Properties

Label 729.2.a.e.1.2
Level $729$
Weight $2$
Character 729.1
Self dual yes
Analytic conductor $5.821$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.7459857.1
Defining polynomial: \( x^{6} - 3x^{5} - 6x^{4} + 13x^{3} + 12x^{2} - 12x - 8 \) Copy content Toggle raw display
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 1.2
Root \(-1.12503\) of defining polynomial
Character \(\chi\) \(=\) 729.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.777732 q^{2} -1.39513 q^{4} -2.37635 q^{5} -2.50138 q^{7} +2.64050 q^{8} +O(q^{10})\) \(q-0.777732 q^{2} -1.39513 q^{4} -2.37635 q^{5} -2.50138 q^{7} +2.64050 q^{8} +1.84816 q^{10} -3.14137 q^{11} +1.33663 q^{13} +1.94540 q^{14} +0.736659 q^{16} -6.27452 q^{17} +8.06469 q^{19} +3.31532 q^{20} +2.44315 q^{22} -4.05460 q^{23} +0.647028 q^{25} -1.03954 q^{26} +3.48975 q^{28} +9.28723 q^{29} +2.83182 q^{31} -5.85393 q^{32} +4.87990 q^{34} +5.94414 q^{35} +5.53191 q^{37} -6.27217 q^{38} -6.27476 q^{40} +7.10576 q^{41} +2.33690 q^{43} +4.38263 q^{44} +3.15339 q^{46} +4.61421 q^{47} -0.743116 q^{49} -0.503215 q^{50} -1.86478 q^{52} -0.135496 q^{53} +7.46499 q^{55} -6.60490 q^{56} -7.22298 q^{58} +3.99874 q^{59} +0.341798 q^{61} -2.20240 q^{62} +3.07947 q^{64} -3.17630 q^{65} +10.1229 q^{67} +8.75378 q^{68} -4.62295 q^{70} -8.19080 q^{71} -12.3144 q^{73} -4.30235 q^{74} -11.2513 q^{76} +7.85775 q^{77} +4.08070 q^{79} -1.75056 q^{80} -5.52638 q^{82} -0.913228 q^{83} +14.9104 q^{85} -1.81748 q^{86} -8.29480 q^{88} +3.72875 q^{89} -3.34341 q^{91} +5.65670 q^{92} -3.58862 q^{94} -19.1645 q^{95} -5.99630 q^{97} +0.577945 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{11} + 6 q^{13} + 24 q^{14} + 15 q^{16} - 9 q^{17} + 12 q^{19} - 21 q^{20} + 3 q^{22} - 12 q^{23} + 9 q^{25} + 24 q^{26} + 3 q^{28} + 21 q^{29} + 15 q^{31} + 30 q^{35} + 3 q^{37} + 15 q^{38} + 3 q^{40} - 12 q^{41} + 6 q^{43} - 33 q^{44} - 3 q^{46} - 15 q^{47} + 12 q^{49} - 24 q^{50} + 3 q^{52} - 9 q^{53} + 15 q^{55} + 12 q^{56} - 15 q^{58} + 6 q^{59} + 24 q^{61} - 30 q^{62} + 6 q^{64} - 15 q^{65} + 15 q^{67} + 36 q^{68} - 15 q^{70} + 12 q^{73} + 24 q^{74} + 9 q^{76} + 15 q^{77} + 24 q^{79} - 21 q^{80} - 21 q^{82} - 6 q^{83} - 18 q^{85} - 30 q^{86} - 21 q^{88} - 9 q^{89} + 18 q^{91} + 6 q^{92} - 6 q^{94} - 33 q^{95} - 21 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.777732 −0.549940 −0.274970 0.961453i \(-0.588668\pi\)
−0.274970 + 0.961453i \(0.588668\pi\)
\(3\) 0 0
\(4\) −1.39513 −0.697566
\(5\) −2.37635 −1.06273 −0.531367 0.847141i \(-0.678322\pi\)
−0.531367 + 0.847141i \(0.678322\pi\)
\(6\) 0 0
\(7\) −2.50138 −0.945431 −0.472716 0.881215i \(-0.656726\pi\)
−0.472716 + 0.881215i \(0.656726\pi\)
\(8\) 2.64050 0.933559
\(9\) 0 0
\(10\) 1.84816 0.584440
\(11\) −3.14137 −0.947159 −0.473579 0.880751i \(-0.657038\pi\)
−0.473579 + 0.880751i \(0.657038\pi\)
\(12\) 0 0
\(13\) 1.33663 0.370714 0.185357 0.982671i \(-0.440656\pi\)
0.185357 + 0.982671i \(0.440656\pi\)
\(14\) 1.94540 0.519930
\(15\) 0 0
\(16\) 0.736659 0.184165
\(17\) −6.27452 −1.52179 −0.760897 0.648873i \(-0.775241\pi\)
−0.760897 + 0.648873i \(0.775241\pi\)
\(18\) 0 0
\(19\) 8.06469 1.85017 0.925083 0.379765i \(-0.123995\pi\)
0.925083 + 0.379765i \(0.123995\pi\)
\(20\) 3.31532 0.741328
\(21\) 0 0
\(22\) 2.44315 0.520880
\(23\) −4.05460 −0.845442 −0.422721 0.906260i \(-0.638925\pi\)
−0.422721 + 0.906260i \(0.638925\pi\)
\(24\) 0 0
\(25\) 0.647028 0.129406
\(26\) −1.03954 −0.203871
\(27\) 0 0
\(28\) 3.48975 0.659501
\(29\) 9.28723 1.72459 0.862297 0.506402i \(-0.169025\pi\)
0.862297 + 0.506402i \(0.169025\pi\)
\(30\) 0 0
\(31\) 2.83182 0.508610 0.254305 0.967124i \(-0.418153\pi\)
0.254305 + 0.967124i \(0.418153\pi\)
\(32\) −5.85393 −1.03484
\(33\) 0 0
\(34\) 4.87990 0.836895
\(35\) 5.94414 1.00474
\(36\) 0 0
\(37\) 5.53191 0.909441 0.454720 0.890634i \(-0.349739\pi\)
0.454720 + 0.890634i \(0.349739\pi\)
\(38\) −6.27217 −1.01748
\(39\) 0 0
\(40\) −6.27476 −0.992126
\(41\) 7.10576 1.10973 0.554867 0.831939i \(-0.312769\pi\)
0.554867 + 0.831939i \(0.312769\pi\)
\(42\) 0 0
\(43\) 2.33690 0.356374 0.178187 0.983997i \(-0.442977\pi\)
0.178187 + 0.983997i \(0.442977\pi\)
\(44\) 4.38263 0.660706
\(45\) 0 0
\(46\) 3.15339 0.464942
\(47\) 4.61421 0.673051 0.336526 0.941674i \(-0.390748\pi\)
0.336526 + 0.941674i \(0.390748\pi\)
\(48\) 0 0
\(49\) −0.743116 −0.106159
\(50\) −0.503215 −0.0711653
\(51\) 0 0
\(52\) −1.86478 −0.258598
\(53\) −0.135496 −0.0186118 −0.00930588 0.999957i \(-0.502962\pi\)
−0.00930588 + 0.999957i \(0.502962\pi\)
\(54\) 0 0
\(55\) 7.46499 1.00658
\(56\) −6.60490 −0.882616
\(57\) 0 0
\(58\) −7.22298 −0.948423
\(59\) 3.99874 0.520591 0.260296 0.965529i \(-0.416180\pi\)
0.260296 + 0.965529i \(0.416180\pi\)
\(60\) 0 0
\(61\) 0.341798 0.0437628 0.0218814 0.999761i \(-0.493034\pi\)
0.0218814 + 0.999761i \(0.493034\pi\)
\(62\) −2.20240 −0.279705
\(63\) 0 0
\(64\) 3.07947 0.384934
\(65\) −3.17630 −0.393971
\(66\) 0 0
\(67\) 10.1229 1.23671 0.618356 0.785898i \(-0.287799\pi\)
0.618356 + 0.785898i \(0.287799\pi\)
\(68\) 8.75378 1.06155
\(69\) 0 0
\(70\) −4.62295 −0.552548
\(71\) −8.19080 −0.972069 −0.486035 0.873940i \(-0.661557\pi\)
−0.486035 + 0.873940i \(0.661557\pi\)
\(72\) 0 0
\(73\) −12.3144 −1.44130 −0.720648 0.693301i \(-0.756156\pi\)
−0.720648 + 0.693301i \(0.756156\pi\)
\(74\) −4.30235 −0.500138
\(75\) 0 0
\(76\) −11.2513 −1.29061
\(77\) 7.85775 0.895474
\(78\) 0 0
\(79\) 4.08070 0.459114 0.229557 0.973295i \(-0.426272\pi\)
0.229557 + 0.973295i \(0.426272\pi\)
\(80\) −1.75056 −0.195718
\(81\) 0 0
\(82\) −5.52638 −0.610287
\(83\) −0.913228 −0.100240 −0.0501199 0.998743i \(-0.515960\pi\)
−0.0501199 + 0.998743i \(0.515960\pi\)
\(84\) 0 0
\(85\) 14.9104 1.61726
\(86\) −1.81748 −0.195984
\(87\) 0 0
\(88\) −8.29480 −0.884229
\(89\) 3.72875 0.395246 0.197623 0.980278i \(-0.436678\pi\)
0.197623 + 0.980278i \(0.436678\pi\)
\(90\) 0 0
\(91\) −3.34341 −0.350485
\(92\) 5.65670 0.589752
\(93\) 0 0
\(94\) −3.58862 −0.370138
\(95\) −19.1645 −1.96624
\(96\) 0 0
\(97\) −5.99630 −0.608832 −0.304416 0.952539i \(-0.598461\pi\)
−0.304416 + 0.952539i \(0.598461\pi\)
\(98\) 0.577945 0.0583813
\(99\) 0 0
\(100\) −0.902690 −0.0902690
\(101\) −10.2217 −1.01710 −0.508549 0.861033i \(-0.669818\pi\)
−0.508549 + 0.861033i \(0.669818\pi\)
\(102\) 0 0
\(103\) 8.53406 0.840886 0.420443 0.907319i \(-0.361875\pi\)
0.420443 + 0.907319i \(0.361875\pi\)
\(104\) 3.52938 0.346084
\(105\) 0 0
\(106\) 0.105379 0.0102354
\(107\) 7.74500 0.748738 0.374369 0.927280i \(-0.377859\pi\)
0.374369 + 0.927280i \(0.377859\pi\)
\(108\) 0 0
\(109\) 1.25438 0.120148 0.0600738 0.998194i \(-0.480866\pi\)
0.0600738 + 0.998194i \(0.480866\pi\)
\(110\) −5.80576 −0.553558
\(111\) 0 0
\(112\) −1.84266 −0.174115
\(113\) 17.7608 1.67079 0.835396 0.549648i \(-0.185238\pi\)
0.835396 + 0.549648i \(0.185238\pi\)
\(114\) 0 0
\(115\) 9.63514 0.898481
\(116\) −12.9569 −1.20302
\(117\) 0 0
\(118\) −3.10995 −0.286294
\(119\) 15.6949 1.43875
\(120\) 0 0
\(121\) −1.13179 −0.102890
\(122\) −0.265827 −0.0240669
\(123\) 0 0
\(124\) −3.95076 −0.354789
\(125\) 10.3442 0.925211
\(126\) 0 0
\(127\) −3.96558 −0.351888 −0.175944 0.984400i \(-0.556298\pi\)
−0.175944 + 0.984400i \(0.556298\pi\)
\(128\) 9.31286 0.823148
\(129\) 0 0
\(130\) 2.47031 0.216660
\(131\) 0.102498 0.00895533 0.00447766 0.999990i \(-0.498575\pi\)
0.00447766 + 0.999990i \(0.498575\pi\)
\(132\) 0 0
\(133\) −20.1728 −1.74921
\(134\) −7.87292 −0.680117
\(135\) 0 0
\(136\) −16.5679 −1.42068
\(137\) 7.61955 0.650982 0.325491 0.945545i \(-0.394470\pi\)
0.325491 + 0.945545i \(0.394470\pi\)
\(138\) 0 0
\(139\) −10.4407 −0.885571 −0.442786 0.896628i \(-0.646010\pi\)
−0.442786 + 0.896628i \(0.646010\pi\)
\(140\) −8.29286 −0.700875
\(141\) 0 0
\(142\) 6.37025 0.534580
\(143\) −4.19885 −0.351125
\(144\) 0 0
\(145\) −22.0697 −1.83279
\(146\) 9.57734 0.792626
\(147\) 0 0
\(148\) −7.71775 −0.634395
\(149\) −9.03258 −0.739978 −0.369989 0.929036i \(-0.620638\pi\)
−0.369989 + 0.929036i \(0.620638\pi\)
\(150\) 0 0
\(151\) 23.8904 1.94417 0.972086 0.234624i \(-0.0753860\pi\)
0.972086 + 0.234624i \(0.0753860\pi\)
\(152\) 21.2948 1.72724
\(153\) 0 0
\(154\) −6.11123 −0.492457
\(155\) −6.72939 −0.540518
\(156\) 0 0
\(157\) 2.71199 0.216440 0.108220 0.994127i \(-0.465485\pi\)
0.108220 + 0.994127i \(0.465485\pi\)
\(158\) −3.17369 −0.252485
\(159\) 0 0
\(160\) 13.9110 1.09976
\(161\) 10.1421 0.799308
\(162\) 0 0
\(163\) −22.0489 −1.72701 −0.863504 0.504343i \(-0.831735\pi\)
−0.863504 + 0.504343i \(0.831735\pi\)
\(164\) −9.91348 −0.774113
\(165\) 0 0
\(166\) 0.710247 0.0551259
\(167\) 8.95081 0.692634 0.346317 0.938118i \(-0.387432\pi\)
0.346317 + 0.938118i \(0.387432\pi\)
\(168\) 0 0
\(169\) −11.2134 −0.862571
\(170\) −11.5963 −0.889398
\(171\) 0 0
\(172\) −3.26029 −0.248595
\(173\) 2.63425 0.200278 0.100139 0.994973i \(-0.468071\pi\)
0.100139 + 0.994973i \(0.468071\pi\)
\(174\) 0 0
\(175\) −1.61846 −0.122344
\(176\) −2.31412 −0.174433
\(177\) 0 0
\(178\) −2.89997 −0.217362
\(179\) 3.68453 0.275395 0.137697 0.990474i \(-0.456030\pi\)
0.137697 + 0.990474i \(0.456030\pi\)
\(180\) 0 0
\(181\) −0.268509 −0.0199581 −0.00997906 0.999950i \(-0.503176\pi\)
−0.00997906 + 0.999950i \(0.503176\pi\)
\(182\) 2.60028 0.192746
\(183\) 0 0
\(184\) −10.7062 −0.789270
\(185\) −13.1457 −0.966494
\(186\) 0 0
\(187\) 19.7106 1.44138
\(188\) −6.43743 −0.469498
\(189\) 0 0
\(190\) 14.9049 1.08131
\(191\) −2.39799 −0.173512 −0.0867561 0.996230i \(-0.527650\pi\)
−0.0867561 + 0.996230i \(0.527650\pi\)
\(192\) 0 0
\(193\) 0.496203 0.0357175 0.0178587 0.999841i \(-0.494315\pi\)
0.0178587 + 0.999841i \(0.494315\pi\)
\(194\) 4.66351 0.334821
\(195\) 0 0
\(196\) 1.03675 0.0740532
\(197\) −22.1468 −1.57789 −0.788946 0.614462i \(-0.789373\pi\)
−0.788946 + 0.614462i \(0.789373\pi\)
\(198\) 0 0
\(199\) 2.13247 0.151167 0.0755834 0.997139i \(-0.475918\pi\)
0.0755834 + 0.997139i \(0.475918\pi\)
\(200\) 1.70848 0.120808
\(201\) 0 0
\(202\) 7.94976 0.559343
\(203\) −23.2309 −1.63049
\(204\) 0 0
\(205\) −16.8858 −1.17935
\(206\) −6.63721 −0.462437
\(207\) 0 0
\(208\) 0.984641 0.0682725
\(209\) −25.3342 −1.75240
\(210\) 0 0
\(211\) 20.0086 1.37745 0.688724 0.725024i \(-0.258171\pi\)
0.688724 + 0.725024i \(0.258171\pi\)
\(212\) 0.189034 0.0129829
\(213\) 0 0
\(214\) −6.02354 −0.411761
\(215\) −5.55329 −0.378731
\(216\) 0 0
\(217\) −7.08345 −0.480856
\(218\) −0.975570 −0.0660739
\(219\) 0 0
\(220\) −10.4146 −0.702155
\(221\) −8.38671 −0.564151
\(222\) 0 0
\(223\) −13.2785 −0.889192 −0.444596 0.895731i \(-0.646653\pi\)
−0.444596 + 0.895731i \(0.646653\pi\)
\(224\) 14.6429 0.978369
\(225\) 0 0
\(226\) −13.8131 −0.918835
\(227\) −12.4709 −0.827725 −0.413862 0.910339i \(-0.635821\pi\)
−0.413862 + 0.910339i \(0.635821\pi\)
\(228\) 0 0
\(229\) 25.6616 1.69576 0.847882 0.530185i \(-0.177878\pi\)
0.847882 + 0.530185i \(0.177878\pi\)
\(230\) −7.49356 −0.494111
\(231\) 0 0
\(232\) 24.5230 1.61001
\(233\) −5.39642 −0.353532 −0.176766 0.984253i \(-0.556564\pi\)
−0.176766 + 0.984253i \(0.556564\pi\)
\(234\) 0 0
\(235\) −10.9650 −0.715275
\(236\) −5.57877 −0.363147
\(237\) 0 0
\(238\) −12.2065 −0.791227
\(239\) 8.37104 0.541478 0.270739 0.962653i \(-0.412732\pi\)
0.270739 + 0.962653i \(0.412732\pi\)
\(240\) 0 0
\(241\) −0.442190 −0.0284839 −0.0142420 0.999899i \(-0.504534\pi\)
−0.0142420 + 0.999899i \(0.504534\pi\)
\(242\) 0.880231 0.0565834
\(243\) 0 0
\(244\) −0.476854 −0.0305274
\(245\) 1.76590 0.112819
\(246\) 0 0
\(247\) 10.7795 0.685883
\(248\) 7.47743 0.474818
\(249\) 0 0
\(250\) −8.04500 −0.508810
\(251\) 17.0285 1.07483 0.537416 0.843317i \(-0.319401\pi\)
0.537416 + 0.843317i \(0.319401\pi\)
\(252\) 0 0
\(253\) 12.7370 0.800768
\(254\) 3.08416 0.193517
\(255\) 0 0
\(256\) −13.4019 −0.837616
\(257\) 20.8767 1.30225 0.651127 0.758969i \(-0.274297\pi\)
0.651127 + 0.758969i \(0.274297\pi\)
\(258\) 0 0
\(259\) −13.8374 −0.859814
\(260\) 4.43136 0.274821
\(261\) 0 0
\(262\) −0.0797163 −0.00492489
\(263\) 19.3916 1.19573 0.597867 0.801595i \(-0.296015\pi\)
0.597867 + 0.801595i \(0.296015\pi\)
\(264\) 0 0
\(265\) 0.321985 0.0197794
\(266\) 15.6891 0.961958
\(267\) 0 0
\(268\) −14.1228 −0.862688
\(269\) 18.6791 1.13889 0.569443 0.822031i \(-0.307159\pi\)
0.569443 + 0.822031i \(0.307159\pi\)
\(270\) 0 0
\(271\) 12.9378 0.785917 0.392958 0.919556i \(-0.371452\pi\)
0.392958 + 0.919556i \(0.371452\pi\)
\(272\) −4.62218 −0.280261
\(273\) 0 0
\(274\) −5.92597 −0.358001
\(275\) −2.03256 −0.122568
\(276\) 0 0
\(277\) 10.4413 0.627359 0.313679 0.949529i \(-0.398438\pi\)
0.313679 + 0.949529i \(0.398438\pi\)
\(278\) 8.12009 0.487011
\(279\) 0 0
\(280\) 15.6955 0.937987
\(281\) 14.3458 0.855798 0.427899 0.903826i \(-0.359254\pi\)
0.427899 + 0.903826i \(0.359254\pi\)
\(282\) 0 0
\(283\) −18.6926 −1.11116 −0.555580 0.831463i \(-0.687504\pi\)
−0.555580 + 0.831463i \(0.687504\pi\)
\(284\) 11.4273 0.678083
\(285\) 0 0
\(286\) 3.26558 0.193098
\(287\) −17.7742 −1.04918
\(288\) 0 0
\(289\) 22.3696 1.31586
\(290\) 17.1643 1.00792
\(291\) 0 0
\(292\) 17.1803 1.00540
\(293\) −10.7882 −0.630252 −0.315126 0.949050i \(-0.602047\pi\)
−0.315126 + 0.949050i \(0.602047\pi\)
\(294\) 0 0
\(295\) −9.50239 −0.553251
\(296\) 14.6070 0.849017
\(297\) 0 0
\(298\) 7.02493 0.406943
\(299\) −5.41950 −0.313418
\(300\) 0 0
\(301\) −5.84547 −0.336927
\(302\) −18.5803 −1.06918
\(303\) 0 0
\(304\) 5.94092 0.340735
\(305\) −0.812231 −0.0465082
\(306\) 0 0
\(307\) 0.0497494 0.00283935 0.00141967 0.999999i \(-0.499548\pi\)
0.00141967 + 0.999999i \(0.499548\pi\)
\(308\) −10.9626 −0.624652
\(309\) 0 0
\(310\) 5.23366 0.297252
\(311\) 13.2355 0.750514 0.375257 0.926921i \(-0.377554\pi\)
0.375257 + 0.926921i \(0.377554\pi\)
\(312\) 0 0
\(313\) −15.0829 −0.852537 −0.426268 0.904597i \(-0.640172\pi\)
−0.426268 + 0.904597i \(0.640172\pi\)
\(314\) −2.10920 −0.119029
\(315\) 0 0
\(316\) −5.69311 −0.320263
\(317\) 8.63082 0.484755 0.242378 0.970182i \(-0.422073\pi\)
0.242378 + 0.970182i \(0.422073\pi\)
\(318\) 0 0
\(319\) −29.1746 −1.63347
\(320\) −7.31790 −0.409083
\(321\) 0 0
\(322\) −7.88782 −0.439571
\(323\) −50.6020 −2.81557
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) 17.1482 0.949750
\(327\) 0 0
\(328\) 18.7628 1.03600
\(329\) −11.5419 −0.636324
\(330\) 0 0
\(331\) 31.0255 1.70531 0.852657 0.522471i \(-0.174990\pi\)
0.852657 + 0.522471i \(0.174990\pi\)
\(332\) 1.27407 0.0699239
\(333\) 0 0
\(334\) −6.96133 −0.380907
\(335\) −24.0556 −1.31430
\(336\) 0 0
\(337\) −23.8673 −1.30014 −0.650068 0.759876i \(-0.725260\pi\)
−0.650068 + 0.759876i \(0.725260\pi\)
\(338\) 8.72104 0.474362
\(339\) 0 0
\(340\) −20.8020 −1.12815
\(341\) −8.89580 −0.481734
\(342\) 0 0
\(343\) 19.3684 1.04580
\(344\) 6.17060 0.332696
\(345\) 0 0
\(346\) −2.04874 −0.110141
\(347\) 21.9112 1.17626 0.588128 0.808768i \(-0.299865\pi\)
0.588128 + 0.808768i \(0.299865\pi\)
\(348\) 0 0
\(349\) 15.8469 0.848263 0.424132 0.905601i \(-0.360579\pi\)
0.424132 + 0.905601i \(0.360579\pi\)
\(350\) 1.25873 0.0672819
\(351\) 0 0
\(352\) 18.3894 0.980157
\(353\) 12.9069 0.686964 0.343482 0.939159i \(-0.388394\pi\)
0.343482 + 0.939159i \(0.388394\pi\)
\(354\) 0 0
\(355\) 19.4642 1.03305
\(356\) −5.20209 −0.275710
\(357\) 0 0
\(358\) −2.86558 −0.151451
\(359\) 25.8285 1.36318 0.681588 0.731736i \(-0.261290\pi\)
0.681588 + 0.731736i \(0.261290\pi\)
\(360\) 0 0
\(361\) 46.0392 2.42312
\(362\) 0.208828 0.0109758
\(363\) 0 0
\(364\) 4.66451 0.244487
\(365\) 29.2634 1.53172
\(366\) 0 0
\(367\) 15.9746 0.833866 0.416933 0.908937i \(-0.363105\pi\)
0.416933 + 0.908937i \(0.363105\pi\)
\(368\) −2.98686 −0.155701
\(369\) 0 0
\(370\) 10.2239 0.531514
\(371\) 0.338926 0.0175961
\(372\) 0 0
\(373\) 1.82657 0.0945760 0.0472880 0.998881i \(-0.484942\pi\)
0.0472880 + 0.998881i \(0.484942\pi\)
\(374\) −15.3296 −0.792673
\(375\) 0 0
\(376\) 12.1838 0.628333
\(377\) 12.4136 0.639332
\(378\) 0 0
\(379\) 1.14694 0.0589141 0.0294571 0.999566i \(-0.490622\pi\)
0.0294571 + 0.999566i \(0.490622\pi\)
\(380\) 26.7370 1.37158
\(381\) 0 0
\(382\) 1.86499 0.0954212
\(383\) 21.8275 1.11534 0.557668 0.830064i \(-0.311696\pi\)
0.557668 + 0.830064i \(0.311696\pi\)
\(384\) 0 0
\(385\) −18.6727 −0.951651
\(386\) −0.385913 −0.0196425
\(387\) 0 0
\(388\) 8.36563 0.424700
\(389\) −26.1962 −1.32820 −0.664099 0.747644i \(-0.731185\pi\)
−0.664099 + 0.747644i \(0.731185\pi\)
\(390\) 0 0
\(391\) 25.4407 1.28659
\(392\) −1.96220 −0.0991061
\(393\) 0 0
\(394\) 17.2243 0.867746
\(395\) −9.69715 −0.487917
\(396\) 0 0
\(397\) 4.19831 0.210707 0.105353 0.994435i \(-0.466403\pi\)
0.105353 + 0.994435i \(0.466403\pi\)
\(398\) −1.65849 −0.0831327
\(399\) 0 0
\(400\) 0.476639 0.0238320
\(401\) −7.82981 −0.391002 −0.195501 0.980703i \(-0.562633\pi\)
−0.195501 + 0.980703i \(0.562633\pi\)
\(402\) 0 0
\(403\) 3.78510 0.188549
\(404\) 14.2606 0.709493
\(405\) 0 0
\(406\) 18.0674 0.896669
\(407\) −17.3778 −0.861385
\(408\) 0 0
\(409\) −17.4290 −0.861808 −0.430904 0.902398i \(-0.641805\pi\)
−0.430904 + 0.902398i \(0.641805\pi\)
\(410\) 13.1326 0.648573
\(411\) 0 0
\(412\) −11.9061 −0.586574
\(413\) −10.0024 −0.492183
\(414\) 0 0
\(415\) 2.17015 0.106528
\(416\) −7.82454 −0.383630
\(417\) 0 0
\(418\) 19.7032 0.963715
\(419\) 11.4832 0.560990 0.280495 0.959856i \(-0.409501\pi\)
0.280495 + 0.959856i \(0.409501\pi\)
\(420\) 0 0
\(421\) 7.29123 0.355353 0.177676 0.984089i \(-0.443142\pi\)
0.177676 + 0.984089i \(0.443142\pi\)
\(422\) −15.5613 −0.757513
\(423\) 0 0
\(424\) −0.357777 −0.0173752
\(425\) −4.05979 −0.196929
\(426\) 0 0
\(427\) −0.854966 −0.0413747
\(428\) −10.8053 −0.522294
\(429\) 0 0
\(430\) 4.31897 0.208279
\(431\) 0.389084 0.0187415 0.00937075 0.999956i \(-0.497017\pi\)
0.00937075 + 0.999956i \(0.497017\pi\)
\(432\) 0 0
\(433\) 24.1011 1.15822 0.579112 0.815248i \(-0.303400\pi\)
0.579112 + 0.815248i \(0.303400\pi\)
\(434\) 5.50903 0.264442
\(435\) 0 0
\(436\) −1.75002 −0.0838109
\(437\) −32.6991 −1.56421
\(438\) 0 0
\(439\) 36.6656 1.74995 0.874977 0.484165i \(-0.160877\pi\)
0.874977 + 0.484165i \(0.160877\pi\)
\(440\) 19.7113 0.939701
\(441\) 0 0
\(442\) 6.52261 0.310249
\(443\) −37.7867 −1.79530 −0.897649 0.440711i \(-0.854726\pi\)
−0.897649 + 0.440711i \(0.854726\pi\)
\(444\) 0 0
\(445\) −8.86080 −0.420042
\(446\) 10.3271 0.489002
\(447\) 0 0
\(448\) −7.70293 −0.363929
\(449\) 11.7858 0.556205 0.278103 0.960551i \(-0.410294\pi\)
0.278103 + 0.960551i \(0.410294\pi\)
\(450\) 0 0
\(451\) −22.3218 −1.05109
\(452\) −24.7786 −1.16549
\(453\) 0 0
\(454\) 9.69905 0.455199
\(455\) 7.94512 0.372473
\(456\) 0 0
\(457\) −19.8559 −0.928820 −0.464410 0.885620i \(-0.653734\pi\)
−0.464410 + 0.885620i \(0.653734\pi\)
\(458\) −19.9578 −0.932568
\(459\) 0 0
\(460\) −13.4423 −0.626750
\(461\) −7.64183 −0.355915 −0.177958 0.984038i \(-0.556949\pi\)
−0.177958 + 0.984038i \(0.556949\pi\)
\(462\) 0 0
\(463\) −15.9544 −0.741465 −0.370732 0.928740i \(-0.620893\pi\)
−0.370732 + 0.928740i \(0.620893\pi\)
\(464\) 6.84152 0.317610
\(465\) 0 0
\(466\) 4.19697 0.194421
\(467\) 26.1406 1.20964 0.604822 0.796360i \(-0.293244\pi\)
0.604822 + 0.796360i \(0.293244\pi\)
\(468\) 0 0
\(469\) −25.3212 −1.16923
\(470\) 8.52780 0.393358
\(471\) 0 0
\(472\) 10.5587 0.486003
\(473\) −7.34107 −0.337543
\(474\) 0 0
\(475\) 5.21808 0.239422
\(476\) −21.8965 −1.00362
\(477\) 0 0
\(478\) −6.51043 −0.297780
\(479\) 39.3503 1.79796 0.898980 0.437989i \(-0.144309\pi\)
0.898980 + 0.437989i \(0.144309\pi\)
\(480\) 0 0
\(481\) 7.39412 0.337143
\(482\) 0.343905 0.0156644
\(483\) 0 0
\(484\) 1.57900 0.0717727
\(485\) 14.2493 0.647027
\(486\) 0 0
\(487\) 11.7133 0.530779 0.265389 0.964141i \(-0.414500\pi\)
0.265389 + 0.964141i \(0.414500\pi\)
\(488\) 0.902519 0.0408551
\(489\) 0 0
\(490\) −1.37340 −0.0620439
\(491\) −38.5498 −1.73973 −0.869865 0.493290i \(-0.835794\pi\)
−0.869865 + 0.493290i \(0.835794\pi\)
\(492\) 0 0
\(493\) −58.2729 −2.62448
\(494\) −8.38357 −0.377195
\(495\) 0 0
\(496\) 2.08609 0.0936680
\(497\) 20.4883 0.919025
\(498\) 0 0
\(499\) −29.5616 −1.32336 −0.661679 0.749787i \(-0.730156\pi\)
−0.661679 + 0.749787i \(0.730156\pi\)
\(500\) −14.4315 −0.645396
\(501\) 0 0
\(502\) −13.2436 −0.591093
\(503\) 35.5775 1.58632 0.793161 0.609011i \(-0.208434\pi\)
0.793161 + 0.609011i \(0.208434\pi\)
\(504\) 0 0
\(505\) 24.2903 1.08091
\(506\) −9.90597 −0.440374
\(507\) 0 0
\(508\) 5.53251 0.245465
\(509\) −28.3823 −1.25803 −0.629013 0.777395i \(-0.716541\pi\)
−0.629013 + 0.777395i \(0.716541\pi\)
\(510\) 0 0
\(511\) 30.8030 1.36265
\(512\) −8.20265 −0.362510
\(513\) 0 0
\(514\) −16.2365 −0.716161
\(515\) −20.2799 −0.893639
\(516\) 0 0
\(517\) −14.4949 −0.637486
\(518\) 10.7618 0.472846
\(519\) 0 0
\(520\) −8.38703 −0.367795
\(521\) −25.4351 −1.11433 −0.557167 0.830401i \(-0.688112\pi\)
−0.557167 + 0.830401i \(0.688112\pi\)
\(522\) 0 0
\(523\) 8.40790 0.367652 0.183826 0.982959i \(-0.441152\pi\)
0.183826 + 0.982959i \(0.441152\pi\)
\(524\) −0.142999 −0.00624693
\(525\) 0 0
\(526\) −15.0814 −0.657582
\(527\) −17.7683 −0.774000
\(528\) 0 0
\(529\) −6.56023 −0.285227
\(530\) −0.250418 −0.0108775
\(531\) 0 0
\(532\) 28.1438 1.22019
\(533\) 9.49777 0.411394
\(534\) 0 0
\(535\) −18.4048 −0.795710
\(536\) 26.7296 1.15454
\(537\) 0 0
\(538\) −14.5274 −0.626319
\(539\) 2.33440 0.100550
\(540\) 0 0
\(541\) −12.8635 −0.553043 −0.276522 0.961008i \(-0.589182\pi\)
−0.276522 + 0.961008i \(0.589182\pi\)
\(542\) −10.0622 −0.432207
\(543\) 0 0
\(544\) 36.7306 1.57481
\(545\) −2.98084 −0.127685
\(546\) 0 0
\(547\) 13.0920 0.559772 0.279886 0.960033i \(-0.409703\pi\)
0.279886 + 0.960033i \(0.409703\pi\)
\(548\) −10.6303 −0.454103
\(549\) 0 0
\(550\) 1.58078 0.0674049
\(551\) 74.8986 3.19079
\(552\) 0 0
\(553\) −10.2074 −0.434061
\(554\) −8.12056 −0.345010
\(555\) 0 0
\(556\) 14.5662 0.617745
\(557\) 4.58220 0.194154 0.0970769 0.995277i \(-0.469051\pi\)
0.0970769 + 0.995277i \(0.469051\pi\)
\(558\) 0 0
\(559\) 3.12357 0.132113
\(560\) 4.37880 0.185038
\(561\) 0 0
\(562\) −11.1572 −0.470638
\(563\) 12.2839 0.517705 0.258853 0.965917i \(-0.416656\pi\)
0.258853 + 0.965917i \(0.416656\pi\)
\(564\) 0 0
\(565\) −42.2058 −1.77561
\(566\) 14.5378 0.611071
\(567\) 0 0
\(568\) −21.6278 −0.907484
\(569\) 14.4937 0.607606 0.303803 0.952735i \(-0.401744\pi\)
0.303803 + 0.952735i \(0.401744\pi\)
\(570\) 0 0
\(571\) −22.0454 −0.922569 −0.461285 0.887252i \(-0.652611\pi\)
−0.461285 + 0.887252i \(0.652611\pi\)
\(572\) 5.85795 0.244933
\(573\) 0 0
\(574\) 13.8236 0.576984
\(575\) −2.62344 −0.109405
\(576\) 0 0
\(577\) −31.4835 −1.31068 −0.655338 0.755336i \(-0.727474\pi\)
−0.655338 + 0.755336i \(0.727474\pi\)
\(578\) −17.3975 −0.723642
\(579\) 0 0
\(580\) 30.7901 1.27849
\(581\) 2.28433 0.0947699
\(582\) 0 0
\(583\) 0.425642 0.0176283
\(584\) −32.5163 −1.34554
\(585\) 0 0
\(586\) 8.39032 0.346601
\(587\) −14.3694 −0.593090 −0.296545 0.955019i \(-0.595835\pi\)
−0.296545 + 0.955019i \(0.595835\pi\)
\(588\) 0 0
\(589\) 22.8378 0.941013
\(590\) 7.39032 0.304255
\(591\) 0 0
\(592\) 4.07513 0.167487
\(593\) −41.0988 −1.68772 −0.843862 0.536560i \(-0.819724\pi\)
−0.843862 + 0.536560i \(0.819724\pi\)
\(594\) 0 0
\(595\) −37.2966 −1.52901
\(596\) 12.6016 0.516183
\(597\) 0 0
\(598\) 4.21492 0.172361
\(599\) 8.56216 0.349840 0.174920 0.984583i \(-0.444033\pi\)
0.174920 + 0.984583i \(0.444033\pi\)
\(600\) 0 0
\(601\) −1.63521 −0.0667016 −0.0333508 0.999444i \(-0.510618\pi\)
−0.0333508 + 0.999444i \(0.510618\pi\)
\(602\) 4.54621 0.185290
\(603\) 0 0
\(604\) −33.3303 −1.35619
\(605\) 2.68953 0.109345
\(606\) 0 0
\(607\) 6.56943 0.266645 0.133322 0.991073i \(-0.457435\pi\)
0.133322 + 0.991073i \(0.457435\pi\)
\(608\) −47.2101 −1.91462
\(609\) 0 0
\(610\) 0.631698 0.0255767
\(611\) 6.16749 0.249510
\(612\) 0 0
\(613\) −26.2726 −1.06114 −0.530569 0.847642i \(-0.678022\pi\)
−0.530569 + 0.847642i \(0.678022\pi\)
\(614\) −0.0386917 −0.00156147
\(615\) 0 0
\(616\) 20.7484 0.835978
\(617\) −6.27303 −0.252542 −0.126271 0.991996i \(-0.540301\pi\)
−0.126271 + 0.991996i \(0.540301\pi\)
\(618\) 0 0
\(619\) 4.94087 0.198590 0.0992952 0.995058i \(-0.468341\pi\)
0.0992952 + 0.995058i \(0.468341\pi\)
\(620\) 9.38839 0.377047
\(621\) 0 0
\(622\) −10.2936 −0.412738
\(623\) −9.32700 −0.373678
\(624\) 0 0
\(625\) −27.8165 −1.11266
\(626\) 11.7305 0.468844
\(627\) 0 0
\(628\) −3.78358 −0.150981
\(629\) −34.7101 −1.38398
\(630\) 0 0
\(631\) −6.92420 −0.275648 −0.137824 0.990457i \(-0.544011\pi\)
−0.137824 + 0.990457i \(0.544011\pi\)
\(632\) 10.7751 0.428610
\(633\) 0 0
\(634\) −6.71247 −0.266586
\(635\) 9.42360 0.373964
\(636\) 0 0
\(637\) −0.993271 −0.0393548
\(638\) 22.6900 0.898308
\(639\) 0 0
\(640\) −22.1306 −0.874788
\(641\) −33.9189 −1.33972 −0.669858 0.742490i \(-0.733645\pi\)
−0.669858 + 0.742490i \(0.733645\pi\)
\(642\) 0 0
\(643\) 7.72322 0.304574 0.152287 0.988336i \(-0.451336\pi\)
0.152287 + 0.988336i \(0.451336\pi\)
\(644\) −14.1495 −0.557570
\(645\) 0 0
\(646\) 39.3548 1.54840
\(647\) 35.1862 1.38331 0.691655 0.722228i \(-0.256882\pi\)
0.691655 + 0.722228i \(0.256882\pi\)
\(648\) 0 0
\(649\) −12.5615 −0.493083
\(650\) −0.672612 −0.0263820
\(651\) 0 0
\(652\) 30.7612 1.20470
\(653\) 19.5120 0.763562 0.381781 0.924253i \(-0.375311\pi\)
0.381781 + 0.924253i \(0.375311\pi\)
\(654\) 0 0
\(655\) −0.243572 −0.00951714
\(656\) 5.23452 0.204374
\(657\) 0 0
\(658\) 8.97648 0.349940
\(659\) 23.0864 0.899320 0.449660 0.893200i \(-0.351545\pi\)
0.449660 + 0.893200i \(0.351545\pi\)
\(660\) 0 0
\(661\) −6.87636 −0.267459 −0.133730 0.991018i \(-0.542695\pi\)
−0.133730 + 0.991018i \(0.542695\pi\)
\(662\) −24.1295 −0.937820
\(663\) 0 0
\(664\) −2.41138 −0.0935798
\(665\) 47.9376 1.85894
\(666\) 0 0
\(667\) −37.6560 −1.45805
\(668\) −12.4876 −0.483158
\(669\) 0 0
\(670\) 18.7088 0.722784
\(671\) −1.07371 −0.0414503
\(672\) 0 0
\(673\) −30.6723 −1.18233 −0.591166 0.806550i \(-0.701332\pi\)
−0.591166 + 0.806550i \(0.701332\pi\)
\(674\) 18.5624 0.714997
\(675\) 0 0
\(676\) 15.6442 0.601700
\(677\) −13.5840 −0.522074 −0.261037 0.965329i \(-0.584065\pi\)
−0.261037 + 0.965329i \(0.584065\pi\)
\(678\) 0 0
\(679\) 14.9990 0.575608
\(680\) 39.3711 1.50981
\(681\) 0 0
\(682\) 6.91855 0.264925
\(683\) −6.06700 −0.232147 −0.116074 0.993241i \(-0.537031\pi\)
−0.116074 + 0.993241i \(0.537031\pi\)
\(684\) 0 0
\(685\) −18.1067 −0.691821
\(686\) −15.0635 −0.575126
\(687\) 0 0
\(688\) 1.72150 0.0656316
\(689\) −0.181108 −0.00689965
\(690\) 0 0
\(691\) 20.6651 0.786137 0.393068 0.919509i \(-0.371414\pi\)
0.393068 + 0.919509i \(0.371414\pi\)
\(692\) −3.67513 −0.139707
\(693\) 0 0
\(694\) −17.0411 −0.646871
\(695\) 24.8108 0.941127
\(696\) 0 0
\(697\) −44.5852 −1.68879
\(698\) −12.3246 −0.466494
\(699\) 0 0
\(700\) 2.25797 0.0853431
\(701\) 11.0222 0.416303 0.208151 0.978097i \(-0.433255\pi\)
0.208151 + 0.978097i \(0.433255\pi\)
\(702\) 0 0
\(703\) 44.6131 1.68262
\(704\) −9.67377 −0.364594
\(705\) 0 0
\(706\) −10.0381 −0.377789
\(707\) 25.5684 0.961597
\(708\) 0 0
\(709\) −10.9874 −0.412642 −0.206321 0.978484i \(-0.566149\pi\)
−0.206321 + 0.978484i \(0.566149\pi\)
\(710\) −15.1379 −0.568116
\(711\) 0 0
\(712\) 9.84577 0.368986
\(713\) −11.4819 −0.430000
\(714\) 0 0
\(715\) 9.97793 0.373153
\(716\) −5.14041 −0.192106
\(717\) 0 0
\(718\) −20.0877 −0.749664
\(719\) 32.7057 1.21972 0.609859 0.792510i \(-0.291226\pi\)
0.609859 + 0.792510i \(0.291226\pi\)
\(720\) 0 0
\(721\) −21.3469 −0.795000
\(722\) −35.8062 −1.33257
\(723\) 0 0
\(724\) 0.374606 0.0139221
\(725\) 6.00910 0.223172
\(726\) 0 0
\(727\) 38.4606 1.42643 0.713213 0.700948i \(-0.247239\pi\)
0.713213 + 0.700948i \(0.247239\pi\)
\(728\) −8.82830 −0.327199
\(729\) 0 0
\(730\) −22.7591 −0.842352
\(731\) −14.6629 −0.542328
\(732\) 0 0
\(733\) 14.1077 0.521082 0.260541 0.965463i \(-0.416099\pi\)
0.260541 + 0.965463i \(0.416099\pi\)
\(734\) −12.4239 −0.458576
\(735\) 0 0
\(736\) 23.7353 0.874896
\(737\) −31.7998 −1.17136
\(738\) 0 0
\(739\) −11.8457 −0.435752 −0.217876 0.975977i \(-0.569913\pi\)
−0.217876 + 0.975977i \(0.569913\pi\)
\(740\) 18.3401 0.674194
\(741\) 0 0
\(742\) −0.263594 −0.00967682
\(743\) −21.7676 −0.798574 −0.399287 0.916826i \(-0.630742\pi\)
−0.399287 + 0.916826i \(0.630742\pi\)
\(744\) 0 0
\(745\) 21.4645 0.786400
\(746\) −1.42058 −0.0520111
\(747\) 0 0
\(748\) −27.4989 −1.00546
\(749\) −19.3732 −0.707880
\(750\) 0 0
\(751\) −42.5490 −1.55264 −0.776318 0.630341i \(-0.782915\pi\)
−0.776318 + 0.630341i \(0.782915\pi\)
\(752\) 3.39910 0.123952
\(753\) 0 0
\(754\) −9.65445 −0.351594
\(755\) −56.7719 −2.06614
\(756\) 0 0
\(757\) −20.6382 −0.750110 −0.375055 0.927003i \(-0.622376\pi\)
−0.375055 + 0.927003i \(0.622376\pi\)
\(758\) −0.892009 −0.0323992
\(759\) 0 0
\(760\) −50.6040 −1.83560
\(761\) −49.4450 −1.79238 −0.896190 0.443670i \(-0.853676\pi\)
−0.896190 + 0.443670i \(0.853676\pi\)
\(762\) 0 0
\(763\) −3.13767 −0.113591
\(764\) 3.34551 0.121036
\(765\) 0 0
\(766\) −16.9760 −0.613367
\(767\) 5.34483 0.192991
\(768\) 0 0
\(769\) 22.1336 0.798158 0.399079 0.916917i \(-0.369330\pi\)
0.399079 + 0.916917i \(0.369330\pi\)
\(770\) 14.5224 0.523351
\(771\) 0 0
\(772\) −0.692269 −0.0249153
\(773\) 21.9671 0.790102 0.395051 0.918659i \(-0.370727\pi\)
0.395051 + 0.918659i \(0.370727\pi\)
\(774\) 0 0
\(775\) 1.83227 0.0658170
\(776\) −15.8332 −0.568380
\(777\) 0 0
\(778\) 20.3736 0.730430
\(779\) 57.3057 2.05319
\(780\) 0 0
\(781\) 25.7303 0.920704
\(782\) −19.7860 −0.707547
\(783\) 0 0
\(784\) −0.547423 −0.0195508
\(785\) −6.44463 −0.230019
\(786\) 0 0
\(787\) 0.535531 0.0190896 0.00954480 0.999954i \(-0.496962\pi\)
0.00954480 + 0.999954i \(0.496962\pi\)
\(788\) 30.8977 1.10068
\(789\) 0 0
\(790\) 7.54179 0.268325
\(791\) −44.4264 −1.57962
\(792\) 0 0
\(793\) 0.456858 0.0162235
\(794\) −3.26516 −0.115876
\(795\) 0 0
\(796\) −2.97508 −0.105449
\(797\) 40.0990 1.42038 0.710189 0.704011i \(-0.248609\pi\)
0.710189 + 0.704011i \(0.248609\pi\)
\(798\) 0 0
\(799\) −28.9519 −1.02425
\(800\) −3.78766 −0.133914
\(801\) 0 0
\(802\) 6.08950 0.215028
\(803\) 38.6842 1.36514
\(804\) 0 0
\(805\) −24.1011 −0.849452
\(806\) −2.94379 −0.103691
\(807\) 0 0
\(808\) −26.9905 −0.949522
\(809\) 17.1826 0.604110 0.302055 0.953291i \(-0.402327\pi\)
0.302055 + 0.953291i \(0.402327\pi\)
\(810\) 0 0
\(811\) −19.6169 −0.688842 −0.344421 0.938815i \(-0.611925\pi\)
−0.344421 + 0.938815i \(0.611925\pi\)
\(812\) 32.4101 1.13737
\(813\) 0 0
\(814\) 13.5153 0.473710
\(815\) 52.3960 1.83535
\(816\) 0 0
\(817\) 18.8464 0.659351
\(818\) 13.5551 0.473943
\(819\) 0 0
\(820\) 23.5579 0.822676
\(821\) 35.9059 1.25313 0.626563 0.779371i \(-0.284461\pi\)
0.626563 + 0.779371i \(0.284461\pi\)
\(822\) 0 0
\(823\) −25.8181 −0.899961 −0.449980 0.893038i \(-0.648569\pi\)
−0.449980 + 0.893038i \(0.648569\pi\)
\(824\) 22.5342 0.785017
\(825\) 0 0
\(826\) 7.77915 0.270671
\(827\) −24.9586 −0.867895 −0.433948 0.900938i \(-0.642880\pi\)
−0.433948 + 0.900938i \(0.642880\pi\)
\(828\) 0 0
\(829\) 2.79927 0.0972228 0.0486114 0.998818i \(-0.484520\pi\)
0.0486114 + 0.998818i \(0.484520\pi\)
\(830\) −1.68779 −0.0585842
\(831\) 0 0
\(832\) 4.11612 0.142701
\(833\) 4.66270 0.161553
\(834\) 0 0
\(835\) −21.2702 −0.736087
\(836\) 35.3445 1.22242
\(837\) 0 0
\(838\) −8.93083 −0.308511
\(839\) −44.7079 −1.54349 −0.771744 0.635934i \(-0.780615\pi\)
−0.771744 + 0.635934i \(0.780615\pi\)
\(840\) 0 0
\(841\) 57.2526 1.97423
\(842\) −5.67062 −0.195423
\(843\) 0 0
\(844\) −27.9146 −0.960861
\(845\) 26.6470 0.916684
\(846\) 0 0
\(847\) 2.83104 0.0972756
\(848\) −0.0998141 −0.00342763
\(849\) 0 0
\(850\) 3.15743 0.108299
\(851\) −22.4297 −0.768880
\(852\) 0 0
\(853\) −43.5150 −1.48992 −0.744962 0.667107i \(-0.767532\pi\)
−0.744962 + 0.667107i \(0.767532\pi\)
\(854\) 0.664935 0.0227536
\(855\) 0 0
\(856\) 20.4507 0.698991
\(857\) 7.31050 0.249722 0.124861 0.992174i \(-0.460152\pi\)
0.124861 + 0.992174i \(0.460152\pi\)
\(858\) 0 0
\(859\) −9.66310 −0.329701 −0.164850 0.986319i \(-0.552714\pi\)
−0.164850 + 0.986319i \(0.552714\pi\)
\(860\) 7.74758 0.264190
\(861\) 0 0
\(862\) −0.302603 −0.0103067
\(863\) 3.15525 0.107406 0.0537030 0.998557i \(-0.482898\pi\)
0.0537030 + 0.998557i \(0.482898\pi\)
\(864\) 0 0
\(865\) −6.25989 −0.212843
\(866\) −18.7442 −0.636953
\(867\) 0 0
\(868\) 9.88235 0.335429
\(869\) −12.8190 −0.434854
\(870\) 0 0
\(871\) 13.5306 0.458467
\(872\) 3.31219 0.112165
\(873\) 0 0
\(874\) 25.4311 0.860221
\(875\) −25.8747 −0.874724
\(876\) 0 0
\(877\) −52.9229 −1.78708 −0.893539 0.448986i \(-0.851785\pi\)
−0.893539 + 0.448986i \(0.851785\pi\)
\(878\) −28.5160 −0.962369
\(879\) 0 0
\(880\) 5.49915 0.185376
\(881\) −36.7014 −1.23650 −0.618250 0.785981i \(-0.712158\pi\)
−0.618250 + 0.785981i \(0.712158\pi\)
\(882\) 0 0
\(883\) 29.9103 1.00656 0.503280 0.864123i \(-0.332126\pi\)
0.503280 + 0.864123i \(0.332126\pi\)
\(884\) 11.7006 0.393533
\(885\) 0 0
\(886\) 29.3879 0.987306
\(887\) −55.7515 −1.87195 −0.935976 0.352064i \(-0.885480\pi\)
−0.935976 + 0.352064i \(0.885480\pi\)
\(888\) 0 0
\(889\) 9.91941 0.332686
\(890\) 6.89133 0.230998
\(891\) 0 0
\(892\) 18.5252 0.620270
\(893\) 37.2121 1.24526
\(894\) 0 0
\(895\) −8.75573 −0.292672
\(896\) −23.2950 −0.778230
\(897\) 0 0
\(898\) −9.16618 −0.305880
\(899\) 26.2998 0.877146
\(900\) 0 0
\(901\) 0.850170 0.0283233
\(902\) 17.3604 0.578038
\(903\) 0 0
\(904\) 46.8974 1.55978
\(905\) 0.638071 0.0212102
\(906\) 0 0
\(907\) 36.0017 1.19542 0.597708 0.801714i \(-0.296078\pi\)
0.597708 + 0.801714i \(0.296078\pi\)
\(908\) 17.3986 0.577393
\(909\) 0 0
\(910\) −6.17917 −0.204838
\(911\) 16.3768 0.542589 0.271294 0.962496i \(-0.412548\pi\)
0.271294 + 0.962496i \(0.412548\pi\)
\(912\) 0 0
\(913\) 2.86879 0.0949430
\(914\) 15.4426 0.510795
\(915\) 0 0
\(916\) −35.8013 −1.18291
\(917\) −0.256387 −0.00846665
\(918\) 0 0
\(919\) 19.5368 0.644461 0.322231 0.946661i \(-0.395567\pi\)
0.322231 + 0.946661i \(0.395567\pi\)
\(920\) 25.4416 0.838785
\(921\) 0 0
\(922\) 5.94330 0.195732
\(923\) −10.9481 −0.360360
\(924\) 0 0
\(925\) 3.57930 0.117687
\(926\) 12.4083 0.407761
\(927\) 0 0
\(928\) −54.3668 −1.78468
\(929\) 10.7511 0.352733 0.176367 0.984325i \(-0.443566\pi\)
0.176367 + 0.984325i \(0.443566\pi\)
\(930\) 0 0
\(931\) −5.99300 −0.196413
\(932\) 7.52873 0.246612
\(933\) 0 0
\(934\) −20.3304 −0.665232
\(935\) −46.8392 −1.53181
\(936\) 0 0
\(937\) −28.4438 −0.929218 −0.464609 0.885516i \(-0.653805\pi\)
−0.464609 + 0.885516i \(0.653805\pi\)
\(938\) 19.6931 0.643004
\(939\) 0 0
\(940\) 15.2976 0.498952
\(941\) 27.7605 0.904968 0.452484 0.891773i \(-0.350538\pi\)
0.452484 + 0.891773i \(0.350538\pi\)
\(942\) 0 0
\(943\) −28.8110 −0.938216
\(944\) 2.94571 0.0958746
\(945\) 0 0
\(946\) 5.70939 0.185628
\(947\) 42.4755 1.38027 0.690135 0.723681i \(-0.257551\pi\)
0.690135 + 0.723681i \(0.257551\pi\)
\(948\) 0 0
\(949\) −16.4599 −0.534309
\(950\) −4.05827 −0.131668
\(951\) 0 0
\(952\) 41.4425 1.34316
\(953\) 49.1516 1.59218 0.796088 0.605181i \(-0.206899\pi\)
0.796088 + 0.605181i \(0.206899\pi\)
\(954\) 0 0
\(955\) 5.69845 0.184397
\(956\) −11.6787 −0.377717
\(957\) 0 0
\(958\) −30.6040 −0.988770
\(959\) −19.0594 −0.615459
\(960\) 0 0
\(961\) −22.9808 −0.741316
\(962\) −5.75065 −0.185408
\(963\) 0 0
\(964\) 0.616913 0.0198694
\(965\) −1.17915 −0.0379582
\(966\) 0 0
\(967\) 47.9870 1.54316 0.771579 0.636134i \(-0.219467\pi\)
0.771579 + 0.636134i \(0.219467\pi\)
\(968\) −2.98850 −0.0960540
\(969\) 0 0
\(970\) −11.0821 −0.355826
\(971\) −28.9682 −0.929633 −0.464817 0.885407i \(-0.653880\pi\)
−0.464817 + 0.885407i \(0.653880\pi\)
\(972\) 0 0
\(973\) 26.1162 0.837247
\(974\) −9.10979 −0.291896
\(975\) 0 0
\(976\) 0.251789 0.00805956
\(977\) −15.1972 −0.486201 −0.243100 0.970001i \(-0.578164\pi\)
−0.243100 + 0.970001i \(0.578164\pi\)
\(978\) 0 0
\(979\) −11.7134 −0.374361
\(980\) −2.46367 −0.0786990
\(981\) 0 0
\(982\) 29.9815 0.956747
\(983\) −38.5722 −1.23026 −0.615131 0.788425i \(-0.710897\pi\)
−0.615131 + 0.788425i \(0.710897\pi\)
\(984\) 0 0
\(985\) 52.6284 1.67688
\(986\) 45.3207 1.44331
\(987\) 0 0
\(988\) −15.0388 −0.478449
\(989\) −9.47520 −0.301294
\(990\) 0 0
\(991\) 51.0341 1.62115 0.810576 0.585633i \(-0.199154\pi\)
0.810576 + 0.585633i \(0.199154\pi\)
\(992\) −16.5773 −0.526329
\(993\) 0 0
\(994\) −15.9344 −0.505408
\(995\) −5.06749 −0.160650
\(996\) 0 0
\(997\) 31.7973 1.00703 0.503515 0.863987i \(-0.332040\pi\)
0.503515 + 0.863987i \(0.332040\pi\)
\(998\) 22.9910 0.727768
\(999\) 0 0
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 729.2.a.e.1.2 yes 6
3.2 odd 2 729.2.a.b.1.5 6
9.2 odd 6 729.2.c.d.244.2 12
9.4 even 3 729.2.c.a.487.5 12
9.5 odd 6 729.2.c.d.487.2 12
9.7 even 3 729.2.c.a.244.5 12
27.2 odd 18 729.2.e.s.568.1 12
27.4 even 9 729.2.e.k.406.1 12
27.5 odd 18 729.2.e.j.649.2 12
27.7 even 9 729.2.e.k.325.1 12
27.11 odd 18 729.2.e.j.82.2 12
27.13 even 9 729.2.e.l.163.2 12
27.14 odd 18 729.2.e.s.163.1 12
27.16 even 9 729.2.e.u.82.1 12
27.20 odd 18 729.2.e.t.325.2 12
27.22 even 9 729.2.e.u.649.1 12
27.23 odd 18 729.2.e.t.406.2 12
27.25 even 9 729.2.e.l.568.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.5 6 3.2 odd 2
729.2.a.e.1.2 yes 6 1.1 even 1 trivial
729.2.c.a.244.5 12 9.7 even 3
729.2.c.a.487.5 12 9.4 even 3
729.2.c.d.244.2 12 9.2 odd 6
729.2.c.d.487.2 12 9.5 odd 6
729.2.e.j.82.2 12 27.11 odd 18
729.2.e.j.649.2 12 27.5 odd 18
729.2.e.k.325.1 12 27.7 even 9
729.2.e.k.406.1 12 27.4 even 9
729.2.e.l.163.2 12 27.13 even 9
729.2.e.l.568.2 12 27.25 even 9
729.2.e.s.163.1 12 27.14 odd 18
729.2.e.s.568.1 12 27.2 odd 18
729.2.e.t.325.2 12 27.20 odd 18
729.2.e.t.406.2 12 27.23 odd 18
729.2.e.u.82.1 12 27.16 even 9
729.2.e.u.649.1 12 27.22 even 9