Properties

Label 1150.2.a.j.1.2
Level $1150$
Weight $2$
Character 1150.1
Self dual yes
Analytic conductor $9.183$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.18279623245\)
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 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} -0.618034 q^{6} -1.61803 q^{7} -1.00000 q^{8} -2.61803 q^{9} +3.85410 q^{11} +0.618034 q^{12} -4.09017 q^{13} +1.61803 q^{14} +1.00000 q^{16} +5.09017 q^{17} +2.61803 q^{18} -4.85410 q^{19} -1.00000 q^{21} -3.85410 q^{22} -1.00000 q^{23} -0.618034 q^{24} +4.09017 q^{26} -3.47214 q^{27} -1.61803 q^{28} -4.76393 q^{29} -2.09017 q^{31} -1.00000 q^{32} +2.38197 q^{33} -5.09017 q^{34} -2.61803 q^{36} +2.47214 q^{37} +4.85410 q^{38} -2.52786 q^{39} -12.3262 q^{41} +1.00000 q^{42} +3.85410 q^{44} +1.00000 q^{46} -9.70820 q^{47} +0.618034 q^{48} -4.38197 q^{49} +3.14590 q^{51} -4.09017 q^{52} +8.47214 q^{53} +3.47214 q^{54} +1.61803 q^{56} -3.00000 q^{57} +4.76393 q^{58} -11.7082 q^{59} +6.32624 q^{61} +2.09017 q^{62} +4.23607 q^{63} +1.00000 q^{64} -2.38197 q^{66} -5.52786 q^{67} +5.09017 q^{68} -0.618034 q^{69} +7.09017 q^{71} +2.61803 q^{72} +1.23607 q^{73} -2.47214 q^{74} -4.85410 q^{76} -6.23607 q^{77} +2.52786 q^{78} +10.4721 q^{79} +5.70820 q^{81} +12.3262 q^{82} -10.9443 q^{83} -1.00000 q^{84} -2.94427 q^{87} -3.85410 q^{88} -1.52786 q^{89} +6.61803 q^{91} -1.00000 q^{92} -1.29180 q^{93} +9.70820 q^{94} -0.618034 q^{96} -14.6180 q^{97} +4.38197 q^{98} -10.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{6} - q^{7} - 2 q^{8} - 3 q^{9} + q^{11} - q^{12} + 3 q^{13} + q^{14} + 2 q^{16} - q^{17} + 3 q^{18} - 3 q^{19} - 2 q^{21} - q^{22} - 2 q^{23} + q^{24} - 3 q^{26} + 2 q^{27} - q^{28} - 14 q^{29} + 7 q^{31} - 2 q^{32} + 7 q^{33} + q^{34} - 3 q^{36} - 4 q^{37} + 3 q^{38} - 14 q^{39} - 9 q^{41} + 2 q^{42} + q^{44} + 2 q^{46} - 6 q^{47} - q^{48} - 11 q^{49} + 13 q^{51} + 3 q^{52} + 8 q^{53} - 2 q^{54} + q^{56} - 6 q^{57} + 14 q^{58} - 10 q^{59} - 3 q^{61} - 7 q^{62} + 4 q^{63} + 2 q^{64} - 7 q^{66} - 20 q^{67} - q^{68} + q^{69} + 3 q^{71} + 3 q^{72} - 2 q^{73} + 4 q^{74} - 3 q^{76} - 8 q^{77} + 14 q^{78} + 12 q^{79} - 2 q^{81} + 9 q^{82} - 4 q^{83} - 2 q^{84} + 12 q^{87} - q^{88} - 12 q^{89} + 11 q^{91} - 2 q^{92} - 16 q^{93} + 6 q^{94} + q^{96} - 27 q^{97} + 11 q^{98} - 9 q^{99} + O(q^{100}) \)

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 \(-0.442904\pi\)
0.178411 + 0.983956i \(0.442904\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −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
\(10\) 0 0
\(11\) 3.85410 1.16206 0.581028 0.813884i \(-0.302651\pi\)
0.581028 + 0.813884i \(0.302651\pi\)
\(12\) 0.618034 0.178411
\(13\) −4.09017 −1.13441 −0.567205 0.823577i \(-0.691975\pi\)
−0.567205 + 0.823577i \(0.691975\pi\)
\(14\) 1.61803 0.432438
\(15\) 0 0
\(16\) 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 \(-0.687972\pi\)
−0.556804 + 0.830644i \(0.687972\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) −3.85410 −0.821697
\(23\) −1.00000 −0.208514
\(24\) −0.618034 −0.126156
\(25\) 0 0
\(26\) 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 0
\(31\) −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
\(35\) 0 0
\(36\) −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
\(40\) 0 0
\(41\) −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
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) −9.70820 −1.41609 −0.708044 0.706169i \(-0.750422\pi\)
−0.708044 + 0.706169i \(0.750422\pi\)
\(48\) 0.618034 0.0892055
\(49\) −4.38197 −0.625995
\(50\) 0 0
\(51\) 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
\(55\) 0 0
\(56\) 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 0
\(61\) 6.32624 0.809992 0.404996 0.914319i \(-0.367273\pi\)
0.404996 + 0.914319i \(0.367273\pi\)
\(62\) 2.09017 0.265452
\(63\) 4.23607 0.533694
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −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
\(69\) −0.618034 −0.0744025
\(70\) 0 0
\(71\) 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 \(-0.476955\pi\)
0.0723354 + 0.997380i \(0.476955\pi\)
\(74\) −2.47214 −0.287380
\(75\) 0 0
\(76\) −4.85410 −0.556804
\(77\) −6.23607 −0.710666
\(78\) 2.52786 0.286224
\(79\) 10.4721 1.17821 0.589104 0.808057i \(-0.299481\pi\)
0.589104 + 0.808057i \(0.299481\pi\)
\(80\) 0 0
\(81\) 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
\(85\) 0 0
\(86\) 0 0
\(87\) −2.94427 −0.315659
\(88\) −3.85410 −0.410849
\(89\) −1.52786 −0.161953 −0.0809766 0.996716i \(-0.525804\pi\)
−0.0809766 + 0.996716i \(0.525804\pi\)
\(90\) 0 0
\(91\) 6.61803 0.693758
\(92\) −1.00000 −0.104257
\(93\) −1.29180 −0.133953
\(94\) 9.70820 1.00132
\(95\) 0 0
\(96\) −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
\(100\) 0 0
\(101\) −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
\(105\) 0 0
\(106\) −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 \(-0.365508\pi\)
0.410060 + 0.912059i \(0.365508\pi\)
\(110\) 0 0
\(111\) 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 0
\(121\) 3.85410 0.350373
\(122\) −6.32624 −0.572751
\(123\) −7.61803 −0.686895
\(124\) −2.09017 −0.187703
\(125\) 0 0
\(126\) −4.23607 −0.377379
\(127\) 6.18034 0.548416 0.274208 0.961670i \(-0.411584\pi\)
0.274208 + 0.961670i \(0.411584\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −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
\(135\) 0 0
\(136\) −5.09017 −0.436478
\(137\) −5.32624 −0.455051 −0.227526 0.973772i \(-0.573064\pi\)
−0.227526 + 0.973772i \(0.573064\pi\)
\(138\) 0.618034 0.0526105
\(139\) 17.2361 1.46194 0.730972 0.682407i \(-0.239067\pi\)
0.730972 + 0.682407i \(0.239067\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −7.09017 −0.594994
\(143\) −15.7639 −1.31825
\(144\) −2.61803 −0.218169
\(145\) 0 0
\(146\) −1.23607 −0.102298
\(147\) −2.70820 −0.223369
\(148\) 2.47214 0.203208
\(149\) −1.14590 −0.0938756 −0.0469378 0.998898i \(-0.514946\pi\)
−0.0469378 + 0.998898i \(0.514946\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) −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
\(160\) 0 0
\(161\) 1.61803 0.127519
\(162\) −5.70820 −0.448479
\(163\) −3.61803 −0.283386 −0.141693 0.989911i \(-0.545255\pi\)
−0.141693 + 0.989911i \(0.545255\pi\)
\(164\) −12.3262 −0.962517
\(165\) 0 0
\(166\) 10.9443 0.849440
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 1.00000 0.0771517
\(169\) 3.72949 0.286884
\(170\) 0 0
\(171\) 12.7082 0.971821
\(172\) 0 0
\(173\) 21.5623 1.63935 0.819676 0.572828i \(-0.194154\pi\)
0.819676 + 0.572828i \(0.194154\pi\)
\(174\) 2.94427 0.223205
\(175\) 0 0
\(176\) 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 \(0.771963\pi\)
\(180\) 0 0
\(181\) −18.8541 −1.40141 −0.700707 0.713449i \(-0.747132\pi\)
−0.700707 + 0.713449i \(0.747132\pi\)
\(182\) −6.61803 −0.490561
\(183\) 3.90983 0.289023
\(184\) 1.00000 0.0737210
\(185\) 0 0
\(186\) 1.29180 0.0947191
\(187\) 19.6180 1.43461
\(188\) −9.70820 −0.708044
\(189\) 5.61803 0.408652
\(190\) 0 0
\(191\) −0.291796 −0.0211136 −0.0105568 0.999944i \(-0.503360\pi\)
−0.0105568 + 0.999944i \(0.503360\pi\)
\(192\) 0.618034 0.0446028
\(193\) −5.23607 −0.376900 −0.188450 0.982083i \(-0.560346\pi\)
−0.188450 + 0.982083i \(0.560346\pi\)
\(194\) 14.6180 1.04951
\(195\) 0 0
\(196\) −4.38197 −0.312998
\(197\) 2.43769 0.173679 0.0868393 0.996222i \(-0.472323\pi\)
0.0868393 + 0.996222i \(0.472323\pi\)
\(198\) 10.0902 0.717077
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 0 0
\(201\) −3.41641 −0.240975
\(202\) 13.7082 0.964506
\(203\) 7.70820 0.541010
\(204\) 3.14590 0.220257
\(205\) 0 0
\(206\) −3.56231 −0.248198
\(207\) 2.61803 0.181966
\(208\) −4.09017 −0.283602
\(209\) −18.7082 −1.29407
\(210\) 0 0
\(211\) 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
\(220\) 0 0
\(221\) −20.8197 −1.40048
\(222\) −1.52786 −0.102544
\(223\) 3.05573 0.204627 0.102313 0.994752i \(-0.467376\pi\)
0.102313 + 0.994752i \(0.467376\pi\)
\(224\) 1.61803 0.108109
\(225\) 0 0
\(226\) 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 \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −3.85410 −0.253581
\(232\) 4.76393 0.312767
\(233\) −19.7082 −1.29113 −0.645564 0.763706i \(-0.723378\pi\)
−0.645564 + 0.763706i \(0.723378\pi\)
\(234\) −10.7082 −0.700017
\(235\) 0 0
\(236\) −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 0
\(241\) 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
\(245\) 0 0
\(246\) 7.61803 0.485708
\(247\) 19.8541 1.26329
\(248\) 2.09017 0.132726
\(249\) −6.76393 −0.428647
\(250\) 0 0
\(251\) 12.8541 0.811344 0.405672 0.914019i \(-0.367038\pi\)
0.405672 + 0.914019i \(0.367038\pi\)
\(252\) 4.23607 0.266847
\(253\) −3.85410 −0.242305
\(254\) −6.18034 −0.387789
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 30.1803 1.88260 0.941299 0.337574i \(-0.109606\pi\)
0.941299 + 0.337574i \(0.109606\pi\)
\(258\) 0 0
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) 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
\(265\) 0 0
\(266\) −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 \(0.419773\pi\)
\(270\) 0 0
\(271\) −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
\(275\) 0 0
\(276\) −0.618034 −0.0372013
\(277\) −2.58359 −0.155233 −0.0776165 0.996983i \(-0.524731\pi\)
−0.0776165 + 0.996983i \(0.524731\pi\)
\(278\) −17.2361 −1.03375
\(279\) 5.47214 0.327608
\(280\) 0 0
\(281\) 27.2361 1.62477 0.812384 0.583123i \(-0.198169\pi\)
0.812384 + 0.583123i \(0.198169\pi\)
\(282\) 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
\(285\) 0 0
\(286\) 15.7639 0.932141
\(287\) 19.9443 1.17727
\(288\) 2.61803 0.154269
\(289\) 8.90983 0.524108
\(290\) 0 0
\(291\) −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
\(295\) 0 0
\(296\) −2.47214 −0.143690
\(297\) −13.3820 −0.776500
\(298\) 1.14590 0.0663801
\(299\) 4.09017 0.236541
\(300\) 0 0
\(301\) 0 0
\(302\) −17.5623 −1.01060
\(303\) −8.47214 −0.486711
\(304\) −4.85410 −0.278402
\(305\) 0 0
\(306\) 13.3262 0.761810
\(307\) −27.4508 −1.56670 −0.783351 0.621579i \(-0.786491\pi\)
−0.783351 + 0.621579i \(0.786491\pi\)
\(308\) −6.23607 −0.355333
\(309\) 2.20163 0.125246
\(310\) 0 0
\(311\) 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
\(315\) 0 0
\(316\) 10.4721 0.589104
\(317\) −0.0901699 −0.00506445 −0.00253222 0.999997i \(-0.500806\pi\)
−0.00253222 + 0.999997i \(0.500806\pi\)
\(318\) −5.23607 −0.293624
\(319\) −18.3607 −1.02800
\(320\) 0 0
\(321\) 2.58359 0.144202
\(322\) −1.61803 −0.0901695
\(323\) −24.7082 −1.37480
\(324\) 5.70820 0.317122
\(325\) 0 0
\(326\) 3.61803 0.200384
\(327\) 5.29180 0.292637
\(328\) 12.3262 0.680603
\(329\) 15.7082 0.866021
\(330\) 0 0
\(331\) 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
\(335\) 0 0
\(336\) −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
\(340\) 0 0
\(341\) −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 \(-0.425696\pi\)
0.231320 + 0.972878i \(0.425696\pi\)
\(348\) −2.94427 −0.157830
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 14.2016 0.758027
\(352\) −3.85410 −0.205424
\(353\) −24.0000 −1.27739 −0.638696 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 7.23607 0.384593
\(355\) 0 0
\(356\) −1.52786 −0.0809766
\(357\) −5.09017 −0.269400
\(358\) 20.1803 1.06656
\(359\) −18.3607 −0.969040 −0.484520 0.874780i \(-0.661006\pi\)
−0.484520 + 0.874780i \(0.661006\pi\)
\(360\) 0 0
\(361\) 4.56231 0.240121
\(362\) 18.8541 0.990950
\(363\) 2.38197 0.125021
\(364\) 6.61803 0.346879
\(365\) 0 0
\(366\) −3.90983 −0.204370
\(367\) 2.47214 0.129044 0.0645222 0.997916i \(-0.479448\pi\)
0.0645222 + 0.997916i \(0.479448\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 32.2705 1.67994
\(370\) 0 0
\(371\) −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 0
\(376\) 9.70820 0.500662
\(377\) 19.4853 1.00354
\(378\) −5.61803 −0.288960
\(379\) 33.4508 1.71825 0.859127 0.511762i \(-0.171007\pi\)
0.859127 + 0.511762i \(0.171007\pi\)
\(380\) 0 0
\(381\) 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
\(385\) 0 0
\(386\) 5.23607 0.266509
\(387\) 0 0
\(388\) −14.6180 −0.742118
\(389\) 5.67376 0.287671 0.143836 0.989602i \(-0.454056\pi\)
0.143836 + 0.989602i \(0.454056\pi\)
\(390\) 0 0
\(391\) −5.09017 −0.257421
\(392\) 4.38197 0.221323
\(393\) −9.23607 −0.465898
\(394\) −2.43769 −0.122809
\(395\) 0 0
\(396\) −10.0902 −0.507050
\(397\) 8.32624 0.417882 0.208941 0.977928i \(-0.432998\pi\)
0.208941 + 0.977928i \(0.432998\pi\)
\(398\) −2.00000 −0.100251
\(399\) 4.85410 0.243009
\(400\) 0 0
\(401\) 11.7082 0.584680 0.292340 0.956314i \(-0.405566\pi\)
0.292340 + 0.956314i \(0.405566\pi\)
\(402\) 3.41641 0.170395
\(403\) 8.54915 0.425864
\(404\) −13.7082 −0.682009
\(405\) 0 0
\(406\) −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 \(0.324252\pi\)
\(410\) 0 0
\(411\) −3.29180 −0.162372
\(412\) 3.56231 0.175502
\(413\) 18.9443 0.932187
\(414\) −2.61803 −0.128669
\(415\) 0 0
\(416\) 4.09017 0.200537
\(417\) 10.6525 0.521654
\(418\) 18.7082 0.915048
\(419\) 5.52786 0.270054 0.135027 0.990842i \(-0.456888\pi\)
0.135027 + 0.990842i \(0.456888\pi\)
\(420\) 0 0
\(421\) −28.7426 −1.40083 −0.700415 0.713735i \(-0.747002\pi\)
−0.700415 + 0.713735i \(0.747002\pi\)
\(422\) −14.0000 −0.681509
\(423\) 25.4164 1.23579
\(424\) −8.47214 −0.411443
\(425\) 0 0
\(426\) −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 \(-0.185713\pi\)
0.834576 + 0.550894i \(0.185713\pi\)
\(432\) −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
\(435\) 0 0
\(436\) 8.56231 0.410060
\(437\) 4.85410 0.232203
\(438\) −0.763932 −0.0365021
\(439\) −15.6180 −0.745408 −0.372704 0.927950i \(-0.621569\pi\)
−0.372704 + 0.927950i \(0.621569\pi\)
\(440\) 0 0
\(441\) 11.4721 0.546292
\(442\) 20.8197 0.990290
\(443\) −13.9098 −0.660876 −0.330438 0.943828i \(-0.607196\pi\)
−0.330438 + 0.943828i \(0.607196\pi\)
\(444\) 1.52786 0.0725092
\(445\) 0 0
\(446\) −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 \(0.355685\pi\)
\(450\) 0 0
\(451\) −47.5066 −2.23700
\(452\) −18.9443 −0.891064
\(453\) 10.8541 0.509970
\(454\) −23.2361 −1.09052
\(455\) 0 0
\(456\) 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 \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) −4.76393 −0.221160
\(465\) 0 0
\(466\) 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
\(470\) 0 0
\(471\) −6.00000 −0.276465
\(472\) 11.7082 0.538914
\(473\) 0 0
\(474\) −6.47214 −0.297275
\(475\) 0 0
\(476\) −8.23607 −0.377500
\(477\) −22.1803 −1.01557
\(478\) −24.3607 −1.11423
\(479\) 3.88854 0.177672 0.0888361 0.996046i \(-0.471685\pi\)
0.0888361 + 0.996046i \(0.471685\pi\)
\(480\) 0 0
\(481\) −10.1115 −0.461043
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 3.85410 0.175186
\(485\) 0 0
\(486\) −13.9443 −0.632525
\(487\) 42.1803 1.91137 0.955687 0.294385i \(-0.0951149\pi\)
0.955687 + 0.294385i \(0.0951149\pi\)
\(488\) −6.32624 −0.286375
\(489\) −2.23607 −0.101118
\(490\) 0 0
\(491\) −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
\(495\) 0 0
\(496\) −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 \(0.757851\pi\)
\(500\) 0 0
\(501\) 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
\(505\) 0 0
\(506\) 3.85410 0.171336
\(507\) 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 \(0.462187\pi\)
\(510\) 0 0
\(511\) −2.00000 −0.0884748
\(512\) −1.00000 −0.0441942
\(513\) 16.8541 0.744127
\(514\) −30.1803 −1.33120
\(515\) 0 0
\(516\) 0 0
\(517\) −37.4164 −1.64557
\(518\) 4.00000 0.175750
\(519\) 13.3262 0.584957
\(520\) 0 0
\(521\) −24.4721 −1.07214 −0.536072 0.844172i \(-0.680092\pi\)
−0.536072 + 0.844172i \(0.680092\pi\)
\(522\) −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
\(525\) 0 0
\(526\) −21.7426 −0.948024
\(527\) −10.6393 −0.463456
\(528\) 2.38197 0.103662
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 30.6525 1.33020
\(532\) 7.85410 0.340519
\(533\) 50.4164 2.18378
\(534\) 0.944272 0.0408626
\(535\) 0 0
\(536\) 5.52786 0.238767
\(537\) −12.4721 −0.538212
\(538\) −8.18034 −0.352679
\(539\) −16.8885 −0.727441
\(540\) 0 0
\(541\) −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
\(545\) 0 0
\(546\) −4.09017 −0.175043
\(547\) 36.9230 1.57871 0.789356 0.613935i \(-0.210414\pi\)
0.789356 + 0.613935i \(0.210414\pi\)
\(548\) −5.32624 −0.227526
\(549\) −16.5623 −0.706862
\(550\) 0 0
\(551\) 23.1246 0.985142
\(552\) 0.618034 0.0263053
\(553\) −16.9443 −0.720544
\(554\) 2.58359 0.109766
\(555\) 0 0
\(556\) 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
\(560\) 0 0
\(561\) 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
\(565\) 0 0
\(566\) −9.05573 −0.380641
\(567\) −9.23607 −0.387878
\(568\) −7.09017 −0.297497
\(569\) −2.00000 −0.0838444 −0.0419222 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) 0 0
\(571\) −30.9787 −1.29642 −0.648209 0.761462i \(-0.724482\pi\)
−0.648209 + 0.761462i \(0.724482\pi\)
\(572\) −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 \(-0.416406\pi\)
0.259611 + 0.965713i \(0.416406\pi\)
\(578\) −8.90983 −0.370600
\(579\) −3.23607 −0.134486
\(580\) 0 0
\(581\) 17.7082 0.734660
\(582\) 9.03444 0.374490
\(583\) 32.6525 1.35233
\(584\) −1.23607 −0.0511489
\(585\) 0 0
\(586\) 15.8885 0.656350
\(587\) −11.3820 −0.469784 −0.234892 0.972021i \(-0.575474\pi\)
−0.234892 + 0.972021i \(0.575474\pi\)
\(588\) −2.70820 −0.111684
\(589\) 10.1459 0.418054
\(590\) 0 0
\(591\) 1.50658 0.0619723
\(592\) 2.47214 0.101604
\(593\) −34.7639 −1.42758 −0.713792 0.700358i \(-0.753024\pi\)
−0.713792 + 0.700358i \(0.753024\pi\)
\(594\) 13.3820 0.549069
\(595\) 0 0
\(596\) −1.14590 −0.0469378
\(597\) 1.23607 0.0505889
\(598\) −4.09017 −0.167259
\(599\) −20.6180 −0.842430 −0.421215 0.906961i \(-0.638396\pi\)
−0.421215 + 0.906961i \(0.638396\pi\)
\(600\) 0 0
\(601\) 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
\(605\) 0 0
\(606\) 8.47214 0.344157
\(607\) −17.5279 −0.711434 −0.355717 0.934594i \(-0.615763\pi\)
−0.355717 + 0.934594i \(0.615763\pi\)
\(608\) 4.85410 0.196860
\(609\) 4.76393 0.193044
\(610\) 0 0
\(611\) 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
\(615\) 0 0
\(616\) 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 \(-0.355660\pi\)
0.438075 + 0.898938i \(0.355660\pi\)
\(620\) 0 0
\(621\) 3.47214 0.139332
\(622\) −4.00000 −0.160385
\(623\) 2.47214 0.0990440
\(624\) −2.52786 −0.101196
\(625\) 0 0
\(626\) −11.7984 −0.471558
\(627\) −11.5623 −0.461754
\(628\) −9.70820 −0.387400
\(629\) 12.5836 0.501741
\(630\) 0 0
\(631\) −16.0689 −0.639692 −0.319846 0.947470i \(-0.603631\pi\)
−0.319846 + 0.947470i \(0.603631\pi\)
\(632\) −10.4721 −0.416559
\(633\) 8.65248 0.343905
\(634\) 0.0901699 0.00358111
\(635\) 0 0
\(636\) 5.23607 0.207624
\(637\) 17.9230 0.710135
\(638\) 18.3607 0.726906
\(639\) −18.5623 −0.734313
\(640\) 0 0
\(641\) −44.3607 −1.75214 −0.876071 0.482183i \(-0.839844\pi\)
−0.876071 + 0.482183i \(0.839844\pi\)
\(642\) −2.58359 −0.101966
\(643\) 21.7082 0.856088 0.428044 0.903758i \(-0.359203\pi\)
0.428044 + 0.903758i \(0.359203\pi\)
\(644\) 1.61803 0.0637595
\(645\) 0 0
\(646\) 24.7082 0.972131
\(647\) −44.2492 −1.73962 −0.869808 0.493390i \(-0.835758\pi\)
−0.869808 + 0.493390i \(0.835758\pi\)
\(648\) −5.70820 −0.224239
\(649\) −45.1246 −1.77130
\(650\) 0 0
\(651\) 2.09017 0.0819202
\(652\) −3.61803 −0.141693
\(653\) −21.0344 −0.823141 −0.411571 0.911378i \(-0.635020\pi\)
−0.411571 + 0.911378i \(0.635020\pi\)
\(654\) −5.29180 −0.206926
\(655\) 0 0
\(656\) −12.3262 −0.481259
\(657\) −3.23607 −0.126251
\(658\) −15.7082 −0.612370
\(659\) 34.2492 1.33416 0.667080 0.744986i \(-0.267544\pi\)
0.667080 + 0.744986i \(0.267544\pi\)
\(660\) 0 0
\(661\) 34.3262 1.33514 0.667568 0.744549i \(-0.267335\pi\)
0.667568 + 0.744549i \(0.267335\pi\)
\(662\) −14.7639 −0.573817
\(663\) −12.8673 −0.499723
\(664\) 10.9443 0.424720
\(665\) 0 0
\(666\) 6.47214 0.250790
\(667\) 4.76393 0.184460
\(668\) 8.00000 0.309529
\(669\) 1.88854 0.0730153
\(670\) 0 0
\(671\) 24.3820 0.941255
\(672\) 1.00000 0.0385758
\(673\) −6.94427 −0.267682 −0.133841 0.991003i \(-0.542731\pi\)
−0.133841 + 0.991003i \(0.542731\pi\)
\(674\) 29.3262 1.12960
\(675\) 0 0
\(676\) 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
\(680\) 0 0
\(681\) 14.3607 0.550302
\(682\) 8.05573 0.308470
\(683\) 11.4377 0.437651 0.218826 0.975764i \(-0.429777\pi\)
0.218826 + 0.975764i \(0.429777\pi\)
\(684\) 12.7082 0.485910
\(685\) 0 0
\(686\) −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
\(695\) 0 0
\(696\) 2.94427 0.111602
\(697\) −62.7426 −2.37655
\(698\) 2.00000 0.0757011
\(699\) −12.1803 −0.460703
\(700\) 0 0
\(701\) −48.3394 −1.82575 −0.912877 0.408235i \(-0.866144\pi\)
−0.912877 + 0.408235i \(0.866144\pi\)
\(702\) −14.2016 −0.536006
\(703\) −12.0000 −0.452589
\(704\) 3.85410 0.145257
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 22.1803 0.834178
\(708\) −7.23607 −0.271948
\(709\) −14.9098 −0.559950 −0.279975 0.960007i \(-0.590326\pi\)
−0.279975 + 0.960007i \(0.590326\pi\)
\(710\) 0 0
\(711\) −27.4164 −1.02820
\(712\) 1.52786 0.0572591
\(713\) 2.09017 0.0782775
\(714\) 5.09017 0.190495
\(715\) 0 0
\(716\) −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 \(0.489733\pi\)
\(720\) 0 0
\(721\) −5.76393 −0.214660
\(722\) −4.56231 −0.169791
\(723\) 0 0
\(724\) −18.8541 −0.700707
\(725\) 0 0
\(726\) −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
\(730\) 0 0
\(731\) 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
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −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 \(0.368110\pi\)
\(740\) 0 0
\(741\) 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
\(745\) 0 0
\(746\) −2.18034 −0.0798279
\(747\) 28.6525 1.04834
\(748\) 19.6180 0.717306
\(749\) −6.76393 −0.247149
\(750\) 0 0
\(751\) 29.0132 1.05871 0.529353 0.848402i \(-0.322435\pi\)
0.529353 + 0.848402i \(0.322435\pi\)
\(752\) −9.70820 −0.354022
\(753\) 7.94427 0.289505
\(754\) −19.4853 −0.709612
\(755\) 0 0
\(756\) 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
\(759\) −2.38197 −0.0864599
\(760\) 0 0
\(761\) −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
\(765\) 0 0
\(766\) 17.8885 0.646339
\(767\) 47.8885 1.72916
\(768\) 0.618034 0.0223014
\(769\) −33.4164 −1.20503 −0.602513 0.798109i \(-0.705834\pi\)
−0.602513 + 0.798109i \(0.705834\pi\)
\(770\) 0 0
\(771\) 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
\(775\) 0 0
\(776\) 14.6180 0.524757
\(777\) −2.47214 −0.0886874
\(778\) −5.67376 −0.203414
\(779\) 59.8328 2.14373
\(780\) 0 0
\(781\) 27.3262 0.977810
\(782\) 5.09017 0.182024
\(783\) 16.5410 0.591128
\(784\) −4.38197 −0.156499
\(785\) 0 0
\(786\) 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
\(790\) 0 0
\(791\) 30.6525 1.08988
\(792\) 10.0902 0.358539
\(793\) −25.8754 −0.918862
\(794\) −8.32624 −0.295487
\(795\) 0 0
\(796\) 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
\(800\) 0 0
\(801\) 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 \(0.523845\pi\)
\(810\) 0 0
\(811\) 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
\(815\) 0 0
\(816\) 3.14590 0.110128
\(817\) 0 0
\(818\) −21.2148 −0.741757
\(819\) −17.3262 −0.605428
\(820\) 0 0
\(821\) −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 \(-0.492141\pi\)
0.0246864 + 0.999695i \(0.492141\pi\)
\(824\) −3.56231 −0.124099
\(825\) 0 0
\(826\) −18.9443 −0.659156
\(827\) −8.29180 −0.288334 −0.144167 0.989553i \(-0.546050\pi\)
−0.144167 + 0.989553i \(0.546050\pi\)
\(828\) 2.61803 0.0909830
\(829\) 1.05573 0.0366670 0.0183335 0.999832i \(-0.494164\pi\)
0.0183335 + 0.999832i \(0.494164\pi\)
\(830\) 0 0
\(831\) −1.59675 −0.0553906
\(832\) −4.09017 −0.141801
\(833\) −22.3050 −0.772821
\(834\) −10.6525 −0.368865
\(835\) 0 0
\(836\) −18.7082 −0.647037
\(837\) 7.25735 0.250851
\(838\) −5.52786 −0.190957
\(839\) −43.0132 −1.48498 −0.742490 0.669858i \(-0.766355\pi\)
−0.742490 + 0.669858i \(0.766355\pi\)
\(840\) 0 0
\(841\) −6.30495 −0.217412
\(842\) 28.7426 0.990537
\(843\) 16.8328 0.579753
\(844\) 14.0000 0.481900
\(845\) 0 0
\(846\) −25.4164 −0.873834
\(847\) −6.23607 −0.214274
\(848\) 8.47214 0.290934
\(849\) 5.59675 0.192080
\(850\) 0 0
\(851\) −2.47214 −0.0847437
\(852\) 4.38197 0.150124
\(853\) −13.7984 −0.472447 −0.236224 0.971699i \(-0.575910\pi\)
−0.236224 + 0.971699i \(0.575910\pi\)
\(854\) 10.2361 0.350271
\(855\) 0 0
\(856\) −4.18034 −0.142881
\(857\) 33.4164 1.14148 0.570741 0.821130i \(-0.306656\pi\)
0.570741 + 0.821130i \(0.306656\pi\)
\(858\) 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 \(-0.718491\pi\)
−0.633765 + 0.773525i \(0.718491\pi\)
\(864\) 3.47214 0.118124
\(865\) 0 0
\(866\) −29.5066 −1.00267
\(867\) 5.50658 0.187013
\(868\) 3.38197 0.114791
\(869\) 40.3607 1.36914
\(870\) 0 0
\(871\) 22.6099 0.766107
\(872\) −8.56231 −0.289956
\(873\) 38.2705 1.29526
\(874\) −4.85410 −0.164192
\(875\) 0 0
\(876\) 0.763932 0.0258109
\(877\) 23.7426 0.801732 0.400866 0.916137i \(-0.368709\pi\)
0.400866 + 0.916137i \(0.368709\pi\)
\(878\) 15.6180 0.527083
\(879\) −9.81966 −0.331209
\(880\) 0 0
\(881\) 35.4164 1.19321 0.596605 0.802535i \(-0.296516\pi\)
0.596605 + 0.802535i \(0.296516\pi\)
\(882\) −11.4721 −0.386287
\(883\) 4.56231 0.153534 0.0767669 0.997049i \(-0.475540\pi\)
0.0767669 + 0.997049i \(0.475540\pi\)
\(884\) −20.8197 −0.700241
\(885\) 0 0
\(886\) 13.9098 0.467310
\(887\) 58.8328 1.97541 0.987706 0.156321i \(-0.0499634\pi\)
0.987706 + 0.156321i \(0.0499634\pi\)
\(888\) −1.52786 −0.0512718
\(889\) −10.0000 −0.335389
\(890\) 0 0
\(891\) 22.0000 0.737028
\(892\) 3.05573 0.102313
\(893\) 47.1246 1.57697
\(894\) 0.708204 0.0236859
\(895\) 0 0
\(896\) 1.61803 0.0540547
\(897\) 2.52786 0.0844029
\(898\) −18.5623 −0.619432
\(899\) 9.95743 0.332099
\(900\) 0 0
\(901\) 43.1246 1.43669
\(902\) 47.5066 1.58180
\(903\) 0 0
\(904\) 18.9443 0.630077
\(905\) 0 0
\(906\) −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
\(910\) 0 0
\(911\) −22.0689 −0.731175 −0.365587 0.930777i \(-0.619132\pi\)
−0.365587 + 0.930777i \(0.619132\pi\)
\(912\) −3.00000 −0.0993399
\(913\) −42.1803 −1.39597
\(914\) 33.7771 1.11725
\(915\) 0 0
\(916\) 10.0000 0.330409
\(917\) 24.1803 0.798505
\(918\) 17.6738 0.583321
\(919\) 40.0000 1.31948 0.659739 0.751495i \(-0.270667\pi\)
0.659739 + 0.751495i \(0.270667\pi\)
\(920\) 0 0
\(921\) −16.9656 −0.559034
\(922\) 34.7639 1.14489
\(923\) −29.0000 −0.954547
\(924\) −3.85410 −0.126791
\(925\) 0 0
\(926\) 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 \(0.565589\pi\)
\(930\) 0 0
\(931\) 21.2705 0.697113
\(932\) −19.7082 −0.645564
\(933\) 2.47214 0.0809341
\(934\) 23.1246 0.756660
\(935\) 0 0
\(936\) −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
\(940\) 0 0
\(941\) −60.5066 −1.97246 −0.986229 0.165385i \(-0.947113\pi\)
−0.986229 + 0.165385i \(0.947113\pi\)
\(942\) 6.00000 0.195491
\(943\) 12.3262 0.401398
\(944\) −11.7082 −0.381070
\(945\) 0 0
\(946\) 0 0
\(947\) −5.68692 −0.184800 −0.0924000 0.995722i \(-0.529454\pi\)
−0.0924000 + 0.995722i \(0.529454\pi\)
\(948\) 6.47214 0.210205
\(949\) −5.05573 −0.164116
\(950\) 0 0
\(951\) −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 0
\(956\) 24.3607 0.787881
\(957\) −11.3475 −0.366813
\(958\) −3.88854 −0.125633
\(959\) 8.61803 0.278291
\(960\) 0 0
\(961\) −26.6312 −0.859071
\(962\) 10.1115 0.326006
\(963\) −10.9443 −0.352674
\(964\) 0 0
\(965\) 0 0
\(966\) −1.00000 −0.0321745
\(967\) −50.5410 −1.62529 −0.812645 0.582759i \(-0.801973\pi\)
−0.812645 + 0.582759i \(0.801973\pi\)
\(968\) −3.85410 −0.123876
\(969\) −15.2705 −0.490559
\(970\) 0 0
\(971\) 0.729490 0.0234105 0.0117052 0.999931i \(-0.496274\pi\)
0.0117052 + 0.999931i \(0.496274\pi\)
\(972\) 13.9443 0.447263
\(973\) −27.8885 −0.894066
\(974\) −42.1803 −1.35155
\(975\) 0 0
\(976\) 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
\(980\) 0 0
\(981\) −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
\(985\) 0 0
\(986\) 24.2492 0.772253
\(987\) 9.70820 0.309016
\(988\) 19.8541 0.631643
\(989\) 0 0
\(990\) 0 0
\(991\) −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
\(995\) 0 0
\(996\) −6.76393 −0.214323
\(997\) 41.1935 1.30461 0.652306 0.757956i \(-0.273802\pi\)
0.652306 + 0.757956i \(0.273802\pi\)
\(998\) 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 1150.2.a.j.1.2 2
4.3 odd 2 9200.2.a.bu.1.1 2
5.2 odd 4 1150.2.b.i.599.1 4
5.3 odd 4 1150.2.b.i.599.4 4
5.4 even 2 230.2.a.c.1.1 2
15.14 odd 2 2070.2.a.u.1.2 2
20.19 odd 2 1840.2.a.l.1.2 2
40.19 odd 2 7360.2.a.bn.1.1 2
40.29 even 2 7360.2.a.bh.1.2 2
115.114 odd 2 5290.2.a.o.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.c.1.1 2 5.4 even 2
1150.2.a.j.1.2 2 1.1 even 1 trivial
1150.2.b.i.599.1 4 5.2 odd 4
1150.2.b.i.599.4 4 5.3 odd 4
1840.2.a.l.1.2 2 20.19 odd 2
2070.2.a.u.1.2 2 15.14 odd 2
5290.2.a.o.1.1 2 115.114 odd 2
7360.2.a.bh.1.2 2 40.29 even 2
7360.2.a.bn.1.1 2 40.19 odd 2
9200.2.a.bu.1.1 2 4.3 odd 2