Properties

Label 2151.4.a.h.1.14
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 1.14
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.10672 q^{2} +1.65170 q^{4} -17.8784 q^{5} +0.745718 q^{7} +19.7224 q^{8} +O(q^{10})\) \(q-3.10672 q^{2} +1.65170 q^{4} -17.8784 q^{5} +0.745718 q^{7} +19.7224 q^{8} +55.5430 q^{10} -24.7007 q^{11} -48.8856 q^{13} -2.31673 q^{14} -74.4855 q^{16} +98.7517 q^{17} +29.0037 q^{19} -29.5297 q^{20} +76.7380 q^{22} +104.592 q^{23} +194.636 q^{25} +151.874 q^{26} +1.23170 q^{28} -143.025 q^{29} -9.12534 q^{31} +73.6264 q^{32} -306.794 q^{34} -13.3322 q^{35} -280.097 q^{37} -90.1064 q^{38} -352.604 q^{40} +350.333 q^{41} -161.036 q^{43} -40.7981 q^{44} -324.938 q^{46} -160.894 q^{47} -342.444 q^{49} -604.679 q^{50} -80.7443 q^{52} -316.963 q^{53} +441.607 q^{55} +14.7073 q^{56} +444.339 q^{58} +295.547 q^{59} -431.505 q^{61} +28.3499 q^{62} +367.147 q^{64} +873.994 q^{65} -547.646 q^{67} +163.108 q^{68} +41.4194 q^{70} +841.853 q^{71} +189.720 q^{73} +870.184 q^{74} +47.9054 q^{76} -18.4197 q^{77} -587.506 q^{79} +1331.68 q^{80} -1088.39 q^{82} +237.277 q^{83} -1765.52 q^{85} +500.292 q^{86} -487.156 q^{88} -1303.76 q^{89} -36.4548 q^{91} +172.754 q^{92} +499.854 q^{94} -518.539 q^{95} -364.918 q^{97} +1063.88 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.10672 −1.09839 −0.549195 0.835694i \(-0.685066\pi\)
−0.549195 + 0.835694i \(0.685066\pi\)
\(3\) 0 0
\(4\) 1.65170 0.206462
\(5\) −17.8784 −1.59909 −0.799545 0.600607i \(-0.794926\pi\)
−0.799545 + 0.600607i \(0.794926\pi\)
\(6\) 0 0
\(7\) 0.745718 0.0402650 0.0201325 0.999797i \(-0.493591\pi\)
0.0201325 + 0.999797i \(0.493591\pi\)
\(8\) 19.7224 0.871614
\(9\) 0 0
\(10\) 55.5430 1.75643
\(11\) −24.7007 −0.677048 −0.338524 0.940958i \(-0.609928\pi\)
−0.338524 + 0.940958i \(0.609928\pi\)
\(12\) 0 0
\(13\) −48.8856 −1.04296 −0.521478 0.853265i \(-0.674619\pi\)
−0.521478 + 0.853265i \(0.674619\pi\)
\(14\) −2.31673 −0.0442267
\(15\) 0 0
\(16\) −74.4855 −1.16384
\(17\) 98.7517 1.40887 0.704435 0.709768i \(-0.251200\pi\)
0.704435 + 0.709768i \(0.251200\pi\)
\(18\) 0 0
\(19\) 29.0037 0.350206 0.175103 0.984550i \(-0.443974\pi\)
0.175103 + 0.984550i \(0.443974\pi\)
\(20\) −29.5297 −0.330152
\(21\) 0 0
\(22\) 76.7380 0.743664
\(23\) 104.592 0.948214 0.474107 0.880467i \(-0.342771\pi\)
0.474107 + 0.880467i \(0.342771\pi\)
\(24\) 0 0
\(25\) 194.636 1.55709
\(26\) 151.874 1.14557
\(27\) 0 0
\(28\) 1.23170 0.00831320
\(29\) −143.025 −0.915831 −0.457915 0.888996i \(-0.651404\pi\)
−0.457915 + 0.888996i \(0.651404\pi\)
\(30\) 0 0
\(31\) −9.12534 −0.0528697 −0.0264348 0.999651i \(-0.508415\pi\)
−0.0264348 + 0.999651i \(0.508415\pi\)
\(32\) 73.6264 0.406732
\(33\) 0 0
\(34\) −306.794 −1.54749
\(35\) −13.3322 −0.0643873
\(36\) 0 0
\(37\) −280.097 −1.24453 −0.622267 0.782805i \(-0.713788\pi\)
−0.622267 + 0.782805i \(0.713788\pi\)
\(38\) −90.1064 −0.384663
\(39\) 0 0
\(40\) −352.604 −1.39379
\(41\) 350.333 1.33446 0.667230 0.744852i \(-0.267480\pi\)
0.667230 + 0.744852i \(0.267480\pi\)
\(42\) 0 0
\(43\) −161.036 −0.571109 −0.285555 0.958362i \(-0.592178\pi\)
−0.285555 + 0.958362i \(0.592178\pi\)
\(44\) −40.7981 −0.139785
\(45\) 0 0
\(46\) −324.938 −1.04151
\(47\) −160.894 −0.499337 −0.249669 0.968331i \(-0.580322\pi\)
−0.249669 + 0.968331i \(0.580322\pi\)
\(48\) 0 0
\(49\) −342.444 −0.998379
\(50\) −604.679 −1.71029
\(51\) 0 0
\(52\) −80.7443 −0.215331
\(53\) −316.963 −0.821476 −0.410738 0.911754i \(-0.634729\pi\)
−0.410738 + 0.911754i \(0.634729\pi\)
\(54\) 0 0
\(55\) 441.607 1.08266
\(56\) 14.7073 0.0350955
\(57\) 0 0
\(58\) 444.339 1.00594
\(59\) 295.547 0.652151 0.326076 0.945344i \(-0.394274\pi\)
0.326076 + 0.945344i \(0.394274\pi\)
\(60\) 0 0
\(61\) −431.505 −0.905713 −0.452857 0.891583i \(-0.649595\pi\)
−0.452857 + 0.891583i \(0.649595\pi\)
\(62\) 28.3499 0.0580715
\(63\) 0 0
\(64\) 367.147 0.717085
\(65\) 873.994 1.66778
\(66\) 0 0
\(67\) −547.646 −0.998591 −0.499296 0.866432i \(-0.666408\pi\)
−0.499296 + 0.866432i \(0.666408\pi\)
\(68\) 163.108 0.290879
\(69\) 0 0
\(70\) 41.4194 0.0707224
\(71\) 841.853 1.40718 0.703588 0.710608i \(-0.251580\pi\)
0.703588 + 0.710608i \(0.251580\pi\)
\(72\) 0 0
\(73\) 189.720 0.304178 0.152089 0.988367i \(-0.451400\pi\)
0.152089 + 0.988367i \(0.451400\pi\)
\(74\) 870.184 1.36698
\(75\) 0 0
\(76\) 47.9054 0.0723043
\(77\) −18.4197 −0.0272613
\(78\) 0 0
\(79\) −587.506 −0.836703 −0.418352 0.908285i \(-0.637392\pi\)
−0.418352 + 0.908285i \(0.637392\pi\)
\(80\) 1331.68 1.86108
\(81\) 0 0
\(82\) −1088.39 −1.46576
\(83\) 237.277 0.313790 0.156895 0.987615i \(-0.449852\pi\)
0.156895 + 0.987615i \(0.449852\pi\)
\(84\) 0 0
\(85\) −1765.52 −2.25291
\(86\) 500.292 0.627301
\(87\) 0 0
\(88\) −487.156 −0.590125
\(89\) −1303.76 −1.55279 −0.776394 0.630248i \(-0.782953\pi\)
−0.776394 + 0.630248i \(0.782953\pi\)
\(90\) 0 0
\(91\) −36.4548 −0.0419946
\(92\) 172.754 0.195771
\(93\) 0 0
\(94\) 499.854 0.548468
\(95\) −518.539 −0.560010
\(96\) 0 0
\(97\) −364.918 −0.381977 −0.190989 0.981592i \(-0.561169\pi\)
−0.190989 + 0.981592i \(0.561169\pi\)
\(98\) 1063.88 1.09661
\(99\) 0 0
\(100\) 321.480 0.321480
\(101\) −1684.17 −1.65922 −0.829610 0.558344i \(-0.811437\pi\)
−0.829610 + 0.558344i \(0.811437\pi\)
\(102\) 0 0
\(103\) −29.1605 −0.0278958 −0.0139479 0.999903i \(-0.504440\pi\)
−0.0139479 + 0.999903i \(0.504440\pi\)
\(104\) −964.140 −0.909055
\(105\) 0 0
\(106\) 984.715 0.902301
\(107\) −1521.44 −1.37461 −0.687304 0.726370i \(-0.741206\pi\)
−0.687304 + 0.726370i \(0.741206\pi\)
\(108\) 0 0
\(109\) 1470.92 1.29256 0.646278 0.763102i \(-0.276325\pi\)
0.646278 + 0.763102i \(0.276325\pi\)
\(110\) −1371.95 −1.18918
\(111\) 0 0
\(112\) −55.5451 −0.0468618
\(113\) −28.8054 −0.0239804 −0.0119902 0.999928i \(-0.503817\pi\)
−0.0119902 + 0.999928i \(0.503817\pi\)
\(114\) 0 0
\(115\) −1869.93 −1.51628
\(116\) −236.235 −0.189085
\(117\) 0 0
\(118\) −918.181 −0.716317
\(119\) 73.6409 0.0567281
\(120\) 0 0
\(121\) −720.877 −0.541606
\(122\) 1340.56 0.994827
\(123\) 0 0
\(124\) −15.0723 −0.0109156
\(125\) −1244.98 −0.890832
\(126\) 0 0
\(127\) 1705.66 1.19175 0.595877 0.803076i \(-0.296805\pi\)
0.595877 + 0.803076i \(0.296805\pi\)
\(128\) −1729.63 −1.19437
\(129\) 0 0
\(130\) −2715.25 −1.83187
\(131\) 920.292 0.613789 0.306894 0.951744i \(-0.400710\pi\)
0.306894 + 0.951744i \(0.400710\pi\)
\(132\) 0 0
\(133\) 21.6286 0.0141010
\(134\) 1701.38 1.09684
\(135\) 0 0
\(136\) 1947.62 1.22799
\(137\) −163.174 −0.101758 −0.0508791 0.998705i \(-0.516202\pi\)
−0.0508791 + 0.998705i \(0.516202\pi\)
\(138\) 0 0
\(139\) −2133.81 −1.30207 −0.651035 0.759048i \(-0.725665\pi\)
−0.651035 + 0.759048i \(0.725665\pi\)
\(140\) −22.0208 −0.0132936
\(141\) 0 0
\(142\) −2615.40 −1.54563
\(143\) 1207.51 0.706131
\(144\) 0 0
\(145\) 2557.06 1.46450
\(146\) −589.406 −0.334107
\(147\) 0 0
\(148\) −462.637 −0.256949
\(149\) −1922.08 −1.05680 −0.528398 0.848997i \(-0.677207\pi\)
−0.528398 + 0.848997i \(0.677207\pi\)
\(150\) 0 0
\(151\) −2674.86 −1.44157 −0.720784 0.693159i \(-0.756218\pi\)
−0.720784 + 0.693159i \(0.756218\pi\)
\(152\) 572.022 0.305244
\(153\) 0 0
\(154\) 57.2249 0.0299436
\(155\) 163.146 0.0845433
\(156\) 0 0
\(157\) −1031.87 −0.524536 −0.262268 0.964995i \(-0.584470\pi\)
−0.262268 + 0.964995i \(0.584470\pi\)
\(158\) 1825.21 0.919027
\(159\) 0 0
\(160\) −1316.32 −0.650401
\(161\) 77.9960 0.0381798
\(162\) 0 0
\(163\) −1046.99 −0.503106 −0.251553 0.967843i \(-0.580941\pi\)
−0.251553 + 0.967843i \(0.580941\pi\)
\(164\) 578.645 0.275516
\(165\) 0 0
\(166\) −737.153 −0.344664
\(167\) −476.791 −0.220929 −0.110465 0.993880i \(-0.535234\pi\)
−0.110465 + 0.993880i \(0.535234\pi\)
\(168\) 0 0
\(169\) 192.801 0.0877565
\(170\) 5484.97 2.47458
\(171\) 0 0
\(172\) −265.982 −0.117913
\(173\) 1492.14 0.655754 0.327877 0.944720i \(-0.393667\pi\)
0.327877 + 0.944720i \(0.393667\pi\)
\(174\) 0 0
\(175\) 145.143 0.0626961
\(176\) 1839.84 0.787973
\(177\) 0 0
\(178\) 4050.41 1.70557
\(179\) −1851.15 −0.772968 −0.386484 0.922296i \(-0.626311\pi\)
−0.386484 + 0.922296i \(0.626311\pi\)
\(180\) 0 0
\(181\) −2034.86 −0.835633 −0.417817 0.908531i \(-0.637205\pi\)
−0.417817 + 0.908531i \(0.637205\pi\)
\(182\) 113.255 0.0461265
\(183\) 0 0
\(184\) 2062.80 0.826477
\(185\) 5007.68 1.99012
\(186\) 0 0
\(187\) −2439.23 −0.953873
\(188\) −265.749 −0.103094
\(189\) 0 0
\(190\) 1610.95 0.615110
\(191\) 3100.11 1.17443 0.587214 0.809431i \(-0.300225\pi\)
0.587214 + 0.809431i \(0.300225\pi\)
\(192\) 0 0
\(193\) 1287.94 0.480353 0.240177 0.970729i \(-0.422795\pi\)
0.240177 + 0.970729i \(0.422795\pi\)
\(194\) 1133.70 0.419560
\(195\) 0 0
\(196\) −565.614 −0.206128
\(197\) 4343.12 1.57073 0.785367 0.619031i \(-0.212474\pi\)
0.785367 + 0.619031i \(0.212474\pi\)
\(198\) 0 0
\(199\) −30.9425 −0.0110224 −0.00551120 0.999985i \(-0.501754\pi\)
−0.00551120 + 0.999985i \(0.501754\pi\)
\(200\) 3838.68 1.35718
\(201\) 0 0
\(202\) 5232.24 1.82247
\(203\) −106.656 −0.0368759
\(204\) 0 0
\(205\) −6263.39 −2.13392
\(206\) 90.5935 0.0306405
\(207\) 0 0
\(208\) 3641.27 1.21383
\(209\) −716.411 −0.237106
\(210\) 0 0
\(211\) 3748.26 1.22294 0.611471 0.791267i \(-0.290578\pi\)
0.611471 + 0.791267i \(0.290578\pi\)
\(212\) −523.527 −0.169604
\(213\) 0 0
\(214\) 4726.68 1.50986
\(215\) 2879.05 0.913255
\(216\) 0 0
\(217\) −6.80493 −0.00212879
\(218\) −4569.73 −1.41973
\(219\) 0 0
\(220\) 729.403 0.223529
\(221\) −4827.53 −1.46939
\(222\) 0 0
\(223\) −2771.21 −0.832171 −0.416085 0.909326i \(-0.636598\pi\)
−0.416085 + 0.909326i \(0.636598\pi\)
\(224\) 54.9045 0.0163771
\(225\) 0 0
\(226\) 89.4902 0.0263398
\(227\) 236.430 0.0691296 0.0345648 0.999402i \(-0.488995\pi\)
0.0345648 + 0.999402i \(0.488995\pi\)
\(228\) 0 0
\(229\) 322.526 0.0930705 0.0465352 0.998917i \(-0.485182\pi\)
0.0465352 + 0.998917i \(0.485182\pi\)
\(230\) 5809.35 1.66547
\(231\) 0 0
\(232\) −2820.80 −0.798251
\(233\) 1999.92 0.562312 0.281156 0.959662i \(-0.409282\pi\)
0.281156 + 0.959662i \(0.409282\pi\)
\(234\) 0 0
\(235\) 2876.53 0.798485
\(236\) 488.154 0.134645
\(237\) 0 0
\(238\) −228.781 −0.0623097
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −5112.71 −1.36655 −0.683275 0.730161i \(-0.739445\pi\)
−0.683275 + 0.730161i \(0.739445\pi\)
\(242\) 2239.56 0.594895
\(243\) 0 0
\(244\) −712.716 −0.186996
\(245\) 6122.34 1.59650
\(246\) 0 0
\(247\) −1417.86 −0.365249
\(248\) −179.973 −0.0460820
\(249\) 0 0
\(250\) 3867.79 0.978482
\(251\) −2554.30 −0.642334 −0.321167 0.947023i \(-0.604075\pi\)
−0.321167 + 0.947023i \(0.604075\pi\)
\(252\) 0 0
\(253\) −2583.49 −0.641987
\(254\) −5299.00 −1.30901
\(255\) 0 0
\(256\) 2436.31 0.594802
\(257\) 4075.19 0.989119 0.494559 0.869144i \(-0.335329\pi\)
0.494559 + 0.869144i \(0.335329\pi\)
\(258\) 0 0
\(259\) −208.874 −0.0501111
\(260\) 1443.58 0.344334
\(261\) 0 0
\(262\) −2859.09 −0.674180
\(263\) 737.047 0.172807 0.0864035 0.996260i \(-0.472463\pi\)
0.0864035 + 0.996260i \(0.472463\pi\)
\(264\) 0 0
\(265\) 5666.78 1.31361
\(266\) −67.1939 −0.0154884
\(267\) 0 0
\(268\) −904.547 −0.206172
\(269\) 3909.75 0.886178 0.443089 0.896478i \(-0.353883\pi\)
0.443089 + 0.896478i \(0.353883\pi\)
\(270\) 0 0
\(271\) −843.576 −0.189091 −0.0945454 0.995521i \(-0.530140\pi\)
−0.0945454 + 0.995521i \(0.530140\pi\)
\(272\) −7355.57 −1.63969
\(273\) 0 0
\(274\) 506.935 0.111770
\(275\) −4807.64 −1.05422
\(276\) 0 0
\(277\) 1297.21 0.281379 0.140690 0.990054i \(-0.455068\pi\)
0.140690 + 0.990054i \(0.455068\pi\)
\(278\) 6629.16 1.43018
\(279\) 0 0
\(280\) −262.943 −0.0561209
\(281\) −6877.66 −1.46010 −0.730048 0.683396i \(-0.760502\pi\)
−0.730048 + 0.683396i \(0.760502\pi\)
\(282\) 0 0
\(283\) 177.597 0.0373041 0.0186520 0.999826i \(-0.494063\pi\)
0.0186520 + 0.999826i \(0.494063\pi\)
\(284\) 1390.49 0.290529
\(285\) 0 0
\(286\) −3751.38 −0.775608
\(287\) 261.250 0.0537320
\(288\) 0 0
\(289\) 4838.90 0.984917
\(290\) −7944.05 −1.60859
\(291\) 0 0
\(292\) 313.360 0.0628014
\(293\) −231.891 −0.0462362 −0.0231181 0.999733i \(-0.507359\pi\)
−0.0231181 + 0.999733i \(0.507359\pi\)
\(294\) 0 0
\(295\) −5283.89 −1.04285
\(296\) −5524.19 −1.08475
\(297\) 0 0
\(298\) 5971.35 1.16078
\(299\) −5113.04 −0.988945
\(300\) 0 0
\(301\) −120.087 −0.0229957
\(302\) 8310.03 1.58341
\(303\) 0 0
\(304\) −2160.36 −0.407582
\(305\) 7714.60 1.44832
\(306\) 0 0
\(307\) 1985.03 0.369029 0.184514 0.982830i \(-0.440929\pi\)
0.184514 + 0.982830i \(0.440929\pi\)
\(308\) −30.4238 −0.00562844
\(309\) 0 0
\(310\) −506.849 −0.0928616
\(311\) 3843.49 0.700786 0.350393 0.936603i \(-0.386048\pi\)
0.350393 + 0.936603i \(0.386048\pi\)
\(312\) 0 0
\(313\) 3979.76 0.718688 0.359344 0.933205i \(-0.383001\pi\)
0.359344 + 0.933205i \(0.383001\pi\)
\(314\) 3205.73 0.576145
\(315\) 0 0
\(316\) −970.383 −0.172748
\(317\) −8025.86 −1.42201 −0.711005 0.703187i \(-0.751760\pi\)
−0.711005 + 0.703187i \(0.751760\pi\)
\(318\) 0 0
\(319\) 3532.82 0.620062
\(320\) −6564.00 −1.14668
\(321\) 0 0
\(322\) −242.312 −0.0419364
\(323\) 2864.17 0.493395
\(324\) 0 0
\(325\) −9514.89 −1.62397
\(326\) 3252.69 0.552607
\(327\) 0 0
\(328\) 6909.41 1.16313
\(329\) −119.982 −0.0201058
\(330\) 0 0
\(331\) 2201.00 0.365493 0.182746 0.983160i \(-0.441501\pi\)
0.182746 + 0.983160i \(0.441501\pi\)
\(332\) 391.910 0.0647858
\(333\) 0 0
\(334\) 1481.26 0.242667
\(335\) 9791.02 1.59684
\(336\) 0 0
\(337\) 9699.26 1.56781 0.783905 0.620880i \(-0.213225\pi\)
0.783905 + 0.620880i \(0.213225\pi\)
\(338\) −598.978 −0.0963909
\(339\) 0 0
\(340\) −2916.11 −0.465141
\(341\) 225.402 0.0357953
\(342\) 0 0
\(343\) −511.148 −0.0804646
\(344\) −3176.01 −0.497787
\(345\) 0 0
\(346\) −4635.67 −0.720274
\(347\) 9863.87 1.52599 0.762997 0.646402i \(-0.223727\pi\)
0.762997 + 0.646402i \(0.223727\pi\)
\(348\) 0 0
\(349\) −11050.6 −1.69491 −0.847454 0.530869i \(-0.821866\pi\)
−0.847454 + 0.530869i \(0.821866\pi\)
\(350\) −450.920 −0.0688648
\(351\) 0 0
\(352\) −1818.62 −0.275377
\(353\) −511.811 −0.0771698 −0.0385849 0.999255i \(-0.512285\pi\)
−0.0385849 + 0.999255i \(0.512285\pi\)
\(354\) 0 0
\(355\) −15051.0 −2.25020
\(356\) −2153.42 −0.320592
\(357\) 0 0
\(358\) 5750.99 0.849021
\(359\) 12746.3 1.87389 0.936943 0.349481i \(-0.113642\pi\)
0.936943 + 0.349481i \(0.113642\pi\)
\(360\) 0 0
\(361\) −6017.78 −0.877356
\(362\) 6321.72 0.917852
\(363\) 0 0
\(364\) −60.2124 −0.00867030
\(365\) −3391.88 −0.486409
\(366\) 0 0
\(367\) 7419.01 1.05523 0.527615 0.849484i \(-0.323086\pi\)
0.527615 + 0.849484i \(0.323086\pi\)
\(368\) −7790.58 −1.10357
\(369\) 0 0
\(370\) −15557.5 −2.18593
\(371\) −236.365 −0.0330767
\(372\) 0 0
\(373\) −1108.86 −0.153927 −0.0769633 0.997034i \(-0.524522\pi\)
−0.0769633 + 0.997034i \(0.524522\pi\)
\(374\) 7578.01 1.04773
\(375\) 0 0
\(376\) −3173.22 −0.435230
\(377\) 6991.87 0.955171
\(378\) 0 0
\(379\) 10686.4 1.44835 0.724173 0.689618i \(-0.242222\pi\)
0.724173 + 0.689618i \(0.242222\pi\)
\(380\) −856.471 −0.115621
\(381\) 0 0
\(382\) −9631.16 −1.28998
\(383\) −12048.2 −1.60740 −0.803702 0.595031i \(-0.797140\pi\)
−0.803702 + 0.595031i \(0.797140\pi\)
\(384\) 0 0
\(385\) 329.314 0.0435933
\(386\) −4001.28 −0.527615
\(387\) 0 0
\(388\) −602.734 −0.0788639
\(389\) −1473.17 −0.192011 −0.0960057 0.995381i \(-0.530607\pi\)
−0.0960057 + 0.995381i \(0.530607\pi\)
\(390\) 0 0
\(391\) 10328.6 1.33591
\(392\) −6753.81 −0.870201
\(393\) 0 0
\(394\) −13492.9 −1.72528
\(395\) 10503.6 1.33796
\(396\) 0 0
\(397\) 5818.69 0.735596 0.367798 0.929906i \(-0.380112\pi\)
0.367798 + 0.929906i \(0.380112\pi\)
\(398\) 96.1297 0.0121069
\(399\) 0 0
\(400\) −14497.5 −1.81219
\(401\) −3009.09 −0.374730 −0.187365 0.982290i \(-0.559995\pi\)
−0.187365 + 0.982290i \(0.559995\pi\)
\(402\) 0 0
\(403\) 446.098 0.0551407
\(404\) −2781.74 −0.342566
\(405\) 0 0
\(406\) 331.351 0.0405042
\(407\) 6918.59 0.842609
\(408\) 0 0
\(409\) −12146.2 −1.46844 −0.734218 0.678914i \(-0.762451\pi\)
−0.734218 + 0.678914i \(0.762451\pi\)
\(410\) 19458.6 2.34388
\(411\) 0 0
\(412\) −48.1644 −0.00575944
\(413\) 220.394 0.0262588
\(414\) 0 0
\(415\) −4242.13 −0.501778
\(416\) −3599.27 −0.424203
\(417\) 0 0
\(418\) 2225.69 0.260435
\(419\) 7078.38 0.825302 0.412651 0.910889i \(-0.364603\pi\)
0.412651 + 0.910889i \(0.364603\pi\)
\(420\) 0 0
\(421\) −1350.43 −0.156332 −0.0781662 0.996940i \(-0.524906\pi\)
−0.0781662 + 0.996940i \(0.524906\pi\)
\(422\) −11644.8 −1.34327
\(423\) 0 0
\(424\) −6251.26 −0.716010
\(425\) 19220.6 2.19373
\(426\) 0 0
\(427\) −321.781 −0.0364685
\(428\) −2512.96 −0.283805
\(429\) 0 0
\(430\) −8944.41 −1.00311
\(431\) −6841.23 −0.764572 −0.382286 0.924044i \(-0.624863\pi\)
−0.382286 + 0.924044i \(0.624863\pi\)
\(432\) 0 0
\(433\) 14287.5 1.58572 0.792859 0.609406i \(-0.208592\pi\)
0.792859 + 0.609406i \(0.208592\pi\)
\(434\) 21.1410 0.00233825
\(435\) 0 0
\(436\) 2429.52 0.266864
\(437\) 3033.56 0.332070
\(438\) 0 0
\(439\) 1490.40 0.162034 0.0810171 0.996713i \(-0.474183\pi\)
0.0810171 + 0.996713i \(0.474183\pi\)
\(440\) 8709.55 0.943663
\(441\) 0 0
\(442\) 14997.8 1.61396
\(443\) 11204.7 1.20169 0.600847 0.799364i \(-0.294830\pi\)
0.600847 + 0.799364i \(0.294830\pi\)
\(444\) 0 0
\(445\) 23309.1 2.48305
\(446\) 8609.37 0.914049
\(447\) 0 0
\(448\) 273.788 0.0288734
\(449\) 15726.5 1.65296 0.826480 0.562966i \(-0.190340\pi\)
0.826480 + 0.562966i \(0.190340\pi\)
\(450\) 0 0
\(451\) −8653.47 −0.903494
\(452\) −47.5778 −0.00495104
\(453\) 0 0
\(454\) −734.522 −0.0759313
\(455\) 651.753 0.0671531
\(456\) 0 0
\(457\) 9442.99 0.966574 0.483287 0.875462i \(-0.339443\pi\)
0.483287 + 0.875462i \(0.339443\pi\)
\(458\) −1002.00 −0.102228
\(459\) 0 0
\(460\) −3088.57 −0.313055
\(461\) 4345.33 0.439007 0.219504 0.975612i \(-0.429556\pi\)
0.219504 + 0.975612i \(0.429556\pi\)
\(462\) 0 0
\(463\) 11702.1 1.17461 0.587303 0.809367i \(-0.300190\pi\)
0.587303 + 0.809367i \(0.300190\pi\)
\(464\) 10653.3 1.06588
\(465\) 0 0
\(466\) −6213.17 −0.617639
\(467\) −10980.5 −1.08805 −0.544023 0.839070i \(-0.683100\pi\)
−0.544023 + 0.839070i \(0.683100\pi\)
\(468\) 0 0
\(469\) −408.389 −0.0402082
\(470\) −8936.56 −0.877049
\(471\) 0 0
\(472\) 5828.89 0.568424
\(473\) 3977.69 0.386669
\(474\) 0 0
\(475\) 5645.16 0.545301
\(476\) 121.633 0.0117122
\(477\) 0 0
\(478\) 742.506 0.0710490
\(479\) 16368.3 1.56135 0.780673 0.624939i \(-0.214876\pi\)
0.780673 + 0.624939i \(0.214876\pi\)
\(480\) 0 0
\(481\) 13692.7 1.29799
\(482\) 15883.8 1.50101
\(483\) 0 0
\(484\) −1190.67 −0.111821
\(485\) 6524.13 0.610815
\(486\) 0 0
\(487\) −5105.40 −0.475047 −0.237523 0.971382i \(-0.576336\pi\)
−0.237523 + 0.971382i \(0.576336\pi\)
\(488\) −8510.30 −0.789433
\(489\) 0 0
\(490\) −19020.4 −1.75358
\(491\) 1265.56 0.116322 0.0581608 0.998307i \(-0.481476\pi\)
0.0581608 + 0.998307i \(0.481476\pi\)
\(492\) 0 0
\(493\) −14124.0 −1.29029
\(494\) 4404.90 0.401186
\(495\) 0 0
\(496\) 679.705 0.0615316
\(497\) 627.784 0.0566599
\(498\) 0 0
\(499\) 4373.23 0.392330 0.196165 0.980571i \(-0.437151\pi\)
0.196165 + 0.980571i \(0.437151\pi\)
\(500\) −2056.33 −0.183923
\(501\) 0 0
\(502\) 7935.48 0.705534
\(503\) −19926.2 −1.76633 −0.883164 0.469064i \(-0.844591\pi\)
−0.883164 + 0.469064i \(0.844591\pi\)
\(504\) 0 0
\(505\) 30110.2 2.65324
\(506\) 8026.18 0.705152
\(507\) 0 0
\(508\) 2817.23 0.246052
\(509\) −15679.4 −1.36538 −0.682691 0.730708i \(-0.739190\pi\)
−0.682691 + 0.730708i \(0.739190\pi\)
\(510\) 0 0
\(511\) 141.477 0.0122477
\(512\) 6268.15 0.541047
\(513\) 0 0
\(514\) −12660.5 −1.08644
\(515\) 521.343 0.0446080
\(516\) 0 0
\(517\) 3974.20 0.338075
\(518\) 648.911 0.0550416
\(519\) 0 0
\(520\) 17237.3 1.45366
\(521\) 16954.5 1.42570 0.712850 0.701316i \(-0.247404\pi\)
0.712850 + 0.701316i \(0.247404\pi\)
\(522\) 0 0
\(523\) 20850.4 1.74326 0.871628 0.490167i \(-0.163064\pi\)
0.871628 + 0.490167i \(0.163064\pi\)
\(524\) 1520.05 0.126724
\(525\) 0 0
\(526\) −2289.80 −0.189810
\(527\) −901.143 −0.0744865
\(528\) 0 0
\(529\) −1227.53 −0.100890
\(530\) −17605.1 −1.44286
\(531\) 0 0
\(532\) 35.7239 0.00291133
\(533\) −17126.3 −1.39178
\(534\) 0 0
\(535\) 27200.8 2.19812
\(536\) −10800.9 −0.870387
\(537\) 0 0
\(538\) −12146.5 −0.973370
\(539\) 8458.59 0.675951
\(540\) 0 0
\(541\) 3440.60 0.273425 0.136712 0.990611i \(-0.456346\pi\)
0.136712 + 0.990611i \(0.456346\pi\)
\(542\) 2620.75 0.207696
\(543\) 0 0
\(544\) 7270.73 0.573033
\(545\) −26297.6 −2.06691
\(546\) 0 0
\(547\) 11784.0 0.921113 0.460556 0.887630i \(-0.347650\pi\)
0.460556 + 0.887630i \(0.347650\pi\)
\(548\) −269.514 −0.0210092
\(549\) 0 0
\(550\) 14936.0 1.15795
\(551\) −4148.26 −0.320729
\(552\) 0 0
\(553\) −438.113 −0.0336898
\(554\) −4030.08 −0.309064
\(555\) 0 0
\(556\) −3524.42 −0.268829
\(557\) −620.891 −0.0472316 −0.0236158 0.999721i \(-0.507518\pi\)
−0.0236158 + 0.999721i \(0.507518\pi\)
\(558\) 0 0
\(559\) 7872.32 0.595642
\(560\) 993.056 0.0749362
\(561\) 0 0
\(562\) 21366.9 1.60376
\(563\) 26002.2 1.94647 0.973233 0.229821i \(-0.0738140\pi\)
0.973233 + 0.229821i \(0.0738140\pi\)
\(564\) 0 0
\(565\) 514.993 0.0383467
\(566\) −551.744 −0.0409745
\(567\) 0 0
\(568\) 16603.3 1.22652
\(569\) −10004.8 −0.737120 −0.368560 0.929604i \(-0.620149\pi\)
−0.368560 + 0.929604i \(0.620149\pi\)
\(570\) 0 0
\(571\) −9283.06 −0.680357 −0.340179 0.940361i \(-0.610488\pi\)
−0.340179 + 0.940361i \(0.610488\pi\)
\(572\) 1994.44 0.145790
\(573\) 0 0
\(574\) −811.629 −0.0590187
\(575\) 20357.3 1.47645
\(576\) 0 0
\(577\) −4371.52 −0.315405 −0.157703 0.987487i \(-0.550409\pi\)
−0.157703 + 0.987487i \(0.550409\pi\)
\(578\) −15033.1 −1.08182
\(579\) 0 0
\(580\) 4223.49 0.302363
\(581\) 176.942 0.0126347
\(582\) 0 0
\(583\) 7829.19 0.556179
\(584\) 3741.73 0.265126
\(585\) 0 0
\(586\) 720.419 0.0507854
\(587\) 5076.25 0.356932 0.178466 0.983946i \(-0.442886\pi\)
0.178466 + 0.983946i \(0.442886\pi\)
\(588\) 0 0
\(589\) −264.669 −0.0185153
\(590\) 16415.6 1.14545
\(591\) 0 0
\(592\) 20863.2 1.44843
\(593\) −14397.4 −0.997019 −0.498509 0.866884i \(-0.666119\pi\)
−0.498509 + 0.866884i \(0.666119\pi\)
\(594\) 0 0
\(595\) −1316.58 −0.0907134
\(596\) −3174.69 −0.218189
\(597\) 0 0
\(598\) 15884.8 1.08625
\(599\) −13497.3 −0.920676 −0.460338 0.887744i \(-0.652272\pi\)
−0.460338 + 0.887744i \(0.652272\pi\)
\(600\) 0 0
\(601\) 7012.74 0.475966 0.237983 0.971269i \(-0.423514\pi\)
0.237983 + 0.971269i \(0.423514\pi\)
\(602\) 373.077 0.0252583
\(603\) 0 0
\(604\) −4418.06 −0.297630
\(605\) 12888.1 0.866076
\(606\) 0 0
\(607\) −22822.2 −1.52607 −0.763035 0.646357i \(-0.776292\pi\)
−0.763035 + 0.646357i \(0.776292\pi\)
\(608\) 2135.44 0.142440
\(609\) 0 0
\(610\) −23967.1 −1.59082
\(611\) 7865.42 0.520787
\(612\) 0 0
\(613\) −12441.8 −0.819771 −0.409885 0.912137i \(-0.634431\pi\)
−0.409885 + 0.912137i \(0.634431\pi\)
\(614\) −6166.94 −0.405338
\(615\) 0 0
\(616\) −363.281 −0.0237614
\(617\) 8903.80 0.580962 0.290481 0.956881i \(-0.406185\pi\)
0.290481 + 0.956881i \(0.406185\pi\)
\(618\) 0 0
\(619\) −1315.39 −0.0854120 −0.0427060 0.999088i \(-0.513598\pi\)
−0.0427060 + 0.999088i \(0.513598\pi\)
\(620\) 269.468 0.0174550
\(621\) 0 0
\(622\) −11940.7 −0.769737
\(623\) −972.236 −0.0625230
\(624\) 0 0
\(625\) −2071.36 −0.132567
\(626\) −12364.0 −0.789400
\(627\) 0 0
\(628\) −1704.34 −0.108297
\(629\) −27660.1 −1.75339
\(630\) 0 0
\(631\) 27108.3 1.71024 0.855121 0.518429i \(-0.173483\pi\)
0.855121 + 0.518429i \(0.173483\pi\)
\(632\) −11587.0 −0.729282
\(633\) 0 0
\(634\) 24934.1 1.56192
\(635\) −30494.4 −1.90572
\(636\) 0 0
\(637\) 16740.6 1.04126
\(638\) −10975.5 −0.681070
\(639\) 0 0
\(640\) 30923.0 1.90991
\(641\) 11334.4 0.698409 0.349204 0.937047i \(-0.386452\pi\)
0.349204 + 0.937047i \(0.386452\pi\)
\(642\) 0 0
\(643\) 1526.23 0.0936063 0.0468031 0.998904i \(-0.485097\pi\)
0.0468031 + 0.998904i \(0.485097\pi\)
\(644\) 128.826 0.00788270
\(645\) 0 0
\(646\) −8898.16 −0.541940
\(647\) −1836.25 −0.111577 −0.0557886 0.998443i \(-0.517767\pi\)
−0.0557886 + 0.998443i \(0.517767\pi\)
\(648\) 0 0
\(649\) −7300.20 −0.441538
\(650\) 29560.1 1.78376
\(651\) 0 0
\(652\) −1729.31 −0.103873
\(653\) −18006.4 −1.07909 −0.539543 0.841958i \(-0.681403\pi\)
−0.539543 + 0.841958i \(0.681403\pi\)
\(654\) 0 0
\(655\) −16453.3 −0.981503
\(656\) −26094.7 −1.55309
\(657\) 0 0
\(658\) 372.750 0.0220840
\(659\) 13881.1 0.820531 0.410266 0.911966i \(-0.365436\pi\)
0.410266 + 0.911966i \(0.365436\pi\)
\(660\) 0 0
\(661\) −13229.9 −0.778495 −0.389247 0.921133i \(-0.627265\pi\)
−0.389247 + 0.921133i \(0.627265\pi\)
\(662\) −6837.90 −0.401454
\(663\) 0 0
\(664\) 4679.67 0.273504
\(665\) −386.684 −0.0225488
\(666\) 0 0
\(667\) −14959.3 −0.868404
\(668\) −787.515 −0.0456136
\(669\) 0 0
\(670\) −30417.9 −1.75395
\(671\) 10658.4 0.613211
\(672\) 0 0
\(673\) 6521.08 0.373505 0.186753 0.982407i \(-0.440204\pi\)
0.186753 + 0.982407i \(0.440204\pi\)
\(674\) −30132.9 −1.72207
\(675\) 0 0
\(676\) 318.449 0.0181184
\(677\) −14707.0 −0.834914 −0.417457 0.908697i \(-0.637079\pi\)
−0.417457 + 0.908697i \(0.637079\pi\)
\(678\) 0 0
\(679\) −272.125 −0.0153803
\(680\) −34820.2 −1.96367
\(681\) 0 0
\(682\) −700.260 −0.0393172
\(683\) −30336.2 −1.69954 −0.849768 0.527157i \(-0.823258\pi\)
−0.849768 + 0.527157i \(0.823258\pi\)
\(684\) 0 0
\(685\) 2917.28 0.162720
\(686\) 1587.99 0.0883816
\(687\) 0 0
\(688\) 11994.8 0.664677
\(689\) 15494.9 0.856763
\(690\) 0 0
\(691\) 22793.2 1.25484 0.627421 0.778680i \(-0.284110\pi\)
0.627421 + 0.778680i \(0.284110\pi\)
\(692\) 2464.57 0.135389
\(693\) 0 0
\(694\) −30644.3 −1.67614
\(695\) 38149.1 2.08213
\(696\) 0 0
\(697\) 34596.0 1.88008
\(698\) 34331.0 1.86167
\(699\) 0 0
\(700\) 239.733 0.0129444
\(701\) 4226.10 0.227700 0.113850 0.993498i \(-0.463682\pi\)
0.113850 + 0.993498i \(0.463682\pi\)
\(702\) 0 0
\(703\) −8123.87 −0.435843
\(704\) −9068.79 −0.485501
\(705\) 0 0
\(706\) 1590.05 0.0847626
\(707\) −1255.91 −0.0668084
\(708\) 0 0
\(709\) −29662.6 −1.57123 −0.785615 0.618715i \(-0.787653\pi\)
−0.785615 + 0.618715i \(0.787653\pi\)
\(710\) 46759.1 2.47160
\(711\) 0 0
\(712\) −25713.2 −1.35343
\(713\) −954.437 −0.0501318
\(714\) 0 0
\(715\) −21588.2 −1.12917
\(716\) −3057.54 −0.159589
\(717\) 0 0
\(718\) −39599.2 −2.05826
\(719\) −28079.9 −1.45647 −0.728237 0.685325i \(-0.759660\pi\)
−0.728237 + 0.685325i \(0.759660\pi\)
\(720\) 0 0
\(721\) −21.7455 −0.00112323
\(722\) 18695.6 0.963680
\(723\) 0 0
\(724\) −3360.97 −0.172527
\(725\) −27837.8 −1.42603
\(726\) 0 0
\(727\) 6488.86 0.331030 0.165515 0.986207i \(-0.447071\pi\)
0.165515 + 0.986207i \(0.447071\pi\)
\(728\) −718.976 −0.0366031
\(729\) 0 0
\(730\) 10537.6 0.534267
\(731\) −15902.5 −0.804619
\(732\) 0 0
\(733\) 5082.45 0.256104 0.128052 0.991767i \(-0.459127\pi\)
0.128052 + 0.991767i \(0.459127\pi\)
\(734\) −23048.8 −1.15905
\(735\) 0 0
\(736\) 7700.72 0.385669
\(737\) 13527.2 0.676094
\(738\) 0 0
\(739\) −2586.05 −0.128727 −0.0643635 0.997927i \(-0.520502\pi\)
−0.0643635 + 0.997927i \(0.520502\pi\)
\(740\) 8271.19 0.410885
\(741\) 0 0
\(742\) 734.319 0.0363311
\(743\) −13473.8 −0.665283 −0.332641 0.943053i \(-0.607940\pi\)
−0.332641 + 0.943053i \(0.607940\pi\)
\(744\) 0 0
\(745\) 34363.6 1.68991
\(746\) 3444.92 0.169072
\(747\) 0 0
\(748\) −4028.88 −0.196939
\(749\) −1134.56 −0.0553486
\(750\) 0 0
\(751\) 17858.4 0.867724 0.433862 0.900979i \(-0.357150\pi\)
0.433862 + 0.900979i \(0.357150\pi\)
\(752\) 11984.3 0.581147
\(753\) 0 0
\(754\) −21721.8 −1.04915
\(755\) 47822.1 2.30520
\(756\) 0 0
\(757\) −3622.31 −0.173917 −0.0869583 0.996212i \(-0.527715\pi\)
−0.0869583 + 0.996212i \(0.527715\pi\)
\(758\) −33199.6 −1.59085
\(759\) 0 0
\(760\) −10226.8 −0.488113
\(761\) −2386.44 −0.113677 −0.0568386 0.998383i \(-0.518102\pi\)
−0.0568386 + 0.998383i \(0.518102\pi\)
\(762\) 0 0
\(763\) 1096.89 0.0520447
\(764\) 5120.45 0.242475
\(765\) 0 0
\(766\) 37430.5 1.76556
\(767\) −14448.0 −0.680165
\(768\) 0 0
\(769\) 4038.92 0.189398 0.0946990 0.995506i \(-0.469811\pi\)
0.0946990 + 0.995506i \(0.469811\pi\)
\(770\) −1023.09 −0.0478825
\(771\) 0 0
\(772\) 2127.29 0.0991749
\(773\) −17780.2 −0.827306 −0.413653 0.910435i \(-0.635747\pi\)
−0.413653 + 0.910435i \(0.635747\pi\)
\(774\) 0 0
\(775\) −1776.12 −0.0823227
\(776\) −7197.04 −0.332937
\(777\) 0 0
\(778\) 4576.71 0.210904
\(779\) 10161.0 0.467336
\(780\) 0 0
\(781\) −20794.3 −0.952727
\(782\) −32088.1 −1.46735
\(783\) 0 0
\(784\) 25507.1 1.16195
\(785\) 18448.1 0.838779
\(786\) 0 0
\(787\) 28216.2 1.27802 0.639009 0.769199i \(-0.279345\pi\)
0.639009 + 0.769199i \(0.279345\pi\)
\(788\) 7173.53 0.324298
\(789\) 0 0
\(790\) −32631.8 −1.46961
\(791\) −21.4807 −0.000965568 0
\(792\) 0 0
\(793\) 21094.4 0.944619
\(794\) −18077.0 −0.807972
\(795\) 0 0
\(796\) −51.1077 −0.00227571
\(797\) 8810.39 0.391568 0.195784 0.980647i \(-0.437275\pi\)
0.195784 + 0.980647i \(0.437275\pi\)
\(798\) 0 0
\(799\) −15888.6 −0.703502
\(800\) 14330.3 0.633317
\(801\) 0 0
\(802\) 9348.38 0.411600
\(803\) −4686.21 −0.205943
\(804\) 0 0
\(805\) −1394.44 −0.0610529
\(806\) −1385.90 −0.0605660
\(807\) 0 0
\(808\) −33215.8 −1.44620
\(809\) −5436.82 −0.236277 −0.118139 0.992997i \(-0.537693\pi\)
−0.118139 + 0.992997i \(0.537693\pi\)
\(810\) 0 0
\(811\) 11563.5 0.500678 0.250339 0.968158i \(-0.419458\pi\)
0.250339 + 0.968158i \(0.419458\pi\)
\(812\) −176.164 −0.00761349
\(813\) 0 0
\(814\) −21494.1 −0.925514
\(815\) 18718.4 0.804512
\(816\) 0 0
\(817\) −4670.63 −0.200006
\(818\) 37734.8 1.61292
\(819\) 0 0
\(820\) −10345.2 −0.440575
\(821\) 25869.9 1.09972 0.549858 0.835258i \(-0.314682\pi\)
0.549858 + 0.835258i \(0.314682\pi\)
\(822\) 0 0
\(823\) −6191.18 −0.262225 −0.131112 0.991368i \(-0.541855\pi\)
−0.131112 + 0.991368i \(0.541855\pi\)
\(824\) −575.115 −0.0243144
\(825\) 0 0
\(826\) −684.703 −0.0288425
\(827\) −33775.3 −1.42017 −0.710086 0.704115i \(-0.751344\pi\)
−0.710086 + 0.704115i \(0.751344\pi\)
\(828\) 0 0
\(829\) −9016.25 −0.377741 −0.188871 0.982002i \(-0.560483\pi\)
−0.188871 + 0.982002i \(0.560483\pi\)
\(830\) 13179.1 0.551148
\(831\) 0 0
\(832\) −17948.2 −0.747888
\(833\) −33816.9 −1.40659
\(834\) 0 0
\(835\) 8524.24 0.353286
\(836\) −1183.30 −0.0489535
\(837\) 0 0
\(838\) −21990.5 −0.906504
\(839\) 45095.2 1.85561 0.927806 0.373062i \(-0.121692\pi\)
0.927806 + 0.373062i \(0.121692\pi\)
\(840\) 0 0
\(841\) −3932.81 −0.161254
\(842\) 4195.41 0.171714
\(843\) 0 0
\(844\) 6191.00 0.252492
\(845\) −3446.97 −0.140330
\(846\) 0 0
\(847\) −537.571 −0.0218077
\(848\) 23609.1 0.956063
\(849\) 0 0
\(850\) −59713.1 −2.40958
\(851\) −29295.9 −1.18008
\(852\) 0 0
\(853\) −49211.7 −1.97535 −0.987676 0.156513i \(-0.949975\pi\)
−0.987676 + 0.156513i \(0.949975\pi\)
\(854\) 999.682 0.0400567
\(855\) 0 0
\(856\) −30006.4 −1.19813
\(857\) −23038.6 −0.918300 −0.459150 0.888359i \(-0.651846\pi\)
−0.459150 + 0.888359i \(0.651846\pi\)
\(858\) 0 0
\(859\) −6529.39 −0.259348 −0.129674 0.991557i \(-0.541393\pi\)
−0.129674 + 0.991557i \(0.541393\pi\)
\(860\) 4755.33 0.188553
\(861\) 0 0
\(862\) 21253.8 0.839799
\(863\) −18172.1 −0.716786 −0.358393 0.933571i \(-0.616675\pi\)
−0.358393 + 0.933571i \(0.616675\pi\)
\(864\) 0 0
\(865\) −26677.1 −1.04861
\(866\) −44387.4 −1.74174
\(867\) 0 0
\(868\) −11.2397 −0.000439516 0
\(869\) 14511.8 0.566488
\(870\) 0 0
\(871\) 26772.0 1.04149
\(872\) 29010.0 1.12661
\(873\) 0 0
\(874\) −9424.40 −0.364743
\(875\) −928.400 −0.0358693
\(876\) 0 0
\(877\) 9910.10 0.381574 0.190787 0.981631i \(-0.438896\pi\)
0.190787 + 0.981631i \(0.438896\pi\)
\(878\) −4630.26 −0.177977
\(879\) 0 0
\(880\) −32893.3 −1.26004
\(881\) 3153.32 0.120588 0.0602940 0.998181i \(-0.480796\pi\)
0.0602940 + 0.998181i \(0.480796\pi\)
\(882\) 0 0
\(883\) −11764.5 −0.448366 −0.224183 0.974547i \(-0.571971\pi\)
−0.224183 + 0.974547i \(0.571971\pi\)
\(884\) −7973.64 −0.303374
\(885\) 0 0
\(886\) −34809.8 −1.31993
\(887\) −35545.6 −1.34555 −0.672777 0.739846i \(-0.734899\pi\)
−0.672777 + 0.739846i \(0.734899\pi\)
\(888\) 0 0
\(889\) 1271.94 0.0479859
\(890\) −72414.7 −2.72736
\(891\) 0 0
\(892\) −4577.21 −0.171812
\(893\) −4666.54 −0.174871
\(894\) 0 0
\(895\) 33095.5 1.23604
\(896\) −1289.82 −0.0480913
\(897\) 0 0
\(898\) −48857.8 −1.81560
\(899\) 1305.15 0.0484197
\(900\) 0 0
\(901\) −31300.6 −1.15735
\(902\) 26883.9 0.992390
\(903\) 0 0
\(904\) −568.110 −0.0209016
\(905\) 36379.9 1.33625
\(906\) 0 0
\(907\) 7842.99 0.287125 0.143562 0.989641i \(-0.454144\pi\)
0.143562 + 0.989641i \(0.454144\pi\)
\(908\) 390.511 0.0142727
\(909\) 0 0
\(910\) −2024.81 −0.0737603
\(911\) −17676.5 −0.642862 −0.321431 0.946933i \(-0.604164\pi\)
−0.321431 + 0.946933i \(0.604164\pi\)
\(912\) 0 0
\(913\) −5860.90 −0.212451
\(914\) −29336.7 −1.06168
\(915\) 0 0
\(916\) 532.716 0.0192156
\(917\) 686.278 0.0247142
\(918\) 0 0
\(919\) 40448.5 1.45187 0.725937 0.687761i \(-0.241406\pi\)
0.725937 + 0.687761i \(0.241406\pi\)
\(920\) −36879.5 −1.32161
\(921\) 0 0
\(922\) −13499.7 −0.482202
\(923\) −41154.5 −1.46762
\(924\) 0 0
\(925\) −54517.0 −1.93785
\(926\) −36355.1 −1.29018
\(927\) 0 0
\(928\) −10530.4 −0.372498
\(929\) 18479.7 0.652635 0.326317 0.945260i \(-0.394192\pi\)
0.326317 + 0.945260i \(0.394192\pi\)
\(930\) 0 0
\(931\) −9932.15 −0.349638
\(932\) 3303.26 0.116096
\(933\) 0 0
\(934\) 34113.4 1.19510
\(935\) 43609.5 1.52533
\(936\) 0 0
\(937\) −12551.8 −0.437620 −0.218810 0.975767i \(-0.570218\pi\)
−0.218810 + 0.975767i \(0.570218\pi\)
\(938\) 1268.75 0.0441644
\(939\) 0 0
\(940\) 4751.16 0.164857
\(941\) 42332.5 1.46652 0.733262 0.679946i \(-0.237997\pi\)
0.733262 + 0.679946i \(0.237997\pi\)
\(942\) 0 0
\(943\) 36642.0 1.26535
\(944\) −22013.9 −0.758997
\(945\) 0 0
\(946\) −12357.6 −0.424713
\(947\) 12726.8 0.436710 0.218355 0.975869i \(-0.429931\pi\)
0.218355 + 0.975869i \(0.429931\pi\)
\(948\) 0 0
\(949\) −9274.57 −0.317245
\(950\) −17537.9 −0.598953
\(951\) 0 0
\(952\) 1452.37 0.0494451
\(953\) −14939.7 −0.507812 −0.253906 0.967229i \(-0.581715\pi\)
−0.253906 + 0.967229i \(0.581715\pi\)
\(954\) 0 0
\(955\) −55424.8 −1.87802
\(956\) −394.756 −0.0133549
\(957\) 0 0
\(958\) −50851.6 −1.71497
\(959\) −121.682 −0.00409729
\(960\) 0 0
\(961\) −29707.7 −0.997205
\(962\) −42539.4 −1.42570
\(963\) 0 0
\(964\) −8444.66 −0.282141
\(965\) −23026.3 −0.768128
\(966\) 0 0
\(967\) 3191.74 0.106142 0.0530710 0.998591i \(-0.483099\pi\)
0.0530710 + 0.998591i \(0.483099\pi\)
\(968\) −14217.4 −0.472071
\(969\) 0 0
\(970\) −20268.6 −0.670914
\(971\) −43380.7 −1.43373 −0.716866 0.697211i \(-0.754424\pi\)
−0.716866 + 0.697211i \(0.754424\pi\)
\(972\) 0 0
\(973\) −1591.22 −0.0524278
\(974\) 15861.0 0.521787
\(975\) 0 0
\(976\) 32140.8 1.05410
\(977\) 57824.4 1.89352 0.946759 0.321945i \(-0.104336\pi\)
0.946759 + 0.321945i \(0.104336\pi\)
\(978\) 0 0
\(979\) 32203.7 1.05131
\(980\) 10112.3 0.329617
\(981\) 0 0
\(982\) −3931.74 −0.127767
\(983\) 36789.7 1.19370 0.596851 0.802352i \(-0.296418\pi\)
0.596851 + 0.802352i \(0.296418\pi\)
\(984\) 0 0
\(985\) −77647.9 −2.51174
\(986\) 43879.2 1.41724
\(987\) 0 0
\(988\) −2341.88 −0.0754102
\(989\) −16843.0 −0.541534
\(990\) 0 0
\(991\) 59886.2 1.91963 0.959813 0.280641i \(-0.0905470\pi\)
0.959813 + 0.280641i \(0.0905470\pi\)
\(992\) −671.866 −0.0215038
\(993\) 0 0
\(994\) −1950.35 −0.0622347
\(995\) 553.202 0.0176258
\(996\) 0 0
\(997\) 39148.2 1.24357 0.621784 0.783189i \(-0.286408\pi\)
0.621784 + 0.783189i \(0.286408\pi\)
\(998\) −13586.4 −0.430932
\(999\) 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.1.14 yes 59
3.2 odd 2 2151.4.a.g.1.46 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.46 59 3.2 odd 2
2151.4.a.h.1.14 yes 59 1.1 even 1 trivial