Properties

Label 8016.2.a.bb.1.3
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 29 x^{7} - 7 x^{6} + 266 x^{5} + 69 x^{4} - 901 x^{3} - 199 x^{2} + 875 x + 391\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.79204\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -0.792043 q^{5} -3.80237 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -0.792043 q^{5} -3.80237 q^{7} +1.00000 q^{9} -5.89024 q^{11} -0.555473 q^{13} +0.792043 q^{15} -1.29236 q^{17} +0.877845 q^{19} +3.80237 q^{21} -1.89018 q^{23} -4.37267 q^{25} -1.00000 q^{27} +4.21505 q^{29} -6.06288 q^{31} +5.89024 q^{33} +3.01164 q^{35} -8.81590 q^{37} +0.555473 q^{39} +0.966875 q^{41} -1.48271 q^{43} -0.792043 q^{45} -4.12328 q^{47} +7.45799 q^{49} +1.29236 q^{51} -13.1556 q^{53} +4.66532 q^{55} -0.877845 q^{57} -10.0336 q^{59} -7.38784 q^{61} -3.80237 q^{63} +0.439959 q^{65} +6.38640 q^{67} +1.89018 q^{69} -12.6943 q^{71} -11.0478 q^{73} +4.37267 q^{75} +22.3968 q^{77} -0.414580 q^{79} +1.00000 q^{81} +2.57849 q^{83} +1.02360 q^{85} -4.21505 q^{87} +0.384059 q^{89} +2.11211 q^{91} +6.06288 q^{93} -0.695291 q^{95} -3.26789 q^{97} -5.89024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.792043 −0.354212 −0.177106 0.984192i \(-0.556674\pi\)
−0.177106 + 0.984192i \(0.556674\pi\)
\(6\) 0 0
\(7\) −3.80237 −1.43716 −0.718580 0.695445i \(-0.755207\pi\)
−0.718580 + 0.695445i \(0.755207\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.89024 −1.77597 −0.887987 0.459869i \(-0.847896\pi\)
−0.887987 + 0.459869i \(0.847896\pi\)
\(12\) 0 0
\(13\) −0.555473 −0.154061 −0.0770303 0.997029i \(-0.524544\pi\)
−0.0770303 + 0.997029i \(0.524544\pi\)
\(14\) 0 0
\(15\) 0.792043 0.204505
\(16\) 0 0
\(17\) −1.29236 −0.313443 −0.156721 0.987643i \(-0.550092\pi\)
−0.156721 + 0.987643i \(0.550092\pi\)
\(18\) 0 0
\(19\) 0.877845 0.201391 0.100696 0.994917i \(-0.467893\pi\)
0.100696 + 0.994917i \(0.467893\pi\)
\(20\) 0 0
\(21\) 3.80237 0.829744
\(22\) 0 0
\(23\) −1.89018 −0.394131 −0.197065 0.980390i \(-0.563141\pi\)
−0.197065 + 0.980390i \(0.563141\pi\)
\(24\) 0 0
\(25\) −4.37267 −0.874534
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 4.21505 0.782715 0.391358 0.920239i \(-0.372006\pi\)
0.391358 + 0.920239i \(0.372006\pi\)
\(30\) 0 0
\(31\) −6.06288 −1.08893 −0.544463 0.838785i \(-0.683266\pi\)
−0.544463 + 0.838785i \(0.683266\pi\)
\(32\) 0 0
\(33\) 5.89024 1.02536
\(34\) 0 0
\(35\) 3.01164 0.509060
\(36\) 0 0
\(37\) −8.81590 −1.44932 −0.724662 0.689104i \(-0.758004\pi\)
−0.724662 + 0.689104i \(0.758004\pi\)
\(38\) 0 0
\(39\) 0.555473 0.0889469
\(40\) 0 0
\(41\) 0.966875 0.151001 0.0755003 0.997146i \(-0.475945\pi\)
0.0755003 + 0.997146i \(0.475945\pi\)
\(42\) 0 0
\(43\) −1.48271 −0.226111 −0.113056 0.993589i \(-0.536064\pi\)
−0.113056 + 0.993589i \(0.536064\pi\)
\(44\) 0 0
\(45\) −0.792043 −0.118071
\(46\) 0 0
\(47\) −4.12328 −0.601442 −0.300721 0.953712i \(-0.597227\pi\)
−0.300721 + 0.953712i \(0.597227\pi\)
\(48\) 0 0
\(49\) 7.45799 1.06543
\(50\) 0 0
\(51\) 1.29236 0.180966
\(52\) 0 0
\(53\) −13.1556 −1.80706 −0.903532 0.428521i \(-0.859035\pi\)
−0.903532 + 0.428521i \(0.859035\pi\)
\(54\) 0 0
\(55\) 4.66532 0.629072
\(56\) 0 0
\(57\) −0.877845 −0.116273
\(58\) 0 0
\(59\) −10.0336 −1.30627 −0.653133 0.757243i \(-0.726546\pi\)
−0.653133 + 0.757243i \(0.726546\pi\)
\(60\) 0 0
\(61\) −7.38784 −0.945916 −0.472958 0.881085i \(-0.656814\pi\)
−0.472958 + 0.881085i \(0.656814\pi\)
\(62\) 0 0
\(63\) −3.80237 −0.479053
\(64\) 0 0
\(65\) 0.439959 0.0545702
\(66\) 0 0
\(67\) 6.38640 0.780223 0.390111 0.920768i \(-0.372437\pi\)
0.390111 + 0.920768i \(0.372437\pi\)
\(68\) 0 0
\(69\) 1.89018 0.227551
\(70\) 0 0
\(71\) −12.6943 −1.50654 −0.753270 0.657712i \(-0.771525\pi\)
−0.753270 + 0.657712i \(0.771525\pi\)
\(72\) 0 0
\(73\) −11.0478 −1.29305 −0.646523 0.762895i \(-0.723778\pi\)
−0.646523 + 0.762895i \(0.723778\pi\)
\(74\) 0 0
\(75\) 4.37267 0.504912
\(76\) 0 0
\(77\) 22.3968 2.55236
\(78\) 0 0
\(79\) −0.414580 −0.0466439 −0.0233219 0.999728i \(-0.507424\pi\)
−0.0233219 + 0.999728i \(0.507424\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.57849 0.283026 0.141513 0.989936i \(-0.454803\pi\)
0.141513 + 0.989936i \(0.454803\pi\)
\(84\) 0 0
\(85\) 1.02360 0.111025
\(86\) 0 0
\(87\) −4.21505 −0.451901
\(88\) 0 0
\(89\) 0.384059 0.0407102 0.0203551 0.999793i \(-0.493520\pi\)
0.0203551 + 0.999793i \(0.493520\pi\)
\(90\) 0 0
\(91\) 2.11211 0.221410
\(92\) 0 0
\(93\) 6.06288 0.628691
\(94\) 0 0
\(95\) −0.695291 −0.0713353
\(96\) 0 0
\(97\) −3.26789 −0.331804 −0.165902 0.986142i \(-0.553054\pi\)
−0.165902 + 0.986142i \(0.553054\pi\)
\(98\) 0 0
\(99\) −5.89024 −0.591991
\(100\) 0 0
\(101\) 8.49046 0.844832 0.422416 0.906402i \(-0.361182\pi\)
0.422416 + 0.906402i \(0.361182\pi\)
\(102\) 0 0
\(103\) −14.0009 −1.37955 −0.689776 0.724023i \(-0.742291\pi\)
−0.689776 + 0.724023i \(0.742291\pi\)
\(104\) 0 0
\(105\) −3.01164 −0.293906
\(106\) 0 0
\(107\) −15.4921 −1.49767 −0.748837 0.662754i \(-0.769387\pi\)
−0.748837 + 0.662754i \(0.769387\pi\)
\(108\) 0 0
\(109\) 11.8458 1.13462 0.567311 0.823504i \(-0.307984\pi\)
0.567311 + 0.823504i \(0.307984\pi\)
\(110\) 0 0
\(111\) 8.81590 0.836768
\(112\) 0 0
\(113\) −13.1420 −1.23630 −0.618148 0.786062i \(-0.712117\pi\)
−0.618148 + 0.786062i \(0.712117\pi\)
\(114\) 0 0
\(115\) 1.49711 0.139606
\(116\) 0 0
\(117\) −0.555473 −0.0513535
\(118\) 0 0
\(119\) 4.91401 0.450467
\(120\) 0 0
\(121\) 23.6949 2.15408
\(122\) 0 0
\(123\) −0.966875 −0.0871802
\(124\) 0 0
\(125\) 7.42355 0.663983
\(126\) 0 0
\(127\) 1.48314 0.131607 0.0658037 0.997833i \(-0.479039\pi\)
0.0658037 + 0.997833i \(0.479039\pi\)
\(128\) 0 0
\(129\) 1.48271 0.130545
\(130\) 0 0
\(131\) −0.619826 −0.0541545 −0.0270772 0.999633i \(-0.508620\pi\)
−0.0270772 + 0.999633i \(0.508620\pi\)
\(132\) 0 0
\(133\) −3.33789 −0.289432
\(134\) 0 0
\(135\) 0.792043 0.0681682
\(136\) 0 0
\(137\) 10.3559 0.884760 0.442380 0.896828i \(-0.354134\pi\)
0.442380 + 0.896828i \(0.354134\pi\)
\(138\) 0 0
\(139\) 4.31897 0.366330 0.183165 0.983082i \(-0.441366\pi\)
0.183165 + 0.983082i \(0.441366\pi\)
\(140\) 0 0
\(141\) 4.12328 0.347243
\(142\) 0 0
\(143\) 3.27187 0.273608
\(144\) 0 0
\(145\) −3.33850 −0.277247
\(146\) 0 0
\(147\) −7.45799 −0.615125
\(148\) 0 0
\(149\) 0.416459 0.0341177 0.0170588 0.999854i \(-0.494570\pi\)
0.0170588 + 0.999854i \(0.494570\pi\)
\(150\) 0 0
\(151\) 10.4266 0.848501 0.424250 0.905545i \(-0.360538\pi\)
0.424250 + 0.905545i \(0.360538\pi\)
\(152\) 0 0
\(153\) −1.29236 −0.104481
\(154\) 0 0
\(155\) 4.80206 0.385711
\(156\) 0 0
\(157\) 10.6346 0.848736 0.424368 0.905490i \(-0.360496\pi\)
0.424368 + 0.905490i \(0.360496\pi\)
\(158\) 0 0
\(159\) 13.1556 1.04331
\(160\) 0 0
\(161\) 7.18717 0.566429
\(162\) 0 0
\(163\) 10.6617 0.835092 0.417546 0.908656i \(-0.362890\pi\)
0.417546 + 0.908656i \(0.362890\pi\)
\(164\) 0 0
\(165\) −4.66532 −0.363195
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −12.6914 −0.976265
\(170\) 0 0
\(171\) 0.877845 0.0671305
\(172\) 0 0
\(173\) −9.69755 −0.737291 −0.368645 0.929570i \(-0.620178\pi\)
−0.368645 + 0.929570i \(0.620178\pi\)
\(174\) 0 0
\(175\) 16.6265 1.25684
\(176\) 0 0
\(177\) 10.0336 0.754173
\(178\) 0 0
\(179\) −9.09640 −0.679897 −0.339948 0.940444i \(-0.610410\pi\)
−0.339948 + 0.940444i \(0.610410\pi\)
\(180\) 0 0
\(181\) 3.40901 0.253390 0.126695 0.991942i \(-0.459563\pi\)
0.126695 + 0.991942i \(0.459563\pi\)
\(182\) 0 0
\(183\) 7.38784 0.546125
\(184\) 0 0
\(185\) 6.98257 0.513369
\(186\) 0 0
\(187\) 7.61229 0.556666
\(188\) 0 0
\(189\) 3.80237 0.276581
\(190\) 0 0
\(191\) 7.76442 0.561814 0.280907 0.959735i \(-0.409365\pi\)
0.280907 + 0.959735i \(0.409365\pi\)
\(192\) 0 0
\(193\) 1.67335 0.120450 0.0602250 0.998185i \(-0.480818\pi\)
0.0602250 + 0.998185i \(0.480818\pi\)
\(194\) 0 0
\(195\) −0.439959 −0.0315061
\(196\) 0 0
\(197\) −9.01551 −0.642329 −0.321164 0.947023i \(-0.604074\pi\)
−0.321164 + 0.947023i \(0.604074\pi\)
\(198\) 0 0
\(199\) −7.27504 −0.515714 −0.257857 0.966183i \(-0.583016\pi\)
−0.257857 + 0.966183i \(0.583016\pi\)
\(200\) 0 0
\(201\) −6.38640 −0.450462
\(202\) 0 0
\(203\) −16.0272 −1.12489
\(204\) 0 0
\(205\) −0.765807 −0.0534863
\(206\) 0 0
\(207\) −1.89018 −0.131377
\(208\) 0 0
\(209\) −5.17072 −0.357666
\(210\) 0 0
\(211\) 2.15224 0.148166 0.0740831 0.997252i \(-0.476397\pi\)
0.0740831 + 0.997252i \(0.476397\pi\)
\(212\) 0 0
\(213\) 12.6943 0.869801
\(214\) 0 0
\(215\) 1.17437 0.0800914
\(216\) 0 0
\(217\) 23.0533 1.56496
\(218\) 0 0
\(219\) 11.0478 0.746540
\(220\) 0 0
\(221\) 0.717870 0.0482892
\(222\) 0 0
\(223\) 14.5871 0.976823 0.488412 0.872613i \(-0.337577\pi\)
0.488412 + 0.872613i \(0.337577\pi\)
\(224\) 0 0
\(225\) −4.37267 −0.291511
\(226\) 0 0
\(227\) 19.2690 1.27893 0.639466 0.768819i \(-0.279156\pi\)
0.639466 + 0.768819i \(0.279156\pi\)
\(228\) 0 0
\(229\) −14.8221 −0.979469 −0.489735 0.871872i \(-0.662906\pi\)
−0.489735 + 0.871872i \(0.662906\pi\)
\(230\) 0 0
\(231\) −22.3968 −1.47360
\(232\) 0 0
\(233\) −7.73508 −0.506742 −0.253371 0.967369i \(-0.581539\pi\)
−0.253371 + 0.967369i \(0.581539\pi\)
\(234\) 0 0
\(235\) 3.26581 0.213038
\(236\) 0 0
\(237\) 0.414580 0.0269299
\(238\) 0 0
\(239\) 11.7199 0.758096 0.379048 0.925377i \(-0.376252\pi\)
0.379048 + 0.925377i \(0.376252\pi\)
\(240\) 0 0
\(241\) −0.783620 −0.0504774 −0.0252387 0.999681i \(-0.508035\pi\)
−0.0252387 + 0.999681i \(0.508035\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −5.90705 −0.377387
\(246\) 0 0
\(247\) −0.487620 −0.0310265
\(248\) 0 0
\(249\) −2.57849 −0.163405
\(250\) 0 0
\(251\) 1.99474 0.125907 0.0629533 0.998016i \(-0.479948\pi\)
0.0629533 + 0.998016i \(0.479948\pi\)
\(252\) 0 0
\(253\) 11.1336 0.699966
\(254\) 0 0
\(255\) −1.02360 −0.0641004
\(256\) 0 0
\(257\) −12.9694 −0.809012 −0.404506 0.914535i \(-0.632556\pi\)
−0.404506 + 0.914535i \(0.632556\pi\)
\(258\) 0 0
\(259\) 33.5213 2.08291
\(260\) 0 0
\(261\) 4.21505 0.260905
\(262\) 0 0
\(263\) 1.41225 0.0870832 0.0435416 0.999052i \(-0.486136\pi\)
0.0435416 + 0.999052i \(0.486136\pi\)
\(264\) 0 0
\(265\) 10.4198 0.640084
\(266\) 0 0
\(267\) −0.384059 −0.0235040
\(268\) 0 0
\(269\) −0.320518 −0.0195423 −0.00977116 0.999952i \(-0.503110\pi\)
−0.00977116 + 0.999952i \(0.503110\pi\)
\(270\) 0 0
\(271\) −16.4920 −1.00182 −0.500908 0.865501i \(-0.667000\pi\)
−0.500908 + 0.865501i \(0.667000\pi\)
\(272\) 0 0
\(273\) −2.11211 −0.127831
\(274\) 0 0
\(275\) 25.7561 1.55315
\(276\) 0 0
\(277\) 21.5960 1.29758 0.648788 0.760969i \(-0.275276\pi\)
0.648788 + 0.760969i \(0.275276\pi\)
\(278\) 0 0
\(279\) −6.06288 −0.362975
\(280\) 0 0
\(281\) 18.5310 1.10547 0.552734 0.833358i \(-0.313585\pi\)
0.552734 + 0.833358i \(0.313585\pi\)
\(282\) 0 0
\(283\) 17.7434 1.05473 0.527367 0.849637i \(-0.323179\pi\)
0.527367 + 0.849637i \(0.323179\pi\)
\(284\) 0 0
\(285\) 0.695291 0.0411855
\(286\) 0 0
\(287\) −3.67641 −0.217012
\(288\) 0 0
\(289\) −15.3298 −0.901754
\(290\) 0 0
\(291\) 3.26789 0.191567
\(292\) 0 0
\(293\) 10.7896 0.630337 0.315169 0.949036i \(-0.397939\pi\)
0.315169 + 0.949036i \(0.397939\pi\)
\(294\) 0 0
\(295\) 7.94706 0.462696
\(296\) 0 0
\(297\) 5.89024 0.341786
\(298\) 0 0
\(299\) 1.04995 0.0607200
\(300\) 0 0
\(301\) 5.63781 0.324958
\(302\) 0 0
\(303\) −8.49046 −0.487764
\(304\) 0 0
\(305\) 5.85149 0.335055
\(306\) 0 0
\(307\) 4.09400 0.233657 0.116829 0.993152i \(-0.462727\pi\)
0.116829 + 0.993152i \(0.462727\pi\)
\(308\) 0 0
\(309\) 14.0009 0.796485
\(310\) 0 0
\(311\) 3.47522 0.197062 0.0985309 0.995134i \(-0.468586\pi\)
0.0985309 + 0.995134i \(0.468586\pi\)
\(312\) 0 0
\(313\) −7.74695 −0.437883 −0.218942 0.975738i \(-0.570260\pi\)
−0.218942 + 0.975738i \(0.570260\pi\)
\(314\) 0 0
\(315\) 3.01164 0.169687
\(316\) 0 0
\(317\) −19.6818 −1.10544 −0.552720 0.833367i \(-0.686410\pi\)
−0.552720 + 0.833367i \(0.686410\pi\)
\(318\) 0 0
\(319\) −24.8277 −1.39008
\(320\) 0 0
\(321\) 15.4921 0.864683
\(322\) 0 0
\(323\) −1.13449 −0.0631247
\(324\) 0 0
\(325\) 2.42890 0.134731
\(326\) 0 0
\(327\) −11.8458 −0.655074
\(328\) 0 0
\(329\) 15.6782 0.864368
\(330\) 0 0
\(331\) 33.7021 1.85244 0.926219 0.376987i \(-0.123040\pi\)
0.926219 + 0.376987i \(0.123040\pi\)
\(332\) 0 0
\(333\) −8.81590 −0.483108
\(334\) 0 0
\(335\) −5.05830 −0.276364
\(336\) 0 0
\(337\) 9.85356 0.536758 0.268379 0.963313i \(-0.413512\pi\)
0.268379 + 0.963313i \(0.413512\pi\)
\(338\) 0 0
\(339\) 13.1420 0.713776
\(340\) 0 0
\(341\) 35.7118 1.93390
\(342\) 0 0
\(343\) −1.74145 −0.0940295
\(344\) 0 0
\(345\) −1.49711 −0.0806015
\(346\) 0 0
\(347\) −5.82717 −0.312819 −0.156409 0.987692i \(-0.549992\pi\)
−0.156409 + 0.987692i \(0.549992\pi\)
\(348\) 0 0
\(349\) −4.76718 −0.255181 −0.127591 0.991827i \(-0.540724\pi\)
−0.127591 + 0.991827i \(0.540724\pi\)
\(350\) 0 0
\(351\) 0.555473 0.0296490
\(352\) 0 0
\(353\) −8.19037 −0.435930 −0.217965 0.975957i \(-0.569942\pi\)
−0.217965 + 0.975957i \(0.569942\pi\)
\(354\) 0 0
\(355\) 10.0545 0.533635
\(356\) 0 0
\(357\) −4.91401 −0.260077
\(358\) 0 0
\(359\) −4.07201 −0.214912 −0.107456 0.994210i \(-0.534271\pi\)
−0.107456 + 0.994210i \(0.534271\pi\)
\(360\) 0 0
\(361\) −18.2294 −0.959441
\(362\) 0 0
\(363\) −23.6949 −1.24366
\(364\) 0 0
\(365\) 8.75032 0.458013
\(366\) 0 0
\(367\) −32.3570 −1.68902 −0.844511 0.535539i \(-0.820109\pi\)
−0.844511 + 0.535539i \(0.820109\pi\)
\(368\) 0 0
\(369\) 0.966875 0.0503335
\(370\) 0 0
\(371\) 50.0225 2.59704
\(372\) 0 0
\(373\) −36.8166 −1.90629 −0.953147 0.302509i \(-0.902176\pi\)
−0.953147 + 0.302509i \(0.902176\pi\)
\(374\) 0 0
\(375\) −7.42355 −0.383351
\(376\) 0 0
\(377\) −2.34135 −0.120586
\(378\) 0 0
\(379\) 32.7057 1.67998 0.839989 0.542604i \(-0.182561\pi\)
0.839989 + 0.542604i \(0.182561\pi\)
\(380\) 0 0
\(381\) −1.48314 −0.0759836
\(382\) 0 0
\(383\) −13.0798 −0.668346 −0.334173 0.942512i \(-0.608457\pi\)
−0.334173 + 0.942512i \(0.608457\pi\)
\(384\) 0 0
\(385\) −17.7393 −0.904076
\(386\) 0 0
\(387\) −1.48271 −0.0753705
\(388\) 0 0
\(389\) −30.1800 −1.53019 −0.765094 0.643919i \(-0.777308\pi\)
−0.765094 + 0.643919i \(0.777308\pi\)
\(390\) 0 0
\(391\) 2.44279 0.123537
\(392\) 0 0
\(393\) 0.619826 0.0312661
\(394\) 0 0
\(395\) 0.328365 0.0165218
\(396\) 0 0
\(397\) −33.9012 −1.70145 −0.850727 0.525608i \(-0.823838\pi\)
−0.850727 + 0.525608i \(0.823838\pi\)
\(398\) 0 0
\(399\) 3.33789 0.167103
\(400\) 0 0
\(401\) −10.9947 −0.549047 −0.274524 0.961580i \(-0.588520\pi\)
−0.274524 + 0.961580i \(0.588520\pi\)
\(402\) 0 0
\(403\) 3.36777 0.167761
\(404\) 0 0
\(405\) −0.792043 −0.0393569
\(406\) 0 0
\(407\) 51.9278 2.57396
\(408\) 0 0
\(409\) −38.5602 −1.90668 −0.953340 0.301899i \(-0.902380\pi\)
−0.953340 + 0.301899i \(0.902380\pi\)
\(410\) 0 0
\(411\) −10.3559 −0.510817
\(412\) 0 0
\(413\) 38.1515 1.87731
\(414\) 0 0
\(415\) −2.04227 −0.100251
\(416\) 0 0
\(417\) −4.31897 −0.211501
\(418\) 0 0
\(419\) −15.4499 −0.754777 −0.377388 0.926055i \(-0.623178\pi\)
−0.377388 + 0.926055i \(0.623178\pi\)
\(420\) 0 0
\(421\) 32.2837 1.57341 0.786706 0.617328i \(-0.211785\pi\)
0.786706 + 0.617328i \(0.211785\pi\)
\(422\) 0 0
\(423\) −4.12328 −0.200481
\(424\) 0 0
\(425\) 5.65105 0.274116
\(426\) 0 0
\(427\) 28.0913 1.35943
\(428\) 0 0
\(429\) −3.27187 −0.157967
\(430\) 0 0
\(431\) −6.55545 −0.315765 −0.157882 0.987458i \(-0.550467\pi\)
−0.157882 + 0.987458i \(0.550467\pi\)
\(432\) 0 0
\(433\) 29.1380 1.40028 0.700140 0.714005i \(-0.253121\pi\)
0.700140 + 0.714005i \(0.253121\pi\)
\(434\) 0 0
\(435\) 3.33850 0.160069
\(436\) 0 0
\(437\) −1.65929 −0.0793746
\(438\) 0 0
\(439\) −29.3375 −1.40020 −0.700102 0.714043i \(-0.746862\pi\)
−0.700102 + 0.714043i \(0.746862\pi\)
\(440\) 0 0
\(441\) 7.45799 0.355142
\(442\) 0 0
\(443\) −18.6272 −0.885004 −0.442502 0.896768i \(-0.645909\pi\)
−0.442502 + 0.896768i \(0.645909\pi\)
\(444\) 0 0
\(445\) −0.304191 −0.0144200
\(446\) 0 0
\(447\) −0.416459 −0.0196978
\(448\) 0 0
\(449\) 4.79727 0.226397 0.113199 0.993572i \(-0.463890\pi\)
0.113199 + 0.993572i \(0.463890\pi\)
\(450\) 0 0
\(451\) −5.69513 −0.268173
\(452\) 0 0
\(453\) −10.4266 −0.489882
\(454\) 0 0
\(455\) −1.67288 −0.0784260
\(456\) 0 0
\(457\) 14.7293 0.689009 0.344505 0.938785i \(-0.388047\pi\)
0.344505 + 0.938785i \(0.388047\pi\)
\(458\) 0 0
\(459\) 1.29236 0.0603221
\(460\) 0 0
\(461\) 28.1180 1.30959 0.654793 0.755808i \(-0.272756\pi\)
0.654793 + 0.755808i \(0.272756\pi\)
\(462\) 0 0
\(463\) −5.00233 −0.232478 −0.116239 0.993221i \(-0.537084\pi\)
−0.116239 + 0.993221i \(0.537084\pi\)
\(464\) 0 0
\(465\) −4.80206 −0.222690
\(466\) 0 0
\(467\) 28.7693 1.33128 0.665642 0.746271i \(-0.268158\pi\)
0.665642 + 0.746271i \(0.268158\pi\)
\(468\) 0 0
\(469\) −24.2834 −1.12130
\(470\) 0 0
\(471\) −10.6346 −0.490018
\(472\) 0 0
\(473\) 8.73353 0.401568
\(474\) 0 0
\(475\) −3.83853 −0.176124
\(476\) 0 0
\(477\) −13.1556 −0.602354
\(478\) 0 0
\(479\) −18.3805 −0.839825 −0.419912 0.907565i \(-0.637939\pi\)
−0.419912 + 0.907565i \(0.637939\pi\)
\(480\) 0 0
\(481\) 4.89700 0.223284
\(482\) 0 0
\(483\) −7.18717 −0.327028
\(484\) 0 0
\(485\) 2.58831 0.117529
\(486\) 0 0
\(487\) −6.59228 −0.298725 −0.149362 0.988783i \(-0.547722\pi\)
−0.149362 + 0.988783i \(0.547722\pi\)
\(488\) 0 0
\(489\) −10.6617 −0.482141
\(490\) 0 0
\(491\) −1.84351 −0.0831966 −0.0415983 0.999134i \(-0.513245\pi\)
−0.0415983 + 0.999134i \(0.513245\pi\)
\(492\) 0 0
\(493\) −5.44735 −0.245336
\(494\) 0 0
\(495\) 4.66532 0.209691
\(496\) 0 0
\(497\) 48.2685 2.16514
\(498\) 0 0
\(499\) 5.85805 0.262242 0.131121 0.991366i \(-0.458142\pi\)
0.131121 + 0.991366i \(0.458142\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 21.3257 0.950868 0.475434 0.879751i \(-0.342291\pi\)
0.475434 + 0.879751i \(0.342291\pi\)
\(504\) 0 0
\(505\) −6.72481 −0.299250
\(506\) 0 0
\(507\) 12.6914 0.563647
\(508\) 0 0
\(509\) 30.5669 1.35485 0.677426 0.735591i \(-0.263095\pi\)
0.677426 + 0.735591i \(0.263095\pi\)
\(510\) 0 0
\(511\) 42.0077 1.85831
\(512\) 0 0
\(513\) −0.877845 −0.0387578
\(514\) 0 0
\(515\) 11.0893 0.488654
\(516\) 0 0
\(517\) 24.2871 1.06815
\(518\) 0 0
\(519\) 9.69755 0.425675
\(520\) 0 0
\(521\) 27.9492 1.22448 0.612238 0.790674i \(-0.290269\pi\)
0.612238 + 0.790674i \(0.290269\pi\)
\(522\) 0 0
\(523\) 45.2812 1.98001 0.990005 0.141035i \(-0.0450430\pi\)
0.990005 + 0.141035i \(0.0450430\pi\)
\(524\) 0 0
\(525\) −16.6265 −0.725639
\(526\) 0 0
\(527\) 7.83541 0.341316
\(528\) 0 0
\(529\) −19.4272 −0.844661
\(530\) 0 0
\(531\) −10.0336 −0.435422
\(532\) 0 0
\(533\) −0.537074 −0.0232632
\(534\) 0 0
\(535\) 12.2704 0.530495
\(536\) 0 0
\(537\) 9.09640 0.392538
\(538\) 0 0
\(539\) −43.9294 −1.89217
\(540\) 0 0
\(541\) −39.2895 −1.68919 −0.844594 0.535407i \(-0.820158\pi\)
−0.844594 + 0.535407i \(0.820158\pi\)
\(542\) 0 0
\(543\) −3.40901 −0.146295
\(544\) 0 0
\(545\) −9.38237 −0.401897
\(546\) 0 0
\(547\) 35.2105 1.50549 0.752745 0.658312i \(-0.228729\pi\)
0.752745 + 0.658312i \(0.228729\pi\)
\(548\) 0 0
\(549\) −7.38784 −0.315305
\(550\) 0 0
\(551\) 3.70016 0.157632
\(552\) 0 0
\(553\) 1.57639 0.0670347
\(554\) 0 0
\(555\) −6.98257 −0.296394
\(556\) 0 0
\(557\) −43.6784 −1.85071 −0.925356 0.379099i \(-0.876234\pi\)
−0.925356 + 0.379099i \(0.876234\pi\)
\(558\) 0 0
\(559\) 0.823607 0.0348349
\(560\) 0 0
\(561\) −7.61229 −0.321391
\(562\) 0 0
\(563\) −45.6949 −1.92581 −0.962905 0.269839i \(-0.913030\pi\)
−0.962905 + 0.269839i \(0.913030\pi\)
\(564\) 0 0
\(565\) 10.4090 0.437911
\(566\) 0 0
\(567\) −3.80237 −0.159684
\(568\) 0 0
\(569\) −39.9641 −1.67538 −0.837690 0.546145i \(-0.816095\pi\)
−0.837690 + 0.546145i \(0.816095\pi\)
\(570\) 0 0
\(571\) −14.3873 −0.602091 −0.301045 0.953610i \(-0.597336\pi\)
−0.301045 + 0.953610i \(0.597336\pi\)
\(572\) 0 0
\(573\) −7.76442 −0.324363
\(574\) 0 0
\(575\) 8.26515 0.344681
\(576\) 0 0
\(577\) 9.63964 0.401303 0.200652 0.979663i \(-0.435694\pi\)
0.200652 + 0.979663i \(0.435694\pi\)
\(578\) 0 0
\(579\) −1.67335 −0.0695419
\(580\) 0 0
\(581\) −9.80435 −0.406753
\(582\) 0 0
\(583\) 77.4897 3.20930
\(584\) 0 0
\(585\) 0.439959 0.0181901
\(586\) 0 0
\(587\) −25.9969 −1.07301 −0.536504 0.843898i \(-0.680255\pi\)
−0.536504 + 0.843898i \(0.680255\pi\)
\(588\) 0 0
\(589\) −5.32227 −0.219300
\(590\) 0 0
\(591\) 9.01551 0.370849
\(592\) 0 0
\(593\) −25.5448 −1.04900 −0.524499 0.851411i \(-0.675747\pi\)
−0.524499 + 0.851411i \(0.675747\pi\)
\(594\) 0 0
\(595\) −3.89211 −0.159561
\(596\) 0 0
\(597\) 7.27504 0.297748
\(598\) 0 0
\(599\) 22.2348 0.908491 0.454245 0.890877i \(-0.349909\pi\)
0.454245 + 0.890877i \(0.349909\pi\)
\(600\) 0 0
\(601\) −4.94235 −0.201602 −0.100801 0.994907i \(-0.532141\pi\)
−0.100801 + 0.994907i \(0.532141\pi\)
\(602\) 0 0
\(603\) 6.38640 0.260074
\(604\) 0 0
\(605\) −18.7674 −0.763003
\(606\) 0 0
\(607\) −16.2877 −0.661095 −0.330548 0.943789i \(-0.607233\pi\)
−0.330548 + 0.943789i \(0.607233\pi\)
\(608\) 0 0
\(609\) 16.0272 0.649454
\(610\) 0 0
\(611\) 2.29037 0.0926585
\(612\) 0 0
\(613\) 21.2986 0.860240 0.430120 0.902772i \(-0.358471\pi\)
0.430120 + 0.902772i \(0.358471\pi\)
\(614\) 0 0
\(615\) 0.765807 0.0308803
\(616\) 0 0
\(617\) 2.94116 0.118406 0.0592032 0.998246i \(-0.481144\pi\)
0.0592032 + 0.998246i \(0.481144\pi\)
\(618\) 0 0
\(619\) 15.9182 0.639805 0.319903 0.947450i \(-0.396350\pi\)
0.319903 + 0.947450i \(0.396350\pi\)
\(620\) 0 0
\(621\) 1.89018 0.0758505
\(622\) 0 0
\(623\) −1.46033 −0.0585070
\(624\) 0 0
\(625\) 15.9836 0.639343
\(626\) 0 0
\(627\) 5.17072 0.206499
\(628\) 0 0
\(629\) 11.3933 0.454280
\(630\) 0 0
\(631\) 24.0346 0.956801 0.478400 0.878142i \(-0.341217\pi\)
0.478400 + 0.878142i \(0.341217\pi\)
\(632\) 0 0
\(633\) −2.15224 −0.0855438
\(634\) 0 0
\(635\) −1.17471 −0.0466170
\(636\) 0 0
\(637\) −4.14272 −0.164140
\(638\) 0 0
\(639\) −12.6943 −0.502180
\(640\) 0 0
\(641\) −22.1395 −0.874460 −0.437230 0.899350i \(-0.644040\pi\)
−0.437230 + 0.899350i \(0.644040\pi\)
\(642\) 0 0
\(643\) 29.2492 1.15348 0.576738 0.816929i \(-0.304325\pi\)
0.576738 + 0.816929i \(0.304325\pi\)
\(644\) 0 0
\(645\) −1.17437 −0.0462408
\(646\) 0 0
\(647\) −38.1852 −1.50121 −0.750607 0.660749i \(-0.770239\pi\)
−0.750607 + 0.660749i \(0.770239\pi\)
\(648\) 0 0
\(649\) 59.1004 2.31990
\(650\) 0 0
\(651\) −23.0533 −0.903530
\(652\) 0 0
\(653\) −48.3317 −1.89137 −0.945684 0.325088i \(-0.894606\pi\)
−0.945684 + 0.325088i \(0.894606\pi\)
\(654\) 0 0
\(655\) 0.490929 0.0191822
\(656\) 0 0
\(657\) −11.0478 −0.431015
\(658\) 0 0
\(659\) 25.6331 0.998525 0.499262 0.866451i \(-0.333604\pi\)
0.499262 + 0.866451i \(0.333604\pi\)
\(660\) 0 0
\(661\) −14.4566 −0.562297 −0.281149 0.959664i \(-0.590715\pi\)
−0.281149 + 0.959664i \(0.590715\pi\)
\(662\) 0 0
\(663\) −0.717870 −0.0278798
\(664\) 0 0
\(665\) 2.64375 0.102520
\(666\) 0 0
\(667\) −7.96722 −0.308492
\(668\) 0 0
\(669\) −14.5871 −0.563969
\(670\) 0 0
\(671\) 43.5162 1.67992
\(672\) 0 0
\(673\) 46.7998 1.80400 0.902000 0.431735i \(-0.142098\pi\)
0.902000 + 0.431735i \(0.142098\pi\)
\(674\) 0 0
\(675\) 4.37267 0.168304
\(676\) 0 0
\(677\) 5.07773 0.195153 0.0975765 0.995228i \(-0.468891\pi\)
0.0975765 + 0.995228i \(0.468891\pi\)
\(678\) 0 0
\(679\) 12.4257 0.476855
\(680\) 0 0
\(681\) −19.2690 −0.738392
\(682\) 0 0
\(683\) 11.3830 0.435557 0.217779 0.975998i \(-0.430119\pi\)
0.217779 + 0.975998i \(0.430119\pi\)
\(684\) 0 0
\(685\) −8.20228 −0.313393
\(686\) 0 0
\(687\) 14.8221 0.565497
\(688\) 0 0
\(689\) 7.30760 0.278397
\(690\) 0 0
\(691\) 23.9443 0.910883 0.455441 0.890266i \(-0.349481\pi\)
0.455441 + 0.890266i \(0.349481\pi\)
\(692\) 0 0
\(693\) 22.3968 0.850786
\(694\) 0 0
\(695\) −3.42081 −0.129759
\(696\) 0 0
\(697\) −1.24955 −0.0473300
\(698\) 0 0
\(699\) 7.73508 0.292568
\(700\) 0 0
\(701\) −28.5154 −1.07701 −0.538506 0.842622i \(-0.681011\pi\)
−0.538506 + 0.842622i \(0.681011\pi\)
\(702\) 0 0
\(703\) −7.73899 −0.291882
\(704\) 0 0
\(705\) −3.26581 −0.122998
\(706\) 0 0
\(707\) −32.2838 −1.21416
\(708\) 0 0
\(709\) 21.7312 0.816132 0.408066 0.912953i \(-0.366203\pi\)
0.408066 + 0.912953i \(0.366203\pi\)
\(710\) 0 0
\(711\) −0.414580 −0.0155480
\(712\) 0 0
\(713\) 11.4600 0.429179
\(714\) 0 0
\(715\) −2.59146 −0.0969152
\(716\) 0 0
\(717\) −11.7199 −0.437687
\(718\) 0 0
\(719\) −16.3856 −0.611078 −0.305539 0.952180i \(-0.598837\pi\)
−0.305539 + 0.952180i \(0.598837\pi\)
\(720\) 0 0
\(721\) 53.2367 1.98264
\(722\) 0 0
\(723\) 0.783620 0.0291431
\(724\) 0 0
\(725\) −18.4310 −0.684511
\(726\) 0 0
\(727\) −2.36008 −0.0875304 −0.0437652 0.999042i \(-0.513935\pi\)
−0.0437652 + 0.999042i \(0.513935\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.91619 0.0708730
\(732\) 0 0
\(733\) 19.6007 0.723967 0.361983 0.932185i \(-0.382100\pi\)
0.361983 + 0.932185i \(0.382100\pi\)
\(734\) 0 0
\(735\) 5.90705 0.217885
\(736\) 0 0
\(737\) −37.6174 −1.38565
\(738\) 0 0
\(739\) 24.5195 0.901965 0.450982 0.892533i \(-0.351074\pi\)
0.450982 + 0.892533i \(0.351074\pi\)
\(740\) 0 0
\(741\) 0.487620 0.0179132
\(742\) 0 0
\(743\) −17.3096 −0.635028 −0.317514 0.948254i \(-0.602848\pi\)
−0.317514 + 0.948254i \(0.602848\pi\)
\(744\) 0 0
\(745\) −0.329853 −0.0120849
\(746\) 0 0
\(747\) 2.57849 0.0943419
\(748\) 0 0
\(749\) 58.9065 2.15240
\(750\) 0 0
\(751\) −14.8116 −0.540481 −0.270241 0.962793i \(-0.587103\pi\)
−0.270241 + 0.962793i \(0.587103\pi\)
\(752\) 0 0
\(753\) −1.99474 −0.0726922
\(754\) 0 0
\(755\) −8.25828 −0.300549
\(756\) 0 0
\(757\) 39.6516 1.44116 0.720580 0.693371i \(-0.243875\pi\)
0.720580 + 0.693371i \(0.243875\pi\)
\(758\) 0 0
\(759\) −11.1336 −0.404125
\(760\) 0 0
\(761\) −44.3103 −1.60625 −0.803124 0.595812i \(-0.796830\pi\)
−0.803124 + 0.595812i \(0.796830\pi\)
\(762\) 0 0
\(763\) −45.0420 −1.63063
\(764\) 0 0
\(765\) 1.02360 0.0370084
\(766\) 0 0
\(767\) 5.57341 0.201244
\(768\) 0 0
\(769\) −1.55817 −0.0561891 −0.0280946 0.999605i \(-0.508944\pi\)
−0.0280946 + 0.999605i \(0.508944\pi\)
\(770\) 0 0
\(771\) 12.9694 0.467083
\(772\) 0 0
\(773\) −29.8336 −1.07304 −0.536520 0.843888i \(-0.680261\pi\)
−0.536520 + 0.843888i \(0.680261\pi\)
\(774\) 0 0
\(775\) 26.5110 0.952302
\(776\) 0 0
\(777\) −33.5213 −1.20257
\(778\) 0 0
\(779\) 0.848767 0.0304102
\(780\) 0 0
\(781\) 74.7726 2.67558
\(782\) 0 0
\(783\) −4.21505 −0.150634
\(784\) 0 0
\(785\) −8.42308 −0.300633
\(786\) 0 0
\(787\) −31.9000 −1.13711 −0.568556 0.822644i \(-0.692498\pi\)
−0.568556 + 0.822644i \(0.692498\pi\)
\(788\) 0 0
\(789\) −1.41225 −0.0502775
\(790\) 0 0
\(791\) 49.9707 1.77676
\(792\) 0 0
\(793\) 4.10375 0.145728
\(794\) 0 0
\(795\) −10.4198 −0.369553
\(796\) 0 0
\(797\) −41.7901 −1.48028 −0.740140 0.672453i \(-0.765241\pi\)
−0.740140 + 0.672453i \(0.765241\pi\)
\(798\) 0 0
\(799\) 5.32875 0.188518
\(800\) 0 0
\(801\) 0.384059 0.0135701
\(802\) 0 0
\(803\) 65.0741 2.29642
\(804\) 0 0
\(805\) −5.69255 −0.200636
\(806\) 0 0
\(807\) 0.320518 0.0112828
\(808\) 0 0
\(809\) 20.3756 0.716366 0.358183 0.933651i \(-0.383396\pi\)
0.358183 + 0.933651i \(0.383396\pi\)
\(810\) 0 0
\(811\) 20.4734 0.718917 0.359458 0.933161i \(-0.382961\pi\)
0.359458 + 0.933161i \(0.382961\pi\)
\(812\) 0 0
\(813\) 16.4920 0.578398
\(814\) 0 0
\(815\) −8.44456 −0.295800
\(816\) 0 0
\(817\) −1.30159 −0.0455369
\(818\) 0 0
\(819\) 2.11211 0.0738032
\(820\) 0 0
\(821\) 26.8617 0.937481 0.468741 0.883336i \(-0.344708\pi\)
0.468741 + 0.883336i \(0.344708\pi\)
\(822\) 0 0
\(823\) −24.2379 −0.844879 −0.422440 0.906391i \(-0.638826\pi\)
−0.422440 + 0.906391i \(0.638826\pi\)
\(824\) 0 0
\(825\) −25.7561 −0.896711
\(826\) 0 0
\(827\) −23.7526 −0.825958 −0.412979 0.910740i \(-0.635512\pi\)
−0.412979 + 0.910740i \(0.635512\pi\)
\(828\) 0 0
\(829\) 41.3698 1.43683 0.718417 0.695613i \(-0.244867\pi\)
0.718417 + 0.695613i \(0.244867\pi\)
\(830\) 0 0
\(831\) −21.5960 −0.749156
\(832\) 0 0
\(833\) −9.63839 −0.333950
\(834\) 0 0
\(835\) 0.792043 0.0274098
\(836\) 0 0
\(837\) 6.06288 0.209564
\(838\) 0 0
\(839\) −3.11634 −0.107588 −0.0537940 0.998552i \(-0.517131\pi\)
−0.0537940 + 0.998552i \(0.517131\pi\)
\(840\) 0 0
\(841\) −11.2333 −0.387357
\(842\) 0 0
\(843\) −18.5310 −0.638242
\(844\) 0 0
\(845\) 10.0522 0.345805
\(846\) 0 0
\(847\) −90.0968 −3.09576
\(848\) 0 0
\(849\) −17.7434 −0.608951
\(850\) 0 0
\(851\) 16.6637 0.571223
\(852\) 0 0
\(853\) −17.5784 −0.601874 −0.300937 0.953644i \(-0.597299\pi\)
−0.300937 + 0.953644i \(0.597299\pi\)
\(854\) 0 0
\(855\) −0.695291 −0.0237784
\(856\) 0 0
\(857\) 39.7135 1.35659 0.678294 0.734790i \(-0.262719\pi\)
0.678294 + 0.734790i \(0.262719\pi\)
\(858\) 0 0
\(859\) −20.4277 −0.696985 −0.348492 0.937312i \(-0.613306\pi\)
−0.348492 + 0.937312i \(0.613306\pi\)
\(860\) 0 0
\(861\) 3.67641 0.125292
\(862\) 0 0
\(863\) −33.9054 −1.15415 −0.577076 0.816690i \(-0.695806\pi\)
−0.577076 + 0.816690i \(0.695806\pi\)
\(864\) 0 0
\(865\) 7.68087 0.261157
\(866\) 0 0
\(867\) 15.3298 0.520628
\(868\) 0 0
\(869\) 2.44198 0.0828383
\(870\) 0 0
\(871\) −3.54747 −0.120202
\(872\) 0 0
\(873\) −3.26789 −0.110601
\(874\) 0 0
\(875\) −28.2271 −0.954249
\(876\) 0 0
\(877\) 26.8020 0.905040 0.452520 0.891754i \(-0.350525\pi\)
0.452520 + 0.891754i \(0.350525\pi\)
\(878\) 0 0
\(879\) −10.7896 −0.363925
\(880\) 0 0
\(881\) 50.1242 1.68873 0.844364 0.535770i \(-0.179978\pi\)
0.844364 + 0.535770i \(0.179978\pi\)
\(882\) 0 0
\(883\) 5.39331 0.181499 0.0907496 0.995874i \(-0.471074\pi\)
0.0907496 + 0.995874i \(0.471074\pi\)
\(884\) 0 0
\(885\) −7.94706 −0.267137
\(886\) 0 0
\(887\) −15.0636 −0.505786 −0.252893 0.967494i \(-0.581382\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(888\) 0 0
\(889\) −5.63944 −0.189141
\(890\) 0 0
\(891\) −5.89024 −0.197330
\(892\) 0 0
\(893\) −3.61960 −0.121125
\(894\) 0 0
\(895\) 7.20473 0.240828
\(896\) 0 0
\(897\) −1.04995 −0.0350567
\(898\) 0 0
\(899\) −25.5554 −0.852319
\(900\) 0 0
\(901\) 17.0018 0.566411
\(902\) 0 0
\(903\) −5.63781 −0.187615
\(904\) 0 0
\(905\) −2.70008 −0.0897537
\(906\) 0 0
\(907\) −49.2144 −1.63414 −0.817069 0.576540i \(-0.804402\pi\)
−0.817069 + 0.576540i \(0.804402\pi\)
\(908\) 0 0
\(909\) 8.49046 0.281611
\(910\) 0 0
\(911\) 6.92136 0.229315 0.114657 0.993405i \(-0.463423\pi\)
0.114657 + 0.993405i \(0.463423\pi\)
\(912\) 0 0
\(913\) −15.1879 −0.502646
\(914\) 0 0
\(915\) −5.85149 −0.193444
\(916\) 0 0
\(917\) 2.35681 0.0778286
\(918\) 0 0
\(919\) −13.2852 −0.438238 −0.219119 0.975698i \(-0.570318\pi\)
−0.219119 + 0.975698i \(0.570318\pi\)
\(920\) 0 0
\(921\) −4.09400 −0.134902
\(922\) 0 0
\(923\) 7.05136 0.232098
\(924\) 0 0
\(925\) 38.5490 1.26748
\(926\) 0 0
\(927\) −14.0009 −0.459851
\(928\) 0 0
\(929\) −4.83070 −0.158490 −0.0792451 0.996855i \(-0.525251\pi\)
−0.0792451 + 0.996855i \(0.525251\pi\)
\(930\) 0 0
\(931\) 6.54696 0.214568
\(932\) 0 0
\(933\) −3.47522 −0.113774
\(934\) 0 0
\(935\) −6.02926 −0.197178
\(936\) 0 0
\(937\) 19.8142 0.647303 0.323651 0.946176i \(-0.395089\pi\)
0.323651 + 0.946176i \(0.395089\pi\)
\(938\) 0 0
\(939\) 7.74695 0.252812
\(940\) 0 0
\(941\) 36.3964 1.18649 0.593245 0.805022i \(-0.297846\pi\)
0.593245 + 0.805022i \(0.297846\pi\)
\(942\) 0 0
\(943\) −1.82757 −0.0595140
\(944\) 0 0
\(945\) −3.01164 −0.0979686
\(946\) 0 0
\(947\) −14.7560 −0.479505 −0.239753 0.970834i \(-0.577066\pi\)
−0.239753 + 0.970834i \(0.577066\pi\)
\(948\) 0 0
\(949\) 6.13675 0.199207
\(950\) 0 0
\(951\) 19.6818 0.638226
\(952\) 0 0
\(953\) −1.59837 −0.0517764 −0.0258882 0.999665i \(-0.508241\pi\)
−0.0258882 + 0.999665i \(0.508241\pi\)
\(954\) 0 0
\(955\) −6.14975 −0.199001
\(956\) 0 0
\(957\) 24.8277 0.802564
\(958\) 0 0
\(959\) −39.3768 −1.27154
\(960\) 0 0
\(961\) 5.75852 0.185759
\(962\) 0 0
\(963\) −15.4921 −0.499225
\(964\) 0 0
\(965\) −1.32536 −0.0426649
\(966\) 0 0
\(967\) −4.37787 −0.140783 −0.0703914 0.997519i \(-0.522425\pi\)
−0.0703914 + 0.997519i \(0.522425\pi\)
\(968\) 0 0
\(969\) 1.13449 0.0364450
\(970\) 0 0
\(971\) −7.68220 −0.246534 −0.123267 0.992374i \(-0.539337\pi\)
−0.123267 + 0.992374i \(0.539337\pi\)
\(972\) 0 0
\(973\) −16.4223 −0.526475
\(974\) 0 0
\(975\) −2.42890 −0.0777871
\(976\) 0 0
\(977\) −8.62319 −0.275880 −0.137940 0.990441i \(-0.544048\pi\)
−0.137940 + 0.990441i \(0.544048\pi\)
\(978\) 0 0
\(979\) −2.26220 −0.0723002
\(980\) 0 0
\(981\) 11.8458 0.378207
\(982\) 0 0
\(983\) −39.6553 −1.26481 −0.632404 0.774638i \(-0.717932\pi\)
−0.632404 + 0.774638i \(0.717932\pi\)
\(984\) 0 0
\(985\) 7.14067 0.227521
\(986\) 0 0
\(987\) −15.6782 −0.499043
\(988\) 0 0
\(989\) 2.80260 0.0891174
\(990\) 0 0
\(991\) −21.3832 −0.679259 −0.339629 0.940559i \(-0.610302\pi\)
−0.339629 + 0.940559i \(0.610302\pi\)
\(992\) 0 0
\(993\) −33.7021 −1.06951
\(994\) 0 0
\(995\) 5.76214 0.182672
\(996\) 0 0
\(997\) 30.8641 0.977477 0.488738 0.872430i \(-0.337457\pi\)
0.488738 + 0.872430i \(0.337457\pi\)
\(998\) 0 0
\(999\) 8.81590 0.278923
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 8016.2.a.bb.1.3 9
4.3 odd 2 2004.2.a.d.1.3 9
12.11 even 2 6012.2.a.h.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.3 9 4.3 odd 2
6012.2.a.h.1.7 9 12.11 even 2
8016.2.a.bb.1.3 9 1.1 even 1 trivial