Properties

Label 1900.2.a.e.1.1
Level $1900$
Weight $2$
Character 1900.1
Self dual yes
Analytic conductor $15.172$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 380)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 1900.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.585786 q^{3} +4.82843 q^{7} -2.65685 q^{9} +O(q^{10})\) \(q+0.585786 q^{3} +4.82843 q^{7} -2.65685 q^{9} -2.00000 q^{11} -2.24264 q^{13} +4.82843 q^{17} -1.00000 q^{19} +2.82843 q^{21} +6.00000 q^{23} -3.31371 q^{27} +10.4853 q^{29} -1.17157 q^{31} -1.17157 q^{33} +10.2426 q^{37} -1.31371 q^{39} -7.65685 q^{41} +0.828427 q^{43} -0.828427 q^{47} +16.3137 q^{49} +2.82843 q^{51} +5.07107 q^{53} -0.585786 q^{57} +2.34315 q^{59} -2.34315 q^{61} -12.8284 q^{63} +0.585786 q^{67} +3.51472 q^{69} +10.8284 q^{71} -14.4853 q^{73} -9.65685 q^{77} -9.65685 q^{79} +6.02944 q^{81} -9.31371 q^{83} +6.14214 q^{87} +10.4853 q^{89} -10.8284 q^{91} -0.686292 q^{93} +1.75736 q^{97} +5.31371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{3} + 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{3} + 4 q^{7} + 6 q^{9} - 4 q^{11} + 4 q^{13} + 4 q^{17} - 2 q^{19} + 12 q^{23} + 16 q^{27} + 4 q^{29} - 8 q^{31} - 8 q^{33} + 12 q^{37} + 20 q^{39} - 4 q^{41} - 4 q^{43} + 4 q^{47} + 10 q^{49} - 4 q^{53} - 4 q^{57} + 16 q^{59} - 16 q^{61} - 20 q^{63} + 4 q^{67} + 24 q^{69} + 16 q^{71} - 12 q^{73} - 8 q^{77} - 8 q^{79} + 46 q^{81} + 4 q^{83} - 16 q^{87} + 4 q^{89} - 16 q^{91} - 24 q^{93} + 12 q^{97} - 12 q^{99} + O(q^{100}) \)

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
\(3\) 0.585786 0.338204 0.169102 0.985599i \(-0.445913\pi\)
0.169102 + 0.985599i \(0.445913\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.82843 1.82497 0.912487 0.409106i \(-0.134159\pi\)
0.912487 + 0.409106i \(0.134159\pi\)
\(8\) 0 0
\(9\) −2.65685 −0.885618
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −2.24264 −0.621997 −0.310998 0.950410i \(-0.600663\pi\)
−0.310998 + 0.950410i \(0.600663\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.82843 1.17107 0.585533 0.810649i \(-0.300885\pi\)
0.585533 + 0.810649i \(0.300885\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 2.82843 0.617213
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.31371 −0.637723
\(28\) 0 0
\(29\) 10.4853 1.94707 0.973534 0.228543i \(-0.0733960\pi\)
0.973534 + 0.228543i \(0.0733960\pi\)
\(30\) 0 0
\(31\) −1.17157 −0.210421 −0.105210 0.994450i \(-0.533552\pi\)
−0.105210 + 0.994450i \(0.533552\pi\)
\(32\) 0 0
\(33\) −1.17157 −0.203945
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.2426 1.68388 0.841940 0.539571i \(-0.181414\pi\)
0.841940 + 0.539571i \(0.181414\pi\)
\(38\) 0 0
\(39\) −1.31371 −0.210362
\(40\) 0 0
\(41\) −7.65685 −1.19580 −0.597900 0.801571i \(-0.703998\pi\)
−0.597900 + 0.801571i \(0.703998\pi\)
\(42\) 0 0
\(43\) 0.828427 0.126334 0.0631670 0.998003i \(-0.479880\pi\)
0.0631670 + 0.998003i \(0.479880\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.828427 −0.120839 −0.0604193 0.998173i \(-0.519244\pi\)
−0.0604193 + 0.998173i \(0.519244\pi\)
\(48\) 0 0
\(49\) 16.3137 2.33053
\(50\) 0 0
\(51\) 2.82843 0.396059
\(52\) 0 0
\(53\) 5.07107 0.696565 0.348282 0.937390i \(-0.386765\pi\)
0.348282 + 0.937390i \(0.386765\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.585786 −0.0775893
\(58\) 0 0
\(59\) 2.34315 0.305052 0.152526 0.988299i \(-0.451259\pi\)
0.152526 + 0.988299i \(0.451259\pi\)
\(60\) 0 0
\(61\) −2.34315 −0.300009 −0.150005 0.988685i \(-0.547929\pi\)
−0.150005 + 0.988685i \(0.547929\pi\)
\(62\) 0 0
\(63\) −12.8284 −1.61623
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0.585786 0.0715652 0.0357826 0.999360i \(-0.488608\pi\)
0.0357826 + 0.999360i \(0.488608\pi\)
\(68\) 0 0
\(69\) 3.51472 0.423122
\(70\) 0 0
\(71\) 10.8284 1.28510 0.642549 0.766245i \(-0.277877\pi\)
0.642549 + 0.766245i \(0.277877\pi\)
\(72\) 0 0
\(73\) −14.4853 −1.69537 −0.847687 0.530497i \(-0.822005\pi\)
−0.847687 + 0.530497i \(0.822005\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.65685 −1.10050
\(78\) 0 0
\(79\) −9.65685 −1.08648 −0.543240 0.839577i \(-0.682803\pi\)
−0.543240 + 0.839577i \(0.682803\pi\)
\(80\) 0 0
\(81\) 6.02944 0.669937
\(82\) 0 0
\(83\) −9.31371 −1.02231 −0.511156 0.859488i \(-0.670783\pi\)
−0.511156 + 0.859488i \(0.670783\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.14214 0.658506
\(88\) 0 0
\(89\) 10.4853 1.11144 0.555719 0.831370i \(-0.312443\pi\)
0.555719 + 0.831370i \(0.312443\pi\)
\(90\) 0 0
\(91\) −10.8284 −1.13513
\(92\) 0 0
\(93\) −0.686292 −0.0711651
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.75736 0.178433 0.0892164 0.996012i \(-0.471564\pi\)
0.0892164 + 0.996012i \(0.471564\pi\)
\(98\) 0 0
\(99\) 5.31371 0.534048
\(100\) 0 0
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 0 0
\(103\) 15.8995 1.56662 0.783312 0.621629i \(-0.213529\pi\)
0.783312 + 0.621629i \(0.213529\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.58579 −0.443325 −0.221662 0.975123i \(-0.571148\pi\)
−0.221662 + 0.975123i \(0.571148\pi\)
\(108\) 0 0
\(109\) −8.82843 −0.845610 −0.422805 0.906221i \(-0.638954\pi\)
−0.422805 + 0.906221i \(0.638954\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −5.07107 −0.477046 −0.238523 0.971137i \(-0.576663\pi\)
−0.238523 + 0.971137i \(0.576663\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.95837 0.550851
\(118\) 0 0
\(119\) 23.3137 2.13716
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) −4.48528 −0.404424
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 21.5563 1.91282 0.956408 0.292033i \(-0.0943316\pi\)
0.956408 + 0.292033i \(0.0943316\pi\)
\(128\) 0 0
\(129\) 0.485281 0.0427266
\(130\) 0 0
\(131\) −5.65685 −0.494242 −0.247121 0.968985i \(-0.579484\pi\)
−0.247121 + 0.968985i \(0.579484\pi\)
\(132\) 0 0
\(133\) −4.82843 −0.418678
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 20.1421 1.72086 0.860429 0.509570i \(-0.170195\pi\)
0.860429 + 0.509570i \(0.170195\pi\)
\(138\) 0 0
\(139\) −17.3137 −1.46853 −0.734265 0.678863i \(-0.762473\pi\)
−0.734265 + 0.678863i \(0.762473\pi\)
\(140\) 0 0
\(141\) −0.485281 −0.0408681
\(142\) 0 0
\(143\) 4.48528 0.375078
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.55635 0.788194
\(148\) 0 0
\(149\) −8.00000 −0.655386 −0.327693 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(150\) 0 0
\(151\) 18.1421 1.47639 0.738193 0.674590i \(-0.235679\pi\)
0.738193 + 0.674590i \(0.235679\pi\)
\(152\) 0 0
\(153\) −12.8284 −1.03712
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.17157 −0.253119 −0.126560 0.991959i \(-0.540393\pi\)
−0.126560 + 0.991959i \(0.540393\pi\)
\(158\) 0 0
\(159\) 2.97056 0.235581
\(160\) 0 0
\(161\) 28.9706 2.28320
\(162\) 0 0
\(163\) 2.48528 0.194662 0.0973311 0.995252i \(-0.468969\pi\)
0.0973311 + 0.995252i \(0.468969\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.7279 0.830152 0.415076 0.909787i \(-0.363755\pi\)
0.415076 + 0.909787i \(0.363755\pi\)
\(168\) 0 0
\(169\) −7.97056 −0.613120
\(170\) 0 0
\(171\) 2.65685 0.203175
\(172\) 0 0
\(173\) 3.89949 0.296473 0.148237 0.988952i \(-0.452640\pi\)
0.148237 + 0.988952i \(0.452640\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.37258 0.103170
\(178\) 0 0
\(179\) 21.6569 1.61871 0.809355 0.587320i \(-0.199817\pi\)
0.809355 + 0.587320i \(0.199817\pi\)
\(180\) 0 0
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) −1.37258 −0.101464
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.65685 −0.706179
\(188\) 0 0
\(189\) −16.0000 −1.16383
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) −0.585786 −0.0421658 −0.0210829 0.999778i \(-0.506711\pi\)
−0.0210829 + 0.999778i \(0.506711\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.31371 0.378586 0.189293 0.981921i \(-0.439380\pi\)
0.189293 + 0.981921i \(0.439380\pi\)
\(198\) 0 0
\(199\) −10.3431 −0.733206 −0.366603 0.930377i \(-0.619479\pi\)
−0.366603 + 0.930377i \(0.619479\pi\)
\(200\) 0 0
\(201\) 0.343146 0.0242036
\(202\) 0 0
\(203\) 50.6274 3.55335
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −15.9411 −1.10798
\(208\) 0 0
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −11.5147 −0.792706 −0.396353 0.918098i \(-0.629724\pi\)
−0.396353 + 0.918098i \(0.629724\pi\)
\(212\) 0 0
\(213\) 6.34315 0.434625
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −5.65685 −0.384012
\(218\) 0 0
\(219\) −8.48528 −0.573382
\(220\) 0 0
\(221\) −10.8284 −0.728399
\(222\) 0 0
\(223\) −19.2132 −1.28661 −0.643306 0.765609i \(-0.722438\pi\)
−0.643306 + 0.765609i \(0.722438\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.5858 −1.36633 −0.683163 0.730266i \(-0.739396\pi\)
−0.683163 + 0.730266i \(0.739396\pi\)
\(228\) 0 0
\(229\) −21.6569 −1.43113 −0.715563 0.698549i \(-0.753830\pi\)
−0.715563 + 0.698549i \(0.753830\pi\)
\(230\) 0 0
\(231\) −5.65685 −0.372194
\(232\) 0 0
\(233\) −10.0000 −0.655122 −0.327561 0.944830i \(-0.606227\pi\)
−0.327561 + 0.944830i \(0.606227\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.65685 −0.367452
\(238\) 0 0
\(239\) 10.3431 0.669042 0.334521 0.942388i \(-0.391425\pi\)
0.334521 + 0.942388i \(0.391425\pi\)
\(240\) 0 0
\(241\) −30.2843 −1.95078 −0.975391 0.220484i \(-0.929236\pi\)
−0.975391 + 0.220484i \(0.929236\pi\)
\(242\) 0 0
\(243\) 13.4731 0.864299
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.24264 0.142696
\(248\) 0 0
\(249\) −5.45584 −0.345750
\(250\) 0 0
\(251\) −13.6569 −0.862013 −0.431006 0.902349i \(-0.641841\pi\)
−0.431006 + 0.902349i \(0.641841\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.24264 0.139892 0.0699460 0.997551i \(-0.477717\pi\)
0.0699460 + 0.997551i \(0.477717\pi\)
\(258\) 0 0
\(259\) 49.4558 3.07304
\(260\) 0 0
\(261\) −27.8579 −1.72436
\(262\) 0 0
\(263\) −3.65685 −0.225491 −0.112746 0.993624i \(-0.535965\pi\)
−0.112746 + 0.993624i \(0.535965\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 6.14214 0.375893
\(268\) 0 0
\(269\) −22.4853 −1.37095 −0.685476 0.728095i \(-0.740406\pi\)
−0.685476 + 0.728095i \(0.740406\pi\)
\(270\) 0 0
\(271\) 23.6569 1.43705 0.718526 0.695500i \(-0.244817\pi\)
0.718526 + 0.695500i \(0.244817\pi\)
\(272\) 0 0
\(273\) −6.34315 −0.383905
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −16.8284 −1.01112 −0.505561 0.862791i \(-0.668714\pi\)
−0.505561 + 0.862791i \(0.668714\pi\)
\(278\) 0 0
\(279\) 3.11270 0.186352
\(280\) 0 0
\(281\) 18.9706 1.13169 0.565844 0.824512i \(-0.308550\pi\)
0.565844 + 0.824512i \(0.308550\pi\)
\(282\) 0 0
\(283\) 2.68629 0.159683 0.0798417 0.996808i \(-0.474559\pi\)
0.0798417 + 0.996808i \(0.474559\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −36.9706 −2.18230
\(288\) 0 0
\(289\) 6.31371 0.371395
\(290\) 0 0
\(291\) 1.02944 0.0603467
\(292\) 0 0
\(293\) 23.4142 1.36787 0.683936 0.729542i \(-0.260267\pi\)
0.683936 + 0.729542i \(0.260267\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.62742 0.384562
\(298\) 0 0
\(299\) −13.4558 −0.778172
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 0 0
\(303\) 2.34315 0.134610
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7.89949 −0.450848 −0.225424 0.974261i \(-0.572377\pi\)
−0.225424 + 0.974261i \(0.572377\pi\)
\(308\) 0 0
\(309\) 9.31371 0.529838
\(310\) 0 0
\(311\) −14.0000 −0.793867 −0.396934 0.917847i \(-0.629926\pi\)
−0.396934 + 0.917847i \(0.629926\pi\)
\(312\) 0 0
\(313\) −18.0000 −1.01742 −0.508710 0.860938i \(-0.669877\pi\)
−0.508710 + 0.860938i \(0.669877\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.75736 0.323366 0.161683 0.986843i \(-0.448308\pi\)
0.161683 + 0.986843i \(0.448308\pi\)
\(318\) 0 0
\(319\) −20.9706 −1.17413
\(320\) 0 0
\(321\) −2.68629 −0.149934
\(322\) 0 0
\(323\) −4.82843 −0.268661
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −5.17157 −0.285989
\(328\) 0 0
\(329\) −4.00000 −0.220527
\(330\) 0 0
\(331\) 1.17157 0.0643955 0.0321977 0.999482i \(-0.489749\pi\)
0.0321977 + 0.999482i \(0.489749\pi\)
\(332\) 0 0
\(333\) −27.2132 −1.49127
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −17.7574 −0.967305 −0.483652 0.875260i \(-0.660690\pi\)
−0.483652 + 0.875260i \(0.660690\pi\)
\(338\) 0 0
\(339\) −2.97056 −0.161339
\(340\) 0 0
\(341\) 2.34315 0.126888
\(342\) 0 0
\(343\) 44.9706 2.42818
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −22.9706 −1.23312 −0.616562 0.787306i \(-0.711475\pi\)
−0.616562 + 0.787306i \(0.711475\pi\)
\(348\) 0 0
\(349\) −0.343146 −0.0183682 −0.00918409 0.999958i \(-0.502923\pi\)
−0.00918409 + 0.999958i \(0.502923\pi\)
\(350\) 0 0
\(351\) 7.43146 0.396662
\(352\) 0 0
\(353\) 3.85786 0.205333 0.102667 0.994716i \(-0.467262\pi\)
0.102667 + 0.994716i \(0.467262\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 13.6569 0.722797
\(358\) 0 0
\(359\) −21.3137 −1.12489 −0.562447 0.826833i \(-0.690140\pi\)
−0.562447 + 0.826833i \(0.690140\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −4.10051 −0.215221
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 28.1421 1.46901 0.734504 0.678605i \(-0.237415\pi\)
0.734504 + 0.678605i \(0.237415\pi\)
\(368\) 0 0
\(369\) 20.3431 1.05902
\(370\) 0 0
\(371\) 24.4853 1.27121
\(372\) 0 0
\(373\) −9.55635 −0.494809 −0.247405 0.968912i \(-0.579578\pi\)
−0.247405 + 0.968912i \(0.579578\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −23.5147 −1.21107
\(378\) 0 0
\(379\) 22.3431 1.14769 0.573845 0.818964i \(-0.305451\pi\)
0.573845 + 0.818964i \(0.305451\pi\)
\(380\) 0 0
\(381\) 12.6274 0.646922
\(382\) 0 0
\(383\) −2.92893 −0.149661 −0.0748307 0.997196i \(-0.523842\pi\)
−0.0748307 + 0.997196i \(0.523842\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2.20101 −0.111884
\(388\) 0 0
\(389\) −28.6274 −1.45147 −0.725734 0.687976i \(-0.758500\pi\)
−0.725734 + 0.687976i \(0.758500\pi\)
\(390\) 0 0
\(391\) 28.9706 1.46510
\(392\) 0 0
\(393\) −3.31371 −0.167154
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 32.1421 1.61317 0.806584 0.591120i \(-0.201314\pi\)
0.806584 + 0.591120i \(0.201314\pi\)
\(398\) 0 0
\(399\) −2.82843 −0.141598
\(400\) 0 0
\(401\) −6.68629 −0.333897 −0.166949 0.985966i \(-0.553391\pi\)
−0.166949 + 0.985966i \(0.553391\pi\)
\(402\) 0 0
\(403\) 2.62742 0.130881
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −20.4853 −1.01542
\(408\) 0 0
\(409\) 9.51472 0.470473 0.235236 0.971938i \(-0.424414\pi\)
0.235236 + 0.971938i \(0.424414\pi\)
\(410\) 0 0
\(411\) 11.7990 0.582001
\(412\) 0 0
\(413\) 11.3137 0.556711
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.1421 −0.496663
\(418\) 0 0
\(419\) 9.65685 0.471768 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(420\) 0 0
\(421\) −8.34315 −0.406620 −0.203310 0.979114i \(-0.565170\pi\)
−0.203310 + 0.979114i \(0.565170\pi\)
\(422\) 0 0
\(423\) 2.20101 0.107017
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −11.3137 −0.547509
\(428\) 0 0
\(429\) 2.62742 0.126853
\(430\) 0 0
\(431\) 33.4558 1.61151 0.805756 0.592248i \(-0.201759\pi\)
0.805756 + 0.592248i \(0.201759\pi\)
\(432\) 0 0
\(433\) 15.2132 0.731100 0.365550 0.930792i \(-0.380881\pi\)
0.365550 + 0.930792i \(0.380881\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) −29.6569 −1.41544 −0.707722 0.706491i \(-0.750277\pi\)
−0.707722 + 0.706491i \(0.750277\pi\)
\(440\) 0 0
\(441\) −43.3431 −2.06396
\(442\) 0 0
\(443\) −34.2843 −1.62889 −0.814447 0.580237i \(-0.802960\pi\)
−0.814447 + 0.580237i \(0.802960\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.68629 −0.221654
\(448\) 0 0
\(449\) −13.5147 −0.637799 −0.318900 0.947789i \(-0.603313\pi\)
−0.318900 + 0.947789i \(0.603313\pi\)
\(450\) 0 0
\(451\) 15.3137 0.721094
\(452\) 0 0
\(453\) 10.6274 0.499320
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.9706 −0.887405 −0.443703 0.896174i \(-0.646335\pi\)
−0.443703 + 0.896174i \(0.646335\pi\)
\(458\) 0 0
\(459\) −16.0000 −0.746816
\(460\) 0 0
\(461\) −5.31371 −0.247484 −0.123742 0.992314i \(-0.539490\pi\)
−0.123742 + 0.992314i \(0.539490\pi\)
\(462\) 0 0
\(463\) 9.31371 0.432845 0.216422 0.976300i \(-0.430561\pi\)
0.216422 + 0.976300i \(0.430561\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.31371 −0.430987 −0.215494 0.976505i \(-0.569136\pi\)
−0.215494 + 0.976505i \(0.569136\pi\)
\(468\) 0 0
\(469\) 2.82843 0.130605
\(470\) 0 0
\(471\) −1.85786 −0.0856059
\(472\) 0 0
\(473\) −1.65685 −0.0761822
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −13.4731 −0.616890
\(478\) 0 0
\(479\) −10.0000 −0.456912 −0.228456 0.973554i \(-0.573368\pi\)
−0.228456 + 0.973554i \(0.573368\pi\)
\(480\) 0 0
\(481\) −22.9706 −1.04737
\(482\) 0 0
\(483\) 16.9706 0.772187
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −24.3848 −1.10498 −0.552490 0.833520i \(-0.686322\pi\)
−0.552490 + 0.833520i \(0.686322\pi\)
\(488\) 0 0
\(489\) 1.45584 0.0658355
\(490\) 0 0
\(491\) 35.3137 1.59369 0.796843 0.604187i \(-0.206502\pi\)
0.796843 + 0.604187i \(0.206502\pi\)
\(492\) 0 0
\(493\) 50.6274 2.28014
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 52.2843 2.34527
\(498\) 0 0
\(499\) −26.9706 −1.20737 −0.603684 0.797224i \(-0.706301\pi\)
−0.603684 + 0.797224i \(0.706301\pi\)
\(500\) 0 0
\(501\) 6.28427 0.280761
\(502\) 0 0
\(503\) −2.97056 −0.132451 −0.0662254 0.997805i \(-0.521096\pi\)
−0.0662254 + 0.997805i \(0.521096\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −4.66905 −0.207360
\(508\) 0 0
\(509\) −33.7990 −1.49811 −0.749057 0.662506i \(-0.769493\pi\)
−0.749057 + 0.662506i \(0.769493\pi\)
\(510\) 0 0
\(511\) −69.9411 −3.09401
\(512\) 0 0
\(513\) 3.31371 0.146304
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.65685 0.0728684
\(518\) 0 0
\(519\) 2.28427 0.100268
\(520\) 0 0
\(521\) 28.3431 1.24174 0.620868 0.783915i \(-0.286780\pi\)
0.620868 + 0.783915i \(0.286780\pi\)
\(522\) 0 0
\(523\) 6.72792 0.294191 0.147096 0.989122i \(-0.453007\pi\)
0.147096 + 0.989122i \(0.453007\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.65685 −0.246416
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −6.22540 −0.270159
\(532\) 0 0
\(533\) 17.1716 0.743783
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 12.6863 0.547454
\(538\) 0 0
\(539\) −32.6274 −1.40536
\(540\) 0 0
\(541\) 11.3137 0.486414 0.243207 0.969974i \(-0.421801\pi\)
0.243207 + 0.969974i \(0.421801\pi\)
\(542\) 0 0
\(543\) −10.5442 −0.452493
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −36.3848 −1.55570 −0.777850 0.628450i \(-0.783690\pi\)
−0.777850 + 0.628450i \(0.783690\pi\)
\(548\) 0 0
\(549\) 6.22540 0.265693
\(550\) 0 0
\(551\) −10.4853 −0.446688
\(552\) 0 0
\(553\) −46.6274 −1.98280
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −41.7990 −1.77108 −0.885540 0.464563i \(-0.846211\pi\)
−0.885540 + 0.464563i \(0.846211\pi\)
\(558\) 0 0
\(559\) −1.85786 −0.0785793
\(560\) 0 0
\(561\) −5.65685 −0.238833
\(562\) 0 0
\(563\) 11.4142 0.481052 0.240526 0.970643i \(-0.422680\pi\)
0.240526 + 0.970643i \(0.422680\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 29.1127 1.22262
\(568\) 0 0
\(569\) 0.828427 0.0347295 0.0173647 0.999849i \(-0.494472\pi\)
0.0173647 + 0.999849i \(0.494472\pi\)
\(570\) 0 0
\(571\) −14.6863 −0.614602 −0.307301 0.951612i \(-0.599426\pi\)
−0.307301 + 0.951612i \(0.599426\pi\)
\(572\) 0 0
\(573\) 2.34315 0.0978863
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) 0 0
\(579\) −0.343146 −0.0142607
\(580\) 0 0
\(581\) −44.9706 −1.86569
\(582\) 0 0
\(583\) −10.1421 −0.420044
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 14.9706 0.617901 0.308951 0.951078i \(-0.400022\pi\)
0.308951 + 0.951078i \(0.400022\pi\)
\(588\) 0 0
\(589\) 1.17157 0.0482738
\(590\) 0 0
\(591\) 3.11270 0.128039
\(592\) 0 0
\(593\) −8.62742 −0.354286 −0.177143 0.984185i \(-0.556685\pi\)
−0.177143 + 0.984185i \(0.556685\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.05887 −0.247973
\(598\) 0 0
\(599\) −4.68629 −0.191477 −0.0957383 0.995407i \(-0.530521\pi\)
−0.0957383 + 0.995407i \(0.530521\pi\)
\(600\) 0 0
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) 0 0
\(603\) −1.55635 −0.0633794
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −5.07107 −0.205828 −0.102914 0.994690i \(-0.532817\pi\)
−0.102914 + 0.994690i \(0.532817\pi\)
\(608\) 0 0
\(609\) 29.6569 1.20176
\(610\) 0 0
\(611\) 1.85786 0.0751611
\(612\) 0 0
\(613\) −17.5147 −0.707413 −0.353706 0.935356i \(-0.615079\pi\)
−0.353706 + 0.935356i \(0.615079\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.20101 0.249643 0.124822 0.992179i \(-0.460164\pi\)
0.124822 + 0.992179i \(0.460164\pi\)
\(618\) 0 0
\(619\) 18.0000 0.723481 0.361741 0.932279i \(-0.382183\pi\)
0.361741 + 0.932279i \(0.382183\pi\)
\(620\) 0 0
\(621\) −19.8823 −0.797847
\(622\) 0 0
\(623\) 50.6274 2.02834
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.17157 0.0467881
\(628\) 0 0
\(629\) 49.4558 1.97193
\(630\) 0 0
\(631\) −3.65685 −0.145577 −0.0727885 0.997347i \(-0.523190\pi\)
−0.0727885 + 0.997347i \(0.523190\pi\)
\(632\) 0 0
\(633\) −6.74517 −0.268096
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −36.5858 −1.44958
\(638\) 0 0
\(639\) −28.7696 −1.13811
\(640\) 0 0
\(641\) −21.3137 −0.841841 −0.420920 0.907098i \(-0.638293\pi\)
−0.420920 + 0.907098i \(0.638293\pi\)
\(642\) 0 0
\(643\) −24.6274 −0.971211 −0.485605 0.874178i \(-0.661401\pi\)
−0.485605 + 0.874178i \(0.661401\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.68629 −0.262865 −0.131433 0.991325i \(-0.541958\pi\)
−0.131433 + 0.991325i \(0.541958\pi\)
\(648\) 0 0
\(649\) −4.68629 −0.183953
\(650\) 0 0
\(651\) −3.31371 −0.129874
\(652\) 0 0
\(653\) −13.7990 −0.539996 −0.269998 0.962861i \(-0.587023\pi\)
−0.269998 + 0.962861i \(0.587023\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 38.4853 1.50145
\(658\) 0 0
\(659\) −34.6274 −1.34889 −0.674446 0.738324i \(-0.735618\pi\)
−0.674446 + 0.738324i \(0.735618\pi\)
\(660\) 0 0
\(661\) −12.6274 −0.491150 −0.245575 0.969378i \(-0.578977\pi\)
−0.245575 + 0.969378i \(0.578977\pi\)
\(662\) 0 0
\(663\) −6.34315 −0.246347
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 62.9117 2.43595
\(668\) 0 0
\(669\) −11.2548 −0.435137
\(670\) 0 0
\(671\) 4.68629 0.180912
\(672\) 0 0
\(673\) −10.2426 −0.394825 −0.197412 0.980321i \(-0.563254\pi\)
−0.197412 + 0.980321i \(0.563254\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −25.5563 −0.982210 −0.491105 0.871100i \(-0.663407\pi\)
−0.491105 + 0.871100i \(0.663407\pi\)
\(678\) 0 0
\(679\) 8.48528 0.325635
\(680\) 0 0
\(681\) −12.0589 −0.462097
\(682\) 0 0
\(683\) 38.7279 1.48188 0.740941 0.671570i \(-0.234380\pi\)
0.740941 + 0.671570i \(0.234380\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −12.6863 −0.484012
\(688\) 0 0
\(689\) −11.3726 −0.433261
\(690\) 0 0
\(691\) −15.6569 −0.595615 −0.297807 0.954626i \(-0.596255\pi\)
−0.297807 + 0.954626i \(0.596255\pi\)
\(692\) 0 0
\(693\) 25.6569 0.974623
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −36.9706 −1.40036
\(698\) 0 0
\(699\) −5.85786 −0.221565
\(700\) 0 0
\(701\) 49.6569 1.87551 0.937757 0.347293i \(-0.112899\pi\)
0.937757 + 0.347293i \(0.112899\pi\)
\(702\) 0 0
\(703\) −10.2426 −0.386309
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19.3137 0.726367
\(708\) 0 0
\(709\) 18.9706 0.712454 0.356227 0.934399i \(-0.384063\pi\)
0.356227 + 0.934399i \(0.384063\pi\)
\(710\) 0 0
\(711\) 25.6569 0.962207
\(712\) 0 0
\(713\) −7.02944 −0.263254
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 6.05887 0.226273
\(718\) 0 0
\(719\) 38.2843 1.42776 0.713881 0.700267i \(-0.246936\pi\)
0.713881 + 0.700267i \(0.246936\pi\)
\(720\) 0 0
\(721\) 76.7696 2.85905
\(722\) 0 0
\(723\) −17.7401 −0.659762
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 29.5147 1.09464 0.547320 0.836923i \(-0.315648\pi\)
0.547320 + 0.836923i \(0.315648\pi\)
\(728\) 0 0
\(729\) −10.1960 −0.377628
\(730\) 0 0
\(731\) 4.00000 0.147945
\(732\) 0 0
\(733\) −39.6569 −1.46476 −0.732380 0.680896i \(-0.761590\pi\)
−0.732380 + 0.680896i \(0.761590\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.17157 −0.0431554
\(738\) 0 0
\(739\) 34.6274 1.27379 0.636895 0.770951i \(-0.280218\pi\)
0.636895 + 0.770951i \(0.280218\pi\)
\(740\) 0 0
\(741\) 1.31371 0.0482603
\(742\) 0 0
\(743\) −14.0416 −0.515137 −0.257569 0.966260i \(-0.582921\pi\)
−0.257569 + 0.966260i \(0.582921\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 24.7452 0.905378
\(748\) 0 0
\(749\) −22.1421 −0.809056
\(750\) 0 0
\(751\) 14.1421 0.516054 0.258027 0.966138i \(-0.416928\pi\)
0.258027 + 0.966138i \(0.416928\pi\)
\(752\) 0 0
\(753\) −8.00000 −0.291536
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −19.6569 −0.714441 −0.357220 0.934020i \(-0.616275\pi\)
−0.357220 + 0.934020i \(0.616275\pi\)
\(758\) 0 0
\(759\) −7.02944 −0.255152
\(760\) 0 0
\(761\) 30.6274 1.11024 0.555121 0.831769i \(-0.312672\pi\)
0.555121 + 0.831769i \(0.312672\pi\)
\(762\) 0 0
\(763\) −42.6274 −1.54322
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.25483 −0.189741
\(768\) 0 0
\(769\) 38.6274 1.39294 0.696470 0.717586i \(-0.254753\pi\)
0.696470 + 0.717586i \(0.254753\pi\)
\(770\) 0 0
\(771\) 1.31371 0.0473121
\(772\) 0 0
\(773\) 0.100505 0.00361492 0.00180746 0.999998i \(-0.499425\pi\)
0.00180746 + 0.999998i \(0.499425\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 28.9706 1.03931
\(778\) 0 0
\(779\) 7.65685 0.274335
\(780\) 0 0
\(781\) −21.6569 −0.774943
\(782\) 0 0
\(783\) −34.7452 −1.24169
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 41.8406 1.49146 0.745729 0.666250i \(-0.232102\pi\)
0.745729 + 0.666250i \(0.232102\pi\)
\(788\) 0 0
\(789\) −2.14214 −0.0762620
\(790\) 0 0
\(791\) −24.4853 −0.870596
\(792\) 0 0
\(793\) 5.25483 0.186605
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −11.8995 −0.421502 −0.210751 0.977540i \(-0.567591\pi\)
−0.210751 + 0.977540i \(0.567591\pi\)
\(798\) 0 0
\(799\) −4.00000 −0.141510
\(800\) 0 0
\(801\) −27.8579 −0.984309
\(802\) 0 0
\(803\) 28.9706 1.02235
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −13.1716 −0.463661
\(808\) 0 0
\(809\) −39.2548 −1.38013 −0.690063 0.723749i \(-0.742417\pi\)
−0.690063 + 0.723749i \(0.742417\pi\)
\(810\) 0 0
\(811\) 19.7990 0.695237 0.347618 0.937636i \(-0.386991\pi\)
0.347618 + 0.937636i \(0.386991\pi\)
\(812\) 0 0
\(813\) 13.8579 0.486017
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.828427 −0.0289830
\(818\) 0 0
\(819\) 28.7696 1.00529
\(820\) 0 0
\(821\) 10.0000 0.349002 0.174501 0.984657i \(-0.444169\pi\)
0.174501 + 0.984657i \(0.444169\pi\)
\(822\) 0 0
\(823\) 15.1716 0.528848 0.264424 0.964407i \(-0.414818\pi\)
0.264424 + 0.964407i \(0.414818\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 29.0711 1.01090 0.505450 0.862856i \(-0.331326\pi\)
0.505450 + 0.862856i \(0.331326\pi\)
\(828\) 0 0
\(829\) −40.4264 −1.40407 −0.702034 0.712144i \(-0.747724\pi\)
−0.702034 + 0.712144i \(0.747724\pi\)
\(830\) 0 0
\(831\) −9.85786 −0.341966
\(832\) 0 0
\(833\) 78.7696 2.72920
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.88225 0.134190
\(838\) 0 0
\(839\) 43.5980 1.50517 0.752585 0.658495i \(-0.228807\pi\)
0.752585 + 0.658495i \(0.228807\pi\)
\(840\) 0 0
\(841\) 80.9411 2.79107
\(842\) 0 0
\(843\) 11.1127 0.382742
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −33.7990 −1.16135
\(848\) 0 0
\(849\) 1.57359 0.0540056
\(850\) 0 0
\(851\) 61.4558 2.10668
\(852\) 0 0
\(853\) −42.0000 −1.43805 −0.719026 0.694983i \(-0.755412\pi\)
−0.719026 + 0.694983i \(0.755412\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 27.2132 0.929585 0.464793 0.885420i \(-0.346129\pi\)
0.464793 + 0.885420i \(0.346129\pi\)
\(858\) 0 0
\(859\) −24.2843 −0.828569 −0.414284 0.910148i \(-0.635968\pi\)
−0.414284 + 0.910148i \(0.635968\pi\)
\(860\) 0 0
\(861\) −21.6569 −0.738064
\(862\) 0 0
\(863\) 3.89949 0.132740 0.0663702 0.997795i \(-0.478858\pi\)
0.0663702 + 0.997795i \(0.478858\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 3.69848 0.125607
\(868\) 0 0
\(869\) 19.3137 0.655173
\(870\) 0 0
\(871\) −1.31371 −0.0445133
\(872\) 0 0
\(873\) −4.66905 −0.158023
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 37.0711 1.25180 0.625901 0.779903i \(-0.284732\pi\)
0.625901 + 0.779903i \(0.284732\pi\)
\(878\) 0 0
\(879\) 13.7157 0.462620
\(880\) 0 0
\(881\) 44.2843 1.49198 0.745988 0.665960i \(-0.231978\pi\)
0.745988 + 0.665960i \(0.231978\pi\)
\(882\) 0 0
\(883\) 39.1716 1.31823 0.659114 0.752043i \(-0.270931\pi\)
0.659114 + 0.752043i \(0.270931\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 49.0711 1.64765 0.823823 0.566848i \(-0.191837\pi\)
0.823823 + 0.566848i \(0.191837\pi\)
\(888\) 0 0
\(889\) 104.083 3.49084
\(890\) 0 0
\(891\) −12.0589 −0.403987
\(892\) 0 0
\(893\) 0.828427 0.0277223
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −7.88225 −0.263181
\(898\) 0 0
\(899\) −12.2843 −0.409703
\(900\) 0 0
\(901\) 24.4853 0.815723
\(902\) 0 0
\(903\) 2.34315 0.0779750
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 20.3848 0.676865 0.338433 0.940991i \(-0.390103\pi\)
0.338433 + 0.940991i \(0.390103\pi\)
\(908\) 0 0
\(909\) −10.6274 −0.352489
\(910\) 0 0
\(911\) 4.20101 0.139186 0.0695928 0.997575i \(-0.477830\pi\)
0.0695928 + 0.997575i \(0.477830\pi\)
\(912\) 0 0
\(913\) 18.6274 0.616478
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −27.3137 −0.901978
\(918\) 0 0
\(919\) 35.3137 1.16489 0.582446 0.812869i \(-0.302096\pi\)
0.582446 + 0.812869i \(0.302096\pi\)
\(920\) 0 0
\(921\) −4.62742 −0.152479
\(922\) 0 0
\(923\) −24.2843 −0.799327
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −42.2426 −1.38743
\(928\) 0 0
\(929\) 6.68629 0.219370 0.109685 0.993966i \(-0.465016\pi\)
0.109685 + 0.993966i \(0.465016\pi\)
\(930\) 0 0
\(931\) −16.3137 −0.534660
\(932\) 0 0
\(933\) −8.20101 −0.268489
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 40.1421 1.31139 0.655693 0.755027i \(-0.272376\pi\)
0.655693 + 0.755027i \(0.272376\pi\)
\(938\) 0 0
\(939\) −10.5442 −0.344096
\(940\) 0 0
\(941\) −30.2843 −0.987239 −0.493620 0.869678i \(-0.664326\pi\)
−0.493620 + 0.869678i \(0.664326\pi\)
\(942\) 0 0
\(943\) −45.9411 −1.49605
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8.34315 0.271116 0.135558 0.990769i \(-0.456717\pi\)
0.135558 + 0.990769i \(0.456717\pi\)
\(948\) 0 0
\(949\) 32.4853 1.05452
\(950\) 0 0
\(951\) 3.37258 0.109363
\(952\) 0 0
\(953\) −5.75736 −0.186499 −0.0932496 0.995643i \(-0.529725\pi\)
−0.0932496 + 0.995643i \(0.529725\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −12.2843 −0.397094
\(958\) 0 0
\(959\) 97.2548 3.14052
\(960\) 0 0
\(961\) −29.6274 −0.955723
\(962\) 0 0
\(963\) 12.1838 0.392616
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −20.6274 −0.663333 −0.331667 0.943397i \(-0.607611\pi\)
−0.331667 + 0.943397i \(0.607611\pi\)
\(968\) 0 0
\(969\) −2.82843 −0.0908622
\(970\) 0 0
\(971\) −35.1127 −1.12682 −0.563410 0.826177i \(-0.690511\pi\)
−0.563410 + 0.826177i \(0.690511\pi\)
\(972\) 0 0
\(973\) −83.5980 −2.68003
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −9.27208 −0.296640 −0.148320 0.988939i \(-0.547387\pi\)
−0.148320 + 0.988939i \(0.547387\pi\)
\(978\) 0 0
\(979\) −20.9706 −0.670222
\(980\) 0 0
\(981\) 23.4558 0.748887
\(982\) 0 0
\(983\) 23.4142 0.746797 0.373399 0.927671i \(-0.378192\pi\)
0.373399 + 0.927671i \(0.378192\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −2.34315 −0.0745832
\(988\) 0 0
\(989\) 4.97056 0.158055
\(990\) 0 0
\(991\) −51.1127 −1.62365 −0.811824 0.583902i \(-0.801525\pi\)
−0.811824 + 0.583902i \(0.801525\pi\)
\(992\) 0 0
\(993\) 0.686292 0.0217788
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 13.5147 0.428015 0.214008 0.976832i \(-0.431348\pi\)
0.214008 + 0.976832i \(0.431348\pi\)
\(998\) 0 0
\(999\) −33.9411 −1.07385
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 1900.2.a.e.1.1 2
4.3 odd 2 7600.2.a.u.1.2 2
5.2 odd 4 1900.2.c.d.1749.2 4
5.3 odd 4 1900.2.c.d.1749.3 4
5.4 even 2 380.2.a.c.1.2 2
15.14 odd 2 3420.2.a.g.1.1 2
20.19 odd 2 1520.2.a.o.1.1 2
40.19 odd 2 6080.2.a.y.1.2 2
40.29 even 2 6080.2.a.bl.1.1 2
95.94 odd 2 7220.2.a.m.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.2.a.c.1.2 2 5.4 even 2
1520.2.a.o.1.1 2 20.19 odd 2
1900.2.a.e.1.1 2 1.1 even 1 trivial
1900.2.c.d.1749.2 4 5.2 odd 4
1900.2.c.d.1749.3 4 5.3 odd 4
3420.2.a.g.1.1 2 15.14 odd 2
6080.2.a.y.1.2 2 40.19 odd 2
6080.2.a.bl.1.1 2 40.29 even 2
7220.2.a.m.1.1 2 95.94 odd 2
7600.2.a.u.1.2 2 4.3 odd 2