Properties

Label 7600.2.a.bk.1.1
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.993.1
Defining polynomial: \(x^{3} - x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.25342\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.25342 q^{3} +0.0778929 q^{7} +7.58473 q^{9} +O(q^{10})\) \(q-3.25342 q^{3} +0.0778929 q^{7} +7.58473 q^{9} +4.50684 q^{11} -5.33131 q^{13} +7.33131 q^{17} -1.00000 q^{19} -0.253418 q^{21} -3.40920 q^{23} -14.9160 q^{27} -1.33131 q^{29} +2.50684 q^{31} -14.6626 q^{33} -5.50684 q^{37} +17.3450 q^{39} -0.506836 q^{43} +5.66262 q^{47} -6.99393 q^{49} -23.8518 q^{51} -12.9358 q^{53} +3.25342 q^{57} -7.56499 q^{59} -2.15579 q^{61} +0.590796 q^{63} +4.58473 q^{67} +11.0916 q^{69} +10.8579 q^{71} -5.09763 q^{73} +0.351050 q^{77} -17.0137 q^{79} +25.7739 q^{81} +13.1695 q^{83} +4.33131 q^{87} +15.0137 q^{89} -0.415271 q^{91} -8.15579 q^{93} +7.67629 q^{97} +34.1831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} + O(q^{10}) \) \( 3q - 2q^{3} - 2q^{7} + 5q^{9} - 2q^{11} - 6q^{13} + 12q^{17} - 3q^{19} + 7q^{21} + 2q^{23} - 17q^{27} + 6q^{29} - 8q^{31} - 24q^{33} - q^{37} + 11q^{39} + 14q^{43} - 3q^{47} + 9q^{49} - 15q^{51} - 10q^{53} + 2q^{57} - 6q^{59} - 2q^{61} + 14q^{63} - 4q^{67} + 6q^{71} - 12q^{73} - 10q^{77} - 20q^{79} + 23q^{81} + 4q^{83} + 3q^{87} + 14q^{89} - 19q^{91} - 20q^{93} - 28q^{97} + 36q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.25342 −1.87836 −0.939181 0.343423i \(-0.888414\pi\)
−0.939181 + 0.343423i \(0.888414\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.0778929 0.0294407 0.0147204 0.999892i \(-0.495314\pi\)
0.0147204 + 0.999892i \(0.495314\pi\)
\(8\) 0 0
\(9\) 7.58473 2.52824
\(10\) 0 0
\(11\) 4.50684 1.35886 0.679431 0.733739i \(-0.262227\pi\)
0.679431 + 0.733739i \(0.262227\pi\)
\(12\) 0 0
\(13\) −5.33131 −1.47864 −0.739320 0.673354i \(-0.764853\pi\)
−0.739320 + 0.673354i \(0.764853\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.33131 1.77810 0.889052 0.457806i \(-0.151365\pi\)
0.889052 + 0.457806i \(0.151365\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −0.253418 −0.0553003
\(22\) 0 0
\(23\) −3.40920 −0.710868 −0.355434 0.934701i \(-0.615667\pi\)
−0.355434 + 0.934701i \(0.615667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −14.9160 −2.87059
\(28\) 0 0
\(29\) −1.33131 −0.247218 −0.123609 0.992331i \(-0.539447\pi\)
−0.123609 + 0.992331i \(0.539447\pi\)
\(30\) 0 0
\(31\) 2.50684 0.450241 0.225121 0.974331i \(-0.427722\pi\)
0.225121 + 0.974331i \(0.427722\pi\)
\(32\) 0 0
\(33\) −14.6626 −2.55243
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.50684 −0.905318 −0.452659 0.891684i \(-0.649525\pi\)
−0.452659 + 0.891684i \(0.649525\pi\)
\(38\) 0 0
\(39\) 17.3450 2.77742
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) −0.506836 −0.0772918 −0.0386459 0.999253i \(-0.512304\pi\)
−0.0386459 + 0.999253i \(0.512304\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.66262 0.825978 0.412989 0.910736i \(-0.364485\pi\)
0.412989 + 0.910736i \(0.364485\pi\)
\(48\) 0 0
\(49\) −6.99393 −0.999133
\(50\) 0 0
\(51\) −23.8518 −3.33992
\(52\) 0 0
\(53\) −12.9358 −1.77687 −0.888433 0.459006i \(-0.848206\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.25342 0.430926
\(58\) 0 0
\(59\) −7.56499 −0.984878 −0.492439 0.870347i \(-0.663894\pi\)
−0.492439 + 0.870347i \(0.663894\pi\)
\(60\) 0 0
\(61\) −2.15579 −0.276020 −0.138010 0.990431i \(-0.544071\pi\)
−0.138010 + 0.990431i \(0.544071\pi\)
\(62\) 0 0
\(63\) 0.590796 0.0744333
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.58473 0.560114 0.280057 0.959983i \(-0.409647\pi\)
0.280057 + 0.959983i \(0.409647\pi\)
\(68\) 0 0
\(69\) 11.0916 1.33527
\(70\) 0 0
\(71\) 10.8579 1.28859 0.644297 0.764775i \(-0.277150\pi\)
0.644297 + 0.764775i \(0.277150\pi\)
\(72\) 0 0
\(73\) −5.09763 −0.596633 −0.298316 0.954467i \(-0.596425\pi\)
−0.298316 + 0.954467i \(0.596425\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.351050 0.0400059
\(78\) 0 0
\(79\) −17.0137 −1.91419 −0.957094 0.289778i \(-0.906418\pi\)
−0.957094 + 0.289778i \(0.906418\pi\)
\(80\) 0 0
\(81\) 25.7739 2.86377
\(82\) 0 0
\(83\) 13.1695 1.44554 0.722768 0.691091i \(-0.242870\pi\)
0.722768 + 0.691091i \(0.242870\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.33131 0.464365
\(88\) 0 0
\(89\) 15.0137 1.59145 0.795723 0.605661i \(-0.207091\pi\)
0.795723 + 0.605661i \(0.207091\pi\)
\(90\) 0 0
\(91\) −0.415271 −0.0435322
\(92\) 0 0
\(93\) −8.15579 −0.845716
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.67629 0.779410 0.389705 0.920940i \(-0.372577\pi\)
0.389705 + 0.920940i \(0.372577\pi\)
\(98\) 0 0
\(99\) 34.1831 3.43553
\(100\) 0 0
\(101\) −4.15579 −0.413516 −0.206758 0.978392i \(-0.566291\pi\)
−0.206758 + 0.978392i \(0.566291\pi\)
\(102\) 0 0
\(103\) −2.35105 −0.231656 −0.115828 0.993269i \(-0.536952\pi\)
−0.115828 + 0.993269i \(0.536952\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 14.0334 1.35666 0.678331 0.734757i \(-0.262704\pi\)
0.678331 + 0.734757i \(0.262704\pi\)
\(108\) 0 0
\(109\) −0.0778929 −0.00746078 −0.00373039 0.999993i \(-0.501187\pi\)
−0.00373039 + 0.999993i \(0.501187\pi\)
\(110\) 0 0
\(111\) 17.9160 1.70052
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −40.4365 −3.73836
\(118\) 0 0
\(119\) 0.571057 0.0523487
\(120\) 0 0
\(121\) 9.31157 0.846506
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −17.8321 −1.58234 −0.791171 0.611596i \(-0.790528\pi\)
−0.791171 + 0.611596i \(0.790528\pi\)
\(128\) 0 0
\(129\) 1.64895 0.145182
\(130\) 0 0
\(131\) 1.49316 0.130458 0.0652292 0.997870i \(-0.479222\pi\)
0.0652292 + 0.997870i \(0.479222\pi\)
\(132\) 0 0
\(133\) −0.0778929 −0.00675417
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.42894 −0.720133 −0.360067 0.932927i \(-0.617246\pi\)
−0.360067 + 0.932927i \(0.617246\pi\)
\(138\) 0 0
\(139\) −8.81841 −0.747968 −0.373984 0.927435i \(-0.622008\pi\)
−0.373984 + 0.927435i \(0.622008\pi\)
\(140\) 0 0
\(141\) −18.4229 −1.55149
\(142\) 0 0
\(143\) −24.0273 −2.00927
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 22.7542 1.87673
\(148\) 0 0
\(149\) 17.6763 1.44810 0.724049 0.689748i \(-0.242279\pi\)
0.724049 + 0.689748i \(0.242279\pi\)
\(150\) 0 0
\(151\) −20.0000 −1.62758 −0.813788 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 55.6060 4.49548
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.506836 0.0404499 0.0202250 0.999795i \(-0.493562\pi\)
0.0202250 + 0.999795i \(0.493562\pi\)
\(158\) 0 0
\(159\) 42.0855 3.33760
\(160\) 0 0
\(161\) −0.265553 −0.0209285
\(162\) 0 0
\(163\) −0.830542 −0.0650531 −0.0325265 0.999471i \(-0.510355\pi\)
−0.0325265 + 0.999471i \(0.510355\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −16.5068 −1.27734 −0.638669 0.769482i \(-0.720515\pi\)
−0.638669 + 0.769482i \(0.720515\pi\)
\(168\) 0 0
\(169\) 15.4229 1.18638
\(170\) 0 0
\(171\) −7.58473 −0.580019
\(172\) 0 0
\(173\) 18.8321 1.43178 0.715888 0.698215i \(-0.246022\pi\)
0.715888 + 0.698215i \(0.246022\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 24.6121 1.84996
\(178\) 0 0
\(179\) 7.15579 0.534849 0.267424 0.963579i \(-0.413827\pi\)
0.267424 + 0.963579i \(0.413827\pi\)
\(180\) 0 0
\(181\) 12.5205 0.930642 0.465321 0.885142i \(-0.345939\pi\)
0.465321 + 0.885142i \(0.345939\pi\)
\(182\) 0 0
\(183\) 7.01367 0.518466
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 33.0410 2.41620
\(188\) 0 0
\(189\) −1.16185 −0.0845124
\(190\) 0 0
\(191\) 4.90237 0.354723 0.177361 0.984146i \(-0.443244\pi\)
0.177361 + 0.984146i \(0.443244\pi\)
\(192\) 0 0
\(193\) 18.1558 1.30688 0.653441 0.756977i \(-0.273325\pi\)
0.653441 + 0.756977i \(0.273325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.98633 −0.212767 −0.106384 0.994325i \(-0.533927\pi\)
−0.106384 + 0.994325i \(0.533927\pi\)
\(198\) 0 0
\(199\) 3.06422 0.217217 0.108608 0.994085i \(-0.465361\pi\)
0.108608 + 0.994085i \(0.465361\pi\)
\(200\) 0 0
\(201\) −14.9160 −1.05210
\(202\) 0 0
\(203\) −0.103700 −0.00727829
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −25.8579 −1.79725
\(208\) 0 0
\(209\) −4.50684 −0.311744
\(210\) 0 0
\(211\) −19.2534 −1.32546 −0.662730 0.748858i \(-0.730602\pi\)
−0.662730 + 0.748858i \(0.730602\pi\)
\(212\) 0 0
\(213\) −35.3252 −2.42045
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.195265 0.0132554
\(218\) 0 0
\(219\) 16.5847 1.12069
\(220\) 0 0
\(221\) −39.0855 −2.62918
\(222\) 0 0
\(223\) 14.5068 0.971450 0.485725 0.874112i \(-0.338556\pi\)
0.485725 + 0.874112i \(0.338556\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 21.5984 1.43354 0.716768 0.697312i \(-0.245621\pi\)
0.716768 + 0.697312i \(0.245621\pi\)
\(228\) 0 0
\(229\) −19.0137 −1.25646 −0.628229 0.778028i \(-0.716220\pi\)
−0.628229 + 0.778028i \(0.716220\pi\)
\(230\) 0 0
\(231\) −1.14211 −0.0751456
\(232\) 0 0
\(233\) −6.01367 −0.393969 −0.196984 0.980407i \(-0.563115\pi\)
−0.196984 + 0.980407i \(0.563115\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 55.3526 3.59554
\(238\) 0 0
\(239\) −15.4092 −0.996739 −0.498369 0.866965i \(-0.666068\pi\)
−0.498369 + 0.866965i \(0.666068\pi\)
\(240\) 0 0
\(241\) −4.81841 −0.310381 −0.155190 0.987885i \(-0.549599\pi\)
−0.155190 + 0.987885i \(0.549599\pi\)
\(242\) 0 0
\(243\) −39.1052 −2.50860
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.33131 0.339223
\(248\) 0 0
\(249\) −42.8458 −2.71524
\(250\) 0 0
\(251\) −1.52051 −0.0959736 −0.0479868 0.998848i \(-0.515281\pi\)
−0.0479868 + 0.998848i \(0.515281\pi\)
\(252\) 0 0
\(253\) −15.3647 −0.965972
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.5068 1.02967 0.514834 0.857290i \(-0.327854\pi\)
0.514834 + 0.857290i \(0.327854\pi\)
\(258\) 0 0
\(259\) −0.428943 −0.0266532
\(260\) 0 0
\(261\) −10.0976 −0.625028
\(262\) 0 0
\(263\) 18.0273 1.11161 0.555807 0.831311i \(-0.312409\pi\)
0.555807 + 0.831311i \(0.312409\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −48.8458 −2.98931
\(268\) 0 0
\(269\) 20.2089 1.23216 0.616080 0.787683i \(-0.288720\pi\)
0.616080 + 0.787683i \(0.288720\pi\)
\(270\) 0 0
\(271\) −6.08396 −0.369574 −0.184787 0.982779i \(-0.559160\pi\)
−0.184787 + 0.982779i \(0.559160\pi\)
\(272\) 0 0
\(273\) 1.35105 0.0817693
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −31.3647 −1.88452 −0.942262 0.334877i \(-0.891305\pi\)
−0.942262 + 0.334877i \(0.891305\pi\)
\(278\) 0 0
\(279\) 19.0137 1.13832
\(280\) 0 0
\(281\) 11.3252 0.675607 0.337804 0.941217i \(-0.390316\pi\)
0.337804 + 0.941217i \(0.390316\pi\)
\(282\) 0 0
\(283\) −26.1437 −1.55408 −0.777039 0.629452i \(-0.783279\pi\)
−0.777039 + 0.629452i \(0.783279\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 36.7481 2.16165
\(290\) 0 0
\(291\) −24.9742 −1.46401
\(292\) 0 0
\(293\) 1.33131 0.0777760 0.0388880 0.999244i \(-0.487618\pi\)
0.0388880 + 0.999244i \(0.487618\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −67.2241 −3.90074
\(298\) 0 0
\(299\) 18.1755 1.05112
\(300\) 0 0
\(301\) −0.0394789 −0.00227553
\(302\) 0 0
\(303\) 13.5205 0.776733
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.84421 0.162328 0.0811639 0.996701i \(-0.474136\pi\)
0.0811639 + 0.996701i \(0.474136\pi\)
\(308\) 0 0
\(309\) 7.64895 0.435134
\(310\) 0 0
\(311\) 16.3895 0.929361 0.464681 0.885478i \(-0.346169\pi\)
0.464681 + 0.885478i \(0.346169\pi\)
\(312\) 0 0
\(313\) −21.0471 −1.18965 −0.594826 0.803855i \(-0.702779\pi\)
−0.594826 + 0.803855i \(0.702779\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.8902 −1.73497 −0.867484 0.497465i \(-0.834264\pi\)
−0.867484 + 0.497465i \(0.834264\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) −45.6566 −2.54830
\(322\) 0 0
\(323\) −7.33131 −0.407925
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.253418 0.0140140
\(328\) 0 0
\(329\) 0.441078 0.0243174
\(330\) 0 0
\(331\) −28.3845 −1.56015 −0.780076 0.625685i \(-0.784819\pi\)
−0.780076 + 0.625685i \(0.784819\pi\)
\(332\) 0 0
\(333\) −41.7679 −2.28886
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −17.8716 −0.973526 −0.486763 0.873534i \(-0.661822\pi\)
−0.486763 + 0.873534i \(0.661822\pi\)
\(338\) 0 0
\(339\) 19.5205 1.06021
\(340\) 0 0
\(341\) 11.2979 0.611816
\(342\) 0 0
\(343\) −1.09003 −0.0588560
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −33.0410 −1.77373 −0.886867 0.462024i \(-0.847123\pi\)
−0.886867 + 0.462024i \(0.847123\pi\)
\(348\) 0 0
\(349\) −19.7158 −1.05536 −0.527681 0.849443i \(-0.676938\pi\)
−0.527681 + 0.849443i \(0.676938\pi\)
\(350\) 0 0
\(351\) 79.5220 4.24457
\(352\) 0 0
\(353\) −5.90997 −0.314556 −0.157278 0.987554i \(-0.550272\pi\)
−0.157278 + 0.987554i \(0.550272\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.85789 −0.0983298
\(358\) 0 0
\(359\) 7.00760 0.369847 0.184924 0.982753i \(-0.440796\pi\)
0.184924 + 0.982753i \(0.440796\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −30.2944 −1.59005
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.7158 −0.924756 −0.462378 0.886683i \(-0.653004\pi\)
−0.462378 + 0.886683i \(0.653004\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.00760 −0.0523122
\(372\) 0 0
\(373\) 15.4487 0.799902 0.399951 0.916536i \(-0.369027\pi\)
0.399951 + 0.916536i \(0.369027\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 7.09763 0.365547
\(378\) 0 0
\(379\) −34.4563 −1.76990 −0.884950 0.465685i \(-0.845808\pi\)
−0.884950 + 0.465685i \(0.845808\pi\)
\(380\) 0 0
\(381\) 58.0152 2.97221
\(382\) 0 0
\(383\) 12.0273 0.614569 0.307284 0.951618i \(-0.400580\pi\)
0.307284 + 0.951618i \(0.400580\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.84421 −0.195412
\(388\) 0 0
\(389\) −15.3647 −0.779022 −0.389511 0.921022i \(-0.627356\pi\)
−0.389511 + 0.921022i \(0.627356\pi\)
\(390\) 0 0
\(391\) −24.9939 −1.26400
\(392\) 0 0
\(393\) −4.85789 −0.245048
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.32524 0.0665121 0.0332560 0.999447i \(-0.489412\pi\)
0.0332560 + 0.999447i \(0.489412\pi\)
\(398\) 0 0
\(399\) 0.253418 0.0126868
\(400\) 0 0
\(401\) −6.46736 −0.322964 −0.161482 0.986876i \(-0.551627\pi\)
−0.161482 + 0.986876i \(0.551627\pi\)
\(402\) 0 0
\(403\) −13.3647 −0.665744
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −24.8184 −1.23020
\(408\) 0 0
\(409\) −1.36472 −0.0674812 −0.0337406 0.999431i \(-0.510742\pi\)
−0.0337406 + 0.999431i \(0.510742\pi\)
\(410\) 0 0
\(411\) 27.4229 1.35267
\(412\) 0 0
\(413\) −0.589259 −0.0289955
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 28.6900 1.40495
\(418\) 0 0
\(419\) −16.6231 −0.812094 −0.406047 0.913852i \(-0.633093\pi\)
−0.406047 + 0.913852i \(0.633093\pi\)
\(420\) 0 0
\(421\) −31.1128 −1.51635 −0.758174 0.652053i \(-0.773908\pi\)
−0.758174 + 0.652053i \(0.773908\pi\)
\(422\) 0 0
\(423\) 42.9495 2.08827
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.167920 −0.00812623
\(428\) 0 0
\(429\) 78.1710 3.77413
\(430\) 0 0
\(431\) 10.1831 0.490504 0.245252 0.969459i \(-0.421129\pi\)
0.245252 + 0.969459i \(0.421129\pi\)
\(432\) 0 0
\(433\) 22.1953 1.06664 0.533318 0.845915i \(-0.320945\pi\)
0.533318 + 0.845915i \(0.320945\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.40920 0.163084
\(438\) 0 0
\(439\) 9.32524 0.445070 0.222535 0.974925i \(-0.428567\pi\)
0.222535 + 0.974925i \(0.428567\pi\)
\(440\) 0 0
\(441\) −53.0471 −2.52605
\(442\) 0 0
\(443\) 13.9879 0.664584 0.332292 0.943177i \(-0.392178\pi\)
0.332292 + 0.943177i \(0.392178\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −57.5084 −2.72005
\(448\) 0 0
\(449\) 13.4932 0.636782 0.318391 0.947960i \(-0.396858\pi\)
0.318391 + 0.947960i \(0.396858\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 65.0684 3.05718
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.68236 0.452922 0.226461 0.974020i \(-0.427284\pi\)
0.226461 + 0.974020i \(0.427284\pi\)
\(458\) 0 0
\(459\) −109.354 −5.10421
\(460\) 0 0
\(461\) 8.66262 0.403459 0.201729 0.979441i \(-0.435344\pi\)
0.201729 + 0.979441i \(0.435344\pi\)
\(462\) 0 0
\(463\) −28.0015 −1.30134 −0.650671 0.759360i \(-0.725512\pi\)
−0.650671 + 0.759360i \(0.725512\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.9742 −0.785472 −0.392736 0.919651i \(-0.628471\pi\)
−0.392736 + 0.919651i \(0.628471\pi\)
\(468\) 0 0
\(469\) 0.357118 0.0164902
\(470\) 0 0
\(471\) −1.64895 −0.0759796
\(472\) 0 0
\(473\) −2.28423 −0.105029
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −98.1144 −4.49235
\(478\) 0 0
\(479\) −10.0532 −0.459340 −0.229670 0.973269i \(-0.573765\pi\)
−0.229670 + 0.973269i \(0.573765\pi\)
\(480\) 0 0
\(481\) 29.3587 1.33864
\(482\) 0 0
\(483\) 0.863954 0.0393113
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −19.2089 −0.870440 −0.435220 0.900324i \(-0.643329\pi\)
−0.435220 + 0.900324i \(0.643329\pi\)
\(488\) 0 0
\(489\) 2.70210 0.122193
\(490\) 0 0
\(491\) −5.32524 −0.240325 −0.120162 0.992754i \(-0.538342\pi\)
−0.120162 + 0.992754i \(0.538342\pi\)
\(492\) 0 0
\(493\) −9.76025 −0.439580
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.845752 0.0379372
\(498\) 0 0
\(499\) 11.9605 0.535426 0.267713 0.963499i \(-0.413732\pi\)
0.267713 + 0.963499i \(0.413732\pi\)
\(500\) 0 0
\(501\) 53.7036 2.39930
\(502\) 0 0
\(503\) 19.3313 0.861941 0.430970 0.902366i \(-0.358171\pi\)
0.430970 + 0.902366i \(0.358171\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −50.1771 −2.22844
\(508\) 0 0
\(509\) −36.1573 −1.60265 −0.801323 0.598232i \(-0.795870\pi\)
−0.801323 + 0.598232i \(0.795870\pi\)
\(510\) 0 0
\(511\) −0.397069 −0.0175653
\(512\) 0 0
\(513\) 14.9160 0.658559
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 25.5205 1.12239
\(518\) 0 0
\(519\) −61.2686 −2.68939
\(520\) 0 0
\(521\) −31.5205 −1.38094 −0.690469 0.723362i \(-0.742596\pi\)
−0.690469 + 0.723362i \(0.742596\pi\)
\(522\) 0 0
\(523\) −5.59840 −0.244801 −0.122400 0.992481i \(-0.539059\pi\)
−0.122400 + 0.992481i \(0.539059\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.3784 0.800575
\(528\) 0 0
\(529\) −11.3773 −0.494667
\(530\) 0 0
\(531\) −57.3784 −2.49001
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −23.2808 −1.00464
\(538\) 0 0
\(539\) −31.5205 −1.35768
\(540\) 0 0
\(541\) 15.1968 0.653362 0.326681 0.945135i \(-0.394070\pi\)
0.326681 + 0.945135i \(0.394070\pi\)
\(542\) 0 0
\(543\) −40.7344 −1.74808
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 26.6505 1.13949 0.569746 0.821821i \(-0.307041\pi\)
0.569746 + 0.821821i \(0.307041\pi\)
\(548\) 0 0
\(549\) −16.3511 −0.697846
\(550\) 0 0
\(551\) 1.33131 0.0567158
\(552\) 0 0
\(553\) −1.32524 −0.0563551
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.8458 0.544292 0.272146 0.962256i \(-0.412267\pi\)
0.272146 + 0.962256i \(0.412267\pi\)
\(558\) 0 0
\(559\) 2.70210 0.114287
\(560\) 0 0
\(561\) −107.496 −4.53849
\(562\) 0 0
\(563\) −10.1968 −0.429744 −0.214872 0.976642i \(-0.568933\pi\)
−0.214872 + 0.976642i \(0.568933\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.00760 0.0843115
\(568\) 0 0
\(569\) −24.3784 −1.02200 −0.510998 0.859582i \(-0.670724\pi\)
−0.510998 + 0.859582i \(0.670724\pi\)
\(570\) 0 0
\(571\) −8.32371 −0.348336 −0.174168 0.984716i \(-0.555724\pi\)
−0.174168 + 0.984716i \(0.555724\pi\)
\(572\) 0 0
\(573\) −15.9495 −0.666298
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −7.29290 −0.303607 −0.151804 0.988411i \(-0.548508\pi\)
−0.151804 + 0.988411i \(0.548508\pi\)
\(578\) 0 0
\(579\) −59.0684 −2.45480
\(580\) 0 0
\(581\) 1.02581 0.0425576
\(582\) 0 0
\(583\) −58.2994 −2.41452
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.53264 −0.228357 −0.114178 0.993460i \(-0.536424\pi\)
−0.114178 + 0.993460i \(0.536424\pi\)
\(588\) 0 0
\(589\) −2.50684 −0.103292
\(590\) 0 0
\(591\) 9.71577 0.399653
\(592\) 0 0
\(593\) −26.3252 −1.08105 −0.540524 0.841329i \(-0.681774\pi\)
−0.540524 + 0.841329i \(0.681774\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −9.96919 −0.408012
\(598\) 0 0
\(599\) −22.2994 −0.911130 −0.455565 0.890202i \(-0.650563\pi\)
−0.455565 + 0.890202i \(0.650563\pi\)
\(600\) 0 0
\(601\) 32.4947 1.32549 0.662743 0.748847i \(-0.269392\pi\)
0.662743 + 0.748847i \(0.269392\pi\)
\(602\) 0 0
\(603\) 34.7739 1.41610
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −8.35105 −0.338959 −0.169479 0.985534i \(-0.554209\pi\)
−0.169479 + 0.985534i \(0.554209\pi\)
\(608\) 0 0
\(609\) 0.337378 0.0136713
\(610\) 0 0
\(611\) −30.1892 −1.22132
\(612\) 0 0
\(613\) −38.2994 −1.54690 −0.773450 0.633858i \(-0.781471\pi\)
−0.773450 + 0.633858i \(0.781471\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −14.3526 −0.577813 −0.288907 0.957357i \(-0.593292\pi\)
−0.288907 + 0.957357i \(0.593292\pi\)
\(618\) 0 0
\(619\) 8.62314 0.346593 0.173297 0.984870i \(-0.444558\pi\)
0.173297 + 0.984870i \(0.444558\pi\)
\(620\) 0 0
\(621\) 50.8518 2.04061
\(622\) 0 0
\(623\) 1.16946 0.0468533
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 14.6626 0.585569
\(628\) 0 0
\(629\) −40.3723 −1.60975
\(630\) 0 0
\(631\) 10.3374 0.411525 0.205762 0.978602i \(-0.434033\pi\)
0.205762 + 0.978602i \(0.434033\pi\)
\(632\) 0 0
\(633\) 62.6394 2.48969
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 37.2868 1.47736
\(638\) 0 0
\(639\) 82.3541 3.25788
\(640\) 0 0
\(641\) 5.88369 0.232392 0.116196 0.993226i \(-0.462930\pi\)
0.116196 + 0.993226i \(0.462930\pi\)
\(642\) 0 0
\(643\) 25.5084 1.00595 0.502976 0.864300i \(-0.332238\pi\)
0.502976 + 0.864300i \(0.332238\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.09157 0.200170 0.100085 0.994979i \(-0.468089\pi\)
0.100085 + 0.994979i \(0.468089\pi\)
\(648\) 0 0
\(649\) −34.0942 −1.33831
\(650\) 0 0
\(651\) −0.635277 −0.0248985
\(652\) 0 0
\(653\) −11.1816 −0.437570 −0.218785 0.975773i \(-0.570209\pi\)
−0.218785 + 0.975773i \(0.570209\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −38.6642 −1.50843
\(658\) 0 0
\(659\) 13.7542 0.535787 0.267894 0.963449i \(-0.413672\pi\)
0.267894 + 0.963449i \(0.413672\pi\)
\(660\) 0 0
\(661\) −12.6171 −0.490747 −0.245374 0.969429i \(-0.578911\pi\)
−0.245374 + 0.969429i \(0.578911\pi\)
\(662\) 0 0
\(663\) 127.161 4.93854
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4.53871 0.175740
\(668\) 0 0
\(669\) −47.1968 −1.82473
\(670\) 0 0
\(671\) −9.71577 −0.375073
\(672\) 0 0
\(673\) 2.35105 0.0906263 0.0453132 0.998973i \(-0.485571\pi\)
0.0453132 + 0.998973i \(0.485571\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −23.7663 −0.913414 −0.456707 0.889617i \(-0.650971\pi\)
−0.456707 + 0.889617i \(0.650971\pi\)
\(678\) 0 0
\(679\) 0.597928 0.0229464
\(680\) 0 0
\(681\) −70.2686 −2.69270
\(682\) 0 0
\(683\) −28.1695 −1.07787 −0.538937 0.842346i \(-0.681174\pi\)
−0.538937 + 0.842346i \(0.681174\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 61.8594 2.36008
\(688\) 0 0
\(689\) 68.9647 2.62734
\(690\) 0 0
\(691\) −2.32371 −0.0883979 −0.0441990 0.999023i \(-0.514074\pi\)
−0.0441990 + 0.999023i \(0.514074\pi\)
\(692\) 0 0
\(693\) 2.66262 0.101145
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 19.5650 0.740016
\(700\) 0 0
\(701\) 23.7036 0.895274 0.447637 0.894215i \(-0.352266\pi\)
0.447637 + 0.894215i \(0.352266\pi\)
\(702\) 0 0
\(703\) 5.50684 0.207694
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.323706 −0.0121742
\(708\) 0 0
\(709\) 9.05315 0.339998 0.169999 0.985444i \(-0.445624\pi\)
0.169999 + 0.985444i \(0.445624\pi\)
\(710\) 0 0
\(711\) −129.044 −4.83953
\(712\) 0 0
\(713\) −8.54631 −0.320062
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 50.1326 1.87224
\(718\) 0 0
\(719\) −35.0734 −1.30802 −0.654008 0.756488i \(-0.726914\pi\)
−0.654008 + 0.756488i \(0.726914\pi\)
\(720\) 0 0
\(721\) −0.183130 −0.00682012
\(722\) 0 0
\(723\) 15.6763 0.583008
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −30.1386 −1.11778 −0.558890 0.829242i \(-0.688773\pi\)
−0.558890 + 0.829242i \(0.688773\pi\)
\(728\) 0 0
\(729\) 49.9039 1.84829
\(730\) 0 0
\(731\) −3.71577 −0.137433
\(732\) 0 0
\(733\) 47.8321 1.76672 0.883359 0.468697i \(-0.155276\pi\)
0.883359 + 0.468697i \(0.155276\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 20.6626 0.761117
\(738\) 0 0
\(739\) 22.4674 0.826475 0.413238 0.910623i \(-0.364398\pi\)
0.413238 + 0.910623i \(0.364398\pi\)
\(740\) 0 0
\(741\) −17.3450 −0.637184
\(742\) 0 0
\(743\) 11.7926 0.432629 0.216314 0.976324i \(-0.430596\pi\)
0.216314 + 0.976324i \(0.430596\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 99.8868 3.65467
\(748\) 0 0
\(749\) 1.09310 0.0399411
\(750\) 0 0
\(751\) 2.03948 0.0744216 0.0372108 0.999307i \(-0.488153\pi\)
0.0372108 + 0.999307i \(0.488153\pi\)
\(752\) 0 0
\(753\) 4.94685 0.180273
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 43.3526 1.57568 0.787838 0.615882i \(-0.211200\pi\)
0.787838 + 0.615882i \(0.211200\pi\)
\(758\) 0 0
\(759\) 49.9879 1.81444
\(760\) 0 0
\(761\) 6.62921 0.240309 0.120154 0.992755i \(-0.461661\pi\)
0.120154 + 0.992755i \(0.461661\pi\)
\(762\) 0 0
\(763\) −0.00606730 −0.000219651 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 40.3313 1.45628
\(768\) 0 0
\(769\) −19.6429 −0.708340 −0.354170 0.935181i \(-0.615237\pi\)
−0.354170 + 0.935181i \(0.615237\pi\)
\(770\) 0 0
\(771\) −53.7036 −1.93409
\(772\) 0 0
\(773\) 14.4107 0.518318 0.259159 0.965835i \(-0.416555\pi\)
0.259159 + 0.965835i \(0.416555\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.39553 0.0500644
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 48.9347 1.75102
\(782\) 0 0
\(783\) 19.8579 0.709663
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −24.3176 −0.866830 −0.433415 0.901194i \(-0.642692\pi\)
−0.433415 + 0.901194i \(0.642692\pi\)
\(788\) 0 0
\(789\) −58.6505 −2.08801
\(790\) 0 0
\(791\) −0.467357 −0.0166173
\(792\) 0 0
\(793\) 11.4932 0.408134
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −7.30397 −0.258720 −0.129360 0.991598i \(-0.541292\pi\)
−0.129360 + 0.991598i \(0.541292\pi\)
\(798\) 0 0
\(799\) 41.5144 1.46868
\(800\) 0 0
\(801\) 113.875 4.02356
\(802\) 0 0
\(803\) −22.9742 −0.810742
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −65.7481 −2.31444
\(808\) 0 0
\(809\) −0.584729 −0.0205580 −0.0102790 0.999947i \(-0.503272\pi\)
−0.0102790 + 0.999947i \(0.503272\pi\)
\(810\) 0 0
\(811\) −1.90997 −0.0670682 −0.0335341 0.999438i \(-0.510676\pi\)
−0.0335341 + 0.999438i \(0.510676\pi\)
\(812\) 0 0
\(813\) 19.7937 0.694194
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0.506836 0.0177319
\(818\) 0 0
\(819\) −3.14972 −0.110060
\(820\) 0 0
\(821\) −38.2226 −1.33398 −0.666989 0.745067i \(-0.732417\pi\)
−0.666989 + 0.745067i \(0.732417\pi\)
\(822\) 0 0
\(823\) 45.7481 1.59468 0.797340 0.603531i \(-0.206240\pi\)
0.797340 + 0.603531i \(0.206240\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.6687 0.788268 0.394134 0.919053i \(-0.371045\pi\)
0.394134 + 0.919053i \(0.371045\pi\)
\(828\) 0 0
\(829\) −4.63028 −0.160816 −0.0804081 0.996762i \(-0.525622\pi\)
−0.0804081 + 0.996762i \(0.525622\pi\)
\(830\) 0 0
\(831\) 102.043 3.53982
\(832\) 0 0
\(833\) −51.2747 −1.77656
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −37.3921 −1.29246
\(838\) 0 0
\(839\) 50.4826 1.74285 0.871426 0.490527i \(-0.163196\pi\)
0.871426 + 0.490527i \(0.163196\pi\)
\(840\) 0 0
\(841\) −27.2276 −0.938883
\(842\) 0 0
\(843\) −36.8458 −1.26904
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0.725305 0.0249218
\(848\) 0 0
\(849\) 85.0562 2.91912
\(850\) 0 0
\(851\) 18.7739 0.643562
\(852\) 0 0
\(853\) 36.2105 1.23982 0.619912 0.784672i \(-0.287168\pi\)
0.619912 + 0.784672i \(0.287168\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 25.1968 0.860706 0.430353 0.902661i \(-0.358389\pi\)
0.430353 + 0.902661i \(0.358389\pi\)
\(858\) 0 0
\(859\) −18.8579 −0.643423 −0.321711 0.946838i \(-0.604258\pi\)
−0.321711 + 0.946838i \(0.604258\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −15.0137 −0.511071 −0.255536 0.966800i \(-0.582252\pi\)
−0.255536 + 0.966800i \(0.582252\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −119.557 −4.06037
\(868\) 0 0
\(869\) −76.6778 −2.60112
\(870\) 0 0
\(871\) −24.4426 −0.828206
\(872\) 0 0
\(873\) 58.2226 1.97054
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 35.1128 1.18568 0.592838 0.805322i \(-0.298007\pi\)
0.592838 + 0.805322i \(0.298007\pi\)
\(878\) 0 0
\(879\) −4.33131 −0.146091
\(880\) 0 0
\(881\) −41.3389 −1.39274 −0.696372 0.717681i \(-0.745203\pi\)
−0.696372 + 0.717681i \(0.745203\pi\)
\(882\) 0 0
\(883\) 12.6353 0.425211 0.212605 0.977138i \(-0.431805\pi\)
0.212605 + 0.977138i \(0.431805\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.15579 −0.139538 −0.0697688 0.997563i \(-0.522226\pi\)
−0.0697688 + 0.997563i \(0.522226\pi\)
\(888\) 0 0
\(889\) −1.38899 −0.0465853
\(890\) 0 0
\(891\) 116.159 3.89147
\(892\) 0 0
\(893\) −5.66262 −0.189492
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −59.1326 −1.97438
\(898\) 0 0
\(899\) −3.33738 −0.111308
\(900\) 0 0
\(901\) −94.8362 −3.15945
\(902\) 0 0
\(903\) 0.128441 0.00427426
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 41.7542 1.38643 0.693213 0.720733i \(-0.256195\pi\)
0.693213 + 0.720733i \(0.256195\pi\)
\(908\) 0 0
\(909\) −31.5205 −1.04547
\(910\) 0 0
\(911\) 9.12998 0.302490 0.151245 0.988496i \(-0.451672\pi\)
0.151245 + 0.988496i \(0.451672\pi\)
\(912\) 0 0
\(913\) 59.3526 1.96428
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.116307 0.00384079
\(918\) 0 0
\(919\) −19.0197 −0.627403 −0.313702 0.949522i \(-0.601569\pi\)
−0.313702 + 0.949522i \(0.601569\pi\)
\(920\) 0 0
\(921\) −9.25342 −0.304910
\(922\) 0 0
\(923\) −57.8868 −1.90537
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −17.8321 −0.585682
\(928\) 0 0
\(929\) −7.77239 −0.255004 −0.127502 0.991838i \(-0.540696\pi\)
−0.127502 + 0.991838i \(0.540696\pi\)
\(930\) 0 0
\(931\) 6.99393 0.229217
\(932\) 0 0
\(933\) −53.3218 −1.74568
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −45.9818 −1.50216 −0.751080 0.660211i \(-0.770467\pi\)
−0.751080 + 0.660211i \(0.770467\pi\)
\(938\) 0 0
\(939\) 68.4750 2.23460
\(940\) 0 0
\(941\) −40.6242 −1.32431 −0.662156 0.749366i \(-0.730358\pi\)
−0.662156 + 0.749366i \(0.730358\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.28423 0.0742274 0.0371137 0.999311i \(-0.488184\pi\)
0.0371137 + 0.999311i \(0.488184\pi\)
\(948\) 0 0
\(949\) 27.1771 0.882205
\(950\) 0 0
\(951\) 100.499 3.25890
\(952\) 0 0
\(953\) −57.5084 −1.86288 −0.931439 0.363896i \(-0.881446\pi\)
−0.931439 + 0.363896i \(0.881446\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 19.5205 0.631008
\(958\) 0 0
\(959\) −0.656555 −0.0212013
\(960\) 0 0
\(961\) −24.7158 −0.797283
\(962\) 0 0
\(963\) 106.440 3.42997
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 4.70210 0.151209 0.0756047 0.997138i \(-0.475911\pi\)
0.0756047 + 0.997138i \(0.475911\pi\)
\(968\) 0 0
\(969\) 23.8518 0.766231
\(970\) 0 0
\(971\) −14.9863 −0.480934 −0.240467 0.970657i \(-0.577301\pi\)
−0.240467 + 0.970657i \(0.577301\pi\)
\(972\) 0 0
\(973\) −0.686891 −0.0220207
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 8.89737 0.284652 0.142326 0.989820i \(-0.454542\pi\)
0.142326 + 0.989820i \(0.454542\pi\)
\(978\) 0 0
\(979\) 67.6642 2.16256
\(980\) 0 0
\(981\) −0.590796 −0.0188627
\(982\) 0 0
\(983\) 1.60947 0.0513341 0.0256671 0.999671i \(-0.491829\pi\)
0.0256671 + 0.999671i \(0.491829\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −1.43501 −0.0456769
\(988\) 0 0
\(989\) 1.72791 0.0549443
\(990\) 0 0
\(991\) −16.8974 −0.536763 −0.268381 0.963313i \(-0.586489\pi\)
−0.268381 + 0.963313i \(0.586489\pi\)
\(992\) 0 0
\(993\) 92.3465 2.93053
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 24.1558 0.765021 0.382511 0.923951i \(-0.375060\pi\)
0.382511 + 0.923951i \(0.375060\pi\)
\(998\) 0 0
\(999\) 82.1402 2.59880
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 7600.2.a.bk.1.1 3
4.3 odd 2 950.2.a.l.1.3 yes 3
5.4 even 2 7600.2.a.bz.1.3 3
12.11 even 2 8550.2.a.ci.1.2 3
20.3 even 4 950.2.b.h.799.3 6
20.7 even 4 950.2.b.h.799.4 6
20.19 odd 2 950.2.a.j.1.1 3
60.59 even 2 8550.2.a.cp.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.j.1.1 3 20.19 odd 2
950.2.a.l.1.3 yes 3 4.3 odd 2
950.2.b.h.799.3 6 20.3 even 4
950.2.b.h.799.4 6 20.7 even 4
7600.2.a.bk.1.1 3 1.1 even 1 trivial
7600.2.a.bz.1.3 3 5.4 even 2
8550.2.a.ci.1.2 3 12.11 even 2
8550.2.a.cp.1.2 3 60.59 even 2