Properties

Label 7800.2.a.bi.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.940.1
Defining polynomial: \( x^{3} - 7x - 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 1560)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-2.29240\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +4.83991 q^{7} +1.00000 q^{9} +2.25511 q^{11} +1.00000 q^{13} -6.32970 q^{17} -2.58480 q^{19} -4.83991 q^{21} -4.83991 q^{23} -1.00000 q^{27} +9.09501 q^{29} -0.510210 q^{31} -2.25511 q^{33} -4.25511 q^{37} -1.00000 q^{39} +0.255105 q^{41} -9.16961 q^{43} +4.51021 q^{47} +16.4247 q^{49} +6.32970 q^{51} +9.93492 q^{53} +2.58480 q^{57} +14.1900 q^{59} +9.93492 q^{61} +4.83991 q^{63} +13.1696 q^{67} +4.83991 q^{69} -5.74489 q^{71} -2.90499 q^{73} +10.9145 q^{77} +5.74489 q^{79} +1.00000 q^{81} -10.1900 q^{83} -9.09501 q^{87} +3.74489 q^{89} +4.83991 q^{91} +0.510210 q^{93} +12.5197 q^{97} +2.25511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - q^{7} + 3 q^{9} + 5 q^{11} + 3 q^{13} - 7 q^{17} + 6 q^{19} + q^{21} + q^{23} - 3 q^{27} + 10 q^{29} + 2 q^{31} - 5 q^{33} - 11 q^{37} - 3 q^{39} - q^{41} + 10 q^{47} + 20 q^{49} + 7 q^{51} - 3 q^{53} - 6 q^{57} + 8 q^{59} - 3 q^{61} - q^{63} + 12 q^{67} - q^{69} - 19 q^{71} - 26 q^{73} + 7 q^{77} + 19 q^{79} + 3 q^{81} + 4 q^{83} - 10 q^{87} + 13 q^{89} - q^{91} - 2 q^{93} - 9 q^{97} + 5 q^{99}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.83991 1.82931 0.914657 0.404232i \(-0.132461\pi\)
0.914657 + 0.404232i \(0.132461\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.25511 0.679940 0.339970 0.940436i \(-0.389583\pi\)
0.339970 + 0.940436i \(0.389583\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.32970 −1.53518 −0.767589 0.640943i \(-0.778544\pi\)
−0.767589 + 0.640943i \(0.778544\pi\)
\(18\) 0 0
\(19\) −2.58480 −0.592995 −0.296497 0.955034i \(-0.595819\pi\)
−0.296497 + 0.955034i \(0.595819\pi\)
\(20\) 0 0
\(21\) −4.83991 −1.05615
\(22\) 0 0
\(23\) −4.83991 −1.00919 −0.504595 0.863356i \(-0.668358\pi\)
−0.504595 + 0.863356i \(0.668358\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 9.09501 1.68890 0.844451 0.535633i \(-0.179927\pi\)
0.844451 + 0.535633i \(0.179927\pi\)
\(30\) 0 0
\(31\) −0.510210 −0.0916364 −0.0458182 0.998950i \(-0.514589\pi\)
−0.0458182 + 0.998950i \(0.514589\pi\)
\(32\) 0 0
\(33\) −2.25511 −0.392563
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.25511 −0.699535 −0.349767 0.936837i \(-0.613739\pi\)
−0.349767 + 0.936837i \(0.613739\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 0.255105 0.0398407 0.0199204 0.999802i \(-0.493659\pi\)
0.0199204 + 0.999802i \(0.493659\pi\)
\(42\) 0 0
\(43\) −9.16961 −1.39835 −0.699176 0.714950i \(-0.746450\pi\)
−0.699176 + 0.714950i \(0.746450\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.51021 0.657882 0.328941 0.944351i \(-0.393308\pi\)
0.328941 + 0.944351i \(0.393308\pi\)
\(48\) 0 0
\(49\) 16.4247 2.34639
\(50\) 0 0
\(51\) 6.32970 0.886335
\(52\) 0 0
\(53\) 9.93492 1.36467 0.682333 0.731041i \(-0.260965\pi\)
0.682333 + 0.731041i \(0.260965\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.58480 0.342366
\(58\) 0 0
\(59\) 14.1900 1.84738 0.923692 0.383136i \(-0.125156\pi\)
0.923692 + 0.383136i \(0.125156\pi\)
\(60\) 0 0
\(61\) 9.93492 1.27204 0.636018 0.771674i \(-0.280580\pi\)
0.636018 + 0.771674i \(0.280580\pi\)
\(62\) 0 0
\(63\) 4.83991 0.609771
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 13.1696 1.60892 0.804462 0.594004i \(-0.202454\pi\)
0.804462 + 0.594004i \(0.202454\pi\)
\(68\) 0 0
\(69\) 4.83991 0.582656
\(70\) 0 0
\(71\) −5.74489 −0.681794 −0.340897 0.940101i \(-0.610731\pi\)
−0.340897 + 0.940101i \(0.610731\pi\)
\(72\) 0 0
\(73\) −2.90499 −0.340003 −0.170001 0.985444i \(-0.554377\pi\)
−0.170001 + 0.985444i \(0.554377\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.9145 1.24382
\(78\) 0 0
\(79\) 5.74489 0.646351 0.323176 0.946339i \(-0.395250\pi\)
0.323176 + 0.946339i \(0.395250\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −10.1900 −1.11850 −0.559250 0.828999i \(-0.688911\pi\)
−0.559250 + 0.828999i \(0.688911\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.09501 −0.975088
\(88\) 0 0
\(89\) 3.74489 0.396958 0.198479 0.980105i \(-0.436400\pi\)
0.198479 + 0.980105i \(0.436400\pi\)
\(90\) 0 0
\(91\) 4.83991 0.507360
\(92\) 0 0
\(93\) 0.510210 0.0529063
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 12.5197 1.27119 0.635593 0.772025i \(-0.280756\pi\)
0.635593 + 0.772025i \(0.280756\pi\)
\(98\) 0 0
\(99\) 2.25511 0.226647
\(100\) 0 0
\(101\) −17.6052 −1.75179 −0.875893 0.482506i \(-0.839727\pi\)
−0.875893 + 0.482506i \(0.839727\pi\)
\(102\) 0 0
\(103\) 17.1696 1.69177 0.845886 0.533364i \(-0.179072\pi\)
0.845886 + 0.533364i \(0.179072\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.91450 −0.668450 −0.334225 0.942493i \(-0.608475\pi\)
−0.334225 + 0.942493i \(0.608475\pi\)
\(108\) 0 0
\(109\) 3.41520 0.327117 0.163558 0.986534i \(-0.447703\pi\)
0.163558 + 0.986534i \(0.447703\pi\)
\(110\) 0 0
\(111\) 4.25511 0.403877
\(112\) 0 0
\(113\) −5.09501 −0.479299 −0.239649 0.970860i \(-0.577032\pi\)
−0.239649 + 0.970860i \(0.577032\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −30.6352 −2.80832
\(120\) 0 0
\(121\) −5.91450 −0.537682
\(122\) 0 0
\(123\) −0.255105 −0.0230020
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.6594 1.12334 0.561670 0.827361i \(-0.310159\pi\)
0.561670 + 0.827361i \(0.310159\pi\)
\(128\) 0 0
\(129\) 9.16961 0.807339
\(130\) 0 0
\(131\) −16.7748 −1.46562 −0.732812 0.680431i \(-0.761792\pi\)
−0.732812 + 0.680431i \(0.761792\pi\)
\(132\) 0 0
\(133\) −12.5102 −1.08477
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.00000 −0.170872 −0.0854358 0.996344i \(-0.527228\pi\)
−0.0854358 + 0.996344i \(0.527228\pi\)
\(138\) 0 0
\(139\) 5.23468 0.444000 0.222000 0.975047i \(-0.428741\pi\)
0.222000 + 0.975047i \(0.428741\pi\)
\(140\) 0 0
\(141\) −4.51021 −0.379828
\(142\) 0 0
\(143\) 2.25511 0.188581
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −16.4247 −1.35469
\(148\) 0 0
\(149\) 3.74489 0.306794 0.153397 0.988165i \(-0.450979\pi\)
0.153397 + 0.988165i \(0.450979\pi\)
\(150\) 0 0
\(151\) 15.3596 1.24995 0.624975 0.780645i \(-0.285109\pi\)
0.624975 + 0.780645i \(0.285109\pi\)
\(152\) 0 0
\(153\) −6.32970 −0.511726
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.979580 −0.0781790 −0.0390895 0.999236i \(-0.512446\pi\)
−0.0390895 + 0.999236i \(0.512446\pi\)
\(158\) 0 0
\(159\) −9.93492 −0.787891
\(160\) 0 0
\(161\) −23.4247 −1.84613
\(162\) 0 0
\(163\) −7.42471 −0.581548 −0.290774 0.956792i \(-0.593913\pi\)
−0.290774 + 0.956792i \(0.593913\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 21.1696 1.63815 0.819077 0.573684i \(-0.194486\pi\)
0.819077 + 0.573684i \(0.194486\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.58480 −0.197665
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −14.1900 −1.06659
\(178\) 0 0
\(179\) 8.77483 0.655862 0.327931 0.944702i \(-0.393649\pi\)
0.327931 + 0.944702i \(0.393649\pi\)
\(180\) 0 0
\(181\) 23.1045 1.71735 0.858673 0.512524i \(-0.171289\pi\)
0.858673 + 0.512524i \(0.171289\pi\)
\(182\) 0 0
\(183\) −9.93492 −0.734411
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −14.2741 −1.04383
\(188\) 0 0
\(189\) −4.83991 −0.352052
\(190\) 0 0
\(191\) 19.3596 1.40081 0.700407 0.713744i \(-0.253002\pi\)
0.700407 + 0.713744i \(0.253002\pi\)
\(192\) 0 0
\(193\) −6.18051 −0.444883 −0.222441 0.974946i \(-0.571403\pi\)
−0.222441 + 0.974946i \(0.571403\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −21.8698 −1.55816 −0.779081 0.626923i \(-0.784314\pi\)
−0.779081 + 0.626923i \(0.784314\pi\)
\(198\) 0 0
\(199\) 2.83039 0.200641 0.100321 0.994955i \(-0.468013\pi\)
0.100321 + 0.994955i \(0.468013\pi\)
\(200\) 0 0
\(201\) −13.1696 −0.928912
\(202\) 0 0
\(203\) 44.0190 3.08953
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.83991 −0.336397
\(208\) 0 0
\(209\) −5.82900 −0.403201
\(210\) 0 0
\(211\) −22.3392 −1.53789 −0.768947 0.639312i \(-0.779219\pi\)
−0.768947 + 0.639312i \(0.779219\pi\)
\(212\) 0 0
\(213\) 5.74489 0.393634
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −2.46937 −0.167632
\(218\) 0 0
\(219\) 2.90499 0.196301
\(220\) 0 0
\(221\) −6.32970 −0.425782
\(222\) 0 0
\(223\) 23.0950 1.54656 0.773278 0.634067i \(-0.218616\pi\)
0.773278 + 0.634067i \(0.218616\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.510210 0.0338638 0.0169319 0.999857i \(-0.494610\pi\)
0.0169319 + 0.999857i \(0.494610\pi\)
\(228\) 0 0
\(229\) −1.09501 −0.0723605 −0.0361803 0.999345i \(-0.511519\pi\)
−0.0361803 + 0.999345i \(0.511519\pi\)
\(230\) 0 0
\(231\) −10.9145 −0.718121
\(232\) 0 0
\(233\) −1.81949 −0.119199 −0.0595993 0.998222i \(-0.518982\pi\)
−0.0595993 + 0.998222i \(0.518982\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.74489 −0.373171
\(238\) 0 0
\(239\) 8.44513 0.546270 0.273135 0.961976i \(-0.411939\pi\)
0.273135 + 0.961976i \(0.411939\pi\)
\(240\) 0 0
\(241\) 20.3392 1.31016 0.655082 0.755558i \(-0.272634\pi\)
0.655082 + 0.755558i \(0.272634\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.58480 −0.164467
\(248\) 0 0
\(249\) 10.1900 0.645767
\(250\) 0 0
\(251\) −17.4342 −1.10044 −0.550219 0.835020i \(-0.685456\pi\)
−0.550219 + 0.835020i \(0.685456\pi\)
\(252\) 0 0
\(253\) −10.9145 −0.686189
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −15.4342 −0.962761 −0.481380 0.876512i \(-0.659864\pi\)
−0.481380 + 0.876512i \(0.659864\pi\)
\(258\) 0 0
\(259\) −20.5943 −1.27967
\(260\) 0 0
\(261\) 9.09501 0.562967
\(262\) 0 0
\(263\) 8.90499 0.549105 0.274553 0.961572i \(-0.411470\pi\)
0.274553 + 0.961572i \(0.411470\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −3.74489 −0.229184
\(268\) 0 0
\(269\) −16.5848 −1.01119 −0.505597 0.862770i \(-0.668728\pi\)
−0.505597 + 0.862770i \(0.668728\pi\)
\(270\) 0 0
\(271\) 17.8290 1.08303 0.541517 0.840690i \(-0.317850\pi\)
0.541517 + 0.840690i \(0.317850\pi\)
\(272\) 0 0
\(273\) −4.83991 −0.292925
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −22.3801 −1.34469 −0.672344 0.740239i \(-0.734712\pi\)
−0.672344 + 0.740239i \(0.734712\pi\)
\(278\) 0 0
\(279\) −0.510210 −0.0305455
\(280\) 0 0
\(281\) −24.1900 −1.44306 −0.721528 0.692385i \(-0.756560\pi\)
−0.721528 + 0.692385i \(0.756560\pi\)
\(282\) 0 0
\(283\) 26.1900 1.55684 0.778418 0.627747i \(-0.216023\pi\)
0.778418 + 0.627747i \(0.216023\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.23468 0.0728811
\(288\) 0 0
\(289\) 23.0651 1.35677
\(290\) 0 0
\(291\) −12.5197 −0.733919
\(292\) 0 0
\(293\) 5.48979 0.320717 0.160358 0.987059i \(-0.448735\pi\)
0.160358 + 0.987059i \(0.448735\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −2.25511 −0.130854
\(298\) 0 0
\(299\) −4.83991 −0.279899
\(300\) 0 0
\(301\) −44.3801 −2.55802
\(302\) 0 0
\(303\) 17.6052 1.01139
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 6.76532 0.386117 0.193058 0.981187i \(-0.438159\pi\)
0.193058 + 0.981187i \(0.438159\pi\)
\(308\) 0 0
\(309\) −17.1696 −0.976745
\(310\) 0 0
\(311\) −17.0204 −0.965139 −0.482570 0.875858i \(-0.660297\pi\)
−0.482570 + 0.875858i \(0.660297\pi\)
\(312\) 0 0
\(313\) −12.8304 −0.725217 −0.362608 0.931942i \(-0.618114\pi\)
−0.362608 + 0.931942i \(0.618114\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.4898 0.757662 0.378831 0.925466i \(-0.376326\pi\)
0.378831 + 0.925466i \(0.376326\pi\)
\(318\) 0 0
\(319\) 20.5102 1.14835
\(320\) 0 0
\(321\) 6.91450 0.385930
\(322\) 0 0
\(323\) 16.3610 0.910352
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −3.41520 −0.188861
\(328\) 0 0
\(329\) 21.8290 1.20347
\(330\) 0 0
\(331\) −14.0746 −0.773610 −0.386805 0.922162i \(-0.626421\pi\)
−0.386805 + 0.922162i \(0.626421\pi\)
\(332\) 0 0
\(333\) −4.25511 −0.233178
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.6594 1.23434 0.617168 0.786831i \(-0.288280\pi\)
0.617168 + 0.786831i \(0.288280\pi\)
\(338\) 0 0
\(339\) 5.09501 0.276723
\(340\) 0 0
\(341\) −1.15058 −0.0623073
\(342\) 0 0
\(343\) 45.6147 2.46296
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.59432 0.461367 0.230684 0.973029i \(-0.425904\pi\)
0.230684 + 0.973029i \(0.425904\pi\)
\(348\) 0 0
\(349\) −23.9444 −1.28172 −0.640858 0.767659i \(-0.721421\pi\)
−0.640858 + 0.767659i \(0.721421\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 30.6352 1.62138
\(358\) 0 0
\(359\) −1.80997 −0.0955268 −0.0477634 0.998859i \(-0.515209\pi\)
−0.0477634 + 0.998859i \(0.515209\pi\)
\(360\) 0 0
\(361\) −12.3188 −0.648358
\(362\) 0 0
\(363\) 5.91450 0.310431
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −9.16961 −0.478650 −0.239325 0.970940i \(-0.576926\pi\)
−0.239325 + 0.970940i \(0.576926\pi\)
\(368\) 0 0
\(369\) 0.255105 0.0132802
\(370\) 0 0
\(371\) 48.0841 2.49640
\(372\) 0 0
\(373\) 28.8494 1.49377 0.746883 0.664955i \(-0.231549\pi\)
0.746883 + 0.664955i \(0.231549\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.09501 0.468417
\(378\) 0 0
\(379\) 21.9444 1.12721 0.563605 0.826044i \(-0.309414\pi\)
0.563605 + 0.826044i \(0.309414\pi\)
\(380\) 0 0
\(381\) −12.6594 −0.648561
\(382\) 0 0
\(383\) 6.32018 0.322946 0.161473 0.986877i \(-0.448375\pi\)
0.161473 + 0.986877i \(0.448375\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −9.16961 −0.466117
\(388\) 0 0
\(389\) −17.6052 −0.892620 −0.446310 0.894878i \(-0.647262\pi\)
−0.446310 + 0.894878i \(0.647262\pi\)
\(390\) 0 0
\(391\) 30.6352 1.54929
\(392\) 0 0
\(393\) 16.7748 0.846178
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 30.0841 1.50988 0.754939 0.655795i \(-0.227666\pi\)
0.754939 + 0.655795i \(0.227666\pi\)
\(398\) 0 0
\(399\) 12.5102 0.626294
\(400\) 0 0
\(401\) 22.5292 1.12506 0.562528 0.826778i \(-0.309829\pi\)
0.562528 + 0.826778i \(0.309829\pi\)
\(402\) 0 0
\(403\) −0.510210 −0.0254154
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.59571 −0.475642
\(408\) 0 0
\(409\) 23.1696 1.14566 0.572832 0.819673i \(-0.305845\pi\)
0.572832 + 0.819673i \(0.305845\pi\)
\(410\) 0 0
\(411\) 2.00000 0.0986527
\(412\) 0 0
\(413\) 68.6784 3.37944
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −5.23468 −0.256344
\(418\) 0 0
\(419\) 9.56438 0.467251 0.233625 0.972327i \(-0.424941\pi\)
0.233625 + 0.972327i \(0.424941\pi\)
\(420\) 0 0
\(421\) −35.7952 −1.74455 −0.872277 0.489012i \(-0.837357\pi\)
−0.872277 + 0.489012i \(0.837357\pi\)
\(422\) 0 0
\(423\) 4.51021 0.219294
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 48.0841 2.32695
\(428\) 0 0
\(429\) −2.25511 −0.108877
\(430\) 0 0
\(431\) 28.3801 1.36702 0.683510 0.729942i \(-0.260453\pi\)
0.683510 + 0.729942i \(0.260453\pi\)
\(432\) 0 0
\(433\) −19.6798 −0.945752 −0.472876 0.881129i \(-0.656784\pi\)
−0.472876 + 0.881129i \(0.656784\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.5102 0.598445
\(438\) 0 0
\(439\) 33.7639 1.61146 0.805732 0.592280i \(-0.201772\pi\)
0.805732 + 0.592280i \(0.201772\pi\)
\(440\) 0 0
\(441\) 16.4247 0.782129
\(442\) 0 0
\(443\) −29.1045 −1.38280 −0.691399 0.722473i \(-0.743005\pi\)
−0.691399 + 0.722473i \(0.743005\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.74489 −0.177127
\(448\) 0 0
\(449\) −22.4642 −1.06015 −0.530075 0.847951i \(-0.677836\pi\)
−0.530075 + 0.847951i \(0.677836\pi\)
\(450\) 0 0
\(451\) 0.575289 0.0270893
\(452\) 0 0
\(453\) −15.3596 −0.721659
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.4993 0.537915 0.268957 0.963152i \(-0.413321\pi\)
0.268957 + 0.963152i \(0.413321\pi\)
\(458\) 0 0
\(459\) 6.32970 0.295445
\(460\) 0 0
\(461\) 16.7843 0.781725 0.390862 0.920449i \(-0.372177\pi\)
0.390862 + 0.920449i \(0.372177\pi\)
\(462\) 0 0
\(463\) −19.6893 −0.915041 −0.457520 0.889199i \(-0.651262\pi\)
−0.457520 + 0.889199i \(0.651262\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.38387 0.0640379 0.0320190 0.999487i \(-0.489806\pi\)
0.0320190 + 0.999487i \(0.489806\pi\)
\(468\) 0 0
\(469\) 63.7397 2.94323
\(470\) 0 0
\(471\) 0.979580 0.0451367
\(472\) 0 0
\(473\) −20.6784 −0.950795
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 9.93492 0.454889
\(478\) 0 0
\(479\) 28.9553 1.32300 0.661502 0.749944i \(-0.269919\pi\)
0.661502 + 0.749944i \(0.269919\pi\)
\(480\) 0 0
\(481\) −4.25511 −0.194016
\(482\) 0 0
\(483\) 23.4247 1.06586
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 26.3705 1.19496 0.597482 0.801883i \(-0.296168\pi\)
0.597482 + 0.801883i \(0.296168\pi\)
\(488\) 0 0
\(489\) 7.42471 0.335757
\(490\) 0 0
\(491\) 5.05417 0.228092 0.114046 0.993475i \(-0.463619\pi\)
0.114046 + 0.993475i \(0.463619\pi\)
\(492\) 0 0
\(493\) −57.5687 −2.59276
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.8048 −1.24721
\(498\) 0 0
\(499\) −15.7544 −0.705264 −0.352632 0.935762i \(-0.614713\pi\)
−0.352632 + 0.935762i \(0.614713\pi\)
\(500\) 0 0
\(501\) −21.1696 −0.945788
\(502\) 0 0
\(503\) 9.92541 0.442552 0.221276 0.975211i \(-0.428978\pi\)
0.221276 + 0.975211i \(0.428978\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) −25.4247 −1.12693 −0.563465 0.826140i \(-0.690532\pi\)
−0.563465 + 0.826140i \(0.690532\pi\)
\(510\) 0 0
\(511\) −14.0599 −0.621972
\(512\) 0 0
\(513\) 2.58480 0.114122
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.1710 0.447320
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) −14.5292 −0.636538 −0.318269 0.948001i \(-0.603101\pi\)
−0.318269 + 0.948001i \(0.603101\pi\)
\(522\) 0 0
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.22948 0.140678
\(528\) 0 0
\(529\) 0.424711 0.0184657
\(530\) 0 0
\(531\) 14.1900 0.615795
\(532\) 0 0
\(533\) 0.255105 0.0110498
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −8.77483 −0.378662
\(538\) 0 0
\(539\) 37.0394 1.59540
\(540\) 0 0
\(541\) 6.11543 0.262923 0.131462 0.991321i \(-0.458033\pi\)
0.131462 + 0.991321i \(0.458033\pi\)
\(542\) 0 0
\(543\) −23.1045 −0.991510
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −15.3596 −0.656730 −0.328365 0.944551i \(-0.606498\pi\)
−0.328365 + 0.944551i \(0.606498\pi\)
\(548\) 0 0
\(549\) 9.93492 0.424012
\(550\) 0 0
\(551\) −23.5088 −1.00151
\(552\) 0 0
\(553\) 27.8048 1.18238
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.3801 0.948273 0.474137 0.880451i \(-0.342760\pi\)
0.474137 + 0.880451i \(0.342760\pi\)
\(558\) 0 0
\(559\) −9.16961 −0.387833
\(560\) 0 0
\(561\) 14.2741 0.602654
\(562\) 0 0
\(563\) −17.7449 −0.747858 −0.373929 0.927457i \(-0.621990\pi\)
−0.373929 + 0.927457i \(0.621990\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.83991 0.203257
\(568\) 0 0
\(569\) −10.0190 −0.420020 −0.210010 0.977699i \(-0.567350\pi\)
−0.210010 + 0.977699i \(0.567350\pi\)
\(570\) 0 0
\(571\) −17.6147 −0.737154 −0.368577 0.929597i \(-0.620155\pi\)
−0.368577 + 0.929597i \(0.620155\pi\)
\(572\) 0 0
\(573\) −19.3596 −0.808760
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 15.3501 0.639034 0.319517 0.947581i \(-0.396479\pi\)
0.319517 + 0.947581i \(0.396479\pi\)
\(578\) 0 0
\(579\) 6.18051 0.256853
\(580\) 0 0
\(581\) −49.3188 −2.04609
\(582\) 0 0
\(583\) 22.4043 0.927891
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23.4898 −0.969527 −0.484764 0.874645i \(-0.661094\pi\)
−0.484764 + 0.874645i \(0.661094\pi\)
\(588\) 0 0
\(589\) 1.31879 0.0543399
\(590\) 0 0
\(591\) 21.8698 0.899605
\(592\) 0 0
\(593\) 5.63898 0.231565 0.115782 0.993275i \(-0.463062\pi\)
0.115782 + 0.993275i \(0.463062\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.83039 −0.115840
\(598\) 0 0
\(599\) −10.0408 −0.410258 −0.205129 0.978735i \(-0.565761\pi\)
−0.205129 + 0.978735i \(0.565761\pi\)
\(600\) 0 0
\(601\) 5.04466 0.205776 0.102888 0.994693i \(-0.467192\pi\)
0.102888 + 0.994693i \(0.467192\pi\)
\(602\) 0 0
\(603\) 13.1696 0.536308
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2.19003 0.0888904 0.0444452 0.999012i \(-0.485848\pi\)
0.0444452 + 0.999012i \(0.485848\pi\)
\(608\) 0 0
\(609\) −44.0190 −1.78374
\(610\) 0 0
\(611\) 4.51021 0.182464
\(612\) 0 0
\(613\) −45.4437 −1.83546 −0.917728 0.397210i \(-0.869978\pi\)
−0.917728 + 0.397210i \(0.869978\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.31879 0.294643 0.147322 0.989089i \(-0.452935\pi\)
0.147322 + 0.989089i \(0.452935\pi\)
\(618\) 0 0
\(619\) 20.6256 0.829015 0.414507 0.910046i \(-0.363954\pi\)
0.414507 + 0.910046i \(0.363954\pi\)
\(620\) 0 0
\(621\) 4.83991 0.194219
\(622\) 0 0
\(623\) 18.1249 0.726161
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 5.82900 0.232788
\(628\) 0 0
\(629\) 26.9335 1.07391
\(630\) 0 0
\(631\) 14.8304 0.590389 0.295194 0.955437i \(-0.404616\pi\)
0.295194 + 0.955437i \(0.404616\pi\)
\(632\) 0 0
\(633\) 22.3392 0.887904
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 16.4247 0.650771
\(638\) 0 0
\(639\) −5.74489 −0.227265
\(640\) 0 0
\(641\) −28.8494 −1.13948 −0.569742 0.821824i \(-0.692957\pi\)
−0.569742 + 0.821824i \(0.692957\pi\)
\(642\) 0 0
\(643\) 29.7449 1.17302 0.586512 0.809940i \(-0.300501\pi\)
0.586512 + 0.809940i \(0.300501\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.13967 −0.0841192 −0.0420596 0.999115i \(-0.513392\pi\)
−0.0420596 + 0.999115i \(0.513392\pi\)
\(648\) 0 0
\(649\) 32.0000 1.25611
\(650\) 0 0
\(651\) 2.46937 0.0967822
\(652\) 0 0
\(653\) 13.2104 0.516965 0.258482 0.966016i \(-0.416778\pi\)
0.258482 + 0.966016i \(0.416778\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.90499 −0.113334
\(658\) 0 0
\(659\) −48.6447 −1.89493 −0.947464 0.319863i \(-0.896363\pi\)
−0.947464 + 0.319863i \(0.896363\pi\)
\(660\) 0 0
\(661\) −24.7340 −0.962041 −0.481020 0.876709i \(-0.659734\pi\)
−0.481020 + 0.876709i \(0.659734\pi\)
\(662\) 0 0
\(663\) 6.32970 0.245825
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −44.0190 −1.70442
\(668\) 0 0
\(669\) −23.0950 −0.892905
\(670\) 0 0
\(671\) 22.4043 0.864908
\(672\) 0 0
\(673\) −39.6988 −1.53028 −0.765139 0.643865i \(-0.777330\pi\)
−0.765139 + 0.643865i \(0.777330\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −28.5535 −1.09740 −0.548700 0.836020i \(-0.684877\pi\)
−0.548700 + 0.836020i \(0.684877\pi\)
\(678\) 0 0
\(679\) 60.5943 2.32540
\(680\) 0 0
\(681\) −0.510210 −0.0195513
\(682\) 0 0
\(683\) −15.8508 −0.606515 −0.303257 0.952909i \(-0.598074\pi\)
−0.303257 + 0.952909i \(0.598074\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 1.09501 0.0417774
\(688\) 0 0
\(689\) 9.93492 0.378490
\(690\) 0 0
\(691\) −28.6256 −1.08897 −0.544485 0.838770i \(-0.683275\pi\)
−0.544485 + 0.838770i \(0.683275\pi\)
\(692\) 0 0
\(693\) 10.9145 0.414608
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.61474 −0.0611626
\(698\) 0 0
\(699\) 1.81949 0.0688194
\(700\) 0 0
\(701\) −8.58480 −0.324244 −0.162122 0.986771i \(-0.551834\pi\)
−0.162122 + 0.986771i \(0.551834\pi\)
\(702\) 0 0
\(703\) 10.9986 0.414820
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −85.2077 −3.20456
\(708\) 0 0
\(709\) −3.56438 −0.133863 −0.0669316 0.997758i \(-0.521321\pi\)
−0.0669316 + 0.997758i \(0.521321\pi\)
\(710\) 0 0
\(711\) 5.74489 0.215450
\(712\) 0 0
\(713\) 2.46937 0.0924786
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.44513 −0.315389
\(718\) 0 0
\(719\) 22.1900 0.827548 0.413774 0.910380i \(-0.364210\pi\)
0.413774 + 0.910380i \(0.364210\pi\)
\(720\) 0 0
\(721\) 83.0993 3.09478
\(722\) 0 0
\(723\) −20.3392 −0.756423
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −9.82900 −0.364538 −0.182269 0.983249i \(-0.558344\pi\)
−0.182269 + 0.983249i \(0.558344\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 58.0408 2.14672
\(732\) 0 0
\(733\) 29.0637 1.07349 0.536746 0.843744i \(-0.319653\pi\)
0.536746 + 0.843744i \(0.319653\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.6988 1.09397
\(738\) 0 0
\(739\) 28.9240 1.06399 0.531994 0.846748i \(-0.321443\pi\)
0.531994 + 0.846748i \(0.321443\pi\)
\(740\) 0 0
\(741\) 2.58480 0.0949551
\(742\) 0 0
\(743\) 20.0190 0.734427 0.367213 0.930137i \(-0.380312\pi\)
0.367213 + 0.930137i \(0.380312\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −10.1900 −0.372834
\(748\) 0 0
\(749\) −33.4656 −1.22280
\(750\) 0 0
\(751\) −22.2741 −0.812795 −0.406397 0.913696i \(-0.633215\pi\)
−0.406397 + 0.913696i \(0.633215\pi\)
\(752\) 0 0
\(753\) 17.4342 0.635339
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 23.1886 0.842805 0.421403 0.906874i \(-0.361538\pi\)
0.421403 + 0.906874i \(0.361538\pi\)
\(758\) 0 0
\(759\) 10.9145 0.396171
\(760\) 0 0
\(761\) 47.5497 1.72367 0.861837 0.507186i \(-0.169314\pi\)
0.861837 + 0.507186i \(0.169314\pi\)
\(762\) 0 0
\(763\) 16.5292 0.598399
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 14.1900 0.512372
\(768\) 0 0
\(769\) −21.8698 −0.788647 −0.394323 0.918972i \(-0.629021\pi\)
−0.394323 + 0.918972i \(0.629021\pi\)
\(770\) 0 0
\(771\) 15.4342 0.555850
\(772\) 0 0
\(773\) 8.84942 0.318292 0.159146 0.987255i \(-0.449126\pi\)
0.159146 + 0.987255i \(0.449126\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 20.5943 0.738817
\(778\) 0 0
\(779\) −0.659396 −0.0236253
\(780\) 0 0
\(781\) −12.9553 −0.463579
\(782\) 0 0
\(783\) −9.09501 −0.325029
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −9.02042 −0.321543 −0.160772 0.986992i \(-0.551398\pi\)
−0.160772 + 0.986992i \(0.551398\pi\)
\(788\) 0 0
\(789\) −8.90499 −0.317026
\(790\) 0 0
\(791\) −24.6594 −0.876787
\(792\) 0 0
\(793\) 9.93492 0.352799
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −9.55487 −0.338451 −0.169225 0.985577i \(-0.554127\pi\)
−0.169225 + 0.985577i \(0.554127\pi\)
\(798\) 0 0
\(799\) −28.5483 −1.00997
\(800\) 0 0
\(801\) 3.74489 0.132319
\(802\) 0 0
\(803\) −6.55105 −0.231182
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 16.5848 0.583813
\(808\) 0 0
\(809\) 53.3596 1.87602 0.938012 0.346602i \(-0.112664\pi\)
0.938012 + 0.346602i \(0.112664\pi\)
\(810\) 0 0
\(811\) 10.9458 0.384360 0.192180 0.981360i \(-0.438444\pi\)
0.192180 + 0.981360i \(0.438444\pi\)
\(812\) 0 0
\(813\) −17.8290 −0.625290
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 23.7016 0.829215
\(818\) 0 0
\(819\) 4.83991 0.169120
\(820\) 0 0
\(821\) 35.6147 1.24296 0.621481 0.783429i \(-0.286531\pi\)
0.621481 + 0.783429i \(0.286531\pi\)
\(822\) 0 0
\(823\) −10.1900 −0.355202 −0.177601 0.984103i \(-0.556834\pi\)
−0.177601 + 0.984103i \(0.556834\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 25.0394 0.870707 0.435353 0.900260i \(-0.356623\pi\)
0.435353 + 0.900260i \(0.356623\pi\)
\(828\) 0 0
\(829\) −36.3392 −1.26211 −0.631057 0.775737i \(-0.717378\pi\)
−0.631057 + 0.775737i \(0.717378\pi\)
\(830\) 0 0
\(831\) 22.3801 0.776355
\(832\) 0 0
\(833\) −103.963 −3.60212
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.510210 0.0176354
\(838\) 0 0
\(839\) 38.4043 1.32586 0.662932 0.748680i \(-0.269312\pi\)
0.662932 + 0.748680i \(0.269312\pi\)
\(840\) 0 0
\(841\) 53.7193 1.85239
\(842\) 0 0
\(843\) 24.1900 0.833149
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −28.6256 −0.983589
\(848\) 0 0
\(849\) −26.1900 −0.898839
\(850\) 0 0
\(851\) 20.5943 0.705964
\(852\) 0 0
\(853\) −22.7245 −0.778071 −0.389036 0.921223i \(-0.627192\pi\)
−0.389036 + 0.921223i \(0.627192\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 10.3297 0.352856 0.176428 0.984314i \(-0.443546\pi\)
0.176428 + 0.984314i \(0.443546\pi\)
\(858\) 0 0
\(859\) 2.40429 0.0820334 0.0410167 0.999158i \(-0.486940\pi\)
0.0410167 + 0.999158i \(0.486940\pi\)
\(860\) 0 0
\(861\) −1.23468 −0.0420779
\(862\) 0 0
\(863\) −17.6798 −0.601828 −0.300914 0.953651i \(-0.597292\pi\)
−0.300914 + 0.953651i \(0.597292\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −23.0651 −0.783331
\(868\) 0 0
\(869\) 12.9553 0.439480
\(870\) 0 0
\(871\) 13.1696 0.446235
\(872\) 0 0
\(873\) 12.5197 0.423728
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −50.7601 −1.71405 −0.857023 0.515277i \(-0.827689\pi\)
−0.857023 + 0.515277i \(0.827689\pi\)
\(878\) 0 0
\(879\) −5.48979 −0.185166
\(880\) 0 0
\(881\) −49.5905 −1.67075 −0.835373 0.549683i \(-0.814748\pi\)
−0.835373 + 0.549683i \(0.814748\pi\)
\(882\) 0 0
\(883\) −21.3188 −0.717434 −0.358717 0.933446i \(-0.616786\pi\)
−0.358717 + 0.933446i \(0.616786\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 16.9891 0.570438 0.285219 0.958462i \(-0.407934\pi\)
0.285219 + 0.958462i \(0.407934\pi\)
\(888\) 0 0
\(889\) 61.2703 2.05494
\(890\) 0 0
\(891\) 2.25511 0.0755489
\(892\) 0 0
\(893\) −11.6580 −0.390120
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 4.83991 0.161600
\(898\) 0 0
\(899\) −4.64037 −0.154765
\(900\) 0 0
\(901\) −62.8851 −2.09500
\(902\) 0 0
\(903\) 44.3801 1.47688
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 36.6594 1.21726 0.608628 0.793456i \(-0.291720\pi\)
0.608628 + 0.793456i \(0.291720\pi\)
\(908\) 0 0
\(909\) −17.6052 −0.583928
\(910\) 0 0
\(911\) 22.1900 0.735188 0.367594 0.929986i \(-0.380182\pi\)
0.367594 + 0.929986i \(0.380182\pi\)
\(912\) 0 0
\(913\) −22.9796 −0.760513
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −81.1886 −2.68108
\(918\) 0 0
\(919\) 25.5957 0.844325 0.422162 0.906520i \(-0.361271\pi\)
0.422162 + 0.906520i \(0.361271\pi\)
\(920\) 0 0
\(921\) −6.76532 −0.222925
\(922\) 0 0
\(923\) −5.74489 −0.189096
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 17.1696 0.563924
\(928\) 0 0
\(929\) 9.40568 0.308590 0.154295 0.988025i \(-0.450689\pi\)
0.154295 + 0.988025i \(0.450689\pi\)
\(930\) 0 0
\(931\) −42.4546 −1.39139
\(932\) 0 0
\(933\) 17.0204 0.557224
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −50.7601 −1.65826 −0.829130 0.559056i \(-0.811164\pi\)
−0.829130 + 0.559056i \(0.811164\pi\)
\(938\) 0 0
\(939\) 12.8304 0.418704
\(940\) 0 0
\(941\) −30.5943 −0.997346 −0.498673 0.866790i \(-0.666179\pi\)
−0.498673 + 0.866790i \(0.666179\pi\)
\(942\) 0 0
\(943\) −1.23468 −0.0402069
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7.12877 −0.231654 −0.115827 0.993269i \(-0.536952\pi\)
−0.115827 + 0.993269i \(0.536952\pi\)
\(948\) 0 0
\(949\) −2.90499 −0.0942999
\(950\) 0 0
\(951\) −13.4898 −0.437436
\(952\) 0 0
\(953\) −3.99049 −0.129265 −0.0646323 0.997909i \(-0.520587\pi\)
−0.0646323 + 0.997909i \(0.520587\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −20.5102 −0.663001
\(958\) 0 0
\(959\) −9.67982 −0.312578
\(960\) 0 0
\(961\) −30.7397 −0.991603
\(962\) 0 0
\(963\) −6.91450 −0.222817
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −27.4751 −0.883539 −0.441769 0.897129i \(-0.645649\pi\)
−0.441769 + 0.897129i \(0.645649\pi\)
\(968\) 0 0
\(969\) −16.3610 −0.525592
\(970\) 0 0
\(971\) 29.5834 0.949377 0.474688 0.880154i \(-0.342561\pi\)
0.474688 + 0.880154i \(0.342561\pi\)
\(972\) 0 0
\(973\) 25.3354 0.812215
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.72066 0.0550487 0.0275243 0.999621i \(-0.491238\pi\)
0.0275243 + 0.999621i \(0.491238\pi\)
\(978\) 0 0
\(979\) 8.44513 0.269908
\(980\) 0 0
\(981\) 3.41520 0.109039
\(982\) 0 0
\(983\) −27.8889 −0.889517 −0.444758 0.895651i \(-0.646710\pi\)
−0.444758 + 0.895651i \(0.646710\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −21.8290 −0.694825
\(988\) 0 0
\(989\) 44.3801 1.41120
\(990\) 0 0
\(991\) 45.6147 1.44900 0.724500 0.689275i \(-0.242071\pi\)
0.724500 + 0.689275i \(0.242071\pi\)
\(992\) 0 0
\(993\) 14.0746 0.446644
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 19.8290 0.627991 0.313995 0.949425i \(-0.398332\pi\)
0.313995 + 0.949425i \(0.398332\pi\)
\(998\) 0 0
\(999\) 4.25511 0.134626
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 7800.2.a.bi.1.3 3
5.4 even 2 1560.2.a.q.1.1 3
15.14 odd 2 4680.2.a.bh.1.1 3
20.19 odd 2 3120.2.a.bi.1.3 3
60.59 even 2 9360.2.a.cy.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1560.2.a.q.1.1 3 5.4 even 2
3120.2.a.bi.1.3 3 20.19 odd 2
4680.2.a.bh.1.1 3 15.14 odd 2
7800.2.a.bi.1.3 3 1.1 even 1 trivial
9360.2.a.cy.1.3 3 60.59 even 2