Properties

Label 4598.2.a.bv.1.2
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.258228.1
Defining polynomial: \(x^{4} - 2 x^{3} - 12 x^{2} + 6 x + 24\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.63927\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.639273 q^{3} +1.00000 q^{4} -1.63927 q^{5} -0.639273 q^{6} +1.54956 q^{7} +1.00000 q^{8} -2.59133 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.639273 q^{3} +1.00000 q^{4} -1.63927 q^{5} -0.639273 q^{6} +1.54956 q^{7} +1.00000 q^{8} -2.59133 q^{9} -1.63927 q^{10} -0.639273 q^{12} +6.04177 q^{13} +1.54956 q^{14} +1.04794 q^{15} +1.00000 q^{16} -2.54956 q^{17} -2.59133 q^{18} +1.00000 q^{19} -1.63927 q^{20} -0.990593 q^{21} -7.04177 q^{23} -0.639273 q^{24} -2.31278 q^{25} +6.04177 q^{26} +3.57439 q^{27} +1.54956 q^{28} +1.95206 q^{29} +1.04794 q^{30} -1.27855 q^{31} +1.00000 q^{32} -2.54956 q^{34} -2.54015 q^{35} -2.59133 q^{36} +5.73839 q^{37} +1.00000 q^{38} -3.86234 q^{39} -1.63927 q^{40} +9.13148 q^{41} -0.990593 q^{42} +12.8050 q^{43} +4.24790 q^{45} -7.04177 q^{46} +3.59133 q^{47} -0.639273 q^{48} -4.59886 q^{49} -2.31278 q^{50} +1.62987 q^{51} +6.04177 q^{52} -7.95206 q^{53} +3.57439 q^{54} +1.54956 q^{56} -0.639273 q^{57} +1.95206 q^{58} +5.40250 q^{59} +1.04794 q^{60} +13.5434 q^{61} -1.27855 q^{62} -4.01542 q^{63} +1.00000 q^{64} -9.90411 q^{65} +10.2212 q^{67} -2.54956 q^{68} +4.50162 q^{69} -2.54015 q^{70} -12.4100 q^{71} -2.59133 q^{72} -1.45044 q^{73} +5.73839 q^{74} +1.47850 q^{75} +1.00000 q^{76} -3.86234 q^{78} -1.13148 q^{79} -1.63927 q^{80} +5.48898 q^{81} +9.13148 q^{82} -4.36073 q^{83} -0.990593 q^{84} +4.17943 q^{85} +12.8050 q^{86} -1.24790 q^{87} -5.85294 q^{89} +4.24790 q^{90} +9.36209 q^{91} -7.04177 q^{92} +0.817341 q^{93} +3.59133 q^{94} -1.63927 q^{95} -0.639273 q^{96} -10.0000 q^{97} -4.59886 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} + 2q^{3} + 4q^{4} - 2q^{5} + 2q^{6} + 3q^{7} + 4q^{8} + 16q^{9} + O(q^{10}) \) \( 4q + 4q^{2} + 2q^{3} + 4q^{4} - 2q^{5} + 2q^{6} + 3q^{7} + 4q^{8} + 16q^{9} - 2q^{10} + 2q^{12} + q^{13} + 3q^{14} + 26q^{15} + 4q^{16} - 7q^{17} + 16q^{18} + 4q^{19} - 2q^{20} - 9q^{21} - 5q^{23} + 2q^{24} + 8q^{25} + q^{26} + 8q^{27} + 3q^{28} - 14q^{29} + 26q^{30} + 4q^{31} + 4q^{32} - 7q^{34} - 12q^{35} + 16q^{36} + 12q^{37} + 4q^{38} + 5q^{39} - 2q^{40} + 12q^{41} - 9q^{42} + 14q^{43} - 2q^{45} - 5q^{46} - 12q^{47} + 2q^{48} + 23q^{49} + 8q^{50} + 7q^{51} + q^{52} - 10q^{53} + 8q^{54} + 3q^{56} + 2q^{57} - 14q^{58} + 3q^{59} + 26q^{60} + 6q^{61} + 4q^{62} - 18q^{63} + 4q^{64} + 4q^{65} + 15q^{67} - 7q^{68} - 7q^{69} - 12q^{70} - 16q^{71} + 16q^{72} - 9q^{73} + 12q^{74} - 44q^{75} + 4q^{76} + 5q^{78} + 20q^{79} - 2q^{80} + 52q^{81} + 12q^{82} - 22q^{83} - 9q^{84} + 14q^{85} + 14q^{86} + 14q^{87} - 8q^{89} - 2q^{90} - 18q^{91} - 5q^{92} + 56q^{93} - 12q^{94} - 2q^{95} + 2q^{96} - 40q^{97} + 23q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.639273 −0.369085 −0.184542 0.982825i \(-0.559080\pi\)
−0.184542 + 0.982825i \(0.559080\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.63927 −0.733105 −0.366553 0.930397i \(-0.619462\pi\)
−0.366553 + 0.930397i \(0.619462\pi\)
\(6\) −0.639273 −0.260982
\(7\) 1.54956 0.585679 0.292839 0.956162i \(-0.405400\pi\)
0.292839 + 0.956162i \(0.405400\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.59133 −0.863776
\(10\) −1.63927 −0.518384
\(11\) 0 0
\(12\) −0.639273 −0.184542
\(13\) 6.04177 1.67569 0.837843 0.545912i \(-0.183817\pi\)
0.837843 + 0.545912i \(0.183817\pi\)
\(14\) 1.54956 0.414137
\(15\) 1.04794 0.270578
\(16\) 1.00000 0.250000
\(17\) −2.54956 −0.618359 −0.309180 0.951004i \(-0.600054\pi\)
−0.309180 + 0.951004i \(0.600054\pi\)
\(18\) −2.59133 −0.610782
\(19\) 1.00000 0.229416
\(20\) −1.63927 −0.366553
\(21\) −0.990593 −0.216165
\(22\) 0 0
\(23\) −7.04177 −1.46831 −0.734155 0.678982i \(-0.762422\pi\)
−0.734155 + 0.678982i \(0.762422\pi\)
\(24\) −0.639273 −0.130491
\(25\) −2.31278 −0.462557
\(26\) 6.04177 1.18489
\(27\) 3.57439 0.687891
\(28\) 1.54956 0.292839
\(29\) 1.95206 0.362488 0.181244 0.983438i \(-0.441988\pi\)
0.181244 + 0.983438i \(0.441988\pi\)
\(30\) 1.04794 0.191328
\(31\) −1.27855 −0.229634 −0.114817 0.993387i \(-0.536628\pi\)
−0.114817 + 0.993387i \(0.536628\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −2.54956 −0.437246
\(35\) −2.54015 −0.429364
\(36\) −2.59133 −0.431888
\(37\) 5.73839 0.943386 0.471693 0.881763i \(-0.343643\pi\)
0.471693 + 0.881763i \(0.343643\pi\)
\(38\) 1.00000 0.162221
\(39\) −3.86234 −0.618470
\(40\) −1.63927 −0.259192
\(41\) 9.13148 1.42610 0.713049 0.701114i \(-0.247314\pi\)
0.713049 + 0.701114i \(0.247314\pi\)
\(42\) −0.990593 −0.152852
\(43\) 12.8050 1.95274 0.976371 0.216099i \(-0.0693334\pi\)
0.976371 + 0.216099i \(0.0693334\pi\)
\(44\) 0 0
\(45\) 4.24790 0.633239
\(46\) −7.04177 −1.03825
\(47\) 3.59133 0.523849 0.261925 0.965088i \(-0.415643\pi\)
0.261925 + 0.965088i \(0.415643\pi\)
\(48\) −0.639273 −0.0922712
\(49\) −4.59886 −0.656980
\(50\) −2.31278 −0.327077
\(51\) 1.62987 0.228227
\(52\) 6.04177 0.837843
\(53\) −7.95206 −1.09230 −0.546149 0.837688i \(-0.683907\pi\)
−0.546149 + 0.837688i \(0.683907\pi\)
\(54\) 3.57439 0.486413
\(55\) 0 0
\(56\) 1.54956 0.207069
\(57\) −0.639273 −0.0846738
\(58\) 1.95206 0.256318
\(59\) 5.40250 0.703345 0.351673 0.936123i \(-0.385613\pi\)
0.351673 + 0.936123i \(0.385613\pi\)
\(60\) 1.04794 0.135289
\(61\) 13.5434 1.73405 0.867026 0.498262i \(-0.166028\pi\)
0.867026 + 0.498262i \(0.166028\pi\)
\(62\) −1.27855 −0.162376
\(63\) −4.01542 −0.505896
\(64\) 1.00000 0.125000
\(65\) −9.90411 −1.22845
\(66\) 0 0
\(67\) 10.2212 1.24872 0.624359 0.781138i \(-0.285360\pi\)
0.624359 + 0.781138i \(0.285360\pi\)
\(68\) −2.54956 −0.309180
\(69\) 4.50162 0.541931
\(70\) −2.54015 −0.303606
\(71\) −12.4100 −1.47280 −0.736400 0.676547i \(-0.763476\pi\)
−0.736400 + 0.676547i \(0.763476\pi\)
\(72\) −2.59133 −0.305391
\(73\) −1.45044 −0.169761 −0.0848806 0.996391i \(-0.527051\pi\)
−0.0848806 + 0.996391i \(0.527051\pi\)
\(74\) 5.73839 0.667075
\(75\) 1.47850 0.170723
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −3.86234 −0.437324
\(79\) −1.13148 −0.127302 −0.0636509 0.997972i \(-0.520274\pi\)
−0.0636509 + 0.997972i \(0.520274\pi\)
\(80\) −1.63927 −0.183276
\(81\) 5.48898 0.609886
\(82\) 9.13148 1.00840
\(83\) −4.36073 −0.478652 −0.239326 0.970939i \(-0.576926\pi\)
−0.239326 + 0.970939i \(0.576926\pi\)
\(84\) −0.990593 −0.108083
\(85\) 4.17943 0.453322
\(86\) 12.8050 1.38080
\(87\) −1.24790 −0.133789
\(88\) 0 0
\(89\) −5.85294 −0.620410 −0.310205 0.950670i \(-0.600398\pi\)
−0.310205 + 0.950670i \(0.600398\pi\)
\(90\) 4.24790 0.447768
\(91\) 9.36209 0.981413
\(92\) −7.04177 −0.734155
\(93\) 0.817341 0.0847543
\(94\) 3.59133 0.370417
\(95\) −1.63927 −0.168186
\(96\) −0.639273 −0.0652456
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) −4.59886 −0.464555
\(99\) 0 0
\(100\) −2.31278 −0.231278
\(101\) −8.26484 −0.822382 −0.411191 0.911549i \(-0.634887\pi\)
−0.411191 + 0.911549i \(0.634887\pi\)
\(102\) 1.62987 0.161381
\(103\) 8.14706 0.802754 0.401377 0.915913i \(-0.368532\pi\)
0.401377 + 0.915913i \(0.368532\pi\)
\(104\) 6.04177 0.592444
\(105\) 1.62385 0.158472
\(106\) −7.95206 −0.772372
\(107\) 12.5509 1.21334 0.606672 0.794953i \(-0.292504\pi\)
0.606672 + 0.794953i \(0.292504\pi\)
\(108\) 3.57439 0.343946
\(109\) −3.40250 −0.325900 −0.162950 0.986634i \(-0.552101\pi\)
−0.162950 + 0.986634i \(0.552101\pi\)
\(110\) 0 0
\(111\) −3.66840 −0.348189
\(112\) 1.54956 0.146420
\(113\) −3.13148 −0.294585 −0.147293 0.989093i \(-0.547056\pi\)
−0.147293 + 0.989093i \(0.547056\pi\)
\(114\) −0.639273 −0.0598734
\(115\) 11.5434 1.07643
\(116\) 1.95206 0.181244
\(117\) −15.6562 −1.44742
\(118\) 5.40250 0.497340
\(119\) −3.95070 −0.362160
\(120\) 1.04794 0.0956638
\(121\) 0 0
\(122\) 13.5434 1.22616
\(123\) −5.83751 −0.526351
\(124\) −1.27855 −0.114817
\(125\) 11.9877 1.07221
\(126\) −4.01542 −0.357722
\(127\) −5.82057 −0.516492 −0.258246 0.966079i \(-0.583145\pi\)
−0.258246 + 0.966079i \(0.583145\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.18589 −0.720728
\(130\) −9.90411 −0.868648
\(131\) 14.9844 1.30919 0.654597 0.755978i \(-0.272838\pi\)
0.654597 + 0.755978i \(0.272838\pi\)
\(132\) 0 0
\(133\) 1.54956 0.134364
\(134\) 10.2212 0.882977
\(135\) −5.85940 −0.504297
\(136\) −2.54956 −0.218623
\(137\) 19.3546 1.65357 0.826785 0.562517i \(-0.190167\pi\)
0.826785 + 0.562517i \(0.190167\pi\)
\(138\) 4.50162 0.383203
\(139\) 15.7398 1.33503 0.667514 0.744597i \(-0.267358\pi\)
0.667514 + 0.744597i \(0.267358\pi\)
\(140\) −2.54015 −0.214682
\(141\) −2.29584 −0.193345
\(142\) −12.4100 −1.04143
\(143\) 0 0
\(144\) −2.59133 −0.215944
\(145\) −3.19995 −0.265742
\(146\) −1.45044 −0.120039
\(147\) 2.93993 0.242481
\(148\) 5.73839 0.471693
\(149\) 19.4456 1.59305 0.796524 0.604607i \(-0.206670\pi\)
0.796524 + 0.604607i \(0.206670\pi\)
\(150\) 1.47850 0.120719
\(151\) −12.2306 −0.995312 −0.497656 0.867374i \(-0.665806\pi\)
−0.497656 + 0.867374i \(0.665806\pi\)
\(152\) 1.00000 0.0811107
\(153\) 6.60675 0.534124
\(154\) 0 0
\(155\) 2.09589 0.168346
\(156\) −3.86234 −0.309235
\(157\) 24.6425 1.96669 0.983343 0.181759i \(-0.0581792\pi\)
0.983343 + 0.181759i \(0.0581792\pi\)
\(158\) −1.13148 −0.0900159
\(159\) 5.08354 0.403151
\(160\) −1.63927 −0.129596
\(161\) −10.9116 −0.859958
\(162\) 5.48898 0.431255
\(163\) −19.0032 −1.48845 −0.744224 0.667930i \(-0.767181\pi\)
−0.744224 + 0.667930i \(0.767181\pi\)
\(164\) 9.13148 0.713049
\(165\) 0 0
\(166\) −4.36073 −0.338458
\(167\) −1.82057 −0.140880 −0.0704401 0.997516i \(-0.522440\pi\)
−0.0704401 + 0.997516i \(0.522440\pi\)
\(168\) −0.990593 −0.0764259
\(169\) 23.5030 1.80792
\(170\) 4.17943 0.320547
\(171\) −2.59133 −0.198164
\(172\) 12.8050 0.976371
\(173\) 10.3109 0.783924 0.391962 0.919981i \(-0.371796\pi\)
0.391962 + 0.919981i \(0.371796\pi\)
\(174\) −1.24790 −0.0946029
\(175\) −3.58380 −0.270909
\(176\) 0 0
\(177\) −3.45367 −0.259594
\(178\) −5.85294 −0.438696
\(179\) 5.78770 0.432593 0.216296 0.976328i \(-0.430602\pi\)
0.216296 + 0.976328i \(0.430602\pi\)
\(180\) 4.24790 0.316620
\(181\) 15.4768 1.15038 0.575190 0.818020i \(-0.304928\pi\)
0.575190 + 0.818020i \(0.304928\pi\)
\(182\) 9.36209 0.693964
\(183\) −8.65793 −0.640012
\(184\) −7.04177 −0.519126
\(185\) −9.40680 −0.691601
\(186\) 0.817341 0.0599304
\(187\) 0 0
\(188\) 3.59133 0.261925
\(189\) 5.53873 0.402883
\(190\) −1.63927 −0.118925
\(191\) 15.4537 1.11819 0.559094 0.829104i \(-0.311149\pi\)
0.559094 + 0.829104i \(0.311149\pi\)
\(192\) −0.639273 −0.0461356
\(193\) 8.00000 0.575853 0.287926 0.957653i \(-0.407034\pi\)
0.287926 + 0.957653i \(0.407034\pi\)
\(194\) −10.0000 −0.717958
\(195\) 6.33144 0.453404
\(196\) −4.59886 −0.328490
\(197\) 5.72469 0.407867 0.203933 0.978985i \(-0.434627\pi\)
0.203933 + 0.978985i \(0.434627\pi\)
\(198\) 0 0
\(199\) 4.18696 0.296806 0.148403 0.988927i \(-0.452587\pi\)
0.148403 + 0.988927i \(0.452587\pi\)
\(200\) −2.31278 −0.163538
\(201\) −6.53414 −0.460883
\(202\) −8.26484 −0.581512
\(203\) 3.02483 0.212301
\(204\) 1.62987 0.114113
\(205\) −14.9690 −1.04548
\(206\) 8.14706 0.567633
\(207\) 18.2475 1.26829
\(208\) 6.04177 0.418921
\(209\) 0 0
\(210\) 1.62385 0.112056
\(211\) 12.9022 0.888227 0.444113 0.895971i \(-0.353519\pi\)
0.444113 + 0.895971i \(0.353519\pi\)
\(212\) −7.95206 −0.546149
\(213\) 7.93340 0.543588
\(214\) 12.5509 0.857963
\(215\) −20.9909 −1.43157
\(216\) 3.57439 0.243206
\(217\) −1.98119 −0.134492
\(218\) −3.40250 −0.230446
\(219\) 0.927228 0.0626562
\(220\) 0 0
\(221\) −15.4039 −1.03618
\(222\) −3.66840 −0.246207
\(223\) 21.3109 1.42708 0.713542 0.700612i \(-0.247090\pi\)
0.713542 + 0.700612i \(0.247090\pi\)
\(224\) 1.54956 0.103534
\(225\) 5.99318 0.399545
\(226\) −3.13148 −0.208303
\(227\) −20.5030 −1.36083 −0.680415 0.732827i \(-0.738201\pi\)
−0.680415 + 0.732827i \(0.738201\pi\)
\(228\) −0.639273 −0.0423369
\(229\) 16.6406 1.09964 0.549822 0.835282i \(-0.314696\pi\)
0.549822 + 0.835282i \(0.314696\pi\)
\(230\) 11.5434 0.761148
\(231\) 0 0
\(232\) 1.95206 0.128159
\(233\) 6.57575 0.430792 0.215396 0.976527i \(-0.430896\pi\)
0.215396 + 0.976527i \(0.430896\pi\)
\(234\) −15.6562 −1.02348
\(235\) −5.88717 −0.384037
\(236\) 5.40250 0.351673
\(237\) 0.723327 0.0469851
\(238\) −3.95070 −0.256086
\(239\) 3.63791 0.235317 0.117659 0.993054i \(-0.462461\pi\)
0.117659 + 0.993054i \(0.462461\pi\)
\(240\) 1.04794 0.0676445
\(241\) 28.1498 1.81329 0.906643 0.421898i \(-0.138636\pi\)
0.906643 + 0.421898i \(0.138636\pi\)
\(242\) 0 0
\(243\) −14.2321 −0.912991
\(244\) 13.5434 0.867026
\(245\) 7.53879 0.481636
\(246\) −5.83751 −0.372186
\(247\) 6.04177 0.384429
\(248\) −1.27855 −0.0811878
\(249\) 2.78770 0.176663
\(250\) 11.9877 0.758166
\(251\) −10.8050 −0.682005 −0.341003 0.940062i \(-0.610766\pi\)
−0.341003 + 0.940062i \(0.610766\pi\)
\(252\) −4.01542 −0.252948
\(253\) 0 0
\(254\) −5.82057 −0.365215
\(255\) −2.67180 −0.167314
\(256\) 1.00000 0.0625000
\(257\) −15.0032 −0.935876 −0.467938 0.883761i \(-0.655003\pi\)
−0.467938 + 0.883761i \(0.655003\pi\)
\(258\) −8.18589 −0.509631
\(259\) 8.89199 0.552521
\(260\) −9.90411 −0.614227
\(261\) −5.05842 −0.313108
\(262\) 14.9844 0.925740
\(263\) −3.57575 −0.220490 −0.110245 0.993904i \(-0.535164\pi\)
−0.110245 + 0.993904i \(0.535164\pi\)
\(264\) 0 0
\(265\) 13.0356 0.800770
\(266\) 1.54956 0.0950096
\(267\) 3.74163 0.228984
\(268\) 10.2212 0.624359
\(269\) −25.5895 −1.56022 −0.780108 0.625644i \(-0.784836\pi\)
−0.780108 + 0.625644i \(0.784836\pi\)
\(270\) −5.85940 −0.356592
\(271\) 10.8125 0.656814 0.328407 0.944536i \(-0.393488\pi\)
0.328407 + 0.944536i \(0.393488\pi\)
\(272\) −2.54956 −0.154590
\(273\) −5.98493 −0.362225
\(274\) 19.3546 1.16925
\(275\) 0 0
\(276\) 4.50162 0.270965
\(277\) −0.277188 −0.0166546 −0.00832731 0.999965i \(-0.502651\pi\)
−0.00832731 + 0.999965i \(0.502651\pi\)
\(278\) 15.7398 0.944008
\(279\) 3.31314 0.198352
\(280\) −2.54015 −0.151803
\(281\) −8.23060 −0.490997 −0.245498 0.969397i \(-0.578952\pi\)
−0.245498 + 0.969397i \(0.578952\pi\)
\(282\) −2.29584 −0.136715
\(283\) −20.4612 −1.21629 −0.608146 0.793825i \(-0.708087\pi\)
−0.608146 + 0.793825i \(0.708087\pi\)
\(284\) −12.4100 −0.736400
\(285\) 1.04794 0.0620748
\(286\) 0 0
\(287\) 14.1498 0.835235
\(288\) −2.59133 −0.152696
\(289\) −10.4997 −0.617632
\(290\) −3.19995 −0.187908
\(291\) 6.39273 0.374749
\(292\) −1.45044 −0.0848806
\(293\) 11.5402 0.674183 0.337091 0.941472i \(-0.390557\pi\)
0.337091 + 0.941472i \(0.390557\pi\)
\(294\) 2.93993 0.171460
\(295\) −8.85617 −0.515626
\(296\) 5.73839 0.333537
\(297\) 0 0
\(298\) 19.4456 1.12645
\(299\) −42.5447 −2.46043
\(300\) 1.47850 0.0853613
\(301\) 19.8421 1.14368
\(302\) −12.2306 −0.703792
\(303\) 5.28349 0.303529
\(304\) 1.00000 0.0573539
\(305\) −22.2013 −1.27124
\(306\) 6.60675 0.377683
\(307\) −1.75382 −0.100096 −0.0500478 0.998747i \(-0.515937\pi\)
−0.0500478 + 0.998747i \(0.515937\pi\)
\(308\) 0 0
\(309\) −5.20820 −0.296284
\(310\) 2.09589 0.119038
\(311\) −17.7473 −1.00636 −0.503178 0.864183i \(-0.667836\pi\)
−0.503178 + 0.864183i \(0.667836\pi\)
\(312\) −3.86234 −0.218662
\(313\) −16.4381 −0.929136 −0.464568 0.885538i \(-0.653790\pi\)
−0.464568 + 0.885538i \(0.653790\pi\)
\(314\) 24.6425 1.39066
\(315\) 6.58237 0.370875
\(316\) −1.13148 −0.0636509
\(317\) 6.78204 0.380917 0.190459 0.981695i \(-0.439003\pi\)
0.190459 + 0.981695i \(0.439003\pi\)
\(318\) 5.08354 0.285071
\(319\) 0 0
\(320\) −1.63927 −0.0916382
\(321\) −8.02347 −0.447826
\(322\) −10.9116 −0.608082
\(323\) −2.54956 −0.141861
\(324\) 5.48898 0.304943
\(325\) −13.9733 −0.775099
\(326\) −19.0032 −1.05249
\(327\) 2.17513 0.120285
\(328\) 9.13148 0.504202
\(329\) 5.56498 0.306807
\(330\) 0 0
\(331\) −7.61616 −0.418622 −0.209311 0.977849i \(-0.567122\pi\)
−0.209311 + 0.977849i \(0.567122\pi\)
\(332\) −4.36073 −0.239326
\(333\) −14.8701 −0.814875
\(334\) −1.82057 −0.0996174
\(335\) −16.7553 −0.915442
\(336\) −0.990593 −0.0540413
\(337\) −20.0200 −1.09056 −0.545280 0.838254i \(-0.683577\pi\)
−0.545280 + 0.838254i \(0.683577\pi\)
\(338\) 23.5030 1.27839
\(339\) 2.00187 0.108727
\(340\) 4.17943 0.226661
\(341\) 0 0
\(342\) −2.59133 −0.140123
\(343\) −17.9731 −0.970458
\(344\) 12.8050 0.690399
\(345\) −7.37938 −0.397292
\(346\) 10.3109 0.554318
\(347\) −16.3296 −0.876617 −0.438308 0.898825i \(-0.644422\pi\)
−0.438308 + 0.898825i \(0.644422\pi\)
\(348\) −1.24790 −0.0668943
\(349\) −26.9995 −1.44525 −0.722625 0.691241i \(-0.757064\pi\)
−0.722625 + 0.691241i \(0.757064\pi\)
\(350\) −3.58380 −0.191562
\(351\) 21.5956 1.15269
\(352\) 0 0
\(353\) 14.0525 0.747941 0.373970 0.927441i \(-0.377996\pi\)
0.373970 + 0.927441i \(0.377996\pi\)
\(354\) −3.45367 −0.183561
\(355\) 20.3434 1.07972
\(356\) −5.85294 −0.310205
\(357\) 2.52558 0.133668
\(358\) 5.78770 0.305889
\(359\) 25.3546 1.33816 0.669081 0.743189i \(-0.266688\pi\)
0.669081 + 0.743189i \(0.266688\pi\)
\(360\) 4.24790 0.223884
\(361\) 1.00000 0.0526316
\(362\) 15.4768 0.813442
\(363\) 0 0
\(364\) 9.36209 0.490707
\(365\) 2.37767 0.124453
\(366\) −8.65793 −0.452557
\(367\) 19.3931 1.01231 0.506155 0.862442i \(-0.331066\pi\)
0.506155 + 0.862442i \(0.331066\pi\)
\(368\) −7.04177 −0.367078
\(369\) −23.6627 −1.23183
\(370\) −9.40680 −0.489036
\(371\) −12.3222 −0.639736
\(372\) 0.817341 0.0423772
\(373\) −35.3018 −1.82786 −0.913929 0.405875i \(-0.866967\pi\)
−0.913929 + 0.405875i \(0.866967\pi\)
\(374\) 0 0
\(375\) −7.66339 −0.395736
\(376\) 3.59133 0.185209
\(377\) 11.7939 0.607415
\(378\) 5.53873 0.284882
\(379\) −5.17002 −0.265566 −0.132783 0.991145i \(-0.542391\pi\)
−0.132783 + 0.991145i \(0.542391\pi\)
\(380\) −1.63927 −0.0840930
\(381\) 3.72094 0.190629
\(382\) 15.4537 0.790679
\(383\) −5.16759 −0.264052 −0.132026 0.991246i \(-0.542148\pi\)
−0.132026 + 0.991246i \(0.542148\pi\)
\(384\) −0.639273 −0.0326228
\(385\) 0 0
\(386\) 8.00000 0.407189
\(387\) −33.1820 −1.68673
\(388\) −10.0000 −0.507673
\(389\) 4.91782 0.249343 0.124672 0.992198i \(-0.460212\pi\)
0.124672 + 0.992198i \(0.460212\pi\)
\(390\) 6.33144 0.320605
\(391\) 17.9534 0.907943
\(392\) −4.59886 −0.232278
\(393\) −9.57914 −0.483204
\(394\) 5.72469 0.288405
\(395\) 1.85481 0.0933256
\(396\) 0 0
\(397\) −7.54151 −0.378498 −0.189249 0.981929i \(-0.560605\pi\)
−0.189249 + 0.981929i \(0.560605\pi\)
\(398\) 4.18696 0.209873
\(399\) −0.990593 −0.0495917
\(400\) −2.31278 −0.115639
\(401\) 4.03236 0.201367 0.100683 0.994919i \(-0.467897\pi\)
0.100683 + 0.994919i \(0.467897\pi\)
\(402\) −6.53414 −0.325893
\(403\) −7.72469 −0.384794
\(404\) −8.26484 −0.411191
\(405\) −8.99793 −0.447111
\(406\) 3.02483 0.150120
\(407\) 0 0
\(408\) 1.62987 0.0806904
\(409\) −0.358853 −0.0177441 −0.00887207 0.999961i \(-0.502824\pi\)
−0.00887207 + 0.999961i \(0.502824\pi\)
\(410\) −14.9690 −0.739266
\(411\) −12.3729 −0.610308
\(412\) 8.14706 0.401377
\(413\) 8.37149 0.411934
\(414\) 18.2475 0.896818
\(415\) 7.14842 0.350902
\(416\) 6.04177 0.296222
\(417\) −10.0620 −0.492739
\(418\) 0 0
\(419\) 31.2643 1.52736 0.763681 0.645594i \(-0.223390\pi\)
0.763681 + 0.645594i \(0.223390\pi\)
\(420\) 1.62385 0.0792359
\(421\) 18.7303 0.912861 0.456431 0.889759i \(-0.349128\pi\)
0.456431 + 0.889759i \(0.349128\pi\)
\(422\) 12.9022 0.628071
\(423\) −9.30632 −0.452489
\(424\) −7.95206 −0.386186
\(425\) 5.89658 0.286026
\(426\) 7.93340 0.384375
\(427\) 20.9863 1.01560
\(428\) 12.5509 0.606672
\(429\) 0 0
\(430\) −20.9909 −1.01227
\(431\) −7.03559 −0.338893 −0.169446 0.985539i \(-0.554198\pi\)
−0.169446 + 0.985539i \(0.554198\pi\)
\(432\) 3.57439 0.171973
\(433\) 11.2785 0.542012 0.271006 0.962578i \(-0.412644\pi\)
0.271006 + 0.962578i \(0.412644\pi\)
\(434\) −1.98119 −0.0950999
\(435\) 2.04565 0.0980812
\(436\) −3.40250 −0.162950
\(437\) −7.04177 −0.336854
\(438\) 0.927228 0.0443047
\(439\) −2.47356 −0.118056 −0.0590282 0.998256i \(-0.518800\pi\)
−0.0590282 + 0.998256i \(0.518800\pi\)
\(440\) 0 0
\(441\) 11.9172 0.567484
\(442\) −15.4039 −0.732687
\(443\) 23.0680 1.09599 0.547996 0.836481i \(-0.315391\pi\)
0.547996 + 0.836481i \(0.315391\pi\)
\(444\) −3.66840 −0.174095
\(445\) 9.59456 0.454826
\(446\) 21.3109 1.00910
\(447\) −12.4311 −0.587969
\(448\) 1.54956 0.0732098
\(449\) −22.8050 −1.07623 −0.538117 0.842870i \(-0.680864\pi\)
−0.538117 + 0.842870i \(0.680864\pi\)
\(450\) 5.99318 0.282521
\(451\) 0 0
\(452\) −3.13148 −0.147293
\(453\) 7.81870 0.367355
\(454\) −20.5030 −0.962252
\(455\) −15.3470 −0.719479
\(456\) −0.639273 −0.0299367
\(457\) −19.1253 −0.894644 −0.447322 0.894373i \(-0.647622\pi\)
−0.447322 + 0.894373i \(0.647622\pi\)
\(458\) 16.6406 0.777566
\(459\) −9.11312 −0.425364
\(460\) 11.5434 0.538213
\(461\) −16.2799 −0.758231 −0.379115 0.925349i \(-0.623772\pi\)
−0.379115 + 0.925349i \(0.623772\pi\)
\(462\) 0 0
\(463\) −21.0525 −0.978394 −0.489197 0.872173i \(-0.662710\pi\)
−0.489197 + 0.872173i \(0.662710\pi\)
\(464\) 1.95206 0.0906219
\(465\) −1.33985 −0.0621339
\(466\) 6.57575 0.304616
\(467\) −32.9909 −1.52664 −0.763318 0.646023i \(-0.776431\pi\)
−0.763318 + 0.646023i \(0.776431\pi\)
\(468\) −15.6562 −0.723709
\(469\) 15.8384 0.731347
\(470\) −5.88717 −0.271555
\(471\) −15.7533 −0.725874
\(472\) 5.40250 0.248670
\(473\) 0 0
\(474\) 0.723327 0.0332235
\(475\) −2.31278 −0.106118
\(476\) −3.95070 −0.181080
\(477\) 20.6064 0.943502
\(478\) 3.63791 0.166394
\(479\) −21.2630 −0.971530 −0.485765 0.874090i \(-0.661459\pi\)
−0.485765 + 0.874090i \(0.661459\pi\)
\(480\) 1.04794 0.0478319
\(481\) 34.6701 1.58082
\(482\) 28.1498 1.28219
\(483\) 6.97553 0.317397
\(484\) 0 0
\(485\) 16.3927 0.744356
\(486\) −14.2321 −0.645582
\(487\) 19.4306 0.880483 0.440241 0.897880i \(-0.354893\pi\)
0.440241 + 0.897880i \(0.354893\pi\)
\(488\) 13.5434 0.613080
\(489\) 12.1483 0.549363
\(490\) 7.53879 0.340568
\(491\) 32.2968 1.45754 0.728768 0.684761i \(-0.240093\pi\)
0.728768 + 0.684761i \(0.240093\pi\)
\(492\) −5.83751 −0.263175
\(493\) −4.97688 −0.224148
\(494\) 6.04177 0.271832
\(495\) 0 0
\(496\) −1.27855 −0.0574085
\(497\) −19.2301 −0.862587
\(498\) 2.78770 0.124920
\(499\) 4.26484 0.190920 0.0954602 0.995433i \(-0.469568\pi\)
0.0954602 + 0.995433i \(0.469568\pi\)
\(500\) 11.9877 0.536104
\(501\) 1.16384 0.0519967
\(502\) −10.8050 −0.482250
\(503\) 22.0108 0.981412 0.490706 0.871325i \(-0.336739\pi\)
0.490706 + 0.871325i \(0.336739\pi\)
\(504\) −4.01542 −0.178861
\(505\) 13.5483 0.602893
\(506\) 0 0
\(507\) −15.0248 −0.667276
\(508\) −5.82057 −0.258246
\(509\) −7.31107 −0.324057 −0.162029 0.986786i \(-0.551804\pi\)
−0.162029 + 0.986786i \(0.551804\pi\)
\(510\) −2.67180 −0.118309
\(511\) −2.24754 −0.0994255
\(512\) 1.00000 0.0441942
\(513\) 3.57439 0.157813
\(514\) −15.0032 −0.661764
\(515\) −13.3553 −0.588503
\(516\) −8.18589 −0.360364
\(517\) 0 0
\(518\) 8.89199 0.390691
\(519\) −6.59149 −0.289334
\(520\) −9.90411 −0.434324
\(521\) −31.4644 −1.37848 −0.689241 0.724532i \(-0.742056\pi\)
−0.689241 + 0.724532i \(0.742056\pi\)
\(522\) −5.05842 −0.221401
\(523\) −4.01264 −0.175460 −0.0877302 0.996144i \(-0.527961\pi\)
−0.0877302 + 0.996144i \(0.527961\pi\)
\(524\) 14.9844 0.654597
\(525\) 2.29103 0.0999886
\(526\) −3.57575 −0.155910
\(527\) 3.25973 0.141996
\(528\) 0 0
\(529\) 26.5865 1.15594
\(530\) 13.0356 0.566230
\(531\) −13.9996 −0.607533
\(532\) 1.54956 0.0671820
\(533\) 55.1703 2.38969
\(534\) 3.74163 0.161916
\(535\) −20.5744 −0.889508
\(536\) 10.2212 0.441488
\(537\) −3.69992 −0.159663
\(538\) −25.5895 −1.10324
\(539\) 0 0
\(540\) −5.85940 −0.252148
\(541\) −6.65298 −0.286034 −0.143017 0.989720i \(-0.545680\pi\)
−0.143017 + 0.989720i \(0.545680\pi\)
\(542\) 10.8125 0.464438
\(543\) −9.89390 −0.424588
\(544\) −2.54956 −0.109311
\(545\) 5.57762 0.238919
\(546\) −5.98493 −0.256131
\(547\) 22.5622 0.964690 0.482345 0.875981i \(-0.339785\pi\)
0.482345 + 0.875981i \(0.339785\pi\)
\(548\) 19.3546 0.826785
\(549\) −35.0954 −1.49783
\(550\) 0 0
\(551\) 1.95206 0.0831604
\(552\) 4.50162 0.191602
\(553\) −1.75330 −0.0745579
\(554\) −0.277188 −0.0117766
\(555\) 6.01352 0.255260
\(556\) 15.7398 0.667514
\(557\) 25.8270 1.09433 0.547163 0.837026i \(-0.315708\pi\)
0.547163 + 0.837026i \(0.315708\pi\)
\(558\) 3.31314 0.140256
\(559\) 77.3648 3.27218
\(560\) −2.54015 −0.107341
\(561\) 0 0
\(562\) −8.23060 −0.347187
\(563\) 22.0698 0.930132 0.465066 0.885276i \(-0.346031\pi\)
0.465066 + 0.885276i \(0.346031\pi\)
\(564\) −2.29584 −0.0966724
\(565\) 5.13336 0.215962
\(566\) −20.4612 −0.860049
\(567\) 8.50550 0.357197
\(568\) −12.4100 −0.520713
\(569\) −0.275315 −0.0115418 −0.00577089 0.999983i \(-0.501837\pi\)
−0.00577089 + 0.999983i \(0.501837\pi\)
\(570\) 1.04794 0.0438935
\(571\) −37.4287 −1.56634 −0.783171 0.621807i \(-0.786399\pi\)
−0.783171 + 0.621807i \(0.786399\pi\)
\(572\) 0 0
\(573\) −9.87912 −0.412706
\(574\) 14.1498 0.590600
\(575\) 16.2861 0.679177
\(576\) −2.59133 −0.107972
\(577\) −14.2893 −0.594872 −0.297436 0.954742i \(-0.596131\pi\)
−0.297436 + 0.954742i \(0.596131\pi\)
\(578\) −10.4997 −0.436732
\(579\) −5.11419 −0.212538
\(580\) −3.19995 −0.132871
\(581\) −6.75721 −0.280336
\(582\) 6.39273 0.264987
\(583\) 0 0
\(584\) −1.45044 −0.0600196
\(585\) 25.6648 1.06111
\(586\) 11.5402 0.476719
\(587\) 0.100479 0.00414722 0.00207361 0.999998i \(-0.499340\pi\)
0.00207361 + 0.999998i \(0.499340\pi\)
\(588\) 2.93993 0.121241
\(589\) −1.27855 −0.0526816
\(590\) −8.85617 −0.364603
\(591\) −3.65964 −0.150537
\(592\) 5.73839 0.235847
\(593\) −19.4270 −0.797770 −0.398885 0.917001i \(-0.630603\pi\)
−0.398885 + 0.917001i \(0.630603\pi\)
\(594\) 0 0
\(595\) 6.47627 0.265501
\(596\) 19.4456 0.796524
\(597\) −2.67661 −0.109546
\(598\) −42.5447 −1.73978
\(599\) −36.8389 −1.50520 −0.752598 0.658481i \(-0.771199\pi\)
−0.752598 + 0.658481i \(0.771199\pi\)
\(600\) 1.47850 0.0603595
\(601\) 2.98170 0.121626 0.0608130 0.998149i \(-0.480631\pi\)
0.0608130 + 0.998149i \(0.480631\pi\)
\(602\) 19.8421 0.808704
\(603\) −26.4865 −1.07861
\(604\) −12.2306 −0.497656
\(605\) 0 0
\(606\) 5.28349 0.214627
\(607\) 28.2118 1.14508 0.572541 0.819876i \(-0.305958\pi\)
0.572541 + 0.819876i \(0.305958\pi\)
\(608\) 1.00000 0.0405554
\(609\) −1.93369 −0.0783572
\(610\) −22.2013 −0.898905
\(611\) 21.6980 0.877806
\(612\) 6.60675 0.267062
\(613\) −33.8872 −1.36869 −0.684345 0.729158i \(-0.739912\pi\)
−0.684345 + 0.729158i \(0.739912\pi\)
\(614\) −1.75382 −0.0707782
\(615\) 9.56928 0.385871
\(616\) 0 0
\(617\) −14.9346 −0.601244 −0.300622 0.953743i \(-0.597194\pi\)
−0.300622 + 0.953743i \(0.597194\pi\)
\(618\) −5.20820 −0.209505
\(619\) −30.9909 −1.24563 −0.622814 0.782370i \(-0.714011\pi\)
−0.622814 + 0.782370i \(0.714011\pi\)
\(620\) 2.09589 0.0841729
\(621\) −25.1700 −1.01004
\(622\) −17.7473 −0.711601
\(623\) −9.06948 −0.363361
\(624\) −3.86234 −0.154617
\(625\) −8.08712 −0.323485
\(626\) −16.4381 −0.656998
\(627\) 0 0
\(628\) 24.6425 0.983343
\(629\) −14.6304 −0.583351
\(630\) 6.58237 0.262248
\(631\) −8.54526 −0.340181 −0.170091 0.985428i \(-0.554406\pi\)
−0.170091 + 0.985428i \(0.554406\pi\)
\(632\) −1.13148 −0.0450080
\(633\) −8.24806 −0.327831
\(634\) 6.78204 0.269349
\(635\) 9.54151 0.378643
\(636\) 5.08354 0.201575
\(637\) −27.7853 −1.10089
\(638\) 0 0
\(639\) 32.1585 1.27217
\(640\) −1.63927 −0.0647980
\(641\) −41.5776 −1.64222 −0.821109 0.570772i \(-0.806644\pi\)
−0.821109 + 0.570772i \(0.806644\pi\)
\(642\) −8.02347 −0.316661
\(643\) −9.38090 −0.369947 −0.184973 0.982744i \(-0.559220\pi\)
−0.184973 + 0.982744i \(0.559220\pi\)
\(644\) −10.9116 −0.429979
\(645\) 13.4189 0.528369
\(646\) −2.54956 −0.100311
\(647\) −44.9256 −1.76621 −0.883105 0.469176i \(-0.844551\pi\)
−0.883105 + 0.469176i \(0.844551\pi\)
\(648\) 5.48898 0.215627
\(649\) 0 0
\(650\) −13.9733 −0.548078
\(651\) 1.26652 0.0496388
\(652\) −19.0032 −0.744224
\(653\) 4.78618 0.187298 0.0936488 0.995605i \(-0.470147\pi\)
0.0936488 + 0.995605i \(0.470147\pi\)
\(654\) 2.17513 0.0850541
\(655\) −24.5636 −0.959778
\(656\) 9.13148 0.356524
\(657\) 3.75857 0.146636
\(658\) 5.56498 0.216946
\(659\) 32.1934 1.25408 0.627039 0.778988i \(-0.284267\pi\)
0.627039 + 0.778988i \(0.284267\pi\)
\(660\) 0 0
\(661\) −42.1684 −1.64016 −0.820081 0.572247i \(-0.806072\pi\)
−0.820081 + 0.572247i \(0.806072\pi\)
\(662\) −7.61616 −0.296010
\(663\) 9.84728 0.382436
\(664\) −4.36073 −0.169229
\(665\) −2.54015 −0.0985029
\(666\) −14.8701 −0.576203
\(667\) −13.7459 −0.532244
\(668\) −1.82057 −0.0704401
\(669\) −13.6235 −0.526715
\(670\) −16.7553 −0.647315
\(671\) 0 0
\(672\) −0.990593 −0.0382129
\(673\) −37.4009 −1.44170 −0.720850 0.693092i \(-0.756248\pi\)
−0.720850 + 0.693092i \(0.756248\pi\)
\(674\) −20.0200 −0.771142
\(675\) −8.26678 −0.318189
\(676\) 23.5030 0.903961
\(677\) −40.3742 −1.55171 −0.775853 0.630913i \(-0.782680\pi\)
−0.775853 + 0.630913i \(0.782680\pi\)
\(678\) 2.00187 0.0768815
\(679\) −15.4956 −0.594667
\(680\) 4.17943 0.160274
\(681\) 13.1070 0.502262
\(682\) 0 0
\(683\) −8.06472 −0.308588 −0.154294 0.988025i \(-0.549310\pi\)
−0.154294 + 0.988025i \(0.549310\pi\)
\(684\) −2.59133 −0.0990820
\(685\) −31.7274 −1.21224
\(686\) −17.9731 −0.686218
\(687\) −10.6379 −0.405862
\(688\) 12.8050 0.488186
\(689\) −48.0445 −1.83035
\(690\) −7.37938 −0.280928
\(691\) 27.8402 1.05909 0.529546 0.848281i \(-0.322362\pi\)
0.529546 + 0.848281i \(0.322362\pi\)
\(692\) 10.3109 0.391962
\(693\) 0 0
\(694\) −16.3296 −0.619862
\(695\) −25.8018 −0.978717
\(696\) −1.24790 −0.0473014
\(697\) −23.2813 −0.881841
\(698\) −26.9995 −1.02195
\(699\) −4.20370 −0.158999
\(700\) −3.58380 −0.135455
\(701\) −36.2010 −1.36729 −0.683646 0.729814i \(-0.739607\pi\)
−0.683646 + 0.729814i \(0.739607\pi\)
\(702\) 21.5956 0.815075
\(703\) 5.73839 0.216428
\(704\) 0 0
\(705\) 3.76351 0.141742
\(706\) 14.0525 0.528874
\(707\) −12.8069 −0.481652
\(708\) −3.45367 −0.129797
\(709\) 22.7091 0.852858 0.426429 0.904521i \(-0.359771\pi\)
0.426429 + 0.904521i \(0.359771\pi\)
\(710\) 20.3434 0.763475
\(711\) 2.93204 0.109960
\(712\) −5.85294 −0.219348
\(713\) 9.00323 0.337174
\(714\) 2.52558 0.0945173
\(715\) 0 0
\(716\) 5.78770 0.216296
\(717\) −2.32562 −0.0868520
\(718\) 25.3546 0.946223
\(719\) 22.2859 0.831125 0.415562 0.909565i \(-0.363585\pi\)
0.415562 + 0.909565i \(0.363585\pi\)
\(720\) 4.24790 0.158310
\(721\) 12.6244 0.470156
\(722\) 1.00000 0.0372161
\(723\) −17.9954 −0.669256
\(724\) 15.4768 0.575190
\(725\) −4.51468 −0.167671
\(726\) 0 0
\(727\) −4.03100 −0.149502 −0.0747508 0.997202i \(-0.523816\pi\)
−0.0747508 + 0.997202i \(0.523816\pi\)
\(728\) 9.36209 0.346982
\(729\) −7.36871 −0.272915
\(730\) 2.37767 0.0880014
\(731\) −32.6471 −1.20750
\(732\) −8.65793 −0.320006
\(733\) −36.0712 −1.33232 −0.666160 0.745809i \(-0.732063\pi\)
−0.666160 + 0.745809i \(0.732063\pi\)
\(734\) 19.3931 0.715812
\(735\) −4.81935 −0.177764
\(736\) −7.04177 −0.259563
\(737\) 0 0
\(738\) −23.6627 −0.871035
\(739\) 38.6388 1.42135 0.710675 0.703521i \(-0.248390\pi\)
0.710675 + 0.703521i \(0.248390\pi\)
\(740\) −9.40680 −0.345801
\(741\) −3.86234 −0.141887
\(742\) −12.3222 −0.452362
\(743\) 50.8416 1.86520 0.932599 0.360915i \(-0.117536\pi\)
0.932599 + 0.360915i \(0.117536\pi\)
\(744\) 0.817341 0.0299652
\(745\) −31.8767 −1.16787
\(746\) −35.3018 −1.29249
\(747\) 11.3001 0.413448
\(748\) 0 0
\(749\) 19.4484 0.710629
\(750\) −7.66339 −0.279827
\(751\) 39.4521 1.43963 0.719814 0.694167i \(-0.244227\pi\)
0.719814 + 0.694167i \(0.244227\pi\)
\(752\) 3.59133 0.130962
\(753\) 6.90734 0.251718
\(754\) 11.7939 0.429507
\(755\) 20.0493 0.729669
\(756\) 5.53873 0.201442
\(757\) 16.5402 0.601162 0.300581 0.953756i \(-0.402819\pi\)
0.300581 + 0.953756i \(0.402819\pi\)
\(758\) −5.17002 −0.187784
\(759\) 0 0
\(760\) −1.63927 −0.0594627
\(761\) −23.5341 −0.853112 −0.426556 0.904461i \(-0.640273\pi\)
−0.426556 + 0.904461i \(0.640273\pi\)
\(762\) 3.72094 0.134795
\(763\) −5.27237 −0.190873
\(764\) 15.4537 0.559094
\(765\) −10.8303 −0.391569
\(766\) −5.16759 −0.186713
\(767\) 32.6406 1.17858
\(768\) −0.639273 −0.0230678
\(769\) −0.0803060 −0.00289591 −0.00144795 0.999999i \(-0.500461\pi\)
−0.00144795 + 0.999999i \(0.500461\pi\)
\(770\) 0 0
\(771\) 9.59117 0.345417
\(772\) 8.00000 0.287926
\(773\) 16.2541 0.584618 0.292309 0.956324i \(-0.405576\pi\)
0.292309 + 0.956324i \(0.405576\pi\)
\(774\) −33.1820 −1.19270
\(775\) 2.95700 0.106219
\(776\) −10.0000 −0.358979
\(777\) −5.68441 −0.203927
\(778\) 4.91782 0.176312
\(779\) 9.13148 0.327169
\(780\) 6.33144 0.226702
\(781\) 0 0
\(782\) 17.9534 0.642013
\(783\) 6.97741 0.249352
\(784\) −4.59886 −0.164245
\(785\) −40.3958 −1.44179
\(786\) −9.57914 −0.341677
\(787\) 11.7726 0.419649 0.209824 0.977739i \(-0.432711\pi\)
0.209824 + 0.977739i \(0.432711\pi\)
\(788\) 5.72469 0.203933
\(789\) 2.28588 0.0813795
\(790\) 1.85481 0.0659911
\(791\) −4.85242 −0.172532
\(792\) 0 0
\(793\) 81.8260 2.90573
\(794\) −7.54151 −0.267638
\(795\) −8.33331 −0.295552
\(796\) 4.18696 0.148403
\(797\) 12.5003 0.442782 0.221391 0.975185i \(-0.428940\pi\)
0.221391 + 0.975185i \(0.428940\pi\)
\(798\) −0.990593 −0.0350666
\(799\) −9.15631 −0.323927
\(800\) −2.31278 −0.0817692
\(801\) 15.1669 0.535895
\(802\) 4.03236 0.142388
\(803\) 0 0
\(804\) −6.53414 −0.230441
\(805\) 17.8872 0.630440
\(806\) −7.72469 −0.272090
\(807\) 16.3587 0.575852
\(808\) −8.26484 −0.290756
\(809\) −6.86988 −0.241532 −0.120766 0.992681i \(-0.538535\pi\)
−0.120766 + 0.992681i \(0.538535\pi\)
\(810\) −8.99793 −0.316155
\(811\) −34.8255 −1.22289 −0.611445 0.791287i \(-0.709411\pi\)
−0.611445 + 0.791287i \(0.709411\pi\)
\(812\) 3.02483 0.106151
\(813\) −6.91216 −0.242420
\(814\) 0 0
\(815\) 31.1515 1.09119
\(816\) 1.62987 0.0570567
\(817\) 12.8050 0.447990
\(818\) −0.358853 −0.0125470
\(819\) −24.2602 −0.847722
\(820\) −14.9690 −0.522740
\(821\) −8.45933 −0.295233 −0.147616 0.989045i \(-0.547160\pi\)
−0.147616 + 0.989045i \(0.547160\pi\)
\(822\) −12.3729 −0.431553
\(823\) −7.47627 −0.260606 −0.130303 0.991474i \(-0.541595\pi\)
−0.130303 + 0.991474i \(0.541595\pi\)
\(824\) 8.14706 0.283816
\(825\) 0 0
\(826\) 8.37149 0.291281
\(827\) 16.4386 0.571626 0.285813 0.958285i \(-0.407736\pi\)
0.285813 + 0.958285i \(0.407736\pi\)
\(828\) 18.2475 0.634146
\(829\) 7.49974 0.260477 0.130238 0.991483i \(-0.458426\pi\)
0.130238 + 0.991483i \(0.458426\pi\)
\(830\) 7.14842 0.248125
\(831\) 0.177199 0.00614697
\(832\) 6.04177 0.209461
\(833\) 11.7251 0.406250
\(834\) −10.0620 −0.348419
\(835\) 2.98442 0.103280
\(836\) 0 0
\(837\) −4.57002 −0.157963
\(838\) 31.2643 1.08001
\(839\) 5.60879 0.193637 0.0968184 0.995302i \(-0.469133\pi\)
0.0968184 + 0.995302i \(0.469133\pi\)
\(840\) 1.62385 0.0560282
\(841\) −25.1895 −0.868603
\(842\) 18.7303 0.645490
\(843\) 5.26161 0.181219
\(844\) 12.9022 0.444113
\(845\) −38.5278 −1.32540
\(846\) −9.30632 −0.319958
\(847\) 0 0
\(848\) −7.95206 −0.273075
\(849\) 13.0803 0.448915
\(850\) 5.89658 0.202251
\(851\) −40.4084 −1.38518
\(852\) 7.93340 0.271794
\(853\) −5.80176 −0.198648 −0.0993242 0.995055i \(-0.531668\pi\)
−0.0993242 + 0.995055i \(0.531668\pi\)
\(854\) 20.9863 0.718136
\(855\) 4.24790 0.145275
\(856\) 12.5509 0.428982
\(857\) −18.6444 −0.636880 −0.318440 0.947943i \(-0.603159\pi\)
−0.318440 + 0.947943i \(0.603159\pi\)
\(858\) 0 0
\(859\) −33.4502 −1.14131 −0.570653 0.821191i \(-0.693310\pi\)
−0.570653 + 0.821191i \(0.693310\pi\)
\(860\) −20.9909 −0.715783
\(861\) −9.04558 −0.308273
\(862\) −7.03559 −0.239633
\(863\) −29.9256 −1.01868 −0.509340 0.860565i \(-0.670111\pi\)
−0.509340 + 0.860565i \(0.670111\pi\)
\(864\) 3.57439 0.121603
\(865\) −16.9024 −0.574699
\(866\) 11.2785 0.383261
\(867\) 6.71221 0.227958
\(868\) −1.98119 −0.0672458
\(869\) 0 0
\(870\) 2.04565 0.0693539
\(871\) 61.7541 2.09246
\(872\) −3.40250 −0.115223
\(873\) 25.9133 0.877032
\(874\) −7.04177 −0.238191
\(875\) 18.5756 0.627969
\(876\) 0.927228 0.0313281
\(877\) −15.6024 −0.526857 −0.263429 0.964679i \(-0.584853\pi\)
−0.263429 + 0.964679i \(0.584853\pi\)
\(878\) −2.47356 −0.0834785
\(879\) −7.37731 −0.248831
\(880\) 0 0
\(881\) −8.93799 −0.301129 −0.150564 0.988600i \(-0.548109\pi\)
−0.150564 + 0.988600i \(0.548109\pi\)
\(882\) 11.9172 0.401272
\(883\) 32.7196 1.10110 0.550551 0.834802i \(-0.314418\pi\)
0.550551 + 0.834802i \(0.314418\pi\)
\(884\) −15.4039 −0.518088
\(885\) 5.66151 0.190310
\(886\) 23.0680 0.774983
\(887\) 56.4812 1.89645 0.948227 0.317594i \(-0.102875\pi\)
0.948227 + 0.317594i \(0.102875\pi\)
\(888\) −3.66840 −0.123104
\(889\) −9.01933 −0.302499
\(890\) 9.59456 0.321610
\(891\) 0 0
\(892\) 21.3109 0.713542
\(893\) 3.59133 0.120179
\(894\) −12.4311 −0.415757
\(895\) −9.48762 −0.317136
\(896\) 1.54956 0.0517672
\(897\) 27.1977 0.908106
\(898\) −22.8050 −0.761012
\(899\) −2.49580 −0.0832394
\(900\) 5.99318 0.199773
\(901\) 20.2742 0.675433
\(902\) 0 0
\(903\) −12.6845 −0.422115
\(904\) −3.13148 −0.104152
\(905\) −25.3707 −0.843350
\(906\) 7.81870 0.259759
\(907\) −5.76135 −0.191302 −0.0956512 0.995415i \(-0.530493\pi\)
−0.0956512 + 0.995415i \(0.530493\pi\)
\(908\) −20.5030 −0.680415
\(909\) 21.4169 0.710354
\(910\) −15.3470 −0.508749
\(911\) 9.78821 0.324298 0.162149 0.986766i \(-0.448157\pi\)
0.162149 + 0.986766i \(0.448157\pi\)
\(912\) −0.639273 −0.0211685
\(913\) 0 0
\(914\) −19.1253 −0.632609
\(915\) 14.1927 0.469197
\(916\) 16.6406 0.549822
\(917\) 23.2193 0.766767
\(918\) −9.11312 −0.300778
\(919\) −33.1748 −1.09433 −0.547167 0.837023i \(-0.684294\pi\)
−0.547167 + 0.837023i \(0.684294\pi\)
\(920\) 11.5434 0.380574
\(921\) 1.12117 0.0369437
\(922\) −16.2799 −0.536150
\(923\) −74.9785 −2.46795
\(924\) 0 0
\(925\) −13.2717 −0.436369
\(926\) −21.0525 −0.691829
\(927\) −21.1117 −0.693400
\(928\) 1.95206 0.0640794
\(929\) −12.5415 −0.411474 −0.205737 0.978607i \(-0.565959\pi\)
−0.205737 + 0.978607i \(0.565959\pi\)
\(930\) −1.33985 −0.0439353
\(931\) −4.59886 −0.150722
\(932\) 6.57575 0.215396
\(933\) 11.3454 0.371431
\(934\) −32.9909 −1.07949
\(935\) 0 0
\(936\) −15.6562 −0.511739
\(937\) 52.2470 1.70684 0.853418 0.521227i \(-0.174526\pi\)
0.853418 + 0.521227i \(0.174526\pi\)
\(938\) 15.8384 0.517141
\(939\) 10.5084 0.342930
\(940\) −5.88717 −0.192018
\(941\) 29.4189 0.959029 0.479515 0.877534i \(-0.340813\pi\)
0.479515 + 0.877534i \(0.340813\pi\)
\(942\) −15.7533 −0.513270
\(943\) −64.3018 −2.09395
\(944\) 5.40250 0.175836
\(945\) −9.07949 −0.295356
\(946\) 0 0
\(947\) −47.4370 −1.54150 −0.770748 0.637140i \(-0.780117\pi\)
−0.770748 + 0.637140i \(0.780117\pi\)
\(948\) 0.723327 0.0234926
\(949\) −8.76322 −0.284466
\(950\) −2.31278 −0.0750366
\(951\) −4.33558 −0.140591
\(952\) −3.95070 −0.128043
\(953\) 42.4785 1.37601 0.688007 0.725704i \(-0.258486\pi\)
0.688007 + 0.725704i \(0.258486\pi\)
\(954\) 20.6064 0.667157
\(955\) −25.3328 −0.819750
\(956\) 3.63791 0.117659
\(957\) 0 0
\(958\) −21.2630 −0.686975
\(959\) 29.9910 0.968461
\(960\) 1.04794 0.0338222
\(961\) −29.3653 −0.947268
\(962\) 34.6701 1.11781
\(963\) −32.5236 −1.04806
\(964\) 28.1498 0.906643
\(965\) −13.1142 −0.422161
\(966\) 6.97553 0.224434
\(967\) 40.6096 1.30592 0.652959 0.757393i \(-0.273527\pi\)
0.652959 + 0.757393i \(0.273527\pi\)
\(968\) 0 0
\(969\) 1.62987 0.0523588
\(970\) 16.3927 0.526339
\(971\) 35.5000 1.13925 0.569625 0.821905i \(-0.307088\pi\)
0.569625 + 0.821905i \(0.307088\pi\)
\(972\) −14.2321 −0.456496
\(973\) 24.3897 0.781898
\(974\) 19.4306 0.622595
\(975\) 8.93276 0.286077
\(976\) 13.5434 0.433513
\(977\) 22.0986 0.706997 0.353499 0.935435i \(-0.384992\pi\)
0.353499 + 0.935435i \(0.384992\pi\)
\(978\) 12.1483 0.388459
\(979\) 0 0
\(980\) 7.53879 0.240818
\(981\) 8.81699 0.281505
\(982\) 32.2968 1.03063
\(983\) −26.1310 −0.833448 −0.416724 0.909033i \(-0.636822\pi\)
−0.416724 + 0.909033i \(0.636822\pi\)
\(984\) −5.83751 −0.186093
\(985\) −9.38433 −0.299009
\(986\) −4.97688 −0.158496
\(987\) −3.55754 −0.113238
\(988\) 6.04177 0.192214
\(989\) −90.1698 −2.86723
\(990\) 0 0
\(991\) −11.0168 −0.349960 −0.174980 0.984572i \(-0.555986\pi\)
−0.174980 + 0.984572i \(0.555986\pi\)
\(992\) −1.27855 −0.0405939
\(993\) 4.86881 0.154507
\(994\) −19.2301 −0.609941
\(995\) −6.86357 −0.217590
\(996\) 2.78770 0.0883316
\(997\) −11.0945 −0.351367 −0.175684 0.984447i \(-0.556214\pi\)
−0.175684 + 0.984447i \(0.556214\pi\)
\(998\) 4.26484 0.135001
\(999\) 20.5112 0.648947
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 4598.2.a.bv.1.2 yes 4
11.10 odd 2 4598.2.a.bs.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bs.1.2 4 11.10 odd 2
4598.2.a.bv.1.2 yes 4 1.1 even 1 trivial