Properties

Label 2601.2.a.t.1.2
Level $2601$
Weight $2$
Character 2601.1
Self dual yes
Analytic conductor $20.769$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.7690895657\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 51)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 2601.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56155 q^{2} +4.56155 q^{4} +3.56155 q^{5} +6.56155 q^{8} +O(q^{10})\) \(q+2.56155 q^{2} +4.56155 q^{4} +3.56155 q^{5} +6.56155 q^{8} +9.12311 q^{10} +1.56155 q^{11} +0.438447 q^{13} +7.68466 q^{16} -4.68466 q^{19} +16.2462 q^{20} +4.00000 q^{22} -2.43845 q^{23} +7.68466 q^{25} +1.12311 q^{26} -8.24621 q^{29} -3.12311 q^{31} +6.56155 q^{32} +5.12311 q^{37} -12.0000 q^{38} +23.3693 q^{40} -3.56155 q^{41} +4.68466 q^{43} +7.12311 q^{44} -6.24621 q^{46} +11.1231 q^{47} -7.00000 q^{49} +19.6847 q^{50} +2.00000 q^{52} -12.2462 q^{53} +5.56155 q^{55} -21.1231 q^{58} -7.12311 q^{59} -9.12311 q^{61} -8.00000 q^{62} +1.43845 q^{64} +1.56155 q^{65} +4.00000 q^{67} -6.24621 q^{71} +12.2462 q^{73} +13.1231 q^{74} -21.3693 q^{76} +9.36932 q^{79} +27.3693 q^{80} -9.12311 q^{82} +0.876894 q^{83} +12.0000 q^{86} +10.2462 q^{88} +1.12311 q^{89} -11.1231 q^{92} +28.4924 q^{94} -16.6847 q^{95} +2.87689 q^{97} -17.9309 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 5q^{4} + 3q^{5} + 9q^{8} + O(q^{10}) \) \( 2q + q^{2} + 5q^{4} + 3q^{5} + 9q^{8} + 10q^{10} - q^{11} + 5q^{13} + 3q^{16} + 3q^{19} + 16q^{20} + 8q^{22} - 9q^{23} + 3q^{25} - 6q^{26} + 2q^{31} + 9q^{32} + 2q^{37} - 24q^{38} + 22q^{40} - 3q^{41} - 3q^{43} + 6q^{44} + 4q^{46} + 14q^{47} - 14q^{49} + 27q^{50} + 4q^{52} - 8q^{53} + 7q^{55} - 34q^{58} - 6q^{59} - 10q^{61} - 16q^{62} + 7q^{64} - q^{65} + 8q^{67} + 4q^{71} + 8q^{73} + 18q^{74} - 18q^{76} - 6q^{79} + 30q^{80} - 10q^{82} + 10q^{83} + 24q^{86} + 4q^{88} - 6q^{89} - 14q^{92} + 24q^{94} - 21q^{95} + 14q^{97} - 7q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56155 1.81129 0.905646 0.424035i \(-0.139387\pi\)
0.905646 + 0.424035i \(0.139387\pi\)
\(3\) 0 0
\(4\) 4.56155 2.28078
\(5\) 3.56155 1.59277 0.796387 0.604787i \(-0.206742\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 6.56155 2.31986
\(9\) 0 0
\(10\) 9.12311 2.88498
\(11\) 1.56155 0.470826 0.235413 0.971895i \(-0.424356\pi\)
0.235413 + 0.971895i \(0.424356\pi\)
\(12\) 0 0
\(13\) 0.438447 0.121603 0.0608017 0.998150i \(-0.480634\pi\)
0.0608017 + 0.998150i \(0.480634\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 7.68466 1.92116
\(17\) 0 0
\(18\) 0 0
\(19\) −4.68466 −1.07473 −0.537367 0.843348i \(-0.680581\pi\)
−0.537367 + 0.843348i \(0.680581\pi\)
\(20\) 16.2462 3.63276
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) −2.43845 −0.508451 −0.254226 0.967145i \(-0.581821\pi\)
−0.254226 + 0.967145i \(0.581821\pi\)
\(24\) 0 0
\(25\) 7.68466 1.53693
\(26\) 1.12311 0.220259
\(27\) 0 0
\(28\) 0 0
\(29\) −8.24621 −1.53128 −0.765641 0.643268i \(-0.777578\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) 0 0
\(31\) −3.12311 −0.560926 −0.280463 0.959865i \(-0.590488\pi\)
−0.280463 + 0.959865i \(0.590488\pi\)
\(32\) 6.56155 1.15993
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.12311 0.842233 0.421117 0.907006i \(-0.361638\pi\)
0.421117 + 0.907006i \(0.361638\pi\)
\(38\) −12.0000 −1.94666
\(39\) 0 0
\(40\) 23.3693 3.69501
\(41\) −3.56155 −0.556221 −0.278111 0.960549i \(-0.589708\pi\)
−0.278111 + 0.960549i \(0.589708\pi\)
\(42\) 0 0
\(43\) 4.68466 0.714404 0.357202 0.934027i \(-0.383731\pi\)
0.357202 + 0.934027i \(0.383731\pi\)
\(44\) 7.12311 1.07385
\(45\) 0 0
\(46\) −6.24621 −0.920954
\(47\) 11.1231 1.62247 0.811236 0.584719i \(-0.198795\pi\)
0.811236 + 0.584719i \(0.198795\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 19.6847 2.78383
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) −12.2462 −1.68215 −0.841073 0.540921i \(-0.818076\pi\)
−0.841073 + 0.540921i \(0.818076\pi\)
\(54\) 0 0
\(55\) 5.56155 0.749920
\(56\) 0 0
\(57\) 0 0
\(58\) −21.1231 −2.77360
\(59\) −7.12311 −0.927349 −0.463675 0.886006i \(-0.653469\pi\)
−0.463675 + 0.886006i \(0.653469\pi\)
\(60\) 0 0
\(61\) −9.12311 −1.16809 −0.584047 0.811720i \(-0.698532\pi\)
−0.584047 + 0.811720i \(0.698532\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.43845 0.179806
\(65\) 1.56155 0.193687
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −6.24621 −0.741289 −0.370644 0.928775i \(-0.620863\pi\)
−0.370644 + 0.928775i \(0.620863\pi\)
\(72\) 0 0
\(73\) 12.2462 1.43331 0.716655 0.697428i \(-0.245672\pi\)
0.716655 + 0.697428i \(0.245672\pi\)
\(74\) 13.1231 1.52553
\(75\) 0 0
\(76\) −21.3693 −2.45123
\(77\) 0 0
\(78\) 0 0
\(79\) 9.36932 1.05413 0.527065 0.849825i \(-0.323292\pi\)
0.527065 + 0.849825i \(0.323292\pi\)
\(80\) 27.3693 3.05998
\(81\) 0 0
\(82\) −9.12311 −1.00748
\(83\) 0.876894 0.0962517 0.0481258 0.998841i \(-0.484675\pi\)
0.0481258 + 0.998841i \(0.484675\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 12.0000 1.29399
\(87\) 0 0
\(88\) 10.2462 1.09225
\(89\) 1.12311 0.119049 0.0595245 0.998227i \(-0.481042\pi\)
0.0595245 + 0.998227i \(0.481042\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −11.1231 −1.15966
\(93\) 0 0
\(94\) 28.4924 2.93877
\(95\) −16.6847 −1.71181
\(96\) 0 0
\(97\) 2.87689 0.292104 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(98\) −17.9309 −1.81129
\(99\) 0 0
\(100\) 35.0540 3.50540
\(101\) −10.8769 −1.08229 −0.541146 0.840929i \(-0.682009\pi\)
−0.541146 + 0.840929i \(0.682009\pi\)
\(102\) 0 0
\(103\) 16.6847 1.64399 0.821994 0.569496i \(-0.192862\pi\)
0.821994 + 0.569496i \(0.192862\pi\)
\(104\) 2.87689 0.282103
\(105\) 0 0
\(106\) −31.3693 −3.04686
\(107\) −4.68466 −0.452883 −0.226442 0.974025i \(-0.572709\pi\)
−0.226442 + 0.974025i \(0.572709\pi\)
\(108\) 0 0
\(109\) 6.87689 0.658687 0.329344 0.944210i \(-0.393173\pi\)
0.329344 + 0.944210i \(0.393173\pi\)
\(110\) 14.2462 1.35832
\(111\) 0 0
\(112\) 0 0
\(113\) −0.438447 −0.0412456 −0.0206228 0.999787i \(-0.506565\pi\)
−0.0206228 + 0.999787i \(0.506565\pi\)
\(114\) 0 0
\(115\) −8.68466 −0.809849
\(116\) −37.6155 −3.49251
\(117\) 0 0
\(118\) −18.2462 −1.67970
\(119\) 0 0
\(120\) 0 0
\(121\) −8.56155 −0.778323
\(122\) −23.3693 −2.11576
\(123\) 0 0
\(124\) −14.2462 −1.27935
\(125\) 9.56155 0.855211
\(126\) 0 0
\(127\) 19.8078 1.75765 0.878827 0.477140i \(-0.158326\pi\)
0.878827 + 0.477140i \(0.158326\pi\)
\(128\) −9.43845 −0.834249
\(129\) 0 0
\(130\) 4.00000 0.350823
\(131\) 14.4384 1.26149 0.630746 0.775989i \(-0.282749\pi\)
0.630746 + 0.775989i \(0.282749\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.2462 0.885138
\(135\) 0 0
\(136\) 0 0
\(137\) −0.246211 −0.0210352 −0.0105176 0.999945i \(-0.503348\pi\)
−0.0105176 + 0.999945i \(0.503348\pi\)
\(138\) 0 0
\(139\) 0.876894 0.0743772 0.0371886 0.999308i \(-0.488160\pi\)
0.0371886 + 0.999308i \(0.488160\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −16.0000 −1.34269
\(143\) 0.684658 0.0572540
\(144\) 0 0
\(145\) −29.3693 −2.43899
\(146\) 31.3693 2.59614
\(147\) 0 0
\(148\) 23.3693 1.92095
\(149\) −12.2462 −1.00325 −0.501624 0.865086i \(-0.667264\pi\)
−0.501624 + 0.865086i \(0.667264\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −30.7386 −2.49323
\(153\) 0 0
\(154\) 0 0
\(155\) −11.1231 −0.893429
\(156\) 0 0
\(157\) 6.68466 0.533494 0.266747 0.963767i \(-0.414051\pi\)
0.266747 + 0.963767i \(0.414051\pi\)
\(158\) 24.0000 1.90934
\(159\) 0 0
\(160\) 23.3693 1.84751
\(161\) 0 0
\(162\) 0 0
\(163\) 15.1231 1.18453 0.592267 0.805742i \(-0.298233\pi\)
0.592267 + 0.805742i \(0.298233\pi\)
\(164\) −16.2462 −1.26862
\(165\) 0 0
\(166\) 2.24621 0.174340
\(167\) 19.8078 1.53277 0.766385 0.642381i \(-0.222053\pi\)
0.766385 + 0.642381i \(0.222053\pi\)
\(168\) 0 0
\(169\) −12.8078 −0.985213
\(170\) 0 0
\(171\) 0 0
\(172\) 21.3693 1.62940
\(173\) 1.80776 0.137442 0.0687209 0.997636i \(-0.478108\pi\)
0.0687209 + 0.997636i \(0.478108\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 12.0000 0.904534
\(177\) 0 0
\(178\) 2.87689 0.215632
\(179\) 0.876894 0.0655422 0.0327711 0.999463i \(-0.489567\pi\)
0.0327711 + 0.999463i \(0.489567\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −16.0000 −1.17954
\(185\) 18.2462 1.34149
\(186\) 0 0
\(187\) 0 0
\(188\) 50.7386 3.70050
\(189\) 0 0
\(190\) −42.7386 −3.10059
\(191\) 4.87689 0.352880 0.176440 0.984311i \(-0.443542\pi\)
0.176440 + 0.984311i \(0.443542\pi\)
\(192\) 0 0
\(193\) 7.75379 0.558130 0.279065 0.960272i \(-0.409976\pi\)
0.279065 + 0.960272i \(0.409976\pi\)
\(194\) 7.36932 0.529086
\(195\) 0 0
\(196\) −31.9309 −2.28078
\(197\) −8.93087 −0.636298 −0.318149 0.948041i \(-0.603061\pi\)
−0.318149 + 0.948041i \(0.603061\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 50.4233 3.56547
\(201\) 0 0
\(202\) −27.8617 −1.96035
\(203\) 0 0
\(204\) 0 0
\(205\) −12.6847 −0.885935
\(206\) 42.7386 2.97774
\(207\) 0 0
\(208\) 3.36932 0.233620
\(209\) −7.31534 −0.506013
\(210\) 0 0
\(211\) −13.3693 −0.920382 −0.460191 0.887820i \(-0.652219\pi\)
−0.460191 + 0.887820i \(0.652219\pi\)
\(212\) −55.8617 −3.83660
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 16.6847 1.13788
\(216\) 0 0
\(217\) 0 0
\(218\) 17.6155 1.19307
\(219\) 0 0
\(220\) 25.3693 1.71040
\(221\) 0 0
\(222\) 0 0
\(223\) −14.9309 −0.999845 −0.499922 0.866070i \(-0.666638\pi\)
−0.499922 + 0.866070i \(0.666638\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.12311 −0.0747079
\(227\) −14.0540 −0.932795 −0.466398 0.884575i \(-0.654448\pi\)
−0.466398 + 0.884575i \(0.654448\pi\)
\(228\) 0 0
\(229\) 6.00000 0.396491 0.198246 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −22.2462 −1.46687
\(231\) 0 0
\(232\) −54.1080 −3.55236
\(233\) −3.56155 −0.233325 −0.116663 0.993172i \(-0.537220\pi\)
−0.116663 + 0.993172i \(0.537220\pi\)
\(234\) 0 0
\(235\) 39.6155 2.58423
\(236\) −32.4924 −2.11508
\(237\) 0 0
\(238\) 0 0
\(239\) 6.24621 0.404034 0.202017 0.979382i \(-0.435250\pi\)
0.202017 + 0.979382i \(0.435250\pi\)
\(240\) 0 0
\(241\) −3.36932 −0.217037 −0.108518 0.994094i \(-0.534611\pi\)
−0.108518 + 0.994094i \(0.534611\pi\)
\(242\) −21.9309 −1.40977
\(243\) 0 0
\(244\) −41.6155 −2.66416
\(245\) −24.9309 −1.59277
\(246\) 0 0
\(247\) −2.05398 −0.130691
\(248\) −20.4924 −1.30127
\(249\) 0 0
\(250\) 24.4924 1.54904
\(251\) −8.49242 −0.536037 −0.268018 0.963414i \(-0.586369\pi\)
−0.268018 + 0.963414i \(0.586369\pi\)
\(252\) 0 0
\(253\) −3.80776 −0.239392
\(254\) 50.7386 3.18363
\(255\) 0 0
\(256\) −27.0540 −1.69087
\(257\) 15.3693 0.958712 0.479356 0.877621i \(-0.340870\pi\)
0.479356 + 0.877621i \(0.340870\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.12311 0.441756
\(261\) 0 0
\(262\) 36.9848 2.28493
\(263\) 20.4924 1.26362 0.631808 0.775125i \(-0.282313\pi\)
0.631808 + 0.775125i \(0.282313\pi\)
\(264\) 0 0
\(265\) −43.6155 −2.67928
\(266\) 0 0
\(267\) 0 0
\(268\) 18.2462 1.11456
\(269\) 16.4384 1.00227 0.501135 0.865369i \(-0.332916\pi\)
0.501135 + 0.865369i \(0.332916\pi\)
\(270\) 0 0
\(271\) 19.8078 1.20324 0.601618 0.798784i \(-0.294523\pi\)
0.601618 + 0.798784i \(0.294523\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.630683 −0.0381010
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) −6.00000 −0.360505 −0.180253 0.983620i \(-0.557691\pi\)
−0.180253 + 0.983620i \(0.557691\pi\)
\(278\) 2.24621 0.134719
\(279\) 0 0
\(280\) 0 0
\(281\) 10.8769 0.648861 0.324431 0.945910i \(-0.394827\pi\)
0.324431 + 0.945910i \(0.394827\pi\)
\(282\) 0 0
\(283\) −21.3693 −1.27027 −0.635137 0.772399i \(-0.719056\pi\)
−0.635137 + 0.772399i \(0.719056\pi\)
\(284\) −28.4924 −1.69071
\(285\) 0 0
\(286\) 1.75379 0.103704
\(287\) 0 0
\(288\) 0 0
\(289\) 0 0
\(290\) −75.2311 −4.41772
\(291\) 0 0
\(292\) 55.8617 3.26906
\(293\) −1.12311 −0.0656125 −0.0328063 0.999462i \(-0.510444\pi\)
−0.0328063 + 0.999462i \(0.510444\pi\)
\(294\) 0 0
\(295\) −25.3693 −1.47706
\(296\) 33.6155 1.95386
\(297\) 0 0
\(298\) −31.3693 −1.81718
\(299\) −1.06913 −0.0618294
\(300\) 0 0
\(301\) 0 0
\(302\) 20.4924 1.17921
\(303\) 0 0
\(304\) −36.0000 −2.06474
\(305\) −32.4924 −1.86051
\(306\) 0 0
\(307\) 32.4924 1.85444 0.927220 0.374516i \(-0.122191\pi\)
0.927220 + 0.374516i \(0.122191\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −28.4924 −1.61826
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −33.6155 −1.90006 −0.950031 0.312156i \(-0.898949\pi\)
−0.950031 + 0.312156i \(0.898949\pi\)
\(314\) 17.1231 0.966313
\(315\) 0 0
\(316\) 42.7386 2.40424
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) 0 0
\(319\) −12.8769 −0.720968
\(320\) 5.12311 0.286390
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 3.36932 0.186896
\(326\) 38.7386 2.14553
\(327\) 0 0
\(328\) −23.3693 −1.29035
\(329\) 0 0
\(330\) 0 0
\(331\) −34.9309 −1.91997 −0.959987 0.280044i \(-0.909651\pi\)
−0.959987 + 0.280044i \(0.909651\pi\)
\(332\) 4.00000 0.219529
\(333\) 0 0
\(334\) 50.7386 2.77629
\(335\) 14.2462 0.778354
\(336\) 0 0
\(337\) 16.7386 0.911811 0.455906 0.890028i \(-0.349315\pi\)
0.455906 + 0.890028i \(0.349315\pi\)
\(338\) −32.8078 −1.78451
\(339\) 0 0
\(340\) 0 0
\(341\) −4.87689 −0.264099
\(342\) 0 0
\(343\) 0 0
\(344\) 30.7386 1.65732
\(345\) 0 0
\(346\) 4.63068 0.248947
\(347\) −8.49242 −0.455897 −0.227949 0.973673i \(-0.573202\pi\)
−0.227949 + 0.973673i \(0.573202\pi\)
\(348\) 0 0
\(349\) 11.5616 0.618876 0.309438 0.950920i \(-0.399859\pi\)
0.309438 + 0.950920i \(0.399859\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.2462 0.546125
\(353\) 10.4924 0.558455 0.279228 0.960225i \(-0.409922\pi\)
0.279228 + 0.960225i \(0.409922\pi\)
\(354\) 0 0
\(355\) −22.2462 −1.18071
\(356\) 5.12311 0.271524
\(357\) 0 0
\(358\) 2.24621 0.118716
\(359\) −14.2462 −0.751886 −0.375943 0.926643i \(-0.622681\pi\)
−0.375943 + 0.926643i \(0.622681\pi\)
\(360\) 0 0
\(361\) 2.94602 0.155054
\(362\) −15.3693 −0.807793
\(363\) 0 0
\(364\) 0 0
\(365\) 43.6155 2.28294
\(366\) 0 0
\(367\) 1.75379 0.0915470 0.0457735 0.998952i \(-0.485425\pi\)
0.0457735 + 0.998952i \(0.485425\pi\)
\(368\) −18.7386 −0.976819
\(369\) 0 0
\(370\) 46.7386 2.42983
\(371\) 0 0
\(372\) 0 0
\(373\) −0.246211 −0.0127483 −0.00637417 0.999980i \(-0.502029\pi\)
−0.00637417 + 0.999980i \(0.502029\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 72.9848 3.76391
\(377\) −3.61553 −0.186209
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) −76.1080 −3.90426
\(381\) 0 0
\(382\) 12.4924 0.639168
\(383\) −6.24621 −0.319166 −0.159583 0.987184i \(-0.551015\pi\)
−0.159583 + 0.987184i \(0.551015\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.8617 1.01094
\(387\) 0 0
\(388\) 13.1231 0.666225
\(389\) −35.8617 −1.81826 −0.909131 0.416510i \(-0.863253\pi\)
−0.909131 + 0.416510i \(0.863253\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −45.9309 −2.31986
\(393\) 0 0
\(394\) −22.8769 −1.15252
\(395\) 33.3693 1.67899
\(396\) 0 0
\(397\) 19.3693 0.972118 0.486059 0.873926i \(-0.338434\pi\)
0.486059 + 0.873926i \(0.338434\pi\)
\(398\) −40.9848 −2.05438
\(399\) 0 0
\(400\) 59.0540 2.95270
\(401\) 39.1771 1.95641 0.978205 0.207641i \(-0.0665787\pi\)
0.978205 + 0.207641i \(0.0665787\pi\)
\(402\) 0 0
\(403\) −1.36932 −0.0682105
\(404\) −49.6155 −2.46846
\(405\) 0 0
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −14.6847 −0.726110 −0.363055 0.931768i \(-0.618266\pi\)
−0.363055 + 0.931768i \(0.618266\pi\)
\(410\) −32.4924 −1.60469
\(411\) 0 0
\(412\) 76.1080 3.74957
\(413\) 0 0
\(414\) 0 0
\(415\) 3.12311 0.153307
\(416\) 2.87689 0.141051
\(417\) 0 0
\(418\) −18.7386 −0.916537
\(419\) −0.492423 −0.0240564 −0.0120282 0.999928i \(-0.503829\pi\)
−0.0120282 + 0.999928i \(0.503829\pi\)
\(420\) 0 0
\(421\) 24.4384 1.19106 0.595529 0.803334i \(-0.296943\pi\)
0.595529 + 0.803334i \(0.296943\pi\)
\(422\) −34.2462 −1.66708
\(423\) 0 0
\(424\) −80.3542 −3.90234
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −21.3693 −1.03292
\(429\) 0 0
\(430\) 42.7386 2.06104
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 26.6847 1.28238 0.641191 0.767381i \(-0.278440\pi\)
0.641191 + 0.767381i \(0.278440\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 31.3693 1.50232
\(437\) 11.4233 0.546450
\(438\) 0 0
\(439\) 22.2462 1.06175 0.530877 0.847449i \(-0.321863\pi\)
0.530877 + 0.847449i \(0.321863\pi\)
\(440\) 36.4924 1.73971
\(441\) 0 0
\(442\) 0 0
\(443\) 31.1231 1.47870 0.739352 0.673319i \(-0.235132\pi\)
0.739352 + 0.673319i \(0.235132\pi\)
\(444\) 0 0
\(445\) 4.00000 0.189618
\(446\) −38.2462 −1.81101
\(447\) 0 0
\(448\) 0 0
\(449\) 36.7386 1.73380 0.866902 0.498479i \(-0.166108\pi\)
0.866902 + 0.498479i \(0.166108\pi\)
\(450\) 0 0
\(451\) −5.56155 −0.261883
\(452\) −2.00000 −0.0940721
\(453\) 0 0
\(454\) −36.0000 −1.68956
\(455\) 0 0
\(456\) 0 0
\(457\) 13.8078 0.645900 0.322950 0.946416i \(-0.395325\pi\)
0.322950 + 0.946416i \(0.395325\pi\)
\(458\) 15.3693 0.718161
\(459\) 0 0
\(460\) −39.6155 −1.84708
\(461\) 8.24621 0.384064 0.192032 0.981389i \(-0.438492\pi\)
0.192032 + 0.981389i \(0.438492\pi\)
\(462\) 0 0
\(463\) −40.9848 −1.90473 −0.952364 0.304965i \(-0.901355\pi\)
−0.952364 + 0.304965i \(0.901355\pi\)
\(464\) −63.3693 −2.94185
\(465\) 0 0
\(466\) −9.12311 −0.422620
\(467\) −21.3693 −0.988854 −0.494427 0.869219i \(-0.664622\pi\)
−0.494427 + 0.869219i \(0.664622\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 101.477 4.68080
\(471\) 0 0
\(472\) −46.7386 −2.15132
\(473\) 7.31534 0.336360
\(474\) 0 0
\(475\) −36.0000 −1.65179
\(476\) 0 0
\(477\) 0 0
\(478\) 16.0000 0.731823
\(479\) 24.3002 1.11030 0.555152 0.831749i \(-0.312660\pi\)
0.555152 + 0.831749i \(0.312660\pi\)
\(480\) 0 0
\(481\) 2.24621 0.102418
\(482\) −8.63068 −0.393117
\(483\) 0 0
\(484\) −39.0540 −1.77518
\(485\) 10.2462 0.465256
\(486\) 0 0
\(487\) −17.3693 −0.787079 −0.393539 0.919308i \(-0.628750\pi\)
−0.393539 + 0.919308i \(0.628750\pi\)
\(488\) −59.8617 −2.70981
\(489\) 0 0
\(490\) −63.8617 −2.88498
\(491\) 21.3693 0.964384 0.482192 0.876066i \(-0.339841\pi\)
0.482192 + 0.876066i \(0.339841\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −5.26137 −0.236720
\(495\) 0 0
\(496\) −24.0000 −1.07763
\(497\) 0 0
\(498\) 0 0
\(499\) −13.3693 −0.598493 −0.299246 0.954176i \(-0.596735\pi\)
−0.299246 + 0.954176i \(0.596735\pi\)
\(500\) 43.6155 1.95055
\(501\) 0 0
\(502\) −21.7538 −0.970919
\(503\) −29.5616 −1.31808 −0.659042 0.752106i \(-0.729038\pi\)
−0.659042 + 0.752106i \(0.729038\pi\)
\(504\) 0 0
\(505\) −38.7386 −1.72385
\(506\) −9.75379 −0.433609
\(507\) 0 0
\(508\) 90.3542 4.00882
\(509\) −25.1231 −1.11356 −0.556781 0.830659i \(-0.687964\pi\)
−0.556781 + 0.830659i \(0.687964\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −50.4233 −2.22842
\(513\) 0 0
\(514\) 39.3693 1.73651
\(515\) 59.4233 2.61850
\(516\) 0 0
\(517\) 17.3693 0.763902
\(518\) 0 0
\(519\) 0 0
\(520\) 10.2462 0.449326
\(521\) −35.5616 −1.55798 −0.778990 0.627036i \(-0.784268\pi\)
−0.778990 + 0.627036i \(0.784268\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 65.8617 2.87718
\(525\) 0 0
\(526\) 52.4924 2.28878
\(527\) 0 0
\(528\) 0 0
\(529\) −17.0540 −0.741477
\(530\) −111.723 −4.85296
\(531\) 0 0
\(532\) 0 0
\(533\) −1.56155 −0.0676384
\(534\) 0 0
\(535\) −16.6847 −0.721341
\(536\) 26.2462 1.13366
\(537\) 0 0
\(538\) 42.1080 1.81540
\(539\) −10.9309 −0.470826
\(540\) 0 0
\(541\) −34.1080 −1.46642 −0.733208 0.680005i \(-0.761978\pi\)
−0.733208 + 0.680005i \(0.761978\pi\)
\(542\) 50.7386 2.17941
\(543\) 0 0
\(544\) 0 0
\(545\) 24.4924 1.04914
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −1.12311 −0.0479767
\(549\) 0 0
\(550\) 30.7386 1.31070
\(551\) 38.6307 1.64572
\(552\) 0 0
\(553\) 0 0
\(554\) −15.3693 −0.652980
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) −26.4924 −1.12252 −0.561260 0.827640i \(-0.689683\pi\)
−0.561260 + 0.827640i \(0.689683\pi\)
\(558\) 0 0
\(559\) 2.05398 0.0868739
\(560\) 0 0
\(561\) 0 0
\(562\) 27.8617 1.17528
\(563\) −31.1231 −1.31168 −0.655841 0.754899i \(-0.727686\pi\)
−0.655841 + 0.754899i \(0.727686\pi\)
\(564\) 0 0
\(565\) −1.56155 −0.0656950
\(566\) −54.7386 −2.30084
\(567\) 0 0
\(568\) −40.9848 −1.71969
\(569\) −21.1231 −0.885527 −0.442763 0.896639i \(-0.646002\pi\)
−0.442763 + 0.896639i \(0.646002\pi\)
\(570\) 0 0
\(571\) 30.7386 1.28637 0.643186 0.765710i \(-0.277612\pi\)
0.643186 + 0.765710i \(0.277612\pi\)
\(572\) 3.12311 0.130584
\(573\) 0 0
\(574\) 0 0
\(575\) −18.7386 −0.781455
\(576\) 0 0
\(577\) −3.94602 −0.164275 −0.0821376 0.996621i \(-0.526175\pi\)
−0.0821376 + 0.996621i \(0.526175\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) −133.970 −5.56279
\(581\) 0 0
\(582\) 0 0
\(583\) −19.1231 −0.791998
\(584\) 80.3542 3.32508
\(585\) 0 0
\(586\) −2.87689 −0.118843
\(587\) 28.9848 1.19633 0.598166 0.801372i \(-0.295896\pi\)
0.598166 + 0.801372i \(0.295896\pi\)
\(588\) 0 0
\(589\) 14.6307 0.602847
\(590\) −64.9848 −2.67538
\(591\) 0 0
\(592\) 39.3693 1.61807
\(593\) −27.7538 −1.13971 −0.569856 0.821745i \(-0.693001\pi\)
−0.569856 + 0.821745i \(0.693001\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −55.8617 −2.28819
\(597\) 0 0
\(598\) −2.73863 −0.111991
\(599\) 0.384472 0.0157091 0.00785455 0.999969i \(-0.497500\pi\)
0.00785455 + 0.999969i \(0.497500\pi\)
\(600\) 0 0
\(601\) 30.9848 1.26390 0.631949 0.775010i \(-0.282255\pi\)
0.631949 + 0.775010i \(0.282255\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 36.4924 1.48486
\(605\) −30.4924 −1.23969
\(606\) 0 0
\(607\) 9.36932 0.380289 0.190144 0.981756i \(-0.439104\pi\)
0.190144 + 0.981756i \(0.439104\pi\)
\(608\) −30.7386 −1.24662
\(609\) 0 0
\(610\) −83.2311 −3.36993
\(611\) 4.87689 0.197298
\(612\) 0 0
\(613\) 14.6847 0.593108 0.296554 0.955016i \(-0.404163\pi\)
0.296554 + 0.955016i \(0.404163\pi\)
\(614\) 83.2311 3.35893
\(615\) 0 0
\(616\) 0 0
\(617\) −44.2462 −1.78129 −0.890643 0.454704i \(-0.849745\pi\)
−0.890643 + 0.454704i \(0.849745\pi\)
\(618\) 0 0
\(619\) −5.36932 −0.215811 −0.107906 0.994161i \(-0.534414\pi\)
−0.107906 + 0.994161i \(0.534414\pi\)
\(620\) −50.7386 −2.03771
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −4.36932 −0.174773
\(626\) −86.1080 −3.44157
\(627\) 0 0
\(628\) 30.4924 1.21678
\(629\) 0 0
\(630\) 0 0
\(631\) −0.684658 −0.0272558 −0.0136279 0.999907i \(-0.504338\pi\)
−0.0136279 + 0.999907i \(0.504338\pi\)
\(632\) 61.4773 2.44543
\(633\) 0 0
\(634\) −46.1080 −1.83118
\(635\) 70.5464 2.79955
\(636\) 0 0
\(637\) −3.06913 −0.121603
\(638\) −32.9848 −1.30588
\(639\) 0 0
\(640\) −33.6155 −1.32877
\(641\) −28.9309 −1.14270 −0.571350 0.820706i \(-0.693580\pi\)
−0.571350 + 0.820706i \(0.693580\pi\)
\(642\) 0 0
\(643\) 13.7538 0.542396 0.271198 0.962524i \(-0.412580\pi\)
0.271198 + 0.962524i \(0.412580\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 9.36932 0.368346 0.184173 0.982894i \(-0.441039\pi\)
0.184173 + 0.982894i \(0.441039\pi\)
\(648\) 0 0
\(649\) −11.1231 −0.436620
\(650\) 8.63068 0.338523
\(651\) 0 0
\(652\) 68.9848 2.70166
\(653\) −32.9309 −1.28868 −0.644342 0.764737i \(-0.722869\pi\)
−0.644342 + 0.764737i \(0.722869\pi\)
\(654\) 0 0
\(655\) 51.4233 2.00927
\(656\) −27.3693 −1.06859
\(657\) 0 0
\(658\) 0 0
\(659\) 9.86174 0.384159 0.192079 0.981379i \(-0.438477\pi\)
0.192079 + 0.981379i \(0.438477\pi\)
\(660\) 0 0
\(661\) 13.3153 0.517907 0.258953 0.965890i \(-0.416622\pi\)
0.258953 + 0.965890i \(0.416622\pi\)
\(662\) −89.4773 −3.47763
\(663\) 0 0
\(664\) 5.75379 0.223290
\(665\) 0 0
\(666\) 0 0
\(667\) 20.1080 0.778583
\(668\) 90.3542 3.49591
\(669\) 0 0
\(670\) 36.4924 1.40983
\(671\) −14.2462 −0.549969
\(672\) 0 0
\(673\) 0.738634 0.0284722 0.0142361 0.999899i \(-0.495468\pi\)
0.0142361 + 0.999899i \(0.495468\pi\)
\(674\) 42.8769 1.65156
\(675\) 0 0
\(676\) −58.4233 −2.24705
\(677\) −1.31534 −0.0505527 −0.0252763 0.999681i \(-0.508047\pi\)
−0.0252763 + 0.999681i \(0.508047\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −12.4924 −0.478360
\(683\) −9.56155 −0.365863 −0.182931 0.983126i \(-0.558559\pi\)
−0.182931 + 0.983126i \(0.558559\pi\)
\(684\) 0 0
\(685\) −0.876894 −0.0335044
\(686\) 0 0
\(687\) 0 0
\(688\) 36.0000 1.37249
\(689\) −5.36932 −0.204555
\(690\) 0 0
\(691\) 28.9848 1.10264 0.551318 0.834295i \(-0.314125\pi\)
0.551318 + 0.834295i \(0.314125\pi\)
\(692\) 8.24621 0.313474
\(693\) 0 0
\(694\) −21.7538 −0.825763
\(695\) 3.12311 0.118466
\(696\) 0 0
\(697\) 0 0
\(698\) 29.6155 1.12096
\(699\) 0 0
\(700\) 0 0
\(701\) −15.3693 −0.580491 −0.290246 0.956952i \(-0.593737\pi\)
−0.290246 + 0.956952i \(0.593737\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) 2.24621 0.0846573
\(705\) 0 0
\(706\) 26.8769 1.01153
\(707\) 0 0
\(708\) 0 0
\(709\) 44.7386 1.68019 0.840097 0.542436i \(-0.182498\pi\)
0.840097 + 0.542436i \(0.182498\pi\)
\(710\) −56.9848 −2.13860
\(711\) 0 0
\(712\) 7.36932 0.276177
\(713\) 7.61553 0.285204
\(714\) 0 0
\(715\) 2.43845 0.0911928
\(716\) 4.00000 0.149487
\(717\) 0 0
\(718\) −36.4924 −1.36189
\(719\) −11.8078 −0.440355 −0.220178 0.975460i \(-0.570664\pi\)
−0.220178 + 0.975460i \(0.570664\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7.54640 0.280848
\(723\) 0 0
\(724\) −27.3693 −1.01717
\(725\) −63.3693 −2.35348
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 111.723 4.13507
\(731\) 0 0
\(732\) 0 0
\(733\) −11.7538 −0.434136 −0.217068 0.976156i \(-0.569649\pi\)
−0.217068 + 0.976156i \(0.569649\pi\)
\(734\) 4.49242 0.165818
\(735\) 0 0
\(736\) −16.0000 −0.589768
\(737\) 6.24621 0.230082
\(738\) 0 0
\(739\) −20.6847 −0.760897 −0.380449 0.924802i \(-0.624230\pi\)
−0.380449 + 0.924802i \(0.624230\pi\)
\(740\) 83.2311 3.05963
\(741\) 0 0
\(742\) 0 0
\(743\) 28.4924 1.04529 0.522643 0.852552i \(-0.324946\pi\)
0.522643 + 0.852552i \(0.324946\pi\)
\(744\) 0 0
\(745\) −43.6155 −1.59795
\(746\) −0.630683 −0.0230909
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 25.3693 0.925740 0.462870 0.886426i \(-0.346820\pi\)
0.462870 + 0.886426i \(0.346820\pi\)
\(752\) 85.4773 3.11704
\(753\) 0 0
\(754\) −9.26137 −0.337279
\(755\) 28.4924 1.03695
\(756\) 0 0
\(757\) 16.0540 0.583492 0.291746 0.956496i \(-0.405764\pi\)
0.291746 + 0.956496i \(0.405764\pi\)
\(758\) 30.7386 1.11648
\(759\) 0 0
\(760\) −109.477 −3.97116
\(761\) 15.7538 0.571074 0.285537 0.958368i \(-0.407828\pi\)
0.285537 + 0.958368i \(0.407828\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 22.2462 0.804840
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −3.12311 −0.112769
\(768\) 0 0
\(769\) 40.5464 1.46214 0.731070 0.682302i \(-0.239021\pi\)
0.731070 + 0.682302i \(0.239021\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 35.3693 1.27297
\(773\) 8.63068 0.310424 0.155212 0.987881i \(-0.450394\pi\)
0.155212 + 0.987881i \(0.450394\pi\)
\(774\) 0 0
\(775\) −24.0000 −0.862105
\(776\) 18.8769 0.677641
\(777\) 0 0
\(778\) −91.8617 −3.29340
\(779\) 16.6847 0.597790
\(780\) 0 0
\(781\) −9.75379 −0.349018
\(782\) 0 0
\(783\) 0 0
\(784\) −53.7926 −1.92116
\(785\) 23.8078 0.849736
\(786\) 0 0
\(787\) 10.2462 0.365238 0.182619 0.983184i \(-0.441543\pi\)
0.182619 + 0.983184i \(0.441543\pi\)
\(788\) −40.7386 −1.45125
\(789\) 0 0
\(790\) 85.4773 3.04114
\(791\) 0 0
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) 49.6155 1.76079
\(795\) 0 0
\(796\) −72.9848 −2.58688
\(797\) 9.61553 0.340599 0.170300 0.985392i \(-0.445526\pi\)
0.170300 + 0.985392i \(0.445526\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 50.4233 1.78273
\(801\) 0 0
\(802\) 100.354 3.54363
\(803\) 19.1231 0.674840
\(804\) 0 0
\(805\) 0 0
\(806\) −3.50758 −0.123549
\(807\) 0 0
\(808\) −71.3693 −2.51076
\(809\) 15.9460 0.560632 0.280316 0.959908i \(-0.409561\pi\)
0.280316 + 0.959908i \(0.409561\pi\)
\(810\) 0 0
\(811\) 45.3693 1.59313 0.796566 0.604551i \(-0.206648\pi\)
0.796566 + 0.604551i \(0.206648\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 20.4924 0.718259
\(815\) 53.8617 1.88669
\(816\) 0 0
\(817\) −21.9460 −0.767794
\(818\) −37.6155 −1.31520
\(819\) 0 0
\(820\) −57.8617 −2.02062
\(821\) −12.4384 −0.434105 −0.217052 0.976160i \(-0.569644\pi\)
−0.217052 + 0.976160i \(0.569644\pi\)
\(822\) 0 0
\(823\) −3.50758 −0.122266 −0.0611332 0.998130i \(-0.519471\pi\)
−0.0611332 + 0.998130i \(0.519471\pi\)
\(824\) 109.477 3.81382
\(825\) 0 0
\(826\) 0 0
\(827\) 47.4233 1.64907 0.824535 0.565811i \(-0.191437\pi\)
0.824535 + 0.565811i \(0.191437\pi\)
\(828\) 0 0
\(829\) 17.5076 0.608063 0.304032 0.952662i \(-0.401667\pi\)
0.304032 + 0.952662i \(0.401667\pi\)
\(830\) 8.00000 0.277684
\(831\) 0 0
\(832\) 0.630683 0.0218650
\(833\) 0 0
\(834\) 0 0
\(835\) 70.5464 2.44136
\(836\) −33.3693 −1.15410
\(837\) 0 0
\(838\) −1.26137 −0.0435732
\(839\) −26.0540 −0.899483 −0.449742 0.893159i \(-0.648484\pi\)
−0.449742 + 0.893159i \(0.648484\pi\)
\(840\) 0 0
\(841\) 39.0000 1.34483
\(842\) 62.6004 2.15735
\(843\) 0 0
\(844\) −60.9848 −2.09918
\(845\) −45.6155 −1.56922
\(846\) 0 0
\(847\) 0 0
\(848\) −94.1080 −3.23168
\(849\) 0 0
\(850\) 0 0
\(851\) −12.4924 −0.428235
\(852\) 0 0
\(853\) 28.7386 0.983992 0.491996 0.870597i \(-0.336267\pi\)
0.491996 + 0.870597i \(0.336267\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −30.7386 −1.05062
\(857\) −6.00000 −0.204956 −0.102478 0.994735i \(-0.532677\pi\)
−0.102478 + 0.994735i \(0.532677\pi\)
\(858\) 0 0
\(859\) 12.0000 0.409435 0.204717 0.978821i \(-0.434372\pi\)
0.204717 + 0.978821i \(0.434372\pi\)
\(860\) 76.1080 2.59526
\(861\) 0 0
\(862\) −61.4773 −2.09392
\(863\) 9.75379 0.332023 0.166011 0.986124i \(-0.446911\pi\)
0.166011 + 0.986124i \(0.446911\pi\)
\(864\) 0 0
\(865\) 6.43845 0.218914
\(866\) 68.3542 2.32277
\(867\) 0 0
\(868\) 0 0
\(869\) 14.6307 0.496312
\(870\) 0 0
\(871\) 1.75379 0.0594249
\(872\) 45.1231 1.52806
\(873\) 0 0
\(874\) 29.2614 0.989780
\(875\) 0 0
\(876\) 0 0
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 56.9848 1.92315
\(879\) 0 0
\(880\) 42.7386 1.44072
\(881\) 40.2462 1.35593 0.677965 0.735095i \(-0.262862\pi\)
0.677965 + 0.735095i \(0.262862\pi\)
\(882\) 0 0
\(883\) −23.4233 −0.788257 −0.394128 0.919055i \(-0.628953\pi\)
−0.394128 + 0.919055i \(0.628953\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 79.7235 2.67836
\(887\) 18.4384 0.619102 0.309551 0.950883i \(-0.399821\pi\)
0.309551 + 0.950883i \(0.399821\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 10.2462 0.343454
\(891\) 0 0
\(892\) −68.1080 −2.28042
\(893\) −52.1080 −1.74373
\(894\) 0 0
\(895\) 3.12311 0.104394
\(896\) 0 0
\(897\) 0 0
\(898\) 94.1080 3.14042
\(899\) 25.7538 0.858937
\(900\) 0 0
\(901\) 0 0
\(902\) −14.2462 −0.474347
\(903\) 0 0
\(904\) −2.87689 −0.0956841
\(905\) −21.3693 −0.710340
\(906\) 0 0
\(907\) 9.86174 0.327454 0.163727 0.986506i \(-0.447648\pi\)
0.163727 + 0.986506i \(0.447648\pi\)
\(908\) −64.1080 −2.12750
\(909\) 0 0
\(910\) 0 0
\(911\) 24.3002 0.805101 0.402551 0.915398i \(-0.368124\pi\)
0.402551 + 0.915398i \(0.368124\pi\)
\(912\) 0 0
\(913\) 1.36932 0.0453178
\(914\) 35.3693 1.16991
\(915\) 0 0
\(916\) 27.3693 0.904308
\(917\) 0 0
\(918\) 0 0
\(919\) −16.6847 −0.550376 −0.275188 0.961390i \(-0.588740\pi\)
−0.275188 + 0.961390i \(0.588740\pi\)
\(920\) −56.9848 −1.87873
\(921\) 0 0
\(922\) 21.1231 0.695652
\(923\) −2.73863 −0.0901432
\(924\) 0 0
\(925\) 39.3693 1.29446
\(926\) −104.985 −3.45002
\(927\) 0 0
\(928\) −54.1080 −1.77618
\(929\) 3.06913 0.100695 0.0503474 0.998732i \(-0.483967\pi\)
0.0503474 + 0.998732i \(0.483967\pi\)
\(930\) 0 0
\(931\) 32.7926 1.07473
\(932\) −16.2462 −0.532162
\(933\) 0 0
\(934\) −54.7386 −1.79110
\(935\) 0 0
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 180.708 5.89406
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) 0 0
\(943\) 8.68466 0.282811
\(944\) −54.7386 −1.78159
\(945\) 0 0
\(946\) 18.7386 0.609246
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 5.36932 0.174295
\(950\) −92.2159 −2.99188
\(951\) 0 0
\(952\) 0 0
\(953\) −36.3542 −1.17763 −0.588813 0.808269i \(-0.700405\pi\)
−0.588813 + 0.808269i \(0.700405\pi\)
\(954\) 0 0
\(955\) 17.3693 0.562058
\(956\) 28.4924 0.921511
\(957\) 0 0
\(958\) 62.2462 2.01108
\(959\) 0 0
\(960\) 0 0
\(961\) −21.2462 −0.685362
\(962\) 5.75379 0.185510
\(963\) 0 0
\(964\) −15.3693 −0.495012
\(965\) 27.6155 0.888975
\(966\) 0 0
\(967\) 42.4384 1.36473 0.682364 0.731012i \(-0.260952\pi\)
0.682364 + 0.731012i \(0.260952\pi\)
\(968\) −56.1771 −1.80560
\(969\) 0 0
\(970\) 26.2462 0.842715
\(971\) 43.6155 1.39969 0.699844 0.714295i \(-0.253253\pi\)
0.699844 + 0.714295i \(0.253253\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −44.4924 −1.42563
\(975\) 0 0
\(976\) −70.1080 −2.24410
\(977\) −8.24621 −0.263820 −0.131910 0.991262i \(-0.542111\pi\)
−0.131910 + 0.991262i \(0.542111\pi\)
\(978\) 0 0
\(979\) 1.75379 0.0560513
\(980\) −113.723 −3.63276
\(981\) 0 0
\(982\) 54.7386 1.74678
\(983\) 30.9309 0.986542 0.493271 0.869876i \(-0.335801\pi\)
0.493271 + 0.869876i \(0.335801\pi\)
\(984\) 0 0
\(985\) −31.8078 −1.01348
\(986\) 0 0
\(987\) 0 0
\(988\) −9.36932 −0.298078
\(989\) −11.4233 −0.363240
\(990\) 0 0
\(991\) −42.7386 −1.35764 −0.678819 0.734306i \(-0.737508\pi\)
−0.678819 + 0.734306i \(0.737508\pi\)
\(992\) −20.4924 −0.650635
\(993\) 0 0
\(994\) 0 0
\(995\) −56.9848 −1.80654
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) −34.2462 −1.08404
\(999\) 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 2601.2.a.t.1.2 2
3.2 odd 2 867.2.a.f.1.1 2
17.16 even 2 153.2.a.e.1.2 2
51.2 odd 8 867.2.e.f.616.2 8
51.5 even 16 867.2.h.j.688.3 16
51.8 odd 8 867.2.e.f.829.3 8
51.11 even 16 867.2.h.j.733.1 16
51.14 even 16 867.2.h.j.757.1 16
51.20 even 16 867.2.h.j.757.2 16
51.23 even 16 867.2.h.j.733.2 16
51.26 odd 8 867.2.e.f.829.4 8
51.29 even 16 867.2.h.j.688.4 16
51.32 odd 8 867.2.e.f.616.1 8
51.38 odd 4 867.2.d.c.577.3 4
51.41 even 16 867.2.h.j.712.3 16
51.44 even 16 867.2.h.j.712.4 16
51.47 odd 4 867.2.d.c.577.4 4
51.50 odd 2 51.2.a.b.1.1 2
68.67 odd 2 2448.2.a.v.1.1 2
85.84 even 2 3825.2.a.s.1.1 2
119.118 odd 2 7497.2.a.v.1.2 2
136.67 odd 2 9792.2.a.cz.1.2 2
136.101 even 2 9792.2.a.cy.1.2 2
204.203 even 2 816.2.a.m.1.2 2
255.152 even 4 1275.2.b.d.1174.1 4
255.203 even 4 1275.2.b.d.1174.4 4
255.254 odd 2 1275.2.a.n.1.2 2
357.356 even 2 2499.2.a.o.1.1 2
408.101 odd 2 3264.2.a.bl.1.1 2
408.203 even 2 3264.2.a.bg.1.1 2
561.560 even 2 6171.2.a.p.1.2 2
663.662 odd 2 8619.2.a.q.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.2.a.b.1.1 2 51.50 odd 2
153.2.a.e.1.2 2 17.16 even 2
816.2.a.m.1.2 2 204.203 even 2
867.2.a.f.1.1 2 3.2 odd 2
867.2.d.c.577.3 4 51.38 odd 4
867.2.d.c.577.4 4 51.47 odd 4
867.2.e.f.616.1 8 51.32 odd 8
867.2.e.f.616.2 8 51.2 odd 8
867.2.e.f.829.3 8 51.8 odd 8
867.2.e.f.829.4 8 51.26 odd 8
867.2.h.j.688.3 16 51.5 even 16
867.2.h.j.688.4 16 51.29 even 16
867.2.h.j.712.3 16 51.41 even 16
867.2.h.j.712.4 16 51.44 even 16
867.2.h.j.733.1 16 51.11 even 16
867.2.h.j.733.2 16 51.23 even 16
867.2.h.j.757.1 16 51.14 even 16
867.2.h.j.757.2 16 51.20 even 16
1275.2.a.n.1.2 2 255.254 odd 2
1275.2.b.d.1174.1 4 255.152 even 4
1275.2.b.d.1174.4 4 255.203 even 4
2448.2.a.v.1.1 2 68.67 odd 2
2499.2.a.o.1.1 2 357.356 even 2
2601.2.a.t.1.2 2 1.1 even 1 trivial
3264.2.a.bg.1.1 2 408.203 even 2
3264.2.a.bl.1.1 2 408.101 odd 2
3825.2.a.s.1.1 2 85.84 even 2
6171.2.a.p.1.2 2 561.560 even 2
7497.2.a.v.1.2 2 119.118 odd 2
8619.2.a.q.1.2 2 663.662 odd 2
9792.2.a.cy.1.2 2 136.101 even 2
9792.2.a.cz.1.2 2 136.67 odd 2