Properties

Label 1805.2.a.d.1.2
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+2.23607 q^{2} +3.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +2.23607 q^{8} -3.00000 q^{9} -2.23607 q^{10} -4.47214 q^{13} -4.47214 q^{14} -1.00000 q^{16} -2.00000 q^{17} -6.70820 q^{18} -3.00000 q^{20} +6.00000 q^{23} +1.00000 q^{25} -10.0000 q^{26} -6.00000 q^{28} -8.94427 q^{29} +8.94427 q^{31} -6.70820 q^{32} -4.47214 q^{34} +2.00000 q^{35} -9.00000 q^{36} -4.47214 q^{37} -2.23607 q^{40} -8.94427 q^{41} -6.00000 q^{43} +3.00000 q^{45} +13.4164 q^{46} -2.00000 q^{47} -3.00000 q^{49} +2.23607 q^{50} -13.4164 q^{52} +4.47214 q^{53} -4.47214 q^{56} -20.0000 q^{58} +8.94427 q^{59} -10.0000 q^{61} +20.0000 q^{62} +6.00000 q^{63} -13.0000 q^{64} +4.47214 q^{65} -6.00000 q^{68} +4.47214 q^{70} +8.94427 q^{71} -6.70820 q^{72} +14.0000 q^{73} -10.0000 q^{74} +8.94427 q^{79} +1.00000 q^{80} +9.00000 q^{81} -20.0000 q^{82} +14.0000 q^{83} +2.00000 q^{85} -13.4164 q^{86} -8.94427 q^{89} +6.70820 q^{90} +8.94427 q^{91} +18.0000 q^{92} -4.47214 q^{94} +13.4164 q^{97} -6.70820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{4} - 2 q^{5} - 4 q^{7} - 6 q^{9} - 2 q^{16} - 4 q^{17} - 6 q^{20} + 12 q^{23} + 2 q^{25} - 20 q^{26} - 12 q^{28} + 4 q^{35} - 18 q^{36} - 12 q^{43} + 6 q^{45} - 4 q^{47} - 6 q^{49} - 40 q^{58} - 20 q^{61} + 40 q^{62} + 12 q^{63} - 26 q^{64} - 12 q^{68} + 28 q^{73} - 20 q^{74} + 2 q^{80} + 18 q^{81} - 40 q^{82} + 28 q^{83} + 4 q^{85} + 36 q^{92}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607 1.58114 0.790569 0.612372i \(-0.209785\pi\)
0.790569 + 0.612372i \(0.209785\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 3.00000 1.50000
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 2.23607 0.790569
\(9\) −3.00000 −1.00000
\(10\) −2.23607 −0.707107
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) −4.47214 −1.24035 −0.620174 0.784465i \(-0.712938\pi\)
−0.620174 + 0.784465i \(0.712938\pi\)
\(14\) −4.47214 −1.19523
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −6.70820 −1.58114
\(19\) 0 0
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −10.0000 −1.96116
\(27\) 0 0
\(28\) −6.00000 −1.13389
\(29\) −8.94427 −1.66091 −0.830455 0.557086i \(-0.811919\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 0 0
\(31\) 8.94427 1.60644 0.803219 0.595683i \(-0.203119\pi\)
0.803219 + 0.595683i \(0.203119\pi\)
\(32\) −6.70820 −1.18585
\(33\) 0 0
\(34\) −4.47214 −0.766965
\(35\) 2.00000 0.338062
\(36\) −9.00000 −1.50000
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −2.23607 −0.353553
\(41\) −8.94427 −1.39686 −0.698430 0.715678i \(-0.746118\pi\)
−0.698430 + 0.715678i \(0.746118\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 3.00000 0.447214
\(46\) 13.4164 1.97814
\(47\) −2.00000 −0.291730 −0.145865 0.989305i \(-0.546597\pi\)
−0.145865 + 0.989305i \(0.546597\pi\)
\(48\) 0 0
\(49\) −3.00000 −0.428571
\(50\) 2.23607 0.316228
\(51\) 0 0
\(52\) −13.4164 −1.86052
\(53\) 4.47214 0.614295 0.307148 0.951662i \(-0.400625\pi\)
0.307148 + 0.951662i \(0.400625\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −4.47214 −0.597614
\(57\) 0 0
\(58\) −20.0000 −2.62613
\(59\) 8.94427 1.16445 0.582223 0.813029i \(-0.302183\pi\)
0.582223 + 0.813029i \(0.302183\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 20.0000 2.54000
\(63\) 6.00000 0.755929
\(64\) −13.0000 −1.62500
\(65\) 4.47214 0.554700
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 4.47214 0.534522
\(71\) 8.94427 1.06149 0.530745 0.847532i \(-0.321912\pi\)
0.530745 + 0.847532i \(0.321912\pi\)
\(72\) −6.70820 −0.790569
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 8.94427 1.00631 0.503155 0.864196i \(-0.332173\pi\)
0.503155 + 0.864196i \(0.332173\pi\)
\(80\) 1.00000 0.111803
\(81\) 9.00000 1.00000
\(82\) −20.0000 −2.20863
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) −13.4164 −1.44673
\(87\) 0 0
\(88\) 0 0
\(89\) −8.94427 −0.948091 −0.474045 0.880500i \(-0.657207\pi\)
−0.474045 + 0.880500i \(0.657207\pi\)
\(90\) 6.70820 0.707107
\(91\) 8.94427 0.937614
\(92\) 18.0000 1.87663
\(93\) 0 0
\(94\) −4.47214 −0.461266
\(95\) 0 0
\(96\) 0 0
\(97\) 13.4164 1.36223 0.681115 0.732177i \(-0.261495\pi\)
0.681115 + 0.732177i \(0.261495\pi\)
\(98\) −6.70820 −0.677631
\(99\) 0 0
\(100\) 3.00000 0.300000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) −8.94427 −0.881305 −0.440653 0.897678i \(-0.645253\pi\)
−0.440653 + 0.897678i \(0.645253\pi\)
\(104\) −10.0000 −0.980581
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) −17.8885 −1.72935 −0.864675 0.502331i \(-0.832476\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 0.188982
\(113\) 13.4164 1.26211 0.631055 0.775738i \(-0.282622\pi\)
0.631055 + 0.775738i \(0.282622\pi\)
\(114\) 0 0
\(115\) −6.00000 −0.559503
\(116\) −26.8328 −2.49136
\(117\) 13.4164 1.24035
\(118\) 20.0000 1.84115
\(119\) 4.00000 0.366679
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −22.3607 −2.02444
\(123\) 0 0
\(124\) 26.8328 2.40966
\(125\) −1.00000 −0.0894427
\(126\) 13.4164 1.19523
\(127\) −8.94427 −0.793676 −0.396838 0.917889i \(-0.629892\pi\)
−0.396838 + 0.917889i \(0.629892\pi\)
\(128\) −15.6525 −1.38350
\(129\) 0 0
\(130\) 10.0000 0.877058
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −4.47214 −0.383482
\(137\) −18.0000 −1.53784 −0.768922 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 6.00000 0.507093
\(141\) 0 0
\(142\) 20.0000 1.67836
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 8.94427 0.742781
\(146\) 31.3050 2.59082
\(147\) 0 0
\(148\) −13.4164 −1.10282
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 17.8885 1.45575 0.727875 0.685710i \(-0.240508\pi\)
0.727875 + 0.685710i \(0.240508\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) −8.94427 −0.718421
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 20.0000 1.59111
\(159\) 0 0
\(160\) 6.70820 0.530330
\(161\) −12.0000 −0.945732
\(162\) 20.1246 1.58114
\(163\) −14.0000 −1.09656 −0.548282 0.836293i \(-0.684718\pi\)
−0.548282 + 0.836293i \(0.684718\pi\)
\(164\) −26.8328 −2.09529
\(165\) 0 0
\(166\) 31.3050 2.42974
\(167\) 8.94427 0.692129 0.346064 0.938211i \(-0.387518\pi\)
0.346064 + 0.938211i \(0.387518\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 4.47214 0.342997
\(171\) 0 0
\(172\) −18.0000 −1.37249
\(173\) 4.47214 0.340010 0.170005 0.985443i \(-0.445622\pi\)
0.170005 + 0.985443i \(0.445622\pi\)
\(174\) 0 0
\(175\) −2.00000 −0.151186
\(176\) 0 0
\(177\) 0 0
\(178\) −20.0000 −1.49906
\(179\) −8.94427 −0.668526 −0.334263 0.942480i \(-0.608487\pi\)
−0.334263 + 0.942480i \(0.608487\pi\)
\(180\) 9.00000 0.670820
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 20.0000 1.48250
\(183\) 0 0
\(184\) 13.4164 0.989071
\(185\) 4.47214 0.328798
\(186\) 0 0
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 13.4164 0.965734 0.482867 0.875694i \(-0.339595\pi\)
0.482867 + 0.875694i \(0.339595\pi\)
\(194\) 30.0000 2.15387
\(195\) 0 0
\(196\) −9.00000 −0.642857
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 2.23607 0.158114
\(201\) 0 0
\(202\) −22.3607 −1.57329
\(203\) 17.8885 1.25553
\(204\) 0 0
\(205\) 8.94427 0.624695
\(206\) −20.0000 −1.39347
\(207\) −18.0000 −1.25109
\(208\) 4.47214 0.310087
\(209\) 0 0
\(210\) 0 0
\(211\) −17.8885 −1.23150 −0.615749 0.787942i \(-0.711146\pi\)
−0.615749 + 0.787942i \(0.711146\pi\)
\(212\) 13.4164 0.921443
\(213\) 0 0
\(214\) −40.0000 −2.73434
\(215\) 6.00000 0.409197
\(216\) 0 0
\(217\) −17.8885 −1.21435
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.94427 0.601657
\(222\) 0 0
\(223\) 26.8328 1.79686 0.898429 0.439119i \(-0.144709\pi\)
0.898429 + 0.439119i \(0.144709\pi\)
\(224\) 13.4164 0.896421
\(225\) −3.00000 −0.200000
\(226\) 30.0000 1.99557
\(227\) 17.8885 1.18730 0.593652 0.804722i \(-0.297686\pi\)
0.593652 + 0.804722i \(0.297686\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −13.4164 −0.884652
\(231\) 0 0
\(232\) −20.0000 −1.31306
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 30.0000 1.96116
\(235\) 2.00000 0.130466
\(236\) 26.8328 1.74667
\(237\) 0 0
\(238\) 8.94427 0.579771
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 0 0
\(241\) 8.94427 0.576151 0.288076 0.957608i \(-0.406985\pi\)
0.288076 + 0.957608i \(0.406985\pi\)
\(242\) −24.5967 −1.58114
\(243\) 0 0
\(244\) −30.0000 −1.92055
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) 0 0
\(248\) 20.0000 1.27000
\(249\) 0 0
\(250\) −2.23607 −0.141421
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 18.0000 1.13389
\(253\) 0 0
\(254\) −20.0000 −1.25491
\(255\) 0 0
\(256\) −9.00000 −0.562500
\(257\) 4.47214 0.278964 0.139482 0.990225i \(-0.455456\pi\)
0.139482 + 0.990225i \(0.455456\pi\)
\(258\) 0 0
\(259\) 8.94427 0.555770
\(260\) 13.4164 0.832050
\(261\) 26.8328 1.66091
\(262\) −26.8328 −1.65774
\(263\) −26.0000 −1.60323 −0.801614 0.597841i \(-0.796025\pi\)
−0.801614 + 0.597841i \(0.796025\pi\)
\(264\) 0 0
\(265\) −4.47214 −0.274721
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −17.8885 −1.09068 −0.545342 0.838214i \(-0.683600\pi\)
−0.545342 + 0.838214i \(0.683600\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −40.2492 −2.43154
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −8.94427 −0.536442
\(279\) −26.8328 −1.60644
\(280\) 4.47214 0.267261
\(281\) 8.94427 0.533571 0.266785 0.963756i \(-0.414039\pi\)
0.266785 + 0.963756i \(0.414039\pi\)
\(282\) 0 0
\(283\) 6.00000 0.356663 0.178331 0.983970i \(-0.442930\pi\)
0.178331 + 0.983970i \(0.442930\pi\)
\(284\) 26.8328 1.59223
\(285\) 0 0
\(286\) 0 0
\(287\) 17.8885 1.05593
\(288\) 20.1246 1.18585
\(289\) −13.0000 −0.764706
\(290\) 20.0000 1.17444
\(291\) 0 0
\(292\) 42.0000 2.45786
\(293\) −13.4164 −0.783795 −0.391897 0.920009i \(-0.628181\pi\)
−0.391897 + 0.920009i \(0.628181\pi\)
\(294\) 0 0
\(295\) −8.94427 −0.520756
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) −13.4164 −0.777192
\(299\) −26.8328 −1.55178
\(300\) 0 0
\(301\) 12.0000 0.691669
\(302\) 40.0000 2.30174
\(303\) 0 0
\(304\) 0 0
\(305\) 10.0000 0.572598
\(306\) 13.4164 0.766965
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −20.0000 −1.13592
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −4.47214 −0.252377
\(315\) −6.00000 −0.338062
\(316\) 26.8328 1.50946
\(317\) −4.47214 −0.251180 −0.125590 0.992082i \(-0.540082\pi\)
−0.125590 + 0.992082i \(0.540082\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 13.0000 0.726722
\(321\) 0 0
\(322\) −26.8328 −1.49533
\(323\) 0 0
\(324\) 27.0000 1.50000
\(325\) −4.47214 −0.248069
\(326\) −31.3050 −1.73382
\(327\) 0 0
\(328\) −20.0000 −1.10432
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) 17.8885 0.983243 0.491622 0.870809i \(-0.336404\pi\)
0.491622 + 0.870809i \(0.336404\pi\)
\(332\) 42.0000 2.30505
\(333\) 13.4164 0.735215
\(334\) 20.0000 1.09435
\(335\) 0 0
\(336\) 0 0
\(337\) −4.47214 −0.243613 −0.121806 0.992554i \(-0.538869\pi\)
−0.121806 + 0.992554i \(0.538869\pi\)
\(338\) 15.6525 0.851382
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) −13.4164 −0.723364
\(345\) 0 0
\(346\) 10.0000 0.537603
\(347\) 2.00000 0.107366 0.0536828 0.998558i \(-0.482904\pi\)
0.0536828 + 0.998558i \(0.482904\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −4.47214 −0.239046
\(351\) 0 0
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) −8.94427 −0.474713
\(356\) −26.8328 −1.42214
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 6.70820 0.353553
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 26.8328 1.40642
\(365\) −14.0000 −0.732793
\(366\) 0 0
\(367\) −18.0000 −0.939592 −0.469796 0.882775i \(-0.655673\pi\)
−0.469796 + 0.882775i \(0.655673\pi\)
\(368\) −6.00000 −0.312772
\(369\) 26.8328 1.39686
\(370\) 10.0000 0.519875
\(371\) −8.94427 −0.464363
\(372\) 0 0
\(373\) −31.3050 −1.62091 −0.810454 0.585802i \(-0.800780\pi\)
−0.810454 + 0.585802i \(0.800780\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −4.47214 −0.230633
\(377\) 40.0000 2.06010
\(378\) 0 0
\(379\) −35.7771 −1.83775 −0.918873 0.394554i \(-0.870899\pi\)
−0.918873 + 0.394554i \(0.870899\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 17.8885 0.915258
\(383\) −8.94427 −0.457031 −0.228515 0.973540i \(-0.573387\pi\)
−0.228515 + 0.973540i \(0.573387\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 30.0000 1.52696
\(387\) 18.0000 0.914991
\(388\) 40.2492 2.04334
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) −6.70820 −0.338815
\(393\) 0 0
\(394\) 4.47214 0.225303
\(395\) −8.94427 −0.450035
\(396\) 0 0
\(397\) −2.00000 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) −44.7214 −2.24168
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −40.0000 −1.99254
\(404\) −30.0000 −1.49256
\(405\) −9.00000 −0.447214
\(406\) 40.0000 1.98517
\(407\) 0 0
\(408\) 0 0
\(409\) −17.8885 −0.884532 −0.442266 0.896884i \(-0.645825\pi\)
−0.442266 + 0.896884i \(0.645825\pi\)
\(410\) 20.0000 0.987730
\(411\) 0 0
\(412\) −26.8328 −1.32196
\(413\) −17.8885 −0.880238
\(414\) −40.2492 −1.97814
\(415\) −14.0000 −0.687233
\(416\) 30.0000 1.47087
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 8.94427 0.435917 0.217959 0.975958i \(-0.430060\pi\)
0.217959 + 0.975958i \(0.430060\pi\)
\(422\) −40.0000 −1.94717
\(423\) 6.00000 0.291730
\(424\) 10.0000 0.485643
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 20.0000 0.967868
\(428\) −53.6656 −2.59403
\(429\) 0 0
\(430\) 13.4164 0.646997
\(431\) 17.8885 0.861661 0.430830 0.902433i \(-0.358221\pi\)
0.430830 + 0.902433i \(0.358221\pi\)
\(432\) 0 0
\(433\) −4.47214 −0.214917 −0.107459 0.994210i \(-0.534271\pi\)
−0.107459 + 0.994210i \(0.534271\pi\)
\(434\) −40.0000 −1.92006
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 26.8328 1.28066 0.640330 0.768100i \(-0.278798\pi\)
0.640330 + 0.768100i \(0.278798\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 20.0000 0.951303
\(443\) −26.0000 −1.23530 −0.617649 0.786454i \(-0.711915\pi\)
−0.617649 + 0.786454i \(0.711915\pi\)
\(444\) 0 0
\(445\) 8.94427 0.423999
\(446\) 60.0000 2.84108
\(447\) 0 0
\(448\) 26.0000 1.22838
\(449\) 17.8885 0.844213 0.422106 0.906546i \(-0.361291\pi\)
0.422106 + 0.906546i \(0.361291\pi\)
\(450\) −6.70820 −0.316228
\(451\) 0 0
\(452\) 40.2492 1.89316
\(453\) 0 0
\(454\) 40.0000 1.87729
\(455\) −8.94427 −0.419314
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 13.4164 0.626908
\(459\) 0 0
\(460\) −18.0000 −0.839254
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) 6.00000 0.278844 0.139422 0.990233i \(-0.455476\pi\)
0.139422 + 0.990233i \(0.455476\pi\)
\(464\) 8.94427 0.415227
\(465\) 0 0
\(466\) −13.4164 −0.621503
\(467\) 2.00000 0.0925490 0.0462745 0.998929i \(-0.485265\pi\)
0.0462745 + 0.998929i \(0.485265\pi\)
\(468\) 40.2492 1.86052
\(469\) 0 0
\(470\) 4.47214 0.206284
\(471\) 0 0
\(472\) 20.0000 0.920575
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 12.0000 0.550019
\(477\) −13.4164 −0.614295
\(478\) −44.7214 −2.04551
\(479\) 16.0000 0.731059 0.365529 0.930800i \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 20.0000 0.910975
\(483\) 0 0
\(484\) −33.0000 −1.50000
\(485\) −13.4164 −0.609208
\(486\) 0 0
\(487\) 26.8328 1.21591 0.607955 0.793971i \(-0.291990\pi\)
0.607955 + 0.793971i \(0.291990\pi\)
\(488\) −22.3607 −1.01222
\(489\) 0 0
\(490\) 6.70820 0.303046
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0 0
\(493\) 17.8885 0.805659
\(494\) 0 0
\(495\) 0 0
\(496\) −8.94427 −0.401610
\(497\) −17.8885 −0.802411
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) −3.00000 −0.134164
\(501\) 0 0
\(502\) 26.8328 1.19761
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 13.4164 0.597614
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 0 0
\(508\) −26.8328 −1.19051
\(509\) −8.94427 −0.396448 −0.198224 0.980157i \(-0.563517\pi\)
−0.198224 + 0.980157i \(0.563517\pi\)
\(510\) 0 0
\(511\) −28.0000 −1.23865
\(512\) 11.1803 0.494106
\(513\) 0 0
\(514\) 10.0000 0.441081
\(515\) 8.94427 0.394132
\(516\) 0 0
\(517\) 0 0
\(518\) 20.0000 0.878750
\(519\) 0 0
\(520\) 10.0000 0.438529
\(521\) −17.8885 −0.783711 −0.391856 0.920027i \(-0.628167\pi\)
−0.391856 + 0.920027i \(0.628167\pi\)
\(522\) 60.0000 2.62613
\(523\) 17.8885 0.782211 0.391106 0.920346i \(-0.372093\pi\)
0.391106 + 0.920346i \(0.372093\pi\)
\(524\) −36.0000 −1.57267
\(525\) 0 0
\(526\) −58.1378 −2.53493
\(527\) −17.8885 −0.779237
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −10.0000 −0.434372
\(531\) −26.8328 −1.16445
\(532\) 0 0
\(533\) 40.0000 1.73259
\(534\) 0 0
\(535\) 17.8885 0.773389
\(536\) 0 0
\(537\) 0 0
\(538\) −40.0000 −1.72452
\(539\) 0 0
\(540\) 0 0
\(541\) −30.0000 −1.28980 −0.644900 0.764267i \(-0.723101\pi\)
−0.644900 + 0.764267i \(0.723101\pi\)
\(542\) −44.7214 −1.92095
\(543\) 0 0
\(544\) 13.4164 0.575224
\(545\) 0 0
\(546\) 0 0
\(547\) −35.7771 −1.52972 −0.764859 0.644198i \(-0.777191\pi\)
−0.764859 + 0.644198i \(0.777191\pi\)
\(548\) −54.0000 −2.30677
\(549\) 30.0000 1.28037
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −17.8885 −0.760698
\(554\) −4.47214 −0.190003
\(555\) 0 0
\(556\) −12.0000 −0.508913
\(557\) 38.0000 1.61011 0.805056 0.593199i \(-0.202135\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) −60.0000 −2.54000
\(559\) 26.8328 1.13491
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 20.0000 0.843649
\(563\) 17.8885 0.753912 0.376956 0.926231i \(-0.376971\pi\)
0.376956 + 0.926231i \(0.376971\pi\)
\(564\) 0 0
\(565\) −13.4164 −0.564433
\(566\) 13.4164 0.563934
\(567\) −18.0000 −0.755929
\(568\) 20.0000 0.839181
\(569\) −17.8885 −0.749927 −0.374963 0.927040i \(-0.622345\pi\)
−0.374963 + 0.927040i \(0.622345\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 40.0000 1.66957
\(575\) 6.00000 0.250217
\(576\) 39.0000 1.62500
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −29.0689 −1.20911
\(579\) 0 0
\(580\) 26.8328 1.11417
\(581\) −28.0000 −1.16164
\(582\) 0 0
\(583\) 0 0
\(584\) 31.3050 1.29541
\(585\) −13.4164 −0.554700
\(586\) −30.0000 −1.23929
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −20.0000 −0.823387
\(591\) 0 0
\(592\) 4.47214 0.183804
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) −4.00000 −0.163984
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −60.0000 −2.45358
\(599\) −26.8328 −1.09636 −0.548180 0.836361i \(-0.684679\pi\)
−0.548180 + 0.836361i \(0.684679\pi\)
\(600\) 0 0
\(601\) −44.7214 −1.82422 −0.912111 0.409943i \(-0.865549\pi\)
−0.912111 + 0.409943i \(0.865549\pi\)
\(602\) 26.8328 1.09362
\(603\) 0 0
\(604\) 53.6656 2.18362
\(605\) 11.0000 0.447214
\(606\) 0 0
\(607\) −26.8328 −1.08911 −0.544555 0.838725i \(-0.683302\pi\)
−0.544555 + 0.838725i \(0.683302\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 22.3607 0.905357
\(611\) 8.94427 0.361847
\(612\) 18.0000 0.727607
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −26.8328 −1.07763
\(621\) 0 0
\(622\) 44.7214 1.79316
\(623\) 17.8885 0.716689
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −13.4164 −0.536228
\(627\) 0 0
\(628\) −6.00000 −0.239426
\(629\) 8.94427 0.356631
\(630\) −13.4164 −0.534522
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 20.0000 0.795557
\(633\) 0 0
\(634\) −10.0000 −0.397151
\(635\) 8.94427 0.354943
\(636\) 0 0
\(637\) 13.4164 0.531577
\(638\) 0 0
\(639\) −26.8328 −1.06149
\(640\) 15.6525 0.618718
\(641\) −26.8328 −1.05983 −0.529916 0.848050i \(-0.677777\pi\)
−0.529916 + 0.848050i \(0.677777\pi\)
\(642\) 0 0
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) −36.0000 −1.41860
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 20.1246 0.790569
\(649\) 0 0
\(650\) −10.0000 −0.392232
\(651\) 0 0
\(652\) −42.0000 −1.64485
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 8.94427 0.349215
\(657\) −42.0000 −1.63858
\(658\) 8.94427 0.348684
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) 0 0
\(661\) −26.8328 −1.04368 −0.521838 0.853045i \(-0.674753\pi\)
−0.521838 + 0.853045i \(0.674753\pi\)
\(662\) 40.0000 1.55464
\(663\) 0 0
\(664\) 31.3050 1.21487
\(665\) 0 0
\(666\) 30.0000 1.16248
\(667\) −53.6656 −2.07794
\(668\) 26.8328 1.03819
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −13.4164 −0.517165 −0.258582 0.965989i \(-0.583255\pi\)
−0.258582 + 0.965989i \(0.583255\pi\)
\(674\) −10.0000 −0.385186
\(675\) 0 0
\(676\) 21.0000 0.807692
\(677\) 4.47214 0.171878 0.0859391 0.996300i \(-0.472611\pi\)
0.0859391 + 0.996300i \(0.472611\pi\)
\(678\) 0 0
\(679\) −26.8328 −1.02975
\(680\) 4.47214 0.171499
\(681\) 0 0
\(682\) 0 0
\(683\) 35.7771 1.36897 0.684486 0.729026i \(-0.260027\pi\)
0.684486 + 0.729026i \(0.260027\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 44.7214 1.70747
\(687\) 0 0
\(688\) 6.00000 0.228748
\(689\) −20.0000 −0.761939
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 13.4164 0.510015
\(693\) 0 0
\(694\) 4.47214 0.169760
\(695\) 4.00000 0.151729
\(696\) 0 0
\(697\) 17.8885 0.677577
\(698\) 22.3607 0.846364
\(699\) 0 0
\(700\) −6.00000 −0.226779
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 31.3050 1.17818
\(707\) 20.0000 0.752177
\(708\) 0 0
\(709\) 50.0000 1.87779 0.938895 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) −20.0000 −0.750587
\(711\) −26.8328 −1.00631
\(712\) −20.0000 −0.749532
\(713\) 53.6656 2.00979
\(714\) 0 0
\(715\) 0 0
\(716\) −26.8328 −1.00279
\(717\) 0 0
\(718\) −53.6656 −2.00278
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) −3.00000 −0.111803
\(721\) 17.8885 0.666204
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.94427 −0.332182
\(726\) 0 0
\(727\) 22.0000 0.815935 0.407967 0.912996i \(-0.366238\pi\)
0.407967 + 0.912996i \(0.366238\pi\)
\(728\) 20.0000 0.741249
\(729\) −27.0000 −1.00000
\(730\) −31.3050 −1.15865
\(731\) 12.0000 0.443836
\(732\) 0 0
\(733\) 34.0000 1.25582 0.627909 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) −40.2492 −1.48563
\(735\) 0 0
\(736\) −40.2492 −1.48361
\(737\) 0 0
\(738\) 60.0000 2.20863
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 13.4164 0.493197
\(741\) 0 0
\(742\) −20.0000 −0.734223
\(743\) −44.7214 −1.64067 −0.820334 0.571885i \(-0.806212\pi\)
−0.820334 + 0.571885i \(0.806212\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) −70.0000 −2.56288
\(747\) −42.0000 −1.53670
\(748\) 0 0
\(749\) 35.7771 1.30727
\(750\) 0 0
\(751\) 35.7771 1.30552 0.652762 0.757563i \(-0.273610\pi\)
0.652762 + 0.757563i \(0.273610\pi\)
\(752\) 2.00000 0.0729325
\(753\) 0 0
\(754\) 89.4427 3.25731
\(755\) −17.8885 −0.651031
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −80.0000 −2.90573
\(759\) 0 0
\(760\) 0 0
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) −6.00000 −0.216930
\(766\) −20.0000 −0.722629
\(767\) −40.0000 −1.44432
\(768\) 0 0
\(769\) −34.0000 −1.22607 −0.613036 0.790055i \(-0.710052\pi\)
−0.613036 + 0.790055i \(0.710052\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 40.2492 1.44860
\(773\) 49.1935 1.76937 0.884684 0.466192i \(-0.154374\pi\)
0.884684 + 0.466192i \(0.154374\pi\)
\(774\) 40.2492 1.44673
\(775\) 8.94427 0.321288
\(776\) 30.0000 1.07694
\(777\) 0 0
\(778\) 22.3607 0.801669
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) −26.8328 −0.959540
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 6.00000 0.213741
\(789\) 0 0
\(790\) −20.0000 −0.711568
\(791\) −26.8328 −0.954065
\(792\) 0 0
\(793\) 44.7214 1.58810
\(794\) −4.47214 −0.158710
\(795\) 0 0
\(796\) −60.0000 −2.12664
\(797\) 22.3607 0.792056 0.396028 0.918238i \(-0.370388\pi\)
0.396028 + 0.918238i \(0.370388\pi\)
\(798\) 0 0
\(799\) 4.00000 0.141510
\(800\) −6.70820 −0.237171
\(801\) 26.8328 0.948091
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 12.0000 0.422944
\(806\) −89.4427 −3.15049
\(807\) 0 0
\(808\) −22.3607 −0.786646
\(809\) 10.0000 0.351581 0.175791 0.984428i \(-0.443752\pi\)
0.175791 + 0.984428i \(0.443752\pi\)
\(810\) −20.1246 −0.707107
\(811\) 8.94427 0.314076 0.157038 0.987593i \(-0.449806\pi\)
0.157038 + 0.987593i \(0.449806\pi\)
\(812\) 53.6656 1.88329
\(813\) 0 0
\(814\) 0 0
\(815\) 14.0000 0.490399
\(816\) 0 0
\(817\) 0 0
\(818\) −40.0000 −1.39857
\(819\) −26.8328 −0.937614
\(820\) 26.8328 0.937043
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) 26.0000 0.906303 0.453152 0.891434i \(-0.350300\pi\)
0.453152 + 0.891434i \(0.350300\pi\)
\(824\) −20.0000 −0.696733
\(825\) 0 0
\(826\) −40.0000 −1.39178
\(827\) 17.8885 0.622046 0.311023 0.950402i \(-0.399328\pi\)
0.311023 + 0.950402i \(0.399328\pi\)
\(828\) −54.0000 −1.87663
\(829\) 53.6656 1.86388 0.931942 0.362607i \(-0.118113\pi\)
0.931942 + 0.362607i \(0.118113\pi\)
\(830\) −31.3050 −1.08661
\(831\) 0 0
\(832\) 58.1378 2.01556
\(833\) 6.00000 0.207888
\(834\) 0 0
\(835\) −8.94427 −0.309529
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −44.7214 −1.54395 −0.771976 0.635651i \(-0.780732\pi\)
−0.771976 + 0.635651i \(0.780732\pi\)
\(840\) 0 0
\(841\) 51.0000 1.75862
\(842\) 20.0000 0.689246
\(843\) 0 0
\(844\) −53.6656 −1.84725
\(845\) −7.00000 −0.240807
\(846\) 13.4164 0.461266
\(847\) 22.0000 0.755929
\(848\) −4.47214 −0.153574
\(849\) 0 0
\(850\) −4.47214 −0.153393
\(851\) −26.8328 −0.919817
\(852\) 0 0
\(853\) 34.0000 1.16414 0.582069 0.813139i \(-0.302243\pi\)
0.582069 + 0.813139i \(0.302243\pi\)
\(854\) 44.7214 1.53033
\(855\) 0 0
\(856\) −40.0000 −1.36717
\(857\) −31.3050 −1.06936 −0.534678 0.845056i \(-0.679567\pi\)
−0.534678 + 0.845056i \(0.679567\pi\)
\(858\) 0 0
\(859\) −40.0000 −1.36478 −0.682391 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) 18.0000 0.613795
\(861\) 0 0
\(862\) 40.0000 1.36241
\(863\) 8.94427 0.304467 0.152233 0.988345i \(-0.451353\pi\)
0.152233 + 0.988345i \(0.451353\pi\)
\(864\) 0 0
\(865\) −4.47214 −0.152057
\(866\) −10.0000 −0.339814
\(867\) 0 0
\(868\) −53.6656 −1.82153
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −40.2492 −1.36223
\(874\) 0 0
\(875\) 2.00000 0.0676123
\(876\) 0 0
\(877\) −13.4164 −0.453040 −0.226520 0.974007i \(-0.572735\pi\)
−0.226520 + 0.974007i \(0.572735\pi\)
\(878\) 60.0000 2.02490
\(879\) 0 0
\(880\) 0 0
\(881\) −50.0000 −1.68454 −0.842271 0.539054i \(-0.818782\pi\)
−0.842271 + 0.539054i \(0.818782\pi\)
\(882\) 20.1246 0.677631
\(883\) 26.0000 0.874970 0.437485 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 26.8328 0.902485
\(885\) 0 0
\(886\) −58.1378 −1.95318
\(887\) 44.7214 1.50160 0.750798 0.660532i \(-0.229669\pi\)
0.750798 + 0.660532i \(0.229669\pi\)
\(888\) 0 0
\(889\) 17.8885 0.599963
\(890\) 20.0000 0.670402
\(891\) 0 0
\(892\) 80.4984 2.69529
\(893\) 0 0
\(894\) 0 0
\(895\) 8.94427 0.298974
\(896\) 31.3050 1.04583
\(897\) 0 0
\(898\) 40.0000 1.33482
\(899\) −80.0000 −2.66815
\(900\) −9.00000 −0.300000
\(901\) −8.94427 −0.297977
\(902\) 0 0
\(903\) 0 0
\(904\) 30.0000 0.997785
\(905\) 0 0
\(906\) 0 0
\(907\) 53.6656 1.78194 0.890969 0.454064i \(-0.150026\pi\)
0.890969 + 0.454064i \(0.150026\pi\)
\(908\) 53.6656 1.78096
\(909\) 30.0000 0.995037
\(910\) −20.0000 −0.662994
\(911\) 35.7771 1.18535 0.592674 0.805443i \(-0.298072\pi\)
0.592674 + 0.805443i \(0.298072\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −49.1935 −1.62718
\(915\) 0 0
\(916\) 18.0000 0.594737
\(917\) 24.0000 0.792550
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) −13.4164 −0.442326
\(921\) 0 0
\(922\) 4.47214 0.147282
\(923\) −40.0000 −1.31662
\(924\) 0 0
\(925\) −4.47214 −0.147043
\(926\) 13.4164 0.440891
\(927\) 26.8328 0.881305
\(928\) 60.0000 1.96960
\(929\) −10.0000 −0.328089 −0.164045 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −18.0000 −0.589610
\(933\) 0 0
\(934\) 4.47214 0.146333
\(935\) 0 0
\(936\) 30.0000 0.980581
\(937\) −2.00000 −0.0653372 −0.0326686 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 6.00000 0.195698
\(941\) 53.6656 1.74945 0.874725 0.484620i \(-0.161042\pi\)
0.874725 + 0.484620i \(0.161042\pi\)
\(942\) 0 0
\(943\) −53.6656 −1.74759
\(944\) −8.94427 −0.291111
\(945\) 0 0
\(946\) 0 0
\(947\) 18.0000 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(948\) 0 0
\(949\) −62.6099 −2.03240
\(950\) 0 0
\(951\) 0 0
\(952\) 8.94427 0.289886
\(953\) 22.3607 0.724333 0.362167 0.932113i \(-0.382037\pi\)
0.362167 + 0.932113i \(0.382037\pi\)
\(954\) −30.0000 −0.971286
\(955\) −8.00000 −0.258874
\(956\) −60.0000 −1.94054
\(957\) 0 0
\(958\) 35.7771 1.15591
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) 49.0000 1.58065
\(962\) 44.7214 1.44187
\(963\) 53.6656 1.72935
\(964\) 26.8328 0.864227
\(965\) −13.4164 −0.431889
\(966\) 0 0
\(967\) −38.0000 −1.22200 −0.610999 0.791632i \(-0.709232\pi\)
−0.610999 + 0.791632i \(0.709232\pi\)
\(968\) −24.5967 −0.790569
\(969\) 0 0
\(970\) −30.0000 −0.963242
\(971\) 44.7214 1.43518 0.717588 0.696467i \(-0.245246\pi\)
0.717588 + 0.696467i \(0.245246\pi\)
\(972\) 0 0
\(973\) 8.00000 0.256468
\(974\) 60.0000 1.92252
\(975\) 0 0
\(976\) 10.0000 0.320092
\(977\) 40.2492 1.28769 0.643843 0.765157i \(-0.277339\pi\)
0.643843 + 0.765157i \(0.277339\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 9.00000 0.287494
\(981\) 0 0
\(982\) 62.6099 1.99796
\(983\) −8.94427 −0.285278 −0.142639 0.989775i \(-0.545559\pi\)
−0.142639 + 0.989775i \(0.545559\pi\)
\(984\) 0 0
\(985\) −2.00000 −0.0637253
\(986\) 40.0000 1.27386
\(987\) 0 0
\(988\) 0 0
\(989\) −36.0000 −1.14473
\(990\) 0 0
\(991\) −17.8885 −0.568248 −0.284124 0.958787i \(-0.591703\pi\)
−0.284124 + 0.958787i \(0.591703\pi\)
\(992\) −60.0000 −1.90500
\(993\) 0 0
\(994\) −40.0000 −1.26872
\(995\) 20.0000 0.634043
\(996\) 0 0
\(997\) −18.0000 −0.570066 −0.285033 0.958518i \(-0.592005\pi\)
−0.285033 + 0.958518i \(0.592005\pi\)
\(998\) −8.94427 −0.283126
\(999\) 0 0
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 1805.2.a.d.1.2 yes 2
5.4 even 2 9025.2.a.q.1.1 2
19.18 odd 2 inner 1805.2.a.d.1.1 2
95.94 odd 2 9025.2.a.q.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.a.d.1.1 2 19.18 odd 2 inner
1805.2.a.d.1.2 yes 2 1.1 even 1 trivial
9025.2.a.q.1.1 2 5.4 even 2
9025.2.a.q.1.2 2 95.94 odd 2