Properties

Label 2800.2.a.bp.1.1
Level $2800$
Weight $2$
Character 2800.1
Self dual yes
Analytic conductor $22.358$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 2800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.23607 q^{3} -1.00000 q^{7} -1.47214 q^{9} +O(q^{10})\) \(q-1.23607 q^{3} -1.00000 q^{7} -1.47214 q^{9} -4.23607 q^{11} -3.23607 q^{13} -6.47214 q^{17} -4.47214 q^{19} +1.23607 q^{21} -1.76393 q^{23} +5.52786 q^{27} +5.00000 q^{29} +9.70820 q^{31} +5.23607 q^{33} +3.00000 q^{37} +4.00000 q^{39} +9.23607 q^{41} -6.23607 q^{43} +2.00000 q^{47} +1.00000 q^{49} +8.00000 q^{51} -0.472136 q^{53} +5.52786 q^{57} +1.70820 q^{59} +3.70820 q^{61} +1.47214 q^{63} -0.236068 q^{67} +2.18034 q^{69} +4.70820 q^{71} -13.2361 q^{73} +4.23607 q^{77} -11.1803 q^{79} -2.41641 q^{81} -5.70820 q^{83} -6.18034 q^{87} +12.7639 q^{89} +3.23607 q^{91} -12.0000 q^{93} +0.763932 q^{97} +6.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 2q^{7} + 6q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{7} + 6q^{9} - 4q^{11} - 2q^{13} - 4q^{17} - 2q^{21} - 8q^{23} + 20q^{27} + 10q^{29} + 6q^{31} + 6q^{33} + 6q^{37} + 8q^{39} + 14q^{41} - 8q^{43} + 4q^{47} + 2q^{49} + 16q^{51} + 8q^{53} + 20q^{57} - 10q^{59} - 6q^{61} - 6q^{63} + 4q^{67} - 18q^{69} - 4q^{71} - 22q^{73} + 4q^{77} + 22q^{81} + 2q^{83} + 10q^{87} + 30q^{89} + 2q^{91} - 24q^{93} + 6q^{97} + 8q^{99} + O(q^{100}) \)

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
\(3\) −1.23607 −0.713644 −0.356822 0.934172i \(-0.616140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) −1.47214 −0.490712
\(10\) 0 0
\(11\) −4.23607 −1.27722 −0.638611 0.769529i \(-0.720491\pi\)
−0.638611 + 0.769529i \(0.720491\pi\)
\(12\) 0 0
\(13\) −3.23607 −0.897524 −0.448762 0.893651i \(-0.648135\pi\)
−0.448762 + 0.893651i \(0.648135\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.47214 −1.56972 −0.784862 0.619671i \(-0.787266\pi\)
−0.784862 + 0.619671i \(0.787266\pi\)
\(18\) 0 0
\(19\) −4.47214 −1.02598 −0.512989 0.858395i \(-0.671462\pi\)
−0.512989 + 0.858395i \(0.671462\pi\)
\(20\) 0 0
\(21\) 1.23607 0.269732
\(22\) 0 0
\(23\) −1.76393 −0.367805 −0.183903 0.982944i \(-0.558873\pi\)
−0.183903 + 0.982944i \(0.558873\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.52786 1.06384
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 9.70820 1.74364 0.871822 0.489822i \(-0.162938\pi\)
0.871822 + 0.489822i \(0.162938\pi\)
\(32\) 0 0
\(33\) 5.23607 0.911482
\(34\) 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
\(41\) 9.23607 1.44243 0.721216 0.692711i \(-0.243584\pi\)
0.721216 + 0.692711i \(0.243584\pi\)
\(42\) 0 0
\(43\) −6.23607 −0.950991 −0.475496 0.879718i \(-0.657731\pi\)
−0.475496 + 0.879718i \(0.657731\pi\)
\(44\) 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
\(53\) −0.472136 −0.0648529 −0.0324264 0.999474i \(-0.510323\pi\)
−0.0324264 + 0.999474i \(0.510323\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.52786 0.732183
\(58\) 0 0
\(59\) 1.70820 0.222389 0.111195 0.993799i \(-0.464532\pi\)
0.111195 + 0.993799i \(0.464532\pi\)
\(60\) 0 0
\(61\) 3.70820 0.474787 0.237393 0.971414i \(-0.423707\pi\)
0.237393 + 0.971414i \(0.423707\pi\)
\(62\) 0 0
\(63\) 1.47214 0.185472
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.236068 −0.0288403 −0.0144201 0.999896i \(-0.504590\pi\)
−0.0144201 + 0.999896i \(0.504590\pi\)
\(68\) 0 0
\(69\) 2.18034 0.262482
\(70\) 0 0
\(71\) 4.70820 0.558761 0.279381 0.960180i \(-0.409871\pi\)
0.279381 + 0.960180i \(0.409871\pi\)
\(72\) 0 0
\(73\) −13.2361 −1.54916 −0.774582 0.632473i \(-0.782040\pi\)
−0.774582 + 0.632473i \(0.782040\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.23607 0.482745
\(78\) 0 0
\(79\) −11.1803 −1.25789 −0.628943 0.777451i \(-0.716512\pi\)
−0.628943 + 0.777451i \(0.716512\pi\)
\(80\) 0 0
\(81\) −2.41641 −0.268490
\(82\) 0 0
\(83\) −5.70820 −0.626557 −0.313278 0.949661i \(-0.601427\pi\)
−0.313278 + 0.949661i \(0.601427\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.18034 −0.662602
\(88\) 0 0
\(89\) 12.7639 1.35297 0.676487 0.736455i \(-0.263501\pi\)
0.676487 + 0.736455i \(0.263501\pi\)
\(90\) 0 0
\(91\) 3.23607 0.339232
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.763932 0.0775655 0.0387828 0.999248i \(-0.487652\pi\)
0.0387828 + 0.999248i \(0.487652\pi\)
\(98\) 0 0
\(99\) 6.23607 0.626748
\(100\) 0 0
\(101\) 9.23607 0.919023 0.459512 0.888172i \(-0.348024\pi\)
0.459512 + 0.888172i \(0.348024\pi\)
\(102\) 0 0
\(103\) 0.472136 0.0465209 0.0232605 0.999729i \(-0.492595\pi\)
0.0232605 + 0.999729i \(0.492595\pi\)
\(104\) 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
\(109\) −18.4164 −1.76397 −0.881986 0.471276i \(-0.843794\pi\)
−0.881986 + 0.471276i \(0.843794\pi\)
\(110\) 0 0
\(111\) −3.70820 −0.351967
\(112\) 0 0
\(113\) 12.4164 1.16804 0.584019 0.811740i \(-0.301479\pi\)
0.584019 + 0.811740i \(0.301479\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.76393 0.440426
\(118\) 0 0
\(119\) 6.47214 0.593300
\(120\) 0 0
\(121\) 6.94427 0.631297
\(122\) 0 0
\(123\) −11.4164 −1.02938
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 17.6525 1.56640 0.783202 0.621767i \(-0.213585\pi\)
0.783202 + 0.621767i \(0.213585\pi\)
\(128\) 0 0
\(129\) 7.70820 0.678670
\(130\) 0 0
\(131\) −0.944272 −0.0825014 −0.0412507 0.999149i \(-0.513134\pi\)
−0.0412507 + 0.999149i \(0.513134\pi\)
\(132\) 0 0
\(133\) 4.47214 0.387783
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.94427 0.593289 0.296645 0.954988i \(-0.404132\pi\)
0.296645 + 0.954988i \(0.404132\pi\)
\(138\) 0 0
\(139\) 20.6525 1.75172 0.875860 0.482565i \(-0.160295\pi\)
0.875860 + 0.482565i \(0.160295\pi\)
\(140\) 0 0
\(141\) −2.47214 −0.208191
\(142\) 0 0
\(143\) 13.7082 1.14634
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.23607 −0.101949
\(148\) 0 0
\(149\) −13.9443 −1.14236 −0.571180 0.820825i \(-0.693514\pi\)
−0.571180 + 0.820825i \(0.693514\pi\)
\(150\) 0 0
\(151\) 15.7639 1.28285 0.641425 0.767185i \(-0.278343\pi\)
0.641425 + 0.767185i \(0.278343\pi\)
\(152\) 0 0
\(153\) 9.52786 0.770282
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.23607 0.417884 0.208942 0.977928i \(-0.432998\pi\)
0.208942 + 0.977928i \(0.432998\pi\)
\(158\) 0 0
\(159\) 0.583592 0.0462819
\(160\) 0 0
\(161\) 1.76393 0.139017
\(162\) 0 0
\(163\) 10.4721 0.820241 0.410120 0.912031i \(-0.365487\pi\)
0.410120 + 0.912031i \(0.365487\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.763932 −0.0591148 −0.0295574 0.999563i \(-0.509410\pi\)
−0.0295574 + 0.999563i \(0.509410\pi\)
\(168\) 0 0
\(169\) −2.52786 −0.194451
\(170\) 0 0
\(171\) 6.58359 0.503460
\(172\) 0 0
\(173\) −20.4721 −1.55647 −0.778234 0.627975i \(-0.783884\pi\)
−0.778234 + 0.627975i \(0.783884\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.11146 −0.158707
\(178\) 0 0
\(179\) −3.41641 −0.255354 −0.127677 0.991816i \(-0.540752\pi\)
−0.127677 + 0.991816i \(0.540752\pi\)
\(180\) 0 0
\(181\) −14.1803 −1.05402 −0.527008 0.849860i \(-0.676686\pi\)
−0.527008 + 0.849860i \(0.676686\pi\)
\(182\) 0 0
\(183\) −4.58359 −0.338829
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 27.4164 2.00489
\(188\) 0 0
\(189\) −5.52786 −0.402093
\(190\) 0 0
\(191\) 2.47214 0.178877 0.0894387 0.995992i \(-0.471493\pi\)
0.0894387 + 0.995992i \(0.471493\pi\)
\(192\) 0 0
\(193\) −14.4164 −1.03772 −0.518858 0.854861i \(-0.673643\pi\)
−0.518858 + 0.854861i \(0.673643\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.47214 0.532368 0.266184 0.963922i \(-0.414237\pi\)
0.266184 + 0.963922i \(0.414237\pi\)
\(198\) 0 0
\(199\) −2.76393 −0.195930 −0.0979650 0.995190i \(-0.531233\pi\)
−0.0979650 + 0.995190i \(0.531233\pi\)
\(200\) 0 0
\(201\) 0.291796 0.0205817
\(202\) 0 0
\(203\) −5.00000 −0.350931
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.59675 0.180486
\(208\) 0 0
\(209\) 18.9443 1.31040
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 0 0
\(213\) −5.81966 −0.398757
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −9.70820 −0.659036
\(218\) 0 0
\(219\) 16.3607 1.10555
\(220\) 0 0
\(221\) 20.9443 1.40886
\(222\) 0 0
\(223\) 2.18034 0.146006 0.0730032 0.997332i \(-0.476742\pi\)
0.0730032 + 0.997332i \(0.476742\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.41641 0.359500 0.179750 0.983712i \(-0.442471\pi\)
0.179750 + 0.983712i \(0.442471\pi\)
\(228\) 0 0
\(229\) 4.47214 0.295527 0.147764 0.989023i \(-0.452793\pi\)
0.147764 + 0.989023i \(0.452793\pi\)
\(230\) 0 0
\(231\) −5.23607 −0.344508
\(232\) 0 0
\(233\) −9.94427 −0.651471 −0.325735 0.945461i \(-0.605612\pi\)
−0.325735 + 0.945461i \(0.605612\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 13.8197 0.897683
\(238\) 0 0
\(239\) 14.4721 0.936125 0.468062 0.883695i \(-0.344952\pi\)
0.468062 + 0.883695i \(0.344952\pi\)
\(240\) 0 0
\(241\) −12.4721 −0.803401 −0.401700 0.915771i \(-0.631581\pi\)
−0.401700 + 0.915771i \(0.631581\pi\)
\(242\) 0 0
\(243\) −13.5967 −0.872232
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 14.4721 0.920840
\(248\) 0 0
\(249\) 7.05573 0.447139
\(250\) 0 0
\(251\) 2.47214 0.156040 0.0780199 0.996952i \(-0.475140\pi\)
0.0780199 + 0.996952i \(0.475140\pi\)
\(252\) 0 0
\(253\) 7.47214 0.469769
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 18.6525 1.16351 0.581755 0.813364i \(-0.302366\pi\)
0.581755 + 0.813364i \(0.302366\pi\)
\(258\) 0 0
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) −7.36068 −0.455615
\(262\) 0 0
\(263\) −11.7639 −0.725395 −0.362698 0.931907i \(-0.618144\pi\)
−0.362698 + 0.931907i \(0.618144\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −15.7771 −0.965542
\(268\) 0 0
\(269\) 1.70820 0.104151 0.0520755 0.998643i \(-0.483416\pi\)
0.0520755 + 0.998643i \(0.483416\pi\)
\(270\) 0 0
\(271\) −10.2918 −0.625182 −0.312591 0.949888i \(-0.601197\pi\)
−0.312591 + 0.949888i \(0.601197\pi\)
\(272\) 0 0
\(273\) −4.00000 −0.242091
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 15.8885 0.954650 0.477325 0.878727i \(-0.341606\pi\)
0.477325 + 0.878727i \(0.341606\pi\)
\(278\) 0 0
\(279\) −14.2918 −0.855627
\(280\) 0 0
\(281\) 29.3607 1.75151 0.875756 0.482755i \(-0.160364\pi\)
0.875756 + 0.482755i \(0.160364\pi\)
\(282\) 0 0
\(283\) 9.41641 0.559747 0.279874 0.960037i \(-0.409707\pi\)
0.279874 + 0.960037i \(0.409707\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.23607 −0.545188
\(288\) 0 0
\(289\) 24.8885 1.46403
\(290\) 0 0
\(291\) −0.944272 −0.0553542
\(292\) 0 0
\(293\) 9.12461 0.533066 0.266533 0.963826i \(-0.414122\pi\)
0.266533 + 0.963826i \(0.414122\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −23.4164 −1.35876
\(298\) 0 0
\(299\) 5.70820 0.330114
\(300\) 0 0
\(301\) 6.23607 0.359441
\(302\) 0 0
\(303\) −11.4164 −0.655855
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −31.4164 −1.79303 −0.896515 0.443014i \(-0.853909\pi\)
−0.896515 + 0.443014i \(0.853909\pi\)
\(308\) 0 0
\(309\) −0.583592 −0.0331994
\(310\) 0 0
\(311\) 20.3607 1.15455 0.577274 0.816550i \(-0.304116\pi\)
0.577274 + 0.816550i \(0.304116\pi\)
\(312\) 0 0
\(313\) 28.4721 1.60934 0.804670 0.593722i \(-0.202342\pi\)
0.804670 + 0.593722i \(0.202342\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −19.3607 −1.08740 −0.543702 0.839278i \(-0.682978\pi\)
−0.543702 + 0.839278i \(0.682978\pi\)
\(318\) 0 0
\(319\) −21.1803 −1.18587
\(320\) 0 0
\(321\) 9.88854 0.551925
\(322\) 0 0
\(323\) 28.9443 1.61050
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 22.7639 1.25885
\(328\) 0 0
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 11.2918 0.620653 0.310327 0.950630i \(-0.399562\pi\)
0.310327 + 0.950630i \(0.399562\pi\)
\(332\) 0 0
\(333\) −4.41641 −0.242018
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −7.52786 −0.410069 −0.205034 0.978755i \(-0.565731\pi\)
−0.205034 + 0.978755i \(0.565731\pi\)
\(338\) 0 0
\(339\) −15.3475 −0.833563
\(340\) 0 0
\(341\) −41.1246 −2.22702
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.7639 −0.846252 −0.423126 0.906071i \(-0.639067\pi\)
−0.423126 + 0.906071i \(0.639067\pi\)
\(348\) 0 0
\(349\) −4.47214 −0.239388 −0.119694 0.992811i \(-0.538191\pi\)
−0.119694 + 0.992811i \(0.538191\pi\)
\(350\) 0 0
\(351\) −17.8885 −0.954820
\(352\) 0 0
\(353\) 20.1803 1.07409 0.537046 0.843553i \(-0.319540\pi\)
0.537046 + 0.843553i \(0.319540\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −8.00000 −0.423405
\(358\) 0 0
\(359\) −10.1246 −0.534357 −0.267178 0.963647i \(-0.586091\pi\)
−0.267178 + 0.963647i \(0.586091\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −8.58359 −0.450522
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −3.12461 −0.163103 −0.0815517 0.996669i \(-0.525988\pi\)
−0.0815517 + 0.996669i \(0.525988\pi\)
\(368\) 0 0
\(369\) −13.5967 −0.707818
\(370\) 0 0
\(371\) 0.472136 0.0245121
\(372\) 0 0
\(373\) 15.8328 0.819792 0.409896 0.912132i \(-0.365565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.1803 −0.833330
\(378\) 0 0
\(379\) −11.1803 −0.574295 −0.287148 0.957886i \(-0.592707\pi\)
−0.287148 + 0.957886i \(0.592707\pi\)
\(380\) 0 0
\(381\) −21.8197 −1.11786
\(382\) 0 0
\(383\) 28.7639 1.46977 0.734884 0.678193i \(-0.237237\pi\)
0.734884 + 0.678193i \(0.237237\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.18034 0.466663
\(388\) 0 0
\(389\) −32.8885 −1.66752 −0.833758 0.552131i \(-0.813815\pi\)
−0.833758 + 0.552131i \(0.813815\pi\)
\(390\) 0 0
\(391\) 11.4164 0.577353
\(392\) 0 0
\(393\) 1.16718 0.0588767
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 26.9443 1.35229 0.676147 0.736767i \(-0.263648\pi\)
0.676147 + 0.736767i \(0.263648\pi\)
\(398\) 0 0
\(399\) −5.52786 −0.276739
\(400\) 0 0
\(401\) 11.4721 0.572891 0.286446 0.958097i \(-0.407526\pi\)
0.286446 + 0.958097i \(0.407526\pi\)
\(402\) 0 0
\(403\) −31.4164 −1.56496
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12.7082 −0.629922
\(408\) 0 0
\(409\) 15.5279 0.767803 0.383902 0.923374i \(-0.374580\pi\)
0.383902 + 0.923374i \(0.374580\pi\)
\(410\) 0 0
\(411\) −8.58359 −0.423397
\(412\) 0 0
\(413\) −1.70820 −0.0840552
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −25.5279 −1.25010
\(418\) 0 0
\(419\) 3.81966 0.186603 0.0933013 0.995638i \(-0.470258\pi\)
0.0933013 + 0.995638i \(0.470258\pi\)
\(420\) 0 0
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 0 0
\(423\) −2.94427 −0.143155
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −3.70820 −0.179453
\(428\) 0 0
\(429\) −16.9443 −0.818077
\(430\) 0 0
\(431\) −26.4721 −1.27512 −0.637559 0.770402i \(-0.720056\pi\)
−0.637559 + 0.770402i \(0.720056\pi\)
\(432\) 0 0
\(433\) 16.3607 0.786244 0.393122 0.919486i \(-0.371395\pi\)
0.393122 + 0.919486i \(0.371395\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.88854 0.377360
\(438\) 0 0
\(439\) 21.7082 1.03608 0.518038 0.855358i \(-0.326663\pi\)
0.518038 + 0.855358i \(0.326663\pi\)
\(440\) 0 0
\(441\) −1.47214 −0.0701017
\(442\) 0 0
\(443\) −7.41641 −0.352364 −0.176182 0.984358i \(-0.556375\pi\)
−0.176182 + 0.984358i \(0.556375\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 17.2361 0.815238
\(448\) 0 0
\(449\) 29.4721 1.39088 0.695438 0.718586i \(-0.255210\pi\)
0.695438 + 0.718586i \(0.255210\pi\)
\(450\) 0 0
\(451\) −39.1246 −1.84231
\(452\) 0 0
\(453\) −19.4853 −0.915499
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −21.4721 −1.00442 −0.502212 0.864744i \(-0.667480\pi\)
−0.502212 + 0.864744i \(0.667480\pi\)
\(458\) 0 0
\(459\) −35.7771 −1.66993
\(460\) 0 0
\(461\) 8.18034 0.380996 0.190498 0.981688i \(-0.438990\pi\)
0.190498 + 0.981688i \(0.438990\pi\)
\(462\) 0 0
\(463\) −21.8885 −1.01725 −0.508623 0.860989i \(-0.669845\pi\)
−0.508623 + 0.860989i \(0.669845\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.9443 0.506441 0.253220 0.967409i \(-0.418510\pi\)
0.253220 + 0.967409i \(0.418510\pi\)
\(468\) 0 0
\(469\) 0.236068 0.0109006
\(470\) 0 0
\(471\) −6.47214 −0.298220
\(472\) 0 0
\(473\) 26.4164 1.21463
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.695048 0.0318241
\(478\) 0 0
\(479\) 3.81966 0.174525 0.0872624 0.996185i \(-0.472188\pi\)
0.0872624 + 0.996185i \(0.472188\pi\)
\(480\) 0 0
\(481\) −9.70820 −0.442656
\(482\) 0 0
\(483\) −2.18034 −0.0992089
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −10.2361 −0.463841 −0.231920 0.972735i \(-0.574501\pi\)
−0.231920 + 0.972735i \(0.574501\pi\)
\(488\) 0 0
\(489\) −12.9443 −0.585360
\(490\) 0 0
\(491\) 10.2361 0.461947 0.230974 0.972960i \(-0.425809\pi\)
0.230974 + 0.972960i \(0.425809\pi\)
\(492\) 0 0
\(493\) −32.3607 −1.45745
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.70820 −0.211192
\(498\) 0 0
\(499\) −28.9443 −1.29572 −0.647862 0.761758i \(-0.724337\pi\)
−0.647862 + 0.761758i \(0.724337\pi\)
\(500\) 0 0
\(501\) 0.944272 0.0421870
\(502\) 0 0
\(503\) 43.8885 1.95689 0.978447 0.206499i \(-0.0662072\pi\)
0.978447 + 0.206499i \(0.0662072\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.12461 0.138769
\(508\) 0 0
\(509\) 9.34752 0.414322 0.207161 0.978307i \(-0.433578\pi\)
0.207161 + 0.978307i \(0.433578\pi\)
\(510\) 0 0
\(511\) 13.2361 0.585529
\(512\) 0 0
\(513\) −24.7214 −1.09147
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8.47214 −0.372604
\(518\) 0 0
\(519\) 25.3050 1.11076
\(520\) 0 0
\(521\) 22.0000 0.963837 0.481919 0.876216i \(-0.339940\pi\)
0.481919 + 0.876216i \(0.339940\pi\)
\(522\) 0 0
\(523\) 28.3607 1.24013 0.620063 0.784552i \(-0.287107\pi\)
0.620063 + 0.784552i \(0.287107\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −62.8328 −2.73704
\(528\) 0 0
\(529\) −19.8885 −0.864719
\(530\) 0 0
\(531\) −2.51471 −0.109129
\(532\) 0 0
\(533\) −29.8885 −1.29462
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 4.22291 0.182232
\(538\) 0 0
\(539\) −4.23607 −0.182460
\(540\) 0 0
\(541\) −1.94427 −0.0835908 −0.0417954 0.999126i \(-0.513308\pi\)
−0.0417954 + 0.999126i \(0.513308\pi\)
\(542\) 0 0
\(543\) 17.5279 0.752193
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14.2361 0.608690 0.304345 0.952562i \(-0.401562\pi\)
0.304345 + 0.952562i \(0.401562\pi\)
\(548\) 0 0
\(549\) −5.45898 −0.232984
\(550\) 0 0
\(551\) −22.3607 −0.952597
\(552\) 0 0
\(553\) 11.1803 0.475436
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −44.8885 −1.90199 −0.950994 0.309208i \(-0.899936\pi\)
−0.950994 + 0.309208i \(0.899936\pi\)
\(558\) 0 0
\(559\) 20.1803 0.853537
\(560\) 0 0
\(561\) −33.8885 −1.43078
\(562\) 0 0
\(563\) 9.41641 0.396854 0.198427 0.980116i \(-0.436417\pi\)
0.198427 + 0.980116i \(0.436417\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.41641 0.101480
\(568\) 0 0
\(569\) 13.9443 0.584574 0.292287 0.956331i \(-0.405584\pi\)
0.292287 + 0.956331i \(0.405584\pi\)
\(570\) 0 0
\(571\) 12.5967 0.527157 0.263579 0.964638i \(-0.415097\pi\)
0.263579 + 0.964638i \(0.415097\pi\)
\(572\) 0 0
\(573\) −3.05573 −0.127655
\(574\) 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
\(579\) 17.8197 0.740560
\(580\) 0 0
\(581\) 5.70820 0.236816
\(582\) 0 0
\(583\) 2.00000 0.0828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 29.2361 1.20670 0.603351 0.797476i \(-0.293832\pi\)
0.603351 + 0.797476i \(0.293832\pi\)
\(588\) 0 0
\(589\) −43.4164 −1.78894
\(590\) 0 0
\(591\) −9.23607 −0.379921
\(592\) 0 0
\(593\) 25.3050 1.03915 0.519575 0.854425i \(-0.326090\pi\)
0.519575 + 0.854425i \(0.326090\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.41641 0.139824
\(598\) 0 0
\(599\) −11.1803 −0.456816 −0.228408 0.973565i \(-0.573352\pi\)
−0.228408 + 0.973565i \(0.573352\pi\)
\(600\) 0 0
\(601\) −19.0557 −0.777299 −0.388650 0.921386i \(-0.627058\pi\)
−0.388650 + 0.921386i \(0.627058\pi\)
\(602\) 0 0
\(603\) 0.347524 0.0141523
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −33.1246 −1.34449 −0.672243 0.740330i \(-0.734669\pi\)
−0.672243 + 0.740330i \(0.734669\pi\)
\(608\) 0 0
\(609\) 6.18034 0.250440
\(610\) 0 0
\(611\) −6.47214 −0.261835
\(612\) 0 0
\(613\) −17.5836 −0.710195 −0.355097 0.934829i \(-0.615552\pi\)
−0.355097 + 0.934829i \(0.615552\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.9443 0.480858 0.240429 0.970667i \(-0.422712\pi\)
0.240429 + 0.970667i \(0.422712\pi\)
\(618\) 0 0
\(619\) −1.70820 −0.0686585 −0.0343293 0.999411i \(-0.510929\pi\)
−0.0343293 + 0.999411i \(0.510929\pi\)
\(620\) 0 0
\(621\) −9.75078 −0.391285
\(622\) 0 0
\(623\) −12.7639 −0.511376
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −23.4164 −0.935161
\(628\) 0 0
\(629\) −19.4164 −0.774183
\(630\) 0 0
\(631\) 3.65248 0.145403 0.0727014 0.997354i \(-0.476838\pi\)
0.0727014 + 0.997354i \(0.476838\pi\)
\(632\) 0 0
\(633\) 14.8328 0.589551
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −3.23607 −0.128218
\(638\) 0 0
\(639\) −6.93112 −0.274191
\(640\) 0 0
\(641\) −9.83282 −0.388373 −0.194186 0.980965i \(-0.562207\pi\)
−0.194186 + 0.980965i \(0.562207\pi\)
\(642\) 0 0
\(643\) −9.52786 −0.375742 −0.187871 0.982194i \(-0.560159\pi\)
−0.187871 + 0.982194i \(0.560159\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.8885 −0.624643 −0.312322 0.949976i \(-0.601107\pi\)
−0.312322 + 0.949976i \(0.601107\pi\)
\(648\) 0 0
\(649\) −7.23607 −0.284041
\(650\) 0 0
\(651\) 12.0000 0.470317
\(652\) 0 0
\(653\) 42.9443 1.68054 0.840270 0.542169i \(-0.182397\pi\)
0.840270 + 0.542169i \(0.182397\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 19.4853 0.760194
\(658\) 0 0
\(659\) 17.8885 0.696839 0.348419 0.937339i \(-0.386719\pi\)
0.348419 + 0.937339i \(0.386719\pi\)
\(660\) 0 0
\(661\) 46.7214 1.81725 0.908625 0.417613i \(-0.137133\pi\)
0.908625 + 0.417613i \(0.137133\pi\)
\(662\) 0 0
\(663\) −25.8885 −1.00543
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.81966 −0.341499
\(668\) 0 0
\(669\) −2.69505 −0.104197
\(670\) 0 0
\(671\) −15.7082 −0.606408
\(672\) 0 0
\(673\) 28.4721 1.09752 0.548760 0.835980i \(-0.315100\pi\)
0.548760 + 0.835980i \(0.315100\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.3607 1.16686 0.583428 0.812165i \(-0.301711\pi\)
0.583428 + 0.812165i \(0.301711\pi\)
\(678\) 0 0
\(679\) −0.763932 −0.0293170
\(680\) 0 0
\(681\) −6.69505 −0.256555
\(682\) 0 0
\(683\) 26.1246 0.999630 0.499815 0.866132i \(-0.333401\pi\)
0.499815 + 0.866132i \(0.333401\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −5.52786 −0.210901
\(688\) 0 0
\(689\) 1.52786 0.0582070
\(690\) 0 0
\(691\) −18.1803 −0.691613 −0.345806 0.938306i \(-0.612395\pi\)
−0.345806 + 0.938306i \(0.612395\pi\)
\(692\) 0 0
\(693\) −6.23607 −0.236889
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −59.7771 −2.26422
\(698\) 0 0
\(699\) 12.2918 0.464918
\(700\) 0 0
\(701\) −46.9443 −1.77306 −0.886530 0.462670i \(-0.846891\pi\)
−0.886530 + 0.462670i \(0.846891\pi\)
\(702\) 0 0
\(703\) −13.4164 −0.506009
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.23607 −0.347358
\(708\) 0 0
\(709\) −47.8885 −1.79849 −0.899246 0.437443i \(-0.855884\pi\)
−0.899246 + 0.437443i \(0.855884\pi\)
\(710\) 0 0
\(711\) 16.4590 0.617260
\(712\) 0 0
\(713\) −17.1246 −0.641322
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −17.8885 −0.668060
\(718\) 0 0
\(719\) 6.18034 0.230488 0.115244 0.993337i \(-0.463235\pi\)
0.115244 + 0.993337i \(0.463235\pi\)
\(720\) 0 0
\(721\) −0.472136 −0.0175833
\(722\) 0 0
\(723\) 15.4164 0.573342
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 20.9443 0.776780 0.388390 0.921495i \(-0.373031\pi\)
0.388390 + 0.921495i \(0.373031\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 0 0
\(731\) 40.3607 1.49279
\(732\) 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
\(739\) 5.65248 0.207930 0.103965 0.994581i \(-0.466847\pi\)
0.103965 + 0.994581i \(0.466847\pi\)
\(740\) 0 0
\(741\) −17.8885 −0.657152
\(742\) 0 0
\(743\) 1.52786 0.0560519 0.0280259 0.999607i \(-0.491078\pi\)
0.0280259 + 0.999607i \(0.491078\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 8.40325 0.307459
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) 0 0
\(751\) −20.9443 −0.764267 −0.382134 0.924107i \(-0.624811\pi\)
−0.382134 + 0.924107i \(0.624811\pi\)
\(752\) 0 0
\(753\) −3.05573 −0.111357
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 46.4164 1.68703 0.843517 0.537103i \(-0.180481\pi\)
0.843517 + 0.537103i \(0.180481\pi\)
\(758\) 0 0
\(759\) −9.23607 −0.335248
\(760\) 0 0
\(761\) −43.7771 −1.58692 −0.793459 0.608624i \(-0.791722\pi\)
−0.793459 + 0.608624i \(0.791722\pi\)
\(762\) 0 0
\(763\) 18.4164 0.666719
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.52786 −0.199600
\(768\) 0 0
\(769\) 33.0132 1.19048 0.595242 0.803546i \(-0.297056\pi\)
0.595242 + 0.803546i \(0.297056\pi\)
\(770\) 0 0
\(771\) −23.0557 −0.830332
\(772\) 0 0
\(773\) 27.8197 1.00060 0.500302 0.865851i \(-0.333222\pi\)
0.500302 + 0.865851i \(0.333222\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 3.70820 0.133031
\(778\) 0 0
\(779\) −41.3050 −1.47990
\(780\) 0 0
\(781\) −19.9443 −0.713662
\(782\) 0 0
\(783\) 27.6393 0.987749
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −45.2361 −1.61249 −0.806246 0.591581i \(-0.798504\pi\)
−0.806246 + 0.591581i \(0.798504\pi\)
\(788\) 0 0
\(789\) 14.5410 0.517674
\(790\) 0 0
\(791\) −12.4164 −0.441477
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.58359 −0.304046 −0.152023 0.988377i \(-0.548579\pi\)
−0.152023 + 0.988377i \(0.548579\pi\)
\(798\) 0 0
\(799\) −12.9443 −0.457935
\(800\) 0 0
\(801\) −18.7902 −0.663921
\(802\) 0 0
\(803\) 56.0689 1.97863
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −2.11146 −0.0743268
\(808\) 0 0
\(809\) 20.5279 0.721721 0.360861 0.932620i \(-0.382483\pi\)
0.360861 + 0.932620i \(0.382483\pi\)
\(810\) 0 0
\(811\) −46.7214 −1.64061 −0.820304 0.571927i \(-0.806196\pi\)
−0.820304 + 0.571927i \(0.806196\pi\)
\(812\) 0 0
\(813\) 12.7214 0.446158
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 27.8885 0.975697
\(818\) 0 0
\(819\) −4.76393 −0.166465
\(820\) 0 0
\(821\) −24.8328 −0.866671 −0.433336 0.901233i \(-0.642664\pi\)
−0.433336 + 0.901233i \(0.642664\pi\)
\(822\) 0 0
\(823\) 0.347524 0.0121139 0.00605697 0.999982i \(-0.498072\pi\)
0.00605697 + 0.999982i \(0.498072\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.5410 0.888148 0.444074 0.895990i \(-0.353533\pi\)
0.444074 + 0.895990i \(0.353533\pi\)
\(828\) 0 0
\(829\) −52.3607 −1.81856 −0.909281 0.416183i \(-0.863368\pi\)
−0.909281 + 0.416183i \(0.863368\pi\)
\(830\) 0 0
\(831\) −19.6393 −0.681280
\(832\) 0 0
\(833\) −6.47214 −0.224246
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 53.6656 1.85496
\(838\) 0 0
\(839\) −0.652476 −0.0225260 −0.0112630 0.999937i \(-0.503585\pi\)
−0.0112630 + 0.999937i \(0.503585\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) −36.2918 −1.24996
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −6.94427 −0.238608
\(848\) 0 0
\(849\) −11.6393 −0.399460
\(850\) 0 0
\(851\) −5.29180 −0.181400
\(852\) 0 0
\(853\) 0.583592 0.0199818 0.00999091 0.999950i \(-0.496820\pi\)
0.00999091 + 0.999950i \(0.496820\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −38.1803 −1.30422 −0.652108 0.758126i \(-0.726115\pi\)
−0.652108 + 0.758126i \(0.726115\pi\)
\(858\) 0 0
\(859\) 22.3607 0.762937 0.381468 0.924382i \(-0.375419\pi\)
0.381468 + 0.924382i \(0.375419\pi\)
\(860\) 0 0
\(861\) 11.4164 0.389070
\(862\) 0 0
\(863\) −49.6525 −1.69019 −0.845095 0.534616i \(-0.820456\pi\)
−0.845095 + 0.534616i \(0.820456\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −30.7639 −1.04480
\(868\) 0 0
\(869\) 47.3607 1.60660
\(870\) 0 0
\(871\) 0.763932 0.0258848
\(872\) 0 0
\(873\) −1.12461 −0.0380623
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −14.3607 −0.484926 −0.242463 0.970161i \(-0.577955\pi\)
−0.242463 + 0.970161i \(0.577955\pi\)
\(878\) 0 0
\(879\) −11.2786 −0.380419
\(880\) 0 0
\(881\) 28.1803 0.949420 0.474710 0.880142i \(-0.342553\pi\)
0.474710 + 0.880142i \(0.342553\pi\)
\(882\) 0 0
\(883\) 50.5967 1.70272 0.851358 0.524585i \(-0.175780\pi\)
0.851358 + 0.524585i \(0.175780\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 52.6525 1.76790 0.883949 0.467584i \(-0.154876\pi\)
0.883949 + 0.467584i \(0.154876\pi\)
\(888\) 0 0
\(889\) −17.6525 −0.592045
\(890\) 0 0
\(891\) 10.2361 0.342921
\(892\) 0 0
\(893\) −8.94427 −0.299309
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −7.05573 −0.235584
\(898\) 0 0
\(899\) 48.5410 1.61893
\(900\) 0 0
\(901\) 3.05573 0.101801
\(902\) 0 0
\(903\) −7.70820 −0.256513
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 18.8328 0.625333 0.312667 0.949863i \(-0.398778\pi\)
0.312667 + 0.949863i \(0.398778\pi\)
\(908\) 0 0
\(909\) −13.5967 −0.450976
\(910\) 0 0
\(911\) −23.1803 −0.767999 −0.383999 0.923333i \(-0.625454\pi\)
−0.383999 + 0.923333i \(0.625454\pi\)
\(912\) 0 0
\(913\) 24.1803 0.800252
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.944272 0.0311826
\(918\) 0 0
\(919\) 32.2361 1.06337 0.531685 0.846942i \(-0.321559\pi\)
0.531685 + 0.846942i \(0.321559\pi\)
\(920\) 0 0
\(921\) 38.8328 1.27958
\(922\) 0 0
\(923\) −15.2361 −0.501501
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −0.695048 −0.0228284
\(928\) 0 0
\(929\) 51.7082 1.69649 0.848246 0.529603i \(-0.177659\pi\)
0.848246 + 0.529603i \(0.177659\pi\)
\(930\) 0 0
\(931\) −4.47214 −0.146568
\(932\) 0 0
\(933\) −25.1672 −0.823937
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 30.7639 1.00501 0.502507 0.864573i \(-0.332411\pi\)
0.502507 + 0.864573i \(0.332411\pi\)
\(938\) 0 0
\(939\) −35.1935 −1.14850
\(940\) 0 0
\(941\) −0.763932 −0.0249035 −0.0124517 0.999922i \(-0.503964\pi\)
−0.0124517 + 0.999922i \(0.503964\pi\)
\(942\) 0 0
\(943\) −16.2918 −0.530534
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 18.8328 0.611984 0.305992 0.952034i \(-0.401012\pi\)
0.305992 + 0.952034i \(0.401012\pi\)
\(948\) 0 0
\(949\) 42.8328 1.39041
\(950\) 0 0
\(951\) 23.9311 0.776020
\(952\) 0 0
\(953\) −5.47214 −0.177260 −0.0886299 0.996065i \(-0.528249\pi\)
−0.0886299 + 0.996065i \(0.528249\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 26.1803 0.846290
\(958\) 0 0
\(959\) −6.94427 −0.224242
\(960\) 0 0
\(961\) 63.2492 2.04030
\(962\) 0 0
\(963\) 11.7771 0.379511
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 49.8885 1.60431 0.802154 0.597118i \(-0.203687\pi\)
0.802154 + 0.597118i \(0.203687\pi\)
\(968\) 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
\(973\) −20.6525 −0.662088
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.52786 −0.0808735 −0.0404368 0.999182i \(-0.512875\pi\)
−0.0404368 + 0.999182i \(0.512875\pi\)
\(978\) 0 0
\(979\) −54.0689 −1.72805
\(980\) 0 0
\(981\) 27.1115 0.865602
\(982\) 0 0
\(983\) −32.5410 −1.03790 −0.518949 0.854805i \(-0.673676\pi\)
−0.518949 + 0.854805i \(0.673676\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.47214 0.0786890
\(988\) 0 0
\(989\) 11.0000 0.349780
\(990\) 0 0
\(991\) 9.18034 0.291623 0.145812 0.989312i \(-0.453421\pi\)
0.145812 + 0.989312i \(0.453421\pi\)
\(992\) 0 0
\(993\) −13.9574 −0.442926
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −18.5836 −0.588548 −0.294274 0.955721i \(-0.595078\pi\)
−0.294274 + 0.955721i \(0.595078\pi\)
\(998\) 0 0
\(999\) 16.5836 0.524682
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.1.1 2
4.3 odd 2 175.2.a.e.1.2 yes 2
5.2 odd 4 2800.2.g.s.449.3 4
5.3 odd 4 2800.2.g.s.449.2 4
5.4 even 2 2800.2.a.bh.1.2 2
12.11 even 2 1575.2.a.n.1.1 2
20.3 even 4 175.2.b.c.99.1 4
20.7 even 4 175.2.b.c.99.4 4
20.19 odd 2 175.2.a.d.1.1 2
28.27 even 2 1225.2.a.u.1.2 2
60.23 odd 4 1575.2.d.k.1324.4 4
60.47 odd 4 1575.2.d.k.1324.1 4
60.59 even 2 1575.2.a.s.1.2 2
140.27 odd 4 1225.2.b.k.99.4 4
140.83 odd 4 1225.2.b.k.99.1 4
140.139 even 2 1225.2.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.a.d.1.1 2 20.19 odd 2
175.2.a.e.1.2 yes 2 4.3 odd 2
175.2.b.c.99.1 4 20.3 even 4
175.2.b.c.99.4 4 20.7 even 4
1225.2.a.n.1.1 2 140.139 even 2
1225.2.a.u.1.2 2 28.27 even 2
1225.2.b.k.99.1 4 140.83 odd 4
1225.2.b.k.99.4 4 140.27 odd 4
1575.2.a.n.1.1 2 12.11 even 2
1575.2.a.s.1.2 2 60.59 even 2
1575.2.d.k.1324.1 4 60.47 odd 4
1575.2.d.k.1324.4 4 60.23 odd 4
2800.2.a.bh.1.2 2 5.4 even 2
2800.2.a.bp.1.1 2 1.1 even 1 trivial
2800.2.g.s.449.2 4 5.3 odd 4
2800.2.g.s.449.3 4 5.2 odd 4