Properties

Label 8280.2.a.bw.1.6
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1161328736\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \( x^{7} - 3x^{6} - 18x^{5} + 46x^{4} + 60x^{3} - 76x^{2} - 51x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-0.330805\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{5} +2.34984 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +2.34984 q^{7} -0.333733 q^{11} +3.37929 q^{13} -7.81531 q^{17} +1.20992 q^{19} +1.00000 q^{23} +1.00000 q^{25} -1.35450 q^{29} -10.2907 q^{31} +2.34984 q^{35} +2.83910 q^{37} -7.94371 q^{41} -7.92175 q^{43} -11.7314 q^{47} -1.47824 q^{49} -7.92062 q^{53} -0.333733 q^{55} -13.2728 q^{59} +2.88487 q^{61} +3.37929 q^{65} +7.70597 q^{67} +15.1945 q^{71} -7.02239 q^{73} -0.784221 q^{77} +0.325047 q^{79} -10.4828 q^{83} -7.81531 q^{85} -8.05475 q^{89} +7.94081 q^{91} +1.20992 q^{95} -1.00919 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 7 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 7 q^{5} - 6 q^{7} - 2 q^{11} - 6 q^{13} - 4 q^{17} - 8 q^{19} + 7 q^{23} + 7 q^{25} + 2 q^{29} - 8 q^{31} - 6 q^{35} - 16 q^{37} + 2 q^{41} - 10 q^{43} - 8 q^{47} + 19 q^{49} - 10 q^{53} - 2 q^{55} - 24 q^{59} + 8 q^{61} - 6 q^{65} - 20 q^{67} - 8 q^{71} + 2 q^{73} - 12 q^{77} - 2 q^{79} - 22 q^{83} - 4 q^{85} - 16 q^{89} - 20 q^{91} - 8 q^{95} + 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(7\) 2.34984 0.888157 0.444078 0.895988i \(-0.353531\pi\)
0.444078 + 0.895988i \(0.353531\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.333733 −0.100624 −0.0503122 0.998734i \(-0.516022\pi\)
−0.0503122 + 0.998734i \(0.516022\pi\)
\(12\) 0 0
\(13\) 3.37929 0.937247 0.468624 0.883398i \(-0.344750\pi\)
0.468624 + 0.883398i \(0.344750\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.81531 −1.89549 −0.947746 0.319026i \(-0.896644\pi\)
−0.947746 + 0.319026i \(0.896644\pi\)
\(18\) 0 0
\(19\) 1.20992 0.277575 0.138788 0.990322i \(-0.455679\pi\)
0.138788 + 0.990322i \(0.455679\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.35450 −0.251524 −0.125762 0.992060i \(-0.540138\pi\)
−0.125762 + 0.992060i \(0.540138\pi\)
\(30\) 0 0
\(31\) −10.2907 −1.84827 −0.924134 0.382070i \(-0.875211\pi\)
−0.924134 + 0.382070i \(0.875211\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.34984 0.397196
\(36\) 0 0
\(37\) 2.83910 0.466745 0.233372 0.972387i \(-0.425024\pi\)
0.233372 + 0.972387i \(0.425024\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.94371 −1.24060 −0.620300 0.784365i \(-0.712989\pi\)
−0.620300 + 0.784365i \(0.712989\pi\)
\(42\) 0 0
\(43\) −7.92175 −1.20806 −0.604028 0.796963i \(-0.706438\pi\)
−0.604028 + 0.796963i \(0.706438\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.7314 −1.71120 −0.855600 0.517638i \(-0.826811\pi\)
−0.855600 + 0.517638i \(0.826811\pi\)
\(48\) 0 0
\(49\) −1.47824 −0.211178
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −7.92062 −1.08798 −0.543990 0.839092i \(-0.683087\pi\)
−0.543990 + 0.839092i \(0.683087\pi\)
\(54\) 0 0
\(55\) −0.333733 −0.0450006
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −13.2728 −1.72797 −0.863985 0.503517i \(-0.832039\pi\)
−0.863985 + 0.503517i \(0.832039\pi\)
\(60\) 0 0
\(61\) 2.88487 0.369370 0.184685 0.982798i \(-0.440873\pi\)
0.184685 + 0.982798i \(0.440873\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.37929 0.419150
\(66\) 0 0
\(67\) 7.70597 0.941434 0.470717 0.882284i \(-0.343995\pi\)
0.470717 + 0.882284i \(0.343995\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 15.1945 1.80326 0.901630 0.432508i \(-0.142371\pi\)
0.901630 + 0.432508i \(0.142371\pi\)
\(72\) 0 0
\(73\) −7.02239 −0.821909 −0.410955 0.911656i \(-0.634805\pi\)
−0.410955 + 0.911656i \(0.634805\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.784221 −0.0893703
\(78\) 0 0
\(79\) 0.325047 0.0365707 0.0182853 0.999833i \(-0.494179\pi\)
0.0182853 + 0.999833i \(0.494179\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −10.4828 −1.15063 −0.575317 0.817930i \(-0.695121\pi\)
−0.575317 + 0.817930i \(0.695121\pi\)
\(84\) 0 0
\(85\) −7.81531 −0.847690
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.05475 −0.853802 −0.426901 0.904298i \(-0.640395\pi\)
−0.426901 + 0.904298i \(0.640395\pi\)
\(90\) 0 0
\(91\) 7.94081 0.832423
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.20992 0.124135
\(96\) 0 0
\(97\) −1.00919 −0.102468 −0.0512341 0.998687i \(-0.516315\pi\)
−0.0512341 + 0.998687i \(0.516315\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 11.6145 1.15569 0.577844 0.816147i \(-0.303894\pi\)
0.577844 + 0.816147i \(0.303894\pi\)
\(102\) 0 0
\(103\) 12.8961 1.27069 0.635346 0.772228i \(-0.280858\pi\)
0.635346 + 0.772228i \(0.280858\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.2078 1.47019 0.735097 0.677962i \(-0.237137\pi\)
0.735097 + 0.677962i \(0.237137\pi\)
\(108\) 0 0
\(109\) −12.0680 −1.15590 −0.577950 0.816072i \(-0.696147\pi\)
−0.577950 + 0.816072i \(0.696147\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.15370 0.108531 0.0542657 0.998527i \(-0.482718\pi\)
0.0542657 + 0.998527i \(0.482718\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −18.3648 −1.68349
\(120\) 0 0
\(121\) −10.8886 −0.989875
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −7.77157 −0.689615 −0.344808 0.938673i \(-0.612056\pi\)
−0.344808 + 0.938673i \(0.612056\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.59841 0.139654 0.0698268 0.997559i \(-0.477755\pi\)
0.0698268 + 0.997559i \(0.477755\pi\)
\(132\) 0 0
\(133\) 2.84312 0.246530
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.98666 −0.426039 −0.213019 0.977048i \(-0.568330\pi\)
−0.213019 + 0.977048i \(0.568330\pi\)
\(138\) 0 0
\(139\) −11.3677 −0.964192 −0.482096 0.876118i \(-0.660124\pi\)
−0.482096 + 0.876118i \(0.660124\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.12778 −0.0943100
\(144\) 0 0
\(145\) −1.35450 −0.112485
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 18.4841 1.51428 0.757139 0.653254i \(-0.226596\pi\)
0.757139 + 0.653254i \(0.226596\pi\)
\(150\) 0 0
\(151\) −14.6892 −1.19539 −0.597694 0.801724i \(-0.703916\pi\)
−0.597694 + 0.801724i \(0.703916\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −10.2907 −0.826570
\(156\) 0 0
\(157\) 7.70994 0.615320 0.307660 0.951496i \(-0.400454\pi\)
0.307660 + 0.951496i \(0.400454\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.34984 0.185193
\(162\) 0 0
\(163\) −16.2704 −1.27440 −0.637198 0.770700i \(-0.719907\pi\)
−0.637198 + 0.770700i \(0.719907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.6828 −1.21357 −0.606786 0.794865i \(-0.707542\pi\)
−0.606786 + 0.794865i \(0.707542\pi\)
\(168\) 0 0
\(169\) −1.58037 −0.121567
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 14.7815 1.12382 0.561908 0.827200i \(-0.310068\pi\)
0.561908 + 0.827200i \(0.310068\pi\)
\(174\) 0 0
\(175\) 2.34984 0.177631
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.66161 −0.647399 −0.323700 0.946160i \(-0.604927\pi\)
−0.323700 + 0.946160i \(0.604927\pi\)
\(180\) 0 0
\(181\) 5.53481 0.411400 0.205700 0.978615i \(-0.434053\pi\)
0.205700 + 0.978615i \(0.434053\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.83910 0.208734
\(186\) 0 0
\(187\) 2.60823 0.190733
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.81157 −0.131081 −0.0655403 0.997850i \(-0.520877\pi\)
−0.0655403 + 0.997850i \(0.520877\pi\)
\(192\) 0 0
\(193\) 26.9261 1.93819 0.969093 0.246695i \(-0.0793447\pi\)
0.969093 + 0.246695i \(0.0793447\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.60772 −0.542028 −0.271014 0.962575i \(-0.587359\pi\)
−0.271014 + 0.962575i \(0.587359\pi\)
\(198\) 0 0
\(199\) −7.99167 −0.566515 −0.283257 0.959044i \(-0.591415\pi\)
−0.283257 + 0.959044i \(0.591415\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.18286 −0.223393
\(204\) 0 0
\(205\) −7.94371 −0.554813
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −0.403791 −0.0279308
\(210\) 0 0
\(211\) 4.70950 0.324215 0.162108 0.986773i \(-0.448171\pi\)
0.162108 + 0.986773i \(0.448171\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.92175 −0.540259
\(216\) 0 0
\(217\) −24.1816 −1.64155
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −26.4102 −1.77654
\(222\) 0 0
\(223\) 25.3766 1.69934 0.849670 0.527315i \(-0.176801\pi\)
0.849670 + 0.527315i \(0.176801\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.4820 0.695714 0.347857 0.937548i \(-0.386909\pi\)
0.347857 + 0.937548i \(0.386909\pi\)
\(228\) 0 0
\(229\) 29.3540 1.93977 0.969884 0.243566i \(-0.0783173\pi\)
0.969884 + 0.243566i \(0.0783173\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.9472 −1.37229 −0.686147 0.727463i \(-0.740700\pi\)
−0.686147 + 0.727463i \(0.740700\pi\)
\(234\) 0 0
\(235\) −11.7314 −0.765272
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.00679442 0.000439494 0 0.000219747 1.00000i \(-0.499930\pi\)
0.000219747 1.00000i \(0.499930\pi\)
\(240\) 0 0
\(241\) 28.2482 1.81963 0.909814 0.415017i \(-0.136224\pi\)
0.909814 + 0.415017i \(0.136224\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.47824 −0.0944415
\(246\) 0 0
\(247\) 4.08868 0.260156
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.85470 −0.622023 −0.311011 0.950406i \(-0.600668\pi\)
−0.311011 + 0.950406i \(0.600668\pi\)
\(252\) 0 0
\(253\) −0.333733 −0.0209816
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −7.06873 −0.440935 −0.220467 0.975394i \(-0.570758\pi\)
−0.220467 + 0.975394i \(0.570758\pi\)
\(258\) 0 0
\(259\) 6.67143 0.414542
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −11.9113 −0.734482 −0.367241 0.930126i \(-0.619698\pi\)
−0.367241 + 0.930126i \(0.619698\pi\)
\(264\) 0 0
\(265\) −7.92062 −0.486560
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 30.5465 1.86245 0.931227 0.364440i \(-0.118739\pi\)
0.931227 + 0.364440i \(0.118739\pi\)
\(270\) 0 0
\(271\) 12.1356 0.737183 0.368591 0.929592i \(-0.379840\pi\)
0.368591 + 0.929592i \(0.379840\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.333733 −0.0201249
\(276\) 0 0
\(277\) 13.7470 0.825974 0.412987 0.910737i \(-0.364485\pi\)
0.412987 + 0.910737i \(0.364485\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −21.3351 −1.27275 −0.636374 0.771381i \(-0.719566\pi\)
−0.636374 + 0.771381i \(0.719566\pi\)
\(282\) 0 0
\(283\) 16.1882 0.962287 0.481144 0.876642i \(-0.340222\pi\)
0.481144 + 0.876642i \(0.340222\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.6665 −1.10185
\(288\) 0 0
\(289\) 44.0791 2.59289
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 25.4006 1.48392 0.741959 0.670445i \(-0.233897\pi\)
0.741959 + 0.670445i \(0.233897\pi\)
\(294\) 0 0
\(295\) −13.2728 −0.772772
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.37929 0.195430
\(300\) 0 0
\(301\) −18.6149 −1.07294
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.88487 0.165187
\(306\) 0 0
\(307\) −17.8342 −1.01785 −0.508927 0.860810i \(-0.669958\pi\)
−0.508927 + 0.860810i \(0.669958\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.21196 0.465658 0.232829 0.972518i \(-0.425202\pi\)
0.232829 + 0.972518i \(0.425202\pi\)
\(312\) 0 0
\(313\) 26.6902 1.50862 0.754308 0.656520i \(-0.227972\pi\)
0.754308 + 0.656520i \(0.227972\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.2587 −1.02551 −0.512756 0.858534i \(-0.671375\pi\)
−0.512756 + 0.858534i \(0.671375\pi\)
\(318\) 0 0
\(319\) 0.452042 0.0253095
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −9.45592 −0.526141
\(324\) 0 0
\(325\) 3.37929 0.187449
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −27.5669 −1.51981
\(330\) 0 0
\(331\) −17.2539 −0.948359 −0.474179 0.880428i \(-0.657255\pi\)
−0.474179 + 0.880428i \(0.657255\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.70597 0.421022
\(336\) 0 0
\(337\) −34.1028 −1.85770 −0.928848 0.370460i \(-0.879200\pi\)
−0.928848 + 0.370460i \(0.879200\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.43436 0.185981
\(342\) 0 0
\(343\) −19.9225 −1.07572
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.63528 0.409883 0.204942 0.978774i \(-0.434300\pi\)
0.204942 + 0.978774i \(0.434300\pi\)
\(348\) 0 0
\(349\) 30.9799 1.65832 0.829158 0.559015i \(-0.188820\pi\)
0.829158 + 0.559015i \(0.188820\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −6.93004 −0.368849 −0.184424 0.982847i \(-0.559042\pi\)
−0.184424 + 0.982847i \(0.559042\pi\)
\(354\) 0 0
\(355\) 15.1945 0.806442
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.20979 0.486074 0.243037 0.970017i \(-0.421856\pi\)
0.243037 + 0.970017i \(0.421856\pi\)
\(360\) 0 0
\(361\) −17.5361 −0.922952
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.02239 −0.367569
\(366\) 0 0
\(367\) 17.8092 0.929631 0.464816 0.885408i \(-0.346121\pi\)
0.464816 + 0.885408i \(0.346121\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −18.6122 −0.966297
\(372\) 0 0
\(373\) −27.0055 −1.39829 −0.699145 0.714980i \(-0.746436\pi\)
−0.699145 + 0.714980i \(0.746436\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.57725 −0.235740
\(378\) 0 0
\(379\) −29.9380 −1.53781 −0.768907 0.639361i \(-0.779199\pi\)
−0.768907 + 0.639361i \(0.779199\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.61303 0.0824221 0.0412110 0.999150i \(-0.486878\pi\)
0.0412110 + 0.999150i \(0.486878\pi\)
\(384\) 0 0
\(385\) −0.784221 −0.0399676
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −15.1507 −0.768172 −0.384086 0.923297i \(-0.625483\pi\)
−0.384086 + 0.923297i \(0.625483\pi\)
\(390\) 0 0
\(391\) −7.81531 −0.395237
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.325047 0.0163549
\(396\) 0 0
\(397\) −5.69395 −0.285771 −0.142885 0.989739i \(-0.545638\pi\)
−0.142885 + 0.989739i \(0.545638\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.72660 0.435786 0.217893 0.975973i \(-0.430082\pi\)
0.217893 + 0.975973i \(0.430082\pi\)
\(402\) 0 0
\(403\) −34.7754 −1.73228
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.947501 −0.0469659
\(408\) 0 0
\(409\) 20.0768 0.992733 0.496367 0.868113i \(-0.334667\pi\)
0.496367 + 0.868113i \(0.334667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −31.1890 −1.53471
\(414\) 0 0
\(415\) −10.4828 −0.514579
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.8662 −0.970527 −0.485263 0.874368i \(-0.661276\pi\)
−0.485263 + 0.874368i \(0.661276\pi\)
\(420\) 0 0
\(421\) −20.3892 −0.993708 −0.496854 0.867834i \(-0.665512\pi\)
−0.496854 + 0.867834i \(0.665512\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.81531 −0.379098
\(426\) 0 0
\(427\) 6.77900 0.328059
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.44768 0.117901 0.0589503 0.998261i \(-0.481225\pi\)
0.0589503 + 0.998261i \(0.481225\pi\)
\(432\) 0 0
\(433\) 26.6576 1.28108 0.640542 0.767923i \(-0.278710\pi\)
0.640542 + 0.767923i \(0.278710\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.20992 0.0578784
\(438\) 0 0
\(439\) 14.2544 0.680324 0.340162 0.940367i \(-0.389518\pi\)
0.340162 + 0.940367i \(0.389518\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.350414 −0.0166487 −0.00832433 0.999965i \(-0.502650\pi\)
−0.00832433 + 0.999965i \(0.502650\pi\)
\(444\) 0 0
\(445\) −8.05475 −0.381832
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.04679 0.190980 0.0954900 0.995430i \(-0.469558\pi\)
0.0954900 + 0.995430i \(0.469558\pi\)
\(450\) 0 0
\(451\) 2.65108 0.124835
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7.94081 0.372271
\(456\) 0 0
\(457\) −5.60780 −0.262322 −0.131161 0.991361i \(-0.541870\pi\)
−0.131161 + 0.991361i \(0.541870\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.0088 0.605880 0.302940 0.953010i \(-0.402032\pi\)
0.302940 + 0.953010i \(0.402032\pi\)
\(462\) 0 0
\(463\) 18.6108 0.864918 0.432459 0.901654i \(-0.357646\pi\)
0.432459 + 0.901654i \(0.357646\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −22.4676 −1.03968 −0.519838 0.854265i \(-0.674008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(468\) 0 0
\(469\) 18.1078 0.836141
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.64375 0.121560
\(474\) 0 0
\(475\) 1.20992 0.0555150
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.60035 −0.301578 −0.150789 0.988566i \(-0.548181\pi\)
−0.150789 + 0.988566i \(0.548181\pi\)
\(480\) 0 0
\(481\) 9.59414 0.437455
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.00919 −0.0458252
\(486\) 0 0
\(487\) 0.00974374 0.000441531 0 0.000220765 1.00000i \(-0.499930\pi\)
0.000220765 1.00000i \(0.499930\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −38.1282 −1.72070 −0.860351 0.509702i \(-0.829756\pi\)
−0.860351 + 0.509702i \(0.829756\pi\)
\(492\) 0 0
\(493\) 10.5858 0.476762
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 35.7048 1.60158
\(498\) 0 0
\(499\) 17.1894 0.769505 0.384753 0.923020i \(-0.374287\pi\)
0.384753 + 0.923020i \(0.374287\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −11.7526 −0.524022 −0.262011 0.965065i \(-0.584386\pi\)
−0.262011 + 0.965065i \(0.584386\pi\)
\(504\) 0 0
\(505\) 11.6145 0.516839
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −17.2543 −0.764783 −0.382391 0.924000i \(-0.624899\pi\)
−0.382391 + 0.924000i \(0.624899\pi\)
\(510\) 0 0
\(511\) −16.5015 −0.729984
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 12.8961 0.568270
\(516\) 0 0
\(517\) 3.91516 0.172188
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −36.6710 −1.60658 −0.803292 0.595585i \(-0.796920\pi\)
−0.803292 + 0.595585i \(0.796920\pi\)
\(522\) 0 0
\(523\) −25.3419 −1.10813 −0.554063 0.832475i \(-0.686923\pi\)
−0.554063 + 0.832475i \(0.686923\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 80.4252 3.50338
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −26.8441 −1.16275
\(534\) 0 0
\(535\) 15.2078 0.657491
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.493339 0.0212496
\(540\) 0 0
\(541\) 31.2913 1.34532 0.672658 0.739953i \(-0.265152\pi\)
0.672658 + 0.739953i \(0.265152\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −12.0680 −0.516934
\(546\) 0 0
\(547\) −39.8281 −1.70293 −0.851464 0.524412i \(-0.824285\pi\)
−0.851464 + 0.524412i \(0.824285\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.63884 −0.0698168
\(552\) 0 0
\(553\) 0.763810 0.0324805
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.5055 −1.20782 −0.603908 0.797054i \(-0.706390\pi\)
−0.603908 + 0.797054i \(0.706390\pi\)
\(558\) 0 0
\(559\) −26.7699 −1.13225
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 10.7082 0.451296 0.225648 0.974209i \(-0.427550\pi\)
0.225648 + 0.974209i \(0.427550\pi\)
\(564\) 0 0
\(565\) 1.15370 0.0485367
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 39.8053 1.66873 0.834363 0.551216i \(-0.185836\pi\)
0.834363 + 0.551216i \(0.185836\pi\)
\(570\) 0 0
\(571\) −29.6536 −1.24097 −0.620483 0.784220i \(-0.713063\pi\)
−0.620483 + 0.784220i \(0.713063\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.00000 0.0417029
\(576\) 0 0
\(577\) 11.6699 0.485824 0.242912 0.970048i \(-0.421897\pi\)
0.242912 + 0.970048i \(0.421897\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −24.6329 −1.02194
\(582\) 0 0
\(583\) 2.64338 0.109477
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.01134 0.330663 0.165332 0.986238i \(-0.447131\pi\)
0.165332 + 0.986238i \(0.447131\pi\)
\(588\) 0 0
\(589\) −12.4510 −0.513033
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 6.83280 0.280590 0.140295 0.990110i \(-0.455195\pi\)
0.140295 + 0.990110i \(0.455195\pi\)
\(594\) 0 0
\(595\) −18.3648 −0.752881
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −30.5228 −1.24713 −0.623563 0.781773i \(-0.714316\pi\)
−0.623563 + 0.781773i \(0.714316\pi\)
\(600\) 0 0
\(601\) −22.2373 −0.907080 −0.453540 0.891236i \(-0.649839\pi\)
−0.453540 + 0.891236i \(0.649839\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −10.8886 −0.442685
\(606\) 0 0
\(607\) −45.5255 −1.84782 −0.923912 0.382605i \(-0.875027\pi\)
−0.923912 + 0.382605i \(0.875027\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −39.6438 −1.60382
\(612\) 0 0
\(613\) 0.297344 0.0120096 0.00600481 0.999982i \(-0.498089\pi\)
0.00600481 + 0.999982i \(0.498089\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.4980 −1.18755 −0.593773 0.804633i \(-0.702362\pi\)
−0.593773 + 0.804633i \(0.702362\pi\)
\(618\) 0 0
\(619\) 0.774004 0.0311098 0.0155549 0.999879i \(-0.495049\pi\)
0.0155549 + 0.999879i \(0.495049\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18.9274 −0.758310
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −22.1884 −0.884710
\(630\) 0 0
\(631\) 26.4887 1.05450 0.527249 0.849711i \(-0.323224\pi\)
0.527249 + 0.849711i \(0.323224\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.77157 −0.308405
\(636\) 0 0
\(637\) −4.99542 −0.197926
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −35.5092 −1.40253 −0.701264 0.712901i \(-0.747381\pi\)
−0.701264 + 0.712901i \(0.747381\pi\)
\(642\) 0 0
\(643\) −3.28511 −0.129552 −0.0647761 0.997900i \(-0.520633\pi\)
−0.0647761 + 0.997900i \(0.520633\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.1929 0.479352 0.239676 0.970853i \(-0.422959\pi\)
0.239676 + 0.970853i \(0.422959\pi\)
\(648\) 0 0
\(649\) 4.42957 0.173876
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 18.9398 0.741171 0.370585 0.928798i \(-0.379157\pi\)
0.370585 + 0.928798i \(0.379157\pi\)
\(654\) 0 0
\(655\) 1.59841 0.0624550
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.9980 −0.623192 −0.311596 0.950215i \(-0.600864\pi\)
−0.311596 + 0.950215i \(0.600864\pi\)
\(660\) 0 0
\(661\) 37.2112 1.44735 0.723675 0.690141i \(-0.242452\pi\)
0.723675 + 0.690141i \(0.242452\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.84312 0.110252
\(666\) 0 0
\(667\) −1.35450 −0.0524464
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.962779 −0.0371677
\(672\) 0 0
\(673\) 31.8952 1.22947 0.614736 0.788733i \(-0.289263\pi\)
0.614736 + 0.788733i \(0.289263\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.4331 −0.823743 −0.411871 0.911242i \(-0.635125\pi\)
−0.411871 + 0.911242i \(0.635125\pi\)
\(678\) 0 0
\(679\) −2.37145 −0.0910078
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 30.5938 1.17064 0.585320 0.810802i \(-0.300969\pi\)
0.585320 + 0.810802i \(0.300969\pi\)
\(684\) 0 0
\(685\) −4.98666 −0.190530
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −26.7661 −1.01971
\(690\) 0 0
\(691\) −7.45708 −0.283681 −0.141840 0.989890i \(-0.545302\pi\)
−0.141840 + 0.989890i \(0.545302\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.3677 −0.431200
\(696\) 0 0
\(697\) 62.0826 2.35155
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 44.1300 1.66677 0.833383 0.552696i \(-0.186401\pi\)
0.833383 + 0.552696i \(0.186401\pi\)
\(702\) 0 0
\(703\) 3.43508 0.129557
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27.2923 1.02643
\(708\) 0 0
\(709\) 19.5296 0.733451 0.366726 0.930329i \(-0.380479\pi\)
0.366726 + 0.930329i \(0.380479\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.2907 −0.385390
\(714\) 0 0
\(715\) −1.12778 −0.0421767
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.4663 0.800557 0.400278 0.916394i \(-0.368913\pi\)
0.400278 + 0.916394i \(0.368913\pi\)
\(720\) 0 0
\(721\) 30.3038 1.12857
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.35450 −0.0503048
\(726\) 0 0
\(727\) 5.33502 0.197865 0.0989325 0.995094i \(-0.468457\pi\)
0.0989325 + 0.995094i \(0.468457\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 61.9109 2.28986
\(732\) 0 0
\(733\) −16.2267 −0.599349 −0.299674 0.954042i \(-0.596878\pi\)
−0.299674 + 0.954042i \(0.596878\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.57174 −0.0947313
\(738\) 0 0
\(739\) 47.0855 1.73207 0.866034 0.499985i \(-0.166661\pi\)
0.866034 + 0.499985i \(0.166661\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −44.2973 −1.62511 −0.812555 0.582885i \(-0.801924\pi\)
−0.812555 + 0.582885i \(0.801924\pi\)
\(744\) 0 0
\(745\) 18.4841 0.677206
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 35.7359 1.30576
\(750\) 0 0
\(751\) −36.6518 −1.33744 −0.668721 0.743513i \(-0.733158\pi\)
−0.668721 + 0.743513i \(0.733158\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −14.6892 −0.534594
\(756\) 0 0
\(757\) 3.88129 0.141068 0.0705339 0.997509i \(-0.477530\pi\)
0.0705339 + 0.997509i \(0.477530\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.935040 0.0338952 0.0169476 0.999856i \(-0.494605\pi\)
0.0169476 + 0.999856i \(0.494605\pi\)
\(762\) 0 0
\(763\) −28.3578 −1.02662
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −44.8527 −1.61954
\(768\) 0 0
\(769\) −4.23198 −0.152609 −0.0763046 0.997085i \(-0.524312\pi\)
−0.0763046 + 0.997085i \(0.524312\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.17222 −0.0781293 −0.0390646 0.999237i \(-0.512438\pi\)
−0.0390646 + 0.999237i \(0.512438\pi\)
\(774\) 0 0
\(775\) −10.2907 −0.369653
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.61127 −0.344360
\(780\) 0 0
\(781\) −5.07093 −0.181452
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 7.70994 0.275180
\(786\) 0 0
\(787\) −39.4188 −1.40513 −0.702564 0.711621i \(-0.747961\pi\)
−0.702564 + 0.711621i \(0.747961\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.71102 0.0963928
\(792\) 0 0
\(793\) 9.74884 0.346191
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.30785 −0.188014 −0.0940068 0.995572i \(-0.529968\pi\)
−0.0940068 + 0.995572i \(0.529968\pi\)
\(798\) 0 0
\(799\) 91.6845 3.24356
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.34361 0.0827041
\(804\) 0 0
\(805\) 2.34984 0.0828210
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 52.9515 1.86168 0.930838 0.365431i \(-0.119079\pi\)
0.930838 + 0.365431i \(0.119079\pi\)
\(810\) 0 0
\(811\) −41.8333 −1.46897 −0.734483 0.678627i \(-0.762575\pi\)
−0.734483 + 0.678627i \(0.762575\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −16.2704 −0.569927
\(816\) 0 0
\(817\) −9.58469 −0.335326
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −48.5303 −1.69372 −0.846860 0.531816i \(-0.821510\pi\)
−0.846860 + 0.531816i \(0.821510\pi\)
\(822\) 0 0
\(823\) −32.4844 −1.13233 −0.566167 0.824291i \(-0.691574\pi\)
−0.566167 + 0.824291i \(0.691574\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 44.9416 1.56277 0.781385 0.624049i \(-0.214513\pi\)
0.781385 + 0.624049i \(0.214513\pi\)
\(828\) 0 0
\(829\) 0.782855 0.0271897 0.0135948 0.999908i \(-0.495672\pi\)
0.0135948 + 0.999908i \(0.495672\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 11.5529 0.400285
\(834\) 0 0
\(835\) −15.6828 −0.542726
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −6.55402 −0.226270 −0.113135 0.993580i \(-0.536089\pi\)
−0.113135 + 0.993580i \(0.536089\pi\)
\(840\) 0 0
\(841\) −27.1653 −0.936736
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.58037 −0.0543665
\(846\) 0 0
\(847\) −25.5865 −0.879164
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.83910 0.0973230
\(852\) 0 0
\(853\) −33.8079 −1.15756 −0.578780 0.815484i \(-0.696471\pi\)
−0.578780 + 0.815484i \(0.696471\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.8990 1.67036 0.835180 0.549977i \(-0.185364\pi\)
0.835180 + 0.549977i \(0.185364\pi\)
\(858\) 0 0
\(859\) −8.46428 −0.288797 −0.144399 0.989520i \(-0.546125\pi\)
−0.144399 + 0.989520i \(0.546125\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.62307 0.123331 0.0616654 0.998097i \(-0.480359\pi\)
0.0616654 + 0.998097i \(0.480359\pi\)
\(864\) 0 0
\(865\) 14.7815 0.502586
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −0.108479 −0.00367990
\(870\) 0 0
\(871\) 26.0407 0.882357
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.34984 0.0794392
\(876\) 0 0
\(877\) −10.9308 −0.369108 −0.184554 0.982822i \(-0.559084\pi\)
−0.184554 + 0.982822i \(0.559084\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 16.0740 0.541545 0.270773 0.962643i \(-0.412721\pi\)
0.270773 + 0.962643i \(0.412721\pi\)
\(882\) 0 0
\(883\) 24.7421 0.832639 0.416319 0.909218i \(-0.363320\pi\)
0.416319 + 0.909218i \(0.363320\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −37.8153 −1.26971 −0.634856 0.772630i \(-0.718941\pi\)
−0.634856 + 0.772630i \(0.718941\pi\)
\(888\) 0 0
\(889\) −18.2620 −0.612487
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −14.1941 −0.474986
\(894\) 0 0
\(895\) −8.66161 −0.289526
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 13.9388 0.464884
\(900\) 0 0
\(901\) 61.9021 2.06226
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 5.53481 0.183983
\(906\) 0 0
\(907\) −53.9550 −1.79155 −0.895774 0.444510i \(-0.853378\pi\)
−0.895774 + 0.444510i \(0.853378\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −31.8570 −1.05547 −0.527735 0.849409i \(-0.676959\pi\)
−0.527735 + 0.849409i \(0.676959\pi\)
\(912\) 0 0
\(913\) 3.49845 0.115782
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.75601 0.124034
\(918\) 0 0
\(919\) −26.8032 −0.884157 −0.442078 0.896976i \(-0.645759\pi\)
−0.442078 + 0.896976i \(0.645759\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 51.3468 1.69010
\(924\) 0 0
\(925\) 2.83910 0.0933489
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.25414 0.139574 0.0697870 0.997562i \(-0.477768\pi\)
0.0697870 + 0.997562i \(0.477768\pi\)
\(930\) 0 0
\(931\) −1.78856 −0.0586176
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.60823 0.0852983
\(936\) 0 0
\(937\) 33.6296 1.09863 0.549316 0.835615i \(-0.314888\pi\)
0.549316 + 0.835615i \(0.314888\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 37.3525 1.21766 0.608829 0.793302i \(-0.291640\pi\)
0.608829 + 0.793302i \(0.291640\pi\)
\(942\) 0 0
\(943\) −7.94371 −0.258683
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −52.4779 −1.70530 −0.852652 0.522479i \(-0.825007\pi\)
−0.852652 + 0.522479i \(0.825007\pi\)
\(948\) 0 0
\(949\) −23.7307 −0.770332
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 3.95962 0.128265 0.0641323 0.997941i \(-0.479572\pi\)
0.0641323 + 0.997941i \(0.479572\pi\)
\(954\) 0 0
\(955\) −1.81157 −0.0586210
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −11.7179 −0.378389
\(960\) 0 0
\(961\) 74.8988 2.41609
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 26.9261 0.866783
\(966\) 0 0
\(967\) −24.7487 −0.795864 −0.397932 0.917415i \(-0.630272\pi\)
−0.397932 + 0.917415i \(0.630272\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −20.3608 −0.653408 −0.326704 0.945127i \(-0.605938\pi\)
−0.326704 + 0.945127i \(0.605938\pi\)
\(972\) 0 0
\(973\) −26.7122 −0.856354
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −49.2849 −1.57676 −0.788381 0.615187i \(-0.789081\pi\)
−0.788381 + 0.615187i \(0.789081\pi\)
\(978\) 0 0
\(979\) 2.68814 0.0859134
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −15.9279 −0.508022 −0.254011 0.967201i \(-0.581750\pi\)
−0.254011 + 0.967201i \(0.581750\pi\)
\(984\) 0 0
\(985\) −7.60772 −0.242402
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.92175 −0.251897
\(990\) 0 0
\(991\) 13.8100 0.438688 0.219344 0.975648i \(-0.429608\pi\)
0.219344 + 0.975648i \(0.429608\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −7.99167 −0.253353
\(996\) 0 0
\(997\) −44.7356 −1.41679 −0.708396 0.705815i \(-0.750581\pi\)
−0.708396 + 0.705815i \(0.750581\pi\)
\(998\) 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 8280.2.a.bw.1.6 yes 7
3.2 odd 2 8280.2.a.bv.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bv.1.6 7 3.2 odd 2
8280.2.a.bw.1.6 yes 7 1.1 even 1 trivial