Properties

Label 5577.2.a.x.1.4
Level $5577$
Weight $2$
Character 5577.1
Self dual yes
Analytic conductor $44.533$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.4
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 \(-0.546198\pi\)
−0.144627 + 0.989486i \(0.546198\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.83266 −0.916332
\(5\) −4.13953 −1.85125 −0.925627 0.378437i \(-0.876462\pi\)
−0.925627 + 0.378437i \(0.876462\pi\)
\(6\) −0.409068 −0.167001
\(7\) −5.18273 −1.95889 −0.979445 0.201714i \(-0.935349\pi\)
−0.979445 + 0.201714i \(0.935349\pi\)
\(8\) 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 \(-0.483702\pi\)
0.0511803 + 0.998689i \(0.483702\pi\)
\(20\) 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 \(-0.543753\pi\)
−0.137021 + 0.990568i \(0.543753\pi\)
\(32\) −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 \(-0.276013\pi\)
0.647024 + 0.762470i \(0.276013\pi\)
\(38\) −0.182518 −0.0296083
\(39\) 0 0
\(40\) −6.49004 −1.02617
\(41\) 8.78563 1.37209 0.686043 0.727561i \(-0.259346\pi\)
0.686043 + 0.727561i \(0.259346\pi\)
\(42\) 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 \(-0.629378\pi\)
−0.395354 + 0.918529i \(0.629378\pi\)
\(48\) 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 \(-0.618880\pi\)
−0.364850 + 0.931066i \(0.618880\pi\)
\(60\) 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 \(-0.423940\pi\)
0.236681 + 0.971587i \(0.423940\pi\)
\(68\) 0.895677 0.108617
\(69\) 5.50882 0.663184
\(70\) −8.77618 −1.04895
\(71\) 8.49886 1.00863 0.504315 0.863520i \(-0.331745\pi\)
0.504315 + 0.863520i \(0.331745\pi\)
\(72\) 1.56782 0.184769
\(73\) −5.95291 −0.696735 −0.348368 0.937358i \(-0.613264\pi\)
−0.348368 + 0.937358i \(0.613264\pi\)
\(74\) −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 \(-0.507993\pi\)
−0.0251083 + 0.999685i \(0.507993\pi\)
\(84\) 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 \(-0.420133\pi\)
0.248284 + 0.968687i \(0.420133\pi\)
\(90\) 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 \(-0.466641\pi\)
0.104609 + 0.994513i \(0.466641\pi\)
\(98\) −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 \(-0.429068\pi\)
0.220999 + 0.975274i \(0.429068\pi\)
\(110\) −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 \(-0.429839\pi\)
0.218635 + 0.975807i \(0.429839\pi\)
\(138\) −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 \(-0.557979\pi\)
−0.181140 + 0.983457i \(0.557979\pi\)
\(150\) −4.96433 −0.405336
\(151\) 4.64014 0.377609 0.188805 0.982015i \(-0.439539\pi\)
0.188805 + 0.982015i \(0.439539\pi\)
\(152\) 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 \(-0.0921659\pi\)
0.958373 + 0.285519i \(0.0921659\pi\)
\(164\) −16.1011 −1.25729
\(165\) 4.13953 0.322262
\(166\) 0.187147 0.0145254
\(167\) 1.26722 0.0980603 0.0490302 0.998797i \(-0.484387\pi\)
0.0490302 + 0.998797i \(0.484387\pi\)
\(168\) −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 \(-0.489212\pi\)
0.0338852 + 0.999426i \(0.489212\pi\)
\(194\) −0.842912 −0.0605175
\(195\) 0 0
\(196\) −36.3980 −2.59986
\(197\) −16.7419 −1.19281 −0.596404 0.802684i \(-0.703404\pi\)
−0.596404 + 0.802684i \(0.703404\pi\)
\(198\) 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 \(-0.630130\pi\)
−0.397522 + 0.917593i \(0.630130\pi\)
\(224\) 22.6623 1.51419
\(225\) 12.1357 0.809047
\(226\) −0.910595 −0.0605719
\(227\) 13.0255 0.864532 0.432266 0.901746i \(-0.357714\pi\)
0.432266 + 0.901746i \(0.357714\pi\)
\(228\) −0.817698 −0.0541533
\(229\) −6.45867 −0.426801 −0.213401 0.976965i \(-0.568454\pi\)
−0.213401 + 0.976965i \(0.568454\pi\)
\(230\) 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 \(-0.504386\pi\)
−0.0137791 + 0.999905i \(0.504386\pi\)
\(240\) −12.5179 −0.808024
\(241\) −12.9860 −0.836503 −0.418251 0.908331i \(-0.637357\pi\)
−0.418251 + 0.908331i \(0.637357\pi\)
\(242\) −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 \(-0.377948\pi\)
0.374112 + 0.927384i \(0.377948\pi\)
\(272\) −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 \(-0.436279\pi\)
0.198850 + 0.980030i \(0.436279\pi\)
\(282\) 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 \(-0.367803\pi\)
0.403472 + 0.914992i \(0.367803\pi\)
\(294\) −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 \(-0.705527\pi\)
−0.601743 + 0.798690i \(0.705527\pi\)
\(308\) −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 \(-0.741613\pi\)
−0.688233 + 0.725490i \(0.741613\pi\)
\(318\) −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 \(-0.593146\pi\)
−0.288469 + 0.957489i \(0.593146\pi\)
\(332\) 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 \(-0.265625\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(350\) 25.7288 1.37526
\(351\) 0 0
\(352\) 4.37265 0.233063
\(353\) −9.19662 −0.489486 −0.244743 0.969588i \(-0.578704\pi\)
−0.244743 + 0.969588i \(0.578704\pi\)
\(354\) 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 \(-0.703646\pi\)
−0.597013 + 0.802231i \(0.703646\pi\)
\(360\) −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 \(-0.480956\pi\)
0.0597934 + 0.998211i \(0.480956\pi\)
\(380\) 3.38488 0.173641
\(381\) −18.2528 −0.935118
\(382\) 7.13457 0.365037
\(383\) −27.2203 −1.39089 −0.695447 0.718578i \(-0.744793\pi\)
−0.695447 + 0.718578i \(0.744793\pi\)
\(384\) 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 \(-0.212084\pi\)
0.786126 + 0.618066i \(0.212084\pi\)
\(398\) −5.38222 −0.269786
\(399\) −2.31243 −0.115766
\(400\) 36.6981 1.83491
\(401\) −8.94790 −0.446837 −0.223418 0.974723i \(-0.571722\pi\)
−0.223418 + 0.974723i \(0.571722\pi\)
\(402\) −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 \(-0.232921\pi\)
0.744012 + 0.668166i \(0.232921\pi\)
\(410\) 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 \(-0.256748\pi\)
0.691958 + 0.721938i \(0.256748\pi\)
\(422\) −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 \(-0.610764\pi\)
−0.340996 + 0.940065i \(0.610764\pi\)
\(432\) 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 \(-0.579156\pi\)
−0.246121 + 0.969239i \(0.579156\pi\)
\(450\) −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 \(-0.360660\pi\)
0.423904 + 0.905707i \(0.360660\pi\)
\(458\) 2.64204 0.123454
\(459\) −0.488730 −0.0228120
\(460\) 41.7919 1.94856
\(461\) −28.6242 −1.33316 −0.666581 0.745432i \(-0.732243\pi\)
−0.666581 + 0.745432i \(0.732243\pi\)
\(462\) −2.12009 −0.0986356
\(463\) 9.44955 0.439158 0.219579 0.975595i \(-0.429532\pi\)
0.219579 + 0.975595i \(0.429532\pi\)
\(464\) −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 \(-0.584948\pi\)
−0.263714 + 0.964601i \(0.584948\pi\)
\(480\) 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 \(-0.788327\pi\)
−0.786923 + 0.617051i \(0.788327\pi\)
\(488\) −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 \(-0.425535\pi\)
0.231811 + 0.972761i \(0.425535\pi\)
\(500\) 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 \(-0.567330\pi\)
−0.209950 + 0.977712i \(0.567330\pi\)
\(510\) −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 \(-0.454287\pi\)
0.143118 + 0.989706i \(0.454287\pi\)
\(542\) −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 \(-0.584236\pi\)
−0.261556 + 0.965188i \(0.584236\pi\)
\(558\) 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 \(-0.463215\pi\)
0.115306 + 0.993330i \(0.463215\pi\)
\(578\) 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 \(-0.305088\pi\)
0.574780 + 0.818308i \(0.305088\pi\)
\(588\) −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 \(-0.498051\pi\)
0.00612351 + 0.999981i \(0.498051\pi\)
\(594\) 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 \(-0.573651\pi\)
−0.229323 + 0.973350i \(0.573651\pi\)
\(614\) 8.62593 0.348114
\(615\) −36.3684 −1.46651
\(616\) 8.12559 0.327390
\(617\) 23.6846 0.953507 0.476753 0.879037i \(-0.341814\pi\)
0.476753 + 0.879037i \(0.341814\pi\)
\(618\) −0.143533 −0.00577373
\(619\) 27.4080 1.10162 0.550810 0.834631i \(-0.314319\pi\)
0.550810 + 0.834631i \(0.314319\pi\)
\(620\) −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 \(-0.819698\pi\)
−0.843819 + 0.536627i \(0.819698\pi\)
\(632\) −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 \(-0.503591\pi\)
−0.0112797 + 0.999936i \(0.503591\pi\)
\(644\) 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 \(-0.729925\pi\)
−0.661135 + 0.750267i \(0.729925\pi\)
\(662\) 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 \(-0.688041\pi\)
−0.556984 + 0.830523i \(0.688041\pi\)
\(684\) −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 \(-0.459184\pi\)
0.127875 + 0.991790i \(0.459184\pi\)
\(692\) −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 \(-0.228498\pi\)
0.753224 + 0.657764i \(0.228498\pi\)
\(710\) 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 \(-0.273169\pi\)
0.653811 + 0.756658i \(0.273169\pi\)
\(734\) 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 \(-0.516811\pi\)
−0.0527902 + 0.998606i \(0.516811\pi\)
\(740\) 59.7152 2.19517
\(741\) 0 0
\(742\) 18.3743 0.674543
\(743\) −23.1129 −0.847930 −0.423965 0.905679i \(-0.639362\pi\)
−0.423965 + 0.905679i \(0.639362\pi\)
\(744\) −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 \(-0.637250\pi\)
−0.417947 + 0.908471i \(0.637250\pi\)
\(762\) 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 \(-0.241474\pi\)
0.725792 + 0.687915i \(0.241474\pi\)
\(770\) 8.77618 0.316272
\(771\) −11.2798 −0.406232
\(772\) −1.72545 −0.0621003
\(773\) −25.6183 −0.921426 −0.460713 0.887549i \(-0.652406\pi\)
−0.460713 + 0.887549i \(0.652406\pi\)
\(774\) 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 \(-0.636581\pi\)
−0.416035 + 0.909349i \(0.636581\pi\)
\(788\) 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 \(-0.365057\pi\)
0.411350 + 0.911477i \(0.365057\pi\)
\(812\) −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 \(-0.462403\pi\)
0.117841 + 0.993032i \(0.462403\pi\)
\(822\) −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 \(-0.173163\pi\)
0.855642 + 0.517569i \(0.173163\pi\)
\(828\) −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 \(-0.544962\pi\)
−0.140785 + 0.990040i \(0.544962\pi\)
\(840\) 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 \(-0.569775\pi\)
−0.217455 + 0.976070i \(0.569775\pi\)
\(854\) −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 \(-0.416592\pi\)
0.259047 + 0.965865i \(0.416592\pi\)
\(864\) −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 \(-0.412627\pi\)
0.271057 + 0.962563i \(0.412627\pi\)
\(878\) −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 \(-0.852646\pi\)
−0.894749 + 0.446569i \(0.852646\pi\)
\(930\) −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 \(-0.535212\pi\)
−0.110396 + 0.993888i \(0.535212\pi\)
\(942\) −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 \(-0.476974\pi\)
0.0722756 + 0.997385i \(0.476974\pi\)
\(948\) 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 \(-0.629699\pi\)
−0.396279 + 0.918130i \(0.629699\pi\)
\(968\) 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 \(-0.440541\pi\)
0.185712 + 0.982604i \(0.440541\pi\)
\(978\) −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 \(-0.882738\pi\)
−0.932908 + 0.360114i \(0.882738\pi\)
\(984\) 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.x.1.4 7
13.5 odd 4 429.2.b.b.298.8 yes 14
13.8 odd 4 429.2.b.b.298.7 14
13.12 even 2 5577.2.a.y.1.4 7
39.5 even 4 1287.2.b.c.298.7 14
39.8 even 4 1287.2.b.c.298.8 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.b.b.298.7 14 13.8 odd 4
429.2.b.b.298.8 yes 14 13.5 odd 4
1287.2.b.c.298.7 14 39.5 even 4
1287.2.b.c.298.8 14 39.8 even 4
5577.2.a.x.1.4 7 1.1 even 1 trivial
5577.2.a.y.1.4 7 13.12 even 2