Properties

Label 2151.4.a.h.1.7
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 1.7
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.45221 q^{2} +11.8222 q^{4} +12.0796 q^{5} -15.4984 q^{7} -17.0170 q^{8} +O(q^{10})\) \(q-4.45221 q^{2} +11.8222 q^{4} +12.0796 q^{5} -15.4984 q^{7} -17.0170 q^{8} -53.7808 q^{10} -9.43863 q^{11} +58.4141 q^{13} +69.0020 q^{14} -18.8139 q^{16} -38.5888 q^{17} +155.155 q^{19} +142.807 q^{20} +42.0227 q^{22} -9.96595 q^{23} +20.9160 q^{25} -260.072 q^{26} -183.224 q^{28} +268.647 q^{29} +126.828 q^{31} +219.900 q^{32} +171.805 q^{34} -187.214 q^{35} -392.339 q^{37} -690.781 q^{38} -205.558 q^{40} +336.132 q^{41} -79.3956 q^{43} -111.585 q^{44} +44.3705 q^{46} -43.3712 q^{47} -102.800 q^{49} -93.1225 q^{50} +690.581 q^{52} -23.7667 q^{53} -114.015 q^{55} +263.736 q^{56} -1196.07 q^{58} +17.5671 q^{59} +679.230 q^{61} -564.665 q^{62} -828.527 q^{64} +705.617 q^{65} -890.593 q^{67} -456.203 q^{68} +833.515 q^{70} -237.928 q^{71} +638.534 q^{73} +1746.78 q^{74} +1834.26 q^{76} +146.283 q^{77} -713.642 q^{79} -227.264 q^{80} -1496.53 q^{82} +532.550 q^{83} -466.136 q^{85} +353.486 q^{86} +160.617 q^{88} +1585.59 q^{89} -905.324 q^{91} -117.819 q^{92} +193.098 q^{94} +1874.20 q^{95} +1522.63 q^{97} +457.688 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45221 −1.57409 −0.787047 0.616894i \(-0.788391\pi\)
−0.787047 + 0.616894i \(0.788391\pi\)
\(3\) 0 0
\(4\) 11.8222 1.47777
\(5\) 12.0796 1.08043 0.540215 0.841527i \(-0.318343\pi\)
0.540215 + 0.841527i \(0.318343\pi\)
\(6\) 0 0
\(7\) −15.4984 −0.836834 −0.418417 0.908255i \(-0.637415\pi\)
−0.418417 + 0.908255i \(0.637415\pi\)
\(8\) −17.0170 −0.752053
\(9\) 0 0
\(10\) −53.7808 −1.70070
\(11\) −9.43863 −0.258714 −0.129357 0.991598i \(-0.541291\pi\)
−0.129357 + 0.991598i \(0.541291\pi\)
\(12\) 0 0
\(13\) 58.4141 1.24624 0.623122 0.782125i \(-0.285864\pi\)
0.623122 + 0.782125i \(0.285864\pi\)
\(14\) 69.0020 1.31725
\(15\) 0 0
\(16\) −18.8139 −0.293968
\(17\) −38.5888 −0.550539 −0.275269 0.961367i \(-0.588767\pi\)
−0.275269 + 0.961367i \(0.588767\pi\)
\(18\) 0 0
\(19\) 155.155 1.87342 0.936709 0.350108i \(-0.113855\pi\)
0.936709 + 0.350108i \(0.113855\pi\)
\(20\) 142.807 1.59663
\(21\) 0 0
\(22\) 42.0227 0.407240
\(23\) −9.96595 −0.0903497 −0.0451749 0.998979i \(-0.514384\pi\)
−0.0451749 + 0.998979i \(0.514384\pi\)
\(24\) 0 0
\(25\) 20.9160 0.167328
\(26\) −260.072 −1.96170
\(27\) 0 0
\(28\) −183.224 −1.23665
\(29\) 268.647 1.72023 0.860113 0.510104i \(-0.170393\pi\)
0.860113 + 0.510104i \(0.170393\pi\)
\(30\) 0 0
\(31\) 126.828 0.734807 0.367403 0.930062i \(-0.380247\pi\)
0.367403 + 0.930062i \(0.380247\pi\)
\(32\) 219.900 1.21479
\(33\) 0 0
\(34\) 171.805 0.866599
\(35\) −187.214 −0.904140
\(36\) 0 0
\(37\) −392.339 −1.74325 −0.871624 0.490175i \(-0.836933\pi\)
−0.871624 + 0.490175i \(0.836933\pi\)
\(38\) −690.781 −2.94893
\(39\) 0 0
\(40\) −205.558 −0.812540
\(41\) 336.132 1.28037 0.640183 0.768222i \(-0.278858\pi\)
0.640183 + 0.768222i \(0.278858\pi\)
\(42\) 0 0
\(43\) −79.3956 −0.281575 −0.140787 0.990040i \(-0.544963\pi\)
−0.140787 + 0.990040i \(0.544963\pi\)
\(44\) −111.585 −0.382319
\(45\) 0 0
\(46\) 44.3705 0.142219
\(47\) −43.3712 −0.134603 −0.0673015 0.997733i \(-0.521439\pi\)
−0.0673015 + 0.997733i \(0.521439\pi\)
\(48\) 0 0
\(49\) −102.800 −0.299709
\(50\) −93.1225 −0.263390
\(51\) 0 0
\(52\) 690.581 1.84166
\(53\) −23.7667 −0.0615963 −0.0307982 0.999526i \(-0.509805\pi\)
−0.0307982 + 0.999526i \(0.509805\pi\)
\(54\) 0 0
\(55\) −114.015 −0.279522
\(56\) 263.736 0.629343
\(57\) 0 0
\(58\) −1196.07 −2.70779
\(59\) 17.5671 0.0387634 0.0193817 0.999812i \(-0.493830\pi\)
0.0193817 + 0.999812i \(0.493830\pi\)
\(60\) 0 0
\(61\) 679.230 1.42568 0.712840 0.701327i \(-0.247409\pi\)
0.712840 + 0.701327i \(0.247409\pi\)
\(62\) −564.665 −1.15665
\(63\) 0 0
\(64\) −828.527 −1.61822
\(65\) 705.617 1.34648
\(66\) 0 0
\(67\) −890.593 −1.62393 −0.811964 0.583707i \(-0.801602\pi\)
−0.811964 + 0.583707i \(0.801602\pi\)
\(68\) −456.203 −0.813569
\(69\) 0 0
\(70\) 833.515 1.42320
\(71\) −237.928 −0.397703 −0.198851 0.980030i \(-0.563721\pi\)
−0.198851 + 0.980030i \(0.563721\pi\)
\(72\) 0 0
\(73\) 638.534 1.02376 0.511882 0.859056i \(-0.328949\pi\)
0.511882 + 0.859056i \(0.328949\pi\)
\(74\) 1746.78 2.74403
\(75\) 0 0
\(76\) 1834.26 2.76848
\(77\) 146.283 0.216501
\(78\) 0 0
\(79\) −713.642 −1.01634 −0.508171 0.861256i \(-0.669678\pi\)
−0.508171 + 0.861256i \(0.669678\pi\)
\(80\) −227.264 −0.317611
\(81\) 0 0
\(82\) −1496.53 −2.01542
\(83\) 532.550 0.704277 0.352139 0.935948i \(-0.385455\pi\)
0.352139 + 0.935948i \(0.385455\pi\)
\(84\) 0 0
\(85\) −466.136 −0.594818
\(86\) 353.486 0.443225
\(87\) 0 0
\(88\) 160.617 0.194567
\(89\) 1585.59 1.88845 0.944224 0.329303i \(-0.106814\pi\)
0.944224 + 0.329303i \(0.106814\pi\)
\(90\) 0 0
\(91\) −905.324 −1.04290
\(92\) −117.819 −0.133516
\(93\) 0 0
\(94\) 193.098 0.211878
\(95\) 1874.20 2.02410
\(96\) 0 0
\(97\) 1522.63 1.59381 0.796907 0.604102i \(-0.206468\pi\)
0.796907 + 0.604102i \(0.206468\pi\)
\(98\) 457.688 0.471770
\(99\) 0 0
\(100\) 247.272 0.247272
\(101\) 8.88424 0.00875262 0.00437631 0.999990i \(-0.498607\pi\)
0.00437631 + 0.999990i \(0.498607\pi\)
\(102\) 0 0
\(103\) −1479.46 −1.41530 −0.707650 0.706563i \(-0.750245\pi\)
−0.707650 + 0.706563i \(0.750245\pi\)
\(104\) −994.034 −0.937241
\(105\) 0 0
\(106\) 105.814 0.0969584
\(107\) 1015.63 0.917612 0.458806 0.888536i \(-0.348277\pi\)
0.458806 + 0.888536i \(0.348277\pi\)
\(108\) 0 0
\(109\) 390.042 0.342745 0.171373 0.985206i \(-0.445180\pi\)
0.171373 + 0.985206i \(0.445180\pi\)
\(110\) 507.616 0.439994
\(111\) 0 0
\(112\) 291.585 0.246002
\(113\) 1722.71 1.43415 0.717075 0.696996i \(-0.245480\pi\)
0.717075 + 0.696996i \(0.245480\pi\)
\(114\) 0 0
\(115\) −120.384 −0.0976165
\(116\) 3175.99 2.54210
\(117\) 0 0
\(118\) −78.2123 −0.0610171
\(119\) 598.064 0.460710
\(120\) 0 0
\(121\) −1241.91 −0.933067
\(122\) −3024.07 −2.24415
\(123\) 0 0
\(124\) 1499.38 1.08587
\(125\) −1257.29 −0.899643
\(126\) 0 0
\(127\) −2181.69 −1.52436 −0.762181 0.647364i \(-0.775871\pi\)
−0.762181 + 0.647364i \(0.775871\pi\)
\(128\) 1929.58 1.33244
\(129\) 0 0
\(130\) −3141.56 −2.11948
\(131\) 1785.44 1.19080 0.595400 0.803430i \(-0.296994\pi\)
0.595400 + 0.803430i \(0.296994\pi\)
\(132\) 0 0
\(133\) −2404.65 −1.56774
\(134\) 3965.10 2.55621
\(135\) 0 0
\(136\) 656.666 0.414034
\(137\) −133.999 −0.0835641 −0.0417821 0.999127i \(-0.513304\pi\)
−0.0417821 + 0.999127i \(0.513304\pi\)
\(138\) 0 0
\(139\) 2290.40 1.39762 0.698810 0.715307i \(-0.253713\pi\)
0.698810 + 0.715307i \(0.253713\pi\)
\(140\) −2213.27 −1.33611
\(141\) 0 0
\(142\) 1059.31 0.626021
\(143\) −551.349 −0.322420
\(144\) 0 0
\(145\) 3245.14 1.85858
\(146\) −2842.89 −1.61150
\(147\) 0 0
\(148\) −4638.29 −2.57612
\(149\) −2306.25 −1.26802 −0.634010 0.773325i \(-0.718592\pi\)
−0.634010 + 0.773325i \(0.718592\pi\)
\(150\) 0 0
\(151\) −551.248 −0.297086 −0.148543 0.988906i \(-0.547458\pi\)
−0.148543 + 0.988906i \(0.547458\pi\)
\(152\) −2640.27 −1.40891
\(153\) 0 0
\(154\) −651.284 −0.340792
\(155\) 1532.03 0.793907
\(156\) 0 0
\(157\) 742.891 0.377638 0.188819 0.982012i \(-0.439534\pi\)
0.188819 + 0.982012i \(0.439534\pi\)
\(158\) 3177.28 1.59982
\(159\) 0 0
\(160\) 2656.29 1.31249
\(161\) 154.456 0.0756077
\(162\) 0 0
\(163\) −1676.37 −0.805541 −0.402771 0.915301i \(-0.631953\pi\)
−0.402771 + 0.915301i \(0.631953\pi\)
\(164\) 3973.81 1.89209
\(165\) 0 0
\(166\) −2371.02 −1.10860
\(167\) −1282.24 −0.594150 −0.297075 0.954854i \(-0.596011\pi\)
−0.297075 + 0.954854i \(0.596011\pi\)
\(168\) 0 0
\(169\) 1215.21 0.553122
\(170\) 2075.34 0.936300
\(171\) 0 0
\(172\) −938.627 −0.416102
\(173\) −399.531 −0.175583 −0.0877913 0.996139i \(-0.527981\pi\)
−0.0877913 + 0.996139i \(0.527981\pi\)
\(174\) 0 0
\(175\) −324.164 −0.140026
\(176\) 177.578 0.0760535
\(177\) 0 0
\(178\) −7059.36 −2.97259
\(179\) 3206.34 1.33884 0.669422 0.742882i \(-0.266542\pi\)
0.669422 + 0.742882i \(0.266542\pi\)
\(180\) 0 0
\(181\) −3402.47 −1.39726 −0.698628 0.715485i \(-0.746206\pi\)
−0.698628 + 0.715485i \(0.746206\pi\)
\(182\) 4030.69 1.64162
\(183\) 0 0
\(184\) 169.591 0.0679478
\(185\) −4739.29 −1.88346
\(186\) 0 0
\(187\) 364.225 0.142432
\(188\) −512.741 −0.198912
\(189\) 0 0
\(190\) −8344.34 −3.18612
\(191\) −1298.73 −0.492003 −0.246001 0.969269i \(-0.579117\pi\)
−0.246001 + 0.969269i \(0.579117\pi\)
\(192\) 0 0
\(193\) 2380.31 0.887762 0.443881 0.896086i \(-0.353601\pi\)
0.443881 + 0.896086i \(0.353601\pi\)
\(194\) −6779.08 −2.50881
\(195\) 0 0
\(196\) −1215.32 −0.442901
\(197\) −4261.27 −1.54113 −0.770566 0.637360i \(-0.780026\pi\)
−0.770566 + 0.637360i \(0.780026\pi\)
\(198\) 0 0
\(199\) 373.752 0.133138 0.0665692 0.997782i \(-0.478795\pi\)
0.0665692 + 0.997782i \(0.478795\pi\)
\(200\) −355.928 −0.125840
\(201\) 0 0
\(202\) −39.5545 −0.0137774
\(203\) −4163.60 −1.43954
\(204\) 0 0
\(205\) 4060.33 1.38335
\(206\) 6586.88 2.22782
\(207\) 0 0
\(208\) −1099.00 −0.366355
\(209\) −1464.45 −0.484679
\(210\) 0 0
\(211\) −1747.25 −0.570074 −0.285037 0.958516i \(-0.592006\pi\)
−0.285037 + 0.958516i \(0.592006\pi\)
\(212\) −280.973 −0.0910252
\(213\) 0 0
\(214\) −4521.79 −1.44441
\(215\) −959.065 −0.304222
\(216\) 0 0
\(217\) −1965.63 −0.614911
\(218\) −1736.55 −0.539513
\(219\) 0 0
\(220\) −1347.90 −0.413069
\(221\) −2254.13 −0.686105
\(222\) 0 0
\(223\) −2024.31 −0.607882 −0.303941 0.952691i \(-0.598303\pi\)
−0.303941 + 0.952691i \(0.598303\pi\)
\(224\) −3408.09 −1.01657
\(225\) 0 0
\(226\) −7669.87 −2.25749
\(227\) 4270.42 1.24862 0.624312 0.781175i \(-0.285379\pi\)
0.624312 + 0.781175i \(0.285379\pi\)
\(228\) 0 0
\(229\) −4802.09 −1.38572 −0.692862 0.721070i \(-0.743651\pi\)
−0.692862 + 0.721070i \(0.743651\pi\)
\(230\) 535.976 0.153657
\(231\) 0 0
\(232\) −4571.57 −1.29370
\(233\) −3112.20 −0.875051 −0.437526 0.899206i \(-0.644145\pi\)
−0.437526 + 0.899206i \(0.644145\pi\)
\(234\) 0 0
\(235\) −523.905 −0.145429
\(236\) 207.681 0.0572833
\(237\) 0 0
\(238\) −2662.71 −0.725200
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 4310.85 1.15223 0.576113 0.817370i \(-0.304569\pi\)
0.576113 + 0.817370i \(0.304569\pi\)
\(242\) 5529.25 1.46873
\(243\) 0 0
\(244\) 8029.96 2.10682
\(245\) −1241.78 −0.323815
\(246\) 0 0
\(247\) 9063.23 2.33473
\(248\) −2158.24 −0.552613
\(249\) 0 0
\(250\) 5597.71 1.41612
\(251\) −6020.03 −1.51387 −0.756935 0.653491i \(-0.773304\pi\)
−0.756935 + 0.653491i \(0.773304\pi\)
\(252\) 0 0
\(253\) 94.0648 0.0233747
\(254\) 9713.35 2.39949
\(255\) 0 0
\(256\) −1962.67 −0.479167
\(257\) 1622.09 0.393710 0.196855 0.980433i \(-0.436927\pi\)
0.196855 + 0.980433i \(0.436927\pi\)
\(258\) 0 0
\(259\) 6080.62 1.45881
\(260\) 8341.92 1.98978
\(261\) 0 0
\(262\) −7949.16 −1.87443
\(263\) 5730.73 1.34362 0.671809 0.740724i \(-0.265517\pi\)
0.671809 + 0.740724i \(0.265517\pi\)
\(264\) 0 0
\(265\) −287.091 −0.0665505
\(266\) 10706.0 2.46777
\(267\) 0 0
\(268\) −10528.7 −2.39979
\(269\) 6414.10 1.45381 0.726904 0.686739i \(-0.240959\pi\)
0.726904 + 0.686739i \(0.240959\pi\)
\(270\) 0 0
\(271\) 992.636 0.222503 0.111252 0.993792i \(-0.464514\pi\)
0.111252 + 0.993792i \(0.464514\pi\)
\(272\) 726.007 0.161841
\(273\) 0 0
\(274\) 596.590 0.131538
\(275\) −197.419 −0.0432901
\(276\) 0 0
\(277\) 6606.52 1.43302 0.716511 0.697575i \(-0.245738\pi\)
0.716511 + 0.697575i \(0.245738\pi\)
\(278\) −10197.3 −2.19998
\(279\) 0 0
\(280\) 3185.82 0.679961
\(281\) −6616.73 −1.40470 −0.702351 0.711831i \(-0.747866\pi\)
−0.702351 + 0.711831i \(0.747866\pi\)
\(282\) 0 0
\(283\) −4172.85 −0.876502 −0.438251 0.898853i \(-0.644402\pi\)
−0.438251 + 0.898853i \(0.644402\pi\)
\(284\) −2812.83 −0.587713
\(285\) 0 0
\(286\) 2454.72 0.507520
\(287\) −5209.51 −1.07145
\(288\) 0 0
\(289\) −3423.90 −0.696907
\(290\) −14448.1 −2.92558
\(291\) 0 0
\(292\) 7548.85 1.51289
\(293\) −2788.75 −0.556043 −0.278021 0.960575i \(-0.589679\pi\)
−0.278021 + 0.960575i \(0.589679\pi\)
\(294\) 0 0
\(295\) 212.203 0.0418811
\(296\) 6676.44 1.31101
\(297\) 0 0
\(298\) 10267.9 1.99598
\(299\) −582.152 −0.112598
\(300\) 0 0
\(301\) 1230.50 0.235631
\(302\) 2454.27 0.467641
\(303\) 0 0
\(304\) −2919.07 −0.550724
\(305\) 8204.80 1.54035
\(306\) 0 0
\(307\) 467.489 0.0869088 0.0434544 0.999055i \(-0.486164\pi\)
0.0434544 + 0.999055i \(0.486164\pi\)
\(308\) 1729.38 0.319938
\(309\) 0 0
\(310\) −6820.91 −1.24968
\(311\) 9268.32 1.68990 0.844949 0.534847i \(-0.179631\pi\)
0.844949 + 0.534847i \(0.179631\pi\)
\(312\) 0 0
\(313\) 5146.60 0.929403 0.464702 0.885467i \(-0.346162\pi\)
0.464702 + 0.885467i \(0.346162\pi\)
\(314\) −3307.50 −0.594437
\(315\) 0 0
\(316\) −8436.78 −1.50192
\(317\) −3101.92 −0.549594 −0.274797 0.961502i \(-0.588611\pi\)
−0.274797 + 0.961502i \(0.588611\pi\)
\(318\) 0 0
\(319\) −2535.66 −0.445046
\(320\) −10008.3 −1.74837
\(321\) 0 0
\(322\) −687.670 −0.119014
\(323\) −5987.24 −1.03139
\(324\) 0 0
\(325\) 1221.79 0.208532
\(326\) 7463.54 1.26800
\(327\) 0 0
\(328\) −5719.97 −0.962904
\(329\) 672.183 0.112640
\(330\) 0 0
\(331\) 8290.74 1.37674 0.688369 0.725361i \(-0.258327\pi\)
0.688369 + 0.725361i \(0.258327\pi\)
\(332\) 6295.89 1.04076
\(333\) 0 0
\(334\) 5708.82 0.935247
\(335\) −10758.0 −1.75454
\(336\) 0 0
\(337\) 6843.83 1.10625 0.553126 0.833097i \(-0.313435\pi\)
0.553126 + 0.833097i \(0.313435\pi\)
\(338\) −5410.36 −0.870666
\(339\) 0 0
\(340\) −5510.73 −0.879004
\(341\) −1197.08 −0.190105
\(342\) 0 0
\(343\) 6909.18 1.08764
\(344\) 1351.08 0.211759
\(345\) 0 0
\(346\) 1778.79 0.276383
\(347\) 8518.74 1.31790 0.658948 0.752189i \(-0.271002\pi\)
0.658948 + 0.752189i \(0.271002\pi\)
\(348\) 0 0
\(349\) −5096.98 −0.781762 −0.390881 0.920441i \(-0.627830\pi\)
−0.390881 + 0.920441i \(0.627830\pi\)
\(350\) 1443.25 0.220414
\(351\) 0 0
\(352\) −2075.55 −0.314282
\(353\) 6701.17 1.01039 0.505194 0.863006i \(-0.331421\pi\)
0.505194 + 0.863006i \(0.331421\pi\)
\(354\) 0 0
\(355\) −2874.07 −0.429690
\(356\) 18745.1 2.79069
\(357\) 0 0
\(358\) −14275.3 −2.10746
\(359\) 6336.49 0.931551 0.465776 0.884903i \(-0.345775\pi\)
0.465776 + 0.884903i \(0.345775\pi\)
\(360\) 0 0
\(361\) 17214.0 2.50970
\(362\) 15148.5 2.19941
\(363\) 0 0
\(364\) −10702.9 −1.54116
\(365\) 7713.22 1.10610
\(366\) 0 0
\(367\) 4634.23 0.659142 0.329571 0.944131i \(-0.393096\pi\)
0.329571 + 0.944131i \(0.393096\pi\)
\(368\) 187.499 0.0265599
\(369\) 0 0
\(370\) 21100.3 2.96474
\(371\) 368.345 0.0515459
\(372\) 0 0
\(373\) −12169.6 −1.68933 −0.844665 0.535296i \(-0.820200\pi\)
−0.844665 + 0.535296i \(0.820200\pi\)
\(374\) −1621.61 −0.224201
\(375\) 0 0
\(376\) 738.048 0.101229
\(377\) 15692.8 2.14382
\(378\) 0 0
\(379\) 6615.75 0.896645 0.448322 0.893872i \(-0.352022\pi\)
0.448322 + 0.893872i \(0.352022\pi\)
\(380\) 22157.1 2.99115
\(381\) 0 0
\(382\) 5782.20 0.774458
\(383\) −14005.4 −1.86852 −0.934260 0.356594i \(-0.883938\pi\)
−0.934260 + 0.356594i \(0.883938\pi\)
\(384\) 0 0
\(385\) 1767.04 0.233914
\(386\) −10597.6 −1.39742
\(387\) 0 0
\(388\) 18000.8 2.35529
\(389\) 14343.8 1.86956 0.934779 0.355229i \(-0.115597\pi\)
0.934779 + 0.355229i \(0.115597\pi\)
\(390\) 0 0
\(391\) 384.574 0.0497410
\(392\) 1749.35 0.225397
\(393\) 0 0
\(394\) 18972.1 2.42589
\(395\) −8620.48 −1.09809
\(396\) 0 0
\(397\) 8729.84 1.10362 0.551811 0.833969i \(-0.313937\pi\)
0.551811 + 0.833969i \(0.313937\pi\)
\(398\) −1664.02 −0.209572
\(399\) 0 0
\(400\) −393.513 −0.0491891
\(401\) 3137.18 0.390681 0.195341 0.980735i \(-0.437419\pi\)
0.195341 + 0.980735i \(0.437419\pi\)
\(402\) 0 0
\(403\) 7408.55 0.915748
\(404\) 105.031 0.0129343
\(405\) 0 0
\(406\) 18537.2 2.26597
\(407\) 3703.14 0.451002
\(408\) 0 0
\(409\) −10168.2 −1.22931 −0.614653 0.788798i \(-0.710704\pi\)
−0.614653 + 0.788798i \(0.710704\pi\)
\(410\) −18077.4 −2.17752
\(411\) 0 0
\(412\) −17490.5 −2.09149
\(413\) −272.261 −0.0324385
\(414\) 0 0
\(415\) 6432.98 0.760922
\(416\) 12845.2 1.51392
\(417\) 0 0
\(418\) 6520.03 0.762930
\(419\) −7237.46 −0.843850 −0.421925 0.906631i \(-0.638645\pi\)
−0.421925 + 0.906631i \(0.638645\pi\)
\(420\) 0 0
\(421\) 5373.23 0.622032 0.311016 0.950405i \(-0.399331\pi\)
0.311016 + 0.950405i \(0.399331\pi\)
\(422\) 7779.12 0.897350
\(423\) 0 0
\(424\) 404.438 0.0463237
\(425\) −807.124 −0.0921207
\(426\) 0 0
\(427\) −10527.0 −1.19306
\(428\) 12006.9 1.35602
\(429\) 0 0
\(430\) 4269.95 0.478873
\(431\) 1674.28 0.187117 0.0935585 0.995614i \(-0.470176\pi\)
0.0935585 + 0.995614i \(0.470176\pi\)
\(432\) 0 0
\(433\) −11105.6 −1.23257 −0.616284 0.787524i \(-0.711363\pi\)
−0.616284 + 0.787524i \(0.711363\pi\)
\(434\) 8751.39 0.967927
\(435\) 0 0
\(436\) 4611.13 0.506498
\(437\) −1546.26 −0.169263
\(438\) 0 0
\(439\) 16347.4 1.77726 0.888630 0.458626i \(-0.151658\pi\)
0.888630 + 0.458626i \(0.151658\pi\)
\(440\) 1940.19 0.210215
\(441\) 0 0
\(442\) 10035.9 1.07999
\(443\) −8720.88 −0.935309 −0.467654 0.883911i \(-0.654901\pi\)
−0.467654 + 0.883911i \(0.654901\pi\)
\(444\) 0 0
\(445\) 19153.2 2.04034
\(446\) 9012.64 0.956863
\(447\) 0 0
\(448\) 12840.8 1.35418
\(449\) −6224.16 −0.654201 −0.327101 0.944990i \(-0.606072\pi\)
−0.327101 + 0.944990i \(0.606072\pi\)
\(450\) 0 0
\(451\) −3172.63 −0.331249
\(452\) 20366.2 2.11934
\(453\) 0 0
\(454\) −19012.8 −1.96545
\(455\) −10935.9 −1.12678
\(456\) 0 0
\(457\) 11792.8 1.20709 0.603547 0.797328i \(-0.293754\pi\)
0.603547 + 0.797328i \(0.293754\pi\)
\(458\) 21379.9 2.18126
\(459\) 0 0
\(460\) −1423.20 −0.144255
\(461\) 7664.01 0.774292 0.387146 0.922018i \(-0.373461\pi\)
0.387146 + 0.922018i \(0.373461\pi\)
\(462\) 0 0
\(463\) −2555.99 −0.256559 −0.128279 0.991738i \(-0.540945\pi\)
−0.128279 + 0.991738i \(0.540945\pi\)
\(464\) −5054.31 −0.505691
\(465\) 0 0
\(466\) 13856.2 1.37741
\(467\) −3113.80 −0.308543 −0.154272 0.988028i \(-0.549303\pi\)
−0.154272 + 0.988028i \(0.549303\pi\)
\(468\) 0 0
\(469\) 13802.7 1.35896
\(470\) 2332.54 0.228919
\(471\) 0 0
\(472\) −298.939 −0.0291521
\(473\) 749.385 0.0728473
\(474\) 0 0
\(475\) 3245.22 0.313476
\(476\) 7070.40 0.680822
\(477\) 0 0
\(478\) 1064.08 0.101820
\(479\) −5888.63 −0.561708 −0.280854 0.959750i \(-0.590618\pi\)
−0.280854 + 0.959750i \(0.590618\pi\)
\(480\) 0 0
\(481\) −22918.2 −2.17251
\(482\) −19192.8 −1.81371
\(483\) 0 0
\(484\) −14682.1 −1.37886
\(485\) 18392.8 1.72200
\(486\) 0 0
\(487\) 8277.47 0.770201 0.385100 0.922875i \(-0.374167\pi\)
0.385100 + 0.922875i \(0.374167\pi\)
\(488\) −11558.5 −1.07219
\(489\) 0 0
\(490\) 5528.67 0.509714
\(491\) 13500.7 1.24089 0.620447 0.784248i \(-0.286951\pi\)
0.620447 + 0.784248i \(0.286951\pi\)
\(492\) 0 0
\(493\) −10366.8 −0.947051
\(494\) −40351.4 −3.67509
\(495\) 0 0
\(496\) −2386.14 −0.216009
\(497\) 3687.51 0.332811
\(498\) 0 0
\(499\) −18025.8 −1.61713 −0.808563 0.588410i \(-0.799754\pi\)
−0.808563 + 0.588410i \(0.799754\pi\)
\(500\) −14863.9 −1.32947
\(501\) 0 0
\(502\) 26802.4 2.38297
\(503\) 10382.8 0.920375 0.460187 0.887822i \(-0.347782\pi\)
0.460187 + 0.887822i \(0.347782\pi\)
\(504\) 0 0
\(505\) 107.318 0.00945659
\(506\) −418.796 −0.0367940
\(507\) 0 0
\(508\) −25792.3 −2.25265
\(509\) −2917.87 −0.254091 −0.127045 0.991897i \(-0.540549\pi\)
−0.127045 + 0.991897i \(0.540549\pi\)
\(510\) 0 0
\(511\) −9896.24 −0.856720
\(512\) −6698.43 −0.578187
\(513\) 0 0
\(514\) −7221.89 −0.619736
\(515\) −17871.3 −1.52913
\(516\) 0 0
\(517\) 409.365 0.0348237
\(518\) −27072.2 −2.29630
\(519\) 0 0
\(520\) −12007.5 −1.01262
\(521\) −5398.65 −0.453972 −0.226986 0.973898i \(-0.572887\pi\)
−0.226986 + 0.973898i \(0.572887\pi\)
\(522\) 0 0
\(523\) −4608.30 −0.385290 −0.192645 0.981269i \(-0.561707\pi\)
−0.192645 + 0.981269i \(0.561707\pi\)
\(524\) 21107.8 1.75973
\(525\) 0 0
\(526\) −25514.4 −2.11498
\(527\) −4894.15 −0.404540
\(528\) 0 0
\(529\) −12067.7 −0.991837
\(530\) 1278.19 0.104757
\(531\) 0 0
\(532\) −28428.1 −2.31676
\(533\) 19634.9 1.59565
\(534\) 0 0
\(535\) 12268.4 0.991415
\(536\) 15155.2 1.22128
\(537\) 0 0
\(538\) −28556.9 −2.28843
\(539\) 970.293 0.0775389
\(540\) 0 0
\(541\) −3575.27 −0.284127 −0.142064 0.989858i \(-0.545374\pi\)
−0.142064 + 0.989858i \(0.545374\pi\)
\(542\) −4419.42 −0.350240
\(543\) 0 0
\(544\) −8485.67 −0.668787
\(545\) 4711.54 0.370312
\(546\) 0 0
\(547\) 4167.64 0.325768 0.162884 0.986645i \(-0.447920\pi\)
0.162884 + 0.986645i \(0.447920\pi\)
\(548\) −1584.15 −0.123488
\(549\) 0 0
\(550\) 878.948 0.0681427
\(551\) 41681.9 3.22270
\(552\) 0 0
\(553\) 11060.3 0.850509
\(554\) −29413.6 −2.25571
\(555\) 0 0
\(556\) 27077.5 2.06536
\(557\) 8423.86 0.640809 0.320404 0.947281i \(-0.396181\pi\)
0.320404 + 0.947281i \(0.396181\pi\)
\(558\) 0 0
\(559\) −4637.82 −0.350911
\(560\) 3522.23 0.265788
\(561\) 0 0
\(562\) 29459.1 2.21113
\(563\) 23644.9 1.77000 0.885002 0.465587i \(-0.154157\pi\)
0.885002 + 0.465587i \(0.154157\pi\)
\(564\) 0 0
\(565\) 20809.6 1.54950
\(566\) 18578.4 1.37970
\(567\) 0 0
\(568\) 4048.83 0.299094
\(569\) 14266.1 1.05108 0.525540 0.850769i \(-0.323863\pi\)
0.525540 + 0.850769i \(0.323863\pi\)
\(570\) 0 0
\(571\) 7683.48 0.563124 0.281562 0.959543i \(-0.409148\pi\)
0.281562 + 0.959543i \(0.409148\pi\)
\(572\) −6518.13 −0.476463
\(573\) 0 0
\(574\) 23193.8 1.68657
\(575\) −208.448 −0.0151181
\(576\) 0 0
\(577\) 11833.0 0.853749 0.426874 0.904311i \(-0.359615\pi\)
0.426874 + 0.904311i \(0.359615\pi\)
\(578\) 15243.9 1.09700
\(579\) 0 0
\(580\) 38364.6 2.74656
\(581\) −8253.67 −0.589363
\(582\) 0 0
\(583\) 224.325 0.0159358
\(584\) −10865.9 −0.769925
\(585\) 0 0
\(586\) 12416.1 0.875263
\(587\) −986.552 −0.0693686 −0.0346843 0.999398i \(-0.511043\pi\)
−0.0346843 + 0.999398i \(0.511043\pi\)
\(588\) 0 0
\(589\) 19678.0 1.37660
\(590\) −944.770 −0.0659247
\(591\) 0 0
\(592\) 7381.44 0.512459
\(593\) 6807.18 0.471395 0.235698 0.971826i \(-0.424263\pi\)
0.235698 + 0.971826i \(0.424263\pi\)
\(594\) 0 0
\(595\) 7224.36 0.497764
\(596\) −27264.8 −1.87384
\(597\) 0 0
\(598\) 2591.86 0.177239
\(599\) −54.1935 −0.00369664 −0.00184832 0.999998i \(-0.500588\pi\)
−0.00184832 + 0.999998i \(0.500588\pi\)
\(600\) 0 0
\(601\) 44.6639 0.00303141 0.00151570 0.999999i \(-0.499518\pi\)
0.00151570 + 0.999999i \(0.499518\pi\)
\(602\) −5478.45 −0.370906
\(603\) 0 0
\(604\) −6516.94 −0.439024
\(605\) −15001.8 −1.00811
\(606\) 0 0
\(607\) 1299.31 0.0868818 0.0434409 0.999056i \(-0.486168\pi\)
0.0434409 + 0.999056i \(0.486168\pi\)
\(608\) 34118.5 2.27580
\(609\) 0 0
\(610\) −36529.5 −2.42465
\(611\) −2533.49 −0.167748
\(612\) 0 0
\(613\) 3353.42 0.220951 0.110476 0.993879i \(-0.464763\pi\)
0.110476 + 0.993879i \(0.464763\pi\)
\(614\) −2081.36 −0.136802
\(615\) 0 0
\(616\) −2489.31 −0.162820
\(617\) 24209.6 1.57964 0.789822 0.613336i \(-0.210173\pi\)
0.789822 + 0.613336i \(0.210173\pi\)
\(618\) 0 0
\(619\) 53.0613 0.00344542 0.00172271 0.999999i \(-0.499452\pi\)
0.00172271 + 0.999999i \(0.499452\pi\)
\(620\) 18111.9 1.17321
\(621\) 0 0
\(622\) −41264.5 −2.66006
\(623\) −24574.0 −1.58032
\(624\) 0 0
\(625\) −17802.0 −1.13933
\(626\) −22913.8 −1.46297
\(627\) 0 0
\(628\) 8782.57 0.558061
\(629\) 15139.9 0.959726
\(630\) 0 0
\(631\) 899.565 0.0567530 0.0283765 0.999597i \(-0.490966\pi\)
0.0283765 + 0.999597i \(0.490966\pi\)
\(632\) 12144.1 0.764342
\(633\) 0 0
\(634\) 13810.4 0.865112
\(635\) −26353.9 −1.64697
\(636\) 0 0
\(637\) −6004.98 −0.373510
\(638\) 11289.3 0.700544
\(639\) 0 0
\(640\) 23308.5 1.43961
\(641\) −1537.41 −0.0947331 −0.0473665 0.998878i \(-0.515083\pi\)
−0.0473665 + 0.998878i \(0.515083\pi\)
\(642\) 0 0
\(643\) 25594.7 1.56976 0.784881 0.619647i \(-0.212724\pi\)
0.784881 + 0.619647i \(0.212724\pi\)
\(644\) 1826.00 0.111731
\(645\) 0 0
\(646\) 26656.4 1.62350
\(647\) 15216.0 0.924580 0.462290 0.886729i \(-0.347028\pi\)
0.462290 + 0.886729i \(0.347028\pi\)
\(648\) 0 0
\(649\) −165.809 −0.0100286
\(650\) −5439.67 −0.328248
\(651\) 0 0
\(652\) −19818.3 −1.19040
\(653\) 29819.4 1.78702 0.893510 0.449044i \(-0.148235\pi\)
0.893510 + 0.449044i \(0.148235\pi\)
\(654\) 0 0
\(655\) 21567.4 1.28658
\(656\) −6323.97 −0.376387
\(657\) 0 0
\(658\) −2992.70 −0.177306
\(659\) 28251.3 1.66998 0.834988 0.550269i \(-0.185475\pi\)
0.834988 + 0.550269i \(0.185475\pi\)
\(660\) 0 0
\(661\) 14182.3 0.834534 0.417267 0.908784i \(-0.362988\pi\)
0.417267 + 0.908784i \(0.362988\pi\)
\(662\) −36912.1 −2.16711
\(663\) 0 0
\(664\) −9062.42 −0.529654
\(665\) −29047.1 −1.69383
\(666\) 0 0
\(667\) −2677.32 −0.155422
\(668\) −15158.9 −0.878016
\(669\) 0 0
\(670\) 47896.8 2.76181
\(671\) −6410.99 −0.368843
\(672\) 0 0
\(673\) −22102.0 −1.26593 −0.632963 0.774182i \(-0.718161\pi\)
−0.632963 + 0.774182i \(0.718161\pi\)
\(674\) −30470.2 −1.74134
\(675\) 0 0
\(676\) 14366.4 0.817387
\(677\) 11041.8 0.626839 0.313419 0.949615i \(-0.398525\pi\)
0.313419 + 0.949615i \(0.398525\pi\)
\(678\) 0 0
\(679\) −23598.4 −1.33376
\(680\) 7932.25 0.447335
\(681\) 0 0
\(682\) 5329.66 0.299242
\(683\) −24708.8 −1.38427 −0.692135 0.721768i \(-0.743330\pi\)
−0.692135 + 0.721768i \(0.743330\pi\)
\(684\) 0 0
\(685\) −1618.65 −0.0902851
\(686\) −30761.1 −1.71205
\(687\) 0 0
\(688\) 1493.74 0.0827739
\(689\) −1388.31 −0.0767640
\(690\) 0 0
\(691\) −11954.9 −0.658156 −0.329078 0.944303i \(-0.606738\pi\)
−0.329078 + 0.944303i \(0.606738\pi\)
\(692\) −4723.32 −0.259470
\(693\) 0 0
\(694\) −37927.2 −2.07449
\(695\) 27667.0 1.51003
\(696\) 0 0
\(697\) −12970.9 −0.704892
\(698\) 22692.8 1.23057
\(699\) 0 0
\(700\) −3832.32 −0.206926
\(701\) −4351.75 −0.234470 −0.117235 0.993104i \(-0.537403\pi\)
−0.117235 + 0.993104i \(0.537403\pi\)
\(702\) 0 0
\(703\) −60873.3 −3.26583
\(704\) 7820.16 0.418655
\(705\) 0 0
\(706\) −29835.0 −1.59045
\(707\) −137.691 −0.00732449
\(708\) 0 0
\(709\) 29815.0 1.57931 0.789653 0.613554i \(-0.210261\pi\)
0.789653 + 0.613554i \(0.210261\pi\)
\(710\) 12796.0 0.676372
\(711\) 0 0
\(712\) −26982.0 −1.42021
\(713\) −1263.96 −0.0663896
\(714\) 0 0
\(715\) −6660.06 −0.348353
\(716\) 37905.8 1.97850
\(717\) 0 0
\(718\) −28211.3 −1.46635
\(719\) −29875.8 −1.54962 −0.774811 0.632193i \(-0.782155\pi\)
−0.774811 + 0.632193i \(0.782155\pi\)
\(720\) 0 0
\(721\) 22929.3 1.18437
\(722\) −76640.3 −3.95050
\(723\) 0 0
\(724\) −40224.5 −2.06482
\(725\) 5619.03 0.287842
\(726\) 0 0
\(727\) 21050.1 1.07387 0.536936 0.843623i \(-0.319582\pi\)
0.536936 + 0.843623i \(0.319582\pi\)
\(728\) 15405.9 0.784315
\(729\) 0 0
\(730\) −34340.8 −1.74111
\(731\) 3063.78 0.155018
\(732\) 0 0
\(733\) 18976.2 0.956212 0.478106 0.878302i \(-0.341324\pi\)
0.478106 + 0.878302i \(0.341324\pi\)
\(734\) −20632.6 −1.03755
\(735\) 0 0
\(736\) −2191.51 −0.109756
\(737\) 8405.97 0.420133
\(738\) 0 0
\(739\) 8704.26 0.433277 0.216638 0.976252i \(-0.430491\pi\)
0.216638 + 0.976252i \(0.430491\pi\)
\(740\) −56028.6 −2.78331
\(741\) 0 0
\(742\) −1639.95 −0.0811380
\(743\) −40169.6 −1.98342 −0.991709 0.128502i \(-0.958983\pi\)
−0.991709 + 0.128502i \(0.958983\pi\)
\(744\) 0 0
\(745\) −27858.5 −1.37001
\(746\) 54181.7 2.65916
\(747\) 0 0
\(748\) 4305.93 0.210482
\(749\) −15740.6 −0.767889
\(750\) 0 0
\(751\) 13712.0 0.666255 0.333127 0.942882i \(-0.391896\pi\)
0.333127 + 0.942882i \(0.391896\pi\)
\(752\) 815.983 0.0395689
\(753\) 0 0
\(754\) −69867.6 −3.37457
\(755\) −6658.84 −0.320980
\(756\) 0 0
\(757\) −16061.4 −0.771153 −0.385576 0.922676i \(-0.625997\pi\)
−0.385576 + 0.922676i \(0.625997\pi\)
\(758\) −29454.7 −1.41140
\(759\) 0 0
\(760\) −31893.3 −1.52223
\(761\) 29960.0 1.42713 0.713567 0.700587i \(-0.247078\pi\)
0.713567 + 0.700587i \(0.247078\pi\)
\(762\) 0 0
\(763\) −6045.01 −0.286821
\(764\) −15353.7 −0.727066
\(765\) 0 0
\(766\) 62355.0 2.94122
\(767\) 1026.17 0.0483086
\(768\) 0 0
\(769\) 9759.16 0.457639 0.228819 0.973469i \(-0.426513\pi\)
0.228819 + 0.973469i \(0.426513\pi\)
\(770\) −7867.23 −0.368202
\(771\) 0 0
\(772\) 28140.3 1.31191
\(773\) −25860.4 −1.20328 −0.601638 0.798769i \(-0.705485\pi\)
−0.601638 + 0.798769i \(0.705485\pi\)
\(774\) 0 0
\(775\) 2652.74 0.122954
\(776\) −25910.7 −1.19863
\(777\) 0 0
\(778\) −63861.5 −2.94286
\(779\) 52152.5 2.39866
\(780\) 0 0
\(781\) 2245.72 0.102891
\(782\) −1712.20 −0.0782970
\(783\) 0 0
\(784\) 1934.08 0.0881048
\(785\) 8973.80 0.408011
\(786\) 0 0
\(787\) 28918.2 1.30981 0.654906 0.755710i \(-0.272708\pi\)
0.654906 + 0.755710i \(0.272708\pi\)
\(788\) −50377.4 −2.27744
\(789\) 0 0
\(790\) 38380.2 1.72849
\(791\) −26699.2 −1.20015
\(792\) 0 0
\(793\) 39676.6 1.77674
\(794\) −38867.1 −1.73720
\(795\) 0 0
\(796\) 4418.55 0.196748
\(797\) −17215.9 −0.765142 −0.382571 0.923926i \(-0.624961\pi\)
−0.382571 + 0.923926i \(0.624961\pi\)
\(798\) 0 0
\(799\) 1673.64 0.0741042
\(800\) 4599.43 0.203268
\(801\) 0 0
\(802\) −13967.4 −0.614969
\(803\) −6026.88 −0.264862
\(804\) 0 0
\(805\) 1865.76 0.0816888
\(806\) −32984.4 −1.44147
\(807\) 0 0
\(808\) −151.183 −0.00658243
\(809\) −8937.15 −0.388397 −0.194199 0.980962i \(-0.562211\pi\)
−0.194199 + 0.980962i \(0.562211\pi\)
\(810\) 0 0
\(811\) −31148.1 −1.34865 −0.674326 0.738434i \(-0.735566\pi\)
−0.674326 + 0.738434i \(0.735566\pi\)
\(812\) −49222.7 −2.12731
\(813\) 0 0
\(814\) −16487.2 −0.709920
\(815\) −20249.8 −0.870331
\(816\) 0 0
\(817\) −12318.6 −0.527507
\(818\) 45271.0 1.93504
\(819\) 0 0
\(820\) 48001.9 2.04427
\(821\) −26976.7 −1.14676 −0.573382 0.819288i \(-0.694369\pi\)
−0.573382 + 0.819288i \(0.694369\pi\)
\(822\) 0 0
\(823\) −42010.5 −1.77934 −0.889668 0.456608i \(-0.849064\pi\)
−0.889668 + 0.456608i \(0.849064\pi\)
\(824\) 25176.1 1.06438
\(825\) 0 0
\(826\) 1212.16 0.0510612
\(827\) 19180.8 0.806508 0.403254 0.915088i \(-0.367879\pi\)
0.403254 + 0.915088i \(0.367879\pi\)
\(828\) 0 0
\(829\) 29952.7 1.25489 0.627443 0.778663i \(-0.284102\pi\)
0.627443 + 0.778663i \(0.284102\pi\)
\(830\) −28641.0 −1.19776
\(831\) 0 0
\(832\) −48397.7 −2.01669
\(833\) 3966.94 0.165001
\(834\) 0 0
\(835\) −15489.0 −0.641937
\(836\) −17312.9 −0.716244
\(837\) 0 0
\(838\) 32222.7 1.32830
\(839\) −3668.38 −0.150950 −0.0754748 0.997148i \(-0.524047\pi\)
−0.0754748 + 0.997148i \(0.524047\pi\)
\(840\) 0 0
\(841\) 47782.3 1.95918
\(842\) −23922.7 −0.979136
\(843\) 0 0
\(844\) −20656.3 −0.842438
\(845\) 14679.2 0.597609
\(846\) 0 0
\(847\) 19247.6 0.780822
\(848\) 447.145 0.0181073
\(849\) 0 0
\(850\) 3593.49 0.145007
\(851\) 3910.03 0.157502
\(852\) 0 0
\(853\) 44013.3 1.76669 0.883345 0.468724i \(-0.155286\pi\)
0.883345 + 0.468724i \(0.155286\pi\)
\(854\) 46868.2 1.87798
\(855\) 0 0
\(856\) −17283.0 −0.690093
\(857\) 12232.4 0.487574 0.243787 0.969829i \(-0.421610\pi\)
0.243787 + 0.969829i \(0.421610\pi\)
\(858\) 0 0
\(859\) 45812.7 1.81969 0.909843 0.414954i \(-0.136202\pi\)
0.909843 + 0.414954i \(0.136202\pi\)
\(860\) −11338.2 −0.449569
\(861\) 0 0
\(862\) −7454.26 −0.294540
\(863\) 33.9685 0.00133986 0.000669932 1.00000i \(-0.499787\pi\)
0.000669932 1.00000i \(0.499787\pi\)
\(864\) 0 0
\(865\) −4826.16 −0.189705
\(866\) 49444.5 1.94018
\(867\) 0 0
\(868\) −23238.0 −0.908696
\(869\) 6735.80 0.262942
\(870\) 0 0
\(871\) −52023.2 −2.02381
\(872\) −6637.35 −0.257762
\(873\) 0 0
\(874\) 6884.29 0.266435
\(875\) 19486.0 0.752852
\(876\) 0 0
\(877\) −16690.0 −0.642624 −0.321312 0.946973i \(-0.604124\pi\)
−0.321312 + 0.946973i \(0.604124\pi\)
\(878\) −72781.8 −2.79757
\(879\) 0 0
\(880\) 2145.06 0.0821705
\(881\) 7575.04 0.289682 0.144841 0.989455i \(-0.453733\pi\)
0.144841 + 0.989455i \(0.453733\pi\)
\(882\) 0 0
\(883\) −19841.4 −0.756191 −0.378096 0.925767i \(-0.623421\pi\)
−0.378096 + 0.925767i \(0.623421\pi\)
\(884\) −26648.7 −1.01391
\(885\) 0 0
\(886\) 38827.2 1.47226
\(887\) −6016.47 −0.227749 −0.113874 0.993495i \(-0.536326\pi\)
−0.113874 + 0.993495i \(0.536326\pi\)
\(888\) 0 0
\(889\) 33812.7 1.27564
\(890\) −85274.1 −3.21168
\(891\) 0 0
\(892\) −23931.7 −0.898309
\(893\) −6729.25 −0.252168
\(894\) 0 0
\(895\) 38731.2 1.44653
\(896\) −29905.3 −1.11503
\(897\) 0 0
\(898\) 27711.3 1.02977
\(899\) 34072.0 1.26403
\(900\) 0 0
\(901\) 917.128 0.0339112
\(902\) 14125.2 0.521416
\(903\) 0 0
\(904\) −29315.4 −1.07856
\(905\) −41100.3 −1.50964
\(906\) 0 0
\(907\) −33324.2 −1.21997 −0.609985 0.792413i \(-0.708825\pi\)
−0.609985 + 0.792413i \(0.708825\pi\)
\(908\) 50485.5 1.84518
\(909\) 0 0
\(910\) 48689.0 1.77365
\(911\) −38706.7 −1.40770 −0.703848 0.710351i \(-0.748536\pi\)
−0.703848 + 0.710351i \(0.748536\pi\)
\(912\) 0 0
\(913\) −5026.54 −0.182206
\(914\) −52503.8 −1.90008
\(915\) 0 0
\(916\) −56771.0 −2.04778
\(917\) −27671.5 −0.996501
\(918\) 0 0
\(919\) 32552.7 1.16846 0.584230 0.811588i \(-0.301397\pi\)
0.584230 + 0.811588i \(0.301397\pi\)
\(920\) 2048.58 0.0734128
\(921\) 0 0
\(922\) −34121.8 −1.21881
\(923\) −13898.4 −0.495635
\(924\) 0 0
\(925\) −8206.18 −0.291695
\(926\) 11379.8 0.403848
\(927\) 0 0
\(928\) 59075.4 2.08970
\(929\) 15272.2 0.539358 0.269679 0.962950i \(-0.413082\pi\)
0.269679 + 0.962950i \(0.413082\pi\)
\(930\) 0 0
\(931\) −15949.9 −0.561480
\(932\) −36792.9 −1.29312
\(933\) 0 0
\(934\) 13863.3 0.485676
\(935\) 4399.69 0.153888
\(936\) 0 0
\(937\) −31426.2 −1.09568 −0.547838 0.836584i \(-0.684549\pi\)
−0.547838 + 0.836584i \(0.684549\pi\)
\(938\) −61452.7 −2.13913
\(939\) 0 0
\(940\) −6193.69 −0.214911
\(941\) 28418.9 0.984518 0.492259 0.870449i \(-0.336171\pi\)
0.492259 + 0.870449i \(0.336171\pi\)
\(942\) 0 0
\(943\) −3349.88 −0.115681
\(944\) −330.506 −0.0113952
\(945\) 0 0
\(946\) −3336.42 −0.114668
\(947\) 35394.9 1.21455 0.607275 0.794492i \(-0.292263\pi\)
0.607275 + 0.794492i \(0.292263\pi\)
\(948\) 0 0
\(949\) 37299.4 1.27586
\(950\) −14448.4 −0.493440
\(951\) 0 0
\(952\) −10177.3 −0.346478
\(953\) 20490.3 0.696481 0.348241 0.937405i \(-0.386779\pi\)
0.348241 + 0.937405i \(0.386779\pi\)
\(954\) 0 0
\(955\) −15688.1 −0.531574
\(956\) −2825.49 −0.0955889
\(957\) 0 0
\(958\) 26217.4 0.884181
\(959\) 2076.76 0.0699293
\(960\) 0 0
\(961\) −13705.6 −0.460059
\(962\) 102036. 3.41973
\(963\) 0 0
\(964\) 50963.5 1.70272
\(965\) 28753.1 0.959165
\(966\) 0 0
\(967\) −45429.2 −1.51076 −0.755380 0.655287i \(-0.772548\pi\)
−0.755380 + 0.655287i \(0.772548\pi\)
\(968\) 21133.6 0.701716
\(969\) 0 0
\(970\) −81888.4 −2.71060
\(971\) −32589.7 −1.07709 −0.538544 0.842597i \(-0.681026\pi\)
−0.538544 + 0.842597i \(0.681026\pi\)
\(972\) 0 0
\(973\) −35497.5 −1.16958
\(974\) −36853.0 −1.21237
\(975\) 0 0
\(976\) −12779.0 −0.419104
\(977\) 35416.5 1.15975 0.579874 0.814706i \(-0.303102\pi\)
0.579874 + 0.814706i \(0.303102\pi\)
\(978\) 0 0
\(979\) −14965.8 −0.488568
\(980\) −14680.5 −0.478523
\(981\) 0 0
\(982\) −60108.0 −1.95328
\(983\) −10203.0 −0.331054 −0.165527 0.986205i \(-0.552932\pi\)
−0.165527 + 0.986205i \(0.552932\pi\)
\(984\) 0 0
\(985\) −51474.3 −1.66509
\(986\) 46155.0 1.49075
\(987\) 0 0
\(988\) 107147. 3.45020
\(989\) 791.252 0.0254402
\(990\) 0 0
\(991\) 33015.0 1.05828 0.529141 0.848534i \(-0.322514\pi\)
0.529141 + 0.848534i \(0.322514\pi\)
\(992\) 27889.5 0.892632
\(993\) 0 0
\(994\) −16417.5 −0.523876
\(995\) 4514.76 0.143847
\(996\) 0 0
\(997\) 15027.1 0.477346 0.238673 0.971100i \(-0.423288\pi\)
0.238673 + 0.971100i \(0.423288\pi\)
\(998\) 80254.6 2.54551
\(999\) 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.1.7 yes 59
3.2 odd 2 2151.4.a.g.1.53 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.53 59 3.2 odd 2
2151.4.a.h.1.7 yes 59 1.1 even 1 trivial