Properties

Label 784.4.a.z.1.1
Level $784$
Weight $4$
Character 784.1
Self dual yes
Analytic conductor $46.257$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(46.2574974445\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{22}) \)
Defining polynomial: \(x^{2} - 22\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 98)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.69042\) of defining polynomial
Character \(\chi\) \(=\) 784.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.38083 q^{3} -9.38083 q^{5} +61.0000 q^{9} +O(q^{10})\) \(q-9.38083 q^{3} -9.38083 q^{5} +61.0000 q^{9} -20.0000 q^{11} -65.6658 q^{13} +88.0000 q^{15} -56.2850 q^{17} +9.38083 q^{19} -48.0000 q^{23} -37.0000 q^{25} -318.948 q^{27} -166.000 q^{29} -206.378 q^{31} +187.617 q^{33} -78.0000 q^{37} +616.000 q^{39} -393.995 q^{41} -436.000 q^{43} -572.231 q^{45} +206.378 q^{47} +528.000 q^{51} +62.0000 q^{53} +187.617 q^{55} -88.0000 q^{57} -666.039 q^{59} -272.044 q^{61} +616.000 q^{65} -580.000 q^{67} +450.280 q^{69} +544.000 q^{71} +600.373 q^{73} +347.091 q^{75} +680.000 q^{79} +1345.00 q^{81} +196.997 q^{83} +528.000 q^{85} +1557.22 q^{87} +1500.93 q^{89} +1936.00 q^{93} -88.0000 q^{95} +656.658 q^{97} -1220.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 122q^{9} + O(q^{10}) \) \( 2q + 122q^{9} - 40q^{11} + 176q^{15} - 96q^{23} - 74q^{25} - 332q^{29} - 156q^{37} + 1232q^{39} - 872q^{43} + 1056q^{51} + 124q^{53} - 176q^{57} + 1232q^{65} - 1160q^{67} + 1088q^{71} + 1360q^{79} + 2690q^{81} + 1056q^{85} + 3872q^{93} - 176q^{95} - 2440q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −9.38083 −1.80534 −0.902671 0.430331i \(-0.858397\pi\)
−0.902671 + 0.430331i \(0.858397\pi\)
\(4\) 0 0
\(5\) −9.38083 −0.839047 −0.419524 0.907744i \(-0.637803\pi\)
−0.419524 + 0.907744i \(0.637803\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 61.0000 2.25926
\(10\) 0 0
\(11\) −20.0000 −0.548202 −0.274101 0.961701i \(-0.588380\pi\)
−0.274101 + 0.961701i \(0.588380\pi\)
\(12\) 0 0
\(13\) −65.6658 −1.40096 −0.700478 0.713674i \(-0.747030\pi\)
−0.700478 + 0.713674i \(0.747030\pi\)
\(14\) 0 0
\(15\) 88.0000 1.51477
\(16\) 0 0
\(17\) −56.2850 −0.803007 −0.401503 0.915858i \(-0.631512\pi\)
−0.401503 + 0.915858i \(0.631512\pi\)
\(18\) 0 0
\(19\) 9.38083 0.113269 0.0566345 0.998395i \(-0.481963\pi\)
0.0566345 + 0.998395i \(0.481963\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −48.0000 −0.435161 −0.217580 0.976042i \(-0.569816\pi\)
−0.217580 + 0.976042i \(0.569816\pi\)
\(24\) 0 0
\(25\) −37.0000 −0.296000
\(26\) 0 0
\(27\) −318.948 −2.27339
\(28\) 0 0
\(29\) −166.000 −1.06295 −0.531473 0.847075i \(-0.678361\pi\)
−0.531473 + 0.847075i \(0.678361\pi\)
\(30\) 0 0
\(31\) −206.378 −1.19570 −0.597849 0.801609i \(-0.703978\pi\)
−0.597849 + 0.801609i \(0.703978\pi\)
\(32\) 0 0
\(33\) 187.617 0.989693
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −78.0000 −0.346571 −0.173285 0.984872i \(-0.555438\pi\)
−0.173285 + 0.984872i \(0.555438\pi\)
\(38\) 0 0
\(39\) 616.000 2.52920
\(40\) 0 0
\(41\) −393.995 −1.50077 −0.750386 0.661000i \(-0.770132\pi\)
−0.750386 + 0.661000i \(0.770132\pi\)
\(42\) 0 0
\(43\) −436.000 −1.54626 −0.773132 0.634245i \(-0.781311\pi\)
−0.773132 + 0.634245i \(0.781311\pi\)
\(44\) 0 0
\(45\) −572.231 −1.89562
\(46\) 0 0
\(47\) 206.378 0.640497 0.320249 0.947334i \(-0.396234\pi\)
0.320249 + 0.947334i \(0.396234\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 528.000 1.44970
\(52\) 0 0
\(53\) 62.0000 0.160686 0.0803430 0.996767i \(-0.474398\pi\)
0.0803430 + 0.996767i \(0.474398\pi\)
\(54\) 0 0
\(55\) 187.617 0.459968
\(56\) 0 0
\(57\) −88.0000 −0.204489
\(58\) 0 0
\(59\) −666.039 −1.46968 −0.734838 0.678243i \(-0.762742\pi\)
−0.734838 + 0.678243i \(0.762742\pi\)
\(60\) 0 0
\(61\) −272.044 −0.571011 −0.285506 0.958377i \(-0.592162\pi\)
−0.285506 + 0.958377i \(0.592162\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 616.000 1.17547
\(66\) 0 0
\(67\) −580.000 −1.05759 −0.528793 0.848751i \(-0.677355\pi\)
−0.528793 + 0.848751i \(0.677355\pi\)
\(68\) 0 0
\(69\) 450.280 0.785613
\(70\) 0 0
\(71\) 544.000 0.909309 0.454654 0.890668i \(-0.349763\pi\)
0.454654 + 0.890668i \(0.349763\pi\)
\(72\) 0 0
\(73\) 600.373 0.962580 0.481290 0.876561i \(-0.340168\pi\)
0.481290 + 0.876561i \(0.340168\pi\)
\(74\) 0 0
\(75\) 347.091 0.534381
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 680.000 0.968430 0.484215 0.874949i \(-0.339105\pi\)
0.484215 + 0.874949i \(0.339105\pi\)
\(80\) 0 0
\(81\) 1345.00 1.84499
\(82\) 0 0
\(83\) 196.997 0.260521 0.130261 0.991480i \(-0.458419\pi\)
0.130261 + 0.991480i \(0.458419\pi\)
\(84\) 0 0
\(85\) 528.000 0.673760
\(86\) 0 0
\(87\) 1557.22 1.91898
\(88\) 0 0
\(89\) 1500.93 1.78762 0.893812 0.448441i \(-0.148021\pi\)
0.893812 + 0.448441i \(0.148021\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 1936.00 2.15864
\(94\) 0 0
\(95\) −88.0000 −0.0950380
\(96\) 0 0
\(97\) 656.658 0.687356 0.343678 0.939088i \(-0.388327\pi\)
0.343678 + 0.939088i \(0.388327\pi\)
\(98\) 0 0
\(99\) −1220.00 −1.23853
\(100\) 0 0
\(101\) −121.951 −0.120144 −0.0600721 0.998194i \(-0.519133\pi\)
−0.0600721 + 0.998194i \(0.519133\pi\)
\(102\) 0 0
\(103\) −1369.60 −1.31020 −0.655101 0.755541i \(-0.727374\pi\)
−0.655101 + 0.755541i \(0.727374\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 260.000 0.234908 0.117454 0.993078i \(-0.462527\pi\)
0.117454 + 0.993078i \(0.462527\pi\)
\(108\) 0 0
\(109\) 1882.00 1.65379 0.826894 0.562358i \(-0.190106\pi\)
0.826894 + 0.562358i \(0.190106\pi\)
\(110\) 0 0
\(111\) 731.705 0.625679
\(112\) 0 0
\(113\) −1286.00 −1.07059 −0.535295 0.844665i \(-0.679800\pi\)
−0.535295 + 0.844665i \(0.679800\pi\)
\(114\) 0 0
\(115\) 450.280 0.365120
\(116\) 0 0
\(117\) −4005.62 −3.16512
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −931.000 −0.699474
\(122\) 0 0
\(123\) 3696.00 2.70941
\(124\) 0 0
\(125\) 1519.69 1.08741
\(126\) 0 0
\(127\) −2312.00 −1.61541 −0.807704 0.589588i \(-0.799290\pi\)
−0.807704 + 0.589588i \(0.799290\pi\)
\(128\) 0 0
\(129\) 4090.04 2.79154
\(130\) 0 0
\(131\) −253.282 −0.168927 −0.0844633 0.996427i \(-0.526918\pi\)
−0.0844633 + 0.996427i \(0.526918\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2992.00 1.90748
\(136\) 0 0
\(137\) −1114.00 −0.694711 −0.347356 0.937733i \(-0.612920\pi\)
−0.347356 + 0.937733i \(0.612920\pi\)
\(138\) 0 0
\(139\) 1378.98 0.841466 0.420733 0.907185i \(-0.361773\pi\)
0.420733 + 0.907185i \(0.361773\pi\)
\(140\) 0 0
\(141\) −1936.00 −1.15632
\(142\) 0 0
\(143\) 1313.32 0.768007
\(144\) 0 0
\(145\) 1557.22 0.891862
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −946.000 −0.520130 −0.260065 0.965591i \(-0.583744\pi\)
−0.260065 + 0.965591i \(0.583744\pi\)
\(150\) 0 0
\(151\) −832.000 −0.448392 −0.224196 0.974544i \(-0.571976\pi\)
−0.224196 + 0.974544i \(0.571976\pi\)
\(152\) 0 0
\(153\) −3433.38 −1.81420
\(154\) 0 0
\(155\) 1936.00 1.00325
\(156\) 0 0
\(157\) −2879.92 −1.46396 −0.731982 0.681324i \(-0.761404\pi\)
−0.731982 + 0.681324i \(0.761404\pi\)
\(158\) 0 0
\(159\) −581.612 −0.290093
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −636.000 −0.305616 −0.152808 0.988256i \(-0.548832\pi\)
−0.152808 + 0.988256i \(0.548832\pi\)
\(164\) 0 0
\(165\) −1760.00 −0.830399
\(166\) 0 0
\(167\) −656.658 −0.304274 −0.152137 0.988359i \(-0.548615\pi\)
−0.152137 + 0.988359i \(0.548615\pi\)
\(168\) 0 0
\(169\) 2115.00 0.962676
\(170\) 0 0
\(171\) 572.231 0.255904
\(172\) 0 0
\(173\) −666.039 −0.292705 −0.146353 0.989232i \(-0.546753\pi\)
−0.146353 + 0.989232i \(0.546753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 6248.00 2.65327
\(178\) 0 0
\(179\) 3228.00 1.34789 0.673944 0.738782i \(-0.264599\pi\)
0.673944 + 0.738782i \(0.264599\pi\)
\(180\) 0 0
\(181\) 2823.63 1.15955 0.579776 0.814776i \(-0.303140\pi\)
0.579776 + 0.814776i \(0.303140\pi\)
\(182\) 0 0
\(183\) 2552.00 1.03087
\(184\) 0 0
\(185\) 731.705 0.290789
\(186\) 0 0
\(187\) 1125.70 0.440210
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2136.00 0.809191 0.404596 0.914496i \(-0.367412\pi\)
0.404596 + 0.914496i \(0.367412\pi\)
\(192\) 0 0
\(193\) 1658.00 0.618370 0.309185 0.951002i \(-0.399944\pi\)
0.309185 + 0.951002i \(0.399944\pi\)
\(194\) 0 0
\(195\) −5778.59 −2.12212
\(196\) 0 0
\(197\) −978.000 −0.353704 −0.176852 0.984237i \(-0.556591\pi\)
−0.176852 + 0.984237i \(0.556591\pi\)
\(198\) 0 0
\(199\) −4934.32 −1.75771 −0.878855 0.477088i \(-0.841692\pi\)
−0.878855 + 0.477088i \(0.841692\pi\)
\(200\) 0 0
\(201\) 5440.88 1.90930
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3696.00 1.25922
\(206\) 0 0
\(207\) −2928.00 −0.983140
\(208\) 0 0
\(209\) −187.617 −0.0620943
\(210\) 0 0
\(211\) −1556.00 −0.507675 −0.253838 0.967247i \(-0.581693\pi\)
−0.253838 + 0.967247i \(0.581693\pi\)
\(212\) 0 0
\(213\) −5103.17 −1.64161
\(214\) 0 0
\(215\) 4090.04 1.29739
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −5632.00 −1.73779
\(220\) 0 0
\(221\) 3696.00 1.12498
\(222\) 0 0
\(223\) 2889.30 0.867630 0.433815 0.901002i \(-0.357167\pi\)
0.433815 + 0.901002i \(0.357167\pi\)
\(224\) 0 0
\(225\) −2257.00 −0.668741
\(226\) 0 0
\(227\) −1979.36 −0.578742 −0.289371 0.957217i \(-0.593446\pi\)
−0.289371 + 0.957217i \(0.593446\pi\)
\(228\) 0 0
\(229\) −2767.35 −0.798565 −0.399282 0.916828i \(-0.630741\pi\)
−0.399282 + 0.916828i \(0.630741\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6490.00 −1.82478 −0.912391 0.409321i \(-0.865766\pi\)
−0.912391 + 0.409321i \(0.865766\pi\)
\(234\) 0 0
\(235\) −1936.00 −0.537407
\(236\) 0 0
\(237\) −6378.97 −1.74835
\(238\) 0 0
\(239\) 4296.00 1.16270 0.581350 0.813654i \(-0.302525\pi\)
0.581350 + 0.813654i \(0.302525\pi\)
\(240\) 0 0
\(241\) −4521.56 −1.20854 −0.604272 0.796778i \(-0.706536\pi\)
−0.604272 + 0.796778i \(0.706536\pi\)
\(242\) 0 0
\(243\) −4005.62 −1.05745
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −616.000 −0.158685
\(248\) 0 0
\(249\) −1848.00 −0.470330
\(250\) 0 0
\(251\) 5581.59 1.40361 0.701807 0.712367i \(-0.252377\pi\)
0.701807 + 0.712367i \(0.252377\pi\)
\(252\) 0 0
\(253\) 960.000 0.238556
\(254\) 0 0
\(255\) −4953.08 −1.21637
\(256\) 0 0
\(257\) 1500.93 0.364302 0.182151 0.983271i \(-0.441694\pi\)
0.182151 + 0.983271i \(0.441694\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −10126.0 −2.40147
\(262\) 0 0
\(263\) 400.000 0.0937835 0.0468917 0.998900i \(-0.485068\pi\)
0.0468917 + 0.998900i \(0.485068\pi\)
\(264\) 0 0
\(265\) −581.612 −0.134823
\(266\) 0 0
\(267\) −14080.0 −3.22727
\(268\) 0 0
\(269\) 272.044 0.0616610 0.0308305 0.999525i \(-0.490185\pi\)
0.0308305 + 0.999525i \(0.490185\pi\)
\(270\) 0 0
\(271\) 6904.29 1.54762 0.773812 0.633416i \(-0.218348\pi\)
0.773812 + 0.633416i \(0.218348\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 740.000 0.162268
\(276\) 0 0
\(277\) −6770.00 −1.46848 −0.734242 0.678888i \(-0.762462\pi\)
−0.734242 + 0.678888i \(0.762462\pi\)
\(278\) 0 0
\(279\) −12589.1 −2.70139
\(280\) 0 0
\(281\) 1878.00 0.398691 0.199345 0.979929i \(-0.436118\pi\)
0.199345 + 0.979929i \(0.436118\pi\)
\(282\) 0 0
\(283\) 384.614 0.0807878 0.0403939 0.999184i \(-0.487139\pi\)
0.0403939 + 0.999184i \(0.487139\pi\)
\(284\) 0 0
\(285\) 825.513 0.171576
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −1745.00 −0.355180
\(290\) 0 0
\(291\) −6160.00 −1.24091
\(292\) 0 0
\(293\) 3742.95 0.746299 0.373149 0.927771i \(-0.378278\pi\)
0.373149 + 0.927771i \(0.378278\pi\)
\(294\) 0 0
\(295\) 6248.00 1.23313
\(296\) 0 0
\(297\) 6378.97 1.24628
\(298\) 0 0
\(299\) 3151.96 0.609641
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1144.00 0.216901
\(304\) 0 0
\(305\) 2552.00 0.479105
\(306\) 0 0
\(307\) 722.324 0.134284 0.0671420 0.997743i \(-0.478612\pi\)
0.0671420 + 0.997743i \(0.478612\pi\)
\(308\) 0 0
\(309\) 12848.0 2.36536
\(310\) 0 0
\(311\) 7279.53 1.32728 0.663640 0.748052i \(-0.269011\pi\)
0.663640 + 0.748052i \(0.269011\pi\)
\(312\) 0 0
\(313\) −1519.69 −0.274435 −0.137218 0.990541i \(-0.543816\pi\)
−0.137218 + 0.990541i \(0.543816\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2358.00 0.417787 0.208893 0.977938i \(-0.433014\pi\)
0.208893 + 0.977938i \(0.433014\pi\)
\(318\) 0 0
\(319\) 3320.00 0.582709
\(320\) 0 0
\(321\) −2439.02 −0.424089
\(322\) 0 0
\(323\) −528.000 −0.0909557
\(324\) 0 0
\(325\) 2429.64 0.414683
\(326\) 0 0
\(327\) −17654.7 −2.98565
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2372.00 −0.393888 −0.196944 0.980415i \(-0.563102\pi\)
−0.196944 + 0.980415i \(0.563102\pi\)
\(332\) 0 0
\(333\) −4758.00 −0.782993
\(334\) 0 0
\(335\) 5440.88 0.887365
\(336\) 0 0
\(337\) −250.000 −0.0404106 −0.0202053 0.999796i \(-0.506432\pi\)
−0.0202053 + 0.999796i \(0.506432\pi\)
\(338\) 0 0
\(339\) 12063.7 1.93278
\(340\) 0 0
\(341\) 4127.57 0.655485
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −4224.00 −0.659167
\(346\) 0 0
\(347\) −9540.00 −1.47589 −0.737945 0.674861i \(-0.764204\pi\)
−0.737945 + 0.674861i \(0.764204\pi\)
\(348\) 0 0
\(349\) 5712.93 0.876235 0.438117 0.898918i \(-0.355645\pi\)
0.438117 + 0.898918i \(0.355645\pi\)
\(350\) 0 0
\(351\) 20944.0 3.18492
\(352\) 0 0
\(353\) −4390.23 −0.661950 −0.330975 0.943640i \(-0.607378\pi\)
−0.330975 + 0.943640i \(0.607378\pi\)
\(354\) 0 0
\(355\) −5103.17 −0.762953
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1840.00 −0.270506 −0.135253 0.990811i \(-0.543185\pi\)
−0.135253 + 0.990811i \(0.543185\pi\)
\(360\) 0 0
\(361\) −6771.00 −0.987170
\(362\) 0 0
\(363\) 8733.55 1.26279
\(364\) 0 0
\(365\) −5632.00 −0.807650
\(366\) 0 0
\(367\) −2964.34 −0.421628 −0.210814 0.977526i \(-0.567611\pi\)
−0.210814 + 0.977526i \(0.567611\pi\)
\(368\) 0 0
\(369\) −24033.7 −3.39063
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 3982.00 0.552762 0.276381 0.961048i \(-0.410865\pi\)
0.276381 + 0.961048i \(0.410865\pi\)
\(374\) 0 0
\(375\) −14256.0 −1.96314
\(376\) 0 0
\(377\) 10900.5 1.48914
\(378\) 0 0
\(379\) −2676.00 −0.362683 −0.181342 0.983420i \(-0.558044\pi\)
−0.181342 + 0.983420i \(0.558044\pi\)
\(380\) 0 0
\(381\) 21688.5 2.91636
\(382\) 0 0
\(383\) 7035.62 0.938652 0.469326 0.883025i \(-0.344497\pi\)
0.469326 + 0.883025i \(0.344497\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −26596.0 −3.49341
\(388\) 0 0
\(389\) 8658.00 1.12848 0.564239 0.825611i \(-0.309170\pi\)
0.564239 + 0.825611i \(0.309170\pi\)
\(390\) 0 0
\(391\) 2701.68 0.349437
\(392\) 0 0
\(393\) 2376.00 0.304970
\(394\) 0 0
\(395\) −6378.97 −0.812558
\(396\) 0 0
\(397\) 9052.50 1.14441 0.572207 0.820109i \(-0.306088\pi\)
0.572207 + 0.820109i \(0.306088\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5706.00 −0.710584 −0.355292 0.934755i \(-0.615619\pi\)
−0.355292 + 0.934755i \(0.615619\pi\)
\(402\) 0 0
\(403\) 13552.0 1.67512
\(404\) 0 0
\(405\) −12617.2 −1.54804
\(406\) 0 0
\(407\) 1560.00 0.189991
\(408\) 0 0
\(409\) −2420.25 −0.292601 −0.146301 0.989240i \(-0.546737\pi\)
−0.146301 + 0.989240i \(0.546737\pi\)
\(410\) 0 0
\(411\) 10450.2 1.25419
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −1848.00 −0.218590
\(416\) 0 0
\(417\) −12936.0 −1.51913
\(418\) 0 0
\(419\) −1510.31 −0.176095 −0.0880473 0.996116i \(-0.528063\pi\)
−0.0880473 + 0.996116i \(0.528063\pi\)
\(420\) 0 0
\(421\) −16770.0 −1.94138 −0.970689 0.240341i \(-0.922741\pi\)
−0.970689 + 0.240341i \(0.922741\pi\)
\(422\) 0 0
\(423\) 12589.1 1.44705
\(424\) 0 0
\(425\) 2082.54 0.237690
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −12320.0 −1.38652
\(430\) 0 0
\(431\) −1336.00 −0.149311 −0.0746553 0.997209i \(-0.523786\pi\)
−0.0746553 + 0.997209i \(0.523786\pi\)
\(432\) 0 0
\(433\) 11163.2 1.23896 0.619479 0.785013i \(-0.287344\pi\)
0.619479 + 0.785013i \(0.287344\pi\)
\(434\) 0 0
\(435\) −14608.0 −1.61011
\(436\) 0 0
\(437\) −450.280 −0.0492902
\(438\) 0 0
\(439\) −3602.24 −0.391630 −0.195815 0.980641i \(-0.562735\pi\)
−0.195815 + 0.980641i \(0.562735\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6348.00 −0.680818 −0.340409 0.940277i \(-0.610566\pi\)
−0.340409 + 0.940277i \(0.610566\pi\)
\(444\) 0 0
\(445\) −14080.0 −1.49990
\(446\) 0 0
\(447\) 8874.27 0.939012
\(448\) 0 0
\(449\) 7170.00 0.753615 0.376808 0.926292i \(-0.377022\pi\)
0.376808 + 0.926292i \(0.377022\pi\)
\(450\) 0 0
\(451\) 7879.90 0.822727
\(452\) 0 0
\(453\) 7804.85 0.809501
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6866.00 0.702796 0.351398 0.936226i \(-0.385706\pi\)
0.351398 + 0.936226i \(0.385706\pi\)
\(458\) 0 0
\(459\) 17952.0 1.82555
\(460\) 0 0
\(461\) −1378.98 −0.139318 −0.0696590 0.997571i \(-0.522191\pi\)
−0.0696590 + 0.997571i \(0.522191\pi\)
\(462\) 0 0
\(463\) −2648.00 −0.265795 −0.132897 0.991130i \(-0.542428\pi\)
−0.132897 + 0.991130i \(0.542428\pi\)
\(464\) 0 0
\(465\) −18161.3 −1.81120
\(466\) 0 0
\(467\) −12335.8 −1.22234 −0.611170 0.791500i \(-0.709301\pi\)
−0.611170 + 0.791500i \(0.709301\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 27016.0 2.64295
\(472\) 0 0
\(473\) 8720.00 0.847666
\(474\) 0 0
\(475\) −347.091 −0.0335276
\(476\) 0 0
\(477\) 3782.00 0.363031
\(478\) 0 0
\(479\) −13339.5 −1.27244 −0.636221 0.771507i \(-0.719503\pi\)
−0.636221 + 0.771507i \(0.719503\pi\)
\(480\) 0 0
\(481\) 5121.93 0.485530
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6160.00 −0.576724
\(486\) 0 0
\(487\) −13936.0 −1.29672 −0.648358 0.761336i \(-0.724544\pi\)
−0.648358 + 0.761336i \(0.724544\pi\)
\(488\) 0 0
\(489\) 5966.21 0.551741
\(490\) 0 0
\(491\) 12276.0 1.12833 0.564163 0.825663i \(-0.309199\pi\)
0.564163 + 0.825663i \(0.309199\pi\)
\(492\) 0 0
\(493\) 9343.31 0.853553
\(494\) 0 0
\(495\) 11444.6 1.03919
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2220.00 0.199160 0.0995800 0.995030i \(-0.468250\pi\)
0.0995800 + 0.995030i \(0.468250\pi\)
\(500\) 0 0
\(501\) 6160.00 0.549318
\(502\) 0 0
\(503\) −11294.5 −1.00119 −0.500594 0.865682i \(-0.666885\pi\)
−0.500594 + 0.865682i \(0.666885\pi\)
\(504\) 0 0
\(505\) 1144.00 0.100807
\(506\) 0 0
\(507\) −19840.5 −1.73796
\(508\) 0 0
\(509\) 15881.7 1.38300 0.691499 0.722377i \(-0.256951\pi\)
0.691499 + 0.722377i \(0.256951\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2992.00 −0.257505
\(514\) 0 0
\(515\) 12848.0 1.09932
\(516\) 0 0
\(517\) −4127.57 −0.351122
\(518\) 0 0
\(519\) 6248.00 0.528433
\(520\) 0 0
\(521\) −11613.5 −0.976575 −0.488287 0.872683i \(-0.662378\pi\)
−0.488287 + 0.872683i \(0.662378\pi\)
\(522\) 0 0
\(523\) 12617.2 1.05490 0.527450 0.849586i \(-0.323148\pi\)
0.527450 + 0.849586i \(0.323148\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 11616.0 0.960154
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) −40628.4 −3.32038
\(532\) 0 0
\(533\) 25872.0 2.10252
\(534\) 0 0
\(535\) −2439.02 −0.197099
\(536\) 0 0
\(537\) −30281.3 −2.43340
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1798.00 0.142887 0.0714437 0.997445i \(-0.477239\pi\)
0.0714437 + 0.997445i \(0.477239\pi\)
\(542\) 0 0
\(543\) −26488.0 −2.09339
\(544\) 0 0
\(545\) −17654.7 −1.38761
\(546\) 0 0
\(547\) −1276.00 −0.0997401 −0.0498700 0.998756i \(-0.515881\pi\)
−0.0498700 + 0.998756i \(0.515881\pi\)
\(548\) 0 0
\(549\) −16594.7 −1.29006
\(550\) 0 0
\(551\) −1557.22 −0.120399
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6864.00 −0.524974
\(556\) 0 0
\(557\) 2694.00 0.204934 0.102467 0.994736i \(-0.467326\pi\)
0.102467 + 0.994736i \(0.467326\pi\)
\(558\) 0 0
\(559\) 28630.3 2.16625
\(560\) 0 0
\(561\) −10560.0 −0.794730
\(562\) 0 0
\(563\) −15769.2 −1.18045 −0.590223 0.807240i \(-0.700960\pi\)
−0.590223 + 0.807240i \(0.700960\pi\)
\(564\) 0 0
\(565\) 12063.7 0.898276
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12606.0 0.928772 0.464386 0.885633i \(-0.346275\pi\)
0.464386 + 0.885633i \(0.346275\pi\)
\(570\) 0 0
\(571\) −6852.00 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) −20037.5 −1.46087
\(574\) 0 0
\(575\) 1776.00 0.128808
\(576\) 0 0
\(577\) −14371.4 −1.03690 −0.518449 0.855108i \(-0.673491\pi\)
−0.518449 + 0.855108i \(0.673491\pi\)
\(578\) 0 0
\(579\) −15553.4 −1.11637
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1240.00 −0.0880884
\(584\) 0 0
\(585\) 37576.0 2.65569
\(586\) 0 0
\(587\) 18977.4 1.33438 0.667191 0.744887i \(-0.267497\pi\)
0.667191 + 0.744887i \(0.267497\pi\)
\(588\) 0 0
\(589\) −1936.00 −0.135435
\(590\) 0 0
\(591\) 9174.45 0.638556
\(592\) 0 0
\(593\) −8217.61 −0.569067 −0.284534 0.958666i \(-0.591839\pi\)
−0.284534 + 0.958666i \(0.591839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 46288.0 3.17327
\(598\) 0 0
\(599\) 19104.0 1.30312 0.651559 0.758598i \(-0.274115\pi\)
0.651559 + 0.758598i \(0.274115\pi\)
\(600\) 0 0
\(601\) −21538.4 −1.46185 −0.730923 0.682460i \(-0.760910\pi\)
−0.730923 + 0.682460i \(0.760910\pi\)
\(602\) 0 0
\(603\) −35380.0 −2.38936
\(604\) 0 0
\(605\) 8733.55 0.586892
\(606\) 0 0
\(607\) 13733.5 0.918331 0.459166 0.888351i \(-0.348148\pi\)
0.459166 + 0.888351i \(0.348148\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13552.0 −0.897308
\(612\) 0 0
\(613\) 28034.0 1.84712 0.923558 0.383458i \(-0.125267\pi\)
0.923558 + 0.383458i \(0.125267\pi\)
\(614\) 0 0
\(615\) −34671.6 −2.27332
\(616\) 0 0
\(617\) −8258.00 −0.538824 −0.269412 0.963025i \(-0.586829\pi\)
−0.269412 + 0.963025i \(0.586829\pi\)
\(618\) 0 0
\(619\) −5131.31 −0.333191 −0.166595 0.986025i \(-0.553277\pi\)
−0.166595 + 0.986025i \(0.553277\pi\)
\(620\) 0 0
\(621\) 15309.5 0.989291
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −9631.00 −0.616384
\(626\) 0 0
\(627\) 1760.00 0.112101
\(628\) 0 0
\(629\) 4390.23 0.278299
\(630\) 0 0
\(631\) −912.000 −0.0575375 −0.0287687 0.999586i \(-0.509159\pi\)
−0.0287687 + 0.999586i \(0.509159\pi\)
\(632\) 0 0
\(633\) 14596.6 0.916527
\(634\) 0 0
\(635\) 21688.5 1.35540
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 33184.0 2.05436
\(640\) 0 0
\(641\) −890.000 −0.0548407 −0.0274203 0.999624i \(-0.508729\pi\)
−0.0274203 + 0.999624i \(0.508729\pi\)
\(642\) 0 0
\(643\) −29352.6 −1.80024 −0.900120 0.435642i \(-0.856521\pi\)
−0.900120 + 0.435642i \(0.856521\pi\)
\(644\) 0 0
\(645\) −38368.0 −2.34223
\(646\) 0 0
\(647\) 11876.1 0.721637 0.360818 0.932636i \(-0.382497\pi\)
0.360818 + 0.932636i \(0.382497\pi\)
\(648\) 0 0
\(649\) 13320.8 0.805680
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21526.0 −1.29001 −0.645006 0.764178i \(-0.723145\pi\)
−0.645006 + 0.764178i \(0.723145\pi\)
\(654\) 0 0
\(655\) 2376.00 0.141737
\(656\) 0 0
\(657\) 36622.8 2.17472
\(658\) 0 0
\(659\) −23452.0 −1.38628 −0.693141 0.720802i \(-0.743774\pi\)
−0.693141 + 0.720802i \(0.743774\pi\)
\(660\) 0 0
\(661\) 26669.7 1.56934 0.784668 0.619916i \(-0.212833\pi\)
0.784668 + 0.619916i \(0.212833\pi\)
\(662\) 0 0
\(663\) −34671.6 −2.03097
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7968.00 0.462552
\(668\) 0 0
\(669\) −27104.0 −1.56637
\(670\) 0 0
\(671\) 5440.88 0.313030
\(672\) 0 0
\(673\) −13858.0 −0.793739 −0.396870 0.917875i \(-0.629904\pi\)
−0.396870 + 0.917875i \(0.629904\pi\)
\(674\) 0 0
\(675\) 11801.1 0.672924
\(676\) 0 0
\(677\) −32448.3 −1.84208 −0.921041 0.389466i \(-0.872660\pi\)
−0.921041 + 0.389466i \(0.872660\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 18568.0 1.04483
\(682\) 0 0
\(683\) 27812.0 1.55812 0.779060 0.626949i \(-0.215696\pi\)
0.779060 + 0.626949i \(0.215696\pi\)
\(684\) 0 0
\(685\) 10450.2 0.582895
\(686\) 0 0
\(687\) 25960.0 1.44168
\(688\) 0 0
\(689\) −4071.28 −0.225114
\(690\) 0 0
\(691\) −1303.94 −0.0717859 −0.0358929 0.999356i \(-0.511428\pi\)
−0.0358929 + 0.999356i \(0.511428\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −12936.0 −0.706029
\(696\) 0 0
\(697\) 22176.0 1.20513
\(698\) 0 0
\(699\) 60881.6 3.29435
\(700\) 0 0
\(701\) 22906.0 1.23416 0.617081 0.786900i \(-0.288315\pi\)
0.617081 + 0.786900i \(0.288315\pi\)
\(702\) 0 0
\(703\) −731.705 −0.0392557
\(704\) 0 0
\(705\) 18161.3 0.970204
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −15086.0 −0.799107 −0.399553 0.916710i \(-0.630835\pi\)
−0.399553 + 0.916710i \(0.630835\pi\)
\(710\) 0 0
\(711\) 41480.0 2.18793
\(712\) 0 0
\(713\) 9906.16 0.520321
\(714\) 0 0
\(715\) −12320.0 −0.644394
\(716\) 0 0
\(717\) −40300.1 −2.09907
\(718\) 0 0
\(719\) −20544.0 −1.06559 −0.532797 0.846243i \(-0.678859\pi\)
−0.532797 + 0.846243i \(0.678859\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 42416.0 2.18184
\(724\) 0 0
\(725\) 6142.00 0.314632
\(726\) 0 0
\(727\) −7223.24 −0.368494 −0.184247 0.982880i \(-0.558985\pi\)
−0.184247 + 0.982880i \(0.558985\pi\)
\(728\) 0 0
\(729\) 1261.00 0.0640654
\(730\) 0 0
\(731\) 24540.3 1.24166
\(732\) 0 0
\(733\) −29427.7 −1.48286 −0.741430 0.671031i \(-0.765852\pi\)
−0.741430 + 0.671031i \(0.765852\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 11600.0 0.579771
\(738\) 0 0
\(739\) −32668.0 −1.62613 −0.813066 0.582171i \(-0.802203\pi\)
−0.813066 + 0.582171i \(0.802203\pi\)
\(740\) 0 0
\(741\) 5778.59 0.286480
\(742\) 0 0
\(743\) 37056.0 1.82968 0.914840 0.403816i \(-0.132316\pi\)
0.914840 + 0.403816i \(0.132316\pi\)
\(744\) 0 0
\(745\) 8874.27 0.436413
\(746\) 0 0
\(747\) 12016.8 0.588586
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 19608.0 0.952738 0.476369 0.879246i \(-0.341953\pi\)
0.476369 + 0.879246i \(0.341953\pi\)
\(752\) 0 0
\(753\) −52360.0 −2.53400
\(754\) 0 0
\(755\) 7804.85 0.376222
\(756\) 0 0
\(757\) 19378.0 0.930390 0.465195 0.885208i \(-0.345984\pi\)
0.465195 + 0.885208i \(0.345984\pi\)
\(758\) 0 0
\(759\) −9005.60 −0.430675
\(760\) 0 0
\(761\) 13977.4 0.665810 0.332905 0.942960i \(-0.391971\pi\)
0.332905 + 0.942960i \(0.391971\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 32208.0 1.52220
\(766\) 0 0
\(767\) 43736.0 2.05895
\(768\) 0 0
\(769\) −8536.56 −0.400307 −0.200154 0.979765i \(-0.564144\pi\)
−0.200154 + 0.979765i \(0.564144\pi\)
\(770\) 0 0
\(771\) −14080.0 −0.657690
\(772\) 0 0
\(773\) 29296.3 1.36315 0.681576 0.731748i \(-0.261295\pi\)
0.681576 + 0.731748i \(0.261295\pi\)
\(774\) 0 0
\(775\) 7636.00 0.353927
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −3696.00 −0.169991
\(780\) 0 0
\(781\) −10880.0 −0.498485
\(782\) 0 0
\(783\) 52945.4 2.41649
\(784\) 0 0
\(785\) 27016.0 1.22833
\(786\) 0 0
\(787\) 13780.4 0.624167 0.312084 0.950055i \(-0.398973\pi\)
0.312084 + 0.950055i \(0.398973\pi\)
\(788\) 0 0
\(789\) −3752.33 −0.169311
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 17864.0 0.799961
\(794\) 0 0
\(795\) 5456.00 0.243402
\(796\) 0 0
\(797\) 34868.6 1.54970 0.774848 0.632148i \(-0.217826\pi\)
0.774848 + 0.632148i \(0.217826\pi\)
\(798\) 0 0
\(799\) −11616.0 −0.514324
\(800\) 0 0
\(801\) 91556.9 4.03871
\(802\) 0 0
\(803\) −12007.5 −0.527689
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2552.00 −0.111319
\(808\) 0 0
\(809\) 14034.0 0.609900 0.304950 0.952368i \(-0.401360\pi\)
0.304950 + 0.952368i \(0.401360\pi\)
\(810\) 0 0
\(811\) −6632.25 −0.287164 −0.143582 0.989638i \(-0.545862\pi\)
−0.143582 + 0.989638i \(0.545862\pi\)
\(812\) 0 0
\(813\) −64768.0 −2.79399
\(814\) 0 0
\(815\) 5966.21 0.256426
\(816\) 0 0
\(817\) −4090.04 −0.175144
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 28622.0 1.21670 0.608352 0.793667i \(-0.291831\pi\)
0.608352 + 0.793667i \(0.291831\pi\)
\(822\) 0 0
\(823\) −24688.0 −1.04565 −0.522825 0.852440i \(-0.675122\pi\)
−0.522825 + 0.852440i \(0.675122\pi\)
\(824\) 0 0
\(825\) −6941.82 −0.292949
\(826\) 0 0
\(827\) 30756.0 1.29322 0.646609 0.762822i \(-0.276187\pi\)
0.646609 + 0.762822i \(0.276187\pi\)
\(828\) 0 0
\(829\) −23236.3 −0.973499 −0.486750 0.873542i \(-0.661818\pi\)
−0.486750 + 0.873542i \(0.661818\pi\)
\(830\) 0 0
\(831\) 63508.2 2.65111
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 6160.00 0.255300
\(836\) 0 0
\(837\) 65824.0 2.71829
\(838\) 0 0
\(839\) −24033.7 −0.988957 −0.494479 0.869190i \(-0.664641\pi\)
−0.494479 + 0.869190i \(0.664641\pi\)
\(840\) 0 0
\(841\) 3167.00 0.129854
\(842\) 0 0
\(843\) −17617.2 −0.719773
\(844\) 0 0
\(845\) −19840.5 −0.807731
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −3608.00 −0.145850
\(850\) 0 0
\(851\) 3744.00 0.150814
\(852\) 0 0
\(853\) 23574.0 0.946260 0.473130 0.880993i \(-0.343124\pi\)
0.473130 + 0.880993i \(0.343124\pi\)
\(854\) 0 0
\(855\) −5368.00 −0.214715
\(856\) 0 0
\(857\) −24484.0 −0.975912 −0.487956 0.872868i \(-0.662257\pi\)
−0.487956 + 0.872868i \(0.662257\pi\)
\(858\) 0 0
\(859\) −32954.9 −1.30897 −0.654485 0.756075i \(-0.727115\pi\)
−0.654485 + 0.756075i \(0.727115\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −40872.0 −1.61217 −0.806083 0.591803i \(-0.798416\pi\)
−0.806083 + 0.591803i \(0.798416\pi\)
\(864\) 0 0
\(865\) 6248.00 0.245593
\(866\) 0 0
\(867\) 16369.6 0.641222
\(868\) 0 0
\(869\) −13600.0 −0.530896
\(870\) 0 0
\(871\) 38086.2 1.48163
\(872\) 0 0
\(873\) 40056.2 1.55292
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −12006.0 −0.462273 −0.231137 0.972921i \(-0.574244\pi\)
−0.231137 + 0.972921i \(0.574244\pi\)
\(878\) 0 0
\(879\) −35112.0 −1.34732
\(880\) 0 0
\(881\) −35722.2 −1.36607 −0.683037 0.730383i \(-0.739341\pi\)
−0.683037 + 0.730383i \(0.739341\pi\)
\(882\) 0 0
\(883\) −19588.0 −0.746533 −0.373267 0.927724i \(-0.621762\pi\)
−0.373267 + 0.927724i \(0.621762\pi\)
\(884\) 0 0
\(885\) −58611.4 −2.22622
\(886\) 0 0
\(887\) −40243.8 −1.52340 −0.761699 0.647931i \(-0.775634\pi\)
−0.761699 + 0.647931i \(0.775634\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −26900.0 −1.01143
\(892\) 0 0
\(893\) 1936.00 0.0725485
\(894\) 0 0
\(895\) −30281.3 −1.13094
\(896\) 0 0
\(897\) −29568.0 −1.10061
\(898\) 0 0
\(899\) 34258.8 1.27096
\(900\) 0 0
\(901\) −3489.67 −0.129032
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −26488.0 −0.972918
\(906\) 0 0
\(907\) −15868.0 −0.580913 −0.290457 0.956888i \(-0.593807\pi\)
−0.290457 + 0.956888i \(0.593807\pi\)
\(908\) 0 0
\(909\) −7439.00 −0.271437
\(910\) 0 0
\(911\) −39832.0 −1.44862 −0.724310 0.689474i \(-0.757842\pi\)
−0.724310 + 0.689474i \(0.757842\pi\)
\(912\) 0 0
\(913\) −3939.95 −0.142818
\(914\) 0 0
\(915\) −23939.9 −0.864949
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 30528.0 1.09578 0.547892 0.836549i \(-0.315430\pi\)
0.547892 + 0.836549i \(0.315430\pi\)
\(920\) 0 0
\(921\) −6776.00 −0.242429
\(922\) 0 0
\(923\) −35722.2 −1.27390
\(924\) 0 0
\(925\) 2886.00 0.102585
\(926\) 0 0
\(927\) −83545.7 −2.96009
\(928\) 0 0
\(929\) 16604.1 0.586396 0.293198 0.956052i \(-0.405280\pi\)
0.293198 + 0.956052i \(0.405280\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −68288.0 −2.39619
\(934\) 0 0
\(935\) −10560.0 −0.369357
\(936\) 0 0
\(937\) −29943.6 −1.04399 −0.521993 0.852950i \(-0.674811\pi\)
−0.521993 + 0.852950i \(0.674811\pi\)
\(938\) 0 0
\(939\) 14256.0 0.495449
\(940\) 0 0
\(941\) −5375.22 −0.186214 −0.0931068 0.995656i \(-0.529680\pi\)
−0.0931068 + 0.995656i \(0.529680\pi\)
\(942\) 0 0
\(943\) 18911.8 0.653077
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −45212.0 −1.55142 −0.775709 0.631091i \(-0.782607\pi\)
−0.775709 + 0.631091i \(0.782607\pi\)
\(948\) 0 0
\(949\) −39424.0 −1.34853
\(950\) 0 0
\(951\) −22120.0 −0.754248
\(952\) 0 0
\(953\) 34218.0 1.16310 0.581548 0.813512i \(-0.302447\pi\)
0.581548 + 0.813512i \(0.302447\pi\)
\(954\) 0 0
\(955\) −20037.5 −0.678950
\(956\) 0 0
\(957\) −31144.4 −1.05199
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 12801.0 0.429694
\(962\) 0 0
\(963\) 15860.0 0.530718
\(964\) 0 0
\(965\) −15553.4 −0.518842
\(966\) 0 0
\(967\) −14464.0 −0.481004 −0.240502 0.970649i \(-0.577312\pi\)
−0.240502 + 0.970649i \(0.577312\pi\)
\(968\) 0 0
\(969\) 4953.08 0.164206
\(970\) 0 0
\(971\) 37832.9 1.25038 0.625188 0.780474i \(-0.285022\pi\)
0.625188 + 0.780474i \(0.285022\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −22792.0 −0.748644
\(976\) 0 0
\(977\) 42062.0 1.37736 0.688681 0.725065i \(-0.258190\pi\)
0.688681 + 0.725065i \(0.258190\pi\)
\(978\) 0 0
\(979\) −30018.7 −0.979980
\(980\) 0 0
\(981\) 114802. 3.73634
\(982\) 0 0
\(983\) −43020.5 −1.39587 −0.697935 0.716161i \(-0.745898\pi\)
−0.697935 + 0.716161i \(0.745898\pi\)
\(984\) 0 0
\(985\) 9174.45 0.296774
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 20928.0 0.672873
\(990\) 0 0
\(991\) −21272.0 −0.681864 −0.340932 0.940088i \(-0.610743\pi\)
−0.340932 + 0.940088i \(0.610743\pi\)
\(992\) 0 0
\(993\) 22251.3 0.711102
\(994\) 0 0
\(995\) 46288.0 1.47480
\(996\) 0 0
\(997\) −121.951 −0.00387384 −0.00193692 0.999998i \(-0.500617\pi\)
−0.00193692 + 0.999998i \(0.500617\pi\)
\(998\) 0 0
\(999\) 24878.0 0.787892
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 784.4.a.z.1.1 2
4.3 odd 2 98.4.a.h.1.2 yes 2
7.6 odd 2 inner 784.4.a.z.1.2 2
12.11 even 2 882.4.a.w.1.2 2
20.19 odd 2 2450.4.a.bs.1.1 2
28.3 even 6 98.4.c.g.79.2 4
28.11 odd 6 98.4.c.g.79.1 4
28.19 even 6 98.4.c.g.67.2 4
28.23 odd 6 98.4.c.g.67.1 4
28.27 even 2 98.4.a.h.1.1 2
84.11 even 6 882.4.g.bi.667.1 4
84.23 even 6 882.4.g.bi.361.1 4
84.47 odd 6 882.4.g.bi.361.2 4
84.59 odd 6 882.4.g.bi.667.2 4
84.83 odd 2 882.4.a.w.1.1 2
140.139 even 2 2450.4.a.bs.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
98.4.a.h.1.1 2 28.27 even 2
98.4.a.h.1.2 yes 2 4.3 odd 2
98.4.c.g.67.1 4 28.23 odd 6
98.4.c.g.67.2 4 28.19 even 6
98.4.c.g.79.1 4 28.11 odd 6
98.4.c.g.79.2 4 28.3 even 6
784.4.a.z.1.1 2 1.1 even 1 trivial
784.4.a.z.1.2 2 7.6 odd 2 inner
882.4.a.w.1.1 2 84.83 odd 2
882.4.a.w.1.2 2 12.11 even 2
882.4.g.bi.361.1 4 84.23 even 6
882.4.g.bi.361.2 4 84.47 odd 6
882.4.g.bi.667.1 4 84.11 even 6
882.4.g.bi.667.2 4 84.59 odd 6
2450.4.a.bs.1.1 2 20.19 odd 2
2450.4.a.bs.1.2 2 140.139 even 2