Properties

Label 3549.2.a.bf.1.8
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 11 x^{7} + 8 x^{6} + 37 x^{5} - 18 x^{4} - 41 x^{3} + 12 x^{2} + 6 x - 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(1.90042\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.90042 q^{2} -1.00000 q^{3} +1.61158 q^{4} -1.76582 q^{5} -1.90042 q^{6} -1.00000 q^{7} -0.738153 q^{8} +1.00000 q^{9} -3.35579 q^{10} +3.13241 q^{11} -1.61158 q^{12} -1.90042 q^{14} +1.76582 q^{15} -4.62597 q^{16} -0.934195 q^{17} +1.90042 q^{18} -2.13289 q^{19} -2.84577 q^{20} +1.00000 q^{21} +5.95289 q^{22} +5.87145 q^{23} +0.738153 q^{24} -1.88188 q^{25} -1.00000 q^{27} -1.61158 q^{28} -2.37261 q^{29} +3.35579 q^{30} +6.06765 q^{31} -7.31496 q^{32} -3.13241 q^{33} -1.77536 q^{34} +1.76582 q^{35} +1.61158 q^{36} +2.02644 q^{37} -4.05338 q^{38} +1.30344 q^{40} +6.16399 q^{41} +1.90042 q^{42} +5.68247 q^{43} +5.04815 q^{44} -1.76582 q^{45} +11.1582 q^{46} -5.26708 q^{47} +4.62597 q^{48} +1.00000 q^{49} -3.57636 q^{50} +0.934195 q^{51} +10.5891 q^{53} -1.90042 q^{54} -5.53127 q^{55} +0.738153 q^{56} +2.13289 q^{57} -4.50895 q^{58} -4.83882 q^{59} +2.84577 q^{60} +12.6018 q^{61} +11.5311 q^{62} -1.00000 q^{63} -4.64954 q^{64} -5.95289 q^{66} +6.65056 q^{67} -1.50553 q^{68} -5.87145 q^{69} +3.35579 q^{70} +7.17531 q^{71} -0.738153 q^{72} -4.85580 q^{73} +3.85108 q^{74} +1.88188 q^{75} -3.43733 q^{76} -3.13241 q^{77} +12.0565 q^{79} +8.16862 q^{80} +1.00000 q^{81} +11.7142 q^{82} -11.7189 q^{83} +1.61158 q^{84} +1.64962 q^{85} +10.7991 q^{86} +2.37261 q^{87} -2.31220 q^{88} -8.30211 q^{89} -3.35579 q^{90} +9.46233 q^{92} -6.06765 q^{93} -10.0096 q^{94} +3.76630 q^{95} +7.31496 q^{96} +18.2921 q^{97} +1.90042 q^{98} +3.13241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + O(q^{10}) \) \( 9q + q^{2} - 9q^{3} + 5q^{4} - 9q^{5} - q^{6} - 9q^{7} + 6q^{8} + 9q^{9} + q^{10} + q^{11} - 5q^{12} - q^{14} + 9q^{15} + 5q^{16} + 11q^{17} + q^{18} - 7q^{19} - 23q^{20} + 9q^{21} - 3q^{22} + 22q^{23} - 6q^{24} - 8q^{25} - 9q^{27} - 5q^{28} + 11q^{29} - q^{30} - 7q^{31} + 18q^{32} - q^{33} + 6q^{34} + 9q^{35} + 5q^{36} + q^{37} - 6q^{38} - 14q^{40} - 16q^{41} + q^{42} + 32q^{43} - 18q^{44} - 9q^{45} + 9q^{46} + 12q^{47} - 5q^{48} + 9q^{49} - 10q^{50} - 11q^{51} + 13q^{53} - q^{54} + 9q^{55} - 6q^{56} + 7q^{57} - 4q^{58} - 29q^{59} + 23q^{60} - 12q^{61} + 30q^{62} - 9q^{63} + 6q^{64} + 3q^{66} + 20q^{67} + 34q^{68} - 22q^{69} - q^{70} + 2q^{71} + 6q^{72} - q^{73} + 43q^{74} + 8q^{75} - 13q^{76} - q^{77} + 3q^{79} + 39q^{80} + 9q^{81} - 19q^{82} - 24q^{83} + 5q^{84} - 15q^{85} + 28q^{86} - 11q^{87} - 19q^{88} - 11q^{89} + q^{90} + 73q^{92} + 7q^{93} + 15q^{94} + 39q^{95} - 18q^{96} - 20q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90042 1.34380 0.671899 0.740643i \(-0.265479\pi\)
0.671899 + 0.740643i \(0.265479\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.61158 0.805792
\(5\) −1.76582 −0.789698 −0.394849 0.918746i \(-0.629203\pi\)
−0.394849 + 0.918746i \(0.629203\pi\)
\(6\) −1.90042 −0.775842
\(7\) −1.00000 −0.377964
\(8\) −0.738153 −0.260976
\(9\) 1.00000 0.333333
\(10\) −3.35579 −1.06119
\(11\) 3.13241 0.944458 0.472229 0.881476i \(-0.343450\pi\)
0.472229 + 0.881476i \(0.343450\pi\)
\(12\) −1.61158 −0.465224
\(13\) 0 0
\(14\) −1.90042 −0.507908
\(15\) 1.76582 0.455932
\(16\) −4.62597 −1.15649
\(17\) −0.934195 −0.226576 −0.113288 0.993562i \(-0.536138\pi\)
−0.113288 + 0.993562i \(0.536138\pi\)
\(18\) 1.90042 0.447933
\(19\) −2.13289 −0.489319 −0.244659 0.969609i \(-0.578676\pi\)
−0.244659 + 0.969609i \(0.578676\pi\)
\(20\) −2.84577 −0.636332
\(21\) 1.00000 0.218218
\(22\) 5.95289 1.26916
\(23\) 5.87145 1.22428 0.612141 0.790749i \(-0.290309\pi\)
0.612141 + 0.790749i \(0.290309\pi\)
\(24\) 0.738153 0.150675
\(25\) −1.88188 −0.376377
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.61158 −0.304561
\(29\) −2.37261 −0.440583 −0.220292 0.975434i \(-0.570701\pi\)
−0.220292 + 0.975434i \(0.570701\pi\)
\(30\) 3.35579 0.612681
\(31\) 6.06765 1.08978 0.544891 0.838507i \(-0.316571\pi\)
0.544891 + 0.838507i \(0.316571\pi\)
\(32\) −7.31496 −1.29311
\(33\) −3.13241 −0.545283
\(34\) −1.77536 −0.304472
\(35\) 1.76582 0.298478
\(36\) 1.61158 0.268597
\(37\) 2.02644 0.333145 0.166572 0.986029i \(-0.446730\pi\)
0.166572 + 0.986029i \(0.446730\pi\)
\(38\) −4.05338 −0.657546
\(39\) 0 0
\(40\) 1.30344 0.206093
\(41\) 6.16399 0.962654 0.481327 0.876541i \(-0.340155\pi\)
0.481327 + 0.876541i \(0.340155\pi\)
\(42\) 1.90042 0.293241
\(43\) 5.68247 0.866569 0.433284 0.901257i \(-0.357355\pi\)
0.433284 + 0.901257i \(0.357355\pi\)
\(44\) 5.04815 0.761037
\(45\) −1.76582 −0.263233
\(46\) 11.1582 1.64519
\(47\) −5.26708 −0.768283 −0.384141 0.923274i \(-0.625502\pi\)
−0.384141 + 0.923274i \(0.625502\pi\)
\(48\) 4.62597 0.667701
\(49\) 1.00000 0.142857
\(50\) −3.57636 −0.505774
\(51\) 0.934195 0.130813
\(52\) 0 0
\(53\) 10.5891 1.45452 0.727260 0.686362i \(-0.240794\pi\)
0.727260 + 0.686362i \(0.240794\pi\)
\(54\) −1.90042 −0.258614
\(55\) −5.53127 −0.745837
\(56\) 0.738153 0.0986398
\(57\) 2.13289 0.282508
\(58\) −4.50895 −0.592055
\(59\) −4.83882 −0.629960 −0.314980 0.949098i \(-0.601998\pi\)
−0.314980 + 0.949098i \(0.601998\pi\)
\(60\) 2.84577 0.367387
\(61\) 12.6018 1.61350 0.806749 0.590894i \(-0.201225\pi\)
0.806749 + 0.590894i \(0.201225\pi\)
\(62\) 11.5311 1.46445
\(63\) −1.00000 −0.125988
\(64\) −4.64954 −0.581192
\(65\) 0 0
\(66\) −5.95289 −0.732750
\(67\) 6.65056 0.812495 0.406248 0.913763i \(-0.366837\pi\)
0.406248 + 0.913763i \(0.366837\pi\)
\(68\) −1.50553 −0.182573
\(69\) −5.87145 −0.706839
\(70\) 3.35579 0.401094
\(71\) 7.17531 0.851552 0.425776 0.904829i \(-0.360001\pi\)
0.425776 + 0.904829i \(0.360001\pi\)
\(72\) −0.738153 −0.0869921
\(73\) −4.85580 −0.568328 −0.284164 0.958776i \(-0.591716\pi\)
−0.284164 + 0.958776i \(0.591716\pi\)
\(74\) 3.85108 0.447679
\(75\) 1.88188 0.217301
\(76\) −3.43733 −0.394289
\(77\) −3.13241 −0.356972
\(78\) 0 0
\(79\) 12.0565 1.35646 0.678231 0.734848i \(-0.262747\pi\)
0.678231 + 0.734848i \(0.262747\pi\)
\(80\) 8.16862 0.913279
\(81\) 1.00000 0.111111
\(82\) 11.7142 1.29361
\(83\) −11.7189 −1.28632 −0.643160 0.765732i \(-0.722377\pi\)
−0.643160 + 0.765732i \(0.722377\pi\)
\(84\) 1.61158 0.175838
\(85\) 1.64962 0.178926
\(86\) 10.7991 1.16449
\(87\) 2.37261 0.254371
\(88\) −2.31220 −0.246481
\(89\) −8.30211 −0.880021 −0.440011 0.897993i \(-0.645025\pi\)
−0.440011 + 0.897993i \(0.645025\pi\)
\(90\) −3.35579 −0.353731
\(91\) 0 0
\(92\) 9.46233 0.986516
\(93\) −6.06765 −0.629186
\(94\) −10.0096 −1.03242
\(95\) 3.76630 0.386414
\(96\) 7.31496 0.746580
\(97\) 18.2921 1.85728 0.928642 0.370977i \(-0.120977\pi\)
0.928642 + 0.370977i \(0.120977\pi\)
\(98\) 1.90042 0.191971
\(99\) 3.13241 0.314819
\(100\) −3.03281 −0.303281
\(101\) 12.5967 1.25342 0.626710 0.779252i \(-0.284401\pi\)
0.626710 + 0.779252i \(0.284401\pi\)
\(102\) 1.77536 0.175787
\(103\) −4.92445 −0.485220 −0.242610 0.970124i \(-0.578004\pi\)
−0.242610 + 0.970124i \(0.578004\pi\)
\(104\) 0 0
\(105\) −1.76582 −0.172326
\(106\) 20.1236 1.95458
\(107\) −3.69523 −0.357231 −0.178616 0.983919i \(-0.557162\pi\)
−0.178616 + 0.983919i \(0.557162\pi\)
\(108\) −1.61158 −0.155075
\(109\) 14.6664 1.40479 0.702393 0.711789i \(-0.252115\pi\)
0.702393 + 0.711789i \(0.252115\pi\)
\(110\) −10.5117 −1.00225
\(111\) −2.02644 −0.192341
\(112\) 4.62597 0.437113
\(113\) 14.4311 1.35756 0.678780 0.734342i \(-0.262509\pi\)
0.678780 + 0.734342i \(0.262509\pi\)
\(114\) 4.05338 0.379634
\(115\) −10.3679 −0.966813
\(116\) −3.82366 −0.355018
\(117\) 0 0
\(118\) −9.19577 −0.846539
\(119\) 0.934195 0.0856375
\(120\) −1.30344 −0.118988
\(121\) −1.18799 −0.107999
\(122\) 23.9487 2.16821
\(123\) −6.16399 −0.555789
\(124\) 9.77853 0.878138
\(125\) 12.1522 1.08692
\(126\) −1.90042 −0.169303
\(127\) −4.80045 −0.425971 −0.212986 0.977055i \(-0.568319\pi\)
−0.212986 + 0.977055i \(0.568319\pi\)
\(128\) 5.79386 0.512110
\(129\) −5.68247 −0.500314
\(130\) 0 0
\(131\) −7.33712 −0.641047 −0.320524 0.947241i \(-0.603859\pi\)
−0.320524 + 0.947241i \(0.603859\pi\)
\(132\) −5.04815 −0.439385
\(133\) 2.13289 0.184945
\(134\) 12.6388 1.09183
\(135\) 1.76582 0.151977
\(136\) 0.689579 0.0591309
\(137\) −0.951272 −0.0812726 −0.0406363 0.999174i \(-0.512939\pi\)
−0.0406363 + 0.999174i \(0.512939\pi\)
\(138\) −11.1582 −0.949849
\(139\) −9.89366 −0.839169 −0.419584 0.907716i \(-0.637824\pi\)
−0.419584 + 0.907716i \(0.637824\pi\)
\(140\) 2.84577 0.240511
\(141\) 5.26708 0.443568
\(142\) 13.6361 1.14431
\(143\) 0 0
\(144\) −4.62597 −0.385497
\(145\) 4.18960 0.347928
\(146\) −9.22804 −0.763718
\(147\) −1.00000 −0.0824786
\(148\) 3.26578 0.268445
\(149\) 19.7207 1.61558 0.807792 0.589467i \(-0.200662\pi\)
0.807792 + 0.589467i \(0.200662\pi\)
\(150\) 3.57636 0.292009
\(151\) −12.6508 −1.02951 −0.514753 0.857338i \(-0.672116\pi\)
−0.514753 + 0.857338i \(0.672116\pi\)
\(152\) 1.57440 0.127701
\(153\) −0.934195 −0.0755252
\(154\) −5.95289 −0.479698
\(155\) −10.7144 −0.860599
\(156\) 0 0
\(157\) −15.9485 −1.27283 −0.636413 0.771348i \(-0.719583\pi\)
−0.636413 + 0.771348i \(0.719583\pi\)
\(158\) 22.9124 1.82281
\(159\) −10.5891 −0.839767
\(160\) 12.9169 1.02117
\(161\) −5.87145 −0.462735
\(162\) 1.90042 0.149311
\(163\) 9.44073 0.739455 0.369727 0.929140i \(-0.379451\pi\)
0.369727 + 0.929140i \(0.379451\pi\)
\(164\) 9.93379 0.775699
\(165\) 5.53127 0.430609
\(166\) −22.2708 −1.72855
\(167\) −4.14823 −0.320999 −0.160500 0.987036i \(-0.551311\pi\)
−0.160500 + 0.987036i \(0.551311\pi\)
\(168\) −0.738153 −0.0569497
\(169\) 0 0
\(170\) 3.13496 0.240441
\(171\) −2.13289 −0.163106
\(172\) 9.15778 0.698274
\(173\) 3.23618 0.246042 0.123021 0.992404i \(-0.460742\pi\)
0.123021 + 0.992404i \(0.460742\pi\)
\(174\) 4.50895 0.341823
\(175\) 1.88188 0.142257
\(176\) −14.4904 −1.09226
\(177\) 4.83882 0.363708
\(178\) −15.7775 −1.18257
\(179\) 19.8786 1.48579 0.742896 0.669406i \(-0.233452\pi\)
0.742896 + 0.669406i \(0.233452\pi\)
\(180\) −2.84577 −0.212111
\(181\) 8.91114 0.662360 0.331180 0.943568i \(-0.392553\pi\)
0.331180 + 0.943568i \(0.392553\pi\)
\(182\) 0 0
\(183\) −12.6018 −0.931553
\(184\) −4.33403 −0.319509
\(185\) −3.57833 −0.263084
\(186\) −11.5311 −0.845499
\(187\) −2.92629 −0.213991
\(188\) −8.48834 −0.619076
\(189\) 1.00000 0.0727393
\(190\) 7.15754 0.519262
\(191\) 17.4590 1.26329 0.631646 0.775257i \(-0.282380\pi\)
0.631646 + 0.775257i \(0.282380\pi\)
\(192\) 4.64954 0.335551
\(193\) −19.3101 −1.38997 −0.694984 0.719025i \(-0.744589\pi\)
−0.694984 + 0.719025i \(0.744589\pi\)
\(194\) 34.7627 2.49581
\(195\) 0 0
\(196\) 1.61158 0.115113
\(197\) −25.9848 −1.85134 −0.925669 0.378334i \(-0.876497\pi\)
−0.925669 + 0.378334i \(0.876497\pi\)
\(198\) 5.95289 0.423054
\(199\) 20.1033 1.42508 0.712542 0.701629i \(-0.247544\pi\)
0.712542 + 0.701629i \(0.247544\pi\)
\(200\) 1.38912 0.0982254
\(201\) −6.65056 −0.469094
\(202\) 23.9390 1.68434
\(203\) 2.37261 0.166525
\(204\) 1.50553 0.105408
\(205\) −10.8845 −0.760206
\(206\) −9.35850 −0.652038
\(207\) 5.87145 0.408094
\(208\) 0 0
\(209\) −6.68110 −0.462141
\(210\) −3.35579 −0.231572
\(211\) −7.25390 −0.499379 −0.249689 0.968326i \(-0.580329\pi\)
−0.249689 + 0.968326i \(0.580329\pi\)
\(212\) 17.0652 1.17204
\(213\) −7.17531 −0.491644
\(214\) −7.02247 −0.480046
\(215\) −10.0342 −0.684328
\(216\) 0.738153 0.0502249
\(217\) −6.06765 −0.411899
\(218\) 27.8723 1.88775
\(219\) 4.85580 0.328124
\(220\) −8.91411 −0.600989
\(221\) 0 0
\(222\) −3.85108 −0.258468
\(223\) 8.41784 0.563701 0.281850 0.959458i \(-0.409052\pi\)
0.281850 + 0.959458i \(0.409052\pi\)
\(224\) 7.31496 0.488751
\(225\) −1.88188 −0.125459
\(226\) 27.4250 1.82429
\(227\) 10.4603 0.694275 0.347138 0.937814i \(-0.387154\pi\)
0.347138 + 0.937814i \(0.387154\pi\)
\(228\) 3.43733 0.227643
\(229\) −10.6287 −0.702362 −0.351181 0.936308i \(-0.614220\pi\)
−0.351181 + 0.936308i \(0.614220\pi\)
\(230\) −19.7034 −1.29920
\(231\) 3.13241 0.206098
\(232\) 1.75135 0.114982
\(233\) 22.9731 1.50502 0.752510 0.658580i \(-0.228843\pi\)
0.752510 + 0.658580i \(0.228843\pi\)
\(234\) 0 0
\(235\) 9.30071 0.606711
\(236\) −7.79816 −0.507617
\(237\) −12.0565 −0.783154
\(238\) 1.77536 0.115079
\(239\) −15.7349 −1.01781 −0.508904 0.860823i \(-0.669949\pi\)
−0.508904 + 0.860823i \(0.669949\pi\)
\(240\) −8.16862 −0.527282
\(241\) −9.04536 −0.582663 −0.291331 0.956622i \(-0.594098\pi\)
−0.291331 + 0.956622i \(0.594098\pi\)
\(242\) −2.25767 −0.145128
\(243\) −1.00000 −0.0641500
\(244\) 20.3089 1.30014
\(245\) −1.76582 −0.112814
\(246\) −11.7142 −0.746867
\(247\) 0 0
\(248\) −4.47885 −0.284407
\(249\) 11.7189 0.742657
\(250\) 23.0942 1.46060
\(251\) 17.0593 1.07677 0.538386 0.842698i \(-0.319034\pi\)
0.538386 + 0.842698i \(0.319034\pi\)
\(252\) −1.61158 −0.101520
\(253\) 18.3918 1.15628
\(254\) −9.12286 −0.572419
\(255\) −1.64962 −0.103303
\(256\) 20.3098 1.26936
\(257\) −7.93028 −0.494677 −0.247339 0.968929i \(-0.579556\pi\)
−0.247339 + 0.968929i \(0.579556\pi\)
\(258\) −10.7991 −0.672320
\(259\) −2.02644 −0.125917
\(260\) 0 0
\(261\) −2.37261 −0.146861
\(262\) −13.9436 −0.861438
\(263\) 18.4617 1.13840 0.569199 0.822200i \(-0.307253\pi\)
0.569199 + 0.822200i \(0.307253\pi\)
\(264\) 2.31220 0.142306
\(265\) −18.6984 −1.14863
\(266\) 4.05338 0.248529
\(267\) 8.30211 0.508081
\(268\) 10.7179 0.654702
\(269\) −10.2133 −0.622716 −0.311358 0.950293i \(-0.600784\pi\)
−0.311358 + 0.950293i \(0.600784\pi\)
\(270\) 3.35579 0.204227
\(271\) −24.1804 −1.46886 −0.734428 0.678687i \(-0.762549\pi\)
−0.734428 + 0.678687i \(0.762549\pi\)
\(272\) 4.32155 0.262033
\(273\) 0 0
\(274\) −1.80781 −0.109214
\(275\) −5.89484 −0.355472
\(276\) −9.46233 −0.569565
\(277\) −18.3142 −1.10039 −0.550195 0.835036i \(-0.685447\pi\)
−0.550195 + 0.835036i \(0.685447\pi\)
\(278\) −18.8021 −1.12767
\(279\) 6.06765 0.363261
\(280\) −1.30344 −0.0778957
\(281\) −9.11661 −0.543852 −0.271926 0.962318i \(-0.587661\pi\)
−0.271926 + 0.962318i \(0.587661\pi\)
\(282\) 10.0096 0.596066
\(283\) −9.22502 −0.548371 −0.274185 0.961677i \(-0.588408\pi\)
−0.274185 + 0.961677i \(0.588408\pi\)
\(284\) 11.5636 0.686174
\(285\) −3.76630 −0.223096
\(286\) 0 0
\(287\) −6.16399 −0.363849
\(288\) −7.31496 −0.431038
\(289\) −16.1273 −0.948664
\(290\) 7.96199 0.467544
\(291\) −18.2921 −1.07230
\(292\) −7.82553 −0.457954
\(293\) 18.0748 1.05594 0.527970 0.849263i \(-0.322953\pi\)
0.527970 + 0.849263i \(0.322953\pi\)
\(294\) −1.90042 −0.110835
\(295\) 8.54448 0.497479
\(296\) −1.49582 −0.0869429
\(297\) −3.13241 −0.181761
\(298\) 37.4776 2.17102
\(299\) 0 0
\(300\) 3.03281 0.175100
\(301\) −5.68247 −0.327532
\(302\) −24.0418 −1.38345
\(303\) −12.5967 −0.723663
\(304\) 9.86668 0.565893
\(305\) −22.2525 −1.27418
\(306\) −1.77536 −0.101491
\(307\) −15.5831 −0.889373 −0.444686 0.895686i \(-0.646685\pi\)
−0.444686 + 0.895686i \(0.646685\pi\)
\(308\) −5.04815 −0.287645
\(309\) 4.92445 0.280142
\(310\) −20.3618 −1.15647
\(311\) −2.20637 −0.125112 −0.0625558 0.998041i \(-0.519925\pi\)
−0.0625558 + 0.998041i \(0.519925\pi\)
\(312\) 0 0
\(313\) 26.6495 1.50632 0.753160 0.657837i \(-0.228528\pi\)
0.753160 + 0.657837i \(0.228528\pi\)
\(314\) −30.3087 −1.71042
\(315\) 1.76582 0.0994926
\(316\) 19.4301 1.09303
\(317\) −22.8415 −1.28291 −0.641455 0.767161i \(-0.721669\pi\)
−0.641455 + 0.767161i \(0.721669\pi\)
\(318\) −20.1236 −1.12848
\(319\) −7.43200 −0.416112
\(320\) 8.21024 0.458966
\(321\) 3.69523 0.206247
\(322\) −11.1582 −0.621822
\(323\) 1.99254 0.110868
\(324\) 1.61158 0.0895324
\(325\) 0 0
\(326\) 17.9413 0.993678
\(327\) −14.6664 −0.811054
\(328\) −4.54997 −0.251230
\(329\) 5.26708 0.290383
\(330\) 10.5117 0.578652
\(331\) −3.66559 −0.201479 −0.100739 0.994913i \(-0.532121\pi\)
−0.100739 + 0.994913i \(0.532121\pi\)
\(332\) −18.8860 −1.03651
\(333\) 2.02644 0.111048
\(334\) −7.88336 −0.431358
\(335\) −11.7437 −0.641626
\(336\) −4.62597 −0.252367
\(337\) −32.6505 −1.77859 −0.889293 0.457339i \(-0.848803\pi\)
−0.889293 + 0.457339i \(0.848803\pi\)
\(338\) 0 0
\(339\) −14.4311 −0.783788
\(340\) 2.65850 0.144177
\(341\) 19.0064 1.02925
\(342\) −4.05338 −0.219182
\(343\) −1.00000 −0.0539949
\(344\) −4.19453 −0.226154
\(345\) 10.3679 0.558190
\(346\) 6.15009 0.330631
\(347\) 21.9592 1.17883 0.589417 0.807829i \(-0.299358\pi\)
0.589417 + 0.807829i \(0.299358\pi\)
\(348\) 3.82366 0.204970
\(349\) −35.8913 −1.92121 −0.960607 0.277909i \(-0.910359\pi\)
−0.960607 + 0.277909i \(0.910359\pi\)
\(350\) 3.57636 0.191165
\(351\) 0 0
\(352\) −22.9135 −1.22129
\(353\) 5.10983 0.271969 0.135984 0.990711i \(-0.456580\pi\)
0.135984 + 0.990711i \(0.456580\pi\)
\(354\) 9.19577 0.488750
\(355\) −12.6703 −0.672469
\(356\) −13.3795 −0.709114
\(357\) −0.934195 −0.0494428
\(358\) 37.7775 1.99660
\(359\) 2.15127 0.113540 0.0567698 0.998387i \(-0.481920\pi\)
0.0567698 + 0.998387i \(0.481920\pi\)
\(360\) 1.30344 0.0686975
\(361\) −14.4508 −0.760567
\(362\) 16.9349 0.890077
\(363\) 1.18799 0.0623531
\(364\) 0 0
\(365\) 8.57446 0.448808
\(366\) −23.9487 −1.25182
\(367\) 19.3500 1.01006 0.505031 0.863101i \(-0.331481\pi\)
0.505031 + 0.863101i \(0.331481\pi\)
\(368\) −27.1611 −1.41587
\(369\) 6.16399 0.320885
\(370\) −6.80031 −0.353532
\(371\) −10.5891 −0.549757
\(372\) −9.77853 −0.506993
\(373\) −16.3147 −0.844741 −0.422371 0.906423i \(-0.638802\pi\)
−0.422371 + 0.906423i \(0.638802\pi\)
\(374\) −5.56116 −0.287561
\(375\) −12.1522 −0.627535
\(376\) 3.88791 0.200504
\(377\) 0 0
\(378\) 1.90042 0.0977469
\(379\) 8.99682 0.462135 0.231068 0.972938i \(-0.425778\pi\)
0.231068 + 0.972938i \(0.425778\pi\)
\(380\) 6.06971 0.311369
\(381\) 4.80045 0.245935
\(382\) 33.1794 1.69761
\(383\) −35.9745 −1.83821 −0.919105 0.394012i \(-0.871087\pi\)
−0.919105 + 0.394012i \(0.871087\pi\)
\(384\) −5.79386 −0.295667
\(385\) 5.53127 0.281900
\(386\) −36.6972 −1.86784
\(387\) 5.68247 0.288856
\(388\) 29.4793 1.49658
\(389\) 21.7976 1.10518 0.552591 0.833453i \(-0.313639\pi\)
0.552591 + 0.833453i \(0.313639\pi\)
\(390\) 0 0
\(391\) −5.48508 −0.277392
\(392\) −0.738153 −0.0372823
\(393\) 7.33712 0.370109
\(394\) −49.3819 −2.48782
\(395\) −21.2896 −1.07120
\(396\) 5.04815 0.253679
\(397\) 25.9786 1.30383 0.651913 0.758293i \(-0.273967\pi\)
0.651913 + 0.758293i \(0.273967\pi\)
\(398\) 38.2046 1.91503
\(399\) −2.13289 −0.106778
\(400\) 8.70553 0.435276
\(401\) 24.2479 1.21088 0.605442 0.795890i \(-0.292996\pi\)
0.605442 + 0.795890i \(0.292996\pi\)
\(402\) −12.6388 −0.630368
\(403\) 0 0
\(404\) 20.3007 1.01000
\(405\) −1.76582 −0.0877442
\(406\) 4.50895 0.223776
\(407\) 6.34765 0.314641
\(408\) −0.689579 −0.0341392
\(409\) 21.5639 1.06627 0.533134 0.846031i \(-0.321014\pi\)
0.533134 + 0.846031i \(0.321014\pi\)
\(410\) −20.6851 −1.02156
\(411\) 0.951272 0.0469228
\(412\) −7.93616 −0.390987
\(413\) 4.83882 0.238103
\(414\) 11.1582 0.548396
\(415\) 20.6935 1.01580
\(416\) 0 0
\(417\) 9.89366 0.484494
\(418\) −12.6969 −0.621024
\(419\) 0.199171 0.00973014 0.00486507 0.999988i \(-0.498451\pi\)
0.00486507 + 0.999988i \(0.498451\pi\)
\(420\) −2.84577 −0.138859
\(421\) −20.8702 −1.01715 −0.508576 0.861017i \(-0.669828\pi\)
−0.508576 + 0.861017i \(0.669828\pi\)
\(422\) −13.7854 −0.671064
\(423\) −5.26708 −0.256094
\(424\) −7.81634 −0.379595
\(425\) 1.75805 0.0852778
\(426\) −13.6361 −0.660670
\(427\) −12.6018 −0.609845
\(428\) −5.95517 −0.287854
\(429\) 0 0
\(430\) −19.0692 −0.919598
\(431\) 13.2296 0.637246 0.318623 0.947882i \(-0.396780\pi\)
0.318623 + 0.947882i \(0.396780\pi\)
\(432\) 4.62597 0.222567
\(433\) −31.5518 −1.51628 −0.758142 0.652090i \(-0.773892\pi\)
−0.758142 + 0.652090i \(0.773892\pi\)
\(434\) −11.5311 −0.553509
\(435\) −4.18960 −0.200876
\(436\) 23.6361 1.13197
\(437\) −12.5232 −0.599064
\(438\) 9.22804 0.440933
\(439\) 27.1399 1.29532 0.647658 0.761931i \(-0.275748\pi\)
0.647658 + 0.761931i \(0.275748\pi\)
\(440\) 4.08292 0.194646
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −0.825961 −0.0392426 −0.0196213 0.999807i \(-0.506246\pi\)
−0.0196213 + 0.999807i \(0.506246\pi\)
\(444\) −3.26578 −0.154987
\(445\) 14.6600 0.694951
\(446\) 15.9974 0.757499
\(447\) −19.7207 −0.932758
\(448\) 4.64954 0.219670
\(449\) −27.5595 −1.30061 −0.650306 0.759673i \(-0.725359\pi\)
−0.650306 + 0.759673i \(0.725359\pi\)
\(450\) −3.57636 −0.168591
\(451\) 19.3082 0.909187
\(452\) 23.2569 1.09391
\(453\) 12.6508 0.594386
\(454\) 19.8789 0.932965
\(455\) 0 0
\(456\) −1.57440 −0.0737280
\(457\) 0.0445936 0.00208600 0.00104300 0.999999i \(-0.499668\pi\)
0.00104300 + 0.999999i \(0.499668\pi\)
\(458\) −20.1989 −0.943833
\(459\) 0.934195 0.0436045
\(460\) −16.7088 −0.779050
\(461\) −2.86714 −0.133536 −0.0667680 0.997769i \(-0.521269\pi\)
−0.0667680 + 0.997769i \(0.521269\pi\)
\(462\) 5.95289 0.276954
\(463\) 11.7612 0.546590 0.273295 0.961930i \(-0.411886\pi\)
0.273295 + 0.961930i \(0.411886\pi\)
\(464\) 10.9756 0.509531
\(465\) 10.7144 0.496867
\(466\) 43.6586 2.02244
\(467\) 39.3716 1.82190 0.910949 0.412518i \(-0.135351\pi\)
0.910949 + 0.412518i \(0.135351\pi\)
\(468\) 0 0
\(469\) −6.65056 −0.307094
\(470\) 17.6752 0.815297
\(471\) 15.9485 0.734867
\(472\) 3.57179 0.164405
\(473\) 17.7999 0.818438
\(474\) −22.9124 −1.05240
\(475\) 4.01385 0.184168
\(476\) 1.50553 0.0690060
\(477\) 10.5891 0.484840
\(478\) −29.9029 −1.36773
\(479\) −15.5574 −0.710835 −0.355417 0.934708i \(-0.615661\pi\)
−0.355417 + 0.934708i \(0.615661\pi\)
\(480\) −12.9169 −0.589573
\(481\) 0 0
\(482\) −17.1900 −0.782981
\(483\) 5.87145 0.267160
\(484\) −1.91454 −0.0870245
\(485\) −32.3006 −1.46669
\(486\) −1.90042 −0.0862047
\(487\) −23.7460 −1.07604 −0.538018 0.842933i \(-0.680827\pi\)
−0.538018 + 0.842933i \(0.680827\pi\)
\(488\) −9.30207 −0.421085
\(489\) −9.44073 −0.426924
\(490\) −3.35579 −0.151599
\(491\) −5.86527 −0.264696 −0.132348 0.991203i \(-0.542252\pi\)
−0.132348 + 0.991203i \(0.542252\pi\)
\(492\) −9.93379 −0.447850
\(493\) 2.21648 0.0998254
\(494\) 0 0
\(495\) −5.53127 −0.248612
\(496\) −28.0687 −1.26032
\(497\) −7.17531 −0.321856
\(498\) 22.2708 0.997981
\(499\) −7.79729 −0.349054 −0.174527 0.984652i \(-0.555840\pi\)
−0.174527 + 0.984652i \(0.555840\pi\)
\(500\) 19.5842 0.875833
\(501\) 4.14823 0.185329
\(502\) 32.4197 1.44696
\(503\) −34.3648 −1.53225 −0.766126 0.642690i \(-0.777818\pi\)
−0.766126 + 0.642690i \(0.777818\pi\)
\(504\) 0.738153 0.0328799
\(505\) −22.2435 −0.989824
\(506\) 34.9521 1.55381
\(507\) 0 0
\(508\) −7.73633 −0.343244
\(509\) 10.4900 0.464960 0.232480 0.972601i \(-0.425316\pi\)
0.232480 + 0.972601i \(0.425316\pi\)
\(510\) −3.13496 −0.138819
\(511\) 4.85580 0.214808
\(512\) 27.0094 1.19366
\(513\) 2.13289 0.0941695
\(514\) −15.0708 −0.664746
\(515\) 8.69568 0.383178
\(516\) −9.15778 −0.403149
\(517\) −16.4987 −0.725611
\(518\) −3.85108 −0.169207
\(519\) −3.23618 −0.142053
\(520\) 0 0
\(521\) −2.34072 −0.102549 −0.0512743 0.998685i \(-0.516328\pi\)
−0.0512743 + 0.998685i \(0.516328\pi\)
\(522\) −4.50895 −0.197352
\(523\) 32.9438 1.44053 0.720266 0.693698i \(-0.244020\pi\)
0.720266 + 0.693698i \(0.244020\pi\)
\(524\) −11.8244 −0.516551
\(525\) −1.88188 −0.0821321
\(526\) 35.0849 1.52978
\(527\) −5.66837 −0.246918
\(528\) 14.4904 0.630615
\(529\) 11.4739 0.498866
\(530\) −35.5347 −1.54353
\(531\) −4.83882 −0.209987
\(532\) 3.43733 0.149027
\(533\) 0 0
\(534\) 15.7775 0.682758
\(535\) 6.52510 0.282105
\(536\) −4.90913 −0.212042
\(537\) −19.8786 −0.857823
\(538\) −19.4095 −0.836805
\(539\) 3.13241 0.134923
\(540\) 2.84577 0.122462
\(541\) −7.71023 −0.331489 −0.165744 0.986169i \(-0.553003\pi\)
−0.165744 + 0.986169i \(0.553003\pi\)
\(542\) −45.9529 −1.97384
\(543\) −8.91114 −0.382414
\(544\) 6.83360 0.292988
\(545\) −25.8982 −1.10936
\(546\) 0 0
\(547\) 23.6877 1.01281 0.506407 0.862294i \(-0.330973\pi\)
0.506407 + 0.862294i \(0.330973\pi\)
\(548\) −1.53305 −0.0654888
\(549\) 12.6018 0.537833
\(550\) −11.2027 −0.477683
\(551\) 5.06053 0.215586
\(552\) 4.33403 0.184468
\(553\) −12.0565 −0.512695
\(554\) −34.8045 −1.47870
\(555\) 3.57833 0.151892
\(556\) −15.9445 −0.676195
\(557\) 11.8899 0.503792 0.251896 0.967754i \(-0.418946\pi\)
0.251896 + 0.967754i \(0.418946\pi\)
\(558\) 11.5311 0.488149
\(559\) 0 0
\(560\) −8.16862 −0.345187
\(561\) 2.92629 0.123548
\(562\) −17.3254 −0.730826
\(563\) 45.2378 1.90655 0.953273 0.302109i \(-0.0976907\pi\)
0.953273 + 0.302109i \(0.0976907\pi\)
\(564\) 8.48834 0.357424
\(565\) −25.4826 −1.07206
\(566\) −17.5314 −0.736899
\(567\) −1.00000 −0.0419961
\(568\) −5.29647 −0.222235
\(569\) −17.7145 −0.742629 −0.371314 0.928507i \(-0.621093\pi\)
−0.371314 + 0.928507i \(0.621093\pi\)
\(570\) −7.15754 −0.299796
\(571\) 20.5380 0.859487 0.429743 0.902951i \(-0.358604\pi\)
0.429743 + 0.902951i \(0.358604\pi\)
\(572\) 0 0
\(573\) −17.4590 −0.729361
\(574\) −11.7142 −0.488940
\(575\) −11.0494 −0.460791
\(576\) −4.64954 −0.193731
\(577\) 11.9204 0.496253 0.248127 0.968728i \(-0.420185\pi\)
0.248127 + 0.968728i \(0.420185\pi\)
\(578\) −30.6486 −1.27481
\(579\) 19.3101 0.802499
\(580\) 6.75190 0.280357
\(581\) 11.7189 0.486183
\(582\) −34.7627 −1.44096
\(583\) 33.1693 1.37373
\(584\) 3.58432 0.148320
\(585\) 0 0
\(586\) 34.3496 1.41897
\(587\) −18.9993 −0.784185 −0.392093 0.919926i \(-0.628249\pi\)
−0.392093 + 0.919926i \(0.628249\pi\)
\(588\) −1.61158 −0.0664606
\(589\) −12.9416 −0.533251
\(590\) 16.2381 0.668511
\(591\) 25.9848 1.06887
\(592\) −9.37425 −0.385279
\(593\) 14.9494 0.613899 0.306949 0.951726i \(-0.400692\pi\)
0.306949 + 0.951726i \(0.400692\pi\)
\(594\) −5.95289 −0.244250
\(595\) −1.64962 −0.0676278
\(596\) 31.7816 1.30183
\(597\) −20.1033 −0.822773
\(598\) 0 0
\(599\) 45.5130 1.85961 0.929806 0.368051i \(-0.119975\pi\)
0.929806 + 0.368051i \(0.119975\pi\)
\(600\) −1.38912 −0.0567105
\(601\) 31.0256 1.26556 0.632781 0.774331i \(-0.281913\pi\)
0.632781 + 0.774331i \(0.281913\pi\)
\(602\) −10.7991 −0.440137
\(603\) 6.65056 0.270832
\(604\) −20.3878 −0.829568
\(605\) 2.09777 0.0852864
\(606\) −23.9390 −0.972456
\(607\) −1.55815 −0.0632435 −0.0316218 0.999500i \(-0.510067\pi\)
−0.0316218 + 0.999500i \(0.510067\pi\)
\(608\) 15.6020 0.632745
\(609\) −2.37261 −0.0961431
\(610\) −42.2891 −1.71224
\(611\) 0 0
\(612\) −1.50553 −0.0608576
\(613\) 17.4821 0.706096 0.353048 0.935605i \(-0.385145\pi\)
0.353048 + 0.935605i \(0.385145\pi\)
\(614\) −29.6143 −1.19514
\(615\) 10.8845 0.438905
\(616\) 2.31220 0.0931612
\(617\) 31.7640 1.27877 0.639385 0.768887i \(-0.279189\pi\)
0.639385 + 0.768887i \(0.279189\pi\)
\(618\) 9.35850 0.376454
\(619\) −1.58220 −0.0635941 −0.0317970 0.999494i \(-0.510123\pi\)
−0.0317970 + 0.999494i \(0.510123\pi\)
\(620\) −17.2671 −0.693464
\(621\) −5.87145 −0.235613
\(622\) −4.19301 −0.168125
\(623\) 8.30211 0.332617
\(624\) 0 0
\(625\) −12.0491 −0.481964
\(626\) 50.6452 2.02419
\(627\) 6.68110 0.266817
\(628\) −25.7023 −1.02563
\(629\) −1.89309 −0.0754825
\(630\) 3.35579 0.133698
\(631\) 3.86214 0.153749 0.0768746 0.997041i \(-0.475506\pi\)
0.0768746 + 0.997041i \(0.475506\pi\)
\(632\) −8.89954 −0.354005
\(633\) 7.25390 0.288317
\(634\) −43.4085 −1.72397
\(635\) 8.47673 0.336389
\(636\) −17.0652 −0.676678
\(637\) 0 0
\(638\) −14.1239 −0.559171
\(639\) 7.17531 0.283851
\(640\) −10.2309 −0.404412
\(641\) −17.1008 −0.675442 −0.337721 0.941246i \(-0.609656\pi\)
−0.337721 + 0.941246i \(0.609656\pi\)
\(642\) 7.02247 0.277155
\(643\) 49.0673 1.93503 0.967513 0.252821i \(-0.0813583\pi\)
0.967513 + 0.252821i \(0.0813583\pi\)
\(644\) −9.46233 −0.372868
\(645\) 10.0342 0.395097
\(646\) 3.78665 0.148984
\(647\) −18.3702 −0.722209 −0.361104 0.932525i \(-0.617600\pi\)
−0.361104 + 0.932525i \(0.617600\pi\)
\(648\) −0.738153 −0.0289974
\(649\) −15.1572 −0.594971
\(650\) 0 0
\(651\) 6.06765 0.237810
\(652\) 15.2145 0.595847
\(653\) 18.7518 0.733814 0.366907 0.930258i \(-0.380417\pi\)
0.366907 + 0.930258i \(0.380417\pi\)
\(654\) −27.8723 −1.08989
\(655\) 12.9560 0.506234
\(656\) −28.5144 −1.11330
\(657\) −4.85580 −0.189443
\(658\) 10.0096 0.390217
\(659\) 27.0220 1.05263 0.526315 0.850290i \(-0.323573\pi\)
0.526315 + 0.850290i \(0.323573\pi\)
\(660\) 8.91411 0.346981
\(661\) −17.3755 −0.675830 −0.337915 0.941177i \(-0.609722\pi\)
−0.337915 + 0.941177i \(0.609722\pi\)
\(662\) −6.96614 −0.270747
\(663\) 0 0
\(664\) 8.65036 0.335699
\(665\) −3.76630 −0.146051
\(666\) 3.85108 0.149226
\(667\) −13.9307 −0.539398
\(668\) −6.68522 −0.258659
\(669\) −8.41784 −0.325453
\(670\) −22.3179 −0.862216
\(671\) 39.4741 1.52388
\(672\) −7.31496 −0.282181
\(673\) 8.26424 0.318563 0.159281 0.987233i \(-0.449082\pi\)
0.159281 + 0.987233i \(0.449082\pi\)
\(674\) −62.0495 −2.39006
\(675\) 1.88188 0.0724337
\(676\) 0 0
\(677\) −33.9430 −1.30454 −0.652268 0.757988i \(-0.726182\pi\)
−0.652268 + 0.757988i \(0.726182\pi\)
\(678\) −27.4250 −1.05325
\(679\) −18.2921 −0.701988
\(680\) −1.21767 −0.0466955
\(681\) −10.4603 −0.400840
\(682\) 36.1201 1.38311
\(683\) 3.32745 0.127321 0.0636606 0.997972i \(-0.479722\pi\)
0.0636606 + 0.997972i \(0.479722\pi\)
\(684\) −3.43733 −0.131430
\(685\) 1.67977 0.0641809
\(686\) −1.90042 −0.0725582
\(687\) 10.6287 0.405509
\(688\) −26.2869 −1.00218
\(689\) 0 0
\(690\) 19.7034 0.750094
\(691\) −13.6990 −0.521133 −0.260567 0.965456i \(-0.583909\pi\)
−0.260567 + 0.965456i \(0.583909\pi\)
\(692\) 5.21538 0.198259
\(693\) −3.13241 −0.118991
\(694\) 41.7317 1.58411
\(695\) 17.4704 0.662690
\(696\) −1.75135 −0.0663848
\(697\) −5.75837 −0.218114
\(698\) −68.2083 −2.58172
\(699\) −22.9731 −0.868924
\(700\) 3.03281 0.114630
\(701\) −25.4300 −0.960478 −0.480239 0.877138i \(-0.659450\pi\)
−0.480239 + 0.877138i \(0.659450\pi\)
\(702\) 0 0
\(703\) −4.32218 −0.163014
\(704\) −14.5643 −0.548911
\(705\) −9.30071 −0.350285
\(706\) 9.71081 0.365471
\(707\) −12.5967 −0.473749
\(708\) 7.79816 0.293073
\(709\) −28.2448 −1.06076 −0.530378 0.847761i \(-0.677950\pi\)
−0.530378 + 0.847761i \(0.677950\pi\)
\(710\) −24.0788 −0.903662
\(711\) 12.0565 0.452154
\(712\) 6.12822 0.229665
\(713\) 35.6259 1.33420
\(714\) −1.77536 −0.0664412
\(715\) 0 0
\(716\) 32.0360 1.19724
\(717\) 15.7349 0.587631
\(718\) 4.08831 0.152574
\(719\) 16.4857 0.614812 0.307406 0.951578i \(-0.400539\pi\)
0.307406 + 0.951578i \(0.400539\pi\)
\(720\) 8.16862 0.304426
\(721\) 4.92445 0.183396
\(722\) −27.4625 −1.02205
\(723\) 9.04536 0.336401
\(724\) 14.3610 0.533724
\(725\) 4.46498 0.165825
\(726\) 2.25767 0.0837899
\(727\) −34.4487 −1.27763 −0.638816 0.769359i \(-0.720576\pi\)
−0.638816 + 0.769359i \(0.720576\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 16.2950 0.603107
\(731\) −5.30854 −0.196343
\(732\) −20.3089 −0.750638
\(733\) −51.0217 −1.88453 −0.942265 0.334869i \(-0.891308\pi\)
−0.942265 + 0.334869i \(0.891308\pi\)
\(734\) 36.7731 1.35732
\(735\) 1.76582 0.0651332
\(736\) −42.9494 −1.58314
\(737\) 20.8323 0.767368
\(738\) 11.7142 0.431204
\(739\) 33.2683 1.22379 0.611897 0.790938i \(-0.290407\pi\)
0.611897 + 0.790938i \(0.290407\pi\)
\(740\) −5.76678 −0.211991
\(741\) 0 0
\(742\) −20.1236 −0.738762
\(743\) 48.4232 1.77648 0.888238 0.459384i \(-0.151930\pi\)
0.888238 + 0.459384i \(0.151930\pi\)
\(744\) 4.47885 0.164203
\(745\) −34.8232 −1.27582
\(746\) −31.0047 −1.13516
\(747\) −11.7189 −0.428773
\(748\) −4.71595 −0.172432
\(749\) 3.69523 0.135021
\(750\) −23.0942 −0.843280
\(751\) 51.7999 1.89021 0.945103 0.326771i \(-0.105961\pi\)
0.945103 + 0.326771i \(0.105961\pi\)
\(752\) 24.3653 0.888512
\(753\) −17.0593 −0.621675
\(754\) 0 0
\(755\) 22.3390 0.812999
\(756\) 1.61158 0.0586127
\(757\) −2.92984 −0.106487 −0.0532434 0.998582i \(-0.516956\pi\)
−0.0532434 + 0.998582i \(0.516956\pi\)
\(758\) 17.0977 0.621016
\(759\) −18.3918 −0.667580
\(760\) −2.78010 −0.100845
\(761\) 18.2514 0.661613 0.330806 0.943699i \(-0.392679\pi\)
0.330806 + 0.943699i \(0.392679\pi\)
\(762\) 9.12286 0.330486
\(763\) −14.6664 −0.530959
\(764\) 28.1367 1.01795
\(765\) 1.64962 0.0596421
\(766\) −68.3665 −2.47018
\(767\) 0 0
\(768\) −20.3098 −0.732867
\(769\) −10.3062 −0.371652 −0.185826 0.982583i \(-0.559496\pi\)
−0.185826 + 0.982583i \(0.559496\pi\)
\(770\) 10.5117 0.378816
\(771\) 7.93028 0.285602
\(772\) −31.1198 −1.12003
\(773\) 41.7219 1.50063 0.750316 0.661079i \(-0.229901\pi\)
0.750316 + 0.661079i \(0.229901\pi\)
\(774\) 10.7991 0.388164
\(775\) −11.4186 −0.410169
\(776\) −13.5024 −0.484707
\(777\) 2.02644 0.0726982
\(778\) 41.4245 1.48514
\(779\) −13.1471 −0.471045
\(780\) 0 0
\(781\) 22.4760 0.804255
\(782\) −10.4239 −0.372759
\(783\) 2.37261 0.0847903
\(784\) −4.62597 −0.165213
\(785\) 28.1621 1.00515
\(786\) 13.9436 0.497351
\(787\) −22.8437 −0.814289 −0.407144 0.913364i \(-0.633475\pi\)
−0.407144 + 0.913364i \(0.633475\pi\)
\(788\) −41.8766 −1.49179
\(789\) −18.4617 −0.657254
\(790\) −40.4591 −1.43947
\(791\) −14.4311 −0.513110
\(792\) −2.31220 −0.0821604
\(793\) 0 0
\(794\) 49.3701 1.75208
\(795\) 18.6984 0.663163
\(796\) 32.3981 1.14832
\(797\) 30.3269 1.07423 0.537116 0.843508i \(-0.319514\pi\)
0.537116 + 0.843508i \(0.319514\pi\)
\(798\) −4.05338 −0.143488
\(799\) 4.92048 0.174074
\(800\) 13.7659 0.486698
\(801\) −8.30211 −0.293340
\(802\) 46.0812 1.62718
\(803\) −15.2104 −0.536762
\(804\) −10.7179 −0.377992
\(805\) 10.3679 0.365421
\(806\) 0 0
\(807\) 10.2133 0.359525
\(808\) −9.29830 −0.327113
\(809\) 27.4074 0.963594 0.481797 0.876283i \(-0.339984\pi\)
0.481797 + 0.876283i \(0.339984\pi\)
\(810\) −3.35579 −0.117910
\(811\) −10.9233 −0.383568 −0.191784 0.981437i \(-0.561427\pi\)
−0.191784 + 0.981437i \(0.561427\pi\)
\(812\) 3.82366 0.134184
\(813\) 24.1804 0.848044
\(814\) 12.0632 0.422814
\(815\) −16.6706 −0.583946
\(816\) −4.32155 −0.151285
\(817\) −12.1201 −0.424028
\(818\) 40.9804 1.43285
\(819\) 0 0
\(820\) −17.5413 −0.612568
\(821\) 3.84174 0.134078 0.0670388 0.997750i \(-0.478645\pi\)
0.0670388 + 0.997750i \(0.478645\pi\)
\(822\) 1.80781 0.0630547
\(823\) 46.5183 1.62153 0.810764 0.585373i \(-0.199052\pi\)
0.810764 + 0.585373i \(0.199052\pi\)
\(824\) 3.63499 0.126631
\(825\) 5.89484 0.205232
\(826\) 9.19577 0.319962
\(827\) −1.60867 −0.0559390 −0.0279695 0.999609i \(-0.508904\pi\)
−0.0279695 + 0.999609i \(0.508904\pi\)
\(828\) 9.46233 0.328839
\(829\) 40.8933 1.42028 0.710142 0.704058i \(-0.248631\pi\)
0.710142 + 0.704058i \(0.248631\pi\)
\(830\) 39.3263 1.36504
\(831\) 18.3142 0.635311
\(832\) 0 0
\(833\) −0.934195 −0.0323679
\(834\) 18.8021 0.651062
\(835\) 7.32502 0.253493
\(836\) −10.7671 −0.372390
\(837\) −6.06765 −0.209729
\(838\) 0.378508 0.0130753
\(839\) −45.4468 −1.56900 −0.784499 0.620130i \(-0.787080\pi\)
−0.784499 + 0.620130i \(0.787080\pi\)
\(840\) 1.30344 0.0449731
\(841\) −23.3707 −0.805886
\(842\) −39.6621 −1.36685
\(843\) 9.11661 0.313993
\(844\) −11.6903 −0.402396
\(845\) 0 0
\(846\) −10.0096 −0.344139
\(847\) 1.18799 0.0408197
\(848\) −48.9846 −1.68214
\(849\) 9.22502 0.316602
\(850\) 3.34102 0.114596
\(851\) 11.8981 0.407863
\(852\) −11.5636 −0.396163
\(853\) −34.0573 −1.16610 −0.583050 0.812436i \(-0.698141\pi\)
−0.583050 + 0.812436i \(0.698141\pi\)
\(854\) −23.9487 −0.819508
\(855\) 3.76630 0.128805
\(856\) 2.72764 0.0932289
\(857\) −30.3420 −1.03646 −0.518231 0.855240i \(-0.673409\pi\)
−0.518231 + 0.855240i \(0.673409\pi\)
\(858\) 0 0
\(859\) 54.1644 1.84806 0.924032 0.382315i \(-0.124873\pi\)
0.924032 + 0.382315i \(0.124873\pi\)
\(860\) −16.1710 −0.551426
\(861\) 6.16399 0.210068
\(862\) 25.1417 0.856329
\(863\) −53.2784 −1.81362 −0.906808 0.421543i \(-0.861489\pi\)
−0.906808 + 0.421543i \(0.861489\pi\)
\(864\) 7.31496 0.248860
\(865\) −5.71451 −0.194299
\(866\) −59.9616 −2.03758
\(867\) 16.1273 0.547711
\(868\) −9.77853 −0.331905
\(869\) 37.7660 1.28112
\(870\) −7.96199 −0.269937
\(871\) 0 0
\(872\) −10.8260 −0.366616
\(873\) 18.2921 0.619095
\(874\) −23.7992 −0.805021
\(875\) −12.1522 −0.410818
\(876\) 7.82553 0.264400
\(877\) −32.5325 −1.09854 −0.549272 0.835643i \(-0.685095\pi\)
−0.549272 + 0.835643i \(0.685095\pi\)
\(878\) 51.5771 1.74064
\(879\) −18.0748 −0.609647
\(880\) 25.5875 0.862554
\(881\) −12.1091 −0.407965 −0.203983 0.978975i \(-0.565389\pi\)
−0.203983 + 0.978975i \(0.565389\pi\)
\(882\) 1.90042 0.0639904
\(883\) −39.1408 −1.31719 −0.658596 0.752497i \(-0.728849\pi\)
−0.658596 + 0.752497i \(0.728849\pi\)
\(884\) 0 0
\(885\) −8.54448 −0.287219
\(886\) −1.56967 −0.0527341
\(887\) −18.8647 −0.633414 −0.316707 0.948523i \(-0.602577\pi\)
−0.316707 + 0.948523i \(0.602577\pi\)
\(888\) 1.49582 0.0501965
\(889\) 4.80045 0.161002
\(890\) 27.8601 0.933874
\(891\) 3.13241 0.104940
\(892\) 13.5661 0.454225
\(893\) 11.2341 0.375935
\(894\) −37.4776 −1.25344
\(895\) −35.1019 −1.17333
\(896\) −5.79386 −0.193559
\(897\) 0 0
\(898\) −52.3744 −1.74776
\(899\) −14.3962 −0.480140
\(900\) −3.03281 −0.101094
\(901\) −9.89225 −0.329559
\(902\) 36.6936 1.22176
\(903\) 5.68247 0.189101
\(904\) −10.6523 −0.354291
\(905\) −15.7355 −0.523064
\(906\) 24.0418 0.798734
\(907\) −7.69608 −0.255544 −0.127772 0.991804i \(-0.540783\pi\)
−0.127772 + 0.991804i \(0.540783\pi\)
\(908\) 16.8577 0.559441
\(909\) 12.5967 0.417807
\(910\) 0 0
\(911\) −37.7524 −1.25079 −0.625396 0.780307i \(-0.715063\pi\)
−0.625396 + 0.780307i \(0.715063\pi\)
\(912\) −9.86668 −0.326718
\(913\) −36.7085 −1.21488
\(914\) 0.0847464 0.00280316
\(915\) 22.2525 0.735646
\(916\) −17.1290 −0.565958
\(917\) 7.33712 0.242293
\(918\) 1.77536 0.0585956
\(919\) −55.4581 −1.82939 −0.914696 0.404142i \(-0.867570\pi\)
−0.914696 + 0.404142i \(0.867570\pi\)
\(920\) 7.65310 0.252315
\(921\) 15.5831 0.513480
\(922\) −5.44876 −0.179445
\(923\) 0 0
\(924\) 5.04815 0.166072
\(925\) −3.81353 −0.125388
\(926\) 22.3512 0.734507
\(927\) −4.92445 −0.161740
\(928\) 17.3556 0.569724
\(929\) 25.9014 0.849799 0.424899 0.905241i \(-0.360309\pi\)
0.424899 + 0.905241i \(0.360309\pi\)
\(930\) 20.3618 0.667689
\(931\) −2.13289 −0.0699027
\(932\) 37.0232 1.21273
\(933\) 2.20637 0.0722332
\(934\) 74.8224 2.44826
\(935\) 5.16729 0.168988
\(936\) 0 0
\(937\) −52.0461 −1.70027 −0.850136 0.526562i \(-0.823481\pi\)
−0.850136 + 0.526562i \(0.823481\pi\)
\(938\) −12.6388 −0.412673
\(939\) −26.6495 −0.869675
\(940\) 14.9889 0.488883
\(941\) 16.0103 0.521921 0.260960 0.965349i \(-0.415961\pi\)
0.260960 + 0.965349i \(0.415961\pi\)
\(942\) 30.3087 0.987512
\(943\) 36.1916 1.17856
\(944\) 22.3842 0.728544
\(945\) −1.76582 −0.0574421
\(946\) 33.8271 1.09982
\(947\) 12.0064 0.390155 0.195078 0.980788i \(-0.437504\pi\)
0.195078 + 0.980788i \(0.437504\pi\)
\(948\) −19.4301 −0.631059
\(949\) 0 0
\(950\) 7.62800 0.247485
\(951\) 22.8415 0.740688
\(952\) −0.689579 −0.0223494
\(953\) −0.168086 −0.00544483 −0.00272241 0.999996i \(-0.500867\pi\)
−0.00272241 + 0.999996i \(0.500867\pi\)
\(954\) 20.1236 0.651527
\(955\) −30.8295 −0.997619
\(956\) −25.3581 −0.820141
\(957\) 7.43200 0.240243
\(958\) −29.5655 −0.955218
\(959\) 0.951272 0.0307182
\(960\) −8.21024 −0.264984
\(961\) 5.81638 0.187625
\(962\) 0 0
\(963\) −3.69523 −0.119077
\(964\) −14.5774 −0.469505
\(965\) 34.0981 1.09766
\(966\) 11.1582 0.359009
\(967\) −13.9167 −0.447531 −0.223766 0.974643i \(-0.571835\pi\)
−0.223766 + 0.974643i \(0.571835\pi\)
\(968\) 0.876915 0.0281851
\(969\) −1.99254 −0.0640095
\(970\) −61.3846 −1.97094
\(971\) 46.8956 1.50495 0.752476 0.658619i \(-0.228859\pi\)
0.752476 + 0.658619i \(0.228859\pi\)
\(972\) −1.61158 −0.0516916
\(973\) 9.89366 0.317176
\(974\) −45.1274 −1.44597
\(975\) 0 0
\(976\) −58.2956 −1.86600
\(977\) 5.97584 0.191184 0.0955920 0.995421i \(-0.469526\pi\)
0.0955920 + 0.995421i \(0.469526\pi\)
\(978\) −17.9413 −0.573700
\(979\) −26.0056 −0.831144
\(980\) −2.84577 −0.0909046
\(981\) 14.6664 0.468262
\(982\) −11.1465 −0.355698
\(983\) 36.0862 1.15097 0.575485 0.817812i \(-0.304813\pi\)
0.575485 + 0.817812i \(0.304813\pi\)
\(984\) 4.54997 0.145048
\(985\) 45.8844 1.46200
\(986\) 4.21224 0.134145
\(987\) −5.26708 −0.167653
\(988\) 0 0
\(989\) 33.3643 1.06092
\(990\) −10.5117 −0.334085
\(991\) −45.0778 −1.43194 −0.715972 0.698129i \(-0.754016\pi\)
−0.715972 + 0.698129i \(0.754016\pi\)
\(992\) −44.3846 −1.40921
\(993\) 3.66559 0.116324
\(994\) −13.6361 −0.432510
\(995\) −35.4988 −1.12539
\(996\) 18.8860 0.598427
\(997\) 15.1512 0.479842 0.239921 0.970792i \(-0.422878\pi\)
0.239921 + 0.970792i \(0.422878\pi\)
\(998\) −14.8181 −0.469059
\(999\) −2.02644 −0.0641138
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 3549.2.a.bf.1.8 yes 9
13.12 even 2 3549.2.a.be.1.2 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.2 9 13.12 even 2
3549.2.a.bf.1.8 yes 9 1.1 even 1 trivial