Properties

Label 5577.2.a.y.1.4
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 1.4
Root \(0.409068\) of defining polynomial
Character \(\chi\) \(=\) 5577.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.409068 q^{2} +1.00000 q^{3} -1.83266 q^{4} +4.13953 q^{5} +0.409068 q^{6} +5.18273 q^{7} -1.56782 q^{8} +1.00000 q^{9} +1.69335 q^{10} +1.00000 q^{11} -1.83266 q^{12} +2.12009 q^{14} +4.13953 q^{15} +3.02398 q^{16} -0.488730 q^{17} +0.409068 q^{18} -0.446180 q^{19} -7.58636 q^{20} +5.18273 q^{21} +0.409068 q^{22} +5.50882 q^{23} -1.56782 q^{24} +12.1357 q^{25} +1.00000 q^{27} -9.49821 q^{28} -6.58571 q^{29} +1.69335 q^{30} +1.52580 q^{31} +4.37265 q^{32} +1.00000 q^{33} -0.199924 q^{34} +21.4541 q^{35} -1.83266 q^{36} -7.87139 q^{37} -0.182518 q^{38} -6.49004 q^{40} -8.78563 q^{41} +2.12009 q^{42} -4.57514 q^{43} -1.83266 q^{44} +4.13953 q^{45} +2.25348 q^{46} +5.42082 q^{47} +3.02398 q^{48} +19.8607 q^{49} +4.96433 q^{50} -0.488730 q^{51} +8.66677 q^{53} +0.409068 q^{54} +4.13953 q^{55} -8.12559 q^{56} -0.446180 q^{57} -2.69400 q^{58} +5.60493 q^{59} -7.58636 q^{60} -0.855775 q^{61} +0.624155 q^{62} +5.18273 q^{63} -4.25925 q^{64} +0.409068 q^{66} -3.87464 q^{67} +0.895677 q^{68} +5.50882 q^{69} +8.77618 q^{70} -8.49886 q^{71} -1.56782 q^{72} +5.95291 q^{73} -3.21993 q^{74} +12.1357 q^{75} +0.817698 q^{76} +5.18273 q^{77} -8.91459 q^{79} +12.5179 q^{80} +1.00000 q^{81} -3.59392 q^{82} +0.457495 q^{83} -9.49821 q^{84} -2.02311 q^{85} -1.87154 q^{86} -6.58571 q^{87} -1.56782 q^{88} -4.68461 q^{89} +1.69335 q^{90} -10.0958 q^{92} +1.52580 q^{93} +2.21748 q^{94} -1.84697 q^{95} +4.37265 q^{96} -2.06057 q^{97} +8.12439 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 3q^{2} + 7q^{3} + 9q^{4} + 6q^{5} + 3q^{6} + 6q^{7} + 15q^{8} + 7q^{9} + 7q^{11} + 9q^{12} + 8q^{14} + 6q^{15} + 17q^{16} - 2q^{17} + 3q^{18} + 8q^{19} - 2q^{20} + 6q^{21} + 3q^{22} + 4q^{23} + 15q^{24} + 13q^{25} + 7q^{27} + 12q^{28} - 12q^{29} - 10q^{31} + 33q^{32} + 7q^{33} + 28q^{34} - 4q^{35} + 9q^{36} + 6q^{37} + 16q^{38} - 10q^{40} + 2q^{41} + 8q^{42} - 16q^{43} + 9q^{44} + 6q^{45} - 26q^{46} + 18q^{47} + 17q^{48} + 23q^{49} + 39q^{50} - 2q^{51} + 10q^{53} + 3q^{54} + 6q^{55} + 16q^{56} + 8q^{57} + 10q^{58} + 2q^{59} - 2q^{60} - 10q^{61} - 36q^{62} + 6q^{63} + 29q^{64} + 3q^{66} + 8q^{67} - 10q^{68} + 4q^{69} - 20q^{70} + 36q^{71} + 15q^{72} + 20q^{73} + 13q^{75} + 10q^{76} + 6q^{77} + 6q^{79} - 20q^{80} + 7q^{81} - 10q^{82} + 30q^{83} + 12q^{84} - 40q^{85} + 6q^{86} - 12q^{87} + 15q^{88} + 34q^{89} - 12q^{92} - 10q^{93} + 32q^{94} + 18q^{95} + 33q^{96} + 16q^{97} + q^{98} + 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.409068 0.289255 0.144627 0.989486i \(-0.453802\pi\)
0.144627 + 0.989486i \(0.453802\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.83266 −0.916332
\(5\) 4.13953 1.85125 0.925627 0.378437i \(-0.123538\pi\)
0.925627 + 0.378437i \(0.123538\pi\)
\(6\) 0.409068 0.167001
\(7\) 5.18273 1.95889 0.979445 0.201714i \(-0.0646510\pi\)
0.979445 + 0.201714i \(0.0646510\pi\)
\(8\) −1.56782 −0.554308
\(9\) 1.00000 0.333333
\(10\) 1.69335 0.535484
\(11\) 1.00000 0.301511
\(12\) −1.83266 −0.529044
\(13\) 0 0
\(14\) 2.12009 0.566618
\(15\) 4.13953 1.06882
\(16\) 3.02398 0.755995
\(17\) −0.488730 −0.118534 −0.0592672 0.998242i \(-0.518876\pi\)
−0.0592672 + 0.998242i \(0.518876\pi\)
\(18\) 0.409068 0.0964183
\(19\) −0.446180 −0.102361 −0.0511803 0.998689i \(-0.516298\pi\)
−0.0511803 + 0.998689i \(0.516298\pi\)
\(20\) −7.58636 −1.69636
\(21\) 5.18273 1.13097
\(22\) 0.409068 0.0872136
\(23\) 5.50882 1.14867 0.574334 0.818621i \(-0.305261\pi\)
0.574334 + 0.818621i \(0.305261\pi\)
\(24\) −1.56782 −0.320030
\(25\) 12.1357 2.42714
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −9.49821 −1.79499
\(29\) −6.58571 −1.22294 −0.611468 0.791269i \(-0.709421\pi\)
−0.611468 + 0.791269i \(0.709421\pi\)
\(30\) 1.69335 0.309162
\(31\) 1.52580 0.274041 0.137021 0.990568i \(-0.456247\pi\)
0.137021 + 0.990568i \(0.456247\pi\)
\(32\) 4.37265 0.772983
\(33\) 1.00000 0.174078
\(34\) −0.199924 −0.0342866
\(35\) 21.4541 3.62640
\(36\) −1.83266 −0.305444
\(37\) −7.87139 −1.29405 −0.647024 0.762470i \(-0.723987\pi\)
−0.647024 + 0.762470i \(0.723987\pi\)
\(38\) −0.182518 −0.0296083
\(39\) 0 0
\(40\) −6.49004 −1.02617
\(41\) −8.78563 −1.37209 −0.686043 0.727561i \(-0.740654\pi\)
−0.686043 + 0.727561i \(0.740654\pi\)
\(42\) 2.12009 0.327137
\(43\) −4.57514 −0.697702 −0.348851 0.937178i \(-0.613428\pi\)
−0.348851 + 0.937178i \(0.613428\pi\)
\(44\) −1.83266 −0.276284
\(45\) 4.13953 0.617085
\(46\) 2.25348 0.332258
\(47\) 5.42082 0.790708 0.395354 0.918529i \(-0.370622\pi\)
0.395354 + 0.918529i \(0.370622\pi\)
\(48\) 3.02398 0.436474
\(49\) 19.8607 2.83725
\(50\) 4.96433 0.702062
\(51\) −0.488730 −0.0684359
\(52\) 0 0
\(53\) 8.66677 1.19047 0.595236 0.803551i \(-0.297059\pi\)
0.595236 + 0.803551i \(0.297059\pi\)
\(54\) 0.409068 0.0556671
\(55\) 4.13953 0.558174
\(56\) −8.12559 −1.08583
\(57\) −0.446180 −0.0590980
\(58\) −2.69400 −0.353740
\(59\) 5.60493 0.729700 0.364850 0.931066i \(-0.381120\pi\)
0.364850 + 0.931066i \(0.381120\pi\)
\(60\) −7.58636 −0.979395
\(61\) −0.855775 −0.109571 −0.0547854 0.998498i \(-0.517447\pi\)
−0.0547854 + 0.998498i \(0.517447\pi\)
\(62\) 0.624155 0.0792678
\(63\) 5.18273 0.652963
\(64\) −4.25925 −0.532406
\(65\) 0 0
\(66\) 0.409068 0.0503528
\(67\) −3.87464 −0.473363 −0.236681 0.971587i \(-0.576060\pi\)
−0.236681 + 0.971587i \(0.576060\pi\)
\(68\) 0.895677 0.108617
\(69\) 5.50882 0.663184
\(70\) 8.77618 1.04895
\(71\) −8.49886 −1.00863 −0.504315 0.863520i \(-0.668255\pi\)
−0.504315 + 0.863520i \(0.668255\pi\)
\(72\) −1.56782 −0.184769
\(73\) 5.95291 0.696735 0.348368 0.937358i \(-0.386736\pi\)
0.348368 + 0.937358i \(0.386736\pi\)
\(74\) −3.21993 −0.374310
\(75\) 12.1357 1.40131
\(76\) 0.817698 0.0937963
\(77\) 5.18273 0.590627
\(78\) 0 0
\(79\) −8.91459 −1.00297 −0.501485 0.865166i \(-0.667213\pi\)
−0.501485 + 0.865166i \(0.667213\pi\)
\(80\) 12.5179 1.39954
\(81\) 1.00000 0.111111
\(82\) −3.59392 −0.396882
\(83\) 0.457495 0.0502166 0.0251083 0.999685i \(-0.492007\pi\)
0.0251083 + 0.999685i \(0.492007\pi\)
\(84\) −9.49821 −1.03634
\(85\) −2.02311 −0.219437
\(86\) −1.87154 −0.201814
\(87\) −6.58571 −0.706062
\(88\) −1.56782 −0.167130
\(89\) −4.68461 −0.496568 −0.248284 0.968687i \(-0.579867\pi\)
−0.248284 + 0.968687i \(0.579867\pi\)
\(90\) 1.69335 0.178495
\(91\) 0 0
\(92\) −10.0958 −1.05256
\(93\) 1.52580 0.158218
\(94\) 2.21748 0.228716
\(95\) −1.84697 −0.189496
\(96\) 4.37265 0.446282
\(97\) −2.06057 −0.209219 −0.104609 0.994513i \(-0.533359\pi\)
−0.104609 + 0.994513i \(0.533359\pi\)
\(98\) 8.12439 0.820687
\(99\) 1.00000 0.100504
\(100\) −22.2407 −2.22407
\(101\) 3.86561 0.384642 0.192321 0.981332i \(-0.438398\pi\)
0.192321 + 0.981332i \(0.438398\pi\)
\(102\) −0.199924 −0.0197954
\(103\) 0.350877 0.0345730 0.0172865 0.999851i \(-0.494497\pi\)
0.0172865 + 0.999851i \(0.494497\pi\)
\(104\) 0 0
\(105\) 21.4541 2.09370
\(106\) 3.54530 0.344350
\(107\) −12.5796 −1.21612 −0.608060 0.793891i \(-0.708052\pi\)
−0.608060 + 0.793891i \(0.708052\pi\)
\(108\) −1.83266 −0.176348
\(109\) −4.61460 −0.441999 −0.220999 0.975274i \(-0.570932\pi\)
−0.220999 + 0.975274i \(0.570932\pi\)
\(110\) 1.69335 0.161455
\(111\) −7.87139 −0.747119
\(112\) 15.6725 1.48091
\(113\) 2.22602 0.209407 0.104703 0.994504i \(-0.466611\pi\)
0.104703 + 0.994504i \(0.466611\pi\)
\(114\) −0.182518 −0.0170944
\(115\) 22.8039 2.12648
\(116\) 12.0694 1.12061
\(117\) 0 0
\(118\) 2.29280 0.211069
\(119\) −2.53296 −0.232196
\(120\) −6.49004 −0.592457
\(121\) 1.00000 0.0909091
\(122\) −0.350070 −0.0316939
\(123\) −8.78563 −0.792174
\(124\) −2.79627 −0.251113
\(125\) 29.5385 2.64200
\(126\) 2.12009 0.188873
\(127\) −18.2528 −1.61967 −0.809836 0.586656i \(-0.800444\pi\)
−0.809836 + 0.586656i \(0.800444\pi\)
\(128\) −10.4876 −0.926985
\(129\) −4.57514 −0.402818
\(130\) 0 0
\(131\) 3.18466 0.278245 0.139122 0.990275i \(-0.455572\pi\)
0.139122 + 0.990275i \(0.455572\pi\)
\(132\) −1.83266 −0.159513
\(133\) −2.31243 −0.200513
\(134\) −1.58499 −0.136922
\(135\) 4.13953 0.356274
\(136\) 0.766241 0.0657046
\(137\) −5.11813 −0.437271 −0.218635 0.975807i \(-0.570161\pi\)
−0.218635 + 0.975807i \(0.570161\pi\)
\(138\) 2.25348 0.191829
\(139\) −10.7714 −0.913617 −0.456809 0.889565i \(-0.651008\pi\)
−0.456809 + 0.889565i \(0.651008\pi\)
\(140\) −39.3181 −3.32299
\(141\) 5.42082 0.456515
\(142\) −3.47661 −0.291751
\(143\) 0 0
\(144\) 3.02398 0.251998
\(145\) −27.2617 −2.26396
\(146\) 2.43514 0.201534
\(147\) 19.8607 1.63809
\(148\) 14.4256 1.18578
\(149\) 4.42220 0.362281 0.181140 0.983457i \(-0.442021\pi\)
0.181140 + 0.983457i \(0.442021\pi\)
\(150\) 4.96433 0.405336
\(151\) −4.64014 −0.377609 −0.188805 0.982015i \(-0.560461\pi\)
−0.188805 + 0.982015i \(0.560461\pi\)
\(152\) 0.699530 0.0567394
\(153\) −0.488730 −0.0395115
\(154\) 2.12009 0.170842
\(155\) 6.31608 0.507320
\(156\) 0 0
\(157\) 10.8227 0.863745 0.431873 0.901935i \(-0.357853\pi\)
0.431873 + 0.901935i \(0.357853\pi\)
\(158\) −3.64667 −0.290114
\(159\) 8.66677 0.687319
\(160\) 18.1007 1.43099
\(161\) 28.5508 2.25011
\(162\) 0.409068 0.0321394
\(163\) −24.4714 −1.91675 −0.958373 0.285519i \(-0.907834\pi\)
−0.958373 + 0.285519i \(0.907834\pi\)
\(164\) 16.1011 1.25729
\(165\) 4.13953 0.322262
\(166\) 0.187147 0.0145254
\(167\) −1.26722 −0.0980603 −0.0490302 0.998797i \(-0.515613\pi\)
−0.0490302 + 0.998797i \(0.515613\pi\)
\(168\) −8.12559 −0.626903
\(169\) 0 0
\(170\) −0.827590 −0.0634733
\(171\) −0.446180 −0.0341202
\(172\) 8.38469 0.639326
\(173\) 3.24638 0.246818 0.123409 0.992356i \(-0.460617\pi\)
0.123409 + 0.992356i \(0.460617\pi\)
\(174\) −2.69400 −0.204232
\(175\) 62.8961 4.75450
\(176\) 3.02398 0.227941
\(177\) 5.60493 0.421292
\(178\) −1.91633 −0.143635
\(179\) −16.5303 −1.23553 −0.617765 0.786363i \(-0.711962\pi\)
−0.617765 + 0.786363i \(0.711962\pi\)
\(180\) −7.58636 −0.565454
\(181\) 12.2065 0.907303 0.453651 0.891179i \(-0.350121\pi\)
0.453651 + 0.891179i \(0.350121\pi\)
\(182\) 0 0
\(183\) −0.855775 −0.0632607
\(184\) −8.63684 −0.636717
\(185\) −32.5838 −2.39561
\(186\) 0.624155 0.0457653
\(187\) −0.488730 −0.0357395
\(188\) −9.93454 −0.724551
\(189\) 5.18273 0.376988
\(190\) −0.755539 −0.0548125
\(191\) −17.4410 −1.26199 −0.630995 0.775787i \(-0.717353\pi\)
−0.630995 + 0.775787i \(0.717353\pi\)
\(192\) −4.25925 −0.307385
\(193\) −0.941498 −0.0677705 −0.0338852 0.999426i \(-0.510788\pi\)
−0.0338852 + 0.999426i \(0.510788\pi\)
\(194\) −0.842912 −0.0605175
\(195\) 0 0
\(196\) −36.3980 −2.59986
\(197\) 16.7419 1.19281 0.596404 0.802684i \(-0.296596\pi\)
0.596404 + 0.802684i \(0.296596\pi\)
\(198\) 0.409068 0.0290712
\(199\) 13.1573 0.932693 0.466347 0.884602i \(-0.345570\pi\)
0.466347 + 0.884602i \(0.345570\pi\)
\(200\) −19.0266 −1.34538
\(201\) −3.87464 −0.273296
\(202\) 1.58130 0.111260
\(203\) −34.1320 −2.39560
\(204\) 0.895677 0.0627100
\(205\) −36.3684 −2.54008
\(206\) 0.143533 0.0100004
\(207\) 5.50882 0.382890
\(208\) 0 0
\(209\) −0.446180 −0.0308629
\(210\) 8.77618 0.605614
\(211\) 13.5657 0.933898 0.466949 0.884284i \(-0.345353\pi\)
0.466949 + 0.884284i \(0.345353\pi\)
\(212\) −15.8833 −1.09087
\(213\) −8.49886 −0.582332
\(214\) −5.14593 −0.351768
\(215\) −18.9389 −1.29162
\(216\) −1.56782 −0.106677
\(217\) 7.90780 0.536816
\(218\) −1.88769 −0.127850
\(219\) 5.95291 0.402260
\(220\) −7.58636 −0.511473
\(221\) 0 0
\(222\) −3.21993 −0.216108
\(223\) 11.8725 0.795044 0.397522 0.917593i \(-0.369870\pi\)
0.397522 + 0.917593i \(0.369870\pi\)
\(224\) 22.6623 1.51419
\(225\) 12.1357 0.809047
\(226\) 0.910595 0.0605719
\(227\) −13.0255 −0.864532 −0.432266 0.901746i \(-0.642286\pi\)
−0.432266 + 0.901746i \(0.642286\pi\)
\(228\) 0.817698 0.0541533
\(229\) 6.45867 0.426801 0.213401 0.976965i \(-0.431546\pi\)
0.213401 + 0.976965i \(0.431546\pi\)
\(230\) 9.32836 0.615094
\(231\) 5.18273 0.340999
\(232\) 10.3252 0.677883
\(233\) −13.2616 −0.868795 −0.434397 0.900721i \(-0.643039\pi\)
−0.434397 + 0.900721i \(0.643039\pi\)
\(234\) 0 0
\(235\) 22.4396 1.46380
\(236\) −10.2720 −0.668647
\(237\) −8.91459 −0.579065
\(238\) −1.03615 −0.0671637
\(239\) 0.426040 0.0275583 0.0137791 0.999905i \(-0.495614\pi\)
0.0137791 + 0.999905i \(0.495614\pi\)
\(240\) 12.5179 0.808024
\(241\) 12.9860 0.836503 0.418251 0.908331i \(-0.362643\pi\)
0.418251 + 0.908331i \(0.362643\pi\)
\(242\) 0.409068 0.0262959
\(243\) 1.00000 0.0641500
\(244\) 1.56835 0.100403
\(245\) 82.2141 5.25246
\(246\) −3.59392 −0.229140
\(247\) 0 0
\(248\) −2.39218 −0.151903
\(249\) 0.457495 0.0289926
\(250\) 12.0832 0.764211
\(251\) 4.37202 0.275959 0.137980 0.990435i \(-0.455939\pi\)
0.137980 + 0.990435i \(0.455939\pi\)
\(252\) −9.49821 −0.598331
\(253\) 5.50882 0.346337
\(254\) −7.46663 −0.468498
\(255\) −2.02311 −0.126692
\(256\) 4.22834 0.264271
\(257\) −11.2798 −0.703614 −0.351807 0.936073i \(-0.614433\pi\)
−0.351807 + 0.936073i \(0.614433\pi\)
\(258\) −1.87154 −0.116517
\(259\) −40.7953 −2.53490
\(260\) 0 0
\(261\) −6.58571 −0.407645
\(262\) 1.30274 0.0804836
\(263\) −0.914614 −0.0563975 −0.0281988 0.999602i \(-0.508977\pi\)
−0.0281988 + 0.999602i \(0.508977\pi\)
\(264\) −1.56782 −0.0964927
\(265\) 35.8763 2.20387
\(266\) −0.945942 −0.0579994
\(267\) −4.68461 −0.286694
\(268\) 7.10091 0.433757
\(269\) 13.1384 0.801064 0.400532 0.916283i \(-0.368825\pi\)
0.400532 + 0.916283i \(0.368825\pi\)
\(270\) 1.69335 0.103054
\(271\) −12.3173 −0.748224 −0.374112 0.927384i \(-0.622052\pi\)
−0.374112 + 0.927384i \(0.622052\pi\)
\(272\) −1.47791 −0.0896115
\(273\) 0 0
\(274\) −2.09366 −0.126483
\(275\) 12.1357 0.731810
\(276\) −10.0958 −0.607697
\(277\) −20.1395 −1.21006 −0.605031 0.796202i \(-0.706839\pi\)
−0.605031 + 0.796202i \(0.706839\pi\)
\(278\) −4.40623 −0.264268
\(279\) 1.52580 0.0913471
\(280\) −33.6361 −2.01014
\(281\) −6.66666 −0.397699 −0.198850 0.980030i \(-0.563721\pi\)
−0.198850 + 0.980030i \(0.563721\pi\)
\(282\) 2.21748 0.132049
\(283\) 27.5589 1.63820 0.819102 0.573647i \(-0.194472\pi\)
0.819102 + 0.573647i \(0.194472\pi\)
\(284\) 15.5755 0.924239
\(285\) −1.84697 −0.109405
\(286\) 0 0
\(287\) −45.5336 −2.68776
\(288\) 4.37265 0.257661
\(289\) −16.7611 −0.985950
\(290\) −11.1519 −0.654863
\(291\) −2.06057 −0.120793
\(292\) −10.9097 −0.638440
\(293\) −13.8127 −0.806945 −0.403472 0.914992i \(-0.632197\pi\)
−0.403472 + 0.914992i \(0.632197\pi\)
\(294\) 8.12439 0.473824
\(295\) 23.2018 1.35086
\(296\) 12.3409 0.717301
\(297\) 1.00000 0.0580259
\(298\) 1.80898 0.104791
\(299\) 0 0
\(300\) −22.2407 −1.28406
\(301\) −23.7117 −1.36672
\(302\) −1.89813 −0.109225
\(303\) 3.86561 0.222073
\(304\) −1.34924 −0.0773842
\(305\) −3.54251 −0.202843
\(306\) −0.199924 −0.0114289
\(307\) 21.0868 1.20349 0.601743 0.798690i \(-0.294473\pi\)
0.601743 + 0.798690i \(0.294473\pi\)
\(308\) −9.49821 −0.541210
\(309\) 0.350877 0.0199607
\(310\) 2.58371 0.146745
\(311\) −29.7858 −1.68900 −0.844498 0.535558i \(-0.820101\pi\)
−0.844498 + 0.535558i \(0.820101\pi\)
\(312\) 0 0
\(313\) 26.3709 1.49057 0.745287 0.666744i \(-0.232312\pi\)
0.745287 + 0.666744i \(0.232312\pi\)
\(314\) 4.42722 0.249842
\(315\) 21.4541 1.20880
\(316\) 16.3374 0.919053
\(317\) 24.5073 1.37647 0.688233 0.725490i \(-0.258387\pi\)
0.688233 + 0.725490i \(0.258387\pi\)
\(318\) 3.54530 0.198810
\(319\) −6.58571 −0.368729
\(320\) −17.6313 −0.985619
\(321\) −12.5796 −0.702127
\(322\) 11.6792 0.650857
\(323\) 0.218061 0.0121333
\(324\) −1.83266 −0.101815
\(325\) 0 0
\(326\) −10.0105 −0.554428
\(327\) −4.61460 −0.255188
\(328\) 13.7743 0.760558
\(329\) 28.0947 1.54891
\(330\) 1.69335 0.0932158
\(331\) 10.4965 0.576939 0.288469 0.957489i \(-0.406854\pi\)
0.288469 + 0.957489i \(0.406854\pi\)
\(332\) −0.838434 −0.0460150
\(333\) −7.87139 −0.431349
\(334\) −0.518379 −0.0283644
\(335\) −16.0392 −0.876315
\(336\) 15.6725 0.855004
\(337\) 21.9103 1.19353 0.596765 0.802416i \(-0.296453\pi\)
0.596765 + 0.802416i \(0.296453\pi\)
\(338\) 0 0
\(339\) 2.22602 0.120901
\(340\) 3.70768 0.201077
\(341\) 1.52580 0.0826266
\(342\) −0.182518 −0.00986944
\(343\) 66.6537 3.59896
\(344\) 7.17299 0.386742
\(345\) 22.8039 1.22772
\(346\) 1.32799 0.0713933
\(347\) −16.4119 −0.881036 −0.440518 0.897744i \(-0.645205\pi\)
−0.440518 + 0.897744i \(0.645205\pi\)
\(348\) 12.0694 0.646987
\(349\) −25.0915 −1.34312 −0.671559 0.740951i \(-0.734375\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(350\) 25.7288 1.37526
\(351\) 0 0
\(352\) 4.37265 0.233063
\(353\) 9.19662 0.489486 0.244743 0.969588i \(-0.421296\pi\)
0.244743 + 0.969588i \(0.421296\pi\)
\(354\) 2.29280 0.121861
\(355\) −35.1813 −1.86723
\(356\) 8.58532 0.455021
\(357\) −2.53296 −0.134058
\(358\) −6.76200 −0.357383
\(359\) 22.6236 1.19403 0.597013 0.802231i \(-0.296354\pi\)
0.597013 + 0.802231i \(0.296354\pi\)
\(360\) −6.49004 −0.342055
\(361\) −18.8009 −0.989522
\(362\) 4.99329 0.262442
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 24.6422 1.28983
\(366\) −0.350070 −0.0182985
\(367\) −13.9344 −0.727371 −0.363685 0.931522i \(-0.618482\pi\)
−0.363685 + 0.931522i \(0.618482\pi\)
\(368\) 16.6586 0.868388
\(369\) −8.78563 −0.457362
\(370\) −13.3290 −0.692942
\(371\) 44.9175 2.33200
\(372\) −2.79627 −0.144980
\(373\) 20.5104 1.06199 0.530995 0.847375i \(-0.321818\pi\)
0.530995 + 0.847375i \(0.321818\pi\)
\(374\) −0.199924 −0.0103378
\(375\) 29.5385 1.52536
\(376\) −8.49887 −0.438296
\(377\) 0 0
\(378\) 2.12009 0.109046
\(379\) −2.32811 −0.119587 −0.0597934 0.998211i \(-0.519044\pi\)
−0.0597934 + 0.998211i \(0.519044\pi\)
\(380\) 3.38488 0.173641
\(381\) −18.2528 −0.935118
\(382\) −7.13457 −0.365037
\(383\) 27.2203 1.39089 0.695447 0.718578i \(-0.255207\pi\)
0.695447 + 0.718578i \(0.255207\pi\)
\(384\) −10.4876 −0.535195
\(385\) 21.4541 1.09340
\(386\) −0.385137 −0.0196029
\(387\) −4.57514 −0.232567
\(388\) 3.77632 0.191714
\(389\) −24.9318 −1.26409 −0.632047 0.774930i \(-0.717785\pi\)
−0.632047 + 0.774930i \(0.717785\pi\)
\(390\) 0 0
\(391\) −2.69233 −0.136157
\(392\) −31.1381 −1.57271
\(393\) 3.18466 0.160645
\(394\) 6.84856 0.345026
\(395\) −36.9022 −1.85675
\(396\) −1.83266 −0.0920948
\(397\) −31.3269 −1.57225 −0.786126 0.618066i \(-0.787916\pi\)
−0.786126 + 0.618066i \(0.787916\pi\)
\(398\) 5.38222 0.269786
\(399\) −2.31243 −0.115766
\(400\) 36.6981 1.83491
\(401\) 8.94790 0.446837 0.223418 0.974723i \(-0.428278\pi\)
0.223418 + 0.974723i \(0.428278\pi\)
\(402\) −1.58499 −0.0790522
\(403\) 0 0
\(404\) −7.08435 −0.352460
\(405\) 4.13953 0.205695
\(406\) −13.9623 −0.692937
\(407\) −7.87139 −0.390170
\(408\) 0.766241 0.0379346
\(409\) −30.0934 −1.48802 −0.744012 0.668166i \(-0.767079\pi\)
−0.744012 + 0.668166i \(0.767079\pi\)
\(410\) −14.8771 −0.734730
\(411\) −5.11813 −0.252459
\(412\) −0.643040 −0.0316803
\(413\) 29.0489 1.42940
\(414\) 2.25348 0.110753
\(415\) 1.89381 0.0929636
\(416\) 0 0
\(417\) −10.7714 −0.527477
\(418\) −0.182518 −0.00892725
\(419\) 32.6525 1.59518 0.797588 0.603202i \(-0.206109\pi\)
0.797588 + 0.603202i \(0.206109\pi\)
\(420\) −39.3181 −1.91853
\(421\) −28.3956 −1.38392 −0.691958 0.721938i \(-0.743252\pi\)
−0.691958 + 0.721938i \(0.743252\pi\)
\(422\) 5.54928 0.270135
\(423\) 5.42082 0.263569
\(424\) −13.5879 −0.659888
\(425\) −5.93108 −0.287700
\(426\) −3.47661 −0.168442
\(427\) −4.43525 −0.214637
\(428\) 23.0542 1.11437
\(429\) 0 0
\(430\) −7.74731 −0.373608
\(431\) 14.1585 0.681992 0.340996 0.940065i \(-0.389236\pi\)
0.340996 + 0.940065i \(0.389236\pi\)
\(432\) 3.02398 0.145491
\(433\) 15.5980 0.749590 0.374795 0.927108i \(-0.377713\pi\)
0.374795 + 0.927108i \(0.377713\pi\)
\(434\) 3.23483 0.155277
\(435\) −27.2617 −1.30710
\(436\) 8.45701 0.405017
\(437\) −2.45793 −0.117579
\(438\) 2.43514 0.116356
\(439\) 16.0616 0.766579 0.383289 0.923628i \(-0.374791\pi\)
0.383289 + 0.923628i \(0.374791\pi\)
\(440\) −6.49004 −0.309400
\(441\) 19.8607 0.945749
\(442\) 0 0
\(443\) −8.20834 −0.389990 −0.194995 0.980804i \(-0.562469\pi\)
−0.194995 + 0.980804i \(0.562469\pi\)
\(444\) 14.4256 0.684609
\(445\) −19.3921 −0.919273
\(446\) 4.85668 0.229970
\(447\) 4.42220 0.209163
\(448\) −22.0746 −1.04292
\(449\) 10.4304 0.492242 0.246121 0.969239i \(-0.420844\pi\)
0.246121 + 0.969239i \(0.420844\pi\)
\(450\) 4.96433 0.234021
\(451\) −8.78563 −0.413699
\(452\) −4.07955 −0.191886
\(453\) −4.64014 −0.218013
\(454\) −5.32831 −0.250070
\(455\) 0 0
\(456\) 0.699530 0.0327585
\(457\) −18.1240 −0.847807 −0.423904 0.905707i \(-0.639340\pi\)
−0.423904 + 0.905707i \(0.639340\pi\)
\(458\) 2.64204 0.123454
\(459\) −0.488730 −0.0228120
\(460\) −41.7919 −1.94856
\(461\) 28.6242 1.33316 0.666581 0.745432i \(-0.267757\pi\)
0.666581 + 0.745432i \(0.267757\pi\)
\(462\) 2.12009 0.0986356
\(463\) −9.44955 −0.439158 −0.219579 0.975595i \(-0.570468\pi\)
−0.219579 + 0.975595i \(0.570468\pi\)
\(464\) −19.9151 −0.924534
\(465\) 6.31608 0.292901
\(466\) −5.42489 −0.251303
\(467\) 19.1423 0.885800 0.442900 0.896571i \(-0.353950\pi\)
0.442900 + 0.896571i \(0.353950\pi\)
\(468\) 0 0
\(469\) −20.0812 −0.927265
\(470\) 9.17934 0.423412
\(471\) 10.8227 0.498683
\(472\) −8.78753 −0.404479
\(473\) −4.57514 −0.210365
\(474\) −3.64667 −0.167497
\(475\) −5.41471 −0.248444
\(476\) 4.64206 0.212768
\(477\) 8.66677 0.396824
\(478\) 0.174280 0.00797136
\(479\) 11.5433 0.527428 0.263714 0.964601i \(-0.415052\pi\)
0.263714 + 0.964601i \(0.415052\pi\)
\(480\) 18.1007 0.826182
\(481\) 0 0
\(482\) 5.31216 0.241962
\(483\) 28.5508 1.29910
\(484\) −1.83266 −0.0833029
\(485\) −8.52977 −0.387317
\(486\) 0.409068 0.0185557
\(487\) 34.7318 1.57385 0.786923 0.617051i \(-0.211673\pi\)
0.786923 + 0.617051i \(0.211673\pi\)
\(488\) 1.34170 0.0607360
\(489\) −24.4714 −1.10663
\(490\) 33.6311 1.51930
\(491\) 19.9935 0.902295 0.451148 0.892449i \(-0.351015\pi\)
0.451148 + 0.892449i \(0.351015\pi\)
\(492\) 16.1011 0.725894
\(493\) 3.21863 0.144960
\(494\) 0 0
\(495\) 4.13953 0.186058
\(496\) 4.61398 0.207174
\(497\) −44.0473 −1.97579
\(498\) 0.187147 0.00838624
\(499\) −10.3565 −0.463623 −0.231811 0.972761i \(-0.574465\pi\)
−0.231811 + 0.972761i \(0.574465\pi\)
\(500\) −54.1340 −2.42095
\(501\) −1.26722 −0.0566151
\(502\) 1.78845 0.0798226
\(503\) 41.2438 1.83897 0.919486 0.393124i \(-0.128606\pi\)
0.919486 + 0.393124i \(0.128606\pi\)
\(504\) −8.12559 −0.361943
\(505\) 16.0018 0.712070
\(506\) 2.25348 0.100180
\(507\) 0 0
\(508\) 33.4512 1.48416
\(509\) 9.47338 0.419900 0.209950 0.977712i \(-0.432670\pi\)
0.209950 + 0.977712i \(0.432670\pi\)
\(510\) −0.827590 −0.0366463
\(511\) 30.8523 1.36483
\(512\) 22.7049 1.00343
\(513\) −0.446180 −0.0196993
\(514\) −4.61420 −0.203524
\(515\) 1.45247 0.0640033
\(516\) 8.38469 0.369115
\(517\) 5.42082 0.238407
\(518\) −16.6881 −0.733231
\(519\) 3.24638 0.142500
\(520\) 0 0
\(521\) −6.47023 −0.283466 −0.141733 0.989905i \(-0.545267\pi\)
−0.141733 + 0.989905i \(0.545267\pi\)
\(522\) −2.69400 −0.117913
\(523\) 16.1999 0.708372 0.354186 0.935175i \(-0.384758\pi\)
0.354186 + 0.935175i \(0.384758\pi\)
\(524\) −5.83640 −0.254964
\(525\) 62.8961 2.74501
\(526\) −0.374140 −0.0163133
\(527\) −0.745703 −0.0324833
\(528\) 3.02398 0.131602
\(529\) 7.34712 0.319440
\(530\) 14.6759 0.637479
\(531\) 5.60493 0.243233
\(532\) 4.23791 0.183737
\(533\) 0 0
\(534\) −1.91633 −0.0829275
\(535\) −52.0738 −2.25135
\(536\) 6.07474 0.262389
\(537\) −16.5303 −0.713334
\(538\) 5.37451 0.231712
\(539\) 19.8607 0.855462
\(540\) −7.58636 −0.326465
\(541\) −6.65767 −0.286236 −0.143118 0.989706i \(-0.545713\pi\)
−0.143118 + 0.989706i \(0.545713\pi\)
\(542\) −5.03862 −0.216427
\(543\) 12.2065 0.523832
\(544\) −2.13705 −0.0916251
\(545\) −19.1023 −0.818252
\(546\) 0 0
\(547\) 2.06963 0.0884912 0.0442456 0.999021i \(-0.485912\pi\)
0.0442456 + 0.999021i \(0.485912\pi\)
\(548\) 9.37980 0.400685
\(549\) −0.855775 −0.0365236
\(550\) 4.96433 0.211680
\(551\) 2.93841 0.125181
\(552\) −8.63684 −0.367608
\(553\) −46.2020 −1.96471
\(554\) −8.23841 −0.350016
\(555\) −32.5838 −1.38311
\(556\) 19.7403 0.837176
\(557\) 12.3459 0.523111 0.261556 0.965188i \(-0.415764\pi\)
0.261556 + 0.965188i \(0.415764\pi\)
\(558\) 0.624155 0.0264226
\(559\) 0 0
\(560\) 64.8767 2.74154
\(561\) −0.488730 −0.0206342
\(562\) −2.72712 −0.115037
\(563\) −3.72355 −0.156929 −0.0784645 0.996917i \(-0.525002\pi\)
−0.0784645 + 0.996917i \(0.525002\pi\)
\(564\) −9.93454 −0.418320
\(565\) 9.21469 0.387665
\(566\) 11.2735 0.473859
\(567\) 5.18273 0.217654
\(568\) 13.3247 0.559091
\(569\) 27.2092 1.14067 0.570334 0.821413i \(-0.306814\pi\)
0.570334 + 0.821413i \(0.306814\pi\)
\(570\) −0.755539 −0.0316460
\(571\) 31.1102 1.30192 0.650961 0.759112i \(-0.274366\pi\)
0.650961 + 0.759112i \(0.274366\pi\)
\(572\) 0 0
\(573\) −17.4410 −0.728610
\(574\) −18.6263 −0.777448
\(575\) 66.8534 2.78798
\(576\) −4.25925 −0.177469
\(577\) −5.53948 −0.230611 −0.115306 0.993330i \(-0.536785\pi\)
−0.115306 + 0.993330i \(0.536785\pi\)
\(578\) −6.85645 −0.285191
\(579\) −0.941498 −0.0391273
\(580\) 49.9616 2.07454
\(581\) 2.37107 0.0983687
\(582\) −0.842912 −0.0349398
\(583\) 8.66677 0.358941
\(584\) −9.33309 −0.386206
\(585\) 0 0
\(586\) −5.65032 −0.233413
\(587\) −27.8516 −1.14956 −0.574780 0.818308i \(-0.694912\pi\)
−0.574780 + 0.818308i \(0.694912\pi\)
\(588\) −36.3980 −1.50103
\(589\) −0.680780 −0.0280511
\(590\) 9.49111 0.390743
\(591\) 16.7419 0.688668
\(592\) −23.8029 −0.978294
\(593\) −0.298235 −0.0122470 −0.00612351 0.999981i \(-0.501949\pi\)
−0.00612351 + 0.999981i \(0.501949\pi\)
\(594\) 0.409068 0.0167843
\(595\) −10.4852 −0.429853
\(596\) −8.10440 −0.331969
\(597\) 13.1573 0.538491
\(598\) 0 0
\(599\) 22.8194 0.932375 0.466188 0.884686i \(-0.345627\pi\)
0.466188 + 0.884686i \(0.345627\pi\)
\(600\) −19.0266 −0.776758
\(601\) −2.27297 −0.0927164 −0.0463582 0.998925i \(-0.514762\pi\)
−0.0463582 + 0.998925i \(0.514762\pi\)
\(602\) −9.69971 −0.395331
\(603\) −3.87464 −0.157788
\(604\) 8.50381 0.346015
\(605\) 4.13953 0.168296
\(606\) 1.58130 0.0642358
\(607\) −4.31576 −0.175171 −0.0875857 0.996157i \(-0.527915\pi\)
−0.0875857 + 0.996157i \(0.527915\pi\)
\(608\) −1.95099 −0.0791231
\(609\) −34.1320 −1.38310
\(610\) −1.44913 −0.0586734
\(611\) 0 0
\(612\) 0.895677 0.0362056
\(613\) 11.3555 0.458646 0.229323 0.973350i \(-0.426349\pi\)
0.229323 + 0.973350i \(0.426349\pi\)
\(614\) 8.62593 0.348114
\(615\) −36.3684 −1.46651
\(616\) −8.12559 −0.327390
\(617\) −23.6846 −0.953507 −0.476753 0.879037i \(-0.658186\pi\)
−0.476753 + 0.879037i \(0.658186\pi\)
\(618\) 0.143533 0.00577373
\(619\) −27.4080 −1.10162 −0.550810 0.834631i \(-0.685681\pi\)
−0.550810 + 0.834631i \(0.685681\pi\)
\(620\) −11.5753 −0.464873
\(621\) 5.50882 0.221061
\(622\) −12.1844 −0.488550
\(623\) −24.2791 −0.972721
\(624\) 0 0
\(625\) 61.5968 2.46387
\(626\) 10.7875 0.431156
\(627\) −0.446180 −0.0178187
\(628\) −19.8344 −0.791477
\(629\) 3.84698 0.153389
\(630\) 8.77618 0.349651
\(631\) 42.3930 1.68764 0.843819 0.536627i \(-0.180302\pi\)
0.843819 + 0.536627i \(0.180302\pi\)
\(632\) 13.9765 0.555954
\(633\) 13.5657 0.539186
\(634\) 10.0251 0.398149
\(635\) −75.5579 −2.99842
\(636\) −15.8833 −0.629812
\(637\) 0 0
\(638\) −2.69400 −0.106657
\(639\) −8.49886 −0.336210
\(640\) −43.4139 −1.71608
\(641\) 18.4040 0.726916 0.363458 0.931611i \(-0.381596\pi\)
0.363458 + 0.931611i \(0.381596\pi\)
\(642\) −5.14593 −0.203094
\(643\) 0.572048 0.0225594 0.0112797 0.999936i \(-0.496409\pi\)
0.0112797 + 0.999936i \(0.496409\pi\)
\(644\) −52.3239 −2.06185
\(645\) −18.9389 −0.745719
\(646\) 0.0892020 0.00350961
\(647\) 16.2324 0.638163 0.319082 0.947727i \(-0.396626\pi\)
0.319082 + 0.947727i \(0.396626\pi\)
\(648\) −1.56782 −0.0615898
\(649\) 5.60493 0.220013
\(650\) 0 0
\(651\) 7.90780 0.309931
\(652\) 44.8478 1.75638
\(653\) −2.56096 −0.100218 −0.0501090 0.998744i \(-0.515957\pi\)
−0.0501090 + 0.998744i \(0.515957\pi\)
\(654\) −1.88769 −0.0738144
\(655\) 13.1830 0.515102
\(656\) −26.5676 −1.03729
\(657\) 5.95291 0.232245
\(658\) 11.4926 0.448029
\(659\) −37.8432 −1.47416 −0.737082 0.675804i \(-0.763797\pi\)
−0.737082 + 0.675804i \(0.763797\pi\)
\(660\) −7.58636 −0.295299
\(661\) 33.9955 1.32227 0.661135 0.750267i \(-0.270075\pi\)
0.661135 + 0.750267i \(0.270075\pi\)
\(662\) 4.29378 0.166882
\(663\) 0 0
\(664\) −0.717270 −0.0278355
\(665\) −9.57238 −0.371201
\(666\) −3.21993 −0.124770
\(667\) −36.2795 −1.40475
\(668\) 2.32238 0.0898558
\(669\) 11.8725 0.459019
\(670\) −6.56112 −0.253478
\(671\) −0.855775 −0.0330368
\(672\) 22.6623 0.874217
\(673\) −34.7689 −1.34024 −0.670122 0.742251i \(-0.733758\pi\)
−0.670122 + 0.742251i \(0.733758\pi\)
\(674\) 8.96280 0.345234
\(675\) 12.1357 0.467103
\(676\) 0 0
\(677\) −31.6215 −1.21531 −0.607656 0.794201i \(-0.707890\pi\)
−0.607656 + 0.794201i \(0.707890\pi\)
\(678\) 0.910595 0.0349712
\(679\) −10.6794 −0.409836
\(680\) 3.17188 0.121636
\(681\) −13.0255 −0.499138
\(682\) 0.624155 0.0239001
\(683\) 29.1127 1.11397 0.556984 0.830523i \(-0.311959\pi\)
0.556984 + 0.830523i \(0.311959\pi\)
\(684\) 0.817698 0.0312654
\(685\) −21.1866 −0.809500
\(686\) 27.2659 1.04102
\(687\) 6.45867 0.246414
\(688\) −13.8351 −0.527459
\(689\) 0 0
\(690\) 9.32836 0.355125
\(691\) −6.72289 −0.255751 −0.127875 0.991790i \(-0.540816\pi\)
−0.127875 + 0.991790i \(0.540816\pi\)
\(692\) −5.94953 −0.226167
\(693\) 5.18273 0.196876
\(694\) −6.71357 −0.254844
\(695\) −44.5885 −1.69134
\(696\) 10.3252 0.391376
\(697\) 4.29380 0.162639
\(698\) −10.2641 −0.388503
\(699\) −13.2616 −0.501599
\(700\) −115.267 −4.35670
\(701\) −33.5332 −1.26653 −0.633265 0.773935i \(-0.718286\pi\)
−0.633265 + 0.773935i \(0.718286\pi\)
\(702\) 0 0
\(703\) 3.51205 0.132460
\(704\) −4.25925 −0.160526
\(705\) 22.4396 0.845126
\(706\) 3.76204 0.141586
\(707\) 20.0344 0.753471
\(708\) −10.2720 −0.386044
\(709\) −40.1123 −1.50645 −0.753224 0.657764i \(-0.771502\pi\)
−0.753224 + 0.657764i \(0.771502\pi\)
\(710\) −14.3915 −0.540105
\(711\) −8.91459 −0.334323
\(712\) 7.34463 0.275252
\(713\) 8.40535 0.314783
\(714\) −1.03615 −0.0387770
\(715\) 0 0
\(716\) 30.2944 1.13216
\(717\) 0.426040 0.0159108
\(718\) 9.25458 0.345378
\(719\) 7.15141 0.266703 0.133351 0.991069i \(-0.457426\pi\)
0.133351 + 0.991069i \(0.457426\pi\)
\(720\) 12.5179 0.466513
\(721\) 1.81850 0.0677246
\(722\) −7.69086 −0.286224
\(723\) 12.9860 0.482955
\(724\) −22.3704 −0.831390
\(725\) −79.9222 −2.96824
\(726\) 0.409068 0.0151819
\(727\) −38.2917 −1.42016 −0.710081 0.704120i \(-0.751342\pi\)
−0.710081 + 0.704120i \(0.751342\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 10.0804 0.373091
\(731\) 2.23601 0.0827017
\(732\) 1.56835 0.0579678
\(733\) −35.4025 −1.30762 −0.653811 0.756658i \(-0.726831\pi\)
−0.653811 + 0.756658i \(0.726831\pi\)
\(734\) −5.70013 −0.210395
\(735\) 82.2141 3.03251
\(736\) 24.0882 0.887902
\(737\) −3.87464 −0.142724
\(738\) −3.59392 −0.132294
\(739\) 2.87016 0.105580 0.0527902 0.998606i \(-0.483189\pi\)
0.0527902 + 0.998606i \(0.483189\pi\)
\(740\) 59.7152 2.19517
\(741\) 0 0
\(742\) 18.3743 0.674543
\(743\) 23.1129 0.847930 0.423965 0.905679i \(-0.360638\pi\)
0.423965 + 0.905679i \(0.360638\pi\)
\(744\) −2.39218 −0.0877014
\(745\) 18.3058 0.670673
\(746\) 8.39016 0.307185
\(747\) 0.457495 0.0167389
\(748\) 0.895677 0.0327492
\(749\) −65.1969 −2.38224
\(750\) 12.0832 0.441218
\(751\) −37.5587 −1.37054 −0.685268 0.728291i \(-0.740315\pi\)
−0.685268 + 0.728291i \(0.740315\pi\)
\(752\) 16.3925 0.597771
\(753\) 4.37202 0.159325
\(754\) 0 0
\(755\) −19.2080 −0.699050
\(756\) −9.49821 −0.345446
\(757\) −47.4259 −1.72372 −0.861862 0.507143i \(-0.830702\pi\)
−0.861862 + 0.507143i \(0.830702\pi\)
\(758\) −0.952354 −0.0345910
\(759\) 5.50882 0.199958
\(760\) 2.89572 0.105039
\(761\) 23.0592 0.835895 0.417947 0.908471i \(-0.362750\pi\)
0.417947 + 0.908471i \(0.362750\pi\)
\(762\) −7.46663 −0.270487
\(763\) −23.9163 −0.865826
\(764\) 31.9636 1.15640
\(765\) −2.02311 −0.0731458
\(766\) 11.1350 0.402323
\(767\) 0 0
\(768\) 4.22834 0.152577
\(769\) −40.2536 −1.45158 −0.725792 0.687915i \(-0.758526\pi\)
−0.725792 + 0.687915i \(0.758526\pi\)
\(770\) 8.77618 0.316272
\(771\) −11.2798 −0.406232
\(772\) 1.72545 0.0621003
\(773\) 25.6183 0.921426 0.460713 0.887549i \(-0.347594\pi\)
0.460713 + 0.887549i \(0.347594\pi\)
\(774\) −1.87154 −0.0672712
\(775\) 18.5166 0.665137
\(776\) 3.23060 0.115972
\(777\) −40.7953 −1.46352
\(778\) −10.1988 −0.365645
\(779\) 3.91997 0.140448
\(780\) 0 0
\(781\) −8.49886 −0.304113
\(782\) −1.10134 −0.0393840
\(783\) −6.58571 −0.235354
\(784\) 60.0585 2.14495
\(785\) 44.8009 1.59901
\(786\) 1.30274 0.0464673
\(787\) 23.3425 0.832070 0.416035 0.909349i \(-0.363419\pi\)
0.416035 + 0.909349i \(0.363419\pi\)
\(788\) −30.6822 −1.09301
\(789\) −0.914614 −0.0325611
\(790\) −15.0955 −0.537074
\(791\) 11.5369 0.410204
\(792\) −1.56782 −0.0557101
\(793\) 0 0
\(794\) −12.8148 −0.454781
\(795\) 35.8763 1.27240
\(796\) −24.1128 −0.854656
\(797\) −49.4116 −1.75025 −0.875125 0.483897i \(-0.839221\pi\)
−0.875125 + 0.483897i \(0.839221\pi\)
\(798\) −0.945942 −0.0334860
\(799\) −2.64932 −0.0937261
\(800\) 53.0652 1.87614
\(801\) −4.68461 −0.165523
\(802\) 3.66030 0.129250
\(803\) 5.95291 0.210074
\(804\) 7.10091 0.250430
\(805\) 118.187 4.16553
\(806\) 0 0
\(807\) 13.1384 0.462495
\(808\) −6.06058 −0.213210
\(809\) 22.7489 0.799810 0.399905 0.916556i \(-0.369043\pi\)
0.399905 + 0.916556i \(0.369043\pi\)
\(810\) 1.69335 0.0594982
\(811\) −23.4289 −0.822701 −0.411350 0.911477i \(-0.634943\pi\)
−0.411350 + 0.911477i \(0.634943\pi\)
\(812\) 62.5524 2.19516
\(813\) −12.3173 −0.431987
\(814\) −3.21993 −0.112859
\(815\) −101.300 −3.54838
\(816\) −1.47791 −0.0517372
\(817\) 2.04133 0.0714173
\(818\) −12.3103 −0.430418
\(819\) 0 0
\(820\) 66.6510 2.32755
\(821\) −6.75303 −0.235682 −0.117841 0.993032i \(-0.537597\pi\)
−0.117841 + 0.993032i \(0.537597\pi\)
\(822\) −2.09366 −0.0730248
\(823\) −36.4194 −1.26950 −0.634751 0.772717i \(-0.718897\pi\)
−0.634751 + 0.772717i \(0.718897\pi\)
\(824\) −0.550113 −0.0191641
\(825\) 12.1357 0.422511
\(826\) 11.8830 0.413461
\(827\) −49.2124 −1.71128 −0.855642 0.517569i \(-0.826837\pi\)
−0.855642 + 0.517569i \(0.826837\pi\)
\(828\) −10.0958 −0.350854
\(829\) 2.84332 0.0987525 0.0493762 0.998780i \(-0.484277\pi\)
0.0493762 + 0.998780i \(0.484277\pi\)
\(830\) 0.774699 0.0268902
\(831\) −20.1395 −0.698630
\(832\) 0 0
\(833\) −9.70653 −0.336311
\(834\) −4.40623 −0.152575
\(835\) −5.24569 −0.181535
\(836\) 0.817698 0.0282807
\(837\) 1.52580 0.0527393
\(838\) 13.3571 0.461413
\(839\) 8.15579 0.281569 0.140785 0.990040i \(-0.455038\pi\)
0.140785 + 0.990040i \(0.455038\pi\)
\(840\) −33.6361 −1.16056
\(841\) 14.3716 0.495571
\(842\) −11.6157 −0.400304
\(843\) −6.66666 −0.229612
\(844\) −24.8613 −0.855761
\(845\) 0 0
\(846\) 2.21748 0.0762387
\(847\) 5.18273 0.178081
\(848\) 26.2081 0.899991
\(849\) 27.5589 0.945818
\(850\) −2.42622 −0.0832185
\(851\) −43.3621 −1.48643
\(852\) 15.5755 0.533609
\(853\) 12.7020 0.434910 0.217455 0.976070i \(-0.430225\pi\)
0.217455 + 0.976070i \(0.430225\pi\)
\(854\) −1.81432 −0.0620848
\(855\) −1.84697 −0.0631652
\(856\) 19.7226 0.674105
\(857\) −50.4563 −1.72355 −0.861777 0.507287i \(-0.830648\pi\)
−0.861777 + 0.507287i \(0.830648\pi\)
\(858\) 0 0
\(859\) −8.22512 −0.280637 −0.140319 0.990106i \(-0.544813\pi\)
−0.140319 + 0.990106i \(0.544813\pi\)
\(860\) 34.7087 1.18356
\(861\) −45.5336 −1.55178
\(862\) 5.79180 0.197269
\(863\) −15.2200 −0.518094 −0.259047 0.965865i \(-0.583408\pi\)
−0.259047 + 0.965865i \(0.583408\pi\)
\(864\) 4.37265 0.148761
\(865\) 13.4385 0.456923
\(866\) 6.38063 0.216823
\(867\) −16.7611 −0.569238
\(868\) −14.4923 −0.491902
\(869\) −8.91459 −0.302407
\(870\) −11.1519 −0.378085
\(871\) 0 0
\(872\) 7.23487 0.245003
\(873\) −2.06057 −0.0697396
\(874\) −1.00546 −0.0340102
\(875\) 153.090 5.17538
\(876\) −10.9097 −0.368604
\(877\) −16.0542 −0.542113 −0.271057 0.962563i \(-0.587373\pi\)
−0.271057 + 0.962563i \(0.587373\pi\)
\(878\) 6.57029 0.221737
\(879\) −13.8127 −0.465890
\(880\) 12.5179 0.421977
\(881\) 51.9810 1.75128 0.875642 0.482961i \(-0.160439\pi\)
0.875642 + 0.482961i \(0.160439\pi\)
\(882\) 8.12439 0.273562
\(883\) −21.5188 −0.724164 −0.362082 0.932146i \(-0.617934\pi\)
−0.362082 + 0.932146i \(0.617934\pi\)
\(884\) 0 0
\(885\) 23.2018 0.779919
\(886\) −3.35777 −0.112806
\(887\) −18.2083 −0.611376 −0.305688 0.952132i \(-0.598887\pi\)
−0.305688 + 0.952132i \(0.598887\pi\)
\(888\) 12.3409 0.414134
\(889\) −94.5993 −3.17276
\(890\) −7.93269 −0.265904
\(891\) 1.00000 0.0335013
\(892\) −21.7584 −0.728524
\(893\) −2.41866 −0.0809374
\(894\) 1.80898 0.0605014
\(895\) −68.4275 −2.28728
\(896\) −54.3546 −1.81586
\(897\) 0 0
\(898\) 4.26676 0.142384
\(899\) −10.0485 −0.335135
\(900\) −22.2407 −0.741355
\(901\) −4.23571 −0.141112
\(902\) −3.59392 −0.119665
\(903\) −23.7117 −0.789077
\(904\) −3.49000 −0.116076
\(905\) 50.5292 1.67965
\(906\) −1.89813 −0.0630612
\(907\) −6.58414 −0.218623 −0.109311 0.994008i \(-0.534865\pi\)
−0.109311 + 0.994008i \(0.534865\pi\)
\(908\) 23.8713 0.792198
\(909\) 3.86561 0.128214
\(910\) 0 0
\(911\) −51.4764 −1.70549 −0.852745 0.522328i \(-0.825064\pi\)
−0.852745 + 0.522328i \(0.825064\pi\)
\(912\) −1.34924 −0.0446778
\(913\) 0.457495 0.0151409
\(914\) −7.41397 −0.245232
\(915\) −3.54251 −0.117112
\(916\) −11.8366 −0.391091
\(917\) 16.5052 0.545051
\(918\) −0.199924 −0.00659847
\(919\) −31.1301 −1.02689 −0.513443 0.858123i \(-0.671630\pi\)
−0.513443 + 0.858123i \(0.671630\pi\)
\(920\) −35.7525 −1.17872
\(921\) 21.0868 0.694833
\(922\) 11.7093 0.385624
\(923\) 0 0
\(924\) −9.49821 −0.312468
\(925\) −95.5248 −3.14084
\(926\) −3.86551 −0.127029
\(927\) 0.350877 0.0115243
\(928\) −28.7970 −0.945309
\(929\) 54.5430 1.78950 0.894749 0.446569i \(-0.147354\pi\)
0.894749 + 0.446569i \(0.147354\pi\)
\(930\) 2.58371 0.0847231
\(931\) −8.86146 −0.290423
\(932\) 24.3040 0.796104
\(933\) −29.7858 −0.975142
\(934\) 7.83051 0.256222
\(935\) −2.02311 −0.0661628
\(936\) 0 0
\(937\) −36.4863 −1.19195 −0.595977 0.803001i \(-0.703235\pi\)
−0.595977 + 0.803001i \(0.703235\pi\)
\(938\) −8.21459 −0.268216
\(939\) 26.3709 0.860583
\(940\) −41.1243 −1.34133
\(941\) 6.77293 0.220791 0.110396 0.993888i \(-0.464788\pi\)
0.110396 + 0.993888i \(0.464788\pi\)
\(942\) 4.42722 0.144247
\(943\) −48.3985 −1.57607
\(944\) 16.9492 0.551650
\(945\) 21.4541 0.697901
\(946\) −1.87154 −0.0608491
\(947\) −4.44833 −0.144551 −0.0722756 0.997385i \(-0.523026\pi\)
−0.0722756 + 0.997385i \(0.523026\pi\)
\(948\) 16.3374 0.530616
\(949\) 0 0
\(950\) −2.21498 −0.0718636
\(951\) 24.5073 0.794703
\(952\) 3.97122 0.128708
\(953\) −52.2252 −1.69174 −0.845870 0.533389i \(-0.820918\pi\)
−0.845870 + 0.533389i \(0.820918\pi\)
\(954\) 3.54530 0.114783
\(955\) −72.1977 −2.33626
\(956\) −0.780789 −0.0252525
\(957\) −6.58571 −0.212886
\(958\) 4.72201 0.152561
\(959\) −26.5259 −0.856565
\(960\) −17.6313 −0.569047
\(961\) −28.6719 −0.924901
\(962\) 0 0
\(963\) −12.5796 −0.405373
\(964\) −23.7990 −0.766514
\(965\) −3.89736 −0.125460
\(966\) 11.6792 0.375772
\(967\) 24.6459 0.792559 0.396279 0.918130i \(-0.370301\pi\)
0.396279 + 0.918130i \(0.370301\pi\)
\(968\) −1.56782 −0.0503917
\(969\) 0.218061 0.00700514
\(970\) −3.48926 −0.112033
\(971\) 16.6242 0.533495 0.266748 0.963766i \(-0.414051\pi\)
0.266748 + 0.963766i \(0.414051\pi\)
\(972\) −1.83266 −0.0587827
\(973\) −55.8252 −1.78967
\(974\) 14.2077 0.455243
\(975\) 0 0
\(976\) −2.58785 −0.0828350
\(977\) −11.6096 −0.371425 −0.185712 0.982604i \(-0.559459\pi\)
−0.185712 + 0.982604i \(0.559459\pi\)
\(978\) −10.0105 −0.320099
\(979\) −4.68461 −0.149721
\(980\) −150.671 −4.81300
\(981\) −4.61460 −0.147333
\(982\) 8.17871 0.260993
\(983\) 58.4986 1.86582 0.932908 0.360114i \(-0.117262\pi\)
0.932908 + 0.360114i \(0.117262\pi\)
\(984\) 13.7743 0.439108
\(985\) 69.3034 2.20819
\(986\) 1.31664 0.0419304
\(987\) 28.0947 0.894263
\(988\) 0 0
\(989\) −25.2036 −0.801429
\(990\) 1.69335 0.0538182
\(991\) 24.4396 0.776350 0.388175 0.921586i \(-0.373106\pi\)
0.388175 + 0.921586i \(0.373106\pi\)
\(992\) 6.67178 0.211829
\(993\) 10.4965 0.333096
\(994\) −18.0184 −0.571508
\(995\) 54.4649 1.72665
\(996\) −0.838434 −0.0265668
\(997\) −36.4681 −1.15496 −0.577478 0.816406i \(-0.695963\pi\)
−0.577478 + 0.816406i \(0.695963\pi\)
\(998\) −4.23653 −0.134105
\(999\) −7.87139 −0.249040
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.1.4 7
13.5 odd 4 429.2.b.b.298.7 14
13.8 odd 4 429.2.b.b.298.8 yes 14
13.12 even 2 5577.2.a.x.1.4 7
39.5 even 4 1287.2.b.c.298.8 14
39.8 even 4 1287.2.b.c.298.7 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.7 14 13.5 odd 4
429.2.b.b.298.8 yes 14 13.8 odd 4
1287.2.b.c.298.7 14 39.8 even 4
1287.2.b.c.298.8 14 39.5 even 4
5577.2.a.x.1.4 7 13.12 even 2
5577.2.a.y.1.4 7 1.1 even 1 trivial