Properties

Label 729.2.a.b.1.5
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 1.5
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 \(-0.411332\pi\)
0.274970 + 0.961453i \(0.411332\pi\)
\(3\) 0 0
\(4\) −1.39513 −0.697566
\(5\) 2.37635 1.06273 0.531367 0.847141i \(-0.321678\pi\)
0.531367 + 0.847141i \(0.321678\pi\)
\(6\) 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 \(-0.342962\pi\)
0.473579 + 0.880751i \(0.342962\pi\)
\(12\) 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 \(-0.224759\pi\)
0.760897 + 0.648873i \(0.224759\pi\)
\(18\) 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 \(-0.361075\pi\)
0.422721 + 0.906260i \(0.361075\pi\)
\(24\) 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 \(-0.830975\pi\)
−0.862297 + 0.506402i \(0.830975\pi\)
\(30\) 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 \(-0.687231\pi\)
−0.554867 + 0.831939i \(0.687231\pi\)
\(42\) 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 \(-0.609252\pi\)
−0.336526 + 0.941674i \(0.609252\pi\)
\(48\) 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 \(-0.497038\pi\)
0.00930588 + 0.999957i \(0.497038\pi\)
\(54\) 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 \(-0.583820\pi\)
−0.260296 + 0.965529i \(0.583820\pi\)
\(60\) 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 \(-0.338443\pi\)
0.486035 + 0.873940i \(0.338443\pi\)
\(72\) 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 \(-0.484040\pi\)
0.0501199 + 0.998743i \(0.484040\pi\)
\(84\) 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 \(-0.563322\pi\)
−0.197623 + 0.980278i \(0.563322\pi\)
\(90\) 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 \(-0.330182\pi\)
0.508549 + 0.861033i \(0.330182\pi\)
\(102\) 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 \(-0.622141\pi\)
−0.374369 + 0.927280i \(0.622141\pi\)
\(108\) 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 \(-0.814762\pi\)
−0.835396 + 0.549648i \(0.814762\pi\)
\(114\) 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 \(-0.501425\pi\)
−0.00447766 + 0.999990i \(0.501425\pi\)
\(132\) 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 \(-0.605530\pi\)
−0.325491 + 0.945545i \(0.605530\pi\)
\(138\) 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 \(-0.379362\pi\)
0.369989 + 0.929036i \(0.379362\pi\)
\(150\) 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 \(-0.612568\pi\)
−0.346317 + 0.938118i \(0.612568\pi\)
\(168\) 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 \(-0.531929\pi\)
−0.100139 + 0.994973i \(0.531929\pi\)
\(174\) 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 \(-0.543970\pi\)
−0.137697 + 0.990474i \(0.543970\pi\)
\(180\) 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 \(-0.472350\pi\)
0.0867561 + 0.996230i \(0.472350\pi\)
\(192\) 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 \(-0.210627\pi\)
0.788946 + 0.614462i \(0.210627\pi\)
\(198\) 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 \(-0.364179\pi\)
0.413862 + 0.910339i \(0.364179\pi\)
\(228\) 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 \(-0.443436\pi\)
0.176766 + 0.984253i \(0.443436\pi\)
\(234\) 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 \(-0.587268\pi\)
−0.270739 + 0.962653i \(0.587268\pi\)
\(240\) 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 \(-0.680599\pi\)
−0.537416 + 0.843317i \(0.680599\pi\)
\(252\) 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 \(-0.725703\pi\)
−0.651127 + 0.758969i \(0.725703\pi\)
\(258\) 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 \(-0.703985\pi\)
−0.597867 + 0.801595i \(0.703985\pi\)
\(264\) 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 \(-0.692841\pi\)
−0.569443 + 0.822031i \(0.692841\pi\)
\(270\) 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 \(-0.640746\pi\)
−0.427899 + 0.903826i \(0.640746\pi\)
\(282\) 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 \(-0.397953\pi\)
0.315126 + 0.949050i \(0.397953\pi\)
\(294\) 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 \(-0.622446\pi\)
−0.375257 + 0.926921i \(0.622446\pi\)
\(312\) 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 \(-0.577927\pi\)
−0.242378 + 0.970182i \(0.577927\pi\)
\(318\) 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 \(-0.700135\pi\)
−0.588128 + 0.808768i \(0.700135\pi\)
\(348\) 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 \(-0.611606\pi\)
−0.343482 + 0.939159i \(0.611606\pi\)
\(354\) 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 \(-0.738710\pi\)
−0.681588 + 0.731736i \(0.738710\pi\)
\(360\) 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 \(-0.688304\pi\)
−0.557668 + 0.830064i \(0.688304\pi\)
\(384\) 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 \(-0.268815\pi\)
0.664099 + 0.747644i \(0.268815\pi\)
\(390\) 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 \(-0.437367\pi\)
0.195501 + 0.980703i \(0.437367\pi\)
\(402\) 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 \(-0.590499\pi\)
−0.280495 + 0.959856i \(0.590499\pi\)
\(420\) 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 \(-0.502983\pi\)
−0.00937075 + 0.999956i \(0.502983\pi\)
\(432\) 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 \(-0.145274\pi\)
0.897649 + 0.440711i \(0.145274\pi\)
\(444\) 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 \(-0.589706\pi\)
−0.278103 + 0.960551i \(0.589706\pi\)
\(450\) 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 \(-0.443051\pi\)
0.177958 + 0.984038i \(0.443051\pi\)
\(462\) 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 \(-0.706756\pi\)
−0.604822 + 0.796360i \(0.706756\pi\)
\(468\) 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 \(-0.855691\pi\)
−0.898980 + 0.437989i \(0.855691\pi\)
\(480\) 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 \(-0.164206\pi\)
0.869865 + 0.493290i \(0.164206\pi\)
\(492\) 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 \(-0.791566\pi\)
−0.793161 + 0.609011i \(0.791566\pi\)
\(504\) 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 \(-0.283459\pi\)
0.629013 + 0.777395i \(0.283459\pi\)
\(510\) 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 \(-0.311888\pi\)
0.557167 + 0.830401i \(0.311888\pi\)
\(522\) 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 \(-0.530949\pi\)
−0.0970769 + 0.995277i \(0.530949\pi\)
\(558\) 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 \(-0.583344\pi\)
−0.258853 + 0.965917i \(0.583344\pi\)
\(564\) 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 \(-0.598256\pi\)
−0.303803 + 0.952735i \(0.598256\pi\)
\(570\) 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 \(-0.404165\pi\)
0.296545 + 0.955019i \(0.404165\pi\)
\(588\) 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 \(-0.180276\pi\)
0.843862 + 0.536560i \(0.180276\pi\)
\(594\) 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 \(-0.555967\pi\)
−0.174920 + 0.984583i \(0.555967\pi\)
\(600\) 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 \(-0.459699\pi\)
0.126271 + 0.991996i \(0.459699\pi\)
\(618\) 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 \(-0.266355\pi\)
0.669858 + 0.742490i \(0.266355\pi\)
\(642\) 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 \(-0.743118\pi\)
−0.691655 + 0.722228i \(0.743118\pi\)
\(648\) 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 \(-0.624689\pi\)
−0.381781 + 0.924253i \(0.624689\pi\)
\(654\) 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 \(-0.648455\pi\)
−0.449660 + 0.893200i \(0.648455\pi\)
\(660\) 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 \(-0.415935\pi\)
0.261037 + 0.965329i \(0.415935\pi\)
\(678\) 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 \(-0.462969\pi\)
0.116074 + 0.993241i \(0.462969\pi\)
\(684\) 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 \(-0.566745\pi\)
−0.208151 + 0.978097i \(0.566745\pi\)
\(702\) 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 \(-0.708774\pi\)
−0.609859 + 0.792510i \(0.708774\pi\)
\(720\) 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 \(-0.369258\pi\)
0.399287 + 0.916826i \(0.369258\pi\)
\(744\) 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 \(-0.146324\pi\)
0.896190 + 0.443670i \(0.146324\pi\)
\(762\) 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 \(-0.629273\pi\)
−0.395051 + 0.918659i \(0.629273\pi\)
\(774\) 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 \(-0.751391\pi\)
−0.710189 + 0.704011i \(0.751391\pi\)
\(798\) 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 \(-0.597673\pi\)
−0.302055 + 0.953291i \(0.597673\pi\)
\(810\) 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 \(-0.715539\pi\)
−0.626563 + 0.779371i \(0.715539\pi\)
\(822\) 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 \(-0.357120\pi\)
0.433948 + 0.900938i \(0.357120\pi\)
\(828\) 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 \(-0.219385\pi\)
0.771744 + 0.635934i \(0.219385\pi\)
\(840\) 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 \(-0.539848\pi\)
−0.124861 + 0.992174i \(0.539848\pi\)
\(858\) 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 \(-0.517102\pi\)
−0.0537030 + 0.998557i \(0.517102\pi\)
\(864\) 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 \(-0.287842\pi\)
0.618250 + 0.785981i \(0.287842\pi\)
\(882\) 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 \(-0.114520\pi\)
0.935976 + 0.352064i \(0.114520\pi\)
\(888\) 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 \(-0.587452\pi\)
−0.271294 + 0.962496i \(0.587452\pi\)
\(912\) 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 \(-0.556434\pi\)
−0.176367 + 0.984325i \(0.556434\pi\)
\(930\) 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 \(-0.649462\pi\)
−0.452484 + 0.891773i \(0.649462\pi\)
\(942\) 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 \(-0.742449\pi\)
−0.690135 + 0.723681i \(0.742449\pi\)
\(948\) 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 \(-0.793101\pi\)
−0.796088 + 0.605181i \(0.793101\pi\)
\(954\) 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 \(-0.346120\pi\)
0.464817 + 0.885407i \(0.346120\pi\)
\(972\) 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 \(-0.421836\pi\)
0.243100 + 0.970001i \(0.421836\pi\)
\(978\) 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 \(-0.289103\pi\)
0.615131 + 0.788425i \(0.289103\pi\)
\(984\) 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.b.1.5 6
3.2 odd 2 729.2.a.e.1.2 yes 6
9.2 odd 6 729.2.c.a.244.5 12
9.4 even 3 729.2.c.d.487.2 12
9.5 odd 6 729.2.c.a.487.5 12
9.7 even 3 729.2.c.d.244.2 12
27.2 odd 18 729.2.e.l.568.2 12
27.4 even 9 729.2.e.t.406.2 12
27.5 odd 18 729.2.e.u.649.1 12
27.7 even 9 729.2.e.t.325.2 12
27.11 odd 18 729.2.e.u.82.1 12
27.13 even 9 729.2.e.s.163.1 12
27.14 odd 18 729.2.e.l.163.2 12
27.16 even 9 729.2.e.j.82.2 12
27.20 odd 18 729.2.e.k.325.1 12
27.22 even 9 729.2.e.j.649.2 12
27.23 odd 18 729.2.e.k.406.1 12
27.25 even 9 729.2.e.s.568.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.5 6 1.1 even 1 trivial
729.2.a.e.1.2 yes 6 3.2 odd 2
729.2.c.a.244.5 12 9.2 odd 6
729.2.c.a.487.5 12 9.5 odd 6
729.2.c.d.244.2 12 9.7 even 3
729.2.c.d.487.2 12 9.4 even 3
729.2.e.j.82.2 12 27.16 even 9
729.2.e.j.649.2 12 27.22 even 9
729.2.e.k.325.1 12 27.20 odd 18
729.2.e.k.406.1 12 27.23 odd 18
729.2.e.l.163.2 12 27.14 odd 18
729.2.e.l.568.2 12 27.2 odd 18
729.2.e.s.163.1 12 27.13 even 9
729.2.e.s.568.1 12 27.25 even 9
729.2.e.t.325.2 12 27.7 even 9
729.2.e.t.406.2 12 27.4 even 9
729.2.e.u.82.1 12 27.11 odd 18
729.2.e.u.649.1 12 27.5 odd 18