Properties

Label 1805.2.b.d.1084.2
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $2$
CM discriminant -19
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-19}) \)
Defining polynomial: \( x^{2} - x + 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1084.2
Root \(0.500000 + 2.17945i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.d.1084.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{4} +(-0.500000 + 2.17945i) q^{5} +4.35890i q^{7} +3.00000 q^{9} +O(q^{10})\) \(q+2.00000 q^{4} +(-0.500000 + 2.17945i) q^{5} +4.35890i q^{7} +3.00000 q^{9} +5.00000 q^{11} +4.00000 q^{16} +4.35890i q^{17} +(-1.00000 + 4.35890i) q^{20} -8.71780i q^{23} +(-4.50000 - 2.17945i) q^{25} +8.71780i q^{28} +(-9.50000 - 2.17945i) q^{35} +6.00000 q^{36} -13.0767i q^{43} +10.0000 q^{44} +(-1.50000 + 6.53835i) q^{45} +4.35890i q^{47} -12.0000 q^{49} +(-2.50000 + 10.8972i) q^{55} -15.0000 q^{61} +13.0767i q^{63} +8.00000 q^{64} +8.71780i q^{68} -13.0767i q^{73} +21.7945i q^{77} +(-2.00000 + 8.71780i) q^{80} +9.00000 q^{81} +8.71780i q^{83} +(-9.50000 - 2.17945i) q^{85} -17.4356i q^{92} +15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{4} - q^{5} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{4} - q^{5} + 6 q^{9} + 10 q^{11} + 8 q^{16} - 2 q^{20} - 9 q^{25} - 19 q^{35} + 12 q^{36} + 20 q^{44} - 3 q^{45} - 24 q^{49} - 5 q^{55} - 30 q^{61} + 16 q^{64} - 4 q^{80} + 18 q^{81} - 19 q^{85} + 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

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 1.00000 \(0\)
−1.00000 \(\pi\)
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 2.00000 1.00000
\(5\) −0.500000 + 2.17945i −0.223607 + 0.974679i
\(6\) 0 0
\(7\) 4.35890i 1.64751i 0.566947 + 0.823754i \(0.308125\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 4.35890i 1.05719i 0.848875 + 0.528594i \(0.177281\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) 0 0
\(20\) −1.00000 + 4.35890i −0.223607 + 0.974679i
\(21\) 0 0
\(22\) 0 0
\(23\) 8.71780i 1.81779i −0.417029 0.908893i \(-0.636929\pi\)
0.417029 0.908893i \(-0.363071\pi\)
\(24\) 0 0
\(25\) −4.50000 2.17945i −0.900000 0.435890i
\(26\) 0 0
\(27\) 0 0
\(28\) 8.71780i 1.64751i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.50000 2.17945i −1.60579 0.368394i
\(36\) 6.00000 1.00000
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 13.0767i 1.99418i −0.0762493 0.997089i \(-0.524294\pi\)
0.0762493 0.997089i \(-0.475706\pi\)
\(44\) 10.0000 1.50756
\(45\) −1.50000 + 6.53835i −0.223607 + 0.974679i
\(46\) 0 0
\(47\) 4.35890i 0.635811i 0.948122 + 0.317905i \(0.102979\pi\)
−0.948122 + 0.317905i \(0.897021\pi\)
\(48\) 0 0
\(49\) −12.0000 −1.71429
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) −2.50000 + 10.8972i −0.337100 + 1.46938i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −15.0000 −1.92055 −0.960277 0.279050i \(-0.909981\pi\)
−0.960277 + 0.279050i \(0.909981\pi\)
\(62\) 0 0
\(63\) 13.0767i 1.64751i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 8.71780i 1.05719i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 13.0767i 1.53051i −0.643726 0.765256i \(-0.722612\pi\)
0.643726 0.765256i \(-0.277388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21.7945i 2.48371i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 + 8.71780i −0.223607 + 0.974679i
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 8.71780i 0.956903i 0.878114 + 0.478451i \(0.158802\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) −9.50000 2.17945i −1.03042 0.236394i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 17.4356i 1.81779i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 15.0000 1.50756
\(100\) −9.00000 4.35890i −0.900000 0.435890i
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 17.4356i 1.64751i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 19.0000 + 4.35890i 1.77176 + 0.406469i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −19.0000 −1.74173
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 7.00000 8.71780i 0.626099 0.779744i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.00000 −0.611593 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.35890i 0.372406i −0.982511 0.186203i \(-0.940382\pi\)
0.982511 0.186203i \(-0.0596182\pi\)
\(138\) 0 0
\(139\) 9.00000 0.763370 0.381685 0.924292i \(-0.375344\pi\)
0.381685 + 0.924292i \(0.375344\pi\)
\(140\) −19.0000 4.35890i −1.60579 0.368394i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000 1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.0000 0.901155 0.450578 0.892737i \(-0.351218\pi\)
0.450578 + 0.892737i \(0.351218\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 13.0767i 1.05719i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 17.4356i 1.39151i −0.718278 0.695756i \(-0.755069\pi\)
0.718278 0.695756i \(-0.244931\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 38.0000 2.99482
\(162\) 0 0
\(163\) 8.71780i 0.682831i −0.939913 0.341415i \(-0.889094\pi\)
0.939913 0.341415i \(-0.110906\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 26.1534i 1.99418i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 9.50000 19.6150i 0.718132 1.48276i
\(176\) 20.0000 1.50756
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −3.00000 + 13.0767i −0.223607 + 0.974679i
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 21.7945i 1.59377i
\(188\) 8.71780i 0.635811i
\(189\) 0 0
\(190\) 0 0
\(191\) −17.0000 −1.23008 −0.615038 0.788497i \(-0.710860\pi\)
−0.615038 + 0.788497i \(0.710860\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −24.0000 −1.71429
\(197\) 17.4356i 1.24223i 0.783718 + 0.621117i \(0.213321\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) −25.0000 −1.77220 −0.886102 0.463491i \(-0.846597\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 26.1534i 1.81779i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 28.5000 + 6.53835i 1.94368 + 0.445912i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −5.00000 + 21.7945i −0.337100 + 1.46938i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −13.5000 6.53835i −0.900000 0.435890i
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) −21.0000 −1.38772 −0.693860 0.720110i \(-0.744091\pi\)
−0.693860 + 0.720110i \(0.744091\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 30.5123i 1.99893i 0.0327561 + 0.999463i \(0.489572\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) 0 0
\(235\) −9.50000 2.17945i −0.619712 0.142172i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) −30.0000 −1.92055
\(245\) 6.00000 26.1534i 0.383326 1.67088i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −23.0000 −1.45175 −0.725874 0.687828i \(-0.758564\pi\)
−0.725874 + 0.687828i \(0.758564\pi\)
\(252\) 26.1534i 1.64751i
\(253\) 43.5890i 2.74042i
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 30.5123i 1.88147i 0.339145 + 0.940734i \(0.389862\pi\)
−0.339145 + 0.940734i \(0.610138\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 17.4356i 1.05719i
\(273\) 0 0
\(274\) 0 0
\(275\) −22.5000 10.8972i −1.35680 0.657129i
\(276\) 0 0
\(277\) 4.35890i 0.261901i 0.991389 + 0.130950i \(0.0418029\pi\)
−0.991389 + 0.130950i \(0.958197\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 13.0767i 0.777329i 0.921379 + 0.388664i \(0.127063\pi\)
−0.921379 + 0.388664i \(0.872937\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2.00000 −0.117647
\(290\) 0 0
\(291\) 0 0
\(292\) 26.1534i 1.53051i
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 57.0000 3.28543
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.50000 32.6917i 0.429449 1.87192i
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 43.5890i 2.48371i
\(309\) 0 0
\(310\) 0 0
\(311\) 35.0000 1.98467 0.992334 0.123585i \(-0.0394392\pi\)
0.992334 + 0.123585i \(0.0394392\pi\)
\(312\) 0 0
\(313\) 34.8712i 1.97104i −0.169570 0.985518i \(-0.554238\pi\)
0.169570 0.985518i \(-0.445762\pi\)
\(314\) 0 0
\(315\) −28.5000 6.53835i −1.60579 0.368394i
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −4.00000 + 17.4356i −0.223607 + 0.974679i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000 1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −19.0000 −1.04750
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 17.4356i 0.956903i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −19.0000 4.35890i −1.03042 0.236394i
\(341\) 0 0
\(342\) 0 0
\(343\) 21.7945i 1.17679i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.35890i 0.233998i −0.993132 0.116999i \(-0.962673\pi\)
0.993132 0.116999i \(-0.0373274\pi\)
\(348\) 0 0
\(349\) −35.0000 −1.87351 −0.936754 0.349990i \(-0.886185\pi\)
−0.936754 + 0.349990i \(0.886185\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 34.8712i 1.85601i −0.372572 0.928003i \(-0.621524\pi\)
0.372572 0.928003i \(-0.378476\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.0000 −1.63612 −0.818059 0.575135i \(-0.804950\pi\)
−0.818059 + 0.575135i \(0.804950\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 28.5000 + 6.53835i 1.49176 + 0.342233i
\(366\) 0 0
\(367\) 26.1534i 1.36520i −0.730794 0.682598i \(-0.760850\pi\)
0.730794 0.682598i \(-0.239150\pi\)
\(368\) 34.8712i 1.81779i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) −47.5000 10.8972i −2.42082 0.555375i
\(386\) 0 0
\(387\) 39.2301i 1.99418i
\(388\) 0 0
\(389\) −25.0000 −1.26755 −0.633775 0.773517i \(-0.718496\pi\)
−0.633775 + 0.773517i \(0.718496\pi\)
\(390\) 0 0
\(391\) 38.0000 1.92174
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 30.0000 1.50756
\(397\) 39.2301i 1.96890i −0.175660 0.984451i \(-0.556206\pi\)
0.175660 0.984451i \(-0.443794\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −18.0000 8.71780i −0.900000 0.435890i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −20.0000 −0.995037
\(405\) −4.50000 + 19.6150i −0.223607 + 0.974679i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −19.0000 4.35890i −0.932673 0.213970i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 40.0000 1.95413 0.977064 0.212946i \(-0.0683059\pi\)
0.977064 + 0.212946i \(0.0683059\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 13.0767i 0.635811i
\(424\) 0 0
\(425\) 9.50000 19.6150i 0.460818 0.951469i
\(426\) 0 0
\(427\) 65.3835i 3.16413i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) 30.5123i 1.44968i 0.688916 + 0.724841i \(0.258087\pi\)
−0.688916 + 0.724841i \(0.741913\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 34.8712i 1.64751i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 39.2301i 1.83511i −0.397613 0.917553i \(-0.630161\pi\)
0.397613 0.917553i \(-0.369839\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 38.0000 + 8.71780i 1.77176 + 0.406469i
\(461\) 37.0000 1.72326 0.861631 0.507535i \(-0.169443\pi\)
0.861631 + 0.507535i \(0.169443\pi\)
\(462\) 0 0
\(463\) 13.0767i 0.607726i 0.952716 + 0.303863i \(0.0982765\pi\)
−0.952716 + 0.303863i \(0.901724\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.35890i 0.201706i −0.994901 0.100853i \(-0.967843\pi\)
0.994901 0.100853i \(-0.0321571\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 65.3835i 3.00634i
\(474\) 0 0
\(475\) 0 0
\(476\) −38.0000 −1.74173
\(477\) 0 0
\(478\) 0 0
\(479\) 4.00000 0.182765 0.0913823 0.995816i \(-0.470871\pi\)
0.0913823 + 0.995816i \(0.470871\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 28.0000 1.27273
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −7.50000 + 32.6917i −0.337100 + 1.46938i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 39.0000 1.74588 0.872940 0.487828i \(-0.162211\pi\)
0.872940 + 0.487828i \(0.162211\pi\)
\(500\) 14.0000 17.4356i 0.626099 0.779744i
\(501\) 0 0
\(502\) 0 0
\(503\) 8.71780i 0.388707i −0.980932 0.194354i \(-0.937739\pi\)
0.980932 0.194354i \(-0.0622609\pi\)
\(504\) 0 0
\(505\) 5.00000 21.7945i 0.222497 0.969842i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 57.0000 2.52153
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 21.7945i 0.958521i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −53.0000 −2.30435
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −60.0000 −2.58438
\(540\) 0 0
\(541\) 25.0000 1.07483 0.537417 0.843317i \(-0.319400\pi\)
0.537417 + 0.843317i \(0.319400\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 8.71780i 0.372406i
\(549\) −45.0000 −1.92055
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 18.0000 0.763370
\(557\) 4.35890i 0.184692i 0.995727 + 0.0923462i \(0.0294367\pi\)
−0.995727 + 0.0923462i \(0.970563\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −38.0000 8.71780i −1.60579 0.368394i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 39.2301i 1.64751i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 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
\(574\) 0 0
\(575\) −19.0000 + 39.2301i −0.792355 + 1.63601i
\(576\) 24.0000 1.00000
\(577\) 47.9479i 1.99610i 0.0624458 + 0.998048i \(0.480110\pi\)
−0.0624458 + 0.998048i \(0.519890\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −38.0000 −1.57651
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 47.9479i 1.97902i 0.144460 + 0.989511i \(0.453855\pi\)
−0.144460 + 0.989511i \(0.546145\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 34.8712i 1.43199i −0.698106 0.715994i \(-0.745974\pi\)
0.698106 0.715994i \(-0.254026\pi\)
\(594\) 0 0
\(595\) 9.50000 41.4095i 0.389462 1.69763i
\(596\) 22.0000 0.901155
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7.00000 + 30.5123i −0.284590 + 1.24050i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 26.1534i 1.05719i
\(613\) 30.5123i 1.23238i −0.787598 0.616190i \(-0.788675\pi\)
0.787598 0.616190i \(-0.211325\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 47.9479i 1.93031i 0.261680 + 0.965155i \(0.415723\pi\)
−0.261680 + 0.965155i \(0.584277\pi\)
\(618\) 0 0
\(619\) 24.0000 0.964641 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 + 19.6150i 0.620000 + 0.784602i
\(626\) 0 0
\(627\) 0 0
\(628\) 34.8712i 1.39151i
\(629\) 0 0
\(630\) 0 0
\(631\) −15.0000 −0.597141 −0.298570 0.954388i \(-0.596510\pi\)
−0.298570 + 0.954388i \(0.596510\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) 13.0767i 0.515695i 0.966186 + 0.257847i \(0.0830131\pi\)
−0.966186 + 0.257847i \(0.916987\pi\)
\(644\) 76.0000 2.99482
\(645\) 0 0
\(646\) 0 0
\(647\) 47.9479i 1.88503i 0.334169 + 0.942513i \(0.391544\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 17.4356i 0.682831i
\(653\) 30.5123i 1.19404i −0.802227 0.597019i \(-0.796352\pi\)
0.802227 0.597019i \(-0.203648\pi\)
\(654\) 0 0
\(655\) 3.50000 15.2561i 0.136756 0.596107i
\(656\) 0 0
\(657\) 39.2301i 1.53051i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −75.0000 −2.89534
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 26.0000 1.00000
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 9.50000 + 2.17945i 0.362976 + 0.0832725i
\(686\) 0 0
\(687\) 0 0
\(688\) 52.3068i 1.99418i
\(689\) 0 0
\(690\) 0 0
\(691\) 35.0000 1.33146 0.665731 0.746191i \(-0.268120\pi\)
0.665731 + 0.746191i \(0.268120\pi\)
\(692\) 0 0
\(693\) 65.3835i 2.48371i
\(694\) 0 0
\(695\) −4.50000 + 19.6150i −0.170695 + 0.744041i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 19.0000 39.2301i 0.718132 1.48276i
\(701\) −50.0000 −1.88847 −0.944237 0.329267i \(-0.893198\pi\)
−0.944237 + 0.329267i \(0.893198\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 40.0000 1.50756
\(705\) 0 0
\(706\) 0 0
\(707\) 43.5890i 1.63933i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 49.0000 1.82739 0.913696 0.406399i \(-0.133216\pi\)
0.913696 + 0.406399i \(0.133216\pi\)
\(720\) −6.00000 + 26.1534i −0.223607 + 0.974679i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 39.2301i 1.45496i 0.686127 + 0.727482i \(0.259309\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 57.0000 2.10822
\(732\) 0 0
\(733\) 52.3068i 1.93200i 0.258551 + 0.965998i \(0.416755\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −45.0000 −1.65535 −0.827676 0.561206i \(-0.810337\pi\)
−0.827676 + 0.561206i \(0.810337\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) −5.50000 + 23.9739i −0.201504 + 0.878337i
\(746\) 0 0
\(747\) 26.1534i 0.956903i
\(748\) 43.5890i 1.59377i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 17.4356i 0.635811i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 47.9479i 1.74270i −0.490666 0.871348i \(-0.663246\pi\)
0.490666 0.871348i \(-0.336754\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 55.0000 1.99375 0.996874 0.0790050i \(-0.0251743\pi\)
0.996874 + 0.0790050i \(0.0251743\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −34.0000 −1.23008
\(765\) −28.5000 6.53835i −1.03042 0.236394i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −51.0000 −1.83911 −0.919554 0.392965i \(-0.871449\pi\)
−0.919554 + 0.392965i \(0.871449\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −48.0000 −1.71429
\(785\) 38.0000 + 8.71780i 1.35628 + 0.311152i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 34.8712i 1.24223i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −50.0000 −1.77220
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) −19.0000 −0.672172
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 65.3835i 2.30733i
\(804\) 0 0
\(805\) −19.0000 + 82.8191i −0.669662 + 2.91899i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −5.00000