −0.0778129
\(381\) 0 0
\(382\) 10771.4 1.44270
\(383\) 1522.65 0.203143 0.101571 0.994828i \(-0.467613\pi\)
0.101571 + 0.994828i \(0.467613\pi\)
\(384\) 0 0
\(385\) −3938.08 −0.521307
\(386\) −224.529 −0.0296068
\(387\) 0 0
\(388\) −136.235 −0.0178254
\(389\) −2273.74 −0.296358 −0.148179 0.988961i \(-0.547341\pi\)
−0.148179 + 0.988961i \(0.547341\pi\)
\(390\) 0 0
\(391\) −6166.97 −0.797639
\(392\) 12294.9 1.58415
\(393\) 0 0
\(394\) 10622.8 1.35830
\(395\) 19382.1 2.46891
\(396\) 0 0
\(397\) −10272.7 −1.29867 −0.649337 0.760500i \(-0.724954\pi\)
−0.649337 + 0.760500i \(0.724954\pi\)
\(398\) 11701.9 1.47377
\(399\) 0 0
\(400\) −10495.0 −1.31187
\(401\) 14406.6 1.79409 0.897047 0.441935i \(-0.145708\pi\)
0.897047 + 0.441935i \(0.145708\pi\)
\(402\) 0 0
\(403\) −5982.64 −0.739495
\(404\) 1058.24 0.130321
\(405\) 0 0
\(406\) 12993.0 1.58825
\(407\) 246.553 0.0300275
\(408\) 0 0
\(409\) 5649.95 0.683062 0.341531 0.939871i \(-0.389055\pi\)
0.341531 + 0.939871i \(0.389055\pi\)
\(410\) −6065.83 −0.730658
\(411\) 0 0
\(412\) −909.800 −0.108793
\(413\) 7892.34 0.940331
\(414\) 0 0
\(415\) 579.529 0.0685493
\(416\) 1565.63 0.184523
\(417\) 0 0
\(418\) 1128.37 0.132035
\(419\) −3959.84 −0.461696 −0.230848 0.972990i \(-0.574150\pi\)
−0.230848 + 0.972990i \(0.574150\pi\)
\(420\) 0 0
\(421\) 10821.5 1.25275 0.626375 0.779522i \(-0.284538\pi\)
0.626375 + 0.779522i \(0.284538\pi\)
\(422\) −930.693 −0.107359
\(423\) 0 0
\(424\) 6144.61 0.703793
\(425\) 7162.67 0.817508
\(426\) 0 0
\(427\) 18275.9 2.07127
\(428\) −134.111 −0.0151461
\(429\) 0 0
\(430\) −15031.9 −1.68582
\(431\) −3895.83 −0.435396 −0.217698 0.976016i \(-0.569855\pi\)
−0.217698 + 0.976016i \(0.569855\pi\)
\(432\) 0 0
\(433\) 453.802 0.0503657 0.0251828 0.999683i \(-0.491983\pi\)
0.0251828 + 0.999683i \(0.491983\pi\)
\(434\) −10917.7 −1.20752
\(435\) 0 0
\(436\) −727.567 −0.0799177
\(437\) −6379.90 −0.698380
\(438\) 0 0
\(439\) −3628.86 −0.394525 −0.197262 0.980351i \(-0.563205\pi\)
−0.197262 + 0.980351i \(0.563205\pi\)
\(440\) 2801.96 0.303587
\(441\) 0 0
\(442\) −6813.34 −0.733207
\(443\) 570.512 0.0611870 0.0305935 0.999532i \(-0.490260\pi\)
0.0305935 + 0.999532i \(0.490260\pi\)
\(444\) 0 0
\(445\) −13487.8 −1.43681
\(446\) 12612.1 1.33901
\(447\) 0 0
\(448\) −13876.9 −1.46344
\(449\) −6238.94 −0.655755 −0.327877 0.944720i \(-0.606333\pi\)
−0.327877 + 0.944720i \(0.606333\pi\)
\(450\) 0 0
\(451\) 967.294 0.100994
\(452\) −375.715 −0.0390977
\(453\) 0 0
\(454\) 12500.9 1.29228
\(455\) 24600.0 2.53465
\(456\) 0 0
\(457\) −3469.70 −0.355155 −0.177577 0.984107i \(-0.556826\pi\)
−0.177577 + 0.984107i \(0.556826\pi\)
\(458\) −19103.3 −1.94899
\(459\) 0 0
\(460\) 1541.70 0.156266
\(461\) 8651.26 0.874033 0.437016 0.899454i \(-0.356035\pi\)
0.437016 + 0.899454i \(0.356035\pi\)
\(462\) 0 0
\(463\) −13077.8 −1.31269 −0.656347 0.754459i \(-0.727899\pi\)
−0.656347 + 0.754459i \(0.727899\pi\)
\(464\) −10070.9 −1.00761
\(465\) 0 0
\(466\) −7803.53 −0.775733
\(467\) 16473.1 1.63230 0.816151 0.577839i \(-0.196104\pi\)
0.816151 + 0.577839i \(0.196104\pi\)
\(468\) 0 0
\(469\) 15650.5 1.54088
\(470\) −7035.49 −0.690474
\(471\) 0 0
\(472\) −5615.44 −0.547609
\(473\) 2397.08 0.233019
\(474\) 0 0
\(475\) 7409.99 0.715776
\(476\) −1012.84 −0.0975281
\(477\) 0 0
\(478\) 705.332 0.0674919
\(479\) 13102.4 1.24982 0.624910 0.780697i \(-0.285136\pi\)
0.624910 + 0.780697i \(0.285136\pi\)
\(480\) 0 0
\(481\) −1540.14 −0.145997
\(482\) 6373.21 0.602266
\(483\) 0 0
\(484\) −900.826 −0.0846005
\(485\) 3194.29 0.299062
\(486\) 0 0
\(487\) 2802.96 0.260809 0.130405 0.991461i \(-0.458372\pi\)
0.130405 + 0.991461i \(0.458372\pi\)
\(488\) −13003.4 −1.20622
\(489\) 0 0
\(490\) 28053.5 2.58638
\(491\) −19817.1 −1.82145 −0.910725 0.413013i \(-0.864476\pi\)
−0.910725 + 0.413013i \(0.864476\pi\)
\(492\) 0 0
\(493\) 6873.26 0.627903
\(494\) −7048.59 −0.641966
\(495\) 0 0
\(496\) 8462.32 0.766067
\(497\) 7453.01 0.672663
\(498\) 0 0
\(499\) 15423.6 1.38368 0.691839 0.722052i \(-0.256801\pi\)
0.691839 + 0.722052i \(0.256801\pi\)
\(500\) −315.370 −0.0282076
\(501\) 0 0
\(502\) −16274.1 −1.44691
\(503\) 12841.3 1.13830 0.569150 0.822234i \(-0.307272\pi\)
0.569150 + 0.822234i \(0.307272\pi\)
\(504\) 0 0
\(505\) −24812.6 −2.18642
\(506\) −3018.05 −0.265155
\(507\) 0 0
\(508\) −164.209 −0.0143417
\(509\) −12494.7 −1.08805 −0.544026 0.839068i \(-0.683101\pi\)
−0.544026 + 0.839068i \(0.683101\pi\)
\(510\) 0 0
\(511\) 26671.4 2.30895
\(512\) 9691.77 0.836562
\(513\) 0 0
\(514\) 10101.1 0.866814
\(515\) 21332.0 1.82525
\(516\) 0 0
\(517\) 1121.92 0.0954393
\(518\) −2810.59 −0.238398
\(519\) 0 0
\(520\) −17503.0 −1.47607
\(521\) 3466.21 0.291473 0.145737 0.989323i \(-0.453445\pi\)
0.145737 + 0.989323i \(0.453445\pi\)
\(522\) 0 0
\(523\) 9874.89 0.825619 0.412810 0.910817i \(-0.364548\pi\)
0.412810 + 0.910817i \(0.364548\pi\)
\(524\) −1898.90 −0.158309
\(525\) 0 0
\(526\) 12268.7 1.01700
\(527\) −5775.42 −0.477384
\(528\) 0 0
\(529\) 4897.29 0.402506
\(530\) 14020.3 1.14906
\(531\) 0 0
\(532\) −1047.81 −0.0853916
\(533\) −6042.39 −0.491041
\(534\) 0 0
\(535\) 3144.50 0.254109
\(536\) −11135.4 −0.897346
\(537\) 0 0
\(538\) 218.783 0.0175323
\(539\) −4473.58 −0.357497
\(540\) 0 0
\(541\) 10796.3 0.857983 0.428992 0.903308i \(-0.358869\pi\)
0.428992 + 0.903308i \(0.358869\pi\)
\(542\) 9219.57 0.730654
\(543\) 0 0
\(544\) 1511.41 0.119120
\(545\) 17059.2 1.34080
\(546\) 0 0
\(547\) 8272.86 0.646658 0.323329 0.946287i \(-0.395198\pi\)
0.323329 + 0.946287i \(0.395198\pi\)
\(548\) 1745.27 0.136048
\(549\) 0 0
\(550\) 3505.34 0.271760
\(551\) 7110.59 0.549766
\(552\) 0 0
\(553\) 35233.5 2.70937
\(554\) 10125.9 0.776546
\(555\) 0 0
\(556\) −319.716 −0.0243867
\(557\) 8859.27 0.673931 0.336965 0.941517i \(-0.390599\pi\)
0.336965 + 0.941517i \(0.390599\pi\)
\(558\) 0 0
\(559\) −14973.8 −1.13296
\(560\) −34796.2 −2.62573
\(561\) 0 0
\(562\) 4277.65 0.321071
\(563\) 17887.7 1.33903 0.669516 0.742797i \(-0.266501\pi\)
0.669516 + 0.742797i \(0.266501\pi\)
\(564\) 0 0
\(565\) 8809.38 0.655953
\(566\) 9701.95 0.720501
\(567\) 0 0
\(568\) −5302.85 −0.391730
\(569\) −5355.10 −0.394547 −0.197274 0.980348i \(-0.563209\pi\)
−0.197274 + 0.980348i \(0.563209\pi\)
\(570\) 0 0
\(571\) 16668.1 1.22161 0.610805 0.791781i \(-0.290846\pi\)
0.610805 + 0.791781i \(0.290846\pi\)
\(572\) −271.618 −0.0198547
\(573\) 0 0
\(574\) −11026.7 −0.801821
\(575\) −19819.5 −1.43744
\(576\) 0 0
\(577\) 22341.9 1.61197 0.805985 0.591937i \(-0.201636\pi\)
0.805985 + 0.591937i \(0.201636\pi\)
\(578\) 7921.81 0.570076
\(579\) 0 0
\(580\) −1718.27 −0.123013
\(581\) 1053.49 0.0752257
\(582\) 0 0
\(583\) −2235.76 −0.158826
\(584\) −18976.9 −1.34464
\(585\) 0 0
\(586\) 7964.62 0.561460
\(587\) −13446.6 −0.945487 −0.472744 0.881200i \(-0.656736\pi\)
−0.472744 + 0.881200i \(0.656736\pi\)
\(588\) 0 0
\(589\) −5974.84 −0.417978
\(590\) −12812.9 −0.894063
\(591\) 0 0
\(592\) 2178.50 0.151243
\(593\) −22921.3 −1.58730 −0.793648 0.608377i \(-0.791821\pi\)
−0.793648 + 0.608377i \(0.791821\pi\)
\(594\) 0 0
\(595\) 23748.0 1.63625
\(596\) 305.178 0.0209741
\(597\) 0 0
\(598\) 18852.8 1.28921
\(599\) −25166.7 −1.71667 −0.858334 0.513091i \(-0.828500\pi\)
−0.858334 + 0.513091i \(0.828500\pi\)
\(600\) 0 0
\(601\) −1390.40 −0.0943688 −0.0471844 0.998886i \(-0.515025\pi\)
−0.0471844 + 0.998886i \(0.515025\pi\)
\(602\) −27325.6 −1.85001
\(603\) 0 0
\(604\) 2422.03 0.163164
\(605\) 21121.6 1.41936
\(606\) 0 0
\(607\) 15650.3 1.04650 0.523249 0.852180i \(-0.324720\pi\)
0.523249 + 0.852180i \(0.324720\pi\)
\(608\) 1563.59 0.104296
\(609\) 0 0
\(610\) −29670.0 −1.96935
\(611\) −7008.31 −0.464036
\(612\) 0 0
\(613\) −20202.6 −1.33112 −0.665559 0.746345i \(-0.731807\pi\)
−0.665559 + 0.746345i \(0.731807\pi\)
\(614\) −29973.1 −1.97006
\(615\) 0 0
\(616\) 5093.52 0.333156
\(617\) 3474.03 0.226676 0.113338 0.993556i \(-0.463846\pi\)
0.113338 + 0.993556i \(0.463846\pi\)
\(618\) 0 0
\(619\) 17527.4 1.13810 0.569051 0.822302i \(-0.307311\pi\)
0.569051 + 0.822302i \(0.307311\pi\)
\(620\) 1443.82 0.0935246
\(621\) 0 0
\(622\) 16184.2 1.04329
\(623\) −24518.6 −1.57676
\(624\) 0 0
\(625\) −11570.7 −0.740527
\(626\) 7482.95 0.477761
\(627\) 0 0
\(628\) 613.263 0.0389679
\(629\) −1486.80 −0.0942489
\(630\) 0 0
\(631\) 254.193 0.0160368 0.00801842 0.999968i \(-0.497448\pi\)
0.00801842 + 0.999968i \(0.497448\pi\)
\(632\) −25068.8 −1.57782
\(633\) 0 0
\(634\) −21637.2 −1.35540
\(635\) 3850.19 0.240615
\(636\) 0 0
\(637\) 27945.1 1.73819
\(638\) 3363.70 0.208731
\(639\) 0 0
\(640\) 26789.1 1.65458
\(641\) 16952.1 1.04457 0.522284 0.852772i \(-0.325080\pi\)
0.522284 + 0.852772i \(0.325080\pi\)
\(642\) 0 0
\(643\) 1479.72 0.0907537 0.0453769 0.998970i \(-0.485551\pi\)
0.0453769 + 0.998970i \(0.485551\pi\)
\(644\) 2802.57 0.171486
\(645\) 0 0
\(646\) −6804.45 −0.414424
\(647\) −24399.8 −1.48262 −0.741309 0.671164i \(-0.765795\pi\)
−0.741309 + 0.671164i \(0.765795\pi\)
\(648\) 0 0
\(649\) 2043.22 0.123580
\(650\) −21896.8 −1.32133
\(651\) 0 0
\(652\) 755.974 0.0454083
\(653\) 1626.88 0.0974958 0.0487479 0.998811i \(-0.484477\pi\)
0.0487479 + 0.998811i \(0.484477\pi\)
\(654\) 0 0
\(655\) 44523.4 2.65599
\(656\) 8546.84 0.508686
\(657\) 0 0
\(658\) −12789.4 −0.757724
\(659\) 24392.7 1.44189 0.720946 0.692992i \(-0.243708\pi\)
0.720946 + 0.692992i \(0.243708\pi\)
\(660\) 0 0
\(661\) 13799.8 0.812029 0.406015 0.913867i \(-0.366918\pi\)
0.406015 + 0.913867i \(0.366918\pi\)
\(662\) 28625.0 1.68058
\(663\) 0 0
\(664\) −749.563 −0.0438083
\(665\) 24567.9 1.43264
\(666\) 0 0
\(667\) −19018.6 −1.10406
\(668\) −234.435 −0.0135787
\(669\) 0 0
\(670\) −25408.0 −1.46507
\(671\) 4731.37 0.272209
\(672\) 0 0
\(673\) −11475.4 −0.657271 −0.328635 0.944457i \(-0.606589\pi\)
−0.328635 + 0.944457i \(0.606589\pi\)
\(674\) −8540.24 −0.488068
\(675\) 0 0
\(676\) 138.003 0.00785179
\(677\) −27237.9 −1.54629 −0.773145 0.634229i \(-0.781317\pi\)
−0.773145 + 0.634229i \(0.781317\pi\)
\(678\) 0 0
\(679\) 5806.70 0.328190
\(680\) −16896.8 −0.952885
\(681\) 0 0
\(682\) −2826.43 −0.158694
\(683\) 28388.1 1.59039 0.795197 0.606351i \(-0.207367\pi\)
0.795197 + 0.606351i \(0.207367\pi\)
\(684\) 0 0
\(685\) −40921.3 −2.28251
\(686\) 20386.5 1.13463
\(687\) 0 0
\(688\) 21180.2 1.17367
\(689\) 13966.1 0.772230
\(690\) 0 0
\(691\) −16140.1 −0.888565 −0.444283 0.895887i \(-0.646541\pi\)
−0.444283 + 0.895887i \(0.646541\pi\)
\(692\) 628.194 0.0345092
\(693\) 0 0
\(694\) 10625.2 0.581161
\(695\) 7496.36 0.409141
\(696\) 0 0
\(697\) −5833.11 −0.316994
\(698\) −14491.2 −0.785815
\(699\) 0 0
\(700\) −3255.07 −0.175757
\(701\) 16564.9 0.892506 0.446253 0.894907i \(-0.352758\pi\)
0.446253 + 0.894907i \(0.352758\pi\)
\(702\) 0 0
\(703\) −1538.14 −0.0825205
\(704\) −3592.54 −0.192328
\(705\) 0 0
\(706\) −17427.8 −0.929041
\(707\) −45105.3 −2.39937
\(708\) 0 0
\(709\) −31152.4 −1.65014 −0.825072 0.565028i \(-0.808865\pi\)
−0.825072 + 0.565028i \(0.808865\pi\)
\(710\) −12099.6 −0.639565
\(711\) 0 0
\(712\) 17445.1 0.918236
\(713\) 15980.9 0.839395
\(714\) 0 0
\(715\) 6368.60 0.333108
\(716\) 2215.92 0.115660
\(717\) 0 0
\(718\) 10529.3 0.547284
\(719\) −21689.5 −1.12501 −0.562505 0.826794i \(-0.690162\pi\)
−0.562505 + 0.826794i \(0.690162\pi\)
\(720\) 0 0
\(721\) 38778.2 2.00302
\(722\) 13202.8 0.680548
\(723\) 0 0
\(724\) −434.274 −0.0222924
\(725\) 22089.4 1.13156
\(726\) 0 0
\(727\) −37929.0 −1.93495 −0.967475 0.252968i \(-0.918593\pi\)
−0.967475 + 0.252968i \(0.918593\pi\)
\(728\) −31817.7 −1.61984
\(729\) 0 0
\(730\) −43299.9 −2.19534
\(731\) −14455.2 −0.731388
\(732\) 0 0
\(733\) 30699.1 1.54693 0.773464 0.633840i \(-0.218522\pi\)
0.773464 + 0.633840i \(0.218522\pi\)
\(734\) −8497.89 −0.427334
\(735\) 0 0
\(736\) −4182.13 −0.209450
\(737\) 4051.71 0.202506
\(738\) 0 0
\(739\) 20883.5 1.03953 0.519764 0.854310i \(-0.326020\pi\)
0.519764 + 0.854310i \(0.326020\pi\)
\(740\) 371.691 0.0184644
\(741\) 0 0
\(742\) 25486.6 1.26097
\(743\) 97.0268 0.00479080 0.00239540 0.999997i \(-0.499238\pi\)
0.00239540 + 0.999997i \(0.499238\pi\)
\(744\) 0 0
\(745\) −7155.49 −0.351889
\(746\) 2261.93 0.111012
\(747\) 0 0
\(748\) −262.210 −0.0128173
\(749\) 5716.19 0.278859
\(750\) 0 0
\(751\) 13681.8 0.664787 0.332394 0.943141i \(-0.392144\pi\)
0.332394 + 0.943141i \(0.392144\pi\)
\(752\) 9913.11 0.480710
\(753\) 0 0
\(754\) −21012.0 −1.01487
\(755\) −56789.2 −2.73744
\(756\) 0 0
\(757\) −26818.7 −1.28764 −0.643819 0.765178i \(-0.722651\pi\)
−0.643819 + 0.765178i \(0.722651\pi\)
\(758\) 15830.1 0.758545
\(759\) 0 0
\(760\) −17480.2 −0.834307
\(761\) −6888.48 −0.328130 −0.164065 0.986450i \(-0.552461\pi\)
−0.164065 + 0.986450i \(0.552461\pi\)
\(762\) 0 0
\(763\) 31010.9 1.47139
\(764\) −2589.47 −0.122623
\(765\) 0 0
\(766\) −4493.61 −0.211959
\(767\) −12763.4 −0.600858
\(768\) 0 0
\(769\) −12475.7 −0.585028 −0.292514 0.956261i \(-0.594492\pi\)
−0.292514 + 0.956261i \(0.594492\pi\)
\(770\) 11622.0 0.543932
\(771\) 0 0
\(772\) 53.9773 0.00251643
\(773\) −32256.3 −1.50088 −0.750439 0.660940i \(-0.770158\pi\)
−0.750439 + 0.660940i \(0.770158\pi\)
\(774\) 0 0
\(775\) −18561.1 −0.860303
\(776\) −4131.50 −0.191124
\(777\) 0 0
\(778\) 6710.22 0.309220
\(779\) −6034.51 −0.277547
\(780\) 0 0
\(781\) 1929.48 0.0884024
\(782\) 18199.8 0.832257
\(783\) 0 0
\(784\) −39527.8 −1.80065
\(785\) −14379.1 −0.653775
\(786\) 0 0
\(787\) 37930.8 1.71803 0.859014 0.511952i \(-0.171078\pi\)
0.859014 + 0.511952i \(0.171078\pi\)
\(788\) −2553.76 −0.115449
\(789\) 0 0
\(790\) −57200.1 −2.57606
\(791\) 16014.0 0.719840
\(792\) 0 0
\(793\) −29555.4 −1.32351
\(794\) 30316.7 1.35504
\(795\) 0 0
\(796\) −2813.16 −0.125264
\(797\) 5478.85 0.243502 0.121751 0.992561i \(-0.461149\pi\)
0.121751 + 0.992561i \(0.461149\pi\)
\(798\) 0 0
\(799\) −6765.57 −0.299560
\(800\) 4857.37 0.214668
\(801\) 0 0
\(802\) −42516.5 −1.87196
\(803\) 6904.87 0.303446
\(804\) 0 0
\(805\) −65711.7 −2.87706
\(806\) 17655.9 0.771590
\(807\) 0 0
\(808\) 32092.6 1.39729
\(809\) 15063.1 0.654623 0.327312 0.944916i \(-0.393857\pi\)
0.327312 + 0.944916i \(0.393857\pi\)
\(810\) 0 0
\(811\) 5485.13 0.237496 0.118748 0.992924i \(-0.462112\pi\)
0.118748 + 0.992924i \(0.462112\pi\)
\(812\) −3123.55 −0.134994
\(813\) 0 0
\(814\) −727.623 −0.0313307
\(815\) −17725.3 −0.761827
\(816\) 0 0
\(817\) −14954.3 −0.640373
\(818\) −16674.0 −0.712707
\(819\) 0 0
\(820\) 1458.24 0.0621024
\(821\) −1055.15 −0.0448540 −0.0224270 0.999748i \(-0.507139\pi\)
−0.0224270 + 0.999748i \(0.507139\pi\)
\(822\) 0 0
\(823\) −17419.3 −0.737785 −0.368893 0.929472i \(-0.620263\pi\)
−0.368893 + 0.929472i \(0.620263\pi\)
\(824\) −27590.9 −1.16647
\(825\) 0 0
\(826\) −23291.7 −0.981141
\(827\) 1379.47 0.0580033 0.0290016 0.999579i \(-0.490767\pi\)
0.0290016 + 0.999579i \(0.490767\pi\)
\(828\) 0 0
\(829\) −32409.1 −1.35780 −0.678900 0.734231i \(-0.737543\pi\)
−0.678900 + 0.734231i \(0.737543\pi\)
\(830\) −1710.29 −0.0715243
\(831\) 0 0
\(832\) 22441.5 0.935119
\(833\) 26977.2 1.12209
\(834\) 0 0
\(835\) 5496.78 0.227813
\(836\) −271.263 −0.0112223
\(837\) 0 0
\(838\) 11686.2 0.481734
\(839\) 19286.0 0.793594 0.396797 0.917906i \(-0.370122\pi\)
0.396797 + 0.917906i \(0.370122\pi\)
\(840\) 0 0
\(841\) −3192.17 −0.130886
\(842\) −31936.2 −1.30712
\(843\) 0 0
\(844\) 223.741 0.00912499
\(845\) −3235.75 −0.131732
\(846\) 0 0
\(847\) 38395.7 1.55761
\(848\) −19754.8 −0.799979
\(849\) 0 0
\(850\) −21138.4 −0.852988
\(851\) 4114.04 0.165720
\(852\) 0 0
\(853\) −9711.21 −0.389807 −0.194904 0.980822i \(-0.562439\pi\)
−0.194904 + 0.980822i \(0.562439\pi\)
\(854\) −53935.4 −2.16116
\(855\) 0 0
\(856\) −4067.10 −0.162395
\(857\) −25747.9 −1.02629 −0.513146 0.858301i \(-0.671520\pi\)
−0.513146 + 0.858301i \(0.671520\pi\)
\(858\) 0 0
\(859\) −1199.86 −0.0476584 −0.0238292 0.999716i \(-0.507586\pi\)
−0.0238292 + 0.999716i \(0.507586\pi\)
\(860\) 3613.71 0.143287
\(861\) 0 0
\(862\) 11497.3 0.454292
\(863\) 1332.02 0.0525407 0.0262704 0.999655i \(-0.491637\pi\)
0.0262704 + 0.999655i \(0.491637\pi\)
\(864\) 0 0
\(865\) −14729.2 −0.578970
\(866\) −1339.25 −0.0525515
\(867\) 0 0
\(868\) 2624.64 0.102634
\(869\) 9121.48 0.356070
\(870\) 0 0
\(871\) −25309.8 −0.984604
\(872\) −22064.4 −0.856876
\(873\) 0 0
\(874\) 18828.2 0.728690
\(875\) 13442.0 0.519339
\(876\) 0 0
\(877\) 20443.6 0.787152 0.393576 0.919292i \(-0.371238\pi\)
0.393576 + 0.919292i \(0.371238\pi\)
\(878\) 10709.4 0.411647
\(879\) 0 0
\(880\) −9008.25 −0.345078
\(881\) −30891.8 −1.18135 −0.590676 0.806909i \(-0.701139\pi\)
−0.590676 + 0.806909i \(0.701139\pi\)
\(882\) 0 0
\(883\) 35760.8 1.36291 0.681454 0.731861i \(-0.261348\pi\)
0.681454 + 0.731861i \(0.261348\pi\)
\(884\) 1637.95 0.0623191
\(885\) 0 0
\(886\) −1683.68 −0.0638425
\(887\) −42438.8 −1.60649 −0.803245 0.595649i \(-0.796895\pi\)
−0.803245 + 0.595649i \(0.796895\pi\)
\(888\) 0 0
\(889\) 6999.03 0.264050
\(890\) 39804.9 1.49917
\(891\) 0 0
\(892\) −3031.98 −0.113810
\(893\) −6999.17 −0.262283
\(894\) 0 0
\(895\) −51956.5 −1.94046
\(896\) 48698.3 1.81573
\(897\) 0 0
\(898\) 18412.2 0.684215
\(899\) −17811.1 −0.660773
\(900\) 0 0
\(901\) 13482.4 0.498516
\(902\) −2854.66 −0.105377
\(903\) 0 0
\(904\) −11394.1 −0.419205
\(905\) 10182.4 0.374005
\(906\) 0 0
\(907\) −3380.87 −0.123770 −0.0618852 0.998083i \(-0.519711\pi\)
−0.0618852 + 0.998083i \(0.519711\pi\)
\(908\) −3005.25 −0.109838
\(909\) 0 0
\(910\) −72599.1 −2.64466
\(911\) 17353.3 0.631111 0.315555 0.948907i \(-0.397809\pi\)
0.315555 + 0.948907i \(0.397809\pi\)
\(912\) 0 0
\(913\) 272.734 0.00988629
\(914\) 10239.7 0.370568
\(915\) 0 0
\(916\) 4592.49 0.165655
\(917\) 80936.3 2.91467
\(918\) 0 0
\(919\) −3785.66 −0.135884 −0.0679420 0.997689i \(-0.521643\pi\)
−0.0679420 + 0.997689i \(0.521643\pi\)
\(920\) 46754.2 1.67548
\(921\) 0 0
\(922\) −25531.4 −0.911966
\(923\) −12052.9 −0.429822
\(924\) 0 0
\(925\) −4778.29 −0.169848
\(926\) 38595.0 1.36966
\(927\) 0 0
\(928\) 4661.11 0.164880
\(929\) −3561.15 −0.125767 −0.0628835 0.998021i \(-0.520030\pi\)
−0.0628835 + 0.998021i \(0.520030\pi\)
\(930\) 0 0
\(931\) 27908.7 0.982460
\(932\) 1875.99 0.0659336
\(933\) 0 0
\(934\) −48615.1 −1.70314
\(935\) 6148.02 0.215039
\(936\) 0 0
\(937\) 7357.98 0.256536 0.128268 0.991740i \(-0.459058\pi\)
0.128268 + 0.991740i \(0.459058\pi\)
\(938\) −46187.6 −1.60776
\(939\) 0 0
\(940\) 1691.35 0.0586870
\(941\) 8221.73 0.284826 0.142413 0.989807i \(-0.454514\pi\)
0.142413 + 0.989807i \(0.454514\pi\)
\(942\) 0 0
\(943\) 16140.5 0.557377
\(944\) 18053.5 0.622449
\(945\) 0 0
\(946\) −7074.21 −0.243132
\(947\) −22232.7 −0.762899 −0.381449 0.924390i \(-0.624575\pi\)
−0.381449 + 0.924390i \(0.624575\pi\)
\(948\) 0 0
\(949\) −43132.6 −1.47539
\(950\) −21868.2 −0.746841
\(951\) 0 0
\(952\) −30715.6 −1.04569
\(953\) 5855.90 0.199047 0.0995233 0.995035i \(-0.468268\pi\)
0.0995233 + 0.995035i \(0.468268\pi\)
\(954\) 0 0
\(955\) 60715.1 2.05727
\(956\) −169.564 −0.00573649
\(957\) 0 0
\(958\) −38667.5 −1.30406
\(959\) −74388.3 −2.50482
\(960\) 0 0
\(961\) −14824.8 −0.497625
\(962\) 4545.24 0.152333
\(963\) 0 0
\(964\) −1532.14 −0.0511897
\(965\) −1265.60 −0.0422189
\(966\) 0 0
\(967\) 26083.7 0.867421 0.433710 0.901052i \(-0.357204\pi\)
0.433710 + 0.901052i \(0.357204\pi\)
\(968\) −27318.7 −0.907083
\(969\) 0 0
\(970\) −9426.92 −0.312041
\(971\) 34276.3 1.13283 0.566415 0.824120i \(-0.308330\pi\)
0.566415 + 0.824120i \(0.308330\pi\)
\(972\) 0 0
\(973\) 13627.2 0.448990
\(974\) −8272.04 −0.272129
\(975\) 0 0
\(976\) 41805.5 1.37107
\(977\) −11390.8 −0.373002 −0.186501 0.982455i \(-0.559715\pi\)
−0.186501 + 0.982455i \(0.559715\pi\)
\(978\) 0 0
\(979\) −6347.54 −0.207220
\(980\) −6744.13 −0.219830
\(981\) 0 0
\(982\) 58483.8 1.90050
\(983\) −49563.1 −1.60815 −0.804077 0.594525i \(-0.797340\pi\)
−0.804077 + 0.594525i \(0.797340\pi\)
\(984\) 0 0
\(985\) 59877.9 1.93692
\(986\) −20284.2 −0.655154
\(987\) 0 0
\(988\) 1694.50 0.0545640
\(989\) 39998.2 1.28601
\(990\) 0 0
\(991\) 31276.5 1.00255 0.501277 0.865287i \(-0.332864\pi\)
0.501277 + 0.865287i \(0.332864\pi\)
\(992\) −3916.61 −0.125355
\(993\) 0 0
\(994\) −21995.2 −0.701856
\(995\) 65960.1 2.10158
\(996\) 0 0
\(997\) 22856.0 0.726035 0.363018 0.931782i \(-0.381747\pi\)
0.363018 + 0.931782i \(0.381747\pi\)
\(998\) −45517.9 −1.44373
\(999\) 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.1.17 yes 59
3.2 odd 2 2151.4.a.g.1.43 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.43 59 3.2 odd 2
2151.4.a.h.1.17 yes 59 1.1 even 1 trivial