Properties

Label 4900.2.a.bg.1.2
Level $4900$
Weight $2$
Character 4900.1
Self dual yes
Analytic conductor $39.127$
Analytic rank $1$
Dimension $4$
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] = [4900,2,Mod(1,4900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4900.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4900.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: \(39.1266969904\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{5})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 6x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.874032\) of defining polynomial
Character \(\chi\) \(=\) 4900.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.874032 q^{3} -2.23607 q^{9} +O(q^{10})\) \(q-0.874032 q^{3} -2.23607 q^{9} +3.47214 q^{11} +2.28825 q^{13} -1.74806 q^{17} +0.333851 q^{19} -5.47214 q^{23} +4.57649 q^{27} -4.23607 q^{29} +1.20788 q^{31} -3.03476 q^{33} +0.236068 q^{37} -2.00000 q^{39} -1.95440 q^{41} -8.23607 q^{43} -7.73877 q^{47} +1.52786 q^{51} +1.70820 q^{53} -0.291796 q^{57} +5.11667 q^{59} +14.6035 q^{61} -3.94427 q^{67} +4.78282 q^{69} +3.29180 q^{71} +14.6035 q^{73} -2.52786 q^{79} +2.70820 q^{81} +9.02546 q^{83} +3.70246 q^{87} -15.3500 q^{89} -1.05573 q^{93} -12.1089 q^{97} -7.76393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{11} - 4 q^{23} - 8 q^{29} - 8 q^{37} - 8 q^{39} - 24 q^{43} + 24 q^{51} - 20 q^{53} - 28 q^{57} + 20 q^{67} + 40 q^{71} - 28 q^{79} - 16 q^{81} - 40 q^{93} - 40 q^{99}+O(q^{100}) \) 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
\(3\) −0.874032 −0.504623 −0.252311 0.967646i \(-0.581191\pi\)
−0.252311 + 0.967646i \(0.581191\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.23607 −0.745356
\(10\) 0 0
\(11\) 3.47214 1.04689 0.523444 0.852060i \(-0.324647\pi\)
0.523444 + 0.852060i \(0.324647\pi\)
\(12\) 0 0
\(13\) 2.28825 0.634645 0.317323 0.948318i \(-0.397216\pi\)
0.317323 + 0.948318i \(0.397216\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.74806 −0.423968 −0.211984 0.977273i \(-0.567992\pi\)
−0.211984 + 0.977273i \(0.567992\pi\)
\(18\) 0 0
\(19\) 0.333851 0.0765906 0.0382953 0.999266i \(-0.487807\pi\)
0.0382953 + 0.999266i \(0.487807\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.47214 −1.14102 −0.570510 0.821291i \(-0.693254\pi\)
−0.570510 + 0.821291i \(0.693254\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.57649 0.880746
\(28\) 0 0
\(29\) −4.23607 −0.786618 −0.393309 0.919406i \(-0.628670\pi\)
−0.393309 + 0.919406i \(0.628670\pi\)
\(30\) 0 0
\(31\) 1.20788 0.216942 0.108471 0.994100i \(-0.465405\pi\)
0.108471 + 0.994100i \(0.465405\pi\)
\(32\) 0 0
\(33\) −3.03476 −0.528284
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.236068 0.0388093 0.0194047 0.999812i \(-0.493823\pi\)
0.0194047 + 0.999812i \(0.493823\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) −1.95440 −0.305225 −0.152613 0.988286i \(-0.548769\pi\)
−0.152613 + 0.988286i \(0.548769\pi\)
\(42\) 0 0
\(43\) −8.23607 −1.25599 −0.627994 0.778218i \(-0.716124\pi\)
−0.627994 + 0.778218i \(0.716124\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.73877 −1.12882 −0.564408 0.825496i \(-0.690895\pi\)
−0.564408 + 0.825496i \(0.690895\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.52786 0.213944
\(52\) 0 0
\(53\) 1.70820 0.234640 0.117320 0.993094i \(-0.462570\pi\)
0.117320 + 0.993094i \(0.462570\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.291796 −0.0386493
\(58\) 0 0
\(59\) 5.11667 0.666134 0.333067 0.942903i \(-0.391916\pi\)
0.333067 + 0.942903i \(0.391916\pi\)
\(60\) 0 0
\(61\) 14.6035 1.86979 0.934894 0.354928i \(-0.115495\pi\)
0.934894 + 0.354928i \(0.115495\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.94427 −0.481870 −0.240935 0.970541i \(-0.577454\pi\)
−0.240935 + 0.970541i \(0.577454\pi\)
\(68\) 0 0
\(69\) 4.78282 0.575784
\(70\) 0 0
\(71\) 3.29180 0.390664 0.195332 0.980737i \(-0.437422\pi\)
0.195332 + 0.980737i \(0.437422\pi\)
\(72\) 0 0
\(73\) 14.6035 1.70921 0.854606 0.519278i \(-0.173799\pi\)
0.854606 + 0.519278i \(0.173799\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −2.52786 −0.284407 −0.142203 0.989837i \(-0.545419\pi\)
−0.142203 + 0.989837i \(0.545419\pi\)
\(80\) 0 0
\(81\) 2.70820 0.300912
\(82\) 0 0
\(83\) 9.02546 0.990673 0.495337 0.868701i \(-0.335045\pi\)
0.495337 + 0.868701i \(0.335045\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.70246 0.396945
\(88\) 0 0
\(89\) −15.3500 −1.62710 −0.813549 0.581496i \(-0.802468\pi\)
−0.813549 + 0.581496i \(0.802468\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.05573 −0.109474
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.1089 −1.22948 −0.614738 0.788732i \(-0.710738\pi\)
−0.614738 + 0.788732i \(0.710738\pi\)
\(98\) 0 0
\(99\) −7.76393 −0.780305
\(100\) 0 0
\(101\) −6.53089 −0.649847 −0.324924 0.945740i \(-0.605339\pi\)
−0.324924 + 0.945740i \(0.605339\pi\)
\(102\) 0 0
\(103\) −18.3848 −1.81151 −0.905753 0.423806i \(-0.860694\pi\)
−0.905753 + 0.423806i \(0.860694\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.52786 −0.341051 −0.170526 0.985353i \(-0.554547\pi\)
−0.170526 + 0.985353i \(0.554547\pi\)
\(108\) 0 0
\(109\) 10.4164 0.997711 0.498855 0.866685i \(-0.333754\pi\)
0.498855 + 0.866685i \(0.333754\pi\)
\(110\) 0 0
\(111\) −0.206331 −0.0195841
\(112\) 0 0
\(113\) −18.2361 −1.71550 −0.857752 0.514063i \(-0.828140\pi\)
−0.857752 + 0.514063i \(0.828140\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −5.11667 −0.473037
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.05573 0.0959753
\(122\) 0 0
\(123\) 1.70820 0.154024
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.1803 −0.992095 −0.496047 0.868295i \(-0.665216\pi\)
−0.496047 + 0.868295i \(0.665216\pi\)
\(128\) 0 0
\(129\) 7.19859 0.633800
\(130\) 0 0
\(131\) 14.8098 1.29394 0.646971 0.762515i \(-0.276036\pi\)
0.646971 + 0.762515i \(0.276036\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 0 0
\(139\) 11.7751 0.998749 0.499375 0.866386i \(-0.333563\pi\)
0.499375 + 0.866386i \(0.333563\pi\)
\(140\) 0 0
\(141\) 6.76393 0.569626
\(142\) 0 0
\(143\) 7.94510 0.664403
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −6.70820 −0.549557 −0.274779 0.961507i \(-0.588605\pi\)
−0.274779 + 0.961507i \(0.588605\pi\)
\(150\) 0 0
\(151\) 3.76393 0.306304 0.153152 0.988203i \(-0.451058\pi\)
0.153152 + 0.988203i \(0.451058\pi\)
\(152\) 0 0
\(153\) 3.90879 0.316007
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.1877 0.972688 0.486344 0.873768i \(-0.338330\pi\)
0.486344 + 0.873768i \(0.338330\pi\)
\(158\) 0 0
\(159\) −1.49302 −0.118405
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −20.1803 −1.58065 −0.790323 0.612690i \(-0.790087\pi\)
−0.790323 + 0.612690i \(0.790087\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.9265 1.54196 0.770980 0.636860i \(-0.219767\pi\)
0.770980 + 0.636860i \(0.219767\pi\)
\(168\) 0 0
\(169\) −7.76393 −0.597226
\(170\) 0 0
\(171\) −0.746512 −0.0570872
\(172\) 0 0
\(173\) −18.3848 −1.39777 −0.698884 0.715235i \(-0.746320\pi\)
−0.698884 + 0.715235i \(0.746320\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −4.47214 −0.336146
\(178\) 0 0
\(179\) −11.7082 −0.875112 −0.437556 0.899191i \(-0.644156\pi\)
−0.437556 + 0.899191i \(0.644156\pi\)
\(180\) 0 0
\(181\) −24.8369 −1.84611 −0.923054 0.384670i \(-0.874315\pi\)
−0.923054 + 0.384670i \(0.874315\pi\)
\(182\) 0 0
\(183\) −12.7639 −0.943537
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −6.06952 −0.443847
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.1803 0.736624 0.368312 0.929702i \(-0.379936\pi\)
0.368312 + 0.929702i \(0.379936\pi\)
\(192\) 0 0
\(193\) −15.6525 −1.12669 −0.563345 0.826222i \(-0.690486\pi\)
−0.563345 + 0.826222i \(0.690486\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.5279 −0.750079 −0.375040 0.927009i \(-0.622371\pi\)
−0.375040 + 0.927009i \(0.622371\pi\)
\(198\) 0 0
\(199\) −0.461370 −0.0327057 −0.0163528 0.999866i \(-0.505205\pi\)
−0.0163528 + 0.999866i \(0.505205\pi\)
\(200\) 0 0
\(201\) 3.44742 0.243162
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 12.2361 0.850466
\(208\) 0 0
\(209\) 1.15917 0.0801818
\(210\) 0 0
\(211\) 18.4721 1.27167 0.635837 0.771823i \(-0.280655\pi\)
0.635837 + 0.771823i \(0.280655\pi\)
\(212\) 0 0
\(213\) −2.87714 −0.197138
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −12.7639 −0.862507
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) 15.0162 1.00556 0.502778 0.864415i \(-0.332311\pi\)
0.502778 + 0.864415i \(0.332311\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −19.0525 −1.26456 −0.632279 0.774741i \(-0.717880\pi\)
−0.632279 + 0.774741i \(0.717880\pi\)
\(228\) 0 0
\(229\) −19.7202 −1.30315 −0.651573 0.758586i \(-0.725891\pi\)
−0.651573 + 0.758586i \(0.725891\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −19.4721 −1.27566 −0.637831 0.770176i \(-0.720168\pi\)
−0.637831 + 0.770176i \(0.720168\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.20943 0.143518
\(238\) 0 0
\(239\) −22.6525 −1.46527 −0.732633 0.680623i \(-0.761709\pi\)
−0.732633 + 0.680623i \(0.761709\pi\)
\(240\) 0 0
\(241\) 1.41421 0.0910975 0.0455488 0.998962i \(-0.485496\pi\)
0.0455488 + 0.998962i \(0.485496\pi\)
\(242\) 0 0
\(243\) −16.0965 −1.03259
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.763932 0.0486078
\(248\) 0 0
\(249\) −7.88854 −0.499916
\(250\) 0 0
\(251\) 4.57649 0.288866 0.144433 0.989515i \(-0.453864\pi\)
0.144433 + 0.989515i \(0.453864\pi\)
\(252\) 0 0
\(253\) −19.0000 −1.19452
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.20788 −0.0753456 −0.0376728 0.999290i \(-0.511994\pi\)
−0.0376728 + 0.999290i \(0.511994\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 9.47214 0.586310
\(262\) 0 0
\(263\) −2.70820 −0.166995 −0.0834975 0.996508i \(-0.526609\pi\)
−0.0834975 + 0.996508i \(0.526609\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 13.4164 0.821071
\(268\) 0 0
\(269\) −2.54328 −0.155067 −0.0775334 0.996990i \(-0.524704\pi\)
−0.0775334 + 0.996990i \(0.524704\pi\)
\(270\) 0 0
\(271\) −3.62365 −0.220121 −0.110060 0.993925i \(-0.535104\pi\)
−0.110060 + 0.993925i \(0.535104\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −3.05573 −0.183601 −0.0918005 0.995777i \(-0.529262\pi\)
−0.0918005 + 0.995777i \(0.529262\pi\)
\(278\) 0 0
\(279\) −2.70091 −0.161699
\(280\) 0 0
\(281\) 16.1246 0.961914 0.480957 0.876744i \(-0.340289\pi\)
0.480957 + 0.876744i \(0.340289\pi\)
\(282\) 0 0
\(283\) −2.08191 −0.123757 −0.0618785 0.998084i \(-0.519709\pi\)
−0.0618785 + 0.998084i \(0.519709\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.9443 −0.820251
\(290\) 0 0
\(291\) 10.5836 0.620421
\(292\) 0 0
\(293\) 21.2619 1.24213 0.621067 0.783757i \(-0.286699\pi\)
0.621067 + 0.783757i \(0.286699\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 15.8902 0.922043
\(298\) 0 0
\(299\) −12.5216 −0.724142
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 5.70820 0.327928
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.3941 0.707367 0.353684 0.935365i \(-0.384929\pi\)
0.353684 + 0.935365i \(0.384929\pi\)
\(308\) 0 0
\(309\) 16.0689 0.914127
\(310\) 0 0
\(311\) −34.8639 −1.97695 −0.988474 0.151389i \(-0.951625\pi\)
−0.988474 + 0.151389i \(0.951625\pi\)
\(312\) 0 0
\(313\) −16.2241 −0.917038 −0.458519 0.888685i \(-0.651620\pi\)
−0.458519 + 0.888685i \(0.651620\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.4164 −1.48369 −0.741847 0.670570i \(-0.766050\pi\)
−0.741847 + 0.670570i \(0.766050\pi\)
\(318\) 0 0
\(319\) −14.7082 −0.823501
\(320\) 0 0
\(321\) 3.08347 0.172102
\(322\) 0 0
\(323\) −0.583592 −0.0324719
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −9.10427 −0.503468
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 27.3607 1.50388 0.751939 0.659232i \(-0.229119\pi\)
0.751939 + 0.659232i \(0.229119\pi\)
\(332\) 0 0
\(333\) −0.527864 −0.0289268
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −23.1246 −1.25968 −0.629839 0.776726i \(-0.716879\pi\)
−0.629839 + 0.776726i \(0.716879\pi\)
\(338\) 0 0
\(339\) 15.9389 0.865683
\(340\) 0 0
\(341\) 4.19393 0.227114
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 19.3607 1.03934 0.519668 0.854368i \(-0.326056\pi\)
0.519668 + 0.854368i \(0.326056\pi\)
\(348\) 0 0
\(349\) 15.9690 0.854802 0.427401 0.904062i \(-0.359429\pi\)
0.427401 + 0.904062i \(0.359429\pi\)
\(350\) 0 0
\(351\) 10.4721 0.558961
\(352\) 0 0
\(353\) 10.3609 0.551453 0.275727 0.961236i \(-0.411082\pi\)
0.275727 + 0.961236i \(0.411082\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 29.0689 1.53420 0.767099 0.641529i \(-0.221700\pi\)
0.767099 + 0.641529i \(0.221700\pi\)
\(360\) 0 0
\(361\) −18.8885 −0.994134
\(362\) 0 0
\(363\) −0.922740 −0.0484313
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 10.0270 0.523406 0.261703 0.965148i \(-0.415716\pi\)
0.261703 + 0.965148i \(0.415716\pi\)
\(368\) 0 0
\(369\) 4.37016 0.227501
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10.1246 0.524233 0.262116 0.965036i \(-0.415580\pi\)
0.262116 + 0.965036i \(0.415580\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.69316 −0.499223
\(378\) 0 0
\(379\) −30.1246 −1.54740 −0.773699 0.633554i \(-0.781596\pi\)
−0.773699 + 0.633554i \(0.781596\pi\)
\(380\) 0 0
\(381\) 9.77198 0.500633
\(382\) 0 0
\(383\) −25.8384 −1.32028 −0.660140 0.751142i \(-0.729503\pi\)
−0.660140 + 0.751142i \(0.729503\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 18.4164 0.936159
\(388\) 0 0
\(389\) 19.1803 0.972482 0.486241 0.873825i \(-0.338368\pi\)
0.486241 + 0.873825i \(0.338368\pi\)
\(390\) 0 0
\(391\) 9.56564 0.483755
\(392\) 0 0
\(393\) −12.9443 −0.652952
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.91034 −0.246443 −0.123221 0.992379i \(-0.539323\pi\)
−0.123221 + 0.992379i \(0.539323\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12.7082 −0.634617 −0.317309 0.948322i \(-0.602779\pi\)
−0.317309 + 0.948322i \(0.602779\pi\)
\(402\) 0 0
\(403\) 2.76393 0.137681
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.819660 0.0406290
\(408\) 0 0
\(409\) −9.89949 −0.489499 −0.244749 0.969586i \(-0.578706\pi\)
−0.244749 + 0.969586i \(0.578706\pi\)
\(410\) 0 0
\(411\) 8.74032 0.431128
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.2918 −0.503991
\(418\) 0 0
\(419\) −12.9343 −0.631880 −0.315940 0.948779i \(-0.602320\pi\)
−0.315940 + 0.948779i \(0.602320\pi\)
\(420\) 0 0
\(421\) −18.5967 −0.906350 −0.453175 0.891422i \(-0.649709\pi\)
−0.453175 + 0.891422i \(0.649709\pi\)
\(422\) 0 0
\(423\) 17.3044 0.841369
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −6.94427 −0.335273
\(430\) 0 0
\(431\) −16.6525 −0.802122 −0.401061 0.916051i \(-0.631358\pi\)
−0.401061 + 0.916051i \(0.631358\pi\)
\(432\) 0 0
\(433\) −16.5579 −0.795722 −0.397861 0.917446i \(-0.630247\pi\)
−0.397861 + 0.917446i \(0.630247\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.82688 −0.0873913
\(438\) 0 0
\(439\) −11.0286 −0.526365 −0.263182 0.964746i \(-0.584772\pi\)
−0.263182 + 0.964746i \(0.584772\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.12461 0.0534319 0.0267160 0.999643i \(-0.491495\pi\)
0.0267160 + 0.999643i \(0.491495\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.86319 0.277319
\(448\) 0 0
\(449\) 14.2361 0.671842 0.335921 0.941890i \(-0.390953\pi\)
0.335921 + 0.941890i \(0.390953\pi\)
\(450\) 0 0
\(451\) −6.78593 −0.319537
\(452\) 0 0
\(453\) −3.28980 −0.154568
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −5.65248 −0.264412 −0.132206 0.991222i \(-0.542206\pi\)
−0.132206 + 0.991222i \(0.542206\pi\)
\(458\) 0 0
\(459\) −8.00000 −0.373408
\(460\) 0 0
\(461\) −24.0903 −1.12200 −0.560999 0.827816i \(-0.689583\pi\)
−0.560999 + 0.827816i \(0.689583\pi\)
\(462\) 0 0
\(463\) 13.4164 0.623513 0.311757 0.950162i \(-0.399083\pi\)
0.311757 + 0.950162i \(0.399083\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.3879 0.943439 0.471719 0.881749i \(-0.343634\pi\)
0.471719 + 0.881749i \(0.343634\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −10.6525 −0.490840
\(472\) 0 0
\(473\) −28.5967 −1.31488
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −3.81966 −0.174890
\(478\) 0 0
\(479\) 30.5725 1.39689 0.698447 0.715662i \(-0.253875\pi\)
0.698447 + 0.715662i \(0.253875\pi\)
\(480\) 0 0
\(481\) 0.540182 0.0246302
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 22.5279 1.02083 0.510417 0.859927i \(-0.329491\pi\)
0.510417 + 0.859927i \(0.329491\pi\)
\(488\) 0 0
\(489\) 17.6383 0.797630
\(490\) 0 0
\(491\) 6.23607 0.281430 0.140715 0.990050i \(-0.455060\pi\)
0.140715 + 0.990050i \(0.455060\pi\)
\(492\) 0 0
\(493\) 7.40492 0.333501
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −9.05573 −0.405390 −0.202695 0.979242i \(-0.564970\pi\)
−0.202695 + 0.979242i \(0.564970\pi\)
\(500\) 0 0
\(501\) −17.4164 −0.778108
\(502\) 0 0
\(503\) −6.65841 −0.296884 −0.148442 0.988921i \(-0.547426\pi\)
−0.148442 + 0.988921i \(0.547426\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.78593 0.301374
\(508\) 0 0
\(509\) −11.8539 −0.525414 −0.262707 0.964876i \(-0.584615\pi\)
−0.262707 + 0.964876i \(0.584615\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 1.52786 0.0674568
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −26.8701 −1.18174
\(518\) 0 0
\(519\) 16.0689 0.705346
\(520\) 0 0
\(521\) 3.41732 0.149715 0.0748577 0.997194i \(-0.476150\pi\)
0.0748577 + 0.997194i \(0.476150\pi\)
\(522\) 0 0
\(523\) 10.2333 0.447473 0.223736 0.974650i \(-0.428175\pi\)
0.223736 + 0.974650i \(0.428175\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.11146 −0.0919765
\(528\) 0 0
\(529\) 6.94427 0.301925
\(530\) 0 0
\(531\) −11.4412 −0.496507
\(532\) 0 0
\(533\) −4.47214 −0.193710
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.2333 0.441601
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 2.70820 0.116435 0.0582174 0.998304i \(-0.481458\pi\)
0.0582174 + 0.998304i \(0.481458\pi\)
\(542\) 0 0
\(543\) 21.7082 0.931588
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 16.7082 0.714391 0.357196 0.934030i \(-0.383733\pi\)
0.357196 + 0.934030i \(0.383733\pi\)
\(548\) 0 0
\(549\) −32.6544 −1.39366
\(550\) 0 0
\(551\) −1.41421 −0.0602475
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −45.6525 −1.93436 −0.967179 0.254097i \(-0.918222\pi\)
−0.967179 + 0.254097i \(0.918222\pi\)
\(558\) 0 0
\(559\) −18.8461 −0.797107
\(560\) 0 0
\(561\) 5.30495 0.223975
\(562\) 0 0
\(563\) −29.0308 −1.22350 −0.611751 0.791051i \(-0.709534\pi\)
−0.611751 + 0.791051i \(0.709534\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.05573 0.253869 0.126935 0.991911i \(-0.459486\pi\)
0.126935 + 0.991911i \(0.459486\pi\)
\(570\) 0 0
\(571\) 35.6525 1.49201 0.746005 0.665941i \(-0.231970\pi\)
0.746005 + 0.665941i \(0.231970\pi\)
\(572\) 0 0
\(573\) −8.89794 −0.371717
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 14.2209 0.592026 0.296013 0.955184i \(-0.404343\pi\)
0.296013 + 0.955184i \(0.404343\pi\)
\(578\) 0 0
\(579\) 13.6808 0.568553
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 5.93112 0.245642
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.0857 0.870299 0.435150 0.900358i \(-0.356695\pi\)
0.435150 + 0.900358i \(0.356695\pi\)
\(588\) 0 0
\(589\) 0.403252 0.0166157
\(590\) 0 0
\(591\) 9.20169 0.378507
\(592\) 0 0
\(593\) 39.0277 1.60268 0.801338 0.598212i \(-0.204122\pi\)
0.801338 + 0.598212i \(0.204122\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0.403252 0.0165040
\(598\) 0 0
\(599\) 17.4721 0.713892 0.356946 0.934125i \(-0.383818\pi\)
0.356946 + 0.934125i \(0.383818\pi\)
\(600\) 0 0
\(601\) −7.14988 −0.291650 −0.145825 0.989310i \(-0.546584\pi\)
−0.145825 + 0.989310i \(0.546584\pi\)
\(602\) 0 0
\(603\) 8.81966 0.359164
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −23.4226 −0.950696 −0.475348 0.879798i \(-0.657678\pi\)
−0.475348 + 0.879798i \(0.657678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −17.7082 −0.716397
\(612\) 0 0
\(613\) 8.88854 0.359005 0.179502 0.983758i \(-0.442551\pi\)
0.179502 + 0.983758i \(0.442551\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.3607 −1.18202 −0.591008 0.806666i \(-0.701270\pi\)
−0.591008 + 0.806666i \(0.701270\pi\)
\(618\) 0 0
\(619\) −27.5865 −1.10879 −0.554397 0.832252i \(-0.687051\pi\)
−0.554397 + 0.832252i \(0.687051\pi\)
\(620\) 0 0
\(621\) −25.0432 −1.00495
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.01316 −0.0404615
\(628\) 0 0
\(629\) −0.412662 −0.0164539
\(630\) 0 0
\(631\) −1.00000 −0.0398094 −0.0199047 0.999802i \(-0.506336\pi\)
−0.0199047 + 0.999802i \(0.506336\pi\)
\(632\) 0 0
\(633\) −16.1452 −0.641716
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −7.36068 −0.291184
\(640\) 0 0
\(641\) 5.36068 0.211734 0.105867 0.994380i \(-0.466238\pi\)
0.105867 + 0.994380i \(0.466238\pi\)
\(642\) 0 0
\(643\) 17.8933 0.705643 0.352821 0.935691i \(-0.385222\pi\)
0.352821 + 0.935691i \(0.385222\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −44.0957 −1.73358 −0.866790 0.498674i \(-0.833821\pi\)
−0.866790 + 0.498674i \(0.833821\pi\)
\(648\) 0 0
\(649\) 17.7658 0.697368
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −27.3050 −1.06853 −0.534263 0.845319i \(-0.679411\pi\)
−0.534263 + 0.845319i \(0.679411\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −32.6544 −1.27397
\(658\) 0 0
\(659\) 7.52786 0.293244 0.146622 0.989193i \(-0.453160\pi\)
0.146622 + 0.989193i \(0.453160\pi\)
\(660\) 0 0
\(661\) 12.4729 0.485139 0.242569 0.970134i \(-0.422010\pi\)
0.242569 + 0.970134i \(0.422010\pi\)
\(662\) 0 0
\(663\) 3.49613 0.135778
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 23.1803 0.897546
\(668\) 0 0
\(669\) −13.1246 −0.507427
\(670\) 0 0
\(671\) 50.7054 1.95746
\(672\) 0 0
\(673\) 21.7082 0.836790 0.418395 0.908265i \(-0.362593\pi\)
0.418395 + 0.908265i \(0.362593\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 37.1034 1.42600 0.713000 0.701164i \(-0.247336\pi\)
0.713000 + 0.701164i \(0.247336\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 16.6525 0.638124
\(682\) 0 0
\(683\) −0.527864 −0.0201982 −0.0100991 0.999949i \(-0.503215\pi\)
−0.0100991 + 0.999949i \(0.503215\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 17.2361 0.657597
\(688\) 0 0
\(689\) 3.90879 0.148913
\(690\) 0 0
\(691\) −36.5632 −1.39093 −0.695465 0.718560i \(-0.744802\pi\)
−0.695465 + 0.718560i \(0.744802\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.41641 0.129406
\(698\) 0 0
\(699\) 17.0193 0.643728
\(700\) 0 0
\(701\) −46.2492 −1.74681 −0.873405 0.486995i \(-0.838093\pi\)
−0.873405 + 0.486995i \(0.838093\pi\)
\(702\) 0 0
\(703\) 0.0788114 0.00297243
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 19.8885 0.746930 0.373465 0.927644i \(-0.378170\pi\)
0.373465 + 0.927644i \(0.378170\pi\)
\(710\) 0 0
\(711\) 5.65248 0.211984
\(712\) 0 0
\(713\) −6.60970 −0.247535
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 19.7990 0.739407
\(718\) 0 0
\(719\) 36.4056 1.35770 0.678850 0.734277i \(-0.262479\pi\)
0.678850 + 0.734277i \(0.262479\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −1.23607 −0.0459699
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 37.9473 1.40739 0.703694 0.710503i \(-0.251532\pi\)
0.703694 + 0.710503i \(0.251532\pi\)
\(728\) 0 0
\(729\) 5.94427 0.220158
\(730\) 0 0
\(731\) 14.3972 0.532499
\(732\) 0 0
\(733\) 31.7804 1.17384 0.586918 0.809646i \(-0.300341\pi\)
0.586918 + 0.809646i \(0.300341\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.6950 −0.504464
\(738\) 0 0
\(739\) −35.9443 −1.32223 −0.661116 0.750284i \(-0.729917\pi\)
−0.661116 + 0.750284i \(0.729917\pi\)
\(740\) 0 0
\(741\) −0.667701 −0.0245286
\(742\) 0 0
\(743\) 23.8197 0.873859 0.436929 0.899496i \(-0.356066\pi\)
0.436929 + 0.899496i \(0.356066\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −20.1815 −0.738404
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −12.9443 −0.472343 −0.236172 0.971711i \(-0.575893\pi\)
−0.236172 + 0.971711i \(0.575893\pi\)
\(752\) 0 0
\(753\) −4.00000 −0.145768
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 39.7214 1.44370 0.721849 0.692051i \(-0.243293\pi\)
0.721849 + 0.692051i \(0.243293\pi\)
\(758\) 0 0
\(759\) 16.6066 0.602782
\(760\) 0 0
\(761\) 38.6150 1.39979 0.699897 0.714244i \(-0.253229\pi\)
0.699897 + 0.714244i \(0.253229\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 11.7082 0.422759
\(768\) 0 0
\(769\) −18.0996 −0.652689 −0.326345 0.945251i \(-0.605817\pi\)
−0.326345 + 0.945251i \(0.605817\pi\)
\(770\) 0 0
\(771\) 1.05573 0.0380211
\(772\) 0 0
\(773\) −22.7549 −0.818438 −0.409219 0.912436i \(-0.634199\pi\)
−0.409219 + 0.912436i \(0.634199\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.652476 −0.0233774
\(780\) 0 0
\(781\) 11.4296 0.408982
\(782\) 0 0
\(783\) −19.3863 −0.692811
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −34.2449 −1.22070 −0.610349 0.792133i \(-0.708971\pi\)
−0.610349 + 0.792133i \(0.708971\pi\)
\(788\) 0 0
\(789\) 2.36706 0.0842695
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 33.4164 1.18665
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.2256 −0.610162 −0.305081 0.952326i \(-0.598684\pi\)
−0.305081 + 0.952326i \(0.598684\pi\)
\(798\) 0 0
\(799\) 13.5279 0.478581
\(800\) 0 0
\(801\) 34.3237 1.21277
\(802\) 0 0
\(803\) 50.7054 1.78935
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2.22291 0.0782502
\(808\) 0 0
\(809\) 52.1246 1.83260 0.916302 0.400488i \(-0.131159\pi\)
0.916302 + 0.400488i \(0.131159\pi\)
\(810\) 0 0
\(811\) 21.4682 0.753852 0.376926 0.926243i \(-0.376981\pi\)
0.376926 + 0.926243i \(0.376981\pi\)
\(812\) 0 0
\(813\) 3.16718 0.111078
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.74962 −0.0961969
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −28.4721 −0.993684 −0.496842 0.867841i \(-0.665507\pi\)
−0.496842 + 0.867841i \(0.665507\pi\)
\(822\) 0 0
\(823\) 33.9443 1.18322 0.591611 0.806223i \(-0.298492\pi\)
0.591611 + 0.806223i \(0.298492\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 16.3475 0.568459 0.284230 0.958756i \(-0.408262\pi\)
0.284230 + 0.958756i \(0.408262\pi\)
\(828\) 0 0
\(829\) 0.922740 0.0320481 0.0160240 0.999872i \(-0.494899\pi\)
0.0160240 + 0.999872i \(0.494899\pi\)
\(830\) 0 0
\(831\) 2.67080 0.0926492
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5.52786 0.191071
\(838\) 0 0
\(839\) −45.7162 −1.57830 −0.789149 0.614201i \(-0.789478\pi\)
−0.789149 + 0.614201i \(0.789478\pi\)
\(840\) 0 0
\(841\) −11.0557 −0.381232
\(842\) 0 0
\(843\) −14.0934 −0.485403
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 1.81966 0.0624506
\(850\) 0 0
\(851\) −1.29180 −0.0442822
\(852\) 0 0
\(853\) −31.3677 −1.07401 −0.537005 0.843579i \(-0.680445\pi\)
−0.537005 + 0.843579i \(0.680445\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −41.3948 −1.41402 −0.707009 0.707205i \(-0.749956\pi\)
−0.707009 + 0.707205i \(0.749956\pi\)
\(858\) 0 0
\(859\) 52.8360 1.80274 0.901370 0.433049i \(-0.142562\pi\)
0.901370 + 0.433049i \(0.142562\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 50.1246 1.70626 0.853131 0.521697i \(-0.174701\pi\)
0.853131 + 0.521697i \(0.174701\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 12.1877 0.413917
\(868\) 0 0
\(869\) −8.77709 −0.297742
\(870\) 0 0
\(871\) −9.02546 −0.305816
\(872\) 0 0
\(873\) 27.0764 0.916397
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 58.4296 1.97303 0.986513 0.163682i \(-0.0523372\pi\)
0.986513 + 0.163682i \(0.0523372\pi\)
\(878\) 0 0
\(879\) −18.5836 −0.626809
\(880\) 0 0
\(881\) −6.60970 −0.222686 −0.111343 0.993782i \(-0.535515\pi\)
−0.111343 + 0.993782i \(0.535515\pi\)
\(882\) 0 0
\(883\) 23.9443 0.805789 0.402894 0.915246i \(-0.368004\pi\)
0.402894 + 0.915246i \(0.368004\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.03165 0.0346396 0.0173198 0.999850i \(-0.494487\pi\)
0.0173198 + 0.999850i \(0.494487\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 9.40325 0.315021
\(892\) 0 0
\(893\) −2.58359 −0.0864566
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 10.9443 0.365419
\(898\) 0 0
\(899\) −5.11667 −0.170651
\(900\) 0 0
\(901\) −2.98605 −0.0994797
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 43.7771 1.45359 0.726797 0.686852i \(-0.241008\pi\)
0.726797 + 0.686852i \(0.241008\pi\)
\(908\) 0 0
\(909\) 14.6035 0.484368
\(910\) 0 0
\(911\) −42.8885 −1.42096 −0.710480 0.703717i \(-0.751522\pi\)
−0.710480 + 0.703717i \(0.751522\pi\)
\(912\) 0 0
\(913\) 31.3376 1.03712
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 5.29180 0.174560 0.0872801 0.996184i \(-0.472182\pi\)
0.0872801 + 0.996184i \(0.472182\pi\)
\(920\) 0 0
\(921\) −10.8328 −0.356953
\(922\) 0 0
\(923\) 7.53244 0.247933
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 41.1096 1.35022
\(928\) 0 0
\(929\) −6.78593 −0.222639 −0.111319 0.993785i \(-0.535508\pi\)
−0.111319 + 0.993785i \(0.535508\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 30.4721 0.997613
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −33.4798 −1.09374 −0.546868 0.837219i \(-0.684180\pi\)
−0.546868 + 0.837219i \(0.684180\pi\)
\(938\) 0 0
\(939\) 14.1803 0.462758
\(940\) 0 0
\(941\) −27.9991 −0.912746 −0.456373 0.889789i \(-0.650852\pi\)
−0.456373 + 0.889789i \(0.650852\pi\)
\(942\) 0 0
\(943\) 10.6947 0.348268
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −55.7771 −1.81251 −0.906256 0.422730i \(-0.861072\pi\)
−0.906256 + 0.422730i \(0.861072\pi\)
\(948\) 0 0
\(949\) 33.4164 1.08474
\(950\) 0 0
\(951\) 23.0888 0.748705
\(952\) 0 0
\(953\) 55.9017 1.81083 0.905417 0.424524i \(-0.139558\pi\)
0.905417 + 0.424524i \(0.139558\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 12.8554 0.415557
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −29.5410 −0.952936
\(962\) 0 0
\(963\) 7.88854 0.254205
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 31.4164 1.01028 0.505142 0.863036i \(-0.331440\pi\)
0.505142 + 0.863036i \(0.331440\pi\)
\(968\) 0 0
\(969\) 0.510078 0.0163861
\(970\) 0 0
\(971\) −44.0957 −1.41510 −0.707549 0.706665i \(-0.750199\pi\)
−0.707549 + 0.706665i \(0.750199\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −42.5967 −1.36279 −0.681395 0.731916i \(-0.738627\pi\)
−0.681395 + 0.731916i \(0.738627\pi\)
\(978\) 0 0
\(979\) −53.2974 −1.70339
\(980\) 0 0
\(981\) −23.2918 −0.743650
\(982\) 0 0
\(983\) −1.36551 −0.0435529 −0.0217764 0.999763i \(-0.506932\pi\)
−0.0217764 + 0.999763i \(0.506932\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 45.0689 1.43311
\(990\) 0 0
\(991\) 35.6525 1.13254 0.566269 0.824220i \(-0.308386\pi\)
0.566269 + 0.824220i \(0.308386\pi\)
\(992\) 0 0
\(993\) −23.9141 −0.758891
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 21.8809 0.692975 0.346488 0.938055i \(-0.387374\pi\)
0.346488 + 0.938055i \(0.387374\pi\)
\(998\) 0 0
\(999\) 1.08036 0.0341812
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 4900.2.a.bg.1.2 4
5.2 odd 4 4900.2.e.u.2549.5 8
5.3 odd 4 4900.2.e.u.2549.3 8
5.4 even 2 4900.2.a.bi.1.3 yes 4
7.6 odd 2 inner 4900.2.a.bg.1.3 yes 4
35.13 even 4 4900.2.e.u.2549.6 8
35.27 even 4 4900.2.e.u.2549.4 8
35.34 odd 2 4900.2.a.bi.1.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4900.2.a.bg.1.2 4 1.1 even 1 trivial
4900.2.a.bg.1.3 yes 4 7.6 odd 2 inner
4900.2.a.bi.1.2 yes 4 35.34 odd 2
4900.2.a.bi.1.3 yes 4 5.4 even 2
4900.2.e.u.2549.3 8 5.3 odd 4
4900.2.e.u.2549.4 8 35.27 even 4
4900.2.e.u.2549.5 8 5.2 odd 4
4900.2.e.u.2549.6 8 35.13 even 4