Properties

Label 8280.2.a.bt.1.2
Level $8280$
Weight $2$
Character 8280.1
Self dual yes
Analytic conductor $66.116$
Analytic rank $1$
Dimension $6$
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: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.287750\) of defining polynomial
Character \(\chi\) \(=\) 8280.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{5} -2.73629 q^{7} +O(q^{10})\) \(q-1.00000 q^{5} -2.73629 q^{7} +5.97718 q^{11} -5.40168 q^{13} +6.94546 q^{17} -3.97718 q^{19} -1.00000 q^{23} +1.00000 q^{25} -9.29741 q^{29} -3.54378 q^{31} +2.73629 q^{35} +7.17782 q^{37} +10.1945 q^{41} +1.42450 q^{43} +10.4187 q^{47} +0.487260 q^{49} -4.04839 q^{53} -5.97718 q^{55} -8.13797 q^{59} -3.34516 q^{61} +5.40168 q^{65} -1.70525 q^{67} +7.56247 q^{71} +7.85722 q^{73} -16.3553 q^{77} -1.36798 q^{79} -13.9709 q^{83} -6.94546 q^{85} +6.49805 q^{89} +14.7805 q^{91} +3.97718 q^{95} -13.8769 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{5} - 2 q^{7} + 4 q^{11} - 4 q^{17} + 8 q^{19} - 6 q^{23} + 6 q^{25} - 18 q^{29} - 8 q^{31} + 2 q^{35} + 6 q^{37} - 6 q^{41} + 8 q^{43} + 8 q^{47} + 10 q^{49} - 8 q^{53} - 4 q^{55} - 2 q^{59} - 8 q^{61} - 2 q^{67} - 2 q^{71} + 8 q^{73} - 16 q^{77} - 28 q^{79} - 24 q^{83} + 4 q^{85} - 4 q^{89} - 8 q^{91} - 8 q^{95} + 24 q^{97}+O(q^{100}) \) 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
\(7\) −2.73629 −1.03422 −0.517109 0.855919i \(-0.672992\pi\)
−0.517109 + 0.855919i \(0.672992\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.97718 1.80219 0.901094 0.433624i \(-0.142765\pi\)
0.901094 + 0.433624i \(0.142765\pi\)
\(12\) 0 0
\(13\) −5.40168 −1.49816 −0.749078 0.662482i \(-0.769503\pi\)
−0.749078 + 0.662482i \(0.769503\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.94546 1.68452 0.842261 0.539070i \(-0.181224\pi\)
0.842261 + 0.539070i \(0.181224\pi\)
\(18\) 0 0
\(19\) −3.97718 −0.912428 −0.456214 0.889870i \(-0.650795\pi\)
−0.456214 + 0.889870i \(0.650795\pi\)
\(20\) 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
\(29\) −9.29741 −1.72649 −0.863243 0.504788i \(-0.831571\pi\)
−0.863243 + 0.504788i \(0.831571\pi\)
\(30\) 0 0
\(31\) −3.54378 −0.636482 −0.318241 0.948010i \(-0.603092\pi\)
−0.318241 + 0.948010i \(0.603092\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.73629 0.462517
\(36\) 0 0
\(37\) 7.17782 1.18003 0.590013 0.807394i \(-0.299123\pi\)
0.590013 + 0.807394i \(0.299123\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.1945 1.59211 0.796056 0.605223i \(-0.206916\pi\)
0.796056 + 0.605223i \(0.206916\pi\)
\(42\) 0 0
\(43\) 1.42450 0.217234 0.108617 0.994084i \(-0.465358\pi\)
0.108617 + 0.994084i \(0.465358\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.4187 1.51973 0.759863 0.650084i \(-0.225266\pi\)
0.759863 + 0.650084i \(0.225266\pi\)
\(48\) 0 0
\(49\) 0.487260 0.0696085
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.04839 −0.556089 −0.278044 0.960568i \(-0.589686\pi\)
−0.278044 + 0.960568i \(0.589686\pi\)
\(54\) 0 0
\(55\) −5.97718 −0.805963
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.13797 −1.05947 −0.529736 0.848162i \(-0.677709\pi\)
−0.529736 + 0.848162i \(0.677709\pi\)
\(60\) 0 0
\(61\) −3.34516 −0.428304 −0.214152 0.976800i \(-0.568699\pi\)
−0.214152 + 0.976800i \(0.568699\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.40168 0.669996
\(66\) 0 0
\(67\) −1.70525 −0.208329 −0.104164 0.994560i \(-0.533217\pi\)
−0.104164 + 0.994560i \(0.533217\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.56247 0.897500 0.448750 0.893657i \(-0.351869\pi\)
0.448750 + 0.893657i \(0.351869\pi\)
\(72\) 0 0
\(73\) 7.85722 0.919618 0.459809 0.888018i \(-0.347918\pi\)
0.459809 + 0.888018i \(0.347918\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −16.3553 −1.86386
\(78\) 0 0
\(79\) −1.36798 −0.153910 −0.0769548 0.997035i \(-0.524520\pi\)
−0.0769548 + 0.997035i \(0.524520\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −13.9709 −1.53351 −0.766755 0.641940i \(-0.778130\pi\)
−0.766755 + 0.641940i \(0.778130\pi\)
\(84\) 0 0
\(85\) −6.94546 −0.753341
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.49805 0.688792 0.344396 0.938824i \(-0.388084\pi\)
0.344396 + 0.938824i \(0.388084\pi\)
\(90\) 0 0
\(91\) 14.7805 1.54942
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.97718 0.408050
\(96\) 0 0
\(97\) −13.8769 −1.40899 −0.704493 0.709710i \(-0.748826\pi\)
−0.704493 + 0.709710i \(0.748826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −18.4293 −1.83378 −0.916890 0.399140i \(-0.869309\pi\)
−0.916890 + 0.399140i \(0.869309\pi\)
\(102\) 0 0
\(103\) 8.29130 0.816966 0.408483 0.912766i \(-0.366058\pi\)
0.408483 + 0.912766i \(0.366058\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.583632 0.0564218 0.0282109 0.999602i \(-0.491019\pi\)
0.0282109 + 0.999602i \(0.491019\pi\)
\(108\) 0 0
\(109\) −4.37064 −0.418631 −0.209316 0.977848i \(-0.567124\pi\)
−0.209316 + 0.977848i \(0.567124\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.4504 −1.07717 −0.538583 0.842572i \(-0.681040\pi\)
−0.538583 + 0.842572i \(0.681040\pi\)
\(114\) 0 0
\(115\) 1.00000 0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −19.0048 −1.74216
\(120\) 0 0
\(121\) 24.7267 2.24788
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 16.9710 1.50594 0.752968 0.658058i \(-0.228622\pi\)
0.752968 + 0.658058i \(0.228622\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 18.3727 1.60523 0.802616 0.596497i \(-0.203441\pi\)
0.802616 + 0.596497i \(0.203441\pi\)
\(132\) 0 0
\(133\) 10.8827 0.943650
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.74607 −0.661792 −0.330896 0.943667i \(-0.607351\pi\)
−0.330896 + 0.943667i \(0.607351\pi\)
\(138\) 0 0
\(139\) −10.2906 −0.872839 −0.436419 0.899743i \(-0.643754\pi\)
−0.436419 + 0.899743i \(0.643754\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −32.2868 −2.69996
\(144\) 0 0
\(145\) 9.29741 0.772108
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −17.0647 −1.39800 −0.698999 0.715123i \(-0.746371\pi\)
−0.698999 + 0.715123i \(0.746371\pi\)
\(150\) 0 0
\(151\) −15.9141 −1.29507 −0.647536 0.762035i \(-0.724200\pi\)
−0.647536 + 0.762035i \(0.724200\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.54378 0.284643
\(156\) 0 0
\(157\) 24.5482 1.95916 0.979581 0.201050i \(-0.0644355\pi\)
0.979581 + 0.201050i \(0.0644355\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.73629 0.215650
\(162\) 0 0
\(163\) −7.71580 −0.604348 −0.302174 0.953253i \(-0.597712\pi\)
−0.302174 + 0.953253i \(0.597712\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.0793410 −0.00613959 −0.00306979 0.999995i \(-0.500977\pi\)
−0.00306979 + 0.999995i \(0.500977\pi\)
\(168\) 0 0
\(169\) 16.1781 1.24447
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 19.1590 1.45663 0.728316 0.685242i \(-0.240303\pi\)
0.728316 + 0.685242i \(0.240303\pi\)
\(174\) 0 0
\(175\) −2.73629 −0.206844
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −4.68009 −0.349807 −0.174903 0.984586i \(-0.555961\pi\)
−0.174903 + 0.984586i \(0.555961\pi\)
\(180\) 0 0
\(181\) 7.46476 0.554851 0.277426 0.960747i \(-0.410519\pi\)
0.277426 + 0.960747i \(0.410519\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −7.17782 −0.527724
\(186\) 0 0
\(187\) 41.5143 3.03582
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −26.7805 −1.93777 −0.968886 0.247508i \(-0.920388\pi\)
−0.968886 + 0.247508i \(0.920388\pi\)
\(192\) 0 0
\(193\) 12.8196 0.922777 0.461388 0.887198i \(-0.347351\pi\)
0.461388 + 0.887198i \(0.347351\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.60577 −0.185654 −0.0928268 0.995682i \(-0.529590\pi\)
−0.0928268 + 0.995682i \(0.529590\pi\)
\(198\) 0 0
\(199\) −12.5686 −0.890963 −0.445482 0.895291i \(-0.646968\pi\)
−0.445482 + 0.895291i \(0.646968\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 25.4404 1.78556
\(204\) 0 0
\(205\) −10.1945 −0.712014
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −23.7723 −1.64437
\(210\) 0 0
\(211\) −25.1102 −1.72866 −0.864330 0.502925i \(-0.832257\pi\)
−0.864330 + 0.502925i \(0.832257\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.42450 −0.0971501
\(216\) 0 0
\(217\) 9.69680 0.658261
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −37.5172 −2.52368
\(222\) 0 0
\(223\) −10.4718 −0.701244 −0.350622 0.936517i \(-0.614030\pi\)
−0.350622 + 0.936517i \(0.614030\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 17.2767 1.14669 0.573347 0.819312i \(-0.305645\pi\)
0.573347 + 0.819312i \(0.305645\pi\)
\(228\) 0 0
\(229\) −12.5065 −0.826453 −0.413226 0.910628i \(-0.635598\pi\)
−0.413226 + 0.910628i \(0.635598\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.09678 0.399413 0.199707 0.979856i \(-0.436001\pi\)
0.199707 + 0.979856i \(0.436001\pi\)
\(234\) 0 0
\(235\) −10.4187 −0.679642
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.57168 0.295718 0.147859 0.989008i \(-0.452762\pi\)
0.147859 + 0.989008i \(0.452762\pi\)
\(240\) 0 0
\(241\) −25.9022 −1.66851 −0.834253 0.551383i \(-0.814100\pi\)
−0.834253 + 0.551383i \(0.814100\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.487260 −0.0311299
\(246\) 0 0
\(247\) 21.4835 1.36696
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.803360 0.0507076 0.0253538 0.999679i \(-0.491929\pi\)
0.0253538 + 0.999679i \(0.491929\pi\)
\(252\) 0 0
\(253\) −5.97718 −0.375782
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.20486 −0.387049 −0.193524 0.981095i \(-0.561992\pi\)
−0.193524 + 0.981095i \(0.561992\pi\)
\(258\) 0 0
\(259\) −19.6406 −1.22040
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −20.8348 −1.28473 −0.642366 0.766398i \(-0.722047\pi\)
−0.642366 + 0.766398i \(0.722047\pi\)
\(264\) 0 0
\(265\) 4.04839 0.248691
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 22.8374 1.39242 0.696210 0.717838i \(-0.254868\pi\)
0.696210 + 0.717838i \(0.254868\pi\)
\(270\) 0 0
\(271\) −28.5632 −1.73509 −0.867547 0.497356i \(-0.834304\pi\)
−0.867547 + 0.497356i \(0.834304\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.97718 0.360438
\(276\) 0 0
\(277\) −26.2565 −1.57760 −0.788801 0.614648i \(-0.789298\pi\)
−0.788801 + 0.614648i \(0.789298\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.27463 0.195348 0.0976740 0.995218i \(-0.468860\pi\)
0.0976740 + 0.995218i \(0.468860\pi\)
\(282\) 0 0
\(283\) −8.87870 −0.527784 −0.263892 0.964552i \(-0.585006\pi\)
−0.263892 + 0.964552i \(0.585006\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −27.8950 −1.64659
\(288\) 0 0
\(289\) 31.2394 1.83761
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.3646 0.956029 0.478014 0.878352i \(-0.341357\pi\)
0.478014 + 0.878352i \(0.341357\pi\)
\(294\) 0 0
\(295\) 8.13797 0.473811
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.40168 0.312387
\(300\) 0 0
\(301\) −3.89784 −0.224668
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3.34516 0.191543
\(306\) 0 0
\(307\) −21.0803 −1.20312 −0.601558 0.798829i \(-0.705453\pi\)
−0.601558 + 0.798829i \(0.705453\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −24.9877 −1.41692 −0.708460 0.705751i \(-0.750610\pi\)
−0.708460 + 0.705751i \(0.750610\pi\)
\(312\) 0 0
\(313\) −26.8602 −1.51823 −0.759114 0.650957i \(-0.774368\pi\)
−0.759114 + 0.650957i \(0.774368\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.0456 −1.40670 −0.703350 0.710843i \(-0.748313\pi\)
−0.703350 + 0.710843i \(0.748313\pi\)
\(318\) 0 0
\(319\) −55.5723 −3.11145
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −27.6233 −1.53700
\(324\) 0 0
\(325\) −5.40168 −0.299631
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −28.5086 −1.57173
\(330\) 0 0
\(331\) −13.4803 −0.740947 −0.370473 0.928843i \(-0.620804\pi\)
−0.370473 + 0.928843i \(0.620804\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.70525 0.0931675
\(336\) 0 0
\(337\) 24.3478 1.32631 0.663155 0.748482i \(-0.269217\pi\)
0.663155 + 0.748482i \(0.269217\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −21.1818 −1.14706
\(342\) 0 0
\(343\) 17.8207 0.962228
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.15100 −0.276520 −0.138260 0.990396i \(-0.544151\pi\)
−0.138260 + 0.990396i \(0.544151\pi\)
\(348\) 0 0
\(349\) 23.0646 1.23462 0.617310 0.786720i \(-0.288222\pi\)
0.617310 + 0.786720i \(0.288222\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −2.62321 −0.139619 −0.0698097 0.997560i \(-0.522239\pi\)
−0.0698097 + 0.997560i \(0.522239\pi\)
\(354\) 0 0
\(355\) −7.56247 −0.401374
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.36987 0.0722991 0.0361495 0.999346i \(-0.488491\pi\)
0.0361495 + 0.999346i \(0.488491\pi\)
\(360\) 0 0
\(361\) −3.18204 −0.167476
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −7.85722 −0.411266
\(366\) 0 0
\(367\) −8.01055 −0.418147 −0.209074 0.977900i \(-0.567045\pi\)
−0.209074 + 0.977900i \(0.567045\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 11.0775 0.575118
\(372\) 0 0
\(373\) −7.80815 −0.404291 −0.202145 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 50.2217 2.58655
\(378\) 0 0
\(379\) −23.8126 −1.22317 −0.611585 0.791179i \(-0.709468\pi\)
−0.611585 + 0.791179i \(0.709468\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −16.4730 −0.841732 −0.420866 0.907123i \(-0.638274\pi\)
−0.420866 + 0.907123i \(0.638274\pi\)
\(384\) 0 0
\(385\) 16.3553 0.833542
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 5.71444 0.289734 0.144867 0.989451i \(-0.453725\pi\)
0.144867 + 0.989451i \(0.453725\pi\)
\(390\) 0 0
\(391\) −6.94546 −0.351247
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.36798 0.0688305
\(396\) 0 0
\(397\) −14.6525 −0.735388 −0.367694 0.929947i \(-0.619853\pi\)
−0.367694 + 0.929947i \(0.619853\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −21.2851 −1.06293 −0.531465 0.847080i \(-0.678358\pi\)
−0.531465 + 0.847080i \(0.678358\pi\)
\(402\) 0 0
\(403\) 19.1424 0.953549
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 42.9031 2.12663
\(408\) 0 0
\(409\) 31.1908 1.54228 0.771142 0.636663i \(-0.219686\pi\)
0.771142 + 0.636663i \(0.219686\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 22.2678 1.09573
\(414\) 0 0
\(415\) 13.9709 0.685807
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −36.4950 −1.78290 −0.891448 0.453123i \(-0.850310\pi\)
−0.891448 + 0.453123i \(0.850310\pi\)
\(420\) 0 0
\(421\) −2.94307 −0.143437 −0.0717183 0.997425i \(-0.522848\pi\)
−0.0717183 + 0.997425i \(0.522848\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.94546 0.336904
\(426\) 0 0
\(427\) 9.15331 0.442960
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.53529 −0.170289 −0.0851444 0.996369i \(-0.527135\pi\)
−0.0851444 + 0.996369i \(0.527135\pi\)
\(432\) 0 0
\(433\) 38.5181 1.85106 0.925532 0.378671i \(-0.123619\pi\)
0.925532 + 0.378671i \(0.123619\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.97718 0.190254
\(438\) 0 0
\(439\) −13.3043 −0.634980 −0.317490 0.948262i \(-0.602840\pi\)
−0.317490 + 0.948262i \(0.602840\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −21.1259 −1.00372 −0.501862 0.864948i \(-0.667351\pi\)
−0.501862 + 0.864948i \(0.667351\pi\)
\(444\) 0 0
\(445\) −6.49805 −0.308037
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.13932 −0.100961 −0.0504805 0.998725i \(-0.516075\pi\)
−0.0504805 + 0.998725i \(0.516075\pi\)
\(450\) 0 0
\(451\) 60.9343 2.86928
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14.7805 −0.692922
\(456\) 0 0
\(457\) 0.0350873 0.00164131 0.000820657 1.00000i \(-0.499739\pi\)
0.000820657 1.00000i \(0.499739\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.2381 1.40833 0.704164 0.710037i \(-0.251322\pi\)
0.704164 + 0.710037i \(0.251322\pi\)
\(462\) 0 0
\(463\) −4.31412 −0.200494 −0.100247 0.994963i \(-0.531963\pi\)
−0.100247 + 0.994963i \(0.531963\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −19.7680 −0.914753 −0.457376 0.889273i \(-0.651211\pi\)
−0.457376 + 0.889273i \(0.651211\pi\)
\(468\) 0 0
\(469\) 4.66604 0.215458
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.51449 0.391497
\(474\) 0 0
\(475\) −3.97718 −0.182486
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −18.5883 −0.849320 −0.424660 0.905353i \(-0.639606\pi\)
−0.424660 + 0.905353i \(0.639606\pi\)
\(480\) 0 0
\(481\) −38.7723 −1.76786
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 13.8769 0.630118
\(486\) 0 0
\(487\) 15.1337 0.685775 0.342888 0.939376i \(-0.388595\pi\)
0.342888 + 0.939376i \(0.388595\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −29.0762 −1.31219 −0.656095 0.754678i \(-0.727793\pi\)
−0.656095 + 0.754678i \(0.727793\pi\)
\(492\) 0 0
\(493\) −64.5748 −2.90830
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.6931 −0.928211
\(498\) 0 0
\(499\) 13.4060 0.600133 0.300067 0.953918i \(-0.402991\pi\)
0.300067 + 0.953918i \(0.402991\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13.2143 0.589197 0.294598 0.955621i \(-0.404814\pi\)
0.294598 + 0.955621i \(0.404814\pi\)
\(504\) 0 0
\(505\) 18.4293 0.820091
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.41682 −0.373069 −0.186534 0.982448i \(-0.559726\pi\)
−0.186534 + 0.982448i \(0.559726\pi\)
\(510\) 0 0
\(511\) −21.4996 −0.951086
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −8.29130 −0.365358
\(516\) 0 0
\(517\) 62.2745 2.73883
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.03908 0.176955 0.0884777 0.996078i \(-0.471800\pi\)
0.0884777 + 0.996078i \(0.471800\pi\)
\(522\) 0 0
\(523\) 8.85699 0.387289 0.193645 0.981072i \(-0.437969\pi\)
0.193645 + 0.981072i \(0.437969\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24.6132 −1.07217
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −55.0674 −2.38523
\(534\) 0 0
\(535\) −0.583632 −0.0252326
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.91244 0.125448
\(540\) 0 0
\(541\) −28.1566 −1.21055 −0.605274 0.796017i \(-0.706936\pi\)
−0.605274 + 0.796017i \(0.706936\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.37064 0.187218
\(546\) 0 0
\(547\) −19.4765 −0.832756 −0.416378 0.909191i \(-0.636701\pi\)
−0.416378 + 0.909191i \(0.636701\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 36.9775 1.57529
\(552\) 0 0
\(553\) 3.74318 0.159176
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.88185 −0.291593 −0.145797 0.989315i \(-0.546575\pi\)
−0.145797 + 0.989315i \(0.546575\pi\)
\(558\) 0 0
\(559\) −7.69469 −0.325451
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.30665 0.392229 0.196114 0.980581i \(-0.437168\pi\)
0.196114 + 0.980581i \(0.437168\pi\)
\(564\) 0 0
\(565\) 11.4504 0.481723
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.5779 0.778827 0.389414 0.921063i \(-0.372678\pi\)
0.389414 + 0.921063i \(0.372678\pi\)
\(570\) 0 0
\(571\) 39.5512 1.65517 0.827583 0.561343i \(-0.189715\pi\)
0.827583 + 0.561343i \(0.189715\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −13.1923 −0.549204 −0.274602 0.961558i \(-0.588546\pi\)
−0.274602 + 0.961558i \(0.588546\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 38.2285 1.58598
\(582\) 0 0
\(583\) −24.1979 −1.00218
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.7066 −0.441908 −0.220954 0.975284i \(-0.570917\pi\)
−0.220954 + 0.975284i \(0.570917\pi\)
\(588\) 0 0
\(589\) 14.0943 0.580744
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 3.98410 0.163607 0.0818036 0.996648i \(-0.473932\pi\)
0.0818036 + 0.996648i \(0.473932\pi\)
\(594\) 0 0
\(595\) 19.0048 0.779119
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 25.9056 1.05847 0.529237 0.848474i \(-0.322478\pi\)
0.529237 + 0.848474i \(0.322478\pi\)
\(600\) 0 0
\(601\) 12.3935 0.505542 0.252771 0.967526i \(-0.418658\pi\)
0.252771 + 0.967526i \(0.418658\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −24.7267 −1.00528
\(606\) 0 0
\(607\) −22.4768 −0.912304 −0.456152 0.889902i \(-0.650773\pi\)
−0.456152 + 0.889902i \(0.650773\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −56.2785 −2.27679
\(612\) 0 0
\(613\) −23.9995 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −30.7574 −1.23825 −0.619123 0.785294i \(-0.712512\pi\)
−0.619123 + 0.785294i \(0.712512\pi\)
\(618\) 0 0
\(619\) −34.4693 −1.38544 −0.692719 0.721207i \(-0.743588\pi\)
−0.692719 + 0.721207i \(0.743588\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −17.7805 −0.712362
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 49.8532 1.98778
\(630\) 0 0
\(631\) −8.22555 −0.327454 −0.163727 0.986506i \(-0.552352\pi\)
−0.163727 + 0.986506i \(0.552352\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −16.9710 −0.673475
\(636\) 0 0
\(637\) −2.63202 −0.104284
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −40.5166 −1.60031 −0.800154 0.599795i \(-0.795249\pi\)
−0.800154 + 0.599795i \(0.795249\pi\)
\(642\) 0 0
\(643\) 0.890308 0.0351103 0.0175552 0.999846i \(-0.494412\pi\)
0.0175552 + 0.999846i \(0.494412\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −31.0168 −1.21940 −0.609699 0.792633i \(-0.708710\pi\)
−0.609699 + 0.792633i \(0.708710\pi\)
\(648\) 0 0
\(649\) −48.6421 −1.90937
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.8735 0.464645 0.232323 0.972639i \(-0.425367\pi\)
0.232323 + 0.972639i \(0.425367\pi\)
\(654\) 0 0
\(655\) −18.3727 −0.717881
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 33.0551 1.28764 0.643822 0.765175i \(-0.277348\pi\)
0.643822 + 0.765175i \(0.277348\pi\)
\(660\) 0 0
\(661\) −4.71253 −0.183296 −0.0916482 0.995791i \(-0.529214\pi\)
−0.0916482 + 0.995791i \(0.529214\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.8827 −0.422013
\(666\) 0 0
\(667\) 9.29741 0.359997
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −19.9946 −0.771884
\(672\) 0 0
\(673\) −13.0906 −0.504605 −0.252303 0.967648i \(-0.581188\pi\)
−0.252303 + 0.967648i \(0.581188\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −0.915188 −0.0351735 −0.0175868 0.999845i \(-0.505598\pi\)
−0.0175868 + 0.999845i \(0.505598\pi\)
\(678\) 0 0
\(679\) 37.9712 1.45720
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 30.1856 1.15502 0.577511 0.816383i \(-0.304024\pi\)
0.577511 + 0.816383i \(0.304024\pi\)
\(684\) 0 0
\(685\) 7.74607 0.295962
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 21.8681 0.833108
\(690\) 0 0
\(691\) −38.8018 −1.47609 −0.738044 0.674752i \(-0.764250\pi\)
−0.738044 + 0.674752i \(0.764250\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.2906 0.390345
\(696\) 0 0
\(697\) 70.8054 2.68195
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.6348 −0.552749 −0.276375 0.961050i \(-0.589133\pi\)
−0.276375 + 0.961050i \(0.589133\pi\)
\(702\) 0 0
\(703\) −28.5475 −1.07669
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 50.4277 1.89653
\(708\) 0 0
\(709\) −6.89807 −0.259062 −0.129531 0.991575i \(-0.541347\pi\)
−0.129531 + 0.991575i \(0.541347\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.54378 0.132716
\(714\) 0 0
\(715\) 32.2868 1.20746
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.9504 0.818610 0.409305 0.912398i \(-0.365771\pi\)
0.409305 + 0.912398i \(0.365771\pi\)
\(720\) 0 0
\(721\) −22.6874 −0.844922
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −9.29741 −0.345297
\(726\) 0 0
\(727\) 39.8620 1.47840 0.739200 0.673486i \(-0.235204\pi\)
0.739200 + 0.673486i \(0.235204\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.89381 0.365936
\(732\) 0 0
\(733\) 50.6101 1.86933 0.934663 0.355536i \(-0.115701\pi\)
0.934663 + 0.355536i \(0.115701\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −10.1926 −0.375448
\(738\) 0 0
\(739\) 11.1158 0.408901 0.204451 0.978877i \(-0.434459\pi\)
0.204451 + 0.978877i \(0.434459\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −40.8523 −1.49873 −0.749363 0.662159i \(-0.769640\pi\)
−0.749363 + 0.662159i \(0.769640\pi\)
\(744\) 0 0
\(745\) 17.0647 0.625204
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.59698 −0.0583525
\(750\) 0 0
\(751\) −5.21900 −0.190444 −0.0952221 0.995456i \(-0.530356\pi\)
−0.0952221 + 0.995456i \(0.530356\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.9141 0.579173
\(756\) 0 0
\(757\) 3.27998 0.119213 0.0596064 0.998222i \(-0.481015\pi\)
0.0596064 + 0.998222i \(0.481015\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −25.5191 −0.925066 −0.462533 0.886602i \(-0.653059\pi\)
−0.462533 + 0.886602i \(0.653059\pi\)
\(762\) 0 0
\(763\) 11.9593 0.432956
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 43.9587 1.58726
\(768\) 0 0
\(769\) 34.5086 1.24441 0.622205 0.782854i \(-0.286237\pi\)
0.622205 + 0.782854i \(0.286237\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 50.8067 1.82739 0.913695 0.406401i \(-0.133216\pi\)
0.913695 + 0.406401i \(0.133216\pi\)
\(774\) 0 0
\(775\) −3.54378 −0.127296
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −40.5453 −1.45269
\(780\) 0 0
\(781\) 45.2022 1.61746
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.5482 −0.876164
\(786\) 0 0
\(787\) −28.9087 −1.03048 −0.515242 0.857045i \(-0.672298\pi\)
−0.515242 + 0.857045i \(0.672298\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 31.3317 1.11403
\(792\) 0 0
\(793\) 18.0695 0.641666
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −41.7056 −1.47729 −0.738644 0.674095i \(-0.764534\pi\)
−0.738644 + 0.674095i \(0.764534\pi\)
\(798\) 0 0
\(799\) 72.3627 2.56001
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 46.9640 1.65732
\(804\) 0 0
\(805\) −2.73629 −0.0964414
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −39.2397 −1.37959 −0.689797 0.724002i \(-0.742300\pi\)
−0.689797 + 0.724002i \(0.742300\pi\)
\(810\) 0 0
\(811\) 32.2340 1.13189 0.565945 0.824443i \(-0.308511\pi\)
0.565945 + 0.824443i \(0.308511\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 7.71580 0.270273
\(816\) 0 0
\(817\) −5.66549 −0.198210
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26.1197 0.911583 0.455792 0.890087i \(-0.349356\pi\)
0.455792 + 0.890087i \(0.349356\pi\)
\(822\) 0 0
\(823\) 14.6734 0.511481 0.255740 0.966745i \(-0.417681\pi\)
0.255740 + 0.966745i \(0.417681\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 14.3498 0.498990 0.249495 0.968376i \(-0.419735\pi\)
0.249495 + 0.968376i \(0.419735\pi\)
\(828\) 0 0
\(829\) −14.9407 −0.518911 −0.259456 0.965755i \(-0.583543\pi\)
−0.259456 + 0.965755i \(0.583543\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.38424 0.117257
\(834\) 0 0
\(835\) 0.0793410 0.00274571
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 38.1982 1.31875 0.659375 0.751814i \(-0.270821\pi\)
0.659375 + 0.751814i \(0.270821\pi\)
\(840\) 0 0
\(841\) 57.4419 1.98076
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −16.1781 −0.556545
\(846\) 0 0
\(847\) −67.6593 −2.32480
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −7.17782 −0.246052
\(852\) 0 0
\(853\) −13.0969 −0.448430 −0.224215 0.974540i \(-0.571982\pi\)
−0.224215 + 0.974540i \(0.571982\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 44.6533 1.52533 0.762664 0.646795i \(-0.223891\pi\)
0.762664 + 0.646795i \(0.223891\pi\)
\(858\) 0 0
\(859\) −23.6964 −0.808512 −0.404256 0.914646i \(-0.632470\pi\)
−0.404256 + 0.914646i \(0.632470\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 28.5825 0.972961 0.486480 0.873692i \(-0.338281\pi\)
0.486480 + 0.873692i \(0.338281\pi\)
\(864\) 0 0
\(865\) −19.1590 −0.651425
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −8.17666 −0.277374
\(870\) 0 0
\(871\) 9.21119 0.312109
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.73629 0.0925033
\(876\) 0 0
\(877\) 29.4797 0.995457 0.497729 0.867333i \(-0.334168\pi\)
0.497729 + 0.867333i \(0.334168\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20.1078 0.677450 0.338725 0.940885i \(-0.390004\pi\)
0.338725 + 0.940885i \(0.390004\pi\)
\(882\) 0 0
\(883\) −50.7789 −1.70885 −0.854424 0.519577i \(-0.826090\pi\)
−0.854424 + 0.519577i \(0.826090\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −0.365439 −0.0122703 −0.00613513 0.999981i \(-0.501953\pi\)
−0.00613513 + 0.999981i \(0.501953\pi\)
\(888\) 0 0
\(889\) −46.4376 −1.55747
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −41.4371 −1.38664
\(894\) 0 0
\(895\) 4.68009 0.156438
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 32.9480 1.09888
\(900\) 0 0
\(901\) −28.1179 −0.936744
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7.46476 −0.248137
\(906\) 0 0
\(907\) 16.9221 0.561890 0.280945 0.959724i \(-0.409352\pi\)
0.280945 + 0.959724i \(0.409352\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −12.0149 −0.398072 −0.199036 0.979992i \(-0.563781\pi\)
−0.199036 + 0.979992i \(0.563781\pi\)
\(912\) 0 0
\(913\) −83.5068 −2.76367
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −50.2730 −1.66016
\(918\) 0 0
\(919\) −12.1340 −0.400263 −0.200131 0.979769i \(-0.564137\pi\)
−0.200131 + 0.979769i \(0.564137\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −40.8500 −1.34459
\(924\) 0 0
\(925\) 7.17782 0.236005
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.70399 −0.0559060 −0.0279530 0.999609i \(-0.508899\pi\)
−0.0279530 + 0.999609i \(0.508899\pi\)
\(930\) 0 0
\(931\) −1.93792 −0.0635127
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −41.5143 −1.35766
\(936\) 0 0
\(937\) 20.1572 0.658505 0.329253 0.944242i \(-0.393203\pi\)
0.329253 + 0.944242i \(0.393203\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −0.934801 −0.0304736 −0.0152368 0.999884i \(-0.504850\pi\)
−0.0152368 + 0.999884i \(0.504850\pi\)
\(942\) 0 0
\(943\) −10.1945 −0.331978
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.0830101 0.00269747 0.00134873 0.999999i \(-0.499571\pi\)
0.00134873 + 0.999999i \(0.499571\pi\)
\(948\) 0 0
\(949\) −42.4422 −1.37773
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −27.0754 −0.877059 −0.438530 0.898717i \(-0.644501\pi\)
−0.438530 + 0.898717i \(0.644501\pi\)
\(954\) 0 0
\(955\) 26.7805 0.866598
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 21.1955 0.684437
\(960\) 0 0
\(961\) −18.4416 −0.594891
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −12.8196 −0.412678
\(966\) 0 0
\(967\) 2.18529 0.0702743 0.0351371 0.999383i \(-0.488813\pi\)
0.0351371 + 0.999383i \(0.488813\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −10.0519 −0.322580 −0.161290 0.986907i \(-0.551565\pi\)
−0.161290 + 0.986907i \(0.551565\pi\)
\(972\) 0 0
\(973\) 28.1581 0.902706
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.22903 −0.103306 −0.0516529 0.998665i \(-0.516449\pi\)
−0.0516529 + 0.998665i \(0.516449\pi\)
\(978\) 0 0
\(979\) 38.8400 1.24133
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −39.6353 −1.26417 −0.632085 0.774899i \(-0.717801\pi\)
−0.632085 + 0.774899i \(0.717801\pi\)
\(984\) 0 0
\(985\) 2.60577 0.0830268
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.42450 −0.0452965
\(990\) 0 0
\(991\) 5.77615 0.183485 0.0917427 0.995783i \(-0.470756\pi\)
0.0917427 + 0.995783i \(0.470756\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 12.5686 0.398451
\(996\) 0 0
\(997\) 57.5757 1.82344 0.911721 0.410810i \(-0.134754\pi\)
0.911721 + 0.410810i \(0.134754\pi\)
\(998\) 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.bt.1.2 6
3.2 odd 2 8280.2.a.bu.1.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8280.2.a.bt.1.2 6 1.1 even 1 trivial
8280.2.a.bu.1.2 yes 6 3.2 odd 2