Properties

Label 5184.2.d.r.2593.6
Level $5184$
Weight $2$
Character 5184.2593
Analytic conductor $41.394$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 576)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2593.6
Root \(-0.180407 - 0.673288i\) of defining polynomial
Character \(\chi\) \(=\) 5184.2593
Dual form 5184.2.d.r.2593.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{5} +4.35461 q^{7} +O(q^{10})\) \(q-1.73205i q^{5} +4.35461 q^{7} -5.83502i q^{11} -4.01989i q^{13} -1.70739 q^{17} -2.00000i q^{19} +6.64245 q^{23} +2.00000 q^{25} -4.68934i q^{29} +4.86143 q^{31} -7.54241i q^{35} +5.75194i q^{37} +1.29261 q^{41} +3.54241i q^{43} -10.6134 q^{47} +11.9627 q^{49} -0.506816i q^{53} -10.1066 q^{55} -1.87237i q^{59} -1.22523i q^{61} -6.96265 q^{65} -1.57976i q^{67} -9.88549 q^{71} -7.96265 q^{73} -25.4093i q^{77} +2.06677 q^{79} +1.54241i q^{83} +2.95729i q^{85} -3.96265 q^{89} -17.5051i q^{91} -3.46410 q^{95} +6.12217 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 24 q^{25} + 36 q^{41} + 48 q^{49} + 12 q^{65} + 48 q^{89} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5184\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(5\) − 1.73205i − 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0 0
\(7\) 4.35461 1.64589 0.822944 0.568122i \(-0.192330\pi\)
0.822944 + 0.568122i \(0.192330\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 5.83502i − 1.75933i −0.475598 0.879663i \(-0.657768\pi\)
0.475598 0.879663i \(-0.342232\pi\)
\(12\) 0 0
\(13\) − 4.01989i − 1.11492i −0.830205 0.557458i \(-0.811777\pi\)
0.830205 0.557458i \(-0.188223\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.70739 −0.414103 −0.207051 0.978330i \(-0.566387\pi\)
−0.207051 + 0.978330i \(0.566387\pi\)
\(18\) 0 0
\(19\) − 2.00000i − 0.458831i −0.973329 0.229416i \(-0.926318\pi\)
0.973329 0.229416i \(-0.0736815\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.64245 1.38505 0.692523 0.721395i \(-0.256499\pi\)
0.692523 + 0.721395i \(0.256499\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 4.68934i − 0.870788i −0.900240 0.435394i \(-0.856609\pi\)
0.900240 0.435394i \(-0.143391\pi\)
\(30\) 0 0
\(31\) 4.86143 0.873138 0.436569 0.899671i \(-0.356193\pi\)
0.436569 + 0.899671i \(0.356193\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 7.54241i − 1.27490i
\(36\) 0 0
\(37\) 5.75194i 0.945613i 0.881166 + 0.472807i \(0.156759\pi\)
−0.881166 + 0.472807i \(0.843241\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.29261 0.201872 0.100936 0.994893i \(-0.467816\pi\)
0.100936 + 0.994893i \(0.467816\pi\)
\(42\) 0 0
\(43\) 3.54241i 0.540213i 0.962831 + 0.270106i \(0.0870588\pi\)
−0.962831 + 0.270106i \(0.912941\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.6134 −1.54812 −0.774060 0.633113i \(-0.781777\pi\)
−0.774060 + 0.633113i \(0.781777\pi\)
\(48\) 0 0
\(49\) 11.9627 1.70895
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 0.506816i − 0.0696166i −0.999394 0.0348083i \(-0.988918\pi\)
0.999394 0.0348083i \(-0.0110821\pi\)
\(54\) 0 0
\(55\) −10.1066 −1.36277
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) − 1.87237i − 0.243762i −0.992545 0.121881i \(-0.961107\pi\)
0.992545 0.121881i \(-0.0388926\pi\)
\(60\) 0 0
\(61\) − 1.22523i − 0.156875i −0.996919 0.0784376i \(-0.975007\pi\)
0.996919 0.0784376i \(-0.0249931\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.96265 −0.863611
\(66\) 0 0
\(67\) − 1.57976i − 0.192998i −0.995333 0.0964990i \(-0.969236\pi\)
0.995333 0.0964990i \(-0.0307645\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9.88549 −1.17319 −0.586596 0.809880i \(-0.699532\pi\)
−0.586596 + 0.809880i \(0.699532\pi\)
\(72\) 0 0
\(73\) −7.96265 −0.931958 −0.465979 0.884796i \(-0.654298\pi\)
−0.465979 + 0.884796i \(0.654298\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 25.4093i − 2.89565i
\(78\) 0 0
\(79\) 2.06677 0.232530 0.116265 0.993218i \(-0.462908\pi\)
0.116265 + 0.993218i \(0.462908\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.54241i 0.169302i 0.996411 + 0.0846508i \(0.0269775\pi\)
−0.996411 + 0.0846508i \(0.973023\pi\)
\(84\) 0 0
\(85\) 2.95729i 0.320763i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.96265 −0.420040 −0.210020 0.977697i \(-0.567353\pi\)
−0.210020 + 0.977697i \(0.567353\pi\)
\(90\) 0 0
\(91\) − 17.5051i − 1.83503i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.46410 −0.355409
\(96\) 0 0
\(97\) 6.12217 0.621612 0.310806 0.950473i \(-0.399401\pi\)
0.310806 + 0.950473i \(0.399401\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 11.5529i 1.14955i 0.818311 + 0.574776i \(0.194911\pi\)
−0.818311 + 0.574776i \(0.805089\pi\)
\(102\) 0 0
\(103\) 0.221065 0.0217822 0.0108911 0.999941i \(-0.496533\pi\)
0.0108911 + 0.999941i \(0.496533\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 0.329957i − 0.0318982i −0.999873 0.0159491i \(-0.994923\pi\)
0.999873 0.0159491i \(-0.00507697\pi\)
\(108\) 0 0
\(109\) 17.9253i 1.71693i 0.512873 + 0.858465i \(0.328581\pi\)
−0.512873 + 0.858465i \(0.671419\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 18.0848 1.70128 0.850638 0.525751i \(-0.176216\pi\)
0.850638 + 0.525751i \(0.176216\pi\)
\(114\) 0 0
\(115\) − 11.5051i − 1.07285i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.43502 −0.681567
\(120\) 0 0
\(121\) −23.0475 −2.09523
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 12.1244i − 1.08444i
\(126\) 0 0
\(127\) −4.57568 −0.406026 −0.203013 0.979176i \(-0.565073\pi\)
−0.203013 + 0.979176i \(0.565073\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 13.5424i 1.18321i 0.806229 + 0.591603i \(0.201505\pi\)
−0.806229 + 0.591603i \(0.798495\pi\)
\(132\) 0 0
\(133\) − 8.70923i − 0.755186i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 22.3774 1.91183 0.955917 0.293639i \(-0.0948662\pi\)
0.955917 + 0.293639i \(0.0948662\pi\)
\(138\) 0 0
\(139\) 11.5424i 0.979015i 0.871999 + 0.489507i \(0.162823\pi\)
−0.871999 + 0.489507i \(0.837177\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −23.4561 −1.96150
\(144\) 0 0
\(145\) −8.12217 −0.674509
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 2.23887i − 0.183415i −0.995786 0.0917076i \(-0.970767\pi\)
0.995786 0.0917076i \(-0.0292325\pi\)
\(150\) 0 0
\(151\) −17.0348 −1.38627 −0.693134 0.720808i \(-0.743771\pi\)
−0.693134 + 0.720808i \(0.743771\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 8.42024i − 0.676330i
\(156\) 0 0
\(157\) 0.0489718i 0.00390837i 0.999998 + 0.00195419i \(0.000622037\pi\)
−0.999998 + 0.00195419i \(0.999378\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 28.9253 2.27963
\(162\) 0 0
\(163\) 19.0848i 1.49484i 0.664353 + 0.747419i \(0.268707\pi\)
−0.664353 + 0.747419i \(0.731293\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −19.9920 −1.54703 −0.773515 0.633778i \(-0.781503\pi\)
−0.773515 + 0.633778i \(0.781503\pi\)
\(168\) 0 0
\(169\) −3.15951 −0.243040
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 12.1244i − 0.921798i −0.887453 0.460899i \(-0.847527\pi\)
0.887453 0.460899i \(-0.152473\pi\)
\(174\) 0 0
\(175\) 8.70923 0.658356
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000i 0.448461i 0.974536 + 0.224231i \(0.0719869\pi\)
−0.974536 + 0.224231i \(0.928013\pi\)
\(180\) 0 0
\(181\) − 5.75194i − 0.427538i −0.976884 0.213769i \(-0.931426\pi\)
0.976884 0.213769i \(-0.0685740\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 9.96265 0.732469
\(186\) 0 0
\(187\) 9.96265i 0.728541i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.221065 0.0159957 0.00799786 0.999968i \(-0.497454\pi\)
0.00799786 + 0.999968i \(0.497454\pi\)
\(192\) 0 0
\(193\) 18.0475 1.29909 0.649543 0.760325i \(-0.274960\pi\)
0.649543 + 0.760325i \(0.274960\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 9.82080i 0.699703i 0.936805 + 0.349852i \(0.113768\pi\)
−0.936805 + 0.349852i \(0.886232\pi\)
\(198\) 0 0
\(199\) 0.604760 0.0428703 0.0214352 0.999770i \(-0.493176\pi\)
0.0214352 + 0.999770i \(0.493176\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) − 20.4202i − 1.43322i
\(204\) 0 0
\(205\) − 2.23887i − 0.156369i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −11.6700 −0.807234
\(210\) 0 0
\(211\) − 0.420243i − 0.0289307i −0.999895 0.0144654i \(-0.995395\pi\)
0.999895 0.0144654i \(-0.00460462\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 6.13564 0.418447
\(216\) 0 0
\(217\) 21.1696 1.43709
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.86352i 0.461690i
\(222\) 0 0
\(223\) 22.7867 1.52591 0.762955 0.646452i \(-0.223748\pi\)
0.762955 + 0.646452i \(0.223748\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.8350i 0.785518i 0.919641 + 0.392759i \(0.128479\pi\)
−0.919641 + 0.392759i \(0.871521\pi\)
\(228\) 0 0
\(229\) − 15.6864i − 1.03659i −0.855203 0.518293i \(-0.826568\pi\)
0.855203 0.518293i \(-0.173432\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.829557 0.0543461 0.0271731 0.999631i \(-0.491349\pi\)
0.0271731 + 0.999631i \(0.491349\pi\)
\(234\) 0 0
\(235\) 18.3829i 1.19917i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.21395 −0.466632 −0.233316 0.972401i \(-0.574958\pi\)
−0.233316 + 0.972401i \(0.574958\pi\)
\(240\) 0 0
\(241\) −20.9253 −1.34792 −0.673959 0.738769i \(-0.735407\pi\)
−0.673959 + 0.738769i \(0.735407\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 20.7199i − 1.32375i
\(246\) 0 0
\(247\) −8.03978 −0.511559
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 20.2553i − 1.27850i −0.768999 0.639250i \(-0.779245\pi\)
0.768999 0.639250i \(-0.220755\pi\)
\(252\) 0 0
\(253\) − 38.7588i − 2.43675i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.74474 0.420725 0.210363 0.977623i \(-0.432536\pi\)
0.210363 + 0.977623i \(0.432536\pi\)
\(258\) 0 0
\(259\) 25.0475i 1.55637i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −26.4134 −1.62872 −0.814361 0.580359i \(-0.802912\pi\)
−0.814361 + 0.580359i \(0.802912\pi\)
\(264\) 0 0
\(265\) −0.877832 −0.0539248
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 23.1704i − 1.41272i −0.707851 0.706362i \(-0.750335\pi\)
0.707851 0.706362i \(-0.249665\pi\)
\(270\) 0 0
\(271\) 17.7626 1.07900 0.539502 0.841984i \(-0.318613\pi\)
0.539502 + 0.841984i \(0.318613\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) − 11.6700i − 0.703730i
\(276\) 0 0
\(277\) 10.4413i 0.627356i 0.949529 + 0.313678i \(0.101561\pi\)
−0.949529 + 0.313678i \(0.898439\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.8880 1.60400 0.802001 0.597323i \(-0.203769\pi\)
0.802001 + 0.597323i \(0.203769\pi\)
\(282\) 0 0
\(283\) − 18.6272i − 1.10727i −0.832758 0.553637i \(-0.813240\pi\)
0.832758 0.553637i \(-0.186760\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.62882 0.332259
\(288\) 0 0
\(289\) −14.0848 −0.828519
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.16055i 0.0678000i 0.999425 + 0.0339000i \(0.0107928\pi\)
−0.999425 + 0.0339000i \(0.989207\pi\)
\(294\) 0 0
\(295\) −3.24304 −0.188817
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) − 26.7019i − 1.54421i
\(300\) 0 0
\(301\) 15.4258i 0.889130i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.12217 −0.121515
\(306\) 0 0
\(307\) − 19.0848i − 1.08923i −0.838687 0.544614i \(-0.816676\pi\)
0.838687 0.544614i \(-0.183324\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −11.1202 −0.630568 −0.315284 0.948997i \(-0.602100\pi\)
−0.315284 + 0.948997i \(0.602100\pi\)
\(312\) 0 0
\(313\) 26.9253 1.52191 0.760954 0.648806i \(-0.224731\pi\)
0.760954 + 0.648806i \(0.224731\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 22.4520i − 1.26103i −0.776178 0.630514i \(-0.782844\pi\)
0.776178 0.630514i \(-0.217156\pi\)
\(318\) 0 0
\(319\) −27.3624 −1.53200
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.41478i 0.190003i
\(324\) 0 0
\(325\) − 8.03978i − 0.445967i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −46.2171 −2.54803
\(330\) 0 0
\(331\) − 22.5899i − 1.24165i −0.783948 0.620826i \(-0.786797\pi\)
0.783948 0.620826i \(-0.213203\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.73622 −0.149496
\(336\) 0 0
\(337\) −14.0848 −0.767249 −0.383625 0.923489i \(-0.625324\pi\)
−0.383625 + 0.923489i \(0.625324\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 28.3665i − 1.53613i
\(342\) 0 0
\(343\) 21.6104 1.16685
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 6.99454i − 0.375486i −0.982218 0.187743i \(-0.939883\pi\)
0.982218 0.187743i \(-0.0601173\pi\)
\(348\) 0 0
\(349\) 9.42764i 0.504650i 0.967643 + 0.252325i \(0.0811952\pi\)
−0.967643 + 0.252325i \(0.918805\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.62257 0.405708 0.202854 0.979209i \(-0.434978\pi\)
0.202854 + 0.979209i \(0.434978\pi\)
\(354\) 0 0
\(355\) 17.1222i 0.908750i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10.8344 −0.571820 −0.285910 0.958257i \(-0.592296\pi\)
−0.285910 + 0.958257i \(0.592296\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 13.7917i 0.721892i
\(366\) 0 0
\(367\) −22.9493 −1.19795 −0.598973 0.800770i \(-0.704424\pi\)
−0.598973 + 0.800770i \(0.704424\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 2.20699i − 0.114581i
\(372\) 0 0
\(373\) − 0.113658i − 0.00588498i −0.999996 0.00294249i \(-0.999063\pi\)
0.999996 0.00294249i \(-0.000936625\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −18.8506 −0.970856
\(378\) 0 0
\(379\) 16.2070i 0.832497i 0.909251 + 0.416249i \(0.136655\pi\)
−0.909251 + 0.416249i \(0.863345\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.0775 −0.719325 −0.359663 0.933082i \(-0.617108\pi\)
−0.359663 + 0.933082i \(0.617108\pi\)
\(384\) 0 0
\(385\) −44.0101 −2.24296
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 28.8734i − 1.46394i −0.681338 0.731969i \(-0.738602\pi\)
0.681338 0.731969i \(-0.261398\pi\)
\(390\) 0 0
\(391\) −11.3413 −0.573552
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 3.57976i − 0.180117i
\(396\) 0 0
\(397\) 2.85934i 0.143506i 0.997422 + 0.0717531i \(0.0228594\pi\)
−0.997422 + 0.0717531i \(0.977141\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −21.5479 −1.07605 −0.538025 0.842929i \(-0.680829\pi\)
−0.538025 + 0.842929i \(0.680829\pi\)
\(402\) 0 0
\(403\) − 19.5424i − 0.973477i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 33.5627 1.66364
\(408\) 0 0
\(409\) −20.9253 −1.03469 −0.517345 0.855777i \(-0.673080\pi\)
−0.517345 + 0.855777i \(0.673080\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 8.15344i − 0.401204i
\(414\) 0 0
\(415\) 2.67153 0.131140
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 12.6646i − 0.618705i −0.950947 0.309353i \(-0.899888\pi\)
0.950947 0.309353i \(-0.100112\pi\)
\(420\) 0 0
\(421\) 26.6835i 1.30047i 0.759732 + 0.650236i \(0.225330\pi\)
−0.759732 + 0.650236i \(0.774670\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.41478 −0.165641
\(426\) 0 0
\(427\) − 5.33542i − 0.258199i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 23.6772 1.14049 0.570246 0.821474i \(-0.306848\pi\)
0.570246 + 0.821474i \(0.306848\pi\)
\(432\) 0 0
\(433\) 7.96265 0.382661 0.191330 0.981526i \(-0.438720\pi\)
0.191330 + 0.981526i \(0.438720\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 13.2849i − 0.635503i
\(438\) 0 0
\(439\) 10.6781 0.509636 0.254818 0.966989i \(-0.417984\pi\)
0.254818 + 0.966989i \(0.417984\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.8825i 0.612066i 0.952021 + 0.306033i \(0.0990018\pi\)
−0.952021 + 0.306033i \(0.900998\pi\)
\(444\) 0 0
\(445\) 6.86352i 0.325362i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.547875 0.0258558 0.0129279 0.999916i \(-0.495885\pi\)
0.0129279 + 0.999916i \(0.495885\pi\)
\(450\) 0 0
\(451\) − 7.54241i − 0.355158i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −30.3197 −1.42141
\(456\) 0 0
\(457\) 19.8031 0.926352 0.463176 0.886266i \(-0.346710\pi\)
0.463176 + 0.886266i \(0.346710\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.0680i 0.655212i 0.944814 + 0.327606i \(0.106242\pi\)
−0.944814 + 0.327606i \(0.893758\pi\)
\(462\) 0 0
\(463\) 12.4591 0.579022 0.289511 0.957175i \(-0.406507\pi\)
0.289511 + 0.957175i \(0.406507\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.3401i 1.35770i 0.734278 + 0.678849i \(0.237521\pi\)
−0.734278 + 0.678849i \(0.762479\pi\)
\(468\) 0 0
\(469\) − 6.87923i − 0.317653i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 20.6700 0.950410
\(474\) 0 0
\(475\) − 4.00000i − 0.183533i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 19.9274 0.910504 0.455252 0.890363i \(-0.349549\pi\)
0.455252 + 0.890363i \(0.349549\pi\)
\(480\) 0 0
\(481\) 23.1222 1.05428
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 10.6039i − 0.481499i
\(486\) 0 0
\(487\) −7.46828 −0.338420 −0.169210 0.985580i \(-0.554122\pi\)
−0.169210 + 0.985580i \(0.554122\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 34.8934i − 1.57472i −0.616495 0.787359i \(-0.711448\pi\)
0.616495 0.787359i \(-0.288552\pi\)
\(492\) 0 0
\(493\) 8.00652i 0.360596i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −43.0475 −1.93094
\(498\) 0 0
\(499\) − 37.4677i − 1.67729i −0.544682 0.838643i \(-0.683350\pi\)
0.544682 0.838643i \(-0.316650\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −10.8991 −0.485968 −0.242984 0.970030i \(-0.578126\pi\)
−0.242984 + 0.970030i \(0.578126\pi\)
\(504\) 0 0
\(505\) 20.0101 0.890439
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.68934i 0.207851i 0.994585 + 0.103926i \(0.0331404\pi\)
−0.994585 + 0.103926i \(0.966860\pi\)
\(510\) 0 0
\(511\) −34.6743 −1.53390
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 0.382896i − 0.0168724i
\(516\) 0 0
\(517\) 61.9292i 2.72364i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.4249 1.15770 0.578848 0.815435i \(-0.303502\pi\)
0.578848 + 0.815435i \(0.303502\pi\)
\(522\) 0 0
\(523\) 13.8880i 0.607278i 0.952787 + 0.303639i \(0.0982017\pi\)
−0.952787 + 0.303639i \(0.901798\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.30035 −0.361569
\(528\) 0 0
\(529\) 21.1222 0.918355
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 5.19615i − 0.225070i
\(534\) 0 0
\(535\) −0.571503 −0.0247082
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 69.8023i − 3.00660i
\(540\) 0 0
\(541\) 25.0161i 1.07553i 0.843096 + 0.537763i \(0.180731\pi\)
−0.843096 + 0.537763i \(0.819269\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 31.0475 1.32993
\(546\) 0 0
\(547\) 14.3455i 0.613371i 0.951811 + 0.306686i \(0.0992200\pi\)
−0.951811 + 0.306686i \(0.900780\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.37867 −0.399545
\(552\) 0 0
\(553\) 9.00000 0.382719
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 32.9912i 1.39788i 0.715179 + 0.698941i \(0.246345\pi\)
−0.715179 + 0.698941i \(0.753655\pi\)
\(558\) 0 0
\(559\) 14.2401 0.602292
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 24.9945i 1.05339i 0.850053 + 0.526697i \(0.176570\pi\)
−0.850053 + 0.526697i \(0.823430\pi\)
\(564\) 0 0
\(565\) − 31.3238i − 1.31780i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.58522 0.234145 0.117072 0.993123i \(-0.462649\pi\)
0.117072 + 0.993123i \(0.462649\pi\)
\(570\) 0 0
\(571\) − 5.57976i − 0.233506i −0.993161 0.116753i \(-0.962751\pi\)
0.993161 0.116753i \(-0.0372485\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 13.2849 0.554019
\(576\) 0 0
\(577\) −9.04748 −0.376651 −0.188326 0.982107i \(-0.560306\pi\)
−0.188326 + 0.982107i \(0.560306\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6.71660i 0.278652i
\(582\) 0 0
\(583\) −2.95729 −0.122478
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.21245i 0.297690i 0.988861 + 0.148845i \(0.0475555\pi\)
−0.988861 + 0.148845i \(0.952444\pi\)
\(588\) 0 0
\(589\) − 9.72286i − 0.400623i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.0475 1.02858 0.514288 0.857617i \(-0.328056\pi\)
0.514288 + 0.857617i \(0.328056\pi\)
\(594\) 0 0
\(595\) 12.8778i 0.527940i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 40.2051 1.64274 0.821369 0.570397i \(-0.193211\pi\)
0.821369 + 0.570397i \(0.193211\pi\)
\(600\) 0 0
\(601\) −10.9627 −0.447176 −0.223588 0.974684i \(-0.571777\pi\)
−0.223588 + 0.974684i \(0.571777\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 39.9194i 1.62295i
\(606\) 0 0
\(607\) 28.4740 1.15572 0.577861 0.816135i \(-0.303888\pi\)
0.577861 + 0.816135i \(0.303888\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 42.6646i 1.72602i
\(612\) 0 0
\(613\) 14.3632i 0.580125i 0.957008 + 0.290063i \(0.0936761\pi\)
−0.957008 + 0.290063i \(0.906324\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.632696 0.0254714 0.0127357 0.999919i \(-0.495946\pi\)
0.0127357 + 0.999919i \(0.495946\pi\)
\(618\) 0 0
\(619\) − 33.4304i − 1.34368i −0.740696 0.671840i \(-0.765504\pi\)
0.740696 0.671840i \(-0.234496\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.2558 −0.691340
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 9.82080i − 0.391581i
\(630\) 0 0
\(631\) −7.59765 −0.302458 −0.151229 0.988499i \(-0.548323\pi\)
−0.151229 + 0.988499i \(0.548323\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7.92531i 0.314506i
\(636\) 0 0
\(637\) − 48.0885i − 1.90534i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 23.7549 0.938261 0.469130 0.883129i \(-0.344567\pi\)
0.469130 + 0.883129i \(0.344567\pi\)
\(642\) 0 0
\(643\) 14.3455i 0.565733i 0.959159 + 0.282867i \(0.0912854\pi\)
−0.959159 + 0.282867i \(0.908715\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28.5781 −1.12352 −0.561761 0.827299i \(-0.689876\pi\)
−0.561761 + 0.827299i \(0.689876\pi\)
\(648\) 0 0
\(649\) −10.9253 −0.428856
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.0253i 0.666251i 0.942882 + 0.333126i \(0.108103\pi\)
−0.942882 + 0.333126i \(0.891897\pi\)
\(654\) 0 0
\(655\) 23.4561 0.916507
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 12.4949i 0.486734i 0.969934 + 0.243367i \(0.0782519\pi\)
−0.969934 + 0.243367i \(0.921748\pi\)
\(660\) 0 0
\(661\) − 34.7879i − 1.35309i −0.736400 0.676547i \(-0.763476\pi\)
0.736400 0.676547i \(-0.236524\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −15.0848 −0.584964
\(666\) 0 0
\(667\) − 31.1487i − 1.20608i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −7.14927 −0.275994
\(672\) 0 0
\(673\) 26.0475 1.00406 0.502028 0.864851i \(-0.332587\pi\)
0.502028 + 0.864851i \(0.332587\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.3511i 1.28179i 0.767630 + 0.640893i \(0.221436\pi\)
−0.767630 + 0.640893i \(0.778564\pi\)
\(678\) 0 0
\(679\) 26.6597 1.02310
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 26.4249i 1.01112i 0.862791 + 0.505560i \(0.168714\pi\)
−0.862791 + 0.505560i \(0.831286\pi\)
\(684\) 0 0
\(685\) − 38.7588i − 1.48090i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2.03735 −0.0776167
\(690\) 0 0
\(691\) − 20.3829i − 0.775402i −0.921785 0.387701i \(-0.873269\pi\)
0.921785 0.387701i \(-0.126731\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 19.9920 0.758341
\(696\) 0 0
\(697\) −2.20699 −0.0835957
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 49.8696i 1.88355i 0.336247 + 0.941774i \(0.390842\pi\)
−0.336247 + 0.941774i \(0.609158\pi\)
\(702\) 0 0
\(703\) 11.5039 0.433877
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 50.3082i 1.89203i
\(708\) 0 0
\(709\) 9.90120i 0.371847i 0.982564 + 0.185924i \(0.0595277\pi\)
−0.982564 + 0.185924i \(0.940472\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 32.2918 1.20934
\(714\) 0 0
\(715\) 40.6272i 1.51937i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −25.5562 −0.953084 −0.476542 0.879152i \(-0.658110\pi\)
−0.476542 + 0.879152i \(0.658110\pi\)
\(720\) 0 0
\(721\) 0.962653 0.0358511
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 9.37867i − 0.348315i
\(726\) 0 0
\(727\) 40.1405 1.48873 0.744364 0.667774i \(-0.232753\pi\)
0.744364 + 0.667774i \(0.232753\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 6.04827i − 0.223704i
\(732\) 0 0
\(733\) − 47.3387i − 1.74849i −0.485481 0.874247i \(-0.661355\pi\)
0.485481 0.874247i \(-0.338645\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.21792 −0.339546
\(738\) 0 0
\(739\) − 37.9627i − 1.39648i −0.715864 0.698239i \(-0.753967\pi\)
0.715864 0.698239i \(-0.246033\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.5196 0.532673 0.266336 0.963880i \(-0.414187\pi\)
0.266336 + 0.963880i \(0.414187\pi\)
\(744\) 0 0
\(745\) −3.87783 −0.142073
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 1.43684i − 0.0525008i
\(750\) 0 0
\(751\) −36.6431 −1.33713 −0.668563 0.743656i \(-0.733090\pi\)
−0.668563 + 0.743656i \(0.733090\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 29.5051i 1.07380i
\(756\) 0 0
\(757\) 2.02727i 0.0736822i 0.999321 + 0.0368411i \(0.0117295\pi\)
−0.999321 + 0.0368411i \(0.988270\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.2070 0.623753 0.311876 0.950123i \(-0.399042\pi\)
0.311876 + 0.950123i \(0.399042\pi\)
\(762\) 0 0
\(763\) 78.0576i 2.82587i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.52671 −0.271774
\(768\) 0 0
\(769\) 26.8506 0.968258 0.484129 0.874997i \(-0.339137\pi\)
0.484129 + 0.874997i \(0.339137\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 4.41305i − 0.158726i −0.996846 0.0793632i \(-0.974711\pi\)
0.996846 0.0793632i \(-0.0252887\pi\)
\(774\) 0 0
\(775\) 9.72286 0.349255
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 2.58522i − 0.0926252i
\(780\) 0 0
\(781\) 57.6820i 2.06403i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.0848216 0.00302741
\(786\) 0 0
\(787\) 34.3829i 1.22562i 0.790231 + 0.612809i \(0.209960\pi\)
−0.790231 + 0.612809i \(0.790040\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 78.7524 2.80011
\(792\) 0 0
\(793\) −4.92531 −0.174903
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 22.8941i − 0.810951i −0.914106 0.405475i \(-0.867106\pi\)
0.914106 0.405475i \(-0.132894\pi\)
\(798\) 0 0
\(799\) 18.1212 0.641080
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 46.4623i 1.63962i
\(804\) 0 0
\(805\) − 50.1001i − 1.76580i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −34.7922 −1.22323 −0.611614 0.791156i \(-0.709480\pi\)
−0.611614 + 0.791156i \(0.709480\pi\)
\(810\) 0 0
\(811\) 11.6810i 0.410174i 0.978744 + 0.205087i \(0.0657478\pi\)
−0.978744 + 0.205087i \(0.934252\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 33.0559 1.15790
\(816\) 0 0
\(817\) 7.08482 0.247867
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 16.0953i 0.561729i 0.959747 + 0.280864i \(0.0906211\pi\)
−0.959747 + 0.280864i \(0.909379\pi\)
\(822\) 0 0
\(823\) 12.8033 0.446294 0.223147 0.974785i \(-0.428367\pi\)
0.223147 + 0.974785i \(0.428367\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 25.9253i − 0.901511i −0.892647 0.450756i \(-0.851155\pi\)
0.892647 0.450756i \(-0.148845\pi\)
\(828\) 0 0
\(829\) 49.0708i 1.70430i 0.523299 + 0.852149i \(0.324701\pi\)
−0.523299 + 0.852149i \(0.675299\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −20.4249 −0.707681
\(834\) 0 0
\(835\) 34.6272i 1.19832i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −30.2550 −1.04452 −0.522259 0.852787i \(-0.674911\pi\)
−0.522259 + 0.852787i \(0.674911\pi\)
\(840\) 0 0
\(841\) 7.01013 0.241729
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 5.47244i 0.188258i
\(846\) 0 0
\(847\) −100.363 −3.44851
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 38.2070i 1.30972i
\(852\) 0 0
\(853\) − 29.9517i − 1.02553i −0.858530 0.512763i \(-0.828622\pi\)
0.858530 0.512763i \(-0.171378\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −23.8031 −0.813100 −0.406550 0.913629i \(-0.633268\pi\)
−0.406550 + 0.913629i \(0.633268\pi\)
\(858\) 0 0
\(859\) − 32.9089i − 1.12284i −0.827532 0.561419i \(-0.810256\pi\)
0.827532 0.561419i \(-0.189744\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −36.3906 −1.23875 −0.619375 0.785095i \(-0.712614\pi\)
−0.619375 + 0.785095i \(0.712614\pi\)
\(864\) 0 0
\(865\) −21.0000 −0.714021
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 12.0597i − 0.409096i
\(870\) 0 0
\(871\) −6.35045 −0.215177
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) − 52.7969i − 1.78486i
\(876\) 0 0
\(877\) 48.9049i 1.65140i 0.564108 + 0.825701i \(0.309220\pi\)
−0.564108 + 0.825701i \(0.690780\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −39.9627 −1.34638 −0.673188 0.739471i \(-0.735076\pi\)
−0.673188 + 0.739471i \(0.735076\pi\)
\(882\) 0 0
\(883\) 10.0000i 0.336527i 0.985742 + 0.168263i \(0.0538159\pi\)
−0.985742 + 0.168263i \(0.946184\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 45.1897 1.51732 0.758661 0.651486i \(-0.225854\pi\)
0.758661 + 0.651486i \(0.225854\pi\)
\(888\) 0 0
\(889\) −19.9253 −0.668273
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 21.2267i 0.710326i
\(894\) 0 0
\(895\) 10.3923 0.347376
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) − 22.7969i − 0.760318i
\(900\) 0 0
\(901\) 0.865333i 0.0288284i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −9.96265 −0.331170
\(906\) 0 0
\(907\) − 40.3829i − 1.34089i −0.741958 0.670446i \(-0.766103\pi\)
0.741958 0.670446i \(-0.233897\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −8.52142 −0.282327 −0.141164 0.989986i \(-0.545084\pi\)
−0.141164 + 0.989986i \(0.545084\pi\)
\(912\) 0 0
\(913\) 9.00000 0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 58.9720i 1.94743i
\(918\) 0 0
\(919\) 2.00834 0.0662490 0.0331245 0.999451i \(-0.489454\pi\)
0.0331245 + 0.999451i \(0.489454\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 39.7386i 1.30801i
\(924\) 0 0
\(925\) 11.5039i 0.378245i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −29.9728 −0.983375 −0.491688 0.870772i \(-0.663620\pi\)
−0.491688 + 0.870772i \(0.663620\pi\)
\(930\) 0 0
\(931\) − 23.9253i − 0.784120i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 17.2558 0.564326
\(936\) 0 0
\(937\) −45.0475 −1.47164 −0.735818 0.677179i \(-0.763202\pi\)
−0.735818 + 0.677179i \(0.763202\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 53.5642i 1.74614i 0.487592 + 0.873072i \(0.337875\pi\)
−0.487592 + 0.873072i \(0.662125\pi\)
\(942\) 0 0
\(943\) 8.58610 0.279602
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 23.8350i 0.774534i 0.921968 + 0.387267i \(0.126581\pi\)
−0.921968 + 0.387267i \(0.873419\pi\)
\(948\) 0 0
\(949\) 32.0090i 1.03906i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 32.4732 1.05191 0.525955 0.850513i \(-0.323708\pi\)
0.525955 + 0.850513i \(0.323708\pi\)
\(954\) 0 0
\(955\) − 0.382896i − 0.0123902i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 97.4451 3.14666
\(960\) 0 0
\(961\) −7.36650 −0.237629
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 31.2591i − 1.00627i
\(966\) 0 0
\(967\) −9.66442 −0.310787 −0.155393 0.987853i \(-0.549665\pi\)
−0.155393 + 0.987853i \(0.549665\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 49.8133i 1.59858i 0.600943 + 0.799292i \(0.294792\pi\)
−0.600943 + 0.799292i \(0.705208\pi\)
\(972\) 0 0
\(973\) 50.2627i 1.61135i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 7.18057 0.229727 0.114863 0.993381i \(-0.463357\pi\)
0.114863 + 0.993381i \(0.463357\pi\)
\(978\) 0 0
\(979\) 23.1222i 0.738988i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.76349 −0.151932 −0.0759658 0.997110i \(-0.524204\pi\)
−0.0759658 + 0.997110i \(0.524204\pi\)
\(984\) 0 0
\(985\) 17.0101 0.541988
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 23.5303i 0.748220i
\(990\) 0 0
\(991\) −28.5781 −0.907815 −0.453907 0.891049i \(-0.649970\pi\)
−0.453907 + 0.891049i \(0.649970\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 1.04748i − 0.0332072i
\(996\) 0 0
\(997\) − 37.2384i − 1.17935i −0.807640 0.589676i \(-0.799255\pi\)
0.807640 0.589676i \(-0.200745\pi\)
\(998\) 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 5184.2.d.r.2593.6 12
3.2 odd 2 5184.2.d.q.2593.12 12
4.3 odd 2 inner 5184.2.d.r.2593.1 12
8.3 odd 2 inner 5184.2.d.r.2593.7 12
8.5 even 2 inner 5184.2.d.r.2593.12 12
9.2 odd 6 576.2.r.e.481.4 yes 12
9.4 even 3 1728.2.r.e.289.1 12
9.5 odd 6 576.2.r.f.97.3 yes 12
9.7 even 3 1728.2.r.f.1441.1 12
12.11 even 2 5184.2.d.q.2593.7 12
24.5 odd 2 5184.2.d.q.2593.6 12
24.11 even 2 5184.2.d.q.2593.1 12
36.7 odd 6 1728.2.r.f.1441.6 12
36.11 even 6 576.2.r.e.481.3 yes 12
36.23 even 6 576.2.r.f.97.4 yes 12
36.31 odd 6 1728.2.r.e.289.6 12
72.5 odd 6 576.2.r.e.97.4 yes 12
72.11 even 6 576.2.r.f.481.4 yes 12
72.13 even 6 1728.2.r.f.289.1 12
72.29 odd 6 576.2.r.f.481.3 yes 12
72.43 odd 6 1728.2.r.e.1441.6 12
72.59 even 6 576.2.r.e.97.3 12
72.61 even 6 1728.2.r.e.1441.1 12
72.67 odd 6 1728.2.r.f.289.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.r.e.97.3 12 72.59 even 6
576.2.r.e.97.4 yes 12 72.5 odd 6
576.2.r.e.481.3 yes 12 36.11 even 6
576.2.r.e.481.4 yes 12 9.2 odd 6
576.2.r.f.97.3 yes 12 9.5 odd 6
576.2.r.f.97.4 yes 12 36.23 even 6
576.2.r.f.481.3 yes 12 72.29 odd 6
576.2.r.f.481.4 yes 12 72.11 even 6
1728.2.r.e.289.1 12 9.4 even 3
1728.2.r.e.289.6 12 36.31 odd 6
1728.2.r.e.1441.1 12 72.61 even 6
1728.2.r.e.1441.6 12 72.43 odd 6
1728.2.r.f.289.1 12 72.13 even 6
1728.2.r.f.289.6 12 72.67 odd 6
1728.2.r.f.1441.1 12 9.7 even 3
1728.2.r.f.1441.6 12 36.7 odd 6
5184.2.d.q.2593.1 12 24.11 even 2
5184.2.d.q.2593.6 12 24.5 odd 2
5184.2.d.q.2593.7 12 12.11 even 2
5184.2.d.q.2593.12 12 3.2 odd 2
5184.2.d.r.2593.1 12 4.3 odd 2 inner
5184.2.d.r.2593.6 12 1.1 even 1 trivial
5184.2.d.r.2593.7 12 8.3 odd 2 inner
5184.2.d.r.2593.12 12 8.5 even 2 inner