Properties

Label 4600.2.a.s.1.2
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 184)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{3} +3.56155 q^{9} +O(q^{10})\) \(q+2.56155 q^{3} +3.56155 q^{9} +5.12311 q^{11} -4.56155 q^{13} +3.12311 q^{17} +5.12311 q^{19} +1.00000 q^{23} +1.43845 q^{27} -0.561553 q^{29} -6.56155 q^{31} +13.1231 q^{33} +8.24621 q^{37} -11.6847 q^{39} +10.8078 q^{41} +8.00000 q^{43} -11.6847 q^{47} -7.00000 q^{49} +8.00000 q^{51} -2.00000 q^{53} +13.1231 q^{57} -6.24621 q^{59} +12.2462 q^{61} +5.12311 q^{67} +2.56155 q^{69} +9.43845 q^{71} +2.31534 q^{73} -5.12311 q^{79} -7.00000 q^{81} +2.24621 q^{83} -1.43845 q^{87} -13.3693 q^{89} -16.8078 q^{93} +13.3693 q^{97} +18.2462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{3} + 3 q^{9} + O(q^{10}) \) \( 2 q + q^{3} + 3 q^{9} + 2 q^{11} - 5 q^{13} - 2 q^{17} + 2 q^{19} + 2 q^{23} + 7 q^{27} + 3 q^{29} - 9 q^{31} + 18 q^{33} - 11 q^{39} + q^{41} + 16 q^{43} - 11 q^{47} - 14 q^{49} + 16 q^{51} - 4 q^{53} + 18 q^{57} + 4 q^{59} + 8 q^{61} + 2 q^{67} + q^{69} + 23 q^{71} + 17 q^{73} - 2 q^{79} - 14 q^{81} - 12 q^{83} - 7 q^{87} - 2 q^{89} - 13 q^{93} + 2 q^{97} + 20 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.56155 1.47891 0.739457 0.673204i \(-0.235083\pi\)
0.739457 + 0.673204i \(0.235083\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 3.56155 1.18718
\(10\) 0 0
\(11\) 5.12311 1.54467 0.772337 0.635213i \(-0.219088\pi\)
0.772337 + 0.635213i \(0.219088\pi\)
\(12\) 0 0
\(13\) −4.56155 −1.26515 −0.632574 0.774500i \(-0.718001\pi\)
−0.632574 + 0.774500i \(0.718001\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.12311 0.757464 0.378732 0.925506i \(-0.376360\pi\)
0.378732 + 0.925506i \(0.376360\pi\)
\(18\) 0 0
\(19\) 5.12311 1.17532 0.587661 0.809108i \(-0.300049\pi\)
0.587661 + 0.809108i \(0.300049\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.43845 0.276829
\(28\) 0 0
\(29\) −0.561553 −0.104278 −0.0521389 0.998640i \(-0.516604\pi\)
−0.0521389 + 0.998640i \(0.516604\pi\)
\(30\) 0 0
\(31\) −6.56155 −1.17849 −0.589245 0.807955i \(-0.700575\pi\)
−0.589245 + 0.807955i \(0.700575\pi\)
\(32\) 0 0
\(33\) 13.1231 2.28444
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.24621 1.35567 0.677834 0.735215i \(-0.262919\pi\)
0.677834 + 0.735215i \(0.262919\pi\)
\(38\) 0 0
\(39\) −11.6847 −1.87104
\(40\) 0 0
\(41\) 10.8078 1.68789 0.843945 0.536430i \(-0.180228\pi\)
0.843945 + 0.536430i \(0.180228\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.6847 −1.70438 −0.852191 0.523230i \(-0.824727\pi\)
−0.852191 + 0.523230i \(0.824727\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 8.00000 1.12022
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 13.1231 1.73820
\(58\) 0 0
\(59\) −6.24621 −0.813187 −0.406594 0.913609i \(-0.633284\pi\)
−0.406594 + 0.913609i \(0.633284\pi\)
\(60\) 0 0
\(61\) 12.2462 1.56797 0.783983 0.620782i \(-0.213185\pi\)
0.783983 + 0.620782i \(0.213185\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.12311 0.625887 0.312943 0.949772i \(-0.398685\pi\)
0.312943 + 0.949772i \(0.398685\pi\)
\(68\) 0 0
\(69\) 2.56155 0.308375
\(70\) 0 0
\(71\) 9.43845 1.12014 0.560069 0.828446i \(-0.310775\pi\)
0.560069 + 0.828446i \(0.310775\pi\)
\(72\) 0 0
\(73\) 2.31534 0.270990 0.135495 0.990778i \(-0.456737\pi\)
0.135495 + 0.990778i \(0.456737\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −5.12311 −0.576394 −0.288197 0.957571i \(-0.593056\pi\)
−0.288197 + 0.957571i \(0.593056\pi\)
\(80\) 0 0
\(81\) −7.00000 −0.777778
\(82\) 0 0
\(83\) 2.24621 0.246554 0.123277 0.992372i \(-0.460660\pi\)
0.123277 + 0.992372i \(0.460660\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.43845 −0.154218
\(88\) 0 0
\(89\) −13.3693 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −16.8078 −1.74288
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.3693 1.35745 0.678724 0.734393i \(-0.262533\pi\)
0.678724 + 0.734393i \(0.262533\pi\)
\(98\) 0 0
\(99\) 18.2462 1.83381
\(100\) 0 0
\(101\) −4.24621 −0.422514 −0.211257 0.977431i \(-0.567756\pi\)
−0.211257 + 0.977431i \(0.567756\pi\)
\(102\) 0 0
\(103\) −2.24621 −0.221326 −0.110663 0.993858i \(-0.535297\pi\)
−0.110663 + 0.993858i \(0.535297\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.87689 −0.278120 −0.139060 0.990284i \(-0.544408\pi\)
−0.139060 + 0.990284i \(0.544408\pi\)
\(108\) 0 0
\(109\) 4.87689 0.467122 0.233561 0.972342i \(-0.424962\pi\)
0.233561 + 0.972342i \(0.424962\pi\)
\(110\) 0 0
\(111\) 21.1231 2.00492
\(112\) 0 0
\(113\) 11.1231 1.04637 0.523187 0.852218i \(-0.324743\pi\)
0.523187 + 0.852218i \(0.324743\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −16.2462 −1.50196
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 15.2462 1.38602
\(122\) 0 0
\(123\) 27.6847 2.49624
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 11.6847 1.03685 0.518423 0.855124i \(-0.326519\pi\)
0.518423 + 0.855124i \(0.326519\pi\)
\(128\) 0 0
\(129\) 20.4924 1.80426
\(130\) 0 0
\(131\) 15.6847 1.37037 0.685187 0.728367i \(-0.259720\pi\)
0.685187 + 0.728367i \(0.259720\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.1231 −1.29205 −0.646027 0.763315i \(-0.723571\pi\)
−0.646027 + 0.763315i \(0.723571\pi\)
\(138\) 0 0
\(139\) −15.6847 −1.33036 −0.665178 0.746685i \(-0.731644\pi\)
−0.665178 + 0.746685i \(0.731644\pi\)
\(140\) 0 0
\(141\) −29.9309 −2.52063
\(142\) 0 0
\(143\) −23.3693 −1.95424
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −17.9309 −1.47891
\(148\) 0 0
\(149\) −3.75379 −0.307522 −0.153761 0.988108i \(-0.549139\pi\)
−0.153761 + 0.988108i \(0.549139\pi\)
\(150\) 0 0
\(151\) −14.5616 −1.18500 −0.592501 0.805570i \(-0.701859\pi\)
−0.592501 + 0.805570i \(0.701859\pi\)
\(152\) 0 0
\(153\) 11.1231 0.899250
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.8769 −1.02769 −0.513844 0.857884i \(-0.671779\pi\)
−0.513844 + 0.857884i \(0.671779\pi\)
\(158\) 0 0
\(159\) −5.12311 −0.406289
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 9.93087 0.777846 0.388923 0.921270i \(-0.372847\pi\)
0.388923 + 0.921270i \(0.372847\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 16.0000 1.23812 0.619059 0.785345i \(-0.287514\pi\)
0.619059 + 0.785345i \(0.287514\pi\)
\(168\) 0 0
\(169\) 7.80776 0.600597
\(170\) 0 0
\(171\) 18.2462 1.39532
\(172\) 0 0
\(173\) 10.0000 0.760286 0.380143 0.924928i \(-0.375875\pi\)
0.380143 + 0.924928i \(0.375875\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −16.0000 −1.20263
\(178\) 0 0
\(179\) −15.6847 −1.17233 −0.586163 0.810193i \(-0.699362\pi\)
−0.586163 + 0.810193i \(0.699362\pi\)
\(180\) 0 0
\(181\) 20.2462 1.50489 0.752445 0.658656i \(-0.228875\pi\)
0.752445 + 0.658656i \(0.228875\pi\)
\(182\) 0 0
\(183\) 31.3693 2.31889
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 16.0000 1.17004
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.630683 0.0456346 0.0228173 0.999740i \(-0.492736\pi\)
0.0228173 + 0.999740i \(0.492736\pi\)
\(192\) 0 0
\(193\) 4.56155 0.328348 0.164174 0.986431i \(-0.447504\pi\)
0.164174 + 0.986431i \(0.447504\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.9309 −0.850039 −0.425020 0.905184i \(-0.639733\pi\)
−0.425020 + 0.905184i \(0.639733\pi\)
\(198\) 0 0
\(199\) 2.87689 0.203938 0.101969 0.994788i \(-0.467486\pi\)
0.101969 + 0.994788i \(0.467486\pi\)
\(200\) 0 0
\(201\) 13.1231 0.925633
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.56155 0.247545
\(208\) 0 0
\(209\) 26.2462 1.81549
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) 24.1771 1.65659
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 5.93087 0.400771
\(220\) 0 0
\(221\) −14.2462 −0.958304
\(222\) 0 0
\(223\) −4.49242 −0.300835 −0.150417 0.988623i \(-0.548062\pi\)
−0.150417 + 0.988623i \(0.548062\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −10.2462 −0.680065 −0.340032 0.940414i \(-0.610438\pi\)
−0.340032 + 0.940414i \(0.610438\pi\)
\(228\) 0 0
\(229\) 23.1231 1.52802 0.764009 0.645206i \(-0.223228\pi\)
0.764009 + 0.645206i \(0.223228\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.0540 −1.37929 −0.689646 0.724147i \(-0.742234\pi\)
−0.689646 + 0.724147i \(0.742234\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −13.1231 −0.852437
\(238\) 0 0
\(239\) −11.0540 −0.715022 −0.357511 0.933909i \(-0.616375\pi\)
−0.357511 + 0.933909i \(0.616375\pi\)
\(240\) 0 0
\(241\) −26.4924 −1.70653 −0.853263 0.521480i \(-0.825380\pi\)
−0.853263 + 0.521480i \(0.825380\pi\)
\(242\) 0 0
\(243\) −22.2462 −1.42710
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −23.3693 −1.48695
\(248\) 0 0
\(249\) 5.75379 0.364632
\(250\) 0 0
\(251\) 10.2462 0.646735 0.323368 0.946273i \(-0.395185\pi\)
0.323368 + 0.946273i \(0.395185\pi\)
\(252\) 0 0
\(253\) 5.12311 0.322087
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.6847 1.10314 0.551569 0.834129i \(-0.314029\pi\)
0.551569 + 0.834129i \(0.314029\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2.00000 −0.123797
\(262\) 0 0
\(263\) 10.8769 0.670698 0.335349 0.942094i \(-0.391146\pi\)
0.335349 + 0.942094i \(0.391146\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −34.2462 −2.09583
\(268\) 0 0
\(269\) 25.6847 1.56602 0.783011 0.622008i \(-0.213683\pi\)
0.783011 + 0.622008i \(0.213683\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2.80776 0.168702 0.0843511 0.996436i \(-0.473118\pi\)
0.0843511 + 0.996436i \(0.473118\pi\)
\(278\) 0 0
\(279\) −23.3693 −1.39908
\(280\) 0 0
\(281\) −3.12311 −0.186309 −0.0931544 0.995652i \(-0.529695\pi\)
−0.0931544 + 0.995652i \(0.529695\pi\)
\(282\) 0 0
\(283\) 5.12311 0.304537 0.152269 0.988339i \(-0.451342\pi\)
0.152269 + 0.988339i \(0.451342\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −7.24621 −0.426248
\(290\) 0 0
\(291\) 34.2462 2.00755
\(292\) 0 0
\(293\) −9.36932 −0.547361 −0.273681 0.961821i \(-0.588241\pi\)
−0.273681 + 0.961821i \(0.588241\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 7.36932 0.427611
\(298\) 0 0
\(299\) −4.56155 −0.263801
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −10.8769 −0.624861
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.75379 0.100094 0.0500470 0.998747i \(-0.484063\pi\)
0.0500470 + 0.998747i \(0.484063\pi\)
\(308\) 0 0
\(309\) −5.75379 −0.327322
\(310\) 0 0
\(311\) 1.43845 0.0815669 0.0407834 0.999168i \(-0.487015\pi\)
0.0407834 + 0.999168i \(0.487015\pi\)
\(312\) 0 0
\(313\) −9.36932 −0.529585 −0.264793 0.964305i \(-0.585303\pi\)
−0.264793 + 0.964305i \(0.585303\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.2462 1.13714 0.568570 0.822635i \(-0.307497\pi\)
0.568570 + 0.822635i \(0.307497\pi\)
\(318\) 0 0
\(319\) −2.87689 −0.161075
\(320\) 0 0
\(321\) −7.36932 −0.411315
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 12.4924 0.690833
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −30.4233 −1.67222 −0.836108 0.548565i \(-0.815174\pi\)
−0.836108 + 0.548565i \(0.815174\pi\)
\(332\) 0 0
\(333\) 29.3693 1.60943
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −19.6155 −1.06853 −0.534263 0.845318i \(-0.679411\pi\)
−0.534263 + 0.845318i \(0.679411\pi\)
\(338\) 0 0
\(339\) 28.4924 1.54750
\(340\) 0 0
\(341\) −33.6155 −1.82038
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.4924 −0.885360 −0.442680 0.896680i \(-0.645972\pi\)
−0.442680 + 0.896680i \(0.645972\pi\)
\(348\) 0 0
\(349\) −22.3153 −1.19451 −0.597256 0.802050i \(-0.703743\pi\)
−0.597256 + 0.802050i \(0.703743\pi\)
\(350\) 0 0
\(351\) −6.56155 −0.350230
\(352\) 0 0
\(353\) −11.4384 −0.608807 −0.304404 0.952543i \(-0.598457\pi\)
−0.304404 + 0.952543i \(0.598457\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.6155 0.929712 0.464856 0.885386i \(-0.346106\pi\)
0.464856 + 0.885386i \(0.346106\pi\)
\(360\) 0 0
\(361\) 7.24621 0.381380
\(362\) 0 0
\(363\) 39.0540 2.04980
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −2.24621 −0.117251 −0.0586256 0.998280i \(-0.518672\pi\)
−0.0586256 + 0.998280i \(0.518672\pi\)
\(368\) 0 0
\(369\) 38.4924 2.00384
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −22.4924 −1.16461 −0.582307 0.812969i \(-0.697850\pi\)
−0.582307 + 0.812969i \(0.697850\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.56155 0.131927
\(378\) 0 0
\(379\) 20.4924 1.05263 0.526313 0.850291i \(-0.323574\pi\)
0.526313 + 0.850291i \(0.323574\pi\)
\(380\) 0 0
\(381\) 29.9309 1.53340
\(382\) 0 0
\(383\) −26.2462 −1.34112 −0.670559 0.741856i \(-0.733946\pi\)
−0.670559 + 0.741856i \(0.733946\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 28.4924 1.44835
\(388\) 0 0
\(389\) 1.36932 0.0694271 0.0347136 0.999397i \(-0.488948\pi\)
0.0347136 + 0.999397i \(0.488948\pi\)
\(390\) 0 0
\(391\) 3.12311 0.157942
\(392\) 0 0
\(393\) 40.1771 2.02667
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −20.5616 −1.03195 −0.515977 0.856602i \(-0.672571\pi\)
−0.515977 + 0.856602i \(0.672571\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.7538 −0.586956 −0.293478 0.955966i \(-0.594813\pi\)
−0.293478 + 0.955966i \(0.594813\pi\)
\(402\) 0 0
\(403\) 29.9309 1.49096
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 42.2462 2.09407
\(408\) 0 0
\(409\) −27.3002 −1.34991 −0.674954 0.737860i \(-0.735836\pi\)
−0.674954 + 0.737860i \(0.735836\pi\)
\(410\) 0 0
\(411\) −38.7386 −1.91084
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −40.1771 −1.96748
\(418\) 0 0
\(419\) −12.4924 −0.610295 −0.305147 0.952305i \(-0.598706\pi\)
−0.305147 + 0.952305i \(0.598706\pi\)
\(420\) 0 0
\(421\) −27.1231 −1.32190 −0.660950 0.750430i \(-0.729846\pi\)
−0.660950 + 0.750430i \(0.729846\pi\)
\(422\) 0 0
\(423\) −41.6155 −2.02342
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −59.8617 −2.89015
\(430\) 0 0
\(431\) −28.4924 −1.37243 −0.686216 0.727398i \(-0.740729\pi\)
−0.686216 + 0.727398i \(0.740729\pi\)
\(432\) 0 0
\(433\) −24.7386 −1.18886 −0.594431 0.804146i \(-0.702623\pi\)
−0.594431 + 0.804146i \(0.702623\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.12311 0.245071
\(438\) 0 0
\(439\) 11.0540 0.527577 0.263789 0.964580i \(-0.415028\pi\)
0.263789 + 0.964580i \(0.415028\pi\)
\(440\) 0 0
\(441\) −24.9309 −1.18718
\(442\) 0 0
\(443\) 6.06913 0.288353 0.144177 0.989552i \(-0.453947\pi\)
0.144177 + 0.989552i \(0.453947\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −9.61553 −0.454799
\(448\) 0 0
\(449\) −8.24621 −0.389163 −0.194581 0.980886i \(-0.562335\pi\)
−0.194581 + 0.980886i \(0.562335\pi\)
\(450\) 0 0
\(451\) 55.3693 2.60724
\(452\) 0 0
\(453\) −37.3002 −1.75252
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 5.36932 0.251166 0.125583 0.992083i \(-0.459920\pi\)
0.125583 + 0.992083i \(0.459920\pi\)
\(458\) 0 0
\(459\) 4.49242 0.209688
\(460\) 0 0
\(461\) −10.8078 −0.503368 −0.251684 0.967809i \(-0.580984\pi\)
−0.251684 + 0.967809i \(0.580984\pi\)
\(462\) 0 0
\(463\) −12.4924 −0.580572 −0.290286 0.956940i \(-0.593750\pi\)
−0.290286 + 0.956940i \(0.593750\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 15.3693 0.711207 0.355604 0.934637i \(-0.384275\pi\)
0.355604 + 0.934637i \(0.384275\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −32.9848 −1.51986
\(472\) 0 0
\(473\) 40.9848 1.88449
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −7.12311 −0.326145
\(478\) 0 0
\(479\) 10.2462 0.468161 0.234081 0.972217i \(-0.424792\pi\)
0.234081 + 0.972217i \(0.424792\pi\)
\(480\) 0 0
\(481\) −37.6155 −1.71512
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −12.3153 −0.558061 −0.279031 0.960282i \(-0.590013\pi\)
−0.279031 + 0.960282i \(0.590013\pi\)
\(488\) 0 0
\(489\) 25.4384 1.15037
\(490\) 0 0
\(491\) 12.8078 0.578006 0.289003 0.957328i \(-0.406676\pi\)
0.289003 + 0.957328i \(0.406676\pi\)
\(492\) 0 0
\(493\) −1.75379 −0.0789867
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −23.0540 −1.03204 −0.516019 0.856577i \(-0.672587\pi\)
−0.516019 + 0.856577i \(0.672587\pi\)
\(500\) 0 0
\(501\) 40.9848 1.83107
\(502\) 0 0
\(503\) −7.36932 −0.328582 −0.164291 0.986412i \(-0.552534\pi\)
−0.164291 + 0.986412i \(0.552534\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 20.0000 0.888231
\(508\) 0 0
\(509\) −15.3002 −0.678169 −0.339084 0.940756i \(-0.610117\pi\)
−0.339084 + 0.940756i \(0.610117\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 7.36932 0.325363
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −59.8617 −2.63272
\(518\) 0 0
\(519\) 25.6155 1.12440
\(520\) 0 0
\(521\) 19.6155 0.859372 0.429686 0.902978i \(-0.358624\pi\)
0.429686 + 0.902978i \(0.358624\pi\)
\(522\) 0 0
\(523\) −5.75379 −0.251596 −0.125798 0.992056i \(-0.540149\pi\)
−0.125798 + 0.992056i \(0.540149\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.4924 −0.892664
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −22.2462 −0.965403
\(532\) 0 0
\(533\) −49.3002 −2.13543
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −40.1771 −1.73377
\(538\) 0 0
\(539\) −35.8617 −1.54467
\(540\) 0 0
\(541\) 35.9309 1.54479 0.772394 0.635143i \(-0.219059\pi\)
0.772394 + 0.635143i \(0.219059\pi\)
\(542\) 0 0
\(543\) 51.8617 2.22560
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −43.5464 −1.86191 −0.930955 0.365135i \(-0.881023\pi\)
−0.930955 + 0.365135i \(0.881023\pi\)
\(548\) 0 0
\(549\) 43.6155 1.86147
\(550\) 0 0
\(551\) −2.87689 −0.122560
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.876894 0.0371552 0.0185776 0.999827i \(-0.494086\pi\)
0.0185776 + 0.999827i \(0.494086\pi\)
\(558\) 0 0
\(559\) −36.4924 −1.54347
\(560\) 0 0
\(561\) 40.9848 1.73038
\(562\) 0 0
\(563\) −5.75379 −0.242493 −0.121247 0.992622i \(-0.538689\pi\)
−0.121247 + 0.992622i \(0.538689\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.24621 −0.345699 −0.172850 0.984948i \(-0.555297\pi\)
−0.172850 + 0.984948i \(0.555297\pi\)
\(570\) 0 0
\(571\) −11.5076 −0.481577 −0.240789 0.970578i \(-0.577406\pi\)
−0.240789 + 0.970578i \(0.577406\pi\)
\(572\) 0 0
\(573\) 1.61553 0.0674897
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −15.9309 −0.663211 −0.331605 0.943418i \(-0.607590\pi\)
−0.331605 + 0.943418i \(0.607590\pi\)
\(578\) 0 0
\(579\) 11.6847 0.485598
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −10.2462 −0.424355
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 23.0540 0.951539 0.475770 0.879570i \(-0.342170\pi\)
0.475770 + 0.879570i \(0.342170\pi\)
\(588\) 0 0
\(589\) −33.6155 −1.38510
\(590\) 0 0
\(591\) −30.5616 −1.25713
\(592\) 0 0
\(593\) 44.7386 1.83720 0.918598 0.395194i \(-0.129323\pi\)
0.918598 + 0.395194i \(0.129323\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 7.36932 0.301606
\(598\) 0 0
\(599\) 8.00000 0.326871 0.163436 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) 0 0
\(601\) −38.8078 −1.58300 −0.791501 0.611168i \(-0.790700\pi\)
−0.791501 + 0.611168i \(0.790700\pi\)
\(602\) 0 0
\(603\) 18.2462 0.743043
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14.7386 0.598223 0.299111 0.954218i \(-0.403310\pi\)
0.299111 + 0.954218i \(0.403310\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 53.3002 2.15629
\(612\) 0 0
\(613\) 28.1080 1.13527 0.567635 0.823281i \(-0.307859\pi\)
0.567635 + 0.823281i \(0.307859\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −34.9848 −1.40844 −0.704218 0.709983i \(-0.748702\pi\)
−0.704218 + 0.709983i \(0.748702\pi\)
\(618\) 0 0
\(619\) 28.4924 1.14521 0.572604 0.819832i \(-0.305933\pi\)
0.572604 + 0.819832i \(0.305933\pi\)
\(620\) 0 0
\(621\) 1.43845 0.0577229
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 67.2311 2.68495
\(628\) 0 0
\(629\) 25.7538 1.02687
\(630\) 0 0
\(631\) −6.73863 −0.268261 −0.134130 0.990964i \(-0.542824\pi\)
−0.134130 + 0.990964i \(0.542824\pi\)
\(632\) 0 0
\(633\) −10.2462 −0.407250
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 31.9309 1.26515
\(638\) 0 0
\(639\) 33.6155 1.32981
\(640\) 0 0
\(641\) −13.3693 −0.528056 −0.264028 0.964515i \(-0.585051\pi\)
−0.264028 + 0.964515i \(0.585051\pi\)
\(642\) 0 0
\(643\) 23.3693 0.921596 0.460798 0.887505i \(-0.347563\pi\)
0.460798 + 0.887505i \(0.347563\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 29.3002 1.15191 0.575955 0.817482i \(-0.304630\pi\)
0.575955 + 0.817482i \(0.304630\pi\)
\(648\) 0 0
\(649\) −32.0000 −1.25611
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −25.0540 −0.980438 −0.490219 0.871599i \(-0.663083\pi\)
−0.490219 + 0.871599i \(0.663083\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 8.24621 0.321715
\(658\) 0 0
\(659\) 2.24621 0.0875000 0.0437500 0.999043i \(-0.486070\pi\)
0.0437500 + 0.999043i \(0.486070\pi\)
\(660\) 0 0
\(661\) −0.246211 −0.00957651 −0.00478825 0.999989i \(-0.501524\pi\)
−0.00478825 + 0.999989i \(0.501524\pi\)
\(662\) 0 0
\(663\) −36.4924 −1.41725
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.561553 −0.0217434
\(668\) 0 0
\(669\) −11.5076 −0.444909
\(670\) 0 0
\(671\) 62.7386 2.42200
\(672\) 0 0
\(673\) 2.94602 0.113561 0.0567805 0.998387i \(-0.481916\pi\)
0.0567805 + 0.998387i \(0.481916\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 38.9848 1.49831 0.749155 0.662395i \(-0.230460\pi\)
0.749155 + 0.662395i \(0.230460\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −26.2462 −1.00576
\(682\) 0 0
\(683\) −16.3153 −0.624289 −0.312145 0.950035i \(-0.601047\pi\)
−0.312145 + 0.950035i \(0.601047\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 59.2311 2.25981
\(688\) 0 0
\(689\) 9.12311 0.347563
\(690\) 0 0
\(691\) 20.9848 0.798301 0.399151 0.916885i \(-0.369305\pi\)
0.399151 + 0.916885i \(0.369305\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 33.7538 1.27852
\(698\) 0 0
\(699\) −53.9309 −2.03985
\(700\) 0 0
\(701\) 29.8617 1.12786 0.563931 0.825822i \(-0.309288\pi\)
0.563931 + 0.825822i \(0.309288\pi\)
\(702\) 0 0
\(703\) 42.2462 1.59335
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −37.3693 −1.40343 −0.701717 0.712456i \(-0.747583\pi\)
−0.701717 + 0.712456i \(0.747583\pi\)
\(710\) 0 0
\(711\) −18.2462 −0.684286
\(712\) 0 0
\(713\) −6.56155 −0.245732
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −28.3153 −1.05746
\(718\) 0 0
\(719\) 4.49242 0.167539 0.0837695 0.996485i \(-0.473304\pi\)
0.0837695 + 0.996485i \(0.473304\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −67.8617 −2.52381
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 39.3693 1.46013 0.730064 0.683379i \(-0.239490\pi\)
0.730064 + 0.683379i \(0.239490\pi\)
\(728\) 0 0
\(729\) −35.9848 −1.33277
\(730\) 0 0
\(731\) 24.9848 0.924098
\(732\) 0 0
\(733\) −49.3693 −1.82350 −0.911749 0.410749i \(-0.865267\pi\)
−0.911749 + 0.410749i \(0.865267\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 26.2462 0.966792
\(738\) 0 0
\(739\) 0.315342 0.0116000 0.00580001 0.999983i \(-0.498154\pi\)
0.00580001 + 0.999983i \(0.498154\pi\)
\(740\) 0 0
\(741\) −59.8617 −2.19908
\(742\) 0 0
\(743\) −34.2462 −1.25637 −0.628186 0.778063i \(-0.716202\pi\)
−0.628186 + 0.778063i \(0.716202\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 8.00000 0.292705
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 40.9848 1.49556 0.747779 0.663948i \(-0.231120\pi\)
0.747779 + 0.663948i \(0.231120\pi\)
\(752\) 0 0
\(753\) 26.2462 0.956465
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.50758 0.0547938 0.0273969 0.999625i \(-0.491278\pi\)
0.0273969 + 0.999625i \(0.491278\pi\)
\(758\) 0 0
\(759\) 13.1231 0.476339
\(760\) 0 0
\(761\) −18.3153 −0.663931 −0.331965 0.943292i \(-0.607712\pi\)
−0.331965 + 0.943292i \(0.607712\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.4924 1.02880
\(768\) 0 0
\(769\) −6.00000 −0.216366 −0.108183 0.994131i \(-0.534503\pi\)
−0.108183 + 0.994131i \(0.534503\pi\)
\(770\) 0 0
\(771\) 45.3002 1.63145
\(772\) 0 0
\(773\) −2.63068 −0.0946191 −0.0473095 0.998880i \(-0.515065\pi\)
−0.0473095 + 0.998880i \(0.515065\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 55.3693 1.98381
\(780\) 0 0
\(781\) 48.3542 1.73025
\(782\) 0 0
\(783\) −0.807764 −0.0288671
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 26.2462 0.935576 0.467788 0.883841i \(-0.345051\pi\)
0.467788 + 0.883841i \(0.345051\pi\)
\(788\) 0 0
\(789\) 27.8617 0.991904
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −55.8617 −1.98371
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.2462 −0.433783 −0.216892 0.976196i \(-0.569592\pi\)
−0.216892 + 0.976196i \(0.569592\pi\)
\(798\) 0 0
\(799\) −36.4924 −1.29101
\(800\) 0 0
\(801\) −47.6155 −1.68241
\(802\) 0 0
\(803\) 11.8617 0.418592
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 65.7926 2.31601
\(808\) 0 0
\(809\) 26.0000 0.914111 0.457056 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 0 0
\(811\) 33.9309 1.19147 0.595737 0.803180i \(-0.296860\pi\)
0.595737 + 0.803180i \(0.296860\pi\)
\(812\) 0 0
\(813\) 61.4773 2.15610
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 40.9848 1.43388
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −24.7386 −0.863384 −0.431692 0.902021i \(-0.642083\pi\)
−0.431692 + 0.902021i \(0.642083\pi\)
\(822\) 0 0
\(823\) −49.4384 −1.72332 −0.861658 0.507489i \(-0.830574\pi\)
−0.861658 + 0.507489i \(0.830574\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −4.49242 −0.156217 −0.0781084 0.996945i \(-0.524888\pi\)
−0.0781084 + 0.996945i \(0.524888\pi\)
\(828\) 0 0
\(829\) −20.2462 −0.703180 −0.351590 0.936154i \(-0.614359\pi\)
−0.351590 + 0.936154i \(0.614359\pi\)
\(830\) 0 0
\(831\) 7.19224 0.249496
\(832\) 0 0
\(833\) −21.8617 −0.757464
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −9.43845 −0.326240
\(838\) 0 0
\(839\) 50.2462 1.73469 0.867346 0.497706i \(-0.165824\pi\)
0.867346 + 0.497706i \(0.165824\pi\)
\(840\) 0 0
\(841\) −28.6847 −0.989126
\(842\) 0 0
\(843\) −8.00000 −0.275535
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 13.1231 0.450384
\(850\) 0 0
\(851\) 8.24621 0.282676
\(852\) 0 0
\(853\) 34.9848 1.19786 0.598929 0.800802i \(-0.295593\pi\)
0.598929 + 0.800802i \(0.295593\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −16.5616 −0.565732 −0.282866 0.959159i \(-0.591285\pi\)
−0.282866 + 0.959159i \(0.591285\pi\)
\(858\) 0 0
\(859\) 16.9460 0.578191 0.289095 0.957300i \(-0.406646\pi\)
0.289095 + 0.957300i \(0.406646\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 8.17708 0.278351 0.139176 0.990268i \(-0.455555\pi\)
0.139176 + 0.990268i \(0.455555\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −18.5616 −0.630383
\(868\) 0 0
\(869\) −26.2462 −0.890342
\(870\) 0 0
\(871\) −23.3693 −0.791839
\(872\) 0 0
\(873\) 47.6155 1.61154
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −30.9848 −1.04628 −0.523142 0.852246i \(-0.675240\pi\)
−0.523142 + 0.852246i \(0.675240\pi\)
\(878\) 0 0
\(879\) −24.0000 −0.809500
\(880\) 0 0
\(881\) 4.87689 0.164307 0.0821534 0.996620i \(-0.473820\pi\)
0.0821534 + 0.996620i \(0.473820\pi\)
\(882\) 0 0
\(883\) −36.9848 −1.24464 −0.622320 0.782763i \(-0.713810\pi\)
−0.622320 + 0.782763i \(0.713810\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −19.6847 −0.660946 −0.330473 0.943815i \(-0.607208\pi\)
−0.330473 + 0.943815i \(0.607208\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −35.8617 −1.20141
\(892\) 0 0
\(893\) −59.8617 −2.00320
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −11.6847 −0.390139
\(898\) 0 0
\(899\) 3.68466 0.122890
\(900\) 0 0
\(901\) −6.24621 −0.208091
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −42.8769 −1.42370 −0.711852 0.702330i \(-0.752143\pi\)
−0.711852 + 0.702330i \(0.752143\pi\)
\(908\) 0 0
\(909\) −15.1231 −0.501602
\(910\) 0 0
\(911\) −37.1231 −1.22994 −0.614972 0.788549i \(-0.710833\pi\)
−0.614972 + 0.788549i \(0.710833\pi\)
\(912\) 0 0
\(913\) 11.5076 0.380845
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 37.7538 1.24538 0.622691 0.782468i \(-0.286039\pi\)
0.622691 + 0.782468i \(0.286039\pi\)
\(920\) 0 0
\(921\) 4.49242 0.148030
\(922\) 0 0
\(923\) −43.0540 −1.41714
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) 34.8078 1.14201 0.571003 0.820948i \(-0.306555\pi\)
0.571003 + 0.820948i \(0.306555\pi\)
\(930\) 0 0
\(931\) −35.8617 −1.17532
\(932\) 0 0
\(933\) 3.68466 0.120630
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −15.7538 −0.514654 −0.257327 0.966324i \(-0.582842\pi\)
−0.257327 + 0.966324i \(0.582842\pi\)
\(938\) 0 0
\(939\) −24.0000 −0.783210
\(940\) 0 0
\(941\) 39.1231 1.27538 0.637688 0.770294i \(-0.279891\pi\)
0.637688 + 0.770294i \(0.279891\pi\)
\(942\) 0 0
\(943\) 10.8078 0.351949
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.56155 0.0832393 0.0416196 0.999134i \(-0.486748\pi\)
0.0416196 + 0.999134i \(0.486748\pi\)
\(948\) 0 0
\(949\) −10.5616 −0.342843
\(950\) 0 0
\(951\) 51.8617 1.68173
\(952\) 0 0
\(953\) −44.2462 −1.43328 −0.716638 0.697446i \(-0.754320\pi\)
−0.716638 + 0.697446i \(0.754320\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −7.36932 −0.238216
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 12.0540 0.388838
\(962\) 0 0
\(963\) −10.2462 −0.330180
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −35.0540 −1.12726 −0.563630 0.826027i \(-0.690596\pi\)
−0.563630 + 0.826027i \(0.690596\pi\)
\(968\) 0 0
\(969\) 40.9848 1.31662
\(970\) 0 0
\(971\) 31.3693 1.00669 0.503345 0.864086i \(-0.332103\pi\)
0.503345 + 0.864086i \(0.332103\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 57.2311 1.83098 0.915492 0.402337i \(-0.131802\pi\)
0.915492 + 0.402337i \(0.131802\pi\)
\(978\) 0 0
\(979\) −68.4924 −2.18903
\(980\) 0 0
\(981\) 17.3693 0.554560
\(982\) 0 0
\(983\) −22.1080 −0.705134 −0.352567 0.935787i \(-0.614691\pi\)
−0.352567 + 0.935787i \(0.614691\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.00000 0.254385
\(990\) 0 0
\(991\) 8.98485 0.285413 0.142707 0.989765i \(-0.454419\pi\)
0.142707 + 0.989765i \(0.454419\pi\)
\(992\) 0 0
\(993\) −77.9309 −2.47306
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −14.0000 −0.443384 −0.221692 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 0 0
\(999\) 11.8617 0.375289
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 4600.2.a.s.1.2 2
4.3 odd 2 9200.2.a.br.1.1 2
5.2 odd 4 4600.2.e.o.4049.1 4
5.3 odd 4 4600.2.e.o.4049.4 4
5.4 even 2 184.2.a.e.1.1 2
15.14 odd 2 1656.2.a.j.1.1 2
20.19 odd 2 368.2.a.i.1.2 2
35.34 odd 2 9016.2.a.w.1.2 2
40.19 odd 2 1472.2.a.p.1.1 2
40.29 even 2 1472.2.a.u.1.2 2
60.59 even 2 3312.2.a.t.1.2 2
115.114 odd 2 4232.2.a.o.1.1 2
460.459 even 2 8464.2.a.bd.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
184.2.a.e.1.1 2 5.4 even 2
368.2.a.i.1.2 2 20.19 odd 2
1472.2.a.p.1.1 2 40.19 odd 2
1472.2.a.u.1.2 2 40.29 even 2
1656.2.a.j.1.1 2 15.14 odd 2
3312.2.a.t.1.2 2 60.59 even 2
4232.2.a.o.1.1 2 115.114 odd 2
4600.2.a.s.1.2 2 1.1 even 1 trivial
4600.2.e.o.4049.1 4 5.2 odd 4
4600.2.e.o.4049.4 4 5.3 odd 4
8464.2.a.bd.1.2 2 460.459 even 2
9016.2.a.w.1.2 2 35.34 odd 2
9200.2.a.br.1.1 2 4.3 odd 2