Properties

Label 8016.2.a.be.1.7
Level 8016
Weight 2
Character 8016.1
Self dual yes
Analytic conductor 64.008
Analytic rank 0
Dimension 11
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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.60189\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +2.60189 q^{5} +3.58131 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +2.60189 q^{5} +3.58131 q^{7} +1.00000 q^{9} +4.72536 q^{11} -0.942538 q^{13} +2.60189 q^{15} -3.64824 q^{17} +2.69214 q^{19} +3.58131 q^{21} +0.381441 q^{23} +1.76983 q^{25} +1.00000 q^{27} +4.31070 q^{29} -0.400729 q^{31} +4.72536 q^{33} +9.31818 q^{35} +0.407293 q^{37} -0.942538 q^{39} +0.759495 q^{41} -4.47426 q^{43} +2.60189 q^{45} -13.2113 q^{47} +5.82578 q^{49} -3.64824 q^{51} +4.41253 q^{53} +12.2949 q^{55} +2.69214 q^{57} +5.47954 q^{59} +10.9868 q^{61} +3.58131 q^{63} -2.45238 q^{65} -4.38579 q^{67} +0.381441 q^{69} +1.17148 q^{71} +12.3989 q^{73} +1.76983 q^{75} +16.9230 q^{77} -8.57361 q^{79} +1.00000 q^{81} -0.551394 q^{83} -9.49231 q^{85} +4.31070 q^{87} +0.764327 q^{89} -3.37552 q^{91} -0.400729 q^{93} +7.00466 q^{95} -4.11552 q^{97} +4.72536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + O(q^{10}) \) \( 11q + 11q^{3} + 10q^{5} + q^{7} + 11q^{9} + q^{11} + 10q^{13} + 10q^{15} + 17q^{17} - 2q^{19} + q^{21} + 3q^{23} + 21q^{25} + 11q^{27} + 17q^{29} + 15q^{31} + q^{33} - 11q^{35} + 4q^{37} + 10q^{39} + 16q^{41} - 10q^{43} + 10q^{45} + 16q^{47} + 22q^{49} + 17q^{51} + 42q^{53} + 5q^{55} - 2q^{57} + 2q^{59} + 12q^{61} + q^{63} + 10q^{65} + q^{67} + 3q^{69} + 9q^{71} + 24q^{73} + 21q^{75} + 22q^{77} + 30q^{79} + 11q^{81} - 16q^{83} + 25q^{85} + 17q^{87} + 37q^{89} - q^{91} + 15q^{93} - 5q^{95} + 4q^{97} + q^{99} + O(q^{100}) \)

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
\(5\) 2.60189 1.16360 0.581800 0.813332i \(-0.302348\pi\)
0.581800 + 0.813332i \(0.302348\pi\)
\(6\) 0 0
\(7\) 3.58131 1.35361 0.676804 0.736163i \(-0.263364\pi\)
0.676804 + 0.736163i \(0.263364\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.72536 1.42475 0.712375 0.701799i \(-0.247619\pi\)
0.712375 + 0.701799i \(0.247619\pi\)
\(12\) 0 0
\(13\) −0.942538 −0.261413 −0.130707 0.991421i \(-0.541725\pi\)
−0.130707 + 0.991421i \(0.541725\pi\)
\(14\) 0 0
\(15\) 2.60189 0.671805
\(16\) 0 0
\(17\) −3.64824 −0.884827 −0.442414 0.896811i \(-0.645878\pi\)
−0.442414 + 0.896811i \(0.645878\pi\)
\(18\) 0 0
\(19\) 2.69214 0.617620 0.308810 0.951124i \(-0.400069\pi\)
0.308810 + 0.951124i \(0.400069\pi\)
\(20\) 0 0
\(21\) 3.58131 0.781506
\(22\) 0 0
\(23\) 0.381441 0.0795360 0.0397680 0.999209i \(-0.487338\pi\)
0.0397680 + 0.999209i \(0.487338\pi\)
\(24\) 0 0
\(25\) 1.76983 0.353967
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.31070 0.800477 0.400239 0.916411i \(-0.368927\pi\)
0.400239 + 0.916411i \(0.368927\pi\)
\(30\) 0 0
\(31\) −0.400729 −0.0719731 −0.0359865 0.999352i \(-0.511457\pi\)
−0.0359865 + 0.999352i \(0.511457\pi\)
\(32\) 0 0
\(33\) 4.72536 0.822580
\(34\) 0 0
\(35\) 9.31818 1.57506
\(36\) 0 0
\(37\) 0.407293 0.0669585 0.0334792 0.999439i \(-0.489341\pi\)
0.0334792 + 0.999439i \(0.489341\pi\)
\(38\) 0 0
\(39\) −0.942538 −0.150927
\(40\) 0 0
\(41\) 0.759495 0.118613 0.0593066 0.998240i \(-0.481111\pi\)
0.0593066 + 0.998240i \(0.481111\pi\)
\(42\) 0 0
\(43\) −4.47426 −0.682319 −0.341159 0.940005i \(-0.610820\pi\)
−0.341159 + 0.940005i \(0.610820\pi\)
\(44\) 0 0
\(45\) 2.60189 0.387867
\(46\) 0 0
\(47\) −13.2113 −1.92707 −0.963534 0.267587i \(-0.913774\pi\)
−0.963534 + 0.267587i \(0.913774\pi\)
\(48\) 0 0
\(49\) 5.82578 0.832255
\(50\) 0 0
\(51\) −3.64824 −0.510855
\(52\) 0 0
\(53\) 4.41253 0.606108 0.303054 0.952973i \(-0.401994\pi\)
0.303054 + 0.952973i \(0.401994\pi\)
\(54\) 0 0
\(55\) 12.2949 1.65784
\(56\) 0 0
\(57\) 2.69214 0.356583
\(58\) 0 0
\(59\) 5.47954 0.713375 0.356687 0.934224i \(-0.383906\pi\)
0.356687 + 0.934224i \(0.383906\pi\)
\(60\) 0 0
\(61\) 10.9868 1.40671 0.703356 0.710838i \(-0.251684\pi\)
0.703356 + 0.710838i \(0.251684\pi\)
\(62\) 0 0
\(63\) 3.58131 0.451203
\(64\) 0 0
\(65\) −2.45238 −0.304180
\(66\) 0 0
\(67\) −4.38579 −0.535809 −0.267905 0.963445i \(-0.586331\pi\)
−0.267905 + 0.963445i \(0.586331\pi\)
\(68\) 0 0
\(69\) 0.381441 0.0459201
\(70\) 0 0
\(71\) 1.17148 0.139029 0.0695143 0.997581i \(-0.477855\pi\)
0.0695143 + 0.997581i \(0.477855\pi\)
\(72\) 0 0
\(73\) 12.3989 1.45118 0.725592 0.688125i \(-0.241566\pi\)
0.725592 + 0.688125i \(0.241566\pi\)
\(74\) 0 0
\(75\) 1.76983 0.204363
\(76\) 0 0
\(77\) 16.9230 1.92855
\(78\) 0 0
\(79\) −8.57361 −0.964607 −0.482303 0.876004i \(-0.660200\pi\)
−0.482303 + 0.876004i \(0.660200\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −0.551394 −0.0605233 −0.0302617 0.999542i \(-0.509634\pi\)
−0.0302617 + 0.999542i \(0.509634\pi\)
\(84\) 0 0
\(85\) −9.49231 −1.02959
\(86\) 0 0
\(87\) 4.31070 0.462156
\(88\) 0 0
\(89\) 0.764327 0.0810185 0.0405092 0.999179i \(-0.487102\pi\)
0.0405092 + 0.999179i \(0.487102\pi\)
\(90\) 0 0
\(91\) −3.37552 −0.353851
\(92\) 0 0
\(93\) −0.400729 −0.0415537
\(94\) 0 0
\(95\) 7.00466 0.718663
\(96\) 0 0
\(97\) −4.11552 −0.417868 −0.208934 0.977930i \(-0.566999\pi\)
−0.208934 + 0.977930i \(0.566999\pi\)
\(98\) 0 0
\(99\) 4.72536 0.474917
\(100\) 0 0
\(101\) 4.37168 0.434999 0.217499 0.976060i \(-0.430210\pi\)
0.217499 + 0.976060i \(0.430210\pi\)
\(102\) 0 0
\(103\) −10.2673 −1.01167 −0.505833 0.862632i \(-0.668815\pi\)
−0.505833 + 0.862632i \(0.668815\pi\)
\(104\) 0 0
\(105\) 9.31818 0.909361
\(106\) 0 0
\(107\) −3.33602 −0.322505 −0.161252 0.986913i \(-0.551553\pi\)
−0.161252 + 0.986913i \(0.551553\pi\)
\(108\) 0 0
\(109\) 6.99888 0.670371 0.335185 0.942152i \(-0.391201\pi\)
0.335185 + 0.942152i \(0.391201\pi\)
\(110\) 0 0
\(111\) 0.407293 0.0386585
\(112\) 0 0
\(113\) −11.1190 −1.04599 −0.522994 0.852336i \(-0.675185\pi\)
−0.522994 + 0.852336i \(0.675185\pi\)
\(114\) 0 0
\(115\) 0.992468 0.0925481
\(116\) 0 0
\(117\) −0.942538 −0.0871377
\(118\) 0 0
\(119\) −13.0655 −1.19771
\(120\) 0 0
\(121\) 11.3290 1.02991
\(122\) 0 0
\(123\) 0.759495 0.0684813
\(124\) 0 0
\(125\) −8.40454 −0.751725
\(126\) 0 0
\(127\) 6.13214 0.544139 0.272070 0.962278i \(-0.412292\pi\)
0.272070 + 0.962278i \(0.412292\pi\)
\(128\) 0 0
\(129\) −4.47426 −0.393937
\(130\) 0 0
\(131\) 12.0777 1.05524 0.527619 0.849481i \(-0.323085\pi\)
0.527619 + 0.849481i \(0.323085\pi\)
\(132\) 0 0
\(133\) 9.64140 0.836016
\(134\) 0 0
\(135\) 2.60189 0.223935
\(136\) 0 0
\(137\) 1.52242 0.130069 0.0650345 0.997883i \(-0.479284\pi\)
0.0650345 + 0.997883i \(0.479284\pi\)
\(138\) 0 0
\(139\) 0.416070 0.0352906 0.0176453 0.999844i \(-0.494383\pi\)
0.0176453 + 0.999844i \(0.494383\pi\)
\(140\) 0 0
\(141\) −13.2113 −1.11259
\(142\) 0 0
\(143\) −4.45383 −0.372448
\(144\) 0 0
\(145\) 11.2160 0.931436
\(146\) 0 0
\(147\) 5.82578 0.480502
\(148\) 0 0
\(149\) 17.3291 1.41965 0.709827 0.704376i \(-0.248773\pi\)
0.709827 + 0.704376i \(0.248773\pi\)
\(150\) 0 0
\(151\) 4.06385 0.330712 0.165356 0.986234i \(-0.447123\pi\)
0.165356 + 0.986234i \(0.447123\pi\)
\(152\) 0 0
\(153\) −3.64824 −0.294942
\(154\) 0 0
\(155\) −1.04265 −0.0837479
\(156\) 0 0
\(157\) −4.55587 −0.363598 −0.181799 0.983336i \(-0.558192\pi\)
−0.181799 + 0.983336i \(0.558192\pi\)
\(158\) 0 0
\(159\) 4.41253 0.349937
\(160\) 0 0
\(161\) 1.36606 0.107661
\(162\) 0 0
\(163\) −0.730514 −0.0572183 −0.0286091 0.999591i \(-0.509108\pi\)
−0.0286091 + 0.999591i \(0.509108\pi\)
\(164\) 0 0
\(165\) 12.2949 0.957155
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −12.1116 −0.931663
\(170\) 0 0
\(171\) 2.69214 0.205873
\(172\) 0 0
\(173\) −0.0679638 −0.00516719 −0.00258359 0.999997i \(-0.500822\pi\)
−0.00258359 + 0.999997i \(0.500822\pi\)
\(174\) 0 0
\(175\) 6.33832 0.479132
\(176\) 0 0
\(177\) 5.47954 0.411867
\(178\) 0 0
\(179\) −2.86435 −0.214092 −0.107046 0.994254i \(-0.534139\pi\)
−0.107046 + 0.994254i \(0.534139\pi\)
\(180\) 0 0
\(181\) −7.39711 −0.549823 −0.274911 0.961470i \(-0.588649\pi\)
−0.274911 + 0.961470i \(0.588649\pi\)
\(182\) 0 0
\(183\) 10.9868 0.812165
\(184\) 0 0
\(185\) 1.05973 0.0779129
\(186\) 0 0
\(187\) −17.2392 −1.26066
\(188\) 0 0
\(189\) 3.58131 0.260502
\(190\) 0 0
\(191\) −1.50228 −0.108701 −0.0543505 0.998522i \(-0.517309\pi\)
−0.0543505 + 0.998522i \(0.517309\pi\)
\(192\) 0 0
\(193\) 11.6710 0.840097 0.420048 0.907502i \(-0.362013\pi\)
0.420048 + 0.907502i \(0.362013\pi\)
\(194\) 0 0
\(195\) −2.45238 −0.175619
\(196\) 0 0
\(197\) −17.0576 −1.21530 −0.607652 0.794203i \(-0.707889\pi\)
−0.607652 + 0.794203i \(0.707889\pi\)
\(198\) 0 0
\(199\) 13.9842 0.991313 0.495656 0.868519i \(-0.334928\pi\)
0.495656 + 0.868519i \(0.334928\pi\)
\(200\) 0 0
\(201\) −4.38579 −0.309350
\(202\) 0 0
\(203\) 15.4380 1.08353
\(204\) 0 0
\(205\) 1.97612 0.138018
\(206\) 0 0
\(207\) 0.381441 0.0265120
\(208\) 0 0
\(209\) 12.7214 0.879955
\(210\) 0 0
\(211\) 2.83616 0.195249 0.0976246 0.995223i \(-0.468876\pi\)
0.0976246 + 0.995223i \(0.468876\pi\)
\(212\) 0 0
\(213\) 1.17148 0.0802682
\(214\) 0 0
\(215\) −11.6415 −0.793947
\(216\) 0 0
\(217\) −1.43514 −0.0974234
\(218\) 0 0
\(219\) 12.3989 0.837841
\(220\) 0 0
\(221\) 3.43860 0.231305
\(222\) 0 0
\(223\) −27.1850 −1.82044 −0.910221 0.414123i \(-0.864088\pi\)
−0.910221 + 0.414123i \(0.864088\pi\)
\(224\) 0 0
\(225\) 1.76983 0.117989
\(226\) 0 0
\(227\) 3.04918 0.202381 0.101191 0.994867i \(-0.467735\pi\)
0.101191 + 0.994867i \(0.467735\pi\)
\(228\) 0 0
\(229\) −18.4941 −1.22213 −0.611063 0.791582i \(-0.709258\pi\)
−0.611063 + 0.791582i \(0.709258\pi\)
\(230\) 0 0
\(231\) 16.9230 1.11345
\(232\) 0 0
\(233\) 0.657303 0.0430614 0.0215307 0.999768i \(-0.493146\pi\)
0.0215307 + 0.999768i \(0.493146\pi\)
\(234\) 0 0
\(235\) −34.3744 −2.24234
\(236\) 0 0
\(237\) −8.57361 −0.556916
\(238\) 0 0
\(239\) −20.0775 −1.29871 −0.649353 0.760488i \(-0.724960\pi\)
−0.649353 + 0.760488i \(0.724960\pi\)
\(240\) 0 0
\(241\) −5.36567 −0.345633 −0.172817 0.984954i \(-0.555287\pi\)
−0.172817 + 0.984954i \(0.555287\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 15.1580 0.968412
\(246\) 0 0
\(247\) −2.53745 −0.161454
\(248\) 0 0
\(249\) −0.551394 −0.0349432
\(250\) 0 0
\(251\) −22.9699 −1.44985 −0.724923 0.688830i \(-0.758125\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(252\) 0 0
\(253\) 1.80245 0.113319
\(254\) 0 0
\(255\) −9.49231 −0.594432
\(256\) 0 0
\(257\) 5.41168 0.337572 0.168786 0.985653i \(-0.446015\pi\)
0.168786 + 0.985653i \(0.446015\pi\)
\(258\) 0 0
\(259\) 1.45864 0.0906355
\(260\) 0 0
\(261\) 4.31070 0.266826
\(262\) 0 0
\(263\) −27.6992 −1.70801 −0.854004 0.520267i \(-0.825832\pi\)
−0.854004 + 0.520267i \(0.825832\pi\)
\(264\) 0 0
\(265\) 11.4809 0.705268
\(266\) 0 0
\(267\) 0.764327 0.0467760
\(268\) 0 0
\(269\) 10.7253 0.653932 0.326966 0.945036i \(-0.393974\pi\)
0.326966 + 0.945036i \(0.393974\pi\)
\(270\) 0 0
\(271\) −8.82097 −0.535836 −0.267918 0.963442i \(-0.586336\pi\)
−0.267918 + 0.963442i \(0.586336\pi\)
\(272\) 0 0
\(273\) −3.37552 −0.204296
\(274\) 0 0
\(275\) 8.36310 0.504314
\(276\) 0 0
\(277\) −18.3165 −1.10053 −0.550265 0.834990i \(-0.685473\pi\)
−0.550265 + 0.834990i \(0.685473\pi\)
\(278\) 0 0
\(279\) −0.400729 −0.0239910
\(280\) 0 0
\(281\) 22.8776 1.36476 0.682382 0.730996i \(-0.260944\pi\)
0.682382 + 0.730996i \(0.260944\pi\)
\(282\) 0 0
\(283\) −14.7628 −0.877556 −0.438778 0.898595i \(-0.644589\pi\)
−0.438778 + 0.898595i \(0.644589\pi\)
\(284\) 0 0
\(285\) 7.00466 0.414920
\(286\) 0 0
\(287\) 2.71999 0.160556
\(288\) 0 0
\(289\) −3.69037 −0.217081
\(290\) 0 0
\(291\) −4.11552 −0.241256
\(292\) 0 0
\(293\) 1.04558 0.0610834 0.0305417 0.999533i \(-0.490277\pi\)
0.0305417 + 0.999533i \(0.490277\pi\)
\(294\) 0 0
\(295\) 14.2572 0.830083
\(296\) 0 0
\(297\) 4.72536 0.274193
\(298\) 0 0
\(299\) −0.359523 −0.0207917
\(300\) 0 0
\(301\) −16.0237 −0.923592
\(302\) 0 0
\(303\) 4.37168 0.251147
\(304\) 0 0
\(305\) 28.5864 1.63685
\(306\) 0 0
\(307\) −10.8164 −0.617326 −0.308663 0.951171i \(-0.599882\pi\)
−0.308663 + 0.951171i \(0.599882\pi\)
\(308\) 0 0
\(309\) −10.2673 −0.584085
\(310\) 0 0
\(311\) 13.1845 0.747625 0.373812 0.927504i \(-0.378050\pi\)
0.373812 + 0.927504i \(0.378050\pi\)
\(312\) 0 0
\(313\) −7.37178 −0.416678 −0.208339 0.978057i \(-0.566806\pi\)
−0.208339 + 0.978057i \(0.566806\pi\)
\(314\) 0 0
\(315\) 9.31818 0.525020
\(316\) 0 0
\(317\) −10.2372 −0.574978 −0.287489 0.957784i \(-0.592821\pi\)
−0.287489 + 0.957784i \(0.592821\pi\)
\(318\) 0 0
\(319\) 20.3696 1.14048
\(320\) 0 0
\(321\) −3.33602 −0.186198
\(322\) 0 0
\(323\) −9.82158 −0.546487
\(324\) 0 0
\(325\) −1.66814 −0.0925315
\(326\) 0 0
\(327\) 6.99888 0.387039
\(328\) 0 0
\(329\) −47.3138 −2.60849
\(330\) 0 0
\(331\) 34.3313 1.88702 0.943509 0.331348i \(-0.107504\pi\)
0.943509 + 0.331348i \(0.107504\pi\)
\(332\) 0 0
\(333\) 0.407293 0.0223195
\(334\) 0 0
\(335\) −11.4113 −0.623468
\(336\) 0 0
\(337\) 1.75514 0.0956088 0.0478044 0.998857i \(-0.484778\pi\)
0.0478044 + 0.998857i \(0.484778\pi\)
\(338\) 0 0
\(339\) −11.1190 −0.603901
\(340\) 0 0
\(341\) −1.89359 −0.102544
\(342\) 0 0
\(343\) −4.20524 −0.227062
\(344\) 0 0
\(345\) 0.992468 0.0534327
\(346\) 0 0
\(347\) −22.0967 −1.18621 −0.593106 0.805125i \(-0.702098\pi\)
−0.593106 + 0.805125i \(0.702098\pi\)
\(348\) 0 0
\(349\) 3.71549 0.198886 0.0994428 0.995043i \(-0.468294\pi\)
0.0994428 + 0.995043i \(0.468294\pi\)
\(350\) 0 0
\(351\) −0.942538 −0.0503090
\(352\) 0 0
\(353\) 12.0789 0.642893 0.321447 0.946928i \(-0.395831\pi\)
0.321447 + 0.946928i \(0.395831\pi\)
\(354\) 0 0
\(355\) 3.04805 0.161774
\(356\) 0 0
\(357\) −13.0655 −0.691498
\(358\) 0 0
\(359\) 15.0369 0.793617 0.396808 0.917902i \(-0.370118\pi\)
0.396808 + 0.917902i \(0.370118\pi\)
\(360\) 0 0
\(361\) −11.7524 −0.618545
\(362\) 0 0
\(363\) 11.3290 0.594621
\(364\) 0 0
\(365\) 32.2606 1.68860
\(366\) 0 0
\(367\) −1.93985 −0.101259 −0.0506295 0.998718i \(-0.516123\pi\)
−0.0506295 + 0.998718i \(0.516123\pi\)
\(368\) 0 0
\(369\) 0.759495 0.0395377
\(370\) 0 0
\(371\) 15.8026 0.820432
\(372\) 0 0
\(373\) 24.3710 1.26188 0.630942 0.775830i \(-0.282669\pi\)
0.630942 + 0.775830i \(0.282669\pi\)
\(374\) 0 0
\(375\) −8.40454 −0.434009
\(376\) 0 0
\(377\) −4.06300 −0.209255
\(378\) 0 0
\(379\) 6.87541 0.353166 0.176583 0.984286i \(-0.443496\pi\)
0.176583 + 0.984286i \(0.443496\pi\)
\(380\) 0 0
\(381\) 6.13214 0.314159
\(382\) 0 0
\(383\) 21.2247 1.08453 0.542267 0.840206i \(-0.317566\pi\)
0.542267 + 0.840206i \(0.317566\pi\)
\(384\) 0 0
\(385\) 44.0318 2.24407
\(386\) 0 0
\(387\) −4.47426 −0.227440
\(388\) 0 0
\(389\) 31.3959 1.59184 0.795918 0.605405i \(-0.206989\pi\)
0.795918 + 0.605405i \(0.206989\pi\)
\(390\) 0 0
\(391\) −1.39159 −0.0703756
\(392\) 0 0
\(393\) 12.0777 0.609242
\(394\) 0 0
\(395\) −22.3076 −1.12242
\(396\) 0 0
\(397\) 24.8691 1.24815 0.624073 0.781366i \(-0.285477\pi\)
0.624073 + 0.781366i \(0.285477\pi\)
\(398\) 0 0
\(399\) 9.64140 0.482674
\(400\) 0 0
\(401\) −5.28088 −0.263714 −0.131857 0.991269i \(-0.542094\pi\)
−0.131857 + 0.991269i \(0.542094\pi\)
\(402\) 0 0
\(403\) 0.377703 0.0188147
\(404\) 0 0
\(405\) 2.60189 0.129289
\(406\) 0 0
\(407\) 1.92460 0.0953991
\(408\) 0 0
\(409\) −21.1368 −1.04515 −0.522575 0.852593i \(-0.675028\pi\)
−0.522575 + 0.852593i \(0.675028\pi\)
\(410\) 0 0
\(411\) 1.52242 0.0750954
\(412\) 0 0
\(413\) 19.6239 0.965630
\(414\) 0 0
\(415\) −1.43467 −0.0704250
\(416\) 0 0
\(417\) 0.416070 0.0203750
\(418\) 0 0
\(419\) −25.0085 −1.22175 −0.610874 0.791728i \(-0.709182\pi\)
−0.610874 + 0.791728i \(0.709182\pi\)
\(420\) 0 0
\(421\) 1.12666 0.0549102 0.0274551 0.999623i \(-0.491260\pi\)
0.0274551 + 0.999623i \(0.491260\pi\)
\(422\) 0 0
\(423\) −13.2113 −0.642356
\(424\) 0 0
\(425\) −6.45677 −0.313199
\(426\) 0 0
\(427\) 39.3470 1.90414
\(428\) 0 0
\(429\) −4.45383 −0.215033
\(430\) 0 0
\(431\) −29.5186 −1.42186 −0.710931 0.703262i \(-0.751726\pi\)
−0.710931 + 0.703262i \(0.751726\pi\)
\(432\) 0 0
\(433\) 2.36702 0.113752 0.0568758 0.998381i \(-0.481886\pi\)
0.0568758 + 0.998381i \(0.481886\pi\)
\(434\) 0 0
\(435\) 11.2160 0.537765
\(436\) 0 0
\(437\) 1.02689 0.0491230
\(438\) 0 0
\(439\) 23.5108 1.12211 0.561056 0.827778i \(-0.310395\pi\)
0.561056 + 0.827778i \(0.310395\pi\)
\(440\) 0 0
\(441\) 5.82578 0.277418
\(442\) 0 0
\(443\) −31.5813 −1.50047 −0.750237 0.661169i \(-0.770060\pi\)
−0.750237 + 0.661169i \(0.770060\pi\)
\(444\) 0 0
\(445\) 1.98869 0.0942731
\(446\) 0 0
\(447\) 17.3291 0.819638
\(448\) 0 0
\(449\) 19.1231 0.902475 0.451237 0.892404i \(-0.350983\pi\)
0.451237 + 0.892404i \(0.350983\pi\)
\(450\) 0 0
\(451\) 3.58889 0.168994
\(452\) 0 0
\(453\) 4.06385 0.190936
\(454\) 0 0
\(455\) −8.78274 −0.411741
\(456\) 0 0
\(457\) −15.1813 −0.710153 −0.355076 0.934837i \(-0.615545\pi\)
−0.355076 + 0.934837i \(0.615545\pi\)
\(458\) 0 0
\(459\) −3.64824 −0.170285
\(460\) 0 0
\(461\) 25.4193 1.18390 0.591948 0.805976i \(-0.298359\pi\)
0.591948 + 0.805976i \(0.298359\pi\)
\(462\) 0 0
\(463\) 21.9175 1.01859 0.509297 0.860591i \(-0.329906\pi\)
0.509297 + 0.860591i \(0.329906\pi\)
\(464\) 0 0
\(465\) −1.04265 −0.0483519
\(466\) 0 0
\(467\) −20.3451 −0.941457 −0.470729 0.882278i \(-0.656009\pi\)
−0.470729 + 0.882278i \(0.656009\pi\)
\(468\) 0 0
\(469\) −15.7069 −0.725276
\(470\) 0 0
\(471\) −4.55587 −0.209924
\(472\) 0 0
\(473\) −21.1425 −0.972134
\(474\) 0 0
\(475\) 4.76465 0.218617
\(476\) 0 0
\(477\) 4.41253 0.202036
\(478\) 0 0
\(479\) 24.7792 1.13219 0.566095 0.824340i \(-0.308454\pi\)
0.566095 + 0.824340i \(0.308454\pi\)
\(480\) 0 0
\(481\) −0.383889 −0.0175038
\(482\) 0 0
\(483\) 1.36606 0.0621579
\(484\) 0 0
\(485\) −10.7081 −0.486232
\(486\) 0 0
\(487\) −18.5285 −0.839605 −0.419802 0.907616i \(-0.637901\pi\)
−0.419802 + 0.907616i \(0.637901\pi\)
\(488\) 0 0
\(489\) −0.730514 −0.0330350
\(490\) 0 0
\(491\) 15.4680 0.698063 0.349031 0.937111i \(-0.386511\pi\)
0.349031 + 0.937111i \(0.386511\pi\)
\(492\) 0 0
\(493\) −15.7265 −0.708284
\(494\) 0 0
\(495\) 12.2949 0.552614
\(496\) 0 0
\(497\) 4.19542 0.188190
\(498\) 0 0
\(499\) −9.82883 −0.439999 −0.219999 0.975500i \(-0.570606\pi\)
−0.219999 + 0.975500i \(0.570606\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −20.7097 −0.923401 −0.461701 0.887036i \(-0.652761\pi\)
−0.461701 + 0.887036i \(0.652761\pi\)
\(504\) 0 0
\(505\) 11.3746 0.506165
\(506\) 0 0
\(507\) −12.1116 −0.537896
\(508\) 0 0
\(509\) 19.6701 0.871863 0.435931 0.899980i \(-0.356419\pi\)
0.435931 + 0.899980i \(0.356419\pi\)
\(510\) 0 0
\(511\) 44.4044 1.96433
\(512\) 0 0
\(513\) 2.69214 0.118861
\(514\) 0 0
\(515\) −26.7143 −1.17717
\(516\) 0 0
\(517\) −62.4282 −2.74559
\(518\) 0 0
\(519\) −0.0679638 −0.00298328
\(520\) 0 0
\(521\) 25.0759 1.09859 0.549297 0.835627i \(-0.314895\pi\)
0.549297 + 0.835627i \(0.314895\pi\)
\(522\) 0 0
\(523\) −27.8230 −1.21661 −0.608307 0.793702i \(-0.708151\pi\)
−0.608307 + 0.793702i \(0.708151\pi\)
\(524\) 0 0
\(525\) 6.33832 0.276627
\(526\) 0 0
\(527\) 1.46195 0.0636838
\(528\) 0 0
\(529\) −22.8545 −0.993674
\(530\) 0 0
\(531\) 5.47954 0.237792
\(532\) 0 0
\(533\) −0.715853 −0.0310070
\(534\) 0 0
\(535\) −8.67995 −0.375267
\(536\) 0 0
\(537\) −2.86435 −0.123606
\(538\) 0 0
\(539\) 27.5289 1.18575
\(540\) 0 0
\(541\) −11.5442 −0.496325 −0.248163 0.968718i \(-0.579827\pi\)
−0.248163 + 0.968718i \(0.579827\pi\)
\(542\) 0 0
\(543\) −7.39711 −0.317440
\(544\) 0 0
\(545\) 18.2103 0.780044
\(546\) 0 0
\(547\) 11.9053 0.509032 0.254516 0.967069i \(-0.418084\pi\)
0.254516 + 0.967069i \(0.418084\pi\)
\(548\) 0 0
\(549\) 10.9868 0.468904
\(550\) 0 0
\(551\) 11.6050 0.494391
\(552\) 0 0
\(553\) −30.7048 −1.30570
\(554\) 0 0
\(555\) 1.05973 0.0449831
\(556\) 0 0
\(557\) 41.1551 1.74380 0.871899 0.489686i \(-0.162888\pi\)
0.871899 + 0.489686i \(0.162888\pi\)
\(558\) 0 0
\(559\) 4.21717 0.178367
\(560\) 0 0
\(561\) −17.2392 −0.727841
\(562\) 0 0
\(563\) 1.33224 0.0561472 0.0280736 0.999606i \(-0.491063\pi\)
0.0280736 + 0.999606i \(0.491063\pi\)
\(564\) 0 0
\(565\) −28.9304 −1.21711
\(566\) 0 0
\(567\) 3.58131 0.150401
\(568\) 0 0
\(569\) 1.31639 0.0551861 0.0275931 0.999619i \(-0.491216\pi\)
0.0275931 + 0.999619i \(0.491216\pi\)
\(570\) 0 0
\(571\) 15.0075 0.628043 0.314022 0.949416i \(-0.398324\pi\)
0.314022 + 0.949416i \(0.398324\pi\)
\(572\) 0 0
\(573\) −1.50228 −0.0627586
\(574\) 0 0
\(575\) 0.675087 0.0281531
\(576\) 0 0
\(577\) 16.9944 0.707487 0.353743 0.935343i \(-0.384909\pi\)
0.353743 + 0.935343i \(0.384909\pi\)
\(578\) 0 0
\(579\) 11.6710 0.485030
\(580\) 0 0
\(581\) −1.97471 −0.0819249
\(582\) 0 0
\(583\) 20.8508 0.863552
\(584\) 0 0
\(585\) −2.45238 −0.101393
\(586\) 0 0
\(587\) 25.0492 1.03389 0.516945 0.856018i \(-0.327069\pi\)
0.516945 + 0.856018i \(0.327069\pi\)
\(588\) 0 0
\(589\) −1.07882 −0.0444520
\(590\) 0 0
\(591\) −17.0576 −0.701656
\(592\) 0 0
\(593\) 20.3612 0.836134 0.418067 0.908416i \(-0.362708\pi\)
0.418067 + 0.908416i \(0.362708\pi\)
\(594\) 0 0
\(595\) −33.9949 −1.39366
\(596\) 0 0
\(597\) 13.9842 0.572335
\(598\) 0 0
\(599\) 13.7622 0.562309 0.281155 0.959663i \(-0.409283\pi\)
0.281155 + 0.959663i \(0.409283\pi\)
\(600\) 0 0
\(601\) −32.7714 −1.33677 −0.668387 0.743814i \(-0.733015\pi\)
−0.668387 + 0.743814i \(0.733015\pi\)
\(602\) 0 0
\(603\) −4.38579 −0.178603
\(604\) 0 0
\(605\) 29.4769 1.19841
\(606\) 0 0
\(607\) −35.7405 −1.45066 −0.725331 0.688401i \(-0.758313\pi\)
−0.725331 + 0.688401i \(0.758313\pi\)
\(608\) 0 0
\(609\) 15.4380 0.625578
\(610\) 0 0
\(611\) 12.4522 0.503761
\(612\) 0 0
\(613\) −5.12576 −0.207028 −0.103514 0.994628i \(-0.533009\pi\)
−0.103514 + 0.994628i \(0.533009\pi\)
\(614\) 0 0
\(615\) 1.97612 0.0796849
\(616\) 0 0
\(617\) −5.86405 −0.236078 −0.118039 0.993009i \(-0.537661\pi\)
−0.118039 + 0.993009i \(0.537661\pi\)
\(618\) 0 0
\(619\) −11.2491 −0.452141 −0.226070 0.974111i \(-0.572588\pi\)
−0.226070 + 0.974111i \(0.572588\pi\)
\(620\) 0 0
\(621\) 0.381441 0.0153067
\(622\) 0 0
\(623\) 2.73729 0.109667
\(624\) 0 0
\(625\) −30.7169 −1.22867
\(626\) 0 0
\(627\) 12.7214 0.508042
\(628\) 0 0
\(629\) −1.48590 −0.0592467
\(630\) 0 0
\(631\) −1.17955 −0.0469573 −0.0234786 0.999724i \(-0.507474\pi\)
−0.0234786 + 0.999724i \(0.507474\pi\)
\(632\) 0 0
\(633\) 2.83616 0.112727
\(634\) 0 0
\(635\) 15.9552 0.633161
\(636\) 0 0
\(637\) −5.49102 −0.217562
\(638\) 0 0
\(639\) 1.17148 0.0463428
\(640\) 0 0
\(641\) −33.1443 −1.30912 −0.654561 0.756009i \(-0.727147\pi\)
−0.654561 + 0.756009i \(0.727147\pi\)
\(642\) 0 0
\(643\) 19.5427 0.770687 0.385344 0.922773i \(-0.374083\pi\)
0.385344 + 0.922773i \(0.374083\pi\)
\(644\) 0 0
\(645\) −11.6415 −0.458385
\(646\) 0 0
\(647\) −3.86419 −0.151917 −0.0759585 0.997111i \(-0.524202\pi\)
−0.0759585 + 0.997111i \(0.524202\pi\)
\(648\) 0 0
\(649\) 25.8928 1.01638
\(650\) 0 0
\(651\) −1.43514 −0.0562474
\(652\) 0 0
\(653\) −3.27995 −0.128354 −0.0641772 0.997939i \(-0.520442\pi\)
−0.0641772 + 0.997939i \(0.520442\pi\)
\(654\) 0 0
\(655\) 31.4250 1.22787
\(656\) 0 0
\(657\) 12.3989 0.483728
\(658\) 0 0
\(659\) 17.6881 0.689031 0.344515 0.938781i \(-0.388043\pi\)
0.344515 + 0.938781i \(0.388043\pi\)
\(660\) 0 0
\(661\) −24.9186 −0.969220 −0.484610 0.874730i \(-0.661038\pi\)
−0.484610 + 0.874730i \(0.661038\pi\)
\(662\) 0 0
\(663\) 3.43860 0.133544
\(664\) 0 0
\(665\) 25.0859 0.972788
\(666\) 0 0
\(667\) 1.64428 0.0636668
\(668\) 0 0
\(669\) −27.1850 −1.05103
\(670\) 0 0
\(671\) 51.9165 2.00421
\(672\) 0 0
\(673\) 15.9326 0.614158 0.307079 0.951684i \(-0.400648\pi\)
0.307079 + 0.951684i \(0.400648\pi\)
\(674\) 0 0
\(675\) 1.76983 0.0681209
\(676\) 0 0
\(677\) 21.0904 0.810569 0.405285 0.914191i \(-0.367172\pi\)
0.405285 + 0.914191i \(0.367172\pi\)
\(678\) 0 0
\(679\) −14.7390 −0.565630
\(680\) 0 0
\(681\) 3.04918 0.116845
\(682\) 0 0
\(683\) −9.92172 −0.379644 −0.189822 0.981819i \(-0.560791\pi\)
−0.189822 + 0.981819i \(0.560791\pi\)
\(684\) 0 0
\(685\) 3.96117 0.151348
\(686\) 0 0
\(687\) −18.4941 −0.705595
\(688\) 0 0
\(689\) −4.15898 −0.158445
\(690\) 0 0
\(691\) 9.68186 0.368315 0.184158 0.982897i \(-0.441044\pi\)
0.184158 + 0.982897i \(0.441044\pi\)
\(692\) 0 0
\(693\) 16.9230 0.642851
\(694\) 0 0
\(695\) 1.08257 0.0410642
\(696\) 0 0
\(697\) −2.77082 −0.104952
\(698\) 0 0
\(699\) 0.657303 0.0248615
\(700\) 0 0
\(701\) 35.5112 1.34124 0.670620 0.741801i \(-0.266028\pi\)
0.670620 + 0.741801i \(0.266028\pi\)
\(702\) 0 0
\(703\) 1.09649 0.0413549
\(704\) 0 0
\(705\) −34.3744 −1.29461
\(706\) 0 0
\(707\) 15.6564 0.588818
\(708\) 0 0
\(709\) 15.2713 0.573525 0.286762 0.958002i \(-0.407421\pi\)
0.286762 + 0.958002i \(0.407421\pi\)
\(710\) 0 0
\(711\) −8.57361 −0.321536
\(712\) 0 0
\(713\) −0.152855 −0.00572445
\(714\) 0 0
\(715\) −11.5884 −0.433381
\(716\) 0 0
\(717\) −20.0775 −0.749808
\(718\) 0 0
\(719\) 43.4707 1.62118 0.810592 0.585612i \(-0.199146\pi\)
0.810592 + 0.585612i \(0.199146\pi\)
\(720\) 0 0
\(721\) −36.7703 −1.36940
\(722\) 0 0
\(723\) −5.36567 −0.199552
\(724\) 0 0
\(725\) 7.62923 0.283342
\(726\) 0 0
\(727\) 21.3900 0.793313 0.396656 0.917967i \(-0.370170\pi\)
0.396656 + 0.917967i \(0.370170\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 16.3232 0.603734
\(732\) 0 0
\(733\) 18.5499 0.685156 0.342578 0.939489i \(-0.388700\pi\)
0.342578 + 0.939489i \(0.388700\pi\)
\(734\) 0 0
\(735\) 15.1580 0.559113
\(736\) 0 0
\(737\) −20.7244 −0.763395
\(738\) 0 0
\(739\) −0.246619 −0.00907202 −0.00453601 0.999990i \(-0.501444\pi\)
−0.00453601 + 0.999990i \(0.501444\pi\)
\(740\) 0 0
\(741\) −2.53745 −0.0932155
\(742\) 0 0
\(743\) 43.8557 1.60891 0.804455 0.594013i \(-0.202457\pi\)
0.804455 + 0.594013i \(0.202457\pi\)
\(744\) 0 0
\(745\) 45.0884 1.65191
\(746\) 0 0
\(747\) −0.551394 −0.0201744
\(748\) 0 0
\(749\) −11.9473 −0.436545
\(750\) 0 0
\(751\) −31.3326 −1.14334 −0.571671 0.820483i \(-0.693705\pi\)
−0.571671 + 0.820483i \(0.693705\pi\)
\(752\) 0 0
\(753\) −22.9699 −0.837069
\(754\) 0 0
\(755\) 10.5737 0.384816
\(756\) 0 0
\(757\) −47.7102 −1.73406 −0.867029 0.498258i \(-0.833973\pi\)
−0.867029 + 0.498258i \(0.833973\pi\)
\(758\) 0 0
\(759\) 1.80245 0.0654247
\(760\) 0 0
\(761\) −33.0321 −1.19741 −0.598706 0.800969i \(-0.704318\pi\)
−0.598706 + 0.800969i \(0.704318\pi\)
\(762\) 0 0
\(763\) 25.0651 0.907419
\(764\) 0 0
\(765\) −9.49231 −0.343195
\(766\) 0 0
\(767\) −5.16467 −0.186485
\(768\) 0 0
\(769\) 2.24259 0.0808698 0.0404349 0.999182i \(-0.487126\pi\)
0.0404349 + 0.999182i \(0.487126\pi\)
\(770\) 0 0
\(771\) 5.41168 0.194897
\(772\) 0 0
\(773\) −33.8407 −1.21716 −0.608582 0.793491i \(-0.708262\pi\)
−0.608582 + 0.793491i \(0.708262\pi\)
\(774\) 0 0
\(775\) −0.709224 −0.0254761
\(776\) 0 0
\(777\) 1.45864 0.0523284
\(778\) 0 0
\(779\) 2.04467 0.0732579
\(780\) 0 0
\(781\) 5.53564 0.198081
\(782\) 0 0
\(783\) 4.31070 0.154052
\(784\) 0 0
\(785\) −11.8539 −0.423083
\(786\) 0 0
\(787\) −22.9925 −0.819596 −0.409798 0.912176i \(-0.634401\pi\)
−0.409798 + 0.912176i \(0.634401\pi\)
\(788\) 0 0
\(789\) −27.6992 −0.986119
\(790\) 0 0
\(791\) −39.8206 −1.41586
\(792\) 0 0
\(793\) −10.3554 −0.367733
\(794\) 0 0
\(795\) 11.4809 0.407186
\(796\) 0 0
\(797\) −25.2005 −0.892649 −0.446324 0.894871i \(-0.647267\pi\)
−0.446324 + 0.894871i \(0.647267\pi\)
\(798\) 0 0
\(799\) 48.1980 1.70512
\(800\) 0 0
\(801\) 0.764327 0.0270062
\(802\) 0 0
\(803\) 58.5894 2.06757
\(804\) 0 0
\(805\) 3.55434 0.125274
\(806\) 0 0
\(807\) 10.7253 0.377548
\(808\) 0 0
\(809\) 3.96709 0.139475 0.0697377 0.997565i \(-0.477784\pi\)
0.0697377 + 0.997565i \(0.477784\pi\)
\(810\) 0 0
\(811\) −8.82118 −0.309753 −0.154877 0.987934i \(-0.549498\pi\)
−0.154877 + 0.987934i \(0.549498\pi\)
\(812\) 0 0
\(813\) −8.82097 −0.309365
\(814\) 0 0
\(815\) −1.90072 −0.0665792
\(816\) 0 0
\(817\) −12.0454 −0.421414
\(818\) 0 0
\(819\) −3.37552 −0.117950
\(820\) 0 0
\(821\) 43.4468 1.51630 0.758151 0.652079i \(-0.226103\pi\)
0.758151 + 0.652079i \(0.226103\pi\)
\(822\) 0 0
\(823\) 51.0625 1.77993 0.889963 0.456033i \(-0.150730\pi\)
0.889963 + 0.456033i \(0.150730\pi\)
\(824\) 0 0
\(825\) 8.36310 0.291166
\(826\) 0 0
\(827\) −13.7322 −0.477516 −0.238758 0.971079i \(-0.576740\pi\)
−0.238758 + 0.971079i \(0.576740\pi\)
\(828\) 0 0
\(829\) 17.6105 0.611637 0.305818 0.952090i \(-0.401070\pi\)
0.305818 + 0.952090i \(0.401070\pi\)
\(830\) 0 0
\(831\) −18.3165 −0.635391
\(832\) 0 0
\(833\) −21.2538 −0.736402
\(834\) 0 0
\(835\) −2.60189 −0.0900421
\(836\) 0 0
\(837\) −0.400729 −0.0138512
\(838\) 0 0
\(839\) 14.8474 0.512591 0.256295 0.966599i \(-0.417498\pi\)
0.256295 + 0.966599i \(0.417498\pi\)
\(840\) 0 0
\(841\) −10.4178 −0.359236
\(842\) 0 0
\(843\) 22.8776 0.787946
\(844\) 0 0
\(845\) −31.5131 −1.08408
\(846\) 0 0
\(847\) 40.5728 1.39410
\(848\) 0 0
\(849\) −14.7628 −0.506657
\(850\) 0 0
\(851\) 0.155358 0.00532561
\(852\) 0 0
\(853\) −14.9949 −0.513414 −0.256707 0.966489i \(-0.582638\pi\)
−0.256707 + 0.966489i \(0.582638\pi\)
\(854\) 0 0
\(855\) 7.00466 0.239554
\(856\) 0 0
\(857\) 46.1967 1.57805 0.789024 0.614363i \(-0.210587\pi\)
0.789024 + 0.614363i \(0.210587\pi\)
\(858\) 0 0
\(859\) −46.7913 −1.59650 −0.798249 0.602327i \(-0.794240\pi\)
−0.798249 + 0.602327i \(0.794240\pi\)
\(860\) 0 0
\(861\) 2.71999 0.0926969
\(862\) 0 0
\(863\) −52.1490 −1.77517 −0.887587 0.460641i \(-0.847620\pi\)
−0.887587 + 0.460641i \(0.847620\pi\)
\(864\) 0 0
\(865\) −0.176834 −0.00601254
\(866\) 0 0
\(867\) −3.69037 −0.125332
\(868\) 0 0
\(869\) −40.5134 −1.37432
\(870\) 0 0
\(871\) 4.13377 0.140068
\(872\) 0 0
\(873\) −4.11552 −0.139289
\(874\) 0 0
\(875\) −30.0993 −1.01754
\(876\) 0 0
\(877\) −25.8887 −0.874199 −0.437099 0.899413i \(-0.643994\pi\)
−0.437099 + 0.899413i \(0.643994\pi\)
\(878\) 0 0
\(879\) 1.04558 0.0352665
\(880\) 0 0
\(881\) −5.07893 −0.171113 −0.0855567 0.996333i \(-0.527267\pi\)
−0.0855567 + 0.996333i \(0.527267\pi\)
\(882\) 0 0
\(883\) −15.9118 −0.535473 −0.267737 0.963492i \(-0.586276\pi\)
−0.267737 + 0.963492i \(0.586276\pi\)
\(884\) 0 0
\(885\) 14.2572 0.479249
\(886\) 0 0
\(887\) 4.59352 0.154235 0.0771177 0.997022i \(-0.475428\pi\)
0.0771177 + 0.997022i \(0.475428\pi\)
\(888\) 0 0
\(889\) 21.9611 0.736551
\(890\) 0 0
\(891\) 4.72536 0.158306
\(892\) 0 0
\(893\) −35.5667 −1.19020
\(894\) 0 0
\(895\) −7.45274 −0.249118
\(896\) 0 0
\(897\) −0.359523 −0.0120041
\(898\) 0 0
\(899\) −1.72742 −0.0576128
\(900\) 0 0
\(901\) −16.0980 −0.536301
\(902\) 0 0
\(903\) −16.0237 −0.533236
\(904\) 0 0
\(905\) −19.2465 −0.639774
\(906\) 0 0
\(907\) −21.5834 −0.716666 −0.358333 0.933594i \(-0.616655\pi\)
−0.358333 + 0.933594i \(0.616655\pi\)
\(908\) 0 0
\(909\) 4.37168 0.145000
\(910\) 0 0
\(911\) −11.9986 −0.397531 −0.198766 0.980047i \(-0.563693\pi\)
−0.198766 + 0.980047i \(0.563693\pi\)
\(912\) 0 0
\(913\) −2.60554 −0.0862306
\(914\) 0 0
\(915\) 28.5864 0.945036
\(916\) 0 0
\(917\) 43.2541 1.42838
\(918\) 0 0
\(919\) 13.9436 0.459955 0.229978 0.973196i \(-0.426135\pi\)
0.229978 + 0.973196i \(0.426135\pi\)
\(920\) 0 0
\(921\) −10.8164 −0.356413
\(922\) 0 0
\(923\) −1.10416 −0.0363439
\(924\) 0 0
\(925\) 0.720840 0.0237011
\(926\) 0 0
\(927\) −10.2673 −0.337222
\(928\) 0 0
\(929\) −1.03719 −0.0340291 −0.0170145 0.999855i \(-0.505416\pi\)
−0.0170145 + 0.999855i \(0.505416\pi\)
\(930\) 0 0
\(931\) 15.6838 0.514017
\(932\) 0 0
\(933\) 13.1845 0.431641
\(934\) 0 0
\(935\) −44.8546 −1.46690
\(936\) 0 0
\(937\) −8.86334 −0.289553 −0.144776 0.989464i \(-0.546246\pi\)
−0.144776 + 0.989464i \(0.546246\pi\)
\(938\) 0 0
\(939\) −7.37178 −0.240569
\(940\) 0 0
\(941\) −26.1467 −0.852357 −0.426178 0.904639i \(-0.640140\pi\)
−0.426178 + 0.904639i \(0.640140\pi\)
\(942\) 0 0
\(943\) 0.289703 0.00943401
\(944\) 0 0
\(945\) 9.31818 0.303120
\(946\) 0 0
\(947\) 13.7102 0.445522 0.222761 0.974873i \(-0.428493\pi\)
0.222761 + 0.974873i \(0.428493\pi\)
\(948\) 0 0
\(949\) −11.6865 −0.379358
\(950\) 0 0
\(951\) −10.2372 −0.331964
\(952\) 0 0
\(953\) −48.4836 −1.57054 −0.785270 0.619154i \(-0.787476\pi\)
−0.785270 + 0.619154i \(0.787476\pi\)
\(954\) 0 0
\(955\) −3.90876 −0.126485
\(956\) 0 0
\(957\) 20.3696 0.658457
\(958\) 0 0
\(959\) 5.45225 0.176062
\(960\) 0 0
\(961\) −30.8394 −0.994820
\(962\) 0 0
\(963\) −3.33602 −0.107502
\(964\) 0 0
\(965\) 30.3666 0.977537
\(966\) 0 0
\(967\) −1.62702 −0.0523214 −0.0261607 0.999658i \(-0.508328\pi\)
−0.0261607 + 0.999658i \(0.508328\pi\)
\(968\) 0 0
\(969\) −9.82158 −0.315515
\(970\) 0 0
\(971\) 23.8897 0.766656 0.383328 0.923612i \(-0.374778\pi\)
0.383328 + 0.923612i \(0.374778\pi\)
\(972\) 0 0
\(973\) 1.49008 0.0477697
\(974\) 0 0
\(975\) −1.66814 −0.0534231
\(976\) 0 0
\(977\) 37.6398 1.20420 0.602102 0.798419i \(-0.294330\pi\)
0.602102 + 0.798419i \(0.294330\pi\)
\(978\) 0 0
\(979\) 3.61172 0.115431
\(980\) 0 0
\(981\) 6.99888 0.223457
\(982\) 0 0
\(983\) 25.8936 0.825877 0.412939 0.910759i \(-0.364502\pi\)
0.412939 + 0.910759i \(0.364502\pi\)
\(984\) 0 0
\(985\) −44.3820 −1.41413
\(986\) 0 0
\(987\) −47.3138 −1.50601
\(988\) 0 0
\(989\) −1.70667 −0.0542689
\(990\) 0 0
\(991\) −43.5439 −1.38322 −0.691609 0.722273i \(-0.743098\pi\)
−0.691609 + 0.722273i \(0.743098\pi\)
\(992\) 0 0
\(993\) 34.3313 1.08947
\(994\) 0 0
\(995\) 36.3853 1.15349
\(996\) 0 0
\(997\) −39.1973 −1.24139 −0.620695 0.784052i \(-0.713150\pi\)
−0.620695 + 0.784052i \(0.713150\pi\)
\(998\) 0 0
\(999\) 0.407293 0.0128862
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.be.1.7 11
4.3 odd 2 4008.2.a.k.1.7 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.k.1.7 11 4.3 odd 2
8016.2.a.be.1.7 11 1.1 even 1 trivial