Properties

Label 2151.4.a.h.1.18
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 1.18
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78319 q^{2} -0.253830 q^{4} +19.2360 q^{5} +27.5534 q^{7} +22.9720 q^{8} +O(q^{10})\) \(q-2.78319 q^{2} -0.253830 q^{4} +19.2360 q^{5} +27.5534 q^{7} +22.9720 q^{8} -53.5375 q^{10} +32.2259 q^{11} +10.3407 q^{13} -76.6866 q^{14} -61.9049 q^{16} +38.8792 q^{17} +137.845 q^{19} -4.88268 q^{20} -89.6910 q^{22} -158.387 q^{23} +245.024 q^{25} -28.7802 q^{26} -6.99390 q^{28} -30.8395 q^{29} +35.0179 q^{31} -11.4827 q^{32} -108.208 q^{34} +530.018 q^{35} +105.071 q^{37} -383.651 q^{38} +441.890 q^{40} +295.652 q^{41} -311.117 q^{43} -8.17992 q^{44} +440.823 q^{46} -122.518 q^{47} +416.192 q^{49} -681.949 q^{50} -2.62478 q^{52} +700.716 q^{53} +619.898 q^{55} +632.958 q^{56} +85.8324 q^{58} -548.102 q^{59} +206.571 q^{61} -97.4616 q^{62} +527.198 q^{64} +198.914 q^{65} +352.913 q^{67} -9.86873 q^{68} -1475.14 q^{70} +759.373 q^{71} -587.570 q^{73} -292.434 q^{74} -34.9894 q^{76} +887.935 q^{77} -149.398 q^{79} -1190.80 q^{80} -822.857 q^{82} +1024.10 q^{83} +747.881 q^{85} +865.900 q^{86} +740.295 q^{88} +1045.70 q^{89} +284.922 q^{91} +40.2035 q^{92} +340.991 q^{94} +2651.60 q^{95} -1808.66 q^{97} -1158.34 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78319 −0.984008 −0.492004 0.870593i \(-0.663735\pi\)
−0.492004 + 0.870593i \(0.663735\pi\)
\(3\) 0 0
\(4\) −0.253830 −0.0317288
\(5\) 19.2360 1.72052 0.860260 0.509855i \(-0.170301\pi\)
0.860260 + 0.509855i \(0.170301\pi\)
\(6\) 0 0
\(7\) 27.5534 1.48775 0.743873 0.668321i \(-0.232987\pi\)
0.743873 + 0.668321i \(0.232987\pi\)
\(8\) 22.9720 1.01523
\(9\) 0 0
\(10\) −53.5375 −1.69301
\(11\) 32.2259 0.883317 0.441658 0.897183i \(-0.354390\pi\)
0.441658 + 0.897183i \(0.354390\pi\)
\(12\) 0 0
\(13\) 10.3407 0.220615 0.110307 0.993898i \(-0.464816\pi\)
0.110307 + 0.993898i \(0.464816\pi\)
\(14\) −76.6866 −1.46395
\(15\) 0 0
\(16\) −61.9049 −0.967264
\(17\) 38.8792 0.554682 0.277341 0.960771i \(-0.410547\pi\)
0.277341 + 0.960771i \(0.410547\pi\)
\(18\) 0 0
\(19\) 137.845 1.66442 0.832208 0.554463i \(-0.187076\pi\)
0.832208 + 0.554463i \(0.187076\pi\)
\(20\) −4.88268 −0.0545901
\(21\) 0 0
\(22\) −89.6910 −0.869191
\(23\) −158.387 −1.43592 −0.717958 0.696087i \(-0.754923\pi\)
−0.717958 + 0.696087i \(0.754923\pi\)
\(24\) 0 0
\(25\) 245.024 1.96019
\(26\) −28.7802 −0.217087
\(27\) 0 0
\(28\) −6.99390 −0.0472044
\(29\) −30.8395 −0.197474 −0.0987372 0.995114i \(-0.531480\pi\)
−0.0987372 + 0.995114i \(0.531480\pi\)
\(30\) 0 0
\(31\) 35.0179 0.202884 0.101442 0.994841i \(-0.467654\pi\)
0.101442 + 0.994841i \(0.467654\pi\)
\(32\) −11.4827 −0.0634334
\(33\) 0 0
\(34\) −108.208 −0.545812
\(35\) 530.018 2.55970
\(36\) 0 0
\(37\) 105.071 0.466855 0.233427 0.972374i \(-0.425006\pi\)
0.233427 + 0.972374i \(0.425006\pi\)
\(38\) −383.651 −1.63780
\(39\) 0 0
\(40\) 441.890 1.74672
\(41\) 295.652 1.12617 0.563086 0.826398i \(-0.309614\pi\)
0.563086 + 0.826398i \(0.309614\pi\)
\(42\) 0 0
\(43\) −311.117 −1.10337 −0.551686 0.834052i \(-0.686015\pi\)
−0.551686 + 0.834052i \(0.686015\pi\)
\(44\) −8.17992 −0.0280266
\(45\) 0 0
\(46\) 440.823 1.41295
\(47\) −122.518 −0.380236 −0.190118 0.981761i \(-0.560887\pi\)
−0.190118 + 0.981761i \(0.560887\pi\)
\(48\) 0 0
\(49\) 416.192 1.21339
\(50\) −681.949 −1.92884
\(51\) 0 0
\(52\) −2.62478 −0.00699984
\(53\) 700.716 1.81605 0.908025 0.418915i \(-0.137590\pi\)
0.908025 + 0.418915i \(0.137590\pi\)
\(54\) 0 0
\(55\) 619.898 1.51977
\(56\) 632.958 1.51040
\(57\) 0 0
\(58\) 85.8324 0.194316
\(59\) −548.102 −1.20944 −0.604718 0.796439i \(-0.706714\pi\)
−0.604718 + 0.796439i \(0.706714\pi\)
\(60\) 0 0
\(61\) 206.571 0.433586 0.216793 0.976218i \(-0.430440\pi\)
0.216793 + 0.976218i \(0.430440\pi\)
\(62\) −97.4616 −0.199639
\(63\) 0 0
\(64\) 527.198 1.02968
\(65\) 198.914 0.379573
\(66\) 0 0
\(67\) 352.913 0.643511 0.321755 0.946823i \(-0.395727\pi\)
0.321755 + 0.946823i \(0.395727\pi\)
\(68\) −9.86873 −0.0175994
\(69\) 0 0
\(70\) −1475.14 −2.51876
\(71\) 759.373 1.26931 0.634655 0.772796i \(-0.281142\pi\)
0.634655 + 0.772796i \(0.281142\pi\)
\(72\) 0 0
\(73\) −587.570 −0.942054 −0.471027 0.882119i \(-0.656116\pi\)
−0.471027 + 0.882119i \(0.656116\pi\)
\(74\) −292.434 −0.459389
\(75\) 0 0
\(76\) −34.9894 −0.0528099
\(77\) 887.935 1.31415
\(78\) 0 0
\(79\) −149.398 −0.212767 −0.106384 0.994325i \(-0.533927\pi\)
−0.106384 + 0.994325i \(0.533927\pi\)
\(80\) −1190.80 −1.66420
\(81\) 0 0
\(82\) −822.857 −1.10816
\(83\) 1024.10 1.35434 0.677168 0.735829i \(-0.263207\pi\)
0.677168 + 0.735829i \(0.263207\pi\)
\(84\) 0 0
\(85\) 747.881 0.954343
\(86\) 865.900 1.08573
\(87\) 0 0
\(88\) 740.295 0.896769
\(89\) 1045.70 1.24544 0.622718 0.782447i \(-0.286029\pi\)
0.622718 + 0.782447i \(0.286029\pi\)
\(90\) 0 0
\(91\) 284.922 0.328219
\(92\) 40.2035 0.0455599
\(93\) 0 0
\(94\) 340.991 0.374155
\(95\) 2651.60 2.86366
\(96\) 0 0
\(97\) −1808.66 −1.89321 −0.946607 0.322390i \(-0.895514\pi\)
−0.946607 + 0.322390i \(0.895514\pi\)
\(98\) −1158.34 −1.19398
\(99\) 0 0
\(100\) −62.1945 −0.0621945
\(101\) 940.319 0.926388 0.463194 0.886257i \(-0.346703\pi\)
0.463194 + 0.886257i \(0.346703\pi\)
\(102\) 0 0
\(103\) −105.854 −0.101263 −0.0506314 0.998717i \(-0.516123\pi\)
−0.0506314 + 0.998717i \(0.516123\pi\)
\(104\) 237.547 0.223975
\(105\) 0 0
\(106\) −1950.23 −1.78701
\(107\) −1946.90 −1.75901 −0.879506 0.475887i \(-0.842127\pi\)
−0.879506 + 0.475887i \(0.842127\pi\)
\(108\) 0 0
\(109\) 1837.70 1.61486 0.807431 0.589961i \(-0.200857\pi\)
0.807431 + 0.589961i \(0.200857\pi\)
\(110\) −1725.30 −1.49546
\(111\) 0 0
\(112\) −1705.69 −1.43904
\(113\) −1446.76 −1.20442 −0.602212 0.798336i \(-0.705714\pi\)
−0.602212 + 0.798336i \(0.705714\pi\)
\(114\) 0 0
\(115\) −3046.74 −2.47052
\(116\) 7.82801 0.00626563
\(117\) 0 0
\(118\) 1525.47 1.19010
\(119\) 1071.26 0.825227
\(120\) 0 0
\(121\) −292.489 −0.219751
\(122\) −574.928 −0.426652
\(123\) 0 0
\(124\) −8.88860 −0.00643726
\(125\) 2308.78 1.65203
\(126\) 0 0
\(127\) −1939.30 −1.35500 −0.677499 0.735524i \(-0.736936\pi\)
−0.677499 + 0.735524i \(0.736936\pi\)
\(128\) −1375.43 −0.949783
\(129\) 0 0
\(130\) −553.616 −0.373502
\(131\) −501.024 −0.334158 −0.167079 0.985944i \(-0.553433\pi\)
−0.167079 + 0.985944i \(0.553433\pi\)
\(132\) 0 0
\(133\) 3798.12 2.47623
\(134\) −982.226 −0.633220
\(135\) 0 0
\(136\) 893.134 0.563130
\(137\) −2450.94 −1.52845 −0.764227 0.644947i \(-0.776879\pi\)
−0.764227 + 0.644947i \(0.776879\pi\)
\(138\) 0 0
\(139\) 257.133 0.156905 0.0784523 0.996918i \(-0.475002\pi\)
0.0784523 + 0.996918i \(0.475002\pi\)
\(140\) −134.535 −0.0812161
\(141\) 0 0
\(142\) −2113.48 −1.24901
\(143\) 333.239 0.194873
\(144\) 0 0
\(145\) −593.230 −0.339759
\(146\) 1635.32 0.926988
\(147\) 0 0
\(148\) −26.6703 −0.0148127
\(149\) 2187.75 1.20287 0.601434 0.798923i \(-0.294596\pi\)
0.601434 + 0.798923i \(0.294596\pi\)
\(150\) 0 0
\(151\) −1250.56 −0.673970 −0.336985 0.941510i \(-0.609407\pi\)
−0.336985 + 0.941510i \(0.609407\pi\)
\(152\) 3166.59 1.68976
\(153\) 0 0
\(154\) −2471.30 −1.29313
\(155\) 673.604 0.349066
\(156\) 0 0
\(157\) −1312.84 −0.667363 −0.333682 0.942686i \(-0.608291\pi\)
−0.333682 + 0.942686i \(0.608291\pi\)
\(158\) 415.804 0.209365
\(159\) 0 0
\(160\) −220.881 −0.109138
\(161\) −4364.12 −2.13628
\(162\) 0 0
\(163\) −1766.12 −0.848670 −0.424335 0.905505i \(-0.639492\pi\)
−0.424335 + 0.905505i \(0.639492\pi\)
\(164\) −75.0454 −0.0357321
\(165\) 0 0
\(166\) −2850.28 −1.33268
\(167\) 780.417 0.361620 0.180810 0.983518i \(-0.442128\pi\)
0.180810 + 0.983518i \(0.442128\pi\)
\(168\) 0 0
\(169\) −2090.07 −0.951329
\(170\) −2081.50 −0.939081
\(171\) 0 0
\(172\) 78.9711 0.0350086
\(173\) −3049.96 −1.34037 −0.670185 0.742194i \(-0.733785\pi\)
−0.670185 + 0.742194i \(0.733785\pi\)
\(174\) 0 0
\(175\) 6751.26 2.91627
\(176\) −1994.94 −0.854401
\(177\) 0 0
\(178\) −2910.38 −1.22552
\(179\) −1950.16 −0.814312 −0.407156 0.913359i \(-0.633480\pi\)
−0.407156 + 0.913359i \(0.633480\pi\)
\(180\) 0 0
\(181\) −2597.95 −1.06687 −0.533436 0.845840i \(-0.679099\pi\)
−0.533436 + 0.845840i \(0.679099\pi\)
\(182\) −792.993 −0.322970
\(183\) 0 0
\(184\) −3638.48 −1.45778
\(185\) 2021.15 0.803234
\(186\) 0 0
\(187\) 1252.92 0.489960
\(188\) 31.0988 0.0120644
\(189\) 0 0
\(190\) −7379.91 −2.81787
\(191\) 1447.23 0.548260 0.274130 0.961693i \(-0.411610\pi\)
0.274130 + 0.961693i \(0.411610\pi\)
\(192\) 0 0
\(193\) −1220.05 −0.455033 −0.227516 0.973774i \(-0.573061\pi\)
−0.227516 + 0.973774i \(0.573061\pi\)
\(194\) 5033.86 1.86294
\(195\) 0 0
\(196\) −105.642 −0.0384994
\(197\) 2862.29 1.03518 0.517588 0.855630i \(-0.326830\pi\)
0.517588 + 0.855630i \(0.326830\pi\)
\(198\) 0 0
\(199\) −267.746 −0.0953771 −0.0476886 0.998862i \(-0.515185\pi\)
−0.0476886 + 0.998862i \(0.515185\pi\)
\(200\) 5628.70 1.99004
\(201\) 0 0
\(202\) −2617.09 −0.911573
\(203\) −849.736 −0.293792
\(204\) 0 0
\(205\) 5687.16 1.93760
\(206\) 294.611 0.0996434
\(207\) 0 0
\(208\) −640.140 −0.213393
\(209\) 4442.20 1.47021
\(210\) 0 0
\(211\) −2491.09 −0.812766 −0.406383 0.913703i \(-0.633210\pi\)
−0.406383 + 0.913703i \(0.633210\pi\)
\(212\) −177.863 −0.0576211
\(213\) 0 0
\(214\) 5418.61 1.73088
\(215\) −5984.66 −1.89837
\(216\) 0 0
\(217\) 964.863 0.301840
\(218\) −5114.69 −1.58904
\(219\) 0 0
\(220\) −157.349 −0.0482203
\(221\) 402.038 0.122371
\(222\) 0 0
\(223\) 5470.72 1.64281 0.821405 0.570346i \(-0.193191\pi\)
0.821405 + 0.570346i \(0.193191\pi\)
\(224\) −316.387 −0.0943728
\(225\) 0 0
\(226\) 4026.62 1.18516
\(227\) 4177.85 1.22156 0.610779 0.791801i \(-0.290856\pi\)
0.610779 + 0.791801i \(0.290856\pi\)
\(228\) 0 0
\(229\) 3049.05 0.879857 0.439928 0.898033i \(-0.355004\pi\)
0.439928 + 0.898033i \(0.355004\pi\)
\(230\) 8479.67 2.43101
\(231\) 0 0
\(232\) −708.446 −0.200482
\(233\) 265.914 0.0747666 0.0373833 0.999301i \(-0.488098\pi\)
0.0373833 + 0.999301i \(0.488098\pi\)
\(234\) 0 0
\(235\) −2356.76 −0.654203
\(236\) 139.125 0.0383740
\(237\) 0 0
\(238\) −2981.52 −0.812029
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −6888.63 −1.84123 −0.920614 0.390475i \(-0.872311\pi\)
−0.920614 + 0.390475i \(0.872311\pi\)
\(242\) 814.054 0.216237
\(243\) 0 0
\(244\) −52.4340 −0.0137571
\(245\) 8005.88 2.08766
\(246\) 0 0
\(247\) 1425.42 0.367195
\(248\) 804.431 0.205973
\(249\) 0 0
\(250\) −6425.79 −1.62561
\(251\) −1646.85 −0.414136 −0.207068 0.978327i \(-0.566392\pi\)
−0.207068 + 0.978327i \(0.566392\pi\)
\(252\) 0 0
\(253\) −5104.18 −1.26837
\(254\) 5397.44 1.33333
\(255\) 0 0
\(256\) −389.487 −0.0950895
\(257\) −5771.91 −1.40094 −0.700471 0.713681i \(-0.747027\pi\)
−0.700471 + 0.713681i \(0.747027\pi\)
\(258\) 0 0
\(259\) 2895.08 0.694562
\(260\) −50.4904 −0.0120434
\(261\) 0 0
\(262\) 1394.45 0.328814
\(263\) 1656.33 0.388341 0.194171 0.980968i \(-0.437798\pi\)
0.194171 + 0.980968i \(0.437798\pi\)
\(264\) 0 0
\(265\) 13479.0 3.12455
\(266\) −10570.9 −2.43663
\(267\) 0 0
\(268\) −89.5801 −0.0204178
\(269\) 2471.45 0.560174 0.280087 0.959975i \(-0.409637\pi\)
0.280087 + 0.959975i \(0.409637\pi\)
\(270\) 0 0
\(271\) 44.2396 0.00991648 0.00495824 0.999988i \(-0.498422\pi\)
0.00495824 + 0.999988i \(0.498422\pi\)
\(272\) −2406.82 −0.536525
\(273\) 0 0
\(274\) 6821.45 1.50401
\(275\) 7896.13 1.73147
\(276\) 0 0
\(277\) −2924.86 −0.634433 −0.317217 0.948353i \(-0.602748\pi\)
−0.317217 + 0.948353i \(0.602748\pi\)
\(278\) −715.651 −0.154395
\(279\) 0 0
\(280\) 12175.6 2.59868
\(281\) 7081.71 1.50341 0.751707 0.659497i \(-0.229231\pi\)
0.751707 + 0.659497i \(0.229231\pi\)
\(282\) 0 0
\(283\) 473.768 0.0995143 0.0497572 0.998761i \(-0.484155\pi\)
0.0497572 + 0.998761i \(0.484155\pi\)
\(284\) −192.752 −0.0402737
\(285\) 0 0
\(286\) −927.468 −0.191756
\(287\) 8146.23 1.67546
\(288\) 0 0
\(289\) −3401.40 −0.692327
\(290\) 1651.07 0.334325
\(291\) 0 0
\(292\) 149.143 0.0298902
\(293\) 9805.59 1.95512 0.977558 0.210668i \(-0.0675637\pi\)
0.977558 + 0.210668i \(0.0675637\pi\)
\(294\) 0 0
\(295\) −10543.3 −2.08086
\(296\) 2413.70 0.473965
\(297\) 0 0
\(298\) −6088.92 −1.18363
\(299\) −1637.84 −0.316784
\(300\) 0 0
\(301\) −8572.36 −1.64154
\(302\) 3480.56 0.663191
\(303\) 0 0
\(304\) −8533.31 −1.60993
\(305\) 3973.60 0.745993
\(306\) 0 0
\(307\) −1384.15 −0.257321 −0.128660 0.991689i \(-0.541068\pi\)
−0.128660 + 0.991689i \(0.541068\pi\)
\(308\) −225.385 −0.0416964
\(309\) 0 0
\(310\) −1874.77 −0.343483
\(311\) −1774.27 −0.323504 −0.161752 0.986831i \(-0.551715\pi\)
−0.161752 + 0.986831i \(0.551715\pi\)
\(312\) 0 0
\(313\) 3700.09 0.668184 0.334092 0.942540i \(-0.391570\pi\)
0.334092 + 0.942540i \(0.391570\pi\)
\(314\) 3653.89 0.656690
\(315\) 0 0
\(316\) 37.9218 0.00675085
\(317\) −3471.60 −0.615093 −0.307547 0.951533i \(-0.599508\pi\)
−0.307547 + 0.951533i \(0.599508\pi\)
\(318\) 0 0
\(319\) −993.833 −0.174433
\(320\) 10141.2 1.77159
\(321\) 0 0
\(322\) 12146.2 2.10211
\(323\) 5359.33 0.923222
\(324\) 0 0
\(325\) 2533.72 0.432448
\(326\) 4915.45 0.835097
\(327\) 0 0
\(328\) 6791.72 1.14332
\(329\) −3375.79 −0.565694
\(330\) 0 0
\(331\) −11769.1 −1.95434 −0.977172 0.212451i \(-0.931855\pi\)
−0.977172 + 0.212451i \(0.931855\pi\)
\(332\) −259.948 −0.0429714
\(333\) 0 0
\(334\) −2172.05 −0.355837
\(335\) 6788.64 1.10717
\(336\) 0 0
\(337\) −10992.7 −1.77689 −0.888444 0.458985i \(-0.848213\pi\)
−0.888444 + 0.458985i \(0.848213\pi\)
\(338\) 5817.07 0.936115
\(339\) 0 0
\(340\) −189.835 −0.0302801
\(341\) 1128.48 0.179211
\(342\) 0 0
\(343\) 2016.70 0.317468
\(344\) −7146.99 −1.12017
\(345\) 0 0
\(346\) 8488.63 1.31893
\(347\) 6679.54 1.03336 0.516681 0.856178i \(-0.327167\pi\)
0.516681 + 0.856178i \(0.327167\pi\)
\(348\) 0 0
\(349\) 7868.92 1.20692 0.603458 0.797395i \(-0.293789\pi\)
0.603458 + 0.797395i \(0.293789\pi\)
\(350\) −18790.1 −2.86963
\(351\) 0 0
\(352\) −370.040 −0.0560318
\(353\) −8705.88 −1.31266 −0.656328 0.754476i \(-0.727891\pi\)
−0.656328 + 0.754476i \(0.727891\pi\)
\(354\) 0 0
\(355\) 14607.3 2.18387
\(356\) −265.430 −0.0395162
\(357\) 0 0
\(358\) 5427.68 0.801290
\(359\) −1128.36 −0.165885 −0.0829425 0.996554i \(-0.526432\pi\)
−0.0829425 + 0.996554i \(0.526432\pi\)
\(360\) 0 0
\(361\) 12142.4 1.77028
\(362\) 7230.59 1.04981
\(363\) 0 0
\(364\) −72.3218 −0.0104140
\(365\) −11302.5 −1.62082
\(366\) 0 0
\(367\) −2218.05 −0.315480 −0.157740 0.987481i \(-0.550421\pi\)
−0.157740 + 0.987481i \(0.550421\pi\)
\(368\) 9804.96 1.38891
\(369\) 0 0
\(370\) −5625.26 −0.790388
\(371\) 19307.1 2.70182
\(372\) 0 0
\(373\) −8888.30 −1.23383 −0.616915 0.787030i \(-0.711618\pi\)
−0.616915 + 0.787030i \(0.711618\pi\)
\(374\) −3487.12 −0.482125
\(375\) 0 0
\(376\) −2814.48 −0.386026
\(377\) −318.902 −0.0435658
\(378\) 0 0
\(379\) 10662.5 1.44511 0.722556 0.691312i \(-0.242967\pi\)
0.722556 + 0.691312i \(0.242967\pi\)
\(380\) −673.056 −0.0908606
\(381\) 0 0
\(382\) −4027.91 −0.539492
\(383\) 3150.75 0.420354 0.210177 0.977663i \(-0.432596\pi\)
0.210177 + 0.977663i \(0.432596\pi\)
\(384\) 0 0
\(385\) 17080.3 2.26102
\(386\) 3395.65 0.447756
\(387\) 0 0
\(388\) 459.093 0.0600694
\(389\) −11728.0 −1.52862 −0.764311 0.644848i \(-0.776921\pi\)
−0.764311 + 0.644848i \(0.776921\pi\)
\(390\) 0 0
\(391\) −6157.98 −0.796477
\(392\) 9560.77 1.23187
\(393\) 0 0
\(394\) −7966.31 −1.01862
\(395\) −2873.83 −0.366070
\(396\) 0 0
\(397\) 6710.89 0.848388 0.424194 0.905571i \(-0.360558\pi\)
0.424194 + 0.905571i \(0.360558\pi\)
\(398\) 745.190 0.0938518
\(399\) 0 0
\(400\) −15168.2 −1.89602
\(401\) 6300.52 0.784621 0.392311 0.919833i \(-0.371676\pi\)
0.392311 + 0.919833i \(0.371676\pi\)
\(402\) 0 0
\(403\) 362.109 0.0447592
\(404\) −238.681 −0.0293932
\(405\) 0 0
\(406\) 2364.98 0.289093
\(407\) 3386.02 0.412381
\(408\) 0 0
\(409\) −1919.04 −0.232006 −0.116003 0.993249i \(-0.537008\pi\)
−0.116003 + 0.993249i \(0.537008\pi\)
\(410\) −15828.5 −1.90662
\(411\) 0 0
\(412\) 26.8689 0.00321295
\(413\) −15102.1 −1.79934
\(414\) 0 0
\(415\) 19699.6 2.33016
\(416\) −118.739 −0.0139943
\(417\) 0 0
\(418\) −12363.5 −1.44669
\(419\) −11720.7 −1.36658 −0.683288 0.730149i \(-0.739450\pi\)
−0.683288 + 0.730149i \(0.739450\pi\)
\(420\) 0 0
\(421\) 11285.6 1.30647 0.653236 0.757154i \(-0.273411\pi\)
0.653236 + 0.757154i \(0.273411\pi\)
\(422\) 6933.18 0.799768
\(423\) 0 0
\(424\) 16096.8 1.84371
\(425\) 9526.35 1.08728
\(426\) 0 0
\(427\) 5691.75 0.645065
\(428\) 494.183 0.0558114
\(429\) 0 0
\(430\) 16656.5 1.86801
\(431\) 12144.7 1.35728 0.678641 0.734471i \(-0.262569\pi\)
0.678641 + 0.734471i \(0.262569\pi\)
\(432\) 0 0
\(433\) −11643.9 −1.29231 −0.646154 0.763207i \(-0.723624\pi\)
−0.646154 + 0.763207i \(0.723624\pi\)
\(434\) −2685.40 −0.297012
\(435\) 0 0
\(436\) −466.465 −0.0512377
\(437\) −21833.0 −2.38996
\(438\) 0 0
\(439\) −4286.79 −0.466054 −0.233027 0.972470i \(-0.574863\pi\)
−0.233027 + 0.972470i \(0.574863\pi\)
\(440\) 14240.3 1.54291
\(441\) 0 0
\(442\) −1118.95 −0.120414
\(443\) −861.239 −0.0923673 −0.0461836 0.998933i \(-0.514706\pi\)
−0.0461836 + 0.998933i \(0.514706\pi\)
\(444\) 0 0
\(445\) 20115.0 2.14280
\(446\) −15226.1 −1.61654
\(447\) 0 0
\(448\) 14526.1 1.53191
\(449\) −4202.34 −0.441694 −0.220847 0.975308i \(-0.570882\pi\)
−0.220847 + 0.975308i \(0.570882\pi\)
\(450\) 0 0
\(451\) 9527.66 0.994767
\(452\) 367.232 0.0382149
\(453\) 0 0
\(454\) −11627.8 −1.20202
\(455\) 5480.76 0.564708
\(456\) 0 0
\(457\) 16451.8 1.68399 0.841993 0.539488i \(-0.181382\pi\)
0.841993 + 0.539488i \(0.181382\pi\)
\(458\) −8486.11 −0.865786
\(459\) 0 0
\(460\) 773.355 0.0783867
\(461\) 3581.86 0.361874 0.180937 0.983495i \(-0.442087\pi\)
0.180937 + 0.983495i \(0.442087\pi\)
\(462\) 0 0
\(463\) −5277.24 −0.529706 −0.264853 0.964289i \(-0.585323\pi\)
−0.264853 + 0.964289i \(0.585323\pi\)
\(464\) 1909.12 0.191010
\(465\) 0 0
\(466\) −740.091 −0.0735709
\(467\) −14263.7 −1.41337 −0.706687 0.707526i \(-0.749811\pi\)
−0.706687 + 0.707526i \(0.749811\pi\)
\(468\) 0 0
\(469\) 9723.98 0.957381
\(470\) 6559.31 0.643741
\(471\) 0 0
\(472\) −12591.0 −1.22786
\(473\) −10026.0 −0.974626
\(474\) 0 0
\(475\) 33775.4 3.26258
\(476\) −271.918 −0.0261834
\(477\) 0 0
\(478\) 665.183 0.0636502
\(479\) 13713.0 1.30807 0.654034 0.756465i \(-0.273075\pi\)
0.654034 + 0.756465i \(0.273075\pi\)
\(480\) 0 0
\(481\) 1086.51 0.102995
\(482\) 19172.4 1.81178
\(483\) 0 0
\(484\) 74.2426 0.00697245
\(485\) −34791.4 −3.25731
\(486\) 0 0
\(487\) −11160.8 −1.03848 −0.519242 0.854627i \(-0.673786\pi\)
−0.519242 + 0.854627i \(0.673786\pi\)
\(488\) 4745.35 0.440189
\(489\) 0 0
\(490\) −22281.9 −2.05427
\(491\) 6933.48 0.637279 0.318639 0.947876i \(-0.396774\pi\)
0.318639 + 0.947876i \(0.396774\pi\)
\(492\) 0 0
\(493\) −1199.02 −0.109536
\(494\) −3967.21 −0.361323
\(495\) 0 0
\(496\) −2167.78 −0.196242
\(497\) 20923.3 1.88841
\(498\) 0 0
\(499\) 134.621 0.0120771 0.00603855 0.999982i \(-0.498078\pi\)
0.00603855 + 0.999982i \(0.498078\pi\)
\(500\) −586.039 −0.0524170
\(501\) 0 0
\(502\) 4583.50 0.407513
\(503\) −4654.45 −0.412588 −0.206294 0.978490i \(-0.566140\pi\)
−0.206294 + 0.978490i \(0.566140\pi\)
\(504\) 0 0
\(505\) 18088.0 1.59387
\(506\) 14205.9 1.24808
\(507\) 0 0
\(508\) 492.252 0.0429925
\(509\) −645.594 −0.0562190 −0.0281095 0.999605i \(-0.508949\pi\)
−0.0281095 + 0.999605i \(0.508949\pi\)
\(510\) 0 0
\(511\) −16189.6 −1.40154
\(512\) 12087.5 1.04335
\(513\) 0 0
\(514\) 16064.3 1.37854
\(515\) −2036.20 −0.174225
\(516\) 0 0
\(517\) −3948.25 −0.335869
\(518\) −8057.57 −0.683454
\(519\) 0 0
\(520\) 4569.45 0.385353
\(521\) −7410.59 −0.623155 −0.311578 0.950221i \(-0.600857\pi\)
−0.311578 + 0.950221i \(0.600857\pi\)
\(522\) 0 0
\(523\) 17542.7 1.46671 0.733356 0.679845i \(-0.237953\pi\)
0.733356 + 0.679845i \(0.237953\pi\)
\(524\) 127.175 0.0106024
\(525\) 0 0
\(526\) −4609.89 −0.382131
\(527\) 1361.47 0.112536
\(528\) 0 0
\(529\) 12919.6 1.06185
\(530\) −37514.6 −3.07458
\(531\) 0 0
\(532\) −964.077 −0.0785678
\(533\) 3057.25 0.248450
\(534\) 0 0
\(535\) −37450.7 −3.02642
\(536\) 8107.13 0.653311
\(537\) 0 0
\(538\) −6878.52 −0.551216
\(539\) 13412.2 1.07181
\(540\) 0 0
\(541\) 9430.61 0.749452 0.374726 0.927136i \(-0.377737\pi\)
0.374726 + 0.927136i \(0.377737\pi\)
\(542\) −123.127 −0.00975789
\(543\) 0 0
\(544\) −446.437 −0.0351854
\(545\) 35350.1 2.77841
\(546\) 0 0
\(547\) 2020.15 0.157908 0.0789539 0.996878i \(-0.474842\pi\)
0.0789539 + 0.996878i \(0.474842\pi\)
\(548\) 622.124 0.0484960
\(549\) 0 0
\(550\) −21976.5 −1.70378
\(551\) −4251.09 −0.328680
\(552\) 0 0
\(553\) −4116.44 −0.316544
\(554\) 8140.46 0.624287
\(555\) 0 0
\(556\) −65.2681 −0.00497839
\(557\) −389.740 −0.0296478 −0.0148239 0.999890i \(-0.504719\pi\)
−0.0148239 + 0.999890i \(0.504719\pi\)
\(558\) 0 0
\(559\) −3217.17 −0.243420
\(560\) −32810.7 −2.47591
\(561\) 0 0
\(562\) −19709.8 −1.47937
\(563\) −1680.19 −0.125775 −0.0628877 0.998021i \(-0.520031\pi\)
−0.0628877 + 0.998021i \(0.520031\pi\)
\(564\) 0 0
\(565\) −27829.9 −2.07224
\(566\) −1318.59 −0.0979229
\(567\) 0 0
\(568\) 17444.3 1.28864
\(569\) −17076.6 −1.25815 −0.629075 0.777345i \(-0.716566\pi\)
−0.629075 + 0.777345i \(0.716566\pi\)
\(570\) 0 0
\(571\) −16649.1 −1.22022 −0.610109 0.792317i \(-0.708875\pi\)
−0.610109 + 0.792317i \(0.708875\pi\)
\(572\) −84.5861 −0.00618308
\(573\) 0 0
\(574\) −22672.5 −1.64866
\(575\) −38808.7 −2.81467
\(576\) 0 0
\(577\) 18039.8 1.30157 0.650784 0.759263i \(-0.274440\pi\)
0.650784 + 0.759263i \(0.274440\pi\)
\(578\) 9466.77 0.681256
\(579\) 0 0
\(580\) 150.580 0.0107801
\(581\) 28217.6 2.01491
\(582\) 0 0
\(583\) 22581.2 1.60415
\(584\) −13497.7 −0.956400
\(585\) 0 0
\(586\) −27290.9 −1.92385
\(587\) 9120.89 0.641328 0.320664 0.947193i \(-0.396094\pi\)
0.320664 + 0.947193i \(0.396094\pi\)
\(588\) 0 0
\(589\) 4827.05 0.337683
\(590\) 29344.0 2.04758
\(591\) 0 0
\(592\) −6504.44 −0.451572
\(593\) −3798.44 −0.263041 −0.131520 0.991313i \(-0.541986\pi\)
−0.131520 + 0.991313i \(0.541986\pi\)
\(594\) 0 0
\(595\) 20606.7 1.41982
\(596\) −555.317 −0.0381655
\(597\) 0 0
\(598\) 4558.41 0.311718
\(599\) 3224.19 0.219928 0.109964 0.993936i \(-0.464926\pi\)
0.109964 + 0.993936i \(0.464926\pi\)
\(600\) 0 0
\(601\) 6429.69 0.436393 0.218197 0.975905i \(-0.429983\pi\)
0.218197 + 0.975905i \(0.429983\pi\)
\(602\) 23858.5 1.61528
\(603\) 0 0
\(604\) 317.431 0.0213842
\(605\) −5626.32 −0.378087
\(606\) 0 0
\(607\) −3889.56 −0.260086 −0.130043 0.991508i \(-0.541512\pi\)
−0.130043 + 0.991508i \(0.541512\pi\)
\(608\) −1582.83 −0.105580
\(609\) 0 0
\(610\) −11059.3 −0.734063
\(611\) −1266.92 −0.0838857
\(612\) 0 0
\(613\) 18334.8 1.20805 0.604025 0.796966i \(-0.293563\pi\)
0.604025 + 0.796966i \(0.293563\pi\)
\(614\) 3852.35 0.253205
\(615\) 0 0
\(616\) 20397.7 1.33416
\(617\) 4169.61 0.272062 0.136031 0.990705i \(-0.456565\pi\)
0.136031 + 0.990705i \(0.456565\pi\)
\(618\) 0 0
\(619\) −5923.21 −0.384610 −0.192305 0.981335i \(-0.561596\pi\)
−0.192305 + 0.981335i \(0.561596\pi\)
\(620\) −170.981 −0.0110754
\(621\) 0 0
\(622\) 4938.15 0.318331
\(623\) 28812.6 1.85289
\(624\) 0 0
\(625\) 13783.8 0.882161
\(626\) −10298.1 −0.657498
\(627\) 0 0
\(628\) 333.239 0.0211746
\(629\) 4085.10 0.258956
\(630\) 0 0
\(631\) −28967.5 −1.82754 −0.913771 0.406229i \(-0.866843\pi\)
−0.913771 + 0.406229i \(0.866843\pi\)
\(632\) −3431.98 −0.216007
\(633\) 0 0
\(634\) 9662.14 0.605256
\(635\) −37304.3 −2.33130
\(636\) 0 0
\(637\) 4303.72 0.267692
\(638\) 2766.03 0.171643
\(639\) 0 0
\(640\) −26457.8 −1.63412
\(641\) −22652.4 −1.39581 −0.697907 0.716188i \(-0.745885\pi\)
−0.697907 + 0.716188i \(0.745885\pi\)
\(642\) 0 0
\(643\) −11734.9 −0.719719 −0.359859 0.933007i \(-0.617175\pi\)
−0.359859 + 0.933007i \(0.617175\pi\)
\(644\) 1107.75 0.0677815
\(645\) 0 0
\(646\) −14916.0 −0.908458
\(647\) 10592.2 0.643621 0.321810 0.946804i \(-0.395709\pi\)
0.321810 + 0.946804i \(0.395709\pi\)
\(648\) 0 0
\(649\) −17663.1 −1.06832
\(650\) −7051.83 −0.425532
\(651\) 0 0
\(652\) 448.295 0.0269273
\(653\) 19626.6 1.17618 0.588091 0.808795i \(-0.299880\pi\)
0.588091 + 0.808795i \(0.299880\pi\)
\(654\) 0 0
\(655\) −9637.71 −0.574926
\(656\) −18302.3 −1.08931
\(657\) 0 0
\(658\) 9395.48 0.556647
\(659\) 5563.31 0.328856 0.164428 0.986389i \(-0.447422\pi\)
0.164428 + 0.986389i \(0.447422\pi\)
\(660\) 0 0
\(661\) −1537.13 −0.0904497 −0.0452249 0.998977i \(-0.514400\pi\)
−0.0452249 + 0.998977i \(0.514400\pi\)
\(662\) 32755.7 1.92309
\(663\) 0 0
\(664\) 23525.7 1.37496
\(665\) 73060.6 4.26040
\(666\) 0 0
\(667\) 4884.59 0.283557
\(668\) −198.094 −0.0114738
\(669\) 0 0
\(670\) −18894.1 −1.08947
\(671\) 6656.95 0.382993
\(672\) 0 0
\(673\) 14786.3 0.846911 0.423456 0.905917i \(-0.360817\pi\)
0.423456 + 0.905917i \(0.360817\pi\)
\(674\) 30594.8 1.74847
\(675\) 0 0
\(676\) 530.523 0.0301845
\(677\) −1268.81 −0.0720298 −0.0360149 0.999351i \(-0.511466\pi\)
−0.0360149 + 0.999351i \(0.511466\pi\)
\(678\) 0 0
\(679\) −49834.9 −2.81662
\(680\) 17180.3 0.968876
\(681\) 0 0
\(682\) −3140.79 −0.176345
\(683\) 13430.8 0.752435 0.376218 0.926531i \(-0.377224\pi\)
0.376218 + 0.926531i \(0.377224\pi\)
\(684\) 0 0
\(685\) −47146.4 −2.62974
\(686\) −5612.87 −0.312391
\(687\) 0 0
\(688\) 19259.7 1.06725
\(689\) 7245.89 0.400648
\(690\) 0 0
\(691\) −29.2231 −0.00160882 −0.000804412 1.00000i \(-0.500256\pi\)
−0.000804412 1.00000i \(0.500256\pi\)
\(692\) 774.172 0.0425283
\(693\) 0 0
\(694\) −18590.5 −1.01684
\(695\) 4946.21 0.269957
\(696\) 0 0
\(697\) 11494.7 0.624668
\(698\) −21900.7 −1.18761
\(699\) 0 0
\(700\) −1713.67 −0.0925297
\(701\) −13868.8 −0.747241 −0.373620 0.927582i \(-0.621884\pi\)
−0.373620 + 0.927582i \(0.621884\pi\)
\(702\) 0 0
\(703\) 14483.6 0.777041
\(704\) 16989.4 0.909537
\(705\) 0 0
\(706\) 24230.2 1.29166
\(707\) 25909.0 1.37823
\(708\) 0 0
\(709\) −12022.0 −0.636808 −0.318404 0.947955i \(-0.603147\pi\)
−0.318404 + 0.947955i \(0.603147\pi\)
\(710\) −40655.0 −2.14895
\(711\) 0 0
\(712\) 24021.8 1.26440
\(713\) −5546.39 −0.291324
\(714\) 0 0
\(715\) 6410.18 0.335283
\(716\) 495.010 0.0258371
\(717\) 0 0
\(718\) 3140.45 0.163232
\(719\) 25462.8 1.32073 0.660363 0.750947i \(-0.270403\pi\)
0.660363 + 0.750947i \(0.270403\pi\)
\(720\) 0 0
\(721\) −2916.63 −0.150653
\(722\) −33794.5 −1.74197
\(723\) 0 0
\(724\) 659.438 0.0338506
\(725\) −7556.43 −0.387088
\(726\) 0 0
\(727\) −16110.0 −0.821850 −0.410925 0.911669i \(-0.634794\pi\)
−0.410925 + 0.911669i \(0.634794\pi\)
\(728\) 6545.23 0.333217
\(729\) 0 0
\(730\) 31457.1 1.59490
\(731\) −12096.0 −0.612021
\(732\) 0 0
\(733\) −11795.4 −0.594372 −0.297186 0.954820i \(-0.596048\pi\)
−0.297186 + 0.954820i \(0.596048\pi\)
\(734\) 6173.25 0.310435
\(735\) 0 0
\(736\) 1818.71 0.0910849
\(737\) 11373.0 0.568424
\(738\) 0 0
\(739\) 859.661 0.0427918 0.0213959 0.999771i \(-0.493189\pi\)
0.0213959 + 0.999771i \(0.493189\pi\)
\(740\) −513.030 −0.0254856
\(741\) 0 0
\(742\) −53735.5 −2.65861
\(743\) 27738.6 1.36962 0.684812 0.728720i \(-0.259884\pi\)
0.684812 + 0.728720i \(0.259884\pi\)
\(744\) 0 0
\(745\) 42083.5 2.06956
\(746\) 24737.9 1.21410
\(747\) 0 0
\(748\) −318.029 −0.0155458
\(749\) −53643.9 −2.61696
\(750\) 0 0
\(751\) −2287.94 −0.111169 −0.0555847 0.998454i \(-0.517702\pi\)
−0.0555847 + 0.998454i \(0.517702\pi\)
\(752\) 7584.46 0.367788
\(753\) 0 0
\(754\) 887.567 0.0428691
\(755\) −24055.8 −1.15958
\(756\) 0 0
\(757\) 23515.8 1.12906 0.564530 0.825413i \(-0.309058\pi\)
0.564530 + 0.825413i \(0.309058\pi\)
\(758\) −29675.9 −1.42200
\(759\) 0 0
\(760\) 60912.5 2.90727
\(761\) −5118.88 −0.243836 −0.121918 0.992540i \(-0.538904\pi\)
−0.121918 + 0.992540i \(0.538904\pi\)
\(762\) 0 0
\(763\) 50635.1 2.40251
\(764\) −367.350 −0.0173956
\(765\) 0 0
\(766\) −8769.14 −0.413632
\(767\) −5667.76 −0.266820
\(768\) 0 0
\(769\) −32713.5 −1.53404 −0.767021 0.641622i \(-0.778262\pi\)
−0.767021 + 0.641622i \(0.778262\pi\)
\(770\) −47537.9 −2.22487
\(771\) 0 0
\(772\) 309.687 0.0144376
\(773\) −1838.02 −0.0855225 −0.0427612 0.999085i \(-0.513615\pi\)
−0.0427612 + 0.999085i \(0.513615\pi\)
\(774\) 0 0
\(775\) 8580.22 0.397691
\(776\) −41548.6 −1.92205
\(777\) 0 0
\(778\) 32641.3 1.50418
\(779\) 40754.3 1.87442
\(780\) 0 0
\(781\) 24471.5 1.12120
\(782\) 17138.9 0.783739
\(783\) 0 0
\(784\) −25764.4 −1.17367
\(785\) −25253.8 −1.14821
\(786\) 0 0
\(787\) 31329.4 1.41902 0.709512 0.704693i \(-0.248915\pi\)
0.709512 + 0.704693i \(0.248915\pi\)
\(788\) −726.536 −0.0328449
\(789\) 0 0
\(790\) 7998.41 0.360216
\(791\) −39863.3 −1.79188
\(792\) 0 0
\(793\) 2136.09 0.0956554
\(794\) −18677.7 −0.834820
\(795\) 0 0
\(796\) 67.9622 0.00302620
\(797\) 7083.13 0.314802 0.157401 0.987535i \(-0.449688\pi\)
0.157401 + 0.987535i \(0.449688\pi\)
\(798\) 0 0
\(799\) −4763.40 −0.210910
\(800\) −2813.53 −0.124342
\(801\) 0 0
\(802\) −17535.6 −0.772073
\(803\) −18935.0 −0.832132
\(804\) 0 0
\(805\) −83948.2 −3.67551
\(806\) −1007.82 −0.0440434
\(807\) 0 0
\(808\) 21601.0 0.940496
\(809\) −40383.7 −1.75502 −0.877512 0.479555i \(-0.840798\pi\)
−0.877512 + 0.479555i \(0.840798\pi\)
\(810\) 0 0
\(811\) −16572.3 −0.717549 −0.358774 0.933424i \(-0.616805\pi\)
−0.358774 + 0.933424i \(0.616805\pi\)
\(812\) 215.689 0.00932166
\(813\) 0 0
\(814\) −9423.96 −0.405786
\(815\) −33973.1 −1.46015
\(816\) 0 0
\(817\) −42886.1 −1.83647
\(818\) 5341.06 0.228296
\(819\) 0 0
\(820\) −1443.57 −0.0614778
\(821\) 2812.98 0.119578 0.0597890 0.998211i \(-0.480957\pi\)
0.0597890 + 0.998211i \(0.480957\pi\)
\(822\) 0 0
\(823\) 14450.1 0.612029 0.306015 0.952027i \(-0.401004\pi\)
0.306015 + 0.952027i \(0.401004\pi\)
\(824\) −2431.67 −0.102805
\(825\) 0 0
\(826\) 42032.1 1.77056
\(827\) −25351.1 −1.06595 −0.532977 0.846130i \(-0.678927\pi\)
−0.532977 + 0.846130i \(0.678927\pi\)
\(828\) 0 0
\(829\) 23430.1 0.981617 0.490808 0.871268i \(-0.336702\pi\)
0.490808 + 0.871268i \(0.336702\pi\)
\(830\) −54827.9 −2.29290
\(831\) 0 0
\(832\) 5451.59 0.227163
\(833\) 16181.2 0.673045
\(834\) 0 0
\(835\) 15012.1 0.622174
\(836\) −1127.56 −0.0466479
\(837\) 0 0
\(838\) 32621.1 1.34472
\(839\) 36286.4 1.49314 0.746572 0.665305i \(-0.231699\pi\)
0.746572 + 0.665305i \(0.231699\pi\)
\(840\) 0 0
\(841\) −23437.9 −0.961004
\(842\) −31409.9 −1.28558
\(843\) 0 0
\(844\) 632.314 0.0257881
\(845\) −40204.6 −1.63678
\(846\) 0 0
\(847\) −8059.08 −0.326934
\(848\) −43377.7 −1.75660
\(849\) 0 0
\(850\) −26513.7 −1.06990
\(851\) −16642.0 −0.670364
\(852\) 0 0
\(853\) −32090.8 −1.28812 −0.644060 0.764975i \(-0.722751\pi\)
−0.644060 + 0.764975i \(0.722751\pi\)
\(854\) −15841.2 −0.634749
\(855\) 0 0
\(856\) −44724.3 −1.78580
\(857\) −13271.5 −0.528992 −0.264496 0.964387i \(-0.585206\pi\)
−0.264496 + 0.964387i \(0.585206\pi\)
\(858\) 0 0
\(859\) −31122.1 −1.23617 −0.618086 0.786110i \(-0.712092\pi\)
−0.618086 + 0.786110i \(0.712092\pi\)
\(860\) 1519.09 0.0602331
\(861\) 0 0
\(862\) −33801.0 −1.33558
\(863\) −29880.8 −1.17863 −0.589313 0.807905i \(-0.700601\pi\)
−0.589313 + 0.807905i \(0.700601\pi\)
\(864\) 0 0
\(865\) −58669.0 −2.30614
\(866\) 32407.2 1.27164
\(867\) 0 0
\(868\) −244.912 −0.00957700
\(869\) −4814.50 −0.187941
\(870\) 0 0
\(871\) 3649.37 0.141968
\(872\) 42215.7 1.63946
\(873\) 0 0
\(874\) 60765.4 2.35174
\(875\) 63614.9 2.45780
\(876\) 0 0
\(877\) 14277.6 0.549737 0.274869 0.961482i \(-0.411366\pi\)
0.274869 + 0.961482i \(0.411366\pi\)
\(878\) 11931.0 0.458600
\(879\) 0 0
\(880\) −38374.8 −1.47001
\(881\) 29068.3 1.11162 0.555809 0.831310i \(-0.312409\pi\)
0.555809 + 0.831310i \(0.312409\pi\)
\(882\) 0 0
\(883\) 19579.3 0.746203 0.373102 0.927790i \(-0.378294\pi\)
0.373102 + 0.927790i \(0.378294\pi\)
\(884\) −102.050 −0.00388269
\(885\) 0 0
\(886\) 2397.00 0.0908901
\(887\) −1135.24 −0.0429738 −0.0214869 0.999769i \(-0.506840\pi\)
−0.0214869 + 0.999769i \(0.506840\pi\)
\(888\) 0 0
\(889\) −53434.3 −2.01589
\(890\) −55984.1 −2.10853
\(891\) 0 0
\(892\) −1388.64 −0.0521244
\(893\) −16888.5 −0.632870
\(894\) 0 0
\(895\) −37513.3 −1.40104
\(896\) −37897.9 −1.41304
\(897\) 0 0
\(898\) 11695.9 0.434631
\(899\) −1079.94 −0.0400644
\(900\) 0 0
\(901\) 27243.3 1.00733
\(902\) −26517.3 −0.978859
\(903\) 0 0
\(904\) −33235.0 −1.22277
\(905\) −49974.1 −1.83558
\(906\) 0 0
\(907\) −42319.8 −1.54929 −0.774645 0.632396i \(-0.782072\pi\)
−0.774645 + 0.632396i \(0.782072\pi\)
\(908\) −1060.47 −0.0387586
\(909\) 0 0
\(910\) −15254.0 −0.555677
\(911\) −20188.8 −0.734233 −0.367116 0.930175i \(-0.619655\pi\)
−0.367116 + 0.930175i \(0.619655\pi\)
\(912\) 0 0
\(913\) 33002.7 1.19631
\(914\) −45788.5 −1.65706
\(915\) 0 0
\(916\) −773.942 −0.0279168
\(917\) −13804.9 −0.497142
\(918\) 0 0
\(919\) 29559.7 1.06103 0.530514 0.847676i \(-0.321999\pi\)
0.530514 + 0.847676i \(0.321999\pi\)
\(920\) −69989.8 −2.50815
\(921\) 0 0
\(922\) −9969.01 −0.356087
\(923\) 7852.44 0.280029
\(924\) 0 0
\(925\) 25745.0 0.915125
\(926\) 14687.6 0.521235
\(927\) 0 0
\(928\) 354.120 0.0125265
\(929\) 35279.7 1.24595 0.622975 0.782242i \(-0.285924\pi\)
0.622975 + 0.782242i \(0.285924\pi\)
\(930\) 0 0
\(931\) 57370.2 2.01958
\(932\) −67.4971 −0.00237225
\(933\) 0 0
\(934\) 39698.7 1.39077
\(935\) 24101.2 0.842987
\(936\) 0 0
\(937\) −33500.7 −1.16801 −0.584003 0.811751i \(-0.698514\pi\)
−0.584003 + 0.811751i \(0.698514\pi\)
\(938\) −27063.7 −0.942070
\(939\) 0 0
\(940\) 598.216 0.0207571
\(941\) 51286.9 1.77673 0.888366 0.459137i \(-0.151841\pi\)
0.888366 + 0.459137i \(0.151841\pi\)
\(942\) 0 0
\(943\) −46827.5 −1.61709
\(944\) 33930.2 1.16985
\(945\) 0 0
\(946\) 27904.4 0.959040
\(947\) −23115.3 −0.793186 −0.396593 0.917995i \(-0.629808\pi\)
−0.396593 + 0.917995i \(0.629808\pi\)
\(948\) 0 0
\(949\) −6075.89 −0.207831
\(950\) −94003.6 −3.21040
\(951\) 0 0
\(952\) 24608.9 0.837794
\(953\) 54712.6 1.85972 0.929861 0.367911i \(-0.119927\pi\)
0.929861 + 0.367911i \(0.119927\pi\)
\(954\) 0 0
\(955\) 27838.9 0.943293
\(956\) 60.6655 0.00205237
\(957\) 0 0
\(958\) −38166.1 −1.28715
\(959\) −67531.9 −2.27395
\(960\) 0 0
\(961\) −28564.7 −0.958838
\(962\) −3023.97 −0.101348
\(963\) 0 0
\(964\) 1748.54 0.0584199
\(965\) −23469.0 −0.782894
\(966\) 0 0
\(967\) −53949.5 −1.79411 −0.897053 0.441923i \(-0.854296\pi\)
−0.897053 + 0.441923i \(0.854296\pi\)
\(968\) −6719.07 −0.223098
\(969\) 0 0
\(970\) 96831.3 3.20522
\(971\) 54124.5 1.78881 0.894407 0.447253i \(-0.147598\pi\)
0.894407 + 0.447253i \(0.147598\pi\)
\(972\) 0 0
\(973\) 7084.90 0.233434
\(974\) 31062.6 1.02188
\(975\) 0 0
\(976\) −12787.8 −0.419392
\(977\) 58614.1 1.91938 0.959688 0.281067i \(-0.0906882\pi\)
0.959688 + 0.281067i \(0.0906882\pi\)
\(978\) 0 0
\(979\) 33698.6 1.10011
\(980\) −2032.14 −0.0662390
\(981\) 0 0
\(982\) −19297.2 −0.627087
\(983\) 18587.9 0.603116 0.301558 0.953448i \(-0.402493\pi\)
0.301558 + 0.953448i \(0.402493\pi\)
\(984\) 0 0
\(985\) 55059.1 1.78104
\(986\) 3337.10 0.107784
\(987\) 0 0
\(988\) −361.814 −0.0116507
\(989\) 49277.1 1.58435
\(990\) 0 0
\(991\) 13247.9 0.424657 0.212328 0.977198i \(-0.431895\pi\)
0.212328 + 0.977198i \(0.431895\pi\)
\(992\) −402.099 −0.0128696
\(993\) 0 0
\(994\) −58233.7 −1.85821
\(995\) −5150.37 −0.164098
\(996\) 0 0
\(997\) 33371.1 1.06005 0.530026 0.847981i \(-0.322182\pi\)
0.530026 + 0.847981i \(0.322182\pi\)
\(998\) −374.677 −0.0118840
\(999\) 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.1.18 yes 59
3.2 odd 2 2151.4.a.g.1.42 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.42 59 3.2 odd 2
2151.4.a.h.1.18 yes 59 1.1 even 1 trivial