Properties

Label 483.2.a.g.1.1
Level $483$
Weight $2$
Character 483.1
Self dual yes
Analytic conductor $3.857$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.85677441763\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 483.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.618034 q^{2} -1.00000 q^{3} -1.61803 q^{4} -0.381966 q^{5} +0.618034 q^{6} +1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +0.236068 q^{10} +2.23607 q^{11} +1.61803 q^{12} -0.145898 q^{13} -0.618034 q^{14} +0.381966 q^{15} +1.85410 q^{16} -5.47214 q^{17} -0.618034 q^{18} -8.23607 q^{19} +0.618034 q^{20} -1.00000 q^{21} -1.38197 q^{22} +1.00000 q^{23} -2.23607 q^{24} -4.85410 q^{25} +0.0901699 q^{26} -1.00000 q^{27} -1.61803 q^{28} -2.70820 q^{29} -0.236068 q^{30} -5.00000 q^{31} -5.61803 q^{32} -2.23607 q^{33} +3.38197 q^{34} -0.381966 q^{35} -1.61803 q^{36} -0.527864 q^{37} +5.09017 q^{38} +0.145898 q^{39} -0.854102 q^{40} +8.70820 q^{41} +0.618034 q^{42} -8.32624 q^{43} -3.61803 q^{44} -0.381966 q^{45} -0.618034 q^{46} +5.23607 q^{47} -1.85410 q^{48} +1.00000 q^{49} +3.00000 q^{50} +5.47214 q^{51} +0.236068 q^{52} -3.61803 q^{53} +0.618034 q^{54} -0.854102 q^{55} +2.23607 q^{56} +8.23607 q^{57} +1.67376 q^{58} -4.85410 q^{59} -0.618034 q^{60} -9.09017 q^{61} +3.09017 q^{62} +1.00000 q^{63} -0.236068 q^{64} +0.0557281 q^{65} +1.38197 q^{66} -6.85410 q^{67} +8.85410 q^{68} -1.00000 q^{69} +0.236068 q^{70} +9.38197 q^{71} +2.23607 q^{72} -3.47214 q^{73} +0.326238 q^{74} +4.85410 q^{75} +13.3262 q^{76} +2.23607 q^{77} -0.0901699 q^{78} +5.94427 q^{79} -0.708204 q^{80} +1.00000 q^{81} -5.38197 q^{82} +7.94427 q^{83} +1.61803 q^{84} +2.09017 q^{85} +5.14590 q^{86} +2.70820 q^{87} +5.00000 q^{88} -16.3262 q^{89} +0.236068 q^{90} -0.145898 q^{91} -1.61803 q^{92} +5.00000 q^{93} -3.23607 q^{94} +3.14590 q^{95} +5.61803 q^{96} -17.1803 q^{97} -0.618034 q^{98} +2.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - 2 q^{3} - q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + 2 q^{9} - 4 q^{10} + q^{12} - 7 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 2 q^{17} + q^{18} - 12 q^{19} - q^{20} - 2 q^{21} - 5 q^{22} + 2 q^{23} - 3 q^{25} - 11 q^{26} - 2 q^{27} - q^{28} + 8 q^{29} + 4 q^{30} - 10 q^{31} - 9 q^{32} + 9 q^{34} - 3 q^{35} - q^{36} - 10 q^{37} - q^{38} + 7 q^{39} + 5 q^{40} + 4 q^{41} - q^{42} - q^{43} - 5 q^{44} - 3 q^{45} + q^{46} + 6 q^{47} + 3 q^{48} + 2 q^{49} + 6 q^{50} + 2 q^{51} - 4 q^{52} - 5 q^{53} - q^{54} + 5 q^{55} + 12 q^{57} + 19 q^{58} - 3 q^{59} + q^{60} - 7 q^{61} - 5 q^{62} + 2 q^{63} + 4 q^{64} + 18 q^{65} + 5 q^{66} - 7 q^{67} + 11 q^{68} - 2 q^{69} - 4 q^{70} + 21 q^{71} + 2 q^{73} - 15 q^{74} + 3 q^{75} + 11 q^{76} + 11 q^{78} - 6 q^{79} + 12 q^{80} + 2 q^{81} - 13 q^{82} - 2 q^{83} + q^{84} - 7 q^{85} + 17 q^{86} - 8 q^{87} + 10 q^{88} - 17 q^{89} - 4 q^{90} - 7 q^{91} - q^{92} + 10 q^{93} - 2 q^{94} + 13 q^{95} + 9 q^{96} - 12 q^{97} + q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.618034 −0.437016 −0.218508 0.975835i \(-0.570119\pi\)
−0.218508 + 0.975835i \(0.570119\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.61803 −0.809017
\(5\) −0.381966 −0.170820 −0.0854102 0.996346i \(-0.527220\pi\)
−0.0854102 + 0.996346i \(0.527220\pi\)
\(6\) 0.618034 0.252311
\(7\) 1.00000 0.377964
\(8\) 2.23607 0.790569
\(9\) 1.00000 0.333333
\(10\) 0.236068 0.0746512
\(11\) 2.23607 0.674200 0.337100 0.941469i \(-0.390554\pi\)
0.337100 + 0.941469i \(0.390554\pi\)
\(12\) 1.61803 0.467086
\(13\) −0.145898 −0.0404648 −0.0202324 0.999795i \(-0.506441\pi\)
−0.0202324 + 0.999795i \(0.506441\pi\)
\(14\) −0.618034 −0.165177
\(15\) 0.381966 0.0986232
\(16\) 1.85410 0.463525
\(17\) −5.47214 −1.32719 −0.663594 0.748093i \(-0.730970\pi\)
−0.663594 + 0.748093i \(0.730970\pi\)
\(18\) −0.618034 −0.145672
\(19\) −8.23607 −1.88948 −0.944742 0.327815i \(-0.893688\pi\)
−0.944742 + 0.327815i \(0.893688\pi\)
\(20\) 0.618034 0.138197
\(21\) −1.00000 −0.218218
\(22\) −1.38197 −0.294636
\(23\) 1.00000 0.208514
\(24\) −2.23607 −0.456435
\(25\) −4.85410 −0.970820
\(26\) 0.0901699 0.0176838
\(27\) −1.00000 −0.192450
\(28\) −1.61803 −0.305780
\(29\) −2.70820 −0.502901 −0.251450 0.967870i \(-0.580908\pi\)
−0.251450 + 0.967870i \(0.580908\pi\)
\(30\) −0.236068 −0.0430999
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −5.61803 −0.993137
\(33\) −2.23607 −0.389249
\(34\) 3.38197 0.580002
\(35\) −0.381966 −0.0645640
\(36\) −1.61803 −0.269672
\(37\) −0.527864 −0.0867803 −0.0433902 0.999058i \(-0.513816\pi\)
−0.0433902 + 0.999058i \(0.513816\pi\)
\(38\) 5.09017 0.825735
\(39\) 0.145898 0.0233624
\(40\) −0.854102 −0.135045
\(41\) 8.70820 1.35999 0.679996 0.733215i \(-0.261981\pi\)
0.679996 + 0.733215i \(0.261981\pi\)
\(42\) 0.618034 0.0953647
\(43\) −8.32624 −1.26974 −0.634870 0.772619i \(-0.718946\pi\)
−0.634870 + 0.772619i \(0.718946\pi\)
\(44\) −3.61803 −0.545439
\(45\) −0.381966 −0.0569401
\(46\) −0.618034 −0.0911241
\(47\) 5.23607 0.763759 0.381880 0.924212i \(-0.375277\pi\)
0.381880 + 0.924212i \(0.375277\pi\)
\(48\) −1.85410 −0.267617
\(49\) 1.00000 0.142857
\(50\) 3.00000 0.424264
\(51\) 5.47214 0.766252
\(52\) 0.236068 0.0327367
\(53\) −3.61803 −0.496975 −0.248488 0.968635i \(-0.579934\pi\)
−0.248488 + 0.968635i \(0.579934\pi\)
\(54\) 0.618034 0.0841038
\(55\) −0.854102 −0.115167
\(56\) 2.23607 0.298807
\(57\) 8.23607 1.09089
\(58\) 1.67376 0.219776
\(59\) −4.85410 −0.631950 −0.315975 0.948767i \(-0.602332\pi\)
−0.315975 + 0.948767i \(0.602332\pi\)
\(60\) −0.618034 −0.0797878
\(61\) −9.09017 −1.16388 −0.581938 0.813233i \(-0.697706\pi\)
−0.581938 + 0.813233i \(0.697706\pi\)
\(62\) 3.09017 0.392452
\(63\) 1.00000 0.125988
\(64\) −0.236068 −0.0295085
\(65\) 0.0557281 0.00691222
\(66\) 1.38197 0.170108
\(67\) −6.85410 −0.837362 −0.418681 0.908133i \(-0.637507\pi\)
−0.418681 + 0.908133i \(0.637507\pi\)
\(68\) 8.85410 1.07372
\(69\) −1.00000 −0.120386
\(70\) 0.236068 0.0282155
\(71\) 9.38197 1.11343 0.556717 0.830702i \(-0.312061\pi\)
0.556717 + 0.830702i \(0.312061\pi\)
\(72\) 2.23607 0.263523
\(73\) −3.47214 −0.406383 −0.203191 0.979139i \(-0.565131\pi\)
−0.203191 + 0.979139i \(0.565131\pi\)
\(74\) 0.326238 0.0379244
\(75\) 4.85410 0.560503
\(76\) 13.3262 1.52862
\(77\) 2.23607 0.254824
\(78\) −0.0901699 −0.0102097
\(79\) 5.94427 0.668783 0.334391 0.942434i \(-0.391469\pi\)
0.334391 + 0.942434i \(0.391469\pi\)
\(80\) −0.708204 −0.0791796
\(81\) 1.00000 0.111111
\(82\) −5.38197 −0.594339
\(83\) 7.94427 0.871997 0.435999 0.899947i \(-0.356395\pi\)
0.435999 + 0.899947i \(0.356395\pi\)
\(84\) 1.61803 0.176542
\(85\) 2.09017 0.226711
\(86\) 5.14590 0.554896
\(87\) 2.70820 0.290350
\(88\) 5.00000 0.533002
\(89\) −16.3262 −1.73058 −0.865289 0.501274i \(-0.832865\pi\)
−0.865289 + 0.501274i \(0.832865\pi\)
\(90\) 0.236068 0.0248837
\(91\) −0.145898 −0.0152943
\(92\) −1.61803 −0.168692
\(93\) 5.00000 0.518476
\(94\) −3.23607 −0.333775
\(95\) 3.14590 0.322762
\(96\) 5.61803 0.573388
\(97\) −17.1803 −1.74440 −0.872200 0.489150i \(-0.837307\pi\)
−0.872200 + 0.489150i \(0.837307\pi\)
\(98\) −0.618034 −0.0624309
\(99\) 2.23607 0.224733
\(100\) 7.85410 0.785410
\(101\) −16.0902 −1.60103 −0.800516 0.599312i \(-0.795441\pi\)
−0.800516 + 0.599312i \(0.795441\pi\)
\(102\) −3.38197 −0.334865
\(103\) 2.47214 0.243587 0.121793 0.992555i \(-0.461135\pi\)
0.121793 + 0.992555i \(0.461135\pi\)
\(104\) −0.326238 −0.0319903
\(105\) 0.381966 0.0372761
\(106\) 2.23607 0.217186
\(107\) 5.85410 0.565937 0.282969 0.959129i \(-0.408681\pi\)
0.282969 + 0.959129i \(0.408681\pi\)
\(108\) 1.61803 0.155695
\(109\) 15.0344 1.44004 0.720019 0.693954i \(-0.244133\pi\)
0.720019 + 0.693954i \(0.244133\pi\)
\(110\) 0.527864 0.0503299
\(111\) 0.527864 0.0501026
\(112\) 1.85410 0.175196
\(113\) 4.09017 0.384771 0.192385 0.981319i \(-0.438378\pi\)
0.192385 + 0.981319i \(0.438378\pi\)
\(114\) −5.09017 −0.476738
\(115\) −0.381966 −0.0356185
\(116\) 4.38197 0.406855
\(117\) −0.145898 −0.0134883
\(118\) 3.00000 0.276172
\(119\) −5.47214 −0.501630
\(120\) 0.854102 0.0779685
\(121\) −6.00000 −0.545455
\(122\) 5.61803 0.508633
\(123\) −8.70820 −0.785192
\(124\) 8.09017 0.726519
\(125\) 3.76393 0.336656
\(126\) −0.618034 −0.0550588
\(127\) −18.3262 −1.62619 −0.813095 0.582131i \(-0.802219\pi\)
−0.813095 + 0.582131i \(0.802219\pi\)
\(128\) 11.3820 1.00603
\(129\) 8.32624 0.733084
\(130\) −0.0344419 −0.00302075
\(131\) 14.4164 1.25957 0.629784 0.776771i \(-0.283144\pi\)
0.629784 + 0.776771i \(0.283144\pi\)
\(132\) 3.61803 0.314909
\(133\) −8.23607 −0.714158
\(134\) 4.23607 0.365941
\(135\) 0.381966 0.0328744
\(136\) −12.2361 −1.04923
\(137\) −2.05573 −0.175633 −0.0878164 0.996137i \(-0.527989\pi\)
−0.0878164 + 0.996137i \(0.527989\pi\)
\(138\) 0.618034 0.0526105
\(139\) 13.1459 1.11502 0.557510 0.830170i \(-0.311757\pi\)
0.557510 + 0.830170i \(0.311757\pi\)
\(140\) 0.618034 0.0522334
\(141\) −5.23607 −0.440956
\(142\) −5.79837 −0.486589
\(143\) −0.326238 −0.0272814
\(144\) 1.85410 0.154508
\(145\) 1.03444 0.0859057
\(146\) 2.14590 0.177596
\(147\) −1.00000 −0.0824786
\(148\) 0.854102 0.0702067
\(149\) 16.6525 1.36422 0.682112 0.731248i \(-0.261062\pi\)
0.682112 + 0.731248i \(0.261062\pi\)
\(150\) −3.00000 −0.244949
\(151\) 11.7082 0.952800 0.476400 0.879229i \(-0.341941\pi\)
0.476400 + 0.879229i \(0.341941\pi\)
\(152\) −18.4164 −1.49377
\(153\) −5.47214 −0.442396
\(154\) −1.38197 −0.111362
\(155\) 1.90983 0.153401
\(156\) −0.236068 −0.0189006
\(157\) 8.18034 0.652862 0.326431 0.945221i \(-0.394154\pi\)
0.326431 + 0.945221i \(0.394154\pi\)
\(158\) −3.67376 −0.292269
\(159\) 3.61803 0.286929
\(160\) 2.14590 0.169648
\(161\) 1.00000 0.0788110
\(162\) −0.618034 −0.0485573
\(163\) 15.5066 1.21457 0.607284 0.794484i \(-0.292259\pi\)
0.607284 + 0.794484i \(0.292259\pi\)
\(164\) −14.0902 −1.10026
\(165\) 0.854102 0.0664917
\(166\) −4.90983 −0.381077
\(167\) 2.52786 0.195612 0.0978060 0.995205i \(-0.468818\pi\)
0.0978060 + 0.995205i \(0.468818\pi\)
\(168\) −2.23607 −0.172516
\(169\) −12.9787 −0.998363
\(170\) −1.29180 −0.0990762
\(171\) −8.23607 −0.629828
\(172\) 13.4721 1.02724
\(173\) −24.7082 −1.87853 −0.939265 0.343193i \(-0.888492\pi\)
−0.939265 + 0.343193i \(0.888492\pi\)
\(174\) −1.67376 −0.126888
\(175\) −4.85410 −0.366936
\(176\) 4.14590 0.312509
\(177\) 4.85410 0.364857
\(178\) 10.0902 0.756290
\(179\) −9.03444 −0.675266 −0.337633 0.941278i \(-0.609626\pi\)
−0.337633 + 0.941278i \(0.609626\pi\)
\(180\) 0.618034 0.0460655
\(181\) 7.18034 0.533710 0.266855 0.963737i \(-0.414015\pi\)
0.266855 + 0.963737i \(0.414015\pi\)
\(182\) 0.0901699 0.00668384
\(183\) 9.09017 0.671965
\(184\) 2.23607 0.164845
\(185\) 0.201626 0.0148238
\(186\) −3.09017 −0.226582
\(187\) −12.2361 −0.894790
\(188\) −8.47214 −0.617894
\(189\) −1.00000 −0.0727393
\(190\) −1.94427 −0.141052
\(191\) 8.29180 0.599973 0.299987 0.953943i \(-0.403018\pi\)
0.299987 + 0.953943i \(0.403018\pi\)
\(192\) 0.236068 0.0170367
\(193\) 4.18034 0.300907 0.150454 0.988617i \(-0.451927\pi\)
0.150454 + 0.988617i \(0.451927\pi\)
\(194\) 10.6180 0.762330
\(195\) −0.0557281 −0.00399077
\(196\) −1.61803 −0.115574
\(197\) −9.67376 −0.689227 −0.344614 0.938745i \(-0.611990\pi\)
−0.344614 + 0.938745i \(0.611990\pi\)
\(198\) −1.38197 −0.0982120
\(199\) 10.5623 0.748742 0.374371 0.927279i \(-0.377859\pi\)
0.374371 + 0.927279i \(0.377859\pi\)
\(200\) −10.8541 −0.767501
\(201\) 6.85410 0.483451
\(202\) 9.94427 0.699677
\(203\) −2.70820 −0.190079
\(204\) −8.85410 −0.619911
\(205\) −3.32624 −0.232315
\(206\) −1.52786 −0.106451
\(207\) 1.00000 0.0695048
\(208\) −0.270510 −0.0187565
\(209\) −18.4164 −1.27389
\(210\) −0.236068 −0.0162902
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) 5.85410 0.402061
\(213\) −9.38197 −0.642842
\(214\) −3.61803 −0.247324
\(215\) 3.18034 0.216897
\(216\) −2.23607 −0.152145
\(217\) −5.00000 −0.339422
\(218\) −9.29180 −0.629320
\(219\) 3.47214 0.234625
\(220\) 1.38197 0.0931721
\(221\) 0.798374 0.0537044
\(222\) −0.326238 −0.0218957
\(223\) 2.67376 0.179048 0.0895242 0.995985i \(-0.471465\pi\)
0.0895242 + 0.995985i \(0.471465\pi\)
\(224\) −5.61803 −0.375371
\(225\) −4.85410 −0.323607
\(226\) −2.52786 −0.168151
\(227\) −18.2705 −1.21266 −0.606328 0.795215i \(-0.707358\pi\)
−0.606328 + 0.795215i \(0.707358\pi\)
\(228\) −13.3262 −0.882552
\(229\) −21.3262 −1.40928 −0.704639 0.709566i \(-0.748891\pi\)
−0.704639 + 0.709566i \(0.748891\pi\)
\(230\) 0.236068 0.0155659
\(231\) −2.23607 −0.147122
\(232\) −6.05573 −0.397578
\(233\) −4.09017 −0.267956 −0.133978 0.990984i \(-0.542775\pi\)
−0.133978 + 0.990984i \(0.542775\pi\)
\(234\) 0.0901699 0.00589459
\(235\) −2.00000 −0.130466
\(236\) 7.85410 0.511258
\(237\) −5.94427 −0.386122
\(238\) 3.38197 0.219220
\(239\) −4.38197 −0.283446 −0.141723 0.989906i \(-0.545264\pi\)
−0.141723 + 0.989906i \(0.545264\pi\)
\(240\) 0.708204 0.0457144
\(241\) 15.2918 0.985031 0.492516 0.870304i \(-0.336077\pi\)
0.492516 + 0.870304i \(0.336077\pi\)
\(242\) 3.70820 0.238372
\(243\) −1.00000 −0.0641500
\(244\) 14.7082 0.941596
\(245\) −0.381966 −0.0244029
\(246\) 5.38197 0.343142
\(247\) 1.20163 0.0764576
\(248\) −11.1803 −0.709952
\(249\) −7.94427 −0.503448
\(250\) −2.32624 −0.147124
\(251\) −25.7082 −1.62269 −0.811344 0.584569i \(-0.801263\pi\)
−0.811344 + 0.584569i \(0.801263\pi\)
\(252\) −1.61803 −0.101927
\(253\) 2.23607 0.140580
\(254\) 11.3262 0.710671
\(255\) −2.09017 −0.130892
\(256\) −6.56231 −0.410144
\(257\) 16.2918 1.01625 0.508127 0.861282i \(-0.330338\pi\)
0.508127 + 0.861282i \(0.330338\pi\)
\(258\) −5.14590 −0.320370
\(259\) −0.527864 −0.0327999
\(260\) −0.0901699 −0.00559210
\(261\) −2.70820 −0.167634
\(262\) −8.90983 −0.550451
\(263\) 5.00000 0.308313 0.154157 0.988046i \(-0.450734\pi\)
0.154157 + 0.988046i \(0.450734\pi\)
\(264\) −5.00000 −0.307729
\(265\) 1.38197 0.0848935
\(266\) 5.09017 0.312098
\(267\) 16.3262 0.999150
\(268\) 11.0902 0.677440
\(269\) 3.85410 0.234989 0.117494 0.993074i \(-0.462514\pi\)
0.117494 + 0.993074i \(0.462514\pi\)
\(270\) −0.236068 −0.0143666
\(271\) 5.18034 0.314683 0.157342 0.987544i \(-0.449708\pi\)
0.157342 + 0.987544i \(0.449708\pi\)
\(272\) −10.1459 −0.615185
\(273\) 0.145898 0.00883015
\(274\) 1.27051 0.0767543
\(275\) −10.8541 −0.654527
\(276\) 1.61803 0.0973942
\(277\) −30.2148 −1.81543 −0.907715 0.419587i \(-0.862175\pi\)
−0.907715 + 0.419587i \(0.862175\pi\)
\(278\) −8.12461 −0.487282
\(279\) −5.00000 −0.299342
\(280\) −0.854102 −0.0510424
\(281\) 27.5967 1.64628 0.823142 0.567836i \(-0.192219\pi\)
0.823142 + 0.567836i \(0.192219\pi\)
\(282\) 3.23607 0.192705
\(283\) −1.32624 −0.0788367 −0.0394183 0.999223i \(-0.512550\pi\)
−0.0394183 + 0.999223i \(0.512550\pi\)
\(284\) −15.1803 −0.900787
\(285\) −3.14590 −0.186347
\(286\) 0.201626 0.0119224
\(287\) 8.70820 0.514029
\(288\) −5.61803 −0.331046
\(289\) 12.9443 0.761428
\(290\) −0.639320 −0.0375422
\(291\) 17.1803 1.00713
\(292\) 5.61803 0.328771
\(293\) −18.4721 −1.07915 −0.539577 0.841936i \(-0.681416\pi\)
−0.539577 + 0.841936i \(0.681416\pi\)
\(294\) 0.618034 0.0360445
\(295\) 1.85410 0.107950
\(296\) −1.18034 −0.0686059
\(297\) −2.23607 −0.129750
\(298\) −10.2918 −0.596188
\(299\) −0.145898 −0.00843750
\(300\) −7.85410 −0.453457
\(301\) −8.32624 −0.479916
\(302\) −7.23607 −0.416389
\(303\) 16.0902 0.924356
\(304\) −15.2705 −0.875824
\(305\) 3.47214 0.198814
\(306\) 3.38197 0.193334
\(307\) 8.05573 0.459765 0.229882 0.973218i \(-0.426166\pi\)
0.229882 + 0.973218i \(0.426166\pi\)
\(308\) −3.61803 −0.206157
\(309\) −2.47214 −0.140635
\(310\) −1.18034 −0.0670388
\(311\) 5.38197 0.305183 0.152592 0.988289i \(-0.451238\pi\)
0.152592 + 0.988289i \(0.451238\pi\)
\(312\) 0.326238 0.0184696
\(313\) −10.4721 −0.591920 −0.295960 0.955200i \(-0.595640\pi\)
−0.295960 + 0.955200i \(0.595640\pi\)
\(314\) −5.05573 −0.285311
\(315\) −0.381966 −0.0215213
\(316\) −9.61803 −0.541057
\(317\) −28.8541 −1.62061 −0.810304 0.586010i \(-0.800698\pi\)
−0.810304 + 0.586010i \(0.800698\pi\)
\(318\) −2.23607 −0.125392
\(319\) −6.05573 −0.339056
\(320\) 0.0901699 0.00504065
\(321\) −5.85410 −0.326744
\(322\) −0.618034 −0.0344417
\(323\) 45.0689 2.50770
\(324\) −1.61803 −0.0898908
\(325\) 0.708204 0.0392841
\(326\) −9.58359 −0.530786
\(327\) −15.0344 −0.831407
\(328\) 19.4721 1.07517
\(329\) 5.23607 0.288674
\(330\) −0.527864 −0.0290580
\(331\) −6.94427 −0.381692 −0.190846 0.981620i \(-0.561123\pi\)
−0.190846 + 0.981620i \(0.561123\pi\)
\(332\) −12.8541 −0.705460
\(333\) −0.527864 −0.0289268
\(334\) −1.56231 −0.0854856
\(335\) 2.61803 0.143038
\(336\) −1.85410 −0.101150
\(337\) 1.56231 0.0851042 0.0425521 0.999094i \(-0.486451\pi\)
0.0425521 + 0.999094i \(0.486451\pi\)
\(338\) 8.02129 0.436300
\(339\) −4.09017 −0.222148
\(340\) −3.38197 −0.183413
\(341\) −11.1803 −0.605449
\(342\) 5.09017 0.275245
\(343\) 1.00000 0.0539949
\(344\) −18.6180 −1.00382
\(345\) 0.381966 0.0205644
\(346\) 15.2705 0.820948
\(347\) 27.6525 1.48446 0.742231 0.670144i \(-0.233768\pi\)
0.742231 + 0.670144i \(0.233768\pi\)
\(348\) −4.38197 −0.234898
\(349\) 31.5066 1.68651 0.843254 0.537515i \(-0.180637\pi\)
0.843254 + 0.537515i \(0.180637\pi\)
\(350\) 3.00000 0.160357
\(351\) 0.145898 0.00778746
\(352\) −12.5623 −0.669573
\(353\) 22.5967 1.20270 0.601352 0.798984i \(-0.294629\pi\)
0.601352 + 0.798984i \(0.294629\pi\)
\(354\) −3.00000 −0.159448
\(355\) −3.58359 −0.190197
\(356\) 26.4164 1.40007
\(357\) 5.47214 0.289616
\(358\) 5.58359 0.295102
\(359\) −1.79837 −0.0949145 −0.0474573 0.998873i \(-0.515112\pi\)
−0.0474573 + 0.998873i \(0.515112\pi\)
\(360\) −0.854102 −0.0450151
\(361\) 48.8328 2.57015
\(362\) −4.43769 −0.233240
\(363\) 6.00000 0.314918
\(364\) 0.236068 0.0123733
\(365\) 1.32624 0.0694185
\(366\) −5.61803 −0.293659
\(367\) 23.4508 1.22412 0.612062 0.790810i \(-0.290340\pi\)
0.612062 + 0.790810i \(0.290340\pi\)
\(368\) 1.85410 0.0966517
\(369\) 8.70820 0.453331
\(370\) −0.124612 −0.00647826
\(371\) −3.61803 −0.187839
\(372\) −8.09017 −0.419456
\(373\) −32.8885 −1.70290 −0.851452 0.524432i \(-0.824278\pi\)
−0.851452 + 0.524432i \(0.824278\pi\)
\(374\) 7.56231 0.391038
\(375\) −3.76393 −0.194369
\(376\) 11.7082 0.603805
\(377\) 0.395122 0.0203498
\(378\) 0.618034 0.0317882
\(379\) −3.05573 −0.156962 −0.0784811 0.996916i \(-0.525007\pi\)
−0.0784811 + 0.996916i \(0.525007\pi\)
\(380\) −5.09017 −0.261120
\(381\) 18.3262 0.938882
\(382\) −5.12461 −0.262198
\(383\) −13.4721 −0.688394 −0.344197 0.938897i \(-0.611849\pi\)
−0.344197 + 0.938897i \(0.611849\pi\)
\(384\) −11.3820 −0.580834
\(385\) −0.854102 −0.0435291
\(386\) −2.58359 −0.131501
\(387\) −8.32624 −0.423246
\(388\) 27.7984 1.41125
\(389\) −18.1246 −0.918954 −0.459477 0.888190i \(-0.651963\pi\)
−0.459477 + 0.888190i \(0.651963\pi\)
\(390\) 0.0344419 0.00174403
\(391\) −5.47214 −0.276738
\(392\) 2.23607 0.112938
\(393\) −14.4164 −0.727212
\(394\) 5.97871 0.301203
\(395\) −2.27051 −0.114242
\(396\) −3.61803 −0.181813
\(397\) 10.7639 0.540226 0.270113 0.962829i \(-0.412939\pi\)
0.270113 + 0.962829i \(0.412939\pi\)
\(398\) −6.52786 −0.327212
\(399\) 8.23607 0.412319
\(400\) −9.00000 −0.450000
\(401\) 29.1803 1.45720 0.728598 0.684941i \(-0.240172\pi\)
0.728598 + 0.684941i \(0.240172\pi\)
\(402\) −4.23607 −0.211276
\(403\) 0.729490 0.0363385
\(404\) 26.0344 1.29526
\(405\) −0.381966 −0.0189800
\(406\) 1.67376 0.0830674
\(407\) −1.18034 −0.0585073
\(408\) 12.2361 0.605776
\(409\) −7.65248 −0.378391 −0.189195 0.981939i \(-0.560588\pi\)
−0.189195 + 0.981939i \(0.560588\pi\)
\(410\) 2.05573 0.101525
\(411\) 2.05573 0.101402
\(412\) −4.00000 −0.197066
\(413\) −4.85410 −0.238855
\(414\) −0.618034 −0.0303747
\(415\) −3.03444 −0.148955
\(416\) 0.819660 0.0401871
\(417\) −13.1459 −0.643757
\(418\) 11.3820 0.556710
\(419\) −0.562306 −0.0274704 −0.0137352 0.999906i \(-0.504372\pi\)
−0.0137352 + 0.999906i \(0.504372\pi\)
\(420\) −0.618034 −0.0301570
\(421\) 26.3262 1.28306 0.641531 0.767097i \(-0.278300\pi\)
0.641531 + 0.767097i \(0.278300\pi\)
\(422\) −9.27051 −0.451281
\(423\) 5.23607 0.254586
\(424\) −8.09017 −0.392893
\(425\) 26.5623 1.28846
\(426\) 5.79837 0.280932
\(427\) −9.09017 −0.439904
\(428\) −9.47214 −0.457853
\(429\) 0.326238 0.0157509
\(430\) −1.96556 −0.0947876
\(431\) 31.0902 1.49756 0.748780 0.662818i \(-0.230640\pi\)
0.748780 + 0.662818i \(0.230640\pi\)
\(432\) −1.85410 −0.0892055
\(433\) −17.1246 −0.822956 −0.411478 0.911420i \(-0.634987\pi\)
−0.411478 + 0.911420i \(0.634987\pi\)
\(434\) 3.09017 0.148333
\(435\) −1.03444 −0.0495977
\(436\) −24.3262 −1.16502
\(437\) −8.23607 −0.393985
\(438\) −2.14590 −0.102535
\(439\) −0.0557281 −0.00265976 −0.00132988 0.999999i \(-0.500423\pi\)
−0.00132988 + 0.999999i \(0.500423\pi\)
\(440\) −1.90983 −0.0910476
\(441\) 1.00000 0.0476190
\(442\) −0.493422 −0.0234697
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) −0.854102 −0.0405339
\(445\) 6.23607 0.295618
\(446\) −1.65248 −0.0782470
\(447\) −16.6525 −0.787635
\(448\) −0.236068 −0.0111532
\(449\) 24.0902 1.13689 0.568443 0.822723i \(-0.307546\pi\)
0.568443 + 0.822723i \(0.307546\pi\)
\(450\) 3.00000 0.141421
\(451\) 19.4721 0.916907
\(452\) −6.61803 −0.311286
\(453\) −11.7082 −0.550099
\(454\) 11.2918 0.529950
\(455\) 0.0557281 0.00261257
\(456\) 18.4164 0.862427
\(457\) −8.20163 −0.383656 −0.191828 0.981429i \(-0.561442\pi\)
−0.191828 + 0.981429i \(0.561442\pi\)
\(458\) 13.1803 0.615877
\(459\) 5.47214 0.255417
\(460\) 0.618034 0.0288160
\(461\) 12.8541 0.598675 0.299338 0.954147i \(-0.403234\pi\)
0.299338 + 0.954147i \(0.403234\pi\)
\(462\) 1.38197 0.0642949
\(463\) −34.5967 −1.60785 −0.803924 0.594733i \(-0.797258\pi\)
−0.803924 + 0.594733i \(0.797258\pi\)
\(464\) −5.02129 −0.233107
\(465\) −1.90983 −0.0885662
\(466\) 2.52786 0.117101
\(467\) −16.8885 −0.781509 −0.390754 0.920495i \(-0.627786\pi\)
−0.390754 + 0.920495i \(0.627786\pi\)
\(468\) 0.236068 0.0109122
\(469\) −6.85410 −0.316493
\(470\) 1.23607 0.0570156
\(471\) −8.18034 −0.376930
\(472\) −10.8541 −0.499601
\(473\) −18.6180 −0.856058
\(474\) 3.67376 0.168741
\(475\) 39.9787 1.83435
\(476\) 8.85410 0.405827
\(477\) −3.61803 −0.165658
\(478\) 2.70820 0.123870
\(479\) 25.6525 1.17209 0.586046 0.810278i \(-0.300684\pi\)
0.586046 + 0.810278i \(0.300684\pi\)
\(480\) −2.14590 −0.0979464
\(481\) 0.0770143 0.00351155
\(482\) −9.45085 −0.430474
\(483\) −1.00000 −0.0455016
\(484\) 9.70820 0.441282
\(485\) 6.56231 0.297979
\(486\) 0.618034 0.0280346
\(487\) 22.2361 1.00761 0.503806 0.863817i \(-0.331933\pi\)
0.503806 + 0.863817i \(0.331933\pi\)
\(488\) −20.3262 −0.920126
\(489\) −15.5066 −0.701232
\(490\) 0.236068 0.0106645
\(491\) 16.9098 0.763130 0.381565 0.924342i \(-0.375385\pi\)
0.381565 + 0.924342i \(0.375385\pi\)
\(492\) 14.0902 0.635234
\(493\) 14.8197 0.667444
\(494\) −0.742646 −0.0334132
\(495\) −0.854102 −0.0383890
\(496\) −9.27051 −0.416258
\(497\) 9.38197 0.420839
\(498\) 4.90983 0.220015
\(499\) −11.7984 −0.528168 −0.264084 0.964500i \(-0.585070\pi\)
−0.264084 + 0.964500i \(0.585070\pi\)
\(500\) −6.09017 −0.272361
\(501\) −2.52786 −0.112937
\(502\) 15.8885 0.709140
\(503\) −9.90983 −0.441857 −0.220929 0.975290i \(-0.570909\pi\)
−0.220929 + 0.975290i \(0.570909\pi\)
\(504\) 2.23607 0.0996024
\(505\) 6.14590 0.273489
\(506\) −1.38197 −0.0614359
\(507\) 12.9787 0.576405
\(508\) 29.6525 1.31562
\(509\) 12.2918 0.544824 0.272412 0.962181i \(-0.412179\pi\)
0.272412 + 0.962181i \(0.412179\pi\)
\(510\) 1.29180 0.0572017
\(511\) −3.47214 −0.153598
\(512\) −18.7082 −0.826794
\(513\) 8.23607 0.363631
\(514\) −10.0689 −0.444119
\(515\) −0.944272 −0.0416096
\(516\) −13.4721 −0.593078
\(517\) 11.7082 0.514926
\(518\) 0.326238 0.0143341
\(519\) 24.7082 1.08457
\(520\) 0.124612 0.00546459
\(521\) −12.4721 −0.546414 −0.273207 0.961955i \(-0.588084\pi\)
−0.273207 + 0.961955i \(0.588084\pi\)
\(522\) 1.67376 0.0732586
\(523\) −20.8328 −0.910955 −0.455478 0.890247i \(-0.650532\pi\)
−0.455478 + 0.890247i \(0.650532\pi\)
\(524\) −23.3262 −1.01901
\(525\) 4.85410 0.211850
\(526\) −3.09017 −0.134738
\(527\) 27.3607 1.19185
\(528\) −4.14590 −0.180427
\(529\) 1.00000 0.0434783
\(530\) −0.854102 −0.0370998
\(531\) −4.85410 −0.210650
\(532\) 13.3262 0.577766
\(533\) −1.27051 −0.0550319
\(534\) −10.0902 −0.436644
\(535\) −2.23607 −0.0966736
\(536\) −15.3262 −0.661993
\(537\) 9.03444 0.389865
\(538\) −2.38197 −0.102694
\(539\) 2.23607 0.0963143
\(540\) −0.618034 −0.0265959
\(541\) −18.7639 −0.806724 −0.403362 0.915040i \(-0.632159\pi\)
−0.403362 + 0.915040i \(0.632159\pi\)
\(542\) −3.20163 −0.137522
\(543\) −7.18034 −0.308138
\(544\) 30.7426 1.31808
\(545\) −5.74265 −0.245988
\(546\) −0.0901699 −0.00385892
\(547\) −24.3820 −1.04250 −0.521249 0.853405i \(-0.674534\pi\)
−0.521249 + 0.853405i \(0.674534\pi\)
\(548\) 3.32624 0.142090
\(549\) −9.09017 −0.387959
\(550\) 6.70820 0.286039
\(551\) 22.3050 0.950223
\(552\) −2.23607 −0.0951734
\(553\) 5.94427 0.252776
\(554\) 18.6738 0.793372
\(555\) −0.201626 −0.00855855
\(556\) −21.2705 −0.902071
\(557\) −12.7639 −0.540825 −0.270413 0.962745i \(-0.587160\pi\)
−0.270413 + 0.962745i \(0.587160\pi\)
\(558\) 3.09017 0.130817
\(559\) 1.21478 0.0513798
\(560\) −0.708204 −0.0299271
\(561\) 12.2361 0.516607
\(562\) −17.0557 −0.719452
\(563\) −11.5623 −0.487293 −0.243647 0.969864i \(-0.578344\pi\)
−0.243647 + 0.969864i \(0.578344\pi\)
\(564\) 8.47214 0.356741
\(565\) −1.56231 −0.0657267
\(566\) 0.819660 0.0344529
\(567\) 1.00000 0.0419961
\(568\) 20.9787 0.880247
\(569\) −43.7771 −1.83523 −0.917615 0.397469i \(-0.869889\pi\)
−0.917615 + 0.397469i \(0.869889\pi\)
\(570\) 1.94427 0.0814366
\(571\) 26.7771 1.12059 0.560293 0.828294i \(-0.310688\pi\)
0.560293 + 0.828294i \(0.310688\pi\)
\(572\) 0.527864 0.0220711
\(573\) −8.29180 −0.346395
\(574\) −5.38197 −0.224639
\(575\) −4.85410 −0.202430
\(576\) −0.236068 −0.00983617
\(577\) 9.41641 0.392010 0.196005 0.980603i \(-0.437203\pi\)
0.196005 + 0.980603i \(0.437203\pi\)
\(578\) −8.00000 −0.332756
\(579\) −4.18034 −0.173729
\(580\) −1.67376 −0.0694992
\(581\) 7.94427 0.329584
\(582\) −10.6180 −0.440132
\(583\) −8.09017 −0.335061
\(584\) −7.76393 −0.321274
\(585\) 0.0557281 0.00230407
\(586\) 11.4164 0.471607
\(587\) −17.5623 −0.724874 −0.362437 0.932008i \(-0.618055\pi\)
−0.362437 + 0.932008i \(0.618055\pi\)
\(588\) 1.61803 0.0667266
\(589\) 41.1803 1.69681
\(590\) −1.14590 −0.0471759
\(591\) 9.67376 0.397925
\(592\) −0.978714 −0.0402249
\(593\) −37.7082 −1.54849 −0.774245 0.632886i \(-0.781870\pi\)
−0.774245 + 0.632886i \(0.781870\pi\)
\(594\) 1.38197 0.0567028
\(595\) 2.09017 0.0856886
\(596\) −26.9443 −1.10368
\(597\) −10.5623 −0.432286
\(598\) 0.0901699 0.00368732
\(599\) 41.2705 1.68627 0.843134 0.537704i \(-0.180708\pi\)
0.843134 + 0.537704i \(0.180708\pi\)
\(600\) 10.8541 0.443117
\(601\) −25.5066 −1.04044 −0.520218 0.854034i \(-0.674149\pi\)
−0.520218 + 0.854034i \(0.674149\pi\)
\(602\) 5.14590 0.209731
\(603\) −6.85410 −0.279121
\(604\) −18.9443 −0.770831
\(605\) 2.29180 0.0931748
\(606\) −9.94427 −0.403958
\(607\) −10.6180 −0.430973 −0.215486 0.976507i \(-0.569134\pi\)
−0.215486 + 0.976507i \(0.569134\pi\)
\(608\) 46.2705 1.87652
\(609\) 2.70820 0.109742
\(610\) −2.14590 −0.0868849
\(611\) −0.763932 −0.0309054
\(612\) 8.85410 0.357906
\(613\) −37.6525 −1.52077 −0.760385 0.649473i \(-0.774990\pi\)
−0.760385 + 0.649473i \(0.774990\pi\)
\(614\) −4.97871 −0.200925
\(615\) 3.32624 0.134127
\(616\) 5.00000 0.201456
\(617\) 37.7426 1.51946 0.759731 0.650238i \(-0.225331\pi\)
0.759731 + 0.650238i \(0.225331\pi\)
\(618\) 1.52786 0.0614597
\(619\) −33.2705 −1.33725 −0.668627 0.743598i \(-0.733118\pi\)
−0.668627 + 0.743598i \(0.733118\pi\)
\(620\) −3.09017 −0.124104
\(621\) −1.00000 −0.0401286
\(622\) −3.32624 −0.133370
\(623\) −16.3262 −0.654097
\(624\) 0.270510 0.0108291
\(625\) 22.8328 0.913313
\(626\) 6.47214 0.258679
\(627\) 18.4164 0.735480
\(628\) −13.2361 −0.528177
\(629\) 2.88854 0.115174
\(630\) 0.236068 0.00940517
\(631\) −38.2361 −1.52215 −0.761077 0.648662i \(-0.775329\pi\)
−0.761077 + 0.648662i \(0.775329\pi\)
\(632\) 13.2918 0.528719
\(633\) −15.0000 −0.596196
\(634\) 17.8328 0.708232
\(635\) 7.00000 0.277787
\(636\) −5.85410 −0.232130
\(637\) −0.145898 −0.00578069
\(638\) 3.74265 0.148173
\(639\) 9.38197 0.371145
\(640\) −4.34752 −0.171851
\(641\) −28.6180 −1.13034 −0.565172 0.824973i \(-0.691190\pi\)
−0.565172 + 0.824973i \(0.691190\pi\)
\(642\) 3.61803 0.142792
\(643\) 2.50658 0.0988498 0.0494249 0.998778i \(-0.484261\pi\)
0.0494249 + 0.998778i \(0.484261\pi\)
\(644\) −1.61803 −0.0637595
\(645\) −3.18034 −0.125226
\(646\) −27.8541 −1.09590
\(647\) 2.09017 0.0821731 0.0410865 0.999156i \(-0.486918\pi\)
0.0410865 + 0.999156i \(0.486918\pi\)
\(648\) 2.23607 0.0878410
\(649\) −10.8541 −0.426061
\(650\) −0.437694 −0.0171678
\(651\) 5.00000 0.195965
\(652\) −25.0902 −0.982607
\(653\) −32.0902 −1.25579 −0.627893 0.778300i \(-0.716082\pi\)
−0.627893 + 0.778300i \(0.716082\pi\)
\(654\) 9.29180 0.363338
\(655\) −5.50658 −0.215160
\(656\) 16.1459 0.630391
\(657\) −3.47214 −0.135461
\(658\) −3.23607 −0.126155
\(659\) −28.5967 −1.11397 −0.556986 0.830522i \(-0.688042\pi\)
−0.556986 + 0.830522i \(0.688042\pi\)
\(660\) −1.38197 −0.0537930
\(661\) 6.81966 0.265254 0.132627 0.991166i \(-0.457659\pi\)
0.132627 + 0.991166i \(0.457659\pi\)
\(662\) 4.29180 0.166805
\(663\) −0.798374 −0.0310063
\(664\) 17.7639 0.689374
\(665\) 3.14590 0.121993
\(666\) 0.326238 0.0126415
\(667\) −2.70820 −0.104862
\(668\) −4.09017 −0.158253
\(669\) −2.67376 −0.103374
\(670\) −1.61803 −0.0625101
\(671\) −20.3262 −0.784686
\(672\) 5.61803 0.216720
\(673\) 21.9443 0.845890 0.422945 0.906155i \(-0.360996\pi\)
0.422945 + 0.906155i \(0.360996\pi\)
\(674\) −0.965558 −0.0371919
\(675\) 4.85410 0.186834
\(676\) 21.0000 0.807692
\(677\) 0.798374 0.0306840 0.0153420 0.999882i \(-0.495116\pi\)
0.0153420 + 0.999882i \(0.495116\pi\)
\(678\) 2.52786 0.0970820
\(679\) −17.1803 −0.659321
\(680\) 4.67376 0.179231
\(681\) 18.2705 0.700127
\(682\) 6.90983 0.264591
\(683\) 40.7082 1.55766 0.778828 0.627237i \(-0.215814\pi\)
0.778828 + 0.627237i \(0.215814\pi\)
\(684\) 13.3262 0.509541
\(685\) 0.785218 0.0300016
\(686\) −0.618034 −0.0235966
\(687\) 21.3262 0.813647
\(688\) −15.4377 −0.588557
\(689\) 0.527864 0.0201100
\(690\) −0.236068 −0.00898695
\(691\) −20.7984 −0.791207 −0.395604 0.918421i \(-0.629465\pi\)
−0.395604 + 0.918421i \(0.629465\pi\)
\(692\) 39.9787 1.51976
\(693\) 2.23607 0.0849412
\(694\) −17.0902 −0.648734
\(695\) −5.02129 −0.190468
\(696\) 6.05573 0.229542
\(697\) −47.6525 −1.80497
\(698\) −19.4721 −0.737031
\(699\) 4.09017 0.154704
\(700\) 7.85410 0.296857
\(701\) −31.7984 −1.20101 −0.600504 0.799622i \(-0.705033\pi\)
−0.600504 + 0.799622i \(0.705033\pi\)
\(702\) −0.0901699 −0.00340325
\(703\) 4.34752 0.163970
\(704\) −0.527864 −0.0198946
\(705\) 2.00000 0.0753244
\(706\) −13.9656 −0.525601
\(707\) −16.0902 −0.605133
\(708\) −7.85410 −0.295175
\(709\) −12.3262 −0.462922 −0.231461 0.972844i \(-0.574350\pi\)
−0.231461 + 0.972844i \(0.574350\pi\)
\(710\) 2.21478 0.0831193
\(711\) 5.94427 0.222928
\(712\) −36.5066 −1.36814
\(713\) −5.00000 −0.187251
\(714\) −3.38197 −0.126567
\(715\) 0.124612 0.00466022
\(716\) 14.6180 0.546302
\(717\) 4.38197 0.163648
\(718\) 1.11146 0.0414792
\(719\) 9.29180 0.346526 0.173263 0.984876i \(-0.444569\pi\)
0.173263 + 0.984876i \(0.444569\pi\)
\(720\) −0.708204 −0.0263932
\(721\) 2.47214 0.0920672
\(722\) −30.1803 −1.12320
\(723\) −15.2918 −0.568708
\(724\) −11.6180 −0.431781
\(725\) 13.1459 0.488226
\(726\) −3.70820 −0.137624
\(727\) −30.2361 −1.12139 −0.560697 0.828021i \(-0.689467\pi\)
−0.560697 + 0.828021i \(0.689467\pi\)
\(728\) −0.326238 −0.0120912
\(729\) 1.00000 0.0370370
\(730\) −0.819660 −0.0303370
\(731\) 45.5623 1.68518
\(732\) −14.7082 −0.543631
\(733\) 28.5410 1.05419 0.527093 0.849807i \(-0.323282\pi\)
0.527093 + 0.849807i \(0.323282\pi\)
\(734\) −14.4934 −0.534962
\(735\) 0.381966 0.0140890
\(736\) −5.61803 −0.207083
\(737\) −15.3262 −0.564549
\(738\) −5.38197 −0.198113
\(739\) −40.4164 −1.48674 −0.743371 0.668880i \(-0.766774\pi\)
−0.743371 + 0.668880i \(0.766774\pi\)
\(740\) −0.326238 −0.0119927
\(741\) −1.20163 −0.0441428
\(742\) 2.23607 0.0820886
\(743\) 25.3951 0.931657 0.465828 0.884875i \(-0.345756\pi\)
0.465828 + 0.884875i \(0.345756\pi\)
\(744\) 11.1803 0.409891
\(745\) −6.36068 −0.233037
\(746\) 20.3262 0.744196
\(747\) 7.94427 0.290666
\(748\) 19.7984 0.723900
\(749\) 5.85410 0.213904
\(750\) 2.32624 0.0849422
\(751\) −32.0902 −1.17099 −0.585493 0.810677i \(-0.699099\pi\)
−0.585493 + 0.810677i \(0.699099\pi\)
\(752\) 9.70820 0.354022
\(753\) 25.7082 0.936859
\(754\) −0.244199 −0.00889319
\(755\) −4.47214 −0.162758
\(756\) 1.61803 0.0588473
\(757\) −32.4164 −1.17819 −0.589097 0.808062i \(-0.700516\pi\)
−0.589097 + 0.808062i \(0.700516\pi\)
\(758\) 1.88854 0.0685950
\(759\) −2.23607 −0.0811641
\(760\) 7.03444 0.255166
\(761\) 53.8885 1.95346 0.976729 0.214477i \(-0.0688046\pi\)
0.976729 + 0.214477i \(0.0688046\pi\)
\(762\) −11.3262 −0.410306
\(763\) 15.0344 0.544283
\(764\) −13.4164 −0.485389
\(765\) 2.09017 0.0755703
\(766\) 8.32624 0.300839
\(767\) 0.708204 0.0255718
\(768\) 6.56231 0.236797
\(769\) 47.9574 1.72939 0.864695 0.502298i \(-0.167512\pi\)
0.864695 + 0.502298i \(0.167512\pi\)
\(770\) 0.527864 0.0190229
\(771\) −16.2918 −0.586735
\(772\) −6.76393 −0.243439
\(773\) −36.0132 −1.29530 −0.647652 0.761937i \(-0.724249\pi\)
−0.647652 + 0.761937i \(0.724249\pi\)
\(774\) 5.14590 0.184965
\(775\) 24.2705 0.871822
\(776\) −38.4164 −1.37907
\(777\) 0.527864 0.0189370
\(778\) 11.2016 0.401598
\(779\) −71.7214 −2.56968
\(780\) 0.0901699 0.00322860
\(781\) 20.9787 0.750677
\(782\) 3.38197 0.120939
\(783\) 2.70820 0.0967833
\(784\) 1.85410 0.0662179
\(785\) −3.12461 −0.111522
\(786\) 8.90983 0.317803
\(787\) −1.79837 −0.0641051 −0.0320526 0.999486i \(-0.510204\pi\)
−0.0320526 + 0.999486i \(0.510204\pi\)
\(788\) 15.6525 0.557596
\(789\) −5.00000 −0.178005
\(790\) 1.40325 0.0499255
\(791\) 4.09017 0.145430
\(792\) 5.00000 0.177667
\(793\) 1.32624 0.0470961
\(794\) −6.65248 −0.236088
\(795\) −1.38197 −0.0490133
\(796\) −17.0902 −0.605745
\(797\) −3.70820 −0.131351 −0.0656757 0.997841i \(-0.520920\pi\)
−0.0656757 + 0.997841i \(0.520920\pi\)
\(798\) −5.09017 −0.180190
\(799\) −28.6525 −1.01365
\(800\) 27.2705 0.964158
\(801\) −16.3262 −0.576859
\(802\) −18.0344 −0.636818
\(803\) −7.76393 −0.273983
\(804\) −11.0902 −0.391120
\(805\) −0.381966 −0.0134625
\(806\) −0.450850 −0.0158805
\(807\) −3.85410 −0.135671
\(808\) −35.9787 −1.26573
\(809\) −2.43769 −0.0857048 −0.0428524 0.999081i \(-0.513645\pi\)
−0.0428524 + 0.999081i \(0.513645\pi\)
\(810\) 0.236068 0.00829458
\(811\) −25.5410 −0.896867 −0.448433 0.893816i \(-0.648018\pi\)
−0.448433 + 0.893816i \(0.648018\pi\)
\(812\) 4.38197 0.153777
\(813\) −5.18034 −0.181682
\(814\) 0.729490 0.0255686
\(815\) −5.92299 −0.207473
\(816\) 10.1459 0.355177
\(817\) 68.5755 2.39915
\(818\) 4.72949 0.165363
\(819\) −0.145898 −0.00509809
\(820\) 5.38197 0.187946
\(821\) 12.2918 0.428987 0.214493 0.976725i \(-0.431190\pi\)
0.214493 + 0.976725i \(0.431190\pi\)
\(822\) −1.27051 −0.0443141
\(823\) 8.02129 0.279604 0.139802 0.990179i \(-0.455353\pi\)
0.139802 + 0.990179i \(0.455353\pi\)
\(824\) 5.52786 0.192572
\(825\) 10.8541 0.377891
\(826\) 3.00000 0.104383
\(827\) −22.8541 −0.794715 −0.397357 0.917664i \(-0.630073\pi\)
−0.397357 + 0.917664i \(0.630073\pi\)
\(828\) −1.61803 −0.0562306
\(829\) 35.0689 1.21799 0.608996 0.793173i \(-0.291572\pi\)
0.608996 + 0.793173i \(0.291572\pi\)
\(830\) 1.87539 0.0650957
\(831\) 30.2148 1.04814
\(832\) 0.0344419 0.00119406
\(833\) −5.47214 −0.189598
\(834\) 8.12461 0.281332
\(835\) −0.965558 −0.0334145
\(836\) 29.7984 1.03060
\(837\) 5.00000 0.172825
\(838\) 0.347524 0.0120050
\(839\) −2.72949 −0.0942325 −0.0471162 0.998889i \(-0.515003\pi\)
−0.0471162 + 0.998889i \(0.515003\pi\)
\(840\) 0.854102 0.0294693
\(841\) −21.6656 −0.747091
\(842\) −16.2705 −0.560719
\(843\) −27.5967 −0.950482
\(844\) −24.2705 −0.835425
\(845\) 4.95743 0.170541
\(846\) −3.23607 −0.111258
\(847\) −6.00000 −0.206162
\(848\) −6.70820 −0.230361
\(849\) 1.32624 0.0455164
\(850\) −16.4164 −0.563078
\(851\) −0.527864 −0.0180949
\(852\) 15.1803 0.520070
\(853\) −42.6525 −1.46039 −0.730196 0.683237i \(-0.760571\pi\)
−0.730196 + 0.683237i \(0.760571\pi\)
\(854\) 5.61803 0.192245
\(855\) 3.14590 0.107587
\(856\) 13.0902 0.447413
\(857\) 43.9574 1.50156 0.750779 0.660554i \(-0.229679\pi\)
0.750779 + 0.660554i \(0.229679\pi\)
\(858\) −0.201626 −0.00688340
\(859\) 1.41641 0.0483272 0.0241636 0.999708i \(-0.492308\pi\)
0.0241636 + 0.999708i \(0.492308\pi\)
\(860\) −5.14590 −0.175474
\(861\) −8.70820 −0.296775
\(862\) −19.2148 −0.654458
\(863\) 31.5967 1.07557 0.537783 0.843083i \(-0.319262\pi\)
0.537783 + 0.843083i \(0.319262\pi\)
\(864\) 5.61803 0.191129
\(865\) 9.43769 0.320891
\(866\) 10.5836 0.359645
\(867\) −12.9443 −0.439611
\(868\) 8.09017 0.274598
\(869\) 13.2918 0.450893
\(870\) 0.639320 0.0216750
\(871\) 1.00000 0.0338837
\(872\) 33.6180 1.13845
\(873\) −17.1803 −0.581466
\(874\) 5.09017 0.172178
\(875\) 3.76393 0.127244
\(876\) −5.61803 −0.189816
\(877\) −26.4721 −0.893901 −0.446950 0.894559i \(-0.647490\pi\)
−0.446950 + 0.894559i \(0.647490\pi\)
\(878\) 0.0344419 0.00116236
\(879\) 18.4721 0.623050
\(880\) −1.58359 −0.0533829
\(881\) −40.5410 −1.36586 −0.682931 0.730483i \(-0.739295\pi\)
−0.682931 + 0.730483i \(0.739295\pi\)
\(882\) −0.618034 −0.0208103
\(883\) 7.74265 0.260561 0.130280 0.991477i \(-0.458412\pi\)
0.130280 + 0.991477i \(0.458412\pi\)
\(884\) −1.29180 −0.0434478
\(885\) −1.85410 −0.0623250
\(886\) 2.47214 0.0830530
\(887\) 22.3262 0.749642 0.374821 0.927097i \(-0.377704\pi\)
0.374821 + 0.927097i \(0.377704\pi\)
\(888\) 1.18034 0.0396096
\(889\) −18.3262 −0.614642
\(890\) −3.85410 −0.129190
\(891\) 2.23607 0.0749111
\(892\) −4.32624 −0.144853
\(893\) −43.1246 −1.44311
\(894\) 10.2918 0.344209
\(895\) 3.45085 0.115349
\(896\) 11.3820 0.380245
\(897\) 0.145898 0.00487139
\(898\) −14.8885 −0.496837
\(899\) 13.5410 0.451618
\(900\) 7.85410 0.261803
\(901\) 19.7984 0.659579
\(902\) −12.0344 −0.400703
\(903\) 8.32624 0.277080
\(904\) 9.14590 0.304188
\(905\) −2.74265 −0.0911686
\(906\) 7.23607 0.240402
\(907\) −0.673762 −0.0223719 −0.0111860 0.999937i \(-0.503561\pi\)
−0.0111860 + 0.999937i \(0.503561\pi\)
\(908\) 29.5623 0.981060
\(909\) −16.0902 −0.533677
\(910\) −0.0344419 −0.00114174
\(911\) −31.7082 −1.05054 −0.525270 0.850936i \(-0.676036\pi\)
−0.525270 + 0.850936i \(0.676036\pi\)
\(912\) 15.2705 0.505657
\(913\) 17.7639 0.587900
\(914\) 5.06888 0.167664
\(915\) −3.47214 −0.114785
\(916\) 34.5066 1.14013
\(917\) 14.4164 0.476072
\(918\) −3.38197 −0.111622
\(919\) −48.4853 −1.59938 −0.799691 0.600412i \(-0.795003\pi\)
−0.799691 + 0.600412i \(0.795003\pi\)
\(920\) −0.854102 −0.0281589
\(921\) −8.05573 −0.265445
\(922\) −7.94427 −0.261631
\(923\) −1.36881 −0.0450549
\(924\) 3.61803 0.119025
\(925\) 2.56231 0.0842481
\(926\) 21.3820 0.702655
\(927\) 2.47214 0.0811956
\(928\) 15.2148 0.499450
\(929\) −8.74265 −0.286837 −0.143418 0.989662i \(-0.545809\pi\)
−0.143418 + 0.989662i \(0.545809\pi\)
\(930\) 1.18034 0.0387049
\(931\) −8.23607 −0.269926
\(932\) 6.61803 0.216781
\(933\) −5.38197 −0.176198
\(934\) 10.4377 0.341532
\(935\) 4.67376 0.152848
\(936\) −0.326238 −0.0106634
\(937\) 11.3607 0.371137 0.185569 0.982631i \(-0.440587\pi\)
0.185569 + 0.982631i \(0.440587\pi\)
\(938\) 4.23607 0.138313
\(939\) 10.4721 0.341745
\(940\) 3.23607 0.105549
\(941\) 18.8328 0.613932 0.306966 0.951720i \(-0.400686\pi\)
0.306966 + 0.951720i \(0.400686\pi\)
\(942\) 5.05573 0.164725
\(943\) 8.70820 0.283578
\(944\) −9.00000 −0.292925
\(945\) 0.381966 0.0124254
\(946\) 11.5066 0.374111
\(947\) 42.7214 1.38826 0.694129 0.719851i \(-0.255790\pi\)
0.694129 + 0.719851i \(0.255790\pi\)
\(948\) 9.61803 0.312379
\(949\) 0.506578 0.0164442
\(950\) −24.7082 −0.801640
\(951\) 28.8541 0.935658
\(952\) −12.2361 −0.396573
\(953\) −15.9230 −0.515796 −0.257898 0.966172i \(-0.583030\pi\)
−0.257898 + 0.966172i \(0.583030\pi\)
\(954\) 2.23607 0.0723954
\(955\) −3.16718 −0.102488
\(956\) 7.09017 0.229312
\(957\) 6.05573 0.195754
\(958\) −15.8541 −0.512223
\(959\) −2.05573 −0.0663829
\(960\) −0.0901699 −0.00291022
\(961\) −6.00000 −0.193548
\(962\) −0.0475975 −0.00153460
\(963\) 5.85410 0.188646
\(964\) −24.7426 −0.796907
\(965\) −1.59675 −0.0514011
\(966\) 0.618034 0.0198849
\(967\) −7.52786 −0.242080 −0.121040 0.992648i \(-0.538623\pi\)
−0.121040 + 0.992648i \(0.538623\pi\)
\(968\) −13.4164 −0.431220
\(969\) −45.0689 −1.44782
\(970\) −4.05573 −0.130222
\(971\) −2.90983 −0.0933809 −0.0466904 0.998909i \(-0.514867\pi\)
−0.0466904 + 0.998909i \(0.514867\pi\)
\(972\) 1.61803 0.0518985
\(973\) 13.1459 0.421438
\(974\) −13.7426 −0.440343
\(975\) −0.708204 −0.0226807
\(976\) −16.8541 −0.539487
\(977\) 7.02129 0.224631 0.112315 0.993673i \(-0.464173\pi\)
0.112315 + 0.993673i \(0.464173\pi\)
\(978\) 9.58359 0.306449
\(979\) −36.5066 −1.16676
\(980\) 0.618034 0.0197424
\(981\) 15.0344 0.480013
\(982\) −10.4508 −0.333500
\(983\) −14.6393 −0.466922 −0.233461 0.972366i \(-0.575005\pi\)
−0.233461 + 0.972366i \(0.575005\pi\)
\(984\) −19.4721 −0.620749
\(985\) 3.69505 0.117734
\(986\) −9.15905 −0.291684
\(987\) −5.23607 −0.166666
\(988\) −1.94427 −0.0618555
\(989\) −8.32624 −0.264759
\(990\) 0.527864 0.0167766
\(991\) 18.3262 0.582152 0.291076 0.956700i \(-0.405987\pi\)
0.291076 + 0.956700i \(0.405987\pi\)
\(992\) 28.0902 0.891864
\(993\) 6.94427 0.220370
\(994\) −5.79837 −0.183913
\(995\) −4.03444 −0.127900
\(996\) 12.8541 0.407298
\(997\) 41.5410 1.31562 0.657809 0.753185i \(-0.271484\pi\)
0.657809 + 0.753185i \(0.271484\pi\)
\(998\) 7.29180 0.230818
\(999\) 0.527864 0.0167009
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 483.2.a.g.1.1 2
3.2 odd 2 1449.2.a.f.1.2 2
4.3 odd 2 7728.2.a.bg.1.2 2
7.6 odd 2 3381.2.a.u.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.g.1.1 2 1.1 even 1 trivial
1449.2.a.f.1.2 2 3.2 odd 2
3381.2.a.u.1.1 2 7.6 odd 2
7728.2.a.bg.1.2 2 4.3 odd 2