Properties

Label 7800.2.a.bz.1.5
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.504568.1
Defining polynomial: \(x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 7 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.28447\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +3.71215 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +3.71215 q^{7} +1.00000 q^{9} +3.31842 q^{11} -1.00000 q^{13} -1.55706 q^{17} -5.33709 q^{19} -3.71215 q^{21} -0.442940 q^{23} -1.00000 q^{27} +2.56894 q^{29} +0.613062 q^{31} -3.31842 q^{33} +0.257322 q^{37} +1.00000 q^{39} -10.6114 q^{41} -12.6935 q^{43} -7.44442 q^{47} +6.78003 q^{49} +1.55706 q^{51} +5.39521 q^{53} +5.33709 q^{57} -13.1358 q^{59} -5.27452 q^{61} +3.71215 q^{63} -10.5384 q^{67} +0.442940 q^{69} +0.311845 q^{71} -9.46841 q^{73} +12.3184 q^{77} +16.1871 q^{79} +1.00000 q^{81} -11.7546 q^{83} -2.56894 q^{87} -4.58762 q^{89} -3.71215 q^{91} -0.613062 q^{93} -10.8500 q^{97} +3.31842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{3} - q^{7} + 5 q^{9} + O(q^{10}) \) \( 5 q - 5 q^{3} - q^{7} + 5 q^{9} + 5 q^{11} - 5 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} - 3 q^{23} - 5 q^{27} + 2 q^{29} - 5 q^{33} - 9 q^{37} + 5 q^{39} - q^{41} - 4 q^{43} - 14 q^{47} + 2 q^{49} + 7 q^{51} - 5 q^{53} - 6 q^{57} + 20 q^{59} - 19 q^{61} - q^{63} - 12 q^{67} + 3 q^{69} + 13 q^{71} - 16 q^{73} - 11 q^{77} + 7 q^{79} + 5 q^{81} + 2 q^{83} - 2 q^{87} + 9 q^{89} + q^{91} - 13 q^{97} + 5 q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.71215 1.40306 0.701530 0.712640i \(-0.252501\pi\)
0.701530 + 0.712640i \(0.252501\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.31842 1.00054 0.500270 0.865869i \(-0.333234\pi\)
0.500270 + 0.865869i \(0.333234\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.55706 −0.377642 −0.188821 0.982011i \(-0.560467\pi\)
−0.188821 + 0.982011i \(0.560467\pi\)
\(18\) 0 0
\(19\) −5.33709 −1.22441 −0.612207 0.790698i \(-0.709718\pi\)
−0.612207 + 0.790698i \(0.709718\pi\)
\(20\) 0 0
\(21\) −3.71215 −0.810057
\(22\) 0 0
\(23\) −0.442940 −0.0923594 −0.0461797 0.998933i \(-0.514705\pi\)
−0.0461797 + 0.998933i \(0.514705\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.56894 0.477041 0.238521 0.971137i \(-0.423338\pi\)
0.238521 + 0.971137i \(0.423338\pi\)
\(30\) 0 0
\(31\) 0.613062 0.110109 0.0550546 0.998483i \(-0.482467\pi\)
0.0550546 + 0.998483i \(0.482467\pi\)
\(32\) 0 0
\(33\) −3.31842 −0.577662
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.257322 0.0423034 0.0211517 0.999776i \(-0.493267\pi\)
0.0211517 + 0.999776i \(0.493267\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −10.6114 −1.65722 −0.828611 0.559826i \(-0.810868\pi\)
−0.828611 + 0.559826i \(0.810868\pi\)
\(42\) 0 0
\(43\) −12.6935 −1.93574 −0.967870 0.251450i \(-0.919093\pi\)
−0.967870 + 0.251450i \(0.919093\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.44442 −1.08588 −0.542940 0.839771i \(-0.682689\pi\)
−0.542940 + 0.839771i \(0.682689\pi\)
\(48\) 0 0
\(49\) 6.78003 0.968576
\(50\) 0 0
\(51\) 1.55706 0.218032
\(52\) 0 0
\(53\) 5.39521 0.741089 0.370545 0.928815i \(-0.379171\pi\)
0.370545 + 0.928815i \(0.379171\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 5.33709 0.706915
\(58\) 0 0
\(59\) −13.1358 −1.71014 −0.855068 0.518516i \(-0.826485\pi\)
−0.855068 + 0.518516i \(0.826485\pi\)
\(60\) 0 0
\(61\) −5.27452 −0.675333 −0.337667 0.941266i \(-0.609638\pi\)
−0.337667 + 0.941266i \(0.609638\pi\)
\(62\) 0 0
\(63\) 3.71215 0.467687
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −10.5384 −1.28747 −0.643736 0.765248i \(-0.722617\pi\)
−0.643736 + 0.765248i \(0.722617\pi\)
\(68\) 0 0
\(69\) 0.442940 0.0533237
\(70\) 0 0
\(71\) 0.311845 0.0370092 0.0185046 0.999829i \(-0.494109\pi\)
0.0185046 + 0.999829i \(0.494109\pi\)
\(72\) 0 0
\(73\) −9.46841 −1.10819 −0.554097 0.832452i \(-0.686936\pi\)
−0.554097 + 0.832452i \(0.686936\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 12.3184 1.40382
\(78\) 0 0
\(79\) 16.1871 1.82119 0.910597 0.413295i \(-0.135622\pi\)
0.910597 + 0.413295i \(0.135622\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.7546 −1.29023 −0.645117 0.764084i \(-0.723191\pi\)
−0.645117 + 0.764084i \(0.723191\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.56894 −0.275420
\(88\) 0 0
\(89\) −4.58762 −0.486287 −0.243144 0.969990i \(-0.578179\pi\)
−0.243144 + 0.969990i \(0.578179\pi\)
\(90\) 0 0
\(91\) −3.71215 −0.389139
\(92\) 0 0
\(93\) −0.613062 −0.0635716
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.8500 −1.10165 −0.550827 0.834619i \(-0.685688\pi\)
−0.550827 + 0.834619i \(0.685688\pi\)
\(98\) 0 0
\(99\) 3.31842 0.333513
\(100\) 0 0
\(101\) 1.68306 0.167471 0.0837356 0.996488i \(-0.473315\pi\)
0.0837356 + 0.996488i \(0.473315\pi\)
\(102\) 0 0
\(103\) −1.78535 −0.175916 −0.0879578 0.996124i \(-0.528034\pi\)
−0.0879578 + 0.996124i \(0.528034\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.11943 −0.108220 −0.0541098 0.998535i \(-0.517232\pi\)
−0.0541098 + 0.998535i \(0.517232\pi\)
\(108\) 0 0
\(109\) −0.914914 −0.0876329 −0.0438164 0.999040i \(-0.513952\pi\)
−0.0438164 + 0.999040i \(0.513952\pi\)
\(110\) 0 0
\(111\) −0.257322 −0.0244239
\(112\) 0 0
\(113\) −2.41386 −0.227077 −0.113538 0.993534i \(-0.536218\pi\)
−0.113538 + 0.993534i \(0.536218\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −5.78003 −0.529855
\(120\) 0 0
\(121\) 0.0118848 0.00108043
\(122\) 0 0
\(123\) 10.6114 0.956797
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 14.0418 1.24601 0.623005 0.782218i \(-0.285912\pi\)
0.623005 + 0.782218i \(0.285912\pi\)
\(128\) 0 0
\(129\) 12.6935 1.11760
\(130\) 0 0
\(131\) 13.7650 1.20265 0.601327 0.799003i \(-0.294639\pi\)
0.601327 + 0.799003i \(0.294639\pi\)
\(132\) 0 0
\(133\) −19.8121 −1.71792
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.50470 0.555734 0.277867 0.960620i \(-0.410373\pi\)
0.277867 + 0.960620i \(0.410373\pi\)
\(138\) 0 0
\(139\) 9.78003 0.829532 0.414766 0.909928i \(-0.363863\pi\)
0.414766 + 0.909928i \(0.363863\pi\)
\(140\) 0 0
\(141\) 7.44442 0.626933
\(142\) 0 0
\(143\) −3.31842 −0.277500
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.78003 −0.559208
\(148\) 0 0
\(149\) −5.93148 −0.485926 −0.242963 0.970036i \(-0.578119\pi\)
−0.242963 + 0.970036i \(0.578119\pi\)
\(150\) 0 0
\(151\) −0.272818 −0.0222016 −0.0111008 0.999938i \(-0.503534\pi\)
−0.0111008 + 0.999938i \(0.503534\pi\)
\(152\) 0 0
\(153\) −1.55706 −0.125881
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.6561 −1.16969 −0.584844 0.811146i \(-0.698844\pi\)
−0.584844 + 0.811146i \(0.698844\pi\)
\(158\) 0 0
\(159\) −5.39521 −0.427868
\(160\) 0 0
\(161\) −1.64426 −0.129586
\(162\) 0 0
\(163\) 3.48345 0.272845 0.136422 0.990651i \(-0.456440\pi\)
0.136422 + 0.990651i \(0.456440\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.69135 −0.363028 −0.181514 0.983388i \(-0.558100\pi\)
−0.181514 + 0.983388i \(0.558100\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −5.33709 −0.408138
\(172\) 0 0
\(173\) −3.26475 −0.248214 −0.124107 0.992269i \(-0.539607\pi\)
−0.124107 + 0.992269i \(0.539607\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 13.1358 0.987348
\(178\) 0 0
\(179\) 19.7204 1.47397 0.736987 0.675907i \(-0.236248\pi\)
0.736987 + 0.675907i \(0.236248\pi\)
\(180\) 0 0
\(181\) −22.0558 −1.63940 −0.819698 0.572796i \(-0.805859\pi\)
−0.819698 + 0.572796i \(0.805859\pi\)
\(182\) 0 0
\(183\) 5.27452 0.389904
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.16697 −0.377846
\(188\) 0 0
\(189\) −3.71215 −0.270019
\(190\) 0 0
\(191\) 22.2729 1.61161 0.805805 0.592182i \(-0.201733\pi\)
0.805805 + 0.592182i \(0.201733\pi\)
\(192\) 0 0
\(193\) 15.7733 1.13539 0.567693 0.823241i \(-0.307836\pi\)
0.567693 + 0.823241i \(0.307836\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.72871 0.194413 0.0972063 0.995264i \(-0.469009\pi\)
0.0972063 + 0.995264i \(0.469009\pi\)
\(198\) 0 0
\(199\) −22.1029 −1.56684 −0.783418 0.621495i \(-0.786526\pi\)
−0.783418 + 0.621495i \(0.786526\pi\)
\(200\) 0 0
\(201\) 10.5384 0.743322
\(202\) 0 0
\(203\) 9.53630 0.669317
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.442940 −0.0307865
\(208\) 0 0
\(209\) −17.7107 −1.22507
\(210\) 0 0
\(211\) 1.01720 0.0700268 0.0350134 0.999387i \(-0.488853\pi\)
0.0350134 + 0.999387i \(0.488853\pi\)
\(212\) 0 0
\(213\) −0.311845 −0.0213672
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.27578 0.154490
\(218\) 0 0
\(219\) 9.46841 0.639816
\(220\) 0 0
\(221\) 1.55706 0.104739
\(222\) 0 0
\(223\) 6.85535 0.459068 0.229534 0.973301i \(-0.426280\pi\)
0.229534 + 0.973301i \(0.426280\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.88224 −0.191301 −0.0956504 0.995415i \(-0.530493\pi\)
−0.0956504 + 0.995415i \(0.530493\pi\)
\(228\) 0 0
\(229\) 14.1857 0.937416 0.468708 0.883353i \(-0.344720\pi\)
0.468708 + 0.883353i \(0.344720\pi\)
\(230\) 0 0
\(231\) −12.3184 −0.810494
\(232\) 0 0
\(233\) −0.429354 −0.0281279 −0.0140639 0.999901i \(-0.504477\pi\)
−0.0140639 + 0.999901i \(0.504477\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −16.1871 −1.05147
\(238\) 0 0
\(239\) 19.7255 1.27594 0.637969 0.770062i \(-0.279775\pi\)
0.637969 + 0.770062i \(0.279775\pi\)
\(240\) 0 0
\(241\) 19.6598 1.26640 0.633200 0.773988i \(-0.281741\pi\)
0.633200 + 0.773988i \(0.281741\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.33709 0.339591
\(248\) 0 0
\(249\) 11.7546 0.744917
\(250\) 0 0
\(251\) 23.4175 1.47810 0.739051 0.673650i \(-0.235274\pi\)
0.739051 + 0.673650i \(0.235274\pi\)
\(252\) 0 0
\(253\) −1.46986 −0.0924093
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −30.7987 −1.92117 −0.960586 0.277981i \(-0.910335\pi\)
−0.960586 + 0.277981i \(0.910335\pi\)
\(258\) 0 0
\(259\) 0.955216 0.0593543
\(260\) 0 0
\(261\) 2.56894 0.159014
\(262\) 0 0
\(263\) 24.1471 1.48897 0.744486 0.667638i \(-0.232695\pi\)
0.744486 + 0.667638i \(0.232695\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 4.58762 0.280758
\(268\) 0 0
\(269\) 12.7557 0.777726 0.388863 0.921295i \(-0.372868\pi\)
0.388863 + 0.921295i \(0.372868\pi\)
\(270\) 0 0
\(271\) −10.4222 −0.633102 −0.316551 0.948575i \(-0.602525\pi\)
−0.316551 + 0.948575i \(0.602525\pi\)
\(272\) 0 0
\(273\) 3.71215 0.224669
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −19.9404 −1.19810 −0.599052 0.800710i \(-0.704456\pi\)
−0.599052 + 0.800710i \(0.704456\pi\)
\(278\) 0 0
\(279\) 0.613062 0.0367031
\(280\) 0 0
\(281\) 28.5272 1.70179 0.850895 0.525336i \(-0.176060\pi\)
0.850895 + 0.525336i \(0.176060\pi\)
\(282\) 0 0
\(283\) −19.1888 −1.14066 −0.570329 0.821416i \(-0.693184\pi\)
−0.570329 + 0.821416i \(0.693184\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −39.3910 −2.32518
\(288\) 0 0
\(289\) −14.5756 −0.857386
\(290\) 0 0
\(291\) 10.8500 0.636040
\(292\) 0 0
\(293\) 11.9828 0.700045 0.350022 0.936741i \(-0.386174\pi\)
0.350022 + 0.936741i \(0.386174\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.31842 −0.192554
\(298\) 0 0
\(299\) 0.442940 0.0256159
\(300\) 0 0
\(301\) −47.1201 −2.71596
\(302\) 0 0
\(303\) −1.68306 −0.0966895
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −25.0299 −1.42853 −0.714267 0.699874i \(-0.753240\pi\)
−0.714267 + 0.699874i \(0.753240\pi\)
\(308\) 0 0
\(309\) 1.78535 0.101565
\(310\) 0 0
\(311\) 27.6360 1.56710 0.783548 0.621331i \(-0.213408\pi\)
0.783548 + 0.621331i \(0.213408\pi\)
\(312\) 0 0
\(313\) −14.5441 −0.822083 −0.411042 0.911617i \(-0.634835\pi\)
−0.411042 + 0.911617i \(0.634835\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.00364 −0.449529 −0.224765 0.974413i \(-0.572161\pi\)
−0.224765 + 0.974413i \(0.572161\pi\)
\(318\) 0 0
\(319\) 8.52483 0.477299
\(320\) 0 0
\(321\) 1.11943 0.0624806
\(322\) 0 0
\(323\) 8.31017 0.462390
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.914914 0.0505949
\(328\) 0 0
\(329\) −27.6348 −1.52355
\(330\) 0 0
\(331\) 5.59929 0.307765 0.153882 0.988089i \(-0.450822\pi\)
0.153882 + 0.988089i \(0.450822\pi\)
\(332\) 0 0
\(333\) 0.257322 0.0141011
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −34.5802 −1.88370 −0.941852 0.336027i \(-0.890917\pi\)
−0.941852 + 0.336027i \(0.890917\pi\)
\(338\) 0 0
\(339\) 2.41386 0.131103
\(340\) 0 0
\(341\) 2.03440 0.110169
\(342\) 0 0
\(343\) −0.816545 −0.0440893
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −31.0537 −1.66705 −0.833525 0.552482i \(-0.813681\pi\)
−0.833525 + 0.552482i \(0.813681\pi\)
\(348\) 0 0
\(349\) 2.94804 0.157805 0.0789026 0.996882i \(-0.474858\pi\)
0.0789026 + 0.996882i \(0.474858\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) −1.80547 −0.0960957 −0.0480478 0.998845i \(-0.515300\pi\)
−0.0480478 + 0.998845i \(0.515300\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 5.78003 0.305912
\(358\) 0 0
\(359\) −9.29216 −0.490422 −0.245211 0.969470i \(-0.578857\pi\)
−0.245211 + 0.969470i \(0.578857\pi\)
\(360\) 0 0
\(361\) 9.48457 0.499188
\(362\) 0 0
\(363\) −0.0118848 −0.000623788 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 18.0955 0.944579 0.472289 0.881444i \(-0.343428\pi\)
0.472289 + 0.881444i \(0.343428\pi\)
\(368\) 0 0
\(369\) −10.6114 −0.552407
\(370\) 0 0
\(371\) 20.0278 1.03979
\(372\) 0 0
\(373\) 29.4689 1.52584 0.762922 0.646491i \(-0.223764\pi\)
0.762922 + 0.646491i \(0.223764\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.56894 −0.132307
\(378\) 0 0
\(379\) −21.2489 −1.09148 −0.545740 0.837954i \(-0.683751\pi\)
−0.545740 + 0.837954i \(0.683751\pi\)
\(380\) 0 0
\(381\) −14.0418 −0.719384
\(382\) 0 0
\(383\) 8.19163 0.418573 0.209286 0.977854i \(-0.432886\pi\)
0.209286 + 0.977854i \(0.432886\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.6935 −0.645247
\(388\) 0 0
\(389\) −24.4557 −1.23995 −0.619976 0.784621i \(-0.712858\pi\)
−0.619976 + 0.784621i \(0.712858\pi\)
\(390\) 0 0
\(391\) 0.689684 0.0348788
\(392\) 0 0
\(393\) −13.7650 −0.694352
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −34.4916 −1.73108 −0.865541 0.500837i \(-0.833025\pi\)
−0.865541 + 0.500837i \(0.833025\pi\)
\(398\) 0 0
\(399\) 19.8121 0.991844
\(400\) 0 0
\(401\) −16.9434 −0.846114 −0.423057 0.906103i \(-0.639043\pi\)
−0.423057 + 0.906103i \(0.639043\pi\)
\(402\) 0 0
\(403\) −0.613062 −0.0305388
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.853901 0.0423263
\(408\) 0 0
\(409\) −3.05299 −0.150961 −0.0754804 0.997147i \(-0.524049\pi\)
−0.0754804 + 0.997147i \(0.524049\pi\)
\(410\) 0 0
\(411\) −6.50470 −0.320853
\(412\) 0 0
\(413\) −48.7620 −2.39942
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −9.78003 −0.478930
\(418\) 0 0
\(419\) 20.9567 1.02380 0.511902 0.859044i \(-0.328941\pi\)
0.511902 + 0.859044i \(0.328941\pi\)
\(420\) 0 0
\(421\) −37.4462 −1.82502 −0.912508 0.409059i \(-0.865857\pi\)
−0.912508 + 0.409059i \(0.865857\pi\)
\(422\) 0 0
\(423\) −7.44442 −0.361960
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −19.5798 −0.947533
\(428\) 0 0
\(429\) 3.31842 0.160215
\(430\) 0 0
\(431\) −27.2671 −1.31341 −0.656706 0.754147i \(-0.728051\pi\)
−0.656706 + 0.754147i \(0.728051\pi\)
\(432\) 0 0
\(433\) −12.5679 −0.603975 −0.301988 0.953312i \(-0.597650\pi\)
−0.301988 + 0.953312i \(0.597650\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.36401 0.113086
\(438\) 0 0
\(439\) 14.7241 0.702742 0.351371 0.936236i \(-0.385716\pi\)
0.351371 + 0.936236i \(0.385716\pi\)
\(440\) 0 0
\(441\) 6.78003 0.322859
\(442\) 0 0
\(443\) −8.65996 −0.411447 −0.205724 0.978610i \(-0.565955\pi\)
−0.205724 + 0.978610i \(0.565955\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 5.93148 0.280549
\(448\) 0 0
\(449\) −21.5690 −1.01791 −0.508953 0.860795i \(-0.669967\pi\)
−0.508953 + 0.860795i \(0.669967\pi\)
\(450\) 0 0
\(451\) −35.2130 −1.65812
\(452\) 0 0
\(453\) 0.272818 0.0128181
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.192394 0.00899982 0.00449991 0.999990i \(-0.498568\pi\)
0.00449991 + 0.999990i \(0.498568\pi\)
\(458\) 0 0
\(459\) 1.55706 0.0726773
\(460\) 0 0
\(461\) −12.0821 −0.562720 −0.281360 0.959602i \(-0.590785\pi\)
−0.281360 + 0.959602i \(0.590785\pi\)
\(462\) 0 0
\(463\) −25.7245 −1.19552 −0.597759 0.801676i \(-0.703942\pi\)
−0.597759 + 0.801676i \(0.703942\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.4317 −0.852918 −0.426459 0.904507i \(-0.640239\pi\)
−0.426459 + 0.904507i \(0.640239\pi\)
\(468\) 0 0
\(469\) −39.1201 −1.80640
\(470\) 0 0
\(471\) 14.6561 0.675319
\(472\) 0 0
\(473\) −42.1223 −1.93679
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.39521 0.247030
\(478\) 0 0
\(479\) 25.5826 1.16890 0.584450 0.811430i \(-0.301310\pi\)
0.584450 + 0.811430i \(0.301310\pi\)
\(480\) 0 0
\(481\) −0.257322 −0.0117329
\(482\) 0 0
\(483\) 1.64426 0.0748164
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 30.1997 1.36848 0.684239 0.729258i \(-0.260134\pi\)
0.684239 + 0.729258i \(0.260134\pi\)
\(488\) 0 0
\(489\) −3.48345 −0.157527
\(490\) 0 0
\(491\) −10.7256 −0.484039 −0.242020 0.970271i \(-0.577810\pi\)
−0.242020 + 0.970271i \(0.577810\pi\)
\(492\) 0 0
\(493\) −4.00000 −0.180151
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.15761 0.0519260
\(498\) 0 0
\(499\) 7.01044 0.313830 0.156915 0.987612i \(-0.449845\pi\)
0.156915 + 0.987612i \(0.449845\pi\)
\(500\) 0 0
\(501\) 4.69135 0.209594
\(502\) 0 0
\(503\) 32.2604 1.43842 0.719210 0.694793i \(-0.244504\pi\)
0.719210 + 0.694793i \(0.244504\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 17.3631 0.769604 0.384802 0.922999i \(-0.374270\pi\)
0.384802 + 0.922999i \(0.374270\pi\)
\(510\) 0 0
\(511\) −35.1481 −1.55486
\(512\) 0 0
\(513\) 5.33709 0.235638
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −24.7037 −1.08647
\(518\) 0 0
\(519\) 3.26475 0.143307
\(520\) 0 0
\(521\) 27.6513 1.21142 0.605712 0.795684i \(-0.292888\pi\)
0.605712 + 0.795684i \(0.292888\pi\)
\(522\) 0 0
\(523\) 7.49745 0.327840 0.163920 0.986474i \(-0.447586\pi\)
0.163920 + 0.986474i \(0.447586\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.954575 −0.0415819
\(528\) 0 0
\(529\) −22.8038 −0.991470
\(530\) 0 0
\(531\) −13.1358 −0.570045
\(532\) 0 0
\(533\) 10.6114 0.459630
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −19.7204 −0.850999
\(538\) 0 0
\(539\) 22.4990 0.969099
\(540\) 0 0
\(541\) 18.8836 0.811871 0.405936 0.913902i \(-0.366946\pi\)
0.405936 + 0.913902i \(0.366946\pi\)
\(542\) 0 0
\(543\) 22.0558 0.946506
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 21.3808 0.914178 0.457089 0.889421i \(-0.348892\pi\)
0.457089 + 0.889421i \(0.348892\pi\)
\(548\) 0 0
\(549\) −5.27452 −0.225111
\(550\) 0 0
\(551\) −13.7107 −0.584095
\(552\) 0 0
\(553\) 60.0890 2.55524
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.80681 −0.161300 −0.0806498 0.996743i \(-0.525700\pi\)
−0.0806498 + 0.996743i \(0.525700\pi\)
\(558\) 0 0
\(559\) 12.6935 0.536878
\(560\) 0 0
\(561\) 5.16697 0.218150
\(562\) 0 0
\(563\) −29.3983 −1.23899 −0.619495 0.785001i \(-0.712662\pi\)
−0.619495 + 0.785001i \(0.712662\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.71215 0.155896
\(568\) 0 0
\(569\) 12.4014 0.519892 0.259946 0.965623i \(-0.416295\pi\)
0.259946 + 0.965623i \(0.416295\pi\)
\(570\) 0 0
\(571\) −4.56899 −0.191206 −0.0956032 0.995420i \(-0.530478\pi\)
−0.0956032 + 0.995420i \(0.530478\pi\)
\(572\) 0 0
\(573\) −22.2729 −0.930463
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −27.4496 −1.14274 −0.571370 0.820692i \(-0.693588\pi\)
−0.571370 + 0.820692i \(0.693588\pi\)
\(578\) 0 0
\(579\) −15.7733 −0.655515
\(580\) 0 0
\(581\) −43.6348 −1.81028
\(582\) 0 0
\(583\) 17.9036 0.741489
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.5191 0.805641 0.402820 0.915279i \(-0.368030\pi\)
0.402820 + 0.915279i \(0.368030\pi\)
\(588\) 0 0
\(589\) −3.27197 −0.134819
\(590\) 0 0
\(591\) −2.72871 −0.112244
\(592\) 0 0
\(593\) 14.8539 0.609975 0.304987 0.952356i \(-0.401348\pi\)
0.304987 + 0.952356i \(0.401348\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 22.1029 0.904613
\(598\) 0 0
\(599\) −42.6098 −1.74099 −0.870494 0.492178i \(-0.836201\pi\)
−0.870494 + 0.492178i \(0.836201\pi\)
\(600\) 0 0
\(601\) 34.4960 1.40712 0.703561 0.710635i \(-0.251592\pi\)
0.703561 + 0.710635i \(0.251592\pi\)
\(602\) 0 0
\(603\) −10.5384 −0.429157
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 44.0061 1.78615 0.893076 0.449906i \(-0.148543\pi\)
0.893076 + 0.449906i \(0.148543\pi\)
\(608\) 0 0
\(609\) −9.53630 −0.386430
\(610\) 0 0
\(611\) 7.44442 0.301169
\(612\) 0 0
\(613\) −11.4907 −0.464104 −0.232052 0.972703i \(-0.574544\pi\)
−0.232052 + 0.972703i \(0.574544\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 47.2506 1.90224 0.951120 0.308823i \(-0.0999350\pi\)
0.951120 + 0.308823i \(0.0999350\pi\)
\(618\) 0 0
\(619\) 25.5964 1.02881 0.514403 0.857549i \(-0.328014\pi\)
0.514403 + 0.857549i \(0.328014\pi\)
\(620\) 0 0
\(621\) 0.442940 0.0177746
\(622\) 0 0
\(623\) −17.0299 −0.682290
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 17.7107 0.707297
\(628\) 0 0
\(629\) −0.400665 −0.0159756
\(630\) 0 0
\(631\) 6.54777 0.260663 0.130331 0.991470i \(-0.458396\pi\)
0.130331 + 0.991470i \(0.458396\pi\)
\(632\) 0 0
\(633\) −1.01720 −0.0404300
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.78003 −0.268635
\(638\) 0 0
\(639\) 0.311845 0.0123364
\(640\) 0 0
\(641\) −0.899023 −0.0355093 −0.0177546 0.999842i \(-0.505652\pi\)
−0.0177546 + 0.999842i \(0.505652\pi\)
\(642\) 0 0
\(643\) 2.48862 0.0981416 0.0490708 0.998795i \(-0.484374\pi\)
0.0490708 + 0.998795i \(0.484374\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.773002 0.0303898 0.0151949 0.999885i \(-0.495163\pi\)
0.0151949 + 0.999885i \(0.495163\pi\)
\(648\) 0 0
\(649\) −43.5901 −1.71106
\(650\) 0 0
\(651\) −2.27578 −0.0891948
\(652\) 0 0
\(653\) 43.1740 1.68953 0.844764 0.535139i \(-0.179741\pi\)
0.844764 + 0.535139i \(0.179741\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −9.46841 −0.369398
\(658\) 0 0
\(659\) −39.3552 −1.53306 −0.766530 0.642208i \(-0.778019\pi\)
−0.766530 + 0.642208i \(0.778019\pi\)
\(660\) 0 0
\(661\) −20.7673 −0.807756 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(662\) 0 0
\(663\) −1.55706 −0.0604712
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.13789 −0.0440592
\(668\) 0 0
\(669\) −6.85535 −0.265043
\(670\) 0 0
\(671\) −17.5031 −0.675698
\(672\) 0 0
\(673\) 49.6479 1.91379 0.956893 0.290439i \(-0.0938014\pi\)
0.956893 + 0.290439i \(0.0938014\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.5884 1.17561 0.587803 0.809004i \(-0.299993\pi\)
0.587803 + 0.809004i \(0.299993\pi\)
\(678\) 0 0
\(679\) −40.2769 −1.54569
\(680\) 0 0
\(681\) 2.88224 0.110448
\(682\) 0 0
\(683\) −28.9405 −1.10738 −0.553688 0.832724i \(-0.686780\pi\)
−0.553688 + 0.832724i \(0.686780\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −14.1857 −0.541218
\(688\) 0 0
\(689\) −5.39521 −0.205541
\(690\) 0 0
\(691\) −31.9739 −1.21635 −0.608173 0.793805i \(-0.708097\pi\)
−0.608173 + 0.793805i \(0.708097\pi\)
\(692\) 0 0
\(693\) 12.3184 0.467939
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 16.5226 0.625837
\(698\) 0 0
\(699\) 0.429354 0.0162396
\(700\) 0 0
\(701\) 4.51673 0.170595 0.0852973 0.996356i \(-0.472816\pi\)
0.0852973 + 0.996356i \(0.472816\pi\)
\(702\) 0 0
\(703\) −1.37335 −0.0517969
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.24778 0.234972
\(708\) 0 0
\(709\) −29.7979 −1.11908 −0.559542 0.828802i \(-0.689023\pi\)
−0.559542 + 0.828802i \(0.689023\pi\)
\(710\) 0 0
\(711\) 16.1871 0.607065
\(712\) 0 0
\(713\) −0.271550 −0.0101696
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −19.7255 −0.736663
\(718\) 0 0
\(719\) 41.8431 1.56049 0.780243 0.625477i \(-0.215096\pi\)
0.780243 + 0.625477i \(0.215096\pi\)
\(720\) 0 0
\(721\) −6.62747 −0.246820
\(722\) 0 0
\(723\) −19.6598 −0.731157
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −15.4317 −0.572330 −0.286165 0.958180i \(-0.592381\pi\)
−0.286165 + 0.958180i \(0.592381\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 19.7645 0.731018
\(732\) 0 0
\(733\) −39.1794 −1.44712 −0.723561 0.690260i \(-0.757496\pi\)
−0.723561 + 0.690260i \(0.757496\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −34.9708 −1.28817
\(738\) 0 0
\(739\) 32.5361 1.19686 0.598430 0.801175i \(-0.295791\pi\)
0.598430 + 0.801175i \(0.295791\pi\)
\(740\) 0 0
\(741\) −5.33709 −0.196063
\(742\) 0 0
\(743\) −8.13346 −0.298388 −0.149194 0.988808i \(-0.547668\pi\)
−0.149194 + 0.988808i \(0.547668\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −11.7546 −0.430078
\(748\) 0 0
\(749\) −4.15550 −0.151839
\(750\) 0 0
\(751\) −48.9359 −1.78570 −0.892848 0.450358i \(-0.851296\pi\)
−0.892848 + 0.450358i \(0.851296\pi\)
\(752\) 0 0
\(753\) −23.4175 −0.853382
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3.54775 0.128945 0.0644726 0.997919i \(-0.479463\pi\)
0.0644726 + 0.997919i \(0.479463\pi\)
\(758\) 0 0
\(759\) 1.46986 0.0533525
\(760\) 0 0
\(761\) 40.8645 1.48134 0.740669 0.671870i \(-0.234509\pi\)
0.740669 + 0.671870i \(0.234509\pi\)
\(762\) 0 0
\(763\) −3.39630 −0.122954
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13.1358 0.474306
\(768\) 0 0
\(769\) −42.6263 −1.53714 −0.768571 0.639764i \(-0.779032\pi\)
−0.768571 + 0.639764i \(0.779032\pi\)
\(770\) 0 0
\(771\) 30.7987 1.10919
\(772\) 0 0
\(773\) −36.3873 −1.30876 −0.654379 0.756166i \(-0.727070\pi\)
−0.654379 + 0.756166i \(0.727070\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −0.955216 −0.0342682
\(778\) 0 0
\(779\) 56.6340 2.02912
\(780\) 0 0
\(781\) 1.03483 0.0370291
\(782\) 0 0
\(783\) −2.56894 −0.0918066
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −12.7280 −0.453705 −0.226853 0.973929i \(-0.572844\pi\)
−0.226853 + 0.973929i \(0.572844\pi\)
\(788\) 0 0
\(789\) −24.1471 −0.859658
\(790\) 0 0
\(791\) −8.96059 −0.318602
\(792\) 0 0
\(793\) 5.27452 0.187304
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20.3707 −0.721566 −0.360783 0.932650i \(-0.617490\pi\)
−0.360783 + 0.932650i \(0.617490\pi\)
\(798\) 0 0
\(799\) 11.5914 0.410074
\(800\) 0 0
\(801\) −4.58762 −0.162096
\(802\) 0 0
\(803\) −31.4201 −1.10879
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −12.7557 −0.449021
\(808\) 0 0
\(809\) −36.4656 −1.28206 −0.641030 0.767516i \(-0.721493\pi\)
−0.641030 + 0.767516i \(0.721493\pi\)
\(810\) 0 0
\(811\) 32.4823 1.14061 0.570304 0.821433i \(-0.306825\pi\)
0.570304 + 0.821433i \(0.306825\pi\)
\(812\) 0 0
\(813\) 10.4222 0.365522
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 67.7464 2.37015
\(818\) 0 0
\(819\) −3.71215 −0.129713
\(820\) 0 0
\(821\) 15.7750 0.550550 0.275275 0.961366i \(-0.411231\pi\)
0.275275 + 0.961366i \(0.411231\pi\)
\(822\) 0 0
\(823\) −33.4570 −1.16624 −0.583120 0.812386i \(-0.698168\pi\)
−0.583120 + 0.812386i \(0.698168\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −30.0516 −1.04500 −0.522499 0.852640i \(-0.675000\pi\)
−0.522499 + 0.852640i \(0.675000\pi\)
\(828\) 0 0
\(829\) 3.52850 0.122550 0.0612750 0.998121i \(-0.480483\pi\)
0.0612750 + 0.998121i \(0.480483\pi\)
\(830\) 0 0
\(831\) 19.9404 0.691726
\(832\) 0 0
\(833\) −10.5569 −0.365776
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −0.613062 −0.0211905
\(838\) 0 0
\(839\) 7.19133 0.248272 0.124136 0.992265i \(-0.460384\pi\)
0.124136 + 0.992265i \(0.460384\pi\)
\(840\) 0 0
\(841\) −22.4005 −0.772432
\(842\) 0 0
\(843\) −28.5272 −0.982529
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.0441180 0.00151591
\(848\) 0 0
\(849\) 19.1888 0.658559
\(850\) 0 0
\(851\) −0.113978 −0.00390712
\(852\) 0 0
\(853\) −16.1780 −0.553924 −0.276962 0.960881i \(-0.589328\pi\)
−0.276962 + 0.960881i \(0.589328\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.79125 −0.0611881 −0.0305940 0.999532i \(-0.509740\pi\)
−0.0305940 + 0.999532i \(0.509740\pi\)
\(858\) 0 0
\(859\) 17.7341 0.605078 0.302539 0.953137i \(-0.402166\pi\)
0.302539 + 0.953137i \(0.402166\pi\)
\(860\) 0 0
\(861\) 39.3910 1.34244
\(862\) 0 0
\(863\) 2.45249 0.0834837 0.0417419 0.999128i \(-0.486709\pi\)
0.0417419 + 0.999128i \(0.486709\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 14.5756 0.495012
\(868\) 0 0
\(869\) 53.7156 1.82218
\(870\) 0 0
\(871\) 10.5384 0.357081
\(872\) 0 0
\(873\) −10.8500 −0.367218
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 48.8367 1.64910 0.824549 0.565791i \(-0.191429\pi\)
0.824549 + 0.565791i \(0.191429\pi\)
\(878\) 0 0
\(879\) −11.9828 −0.404171
\(880\) 0 0
\(881\) 6.25328 0.210678 0.105339 0.994436i \(-0.466407\pi\)
0.105339 + 0.994436i \(0.466407\pi\)
\(882\) 0 0
\(883\) 25.0964 0.844560 0.422280 0.906465i \(-0.361230\pi\)
0.422280 + 0.906465i \(0.361230\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.57354 0.0528344 0.0264172 0.999651i \(-0.491590\pi\)
0.0264172 + 0.999651i \(0.491590\pi\)
\(888\) 0 0
\(889\) 52.1253 1.74823
\(890\) 0 0
\(891\) 3.31842 0.111171
\(892\) 0 0
\(893\) 39.7316 1.32957
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.442940 −0.0147893
\(898\) 0 0
\(899\) 1.57492 0.0525266
\(900\) 0 0
\(901\) −8.40067 −0.279867
\(902\) 0 0
\(903\) 47.1201 1.56806
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 20.6504 0.685686 0.342843 0.939393i \(-0.388610\pi\)
0.342843 + 0.939393i \(0.388610\pi\)
\(908\) 0 0
\(909\) 1.68306 0.0558237
\(910\) 0 0
\(911\) 39.4108 1.30574 0.652869 0.757471i \(-0.273565\pi\)
0.652869 + 0.757471i \(0.273565\pi\)
\(912\) 0 0
\(913\) −39.0066 −1.29093
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 51.0977 1.68739
\(918\) 0 0
\(919\) −7.84896 −0.258913 −0.129457 0.991585i \(-0.541323\pi\)
−0.129457 + 0.991585i \(0.541323\pi\)
\(920\) 0 0
\(921\) 25.0299 0.824764
\(922\) 0 0
\(923\) −0.311845 −0.0102645
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −1.78535 −0.0586385
\(928\) 0 0
\(929\) −29.2279 −0.958935 −0.479467 0.877560i \(-0.659170\pi\)
−0.479467 + 0.877560i \(0.659170\pi\)
\(930\) 0 0
\(931\) −36.1857 −1.18594
\(932\) 0 0
\(933\) −27.6360 −0.904764
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 8.62318 0.281707 0.140853 0.990030i \(-0.455015\pi\)
0.140853 + 0.990030i \(0.455015\pi\)
\(938\) 0 0
\(939\) 14.5441 0.474630
\(940\) 0 0
\(941\) −31.5064 −1.02708 −0.513540 0.858066i \(-0.671666\pi\)
−0.513540 + 0.858066i \(0.671666\pi\)
\(942\) 0 0
\(943\) 4.70021 0.153060
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 31.8565 1.03520 0.517598 0.855624i \(-0.326826\pi\)
0.517598 + 0.855624i \(0.326826\pi\)
\(948\) 0 0
\(949\) 9.46841 0.307358
\(950\) 0 0
\(951\) 8.00364 0.259536
\(952\) 0 0
\(953\) −32.9471 −1.06726 −0.533631 0.845717i \(-0.679173\pi\)
−0.533631 + 0.845717i \(0.679173\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −8.52483 −0.275569
\(958\) 0 0
\(959\) 24.1464 0.779728
\(960\) 0 0
\(961\) −30.6242 −0.987876
\(962\) 0 0
\(963\) −1.11943 −0.0360732
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 17.3801 0.558907 0.279453 0.960159i \(-0.409847\pi\)
0.279453 + 0.960159i \(0.409847\pi\)
\(968\) 0 0
\(969\) −8.31017 −0.266961
\(970\) 0 0
\(971\) −29.4311 −0.944490 −0.472245 0.881467i \(-0.656556\pi\)
−0.472245 + 0.881467i \(0.656556\pi\)
\(972\) 0 0
\(973\) 36.3049 1.16388
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.49492 −0.111812 −0.0559062 0.998436i \(-0.517805\pi\)
−0.0559062 + 0.998436i \(0.517805\pi\)
\(978\) 0 0
\(979\) −15.2236 −0.486550
\(980\) 0 0
\(981\) −0.914914 −0.0292110
\(982\) 0 0
\(983\) 12.1407 0.387230 0.193615 0.981078i \(-0.437979\pi\)
0.193615 + 0.981078i \(0.437979\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 27.6348 0.879625
\(988\) 0 0
\(989\) 5.62246 0.178784
\(990\) 0 0
\(991\) 46.5633 1.47913 0.739566 0.673084i \(-0.235031\pi\)
0.739566 + 0.673084i \(0.235031\pi\)
\(992\) 0 0
\(993\) −5.59929 −0.177688
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 10.8908 0.344915 0.172457 0.985017i \(-0.444829\pi\)
0.172457 + 0.985017i \(0.444829\pi\)
\(998\) 0 0
\(999\) −0.257322 −0.00814130
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 7800.2.a.bz.1.5 5
5.2 odd 4 1560.2.l.f.1249.10 yes 10
5.3 odd 4 1560.2.l.f.1249.5 10
5.4 even 2 7800.2.a.ca.1.1 5
15.2 even 4 4680.2.l.h.2809.1 10
15.8 even 4 4680.2.l.h.2809.2 10
20.3 even 4 3120.2.l.q.1249.10 10
20.7 even 4 3120.2.l.q.1249.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.l.f.1249.5 10 5.3 odd 4
1560.2.l.f.1249.10 yes 10 5.2 odd 4
3120.2.l.q.1249.5 10 20.7 even 4
3120.2.l.q.1249.10 10 20.3 even 4
4680.2.l.h.2809.1 10 15.2 even 4
4680.2.l.h.2809.2 10 15.8 even 4
7800.2.a.bz.1.5 5 1.1 even 1 trivial
7800.2.a.ca.1.1 5 5.4 even 2