Properties

Label 8016.2.a.w.1.1
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 2 x^{6} - 7 x^{5} + 11 x^{4} + 12 x^{3} - 14 x^{2} - 6 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.80982\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} -3.20729 q^{5} -3.68779 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -3.20729 q^{5} -3.68779 q^{7} +1.00000 q^{9} -2.41235 q^{11} -0.292389 q^{13} -3.20729 q^{15} +7.19061 q^{17} +2.96484 q^{19} -3.68779 q^{21} -5.50281 q^{23} +5.28672 q^{25} +1.00000 q^{27} +3.32252 q^{29} +3.32412 q^{31} -2.41235 q^{33} +11.8278 q^{35} -0.357486 q^{37} -0.292389 q^{39} +3.49808 q^{41} +11.1409 q^{43} -3.20729 q^{45} +0.406706 q^{47} +6.59982 q^{49} +7.19061 q^{51} -10.6914 q^{53} +7.73710 q^{55} +2.96484 q^{57} +3.65193 q^{59} +9.48361 q^{61} -3.68779 q^{63} +0.937777 q^{65} -4.18677 q^{67} -5.50281 q^{69} -2.68125 q^{71} -6.27452 q^{73} +5.28672 q^{75} +8.89624 q^{77} -6.66323 q^{79} +1.00000 q^{81} -10.2090 q^{83} -23.0624 q^{85} +3.32252 q^{87} -4.51995 q^{89} +1.07827 q^{91} +3.32412 q^{93} -9.50909 q^{95} +1.77054 q^{97} -2.41235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 7q^{3} - 3q^{5} - 8q^{7} + 7q^{9} + O(q^{10}) \) \( 7q + 7q^{3} - 3q^{5} - 8q^{7} + 7q^{9} - q^{11} - 2q^{13} - 3q^{15} + 11q^{17} - 2q^{19} - 8q^{21} - 17q^{23} + 4q^{25} + 7q^{27} - 7q^{29} - 10q^{31} - q^{33} - 10q^{35} - 21q^{37} - 2q^{39} + 8q^{41} + 12q^{43} - 3q^{45} - 25q^{47} - 7q^{49} + 11q^{51} - 7q^{53} - 15q^{55} - 2q^{57} - 3q^{59} - 14q^{61} - 8q^{63} + 4q^{65} - 4q^{67} - 17q^{69} - 27q^{71} - 12q^{73} + 4q^{75} + 16q^{77} - 8q^{79} + 7q^{81} - 15q^{83} - 3q^{85} - 7q^{87} + 14q^{89} + 3q^{91} - 10q^{93} - 37q^{95} + 3q^{97} - q^{99} + O(q^{100}) \)

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
\(5\) −3.20729 −1.43434 −0.717172 0.696896i \(-0.754564\pi\)
−0.717172 + 0.696896i \(0.754564\pi\)
\(6\) 0 0
\(7\) −3.68779 −1.39385 −0.696927 0.717142i \(-0.745450\pi\)
−0.696927 + 0.717142i \(0.745450\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −2.41235 −0.727350 −0.363675 0.931526i \(-0.618478\pi\)
−0.363675 + 0.931526i \(0.618478\pi\)
\(12\) 0 0
\(13\) −0.292389 −0.0810942 −0.0405471 0.999178i \(-0.512910\pi\)
−0.0405471 + 0.999178i \(0.512910\pi\)
\(14\) 0 0
\(15\) −3.20729 −0.828119
\(16\) 0 0
\(17\) 7.19061 1.74398 0.871989 0.489525i \(-0.162830\pi\)
0.871989 + 0.489525i \(0.162830\pi\)
\(18\) 0 0
\(19\) 2.96484 0.680180 0.340090 0.940393i \(-0.389542\pi\)
0.340090 + 0.940393i \(0.389542\pi\)
\(20\) 0 0
\(21\) −3.68779 −0.804743
\(22\) 0 0
\(23\) −5.50281 −1.14742 −0.573708 0.819060i \(-0.694496\pi\)
−0.573708 + 0.819060i \(0.694496\pi\)
\(24\) 0 0
\(25\) 5.28672 1.05734
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.32252 0.616976 0.308488 0.951228i \(-0.400177\pi\)
0.308488 + 0.951228i \(0.400177\pi\)
\(30\) 0 0
\(31\) 3.32412 0.597029 0.298514 0.954405i \(-0.403509\pi\)
0.298514 + 0.954405i \(0.403509\pi\)
\(32\) 0 0
\(33\) −2.41235 −0.419936
\(34\) 0 0
\(35\) 11.8278 1.99927
\(36\) 0 0
\(37\) −0.357486 −0.0587703 −0.0293852 0.999568i \(-0.509355\pi\)
−0.0293852 + 0.999568i \(0.509355\pi\)
\(38\) 0 0
\(39\) −0.292389 −0.0468197
\(40\) 0 0
\(41\) 3.49808 0.546309 0.273154 0.961970i \(-0.411933\pi\)
0.273154 + 0.961970i \(0.411933\pi\)
\(42\) 0 0
\(43\) 11.1409 1.69898 0.849488 0.527608i \(-0.176911\pi\)
0.849488 + 0.527608i \(0.176911\pi\)
\(44\) 0 0
\(45\) −3.20729 −0.478115
\(46\) 0 0
\(47\) 0.406706 0.0593241 0.0296621 0.999560i \(-0.490557\pi\)
0.0296621 + 0.999560i \(0.490557\pi\)
\(48\) 0 0
\(49\) 6.59982 0.942832
\(50\) 0 0
\(51\) 7.19061 1.00689
\(52\) 0 0
\(53\) −10.6914 −1.46858 −0.734291 0.678834i \(-0.762485\pi\)
−0.734291 + 0.678834i \(0.762485\pi\)
\(54\) 0 0
\(55\) 7.73710 1.04327
\(56\) 0 0
\(57\) 2.96484 0.392702
\(58\) 0 0
\(59\) 3.65193 0.475441 0.237720 0.971334i \(-0.423600\pi\)
0.237720 + 0.971334i \(0.423600\pi\)
\(60\) 0 0
\(61\) 9.48361 1.21425 0.607126 0.794606i \(-0.292322\pi\)
0.607126 + 0.794606i \(0.292322\pi\)
\(62\) 0 0
\(63\) −3.68779 −0.464618
\(64\) 0 0
\(65\) 0.937777 0.116317
\(66\) 0 0
\(67\) −4.18677 −0.511496 −0.255748 0.966744i \(-0.582322\pi\)
−0.255748 + 0.966744i \(0.582322\pi\)
\(68\) 0 0
\(69\) −5.50281 −0.662461
\(70\) 0 0
\(71\) −2.68125 −0.318206 −0.159103 0.987262i \(-0.550860\pi\)
−0.159103 + 0.987262i \(0.550860\pi\)
\(72\) 0 0
\(73\) −6.27452 −0.734377 −0.367189 0.930147i \(-0.619680\pi\)
−0.367189 + 0.930147i \(0.619680\pi\)
\(74\) 0 0
\(75\) 5.28672 0.610457
\(76\) 0 0
\(77\) 8.89624 1.01382
\(78\) 0 0
\(79\) −6.66323 −0.749672 −0.374836 0.927091i \(-0.622301\pi\)
−0.374836 + 0.927091i \(0.622301\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −10.2090 −1.12059 −0.560293 0.828295i \(-0.689311\pi\)
−0.560293 + 0.828295i \(0.689311\pi\)
\(84\) 0 0
\(85\) −23.0624 −2.50147
\(86\) 0 0
\(87\) 3.32252 0.356211
\(88\) 0 0
\(89\) −4.51995 −0.479114 −0.239557 0.970882i \(-0.577002\pi\)
−0.239557 + 0.970882i \(0.577002\pi\)
\(90\) 0 0
\(91\) 1.07827 0.113034
\(92\) 0 0
\(93\) 3.32412 0.344695
\(94\) 0 0
\(95\) −9.50909 −0.975613
\(96\) 0 0
\(97\) 1.77054 0.179771 0.0898853 0.995952i \(-0.471350\pi\)
0.0898853 + 0.995952i \(0.471350\pi\)
\(98\) 0 0
\(99\) −2.41235 −0.242450
\(100\) 0 0
\(101\) 18.8099 1.87165 0.935826 0.352463i \(-0.114656\pi\)
0.935826 + 0.352463i \(0.114656\pi\)
\(102\) 0 0
\(103\) −5.82075 −0.573536 −0.286768 0.958000i \(-0.592581\pi\)
−0.286768 + 0.958000i \(0.592581\pi\)
\(104\) 0 0
\(105\) 11.8278 1.15428
\(106\) 0 0
\(107\) −9.11502 −0.881182 −0.440591 0.897708i \(-0.645231\pi\)
−0.440591 + 0.897708i \(0.645231\pi\)
\(108\) 0 0
\(109\) −18.8744 −1.80784 −0.903922 0.427697i \(-0.859325\pi\)
−0.903922 + 0.427697i \(0.859325\pi\)
\(110\) 0 0
\(111\) −0.357486 −0.0339311
\(112\) 0 0
\(113\) 12.5304 1.17876 0.589381 0.807855i \(-0.299372\pi\)
0.589381 + 0.807855i \(0.299372\pi\)
\(114\) 0 0
\(115\) 17.6491 1.64579
\(116\) 0 0
\(117\) −0.292389 −0.0270314
\(118\) 0 0
\(119\) −26.5175 −2.43085
\(120\) 0 0
\(121\) −5.18058 −0.470962
\(122\) 0 0
\(123\) 3.49808 0.315412
\(124\) 0 0
\(125\) −0.919585 −0.0822502
\(126\) 0 0
\(127\) 1.13671 0.100867 0.0504333 0.998727i \(-0.483940\pi\)
0.0504333 + 0.998727i \(0.483940\pi\)
\(128\) 0 0
\(129\) 11.1409 0.980904
\(130\) 0 0
\(131\) −12.1630 −1.06269 −0.531343 0.847157i \(-0.678312\pi\)
−0.531343 + 0.847157i \(0.678312\pi\)
\(132\) 0 0
\(133\) −10.9337 −0.948072
\(134\) 0 0
\(135\) −3.20729 −0.276040
\(136\) 0 0
\(137\) −14.4346 −1.23323 −0.616616 0.787264i \(-0.711497\pi\)
−0.616616 + 0.787264i \(0.711497\pi\)
\(138\) 0 0
\(139\) 0.433633 0.0367803 0.0183902 0.999831i \(-0.494146\pi\)
0.0183902 + 0.999831i \(0.494146\pi\)
\(140\) 0 0
\(141\) 0.406706 0.0342508
\(142\) 0 0
\(143\) 0.705344 0.0589839
\(144\) 0 0
\(145\) −10.6563 −0.884956
\(146\) 0 0
\(147\) 6.59982 0.544344
\(148\) 0 0
\(149\) −19.0992 −1.56466 −0.782332 0.622862i \(-0.785970\pi\)
−0.782332 + 0.622862i \(0.785970\pi\)
\(150\) 0 0
\(151\) −8.70546 −0.708440 −0.354220 0.935162i \(-0.615254\pi\)
−0.354220 + 0.935162i \(0.615254\pi\)
\(152\) 0 0
\(153\) 7.19061 0.581326
\(154\) 0 0
\(155\) −10.6614 −0.856345
\(156\) 0 0
\(157\) 22.6106 1.80452 0.902261 0.431191i \(-0.141907\pi\)
0.902261 + 0.431191i \(0.141907\pi\)
\(158\) 0 0
\(159\) −10.6914 −0.847887
\(160\) 0 0
\(161\) 20.2932 1.59933
\(162\) 0 0
\(163\) 9.50323 0.744350 0.372175 0.928162i \(-0.378612\pi\)
0.372175 + 0.928162i \(0.378612\pi\)
\(164\) 0 0
\(165\) 7.73710 0.602332
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −12.9145 −0.993424
\(170\) 0 0
\(171\) 2.96484 0.226727
\(172\) 0 0
\(173\) 3.88163 0.295115 0.147557 0.989053i \(-0.452859\pi\)
0.147557 + 0.989053i \(0.452859\pi\)
\(174\) 0 0
\(175\) −19.4963 −1.47378
\(176\) 0 0
\(177\) 3.65193 0.274496
\(178\) 0 0
\(179\) 7.65909 0.572467 0.286234 0.958160i \(-0.407597\pi\)
0.286234 + 0.958160i \(0.407597\pi\)
\(180\) 0 0
\(181\) 9.78926 0.727630 0.363815 0.931471i \(-0.381474\pi\)
0.363815 + 0.931471i \(0.381474\pi\)
\(182\) 0 0
\(183\) 9.48361 0.701048
\(184\) 0 0
\(185\) 1.14656 0.0842969
\(186\) 0 0
\(187\) −17.3462 −1.26848
\(188\) 0 0
\(189\) −3.68779 −0.268248
\(190\) 0 0
\(191\) −14.9580 −1.08232 −0.541162 0.840918i \(-0.682015\pi\)
−0.541162 + 0.840918i \(0.682015\pi\)
\(192\) 0 0
\(193\) −0.569004 −0.0409578 −0.0204789 0.999790i \(-0.506519\pi\)
−0.0204789 + 0.999790i \(0.506519\pi\)
\(194\) 0 0
\(195\) 0.937777 0.0671556
\(196\) 0 0
\(197\) 24.1326 1.71938 0.859688 0.510820i \(-0.170658\pi\)
0.859688 + 0.510820i \(0.170658\pi\)
\(198\) 0 0
\(199\) −10.6151 −0.752482 −0.376241 0.926522i \(-0.622784\pi\)
−0.376241 + 0.926522i \(0.622784\pi\)
\(200\) 0 0
\(201\) −4.18677 −0.295312
\(202\) 0 0
\(203\) −12.2528 −0.859975
\(204\) 0 0
\(205\) −11.2194 −0.783595
\(206\) 0 0
\(207\) −5.50281 −0.382472
\(208\) 0 0
\(209\) −7.15222 −0.494729
\(210\) 0 0
\(211\) −14.9203 −1.02716 −0.513579 0.858042i \(-0.671681\pi\)
−0.513579 + 0.858042i \(0.671681\pi\)
\(212\) 0 0
\(213\) −2.68125 −0.183716
\(214\) 0 0
\(215\) −35.7322 −2.43692
\(216\) 0 0
\(217\) −12.2587 −0.832171
\(218\) 0 0
\(219\) −6.27452 −0.423993
\(220\) 0 0
\(221\) −2.10246 −0.141427
\(222\) 0 0
\(223\) 14.5962 0.977431 0.488715 0.872443i \(-0.337466\pi\)
0.488715 + 0.872443i \(0.337466\pi\)
\(224\) 0 0
\(225\) 5.28672 0.352448
\(226\) 0 0
\(227\) −7.67692 −0.509535 −0.254767 0.967002i \(-0.581999\pi\)
−0.254767 + 0.967002i \(0.581999\pi\)
\(228\) 0 0
\(229\) −7.74042 −0.511501 −0.255751 0.966743i \(-0.582323\pi\)
−0.255751 + 0.966743i \(0.582323\pi\)
\(230\) 0 0
\(231\) 8.89624 0.585330
\(232\) 0 0
\(233\) −15.6688 −1.02650 −0.513250 0.858239i \(-0.671558\pi\)
−0.513250 + 0.858239i \(0.671558\pi\)
\(234\) 0 0
\(235\) −1.30442 −0.0850912
\(236\) 0 0
\(237\) −6.66323 −0.432823
\(238\) 0 0
\(239\) −20.3027 −1.31327 −0.656636 0.754208i \(-0.728021\pi\)
−0.656636 + 0.754208i \(0.728021\pi\)
\(240\) 0 0
\(241\) 7.43764 0.479100 0.239550 0.970884i \(-0.423000\pi\)
0.239550 + 0.970884i \(0.423000\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −21.1675 −1.35235
\(246\) 0 0
\(247\) −0.866886 −0.0551586
\(248\) 0 0
\(249\) −10.2090 −0.646970
\(250\) 0 0
\(251\) −28.3028 −1.78646 −0.893228 0.449604i \(-0.851565\pi\)
−0.893228 + 0.449604i \(0.851565\pi\)
\(252\) 0 0
\(253\) 13.2747 0.834573
\(254\) 0 0
\(255\) −23.0624 −1.44422
\(256\) 0 0
\(257\) −7.82120 −0.487873 −0.243936 0.969791i \(-0.578439\pi\)
−0.243936 + 0.969791i \(0.578439\pi\)
\(258\) 0 0
\(259\) 1.31833 0.0819173
\(260\) 0 0
\(261\) 3.32252 0.205659
\(262\) 0 0
\(263\) 6.44120 0.397182 0.198591 0.980082i \(-0.436364\pi\)
0.198591 + 0.980082i \(0.436364\pi\)
\(264\) 0 0
\(265\) 34.2906 2.10645
\(266\) 0 0
\(267\) −4.51995 −0.276617
\(268\) 0 0
\(269\) 21.7914 1.32865 0.664323 0.747446i \(-0.268720\pi\)
0.664323 + 0.747446i \(0.268720\pi\)
\(270\) 0 0
\(271\) 10.1627 0.617340 0.308670 0.951169i \(-0.400116\pi\)
0.308670 + 0.951169i \(0.400116\pi\)
\(272\) 0 0
\(273\) 1.07827 0.0652599
\(274\) 0 0
\(275\) −12.7534 −0.769059
\(276\) 0 0
\(277\) 5.38295 0.323430 0.161715 0.986838i \(-0.448297\pi\)
0.161715 + 0.986838i \(0.448297\pi\)
\(278\) 0 0
\(279\) 3.32412 0.199010
\(280\) 0 0
\(281\) −17.2566 −1.02945 −0.514723 0.857357i \(-0.672105\pi\)
−0.514723 + 0.857357i \(0.672105\pi\)
\(282\) 0 0
\(283\) 6.13015 0.364399 0.182200 0.983262i \(-0.441678\pi\)
0.182200 + 0.983262i \(0.441678\pi\)
\(284\) 0 0
\(285\) −9.50909 −0.563270
\(286\) 0 0
\(287\) −12.9002 −0.761475
\(288\) 0 0
\(289\) 34.7048 2.04146
\(290\) 0 0
\(291\) 1.77054 0.103791
\(292\) 0 0
\(293\) 17.6848 1.03316 0.516578 0.856240i \(-0.327206\pi\)
0.516578 + 0.856240i \(0.327206\pi\)
\(294\) 0 0
\(295\) −11.7128 −0.681945
\(296\) 0 0
\(297\) −2.41235 −0.139979
\(298\) 0 0
\(299\) 1.60896 0.0930488
\(300\) 0 0
\(301\) −41.0854 −2.36813
\(302\) 0 0
\(303\) 18.8099 1.08060
\(304\) 0 0
\(305\) −30.4167 −1.74165
\(306\) 0 0
\(307\) −11.1101 −0.634085 −0.317042 0.948411i \(-0.602690\pi\)
−0.317042 + 0.948411i \(0.602690\pi\)
\(308\) 0 0
\(309\) −5.82075 −0.331131
\(310\) 0 0
\(311\) −28.3481 −1.60747 −0.803737 0.594985i \(-0.797158\pi\)
−0.803737 + 0.594985i \(0.797158\pi\)
\(312\) 0 0
\(313\) 31.4209 1.77601 0.888006 0.459831i \(-0.152090\pi\)
0.888006 + 0.459831i \(0.152090\pi\)
\(314\) 0 0
\(315\) 11.8278 0.666423
\(316\) 0 0
\(317\) −7.57882 −0.425669 −0.212834 0.977088i \(-0.568269\pi\)
−0.212834 + 0.977088i \(0.568269\pi\)
\(318\) 0 0
\(319\) −8.01507 −0.448758
\(320\) 0 0
\(321\) −9.11502 −0.508751
\(322\) 0 0
\(323\) 21.3190 1.18622
\(324\) 0 0
\(325\) −1.54578 −0.0857444
\(326\) 0 0
\(327\) −18.8744 −1.04376
\(328\) 0 0
\(329\) −1.49985 −0.0826892
\(330\) 0 0
\(331\) −29.3509 −1.61327 −0.806636 0.591049i \(-0.798714\pi\)
−0.806636 + 0.591049i \(0.798714\pi\)
\(332\) 0 0
\(333\) −0.357486 −0.0195901
\(334\) 0 0
\(335\) 13.4282 0.733661
\(336\) 0 0
\(337\) −24.2626 −1.32167 −0.660833 0.750533i \(-0.729797\pi\)
−0.660833 + 0.750533i \(0.729797\pi\)
\(338\) 0 0
\(339\) 12.5304 0.680559
\(340\) 0 0
\(341\) −8.01892 −0.434249
\(342\) 0 0
\(343\) 1.47578 0.0796844
\(344\) 0 0
\(345\) 17.6491 0.950197
\(346\) 0 0
\(347\) −16.9314 −0.908924 −0.454462 0.890766i \(-0.650169\pi\)
−0.454462 + 0.890766i \(0.650169\pi\)
\(348\) 0 0
\(349\) 2.41024 0.129017 0.0645087 0.997917i \(-0.479452\pi\)
0.0645087 + 0.997917i \(0.479452\pi\)
\(350\) 0 0
\(351\) −0.292389 −0.0156066
\(352\) 0 0
\(353\) −12.2607 −0.652570 −0.326285 0.945271i \(-0.605797\pi\)
−0.326285 + 0.945271i \(0.605797\pi\)
\(354\) 0 0
\(355\) 8.59956 0.456417
\(356\) 0 0
\(357\) −26.5175 −1.40345
\(358\) 0 0
\(359\) −12.1673 −0.642166 −0.321083 0.947051i \(-0.604047\pi\)
−0.321083 + 0.947051i \(0.604047\pi\)
\(360\) 0 0
\(361\) −10.2097 −0.537355
\(362\) 0 0
\(363\) −5.18058 −0.271910
\(364\) 0 0
\(365\) 20.1242 1.05335
\(366\) 0 0
\(367\) −7.82364 −0.408391 −0.204195 0.978930i \(-0.565458\pi\)
−0.204195 + 0.978930i \(0.565458\pi\)
\(368\) 0 0
\(369\) 3.49808 0.182103
\(370\) 0 0
\(371\) 39.4278 2.04699
\(372\) 0 0
\(373\) −18.1180 −0.938114 −0.469057 0.883168i \(-0.655406\pi\)
−0.469057 + 0.883168i \(0.655406\pi\)
\(374\) 0 0
\(375\) −0.919585 −0.0474872
\(376\) 0 0
\(377\) −0.971469 −0.0500332
\(378\) 0 0
\(379\) −0.116915 −0.00600553 −0.00300276 0.999995i \(-0.500956\pi\)
−0.00300276 + 0.999995i \(0.500956\pi\)
\(380\) 0 0
\(381\) 1.13671 0.0582354
\(382\) 0 0
\(383\) 0.723537 0.0369710 0.0184855 0.999829i \(-0.494116\pi\)
0.0184855 + 0.999829i \(0.494116\pi\)
\(384\) 0 0
\(385\) −28.5328 −1.45417
\(386\) 0 0
\(387\) 11.1409 0.566325
\(388\) 0 0
\(389\) −24.8520 −1.26004 −0.630022 0.776577i \(-0.716954\pi\)
−0.630022 + 0.776577i \(0.716954\pi\)
\(390\) 0 0
\(391\) −39.5686 −2.00107
\(392\) 0 0
\(393\) −12.1630 −0.613542
\(394\) 0 0
\(395\) 21.3709 1.07529
\(396\) 0 0
\(397\) 14.6468 0.735102 0.367551 0.930003i \(-0.380196\pi\)
0.367551 + 0.930003i \(0.380196\pi\)
\(398\) 0 0
\(399\) −10.9337 −0.547370
\(400\) 0 0
\(401\) −5.34823 −0.267078 −0.133539 0.991044i \(-0.542634\pi\)
−0.133539 + 0.991044i \(0.542634\pi\)
\(402\) 0 0
\(403\) −0.971935 −0.0484156
\(404\) 0 0
\(405\) −3.20729 −0.159372
\(406\) 0 0
\(407\) 0.862380 0.0427466
\(408\) 0 0
\(409\) 16.7435 0.827913 0.413957 0.910297i \(-0.364146\pi\)
0.413957 + 0.910297i \(0.364146\pi\)
\(410\) 0 0
\(411\) −14.4346 −0.712007
\(412\) 0 0
\(413\) −13.4676 −0.662695
\(414\) 0 0
\(415\) 32.7433 1.60731
\(416\) 0 0
\(417\) 0.433633 0.0212351
\(418\) 0 0
\(419\) −5.99429 −0.292840 −0.146420 0.989222i \(-0.546775\pi\)
−0.146420 + 0.989222i \(0.546775\pi\)
\(420\) 0 0
\(421\) 2.60581 0.126999 0.0634996 0.997982i \(-0.479774\pi\)
0.0634996 + 0.997982i \(0.479774\pi\)
\(422\) 0 0
\(423\) 0.406706 0.0197747
\(424\) 0 0
\(425\) 38.0147 1.84398
\(426\) 0 0
\(427\) −34.9736 −1.69249
\(428\) 0 0
\(429\) 0.705344 0.0340543
\(430\) 0 0
\(431\) −3.60689 −0.173738 −0.0868690 0.996220i \(-0.527686\pi\)
−0.0868690 + 0.996220i \(0.527686\pi\)
\(432\) 0 0
\(433\) 11.1030 0.533576 0.266788 0.963755i \(-0.414038\pi\)
0.266788 + 0.963755i \(0.414038\pi\)
\(434\) 0 0
\(435\) −10.6563 −0.510930
\(436\) 0 0
\(437\) −16.3149 −0.780450
\(438\) 0 0
\(439\) 37.7654 1.80245 0.901223 0.433356i \(-0.142671\pi\)
0.901223 + 0.433356i \(0.142671\pi\)
\(440\) 0 0
\(441\) 6.59982 0.314277
\(442\) 0 0
\(443\) 21.3294 1.01339 0.506695 0.862125i \(-0.330867\pi\)
0.506695 + 0.862125i \(0.330867\pi\)
\(444\) 0 0
\(445\) 14.4968 0.687215
\(446\) 0 0
\(447\) −19.0992 −0.903359
\(448\) 0 0
\(449\) 28.7910 1.35873 0.679365 0.733800i \(-0.262255\pi\)
0.679365 + 0.733800i \(0.262255\pi\)
\(450\) 0 0
\(451\) −8.43859 −0.397358
\(452\) 0 0
\(453\) −8.70546 −0.409018
\(454\) 0 0
\(455\) −3.45833 −0.162129
\(456\) 0 0
\(457\) 18.7766 0.878332 0.439166 0.898406i \(-0.355274\pi\)
0.439166 + 0.898406i \(0.355274\pi\)
\(458\) 0 0
\(459\) 7.19061 0.335629
\(460\) 0 0
\(461\) −12.0426 −0.560878 −0.280439 0.959872i \(-0.590480\pi\)
−0.280439 + 0.959872i \(0.590480\pi\)
\(462\) 0 0
\(463\) −21.0030 −0.976094 −0.488047 0.872817i \(-0.662291\pi\)
−0.488047 + 0.872817i \(0.662291\pi\)
\(464\) 0 0
\(465\) −10.6614 −0.494411
\(466\) 0 0
\(467\) 36.3609 1.68258 0.841291 0.540582i \(-0.181796\pi\)
0.841291 + 0.540582i \(0.181796\pi\)
\(468\) 0 0
\(469\) 15.4400 0.712951
\(470\) 0 0
\(471\) 22.6106 1.04184
\(472\) 0 0
\(473\) −26.8758 −1.23575
\(474\) 0 0
\(475\) 15.6743 0.719184
\(476\) 0 0
\(477\) −10.6914 −0.489528
\(478\) 0 0
\(479\) −10.2203 −0.466976 −0.233488 0.972360i \(-0.575014\pi\)
−0.233488 + 0.972360i \(0.575014\pi\)
\(480\) 0 0
\(481\) 0.104525 0.00476593
\(482\) 0 0
\(483\) 20.2932 0.923375
\(484\) 0 0
\(485\) −5.67862 −0.257853
\(486\) 0 0
\(487\) 27.8144 1.26039 0.630195 0.776437i \(-0.282975\pi\)
0.630195 + 0.776437i \(0.282975\pi\)
\(488\) 0 0
\(489\) 9.50323 0.429751
\(490\) 0 0
\(491\) −6.01324 −0.271374 −0.135687 0.990752i \(-0.543324\pi\)
−0.135687 + 0.990752i \(0.543324\pi\)
\(492\) 0 0
\(493\) 23.8909 1.07599
\(494\) 0 0
\(495\) 7.73710 0.347757
\(496\) 0 0
\(497\) 9.88791 0.443533
\(498\) 0 0
\(499\) −6.63868 −0.297188 −0.148594 0.988898i \(-0.547475\pi\)
−0.148594 + 0.988898i \(0.547475\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −42.5316 −1.89639 −0.948195 0.317689i \(-0.897093\pi\)
−0.948195 + 0.317689i \(0.897093\pi\)
\(504\) 0 0
\(505\) −60.3287 −2.68459
\(506\) 0 0
\(507\) −12.9145 −0.573553
\(508\) 0 0
\(509\) −35.1257 −1.55692 −0.778461 0.627693i \(-0.783999\pi\)
−0.778461 + 0.627693i \(0.783999\pi\)
\(510\) 0 0
\(511\) 23.1391 1.02362
\(512\) 0 0
\(513\) 2.96484 0.130901
\(514\) 0 0
\(515\) 18.6689 0.822648
\(516\) 0 0
\(517\) −0.981115 −0.0431494
\(518\) 0 0
\(519\) 3.88163 0.170385
\(520\) 0 0
\(521\) −37.8196 −1.65691 −0.828454 0.560057i \(-0.810779\pi\)
−0.828454 + 0.560057i \(0.810779\pi\)
\(522\) 0 0
\(523\) 2.84372 0.124347 0.0621737 0.998065i \(-0.480197\pi\)
0.0621737 + 0.998065i \(0.480197\pi\)
\(524\) 0 0
\(525\) −19.4963 −0.850889
\(526\) 0 0
\(527\) 23.9024 1.04121
\(528\) 0 0
\(529\) 7.28097 0.316564
\(530\) 0 0
\(531\) 3.65193 0.158480
\(532\) 0 0
\(533\) −1.02280 −0.0443025
\(534\) 0 0
\(535\) 29.2345 1.26392
\(536\) 0 0
\(537\) 7.65909 0.330514
\(538\) 0 0
\(539\) −15.9211 −0.685769
\(540\) 0 0
\(541\) 37.0033 1.59090 0.795448 0.606022i \(-0.207236\pi\)
0.795448 + 0.606022i \(0.207236\pi\)
\(542\) 0 0
\(543\) 9.78926 0.420097
\(544\) 0 0
\(545\) 60.5358 2.59307
\(546\) 0 0
\(547\) 33.2638 1.42226 0.711128 0.703063i \(-0.248185\pi\)
0.711128 + 0.703063i \(0.248185\pi\)
\(548\) 0 0
\(549\) 9.48361 0.404750
\(550\) 0 0
\(551\) 9.85072 0.419655
\(552\) 0 0
\(553\) 24.5726 1.04493
\(554\) 0 0
\(555\) 1.14656 0.0486688
\(556\) 0 0
\(557\) −38.8570 −1.64642 −0.823212 0.567734i \(-0.807820\pi\)
−0.823212 + 0.567734i \(0.807820\pi\)
\(558\) 0 0
\(559\) −3.25749 −0.137777
\(560\) 0 0
\(561\) −17.3462 −0.732359
\(562\) 0 0
\(563\) −15.4700 −0.651984 −0.325992 0.945373i \(-0.605698\pi\)
−0.325992 + 0.945373i \(0.605698\pi\)
\(564\) 0 0
\(565\) −40.1887 −1.69075
\(566\) 0 0
\(567\) −3.68779 −0.154873
\(568\) 0 0
\(569\) −21.7094 −0.910107 −0.455053 0.890464i \(-0.650380\pi\)
−0.455053 + 0.890464i \(0.650380\pi\)
\(570\) 0 0
\(571\) −22.9576 −0.960745 −0.480372 0.877065i \(-0.659498\pi\)
−0.480372 + 0.877065i \(0.659498\pi\)
\(572\) 0 0
\(573\) −14.9580 −0.624880
\(574\) 0 0
\(575\) −29.0918 −1.21321
\(576\) 0 0
\(577\) −23.8858 −0.994381 −0.497190 0.867641i \(-0.665635\pi\)
−0.497190 + 0.867641i \(0.665635\pi\)
\(578\) 0 0
\(579\) −0.569004 −0.0236470
\(580\) 0 0
\(581\) 37.6488 1.56193
\(582\) 0 0
\(583\) 25.7915 1.06817
\(584\) 0 0
\(585\) 0.937777 0.0387723
\(586\) 0 0
\(587\) 18.2904 0.754926 0.377463 0.926025i \(-0.376797\pi\)
0.377463 + 0.926025i \(0.376797\pi\)
\(588\) 0 0
\(589\) 9.85546 0.406087
\(590\) 0 0
\(591\) 24.1326 0.992682
\(592\) 0 0
\(593\) −33.7008 −1.38393 −0.691964 0.721932i \(-0.743254\pi\)
−0.691964 + 0.721932i \(0.743254\pi\)
\(594\) 0 0
\(595\) 85.0493 3.48668
\(596\) 0 0
\(597\) −10.6151 −0.434446
\(598\) 0 0
\(599\) 22.1340 0.904372 0.452186 0.891924i \(-0.350644\pi\)
0.452186 + 0.891924i \(0.350644\pi\)
\(600\) 0 0
\(601\) 6.70740 0.273601 0.136800 0.990599i \(-0.456318\pi\)
0.136800 + 0.990599i \(0.456318\pi\)
\(602\) 0 0
\(603\) −4.18677 −0.170499
\(604\) 0 0
\(605\) 16.6156 0.675521
\(606\) 0 0
\(607\) −30.2730 −1.22874 −0.614371 0.789017i \(-0.710590\pi\)
−0.614371 + 0.789017i \(0.710590\pi\)
\(608\) 0 0
\(609\) −12.2528 −0.496507
\(610\) 0 0
\(611\) −0.118916 −0.00481084
\(612\) 0 0
\(613\) 2.52415 0.101949 0.0509747 0.998700i \(-0.483767\pi\)
0.0509747 + 0.998700i \(0.483767\pi\)
\(614\) 0 0
\(615\) −11.2194 −0.452409
\(616\) 0 0
\(617\) 12.6084 0.507593 0.253797 0.967258i \(-0.418321\pi\)
0.253797 + 0.967258i \(0.418321\pi\)
\(618\) 0 0
\(619\) 3.97122 0.159617 0.0798085 0.996810i \(-0.474569\pi\)
0.0798085 + 0.996810i \(0.474569\pi\)
\(620\) 0 0
\(621\) −5.50281 −0.220820
\(622\) 0 0
\(623\) 16.6687 0.667816
\(624\) 0 0
\(625\) −23.4842 −0.939368
\(626\) 0 0
\(627\) −7.15222 −0.285632
\(628\) 0 0
\(629\) −2.57054 −0.102494
\(630\) 0 0
\(631\) 48.8417 1.94436 0.972179 0.234238i \(-0.0752594\pi\)
0.972179 + 0.234238i \(0.0752594\pi\)
\(632\) 0 0
\(633\) −14.9203 −0.593030
\(634\) 0 0
\(635\) −3.64576 −0.144677
\(636\) 0 0
\(637\) −1.92972 −0.0764582
\(638\) 0 0
\(639\) −2.68125 −0.106069
\(640\) 0 0
\(641\) −11.7538 −0.464246 −0.232123 0.972686i \(-0.574567\pi\)
−0.232123 + 0.972686i \(0.574567\pi\)
\(642\) 0 0
\(643\) 18.9663 0.747958 0.373979 0.927437i \(-0.377993\pi\)
0.373979 + 0.927437i \(0.377993\pi\)
\(644\) 0 0
\(645\) −35.7322 −1.40695
\(646\) 0 0
\(647\) −37.2745 −1.46541 −0.732705 0.680546i \(-0.761743\pi\)
−0.732705 + 0.680546i \(0.761743\pi\)
\(648\) 0 0
\(649\) −8.80972 −0.345812
\(650\) 0 0
\(651\) −12.2587 −0.480454
\(652\) 0 0
\(653\) −9.70587 −0.379820 −0.189910 0.981802i \(-0.560820\pi\)
−0.189910 + 0.981802i \(0.560820\pi\)
\(654\) 0 0
\(655\) 39.0103 1.52426
\(656\) 0 0
\(657\) −6.27452 −0.244792
\(658\) 0 0
\(659\) −21.9798 −0.856211 −0.428105 0.903729i \(-0.640819\pi\)
−0.428105 + 0.903729i \(0.640819\pi\)
\(660\) 0 0
\(661\) −24.2779 −0.944300 −0.472150 0.881518i \(-0.656522\pi\)
−0.472150 + 0.881518i \(0.656522\pi\)
\(662\) 0 0
\(663\) −2.10246 −0.0816526
\(664\) 0 0
\(665\) 35.0676 1.35986
\(666\) 0 0
\(667\) −18.2832 −0.707928
\(668\) 0 0
\(669\) 14.5962 0.564320
\(670\) 0 0
\(671\) −22.8778 −0.883186
\(672\) 0 0
\(673\) 27.1769 1.04759 0.523795 0.851844i \(-0.324516\pi\)
0.523795 + 0.851844i \(0.324516\pi\)
\(674\) 0 0
\(675\) 5.28672 0.203486
\(676\) 0 0
\(677\) 31.2103 1.19951 0.599755 0.800184i \(-0.295265\pi\)
0.599755 + 0.800184i \(0.295265\pi\)
\(678\) 0 0
\(679\) −6.52937 −0.250574
\(680\) 0 0
\(681\) −7.67692 −0.294180
\(682\) 0 0
\(683\) −8.68394 −0.332282 −0.166141 0.986102i \(-0.553131\pi\)
−0.166141 + 0.986102i \(0.553131\pi\)
\(684\) 0 0
\(685\) 46.2960 1.76888
\(686\) 0 0
\(687\) −7.74042 −0.295316
\(688\) 0 0
\(689\) 3.12606 0.119094
\(690\) 0 0
\(691\) 10.3984 0.395573 0.197787 0.980245i \(-0.436625\pi\)
0.197787 + 0.980245i \(0.436625\pi\)
\(692\) 0 0
\(693\) 8.89624 0.337940
\(694\) 0 0
\(695\) −1.39079 −0.0527556
\(696\) 0 0
\(697\) 25.1533 0.952751
\(698\) 0 0
\(699\) −15.6688 −0.592650
\(700\) 0 0
\(701\) 33.3918 1.26119 0.630596 0.776111i \(-0.282811\pi\)
0.630596 + 0.776111i \(0.282811\pi\)
\(702\) 0 0
\(703\) −1.05989 −0.0399744
\(704\) 0 0
\(705\) −1.30442 −0.0491274
\(706\) 0 0
\(707\) −69.3669 −2.60881
\(708\) 0 0
\(709\) −5.92848 −0.222649 −0.111324 0.993784i \(-0.535509\pi\)
−0.111324 + 0.993784i \(0.535509\pi\)
\(710\) 0 0
\(711\) −6.66323 −0.249891
\(712\) 0 0
\(713\) −18.2920 −0.685040
\(714\) 0 0
\(715\) −2.26224 −0.0846032
\(716\) 0 0
\(717\) −20.3027 −0.758218
\(718\) 0 0
\(719\) 4.67728 0.174433 0.0872166 0.996189i \(-0.472203\pi\)
0.0872166 + 0.996189i \(0.472203\pi\)
\(720\) 0 0
\(721\) 21.4657 0.799426
\(722\) 0 0
\(723\) 7.43764 0.276609
\(724\) 0 0
\(725\) 17.5652 0.652356
\(726\) 0 0
\(727\) −27.8553 −1.03310 −0.516548 0.856258i \(-0.672783\pi\)
−0.516548 + 0.856258i \(0.672783\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 80.1101 2.96298
\(732\) 0 0
\(733\) −23.6613 −0.873949 −0.436974 0.899474i \(-0.643950\pi\)
−0.436974 + 0.899474i \(0.643950\pi\)
\(734\) 0 0
\(735\) −21.1675 −0.780777
\(736\) 0 0
\(737\) 10.0999 0.372036
\(738\) 0 0
\(739\) −2.47093 −0.0908945 −0.0454473 0.998967i \(-0.514471\pi\)
−0.0454473 + 0.998967i \(0.514471\pi\)
\(740\) 0 0
\(741\) −0.866886 −0.0318459
\(742\) 0 0
\(743\) −18.8973 −0.693276 −0.346638 0.937999i \(-0.612677\pi\)
−0.346638 + 0.937999i \(0.612677\pi\)
\(744\) 0 0
\(745\) 61.2565 2.24427
\(746\) 0 0
\(747\) −10.2090 −0.373529
\(748\) 0 0
\(749\) 33.6143 1.22824
\(750\) 0 0
\(751\) −39.2273 −1.43142 −0.715712 0.698396i \(-0.753898\pi\)
−0.715712 + 0.698396i \(0.753898\pi\)
\(752\) 0 0
\(753\) −28.3028 −1.03141
\(754\) 0 0
\(755\) 27.9210 1.01615
\(756\) 0 0
\(757\) 34.1963 1.24288 0.621442 0.783460i \(-0.286547\pi\)
0.621442 + 0.783460i \(0.286547\pi\)
\(758\) 0 0
\(759\) 13.2747 0.481841
\(760\) 0 0
\(761\) −11.0455 −0.400398 −0.200199 0.979755i \(-0.564159\pi\)
−0.200199 + 0.979755i \(0.564159\pi\)
\(762\) 0 0
\(763\) 69.6051 2.51987
\(764\) 0 0
\(765\) −23.0624 −0.833822
\(766\) 0 0
\(767\) −1.06778 −0.0385555
\(768\) 0 0
\(769\) 8.17138 0.294668 0.147334 0.989087i \(-0.452931\pi\)
0.147334 + 0.989087i \(0.452931\pi\)
\(770\) 0 0
\(771\) −7.82120 −0.281673
\(772\) 0 0
\(773\) −47.9579 −1.72493 −0.862463 0.506120i \(-0.831079\pi\)
−0.862463 + 0.506120i \(0.831079\pi\)
\(774\) 0 0
\(775\) 17.5737 0.631264
\(776\) 0 0
\(777\) 1.31833 0.0472950
\(778\) 0 0
\(779\) 10.3712 0.371588
\(780\) 0 0
\(781\) 6.46812 0.231447
\(782\) 0 0
\(783\) 3.32252 0.118737
\(784\) 0 0
\(785\) −72.5187 −2.58830
\(786\) 0 0
\(787\) −53.9997 −1.92488 −0.962440 0.271495i \(-0.912482\pi\)
−0.962440 + 0.271495i \(0.912482\pi\)
\(788\) 0 0
\(789\) 6.44120 0.229313
\(790\) 0 0
\(791\) −46.2096 −1.64302
\(792\) 0 0
\(793\) −2.77290 −0.0984687
\(794\) 0 0
\(795\) 34.2906 1.21616
\(796\) 0 0
\(797\) 5.87813 0.208214 0.104107 0.994566i \(-0.466802\pi\)
0.104107 + 0.994566i \(0.466802\pi\)
\(798\) 0 0
\(799\) 2.92446 0.103460
\(800\) 0 0
\(801\) −4.51995 −0.159705
\(802\) 0 0
\(803\) 15.1363 0.534149
\(804\) 0 0
\(805\) −65.0863 −2.29399
\(806\) 0 0
\(807\) 21.7914 0.767094
\(808\) 0 0
\(809\) −3.91670 −0.137704 −0.0688519 0.997627i \(-0.521934\pi\)
−0.0688519 + 0.997627i \(0.521934\pi\)
\(810\) 0 0
\(811\) −13.4761 −0.473211 −0.236605 0.971606i \(-0.576035\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(812\) 0 0
\(813\) 10.1627 0.356421
\(814\) 0 0
\(815\) −30.4796 −1.06765
\(816\) 0 0
\(817\) 33.0310 1.15561
\(818\) 0 0
\(819\) 1.07827 0.0376778
\(820\) 0 0
\(821\) 22.0639 0.770035 0.385018 0.922909i \(-0.374195\pi\)
0.385018 + 0.922909i \(0.374195\pi\)
\(822\) 0 0
\(823\) 12.8677 0.448540 0.224270 0.974527i \(-0.428000\pi\)
0.224270 + 0.974527i \(0.428000\pi\)
\(824\) 0 0
\(825\) −12.7534 −0.444016
\(826\) 0 0
\(827\) 23.6784 0.823380 0.411690 0.911324i \(-0.364939\pi\)
0.411690 + 0.911324i \(0.364939\pi\)
\(828\) 0 0
\(829\) 32.1173 1.11548 0.557741 0.830015i \(-0.311668\pi\)
0.557741 + 0.830015i \(0.311668\pi\)
\(830\) 0 0
\(831\) 5.38295 0.186732
\(832\) 0 0
\(833\) 47.4567 1.64428
\(834\) 0 0
\(835\) −3.20729 −0.110993
\(836\) 0 0
\(837\) 3.32412 0.114898
\(838\) 0 0
\(839\) −4.63931 −0.160167 −0.0800835 0.996788i \(-0.525519\pi\)
−0.0800835 + 0.996788i \(0.525519\pi\)
\(840\) 0 0
\(841\) −17.9609 −0.619340
\(842\) 0 0
\(843\) −17.2566 −0.594351
\(844\) 0 0
\(845\) 41.4206 1.42491
\(846\) 0 0
\(847\) 19.1049 0.656452
\(848\) 0 0
\(849\) 6.13015 0.210386
\(850\) 0 0
\(851\) 1.96718 0.0674340
\(852\) 0 0
\(853\) −4.45984 −0.152702 −0.0763510 0.997081i \(-0.524327\pi\)
−0.0763510 + 0.997081i \(0.524327\pi\)
\(854\) 0 0
\(855\) −9.50909 −0.325204
\(856\) 0 0
\(857\) 48.4705 1.65572 0.827860 0.560935i \(-0.189558\pi\)
0.827860 + 0.560935i \(0.189558\pi\)
\(858\) 0 0
\(859\) 11.3642 0.387741 0.193871 0.981027i \(-0.437896\pi\)
0.193871 + 0.981027i \(0.437896\pi\)
\(860\) 0 0
\(861\) −12.9002 −0.439638
\(862\) 0 0
\(863\) −31.2403 −1.06343 −0.531717 0.846922i \(-0.678453\pi\)
−0.531717 + 0.846922i \(0.678453\pi\)
\(864\) 0 0
\(865\) −12.4495 −0.423296
\(866\) 0 0
\(867\) 34.7048 1.17864
\(868\) 0 0
\(869\) 16.0740 0.545274
\(870\) 0 0
\(871\) 1.22417 0.0414793
\(872\) 0 0
\(873\) 1.77054 0.0599236
\(874\) 0 0
\(875\) 3.39124 0.114645
\(876\) 0 0
\(877\) −3.45334 −0.116611 −0.0583055 0.998299i \(-0.518570\pi\)
−0.0583055 + 0.998299i \(0.518570\pi\)
\(878\) 0 0
\(879\) 17.6848 0.596493
\(880\) 0 0
\(881\) −18.0397 −0.607772 −0.303886 0.952708i \(-0.598284\pi\)
−0.303886 + 0.952708i \(0.598284\pi\)
\(882\) 0 0
\(883\) 19.7645 0.665129 0.332565 0.943081i \(-0.392086\pi\)
0.332565 + 0.943081i \(0.392086\pi\)
\(884\) 0 0
\(885\) −11.7128 −0.393721
\(886\) 0 0
\(887\) −14.0636 −0.472209 −0.236105 0.971728i \(-0.575871\pi\)
−0.236105 + 0.971728i \(0.575871\pi\)
\(888\) 0 0
\(889\) −4.19195 −0.140593
\(890\) 0 0
\(891\) −2.41235 −0.0808167
\(892\) 0 0
\(893\) 1.20582 0.0403511
\(894\) 0 0
\(895\) −24.5649 −0.821115
\(896\) 0 0
\(897\) 1.60896 0.0537217
\(898\) 0 0
\(899\) 11.0444 0.368353
\(900\) 0 0
\(901\) −76.8780 −2.56118
\(902\) 0 0
\(903\) −41.0854 −1.36724
\(904\) 0 0
\(905\) −31.3970 −1.04367
\(906\) 0 0
\(907\) 13.8587 0.460170 0.230085 0.973171i \(-0.426100\pi\)
0.230085 + 0.973171i \(0.426100\pi\)
\(908\) 0 0
\(909\) 18.8099 0.623884
\(910\) 0 0
\(911\) 37.7036 1.24918 0.624588 0.780954i \(-0.285267\pi\)
0.624588 + 0.780954i \(0.285267\pi\)
\(912\) 0 0
\(913\) 24.6277 0.815058
\(914\) 0 0
\(915\) −30.4167 −1.00554
\(916\) 0 0
\(917\) 44.8546 1.48123
\(918\) 0 0
\(919\) 24.6184 0.812086 0.406043 0.913854i \(-0.366908\pi\)
0.406043 + 0.913854i \(0.366908\pi\)
\(920\) 0 0
\(921\) −11.1101 −0.366089
\(922\) 0 0
\(923\) 0.783970 0.0258047
\(924\) 0 0
\(925\) −1.88993 −0.0621404
\(926\) 0 0
\(927\) −5.82075 −0.191179
\(928\) 0 0
\(929\) 28.1432 0.923349 0.461675 0.887049i \(-0.347249\pi\)
0.461675 + 0.887049i \(0.347249\pi\)
\(930\) 0 0
\(931\) 19.5674 0.641295
\(932\) 0 0
\(933\) −28.3481 −0.928076
\(934\) 0 0
\(935\) 55.6345 1.81944
\(936\) 0 0
\(937\) 14.4087 0.470713 0.235357 0.971909i \(-0.424374\pi\)
0.235357 + 0.971909i \(0.424374\pi\)
\(938\) 0 0
\(939\) 31.4209 1.02538
\(940\) 0 0
\(941\) 31.8231 1.03740 0.518702 0.854955i \(-0.326415\pi\)
0.518702 + 0.854955i \(0.326415\pi\)
\(942\) 0 0
\(943\) −19.2493 −0.626844
\(944\) 0 0
\(945\) 11.8278 0.384759
\(946\) 0 0
\(947\) −7.53847 −0.244967 −0.122484 0.992471i \(-0.539086\pi\)
−0.122484 + 0.992471i \(0.539086\pi\)
\(948\) 0 0
\(949\) 1.83460 0.0595537
\(950\) 0 0
\(951\) −7.57882 −0.245760
\(952\) 0 0
\(953\) 9.31282 0.301672 0.150836 0.988559i \(-0.451803\pi\)
0.150836 + 0.988559i \(0.451803\pi\)
\(954\) 0 0
\(955\) 47.9747 1.55242
\(956\) 0 0
\(957\) −8.01507 −0.259090
\(958\) 0 0
\(959\) 53.2319 1.71895
\(960\) 0 0
\(961\) −19.9503 −0.643557
\(962\) 0 0
\(963\) −9.11502 −0.293727
\(964\) 0 0
\(965\) 1.82496 0.0587476
\(966\) 0 0
\(967\) −8.56361 −0.275387 −0.137693 0.990475i \(-0.543969\pi\)
−0.137693 + 0.990475i \(0.543969\pi\)
\(968\) 0 0
\(969\) 21.3190 0.684864
\(970\) 0 0
\(971\) 17.1699 0.551010 0.275505 0.961300i \(-0.411155\pi\)
0.275505 + 0.961300i \(0.411155\pi\)
\(972\) 0 0
\(973\) −1.59915 −0.0512664
\(974\) 0 0
\(975\) −1.54578 −0.0495045
\(976\) 0 0
\(977\) 16.8510 0.539112 0.269556 0.962985i \(-0.413123\pi\)
0.269556 + 0.962985i \(0.413123\pi\)
\(978\) 0 0
\(979\) 10.9037 0.348484
\(980\) 0 0
\(981\) −18.8744 −0.602615
\(982\) 0 0
\(983\) −23.9668 −0.764424 −0.382212 0.924075i \(-0.624838\pi\)
−0.382212 + 0.924075i \(0.624838\pi\)
\(984\) 0 0
\(985\) −77.4002 −2.46618
\(986\) 0 0
\(987\) −1.49985 −0.0477406
\(988\) 0 0
\(989\) −61.3065 −1.94943
\(990\) 0 0
\(991\) 17.7821 0.564867 0.282434 0.959287i \(-0.408858\pi\)
0.282434 + 0.959287i \(0.408858\pi\)
\(992\) 0 0
\(993\) −29.3509 −0.931423
\(994\) 0 0
\(995\) 34.0456 1.07932
\(996\) 0 0
\(997\) −34.0948 −1.07979 −0.539896 0.841732i \(-0.681536\pi\)
−0.539896 + 0.841732i \(0.681536\pi\)
\(998\) 0 0
\(999\) −0.357486 −0.0113104
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.w.1.1 7
4.3 odd 2 4008.2.a.g.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.g.1.1 7 4.3 odd 2
8016.2.a.w.1.1 7 1.1 even 1 trivial