Properties

Label 6008.2.a.b.1.5
Level 6008
Weight 2
Character 6008.1
Self dual yes
Analytic conductor 47.974
Analytic rank 1
Dimension 44
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.5
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.99842 q^{3} +0.770002 q^{5} +1.05287 q^{7} +5.99050 q^{9} +O(q^{10})\) \(q-2.99842 q^{3} +0.770002 q^{5} +1.05287 q^{7} +5.99050 q^{9} +0.959283 q^{11} +2.31044 q^{13} -2.30879 q^{15} +0.658148 q^{17} +0.523355 q^{19} -3.15696 q^{21} +2.38449 q^{23} -4.40710 q^{25} -8.96675 q^{27} -3.71489 q^{29} -10.3577 q^{31} -2.87633 q^{33} +0.810716 q^{35} +3.08029 q^{37} -6.92767 q^{39} +5.97360 q^{41} -5.82472 q^{43} +4.61270 q^{45} -8.50628 q^{47} -5.89146 q^{49} -1.97340 q^{51} -0.661519 q^{53} +0.738650 q^{55} -1.56924 q^{57} -12.5242 q^{59} +5.54917 q^{61} +6.30724 q^{63} +1.77905 q^{65} +9.74536 q^{67} -7.14968 q^{69} +3.51967 q^{71} +10.5936 q^{73} +13.2143 q^{75} +1.01000 q^{77} +0.0967290 q^{79} +8.91457 q^{81} +2.45953 q^{83} +0.506776 q^{85} +11.1388 q^{87} -8.07248 q^{89} +2.43261 q^{91} +31.0566 q^{93} +0.402985 q^{95} -6.95906 q^{97} +5.74658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} + O(q^{10}) \) \( 44q - 14q^{3} + 7q^{5} - 20q^{7} + 38q^{9} - 19q^{11} - 10q^{13} - 17q^{15} - 16q^{17} - 25q^{19} + 16q^{21} - 29q^{23} + 29q^{25} - 50q^{27} + 35q^{29} - 49q^{31} - 28q^{33} - 37q^{35} - 30q^{37} - 28q^{39} - 14q^{41} - 35q^{43} + 6q^{45} - 45q^{47} + 20q^{49} - 17q^{51} + 18q^{53} - 53q^{55} - 31q^{57} - 57q^{59} + 27q^{61} - 77q^{63} - 21q^{65} - 56q^{67} + 36q^{69} - 52q^{71} - 68q^{73} - 77q^{75} + 37q^{77} - 55q^{79} + 28q^{81} - 51q^{83} - 16q^{85} - 67q^{87} - 21q^{89} - 51q^{91} - 14q^{93} - 56q^{95} - 67q^{97} - 58q^{99} + O(q^{100}) \)

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
\(3\) −2.99842 −1.73114 −0.865568 0.500791i \(-0.833042\pi\)
−0.865568 + 0.500791i \(0.833042\pi\)
\(4\) 0 0
\(5\) 0.770002 0.344356 0.172178 0.985066i \(-0.444920\pi\)
0.172178 + 0.985066i \(0.444920\pi\)
\(6\) 0 0
\(7\) 1.05287 0.397949 0.198975 0.980005i \(-0.436239\pi\)
0.198975 + 0.980005i \(0.436239\pi\)
\(8\) 0 0
\(9\) 5.99050 1.99683
\(10\) 0 0
\(11\) 0.959283 0.289235 0.144617 0.989488i \(-0.453805\pi\)
0.144617 + 0.989488i \(0.453805\pi\)
\(12\) 0 0
\(13\) 2.31044 0.640802 0.320401 0.947282i \(-0.396182\pi\)
0.320401 + 0.947282i \(0.396182\pi\)
\(14\) 0 0
\(15\) −2.30879 −0.596126
\(16\) 0 0
\(17\) 0.658148 0.159624 0.0798122 0.996810i \(-0.474568\pi\)
0.0798122 + 0.996810i \(0.474568\pi\)
\(18\) 0 0
\(19\) 0.523355 0.120066 0.0600329 0.998196i \(-0.480879\pi\)
0.0600329 + 0.998196i \(0.480879\pi\)
\(20\) 0 0
\(21\) −3.15696 −0.688904
\(22\) 0 0
\(23\) 2.38449 0.497200 0.248600 0.968606i \(-0.420030\pi\)
0.248600 + 0.968606i \(0.420030\pi\)
\(24\) 0 0
\(25\) −4.40710 −0.881419
\(26\) 0 0
\(27\) −8.96675 −1.72565
\(28\) 0 0
\(29\) −3.71489 −0.689838 −0.344919 0.938633i \(-0.612094\pi\)
−0.344919 + 0.938633i \(0.612094\pi\)
\(30\) 0 0
\(31\) −10.3577 −1.86029 −0.930146 0.367190i \(-0.880320\pi\)
−0.930146 + 0.367190i \(0.880320\pi\)
\(32\) 0 0
\(33\) −2.87633 −0.500704
\(34\) 0 0
\(35\) 0.810716 0.137036
\(36\) 0 0
\(37\) 3.08029 0.506397 0.253198 0.967414i \(-0.418517\pi\)
0.253198 + 0.967414i \(0.418517\pi\)
\(38\) 0 0
\(39\) −6.92767 −1.10931
\(40\) 0 0
\(41\) 5.97360 0.932920 0.466460 0.884542i \(-0.345529\pi\)
0.466460 + 0.884542i \(0.345529\pi\)
\(42\) 0 0
\(43\) −5.82472 −0.888261 −0.444131 0.895962i \(-0.646487\pi\)
−0.444131 + 0.895962i \(0.646487\pi\)
\(44\) 0 0
\(45\) 4.61270 0.687620
\(46\) 0 0
\(47\) −8.50628 −1.24077 −0.620384 0.784298i \(-0.713023\pi\)
−0.620384 + 0.784298i \(0.713023\pi\)
\(48\) 0 0
\(49\) −5.89146 −0.841637
\(50\) 0 0
\(51\) −1.97340 −0.276331
\(52\) 0 0
\(53\) −0.661519 −0.0908667 −0.0454333 0.998967i \(-0.514467\pi\)
−0.0454333 + 0.998967i \(0.514467\pi\)
\(54\) 0 0
\(55\) 0.738650 0.0995995
\(56\) 0 0
\(57\) −1.56924 −0.207850
\(58\) 0 0
\(59\) −12.5242 −1.63051 −0.815256 0.579101i \(-0.803404\pi\)
−0.815256 + 0.579101i \(0.803404\pi\)
\(60\) 0 0
\(61\) 5.54917 0.710499 0.355249 0.934772i \(-0.384396\pi\)
0.355249 + 0.934772i \(0.384396\pi\)
\(62\) 0 0
\(63\) 6.30724 0.794638
\(64\) 0 0
\(65\) 1.77905 0.220664
\(66\) 0 0
\(67\) 9.74536 1.19058 0.595292 0.803509i \(-0.297036\pi\)
0.595292 + 0.803509i \(0.297036\pi\)
\(68\) 0 0
\(69\) −7.14968 −0.860721
\(70\) 0 0
\(71\) 3.51967 0.417708 0.208854 0.977947i \(-0.433027\pi\)
0.208854 + 0.977947i \(0.433027\pi\)
\(72\) 0 0
\(73\) 10.5936 1.23989 0.619946 0.784644i \(-0.287154\pi\)
0.619946 + 0.784644i \(0.287154\pi\)
\(74\) 0 0
\(75\) 13.2143 1.52586
\(76\) 0 0
\(77\) 1.01000 0.115101
\(78\) 0 0
\(79\) 0.0967290 0.0108829 0.00544143 0.999985i \(-0.498268\pi\)
0.00544143 + 0.999985i \(0.498268\pi\)
\(80\) 0 0
\(81\) 8.91457 0.990507
\(82\) 0 0
\(83\) 2.45953 0.269969 0.134984 0.990848i \(-0.456902\pi\)
0.134984 + 0.990848i \(0.456902\pi\)
\(84\) 0 0
\(85\) 0.506776 0.0549675
\(86\) 0 0
\(87\) 11.1388 1.19420
\(88\) 0 0
\(89\) −8.07248 −0.855682 −0.427841 0.903854i \(-0.640726\pi\)
−0.427841 + 0.903854i \(0.640726\pi\)
\(90\) 0 0
\(91\) 2.43261 0.255006
\(92\) 0 0
\(93\) 31.0566 3.22042
\(94\) 0 0
\(95\) 0.402985 0.0413453
\(96\) 0 0
\(97\) −6.95906 −0.706586 −0.353293 0.935513i \(-0.614938\pi\)
−0.353293 + 0.935513i \(0.614938\pi\)
\(98\) 0 0
\(99\) 5.74658 0.577553
\(100\) 0 0
\(101\) −2.79962 −0.278573 −0.139286 0.990252i \(-0.544481\pi\)
−0.139286 + 0.990252i \(0.544481\pi\)
\(102\) 0 0
\(103\) −8.82270 −0.869327 −0.434663 0.900593i \(-0.643133\pi\)
−0.434663 + 0.900593i \(0.643133\pi\)
\(104\) 0 0
\(105\) −2.43086 −0.237228
\(106\) 0 0
\(107\) −6.76228 −0.653734 −0.326867 0.945070i \(-0.605993\pi\)
−0.326867 + 0.945070i \(0.605993\pi\)
\(108\) 0 0
\(109\) 11.8052 1.13073 0.565365 0.824841i \(-0.308735\pi\)
0.565365 + 0.824841i \(0.308735\pi\)
\(110\) 0 0
\(111\) −9.23599 −0.876642
\(112\) 0 0
\(113\) 2.03947 0.191858 0.0959288 0.995388i \(-0.469418\pi\)
0.0959288 + 0.995388i \(0.469418\pi\)
\(114\) 0 0
\(115\) 1.83606 0.171214
\(116\) 0 0
\(117\) 13.8407 1.27957
\(118\) 0 0
\(119\) 0.692947 0.0635224
\(120\) 0 0
\(121\) −10.0798 −0.916343
\(122\) 0 0
\(123\) −17.9113 −1.61501
\(124\) 0 0
\(125\) −7.24349 −0.647877
\(126\) 0 0
\(127\) −17.9176 −1.58993 −0.794964 0.606657i \(-0.792510\pi\)
−0.794964 + 0.606657i \(0.792510\pi\)
\(128\) 0 0
\(129\) 17.4649 1.53770
\(130\) 0 0
\(131\) −11.8525 −1.03556 −0.517781 0.855513i \(-0.673242\pi\)
−0.517781 + 0.855513i \(0.673242\pi\)
\(132\) 0 0
\(133\) 0.551027 0.0477801
\(134\) 0 0
\(135\) −6.90442 −0.594238
\(136\) 0 0
\(137\) 21.0998 1.80267 0.901337 0.433118i \(-0.142587\pi\)
0.901337 + 0.433118i \(0.142587\pi\)
\(138\) 0 0
\(139\) 17.5738 1.49059 0.745295 0.666735i \(-0.232309\pi\)
0.745295 + 0.666735i \(0.232309\pi\)
\(140\) 0 0
\(141\) 25.5054 2.14794
\(142\) 0 0
\(143\) 2.21637 0.185342
\(144\) 0 0
\(145\) −2.86047 −0.237549
\(146\) 0 0
\(147\) 17.6650 1.45699
\(148\) 0 0
\(149\) 12.3468 1.01149 0.505747 0.862682i \(-0.331217\pi\)
0.505747 + 0.862682i \(0.331217\pi\)
\(150\) 0 0
\(151\) 11.3490 0.923571 0.461786 0.886992i \(-0.347209\pi\)
0.461786 + 0.886992i \(0.347209\pi\)
\(152\) 0 0
\(153\) 3.94263 0.318743
\(154\) 0 0
\(155\) −7.97543 −0.640602
\(156\) 0 0
\(157\) 15.7160 1.25427 0.627137 0.778909i \(-0.284227\pi\)
0.627137 + 0.778909i \(0.284227\pi\)
\(158\) 0 0
\(159\) 1.98351 0.157303
\(160\) 0 0
\(161\) 2.51056 0.197860
\(162\) 0 0
\(163\) −12.9136 −1.01147 −0.505735 0.862689i \(-0.668778\pi\)
−0.505735 + 0.862689i \(0.668778\pi\)
\(164\) 0 0
\(165\) −2.21478 −0.172420
\(166\) 0 0
\(167\) −17.7029 −1.36989 −0.684946 0.728594i \(-0.740174\pi\)
−0.684946 + 0.728594i \(0.740174\pi\)
\(168\) 0 0
\(169\) −7.66185 −0.589373
\(170\) 0 0
\(171\) 3.13516 0.239751
\(172\) 0 0
\(173\) −2.22880 −0.169452 −0.0847261 0.996404i \(-0.527002\pi\)
−0.0847261 + 0.996404i \(0.527002\pi\)
\(174\) 0 0
\(175\) −4.64012 −0.350760
\(176\) 0 0
\(177\) 37.5528 2.82264
\(178\) 0 0
\(179\) 2.51593 0.188049 0.0940245 0.995570i \(-0.470027\pi\)
0.0940245 + 0.995570i \(0.470027\pi\)
\(180\) 0 0
\(181\) 2.32065 0.172492 0.0862461 0.996274i \(-0.472513\pi\)
0.0862461 + 0.996274i \(0.472513\pi\)
\(182\) 0 0
\(183\) −16.6387 −1.22997
\(184\) 0 0
\(185\) 2.37183 0.174380
\(186\) 0 0
\(187\) 0.631350 0.0461689
\(188\) 0 0
\(189\) −9.44087 −0.686722
\(190\) 0 0
\(191\) 3.21203 0.232415 0.116207 0.993225i \(-0.462926\pi\)
0.116207 + 0.993225i \(0.462926\pi\)
\(192\) 0 0
\(193\) −26.6807 −1.92052 −0.960259 0.279110i \(-0.909960\pi\)
−0.960259 + 0.279110i \(0.909960\pi\)
\(194\) 0 0
\(195\) −5.33432 −0.381999
\(196\) 0 0
\(197\) −21.6958 −1.54576 −0.772882 0.634549i \(-0.781186\pi\)
−0.772882 + 0.634549i \(0.781186\pi\)
\(198\) 0 0
\(199\) −1.60454 −0.113743 −0.0568714 0.998382i \(-0.518113\pi\)
−0.0568714 + 0.998382i \(0.518113\pi\)
\(200\) 0 0
\(201\) −29.2206 −2.06106
\(202\) 0 0
\(203\) −3.91131 −0.274520
\(204\) 0 0
\(205\) 4.59969 0.321256
\(206\) 0 0
\(207\) 14.2843 0.992825
\(208\) 0 0
\(209\) 0.502045 0.0347272
\(210\) 0 0
\(211\) 15.4534 1.06386 0.531928 0.846790i \(-0.321468\pi\)
0.531928 + 0.846790i \(0.321468\pi\)
\(212\) 0 0
\(213\) −10.5534 −0.723109
\(214\) 0 0
\(215\) −4.48505 −0.305878
\(216\) 0 0
\(217\) −10.9053 −0.740302
\(218\) 0 0
\(219\) −31.7642 −2.14642
\(220\) 0 0
\(221\) 1.52061 0.102288
\(222\) 0 0
\(223\) −8.64062 −0.578619 −0.289309 0.957236i \(-0.593426\pi\)
−0.289309 + 0.957236i \(0.593426\pi\)
\(224\) 0 0
\(225\) −26.4007 −1.76005
\(226\) 0 0
\(227\) −7.49293 −0.497323 −0.248662 0.968590i \(-0.579991\pi\)
−0.248662 + 0.968590i \(0.579991\pi\)
\(228\) 0 0
\(229\) 10.1037 0.667674 0.333837 0.942631i \(-0.391657\pi\)
0.333837 + 0.942631i \(0.391657\pi\)
\(230\) 0 0
\(231\) −3.02841 −0.199255
\(232\) 0 0
\(233\) 20.6694 1.35410 0.677050 0.735937i \(-0.263258\pi\)
0.677050 + 0.735937i \(0.263258\pi\)
\(234\) 0 0
\(235\) −6.54985 −0.427265
\(236\) 0 0
\(237\) −0.290034 −0.0188397
\(238\) 0 0
\(239\) −4.87871 −0.315578 −0.157789 0.987473i \(-0.550437\pi\)
−0.157789 + 0.987473i \(0.550437\pi\)
\(240\) 0 0
\(241\) 26.9054 1.73313 0.866565 0.499064i \(-0.166323\pi\)
0.866565 + 0.499064i \(0.166323\pi\)
\(242\) 0 0
\(243\) 0.170687 0.0109496
\(244\) 0 0
\(245\) −4.53643 −0.289822
\(246\) 0 0
\(247\) 1.20918 0.0769384
\(248\) 0 0
\(249\) −7.37470 −0.467353
\(250\) 0 0
\(251\) −1.70548 −0.107649 −0.0538245 0.998550i \(-0.517141\pi\)
−0.0538245 + 0.998550i \(0.517141\pi\)
\(252\) 0 0
\(253\) 2.28740 0.143807
\(254\) 0 0
\(255\) −1.51952 −0.0951563
\(256\) 0 0
\(257\) −14.2646 −0.889801 −0.444900 0.895580i \(-0.646761\pi\)
−0.444900 + 0.895580i \(0.646761\pi\)
\(258\) 0 0
\(259\) 3.24316 0.201520
\(260\) 0 0
\(261\) −22.2540 −1.37749
\(262\) 0 0
\(263\) 15.5509 0.958909 0.479454 0.877567i \(-0.340835\pi\)
0.479454 + 0.877567i \(0.340835\pi\)
\(264\) 0 0
\(265\) −0.509372 −0.0312904
\(266\) 0 0
\(267\) 24.2047 1.48130
\(268\) 0 0
\(269\) −13.1273 −0.800387 −0.400194 0.916431i \(-0.631057\pi\)
−0.400194 + 0.916431i \(0.631057\pi\)
\(270\) 0 0
\(271\) 3.36151 0.204197 0.102099 0.994774i \(-0.467444\pi\)
0.102099 + 0.994774i \(0.467444\pi\)
\(272\) 0 0
\(273\) −7.29396 −0.441451
\(274\) 0 0
\(275\) −4.22765 −0.254937
\(276\) 0 0
\(277\) −10.5315 −0.632777 −0.316388 0.948630i \(-0.602470\pi\)
−0.316388 + 0.948630i \(0.602470\pi\)
\(278\) 0 0
\(279\) −62.0476 −3.71469
\(280\) 0 0
\(281\) −8.19301 −0.488754 −0.244377 0.969680i \(-0.578583\pi\)
−0.244377 + 0.969680i \(0.578583\pi\)
\(282\) 0 0
\(283\) −8.31414 −0.494224 −0.247112 0.968987i \(-0.579482\pi\)
−0.247112 + 0.968987i \(0.579482\pi\)
\(284\) 0 0
\(285\) −1.20832 −0.0715744
\(286\) 0 0
\(287\) 6.28945 0.371255
\(288\) 0 0
\(289\) −16.5668 −0.974520
\(290\) 0 0
\(291\) 20.8662 1.22320
\(292\) 0 0
\(293\) 13.3670 0.780909 0.390455 0.920622i \(-0.372318\pi\)
0.390455 + 0.920622i \(0.372318\pi\)
\(294\) 0 0
\(295\) −9.64366 −0.561476
\(296\) 0 0
\(297\) −8.60165 −0.499118
\(298\) 0 0
\(299\) 5.50922 0.318606
\(300\) 0 0
\(301\) −6.13270 −0.353483
\(302\) 0 0
\(303\) 8.39444 0.482248
\(304\) 0 0
\(305\) 4.27288 0.244664
\(306\) 0 0
\(307\) 5.77060 0.329346 0.164673 0.986348i \(-0.447343\pi\)
0.164673 + 0.986348i \(0.447343\pi\)
\(308\) 0 0
\(309\) 26.4541 1.50492
\(310\) 0 0
\(311\) −1.75611 −0.0995799 −0.0497900 0.998760i \(-0.515855\pi\)
−0.0497900 + 0.998760i \(0.515855\pi\)
\(312\) 0 0
\(313\) −14.0944 −0.796661 −0.398330 0.917242i \(-0.630410\pi\)
−0.398330 + 0.917242i \(0.630410\pi\)
\(314\) 0 0
\(315\) 4.85659 0.273638
\(316\) 0 0
\(317\) 10.5127 0.590455 0.295227 0.955427i \(-0.404605\pi\)
0.295227 + 0.955427i \(0.404605\pi\)
\(318\) 0 0
\(319\) −3.56363 −0.199525
\(320\) 0 0
\(321\) 20.2761 1.13170
\(322\) 0 0
\(323\) 0.344445 0.0191654
\(324\) 0 0
\(325\) −10.1823 −0.564815
\(326\) 0 0
\(327\) −35.3968 −1.95745
\(328\) 0 0
\(329\) −8.95604 −0.493763
\(330\) 0 0
\(331\) −24.9288 −1.37021 −0.685104 0.728445i \(-0.740243\pi\)
−0.685104 + 0.728445i \(0.740243\pi\)
\(332\) 0 0
\(333\) 18.4525 1.01119
\(334\) 0 0
\(335\) 7.50395 0.409984
\(336\) 0 0
\(337\) −31.4419 −1.71275 −0.856376 0.516353i \(-0.827289\pi\)
−0.856376 + 0.516353i \(0.827289\pi\)
\(338\) 0 0
\(339\) −6.11519 −0.332132
\(340\) 0 0
\(341\) −9.93593 −0.538061
\(342\) 0 0
\(343\) −13.5731 −0.732878
\(344\) 0 0
\(345\) −5.50527 −0.296394
\(346\) 0 0
\(347\) 3.67123 0.197082 0.0985410 0.995133i \(-0.468582\pi\)
0.0985410 + 0.995133i \(0.468582\pi\)
\(348\) 0 0
\(349\) −14.1450 −0.757162 −0.378581 0.925568i \(-0.623588\pi\)
−0.378581 + 0.925568i \(0.623588\pi\)
\(350\) 0 0
\(351\) −20.7172 −1.10580
\(352\) 0 0
\(353\) −7.96177 −0.423763 −0.211881 0.977295i \(-0.567959\pi\)
−0.211881 + 0.977295i \(0.567959\pi\)
\(354\) 0 0
\(355\) 2.71015 0.143840
\(356\) 0 0
\(357\) −2.07774 −0.109966
\(358\) 0 0
\(359\) 10.3075 0.544011 0.272006 0.962296i \(-0.412313\pi\)
0.272006 + 0.962296i \(0.412313\pi\)
\(360\) 0 0
\(361\) −18.7261 −0.985584
\(362\) 0 0
\(363\) 30.2234 1.58632
\(364\) 0 0
\(365\) 8.15713 0.426964
\(366\) 0 0
\(367\) −25.3898 −1.32534 −0.662668 0.748913i \(-0.730576\pi\)
−0.662668 + 0.748913i \(0.730576\pi\)
\(368\) 0 0
\(369\) 35.7848 1.86288
\(370\) 0 0
\(371\) −0.696497 −0.0361603
\(372\) 0 0
\(373\) −17.9732 −0.930616 −0.465308 0.885149i \(-0.654056\pi\)
−0.465308 + 0.885149i \(0.654056\pi\)
\(374\) 0 0
\(375\) 21.7190 1.12156
\(376\) 0 0
\(377\) −8.58304 −0.442049
\(378\) 0 0
\(379\) −1.88815 −0.0969878 −0.0484939 0.998823i \(-0.515442\pi\)
−0.0484939 + 0.998823i \(0.515442\pi\)
\(380\) 0 0
\(381\) 53.7243 2.75238
\(382\) 0 0
\(383\) −31.8380 −1.62684 −0.813422 0.581674i \(-0.802398\pi\)
−0.813422 + 0.581674i \(0.802398\pi\)
\(384\) 0 0
\(385\) 0.777705 0.0396355
\(386\) 0 0
\(387\) −34.8930 −1.77371
\(388\) 0 0
\(389\) 15.9268 0.807523 0.403761 0.914864i \(-0.367703\pi\)
0.403761 + 0.914864i \(0.367703\pi\)
\(390\) 0 0
\(391\) 1.56935 0.0793652
\(392\) 0 0
\(393\) 35.5389 1.79270
\(394\) 0 0
\(395\) 0.0744816 0.00374757
\(396\) 0 0
\(397\) −25.0231 −1.25588 −0.627938 0.778263i \(-0.716101\pi\)
−0.627938 + 0.778263i \(0.716101\pi\)
\(398\) 0 0
\(399\) −1.65221 −0.0827139
\(400\) 0 0
\(401\) −21.7637 −1.08683 −0.543413 0.839465i \(-0.682868\pi\)
−0.543413 + 0.839465i \(0.682868\pi\)
\(402\) 0 0
\(403\) −23.9308 −1.19208
\(404\) 0 0
\(405\) 6.86424 0.341087
\(406\) 0 0
\(407\) 2.95487 0.146467
\(408\) 0 0
\(409\) −4.41727 −0.218420 −0.109210 0.994019i \(-0.534832\pi\)
−0.109210 + 0.994019i \(0.534832\pi\)
\(410\) 0 0
\(411\) −63.2659 −3.12068
\(412\) 0 0
\(413\) −13.1864 −0.648861
\(414\) 0 0
\(415\) 1.89385 0.0929653
\(416\) 0 0
\(417\) −52.6935 −2.58041
\(418\) 0 0
\(419\) 29.2483 1.42887 0.714436 0.699700i \(-0.246683\pi\)
0.714436 + 0.699700i \(0.246683\pi\)
\(420\) 0 0
\(421\) 10.6880 0.520899 0.260449 0.965487i \(-0.416129\pi\)
0.260449 + 0.965487i \(0.416129\pi\)
\(422\) 0 0
\(423\) −50.9568 −2.47761
\(424\) 0 0
\(425\) −2.90052 −0.140696
\(426\) 0 0
\(427\) 5.84258 0.282742
\(428\) 0 0
\(429\) −6.64559 −0.320852
\(430\) 0 0
\(431\) −13.2763 −0.639498 −0.319749 0.947502i \(-0.603599\pi\)
−0.319749 + 0.947502i \(0.603599\pi\)
\(432\) 0 0
\(433\) −21.1711 −1.01742 −0.508710 0.860938i \(-0.669877\pi\)
−0.508710 + 0.860938i \(0.669877\pi\)
\(434\) 0 0
\(435\) 8.57689 0.411230
\(436\) 0 0
\(437\) 1.24793 0.0596967
\(438\) 0 0
\(439\) −5.79351 −0.276509 −0.138255 0.990397i \(-0.544149\pi\)
−0.138255 + 0.990397i \(0.544149\pi\)
\(440\) 0 0
\(441\) −35.2927 −1.68061
\(442\) 0 0
\(443\) 22.1103 1.05049 0.525247 0.850950i \(-0.323973\pi\)
0.525247 + 0.850950i \(0.323973\pi\)
\(444\) 0 0
\(445\) −6.21583 −0.294659
\(446\) 0 0
\(447\) −37.0210 −1.75103
\(448\) 0 0
\(449\) 15.5413 0.733440 0.366720 0.930331i \(-0.380481\pi\)
0.366720 + 0.930331i \(0.380481\pi\)
\(450\) 0 0
\(451\) 5.73037 0.269833
\(452\) 0 0
\(453\) −34.0291 −1.59883
\(454\) 0 0
\(455\) 1.87311 0.0878129
\(456\) 0 0
\(457\) 0.341772 0.0159874 0.00799372 0.999968i \(-0.497455\pi\)
0.00799372 + 0.999968i \(0.497455\pi\)
\(458\) 0 0
\(459\) −5.90145 −0.275456
\(460\) 0 0
\(461\) −37.4906 −1.74611 −0.873056 0.487620i \(-0.837865\pi\)
−0.873056 + 0.487620i \(0.837865\pi\)
\(462\) 0 0
\(463\) −11.0872 −0.515267 −0.257634 0.966243i \(-0.582943\pi\)
−0.257634 + 0.966243i \(0.582943\pi\)
\(464\) 0 0
\(465\) 23.9137 1.10897
\(466\) 0 0
\(467\) −28.6005 −1.32347 −0.661737 0.749736i \(-0.730180\pi\)
−0.661737 + 0.749736i \(0.730180\pi\)
\(468\) 0 0
\(469\) 10.2606 0.473792
\(470\) 0 0
\(471\) −47.1231 −2.17132
\(472\) 0 0
\(473\) −5.58755 −0.256916
\(474\) 0 0
\(475\) −2.30648 −0.105828
\(476\) 0 0
\(477\) −3.96283 −0.181446
\(478\) 0 0
\(479\) 39.9595 1.82580 0.912898 0.408189i \(-0.133839\pi\)
0.912898 + 0.408189i \(0.133839\pi\)
\(480\) 0 0
\(481\) 7.11683 0.324500
\(482\) 0 0
\(483\) −7.52772 −0.342523
\(484\) 0 0
\(485\) −5.35849 −0.243317
\(486\) 0 0
\(487\) 7.25884 0.328929 0.164465 0.986383i \(-0.447410\pi\)
0.164465 + 0.986383i \(0.447410\pi\)
\(488\) 0 0
\(489\) 38.7203 1.75099
\(490\) 0 0
\(491\) −10.4310 −0.470744 −0.235372 0.971905i \(-0.575631\pi\)
−0.235372 + 0.971905i \(0.575631\pi\)
\(492\) 0 0
\(493\) −2.44495 −0.110115
\(494\) 0 0
\(495\) 4.42488 0.198884
\(496\) 0 0
\(497\) 3.70577 0.166226
\(498\) 0 0
\(499\) 36.2097 1.62097 0.810484 0.585761i \(-0.199204\pi\)
0.810484 + 0.585761i \(0.199204\pi\)
\(500\) 0 0
\(501\) 53.0807 2.37147
\(502\) 0 0
\(503\) −11.0925 −0.494588 −0.247294 0.968940i \(-0.579541\pi\)
−0.247294 + 0.968940i \(0.579541\pi\)
\(504\) 0 0
\(505\) −2.15572 −0.0959281
\(506\) 0 0
\(507\) 22.9734 1.02029
\(508\) 0 0
\(509\) 42.2406 1.87228 0.936140 0.351627i \(-0.114371\pi\)
0.936140 + 0.351627i \(0.114371\pi\)
\(510\) 0 0
\(511\) 11.1538 0.493414
\(512\) 0 0
\(513\) −4.69279 −0.207192
\(514\) 0 0
\(515\) −6.79350 −0.299358
\(516\) 0 0
\(517\) −8.15992 −0.358873
\(518\) 0 0
\(519\) 6.68286 0.293345
\(520\) 0 0
\(521\) −32.3459 −1.41710 −0.708551 0.705660i \(-0.750651\pi\)
−0.708551 + 0.705660i \(0.750651\pi\)
\(522\) 0 0
\(523\) −14.9568 −0.654014 −0.327007 0.945022i \(-0.606040\pi\)
−0.327007 + 0.945022i \(0.606040\pi\)
\(524\) 0 0
\(525\) 13.9130 0.607213
\(526\) 0 0
\(527\) −6.81688 −0.296948
\(528\) 0 0
\(529\) −17.3142 −0.752792
\(530\) 0 0
\(531\) −75.0262 −3.25586
\(532\) 0 0
\(533\) 13.8017 0.597817
\(534\) 0 0
\(535\) −5.20697 −0.225117
\(536\) 0 0
\(537\) −7.54379 −0.325539
\(538\) 0 0
\(539\) −5.65157 −0.243430
\(540\) 0 0
\(541\) −8.63314 −0.371168 −0.185584 0.982628i \(-0.559418\pi\)
−0.185584 + 0.982628i \(0.559418\pi\)
\(542\) 0 0
\(543\) −6.95826 −0.298608
\(544\) 0 0
\(545\) 9.09001 0.389373
\(546\) 0 0
\(547\) −27.6534 −1.18237 −0.591187 0.806535i \(-0.701340\pi\)
−0.591187 + 0.806535i \(0.701340\pi\)
\(548\) 0 0
\(549\) 33.2423 1.41875
\(550\) 0 0
\(551\) −1.94421 −0.0828260
\(552\) 0 0
\(553\) 0.101843 0.00433083
\(554\) 0 0
\(555\) −7.11174 −0.301876
\(556\) 0 0
\(557\) 7.68906 0.325796 0.162898 0.986643i \(-0.447916\pi\)
0.162898 + 0.986643i \(0.447916\pi\)
\(558\) 0 0
\(559\) −13.4577 −0.569199
\(560\) 0 0
\(561\) −1.89305 −0.0799246
\(562\) 0 0
\(563\) 11.5043 0.484850 0.242425 0.970170i \(-0.422057\pi\)
0.242425 + 0.970170i \(0.422057\pi\)
\(564\) 0 0
\(565\) 1.57040 0.0660672
\(566\) 0 0
\(567\) 9.38592 0.394172
\(568\) 0 0
\(569\) 42.2693 1.77202 0.886012 0.463663i \(-0.153465\pi\)
0.886012 + 0.463663i \(0.153465\pi\)
\(570\) 0 0
\(571\) −4.80830 −0.201221 −0.100611 0.994926i \(-0.532080\pi\)
−0.100611 + 0.994926i \(0.532080\pi\)
\(572\) 0 0
\(573\) −9.63102 −0.402341
\(574\) 0 0
\(575\) −10.5087 −0.438241
\(576\) 0 0
\(577\) 31.6921 1.31936 0.659679 0.751547i \(-0.270692\pi\)
0.659679 + 0.751547i \(0.270692\pi\)
\(578\) 0 0
\(579\) 79.9998 3.32468
\(580\) 0 0
\(581\) 2.58958 0.107434
\(582\) 0 0
\(583\) −0.634584 −0.0262818
\(584\) 0 0
\(585\) 10.6574 0.440628
\(586\) 0 0
\(587\) 14.7481 0.608717 0.304359 0.952558i \(-0.401558\pi\)
0.304359 + 0.952558i \(0.401558\pi\)
\(588\) 0 0
\(589\) −5.42074 −0.223358
\(590\) 0 0
\(591\) 65.0532 2.67593
\(592\) 0 0
\(593\) −41.3876 −1.69959 −0.849793 0.527117i \(-0.823273\pi\)
−0.849793 + 0.527117i \(0.823273\pi\)
\(594\) 0 0
\(595\) 0.533571 0.0218743
\(596\) 0 0
\(597\) 4.81108 0.196904
\(598\) 0 0
\(599\) −19.6541 −0.803045 −0.401523 0.915849i \(-0.631519\pi\)
−0.401523 + 0.915849i \(0.631519\pi\)
\(600\) 0 0
\(601\) −19.4057 −0.791575 −0.395787 0.918342i \(-0.629528\pi\)
−0.395787 + 0.918342i \(0.629528\pi\)
\(602\) 0 0
\(603\) 58.3795 2.37740
\(604\) 0 0
\(605\) −7.76145 −0.315548
\(606\) 0 0
\(607\) −20.7449 −0.842009 −0.421005 0.907058i \(-0.638322\pi\)
−0.421005 + 0.907058i \(0.638322\pi\)
\(608\) 0 0
\(609\) 11.7277 0.475232
\(610\) 0 0
\(611\) −19.6533 −0.795086
\(612\) 0 0
\(613\) −45.4275 −1.83480 −0.917399 0.397969i \(-0.869715\pi\)
−0.917399 + 0.397969i \(0.869715\pi\)
\(614\) 0 0
\(615\) −13.7918 −0.556138
\(616\) 0 0
\(617\) 4.32561 0.174143 0.0870713 0.996202i \(-0.472249\pi\)
0.0870713 + 0.996202i \(0.472249\pi\)
\(618\) 0 0
\(619\) 17.5465 0.705254 0.352627 0.935764i \(-0.385288\pi\)
0.352627 + 0.935764i \(0.385288\pi\)
\(620\) 0 0
\(621\) −21.3811 −0.857994
\(622\) 0 0
\(623\) −8.49931 −0.340518
\(624\) 0 0
\(625\) 16.4580 0.658319
\(626\) 0 0
\(627\) −1.50534 −0.0601175
\(628\) 0 0
\(629\) 2.02729 0.0808332
\(630\) 0 0
\(631\) 8.47147 0.337244 0.168622 0.985681i \(-0.446068\pi\)
0.168622 + 0.985681i \(0.446068\pi\)
\(632\) 0 0
\(633\) −46.3357 −1.84168
\(634\) 0 0
\(635\) −13.7966 −0.547500
\(636\) 0 0
\(637\) −13.6119 −0.539322
\(638\) 0 0
\(639\) 21.0846 0.834093
\(640\) 0 0
\(641\) 48.3510 1.90975 0.954875 0.297007i \(-0.0959884\pi\)
0.954875 + 0.297007i \(0.0959884\pi\)
\(642\) 0 0
\(643\) 46.2828 1.82521 0.912607 0.408838i \(-0.134066\pi\)
0.912607 + 0.408838i \(0.134066\pi\)
\(644\) 0 0
\(645\) 13.4480 0.529516
\(646\) 0 0
\(647\) −8.86453 −0.348501 −0.174250 0.984701i \(-0.555750\pi\)
−0.174250 + 0.984701i \(0.555750\pi\)
\(648\) 0 0
\(649\) −12.0142 −0.471600
\(650\) 0 0
\(651\) 32.6987 1.28156
\(652\) 0 0
\(653\) −10.9639 −0.429051 −0.214525 0.976718i \(-0.568820\pi\)
−0.214525 + 0.976718i \(0.568820\pi\)
\(654\) 0 0
\(655\) −9.12649 −0.356601
\(656\) 0 0
\(657\) 63.4612 2.47586
\(658\) 0 0
\(659\) 8.39935 0.327192 0.163596 0.986527i \(-0.447691\pi\)
0.163596 + 0.986527i \(0.447691\pi\)
\(660\) 0 0
\(661\) 12.0288 0.467868 0.233934 0.972253i \(-0.424840\pi\)
0.233934 + 0.972253i \(0.424840\pi\)
\(662\) 0 0
\(663\) −4.55943 −0.177074
\(664\) 0 0
\(665\) 0.424292 0.0164533
\(666\) 0 0
\(667\) −8.85810 −0.342987
\(668\) 0 0
\(669\) 25.9082 1.00167
\(670\) 0 0
\(671\) 5.32322 0.205501
\(672\) 0 0
\(673\) 34.6001 1.33374 0.666868 0.745176i \(-0.267634\pi\)
0.666868 + 0.745176i \(0.267634\pi\)
\(674\) 0 0
\(675\) 39.5174 1.52102
\(676\) 0 0
\(677\) −31.5688 −1.21329 −0.606645 0.794973i \(-0.707485\pi\)
−0.606645 + 0.794973i \(0.707485\pi\)
\(678\) 0 0
\(679\) −7.32702 −0.281185
\(680\) 0 0
\(681\) 22.4669 0.860935
\(682\) 0 0
\(683\) 45.2395 1.73104 0.865520 0.500874i \(-0.166988\pi\)
0.865520 + 0.500874i \(0.166988\pi\)
\(684\) 0 0
\(685\) 16.2469 0.620761
\(686\) 0 0
\(687\) −30.2952 −1.15583
\(688\) 0 0
\(689\) −1.52840 −0.0582275
\(690\) 0 0
\(691\) −22.1398 −0.842238 −0.421119 0.907005i \(-0.638363\pi\)
−0.421119 + 0.907005i \(0.638363\pi\)
\(692\) 0 0
\(693\) 6.05043 0.229837
\(694\) 0 0
\(695\) 13.5319 0.513293
\(696\) 0 0
\(697\) 3.93151 0.148917
\(698\) 0 0
\(699\) −61.9755 −2.34413
\(700\) 0 0
\(701\) 8.95277 0.338141 0.169071 0.985604i \(-0.445923\pi\)
0.169071 + 0.985604i \(0.445923\pi\)
\(702\) 0 0
\(703\) 1.61209 0.0608009
\(704\) 0 0
\(705\) 19.6392 0.739654
\(706\) 0 0
\(707\) −2.94765 −0.110858
\(708\) 0 0
\(709\) 7.49269 0.281394 0.140697 0.990053i \(-0.455066\pi\)
0.140697 + 0.990053i \(0.455066\pi\)
\(710\) 0 0
\(711\) 0.579455 0.0217313
\(712\) 0 0
\(713\) −24.6977 −0.924937
\(714\) 0 0
\(715\) 1.70661 0.0638235
\(716\) 0 0
\(717\) 14.6284 0.546308
\(718\) 0 0
\(719\) 0.772991 0.0288277 0.0144138 0.999896i \(-0.495412\pi\)
0.0144138 + 0.999896i \(0.495412\pi\)
\(720\) 0 0
\(721\) −9.28920 −0.345948
\(722\) 0 0
\(723\) −80.6736 −3.00028
\(724\) 0 0
\(725\) 16.3719 0.608036
\(726\) 0 0
\(727\) 4.85925 0.180219 0.0901097 0.995932i \(-0.471278\pi\)
0.0901097 + 0.995932i \(0.471278\pi\)
\(728\) 0 0
\(729\) −27.2555 −1.00946
\(730\) 0 0
\(731\) −3.83353 −0.141788
\(732\) 0 0
\(733\) −12.8065 −0.473019 −0.236509 0.971629i \(-0.576003\pi\)
−0.236509 + 0.971629i \(0.576003\pi\)
\(734\) 0 0
\(735\) 13.6021 0.501722
\(736\) 0 0
\(737\) 9.34855 0.344358
\(738\) 0 0
\(739\) 11.8068 0.434321 0.217160 0.976136i \(-0.430321\pi\)
0.217160 + 0.976136i \(0.430321\pi\)
\(740\) 0 0
\(741\) −3.62563 −0.133191
\(742\) 0 0
\(743\) −48.6896 −1.78625 −0.893124 0.449811i \(-0.851491\pi\)
−0.893124 + 0.449811i \(0.851491\pi\)
\(744\) 0 0
\(745\) 9.50710 0.348313
\(746\) 0 0
\(747\) 14.7338 0.539083
\(748\) 0 0
\(749\) −7.11983 −0.260153
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 5.11374 0.186355
\(754\) 0 0
\(755\) 8.73878 0.318037
\(756\) 0 0
\(757\) −35.8778 −1.30400 −0.652000 0.758219i \(-0.726070\pi\)
−0.652000 + 0.758219i \(0.726070\pi\)
\(758\) 0 0
\(759\) −6.85856 −0.248950
\(760\) 0 0
\(761\) −17.9641 −0.651197 −0.325599 0.945508i \(-0.605566\pi\)
−0.325599 + 0.945508i \(0.605566\pi\)
\(762\) 0 0
\(763\) 12.4294 0.449973
\(764\) 0 0
\(765\) 3.03584 0.109761
\(766\) 0 0
\(767\) −28.9364 −1.04483
\(768\) 0 0
\(769\) −1.16073 −0.0418569 −0.0209285 0.999781i \(-0.506662\pi\)
−0.0209285 + 0.999781i \(0.506662\pi\)
\(770\) 0 0
\(771\) 42.7712 1.54037
\(772\) 0 0
\(773\) −19.9379 −0.717117 −0.358559 0.933507i \(-0.616732\pi\)
−0.358559 + 0.933507i \(0.616732\pi\)
\(774\) 0 0
\(775\) 45.6472 1.63970
\(776\) 0 0
\(777\) −9.72434 −0.348859
\(778\) 0 0
\(779\) 3.12631 0.112012
\(780\) 0 0
\(781\) 3.37636 0.120816
\(782\) 0 0
\(783\) 33.3105 1.19042
\(784\) 0 0
\(785\) 12.1014 0.431916
\(786\) 0 0
\(787\) 24.7188 0.881130 0.440565 0.897721i \(-0.354778\pi\)
0.440565 + 0.897721i \(0.354778\pi\)
\(788\) 0 0
\(789\) −46.6280 −1.66000
\(790\) 0 0
\(791\) 2.14731 0.0763496
\(792\) 0 0
\(793\) 12.8210 0.455289
\(794\) 0 0
\(795\) 1.52731 0.0541680
\(796\) 0 0
\(797\) −9.74400 −0.345150 −0.172575 0.984996i \(-0.555209\pi\)
−0.172575 + 0.984996i \(0.555209\pi\)
\(798\) 0 0
\(799\) −5.59839 −0.198057
\(800\) 0 0
\(801\) −48.3582 −1.70865
\(802\) 0 0
\(803\) 10.1623 0.358620
\(804\) 0 0
\(805\) 1.93314 0.0681343
\(806\) 0 0
\(807\) 39.3612 1.38558
\(808\) 0 0
\(809\) 8.39624 0.295196 0.147598 0.989047i \(-0.452846\pi\)
0.147598 + 0.989047i \(0.452846\pi\)
\(810\) 0 0
\(811\) −32.6840 −1.14769 −0.573846 0.818963i \(-0.694549\pi\)
−0.573846 + 0.818963i \(0.694549\pi\)
\(812\) 0 0
\(813\) −10.0792 −0.353494
\(814\) 0 0
\(815\) −9.94348 −0.348305
\(816\) 0 0
\(817\) −3.04840 −0.106650
\(818\) 0 0
\(819\) 14.5725 0.509205
\(820\) 0 0
\(821\) −26.7719 −0.934347 −0.467174 0.884166i \(-0.654728\pi\)
−0.467174 + 0.884166i \(0.654728\pi\)
\(822\) 0 0
\(823\) 39.2327 1.36757 0.683784 0.729685i \(-0.260333\pi\)
0.683784 + 0.729685i \(0.260333\pi\)
\(824\) 0 0
\(825\) 12.6763 0.441331
\(826\) 0 0
\(827\) −22.1997 −0.771961 −0.385980 0.922507i \(-0.626137\pi\)
−0.385980 + 0.922507i \(0.626137\pi\)
\(828\) 0 0
\(829\) 14.4560 0.502076 0.251038 0.967977i \(-0.419228\pi\)
0.251038 + 0.967977i \(0.419228\pi\)
\(830\) 0 0
\(831\) 31.5778 1.09542
\(832\) 0 0
\(833\) −3.87745 −0.134346
\(834\) 0 0
\(835\) −13.6313 −0.471730
\(836\) 0 0
\(837\) 92.8747 3.21022
\(838\) 0 0
\(839\) 37.8534 1.30684 0.653422 0.756994i \(-0.273333\pi\)
0.653422 + 0.756994i \(0.273333\pi\)
\(840\) 0 0
\(841\) −15.1996 −0.524124
\(842\) 0 0
\(843\) 24.5661 0.846100
\(844\) 0 0
\(845\) −5.89965 −0.202954
\(846\) 0 0
\(847\) −10.6127 −0.364658
\(848\) 0 0
\(849\) 24.9292 0.855569
\(850\) 0 0
\(851\) 7.34491 0.251780
\(852\) 0 0
\(853\) 45.2039 1.54775 0.773876 0.633337i \(-0.218315\pi\)
0.773876 + 0.633337i \(0.218315\pi\)
\(854\) 0 0
\(855\) 2.41408 0.0825597
\(856\) 0 0
\(857\) 10.1451 0.346549 0.173274 0.984874i \(-0.444565\pi\)
0.173274 + 0.984874i \(0.444565\pi\)
\(858\) 0 0
\(859\) −8.58783 −0.293013 −0.146506 0.989210i \(-0.546803\pi\)
−0.146506 + 0.989210i \(0.546803\pi\)
\(860\) 0 0
\(861\) −18.8584 −0.642692
\(862\) 0 0
\(863\) 4.81075 0.163760 0.0818799 0.996642i \(-0.473908\pi\)
0.0818799 + 0.996642i \(0.473908\pi\)
\(864\) 0 0
\(865\) −1.71618 −0.0583518
\(866\) 0 0
\(867\) 49.6743 1.68703
\(868\) 0 0
\(869\) 0.0927905 0.00314770
\(870\) 0 0
\(871\) 22.5161 0.762929
\(872\) 0 0
\(873\) −41.6882 −1.41093
\(874\) 0 0
\(875\) −7.62648 −0.257822
\(876\) 0 0
\(877\) 4.80349 0.162202 0.0811012 0.996706i \(-0.474156\pi\)
0.0811012 + 0.996706i \(0.474156\pi\)
\(878\) 0 0
\(879\) −40.0799 −1.35186
\(880\) 0 0
\(881\) −37.4210 −1.26075 −0.630373 0.776292i \(-0.717098\pi\)
−0.630373 + 0.776292i \(0.717098\pi\)
\(882\) 0 0
\(883\) −29.2253 −0.983510 −0.491755 0.870734i \(-0.663644\pi\)
−0.491755 + 0.870734i \(0.663644\pi\)
\(884\) 0 0
\(885\) 28.9157 0.971991
\(886\) 0 0
\(887\) −9.20098 −0.308939 −0.154469 0.987998i \(-0.549367\pi\)
−0.154469 + 0.987998i \(0.549367\pi\)
\(888\) 0 0
\(889\) −18.8650 −0.632710
\(890\) 0 0
\(891\) 8.55159 0.286489
\(892\) 0 0
\(893\) −4.45180 −0.148974
\(894\) 0 0
\(895\) 1.93727 0.0647557
\(896\) 0 0
\(897\) −16.5189 −0.551551
\(898\) 0 0
\(899\) 38.4776 1.28330
\(900\) 0 0
\(901\) −0.435378 −0.0145045
\(902\) 0 0
\(903\) 18.3884 0.611927
\(904\) 0 0
\(905\) 1.78690 0.0593987
\(906\) 0 0
\(907\) 23.1419 0.768413 0.384206 0.923247i \(-0.374475\pi\)
0.384206 + 0.923247i \(0.374475\pi\)
\(908\) 0 0
\(909\) −16.7711 −0.556264
\(910\) 0 0
\(911\) −28.3804 −0.940283 −0.470142 0.882591i \(-0.655797\pi\)
−0.470142 + 0.882591i \(0.655797\pi\)
\(912\) 0 0
\(913\) 2.35939 0.0780843
\(914\) 0 0
\(915\) −12.8119 −0.423547
\(916\) 0 0
\(917\) −12.4792 −0.412101
\(918\) 0 0
\(919\) −24.0452 −0.793177 −0.396588 0.917997i \(-0.629806\pi\)
−0.396588 + 0.917997i \(0.629806\pi\)
\(920\) 0 0
\(921\) −17.3027 −0.570142
\(922\) 0 0
\(923\) 8.13199 0.267668
\(924\) 0 0
\(925\) −13.5751 −0.446348
\(926\) 0 0
\(927\) −52.8524 −1.73590
\(928\) 0 0
\(929\) 36.7347 1.20523 0.602613 0.798034i \(-0.294126\pi\)
0.602613 + 0.798034i \(0.294126\pi\)
\(930\) 0 0
\(931\) −3.08332 −0.101052
\(932\) 0 0
\(933\) 5.26555 0.172386
\(934\) 0 0
\(935\) 0.486141 0.0158985
\(936\) 0 0
\(937\) −33.0995 −1.08131 −0.540657 0.841243i \(-0.681824\pi\)
−0.540657 + 0.841243i \(0.681824\pi\)
\(938\) 0 0
\(939\) 42.2608 1.37913
\(940\) 0 0
\(941\) −13.3615 −0.435572 −0.217786 0.975997i \(-0.569884\pi\)
−0.217786 + 0.975997i \(0.569884\pi\)
\(942\) 0 0
\(943\) 14.2440 0.463848
\(944\) 0 0
\(945\) −7.26949 −0.236477
\(946\) 0 0
\(947\) 9.53312 0.309785 0.154892 0.987931i \(-0.450497\pi\)
0.154892 + 0.987931i \(0.450497\pi\)
\(948\) 0 0
\(949\) 24.4760 0.794525
\(950\) 0 0
\(951\) −31.5216 −1.02216
\(952\) 0 0
\(953\) 0.848536 0.0274868 0.0137434 0.999906i \(-0.495625\pi\)
0.0137434 + 0.999906i \(0.495625\pi\)
\(954\) 0 0
\(955\) 2.47327 0.0800333
\(956\) 0 0
\(957\) 10.6852 0.345405
\(958\) 0 0
\(959\) 22.2154 0.717373
\(960\) 0 0
\(961\) 76.2813 2.46069
\(962\) 0 0
\(963\) −40.5094 −1.30540
\(964\) 0 0
\(965\) −20.5442 −0.661341
\(966\) 0 0
\(967\) −45.8415 −1.47416 −0.737081 0.675804i \(-0.763796\pi\)
−0.737081 + 0.675804i \(0.763796\pi\)
\(968\) 0 0
\(969\) −1.03279 −0.0331780
\(970\) 0 0
\(971\) 40.0954 1.28672 0.643361 0.765563i \(-0.277540\pi\)
0.643361 + 0.765563i \(0.277540\pi\)
\(972\) 0 0
\(973\) 18.5030 0.593179
\(974\) 0 0
\(975\) 30.5309 0.977771
\(976\) 0 0
\(977\) −1.08594 −0.0347425 −0.0173712 0.999849i \(-0.505530\pi\)
−0.0173712 + 0.999849i \(0.505530\pi\)
\(978\) 0 0
\(979\) −7.74379 −0.247493
\(980\) 0 0
\(981\) 70.7189 2.25788
\(982\) 0 0
\(983\) 9.55358 0.304712 0.152356 0.988326i \(-0.451314\pi\)
0.152356 + 0.988326i \(0.451314\pi\)
\(984\) 0 0
\(985\) −16.7058 −0.532293
\(986\) 0 0
\(987\) 26.8539 0.854770
\(988\) 0 0
\(989\) −13.8890 −0.441643
\(990\) 0 0
\(991\) −25.3302 −0.804640 −0.402320 0.915499i \(-0.631796\pi\)
−0.402320 + 0.915499i \(0.631796\pi\)
\(992\) 0 0
\(993\) 74.7468 2.37202
\(994\) 0 0
\(995\) −1.23550 −0.0391680
\(996\) 0 0
\(997\) 29.1069 0.921824 0.460912 0.887446i \(-0.347522\pi\)
0.460912 + 0.887446i \(0.347522\pi\)
\(998\) 0 0
\(999\) −27.6202 −0.873865
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.1.5 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6008.2.a.b.1.5 44 1.1 even 1 trivial