Properties

Label 1400.2.a.s.1.2
Level $1400$
Weight $2$
Character 1400.1
Self dual yes
Analytic conductor $11.179$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 1400.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.363328 q^{3} +1.00000 q^{7} -2.86799 q^{9} +O(q^{10})\) \(q+0.363328 q^{3} +1.00000 q^{7} -2.86799 q^{9} +5.14134 q^{11} -4.64600 q^{13} +3.86799 q^{17} -0.778008 q^{19} +0.363328 q^{21} +5.00933 q^{23} -2.13201 q^{27} +9.42401 q^{29} +4.72666 q^{31} +1.86799 q^{33} +6.00000 q^{37} -1.68802 q^{39} -1.00933 q^{41} -7.00933 q^{43} -11.4240 q^{47} +1.00000 q^{49} +1.40535 q^{51} +7.55602 q^{53} -0.282672 q^{57} +12.5140 q^{59} +11.5047 q^{61} -2.86799 q^{63} -11.7360 q^{67} +1.82003 q^{69} +2.72666 q^{71} +5.00933 q^{73} +5.14134 q^{77} +5.68802 q^{79} +7.82936 q^{81} -4.67531 q^{83} +3.42401 q^{87} -2.82936 q^{89} -4.64600 q^{91} +1.71733 q^{93} -1.58532 q^{97} -14.7453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{3} + 3q^{7} + 4q^{9} + O(q^{10}) \) \( 3q - q^{3} + 3q^{7} + 4q^{9} + 7q^{11} + 5q^{13} - q^{17} + 4q^{19} - q^{21} - 6q^{23} - 19q^{27} + 3q^{29} + 10q^{31} - 7q^{33} + 18q^{37} - 5q^{39} + 18q^{41} - 9q^{47} + 3q^{49} + 21q^{51} + 10q^{53} + 16q^{57} + 6q^{59} + 24q^{61} + 4q^{63} - 10q^{67} + 18q^{69} + 4q^{71} - 6q^{73} + 7q^{77} + 17q^{79} + 15q^{81} - 12q^{83} - 15q^{87} + 5q^{91} + 22q^{93} - 9q^{97} + 2q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.363328 0.209768 0.104884 0.994484i \(-0.466553\pi\)
0.104884 + 0.994484i \(0.466553\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.86799 −0.955998
\(10\) 0 0
\(11\) 5.14134 1.55017 0.775086 0.631856i \(-0.217707\pi\)
0.775086 + 0.631856i \(0.217707\pi\)
\(12\) 0 0
\(13\) −4.64600 −1.28857 −0.644284 0.764786i \(-0.722845\pi\)
−0.644284 + 0.764786i \(0.722845\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.86799 0.938126 0.469063 0.883165i \(-0.344592\pi\)
0.469063 + 0.883165i \(0.344592\pi\)
\(18\) 0 0
\(19\) −0.778008 −0.178487 −0.0892436 0.996010i \(-0.528445\pi\)
−0.0892436 + 0.996010i \(0.528445\pi\)
\(20\) 0 0
\(21\) 0.363328 0.0792847
\(22\) 0 0
\(23\) 5.00933 1.04452 0.522259 0.852787i \(-0.325090\pi\)
0.522259 + 0.852787i \(0.325090\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.13201 −0.410305
\(28\) 0 0
\(29\) 9.42401 1.74999 0.874997 0.484128i \(-0.160863\pi\)
0.874997 + 0.484128i \(0.160863\pi\)
\(30\) 0 0
\(31\) 4.72666 0.848933 0.424466 0.905444i \(-0.360462\pi\)
0.424466 + 0.905444i \(0.360462\pi\)
\(32\) 0 0
\(33\) 1.86799 0.325176
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) −1.68802 −0.270300
\(40\) 0 0
\(41\) −1.00933 −0.157631 −0.0788153 0.996889i \(-0.525114\pi\)
−0.0788153 + 0.996889i \(0.525114\pi\)
\(42\) 0 0
\(43\) −7.00933 −1.06891 −0.534456 0.845196i \(-0.679484\pi\)
−0.534456 + 0.845196i \(0.679484\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.4240 −1.66636 −0.833181 0.553000i \(-0.813483\pi\)
−0.833181 + 0.553000i \(0.813483\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 1.40535 0.196788
\(52\) 0 0
\(53\) 7.55602 1.03790 0.518949 0.854805i \(-0.326323\pi\)
0.518949 + 0.854805i \(0.326323\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.282672 −0.0374409
\(58\) 0 0
\(59\) 12.5140 1.62918 0.814592 0.580035i \(-0.196961\pi\)
0.814592 + 0.580035i \(0.196961\pi\)
\(60\) 0 0
\(61\) 11.5047 1.47302 0.736511 0.676426i \(-0.236472\pi\)
0.736511 + 0.676426i \(0.236472\pi\)
\(62\) 0 0
\(63\) −2.86799 −0.361333
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −11.7360 −1.43378 −0.716889 0.697187i \(-0.754435\pi\)
−0.716889 + 0.697187i \(0.754435\pi\)
\(68\) 0 0
\(69\) 1.82003 0.219106
\(70\) 0 0
\(71\) 2.72666 0.323595 0.161797 0.986824i \(-0.448271\pi\)
0.161797 + 0.986824i \(0.448271\pi\)
\(72\) 0 0
\(73\) 5.00933 0.586298 0.293149 0.956067i \(-0.405297\pi\)
0.293149 + 0.956067i \(0.405297\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.14134 0.585910
\(78\) 0 0
\(79\) 5.68802 0.639953 0.319976 0.947426i \(-0.396325\pi\)
0.319976 + 0.947426i \(0.396325\pi\)
\(80\) 0 0
\(81\) 7.82936 0.869929
\(82\) 0 0
\(83\) −4.67531 −0.513181 −0.256591 0.966520i \(-0.582599\pi\)
−0.256591 + 0.966520i \(0.582599\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.42401 0.367092
\(88\) 0 0
\(89\) −2.82936 −0.299911 −0.149956 0.988693i \(-0.547913\pi\)
−0.149956 + 0.988693i \(0.547913\pi\)
\(90\) 0 0
\(91\) −4.64600 −0.487033
\(92\) 0 0
\(93\) 1.71733 0.178079
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.58532 −0.160965 −0.0804824 0.996756i \(-0.525646\pi\)
−0.0804824 + 0.996756i \(0.525646\pi\)
\(98\) 0 0
\(99\) −14.7453 −1.48196
\(100\) 0 0
\(101\) −9.06068 −0.901571 −0.450786 0.892632i \(-0.648856\pi\)
−0.450786 + 0.892632i \(0.648856\pi\)
\(102\) 0 0
\(103\) 5.14134 0.506591 0.253295 0.967389i \(-0.418486\pi\)
0.253295 + 0.967389i \(0.418486\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −3.97070 −0.380324 −0.190162 0.981753i \(-0.560901\pi\)
−0.190162 + 0.981753i \(0.560901\pi\)
\(110\) 0 0
\(111\) 2.17997 0.206914
\(112\) 0 0
\(113\) 4.54669 0.427716 0.213858 0.976865i \(-0.431397\pi\)
0.213858 + 0.976865i \(0.431397\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 13.3247 1.23187
\(118\) 0 0
\(119\) 3.86799 0.354578
\(120\) 0 0
\(121\) 15.4333 1.40303
\(122\) 0 0
\(123\) −0.366718 −0.0330658
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.1214 1.43054 0.715270 0.698849i \(-0.246304\pi\)
0.715270 + 0.698849i \(0.246304\pi\)
\(128\) 0 0
\(129\) −2.54669 −0.224223
\(130\) 0 0
\(131\) 0.0513514 0.00448659 0.00224330 0.999997i \(-0.499286\pi\)
0.00224330 + 0.999997i \(0.499286\pi\)
\(132\) 0 0
\(133\) −0.778008 −0.0674618
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.0187 −1.19769 −0.598847 0.800863i \(-0.704374\pi\)
−0.598847 + 0.800863i \(0.704374\pi\)
\(138\) 0 0
\(139\) 12.6167 1.07013 0.535067 0.844810i \(-0.320286\pi\)
0.535067 + 0.844810i \(0.320286\pi\)
\(140\) 0 0
\(141\) −4.15066 −0.349549
\(142\) 0 0
\(143\) −23.8867 −1.99750
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.363328 0.0299668
\(148\) 0 0
\(149\) −11.4533 −0.938292 −0.469146 0.883121i \(-0.655438\pi\)
−0.469146 + 0.883121i \(0.655438\pi\)
\(150\) 0 0
\(151\) 5.86799 0.477530 0.238765 0.971077i \(-0.423257\pi\)
0.238765 + 0.971077i \(0.423257\pi\)
\(152\) 0 0
\(153\) −11.0934 −0.896846
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −5.78734 −0.461880 −0.230940 0.972968i \(-0.574180\pi\)
−0.230940 + 0.972968i \(0.574180\pi\)
\(158\) 0 0
\(159\) 2.74531 0.217718
\(160\) 0 0
\(161\) 5.00933 0.394790
\(162\) 0 0
\(163\) 3.27334 0.256388 0.128194 0.991749i \(-0.459082\pi\)
0.128194 + 0.991749i \(0.459082\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −24.8773 −1.92506 −0.962532 0.271166i \(-0.912591\pi\)
−0.962532 + 0.271166i \(0.912591\pi\)
\(168\) 0 0
\(169\) 8.58532 0.660409
\(170\) 0 0
\(171\) 2.23132 0.170633
\(172\) 0 0
\(173\) 6.62734 0.503868 0.251934 0.967744i \(-0.418933\pi\)
0.251934 + 0.967744i \(0.418933\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.54669 0.341750
\(178\) 0 0
\(179\) −10.0187 −0.748830 −0.374415 0.927261i \(-0.622156\pi\)
−0.374415 + 0.927261i \(0.622156\pi\)
\(180\) 0 0
\(181\) 1.78734 0.132852 0.0664258 0.997791i \(-0.478840\pi\)
0.0664258 + 0.997791i \(0.478840\pi\)
\(182\) 0 0
\(183\) 4.17997 0.308992
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 19.8867 1.45426
\(188\) 0 0
\(189\) −2.13201 −0.155081
\(190\) 0 0
\(191\) −8.59465 −0.621887 −0.310943 0.950428i \(-0.600645\pi\)
−0.310943 + 0.950428i \(0.600645\pi\)
\(192\) 0 0
\(193\) −5.17064 −0.372191 −0.186095 0.982532i \(-0.559583\pi\)
−0.186095 + 0.982532i \(0.559583\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 23.9160 1.70394 0.851971 0.523590i \(-0.175407\pi\)
0.851971 + 0.523590i \(0.175407\pi\)
\(198\) 0 0
\(199\) −15.3107 −1.08534 −0.542672 0.839945i \(-0.682587\pi\)
−0.542672 + 0.839945i \(0.682587\pi\)
\(200\) 0 0
\(201\) −4.26401 −0.300760
\(202\) 0 0
\(203\) 9.42401 0.661436
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −14.3667 −0.998556
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −1.03863 −0.0715025 −0.0357512 0.999361i \(-0.511382\pi\)
−0.0357512 + 0.999361i \(0.511382\pi\)
\(212\) 0 0
\(213\) 0.990671 0.0678797
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 4.72666 0.320866
\(218\) 0 0
\(219\) 1.82003 0.122986
\(220\) 0 0
\(221\) −17.9707 −1.20884
\(222\) 0 0
\(223\) −9.86799 −0.660810 −0.330405 0.943839i \(-0.607185\pi\)
−0.330405 + 0.943839i \(0.607185\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −21.6553 −1.43731 −0.718657 0.695364i \(-0.755243\pi\)
−0.718657 + 0.695364i \(0.755243\pi\)
\(228\) 0 0
\(229\) 20.2313 1.33692 0.668462 0.743747i \(-0.266953\pi\)
0.668462 + 0.743747i \(0.266953\pi\)
\(230\) 0 0
\(231\) 1.86799 0.122905
\(232\) 0 0
\(233\) −5.45331 −0.357258 −0.178629 0.983916i \(-0.557166\pi\)
−0.178629 + 0.983916i \(0.557166\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.06662 0.134241
\(238\) 0 0
\(239\) −11.5853 −0.749392 −0.374696 0.927148i \(-0.622253\pi\)
−0.374696 + 0.927148i \(0.622253\pi\)
\(240\) 0 0
\(241\) −5.00933 −0.322679 −0.161340 0.986899i \(-0.551581\pi\)
−0.161340 + 0.986899i \(0.551581\pi\)
\(242\) 0 0
\(243\) 9.24065 0.592788
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.61462 0.229993
\(248\) 0 0
\(249\) −1.69867 −0.107649
\(250\) 0 0
\(251\) −23.4206 −1.47830 −0.739148 0.673543i \(-0.764772\pi\)
−0.739148 + 0.673543i \(0.764772\pi\)
\(252\) 0 0
\(253\) 25.7546 1.61918
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.0093 0.811500 0.405750 0.913984i \(-0.367010\pi\)
0.405750 + 0.913984i \(0.367010\pi\)
\(258\) 0 0
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) −27.0280 −1.67299
\(262\) 0 0
\(263\) 6.01866 0.371126 0.185563 0.982632i \(-0.440589\pi\)
0.185563 + 0.982632i \(0.440589\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.02799 −0.0629117
\(268\) 0 0
\(269\) 3.24065 0.197586 0.0987929 0.995108i \(-0.468502\pi\)
0.0987929 + 0.995108i \(0.468502\pi\)
\(270\) 0 0
\(271\) −29.1307 −1.76956 −0.884782 0.466006i \(-0.845693\pi\)
−0.884782 + 0.466006i \(0.845693\pi\)
\(272\) 0 0
\(273\) −1.68802 −0.102164
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −4.44398 −0.267013 −0.133507 0.991048i \(-0.542624\pi\)
−0.133507 + 0.991048i \(0.542624\pi\)
\(278\) 0 0
\(279\) −13.5560 −0.811577
\(280\) 0 0
\(281\) −24.6974 −1.47332 −0.736660 0.676263i \(-0.763598\pi\)
−0.736660 + 0.676263i \(0.763598\pi\)
\(282\) 0 0
\(283\) 7.73937 0.460058 0.230029 0.973184i \(-0.426118\pi\)
0.230029 + 0.973184i \(0.426118\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.00933 −0.0595788
\(288\) 0 0
\(289\) −2.03863 −0.119920
\(290\) 0 0
\(291\) −0.575992 −0.0337652
\(292\) 0 0
\(293\) 25.1086 1.46686 0.733431 0.679764i \(-0.237918\pi\)
0.733431 + 0.679764i \(0.237918\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −10.9614 −0.636043
\(298\) 0 0
\(299\) −23.2733 −1.34593
\(300\) 0 0
\(301\) −7.00933 −0.404011
\(302\) 0 0
\(303\) −3.29200 −0.189121
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −33.9193 −1.93588 −0.967940 0.251183i \(-0.919180\pi\)
−0.967940 + 0.251183i \(0.919180\pi\)
\(308\) 0 0
\(309\) 1.86799 0.106266
\(310\) 0 0
\(311\) 0.565344 0.0320577 0.0160289 0.999872i \(-0.494898\pi\)
0.0160289 + 0.999872i \(0.494898\pi\)
\(312\) 0 0
\(313\) −27.3400 −1.54535 −0.772673 0.634804i \(-0.781081\pi\)
−0.772673 + 0.634804i \(0.781081\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.7267 1.27646 0.638228 0.769847i \(-0.279668\pi\)
0.638228 + 0.769847i \(0.279668\pi\)
\(318\) 0 0
\(319\) 48.4520 2.71279
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.00933 −0.167444
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.44267 −0.0797796
\(328\) 0 0
\(329\) −11.4240 −0.629826
\(330\) 0 0
\(331\) 0.462642 0.0254291 0.0127145 0.999919i \(-0.495953\pi\)
0.0127145 + 0.999919i \(0.495953\pi\)
\(332\) 0 0
\(333\) −17.2080 −0.942990
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −10.5653 −0.575531 −0.287765 0.957701i \(-0.592912\pi\)
−0.287765 + 0.957701i \(0.592912\pi\)
\(338\) 0 0
\(339\) 1.65194 0.0897211
\(340\) 0 0
\(341\) 24.3013 1.31599
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 31.8760 1.71119 0.855597 0.517643i \(-0.173190\pi\)
0.855597 + 0.517643i \(0.173190\pi\)
\(348\) 0 0
\(349\) −9.62602 −0.515269 −0.257635 0.966242i \(-0.582943\pi\)
−0.257635 + 0.966242i \(0.582943\pi\)
\(350\) 0 0
\(351\) 9.90531 0.528706
\(352\) 0 0
\(353\) −26.2534 −1.39733 −0.698663 0.715451i \(-0.746221\pi\)
−0.698663 + 0.715451i \(0.746221\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.40535 0.0743791
\(358\) 0 0
\(359\) −4.56534 −0.240950 −0.120475 0.992716i \(-0.538442\pi\)
−0.120475 + 0.992716i \(0.538442\pi\)
\(360\) 0 0
\(361\) −18.3947 −0.968142
\(362\) 0 0
\(363\) 5.60737 0.294310
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3.79073 0.197874 0.0989371 0.995094i \(-0.468456\pi\)
0.0989371 + 0.995094i \(0.468456\pi\)
\(368\) 0 0
\(369\) 2.89475 0.150695
\(370\) 0 0
\(371\) 7.55602 0.392289
\(372\) 0 0
\(373\) 20.7453 1.07415 0.537076 0.843534i \(-0.319529\pi\)
0.537076 + 0.843534i \(0.319529\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −43.7839 −2.25499
\(378\) 0 0
\(379\) 3.00933 0.154579 0.0772894 0.997009i \(-0.475373\pi\)
0.0772894 + 0.997009i \(0.475373\pi\)
\(380\) 0 0
\(381\) 5.85735 0.300081
\(382\) 0 0
\(383\) 7.00933 0.358160 0.179080 0.983835i \(-0.442688\pi\)
0.179080 + 0.983835i \(0.442688\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 20.1027 1.02188
\(388\) 0 0
\(389\) −19.7653 −1.00214 −0.501070 0.865407i \(-0.667060\pi\)
−0.501070 + 0.865407i \(0.667060\pi\)
\(390\) 0 0
\(391\) 19.3760 0.979889
\(392\) 0 0
\(393\) 0.0186574 0.000941142 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.37266 −0.470400 −0.235200 0.971947i \(-0.575575\pi\)
−0.235200 + 0.971947i \(0.575575\pi\)
\(398\) 0 0
\(399\) −0.282672 −0.0141513
\(400\) 0 0
\(401\) −16.1507 −0.806526 −0.403263 0.915084i \(-0.632124\pi\)
−0.403263 + 0.915084i \(0.632124\pi\)
\(402\) 0 0
\(403\) −21.9600 −1.09391
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 30.8480 1.52908
\(408\) 0 0
\(409\) 15.2920 0.756141 0.378070 0.925777i \(-0.376588\pi\)
0.378070 + 0.925777i \(0.376588\pi\)
\(410\) 0 0
\(411\) −5.09337 −0.251238
\(412\) 0 0
\(413\) 12.5140 0.615773
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 4.58400 0.224480
\(418\) 0 0
\(419\) −33.1820 −1.62105 −0.810524 0.585705i \(-0.800818\pi\)
−0.810524 + 0.585705i \(0.800818\pi\)
\(420\) 0 0
\(421\) 27.8094 1.35535 0.677673 0.735363i \(-0.262988\pi\)
0.677673 + 0.735363i \(0.262988\pi\)
\(422\) 0 0
\(423\) 32.7640 1.59304
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 11.5047 0.556750
\(428\) 0 0
\(429\) −8.67869 −0.419011
\(430\) 0 0
\(431\) −21.5454 −1.03780 −0.518902 0.854834i \(-0.673659\pi\)
−0.518902 + 0.854834i \(0.673659\pi\)
\(432\) 0 0
\(433\) −36.0187 −1.73095 −0.865473 0.500955i \(-0.832982\pi\)
−0.865473 + 0.500955i \(0.832982\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.89730 −0.186433
\(438\) 0 0
\(439\) −21.1893 −1.01131 −0.505655 0.862736i \(-0.668749\pi\)
−0.505655 + 0.862736i \(0.668749\pi\)
\(440\) 0 0
\(441\) −2.86799 −0.136571
\(442\) 0 0
\(443\) −11.1120 −0.527949 −0.263974 0.964530i \(-0.585033\pi\)
−0.263974 + 0.964530i \(0.585033\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.16131 −0.196823
\(448\) 0 0
\(449\) 0.961367 0.0453697 0.0226848 0.999743i \(-0.492779\pi\)
0.0226848 + 0.999743i \(0.492779\pi\)
\(450\) 0 0
\(451\) −5.18930 −0.244355
\(452\) 0 0
\(453\) 2.13201 0.100170
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 28.2241 1.32027 0.660133 0.751149i \(-0.270500\pi\)
0.660133 + 0.751149i \(0.270500\pi\)
\(458\) 0 0
\(459\) −8.24659 −0.384918
\(460\) 0 0
\(461\) 26.0887 1.21507 0.607535 0.794293i \(-0.292158\pi\)
0.607535 + 0.794293i \(0.292158\pi\)
\(462\) 0 0
\(463\) −2.90663 −0.135082 −0.0675412 0.997716i \(-0.521515\pi\)
−0.0675412 + 0.997716i \(0.521515\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.2020 0.564642 0.282321 0.959320i \(-0.408896\pi\)
0.282321 + 0.959320i \(0.408896\pi\)
\(468\) 0 0
\(469\) −11.7360 −0.541917
\(470\) 0 0
\(471\) −2.10270 −0.0968874
\(472\) 0 0
\(473\) −36.0373 −1.65700
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −21.6706 −0.992228
\(478\) 0 0
\(479\) −17.6519 −0.806538 −0.403269 0.915082i \(-0.632126\pi\)
−0.403269 + 0.915082i \(0.632126\pi\)
\(480\) 0 0
\(481\) −27.8760 −1.27104
\(482\) 0 0
\(483\) 1.82003 0.0828143
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.57467 −0.0713553 −0.0356776 0.999363i \(-0.511359\pi\)
−0.0356776 + 0.999363i \(0.511359\pi\)
\(488\) 0 0
\(489\) 1.18930 0.0537819
\(490\) 0 0
\(491\) −3.26270 −0.147243 −0.0736217 0.997286i \(-0.523456\pi\)
−0.0736217 + 0.997286i \(0.523456\pi\)
\(492\) 0 0
\(493\) 36.4520 1.64172
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.72666 0.122307
\(498\) 0 0
\(499\) 42.5293 1.90387 0.951936 0.306298i \(-0.0990905\pi\)
0.951936 + 0.306298i \(0.0990905\pi\)
\(500\) 0 0
\(501\) −9.03863 −0.403816
\(502\) 0 0
\(503\) −18.6974 −0.833674 −0.416837 0.908981i \(-0.636861\pi\)
−0.416837 + 0.908981i \(0.636861\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.11929 0.138533
\(508\) 0 0
\(509\) 20.2313 0.896738 0.448369 0.893849i \(-0.352005\pi\)
0.448369 + 0.893849i \(0.352005\pi\)
\(510\) 0 0
\(511\) 5.00933 0.221600
\(512\) 0 0
\(513\) 1.65872 0.0732342
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −58.7347 −2.58315
\(518\) 0 0
\(519\) 2.40790 0.105695
\(520\) 0 0
\(521\) 21.8387 0.956770 0.478385 0.878150i \(-0.341222\pi\)
0.478385 + 0.878150i \(0.341222\pi\)
\(522\) 0 0
\(523\) −20.4554 −0.894451 −0.447226 0.894421i \(-0.647588\pi\)
−0.447226 + 0.894421i \(0.647588\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.2827 0.796406
\(528\) 0 0
\(529\) 2.09337 0.0910163
\(530\) 0 0
\(531\) −35.8900 −1.55750
\(532\) 0 0
\(533\) 4.68934 0.203118
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −3.64006 −0.157080
\(538\) 0 0
\(539\) 5.14134 0.221453
\(540\) 0 0
\(541\) 27.3400 1.17544 0.587718 0.809066i \(-0.300026\pi\)
0.587718 + 0.809066i \(0.300026\pi\)
\(542\) 0 0
\(543\) 0.649390 0.0278680
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −22.6867 −0.970013 −0.485007 0.874510i \(-0.661183\pi\)
−0.485007 + 0.874510i \(0.661183\pi\)
\(548\) 0 0
\(549\) −32.9953 −1.40820
\(550\) 0 0
\(551\) −7.33195 −0.312352
\(552\) 0 0
\(553\) 5.68802 0.241879
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −12.7453 −0.540036 −0.270018 0.962855i \(-0.587030\pi\)
−0.270018 + 0.962855i \(0.587030\pi\)
\(558\) 0 0
\(559\) 32.5653 1.37737
\(560\) 0 0
\(561\) 7.22538 0.305056
\(562\) 0 0
\(563\) −5.20333 −0.219294 −0.109647 0.993971i \(-0.534972\pi\)
−0.109647 + 0.993971i \(0.534972\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 7.82936 0.328802
\(568\) 0 0
\(569\) −7.37605 −0.309220 −0.154610 0.987976i \(-0.549412\pi\)
−0.154610 + 0.987976i \(0.549412\pi\)
\(570\) 0 0
\(571\) 15.8973 0.665281 0.332641 0.943054i \(-0.392060\pi\)
0.332641 + 0.943054i \(0.392060\pi\)
\(572\) 0 0
\(573\) −3.12268 −0.130452
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −19.9707 −0.831391 −0.415695 0.909504i \(-0.636462\pi\)
−0.415695 + 0.909504i \(0.636462\pi\)
\(578\) 0 0
\(579\) −1.87864 −0.0780736
\(580\) 0 0
\(581\) −4.67531 −0.193964
\(582\) 0 0
\(583\) 38.8480 1.60892
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −13.8060 −0.569834 −0.284917 0.958552i \(-0.591966\pi\)
−0.284917 + 0.958552i \(0.591966\pi\)
\(588\) 0 0
\(589\) −3.67738 −0.151524
\(590\) 0 0
\(591\) 8.68934 0.357432
\(592\) 0 0
\(593\) 20.0666 0.824037 0.412019 0.911175i \(-0.364824\pi\)
0.412019 + 0.911175i \(0.364824\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5.56279 −0.227670
\(598\) 0 0
\(599\) 46.0267 1.88060 0.940299 0.340349i \(-0.110545\pi\)
0.940299 + 0.340349i \(0.110545\pi\)
\(600\) 0 0
\(601\) −1.37605 −0.0561301 −0.0280651 0.999606i \(-0.508935\pi\)
−0.0280651 + 0.999606i \(0.508935\pi\)
\(602\) 0 0
\(603\) 33.6587 1.37069
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 18.7933 0.762796 0.381398 0.924411i \(-0.375443\pi\)
0.381398 + 0.924411i \(0.375443\pi\)
\(608\) 0 0
\(609\) 3.42401 0.138748
\(610\) 0 0
\(611\) 53.0759 2.14722
\(612\) 0 0
\(613\) 24.8480 1.00360 0.501801 0.864983i \(-0.332671\pi\)
0.501801 + 0.864983i \(0.332671\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 43.1680 1.73788 0.868939 0.494919i \(-0.164802\pi\)
0.868939 + 0.494919i \(0.164802\pi\)
\(618\) 0 0
\(619\) 31.9486 1.28412 0.642062 0.766652i \(-0.278079\pi\)
0.642062 + 0.766652i \(0.278079\pi\)
\(620\) 0 0
\(621\) −10.6799 −0.428571
\(622\) 0 0
\(623\) −2.82936 −0.113356
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −1.45331 −0.0580397
\(628\) 0 0
\(629\) 23.2080 0.925362
\(630\) 0 0
\(631\) −8.59465 −0.342148 −0.171074 0.985258i \(-0.554724\pi\)
−0.171074 + 0.985258i \(0.554724\pi\)
\(632\) 0 0
\(633\) −0.377365 −0.0149989
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.64600 −0.184081
\(638\) 0 0
\(639\) −7.82003 −0.309356
\(640\) 0 0
\(641\) 33.2266 1.31237 0.656186 0.754599i \(-0.272169\pi\)
0.656186 + 0.754599i \(0.272169\pi\)
\(642\) 0 0
\(643\) 17.4940 0.689897 0.344948 0.938622i \(-0.387896\pi\)
0.344948 + 0.938622i \(0.387896\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.91595 0.389836 0.194918 0.980820i \(-0.437556\pi\)
0.194918 + 0.980820i \(0.437556\pi\)
\(648\) 0 0
\(649\) 64.3386 2.52551
\(650\) 0 0
\(651\) 1.71733 0.0673074
\(652\) 0 0
\(653\) 14.6240 0.572280 0.286140 0.958188i \(-0.407628\pi\)
0.286140 + 0.958188i \(0.407628\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −14.3667 −0.560499
\(658\) 0 0
\(659\) 20.2534 0.788959 0.394480 0.918905i \(-0.370925\pi\)
0.394480 + 0.918905i \(0.370925\pi\)
\(660\) 0 0
\(661\) −12.4299 −0.483469 −0.241734 0.970342i \(-0.577716\pi\)
−0.241734 + 0.970342i \(0.577716\pi\)
\(662\) 0 0
\(663\) −6.52926 −0.253575
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 47.2080 1.82790
\(668\) 0 0
\(669\) −3.58532 −0.138616
\(670\) 0 0
\(671\) 59.1493 2.28344
\(672\) 0 0
\(673\) −47.6774 −1.83783 −0.918914 0.394458i \(-0.870932\pi\)
−0.918914 + 0.394458i \(0.870932\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.00339 0.230729 0.115364 0.993323i \(-0.463196\pi\)
0.115364 + 0.993323i \(0.463196\pi\)
\(678\) 0 0
\(679\) −1.58532 −0.0608390
\(680\) 0 0
\(681\) −7.86799 −0.301502
\(682\) 0 0
\(683\) −28.5653 −1.09302 −0.546511 0.837452i \(-0.684044\pi\)
−0.546511 + 0.837452i \(0.684044\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.35061 0.280443
\(688\) 0 0
\(689\) −35.1053 −1.33740
\(690\) 0 0
\(691\) 47.8247 1.81934 0.909668 0.415337i \(-0.136336\pi\)
0.909668 + 0.415337i \(0.136336\pi\)
\(692\) 0 0
\(693\) −14.7453 −0.560128
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.90408 −0.147877
\(698\) 0 0
\(699\) −1.98134 −0.0749413
\(700\) 0 0
\(701\) −4.80005 −0.181296 −0.0906478 0.995883i \(-0.528894\pi\)
−0.0906478 + 0.995883i \(0.528894\pi\)
\(702\) 0 0
\(703\) −4.66805 −0.176059
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.06068 −0.340762
\(708\) 0 0
\(709\) 11.7653 0.441855 0.220927 0.975290i \(-0.429092\pi\)
0.220927 + 0.975290i \(0.429092\pi\)
\(710\) 0 0
\(711\) −16.3132 −0.611793
\(712\) 0 0
\(713\) 23.6774 0.886725
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −4.20927 −0.157198
\(718\) 0 0
\(719\) −40.7640 −1.52024 −0.760120 0.649783i \(-0.774860\pi\)
−0.760120 + 0.649783i \(0.774860\pi\)
\(720\) 0 0
\(721\) 5.14134 0.191473
\(722\) 0 0
\(723\) −1.82003 −0.0676877
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 22.1214 0.820436 0.410218 0.911988i \(-0.365453\pi\)
0.410218 + 0.911988i \(0.365453\pi\)
\(728\) 0 0
\(729\) −20.1307 −0.745581
\(730\) 0 0
\(731\) −27.1120 −1.00277
\(732\) 0 0
\(733\) 13.0500 0.482014 0.241007 0.970523i \(-0.422522\pi\)
0.241007 + 0.970523i \(0.422522\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −60.3386 −2.22260
\(738\) 0 0
\(739\) −34.5734 −1.27180 −0.635901 0.771771i \(-0.719371\pi\)
−0.635901 + 0.771771i \(0.719371\pi\)
\(740\) 0 0
\(741\) 1.31330 0.0482451
\(742\) 0 0
\(743\) −3.55602 −0.130458 −0.0652288 0.997870i \(-0.520778\pi\)
−0.0652288 + 0.997870i \(0.520778\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 13.4087 0.490600
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −23.6226 −0.862002 −0.431001 0.902351i \(-0.641839\pi\)
−0.431001 + 0.902351i \(0.641839\pi\)
\(752\) 0 0
\(753\) −8.50937 −0.310099
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 15.1893 0.552064 0.276032 0.961148i \(-0.410980\pi\)
0.276032 + 0.961148i \(0.410980\pi\)
\(758\) 0 0
\(759\) 9.35739 0.339652
\(760\) 0 0
\(761\) 34.4626 1.24927 0.624635 0.780917i \(-0.285248\pi\)
0.624635 + 0.780917i \(0.285248\pi\)
\(762\) 0 0
\(763\) −3.97070 −0.143749
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −58.1400 −2.09931
\(768\) 0 0
\(769\) 40.3854 1.45633 0.728167 0.685400i \(-0.240373\pi\)
0.728167 + 0.685400i \(0.240373\pi\)
\(770\) 0 0
\(771\) 4.72666 0.170226
\(772\) 0 0
\(773\) −10.7674 −0.387275 −0.193638 0.981073i \(-0.562029\pi\)
−0.193638 + 0.981073i \(0.562029\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.17997 0.0782060
\(778\) 0 0
\(779\) 0.785266 0.0281351
\(780\) 0 0
\(781\) 14.0187 0.501627
\(782\) 0 0
\(783\) −20.0921 −0.718031
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −9.19269 −0.327684 −0.163842 0.986487i \(-0.552389\pi\)
−0.163842 + 0.986487i \(0.552389\pi\)
\(788\) 0 0
\(789\) 2.18675 0.0778503
\(790\) 0 0
\(791\) 4.54669 0.161662
\(792\) 0 0
\(793\) −53.4507 −1.89809
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 21.1086 0.747706 0.373853 0.927488i \(-0.378036\pi\)
0.373853 + 0.927488i \(0.378036\pi\)
\(798\) 0 0
\(799\) −44.1880 −1.56326
\(800\) 0 0
\(801\) 8.11458 0.286715
\(802\) 0 0
\(803\) 25.7546 0.908862
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 1.17742 0.0414471
\(808\) 0 0
\(809\) −27.8280 −0.978382 −0.489191 0.872177i \(-0.662708\pi\)
−0.489191 + 0.872177i \(0.662708\pi\)
\(810\) 0 0
\(811\) −11.0607 −0.388393 −0.194197 0.980963i \(-0.562210\pi\)
−0.194197 + 0.980963i \(0.562210\pi\)
\(812\) 0 0
\(813\) −10.5840 −0.371197
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 5.45331 0.190787
\(818\) 0 0
\(819\) 13.3247 0.465603
\(820\) 0 0
\(821\) −17.8867 −0.624248 −0.312124 0.950041i \(-0.601041\pi\)
−0.312124 + 0.950041i \(0.601041\pi\)
\(822\) 0 0
\(823\) 52.8667 1.84282 0.921408 0.388596i \(-0.127040\pi\)
0.921408 + 0.388596i \(0.127040\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 36.3013 1.26232 0.631160 0.775652i \(-0.282579\pi\)
0.631160 + 0.775652i \(0.282579\pi\)
\(828\) 0 0
\(829\) −0.759350 −0.0263733 −0.0131867 0.999913i \(-0.504198\pi\)
−0.0131867 + 0.999913i \(0.504198\pi\)
\(830\) 0 0
\(831\) −1.61462 −0.0560107
\(832\) 0 0
\(833\) 3.86799 0.134018
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −10.0773 −0.348321
\(838\) 0 0
\(839\) −43.3107 −1.49525 −0.747625 0.664121i \(-0.768806\pi\)
−0.747625 + 0.664121i \(0.768806\pi\)
\(840\) 0 0
\(841\) 59.8119 2.06248
\(842\) 0 0
\(843\) −8.97325 −0.309055
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 15.4333 0.530296
\(848\) 0 0
\(849\) 2.81193 0.0965053
\(850\) 0 0
\(851\) 30.0560 1.03031
\(852\) 0 0
\(853\) −40.3713 −1.38229 −0.691144 0.722717i \(-0.742893\pi\)
−0.691144 + 0.722717i \(0.742893\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 13.4720 0.460194 0.230097 0.973168i \(-0.426096\pi\)
0.230097 + 0.973168i \(0.426096\pi\)
\(858\) 0 0
\(859\) −34.7313 −1.18502 −0.592508 0.805565i \(-0.701862\pi\)
−0.592508 + 0.805565i \(0.701862\pi\)
\(860\) 0 0
\(861\) −0.366718 −0.0124977
\(862\) 0 0
\(863\) −14.2454 −0.484918 −0.242459 0.970162i \(-0.577954\pi\)
−0.242459 + 0.970162i \(0.577954\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.740693 −0.0251553
\(868\) 0 0
\(869\) 29.2440 0.992036
\(870\) 0 0
\(871\) 54.5254 1.84752
\(872\) 0 0
\(873\) 4.54669 0.153882
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.7546 0.667067 0.333533 0.942738i \(-0.391759\pi\)
0.333533 + 0.942738i \(0.391759\pi\)
\(878\) 0 0
\(879\) 9.12268 0.307700
\(880\) 0 0
\(881\) −9.53058 −0.321093 −0.160547 0.987028i \(-0.551326\pi\)
−0.160547 + 0.987028i \(0.551326\pi\)
\(882\) 0 0
\(883\) 51.1867 1.72257 0.861284 0.508124i \(-0.169661\pi\)
0.861284 + 0.508124i \(0.169661\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 24.4626 0.821375 0.410688 0.911776i \(-0.365289\pi\)
0.410688 + 0.911776i \(0.365289\pi\)
\(888\) 0 0
\(889\) 16.1214 0.540693
\(890\) 0 0
\(891\) 40.2534 1.34854
\(892\) 0 0
\(893\) 8.88797 0.297425
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −8.45586 −0.282333
\(898\) 0 0
\(899\) 44.5441 1.48563
\(900\) 0 0
\(901\) 29.2266 0.973680
\(902\) 0 0
\(903\) −2.54669 −0.0847484
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −8.09592 −0.268821 −0.134410 0.990926i \(-0.542914\pi\)
−0.134410 + 0.990926i \(0.542914\pi\)
\(908\) 0 0
\(909\) 25.9860 0.861900
\(910\) 0 0
\(911\) −59.5093 −1.97163 −0.985815 0.167834i \(-0.946323\pi\)
−0.985815 + 0.167834i \(0.946323\pi\)
\(912\) 0 0
\(913\) −24.0373 −0.795519
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.0513514 0.00169577
\(918\) 0 0
\(919\) 51.7067 1.70565 0.852823 0.522200i \(-0.174889\pi\)
0.852823 + 0.522200i \(0.174889\pi\)
\(920\) 0 0
\(921\) −12.3239 −0.406085
\(922\) 0 0
\(923\) −12.6680 −0.416974
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −14.7453 −0.484300
\(928\) 0 0
\(929\) −3.76142 −0.123408 −0.0617041 0.998094i \(-0.519654\pi\)
−0.0617041 + 0.998094i \(0.519654\pi\)
\(930\) 0 0
\(931\) −0.778008 −0.0254982
\(932\) 0 0
\(933\) 0.205406 0.00672468
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 21.1014 0.689352 0.344676 0.938722i \(-0.387989\pi\)
0.344676 + 0.938722i \(0.387989\pi\)
\(938\) 0 0
\(939\) −9.93338 −0.324164
\(940\) 0 0
\(941\) −1.72873 −0.0563549 −0.0281775 0.999603i \(-0.508970\pi\)
−0.0281775 + 0.999603i \(0.508970\pi\)
\(942\) 0 0
\(943\) −5.05606 −0.164648
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −24.7267 −0.803508 −0.401754 0.915748i \(-0.631599\pi\)
−0.401754 + 0.915748i \(0.631599\pi\)
\(948\) 0 0
\(949\) −23.2733 −0.755485
\(950\) 0 0
\(951\) 8.25724 0.267759
\(952\) 0 0
\(953\) 1.18930 0.0385251 0.0192626 0.999814i \(-0.493868\pi\)
0.0192626 + 0.999814i \(0.493868\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 17.6040 0.569056
\(958\) 0 0
\(959\) −14.0187 −0.452686
\(960\) 0 0
\(961\) −8.65872 −0.279314
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −23.3293 −0.750220 −0.375110 0.926980i \(-0.622395\pi\)
−0.375110 + 0.926980i \(0.622395\pi\)
\(968\) 0 0
\(969\) −1.09337 −0.0351242
\(970\) 0 0
\(971\) −4.61670 −0.148157 −0.0740784 0.997252i \(-0.523602\pi\)
−0.0740784 + 0.997252i \(0.523602\pi\)
\(972\) 0 0
\(973\) 12.6167 0.404473
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19.1120 −0.611448 −0.305724 0.952120i \(-0.598898\pi\)
−0.305724 + 0.952120i \(0.598898\pi\)
\(978\) 0 0
\(979\) −14.5467 −0.464914
\(980\) 0 0
\(981\) 11.3879 0.363588
\(982\) 0 0
\(983\) −52.6506 −1.67929 −0.839647 0.543132i \(-0.817238\pi\)
−0.839647 + 0.543132i \(0.817238\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −4.15066 −0.132117
\(988\) 0 0
\(989\) −35.1120 −1.11650
\(990\) 0 0
\(991\) 52.4227 1.66526 0.832631 0.553828i \(-0.186834\pi\)
0.832631 + 0.553828i \(0.186834\pi\)
\(992\) 0 0
\(993\) 0.168091 0.00533420
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 19.7580 0.625743 0.312872 0.949795i \(-0.398709\pi\)
0.312872 + 0.949795i \(0.398709\pi\)
\(998\) 0 0
\(999\) −12.7920 −0.404722
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 1400.2.a.s.1.2 3
4.3 odd 2 2800.2.a.br.1.2 3
5.2 odd 4 280.2.g.b.169.3 6
5.3 odd 4 280.2.g.b.169.4 yes 6
5.4 even 2 1400.2.a.t.1.2 3
7.6 odd 2 9800.2.a.cg.1.2 3
15.2 even 4 2520.2.t.g.1009.5 6
15.8 even 4 2520.2.t.g.1009.6 6
20.3 even 4 560.2.g.f.449.3 6
20.7 even 4 560.2.g.f.449.4 6
20.19 odd 2 2800.2.a.bq.1.2 3
35.13 even 4 1960.2.g.c.1569.3 6
35.27 even 4 1960.2.g.c.1569.4 6
35.34 odd 2 9800.2.a.cd.1.2 3
40.3 even 4 2240.2.g.m.449.4 6
40.13 odd 4 2240.2.g.l.449.3 6
40.27 even 4 2240.2.g.m.449.3 6
40.37 odd 4 2240.2.g.l.449.4 6
60.23 odd 4 5040.2.t.y.1009.6 6
60.47 odd 4 5040.2.t.y.1009.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.g.b.169.3 6 5.2 odd 4
280.2.g.b.169.4 yes 6 5.3 odd 4
560.2.g.f.449.3 6 20.3 even 4
560.2.g.f.449.4 6 20.7 even 4
1400.2.a.s.1.2 3 1.1 even 1 trivial
1400.2.a.t.1.2 3 5.4 even 2
1960.2.g.c.1569.3 6 35.13 even 4
1960.2.g.c.1569.4 6 35.27 even 4
2240.2.g.l.449.3 6 40.13 odd 4
2240.2.g.l.449.4 6 40.37 odd 4
2240.2.g.m.449.3 6 40.27 even 4
2240.2.g.m.449.4 6 40.3 even 4
2520.2.t.g.1009.5 6 15.2 even 4
2520.2.t.g.1009.6 6 15.8 even 4
2800.2.a.bq.1.2 3 20.19 odd 2
2800.2.a.br.1.2 3 4.3 odd 2
5040.2.t.y.1009.5 6 60.47 odd 4
5040.2.t.y.1009.6 6 60.23 odd 4
9800.2.a.cd.1.2 3 35.34 odd 2
9800.2.a.cg.1.2 3 7.6 odd 2