Properties

Label 9800.2.a.ce.1.1
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(78.2533939809\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1944.1
Defining polynomial: \(x^{3} - 9 x - 6\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.58423\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58423 q^{3} +3.67822 q^{9} +O(q^{10})\) \(q-2.58423 q^{3} +3.67822 q^{9} +1.67822 q^{11} +4.84667 q^{13} -2.00000 q^{17} +6.84667 q^{19} +2.26245 q^{23} -1.75268 q^{27} +3.32178 q^{29} +9.16845 q^{31} -4.33690 q^{33} +2.84667 q^{37} -12.5249 q^{39} +9.52489 q^{41} -6.58423 q^{43} +12.2031 q^{47} +5.16845 q^{51} -7.49023 q^{53} -17.6933 q^{57} +8.00000 q^{59} -6.49023 q^{61} +5.75268 q^{67} -5.84667 q^{69} +11.6933 q^{73} +5.69334 q^{79} -6.50535 q^{81} +12.5842 q^{83} -8.58423 q^{87} -5.84667 q^{89} -23.6933 q^{93} +2.00000 q^{97} +6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 9q^{9} + O(q^{10}) \) \( 3q + 9q^{9} + 3q^{11} - 3q^{13} - 6q^{17} + 3q^{19} - 3q^{23} + 18q^{27} + 12q^{29} + 12q^{31} + 18q^{33} - 9q^{37} - 18q^{39} + 9q^{41} - 12q^{43} + 15q^{47} - 9q^{53} - 18q^{57} + 24q^{59} - 6q^{61} - 6q^{67} - 18q^{79} + 27q^{81} + 30q^{83} - 18q^{87} - 36q^{93} + 6q^{97} + 63q^{99} + O(q^{100}) \)

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
\(3\) −2.58423 −1.49200 −0.746002 0.665944i \(-0.768029\pi\)
−0.746002 + 0.665944i \(0.768029\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 3.67822 1.22607
\(10\) 0 0
\(11\) 1.67822 0.506003 0.253001 0.967466i \(-0.418582\pi\)
0.253001 + 0.967466i \(0.418582\pi\)
\(12\) 0 0
\(13\) 4.84667 1.34422 0.672112 0.740449i \(-0.265387\pi\)
0.672112 + 0.740449i \(0.265387\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 6.84667 1.57073 0.785367 0.619030i \(-0.212474\pi\)
0.785367 + 0.619030i \(0.212474\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.26245 0.471753 0.235876 0.971783i \(-0.424204\pi\)
0.235876 + 0.971783i \(0.424204\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.75268 −0.337303
\(28\) 0 0
\(29\) 3.32178 0.616839 0.308419 0.951250i \(-0.400200\pi\)
0.308419 + 0.951250i \(0.400200\pi\)
\(30\) 0 0
\(31\) 9.16845 1.64670 0.823351 0.567532i \(-0.192102\pi\)
0.823351 + 0.567532i \(0.192102\pi\)
\(32\) 0 0
\(33\) −4.33690 −0.754958
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.84667 0.467990 0.233995 0.972238i \(-0.424820\pi\)
0.233995 + 0.972238i \(0.424820\pi\)
\(38\) 0 0
\(39\) −12.5249 −2.00559
\(40\) 0 0
\(41\) 9.52489 1.48754 0.743769 0.668437i \(-0.233036\pi\)
0.743769 + 0.668437i \(0.233036\pi\)
\(42\) 0 0
\(43\) −6.58423 −1.00408 −0.502042 0.864843i \(-0.667418\pi\)
−0.502042 + 0.864843i \(0.667418\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 12.2031 1.78001 0.890004 0.455954i \(-0.150702\pi\)
0.890004 + 0.455954i \(0.150702\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 5.16845 0.723728
\(52\) 0 0
\(53\) −7.49023 −1.02886 −0.514431 0.857532i \(-0.671997\pi\)
−0.514431 + 0.857532i \(0.671997\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −17.6933 −2.34354
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −6.49023 −0.830989 −0.415494 0.909596i \(-0.636391\pi\)
−0.415494 + 0.909596i \(0.636391\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.75268 0.702801 0.351401 0.936225i \(-0.385706\pi\)
0.351401 + 0.936225i \(0.385706\pi\)
\(68\) 0 0
\(69\) −5.84667 −0.703857
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 11.6933 1.36860 0.684301 0.729199i \(-0.260107\pi\)
0.684301 + 0.729199i \(0.260107\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 5.69334 0.640551 0.320276 0.947324i \(-0.396224\pi\)
0.320276 + 0.947324i \(0.396224\pi\)
\(80\) 0 0
\(81\) −6.50535 −0.722817
\(82\) 0 0
\(83\) 12.5842 1.38130 0.690649 0.723190i \(-0.257325\pi\)
0.690649 + 0.723190i \(0.257325\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −8.58423 −0.920326
\(88\) 0 0
\(89\) −5.84667 −0.619746 −0.309873 0.950778i \(-0.600287\pi\)
−0.309873 + 0.950778i \(0.600287\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −23.6933 −2.45689
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 6.17287 0.620397
\(100\) 0 0
\(101\) −17.0151 −1.69307 −0.846534 0.532335i \(-0.821315\pi\)
−0.846534 + 0.532335i \(0.821315\pi\)
\(102\) 0 0
\(103\) −7.10912 −0.700482 −0.350241 0.936660i \(-0.613900\pi\)
−0.350241 + 0.936660i \(0.613900\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.75268 0.169438 0.0847188 0.996405i \(-0.473001\pi\)
0.0847188 + 0.996405i \(0.473001\pi\)
\(108\) 0 0
\(109\) 19.5400 1.87159 0.935797 0.352539i \(-0.114682\pi\)
0.935797 + 0.352539i \(0.114682\pi\)
\(110\) 0 0
\(111\) −7.35644 −0.698243
\(112\) 0 0
\(113\) −10.3369 −0.972414 −0.486207 0.873844i \(-0.661620\pi\)
−0.486207 + 0.873844i \(0.661620\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 17.8271 1.64812
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −8.18357 −0.743961
\(122\) 0 0
\(123\) −24.6145 −2.21941
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 19.1836 1.70227 0.851133 0.524949i \(-0.175916\pi\)
0.851133 + 0.524949i \(0.175916\pi\)
\(128\) 0 0
\(129\) 17.0151 1.49810
\(130\) 0 0
\(131\) −17.8271 −1.55756 −0.778782 0.627295i \(-0.784162\pi\)
−0.778782 + 0.627295i \(0.784162\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.00000 −0.341743 −0.170872 0.985293i \(-0.554658\pi\)
−0.170872 + 0.985293i \(0.554658\pi\)
\(138\) 0 0
\(139\) −5.16845 −0.438382 −0.219191 0.975682i \(-0.570342\pi\)
−0.219191 + 0.975682i \(0.570342\pi\)
\(140\) 0 0
\(141\) −31.5356 −2.65578
\(142\) 0 0
\(143\) 8.13379 0.680181
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.796886 0.0652834 0.0326417 0.999467i \(-0.489608\pi\)
0.0326417 + 0.999467i \(0.489608\pi\)
\(150\) 0 0
\(151\) −16.5249 −1.34478 −0.672388 0.740199i \(-0.734731\pi\)
−0.672388 + 0.740199i \(0.734731\pi\)
\(152\) 0 0
\(153\) −7.35644 −0.594733
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.20311 −0.654680 −0.327340 0.944907i \(-0.606152\pi\)
−0.327340 + 0.944907i \(0.606152\pi\)
\(158\) 0 0
\(159\) 19.3564 1.53507
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.69334 −0.289285 −0.144643 0.989484i \(-0.546203\pi\)
−0.144643 + 0.989484i \(0.546203\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.262447 0.0203087 0.0101544 0.999948i \(-0.496768\pi\)
0.0101544 + 0.999948i \(0.496768\pi\)
\(168\) 0 0
\(169\) 10.4902 0.806941
\(170\) 0 0
\(171\) 25.1836 1.92584
\(172\) 0 0
\(173\) 18.8467 1.43289 0.716443 0.697646i \(-0.245769\pi\)
0.716443 + 0.697646i \(0.245769\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −20.6738 −1.55394
\(178\) 0 0
\(179\) −12.0151 −0.898052 −0.449026 0.893519i \(-0.648229\pi\)
−0.449026 + 0.893519i \(0.648229\pi\)
\(180\) 0 0
\(181\) −6.03466 −0.448553 −0.224276 0.974526i \(-0.572002\pi\)
−0.224276 + 0.974526i \(0.572002\pi\)
\(182\) 0 0
\(183\) 16.7722 1.23984
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −3.35644 −0.245447
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 2.83155 0.204884 0.102442 0.994739i \(-0.467334\pi\)
0.102442 + 0.994739i \(0.467334\pi\)
\(192\) 0 0
\(193\) −12.9805 −0.934354 −0.467177 0.884164i \(-0.654729\pi\)
−0.467177 + 0.884164i \(0.654729\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.84667 0.345311 0.172656 0.984982i \(-0.444765\pi\)
0.172656 + 0.984982i \(0.444765\pi\)
\(198\) 0 0
\(199\) −15.3867 −1.09073 −0.545367 0.838198i \(-0.683610\pi\)
−0.545367 + 0.838198i \(0.683610\pi\)
\(200\) 0 0
\(201\) −14.8662 −1.04858
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 8.32178 0.578404
\(208\) 0 0
\(209\) 11.4902 0.794796
\(210\) 0 0
\(211\) 9.18357 0.632223 0.316112 0.948722i \(-0.397623\pi\)
0.316112 + 0.948722i \(0.397623\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −30.2182 −2.04196
\(220\) 0 0
\(221\) −9.69334 −0.652045
\(222\) 0 0
\(223\) 12.9805 0.869236 0.434618 0.900615i \(-0.356883\pi\)
0.434618 + 0.900615i \(0.356883\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 22.0302 1.46220 0.731099 0.682271i \(-0.239008\pi\)
0.731099 + 0.682271i \(0.239008\pi\)
\(228\) 0 0
\(229\) 4.30666 0.284592 0.142296 0.989824i \(-0.454552\pi\)
0.142296 + 0.989824i \(0.454552\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −14.7129 −0.955705
\(238\) 0 0
\(239\) 10.8618 0.702591 0.351296 0.936265i \(-0.385741\pi\)
0.351296 + 0.936265i \(0.385741\pi\)
\(240\) 0 0
\(241\) 0.203114 0.0130837 0.00654187 0.999979i \(-0.497918\pi\)
0.00654187 + 0.999979i \(0.497918\pi\)
\(242\) 0 0
\(243\) 22.0693 1.41575
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 33.1836 2.11142
\(248\) 0 0
\(249\) −32.5205 −2.06090
\(250\) 0 0
\(251\) 5.03466 0.317785 0.158893 0.987296i \(-0.449208\pi\)
0.158893 + 0.987296i \(0.449208\pi\)
\(252\) 0 0
\(253\) 3.79689 0.238708
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −23.3867 −1.45882 −0.729411 0.684076i \(-0.760206\pi\)
−0.729411 + 0.684076i \(0.760206\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 12.2182 0.756290
\(262\) 0 0
\(263\) −27.1091 −1.67162 −0.835810 0.549019i \(-0.815001\pi\)
−0.835810 + 0.549019i \(0.815001\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 15.1091 0.924663
\(268\) 0 0
\(269\) 6.49023 0.395716 0.197858 0.980231i \(-0.436601\pi\)
0.197858 + 0.980231i \(0.436601\pi\)
\(270\) 0 0
\(271\) −23.3867 −1.42064 −0.710320 0.703879i \(-0.751450\pi\)
−0.710320 + 0.703879i \(0.751450\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −3.66310 −0.220094 −0.110047 0.993926i \(-0.535100\pi\)
−0.110047 + 0.993926i \(0.535100\pi\)
\(278\) 0 0
\(279\) 33.7236 2.01898
\(280\) 0 0
\(281\) 13.8965 0.828993 0.414497 0.910051i \(-0.363958\pi\)
0.414497 + 0.910051i \(0.363958\pi\)
\(282\) 0 0
\(283\) 20.3369 1.20890 0.604452 0.796642i \(-0.293392\pi\)
0.604452 + 0.796642i \(0.293392\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −5.16845 −0.302980
\(292\) 0 0
\(293\) −18.8467 −1.10103 −0.550517 0.834824i \(-0.685569\pi\)
−0.550517 + 0.834824i \(0.685569\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.94138 −0.170676
\(298\) 0 0
\(299\) 10.9653 0.634142
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 43.9709 2.52606
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.39623 0.136760 0.0683802 0.997659i \(-0.478217\pi\)
0.0683802 + 0.997659i \(0.478217\pi\)
\(308\) 0 0
\(309\) 18.3716 1.04512
\(310\) 0 0
\(311\) −5.66310 −0.321125 −0.160562 0.987026i \(-0.551331\pi\)
−0.160562 + 0.987026i \(0.551331\pi\)
\(312\) 0 0
\(313\) −29.7236 −1.68008 −0.840038 0.542527i \(-0.817468\pi\)
−0.840038 + 0.542527i \(0.817468\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −19.0498 −1.06994 −0.534971 0.844870i \(-0.679678\pi\)
−0.534971 + 0.844870i \(0.679678\pi\)
\(318\) 0 0
\(319\) 5.57468 0.312122
\(320\) 0 0
\(321\) −4.52931 −0.252801
\(322\) 0 0
\(323\) −13.6933 −0.761918
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −50.4958 −2.79242
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.32178 0.127617 0.0638083 0.997962i \(-0.479675\pi\)
0.0638083 + 0.997962i \(0.479675\pi\)
\(332\) 0 0
\(333\) 10.4707 0.573790
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 16.4062 0.893704 0.446852 0.894608i \(-0.352545\pi\)
0.446852 + 0.894608i \(0.352545\pi\)
\(338\) 0 0
\(339\) 26.7129 1.45084
\(340\) 0 0
\(341\) 15.3867 0.833236
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.58423 −0.246094 −0.123047 0.992401i \(-0.539267\pi\)
−0.123047 + 0.992401i \(0.539267\pi\)
\(348\) 0 0
\(349\) 12.3716 0.662235 0.331117 0.943590i \(-0.392574\pi\)
0.331117 + 0.943590i \(0.392574\pi\)
\(350\) 0 0
\(351\) −8.49465 −0.453411
\(352\) 0 0
\(353\) −19.3867 −1.03185 −0.515925 0.856634i \(-0.672552\pi\)
−0.515925 + 0.856634i \(0.672552\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.81201 −0.517858 −0.258929 0.965896i \(-0.583370\pi\)
−0.258929 + 0.965896i \(0.583370\pi\)
\(360\) 0 0
\(361\) 27.8769 1.46721
\(362\) 0 0
\(363\) 21.1482 1.10999
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 12.7180 0.663875 0.331937 0.943301i \(-0.392298\pi\)
0.331937 + 0.943301i \(0.392298\pi\)
\(368\) 0 0
\(369\) 35.0347 1.82383
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 16.4062 0.849482 0.424741 0.905315i \(-0.360365\pi\)
0.424741 + 0.905315i \(0.360365\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 16.0996 0.829170
\(378\) 0 0
\(379\) 14.4707 0.743309 0.371655 0.928371i \(-0.378791\pi\)
0.371655 + 0.928371i \(0.378791\pi\)
\(380\) 0 0
\(381\) −49.5747 −2.53979
\(382\) 0 0
\(383\) 3.54956 0.181374 0.0906871 0.995879i \(-0.471094\pi\)
0.0906871 + 0.995879i \(0.471094\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −24.2182 −1.23108
\(388\) 0 0
\(389\) 8.98046 0.455327 0.227664 0.973740i \(-0.426891\pi\)
0.227664 + 0.973740i \(0.426891\pi\)
\(390\) 0 0
\(391\) −4.52489 −0.228834
\(392\) 0 0
\(393\) 46.0693 2.32389
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 28.0996 1.41028 0.705139 0.709070i \(-0.250885\pi\)
0.705139 + 0.709070i \(0.250885\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −26.6933 −1.33300 −0.666501 0.745504i \(-0.732209\pi\)
−0.666501 + 0.745504i \(0.732209\pi\)
\(402\) 0 0
\(403\) 44.4365 2.21354
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.77735 0.236804
\(408\) 0 0
\(409\) 28.0649 1.38772 0.693860 0.720110i \(-0.255909\pi\)
0.693860 + 0.720110i \(0.255909\pi\)
\(410\) 0 0
\(411\) 10.3369 0.509882
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 13.3564 0.654068
\(418\) 0 0
\(419\) −18.8769 −0.922198 −0.461099 0.887349i \(-0.652545\pi\)
−0.461099 + 0.887349i \(0.652545\pi\)
\(420\) 0 0
\(421\) −28.1836 −1.37358 −0.686792 0.726854i \(-0.740982\pi\)
−0.686792 + 0.726854i \(0.740982\pi\)
\(422\) 0 0
\(423\) 44.8858 2.18242
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −21.0195 −1.01483
\(430\) 0 0
\(431\) 2.83155 0.136391 0.0681955 0.997672i \(-0.478276\pi\)
0.0681955 + 0.997672i \(0.478276\pi\)
\(432\) 0 0
\(433\) 2.33690 0.112304 0.0561522 0.998422i \(-0.482117\pi\)
0.0561522 + 0.998422i \(0.482117\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.4902 0.740998
\(438\) 0 0
\(439\) −6.06933 −0.289673 −0.144837 0.989456i \(-0.546266\pi\)
−0.144837 + 0.989456i \(0.546266\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −11.6038 −0.551312 −0.275656 0.961256i \(-0.588895\pi\)
−0.275656 + 0.961256i \(0.588895\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2.05933 −0.0974031
\(448\) 0 0
\(449\) 4.13821 0.195294 0.0976470 0.995221i \(-0.468868\pi\)
0.0976470 + 0.995221i \(0.468868\pi\)
\(450\) 0 0
\(451\) 15.9849 0.752698
\(452\) 0 0
\(453\) 42.7040 2.00641
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 12.6436 0.591441 0.295720 0.955275i \(-0.404440\pi\)
0.295720 + 0.955275i \(0.404440\pi\)
\(458\) 0 0
\(459\) 3.50535 0.163616
\(460\) 0 0
\(461\) 20.7129 0.964695 0.482348 0.875980i \(-0.339784\pi\)
0.482348 + 0.875980i \(0.339784\pi\)
\(462\) 0 0
\(463\) 16.3811 0.761295 0.380647 0.924720i \(-0.375701\pi\)
0.380647 + 0.924720i \(0.375701\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.72243 0.0797046 0.0398523 0.999206i \(-0.487311\pi\)
0.0398523 + 0.999206i \(0.487311\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 21.1987 0.976784
\(472\) 0 0
\(473\) −11.0498 −0.508070
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −27.5507 −1.26146
\(478\) 0 0
\(479\) −1.78176 −0.0814108 −0.0407054 0.999171i \(-0.512961\pi\)
−0.0407054 + 0.999171i \(0.512961\pi\)
\(480\) 0 0
\(481\) 13.7969 0.629084
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 11.0195 0.499343 0.249672 0.968331i \(-0.419677\pi\)
0.249672 + 0.968331i \(0.419677\pi\)
\(488\) 0 0
\(489\) 9.54443 0.431614
\(490\) 0 0
\(491\) −20.9311 −0.944608 −0.472304 0.881436i \(-0.656578\pi\)
−0.472304 + 0.881436i \(0.656578\pi\)
\(492\) 0 0
\(493\) −6.64356 −0.299211
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −7.50535 −0.335986 −0.167993 0.985788i \(-0.553729\pi\)
−0.167993 + 0.985788i \(0.553729\pi\)
\(500\) 0 0
\(501\) −0.678221 −0.0303007
\(502\) 0 0
\(503\) −20.5842 −0.917805 −0.458903 0.888487i \(-0.651757\pi\)
−0.458903 + 0.888487i \(0.651757\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −27.1091 −1.20396
\(508\) 0 0
\(509\) 13.6587 0.605410 0.302705 0.953084i \(-0.402110\pi\)
0.302705 + 0.953084i \(0.402110\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −12.0000 −0.529813
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 20.4795 0.900688
\(518\) 0 0
\(519\) −48.7040 −2.13787
\(520\) 0 0
\(521\) −42.1640 −1.84724 −0.923620 0.383310i \(-0.874784\pi\)
−0.923620 + 0.383310i \(0.874784\pi\)
\(522\) 0 0
\(523\) 30.6436 1.33995 0.669975 0.742384i \(-0.266305\pi\)
0.669975 + 0.742384i \(0.266305\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.3369 −0.798768
\(528\) 0 0
\(529\) −17.8813 −0.777449
\(530\) 0 0
\(531\) 29.4258 1.27697
\(532\) 0 0
\(533\) 46.1640 1.99959
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 31.0498 1.33990
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −33.6889 −1.44840 −0.724200 0.689590i \(-0.757791\pi\)
−0.724200 + 0.689590i \(0.757791\pi\)
\(542\) 0 0
\(543\) 15.5949 0.669243
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 3.03979 0.129972 0.0649861 0.997886i \(-0.479300\pi\)
0.0649861 + 0.997886i \(0.479300\pi\)
\(548\) 0 0
\(549\) −23.8725 −1.01885
\(550\) 0 0
\(551\) 22.7431 0.968890
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.1640 −0.769635 −0.384817 0.922993i \(-0.625736\pi\)
−0.384817 + 0.922993i \(0.625736\pi\)
\(558\) 0 0
\(559\) −31.9116 −1.34972
\(560\) 0 0
\(561\) 8.67380 0.366208
\(562\) 0 0
\(563\) 36.9905 1.55896 0.779481 0.626426i \(-0.215483\pi\)
0.779481 + 0.626426i \(0.215483\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 32.6093 1.36705 0.683527 0.729925i \(-0.260445\pi\)
0.683527 + 0.729925i \(0.260445\pi\)
\(570\) 0 0
\(571\) 40.4365 1.69221 0.846107 0.533013i \(-0.178940\pi\)
0.846107 + 0.533013i \(0.178940\pi\)
\(572\) 0 0
\(573\) −7.31736 −0.305687
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 38.0302 1.58322 0.791610 0.611027i \(-0.209243\pi\)
0.791610 + 0.611027i \(0.209243\pi\)
\(578\) 0 0
\(579\) 33.5444 1.39406
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −12.5703 −0.520607
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.0302 −1.40458 −0.702289 0.711892i \(-0.747839\pi\)
−0.702289 + 0.711892i \(0.747839\pi\)
\(588\) 0 0
\(589\) 62.7734 2.58653
\(590\) 0 0
\(591\) −12.5249 −0.515205
\(592\) 0 0
\(593\) 33.7236 1.38486 0.692431 0.721484i \(-0.256540\pi\)
0.692431 + 0.721484i \(0.256540\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 39.7627 1.62738
\(598\) 0 0
\(599\) 6.30666 0.257683 0.128841 0.991665i \(-0.458874\pi\)
0.128841 + 0.991665i \(0.458874\pi\)
\(600\) 0 0
\(601\) −11.2871 −0.460411 −0.230206 0.973142i \(-0.573940\pi\)
−0.230206 + 0.973142i \(0.573940\pi\)
\(602\) 0 0
\(603\) 21.1596 0.861686
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 15.4611 0.627548 0.313774 0.949498i \(-0.398406\pi\)
0.313774 + 0.949498i \(0.398406\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 59.1445 2.39273
\(612\) 0 0
\(613\) 22.1640 0.895197 0.447598 0.894235i \(-0.352279\pi\)
0.447598 + 0.894235i \(0.352279\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 14.9805 0.603091 0.301545 0.953452i \(-0.402498\pi\)
0.301545 + 0.953452i \(0.402498\pi\)
\(618\) 0 0
\(619\) 23.6391 0.950137 0.475069 0.879949i \(-0.342423\pi\)
0.475069 + 0.879949i \(0.342423\pi\)
\(620\) 0 0
\(621\) −3.96534 −0.159123
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −29.6933 −1.18584
\(628\) 0 0
\(629\) −5.69334 −0.227008
\(630\) 0 0
\(631\) −13.7818 −0.548643 −0.274322 0.961638i \(-0.588453\pi\)
−0.274322 + 0.961638i \(0.588453\pi\)
\(632\) 0 0
\(633\) −23.7324 −0.943279
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 43.8618 1.73244 0.866218 0.499666i \(-0.166544\pi\)
0.866218 + 0.499666i \(0.166544\pi\)
\(642\) 0 0
\(643\) −7.04979 −0.278016 −0.139008 0.990291i \(-0.544391\pi\)
−0.139008 + 0.990291i \(0.544391\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.4807 0.962435 0.481217 0.876601i \(-0.340195\pi\)
0.481217 + 0.876601i \(0.340195\pi\)
\(648\) 0 0
\(649\) 13.4258 0.527008
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.816426 −0.0319492 −0.0159746 0.999872i \(-0.505085\pi\)
−0.0159746 + 0.999872i \(0.505085\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 43.0107 1.67801
\(658\) 0 0
\(659\) 21.2871 0.829228 0.414614 0.909997i \(-0.363917\pi\)
0.414614 + 0.909997i \(0.363917\pi\)
\(660\) 0 0
\(661\) 25.9462 1.00919 0.504596 0.863356i \(-0.331641\pi\)
0.504596 + 0.863356i \(0.331641\pi\)
\(662\) 0 0
\(663\) 25.0498 0.972853
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 7.51535 0.290995
\(668\) 0 0
\(669\) −33.5444 −1.29690
\(670\) 0 0
\(671\) −10.8920 −0.420483
\(672\) 0 0
\(673\) −22.0693 −0.850710 −0.425355 0.905027i \(-0.639851\pi\)
−0.425355 + 0.905027i \(0.639851\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −5.49023 −0.211007 −0.105503 0.994419i \(-0.533645\pi\)
−0.105503 + 0.994419i \(0.533645\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −56.9311 −2.18161
\(682\) 0 0
\(683\) −19.2278 −0.735731 −0.367865 0.929879i \(-0.619911\pi\)
−0.367865 + 0.929879i \(0.619911\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −11.1294 −0.424612
\(688\) 0 0
\(689\) −36.3027 −1.38302
\(690\) 0 0
\(691\) 14.2182 0.540887 0.270444 0.962736i \(-0.412830\pi\)
0.270444 + 0.962736i \(0.412830\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −19.0498 −0.721562
\(698\) 0 0
\(699\) 46.5161 1.75940
\(700\) 0 0
\(701\) 14.1533 0.534564 0.267282 0.963618i \(-0.413875\pi\)
0.267282 + 0.963618i \(0.413875\pi\)
\(702\) 0 0
\(703\) 19.4902 0.735088
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 17.0454 0.640152 0.320076 0.947392i \(-0.396292\pi\)
0.320076 + 0.947392i \(0.396292\pi\)
\(710\) 0 0
\(711\) 20.9414 0.785363
\(712\) 0 0
\(713\) 20.7431 0.776836
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −28.0693 −1.04827
\(718\) 0 0
\(719\) −11.5054 −0.429077 −0.214539 0.976716i \(-0.568825\pi\)
−0.214539 + 0.976716i \(0.568825\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.524893 −0.0195210
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −16.4114 −0.608664 −0.304332 0.952566i \(-0.598433\pi\)
−0.304332 + 0.952566i \(0.598433\pi\)
\(728\) 0 0
\(729\) −37.5161 −1.38948
\(730\) 0 0
\(731\) 13.1685 0.487053
\(732\) 0 0
\(733\) 9.11425 0.336642 0.168321 0.985732i \(-0.446165\pi\)
0.168321 + 0.985732i \(0.446165\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.65426 0.355619
\(738\) 0 0
\(739\) −34.9956 −1.28733 −0.643667 0.765306i \(-0.722588\pi\)
−0.643667 + 0.765306i \(0.722588\pi\)
\(740\) 0 0
\(741\) −85.7538 −3.15025
\(742\) 0 0
\(743\) 43.5305 1.59698 0.798489 0.602009i \(-0.205633\pi\)
0.798489 + 0.602009i \(0.205633\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 46.2876 1.69357
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 6.30666 0.230133 0.115067 0.993358i \(-0.463292\pi\)
0.115067 + 0.993358i \(0.463292\pi\)
\(752\) 0 0
\(753\) −13.0107 −0.474136
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.3369 −0.884540 −0.442270 0.896882i \(-0.645827\pi\)
−0.442270 + 0.896882i \(0.645827\pi\)
\(758\) 0 0
\(759\) −9.81201 −0.356153
\(760\) 0 0
\(761\) −28.2031 −1.02236 −0.511181 0.859473i \(-0.670792\pi\)
−0.511181 + 0.859473i \(0.670792\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 38.7734 1.40003
\(768\) 0 0
\(769\) −41.8965 −1.51082 −0.755412 0.655250i \(-0.772563\pi\)
−0.755412 + 0.655250i \(0.772563\pi\)
\(770\) 0 0
\(771\) 60.4365 2.17657
\(772\) 0 0
\(773\) −39.8574 −1.43357 −0.716785 0.697294i \(-0.754387\pi\)
−0.716785 + 0.697294i \(0.754387\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 65.2138 2.33653
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −5.82200 −0.208061
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −35.3274 −1.25928 −0.629642 0.776885i \(-0.716798\pi\)
−0.629642 + 0.776885i \(0.716798\pi\)
\(788\) 0 0
\(789\) 70.0561 2.49406
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −31.4560 −1.11704
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −29.6933 −1.05179 −0.525896 0.850549i \(-0.676270\pi\)
−0.525896 + 0.850549i \(0.676270\pi\)
\(798\) 0 0
\(799\) −24.4062 −0.863430
\(800\) 0 0
\(801\) −21.5054 −0.759854
\(802\) 0 0
\(803\) 19.6240 0.692517
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −16.7722 −0.590410
\(808\) 0 0
\(809\) −19.6436 −0.690631 −0.345315 0.938487i \(-0.612228\pi\)
−0.345315 + 0.938487i \(0.612228\pi\)
\(810\) 0 0
\(811\) 0.252452 0.00886479 0.00443239 0.999990i \(-0.498589\pi\)
0.00443239 + 0.999990i \(0.498589\pi\)
\(812\) 0 0
\(813\) 60.4365 2.11960
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −45.0800 −1.57715
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 44.7734 1.56260 0.781301 0.624155i \(-0.214556\pi\)
0.781301 + 0.624155i \(0.214556\pi\)
\(822\) 0 0
\(823\) −3.29711 −0.114930 −0.0574650 0.998348i \(-0.518302\pi\)
−0.0574650 + 0.998348i \(0.518302\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.41577 −0.327419 −0.163709 0.986509i \(-0.552346\pi\)
−0.163709 + 0.986509i \(0.552346\pi\)
\(828\) 0 0
\(829\) −4.71288 −0.163685 −0.0818426 0.996645i \(-0.526080\pi\)
−0.0818426 + 0.996645i \(0.526080\pi\)
\(830\) 0 0
\(831\) 9.46627 0.328381
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −16.0693 −0.555437
\(838\) 0 0
\(839\) 22.1880 0.766015 0.383007 0.923745i \(-0.374888\pi\)
0.383007 + 0.923745i \(0.374888\pi\)
\(840\) 0 0
\(841\) −17.9658 −0.619510
\(842\) 0 0
\(843\) −35.9116 −1.23686
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −52.5551 −1.80369
\(850\) 0 0
\(851\) 6.44044 0.220776
\(852\) 0 0
\(853\) −39.9267 −1.36706 −0.683532 0.729920i \(-0.739557\pi\)
−0.683532 + 0.729920i \(0.739557\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.62402 0.0554754 0.0277377 0.999615i \(-0.491170\pi\)
0.0277377 + 0.999615i \(0.491170\pi\)
\(858\) 0 0
\(859\) 8.00000 0.272956 0.136478 0.990643i \(-0.456422\pi\)
0.136478 + 0.990643i \(0.456422\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −18.2234 −0.620331 −0.310165 0.950683i \(-0.600384\pi\)
−0.310165 + 0.950683i \(0.600384\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 33.5949 1.14094
\(868\) 0 0
\(869\) 9.55469 0.324121
\(870\) 0 0
\(871\) 27.8813 0.944723
\(872\) 0 0
\(873\) 7.35644 0.248978
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 50.8769 1.71799 0.858996 0.511983i \(-0.171089\pi\)
0.858996 + 0.511983i \(0.171089\pi\)
\(878\) 0 0
\(879\) 48.7040 1.64275
\(880\) 0 0
\(881\) −19.1187 −0.644124 −0.322062 0.946719i \(-0.604376\pi\)
−0.322062 + 0.946719i \(0.604376\pi\)
\(882\) 0 0
\(883\) −39.3174 −1.32313 −0.661567 0.749886i \(-0.730108\pi\)
−0.661567 + 0.749886i \(0.730108\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −27.0398 −0.907907 −0.453954 0.891025i \(-0.649987\pi\)
−0.453954 + 0.891025i \(0.649987\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −10.9174 −0.365747
\(892\) 0 0
\(893\) 83.5507 2.79592
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −28.3369 −0.946142
\(898\) 0 0
\(899\) 30.4556 1.01575
\(900\) 0 0
\(901\) 14.9805 0.499071
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −32.8025 −1.08919 −0.544594 0.838700i \(-0.683316\pi\)
−0.544594 + 0.838700i \(0.683316\pi\)
\(908\) 0 0
\(909\) −62.5854 −2.07583
\(910\) 0 0
\(911\) 6.18799 0.205017 0.102509 0.994732i \(-0.467313\pi\)
0.102509 + 0.994732i \(0.467313\pi\)
\(912\) 0 0
\(913\) 21.1191 0.698941
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −47.7929 −1.57654 −0.788271 0.615328i \(-0.789024\pi\)
−0.788271 + 0.615328i \(0.789024\pi\)
\(920\) 0 0
\(921\) −6.19241 −0.204047
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −26.1489 −0.858843
\(928\) 0 0
\(929\) −39.8618 −1.30782 −0.653912 0.756571i \(-0.726873\pi\)
−0.653912 + 0.756571i \(0.726873\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 14.6347 0.479119
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −0.406229 −0.0132709 −0.00663546 0.999978i \(-0.502112\pi\)
−0.00663546 + 0.999978i \(0.502112\pi\)
\(938\) 0 0
\(939\) 76.8125 2.50668
\(940\) 0 0
\(941\) 33.6543 1.09710 0.548549 0.836119i \(-0.315180\pi\)
0.548549 + 0.836119i \(0.315180\pi\)
\(942\) 0 0
\(943\) 21.5496 0.701750
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.84110 −0.189810 −0.0949050 0.995486i \(-0.530255\pi\)
−0.0949050 + 0.995486i \(0.530255\pi\)
\(948\) 0 0
\(949\) 56.6738 1.83971
\(950\) 0 0
\(951\) 49.2289 1.59636
\(952\) 0 0
\(953\) −32.0605 −1.03854 −0.519271 0.854610i \(-0.673796\pi\)
−0.519271 + 0.854610i \(0.673796\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −14.4062 −0.465687
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 53.0605 1.71163
\(962\) 0 0
\(963\) 6.44673 0.207743
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −24.0896 −0.774669 −0.387334 0.921939i \(-0.626604\pi\)
−0.387334 + 0.921939i \(0.626604\pi\)
\(968\) 0 0
\(969\) 35.3867 1.13678
\(970\) 0 0
\(971\) 18.4707 0.592753 0.296376 0.955071i \(-0.404222\pi\)
0.296376 + 0.955071i \(0.404222\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24.3369 −0.778606 −0.389303 0.921110i \(-0.627284\pi\)
−0.389303 + 0.921110i \(0.627284\pi\)
\(978\) 0 0
\(979\) −9.81201 −0.313593
\(980\) 0 0
\(981\) 71.8725 2.29471
\(982\) 0 0
\(983\) −8.66868 −0.276488 −0.138244 0.990398i \(-0.544146\pi\)
−0.138244 + 0.990398i \(0.544146\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −14.8965 −0.473680
\(990\) 0 0
\(991\) −55.5054 −1.76319 −0.881593 0.472011i \(-0.843528\pi\)
−0.881593 + 0.472011i \(0.843528\pi\)
\(992\) 0 0
\(993\) −6.00000 −0.190404
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 35.1191 1.11223 0.556117 0.831104i \(-0.312291\pi\)
0.556117 + 0.831104i \(0.312291\pi\)
\(998\) 0 0
\(999\) −4.98929 −0.157854
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 9800.2.a.ce.1.1 3
5.4 even 2 1960.2.a.w.1.3 3
7.2 even 3 1400.2.q.j.1201.3 6
7.4 even 3 1400.2.q.j.401.3 6
7.6 odd 2 9800.2.a.cf.1.3 3
20.19 odd 2 3920.2.a.cc.1.1 3
35.2 odd 12 1400.2.bh.i.249.2 12
35.4 even 6 280.2.q.e.121.1 yes 6
35.9 even 6 280.2.q.e.81.1 6
35.18 odd 12 1400.2.bh.i.849.2 12
35.19 odd 6 1960.2.q.w.361.3 6
35.23 odd 12 1400.2.bh.i.249.5 12
35.24 odd 6 1960.2.q.w.961.3 6
35.32 odd 12 1400.2.bh.i.849.5 12
35.34 odd 2 1960.2.a.v.1.1 3
105.44 odd 6 2520.2.bi.q.361.1 6
105.74 odd 6 2520.2.bi.q.1801.1 6
140.39 odd 6 560.2.q.l.401.3 6
140.79 odd 6 560.2.q.l.81.3 6
140.139 even 2 3920.2.a.cb.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.q.e.81.1 6 35.9 even 6
280.2.q.e.121.1 yes 6 35.4 even 6
560.2.q.l.81.3 6 140.79 odd 6
560.2.q.l.401.3 6 140.39 odd 6
1400.2.q.j.401.3 6 7.4 even 3
1400.2.q.j.1201.3 6 7.2 even 3
1400.2.bh.i.249.2 12 35.2 odd 12
1400.2.bh.i.249.5 12 35.23 odd 12
1400.2.bh.i.849.2 12 35.18 odd 12
1400.2.bh.i.849.5 12 35.32 odd 12
1960.2.a.v.1.1 3 35.34 odd 2
1960.2.a.w.1.3 3 5.4 even 2
1960.2.q.w.361.3 6 35.19 odd 6
1960.2.q.w.961.3 6 35.24 odd 6
2520.2.bi.q.361.1 6 105.44 odd 6
2520.2.bi.q.1801.1 6 105.74 odd 6
3920.2.a.cb.1.3 3 140.139 even 2
3920.2.a.cc.1.1 3 20.19 odd 2
9800.2.a.ce.1.1 3 1.1 even 1 trivial
9800.2.a.cf.1.3 3 7.6 odd 2