Properties

Label 9200.2.a.cz.1.2
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.78665\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.78665 q^{3} -1.75578 q^{7} +0.192116 q^{9} +O(q^{10})\) \(q-1.78665 q^{3} -1.75578 q^{7} +0.192116 q^{9} +4.77574 q^{11} +1.72967 q^{13} -7.81453 q^{17} +2.43970 q^{19} +3.13696 q^{21} +1.00000 q^{23} +5.01670 q^{27} +7.86235 q^{29} -6.14217 q^{31} -8.53258 q^{33} -6.83324 q^{37} -3.09031 q^{39} -2.50416 q^{41} +3.26755 q^{43} -8.46487 q^{47} -3.91724 q^{49} +13.9618 q^{51} -2.76559 q^{53} -4.35889 q^{57} -1.91706 q^{59} -3.50364 q^{61} -0.337313 q^{63} +12.7649 q^{67} -1.78665 q^{69} +13.3973 q^{71} +0.0111737 q^{73} -8.38515 q^{77} +16.6960 q^{79} -9.53944 q^{81} +2.64145 q^{83} -14.0473 q^{87} -13.1729 q^{89} -3.03692 q^{91} +10.9739 q^{93} +15.8568 q^{97} +0.917494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + 7q^{11} - 7q^{13} + 7q^{19} - 6q^{21} + 7q^{23} - 11q^{29} + 10q^{31} - 19q^{33} - 19q^{37} + 24q^{39} - 16q^{41} - 6q^{43} - 6q^{47} - 17q^{49} + 7q^{51} - 15q^{53} - 8q^{57} + 11q^{59} + 5q^{61} - 13q^{63} - 9q^{67} - 3q^{69} + 14q^{71} - 10q^{73} - 6q^{77} + 32q^{79} - 5q^{81} - q^{83} - 10q^{87} - 24q^{89} + 7q^{91} - 26q^{93} + 7q^{97} + 61q^{99} + O(q^{100}) \)

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
\(3\) −1.78665 −1.03152 −0.515761 0.856732i \(-0.672491\pi\)
−0.515761 + 0.856732i \(0.672491\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.75578 −0.663622 −0.331811 0.943346i \(-0.607660\pi\)
−0.331811 + 0.943346i \(0.607660\pi\)
\(8\) 0 0
\(9\) 0.192116 0.0640385
\(10\) 0 0
\(11\) 4.77574 1.43994 0.719970 0.694005i \(-0.244155\pi\)
0.719970 + 0.694005i \(0.244155\pi\)
\(12\) 0 0
\(13\) 1.72967 0.479724 0.239862 0.970807i \(-0.422898\pi\)
0.239862 + 0.970807i \(0.422898\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.81453 −1.89530 −0.947651 0.319309i \(-0.896549\pi\)
−0.947651 + 0.319309i \(0.896549\pi\)
\(18\) 0 0
\(19\) 2.43970 0.559706 0.279853 0.960043i \(-0.409714\pi\)
0.279853 + 0.960043i \(0.409714\pi\)
\(20\) 0 0
\(21\) 3.13696 0.684541
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.01670 0.965465
\(28\) 0 0
\(29\) 7.86235 1.46000 0.730001 0.683446i \(-0.239520\pi\)
0.730001 + 0.683446i \(0.239520\pi\)
\(30\) 0 0
\(31\) −6.14217 −1.10317 −0.551583 0.834120i \(-0.685976\pi\)
−0.551583 + 0.834120i \(0.685976\pi\)
\(32\) 0 0
\(33\) −8.53258 −1.48533
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.83324 −1.12338 −0.561689 0.827349i \(-0.689848\pi\)
−0.561689 + 0.827349i \(0.689848\pi\)
\(38\) 0 0
\(39\) −3.09031 −0.494846
\(40\) 0 0
\(41\) −2.50416 −0.391084 −0.195542 0.980695i \(-0.562647\pi\)
−0.195542 + 0.980695i \(0.562647\pi\)
\(42\) 0 0
\(43\) 3.26755 0.498297 0.249148 0.968465i \(-0.419849\pi\)
0.249148 + 0.968465i \(0.419849\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.46487 −1.23473 −0.617364 0.786678i \(-0.711799\pi\)
−0.617364 + 0.786678i \(0.711799\pi\)
\(48\) 0 0
\(49\) −3.91724 −0.559605
\(50\) 0 0
\(51\) 13.9618 1.95505
\(52\) 0 0
\(53\) −2.76559 −0.379883 −0.189942 0.981795i \(-0.560830\pi\)
−0.189942 + 0.981795i \(0.560830\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.35889 −0.577349
\(58\) 0 0
\(59\) −1.91706 −0.249580 −0.124790 0.992183i \(-0.539826\pi\)
−0.124790 + 0.992183i \(0.539826\pi\)
\(60\) 0 0
\(61\) −3.50364 −0.448595 −0.224297 0.974521i \(-0.572009\pi\)
−0.224297 + 0.974521i \(0.572009\pi\)
\(62\) 0 0
\(63\) −0.337313 −0.0424974
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.7649 1.55948 0.779741 0.626102i \(-0.215351\pi\)
0.779741 + 0.626102i \(0.215351\pi\)
\(68\) 0 0
\(69\) −1.78665 −0.215087
\(70\) 0 0
\(71\) 13.3973 1.58997 0.794984 0.606630i \(-0.207479\pi\)
0.794984 + 0.606630i \(0.207479\pi\)
\(72\) 0 0
\(73\) 0.0111737 0.00130778 0.000653890 1.00000i \(-0.499792\pi\)
0.000653890 1.00000i \(0.499792\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.38515 −0.955577
\(78\) 0 0
\(79\) 16.6960 1.87844 0.939222 0.343310i \(-0.111548\pi\)
0.939222 + 0.343310i \(0.111548\pi\)
\(80\) 0 0
\(81\) −9.53944 −1.05994
\(82\) 0 0
\(83\) 2.64145 0.289937 0.144969 0.989436i \(-0.453692\pi\)
0.144969 + 0.989436i \(0.453692\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −14.0473 −1.50602
\(88\) 0 0
\(89\) −13.1729 −1.39632 −0.698160 0.715942i \(-0.745998\pi\)
−0.698160 + 0.715942i \(0.745998\pi\)
\(90\) 0 0
\(91\) −3.03692 −0.318356
\(92\) 0 0
\(93\) 10.9739 1.13794
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 15.8568 1.61001 0.805005 0.593268i \(-0.202162\pi\)
0.805005 + 0.593268i \(0.202162\pi\)
\(98\) 0 0
\(99\) 0.917494 0.0922117
\(100\) 0 0
\(101\) 15.6987 1.56208 0.781040 0.624481i \(-0.214689\pi\)
0.781040 + 0.624481i \(0.214689\pi\)
\(102\) 0 0
\(103\) −8.37467 −0.825180 −0.412590 0.910917i \(-0.635376\pi\)
−0.412590 + 0.910917i \(0.635376\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.52262 0.630565 0.315283 0.948998i \(-0.397901\pi\)
0.315283 + 0.948998i \(0.397901\pi\)
\(108\) 0 0
\(109\) −8.11474 −0.777251 −0.388626 0.921396i \(-0.627050\pi\)
−0.388626 + 0.921396i \(0.627050\pi\)
\(110\) 0 0
\(111\) 12.2086 1.15879
\(112\) 0 0
\(113\) −12.9224 −1.21563 −0.607817 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.332296 0.0307208
\(118\) 0 0
\(119\) 13.7206 1.25776
\(120\) 0 0
\(121\) 11.8077 1.07343
\(122\) 0 0
\(123\) 4.47406 0.403412
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.05406 −0.625947 −0.312973 0.949762i \(-0.601325\pi\)
−0.312973 + 0.949762i \(0.601325\pi\)
\(128\) 0 0
\(129\) −5.83797 −0.514004
\(130\) 0 0
\(131\) 11.1585 0.974923 0.487461 0.873145i \(-0.337923\pi\)
0.487461 + 0.873145i \(0.337923\pi\)
\(132\) 0 0
\(133\) −4.28358 −0.371434
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.71462 0.231926 0.115963 0.993254i \(-0.463005\pi\)
0.115963 + 0.993254i \(0.463005\pi\)
\(138\) 0 0
\(139\) −13.0913 −1.11039 −0.555197 0.831719i \(-0.687357\pi\)
−0.555197 + 0.831719i \(0.687357\pi\)
\(140\) 0 0
\(141\) 15.1238 1.27365
\(142\) 0 0
\(143\) 8.26046 0.690774
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.99873 0.577245
\(148\) 0 0
\(149\) −12.0898 −0.990435 −0.495217 0.868769i \(-0.664912\pi\)
−0.495217 + 0.868769i \(0.664912\pi\)
\(150\) 0 0
\(151\) −14.9430 −1.21604 −0.608021 0.793921i \(-0.708036\pi\)
−0.608021 + 0.793921i \(0.708036\pi\)
\(152\) 0 0
\(153\) −1.50129 −0.121372
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 4.78395 0.381800 0.190900 0.981609i \(-0.438859\pi\)
0.190900 + 0.981609i \(0.438859\pi\)
\(158\) 0 0
\(159\) 4.94114 0.391858
\(160\) 0 0
\(161\) −1.75578 −0.138375
\(162\) 0 0
\(163\) −5.49063 −0.430059 −0.215030 0.976608i \(-0.568985\pi\)
−0.215030 + 0.976608i \(0.568985\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.26932 0.562517 0.281258 0.959632i \(-0.409248\pi\)
0.281258 + 0.959632i \(0.409248\pi\)
\(168\) 0 0
\(169\) −10.0082 −0.769865
\(170\) 0 0
\(171\) 0.468705 0.0358427
\(172\) 0 0
\(173\) −7.50892 −0.570893 −0.285446 0.958395i \(-0.592142\pi\)
−0.285446 + 0.958395i \(0.592142\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.42511 0.257447
\(178\) 0 0
\(179\) 5.73414 0.428590 0.214295 0.976769i \(-0.431255\pi\)
0.214295 + 0.976769i \(0.431255\pi\)
\(180\) 0 0
\(181\) 25.2262 1.87505 0.937523 0.347923i \(-0.113113\pi\)
0.937523 + 0.347923i \(0.113113\pi\)
\(182\) 0 0
\(183\) 6.25977 0.462736
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −37.3202 −2.72912
\(188\) 0 0
\(189\) −8.80823 −0.640704
\(190\) 0 0
\(191\) −3.63151 −0.262767 −0.131383 0.991332i \(-0.541942\pi\)
−0.131383 + 0.991332i \(0.541942\pi\)
\(192\) 0 0
\(193\) 21.7050 1.56236 0.781179 0.624307i \(-0.214619\pi\)
0.781179 + 0.624307i \(0.214619\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.26526 0.517628 0.258814 0.965927i \(-0.416668\pi\)
0.258814 + 0.965927i \(0.416668\pi\)
\(198\) 0 0
\(199\) −6.52705 −0.462690 −0.231345 0.972872i \(-0.574313\pi\)
−0.231345 + 0.972872i \(0.574313\pi\)
\(200\) 0 0
\(201\) −22.8064 −1.60864
\(202\) 0 0
\(203\) −13.8046 −0.968890
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.192116 0.0133530
\(208\) 0 0
\(209\) 11.6514 0.805944
\(210\) 0 0
\(211\) 22.7856 1.56863 0.784313 0.620365i \(-0.213016\pi\)
0.784313 + 0.620365i \(0.213016\pi\)
\(212\) 0 0
\(213\) −23.9363 −1.64009
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.7843 0.732086
\(218\) 0 0
\(219\) −0.0199634 −0.00134900
\(220\) 0 0
\(221\) −13.5165 −0.909221
\(222\) 0 0
\(223\) −6.86315 −0.459591 −0.229795 0.973239i \(-0.573806\pi\)
−0.229795 + 0.973239i \(0.573806\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.5001 −1.16152 −0.580761 0.814074i \(-0.697245\pi\)
−0.580761 + 0.814074i \(0.697245\pi\)
\(228\) 0 0
\(229\) −23.8643 −1.57700 −0.788498 0.615038i \(-0.789141\pi\)
−0.788498 + 0.615038i \(0.789141\pi\)
\(230\) 0 0
\(231\) 14.9813 0.985699
\(232\) 0 0
\(233\) −21.8957 −1.43444 −0.717218 0.696849i \(-0.754585\pi\)
−0.717218 + 0.696849i \(0.754585\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −29.8299 −1.93766
\(238\) 0 0
\(239\) 19.3443 1.25128 0.625639 0.780113i \(-0.284838\pi\)
0.625639 + 0.780113i \(0.284838\pi\)
\(240\) 0 0
\(241\) 11.4761 0.739240 0.369620 0.929183i \(-0.379488\pi\)
0.369620 + 0.929183i \(0.379488\pi\)
\(242\) 0 0
\(243\) 1.99352 0.127884
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 4.21988 0.268504
\(248\) 0 0
\(249\) −4.71935 −0.299077
\(250\) 0 0
\(251\) −17.0040 −1.07328 −0.536641 0.843811i \(-0.680307\pi\)
−0.536641 + 0.843811i \(0.680307\pi\)
\(252\) 0 0
\(253\) 4.77574 0.300248
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.6462 −0.913607 −0.456803 0.889568i \(-0.651006\pi\)
−0.456803 + 0.889568i \(0.651006\pi\)
\(258\) 0 0
\(259\) 11.9977 0.745499
\(260\) 0 0
\(261\) 1.51048 0.0934964
\(262\) 0 0
\(263\) −10.2641 −0.632912 −0.316456 0.948607i \(-0.602493\pi\)
−0.316456 + 0.948607i \(0.602493\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 23.5353 1.44034
\(268\) 0 0
\(269\) −2.61485 −0.159430 −0.0797150 0.996818i \(-0.525401\pi\)
−0.0797150 + 0.996818i \(0.525401\pi\)
\(270\) 0 0
\(271\) −9.87492 −0.599859 −0.299929 0.953961i \(-0.596963\pi\)
−0.299929 + 0.953961i \(0.596963\pi\)
\(272\) 0 0
\(273\) 5.42591 0.328391
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4.21949 −0.253525 −0.126762 0.991933i \(-0.540459\pi\)
−0.126762 + 0.991933i \(0.540459\pi\)
\(278\) 0 0
\(279\) −1.18001 −0.0706451
\(280\) 0 0
\(281\) −13.4058 −0.799724 −0.399862 0.916575i \(-0.630942\pi\)
−0.399862 + 0.916575i \(0.630942\pi\)
\(282\) 0 0
\(283\) 5.66084 0.336502 0.168251 0.985744i \(-0.446188\pi\)
0.168251 + 0.985744i \(0.446188\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.39676 0.259532
\(288\) 0 0
\(289\) 44.0668 2.59217
\(290\) 0 0
\(291\) −28.3305 −1.66076
\(292\) 0 0
\(293\) 5.70404 0.333233 0.166617 0.986022i \(-0.446716\pi\)
0.166617 + 0.986022i \(0.446716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 23.9585 1.39021
\(298\) 0 0
\(299\) 1.72967 0.100029
\(300\) 0 0
\(301\) −5.73710 −0.330681
\(302\) 0 0
\(303\) −28.0481 −1.61132
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −14.8943 −0.850065 −0.425033 0.905178i \(-0.639737\pi\)
−0.425033 + 0.905178i \(0.639737\pi\)
\(308\) 0 0
\(309\) 14.9626 0.851192
\(310\) 0 0
\(311\) 10.0355 0.569059 0.284530 0.958667i \(-0.408163\pi\)
0.284530 + 0.958667i \(0.408163\pi\)
\(312\) 0 0
\(313\) −23.5043 −1.32854 −0.664272 0.747491i \(-0.731258\pi\)
−0.664272 + 0.747491i \(0.731258\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.94093 −0.446007 −0.223004 0.974818i \(-0.571586\pi\)
−0.223004 + 0.974818i \(0.571586\pi\)
\(318\) 0 0
\(319\) 37.5486 2.10232
\(320\) 0 0
\(321\) −11.6536 −0.650442
\(322\) 0 0
\(323\) −19.0651 −1.06081
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 14.4982 0.801752
\(328\) 0 0
\(329\) 14.8625 0.819393
\(330\) 0 0
\(331\) −6.31442 −0.347072 −0.173536 0.984828i \(-0.555519\pi\)
−0.173536 + 0.984828i \(0.555519\pi\)
\(332\) 0 0
\(333\) −1.31277 −0.0719394
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 23.4516 1.27749 0.638746 0.769418i \(-0.279453\pi\)
0.638746 + 0.769418i \(0.279453\pi\)
\(338\) 0 0
\(339\) 23.0877 1.25395
\(340\) 0 0
\(341\) −29.3334 −1.58849
\(342\) 0 0
\(343\) 19.1683 1.03499
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 15.4757 0.830780 0.415390 0.909643i \(-0.363645\pi\)
0.415390 + 0.909643i \(0.363645\pi\)
\(348\) 0 0
\(349\) −25.5514 −1.36773 −0.683867 0.729607i \(-0.739703\pi\)
−0.683867 + 0.729607i \(0.739703\pi\)
\(350\) 0 0
\(351\) 8.67724 0.463157
\(352\) 0 0
\(353\) 23.5917 1.25566 0.627829 0.778352i \(-0.283944\pi\)
0.627829 + 0.778352i \(0.283944\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −24.5139 −1.29741
\(358\) 0 0
\(359\) −3.14840 −0.166166 −0.0830832 0.996543i \(-0.526477\pi\)
−0.0830832 + 0.996543i \(0.526477\pi\)
\(360\) 0 0
\(361\) −13.0479 −0.686729
\(362\) 0 0
\(363\) −21.0963 −1.10727
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −32.4297 −1.69282 −0.846408 0.532534i \(-0.821240\pi\)
−0.846408 + 0.532534i \(0.821240\pi\)
\(368\) 0 0
\(369\) −0.481088 −0.0250445
\(370\) 0 0
\(371\) 4.85577 0.252099
\(372\) 0 0
\(373\) −7.99302 −0.413863 −0.206931 0.978355i \(-0.566348\pi\)
−0.206931 + 0.978355i \(0.566348\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 13.5993 0.700398
\(378\) 0 0
\(379\) −8.96061 −0.460275 −0.230138 0.973158i \(-0.573918\pi\)
−0.230138 + 0.973158i \(0.573918\pi\)
\(380\) 0 0
\(381\) 12.6031 0.645678
\(382\) 0 0
\(383\) −36.7195 −1.87628 −0.938141 0.346255i \(-0.887453\pi\)
−0.938141 + 0.346255i \(0.887453\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.627747 0.0319102
\(388\) 0 0
\(389\) 0.0627294 0.00318051 0.00159025 0.999999i \(-0.499494\pi\)
0.00159025 + 0.999999i \(0.499494\pi\)
\(390\) 0 0
\(391\) −7.81453 −0.395198
\(392\) 0 0
\(393\) −19.9363 −1.00565
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −20.9714 −1.05252 −0.526262 0.850323i \(-0.676407\pi\)
−0.526262 + 0.850323i \(0.676407\pi\)
\(398\) 0 0
\(399\) 7.65326 0.383142
\(400\) 0 0
\(401\) −13.8567 −0.691972 −0.345986 0.938240i \(-0.612456\pi\)
−0.345986 + 0.938240i \(0.612456\pi\)
\(402\) 0 0
\(403\) −10.6239 −0.529215
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −32.6338 −1.61760
\(408\) 0 0
\(409\) 12.5868 0.622378 0.311189 0.950348i \(-0.399273\pi\)
0.311189 + 0.950348i \(0.399273\pi\)
\(410\) 0 0
\(411\) −4.85007 −0.239236
\(412\) 0 0
\(413\) 3.36593 0.165627
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 23.3896 1.14540
\(418\) 0 0
\(419\) 32.4927 1.58737 0.793685 0.608328i \(-0.208160\pi\)
0.793685 + 0.608328i \(0.208160\pi\)
\(420\) 0 0
\(421\) 18.8356 0.917992 0.458996 0.888438i \(-0.348209\pi\)
0.458996 + 0.888438i \(0.348209\pi\)
\(422\) 0 0
\(423\) −1.62623 −0.0790702
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.15162 0.297698
\(428\) 0 0
\(429\) −14.7585 −0.712549
\(430\) 0 0
\(431\) −1.66739 −0.0803155 −0.0401577 0.999193i \(-0.512786\pi\)
−0.0401577 + 0.999193i \(0.512786\pi\)
\(432\) 0 0
\(433\) −5.83595 −0.280458 −0.140229 0.990119i \(-0.544784\pi\)
−0.140229 + 0.990119i \(0.544784\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.43970 0.116707
\(438\) 0 0
\(439\) −30.5742 −1.45923 −0.729614 0.683860i \(-0.760300\pi\)
−0.729614 + 0.683860i \(0.760300\pi\)
\(440\) 0 0
\(441\) −0.752562 −0.0358363
\(442\) 0 0
\(443\) −34.9173 −1.65897 −0.829485 0.558530i \(-0.811366\pi\)
−0.829485 + 0.558530i \(0.811366\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 21.6002 1.02166
\(448\) 0 0
\(449\) −33.1265 −1.56334 −0.781668 0.623694i \(-0.785631\pi\)
−0.781668 + 0.623694i \(0.785631\pi\)
\(450\) 0 0
\(451\) −11.9592 −0.563138
\(452\) 0 0
\(453\) 26.6978 1.25437
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.27252 0.199860 0.0999299 0.994994i \(-0.468138\pi\)
0.0999299 + 0.994994i \(0.468138\pi\)
\(458\) 0 0
\(459\) −39.2032 −1.82985
\(460\) 0 0
\(461\) −38.4702 −1.79173 −0.895867 0.444322i \(-0.853444\pi\)
−0.895867 + 0.444322i \(0.853444\pi\)
\(462\) 0 0
\(463\) 8.94727 0.415815 0.207908 0.978148i \(-0.433335\pi\)
0.207908 + 0.978148i \(0.433335\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.3171 0.755064 0.377532 0.925996i \(-0.376773\pi\)
0.377532 + 0.925996i \(0.376773\pi\)
\(468\) 0 0
\(469\) −22.4124 −1.03491
\(470\) 0 0
\(471\) −8.54723 −0.393836
\(472\) 0 0
\(473\) 15.6050 0.717518
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.531313 −0.0243272
\(478\) 0 0
\(479\) −11.9574 −0.546349 −0.273174 0.961965i \(-0.588074\pi\)
−0.273174 + 0.961965i \(0.588074\pi\)
\(480\) 0 0
\(481\) −11.8192 −0.538911
\(482\) 0 0
\(483\) 3.13696 0.142737
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.19495 −0.0541484 −0.0270742 0.999633i \(-0.508619\pi\)
−0.0270742 + 0.999633i \(0.508619\pi\)
\(488\) 0 0
\(489\) 9.80982 0.443616
\(490\) 0 0
\(491\) 13.6912 0.617874 0.308937 0.951083i \(-0.400027\pi\)
0.308937 + 0.951083i \(0.400027\pi\)
\(492\) 0 0
\(493\) −61.4406 −2.76714
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −23.5227 −1.05514
\(498\) 0 0
\(499\) −11.9774 −0.536184 −0.268092 0.963393i \(-0.586393\pi\)
−0.268092 + 0.963393i \(0.586393\pi\)
\(500\) 0 0
\(501\) −12.9877 −0.580249
\(502\) 0 0
\(503\) −32.3666 −1.44316 −0.721578 0.692333i \(-0.756583\pi\)
−0.721578 + 0.692333i \(0.756583\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 17.8812 0.794133
\(508\) 0 0
\(509\) 15.6507 0.693706 0.346853 0.937919i \(-0.387250\pi\)
0.346853 + 0.937919i \(0.387250\pi\)
\(510\) 0 0
\(511\) −0.0196185 −0.000867872 0
\(512\) 0 0
\(513\) 12.2393 0.540377
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −40.4261 −1.77794
\(518\) 0 0
\(519\) 13.4158 0.588889
\(520\) 0 0
\(521\) 21.7184 0.951499 0.475749 0.879581i \(-0.342177\pi\)
0.475749 + 0.879581i \(0.342177\pi\)
\(522\) 0 0
\(523\) −8.89014 −0.388739 −0.194369 0.980928i \(-0.562266\pi\)
−0.194369 + 0.980928i \(0.562266\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 47.9981 2.09083
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −0.368297 −0.0159827
\(532\) 0 0
\(533\) −4.33137 −0.187613
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −10.2449 −0.442100
\(538\) 0 0
\(539\) −18.7077 −0.805798
\(540\) 0 0
\(541\) −29.0112 −1.24729 −0.623645 0.781708i \(-0.714349\pi\)
−0.623645 + 0.781708i \(0.714349\pi\)
\(542\) 0 0
\(543\) −45.0703 −1.93415
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −24.9089 −1.06503 −0.532514 0.846421i \(-0.678753\pi\)
−0.532514 + 0.846421i \(0.678753\pi\)
\(548\) 0 0
\(549\) −0.673103 −0.0287273
\(550\) 0 0
\(551\) 19.1818 0.817172
\(552\) 0 0
\(553\) −29.3145 −1.24658
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 15.3536 0.650552 0.325276 0.945619i \(-0.394543\pi\)
0.325276 + 0.945619i \(0.394543\pi\)
\(558\) 0 0
\(559\) 5.65178 0.239045
\(560\) 0 0
\(561\) 66.6781 2.81515
\(562\) 0 0
\(563\) 16.8264 0.709146 0.354573 0.935028i \(-0.384626\pi\)
0.354573 + 0.935028i \(0.384626\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 16.7492 0.703398
\(568\) 0 0
\(569\) 1.75646 0.0736344 0.0368172 0.999322i \(-0.488278\pi\)
0.0368172 + 0.999322i \(0.488278\pi\)
\(570\) 0 0
\(571\) −13.4273 −0.561913 −0.280956 0.959721i \(-0.590652\pi\)
−0.280956 + 0.959721i \(0.590652\pi\)
\(572\) 0 0
\(573\) 6.48823 0.271050
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −20.4806 −0.852620 −0.426310 0.904577i \(-0.640187\pi\)
−0.426310 + 0.904577i \(0.640187\pi\)
\(578\) 0 0
\(579\) −38.7792 −1.61161
\(580\) 0 0
\(581\) −4.63781 −0.192409
\(582\) 0 0
\(583\) −13.2078 −0.547010
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −45.3569 −1.87208 −0.936040 0.351893i \(-0.885538\pi\)
−0.936040 + 0.351893i \(0.885538\pi\)
\(588\) 0 0
\(589\) −14.9851 −0.617449
\(590\) 0 0
\(591\) −12.9805 −0.533945
\(592\) 0 0
\(593\) −28.8520 −1.18481 −0.592404 0.805641i \(-0.701821\pi\)
−0.592404 + 0.805641i \(0.701821\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 11.6615 0.477275
\(598\) 0 0
\(599\) −8.78767 −0.359054 −0.179527 0.983753i \(-0.557457\pi\)
−0.179527 + 0.983753i \(0.557457\pi\)
\(600\) 0 0
\(601\) −44.7810 −1.82665 −0.913327 0.407227i \(-0.866496\pi\)
−0.913327 + 0.407227i \(0.866496\pi\)
\(602\) 0 0
\(603\) 2.45234 0.0998669
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −6.96387 −0.282655 −0.141327 0.989963i \(-0.545137\pi\)
−0.141327 + 0.989963i \(0.545137\pi\)
\(608\) 0 0
\(609\) 24.6639 0.999432
\(610\) 0 0
\(611\) −14.6414 −0.592329
\(612\) 0 0
\(613\) 30.6214 1.23679 0.618393 0.785869i \(-0.287784\pi\)
0.618393 + 0.785869i \(0.287784\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 10.6041 0.426905 0.213452 0.976953i \(-0.431529\pi\)
0.213452 + 0.976953i \(0.431529\pi\)
\(618\) 0 0
\(619\) −21.0095 −0.844445 −0.422223 0.906492i \(-0.638750\pi\)
−0.422223 + 0.906492i \(0.638750\pi\)
\(620\) 0 0
\(621\) 5.01670 0.201313
\(622\) 0 0
\(623\) 23.1286 0.926629
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −20.8170 −0.831349
\(628\) 0 0
\(629\) 53.3985 2.12914
\(630\) 0 0
\(631\) −5.45489 −0.217156 −0.108578 0.994088i \(-0.534630\pi\)
−0.108578 + 0.994088i \(0.534630\pi\)
\(632\) 0 0
\(633\) −40.7099 −1.61807
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.77552 −0.268456
\(638\) 0 0
\(639\) 2.57383 0.101819
\(640\) 0 0
\(641\) −28.7734 −1.13648 −0.568241 0.822862i \(-0.692376\pi\)
−0.568241 + 0.822862i \(0.692376\pi\)
\(642\) 0 0
\(643\) 11.5319 0.454775 0.227388 0.973804i \(-0.426982\pi\)
0.227388 + 0.973804i \(0.426982\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.18564 0.125240 0.0626202 0.998037i \(-0.480054\pi\)
0.0626202 + 0.998037i \(0.480054\pi\)
\(648\) 0 0
\(649\) −9.15538 −0.359380
\(650\) 0 0
\(651\) −19.2678 −0.755163
\(652\) 0 0
\(653\) −28.6814 −1.12239 −0.561194 0.827684i \(-0.689658\pi\)
−0.561194 + 0.827684i \(0.689658\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.00214664 8.37483e−5 0
\(658\) 0 0
\(659\) −24.0012 −0.934954 −0.467477 0.884005i \(-0.654837\pi\)
−0.467477 + 0.884005i \(0.654837\pi\)
\(660\) 0 0
\(661\) 31.9043 1.24093 0.620467 0.784232i \(-0.286943\pi\)
0.620467 + 0.784232i \(0.286943\pi\)
\(662\) 0 0
\(663\) 24.1493 0.937882
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.86235 0.304431
\(668\) 0 0
\(669\) 12.2620 0.474078
\(670\) 0 0
\(671\) −16.7325 −0.645950
\(672\) 0 0
\(673\) −1.87848 −0.0724101 −0.0362051 0.999344i \(-0.511527\pi\)
−0.0362051 + 0.999344i \(0.511527\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.6119 1.33024 0.665121 0.746736i \(-0.268380\pi\)
0.665121 + 0.746736i \(0.268380\pi\)
\(678\) 0 0
\(679\) −27.8410 −1.06844
\(680\) 0 0
\(681\) 31.2665 1.19814
\(682\) 0 0
\(683\) 16.0493 0.614110 0.307055 0.951692i \(-0.400656\pi\)
0.307055 + 0.951692i \(0.400656\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 42.6371 1.62671
\(688\) 0 0
\(689\) −4.78356 −0.182239
\(690\) 0 0
\(691\) 19.5985 0.745564 0.372782 0.927919i \(-0.378404\pi\)
0.372782 + 0.927919i \(0.378404\pi\)
\(692\) 0 0
\(693\) −1.61092 −0.0611937
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 19.5688 0.741223
\(698\) 0 0
\(699\) 39.1199 1.47965
\(700\) 0 0
\(701\) −51.5536 −1.94715 −0.973575 0.228366i \(-0.926662\pi\)
−0.973575 + 0.228366i \(0.926662\pi\)
\(702\) 0 0
\(703\) −16.6711 −0.628761
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −27.5635 −1.03663
\(708\) 0 0
\(709\) 8.64772 0.324772 0.162386 0.986727i \(-0.448081\pi\)
0.162386 + 0.986727i \(0.448081\pi\)
\(710\) 0 0
\(711\) 3.20756 0.120293
\(712\) 0 0
\(713\) −6.14217 −0.230026
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −34.5615 −1.29072
\(718\) 0 0
\(719\) 7.50754 0.279984 0.139992 0.990153i \(-0.455292\pi\)
0.139992 + 0.990153i \(0.455292\pi\)
\(720\) 0 0
\(721\) 14.7041 0.547608
\(722\) 0 0
\(723\) −20.5037 −0.762543
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.79852 −0.103791 −0.0518956 0.998653i \(-0.516526\pi\)
−0.0518956 + 0.998653i \(0.516526\pi\)
\(728\) 0 0
\(729\) 25.0566 0.928022
\(730\) 0 0
\(731\) −25.5344 −0.944423
\(732\) 0 0
\(733\) −1.38900 −0.0513038 −0.0256519 0.999671i \(-0.508166\pi\)
−0.0256519 + 0.999671i \(0.508166\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 60.9619 2.24556
\(738\) 0 0
\(739\) −6.31935 −0.232461 −0.116230 0.993222i \(-0.537081\pi\)
−0.116230 + 0.993222i \(0.537081\pi\)
\(740\) 0 0
\(741\) −7.53944 −0.276968
\(742\) 0 0
\(743\) 39.7611 1.45869 0.729347 0.684144i \(-0.239824\pi\)
0.729347 + 0.684144i \(0.239824\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.507464 0.0185671
\(748\) 0 0
\(749\) −11.4523 −0.418457
\(750\) 0 0
\(751\) −7.27267 −0.265384 −0.132692 0.991157i \(-0.542362\pi\)
−0.132692 + 0.991157i \(0.542362\pi\)
\(752\) 0 0
\(753\) 30.3801 1.10711
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 15.8682 0.576739 0.288369 0.957519i \(-0.406887\pi\)
0.288369 + 0.957519i \(0.406887\pi\)
\(758\) 0 0
\(759\) −8.53258 −0.309713
\(760\) 0 0
\(761\) −4.80457 −0.174166 −0.0870828 0.996201i \(-0.527754\pi\)
−0.0870828 + 0.996201i \(0.527754\pi\)
\(762\) 0 0
\(763\) 14.2477 0.515801
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.31588 −0.119729
\(768\) 0 0
\(769\) 30.1358 1.08673 0.543363 0.839498i \(-0.317151\pi\)
0.543363 + 0.839498i \(0.317151\pi\)
\(770\) 0 0
\(771\) 26.1677 0.942406
\(772\) 0 0
\(773\) 3.35253 0.120582 0.0602910 0.998181i \(-0.480797\pi\)
0.0602910 + 0.998181i \(0.480797\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −21.4356 −0.768999
\(778\) 0 0
\(779\) −6.10941 −0.218892
\(780\) 0 0
\(781\) 63.9821 2.28946
\(782\) 0 0
\(783\) 39.4431 1.40958
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −2.36807 −0.0844126 −0.0422063 0.999109i \(-0.513439\pi\)
−0.0422063 + 0.999109i \(0.513439\pi\)
\(788\) 0 0
\(789\) 18.3384 0.652863
\(790\) 0 0
\(791\) 22.6888 0.806722
\(792\) 0 0
\(793\) −6.06013 −0.215202
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.0367 −1.17022 −0.585110 0.810954i \(-0.698949\pi\)
−0.585110 + 0.810954i \(0.698949\pi\)
\(798\) 0 0
\(799\) 66.1490 2.34018
\(800\) 0 0
\(801\) −2.53071 −0.0894183
\(802\) 0 0
\(803\) 0.0533626 0.00188313
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 4.67181 0.164456
\(808\) 0 0
\(809\) −16.7157 −0.587692 −0.293846 0.955853i \(-0.594935\pi\)
−0.293846 + 0.955853i \(0.594935\pi\)
\(810\) 0 0
\(811\) 5.85752 0.205685 0.102843 0.994698i \(-0.467206\pi\)
0.102843 + 0.994698i \(0.467206\pi\)
\(812\) 0 0
\(813\) 17.6430 0.618768
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 7.97185 0.278900
\(818\) 0 0
\(819\) −0.583439 −0.0203870
\(820\) 0 0
\(821\) 26.3966 0.921249 0.460625 0.887595i \(-0.347625\pi\)
0.460625 + 0.887595i \(0.347625\pi\)
\(822\) 0 0
\(823\) 25.5803 0.891672 0.445836 0.895115i \(-0.352906\pi\)
0.445836 + 0.895115i \(0.352906\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.74132 −0.338739 −0.169369 0.985553i \(-0.554173\pi\)
−0.169369 + 0.985553i \(0.554173\pi\)
\(828\) 0 0
\(829\) −54.7679 −1.90217 −0.951085 0.308931i \(-0.900029\pi\)
−0.951085 + 0.308931i \(0.900029\pi\)
\(830\) 0 0
\(831\) 7.53875 0.261516
\(832\) 0 0
\(833\) 30.6114 1.06062
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −30.8134 −1.06507
\(838\) 0 0
\(839\) 51.2171 1.76821 0.884106 0.467286i \(-0.154768\pi\)
0.884106 + 0.467286i \(0.154768\pi\)
\(840\) 0 0
\(841\) 32.8166 1.13161
\(842\) 0 0
\(843\) 23.9515 0.824933
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −20.7318 −0.712352
\(848\) 0 0
\(849\) −10.1139 −0.347109
\(850\) 0 0
\(851\) −6.83324 −0.234240
\(852\) 0 0
\(853\) −23.2520 −0.796135 −0.398067 0.917356i \(-0.630319\pi\)
−0.398067 + 0.917356i \(0.630319\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.8722 1.66944 0.834721 0.550674i \(-0.185629\pi\)
0.834721 + 0.550674i \(0.185629\pi\)
\(858\) 0 0
\(859\) 12.7171 0.433903 0.216952 0.976182i \(-0.430389\pi\)
0.216952 + 0.976182i \(0.430389\pi\)
\(860\) 0 0
\(861\) −7.85546 −0.267713
\(862\) 0 0
\(863\) 13.5511 0.461285 0.230642 0.973039i \(-0.425917\pi\)
0.230642 + 0.973039i \(0.425917\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −78.7320 −2.67388
\(868\) 0 0
\(869\) 79.7357 2.70485
\(870\) 0 0
\(871\) 22.0791 0.748121
\(872\) 0 0
\(873\) 3.04633 0.103103
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −4.88341 −0.164901 −0.0824505 0.996595i \(-0.526275\pi\)
−0.0824505 + 0.996595i \(0.526275\pi\)
\(878\) 0 0
\(879\) −10.1911 −0.343738
\(880\) 0 0
\(881\) −22.5717 −0.760461 −0.380230 0.924892i \(-0.624155\pi\)
−0.380230 + 0.924892i \(0.624155\pi\)
\(882\) 0 0
\(883\) −0.202906 −0.00682834 −0.00341417 0.999994i \(-0.501087\pi\)
−0.00341417 + 0.999994i \(0.501087\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −19.1859 −0.644201 −0.322100 0.946705i \(-0.604389\pi\)
−0.322100 + 0.946705i \(0.604389\pi\)
\(888\) 0 0
\(889\) 12.3854 0.415392
\(890\) 0 0
\(891\) −45.5579 −1.52625
\(892\) 0 0
\(893\) −20.6518 −0.691085
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −3.09031 −0.103183
\(898\) 0 0
\(899\) −48.2919 −1.61062
\(900\) 0 0
\(901\) 21.6118 0.719993
\(902\) 0 0
\(903\) 10.2502 0.341105
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 12.9713 0.430704 0.215352 0.976536i \(-0.430910\pi\)
0.215352 + 0.976536i \(0.430910\pi\)
\(908\) 0 0
\(909\) 3.01597 0.100033
\(910\) 0 0
\(911\) −31.3377 −1.03826 −0.519132 0.854694i \(-0.673745\pi\)
−0.519132 + 0.854694i \(0.673745\pi\)
\(912\) 0 0
\(913\) 12.6149 0.417492
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −19.5919 −0.646980
\(918\) 0 0
\(919\) −38.4577 −1.26860 −0.634302 0.773085i \(-0.718712\pi\)
−0.634302 + 0.773085i \(0.718712\pi\)
\(920\) 0 0
\(921\) 26.6110 0.876861
\(922\) 0 0
\(923\) 23.1729 0.762746
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.60890 −0.0528433
\(928\) 0 0
\(929\) −54.3396 −1.78282 −0.891412 0.453193i \(-0.850285\pi\)
−0.891412 + 0.453193i \(0.850285\pi\)
\(930\) 0 0
\(931\) −9.55689 −0.313215
\(932\) 0 0
\(933\) −17.9299 −0.586998
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −43.1182 −1.40861 −0.704304 0.709898i \(-0.748741\pi\)
−0.704304 + 0.709898i \(0.748741\pi\)
\(938\) 0 0
\(939\) 41.9940 1.37042
\(940\) 0 0
\(941\) 9.22344 0.300676 0.150338 0.988635i \(-0.451964\pi\)
0.150338 + 0.988635i \(0.451964\pi\)
\(942\) 0 0
\(943\) −2.50416 −0.0815467
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 45.8127 1.48871 0.744357 0.667782i \(-0.232756\pi\)
0.744357 + 0.667782i \(0.232756\pi\)
\(948\) 0 0
\(949\) 0.0193268 0.000627374 0
\(950\) 0 0
\(951\) 14.1877 0.460066
\(952\) 0 0
\(953\) 21.2363 0.687913 0.343956 0.938986i \(-0.388233\pi\)
0.343956 + 0.938986i \(0.388233\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −67.0861 −2.16859
\(958\) 0 0
\(959\) −4.76627 −0.153911
\(960\) 0 0
\(961\) 6.72623 0.216975
\(962\) 0 0
\(963\) 1.25310 0.0403805
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.88651 −0.189297 −0.0946486 0.995511i \(-0.530173\pi\)
−0.0946486 + 0.995511i \(0.530173\pi\)
\(968\) 0 0
\(969\) 34.0627 1.09425
\(970\) 0 0
\(971\) −27.1841 −0.872378 −0.436189 0.899855i \(-0.643672\pi\)
−0.436189 + 0.899855i \(0.643672\pi\)
\(972\) 0 0
\(973\) 22.9855 0.736882
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −48.5280 −1.55255 −0.776274 0.630395i \(-0.782893\pi\)
−0.776274 + 0.630395i \(0.782893\pi\)
\(978\) 0 0
\(979\) −62.9102 −2.01062
\(980\) 0 0
\(981\) −1.55897 −0.0497740
\(982\) 0 0
\(983\) −50.7935 −1.62006 −0.810030 0.586388i \(-0.800549\pi\)
−0.810030 + 0.586388i \(0.800549\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −26.5540 −0.845223
\(988\) 0 0
\(989\) 3.26755 0.103902
\(990\) 0 0
\(991\) 9.42740 0.299471 0.149736 0.988726i \(-0.452158\pi\)
0.149736 + 0.988726i \(0.452158\pi\)
\(992\) 0 0
\(993\) 11.2816 0.358012
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 6.78817 0.214984 0.107492 0.994206i \(-0.465718\pi\)
0.107492 + 0.994206i \(0.465718\pi\)
\(998\) 0 0
\(999\) −34.2803 −1.08458
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 9200.2.a.cz.1.2 7
4.3 odd 2 4600.2.a.bi.1.6 7
5.2 odd 4 1840.2.e.g.369.12 14
5.3 odd 4 1840.2.e.g.369.3 14
5.4 even 2 9200.2.a.dc.1.6 7
20.3 even 4 920.2.e.b.369.12 yes 14
20.7 even 4 920.2.e.b.369.3 14
20.19 odd 2 4600.2.a.bh.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.3 14 20.7 even 4
920.2.e.b.369.12 yes 14 20.3 even 4
1840.2.e.g.369.3 14 5.3 odd 4
1840.2.e.g.369.12 14 5.2 odd 4
4600.2.a.bh.1.2 7 20.19 odd 2
4600.2.a.bi.1.6 7 4.3 odd 2
9200.2.a.cz.1.2 7 1.1 even 1 trivial
9200.2.a.dc.1.6 7 5.4 even 2