Properties

Label 3240.2.a.i.1.1
Level $3240$
Weight $2$
Character 3240.1
Self dual yes
Analytic conductor $25.872$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
Defining polynomial: \(x^{2} - x - 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.37228\) of defining polynomial
Character \(\chi\) \(=\) 3240.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -2.37228 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -2.37228 q^{7} +3.37228 q^{11} +2.37228 q^{13} -4.74456 q^{17} +1.00000 q^{19} +0.372281 q^{23} +1.00000 q^{25} +3.37228 q^{29} -6.11684 q^{31} +2.37228 q^{35} +6.00000 q^{37} -11.7446 q^{41} +6.74456 q^{43} +3.62772 q^{47} -1.37228 q^{49} +7.11684 q^{53} -3.37228 q^{55} -5.00000 q^{59} +1.25544 q^{61} -2.37228 q^{65} +10.7446 q^{67} -1.37228 q^{71} +3.25544 q^{73} -8.00000 q^{77} +8.74456 q^{79} +10.0000 q^{83} +4.74456 q^{85} -1.37228 q^{89} -5.62772 q^{91} -1.00000 q^{95} +6.74456 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5} + q^{7} + O(q^{10}) \) \( 2 q - 2 q^{5} + q^{7} + q^{11} - q^{13} + 2 q^{17} + 2 q^{19} - 5 q^{23} + 2 q^{25} + q^{29} + 5 q^{31} - q^{35} + 12 q^{37} - 12 q^{41} + 2 q^{43} + 13 q^{47} + 3 q^{49} - 3 q^{53} - q^{55} - 10 q^{59} + 14 q^{61} + q^{65} + 10 q^{67} + 3 q^{71} + 18 q^{73} - 16 q^{77} + 6 q^{79} + 20 q^{83} - 2 q^{85} + 3 q^{89} - 17 q^{91} - 2 q^{95} + 2 q^{97} + O(q^{100}) \)

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 0
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −2.37228 −0.896638 −0.448319 0.893874i \(-0.647977\pi\)
−0.448319 + 0.893874i \(0.647977\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.37228 1.01678 0.508391 0.861127i \(-0.330241\pi\)
0.508391 + 0.861127i \(0.330241\pi\)
\(12\) 0 0
\(13\) 2.37228 0.657952 0.328976 0.944338i \(-0.393296\pi\)
0.328976 + 0.944338i \(0.393296\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.74456 −1.15073 −0.575363 0.817898i \(-0.695139\pi\)
−0.575363 + 0.817898i \(0.695139\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.372281 0.0776260 0.0388130 0.999246i \(-0.487642\pi\)
0.0388130 + 0.999246i \(0.487642\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.37228 0.626217 0.313108 0.949717i \(-0.398630\pi\)
0.313108 + 0.949717i \(0.398630\pi\)
\(30\) 0 0
\(31\) −6.11684 −1.09862 −0.549309 0.835619i \(-0.685109\pi\)
−0.549309 + 0.835619i \(0.685109\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.37228 0.400989
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11.7446 −1.83419 −0.917096 0.398666i \(-0.869473\pi\)
−0.917096 + 0.398666i \(0.869473\pi\)
\(42\) 0 0
\(43\) 6.74456 1.02854 0.514268 0.857629i \(-0.328064\pi\)
0.514268 + 0.857629i \(0.328064\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.62772 0.529157 0.264579 0.964364i \(-0.414767\pi\)
0.264579 + 0.964364i \(0.414767\pi\)
\(48\) 0 0
\(49\) −1.37228 −0.196040
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.11684 0.977574 0.488787 0.872403i \(-0.337440\pi\)
0.488787 + 0.872403i \(0.337440\pi\)
\(54\) 0 0
\(55\) −3.37228 −0.454718
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −5.00000 −0.650945 −0.325472 0.945552i \(-0.605523\pi\)
−0.325472 + 0.945552i \(0.605523\pi\)
\(60\) 0 0
\(61\) 1.25544 0.160742 0.0803711 0.996765i \(-0.474389\pi\)
0.0803711 + 0.996765i \(0.474389\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.37228 −0.294245
\(66\) 0 0
\(67\) 10.7446 1.31266 0.656329 0.754475i \(-0.272108\pi\)
0.656329 + 0.754475i \(0.272108\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.37228 −0.162860 −0.0814299 0.996679i \(-0.525949\pi\)
−0.0814299 + 0.996679i \(0.525949\pi\)
\(72\) 0 0
\(73\) 3.25544 0.381020 0.190510 0.981685i \(-0.438986\pi\)
0.190510 + 0.981685i \(0.438986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.00000 −0.911685
\(78\) 0 0
\(79\) 8.74456 0.983840 0.491920 0.870640i \(-0.336295\pi\)
0.491920 + 0.870640i \(0.336295\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.0000 1.09764 0.548821 0.835940i \(-0.315077\pi\)
0.548821 + 0.835940i \(0.315077\pi\)
\(84\) 0 0
\(85\) 4.74456 0.514620
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.37228 −0.145462 −0.0727308 0.997352i \(-0.523171\pi\)
−0.0727308 + 0.997352i \(0.523171\pi\)
\(90\) 0 0
\(91\) −5.62772 −0.589945
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.00000 −0.102598
\(96\) 0 0
\(97\) 6.74456 0.684807 0.342403 0.939553i \(-0.388759\pi\)
0.342403 + 0.939553i \(0.388759\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −12.8614 −1.27976 −0.639879 0.768476i \(-0.721015\pi\)
−0.639879 + 0.768476i \(0.721015\pi\)
\(102\) 0 0
\(103\) 17.1168 1.68657 0.843286 0.537464i \(-0.180618\pi\)
0.843286 + 0.537464i \(0.180618\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0 0
\(109\) 18.1168 1.73528 0.867639 0.497194i \(-0.165636\pi\)
0.867639 + 0.497194i \(0.165636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.25544 −0.306246 −0.153123 0.988207i \(-0.548933\pi\)
−0.153123 + 0.988207i \(0.548933\pi\)
\(114\) 0 0
\(115\) −0.372281 −0.0347154
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 11.2554 1.03178
\(120\) 0 0
\(121\) 0.372281 0.0338438
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 15.8614 1.40747 0.703736 0.710461i \(-0.251514\pi\)
0.703736 + 0.710461i \(0.251514\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.7446 −1.55035 −0.775175 0.631747i \(-0.782338\pi\)
−0.775175 + 0.631747i \(0.782338\pi\)
\(132\) 0 0
\(133\) −2.37228 −0.205703
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 16.7446 1.43058 0.715292 0.698825i \(-0.246294\pi\)
0.715292 + 0.698825i \(0.246294\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −3.37228 −0.280053
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.48913 0.285840 0.142920 0.989734i \(-0.454351\pi\)
0.142920 + 0.989734i \(0.454351\pi\)
\(150\) 0 0
\(151\) 18.6277 1.51590 0.757951 0.652311i \(-0.226201\pi\)
0.757951 + 0.652311i \(0.226201\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.11684 0.491317
\(156\) 0 0
\(157\) −5.86141 −0.467791 −0.233896 0.972262i \(-0.575147\pi\)
−0.233896 + 0.972262i \(0.575147\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.883156 −0.0696024
\(162\) 0 0
\(163\) −13.4891 −1.05655 −0.528275 0.849073i \(-0.677161\pi\)
−0.528275 + 0.849073i \(0.677161\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −7.37228 −0.567099
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 13.8614 1.05386 0.526932 0.849908i \(-0.323342\pi\)
0.526932 + 0.849908i \(0.323342\pi\)
\(174\) 0 0
\(175\) −2.37228 −0.179328
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.7446 1.17680 0.588402 0.808569i \(-0.299757\pi\)
0.588402 + 0.808569i \(0.299757\pi\)
\(180\) 0 0
\(181\) 14.8614 1.10464 0.552320 0.833632i \(-0.313743\pi\)
0.552320 + 0.833632i \(0.313743\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) −16.0000 −1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.3723 0.822869 0.411435 0.911439i \(-0.365028\pi\)
0.411435 + 0.911439i \(0.365028\pi\)
\(192\) 0 0
\(193\) −10.7446 −0.773411 −0.386705 0.922203i \(-0.626387\pi\)
−0.386705 + 0.922203i \(0.626387\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.37228 0.454006 0.227003 0.973894i \(-0.427107\pi\)
0.227003 + 0.973894i \(0.427107\pi\)
\(198\) 0 0
\(199\) −9.48913 −0.672666 −0.336333 0.941743i \(-0.609187\pi\)
−0.336333 + 0.941743i \(0.609187\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.00000 −0.561490
\(204\) 0 0
\(205\) 11.7446 0.820276
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.37228 0.233266
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.74456 −0.459975
\(216\) 0 0
\(217\) 14.5109 0.985062
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −11.2554 −0.757123
\(222\) 0 0
\(223\) 2.51087 0.168141 0.0840703 0.996460i \(-0.473208\pi\)
0.0840703 + 0.996460i \(0.473208\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.48913 −0.364326 −0.182163 0.983268i \(-0.558310\pi\)
−0.182163 + 0.983268i \(0.558310\pi\)
\(228\) 0 0
\(229\) −5.25544 −0.347289 −0.173645 0.984808i \(-0.555554\pi\)
−0.173645 + 0.984808i \(0.555554\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.2337 −1.32555 −0.662776 0.748817i \(-0.730622\pi\)
−0.662776 + 0.748817i \(0.730622\pi\)
\(234\) 0 0
\(235\) −3.62772 −0.236646
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −14.2337 −0.920701 −0.460350 0.887737i \(-0.652276\pi\)
−0.460350 + 0.887737i \(0.652276\pi\)
\(240\) 0 0
\(241\) 29.6060 1.90709 0.953544 0.301254i \(-0.0974051\pi\)
0.953544 + 0.301254i \(0.0974051\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.37228 0.0876718
\(246\) 0 0
\(247\) 2.37228 0.150945
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −15.8614 −1.00116 −0.500582 0.865689i \(-0.666880\pi\)
−0.500582 + 0.865689i \(0.666880\pi\)
\(252\) 0 0
\(253\) 1.25544 0.0789287
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −23.4891 −1.46521 −0.732606 0.680653i \(-0.761696\pi\)
−0.732606 + 0.680653i \(0.761696\pi\)
\(258\) 0 0
\(259\) −14.2337 −0.884438
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13.1168 0.808819 0.404410 0.914578i \(-0.367477\pi\)
0.404410 + 0.914578i \(0.367477\pi\)
\(264\) 0 0
\(265\) −7.11684 −0.437184
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.1168 −0.738777 −0.369389 0.929275i \(-0.620433\pi\)
−0.369389 + 0.929275i \(0.620433\pi\)
\(270\) 0 0
\(271\) −20.7446 −1.26014 −0.630071 0.776537i \(-0.716974\pi\)
−0.630071 + 0.776537i \(0.716974\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.37228 0.203356
\(276\) 0 0
\(277\) −17.1168 −1.02845 −0.514226 0.857655i \(-0.671921\pi\)
−0.514226 + 0.857655i \(0.671921\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.6277 −0.693652 −0.346826 0.937930i \(-0.612740\pi\)
−0.346826 + 0.937930i \(0.612740\pi\)
\(282\) 0 0
\(283\) 5.25544 0.312403 0.156202 0.987725i \(-0.450075\pi\)
0.156202 + 0.987725i \(0.450075\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 27.8614 1.64461
\(288\) 0 0
\(289\) 5.51087 0.324169
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.8614 −0.809792 −0.404896 0.914363i \(-0.632692\pi\)
−0.404896 + 0.914363i \(0.632692\pi\)
\(294\) 0 0
\(295\) 5.00000 0.291111
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.883156 0.0510742
\(300\) 0 0
\(301\) −16.0000 −0.922225
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.25544 −0.0718861
\(306\) 0 0
\(307\) −10.7446 −0.613225 −0.306612 0.951834i \(-0.599195\pi\)
−0.306612 + 0.951834i \(0.599195\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 10.8614 0.615894 0.307947 0.951404i \(-0.400358\pi\)
0.307947 + 0.951404i \(0.400358\pi\)
\(312\) 0 0
\(313\) −4.00000 −0.226093 −0.113047 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.3723 0.919559 0.459779 0.888033i \(-0.347928\pi\)
0.459779 + 0.888033i \(0.347928\pi\)
\(318\) 0 0
\(319\) 11.3723 0.636726
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.74456 −0.263995
\(324\) 0 0
\(325\) 2.37228 0.131590
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8.60597 −0.474462
\(330\) 0 0
\(331\) 19.3723 1.06480 0.532398 0.846494i \(-0.321291\pi\)
0.532398 + 0.846494i \(0.321291\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.7446 −0.587038
\(336\) 0 0
\(337\) 0.744563 0.0405589 0.0202795 0.999794i \(-0.493544\pi\)
0.0202795 + 0.999794i \(0.493544\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −20.6277 −1.11705
\(342\) 0 0
\(343\) 19.8614 1.07242
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.2337 1.62303 0.811515 0.584332i \(-0.198643\pi\)
0.811515 + 0.584332i \(0.198643\pi\)
\(348\) 0 0
\(349\) −25.3723 −1.35815 −0.679074 0.734070i \(-0.737618\pi\)
−0.679074 + 0.734070i \(0.737618\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −24.9783 −1.32946 −0.664729 0.747085i \(-0.731453\pi\)
−0.664729 + 0.747085i \(0.731453\pi\)
\(354\) 0 0
\(355\) 1.37228 0.0728331
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.6277 0.560910 0.280455 0.959867i \(-0.409515\pi\)
0.280455 + 0.959867i \(0.409515\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.25544 −0.170397
\(366\) 0 0
\(367\) 4.23369 0.220997 0.110498 0.993876i \(-0.464755\pi\)
0.110498 + 0.993876i \(0.464755\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −16.8832 −0.876530
\(372\) 0 0
\(373\) 0.744563 0.0385520 0.0192760 0.999814i \(-0.493864\pi\)
0.0192760 + 0.999814i \(0.493864\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 25.3505 1.30217 0.651085 0.759005i \(-0.274314\pi\)
0.651085 + 0.759005i \(0.274314\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13.6277 0.696344 0.348172 0.937431i \(-0.386803\pi\)
0.348172 + 0.937431i \(0.386803\pi\)
\(384\) 0 0
\(385\) 8.00000 0.407718
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.25544 −0.469269 −0.234635 0.972084i \(-0.575389\pi\)
−0.234635 + 0.972084i \(0.575389\pi\)
\(390\) 0 0
\(391\) −1.76631 −0.0893262
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.74456 −0.439987
\(396\) 0 0
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.3505 0.766569 0.383284 0.923630i \(-0.374793\pi\)
0.383284 + 0.923630i \(0.374793\pi\)
\(402\) 0 0
\(403\) −14.5109 −0.722838
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 20.2337 1.00295
\(408\) 0 0
\(409\) −15.6277 −0.772741 −0.386370 0.922344i \(-0.626271\pi\)
−0.386370 + 0.922344i \(0.626271\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.8614 0.583662
\(414\) 0 0
\(415\) −10.0000 −0.490881
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.9783 0.536323 0.268161 0.963374i \(-0.413584\pi\)
0.268161 + 0.963374i \(0.413584\pi\)
\(420\) 0 0
\(421\) 22.6277 1.10281 0.551404 0.834239i \(-0.314092\pi\)
0.551404 + 0.834239i \(0.314092\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −4.74456 −0.230145
\(426\) 0 0
\(427\) −2.97825 −0.144128
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.3723 −0.740457 −0.370228 0.928941i \(-0.620721\pi\)
−0.370228 + 0.928941i \(0.620721\pi\)
\(432\) 0 0
\(433\) 39.2119 1.88441 0.942203 0.335043i \(-0.108751\pi\)
0.942203 + 0.335043i \(0.108751\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.372281 0.0178086
\(438\) 0 0
\(439\) 31.0951 1.48409 0.742044 0.670351i \(-0.233857\pi\)
0.742044 + 0.670351i \(0.233857\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −16.9783 −0.806661 −0.403331 0.915054i \(-0.632148\pi\)
−0.403331 + 0.915054i \(0.632148\pi\)
\(444\) 0 0
\(445\) 1.37228 0.0650524
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.7228 1.07236 0.536178 0.844105i \(-0.319868\pi\)
0.536178 + 0.844105i \(0.319868\pi\)
\(450\) 0 0
\(451\) −39.6060 −1.86497
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.62772 0.263832
\(456\) 0 0
\(457\) −40.2337 −1.88205 −0.941026 0.338334i \(-0.890137\pi\)
−0.941026 + 0.338334i \(0.890137\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −13.8832 −0.646603 −0.323302 0.946296i \(-0.604793\pi\)
−0.323302 + 0.946296i \(0.604793\pi\)
\(462\) 0 0
\(463\) −21.8614 −1.01599 −0.507993 0.861361i \(-0.669612\pi\)
−0.507993 + 0.861361i \(0.669612\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.2337 0.843754 0.421877 0.906653i \(-0.361371\pi\)
0.421877 + 0.906653i \(0.361371\pi\)
\(468\) 0 0
\(469\) −25.4891 −1.17698
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 22.7446 1.04580
\(474\) 0 0
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 24.1168 1.10193 0.550963 0.834529i \(-0.314260\pi\)
0.550963 + 0.834529i \(0.314260\pi\)
\(480\) 0 0
\(481\) 14.2337 0.649000
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.74456 −0.306255
\(486\) 0 0
\(487\) −20.6060 −0.933746 −0.466873 0.884324i \(-0.654619\pi\)
−0.466873 + 0.884324i \(0.654619\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −19.9783 −0.901606 −0.450803 0.892624i \(-0.648862\pi\)
−0.450803 + 0.892624i \(0.648862\pi\)
\(492\) 0 0
\(493\) −16.0000 −0.720604
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.25544 0.146026
\(498\) 0 0
\(499\) 8.25544 0.369564 0.184782 0.982780i \(-0.440842\pi\)
0.184782 + 0.982780i \(0.440842\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.9783 1.55960 0.779802 0.626027i \(-0.215320\pi\)
0.779802 + 0.626027i \(0.215320\pi\)
\(504\) 0 0
\(505\) 12.8614 0.572325
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 38.0000 1.68432 0.842160 0.539227i \(-0.181284\pi\)
0.842160 + 0.539227i \(0.181284\pi\)
\(510\) 0 0
\(511\) −7.72281 −0.341637
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −17.1168 −0.754258
\(516\) 0 0
\(517\) 12.2337 0.538037
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −17.1168 −0.749903 −0.374951 0.927045i \(-0.622341\pi\)
−0.374951 + 0.927045i \(0.622341\pi\)
\(522\) 0 0
\(523\) −5.76631 −0.252143 −0.126072 0.992021i \(-0.540237\pi\)
−0.126072 + 0.992021i \(0.540237\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.0217 1.26421
\(528\) 0 0
\(529\) −22.8614 −0.993974
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −27.8614 −1.20681
\(534\) 0 0
\(535\) −6.00000 −0.259403
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.62772 −0.199330
\(540\) 0 0
\(541\) −38.3505 −1.64882 −0.824409 0.565994i \(-0.808492\pi\)
−0.824409 + 0.565994i \(0.808492\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −18.1168 −0.776040
\(546\) 0 0
\(547\) −40.0000 −1.71028 −0.855138 0.518400i \(-0.826528\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.37228 0.143664
\(552\) 0 0
\(553\) −20.7446 −0.882149
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.60597 −0.364647 −0.182323 0.983239i \(-0.558362\pi\)
−0.182323 + 0.983239i \(0.558362\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −24.2337 −1.02133 −0.510664 0.859780i \(-0.670600\pi\)
−0.510664 + 0.859780i \(0.670600\pi\)
\(564\) 0 0
\(565\) 3.25544 0.136957
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −43.2337 −1.81245 −0.906225 0.422795i \(-0.861049\pi\)
−0.906225 + 0.422795i \(0.861049\pi\)
\(570\) 0 0
\(571\) 14.1168 0.590772 0.295386 0.955378i \(-0.404552\pi\)
0.295386 + 0.955378i \(0.404552\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.372281 0.0155252
\(576\) 0 0
\(577\) 13.4891 0.561560 0.280780 0.959772i \(-0.409407\pi\)
0.280780 + 0.959772i \(0.409407\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −23.7228 −0.984188
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) 0 0
\(589\) −6.11684 −0.252040
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16.9783 −0.697213 −0.348607 0.937269i \(-0.613345\pi\)
−0.348607 + 0.937269i \(0.613345\pi\)
\(594\) 0 0
\(595\) −11.2554 −0.461428
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 36.3505 1.48524 0.742621 0.669712i \(-0.233582\pi\)
0.742621 + 0.669712i \(0.233582\pi\)
\(600\) 0 0
\(601\) 13.0000 0.530281 0.265141 0.964210i \(-0.414582\pi\)
0.265141 + 0.964210i \(0.414582\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.372281 −0.0151354
\(606\) 0 0
\(607\) −33.2554 −1.34980 −0.674898 0.737911i \(-0.735813\pi\)
−0.674898 + 0.737911i \(0.735813\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.60597 0.348160
\(612\) 0 0
\(613\) −33.3505 −1.34702 −0.673508 0.739180i \(-0.735213\pi\)
−0.673508 + 0.739180i \(0.735213\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 43.7228 1.76021 0.880107 0.474775i \(-0.157471\pi\)
0.880107 + 0.474775i \(0.157471\pi\)
\(618\) 0 0
\(619\) −38.3723 −1.54231 −0.771156 0.636646i \(-0.780321\pi\)
−0.771156 + 0.636646i \(0.780321\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.25544 0.130426
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28.4674 −1.13507
\(630\) 0 0
\(631\) −36.6277 −1.45813 −0.729063 0.684446i \(-0.760044\pi\)
−0.729063 + 0.684446i \(0.760044\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15.8614 −0.629441
\(636\) 0 0
\(637\) −3.25544 −0.128985
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.39403 −0.0945585 −0.0472793 0.998882i \(-0.515055\pi\)
−0.0472793 + 0.998882i \(0.515055\pi\)
\(642\) 0 0
\(643\) 21.2554 0.838233 0.419116 0.907933i \(-0.362340\pi\)
0.419116 + 0.907933i \(0.362340\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.7228 −1.01127 −0.505634 0.862748i \(-0.668741\pi\)
−0.505634 + 0.862748i \(0.668741\pi\)
\(648\) 0 0
\(649\) −16.8614 −0.661868
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24.7446 0.968330 0.484165 0.874977i \(-0.339124\pi\)
0.484165 + 0.874977i \(0.339124\pi\)
\(654\) 0 0
\(655\) 17.7446 0.693337
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 47.5842 1.85362 0.926809 0.375533i \(-0.122540\pi\)
0.926809 + 0.375533i \(0.122540\pi\)
\(660\) 0 0
\(661\) −45.0951 −1.75400 −0.876998 0.480494i \(-0.840457\pi\)
−0.876998 + 0.480494i \(0.840457\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.37228 0.0919931
\(666\) 0 0
\(667\) 1.25544 0.0486107
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.23369 0.163440
\(672\) 0 0
\(673\) −0.510875 −0.0196928 −0.00984639 0.999952i \(-0.503134\pi\)
−0.00984639 + 0.999952i \(0.503134\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21.1168 0.811586 0.405793 0.913965i \(-0.366995\pi\)
0.405793 + 0.913965i \(0.366995\pi\)
\(678\) 0 0
\(679\) −16.0000 −0.614024
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −38.2337 −1.46297 −0.731486 0.681857i \(-0.761173\pi\)
−0.731486 + 0.681857i \(0.761173\pi\)
\(684\) 0 0
\(685\) −16.7446 −0.639777
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.8832 0.643197
\(690\) 0 0
\(691\) 41.3505 1.57305 0.786524 0.617559i \(-0.211879\pi\)
0.786524 + 0.617559i \(0.211879\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −15.0000 −0.568982
\(696\) 0 0
\(697\) 55.7228 2.11065
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.11684 0.306569 0.153284 0.988182i \(-0.451015\pi\)
0.153284 + 0.988182i \(0.451015\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 30.5109 1.14748
\(708\) 0 0
\(709\) 18.4674 0.693557 0.346778 0.937947i \(-0.387276\pi\)
0.346778 + 0.937947i \(0.387276\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.27719 −0.0852813
\(714\) 0 0
\(715\) −8.00000 −0.299183
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.3940 0.387632 0.193816 0.981038i \(-0.437914\pi\)
0.193816 + 0.981038i \(0.437914\pi\)
\(720\) 0 0
\(721\) −40.6060 −1.51225
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.37228 0.125243
\(726\) 0 0
\(727\) −47.1168 −1.74747 −0.873734 0.486405i \(-0.838308\pi\)
−0.873734 + 0.486405i \(0.838308\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −32.0000 −1.18356
\(732\) 0 0
\(733\) −28.9783 −1.07034 −0.535168 0.844746i \(-0.679752\pi\)
−0.535168 + 0.844746i \(0.679752\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.2337 1.33469
\(738\) 0 0
\(739\) −12.8614 −0.473114 −0.236557 0.971618i \(-0.576019\pi\)
−0.236557 + 0.971618i \(0.576019\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 29.4891 1.08185 0.540926 0.841070i \(-0.318074\pi\)
0.540926 + 0.841070i \(0.318074\pi\)
\(744\) 0 0
\(745\) −3.48913 −0.127832
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14.2337 −0.520088
\(750\) 0 0
\(751\) −38.2337 −1.39517 −0.697584 0.716503i \(-0.745741\pi\)
−0.697584 + 0.716503i \(0.745741\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −18.6277 −0.677932
\(756\) 0 0
\(757\) 27.1168 0.985578 0.492789 0.870149i \(-0.335977\pi\)
0.492789 + 0.870149i \(0.335977\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.2337 0.624721 0.312360 0.949964i \(-0.398880\pi\)
0.312360 + 0.949964i \(0.398880\pi\)
\(762\) 0 0
\(763\) −42.9783 −1.55592
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.8614 −0.428291
\(768\) 0 0
\(769\) −32.3505 −1.16659 −0.583295 0.812260i \(-0.698237\pi\)
−0.583295 + 0.812260i \(0.698237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) −6.11684 −0.219724
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11.7446 −0.420793
\(780\) 0 0
\(781\) −4.62772 −0.165593
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.86141 0.209203
\(786\) 0 0
\(787\) 15.7228 0.560458 0.280229 0.959933i \(-0.409590\pi\)
0.280229 + 0.959933i \(0.409590\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.72281 0.274592
\(792\) 0 0
\(793\) 2.97825 0.105761
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.2337 −0.504183 −0.252092 0.967703i \(-0.581118\pi\)
−0.252092 + 0.967703i \(0.581118\pi\)
\(798\) 0 0
\(799\) −17.2119 −0.608915
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 10.9783 0.387414
\(804\) 0 0
\(805\) 0.883156 0.0311272
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 34.2119 1.20283 0.601414 0.798938i \(-0.294604\pi\)
0.601414 + 0.798938i \(0.294604\pi\)
\(810\) 0 0
\(811\) 14.3505 0.503915 0.251958 0.967738i \(-0.418926\pi\)
0.251958 + 0.967738i \(0.418926\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 13.4891 0.472503
\(816\) 0 0
\(817\) 6.74456 0.235962
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −41.3723 −1.44390 −0.721951 0.691944i \(-0.756755\pi\)
−0.721951 + 0.691944i \(0.756755\pi\)
\(822\) 0 0
\(823\) −34.7446 −1.21112 −0.605560 0.795800i \(-0.707051\pi\)
−0.605560 + 0.795800i \(0.707051\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −45.9565 −1.59806 −0.799032 0.601288i \(-0.794654\pi\)
−0.799032 + 0.601288i \(0.794654\pi\)
\(828\) 0 0
\(829\) 42.5842 1.47901 0.739506 0.673150i \(-0.235059\pi\)
0.739506 + 0.673150i \(0.235059\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 6.51087 0.225588
\(834\) 0 0
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −11.6060 −0.400683 −0.200341 0.979726i \(-0.564205\pi\)
−0.200341 + 0.979726i \(0.564205\pi\)
\(840\) 0 0
\(841\) −17.6277 −0.607852
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.37228 0.253614
\(846\) 0 0
\(847\) −0.883156 −0.0303456
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.23369 0.0765698
\(852\) 0 0
\(853\) −0.744563 −0.0254933 −0.0127467 0.999919i \(-0.504058\pi\)
−0.0127467 + 0.999919i \(0.504058\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 44.7446 1.52845 0.764223 0.644953i \(-0.223123\pi\)
0.764223 + 0.644953i \(0.223123\pi\)
\(858\) 0 0
\(859\) 50.3505 1.71794 0.858969 0.512028i \(-0.171105\pi\)
0.858969 + 0.512028i \(0.171105\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11.3940 0.387857 0.193929 0.981016i \(-0.437877\pi\)
0.193929 + 0.981016i \(0.437877\pi\)
\(864\) 0 0
\(865\) −13.8614 −0.471302
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 29.4891 1.00035
\(870\) 0 0
\(871\) 25.4891 0.863666
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.37228 0.0801977
\(876\) 0 0
\(877\) 8.88316 0.299963 0.149981 0.988689i \(-0.452079\pi\)
0.149981 + 0.988689i \(0.452079\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −25.3723 −0.854814 −0.427407 0.904059i \(-0.640573\pi\)
−0.427407 + 0.904059i \(0.640573\pi\)
\(882\) 0 0
\(883\) 5.76631 0.194052 0.0970259 0.995282i \(-0.469067\pi\)
0.0970259 + 0.995282i \(0.469067\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 41.8614 1.40557 0.702784 0.711403i \(-0.251940\pi\)
0.702784 + 0.711403i \(0.251940\pi\)
\(888\) 0 0
\(889\) −37.6277 −1.26199
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 3.62772 0.121397
\(894\) 0 0
\(895\) −15.7446 −0.526283
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −20.6277 −0.687973
\(900\) 0 0
\(901\) −33.7663 −1.12492
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −14.8614 −0.494010
\(906\) 0 0
\(907\) −35.4891 −1.17840 −0.589199 0.807988i \(-0.700556\pi\)
−0.589199 + 0.807988i \(0.700556\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −54.0733 −1.79153 −0.895765 0.444528i \(-0.853371\pi\)
−0.895765 + 0.444528i \(0.853371\pi\)
\(912\) 0 0
\(913\) 33.7228 1.11606
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 42.0951 1.39010
\(918\) 0 0
\(919\) 42.1168 1.38931 0.694653 0.719345i \(-0.255558\pi\)
0.694653 + 0.719345i \(0.255558\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.25544 −0.107154
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.86141 0.0938797 0.0469399 0.998898i \(-0.485053\pi\)
0.0469399 + 0.998898i \(0.485053\pi\)
\(930\) 0 0
\(931\) −1.37228 −0.0449747
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 16.0000 0.523256
\(936\) 0 0
\(937\) 42.7446 1.39640 0.698202 0.715901i \(-0.253984\pi\)
0.698202 + 0.715901i \(0.253984\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −26.4674 −0.862812 −0.431406 0.902158i \(-0.641982\pi\)
−0.431406 + 0.902158i \(0.641982\pi\)
\(942\) 0 0
\(943\) −4.37228 −0.142381
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −37.2554 −1.21064 −0.605320 0.795983i \(-0.706955\pi\)
−0.605320 + 0.795983i \(0.706955\pi\)
\(948\) 0 0
\(949\) 7.72281 0.250693
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 12.0000 0.388718 0.194359 0.980930i \(-0.437737\pi\)
0.194359 + 0.980930i \(0.437737\pi\)
\(954\) 0 0
\(955\) −11.3723 −0.367998
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −39.7228 −1.28272
\(960\) 0 0
\(961\) 6.41578 0.206961
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10.7446 0.345880
\(966\) 0 0
\(967\) −18.5109 −0.595270 −0.297635 0.954680i \(-0.596198\pi\)
−0.297635 + 0.954680i \(0.596198\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 8.72281 0.279928 0.139964 0.990157i \(-0.455301\pi\)
0.139964 + 0.990157i \(0.455301\pi\)
\(972\) 0 0
\(973\) −35.5842 −1.14078
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −17.7663 −0.568395 −0.284197 0.958766i \(-0.591727\pi\)
−0.284197 + 0.958766i \(0.591727\pi\)
\(978\) 0 0
\(979\) −4.62772 −0.147903
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5.48913 0.175076 0.0875380 0.996161i \(-0.472100\pi\)
0.0875380 + 0.996161i \(0.472100\pi\)
\(984\) 0 0
\(985\) −6.37228 −0.203038
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.51087 0.0798412
\(990\) 0 0
\(991\) 3.37228 0.107124 0.0535620 0.998565i \(-0.482943\pi\)
0.0535620 + 0.998565i \(0.482943\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9.48913 0.300825
\(996\) 0 0
\(997\) 9.35053 0.296134 0.148067 0.988977i \(-0.452695\pi\)
0.148067 + 0.988977i \(0.452695\pi\)
\(998\) 0 0
\(999\) 0 0
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 3240.2.a.i.1.1 2
3.2 odd 2 3240.2.a.m.1.1 yes 2
4.3 odd 2 6480.2.a.bd.1.2 2
9.2 odd 6 3240.2.q.ba.1081.2 4
9.4 even 3 3240.2.q.bd.2161.2 4
9.5 odd 6 3240.2.q.ba.2161.2 4
9.7 even 3 3240.2.q.bd.1081.2 4
12.11 even 2 6480.2.a.bo.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3240.2.a.i.1.1 2 1.1 even 1 trivial
3240.2.a.m.1.1 yes 2 3.2 odd 2
3240.2.q.ba.1081.2 4 9.2 odd 6
3240.2.q.ba.2161.2 4 9.5 odd 6
3240.2.q.bd.1081.2 4 9.7 even 3
3240.2.q.bd.2161.2 4 9.4 even 3
6480.2.a.bd.1.2 2 4.3 odd 2
6480.2.a.bo.1.2 2 12.11 even 2