Properties

Label 6008.2.a.b.1.7
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 1.7
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46379 q^{3} +1.54615 q^{5} -4.51355 q^{7} +3.07028 q^{9} +O(q^{10})\) \(q-2.46379 q^{3} +1.54615 q^{5} -4.51355 q^{7} +3.07028 q^{9} -1.39622 q^{11} -1.88688 q^{13} -3.80940 q^{15} +5.81705 q^{17} -5.42202 q^{19} +11.1205 q^{21} +1.48892 q^{23} -2.60942 q^{25} -0.173161 q^{27} +6.06659 q^{29} +2.12645 q^{31} +3.43999 q^{33} -6.97863 q^{35} +5.90324 q^{37} +4.64888 q^{39} +0.00128388 q^{41} +1.74065 q^{43} +4.74712 q^{45} -4.47451 q^{47} +13.3722 q^{49} -14.3320 q^{51} +1.11696 q^{53} -2.15876 q^{55} +13.3587 q^{57} +3.60544 q^{59} -7.40424 q^{61} -13.8579 q^{63} -2.91740 q^{65} +10.7106 q^{67} -3.66840 q^{69} +6.58932 q^{71} -8.24164 q^{73} +6.42907 q^{75} +6.30190 q^{77} +7.11435 q^{79} -8.78421 q^{81} +3.52854 q^{83} +8.99404 q^{85} -14.9468 q^{87} -10.6326 q^{89} +8.51653 q^{91} -5.23914 q^{93} -8.38325 q^{95} +15.2081 q^{97} -4.28678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.46379 −1.42247 −0.711236 0.702953i \(-0.751864\pi\)
−0.711236 + 0.702953i \(0.751864\pi\)
\(4\) 0 0
\(5\) 1.54615 0.691460 0.345730 0.938334i \(-0.387631\pi\)
0.345730 + 0.938334i \(0.387631\pi\)
\(6\) 0 0
\(7\) −4.51355 −1.70596 −0.852981 0.521941i \(-0.825208\pi\)
−0.852981 + 0.521941i \(0.825208\pi\)
\(8\) 0 0
\(9\) 3.07028 1.02343
\(10\) 0 0
\(11\) −1.39622 −0.420975 −0.210488 0.977597i \(-0.567505\pi\)
−0.210488 + 0.977597i \(0.567505\pi\)
\(12\) 0 0
\(13\) −1.88688 −0.523326 −0.261663 0.965159i \(-0.584271\pi\)
−0.261663 + 0.965159i \(0.584271\pi\)
\(14\) 0 0
\(15\) −3.80940 −0.983582
\(16\) 0 0
\(17\) 5.81705 1.41084 0.705421 0.708788i \(-0.250758\pi\)
0.705421 + 0.708788i \(0.250758\pi\)
\(18\) 0 0
\(19\) −5.42202 −1.24390 −0.621948 0.783059i \(-0.713658\pi\)
−0.621948 + 0.783059i \(0.713658\pi\)
\(20\) 0 0
\(21\) 11.1205 2.42668
\(22\) 0 0
\(23\) 1.48892 0.310462 0.155231 0.987878i \(-0.450388\pi\)
0.155231 + 0.987878i \(0.450388\pi\)
\(24\) 0 0
\(25\) −2.60942 −0.521883
\(26\) 0 0
\(27\) −0.173161 −0.0333249
\(28\) 0 0
\(29\) 6.06659 1.12654 0.563269 0.826274i \(-0.309543\pi\)
0.563269 + 0.826274i \(0.309543\pi\)
\(30\) 0 0
\(31\) 2.12645 0.381922 0.190961 0.981598i \(-0.438840\pi\)
0.190961 + 0.981598i \(0.438840\pi\)
\(32\) 0 0
\(33\) 3.43999 0.598826
\(34\) 0 0
\(35\) −6.97863 −1.17960
\(36\) 0 0
\(37\) 5.90324 0.970487 0.485244 0.874379i \(-0.338731\pi\)
0.485244 + 0.874379i \(0.338731\pi\)
\(38\) 0 0
\(39\) 4.64888 0.744417
\(40\) 0 0
\(41\) 0.00128388 0.000200509 0 0.000100254 1.00000i \(-0.499968\pi\)
0.000100254 1.00000i \(0.499968\pi\)
\(42\) 0 0
\(43\) 1.74065 0.265446 0.132723 0.991153i \(-0.457628\pi\)
0.132723 + 0.991153i \(0.457628\pi\)
\(44\) 0 0
\(45\) 4.74712 0.707659
\(46\) 0 0
\(47\) −4.47451 −0.652674 −0.326337 0.945253i \(-0.605814\pi\)
−0.326337 + 0.945253i \(0.605814\pi\)
\(48\) 0 0
\(49\) 13.3722 1.91031
\(50\) 0 0
\(51\) −14.3320 −2.00688
\(52\) 0 0
\(53\) 1.11696 0.153426 0.0767132 0.997053i \(-0.475557\pi\)
0.0767132 + 0.997053i \(0.475557\pi\)
\(54\) 0 0
\(55\) −2.15876 −0.291087
\(56\) 0 0
\(57\) 13.3587 1.76941
\(58\) 0 0
\(59\) 3.60544 0.469389 0.234694 0.972069i \(-0.424591\pi\)
0.234694 + 0.972069i \(0.424591\pi\)
\(60\) 0 0
\(61\) −7.40424 −0.948016 −0.474008 0.880521i \(-0.657193\pi\)
−0.474008 + 0.880521i \(0.657193\pi\)
\(62\) 0 0
\(63\) −13.8579 −1.74593
\(64\) 0 0
\(65\) −2.91740 −0.361859
\(66\) 0 0
\(67\) 10.7106 1.30851 0.654254 0.756275i \(-0.272983\pi\)
0.654254 + 0.756275i \(0.272983\pi\)
\(68\) 0 0
\(69\) −3.66840 −0.441623
\(70\) 0 0
\(71\) 6.58932 0.782008 0.391004 0.920389i \(-0.372128\pi\)
0.391004 + 0.920389i \(0.372128\pi\)
\(72\) 0 0
\(73\) −8.24164 −0.964611 −0.482305 0.876003i \(-0.660200\pi\)
−0.482305 + 0.876003i \(0.660200\pi\)
\(74\) 0 0
\(75\) 6.42907 0.742365
\(76\) 0 0
\(77\) 6.30190 0.718168
\(78\) 0 0
\(79\) 7.11435 0.800427 0.400213 0.916422i \(-0.368936\pi\)
0.400213 + 0.916422i \(0.368936\pi\)
\(80\) 0 0
\(81\) −8.78421 −0.976024
\(82\) 0 0
\(83\) 3.52854 0.387308 0.193654 0.981070i \(-0.437966\pi\)
0.193654 + 0.981070i \(0.437966\pi\)
\(84\) 0 0
\(85\) 8.99404 0.975541
\(86\) 0 0
\(87\) −14.9468 −1.60247
\(88\) 0 0
\(89\) −10.6326 −1.12706 −0.563529 0.826096i \(-0.690557\pi\)
−0.563529 + 0.826096i \(0.690557\pi\)
\(90\) 0 0
\(91\) 8.51653 0.892775
\(92\) 0 0
\(93\) −5.23914 −0.543274
\(94\) 0 0
\(95\) −8.38325 −0.860104
\(96\) 0 0
\(97\) 15.2081 1.54415 0.772074 0.635532i \(-0.219219\pi\)
0.772074 + 0.635532i \(0.219219\pi\)
\(98\) 0 0
\(99\) −4.28678 −0.430838
\(100\) 0 0
\(101\) −19.6441 −1.95466 −0.977332 0.211711i \(-0.932097\pi\)
−0.977332 + 0.211711i \(0.932097\pi\)
\(102\) 0 0
\(103\) −1.27909 −0.126032 −0.0630161 0.998013i \(-0.520072\pi\)
−0.0630161 + 0.998013i \(0.520072\pi\)
\(104\) 0 0
\(105\) 17.1939 1.67795
\(106\) 0 0
\(107\) −10.0003 −0.966764 −0.483382 0.875409i \(-0.660592\pi\)
−0.483382 + 0.875409i \(0.660592\pi\)
\(108\) 0 0
\(109\) 12.9577 1.24112 0.620560 0.784159i \(-0.286906\pi\)
0.620560 + 0.784159i \(0.286906\pi\)
\(110\) 0 0
\(111\) −14.5444 −1.38049
\(112\) 0 0
\(113\) 6.64548 0.625154 0.312577 0.949892i \(-0.398808\pi\)
0.312577 + 0.949892i \(0.398808\pi\)
\(114\) 0 0
\(115\) 2.30210 0.214672
\(116\) 0 0
\(117\) −5.79325 −0.535586
\(118\) 0 0
\(119\) −26.2556 −2.40684
\(120\) 0 0
\(121\) −9.05058 −0.822780
\(122\) 0 0
\(123\) −0.00316322 −0.000285218 0
\(124\) 0 0
\(125\) −11.7653 −1.05232
\(126\) 0 0
\(127\) −8.26613 −0.733501 −0.366750 0.930319i \(-0.619530\pi\)
−0.366750 + 0.930319i \(0.619530\pi\)
\(128\) 0 0
\(129\) −4.28860 −0.377590
\(130\) 0 0
\(131\) 20.4110 1.78332 0.891659 0.452707i \(-0.149542\pi\)
0.891659 + 0.452707i \(0.149542\pi\)
\(132\) 0 0
\(133\) 24.4726 2.12204
\(134\) 0 0
\(135\) −0.267733 −0.0230428
\(136\) 0 0
\(137\) −12.8555 −1.09832 −0.549158 0.835718i \(-0.685052\pi\)
−0.549158 + 0.835718i \(0.685052\pi\)
\(138\) 0 0
\(139\) 9.49073 0.804993 0.402497 0.915422i \(-0.368143\pi\)
0.402497 + 0.915422i \(0.368143\pi\)
\(140\) 0 0
\(141\) 11.0243 0.928411
\(142\) 0 0
\(143\) 2.63449 0.220307
\(144\) 0 0
\(145\) 9.37987 0.778956
\(146\) 0 0
\(147\) −32.9463 −2.71736
\(148\) 0 0
\(149\) −0.941426 −0.0771246 −0.0385623 0.999256i \(-0.512278\pi\)
−0.0385623 + 0.999256i \(0.512278\pi\)
\(150\) 0 0
\(151\) 0.737818 0.0600428 0.0300214 0.999549i \(-0.490442\pi\)
0.0300214 + 0.999549i \(0.490442\pi\)
\(152\) 0 0
\(153\) 17.8600 1.44389
\(154\) 0 0
\(155\) 3.28782 0.264084
\(156\) 0 0
\(157\) −8.92195 −0.712049 −0.356025 0.934477i \(-0.615868\pi\)
−0.356025 + 0.934477i \(0.615868\pi\)
\(158\) 0 0
\(159\) −2.75196 −0.218245
\(160\) 0 0
\(161\) −6.72033 −0.529636
\(162\) 0 0
\(163\) −19.9660 −1.56386 −0.781930 0.623366i \(-0.785765\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(164\) 0 0
\(165\) 5.31875 0.414064
\(166\) 0 0
\(167\) −15.6345 −1.20984 −0.604918 0.796287i \(-0.706794\pi\)
−0.604918 + 0.796287i \(0.706794\pi\)
\(168\) 0 0
\(169\) −9.43969 −0.726130
\(170\) 0 0
\(171\) −16.6471 −1.27304
\(172\) 0 0
\(173\) 0.265640 0.0201962 0.0100981 0.999949i \(-0.496786\pi\)
0.0100981 + 0.999949i \(0.496786\pi\)
\(174\) 0 0
\(175\) 11.7777 0.890314
\(176\) 0 0
\(177\) −8.88307 −0.667693
\(178\) 0 0
\(179\) 10.7752 0.805377 0.402689 0.915337i \(-0.368076\pi\)
0.402689 + 0.915337i \(0.368076\pi\)
\(180\) 0 0
\(181\) 10.2154 0.759307 0.379653 0.925129i \(-0.376043\pi\)
0.379653 + 0.925129i \(0.376043\pi\)
\(182\) 0 0
\(183\) 18.2425 1.34853
\(184\) 0 0
\(185\) 9.12731 0.671053
\(186\) 0 0
\(187\) −8.12187 −0.593930
\(188\) 0 0
\(189\) 0.781572 0.0568510
\(190\) 0 0
\(191\) 7.80245 0.564566 0.282283 0.959331i \(-0.408908\pi\)
0.282283 + 0.959331i \(0.408908\pi\)
\(192\) 0 0
\(193\) 22.5406 1.62251 0.811255 0.584692i \(-0.198785\pi\)
0.811255 + 0.584692i \(0.198785\pi\)
\(194\) 0 0
\(195\) 7.18787 0.514734
\(196\) 0 0
\(197\) −6.00587 −0.427900 −0.213950 0.976845i \(-0.568633\pi\)
−0.213950 + 0.976845i \(0.568633\pi\)
\(198\) 0 0
\(199\) 9.88724 0.700888 0.350444 0.936584i \(-0.386031\pi\)
0.350444 + 0.936584i \(0.386031\pi\)
\(200\) 0 0
\(201\) −26.3887 −1.86132
\(202\) 0 0
\(203\) −27.3819 −1.92183
\(204\) 0 0
\(205\) 0.00198508 0.000138644 0
\(206\) 0 0
\(207\) 4.57141 0.317735
\(208\) 0 0
\(209\) 7.57031 0.523649
\(210\) 0 0
\(211\) 5.04377 0.347227 0.173614 0.984814i \(-0.444456\pi\)
0.173614 + 0.984814i \(0.444456\pi\)
\(212\) 0 0
\(213\) −16.2347 −1.11238
\(214\) 0 0
\(215\) 2.69131 0.183546
\(216\) 0 0
\(217\) −9.59786 −0.651545
\(218\) 0 0
\(219\) 20.3057 1.37213
\(220\) 0 0
\(221\) −10.9761 −0.738330
\(222\) 0 0
\(223\) −10.7691 −0.721151 −0.360575 0.932730i \(-0.617420\pi\)
−0.360575 + 0.932730i \(0.617420\pi\)
\(224\) 0 0
\(225\) −8.01165 −0.534110
\(226\) 0 0
\(227\) −28.4526 −1.88846 −0.944232 0.329280i \(-0.893194\pi\)
−0.944232 + 0.329280i \(0.893194\pi\)
\(228\) 0 0
\(229\) −6.54581 −0.432559 −0.216280 0.976331i \(-0.569392\pi\)
−0.216280 + 0.976331i \(0.569392\pi\)
\(230\) 0 0
\(231\) −15.5266 −1.02157
\(232\) 0 0
\(233\) −13.6326 −0.893104 −0.446552 0.894758i \(-0.647348\pi\)
−0.446552 + 0.894758i \(0.647348\pi\)
\(234\) 0 0
\(235\) −6.91826 −0.451298
\(236\) 0 0
\(237\) −17.5283 −1.13858
\(238\) 0 0
\(239\) 8.68138 0.561552 0.280776 0.959773i \(-0.409408\pi\)
0.280776 + 0.959773i \(0.409408\pi\)
\(240\) 0 0
\(241\) 6.08055 0.391683 0.195841 0.980636i \(-0.437256\pi\)
0.195841 + 0.980636i \(0.437256\pi\)
\(242\) 0 0
\(243\) 22.1620 1.42169
\(244\) 0 0
\(245\) 20.6754 1.32090
\(246\) 0 0
\(247\) 10.2307 0.650963
\(248\) 0 0
\(249\) −8.69360 −0.550934
\(250\) 0 0
\(251\) 1.74489 0.110137 0.0550683 0.998483i \(-0.482462\pi\)
0.0550683 + 0.998483i \(0.482462\pi\)
\(252\) 0 0
\(253\) −2.07886 −0.130697
\(254\) 0 0
\(255\) −22.1595 −1.38768
\(256\) 0 0
\(257\) 11.8713 0.740513 0.370257 0.928930i \(-0.379270\pi\)
0.370257 + 0.928930i \(0.379270\pi\)
\(258\) 0 0
\(259\) −26.6446 −1.65561
\(260\) 0 0
\(261\) 18.6262 1.15293
\(262\) 0 0
\(263\) 11.0704 0.682628 0.341314 0.939949i \(-0.389128\pi\)
0.341314 + 0.939949i \(0.389128\pi\)
\(264\) 0 0
\(265\) 1.72699 0.106088
\(266\) 0 0
\(267\) 26.1967 1.60321
\(268\) 0 0
\(269\) 14.1665 0.863747 0.431873 0.901934i \(-0.357853\pi\)
0.431873 + 0.901934i \(0.357853\pi\)
\(270\) 0 0
\(271\) 15.5830 0.946600 0.473300 0.880901i \(-0.343063\pi\)
0.473300 + 0.880901i \(0.343063\pi\)
\(272\) 0 0
\(273\) −20.9830 −1.26995
\(274\) 0 0
\(275\) 3.64331 0.219700
\(276\) 0 0
\(277\) 0.412937 0.0248110 0.0124055 0.999923i \(-0.496051\pi\)
0.0124055 + 0.999923i \(0.496051\pi\)
\(278\) 0 0
\(279\) 6.52881 0.390870
\(280\) 0 0
\(281\) −18.9951 −1.13315 −0.566577 0.824009i \(-0.691733\pi\)
−0.566577 + 0.824009i \(0.691733\pi\)
\(282\) 0 0
\(283\) −1.39753 −0.0830748 −0.0415374 0.999137i \(-0.513226\pi\)
−0.0415374 + 0.999137i \(0.513226\pi\)
\(284\) 0 0
\(285\) 20.6546 1.22347
\(286\) 0 0
\(287\) −0.00579487 −0.000342060 0
\(288\) 0 0
\(289\) 16.8381 0.990476
\(290\) 0 0
\(291\) −37.4696 −2.19651
\(292\) 0 0
\(293\) −5.10362 −0.298156 −0.149078 0.988825i \(-0.547631\pi\)
−0.149078 + 0.988825i \(0.547631\pi\)
\(294\) 0 0
\(295\) 5.57456 0.324564
\(296\) 0 0
\(297\) 0.241770 0.0140289
\(298\) 0 0
\(299\) −2.80942 −0.162473
\(300\) 0 0
\(301\) −7.85651 −0.452842
\(302\) 0 0
\(303\) 48.3991 2.78046
\(304\) 0 0
\(305\) −11.4481 −0.655515
\(306\) 0 0
\(307\) −16.4210 −0.937197 −0.468599 0.883411i \(-0.655241\pi\)
−0.468599 + 0.883411i \(0.655241\pi\)
\(308\) 0 0
\(309\) 3.15141 0.179277
\(310\) 0 0
\(311\) −13.1430 −0.745269 −0.372635 0.927978i \(-0.621545\pi\)
−0.372635 + 0.927978i \(0.621545\pi\)
\(312\) 0 0
\(313\) −25.8920 −1.46350 −0.731750 0.681573i \(-0.761296\pi\)
−0.731750 + 0.681573i \(0.761296\pi\)
\(314\) 0 0
\(315\) −21.4264 −1.20724
\(316\) 0 0
\(317\) −15.7475 −0.884468 −0.442234 0.896900i \(-0.645814\pi\)
−0.442234 + 0.896900i \(0.645814\pi\)
\(318\) 0 0
\(319\) −8.47028 −0.474245
\(320\) 0 0
\(321\) 24.6387 1.37520
\(322\) 0 0
\(323\) −31.5401 −1.75494
\(324\) 0 0
\(325\) 4.92365 0.273115
\(326\) 0 0
\(327\) −31.9250 −1.76546
\(328\) 0 0
\(329\) 20.1959 1.11344
\(330\) 0 0
\(331\) −6.21265 −0.341478 −0.170739 0.985316i \(-0.554615\pi\)
−0.170739 + 0.985316i \(0.554615\pi\)
\(332\) 0 0
\(333\) 18.1246 0.993223
\(334\) 0 0
\(335\) 16.5602 0.904781
\(336\) 0 0
\(337\) −1.31220 −0.0714798 −0.0357399 0.999361i \(-0.511379\pi\)
−0.0357399 + 0.999361i \(0.511379\pi\)
\(338\) 0 0
\(339\) −16.3731 −0.889265
\(340\) 0 0
\(341\) −2.96899 −0.160780
\(342\) 0 0
\(343\) −28.7611 −1.55295
\(344\) 0 0
\(345\) −5.67190 −0.305365
\(346\) 0 0
\(347\) −31.3057 −1.68058 −0.840290 0.542138i \(-0.817615\pi\)
−0.840290 + 0.542138i \(0.817615\pi\)
\(348\) 0 0
\(349\) 4.59932 0.246196 0.123098 0.992395i \(-0.460717\pi\)
0.123098 + 0.992395i \(0.460717\pi\)
\(350\) 0 0
\(351\) 0.326734 0.0174398
\(352\) 0 0
\(353\) −19.6863 −1.04779 −0.523897 0.851782i \(-0.675522\pi\)
−0.523897 + 0.851782i \(0.675522\pi\)
\(354\) 0 0
\(355\) 10.1881 0.540727
\(356\) 0 0
\(357\) 64.6883 3.42367
\(358\) 0 0
\(359\) −23.9206 −1.26248 −0.631241 0.775587i \(-0.717454\pi\)
−0.631241 + 0.775587i \(0.717454\pi\)
\(360\) 0 0
\(361\) 10.3982 0.547276
\(362\) 0 0
\(363\) 22.2988 1.17038
\(364\) 0 0
\(365\) −12.7428 −0.666989
\(366\) 0 0
\(367\) −25.8401 −1.34884 −0.674421 0.738347i \(-0.735607\pi\)
−0.674421 + 0.738347i \(0.735607\pi\)
\(368\) 0 0
\(369\) 0.00394188 0.000205206 0
\(370\) 0 0
\(371\) −5.04147 −0.261740
\(372\) 0 0
\(373\) 2.91153 0.150753 0.0753767 0.997155i \(-0.475984\pi\)
0.0753767 + 0.997155i \(0.475984\pi\)
\(374\) 0 0
\(375\) 28.9873 1.49690
\(376\) 0 0
\(377\) −11.4469 −0.589547
\(378\) 0 0
\(379\) −7.47288 −0.383856 −0.191928 0.981409i \(-0.561474\pi\)
−0.191928 + 0.981409i \(0.561474\pi\)
\(380\) 0 0
\(381\) 20.3660 1.04338
\(382\) 0 0
\(383\) −21.1650 −1.08148 −0.540740 0.841190i \(-0.681856\pi\)
−0.540740 + 0.841190i \(0.681856\pi\)
\(384\) 0 0
\(385\) 9.74369 0.496584
\(386\) 0 0
\(387\) 5.34428 0.271665
\(388\) 0 0
\(389\) 25.8454 1.31041 0.655207 0.755450i \(-0.272582\pi\)
0.655207 + 0.755450i \(0.272582\pi\)
\(390\) 0 0
\(391\) 8.66114 0.438013
\(392\) 0 0
\(393\) −50.2885 −2.53672
\(394\) 0 0
\(395\) 10.9999 0.553463
\(396\) 0 0
\(397\) −8.17611 −0.410347 −0.205174 0.978726i \(-0.565776\pi\)
−0.205174 + 0.978726i \(0.565776\pi\)
\(398\) 0 0
\(399\) −60.2953 −3.01854
\(400\) 0 0
\(401\) 11.8114 0.589832 0.294916 0.955523i \(-0.404708\pi\)
0.294916 + 0.955523i \(0.404708\pi\)
\(402\) 0 0
\(403\) −4.01236 −0.199870
\(404\) 0 0
\(405\) −13.5817 −0.674881
\(406\) 0 0
\(407\) −8.24221 −0.408551
\(408\) 0 0
\(409\) 19.2109 0.949918 0.474959 0.880008i \(-0.342463\pi\)
0.474959 + 0.880008i \(0.342463\pi\)
\(410\) 0 0
\(411\) 31.6732 1.56232
\(412\) 0 0
\(413\) −16.2734 −0.800760
\(414\) 0 0
\(415\) 5.45566 0.267808
\(416\) 0 0
\(417\) −23.3832 −1.14508
\(418\) 0 0
\(419\) −18.6162 −0.909459 −0.454730 0.890629i \(-0.650264\pi\)
−0.454730 + 0.890629i \(0.650264\pi\)
\(420\) 0 0
\(421\) −34.4681 −1.67987 −0.839937 0.542684i \(-0.817408\pi\)
−0.839937 + 0.542684i \(0.817408\pi\)
\(422\) 0 0
\(423\) −13.7380 −0.667965
\(424\) 0 0
\(425\) −15.1791 −0.736295
\(426\) 0 0
\(427\) 33.4194 1.61728
\(428\) 0 0
\(429\) −6.49085 −0.313381
\(430\) 0 0
\(431\) 20.1809 0.972081 0.486040 0.873936i \(-0.338441\pi\)
0.486040 + 0.873936i \(0.338441\pi\)
\(432\) 0 0
\(433\) −33.5443 −1.61204 −0.806019 0.591889i \(-0.798382\pi\)
−0.806019 + 0.591889i \(0.798382\pi\)
\(434\) 0 0
\(435\) −23.1101 −1.10804
\(436\) 0 0
\(437\) −8.07296 −0.386182
\(438\) 0 0
\(439\) 4.27741 0.204150 0.102075 0.994777i \(-0.467452\pi\)
0.102075 + 0.994777i \(0.467452\pi\)
\(440\) 0 0
\(441\) 41.0563 1.95506
\(442\) 0 0
\(443\) −26.1991 −1.24476 −0.622378 0.782716i \(-0.713833\pi\)
−0.622378 + 0.782716i \(0.713833\pi\)
\(444\) 0 0
\(445\) −16.4397 −0.779315
\(446\) 0 0
\(447\) 2.31948 0.109708
\(448\) 0 0
\(449\) −10.8570 −0.512373 −0.256186 0.966627i \(-0.582466\pi\)
−0.256186 + 0.966627i \(0.582466\pi\)
\(450\) 0 0
\(451\) −0.00179258 −8.44092e−5 0
\(452\) 0 0
\(453\) −1.81783 −0.0854092
\(454\) 0 0
\(455\) 13.1678 0.617318
\(456\) 0 0
\(457\) −34.0541 −1.59298 −0.796492 0.604649i \(-0.793313\pi\)
−0.796492 + 0.604649i \(0.793313\pi\)
\(458\) 0 0
\(459\) −1.00729 −0.0470161
\(460\) 0 0
\(461\) −21.7221 −1.01170 −0.505851 0.862621i \(-0.668821\pi\)
−0.505851 + 0.862621i \(0.668821\pi\)
\(462\) 0 0
\(463\) −18.8802 −0.877437 −0.438719 0.898624i \(-0.644568\pi\)
−0.438719 + 0.898624i \(0.644568\pi\)
\(464\) 0 0
\(465\) −8.10050 −0.375652
\(466\) 0 0
\(467\) 9.44774 0.437189 0.218595 0.975816i \(-0.429853\pi\)
0.218595 + 0.975816i \(0.429853\pi\)
\(468\) 0 0
\(469\) −48.3429 −2.23227
\(470\) 0 0
\(471\) 21.9819 1.01287
\(472\) 0 0
\(473\) −2.43032 −0.111746
\(474\) 0 0
\(475\) 14.1483 0.649168
\(476\) 0 0
\(477\) 3.42939 0.157021
\(478\) 0 0
\(479\) 3.66074 0.167263 0.0836317 0.996497i \(-0.473348\pi\)
0.0836317 + 0.996497i \(0.473348\pi\)
\(480\) 0 0
\(481\) −11.1387 −0.507881
\(482\) 0 0
\(483\) 16.5575 0.753393
\(484\) 0 0
\(485\) 23.5140 1.06772
\(486\) 0 0
\(487\) −9.16552 −0.415329 −0.207665 0.978200i \(-0.566586\pi\)
−0.207665 + 0.978200i \(0.566586\pi\)
\(488\) 0 0
\(489\) 49.1922 2.22455
\(490\) 0 0
\(491\) 24.2323 1.09359 0.546794 0.837267i \(-0.315848\pi\)
0.546794 + 0.837267i \(0.315848\pi\)
\(492\) 0 0
\(493\) 35.2897 1.58937
\(494\) 0 0
\(495\) −6.62801 −0.297907
\(496\) 0 0
\(497\) −29.7412 −1.33408
\(498\) 0 0
\(499\) −0.463648 −0.0207557 −0.0103779 0.999946i \(-0.503303\pi\)
−0.0103779 + 0.999946i \(0.503303\pi\)
\(500\) 0 0
\(501\) 38.5203 1.72096
\(502\) 0 0
\(503\) −18.5312 −0.826265 −0.413133 0.910671i \(-0.635565\pi\)
−0.413133 + 0.910671i \(0.635565\pi\)
\(504\) 0 0
\(505\) −30.3728 −1.35157
\(506\) 0 0
\(507\) 23.2575 1.03290
\(508\) 0 0
\(509\) −1.92753 −0.0854362 −0.0427181 0.999087i \(-0.513602\pi\)
−0.0427181 + 0.999087i \(0.513602\pi\)
\(510\) 0 0
\(511\) 37.1991 1.64559
\(512\) 0 0
\(513\) 0.938882 0.0414527
\(514\) 0 0
\(515\) −1.97766 −0.0871462
\(516\) 0 0
\(517\) 6.24738 0.274760
\(518\) 0 0
\(519\) −0.654483 −0.0287286
\(520\) 0 0
\(521\) 17.3717 0.761066 0.380533 0.924767i \(-0.375741\pi\)
0.380533 + 0.924767i \(0.375741\pi\)
\(522\) 0 0
\(523\) 23.3181 1.01963 0.509815 0.860284i \(-0.329714\pi\)
0.509815 + 0.860284i \(0.329714\pi\)
\(524\) 0 0
\(525\) −29.0179 −1.26645
\(526\) 0 0
\(527\) 12.3697 0.538832
\(528\) 0 0
\(529\) −20.7831 −0.903613
\(530\) 0 0
\(531\) 11.0697 0.480386
\(532\) 0 0
\(533\) −0.00242253 −0.000104931 0
\(534\) 0 0
\(535\) −15.4620 −0.668479
\(536\) 0 0
\(537\) −26.5479 −1.14563
\(538\) 0 0
\(539\) −18.6704 −0.804193
\(540\) 0 0
\(541\) 16.6818 0.717207 0.358603 0.933490i \(-0.383253\pi\)
0.358603 + 0.933490i \(0.383253\pi\)
\(542\) 0 0
\(543\) −25.1687 −1.08009
\(544\) 0 0
\(545\) 20.0345 0.858184
\(546\) 0 0
\(547\) 19.8737 0.849740 0.424870 0.905254i \(-0.360320\pi\)
0.424870 + 0.905254i \(0.360320\pi\)
\(548\) 0 0
\(549\) −22.7331 −0.970226
\(550\) 0 0
\(551\) −32.8932 −1.40130
\(552\) 0 0
\(553\) −32.1110 −1.36550
\(554\) 0 0
\(555\) −22.4878 −0.954554
\(556\) 0 0
\(557\) 37.2954 1.58026 0.790128 0.612941i \(-0.210014\pi\)
0.790128 + 0.612941i \(0.210014\pi\)
\(558\) 0 0
\(559\) −3.28439 −0.138915
\(560\) 0 0
\(561\) 20.0106 0.844848
\(562\) 0 0
\(563\) 18.0505 0.760737 0.380369 0.924835i \(-0.375797\pi\)
0.380369 + 0.924835i \(0.375797\pi\)
\(564\) 0 0
\(565\) 10.2749 0.432269
\(566\) 0 0
\(567\) 39.6480 1.66506
\(568\) 0 0
\(569\) −12.6665 −0.531007 −0.265503 0.964110i \(-0.585538\pi\)
−0.265503 + 0.964110i \(0.585538\pi\)
\(570\) 0 0
\(571\) 35.1787 1.47218 0.736092 0.676882i \(-0.236669\pi\)
0.736092 + 0.676882i \(0.236669\pi\)
\(572\) 0 0
\(573\) −19.2236 −0.803079
\(574\) 0 0
\(575\) −3.88522 −0.162025
\(576\) 0 0
\(577\) 10.3487 0.430823 0.215411 0.976523i \(-0.430891\pi\)
0.215411 + 0.976523i \(0.430891\pi\)
\(578\) 0 0
\(579\) −55.5355 −2.30798
\(580\) 0 0
\(581\) −15.9263 −0.660732
\(582\) 0 0
\(583\) −1.55952 −0.0645888
\(584\) 0 0
\(585\) −8.95724 −0.370336
\(586\) 0 0
\(587\) −33.9217 −1.40010 −0.700050 0.714094i \(-0.746839\pi\)
−0.700050 + 0.714094i \(0.746839\pi\)
\(588\) 0 0
\(589\) −11.5297 −0.475071
\(590\) 0 0
\(591\) 14.7972 0.608677
\(592\) 0 0
\(593\) −32.9176 −1.35176 −0.675882 0.737010i \(-0.736237\pi\)
−0.675882 + 0.737010i \(0.736237\pi\)
\(594\) 0 0
\(595\) −40.5951 −1.66424
\(596\) 0 0
\(597\) −24.3601 −0.996993
\(598\) 0 0
\(599\) 3.31308 0.135369 0.0676844 0.997707i \(-0.478439\pi\)
0.0676844 + 0.997707i \(0.478439\pi\)
\(600\) 0 0
\(601\) 20.3412 0.829734 0.414867 0.909882i \(-0.363828\pi\)
0.414867 + 0.909882i \(0.363828\pi\)
\(602\) 0 0
\(603\) 32.8846 1.33916
\(604\) 0 0
\(605\) −13.9936 −0.568919
\(606\) 0 0
\(607\) −12.5095 −0.507747 −0.253873 0.967237i \(-0.581705\pi\)
−0.253873 + 0.967237i \(0.581705\pi\)
\(608\) 0 0
\(609\) 67.4633 2.73375
\(610\) 0 0
\(611\) 8.44285 0.341561
\(612\) 0 0
\(613\) 39.6818 1.60273 0.801367 0.598173i \(-0.204107\pi\)
0.801367 + 0.598173i \(0.204107\pi\)
\(614\) 0 0
\(615\) −0.00489082 −0.000197217 0
\(616\) 0 0
\(617\) −21.4096 −0.861919 −0.430959 0.902371i \(-0.641825\pi\)
−0.430959 + 0.902371i \(0.641825\pi\)
\(618\) 0 0
\(619\) −12.5691 −0.505195 −0.252597 0.967571i \(-0.581285\pi\)
−0.252597 + 0.967571i \(0.581285\pi\)
\(620\) 0 0
\(621\) −0.257823 −0.0103461
\(622\) 0 0
\(623\) 47.9910 1.92272
\(624\) 0 0
\(625\) −5.14386 −0.205754
\(626\) 0 0
\(627\) −18.6517 −0.744877
\(628\) 0 0
\(629\) 34.3395 1.36920
\(630\) 0 0
\(631\) −42.1760 −1.67900 −0.839499 0.543361i \(-0.817152\pi\)
−0.839499 + 0.543361i \(0.817152\pi\)
\(632\) 0 0
\(633\) −12.4268 −0.493921
\(634\) 0 0
\(635\) −12.7807 −0.507186
\(636\) 0 0
\(637\) −25.2316 −0.999714
\(638\) 0 0
\(639\) 20.2311 0.800328
\(640\) 0 0
\(641\) −4.85892 −0.191916 −0.0959579 0.995385i \(-0.530591\pi\)
−0.0959579 + 0.995385i \(0.530591\pi\)
\(642\) 0 0
\(643\) −23.8815 −0.941795 −0.470897 0.882188i \(-0.656070\pi\)
−0.470897 + 0.882188i \(0.656070\pi\)
\(644\) 0 0
\(645\) −6.63082 −0.261088
\(646\) 0 0
\(647\) −3.71552 −0.146072 −0.0730361 0.997329i \(-0.523269\pi\)
−0.0730361 + 0.997329i \(0.523269\pi\)
\(648\) 0 0
\(649\) −5.03398 −0.197601
\(650\) 0 0
\(651\) 23.6471 0.926805
\(652\) 0 0
\(653\) 23.7542 0.929574 0.464787 0.885422i \(-0.346131\pi\)
0.464787 + 0.885422i \(0.346131\pi\)
\(654\) 0 0
\(655\) 31.5585 1.23309
\(656\) 0 0
\(657\) −25.3041 −0.987209
\(658\) 0 0
\(659\) 23.0706 0.898704 0.449352 0.893355i \(-0.351655\pi\)
0.449352 + 0.893355i \(0.351655\pi\)
\(660\) 0 0
\(661\) 0.154231 0.00599891 0.00299945 0.999996i \(-0.499045\pi\)
0.00299945 + 0.999996i \(0.499045\pi\)
\(662\) 0 0
\(663\) 27.0428 1.05025
\(664\) 0 0
\(665\) 37.8383 1.46730
\(666\) 0 0
\(667\) 9.03269 0.349747
\(668\) 0 0
\(669\) 26.5328 1.02582
\(670\) 0 0
\(671\) 10.3379 0.399091
\(672\) 0 0
\(673\) −25.5536 −0.985021 −0.492510 0.870307i \(-0.663921\pi\)
−0.492510 + 0.870307i \(0.663921\pi\)
\(674\) 0 0
\(675\) 0.451849 0.0173917
\(676\) 0 0
\(677\) 34.1875 1.31393 0.656965 0.753921i \(-0.271840\pi\)
0.656965 + 0.753921i \(0.271840\pi\)
\(678\) 0 0
\(679\) −68.6426 −2.63426
\(680\) 0 0
\(681\) 70.1013 2.68629
\(682\) 0 0
\(683\) −26.7749 −1.02451 −0.512257 0.858832i \(-0.671190\pi\)
−0.512257 + 0.858832i \(0.671190\pi\)
\(684\) 0 0
\(685\) −19.8765 −0.759442
\(686\) 0 0
\(687\) 16.1275 0.615303
\(688\) 0 0
\(689\) −2.10757 −0.0802921
\(690\) 0 0
\(691\) 15.5457 0.591387 0.295693 0.955283i \(-0.404449\pi\)
0.295693 + 0.955283i \(0.404449\pi\)
\(692\) 0 0
\(693\) 19.3486 0.734993
\(694\) 0 0
\(695\) 14.6741 0.556620
\(696\) 0 0
\(697\) 0.00746841 0.000282886 0
\(698\) 0 0
\(699\) 33.5880 1.27042
\(700\) 0 0
\(701\) −5.54151 −0.209300 −0.104650 0.994509i \(-0.533372\pi\)
−0.104650 + 0.994509i \(0.533372\pi\)
\(702\) 0 0
\(703\) −32.0075 −1.20718
\(704\) 0 0
\(705\) 17.0452 0.641959
\(706\) 0 0
\(707\) 88.6649 3.33458
\(708\) 0 0
\(709\) −0.343763 −0.0129103 −0.00645514 0.999979i \(-0.502055\pi\)
−0.00645514 + 0.999979i \(0.502055\pi\)
\(710\) 0 0
\(711\) 21.8431 0.819179
\(712\) 0 0
\(713\) 3.16612 0.118572
\(714\) 0 0
\(715\) 4.07332 0.152334
\(716\) 0 0
\(717\) −21.3891 −0.798792
\(718\) 0 0
\(719\) −33.2707 −1.24079 −0.620394 0.784290i \(-0.713027\pi\)
−0.620394 + 0.784290i \(0.713027\pi\)
\(720\) 0 0
\(721\) 5.77323 0.215006
\(722\) 0 0
\(723\) −14.9812 −0.557158
\(724\) 0 0
\(725\) −15.8303 −0.587921
\(726\) 0 0
\(727\) −50.5555 −1.87500 −0.937499 0.347988i \(-0.886865\pi\)
−0.937499 + 0.347988i \(0.886865\pi\)
\(728\) 0 0
\(729\) −28.2499 −1.04629
\(730\) 0 0
\(731\) 10.1254 0.374503
\(732\) 0 0
\(733\) −39.1140 −1.44471 −0.722354 0.691523i \(-0.756940\pi\)
−0.722354 + 0.691523i \(0.756940\pi\)
\(734\) 0 0
\(735\) −50.9399 −1.87895
\(736\) 0 0
\(737\) −14.9543 −0.550850
\(738\) 0 0
\(739\) 42.9975 1.58169 0.790844 0.612018i \(-0.209642\pi\)
0.790844 + 0.612018i \(0.209642\pi\)
\(740\) 0 0
\(741\) −25.2063 −0.925977
\(742\) 0 0
\(743\) 48.7392 1.78807 0.894035 0.447998i \(-0.147863\pi\)
0.894035 + 0.447998i \(0.147863\pi\)
\(744\) 0 0
\(745\) −1.45559 −0.0533286
\(746\) 0 0
\(747\) 10.8336 0.396381
\(748\) 0 0
\(749\) 45.1368 1.64926
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −4.29905 −0.156666
\(754\) 0 0
\(755\) 1.14078 0.0415172
\(756\) 0 0
\(757\) −31.0828 −1.12973 −0.564863 0.825185i \(-0.691071\pi\)
−0.564863 + 0.825185i \(0.691071\pi\)
\(758\) 0 0
\(759\) 5.12188 0.185913
\(760\) 0 0
\(761\) −5.55942 −0.201529 −0.100764 0.994910i \(-0.532129\pi\)
−0.100764 + 0.994910i \(0.532129\pi\)
\(762\) 0 0
\(763\) −58.4851 −2.11730
\(764\) 0 0
\(765\) 27.6142 0.998395
\(766\) 0 0
\(767\) −6.80304 −0.245643
\(768\) 0 0
\(769\) 13.8881 0.500816 0.250408 0.968140i \(-0.419435\pi\)
0.250408 + 0.968140i \(0.419435\pi\)
\(770\) 0 0
\(771\) −29.2485 −1.05336
\(772\) 0 0
\(773\) 25.7487 0.926117 0.463059 0.886328i \(-0.346752\pi\)
0.463059 + 0.886328i \(0.346752\pi\)
\(774\) 0 0
\(775\) −5.54880 −0.199319
\(776\) 0 0
\(777\) 65.6468 2.35507
\(778\) 0 0
\(779\) −0.00696123 −0.000249412 0
\(780\) 0 0
\(781\) −9.20012 −0.329206
\(782\) 0 0
\(783\) −1.05050 −0.0375417
\(784\) 0 0
\(785\) −13.7947 −0.492354
\(786\) 0 0
\(787\) 27.9233 0.995358 0.497679 0.867361i \(-0.334186\pi\)
0.497679 + 0.867361i \(0.334186\pi\)
\(788\) 0 0
\(789\) −27.2751 −0.971019
\(790\) 0 0
\(791\) −29.9947 −1.06649
\(792\) 0 0
\(793\) 13.9709 0.496121
\(794\) 0 0
\(795\) −4.25495 −0.150908
\(796\) 0 0
\(797\) 52.5312 1.86075 0.930375 0.366609i \(-0.119481\pi\)
0.930375 + 0.366609i \(0.119481\pi\)
\(798\) 0 0
\(799\) −26.0284 −0.920820
\(800\) 0 0
\(801\) −32.6452 −1.15346
\(802\) 0 0
\(803\) 11.5071 0.406077
\(804\) 0 0
\(805\) −10.3906 −0.366222
\(806\) 0 0
\(807\) −34.9033 −1.22866
\(808\) 0 0
\(809\) −32.3488 −1.13732 −0.568661 0.822572i \(-0.692539\pi\)
−0.568661 + 0.822572i \(0.692539\pi\)
\(810\) 0 0
\(811\) 32.4210 1.13846 0.569229 0.822179i \(-0.307242\pi\)
0.569229 + 0.822179i \(0.307242\pi\)
\(812\) 0 0
\(813\) −38.3933 −1.34651
\(814\) 0 0
\(815\) −30.8705 −1.08135
\(816\) 0 0
\(817\) −9.43782 −0.330188
\(818\) 0 0
\(819\) 26.1481 0.913690
\(820\) 0 0
\(821\) 32.4244 1.13162 0.565810 0.824536i \(-0.308563\pi\)
0.565810 + 0.824536i \(0.308563\pi\)
\(822\) 0 0
\(823\) −45.2888 −1.57867 −0.789335 0.613963i \(-0.789574\pi\)
−0.789335 + 0.613963i \(0.789574\pi\)
\(824\) 0 0
\(825\) −8.97637 −0.312517
\(826\) 0 0
\(827\) 6.20933 0.215919 0.107960 0.994155i \(-0.465568\pi\)
0.107960 + 0.994155i \(0.465568\pi\)
\(828\) 0 0
\(829\) −26.6197 −0.924542 −0.462271 0.886739i \(-0.652965\pi\)
−0.462271 + 0.886739i \(0.652965\pi\)
\(830\) 0 0
\(831\) −1.01739 −0.0352930
\(832\) 0 0
\(833\) 77.7865 2.69514
\(834\) 0 0
\(835\) −24.1734 −0.836553
\(836\) 0 0
\(837\) −0.368219 −0.0127275
\(838\) 0 0
\(839\) −38.1136 −1.31583 −0.657914 0.753093i \(-0.728561\pi\)
−0.657914 + 0.753093i \(0.728561\pi\)
\(840\) 0 0
\(841\) 7.80355 0.269088
\(842\) 0 0
\(843\) 46.8000 1.61188
\(844\) 0 0
\(845\) −14.5952 −0.502090
\(846\) 0 0
\(847\) 40.8503 1.40363
\(848\) 0 0
\(849\) 3.44324 0.118172
\(850\) 0 0
\(851\) 8.78947 0.301299
\(852\) 0 0
\(853\) 41.0705 1.40623 0.703113 0.711078i \(-0.251793\pi\)
0.703113 + 0.711078i \(0.251793\pi\)
\(854\) 0 0
\(855\) −25.7390 −0.880254
\(856\) 0 0
\(857\) 9.40547 0.321285 0.160642 0.987013i \(-0.448643\pi\)
0.160642 + 0.987013i \(0.448643\pi\)
\(858\) 0 0
\(859\) 8.74773 0.298469 0.149234 0.988802i \(-0.452319\pi\)
0.149234 + 0.988802i \(0.452319\pi\)
\(860\) 0 0
\(861\) 0.0142774 0.000486571 0
\(862\) 0 0
\(863\) −29.6683 −1.00992 −0.504960 0.863143i \(-0.668493\pi\)
−0.504960 + 0.863143i \(0.668493\pi\)
\(864\) 0 0
\(865\) 0.410720 0.0139649
\(866\) 0 0
\(867\) −41.4856 −1.40892
\(868\) 0 0
\(869\) −9.93317 −0.336960
\(870\) 0 0
\(871\) −20.2096 −0.684776
\(872\) 0 0
\(873\) 46.6932 1.58032
\(874\) 0 0
\(875\) 53.1033 1.79522
\(876\) 0 0
\(877\) −50.7500 −1.71370 −0.856852 0.515562i \(-0.827583\pi\)
−0.856852 + 0.515562i \(0.827583\pi\)
\(878\) 0 0
\(879\) 12.5743 0.424119
\(880\) 0 0
\(881\) −9.19753 −0.309873 −0.154936 0.987924i \(-0.549517\pi\)
−0.154936 + 0.987924i \(0.549517\pi\)
\(882\) 0 0
\(883\) 25.8988 0.871564 0.435782 0.900052i \(-0.356472\pi\)
0.435782 + 0.900052i \(0.356472\pi\)
\(884\) 0 0
\(885\) −13.7346 −0.461683
\(886\) 0 0
\(887\) 40.0363 1.34429 0.672144 0.740420i \(-0.265374\pi\)
0.672144 + 0.740420i \(0.265374\pi\)
\(888\) 0 0
\(889\) 37.3096 1.25132
\(890\) 0 0
\(891\) 12.2647 0.410882
\(892\) 0 0
\(893\) 24.2608 0.811858
\(894\) 0 0
\(895\) 16.6601 0.556886
\(896\) 0 0
\(897\) 6.92182 0.231113
\(898\) 0 0
\(899\) 12.9003 0.430250
\(900\) 0 0
\(901\) 6.49742 0.216461
\(902\) 0 0
\(903\) 19.3568 0.644155
\(904\) 0 0
\(905\) 15.7946 0.525030
\(906\) 0 0
\(907\) −16.3952 −0.544393 −0.272197 0.962242i \(-0.587750\pi\)
−0.272197 + 0.962242i \(0.587750\pi\)
\(908\) 0 0
\(909\) −60.3130 −2.00046
\(910\) 0 0
\(911\) −45.3056 −1.50104 −0.750521 0.660846i \(-0.770198\pi\)
−0.750521 + 0.660846i \(0.770198\pi\)
\(912\) 0 0
\(913\) −4.92661 −0.163047
\(914\) 0 0
\(915\) 28.2057 0.932452
\(916\) 0 0
\(917\) −92.1262 −3.04227
\(918\) 0 0
\(919\) 13.2689 0.437699 0.218850 0.975759i \(-0.429770\pi\)
0.218850 + 0.975759i \(0.429770\pi\)
\(920\) 0 0
\(921\) 40.4580 1.33314
\(922\) 0 0
\(923\) −12.4332 −0.409245
\(924\) 0 0
\(925\) −15.4040 −0.506481
\(926\) 0 0
\(927\) −3.92716 −0.128985
\(928\) 0 0
\(929\) 26.3443 0.864328 0.432164 0.901795i \(-0.357750\pi\)
0.432164 + 0.901795i \(0.357750\pi\)
\(930\) 0 0
\(931\) −72.5041 −2.37622
\(932\) 0 0
\(933\) 32.3816 1.06012
\(934\) 0 0
\(935\) −12.5576 −0.410678
\(936\) 0 0
\(937\) 1.65737 0.0541440 0.0270720 0.999633i \(-0.491382\pi\)
0.0270720 + 0.999633i \(0.491382\pi\)
\(938\) 0 0
\(939\) 63.7924 2.08179
\(940\) 0 0
\(941\) −7.52502 −0.245309 −0.122654 0.992449i \(-0.539141\pi\)
−0.122654 + 0.992449i \(0.539141\pi\)
\(942\) 0 0
\(943\) 0.00191160 6.22503e−5 0
\(944\) 0 0
\(945\) 1.20843 0.0393102
\(946\) 0 0
\(947\) −51.6190 −1.67739 −0.838696 0.544599i \(-0.816682\pi\)
−0.838696 + 0.544599i \(0.816682\pi\)
\(948\) 0 0
\(949\) 15.5510 0.504806
\(950\) 0 0
\(951\) 38.7986 1.25813
\(952\) 0 0
\(953\) 13.2680 0.429793 0.214897 0.976637i \(-0.431059\pi\)
0.214897 + 0.976637i \(0.431059\pi\)
\(954\) 0 0
\(955\) 12.0638 0.390374
\(956\) 0 0
\(957\) 20.8690 0.674600
\(958\) 0 0
\(959\) 58.0238 1.87369
\(960\) 0 0
\(961\) −26.4782 −0.854135
\(962\) 0 0
\(963\) −30.7037 −0.989413
\(964\) 0 0
\(965\) 34.8512 1.12190
\(966\) 0 0
\(967\) 9.82786 0.316043 0.158021 0.987436i \(-0.449489\pi\)
0.158021 + 0.987436i \(0.449489\pi\)
\(968\) 0 0
\(969\) 77.7084 2.49635
\(970\) 0 0
\(971\) −41.3998 −1.32858 −0.664292 0.747473i \(-0.731267\pi\)
−0.664292 + 0.747473i \(0.731267\pi\)
\(972\) 0 0
\(973\) −42.8369 −1.37329
\(974\) 0 0
\(975\) −12.1309 −0.388499
\(976\) 0 0
\(977\) −12.3075 −0.393751 −0.196876 0.980428i \(-0.563080\pi\)
−0.196876 + 0.980428i \(0.563080\pi\)
\(978\) 0 0
\(979\) 14.8455 0.474464
\(980\) 0 0
\(981\) 39.7837 1.27020
\(982\) 0 0
\(983\) 57.4653 1.83286 0.916429 0.400198i \(-0.131059\pi\)
0.916429 + 0.400198i \(0.131059\pi\)
\(984\) 0 0
\(985\) −9.28598 −0.295876
\(986\) 0 0
\(987\) −49.7586 −1.58383
\(988\) 0 0
\(989\) 2.59169 0.0824110
\(990\) 0 0
\(991\) 58.8952 1.87087 0.935433 0.353503i \(-0.115010\pi\)
0.935433 + 0.353503i \(0.115010\pi\)
\(992\) 0 0
\(993\) 15.3067 0.485743
\(994\) 0 0
\(995\) 15.2872 0.484636
\(996\) 0 0
\(997\) −33.5055 −1.06113 −0.530566 0.847644i \(-0.678020\pi\)
−0.530566 + 0.847644i \(0.678020\pi\)
\(998\) 0 0
\(999\) −1.02221 −0.0323414
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.1.7 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.7 44 1.1 even 1 trivial