Properties

Label 9800.2.a.db.1.5
Level $9800$
Weight $2$
Character 9800.1
Self dual yes
Analytic conductor $78.253$
Analytic rank $1$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9800,2,Mod(1,9800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9800.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9800.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(78.2533939809\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{41}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 1960)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.61569\) of defining polynomial
Character \(\chi\) \(=\) 9800.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.836591 q^{3} -2.30012 q^{9} +O(q^{10})\) \(q-0.836591 q^{3} -2.30012 q^{9} +0.403442 q^{11} -6.20918 q^{13} -2.62588 q^{17} +6.41173 q^{19} -6.54712 q^{23} +4.43403 q^{27} +1.96279 q^{29} +4.66707 q^{31} -0.337516 q^{33} +3.44379 q^{37} +5.19455 q^{39} +2.68230 q^{41} +10.8609 q^{43} +9.67165 q^{47} +2.19679 q^{51} +5.97422 q^{53} -5.36400 q^{57} +9.18754 q^{59} +5.69505 q^{61} -11.8844 q^{67} +5.47726 q^{69} -0.530435 q^{71} -8.20102 q^{73} -9.12014 q^{79} +3.19087 q^{81} -2.96013 q^{83} -1.64206 q^{87} -10.8387 q^{89} -3.90443 q^{93} +13.5581 q^{97} -0.927964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 14 q^{9} - 12 q^{11} - 16 q^{23} + 12 q^{29} - 36 q^{37} - 20 q^{39} - 24 q^{43} - 36 q^{51} - 8 q^{53} - 16 q^{57} - 40 q^{67} - 8 q^{71} - 4 q^{79} + 50 q^{81} - 48 q^{93} - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −0.836591 −0.483006 −0.241503 0.970400i \(-0.577640\pi\)
−0.241503 + 0.970400i \(0.577640\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.30012 −0.766705
\(10\) 0 0
\(11\) 0.403442 0.121642 0.0608212 0.998149i \(-0.480628\pi\)
0.0608212 + 0.998149i \(0.480628\pi\)
\(12\) 0 0
\(13\) −6.20918 −1.72212 −0.861058 0.508506i \(-0.830198\pi\)
−0.861058 + 0.508506i \(0.830198\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.62588 −0.636869 −0.318435 0.947945i \(-0.603157\pi\)
−0.318435 + 0.947945i \(0.603157\pi\)
\(18\) 0 0
\(19\) 6.41173 1.47095 0.735476 0.677551i \(-0.236959\pi\)
0.735476 + 0.677551i \(0.236959\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.54712 −1.36517 −0.682584 0.730807i \(-0.739144\pi\)
−0.682584 + 0.730807i \(0.739144\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.43403 0.853329
\(28\) 0 0
\(29\) 1.96279 0.364482 0.182241 0.983254i \(-0.441665\pi\)
0.182241 + 0.983254i \(0.441665\pi\)
\(30\) 0 0
\(31\) 4.66707 0.838230 0.419115 0.907933i \(-0.362340\pi\)
0.419115 + 0.907933i \(0.362340\pi\)
\(32\) 0 0
\(33\) −0.337516 −0.0587541
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.44379 0.566155 0.283078 0.959097i \(-0.408645\pi\)
0.283078 + 0.959097i \(0.408645\pi\)
\(38\) 0 0
\(39\) 5.19455 0.831793
\(40\) 0 0
\(41\) 2.68230 0.418905 0.209452 0.977819i \(-0.432832\pi\)
0.209452 + 0.977819i \(0.432832\pi\)
\(42\) 0 0
\(43\) 10.8609 1.65627 0.828136 0.560528i \(-0.189402\pi\)
0.828136 + 0.560528i \(0.189402\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.67165 1.41076 0.705378 0.708832i \(-0.250777\pi\)
0.705378 + 0.708832i \(0.250777\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 2.19679 0.307612
\(52\) 0 0
\(53\) 5.97422 0.820623 0.410311 0.911946i \(-0.365420\pi\)
0.410311 + 0.911946i \(0.365420\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.36400 −0.710479
\(58\) 0 0
\(59\) 9.18754 1.19612 0.598058 0.801453i \(-0.295939\pi\)
0.598058 + 0.801453i \(0.295939\pi\)
\(60\) 0 0
\(61\) 5.69505 0.729176 0.364588 0.931169i \(-0.381210\pi\)
0.364588 + 0.931169i \(0.381210\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.8844 −1.45191 −0.725957 0.687740i \(-0.758603\pi\)
−0.725957 + 0.687740i \(0.758603\pi\)
\(68\) 0 0
\(69\) 5.47726 0.659385
\(70\) 0 0
\(71\) −0.530435 −0.0629511 −0.0314755 0.999505i \(-0.510021\pi\)
−0.0314755 + 0.999505i \(0.510021\pi\)
\(72\) 0 0
\(73\) −8.20102 −0.959856 −0.479928 0.877308i \(-0.659337\pi\)
−0.479928 + 0.877308i \(0.659337\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −9.12014 −1.02610 −0.513048 0.858360i \(-0.671484\pi\)
−0.513048 + 0.858360i \(0.671484\pi\)
\(80\) 0 0
\(81\) 3.19087 0.354542
\(82\) 0 0
\(83\) −2.96013 −0.324917 −0.162458 0.986715i \(-0.551942\pi\)
−0.162458 + 0.986715i \(0.551942\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.64206 −0.176047
\(88\) 0 0
\(89\) −10.8387 −1.14890 −0.574449 0.818540i \(-0.694784\pi\)
−0.574449 + 0.818540i \(0.694784\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.90443 −0.404870
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.5581 1.37661 0.688307 0.725419i \(-0.258354\pi\)
0.688307 + 0.725419i \(0.258354\pi\)
\(98\) 0 0
\(99\) −0.927964 −0.0932639
\(100\) 0 0
\(101\) −1.56081 −0.155306 −0.0776531 0.996980i \(-0.524743\pi\)
−0.0776531 + 0.996980i \(0.524743\pi\)
\(102\) 0 0
\(103\) −2.12354 −0.209239 −0.104619 0.994512i \(-0.533362\pi\)
−0.104619 + 0.994512i \(0.533362\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.15510 0.208341 0.104171 0.994559i \(-0.466781\pi\)
0.104171 + 0.994559i \(0.466781\pi\)
\(108\) 0 0
\(109\) −11.2910 −1.08148 −0.540742 0.841189i \(-0.681856\pi\)
−0.540742 + 0.841189i \(0.681856\pi\)
\(110\) 0 0
\(111\) −2.88104 −0.273456
\(112\) 0 0
\(113\) −4.88668 −0.459700 −0.229850 0.973226i \(-0.573824\pi\)
−0.229850 + 0.973226i \(0.573824\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 14.2818 1.32036
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.8372 −0.985203
\(122\) 0 0
\(123\) −2.24399 −0.202334
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.97422 −0.885069 −0.442535 0.896751i \(-0.645921\pi\)
−0.442535 + 0.896751i \(0.645921\pi\)
\(128\) 0 0
\(129\) −9.08613 −0.799989
\(130\) 0 0
\(131\) −11.8667 −1.03680 −0.518398 0.855140i \(-0.673471\pi\)
−0.518398 + 0.855140i \(0.673471\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.7167 −1.25733 −0.628666 0.777675i \(-0.716399\pi\)
−0.628666 + 0.777675i \(0.716399\pi\)
\(138\) 0 0
\(139\) −5.80345 −0.492242 −0.246121 0.969239i \(-0.579156\pi\)
−0.246121 + 0.969239i \(0.579156\pi\)
\(140\) 0 0
\(141\) −8.09122 −0.681404
\(142\) 0 0
\(143\) −2.50505 −0.209483
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 14.5957 1.19573 0.597865 0.801597i \(-0.296016\pi\)
0.597865 + 0.801597i \(0.296016\pi\)
\(150\) 0 0
\(151\) −21.1854 −1.72405 −0.862024 0.506868i \(-0.830803\pi\)
−0.862024 + 0.506868i \(0.830803\pi\)
\(152\) 0 0
\(153\) 6.03982 0.488291
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −19.2637 −1.53741 −0.768703 0.639605i \(-0.779098\pi\)
−0.768703 + 0.639605i \(0.779098\pi\)
\(158\) 0 0
\(159\) −4.99798 −0.396366
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −13.3427 −1.04508 −0.522541 0.852614i \(-0.675016\pi\)
−0.522541 + 0.852614i \(0.675016\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.3731 0.957459 0.478730 0.877962i \(-0.341097\pi\)
0.478730 + 0.877962i \(0.341097\pi\)
\(168\) 0 0
\(169\) 25.5539 1.96569
\(170\) 0 0
\(171\) −14.7477 −1.12779
\(172\) 0 0
\(173\) 6.00524 0.456570 0.228285 0.973594i \(-0.426688\pi\)
0.228285 + 0.973594i \(0.426688\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.68622 −0.577731
\(178\) 0 0
\(179\) −12.8069 −0.957232 −0.478616 0.878024i \(-0.658861\pi\)
−0.478616 + 0.878024i \(0.658861\pi\)
\(180\) 0 0
\(181\) 13.0636 0.971007 0.485504 0.874235i \(-0.338636\pi\)
0.485504 + 0.874235i \(0.338636\pi\)
\(182\) 0 0
\(183\) −4.76443 −0.352197
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −1.05939 −0.0774704
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 21.7159 1.57131 0.785653 0.618667i \(-0.212327\pi\)
0.785653 + 0.618667i \(0.212327\pi\)
\(192\) 0 0
\(193\) −15.7302 −1.13229 −0.566144 0.824307i \(-0.691565\pi\)
−0.566144 + 0.824307i \(0.691565\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.18536 −0.155700 −0.0778502 0.996965i \(-0.524806\pi\)
−0.0778502 + 0.996965i \(0.524806\pi\)
\(198\) 0 0
\(199\) 13.6703 0.969061 0.484530 0.874774i \(-0.338990\pi\)
0.484530 + 0.874774i \(0.338990\pi\)
\(200\) 0 0
\(201\) 9.94242 0.701284
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 15.0591 1.04668
\(208\) 0 0
\(209\) 2.58676 0.178930
\(210\) 0 0
\(211\) 23.7857 1.63747 0.818737 0.574169i \(-0.194675\pi\)
0.818737 + 0.574169i \(0.194675\pi\)
\(212\) 0 0
\(213\) 0.443757 0.0304058
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.86090 0.463617
\(220\) 0 0
\(221\) 16.3046 1.09676
\(222\) 0 0
\(223\) −12.1550 −0.813961 −0.406980 0.913437i \(-0.633418\pi\)
−0.406980 + 0.913437i \(0.633418\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −28.9574 −1.92197 −0.960986 0.276597i \(-0.910793\pi\)
−0.960986 + 0.276597i \(0.910793\pi\)
\(228\) 0 0
\(229\) −7.43498 −0.491318 −0.245659 0.969356i \(-0.579004\pi\)
−0.245659 + 0.969356i \(0.579004\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.6389 −1.09005 −0.545024 0.838420i \(-0.683480\pi\)
−0.545024 + 0.838420i \(0.683480\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 7.62983 0.495611
\(238\) 0 0
\(239\) −3.80387 −0.246052 −0.123026 0.992403i \(-0.539260\pi\)
−0.123026 + 0.992403i \(0.539260\pi\)
\(240\) 0 0
\(241\) 13.4275 0.864940 0.432470 0.901648i \(-0.357642\pi\)
0.432470 + 0.901648i \(0.357642\pi\)
\(242\) 0 0
\(243\) −15.9715 −1.02458
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −39.8116 −2.53315
\(248\) 0 0
\(249\) 2.47642 0.156937
\(250\) 0 0
\(251\) −15.2130 −0.960238 −0.480119 0.877203i \(-0.659407\pi\)
−0.480119 + 0.877203i \(0.659407\pi\)
\(252\) 0 0
\(253\) −2.64138 −0.166062
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.75756 −0.109634 −0.0548168 0.998496i \(-0.517457\pi\)
−0.0548168 + 0.998496i \(0.517457\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −4.51465 −0.279450
\(262\) 0 0
\(263\) 10.7280 0.661516 0.330758 0.943716i \(-0.392696\pi\)
0.330758 + 0.943716i \(0.392696\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.06755 0.554925
\(268\) 0 0
\(269\) −9.38628 −0.572292 −0.286146 0.958186i \(-0.592374\pi\)
−0.286146 + 0.958186i \(0.592374\pi\)
\(270\) 0 0
\(271\) −5.23762 −0.318163 −0.159081 0.987265i \(-0.550853\pi\)
−0.159081 + 0.987265i \(0.550853\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −16.2871 −0.978597 −0.489299 0.872116i \(-0.662747\pi\)
−0.489299 + 0.872116i \(0.662747\pi\)
\(278\) 0 0
\(279\) −10.7348 −0.642675
\(280\) 0 0
\(281\) 3.49547 0.208522 0.104261 0.994550i \(-0.466752\pi\)
0.104261 + 0.994550i \(0.466752\pi\)
\(282\) 0 0
\(283\) −13.6600 −0.812006 −0.406003 0.913872i \(-0.633078\pi\)
−0.406003 + 0.913872i \(0.633078\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −10.1048 −0.594398
\(290\) 0 0
\(291\) −11.3426 −0.664913
\(292\) 0 0
\(293\) 30.5720 1.78604 0.893019 0.450020i \(-0.148583\pi\)
0.893019 + 0.450020i \(0.148583\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.78888 0.103801
\(298\) 0 0
\(299\) 40.6522 2.35098
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.30576 0.0750139
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.3514 −0.590786 −0.295393 0.955376i \(-0.595451\pi\)
−0.295393 + 0.955376i \(0.595451\pi\)
\(308\) 0 0
\(309\) 1.77654 0.101064
\(310\) 0 0
\(311\) 12.8740 0.730020 0.365010 0.931004i \(-0.381066\pi\)
0.365010 + 0.931004i \(0.381066\pi\)
\(312\) 0 0
\(313\) 6.37734 0.360469 0.180234 0.983624i \(-0.442314\pi\)
0.180234 + 0.983624i \(0.442314\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −32.5333 −1.82725 −0.913626 0.406556i \(-0.866730\pi\)
−0.913626 + 0.406556i \(0.866730\pi\)
\(318\) 0 0
\(319\) 0.791875 0.0443365
\(320\) 0 0
\(321\) −1.80294 −0.100630
\(322\) 0 0
\(323\) −16.8364 −0.936804
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 9.44597 0.522363
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −32.3687 −1.77914 −0.889572 0.456794i \(-0.848997\pi\)
−0.889572 + 0.456794i \(0.848997\pi\)
\(332\) 0 0
\(333\) −7.92111 −0.434074
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 4.17626 0.227496 0.113748 0.993510i \(-0.463714\pi\)
0.113748 + 0.993510i \(0.463714\pi\)
\(338\) 0 0
\(339\) 4.08815 0.222038
\(340\) 0 0
\(341\) 1.88289 0.101964
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −27.8062 −1.49272 −0.746358 0.665545i \(-0.768199\pi\)
−0.746358 + 0.665545i \(0.768199\pi\)
\(348\) 0 0
\(349\) 33.4108 1.78844 0.894219 0.447629i \(-0.147732\pi\)
0.894219 + 0.447629i \(0.147732\pi\)
\(350\) 0 0
\(351\) −27.5317 −1.46953
\(352\) 0 0
\(353\) 10.6932 0.569142 0.284571 0.958655i \(-0.408149\pi\)
0.284571 + 0.958655i \(0.408149\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −34.0636 −1.79781 −0.898903 0.438148i \(-0.855635\pi\)
−0.898903 + 0.438148i \(0.855635\pi\)
\(360\) 0 0
\(361\) 22.1103 1.16370
\(362\) 0 0
\(363\) 9.06634 0.475859
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −19.0564 −0.994735 −0.497367 0.867540i \(-0.665700\pi\)
−0.497367 + 0.867540i \(0.665700\pi\)
\(368\) 0 0
\(369\) −6.16960 −0.321176
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 29.4787 1.52635 0.763175 0.646192i \(-0.223639\pi\)
0.763175 + 0.646192i \(0.223639\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.1873 −0.627680
\(378\) 0 0
\(379\) −27.7211 −1.42394 −0.711970 0.702210i \(-0.752197\pi\)
−0.711970 + 0.702210i \(0.752197\pi\)
\(380\) 0 0
\(381\) 8.34435 0.427494
\(382\) 0 0
\(383\) 27.8299 1.42204 0.711020 0.703172i \(-0.248234\pi\)
0.711020 + 0.703172i \(0.248234\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −24.9813 −1.26987
\(388\) 0 0
\(389\) 35.7590 1.81305 0.906527 0.422148i \(-0.138724\pi\)
0.906527 + 0.422148i \(0.138724\pi\)
\(390\) 0 0
\(391\) 17.1919 0.869433
\(392\) 0 0
\(393\) 9.92755 0.500779
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 13.5015 0.677620 0.338810 0.940855i \(-0.389976\pi\)
0.338810 + 0.940855i \(0.389976\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.97476 0.498115 0.249058 0.968489i \(-0.419879\pi\)
0.249058 + 0.968489i \(0.419879\pi\)
\(402\) 0 0
\(403\) −28.9787 −1.44353
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.38937 0.0688685
\(408\) 0 0
\(409\) 5.03254 0.248843 0.124422 0.992229i \(-0.460292\pi\)
0.124422 + 0.992229i \(0.460292\pi\)
\(410\) 0 0
\(411\) 12.3119 0.607299
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.85511 0.237756
\(418\) 0 0
\(419\) 3.23209 0.157898 0.0789491 0.996879i \(-0.474844\pi\)
0.0789491 + 0.996879i \(0.474844\pi\)
\(420\) 0 0
\(421\) 18.3052 0.892142 0.446071 0.894998i \(-0.352823\pi\)
0.446071 + 0.894998i \(0.352823\pi\)
\(422\) 0 0
\(423\) −22.2459 −1.08163
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 2.09570 0.101181
\(430\) 0 0
\(431\) 6.87077 0.330953 0.165477 0.986214i \(-0.447084\pi\)
0.165477 + 0.986214i \(0.447084\pi\)
\(432\) 0 0
\(433\) 25.2716 1.21447 0.607237 0.794521i \(-0.292278\pi\)
0.607237 + 0.794521i \(0.292278\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −41.9783 −2.00810
\(438\) 0 0
\(439\) −7.63193 −0.364252 −0.182126 0.983275i \(-0.558298\pi\)
−0.182126 + 0.983275i \(0.558298\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.03640 0.334309 0.167155 0.985931i \(-0.446542\pi\)
0.167155 + 0.985931i \(0.446542\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −12.2107 −0.577545
\(448\) 0 0
\(449\) −21.1384 −0.997582 −0.498791 0.866722i \(-0.666222\pi\)
−0.498791 + 0.866722i \(0.666222\pi\)
\(450\) 0 0
\(451\) 1.08215 0.0509566
\(452\) 0 0
\(453\) 17.7236 0.832726
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −27.7942 −1.30016 −0.650080 0.759866i \(-0.725265\pi\)
−0.650080 + 0.759866i \(0.725265\pi\)
\(458\) 0 0
\(459\) −11.6432 −0.543459
\(460\) 0 0
\(461\) −8.74916 −0.407489 −0.203744 0.979024i \(-0.565311\pi\)
−0.203744 + 0.979024i \(0.565311\pi\)
\(462\) 0 0
\(463\) −22.1551 −1.02963 −0.514817 0.857300i \(-0.672140\pi\)
−0.514817 + 0.857300i \(0.672140\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.90576 −0.365835 −0.182918 0.983128i \(-0.558554\pi\)
−0.182918 + 0.983128i \(0.558554\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 16.1158 0.742577
\(472\) 0 0
\(473\) 4.38175 0.201473
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −13.7414 −0.629175
\(478\) 0 0
\(479\) 17.8720 0.816594 0.408297 0.912849i \(-0.366123\pi\)
0.408297 + 0.912849i \(0.366123\pi\)
\(480\) 0 0
\(481\) −21.3831 −0.974986
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.28891 0.375606 0.187803 0.982207i \(-0.439863\pi\)
0.187803 + 0.982207i \(0.439863\pi\)
\(488\) 0 0
\(489\) 11.1624 0.504781
\(490\) 0 0
\(491\) −20.7385 −0.935916 −0.467958 0.883751i \(-0.655010\pi\)
−0.467958 + 0.883751i \(0.655010\pi\)
\(492\) 0 0
\(493\) −5.15406 −0.232127
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 29.2935 1.31136 0.655678 0.755041i \(-0.272383\pi\)
0.655678 + 0.755041i \(0.272383\pi\)
\(500\) 0 0
\(501\) −10.3512 −0.462459
\(502\) 0 0
\(503\) 31.3632 1.39841 0.699207 0.714919i \(-0.253536\pi\)
0.699207 + 0.714919i \(0.253536\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −21.3782 −0.949439
\(508\) 0 0
\(509\) −6.18921 −0.274332 −0.137166 0.990548i \(-0.543799\pi\)
−0.137166 + 0.990548i \(0.543799\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 28.4298 1.25521
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 3.90196 0.171608
\(518\) 0 0
\(519\) −5.02394 −0.220526
\(520\) 0 0
\(521\) −36.3709 −1.59344 −0.796720 0.604349i \(-0.793433\pi\)
−0.796720 + 0.604349i \(0.793433\pi\)
\(522\) 0 0
\(523\) 24.7114 1.08055 0.540276 0.841488i \(-0.318320\pi\)
0.540276 + 0.841488i \(0.318320\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.2552 −0.533843
\(528\) 0 0
\(529\) 19.8647 0.863683
\(530\) 0 0
\(531\) −21.1324 −0.917068
\(532\) 0 0
\(533\) −16.6549 −0.721403
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.7141 0.462349
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 20.8192 0.895088 0.447544 0.894262i \(-0.352299\pi\)
0.447544 + 0.894262i \(0.352299\pi\)
\(542\) 0 0
\(543\) −10.9289 −0.469002
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.09203 −0.132206 −0.0661028 0.997813i \(-0.521057\pi\)
−0.0661028 + 0.997813i \(0.521057\pi\)
\(548\) 0 0
\(549\) −13.0993 −0.559063
\(550\) 0 0
\(551\) 12.5849 0.536135
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.23109 −0.221648 −0.110824 0.993840i \(-0.535349\pi\)
−0.110824 + 0.993840i \(0.535349\pi\)
\(558\) 0 0
\(559\) −67.4373 −2.85229
\(560\) 0 0
\(561\) 0.886277 0.0374187
\(562\) 0 0
\(563\) 0.260526 0.0109799 0.00548994 0.999985i \(-0.498252\pi\)
0.00548994 + 0.999985i \(0.498252\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 30.5445 1.28049 0.640245 0.768171i \(-0.278833\pi\)
0.640245 + 0.768171i \(0.278833\pi\)
\(570\) 0 0
\(571\) 8.45361 0.353773 0.176886 0.984231i \(-0.443398\pi\)
0.176886 + 0.984231i \(0.443398\pi\)
\(572\) 0 0
\(573\) −18.1673 −0.758951
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.6074 −0.483220 −0.241610 0.970373i \(-0.577676\pi\)
−0.241610 + 0.970373i \(0.577676\pi\)
\(578\) 0 0
\(579\) 13.1598 0.546902
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.41026 0.0998226
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 29.5957 1.22155 0.610774 0.791805i \(-0.290859\pi\)
0.610774 + 0.791805i \(0.290859\pi\)
\(588\) 0 0
\(589\) 29.9240 1.23300
\(590\) 0 0
\(591\) 1.82825 0.0752043
\(592\) 0 0
\(593\) 34.4394 1.41426 0.707128 0.707085i \(-0.249990\pi\)
0.707128 + 0.707085i \(0.249990\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.4364 −0.468062
\(598\) 0 0
\(599\) −29.6107 −1.20986 −0.604931 0.796278i \(-0.706799\pi\)
−0.604931 + 0.796278i \(0.706799\pi\)
\(600\) 0 0
\(601\) −1.91726 −0.0782068 −0.0391034 0.999235i \(-0.512450\pi\)
−0.0391034 + 0.999235i \(0.512450\pi\)
\(602\) 0 0
\(603\) 27.3356 1.11319
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 34.6190 1.40514 0.702571 0.711614i \(-0.252035\pi\)
0.702571 + 0.711614i \(0.252035\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −60.0530 −2.42949
\(612\) 0 0
\(613\) −39.9758 −1.61461 −0.807303 0.590137i \(-0.799074\pi\)
−0.807303 + 0.590137i \(0.799074\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 44.8372 1.80508 0.902539 0.430609i \(-0.141701\pi\)
0.902539 + 0.430609i \(0.141701\pi\)
\(618\) 0 0
\(619\) −31.6368 −1.27159 −0.635796 0.771858i \(-0.719328\pi\)
−0.635796 + 0.771858i \(0.719328\pi\)
\(620\) 0 0
\(621\) −29.0301 −1.16494
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.16406 −0.0864244
\(628\) 0 0
\(629\) −9.04297 −0.360567
\(630\) 0 0
\(631\) 7.14722 0.284526 0.142263 0.989829i \(-0.454562\pi\)
0.142263 + 0.989829i \(0.454562\pi\)
\(632\) 0 0
\(633\) −19.8989 −0.790910
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 1.22006 0.0482649
\(640\) 0 0
\(641\) −29.9734 −1.18388 −0.591938 0.805983i \(-0.701637\pi\)
−0.591938 + 0.805983i \(0.701637\pi\)
\(642\) 0 0
\(643\) −16.1717 −0.637750 −0.318875 0.947797i \(-0.603305\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −14.3068 −0.562460 −0.281230 0.959640i \(-0.590742\pi\)
−0.281230 + 0.959640i \(0.590742\pi\)
\(648\) 0 0
\(649\) 3.70664 0.145499
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −32.7309 −1.28086 −0.640429 0.768018i \(-0.721243\pi\)
−0.640429 + 0.768018i \(0.721243\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 18.8633 0.735927
\(658\) 0 0
\(659\) −0.326169 −0.0127057 −0.00635287 0.999980i \(-0.502022\pi\)
−0.00635287 + 0.999980i \(0.502022\pi\)
\(660\) 0 0
\(661\) −21.2200 −0.825361 −0.412680 0.910876i \(-0.635407\pi\)
−0.412680 + 0.910876i \(0.635407\pi\)
\(662\) 0 0
\(663\) −13.6403 −0.529743
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12.8506 −0.497579
\(668\) 0 0
\(669\) 10.1688 0.393148
\(670\) 0 0
\(671\) 2.29762 0.0886988
\(672\) 0 0
\(673\) −15.9064 −0.613146 −0.306573 0.951847i \(-0.599182\pi\)
−0.306573 + 0.951847i \(0.599182\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −33.5811 −1.29063 −0.645314 0.763917i \(-0.723273\pi\)
−0.645314 + 0.763917i \(0.723273\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 24.2255 0.928324
\(682\) 0 0
\(683\) 39.7281 1.52015 0.760076 0.649834i \(-0.225162\pi\)
0.760076 + 0.649834i \(0.225162\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 6.22004 0.237309
\(688\) 0 0
\(689\) −37.0950 −1.41321
\(690\) 0 0
\(691\) 36.8959 1.40358 0.701792 0.712382i \(-0.252383\pi\)
0.701792 + 0.712382i \(0.252383\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −7.04340 −0.266788
\(698\) 0 0
\(699\) 13.9199 0.526500
\(700\) 0 0
\(701\) 11.0237 0.416358 0.208179 0.978091i \(-0.433246\pi\)
0.208179 + 0.978091i \(0.433246\pi\)
\(702\) 0 0
\(703\) 22.0806 0.832787
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −6.55854 −0.246311 −0.123156 0.992387i \(-0.539301\pi\)
−0.123156 + 0.992387i \(0.539301\pi\)
\(710\) 0 0
\(711\) 20.9774 0.786713
\(712\) 0 0
\(713\) −30.5558 −1.14432
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 3.18229 0.118845
\(718\) 0 0
\(719\) −49.4169 −1.84294 −0.921470 0.388450i \(-0.873010\pi\)
−0.921470 + 0.388450i \(0.873010\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −11.2333 −0.417771
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −9.05602 −0.335869 −0.167935 0.985798i \(-0.553710\pi\)
−0.167935 + 0.985798i \(0.553710\pi\)
\(728\) 0 0
\(729\) 3.78904 0.140335
\(730\) 0 0
\(731\) −28.5194 −1.05483
\(732\) 0 0
\(733\) −36.9803 −1.36590 −0.682949 0.730466i \(-0.739303\pi\)
−0.682949 + 0.730466i \(0.739303\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.79469 −0.176615
\(738\) 0 0
\(739\) −48.0463 −1.76741 −0.883707 0.468041i \(-0.844960\pi\)
−0.883707 + 0.468041i \(0.844960\pi\)
\(740\) 0 0
\(741\) 33.3060 1.22353
\(742\) 0 0
\(743\) 44.9706 1.64981 0.824906 0.565270i \(-0.191228\pi\)
0.824906 + 0.565270i \(0.191228\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.80864 0.249115
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 40.6670 1.48396 0.741979 0.670423i \(-0.233887\pi\)
0.741979 + 0.670423i \(0.233887\pi\)
\(752\) 0 0
\(753\) 12.7271 0.463801
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −32.2736 −1.17301 −0.586503 0.809947i \(-0.699496\pi\)
−0.586503 + 0.809947i \(0.699496\pi\)
\(758\) 0 0
\(759\) 2.20976 0.0802092
\(760\) 0 0
\(761\) −16.7233 −0.606217 −0.303109 0.952956i \(-0.598025\pi\)
−0.303109 + 0.952956i \(0.598025\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −57.0471 −2.05985
\(768\) 0 0
\(769\) 38.7197 1.39627 0.698134 0.715967i \(-0.254014\pi\)
0.698134 + 0.715967i \(0.254014\pi\)
\(770\) 0 0
\(771\) 1.47036 0.0529537
\(772\) 0 0
\(773\) −32.4246 −1.16623 −0.583116 0.812389i \(-0.698167\pi\)
−0.583116 + 0.812389i \(0.698167\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17.1982 0.616189
\(780\) 0 0
\(781\) −0.214000 −0.00765752
\(782\) 0 0
\(783\) 8.70309 0.311023
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 15.1453 0.539871 0.269935 0.962878i \(-0.412998\pi\)
0.269935 + 0.962878i \(0.412998\pi\)
\(788\) 0 0
\(789\) −8.97495 −0.319517
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −35.3616 −1.25573
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.0776 −0.427810 −0.213905 0.976854i \(-0.568618\pi\)
−0.213905 + 0.976854i \(0.568618\pi\)
\(798\) 0 0
\(799\) −25.3966 −0.898467
\(800\) 0 0
\(801\) 24.9302 0.880867
\(802\) 0 0
\(803\) −3.30864 −0.116759
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7.85248 0.276420
\(808\) 0 0
\(809\) 43.9340 1.54464 0.772318 0.635236i \(-0.219097\pi\)
0.772318 + 0.635236i \(0.219097\pi\)
\(810\) 0 0
\(811\) −37.1167 −1.30334 −0.651671 0.758501i \(-0.725932\pi\)
−0.651671 + 0.758501i \(0.725932\pi\)
\(812\) 0 0
\(813\) 4.38175 0.153675
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 69.6371 2.43630
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24.3112 −0.848468 −0.424234 0.905553i \(-0.639457\pi\)
−0.424234 + 0.905553i \(0.639457\pi\)
\(822\) 0 0
\(823\) −14.0685 −0.490397 −0.245198 0.969473i \(-0.578853\pi\)
−0.245198 + 0.969473i \(0.578853\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.8782 −0.795554 −0.397777 0.917482i \(-0.630218\pi\)
−0.397777 + 0.917482i \(0.630218\pi\)
\(828\) 0 0
\(829\) 10.0626 0.349488 0.174744 0.984614i \(-0.444090\pi\)
0.174744 + 0.984614i \(0.444090\pi\)
\(830\) 0 0
\(831\) 13.6257 0.472669
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 20.6939 0.715286
\(838\) 0 0
\(839\) −49.3245 −1.70287 −0.851436 0.524459i \(-0.824268\pi\)
−0.851436 + 0.524459i \(0.824268\pi\)
\(840\) 0 0
\(841\) −25.1474 −0.867153
\(842\) 0 0
\(843\) −2.92428 −0.100718
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 11.4279 0.392204
\(850\) 0 0
\(851\) −22.5469 −0.772897
\(852\) 0 0
\(853\) −24.3633 −0.834185 −0.417092 0.908864i \(-0.636951\pi\)
−0.417092 + 0.908864i \(0.636951\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −37.6446 −1.28591 −0.642957 0.765902i \(-0.722293\pi\)
−0.642957 + 0.765902i \(0.722293\pi\)
\(858\) 0 0
\(859\) −10.4954 −0.358098 −0.179049 0.983840i \(-0.557302\pi\)
−0.179049 + 0.983840i \(0.557302\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −32.9271 −1.12085 −0.560426 0.828205i \(-0.689363\pi\)
−0.560426 + 0.828205i \(0.689363\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 8.45355 0.287098
\(868\) 0 0
\(869\) −3.67945 −0.124817
\(870\) 0 0
\(871\) 73.7926 2.50037
\(872\) 0 0
\(873\) −31.1851 −1.05546
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 14.2674 0.481774 0.240887 0.970553i \(-0.422562\pi\)
0.240887 + 0.970553i \(0.422562\pi\)
\(878\) 0 0
\(879\) −25.5763 −0.862667
\(880\) 0 0
\(881\) 15.9553 0.537547 0.268774 0.963203i \(-0.413382\pi\)
0.268774 + 0.963203i \(0.413382\pi\)
\(882\) 0 0
\(883\) −5.32356 −0.179152 −0.0895760 0.995980i \(-0.528551\pi\)
−0.0895760 + 0.995980i \(0.528551\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −39.9406 −1.34107 −0.670536 0.741877i \(-0.733936\pi\)
−0.670536 + 0.741877i \(0.733936\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 1.28733 0.0431273
\(892\) 0 0
\(893\) 62.0120 2.07515
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −34.0093 −1.13554
\(898\) 0 0
\(899\) 9.16050 0.305520
\(900\) 0 0
\(901\) −15.6876 −0.522629
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 25.9996 0.863301 0.431650 0.902041i \(-0.357931\pi\)
0.431650 + 0.902041i \(0.357931\pi\)
\(908\) 0 0
\(909\) 3.59004 0.119074
\(910\) 0 0
\(911\) −24.5747 −0.814196 −0.407098 0.913385i \(-0.633459\pi\)
−0.407098 + 0.913385i \(0.633459\pi\)
\(912\) 0 0
\(913\) −1.19424 −0.0395237
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −1.92702 −0.0635666 −0.0317833 0.999495i \(-0.510119\pi\)
−0.0317833 + 0.999495i \(0.510119\pi\)
\(920\) 0 0
\(921\) 8.65990 0.285353
\(922\) 0 0
\(923\) 3.29357 0.108409
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 4.88439 0.160424
\(928\) 0 0
\(929\) 13.5639 0.445017 0.222509 0.974931i \(-0.428575\pi\)
0.222509 + 0.974931i \(0.428575\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −10.7703 −0.352604
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 31.8976 1.04205 0.521025 0.853541i \(-0.325550\pi\)
0.521025 + 0.853541i \(0.325550\pi\)
\(938\) 0 0
\(939\) −5.33523 −0.174109
\(940\) 0 0
\(941\) −7.46416 −0.243325 −0.121662 0.992572i \(-0.538822\pi\)
−0.121662 + 0.992572i \(0.538822\pi\)
\(942\) 0 0
\(943\) −17.5613 −0.571876
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 37.0934 1.20537 0.602686 0.797978i \(-0.294097\pi\)
0.602686 + 0.797978i \(0.294097\pi\)
\(948\) 0 0
\(949\) 50.9216 1.65299
\(950\) 0 0
\(951\) 27.2171 0.882574
\(952\) 0 0
\(953\) 12.1489 0.393542 0.196771 0.980449i \(-0.436954\pi\)
0.196771 + 0.980449i \(0.436954\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −0.662476 −0.0214148
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −9.21848 −0.297370
\(962\) 0 0
\(963\) −4.95698 −0.159736
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.16851 −0.166208 −0.0831040 0.996541i \(-0.526483\pi\)
−0.0831040 + 0.996541i \(0.526483\pi\)
\(968\) 0 0
\(969\) 14.0852 0.452482
\(970\) 0 0
\(971\) −26.3784 −0.846523 −0.423261 0.906008i \(-0.639115\pi\)
−0.423261 + 0.906008i \(0.639115\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −40.2923 −1.28906 −0.644532 0.764577i \(-0.722948\pi\)
−0.644532 + 0.764577i \(0.722948\pi\)
\(978\) 0 0
\(979\) −4.37279 −0.139755
\(980\) 0 0
\(981\) 25.9706 0.829179
\(982\) 0 0
\(983\) 14.3832 0.458751 0.229376 0.973338i \(-0.426332\pi\)
0.229376 + 0.973338i \(0.426332\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −71.1076 −2.26109
\(990\) 0 0
\(991\) 2.09085 0.0664181 0.0332090 0.999448i \(-0.489427\pi\)
0.0332090 + 0.999448i \(0.489427\pi\)
\(992\) 0 0
\(993\) 27.0794 0.859338
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 28.4579 0.901270 0.450635 0.892708i \(-0.351198\pi\)
0.450635 + 0.892708i \(0.351198\pi\)
\(998\) 0 0
\(999\) 15.2699 0.483117
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.db.1.5 10
5.2 odd 4 1960.2.g.g.1569.12 yes 20
5.3 odd 4 1960.2.g.g.1569.10 yes 20
5.4 even 2 9800.2.a.dc.1.6 10
7.6 odd 2 inner 9800.2.a.db.1.6 10
35.13 even 4 1960.2.g.g.1569.11 yes 20
35.27 even 4 1960.2.g.g.1569.9 20
35.34 odd 2 9800.2.a.dc.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1960.2.g.g.1569.9 20 35.27 even 4
1960.2.g.g.1569.10 yes 20 5.3 odd 4
1960.2.g.g.1569.11 yes 20 35.13 even 4
1960.2.g.g.1569.12 yes 20 5.2 odd 4
9800.2.a.db.1.5 10 1.1 even 1 trivial
9800.2.a.db.1.6 10 7.6 odd 2 inner
9800.2.a.dc.1.5 10 35.34 odd 2
9800.2.a.dc.1.6 10 5.4 even 2