Properties

Label 1386.4.a.d.1.1
Level $1386$
Weight $4$
Character 1386.1
Self dual yes
Analytic conductor $81.777$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(81.7766472680\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1386.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} -1.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +2.00000 q^{10} +11.0000 q^{11} -43.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -100.000 q^{17} -87.0000 q^{19} -4.00000 q^{20} -22.0000 q^{22} +58.0000 q^{23} -124.000 q^{25} +86.0000 q^{26} -28.0000 q^{28} +223.000 q^{29} +88.0000 q^{31} -32.0000 q^{32} +200.000 q^{34} +7.00000 q^{35} +37.0000 q^{37} +174.000 q^{38} +8.00000 q^{40} -128.000 q^{41} -458.000 q^{43} +44.0000 q^{44} -116.000 q^{46} +341.000 q^{47} +49.0000 q^{49} +248.000 q^{50} -172.000 q^{52} +342.000 q^{53} -11.0000 q^{55} +56.0000 q^{56} -446.000 q^{58} +105.000 q^{59} +190.000 q^{61} -176.000 q^{62} +64.0000 q^{64} +43.0000 q^{65} -579.000 q^{67} -400.000 q^{68} -14.0000 q^{70} -128.000 q^{71} -161.000 q^{73} -74.0000 q^{74} -348.000 q^{76} -77.0000 q^{77} -396.000 q^{79} -16.0000 q^{80} +256.000 q^{82} +420.000 q^{83} +100.000 q^{85} +916.000 q^{86} -88.0000 q^{88} +798.000 q^{89} +301.000 q^{91} +232.000 q^{92} -682.000 q^{94} +87.0000 q^{95} +1414.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 0 0
\(4\) 4.00000 0.500000
\(5\) −1.00000 −0.0894427 −0.0447214 0.998999i \(-0.514240\pi\)
−0.0447214 + 0.998999i \(0.514240\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 2.00000 0.0632456
\(11\) 11.0000 0.301511
\(12\) 0 0
\(13\) −43.0000 −0.917389 −0.458694 0.888594i \(-0.651683\pi\)
−0.458694 + 0.888594i \(0.651683\pi\)
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −100.000 −1.42668 −0.713340 0.700818i \(-0.752818\pi\)
−0.713340 + 0.700818i \(0.752818\pi\)
\(18\) 0 0
\(19\) −87.0000 −1.05048 −0.525241 0.850953i \(-0.676025\pi\)
−0.525241 + 0.850953i \(0.676025\pi\)
\(20\) −4.00000 −0.0447214
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) 58.0000 0.525819 0.262909 0.964821i \(-0.415318\pi\)
0.262909 + 0.964821i \(0.415318\pi\)
\(24\) 0 0
\(25\) −124.000 −0.992000
\(26\) 86.0000 0.648692
\(27\) 0 0
\(28\) −28.0000 −0.188982
\(29\) 223.000 1.42793 0.713967 0.700180i \(-0.246897\pi\)
0.713967 + 0.700180i \(0.246897\pi\)
\(30\) 0 0
\(31\) 88.0000 0.509847 0.254924 0.966961i \(-0.417950\pi\)
0.254924 + 0.966961i \(0.417950\pi\)
\(32\) −32.0000 −0.176777
\(33\) 0 0
\(34\) 200.000 1.00882
\(35\) 7.00000 0.0338062
\(36\) 0 0
\(37\) 37.0000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 174.000 0.742803
\(39\) 0 0
\(40\) 8.00000 0.0316228
\(41\) −128.000 −0.487567 −0.243783 0.969830i \(-0.578389\pi\)
−0.243783 + 0.969830i \(0.578389\pi\)
\(42\) 0 0
\(43\) −458.000 −1.62429 −0.812144 0.583458i \(-0.801699\pi\)
−0.812144 + 0.583458i \(0.801699\pi\)
\(44\) 44.0000 0.150756
\(45\) 0 0
\(46\) −116.000 −0.371810
\(47\) 341.000 1.05830 0.529149 0.848529i \(-0.322511\pi\)
0.529149 + 0.848529i \(0.322511\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 248.000 0.701450
\(51\) 0 0
\(52\) −172.000 −0.458694
\(53\) 342.000 0.886364 0.443182 0.896432i \(-0.353849\pi\)
0.443182 + 0.896432i \(0.353849\pi\)
\(54\) 0 0
\(55\) −11.0000 −0.0269680
\(56\) 56.0000 0.133631
\(57\) 0 0
\(58\) −446.000 −1.00970
\(59\) 105.000 0.231692 0.115846 0.993267i \(-0.463042\pi\)
0.115846 + 0.993267i \(0.463042\pi\)
\(60\) 0 0
\(61\) 190.000 0.398803 0.199402 0.979918i \(-0.436100\pi\)
0.199402 + 0.979918i \(0.436100\pi\)
\(62\) −176.000 −0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 43.0000 0.0820537
\(66\) 0 0
\(67\) −579.000 −1.05576 −0.527881 0.849318i \(-0.677013\pi\)
−0.527881 + 0.849318i \(0.677013\pi\)
\(68\) −400.000 −0.713340
\(69\) 0 0
\(70\) −14.0000 −0.0239046
\(71\) −128.000 −0.213955 −0.106978 0.994261i \(-0.534117\pi\)
−0.106978 + 0.994261i \(0.534117\pi\)
\(72\) 0 0
\(73\) −161.000 −0.258132 −0.129066 0.991636i \(-0.541198\pi\)
−0.129066 + 0.991636i \(0.541198\pi\)
\(74\) −74.0000 −0.116248
\(75\) 0 0
\(76\) −348.000 −0.525241
\(77\) −77.0000 −0.113961
\(78\) 0 0
\(79\) −396.000 −0.563968 −0.281984 0.959419i \(-0.590993\pi\)
−0.281984 + 0.959419i \(0.590993\pi\)
\(80\) −16.0000 −0.0223607
\(81\) 0 0
\(82\) 256.000 0.344762
\(83\) 420.000 0.555434 0.277717 0.960663i \(-0.410422\pi\)
0.277717 + 0.960663i \(0.410422\pi\)
\(84\) 0 0
\(85\) 100.000 0.127606
\(86\) 916.000 1.14854
\(87\) 0 0
\(88\) −88.0000 −0.106600
\(89\) 798.000 0.950425 0.475213 0.879871i \(-0.342371\pi\)
0.475213 + 0.879871i \(0.342371\pi\)
\(90\) 0 0
\(91\) 301.000 0.346740
\(92\) 232.000 0.262909
\(93\) 0 0
\(94\) −682.000 −0.748329
\(95\) 87.0000 0.0939580
\(96\) 0 0
\(97\) 1414.00 1.48010 0.740051 0.672550i \(-0.234801\pi\)
0.740051 + 0.672550i \(0.234801\pi\)
\(98\) −98.0000 −0.101015
\(99\) 0 0
\(100\) −496.000 −0.496000
\(101\) 1764.00 1.73787 0.868933 0.494929i \(-0.164806\pi\)
0.868933 + 0.494929i \(0.164806\pi\)
\(102\) 0 0
\(103\) 978.000 0.935584 0.467792 0.883838i \(-0.345050\pi\)
0.467792 + 0.883838i \(0.345050\pi\)
\(104\) 344.000 0.324346
\(105\) 0 0
\(106\) −684.000 −0.626754
\(107\) −481.000 −0.434580 −0.217290 0.976107i \(-0.569722\pi\)
−0.217290 + 0.976107i \(0.569722\pi\)
\(108\) 0 0
\(109\) −284.000 −0.249562 −0.124781 0.992184i \(-0.539823\pi\)
−0.124781 + 0.992184i \(0.539823\pi\)
\(110\) 22.0000 0.0190693
\(111\) 0 0
\(112\) −112.000 −0.0944911
\(113\) −1498.00 −1.24708 −0.623540 0.781792i \(-0.714306\pi\)
−0.623540 + 0.781792i \(0.714306\pi\)
\(114\) 0 0
\(115\) −58.0000 −0.0470307
\(116\) 892.000 0.713967
\(117\) 0 0
\(118\) −210.000 −0.163831
\(119\) 700.000 0.539234
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) −380.000 −0.281997
\(123\) 0 0
\(124\) 352.000 0.254924
\(125\) 249.000 0.178170
\(126\) 0 0
\(127\) −616.000 −0.430403 −0.215201 0.976570i \(-0.569041\pi\)
−0.215201 + 0.976570i \(0.569041\pi\)
\(128\) −128.000 −0.0883883
\(129\) 0 0
\(130\) −86.0000 −0.0580208
\(131\) −2748.00 −1.83278 −0.916389 0.400289i \(-0.868910\pi\)
−0.916389 + 0.400289i \(0.868910\pi\)
\(132\) 0 0
\(133\) 609.000 0.397045
\(134\) 1158.00 0.746537
\(135\) 0 0
\(136\) 800.000 0.504408
\(137\) −2184.00 −1.36198 −0.680992 0.732291i \(-0.738451\pi\)
−0.680992 + 0.732291i \(0.738451\pi\)
\(138\) 0 0
\(139\) 908.000 0.554069 0.277034 0.960860i \(-0.410648\pi\)
0.277034 + 0.960860i \(0.410648\pi\)
\(140\) 28.0000 0.0169031
\(141\) 0 0
\(142\) 256.000 0.151289
\(143\) −473.000 −0.276603
\(144\) 0 0
\(145\) −223.000 −0.127718
\(146\) 322.000 0.182527
\(147\) 0 0
\(148\) 148.000 0.0821995
\(149\) −421.000 −0.231474 −0.115737 0.993280i \(-0.536923\pi\)
−0.115737 + 0.993280i \(0.536923\pi\)
\(150\) 0 0
\(151\) 948.000 0.510908 0.255454 0.966821i \(-0.417775\pi\)
0.255454 + 0.966821i \(0.417775\pi\)
\(152\) 696.000 0.371402
\(153\) 0 0
\(154\) 154.000 0.0805823
\(155\) −88.0000 −0.0456021
\(156\) 0 0
\(157\) 2368.00 1.20374 0.601869 0.798595i \(-0.294423\pi\)
0.601869 + 0.798595i \(0.294423\pi\)
\(158\) 792.000 0.398786
\(159\) 0 0
\(160\) 32.0000 0.0158114
\(161\) −406.000 −0.198741
\(162\) 0 0
\(163\) −2603.00 −1.25081 −0.625407 0.780299i \(-0.715067\pi\)
−0.625407 + 0.780299i \(0.715067\pi\)
\(164\) −512.000 −0.243783
\(165\) 0 0
\(166\) −840.000 −0.392751
\(167\) 1402.00 0.649641 0.324820 0.945776i \(-0.394696\pi\)
0.324820 + 0.945776i \(0.394696\pi\)
\(168\) 0 0
\(169\) −348.000 −0.158398
\(170\) −200.000 −0.0902312
\(171\) 0 0
\(172\) −1832.00 −0.812144
\(173\) −836.000 −0.367398 −0.183699 0.982983i \(-0.558807\pi\)
−0.183699 + 0.982983i \(0.558807\pi\)
\(174\) 0 0
\(175\) 868.000 0.374941
\(176\) 176.000 0.0753778
\(177\) 0 0
\(178\) −1596.00 −0.672052
\(179\) 3292.00 1.37461 0.687306 0.726368i \(-0.258793\pi\)
0.687306 + 0.726368i \(0.258793\pi\)
\(180\) 0 0
\(181\) 4838.00 1.98677 0.993386 0.114823i \(-0.0366302\pi\)
0.993386 + 0.114823i \(0.0366302\pi\)
\(182\) −602.000 −0.245182
\(183\) 0 0
\(184\) −464.000 −0.185905
\(185\) −37.0000 −0.0147043
\(186\) 0 0
\(187\) −1100.00 −0.430160
\(188\) 1364.00 0.529149
\(189\) 0 0
\(190\) −174.000 −0.0664384
\(191\) 1232.00 0.466725 0.233362 0.972390i \(-0.425027\pi\)
0.233362 + 0.972390i \(0.425027\pi\)
\(192\) 0 0
\(193\) 2366.00 0.882427 0.441213 0.897402i \(-0.354548\pi\)
0.441213 + 0.897402i \(0.354548\pi\)
\(194\) −2828.00 −1.04659
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) −318.000 −0.115008 −0.0575040 0.998345i \(-0.518314\pi\)
−0.0575040 + 0.998345i \(0.518314\pi\)
\(198\) 0 0
\(199\) −806.000 −0.287115 −0.143557 0.989642i \(-0.545854\pi\)
−0.143557 + 0.989642i \(0.545854\pi\)
\(200\) 992.000 0.350725
\(201\) 0 0
\(202\) −3528.00 −1.22886
\(203\) −1561.00 −0.539708
\(204\) 0 0
\(205\) 128.000 0.0436093
\(206\) −1956.00 −0.661558
\(207\) 0 0
\(208\) −688.000 −0.229347
\(209\) −957.000 −0.316732
\(210\) 0 0
\(211\) 4462.00 1.45581 0.727907 0.685676i \(-0.240493\pi\)
0.727907 + 0.685676i \(0.240493\pi\)
\(212\) 1368.00 0.443182
\(213\) 0 0
\(214\) 962.000 0.307294
\(215\) 458.000 0.145281
\(216\) 0 0
\(217\) −616.000 −0.192704
\(218\) 568.000 0.176467
\(219\) 0 0
\(220\) −44.0000 −0.0134840
\(221\) 4300.00 1.30882
\(222\) 0 0
\(223\) 3802.00 1.14171 0.570854 0.821052i \(-0.306612\pi\)
0.570854 + 0.821052i \(0.306612\pi\)
\(224\) 224.000 0.0668153
\(225\) 0 0
\(226\) 2996.00 0.881818
\(227\) 3370.00 0.985351 0.492676 0.870213i \(-0.336019\pi\)
0.492676 + 0.870213i \(0.336019\pi\)
\(228\) 0 0
\(229\) −898.000 −0.259133 −0.129567 0.991571i \(-0.541359\pi\)
−0.129567 + 0.991571i \(0.541359\pi\)
\(230\) 116.000 0.0332557
\(231\) 0 0
\(232\) −1784.00 −0.504851
\(233\) 462.000 0.129900 0.0649498 0.997889i \(-0.479311\pi\)
0.0649498 + 0.997889i \(0.479311\pi\)
\(234\) 0 0
\(235\) −341.000 −0.0946570
\(236\) 420.000 0.115846
\(237\) 0 0
\(238\) −1400.00 −0.381296
\(239\) 5665.00 1.53322 0.766608 0.642116i \(-0.221943\pi\)
0.766608 + 0.642116i \(0.221943\pi\)
\(240\) 0 0
\(241\) 1593.00 0.425785 0.212892 0.977076i \(-0.431712\pi\)
0.212892 + 0.977076i \(0.431712\pi\)
\(242\) −242.000 −0.0642824
\(243\) 0 0
\(244\) 760.000 0.199402
\(245\) −49.0000 −0.0127775
\(246\) 0 0
\(247\) 3741.00 0.963701
\(248\) −704.000 −0.180258
\(249\) 0 0
\(250\) −498.000 −0.125985
\(251\) −4545.00 −1.14294 −0.571470 0.820623i \(-0.693627\pi\)
−0.571470 + 0.820623i \(0.693627\pi\)
\(252\) 0 0
\(253\) 638.000 0.158540
\(254\) 1232.00 0.304341
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 2859.00 0.693928 0.346964 0.937878i \(-0.387213\pi\)
0.346964 + 0.937878i \(0.387213\pi\)
\(258\) 0 0
\(259\) −259.000 −0.0621370
\(260\) 172.000 0.0410269
\(261\) 0 0
\(262\) 5496.00 1.29597
\(263\) 6279.00 1.47217 0.736083 0.676891i \(-0.236673\pi\)
0.736083 + 0.676891i \(0.236673\pi\)
\(264\) 0 0
\(265\) −342.000 −0.0792788
\(266\) −1218.00 −0.280753
\(267\) 0 0
\(268\) −2316.00 −0.527881
\(269\) 6270.00 1.42115 0.710574 0.703623i \(-0.248435\pi\)
0.710574 + 0.703623i \(0.248435\pi\)
\(270\) 0 0
\(271\) 6721.00 1.50654 0.753269 0.657713i \(-0.228476\pi\)
0.753269 + 0.657713i \(0.228476\pi\)
\(272\) −1600.00 −0.356670
\(273\) 0 0
\(274\) 4368.00 0.963068
\(275\) −1364.00 −0.299099
\(276\) 0 0
\(277\) −5388.00 −1.16871 −0.584357 0.811497i \(-0.698653\pi\)
−0.584357 + 0.811497i \(0.698653\pi\)
\(278\) −1816.00 −0.391786
\(279\) 0 0
\(280\) −56.0000 −0.0119523
\(281\) −4765.00 −1.01159 −0.505794 0.862654i \(-0.668800\pi\)
−0.505794 + 0.862654i \(0.668800\pi\)
\(282\) 0 0
\(283\) −903.000 −0.189674 −0.0948371 0.995493i \(-0.530233\pi\)
−0.0948371 + 0.995493i \(0.530233\pi\)
\(284\) −512.000 −0.106978
\(285\) 0 0
\(286\) 946.000 0.195588
\(287\) 896.000 0.184283
\(288\) 0 0
\(289\) 5087.00 1.03542
\(290\) 446.000 0.0903104
\(291\) 0 0
\(292\) −644.000 −0.129066
\(293\) −672.000 −0.133989 −0.0669943 0.997753i \(-0.521341\pi\)
−0.0669943 + 0.997753i \(0.521341\pi\)
\(294\) 0 0
\(295\) −105.000 −0.0207232
\(296\) −296.000 −0.0581238
\(297\) 0 0
\(298\) 842.000 0.163677
\(299\) −2494.00 −0.482380
\(300\) 0 0
\(301\) 3206.00 0.613923
\(302\) −1896.00 −0.361267
\(303\) 0 0
\(304\) −1392.00 −0.262621
\(305\) −190.000 −0.0356701
\(306\) 0 0
\(307\) −1876.00 −0.348759 −0.174379 0.984679i \(-0.555792\pi\)
−0.174379 + 0.984679i \(0.555792\pi\)
\(308\) −308.000 −0.0569803
\(309\) 0 0
\(310\) 176.000 0.0322456
\(311\) 4688.00 0.854766 0.427383 0.904071i \(-0.359436\pi\)
0.427383 + 0.904071i \(0.359436\pi\)
\(312\) 0 0
\(313\) 4912.00 0.887037 0.443519 0.896265i \(-0.353730\pi\)
0.443519 + 0.896265i \(0.353730\pi\)
\(314\) −4736.00 −0.851172
\(315\) 0 0
\(316\) −1584.00 −0.281984
\(317\) 558.000 0.0988656 0.0494328 0.998777i \(-0.484259\pi\)
0.0494328 + 0.998777i \(0.484259\pi\)
\(318\) 0 0
\(319\) 2453.00 0.430538
\(320\) −64.0000 −0.0111803
\(321\) 0 0
\(322\) 812.000 0.140531
\(323\) 8700.00 1.49870
\(324\) 0 0
\(325\) 5332.00 0.910050
\(326\) 5206.00 0.884459
\(327\) 0 0
\(328\) 1024.00 0.172381
\(329\) −2387.00 −0.399999
\(330\) 0 0
\(331\) 4660.00 0.773827 0.386914 0.922116i \(-0.373541\pi\)
0.386914 + 0.922116i \(0.373541\pi\)
\(332\) 1680.00 0.277717
\(333\) 0 0
\(334\) −2804.00 −0.459365
\(335\) 579.000 0.0944303
\(336\) 0 0
\(337\) −9906.00 −1.60123 −0.800615 0.599180i \(-0.795493\pi\)
−0.800615 + 0.599180i \(0.795493\pi\)
\(338\) 696.000 0.112004
\(339\) 0 0
\(340\) 400.000 0.0638031
\(341\) 968.000 0.153725
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 3664.00 0.574272
\(345\) 0 0
\(346\) 1672.00 0.259790
\(347\) 10664.0 1.64978 0.824890 0.565294i \(-0.191237\pi\)
0.824890 + 0.565294i \(0.191237\pi\)
\(348\) 0 0
\(349\) 5489.00 0.841889 0.420945 0.907086i \(-0.361699\pi\)
0.420945 + 0.907086i \(0.361699\pi\)
\(350\) −1736.00 −0.265123
\(351\) 0 0
\(352\) −352.000 −0.0533002
\(353\) 1845.00 0.278185 0.139093 0.990279i \(-0.455581\pi\)
0.139093 + 0.990279i \(0.455581\pi\)
\(354\) 0 0
\(355\) 128.000 0.0191367
\(356\) 3192.00 0.475213
\(357\) 0 0
\(358\) −6584.00 −0.971998
\(359\) 848.000 0.124668 0.0623339 0.998055i \(-0.480146\pi\)
0.0623339 + 0.998055i \(0.480146\pi\)
\(360\) 0 0
\(361\) 710.000 0.103514
\(362\) −9676.00 −1.40486
\(363\) 0 0
\(364\) 1204.00 0.173370
\(365\) 161.000 0.0230880
\(366\) 0 0
\(367\) −8474.00 −1.20528 −0.602642 0.798012i \(-0.705885\pi\)
−0.602642 + 0.798012i \(0.705885\pi\)
\(368\) 928.000 0.131455
\(369\) 0 0
\(370\) 74.0000 0.0103975
\(371\) −2394.00 −0.335014
\(372\) 0 0
\(373\) 11396.0 1.58194 0.790969 0.611857i \(-0.209577\pi\)
0.790969 + 0.611857i \(0.209577\pi\)
\(374\) 2200.00 0.304169
\(375\) 0 0
\(376\) −2728.00 −0.374165
\(377\) −9589.00 −1.30997
\(378\) 0 0
\(379\) 2155.00 0.292071 0.146036 0.989279i \(-0.453349\pi\)
0.146036 + 0.989279i \(0.453349\pi\)
\(380\) 348.000 0.0469790
\(381\) 0 0
\(382\) −2464.00 −0.330024
\(383\) 5864.00 0.782340 0.391170 0.920318i \(-0.372070\pi\)
0.391170 + 0.920318i \(0.372070\pi\)
\(384\) 0 0
\(385\) 77.0000 0.0101929
\(386\) −4732.00 −0.623970
\(387\) 0 0
\(388\) 5656.00 0.740051
\(389\) −10104.0 −1.31695 −0.658474 0.752603i \(-0.728798\pi\)
−0.658474 + 0.752603i \(0.728798\pi\)
\(390\) 0 0
\(391\) −5800.00 −0.750175
\(392\) −392.000 −0.0505076
\(393\) 0 0
\(394\) 636.000 0.0813229
\(395\) 396.000 0.0504428
\(396\) 0 0
\(397\) −5868.00 −0.741830 −0.370915 0.928667i \(-0.620956\pi\)
−0.370915 + 0.928667i \(0.620956\pi\)
\(398\) 1612.00 0.203021
\(399\) 0 0
\(400\) −1984.00 −0.248000
\(401\) 2418.00 0.301120 0.150560 0.988601i \(-0.451892\pi\)
0.150560 + 0.988601i \(0.451892\pi\)
\(402\) 0 0
\(403\) −3784.00 −0.467728
\(404\) 7056.00 0.868933
\(405\) 0 0
\(406\) 3122.00 0.381631
\(407\) 407.000 0.0495682
\(408\) 0 0
\(409\) −2354.00 −0.284591 −0.142296 0.989824i \(-0.545448\pi\)
−0.142296 + 0.989824i \(0.545448\pi\)
\(410\) −256.000 −0.0308364
\(411\) 0 0
\(412\) 3912.00 0.467792
\(413\) −735.000 −0.0875714
\(414\) 0 0
\(415\) −420.000 −0.0496795
\(416\) 1376.00 0.162173
\(417\) 0 0
\(418\) 1914.00 0.223964
\(419\) 11443.0 1.33419 0.667097 0.744971i \(-0.267537\pi\)
0.667097 + 0.744971i \(0.267537\pi\)
\(420\) 0 0
\(421\) −13325.0 −1.54257 −0.771284 0.636492i \(-0.780385\pi\)
−0.771284 + 0.636492i \(0.780385\pi\)
\(422\) −8924.00 −1.02942
\(423\) 0 0
\(424\) −2736.00 −0.313377
\(425\) 12400.0 1.41527
\(426\) 0 0
\(427\) −1330.00 −0.150734
\(428\) −1924.00 −0.217290
\(429\) 0 0
\(430\) −916.000 −0.102729
\(431\) 8503.00 0.950290 0.475145 0.879907i \(-0.342396\pi\)
0.475145 + 0.879907i \(0.342396\pi\)
\(432\) 0 0
\(433\) 4496.00 0.498993 0.249497 0.968376i \(-0.419735\pi\)
0.249497 + 0.968376i \(0.419735\pi\)
\(434\) 1232.00 0.136262
\(435\) 0 0
\(436\) −1136.00 −0.124781
\(437\) −5046.00 −0.552364
\(438\) 0 0
\(439\) −7247.00 −0.787883 −0.393941 0.919136i \(-0.628889\pi\)
−0.393941 + 0.919136i \(0.628889\pi\)
\(440\) 88.0000 0.00953463
\(441\) 0 0
\(442\) −8600.00 −0.925476
\(443\) −8568.00 −0.918912 −0.459456 0.888201i \(-0.651956\pi\)
−0.459456 + 0.888201i \(0.651956\pi\)
\(444\) 0 0
\(445\) −798.000 −0.0850086
\(446\) −7604.00 −0.807309
\(447\) 0 0
\(448\) −448.000 −0.0472456
\(449\) 7812.00 0.821094 0.410547 0.911840i \(-0.365338\pi\)
0.410547 + 0.911840i \(0.365338\pi\)
\(450\) 0 0
\(451\) −1408.00 −0.147007
\(452\) −5992.00 −0.623540
\(453\) 0 0
\(454\) −6740.00 −0.696749
\(455\) −301.000 −0.0310134
\(456\) 0 0
\(457\) 4262.00 0.436254 0.218127 0.975920i \(-0.430005\pi\)
0.218127 + 0.975920i \(0.430005\pi\)
\(458\) 1796.00 0.183235
\(459\) 0 0
\(460\) −232.000 −0.0235153
\(461\) −8316.00 −0.840162 −0.420081 0.907487i \(-0.637998\pi\)
−0.420081 + 0.907487i \(0.637998\pi\)
\(462\) 0 0
\(463\) −16103.0 −1.61635 −0.808175 0.588943i \(-0.799544\pi\)
−0.808175 + 0.588943i \(0.799544\pi\)
\(464\) 3568.00 0.356983
\(465\) 0 0
\(466\) −924.000 −0.0918529
\(467\) 8913.00 0.883179 0.441589 0.897217i \(-0.354415\pi\)
0.441589 + 0.897217i \(0.354415\pi\)
\(468\) 0 0
\(469\) 4053.00 0.399041
\(470\) 682.000 0.0669326
\(471\) 0 0
\(472\) −840.000 −0.0819155
\(473\) −5038.00 −0.489741
\(474\) 0 0
\(475\) 10788.0 1.04208
\(476\) 2800.00 0.269617
\(477\) 0 0
\(478\) −11330.0 −1.08415
\(479\) 4100.00 0.391093 0.195547 0.980694i \(-0.437352\pi\)
0.195547 + 0.980694i \(0.437352\pi\)
\(480\) 0 0
\(481\) −1591.00 −0.150818
\(482\) −3186.00 −0.301075
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) −1414.00 −0.132384
\(486\) 0 0
\(487\) 10496.0 0.976631 0.488315 0.872667i \(-0.337612\pi\)
0.488315 + 0.872667i \(0.337612\pi\)
\(488\) −1520.00 −0.140998
\(489\) 0 0
\(490\) 98.0000 0.00903508
\(491\) −2625.00 −0.241272 −0.120636 0.992697i \(-0.538493\pi\)
−0.120636 + 0.992697i \(0.538493\pi\)
\(492\) 0 0
\(493\) −22300.0 −2.03720
\(494\) −7482.00 −0.681439
\(495\) 0 0
\(496\) 1408.00 0.127462
\(497\) 896.000 0.0808674
\(498\) 0 0
\(499\) −12397.0 −1.11216 −0.556078 0.831130i \(-0.687694\pi\)
−0.556078 + 0.831130i \(0.687694\pi\)
\(500\) 996.000 0.0890849
\(501\) 0 0
\(502\) 9090.00 0.808180
\(503\) 1854.00 0.164345 0.0821727 0.996618i \(-0.473814\pi\)
0.0821727 + 0.996618i \(0.473814\pi\)
\(504\) 0 0
\(505\) −1764.00 −0.155440
\(506\) −1276.00 −0.112105
\(507\) 0 0
\(508\) −2464.00 −0.215201
\(509\) −17530.0 −1.52653 −0.763265 0.646086i \(-0.776405\pi\)
−0.763265 + 0.646086i \(0.776405\pi\)
\(510\) 0 0
\(511\) 1127.00 0.0975647
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −5718.00 −0.490681
\(515\) −978.000 −0.0836812
\(516\) 0 0
\(517\) 3751.00 0.319089
\(518\) 518.000 0.0439375
\(519\) 0 0
\(520\) −344.000 −0.0290104
\(521\) 22255.0 1.87142 0.935709 0.352772i \(-0.114761\pi\)
0.935709 + 0.352772i \(0.114761\pi\)
\(522\) 0 0
\(523\) −7789.00 −0.651222 −0.325611 0.945504i \(-0.605570\pi\)
−0.325611 + 0.945504i \(0.605570\pi\)
\(524\) −10992.0 −0.916389
\(525\) 0 0
\(526\) −12558.0 −1.04098
\(527\) −8800.00 −0.727389
\(528\) 0 0
\(529\) −8803.00 −0.723514
\(530\) 684.000 0.0560586
\(531\) 0 0
\(532\) 2436.00 0.198523
\(533\) 5504.00 0.447288
\(534\) 0 0
\(535\) 481.000 0.0388700
\(536\) 4632.00 0.373269
\(537\) 0 0
\(538\) −12540.0 −1.00490
\(539\) 539.000 0.0430730
\(540\) 0 0
\(541\) 8288.00 0.658649 0.329324 0.944217i \(-0.393179\pi\)
0.329324 + 0.944217i \(0.393179\pi\)
\(542\) −13442.0 −1.06528
\(543\) 0 0
\(544\) 3200.00 0.252204
\(545\) 284.000 0.0223215
\(546\) 0 0
\(547\) −6432.00 −0.502765 −0.251383 0.967888i \(-0.580885\pi\)
−0.251383 + 0.967888i \(0.580885\pi\)
\(548\) −8736.00 −0.680992
\(549\) 0 0
\(550\) 2728.00 0.211495
\(551\) −19401.0 −1.50002
\(552\) 0 0
\(553\) 2772.00 0.213160
\(554\) 10776.0 0.826405
\(555\) 0 0
\(556\) 3632.00 0.277034
\(557\) 9815.00 0.746634 0.373317 0.927704i \(-0.378220\pi\)
0.373317 + 0.927704i \(0.378220\pi\)
\(558\) 0 0
\(559\) 19694.0 1.49010
\(560\) 112.000 0.00845154
\(561\) 0 0
\(562\) 9530.00 0.715300
\(563\) 20042.0 1.50030 0.750151 0.661267i \(-0.229981\pi\)
0.750151 + 0.661267i \(0.229981\pi\)
\(564\) 0 0
\(565\) 1498.00 0.111542
\(566\) 1806.00 0.134120
\(567\) 0 0
\(568\) 1024.00 0.0756445
\(569\) 8562.00 0.630822 0.315411 0.948955i \(-0.397858\pi\)
0.315411 + 0.948955i \(0.397858\pi\)
\(570\) 0 0
\(571\) 27004.0 1.97913 0.989564 0.144093i \(-0.0460265\pi\)
0.989564 + 0.144093i \(0.0460265\pi\)
\(572\) −1892.00 −0.138302
\(573\) 0 0
\(574\) −1792.00 −0.130308
\(575\) −7192.00 −0.521612
\(576\) 0 0
\(577\) 14360.0 1.03607 0.518037 0.855358i \(-0.326663\pi\)
0.518037 + 0.855358i \(0.326663\pi\)
\(578\) −10174.0 −0.732150
\(579\) 0 0
\(580\) −892.000 −0.0638591
\(581\) −2940.00 −0.209934
\(582\) 0 0
\(583\) 3762.00 0.267249
\(584\) 1288.00 0.0912634
\(585\) 0 0
\(586\) 1344.00 0.0947442
\(587\) −15453.0 −1.08656 −0.543282 0.839550i \(-0.682819\pi\)
−0.543282 + 0.839550i \(0.682819\pi\)
\(588\) 0 0
\(589\) −7656.00 −0.535586
\(590\) 210.000 0.0146535
\(591\) 0 0
\(592\) 592.000 0.0410997
\(593\) −18000.0 −1.24649 −0.623247 0.782025i \(-0.714187\pi\)
−0.623247 + 0.782025i \(0.714187\pi\)
\(594\) 0 0
\(595\) −700.000 −0.0482306
\(596\) −1684.00 −0.115737
\(597\) 0 0
\(598\) 4988.00 0.341094
\(599\) −27180.0 −1.85400 −0.926999 0.375064i \(-0.877621\pi\)
−0.926999 + 0.375064i \(0.877621\pi\)
\(600\) 0 0
\(601\) −16153.0 −1.09633 −0.548165 0.836370i \(-0.684674\pi\)
−0.548165 + 0.836370i \(0.684674\pi\)
\(602\) −6412.00 −0.434109
\(603\) 0 0
\(604\) 3792.00 0.255454
\(605\) −121.000 −0.00813116
\(606\) 0 0
\(607\) −11443.0 −0.765168 −0.382584 0.923921i \(-0.624966\pi\)
−0.382584 + 0.923921i \(0.624966\pi\)
\(608\) 2784.00 0.185701
\(609\) 0 0
\(610\) 380.000 0.0252225
\(611\) −14663.0 −0.970870
\(612\) 0 0
\(613\) −9488.00 −0.625150 −0.312575 0.949893i \(-0.601191\pi\)
−0.312575 + 0.949893i \(0.601191\pi\)
\(614\) 3752.00 0.246610
\(615\) 0 0
\(616\) 616.000 0.0402911
\(617\) −22902.0 −1.49433 −0.747164 0.664640i \(-0.768585\pi\)
−0.747164 + 0.664640i \(0.768585\pi\)
\(618\) 0 0
\(619\) 19448.0 1.26281 0.631406 0.775452i \(-0.282478\pi\)
0.631406 + 0.775452i \(0.282478\pi\)
\(620\) −352.000 −0.0228011
\(621\) 0 0
\(622\) −9376.00 −0.604411
\(623\) −5586.00 −0.359227
\(624\) 0 0
\(625\) 15251.0 0.976064
\(626\) −9824.00 −0.627230
\(627\) 0 0
\(628\) 9472.00 0.601869
\(629\) −3700.00 −0.234545
\(630\) 0 0
\(631\) −13608.0 −0.858520 −0.429260 0.903181i \(-0.641226\pi\)
−0.429260 + 0.903181i \(0.641226\pi\)
\(632\) 3168.00 0.199393
\(633\) 0 0
\(634\) −1116.00 −0.0699086
\(635\) 616.000 0.0384964
\(636\) 0 0
\(637\) −2107.00 −0.131056
\(638\) −4906.00 −0.304436
\(639\) 0 0
\(640\) 128.000 0.00790569
\(641\) −17628.0 −1.08622 −0.543108 0.839663i \(-0.682752\pi\)
−0.543108 + 0.839663i \(0.682752\pi\)
\(642\) 0 0
\(643\) −21074.0 −1.29250 −0.646250 0.763126i \(-0.723664\pi\)
−0.646250 + 0.763126i \(0.723664\pi\)
\(644\) −1624.00 −0.0993704
\(645\) 0 0
\(646\) −17400.0 −1.05974
\(647\) 4899.00 0.297681 0.148840 0.988861i \(-0.452446\pi\)
0.148840 + 0.988861i \(0.452446\pi\)
\(648\) 0 0
\(649\) 1155.00 0.0698578
\(650\) −10664.0 −0.643502
\(651\) 0 0
\(652\) −10412.0 −0.625407
\(653\) −7760.00 −0.465042 −0.232521 0.972591i \(-0.574697\pi\)
−0.232521 + 0.972591i \(0.574697\pi\)
\(654\) 0 0
\(655\) 2748.00 0.163929
\(656\) −2048.00 −0.121892
\(657\) 0 0
\(658\) 4774.00 0.282842
\(659\) −18365.0 −1.08558 −0.542791 0.839868i \(-0.682633\pi\)
−0.542791 + 0.839868i \(0.682633\pi\)
\(660\) 0 0
\(661\) 13286.0 0.781794 0.390897 0.920435i \(-0.372165\pi\)
0.390897 + 0.920435i \(0.372165\pi\)
\(662\) −9320.00 −0.547178
\(663\) 0 0
\(664\) −3360.00 −0.196375
\(665\) −609.000 −0.0355128
\(666\) 0 0
\(667\) 12934.0 0.750834
\(668\) 5608.00 0.324820
\(669\) 0 0
\(670\) −1158.00 −0.0667723
\(671\) 2090.00 0.120244
\(672\) 0 0
\(673\) −15242.0 −0.873010 −0.436505 0.899702i \(-0.643784\pi\)
−0.436505 + 0.899702i \(0.643784\pi\)
\(674\) 19812.0 1.13224
\(675\) 0 0
\(676\) −1392.00 −0.0791989
\(677\) −14170.0 −0.804427 −0.402214 0.915546i \(-0.631759\pi\)
−0.402214 + 0.915546i \(0.631759\pi\)
\(678\) 0 0
\(679\) −9898.00 −0.559426
\(680\) −800.000 −0.0451156
\(681\) 0 0
\(682\) −1936.00 −0.108700
\(683\) 7116.00 0.398662 0.199331 0.979932i \(-0.436123\pi\)
0.199331 + 0.979932i \(0.436123\pi\)
\(684\) 0 0
\(685\) 2184.00 0.121819
\(686\) 686.000 0.0381802
\(687\) 0 0
\(688\) −7328.00 −0.406072
\(689\) −14706.0 −0.813141
\(690\) 0 0
\(691\) 2010.00 0.110657 0.0553285 0.998468i \(-0.482379\pi\)
0.0553285 + 0.998468i \(0.482379\pi\)
\(692\) −3344.00 −0.183699
\(693\) 0 0
\(694\) −21328.0 −1.16657
\(695\) −908.000 −0.0495574
\(696\) 0 0
\(697\) 12800.0 0.695602
\(698\) −10978.0 −0.595306
\(699\) 0 0
\(700\) 3472.00 0.187470
\(701\) −7794.00 −0.419936 −0.209968 0.977708i \(-0.567336\pi\)
−0.209968 + 0.977708i \(0.567336\pi\)
\(702\) 0 0
\(703\) −3219.00 −0.172698
\(704\) 704.000 0.0376889
\(705\) 0 0
\(706\) −3690.00 −0.196707
\(707\) −12348.0 −0.656852
\(708\) 0 0
\(709\) 29991.0 1.58863 0.794313 0.607509i \(-0.207831\pi\)
0.794313 + 0.607509i \(0.207831\pi\)
\(710\) −256.000 −0.0135317
\(711\) 0 0
\(712\) −6384.00 −0.336026
\(713\) 5104.00 0.268087
\(714\) 0 0
\(715\) 473.000 0.0247401
\(716\) 13168.0 0.687306
\(717\) 0 0
\(718\) −1696.00 −0.0881534
\(719\) −19613.0 −1.01730 −0.508652 0.860972i \(-0.669856\pi\)
−0.508652 + 0.860972i \(0.669856\pi\)
\(720\) 0 0
\(721\) −6846.00 −0.353618
\(722\) −1420.00 −0.0731952
\(723\) 0 0
\(724\) 19352.0 0.993386
\(725\) −27652.0 −1.41651
\(726\) 0 0
\(727\) 16646.0 0.849197 0.424598 0.905382i \(-0.360415\pi\)
0.424598 + 0.905382i \(0.360415\pi\)
\(728\) −2408.00 −0.122591
\(729\) 0 0
\(730\) −322.000 −0.0163257
\(731\) 45800.0 2.31734
\(732\) 0 0
\(733\) −36346.0 −1.83147 −0.915737 0.401779i \(-0.868392\pi\)
−0.915737 + 0.401779i \(0.868392\pi\)
\(734\) 16948.0 0.852264
\(735\) 0 0
\(736\) −1856.00 −0.0929525
\(737\) −6369.00 −0.318324
\(738\) 0 0
\(739\) −25698.0 −1.27918 −0.639591 0.768715i \(-0.720896\pi\)
−0.639591 + 0.768715i \(0.720896\pi\)
\(740\) −148.000 −0.00735215
\(741\) 0 0
\(742\) 4788.00 0.236891
\(743\) 27543.0 1.35997 0.679983 0.733228i \(-0.261987\pi\)
0.679983 + 0.733228i \(0.261987\pi\)
\(744\) 0 0
\(745\) 421.000 0.0207037
\(746\) −22792.0 −1.11860
\(747\) 0 0
\(748\) −4400.00 −0.215080
\(749\) 3367.00 0.164256
\(750\) 0 0
\(751\) 26005.0 1.26356 0.631782 0.775146i \(-0.282324\pi\)
0.631782 + 0.775146i \(0.282324\pi\)
\(752\) 5456.00 0.264574
\(753\) 0 0
\(754\) 19178.0 0.926289
\(755\) −948.000 −0.0456970
\(756\) 0 0
\(757\) 17621.0 0.846032 0.423016 0.906122i \(-0.360971\pi\)
0.423016 + 0.906122i \(0.360971\pi\)
\(758\) −4310.00 −0.206525
\(759\) 0 0
\(760\) −696.000 −0.0332192
\(761\) −22968.0 −1.09407 −0.547036 0.837109i \(-0.684244\pi\)
−0.547036 + 0.837109i \(0.684244\pi\)
\(762\) 0 0
\(763\) 1988.00 0.0943256
\(764\) 4928.00 0.233362
\(765\) 0 0
\(766\) −11728.0 −0.553198
\(767\) −4515.00 −0.212552
\(768\) 0 0
\(769\) 28273.0 1.32581 0.662907 0.748702i \(-0.269323\pi\)
0.662907 + 0.748702i \(0.269323\pi\)
\(770\) −154.000 −0.00720750
\(771\) 0 0
\(772\) 9464.00 0.441213
\(773\) 13239.0 0.616007 0.308004 0.951385i \(-0.400339\pi\)
0.308004 + 0.951385i \(0.400339\pi\)
\(774\) 0 0
\(775\) −10912.0 −0.505769
\(776\) −11312.0 −0.523295
\(777\) 0 0
\(778\) 20208.0 0.931224
\(779\) 11136.0 0.512180
\(780\) 0 0
\(781\) −1408.00 −0.0645099
\(782\) 11600.0 0.530454
\(783\) 0 0
\(784\) 784.000 0.0357143
\(785\) −2368.00 −0.107666
\(786\) 0 0
\(787\) 1775.00 0.0803963 0.0401982 0.999192i \(-0.487201\pi\)
0.0401982 + 0.999192i \(0.487201\pi\)
\(788\) −1272.00 −0.0575040
\(789\) 0 0
\(790\) −792.000 −0.0356685
\(791\) 10486.0 0.471352
\(792\) 0 0
\(793\) −8170.00 −0.365858
\(794\) 11736.0 0.524553
\(795\) 0 0
\(796\) −3224.00 −0.143557
\(797\) 16481.0 0.732481 0.366240 0.930520i \(-0.380645\pi\)
0.366240 + 0.930520i \(0.380645\pi\)
\(798\) 0 0
\(799\) −34100.0 −1.50985
\(800\) 3968.00 0.175362
\(801\) 0 0
\(802\) −4836.00 −0.212924
\(803\) −1771.00 −0.0778297
\(804\) 0 0
\(805\) 406.000 0.0177759
\(806\) 7568.00 0.330734
\(807\) 0 0
\(808\) −14112.0 −0.614429
\(809\) 29079.0 1.26374 0.631868 0.775076i \(-0.282288\pi\)
0.631868 + 0.775076i \(0.282288\pi\)
\(810\) 0 0
\(811\) −40381.0 −1.74842 −0.874210 0.485548i \(-0.838620\pi\)
−0.874210 + 0.485548i \(0.838620\pi\)
\(812\) −6244.00 −0.269854
\(813\) 0 0
\(814\) −814.000 −0.0350500
\(815\) 2603.00 0.111876
\(816\) 0 0
\(817\) 39846.0 1.70629
\(818\) 4708.00 0.201236
\(819\) 0 0
\(820\) 512.000 0.0218047
\(821\) 6345.00 0.269722 0.134861 0.990865i \(-0.456941\pi\)
0.134861 + 0.990865i \(0.456941\pi\)
\(822\) 0 0
\(823\) 7757.00 0.328544 0.164272 0.986415i \(-0.447472\pi\)
0.164272 + 0.986415i \(0.447472\pi\)
\(824\) −7824.00 −0.330779
\(825\) 0 0
\(826\) 1470.00 0.0619223
\(827\) 15659.0 0.658424 0.329212 0.944256i \(-0.393217\pi\)
0.329212 + 0.944256i \(0.393217\pi\)
\(828\) 0 0
\(829\) −5384.00 −0.225566 −0.112783 0.993620i \(-0.535976\pi\)
−0.112783 + 0.993620i \(0.535976\pi\)
\(830\) 840.000 0.0351287
\(831\) 0 0
\(832\) −2752.00 −0.114674
\(833\) −4900.00 −0.203811
\(834\) 0 0
\(835\) −1402.00 −0.0581056
\(836\) −3828.00 −0.158366
\(837\) 0 0
\(838\) −22886.0 −0.943417
\(839\) −40395.0 −1.66221 −0.831103 0.556119i \(-0.812290\pi\)
−0.831103 + 0.556119i \(0.812290\pi\)
\(840\) 0 0
\(841\) 25340.0 1.03899
\(842\) 26650.0 1.09076
\(843\) 0 0
\(844\) 17848.0 0.727907
\(845\) 348.000 0.0141675
\(846\) 0 0
\(847\) −847.000 −0.0343604
\(848\) 5472.00 0.221591
\(849\) 0 0
\(850\) −24800.0 −1.00074
\(851\) 2146.00 0.0864441
\(852\) 0 0
\(853\) −33202.0 −1.33273 −0.666363 0.745628i \(-0.732150\pi\)
−0.666363 + 0.745628i \(0.732150\pi\)
\(854\) 2660.00 0.106585
\(855\) 0 0
\(856\) 3848.00 0.153647
\(857\) −21034.0 −0.838399 −0.419199 0.907894i \(-0.637689\pi\)
−0.419199 + 0.907894i \(0.637689\pi\)
\(858\) 0 0
\(859\) 20920.0 0.830944 0.415472 0.909606i \(-0.363616\pi\)
0.415472 + 0.909606i \(0.363616\pi\)
\(860\) 1832.00 0.0726403
\(861\) 0 0
\(862\) −17006.0 −0.671957
\(863\) −8354.00 −0.329517 −0.164759 0.986334i \(-0.552685\pi\)
−0.164759 + 0.986334i \(0.552685\pi\)
\(864\) 0 0
\(865\) 836.000 0.0328611
\(866\) −8992.00 −0.352841
\(867\) 0 0
\(868\) −2464.00 −0.0963521
\(869\) −4356.00 −0.170043
\(870\) 0 0
\(871\) 24897.0 0.968545
\(872\) 2272.00 0.0882335
\(873\) 0 0
\(874\) 10092.0 0.390580
\(875\) −1743.00 −0.0673419
\(876\) 0 0
\(877\) 19564.0 0.753283 0.376642 0.926359i \(-0.377079\pi\)
0.376642 + 0.926359i \(0.377079\pi\)
\(878\) 14494.0 0.557117
\(879\) 0 0
\(880\) −176.000 −0.00674200
\(881\) −32061.0 −1.22606 −0.613032 0.790058i \(-0.710050\pi\)
−0.613032 + 0.790058i \(0.710050\pi\)
\(882\) 0 0
\(883\) 46711.0 1.78024 0.890119 0.455728i \(-0.150621\pi\)
0.890119 + 0.455728i \(0.150621\pi\)
\(884\) 17200.0 0.654410
\(885\) 0 0
\(886\) 17136.0 0.649769
\(887\) 7120.00 0.269522 0.134761 0.990878i \(-0.456973\pi\)
0.134761 + 0.990878i \(0.456973\pi\)
\(888\) 0 0
\(889\) 4312.00 0.162677
\(890\) 1596.00 0.0601102
\(891\) 0 0
\(892\) 15208.0 0.570854
\(893\) −29667.0 −1.11172
\(894\) 0 0
\(895\) −3292.00 −0.122949
\(896\) 896.000 0.0334077
\(897\) 0 0
\(898\) −15624.0 −0.580601
\(899\) 19624.0 0.728028
\(900\) 0 0
\(901\) −34200.0 −1.26456
\(902\) 2816.00 0.103950
\(903\) 0 0
\(904\) 11984.0 0.440909
\(905\) −4838.00 −0.177702
\(906\) 0 0
\(907\) −21940.0 −0.803204 −0.401602 0.915814i \(-0.631546\pi\)
−0.401602 + 0.915814i \(0.631546\pi\)
\(908\) 13480.0 0.492676
\(909\) 0 0
\(910\) 602.000 0.0219298
\(911\) −66.0000 −0.00240030 −0.00120015 0.999999i \(-0.500382\pi\)
−0.00120015 + 0.999999i \(0.500382\pi\)
\(912\) 0 0
\(913\) 4620.00 0.167470
\(914\) −8524.00 −0.308478
\(915\) 0 0
\(916\) −3592.00 −0.129567
\(917\) 19236.0 0.692725
\(918\) 0 0
\(919\) −42594.0 −1.52889 −0.764443 0.644691i \(-0.776986\pi\)
−0.764443 + 0.644691i \(0.776986\pi\)
\(920\) 464.000 0.0166279
\(921\) 0 0
\(922\) 16632.0 0.594084
\(923\) 5504.00 0.196280
\(924\) 0 0
\(925\) −4588.00 −0.163084
\(926\) 32206.0 1.14293
\(927\) 0 0
\(928\) −7136.00 −0.252425
\(929\) 6609.00 0.233406 0.116703 0.993167i \(-0.462767\pi\)
0.116703 + 0.993167i \(0.462767\pi\)
\(930\) 0 0
\(931\) −4263.00 −0.150069
\(932\) 1848.00 0.0649498
\(933\) 0 0
\(934\) −17826.0 −0.624502
\(935\) 1100.00 0.0384747
\(936\) 0 0
\(937\) 10098.0 0.352068 0.176034 0.984384i \(-0.443673\pi\)
0.176034 + 0.984384i \(0.443673\pi\)
\(938\) −8106.00 −0.282164
\(939\) 0 0
\(940\) −1364.00 −0.0473285
\(941\) 41824.0 1.44891 0.724455 0.689323i \(-0.242092\pi\)
0.724455 + 0.689323i \(0.242092\pi\)
\(942\) 0 0
\(943\) −7424.00 −0.256372
\(944\) 1680.00 0.0579230
\(945\) 0 0
\(946\) 10076.0 0.346299
\(947\) 28838.0 0.989556 0.494778 0.869020i \(-0.335249\pi\)
0.494778 + 0.869020i \(0.335249\pi\)
\(948\) 0 0
\(949\) 6923.00 0.236807
\(950\) −21576.0 −0.736861
\(951\) 0 0
\(952\) −5600.00 −0.190648
\(953\) −16165.0 −0.549460 −0.274730 0.961521i \(-0.588589\pi\)
−0.274730 + 0.961521i \(0.588589\pi\)
\(954\) 0 0
\(955\) −1232.00 −0.0417451
\(956\) 22660.0 0.766608
\(957\) 0 0
\(958\) −8200.00 −0.276545
\(959\) 15288.0 0.514781
\(960\) 0 0
\(961\) −22047.0 −0.740056
\(962\) 3182.00 0.106644
\(963\) 0 0
\(964\) 6372.00 0.212892
\(965\) −2366.00 −0.0789267
\(966\) 0 0
\(967\) −40114.0 −1.33400 −0.667001 0.745057i \(-0.732422\pi\)
−0.667001 + 0.745057i \(0.732422\pi\)
\(968\) −968.000 −0.0321412
\(969\) 0 0
\(970\) 2828.00 0.0936099
\(971\) 6515.00 0.215321 0.107660 0.994188i \(-0.465664\pi\)
0.107660 + 0.994188i \(0.465664\pi\)
\(972\) 0 0
\(973\) −6356.00 −0.209418
\(974\) −20992.0 −0.690582
\(975\) 0 0
\(976\) 3040.00 0.0997008
\(977\) −12790.0 −0.418821 −0.209411 0.977828i \(-0.567155\pi\)
−0.209411 + 0.977828i \(0.567155\pi\)
\(978\) 0 0
\(979\) 8778.00 0.286564
\(980\) −196.000 −0.00638877
\(981\) 0 0
\(982\) 5250.00 0.170605
\(983\) −4788.00 −0.155355 −0.0776773 0.996979i \(-0.524750\pi\)
−0.0776773 + 0.996979i \(0.524750\pi\)
\(984\) 0 0
\(985\) 318.000 0.0102866
\(986\) 44600.0 1.44052
\(987\) 0 0
\(988\) 14964.0 0.481850
\(989\) −26564.0 −0.854081
\(990\) 0 0
\(991\) 26989.0 0.865120 0.432560 0.901605i \(-0.357610\pi\)
0.432560 + 0.901605i \(0.357610\pi\)
\(992\) −2816.00 −0.0901291
\(993\) 0 0
\(994\) −1792.00 −0.0571819
\(995\) 806.000 0.0256803
\(996\) 0 0
\(997\) −55518.0 −1.76356 −0.881782 0.471658i \(-0.843656\pi\)
−0.881782 + 0.471658i \(0.843656\pi\)
\(998\) 24794.0 0.786413
\(999\) 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 1386.4.a.d.1.1 1
3.2 odd 2 462.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.4.a.f.1.1 1 3.2 odd 2
1386.4.a.d.1.1 1 1.1 even 1 trivial