Properties

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

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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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
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 \(3.12489\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.12489 q^{3} +6.76491 q^{9} +O(q^{10})\) \(q-3.12489 q^{3} +6.76491 q^{9} +2.48486 q^{11} +4.15516 q^{13} -5.76491 q^{17} +1.60975 q^{19} +7.28005 q^{23} -11.7649 q^{27} +1.45459 q^{29} +2.24977 q^{31} -7.76491 q^{33} -6.00000 q^{37} -12.9844 q^{39} -11.2800 q^{41} -5.28005 q^{43} -3.45459 q^{47} +18.0147 q^{51} -9.21949 q^{53} -5.03028 q^{57} +5.92007 q^{59} -5.35998 q^{61} -7.52982 q^{67} -22.7493 q^{69} -4.24977 q^{71} -7.28005 q^{73} +16.9844 q^{79} +16.4693 q^{81} +10.1093 q^{83} -4.54541 q^{87} +11.4693 q^{89} -7.03028 q^{93} +2.73463 q^{97} +16.8099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{3} + 4q^{9} + O(q^{10}) \) \( 3q - q^{3} + 4q^{9} + 7q^{11} + 5q^{13} - q^{17} - 4q^{19} + 6q^{23} - 19q^{27} + 3q^{29} - 10q^{31} - 7q^{33} - 18q^{37} - 5q^{39} - 18q^{41} - 9q^{47} + 21q^{51} - 10q^{53} - 16q^{57} - 6q^{59} - 24q^{61} + 10q^{67} - 18q^{69} + 4q^{71} - 6q^{73} + 17q^{79} + 15q^{81} - 12q^{83} - 15q^{87} - 22q^{93} - 9q^{97} + 2q^{99} + O(q^{100}) \)

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
\(3\) −3.12489 −1.80415 −0.902077 0.431576i \(-0.857958\pi\)
−0.902077 + 0.431576i \(0.857958\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 6.76491 2.25497
\(10\) 0 0
\(11\) 2.48486 0.749214 0.374607 0.927184i \(-0.377778\pi\)
0.374607 + 0.927184i \(0.377778\pi\)
\(12\) 0 0
\(13\) 4.15516 1.15243 0.576217 0.817297i \(-0.304528\pi\)
0.576217 + 0.817297i \(0.304528\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.76491 −1.39820 −0.699098 0.715026i \(-0.746415\pi\)
−0.699098 + 0.715026i \(0.746415\pi\)
\(18\) 0 0
\(19\) 1.60975 0.369301 0.184651 0.982804i \(-0.440885\pi\)
0.184651 + 0.982804i \(0.440885\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.28005 1.51799 0.758997 0.651094i \(-0.225690\pi\)
0.758997 + 0.651094i \(0.225690\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −11.7649 −2.26416
\(28\) 0 0
\(29\) 1.45459 0.270110 0.135055 0.990838i \(-0.456879\pi\)
0.135055 + 0.990838i \(0.456879\pi\)
\(30\) 0 0
\(31\) 2.24977 0.404071 0.202035 0.979378i \(-0.435244\pi\)
0.202035 + 0.979378i \(0.435244\pi\)
\(32\) 0 0
\(33\) −7.76491 −1.35170
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) −12.9844 −2.07917
\(40\) 0 0
\(41\) −11.2800 −1.76165 −0.880824 0.473444i \(-0.843010\pi\)
−0.880824 + 0.473444i \(0.843010\pi\)
\(42\) 0 0
\(43\) −5.28005 −0.805200 −0.402600 0.915376i \(-0.631893\pi\)
−0.402600 + 0.915376i \(0.631893\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.45459 −0.503903 −0.251952 0.967740i \(-0.581072\pi\)
−0.251952 + 0.967740i \(0.581072\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 18.0147 2.52256
\(52\) 0 0
\(53\) −9.21949 −1.26639 −0.633197 0.773990i \(-0.718258\pi\)
−0.633197 + 0.773990i \(0.718258\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.03028 −0.666276
\(58\) 0 0
\(59\) 5.92007 0.770728 0.385364 0.922765i \(-0.374076\pi\)
0.385364 + 0.922765i \(0.374076\pi\)
\(60\) 0 0
\(61\) −5.35998 −0.686275 −0.343137 0.939285i \(-0.611490\pi\)
−0.343137 + 0.939285i \(0.611490\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.52982 −0.919914 −0.459957 0.887941i \(-0.652135\pi\)
−0.459957 + 0.887941i \(0.652135\pi\)
\(68\) 0 0
\(69\) −22.7493 −2.73870
\(70\) 0 0
\(71\) −4.24977 −0.504355 −0.252178 0.967681i \(-0.581147\pi\)
−0.252178 + 0.967681i \(0.581147\pi\)
\(72\) 0 0
\(73\) −7.28005 −0.852065 −0.426033 0.904708i \(-0.640089\pi\)
−0.426033 + 0.904708i \(0.640089\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 16.9844 1.91089 0.955447 0.295162i \(-0.0953735\pi\)
0.955447 + 0.295162i \(0.0953735\pi\)
\(80\) 0 0
\(81\) 16.4693 1.82992
\(82\) 0 0
\(83\) 10.1093 1.10964 0.554819 0.831971i \(-0.312787\pi\)
0.554819 + 0.831971i \(0.312787\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.54541 −0.487320
\(88\) 0 0
\(89\) 11.4693 1.21574 0.607870 0.794037i \(-0.292024\pi\)
0.607870 + 0.794037i \(0.292024\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.03028 −0.729006
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.73463 0.277660 0.138830 0.990316i \(-0.455666\pi\)
0.138830 + 0.990316i \(0.455666\pi\)
\(98\) 0 0
\(99\) 16.8099 1.68945
\(100\) 0 0
\(101\) 4.57947 0.455674 0.227837 0.973699i \(-0.426835\pi\)
0.227837 + 0.973699i \(0.426835\pi\)
\(102\) 0 0
\(103\) 2.48486 0.244841 0.122420 0.992478i \(-0.460934\pi\)
0.122420 + 0.992478i \(0.460934\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −9.95413 −0.953433 −0.476716 0.879057i \(-0.658173\pi\)
−0.476716 + 0.879057i \(0.658173\pi\)
\(110\) 0 0
\(111\) 18.7493 1.77961
\(112\) 0 0
\(113\) −18.4995 −1.74029 −0.870145 0.492795i \(-0.835975\pi\)
−0.870145 + 0.492795i \(0.835975\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 28.1093 2.59870
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.82546 −0.438678
\(122\) 0 0
\(123\) 35.2489 3.17828
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.15894 −0.635253 −0.317627 0.948216i \(-0.602886\pi\)
−0.317627 + 0.948216i \(0.602886\pi\)
\(128\) 0 0
\(129\) 16.4995 1.45270
\(130\) 0 0
\(131\) −7.85952 −0.686689 −0.343345 0.939209i \(-0.611560\pi\)
−0.343345 + 0.939209i \(0.611560\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.5601 −0.902210 −0.451105 0.892471i \(-0.648970\pi\)
−0.451105 + 0.892471i \(0.648970\pi\)
\(138\) 0 0
\(139\) −9.79897 −0.831137 −0.415569 0.909562i \(-0.636417\pi\)
−0.415569 + 0.909562i \(0.636417\pi\)
\(140\) 0 0
\(141\) 10.7952 0.909119
\(142\) 0 0
\(143\) 10.3250 0.863420
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.49954 0.204770 0.102385 0.994745i \(-0.467353\pi\)
0.102385 + 0.994745i \(0.467353\pi\)
\(150\) 0 0
\(151\) −3.76491 −0.306384 −0.153192 0.988196i \(-0.548955\pi\)
−0.153192 + 0.988196i \(0.548955\pi\)
\(152\) 0 0
\(153\) −38.9991 −3.15289
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.67030 0.452539 0.226270 0.974065i \(-0.427347\pi\)
0.226270 + 0.974065i \(0.427347\pi\)
\(158\) 0 0
\(159\) 28.8099 2.28477
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.2498 −0.802824 −0.401412 0.915898i \(-0.631480\pi\)
−0.401412 + 0.915898i \(0.631480\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.95504 −0.228668 −0.114334 0.993442i \(-0.536473\pi\)
−0.114334 + 0.993442i \(0.536473\pi\)
\(168\) 0 0
\(169\) 4.26537 0.328105
\(170\) 0 0
\(171\) 10.8898 0.832763
\(172\) 0 0
\(173\) 22.4049 1.70342 0.851708 0.524017i \(-0.175567\pi\)
0.851708 + 0.524017i \(0.175567\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −18.4995 −1.39051
\(178\) 0 0
\(179\) 14.5601 1.08827 0.544136 0.838997i \(-0.316857\pi\)
0.544136 + 0.838997i \(0.316857\pi\)
\(180\) 0 0
\(181\) 9.67030 0.718788 0.359394 0.933186i \(-0.382983\pi\)
0.359394 + 0.933186i \(0.382983\pi\)
\(182\) 0 0
\(183\) 16.7493 1.23814
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −14.3250 −1.04755
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.01468 0.579922 0.289961 0.957038i \(-0.406358\pi\)
0.289961 + 0.957038i \(0.406358\pi\)
\(192\) 0 0
\(193\) −3.46927 −0.249723 −0.124862 0.992174i \(-0.539849\pi\)
−0.124862 + 0.992174i \(0.539849\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2791 1.15984 0.579920 0.814673i \(-0.303084\pi\)
0.579920 + 0.814673i \(0.303084\pi\)
\(198\) 0 0
\(199\) −26.8704 −1.90479 −0.952397 0.304862i \(-0.901390\pi\)
−0.952397 + 0.304862i \(0.901390\pi\)
\(200\) 0 0
\(201\) 23.5298 1.65967
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 49.2489 3.42303
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 17.2342 1.18645 0.593225 0.805037i \(-0.297855\pi\)
0.593225 + 0.805037i \(0.297855\pi\)
\(212\) 0 0
\(213\) 13.2800 0.909934
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 22.7493 1.53726
\(220\) 0 0
\(221\) −23.9541 −1.61133
\(222\) 0 0
\(223\) −0.235091 −0.0157429 −0.00787143 0.999969i \(-0.502506\pi\)
−0.00787143 + 0.999969i \(0.502506\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.564792 −0.0374865 −0.0187433 0.999824i \(-0.505967\pi\)
−0.0187433 + 0.999824i \(0.505967\pi\)
\(228\) 0 0
\(229\) −7.11021 −0.469856 −0.234928 0.972013i \(-0.575485\pi\)
−0.234928 + 0.972013i \(0.575485\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.49954 −0.556823 −0.278412 0.960462i \(-0.589808\pi\)
−0.278412 + 0.960462i \(0.589808\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −53.0743 −3.44755
\(238\) 0 0
\(239\) −7.26537 −0.469958 −0.234979 0.972001i \(-0.575502\pi\)
−0.234979 + 0.972001i \(0.575502\pi\)
\(240\) 0 0
\(241\) −7.28005 −0.468949 −0.234475 0.972122i \(-0.575337\pi\)
−0.234475 + 0.972122i \(0.575337\pi\)
\(242\) 0 0
\(243\) −16.1698 −1.03730
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.68876 0.425596
\(248\) 0 0
\(249\) −31.5904 −2.00196
\(250\) 0 0
\(251\) −22.9192 −1.44664 −0.723322 0.690511i \(-0.757386\pi\)
−0.723322 + 0.690511i \(0.757386\pi\)
\(252\) 0 0
\(253\) 18.0899 1.13730
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0.719953 0.0449094 0.0224547 0.999748i \(-0.492852\pi\)
0.0224547 + 0.999748i \(0.492852\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.84014 0.609089
\(262\) 0 0
\(263\) 18.5601 1.14446 0.572232 0.820092i \(-0.306078\pi\)
0.572232 + 0.820092i \(0.306078\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −35.8401 −2.19338
\(268\) 0 0
\(269\) 22.1698 1.35172 0.675860 0.737030i \(-0.263773\pi\)
0.675860 + 0.737030i \(0.263773\pi\)
\(270\) 0 0
\(271\) 7.87890 0.478609 0.239304 0.970945i \(-0.423081\pi\)
0.239304 + 0.970945i \(0.423081\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.78051 0.167064 0.0835322 0.996505i \(-0.473380\pi\)
0.0835322 + 0.996505i \(0.473380\pi\)
\(278\) 0 0
\(279\) 15.2195 0.911167
\(280\) 0 0
\(281\) −23.7044 −1.41408 −0.707042 0.707172i \(-0.749971\pi\)
−0.707042 + 0.707172i \(0.749971\pi\)
\(282\) 0 0
\(283\) 26.8439 1.59571 0.797853 0.602852i \(-0.205969\pi\)
0.797853 + 0.602852i \(0.205969\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.2342 0.954951
\(290\) 0 0
\(291\) −8.54541 −0.500941
\(292\) 0 0
\(293\) −9.93475 −0.580394 −0.290197 0.956967i \(-0.593721\pi\)
−0.290197 + 0.956967i \(0.593721\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −29.2342 −1.69634
\(298\) 0 0
\(299\) 30.2498 1.74939
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −14.3103 −0.822107
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −32.0946 −1.83174 −0.915868 0.401479i \(-0.868496\pi\)
−0.915868 + 0.401479i \(0.868496\pi\)
\(308\) 0 0
\(309\) −7.76491 −0.441730
\(310\) 0 0
\(311\) 10.0606 0.570482 0.285241 0.958456i \(-0.407926\pi\)
0.285241 + 0.958456i \(0.407926\pi\)
\(312\) 0 0
\(313\) 20.8245 1.17707 0.588536 0.808471i \(-0.299704\pi\)
0.588536 + 0.808471i \(0.299704\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.7502 −0.884621 −0.442311 0.896862i \(-0.645841\pi\)
−0.442311 + 0.896862i \(0.645841\pi\)
\(318\) 0 0
\(319\) 3.61445 0.202370
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −9.28005 −0.516356
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 31.1055 1.72014
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −25.7796 −1.41697 −0.708487 0.705724i \(-0.750622\pi\)
−0.708487 + 0.705724i \(0.750622\pi\)
\(332\) 0 0
\(333\) −40.5895 −2.22429
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.0605522 −0.00329849 −0.00164924 0.999999i \(-0.500525\pi\)
−0.00164924 + 0.999999i \(0.500525\pi\)
\(338\) 0 0
\(339\) 57.8089 3.13975
\(340\) 0 0
\(341\) 5.59037 0.302736
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.9310 1.12363 0.561817 0.827262i \(-0.310103\pi\)
0.561817 + 0.827262i \(0.310103\pi\)
\(348\) 0 0
\(349\) −5.48108 −0.293396 −0.146698 0.989181i \(-0.546864\pi\)
−0.146698 + 0.989181i \(0.546864\pi\)
\(350\) 0 0
\(351\) −48.8851 −2.60929
\(352\) 0 0
\(353\) −26.9239 −1.43301 −0.716506 0.697581i \(-0.754260\pi\)
−0.716506 + 0.697581i \(0.754260\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.06055 0.319864 0.159932 0.987128i \(-0.448873\pi\)
0.159932 + 0.987128i \(0.448873\pi\)
\(360\) 0 0
\(361\) −16.4087 −0.863616
\(362\) 0 0
\(363\) 15.0790 0.791443
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 30.7034 1.60271 0.801353 0.598191i \(-0.204114\pi\)
0.801353 + 0.598191i \(0.204114\pi\)
\(368\) 0 0
\(369\) −76.3085 −3.97246
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.8099 0.559714 0.279857 0.960042i \(-0.409713\pi\)
0.279857 + 0.960042i \(0.409713\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.04404 0.311284
\(378\) 0 0
\(379\) −9.28005 −0.476684 −0.238342 0.971181i \(-0.576604\pi\)
−0.238342 + 0.971181i \(0.576604\pi\)
\(380\) 0 0
\(381\) 22.3709 1.14609
\(382\) 0 0
\(383\) −5.28005 −0.269798 −0.134899 0.990859i \(-0.543071\pi\)
−0.134899 + 0.990859i \(0.543071\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −35.7190 −1.81570
\(388\) 0 0
\(389\) 5.48395 0.278047 0.139024 0.990289i \(-0.455604\pi\)
0.139024 + 0.990289i \(0.455604\pi\)
\(390\) 0 0
\(391\) −41.9688 −2.12245
\(392\) 0 0
\(393\) 24.5601 1.23889
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 6.40493 0.321454 0.160727 0.986999i \(-0.448616\pi\)
0.160727 + 0.986999i \(0.448616\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.20482 −0.0601656 −0.0300828 0.999547i \(-0.509577\pi\)
−0.0300828 + 0.999547i \(0.509577\pi\)
\(402\) 0 0
\(403\) 9.34816 0.465665
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.9092 −0.739020
\(408\) 0 0
\(409\) 2.31032 0.114238 0.0571191 0.998367i \(-0.481809\pi\)
0.0571191 + 0.998367i \(0.481809\pi\)
\(410\) 0 0
\(411\) 32.9991 1.62772
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 30.6206 1.49950
\(418\) 0 0
\(419\) 19.7384 0.964285 0.482142 0.876093i \(-0.339859\pi\)
0.482142 + 0.876093i \(0.339859\pi\)
\(420\) 0 0
\(421\) 30.1433 1.46910 0.734548 0.678556i \(-0.237394\pi\)
0.734548 + 0.678556i \(0.237394\pi\)
\(422\) 0 0
\(423\) −23.3700 −1.13629
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −32.2645 −1.55774
\(430\) 0 0
\(431\) −4.61353 −0.222226 −0.111113 0.993808i \(-0.535442\pi\)
−0.111113 + 0.993808i \(0.535442\pi\)
\(432\) 0 0
\(433\) −11.4399 −0.549767 −0.274883 0.961478i \(-0.588639\pi\)
−0.274883 + 0.961478i \(0.588639\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 11.7190 0.560598
\(438\) 0 0
\(439\) −12.0294 −0.574130 −0.287065 0.957911i \(-0.592680\pi\)
−0.287065 + 0.957911i \(0.592680\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.4390 0.686017 0.343009 0.939332i \(-0.388554\pi\)
0.343009 + 0.939332i \(0.388554\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −7.81078 −0.369437
\(448\) 0 0
\(449\) 19.2342 0.907717 0.453858 0.891074i \(-0.350047\pi\)
0.453858 + 0.891074i \(0.350047\pi\)
\(450\) 0 0
\(451\) −28.0294 −1.31985
\(452\) 0 0
\(453\) 11.7649 0.552764
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −34.8780 −1.63152 −0.815762 0.578388i \(-0.803682\pi\)
−0.815762 + 0.578388i \(0.803682\pi\)
\(458\) 0 0
\(459\) 67.8236 3.16574
\(460\) 0 0
\(461\) 15.2607 0.710760 0.355380 0.934722i \(-0.384351\pi\)
0.355380 + 0.934722i \(0.384351\pi\)
\(462\) 0 0
\(463\) −24.9991 −1.16181 −0.580903 0.813973i \(-0.697300\pi\)
−0.580903 + 0.813973i \(0.697300\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 5.06433 0.234349 0.117175 0.993111i \(-0.462616\pi\)
0.117175 + 0.993111i \(0.462616\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −17.7190 −0.816450
\(472\) 0 0
\(473\) −13.1202 −0.603267
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −62.3690 −2.85568
\(478\) 0 0
\(479\) −41.8089 −1.91030 −0.955150 0.296123i \(-0.904306\pi\)
−0.955150 + 0.296123i \(0.904306\pi\)
\(480\) 0 0
\(481\) −24.9310 −1.13675
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −21.3406 −0.967035 −0.483517 0.875335i \(-0.660641\pi\)
−0.483517 + 0.875335i \(0.660641\pi\)
\(488\) 0 0
\(489\) 32.0294 1.44842
\(490\) 0 0
\(491\) 8.35620 0.377110 0.188555 0.982063i \(-0.439620\pi\)
0.188555 + 0.982063i \(0.439620\pi\)
\(492\) 0 0
\(493\) −8.38555 −0.377666
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −38.8539 −1.73934 −0.869670 0.493634i \(-0.835668\pi\)
−0.869670 + 0.493634i \(0.835668\pi\)
\(500\) 0 0
\(501\) 9.23417 0.412552
\(502\) 0 0
\(503\) −17.7044 −0.789398 −0.394699 0.918810i \(-0.629151\pi\)
−0.394699 + 0.918810i \(0.629151\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −13.3288 −0.591952
\(508\) 0 0
\(509\) −7.11021 −0.315154 −0.157577 0.987507i \(-0.550368\pi\)
−0.157577 + 0.987507i \(0.550368\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −18.9385 −0.836157
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8.58417 −0.377531
\(518\) 0 0
\(519\) −70.0128 −3.07322
\(520\) 0 0
\(521\) −18.1892 −0.796884 −0.398442 0.917194i \(-0.630449\pi\)
−0.398442 + 0.917194i \(0.630449\pi\)
\(522\) 0 0
\(523\) −13.9882 −0.611661 −0.305830 0.952086i \(-0.598934\pi\)
−0.305830 + 0.952086i \(0.598934\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.9697 −0.564970
\(528\) 0 0
\(529\) 29.9991 1.30431
\(530\) 0 0
\(531\) 40.0487 1.73797
\(532\) 0 0
\(533\) −46.8704 −2.03018
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −45.4986 −1.96341
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −20.8245 −0.895317 −0.447659 0.894205i \(-0.647742\pi\)
−0.447659 + 0.894205i \(0.647742\pi\)
\(542\) 0 0
\(543\) −30.2186 −1.29680
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 3.09839 0.132478 0.0662388 0.997804i \(-0.478900\pi\)
0.0662388 + 0.997804i \(0.478900\pi\)
\(548\) 0 0
\(549\) −36.2598 −1.54753
\(550\) 0 0
\(551\) 2.34152 0.0997519
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −18.8099 −0.797000 −0.398500 0.917168i \(-0.630469\pi\)
−0.398500 + 0.917168i \(0.630469\pi\)
\(558\) 0 0
\(559\) −21.9394 −0.927940
\(560\) 0 0
\(561\) 44.7640 1.88994
\(562\) 0 0
\(563\) −28.9503 −1.22011 −0.610056 0.792358i \(-0.708853\pi\)
−0.610056 + 0.792358i \(0.708853\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −29.9688 −1.25636 −0.628179 0.778069i \(-0.716199\pi\)
−0.628179 + 0.778069i \(0.716199\pi\)
\(570\) 0 0
\(571\) 0.280964 0.0117580 0.00587898 0.999983i \(-0.498129\pi\)
0.00587898 + 0.999983i \(0.498129\pi\)
\(572\) 0 0
\(573\) −25.0450 −1.04627
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −25.9541 −1.08048 −0.540242 0.841510i \(-0.681667\pi\)
−0.540242 + 0.841510i \(0.681667\pi\)
\(578\) 0 0
\(579\) 10.8411 0.450539
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −22.9092 −0.948801
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.2304 0.917547 0.458773 0.888553i \(-0.348289\pi\)
0.458773 + 0.888553i \(0.348289\pi\)
\(588\) 0 0
\(589\) 3.62156 0.149224
\(590\) 0 0
\(591\) −50.8704 −2.09253
\(592\) 0 0
\(593\) −35.0743 −1.44033 −0.720165 0.693803i \(-0.755934\pi\)
−0.720165 + 0.693803i \(0.755934\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 83.9670 3.43654
\(598\) 0 0
\(599\) −21.7262 −0.887707 −0.443853 0.896099i \(-0.646389\pi\)
−0.443853 + 0.896099i \(0.646389\pi\)
\(600\) 0 0
\(601\) 23.9688 0.977708 0.488854 0.872366i \(-0.337415\pi\)
0.488854 + 0.872366i \(0.337415\pi\)
\(602\) 0 0
\(603\) −50.9385 −2.07438
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −43.3241 −1.75847 −0.879235 0.476388i \(-0.841946\pi\)
−0.879235 + 0.476388i \(0.841946\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −14.3544 −0.580715
\(612\) 0 0
\(613\) −8.90917 −0.359838 −0.179919 0.983681i \(-0.557584\pi\)
−0.179919 + 0.983681i \(0.557584\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 27.2413 1.09669 0.548347 0.836251i \(-0.315257\pi\)
0.548347 + 0.836251i \(0.315257\pi\)
\(618\) 0 0
\(619\) −24.1405 −0.970288 −0.485144 0.874434i \(-0.661233\pi\)
−0.485144 + 0.874434i \(0.661233\pi\)
\(620\) 0 0
\(621\) −85.6491 −3.43698
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −12.4995 −0.499184
\(628\) 0 0
\(629\) 34.5895 1.37917
\(630\) 0 0
\(631\) 8.01468 0.319059 0.159530 0.987193i \(-0.449002\pi\)
0.159530 + 0.987193i \(0.449002\pi\)
\(632\) 0 0
\(633\) −53.8548 −2.14054
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −28.7493 −1.13731
\(640\) 0 0
\(641\) −49.1495 −1.94129 −0.970645 0.240516i \(-0.922683\pi\)
−0.970645 + 0.240516i \(0.922683\pi\)
\(642\) 0 0
\(643\) −7.24599 −0.285754 −0.142877 0.989740i \(-0.545635\pi\)
−0.142877 + 0.989740i \(0.545635\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.2791 −1.19040 −0.595198 0.803579i \(-0.702926\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(648\) 0 0
\(649\) 14.7106 0.577440
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.96881 0.311844 0.155922 0.987769i \(-0.450165\pi\)
0.155922 + 0.987769i \(0.450165\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −49.2489 −1.92138
\(658\) 0 0
\(659\) 20.9239 0.815078 0.407539 0.913188i \(-0.366387\pi\)
0.407539 + 0.913188i \(0.366387\pi\)
\(660\) 0 0
\(661\) −46.1992 −1.79694 −0.898470 0.439034i \(-0.855321\pi\)
−0.898470 + 0.439034i \(0.855321\pi\)
\(662\) 0 0
\(663\) 74.8539 2.90708
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.5895 0.410025
\(668\) 0 0
\(669\) 0.734633 0.0284025
\(670\) 0 0
\(671\) −13.3188 −0.514167
\(672\) 0 0
\(673\) 40.3784 1.55647 0.778237 0.627970i \(-0.216114\pi\)
0.778237 + 0.627970i \(0.216114\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 44.3737 1.70542 0.852711 0.522383i \(-0.174957\pi\)
0.852711 + 0.522383i \(0.174957\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.76491 0.0676315
\(682\) 0 0
\(683\) 17.9394 0.686434 0.343217 0.939256i \(-0.388483\pi\)
0.343217 + 0.939256i \(0.388483\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 22.2186 0.847692
\(688\) 0 0
\(689\) −38.3085 −1.45944
\(690\) 0 0
\(691\) 12.7905 0.486573 0.243287 0.969954i \(-0.421774\pi\)
0.243287 + 0.969954i \(0.421774\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 65.0284 2.46313
\(698\) 0 0
\(699\) 26.5601 1.00460
\(700\) 0 0
\(701\) −19.4234 −0.733611 −0.366806 0.930298i \(-0.619549\pi\)
−0.366806 + 0.930298i \(0.619549\pi\)
\(702\) 0 0
\(703\) −9.65848 −0.364277
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.4839 −0.506400 −0.253200 0.967414i \(-0.581483\pi\)
−0.253200 + 0.967414i \(0.581483\pi\)
\(710\) 0 0
\(711\) 114.898 4.30901
\(712\) 0 0
\(713\) 16.3784 0.613377
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 22.7034 0.847876
\(718\) 0 0
\(719\) −15.3700 −0.573203 −0.286601 0.958050i \(-0.592526\pi\)
−0.286601 + 0.958050i \(0.592526\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 22.7493 0.846056
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 13.1589 0.488038 0.244019 0.969770i \(-0.421534\pi\)
0.244019 + 0.969770i \(0.421534\pi\)
\(728\) 0 0
\(729\) 1.12110 0.0415224
\(730\) 0 0
\(731\) 30.4390 1.12583
\(732\) 0 0
\(733\) −10.0265 −0.370337 −0.185169 0.982707i \(-0.559283\pi\)
−0.185169 + 0.982707i \(0.559283\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.7106 −0.689212
\(738\) 0 0
\(739\) 19.2266 0.707262 0.353631 0.935385i \(-0.384947\pi\)
0.353631 + 0.935385i \(0.384947\pi\)
\(740\) 0 0
\(741\) −20.9016 −0.767840
\(742\) 0 0
\(743\) 5.21949 0.191485 0.0957423 0.995406i \(-0.469478\pi\)
0.0957423 + 0.995406i \(0.469478\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 68.3884 2.50220
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 29.8548 1.08942 0.544709 0.838625i \(-0.316640\pi\)
0.544709 + 0.838625i \(0.316640\pi\)
\(752\) 0 0
\(753\) 71.6197 2.60997
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 18.0294 0.655288 0.327644 0.944801i \(-0.393745\pi\)
0.327644 + 0.944801i \(0.393745\pi\)
\(758\) 0 0
\(759\) −56.5289 −2.05187
\(760\) 0 0
\(761\) −8.22041 −0.297990 −0.148995 0.988838i \(-0.547604\pi\)
−0.148995 + 0.988838i \(0.547604\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24.5988 0.888213
\(768\) 0 0
\(769\) −50.6888 −1.82788 −0.913942 0.405845i \(-0.866977\pi\)
−0.913942 + 0.405845i \(0.866977\pi\)
\(770\) 0 0
\(771\) −2.24977 −0.0810235
\(772\) 0 0
\(773\) 6.99622 0.251637 0.125818 0.992053i \(-0.459844\pi\)
0.125818 + 0.992053i \(0.459844\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −18.1580 −0.650579
\(780\) 0 0
\(781\) −10.5601 −0.377870
\(782\) 0 0
\(783\) −17.1131 −0.611571
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −14.3444 −0.511322 −0.255661 0.966767i \(-0.582293\pi\)
−0.255661 + 0.966767i \(0.582293\pi\)
\(788\) 0 0
\(789\) −57.9982 −2.06479
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −22.2716 −0.790887
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −13.9348 −0.493594 −0.246797 0.969067i \(-0.579378\pi\)
−0.246797 + 0.969067i \(0.579378\pi\)
\(798\) 0 0
\(799\) 19.9154 0.704555
\(800\) 0 0
\(801\) 77.5885 2.74146
\(802\) 0 0
\(803\) −18.0899 −0.638379
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −69.2782 −2.43871
\(808\) 0 0
\(809\) −5.58325 −0.196297 −0.0981483 0.995172i \(-0.531292\pi\)
−0.0981483 + 0.995172i \(0.531292\pi\)
\(810\) 0 0
\(811\) 6.57947 0.231036 0.115518 0.993305i \(-0.463147\pi\)
0.115518 + 0.993305i \(0.463147\pi\)
\(812\) 0 0
\(813\) −24.6206 −0.863484
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −8.49954 −0.297361
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 16.3250 0.569747 0.284873 0.958565i \(-0.408048\pi\)
0.284873 + 0.958565i \(0.408048\pi\)
\(822\) 0 0
\(823\) −12.3491 −0.430462 −0.215231 0.976563i \(-0.569050\pi\)
−0.215231 + 0.976563i \(0.569050\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −6.40963 −0.222885 −0.111442 0.993771i \(-0.535547\pi\)
−0.111442 + 0.993771i \(0.535547\pi\)
\(828\) 0 0
\(829\) 26.1698 0.908916 0.454458 0.890768i \(-0.349833\pi\)
0.454458 + 0.890768i \(0.349833\pi\)
\(830\) 0 0
\(831\) −8.68876 −0.301410
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −26.4683 −0.914880
\(838\) 0 0
\(839\) 1.12958 0.0389975 0.0194988 0.999810i \(-0.493793\pi\)
0.0194988 + 0.999810i \(0.493793\pi\)
\(840\) 0 0
\(841\) −26.8842 −0.927041
\(842\) 0 0
\(843\) 74.0734 2.55122
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −83.8842 −2.87890
\(850\) 0 0
\(851\) −43.6803 −1.49734
\(852\) 0 0
\(853\) 6.29095 0.215398 0.107699 0.994184i \(-0.465652\pi\)
0.107699 + 0.994184i \(0.465652\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.0596 −0.856021 −0.428010 0.903774i \(-0.640785\pi\)
−0.428010 + 0.903774i \(0.640785\pi\)
\(858\) 0 0
\(859\) −53.7896 −1.83528 −0.917638 0.397417i \(-0.869907\pi\)
−0.917638 + 0.397417i \(0.869907\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 58.0899 1.97740 0.988702 0.149896i \(-0.0478938\pi\)
0.988702 + 0.149896i \(0.0478938\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −50.7299 −1.72288
\(868\) 0 0
\(869\) 42.2039 1.43167
\(870\) 0 0
\(871\) −31.2876 −1.06014
\(872\) 0 0
\(873\) 18.4995 0.626115
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 24.0899 0.813459 0.406729 0.913549i \(-0.366669\pi\)
0.406729 + 0.913549i \(0.366669\pi\)
\(878\) 0 0
\(879\) 31.0450 1.04712
\(880\) 0 0
\(881\) −40.9679 −1.38024 −0.690122 0.723693i \(-0.742443\pi\)
−0.690122 + 0.723693i \(0.742443\pi\)
\(882\) 0 0
\(883\) 43.8014 1.47403 0.737017 0.675874i \(-0.236234\pi\)
0.737017 + 0.675874i \(0.236234\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.77959 −0.0597527 −0.0298764 0.999554i \(-0.509511\pi\)
−0.0298764 + 0.999554i \(0.509511\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 40.9239 1.37100
\(892\) 0 0
\(893\) −5.56101 −0.186092
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −94.5271 −3.15617
\(898\) 0 0
\(899\) 3.27248 0.109143
\(900\) 0 0
\(901\) 53.1495 1.77067
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −53.0284 −1.76078 −0.880390 0.474250i \(-0.842719\pi\)
−0.880390 + 0.474250i \(0.842719\pi\)
\(908\) 0 0
\(909\) 30.9797 1.02753
\(910\) 0 0
\(911\) 28.1798 0.933639 0.466820 0.884353i \(-0.345400\pi\)
0.466820 + 0.884353i \(0.345400\pi\)
\(912\) 0 0
\(913\) 25.1202 0.831357
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 38.4243 1.26750 0.633751 0.773538i \(-0.281515\pi\)
0.633751 + 0.773538i \(0.281515\pi\)
\(920\) 0 0
\(921\) 100.292 3.30473
\(922\) 0 0
\(923\) −17.6585 −0.581236
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 16.8099 0.552108
\(928\) 0 0
\(929\) 36.6576 1.20270 0.601348 0.798987i \(-0.294631\pi\)
0.601348 + 0.798987i \(0.294631\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −31.4381 −1.02924
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.83302 0.190557 0.0952783 0.995451i \(-0.469626\pi\)
0.0952783 + 0.995451i \(0.469626\pi\)
\(938\) 0 0
\(939\) −65.0743 −2.12362
\(940\) 0 0
\(941\) 2.23796 0.0729553 0.0364776 0.999334i \(-0.488386\pi\)
0.0364776 + 0.999334i \(0.488386\pi\)
\(942\) 0 0
\(943\) −82.1193 −2.67417
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 17.7502 0.576805 0.288402 0.957509i \(-0.406876\pi\)
0.288402 + 0.957509i \(0.406876\pi\)
\(948\) 0 0
\(949\) −30.2498 −0.981949
\(950\) 0 0
\(951\) 49.2177 1.59599
\(952\) 0 0
\(953\) 32.0294 1.03753 0.518766 0.854916i \(-0.326391\pi\)
0.518766 + 0.854916i \(0.326391\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −11.2947 −0.365107
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −25.9385 −0.836727
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −43.4305 −1.39663 −0.698316 0.715790i \(-0.746067\pi\)
−0.698316 + 0.715790i \(0.746067\pi\)
\(968\) 0 0
\(969\) 28.9991 0.931585
\(970\) 0 0
\(971\) 1.79897 0.0577316 0.0288658 0.999583i \(-0.490810\pi\)
0.0288658 + 0.999583i \(0.490810\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 22.4390 0.717887 0.358943 0.933359i \(-0.383137\pi\)
0.358943 + 0.933359i \(0.383137\pi\)
\(978\) 0 0
\(979\) 28.4995 0.910849
\(980\) 0 0
\(981\) −67.3388 −2.14996
\(982\) 0 0
\(983\) 37.6950 1.20228 0.601141 0.799143i \(-0.294713\pi\)
0.601141 + 0.799143i \(0.294713\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −38.4390 −1.22229
\(990\) 0 0
\(991\) 13.5686 0.431020 0.215510 0.976502i \(-0.430859\pi\)
0.215510 + 0.976502i \(0.430859\pi\)
\(992\) 0 0
\(993\) 80.5583 2.55644
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 14.2838 0.452373 0.226187 0.974084i \(-0.427374\pi\)
0.226187 + 0.974084i \(0.427374\pi\)
\(998\) 0 0
\(999\) 70.5895 2.23335
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.cd.1.1 3
5.2 odd 4 1960.2.g.c.1569.6 6
5.3 odd 4 1960.2.g.c.1569.1 6
5.4 even 2 9800.2.a.cg.1.3 3
7.6 odd 2 1400.2.a.t.1.3 3
28.27 even 2 2800.2.a.bq.1.1 3
35.13 even 4 280.2.g.b.169.6 yes 6
35.27 even 4 280.2.g.b.169.1 6
35.34 odd 2 1400.2.a.s.1.1 3
105.62 odd 4 2520.2.t.g.1009.2 6
105.83 odd 4 2520.2.t.g.1009.1 6
140.27 odd 4 560.2.g.f.449.6 6
140.83 odd 4 560.2.g.f.449.1 6
140.139 even 2 2800.2.a.br.1.3 3
280.13 even 4 2240.2.g.l.449.1 6
280.27 odd 4 2240.2.g.m.449.1 6
280.83 odd 4 2240.2.g.m.449.6 6
280.237 even 4 2240.2.g.l.449.6 6
420.83 even 4 5040.2.t.y.1009.1 6
420.167 even 4 5040.2.t.y.1009.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.g.b.169.1 6 35.27 even 4
280.2.g.b.169.6 yes 6 35.13 even 4
560.2.g.f.449.1 6 140.83 odd 4
560.2.g.f.449.6 6 140.27 odd 4
1400.2.a.s.1.1 3 35.34 odd 2
1400.2.a.t.1.3 3 7.6 odd 2
1960.2.g.c.1569.1 6 5.3 odd 4
1960.2.g.c.1569.6 6 5.2 odd 4
2240.2.g.l.449.1 6 280.13 even 4
2240.2.g.l.449.6 6 280.237 even 4
2240.2.g.m.449.1 6 280.27 odd 4
2240.2.g.m.449.6 6 280.83 odd 4
2520.2.t.g.1009.1 6 105.83 odd 4
2520.2.t.g.1009.2 6 105.62 odd 4
2800.2.a.bq.1.1 3 28.27 even 2
2800.2.a.br.1.3 3 140.139 even 2
5040.2.t.y.1009.1 6 420.83 even 4
5040.2.t.y.1009.2 6 420.167 even 4
9800.2.a.cd.1.1 3 1.1 even 1 trivial
9800.2.a.cg.1.3 3 5.4 even 2