Properties

Label 6008.2.a.b.1.17
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(1\)
Dimension: \(44\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.09930 q^{3} -2.74603 q^{5} +2.16897 q^{7} -1.79154 q^{9} +O(q^{10})\) \(q-1.09930 q^{3} -2.74603 q^{5} +2.16897 q^{7} -1.79154 q^{9} -1.58452 q^{11} -1.73180 q^{13} +3.01872 q^{15} +2.86954 q^{17} +1.23160 q^{19} -2.38435 q^{21} +1.19367 q^{23} +2.54071 q^{25} +5.26734 q^{27} -0.223779 q^{29} -1.89585 q^{31} +1.74187 q^{33} -5.95606 q^{35} +8.49852 q^{37} +1.90377 q^{39} -10.1205 q^{41} +6.87393 q^{43} +4.91962 q^{45} -2.10996 q^{47} -2.29559 q^{49} -3.15449 q^{51} +10.0047 q^{53} +4.35115 q^{55} -1.35390 q^{57} +4.74701 q^{59} -7.90097 q^{61} -3.88578 q^{63} +4.75557 q^{65} +3.43609 q^{67} -1.31221 q^{69} +11.9228 q^{71} -10.4927 q^{73} -2.79300 q^{75} -3.43677 q^{77} -4.30406 q^{79} -0.415792 q^{81} +17.4052 q^{83} -7.87986 q^{85} +0.246001 q^{87} +6.11597 q^{89} -3.75621 q^{91} +2.08411 q^{93} -3.38201 q^{95} -4.33364 q^{97} +2.83873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −1.09930 −0.634682 −0.317341 0.948311i \(-0.602790\pi\)
−0.317341 + 0.948311i \(0.602790\pi\)
\(4\) 0 0
\(5\) −2.74603 −1.22806 −0.614032 0.789281i \(-0.710453\pi\)
−0.614032 + 0.789281i \(0.710453\pi\)
\(6\) 0 0
\(7\) 2.16897 0.819792 0.409896 0.912132i \(-0.365565\pi\)
0.409896 + 0.912132i \(0.365565\pi\)
\(8\) 0 0
\(9\) −1.79154 −0.597179
\(10\) 0 0
\(11\) −1.58452 −0.477751 −0.238876 0.971050i \(-0.576779\pi\)
−0.238876 + 0.971050i \(0.576779\pi\)
\(12\) 0 0
\(13\) −1.73180 −0.480314 −0.240157 0.970734i \(-0.577199\pi\)
−0.240157 + 0.970734i \(0.577199\pi\)
\(14\) 0 0
\(15\) 3.01872 0.779430
\(16\) 0 0
\(17\) 2.86954 0.695966 0.347983 0.937501i \(-0.386867\pi\)
0.347983 + 0.937501i \(0.386867\pi\)
\(18\) 0 0
\(19\) 1.23160 0.282548 0.141274 0.989971i \(-0.454880\pi\)
0.141274 + 0.989971i \(0.454880\pi\)
\(20\) 0 0
\(21\) −2.38435 −0.520307
\(22\) 0 0
\(23\) 1.19367 0.248898 0.124449 0.992226i \(-0.460284\pi\)
0.124449 + 0.992226i \(0.460284\pi\)
\(24\) 0 0
\(25\) 2.54071 0.508142
\(26\) 0 0
\(27\) 5.26734 1.01370
\(28\) 0 0
\(29\) −0.223779 −0.0415548 −0.0207774 0.999784i \(-0.506614\pi\)
−0.0207774 + 0.999784i \(0.506614\pi\)
\(30\) 0 0
\(31\) −1.89585 −0.340505 −0.170253 0.985400i \(-0.554458\pi\)
−0.170253 + 0.985400i \(0.554458\pi\)
\(32\) 0 0
\(33\) 1.74187 0.303220
\(34\) 0 0
\(35\) −5.95606 −1.00676
\(36\) 0 0
\(37\) 8.49852 1.39715 0.698574 0.715538i \(-0.253818\pi\)
0.698574 + 0.715538i \(0.253818\pi\)
\(38\) 0 0
\(39\) 1.90377 0.304846
\(40\) 0 0
\(41\) −10.1205 −1.58056 −0.790280 0.612745i \(-0.790065\pi\)
−0.790280 + 0.612745i \(0.790065\pi\)
\(42\) 0 0
\(43\) 6.87393 1.04826 0.524132 0.851637i \(-0.324390\pi\)
0.524132 + 0.851637i \(0.324390\pi\)
\(44\) 0 0
\(45\) 4.91962 0.733374
\(46\) 0 0
\(47\) −2.10996 −0.307769 −0.153885 0.988089i \(-0.549178\pi\)
−0.153885 + 0.988089i \(0.549178\pi\)
\(48\) 0 0
\(49\) −2.29559 −0.327941
\(50\) 0 0
\(51\) −3.15449 −0.441717
\(52\) 0 0
\(53\) 10.0047 1.37425 0.687127 0.726537i \(-0.258872\pi\)
0.687127 + 0.726537i \(0.258872\pi\)
\(54\) 0 0
\(55\) 4.35115 0.586709
\(56\) 0 0
\(57\) −1.35390 −0.179328
\(58\) 0 0
\(59\) 4.74701 0.618008 0.309004 0.951061i \(-0.400004\pi\)
0.309004 + 0.951061i \(0.400004\pi\)
\(60\) 0 0
\(61\) −7.90097 −1.01162 −0.505808 0.862646i \(-0.668806\pi\)
−0.505808 + 0.862646i \(0.668806\pi\)
\(62\) 0 0
\(63\) −3.88578 −0.489562
\(64\) 0 0
\(65\) 4.75557 0.589856
\(66\) 0 0
\(67\) 3.43609 0.419785 0.209893 0.977724i \(-0.432689\pi\)
0.209893 + 0.977724i \(0.432689\pi\)
\(68\) 0 0
\(69\) −1.31221 −0.157971
\(70\) 0 0
\(71\) 11.9228 1.41497 0.707487 0.706727i \(-0.249829\pi\)
0.707487 + 0.706727i \(0.249829\pi\)
\(72\) 0 0
\(73\) −10.4927 −1.22808 −0.614038 0.789276i \(-0.710456\pi\)
−0.614038 + 0.789276i \(0.710456\pi\)
\(74\) 0 0
\(75\) −2.79300 −0.322508
\(76\) 0 0
\(77\) −3.43677 −0.391657
\(78\) 0 0
\(79\) −4.30406 −0.484244 −0.242122 0.970246i \(-0.577843\pi\)
−0.242122 + 0.970246i \(0.577843\pi\)
\(80\) 0 0
\(81\) −0.415792 −0.0461991
\(82\) 0 0
\(83\) 17.4052 1.91047 0.955235 0.295849i \(-0.0956025\pi\)
0.955235 + 0.295849i \(0.0956025\pi\)
\(84\) 0 0
\(85\) −7.87986 −0.854691
\(86\) 0 0
\(87\) 0.246001 0.0263741
\(88\) 0 0
\(89\) 6.11597 0.648292 0.324146 0.946007i \(-0.394923\pi\)
0.324146 + 0.946007i \(0.394923\pi\)
\(90\) 0 0
\(91\) −3.75621 −0.393757
\(92\) 0 0
\(93\) 2.08411 0.216113
\(94\) 0 0
\(95\) −3.38201 −0.346987
\(96\) 0 0
\(97\) −4.33364 −0.440014 −0.220007 0.975498i \(-0.570608\pi\)
−0.220007 + 0.975498i \(0.570608\pi\)
\(98\) 0 0
\(99\) 2.83873 0.285303
\(100\) 0 0
\(101\) −8.97014 −0.892562 −0.446281 0.894893i \(-0.647252\pi\)
−0.446281 + 0.894893i \(0.647252\pi\)
\(102\) 0 0
\(103\) −18.0865 −1.78212 −0.891059 0.453888i \(-0.850037\pi\)
−0.891059 + 0.453888i \(0.850037\pi\)
\(104\) 0 0
\(105\) 6.54750 0.638971
\(106\) 0 0
\(107\) 15.4337 1.49203 0.746017 0.665927i \(-0.231964\pi\)
0.746017 + 0.665927i \(0.231964\pi\)
\(108\) 0 0
\(109\) −5.54369 −0.530989 −0.265495 0.964112i \(-0.585535\pi\)
−0.265495 + 0.964112i \(0.585535\pi\)
\(110\) 0 0
\(111\) −9.34244 −0.886745
\(112\) 0 0
\(113\) 12.8618 1.20994 0.604968 0.796250i \(-0.293186\pi\)
0.604968 + 0.796250i \(0.293186\pi\)
\(114\) 0 0
\(115\) −3.27787 −0.305663
\(116\) 0 0
\(117\) 3.10257 0.286833
\(118\) 0 0
\(119\) 6.22394 0.570547
\(120\) 0 0
\(121\) −8.48929 −0.771754
\(122\) 0 0
\(123\) 11.1255 1.00315
\(124\) 0 0
\(125\) 6.75330 0.604034
\(126\) 0 0
\(127\) −9.77630 −0.867506 −0.433753 0.901032i \(-0.642811\pi\)
−0.433753 + 0.901032i \(0.642811\pi\)
\(128\) 0 0
\(129\) −7.55652 −0.665315
\(130\) 0 0
\(131\) −14.9727 −1.30817 −0.654084 0.756422i \(-0.726946\pi\)
−0.654084 + 0.756422i \(0.726946\pi\)
\(132\) 0 0
\(133\) 2.67130 0.231631
\(134\) 0 0
\(135\) −14.4643 −1.24489
\(136\) 0 0
\(137\) 2.50628 0.214126 0.107063 0.994252i \(-0.465855\pi\)
0.107063 + 0.994252i \(0.465855\pi\)
\(138\) 0 0
\(139\) −13.1374 −1.11430 −0.557150 0.830412i \(-0.688105\pi\)
−0.557150 + 0.830412i \(0.688105\pi\)
\(140\) 0 0
\(141\) 2.31948 0.195336
\(142\) 0 0
\(143\) 2.74407 0.229470
\(144\) 0 0
\(145\) 0.614506 0.0510320
\(146\) 0 0
\(147\) 2.52354 0.208138
\(148\) 0 0
\(149\) 6.30286 0.516350 0.258175 0.966098i \(-0.416879\pi\)
0.258175 + 0.966098i \(0.416879\pi\)
\(150\) 0 0
\(151\) −19.7337 −1.60591 −0.802954 0.596041i \(-0.796740\pi\)
−0.802954 + 0.596041i \(0.796740\pi\)
\(152\) 0 0
\(153\) −5.14089 −0.415616
\(154\) 0 0
\(155\) 5.20608 0.418162
\(156\) 0 0
\(157\) 3.27204 0.261137 0.130569 0.991439i \(-0.458320\pi\)
0.130569 + 0.991439i \(0.458320\pi\)
\(158\) 0 0
\(159\) −10.9982 −0.872215
\(160\) 0 0
\(161\) 2.58904 0.204045
\(162\) 0 0
\(163\) −12.7780 −1.00085 −0.500425 0.865780i \(-0.666823\pi\)
−0.500425 + 0.865780i \(0.666823\pi\)
\(164\) 0 0
\(165\) −4.78323 −0.372374
\(166\) 0 0
\(167\) 8.37846 0.648344 0.324172 0.945998i \(-0.394914\pi\)
0.324172 + 0.945998i \(0.394914\pi\)
\(168\) 0 0
\(169\) −10.0009 −0.769299
\(170\) 0 0
\(171\) −2.20645 −0.168732
\(172\) 0 0
\(173\) 17.0971 1.29987 0.649934 0.759990i \(-0.274796\pi\)
0.649934 + 0.759990i \(0.274796\pi\)
\(174\) 0 0
\(175\) 5.51071 0.416570
\(176\) 0 0
\(177\) −5.21840 −0.392239
\(178\) 0 0
\(179\) −6.01037 −0.449237 −0.224618 0.974447i \(-0.572114\pi\)
−0.224618 + 0.974447i \(0.572114\pi\)
\(180\) 0 0
\(181\) 2.72597 0.202620 0.101310 0.994855i \(-0.467697\pi\)
0.101310 + 0.994855i \(0.467697\pi\)
\(182\) 0 0
\(183\) 8.68555 0.642054
\(184\) 0 0
\(185\) −23.3372 −1.71579
\(186\) 0 0
\(187\) −4.54685 −0.332499
\(188\) 0 0
\(189\) 11.4247 0.831024
\(190\) 0 0
\(191\) −11.7434 −0.849725 −0.424862 0.905258i \(-0.639678\pi\)
−0.424862 + 0.905258i \(0.639678\pi\)
\(192\) 0 0
\(193\) −7.73685 −0.556911 −0.278455 0.960449i \(-0.589822\pi\)
−0.278455 + 0.960449i \(0.589822\pi\)
\(194\) 0 0
\(195\) −5.22781 −0.374371
\(196\) 0 0
\(197\) −8.37966 −0.597026 −0.298513 0.954406i \(-0.596491\pi\)
−0.298513 + 0.954406i \(0.596491\pi\)
\(198\) 0 0
\(199\) −11.7130 −0.830310 −0.415155 0.909751i \(-0.636273\pi\)
−0.415155 + 0.909751i \(0.636273\pi\)
\(200\) 0 0
\(201\) −3.77730 −0.266430
\(202\) 0 0
\(203\) −0.485370 −0.0340663
\(204\) 0 0
\(205\) 27.7913 1.94103
\(206\) 0 0
\(207\) −2.13851 −0.148637
\(208\) 0 0
\(209\) −1.95149 −0.134988
\(210\) 0 0
\(211\) 3.02947 0.208557 0.104279 0.994548i \(-0.466747\pi\)
0.104279 + 0.994548i \(0.466747\pi\)
\(212\) 0 0
\(213\) −13.1067 −0.898058
\(214\) 0 0
\(215\) −18.8760 −1.28734
\(216\) 0 0
\(217\) −4.11204 −0.279144
\(218\) 0 0
\(219\) 11.5346 0.779438
\(220\) 0 0
\(221\) −4.96946 −0.334282
\(222\) 0 0
\(223\) 11.2040 0.750272 0.375136 0.926970i \(-0.377596\pi\)
0.375136 + 0.926970i \(0.377596\pi\)
\(224\) 0 0
\(225\) −4.55177 −0.303451
\(226\) 0 0
\(227\) −16.3342 −1.08414 −0.542069 0.840334i \(-0.682359\pi\)
−0.542069 + 0.840334i \(0.682359\pi\)
\(228\) 0 0
\(229\) 22.5748 1.49179 0.745893 0.666066i \(-0.232023\pi\)
0.745893 + 0.666066i \(0.232023\pi\)
\(230\) 0 0
\(231\) 3.77805 0.248577
\(232\) 0 0
\(233\) 2.64135 0.173041 0.0865204 0.996250i \(-0.472425\pi\)
0.0865204 + 0.996250i \(0.472425\pi\)
\(234\) 0 0
\(235\) 5.79402 0.377960
\(236\) 0 0
\(237\) 4.73146 0.307341
\(238\) 0 0
\(239\) 4.24441 0.274548 0.137274 0.990533i \(-0.456166\pi\)
0.137274 + 0.990533i \(0.456166\pi\)
\(240\) 0 0
\(241\) 17.2000 1.10795 0.553975 0.832534i \(-0.313110\pi\)
0.553975 + 0.832534i \(0.313110\pi\)
\(242\) 0 0
\(243\) −15.3449 −0.984379
\(244\) 0 0
\(245\) 6.30376 0.402732
\(246\) 0 0
\(247\) −2.13288 −0.135712
\(248\) 0 0
\(249\) −19.1336 −1.21254
\(250\) 0 0
\(251\) −11.0296 −0.696184 −0.348092 0.937460i \(-0.613170\pi\)
−0.348092 + 0.937460i \(0.613170\pi\)
\(252\) 0 0
\(253\) −1.89140 −0.118911
\(254\) 0 0
\(255\) 8.66234 0.542457
\(256\) 0 0
\(257\) −3.98414 −0.248524 −0.124262 0.992249i \(-0.539656\pi\)
−0.124262 + 0.992249i \(0.539656\pi\)
\(258\) 0 0
\(259\) 18.4330 1.14537
\(260\) 0 0
\(261\) 0.400909 0.0248156
\(262\) 0 0
\(263\) −14.8103 −0.913244 −0.456622 0.889661i \(-0.650941\pi\)
−0.456622 + 0.889661i \(0.650941\pi\)
\(264\) 0 0
\(265\) −27.4733 −1.68767
\(266\) 0 0
\(267\) −6.72330 −0.411459
\(268\) 0 0
\(269\) −24.3355 −1.48376 −0.741882 0.670531i \(-0.766066\pi\)
−0.741882 + 0.670531i \(0.766066\pi\)
\(270\) 0 0
\(271\) −19.6056 −1.19096 −0.595479 0.803371i \(-0.703038\pi\)
−0.595479 + 0.803371i \(0.703038\pi\)
\(272\) 0 0
\(273\) 4.12920 0.249911
\(274\) 0 0
\(275\) −4.02581 −0.242765
\(276\) 0 0
\(277\) 27.7508 1.66738 0.833691 0.552231i \(-0.186223\pi\)
0.833691 + 0.552231i \(0.186223\pi\)
\(278\) 0 0
\(279\) 3.39649 0.203343
\(280\) 0 0
\(281\) −8.25163 −0.492251 −0.246126 0.969238i \(-0.579158\pi\)
−0.246126 + 0.969238i \(0.579158\pi\)
\(282\) 0 0
\(283\) −15.4690 −0.919539 −0.459770 0.888038i \(-0.652068\pi\)
−0.459770 + 0.888038i \(0.652068\pi\)
\(284\) 0 0
\(285\) 3.71785 0.220227
\(286\) 0 0
\(287\) −21.9511 −1.29573
\(288\) 0 0
\(289\) −8.76573 −0.515631
\(290\) 0 0
\(291\) 4.76398 0.279269
\(292\) 0 0
\(293\) 12.2695 0.716790 0.358395 0.933570i \(-0.383324\pi\)
0.358395 + 0.933570i \(0.383324\pi\)
\(294\) 0 0
\(295\) −13.0355 −0.758954
\(296\) 0 0
\(297\) −8.34622 −0.484297
\(298\) 0 0
\(299\) −2.06720 −0.119549
\(300\) 0 0
\(301\) 14.9093 0.859359
\(302\) 0 0
\(303\) 9.86089 0.566493
\(304\) 0 0
\(305\) 21.6963 1.24233
\(306\) 0 0
\(307\) −6.68631 −0.381608 −0.190804 0.981628i \(-0.561109\pi\)
−0.190804 + 0.981628i \(0.561109\pi\)
\(308\) 0 0
\(309\) 19.8825 1.13108
\(310\) 0 0
\(311\) 1.04846 0.0594526 0.0297263 0.999558i \(-0.490536\pi\)
0.0297263 + 0.999558i \(0.490536\pi\)
\(312\) 0 0
\(313\) 16.0115 0.905026 0.452513 0.891758i \(-0.350528\pi\)
0.452513 + 0.891758i \(0.350528\pi\)
\(314\) 0 0
\(315\) 10.6705 0.601214
\(316\) 0 0
\(317\) 18.1094 1.01712 0.508562 0.861025i \(-0.330177\pi\)
0.508562 + 0.861025i \(0.330177\pi\)
\(318\) 0 0
\(319\) 0.354583 0.0198529
\(320\) 0 0
\(321\) −16.9663 −0.946967
\(322\) 0 0
\(323\) 3.53412 0.196644
\(324\) 0 0
\(325\) −4.39999 −0.244067
\(326\) 0 0
\(327\) 6.09419 0.337009
\(328\) 0 0
\(329\) −4.57643 −0.252307
\(330\) 0 0
\(331\) 24.7980 1.36302 0.681509 0.731809i \(-0.261324\pi\)
0.681509 + 0.731809i \(0.261324\pi\)
\(332\) 0 0
\(333\) −15.2254 −0.834347
\(334\) 0 0
\(335\) −9.43562 −0.515523
\(336\) 0 0
\(337\) −32.2436 −1.75642 −0.878212 0.478272i \(-0.841263\pi\)
−0.878212 + 0.478272i \(0.841263\pi\)
\(338\) 0 0
\(339\) −14.1390 −0.767924
\(340\) 0 0
\(341\) 3.00402 0.162677
\(342\) 0 0
\(343\) −20.1618 −1.08864
\(344\) 0 0
\(345\) 3.60337 0.193999
\(346\) 0 0
\(347\) −24.8657 −1.33486 −0.667431 0.744672i \(-0.732606\pi\)
−0.667431 + 0.744672i \(0.732606\pi\)
\(348\) 0 0
\(349\) −20.9262 −1.12015 −0.560077 0.828441i \(-0.689228\pi\)
−0.560077 + 0.828441i \(0.689228\pi\)
\(350\) 0 0
\(351\) −9.12196 −0.486894
\(352\) 0 0
\(353\) 0.785093 0.0417863 0.0208932 0.999782i \(-0.493349\pi\)
0.0208932 + 0.999782i \(0.493349\pi\)
\(354\) 0 0
\(355\) −32.7404 −1.73768
\(356\) 0 0
\(357\) −6.84199 −0.362116
\(358\) 0 0
\(359\) −20.9711 −1.10681 −0.553406 0.832912i \(-0.686672\pi\)
−0.553406 + 0.832912i \(0.686672\pi\)
\(360\) 0 0
\(361\) −17.4832 −0.920167
\(362\) 0 0
\(363\) 9.33229 0.489818
\(364\) 0 0
\(365\) 28.8133 1.50816
\(366\) 0 0
\(367\) −36.2502 −1.89224 −0.946122 0.323811i \(-0.895036\pi\)
−0.946122 + 0.323811i \(0.895036\pi\)
\(368\) 0 0
\(369\) 18.1313 0.943877
\(370\) 0 0
\(371\) 21.6999 1.12660
\(372\) 0 0
\(373\) −18.7117 −0.968855 −0.484427 0.874831i \(-0.660972\pi\)
−0.484427 + 0.874831i \(0.660972\pi\)
\(374\) 0 0
\(375\) −7.42392 −0.383369
\(376\) 0 0
\(377\) 0.387540 0.0199593
\(378\) 0 0
\(379\) 16.5080 0.847957 0.423979 0.905672i \(-0.360633\pi\)
0.423979 + 0.905672i \(0.360633\pi\)
\(380\) 0 0
\(381\) 10.7471 0.550591
\(382\) 0 0
\(383\) 21.7893 1.11338 0.556690 0.830720i \(-0.312071\pi\)
0.556690 + 0.830720i \(0.312071\pi\)
\(384\) 0 0
\(385\) 9.43750 0.480979
\(386\) 0 0
\(387\) −12.3149 −0.626001
\(388\) 0 0
\(389\) 9.66257 0.489912 0.244956 0.969534i \(-0.421227\pi\)
0.244956 + 0.969534i \(0.421227\pi\)
\(390\) 0 0
\(391\) 3.42530 0.173225
\(392\) 0 0
\(393\) 16.4595 0.830271
\(394\) 0 0
\(395\) 11.8191 0.594683
\(396\) 0 0
\(397\) −14.6358 −0.734548 −0.367274 0.930113i \(-0.619709\pi\)
−0.367274 + 0.930113i \(0.619709\pi\)
\(398\) 0 0
\(399\) −2.93656 −0.147012
\(400\) 0 0
\(401\) −19.3109 −0.964341 −0.482170 0.876077i \(-0.660151\pi\)
−0.482170 + 0.876077i \(0.660151\pi\)
\(402\) 0 0
\(403\) 3.28323 0.163549
\(404\) 0 0
\(405\) 1.14178 0.0567355
\(406\) 0 0
\(407\) −13.4661 −0.667489
\(408\) 0 0
\(409\) 27.9970 1.38436 0.692182 0.721723i \(-0.256649\pi\)
0.692182 + 0.721723i \(0.256649\pi\)
\(410\) 0 0
\(411\) −2.75516 −0.135902
\(412\) 0 0
\(413\) 10.2961 0.506638
\(414\) 0 0
\(415\) −47.7953 −2.34618
\(416\) 0 0
\(417\) 14.4420 0.707226
\(418\) 0 0
\(419\) −30.7660 −1.50302 −0.751508 0.659724i \(-0.770673\pi\)
−0.751508 + 0.659724i \(0.770673\pi\)
\(420\) 0 0
\(421\) −31.1246 −1.51692 −0.758459 0.651720i \(-0.774048\pi\)
−0.758459 + 0.651720i \(0.774048\pi\)
\(422\) 0 0
\(423\) 3.78007 0.183793
\(424\) 0 0
\(425\) 7.29067 0.353649
\(426\) 0 0
\(427\) −17.1369 −0.829315
\(428\) 0 0
\(429\) −3.01656 −0.145641
\(430\) 0 0
\(431\) −39.5001 −1.90265 −0.951327 0.308182i \(-0.900279\pi\)
−0.951327 + 0.308182i \(0.900279\pi\)
\(432\) 0 0
\(433\) 29.8505 1.43452 0.717261 0.696805i \(-0.245396\pi\)
0.717261 + 0.696805i \(0.245396\pi\)
\(434\) 0 0
\(435\) −0.675528 −0.0323891
\(436\) 0 0
\(437\) 1.47013 0.0703258
\(438\) 0 0
\(439\) 25.1976 1.20262 0.601308 0.799017i \(-0.294646\pi\)
0.601308 + 0.799017i \(0.294646\pi\)
\(440\) 0 0
\(441\) 4.11262 0.195839
\(442\) 0 0
\(443\) 10.1704 0.483212 0.241606 0.970374i \(-0.422326\pi\)
0.241606 + 0.970374i \(0.422326\pi\)
\(444\) 0 0
\(445\) −16.7947 −0.796144
\(446\) 0 0
\(447\) −6.92874 −0.327718
\(448\) 0 0
\(449\) −31.8335 −1.50232 −0.751158 0.660123i \(-0.770504\pi\)
−0.751158 + 0.660123i \(0.770504\pi\)
\(450\) 0 0
\(451\) 16.0362 0.755115
\(452\) 0 0
\(453\) 21.6933 1.01924
\(454\) 0 0
\(455\) 10.3147 0.483559
\(456\) 0 0
\(457\) 23.9539 1.12052 0.560258 0.828318i \(-0.310702\pi\)
0.560258 + 0.828318i \(0.310702\pi\)
\(458\) 0 0
\(459\) 15.1149 0.705501
\(460\) 0 0
\(461\) −7.67836 −0.357617 −0.178808 0.983884i \(-0.557224\pi\)
−0.178808 + 0.983884i \(0.557224\pi\)
\(462\) 0 0
\(463\) 10.6720 0.495969 0.247984 0.968764i \(-0.420232\pi\)
0.247984 + 0.968764i \(0.420232\pi\)
\(464\) 0 0
\(465\) −5.72305 −0.265400
\(466\) 0 0
\(467\) −1.31574 −0.0608854 −0.0304427 0.999537i \(-0.509692\pi\)
−0.0304427 + 0.999537i \(0.509692\pi\)
\(468\) 0 0
\(469\) 7.45276 0.344137
\(470\) 0 0
\(471\) −3.59696 −0.165739
\(472\) 0 0
\(473\) −10.8919 −0.500809
\(474\) 0 0
\(475\) 3.12913 0.143574
\(476\) 0 0
\(477\) −17.9238 −0.820675
\(478\) 0 0
\(479\) −26.0250 −1.18911 −0.594557 0.804053i \(-0.702673\pi\)
−0.594557 + 0.804053i \(0.702673\pi\)
\(480\) 0 0
\(481\) −14.7177 −0.671069
\(482\) 0 0
\(483\) −2.84614 −0.129504
\(484\) 0 0
\(485\) 11.9003 0.540366
\(486\) 0 0
\(487\) 36.4637 1.65233 0.826164 0.563430i \(-0.190519\pi\)
0.826164 + 0.563430i \(0.190519\pi\)
\(488\) 0 0
\(489\) 14.0469 0.635222
\(490\) 0 0
\(491\) −26.9479 −1.21614 −0.608070 0.793883i \(-0.708056\pi\)
−0.608070 + 0.793883i \(0.708056\pi\)
\(492\) 0 0
\(493\) −0.642144 −0.0289207
\(494\) 0 0
\(495\) −7.79524 −0.350370
\(496\) 0 0
\(497\) 25.8601 1.15998
\(498\) 0 0
\(499\) −22.4133 −1.00336 −0.501678 0.865055i \(-0.667284\pi\)
−0.501678 + 0.865055i \(0.667284\pi\)
\(500\) 0 0
\(501\) −9.21045 −0.411493
\(502\) 0 0
\(503\) 8.78473 0.391692 0.195846 0.980635i \(-0.437255\pi\)
0.195846 + 0.980635i \(0.437255\pi\)
\(504\) 0 0
\(505\) 24.6323 1.09612
\(506\) 0 0
\(507\) 10.9940 0.488260
\(508\) 0 0
\(509\) −40.6673 −1.80255 −0.901273 0.433252i \(-0.857366\pi\)
−0.901273 + 0.433252i \(0.857366\pi\)
\(510\) 0 0
\(511\) −22.7583 −1.00677
\(512\) 0 0
\(513\) 6.48725 0.286419
\(514\) 0 0
\(515\) 49.6662 2.18855
\(516\) 0 0
\(517\) 3.34328 0.147037
\(518\) 0 0
\(519\) −18.7949 −0.825003
\(520\) 0 0
\(521\) −40.6019 −1.77880 −0.889400 0.457130i \(-0.848877\pi\)
−0.889400 + 0.457130i \(0.848877\pi\)
\(522\) 0 0
\(523\) −35.3124 −1.54410 −0.772052 0.635559i \(-0.780770\pi\)
−0.772052 + 0.635559i \(0.780770\pi\)
\(524\) 0 0
\(525\) −6.05793 −0.264390
\(526\) 0 0
\(527\) −5.44023 −0.236980
\(528\) 0 0
\(529\) −21.5751 −0.938050
\(530\) 0 0
\(531\) −8.50444 −0.369061
\(532\) 0 0
\(533\) 17.5267 0.759165
\(534\) 0 0
\(535\) −42.3815 −1.83231
\(536\) 0 0
\(537\) 6.60722 0.285122
\(538\) 0 0
\(539\) 3.63740 0.156674
\(540\) 0 0
\(541\) −5.07096 −0.218018 −0.109009 0.994041i \(-0.534768\pi\)
−0.109009 + 0.994041i \(0.534768\pi\)
\(542\) 0 0
\(543\) −2.99666 −0.128599
\(544\) 0 0
\(545\) 15.2232 0.652089
\(546\) 0 0
\(547\) −1.61212 −0.0689291 −0.0344646 0.999406i \(-0.510973\pi\)
−0.0344646 + 0.999406i \(0.510973\pi\)
\(548\) 0 0
\(549\) 14.1549 0.604115
\(550\) 0 0
\(551\) −0.275606 −0.0117412
\(552\) 0 0
\(553\) −9.33535 −0.396980
\(554\) 0 0
\(555\) 25.6547 1.08898
\(556\) 0 0
\(557\) 12.4610 0.527988 0.263994 0.964524i \(-0.414960\pi\)
0.263994 + 0.964524i \(0.414960\pi\)
\(558\) 0 0
\(559\) −11.9042 −0.503496
\(560\) 0 0
\(561\) 4.99836 0.211031
\(562\) 0 0
\(563\) −10.7354 −0.452442 −0.226221 0.974076i \(-0.572637\pi\)
−0.226221 + 0.974076i \(0.572637\pi\)
\(564\) 0 0
\(565\) −35.3189 −1.48588
\(566\) 0 0
\(567\) −0.901839 −0.0378737
\(568\) 0 0
\(569\) 43.9395 1.84204 0.921020 0.389515i \(-0.127357\pi\)
0.921020 + 0.389515i \(0.127357\pi\)
\(570\) 0 0
\(571\) 6.99777 0.292848 0.146424 0.989222i \(-0.453224\pi\)
0.146424 + 0.989222i \(0.453224\pi\)
\(572\) 0 0
\(573\) 12.9096 0.539305
\(574\) 0 0
\(575\) 3.03278 0.126476
\(576\) 0 0
\(577\) −8.57486 −0.356976 −0.178488 0.983942i \(-0.557121\pi\)
−0.178488 + 0.983942i \(0.557121\pi\)
\(578\) 0 0
\(579\) 8.50514 0.353461
\(580\) 0 0
\(581\) 37.7513 1.56619
\(582\) 0 0
\(583\) −15.8527 −0.656551
\(584\) 0 0
\(585\) −8.51977 −0.352249
\(586\) 0 0
\(587\) −43.1314 −1.78022 −0.890111 0.455744i \(-0.849373\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(588\) 0 0
\(589\) −2.33493 −0.0962091
\(590\) 0 0
\(591\) 9.21177 0.378922
\(592\) 0 0
\(593\) 29.5291 1.21261 0.606306 0.795231i \(-0.292650\pi\)
0.606306 + 0.795231i \(0.292650\pi\)
\(594\) 0 0
\(595\) −17.0912 −0.700669
\(596\) 0 0
\(597\) 12.8761 0.526983
\(598\) 0 0
\(599\) 37.9585 1.55094 0.775471 0.631383i \(-0.217512\pi\)
0.775471 + 0.631383i \(0.217512\pi\)
\(600\) 0 0
\(601\) 0.0309671 0.00126318 0.000631588 1.00000i \(-0.499799\pi\)
0.000631588 1.00000i \(0.499799\pi\)
\(602\) 0 0
\(603\) −6.15588 −0.250687
\(604\) 0 0
\(605\) 23.3119 0.947763
\(606\) 0 0
\(607\) 12.6469 0.513323 0.256662 0.966501i \(-0.417377\pi\)
0.256662 + 0.966501i \(0.417377\pi\)
\(608\) 0 0
\(609\) 0.533568 0.0216213
\(610\) 0 0
\(611\) 3.65402 0.147826
\(612\) 0 0
\(613\) −30.5519 −1.23398 −0.616989 0.786971i \(-0.711648\pi\)
−0.616989 + 0.786971i \(0.711648\pi\)
\(614\) 0 0
\(615\) −30.5510 −1.23194
\(616\) 0 0
\(617\) −26.5044 −1.06703 −0.533513 0.845792i \(-0.679128\pi\)
−0.533513 + 0.845792i \(0.679128\pi\)
\(618\) 0 0
\(619\) −47.5115 −1.90965 −0.954824 0.297172i \(-0.903957\pi\)
−0.954824 + 0.297172i \(0.903957\pi\)
\(620\) 0 0
\(621\) 6.28750 0.252309
\(622\) 0 0
\(623\) 13.2653 0.531465
\(624\) 0 0
\(625\) −31.2483 −1.24993
\(626\) 0 0
\(627\) 2.14528 0.0856743
\(628\) 0 0
\(629\) 24.3869 0.972368
\(630\) 0 0
\(631\) −0.276788 −0.0110187 −0.00550937 0.999985i \(-0.501754\pi\)
−0.00550937 + 0.999985i \(0.501754\pi\)
\(632\) 0 0
\(633\) −3.33030 −0.132368
\(634\) 0 0
\(635\) 26.8461 1.06535
\(636\) 0 0
\(637\) 3.97548 0.157514
\(638\) 0 0
\(639\) −21.3601 −0.844992
\(640\) 0 0
\(641\) 43.7215 1.72690 0.863448 0.504438i \(-0.168300\pi\)
0.863448 + 0.504438i \(0.168300\pi\)
\(642\) 0 0
\(643\) −12.1504 −0.479166 −0.239583 0.970876i \(-0.577011\pi\)
−0.239583 + 0.970876i \(0.577011\pi\)
\(644\) 0 0
\(645\) 20.7505 0.817049
\(646\) 0 0
\(647\) 20.8906 0.821295 0.410647 0.911794i \(-0.365303\pi\)
0.410647 + 0.911794i \(0.365303\pi\)
\(648\) 0 0
\(649\) −7.52174 −0.295254
\(650\) 0 0
\(651\) 4.52037 0.177167
\(652\) 0 0
\(653\) −0.341625 −0.0133688 −0.00668441 0.999978i \(-0.502128\pi\)
−0.00668441 + 0.999978i \(0.502128\pi\)
\(654\) 0 0
\(655\) 41.1155 1.60651
\(656\) 0 0
\(657\) 18.7980 0.733381
\(658\) 0 0
\(659\) 15.9077 0.619675 0.309837 0.950790i \(-0.399725\pi\)
0.309837 + 0.950790i \(0.399725\pi\)
\(660\) 0 0
\(661\) 29.8124 1.15957 0.579784 0.814770i \(-0.303137\pi\)
0.579784 + 0.814770i \(0.303137\pi\)
\(662\) 0 0
\(663\) 5.46293 0.212163
\(664\) 0 0
\(665\) −7.33547 −0.284457
\(666\) 0 0
\(667\) −0.267120 −0.0103429
\(668\) 0 0
\(669\) −12.3165 −0.476185
\(670\) 0 0
\(671\) 12.5193 0.483301
\(672\) 0 0
\(673\) 33.7290 1.30016 0.650079 0.759867i \(-0.274736\pi\)
0.650079 + 0.759867i \(0.274736\pi\)
\(674\) 0 0
\(675\) 13.3828 0.515103
\(676\) 0 0
\(677\) −42.5081 −1.63372 −0.816859 0.576837i \(-0.804287\pi\)
−0.816859 + 0.576837i \(0.804287\pi\)
\(678\) 0 0
\(679\) −9.39952 −0.360720
\(680\) 0 0
\(681\) 17.9562 0.688083
\(682\) 0 0
\(683\) −43.2500 −1.65492 −0.827459 0.561527i \(-0.810214\pi\)
−0.827459 + 0.561527i \(0.810214\pi\)
\(684\) 0 0
\(685\) −6.88233 −0.262960
\(686\) 0 0
\(687\) −24.8165 −0.946809
\(688\) 0 0
\(689\) −17.3261 −0.660073
\(690\) 0 0
\(691\) 27.9817 1.06447 0.532236 0.846596i \(-0.321352\pi\)
0.532236 + 0.846596i \(0.321352\pi\)
\(692\) 0 0
\(693\) 6.15710 0.233889
\(694\) 0 0
\(695\) 36.0758 1.36843
\(696\) 0 0
\(697\) −29.0413 −1.10002
\(698\) 0 0
\(699\) −2.90364 −0.109826
\(700\) 0 0
\(701\) 13.9590 0.527226 0.263613 0.964629i \(-0.415086\pi\)
0.263613 + 0.964629i \(0.415086\pi\)
\(702\) 0 0
\(703\) 10.4668 0.394762
\(704\) 0 0
\(705\) −6.36938 −0.239885
\(706\) 0 0
\(707\) −19.4559 −0.731716
\(708\) 0 0
\(709\) −2.14351 −0.0805013 −0.0402506 0.999190i \(-0.512816\pi\)
−0.0402506 + 0.999190i \(0.512816\pi\)
\(710\) 0 0
\(711\) 7.71087 0.289180
\(712\) 0 0
\(713\) −2.26303 −0.0847512
\(714\) 0 0
\(715\) −7.53530 −0.281804
\(716\) 0 0
\(717\) −4.66588 −0.174251
\(718\) 0 0
\(719\) −12.2714 −0.457646 −0.228823 0.973468i \(-0.573488\pi\)
−0.228823 + 0.973468i \(0.573488\pi\)
\(720\) 0 0
\(721\) −39.2290 −1.46097
\(722\) 0 0
\(723\) −18.9080 −0.703195
\(724\) 0 0
\(725\) −0.568558 −0.0211157
\(726\) 0 0
\(727\) −3.20764 −0.118965 −0.0594824 0.998229i \(-0.518945\pi\)
−0.0594824 + 0.998229i \(0.518945\pi\)
\(728\) 0 0
\(729\) 18.1161 0.670967
\(730\) 0 0
\(731\) 19.7250 0.729556
\(732\) 0 0
\(733\) 10.1991 0.376711 0.188356 0.982101i \(-0.439684\pi\)
0.188356 + 0.982101i \(0.439684\pi\)
\(734\) 0 0
\(735\) −6.92973 −0.255607
\(736\) 0 0
\(737\) −5.44456 −0.200553
\(738\) 0 0
\(739\) 39.4814 1.45235 0.726174 0.687511i \(-0.241297\pi\)
0.726174 + 0.687511i \(0.241297\pi\)
\(740\) 0 0
\(741\) 2.34467 0.0861338
\(742\) 0 0
\(743\) 42.7144 1.56704 0.783520 0.621367i \(-0.213422\pi\)
0.783520 + 0.621367i \(0.213422\pi\)
\(744\) 0 0
\(745\) −17.3079 −0.634111
\(746\) 0 0
\(747\) −31.1820 −1.14089
\(748\) 0 0
\(749\) 33.4752 1.22316
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 12.1249 0.441855
\(754\) 0 0
\(755\) 54.1895 1.97216
\(756\) 0 0
\(757\) −21.6557 −0.787091 −0.393546 0.919305i \(-0.628752\pi\)
−0.393546 + 0.919305i \(0.628752\pi\)
\(758\) 0 0
\(759\) 2.07922 0.0754710
\(760\) 0 0
\(761\) 29.7939 1.08003 0.540013 0.841657i \(-0.318419\pi\)
0.540013 + 0.841657i \(0.318419\pi\)
\(762\) 0 0
\(763\) −12.0241 −0.435301
\(764\) 0 0
\(765\) 14.1171 0.510403
\(766\) 0 0
\(767\) −8.22085 −0.296838
\(768\) 0 0
\(769\) 10.4364 0.376348 0.188174 0.982136i \(-0.439743\pi\)
0.188174 + 0.982136i \(0.439743\pi\)
\(770\) 0 0
\(771\) 4.37977 0.157734
\(772\) 0 0
\(773\) 25.8927 0.931295 0.465648 0.884970i \(-0.345821\pi\)
0.465648 + 0.884970i \(0.345821\pi\)
\(774\) 0 0
\(775\) −4.81681 −0.173025
\(776\) 0 0
\(777\) −20.2634 −0.726947
\(778\) 0 0
\(779\) −12.4644 −0.446584
\(780\) 0 0
\(781\) −18.8919 −0.676005
\(782\) 0 0
\(783\) −1.17872 −0.0421241
\(784\) 0 0
\(785\) −8.98514 −0.320693
\(786\) 0 0
\(787\) 31.3764 1.11845 0.559224 0.829017i \(-0.311099\pi\)
0.559224 + 0.829017i \(0.311099\pi\)
\(788\) 0 0
\(789\) 16.2810 0.579619
\(790\) 0 0
\(791\) 27.8968 0.991896
\(792\) 0 0
\(793\) 13.6829 0.485893
\(794\) 0 0
\(795\) 30.2015 1.07114
\(796\) 0 0
\(797\) −30.5511 −1.08217 −0.541087 0.840966i \(-0.681987\pi\)
−0.541087 + 0.840966i \(0.681987\pi\)
\(798\) 0 0
\(799\) −6.05462 −0.214197
\(800\) 0 0
\(801\) −10.9570 −0.387146
\(802\) 0 0
\(803\) 16.6259 0.586715
\(804\) 0 0
\(805\) −7.10960 −0.250580
\(806\) 0 0
\(807\) 26.7521 0.941718
\(808\) 0 0
\(809\) 34.0041 1.19552 0.597760 0.801675i \(-0.296058\pi\)
0.597760 + 0.801675i \(0.296058\pi\)
\(810\) 0 0
\(811\) −16.6465 −0.584538 −0.292269 0.956336i \(-0.594410\pi\)
−0.292269 + 0.956336i \(0.594410\pi\)
\(812\) 0 0
\(813\) 21.5525 0.755879
\(814\) 0 0
\(815\) 35.0889 1.22911
\(816\) 0 0
\(817\) 8.46592 0.296185
\(818\) 0 0
\(819\) 6.72938 0.235143
\(820\) 0 0
\(821\) −3.44212 −0.120131 −0.0600655 0.998194i \(-0.519131\pi\)
−0.0600655 + 0.998194i \(0.519131\pi\)
\(822\) 0 0
\(823\) 37.5459 1.30877 0.654384 0.756163i \(-0.272928\pi\)
0.654384 + 0.756163i \(0.272928\pi\)
\(824\) 0 0
\(825\) 4.42557 0.154079
\(826\) 0 0
\(827\) 35.6422 1.23940 0.619700 0.784839i \(-0.287254\pi\)
0.619700 + 0.784839i \(0.287254\pi\)
\(828\) 0 0
\(829\) −11.8902 −0.412963 −0.206482 0.978450i \(-0.566201\pi\)
−0.206482 + 0.978450i \(0.566201\pi\)
\(830\) 0 0
\(831\) −30.5065 −1.05826
\(832\) 0 0
\(833\) −6.58728 −0.228236
\(834\) 0 0
\(835\) −23.0075 −0.796209
\(836\) 0 0
\(837\) −9.98611 −0.345171
\(838\) 0 0
\(839\) 47.2189 1.63018 0.815089 0.579335i \(-0.196688\pi\)
0.815089 + 0.579335i \(0.196688\pi\)
\(840\) 0 0
\(841\) −28.9499 −0.998273
\(842\) 0 0
\(843\) 9.07103 0.312423
\(844\) 0 0
\(845\) 27.4628 0.944748
\(846\) 0 0
\(847\) −18.4130 −0.632678
\(848\) 0 0
\(849\) 17.0051 0.583615
\(850\) 0 0
\(851\) 10.1445 0.347748
\(852\) 0 0
\(853\) 42.9014 1.46892 0.734458 0.678654i \(-0.237436\pi\)
0.734458 + 0.678654i \(0.237436\pi\)
\(854\) 0 0
\(855\) 6.05900 0.207213
\(856\) 0 0
\(857\) −21.4026 −0.731099 −0.365549 0.930792i \(-0.619119\pi\)
−0.365549 + 0.930792i \(0.619119\pi\)
\(858\) 0 0
\(859\) 6.70785 0.228869 0.114434 0.993431i \(-0.463494\pi\)
0.114434 + 0.993431i \(0.463494\pi\)
\(860\) 0 0
\(861\) 24.1309 0.822377
\(862\) 0 0
\(863\) 46.3084 1.57636 0.788178 0.615448i \(-0.211025\pi\)
0.788178 + 0.615448i \(0.211025\pi\)
\(864\) 0 0
\(865\) −46.9492 −1.59632
\(866\) 0 0
\(867\) 9.63618 0.327262
\(868\) 0 0
\(869\) 6.81987 0.231348
\(870\) 0 0
\(871\) −5.95060 −0.201629
\(872\) 0 0
\(873\) 7.76387 0.262767
\(874\) 0 0
\(875\) 14.6477 0.495182
\(876\) 0 0
\(877\) 21.2141 0.716351 0.358175 0.933654i \(-0.383399\pi\)
0.358175 + 0.933654i \(0.383399\pi\)
\(878\) 0 0
\(879\) −13.4878 −0.454934
\(880\) 0 0
\(881\) 25.0157 0.842800 0.421400 0.906875i \(-0.361539\pi\)
0.421400 + 0.906875i \(0.361539\pi\)
\(882\) 0 0
\(883\) 14.1355 0.475699 0.237849 0.971302i \(-0.423557\pi\)
0.237849 + 0.971302i \(0.423557\pi\)
\(884\) 0 0
\(885\) 14.3299 0.481694
\(886\) 0 0
\(887\) −18.9050 −0.634769 −0.317384 0.948297i \(-0.602805\pi\)
−0.317384 + 0.948297i \(0.602805\pi\)
\(888\) 0 0
\(889\) −21.2045 −0.711175
\(890\) 0 0
\(891\) 0.658831 0.0220717
\(892\) 0 0
\(893\) −2.59862 −0.0869596
\(894\) 0 0
\(895\) 16.5047 0.551691
\(896\) 0 0
\(897\) 2.27248 0.0758758
\(898\) 0 0
\(899\) 0.424253 0.0141496
\(900\) 0 0
\(901\) 28.7090 0.956434
\(902\) 0 0
\(903\) −16.3898 −0.545420
\(904\) 0 0
\(905\) −7.48560 −0.248830
\(906\) 0 0
\(907\) 23.6291 0.784591 0.392296 0.919839i \(-0.371681\pi\)
0.392296 + 0.919839i \(0.371681\pi\)
\(908\) 0 0
\(909\) 16.0703 0.533019
\(910\) 0 0
\(911\) −11.8946 −0.394087 −0.197044 0.980395i \(-0.563134\pi\)
−0.197044 + 0.980395i \(0.563134\pi\)
\(912\) 0 0
\(913\) −27.5789 −0.912729
\(914\) 0 0
\(915\) −23.8508 −0.788484
\(916\) 0 0
\(917\) −32.4752 −1.07243
\(918\) 0 0
\(919\) −29.4710 −0.972160 −0.486080 0.873914i \(-0.661574\pi\)
−0.486080 + 0.873914i \(0.661574\pi\)
\(920\) 0 0
\(921\) 7.35027 0.242200
\(922\) 0 0
\(923\) −20.6478 −0.679631
\(924\) 0 0
\(925\) 21.5923 0.709949
\(926\) 0 0
\(927\) 32.4026 1.06424
\(928\) 0 0
\(929\) 12.9547 0.425029 0.212515 0.977158i \(-0.431835\pi\)
0.212515 + 0.977158i \(0.431835\pi\)
\(930\) 0 0
\(931\) −2.82724 −0.0926591
\(932\) 0 0
\(933\) −1.15257 −0.0377335
\(934\) 0 0
\(935\) 12.4858 0.408330
\(936\) 0 0
\(937\) 43.2695 1.41355 0.706776 0.707438i \(-0.250149\pi\)
0.706776 + 0.707438i \(0.250149\pi\)
\(938\) 0 0
\(939\) −17.6015 −0.574404
\(940\) 0 0
\(941\) 13.0194 0.424420 0.212210 0.977224i \(-0.431934\pi\)
0.212210 + 0.977224i \(0.431934\pi\)
\(942\) 0 0
\(943\) −12.0806 −0.393399
\(944\) 0 0
\(945\) −31.3726 −1.02055
\(946\) 0 0
\(947\) −25.5145 −0.829111 −0.414555 0.910024i \(-0.636063\pi\)
−0.414555 + 0.910024i \(0.636063\pi\)
\(948\) 0 0
\(949\) 18.1712 0.589862
\(950\) 0 0
\(951\) −19.9077 −0.645551
\(952\) 0 0
\(953\) 19.0101 0.615796 0.307898 0.951419i \(-0.400374\pi\)
0.307898 + 0.951419i \(0.400374\pi\)
\(954\) 0 0
\(955\) 32.2479 1.04352
\(956\) 0 0
\(957\) −0.389794 −0.0126002
\(958\) 0 0
\(959\) 5.43603 0.175539
\(960\) 0 0
\(961\) −27.4057 −0.884056
\(962\) 0 0
\(963\) −27.6501 −0.891010
\(964\) 0 0
\(965\) 21.2457 0.683922
\(966\) 0 0
\(967\) 12.2436 0.393728 0.196864 0.980431i \(-0.436924\pi\)
0.196864 + 0.980431i \(0.436924\pi\)
\(968\) 0 0
\(969\) −3.88507 −0.124806
\(970\) 0 0
\(971\) −0.946139 −0.0303630 −0.0151815 0.999885i \(-0.504833\pi\)
−0.0151815 + 0.999885i \(0.504833\pi\)
\(972\) 0 0
\(973\) −28.4946 −0.913495
\(974\) 0 0
\(975\) 4.83691 0.154905
\(976\) 0 0
\(977\) −51.0007 −1.63166 −0.815829 0.578294i \(-0.803719\pi\)
−0.815829 + 0.578294i \(0.803719\pi\)
\(978\) 0 0
\(979\) −9.69089 −0.309722
\(980\) 0 0
\(981\) 9.93172 0.317095
\(982\) 0 0
\(983\) −17.2201 −0.549236 −0.274618 0.961553i \(-0.588551\pi\)
−0.274618 + 0.961553i \(0.588551\pi\)
\(984\) 0 0
\(985\) 23.0108 0.733186
\(986\) 0 0
\(987\) 5.03088 0.160135
\(988\) 0 0
\(989\) 8.20524 0.260911
\(990\) 0 0
\(991\) 43.8871 1.39412 0.697060 0.717013i \(-0.254491\pi\)
0.697060 + 0.717013i \(0.254491\pi\)
\(992\) 0 0
\(993\) −27.2604 −0.865084
\(994\) 0 0
\(995\) 32.1642 1.01967
\(996\) 0 0
\(997\) 16.0745 0.509086 0.254543 0.967061i \(-0.418075\pi\)
0.254543 + 0.967061i \(0.418075\pi\)
\(998\) 0 0
\(999\) 44.7646 1.41629
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 6008.2.a.b.1.17 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.17 44 1.1 even 1 trivial