Properties

Label 287.2.a.e.1.1
Level $287$
Weight $2$
Character 287.1
Self dual yes
Analytic conductor $2.292$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [287,2,Mod(1,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 287.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.633117.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 \) 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 \(2.45719\) of defining polynomial
Character \(\chi\) \(=\) 287.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.45719 q^{2} -1.45719 q^{3} +4.03778 q^{4} -2.26685 q^{5} +3.58059 q^{6} +1.00000 q^{7} -5.00722 q^{8} -0.876597 q^{9} +O(q^{10})\) \(q-2.45719 q^{2} -1.45719 q^{3} +4.03778 q^{4} -2.26685 q^{5} +3.58059 q^{6} +1.00000 q^{7} -5.00722 q^{8} -0.876597 q^{9} +5.57007 q^{10} -5.41988 q^{11} -5.88382 q^{12} +3.23628 q^{13} -2.45719 q^{14} +3.30322 q^{15} +4.22813 q^{16} +2.83206 q^{17} +2.15397 q^{18} -4.32097 q^{19} -9.15303 q^{20} -1.45719 q^{21} +13.3177 q^{22} +6.99907 q^{23} +7.29647 q^{24} +0.138589 q^{25} -7.95216 q^{26} +5.64894 q^{27} +4.03778 q^{28} +8.06741 q^{29} -8.11665 q^{30} +9.18123 q^{31} -0.374872 q^{32} +7.89779 q^{33} -6.95892 q^{34} -2.26685 q^{35} -3.53951 q^{36} -0.0469023 q^{37} +10.6174 q^{38} -4.71588 q^{39} +11.3506 q^{40} -1.00000 q^{41} +3.58059 q^{42} -6.31281 q^{43} -21.8843 q^{44} +1.98711 q^{45} -17.1980 q^{46} +5.26448 q^{47} -6.16119 q^{48} +1.00000 q^{49} -0.340538 q^{50} -4.12685 q^{51} +13.0674 q^{52} +6.43622 q^{53} -13.8805 q^{54} +12.2860 q^{55} -5.00722 q^{56} +6.29647 q^{57} -19.8232 q^{58} +2.45253 q^{59} +13.3377 q^{60} +5.28319 q^{61} -22.5600 q^{62} -0.876597 q^{63} -7.53512 q^{64} -7.33615 q^{65} -19.4064 q^{66} -8.78423 q^{67} +11.4353 q^{68} -10.1990 q^{69} +5.57007 q^{70} -12.1364 q^{71} +4.38931 q^{72} +2.42993 q^{73} +0.115248 q^{74} -0.201950 q^{75} -17.4471 q^{76} -5.41988 q^{77} +11.5878 q^{78} +4.92882 q^{79} -9.58451 q^{80} -5.60179 q^{81} +2.45719 q^{82} -1.63593 q^{83} -5.88382 q^{84} -6.41985 q^{85} +15.5118 q^{86} -11.7558 q^{87} +27.1385 q^{88} +1.68625 q^{89} -4.88271 q^{90} +3.23628 q^{91} +28.2607 q^{92} -13.3788 q^{93} -12.9358 q^{94} +9.79497 q^{95} +0.546260 q^{96} +18.8278 q^{97} -2.45719 q^{98} +4.75105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - q^{2} + 4 q^{3} + 3 q^{4} - 5 q^{5} + 12 q^{6} + 5 q^{7} - 3 q^{8} + q^{9} + 2 q^{11} - 2 q^{12} + 5 q^{13} - q^{14} - 5 q^{15} - q^{16} + 13 q^{17} + 21 q^{18} - 23 q^{20} + 4 q^{21} + q^{22} + 2 q^{23} + 2 q^{24} + 22 q^{25} + 10 q^{27} + 3 q^{28} - 5 q^{29} - 33 q^{30} + 17 q^{31} - 12 q^{32} + 3 q^{33} - 8 q^{34} - 5 q^{35} + 15 q^{36} - 7 q^{37} - 3 q^{38} + 5 q^{39} + 7 q^{40} - 5 q^{41} + 12 q^{42} + q^{43} - 47 q^{44} - 23 q^{45} - 24 q^{46} + 9 q^{47} - 19 q^{48} + 5 q^{49} + 2 q^{50} + 5 q^{51} + 20 q^{52} + 5 q^{53} + 2 q^{54} + 33 q^{55} - 3 q^{56} - 3 q^{57} - 27 q^{58} + 7 q^{59} - 16 q^{60} + 22 q^{61} - 28 q^{62} + q^{63} - 3 q^{64} - 31 q^{65} - 42 q^{66} - 3 q^{67} + 17 q^{68} - 22 q^{69} - 24 q^{71} - 12 q^{72} + 40 q^{73} - 5 q^{74} + 24 q^{75} - 19 q^{76} + 2 q^{77} + 30 q^{78} - 42 q^{79} + 24 q^{80} + 9 q^{81} + q^{82} - 12 q^{83} - 2 q^{84} - 23 q^{85} + 16 q^{86} - 32 q^{87} + 26 q^{88} + 8 q^{89} - 59 q^{90} + 5 q^{91} + 12 q^{92} - 11 q^{93} - 23 q^{94} - 17 q^{95} - 17 q^{96} + 16 q^{97} - q^{98} - 45 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45719 −1.73750 −0.868748 0.495255i \(-0.835075\pi\)
−0.868748 + 0.495255i \(0.835075\pi\)
\(3\) −1.45719 −0.841309 −0.420655 0.907221i \(-0.638200\pi\)
−0.420655 + 0.907221i \(0.638200\pi\)
\(4\) 4.03778 2.01889
\(5\) −2.26685 −1.01376 −0.506882 0.862015i \(-0.669202\pi\)
−0.506882 + 0.862015i \(0.669202\pi\)
\(6\) 3.58059 1.46177
\(7\) 1.00000 0.377964
\(8\) −5.00722 −1.77032
\(9\) −0.876597 −0.292199
\(10\) 5.57007 1.76141
\(11\) −5.41988 −1.63415 −0.817077 0.576528i \(-0.804407\pi\)
−0.817077 + 0.576528i \(0.804407\pi\)
\(12\) −5.88382 −1.69851
\(13\) 3.23628 0.897584 0.448792 0.893636i \(-0.351854\pi\)
0.448792 + 0.893636i \(0.351854\pi\)
\(14\) −2.45719 −0.656712
\(15\) 3.30322 0.852889
\(16\) 4.22813 1.05703
\(17\) 2.83206 0.686876 0.343438 0.939175i \(-0.388408\pi\)
0.343438 + 0.939175i \(0.388408\pi\)
\(18\) 2.15397 0.507694
\(19\) −4.32097 −0.991298 −0.495649 0.868523i \(-0.665070\pi\)
−0.495649 + 0.868523i \(0.665070\pi\)
\(20\) −9.15303 −2.04668
\(21\) −1.45719 −0.317985
\(22\) 13.3177 2.83934
\(23\) 6.99907 1.45941 0.729703 0.683764i \(-0.239658\pi\)
0.729703 + 0.683764i \(0.239658\pi\)
\(24\) 7.29647 1.48939
\(25\) 0.138589 0.0277177
\(26\) −7.95216 −1.55955
\(27\) 5.64894 1.08714
\(28\) 4.03778 0.763069
\(29\) 8.06741 1.49808 0.749040 0.662524i \(-0.230515\pi\)
0.749040 + 0.662524i \(0.230515\pi\)
\(30\) −8.11665 −1.48189
\(31\) 9.18123 1.64900 0.824498 0.565864i \(-0.191457\pi\)
0.824498 + 0.565864i \(0.191457\pi\)
\(32\) −0.374872 −0.0662686
\(33\) 7.89779 1.37483
\(34\) −6.95892 −1.19344
\(35\) −2.26685 −0.383167
\(36\) −3.53951 −0.589918
\(37\) −0.0469023 −0.00771068 −0.00385534 0.999993i \(-0.501227\pi\)
−0.00385534 + 0.999993i \(0.501227\pi\)
\(38\) 10.6174 1.72238
\(39\) −4.71588 −0.755145
\(40\) 11.3506 1.79469
\(41\) −1.00000 −0.156174
\(42\) 3.58059 0.552498
\(43\) −6.31281 −0.962695 −0.481348 0.876530i \(-0.659852\pi\)
−0.481348 + 0.876530i \(0.659852\pi\)
\(44\) −21.8843 −3.29918
\(45\) 1.98711 0.296221
\(46\) −17.1980 −2.53571
\(47\) 5.26448 0.767903 0.383952 0.923353i \(-0.374563\pi\)
0.383952 + 0.923353i \(0.374563\pi\)
\(48\) −6.16119 −0.889291
\(49\) 1.00000 0.142857
\(50\) −0.340538 −0.0481594
\(51\) −4.12685 −0.577875
\(52\) 13.0674 1.81212
\(53\) 6.43622 0.884082 0.442041 0.896995i \(-0.354255\pi\)
0.442041 + 0.896995i \(0.354255\pi\)
\(54\) −13.8805 −1.88890
\(55\) 12.2860 1.65665
\(56\) −5.00722 −0.669118
\(57\) 6.29647 0.833988
\(58\) −19.8232 −2.60291
\(59\) 2.45253 0.319292 0.159646 0.987174i \(-0.448965\pi\)
0.159646 + 0.987174i \(0.448965\pi\)
\(60\) 13.3377 1.72189
\(61\) 5.28319 0.676443 0.338221 0.941067i \(-0.390175\pi\)
0.338221 + 0.941067i \(0.390175\pi\)
\(62\) −22.5600 −2.86513
\(63\) −0.876597 −0.110441
\(64\) −7.53512 −0.941891
\(65\) −7.33615 −0.909938
\(66\) −19.4064 −2.38876
\(67\) −8.78423 −1.07316 −0.536582 0.843848i \(-0.680285\pi\)
−0.536582 + 0.843848i \(0.680285\pi\)
\(68\) 11.4353 1.38673
\(69\) −10.1990 −1.22781
\(70\) 5.57007 0.665751
\(71\) −12.1364 −1.44033 −0.720165 0.693802i \(-0.755934\pi\)
−0.720165 + 0.693802i \(0.755934\pi\)
\(72\) 4.38931 0.517286
\(73\) 2.42993 0.284402 0.142201 0.989838i \(-0.454582\pi\)
0.142201 + 0.989838i \(0.454582\pi\)
\(74\) 0.115248 0.0133973
\(75\) −0.201950 −0.0233192
\(76\) −17.4471 −2.00132
\(77\) −5.41988 −0.617652
\(78\) 11.5878 1.31206
\(79\) 4.92882 0.554536 0.277268 0.960793i \(-0.410571\pi\)
0.277268 + 0.960793i \(0.410571\pi\)
\(80\) −9.58451 −1.07158
\(81\) −5.60179 −0.622421
\(82\) 2.45719 0.271351
\(83\) −1.63593 −0.179567 −0.0897833 0.995961i \(-0.528617\pi\)
−0.0897833 + 0.995961i \(0.528617\pi\)
\(84\) −5.88382 −0.641977
\(85\) −6.41985 −0.696330
\(86\) 15.5118 1.67268
\(87\) −11.7558 −1.26035
\(88\) 27.1385 2.89298
\(89\) 1.68625 0.178742 0.0893712 0.995998i \(-0.471514\pi\)
0.0893712 + 0.995998i \(0.471514\pi\)
\(90\) −4.88271 −0.514682
\(91\) 3.23628 0.339255
\(92\) 28.2607 2.94638
\(93\) −13.3788 −1.38732
\(94\) −12.9358 −1.33423
\(95\) 9.79497 1.00494
\(96\) 0.546260 0.0557524
\(97\) 18.8278 1.91168 0.955838 0.293894i \(-0.0949512\pi\)
0.955838 + 0.293894i \(0.0949512\pi\)
\(98\) −2.45719 −0.248214
\(99\) 4.75105 0.477498
\(100\) 0.559591 0.0559591
\(101\) 7.44903 0.741207 0.370603 0.928791i \(-0.379151\pi\)
0.370603 + 0.928791i \(0.379151\pi\)
\(102\) 10.1405 1.00406
\(103\) 3.68672 0.363264 0.181632 0.983367i \(-0.441862\pi\)
0.181632 + 0.983367i \(0.441862\pi\)
\(104\) −16.2048 −1.58901
\(105\) 3.30322 0.322362
\(106\) −15.8150 −1.53609
\(107\) −8.58781 −0.830215 −0.415108 0.909772i \(-0.636256\pi\)
−0.415108 + 0.909772i \(0.636256\pi\)
\(108\) 22.8092 2.19482
\(109\) −2.91912 −0.279601 −0.139800 0.990180i \(-0.544646\pi\)
−0.139800 + 0.990180i \(0.544646\pi\)
\(110\) −30.1891 −2.87842
\(111\) 0.0683455 0.00648707
\(112\) 4.22813 0.399521
\(113\) −7.03990 −0.662258 −0.331129 0.943585i \(-0.607430\pi\)
−0.331129 + 0.943585i \(0.607430\pi\)
\(114\) −15.4716 −1.44905
\(115\) −15.8658 −1.47949
\(116\) 32.5745 3.02446
\(117\) −2.83692 −0.262273
\(118\) −6.02633 −0.554768
\(119\) 2.83206 0.259615
\(120\) −16.5400 −1.50989
\(121\) 18.3751 1.67046
\(122\) −12.9818 −1.17532
\(123\) 1.45719 0.131390
\(124\) 37.0718 3.32915
\(125\) 11.0201 0.985665
\(126\) 2.15397 0.191890
\(127\) 19.1099 1.69573 0.847863 0.530216i \(-0.177889\pi\)
0.847863 + 0.530216i \(0.177889\pi\)
\(128\) 19.2650 1.70280
\(129\) 9.19897 0.809924
\(130\) 18.0263 1.58101
\(131\) 9.99440 0.873215 0.436608 0.899652i \(-0.356180\pi\)
0.436608 + 0.899652i \(0.356180\pi\)
\(132\) 31.8896 2.77563
\(133\) −4.32097 −0.374676
\(134\) 21.5845 1.86462
\(135\) −12.8053 −1.10210
\(136\) −14.1808 −1.21599
\(137\) 4.66385 0.398459 0.199230 0.979953i \(-0.436156\pi\)
0.199230 + 0.979953i \(0.436156\pi\)
\(138\) 25.0608 2.13332
\(139\) −10.3954 −0.881725 −0.440862 0.897575i \(-0.645327\pi\)
−0.440862 + 0.897575i \(0.645327\pi\)
\(140\) −9.15303 −0.773572
\(141\) −7.67135 −0.646044
\(142\) 29.8215 2.50257
\(143\) −17.5403 −1.46679
\(144\) −3.70636 −0.308864
\(145\) −18.2876 −1.51870
\(146\) −5.97080 −0.494147
\(147\) −1.45719 −0.120187
\(148\) −0.189381 −0.0155670
\(149\) 6.23050 0.510422 0.255211 0.966885i \(-0.417855\pi\)
0.255211 + 0.966885i \(0.417855\pi\)
\(150\) 0.496229 0.0405169
\(151\) −21.1548 −1.72156 −0.860778 0.508981i \(-0.830022\pi\)
−0.860778 + 0.508981i \(0.830022\pi\)
\(152\) 21.6360 1.75492
\(153\) −2.48258 −0.200704
\(154\) 13.3177 1.07317
\(155\) −20.8124 −1.67169
\(156\) −19.0417 −1.52456
\(157\) 20.4912 1.63538 0.817688 0.575662i \(-0.195255\pi\)
0.817688 + 0.575662i \(0.195255\pi\)
\(158\) −12.1111 −0.963504
\(159\) −9.37879 −0.743787
\(160\) 0.849777 0.0671808
\(161\) 6.99907 0.551604
\(162\) 13.7647 1.08145
\(163\) −1.63497 −0.128060 −0.0640302 0.997948i \(-0.520395\pi\)
−0.0640302 + 0.997948i \(0.520395\pi\)
\(164\) −4.03778 −0.315298
\(165\) −17.9031 −1.39375
\(166\) 4.01979 0.311996
\(167\) −19.8243 −1.53405 −0.767026 0.641616i \(-0.778264\pi\)
−0.767026 + 0.641616i \(0.778264\pi\)
\(168\) 7.29647 0.562935
\(169\) −2.52647 −0.194344
\(170\) 15.7748 1.20987
\(171\) 3.78775 0.289656
\(172\) −25.4898 −1.94358
\(173\) −9.31394 −0.708126 −0.354063 0.935222i \(-0.615200\pi\)
−0.354063 + 0.935222i \(0.615200\pi\)
\(174\) 28.8861 2.18985
\(175\) 0.138589 0.0104763
\(176\) −22.9159 −1.72735
\(177\) −3.57380 −0.268623
\(178\) −4.14344 −0.310564
\(179\) −17.3459 −1.29649 −0.648245 0.761432i \(-0.724497\pi\)
−0.648245 + 0.761432i \(0.724497\pi\)
\(180\) 8.02352 0.598038
\(181\) 10.1355 0.753364 0.376682 0.926343i \(-0.377065\pi\)
0.376682 + 0.926343i \(0.377065\pi\)
\(182\) −7.95216 −0.589454
\(183\) −7.69861 −0.569097
\(184\) −35.0459 −2.58362
\(185\) 0.106320 0.00781681
\(186\) 32.8742 2.41046
\(187\) −15.3494 −1.12246
\(188\) 21.2568 1.55031
\(189\) 5.64894 0.410900
\(190\) −24.0681 −1.74608
\(191\) 18.1959 1.31661 0.658306 0.752750i \(-0.271273\pi\)
0.658306 + 0.752750i \(0.271273\pi\)
\(192\) 10.9801 0.792421
\(193\) 1.29950 0.0935398 0.0467699 0.998906i \(-0.485107\pi\)
0.0467699 + 0.998906i \(0.485107\pi\)
\(194\) −46.2635 −3.32153
\(195\) 10.6902 0.765539
\(196\) 4.03778 0.288413
\(197\) 5.64679 0.402317 0.201159 0.979559i \(-0.435529\pi\)
0.201159 + 0.979559i \(0.435529\pi\)
\(198\) −11.6742 −0.829651
\(199\) −11.5069 −0.815699 −0.407850 0.913049i \(-0.633721\pi\)
−0.407850 + 0.913049i \(0.633721\pi\)
\(200\) −0.693943 −0.0490692
\(201\) 12.8003 0.902863
\(202\) −18.3037 −1.28784
\(203\) 8.06741 0.566221
\(204\) −16.6633 −1.16667
\(205\) 2.26685 0.158323
\(206\) −9.05898 −0.631169
\(207\) −6.13536 −0.426437
\(208\) 13.6834 0.948775
\(209\) 23.4191 1.61993
\(210\) −8.11665 −0.560102
\(211\) −9.92599 −0.683333 −0.341667 0.939821i \(-0.610991\pi\)
−0.341667 + 0.939821i \(0.610991\pi\)
\(212\) 25.9880 1.78487
\(213\) 17.6851 1.21176
\(214\) 21.1019 1.44250
\(215\) 14.3102 0.975946
\(216\) −28.2855 −1.92458
\(217\) 9.18123 0.623262
\(218\) 7.17282 0.485805
\(219\) −3.54087 −0.239270
\(220\) 49.6083 3.34459
\(221\) 9.16536 0.616529
\(222\) −0.167938 −0.0112713
\(223\) −11.8232 −0.791738 −0.395869 0.918307i \(-0.629557\pi\)
−0.395869 + 0.918307i \(0.629557\pi\)
\(224\) −0.374872 −0.0250472
\(225\) −0.121486 −0.00809909
\(226\) 17.2984 1.15067
\(227\) 1.60275 0.106378 0.0531892 0.998584i \(-0.483061\pi\)
0.0531892 + 0.998584i \(0.483061\pi\)
\(228\) 25.4238 1.68373
\(229\) −9.93349 −0.656423 −0.328212 0.944604i \(-0.606446\pi\)
−0.328212 + 0.944604i \(0.606446\pi\)
\(230\) 38.9853 2.57061
\(231\) 7.89779 0.519636
\(232\) −40.3953 −2.65208
\(233\) −7.91248 −0.518364 −0.259182 0.965829i \(-0.583453\pi\)
−0.259182 + 0.965829i \(0.583453\pi\)
\(234\) 6.97084 0.455698
\(235\) −11.9338 −0.778473
\(236\) 9.90278 0.644616
\(237\) −7.18223 −0.466536
\(238\) −6.95892 −0.451079
\(239\) 27.1893 1.75873 0.879365 0.476148i \(-0.157967\pi\)
0.879365 + 0.476148i \(0.157967\pi\)
\(240\) 13.9665 0.901531
\(241\) 19.4014 1.24975 0.624877 0.780723i \(-0.285149\pi\)
0.624877 + 0.780723i \(0.285149\pi\)
\(242\) −45.1510 −2.90242
\(243\) −8.78395 −0.563490
\(244\) 21.3324 1.36566
\(245\) −2.26685 −0.144823
\(246\) −3.58059 −0.228290
\(247\) −13.9839 −0.889773
\(248\) −45.9724 −2.91925
\(249\) 2.38386 0.151071
\(250\) −27.0784 −1.71259
\(251\) 27.4697 1.73387 0.866935 0.498421i \(-0.166087\pi\)
0.866935 + 0.498421i \(0.166087\pi\)
\(252\) −3.53951 −0.222968
\(253\) −37.9341 −2.38489
\(254\) −46.9566 −2.94632
\(255\) 9.35494 0.585829
\(256\) −32.2675 −2.01672
\(257\) 21.6328 1.34942 0.674710 0.738083i \(-0.264269\pi\)
0.674710 + 0.738083i \(0.264269\pi\)
\(258\) −22.6036 −1.40724
\(259\) −0.0469023 −0.00291436
\(260\) −29.6218 −1.83707
\(261\) −7.07187 −0.437738
\(262\) −24.5581 −1.51721
\(263\) −9.84482 −0.607058 −0.303529 0.952822i \(-0.598165\pi\)
−0.303529 + 0.952822i \(0.598165\pi\)
\(264\) −39.5460 −2.43389
\(265\) −14.5899 −0.896251
\(266\) 10.6174 0.650997
\(267\) −2.45719 −0.150378
\(268\) −35.4688 −2.16660
\(269\) −26.0627 −1.58907 −0.794535 0.607219i \(-0.792285\pi\)
−0.794535 + 0.607219i \(0.792285\pi\)
\(270\) 31.4650 1.91490
\(271\) 25.4506 1.54602 0.773008 0.634396i \(-0.218751\pi\)
0.773008 + 0.634396i \(0.218751\pi\)
\(272\) 11.9743 0.726050
\(273\) −4.71588 −0.285418
\(274\) −11.4600 −0.692321
\(275\) −0.751133 −0.0452950
\(276\) −41.1812 −2.47882
\(277\) 29.3678 1.76454 0.882270 0.470743i \(-0.156014\pi\)
0.882270 + 0.470743i \(0.156014\pi\)
\(278\) 25.5434 1.53199
\(279\) −8.04823 −0.481835
\(280\) 11.3506 0.678328
\(281\) 24.2120 1.44437 0.722184 0.691701i \(-0.243139\pi\)
0.722184 + 0.691701i \(0.243139\pi\)
\(282\) 18.8500 1.12250
\(283\) 8.91251 0.529794 0.264897 0.964277i \(-0.414662\pi\)
0.264897 + 0.964277i \(0.414662\pi\)
\(284\) −49.0043 −2.90787
\(285\) −14.2731 −0.845467
\(286\) 43.0997 2.54854
\(287\) −1.00000 −0.0590281
\(288\) 0.328612 0.0193636
\(289\) −8.97942 −0.528201
\(290\) 44.9361 2.63874
\(291\) −27.4357 −1.60831
\(292\) 9.81153 0.574176
\(293\) −8.79238 −0.513656 −0.256828 0.966457i \(-0.582677\pi\)
−0.256828 + 0.966457i \(0.582677\pi\)
\(294\) 3.58059 0.208824
\(295\) −5.55950 −0.323687
\(296\) 0.234850 0.0136504
\(297\) −30.6166 −1.77655
\(298\) −15.3095 −0.886856
\(299\) 22.6510 1.30994
\(300\) −0.815430 −0.0470789
\(301\) −6.31281 −0.363865
\(302\) 51.9814 2.99120
\(303\) −10.8547 −0.623584
\(304\) −18.2696 −1.04783
\(305\) −11.9762 −0.685753
\(306\) 6.10016 0.348723
\(307\) 25.4509 1.45256 0.726281 0.687398i \(-0.241247\pi\)
0.726281 + 0.687398i \(0.241247\pi\)
\(308\) −21.8843 −1.24697
\(309\) −5.37226 −0.305617
\(310\) 51.1401 2.90456
\(311\) −8.20774 −0.465418 −0.232709 0.972546i \(-0.574759\pi\)
−0.232709 + 0.972546i \(0.574759\pi\)
\(312\) 23.6135 1.33685
\(313\) 7.84025 0.443157 0.221578 0.975143i \(-0.428879\pi\)
0.221578 + 0.975143i \(0.428879\pi\)
\(314\) −50.3508 −2.84146
\(315\) 1.98711 0.111961
\(316\) 19.9015 1.11955
\(317\) 32.4359 1.82178 0.910891 0.412647i \(-0.135396\pi\)
0.910891 + 0.412647i \(0.135396\pi\)
\(318\) 23.0455 1.29233
\(319\) −43.7244 −2.44810
\(320\) 17.0810 0.954855
\(321\) 12.5141 0.698468
\(322\) −17.1980 −0.958409
\(323\) −12.2373 −0.680899
\(324\) −22.6188 −1.25660
\(325\) 0.448512 0.0248790
\(326\) 4.01742 0.222504
\(327\) 4.25371 0.235230
\(328\) 5.00722 0.276478
\(329\) 5.26448 0.290240
\(330\) 43.9913 2.42164
\(331\) 13.8576 0.761685 0.380843 0.924640i \(-0.375634\pi\)
0.380843 + 0.924640i \(0.375634\pi\)
\(332\) −6.60553 −0.362526
\(333\) 0.0411144 0.00225305
\(334\) 48.7121 2.66541
\(335\) 19.9125 1.08794
\(336\) −6.16119 −0.336120
\(337\) 18.6080 1.01364 0.506822 0.862050i \(-0.330820\pi\)
0.506822 + 0.862050i \(0.330820\pi\)
\(338\) 6.20802 0.337672
\(339\) 10.2585 0.557164
\(340\) −25.9220 −1.40582
\(341\) −49.7611 −2.69472
\(342\) −9.30722 −0.503277
\(343\) 1.00000 0.0539949
\(344\) 31.6097 1.70428
\(345\) 23.1195 1.24471
\(346\) 22.8861 1.23037
\(347\) 23.3306 1.25245 0.626225 0.779642i \(-0.284599\pi\)
0.626225 + 0.779642i \(0.284599\pi\)
\(348\) −47.4672 −2.54451
\(349\) −5.59571 −0.299531 −0.149766 0.988722i \(-0.547852\pi\)
−0.149766 + 0.988722i \(0.547852\pi\)
\(350\) −0.340538 −0.0182025
\(351\) 18.2816 0.975798
\(352\) 2.03176 0.108293
\(353\) −19.4280 −1.03405 −0.517023 0.855971i \(-0.672960\pi\)
−0.517023 + 0.855971i \(0.672960\pi\)
\(354\) 8.78150 0.466732
\(355\) 27.5114 1.46016
\(356\) 6.80872 0.360862
\(357\) −4.12685 −0.218416
\(358\) 42.6221 2.25265
\(359\) 14.3127 0.755398 0.377699 0.925929i \(-0.376715\pi\)
0.377699 + 0.925929i \(0.376715\pi\)
\(360\) −9.94990 −0.524406
\(361\) −0.329226 −0.0173277
\(362\) −24.9048 −1.30897
\(363\) −26.7760 −1.40537
\(364\) 13.0674 0.684918
\(365\) −5.50827 −0.288316
\(366\) 18.9169 0.988804
\(367\) −21.2458 −1.10902 −0.554512 0.832176i \(-0.687095\pi\)
−0.554512 + 0.832176i \(0.687095\pi\)
\(368\) 29.5929 1.54264
\(369\) 0.876597 0.0456338
\(370\) −0.261249 −0.0135817
\(371\) 6.43622 0.334152
\(372\) −54.0207 −2.80084
\(373\) 28.2272 1.46155 0.730774 0.682620i \(-0.239160\pi\)
0.730774 + 0.682620i \(0.239160\pi\)
\(374\) 37.7165 1.95027
\(375\) −16.0583 −0.829249
\(376\) −26.3604 −1.35943
\(377\) 26.1084 1.34465
\(378\) −13.8805 −0.713937
\(379\) −8.57635 −0.440538 −0.220269 0.975439i \(-0.570693\pi\)
−0.220269 + 0.975439i \(0.570693\pi\)
\(380\) 39.5500 2.02887
\(381\) −27.8467 −1.42663
\(382\) −44.7109 −2.28761
\(383\) 2.63393 0.134588 0.0672938 0.997733i \(-0.478564\pi\)
0.0672938 + 0.997733i \(0.478564\pi\)
\(384\) −28.0727 −1.43258
\(385\) 12.2860 0.626154
\(386\) −3.19311 −0.162525
\(387\) 5.53379 0.281298
\(388\) 76.0227 3.85947
\(389\) −13.2656 −0.672595 −0.336298 0.941756i \(-0.609175\pi\)
−0.336298 + 0.941756i \(0.609175\pi\)
\(390\) −26.2678 −1.33012
\(391\) 19.8218 1.00243
\(392\) −5.00722 −0.252903
\(393\) −14.5637 −0.734644
\(394\) −13.8752 −0.699025
\(395\) −11.1729 −0.562169
\(396\) 19.1837 0.964017
\(397\) 2.28602 0.114732 0.0573661 0.998353i \(-0.481730\pi\)
0.0573661 + 0.998353i \(0.481730\pi\)
\(398\) 28.2745 1.41727
\(399\) 6.29647 0.315218
\(400\) 0.585970 0.0292985
\(401\) 2.79191 0.139421 0.0697107 0.997567i \(-0.477792\pi\)
0.0697107 + 0.997567i \(0.477792\pi\)
\(402\) −31.4527 −1.56872
\(403\) 29.7130 1.48011
\(404\) 30.0776 1.49642
\(405\) 12.6984 0.630988
\(406\) −19.8232 −0.983807
\(407\) 0.254204 0.0126004
\(408\) 20.6641 1.02302
\(409\) −10.8769 −0.537826 −0.268913 0.963164i \(-0.586664\pi\)
−0.268913 + 0.963164i \(0.586664\pi\)
\(410\) −5.57007 −0.275086
\(411\) −6.79611 −0.335227
\(412\) 14.8862 0.733390
\(413\) 2.45253 0.120681
\(414\) 15.0757 0.740932
\(415\) 3.70840 0.182038
\(416\) −1.21319 −0.0594816
\(417\) 15.1480 0.741803
\(418\) −57.5452 −2.81463
\(419\) −24.9047 −1.21668 −0.608338 0.793678i \(-0.708164\pi\)
−0.608338 + 0.793678i \(0.708164\pi\)
\(420\) 13.3377 0.650813
\(421\) −7.16405 −0.349155 −0.174577 0.984643i \(-0.555856\pi\)
−0.174577 + 0.984643i \(0.555856\pi\)
\(422\) 24.3900 1.18729
\(423\) −4.61483 −0.224380
\(424\) −32.2276 −1.56511
\(425\) 0.392491 0.0190386
\(426\) −43.4557 −2.10543
\(427\) 5.28319 0.255671
\(428\) −34.6757 −1.67611
\(429\) 25.5595 1.23402
\(430\) −35.1628 −1.69570
\(431\) −14.6538 −0.705850 −0.352925 0.935652i \(-0.614813\pi\)
−0.352925 + 0.935652i \(0.614813\pi\)
\(432\) 23.8844 1.14914
\(433\) −29.4173 −1.41370 −0.706851 0.707362i \(-0.749885\pi\)
−0.706851 + 0.707362i \(0.749885\pi\)
\(434\) −22.5600 −1.08292
\(435\) 26.6485 1.27770
\(436\) −11.7868 −0.564483
\(437\) −30.2427 −1.44671
\(438\) 8.70059 0.415730
\(439\) 26.5607 1.26767 0.633837 0.773466i \(-0.281479\pi\)
0.633837 + 0.773466i \(0.281479\pi\)
\(440\) −61.5188 −2.93280
\(441\) −0.876597 −0.0417427
\(442\) −22.5210 −1.07122
\(443\) −12.2373 −0.581409 −0.290705 0.956813i \(-0.593890\pi\)
−0.290705 + 0.956813i \(0.593890\pi\)
\(444\) 0.275964 0.0130967
\(445\) −3.82247 −0.181203
\(446\) 29.0518 1.37564
\(447\) −9.07902 −0.429423
\(448\) −7.53512 −0.356001
\(449\) −23.4334 −1.10589 −0.552944 0.833218i \(-0.686496\pi\)
−0.552944 + 0.833218i \(0.686496\pi\)
\(450\) 0.298515 0.0140721
\(451\) 5.41988 0.255212
\(452\) −28.4256 −1.33703
\(453\) 30.8266 1.44836
\(454\) −3.93826 −0.184832
\(455\) −7.33615 −0.343924
\(456\) −31.5278 −1.47643
\(457\) −8.25626 −0.386212 −0.193106 0.981178i \(-0.561856\pi\)
−0.193106 + 0.981178i \(0.561856\pi\)
\(458\) 24.4085 1.14053
\(459\) 15.9981 0.746729
\(460\) −64.0627 −2.98694
\(461\) −8.79238 −0.409502 −0.204751 0.978814i \(-0.565638\pi\)
−0.204751 + 0.978814i \(0.565638\pi\)
\(462\) −19.4064 −0.902866
\(463\) 36.8884 1.71435 0.857175 0.515025i \(-0.172217\pi\)
0.857175 + 0.515025i \(0.172217\pi\)
\(464\) 34.1100 1.58352
\(465\) 30.3277 1.40641
\(466\) 19.4425 0.900655
\(467\) −21.8803 −1.01250 −0.506250 0.862387i \(-0.668969\pi\)
−0.506250 + 0.862387i \(0.668969\pi\)
\(468\) −11.4549 −0.529501
\(469\) −8.78423 −0.405618
\(470\) 29.3235 1.35259
\(471\) −29.8596 −1.37586
\(472\) −12.2803 −0.565249
\(473\) 34.2147 1.57319
\(474\) 17.6481 0.810605
\(475\) −0.598837 −0.0274765
\(476\) 11.4353 0.524134
\(477\) −5.64197 −0.258328
\(478\) −66.8093 −3.05579
\(479\) 34.3678 1.57030 0.785152 0.619303i \(-0.212585\pi\)
0.785152 + 0.619303i \(0.212585\pi\)
\(480\) −1.23829 −0.0565198
\(481\) −0.151789 −0.00692098
\(482\) −47.6729 −2.17144
\(483\) −10.1990 −0.464069
\(484\) 74.1945 3.37248
\(485\) −42.6798 −1.93799
\(486\) 21.5838 0.979062
\(487\) 15.9585 0.723146 0.361573 0.932344i \(-0.382240\pi\)
0.361573 + 0.932344i \(0.382240\pi\)
\(488\) −26.4541 −1.19752
\(489\) 2.38246 0.107738
\(490\) 5.57007 0.251630
\(491\) −1.69863 −0.0766581 −0.0383290 0.999265i \(-0.512204\pi\)
−0.0383290 + 0.999265i \(0.512204\pi\)
\(492\) 5.88382 0.265263
\(493\) 22.8474 1.02900
\(494\) 34.3611 1.54598
\(495\) −10.7699 −0.484071
\(496\) 38.8194 1.74304
\(497\) −12.1364 −0.544394
\(498\) −5.85760 −0.262485
\(499\) −23.0520 −1.03195 −0.515975 0.856604i \(-0.672570\pi\)
−0.515975 + 0.856604i \(0.672570\pi\)
\(500\) 44.4967 1.98995
\(501\) 28.8878 1.29061
\(502\) −67.4982 −3.01259
\(503\) 34.6937 1.54692 0.773458 0.633848i \(-0.218526\pi\)
0.773458 + 0.633848i \(0.218526\pi\)
\(504\) 4.38931 0.195516
\(505\) −16.8858 −0.751409
\(506\) 93.2112 4.14374
\(507\) 3.68155 0.163503
\(508\) 77.1615 3.42349
\(509\) −7.41125 −0.328498 −0.164249 0.986419i \(-0.552520\pi\)
−0.164249 + 0.986419i \(0.552520\pi\)
\(510\) −22.9869 −1.01788
\(511\) 2.42993 0.107494
\(512\) 40.7573 1.80124
\(513\) −24.4089 −1.07768
\(514\) −53.1560 −2.34461
\(515\) −8.35723 −0.368264
\(516\) 37.1434 1.63515
\(517\) −28.5328 −1.25487
\(518\) 0.115248 0.00506370
\(519\) 13.5722 0.595753
\(520\) 36.7337 1.61088
\(521\) −24.2278 −1.06144 −0.530719 0.847548i \(-0.678078\pi\)
−0.530719 + 0.847548i \(0.678078\pi\)
\(522\) 17.3769 0.760567
\(523\) −43.3265 −1.89454 −0.947268 0.320442i \(-0.896169\pi\)
−0.947268 + 0.320442i \(0.896169\pi\)
\(524\) 40.3552 1.76293
\(525\) −0.201950 −0.00881381
\(526\) 24.1906 1.05476
\(527\) 26.0018 1.13266
\(528\) 33.3929 1.45324
\(529\) 25.9869 1.12987
\(530\) 35.8502 1.55723
\(531\) −2.14988 −0.0932968
\(532\) −17.4471 −0.756429
\(533\) −3.23628 −0.140179
\(534\) 6.03778 0.261280
\(535\) 19.4672 0.841643
\(536\) 43.9846 1.89984
\(537\) 25.2762 1.09075
\(538\) 64.0410 2.76100
\(539\) −5.41988 −0.233451
\(540\) −51.7049 −2.22503
\(541\) −12.7180 −0.546788 −0.273394 0.961902i \(-0.588146\pi\)
−0.273394 + 0.961902i \(0.588146\pi\)
\(542\) −62.5370 −2.68620
\(543\) −14.7693 −0.633812
\(544\) −1.06166 −0.0455183
\(545\) 6.61718 0.283449
\(546\) 11.5878 0.495913
\(547\) −4.71489 −0.201594 −0.100797 0.994907i \(-0.532139\pi\)
−0.100797 + 0.994907i \(0.532139\pi\)
\(548\) 18.8316 0.804446
\(549\) −4.63122 −0.197656
\(550\) 1.84568 0.0786999
\(551\) −34.8590 −1.48504
\(552\) 51.0685 2.17362
\(553\) 4.92882 0.209595
\(554\) −72.1623 −3.06588
\(555\) −0.154929 −0.00657636
\(556\) −41.9743 −1.78011
\(557\) −11.0756 −0.469288 −0.234644 0.972081i \(-0.575392\pi\)
−0.234644 + 0.972081i \(0.575392\pi\)
\(558\) 19.7760 0.837187
\(559\) −20.4301 −0.864099
\(560\) −9.58451 −0.405020
\(561\) 22.3670 0.944337
\(562\) −59.4935 −2.50958
\(563\) 24.9735 1.05251 0.526255 0.850327i \(-0.323596\pi\)
0.526255 + 0.850327i \(0.323596\pi\)
\(564\) −30.9752 −1.30429
\(565\) 15.9584 0.671374
\(566\) −21.8997 −0.920515
\(567\) −5.60179 −0.235253
\(568\) 60.7698 2.54985
\(569\) 3.14116 0.131684 0.0658422 0.997830i \(-0.479027\pi\)
0.0658422 + 0.997830i \(0.479027\pi\)
\(570\) 35.0718 1.46900
\(571\) 7.13418 0.298556 0.149278 0.988795i \(-0.452305\pi\)
0.149278 + 0.988795i \(0.452305\pi\)
\(572\) −70.8238 −2.96129
\(573\) −26.5150 −1.10768
\(574\) 2.45719 0.102561
\(575\) 0.969990 0.0404514
\(576\) 6.60527 0.275219
\(577\) 4.41995 0.184005 0.0920024 0.995759i \(-0.470673\pi\)
0.0920024 + 0.995759i \(0.470673\pi\)
\(578\) 22.0642 0.917748
\(579\) −1.89361 −0.0786959
\(580\) −73.8413 −3.06609
\(581\) −1.63593 −0.0678698
\(582\) 67.4148 2.79443
\(583\) −34.8835 −1.44473
\(584\) −12.1672 −0.503482
\(585\) 6.43085 0.265883
\(586\) 21.6046 0.892476
\(587\) 29.7123 1.22636 0.613178 0.789944i \(-0.289891\pi\)
0.613178 + 0.789944i \(0.289891\pi\)
\(588\) −5.88382 −0.242645
\(589\) −39.6718 −1.63465
\(590\) 13.6608 0.562404
\(591\) −8.22845 −0.338473
\(592\) −0.198309 −0.00815044
\(593\) −14.3020 −0.587315 −0.293657 0.955911i \(-0.594872\pi\)
−0.293657 + 0.955911i \(0.594872\pi\)
\(594\) 75.2307 3.08675
\(595\) −6.41985 −0.263188
\(596\) 25.1574 1.03049
\(597\) 16.7677 0.686255
\(598\) −55.6577 −2.27601
\(599\) 38.6159 1.57780 0.788902 0.614518i \(-0.210650\pi\)
0.788902 + 0.614518i \(0.210650\pi\)
\(600\) 1.01121 0.0412824
\(601\) 2.04839 0.0835557 0.0417779 0.999127i \(-0.486698\pi\)
0.0417779 + 0.999127i \(0.486698\pi\)
\(602\) 15.5118 0.632213
\(603\) 7.70022 0.313577
\(604\) −85.4186 −3.47563
\(605\) −41.6534 −1.69345
\(606\) 26.6720 1.08347
\(607\) 5.79770 0.235321 0.117661 0.993054i \(-0.462460\pi\)
0.117661 + 0.993054i \(0.462460\pi\)
\(608\) 1.61981 0.0656920
\(609\) −11.7558 −0.476367
\(610\) 29.4277 1.19149
\(611\) 17.0373 0.689257
\(612\) −10.0241 −0.405201
\(613\) 45.3061 1.82989 0.914947 0.403573i \(-0.132232\pi\)
0.914947 + 0.403573i \(0.132232\pi\)
\(614\) −62.5378 −2.52382
\(615\) −3.30322 −0.133199
\(616\) 27.1385 1.09344
\(617\) −22.8349 −0.919300 −0.459650 0.888100i \(-0.652025\pi\)
−0.459650 + 0.888100i \(0.652025\pi\)
\(618\) 13.2007 0.531008
\(619\) 15.2514 0.613007 0.306503 0.951870i \(-0.400841\pi\)
0.306503 + 0.951870i \(0.400841\pi\)
\(620\) −84.0360 −3.37497
\(621\) 39.5373 1.58658
\(622\) 20.1680 0.808662
\(623\) 1.68625 0.0675583
\(624\) −19.9393 −0.798213
\(625\) −25.6737 −1.02695
\(626\) −19.2650 −0.769983
\(627\) −34.1261 −1.36287
\(628\) 82.7390 3.30165
\(629\) −0.132830 −0.00529628
\(630\) −4.88271 −0.194532
\(631\) −40.2426 −1.60203 −0.801016 0.598643i \(-0.795707\pi\)
−0.801016 + 0.598643i \(0.795707\pi\)
\(632\) −24.6797 −0.981706
\(633\) 14.4640 0.574894
\(634\) −79.7012 −3.16534
\(635\) −43.3191 −1.71907
\(636\) −37.8695 −1.50162
\(637\) 3.23628 0.128226
\(638\) 107.439 4.25355
\(639\) 10.6388 0.420863
\(640\) −43.6707 −1.72624
\(641\) 8.41075 0.332205 0.166102 0.986109i \(-0.446882\pi\)
0.166102 + 0.986109i \(0.446882\pi\)
\(642\) −30.7495 −1.21358
\(643\) −23.9146 −0.943101 −0.471550 0.881839i \(-0.656305\pi\)
−0.471550 + 0.881839i \(0.656305\pi\)
\(644\) 28.2607 1.11363
\(645\) −20.8526 −0.821072
\(646\) 30.0693 1.18306
\(647\) 10.9669 0.431152 0.215576 0.976487i \(-0.430837\pi\)
0.215576 + 0.976487i \(0.430837\pi\)
\(648\) 28.0494 1.10188
\(649\) −13.2924 −0.521772
\(650\) −1.10208 −0.0432271
\(651\) −13.3788 −0.524356
\(652\) −6.60164 −0.258540
\(653\) 29.3523 1.14865 0.574323 0.818629i \(-0.305265\pi\)
0.574323 + 0.818629i \(0.305265\pi\)
\(654\) −10.4522 −0.408712
\(655\) −22.6558 −0.885234
\(656\) −4.22813 −0.165081
\(657\) −2.13007 −0.0831019
\(658\) −12.9358 −0.504291
\(659\) −12.7905 −0.498245 −0.249123 0.968472i \(-0.580142\pi\)
−0.249123 + 0.968472i \(0.580142\pi\)
\(660\) −72.2887 −2.81383
\(661\) 15.1159 0.587942 0.293971 0.955814i \(-0.405023\pi\)
0.293971 + 0.955814i \(0.405023\pi\)
\(662\) −34.0509 −1.32342
\(663\) −13.3557 −0.518691
\(664\) 8.19146 0.317890
\(665\) 9.79497 0.379833
\(666\) −0.101026 −0.00391467
\(667\) 56.4643 2.18631
\(668\) −80.0463 −3.09708
\(669\) 17.2286 0.666096
\(670\) −48.9288 −1.89028
\(671\) −28.6342 −1.10541
\(672\) 0.546260 0.0210724
\(673\) 10.3101 0.397425 0.198713 0.980058i \(-0.436324\pi\)
0.198713 + 0.980058i \(0.436324\pi\)
\(674\) −45.7235 −1.76120
\(675\) 0.782878 0.0301330
\(676\) −10.2013 −0.392359
\(677\) −1.97105 −0.0757535 −0.0378768 0.999282i \(-0.512059\pi\)
−0.0378768 + 0.999282i \(0.512059\pi\)
\(678\) −25.2070 −0.968070
\(679\) 18.8278 0.722546
\(680\) 32.1456 1.23273
\(681\) −2.33551 −0.0894970
\(682\) 122.273 4.68206
\(683\) −9.53970 −0.365026 −0.182513 0.983203i \(-0.558423\pi\)
−0.182513 + 0.983203i \(0.558423\pi\)
\(684\) 15.2941 0.584785
\(685\) −10.5722 −0.403944
\(686\) −2.45719 −0.0938160
\(687\) 14.4750 0.552255
\(688\) −26.6914 −1.01760
\(689\) 20.8294 0.793538
\(690\) −56.8090 −2.16268
\(691\) 16.3915 0.623562 0.311781 0.950154i \(-0.399075\pi\)
0.311781 + 0.950154i \(0.399075\pi\)
\(692\) −37.6077 −1.42963
\(693\) 4.75105 0.180477
\(694\) −57.3276 −2.17613
\(695\) 23.5647 0.893861
\(696\) 58.8637 2.23122
\(697\) −2.83206 −0.107272
\(698\) 13.7497 0.520434
\(699\) 11.5300 0.436104
\(700\) 0.559591 0.0211505
\(701\) 12.1383 0.458457 0.229229 0.973373i \(-0.426380\pi\)
0.229229 + 0.973373i \(0.426380\pi\)
\(702\) −44.9213 −1.69544
\(703\) 0.202663 0.00764359
\(704\) 40.8394 1.53919
\(705\) 17.3898 0.654936
\(706\) 47.7382 1.79665
\(707\) 7.44903 0.280150
\(708\) −14.4302 −0.542321
\(709\) −29.6150 −1.11222 −0.556108 0.831110i \(-0.687706\pi\)
−0.556108 + 0.831110i \(0.687706\pi\)
\(710\) −67.6008 −2.53701
\(711\) −4.32059 −0.162035
\(712\) −8.44344 −0.316431
\(713\) 64.2600 2.40656
\(714\) 10.1405 0.379497
\(715\) 39.7611 1.48698
\(716\) −70.0388 −2.61747
\(717\) −39.6200 −1.47964
\(718\) −35.1691 −1.31250
\(719\) 42.0273 1.56735 0.783676 0.621169i \(-0.213342\pi\)
0.783676 + 0.621169i \(0.213342\pi\)
\(720\) 8.40175 0.313115
\(721\) 3.68672 0.137301
\(722\) 0.808971 0.0301068
\(723\) −28.2715 −1.05143
\(724\) 40.9249 1.52096
\(725\) 1.11805 0.0415234
\(726\) 65.7936 2.44183
\(727\) −41.0718 −1.52327 −0.761635 0.648007i \(-0.775603\pi\)
−0.761635 + 0.648007i \(0.775603\pi\)
\(728\) −16.2048 −0.600589
\(729\) 29.6052 1.09649
\(730\) 13.5349 0.500948
\(731\) −17.8783 −0.661252
\(732\) −31.0853 −1.14895
\(733\) 9.51418 0.351414 0.175707 0.984442i \(-0.443779\pi\)
0.175707 + 0.984442i \(0.443779\pi\)
\(734\) 52.2051 1.92693
\(735\) 3.30322 0.121841
\(736\) −2.62375 −0.0967128
\(737\) 47.6094 1.75372
\(738\) −2.15397 −0.0792886
\(739\) −45.4606 −1.67230 −0.836148 0.548504i \(-0.815197\pi\)
−0.836148 + 0.548504i \(0.815197\pi\)
\(740\) 0.429298 0.0157813
\(741\) 20.3772 0.748574
\(742\) −15.8150 −0.580587
\(743\) −51.1920 −1.87805 −0.939027 0.343845i \(-0.888271\pi\)
−0.939027 + 0.343845i \(0.888271\pi\)
\(744\) 66.9906 2.45599
\(745\) −14.1236 −0.517448
\(746\) −69.3595 −2.53943
\(747\) 1.43405 0.0524692
\(748\) −61.9777 −2.26613
\(749\) −8.58781 −0.313792
\(750\) 39.4584 1.44082
\(751\) −32.2359 −1.17631 −0.588153 0.808750i \(-0.700145\pi\)
−0.588153 + 0.808750i \(0.700145\pi\)
\(752\) 22.2589 0.811698
\(753\) −40.0285 −1.45872
\(754\) −64.1534 −2.33633
\(755\) 47.9547 1.74525
\(756\) 22.8092 0.829562
\(757\) −26.3465 −0.957581 −0.478790 0.877929i \(-0.658925\pi\)
−0.478790 + 0.877929i \(0.658925\pi\)
\(758\) 21.0737 0.765432
\(759\) 55.2772 2.00643
\(760\) −49.0456 −1.77907
\(761\) −30.0811 −1.09044 −0.545219 0.838293i \(-0.683554\pi\)
−0.545219 + 0.838293i \(0.683554\pi\)
\(762\) 68.4246 2.47876
\(763\) −2.91912 −0.105679
\(764\) 73.4713 2.65810
\(765\) 5.62762 0.203467
\(766\) −6.47207 −0.233845
\(767\) 7.93707 0.286591
\(768\) 47.0198 1.69668
\(769\) −0.608700 −0.0219503 −0.0109751 0.999940i \(-0.503494\pi\)
−0.0109751 + 0.999940i \(0.503494\pi\)
\(770\) −30.1891 −1.08794
\(771\) −31.5232 −1.13528
\(772\) 5.24708 0.188847
\(773\) −8.67944 −0.312178 −0.156089 0.987743i \(-0.549889\pi\)
−0.156089 + 0.987743i \(0.549889\pi\)
\(774\) −13.5976 −0.488755
\(775\) 1.27241 0.0457064
\(776\) −94.2751 −3.38428
\(777\) 0.0683455 0.00245188
\(778\) 32.5962 1.16863
\(779\) 4.32097 0.154815
\(780\) 43.1646 1.54554
\(781\) 65.7780 2.35372
\(782\) −48.7059 −1.74172
\(783\) 45.5723 1.62862
\(784\) 4.22813 0.151005
\(785\) −46.4504 −1.65789
\(786\) 35.7859 1.27644
\(787\) 34.2640 1.22138 0.610689 0.791870i \(-0.290892\pi\)
0.610689 + 0.791870i \(0.290892\pi\)
\(788\) 22.8005 0.812235
\(789\) 14.3458 0.510723
\(790\) 27.4539 0.976766
\(791\) −7.03990 −0.250310
\(792\) −23.7895 −0.845325
\(793\) 17.0979 0.607164
\(794\) −5.61719 −0.199347
\(795\) 21.2603 0.754024
\(796\) −46.4622 −1.64681
\(797\) 13.1568 0.466036 0.233018 0.972472i \(-0.425140\pi\)
0.233018 + 0.972472i \(0.425140\pi\)
\(798\) −15.4716 −0.547690
\(799\) 14.9093 0.527454
\(800\) −0.0519530 −0.00183681
\(801\) −1.47816 −0.0522283
\(802\) −6.86026 −0.242244
\(803\) −13.1699 −0.464756
\(804\) 51.6848 1.82278
\(805\) −15.8658 −0.559196
\(806\) −73.0106 −2.57169
\(807\) 37.9783 1.33690
\(808\) −37.2990 −1.31217
\(809\) −2.04798 −0.0720033 −0.0360017 0.999352i \(-0.511462\pi\)
−0.0360017 + 0.999352i \(0.511462\pi\)
\(810\) −31.2023 −1.09634
\(811\) 5.48050 0.192446 0.0962232 0.995360i \(-0.469324\pi\)
0.0962232 + 0.995360i \(0.469324\pi\)
\(812\) 32.5745 1.14314
\(813\) −37.0864 −1.30068
\(814\) −0.624629 −0.0218932
\(815\) 3.70622 0.129823
\(816\) −17.4489 −0.610832
\(817\) 27.2775 0.954318
\(818\) 26.7265 0.934471
\(819\) −2.83692 −0.0991299
\(820\) 9.15303 0.319638
\(821\) −1.55848 −0.0543913 −0.0271957 0.999630i \(-0.508658\pi\)
−0.0271957 + 0.999630i \(0.508658\pi\)
\(822\) 16.6993 0.582456
\(823\) 39.3703 1.37236 0.686182 0.727430i \(-0.259286\pi\)
0.686182 + 0.727430i \(0.259286\pi\)
\(824\) −18.4602 −0.643093
\(825\) 1.09454 0.0381071
\(826\) −6.02633 −0.209683
\(827\) −26.3888 −0.917628 −0.458814 0.888532i \(-0.651726\pi\)
−0.458814 + 0.888532i \(0.651726\pi\)
\(828\) −24.7733 −0.860930
\(829\) 45.0610 1.56503 0.782517 0.622629i \(-0.213935\pi\)
0.782517 + 0.622629i \(0.213935\pi\)
\(830\) −9.11224 −0.316291
\(831\) −42.7945 −1.48452
\(832\) −24.3858 −0.845425
\(833\) 2.83206 0.0981251
\(834\) −37.2216 −1.28888
\(835\) 44.9387 1.55517
\(836\) 94.5613 3.27047
\(837\) 51.8642 1.79269
\(838\) 61.1957 2.11397
\(839\) −42.0761 −1.45263 −0.726314 0.687363i \(-0.758768\pi\)
−0.726314 + 0.687363i \(0.758768\pi\)
\(840\) −16.5400 −0.570683
\(841\) 36.0831 1.24425
\(842\) 17.6034 0.606655
\(843\) −35.2815 −1.21516
\(844\) −40.0790 −1.37958
\(845\) 5.72712 0.197019
\(846\) 11.3395 0.389860
\(847\) 18.3751 0.631375
\(848\) 27.2131 0.934503
\(849\) −12.9872 −0.445720
\(850\) −0.964426 −0.0330795
\(851\) −0.328272 −0.0112530
\(852\) 71.4086 2.44642
\(853\) −20.2803 −0.694384 −0.347192 0.937794i \(-0.612865\pi\)
−0.347192 + 0.937794i \(0.612865\pi\)
\(854\) −12.9818 −0.444228
\(855\) −8.58624 −0.293643
\(856\) 43.0011 1.46975
\(857\) −49.2604 −1.68270 −0.841351 0.540490i \(-0.818239\pi\)
−0.841351 + 0.540490i \(0.818239\pi\)
\(858\) −62.8045 −2.14411
\(859\) −12.7326 −0.434430 −0.217215 0.976124i \(-0.569697\pi\)
−0.217215 + 0.976124i \(0.569697\pi\)
\(860\) 57.7814 1.97033
\(861\) 1.45719 0.0496609
\(862\) 36.0072 1.22641
\(863\) −14.7535 −0.502216 −0.251108 0.967959i \(-0.580795\pi\)
−0.251108 + 0.967959i \(0.580795\pi\)
\(864\) −2.11763 −0.0720432
\(865\) 21.1133 0.717872
\(866\) 72.2838 2.45630
\(867\) 13.0847 0.444381
\(868\) 37.0718 1.25830
\(869\) −26.7136 −0.906197
\(870\) −65.4804 −2.21999
\(871\) −28.4282 −0.963254
\(872\) 14.6167 0.494982
\(873\) −16.5044 −0.558590
\(874\) 74.3122 2.51365
\(875\) 11.0201 0.372546
\(876\) −14.2973 −0.483060
\(877\) −20.7432 −0.700450 −0.350225 0.936666i \(-0.613895\pi\)
−0.350225 + 0.936666i \(0.613895\pi\)
\(878\) −65.2648 −2.20258
\(879\) 12.8122 0.432144
\(880\) 51.9469 1.75113
\(881\) −19.5041 −0.657110 −0.328555 0.944485i \(-0.606562\pi\)
−0.328555 + 0.944485i \(0.606562\pi\)
\(882\) 2.15397 0.0725278
\(883\) 27.7626 0.934286 0.467143 0.884182i \(-0.345283\pi\)
0.467143 + 0.884182i \(0.345283\pi\)
\(884\) 37.0077 1.24470
\(885\) 8.10125 0.272321
\(886\) 30.0693 1.01020
\(887\) 35.3228 1.18602 0.593012 0.805194i \(-0.297939\pi\)
0.593012 + 0.805194i \(0.297939\pi\)
\(888\) −0.342221 −0.0114842
\(889\) 19.1099 0.640924
\(890\) 9.39254 0.314839
\(891\) 30.3610 1.01713
\(892\) −47.7394 −1.59843
\(893\) −22.7476 −0.761221
\(894\) 22.3089 0.746120
\(895\) 39.3204 1.31434
\(896\) 19.2650 0.643598
\(897\) −33.0068 −1.10206
\(898\) 57.5802 1.92148
\(899\) 74.0687 2.47033
\(900\) −0.490535 −0.0163512
\(901\) 18.2278 0.607255
\(902\) −13.3177 −0.443430
\(903\) 9.19897 0.306123
\(904\) 35.2503 1.17241
\(905\) −22.9756 −0.763734
\(906\) −75.7469 −2.51652
\(907\) 10.5803 0.351312 0.175656 0.984452i \(-0.443795\pi\)
0.175656 + 0.984452i \(0.443795\pi\)
\(908\) 6.47156 0.214766
\(909\) −6.52980 −0.216580
\(910\) 18.0263 0.597567
\(911\) −18.0853 −0.599192 −0.299596 0.954066i \(-0.596852\pi\)
−0.299596 + 0.954066i \(0.596852\pi\)
\(912\) 26.6223 0.881552
\(913\) 8.86654 0.293440
\(914\) 20.2872 0.671041
\(915\) 17.4516 0.576930
\(916\) −40.1093 −1.32525
\(917\) 9.99440 0.330044
\(918\) −39.3105 −1.29744
\(919\) 9.90775 0.326826 0.163413 0.986558i \(-0.447750\pi\)
0.163413 + 0.986558i \(0.447750\pi\)
\(920\) 79.4436 2.61918
\(921\) −37.0869 −1.22205
\(922\) 21.6046 0.711508
\(923\) −39.2770 −1.29282
\(924\) 31.8896 1.04909
\(925\) −0.00650012 −0.000213722 0
\(926\) −90.6419 −2.97868
\(927\) −3.23177 −0.106145
\(928\) −3.02425 −0.0992757
\(929\) −15.2665 −0.500878 −0.250439 0.968132i \(-0.580575\pi\)
−0.250439 + 0.968132i \(0.580575\pi\)
\(930\) −74.5208 −2.44363
\(931\) −4.32097 −0.141614
\(932\) −31.9489 −1.04652
\(933\) 11.9602 0.391561
\(934\) 53.7641 1.75921
\(935\) 34.7948 1.13791
\(936\) 14.2051 0.464307
\(937\) 21.2126 0.692985 0.346492 0.938053i \(-0.387373\pi\)
0.346492 + 0.938053i \(0.387373\pi\)
\(938\) 21.5845 0.704759
\(939\) −11.4247 −0.372832
\(940\) −48.1859 −1.57165
\(941\) −34.1282 −1.11255 −0.556274 0.830999i \(-0.687770\pi\)
−0.556274 + 0.830999i \(0.687770\pi\)
\(942\) 73.3707 2.39055
\(943\) −6.99907 −0.227921
\(944\) 10.3696 0.337502
\(945\) −12.8053 −0.416556
\(946\) −84.0720 −2.73342
\(947\) −18.3584 −0.596567 −0.298284 0.954477i \(-0.596414\pi\)
−0.298284 + 0.954477i \(0.596414\pi\)
\(948\) −29.0003 −0.941886
\(949\) 7.86394 0.255274
\(950\) 1.47146 0.0477403
\(951\) −47.2653 −1.53268
\(952\) −14.1808 −0.459601
\(953\) −16.0790 −0.520849 −0.260424 0.965494i \(-0.583862\pi\)
−0.260424 + 0.965494i \(0.583862\pi\)
\(954\) 13.8634 0.448844
\(955\) −41.2474 −1.33473
\(956\) 109.785 3.55069
\(957\) 63.7147 2.05960
\(958\) −84.4482 −2.72840
\(959\) 4.66385 0.150603
\(960\) −24.8902 −0.803328
\(961\) 53.2949 1.71919
\(962\) 0.372974 0.0120252
\(963\) 7.52805 0.242588
\(964\) 78.3386 2.52312
\(965\) −2.94576 −0.0948273
\(966\) 25.0608 0.806318
\(967\) 38.0340 1.22309 0.611546 0.791209i \(-0.290548\pi\)
0.611546 + 0.791209i \(0.290548\pi\)
\(968\) −92.0080 −2.95725
\(969\) 17.8320 0.572847
\(970\) 104.872 3.36725
\(971\) 60.7488 1.94952 0.974761 0.223250i \(-0.0716667\pi\)
0.974761 + 0.223250i \(0.0716667\pi\)
\(972\) −35.4677 −1.13763
\(973\) −10.3954 −0.333261
\(974\) −39.2129 −1.25646
\(975\) −0.653567 −0.0209309
\(976\) 22.3380 0.715021
\(977\) −4.23580 −0.135515 −0.0677576 0.997702i \(-0.521584\pi\)
−0.0677576 + 0.997702i \(0.521584\pi\)
\(978\) −5.85415 −0.187195
\(979\) −9.13928 −0.292093
\(980\) −9.15303 −0.292383
\(981\) 2.55889 0.0816990
\(982\) 4.17386 0.133193
\(983\) −7.21490 −0.230120 −0.115060 0.993359i \(-0.536706\pi\)
−0.115060 + 0.993359i \(0.536706\pi\)
\(984\) −7.29647 −0.232603
\(985\) −12.8004 −0.407855
\(986\) −56.1404 −1.78788
\(987\) −7.67135 −0.244182
\(988\) −56.4639 −1.79636
\(989\) −44.1838 −1.40496
\(990\) 26.4637 0.841071
\(991\) −20.9196 −0.664533 −0.332267 0.943186i \(-0.607813\pi\)
−0.332267 + 0.943186i \(0.607813\pi\)
\(992\) −3.44178 −0.109277
\(993\) −20.1932 −0.640813
\(994\) 29.8215 0.945882
\(995\) 26.0843 0.826927
\(996\) 9.62551 0.304996
\(997\) −18.4455 −0.584175 −0.292088 0.956392i \(-0.594350\pi\)
−0.292088 + 0.956392i \(0.594350\pi\)
\(998\) 56.6432 1.79301
\(999\) −0.264948 −0.00838258
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 287.2.a.e.1.1 5
3.2 odd 2 2583.2.a.r.1.5 5
4.3 odd 2 4592.2.a.bb.1.5 5
5.4 even 2 7175.2.a.n.1.5 5
7.6 odd 2 2009.2.a.n.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.2.a.e.1.1 5 1.1 even 1 trivial
2009.2.a.n.1.1 5 7.6 odd 2
2583.2.a.r.1.5 5 3.2 odd 2
4592.2.a.bb.1.5 5 4.3 odd 2
7175.2.a.n.1.5 5 5.4 even 2