Properties

Label 5290.2.a.o.1.1
Level $5290$
Weight $2$
Character 5290.1
Self dual yes
Analytic conductor $42.241$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5290.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.2408626693\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 5290.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.618034 q^{6} -1.61803 q^{7} +1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} -3.85410 q^{11} -0.618034 q^{12} +4.09017 q^{13} -1.61803 q^{14} +0.618034 q^{15} +1.00000 q^{16} +5.09017 q^{17} -2.61803 q^{18} +4.85410 q^{19} -1.00000 q^{20} +1.00000 q^{21} -3.85410 q^{22} -0.618034 q^{24} +1.00000 q^{25} +4.09017 q^{26} +3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} +0.618034 q^{30} -2.09017 q^{31} +1.00000 q^{32} +2.38197 q^{33} +5.09017 q^{34} +1.61803 q^{35} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -1.00000 q^{40} -12.3262 q^{41} +1.00000 q^{42} -3.85410 q^{44} +2.61803 q^{45} +9.70820 q^{47} -0.618034 q^{48} -4.38197 q^{49} +1.00000 q^{50} -3.14590 q^{51} +4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +3.85410 q^{55} -1.61803 q^{56} -3.00000 q^{57} -4.76393 q^{58} -11.7082 q^{59} +0.618034 q^{60} -6.32624 q^{61} -2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -4.09017 q^{65} +2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} +1.61803 q^{70} +7.09017 q^{71} -2.61803 q^{72} -1.23607 q^{73} +2.47214 q^{74} -0.618034 q^{75} +4.85410 q^{76} +6.23607 q^{77} -2.52786 q^{78} -10.4721 q^{79} -1.00000 q^{80} +5.70820 q^{81} -12.3262 q^{82} -10.9443 q^{83} +1.00000 q^{84} -5.09017 q^{85} +2.94427 q^{87} -3.85410 q^{88} +1.52786 q^{89} +2.61803 q^{90} -6.61803 q^{91} +1.29180 q^{93} +9.70820 q^{94} -4.85410 q^{95} -0.618034 q^{96} -14.6180 q^{97} -4.38197 q^{98} +10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} + q^{6} - q^{7} + 2 q^{8} - 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 3 q^{13} - q^{14} - q^{15} + 2 q^{16} - q^{17} - 3 q^{18} + 3 q^{19} - 2 q^{20} + 2 q^{21} - q^{22} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - q^{28} - 14 q^{29} - q^{30} + 7 q^{31} + 2 q^{32} + 7 q^{33} - q^{34} + q^{35} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 2 q^{40} - 9 q^{41} + 2 q^{42} - q^{44} + 3 q^{45} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} - 13 q^{51} - 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{55} - q^{56} - 6 q^{57} - 14 q^{58} - 10 q^{59} - q^{60} + 3 q^{61} + 7 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{65} + 7 q^{66} - 20 q^{67} - q^{68} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} - 4 q^{74} + q^{75} + 3 q^{76} + 8 q^{77} - 14 q^{78} - 12 q^{79} - 2 q^{80} - 2 q^{81} - 9 q^{82} - 4 q^{83} + 2 q^{84} + q^{85} - 12 q^{87} - q^{88} + 12 q^{89} + 3 q^{90} - 11 q^{91} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} - 27 q^{97} - 11 q^{98} + 9 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.618034 −0.356822 −0.178411 0.983956i \(-0.557096\pi\)
−0.178411 + 0.983956i \(0.557096\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −0.618034 −0.252311
\(7\) −1.61803 −0.611559 −0.305780 0.952102i \(-0.598917\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.61803 −0.872678
\(10\) −1.00000 −0.316228
\(11\) −3.85410 −1.16206 −0.581028 0.813884i \(-0.697349\pi\)
−0.581028 + 0.813884i \(0.697349\pi\)
\(12\) −0.618034 −0.178411
\(13\) 4.09017 1.13441 0.567205 0.823577i \(-0.308025\pi\)
0.567205 + 0.823577i \(0.308025\pi\)
\(14\) −1.61803 −0.432438
\(15\) 0.618034 0.159576
\(16\) 1.00000 0.250000
\(17\) 5.09017 1.23455 0.617274 0.786748i \(-0.288237\pi\)
0.617274 + 0.786748i \(0.288237\pi\)
\(18\) −2.61803 −0.617077
\(19\) 4.85410 1.11361 0.556804 0.830644i \(-0.312028\pi\)
0.556804 + 0.830644i \(0.312028\pi\)
\(20\) −1.00000 −0.223607
\(21\) 1.00000 0.218218
\(22\) −3.85410 −0.821697
\(23\) 0 0
\(24\) −0.618034 −0.126156
\(25\) 1.00000 0.200000
\(26\) 4.09017 0.802148
\(27\) 3.47214 0.668213
\(28\) −1.61803 −0.305780
\(29\) −4.76393 −0.884640 −0.442320 0.896857i \(-0.645844\pi\)
−0.442320 + 0.896857i \(0.645844\pi\)
\(30\) 0.618034 0.112837
\(31\) −2.09017 −0.375406 −0.187703 0.982226i \(-0.560104\pi\)
−0.187703 + 0.982226i \(0.560104\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.38197 0.414647
\(34\) 5.09017 0.872957
\(35\) 1.61803 0.273498
\(36\) −2.61803 −0.436339
\(37\) 2.47214 0.406417 0.203208 0.979136i \(-0.434863\pi\)
0.203208 + 0.979136i \(0.434863\pi\)
\(38\) 4.85410 0.787439
\(39\) −2.52786 −0.404782
\(40\) −1.00000 −0.158114
\(41\) −12.3262 −1.92503 −0.962517 0.271220i \(-0.912573\pi\)
−0.962517 + 0.271220i \(0.912573\pi\)
\(42\) 1.00000 0.154303
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) −3.85410 −0.581028
\(45\) 2.61803 0.390273
\(46\) 0 0
\(47\) 9.70820 1.41609 0.708044 0.706169i \(-0.249578\pi\)
0.708044 + 0.706169i \(0.249578\pi\)
\(48\) −0.618034 −0.0892055
\(49\) −4.38197 −0.625995
\(50\) 1.00000 0.141421
\(51\) −3.14590 −0.440514
\(52\) 4.09017 0.567205
\(53\) 8.47214 1.16374 0.581869 0.813283i \(-0.302322\pi\)
0.581869 + 0.813283i \(0.302322\pi\)
\(54\) 3.47214 0.472498
\(55\) 3.85410 0.519687
\(56\) −1.61803 −0.216219
\(57\) −3.00000 −0.397360
\(58\) −4.76393 −0.625535
\(59\) −11.7082 −1.52428 −0.762139 0.647413i \(-0.775851\pi\)
−0.762139 + 0.647413i \(0.775851\pi\)
\(60\) 0.618034 0.0797878
\(61\) −6.32624 −0.809992 −0.404996 0.914319i \(-0.632727\pi\)
−0.404996 + 0.914319i \(0.632727\pi\)
\(62\) −2.09017 −0.265452
\(63\) 4.23607 0.533694
\(64\) 1.00000 0.125000
\(65\) −4.09017 −0.507323
\(66\) 2.38197 0.293200
\(67\) −5.52786 −0.675336 −0.337668 0.941265i \(-0.609638\pi\)
−0.337668 + 0.941265i \(0.609638\pi\)
\(68\) 5.09017 0.617274
\(69\) 0 0
\(70\) 1.61803 0.193392
\(71\) 7.09017 0.841448 0.420724 0.907189i \(-0.361776\pi\)
0.420724 + 0.907189i \(0.361776\pi\)
\(72\) −2.61803 −0.308538
\(73\) −1.23607 −0.144671 −0.0723354 0.997380i \(-0.523045\pi\)
−0.0723354 + 0.997380i \(0.523045\pi\)
\(74\) 2.47214 0.287380
\(75\) −0.618034 −0.0713644
\(76\) 4.85410 0.556804
\(77\) 6.23607 0.710666
\(78\) −2.52786 −0.286224
\(79\) −10.4721 −1.17821 −0.589104 0.808057i \(-0.700519\pi\)
−0.589104 + 0.808057i \(0.700519\pi\)
\(80\) −1.00000 −0.111803
\(81\) 5.70820 0.634245
\(82\) −12.3262 −1.36121
\(83\) −10.9443 −1.20129 −0.600645 0.799516i \(-0.705089\pi\)
−0.600645 + 0.799516i \(0.705089\pi\)
\(84\) 1.00000 0.109109
\(85\) −5.09017 −0.552106
\(86\) 0 0
\(87\) 2.94427 0.315659
\(88\) −3.85410 −0.410849
\(89\) 1.52786 0.161953 0.0809766 0.996716i \(-0.474196\pi\)
0.0809766 + 0.996716i \(0.474196\pi\)
\(90\) 2.61803 0.275965
\(91\) −6.61803 −0.693758
\(92\) 0 0
\(93\) 1.29180 0.133953
\(94\) 9.70820 1.00132
\(95\) −4.85410 −0.498020
\(96\) −0.618034 −0.0630778
\(97\) −14.6180 −1.48424 −0.742118 0.670269i \(-0.766179\pi\)
−0.742118 + 0.670269i \(0.766179\pi\)
\(98\) −4.38197 −0.442645
\(99\) 10.0902 1.01410
\(100\) 1.00000 0.100000
\(101\) −13.7082 −1.36402 −0.682009 0.731344i \(-0.738893\pi\)
−0.682009 + 0.731344i \(0.738893\pi\)
\(102\) −3.14590 −0.311490
\(103\) 3.56231 0.351004 0.175502 0.984479i \(-0.443845\pi\)
0.175502 + 0.984479i \(0.443845\pi\)
\(104\) 4.09017 0.401074
\(105\) −1.00000 −0.0975900
\(106\) 8.47214 0.822887
\(107\) 4.18034 0.404129 0.202064 0.979372i \(-0.435235\pi\)
0.202064 + 0.979372i \(0.435235\pi\)
\(108\) 3.47214 0.334106
\(109\) −8.56231 −0.820120 −0.410060 0.912059i \(-0.634492\pi\)
−0.410060 + 0.912059i \(0.634492\pi\)
\(110\) 3.85410 0.367474
\(111\) −1.52786 −0.145018
\(112\) −1.61803 −0.152890
\(113\) −18.9443 −1.78213 −0.891064 0.453878i \(-0.850040\pi\)
−0.891064 + 0.453878i \(0.850040\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) −4.76393 −0.442320
\(117\) −10.7082 −0.989974
\(118\) −11.7082 −1.07783
\(119\) −8.23607 −0.754999
\(120\) 0.618034 0.0564185
\(121\) 3.85410 0.350373
\(122\) −6.32624 −0.572751
\(123\) 7.61803 0.686895
\(124\) −2.09017 −0.187703
\(125\) −1.00000 −0.0894427
\(126\) 4.23607 0.377379
\(127\) −6.18034 −0.548416 −0.274208 0.961670i \(-0.588416\pi\)
−0.274208 + 0.961670i \(0.588416\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −4.09017 −0.358732
\(131\) −14.9443 −1.30569 −0.652844 0.757493i \(-0.726424\pi\)
−0.652844 + 0.757493i \(0.726424\pi\)
\(132\) 2.38197 0.207324
\(133\) −7.85410 −0.681037
\(134\) −5.52786 −0.477535
\(135\) −3.47214 −0.298834
\(136\) 5.09017 0.436478
\(137\) −5.32624 −0.455051 −0.227526 0.973772i \(-0.573064\pi\)
−0.227526 + 0.973772i \(0.573064\pi\)
\(138\) 0 0
\(139\) 17.2361 1.46194 0.730972 0.682407i \(-0.239067\pi\)
0.730972 + 0.682407i \(0.239067\pi\)
\(140\) 1.61803 0.136749
\(141\) −6.00000 −0.505291
\(142\) 7.09017 0.594994
\(143\) −15.7639 −1.31825
\(144\) −2.61803 −0.218169
\(145\) 4.76393 0.395623
\(146\) −1.23607 −0.102298
\(147\) 2.70820 0.223369
\(148\) 2.47214 0.203208
\(149\) 1.14590 0.0938756 0.0469378 0.998898i \(-0.485054\pi\)
0.0469378 + 0.998898i \(0.485054\pi\)
\(150\) −0.618034 −0.0504623
\(151\) 17.5623 1.42920 0.714600 0.699533i \(-0.246609\pi\)
0.714600 + 0.699533i \(0.246609\pi\)
\(152\) 4.85410 0.393720
\(153\) −13.3262 −1.07736
\(154\) 6.23607 0.502517
\(155\) 2.09017 0.167886
\(156\) −2.52786 −0.202391
\(157\) −9.70820 −0.774799 −0.387400 0.921912i \(-0.626627\pi\)
−0.387400 + 0.921912i \(0.626627\pi\)
\(158\) −10.4721 −0.833118
\(159\) −5.23607 −0.415247
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 5.70820 0.448479
\(163\) 3.61803 0.283386 0.141693 0.989911i \(-0.454745\pi\)
0.141693 + 0.989911i \(0.454745\pi\)
\(164\) −12.3262 −0.962517
\(165\) −2.38197 −0.185436
\(166\) −10.9443 −0.849440
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 1.00000 0.0771517
\(169\) 3.72949 0.286884
\(170\) −5.09017 −0.390398
\(171\) −12.7082 −0.971821
\(172\) 0 0
\(173\) −21.5623 −1.63935 −0.819676 0.572828i \(-0.805846\pi\)
−0.819676 + 0.572828i \(0.805846\pi\)
\(174\) 2.94427 0.223205
\(175\) −1.61803 −0.122312
\(176\) −3.85410 −0.290514
\(177\) 7.23607 0.543896
\(178\) 1.52786 0.114518
\(179\) −20.1803 −1.50835 −0.754175 0.656674i \(-0.771963\pi\)
−0.754175 + 0.656674i \(0.771963\pi\)
\(180\) 2.61803 0.195137
\(181\) 18.8541 1.40141 0.700707 0.713449i \(-0.252868\pi\)
0.700707 + 0.713449i \(0.252868\pi\)
\(182\) −6.61803 −0.490561
\(183\) 3.90983 0.289023
\(184\) 0 0
\(185\) −2.47214 −0.181755
\(186\) 1.29180 0.0947191
\(187\) −19.6180 −1.43461
\(188\) 9.70820 0.708044
\(189\) −5.61803 −0.408652
\(190\) −4.85410 −0.352154
\(191\) 0.291796 0.0211136 0.0105568 0.999944i \(-0.496640\pi\)
0.0105568 + 0.999944i \(0.496640\pi\)
\(192\) −0.618034 −0.0446028
\(193\) 5.23607 0.376900 0.188450 0.982083i \(-0.439654\pi\)
0.188450 + 0.982083i \(0.439654\pi\)
\(194\) −14.6180 −1.04951
\(195\) 2.52786 0.181024
\(196\) −4.38197 −0.312998
\(197\) −2.43769 −0.173679 −0.0868393 0.996222i \(-0.527677\pi\)
−0.0868393 + 0.996222i \(0.527677\pi\)
\(198\) 10.0902 0.717077
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 1.00000 0.0707107
\(201\) 3.41641 0.240975
\(202\) −13.7082 −0.964506
\(203\) 7.70820 0.541010
\(204\) −3.14590 −0.220257
\(205\) 12.3262 0.860902
\(206\) 3.56231 0.248198
\(207\) 0 0
\(208\) 4.09017 0.283602
\(209\) −18.7082 −1.29407
\(210\) −1.00000 −0.0690066
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 8.47214 0.581869
\(213\) −4.38197 −0.300247
\(214\) 4.18034 0.285762
\(215\) 0 0
\(216\) 3.47214 0.236249
\(217\) 3.38197 0.229583
\(218\) −8.56231 −0.579913
\(219\) 0.763932 0.0516217
\(220\) 3.85410 0.259844
\(221\) 20.8197 1.40048
\(222\) −1.52786 −0.102544
\(223\) −3.05573 −0.204627 −0.102313 0.994752i \(-0.532624\pi\)
−0.102313 + 0.994752i \(0.532624\pi\)
\(224\) −1.61803 −0.108109
\(225\) −2.61803 −0.174536
\(226\) −18.9443 −1.26015
\(227\) 23.2361 1.54223 0.771116 0.636695i \(-0.219699\pi\)
0.771116 + 0.636695i \(0.219699\pi\)
\(228\) −3.00000 −0.198680
\(229\) −10.0000 −0.660819 −0.330409 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) −3.85410 −0.253581
\(232\) −4.76393 −0.312767
\(233\) 19.7082 1.29113 0.645564 0.763706i \(-0.276622\pi\)
0.645564 + 0.763706i \(0.276622\pi\)
\(234\) −10.7082 −0.700017
\(235\) −9.70820 −0.633293
\(236\) −11.7082 −0.762139
\(237\) 6.47214 0.420410
\(238\) −8.23607 −0.533865
\(239\) 24.3607 1.57576 0.787881 0.615828i \(-0.211178\pi\)
0.787881 + 0.615828i \(0.211178\pi\)
\(240\) 0.618034 0.0398939
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 3.85410 0.247751
\(243\) −13.9443 −0.894525
\(244\) −6.32624 −0.404996
\(245\) 4.38197 0.279954
\(246\) 7.61803 0.485708
\(247\) 19.8541 1.26329
\(248\) −2.09017 −0.132726
\(249\) 6.76393 0.428647
\(250\) −1.00000 −0.0632456
\(251\) −12.8541 −0.811344 −0.405672 0.914019i \(-0.632962\pi\)
−0.405672 + 0.914019i \(0.632962\pi\)
\(252\) 4.23607 0.266847
\(253\) 0 0
\(254\) −6.18034 −0.387789
\(255\) 3.14590 0.197004
\(256\) 1.00000 0.0625000
\(257\) −30.1803 −1.88260 −0.941299 0.337574i \(-0.890394\pi\)
−0.941299 + 0.337574i \(0.890394\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) −4.09017 −0.253662
\(261\) 12.4721 0.772006
\(262\) −14.9443 −0.923260
\(263\) 21.7426 1.34071 0.670354 0.742041i \(-0.266142\pi\)
0.670354 + 0.742041i \(0.266142\pi\)
\(264\) 2.38197 0.146600
\(265\) −8.47214 −0.520439
\(266\) −7.85410 −0.481566
\(267\) −0.944272 −0.0577885
\(268\) −5.52786 −0.337668
\(269\) 8.18034 0.498764 0.249382 0.968405i \(-0.419773\pi\)
0.249382 + 0.968405i \(0.419773\pi\)
\(270\) −3.47214 −0.211307
\(271\) −14.6738 −0.891368 −0.445684 0.895190i \(-0.647039\pi\)
−0.445684 + 0.895190i \(0.647039\pi\)
\(272\) 5.09017 0.308637
\(273\) 4.09017 0.247548
\(274\) −5.32624 −0.321770
\(275\) −3.85410 −0.232411
\(276\) 0 0
\(277\) 2.58359 0.155233 0.0776165 0.996983i \(-0.475269\pi\)
0.0776165 + 0.996983i \(0.475269\pi\)
\(278\) 17.2361 1.03375
\(279\) 5.47214 0.327608
\(280\) 1.61803 0.0966960
\(281\) −27.2361 −1.62477 −0.812384 0.583123i \(-0.801831\pi\)
−0.812384 + 0.583123i \(0.801831\pi\)
\(282\) −6.00000 −0.357295
\(283\) 9.05573 0.538307 0.269154 0.963097i \(-0.413256\pi\)
0.269154 + 0.963097i \(0.413256\pi\)
\(284\) 7.09017 0.420724
\(285\) 3.00000 0.177705
\(286\) −15.7639 −0.932141
\(287\) 19.9443 1.17727
\(288\) −2.61803 −0.154269
\(289\) 8.90983 0.524108
\(290\) 4.76393 0.279748
\(291\) 9.03444 0.529608
\(292\) −1.23607 −0.0723354
\(293\) −15.8885 −0.928219 −0.464109 0.885778i \(-0.653626\pi\)
−0.464109 + 0.885778i \(0.653626\pi\)
\(294\) 2.70820 0.157946
\(295\) 11.7082 0.681678
\(296\) 2.47214 0.143690
\(297\) −13.3820 −0.776500
\(298\) 1.14590 0.0663801
\(299\) 0 0
\(300\) −0.618034 −0.0356822
\(301\) 0 0
\(302\) 17.5623 1.01060
\(303\) 8.47214 0.486711
\(304\) 4.85410 0.278402
\(305\) 6.32624 0.362239
\(306\) −13.3262 −0.761810
\(307\) 27.4508 1.56670 0.783351 0.621579i \(-0.213509\pi\)
0.783351 + 0.621579i \(0.213509\pi\)
\(308\) 6.23607 0.355333
\(309\) −2.20163 −0.125246
\(310\) 2.09017 0.118714
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) −2.52786 −0.143112
\(313\) 11.7984 0.666884 0.333442 0.942771i \(-0.391790\pi\)
0.333442 + 0.942771i \(0.391790\pi\)
\(314\) −9.70820 −0.547866
\(315\) −4.23607 −0.238675
\(316\) −10.4721 −0.589104
\(317\) 0.0901699 0.00506445 0.00253222 0.999997i \(-0.499194\pi\)
0.00253222 + 0.999997i \(0.499194\pi\)
\(318\) −5.23607 −0.293624
\(319\) 18.3607 1.02800
\(320\) −1.00000 −0.0559017
\(321\) −2.58359 −0.144202
\(322\) 0 0
\(323\) 24.7082 1.37480
\(324\) 5.70820 0.317122
\(325\) 4.09017 0.226882
\(326\) 3.61803 0.200384
\(327\) 5.29180 0.292637
\(328\) −12.3262 −0.680603
\(329\) −15.7082 −0.866021
\(330\) −2.38197 −0.131123
\(331\) 14.7639 0.811499 0.405750 0.913984i \(-0.367011\pi\)
0.405750 + 0.913984i \(0.367011\pi\)
\(332\) −10.9443 −0.600645
\(333\) −6.47214 −0.354671
\(334\) −8.00000 −0.437741
\(335\) 5.52786 0.302019
\(336\) 1.00000 0.0545545
\(337\) −29.3262 −1.59750 −0.798751 0.601662i \(-0.794506\pi\)
−0.798751 + 0.601662i \(0.794506\pi\)
\(338\) 3.72949 0.202858
\(339\) 11.7082 0.635902
\(340\) −5.09017 −0.276053
\(341\) 8.05573 0.436242
\(342\) −12.7082 −0.687181
\(343\) 18.4164 0.994393
\(344\) 0 0
\(345\) 0 0
\(346\) −21.5623 −1.15920
\(347\) −8.61803 −0.462640 −0.231320 0.972878i \(-0.574304\pi\)
−0.231320 + 0.972878i \(0.574304\pi\)
\(348\) 2.94427 0.157830
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) −1.61803 −0.0864876
\(351\) 14.2016 0.758027
\(352\) −3.85410 −0.205424
\(353\) 24.0000 1.27739 0.638696 0.769460i \(-0.279474\pi\)
0.638696 + 0.769460i \(0.279474\pi\)
\(354\) 7.23607 0.384593
\(355\) −7.09017 −0.376307
\(356\) 1.52786 0.0809766
\(357\) 5.09017 0.269400
\(358\) −20.1803 −1.06656
\(359\) 18.3607 0.969040 0.484520 0.874780i \(-0.338994\pi\)
0.484520 + 0.874780i \(0.338994\pi\)
\(360\) 2.61803 0.137983
\(361\) 4.56231 0.240121
\(362\) 18.8541 0.990950
\(363\) −2.38197 −0.125021
\(364\) −6.61803 −0.346879
\(365\) 1.23607 0.0646988
\(366\) 3.90983 0.204370
\(367\) 2.47214 0.129044 0.0645222 0.997916i \(-0.479448\pi\)
0.0645222 + 0.997916i \(0.479448\pi\)
\(368\) 0 0
\(369\) 32.2705 1.67994
\(370\) −2.47214 −0.128520
\(371\) −13.7082 −0.711694
\(372\) 1.29180 0.0669765
\(373\) 2.18034 0.112894 0.0564469 0.998406i \(-0.482023\pi\)
0.0564469 + 0.998406i \(0.482023\pi\)
\(374\) −19.6180 −1.01442
\(375\) 0.618034 0.0319151
\(376\) 9.70820 0.500662
\(377\) −19.4853 −1.00354
\(378\) −5.61803 −0.288960
\(379\) −33.4508 −1.71825 −0.859127 0.511762i \(-0.828993\pi\)
−0.859127 + 0.511762i \(0.828993\pi\)
\(380\) −4.85410 −0.249010
\(381\) 3.81966 0.195687
\(382\) 0.291796 0.0149296
\(383\) −17.8885 −0.914062 −0.457031 0.889451i \(-0.651087\pi\)
−0.457031 + 0.889451i \(0.651087\pi\)
\(384\) −0.618034 −0.0315389
\(385\) −6.23607 −0.317819
\(386\) 5.23607 0.266509
\(387\) 0 0
\(388\) −14.6180 −0.742118
\(389\) −5.67376 −0.287671 −0.143836 0.989602i \(-0.545944\pi\)
−0.143836 + 0.989602i \(0.545944\pi\)
\(390\) 2.52786 0.128003
\(391\) 0 0
\(392\) −4.38197 −0.221323
\(393\) 9.23607 0.465898
\(394\) −2.43769 −0.122809
\(395\) 10.4721 0.526910
\(396\) 10.0902 0.507050
\(397\) −8.32624 −0.417882 −0.208941 0.977928i \(-0.567002\pi\)
−0.208941 + 0.977928i \(0.567002\pi\)
\(398\) −2.00000 −0.100251
\(399\) 4.85410 0.243009
\(400\) 1.00000 0.0500000
\(401\) −11.7082 −0.584680 −0.292340 0.956314i \(-0.594434\pi\)
−0.292340 + 0.956314i \(0.594434\pi\)
\(402\) 3.41641 0.170395
\(403\) −8.54915 −0.425864
\(404\) −13.7082 −0.682009
\(405\) −5.70820 −0.283643
\(406\) 7.70820 0.382552
\(407\) −9.52786 −0.472279
\(408\) −3.14590 −0.155745
\(409\) 21.2148 1.04900 0.524502 0.851409i \(-0.324252\pi\)
0.524502 + 0.851409i \(0.324252\pi\)
\(410\) 12.3262 0.608750
\(411\) 3.29180 0.162372
\(412\) 3.56231 0.175502
\(413\) 18.9443 0.932187
\(414\) 0 0
\(415\) 10.9443 0.537233
\(416\) 4.09017 0.200537
\(417\) −10.6525 −0.521654
\(418\) −18.7082 −0.915048
\(419\) −5.52786 −0.270054 −0.135027 0.990842i \(-0.543112\pi\)
−0.135027 + 0.990842i \(0.543112\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 28.7426 1.40083 0.700415 0.713735i \(-0.252998\pi\)
0.700415 + 0.713735i \(0.252998\pi\)
\(422\) 14.0000 0.681509
\(423\) −25.4164 −1.23579
\(424\) 8.47214 0.411443
\(425\) 5.09017 0.246910
\(426\) −4.38197 −0.212307
\(427\) 10.2361 0.495358
\(428\) 4.18034 0.202064
\(429\) 9.74265 0.470379
\(430\) 0 0
\(431\) −34.6525 −1.66915 −0.834576 0.550894i \(-0.814287\pi\)
−0.834576 + 0.550894i \(0.814287\pi\)
\(432\) 3.47214 0.167053
\(433\) 29.5066 1.41800 0.708998 0.705211i \(-0.249148\pi\)
0.708998 + 0.705211i \(0.249148\pi\)
\(434\) 3.38197 0.162340
\(435\) −2.94427 −0.141167
\(436\) −8.56231 −0.410060
\(437\) 0 0
\(438\) 0.763932 0.0365021
\(439\) −15.6180 −0.745408 −0.372704 0.927950i \(-0.621569\pi\)
−0.372704 + 0.927950i \(0.621569\pi\)
\(440\) 3.85410 0.183737
\(441\) 11.4721 0.546292
\(442\) 20.8197 0.990290
\(443\) 13.9098 0.660876 0.330438 0.943828i \(-0.392804\pi\)
0.330438 + 0.943828i \(0.392804\pi\)
\(444\) −1.52786 −0.0725092
\(445\) −1.52786 −0.0724277
\(446\) −3.05573 −0.144693
\(447\) −0.708204 −0.0334969
\(448\) −1.61803 −0.0764449
\(449\) 18.5623 0.876009 0.438005 0.898973i \(-0.355685\pi\)
0.438005 + 0.898973i \(0.355685\pi\)
\(450\) −2.61803 −0.123415
\(451\) 47.5066 2.23700
\(452\) −18.9443 −0.891064
\(453\) −10.8541 −0.509970
\(454\) 23.2361 1.09052
\(455\) 6.61803 0.310258
\(456\) −3.00000 −0.140488
\(457\) −33.7771 −1.58003 −0.790013 0.613090i \(-0.789926\pi\)
−0.790013 + 0.613090i \(0.789926\pi\)
\(458\) −10.0000 −0.467269
\(459\) 17.6738 0.824941
\(460\) 0 0
\(461\) −34.7639 −1.61912 −0.809559 0.587039i \(-0.800294\pi\)
−0.809559 + 0.587039i \(0.800294\pi\)
\(462\) −3.85410 −0.179309
\(463\) 2.00000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) −4.76393 −0.221160
\(465\) −1.29180 −0.0599056
\(466\) 19.7082 0.912965
\(467\) −23.1246 −1.07008 −0.535040 0.844827i \(-0.679703\pi\)
−0.535040 + 0.844827i \(0.679703\pi\)
\(468\) −10.7082 −0.494987
\(469\) 8.94427 0.413008
\(470\) −9.70820 −0.447806
\(471\) 6.00000 0.276465
\(472\) −11.7082 −0.538914
\(473\) 0 0
\(474\) 6.47214 0.297275
\(475\) 4.85410 0.222721
\(476\) −8.23607 −0.377500
\(477\) −22.1803 −1.01557
\(478\) 24.3607 1.11423
\(479\) −3.88854 −0.177672 −0.0888361 0.996046i \(-0.528315\pi\)
−0.0888361 + 0.996046i \(0.528315\pi\)
\(480\) 0.618034 0.0282093
\(481\) 10.1115 0.461043
\(482\) 0 0
\(483\) 0 0
\(484\) 3.85410 0.175186
\(485\) 14.6180 0.663771
\(486\) −13.9443 −0.632525
\(487\) −42.1803 −1.91137 −0.955687 0.294385i \(-0.904885\pi\)
−0.955687 + 0.294385i \(0.904885\pi\)
\(488\) −6.32624 −0.286375
\(489\) −2.23607 −0.101118
\(490\) 4.38197 0.197957
\(491\) −16.1803 −0.730209 −0.365104 0.930967i \(-0.618967\pi\)
−0.365104 + 0.930967i \(0.618967\pi\)
\(492\) 7.61803 0.343447
\(493\) −24.2492 −1.09213
\(494\) 19.8541 0.893278
\(495\) −10.0902 −0.453519
\(496\) −2.09017 −0.0938514
\(497\) −11.4721 −0.514596
\(498\) 6.76393 0.303099
\(499\) −32.3607 −1.44866 −0.724331 0.689452i \(-0.757851\pi\)
−0.724331 + 0.689452i \(0.757851\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 4.94427 0.220894
\(502\) −12.8541 −0.573707
\(503\) −20.6738 −0.921797 −0.460899 0.887453i \(-0.652473\pi\)
−0.460899 + 0.887453i \(0.652473\pi\)
\(504\) 4.23607 0.188689
\(505\) 13.7082 0.610007
\(506\) 0 0
\(507\) −2.30495 −0.102366
\(508\) −6.18034 −0.274208
\(509\) 5.34752 0.237025 0.118512 0.992953i \(-0.462187\pi\)
0.118512 + 0.992953i \(0.462187\pi\)
\(510\) 3.14590 0.139303
\(511\) 2.00000 0.0884748
\(512\) 1.00000 0.0441942
\(513\) 16.8541 0.744127
\(514\) −30.1803 −1.33120
\(515\) −3.56231 −0.156974
\(516\) 0 0
\(517\) −37.4164 −1.64557
\(518\) −4.00000 −0.175750
\(519\) 13.3262 0.584957
\(520\) −4.09017 −0.179366
\(521\) 24.4721 1.07214 0.536072 0.844172i \(-0.319908\pi\)
0.536072 + 0.844172i \(0.319908\pi\)
\(522\) 12.4721 0.545891
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) −14.9443 −0.652844
\(525\) 1.00000 0.0436436
\(526\) 21.7426 0.948024
\(527\) −10.6393 −0.463456
\(528\) 2.38197 0.103662
\(529\) 0 0
\(530\) −8.47214 −0.368006
\(531\) 30.6525 1.33020
\(532\) −7.85410 −0.340519
\(533\) −50.4164 −2.18378
\(534\) −0.944272 −0.0408626
\(535\) −4.18034 −0.180732
\(536\) −5.52786 −0.238767
\(537\) 12.4721 0.538212
\(538\) 8.18034 0.352679
\(539\) 16.8885 0.727441
\(540\) −3.47214 −0.149417
\(541\) −30.8328 −1.32561 −0.662803 0.748794i \(-0.730633\pi\)
−0.662803 + 0.748794i \(0.730633\pi\)
\(542\) −14.6738 −0.630292
\(543\) −11.6525 −0.500056
\(544\) 5.09017 0.218239
\(545\) 8.56231 0.366769
\(546\) 4.09017 0.175043
\(547\) −36.9230 −1.57871 −0.789356 0.613935i \(-0.789586\pi\)
−0.789356 + 0.613935i \(0.789586\pi\)
\(548\) −5.32624 −0.227526
\(549\) 16.5623 0.706862
\(550\) −3.85410 −0.164339
\(551\) −23.1246 −0.985142
\(552\) 0 0
\(553\) 16.9443 0.720544
\(554\) 2.58359 0.109766
\(555\) 1.52786 0.0648542
\(556\) 17.2361 0.730972
\(557\) −30.8328 −1.30643 −0.653214 0.757173i \(-0.726580\pi\)
−0.653214 + 0.757173i \(0.726580\pi\)
\(558\) 5.47214 0.231654
\(559\) 0 0
\(560\) 1.61803 0.0683744
\(561\) 12.1246 0.511902
\(562\) −27.2361 −1.14888
\(563\) −21.8885 −0.922492 −0.461246 0.887272i \(-0.652597\pi\)
−0.461246 + 0.887272i \(0.652597\pi\)
\(564\) −6.00000 −0.252646
\(565\) 18.9443 0.796992
\(566\) 9.05573 0.380641
\(567\) −9.23607 −0.387878
\(568\) 7.09017 0.297497
\(569\) 2.00000 0.0838444 0.0419222 0.999121i \(-0.486652\pi\)
0.0419222 + 0.999121i \(0.486652\pi\)
\(570\) 3.00000 0.125656
\(571\) 30.9787 1.29642 0.648209 0.761462i \(-0.275518\pi\)
0.648209 + 0.761462i \(0.275518\pi\)
\(572\) −15.7639 −0.659123
\(573\) −0.180340 −0.00753381
\(574\) 19.9443 0.832458
\(575\) 0 0
\(576\) −2.61803 −0.109085
\(577\) −12.4721 −0.519222 −0.259611 0.965713i \(-0.583594\pi\)
−0.259611 + 0.965713i \(0.583594\pi\)
\(578\) 8.90983 0.370600
\(579\) −3.23607 −0.134486
\(580\) 4.76393 0.197812
\(581\) 17.7082 0.734660
\(582\) 9.03444 0.374490
\(583\) −32.6525 −1.35233
\(584\) −1.23607 −0.0511489
\(585\) 10.7082 0.442730
\(586\) −15.8885 −0.656350
\(587\) 11.3820 0.469784 0.234892 0.972021i \(-0.424526\pi\)
0.234892 + 0.972021i \(0.424526\pi\)
\(588\) 2.70820 0.111684
\(589\) −10.1459 −0.418054
\(590\) 11.7082 0.482019
\(591\) 1.50658 0.0619723
\(592\) 2.47214 0.101604
\(593\) 34.7639 1.42758 0.713792 0.700358i \(-0.246976\pi\)
0.713792 + 0.700358i \(0.246976\pi\)
\(594\) −13.3820 −0.549069
\(595\) 8.23607 0.337646
\(596\) 1.14590 0.0469378
\(597\) 1.23607 0.0505889
\(598\) 0 0
\(599\) −20.6180 −0.842430 −0.421215 0.906961i \(-0.638396\pi\)
−0.421215 + 0.906961i \(0.638396\pi\)
\(600\) −0.618034 −0.0252311
\(601\) 0.270510 0.0110343 0.00551716 0.999985i \(-0.498244\pi\)
0.00551716 + 0.999985i \(0.498244\pi\)
\(602\) 0 0
\(603\) 14.4721 0.589351
\(604\) 17.5623 0.714600
\(605\) −3.85410 −0.156692
\(606\) 8.47214 0.344157
\(607\) 17.5279 0.711434 0.355717 0.934594i \(-0.384237\pi\)
0.355717 + 0.934594i \(0.384237\pi\)
\(608\) 4.85410 0.196860
\(609\) −4.76393 −0.193044
\(610\) 6.32624 0.256142
\(611\) 39.7082 1.60642
\(612\) −13.3262 −0.538681
\(613\) 43.3050 1.74907 0.874535 0.484962i \(-0.161167\pi\)
0.874535 + 0.484962i \(0.161167\pi\)
\(614\) 27.4508 1.10783
\(615\) −7.61803 −0.307189
\(616\) 6.23607 0.251258
\(617\) −22.9098 −0.922315 −0.461158 0.887318i \(-0.652566\pi\)
−0.461158 + 0.887318i \(0.652566\pi\)
\(618\) −2.20163 −0.0885624
\(619\) −21.7984 −0.876151 −0.438075 0.898938i \(-0.644340\pi\)
−0.438075 + 0.898938i \(0.644340\pi\)
\(620\) 2.09017 0.0839432
\(621\) 0 0
\(622\) 4.00000 0.160385
\(623\) −2.47214 −0.0990440
\(624\) −2.52786 −0.101196
\(625\) 1.00000 0.0400000
\(626\) 11.7984 0.471558
\(627\) 11.5623 0.461754
\(628\) −9.70820 −0.387400
\(629\) 12.5836 0.501741
\(630\) −4.23607 −0.168769
\(631\) 16.0689 0.639692 0.319846 0.947470i \(-0.396369\pi\)
0.319846 + 0.947470i \(0.396369\pi\)
\(632\) −10.4721 −0.416559
\(633\) −8.65248 −0.343905
\(634\) 0.0901699 0.00358111
\(635\) 6.18034 0.245259
\(636\) −5.23607 −0.207624
\(637\) −17.9230 −0.710135
\(638\) 18.3607 0.726906
\(639\) −18.5623 −0.734313
\(640\) −1.00000 −0.0395285
\(641\) 44.3607 1.75214 0.876071 0.482183i \(-0.160156\pi\)
0.876071 + 0.482183i \(0.160156\pi\)
\(642\) −2.58359 −0.101966
\(643\) 21.7082 0.856088 0.428044 0.903758i \(-0.359203\pi\)
0.428044 + 0.903758i \(0.359203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 24.7082 0.972131
\(647\) 44.2492 1.73962 0.869808 0.493390i \(-0.164242\pi\)
0.869808 + 0.493390i \(0.164242\pi\)
\(648\) 5.70820 0.224239
\(649\) 45.1246 1.77130
\(650\) 4.09017 0.160430
\(651\) −2.09017 −0.0819202
\(652\) 3.61803 0.141693
\(653\) 21.0344 0.823141 0.411571 0.911378i \(-0.364980\pi\)
0.411571 + 0.911378i \(0.364980\pi\)
\(654\) 5.29180 0.206926
\(655\) 14.9443 0.583921
\(656\) −12.3262 −0.481259
\(657\) 3.23607 0.126251
\(658\) −15.7082 −0.612370
\(659\) −34.2492 −1.33416 −0.667080 0.744986i \(-0.732456\pi\)
−0.667080 + 0.744986i \(0.732456\pi\)
\(660\) −2.38197 −0.0927179
\(661\) −34.3262 −1.33514 −0.667568 0.744549i \(-0.732665\pi\)
−0.667568 + 0.744549i \(0.732665\pi\)
\(662\) 14.7639 0.573817
\(663\) −12.8673 −0.499723
\(664\) −10.9443 −0.424720
\(665\) 7.85410 0.304569
\(666\) −6.47214 −0.250790
\(667\) 0 0
\(668\) −8.00000 −0.309529
\(669\) 1.88854 0.0730153
\(670\) 5.52786 0.213560
\(671\) 24.3820 0.941255
\(672\) 1.00000 0.0385758
\(673\) 6.94427 0.267682 0.133841 0.991003i \(-0.457269\pi\)
0.133841 + 0.991003i \(0.457269\pi\)
\(674\) −29.3262 −1.12960
\(675\) 3.47214 0.133643
\(676\) 3.72949 0.143442
\(677\) 33.0557 1.27043 0.635217 0.772333i \(-0.280910\pi\)
0.635217 + 0.772333i \(0.280910\pi\)
\(678\) 11.7082 0.449651
\(679\) 23.6525 0.907699
\(680\) −5.09017 −0.195199
\(681\) −14.3607 −0.550302
\(682\) 8.05573 0.308470
\(683\) −11.4377 −0.437651 −0.218826 0.975764i \(-0.570223\pi\)
−0.218826 + 0.975764i \(0.570223\pi\)
\(684\) −12.7082 −0.485910
\(685\) 5.32624 0.203505
\(686\) 18.4164 0.703142
\(687\) 6.18034 0.235795
\(688\) 0 0
\(689\) 34.6525 1.32015
\(690\) 0 0
\(691\) −24.7639 −0.942064 −0.471032 0.882116i \(-0.656118\pi\)
−0.471032 + 0.882116i \(0.656118\pi\)
\(692\) −21.5623 −0.819676
\(693\) −16.3262 −0.620182
\(694\) −8.61803 −0.327136
\(695\) −17.2361 −0.653801
\(696\) 2.94427 0.111602
\(697\) −62.7426 −2.37655
\(698\) −2.00000 −0.0757011
\(699\) −12.1803 −0.460703
\(700\) −1.61803 −0.0611559
\(701\) 48.3394 1.82575 0.912877 0.408235i \(-0.133856\pi\)
0.912877 + 0.408235i \(0.133856\pi\)
\(702\) 14.2016 0.536006
\(703\) 12.0000 0.452589
\(704\) −3.85410 −0.145257
\(705\) 6.00000 0.225973
\(706\) 24.0000 0.903252
\(707\) 22.1803 0.834178
\(708\) 7.23607 0.271948
\(709\) 14.9098 0.559950 0.279975 0.960007i \(-0.409674\pi\)
0.279975 + 0.960007i \(0.409674\pi\)
\(710\) −7.09017 −0.266089
\(711\) 27.4164 1.02820
\(712\) 1.52786 0.0572591
\(713\) 0 0
\(714\) 5.09017 0.190495
\(715\) 15.7639 0.589538
\(716\) −20.1803 −0.754175
\(717\) −15.0557 −0.562266
\(718\) 18.3607 0.685214
\(719\) 1.72949 0.0644991 0.0322495 0.999480i \(-0.489733\pi\)
0.0322495 + 0.999480i \(0.489733\pi\)
\(720\) 2.61803 0.0975684
\(721\) −5.76393 −0.214660
\(722\) 4.56231 0.169791
\(723\) 0 0
\(724\) 18.8541 0.700707
\(725\) −4.76393 −0.176928
\(726\) −2.38197 −0.0884031
\(727\) −52.7984 −1.95818 −0.979092 0.203420i \(-0.934794\pi\)
−0.979092 + 0.203420i \(0.934794\pi\)
\(728\) −6.61803 −0.245281
\(729\) −8.50658 −0.315058
\(730\) 1.23607 0.0457489
\(731\) 0 0
\(732\) 3.90983 0.144511
\(733\) 2.58359 0.0954272 0.0477136 0.998861i \(-0.484807\pi\)
0.0477136 + 0.998861i \(0.484807\pi\)
\(734\) 2.47214 0.0912482
\(735\) −2.70820 −0.0998936
\(736\) 0 0
\(737\) 21.3050 0.784778
\(738\) 32.2705 1.18789
\(739\) 21.8885 0.805183 0.402592 0.915380i \(-0.368110\pi\)
0.402592 + 0.915380i \(0.368110\pi\)
\(740\) −2.47214 −0.0908775
\(741\) −12.2705 −0.450768
\(742\) −13.7082 −0.503244
\(743\) 44.6312 1.63736 0.818680 0.574250i \(-0.194706\pi\)
0.818680 + 0.574250i \(0.194706\pi\)
\(744\) 1.29180 0.0473595
\(745\) −1.14590 −0.0419825
\(746\) 2.18034 0.0798279
\(747\) 28.6525 1.04834
\(748\) −19.6180 −0.717306
\(749\) −6.76393 −0.247149
\(750\) 0.618034 0.0225674
\(751\) −29.0132 −1.05871 −0.529353 0.848402i \(-0.677565\pi\)
−0.529353 + 0.848402i \(0.677565\pi\)
\(752\) 9.70820 0.354022
\(753\) 7.94427 0.289505
\(754\) −19.4853 −0.709612
\(755\) −17.5623 −0.639158
\(756\) −5.61803 −0.204326
\(757\) −17.8885 −0.650170 −0.325085 0.945685i \(-0.605393\pi\)
−0.325085 + 0.945685i \(0.605393\pi\)
\(758\) −33.4508 −1.21499
\(759\) 0 0
\(760\) −4.85410 −0.176077
\(761\) −35.8673 −1.30019 −0.650094 0.759854i \(-0.725270\pi\)
−0.650094 + 0.759854i \(0.725270\pi\)
\(762\) 3.81966 0.138372
\(763\) 13.8541 0.501552
\(764\) 0.291796 0.0105568
\(765\) 13.3262 0.481811
\(766\) −17.8885 −0.646339
\(767\) −47.8885 −1.72916
\(768\) −0.618034 −0.0223014
\(769\) 33.4164 1.20503 0.602513 0.798109i \(-0.294166\pi\)
0.602513 + 0.798109i \(0.294166\pi\)
\(770\) −6.23607 −0.224732
\(771\) 18.6525 0.671753
\(772\) 5.23607 0.188450
\(773\) −11.0557 −0.397647 −0.198823 0.980035i \(-0.563712\pi\)
−0.198823 + 0.980035i \(0.563712\pi\)
\(774\) 0 0
\(775\) −2.09017 −0.0750811
\(776\) −14.6180 −0.524757
\(777\) 2.47214 0.0886874
\(778\) −5.67376 −0.203414
\(779\) −59.8328 −2.14373
\(780\) 2.52786 0.0905121
\(781\) −27.3262 −0.977810
\(782\) 0 0
\(783\) −16.5410 −0.591128
\(784\) −4.38197 −0.156499
\(785\) 9.70820 0.346501
\(786\) 9.23607 0.329440
\(787\) 43.1246 1.53723 0.768613 0.639714i \(-0.220947\pi\)
0.768613 + 0.639714i \(0.220947\pi\)
\(788\) −2.43769 −0.0868393
\(789\) −13.4377 −0.478395
\(790\) 10.4721 0.372582
\(791\) 30.6525 1.08988
\(792\) 10.0902 0.358539
\(793\) −25.8754 −0.918862
\(794\) −8.32624 −0.295487
\(795\) 5.23607 0.185704
\(796\) −2.00000 −0.0708881
\(797\) −0.291796 −0.0103359 −0.00516797 0.999987i \(-0.501645\pi\)
−0.00516797 + 0.999987i \(0.501645\pi\)
\(798\) 4.85410 0.171833
\(799\) 49.4164 1.74823
\(800\) 1.00000 0.0353553
\(801\) −4.00000 −0.141333
\(802\) −11.7082 −0.413431
\(803\) 4.76393 0.168116
\(804\) 3.41641 0.120487
\(805\) 0 0
\(806\) −8.54915 −0.301131
\(807\) −5.05573 −0.177970
\(808\) −13.7082 −0.482253
\(809\) −4.25735 −0.149681 −0.0748403 0.997196i \(-0.523845\pi\)
−0.0748403 + 0.997196i \(0.523845\pi\)
\(810\) −5.70820 −0.200566
\(811\) 44.1803 1.55138 0.775691 0.631113i \(-0.217402\pi\)
0.775691 + 0.631113i \(0.217402\pi\)
\(812\) 7.70820 0.270505
\(813\) 9.06888 0.318060
\(814\) −9.52786 −0.333951
\(815\) −3.61803 −0.126734
\(816\) −3.14590 −0.110128
\(817\) 0 0
\(818\) 21.2148 0.741757
\(819\) 17.3262 0.605428
\(820\) 12.3262 0.430451
\(821\) −50.9443 −1.77797 −0.888984 0.457939i \(-0.848588\pi\)
−0.888984 + 0.457939i \(0.848588\pi\)
\(822\) 3.29180 0.114815
\(823\) −1.41641 −0.0493729 −0.0246864 0.999695i \(-0.507859\pi\)
−0.0246864 + 0.999695i \(0.507859\pi\)
\(824\) 3.56231 0.124099
\(825\) 2.38197 0.0829294
\(826\) 18.9443 0.659156
\(827\) −8.29180 −0.288334 −0.144167 0.989553i \(-0.546050\pi\)
−0.144167 + 0.989553i \(0.546050\pi\)
\(828\) 0 0
\(829\) 1.05573 0.0366670 0.0183335 0.999832i \(-0.494164\pi\)
0.0183335 + 0.999832i \(0.494164\pi\)
\(830\) 10.9443 0.379881
\(831\) −1.59675 −0.0553906
\(832\) 4.09017 0.141801
\(833\) −22.3050 −0.772821
\(834\) −10.6525 −0.368865
\(835\) 8.00000 0.276851
\(836\) −18.7082 −0.647037
\(837\) −7.25735 −0.250851
\(838\) −5.52786 −0.190957
\(839\) 43.0132 1.48498 0.742490 0.669858i \(-0.233645\pi\)
0.742490 + 0.669858i \(0.233645\pi\)
\(840\) −1.00000 −0.0345033
\(841\) −6.30495 −0.217412
\(842\) 28.7426 0.990537
\(843\) 16.8328 0.579753
\(844\) 14.0000 0.481900
\(845\) −3.72949 −0.128298
\(846\) −25.4164 −0.873834
\(847\) −6.23607 −0.214274
\(848\) 8.47214 0.290934
\(849\) −5.59675 −0.192080
\(850\) 5.09017 0.174591
\(851\) 0 0
\(852\) −4.38197 −0.150124
\(853\) 13.7984 0.472447 0.236224 0.971699i \(-0.424090\pi\)
0.236224 + 0.971699i \(0.424090\pi\)
\(854\) 10.2361 0.350271
\(855\) 12.7082 0.434611
\(856\) 4.18034 0.142881
\(857\) −33.4164 −1.14148 −0.570741 0.821130i \(-0.693344\pi\)
−0.570741 + 0.821130i \(0.693344\pi\)
\(858\) 9.74265 0.332608
\(859\) 34.0689 1.16242 0.581208 0.813755i \(-0.302580\pi\)
0.581208 + 0.813755i \(0.302580\pi\)
\(860\) 0 0
\(861\) −12.3262 −0.420077
\(862\) −34.6525 −1.18027
\(863\) 37.2361 1.26753 0.633765 0.773525i \(-0.281509\pi\)
0.633765 + 0.773525i \(0.281509\pi\)
\(864\) 3.47214 0.118124
\(865\) 21.5623 0.733140
\(866\) 29.5066 1.00267
\(867\) −5.50658 −0.187013
\(868\) 3.38197 0.114791
\(869\) 40.3607 1.36914
\(870\) −2.94427 −0.0998202
\(871\) −22.6099 −0.766107
\(872\) −8.56231 −0.289956
\(873\) 38.2705 1.29526
\(874\) 0 0
\(875\) 1.61803 0.0546995
\(876\) 0.763932 0.0258109
\(877\) −23.7426 −0.801732 −0.400866 0.916137i \(-0.631291\pi\)
−0.400866 + 0.916137i \(0.631291\pi\)
\(878\) −15.6180 −0.527083
\(879\) 9.81966 0.331209
\(880\) 3.85410 0.129922
\(881\) −35.4164 −1.19321 −0.596605 0.802535i \(-0.703484\pi\)
−0.596605 + 0.802535i \(0.703484\pi\)
\(882\) 11.4721 0.386287
\(883\) −4.56231 −0.153534 −0.0767669 0.997049i \(-0.524460\pi\)
−0.0767669 + 0.997049i \(0.524460\pi\)
\(884\) 20.8197 0.700241
\(885\) −7.23607 −0.243238
\(886\) 13.9098 0.467310
\(887\) −58.8328 −1.97541 −0.987706 0.156321i \(-0.950037\pi\)
−0.987706 + 0.156321i \(0.950037\pi\)
\(888\) −1.52786 −0.0512718
\(889\) 10.0000 0.335389
\(890\) −1.52786 −0.0512141
\(891\) −22.0000 −0.737028
\(892\) −3.05573 −0.102313
\(893\) 47.1246 1.57697
\(894\) −0.708204 −0.0236859
\(895\) 20.1803 0.674554
\(896\) −1.61803 −0.0540547
\(897\) 0 0
\(898\) 18.5623 0.619432
\(899\) 9.95743 0.332099
\(900\) −2.61803 −0.0872678
\(901\) 43.1246 1.43669
\(902\) 47.5066 1.58180
\(903\) 0 0
\(904\) −18.9443 −0.630077
\(905\) −18.8541 −0.626732
\(906\) −10.8541 −0.360603
\(907\) 33.1246 1.09988 0.549942 0.835203i \(-0.314650\pi\)
0.549942 + 0.835203i \(0.314650\pi\)
\(908\) 23.2361 0.771116
\(909\) 35.8885 1.19035
\(910\) 6.61803 0.219386
\(911\) 22.0689 0.731175 0.365587 0.930777i \(-0.380868\pi\)
0.365587 + 0.930777i \(0.380868\pi\)
\(912\) −3.00000 −0.0993399
\(913\) 42.1803 1.39597
\(914\) −33.7771 −1.11725
\(915\) −3.90983 −0.129255
\(916\) −10.0000 −0.330409
\(917\) 24.1803 0.798505
\(918\) 17.6738 0.583321
\(919\) −40.0000 −1.31948 −0.659739 0.751495i \(-0.729333\pi\)
−0.659739 + 0.751495i \(0.729333\pi\)
\(920\) 0 0
\(921\) −16.9656 −0.559034
\(922\) −34.7639 −1.14489
\(923\) 29.0000 0.954547
\(924\) −3.85410 −0.126791
\(925\) 2.47214 0.0812833
\(926\) 2.00000 0.0657241
\(927\) −9.32624 −0.306314
\(928\) −4.76393 −0.156384
\(929\) −12.4721 −0.409198 −0.204599 0.978846i \(-0.565589\pi\)
−0.204599 + 0.978846i \(0.565589\pi\)
\(930\) −1.29180 −0.0423597
\(931\) −21.2705 −0.697113
\(932\) 19.7082 0.645564
\(933\) −2.47214 −0.0809341
\(934\) −23.1246 −0.756660
\(935\) 19.6180 0.641578
\(936\) −10.7082 −0.350009
\(937\) 12.2016 0.398610 0.199305 0.979938i \(-0.436132\pi\)
0.199305 + 0.979938i \(0.436132\pi\)
\(938\) 8.94427 0.292041
\(939\) −7.29180 −0.237959
\(940\) −9.70820 −0.316647
\(941\) 60.5066 1.97246 0.986229 0.165385i \(-0.0528868\pi\)
0.986229 + 0.165385i \(0.0528868\pi\)
\(942\) 6.00000 0.195491
\(943\) 0 0
\(944\) −11.7082 −0.381070
\(945\) 5.61803 0.182755
\(946\) 0 0
\(947\) 5.68692 0.184800 0.0924000 0.995722i \(-0.470546\pi\)
0.0924000 + 0.995722i \(0.470546\pi\)
\(948\) 6.47214 0.210205
\(949\) −5.05573 −0.164116
\(950\) 4.85410 0.157488
\(951\) −0.0557281 −0.00180711
\(952\) −8.23607 −0.266932
\(953\) 20.7984 0.673725 0.336863 0.941554i \(-0.390634\pi\)
0.336863 + 0.941554i \(0.390634\pi\)
\(954\) −22.1803 −0.718115
\(955\) −0.291796 −0.00944230
\(956\) 24.3607 0.787881
\(957\) −11.3475 −0.366813
\(958\) −3.88854 −0.125633
\(959\) 8.61803 0.278291
\(960\) 0.618034 0.0199470
\(961\) −26.6312 −0.859071
\(962\) 10.1115 0.326006
\(963\) −10.9443 −0.352674
\(964\) 0 0
\(965\) −5.23607 −0.168555
\(966\) 0 0
\(967\) 50.5410 1.62529 0.812645 0.582759i \(-0.198027\pi\)
0.812645 + 0.582759i \(0.198027\pi\)
\(968\) 3.85410 0.123876
\(969\) −15.2705 −0.490559
\(970\) 14.6180 0.469357
\(971\) −0.729490 −0.0234105 −0.0117052 0.999931i \(-0.503726\pi\)
−0.0117052 + 0.999931i \(0.503726\pi\)
\(972\) −13.9443 −0.447263
\(973\) −27.8885 −0.894066
\(974\) −42.1803 −1.35155
\(975\) −2.52786 −0.0809564
\(976\) −6.32624 −0.202498
\(977\) 3.43769 0.109982 0.0549908 0.998487i \(-0.482487\pi\)
0.0549908 + 0.998487i \(0.482487\pi\)
\(978\) −2.23607 −0.0715016
\(979\) −5.88854 −0.188199
\(980\) 4.38197 0.139977
\(981\) 22.4164 0.715701
\(982\) −16.1803 −0.516335
\(983\) −19.2705 −0.614634 −0.307317 0.951607i \(-0.599431\pi\)
−0.307317 + 0.951607i \(0.599431\pi\)
\(984\) 7.61803 0.242854
\(985\) 2.43769 0.0776714
\(986\) −24.2492 −0.772253
\(987\) 9.70820 0.309016
\(988\) 19.8541 0.631643
\(989\) 0 0
\(990\) −10.0902 −0.320687
\(991\) −10.5066 −0.333752 −0.166876 0.985978i \(-0.553368\pi\)
−0.166876 + 0.985978i \(0.553368\pi\)
\(992\) −2.09017 −0.0663630
\(993\) −9.12461 −0.289561
\(994\) −11.4721 −0.363874
\(995\) 2.00000 0.0634043
\(996\) 6.76393 0.214323
\(997\) −41.1935 −1.30461 −0.652306 0.757956i \(-0.726198\pi\)
−0.652306 + 0.757956i \(0.726198\pi\)
\(998\) −32.3607 −1.02436
\(999\) 8.58359 0.271573
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 5290.2.a.o.1.1 2
23.22 odd 2 230.2.a.c.1.1 2
69.68 even 2 2070.2.a.u.1.2 2
92.91 even 2 1840.2.a.l.1.2 2
115.22 even 4 1150.2.b.i.599.4 4
115.68 even 4 1150.2.b.i.599.1 4
115.114 odd 2 1150.2.a.j.1.2 2
184.45 odd 2 7360.2.a.bh.1.2 2
184.91 even 2 7360.2.a.bn.1.1 2
460.459 even 2 9200.2.a.bu.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.1 2 23.22 odd 2
1150.2.a.j.1.2 2 115.114 odd 2
1150.2.b.i.599.1 4 115.68 even 4
1150.2.b.i.599.4 4 115.22 even 4
1840.2.a.l.1.2 2 92.91 even 2
2070.2.a.u.1.2 2 69.68 even 2
5290.2.a.o.1.1 2 1.1 even 1 trivial
7360.2.a.bh.1.2 2 184.45 odd 2
7360.2.a.bn.1.1 2 184.91 even 2
9200.2.a.bu.1.1 2 460.459 even 2