Properties

Label 2151.4.a.h.1.6
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 1.6
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.50896 q^{2} +12.3307 q^{4} -9.52144 q^{5} -13.3640 q^{7} -19.5269 q^{8} +O(q^{10})\) \(q-4.50896 q^{2} +12.3307 q^{4} -9.52144 q^{5} -13.3640 q^{7} -19.5269 q^{8} +42.9318 q^{10} +2.94125 q^{11} +33.8562 q^{13} +60.2578 q^{14} -10.5995 q^{16} +28.2145 q^{17} -135.304 q^{19} -117.406 q^{20} -13.2620 q^{22} +84.3598 q^{23} -34.3422 q^{25} -152.656 q^{26} -164.788 q^{28} +107.051 q^{29} -131.876 q^{31} +204.008 q^{32} -127.218 q^{34} +127.245 q^{35} -139.270 q^{37} +610.080 q^{38} +185.924 q^{40} +173.525 q^{41} +476.983 q^{43} +36.2677 q^{44} -380.375 q^{46} +323.326 q^{47} -164.403 q^{49} +154.847 q^{50} +417.471 q^{52} -601.871 q^{53} -28.0049 q^{55} +260.958 q^{56} -482.690 q^{58} -430.427 q^{59} -651.074 q^{61} +594.622 q^{62} -835.068 q^{64} -322.360 q^{65} +1013.18 q^{67} +347.905 q^{68} -573.741 q^{70} -935.109 q^{71} -271.689 q^{73} +627.964 q^{74} -1668.39 q^{76} -39.3069 q^{77} -301.342 q^{79} +100.923 q^{80} -782.415 q^{82} +689.562 q^{83} -268.643 q^{85} -2150.70 q^{86} -57.4335 q^{88} +650.347 q^{89} -452.455 q^{91} +1040.22 q^{92} -1457.87 q^{94} +1288.29 q^{95} +211.167 q^{97} +741.287 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.50896 −1.59416 −0.797079 0.603876i \(-0.793622\pi\)
−0.797079 + 0.603876i \(0.793622\pi\)
\(3\) 0 0
\(4\) 12.3307 1.54134
\(5\) −9.52144 −0.851624 −0.425812 0.904812i \(-0.640011\pi\)
−0.425812 + 0.904812i \(0.640011\pi\)
\(6\) 0 0
\(7\) −13.3640 −0.721589 −0.360794 0.932645i \(-0.617494\pi\)
−0.360794 + 0.932645i \(0.617494\pi\)
\(8\) −19.5269 −0.862976
\(9\) 0 0
\(10\) 42.9318 1.35762
\(11\) 2.94125 0.0806200 0.0403100 0.999187i \(-0.487165\pi\)
0.0403100 + 0.999187i \(0.487165\pi\)
\(12\) 0 0
\(13\) 33.8562 0.722310 0.361155 0.932506i \(-0.382383\pi\)
0.361155 + 0.932506i \(0.382383\pi\)
\(14\) 60.2578 1.15033
\(15\) 0 0
\(16\) −10.5995 −0.165618
\(17\) 28.2145 0.402531 0.201265 0.979537i \(-0.435495\pi\)
0.201265 + 0.979537i \(0.435495\pi\)
\(18\) 0 0
\(19\) −135.304 −1.63373 −0.816865 0.576829i \(-0.804290\pi\)
−0.816865 + 0.576829i \(0.804290\pi\)
\(20\) −117.406 −1.31264
\(21\) 0 0
\(22\) −13.2620 −0.128521
\(23\) 84.3598 0.764793 0.382397 0.923998i \(-0.375099\pi\)
0.382397 + 0.923998i \(0.375099\pi\)
\(24\) 0 0
\(25\) −34.3422 −0.274737
\(26\) −152.656 −1.15147
\(27\) 0 0
\(28\) −164.788 −1.11221
\(29\) 107.051 0.685481 0.342741 0.939430i \(-0.388645\pi\)
0.342741 + 0.939430i \(0.388645\pi\)
\(30\) 0 0
\(31\) −131.876 −0.764051 −0.382025 0.924152i \(-0.624773\pi\)
−0.382025 + 0.924152i \(0.624773\pi\)
\(32\) 204.008 1.12700
\(33\) 0 0
\(34\) −127.218 −0.641697
\(35\) 127.245 0.614522
\(36\) 0 0
\(37\) −139.270 −0.618808 −0.309404 0.950931i \(-0.600129\pi\)
−0.309404 + 0.950931i \(0.600129\pi\)
\(38\) 610.080 2.60442
\(39\) 0 0
\(40\) 185.924 0.734931
\(41\) 173.525 0.660975 0.330488 0.943810i \(-0.392787\pi\)
0.330488 + 0.943810i \(0.392787\pi\)
\(42\) 0 0
\(43\) 476.983 1.69161 0.845805 0.533492i \(-0.179121\pi\)
0.845805 + 0.533492i \(0.179121\pi\)
\(44\) 36.2677 0.124263
\(45\) 0 0
\(46\) −380.375 −1.21920
\(47\) 323.326 1.00345 0.501723 0.865028i \(-0.332699\pi\)
0.501723 + 0.865028i \(0.332699\pi\)
\(48\) 0 0
\(49\) −164.403 −0.479310
\(50\) 154.847 0.437974
\(51\) 0 0
\(52\) 417.471 1.11332
\(53\) −601.871 −1.55987 −0.779937 0.625858i \(-0.784749\pi\)
−0.779937 + 0.625858i \(0.784749\pi\)
\(54\) 0 0
\(55\) −28.0049 −0.0686579
\(56\) 260.958 0.622714
\(57\) 0 0
\(58\) −482.690 −1.09276
\(59\) −430.427 −0.949776 −0.474888 0.880046i \(-0.657511\pi\)
−0.474888 + 0.880046i \(0.657511\pi\)
\(60\) 0 0
\(61\) −651.074 −1.36658 −0.683291 0.730147i \(-0.739452\pi\)
−0.683291 + 0.730147i \(0.739452\pi\)
\(62\) 594.622 1.21802
\(63\) 0 0
\(64\) −835.068 −1.63099
\(65\) −322.360 −0.615136
\(66\) 0 0
\(67\) 1013.18 1.84745 0.923727 0.383052i \(-0.125127\pi\)
0.923727 + 0.383052i \(0.125127\pi\)
\(68\) 347.905 0.620436
\(69\) 0 0
\(70\) −573.741 −0.979645
\(71\) −935.109 −1.56306 −0.781528 0.623870i \(-0.785560\pi\)
−0.781528 + 0.623870i \(0.785560\pi\)
\(72\) 0 0
\(73\) −271.689 −0.435600 −0.217800 0.975993i \(-0.569888\pi\)
−0.217800 + 0.975993i \(0.569888\pi\)
\(74\) 627.964 0.986477
\(75\) 0 0
\(76\) −1668.39 −2.51813
\(77\) −39.3069 −0.0581745
\(78\) 0 0
\(79\) −301.342 −0.429159 −0.214580 0.976706i \(-0.568838\pi\)
−0.214580 + 0.976706i \(0.568838\pi\)
\(80\) 100.923 0.141044
\(81\) 0 0
\(82\) −782.415 −1.05370
\(83\) 689.562 0.911919 0.455960 0.890001i \(-0.349296\pi\)
0.455960 + 0.890001i \(0.349296\pi\)
\(84\) 0 0
\(85\) −268.643 −0.342805
\(86\) −2150.70 −2.69669
\(87\) 0 0
\(88\) −57.4335 −0.0695731
\(89\) 650.347 0.774568 0.387284 0.921960i \(-0.373413\pi\)
0.387284 + 0.921960i \(0.373413\pi\)
\(90\) 0 0
\(91\) −452.455 −0.521210
\(92\) 1040.22 1.17880
\(93\) 0 0
\(94\) −1457.87 −1.59965
\(95\) 1288.29 1.39132
\(96\) 0 0
\(97\) 211.167 0.221039 0.110520 0.993874i \(-0.464749\pi\)
0.110520 + 0.993874i \(0.464749\pi\)
\(98\) 741.287 0.764095
\(99\) 0 0
\(100\) −423.463 −0.423463
\(101\) −526.291 −0.518494 −0.259247 0.965811i \(-0.583474\pi\)
−0.259247 + 0.965811i \(0.583474\pi\)
\(102\) 0 0
\(103\) −1107.17 −1.05916 −0.529578 0.848261i \(-0.677650\pi\)
−0.529578 + 0.848261i \(0.677650\pi\)
\(104\) −661.107 −0.623336
\(105\) 0 0
\(106\) 2713.81 2.48668
\(107\) 284.273 0.256838 0.128419 0.991720i \(-0.459010\pi\)
0.128419 + 0.991720i \(0.459010\pi\)
\(108\) 0 0
\(109\) 1109.29 0.974780 0.487390 0.873184i \(-0.337949\pi\)
0.487390 + 0.873184i \(0.337949\pi\)
\(110\) 126.273 0.109451
\(111\) 0 0
\(112\) 141.652 0.119508
\(113\) −891.630 −0.742279 −0.371140 0.928577i \(-0.621033\pi\)
−0.371140 + 0.928577i \(0.621033\pi\)
\(114\) 0 0
\(115\) −803.227 −0.651316
\(116\) 1320.02 1.05656
\(117\) 0 0
\(118\) 1940.78 1.51409
\(119\) −377.059 −0.290462
\(120\) 0 0
\(121\) −1322.35 −0.993500
\(122\) 2935.66 2.17855
\(123\) 0 0
\(124\) −1626.12 −1.17766
\(125\) 1517.17 1.08560
\(126\) 0 0
\(127\) −1211.31 −0.846347 −0.423174 0.906049i \(-0.639084\pi\)
−0.423174 + 0.906049i \(0.639084\pi\)
\(128\) 2133.22 1.47306
\(129\) 0 0
\(130\) 1453.51 0.980623
\(131\) 1226.76 0.818188 0.409094 0.912492i \(-0.365845\pi\)
0.409094 + 0.912492i \(0.365845\pi\)
\(132\) 0 0
\(133\) 1808.21 1.17888
\(134\) −4568.38 −2.94513
\(135\) 0 0
\(136\) −550.943 −0.347374
\(137\) −1736.26 −1.08276 −0.541382 0.840776i \(-0.682099\pi\)
−0.541382 + 0.840776i \(0.682099\pi\)
\(138\) 0 0
\(139\) 318.169 0.194149 0.0970745 0.995277i \(-0.469051\pi\)
0.0970745 + 0.995277i \(0.469051\pi\)
\(140\) 1569.01 0.947185
\(141\) 0 0
\(142\) 4216.37 2.49176
\(143\) 99.5796 0.0582326
\(144\) 0 0
\(145\) −1019.28 −0.583772
\(146\) 1225.03 0.694415
\(147\) 0 0
\(148\) −1717.30 −0.953791
\(149\) −1076.64 −0.591956 −0.295978 0.955195i \(-0.595645\pi\)
−0.295978 + 0.955195i \(0.595645\pi\)
\(150\) 0 0
\(151\) −1156.90 −0.623491 −0.311745 0.950166i \(-0.600914\pi\)
−0.311745 + 0.950166i \(0.600914\pi\)
\(152\) 2642.07 1.40987
\(153\) 0 0
\(154\) 177.233 0.0927393
\(155\) 1255.65 0.650684
\(156\) 0 0
\(157\) −2167.66 −1.10190 −0.550950 0.834538i \(-0.685735\pi\)
−0.550950 + 0.834538i \(0.685735\pi\)
\(158\) 1358.74 0.684147
\(159\) 0 0
\(160\) −1942.45 −0.959777
\(161\) −1127.39 −0.551866
\(162\) 0 0
\(163\) −1150.19 −0.552696 −0.276348 0.961058i \(-0.589124\pi\)
−0.276348 + 0.961058i \(0.589124\pi\)
\(164\) 2139.68 1.01879
\(165\) 0 0
\(166\) −3109.21 −1.45374
\(167\) −2654.37 −1.22995 −0.614974 0.788547i \(-0.710834\pi\)
−0.614974 + 0.788547i \(0.710834\pi\)
\(168\) 0 0
\(169\) −1050.76 −0.478269
\(170\) 1211.30 0.546485
\(171\) 0 0
\(172\) 5881.53 2.60734
\(173\) 849.869 0.373493 0.186747 0.982408i \(-0.440206\pi\)
0.186747 + 0.982408i \(0.440206\pi\)
\(174\) 0 0
\(175\) 458.949 0.198247
\(176\) −31.1758 −0.0133521
\(177\) 0 0
\(178\) −2932.38 −1.23478
\(179\) 2819.54 1.17733 0.588666 0.808376i \(-0.299653\pi\)
0.588666 + 0.808376i \(0.299653\pi\)
\(180\) 0 0
\(181\) 1234.91 0.507128 0.253564 0.967319i \(-0.418397\pi\)
0.253564 + 0.967319i \(0.418397\pi\)
\(182\) 2040.10 0.830891
\(183\) 0 0
\(184\) −1647.29 −0.659998
\(185\) 1326.05 0.526991
\(186\) 0 0
\(187\) 82.9859 0.0324520
\(188\) 3986.84 1.54665
\(189\) 0 0
\(190\) −5808.84 −2.21799
\(191\) −2491.75 −0.943963 −0.471981 0.881609i \(-0.656461\pi\)
−0.471981 + 0.881609i \(0.656461\pi\)
\(192\) 0 0
\(193\) −4237.89 −1.58057 −0.790284 0.612740i \(-0.790067\pi\)
−0.790284 + 0.612740i \(0.790067\pi\)
\(194\) −952.144 −0.352371
\(195\) 0 0
\(196\) −2027.21 −0.738778
\(197\) 5180.33 1.87352 0.936760 0.349973i \(-0.113809\pi\)
0.936760 + 0.349973i \(0.113809\pi\)
\(198\) 0 0
\(199\) 4099.35 1.46028 0.730139 0.683299i \(-0.239455\pi\)
0.730139 + 0.683299i \(0.239455\pi\)
\(200\) 670.597 0.237092
\(201\) 0 0
\(202\) 2373.02 0.826561
\(203\) −1430.64 −0.494636
\(204\) 0 0
\(205\) −1652.20 −0.562902
\(206\) 4992.20 1.68846
\(207\) 0 0
\(208\) −358.860 −0.119627
\(209\) −397.963 −0.131711
\(210\) 0 0
\(211\) 3788.99 1.23623 0.618116 0.786087i \(-0.287896\pi\)
0.618116 + 0.786087i \(0.287896\pi\)
\(212\) −7421.49 −2.40429
\(213\) 0 0
\(214\) −1281.77 −0.409440
\(215\) −4541.57 −1.44061
\(216\) 0 0
\(217\) 1762.39 0.551331
\(218\) −5001.76 −1.55395
\(219\) 0 0
\(220\) −345.320 −0.105825
\(221\) 955.237 0.290752
\(222\) 0 0
\(223\) −4451.92 −1.33687 −0.668437 0.743769i \(-0.733036\pi\)
−0.668437 + 0.743769i \(0.733036\pi\)
\(224\) −2726.37 −0.813228
\(225\) 0 0
\(226\) 4020.32 1.18331
\(227\) −1524.03 −0.445611 −0.222805 0.974863i \(-0.571521\pi\)
−0.222805 + 0.974863i \(0.571521\pi\)
\(228\) 0 0
\(229\) −3437.46 −0.991939 −0.495969 0.868340i \(-0.665187\pi\)
−0.495969 + 0.868340i \(0.665187\pi\)
\(230\) 3621.72 1.03830
\(231\) 0 0
\(232\) −2090.39 −0.591554
\(233\) 3451.71 0.970510 0.485255 0.874373i \(-0.338727\pi\)
0.485255 + 0.874373i \(0.338727\pi\)
\(234\) 0 0
\(235\) −3078.53 −0.854559
\(236\) −5307.46 −1.46392
\(237\) 0 0
\(238\) 1700.14 0.463042
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 2828.41 0.755990 0.377995 0.925808i \(-0.376614\pi\)
0.377995 + 0.925808i \(0.376614\pi\)
\(242\) 5962.42 1.58380
\(243\) 0 0
\(244\) −8028.19 −2.10636
\(245\) 1565.36 0.408191
\(246\) 0 0
\(247\) −4580.88 −1.18006
\(248\) 2575.13 0.659358
\(249\) 0 0
\(250\) −6840.84 −1.73061
\(251\) −7281.21 −1.83102 −0.915509 0.402297i \(-0.868212\pi\)
−0.915509 + 0.402297i \(0.868212\pi\)
\(252\) 0 0
\(253\) 248.123 0.0616576
\(254\) 5461.73 1.34921
\(255\) 0 0
\(256\) −2938.05 −0.717298
\(257\) −5028.04 −1.22039 −0.610196 0.792250i \(-0.708909\pi\)
−0.610196 + 0.792250i \(0.708909\pi\)
\(258\) 0 0
\(259\) 1861.21 0.446525
\(260\) −3974.92 −0.948131
\(261\) 0 0
\(262\) −5531.41 −1.30432
\(263\) −7977.18 −1.87032 −0.935160 0.354225i \(-0.884745\pi\)
−0.935160 + 0.354225i \(0.884745\pi\)
\(264\) 0 0
\(265\) 5730.68 1.32843
\(266\) −8153.12 −1.87932
\(267\) 0 0
\(268\) 12493.2 2.84755
\(269\) 1734.11 0.393051 0.196525 0.980499i \(-0.437034\pi\)
0.196525 + 0.980499i \(0.437034\pi\)
\(270\) 0 0
\(271\) 6903.99 1.54756 0.773778 0.633457i \(-0.218365\pi\)
0.773778 + 0.633457i \(0.218365\pi\)
\(272\) −299.060 −0.0666662
\(273\) 0 0
\(274\) 7828.73 1.72610
\(275\) −101.009 −0.0221493
\(276\) 0 0
\(277\) −3699.16 −0.802387 −0.401193 0.915993i \(-0.631404\pi\)
−0.401193 + 0.915993i \(0.631404\pi\)
\(278\) −1434.61 −0.309504
\(279\) 0 0
\(280\) −2484.70 −0.530318
\(281\) 7660.30 1.62625 0.813123 0.582091i \(-0.197765\pi\)
0.813123 + 0.582091i \(0.197765\pi\)
\(282\) 0 0
\(283\) −2988.83 −0.627801 −0.313900 0.949456i \(-0.601636\pi\)
−0.313900 + 0.949456i \(0.601636\pi\)
\(284\) −11530.5 −2.40920
\(285\) 0 0
\(286\) −449.000 −0.0928319
\(287\) −2318.98 −0.476952
\(288\) 0 0
\(289\) −4116.94 −0.837969
\(290\) 4595.91 0.930624
\(291\) 0 0
\(292\) −3350.12 −0.671406
\(293\) 2649.48 0.528275 0.264137 0.964485i \(-0.414913\pi\)
0.264137 + 0.964485i \(0.414913\pi\)
\(294\) 0 0
\(295\) 4098.28 0.808852
\(296\) 2719.52 0.534016
\(297\) 0 0
\(298\) 4854.50 0.943670
\(299\) 2856.10 0.552417
\(300\) 0 0
\(301\) −6374.41 −1.22065
\(302\) 5216.41 0.993943
\(303\) 0 0
\(304\) 1434.16 0.270574
\(305\) 6199.16 1.16381
\(306\) 0 0
\(307\) −3164.53 −0.588304 −0.294152 0.955759i \(-0.595037\pi\)
−0.294152 + 0.955759i \(0.595037\pi\)
\(308\) −484.681 −0.0896665
\(309\) 0 0
\(310\) −5661.66 −1.03729
\(311\) −8788.76 −1.60246 −0.801230 0.598357i \(-0.795820\pi\)
−0.801230 + 0.598357i \(0.795820\pi\)
\(312\) 0 0
\(313\) 6066.85 1.09559 0.547794 0.836613i \(-0.315468\pi\)
0.547794 + 0.836613i \(0.315468\pi\)
\(314\) 9773.90 1.75660
\(315\) 0 0
\(316\) −3715.75 −0.661479
\(317\) 341.345 0.0604789 0.0302395 0.999543i \(-0.490373\pi\)
0.0302395 + 0.999543i \(0.490373\pi\)
\(318\) 0 0
\(319\) 314.865 0.0552635
\(320\) 7951.05 1.38899
\(321\) 0 0
\(322\) 5083.33 0.879761
\(323\) −3817.54 −0.657627
\(324\) 0 0
\(325\) −1162.70 −0.198445
\(326\) 5186.14 0.881085
\(327\) 0 0
\(328\) −3388.40 −0.570406
\(329\) −4320.94 −0.724076
\(330\) 0 0
\(331\) −1591.92 −0.264351 −0.132175 0.991226i \(-0.542196\pi\)
−0.132175 + 0.991226i \(0.542196\pi\)
\(332\) 8502.78 1.40557
\(333\) 0 0
\(334\) 11968.4 1.96073
\(335\) −9646.91 −1.57333
\(336\) 0 0
\(337\) 7329.03 1.18468 0.592341 0.805688i \(-0.298204\pi\)
0.592341 + 0.805688i \(0.298204\pi\)
\(338\) 4737.82 0.762436
\(339\) 0 0
\(340\) −3312.55 −0.528378
\(341\) −387.879 −0.0615978
\(342\) 0 0
\(343\) 6780.94 1.06745
\(344\) −9314.01 −1.45982
\(345\) 0 0
\(346\) −3832.02 −0.595407
\(347\) −4172.50 −0.645509 −0.322755 0.946483i \(-0.604609\pi\)
−0.322755 + 0.946483i \(0.604609\pi\)
\(348\) 0 0
\(349\) 9998.71 1.53358 0.766789 0.641899i \(-0.221853\pi\)
0.766789 + 0.641899i \(0.221853\pi\)
\(350\) −2069.38 −0.316037
\(351\) 0 0
\(352\) 600.039 0.0908585
\(353\) 12562.4 1.89413 0.947063 0.321048i \(-0.104035\pi\)
0.947063 + 0.321048i \(0.104035\pi\)
\(354\) 0 0
\(355\) 8903.59 1.33114
\(356\) 8019.22 1.19387
\(357\) 0 0
\(358\) −12713.2 −1.87685
\(359\) 7210.95 1.06011 0.530055 0.847963i \(-0.322171\pi\)
0.530055 + 0.847963i \(0.322171\pi\)
\(360\) 0 0
\(361\) 11448.2 1.66908
\(362\) −5568.16 −0.808441
\(363\) 0 0
\(364\) −5579.08 −0.803361
\(365\) 2586.87 0.370967
\(366\) 0 0
\(367\) 10963.6 1.55938 0.779692 0.626163i \(-0.215376\pi\)
0.779692 + 0.626163i \(0.215376\pi\)
\(368\) −894.174 −0.126663
\(369\) 0 0
\(370\) −5979.12 −0.840107
\(371\) 8043.41 1.12559
\(372\) 0 0
\(373\) 5992.61 0.831865 0.415932 0.909396i \(-0.363455\pi\)
0.415932 + 0.909396i \(0.363455\pi\)
\(374\) −374.180 −0.0517337
\(375\) 0 0
\(376\) −6313.57 −0.865951
\(377\) 3624.36 0.495130
\(378\) 0 0
\(379\) −5911.11 −0.801144 −0.400572 0.916265i \(-0.631188\pi\)
−0.400572 + 0.916265i \(0.631188\pi\)
\(380\) 15885.5 2.14450
\(381\) 0 0
\(382\) 11235.2 1.50482
\(383\) 11200.1 1.49426 0.747129 0.664679i \(-0.231432\pi\)
0.747129 + 0.664679i \(0.231432\pi\)
\(384\) 0 0
\(385\) 374.258 0.0495428
\(386\) 19108.4 2.51967
\(387\) 0 0
\(388\) 2603.84 0.340696
\(389\) −554.700 −0.0722992 −0.0361496 0.999346i \(-0.511509\pi\)
−0.0361496 + 0.999346i \(0.511509\pi\)
\(390\) 0 0
\(391\) 2380.17 0.307853
\(392\) 3210.29 0.413633
\(393\) 0 0
\(394\) −23357.9 −2.98668
\(395\) 2869.21 0.365482
\(396\) 0 0
\(397\) −6188.23 −0.782314 −0.391157 0.920324i \(-0.627925\pi\)
−0.391157 + 0.920324i \(0.627925\pi\)
\(398\) −18483.8 −2.32791
\(399\) 0 0
\(400\) 364.011 0.0455013
\(401\) 401.406 0.0499881 0.0249941 0.999688i \(-0.492043\pi\)
0.0249941 + 0.999688i \(0.492043\pi\)
\(402\) 0 0
\(403\) −4464.81 −0.551881
\(404\) −6489.53 −0.799174
\(405\) 0 0
\(406\) 6450.68 0.788527
\(407\) −409.629 −0.0498883
\(408\) 0 0
\(409\) 13706.7 1.65709 0.828546 0.559921i \(-0.189168\pi\)
0.828546 + 0.559921i \(0.189168\pi\)
\(410\) 7449.72 0.897354
\(411\) 0 0
\(412\) −13652.2 −1.63252
\(413\) 5752.23 0.685348
\(414\) 0 0
\(415\) −6565.63 −0.776612
\(416\) 6906.94 0.814040
\(417\) 0 0
\(418\) 1794.40 0.209969
\(419\) −5143.37 −0.599690 −0.299845 0.953988i \(-0.596935\pi\)
−0.299845 + 0.953988i \(0.596935\pi\)
\(420\) 0 0
\(421\) 12319.4 1.42615 0.713077 0.701086i \(-0.247301\pi\)
0.713077 + 0.701086i \(0.247301\pi\)
\(422\) −17084.4 −1.97075
\(423\) 0 0
\(424\) 11752.7 1.34613
\(425\) −968.948 −0.110590
\(426\) 0 0
\(427\) 8700.96 0.986110
\(428\) 3505.28 0.395874
\(429\) 0 0
\(430\) 20477.7 2.29657
\(431\) 4201.09 0.469512 0.234756 0.972054i \(-0.424571\pi\)
0.234756 + 0.972054i \(0.424571\pi\)
\(432\) 0 0
\(433\) −15710.6 −1.74365 −0.871826 0.489816i \(-0.837064\pi\)
−0.871826 + 0.489816i \(0.837064\pi\)
\(434\) −7946.54 −0.878908
\(435\) 0 0
\(436\) 13678.4 1.50247
\(437\) −11414.2 −1.24947
\(438\) 0 0
\(439\) −3398.57 −0.369487 −0.184743 0.982787i \(-0.559145\pi\)
−0.184743 + 0.982787i \(0.559145\pi\)
\(440\) 546.850 0.0592501
\(441\) 0 0
\(442\) −4307.12 −0.463504
\(443\) 17894.5 1.91917 0.959585 0.281421i \(-0.0908056\pi\)
0.959585 + 0.281421i \(0.0908056\pi\)
\(444\) 0 0
\(445\) −6192.24 −0.659641
\(446\) 20073.5 2.13119
\(447\) 0 0
\(448\) 11159.9 1.17691
\(449\) 18018.6 1.89387 0.946936 0.321423i \(-0.104161\pi\)
0.946936 + 0.321423i \(0.104161\pi\)
\(450\) 0 0
\(451\) 510.379 0.0532878
\(452\) −10994.4 −1.14410
\(453\) 0 0
\(454\) 6871.80 0.710374
\(455\) 4308.02 0.443875
\(456\) 0 0
\(457\) 676.858 0.0692824 0.0346412 0.999400i \(-0.488971\pi\)
0.0346412 + 0.999400i \(0.488971\pi\)
\(458\) 15499.4 1.58131
\(459\) 0 0
\(460\) −9904.35 −1.00390
\(461\) −4958.46 −0.500951 −0.250476 0.968123i \(-0.580587\pi\)
−0.250476 + 0.968123i \(0.580587\pi\)
\(462\) 0 0
\(463\) 7946.43 0.797629 0.398814 0.917032i \(-0.369422\pi\)
0.398814 + 0.917032i \(0.369422\pi\)
\(464\) −1134.69 −0.113528
\(465\) 0 0
\(466\) −15563.6 −1.54715
\(467\) 1079.41 0.106958 0.0534788 0.998569i \(-0.482969\pi\)
0.0534788 + 0.998569i \(0.482969\pi\)
\(468\) 0 0
\(469\) −13540.1 −1.33310
\(470\) 13881.0 1.36230
\(471\) 0 0
\(472\) 8404.91 0.819634
\(473\) 1402.93 0.136378
\(474\) 0 0
\(475\) 4646.63 0.448847
\(476\) −4649.40 −0.447699
\(477\) 0 0
\(478\) 1077.64 0.103117
\(479\) −929.575 −0.0886709 −0.0443355 0.999017i \(-0.514117\pi\)
−0.0443355 + 0.999017i \(0.514117\pi\)
\(480\) 0 0
\(481\) −4715.16 −0.446971
\(482\) −12753.2 −1.20517
\(483\) 0 0
\(484\) −16305.5 −1.53132
\(485\) −2010.62 −0.188242
\(486\) 0 0
\(487\) −386.533 −0.0359661 −0.0179830 0.999838i \(-0.505724\pi\)
−0.0179830 + 0.999838i \(0.505724\pi\)
\(488\) 12713.5 1.17933
\(489\) 0 0
\(490\) −7058.12 −0.650721
\(491\) 9376.47 0.861821 0.430911 0.902395i \(-0.358192\pi\)
0.430911 + 0.902395i \(0.358192\pi\)
\(492\) 0 0
\(493\) 3020.41 0.275927
\(494\) 20655.0 1.88120
\(495\) 0 0
\(496\) 1397.82 0.126540
\(497\) 12496.8 1.12788
\(498\) 0 0
\(499\) 4239.68 0.380349 0.190174 0.981750i \(-0.439095\pi\)
0.190174 + 0.981750i \(0.439095\pi\)
\(500\) 18707.7 1.67327
\(501\) 0 0
\(502\) 32830.6 2.91893
\(503\) 10396.2 0.921557 0.460779 0.887515i \(-0.347570\pi\)
0.460779 + 0.887515i \(0.347570\pi\)
\(504\) 0 0
\(505\) 5011.05 0.441562
\(506\) −1118.78 −0.0982919
\(507\) 0 0
\(508\) −14936.3 −1.30451
\(509\) −1506.46 −0.131184 −0.0655922 0.997847i \(-0.520894\pi\)
−0.0655922 + 0.997847i \(0.520894\pi\)
\(510\) 0 0
\(511\) 3630.86 0.314324
\(512\) −3818.20 −0.329574
\(513\) 0 0
\(514\) 22671.2 1.94550
\(515\) 10541.9 0.902003
\(516\) 0 0
\(517\) 950.984 0.0808979
\(518\) −8392.11 −0.711831
\(519\) 0 0
\(520\) 6294.70 0.530847
\(521\) 20112.3 1.69124 0.845619 0.533787i \(-0.179232\pi\)
0.845619 + 0.533787i \(0.179232\pi\)
\(522\) 0 0
\(523\) −22514.3 −1.88238 −0.941188 0.337884i \(-0.890289\pi\)
−0.941188 + 0.337884i \(0.890289\pi\)
\(524\) 15126.8 1.26110
\(525\) 0 0
\(526\) 35968.8 2.98158
\(527\) −3720.81 −0.307554
\(528\) 0 0
\(529\) −5050.42 −0.415092
\(530\) −25839.4 −2.11772
\(531\) 0 0
\(532\) 22296.4 1.81705
\(533\) 5874.89 0.477429
\(534\) 0 0
\(535\) −2706.69 −0.218729
\(536\) −19784.2 −1.59431
\(537\) 0 0
\(538\) −7819.04 −0.626585
\(539\) −483.551 −0.0386419
\(540\) 0 0
\(541\) −7007.02 −0.556849 −0.278425 0.960458i \(-0.589812\pi\)
−0.278425 + 0.960458i \(0.589812\pi\)
\(542\) −31129.8 −2.46705
\(543\) 0 0
\(544\) 5755.99 0.453651
\(545\) −10562.1 −0.830146
\(546\) 0 0
\(547\) 18716.5 1.46300 0.731501 0.681841i \(-0.238820\pi\)
0.731501 + 0.681841i \(0.238820\pi\)
\(548\) −21409.3 −1.66891
\(549\) 0 0
\(550\) 455.445 0.0353095
\(551\) −14484.5 −1.11989
\(552\) 0 0
\(553\) 4027.13 0.309677
\(554\) 16679.4 1.27913
\(555\) 0 0
\(556\) 3923.24 0.299249
\(557\) 15671.3 1.19213 0.596063 0.802937i \(-0.296731\pi\)
0.596063 + 0.802937i \(0.296731\pi\)
\(558\) 0 0
\(559\) 16148.8 1.22187
\(560\) −1348.73 −0.101776
\(561\) 0 0
\(562\) −34540.0 −2.59249
\(563\) −19848.8 −1.48584 −0.742919 0.669381i \(-0.766559\pi\)
−0.742919 + 0.669381i \(0.766559\pi\)
\(564\) 0 0
\(565\) 8489.61 0.632142
\(566\) 13476.5 1.00081
\(567\) 0 0
\(568\) 18259.8 1.34888
\(569\) 6192.68 0.456258 0.228129 0.973631i \(-0.426739\pi\)
0.228129 + 0.973631i \(0.426739\pi\)
\(570\) 0 0
\(571\) 19889.3 1.45769 0.728847 0.684677i \(-0.240057\pi\)
0.728847 + 0.684677i \(0.240057\pi\)
\(572\) 1227.89 0.0897561
\(573\) 0 0
\(574\) 10456.2 0.760337
\(575\) −2897.10 −0.210117
\(576\) 0 0
\(577\) −812.698 −0.0586362 −0.0293181 0.999570i \(-0.509334\pi\)
−0.0293181 + 0.999570i \(0.509334\pi\)
\(578\) 18563.1 1.33585
\(579\) 0 0
\(580\) −12568.5 −0.899789
\(581\) −9215.32 −0.658031
\(582\) 0 0
\(583\) −1770.25 −0.125757
\(584\) 5305.25 0.375912
\(585\) 0 0
\(586\) −11946.4 −0.842153
\(587\) 12737.5 0.895625 0.447813 0.894127i \(-0.352203\pi\)
0.447813 + 0.894127i \(0.352203\pi\)
\(588\) 0 0
\(589\) 17843.3 1.24825
\(590\) −18479.0 −1.28944
\(591\) 0 0
\(592\) 1476.20 0.102485
\(593\) −2724.99 −0.188705 −0.0943525 0.995539i \(-0.530078\pi\)
−0.0943525 + 0.995539i \(0.530078\pi\)
\(594\) 0 0
\(595\) 3590.15 0.247364
\(596\) −13275.7 −0.912403
\(597\) 0 0
\(598\) −12878.1 −0.880640
\(599\) 2202.04 0.150205 0.0751027 0.997176i \(-0.476072\pi\)
0.0751027 + 0.997176i \(0.476072\pi\)
\(600\) 0 0
\(601\) 27419.9 1.86103 0.930516 0.366251i \(-0.119359\pi\)
0.930516 + 0.366251i \(0.119359\pi\)
\(602\) 28741.9 1.94590
\(603\) 0 0
\(604\) −14265.4 −0.961010
\(605\) 12590.7 0.846088
\(606\) 0 0
\(607\) 19222.9 1.28539 0.642697 0.766120i \(-0.277815\pi\)
0.642697 + 0.766120i \(0.277815\pi\)
\(608\) −27603.1 −1.84121
\(609\) 0 0
\(610\) −27951.7 −1.85530
\(611\) 10946.6 0.724799
\(612\) 0 0
\(613\) −9914.28 −0.653236 −0.326618 0.945156i \(-0.605909\pi\)
−0.326618 + 0.945156i \(0.605909\pi\)
\(614\) 14268.7 0.937850
\(615\) 0 0
\(616\) 767.543 0.0502032
\(617\) −11380.3 −0.742552 −0.371276 0.928523i \(-0.621080\pi\)
−0.371276 + 0.928523i \(0.621080\pi\)
\(618\) 0 0
\(619\) −9959.91 −0.646725 −0.323362 0.946275i \(-0.604813\pi\)
−0.323362 + 0.946275i \(0.604813\pi\)
\(620\) 15483.0 1.00292
\(621\) 0 0
\(622\) 39628.1 2.55457
\(623\) −8691.24 −0.558920
\(624\) 0 0
\(625\) −10152.8 −0.649782
\(626\) −27355.2 −1.74654
\(627\) 0 0
\(628\) −26728.8 −1.69840
\(629\) −3929.44 −0.249089
\(630\) 0 0
\(631\) 20723.6 1.30744 0.653720 0.756737i \(-0.273208\pi\)
0.653720 + 0.756737i \(0.273208\pi\)
\(632\) 5884.27 0.370354
\(633\) 0 0
\(634\) −1539.11 −0.0964129
\(635\) 11533.4 0.720769
\(636\) 0 0
\(637\) −5566.07 −0.346210
\(638\) −1419.71 −0.0880987
\(639\) 0 0
\(640\) −20311.3 −1.25449
\(641\) −8283.61 −0.510426 −0.255213 0.966885i \(-0.582146\pi\)
−0.255213 + 0.966885i \(0.582146\pi\)
\(642\) 0 0
\(643\) −10978.6 −0.673337 −0.336668 0.941623i \(-0.609300\pi\)
−0.336668 + 0.941623i \(0.609300\pi\)
\(644\) −13901.4 −0.850612
\(645\) 0 0
\(646\) 17213.1 1.04836
\(647\) 19305.5 1.17307 0.586536 0.809923i \(-0.300491\pi\)
0.586536 + 0.809923i \(0.300491\pi\)
\(648\) 0 0
\(649\) −1265.99 −0.0765710
\(650\) 5242.54 0.316353
\(651\) 0 0
\(652\) −14182.6 −0.851891
\(653\) 12072.8 0.723497 0.361748 0.932276i \(-0.382180\pi\)
0.361748 + 0.932276i \(0.382180\pi\)
\(654\) 0 0
\(655\) −11680.5 −0.696788
\(656\) −1839.28 −0.109469
\(657\) 0 0
\(658\) 19482.9 1.15429
\(659\) −24979.0 −1.47655 −0.738274 0.674501i \(-0.764359\pi\)
−0.738274 + 0.674501i \(0.764359\pi\)
\(660\) 0 0
\(661\) −5431.43 −0.319604 −0.159802 0.987149i \(-0.551086\pi\)
−0.159802 + 0.987149i \(0.551086\pi\)
\(662\) 7177.92 0.421416
\(663\) 0 0
\(664\) −13465.0 −0.786964
\(665\) −17216.7 −1.00396
\(666\) 0 0
\(667\) 9030.84 0.524251
\(668\) −32730.2 −1.89577
\(669\) 0 0
\(670\) 43497.5 2.50814
\(671\) −1914.97 −0.110174
\(672\) 0 0
\(673\) 439.624 0.0251802 0.0125901 0.999921i \(-0.495992\pi\)
0.0125901 + 0.999921i \(0.495992\pi\)
\(674\) −33046.3 −1.88857
\(675\) 0 0
\(676\) −12956.6 −0.737174
\(677\) 24517.3 1.39184 0.695922 0.718117i \(-0.254996\pi\)
0.695922 + 0.718117i \(0.254996\pi\)
\(678\) 0 0
\(679\) −2822.04 −0.159499
\(680\) 5245.77 0.295832
\(681\) 0 0
\(682\) 1748.93 0.0981966
\(683\) −15501.9 −0.868466 −0.434233 0.900801i \(-0.642981\pi\)
−0.434233 + 0.900801i \(0.642981\pi\)
\(684\) 0 0
\(685\) 16531.7 0.922108
\(686\) −30575.0 −1.70169
\(687\) 0 0
\(688\) −5055.79 −0.280160
\(689\) −20377.1 −1.12671
\(690\) 0 0
\(691\) 23007.6 1.26664 0.633322 0.773888i \(-0.281691\pi\)
0.633322 + 0.773888i \(0.281691\pi\)
\(692\) 10479.5 0.575679
\(693\) 0 0
\(694\) 18813.6 1.02904
\(695\) −3029.42 −0.165342
\(696\) 0 0
\(697\) 4895.91 0.266063
\(698\) −45083.8 −2.44476
\(699\) 0 0
\(700\) 5659.16 0.305566
\(701\) −33032.5 −1.77977 −0.889886 0.456184i \(-0.849216\pi\)
−0.889886 + 0.456184i \(0.849216\pi\)
\(702\) 0 0
\(703\) 18843.8 1.01097
\(704\) −2456.14 −0.131491
\(705\) 0 0
\(706\) −56643.1 −3.01953
\(707\) 7033.36 0.374140
\(708\) 0 0
\(709\) −7523.49 −0.398520 −0.199260 0.979947i \(-0.563854\pi\)
−0.199260 + 0.979947i \(0.563854\pi\)
\(710\) −40145.9 −2.12204
\(711\) 0 0
\(712\) −12699.3 −0.668434
\(713\) −11125.0 −0.584341
\(714\) 0 0
\(715\) −948.141 −0.0495923
\(716\) 34766.9 1.81467
\(717\) 0 0
\(718\) −32513.9 −1.68998
\(719\) 16846.3 0.873800 0.436900 0.899510i \(-0.356076\pi\)
0.436900 + 0.899510i \(0.356076\pi\)
\(720\) 0 0
\(721\) 14796.3 0.764276
\(722\) −51619.4 −2.66077
\(723\) 0 0
\(724\) 15227.3 0.781655
\(725\) −3676.38 −0.188327
\(726\) 0 0
\(727\) 2903.64 0.148129 0.0740647 0.997253i \(-0.476403\pi\)
0.0740647 + 0.997253i \(0.476403\pi\)
\(728\) 8835.05 0.449792
\(729\) 0 0
\(730\) −11664.1 −0.591380
\(731\) 13457.8 0.680925
\(732\) 0 0
\(733\) −25017.0 −1.26060 −0.630302 0.776350i \(-0.717069\pi\)
−0.630302 + 0.776350i \(0.717069\pi\)
\(734\) −49434.3 −2.48590
\(735\) 0 0
\(736\) 17210.1 0.861919
\(737\) 2980.01 0.148942
\(738\) 0 0
\(739\) 28998.8 1.44349 0.721745 0.692159i \(-0.243340\pi\)
0.721745 + 0.692159i \(0.243340\pi\)
\(740\) 16351.2 0.812271
\(741\) 0 0
\(742\) −36267.4 −1.79436
\(743\) −17862.0 −0.881958 −0.440979 0.897518i \(-0.645369\pi\)
−0.440979 + 0.897518i \(0.645369\pi\)
\(744\) 0 0
\(745\) 10251.1 0.504123
\(746\) −27020.4 −1.32612
\(747\) 0 0
\(748\) 1023.27 0.0500195
\(749\) −3799.03 −0.185332
\(750\) 0 0
\(751\) −15428.4 −0.749656 −0.374828 0.927094i \(-0.622298\pi\)
−0.374828 + 0.927094i \(0.622298\pi\)
\(752\) −3427.11 −0.166188
\(753\) 0 0
\(754\) −16342.1 −0.789314
\(755\) 11015.3 0.530980
\(756\) 0 0
\(757\) 27126.6 1.30242 0.651211 0.758896i \(-0.274261\pi\)
0.651211 + 0.758896i \(0.274261\pi\)
\(758\) 26653.0 1.27715
\(759\) 0 0
\(760\) −25156.3 −1.20068
\(761\) 17958.1 0.855426 0.427713 0.903914i \(-0.359319\pi\)
0.427713 + 0.903914i \(0.359319\pi\)
\(762\) 0 0
\(763\) −14824.6 −0.703391
\(764\) −30725.0 −1.45496
\(765\) 0 0
\(766\) −50501.0 −2.38208
\(767\) −14572.6 −0.686032
\(768\) 0 0
\(769\) 15157.7 0.710796 0.355398 0.934715i \(-0.384345\pi\)
0.355398 + 0.934715i \(0.384345\pi\)
\(770\) −1687.51 −0.0789790
\(771\) 0 0
\(772\) −52256.1 −2.43619
\(773\) 33668.1 1.56657 0.783285 0.621663i \(-0.213543\pi\)
0.783285 + 0.621663i \(0.213543\pi\)
\(774\) 0 0
\(775\) 4528.90 0.209913
\(776\) −4123.45 −0.190751
\(777\) 0 0
\(778\) 2501.12 0.115256
\(779\) −23478.6 −1.07986
\(780\) 0 0
\(781\) −2750.39 −0.126014
\(782\) −10732.1 −0.490766
\(783\) 0 0
\(784\) 1742.60 0.0793821
\(785\) 20639.3 0.938405
\(786\) 0 0
\(787\) 22259.6 1.00822 0.504110 0.863640i \(-0.331821\pi\)
0.504110 + 0.863640i \(0.331821\pi\)
\(788\) 63877.1 2.88772
\(789\) 0 0
\(790\) −12937.1 −0.582636
\(791\) 11915.8 0.535620
\(792\) 0 0
\(793\) −22042.9 −0.987095
\(794\) 27902.5 1.24713
\(795\) 0 0
\(796\) 50547.8 2.25078
\(797\) 24064.3 1.06951 0.534757 0.845006i \(-0.320403\pi\)
0.534757 + 0.845006i \(0.320403\pi\)
\(798\) 0 0
\(799\) 9122.50 0.403918
\(800\) −7006.08 −0.309628
\(801\) 0 0
\(802\) −1809.92 −0.0796889
\(803\) −799.105 −0.0351181
\(804\) 0 0
\(805\) 10734.3 0.469982
\(806\) 20131.6 0.879785
\(807\) 0 0
\(808\) 10276.8 0.447448
\(809\) −29725.2 −1.29182 −0.645910 0.763414i \(-0.723522\pi\)
−0.645910 + 0.763414i \(0.723522\pi\)
\(810\) 0 0
\(811\) 24720.6 1.07036 0.535178 0.844739i \(-0.320245\pi\)
0.535178 + 0.844739i \(0.320245\pi\)
\(812\) −17640.7 −0.762400
\(813\) 0 0
\(814\) 1847.00 0.0795298
\(815\) 10951.4 0.470689
\(816\) 0 0
\(817\) −64537.7 −2.76363
\(818\) −61802.7 −2.64167
\(819\) 0 0
\(820\) −20372.8 −0.867622
\(821\) −95.7985 −0.00407234 −0.00203617 0.999998i \(-0.500648\pi\)
−0.00203617 + 0.999998i \(0.500648\pi\)
\(822\) 0 0
\(823\) 16210.6 0.686595 0.343298 0.939227i \(-0.388456\pi\)
0.343298 + 0.939227i \(0.388456\pi\)
\(824\) 21619.7 0.914027
\(825\) 0 0
\(826\) −25936.6 −1.09255
\(827\) −324.820 −0.0136579 −0.00682895 0.999977i \(-0.502174\pi\)
−0.00682895 + 0.999977i \(0.502174\pi\)
\(828\) 0 0
\(829\) 21670.0 0.907877 0.453938 0.891033i \(-0.350019\pi\)
0.453938 + 0.891033i \(0.350019\pi\)
\(830\) 29604.1 1.23804
\(831\) 0 0
\(832\) −28272.2 −1.17808
\(833\) −4638.56 −0.192937
\(834\) 0 0
\(835\) 25273.4 1.04745
\(836\) −4907.16 −0.203012
\(837\) 0 0
\(838\) 23191.2 0.956000
\(839\) 19402.4 0.798386 0.399193 0.916867i \(-0.369290\pi\)
0.399193 + 0.916867i \(0.369290\pi\)
\(840\) 0 0
\(841\) −12929.0 −0.530115
\(842\) −55547.6 −2.27351
\(843\) 0 0
\(844\) 46720.9 1.90545
\(845\) 10004.7 0.407305
\(846\) 0 0
\(847\) 17671.9 0.716899
\(848\) 6379.54 0.258343
\(849\) 0 0
\(850\) 4368.94 0.176298
\(851\) −11748.8 −0.473260
\(852\) 0 0
\(853\) 40326.6 1.61871 0.809353 0.587323i \(-0.199818\pi\)
0.809353 + 0.587323i \(0.199818\pi\)
\(854\) −39232.2 −1.57201
\(855\) 0 0
\(856\) −5550.97 −0.221645
\(857\) 33139.5 1.32092 0.660458 0.750863i \(-0.270362\pi\)
0.660458 + 0.750863i \(0.270362\pi\)
\(858\) 0 0
\(859\) −38149.5 −1.51530 −0.757651 0.652659i \(-0.773653\pi\)
−0.757651 + 0.652659i \(0.773653\pi\)
\(860\) −56000.7 −2.22047
\(861\) 0 0
\(862\) −18942.6 −0.748476
\(863\) −3945.03 −0.155609 −0.0778044 0.996969i \(-0.524791\pi\)
−0.0778044 + 0.996969i \(0.524791\pi\)
\(864\) 0 0
\(865\) −8091.98 −0.318076
\(866\) 70838.2 2.77965
\(867\) 0 0
\(868\) 21731.5 0.849786
\(869\) −886.321 −0.0345988
\(870\) 0 0
\(871\) 34302.4 1.33443
\(872\) −21661.1 −0.841212
\(873\) 0 0
\(874\) 51466.3 1.99184
\(875\) −20275.4 −0.783354
\(876\) 0 0
\(877\) −13862.9 −0.533771 −0.266886 0.963728i \(-0.585995\pi\)
−0.266886 + 0.963728i \(0.585995\pi\)
\(878\) 15324.0 0.589020
\(879\) 0 0
\(880\) 296.839 0.0113710
\(881\) −5631.94 −0.215374 −0.107687 0.994185i \(-0.534345\pi\)
−0.107687 + 0.994185i \(0.534345\pi\)
\(882\) 0 0
\(883\) −17981.2 −0.685294 −0.342647 0.939464i \(-0.611323\pi\)
−0.342647 + 0.939464i \(0.611323\pi\)
\(884\) 11778.7 0.448147
\(885\) 0 0
\(886\) −80685.4 −3.05946
\(887\) 14979.6 0.567041 0.283521 0.958966i \(-0.408498\pi\)
0.283521 + 0.958966i \(0.408498\pi\)
\(888\) 0 0
\(889\) 16187.9 0.610715
\(890\) 27920.5 1.05157
\(891\) 0 0
\(892\) −54895.3 −2.06057
\(893\) −43747.4 −1.63936
\(894\) 0 0
\(895\) −26846.1 −1.00264
\(896\) −28508.4 −1.06294
\(897\) 0 0
\(898\) −81244.9 −3.01913
\(899\) −14117.5 −0.523743
\(900\) 0 0
\(901\) −16981.5 −0.627898
\(902\) −2301.28 −0.0849492
\(903\) 0 0
\(904\) 17410.8 0.640569
\(905\) −11758.1 −0.431882
\(906\) 0 0
\(907\) −53497.6 −1.95850 −0.979249 0.202661i \(-0.935041\pi\)
−0.979249 + 0.202661i \(0.935041\pi\)
\(908\) −18792.4 −0.686836
\(909\) 0 0
\(910\) −19424.7 −0.707607
\(911\) −23406.8 −0.851265 −0.425633 0.904896i \(-0.639948\pi\)
−0.425633 + 0.904896i \(0.639948\pi\)
\(912\) 0 0
\(913\) 2028.17 0.0735189
\(914\) −3051.92 −0.110447
\(915\) 0 0
\(916\) −42386.3 −1.52891
\(917\) −16394.4 −0.590395
\(918\) 0 0
\(919\) 9513.83 0.341493 0.170747 0.985315i \(-0.445382\pi\)
0.170747 + 0.985315i \(0.445382\pi\)
\(920\) 15684.5 0.562070
\(921\) 0 0
\(922\) 22357.5 0.798595
\(923\) −31659.3 −1.12901
\(924\) 0 0
\(925\) 4782.84 0.170010
\(926\) −35830.1 −1.27155
\(927\) 0 0
\(928\) 21839.4 0.772535
\(929\) −33262.4 −1.17471 −0.587353 0.809331i \(-0.699830\pi\)
−0.587353 + 0.809331i \(0.699830\pi\)
\(930\) 0 0
\(931\) 22244.4 0.783063
\(932\) 42562.0 1.49588
\(933\) 0 0
\(934\) −4867.02 −0.170507
\(935\) −790.146 −0.0276369
\(936\) 0 0
\(937\) 25966.8 0.905333 0.452666 0.891680i \(-0.350473\pi\)
0.452666 + 0.891680i \(0.350473\pi\)
\(938\) 61051.8 2.12517
\(939\) 0 0
\(940\) −37960.5 −1.31716
\(941\) −4390.79 −0.152110 −0.0760552 0.997104i \(-0.524233\pi\)
−0.0760552 + 0.997104i \(0.524233\pi\)
\(942\) 0 0
\(943\) 14638.5 0.505509
\(944\) 4562.32 0.157300
\(945\) 0 0
\(946\) −6325.73 −0.217407
\(947\) −54191.6 −1.85955 −0.929774 0.368131i \(-0.879998\pi\)
−0.929774 + 0.368131i \(0.879998\pi\)
\(948\) 0 0
\(949\) −9198.36 −0.314638
\(950\) −20951.5 −0.715532
\(951\) 0 0
\(952\) 7362.80 0.250662
\(953\) −42172.3 −1.43347 −0.716734 0.697346i \(-0.754364\pi\)
−0.716734 + 0.697346i \(0.754364\pi\)
\(954\) 0 0
\(955\) 23725.1 0.803901
\(956\) −2947.04 −0.0997008
\(957\) 0 0
\(958\) 4191.42 0.141355
\(959\) 23203.4 0.781311
\(960\) 0 0
\(961\) −12399.8 −0.416226
\(962\) 21260.5 0.712541
\(963\) 0 0
\(964\) 34876.2 1.16524
\(965\) 40350.8 1.34605
\(966\) 0 0
\(967\) −53176.0 −1.76838 −0.884190 0.467127i \(-0.845289\pi\)
−0.884190 + 0.467127i \(0.845289\pi\)
\(968\) 25821.4 0.857367
\(969\) 0 0
\(970\) 9065.78 0.300087
\(971\) 10197.8 0.337036 0.168518 0.985699i \(-0.446102\pi\)
0.168518 + 0.985699i \(0.446102\pi\)
\(972\) 0 0
\(973\) −4252.01 −0.140096
\(974\) 1742.86 0.0573356
\(975\) 0 0
\(976\) 6901.07 0.226330
\(977\) 4263.95 0.139627 0.0698136 0.997560i \(-0.477760\pi\)
0.0698136 + 0.997560i \(0.477760\pi\)
\(978\) 0 0
\(979\) 1912.83 0.0624457
\(980\) 19301.9 0.629160
\(981\) 0 0
\(982\) −42278.1 −1.37388
\(983\) 9411.52 0.305372 0.152686 0.988275i \(-0.451208\pi\)
0.152686 + 0.988275i \(0.451208\pi\)
\(984\) 0 0
\(985\) −49324.2 −1.59553
\(986\) −13618.9 −0.439872
\(987\) 0 0
\(988\) −56485.5 −1.81887
\(989\) 40238.2 1.29373
\(990\) 0 0
\(991\) −47766.3 −1.53113 −0.765563 0.643361i \(-0.777539\pi\)
−0.765563 + 0.643361i \(0.777539\pi\)
\(992\) −26903.7 −0.861083
\(993\) 0 0
\(994\) −56347.6 −1.79802
\(995\) −39031.7 −1.24361
\(996\) 0 0
\(997\) −50485.2 −1.60369 −0.801847 0.597530i \(-0.796149\pi\)
−0.801847 + 0.597530i \(0.796149\pi\)
\(998\) −19116.5 −0.606336
\(999\) 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.1.6 yes 59
3.2 odd 2 2151.4.a.g.1.54 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.54 59 3.2 odd 2
2151.4.a.h.1.6 yes 59 1.1 even 1 trivial