Properties

Label 2151.4.a.h.1.4
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 1.4
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.11618 q^{2} +18.1753 q^{4} +6.15957 q^{5} +24.2123 q^{7} -52.0584 q^{8} +O(q^{10})\) \(q-5.11618 q^{2} +18.1753 q^{4} +6.15957 q^{5} +24.2123 q^{7} -52.0584 q^{8} -31.5134 q^{10} +60.5329 q^{11} -2.25761 q^{13} -123.874 q^{14} +120.938 q^{16} +114.457 q^{17} -56.9025 q^{19} +111.952 q^{20} -309.697 q^{22} +11.1459 q^{23} -87.0598 q^{25} +11.5503 q^{26} +440.064 q^{28} +177.408 q^{29} -199.533 q^{31} -202.272 q^{32} -585.582 q^{34} +149.137 q^{35} +267.387 q^{37} +291.123 q^{38} -320.657 q^{40} +475.722 q^{41} -207.667 q^{43} +1100.20 q^{44} -57.0244 q^{46} -598.232 q^{47} +243.233 q^{49} +445.413 q^{50} -41.0325 q^{52} -275.859 q^{53} +372.856 q^{55} -1260.45 q^{56} -907.651 q^{58} +25.8847 q^{59} +247.309 q^{61} +1020.85 q^{62} +67.3571 q^{64} -13.9059 q^{65} -24.8585 q^{67} +2080.29 q^{68} -763.011 q^{70} +260.252 q^{71} +1076.96 q^{73} -1368.00 q^{74} -1034.22 q^{76} +1465.64 q^{77} +644.964 q^{79} +744.925 q^{80} -2433.88 q^{82} -276.207 q^{83} +705.006 q^{85} +1062.46 q^{86} -3151.25 q^{88} +446.913 q^{89} -54.6617 q^{91} +202.580 q^{92} +3060.66 q^{94} -350.494 q^{95} +1294.37 q^{97} -1244.42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.11618 −1.80884 −0.904421 0.426642i \(-0.859696\pi\)
−0.904421 + 0.426642i \(0.859696\pi\)
\(3\) 0 0
\(4\) 18.1753 2.27191
\(5\) 6.15957 0.550928 0.275464 0.961311i \(-0.411168\pi\)
0.275464 + 0.961311i \(0.411168\pi\)
\(6\) 0 0
\(7\) 24.2123 1.30734 0.653669 0.756780i \(-0.273229\pi\)
0.653669 + 0.756780i \(0.273229\pi\)
\(8\) −52.0584 −2.30068
\(9\) 0 0
\(10\) −31.5134 −0.996542
\(11\) 60.5329 1.65921 0.829607 0.558348i \(-0.188564\pi\)
0.829607 + 0.558348i \(0.188564\pi\)
\(12\) 0 0
\(13\) −2.25761 −0.0481652 −0.0240826 0.999710i \(-0.507666\pi\)
−0.0240826 + 0.999710i \(0.507666\pi\)
\(14\) −123.874 −2.36477
\(15\) 0 0
\(16\) 120.938 1.88965
\(17\) 114.457 1.63294 0.816468 0.577391i \(-0.195929\pi\)
0.816468 + 0.577391i \(0.195929\pi\)
\(18\) 0 0
\(19\) −56.9025 −0.687070 −0.343535 0.939140i \(-0.611624\pi\)
−0.343535 + 0.939140i \(0.611624\pi\)
\(20\) 111.952 1.25166
\(21\) 0 0
\(22\) −309.697 −3.00126
\(23\) 11.1459 0.101047 0.0505235 0.998723i \(-0.483911\pi\)
0.0505235 + 0.998723i \(0.483911\pi\)
\(24\) 0 0
\(25\) −87.0598 −0.696478
\(26\) 11.5503 0.0871231
\(27\) 0 0
\(28\) 440.064 2.97015
\(29\) 177.408 1.13600 0.567998 0.823030i \(-0.307718\pi\)
0.567998 + 0.823030i \(0.307718\pi\)
\(30\) 0 0
\(31\) −199.533 −1.15604 −0.578020 0.816022i \(-0.696175\pi\)
−0.578020 + 0.816022i \(0.696175\pi\)
\(32\) −202.272 −1.11741
\(33\) 0 0
\(34\) −585.582 −2.95372
\(35\) 149.137 0.720250
\(36\) 0 0
\(37\) 267.387 1.18806 0.594028 0.804444i \(-0.297537\pi\)
0.594028 + 0.804444i \(0.297537\pi\)
\(38\) 291.123 1.24280
\(39\) 0 0
\(40\) −320.657 −1.26751
\(41\) 475.722 1.81208 0.906040 0.423192i \(-0.139090\pi\)
0.906040 + 0.423192i \(0.139090\pi\)
\(42\) 0 0
\(43\) −207.667 −0.736487 −0.368244 0.929729i \(-0.620041\pi\)
−0.368244 + 0.929729i \(0.620041\pi\)
\(44\) 1100.20 3.76958
\(45\) 0 0
\(46\) −57.0244 −0.182778
\(47\) −598.232 −1.85662 −0.928309 0.371809i \(-0.878737\pi\)
−0.928309 + 0.371809i \(0.878737\pi\)
\(48\) 0 0
\(49\) 243.233 0.709135
\(50\) 445.413 1.25982
\(51\) 0 0
\(52\) −41.0325 −0.109427
\(53\) −275.859 −0.714947 −0.357473 0.933923i \(-0.616362\pi\)
−0.357473 + 0.933923i \(0.616362\pi\)
\(54\) 0 0
\(55\) 372.856 0.914108
\(56\) −1260.45 −3.00777
\(57\) 0 0
\(58\) −907.651 −2.05484
\(59\) 25.8847 0.0571169 0.0285585 0.999592i \(-0.490908\pi\)
0.0285585 + 0.999592i \(0.490908\pi\)
\(60\) 0 0
\(61\) 247.309 0.519092 0.259546 0.965731i \(-0.416427\pi\)
0.259546 + 0.965731i \(0.416427\pi\)
\(62\) 1020.85 2.09109
\(63\) 0 0
\(64\) 67.3571 0.131557
\(65\) −13.9059 −0.0265355
\(66\) 0 0
\(67\) −24.8585 −0.0453276 −0.0226638 0.999743i \(-0.507215\pi\)
−0.0226638 + 0.999743i \(0.507215\pi\)
\(68\) 2080.29 3.70988
\(69\) 0 0
\(70\) −763.011 −1.30282
\(71\) 260.252 0.435017 0.217509 0.976058i \(-0.430207\pi\)
0.217509 + 0.976058i \(0.430207\pi\)
\(72\) 0 0
\(73\) 1076.96 1.72670 0.863349 0.504607i \(-0.168363\pi\)
0.863349 + 0.504607i \(0.168363\pi\)
\(74\) −1368.00 −2.14900
\(75\) 0 0
\(76\) −1034.22 −1.56096
\(77\) 1465.64 2.16915
\(78\) 0 0
\(79\) 644.964 0.918533 0.459266 0.888299i \(-0.348112\pi\)
0.459266 + 0.888299i \(0.348112\pi\)
\(80\) 744.925 1.04106
\(81\) 0 0
\(82\) −2433.88 −3.27777
\(83\) −276.207 −0.365274 −0.182637 0.983180i \(-0.558463\pi\)
−0.182637 + 0.983180i \(0.558463\pi\)
\(84\) 0 0
\(85\) 705.006 0.899631
\(86\) 1062.46 1.33219
\(87\) 0 0
\(88\) −3151.25 −3.81732
\(89\) 446.913 0.532278 0.266139 0.963935i \(-0.414252\pi\)
0.266139 + 0.963935i \(0.414252\pi\)
\(90\) 0 0
\(91\) −54.6617 −0.0629682
\(92\) 202.580 0.229570
\(93\) 0 0
\(94\) 3060.66 3.35833
\(95\) −350.494 −0.378526
\(96\) 0 0
\(97\) 1294.37 1.35488 0.677438 0.735580i \(-0.263090\pi\)
0.677438 + 0.735580i \(0.263090\pi\)
\(98\) −1244.42 −1.28271
\(99\) 0 0
\(100\) −1582.33 −1.58233
\(101\) 973.935 0.959506 0.479753 0.877404i \(-0.340726\pi\)
0.479753 + 0.877404i \(0.340726\pi\)
\(102\) 0 0
\(103\) 478.119 0.457383 0.228692 0.973499i \(-0.426555\pi\)
0.228692 + 0.973499i \(0.426555\pi\)
\(104\) 117.527 0.110812
\(105\) 0 0
\(106\) 1411.34 1.29323
\(107\) −337.772 −0.305174 −0.152587 0.988290i \(-0.548760\pi\)
−0.152587 + 0.988290i \(0.548760\pi\)
\(108\) 0 0
\(109\) −71.4379 −0.0627754 −0.0313877 0.999507i \(-0.509993\pi\)
−0.0313877 + 0.999507i \(0.509993\pi\)
\(110\) −1907.60 −1.65348
\(111\) 0 0
\(112\) 2928.18 2.47042
\(113\) 952.662 0.793088 0.396544 0.918016i \(-0.370209\pi\)
0.396544 + 0.918016i \(0.370209\pi\)
\(114\) 0 0
\(115\) 68.6539 0.0556697
\(116\) 3224.44 2.58088
\(117\) 0 0
\(118\) −132.431 −0.103315
\(119\) 2771.26 2.13480
\(120\) 0 0
\(121\) 2333.23 1.75299
\(122\) −1265.27 −0.938955
\(123\) 0 0
\(124\) −3626.57 −2.62642
\(125\) −1306.20 −0.934638
\(126\) 0 0
\(127\) −565.205 −0.394912 −0.197456 0.980312i \(-0.563268\pi\)
−0.197456 + 0.980312i \(0.563268\pi\)
\(128\) 1273.57 0.879441
\(129\) 0 0
\(130\) 71.1449 0.0479986
\(131\) 1729.24 1.15331 0.576657 0.816986i \(-0.304357\pi\)
0.576657 + 0.816986i \(0.304357\pi\)
\(132\) 0 0
\(133\) −1377.74 −0.898233
\(134\) 127.181 0.0819905
\(135\) 0 0
\(136\) −5958.45 −3.75686
\(137\) 1709.34 1.06597 0.532987 0.846123i \(-0.321069\pi\)
0.532987 + 0.846123i \(0.321069\pi\)
\(138\) 0 0
\(139\) −2291.12 −1.39806 −0.699030 0.715092i \(-0.746385\pi\)
−0.699030 + 0.715092i \(0.746385\pi\)
\(140\) 2710.60 1.63634
\(141\) 0 0
\(142\) −1331.49 −0.786877
\(143\) −136.659 −0.0799163
\(144\) 0 0
\(145\) 1092.76 0.625852
\(146\) −5509.93 −3.12332
\(147\) 0 0
\(148\) 4859.82 2.69915
\(149\) −2879.38 −1.58314 −0.791570 0.611079i \(-0.790736\pi\)
−0.791570 + 0.611079i \(0.790736\pi\)
\(150\) 0 0
\(151\) −869.813 −0.468771 −0.234385 0.972144i \(-0.575308\pi\)
−0.234385 + 0.972144i \(0.575308\pi\)
\(152\) 2962.25 1.58073
\(153\) 0 0
\(154\) −7498.46 −3.92366
\(155\) −1229.04 −0.636896
\(156\) 0 0
\(157\) −61.0278 −0.0310226 −0.0155113 0.999880i \(-0.504938\pi\)
−0.0155113 + 0.999880i \(0.504938\pi\)
\(158\) −3299.75 −1.66148
\(159\) 0 0
\(160\) −1245.91 −0.615611
\(161\) 269.868 0.132103
\(162\) 0 0
\(163\) −566.997 −0.272458 −0.136229 0.990677i \(-0.543498\pi\)
−0.136229 + 0.990677i \(0.543498\pi\)
\(164\) 8646.37 4.11688
\(165\) 0 0
\(166\) 1413.13 0.660722
\(167\) −833.335 −0.386140 −0.193070 0.981185i \(-0.561844\pi\)
−0.193070 + 0.981185i \(0.561844\pi\)
\(168\) 0 0
\(169\) −2191.90 −0.997680
\(170\) −3606.93 −1.62729
\(171\) 0 0
\(172\) −3774.40 −1.67323
\(173\) 2726.65 1.19829 0.599143 0.800642i \(-0.295508\pi\)
0.599143 + 0.800642i \(0.295508\pi\)
\(174\) 0 0
\(175\) −2107.91 −0.910533
\(176\) 7320.72 3.13534
\(177\) 0 0
\(178\) −2286.49 −0.962806
\(179\) −2310.94 −0.964958 −0.482479 0.875907i \(-0.660264\pi\)
−0.482479 + 0.875907i \(0.660264\pi\)
\(180\) 0 0
\(181\) −258.541 −0.106173 −0.0530863 0.998590i \(-0.516906\pi\)
−0.0530863 + 0.998590i \(0.516906\pi\)
\(182\) 279.659 0.113899
\(183\) 0 0
\(184\) −580.238 −0.232477
\(185\) 1646.98 0.654534
\(186\) 0 0
\(187\) 6928.42 2.70939
\(188\) −10873.0 −4.21806
\(189\) 0 0
\(190\) 1793.19 0.684694
\(191\) −3180.80 −1.20500 −0.602499 0.798119i \(-0.705828\pi\)
−0.602499 + 0.798119i \(0.705828\pi\)
\(192\) 0 0
\(193\) 1964.34 0.732624 0.366312 0.930492i \(-0.380620\pi\)
0.366312 + 0.930492i \(0.380620\pi\)
\(194\) −6622.20 −2.45075
\(195\) 0 0
\(196\) 4420.82 1.61109
\(197\) −3229.80 −1.16809 −0.584045 0.811721i \(-0.698531\pi\)
−0.584045 + 0.811721i \(0.698531\pi\)
\(198\) 0 0
\(199\) −1069.53 −0.380991 −0.190495 0.981688i \(-0.561009\pi\)
−0.190495 + 0.981688i \(0.561009\pi\)
\(200\) 4532.19 1.60237
\(201\) 0 0
\(202\) −4982.82 −1.73559
\(203\) 4295.45 1.48513
\(204\) 0 0
\(205\) 2930.24 0.998326
\(206\) −2446.14 −0.827334
\(207\) 0 0
\(208\) −273.030 −0.0910155
\(209\) −3444.47 −1.14000
\(210\) 0 0
\(211\) 3260.16 1.06369 0.531845 0.846842i \(-0.321499\pi\)
0.531845 + 0.846842i \(0.321499\pi\)
\(212\) −5013.81 −1.62429
\(213\) 0 0
\(214\) 1728.10 0.552012
\(215\) −1279.14 −0.405752
\(216\) 0 0
\(217\) −4831.15 −1.51134
\(218\) 365.489 0.113551
\(219\) 0 0
\(220\) 6776.76 2.07677
\(221\) −258.399 −0.0786506
\(222\) 0 0
\(223\) −5181.92 −1.55609 −0.778043 0.628211i \(-0.783787\pi\)
−0.778043 + 0.628211i \(0.783787\pi\)
\(224\) −4897.46 −1.46083
\(225\) 0 0
\(226\) −4873.99 −1.43457
\(227\) −3885.67 −1.13613 −0.568064 0.822984i \(-0.692307\pi\)
−0.568064 + 0.822984i \(0.692307\pi\)
\(228\) 0 0
\(229\) −996.362 −0.287517 −0.143759 0.989613i \(-0.545919\pi\)
−0.143759 + 0.989613i \(0.545919\pi\)
\(230\) −351.246 −0.100698
\(231\) 0 0
\(232\) −9235.58 −2.61356
\(233\) 4588.29 1.29008 0.645040 0.764149i \(-0.276841\pi\)
0.645040 + 0.764149i \(0.276841\pi\)
\(234\) 0 0
\(235\) −3684.85 −1.02286
\(236\) 470.461 0.129764
\(237\) 0 0
\(238\) −14178.3 −3.86151
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −862.038 −0.230410 −0.115205 0.993342i \(-0.536752\pi\)
−0.115205 + 0.993342i \(0.536752\pi\)
\(242\) −11937.2 −3.17088
\(243\) 0 0
\(244\) 4494.90 1.17933
\(245\) 1498.21 0.390682
\(246\) 0 0
\(247\) 128.463 0.0330928
\(248\) 10387.4 2.65968
\(249\) 0 0
\(250\) 6682.73 1.69061
\(251\) 2970.96 0.747113 0.373557 0.927607i \(-0.378138\pi\)
0.373557 + 0.927607i \(0.378138\pi\)
\(252\) 0 0
\(253\) 674.694 0.167659
\(254\) 2891.69 0.714334
\(255\) 0 0
\(256\) −7054.65 −1.72233
\(257\) −3291.02 −0.798787 −0.399393 0.916780i \(-0.630779\pi\)
−0.399393 + 0.916780i \(0.630779\pi\)
\(258\) 0 0
\(259\) 6474.03 1.55319
\(260\) −252.743 −0.0602863
\(261\) 0 0
\(262\) −8847.09 −2.08616
\(263\) 5559.72 1.30353 0.651763 0.758423i \(-0.274030\pi\)
0.651763 + 0.758423i \(0.274030\pi\)
\(264\) 0 0
\(265\) −1699.17 −0.393884
\(266\) 7048.74 1.62476
\(267\) 0 0
\(268\) −451.810 −0.102980
\(269\) −4835.44 −1.09599 −0.547996 0.836481i \(-0.684609\pi\)
−0.547996 + 0.836481i \(0.684609\pi\)
\(270\) 0 0
\(271\) 4159.85 0.932447 0.466223 0.884667i \(-0.345614\pi\)
0.466223 + 0.884667i \(0.345614\pi\)
\(272\) 13842.2 3.08568
\(273\) 0 0
\(274\) −8745.27 −1.92818
\(275\) −5269.98 −1.15561
\(276\) 0 0
\(277\) −1547.96 −0.335768 −0.167884 0.985807i \(-0.553693\pi\)
−0.167884 + 0.985807i \(0.553693\pi\)
\(278\) 11721.8 2.52887
\(279\) 0 0
\(280\) −7763.83 −1.65706
\(281\) 6222.21 1.32095 0.660474 0.750849i \(-0.270356\pi\)
0.660474 + 0.750849i \(0.270356\pi\)
\(282\) 0 0
\(283\) −7453.16 −1.56553 −0.782764 0.622319i \(-0.786191\pi\)
−0.782764 + 0.622319i \(0.786191\pi\)
\(284\) 4730.15 0.988319
\(285\) 0 0
\(286\) 699.173 0.144556
\(287\) 11518.3 2.36900
\(288\) 0 0
\(289\) 8187.41 1.66648
\(290\) −5590.74 −1.13207
\(291\) 0 0
\(292\) 19574.1 3.92290
\(293\) 9507.05 1.89559 0.947795 0.318881i \(-0.103307\pi\)
0.947795 + 0.318881i \(0.103307\pi\)
\(294\) 0 0
\(295\) 159.438 0.0314673
\(296\) −13919.7 −2.73333
\(297\) 0 0
\(298\) 14731.4 2.86365
\(299\) −25.1631 −0.00486695
\(300\) 0 0
\(301\) −5028.09 −0.962838
\(302\) 4450.12 0.847932
\(303\) 0 0
\(304\) −6881.66 −1.29832
\(305\) 1523.31 0.285982
\(306\) 0 0
\(307\) −4201.33 −0.781051 −0.390526 0.920592i \(-0.627707\pi\)
−0.390526 + 0.920592i \(0.627707\pi\)
\(308\) 26638.3 4.92812
\(309\) 0 0
\(310\) 6287.98 1.15204
\(311\) −1055.44 −0.192438 −0.0962190 0.995360i \(-0.530675\pi\)
−0.0962190 + 0.995360i \(0.530675\pi\)
\(312\) 0 0
\(313\) −9121.61 −1.64723 −0.823617 0.567147i \(-0.808047\pi\)
−0.823617 + 0.567147i \(0.808047\pi\)
\(314\) 312.229 0.0561149
\(315\) 0 0
\(316\) 11722.4 2.08682
\(317\) −5793.06 −1.02641 −0.513203 0.858267i \(-0.671541\pi\)
−0.513203 + 0.858267i \(0.671541\pi\)
\(318\) 0 0
\(319\) 10739.0 1.88486
\(320\) 414.891 0.0724784
\(321\) 0 0
\(322\) −1380.69 −0.238953
\(323\) −6512.89 −1.12194
\(324\) 0 0
\(325\) 196.547 0.0335460
\(326\) 2900.86 0.492833
\(327\) 0 0
\(328\) −24765.3 −4.16901
\(329\) −14484.5 −2.42723
\(330\) 0 0
\(331\) −3979.44 −0.660815 −0.330408 0.943838i \(-0.607186\pi\)
−0.330408 + 0.943838i \(0.607186\pi\)
\(332\) −5020.14 −0.829868
\(333\) 0 0
\(334\) 4263.49 0.698466
\(335\) −153.118 −0.0249723
\(336\) 0 0
\(337\) 2938.64 0.475009 0.237504 0.971386i \(-0.423671\pi\)
0.237504 + 0.971386i \(0.423671\pi\)
\(338\) 11214.2 1.80465
\(339\) 0 0
\(340\) 12813.7 2.04388
\(341\) −12078.3 −1.91812
\(342\) 0 0
\(343\) −2415.58 −0.380260
\(344\) 10810.8 1.69442
\(345\) 0 0
\(346\) −13950.0 −2.16751
\(347\) −3152.37 −0.487688 −0.243844 0.969814i \(-0.578409\pi\)
−0.243844 + 0.969814i \(0.578409\pi\)
\(348\) 0 0
\(349\) −4348.01 −0.666887 −0.333444 0.942770i \(-0.608211\pi\)
−0.333444 + 0.942770i \(0.608211\pi\)
\(350\) 10784.5 1.64701
\(351\) 0 0
\(352\) −12244.1 −1.85402
\(353\) 10646.0 1.60518 0.802589 0.596532i \(-0.203455\pi\)
0.802589 + 0.596532i \(0.203455\pi\)
\(354\) 0 0
\(355\) 1603.04 0.239663
\(356\) 8122.76 1.20929
\(357\) 0 0
\(358\) 11823.2 1.74546
\(359\) 7666.22 1.12704 0.563520 0.826102i \(-0.309447\pi\)
0.563520 + 0.826102i \(0.309447\pi\)
\(360\) 0 0
\(361\) −3621.11 −0.527935
\(362\) 1322.74 0.192049
\(363\) 0 0
\(364\) −993.490 −0.143058
\(365\) 6633.62 0.951287
\(366\) 0 0
\(367\) −9305.91 −1.32361 −0.661805 0.749676i \(-0.730209\pi\)
−0.661805 + 0.749676i \(0.730209\pi\)
\(368\) 1347.96 0.190944
\(369\) 0 0
\(370\) −8426.26 −1.18395
\(371\) −6679.17 −0.934678
\(372\) 0 0
\(373\) 13038.1 1.80989 0.904943 0.425533i \(-0.139913\pi\)
0.904943 + 0.425533i \(0.139913\pi\)
\(374\) −35447.0 −4.90086
\(375\) 0 0
\(376\) 31143.0 4.27148
\(377\) −400.518 −0.0547154
\(378\) 0 0
\(379\) 7405.15 1.00363 0.501816 0.864974i \(-0.332665\pi\)
0.501816 + 0.864974i \(0.332665\pi\)
\(380\) −6370.33 −0.859976
\(381\) 0 0
\(382\) 16273.5 2.17965
\(383\) −8586.05 −1.14550 −0.572750 0.819730i \(-0.694123\pi\)
−0.572750 + 0.819730i \(0.694123\pi\)
\(384\) 0 0
\(385\) 9027.69 1.19505
\(386\) −10049.9 −1.32520
\(387\) 0 0
\(388\) 23525.4 3.07815
\(389\) −6051.43 −0.788740 −0.394370 0.918952i \(-0.629037\pi\)
−0.394370 + 0.918952i \(0.629037\pi\)
\(390\) 0 0
\(391\) 1275.73 0.165003
\(392\) −12662.3 −1.63149
\(393\) 0 0
\(394\) 16524.2 2.11289
\(395\) 3972.70 0.506046
\(396\) 0 0
\(397\) −5248.00 −0.663450 −0.331725 0.943376i \(-0.607631\pi\)
−0.331725 + 0.943376i \(0.607631\pi\)
\(398\) 5471.91 0.689151
\(399\) 0 0
\(400\) −10528.8 −1.31610
\(401\) −10290.3 −1.28147 −0.640737 0.767760i \(-0.721371\pi\)
−0.640737 + 0.767760i \(0.721371\pi\)
\(402\) 0 0
\(403\) 450.468 0.0556809
\(404\) 17701.5 2.17991
\(405\) 0 0
\(406\) −21976.3 −2.68637
\(407\) 16185.7 1.97124
\(408\) 0 0
\(409\) 8720.00 1.05422 0.527111 0.849797i \(-0.323275\pi\)
0.527111 + 0.849797i \(0.323275\pi\)
\(410\) −14991.6 −1.80581
\(411\) 0 0
\(412\) 8689.94 1.03913
\(413\) 626.726 0.0746712
\(414\) 0 0
\(415\) −1701.32 −0.201240
\(416\) 456.651 0.0538201
\(417\) 0 0
\(418\) 17622.5 2.06207
\(419\) 7078.88 0.825361 0.412680 0.910876i \(-0.364593\pi\)
0.412680 + 0.910876i \(0.364593\pi\)
\(420\) 0 0
\(421\) 14011.5 1.62203 0.811017 0.585022i \(-0.198914\pi\)
0.811017 + 0.585022i \(0.198914\pi\)
\(422\) −16679.5 −1.92405
\(423\) 0 0
\(424\) 14360.8 1.64486
\(425\) −9964.60 −1.13730
\(426\) 0 0
\(427\) 5987.90 0.678629
\(428\) −6139.09 −0.693327
\(429\) 0 0
\(430\) 6544.30 0.733940
\(431\) 15783.4 1.76394 0.881970 0.471305i \(-0.156217\pi\)
0.881970 + 0.471305i \(0.156217\pi\)
\(432\) 0 0
\(433\) 11461.2 1.27203 0.636014 0.771677i \(-0.280582\pi\)
0.636014 + 0.771677i \(0.280582\pi\)
\(434\) 24717.0 2.73377
\(435\) 0 0
\(436\) −1298.40 −0.142620
\(437\) −634.230 −0.0694264
\(438\) 0 0
\(439\) 6354.81 0.690885 0.345442 0.938440i \(-0.387729\pi\)
0.345442 + 0.938440i \(0.387729\pi\)
\(440\) −19410.3 −2.10307
\(441\) 0 0
\(442\) 1322.01 0.142266
\(443\) 1129.37 0.121124 0.0605619 0.998164i \(-0.480711\pi\)
0.0605619 + 0.998164i \(0.480711\pi\)
\(444\) 0 0
\(445\) 2752.79 0.293247
\(446\) 26511.6 2.81471
\(447\) 0 0
\(448\) 1630.87 0.171989
\(449\) −5699.02 −0.599006 −0.299503 0.954095i \(-0.596821\pi\)
−0.299503 + 0.954095i \(0.596821\pi\)
\(450\) 0 0
\(451\) 28796.8 3.00663
\(452\) 17314.9 1.80182
\(453\) 0 0
\(454\) 19879.8 2.05508
\(455\) −336.692 −0.0346909
\(456\) 0 0
\(457\) −9585.31 −0.981142 −0.490571 0.871401i \(-0.663212\pi\)
−0.490571 + 0.871401i \(0.663212\pi\)
\(458\) 5097.57 0.520073
\(459\) 0 0
\(460\) 1247.80 0.126476
\(461\) 15284.2 1.54416 0.772078 0.635527i \(-0.219217\pi\)
0.772078 + 0.635527i \(0.219217\pi\)
\(462\) 0 0
\(463\) 3329.90 0.334241 0.167121 0.985936i \(-0.446553\pi\)
0.167121 + 0.985936i \(0.446553\pi\)
\(464\) 21455.4 2.14664
\(465\) 0 0
\(466\) −23474.5 −2.33355
\(467\) −459.551 −0.0455364 −0.0227682 0.999741i \(-0.507248\pi\)
−0.0227682 + 0.999741i \(0.507248\pi\)
\(468\) 0 0
\(469\) −601.881 −0.0592586
\(470\) 18852.3 1.85020
\(471\) 0 0
\(472\) −1347.51 −0.131408
\(473\) −12570.7 −1.22199
\(474\) 0 0
\(475\) 4953.92 0.478529
\(476\) 50368.4 4.85007
\(477\) 0 0
\(478\) 1222.77 0.117004
\(479\) −4162.34 −0.397040 −0.198520 0.980097i \(-0.563613\pi\)
−0.198520 + 0.980097i \(0.563613\pi\)
\(480\) 0 0
\(481\) −603.653 −0.0572229
\(482\) 4410.34 0.416775
\(483\) 0 0
\(484\) 42407.1 3.98263
\(485\) 7972.73 0.746439
\(486\) 0 0
\(487\) −6565.21 −0.610879 −0.305439 0.952211i \(-0.598803\pi\)
−0.305439 + 0.952211i \(0.598803\pi\)
\(488\) −12874.5 −1.19426
\(489\) 0 0
\(490\) −7665.11 −0.706682
\(491\) 6302.45 0.579278 0.289639 0.957136i \(-0.406465\pi\)
0.289639 + 0.957136i \(0.406465\pi\)
\(492\) 0 0
\(493\) 20305.6 1.85501
\(494\) −657.241 −0.0598596
\(495\) 0 0
\(496\) −24131.1 −2.18452
\(497\) 6301.29 0.568715
\(498\) 0 0
\(499\) 10128.2 0.908620 0.454310 0.890844i \(-0.349886\pi\)
0.454310 + 0.890844i \(0.349886\pi\)
\(500\) −23740.4 −2.12341
\(501\) 0 0
\(502\) −15200.0 −1.35141
\(503\) 10440.7 0.925499 0.462750 0.886489i \(-0.346863\pi\)
0.462750 + 0.886489i \(0.346863\pi\)
\(504\) 0 0
\(505\) 5999.01 0.528619
\(506\) −3451.85 −0.303268
\(507\) 0 0
\(508\) −10272.8 −0.897204
\(509\) 7114.47 0.619535 0.309767 0.950812i \(-0.399749\pi\)
0.309767 + 0.950812i \(0.399749\pi\)
\(510\) 0 0
\(511\) 26075.7 2.25738
\(512\) 25904.3 2.23597
\(513\) 0 0
\(514\) 16837.4 1.44488
\(515\) 2945.01 0.251985
\(516\) 0 0
\(517\) −36212.7 −3.08053
\(518\) −33122.3 −2.80948
\(519\) 0 0
\(520\) 723.917 0.0610497
\(521\) 17164.2 1.44333 0.721665 0.692242i \(-0.243377\pi\)
0.721665 + 0.692242i \(0.243377\pi\)
\(522\) 0 0
\(523\) 7814.01 0.653313 0.326657 0.945143i \(-0.394078\pi\)
0.326657 + 0.945143i \(0.394078\pi\)
\(524\) 31429.3 2.62022
\(525\) 0 0
\(526\) −28444.5 −2.35787
\(527\) −22838.0 −1.88774
\(528\) 0 0
\(529\) −12042.8 −0.989789
\(530\) 8693.27 0.712474
\(531\) 0 0
\(532\) −25040.7 −2.04070
\(533\) −1073.99 −0.0872791
\(534\) 0 0
\(535\) −2080.53 −0.168129
\(536\) 1294.09 0.104284
\(537\) 0 0
\(538\) 24739.0 1.98248
\(539\) 14723.6 1.17661
\(540\) 0 0
\(541\) −5367.07 −0.426522 −0.213261 0.976995i \(-0.568409\pi\)
−0.213261 + 0.976995i \(0.568409\pi\)
\(542\) −21282.5 −1.68665
\(543\) 0 0
\(544\) −23151.5 −1.82465
\(545\) −440.027 −0.0345847
\(546\) 0 0
\(547\) 21500.9 1.68064 0.840322 0.542088i \(-0.182366\pi\)
0.840322 + 0.542088i \(0.182366\pi\)
\(548\) 31067.6 2.42180
\(549\) 0 0
\(550\) 26962.1 2.09031
\(551\) −10095.0 −0.780508
\(552\) 0 0
\(553\) 15616.0 1.20083
\(554\) 7919.61 0.607350
\(555\) 0 0
\(556\) −41641.7 −3.17626
\(557\) −17048.6 −1.29690 −0.648449 0.761258i \(-0.724582\pi\)
−0.648449 + 0.761258i \(0.724582\pi\)
\(558\) 0 0
\(559\) 468.831 0.0354730
\(560\) 18036.3 1.36102
\(561\) 0 0
\(562\) −31833.9 −2.38938
\(563\) −613.122 −0.0458970 −0.0229485 0.999737i \(-0.507305\pi\)
−0.0229485 + 0.999737i \(0.507305\pi\)
\(564\) 0 0
\(565\) 5867.99 0.436935
\(566\) 38131.7 2.83179
\(567\) 0 0
\(568\) −13548.3 −1.00083
\(569\) −16212.2 −1.19446 −0.597232 0.802069i \(-0.703733\pi\)
−0.597232 + 0.802069i \(0.703733\pi\)
\(570\) 0 0
\(571\) −16513.8 −1.21030 −0.605150 0.796112i \(-0.706887\pi\)
−0.605150 + 0.796112i \(0.706887\pi\)
\(572\) −2483.82 −0.181562
\(573\) 0 0
\(574\) −58929.7 −4.28515
\(575\) −970.360 −0.0703771
\(576\) 0 0
\(577\) −1929.46 −0.139210 −0.0696051 0.997575i \(-0.522174\pi\)
−0.0696051 + 0.997575i \(0.522174\pi\)
\(578\) −41888.2 −3.01440
\(579\) 0 0
\(580\) 19861.1 1.42188
\(581\) −6687.60 −0.477536
\(582\) 0 0
\(583\) −16698.6 −1.18625
\(584\) −56065.0 −3.97258
\(585\) 0 0
\(586\) −48639.7 −3.42882
\(587\) −7835.41 −0.550941 −0.275470 0.961310i \(-0.588834\pi\)
−0.275470 + 0.961310i \(0.588834\pi\)
\(588\) 0 0
\(589\) 11353.9 0.794281
\(590\) −815.715 −0.0569194
\(591\) 0 0
\(592\) 32337.2 2.24501
\(593\) −11655.4 −0.807131 −0.403566 0.914951i \(-0.632229\pi\)
−0.403566 + 0.914951i \(0.632229\pi\)
\(594\) 0 0
\(595\) 17069.8 1.17612
\(596\) −52333.4 −3.59675
\(597\) 0 0
\(598\) 128.739 0.00880354
\(599\) 8154.09 0.556205 0.278103 0.960551i \(-0.410294\pi\)
0.278103 + 0.960551i \(0.410294\pi\)
\(600\) 0 0
\(601\) −3889.65 −0.263997 −0.131999 0.991250i \(-0.542139\pi\)
−0.131999 + 0.991250i \(0.542139\pi\)
\(602\) 25724.6 1.74162
\(603\) 0 0
\(604\) −15809.1 −1.06500
\(605\) 14371.7 0.965773
\(606\) 0 0
\(607\) −15961.4 −1.06730 −0.533651 0.845705i \(-0.679180\pi\)
−0.533651 + 0.845705i \(0.679180\pi\)
\(608\) 11509.8 0.767736
\(609\) 0 0
\(610\) −7793.54 −0.517297
\(611\) 1350.57 0.0894243
\(612\) 0 0
\(613\) −8958.59 −0.590268 −0.295134 0.955456i \(-0.595364\pi\)
−0.295134 + 0.955456i \(0.595364\pi\)
\(614\) 21494.8 1.41280
\(615\) 0 0
\(616\) −76298.7 −4.99053
\(617\) −25935.8 −1.69228 −0.846139 0.532962i \(-0.821079\pi\)
−0.846139 + 0.532962i \(0.821079\pi\)
\(618\) 0 0
\(619\) 28793.1 1.86962 0.934810 0.355149i \(-0.115570\pi\)
0.934810 + 0.355149i \(0.115570\pi\)
\(620\) −22338.1 −1.44697
\(621\) 0 0
\(622\) 5399.79 0.348090
\(623\) 10820.8 0.695867
\(624\) 0 0
\(625\) 2836.87 0.181560
\(626\) 46667.8 2.97958
\(627\) 0 0
\(628\) −1109.20 −0.0704804
\(629\) 30604.3 1.94002
\(630\) 0 0
\(631\) −10699.7 −0.675034 −0.337517 0.941319i \(-0.609587\pi\)
−0.337517 + 0.941319i \(0.609587\pi\)
\(632\) −33575.8 −2.11325
\(633\) 0 0
\(634\) 29638.3 1.85661
\(635\) −3481.42 −0.217568
\(636\) 0 0
\(637\) −549.124 −0.0341556
\(638\) −54942.8 −3.40941
\(639\) 0 0
\(640\) 7844.61 0.484509
\(641\) −18742.7 −1.15490 −0.577450 0.816426i \(-0.695952\pi\)
−0.577450 + 0.816426i \(0.695952\pi\)
\(642\) 0 0
\(643\) −1338.90 −0.0821166 −0.0410583 0.999157i \(-0.513073\pi\)
−0.0410583 + 0.999157i \(0.513073\pi\)
\(644\) 4904.91 0.300125
\(645\) 0 0
\(646\) 33321.1 2.02941
\(647\) −14253.8 −0.866112 −0.433056 0.901367i \(-0.642565\pi\)
−0.433056 + 0.901367i \(0.642565\pi\)
\(648\) 0 0
\(649\) 1566.87 0.0947692
\(650\) −1005.57 −0.0606793
\(651\) 0 0
\(652\) −10305.3 −0.618999
\(653\) 7106.59 0.425884 0.212942 0.977065i \(-0.431695\pi\)
0.212942 + 0.977065i \(0.431695\pi\)
\(654\) 0 0
\(655\) 10651.4 0.635394
\(656\) 57532.8 3.42420
\(657\) 0 0
\(658\) 74105.4 4.39047
\(659\) 32587.0 1.92627 0.963133 0.269024i \(-0.0867011\pi\)
0.963133 + 0.269024i \(0.0867011\pi\)
\(660\) 0 0
\(661\) −29315.3 −1.72501 −0.862506 0.506046i \(-0.831106\pi\)
−0.862506 + 0.506046i \(0.831106\pi\)
\(662\) 20359.5 1.19531
\(663\) 0 0
\(664\) 14378.9 0.840377
\(665\) −8486.26 −0.494862
\(666\) 0 0
\(667\) 1977.37 0.114789
\(668\) −15146.1 −0.877275
\(669\) 0 0
\(670\) 783.377 0.0451709
\(671\) 14970.3 0.861285
\(672\) 0 0
\(673\) 4257.99 0.243884 0.121942 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(674\) −15034.6 −0.859215
\(675\) 0 0
\(676\) −39838.4 −2.26664
\(677\) −10449.7 −0.593227 −0.296613 0.954998i \(-0.595857\pi\)
−0.296613 + 0.954998i \(0.595857\pi\)
\(678\) 0 0
\(679\) 31339.5 1.77128
\(680\) −36701.5 −2.06976
\(681\) 0 0
\(682\) 61794.9 3.46957
\(683\) 20866.7 1.16902 0.584510 0.811386i \(-0.301287\pi\)
0.584510 + 0.811386i \(0.301287\pi\)
\(684\) 0 0
\(685\) 10528.8 0.587276
\(686\) 12358.5 0.687829
\(687\) 0 0
\(688\) −25114.8 −1.39171
\(689\) 622.781 0.0344355
\(690\) 0 0
\(691\) 31753.3 1.74812 0.874061 0.485815i \(-0.161477\pi\)
0.874061 + 0.485815i \(0.161477\pi\)
\(692\) 49557.6 2.72239
\(693\) 0 0
\(694\) 16128.1 0.882151
\(695\) −14112.3 −0.770231
\(696\) 0 0
\(697\) 54449.7 2.95901
\(698\) 22245.2 1.20629
\(699\) 0 0
\(700\) −38311.9 −2.06865
\(701\) 33086.2 1.78266 0.891332 0.453350i \(-0.149771\pi\)
0.891332 + 0.453350i \(0.149771\pi\)
\(702\) 0 0
\(703\) −15215.0 −0.816277
\(704\) 4077.32 0.218281
\(705\) 0 0
\(706\) −54466.7 −2.90351
\(707\) 23581.2 1.25440
\(708\) 0 0
\(709\) 13001.5 0.688689 0.344345 0.938843i \(-0.388101\pi\)
0.344345 + 0.938843i \(0.388101\pi\)
\(710\) −8201.43 −0.433513
\(711\) 0 0
\(712\) −23265.6 −1.22460
\(713\) −2223.98 −0.116815
\(714\) 0 0
\(715\) −841.762 −0.0440281
\(716\) −42001.9 −2.19230
\(717\) 0 0
\(718\) −39221.7 −2.03864
\(719\) −22832.0 −1.18427 −0.592136 0.805838i \(-0.701715\pi\)
−0.592136 + 0.805838i \(0.701715\pi\)
\(720\) 0 0
\(721\) 11576.3 0.597955
\(722\) 18526.2 0.954951
\(723\) 0 0
\(724\) −4699.05 −0.241214
\(725\) −15445.1 −0.791196
\(726\) 0 0
\(727\) −12675.4 −0.646634 −0.323317 0.946291i \(-0.604798\pi\)
−0.323317 + 0.946291i \(0.604798\pi\)
\(728\) 2845.60 0.144869
\(729\) 0 0
\(730\) −33938.8 −1.72073
\(731\) −23769.0 −1.20264
\(732\) 0 0
\(733\) 12531.2 0.631448 0.315724 0.948851i \(-0.397753\pi\)
0.315724 + 0.948851i \(0.397753\pi\)
\(734\) 47610.7 2.39420
\(735\) 0 0
\(736\) −2254.51 −0.112911
\(737\) −1504.76 −0.0752082
\(738\) 0 0
\(739\) 28474.9 1.41741 0.708706 0.705504i \(-0.249279\pi\)
0.708706 + 0.705504i \(0.249279\pi\)
\(740\) 29934.4 1.48704
\(741\) 0 0
\(742\) 34171.8 1.69068
\(743\) −33823.3 −1.67006 −0.835032 0.550202i \(-0.814551\pi\)
−0.835032 + 0.550202i \(0.814551\pi\)
\(744\) 0 0
\(745\) −17735.7 −0.872196
\(746\) −66705.2 −3.27380
\(747\) 0 0
\(748\) 125926. 6.15548
\(749\) −8178.22 −0.398966
\(750\) 0 0
\(751\) −32411.1 −1.57483 −0.787414 0.616424i \(-0.788581\pi\)
−0.787414 + 0.616424i \(0.788581\pi\)
\(752\) −72348.8 −3.50837
\(753\) 0 0
\(754\) 2049.12 0.0989715
\(755\) −5357.67 −0.258259
\(756\) 0 0
\(757\) −19616.4 −0.941834 −0.470917 0.882178i \(-0.656077\pi\)
−0.470917 + 0.882178i \(0.656077\pi\)
\(758\) −37886.0 −1.81541
\(759\) 0 0
\(760\) 18246.2 0.870866
\(761\) 11000.9 0.524025 0.262012 0.965065i \(-0.415614\pi\)
0.262012 + 0.965065i \(0.415614\pi\)
\(762\) 0 0
\(763\) −1729.67 −0.0820687
\(764\) −57811.9 −2.73764
\(765\) 0 0
\(766\) 43927.7 2.07203
\(767\) −58.4374 −0.00275104
\(768\) 0 0
\(769\) 23498.7 1.10193 0.550966 0.834528i \(-0.314260\pi\)
0.550966 + 0.834528i \(0.314260\pi\)
\(770\) −46187.3 −2.16165
\(771\) 0 0
\(772\) 35702.4 1.66445
\(773\) −20105.2 −0.935489 −0.467745 0.883864i \(-0.654933\pi\)
−0.467745 + 0.883864i \(0.654933\pi\)
\(774\) 0 0
\(775\) 17371.3 0.805157
\(776\) −67382.6 −3.11713
\(777\) 0 0
\(778\) 30960.2 1.42670
\(779\) −27069.8 −1.24503
\(780\) 0 0
\(781\) 15753.8 0.721787
\(782\) −6526.85 −0.298465
\(783\) 0 0
\(784\) 29416.1 1.34002
\(785\) −375.904 −0.0170912
\(786\) 0 0
\(787\) −34093.2 −1.54421 −0.772103 0.635497i \(-0.780795\pi\)
−0.772103 + 0.635497i \(0.780795\pi\)
\(788\) −58702.5 −2.65379
\(789\) 0 0
\(790\) −20325.0 −0.915356
\(791\) 23066.1 1.03683
\(792\) 0 0
\(793\) −558.325 −0.0250021
\(794\) 26849.7 1.20008
\(795\) 0 0
\(796\) −19439.0 −0.865575
\(797\) −9128.51 −0.405707 −0.202853 0.979209i \(-0.565021\pi\)
−0.202853 + 0.979209i \(0.565021\pi\)
\(798\) 0 0
\(799\) −68471.8 −3.03174
\(800\) 17609.8 0.778249
\(801\) 0 0
\(802\) 52646.8 2.31798
\(803\) 65191.7 2.86496
\(804\) 0 0
\(805\) 1662.27 0.0727791
\(806\) −2304.67 −0.100718
\(807\) 0 0
\(808\) −50701.5 −2.20751
\(809\) −8581.63 −0.372947 −0.186474 0.982460i \(-0.559706\pi\)
−0.186474 + 0.982460i \(0.559706\pi\)
\(810\) 0 0
\(811\) −7419.25 −0.321239 −0.160620 0.987016i \(-0.551349\pi\)
−0.160620 + 0.987016i \(0.551349\pi\)
\(812\) 78070.9 3.37408
\(813\) 0 0
\(814\) −82808.8 −3.56566
\(815\) −3492.46 −0.150105
\(816\) 0 0
\(817\) 11816.8 0.506018
\(818\) −44613.1 −1.90692
\(819\) 0 0
\(820\) 53257.9 2.26810
\(821\) −395.175 −0.0167987 −0.00839933 0.999965i \(-0.502674\pi\)
−0.00839933 + 0.999965i \(0.502674\pi\)
\(822\) 0 0
\(823\) −13815.4 −0.585145 −0.292572 0.956243i \(-0.594511\pi\)
−0.292572 + 0.956243i \(0.594511\pi\)
\(824\) −24890.1 −1.05229
\(825\) 0 0
\(826\) −3206.44 −0.135068
\(827\) −4972.77 −0.209093 −0.104547 0.994520i \(-0.533339\pi\)
−0.104547 + 0.994520i \(0.533339\pi\)
\(828\) 0 0
\(829\) −2223.76 −0.0931656 −0.0465828 0.998914i \(-0.514833\pi\)
−0.0465828 + 0.998914i \(0.514833\pi\)
\(830\) 8704.24 0.364010
\(831\) 0 0
\(832\) −152.066 −0.00633646
\(833\) 27839.7 1.15797
\(834\) 0 0
\(835\) −5132.98 −0.212736
\(836\) −62604.1 −2.58996
\(837\) 0 0
\(838\) −36216.8 −1.49295
\(839\) 6945.72 0.285808 0.142904 0.989737i \(-0.454356\pi\)
0.142904 + 0.989737i \(0.454356\pi\)
\(840\) 0 0
\(841\) 7084.65 0.290486
\(842\) −71685.1 −2.93400
\(843\) 0 0
\(844\) 59254.2 2.41660
\(845\) −13501.2 −0.549650
\(846\) 0 0
\(847\) 56492.8 2.29175
\(848\) −33361.8 −1.35100
\(849\) 0 0
\(850\) 50980.7 2.05720
\(851\) 2980.27 0.120050
\(852\) 0 0
\(853\) −21002.3 −0.843029 −0.421515 0.906822i \(-0.638501\pi\)
−0.421515 + 0.906822i \(0.638501\pi\)
\(854\) −30635.1 −1.22753
\(855\) 0 0
\(856\) 17583.9 0.702107
\(857\) 17224.3 0.686545 0.343273 0.939236i \(-0.388465\pi\)
0.343273 + 0.939236i \(0.388465\pi\)
\(858\) 0 0
\(859\) −39760.0 −1.57927 −0.789635 0.613576i \(-0.789730\pi\)
−0.789635 + 0.613576i \(0.789730\pi\)
\(860\) −23248.7 −0.921830
\(861\) 0 0
\(862\) −80750.5 −3.19069
\(863\) 32018.9 1.26296 0.631480 0.775392i \(-0.282448\pi\)
0.631480 + 0.775392i \(0.282448\pi\)
\(864\) 0 0
\(865\) 16795.0 0.660170
\(866\) −58637.3 −2.30090
\(867\) 0 0
\(868\) −87807.5 −3.43362
\(869\) 39041.5 1.52404
\(870\) 0 0
\(871\) 56.1207 0.00218321
\(872\) 3718.94 0.144426
\(873\) 0 0
\(874\) 3244.83 0.125581
\(875\) −31625.9 −1.22189
\(876\) 0 0
\(877\) 24682.8 0.950376 0.475188 0.879884i \(-0.342380\pi\)
0.475188 + 0.879884i \(0.342380\pi\)
\(878\) −32512.3 −1.24970
\(879\) 0 0
\(880\) 45092.4 1.72735
\(881\) 11864.7 0.453726 0.226863 0.973927i \(-0.427153\pi\)
0.226863 + 0.973927i \(0.427153\pi\)
\(882\) 0 0
\(883\) 16157.7 0.615797 0.307899 0.951419i \(-0.400374\pi\)
0.307899 + 0.951419i \(0.400374\pi\)
\(884\) −4696.46 −0.178687
\(885\) 0 0
\(886\) −5778.04 −0.219094
\(887\) 26782.5 1.01383 0.506916 0.861995i \(-0.330785\pi\)
0.506916 + 0.861995i \(0.330785\pi\)
\(888\) 0 0
\(889\) −13684.9 −0.516284
\(890\) −14083.8 −0.530437
\(891\) 0 0
\(892\) −94182.7 −3.53528
\(893\) 34040.9 1.27563
\(894\) 0 0
\(895\) −14234.4 −0.531623
\(896\) 30835.9 1.14973
\(897\) 0 0
\(898\) 29157.2 1.08351
\(899\) −35398.9 −1.31326
\(900\) 0 0
\(901\) −31574.0 −1.16746
\(902\) −147330. −5.43852
\(903\) 0 0
\(904\) −49594.1 −1.82464
\(905\) −1592.50 −0.0584934
\(906\) 0 0
\(907\) −16780.3 −0.614312 −0.307156 0.951659i \(-0.599377\pi\)
−0.307156 + 0.951659i \(0.599377\pi\)
\(908\) −70623.1 −2.58118
\(909\) 0 0
\(910\) 1722.58 0.0627504
\(911\) 47243.2 1.71815 0.859076 0.511848i \(-0.171039\pi\)
0.859076 + 0.511848i \(0.171039\pi\)
\(912\) 0 0
\(913\) −16719.6 −0.606067
\(914\) 49040.1 1.77473
\(915\) 0 0
\(916\) −18109.1 −0.653213
\(917\) 41868.8 1.50777
\(918\) 0 0
\(919\) 16832.5 0.604191 0.302095 0.953278i \(-0.402314\pi\)
0.302095 + 0.953278i \(0.402314\pi\)
\(920\) −3574.01 −0.128078
\(921\) 0 0
\(922\) −78196.7 −2.79313
\(923\) −587.546 −0.0209527
\(924\) 0 0
\(925\) −23278.6 −0.827455
\(926\) −17036.4 −0.604590
\(927\) 0 0
\(928\) −35884.7 −1.26937
\(929\) 44392.4 1.56778 0.783890 0.620900i \(-0.213233\pi\)
0.783890 + 0.620900i \(0.213233\pi\)
\(930\) 0 0
\(931\) −13840.6 −0.487225
\(932\) 83393.3 2.93094
\(933\) 0 0
\(934\) 2351.14 0.0823681
\(935\) 42676.0 1.49268
\(936\) 0 0
\(937\) 26352.9 0.918797 0.459399 0.888230i \(-0.348065\pi\)
0.459399 + 0.888230i \(0.348065\pi\)
\(938\) 3079.33 0.107189
\(939\) 0 0
\(940\) −66973.0 −2.32385
\(941\) −12263.8 −0.424853 −0.212427 0.977177i \(-0.568137\pi\)
−0.212427 + 0.977177i \(0.568137\pi\)
\(942\) 0 0
\(943\) 5302.35 0.183105
\(944\) 3130.44 0.107931
\(945\) 0 0
\(946\) 64313.9 2.21039
\(947\) 19599.5 0.672542 0.336271 0.941765i \(-0.390834\pi\)
0.336271 + 0.941765i \(0.390834\pi\)
\(948\) 0 0
\(949\) −2431.36 −0.0831667
\(950\) −25345.1 −0.865583
\(951\) 0 0
\(952\) −144267. −4.91149
\(953\) 26505.2 0.900932 0.450466 0.892794i \(-0.351258\pi\)
0.450466 + 0.892794i \(0.351258\pi\)
\(954\) 0 0
\(955\) −19592.4 −0.663868
\(956\) −4343.89 −0.146957
\(957\) 0 0
\(958\) 21295.3 0.718183
\(959\) 41386.9 1.39359
\(960\) 0 0
\(961\) 10022.6 0.336430
\(962\) 3088.40 0.103507
\(963\) 0 0
\(964\) −15667.8 −0.523470
\(965\) 12099.5 0.403623
\(966\) 0 0
\(967\) 2628.01 0.0873951 0.0436976 0.999045i \(-0.486086\pi\)
0.0436976 + 0.999045i \(0.486086\pi\)
\(968\) −121464. −4.03307
\(969\) 0 0
\(970\) −40789.9 −1.35019
\(971\) −4466.94 −0.147632 −0.0738161 0.997272i \(-0.523518\pi\)
−0.0738161 + 0.997272i \(0.523518\pi\)
\(972\) 0 0
\(973\) −55473.2 −1.82774
\(974\) 33588.8 1.10498
\(975\) 0 0
\(976\) 29909.0 0.980904
\(977\) 4528.27 0.148283 0.0741413 0.997248i \(-0.476378\pi\)
0.0741413 + 0.997248i \(0.476378\pi\)
\(978\) 0 0
\(979\) 27053.0 0.883163
\(980\) 27230.4 0.887594
\(981\) 0 0
\(982\) −32244.4 −1.04782
\(983\) −37570.4 −1.21903 −0.609517 0.792773i \(-0.708637\pi\)
−0.609517 + 0.792773i \(0.708637\pi\)
\(984\) 0 0
\(985\) −19894.2 −0.643534
\(986\) −103887. −3.35541
\(987\) 0 0
\(988\) 2334.85 0.0751838
\(989\) −2314.64 −0.0744199
\(990\) 0 0
\(991\) 30386.3 0.974018 0.487009 0.873397i \(-0.338088\pi\)
0.487009 + 0.873397i \(0.338088\pi\)
\(992\) 40360.1 1.29177
\(993\) 0 0
\(994\) −32238.5 −1.02871
\(995\) −6587.85 −0.209898
\(996\) 0 0
\(997\) −30865.5 −0.980462 −0.490231 0.871593i \(-0.663088\pi\)
−0.490231 + 0.871593i \(0.663088\pi\)
\(998\) −51817.8 −1.64355
\(999\) 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.1.4 yes 59
3.2 odd 2 2151.4.a.g.1.56 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.56 59 3.2 odd 2
2151.4.a.h.1.4 yes 59 1.1 even 1 trivial