Properties

Label 5577.2.a.x.1.6
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $1$
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: \(1\)
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 1.6
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 \(-0.339289\pi\)
0.483710 + 0.875228i \(0.339289\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.128197 −0.0640985
\(5\) −2.18365 −0.976558 −0.488279 0.872688i \(-0.662375\pi\)
−0.488279 + 0.872688i \(0.662375\pi\)
\(6\) 1.36814 0.558540
\(7\) 4.27070 1.61417 0.807087 0.590433i \(-0.201043\pi\)
0.807087 + 0.590433i \(0.201043\pi\)
\(8\) −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 \(-0.381493\pi\)
0.363760 + 0.931493i \(0.381493\pi\)
\(20\) 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 \(-0.502079\pi\)
−0.00653268 + 0.999979i \(0.502079\pi\)
\(32\) 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 \(-0.597451\pi\)
−0.301391 + 0.953501i \(0.597451\pi\)
\(38\) 4.33862 0.703817
\(39\) 0 0
\(40\) 6.35806 1.00530
\(41\) 4.16722 0.650811 0.325405 0.945575i \(-0.394499\pi\)
0.325405 + 0.945575i \(0.394499\pi\)
\(42\) 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 \(-0.822480\pi\)
−0.848477 + 0.529232i \(0.822480\pi\)
\(48\) −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 \(-0.619386\pi\)
−0.366329 + 0.930485i \(0.619386\pi\)
\(60\) 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 \(-0.711993\pi\)
−0.617843 + 0.786302i \(0.711993\pi\)
\(68\) 0.486088 0.0589469
\(69\) −4.94243 −0.594998
\(70\) −12.7589 −1.52498
\(71\) −9.62239 −1.14197 −0.570984 0.820961i \(-0.693438\pi\)
−0.570984 + 0.820961i \(0.693438\pi\)
\(72\) −2.91167 −0.343143
\(73\) −6.44736 −0.754607 −0.377303 0.926090i \(-0.623149\pi\)
−0.377303 + 0.926090i \(0.623149\pi\)
\(74\) −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 \(-0.359012\pi\)
0.428585 + 0.903502i \(0.359012\pi\)
\(84\) −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 \(-0.548762\pi\)
−0.152593 + 0.988289i \(0.548762\pi\)
\(90\) −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 \(-0.561676\pi\)
−0.192551 + 0.981287i \(0.561676\pi\)
\(98\) 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 \(-0.640093\pi\)
−0.426045 + 0.904702i \(0.640093\pi\)
\(110\) 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 \(-0.554122\pi\)
−0.169211 + 0.985580i \(0.554122\pi\)
\(138\) −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 \(-0.692785\pi\)
−0.569299 + 0.822131i \(0.692785\pi\)
\(150\) −0.316965 −0.0258801
\(151\) 2.29739 0.186959 0.0934795 0.995621i \(-0.470201\pi\)
0.0934795 + 0.995621i \(0.470201\pi\)
\(152\) −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 \(-0.515661\pi\)
−0.0491822 + 0.998790i \(0.515661\pi\)
\(164\) −0.534226 −0.0417160
\(165\) 2.18365 0.169997
\(166\) 10.6840 0.829243
\(167\) −17.3823 −1.34509 −0.672543 0.740058i \(-0.734798\pi\)
−0.672543 + 0.740058i \(0.734798\pi\)
\(168\) −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 \(-0.813827\pi\)
−0.833778 + 0.552099i \(0.813827\pi\)
\(194\) −5.18909 −0.372555
\(195\) 0 0
\(196\) −1.44079 −0.102914
\(197\) −9.18435 −0.654358 −0.327179 0.944962i \(-0.606098\pi\)
−0.327179 + 0.944962i \(0.606098\pi\)
\(198\) −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 \(-0.313249\pi\)
0.553611 + 0.832775i \(0.313249\pi\)
\(224\) 3.09220 0.206606
\(225\) −0.231676 −0.0154451
\(226\) 1.86822 0.124272
\(227\) 19.9826 1.32630 0.663148 0.748489i \(-0.269220\pi\)
0.663148 + 0.748489i \(0.269220\pi\)
\(228\) −0.406536 −0.0269235
\(229\) −15.8459 −1.04713 −0.523564 0.851986i \(-0.675398\pi\)
−0.523564 + 0.851986i \(0.675398\pi\)
\(230\) 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 \(-0.685178\pi\)
−0.549491 + 0.835500i \(0.685178\pi\)
\(240\) 8.13884 0.525360
\(241\) 21.9883 1.41639 0.708197 0.706015i \(-0.249509\pi\)
0.708197 + 0.706015i \(0.249509\pi\)
\(242\) 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 \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(272\) 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 \(-0.479802\pi\)
0.0634100 + 0.997988i \(0.479802\pi\)
\(282\) −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 \(-0.664349\pi\)
−0.493682 + 0.869643i \(0.664349\pi\)
\(294\) 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 \(-0.252151\pi\)
0.702312 + 0.711869i \(0.252151\pi\)
\(308\) 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 \(-0.644749\pi\)
−0.439230 + 0.898375i \(0.644749\pi\)
\(318\) 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 \(-0.719419\pi\)
−0.636017 + 0.771675i \(0.719419\pi\)
\(332\) −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 \(-0.215698\pi\)
0.779058 + 0.626952i \(0.215698\pi\)
\(350\) −1.35366 −0.0723562
\(351\) 0 0
\(352\) −0.724050 −0.0385920
\(353\) −29.1723 −1.55268 −0.776342 0.630312i \(-0.782927\pi\)
−0.776342 + 0.630312i \(0.782927\pi\)
\(354\) −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 \(-0.341675\pi\)
0.477136 + 0.878830i \(0.341675\pi\)
\(360\) 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 \(-0.343853\pi\)
0.471112 + 0.882073i \(0.343853\pi\)
\(380\) 0.887733 0.0455397
\(381\) 10.4027 0.532948
\(382\) 15.2179 0.778617
\(383\) −16.1019 −0.822768 −0.411384 0.911462i \(-0.634954\pi\)
−0.411384 + 0.911462i \(0.634954\pi\)
\(384\) 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 \(-0.528128\pi\)
−0.0882529 + 0.996098i \(0.528128\pi\)
\(398\) 8.74154 0.438174
\(399\) 13.5432 0.678007
\(400\) 0.863496 0.0431748
\(401\) 18.6231 0.929992 0.464996 0.885313i \(-0.346056\pi\)
0.464996 + 0.885313i \(0.346056\pi\)
\(402\) −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 \(-0.644005\pi\)
−0.437131 + 0.899398i \(0.644005\pi\)
\(410\) −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 \(-0.443724\pi\)
0.175878 + 0.984412i \(0.443724\pi\)
\(422\) 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 \(-0.245328\pi\)
0.717408 + 0.696653i \(0.245328\pi\)
\(432\) −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 \(-0.567690\pi\)
−0.211056 + 0.977474i \(0.567690\pi\)
\(450\) −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 \(-0.267780\pi\)
0.666527 + 0.745481i \(0.267780\pi\)
\(458\) −21.6794 −1.01301
\(459\) −3.79173 −0.176983
\(460\) −1.38357 −0.0645093
\(461\) 19.2580 0.896932 0.448466 0.893800i \(-0.351970\pi\)
0.448466 + 0.893800i \(0.351970\pi\)
\(462\) −5.84291 −0.271837
\(463\) −36.3639 −1.68997 −0.844987 0.534787i \(-0.820392\pi\)
−0.844987 + 0.534787i \(0.820392\pi\)
\(464\) 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 \(-0.310197\pi\)
0.561571 + 0.827429i \(0.310197\pi\)
\(480\) −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 \(-0.870380\pi\)
−0.918228 + 0.396053i \(0.870380\pi\)
\(488\) 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 \(-0.720343\pi\)
−0.638254 + 0.769826i \(0.720343\pi\)
\(500\) −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 \(-0.309116\pi\)
0.564378 + 0.825516i \(0.309116\pi\)
\(510\) 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 \(-0.281352\pi\)
0.634145 + 0.773214i \(0.281352\pi\)
\(542\) −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 \(-0.358596\pi\)
0.429767 + 0.902940i \(0.358596\pi\)
\(558\) −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 \(-0.679736\pi\)
−0.535127 + 0.844772i \(0.679736\pi\)
\(578\) −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 \(-0.509514\pi\)
−0.0298837 + 0.999553i \(0.509514\pi\)
\(588\) −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 \(-0.527979\pi\)
−0.0877845 + 0.996139i \(0.527979\pi\)
\(594\) −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 \(-0.605832\pi\)
−0.326388 + 0.945236i \(0.605832\pi\)
\(614\) 33.6713 1.35886
\(615\) −9.09975 −0.366937
\(616\) 12.4349 0.501015
\(617\) −8.12561 −0.327125 −0.163562 0.986533i \(-0.552299\pi\)
−0.163562 + 0.986533i \(0.552299\pi\)
\(618\) −23.2550 −0.935453
\(619\) −7.09593 −0.285209 −0.142605 0.989780i \(-0.545548\pi\)
−0.142605 + 0.989780i \(0.545548\pi\)
\(620\) −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 \(-0.522965\pi\)
−0.0720854 + 0.997398i \(0.522965\pi\)
\(632\) −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 \(-0.118755\pi\)
0.931210 + 0.364484i \(0.118755\pi\)
\(644\) 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 \(-0.360214\pi\)
0.425171 + 0.905113i \(0.360214\pi\)
\(662\) −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 \(-0.343053\pi\)
0.473327 + 0.880887i \(0.343053\pi\)
\(684\) −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 \(-0.642377\pi\)
−0.432523 + 0.901623i \(0.642377\pi\)
\(692\) 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 \(-0.596448\pi\)
−0.298385 + 0.954446i \(0.596448\pi\)
\(710\) 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 \(-0.717963\pi\)
−0.632480 + 0.774576i \(0.717963\pi\)
\(734\) 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 \(-0.310194\pi\)
0.561578 + 0.827424i \(0.310194\pi\)
\(740\) −1.02641 −0.0377317
\(741\) 0 0
\(742\) 29.8729 1.09667
\(743\) −2.86476 −0.105098 −0.0525490 0.998618i \(-0.516735\pi\)
−0.0525490 + 0.998618i \(0.516735\pi\)
\(744\) 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 \(-0.337649\pi\)
0.488214 + 0.872724i \(0.337649\pi\)
\(762\) 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 \(-0.522032\pi\)
−0.0691603 + 0.997606i \(0.522032\pi\)
\(770\) 12.7589 0.459798
\(771\) 28.3671 1.02162
\(772\) 2.96987 0.106888
\(773\) −21.7215 −0.781267 −0.390633 0.920546i \(-0.627744\pi\)
−0.390633 + 0.920546i \(0.627744\pi\)
\(774\) 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 \(-0.699240\pi\)
−0.585853 + 0.810417i \(0.699240\pi\)
\(788\) 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 \(-0.305220\pi\)
0.574439 + 0.818548i \(0.305220\pi\)
\(812\) 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 \(-0.316502\pi\)
0.545073 + 0.838388i \(0.316502\pi\)
\(822\) −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 \(-0.333914\pi\)
0.498419 + 0.866936i \(0.333914\pi\)
\(828\) 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 \(-0.784756\pi\)
−0.779951 + 0.625840i \(0.784756\pi\)
\(840\) 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 \(-0.427118\pi\)
0.226972 + 0.973901i \(0.427118\pi\)
\(854\) −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 \(-0.451350\pi\)
0.152245 + 0.988343i \(0.451350\pi\)
\(864\) 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 \(-0.562581\pi\)
−0.195340 + 0.980736i \(0.562581\pi\)
\(878\) −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 \(-0.340589\pi\)
0.480132 + 0.877196i \(0.340589\pi\)
\(930\) 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 \(-0.592085\pi\)
−0.285276 + 0.958445i \(0.592085\pi\)
\(942\) −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 \(-0.677686\pi\)
−0.529675 + 0.848201i \(0.677686\pi\)
\(948\) −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 \(-0.613572\pi\)
−0.349275 + 0.937020i \(0.613572\pi\)
\(968\) −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 \(-0.570782\pi\)
−0.220539 + 0.975378i \(0.570782\pi\)
\(978\) −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 \(-0.326284\pi\)
0.519056 + 0.854740i \(0.326284\pi\)
\(984\) −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.x.1.6 7
13.5 odd 4 429.2.b.b.298.5 14
13.8 odd 4 429.2.b.b.298.10 yes 14
13.12 even 2 5577.2.a.y.1.2 7
39.5 even 4 1287.2.b.c.298.10 14
39.8 even 4 1287.2.b.c.298.5 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.5 14 13.5 odd 4
429.2.b.b.298.10 yes 14 13.8 odd 4
1287.2.b.c.298.5 14 39.8 even 4
1287.2.b.c.298.10 14 39.5 even 4
5577.2.a.x.1.6 7 1.1 even 1 trivial
5577.2.a.y.1.2 7 13.12 even 2