Properties

Label 5577.2.a.y.1.2
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 1.2
Root \(-1.36814\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} -2.98753 q^{10} +1.00000 q^{11} -0.128197 q^{12} +5.84291 q^{14} +2.18365 q^{15} -3.72717 q^{16} -3.79173 q^{17} -1.36814 q^{18} -3.17118 q^{19} -0.279937 q^{20} -4.27070 q^{21} -1.36814 q^{22} -4.94243 q^{23} +2.91167 q^{24} -0.231676 q^{25} +1.00000 q^{27} +0.547491 q^{28} -7.35483 q^{29} -2.98753 q^{30} +0.0727448 q^{31} -0.724050 q^{32} +1.00000 q^{33} +5.18761 q^{34} -9.32571 q^{35} -0.128197 q^{36} +3.66658 q^{37} +4.33862 q^{38} +6.35806 q^{40} -4.16722 q^{41} +5.84291 q^{42} +7.11697 q^{43} -0.128197 q^{44} +2.18365 q^{45} +6.76193 q^{46} +11.6337 q^{47} -3.72717 q^{48} +11.2389 q^{49} +0.316965 q^{50} -3.79173 q^{51} +5.11268 q^{53} -1.36814 q^{54} +2.18365 q^{55} -12.4349 q^{56} -3.17118 q^{57} +10.0624 q^{58} +5.62765 q^{59} -0.279937 q^{60} -5.40800 q^{61} -0.0995250 q^{62} -4.27070 q^{63} +8.44494 q^{64} -1.36814 q^{66} +10.1145 q^{67} +0.486088 q^{68} -4.94243 q^{69} +12.7589 q^{70} +9.62239 q^{71} +2.91167 q^{72} +6.44736 q^{73} -5.01639 q^{74} -0.231676 q^{75} +0.406536 q^{76} -4.27070 q^{77} +10.1209 q^{79} -8.13884 q^{80} +1.00000 q^{81} +5.70134 q^{82} -7.80918 q^{83} +0.547491 q^{84} -8.27981 q^{85} -9.73700 q^{86} -7.35483 q^{87} +2.91167 q^{88} +2.87912 q^{89} -2.98753 q^{90} +0.633605 q^{92} +0.0727448 q^{93} -15.9166 q^{94} -6.92475 q^{95} -0.724050 q^{96} +3.79281 q^{97} -15.3764 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + 7q^{11} + 9q^{12} + 8q^{14} + 6q^{15} + 17q^{16} - 2q^{17} + 3q^{18} + 8q^{19} - 2q^{20} + 6q^{21} + 3q^{22} + 4q^{23} + 15q^{24} + 13q^{25} + 7q^{27} + 12q^{28} - 12q^{29} - 10q^{31} + 33q^{32} + 7q^{33} + 28q^{34} - 4q^{35} + 9q^{36} + 6q^{37} + 16q^{38} - 10q^{40} + 2q^{41} + 8q^{42} - 16q^{43} + 9q^{44} + 6q^{45} - 26q^{46} + 18q^{47} + 17q^{48} + 23q^{49} + 39q^{50} - 2q^{51} + 10q^{53} + 3q^{54} + 6q^{55} + 16q^{56} + 8q^{57} + 10q^{58} + 2q^{59} - 2q^{60} - 10q^{61} - 36q^{62} + 6q^{63} + 29q^{64} + 3q^{66} + 8q^{67} - 10q^{68} + 4q^{69} - 20q^{70} + 36q^{71} + 15q^{72} + 20q^{73} + 13q^{75} + 10q^{76} + 6q^{77} + 6q^{79} - 20q^{80} + 7q^{81} - 10q^{82} + 30q^{83} + 12q^{84} - 40q^{85} + 6q^{86} - 12q^{87} + 15q^{88} + 34q^{89} - 12q^{92} - 10q^{93} + 32q^{94} + 18q^{95} + 33q^{96} + 16q^{97} + q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36814 −0.967420 −0.483710 0.875228i \(-0.660711\pi\)
−0.483710 + 0.875228i \(0.660711\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.128197 −0.0640985
\(5\) 2.18365 0.976558 0.488279 0.872688i \(-0.337625\pi\)
0.488279 + 0.872688i \(0.337625\pi\)
\(6\) −1.36814 −0.558540
\(7\) −4.27070 −1.61417 −0.807087 0.590433i \(-0.798957\pi\)
−0.807087 + 0.590433i \(0.798957\pi\)
\(8\) 2.91167 1.02943
\(9\) 1.00000 0.333333
\(10\) −2.98753 −0.944741
\(11\) 1.00000 0.301511
\(12\) −0.128197 −0.0370073
\(13\) 0 0
\(14\) 5.84291 1.56158
\(15\) 2.18365 0.563816
\(16\) −3.72717 −0.931793
\(17\) −3.79173 −0.919629 −0.459815 0.888015i \(-0.652084\pi\)
−0.459815 + 0.888015i \(0.652084\pi\)
\(18\) −1.36814 −0.322473
\(19\) −3.17118 −0.727519 −0.363760 0.931493i \(-0.618507\pi\)
−0.363760 + 0.931493i \(0.618507\pi\)
\(20\) −0.279937 −0.0625959
\(21\) −4.27070 −0.931943
\(22\) −1.36814 −0.291688
\(23\) −4.94243 −1.03057 −0.515284 0.857020i \(-0.672313\pi\)
−0.515284 + 0.857020i \(0.672313\pi\)
\(24\) 2.91167 0.594342
\(25\) −0.231676 −0.0463352
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.547491 0.103466
\(29\) −7.35483 −1.36576 −0.682879 0.730531i \(-0.739272\pi\)
−0.682879 + 0.730531i \(0.739272\pi\)
\(30\) −2.98753 −0.545447
\(31\) 0.0727448 0.0130654 0.00653268 0.999979i \(-0.497921\pi\)
0.00653268 + 0.999979i \(0.497921\pi\)
\(32\) −0.724050 −0.127995
\(33\) 1.00000 0.174078
\(34\) 5.18761 0.889668
\(35\) −9.32571 −1.57633
\(36\) −0.128197 −0.0213662
\(37\) 3.66658 0.602782 0.301391 0.953501i \(-0.402549\pi\)
0.301391 + 0.953501i \(0.402549\pi\)
\(38\) 4.33862 0.703817
\(39\) 0 0
\(40\) 6.35806 1.00530
\(41\) −4.16722 −0.650811 −0.325405 0.945575i \(-0.605501\pi\)
−0.325405 + 0.945575i \(0.605501\pi\)
\(42\) 5.84291 0.901581
\(43\) 7.11697 1.08533 0.542664 0.839950i \(-0.317416\pi\)
0.542664 + 0.839950i \(0.317416\pi\)
\(44\) −0.128197 −0.0193264
\(45\) 2.18365 0.325519
\(46\) 6.76193 0.996992
\(47\) 11.6337 1.69695 0.848477 0.529232i \(-0.177520\pi\)
0.848477 + 0.529232i \(0.177520\pi\)
\(48\) −3.72717 −0.537971
\(49\) 11.2389 1.60556
\(50\) 0.316965 0.0448256
\(51\) −3.79173 −0.530948
\(52\) 0 0
\(53\) 5.11268 0.702281 0.351140 0.936323i \(-0.385794\pi\)
0.351140 + 0.936323i \(0.385794\pi\)
\(54\) −1.36814 −0.186180
\(55\) 2.18365 0.294443
\(56\) −12.4349 −1.66168
\(57\) −3.17118 −0.420034
\(58\) 10.0624 1.32126
\(59\) 5.62765 0.732658 0.366329 0.930485i \(-0.380614\pi\)
0.366329 + 0.930485i \(0.380614\pi\)
\(60\) −0.279937 −0.0361398
\(61\) −5.40800 −0.692424 −0.346212 0.938156i \(-0.612532\pi\)
−0.346212 + 0.938156i \(0.612532\pi\)
\(62\) −0.0995250 −0.0126397
\(63\) −4.27070 −0.538058
\(64\) 8.44494 1.05562
\(65\) 0 0
\(66\) −1.36814 −0.168406
\(67\) 10.1145 1.23569 0.617843 0.786302i \(-0.288007\pi\)
0.617843 + 0.786302i \(0.288007\pi\)
\(68\) 0.486088 0.0589469
\(69\) −4.94243 −0.594998
\(70\) 12.7589 1.52498
\(71\) 9.62239 1.14197 0.570984 0.820961i \(-0.306562\pi\)
0.570984 + 0.820961i \(0.306562\pi\)
\(72\) 2.91167 0.343143
\(73\) 6.44736 0.754607 0.377303 0.926090i \(-0.376851\pi\)
0.377303 + 0.926090i \(0.376851\pi\)
\(74\) −5.01639 −0.583144
\(75\) −0.231676 −0.0267516
\(76\) 0.406536 0.0466329
\(77\) −4.27070 −0.486692
\(78\) 0 0
\(79\) 10.1209 1.13869 0.569347 0.822097i \(-0.307196\pi\)
0.569347 + 0.822097i \(0.307196\pi\)
\(80\) −8.13884 −0.909949
\(81\) 1.00000 0.111111
\(82\) 5.70134 0.629607
\(83\) −7.80918 −0.857169 −0.428585 0.903502i \(-0.640988\pi\)
−0.428585 + 0.903502i \(0.640988\pi\)
\(84\) 0.547491 0.0597362
\(85\) −8.27981 −0.898071
\(86\) −9.73700 −1.04997
\(87\) −7.35483 −0.788521
\(88\) 2.91167 0.310385
\(89\) 2.87912 0.305187 0.152593 0.988289i \(-0.451238\pi\)
0.152593 + 0.988289i \(0.451238\pi\)
\(90\) −2.98753 −0.314914
\(91\) 0 0
\(92\) 0.633605 0.0660579
\(93\) 0.0727448 0.00754329
\(94\) −15.9166 −1.64167
\(95\) −6.92475 −0.710465
\(96\) −0.724050 −0.0738980
\(97\) 3.79281 0.385101 0.192551 0.981287i \(-0.438324\pi\)
0.192551 + 0.981287i \(0.438324\pi\)
\(98\) −15.3764 −1.55325
\(99\) 1.00000 0.100504
\(100\) 0.0297002 0.00297002
\(101\) 12.8641 1.28003 0.640014 0.768363i \(-0.278928\pi\)
0.640014 + 0.768363i \(0.278928\pi\)
\(102\) 5.18761 0.513650
\(103\) −16.9975 −1.67482 −0.837409 0.546577i \(-0.815930\pi\)
−0.837409 + 0.546577i \(0.815930\pi\)
\(104\) 0 0
\(105\) −9.32571 −0.910096
\(106\) −6.99486 −0.679400
\(107\) −12.6819 −1.22600 −0.613001 0.790082i \(-0.710038\pi\)
−0.613001 + 0.790082i \(0.710038\pi\)
\(108\) −0.128197 −0.0123358
\(109\) 8.89607 0.852089 0.426045 0.904702i \(-0.359907\pi\)
0.426045 + 0.904702i \(0.359907\pi\)
\(110\) −2.98753 −0.284850
\(111\) 3.66658 0.348017
\(112\) 15.9176 1.50408
\(113\) 1.36552 0.128457 0.0642287 0.997935i \(-0.479541\pi\)
0.0642287 + 0.997935i \(0.479541\pi\)
\(114\) 4.33862 0.406349
\(115\) −10.7925 −1.00641
\(116\) 0.942868 0.0875431
\(117\) 0 0
\(118\) −7.69941 −0.708788
\(119\) 16.1933 1.48444
\(120\) 6.35806 0.580409
\(121\) 1.00000 0.0909091
\(122\) 7.39890 0.669865
\(123\) −4.16722 −0.375746
\(124\) −0.00932567 −0.000837470 0
\(125\) −11.4241 −1.02181
\(126\) 5.84291 0.520528
\(127\) 10.4027 0.923093 0.461546 0.887116i \(-0.347295\pi\)
0.461546 + 0.887116i \(0.347295\pi\)
\(128\) −10.1058 −0.893231
\(129\) 7.11697 0.626614
\(130\) 0 0
\(131\) −12.0678 −1.05437 −0.527183 0.849752i \(-0.676752\pi\)
−0.527183 + 0.849752i \(0.676752\pi\)
\(132\) −0.128197 −0.0111581
\(133\) 13.5432 1.17434
\(134\) −13.8381 −1.19543
\(135\) 2.18365 0.187939
\(136\) −11.0403 −0.946694
\(137\) 3.96114 0.338423 0.169211 0.985580i \(-0.445878\pi\)
0.169211 + 0.985580i \(0.445878\pi\)
\(138\) 6.76193 0.575613
\(139\) 18.2437 1.54741 0.773703 0.633548i \(-0.218402\pi\)
0.773703 + 0.633548i \(0.218402\pi\)
\(140\) 1.19553 0.101041
\(141\) 11.6337 0.979737
\(142\) −13.1648 −1.10476
\(143\) 0 0
\(144\) −3.72717 −0.310598
\(145\) −16.0604 −1.33374
\(146\) −8.82089 −0.730022
\(147\) 11.2389 0.926968
\(148\) −0.470045 −0.0386375
\(149\) 13.8984 1.13860 0.569299 0.822131i \(-0.307215\pi\)
0.569299 + 0.822131i \(0.307215\pi\)
\(150\) 0.316965 0.0258801
\(151\) −2.29739 −0.186959 −0.0934795 0.995621i \(-0.529799\pi\)
−0.0934795 + 0.995621i \(0.529799\pi\)
\(152\) −9.23344 −0.748931
\(153\) −3.79173 −0.306543
\(154\) 5.84291 0.470835
\(155\) 0.158849 0.0127591
\(156\) 0 0
\(157\) −15.6293 −1.24736 −0.623678 0.781682i \(-0.714362\pi\)
−0.623678 + 0.781682i \(0.714362\pi\)
\(158\) −13.8468 −1.10160
\(159\) 5.11268 0.405462
\(160\) −1.58107 −0.124995
\(161\) 21.1076 1.66351
\(162\) −1.36814 −0.107491
\(163\) 1.25583 0.0983643 0.0491822 0.998790i \(-0.484339\pi\)
0.0491822 + 0.998790i \(0.484339\pi\)
\(164\) 0.534226 0.0417160
\(165\) 2.18365 0.169997
\(166\) 10.6840 0.829243
\(167\) 17.3823 1.34509 0.672543 0.740058i \(-0.265202\pi\)
0.672543 + 0.740058i \(0.265202\pi\)
\(168\) −12.4349 −0.959371
\(169\) 0 0
\(170\) 11.3279 0.868812
\(171\) −3.17118 −0.242506
\(172\) −0.912375 −0.0695679
\(173\) −12.0899 −0.919178 −0.459589 0.888132i \(-0.652003\pi\)
−0.459589 + 0.888132i \(0.652003\pi\)
\(174\) 10.0624 0.762831
\(175\) 0.989418 0.0747930
\(176\) −3.72717 −0.280946
\(177\) 5.62765 0.423000
\(178\) −3.93904 −0.295244
\(179\) −5.13094 −0.383504 −0.191752 0.981443i \(-0.561417\pi\)
−0.191752 + 0.981443i \(0.561417\pi\)
\(180\) −0.279937 −0.0208653
\(181\) −23.3170 −1.73314 −0.866568 0.499059i \(-0.833679\pi\)
−0.866568 + 0.499059i \(0.833679\pi\)
\(182\) 0 0
\(183\) −5.40800 −0.399771
\(184\) −14.3907 −1.06090
\(185\) 8.00653 0.588652
\(186\) −0.0995250 −0.00729753
\(187\) −3.79173 −0.277279
\(188\) −1.49141 −0.108772
\(189\) −4.27070 −0.310648
\(190\) 9.47402 0.687318
\(191\) 11.1231 0.804838 0.402419 0.915456i \(-0.368169\pi\)
0.402419 + 0.915456i \(0.368169\pi\)
\(192\) 8.44494 0.609461
\(193\) 23.1664 1.66756 0.833778 0.552099i \(-0.186173\pi\)
0.833778 + 0.552099i \(0.186173\pi\)
\(194\) −5.18909 −0.372555
\(195\) 0 0
\(196\) −1.44079 −0.102914
\(197\) 9.18435 0.654358 0.327179 0.944962i \(-0.393902\pi\)
0.327179 + 0.944962i \(0.393902\pi\)
\(198\) −1.36814 −0.0972294
\(199\) 6.38937 0.452930 0.226465 0.974019i \(-0.427283\pi\)
0.226465 + 0.974019i \(0.427283\pi\)
\(200\) −0.674563 −0.0476988
\(201\) 10.1145 0.713423
\(202\) −17.5999 −1.23833
\(203\) 31.4103 2.20457
\(204\) 0.486088 0.0340330
\(205\) −9.09975 −0.635554
\(206\) 23.2550 1.62025
\(207\) −4.94243 −0.343522
\(208\) 0 0
\(209\) −3.17118 −0.219355
\(210\) 12.7589 0.880446
\(211\) 22.4436 1.54508 0.772541 0.634965i \(-0.218985\pi\)
0.772541 + 0.634965i \(0.218985\pi\)
\(212\) −0.655431 −0.0450152
\(213\) 9.62239 0.659315
\(214\) 17.3505 1.18606
\(215\) 15.5410 1.05989
\(216\) 2.91167 0.198114
\(217\) −0.310671 −0.0210897
\(218\) −12.1711 −0.824328
\(219\) 6.44736 0.435673
\(220\) −0.279937 −0.0188734
\(221\) 0 0
\(222\) −5.01639 −0.336678
\(223\) −16.5344 −1.10722 −0.553611 0.832775i \(-0.686751\pi\)
−0.553611 + 0.832775i \(0.686751\pi\)
\(224\) 3.09220 0.206606
\(225\) −0.231676 −0.0154451
\(226\) −1.86822 −0.124272
\(227\) −19.9826 −1.32630 −0.663148 0.748489i \(-0.730780\pi\)
−0.663148 + 0.748489i \(0.730780\pi\)
\(228\) 0.406536 0.0269235
\(229\) 15.8459 1.04713 0.523564 0.851986i \(-0.324602\pi\)
0.523564 + 0.851986i \(0.324602\pi\)
\(230\) 14.7657 0.973620
\(231\) −4.27070 −0.280992
\(232\) −21.4148 −1.40595
\(233\) 15.9195 1.04292 0.521460 0.853276i \(-0.325388\pi\)
0.521460 + 0.853276i \(0.325388\pi\)
\(234\) 0 0
\(235\) 25.4040 1.65717
\(236\) −0.721449 −0.0469623
\(237\) 10.1209 0.657425
\(238\) −22.1547 −1.43608
\(239\) 16.9898 1.09898 0.549491 0.835500i \(-0.314822\pi\)
0.549491 + 0.835500i \(0.314822\pi\)
\(240\) −8.13884 −0.525360
\(241\) −21.9883 −1.41639 −0.708197 0.706015i \(-0.750491\pi\)
−0.708197 + 0.706015i \(0.750491\pi\)
\(242\) −1.36814 −0.0879473
\(243\) 1.00000 0.0641500
\(244\) 0.693290 0.0443834
\(245\) 24.5418 1.56792
\(246\) 5.70134 0.363504
\(247\) 0 0
\(248\) 0.211809 0.0134499
\(249\) −7.80918 −0.494887
\(250\) 15.6298 0.988516
\(251\) 11.9461 0.754029 0.377015 0.926207i \(-0.376951\pi\)
0.377015 + 0.926207i \(0.376951\pi\)
\(252\) 0.547491 0.0344887
\(253\) −4.94243 −0.310728
\(254\) −14.2324 −0.893019
\(255\) −8.27981 −0.518502
\(256\) −3.06382 −0.191489
\(257\) 28.3671 1.76949 0.884746 0.466074i \(-0.154332\pi\)
0.884746 + 0.466074i \(0.154332\pi\)
\(258\) −9.73700 −0.606199
\(259\) −15.6589 −0.972995
\(260\) 0 0
\(261\) −7.35483 −0.455253
\(262\) 16.5104 1.02001
\(263\) −1.37798 −0.0849699 −0.0424849 0.999097i \(-0.513527\pi\)
−0.0424849 + 0.999097i \(0.513527\pi\)
\(264\) 2.91167 0.179201
\(265\) 11.1643 0.685818
\(266\) −18.5289 −1.13608
\(267\) 2.87912 0.176200
\(268\) −1.29665 −0.0792056
\(269\) −14.6274 −0.891847 −0.445923 0.895071i \(-0.647125\pi\)
−0.445923 + 0.895071i \(0.647125\pi\)
\(270\) −2.98753 −0.181816
\(271\) 13.3040 0.808158 0.404079 0.914724i \(-0.367592\pi\)
0.404079 + 0.914724i \(0.367592\pi\)
\(272\) 14.1324 0.856904
\(273\) 0 0
\(274\) −5.41938 −0.327397
\(275\) −0.231676 −0.0139706
\(276\) 0.633605 0.0381385
\(277\) 22.1581 1.33135 0.665676 0.746241i \(-0.268143\pi\)
0.665676 + 0.746241i \(0.268143\pi\)
\(278\) −24.9598 −1.49699
\(279\) 0.0727448 0.00435512
\(280\) −27.1534 −1.62273
\(281\) −2.12589 −0.126820 −0.0634100 0.997988i \(-0.520198\pi\)
−0.0634100 + 0.997988i \(0.520198\pi\)
\(282\) −15.9166 −0.947817
\(283\) −31.1036 −1.84892 −0.924458 0.381283i \(-0.875482\pi\)
−0.924458 + 0.381283i \(0.875482\pi\)
\(284\) −1.23356 −0.0731984
\(285\) −6.92475 −0.410187
\(286\) 0 0
\(287\) 17.7970 1.05052
\(288\) −0.724050 −0.0426650
\(289\) −2.62279 −0.154282
\(290\) 21.9728 1.29029
\(291\) 3.79281 0.222338
\(292\) −0.826533 −0.0483692
\(293\) 16.9009 0.987363 0.493682 0.869643i \(-0.335651\pi\)
0.493682 + 0.869643i \(0.335651\pi\)
\(294\) −15.3764 −0.896767
\(295\) 12.2888 0.715483
\(296\) 10.6759 0.620523
\(297\) 1.00000 0.0580259
\(298\) −19.0149 −1.10150
\(299\) 0 0
\(300\) 0.0297002 0.00171474
\(301\) −30.3945 −1.75191
\(302\) 3.14315 0.180868
\(303\) 12.8641 0.739025
\(304\) 11.8195 0.677897
\(305\) −11.8092 −0.676192
\(306\) 5.18761 0.296556
\(307\) −24.6110 −1.40462 −0.702312 0.711869i \(-0.747849\pi\)
−0.702312 + 0.711869i \(0.747849\pi\)
\(308\) 0.547491 0.0311962
\(309\) −16.9975 −0.966956
\(310\) −0.217328 −0.0123434
\(311\) −1.00504 −0.0569904 −0.0284952 0.999594i \(-0.509072\pi\)
−0.0284952 + 0.999594i \(0.509072\pi\)
\(312\) 0 0
\(313\) −13.8744 −0.784227 −0.392114 0.919917i \(-0.628256\pi\)
−0.392114 + 0.919917i \(0.628256\pi\)
\(314\) 21.3831 1.20672
\(315\) −9.32571 −0.525444
\(316\) −1.29747 −0.0729886
\(317\) 15.6405 0.878460 0.439230 0.898375i \(-0.355251\pi\)
0.439230 + 0.898375i \(0.355251\pi\)
\(318\) −6.99486 −0.392252
\(319\) −7.35483 −0.411792
\(320\) 18.4408 1.03087
\(321\) −12.6819 −0.707832
\(322\) −28.8782 −1.60932
\(323\) 12.0243 0.669048
\(324\) −0.128197 −0.00712206
\(325\) 0 0
\(326\) −1.71815 −0.0951596
\(327\) 8.89607 0.491954
\(328\) −12.1336 −0.669964
\(329\) −49.6842 −2.73918
\(330\) −2.98753 −0.164458
\(331\) 23.1426 1.27203 0.636017 0.771675i \(-0.280581\pi\)
0.636017 + 0.771675i \(0.280581\pi\)
\(332\) 1.00111 0.0549433
\(333\) 3.66658 0.200927
\(334\) −23.7814 −1.30126
\(335\) 22.0866 1.20672
\(336\) 15.9176 0.868378
\(337\) 15.1946 0.827705 0.413853 0.910344i \(-0.364183\pi\)
0.413853 + 0.910344i \(0.364183\pi\)
\(338\) 0 0
\(339\) 1.36552 0.0741650
\(340\) 1.06145 0.0575650
\(341\) 0.0727448 0.00393935
\(342\) 4.33862 0.234606
\(343\) −18.1030 −0.977472
\(344\) 20.7223 1.11727
\(345\) −10.7925 −0.581050
\(346\) 16.5407 0.889231
\(347\) 16.6545 0.894061 0.447030 0.894519i \(-0.352482\pi\)
0.447030 + 0.894519i \(0.352482\pi\)
\(348\) 0.942868 0.0505430
\(349\) −29.1080 −1.55812 −0.779058 0.626952i \(-0.784302\pi\)
−0.779058 + 0.626952i \(0.784302\pi\)
\(350\) −1.35366 −0.0723562
\(351\) 0 0
\(352\) −0.724050 −0.0385920
\(353\) 29.1723 1.55268 0.776342 0.630312i \(-0.217073\pi\)
0.776342 + 0.630312i \(0.217073\pi\)
\(354\) −7.69941 −0.409219
\(355\) 21.0119 1.11520
\(356\) −0.369095 −0.0195620
\(357\) 16.1933 0.857043
\(358\) 7.01983 0.371010
\(359\) −18.0809 −0.954271 −0.477136 0.878830i \(-0.658325\pi\)
−0.477136 + 0.878830i \(0.658325\pi\)
\(360\) 6.35806 0.335099
\(361\) −8.94359 −0.470715
\(362\) 31.9008 1.67667
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 14.0788 0.736917
\(366\) 7.39890 0.386747
\(367\) 18.1338 0.946578 0.473289 0.880907i \(-0.343067\pi\)
0.473289 + 0.880907i \(0.343067\pi\)
\(368\) 18.4213 0.960275
\(369\) −4.16722 −0.216937
\(370\) −10.9540 −0.569474
\(371\) −21.8347 −1.13360
\(372\) −0.00932567 −0.000483513 0
\(373\) −15.8564 −0.821012 −0.410506 0.911858i \(-0.634648\pi\)
−0.410506 + 0.911858i \(0.634648\pi\)
\(374\) 5.18761 0.268245
\(375\) −11.4241 −0.589940
\(376\) 33.8736 1.74690
\(377\) 0 0
\(378\) 5.84291 0.300527
\(379\) −18.3431 −0.942224 −0.471112 0.882073i \(-0.656147\pi\)
−0.471112 + 0.882073i \(0.656147\pi\)
\(380\) 0.887733 0.0455397
\(381\) 10.4027 0.532948
\(382\) −15.2179 −0.778617
\(383\) 16.1019 0.822768 0.411384 0.911462i \(-0.365046\pi\)
0.411384 + 0.911462i \(0.365046\pi\)
\(384\) −10.1058 −0.515707
\(385\) −9.32571 −0.475282
\(386\) −31.6949 −1.61323
\(387\) 7.11697 0.361776
\(388\) −0.486227 −0.0246844
\(389\) 32.7166 1.65880 0.829400 0.558655i \(-0.188683\pi\)
0.829400 + 0.558655i \(0.188683\pi\)
\(390\) 0 0
\(391\) 18.7403 0.947740
\(392\) 32.7239 1.65281
\(393\) −12.0678 −0.608738
\(394\) −12.5655 −0.633039
\(395\) 22.1006 1.11200
\(396\) −0.128197 −0.00644214
\(397\) 3.51685 0.176506 0.0882529 0.996098i \(-0.471872\pi\)
0.0882529 + 0.996098i \(0.471872\pi\)
\(398\) −8.74154 −0.438174
\(399\) 13.5432 0.678007
\(400\) 0.863496 0.0431748
\(401\) −18.6231 −0.929992 −0.464996 0.885313i \(-0.653944\pi\)
−0.464996 + 0.885313i \(0.653944\pi\)
\(402\) −13.8381 −0.690180
\(403\) 0 0
\(404\) −1.64914 −0.0820480
\(405\) 2.18365 0.108506
\(406\) −42.9736 −2.13275
\(407\) 3.66658 0.181746
\(408\) −11.0403 −0.546574
\(409\) 17.6809 0.874262 0.437131 0.899398i \(-0.355995\pi\)
0.437131 + 0.899398i \(0.355995\pi\)
\(410\) 12.4497 0.614848
\(411\) 3.96114 0.195388
\(412\) 2.17903 0.107353
\(413\) −24.0340 −1.18264
\(414\) 6.76193 0.332331
\(415\) −17.0525 −0.837075
\(416\) 0 0
\(417\) 18.2437 0.893395
\(418\) 4.33862 0.212209
\(419\) −1.93036 −0.0943044 −0.0471522 0.998888i \(-0.515015\pi\)
−0.0471522 + 0.998888i \(0.515015\pi\)
\(420\) 1.19553 0.0583358
\(421\) −7.21742 −0.351756 −0.175878 0.984412i \(-0.556276\pi\)
−0.175878 + 0.984412i \(0.556276\pi\)
\(422\) −30.7060 −1.49474
\(423\) 11.6337 0.565651
\(424\) 14.8864 0.722949
\(425\) 0.878452 0.0426112
\(426\) −13.1648 −0.637835
\(427\) 23.0960 1.11769
\(428\) 1.62578 0.0785849
\(429\) 0 0
\(430\) −21.2622 −1.02535
\(431\) −29.7876 −1.43482 −0.717408 0.696653i \(-0.754672\pi\)
−0.717408 + 0.696653i \(0.754672\pi\)
\(432\) −3.72717 −0.179324
\(433\) −25.2468 −1.21329 −0.606643 0.794975i \(-0.707484\pi\)
−0.606643 + 0.794975i \(0.707484\pi\)
\(434\) 0.425041 0.0204026
\(435\) −16.0604 −0.770036
\(436\) −1.14045 −0.0546177
\(437\) 15.6733 0.749758
\(438\) −8.82089 −0.421478
\(439\) −9.07110 −0.432940 −0.216470 0.976289i \(-0.569454\pi\)
−0.216470 + 0.976289i \(0.569454\pi\)
\(440\) 6.35806 0.303109
\(441\) 11.2389 0.535185
\(442\) 0 0
\(443\) −12.0753 −0.573715 −0.286858 0.957973i \(-0.592611\pi\)
−0.286858 + 0.957973i \(0.592611\pi\)
\(444\) −0.470045 −0.0223074
\(445\) 6.28700 0.298032
\(446\) 22.6213 1.07115
\(447\) 13.8984 0.657370
\(448\) −36.0658 −1.70395
\(449\) 8.94438 0.422111 0.211056 0.977474i \(-0.432310\pi\)
0.211056 + 0.977474i \(0.432310\pi\)
\(450\) 0.316965 0.0149419
\(451\) −4.16722 −0.196227
\(452\) −0.175056 −0.00823394
\(453\) −2.29739 −0.107941
\(454\) 27.3390 1.28308
\(455\) 0 0
\(456\) −9.23344 −0.432395
\(457\) −28.4975 −1.33305 −0.666527 0.745481i \(-0.732220\pi\)
−0.666527 + 0.745481i \(0.732220\pi\)
\(458\) −21.6794 −1.01301
\(459\) −3.79173 −0.176983
\(460\) 1.38357 0.0645093
\(461\) −19.2580 −0.896932 −0.448466 0.893800i \(-0.648030\pi\)
−0.448466 + 0.893800i \(0.648030\pi\)
\(462\) 5.84291 0.271837
\(463\) 36.3639 1.68997 0.844987 0.534787i \(-0.179608\pi\)
0.844987 + 0.534787i \(0.179608\pi\)
\(464\) 27.4127 1.27260
\(465\) 0.158849 0.00736645
\(466\) −21.7801 −1.00894
\(467\) 1.70345 0.0788264 0.0394132 0.999223i \(-0.487451\pi\)
0.0394132 + 0.999223i \(0.487451\pi\)
\(468\) 0 0
\(469\) −43.1961 −1.99461
\(470\) −34.7562 −1.60318
\(471\) −15.6293 −0.720161
\(472\) 16.3859 0.754220
\(473\) 7.11697 0.327239
\(474\) −13.8468 −0.636006
\(475\) 0.734687 0.0337097
\(476\) −2.07594 −0.0951505
\(477\) 5.11268 0.234094
\(478\) −23.2444 −1.06318
\(479\) −24.5812 −1.12314 −0.561571 0.827429i \(-0.689803\pi\)
−0.561571 + 0.827429i \(0.689803\pi\)
\(480\) −1.58107 −0.0721657
\(481\) 0 0
\(482\) 30.0831 1.37025
\(483\) 21.1076 0.960431
\(484\) −0.128197 −0.00582714
\(485\) 8.28216 0.376074
\(486\) −1.36814 −0.0620600
\(487\) 40.5270 1.83646 0.918228 0.396053i \(-0.129620\pi\)
0.918228 + 0.396053i \(0.129620\pi\)
\(488\) −15.7463 −0.712802
\(489\) 1.25583 0.0567907
\(490\) −33.5766 −1.51683
\(491\) 16.8245 0.759277 0.379639 0.925135i \(-0.376048\pi\)
0.379639 + 0.925135i \(0.376048\pi\)
\(492\) 0.534226 0.0240848
\(493\) 27.8875 1.25599
\(494\) 0 0
\(495\) 2.18365 0.0981477
\(496\) −0.271132 −0.0121742
\(497\) −41.0943 −1.84333
\(498\) 10.6840 0.478764
\(499\) 28.5150 1.27651 0.638254 0.769826i \(-0.279657\pi\)
0.638254 + 0.769826i \(0.279657\pi\)
\(500\) 1.46454 0.0654963
\(501\) 17.3823 0.776586
\(502\) −16.3439 −0.729463
\(503\) 27.4200 1.22260 0.611299 0.791400i \(-0.290647\pi\)
0.611299 + 0.791400i \(0.290647\pi\)
\(504\) −12.4349 −0.553893
\(505\) 28.0908 1.25002
\(506\) 6.76193 0.300604
\(507\) 0 0
\(508\) −1.33360 −0.0591689
\(509\) −25.4659 −1.12876 −0.564378 0.825516i \(-0.690884\pi\)
−0.564378 + 0.825516i \(0.690884\pi\)
\(510\) 11.3279 0.501609
\(511\) −27.5348 −1.21807
\(512\) 24.4032 1.07848
\(513\) −3.17118 −0.140011
\(514\) −38.8101 −1.71184
\(515\) −37.1167 −1.63556
\(516\) −0.912375 −0.0401651
\(517\) 11.6337 0.511651
\(518\) 21.4235 0.941295
\(519\) −12.0899 −0.530688
\(520\) 0 0
\(521\) 2.38806 0.104623 0.0523113 0.998631i \(-0.483341\pi\)
0.0523113 + 0.998631i \(0.483341\pi\)
\(522\) 10.0624 0.440421
\(523\) 45.6041 1.99413 0.997064 0.0765769i \(-0.0243991\pi\)
0.997064 + 0.0765769i \(0.0243991\pi\)
\(524\) 1.54705 0.0675833
\(525\) 0.989418 0.0431818
\(526\) 1.88527 0.0822015
\(527\) −0.275829 −0.0120153
\(528\) −3.72717 −0.162204
\(529\) 1.42760 0.0620694
\(530\) −15.2743 −0.663474
\(531\) 5.62765 0.244219
\(532\) −1.73620 −0.0752736
\(533\) 0 0
\(534\) −3.93904 −0.170459
\(535\) −27.6927 −1.19726
\(536\) 29.4501 1.27205
\(537\) −5.13094 −0.221416
\(538\) 20.0123 0.862791
\(539\) 11.2389 0.484093
\(540\) −0.279937 −0.0120466
\(541\) −29.4997 −1.26829 −0.634145 0.773214i \(-0.718648\pi\)
−0.634145 + 0.773214i \(0.718648\pi\)
\(542\) −18.2017 −0.781828
\(543\) −23.3170 −1.00063
\(544\) 2.74540 0.117708
\(545\) 19.4259 0.832114
\(546\) 0 0
\(547\) 7.75142 0.331427 0.165713 0.986174i \(-0.447007\pi\)
0.165713 + 0.986174i \(0.447007\pi\)
\(548\) −0.507806 −0.0216924
\(549\) −5.40800 −0.230808
\(550\) 0.316965 0.0135154
\(551\) 23.3235 0.993616
\(552\) −14.3907 −0.612509
\(553\) −43.2235 −1.83805
\(554\) −30.3153 −1.28798
\(555\) 8.00653 0.339858
\(556\) −2.33878 −0.0991865
\(557\) −20.2857 −0.859534 −0.429767 0.902940i \(-0.641404\pi\)
−0.429767 + 0.902940i \(0.641404\pi\)
\(558\) −0.0995250 −0.00421323
\(559\) 0 0
\(560\) 34.7585 1.46882
\(561\) −3.79173 −0.160087
\(562\) 2.90851 0.122688
\(563\) −32.7633 −1.38081 −0.690403 0.723425i \(-0.742567\pi\)
−0.690403 + 0.723425i \(0.742567\pi\)
\(564\) −1.49141 −0.0627997
\(565\) 2.98182 0.125446
\(566\) 42.5540 1.78868
\(567\) −4.27070 −0.179353
\(568\) 28.0172 1.17558
\(569\) 27.8002 1.16545 0.582723 0.812671i \(-0.301987\pi\)
0.582723 + 0.812671i \(0.301987\pi\)
\(570\) 9.47402 0.396823
\(571\) 43.4425 1.81801 0.909007 0.416782i \(-0.136842\pi\)
0.909007 + 0.416782i \(0.136842\pi\)
\(572\) 0 0
\(573\) 11.1231 0.464674
\(574\) −24.3487 −1.01630
\(575\) 1.14504 0.0477515
\(576\) 8.44494 0.351873
\(577\) 25.7084 1.07025 0.535127 0.844772i \(-0.320264\pi\)
0.535127 + 0.844772i \(0.320264\pi\)
\(578\) 3.58834 0.149255
\(579\) 23.1664 0.962764
\(580\) 2.05889 0.0854909
\(581\) 33.3507 1.38362
\(582\) −5.18909 −0.215095
\(583\) 5.11268 0.211746
\(584\) 18.7726 0.776815
\(585\) 0 0
\(586\) −23.1228 −0.955195
\(587\) 1.44805 0.0597673 0.0298837 0.999553i \(-0.490486\pi\)
0.0298837 + 0.999553i \(0.490486\pi\)
\(588\) −1.44079 −0.0594173
\(589\) −0.230687 −0.00950530
\(590\) −16.8128 −0.692173
\(591\) 9.18435 0.377794
\(592\) −13.6660 −0.561668
\(593\) 4.27539 0.175569 0.0877845 0.996139i \(-0.472021\pi\)
0.0877845 + 0.996139i \(0.472021\pi\)
\(594\) −1.36814 −0.0561354
\(595\) 35.3606 1.44964
\(596\) −1.78173 −0.0729824
\(597\) 6.38937 0.261499
\(598\) 0 0
\(599\) 15.9807 0.652953 0.326476 0.945205i \(-0.394139\pi\)
0.326476 + 0.945205i \(0.394139\pi\)
\(600\) −0.674563 −0.0275389
\(601\) −25.2647 −1.03057 −0.515283 0.857020i \(-0.672313\pi\)
−0.515283 + 0.857020i \(0.672313\pi\)
\(602\) 41.5838 1.69483
\(603\) 10.1145 0.411895
\(604\) 0.294519 0.0119838
\(605\) 2.18365 0.0887780
\(606\) −17.5999 −0.714948
\(607\) 41.6506 1.69055 0.845273 0.534334i \(-0.179437\pi\)
0.845273 + 0.534334i \(0.179437\pi\)
\(608\) 2.29610 0.0931190
\(609\) 31.4103 1.27281
\(610\) 16.1566 0.654162
\(611\) 0 0
\(612\) 0.486088 0.0196490
\(613\) 16.1620 0.652777 0.326388 0.945236i \(-0.394168\pi\)
0.326388 + 0.945236i \(0.394168\pi\)
\(614\) 33.6713 1.35886
\(615\) −9.09975 −0.366937
\(616\) −12.4349 −0.501015
\(617\) 8.12561 0.327125 0.163562 0.986533i \(-0.447701\pi\)
0.163562 + 0.986533i \(0.447701\pi\)
\(618\) 23.2550 0.935453
\(619\) 7.09593 0.285209 0.142605 0.989780i \(-0.454452\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(620\) −0.0203640 −0.000817838 0
\(621\) −4.94243 −0.198333
\(622\) 1.37503 0.0551337
\(623\) −12.2959 −0.492624
\(624\) 0 0
\(625\) −23.7879 −0.951518
\(626\) 18.9821 0.758677
\(627\) −3.17118 −0.126645
\(628\) 2.00363 0.0799536
\(629\) −13.9027 −0.554337
\(630\) 12.7589 0.508325
\(631\) 3.62153 0.144171 0.0720854 0.997398i \(-0.477035\pi\)
0.0720854 + 0.997398i \(0.477035\pi\)
\(632\) 29.4688 1.17221
\(633\) 22.4436 0.892053
\(634\) −21.3984 −0.849840
\(635\) 22.7159 0.901453
\(636\) −0.655431 −0.0259895
\(637\) 0 0
\(638\) 10.0624 0.398375
\(639\) 9.62239 0.380656
\(640\) −22.0674 −0.872291
\(641\) −8.81244 −0.348070 −0.174035 0.984739i \(-0.555681\pi\)
−0.174035 + 0.984739i \(0.555681\pi\)
\(642\) 17.3505 0.684771
\(643\) −47.2262 −1.86242 −0.931210 0.364484i \(-0.881245\pi\)
−0.931210 + 0.364484i \(0.881245\pi\)
\(644\) −2.70594 −0.106629
\(645\) 15.5410 0.611925
\(646\) −16.4509 −0.647251
\(647\) 41.0552 1.61405 0.807023 0.590520i \(-0.201077\pi\)
0.807023 + 0.590520i \(0.201077\pi\)
\(648\) 2.91167 0.114381
\(649\) 5.62765 0.220905
\(650\) 0 0
\(651\) −0.310671 −0.0121762
\(652\) −0.160994 −0.00630501
\(653\) 36.9362 1.44542 0.722712 0.691149i \(-0.242895\pi\)
0.722712 + 0.691149i \(0.242895\pi\)
\(654\) −12.1711 −0.475926
\(655\) −26.3518 −1.02965
\(656\) 15.5320 0.606421
\(657\) 6.44736 0.251536
\(658\) 67.9748 2.64994
\(659\) 39.7980 1.55031 0.775154 0.631772i \(-0.217672\pi\)
0.775154 + 0.631772i \(0.217672\pi\)
\(660\) −0.279937 −0.0108965
\(661\) −21.8622 −0.850342 −0.425171 0.905113i \(-0.639786\pi\)
−0.425171 + 0.905113i \(0.639786\pi\)
\(662\) −31.6623 −1.23059
\(663\) 0 0
\(664\) −22.7378 −0.882396
\(665\) 29.5736 1.14681
\(666\) −5.01639 −0.194381
\(667\) 36.3507 1.40751
\(668\) −2.22836 −0.0862180
\(669\) −16.5344 −0.639255
\(670\) −30.2175 −1.16740
\(671\) −5.40800 −0.208774
\(672\) 3.09220 0.119284
\(673\) −32.3152 −1.24566 −0.622830 0.782357i \(-0.714017\pi\)
−0.622830 + 0.782357i \(0.714017\pi\)
\(674\) −20.7884 −0.800739
\(675\) −0.231676 −0.00891721
\(676\) 0 0
\(677\) −21.1472 −0.812753 −0.406376 0.913706i \(-0.633208\pi\)
−0.406376 + 0.913706i \(0.633208\pi\)
\(678\) −1.86822 −0.0717487
\(679\) −16.1979 −0.621620
\(680\) −24.1081 −0.924502
\(681\) −19.9826 −0.765737
\(682\) −0.0995250 −0.00381101
\(683\) −24.7401 −0.946654 −0.473327 0.880887i \(-0.656947\pi\)
−0.473327 + 0.880887i \(0.656947\pi\)
\(684\) 0.406536 0.0155443
\(685\) 8.64973 0.330489
\(686\) 24.7675 0.945626
\(687\) 15.8459 0.604560
\(688\) −26.5262 −1.01130
\(689\) 0 0
\(690\) 14.7657 0.562120
\(691\) 22.7394 0.865047 0.432523 0.901623i \(-0.357623\pi\)
0.432523 + 0.901623i \(0.357623\pi\)
\(692\) 1.54989 0.0589180
\(693\) −4.27070 −0.162231
\(694\) −22.7857 −0.864932
\(695\) 39.8377 1.51113
\(696\) −21.4148 −0.811727
\(697\) 15.8010 0.598505
\(698\) 39.8238 1.50735
\(699\) 15.9195 0.602130
\(700\) −0.126840 −0.00479412
\(701\) −23.8173 −0.899567 −0.449783 0.893138i \(-0.648499\pi\)
−0.449783 + 0.893138i \(0.648499\pi\)
\(702\) 0 0
\(703\) −11.6274 −0.438536
\(704\) 8.44494 0.318281
\(705\) 25.4040 0.956769
\(706\) −39.9117 −1.50210
\(707\) −54.9389 −2.06619
\(708\) −0.721449 −0.0271137
\(709\) 15.8902 0.596770 0.298385 0.954446i \(-0.403552\pi\)
0.298385 + 0.954446i \(0.403552\pi\)
\(710\) −28.7472 −1.07886
\(711\) 10.1209 0.379565
\(712\) 8.38305 0.314168
\(713\) −0.359536 −0.0134647
\(714\) −22.1547 −0.829120
\(715\) 0 0
\(716\) 0.657771 0.0245821
\(717\) 16.9898 0.634497
\(718\) 24.7371 0.923181
\(719\) 4.64051 0.173062 0.0865309 0.996249i \(-0.472422\pi\)
0.0865309 + 0.996249i \(0.472422\pi\)
\(720\) −8.13884 −0.303316
\(721\) 72.5914 2.70345
\(722\) 12.2361 0.455379
\(723\) −21.9883 −0.817755
\(724\) 2.98917 0.111091
\(725\) 1.70394 0.0632826
\(726\) −1.36814 −0.0507764
\(727\) −14.5583 −0.539938 −0.269969 0.962869i \(-0.587013\pi\)
−0.269969 + 0.962869i \(0.587013\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −19.2617 −0.712908
\(731\) −26.9856 −0.998100
\(732\) 0.693290 0.0256247
\(733\) 34.2475 1.26496 0.632480 0.774576i \(-0.282037\pi\)
0.632480 + 0.774576i \(0.282037\pi\)
\(734\) −24.8096 −0.915738
\(735\) 24.5418 0.905238
\(736\) 3.57856 0.131908
\(737\) 10.1145 0.372573
\(738\) 5.70134 0.209869
\(739\) −30.5325 −1.12316 −0.561578 0.827424i \(-0.689806\pi\)
−0.561578 + 0.827424i \(0.689806\pi\)
\(740\) −1.02641 −0.0377317
\(741\) 0 0
\(742\) 29.8729 1.09667
\(743\) 2.86476 0.105098 0.0525490 0.998618i \(-0.483265\pi\)
0.0525490 + 0.998618i \(0.483265\pi\)
\(744\) 0.211809 0.00776529
\(745\) 30.3491 1.11191
\(746\) 21.6937 0.794263
\(747\) −7.80918 −0.285723
\(748\) 0.486088 0.0177732
\(749\) 54.1604 1.97898
\(750\) 15.6298 0.570720
\(751\) 38.1810 1.39324 0.696621 0.717439i \(-0.254686\pi\)
0.696621 + 0.717439i \(0.254686\pi\)
\(752\) −43.3609 −1.58121
\(753\) 11.9461 0.435339
\(754\) 0 0
\(755\) −5.01670 −0.182576
\(756\) 0.547491 0.0199121
\(757\) −38.9456 −1.41550 −0.707750 0.706463i \(-0.750290\pi\)
−0.707750 + 0.706463i \(0.750290\pi\)
\(758\) 25.0960 0.911526
\(759\) −4.94243 −0.179399
\(760\) −20.1626 −0.731374
\(761\) −26.9359 −0.976427 −0.488214 0.872724i \(-0.662351\pi\)
−0.488214 + 0.872724i \(0.662351\pi\)
\(762\) −14.2324 −0.515585
\(763\) −37.9925 −1.37542
\(764\) −1.42595 −0.0515889
\(765\) −8.27981 −0.299357
\(766\) −22.0296 −0.795962
\(767\) 0 0
\(768\) −3.06382 −0.110556
\(769\) 3.83575 0.138321 0.0691603 0.997606i \(-0.477968\pi\)
0.0691603 + 0.997606i \(0.477968\pi\)
\(770\) 12.7589 0.459798
\(771\) 28.3671 1.02162
\(772\) −2.96987 −0.106888
\(773\) 21.7215 0.781267 0.390633 0.920546i \(-0.372256\pi\)
0.390633 + 0.920546i \(0.372256\pi\)
\(774\) −9.73700 −0.349989
\(775\) −0.0168532 −0.000605385 0
\(776\) 11.0434 0.396435
\(777\) −15.6589 −0.561759
\(778\) −44.7609 −1.60476
\(779\) 13.2150 0.473478
\(780\) 0 0
\(781\) 9.62239 0.344316
\(782\) −25.6394 −0.916863
\(783\) −7.35483 −0.262840
\(784\) −41.8893 −1.49605
\(785\) −34.1290 −1.21811
\(786\) 16.5104 0.588905
\(787\) 32.8705 1.17171 0.585853 0.810417i \(-0.300760\pi\)
0.585853 + 0.810417i \(0.300760\pi\)
\(788\) −1.17741 −0.0419434
\(789\) −1.37798 −0.0490574
\(790\) −30.2366 −1.07577
\(791\) −5.83174 −0.207353
\(792\) 2.91167 0.103462
\(793\) 0 0
\(794\) −4.81154 −0.170755
\(795\) 11.1643 0.395957
\(796\) −0.819098 −0.0290322
\(797\) −2.27867 −0.0807147 −0.0403573 0.999185i \(-0.512850\pi\)
−0.0403573 + 0.999185i \(0.512850\pi\)
\(798\) −18.5289 −0.655918
\(799\) −44.1120 −1.56057
\(800\) 0.167745 0.00593068
\(801\) 2.87912 0.101729
\(802\) 25.4789 0.899693
\(803\) 6.44736 0.227523
\(804\) −1.29665 −0.0457294
\(805\) 46.0917 1.62452
\(806\) 0 0
\(807\) −14.6274 −0.514908
\(808\) 37.4561 1.31770
\(809\) 25.3935 0.892786 0.446393 0.894837i \(-0.352708\pi\)
0.446393 + 0.894837i \(0.352708\pi\)
\(810\) −2.98753 −0.104971
\(811\) −32.7178 −1.14888 −0.574439 0.818548i \(-0.694780\pi\)
−0.574439 + 0.818548i \(0.694780\pi\)
\(812\) −4.02671 −0.141310
\(813\) 13.3040 0.466590
\(814\) −5.01639 −0.175824
\(815\) 2.74230 0.0960584
\(816\) 14.1324 0.494734
\(817\) −22.5692 −0.789597
\(818\) −24.1899 −0.845779
\(819\) 0 0
\(820\) 1.16656 0.0407381
\(821\) −31.2361 −1.09015 −0.545073 0.838388i \(-0.683498\pi\)
−0.545073 + 0.838388i \(0.683498\pi\)
\(822\) −5.41938 −0.189023
\(823\) 8.94424 0.311777 0.155888 0.987775i \(-0.450176\pi\)
0.155888 + 0.987775i \(0.450176\pi\)
\(824\) −49.4912 −1.72411
\(825\) −0.231676 −0.00806592
\(826\) 32.8819 1.14411
\(827\) −28.6667 −0.996838 −0.498419 0.866936i \(-0.666086\pi\)
−0.498419 + 0.866936i \(0.666086\pi\)
\(828\) 0.633605 0.0220193
\(829\) 39.5515 1.37368 0.686839 0.726809i \(-0.258998\pi\)
0.686839 + 0.726809i \(0.258998\pi\)
\(830\) 23.3302 0.809803
\(831\) 22.1581 0.768656
\(832\) 0 0
\(833\) −42.6148 −1.47652
\(834\) −24.9598 −0.864289
\(835\) 37.9569 1.31355
\(836\) 0.406536 0.0140604
\(837\) 0.0727448 0.00251443
\(838\) 2.64100 0.0912320
\(839\) 45.1833 1.55990 0.779951 0.625840i \(-0.215244\pi\)
0.779951 + 0.625840i \(0.215244\pi\)
\(840\) −27.1534 −0.936881
\(841\) 25.0936 0.865296
\(842\) 9.87443 0.340295
\(843\) −2.12589 −0.0732195
\(844\) −2.87720 −0.0990375
\(845\) 0 0
\(846\) −15.9166 −0.547222
\(847\) −4.27070 −0.146743
\(848\) −19.0558 −0.654380
\(849\) −31.1036 −1.06747
\(850\) −1.20184 −0.0412229
\(851\) −18.1218 −0.621208
\(852\) −1.23356 −0.0422611
\(853\) −13.2579 −0.453943 −0.226972 0.973901i \(-0.572882\pi\)
−0.226972 + 0.973901i \(0.572882\pi\)
\(854\) −31.5985 −1.08128
\(855\) −6.92475 −0.236822
\(856\) −36.9254 −1.26208
\(857\) 38.9268 1.32971 0.664857 0.746971i \(-0.268493\pi\)
0.664857 + 0.746971i \(0.268493\pi\)
\(858\) 0 0
\(859\) −21.2750 −0.725893 −0.362947 0.931810i \(-0.618229\pi\)
−0.362947 + 0.931810i \(0.618229\pi\)
\(860\) −1.99231 −0.0679371
\(861\) 17.7970 0.606519
\(862\) 40.7535 1.38807
\(863\) −8.94497 −0.304490 −0.152245 0.988343i \(-0.548650\pi\)
−0.152245 + 0.988343i \(0.548650\pi\)
\(864\) −0.724050 −0.0246327
\(865\) −26.4001 −0.897630
\(866\) 34.5412 1.17376
\(867\) −2.62279 −0.0890746
\(868\) 0.0398271 0.00135182
\(869\) 10.1209 0.343329
\(870\) 21.9728 0.744948
\(871\) 0 0
\(872\) 25.9024 0.877166
\(873\) 3.79281 0.128367
\(874\) −21.4433 −0.725331
\(875\) 48.7891 1.64937
\(876\) −0.826533 −0.0279260
\(877\) 11.5696 0.390679 0.195340 0.980736i \(-0.437419\pi\)
0.195340 + 0.980736i \(0.437419\pi\)
\(878\) 12.4105 0.418835
\(879\) 16.9009 0.570055
\(880\) −8.13884 −0.274360
\(881\) −13.2958 −0.447947 −0.223974 0.974595i \(-0.571903\pi\)
−0.223974 + 0.974595i \(0.571903\pi\)
\(882\) −15.3764 −0.517749
\(883\) −18.7422 −0.630726 −0.315363 0.948971i \(-0.602126\pi\)
−0.315363 + 0.948971i \(0.602126\pi\)
\(884\) 0 0
\(885\) 12.2888 0.413084
\(886\) 16.5207 0.555024
\(887\) 41.6306 1.39782 0.698910 0.715210i \(-0.253669\pi\)
0.698910 + 0.715210i \(0.253669\pi\)
\(888\) 10.6759 0.358259
\(889\) −44.4269 −1.49003
\(890\) −8.60148 −0.288322
\(891\) 1.00000 0.0335013
\(892\) 2.11966 0.0709713
\(893\) −36.8927 −1.23457
\(894\) −19.0149 −0.635953
\(895\) −11.2042 −0.374514
\(896\) 43.1586 1.44183
\(897\) 0 0
\(898\) −12.2372 −0.408359
\(899\) −0.535026 −0.0178441
\(900\) 0.0297002 0.000990005 0
\(901\) −19.3859 −0.645838
\(902\) 5.70134 0.189834
\(903\) −30.3945 −1.01146
\(904\) 3.97595 0.132238
\(905\) −50.9161 −1.69251
\(906\) 3.14315 0.104424
\(907\) 37.0540 1.23036 0.615179 0.788387i \(-0.289084\pi\)
0.615179 + 0.788387i \(0.289084\pi\)
\(908\) 2.56172 0.0850136
\(909\) 12.8641 0.426676
\(910\) 0 0
\(911\) −43.8739 −1.45361 −0.726804 0.686845i \(-0.758995\pi\)
−0.726804 + 0.686845i \(0.758995\pi\)
\(912\) 11.8195 0.391384
\(913\) −7.80918 −0.258446
\(914\) 38.9885 1.28962
\(915\) −11.8092 −0.390400
\(916\) −2.03140 −0.0671194
\(917\) 51.5378 1.70193
\(918\) 5.18761 0.171217
\(919\) −30.1561 −0.994759 −0.497380 0.867533i \(-0.665704\pi\)
−0.497380 + 0.867533i \(0.665704\pi\)
\(920\) −31.4243 −1.03603
\(921\) −24.6110 −0.810961
\(922\) 26.3475 0.867710
\(923\) 0 0
\(924\) 0.547491 0.0180111
\(925\) −0.849459 −0.0279300
\(926\) −49.7508 −1.63491
\(927\) −16.9975 −0.558272
\(928\) 5.32527 0.174810
\(929\) −29.2684 −0.960264 −0.480132 0.877196i \(-0.659411\pi\)
−0.480132 + 0.877196i \(0.659411\pi\)
\(930\) −0.217328 −0.00712645
\(931\) −35.6406 −1.16807
\(932\) −2.04083 −0.0668496
\(933\) −1.00504 −0.0329034
\(934\) −2.33056 −0.0762583
\(935\) −8.27981 −0.270779
\(936\) 0 0
\(937\) −14.7979 −0.483427 −0.241713 0.970348i \(-0.577709\pi\)
−0.241713 + 0.970348i \(0.577709\pi\)
\(938\) 59.0983 1.92963
\(939\) −13.8744 −0.452774
\(940\) −3.25672 −0.106222
\(941\) 17.5021 0.570553 0.285276 0.958445i \(-0.407915\pi\)
0.285276 + 0.958445i \(0.407915\pi\)
\(942\) 21.3831 0.696698
\(943\) 20.5962 0.670704
\(944\) −20.9752 −0.682686
\(945\) −9.32571 −0.303365
\(946\) −9.73700 −0.316577
\(947\) 32.5998 1.05935 0.529675 0.848201i \(-0.322314\pi\)
0.529675 + 0.848201i \(0.322314\pi\)
\(948\) −1.29747 −0.0421400
\(949\) 0 0
\(950\) −1.00515 −0.0326115
\(951\) 15.6405 0.507179
\(952\) 47.1496 1.52813
\(953\) −44.8368 −1.45241 −0.726204 0.687479i \(-0.758717\pi\)
−0.726204 + 0.687479i \(0.758717\pi\)
\(954\) −6.99486 −0.226467
\(955\) 24.2889 0.785971
\(956\) −2.17805 −0.0704431
\(957\) −7.35483 −0.237748
\(958\) 33.6304 1.08655
\(959\) −16.9168 −0.546273
\(960\) 18.4408 0.595174
\(961\) −30.9947 −0.999829
\(962\) 0 0
\(963\) −12.6819 −0.408667
\(964\) 2.81884 0.0907887
\(965\) 50.5874 1.62847
\(966\) −28.8782 −0.929140
\(967\) 21.7225 0.698550 0.349275 0.937020i \(-0.386428\pi\)
0.349275 + 0.937020i \(0.386428\pi\)
\(968\) 2.91167 0.0935846
\(969\) 12.0243 0.386275
\(970\) −11.3311 −0.363821
\(971\) −28.7521 −0.922699 −0.461349 0.887219i \(-0.652635\pi\)
−0.461349 + 0.887219i \(0.652635\pi\)
\(972\) −0.128197 −0.00411192
\(973\) −77.9132 −2.49778
\(974\) −55.4466 −1.77662
\(975\) 0 0
\(976\) 20.1566 0.645196
\(977\) 13.7868 0.441077 0.220539 0.975378i \(-0.429218\pi\)
0.220539 + 0.975378i \(0.429218\pi\)
\(978\) −1.71815 −0.0549404
\(979\) 2.87912 0.0920172
\(980\) −3.14619 −0.100501
\(981\) 8.89607 0.284030
\(982\) −23.0182 −0.734540
\(983\) −32.5478 −1.03811 −0.519056 0.854740i \(-0.673716\pi\)
−0.519056 + 0.854740i \(0.673716\pi\)
\(984\) −12.1336 −0.386804
\(985\) 20.0554 0.639018
\(986\) −38.1540 −1.21507
\(987\) −49.6842 −1.58146
\(988\) 0 0
\(989\) −35.1751 −1.11850
\(990\) −2.98753 −0.0949501
\(991\) −3.97937 −0.126409 −0.0632044 0.998001i \(-0.520132\pi\)
−0.0632044 + 0.998001i \(0.520132\pi\)
\(992\) −0.0526709 −0.00167230
\(993\) 23.1426 0.734409
\(994\) 56.2227 1.78328
\(995\) 13.9521 0.442312
\(996\) 1.00111 0.0317215
\(997\) −24.9767 −0.791021 −0.395511 0.918461i \(-0.629432\pi\)
−0.395511 + 0.918461i \(0.629432\pi\)
\(998\) −39.0125 −1.23492
\(999\) 3.66658 0.116006
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.1.2 7
13.5 odd 4 429.2.b.b.298.10 yes 14
13.8 odd 4 429.2.b.b.298.5 14
13.12 even 2 5577.2.a.x.1.6 7
39.5 even 4 1287.2.b.c.298.5 14
39.8 even 4 1287.2.b.c.298.10 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.5 14 13.8 odd 4
429.2.b.b.298.10 yes 14 13.5 odd 4
1287.2.b.c.298.5 14 39.5 even 4
1287.2.b.c.298.10 14 39.8 even 4
5577.2.a.x.1.6 7 13.12 even 2
5577.2.a.y.1.2 7 1.1 even 1 trivial