Properties

Label 2800.2.a.bp.1.2
Level $2800$
Weight $2$
Character 2800.1
Self dual yes
Analytic conductor $22.358$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.3581125660\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 175)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 2800.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.23607 q^{3} -1.00000 q^{7} +7.47214 q^{9} +O(q^{10})\) \(q+3.23607 q^{3} -1.00000 q^{7} +7.47214 q^{9} +0.236068 q^{11} +1.23607 q^{13} +2.47214 q^{17} +4.47214 q^{19} -3.23607 q^{21} -6.23607 q^{23} +14.4721 q^{27} +5.00000 q^{29} -3.70820 q^{31} +0.763932 q^{33} +3.00000 q^{37} +4.00000 q^{39} +4.76393 q^{41} -1.76393 q^{43} +2.00000 q^{47} +1.00000 q^{49} +8.00000 q^{51} +8.47214 q^{53} +14.4721 q^{57} -11.7082 q^{59} -9.70820 q^{61} -7.47214 q^{63} +4.23607 q^{67} -20.1803 q^{69} -8.70820 q^{71} -8.76393 q^{73} -0.236068 q^{77} +11.1803 q^{79} +24.4164 q^{81} +7.70820 q^{83} +16.1803 q^{87} +17.2361 q^{89} -1.23607 q^{91} -12.0000 q^{93} +5.23607 q^{97} +1.76393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 2 q^{7} + 6 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{3} - 2 q^{7} + 6 q^{9} - 4 q^{11} - 2 q^{13} - 4 q^{17} - 2 q^{21} - 8 q^{23} + 20 q^{27} + 10 q^{29} + 6 q^{31} + 6 q^{33} + 6 q^{37} + 8 q^{39} + 14 q^{41} - 8 q^{43} + 4 q^{47} + 2 q^{49} + 16 q^{51} + 8 q^{53} + 20 q^{57} - 10 q^{59} - 6 q^{61} - 6 q^{63} + 4 q^{67} - 18 q^{69} - 4 q^{71} - 22 q^{73} + 4 q^{77} + 22 q^{81} + 2 q^{83} + 10 q^{87} + 30 q^{89} + 2 q^{91} - 24 q^{93} + 6 q^{97} + 8 q^{99} + O(q^{100}) \)

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
\(3\) 3.23607 1.86834 0.934172 0.356822i \(-0.116140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 7.47214 2.49071
\(10\) 0 0
\(11\) 0.236068 0.0711772 0.0355886 0.999367i \(-0.488669\pi\)
0.0355886 + 0.999367i \(0.488669\pi\)
\(12\) 0 0
\(13\) 1.23607 0.342824 0.171412 0.985199i \(-0.445167\pi\)
0.171412 + 0.985199i \(0.445167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.47214 0.599581 0.299791 0.954005i \(-0.403083\pi\)
0.299791 + 0.954005i \(0.403083\pi\)
\(18\) 0 0
\(19\) 4.47214 1.02598 0.512989 0.858395i \(-0.328538\pi\)
0.512989 + 0.858395i \(0.328538\pi\)
\(20\) 0 0
\(21\) −3.23607 −0.706168
\(22\) 0 0
\(23\) −6.23607 −1.30031 −0.650155 0.759802i \(-0.725296\pi\)
−0.650155 + 0.759802i \(0.725296\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 14.4721 2.78516
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) −3.70820 −0.666013 −0.333007 0.942925i \(-0.608063\pi\)
−0.333007 + 0.942925i \(0.608063\pi\)
\(32\) 0 0
\(33\) 0.763932 0.132983
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 0.493197 0.246598 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) 0 0
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 4.76393 0.744001 0.372001 0.928232i \(-0.378672\pi\)
0.372001 + 0.928232i \(0.378672\pi\)
\(42\) 0 0
\(43\) −1.76393 −0.268997 −0.134499 0.990914i \(-0.542942\pi\)
−0.134499 + 0.990914i \(0.542942\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 8.00000 1.12022
\(52\) 0 0
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 14.4721 1.91688
\(58\) 0 0
\(59\) −11.7082 −1.52428 −0.762139 0.647413i \(-0.775851\pi\)
−0.762139 + 0.647413i \(0.775851\pi\)
\(60\) 0 0
\(61\) −9.70820 −1.24301 −0.621504 0.783411i \(-0.713478\pi\)
−0.621504 + 0.783411i \(0.713478\pi\)
\(62\) 0 0
\(63\) −7.47214 −0.941401
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.23607 0.517518 0.258759 0.965942i \(-0.416686\pi\)
0.258759 + 0.965942i \(0.416686\pi\)
\(68\) 0 0
\(69\) −20.1803 −2.42943
\(70\) 0 0
\(71\) −8.70820 −1.03347 −0.516737 0.856144i \(-0.672853\pi\)
−0.516737 + 0.856144i \(0.672853\pi\)
\(72\) 0 0
\(73\) −8.76393 −1.02574 −0.512870 0.858466i \(-0.671418\pi\)
−0.512870 + 0.858466i \(0.671418\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.236068 −0.0269024
\(78\) 0 0
\(79\) 11.1803 1.25789 0.628943 0.777451i \(-0.283488\pi\)
0.628943 + 0.777451i \(0.283488\pi\)
\(80\) 0 0
\(81\) 24.4164 2.71293
\(82\) 0 0
\(83\) 7.70820 0.846085 0.423043 0.906110i \(-0.360962\pi\)
0.423043 + 0.906110i \(0.360962\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 16.1803 1.73471
\(88\) 0 0
\(89\) 17.2361 1.82702 0.913510 0.406817i \(-0.133361\pi\)
0.913510 + 0.406817i \(0.133361\pi\)
\(90\) 0 0
\(91\) −1.23607 −0.129575
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 5.23607 0.531642 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(98\) 0 0
\(99\) 1.76393 0.177282
\(100\) 0 0
\(101\) 4.76393 0.474029 0.237014 0.971506i \(-0.423831\pi\)
0.237014 + 0.971506i \(0.423831\pi\)
\(102\) 0 0
\(103\) −8.47214 −0.834784 −0.417392 0.908726i \(-0.637056\pi\)
−0.417392 + 0.908726i \(0.637056\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.00000 −0.773389 −0.386695 0.922208i \(-0.626383\pi\)
−0.386695 + 0.922208i \(0.626383\pi\)
\(108\) 0 0
\(109\) 8.41641 0.806146 0.403073 0.915168i \(-0.367942\pi\)
0.403073 + 0.915168i \(0.367942\pi\)
\(110\) 0 0
\(111\) 9.70820 0.921462
\(112\) 0 0
\(113\) −14.4164 −1.35618 −0.678091 0.734978i \(-0.737192\pi\)
−0.678091 + 0.734978i \(0.737192\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9.23607 0.853875
\(118\) 0 0
\(119\) −2.47214 −0.226620
\(120\) 0 0
\(121\) −10.9443 −0.994934
\(122\) 0 0
\(123\) 15.4164 1.39005
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −13.6525 −1.21146 −0.605731 0.795670i \(-0.707119\pi\)
−0.605731 + 0.795670i \(0.707119\pi\)
\(128\) 0 0
\(129\) −5.70820 −0.502579
\(130\) 0 0
\(131\) 16.9443 1.48043 0.740214 0.672371i \(-0.234724\pi\)
0.740214 + 0.672371i \(0.234724\pi\)
\(132\) 0 0
\(133\) −4.47214 −0.387783
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.9443 −0.935032 −0.467516 0.883985i \(-0.654851\pi\)
−0.467516 + 0.883985i \(0.654851\pi\)
\(138\) 0 0
\(139\) −10.6525 −0.903531 −0.451766 0.892137i \(-0.649206\pi\)
−0.451766 + 0.892137i \(0.649206\pi\)
\(140\) 0 0
\(141\) 6.47214 0.545052
\(142\) 0 0
\(143\) 0.291796 0.0244012
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.23607 0.266906
\(148\) 0 0
\(149\) 3.94427 0.323127 0.161564 0.986862i \(-0.448346\pi\)
0.161564 + 0.986862i \(0.448346\pi\)
\(150\) 0 0
\(151\) 20.2361 1.64679 0.823394 0.567470i \(-0.192078\pi\)
0.823394 + 0.567470i \(0.192078\pi\)
\(152\) 0 0
\(153\) 18.4721 1.49338
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.763932 0.0609684 0.0304842 0.999535i \(-0.490295\pi\)
0.0304842 + 0.999535i \(0.490295\pi\)
\(158\) 0 0
\(159\) 27.4164 2.17426
\(160\) 0 0
\(161\) 6.23607 0.491471
\(162\) 0 0
\(163\) 1.52786 0.119672 0.0598358 0.998208i \(-0.480942\pi\)
0.0598358 + 0.998208i \(0.480942\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.23607 −0.405179 −0.202590 0.979264i \(-0.564936\pi\)
−0.202590 + 0.979264i \(0.564936\pi\)
\(168\) 0 0
\(169\) −11.4721 −0.882472
\(170\) 0 0
\(171\) 33.4164 2.55542
\(172\) 0 0
\(173\) −11.5279 −0.876447 −0.438224 0.898866i \(-0.644392\pi\)
−0.438224 + 0.898866i \(0.644392\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −37.8885 −2.84788
\(178\) 0 0
\(179\) 23.4164 1.75022 0.875112 0.483920i \(-0.160787\pi\)
0.875112 + 0.483920i \(0.160787\pi\)
\(180\) 0 0
\(181\) 8.18034 0.608040 0.304020 0.952666i \(-0.401671\pi\)
0.304020 + 0.952666i \(0.401671\pi\)
\(182\) 0 0
\(183\) −31.4164 −2.32237
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.583592 0.0426765
\(188\) 0 0
\(189\) −14.4721 −1.05269
\(190\) 0 0
\(191\) −6.47214 −0.468307 −0.234154 0.972200i \(-0.575232\pi\)
−0.234154 + 0.972200i \(0.575232\pi\)
\(192\) 0 0
\(193\) 12.4164 0.893753 0.446876 0.894596i \(-0.352536\pi\)
0.446876 + 0.894596i \(0.352536\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.47214 −0.104885 −0.0524427 0.998624i \(-0.516701\pi\)
−0.0524427 + 0.998624i \(0.516701\pi\)
\(198\) 0 0
\(199\) −7.23607 −0.512951 −0.256476 0.966551i \(-0.582561\pi\)
−0.256476 + 0.966551i \(0.582561\pi\)
\(200\) 0 0
\(201\) 13.7082 0.966902
\(202\) 0 0
\(203\) −5.00000 −0.350931
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −46.5967 −3.23870
\(208\) 0 0
\(209\) 1.05573 0.0730262
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) −28.1803 −1.93089
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.70820 0.251729
\(218\) 0 0
\(219\) −28.3607 −1.91644
\(220\) 0 0
\(221\) 3.05573 0.205551
\(222\) 0 0
\(223\) −20.1803 −1.35138 −0.675688 0.737188i \(-0.736153\pi\)
−0.675688 + 0.737188i \(0.736153\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.4164 −1.42146 −0.710728 0.703466i \(-0.751635\pi\)
−0.710728 + 0.703466i \(0.751635\pi\)
\(228\) 0 0
\(229\) −4.47214 −0.295527 −0.147764 0.989023i \(-0.547207\pi\)
−0.147764 + 0.989023i \(0.547207\pi\)
\(230\) 0 0
\(231\) −0.763932 −0.0502630
\(232\) 0 0
\(233\) 7.94427 0.520447 0.260223 0.965548i \(-0.416204\pi\)
0.260223 + 0.965548i \(0.416204\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 36.1803 2.35017
\(238\) 0 0
\(239\) 5.52786 0.357568 0.178784 0.983888i \(-0.442784\pi\)
0.178784 + 0.983888i \(0.442784\pi\)
\(240\) 0 0
\(241\) −3.52786 −0.227250 −0.113625 0.993524i \(-0.536246\pi\)
−0.113625 + 0.993524i \(0.536246\pi\)
\(242\) 0 0
\(243\) 35.5967 2.28353
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.52786 0.351730
\(248\) 0 0
\(249\) 24.9443 1.58078
\(250\) 0 0
\(251\) −6.47214 −0.408518 −0.204259 0.978917i \(-0.565478\pi\)
−0.204259 + 0.978917i \(0.565478\pi\)
\(252\) 0 0
\(253\) −1.47214 −0.0925524
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −12.6525 −0.789240 −0.394620 0.918844i \(-0.629124\pi\)
−0.394620 + 0.918844i \(0.629124\pi\)
\(258\) 0 0
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) 37.3607 2.31257
\(262\) 0 0
\(263\) −16.2361 −1.00116 −0.500579 0.865691i \(-0.666880\pi\)
−0.500579 + 0.865691i \(0.666880\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 55.7771 3.41350
\(268\) 0 0
\(269\) −11.7082 −0.713862 −0.356931 0.934131i \(-0.616177\pi\)
−0.356931 + 0.934131i \(0.616177\pi\)
\(270\) 0 0
\(271\) −23.7082 −1.44017 −0.720085 0.693885i \(-0.755897\pi\)
−0.720085 + 0.693885i \(0.755897\pi\)
\(272\) 0 0
\(273\) −4.00000 −0.242091
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −19.8885 −1.19499 −0.597493 0.801874i \(-0.703837\pi\)
−0.597493 + 0.801874i \(0.703837\pi\)
\(278\) 0 0
\(279\) −27.7082 −1.65885
\(280\) 0 0
\(281\) −15.3607 −0.916341 −0.458171 0.888864i \(-0.651495\pi\)
−0.458171 + 0.888864i \(0.651495\pi\)
\(282\) 0 0
\(283\) −17.4164 −1.03530 −0.517649 0.855593i \(-0.673193\pi\)
−0.517649 + 0.855593i \(0.673193\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.76393 −0.281206
\(288\) 0 0
\(289\) −10.8885 −0.640503
\(290\) 0 0
\(291\) 16.9443 0.993291
\(292\) 0 0
\(293\) −31.1246 −1.81832 −0.909160 0.416448i \(-0.863275\pi\)
−0.909160 + 0.416448i \(0.863275\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.41641 0.198240
\(298\) 0 0
\(299\) −7.70820 −0.445777
\(300\) 0 0
\(301\) 1.76393 0.101671
\(302\) 0 0
\(303\) 15.4164 0.885649
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.58359 −0.261599 −0.130800 0.991409i \(-0.541754\pi\)
−0.130800 + 0.991409i \(0.541754\pi\)
\(308\) 0 0
\(309\) −27.4164 −1.55966
\(310\) 0 0
\(311\) −24.3607 −1.38137 −0.690684 0.723157i \(-0.742690\pi\)
−0.690684 + 0.723157i \(0.742690\pi\)
\(312\) 0 0
\(313\) 19.5279 1.10378 0.551890 0.833917i \(-0.313907\pi\)
0.551890 + 0.833917i \(0.313907\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.3607 1.42440 0.712199 0.701978i \(-0.247699\pi\)
0.712199 + 0.701978i \(0.247699\pi\)
\(318\) 0 0
\(319\) 1.18034 0.0660863
\(320\) 0 0
\(321\) −25.8885 −1.44496
\(322\) 0 0
\(323\) 11.0557 0.615157
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 27.2361 1.50616
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 24.7082 1.35809 0.679043 0.734099i \(-0.262395\pi\)
0.679043 + 0.734099i \(0.262395\pi\)
\(332\) 0 0
\(333\) 22.4164 1.22841
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −16.4721 −0.897294 −0.448647 0.893709i \(-0.648094\pi\)
−0.448647 + 0.893709i \(0.648094\pi\)
\(338\) 0 0
\(339\) −46.6525 −2.53381
\(340\) 0 0
\(341\) −0.875388 −0.0474049
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.2361 −1.08633 −0.543165 0.839626i \(-0.682774\pi\)
−0.543165 + 0.839626i \(0.682774\pi\)
\(348\) 0 0
\(349\) 4.47214 0.239388 0.119694 0.992811i \(-0.461809\pi\)
0.119694 + 0.992811i \(0.461809\pi\)
\(350\) 0 0
\(351\) 17.8885 0.954820
\(352\) 0 0
\(353\) −2.18034 −0.116048 −0.0580239 0.998315i \(-0.518480\pi\)
−0.0580239 + 0.998315i \(0.518480\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −8.00000 −0.423405
\(358\) 0 0
\(359\) 30.1246 1.58992 0.794958 0.606664i \(-0.207493\pi\)
0.794958 + 0.606664i \(0.207493\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −35.4164 −1.85888
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 37.1246 1.93789 0.968944 0.247278i \(-0.0795362\pi\)
0.968944 + 0.247278i \(0.0795362\pi\)
\(368\) 0 0
\(369\) 35.5967 1.85309
\(370\) 0 0
\(371\) −8.47214 −0.439851
\(372\) 0 0
\(373\) −37.8328 −1.95891 −0.979454 0.201665i \(-0.935365\pi\)
−0.979454 + 0.201665i \(0.935365\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.18034 0.318304
\(378\) 0 0
\(379\) 11.1803 0.574295 0.287148 0.957886i \(-0.407293\pi\)
0.287148 + 0.957886i \(0.407293\pi\)
\(380\) 0 0
\(381\) −44.1803 −2.26343
\(382\) 0 0
\(383\) 33.2361 1.69828 0.849142 0.528165i \(-0.177120\pi\)
0.849142 + 0.528165i \(0.177120\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.1803 −0.669994
\(388\) 0 0
\(389\) 2.88854 0.146455 0.0732275 0.997315i \(-0.476670\pi\)
0.0732275 + 0.997315i \(0.476670\pi\)
\(390\) 0 0
\(391\) −15.4164 −0.779641
\(392\) 0 0
\(393\) 54.8328 2.76595
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9.05573 0.454494 0.227247 0.973837i \(-0.427028\pi\)
0.227247 + 0.973837i \(0.427028\pi\)
\(398\) 0 0
\(399\) −14.4721 −0.724513
\(400\) 0 0
\(401\) 2.52786 0.126236 0.0631178 0.998006i \(-0.479896\pi\)
0.0631178 + 0.998006i \(0.479896\pi\)
\(402\) 0 0
\(403\) −4.58359 −0.228325
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.708204 0.0351044
\(408\) 0 0
\(409\) 24.4721 1.21007 0.605035 0.796199i \(-0.293159\pi\)
0.605035 + 0.796199i \(0.293159\pi\)
\(410\) 0 0
\(411\) −35.4164 −1.74696
\(412\) 0 0
\(413\) 11.7082 0.576123
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −34.4721 −1.68811
\(418\) 0 0
\(419\) 26.1803 1.27899 0.639497 0.768794i \(-0.279143\pi\)
0.639497 + 0.768794i \(0.279143\pi\)
\(420\) 0 0
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 0 0
\(423\) 14.9443 0.726615
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 9.70820 0.469813
\(428\) 0 0
\(429\) 0.944272 0.0455899
\(430\) 0 0
\(431\) −17.5279 −0.844288 −0.422144 0.906529i \(-0.638722\pi\)
−0.422144 + 0.906529i \(0.638722\pi\)
\(432\) 0 0
\(433\) −28.3607 −1.36293 −0.681464 0.731852i \(-0.738656\pi\)
−0.681464 + 0.731852i \(0.738656\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −27.8885 −1.33409
\(438\) 0 0
\(439\) 8.29180 0.395746 0.197873 0.980228i \(-0.436597\pi\)
0.197873 + 0.980228i \(0.436597\pi\)
\(440\) 0 0
\(441\) 7.47214 0.355816
\(442\) 0 0
\(443\) 19.4164 0.922501 0.461251 0.887270i \(-0.347401\pi\)
0.461251 + 0.887270i \(0.347401\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.7639 0.603713
\(448\) 0 0
\(449\) 20.5279 0.968770 0.484385 0.874855i \(-0.339043\pi\)
0.484385 + 0.874855i \(0.339043\pi\)
\(450\) 0 0
\(451\) 1.12461 0.0529559
\(452\) 0 0
\(453\) 65.4853 3.07677
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −12.5279 −0.586029 −0.293014 0.956108i \(-0.594658\pi\)
−0.293014 + 0.956108i \(0.594658\pi\)
\(458\) 0 0
\(459\) 35.7771 1.66993
\(460\) 0 0
\(461\) −14.1803 −0.660444 −0.330222 0.943903i \(-0.607124\pi\)
−0.330222 + 0.943903i \(0.607124\pi\)
\(462\) 0 0
\(463\) 13.8885 0.645455 0.322728 0.946492i \(-0.395400\pi\)
0.322728 + 0.946492i \(0.395400\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.94427 −0.321343 −0.160671 0.987008i \(-0.551366\pi\)
−0.160671 + 0.987008i \(0.551366\pi\)
\(468\) 0 0
\(469\) −4.23607 −0.195603
\(470\) 0 0
\(471\) 2.47214 0.113910
\(472\) 0 0
\(473\) −0.416408 −0.0191465
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 63.3050 2.89853
\(478\) 0 0
\(479\) 26.1803 1.19621 0.598105 0.801418i \(-0.295921\pi\)
0.598105 + 0.801418i \(0.295921\pi\)
\(480\) 0 0
\(481\) 3.70820 0.169080
\(482\) 0 0
\(483\) 20.1803 0.918237
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −5.76393 −0.261189 −0.130594 0.991436i \(-0.541689\pi\)
−0.130594 + 0.991436i \(0.541689\pi\)
\(488\) 0 0
\(489\) 4.94427 0.223588
\(490\) 0 0
\(491\) 5.76393 0.260123 0.130061 0.991506i \(-0.458483\pi\)
0.130061 + 0.991506i \(0.458483\pi\)
\(492\) 0 0
\(493\) 12.3607 0.556697
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.70820 0.390616
\(498\) 0 0
\(499\) −11.0557 −0.494922 −0.247461 0.968898i \(-0.579596\pi\)
−0.247461 + 0.968898i \(0.579596\pi\)
\(500\) 0 0
\(501\) −16.9443 −0.757014
\(502\) 0 0
\(503\) 8.11146 0.361672 0.180836 0.983513i \(-0.442120\pi\)
0.180836 + 0.983513i \(0.442120\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −37.1246 −1.64876
\(508\) 0 0
\(509\) 40.6525 1.80189 0.900945 0.433934i \(-0.142875\pi\)
0.900945 + 0.433934i \(0.142875\pi\)
\(510\) 0 0
\(511\) 8.76393 0.387694
\(512\) 0 0
\(513\) 64.7214 2.85752
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.472136 0.0207645
\(518\) 0 0
\(519\) −37.3050 −1.63751
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) −16.3607 −0.715403 −0.357701 0.933836i \(-0.616439\pi\)
−0.357701 + 0.933836i \(0.616439\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.16718 −0.399329
\(528\) 0 0
\(529\) 15.8885 0.690806
\(530\) 0 0
\(531\) −87.4853 −3.79654
\(532\) 0 0
\(533\) 5.88854 0.255061
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 75.7771 3.27002
\(538\) 0 0
\(539\) 0.236068 0.0101682
\(540\) 0 0
\(541\) 15.9443 0.685498 0.342749 0.939427i \(-0.388642\pi\)
0.342749 + 0.939427i \(0.388642\pi\)
\(542\) 0 0
\(543\) 26.4721 1.13603
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 9.76393 0.417476 0.208738 0.977972i \(-0.433064\pi\)
0.208738 + 0.977972i \(0.433064\pi\)
\(548\) 0 0
\(549\) −72.5410 −3.09598
\(550\) 0 0
\(551\) 22.3607 0.952597
\(552\) 0 0
\(553\) −11.1803 −0.475436
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.11146 −0.386065 −0.193032 0.981192i \(-0.561832\pi\)
−0.193032 + 0.981192i \(0.561832\pi\)
\(558\) 0 0
\(559\) −2.18034 −0.0922186
\(560\) 0 0
\(561\) 1.88854 0.0797344
\(562\) 0 0
\(563\) −17.4164 −0.734014 −0.367007 0.930218i \(-0.619618\pi\)
−0.367007 + 0.930218i \(0.619618\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −24.4164 −1.02539
\(568\) 0 0
\(569\) −3.94427 −0.165352 −0.0826762 0.996576i \(-0.526347\pi\)
−0.0826762 + 0.996576i \(0.526347\pi\)
\(570\) 0 0
\(571\) −36.5967 −1.53153 −0.765763 0.643123i \(-0.777638\pi\)
−0.765763 + 0.643123i \(0.777638\pi\)
\(572\) 0 0
\(573\) −20.9443 −0.874960
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 0 0
\(579\) 40.1803 1.66984
\(580\) 0 0
\(581\) −7.70820 −0.319790
\(582\) 0 0
\(583\) 2.00000 0.0828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.7639 1.02212 0.511058 0.859546i \(-0.329254\pi\)
0.511058 + 0.859546i \(0.329254\pi\)
\(588\) 0 0
\(589\) −16.5836 −0.683315
\(590\) 0 0
\(591\) −4.76393 −0.195962
\(592\) 0 0
\(593\) −37.3050 −1.53193 −0.765965 0.642882i \(-0.777739\pi\)
−0.765965 + 0.642882i \(0.777739\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −23.4164 −0.958370
\(598\) 0 0
\(599\) 11.1803 0.456816 0.228408 0.973565i \(-0.426648\pi\)
0.228408 + 0.973565i \(0.426648\pi\)
\(600\) 0 0
\(601\) −36.9443 −1.50699 −0.753494 0.657455i \(-0.771633\pi\)
−0.753494 + 0.657455i \(0.771633\pi\)
\(602\) 0 0
\(603\) 31.6525 1.28899
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.12461 0.289179 0.144590 0.989492i \(-0.453814\pi\)
0.144590 + 0.989492i \(0.453814\pi\)
\(608\) 0 0
\(609\) −16.1803 −0.655660
\(610\) 0 0
\(611\) 2.47214 0.100012
\(612\) 0 0
\(613\) −44.4164 −1.79396 −0.896981 0.442069i \(-0.854245\pi\)
−0.896981 + 0.442069i \(0.854245\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.94427 −0.239307 −0.119654 0.992816i \(-0.538178\pi\)
−0.119654 + 0.992816i \(0.538178\pi\)
\(618\) 0 0
\(619\) 11.7082 0.470592 0.235296 0.971924i \(-0.424394\pi\)
0.235296 + 0.971924i \(0.424394\pi\)
\(620\) 0 0
\(621\) −90.2492 −3.62158
\(622\) 0 0
\(623\) −17.2361 −0.690548
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.41641 0.136438
\(628\) 0 0
\(629\) 7.41641 0.295712
\(630\) 0 0
\(631\) −27.6525 −1.10083 −0.550414 0.834892i \(-0.685530\pi\)
−0.550414 + 0.834892i \(0.685530\pi\)
\(632\) 0 0
\(633\) −38.8328 −1.54347
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 1.23607 0.0489748
\(638\) 0 0
\(639\) −65.0689 −2.57409
\(640\) 0 0
\(641\) 43.8328 1.73129 0.865646 0.500656i \(-0.166908\pi\)
0.865646 + 0.500656i \(0.166908\pi\)
\(642\) 0 0
\(643\) −18.4721 −0.728470 −0.364235 0.931307i \(-0.618669\pi\)
−0.364235 + 0.931307i \(0.618669\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.8885 0.781899 0.390950 0.920412i \(-0.372147\pi\)
0.390950 + 0.920412i \(0.372147\pi\)
\(648\) 0 0
\(649\) −2.76393 −0.108494
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 0 0
\(653\) 25.0557 0.980506 0.490253 0.871580i \(-0.336904\pi\)
0.490253 + 0.871580i \(0.336904\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −65.4853 −2.55482
\(658\) 0 0
\(659\) −17.8885 −0.696839 −0.348419 0.937339i \(-0.613281\pi\)
−0.348419 + 0.937339i \(0.613281\pi\)
\(660\) 0 0
\(661\) −42.7214 −1.66167 −0.830834 0.556520i \(-0.812136\pi\)
−0.830834 + 0.556520i \(0.812136\pi\)
\(662\) 0 0
\(663\) 9.88854 0.384039
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −31.1803 −1.20731
\(668\) 0 0
\(669\) −65.3050 −2.52484
\(670\) 0 0
\(671\) −2.29180 −0.0884738
\(672\) 0 0
\(673\) 19.5279 0.752744 0.376372 0.926469i \(-0.377171\pi\)
0.376372 + 0.926469i \(0.377171\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.3607 −0.551926 −0.275963 0.961168i \(-0.588997\pi\)
−0.275963 + 0.961168i \(0.588997\pi\)
\(678\) 0 0
\(679\) −5.23607 −0.200942
\(680\) 0 0
\(681\) −69.3050 −2.65577
\(682\) 0 0
\(683\) −14.1246 −0.540463 −0.270232 0.962795i \(-0.587100\pi\)
−0.270232 + 0.962795i \(0.587100\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −14.4721 −0.552146
\(688\) 0 0
\(689\) 10.4721 0.398957
\(690\) 0 0
\(691\) 4.18034 0.159028 0.0795138 0.996834i \(-0.474663\pi\)
0.0795138 + 0.996834i \(0.474663\pi\)
\(692\) 0 0
\(693\) −1.76393 −0.0670062
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 11.7771 0.446089
\(698\) 0 0
\(699\) 25.7082 0.972374
\(700\) 0 0
\(701\) −29.0557 −1.09742 −0.548710 0.836013i \(-0.684881\pi\)
−0.548710 + 0.836013i \(0.684881\pi\)
\(702\) 0 0
\(703\) 13.4164 0.506009
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.76393 −0.179166
\(708\) 0 0
\(709\) −12.1115 −0.454855 −0.227428 0.973795i \(-0.573032\pi\)
−0.227428 + 0.973795i \(0.573032\pi\)
\(710\) 0 0
\(711\) 83.5410 3.13303
\(712\) 0 0
\(713\) 23.1246 0.866024
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 17.8885 0.668060
\(718\) 0 0
\(719\) −16.1803 −0.603425 −0.301712 0.953399i \(-0.597558\pi\)
−0.301712 + 0.953399i \(0.597558\pi\)
\(720\) 0 0
\(721\) 8.47214 0.315519
\(722\) 0 0
\(723\) −11.4164 −0.424581
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 3.05573 0.113331 0.0566653 0.998393i \(-0.481953\pi\)
0.0566653 + 0.998393i \(0.481953\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 0 0
\(731\) −4.36068 −0.161286
\(732\) 0 0
\(733\) 4.00000 0.147743 0.0738717 0.997268i \(-0.476464\pi\)
0.0738717 + 0.997268i \(0.476464\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.00000 0.0368355
\(738\) 0 0
\(739\) −25.6525 −0.943642 −0.471821 0.881694i \(-0.656403\pi\)
−0.471821 + 0.881694i \(0.656403\pi\)
\(740\) 0 0
\(741\) 17.8885 0.657152
\(742\) 0 0
\(743\) 10.4721 0.384185 0.192093 0.981377i \(-0.438473\pi\)
0.192093 + 0.981377i \(0.438473\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 57.5967 2.10735
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) −3.05573 −0.111505 −0.0557526 0.998445i \(-0.517756\pi\)
−0.0557526 + 0.998445i \(0.517756\pi\)
\(752\) 0 0
\(753\) −20.9443 −0.763252
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 19.5836 0.711778 0.355889 0.934528i \(-0.384178\pi\)
0.355889 + 0.934528i \(0.384178\pi\)
\(758\) 0 0
\(759\) −4.76393 −0.172920
\(760\) 0 0
\(761\) 27.7771 1.00692 0.503459 0.864019i \(-0.332060\pi\)
0.503459 + 0.864019i \(0.332060\pi\)
\(762\) 0 0
\(763\) −8.41641 −0.304694
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.4721 −0.522559
\(768\) 0 0
\(769\) −43.0132 −1.55109 −0.775547 0.631290i \(-0.782526\pi\)
−0.775547 + 0.631290i \(0.782526\pi\)
\(770\) 0 0
\(771\) −40.9443 −1.47457
\(772\) 0 0
\(773\) 50.1803 1.80486 0.902431 0.430835i \(-0.141781\pi\)
0.902431 + 0.430835i \(0.141781\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −9.70820 −0.348280
\(778\) 0 0
\(779\) 21.3050 0.763329
\(780\) 0 0
\(781\) −2.05573 −0.0735597
\(782\) 0 0
\(783\) 72.3607 2.58596
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −40.7639 −1.45308 −0.726539 0.687126i \(-0.758872\pi\)
−0.726539 + 0.687126i \(0.758872\pi\)
\(788\) 0 0
\(789\) −52.5410 −1.87051
\(790\) 0 0
\(791\) 14.4164 0.512588
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −35.4164 −1.25451 −0.627257 0.778813i \(-0.715822\pi\)
−0.627257 + 0.778813i \(0.715822\pi\)
\(798\) 0 0
\(799\) 4.94427 0.174916
\(800\) 0 0
\(801\) 128.790 4.55058
\(802\) 0 0
\(803\) −2.06888 −0.0730093
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −37.8885 −1.33374
\(808\) 0 0
\(809\) 29.4721 1.03619 0.518093 0.855325i \(-0.326642\pi\)
0.518093 + 0.855325i \(0.326642\pi\)
\(810\) 0 0
\(811\) 42.7214 1.50015 0.750075 0.661353i \(-0.230017\pi\)
0.750075 + 0.661353i \(0.230017\pi\)
\(812\) 0 0
\(813\) −76.7214 −2.69074
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −7.88854 −0.275985
\(818\) 0 0
\(819\) −9.23607 −0.322734
\(820\) 0 0
\(821\) 28.8328 1.00627 0.503136 0.864207i \(-0.332179\pi\)
0.503136 + 0.864207i \(0.332179\pi\)
\(822\) 0 0
\(823\) 31.6525 1.10334 0.551668 0.834064i \(-0.313992\pi\)
0.551668 + 0.834064i \(0.313992\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −41.5410 −1.44452 −0.722261 0.691620i \(-0.756897\pi\)
−0.722261 + 0.691620i \(0.756897\pi\)
\(828\) 0 0
\(829\) −7.63932 −0.265325 −0.132662 0.991161i \(-0.542353\pi\)
−0.132662 + 0.991161i \(0.542353\pi\)
\(830\) 0 0
\(831\) −64.3607 −2.23265
\(832\) 0 0
\(833\) 2.47214 0.0856544
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −53.6656 −1.85496
\(838\) 0 0
\(839\) 30.6525 1.05824 0.529120 0.848547i \(-0.322522\pi\)
0.529120 + 0.848547i \(0.322522\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) −49.7082 −1.71204
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 10.9443 0.376050
\(848\) 0 0
\(849\) −56.3607 −1.93429
\(850\) 0 0
\(851\) −18.7082 −0.641309
\(852\) 0 0
\(853\) 27.4164 0.938720 0.469360 0.883007i \(-0.344485\pi\)
0.469360 + 0.883007i \(0.344485\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15.8197 −0.540389 −0.270195 0.962806i \(-0.587088\pi\)
−0.270195 + 0.962806i \(0.587088\pi\)
\(858\) 0 0
\(859\) −22.3607 −0.762937 −0.381468 0.924382i \(-0.624581\pi\)
−0.381468 + 0.924382i \(0.624581\pi\)
\(860\) 0 0
\(861\) −15.4164 −0.525390
\(862\) 0 0
\(863\) −18.3475 −0.624557 −0.312278 0.949991i \(-0.601092\pi\)
−0.312278 + 0.949991i \(0.601092\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −35.2361 −1.19668
\(868\) 0 0
\(869\) 2.63932 0.0895328
\(870\) 0 0
\(871\) 5.23607 0.177417
\(872\) 0 0
\(873\) 39.1246 1.32417
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 30.3607 1.02521 0.512604 0.858625i \(-0.328681\pi\)
0.512604 + 0.858625i \(0.328681\pi\)
\(878\) 0 0
\(879\) −100.721 −3.39725
\(880\) 0 0
\(881\) 5.81966 0.196069 0.0980347 0.995183i \(-0.468744\pi\)
0.0980347 + 0.995183i \(0.468744\pi\)
\(882\) 0 0
\(883\) 1.40325 0.0472232 0.0236116 0.999721i \(-0.492483\pi\)
0.0236116 + 0.999721i \(0.492483\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 21.3475 0.716780 0.358390 0.933572i \(-0.383326\pi\)
0.358390 + 0.933572i \(0.383326\pi\)
\(888\) 0 0
\(889\) 13.6525 0.457889
\(890\) 0 0
\(891\) 5.76393 0.193099
\(892\) 0 0
\(893\) 8.94427 0.299309
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −24.9443 −0.832865
\(898\) 0 0
\(899\) −18.5410 −0.618378
\(900\) 0 0
\(901\) 20.9443 0.697755
\(902\) 0 0
\(903\) 5.70820 0.189957
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −34.8328 −1.15660 −0.578302 0.815823i \(-0.696285\pi\)
−0.578302 + 0.815823i \(0.696285\pi\)
\(908\) 0 0
\(909\) 35.5967 1.18067
\(910\) 0 0
\(911\) −0.819660 −0.0271566 −0.0135783 0.999908i \(-0.504322\pi\)
−0.0135783 + 0.999908i \(0.504322\pi\)
\(912\) 0 0
\(913\) 1.81966 0.0602220
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −16.9443 −0.559549
\(918\) 0 0
\(919\) 27.7639 0.915848 0.457924 0.888991i \(-0.348593\pi\)
0.457924 + 0.888991i \(0.348593\pi\)
\(920\) 0 0
\(921\) −14.8328 −0.488758
\(922\) 0 0
\(923\) −10.7639 −0.354299
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −63.3050 −2.07921
\(928\) 0 0
\(929\) 38.2918 1.25631 0.628157 0.778087i \(-0.283810\pi\)
0.628157 + 0.778087i \(0.283810\pi\)
\(930\) 0 0
\(931\) 4.47214 0.146568
\(932\) 0 0
\(933\) −78.8328 −2.58087
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 35.2361 1.15111 0.575556 0.817762i \(-0.304786\pi\)
0.575556 + 0.817762i \(0.304786\pi\)
\(938\) 0 0
\(939\) 63.1935 2.06224
\(940\) 0 0
\(941\) −5.23607 −0.170691 −0.0853455 0.996351i \(-0.527199\pi\)
−0.0853455 + 0.996351i \(0.527199\pi\)
\(942\) 0 0
\(943\) −29.7082 −0.967432
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −34.8328 −1.13191 −0.565957 0.824435i \(-0.691493\pi\)
−0.565957 + 0.824435i \(0.691493\pi\)
\(948\) 0 0
\(949\) −10.8328 −0.351648
\(950\) 0 0
\(951\) 82.0689 2.66127
\(952\) 0 0
\(953\) 3.47214 0.112474 0.0562368 0.998417i \(-0.482090\pi\)
0.0562368 + 0.998417i \(0.482090\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 3.81966 0.123472
\(958\) 0 0
\(959\) 10.9443 0.353409
\(960\) 0 0
\(961\) −17.2492 −0.556427
\(962\) 0 0
\(963\) −59.7771 −1.92629
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 14.1115 0.453794 0.226897 0.973919i \(-0.427142\pi\)
0.226897 + 0.973919i \(0.427142\pi\)
\(968\) 0 0
\(969\) 35.7771 1.14933
\(970\) 0 0
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) 10.6525 0.341503
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −11.4721 −0.367026 −0.183513 0.983017i \(-0.558747\pi\)
−0.183513 + 0.983017i \(0.558747\pi\)
\(978\) 0 0
\(979\) 4.06888 0.130042
\(980\) 0 0
\(981\) 62.8885 2.00788
\(982\) 0 0
\(983\) 34.5410 1.10169 0.550844 0.834608i \(-0.314306\pi\)
0.550844 + 0.834608i \(0.314306\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −6.47214 −0.206010
\(988\) 0 0
\(989\) 11.0000 0.349780
\(990\) 0 0
\(991\) −13.1803 −0.418687 −0.209344 0.977842i \(-0.567133\pi\)
−0.209344 + 0.977842i \(0.567133\pi\)
\(992\) 0 0
\(993\) 79.9574 2.53737
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −45.4164 −1.43835 −0.719176 0.694828i \(-0.755481\pi\)
−0.719176 + 0.694828i \(0.755481\pi\)
\(998\) 0 0
\(999\) 43.4164 1.37363
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 2800.2.a.bp.1.2 2
4.3 odd 2 175.2.a.e.1.1 yes 2
5.2 odd 4 2800.2.g.s.449.1 4
5.3 odd 4 2800.2.g.s.449.4 4
5.4 even 2 2800.2.a.bh.1.1 2
12.11 even 2 1575.2.a.n.1.2 2
20.3 even 4 175.2.b.c.99.3 4
20.7 even 4 175.2.b.c.99.2 4
20.19 odd 2 175.2.a.d.1.2 2
28.27 even 2 1225.2.a.u.1.1 2
60.23 odd 4 1575.2.d.k.1324.2 4
60.47 odd 4 1575.2.d.k.1324.3 4
60.59 even 2 1575.2.a.s.1.1 2
140.27 odd 4 1225.2.b.k.99.2 4
140.83 odd 4 1225.2.b.k.99.3 4
140.139 even 2 1225.2.a.n.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.a.d.1.2 2 20.19 odd 2
175.2.a.e.1.1 yes 2 4.3 odd 2
175.2.b.c.99.2 4 20.7 even 4
175.2.b.c.99.3 4 20.3 even 4
1225.2.a.n.1.2 2 140.139 even 2
1225.2.a.u.1.1 2 28.27 even 2
1225.2.b.k.99.2 4 140.27 odd 4
1225.2.b.k.99.3 4 140.83 odd 4
1575.2.a.n.1.2 2 12.11 even 2
1575.2.a.s.1.1 2 60.59 even 2
1575.2.d.k.1324.2 4 60.23 odd 4
1575.2.d.k.1324.3 4 60.47 odd 4
2800.2.a.bh.1.1 2 5.4 even 2
2800.2.a.bp.1.2 2 1.1 even 1 trivial
2800.2.g.s.449.1 4 5.2 odd 4
2800.2.g.s.449.4 4 5.3 odd 4