Properties

Label 8016.2.a.ba.1.8
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: \(x^{9} - 3 x^{8} - 16 x^{7} + 45 x^{6} + 67 x^{5} - 166 x^{4} - 83 x^{3} + 152 x^{2} + 51 x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(2.94484\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.94484 q^{5} +3.19705 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.94484 q^{5} +3.19705 q^{7} +1.00000 q^{9} +0.785264 q^{11} -4.88513 q^{13} -1.94484 q^{15} +2.74809 q^{17} -1.67411 q^{19} -3.19705 q^{21} +6.23759 q^{23} -1.21759 q^{25} -1.00000 q^{27} -0.902257 q^{29} -5.13811 q^{31} -0.785264 q^{33} +6.21775 q^{35} +0.279586 q^{37} +4.88513 q^{39} +1.15508 q^{41} -4.50592 q^{43} +1.94484 q^{45} +8.29789 q^{47} +3.22111 q^{49} -2.74809 q^{51} -6.24888 q^{53} +1.52721 q^{55} +1.67411 q^{57} +9.18041 q^{59} +0.717810 q^{61} +3.19705 q^{63} -9.50080 q^{65} +12.0469 q^{67} -6.23759 q^{69} +15.7083 q^{71} +2.50452 q^{73} +1.21759 q^{75} +2.51053 q^{77} +10.2869 q^{79} +1.00000 q^{81} -4.93675 q^{83} +5.34461 q^{85} +0.902257 q^{87} +15.4270 q^{89} -15.6180 q^{91} +5.13811 q^{93} -3.25588 q^{95} +1.53933 q^{97} +0.785264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} - q^{11} - 4q^{13} + 6q^{15} - 9q^{17} + 8q^{19} - 11q^{21} + 7q^{23} - q^{25} - 9q^{27} - 9q^{29} + 25q^{31} + q^{33} - 5q^{35} - 6q^{37} + 4q^{39} - 4q^{41} + 24q^{43} - 6q^{45} + 16q^{47} + 4q^{49} + 9q^{51} - 26q^{53} + 29q^{55} - 8q^{57} + 4q^{59} - 20q^{61} + 11q^{63} - 8q^{65} + 25q^{67} - 7q^{69} + 15q^{71} - 10q^{73} + q^{75} - 20q^{77} + 34q^{79} + 9q^{81} + 4q^{83} - 13q^{85} + 9q^{87} + 13q^{89} + 21q^{91} - 25q^{93} + 7q^{95} - 4q^{97} - q^{99} + O(q^{100}) \)

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
\(5\) 1.94484 0.869760 0.434880 0.900488i \(-0.356791\pi\)
0.434880 + 0.900488i \(0.356791\pi\)
\(6\) 0 0
\(7\) 3.19705 1.20837 0.604185 0.796844i \(-0.293499\pi\)
0.604185 + 0.796844i \(0.293499\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0.785264 0.236766 0.118383 0.992968i \(-0.462229\pi\)
0.118383 + 0.992968i \(0.462229\pi\)
\(12\) 0 0
\(13\) −4.88513 −1.35489 −0.677445 0.735573i \(-0.736913\pi\)
−0.677445 + 0.735573i \(0.736913\pi\)
\(14\) 0 0
\(15\) −1.94484 −0.502156
\(16\) 0 0
\(17\) 2.74809 0.666511 0.333255 0.942837i \(-0.391853\pi\)
0.333255 + 0.942837i \(0.391853\pi\)
\(18\) 0 0
\(19\) −1.67411 −0.384067 −0.192034 0.981388i \(-0.561508\pi\)
−0.192034 + 0.981388i \(0.561508\pi\)
\(20\) 0 0
\(21\) −3.19705 −0.697653
\(22\) 0 0
\(23\) 6.23759 1.30063 0.650314 0.759665i \(-0.274637\pi\)
0.650314 + 0.759665i \(0.274637\pi\)
\(24\) 0 0
\(25\) −1.21759 −0.243518
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −0.902257 −0.167545 −0.0837724 0.996485i \(-0.526697\pi\)
−0.0837724 + 0.996485i \(0.526697\pi\)
\(30\) 0 0
\(31\) −5.13811 −0.922832 −0.461416 0.887184i \(-0.652658\pi\)
−0.461416 + 0.887184i \(0.652658\pi\)
\(32\) 0 0
\(33\) −0.785264 −0.136697
\(34\) 0 0
\(35\) 6.21775 1.05099
\(36\) 0 0
\(37\) 0.279586 0.0459636 0.0229818 0.999736i \(-0.492684\pi\)
0.0229818 + 0.999736i \(0.492684\pi\)
\(38\) 0 0
\(39\) 4.88513 0.782247
\(40\) 0 0
\(41\) 1.15508 0.180393 0.0901965 0.995924i \(-0.471250\pi\)
0.0901965 + 0.995924i \(0.471250\pi\)
\(42\) 0 0
\(43\) −4.50592 −0.687146 −0.343573 0.939126i \(-0.611637\pi\)
−0.343573 + 0.939126i \(0.611637\pi\)
\(44\) 0 0
\(45\) 1.94484 0.289920
\(46\) 0 0
\(47\) 8.29789 1.21037 0.605186 0.796084i \(-0.293099\pi\)
0.605186 + 0.796084i \(0.293099\pi\)
\(48\) 0 0
\(49\) 3.22111 0.460159
\(50\) 0 0
\(51\) −2.74809 −0.384810
\(52\) 0 0
\(53\) −6.24888 −0.858350 −0.429175 0.903221i \(-0.641196\pi\)
−0.429175 + 0.903221i \(0.641196\pi\)
\(54\) 0 0
\(55\) 1.52721 0.205930
\(56\) 0 0
\(57\) 1.67411 0.221741
\(58\) 0 0
\(59\) 9.18041 1.19519 0.597594 0.801799i \(-0.296123\pi\)
0.597594 + 0.801799i \(0.296123\pi\)
\(60\) 0 0
\(61\) 0.717810 0.0919061 0.0459531 0.998944i \(-0.485368\pi\)
0.0459531 + 0.998944i \(0.485368\pi\)
\(62\) 0 0
\(63\) 3.19705 0.402790
\(64\) 0 0
\(65\) −9.50080 −1.17843
\(66\) 0 0
\(67\) 12.0469 1.47176 0.735882 0.677110i \(-0.236768\pi\)
0.735882 + 0.677110i \(0.236768\pi\)
\(68\) 0 0
\(69\) −6.23759 −0.750918
\(70\) 0 0
\(71\) 15.7083 1.86423 0.932116 0.362160i \(-0.117961\pi\)
0.932116 + 0.362160i \(0.117961\pi\)
\(72\) 0 0
\(73\) 2.50452 0.293132 0.146566 0.989201i \(-0.453178\pi\)
0.146566 + 0.989201i \(0.453178\pi\)
\(74\) 0 0
\(75\) 1.21759 0.140595
\(76\) 0 0
\(77\) 2.51053 0.286101
\(78\) 0 0
\(79\) 10.2869 1.15737 0.578683 0.815552i \(-0.303567\pi\)
0.578683 + 0.815552i \(0.303567\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.93675 −0.541879 −0.270939 0.962596i \(-0.587334\pi\)
−0.270939 + 0.962596i \(0.587334\pi\)
\(84\) 0 0
\(85\) 5.34461 0.579704
\(86\) 0 0
\(87\) 0.902257 0.0967321
\(88\) 0 0
\(89\) 15.4270 1.63526 0.817629 0.575746i \(-0.195288\pi\)
0.817629 + 0.575746i \(0.195288\pi\)
\(90\) 0 0
\(91\) −15.6180 −1.63721
\(92\) 0 0
\(93\) 5.13811 0.532797
\(94\) 0 0
\(95\) −3.25588 −0.334046
\(96\) 0 0
\(97\) 1.53933 0.156296 0.0781479 0.996942i \(-0.475099\pi\)
0.0781479 + 0.996942i \(0.475099\pi\)
\(98\) 0 0
\(99\) 0.785264 0.0789220
\(100\) 0 0
\(101\) −0.637664 −0.0634500 −0.0317250 0.999497i \(-0.510100\pi\)
−0.0317250 + 0.999497i \(0.510100\pi\)
\(102\) 0 0
\(103\) −4.83309 −0.476219 −0.238109 0.971238i \(-0.576528\pi\)
−0.238109 + 0.971238i \(0.576528\pi\)
\(104\) 0 0
\(105\) −6.21775 −0.606790
\(106\) 0 0
\(107\) 9.26070 0.895266 0.447633 0.894217i \(-0.352267\pi\)
0.447633 + 0.894217i \(0.352267\pi\)
\(108\) 0 0
\(109\) −0.140018 −0.0134112 −0.00670562 0.999978i \(-0.502134\pi\)
−0.00670562 + 0.999978i \(0.502134\pi\)
\(110\) 0 0
\(111\) −0.279586 −0.0265371
\(112\) 0 0
\(113\) −14.1206 −1.32836 −0.664178 0.747574i \(-0.731218\pi\)
−0.664178 + 0.747574i \(0.731218\pi\)
\(114\) 0 0
\(115\) 12.1311 1.13123
\(116\) 0 0
\(117\) −4.88513 −0.451630
\(118\) 0 0
\(119\) 8.78579 0.805392
\(120\) 0 0
\(121\) −10.3834 −0.943942
\(122\) 0 0
\(123\) −1.15508 −0.104150
\(124\) 0 0
\(125\) −12.0922 −1.08156
\(126\) 0 0
\(127\) 12.0579 1.06996 0.534981 0.844864i \(-0.320319\pi\)
0.534981 + 0.844864i \(0.320319\pi\)
\(128\) 0 0
\(129\) 4.50592 0.396724
\(130\) 0 0
\(131\) 6.67350 0.583066 0.291533 0.956561i \(-0.405835\pi\)
0.291533 + 0.956561i \(0.405835\pi\)
\(132\) 0 0
\(133\) −5.35221 −0.464095
\(134\) 0 0
\(135\) −1.94484 −0.167385
\(136\) 0 0
\(137\) 9.73895 0.832054 0.416027 0.909352i \(-0.363422\pi\)
0.416027 + 0.909352i \(0.363422\pi\)
\(138\) 0 0
\(139\) 7.08219 0.600704 0.300352 0.953828i \(-0.402896\pi\)
0.300352 + 0.953828i \(0.402896\pi\)
\(140\) 0 0
\(141\) −8.29789 −0.698808
\(142\) 0 0
\(143\) −3.83612 −0.320792
\(144\) 0 0
\(145\) −1.75475 −0.145724
\(146\) 0 0
\(147\) −3.22111 −0.265673
\(148\) 0 0
\(149\) 1.98095 0.162285 0.0811427 0.996702i \(-0.474143\pi\)
0.0811427 + 0.996702i \(0.474143\pi\)
\(150\) 0 0
\(151\) 21.5517 1.75385 0.876925 0.480627i \(-0.159591\pi\)
0.876925 + 0.480627i \(0.159591\pi\)
\(152\) 0 0
\(153\) 2.74809 0.222170
\(154\) 0 0
\(155\) −9.99281 −0.802642
\(156\) 0 0
\(157\) 6.14846 0.490701 0.245350 0.969434i \(-0.421097\pi\)
0.245350 + 0.969434i \(0.421097\pi\)
\(158\) 0 0
\(159\) 6.24888 0.495569
\(160\) 0 0
\(161\) 19.9419 1.57164
\(162\) 0 0
\(163\) 0.988706 0.0774414 0.0387207 0.999250i \(-0.487672\pi\)
0.0387207 + 0.999250i \(0.487672\pi\)
\(164\) 0 0
\(165\) −1.52721 −0.118894
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 10.8645 0.835729
\(170\) 0 0
\(171\) −1.67411 −0.128022
\(172\) 0 0
\(173\) 0.748097 0.0568767 0.0284384 0.999596i \(-0.490947\pi\)
0.0284384 + 0.999596i \(0.490947\pi\)
\(174\) 0 0
\(175\) −3.89269 −0.294260
\(176\) 0 0
\(177\) −9.18041 −0.690042
\(178\) 0 0
\(179\) −19.6260 −1.46691 −0.733457 0.679736i \(-0.762095\pi\)
−0.733457 + 0.679736i \(0.762095\pi\)
\(180\) 0 0
\(181\) 10.6840 0.794134 0.397067 0.917790i \(-0.370028\pi\)
0.397067 + 0.917790i \(0.370028\pi\)
\(182\) 0 0
\(183\) −0.717810 −0.0530620
\(184\) 0 0
\(185\) 0.543750 0.0399773
\(186\) 0 0
\(187\) 2.15798 0.157807
\(188\) 0 0
\(189\) −3.19705 −0.232551
\(190\) 0 0
\(191\) −25.6633 −1.85693 −0.928465 0.371420i \(-0.878871\pi\)
−0.928465 + 0.371420i \(0.878871\pi\)
\(192\) 0 0
\(193\) 4.10218 0.295281 0.147641 0.989041i \(-0.452832\pi\)
0.147641 + 0.989041i \(0.452832\pi\)
\(194\) 0 0
\(195\) 9.50080 0.680366
\(196\) 0 0
\(197\) −3.58320 −0.255292 −0.127646 0.991820i \(-0.540742\pi\)
−0.127646 + 0.991820i \(0.540742\pi\)
\(198\) 0 0
\(199\) −1.22740 −0.0870078 −0.0435039 0.999053i \(-0.513852\pi\)
−0.0435039 + 0.999053i \(0.513852\pi\)
\(200\) 0 0
\(201\) −12.0469 −0.849723
\(202\) 0 0
\(203\) −2.88456 −0.202456
\(204\) 0 0
\(205\) 2.24645 0.156899
\(206\) 0 0
\(207\) 6.23759 0.433543
\(208\) 0 0
\(209\) −1.31462 −0.0909341
\(210\) 0 0
\(211\) 5.24358 0.360983 0.180492 0.983577i \(-0.442231\pi\)
0.180492 + 0.983577i \(0.442231\pi\)
\(212\) 0 0
\(213\) −15.7083 −1.07631
\(214\) 0 0
\(215\) −8.76329 −0.597652
\(216\) 0 0
\(217\) −16.4268 −1.11512
\(218\) 0 0
\(219\) −2.50452 −0.169240
\(220\) 0 0
\(221\) −13.4248 −0.903049
\(222\) 0 0
\(223\) −1.10636 −0.0740872 −0.0370436 0.999314i \(-0.511794\pi\)
−0.0370436 + 0.999314i \(0.511794\pi\)
\(224\) 0 0
\(225\) −1.21759 −0.0811727
\(226\) 0 0
\(227\) 17.7395 1.17741 0.588707 0.808347i \(-0.299637\pi\)
0.588707 + 0.808347i \(0.299637\pi\)
\(228\) 0 0
\(229\) 3.65487 0.241521 0.120760 0.992682i \(-0.461467\pi\)
0.120760 + 0.992682i \(0.461467\pi\)
\(230\) 0 0
\(231\) −2.51053 −0.165181
\(232\) 0 0
\(233\) −9.77622 −0.640462 −0.320231 0.947340i \(-0.603760\pi\)
−0.320231 + 0.947340i \(0.603760\pi\)
\(234\) 0 0
\(235\) 16.1381 1.05273
\(236\) 0 0
\(237\) −10.2869 −0.668206
\(238\) 0 0
\(239\) −15.9111 −1.02921 −0.514603 0.857429i \(-0.672061\pi\)
−0.514603 + 0.857429i \(0.672061\pi\)
\(240\) 0 0
\(241\) 26.5185 1.70821 0.854105 0.520101i \(-0.174106\pi\)
0.854105 + 0.520101i \(0.174106\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 6.26455 0.400227
\(246\) 0 0
\(247\) 8.17824 0.520369
\(248\) 0 0
\(249\) 4.93675 0.312854
\(250\) 0 0
\(251\) −23.6017 −1.48973 −0.744865 0.667216i \(-0.767486\pi\)
−0.744865 + 0.667216i \(0.767486\pi\)
\(252\) 0 0
\(253\) 4.89816 0.307945
\(254\) 0 0
\(255\) −5.34461 −0.334692
\(256\) 0 0
\(257\) 24.0027 1.49725 0.748623 0.662996i \(-0.230715\pi\)
0.748623 + 0.662996i \(0.230715\pi\)
\(258\) 0 0
\(259\) 0.893848 0.0555410
\(260\) 0 0
\(261\) −0.902257 −0.0558483
\(262\) 0 0
\(263\) 19.9455 1.22989 0.614946 0.788569i \(-0.289178\pi\)
0.614946 + 0.788569i \(0.289178\pi\)
\(264\) 0 0
\(265\) −12.1531 −0.746558
\(266\) 0 0
\(267\) −15.4270 −0.944116
\(268\) 0 0
\(269\) 14.7796 0.901129 0.450564 0.892744i \(-0.351223\pi\)
0.450564 + 0.892744i \(0.351223\pi\)
\(270\) 0 0
\(271\) −7.89192 −0.479400 −0.239700 0.970847i \(-0.577049\pi\)
−0.239700 + 0.970847i \(0.577049\pi\)
\(272\) 0 0
\(273\) 15.6180 0.945243
\(274\) 0 0
\(275\) −0.956130 −0.0576568
\(276\) 0 0
\(277\) −8.44295 −0.507287 −0.253644 0.967298i \(-0.581629\pi\)
−0.253644 + 0.967298i \(0.581629\pi\)
\(278\) 0 0
\(279\) −5.13811 −0.307611
\(280\) 0 0
\(281\) −3.38998 −0.202229 −0.101114 0.994875i \(-0.532241\pi\)
−0.101114 + 0.994875i \(0.532241\pi\)
\(282\) 0 0
\(283\) −11.5355 −0.685715 −0.342858 0.939387i \(-0.611395\pi\)
−0.342858 + 0.939387i \(0.611395\pi\)
\(284\) 0 0
\(285\) 3.25588 0.192862
\(286\) 0 0
\(287\) 3.69284 0.217982
\(288\) 0 0
\(289\) −9.44797 −0.555763
\(290\) 0 0
\(291\) −1.53933 −0.0902374
\(292\) 0 0
\(293\) −7.92981 −0.463265 −0.231632 0.972803i \(-0.574407\pi\)
−0.231632 + 0.972803i \(0.574407\pi\)
\(294\) 0 0
\(295\) 17.8545 1.03953
\(296\) 0 0
\(297\) −0.785264 −0.0455657
\(298\) 0 0
\(299\) −30.4714 −1.76221
\(300\) 0 0
\(301\) −14.4056 −0.830326
\(302\) 0 0
\(303\) 0.637664 0.0366329
\(304\) 0 0
\(305\) 1.39603 0.0799362
\(306\) 0 0
\(307\) 22.6509 1.29275 0.646377 0.763018i \(-0.276283\pi\)
0.646377 + 0.763018i \(0.276283\pi\)
\(308\) 0 0
\(309\) 4.83309 0.274945
\(310\) 0 0
\(311\) −16.1604 −0.916370 −0.458185 0.888857i \(-0.651500\pi\)
−0.458185 + 0.888857i \(0.651500\pi\)
\(312\) 0 0
\(313\) −3.80949 −0.215325 −0.107663 0.994187i \(-0.534337\pi\)
−0.107663 + 0.994187i \(0.534337\pi\)
\(314\) 0 0
\(315\) 6.21775 0.350331
\(316\) 0 0
\(317\) −6.77439 −0.380488 −0.190244 0.981737i \(-0.560928\pi\)
−0.190244 + 0.981737i \(0.560928\pi\)
\(318\) 0 0
\(319\) −0.708510 −0.0396689
\(320\) 0 0
\(321\) −9.26070 −0.516882
\(322\) 0 0
\(323\) −4.60061 −0.255985
\(324\) 0 0
\(325\) 5.94808 0.329940
\(326\) 0 0
\(327\) 0.140018 0.00774299
\(328\) 0 0
\(329\) 26.5287 1.46258
\(330\) 0 0
\(331\) 27.0240 1.48538 0.742688 0.669638i \(-0.233551\pi\)
0.742688 + 0.669638i \(0.233551\pi\)
\(332\) 0 0
\(333\) 0.279586 0.0153212
\(334\) 0 0
\(335\) 23.4293 1.28008
\(336\) 0 0
\(337\) 26.9667 1.46897 0.734485 0.678625i \(-0.237424\pi\)
0.734485 + 0.678625i \(0.237424\pi\)
\(338\) 0 0
\(339\) 14.1206 0.766927
\(340\) 0 0
\(341\) −4.03477 −0.218495
\(342\) 0 0
\(343\) −12.0813 −0.652328
\(344\) 0 0
\(345\) −12.1311 −0.653118
\(346\) 0 0
\(347\) −3.71182 −0.199261 −0.0996305 0.995025i \(-0.531766\pi\)
−0.0996305 + 0.995025i \(0.531766\pi\)
\(348\) 0 0
\(349\) −35.5718 −1.90412 −0.952058 0.305917i \(-0.901037\pi\)
−0.952058 + 0.305917i \(0.901037\pi\)
\(350\) 0 0
\(351\) 4.88513 0.260749
\(352\) 0 0
\(353\) 7.37584 0.392576 0.196288 0.980546i \(-0.437111\pi\)
0.196288 + 0.980546i \(0.437111\pi\)
\(354\) 0 0
\(355\) 30.5501 1.62143
\(356\) 0 0
\(357\) −8.78579 −0.464993
\(358\) 0 0
\(359\) 3.08145 0.162633 0.0813163 0.996688i \(-0.474088\pi\)
0.0813163 + 0.996688i \(0.474088\pi\)
\(360\) 0 0
\(361\) −16.1974 −0.852492
\(362\) 0 0
\(363\) 10.3834 0.544985
\(364\) 0 0
\(365\) 4.87090 0.254955
\(366\) 0 0
\(367\) −17.9058 −0.934674 −0.467337 0.884079i \(-0.654787\pi\)
−0.467337 + 0.884079i \(0.654787\pi\)
\(368\) 0 0
\(369\) 1.15508 0.0601310
\(370\) 0 0
\(371\) −19.9780 −1.03720
\(372\) 0 0
\(373\) 4.74741 0.245812 0.122906 0.992418i \(-0.460779\pi\)
0.122906 + 0.992418i \(0.460779\pi\)
\(374\) 0 0
\(375\) 12.0922 0.624440
\(376\) 0 0
\(377\) 4.40764 0.227005
\(378\) 0 0
\(379\) −35.8092 −1.83940 −0.919699 0.392625i \(-0.871567\pi\)
−0.919699 + 0.392625i \(0.871567\pi\)
\(380\) 0 0
\(381\) −12.0579 −0.617743
\(382\) 0 0
\(383\) −16.8974 −0.863415 −0.431707 0.902014i \(-0.642089\pi\)
−0.431707 + 0.902014i \(0.642089\pi\)
\(384\) 0 0
\(385\) 4.88258 0.248839
\(386\) 0 0
\(387\) −4.50592 −0.229049
\(388\) 0 0
\(389\) −9.81225 −0.497501 −0.248750 0.968568i \(-0.580020\pi\)
−0.248750 + 0.968568i \(0.580020\pi\)
\(390\) 0 0
\(391\) 17.1415 0.866883
\(392\) 0 0
\(393\) −6.67350 −0.336633
\(394\) 0 0
\(395\) 20.0064 1.00663
\(396\) 0 0
\(397\) 14.5614 0.730818 0.365409 0.930847i \(-0.380929\pi\)
0.365409 + 0.930847i \(0.380929\pi\)
\(398\) 0 0
\(399\) 5.35221 0.267946
\(400\) 0 0
\(401\) −20.4361 −1.02053 −0.510266 0.860017i \(-0.670453\pi\)
−0.510266 + 0.860017i \(0.670453\pi\)
\(402\) 0 0
\(403\) 25.1003 1.25034
\(404\) 0 0
\(405\) 1.94484 0.0966400
\(406\) 0 0
\(407\) 0.219549 0.0108826
\(408\) 0 0
\(409\) −14.4146 −0.712758 −0.356379 0.934341i \(-0.615989\pi\)
−0.356379 + 0.934341i \(0.615989\pi\)
\(410\) 0 0
\(411\) −9.73895 −0.480387
\(412\) 0 0
\(413\) 29.3502 1.44423
\(414\) 0 0
\(415\) −9.60120 −0.471304
\(416\) 0 0
\(417\) −7.08219 −0.346816
\(418\) 0 0
\(419\) 10.8259 0.528881 0.264441 0.964402i \(-0.414813\pi\)
0.264441 + 0.964402i \(0.414813\pi\)
\(420\) 0 0
\(421\) 7.79642 0.379974 0.189987 0.981787i \(-0.439155\pi\)
0.189987 + 0.981787i \(0.439155\pi\)
\(422\) 0 0
\(423\) 8.29789 0.403457
\(424\) 0 0
\(425\) −3.34605 −0.162307
\(426\) 0 0
\(427\) 2.29487 0.111057
\(428\) 0 0
\(429\) 3.83612 0.185209
\(430\) 0 0
\(431\) 1.95879 0.0943518 0.0471759 0.998887i \(-0.484978\pi\)
0.0471759 + 0.998887i \(0.484978\pi\)
\(432\) 0 0
\(433\) 6.77815 0.325737 0.162869 0.986648i \(-0.447925\pi\)
0.162869 + 0.986648i \(0.447925\pi\)
\(434\) 0 0
\(435\) 1.75475 0.0841337
\(436\) 0 0
\(437\) −10.4424 −0.499529
\(438\) 0 0
\(439\) 1.60884 0.0767858 0.0383929 0.999263i \(-0.487776\pi\)
0.0383929 + 0.999263i \(0.487776\pi\)
\(440\) 0 0
\(441\) 3.22111 0.153386
\(442\) 0 0
\(443\) 13.1166 0.623189 0.311594 0.950215i \(-0.399137\pi\)
0.311594 + 0.950215i \(0.399137\pi\)
\(444\) 0 0
\(445\) 30.0030 1.42228
\(446\) 0 0
\(447\) −1.98095 −0.0936955
\(448\) 0 0
\(449\) 20.2340 0.954900 0.477450 0.878659i \(-0.341561\pi\)
0.477450 + 0.878659i \(0.341561\pi\)
\(450\) 0 0
\(451\) 0.907042 0.0427110
\(452\) 0 0
\(453\) −21.5517 −1.01259
\(454\) 0 0
\(455\) −30.3745 −1.42398
\(456\) 0 0
\(457\) −32.8087 −1.53473 −0.767364 0.641212i \(-0.778432\pi\)
−0.767364 + 0.641212i \(0.778432\pi\)
\(458\) 0 0
\(459\) −2.74809 −0.128270
\(460\) 0 0
\(461\) 0.330968 0.0154147 0.00770735 0.999970i \(-0.497547\pi\)
0.00770735 + 0.999970i \(0.497547\pi\)
\(462\) 0 0
\(463\) 22.7776 1.05857 0.529283 0.848445i \(-0.322461\pi\)
0.529283 + 0.848445i \(0.322461\pi\)
\(464\) 0 0
\(465\) 9.99281 0.463405
\(466\) 0 0
\(467\) 24.0969 1.11507 0.557535 0.830153i \(-0.311747\pi\)
0.557535 + 0.830153i \(0.311747\pi\)
\(468\) 0 0
\(469\) 38.5145 1.77844
\(470\) 0 0
\(471\) −6.14846 −0.283306
\(472\) 0 0
\(473\) −3.53833 −0.162693
\(474\) 0 0
\(475\) 2.03838 0.0935273
\(476\) 0 0
\(477\) −6.24888 −0.286117
\(478\) 0 0
\(479\) 1.21205 0.0553800 0.0276900 0.999617i \(-0.491185\pi\)
0.0276900 + 0.999617i \(0.491185\pi\)
\(480\) 0 0
\(481\) −1.36581 −0.0622756
\(482\) 0 0
\(483\) −19.9419 −0.907387
\(484\) 0 0
\(485\) 2.99376 0.135940
\(486\) 0 0
\(487\) −12.1030 −0.548437 −0.274219 0.961667i \(-0.588419\pi\)
−0.274219 + 0.961667i \(0.588419\pi\)
\(488\) 0 0
\(489\) −0.988706 −0.0447108
\(490\) 0 0
\(491\) 2.65281 0.119720 0.0598598 0.998207i \(-0.480935\pi\)
0.0598598 + 0.998207i \(0.480935\pi\)
\(492\) 0 0
\(493\) −2.47949 −0.111670
\(494\) 0 0
\(495\) 1.52721 0.0686432
\(496\) 0 0
\(497\) 50.2202 2.25268
\(498\) 0 0
\(499\) 31.8523 1.42590 0.712952 0.701213i \(-0.247358\pi\)
0.712952 + 0.701213i \(0.247358\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 12.6781 0.565290 0.282645 0.959225i \(-0.408788\pi\)
0.282645 + 0.959225i \(0.408788\pi\)
\(504\) 0 0
\(505\) −1.24016 −0.0551862
\(506\) 0 0
\(507\) −10.8645 −0.482508
\(508\) 0 0
\(509\) 12.9221 0.572764 0.286382 0.958116i \(-0.407547\pi\)
0.286382 + 0.958116i \(0.407547\pi\)
\(510\) 0 0
\(511\) 8.00708 0.354212
\(512\) 0 0
\(513\) 1.67411 0.0739138
\(514\) 0 0
\(515\) −9.39960 −0.414196
\(516\) 0 0
\(517\) 6.51603 0.286575
\(518\) 0 0
\(519\) −0.748097 −0.0328378
\(520\) 0 0
\(521\) 20.3920 0.893390 0.446695 0.894686i \(-0.352601\pi\)
0.446695 + 0.894686i \(0.352601\pi\)
\(522\) 0 0
\(523\) 0.653312 0.0285673 0.0142837 0.999898i \(-0.495453\pi\)
0.0142837 + 0.999898i \(0.495453\pi\)
\(524\) 0 0
\(525\) 3.89269 0.169891
\(526\) 0 0
\(527\) −14.1200 −0.615077
\(528\) 0 0
\(529\) 15.9076 0.691634
\(530\) 0 0
\(531\) 9.18041 0.398396
\(532\) 0 0
\(533\) −5.64271 −0.244413
\(534\) 0 0
\(535\) 18.0106 0.778666
\(536\) 0 0
\(537\) 19.6260 0.846924
\(538\) 0 0
\(539\) 2.52942 0.108950
\(540\) 0 0
\(541\) 21.8468 0.939268 0.469634 0.882861i \(-0.344386\pi\)
0.469634 + 0.882861i \(0.344386\pi\)
\(542\) 0 0
\(543\) −10.6840 −0.458493
\(544\) 0 0
\(545\) −0.272312 −0.0116646
\(546\) 0 0
\(547\) 40.3863 1.72679 0.863397 0.504525i \(-0.168332\pi\)
0.863397 + 0.504525i \(0.168332\pi\)
\(548\) 0 0
\(549\) 0.717810 0.0306354
\(550\) 0 0
\(551\) 1.51048 0.0643485
\(552\) 0 0
\(553\) 32.8877 1.39853
\(554\) 0 0
\(555\) −0.543750 −0.0230809
\(556\) 0 0
\(557\) 15.0593 0.638084 0.319042 0.947741i \(-0.396639\pi\)
0.319042 + 0.947741i \(0.396639\pi\)
\(558\) 0 0
\(559\) 22.0120 0.931007
\(560\) 0 0
\(561\) −2.15798 −0.0911100
\(562\) 0 0
\(563\) 20.5299 0.865232 0.432616 0.901578i \(-0.357591\pi\)
0.432616 + 0.901578i \(0.357591\pi\)
\(564\) 0 0
\(565\) −27.4624 −1.15535
\(566\) 0 0
\(567\) 3.19705 0.134263
\(568\) 0 0
\(569\) 6.59982 0.276679 0.138339 0.990385i \(-0.455824\pi\)
0.138339 + 0.990385i \(0.455824\pi\)
\(570\) 0 0
\(571\) 15.4955 0.648469 0.324234 0.945977i \(-0.394893\pi\)
0.324234 + 0.945977i \(0.394893\pi\)
\(572\) 0 0
\(573\) 25.6633 1.07210
\(574\) 0 0
\(575\) −7.59483 −0.316726
\(576\) 0 0
\(577\) 7.56245 0.314829 0.157415 0.987533i \(-0.449684\pi\)
0.157415 + 0.987533i \(0.449684\pi\)
\(578\) 0 0
\(579\) −4.10218 −0.170481
\(580\) 0 0
\(581\) −15.7830 −0.654790
\(582\) 0 0
\(583\) −4.90702 −0.203228
\(584\) 0 0
\(585\) −9.50080 −0.392810
\(586\) 0 0
\(587\) −40.7031 −1.68000 −0.839999 0.542588i \(-0.817445\pi\)
−0.839999 + 0.542588i \(0.817445\pi\)
\(588\) 0 0
\(589\) 8.60176 0.354429
\(590\) 0 0
\(591\) 3.58320 0.147393
\(592\) 0 0
\(593\) 31.6194 1.29845 0.649227 0.760595i \(-0.275092\pi\)
0.649227 + 0.760595i \(0.275092\pi\)
\(594\) 0 0
\(595\) 17.0870 0.700497
\(596\) 0 0
\(597\) 1.22740 0.0502340
\(598\) 0 0
\(599\) 1.82585 0.0746023 0.0373011 0.999304i \(-0.488124\pi\)
0.0373011 + 0.999304i \(0.488124\pi\)
\(600\) 0 0
\(601\) 36.1032 1.47268 0.736340 0.676611i \(-0.236552\pi\)
0.736340 + 0.676611i \(0.236552\pi\)
\(602\) 0 0
\(603\) 12.0469 0.490588
\(604\) 0 0
\(605\) −20.1940 −0.821003
\(606\) 0 0
\(607\) −9.38030 −0.380735 −0.190367 0.981713i \(-0.560968\pi\)
−0.190367 + 0.981713i \(0.560968\pi\)
\(608\) 0 0
\(609\) 2.88456 0.116888
\(610\) 0 0
\(611\) −40.5362 −1.63992
\(612\) 0 0
\(613\) −31.2542 −1.26234 −0.631172 0.775643i \(-0.717426\pi\)
−0.631172 + 0.775643i \(0.717426\pi\)
\(614\) 0 0
\(615\) −2.24645 −0.0905855
\(616\) 0 0
\(617\) −10.0094 −0.402962 −0.201481 0.979492i \(-0.564575\pi\)
−0.201481 + 0.979492i \(0.564575\pi\)
\(618\) 0 0
\(619\) 8.03107 0.322796 0.161398 0.986889i \(-0.448400\pi\)
0.161398 + 0.986889i \(0.448400\pi\)
\(620\) 0 0
\(621\) −6.23759 −0.250306
\(622\) 0 0
\(623\) 49.3208 1.97600
\(624\) 0 0
\(625\) −17.4295 −0.697181
\(626\) 0 0
\(627\) 1.31462 0.0525008
\(628\) 0 0
\(629\) 0.768328 0.0306352
\(630\) 0 0
\(631\) −11.1105 −0.442302 −0.221151 0.975240i \(-0.570981\pi\)
−0.221151 + 0.975240i \(0.570981\pi\)
\(632\) 0 0
\(633\) −5.24358 −0.208414
\(634\) 0 0
\(635\) 23.4506 0.930610
\(636\) 0 0
\(637\) −15.7355 −0.623465
\(638\) 0 0
\(639\) 15.7083 0.621411
\(640\) 0 0
\(641\) 47.7769 1.88707 0.943537 0.331268i \(-0.107476\pi\)
0.943537 + 0.331268i \(0.107476\pi\)
\(642\) 0 0
\(643\) 24.0665 0.949092 0.474546 0.880231i \(-0.342612\pi\)
0.474546 + 0.880231i \(0.342612\pi\)
\(644\) 0 0
\(645\) 8.76329 0.345054
\(646\) 0 0
\(647\) 41.2896 1.62326 0.811631 0.584170i \(-0.198580\pi\)
0.811631 + 0.584170i \(0.198580\pi\)
\(648\) 0 0
\(649\) 7.20905 0.282980
\(650\) 0 0
\(651\) 16.4268 0.643816
\(652\) 0 0
\(653\) −16.6726 −0.652449 −0.326225 0.945292i \(-0.605777\pi\)
−0.326225 + 0.945292i \(0.605777\pi\)
\(654\) 0 0
\(655\) 12.9789 0.507127
\(656\) 0 0
\(657\) 2.50452 0.0977108
\(658\) 0 0
\(659\) −31.8476 −1.24061 −0.620303 0.784362i \(-0.712990\pi\)
−0.620303 + 0.784362i \(0.712990\pi\)
\(660\) 0 0
\(661\) 41.0798 1.59782 0.798909 0.601452i \(-0.205411\pi\)
0.798909 + 0.601452i \(0.205411\pi\)
\(662\) 0 0
\(663\) 13.4248 0.521376
\(664\) 0 0
\(665\) −10.4092 −0.403652
\(666\) 0 0
\(667\) −5.62791 −0.217914
\(668\) 0 0
\(669\) 1.10636 0.0427742
\(670\) 0 0
\(671\) 0.563670 0.0217602
\(672\) 0 0
\(673\) −45.5600 −1.75621 −0.878105 0.478469i \(-0.841192\pi\)
−0.878105 + 0.478469i \(0.841192\pi\)
\(674\) 0 0
\(675\) 1.21759 0.0468651
\(676\) 0 0
\(677\) −10.1339 −0.389478 −0.194739 0.980855i \(-0.562386\pi\)
−0.194739 + 0.980855i \(0.562386\pi\)
\(678\) 0 0
\(679\) 4.92133 0.188863
\(680\) 0 0
\(681\) −17.7395 −0.679780
\(682\) 0 0
\(683\) −12.0786 −0.462173 −0.231086 0.972933i \(-0.574228\pi\)
−0.231086 + 0.972933i \(0.574228\pi\)
\(684\) 0 0
\(685\) 18.9407 0.723687
\(686\) 0 0
\(687\) −3.65487 −0.139442
\(688\) 0 0
\(689\) 30.5266 1.16297
\(690\) 0 0
\(691\) −11.9988 −0.456457 −0.228228 0.973608i \(-0.573293\pi\)
−0.228228 + 0.973608i \(0.573293\pi\)
\(692\) 0 0
\(693\) 2.51053 0.0953670
\(694\) 0 0
\(695\) 13.7737 0.522468
\(696\) 0 0
\(697\) 3.17427 0.120234
\(698\) 0 0
\(699\) 9.77622 0.369771
\(700\) 0 0
\(701\) 24.9550 0.942537 0.471269 0.881990i \(-0.343796\pi\)
0.471269 + 0.881990i \(0.343796\pi\)
\(702\) 0 0
\(703\) −0.468057 −0.0176531
\(704\) 0 0
\(705\) −16.1381 −0.607795
\(706\) 0 0
\(707\) −2.03864 −0.0766710
\(708\) 0 0
\(709\) −26.9420 −1.01183 −0.505914 0.862584i \(-0.668845\pi\)
−0.505914 + 0.862584i \(0.668845\pi\)
\(710\) 0 0
\(711\) 10.2869 0.385789
\(712\) 0 0
\(713\) −32.0494 −1.20026
\(714\) 0 0
\(715\) −7.46064 −0.279012
\(716\) 0 0
\(717\) 15.9111 0.594212
\(718\) 0 0
\(719\) 25.0824 0.935416 0.467708 0.883883i \(-0.345080\pi\)
0.467708 + 0.883883i \(0.345080\pi\)
\(720\) 0 0
\(721\) −15.4516 −0.575449
\(722\) 0 0
\(723\) −26.5185 −0.986235
\(724\) 0 0
\(725\) 1.09858 0.0408002
\(726\) 0 0
\(727\) 46.0283 1.70709 0.853547 0.521015i \(-0.174447\pi\)
0.853547 + 0.521015i \(0.174447\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.3827 −0.457990
\(732\) 0 0
\(733\) −8.71867 −0.322032 −0.161016 0.986952i \(-0.551477\pi\)
−0.161016 + 0.986952i \(0.551477\pi\)
\(734\) 0 0
\(735\) −6.26455 −0.231071
\(736\) 0 0
\(737\) 9.46001 0.348464
\(738\) 0 0
\(739\) 4.73695 0.174252 0.0871258 0.996197i \(-0.472232\pi\)
0.0871258 + 0.996197i \(0.472232\pi\)
\(740\) 0 0
\(741\) −8.17824 −0.300435
\(742\) 0 0
\(743\) −24.4489 −0.896942 −0.448471 0.893797i \(-0.648031\pi\)
−0.448471 + 0.893797i \(0.648031\pi\)
\(744\) 0 0
\(745\) 3.85263 0.141149
\(746\) 0 0
\(747\) −4.93675 −0.180626
\(748\) 0 0
\(749\) 29.6069 1.08181
\(750\) 0 0
\(751\) −25.8796 −0.944360 −0.472180 0.881502i \(-0.656533\pi\)
−0.472180 + 0.881502i \(0.656533\pi\)
\(752\) 0 0
\(753\) 23.6017 0.860096
\(754\) 0 0
\(755\) 41.9146 1.52543
\(756\) 0 0
\(757\) 45.7756 1.66374 0.831872 0.554968i \(-0.187270\pi\)
0.831872 + 0.554968i \(0.187270\pi\)
\(758\) 0 0
\(759\) −4.89816 −0.177792
\(760\) 0 0
\(761\) −11.9566 −0.433426 −0.216713 0.976235i \(-0.569534\pi\)
−0.216713 + 0.976235i \(0.569534\pi\)
\(762\) 0 0
\(763\) −0.447643 −0.0162058
\(764\) 0 0
\(765\) 5.34461 0.193235
\(766\) 0 0
\(767\) −44.8475 −1.61935
\(768\) 0 0
\(769\) −47.0375 −1.69622 −0.848108 0.529823i \(-0.822258\pi\)
−0.848108 + 0.529823i \(0.822258\pi\)
\(770\) 0 0
\(771\) −24.0027 −0.864436
\(772\) 0 0
\(773\) 27.5761 0.991843 0.495922 0.868367i \(-0.334830\pi\)
0.495922 + 0.868367i \(0.334830\pi\)
\(774\) 0 0
\(775\) 6.25611 0.224726
\(776\) 0 0
\(777\) −0.893848 −0.0320666
\(778\) 0 0
\(779\) −1.93373 −0.0692831
\(780\) 0 0
\(781\) 12.3352 0.441387
\(782\) 0 0
\(783\) 0.902257 0.0322440
\(784\) 0 0
\(785\) 11.9578 0.426792
\(786\) 0 0
\(787\) −41.3548 −1.47414 −0.737069 0.675817i \(-0.763791\pi\)
−0.737069 + 0.675817i \(0.763791\pi\)
\(788\) 0 0
\(789\) −19.9455 −0.710079
\(790\) 0 0
\(791\) −45.1443 −1.60515
\(792\) 0 0
\(793\) −3.50659 −0.124523
\(794\) 0 0
\(795\) 12.1531 0.431026
\(796\) 0 0
\(797\) −52.1923 −1.84875 −0.924374 0.381489i \(-0.875412\pi\)
−0.924374 + 0.381489i \(0.875412\pi\)
\(798\) 0 0
\(799\) 22.8034 0.806726
\(800\) 0 0
\(801\) 15.4270 0.545086
\(802\) 0 0
\(803\) 1.96671 0.0694038
\(804\) 0 0
\(805\) 38.7838 1.36695
\(806\) 0 0
\(807\) −14.7796 −0.520267
\(808\) 0 0
\(809\) 7.72641 0.271646 0.135823 0.990733i \(-0.456632\pi\)
0.135823 + 0.990733i \(0.456632\pi\)
\(810\) 0 0
\(811\) −15.0077 −0.526993 −0.263496 0.964660i \(-0.584876\pi\)
−0.263496 + 0.964660i \(0.584876\pi\)
\(812\) 0 0
\(813\) 7.89192 0.276782
\(814\) 0 0
\(815\) 1.92288 0.0673554
\(816\) 0 0
\(817\) 7.54340 0.263910
\(818\) 0 0
\(819\) −15.6180 −0.545737
\(820\) 0 0
\(821\) 8.08701 0.282239 0.141119 0.989993i \(-0.454930\pi\)
0.141119 + 0.989993i \(0.454930\pi\)
\(822\) 0 0
\(823\) −1.51032 −0.0526465 −0.0263233 0.999653i \(-0.508380\pi\)
−0.0263233 + 0.999653i \(0.508380\pi\)
\(824\) 0 0
\(825\) 0.956130 0.0332882
\(826\) 0 0
\(827\) −43.2284 −1.50320 −0.751599 0.659621i \(-0.770717\pi\)
−0.751599 + 0.659621i \(0.770717\pi\)
\(828\) 0 0
\(829\) 10.1690 0.353185 0.176593 0.984284i \(-0.443493\pi\)
0.176593 + 0.984284i \(0.443493\pi\)
\(830\) 0 0
\(831\) 8.44295 0.292883
\(832\) 0 0
\(833\) 8.85192 0.306701
\(834\) 0 0
\(835\) 1.94484 0.0673040
\(836\) 0 0
\(837\) 5.13811 0.177599
\(838\) 0 0
\(839\) −36.9084 −1.27422 −0.637110 0.770773i \(-0.719870\pi\)
−0.637110 + 0.770773i \(0.719870\pi\)
\(840\) 0 0
\(841\) −28.1859 −0.971929
\(842\) 0 0
\(843\) 3.38998 0.116757
\(844\) 0 0
\(845\) 21.1297 0.726883
\(846\) 0 0
\(847\) −33.1961 −1.14063
\(848\) 0 0
\(849\) 11.5355 0.395898
\(850\) 0 0
\(851\) 1.74394 0.0597815
\(852\) 0 0
\(853\) 4.95854 0.169777 0.0848886 0.996390i \(-0.472947\pi\)
0.0848886 + 0.996390i \(0.472947\pi\)
\(854\) 0 0
\(855\) −3.25588 −0.111349
\(856\) 0 0
\(857\) 16.2261 0.554272 0.277136 0.960831i \(-0.410615\pi\)
0.277136 + 0.960831i \(0.410615\pi\)
\(858\) 0 0
\(859\) −11.7556 −0.401097 −0.200549 0.979684i \(-0.564272\pi\)
−0.200549 + 0.979684i \(0.564272\pi\)
\(860\) 0 0
\(861\) −3.69284 −0.125852
\(862\) 0 0
\(863\) 34.1048 1.16094 0.580470 0.814282i \(-0.302869\pi\)
0.580470 + 0.814282i \(0.302869\pi\)
\(864\) 0 0
\(865\) 1.45493 0.0494691
\(866\) 0 0
\(867\) 9.44797 0.320870
\(868\) 0 0
\(869\) 8.07793 0.274025
\(870\) 0 0
\(871\) −58.8507 −1.99408
\(872\) 0 0
\(873\) 1.53933 0.0520986
\(874\) 0 0
\(875\) −38.6594 −1.30693
\(876\) 0 0
\(877\) 23.5036 0.793662 0.396831 0.917892i \(-0.370110\pi\)
0.396831 + 0.917892i \(0.370110\pi\)
\(878\) 0 0
\(879\) 7.92981 0.267466
\(880\) 0 0
\(881\) 35.4073 1.19290 0.596451 0.802650i \(-0.296577\pi\)
0.596451 + 0.802650i \(0.296577\pi\)
\(882\) 0 0
\(883\) −44.4104 −1.49453 −0.747265 0.664526i \(-0.768633\pi\)
−0.747265 + 0.664526i \(0.768633\pi\)
\(884\) 0 0
\(885\) −17.8545 −0.600171
\(886\) 0 0
\(887\) −0.959427 −0.0322144 −0.0161072 0.999870i \(-0.505127\pi\)
−0.0161072 + 0.999870i \(0.505127\pi\)
\(888\) 0 0
\(889\) 38.5495 1.29291
\(890\) 0 0
\(891\) 0.785264 0.0263073
\(892\) 0 0
\(893\) −13.8916 −0.464864
\(894\) 0 0
\(895\) −38.1694 −1.27586
\(896\) 0 0
\(897\) 30.4714 1.01741
\(898\) 0 0
\(899\) 4.63589 0.154616
\(900\) 0 0
\(901\) −17.1725 −0.572100
\(902\) 0 0
\(903\) 14.4056 0.479389
\(904\) 0 0
\(905\) 20.7786 0.690705
\(906\) 0 0
\(907\) −0.753739 −0.0250275 −0.0125137 0.999922i \(-0.503983\pi\)
−0.0125137 + 0.999922i \(0.503983\pi\)
\(908\) 0 0
\(909\) −0.637664 −0.0211500
\(910\) 0 0
\(911\) 6.87062 0.227634 0.113817 0.993502i \(-0.463692\pi\)
0.113817 + 0.993502i \(0.463692\pi\)
\(912\) 0 0
\(913\) −3.87666 −0.128299
\(914\) 0 0
\(915\) −1.39603 −0.0461512
\(916\) 0 0
\(917\) 21.3355 0.704560
\(918\) 0 0
\(919\) 48.1883 1.58958 0.794792 0.606881i \(-0.207580\pi\)
0.794792 + 0.606881i \(0.207580\pi\)
\(920\) 0 0
\(921\) −22.6509 −0.746372
\(922\) 0 0
\(923\) −76.7370 −2.52583
\(924\) 0 0
\(925\) −0.340421 −0.0111930
\(926\) 0 0
\(927\) −4.83309 −0.158740
\(928\) 0 0
\(929\) −21.0774 −0.691528 −0.345764 0.938322i \(-0.612380\pi\)
−0.345764 + 0.938322i \(0.612380\pi\)
\(930\) 0 0
\(931\) −5.39249 −0.176732
\(932\) 0 0
\(933\) 16.1604 0.529066
\(934\) 0 0
\(935\) 4.19693 0.137254
\(936\) 0 0
\(937\) 22.1319 0.723019 0.361509 0.932368i \(-0.382262\pi\)
0.361509 + 0.932368i \(0.382262\pi\)
\(938\) 0 0
\(939\) 3.80949 0.124318
\(940\) 0 0
\(941\) −5.58967 −0.182218 −0.0911091 0.995841i \(-0.529041\pi\)
−0.0911091 + 0.995841i \(0.529041\pi\)
\(942\) 0 0
\(943\) 7.20491 0.234624
\(944\) 0 0
\(945\) −6.21775 −0.202263
\(946\) 0 0
\(947\) −0.824122 −0.0267804 −0.0133902 0.999910i \(-0.504262\pi\)
−0.0133902 + 0.999910i \(0.504262\pi\)
\(948\) 0 0
\(949\) −12.2349 −0.397162
\(950\) 0 0
\(951\) 6.77439 0.219675
\(952\) 0 0
\(953\) −8.76121 −0.283804 −0.141902 0.989881i \(-0.545322\pi\)
−0.141902 + 0.989881i \(0.545322\pi\)
\(954\) 0 0
\(955\) −49.9110 −1.61508
\(956\) 0 0
\(957\) 0.708510 0.0229029
\(958\) 0 0
\(959\) 31.1359 1.00543
\(960\) 0 0
\(961\) −4.59983 −0.148382
\(962\) 0 0
\(963\) 9.26070 0.298422
\(964\) 0 0
\(965\) 7.97808 0.256824
\(966\) 0 0
\(967\) 21.1756 0.680963 0.340481 0.940251i \(-0.389410\pi\)
0.340481 + 0.940251i \(0.389410\pi\)
\(968\) 0 0
\(969\) 4.60061 0.147793
\(970\) 0 0
\(971\) −23.9748 −0.769388 −0.384694 0.923044i \(-0.625693\pi\)
−0.384694 + 0.923044i \(0.625693\pi\)
\(972\) 0 0
\(973\) 22.6421 0.725872
\(974\) 0 0
\(975\) −5.94808 −0.190491
\(976\) 0 0
\(977\) −8.56075 −0.273883 −0.136941 0.990579i \(-0.543727\pi\)
−0.136941 + 0.990579i \(0.543727\pi\)
\(978\) 0 0
\(979\) 12.1143 0.387173
\(980\) 0 0
\(981\) −0.140018 −0.00447042
\(982\) 0 0
\(983\) −25.5757 −0.815738 −0.407869 0.913040i \(-0.633728\pi\)
−0.407869 + 0.913040i \(0.633728\pi\)
\(984\) 0 0
\(985\) −6.96875 −0.222043
\(986\) 0 0
\(987\) −26.5287 −0.844419
\(988\) 0 0
\(989\) −28.1061 −0.893721
\(990\) 0 0
\(991\) 35.5988 1.13083 0.565416 0.824806i \(-0.308716\pi\)
0.565416 + 0.824806i \(0.308716\pi\)
\(992\) 0 0
\(993\) −27.0240 −0.857582
\(994\) 0 0
\(995\) −2.38709 −0.0756759
\(996\) 0 0
\(997\) −9.21830 −0.291946 −0.145973 0.989289i \(-0.546631\pi\)
−0.145973 + 0.989289i \(0.546631\pi\)
\(998\) 0 0
\(999\) −0.279586 −0.00884570
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.ba.1.8 9
4.3 odd 2 4008.2.a.i.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.i.1.8 9 4.3 odd 2
8016.2.a.ba.1.8 9 1.1 even 1 trivial