Properties

Label 5577.2.a.y.1.7
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5577.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.5325692073\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 21 x^{4} + 13 x^{3} - 33 x^{2} - 7 x + 7\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(2.73878\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.73878 q^{2} +1.00000 q^{3} +5.50093 q^{4} -2.84154 q^{5} +2.73878 q^{6} +3.93129 q^{7} +9.58828 q^{8} +1.00000 q^{9} -7.78236 q^{10} +1.00000 q^{11} +5.50093 q^{12} +10.7670 q^{14} -2.84154 q^{15} +15.2584 q^{16} +3.81818 q^{17} +2.73878 q^{18} -2.94082 q^{19} -15.6311 q^{20} +3.93129 q^{21} +2.73878 q^{22} -1.89484 q^{23} +9.58828 q^{24} +3.07435 q^{25} +1.00000 q^{27} +21.6258 q^{28} -2.09928 q^{29} -7.78236 q^{30} -6.16032 q^{31} +22.6127 q^{32} +1.00000 q^{33} +10.4572 q^{34} -11.1709 q^{35} +5.50093 q^{36} +8.34404 q^{37} -8.05426 q^{38} -27.2455 q^{40} +6.35787 q^{41} +10.7670 q^{42} -11.7275 q^{43} +5.50093 q^{44} -2.84154 q^{45} -5.18956 q^{46} +5.31137 q^{47} +15.2584 q^{48} +8.45506 q^{49} +8.41997 q^{50} +3.81818 q^{51} -2.37985 q^{53} +2.73878 q^{54} -2.84154 q^{55} +37.6943 q^{56} -2.94082 q^{57} -5.74947 q^{58} -5.38624 q^{59} -15.6311 q^{60} -2.34857 q^{61} -16.8718 q^{62} +3.93129 q^{63} +31.4147 q^{64} +2.73878 q^{66} +10.4731 q^{67} +21.0035 q^{68} -1.89484 q^{69} -30.5947 q^{70} +10.0939 q^{71} +9.58828 q^{72} -15.1079 q^{73} +22.8525 q^{74} +3.07435 q^{75} -16.1772 q^{76} +3.93129 q^{77} +1.57120 q^{79} -43.3572 q^{80} +1.00000 q^{81} +17.4128 q^{82} +10.6736 q^{83} +21.6258 q^{84} -10.8495 q^{85} -32.1190 q^{86} -2.09928 q^{87} +9.58828 q^{88} +3.23647 q^{89} -7.78236 q^{90} -10.4234 q^{92} -6.16032 q^{93} +14.5467 q^{94} +8.35645 q^{95} +22.6127 q^{96} -17.7914 q^{97} +23.1566 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + 7q^{11} + 9q^{12} + 8q^{14} + 6q^{15} + 17q^{16} - 2q^{17} + 3q^{18} + 8q^{19} - 2q^{20} + 6q^{21} + 3q^{22} + 4q^{23} + 15q^{24} + 13q^{25} + 7q^{27} + 12q^{28} - 12q^{29} - 10q^{31} + 33q^{32} + 7q^{33} + 28q^{34} - 4q^{35} + 9q^{36} + 6q^{37} + 16q^{38} - 10q^{40} + 2q^{41} + 8q^{42} - 16q^{43} + 9q^{44} + 6q^{45} - 26q^{46} + 18q^{47} + 17q^{48} + 23q^{49} + 39q^{50} - 2q^{51} + 10q^{53} + 3q^{54} + 6q^{55} + 16q^{56} + 8q^{57} + 10q^{58} + 2q^{59} - 2q^{60} - 10q^{61} - 36q^{62} + 6q^{63} + 29q^{64} + 3q^{66} + 8q^{67} - 10q^{68} + 4q^{69} - 20q^{70} + 36q^{71} + 15q^{72} + 20q^{73} + 13q^{75} + 10q^{76} + 6q^{77} + 6q^{79} - 20q^{80} + 7q^{81} - 10q^{82} + 30q^{83} + 12q^{84} - 40q^{85} + 6q^{86} - 12q^{87} + 15q^{88} + 34q^{89} - 12q^{92} - 10q^{93} + 32q^{94} + 18q^{95} + 33q^{96} + 16q^{97} + q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.73878 1.93661 0.968306 0.249768i \(-0.0803543\pi\)
0.968306 + 0.249768i \(0.0803543\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.50093 2.75046
\(5\) −2.84154 −1.27078 −0.635388 0.772193i \(-0.719160\pi\)
−0.635388 + 0.772193i \(0.719160\pi\)
\(6\) 2.73878 1.11810
\(7\) 3.93129 1.48589 0.742944 0.669353i \(-0.233429\pi\)
0.742944 + 0.669353i \(0.233429\pi\)
\(8\) 9.58828 3.38997
\(9\) 1.00000 0.333333
\(10\) −7.78236 −2.46100
\(11\) 1.00000 0.301511
\(12\) 5.50093 1.58798
\(13\) 0 0
\(14\) 10.7670 2.87759
\(15\) −2.84154 −0.733682
\(16\) 15.2584 3.81459
\(17\) 3.81818 0.926044 0.463022 0.886347i \(-0.346765\pi\)
0.463022 + 0.886347i \(0.346765\pi\)
\(18\) 2.73878 0.645537
\(19\) −2.94082 −0.674670 −0.337335 0.941385i \(-0.609526\pi\)
−0.337335 + 0.941385i \(0.609526\pi\)
\(20\) −15.6311 −3.49522
\(21\) 3.93129 0.857878
\(22\) 2.73878 0.583910
\(23\) −1.89484 −0.395102 −0.197551 0.980293i \(-0.563299\pi\)
−0.197551 + 0.980293i \(0.563299\pi\)
\(24\) 9.58828 1.95720
\(25\) 3.07435 0.614869
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 21.6258 4.08688
\(29\) −2.09928 −0.389826 −0.194913 0.980821i \(-0.562443\pi\)
−0.194913 + 0.980821i \(0.562443\pi\)
\(30\) −7.78236 −1.42086
\(31\) −6.16032 −1.10643 −0.553213 0.833040i \(-0.686598\pi\)
−0.553213 + 0.833040i \(0.686598\pi\)
\(32\) 22.6127 3.99741
\(33\) 1.00000 0.174078
\(34\) 10.4572 1.79339
\(35\) −11.1709 −1.88823
\(36\) 5.50093 0.916821
\(37\) 8.34404 1.37175 0.685876 0.727719i \(-0.259419\pi\)
0.685876 + 0.727719i \(0.259419\pi\)
\(38\) −8.05426 −1.30657
\(39\) 0 0
\(40\) −27.2455 −4.30789
\(41\) 6.35787 0.992933 0.496466 0.868056i \(-0.334631\pi\)
0.496466 + 0.868056i \(0.334631\pi\)
\(42\) 10.7670 1.66138
\(43\) −11.7275 −1.78842 −0.894212 0.447643i \(-0.852264\pi\)
−0.894212 + 0.447643i \(0.852264\pi\)
\(44\) 5.50093 0.829296
\(45\) −2.84154 −0.423592
\(46\) −5.18956 −0.765159
\(47\) 5.31137 0.774743 0.387371 0.921924i \(-0.373383\pi\)
0.387371 + 0.921924i \(0.373383\pi\)
\(48\) 15.2584 2.20235
\(49\) 8.45506 1.20787
\(50\) 8.41997 1.19076
\(51\) 3.81818 0.534652
\(52\) 0 0
\(53\) −2.37985 −0.326898 −0.163449 0.986552i \(-0.552262\pi\)
−0.163449 + 0.986552i \(0.552262\pi\)
\(54\) 2.73878 0.372701
\(55\) −2.84154 −0.383153
\(56\) 37.6943 5.03712
\(57\) −2.94082 −0.389521
\(58\) −5.74947 −0.754942
\(59\) −5.38624 −0.701229 −0.350615 0.936520i \(-0.614027\pi\)
−0.350615 + 0.936520i \(0.614027\pi\)
\(60\) −15.6311 −2.01797
\(61\) −2.34857 −0.300703 −0.150352 0.988633i \(-0.548041\pi\)
−0.150352 + 0.988633i \(0.548041\pi\)
\(62\) −16.8718 −2.14272
\(63\) 3.93129 0.495296
\(64\) 31.4147 3.92684
\(65\) 0 0
\(66\) 2.73878 0.337121
\(67\) 10.4731 1.27949 0.639744 0.768588i \(-0.279040\pi\)
0.639744 + 0.768588i \(0.279040\pi\)
\(68\) 21.0035 2.54705
\(69\) −1.89484 −0.228112
\(70\) −30.5947 −3.65677
\(71\) 10.0939 1.19793 0.598964 0.800776i \(-0.295579\pi\)
0.598964 + 0.800776i \(0.295579\pi\)
\(72\) 9.58828 1.12999
\(73\) −15.1079 −1.76824 −0.884120 0.467260i \(-0.845241\pi\)
−0.884120 + 0.467260i \(0.845241\pi\)
\(74\) 22.8525 2.65655
\(75\) 3.07435 0.354995
\(76\) −16.1772 −1.85566
\(77\) 3.93129 0.448012
\(78\) 0 0
\(79\) 1.57120 0.176774 0.0883872 0.996086i \(-0.471829\pi\)
0.0883872 + 0.996086i \(0.471829\pi\)
\(80\) −43.3572 −4.84748
\(81\) 1.00000 0.111111
\(82\) 17.4128 1.92293
\(83\) 10.6736 1.17157 0.585787 0.810465i \(-0.300785\pi\)
0.585787 + 0.810465i \(0.300785\pi\)
\(84\) 21.6258 2.35956
\(85\) −10.8495 −1.17679
\(86\) −32.1190 −3.46348
\(87\) −2.09928 −0.225066
\(88\) 9.58828 1.02211
\(89\) 3.23647 0.343065 0.171533 0.985178i \(-0.445128\pi\)
0.171533 + 0.985178i \(0.445128\pi\)
\(90\) −7.78236 −0.820333
\(91\) 0 0
\(92\) −10.4234 −1.08671
\(93\) −6.16032 −0.638795
\(94\) 14.5467 1.50038
\(95\) 8.35645 0.857354
\(96\) 22.6127 2.30790
\(97\) −17.7914 −1.80645 −0.903223 0.429172i \(-0.858805\pi\)
−0.903223 + 0.429172i \(0.858805\pi\)
\(98\) 23.1566 2.33917
\(99\) 1.00000 0.100504
\(100\) 16.9118 1.69118
\(101\) −12.1229 −1.20627 −0.603136 0.797638i \(-0.706083\pi\)
−0.603136 + 0.797638i \(0.706083\pi\)
\(102\) 10.4572 1.03541
\(103\) −3.40983 −0.335981 −0.167990 0.985789i \(-0.553728\pi\)
−0.167990 + 0.985789i \(0.553728\pi\)
\(104\) 0 0
\(105\) −11.1709 −1.09017
\(106\) −6.51790 −0.633075
\(107\) −12.2352 −1.18282 −0.591411 0.806370i \(-0.701429\pi\)
−0.591411 + 0.806370i \(0.701429\pi\)
\(108\) 5.50093 0.529327
\(109\) −8.72763 −0.835956 −0.417978 0.908457i \(-0.637261\pi\)
−0.417978 + 0.908457i \(0.637261\pi\)
\(110\) −7.78236 −0.742019
\(111\) 8.34404 0.791981
\(112\) 59.9850 5.66805
\(113\) 0.0155525 0.00146305 0.000731527 1.00000i \(-0.499767\pi\)
0.000731527 1.00000i \(0.499767\pi\)
\(114\) −8.05426 −0.754351
\(115\) 5.38427 0.502086
\(116\) −11.5480 −1.07220
\(117\) 0 0
\(118\) −14.7517 −1.35801
\(119\) 15.0104 1.37600
\(120\) −27.2455 −2.48716
\(121\) 1.00000 0.0909091
\(122\) −6.43222 −0.582346
\(123\) 6.35787 0.573270
\(124\) −33.8875 −3.04318
\(125\) 5.47182 0.489414
\(126\) 10.7670 0.959196
\(127\) −5.91514 −0.524883 −0.262442 0.964948i \(-0.584528\pi\)
−0.262442 + 0.964948i \(0.584528\pi\)
\(128\) 40.8125 3.60735
\(129\) −11.7275 −1.03255
\(130\) 0 0
\(131\) −1.32191 −0.115496 −0.0577481 0.998331i \(-0.518392\pi\)
−0.0577481 + 0.998331i \(0.518392\pi\)
\(132\) 5.50093 0.478794
\(133\) −11.5612 −1.00248
\(134\) 28.6835 2.47787
\(135\) −2.84154 −0.244561
\(136\) 36.6097 3.13926
\(137\) 4.82127 0.411909 0.205955 0.978562i \(-0.433970\pi\)
0.205955 + 0.978562i \(0.433970\pi\)
\(138\) −5.18956 −0.441765
\(139\) 17.1877 1.45784 0.728919 0.684600i \(-0.240023\pi\)
0.728919 + 0.684600i \(0.240023\pi\)
\(140\) −61.4504 −5.19351
\(141\) 5.31137 0.447298
\(142\) 27.6451 2.31992
\(143\) 0 0
\(144\) 15.2584 1.27153
\(145\) 5.96518 0.495382
\(146\) −41.3771 −3.42439
\(147\) 8.45506 0.697361
\(148\) 45.8999 3.77295
\(149\) −5.31754 −0.435629 −0.217815 0.975990i \(-0.569893\pi\)
−0.217815 + 0.975990i \(0.569893\pi\)
\(150\) 8.41997 0.687487
\(151\) −6.77573 −0.551401 −0.275700 0.961244i \(-0.588910\pi\)
−0.275700 + 0.961244i \(0.588910\pi\)
\(152\) −28.1974 −2.28711
\(153\) 3.81818 0.308681
\(154\) 10.7670 0.867626
\(155\) 17.5048 1.40602
\(156\) 0 0
\(157\) 16.2884 1.29995 0.649977 0.759954i \(-0.274779\pi\)
0.649977 + 0.759954i \(0.274779\pi\)
\(158\) 4.30319 0.342343
\(159\) −2.37985 −0.188735
\(160\) −64.2550 −5.07981
\(161\) −7.44918 −0.587077
\(162\) 2.73878 0.215179
\(163\) 11.4032 0.893170 0.446585 0.894741i \(-0.352640\pi\)
0.446585 + 0.894741i \(0.352640\pi\)
\(164\) 34.9742 2.73103
\(165\) −2.84154 −0.221214
\(166\) 29.2325 2.26888
\(167\) −14.7302 −1.13985 −0.569927 0.821695i \(-0.693029\pi\)
−0.569927 + 0.821695i \(0.693029\pi\)
\(168\) 37.6943 2.90818
\(169\) 0 0
\(170\) −29.7144 −2.27899
\(171\) −2.94082 −0.224890
\(172\) −64.5121 −4.91900
\(173\) 0.186647 0.0141905 0.00709527 0.999975i \(-0.497741\pi\)
0.00709527 + 0.999975i \(0.497741\pi\)
\(174\) −5.74947 −0.435866
\(175\) 12.0862 0.913627
\(176\) 15.2584 1.15014
\(177\) −5.38624 −0.404855
\(178\) 8.86399 0.664384
\(179\) 10.9555 0.818856 0.409428 0.912342i \(-0.365728\pi\)
0.409428 + 0.912342i \(0.365728\pi\)
\(180\) −15.6311 −1.16507
\(181\) −8.52034 −0.633312 −0.316656 0.948540i \(-0.602560\pi\)
−0.316656 + 0.948540i \(0.602560\pi\)
\(182\) 0 0
\(183\) −2.34857 −0.173611
\(184\) −18.1683 −1.33938
\(185\) −23.7099 −1.74319
\(186\) −16.8718 −1.23710
\(187\) 3.81818 0.279213
\(188\) 29.2175 2.13090
\(189\) 3.93129 0.285959
\(190\) 22.8865 1.66036
\(191\) −11.8003 −0.853840 −0.426920 0.904289i \(-0.640401\pi\)
−0.426920 + 0.904289i \(0.640401\pi\)
\(192\) 31.4147 2.26716
\(193\) 10.9405 0.787518 0.393759 0.919214i \(-0.371174\pi\)
0.393759 + 0.919214i \(0.371174\pi\)
\(194\) −48.7268 −3.49838
\(195\) 0 0
\(196\) 46.5107 3.32219
\(197\) 9.43307 0.672079 0.336039 0.941848i \(-0.390912\pi\)
0.336039 + 0.941848i \(0.390912\pi\)
\(198\) 2.73878 0.194637
\(199\) −15.3198 −1.08599 −0.542996 0.839735i \(-0.682710\pi\)
−0.542996 + 0.839735i \(0.682710\pi\)
\(200\) 29.4777 2.08439
\(201\) 10.4731 0.738713
\(202\) −33.2020 −2.33608
\(203\) −8.25288 −0.579238
\(204\) 21.0035 1.47054
\(205\) −18.0661 −1.26179
\(206\) −9.33878 −0.650664
\(207\) −1.89484 −0.131701
\(208\) 0 0
\(209\) −2.94082 −0.203421
\(210\) −30.5947 −2.11124
\(211\) 2.91243 0.200500 0.100250 0.994962i \(-0.468036\pi\)
0.100250 + 0.994962i \(0.468036\pi\)
\(212\) −13.0914 −0.899122
\(213\) 10.0939 0.691625
\(214\) −33.5096 −2.29067
\(215\) 33.3241 2.27269
\(216\) 9.58828 0.652400
\(217\) −24.2180 −1.64403
\(218\) −23.9031 −1.61892
\(219\) −15.1079 −1.02089
\(220\) −15.6311 −1.05385
\(221\) 0 0
\(222\) 22.8525 1.53376
\(223\) 10.8511 0.726641 0.363320 0.931664i \(-0.381643\pi\)
0.363320 + 0.931664i \(0.381643\pi\)
\(224\) 88.8973 5.93970
\(225\) 3.07435 0.204956
\(226\) 0.0425948 0.00283337
\(227\) 0.322636 0.0214141 0.0107070 0.999943i \(-0.496592\pi\)
0.0107070 + 0.999943i \(0.496592\pi\)
\(228\) −16.1772 −1.07136
\(229\) −5.94060 −0.392566 −0.196283 0.980547i \(-0.562887\pi\)
−0.196283 + 0.980547i \(0.562887\pi\)
\(230\) 14.7463 0.972345
\(231\) 3.93129 0.258660
\(232\) −20.1285 −1.32150
\(233\) −12.6202 −0.826774 −0.413387 0.910555i \(-0.635654\pi\)
−0.413387 + 0.910555i \(0.635654\pi\)
\(234\) 0 0
\(235\) −15.0925 −0.984524
\(236\) −29.6293 −1.92871
\(237\) 1.57120 0.102061
\(238\) 41.1101 2.66477
\(239\) 20.7706 1.34354 0.671768 0.740762i \(-0.265535\pi\)
0.671768 + 0.740762i \(0.265535\pi\)
\(240\) −43.3572 −2.79870
\(241\) −18.2163 −1.17341 −0.586706 0.809800i \(-0.699576\pi\)
−0.586706 + 0.809800i \(0.699576\pi\)
\(242\) 2.73878 0.176056
\(243\) 1.00000 0.0641500
\(244\) −12.9193 −0.827074
\(245\) −24.0254 −1.53492
\(246\) 17.4128 1.11020
\(247\) 0 0
\(248\) −59.0668 −3.75075
\(249\) 10.6736 0.676409
\(250\) 14.9861 0.947806
\(251\) −22.6662 −1.43068 −0.715340 0.698776i \(-0.753728\pi\)
−0.715340 + 0.698776i \(0.753728\pi\)
\(252\) 21.6258 1.36229
\(253\) −1.89484 −0.119128
\(254\) −16.2003 −1.01650
\(255\) −10.8495 −0.679422
\(256\) 48.9471 3.05920
\(257\) 17.7333 1.10617 0.553087 0.833124i \(-0.313450\pi\)
0.553087 + 0.833124i \(0.313450\pi\)
\(258\) −32.1190 −1.99964
\(259\) 32.8028 2.03827
\(260\) 0 0
\(261\) −2.09928 −0.129942
\(262\) −3.62044 −0.223671
\(263\) 29.5107 1.81971 0.909853 0.414930i \(-0.136194\pi\)
0.909853 + 0.414930i \(0.136194\pi\)
\(264\) 9.58828 0.590118
\(265\) 6.76245 0.415414
\(266\) −31.6637 −1.94142
\(267\) 3.23647 0.198069
\(268\) 57.6116 3.51919
\(269\) −9.02091 −0.550015 −0.275007 0.961442i \(-0.588680\pi\)
−0.275007 + 0.961442i \(0.588680\pi\)
\(270\) −7.78236 −0.473619
\(271\) 4.58320 0.278410 0.139205 0.990264i \(-0.455545\pi\)
0.139205 + 0.990264i \(0.455545\pi\)
\(272\) 58.2591 3.53248
\(273\) 0 0
\(274\) 13.2044 0.797708
\(275\) 3.07435 0.185390
\(276\) −10.4234 −0.627414
\(277\) 20.9859 1.26092 0.630461 0.776221i \(-0.282866\pi\)
0.630461 + 0.776221i \(0.282866\pi\)
\(278\) 47.0732 2.82327
\(279\) −6.16032 −0.368809
\(280\) −107.110 −6.40104
\(281\) 10.5360 0.628524 0.314262 0.949336i \(-0.398243\pi\)
0.314262 + 0.949336i \(0.398243\pi\)
\(282\) 14.5467 0.866242
\(283\) −2.57169 −0.152871 −0.0764355 0.997075i \(-0.524354\pi\)
−0.0764355 + 0.997075i \(0.524354\pi\)
\(284\) 55.5260 3.29486
\(285\) 8.35645 0.494993
\(286\) 0 0
\(287\) 24.9947 1.47539
\(288\) 22.6127 1.33247
\(289\) −2.42153 −0.142443
\(290\) 16.3373 0.959362
\(291\) −17.7914 −1.04295
\(292\) −83.1072 −4.86348
\(293\) 5.16162 0.301545 0.150772 0.988568i \(-0.451824\pi\)
0.150772 + 0.988568i \(0.451824\pi\)
\(294\) 23.1566 1.35052
\(295\) 15.3052 0.891105
\(296\) 80.0050 4.65019
\(297\) 1.00000 0.0580259
\(298\) −14.5636 −0.843645
\(299\) 0 0
\(300\) 16.9118 0.976401
\(301\) −46.1042 −2.65740
\(302\) −18.5572 −1.06785
\(303\) −12.1229 −0.696442
\(304\) −44.8720 −2.57359
\(305\) 6.67355 0.382126
\(306\) 10.4572 0.597796
\(307\) −30.0561 −1.71539 −0.857697 0.514156i \(-0.828105\pi\)
−0.857697 + 0.514156i \(0.828105\pi\)
\(308\) 21.6258 1.23224
\(309\) −3.40983 −0.193978
\(310\) 47.9418 2.72291
\(311\) −21.7462 −1.23311 −0.616557 0.787310i \(-0.711473\pi\)
−0.616557 + 0.787310i \(0.711473\pi\)
\(312\) 0 0
\(313\) −24.4361 −1.38121 −0.690606 0.723231i \(-0.742656\pi\)
−0.690606 + 0.723231i \(0.742656\pi\)
\(314\) 44.6103 2.51751
\(315\) −11.1709 −0.629410
\(316\) 8.64309 0.486212
\(317\) 21.1040 1.18532 0.592658 0.805454i \(-0.298079\pi\)
0.592658 + 0.805454i \(0.298079\pi\)
\(318\) −6.51790 −0.365506
\(319\) −2.09928 −0.117537
\(320\) −89.2661 −4.99013
\(321\) −12.2352 −0.682903
\(322\) −20.4017 −1.13694
\(323\) −11.2286 −0.624774
\(324\) 5.50093 0.305607
\(325\) 0 0
\(326\) 31.2310 1.72972
\(327\) −8.72763 −0.482639
\(328\) 60.9611 3.36601
\(329\) 20.8805 1.15118
\(330\) −7.78236 −0.428405
\(331\) 0.560518 0.0308089 0.0154044 0.999881i \(-0.495096\pi\)
0.0154044 + 0.999881i \(0.495096\pi\)
\(332\) 58.7144 3.22237
\(333\) 8.34404 0.457250
\(334\) −40.3427 −2.20745
\(335\) −29.7596 −1.62594
\(336\) 59.9850 3.27245
\(337\) −7.76850 −0.423177 −0.211589 0.977359i \(-0.567864\pi\)
−0.211589 + 0.977359i \(0.567864\pi\)
\(338\) 0 0
\(339\) 0.0155525 0.000844695 0
\(340\) −59.6823 −3.23673
\(341\) −6.16032 −0.333600
\(342\) −8.05426 −0.435525
\(343\) 5.72025 0.308864
\(344\) −112.446 −6.06270
\(345\) 5.38427 0.289879
\(346\) 0.511186 0.0274816
\(347\) −10.1357 −0.544110 −0.272055 0.962282i \(-0.587703\pi\)
−0.272055 + 0.962282i \(0.587703\pi\)
\(348\) −11.5480 −0.619037
\(349\) −20.0030 −1.07074 −0.535369 0.844619i \(-0.679827\pi\)
−0.535369 + 0.844619i \(0.679827\pi\)
\(350\) 33.1013 1.76934
\(351\) 0 0
\(352\) 22.6127 1.20526
\(353\) −26.7905 −1.42591 −0.712957 0.701208i \(-0.752645\pi\)
−0.712957 + 0.701208i \(0.752645\pi\)
\(354\) −14.7517 −0.784047
\(355\) −28.6823 −1.52230
\(356\) 17.8036 0.943589
\(357\) 15.0104 0.794433
\(358\) 30.0049 1.58581
\(359\) 26.7347 1.41101 0.705503 0.708707i \(-0.250721\pi\)
0.705503 + 0.708707i \(0.250721\pi\)
\(360\) −27.2455 −1.43596
\(361\) −10.3516 −0.544820
\(362\) −23.3354 −1.22648
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 42.9296 2.24704
\(366\) −6.43222 −0.336218
\(367\) 1.89563 0.0989512 0.0494756 0.998775i \(-0.484245\pi\)
0.0494756 + 0.998775i \(0.484245\pi\)
\(368\) −28.9122 −1.50715
\(369\) 6.35787 0.330978
\(370\) −64.9363 −3.37588
\(371\) −9.35590 −0.485734
\(372\) −33.8875 −1.75698
\(373\) −36.7517 −1.90293 −0.951464 0.307759i \(-0.900421\pi\)
−0.951464 + 0.307759i \(0.900421\pi\)
\(374\) 10.4572 0.540726
\(375\) 5.47182 0.282564
\(376\) 50.9269 2.62635
\(377\) 0 0
\(378\) 10.7670 0.553792
\(379\) −26.1328 −1.34235 −0.671176 0.741298i \(-0.734211\pi\)
−0.671176 + 0.741298i \(0.734211\pi\)
\(380\) 45.9682 2.35812
\(381\) −5.91514 −0.303042
\(382\) −32.3185 −1.65356
\(383\) 16.9211 0.864629 0.432315 0.901723i \(-0.357697\pi\)
0.432315 + 0.901723i \(0.357697\pi\)
\(384\) 40.8125 2.08270
\(385\) −11.1709 −0.569323
\(386\) 29.9638 1.52512
\(387\) −11.7275 −0.596142
\(388\) −97.8693 −4.96856
\(389\) −5.05607 −0.256353 −0.128177 0.991751i \(-0.540912\pi\)
−0.128177 + 0.991751i \(0.540912\pi\)
\(390\) 0 0
\(391\) −7.23484 −0.365882
\(392\) 81.0694 4.09462
\(393\) −1.32191 −0.0666818
\(394\) 25.8351 1.30156
\(395\) −4.46464 −0.224640
\(396\) 5.50093 0.276432
\(397\) 15.7731 0.791631 0.395815 0.918330i \(-0.370462\pi\)
0.395815 + 0.918330i \(0.370462\pi\)
\(398\) −41.9576 −2.10314
\(399\) −11.5612 −0.578785
\(400\) 46.9095 2.34547
\(401\) 8.42218 0.420584 0.210292 0.977639i \(-0.432559\pi\)
0.210292 + 0.977639i \(0.432559\pi\)
\(402\) 28.6835 1.43060
\(403\) 0 0
\(404\) −66.6872 −3.31781
\(405\) −2.84154 −0.141197
\(406\) −22.6028 −1.12176
\(407\) 8.34404 0.413599
\(408\) 36.6097 1.81245
\(409\) 31.3861 1.55194 0.775971 0.630768i \(-0.217260\pi\)
0.775971 + 0.630768i \(0.217260\pi\)
\(410\) −49.4792 −2.44361
\(411\) 4.82127 0.237816
\(412\) −18.7572 −0.924102
\(413\) −21.1749 −1.04195
\(414\) −5.18956 −0.255053
\(415\) −30.3293 −1.48881
\(416\) 0 0
\(417\) 17.1877 0.841683
\(418\) −8.05426 −0.393947
\(419\) −6.62928 −0.323861 −0.161931 0.986802i \(-0.551772\pi\)
−0.161931 + 0.986802i \(0.551772\pi\)
\(420\) −61.4504 −2.99847
\(421\) −2.61327 −0.127363 −0.0636816 0.997970i \(-0.520284\pi\)
−0.0636816 + 0.997970i \(0.520284\pi\)
\(422\) 7.97651 0.388290
\(423\) 5.31137 0.258248
\(424\) −22.8187 −1.10817
\(425\) 11.7384 0.569396
\(426\) 27.6451 1.33941
\(427\) −9.23291 −0.446812
\(428\) −67.3050 −3.25331
\(429\) 0 0
\(430\) 91.2675 4.40131
\(431\) −24.8745 −1.19816 −0.599081 0.800688i \(-0.704467\pi\)
−0.599081 + 0.800688i \(0.704467\pi\)
\(432\) 15.2584 0.734118
\(433\) 6.55556 0.315040 0.157520 0.987516i \(-0.449650\pi\)
0.157520 + 0.987516i \(0.449650\pi\)
\(434\) −66.3278 −3.18384
\(435\) 5.96518 0.286009
\(436\) −48.0101 −2.29927
\(437\) 5.57239 0.266563
\(438\) −41.3771 −1.97707
\(439\) −38.2180 −1.82405 −0.912023 0.410138i \(-0.865480\pi\)
−0.912023 + 0.410138i \(0.865480\pi\)
\(440\) −27.2455 −1.29888
\(441\) 8.45506 0.402622
\(442\) 0 0
\(443\) −12.7407 −0.605330 −0.302665 0.953097i \(-0.597876\pi\)
−0.302665 + 0.953097i \(0.597876\pi\)
\(444\) 45.8999 2.17831
\(445\) −9.19656 −0.435959
\(446\) 29.7187 1.40722
\(447\) −5.31754 −0.251511
\(448\) 123.500 5.83484
\(449\) 25.9513 1.22472 0.612358 0.790581i \(-0.290221\pi\)
0.612358 + 0.790581i \(0.290221\pi\)
\(450\) 8.41997 0.396921
\(451\) 6.35787 0.299381
\(452\) 0.0855531 0.00402408
\(453\) −6.77573 −0.318351
\(454\) 0.883629 0.0414708
\(455\) 0 0
\(456\) −28.1974 −1.32046
\(457\) 16.0372 0.750190 0.375095 0.926986i \(-0.377610\pi\)
0.375095 + 0.926986i \(0.377610\pi\)
\(458\) −16.2700 −0.760247
\(459\) 3.81818 0.178217
\(460\) 29.6185 1.38097
\(461\) 3.48566 0.162343 0.0811716 0.996700i \(-0.474134\pi\)
0.0811716 + 0.996700i \(0.474134\pi\)
\(462\) 10.7670 0.500924
\(463\) −27.0784 −1.25844 −0.629220 0.777227i \(-0.716626\pi\)
−0.629220 + 0.777227i \(0.716626\pi\)
\(464\) −32.0315 −1.48703
\(465\) 17.5048 0.811765
\(466\) −34.5639 −1.60114
\(467\) −15.6899 −0.726041 −0.363020 0.931781i \(-0.618254\pi\)
−0.363020 + 0.931781i \(0.618254\pi\)
\(468\) 0 0
\(469\) 41.1727 1.90118
\(470\) −41.3350 −1.90664
\(471\) 16.2884 0.750529
\(472\) −51.6448 −2.37715
\(473\) −11.7275 −0.539230
\(474\) 4.30319 0.197652
\(475\) −9.04109 −0.414834
\(476\) 82.5709 3.78463
\(477\) −2.37985 −0.108966
\(478\) 56.8860 2.60191
\(479\) 33.0061 1.50809 0.754043 0.656825i \(-0.228101\pi\)
0.754043 + 0.656825i \(0.228101\pi\)
\(480\) −64.2550 −2.93283
\(481\) 0 0
\(482\) −49.8904 −2.27244
\(483\) −7.44918 −0.338949
\(484\) 5.50093 0.250042
\(485\) 50.5550 2.29559
\(486\) 2.73878 0.124234
\(487\) 18.6684 0.845945 0.422973 0.906142i \(-0.360987\pi\)
0.422973 + 0.906142i \(0.360987\pi\)
\(488\) −22.5187 −1.01938
\(489\) 11.4032 0.515672
\(490\) −65.8003 −2.97255
\(491\) −6.78238 −0.306084 −0.153042 0.988220i \(-0.548907\pi\)
−0.153042 + 0.988220i \(0.548907\pi\)
\(492\) 34.9742 1.57676
\(493\) −8.01542 −0.360996
\(494\) 0 0
\(495\) −2.84154 −0.127718
\(496\) −93.9963 −4.22056
\(497\) 39.6822 1.77999
\(498\) 29.2325 1.30994
\(499\) −0.212900 −0.00953070 −0.00476535 0.999989i \(-0.501517\pi\)
−0.00476535 + 0.999989i \(0.501517\pi\)
\(500\) 30.1001 1.34612
\(501\) −14.7302 −0.658095
\(502\) −62.0779 −2.77067
\(503\) −10.5282 −0.469430 −0.234715 0.972064i \(-0.575416\pi\)
−0.234715 + 0.972064i \(0.575416\pi\)
\(504\) 37.6943 1.67904
\(505\) 34.4477 1.53290
\(506\) −5.18956 −0.230704
\(507\) 0 0
\(508\) −32.5387 −1.44367
\(509\) −26.1335 −1.15835 −0.579175 0.815204i \(-0.696625\pi\)
−0.579175 + 0.815204i \(0.696625\pi\)
\(510\) −29.7144 −1.31578
\(511\) −59.3934 −2.62741
\(512\) 52.4306 2.31713
\(513\) −2.94082 −0.129840
\(514\) 48.5677 2.14223
\(515\) 9.68917 0.426956
\(516\) −64.5121 −2.83999
\(517\) 5.31137 0.233594
\(518\) 89.8398 3.94734
\(519\) 0.186647 0.00819291
\(520\) 0 0
\(521\) 44.5983 1.95389 0.976944 0.213495i \(-0.0684847\pi\)
0.976944 + 0.213495i \(0.0684847\pi\)
\(522\) −5.74947 −0.251647
\(523\) −35.9788 −1.57324 −0.786622 0.617435i \(-0.788172\pi\)
−0.786622 + 0.617435i \(0.788172\pi\)
\(524\) −7.27176 −0.317668
\(525\) 12.0862 0.527483
\(526\) 80.8233 3.52406
\(527\) −23.5212 −1.02460
\(528\) 15.2584 0.664035
\(529\) −19.4096 −0.843895
\(530\) 18.5209 0.804495
\(531\) −5.38624 −0.233743
\(532\) −63.5974 −2.75730
\(533\) 0 0
\(534\) 8.86399 0.383583
\(535\) 34.7668 1.50310
\(536\) 100.419 4.33743
\(537\) 10.9555 0.472767
\(538\) −24.7063 −1.06516
\(539\) 8.45506 0.364185
\(540\) −15.6311 −0.672656
\(541\) 19.2806 0.828937 0.414469 0.910064i \(-0.363967\pi\)
0.414469 + 0.910064i \(0.363967\pi\)
\(542\) 12.5524 0.539172
\(543\) −8.52034 −0.365643
\(544\) 86.3395 3.70177
\(545\) 24.7999 1.06231
\(546\) 0 0
\(547\) −18.3680 −0.785359 −0.392679 0.919675i \(-0.628452\pi\)
−0.392679 + 0.919675i \(0.628452\pi\)
\(548\) 26.5215 1.13294
\(549\) −2.34857 −0.100234
\(550\) 8.41997 0.359029
\(551\) 6.17360 0.263004
\(552\) −18.1683 −0.773293
\(553\) 6.17686 0.262667
\(554\) 57.4759 2.44192
\(555\) −23.7099 −1.00643
\(556\) 94.5481 4.00973
\(557\) −20.9920 −0.889459 −0.444730 0.895665i \(-0.646700\pi\)
−0.444730 + 0.895665i \(0.646700\pi\)
\(558\) −16.8718 −0.714239
\(559\) 0 0
\(560\) −170.450 −7.20282
\(561\) 3.81818 0.161204
\(562\) 28.8558 1.21721
\(563\) 3.18924 0.134411 0.0672053 0.997739i \(-0.478592\pi\)
0.0672053 + 0.997739i \(0.478592\pi\)
\(564\) 29.2175 1.23028
\(565\) −0.0441930 −0.00185921
\(566\) −7.04329 −0.296052
\(567\) 3.93129 0.165099
\(568\) 96.7834 4.06094
\(569\) 19.0570 0.798909 0.399455 0.916753i \(-0.369200\pi\)
0.399455 + 0.916753i \(0.369200\pi\)
\(570\) 22.8865 0.958610
\(571\) 13.1418 0.549967 0.274984 0.961449i \(-0.411328\pi\)
0.274984 + 0.961449i \(0.411328\pi\)
\(572\) 0 0
\(573\) −11.8003 −0.492965
\(574\) 68.4549 2.85725
\(575\) −5.82540 −0.242936
\(576\) 31.4147 1.30895
\(577\) 6.38825 0.265946 0.132973 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(578\) −6.63205 −0.275857
\(579\) 10.9405 0.454674
\(580\) 32.8140 1.36253
\(581\) 41.9608 1.74083
\(582\) −48.7268 −2.01979
\(583\) −2.37985 −0.0985635
\(584\) −144.858 −5.99428
\(585\) 0 0
\(586\) 14.1365 0.583975
\(587\) −8.66483 −0.357636 −0.178818 0.983882i \(-0.557227\pi\)
−0.178818 + 0.983882i \(0.557227\pi\)
\(588\) 46.5107 1.91807
\(589\) 18.1164 0.746472
\(590\) 41.9177 1.72572
\(591\) 9.43307 0.388025
\(592\) 127.316 5.23267
\(593\) 5.41552 0.222389 0.111194 0.993799i \(-0.464532\pi\)
0.111194 + 0.993799i \(0.464532\pi\)
\(594\) 2.73878 0.112374
\(595\) −42.6525 −1.74858
\(596\) −29.2514 −1.19818
\(597\) −15.3198 −0.626997
\(598\) 0 0
\(599\) 17.1821 0.702041 0.351021 0.936368i \(-0.385835\pi\)
0.351021 + 0.936368i \(0.385835\pi\)
\(600\) 29.4777 1.20342
\(601\) 4.44618 0.181364 0.0906818 0.995880i \(-0.471095\pi\)
0.0906818 + 0.995880i \(0.471095\pi\)
\(602\) −126.269 −5.14635
\(603\) 10.4731 0.426496
\(604\) −37.2728 −1.51661
\(605\) −2.84154 −0.115525
\(606\) −33.2020 −1.34874
\(607\) 12.1499 0.493148 0.246574 0.969124i \(-0.420695\pi\)
0.246574 + 0.969124i \(0.420695\pi\)
\(608\) −66.5000 −2.69693
\(609\) −8.25288 −0.334423
\(610\) 18.2774 0.740031
\(611\) 0 0
\(612\) 21.0035 0.849017
\(613\) −30.6073 −1.23622 −0.618108 0.786093i \(-0.712101\pi\)
−0.618108 + 0.786093i \(0.712101\pi\)
\(614\) −82.3172 −3.32205
\(615\) −18.0661 −0.728497
\(616\) 37.6943 1.51875
\(617\) 15.3414 0.617622 0.308811 0.951123i \(-0.400069\pi\)
0.308811 + 0.951123i \(0.400069\pi\)
\(618\) −9.33878 −0.375661
\(619\) −10.0391 −0.403505 −0.201752 0.979437i \(-0.564664\pi\)
−0.201752 + 0.979437i \(0.564664\pi\)
\(620\) 96.2926 3.86720
\(621\) −1.89484 −0.0760374
\(622\) −59.5581 −2.38806
\(623\) 12.7235 0.509757
\(624\) 0 0
\(625\) −30.9201 −1.23681
\(626\) −66.9253 −2.67487
\(627\) −2.94082 −0.117445
\(628\) 89.6012 3.57548
\(629\) 31.8590 1.27030
\(630\) −30.5947 −1.21892
\(631\) 20.8523 0.830119 0.415059 0.909794i \(-0.363761\pi\)
0.415059 + 0.909794i \(0.363761\pi\)
\(632\) 15.0652 0.599260
\(633\) 2.91243 0.115759
\(634\) 57.7991 2.29550
\(635\) 16.8081 0.667009
\(636\) −13.0914 −0.519108
\(637\) 0 0
\(638\) −5.74947 −0.227624
\(639\) 10.0939 0.399310
\(640\) −115.970 −4.58413
\(641\) 29.3934 1.16097 0.580484 0.814272i \(-0.302863\pi\)
0.580484 + 0.814272i \(0.302863\pi\)
\(642\) −33.5096 −1.32252
\(643\) −7.23812 −0.285444 −0.142722 0.989763i \(-0.545585\pi\)
−0.142722 + 0.989763i \(0.545585\pi\)
\(644\) −40.9774 −1.61474
\(645\) 33.3241 1.31214
\(646\) −30.7526 −1.20994
\(647\) −25.4069 −0.998848 −0.499424 0.866358i \(-0.666455\pi\)
−0.499424 + 0.866358i \(0.666455\pi\)
\(648\) 9.58828 0.376663
\(649\) −5.38624 −0.211429
\(650\) 0 0
\(651\) −24.2180 −0.949178
\(652\) 62.7284 2.45663
\(653\) −10.1486 −0.397146 −0.198573 0.980086i \(-0.563631\pi\)
−0.198573 + 0.980086i \(0.563631\pi\)
\(654\) −23.9031 −0.934685
\(655\) 3.75627 0.146770
\(656\) 97.0107 3.78763
\(657\) −15.1079 −0.589413
\(658\) 57.1873 2.22939
\(659\) −18.8648 −0.734869 −0.367434 0.930049i \(-0.619764\pi\)
−0.367434 + 0.930049i \(0.619764\pi\)
\(660\) −15.6311 −0.608440
\(661\) −7.39059 −0.287461 −0.143730 0.989617i \(-0.545910\pi\)
−0.143730 + 0.989617i \(0.545910\pi\)
\(662\) 1.53514 0.0596648
\(663\) 0 0
\(664\) 102.341 3.97160
\(665\) 32.8516 1.27393
\(666\) 22.8525 0.885516
\(667\) 3.97780 0.154021
\(668\) −81.0296 −3.13513
\(669\) 10.8511 0.419526
\(670\) −81.5052 −3.14882
\(671\) −2.34857 −0.0906655
\(672\) 88.8973 3.42929
\(673\) −13.8241 −0.532879 −0.266439 0.963852i \(-0.585847\pi\)
−0.266439 + 0.963852i \(0.585847\pi\)
\(674\) −21.2762 −0.819530
\(675\) 3.07435 0.118332
\(676\) 0 0
\(677\) −28.1714 −1.08272 −0.541358 0.840792i \(-0.682090\pi\)
−0.541358 + 0.840792i \(0.682090\pi\)
\(678\) 0.0425948 0.00163585
\(679\) −69.9433 −2.68418
\(680\) −104.028 −3.98929
\(681\) 0.322636 0.0123634
\(682\) −16.8718 −0.646053
\(683\) −20.1458 −0.770856 −0.385428 0.922738i \(-0.625946\pi\)
−0.385428 + 0.922738i \(0.625946\pi\)
\(684\) −16.1772 −0.618552
\(685\) −13.6998 −0.523444
\(686\) 15.6665 0.598150
\(687\) −5.94060 −0.226648
\(688\) −178.942 −6.82211
\(689\) 0 0
\(690\) 14.7463 0.561384
\(691\) −4.60090 −0.175026 −0.0875132 0.996163i \(-0.527892\pi\)
−0.0875132 + 0.996163i \(0.527892\pi\)
\(692\) 1.02673 0.0390306
\(693\) 3.93129 0.149337
\(694\) −27.7593 −1.05373
\(695\) −48.8394 −1.85258
\(696\) −20.1285 −0.762968
\(697\) 24.2755 0.919499
\(698\) −54.7839 −2.07360
\(699\) −12.6202 −0.477338
\(700\) 66.4851 2.51290
\(701\) −2.14477 −0.0810067 −0.0405033 0.999179i \(-0.512896\pi\)
−0.0405033 + 0.999179i \(0.512896\pi\)
\(702\) 0 0
\(703\) −24.5383 −0.925479
\(704\) 31.4147 1.18399
\(705\) −15.0925 −0.568415
\(706\) −73.3733 −2.76144
\(707\) −47.6586 −1.79239
\(708\) −29.6293 −1.11354
\(709\) −18.0751 −0.678826 −0.339413 0.940637i \(-0.610228\pi\)
−0.339413 + 0.940637i \(0.610228\pi\)
\(710\) −78.5546 −2.94810
\(711\) 1.57120 0.0589248
\(712\) 31.0322 1.16298
\(713\) 11.6728 0.437151
\(714\) 41.1101 1.53851
\(715\) 0 0
\(716\) 60.2657 2.25223
\(717\) 20.7706 0.775691
\(718\) 73.2206 2.73257
\(719\) −5.67258 −0.211552 −0.105776 0.994390i \(-0.533733\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(720\) −43.3572 −1.61583
\(721\) −13.4050 −0.499230
\(722\) −28.3507 −1.05511
\(723\) −18.2163 −0.677470
\(724\) −46.8698 −1.74190
\(725\) −6.45391 −0.239692
\(726\) 2.73878 0.101646
\(727\) 20.7279 0.768756 0.384378 0.923176i \(-0.374416\pi\)
0.384378 + 0.923176i \(0.374416\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 117.575 4.35163
\(731\) −44.7776 −1.65616
\(732\) −12.9193 −0.477511
\(733\) 13.8875 0.512945 0.256473 0.966552i \(-0.417440\pi\)
0.256473 + 0.966552i \(0.417440\pi\)
\(734\) 5.19172 0.191630
\(735\) −24.0254 −0.886189
\(736\) −42.8476 −1.57938
\(737\) 10.4731 0.385780
\(738\) 17.4128 0.640975
\(739\) −2.10062 −0.0772725 −0.0386362 0.999253i \(-0.512301\pi\)
−0.0386362 + 0.999253i \(0.512301\pi\)
\(740\) −130.427 −4.79457
\(741\) 0 0
\(742\) −25.6238 −0.940678
\(743\) 39.5255 1.45005 0.725025 0.688722i \(-0.241828\pi\)
0.725025 + 0.688722i \(0.241828\pi\)
\(744\) −59.0668 −2.16550
\(745\) 15.1100 0.553587
\(746\) −100.655 −3.68523
\(747\) 10.6736 0.390525
\(748\) 21.0035 0.767964
\(749\) −48.1002 −1.75754
\(750\) 14.9861 0.547216
\(751\) −7.96076 −0.290492 −0.145246 0.989396i \(-0.546397\pi\)
−0.145246 + 0.989396i \(0.546397\pi\)
\(752\) 81.0427 2.95532
\(753\) −22.6662 −0.826004
\(754\) 0 0
\(755\) 19.2535 0.700707
\(756\) 21.6258 0.786521
\(757\) −21.7720 −0.791316 −0.395658 0.918398i \(-0.629484\pi\)
−0.395658 + 0.918398i \(0.629484\pi\)
\(758\) −71.5721 −2.59962
\(759\) −1.89484 −0.0687784
\(760\) 80.1240 2.90640
\(761\) −25.3978 −0.920668 −0.460334 0.887746i \(-0.652270\pi\)
−0.460334 + 0.887746i \(0.652270\pi\)
\(762\) −16.2003 −0.586874
\(763\) −34.3109 −1.24214
\(764\) −64.9126 −2.34846
\(765\) −10.8495 −0.392264
\(766\) 46.3433 1.67445
\(767\) 0 0
\(768\) 48.9471 1.76623
\(769\) −17.5471 −0.632763 −0.316382 0.948632i \(-0.602468\pi\)
−0.316382 + 0.948632i \(0.602468\pi\)
\(770\) −30.5947 −1.10256
\(771\) 17.7333 0.638649
\(772\) 60.1832 2.16604
\(773\) 16.9181 0.608503 0.304251 0.952592i \(-0.401594\pi\)
0.304251 + 0.952592i \(0.401594\pi\)
\(774\) −32.1190 −1.15449
\(775\) −18.9389 −0.680307
\(776\) −170.589 −6.12379
\(777\) 32.8028 1.17680
\(778\) −13.8475 −0.496456
\(779\) −18.6974 −0.669902
\(780\) 0 0
\(781\) 10.0939 0.361189
\(782\) −19.8147 −0.708570
\(783\) −2.09928 −0.0750221
\(784\) 129.010 4.60751
\(785\) −46.2841 −1.65195
\(786\) −3.62044 −0.129137
\(787\) 27.1659 0.968361 0.484181 0.874968i \(-0.339118\pi\)
0.484181 + 0.874968i \(0.339118\pi\)
\(788\) 51.8907 1.84853
\(789\) 29.5107 1.05061
\(790\) −12.2277 −0.435041
\(791\) 0.0611413 0.00217394
\(792\) 9.58828 0.340705
\(793\) 0 0
\(794\) 43.1992 1.53308
\(795\) 6.76245 0.239839
\(796\) −84.2731 −2.98698
\(797\) 12.3253 0.436583 0.218292 0.975884i \(-0.429952\pi\)
0.218292 + 0.975884i \(0.429952\pi\)
\(798\) −31.6637 −1.12088
\(799\) 20.2797 0.717446
\(800\) 69.5194 2.45788
\(801\) 3.23647 0.114355
\(802\) 23.0665 0.814507
\(803\) −15.1079 −0.533144
\(804\) 57.6116 2.03180
\(805\) 21.1671 0.746043
\(806\) 0 0
\(807\) −9.02091 −0.317551
\(808\) −116.238 −4.08923
\(809\) 51.6306 1.81523 0.907617 0.419798i \(-0.137899\pi\)
0.907617 + 0.419798i \(0.137899\pi\)
\(810\) −7.78236 −0.273444
\(811\) 22.5443 0.791637 0.395818 0.918329i \(-0.370461\pi\)
0.395818 + 0.918329i \(0.370461\pi\)
\(812\) −45.3985 −1.59317
\(813\) 4.58320 0.160740
\(814\) 22.8525 0.800980
\(815\) −32.4027 −1.13502
\(816\) 58.2591 2.03948
\(817\) 34.4884 1.20660
\(818\) 85.9597 3.00551
\(819\) 0 0
\(820\) −99.3806 −3.47052
\(821\) −18.1907 −0.634861 −0.317430 0.948282i \(-0.602820\pi\)
−0.317430 + 0.948282i \(0.602820\pi\)
\(822\) 13.2044 0.460557
\(823\) 44.4631 1.54989 0.774944 0.632030i \(-0.217778\pi\)
0.774944 + 0.632030i \(0.217778\pi\)
\(824\) −32.6944 −1.13896
\(825\) 3.07435 0.107035
\(826\) −57.9934 −2.01785
\(827\) −6.33341 −0.220234 −0.110117 0.993919i \(-0.535123\pi\)
−0.110117 + 0.993919i \(0.535123\pi\)
\(828\) −10.4234 −0.362238
\(829\) 7.54455 0.262033 0.131017 0.991380i \(-0.458176\pi\)
0.131017 + 0.991380i \(0.458176\pi\)
\(830\) −83.0654 −2.88324
\(831\) 20.9859 0.727994
\(832\) 0 0
\(833\) 32.2829 1.11854
\(834\) 47.0732 1.63001
\(835\) 41.8563 1.44850
\(836\) −16.1772 −0.559501
\(837\) −6.16032 −0.212932
\(838\) −18.1561 −0.627194
\(839\) 30.1703 1.04159 0.520797 0.853681i \(-0.325635\pi\)
0.520797 + 0.853681i \(0.325635\pi\)
\(840\) −107.110 −3.69564
\(841\) −24.5930 −0.848035
\(842\) −7.15719 −0.246653
\(843\) 10.5360 0.362878
\(844\) 16.0211 0.551468
\(845\) 0 0
\(846\) 14.5467 0.500125
\(847\) 3.93129 0.135081
\(848\) −36.3127 −1.24698
\(849\) −2.57169 −0.0882601
\(850\) 32.1489 1.10270
\(851\) −15.8106 −0.541981
\(852\) 55.5260 1.90229
\(853\) −14.6801 −0.502637 −0.251319 0.967904i \(-0.580864\pi\)
−0.251319 + 0.967904i \(0.580864\pi\)
\(854\) −25.2869 −0.865301
\(855\) 8.35645 0.285785
\(856\) −117.315 −4.00973
\(857\) −21.1257 −0.721641 −0.360821 0.932635i \(-0.617503\pi\)
−0.360821 + 0.932635i \(0.617503\pi\)
\(858\) 0 0
\(859\) 29.4462 1.00469 0.502346 0.864667i \(-0.332470\pi\)
0.502346 + 0.864667i \(0.332470\pi\)
\(860\) 183.314 6.25094
\(861\) 24.9947 0.851816
\(862\) −68.1258 −2.32038
\(863\) 33.8929 1.15373 0.576865 0.816840i \(-0.304276\pi\)
0.576865 + 0.816840i \(0.304276\pi\)
\(864\) 22.6127 0.769301
\(865\) −0.530366 −0.0180330
\(866\) 17.9543 0.610111
\(867\) −2.42153 −0.0822396
\(868\) −133.221 −4.52183
\(869\) 1.57120 0.0532995
\(870\) 16.3373 0.553888
\(871\) 0 0
\(872\) −83.6830 −2.83386
\(873\) −17.7914 −0.602148
\(874\) 15.2616 0.516230
\(875\) 21.5113 0.727215
\(876\) −83.1072 −2.80793
\(877\) −6.62356 −0.223662 −0.111831 0.993727i \(-0.535671\pi\)
−0.111831 + 0.993727i \(0.535671\pi\)
\(878\) −104.671 −3.53247
\(879\) 5.16162 0.174097
\(880\) −43.3572 −1.46157
\(881\) 18.7993 0.633366 0.316683 0.948531i \(-0.397431\pi\)
0.316683 + 0.948531i \(0.397431\pi\)
\(882\) 23.1566 0.779722
\(883\) −35.0323 −1.17893 −0.589465 0.807794i \(-0.700661\pi\)
−0.589465 + 0.807794i \(0.700661\pi\)
\(884\) 0 0
\(885\) 15.3052 0.514479
\(886\) −34.8941 −1.17229
\(887\) 12.8619 0.431860 0.215930 0.976409i \(-0.430722\pi\)
0.215930 + 0.976409i \(0.430722\pi\)
\(888\) 80.0050 2.68479
\(889\) −23.2541 −0.779918
\(890\) −25.1874 −0.844283
\(891\) 1.00000 0.0335013
\(892\) 59.6909 1.99860
\(893\) −15.6198 −0.522696
\(894\) −14.5636 −0.487079
\(895\) −31.1306 −1.04058
\(896\) 160.446 5.36012
\(897\) 0 0
\(898\) 71.0749 2.37180
\(899\) 12.9322 0.431314
\(900\) 16.9118 0.563725
\(901\) −9.08670 −0.302722
\(902\) 17.4128 0.579784
\(903\) −46.1042 −1.53425
\(904\) 0.149121 0.00495971
\(905\) 24.2109 0.804797
\(906\) −18.5572 −0.616523
\(907\) 47.0378 1.56187 0.780933 0.624615i \(-0.214744\pi\)
0.780933 + 0.624615i \(0.214744\pi\)
\(908\) 1.77480 0.0588987
\(909\) −12.1229 −0.402091
\(910\) 0 0
\(911\) 40.3206 1.33588 0.667940 0.744215i \(-0.267176\pi\)
0.667940 + 0.744215i \(0.267176\pi\)
\(912\) −44.8720 −1.48586
\(913\) 10.6736 0.353243
\(914\) 43.9225 1.45283
\(915\) 6.67355 0.220621
\(916\) −32.6788 −1.07974
\(917\) −5.19683 −0.171614
\(918\) 10.4572 0.345137
\(919\) −1.80179 −0.0594356 −0.0297178 0.999558i \(-0.509461\pi\)
−0.0297178 + 0.999558i \(0.509461\pi\)
\(920\) 51.6259 1.70205
\(921\) −30.0561 −0.990383
\(922\) 9.54646 0.314396
\(923\) 0 0
\(924\) 21.6258 0.711435
\(925\) 25.6525 0.843448
\(926\) −74.1619 −2.43711
\(927\) −3.40983 −0.111994
\(928\) −47.4705 −1.55829
\(929\) 26.3015 0.862924 0.431462 0.902131i \(-0.357998\pi\)
0.431462 + 0.902131i \(0.357998\pi\)
\(930\) 47.9418 1.57207
\(931\) −24.8648 −0.814910
\(932\) −69.4226 −2.27401
\(933\) −21.7462 −0.711939
\(934\) −42.9711 −1.40606
\(935\) −10.8495 −0.354817
\(936\) 0 0
\(937\) 8.45280 0.276141 0.138070 0.990422i \(-0.455910\pi\)
0.138070 + 0.990422i \(0.455910\pi\)
\(938\) 112.763 3.68184
\(939\) −24.4361 −0.797443
\(940\) −83.0226 −2.70790
\(941\) −8.34188 −0.271937 −0.135969 0.990713i \(-0.543415\pi\)
−0.135969 + 0.990713i \(0.543415\pi\)
\(942\) 44.6103 1.45348
\(943\) −12.0472 −0.392310
\(944\) −82.1852 −2.67490
\(945\) −11.1709 −0.363390
\(946\) −32.1190 −1.04428
\(947\) −21.8593 −0.710330 −0.355165 0.934804i \(-0.615575\pi\)
−0.355165 + 0.934804i \(0.615575\pi\)
\(948\) 8.64309 0.280714
\(949\) 0 0
\(950\) −24.7616 −0.803372
\(951\) 21.1040 0.684343
\(952\) 143.924 4.66459
\(953\) 57.6509 1.86750 0.933748 0.357932i \(-0.116518\pi\)
0.933748 + 0.357932i \(0.116518\pi\)
\(954\) −6.51790 −0.211025
\(955\) 33.5310 1.08504
\(956\) 114.257 3.69535
\(957\) −2.09928 −0.0678600
\(958\) 90.3964 2.92058
\(959\) 18.9538 0.612051
\(960\) −89.2661 −2.88105
\(961\) 6.94950 0.224177
\(962\) 0 0
\(963\) −12.2352 −0.394274
\(964\) −100.206 −3.22743
\(965\) −31.0880 −1.00076
\(966\) −20.4017 −0.656413
\(967\) 41.2637 1.32695 0.663476 0.748197i \(-0.269080\pi\)
0.663476 + 0.748197i \(0.269080\pi\)
\(968\) 9.58828 0.308179
\(969\) −11.2286 −0.360713
\(970\) 138.459 4.44566
\(971\) 10.2876 0.330146 0.165073 0.986281i \(-0.447214\pi\)
0.165073 + 0.986281i \(0.447214\pi\)
\(972\) 5.50093 0.176442
\(973\) 67.5697 2.16618
\(974\) 51.1286 1.63827
\(975\) 0 0
\(976\) −35.8353 −1.14706
\(977\) −54.0502 −1.72922 −0.864609 0.502445i \(-0.832434\pi\)
−0.864609 + 0.502445i \(0.832434\pi\)
\(978\) 31.2310 0.998657
\(979\) 3.23647 0.103438
\(980\) −132.162 −4.22176
\(981\) −8.72763 −0.278652
\(982\) −18.5755 −0.592766
\(983\) −33.3316 −1.06311 −0.531557 0.847022i \(-0.678393\pi\)
−0.531557 + 0.847022i \(0.678393\pi\)
\(984\) 60.9611 1.94337
\(985\) −26.8045 −0.854061
\(986\) −21.9525 −0.699109
\(987\) 20.8805 0.664635
\(988\) 0 0
\(989\) 22.2217 0.706610
\(990\) −7.78236 −0.247340
\(991\) 15.1783 0.482155 0.241077 0.970506i \(-0.422499\pi\)
0.241077 + 0.970506i \(0.422499\pi\)
\(992\) −139.302 −4.42283
\(993\) 0.560518 0.0177875
\(994\) 108.681 3.44715
\(995\) 43.5318 1.38005
\(996\) 58.7144 1.86044
\(997\) −23.6131 −0.747834 −0.373917 0.927462i \(-0.621986\pi\)
−0.373917 + 0.927462i \(0.621986\pi\)
\(998\) −0.583086 −0.0184573
\(999\) 8.34404 0.263994
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 5577.2.a.y.1.7 7
13.5 odd 4 429.2.b.b.298.1 14
13.8 odd 4 429.2.b.b.298.14 yes 14
13.12 even 2 5577.2.a.x.1.1 7
39.5 even 4 1287.2.b.c.298.14 14
39.8 even 4 1287.2.b.c.298.1 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.1 14 13.5 odd 4
429.2.b.b.298.14 yes 14 13.8 odd 4
1287.2.b.c.298.1 14 39.8 even 4
1287.2.b.c.298.14 14 39.5 even 4
5577.2.a.x.1.1 7 13.12 even 2
5577.2.a.y.1.7 7 1.1 even 1 trivial