Properties

Label 2151.4.a.h.1.1
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 1.1
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.26507 q^{2} +19.7210 q^{4} +20.1774 q^{5} -13.2314 q^{7} -61.7120 q^{8} +O(q^{10})\) \(q-5.26507 q^{2} +19.7210 q^{4} +20.1774 q^{5} -13.2314 q^{7} -61.7120 q^{8} -106.236 q^{10} -68.0955 q^{11} +33.3968 q^{13} +69.6642 q^{14} +167.150 q^{16} +135.241 q^{17} -37.9908 q^{19} +397.920 q^{20} +358.528 q^{22} +177.852 q^{23} +282.129 q^{25} -175.837 q^{26} -260.936 q^{28} -141.413 q^{29} +105.071 q^{31} -386.362 q^{32} -712.054 q^{34} -266.975 q^{35} +271.247 q^{37} +200.024 q^{38} -1245.19 q^{40} +460.303 q^{41} -187.115 q^{43} -1342.91 q^{44} -936.406 q^{46} +150.225 q^{47} -167.931 q^{49} -1485.43 q^{50} +658.618 q^{52} +92.8507 q^{53} -1373.99 q^{55} +816.534 q^{56} +744.551 q^{58} -171.792 q^{59} -835.237 q^{61} -553.207 q^{62} +697.024 q^{64} +673.862 q^{65} -311.402 q^{67} +2667.09 q^{68} +1405.64 q^{70} +525.740 q^{71} -90.5209 q^{73} -1428.14 q^{74} -749.217 q^{76} +900.996 q^{77} -333.645 q^{79} +3372.66 q^{80} -2423.53 q^{82} +734.292 q^{83} +2728.82 q^{85} +985.175 q^{86} +4202.31 q^{88} +741.275 q^{89} -441.885 q^{91} +3507.43 q^{92} -790.945 q^{94} -766.557 q^{95} -597.767 q^{97} +884.168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.26507 −1.86148 −0.930742 0.365675i \(-0.880838\pi\)
−0.930742 + 0.365675i \(0.880838\pi\)
\(3\) 0 0
\(4\) 19.7210 2.46513
\(5\) 20.1774 1.80473 0.902363 0.430977i \(-0.141831\pi\)
0.902363 + 0.430977i \(0.141831\pi\)
\(6\) 0 0
\(7\) −13.2314 −0.714427 −0.357213 0.934023i \(-0.616273\pi\)
−0.357213 + 0.934023i \(0.616273\pi\)
\(8\) −61.7120 −2.72731
\(9\) 0 0
\(10\) −106.236 −3.35947
\(11\) −68.0955 −1.86651 −0.933253 0.359221i \(-0.883042\pi\)
−0.933253 + 0.359221i \(0.883042\pi\)
\(12\) 0 0
\(13\) 33.3968 0.712508 0.356254 0.934389i \(-0.384054\pi\)
0.356254 + 0.934389i \(0.384054\pi\)
\(14\) 69.6642 1.32989
\(15\) 0 0
\(16\) 167.150 2.61172
\(17\) 135.241 1.92946 0.964729 0.263246i \(-0.0847932\pi\)
0.964729 + 0.263246i \(0.0847932\pi\)
\(18\) 0 0
\(19\) −37.9908 −0.458720 −0.229360 0.973342i \(-0.573663\pi\)
−0.229360 + 0.973342i \(0.573663\pi\)
\(20\) 397.920 4.44888
\(21\) 0 0
\(22\) 358.528 3.47447
\(23\) 177.852 1.61238 0.806191 0.591655i \(-0.201525\pi\)
0.806191 + 0.591655i \(0.201525\pi\)
\(24\) 0 0
\(25\) 282.129 2.25703
\(26\) −175.837 −1.32632
\(27\) 0 0
\(28\) −260.936 −1.76115
\(29\) −141.413 −0.905510 −0.452755 0.891635i \(-0.649559\pi\)
−0.452755 + 0.891635i \(0.649559\pi\)
\(30\) 0 0
\(31\) 105.071 0.608752 0.304376 0.952552i \(-0.401552\pi\)
0.304376 + 0.952552i \(0.401552\pi\)
\(32\) −386.362 −2.13437
\(33\) 0 0
\(34\) −712.054 −3.59166
\(35\) −266.975 −1.28934
\(36\) 0 0
\(37\) 271.247 1.20521 0.602604 0.798040i \(-0.294130\pi\)
0.602604 + 0.798040i \(0.294130\pi\)
\(38\) 200.024 0.853901
\(39\) 0 0
\(40\) −1245.19 −4.92205
\(41\) 460.303 1.75335 0.876673 0.481086i \(-0.159758\pi\)
0.876673 + 0.481086i \(0.159758\pi\)
\(42\) 0 0
\(43\) −187.115 −0.663600 −0.331800 0.943350i \(-0.607656\pi\)
−0.331800 + 0.943350i \(0.607656\pi\)
\(44\) −1342.91 −4.60117
\(45\) 0 0
\(46\) −936.406 −3.00143
\(47\) 150.225 0.466224 0.233112 0.972450i \(-0.425109\pi\)
0.233112 + 0.972450i \(0.425109\pi\)
\(48\) 0 0
\(49\) −167.931 −0.489594
\(50\) −1485.43 −4.20144
\(51\) 0 0
\(52\) 658.618 1.75642
\(53\) 92.8507 0.240642 0.120321 0.992735i \(-0.461608\pi\)
0.120321 + 0.992735i \(0.461608\pi\)
\(54\) 0 0
\(55\) −1373.99 −3.36853
\(56\) 816.534 1.94846
\(57\) 0 0
\(58\) 744.551 1.68559
\(59\) −171.792 −0.379075 −0.189537 0.981874i \(-0.560699\pi\)
−0.189537 + 0.981874i \(0.560699\pi\)
\(60\) 0 0
\(61\) −835.237 −1.75313 −0.876567 0.481281i \(-0.840172\pi\)
−0.876567 + 0.481281i \(0.840172\pi\)
\(62\) −553.207 −1.13318
\(63\) 0 0
\(64\) 697.024 1.36137
\(65\) 673.862 1.28588
\(66\) 0 0
\(67\) −311.402 −0.567819 −0.283909 0.958851i \(-0.591631\pi\)
−0.283909 + 0.958851i \(0.591631\pi\)
\(68\) 2667.09 4.75636
\(69\) 0 0
\(70\) 1405.64 2.40010
\(71\) 525.740 0.878786 0.439393 0.898295i \(-0.355193\pi\)
0.439393 + 0.898295i \(0.355193\pi\)
\(72\) 0 0
\(73\) −90.5209 −0.145132 −0.0725662 0.997364i \(-0.523119\pi\)
−0.0725662 + 0.997364i \(0.523119\pi\)
\(74\) −1428.14 −2.24348
\(75\) 0 0
\(76\) −749.217 −1.13080
\(77\) 900.996 1.33348
\(78\) 0 0
\(79\) −333.645 −0.475164 −0.237582 0.971367i \(-0.576355\pi\)
−0.237582 + 0.971367i \(0.576355\pi\)
\(80\) 3372.66 4.71344
\(81\) 0 0
\(82\) −2423.53 −3.26383
\(83\) 734.292 0.971072 0.485536 0.874217i \(-0.338624\pi\)
0.485536 + 0.874217i \(0.338624\pi\)
\(84\) 0 0
\(85\) 2728.82 3.48214
\(86\) 985.175 1.23528
\(87\) 0 0
\(88\) 4202.31 5.09054
\(89\) 741.275 0.882865 0.441432 0.897295i \(-0.354471\pi\)
0.441432 + 0.897295i \(0.354471\pi\)
\(90\) 0 0
\(91\) −441.885 −0.509035
\(92\) 3507.43 3.97473
\(93\) 0 0
\(94\) −790.945 −0.867869
\(95\) −766.557 −0.827864
\(96\) 0 0
\(97\) −597.767 −0.625712 −0.312856 0.949801i \(-0.601286\pi\)
−0.312856 + 0.949801i \(0.601286\pi\)
\(98\) 884.168 0.911372
\(99\) 0 0
\(100\) 5563.87 5.56387
\(101\) 333.618 0.328675 0.164338 0.986404i \(-0.447451\pi\)
0.164338 + 0.986404i \(0.447451\pi\)
\(102\) 0 0
\(103\) 580.062 0.554905 0.277453 0.960739i \(-0.410510\pi\)
0.277453 + 0.960739i \(0.410510\pi\)
\(104\) −2060.98 −1.94323
\(105\) 0 0
\(106\) −488.866 −0.447951
\(107\) −1481.03 −1.33810 −0.669050 0.743217i \(-0.733299\pi\)
−0.669050 + 0.743217i \(0.733299\pi\)
\(108\) 0 0
\(109\) −1885.54 −1.65690 −0.828451 0.560061i \(-0.810778\pi\)
−0.828451 + 0.560061i \(0.810778\pi\)
\(110\) 7234.17 6.27047
\(111\) 0 0
\(112\) −2211.63 −1.86588
\(113\) −1100.64 −0.916276 −0.458138 0.888881i \(-0.651483\pi\)
−0.458138 + 0.888881i \(0.651483\pi\)
\(114\) 0 0
\(115\) 3588.61 2.90991
\(116\) −2788.81 −2.23220
\(117\) 0 0
\(118\) 904.498 0.705642
\(119\) −1789.42 −1.37846
\(120\) 0 0
\(121\) 3305.99 2.48384
\(122\) 4397.58 3.26343
\(123\) 0 0
\(124\) 2072.11 1.50065
\(125\) 3170.47 2.26860
\(126\) 0 0
\(127\) 608.505 0.425166 0.212583 0.977143i \(-0.431812\pi\)
0.212583 + 0.977143i \(0.431812\pi\)
\(128\) −578.986 −0.399809
\(129\) 0 0
\(130\) −3547.93 −2.39365
\(131\) −741.290 −0.494403 −0.247201 0.968964i \(-0.579511\pi\)
−0.247201 + 0.968964i \(0.579511\pi\)
\(132\) 0 0
\(133\) 502.670 0.327722
\(134\) 1639.56 1.05699
\(135\) 0 0
\(136\) −8345.99 −5.26223
\(137\) 46.8439 0.0292127 0.0146064 0.999893i \(-0.495350\pi\)
0.0146064 + 0.999893i \(0.495350\pi\)
\(138\) 0 0
\(139\) −1210.76 −0.738815 −0.369408 0.929267i \(-0.620439\pi\)
−0.369408 + 0.929267i \(0.620439\pi\)
\(140\) −5265.02 −3.17840
\(141\) 0 0
\(142\) −2768.06 −1.63585
\(143\) −2274.17 −1.32990
\(144\) 0 0
\(145\) −2853.36 −1.63420
\(146\) 476.599 0.270162
\(147\) 0 0
\(148\) 5349.26 2.97099
\(149\) 2779.16 1.52804 0.764019 0.645193i \(-0.223223\pi\)
0.764019 + 0.645193i \(0.223223\pi\)
\(150\) 0 0
\(151\) −1613.32 −0.869471 −0.434736 0.900558i \(-0.643158\pi\)
−0.434736 + 0.900558i \(0.643158\pi\)
\(152\) 2344.49 1.25107
\(153\) 0 0
\(154\) −4743.81 −2.48226
\(155\) 2120.06 1.09863
\(156\) 0 0
\(157\) −990.570 −0.503542 −0.251771 0.967787i \(-0.581013\pi\)
−0.251771 + 0.967787i \(0.581013\pi\)
\(158\) 1756.67 0.884511
\(159\) 0 0
\(160\) −7795.80 −3.85195
\(161\) −2353.23 −1.15193
\(162\) 0 0
\(163\) 1548.67 0.744180 0.372090 0.928197i \(-0.378641\pi\)
0.372090 + 0.928197i \(0.378641\pi\)
\(164\) 9077.63 4.32222
\(165\) 0 0
\(166\) −3866.10 −1.80764
\(167\) −1299.02 −0.601923 −0.300961 0.953636i \(-0.597308\pi\)
−0.300961 + 0.953636i \(0.597308\pi\)
\(168\) 0 0
\(169\) −1081.65 −0.492333
\(170\) −14367.4 −6.48195
\(171\) 0 0
\(172\) −3690.10 −1.63586
\(173\) −363.132 −0.159586 −0.0797930 0.996811i \(-0.525426\pi\)
−0.0797930 + 0.996811i \(0.525426\pi\)
\(174\) 0 0
\(175\) −3732.96 −1.61249
\(176\) −11382.2 −4.87479
\(177\) 0 0
\(178\) −3902.87 −1.64344
\(179\) 600.492 0.250742 0.125371 0.992110i \(-0.459988\pi\)
0.125371 + 0.992110i \(0.459988\pi\)
\(180\) 0 0
\(181\) 3425.37 1.40666 0.703331 0.710863i \(-0.251695\pi\)
0.703331 + 0.710863i \(0.251695\pi\)
\(182\) 2326.56 0.947560
\(183\) 0 0
\(184\) −10975.6 −4.39747
\(185\) 5473.07 2.17507
\(186\) 0 0
\(187\) −9209.30 −3.60134
\(188\) 2962.58 1.14930
\(189\) 0 0
\(190\) 4035.98 1.54106
\(191\) 885.654 0.335517 0.167758 0.985828i \(-0.446347\pi\)
0.167758 + 0.985828i \(0.446347\pi\)
\(192\) 0 0
\(193\) −1354.18 −0.505056 −0.252528 0.967590i \(-0.581262\pi\)
−0.252528 + 0.967590i \(0.581262\pi\)
\(194\) 3147.29 1.16475
\(195\) 0 0
\(196\) −3311.77 −1.20691
\(197\) −1095.00 −0.396019 −0.198009 0.980200i \(-0.563448\pi\)
−0.198009 + 0.980200i \(0.563448\pi\)
\(198\) 0 0
\(199\) 3997.52 1.42400 0.712002 0.702178i \(-0.247789\pi\)
0.712002 + 0.702178i \(0.247789\pi\)
\(200\) −17410.8 −6.15563
\(201\) 0 0
\(202\) −1756.52 −0.611824
\(203\) 1871.09 0.646921
\(204\) 0 0
\(205\) 9287.73 3.16431
\(206\) −3054.07 −1.03295
\(207\) 0 0
\(208\) 5582.28 1.86087
\(209\) 2587.00 0.856204
\(210\) 0 0
\(211\) 2251.18 0.734492 0.367246 0.930124i \(-0.380301\pi\)
0.367246 + 0.930124i \(0.380301\pi\)
\(212\) 1831.11 0.593213
\(213\) 0 0
\(214\) 7797.74 2.49085
\(215\) −3775.51 −1.19762
\(216\) 0 0
\(217\) −1390.23 −0.434909
\(218\) 9927.53 3.08430
\(219\) 0 0
\(220\) −27096.5 −8.30385
\(221\) 4516.62 1.37475
\(222\) 0 0
\(223\) 2793.48 0.838858 0.419429 0.907788i \(-0.362230\pi\)
0.419429 + 0.907788i \(0.362230\pi\)
\(224\) 5112.10 1.52485
\(225\) 0 0
\(226\) 5794.93 1.70563
\(227\) 6450.38 1.88602 0.943010 0.332764i \(-0.107981\pi\)
0.943010 + 0.332764i \(0.107981\pi\)
\(228\) 0 0
\(229\) 722.752 0.208562 0.104281 0.994548i \(-0.466746\pi\)
0.104281 + 0.994548i \(0.466746\pi\)
\(230\) −18894.3 −5.41675
\(231\) 0 0
\(232\) 8726.89 2.46961
\(233\) −3388.50 −0.952738 −0.476369 0.879245i \(-0.658047\pi\)
−0.476369 + 0.879245i \(0.658047\pi\)
\(234\) 0 0
\(235\) 3031.15 0.841407
\(236\) −3387.91 −0.934467
\(237\) 0 0
\(238\) 9421.45 2.56598
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 6482.01 1.73254 0.866272 0.499573i \(-0.166510\pi\)
0.866272 + 0.499573i \(0.166510\pi\)
\(242\) −17406.3 −4.62363
\(243\) 0 0
\(244\) −16471.7 −4.32169
\(245\) −3388.41 −0.883583
\(246\) 0 0
\(247\) −1268.77 −0.326842
\(248\) −6484.14 −1.66026
\(249\) 0 0
\(250\) −16692.7 −4.22297
\(251\) 2013.62 0.506370 0.253185 0.967418i \(-0.418522\pi\)
0.253185 + 0.967418i \(0.418522\pi\)
\(252\) 0 0
\(253\) −12110.9 −3.00952
\(254\) −3203.82 −0.791440
\(255\) 0 0
\(256\) −2527.79 −0.617136
\(257\) 1280.22 0.310731 0.155365 0.987857i \(-0.450345\pi\)
0.155365 + 0.987857i \(0.450345\pi\)
\(258\) 0 0
\(259\) −3588.97 −0.861034
\(260\) 13289.2 3.16986
\(261\) 0 0
\(262\) 3902.95 0.920324
\(263\) 7629.58 1.78882 0.894411 0.447245i \(-0.147595\pi\)
0.894411 + 0.447245i \(0.147595\pi\)
\(264\) 0 0
\(265\) 1873.49 0.434293
\(266\) −2646.60 −0.610050
\(267\) 0 0
\(268\) −6141.17 −1.39974
\(269\) 3449.88 0.781944 0.390972 0.920403i \(-0.372139\pi\)
0.390972 + 0.920403i \(0.372139\pi\)
\(270\) 0 0
\(271\) 409.007 0.0916805 0.0458403 0.998949i \(-0.485403\pi\)
0.0458403 + 0.998949i \(0.485403\pi\)
\(272\) 22605.6 5.03920
\(273\) 0 0
\(274\) −246.636 −0.0543790
\(275\) −19211.7 −4.21277
\(276\) 0 0
\(277\) −2697.20 −0.585052 −0.292526 0.956258i \(-0.594496\pi\)
−0.292526 + 0.956258i \(0.594496\pi\)
\(278\) 6374.74 1.37529
\(279\) 0 0
\(280\) 16475.6 3.51644
\(281\) 2747.53 0.583288 0.291644 0.956527i \(-0.405798\pi\)
0.291644 + 0.956527i \(0.405798\pi\)
\(282\) 0 0
\(283\) −5880.65 −1.23522 −0.617612 0.786483i \(-0.711900\pi\)
−0.617612 + 0.786483i \(0.711900\pi\)
\(284\) 10368.1 2.16632
\(285\) 0 0
\(286\) 11973.7 2.47559
\(287\) −6090.44 −1.25264
\(288\) 0 0
\(289\) 13377.1 2.72281
\(290\) 15023.1 3.04203
\(291\) 0 0
\(292\) −1785.16 −0.357770
\(293\) −8311.20 −1.65715 −0.828576 0.559877i \(-0.810849\pi\)
−0.828576 + 0.559877i \(0.810849\pi\)
\(294\) 0 0
\(295\) −3466.32 −0.684126
\(296\) −16739.2 −3.28698
\(297\) 0 0
\(298\) −14632.5 −2.84442
\(299\) 5939.70 1.14884
\(300\) 0 0
\(301\) 2475.79 0.474094
\(302\) 8494.25 1.61851
\(303\) 0 0
\(304\) −6350.17 −1.19805
\(305\) −16852.9 −3.16392
\(306\) 0 0
\(307\) 2796.23 0.519834 0.259917 0.965631i \(-0.416305\pi\)
0.259917 + 0.965631i \(0.416305\pi\)
\(308\) 17768.6 3.28720
\(309\) 0 0
\(310\) −11162.3 −2.04508
\(311\) −7690.57 −1.40222 −0.701112 0.713051i \(-0.747313\pi\)
−0.701112 + 0.713051i \(0.747313\pi\)
\(312\) 0 0
\(313\) 9300.22 1.67949 0.839743 0.542983i \(-0.182705\pi\)
0.839743 + 0.542983i \(0.182705\pi\)
\(314\) 5215.42 0.937336
\(315\) 0 0
\(316\) −6579.81 −1.17134
\(317\) 428.900 0.0759919 0.0379959 0.999278i \(-0.487903\pi\)
0.0379959 + 0.999278i \(0.487903\pi\)
\(318\) 0 0
\(319\) 9629.60 1.69014
\(320\) 14064.2 2.45691
\(321\) 0 0
\(322\) 12389.9 2.14430
\(323\) −5137.91 −0.885081
\(324\) 0 0
\(325\) 9422.21 1.60815
\(326\) −8153.87 −1.38528
\(327\) 0 0
\(328\) −28406.2 −4.78192
\(329\) −1987.68 −0.333083
\(330\) 0 0
\(331\) −8728.76 −1.44947 −0.724737 0.689025i \(-0.758039\pi\)
−0.724737 + 0.689025i \(0.758039\pi\)
\(332\) 14481.0 2.39382
\(333\) 0 0
\(334\) 6839.43 1.12047
\(335\) −6283.30 −1.02476
\(336\) 0 0
\(337\) 11015.3 1.78053 0.890266 0.455442i \(-0.150519\pi\)
0.890266 + 0.455442i \(0.150519\pi\)
\(338\) 5694.99 0.916470
\(339\) 0 0
\(340\) 53815.1 8.58392
\(341\) −7154.86 −1.13624
\(342\) 0 0
\(343\) 6760.32 1.06421
\(344\) 11547.2 1.80984
\(345\) 0 0
\(346\) 1911.92 0.297067
\(347\) 7148.46 1.10591 0.552953 0.833212i \(-0.313501\pi\)
0.552953 + 0.833212i \(0.313501\pi\)
\(348\) 0 0
\(349\) 3630.38 0.556818 0.278409 0.960463i \(-0.410193\pi\)
0.278409 + 0.960463i \(0.410193\pi\)
\(350\) 19654.3 3.00162
\(351\) 0 0
\(352\) 26309.5 3.98381
\(353\) 3706.20 0.558814 0.279407 0.960173i \(-0.409862\pi\)
0.279407 + 0.960173i \(0.409862\pi\)
\(354\) 0 0
\(355\) 10608.1 1.58597
\(356\) 14618.7 2.17637
\(357\) 0 0
\(358\) −3161.63 −0.466753
\(359\) −5691.48 −0.836727 −0.418363 0.908280i \(-0.637396\pi\)
−0.418363 + 0.908280i \(0.637396\pi\)
\(360\) 0 0
\(361\) −5415.70 −0.789576
\(362\) −18034.8 −2.61848
\(363\) 0 0
\(364\) −8714.42 −1.25483
\(365\) −1826.48 −0.261924
\(366\) 0 0
\(367\) 1962.63 0.279151 0.139575 0.990211i \(-0.455426\pi\)
0.139575 + 0.990211i \(0.455426\pi\)
\(368\) 29728.1 4.21109
\(369\) 0 0
\(370\) −28816.1 −4.04886
\(371\) −1228.54 −0.171921
\(372\) 0 0
\(373\) 1605.24 0.222832 0.111416 0.993774i \(-0.464461\pi\)
0.111416 + 0.993774i \(0.464461\pi\)
\(374\) 48487.7 6.70384
\(375\) 0 0
\(376\) −9270.67 −1.27154
\(377\) −4722.75 −0.645183
\(378\) 0 0
\(379\) −3963.46 −0.537175 −0.268588 0.963255i \(-0.586557\pi\)
−0.268588 + 0.963255i \(0.586557\pi\)
\(380\) −15117.3 −2.04079
\(381\) 0 0
\(382\) −4663.03 −0.624559
\(383\) −582.785 −0.0777518 −0.0388759 0.999244i \(-0.512378\pi\)
−0.0388759 + 0.999244i \(0.512378\pi\)
\(384\) 0 0
\(385\) 18179.8 2.40657
\(386\) 7129.85 0.940155
\(387\) 0 0
\(388\) −11788.6 −1.54246
\(389\) 6856.77 0.893707 0.446853 0.894607i \(-0.352545\pi\)
0.446853 + 0.894607i \(0.352545\pi\)
\(390\) 0 0
\(391\) 24053.0 3.11102
\(392\) 10363.3 1.33528
\(393\) 0 0
\(394\) 5765.27 0.737183
\(395\) −6732.10 −0.857541
\(396\) 0 0
\(397\) 8288.31 1.04780 0.523902 0.851778i \(-0.324476\pi\)
0.523902 + 0.851778i \(0.324476\pi\)
\(398\) −21047.2 −2.65076
\(399\) 0 0
\(400\) 47157.9 5.89474
\(401\) 14917.7 1.85774 0.928871 0.370403i \(-0.120781\pi\)
0.928871 + 0.370403i \(0.120781\pi\)
\(402\) 0 0
\(403\) 3509.03 0.433741
\(404\) 6579.28 0.810226
\(405\) 0 0
\(406\) −9851.44 −1.20423
\(407\) −18470.7 −2.24953
\(408\) 0 0
\(409\) 1787.00 0.216042 0.108021 0.994149i \(-0.465549\pi\)
0.108021 + 0.994149i \(0.465549\pi\)
\(410\) −48900.6 −5.89031
\(411\) 0 0
\(412\) 11439.4 1.36791
\(413\) 2273.04 0.270821
\(414\) 0 0
\(415\) 14816.1 1.75252
\(416\) −12903.2 −1.52075
\(417\) 0 0
\(418\) −13620.8 −1.59381
\(419\) −12421.9 −1.44833 −0.724163 0.689628i \(-0.757774\pi\)
−0.724163 + 0.689628i \(0.757774\pi\)
\(420\) 0 0
\(421\) −7526.06 −0.871254 −0.435627 0.900127i \(-0.643473\pi\)
−0.435627 + 0.900127i \(0.643473\pi\)
\(422\) −11852.7 −1.36725
\(423\) 0 0
\(424\) −5730.00 −0.656305
\(425\) 38155.5 4.35485
\(426\) 0 0
\(427\) 11051.3 1.25249
\(428\) −29207.4 −3.29859
\(429\) 0 0
\(430\) 19878.3 2.22934
\(431\) 17221.9 1.92471 0.962357 0.271790i \(-0.0876154\pi\)
0.962357 + 0.271790i \(0.0876154\pi\)
\(432\) 0 0
\(433\) 9694.62 1.07597 0.537984 0.842955i \(-0.319186\pi\)
0.537984 + 0.842955i \(0.319186\pi\)
\(434\) 7319.68 0.809576
\(435\) 0 0
\(436\) −37184.8 −4.08447
\(437\) −6756.75 −0.739633
\(438\) 0 0
\(439\) 666.978 0.0725128 0.0362564 0.999343i \(-0.488457\pi\)
0.0362564 + 0.999343i \(0.488457\pi\)
\(440\) 84791.8 9.18703
\(441\) 0 0
\(442\) −23780.3 −2.55908
\(443\) −5208.79 −0.558639 −0.279319 0.960198i \(-0.590109\pi\)
−0.279319 + 0.960198i \(0.590109\pi\)
\(444\) 0 0
\(445\) 14957.0 1.59333
\(446\) −14707.9 −1.56152
\(447\) 0 0
\(448\) −9222.58 −0.972602
\(449\) −10865.0 −1.14198 −0.570990 0.820957i \(-0.693441\pi\)
−0.570990 + 0.820957i \(0.693441\pi\)
\(450\) 0 0
\(451\) −31344.5 −3.27263
\(452\) −21705.7 −2.25874
\(453\) 0 0
\(454\) −33961.7 −3.51080
\(455\) −8916.12 −0.918668
\(456\) 0 0
\(457\) 7334.58 0.750759 0.375380 0.926871i \(-0.377512\pi\)
0.375380 + 0.926871i \(0.377512\pi\)
\(458\) −3805.34 −0.388236
\(459\) 0 0
\(460\) 70771.0 7.17329
\(461\) −3797.57 −0.383667 −0.191833 0.981428i \(-0.561443\pi\)
−0.191833 + 0.981428i \(0.561443\pi\)
\(462\) 0 0
\(463\) −12486.0 −1.25329 −0.626646 0.779304i \(-0.715573\pi\)
−0.626646 + 0.779304i \(0.715573\pi\)
\(464\) −23637.2 −2.36494
\(465\) 0 0
\(466\) 17840.7 1.77351
\(467\) 5250.91 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(468\) 0 0
\(469\) 4120.28 0.405665
\(470\) −15959.2 −1.56627
\(471\) 0 0
\(472\) 10601.6 1.03385
\(473\) 12741.7 1.23861
\(474\) 0 0
\(475\) −10718.3 −1.03535
\(476\) −35289.3 −3.39807
\(477\) 0 0
\(478\) 1258.35 0.120409
\(479\) 7322.21 0.698456 0.349228 0.937038i \(-0.386444\pi\)
0.349228 + 0.937038i \(0.386444\pi\)
\(480\) 0 0
\(481\) 9058.78 0.858721
\(482\) −34128.3 −3.22510
\(483\) 0 0
\(484\) 65197.5 6.12298
\(485\) −12061.4 −1.12924
\(486\) 0 0
\(487\) 2735.05 0.254491 0.127246 0.991871i \(-0.459386\pi\)
0.127246 + 0.991871i \(0.459386\pi\)
\(488\) 51544.1 4.78134
\(489\) 0 0
\(490\) 17840.3 1.64478
\(491\) −6821.94 −0.627026 −0.313513 0.949584i \(-0.601506\pi\)
−0.313513 + 0.949584i \(0.601506\pi\)
\(492\) 0 0
\(493\) −19124.9 −1.74714
\(494\) 6680.17 0.608411
\(495\) 0 0
\(496\) 17562.6 1.58989
\(497\) −6956.26 −0.627829
\(498\) 0 0
\(499\) −15541.3 −1.39424 −0.697120 0.716954i \(-0.745536\pi\)
−0.697120 + 0.716954i \(0.745536\pi\)
\(500\) 62524.8 5.59239
\(501\) 0 0
\(502\) −10601.9 −0.942600
\(503\) 2490.11 0.220733 0.110366 0.993891i \(-0.464798\pi\)
0.110366 + 0.993891i \(0.464798\pi\)
\(504\) 0 0
\(505\) 6731.55 0.593169
\(506\) 63765.0 5.60218
\(507\) 0 0
\(508\) 12000.3 1.04809
\(509\) 4863.51 0.423519 0.211759 0.977322i \(-0.432081\pi\)
0.211759 + 0.977322i \(0.432081\pi\)
\(510\) 0 0
\(511\) 1197.72 0.103687
\(512\) 17940.9 1.54860
\(513\) 0 0
\(514\) −6740.44 −0.578420
\(515\) 11704.2 1.00145
\(516\) 0 0
\(517\) −10229.6 −0.870210
\(518\) 18896.2 1.60280
\(519\) 0 0
\(520\) −41585.3 −3.50700
\(521\) −280.964 −0.0236262 −0.0118131 0.999930i \(-0.503760\pi\)
−0.0118131 + 0.999930i \(0.503760\pi\)
\(522\) 0 0
\(523\) −16027.2 −1.34000 −0.669999 0.742362i \(-0.733706\pi\)
−0.669999 + 0.742362i \(0.733706\pi\)
\(524\) −14619.0 −1.21877
\(525\) 0 0
\(526\) −40170.3 −3.32987
\(527\) 14209.9 1.17456
\(528\) 0 0
\(529\) 19464.5 1.59978
\(530\) −9864.06 −0.808429
\(531\) 0 0
\(532\) 9913.16 0.807876
\(533\) 15372.6 1.24927
\(534\) 0 0
\(535\) −29883.4 −2.41490
\(536\) 19217.3 1.54862
\(537\) 0 0
\(538\) −18163.9 −1.45558
\(539\) 11435.3 0.913830
\(540\) 0 0
\(541\) 16591.9 1.31856 0.659282 0.751896i \(-0.270860\pi\)
0.659282 + 0.751896i \(0.270860\pi\)
\(542\) −2153.45 −0.170662
\(543\) 0 0
\(544\) −52252.0 −4.11817
\(545\) −38045.5 −2.99025
\(546\) 0 0
\(547\) 1767.79 0.138181 0.0690906 0.997610i \(-0.477990\pi\)
0.0690906 + 0.997610i \(0.477990\pi\)
\(548\) 923.808 0.0720130
\(549\) 0 0
\(550\) 101151. 7.84200
\(551\) 5372.40 0.415376
\(552\) 0 0
\(553\) 4414.58 0.339470
\(554\) 14201.0 1.08907
\(555\) 0 0
\(556\) −23877.4 −1.82127
\(557\) −13963.8 −1.06223 −0.531117 0.847298i \(-0.678228\pi\)
−0.531117 + 0.847298i \(0.678228\pi\)
\(558\) 0 0
\(559\) −6249.04 −0.472820
\(560\) −44625.0 −3.36741
\(561\) 0 0
\(562\) −14466.0 −1.08578
\(563\) 11204.3 0.838727 0.419364 0.907818i \(-0.362253\pi\)
0.419364 + 0.907818i \(0.362253\pi\)
\(564\) 0 0
\(565\) −22208.0 −1.65363
\(566\) 30962.1 2.29935
\(567\) 0 0
\(568\) −32444.4 −2.39672
\(569\) 17933.8 1.32131 0.660653 0.750691i \(-0.270279\pi\)
0.660653 + 0.750691i \(0.270279\pi\)
\(570\) 0 0
\(571\) 3649.96 0.267506 0.133753 0.991015i \(-0.457297\pi\)
0.133753 + 0.991015i \(0.457297\pi\)
\(572\) −44848.9 −3.27837
\(573\) 0 0
\(574\) 32066.6 2.33177
\(575\) 50177.4 3.63920
\(576\) 0 0
\(577\) −10571.6 −0.762737 −0.381369 0.924423i \(-0.624547\pi\)
−0.381369 + 0.924423i \(0.624547\pi\)
\(578\) −70431.7 −5.06846
\(579\) 0 0
\(580\) −56271.1 −4.02850
\(581\) −9715.69 −0.693760
\(582\) 0 0
\(583\) −6322.71 −0.449159
\(584\) 5586.22 0.395821
\(585\) 0 0
\(586\) 43759.1 3.08476
\(587\) 9237.12 0.649500 0.324750 0.945800i \(-0.394720\pi\)
0.324750 + 0.945800i \(0.394720\pi\)
\(588\) 0 0
\(589\) −3991.73 −0.279247
\(590\) 18250.4 1.27349
\(591\) 0 0
\(592\) 45339.0 3.14767
\(593\) 15168.6 1.05042 0.525210 0.850973i \(-0.323987\pi\)
0.525210 + 0.850973i \(0.323987\pi\)
\(594\) 0 0
\(595\) −36106.0 −2.48773
\(596\) 54807.9 3.76681
\(597\) 0 0
\(598\) −31273.0 −2.13854
\(599\) −21957.6 −1.49777 −0.748884 0.662701i \(-0.769410\pi\)
−0.748884 + 0.662701i \(0.769410\pi\)
\(600\) 0 0
\(601\) 22860.6 1.55158 0.775792 0.630988i \(-0.217350\pi\)
0.775792 + 0.630988i \(0.217350\pi\)
\(602\) −13035.2 −0.882518
\(603\) 0 0
\(604\) −31816.3 −2.14336
\(605\) 66706.5 4.48265
\(606\) 0 0
\(607\) 17516.0 1.17126 0.585629 0.810580i \(-0.300848\pi\)
0.585629 + 0.810580i \(0.300848\pi\)
\(608\) 14678.2 0.979078
\(609\) 0 0
\(610\) 88732.0 5.88960
\(611\) 5017.02 0.332188
\(612\) 0 0
\(613\) 2369.01 0.156090 0.0780452 0.996950i \(-0.475132\pi\)
0.0780452 + 0.996950i \(0.475132\pi\)
\(614\) −14722.3 −0.967664
\(615\) 0 0
\(616\) −55602.3 −3.63682
\(617\) −18863.8 −1.23084 −0.615420 0.788199i \(-0.711014\pi\)
−0.615420 + 0.788199i \(0.711014\pi\)
\(618\) 0 0
\(619\) −25535.7 −1.65810 −0.829051 0.559173i \(-0.811119\pi\)
−0.829051 + 0.559173i \(0.811119\pi\)
\(620\) 41809.8 2.70826
\(621\) 0 0
\(622\) 40491.4 2.61022
\(623\) −9808.08 −0.630742
\(624\) 0 0
\(625\) 28705.8 1.83717
\(626\) −48966.3 −3.12634
\(627\) 0 0
\(628\) −19535.0 −1.24129
\(629\) 36683.7 2.32540
\(630\) 0 0
\(631\) 26395.5 1.66528 0.832638 0.553818i \(-0.186829\pi\)
0.832638 + 0.553818i \(0.186829\pi\)
\(632\) 20589.9 1.29592
\(633\) 0 0
\(634\) −2258.19 −0.141458
\(635\) 12278.1 0.767308
\(636\) 0 0
\(637\) −5608.35 −0.348840
\(638\) −50700.6 −3.14617
\(639\) 0 0
\(640\) −11682.4 −0.721546
\(641\) −796.235 −0.0490630 −0.0245315 0.999699i \(-0.507809\pi\)
−0.0245315 + 0.999699i \(0.507809\pi\)
\(642\) 0 0
\(643\) 28684.2 1.75924 0.879622 0.475674i \(-0.157796\pi\)
0.879622 + 0.475674i \(0.157796\pi\)
\(644\) −46408.1 −2.83965
\(645\) 0 0
\(646\) 27051.5 1.64757
\(647\) −19433.6 −1.18086 −0.590429 0.807090i \(-0.701041\pi\)
−0.590429 + 0.807090i \(0.701041\pi\)
\(648\) 0 0
\(649\) 11698.3 0.707545
\(650\) −49608.6 −2.99356
\(651\) 0 0
\(652\) 30541.4 1.83450
\(653\) −12293.8 −0.736744 −0.368372 0.929678i \(-0.620085\pi\)
−0.368372 + 0.929678i \(0.620085\pi\)
\(654\) 0 0
\(655\) −14957.3 −0.892262
\(656\) 76939.7 4.57925
\(657\) 0 0
\(658\) 10465.3 0.620029
\(659\) 4962.98 0.293369 0.146685 0.989183i \(-0.453140\pi\)
0.146685 + 0.989183i \(0.453140\pi\)
\(660\) 0 0
\(661\) 2665.38 0.156840 0.0784200 0.996920i \(-0.475012\pi\)
0.0784200 + 0.996920i \(0.475012\pi\)
\(662\) 45957.6 2.69817
\(663\) 0 0
\(664\) −45314.6 −2.64842
\(665\) 10142.6 0.591448
\(666\) 0 0
\(667\) −25150.7 −1.46003
\(668\) −25618.0 −1.48382
\(669\) 0 0
\(670\) 33082.1 1.90757
\(671\) 56875.8 3.27223
\(672\) 0 0
\(673\) −14281.1 −0.817972 −0.408986 0.912541i \(-0.634118\pi\)
−0.408986 + 0.912541i \(0.634118\pi\)
\(674\) −57996.1 −3.31443
\(675\) 0 0
\(676\) −21331.3 −1.21366
\(677\) −10640.4 −0.604054 −0.302027 0.953299i \(-0.597663\pi\)
−0.302027 + 0.953299i \(0.597663\pi\)
\(678\) 0 0
\(679\) 7909.28 0.447025
\(680\) −168401. −9.49688
\(681\) 0 0
\(682\) 37670.9 2.11509
\(683\) −5985.39 −0.335322 −0.167661 0.985845i \(-0.553621\pi\)
−0.167661 + 0.985845i \(0.553621\pi\)
\(684\) 0 0
\(685\) 945.189 0.0527209
\(686\) −35593.6 −1.98100
\(687\) 0 0
\(688\) −31276.3 −1.73314
\(689\) 3100.91 0.171459
\(690\) 0 0
\(691\) 6136.31 0.337824 0.168912 0.985631i \(-0.445975\pi\)
0.168912 + 0.985631i \(0.445975\pi\)
\(692\) −7161.32 −0.393400
\(693\) 0 0
\(694\) −37637.2 −2.05863
\(695\) −24430.0 −1.33336
\(696\) 0 0
\(697\) 62251.8 3.38301
\(698\) −19114.2 −1.03651
\(699\) 0 0
\(700\) −73617.7 −3.97498
\(701\) 3702.99 0.199515 0.0997576 0.995012i \(-0.468193\pi\)
0.0997576 + 0.995012i \(0.468193\pi\)
\(702\) 0 0
\(703\) −10304.9 −0.552854
\(704\) −47464.2 −2.54101
\(705\) 0 0
\(706\) −19513.4 −1.04022
\(707\) −4414.22 −0.234814
\(708\) 0 0
\(709\) 22752.4 1.20520 0.602598 0.798045i \(-0.294132\pi\)
0.602598 + 0.798045i \(0.294132\pi\)
\(710\) −55852.4 −2.95226
\(711\) 0 0
\(712\) −45745.5 −2.40785
\(713\) 18687.1 0.981541
\(714\) 0 0
\(715\) −45886.9 −2.40010
\(716\) 11842.3 0.618111
\(717\) 0 0
\(718\) 29966.1 1.55755
\(719\) 31170.0 1.61675 0.808376 0.588666i \(-0.200347\pi\)
0.808376 + 0.588666i \(0.200347\pi\)
\(720\) 0 0
\(721\) −7675.02 −0.396439
\(722\) 28514.1 1.46978
\(723\) 0 0
\(724\) 67551.7 3.46760
\(725\) −39896.8 −2.04377
\(726\) 0 0
\(727\) −9753.18 −0.497559 −0.248780 0.968560i \(-0.580029\pi\)
−0.248780 + 0.968560i \(0.580029\pi\)
\(728\) 27269.6 1.38830
\(729\) 0 0
\(730\) 9616.55 0.487568
\(731\) −25305.6 −1.28039
\(732\) 0 0
\(733\) 24162.4 1.21754 0.608771 0.793346i \(-0.291663\pi\)
0.608771 + 0.793346i \(0.291663\pi\)
\(734\) −10333.4 −0.519635
\(735\) 0 0
\(736\) −68715.4 −3.44142
\(737\) 21205.1 1.05984
\(738\) 0 0
\(739\) −32378.7 −1.61173 −0.805866 0.592099i \(-0.798300\pi\)
−0.805866 + 0.592099i \(0.798300\pi\)
\(740\) 107934. 5.36182
\(741\) 0 0
\(742\) 6468.37 0.320029
\(743\) −30746.0 −1.51812 −0.759060 0.651021i \(-0.774341\pi\)
−0.759060 + 0.651021i \(0.774341\pi\)
\(744\) 0 0
\(745\) 56076.4 2.75769
\(746\) −8451.73 −0.414799
\(747\) 0 0
\(748\) −181617. −8.87776
\(749\) 19596.1 0.955975
\(750\) 0 0
\(751\) −3552.72 −0.172624 −0.0863121 0.996268i \(-0.527508\pi\)
−0.0863121 + 0.996268i \(0.527508\pi\)
\(752\) 25110.1 1.21765
\(753\) 0 0
\(754\) 24865.6 1.20100
\(755\) −32552.7 −1.56916
\(756\) 0 0
\(757\) −10905.3 −0.523594 −0.261797 0.965123i \(-0.584315\pi\)
−0.261797 + 0.965123i \(0.584315\pi\)
\(758\) 20867.9 0.999944
\(759\) 0 0
\(760\) 47305.8 2.25784
\(761\) 1097.56 0.0522818 0.0261409 0.999658i \(-0.491678\pi\)
0.0261409 + 0.999658i \(0.491678\pi\)
\(762\) 0 0
\(763\) 24948.3 1.18374
\(764\) 17466.0 0.827091
\(765\) 0 0
\(766\) 3068.41 0.144734
\(767\) −5737.30 −0.270094
\(768\) 0 0
\(769\) 6373.24 0.298862 0.149431 0.988772i \(-0.452256\pi\)
0.149431 + 0.988772i \(0.452256\pi\)
\(770\) −95718.0 −4.47979
\(771\) 0 0
\(772\) −26705.8 −1.24503
\(773\) −30799.4 −1.43309 −0.716545 0.697541i \(-0.754278\pi\)
−0.716545 + 0.697541i \(0.754278\pi\)
\(774\) 0 0
\(775\) 29643.6 1.37397
\(776\) 36889.4 1.70651
\(777\) 0 0
\(778\) −36101.4 −1.66362
\(779\) −17487.3 −0.804296
\(780\) 0 0
\(781\) −35800.5 −1.64026
\(782\) −126641. −5.79112
\(783\) 0 0
\(784\) −28069.7 −1.27868
\(785\) −19987.2 −0.908755
\(786\) 0 0
\(787\) 28238.3 1.27902 0.639509 0.768783i \(-0.279138\pi\)
0.639509 + 0.768783i \(0.279138\pi\)
\(788\) −21594.6 −0.976236
\(789\) 0 0
\(790\) 35445.0 1.59630
\(791\) 14562.9 0.654612
\(792\) 0 0
\(793\) −27894.2 −1.24912
\(794\) −43638.6 −1.95047
\(795\) 0 0
\(796\) 78835.1 3.51035
\(797\) 30650.8 1.36224 0.681122 0.732170i \(-0.261492\pi\)
0.681122 + 0.732170i \(0.261492\pi\)
\(798\) 0 0
\(799\) 20316.6 0.899559
\(800\) −109004. −4.81734
\(801\) 0 0
\(802\) −78542.8 −3.45816
\(803\) 6164.06 0.270890
\(804\) 0 0
\(805\) −47482.2 −2.07892
\(806\) −18475.3 −0.807401
\(807\) 0 0
\(808\) −20588.2 −0.896399
\(809\) 40477.0 1.75908 0.879541 0.475824i \(-0.157850\pi\)
0.879541 + 0.475824i \(0.157850\pi\)
\(810\) 0 0
\(811\) 12850.5 0.556404 0.278202 0.960523i \(-0.410262\pi\)
0.278202 + 0.960523i \(0.410262\pi\)
\(812\) 36899.8 1.59474
\(813\) 0 0
\(814\) 97249.6 4.18746
\(815\) 31248.2 1.34304
\(816\) 0 0
\(817\) 7108.65 0.304407
\(818\) −9408.68 −0.402160
\(819\) 0 0
\(820\) 183163. 7.80042
\(821\) 34174.1 1.45272 0.726360 0.687314i \(-0.241210\pi\)
0.726360 + 0.687314i \(0.241210\pi\)
\(822\) 0 0
\(823\) −18526.9 −0.784700 −0.392350 0.919816i \(-0.628338\pi\)
−0.392350 + 0.919816i \(0.628338\pi\)
\(824\) −35796.8 −1.51340
\(825\) 0 0
\(826\) −11967.7 −0.504130
\(827\) 13750.8 0.578188 0.289094 0.957301i \(-0.406646\pi\)
0.289094 + 0.957301i \(0.406646\pi\)
\(828\) 0 0
\(829\) 36741.2 1.53930 0.769648 0.638469i \(-0.220432\pi\)
0.769648 + 0.638469i \(0.220432\pi\)
\(830\) −78008.0 −3.26229
\(831\) 0 0
\(832\) 23278.4 0.969990
\(833\) −22711.1 −0.944651
\(834\) 0 0
\(835\) −26210.9 −1.08631
\(836\) 51018.3 2.11065
\(837\) 0 0
\(838\) 65402.2 2.69604
\(839\) 29148.3 1.19942 0.599709 0.800218i \(-0.295283\pi\)
0.599709 + 0.800218i \(0.295283\pi\)
\(840\) 0 0
\(841\) −4391.29 −0.180052
\(842\) 39625.3 1.62183
\(843\) 0 0
\(844\) 44395.6 1.81062
\(845\) −21825.0 −0.888525
\(846\) 0 0
\(847\) −43742.8 −1.77452
\(848\) 15520.0 0.628490
\(849\) 0 0
\(850\) −200891. −8.10649
\(851\) 48241.9 1.94326
\(852\) 0 0
\(853\) −12165.1 −0.488306 −0.244153 0.969737i \(-0.578510\pi\)
−0.244153 + 0.969737i \(0.578510\pi\)
\(854\) −58186.1 −2.33148
\(855\) 0 0
\(856\) 91397.4 3.64941
\(857\) −39605.6 −1.57865 −0.789324 0.613977i \(-0.789569\pi\)
−0.789324 + 0.613977i \(0.789569\pi\)
\(858\) 0 0
\(859\) −1672.71 −0.0664401 −0.0332200 0.999448i \(-0.510576\pi\)
−0.0332200 + 0.999448i \(0.510576\pi\)
\(860\) −74456.8 −2.95227
\(861\) 0 0
\(862\) −90674.8 −3.58283
\(863\) −23847.6 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(864\) 0 0
\(865\) −7327.07 −0.288009
\(866\) −51042.9 −2.00290
\(867\) 0 0
\(868\) −27416.8 −1.07211
\(869\) 22719.7 0.886897
\(870\) 0 0
\(871\) −10399.8 −0.404575
\(872\) 116361. 4.51889
\(873\) 0 0
\(874\) 35574.8 1.37681
\(875\) −41949.6 −1.62075
\(876\) 0 0
\(877\) 5550.23 0.213704 0.106852 0.994275i \(-0.465923\pi\)
0.106852 + 0.994275i \(0.465923\pi\)
\(878\) −3511.69 −0.134981
\(879\) 0 0
\(880\) −229663. −8.79766
\(881\) −39226.6 −1.50009 −0.750044 0.661388i \(-0.769967\pi\)
−0.750044 + 0.661388i \(0.769967\pi\)
\(882\) 0 0
\(883\) 44129.7 1.68186 0.840930 0.541144i \(-0.182008\pi\)
0.840930 + 0.541144i \(0.182008\pi\)
\(884\) 89072.2 3.38894
\(885\) 0 0
\(886\) 27424.6 1.03990
\(887\) 34242.6 1.29623 0.648113 0.761544i \(-0.275558\pi\)
0.648113 + 0.761544i \(0.275558\pi\)
\(888\) 0 0
\(889\) −8051.35 −0.303750
\(890\) −78749.9 −2.96596
\(891\) 0 0
\(892\) 55090.3 2.06789
\(893\) −5707.16 −0.213866
\(894\) 0 0
\(895\) 12116.4 0.452521
\(896\) 7660.77 0.285634
\(897\) 0 0
\(898\) 57204.8 2.12578
\(899\) −14858.4 −0.551231
\(900\) 0 0
\(901\) 12557.2 0.464308
\(902\) 165031. 6.09195
\(903\) 0 0
\(904\) 67922.5 2.49897
\(905\) 69115.2 2.53864
\(906\) 0 0
\(907\) −52054.3 −1.90566 −0.952830 0.303504i \(-0.901843\pi\)
−0.952830 + 0.303504i \(0.901843\pi\)
\(908\) 127208. 4.64928
\(909\) 0 0
\(910\) 46944.0 1.71009
\(911\) 49109.3 1.78602 0.893010 0.450036i \(-0.148589\pi\)
0.893010 + 0.450036i \(0.148589\pi\)
\(912\) 0 0
\(913\) −50001.9 −1.81251
\(914\) −38617.1 −1.39753
\(915\) 0 0
\(916\) 14253.4 0.514133
\(917\) 9808.28 0.353215
\(918\) 0 0
\(919\) −39316.6 −1.41125 −0.705623 0.708587i \(-0.749333\pi\)
−0.705623 + 0.708587i \(0.749333\pi\)
\(920\) −221460. −7.93622
\(921\) 0 0
\(922\) 19994.5 0.714190
\(923\) 17558.0 0.626142
\(924\) 0 0
\(925\) 76526.7 2.72020
\(926\) 65739.7 2.33298
\(927\) 0 0
\(928\) 54636.7 1.93269
\(929\) 43407.2 1.53299 0.766493 0.642253i \(-0.222000\pi\)
0.766493 + 0.642253i \(0.222000\pi\)
\(930\) 0 0
\(931\) 6379.82 0.224587
\(932\) −66824.6 −2.34862
\(933\) 0 0
\(934\) −27646.4 −0.968542
\(935\) −185820. −6.49943
\(936\) 0 0
\(937\) −27279.5 −0.951102 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(938\) −21693.6 −0.755139
\(939\) 0 0
\(940\) 59777.4 2.07417
\(941\) −24741.4 −0.857116 −0.428558 0.903514i \(-0.640978\pi\)
−0.428558 + 0.903514i \(0.640978\pi\)
\(942\) 0 0
\(943\) 81866.0 2.82707
\(944\) −28715.1 −0.990037
\(945\) 0 0
\(946\) −67086.0 −2.30566
\(947\) −44553.0 −1.52880 −0.764402 0.644740i \(-0.776966\pi\)
−0.764402 + 0.644740i \(0.776966\pi\)
\(948\) 0 0
\(949\) −3023.11 −0.103408
\(950\) 56432.7 1.92728
\(951\) 0 0
\(952\) 110429. 3.75948
\(953\) −52298.9 −1.77768 −0.888839 0.458220i \(-0.848487\pi\)
−0.888839 + 0.458220i \(0.848487\pi\)
\(954\) 0 0
\(955\) 17870.2 0.605515
\(956\) −4713.32 −0.159456
\(957\) 0 0
\(958\) −38552.0 −1.30016
\(959\) −619.808 −0.0208703
\(960\) 0 0
\(961\) −18751.1 −0.629421
\(962\) −47695.1 −1.59850
\(963\) 0 0
\(964\) 127832. 4.27094
\(965\) −27323.9 −0.911488
\(966\) 0 0
\(967\) 21652.6 0.720064 0.360032 0.932940i \(-0.382766\pi\)
0.360032 + 0.932940i \(0.382766\pi\)
\(968\) −204019. −6.77421
\(969\) 0 0
\(970\) 63504.2 2.10206
\(971\) 40757.1 1.34702 0.673510 0.739178i \(-0.264786\pi\)
0.673510 + 0.739178i \(0.264786\pi\)
\(972\) 0 0
\(973\) 16020.0 0.527830
\(974\) −14400.3 −0.473731
\(975\) 0 0
\(976\) −139610. −4.57869
\(977\) 57315.1 1.87684 0.938420 0.345497i \(-0.112290\pi\)
0.938420 + 0.345497i \(0.112290\pi\)
\(978\) 0 0
\(979\) −50477.4 −1.64787
\(980\) −66823.0 −2.17814
\(981\) 0 0
\(982\) 35918.0 1.16720
\(983\) −4287.35 −0.139110 −0.0695551 0.997578i \(-0.522158\pi\)
−0.0695551 + 0.997578i \(0.522158\pi\)
\(984\) 0 0
\(985\) −22094.4 −0.714705
\(986\) 100694. 3.25228
\(987\) 0 0
\(988\) −25021.4 −0.805706
\(989\) −33278.9 −1.06998
\(990\) 0 0
\(991\) 5168.68 0.165680 0.0828398 0.996563i \(-0.473601\pi\)
0.0828398 + 0.996563i \(0.473601\pi\)
\(992\) −40595.4 −1.29930
\(993\) 0 0
\(994\) 36625.2 1.16869
\(995\) 80659.7 2.56994
\(996\) 0 0
\(997\) 36154.6 1.14847 0.574237 0.818689i \(-0.305299\pi\)
0.574237 + 0.818689i \(0.305299\pi\)
\(998\) 81826.3 2.59536
\(999\) 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.1.1 yes 59
3.2 odd 2 2151.4.a.g.1.59 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.59 59 3.2 odd 2
2151.4.a.h.1.1 yes 59 1.1 even 1 trivial