Properties

Label 4598.2.a.bq.1.4
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.7488.1
Defining polynomial: \(x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.698857\) of defining polynomial
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} -1.43091 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.952503 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.43091 q^{3} +1.00000 q^{4} -0.301143 q^{5} -1.43091 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.952503 q^{9} +0.301143 q^{10} +1.43091 q^{12} +1.39771 q^{13} -1.00000 q^{14} -0.430908 q^{15} +1.00000 q^{16} +3.90931 q^{17} +0.952503 q^{18} -1.00000 q^{19} -0.301143 q^{20} +1.43091 q^{21} -3.57498 q^{23} -1.43091 q^{24} -4.90931 q^{25} -1.39771 q^{26} -5.65567 q^{27} +1.00000 q^{28} +0.635480 q^{29} +0.430908 q^{30} -8.90089 q^{31} -1.00000 q^{32} -3.90931 q^{34} -0.301143 q^{35} -0.952503 q^{36} -0.187258 q^{37} +1.00000 q^{38} +2.00000 q^{39} +0.301143 q^{40} -8.02908 q^{41} -1.43091 q^{42} +0.641364 q^{43} +0.286840 q^{45} +3.57498 q^{46} -7.55068 q^{47} +1.43091 q^{48} -6.00000 q^{49} +4.90931 q^{50} +5.59387 q^{51} +1.39771 q^{52} -0.919309 q^{53} +5.65567 q^{54} -1.00000 q^{56} -1.43091 q^{57} -0.635480 q^{58} +0.502705 q^{59} -0.430908 q^{60} +1.41072 q^{61} +8.90089 q^{62} -0.952503 q^{63} +1.00000 q^{64} -0.420912 q^{65} +8.14454 q^{67} +3.90931 q^{68} -5.11546 q^{69} +0.301143 q^{70} +7.20634 q^{71} +0.952503 q^{72} -4.86612 q^{73} +0.187258 q^{74} -7.02477 q^{75} -1.00000 q^{76} -2.00000 q^{78} -5.73363 q^{79} -0.301143 q^{80} -5.23523 q^{81} +8.02908 q^{82} +14.9152 q^{83} +1.43091 q^{84} -1.17726 q^{85} -0.641364 q^{86} +0.909313 q^{87} +3.76955 q^{89} -0.286840 q^{90} +1.39771 q^{91} -3.57498 q^{92} -12.7364 q^{93} +7.55068 q^{94} +0.301143 q^{95} -1.43091 q^{96} -1.58641 q^{97} +6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} - 2q^{5} + 2q^{6} + 4q^{7} - 4q^{8} + O(q^{10}) \) \( 4q - 4q^{2} - 2q^{3} + 4q^{4} - 2q^{5} + 2q^{6} + 4q^{7} - 4q^{8} + 2q^{10} - 2q^{12} + 4q^{13} - 4q^{14} + 6q^{15} + 4q^{16} + 4q^{17} - 4q^{19} - 2q^{20} - 2q^{21} - 8q^{23} + 2q^{24} - 8q^{25} - 4q^{26} - 14q^{27} + 4q^{28} - 2q^{29} - 6q^{30} - 4q^{32} - 4q^{34} - 2q^{35} - 10q^{37} + 4q^{38} + 8q^{39} + 2q^{40} + 2q^{41} + 2q^{42} - 16q^{43} - 8q^{45} + 8q^{46} - 2q^{48} - 24q^{49} + 8q^{50} + 4q^{52} - 6q^{53} + 14q^{54} - 4q^{56} + 2q^{57} + 2q^{58} + 22q^{59} + 6q^{60} + 2q^{61} + 4q^{64} + 20q^{65} - 20q^{67} + 4q^{68} - 2q^{69} + 2q^{70} - 10q^{71} + 10q^{74} + 2q^{75} - 4q^{76} - 8q^{78} - 6q^{79} - 2q^{80} + 20q^{81} - 2q^{82} + 34q^{83} - 2q^{84} + 16q^{86} - 8q^{87} - 2q^{89} + 8q^{90} + 4q^{91} - 8q^{92} - 40q^{93} + 2q^{95} + 2q^{96} - 8q^{97} + 24q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.43091 0.826135 0.413068 0.910700i \(-0.364457\pi\)
0.413068 + 0.910700i \(0.364457\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.301143 −0.134675 −0.0673376 0.997730i \(-0.521450\pi\)
−0.0673376 + 0.997730i \(0.521450\pi\)
\(6\) −1.43091 −0.584166
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.952503 −0.317501
\(10\) 0.301143 0.0952298
\(11\) 0 0
\(12\) 1.43091 0.413068
\(13\) 1.39771 0.387656 0.193828 0.981036i \(-0.437910\pi\)
0.193828 + 0.981036i \(0.437910\pi\)
\(14\) −1.00000 −0.267261
\(15\) −0.430908 −0.111260
\(16\) 1.00000 0.250000
\(17\) 3.90931 0.948148 0.474074 0.880485i \(-0.342783\pi\)
0.474074 + 0.880485i \(0.342783\pi\)
\(18\) 0.952503 0.224507
\(19\) −1.00000 −0.229416
\(20\) −0.301143 −0.0673376
\(21\) 1.43091 0.312250
\(22\) 0 0
\(23\) −3.57498 −0.745434 −0.372717 0.927945i \(-0.621574\pi\)
−0.372717 + 0.927945i \(0.621574\pi\)
\(24\) −1.43091 −0.292083
\(25\) −4.90931 −0.981863
\(26\) −1.39771 −0.274114
\(27\) −5.65567 −1.08843
\(28\) 1.00000 0.188982
\(29\) 0.635480 0.118006 0.0590028 0.998258i \(-0.481208\pi\)
0.0590028 + 0.998258i \(0.481208\pi\)
\(30\) 0.430908 0.0786726
\(31\) −8.90089 −1.59865 −0.799324 0.600901i \(-0.794809\pi\)
−0.799324 + 0.600901i \(0.794809\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −3.90931 −0.670442
\(35\) −0.301143 −0.0509025
\(36\) −0.952503 −0.158750
\(37\) −0.187258 −0.0307851 −0.0153925 0.999882i \(-0.504900\pi\)
−0.0153925 + 0.999882i \(0.504900\pi\)
\(38\) 1.00000 0.162221
\(39\) 2.00000 0.320256
\(40\) 0.301143 0.0476149
\(41\) −8.02908 −1.25393 −0.626966 0.779047i \(-0.715703\pi\)
−0.626966 + 0.779047i \(0.715703\pi\)
\(42\) −1.43091 −0.220794
\(43\) 0.641364 0.0978071 0.0489035 0.998804i \(-0.484427\pi\)
0.0489035 + 0.998804i \(0.484427\pi\)
\(44\) 0 0
\(45\) 0.286840 0.0427595
\(46\) 3.57498 0.527101
\(47\) −7.55068 −1.10138 −0.550690 0.834710i \(-0.685635\pi\)
−0.550690 + 0.834710i \(0.685635\pi\)
\(48\) 1.43091 0.206534
\(49\) −6.00000 −0.857143
\(50\) 4.90931 0.694282
\(51\) 5.59387 0.783298
\(52\) 1.39771 0.193828
\(53\) −0.919309 −0.126277 −0.0631384 0.998005i \(-0.520111\pi\)
−0.0631384 + 0.998005i \(0.520111\pi\)
\(54\) 5.65567 0.769639
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) −1.43091 −0.189528
\(58\) −0.635480 −0.0834426
\(59\) 0.502705 0.0654466 0.0327233 0.999464i \(-0.489582\pi\)
0.0327233 + 0.999464i \(0.489582\pi\)
\(60\) −0.430908 −0.0556300
\(61\) 1.41072 0.180624 0.0903121 0.995914i \(-0.471214\pi\)
0.0903121 + 0.995914i \(0.471214\pi\)
\(62\) 8.90089 1.13041
\(63\) −0.952503 −0.120004
\(64\) 1.00000 0.125000
\(65\) −0.420912 −0.0522077
\(66\) 0 0
\(67\) 8.14454 0.995014 0.497507 0.867460i \(-0.334249\pi\)
0.497507 + 0.867460i \(0.334249\pi\)
\(68\) 3.90931 0.474074
\(69\) −5.11546 −0.615829
\(70\) 0.301143 0.0359935
\(71\) 7.20634 0.855236 0.427618 0.903960i \(-0.359353\pi\)
0.427618 + 0.903960i \(0.359353\pi\)
\(72\) 0.952503 0.112254
\(73\) −4.86612 −0.569537 −0.284768 0.958596i \(-0.591917\pi\)
−0.284768 + 0.958596i \(0.591917\pi\)
\(74\) 0.187258 0.0217683
\(75\) −7.02477 −0.811151
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −5.73363 −0.645083 −0.322542 0.946555i \(-0.604537\pi\)
−0.322542 + 0.946555i \(0.604537\pi\)
\(80\) −0.301143 −0.0336688
\(81\) −5.23523 −0.581692
\(82\) 8.02908 0.886664
\(83\) 14.9152 1.63716 0.818578 0.574396i \(-0.194763\pi\)
0.818578 + 0.574396i \(0.194763\pi\)
\(84\) 1.43091 0.156125
\(85\) −1.17726 −0.127692
\(86\) −0.641364 −0.0691600
\(87\) 0.909313 0.0974886
\(88\) 0 0
\(89\) 3.76955 0.399572 0.199786 0.979840i \(-0.435975\pi\)
0.199786 + 0.979840i \(0.435975\pi\)
\(90\) −0.286840 −0.0302355
\(91\) 1.39771 0.146520
\(92\) −3.57498 −0.372717
\(93\) −12.7364 −1.32070
\(94\) 7.55068 0.778793
\(95\) 0.301143 0.0308966
\(96\) −1.43091 −0.146041
\(97\) −1.58641 −0.161075 −0.0805376 0.996752i \(-0.525664\pi\)
−0.0805376 + 0.996752i \(0.525664\pi\)
\(98\) 6.00000 0.606092
\(99\) 0 0
\(100\) −4.90931 −0.490931
\(101\) −6.84751 −0.681353 −0.340676 0.940181i \(-0.610656\pi\)
−0.340676 + 0.940181i \(0.610656\pi\)
\(102\) −5.59387 −0.553875
\(103\) 5.20634 0.512996 0.256498 0.966545i \(-0.417431\pi\)
0.256498 + 0.966545i \(0.417431\pi\)
\(104\) −1.39771 −0.137057
\(105\) −0.430908 −0.0420523
\(106\) 0.919309 0.0892912
\(107\) 7.67997 0.742450 0.371225 0.928543i \(-0.378938\pi\)
0.371225 + 0.928543i \(0.378938\pi\)
\(108\) −5.65567 −0.544217
\(109\) −11.1198 −1.06508 −0.532540 0.846405i \(-0.678763\pi\)
−0.532540 + 0.846405i \(0.678763\pi\)
\(110\) 0 0
\(111\) −0.267949 −0.0254326
\(112\) 1.00000 0.0944911
\(113\) −7.33180 −0.689718 −0.344859 0.938655i \(-0.612073\pi\)
−0.344859 + 0.938655i \(0.612073\pi\)
\(114\) 1.43091 0.134017
\(115\) 1.07658 0.100392
\(116\) 0.635480 0.0590028
\(117\) −1.33133 −0.123081
\(118\) −0.502705 −0.0462777
\(119\) 3.90931 0.358366
\(120\) 0.430908 0.0393363
\(121\) 0 0
\(122\) −1.41072 −0.127721
\(123\) −11.4889 −1.03592
\(124\) −8.90089 −0.799324
\(125\) 2.98412 0.266908
\(126\) 0.952503 0.0848557
\(127\) −4.07816 −0.361878 −0.180939 0.983494i \(-0.557914\pi\)
−0.180939 + 0.983494i \(0.557914\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.917732 0.0808018
\(130\) 0.420912 0.0369164
\(131\) −6.73636 −0.588558 −0.294279 0.955720i \(-0.595080\pi\)
−0.294279 + 0.955720i \(0.595080\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) −8.14454 −0.703581
\(135\) 1.70316 0.146585
\(136\) −3.90931 −0.335221
\(137\) −21.0107 −1.79506 −0.897531 0.440951i \(-0.854641\pi\)
−0.897531 + 0.440951i \(0.854641\pi\)
\(138\) 5.11546 0.435457
\(139\) −1.30272 −0.110495 −0.0552476 0.998473i \(-0.517595\pi\)
−0.0552476 + 0.998473i \(0.517595\pi\)
\(140\) −0.301143 −0.0254512
\(141\) −10.8043 −0.909888
\(142\) −7.20634 −0.604743
\(143\) 0 0
\(144\) −0.952503 −0.0793752
\(145\) −0.191370 −0.0158924
\(146\) 4.86612 0.402723
\(147\) −8.58545 −0.708116
\(148\) −0.187258 −0.0153925
\(149\) 15.9514 1.30679 0.653395 0.757017i \(-0.273344\pi\)
0.653395 + 0.757017i \(0.273344\pi\)
\(150\) 7.02477 0.573570
\(151\) −0.910890 −0.0741271 −0.0370636 0.999313i \(-0.511800\pi\)
−0.0370636 + 0.999313i \(0.511800\pi\)
\(152\) 1.00000 0.0811107
\(153\) −3.72363 −0.301038
\(154\) 0 0
\(155\) 2.68044 0.215298
\(156\) 2.00000 0.160128
\(157\) 14.4848 1.15601 0.578005 0.816033i \(-0.303831\pi\)
0.578005 + 0.816033i \(0.303831\pi\)
\(158\) 5.73363 0.456143
\(159\) −1.31545 −0.104322
\(160\) 0.301143 0.0238074
\(161\) −3.57498 −0.281748
\(162\) 5.23523 0.411319
\(163\) −14.7364 −1.15424 −0.577120 0.816659i \(-0.695824\pi\)
−0.577120 + 0.816659i \(0.695824\pi\)
\(164\) −8.02908 −0.626966
\(165\) 0 0
\(166\) −14.9152 −1.15764
\(167\) −16.4978 −1.27664 −0.638318 0.769773i \(-0.720369\pi\)
−0.638318 + 0.769773i \(0.720369\pi\)
\(168\) −1.43091 −0.110397
\(169\) −11.0464 −0.849723
\(170\) 1.17726 0.0902919
\(171\) 0.952503 0.0728397
\(172\) 0.641364 0.0489035
\(173\) 5.07638 0.385950 0.192975 0.981204i \(-0.438186\pi\)
0.192975 + 0.981204i \(0.438186\pi\)
\(174\) −0.909313 −0.0689348
\(175\) −4.90931 −0.371109
\(176\) 0 0
\(177\) 0.719324 0.0540677
\(178\) −3.76955 −0.282540
\(179\) 4.26111 0.318490 0.159245 0.987239i \(-0.449094\pi\)
0.159245 + 0.987239i \(0.449094\pi\)
\(180\) 0.286840 0.0213798
\(181\) −11.2827 −0.838639 −0.419319 0.907839i \(-0.637731\pi\)
−0.419319 + 0.907839i \(0.637731\pi\)
\(182\) −1.39771 −0.103605
\(183\) 2.01861 0.149220
\(184\) 3.57498 0.263551
\(185\) 0.0563915 0.00414598
\(186\) 12.7364 0.933875
\(187\) 0 0
\(188\) −7.55068 −0.550690
\(189\) −5.65567 −0.411389
\(190\) −0.301143 −0.0218472
\(191\) −0.495719 −0.0358690 −0.0179345 0.999839i \(-0.505709\pi\)
−0.0179345 + 0.999839i \(0.505709\pi\)
\(192\) 1.43091 0.103267
\(193\) 19.3018 1.38937 0.694687 0.719312i \(-0.255543\pi\)
0.694687 + 0.719312i \(0.255543\pi\)
\(194\) 1.58641 0.113897
\(195\) −0.602286 −0.0431306
\(196\) −6.00000 −0.428571
\(197\) 22.9591 1.63577 0.817883 0.575385i \(-0.195148\pi\)
0.817883 + 0.575385i \(0.195148\pi\)
\(198\) 0 0
\(199\) −24.5611 −1.74109 −0.870547 0.492086i \(-0.836235\pi\)
−0.870547 + 0.492086i \(0.836235\pi\)
\(200\) 4.90931 0.347141
\(201\) 11.6541 0.822016
\(202\) 6.84751 0.481789
\(203\) 0.635480 0.0446019
\(204\) 5.59387 0.391649
\(205\) 2.41790 0.168874
\(206\) −5.20634 −0.362743
\(207\) 3.40517 0.236676
\(208\) 1.39771 0.0969140
\(209\) 0 0
\(210\) 0.430908 0.0297355
\(211\) −13.0321 −0.897166 −0.448583 0.893741i \(-0.648071\pi\)
−0.448583 + 0.893741i \(0.648071\pi\)
\(212\) −0.919309 −0.0631384
\(213\) 10.3116 0.706540
\(214\) −7.67997 −0.524992
\(215\) −0.193142 −0.0131722
\(216\) 5.65567 0.384819
\(217\) −8.90089 −0.604232
\(218\) 11.1198 0.753126
\(219\) −6.96297 −0.470514
\(220\) 0 0
\(221\) 5.46410 0.367555
\(222\) 0.267949 0.0179836
\(223\) −7.01450 −0.469726 −0.234863 0.972029i \(-0.575464\pi\)
−0.234863 + 0.972029i \(0.575464\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.67613 0.311742
\(226\) 7.33180 0.487704
\(227\) −2.63089 −0.174618 −0.0873092 0.996181i \(-0.527827\pi\)
−0.0873092 + 0.996181i \(0.527827\pi\)
\(228\) −1.43091 −0.0947642
\(229\) −4.43961 −0.293377 −0.146689 0.989183i \(-0.546862\pi\)
−0.146689 + 0.989183i \(0.546862\pi\)
\(230\) −1.07658 −0.0709875
\(231\) 0 0
\(232\) −0.635480 −0.0417213
\(233\) −15.4482 −1.01205 −0.506023 0.862520i \(-0.668885\pi\)
−0.506023 + 0.862520i \(0.668885\pi\)
\(234\) 1.33133 0.0870315
\(235\) 2.27383 0.148329
\(236\) 0.502705 0.0327233
\(237\) −8.20429 −0.532926
\(238\) −3.90931 −0.253403
\(239\) −13.1489 −0.850528 −0.425264 0.905069i \(-0.639819\pi\)
−0.425264 + 0.905069i \(0.639819\pi\)
\(240\) −0.430908 −0.0278150
\(241\) −16.1545 −1.04061 −0.520303 0.853982i \(-0.674181\pi\)
−0.520303 + 0.853982i \(0.674181\pi\)
\(242\) 0 0
\(243\) 9.47587 0.607877
\(244\) 1.41072 0.0903121
\(245\) 1.80686 0.115436
\(246\) 11.4889 0.732504
\(247\) −1.39771 −0.0889344
\(248\) 8.90089 0.565207
\(249\) 21.3423 1.35251
\(250\) −2.98412 −0.188732
\(251\) 4.74683 0.299617 0.149809 0.988715i \(-0.452134\pi\)
0.149809 + 0.988715i \(0.452134\pi\)
\(252\) −0.952503 −0.0600020
\(253\) 0 0
\(254\) 4.07816 0.255886
\(255\) −1.68455 −0.105491
\(256\) 1.00000 0.0625000
\(257\) 20.6804 1.29001 0.645005 0.764178i \(-0.276855\pi\)
0.645005 + 0.764178i \(0.276855\pi\)
\(258\) −0.917732 −0.0571355
\(259\) −0.187258 −0.0116357
\(260\) −0.420912 −0.0261038
\(261\) −0.605296 −0.0374669
\(262\) 6.73636 0.416174
\(263\) −16.2184 −1.00007 −0.500034 0.866006i \(-0.666679\pi\)
−0.500034 + 0.866006i \(0.666679\pi\)
\(264\) 0 0
\(265\) 0.276843 0.0170064
\(266\) 1.00000 0.0613139
\(267\) 5.39388 0.330100
\(268\) 8.14454 0.497507
\(269\) −1.93074 −0.117719 −0.0588596 0.998266i \(-0.518746\pi\)
−0.0588596 + 0.998266i \(0.518746\pi\)
\(270\) −1.70316 −0.103651
\(271\) −4.51475 −0.274252 −0.137126 0.990554i \(-0.543786\pi\)
−0.137126 + 0.990554i \(0.543786\pi\)
\(272\) 3.90931 0.237037
\(273\) 2.00000 0.121046
\(274\) 21.0107 1.26930
\(275\) 0 0
\(276\) −5.11546 −0.307915
\(277\) −12.6071 −0.757485 −0.378743 0.925502i \(-0.623643\pi\)
−0.378743 + 0.925502i \(0.623643\pi\)
\(278\) 1.30272 0.0781319
\(279\) 8.47813 0.507572
\(280\) 0.301143 0.0179967
\(281\) 13.3200 0.794607 0.397303 0.917687i \(-0.369946\pi\)
0.397303 + 0.917687i \(0.369946\pi\)
\(282\) 10.8043 0.643388
\(283\) 24.5772 1.46096 0.730482 0.682932i \(-0.239295\pi\)
0.730482 + 0.682932i \(0.239295\pi\)
\(284\) 7.20634 0.427618
\(285\) 0.430908 0.0255248
\(286\) 0 0
\(287\) −8.02908 −0.473942
\(288\) 0.952503 0.0561268
\(289\) −1.71727 −0.101016
\(290\) 0.191370 0.0112376
\(291\) −2.27000 −0.133070
\(292\) −4.86612 −0.284768
\(293\) −6.95839 −0.406513 −0.203257 0.979125i \(-0.565153\pi\)
−0.203257 + 0.979125i \(0.565153\pi\)
\(294\) 8.58545 0.500713
\(295\) −0.151386 −0.00881403
\(296\) 0.187258 0.0108842
\(297\) 0 0
\(298\) −15.9514 −0.924040
\(299\) −4.99679 −0.288972
\(300\) −7.02477 −0.405576
\(301\) 0.641364 0.0369676
\(302\) 0.910890 0.0524158
\(303\) −9.79816 −0.562890
\(304\) −1.00000 −0.0573539
\(305\) −0.424829 −0.0243256
\(306\) 3.72363 0.212866
\(307\) 11.0608 0.631276 0.315638 0.948880i \(-0.397782\pi\)
0.315638 + 0.948880i \(0.397782\pi\)
\(308\) 0 0
\(309\) 7.44980 0.423804
\(310\) −2.68044 −0.152239
\(311\) 25.7857 1.46217 0.731087 0.682284i \(-0.239013\pi\)
0.731087 + 0.682284i \(0.239013\pi\)
\(312\) −2.00000 −0.113228
\(313\) −17.3016 −0.977945 −0.488973 0.872299i \(-0.662628\pi\)
−0.488973 + 0.872299i \(0.662628\pi\)
\(314\) −14.4848 −0.817423
\(315\) 0.286840 0.0161616
\(316\) −5.73363 −0.322542
\(317\) −11.8272 −0.664284 −0.332142 0.943229i \(-0.607771\pi\)
−0.332142 + 0.943229i \(0.607771\pi\)
\(318\) 1.31545 0.0737666
\(319\) 0 0
\(320\) −0.301143 −0.0168344
\(321\) 10.9893 0.613364
\(322\) 3.57498 0.199226
\(323\) −3.90931 −0.217520
\(324\) −5.23523 −0.290846
\(325\) −6.86182 −0.380625
\(326\) 14.7364 0.816171
\(327\) −15.9114 −0.879900
\(328\) 8.02908 0.443332
\(329\) −7.55068 −0.416282
\(330\) 0 0
\(331\) −21.1398 −1.16195 −0.580973 0.813923i \(-0.697328\pi\)
−0.580973 + 0.813923i \(0.697328\pi\)
\(332\) 14.9152 0.818578
\(333\) 0.178364 0.00977428
\(334\) 16.4978 0.902718
\(335\) −2.45267 −0.134004
\(336\) 1.43091 0.0780624
\(337\) 3.64725 0.198678 0.0993391 0.995054i \(-0.468327\pi\)
0.0993391 + 0.995054i \(0.468327\pi\)
\(338\) 11.0464 0.600845
\(339\) −10.4911 −0.569800
\(340\) −1.17726 −0.0638460
\(341\) 0 0
\(342\) −0.952503 −0.0515055
\(343\) −13.0000 −0.701934
\(344\) −0.641364 −0.0345800
\(345\) 1.54049 0.0829369
\(346\) −5.07638 −0.272908
\(347\) 5.70933 0.306493 0.153246 0.988188i \(-0.451027\pi\)
0.153246 + 0.988188i \(0.451027\pi\)
\(348\) 0.909313 0.0487443
\(349\) 7.82910 0.419082 0.209541 0.977800i \(-0.432803\pi\)
0.209541 + 0.977800i \(0.432803\pi\)
\(350\) 4.90931 0.262414
\(351\) −7.90501 −0.421938
\(352\) 0 0
\(353\) 3.13708 0.166970 0.0834850 0.996509i \(-0.473395\pi\)
0.0834850 + 0.996509i \(0.473395\pi\)
\(354\) −0.719324 −0.0382316
\(355\) −2.17014 −0.115179
\(356\) 3.76955 0.199786
\(357\) 5.59387 0.296059
\(358\) −4.26111 −0.225206
\(359\) −9.10566 −0.480578 −0.240289 0.970701i \(-0.577242\pi\)
−0.240289 + 0.970701i \(0.577242\pi\)
\(360\) −0.286840 −0.0151178
\(361\) 1.00000 0.0526316
\(362\) 11.2827 0.593007
\(363\) 0 0
\(364\) 1.39771 0.0732601
\(365\) 1.46540 0.0767025
\(366\) −2.01861 −0.105514
\(367\) 1.30291 0.0680116 0.0340058 0.999422i \(-0.489174\pi\)
0.0340058 + 0.999422i \(0.489174\pi\)
\(368\) −3.57498 −0.186359
\(369\) 7.64772 0.398125
\(370\) −0.0563915 −0.00293165
\(371\) −0.919309 −0.0477281
\(372\) −12.7364 −0.660349
\(373\) −0.845461 −0.0437763 −0.0218882 0.999760i \(-0.506968\pi\)
−0.0218882 + 0.999760i \(0.506968\pi\)
\(374\) 0 0
\(375\) 4.27000 0.220502
\(376\) 7.55068 0.389396
\(377\) 0.888219 0.0457456
\(378\) 5.65567 0.290896
\(379\) −16.4689 −0.845950 −0.422975 0.906141i \(-0.639014\pi\)
−0.422975 + 0.906141i \(0.639014\pi\)
\(380\) 0.301143 0.0154483
\(381\) −5.83546 −0.298960
\(382\) 0.495719 0.0253632
\(383\) 14.8014 0.756319 0.378159 0.925741i \(-0.376557\pi\)
0.378159 + 0.925741i \(0.376557\pi\)
\(384\) −1.43091 −0.0730207
\(385\) 0 0
\(386\) −19.3018 −0.982436
\(387\) −0.610901 −0.0310538
\(388\) −1.58641 −0.0805376
\(389\) −3.91931 −0.198717 −0.0993584 0.995052i \(-0.531679\pi\)
−0.0993584 + 0.995052i \(0.531679\pi\)
\(390\) 0.602286 0.0304979
\(391\) −13.9757 −0.706782
\(392\) 6.00000 0.303046
\(393\) −9.63911 −0.486229
\(394\) −22.9591 −1.15666
\(395\) 1.72664 0.0868768
\(396\) 0 0
\(397\) 12.9082 0.647845 0.323922 0.946084i \(-0.394998\pi\)
0.323922 + 0.946084i \(0.394998\pi\)
\(398\) 24.5611 1.23114
\(399\) −1.43091 −0.0716350
\(400\) −4.90931 −0.245466
\(401\) −2.53413 −0.126548 −0.0632741 0.997996i \(-0.520154\pi\)
−0.0632741 + 0.997996i \(0.520154\pi\)
\(402\) −11.6541 −0.581253
\(403\) −12.4409 −0.619726
\(404\) −6.84751 −0.340676
\(405\) 1.57655 0.0783395
\(406\) −0.635480 −0.0315383
\(407\) 0 0
\(408\) −5.59387 −0.276938
\(409\) −28.3472 −1.40168 −0.700841 0.713318i \(-0.747192\pi\)
−0.700841 + 0.713318i \(0.747192\pi\)
\(410\) −2.41790 −0.119412
\(411\) −30.0643 −1.48296
\(412\) 5.20634 0.256498
\(413\) 0.502705 0.0247365
\(414\) −3.40517 −0.167355
\(415\) −4.49161 −0.220484
\(416\) −1.39771 −0.0685286
\(417\) −1.86407 −0.0912840
\(418\) 0 0
\(419\) −1.82561 −0.0891870 −0.0445935 0.999005i \(-0.514199\pi\)
−0.0445935 + 0.999005i \(0.514199\pi\)
\(420\) −0.430908 −0.0210261
\(421\) 24.0238 1.17085 0.585425 0.810727i \(-0.300928\pi\)
0.585425 + 0.810727i \(0.300928\pi\)
\(422\) 13.0321 0.634392
\(423\) 7.19204 0.349689
\(424\) 0.919309 0.0446456
\(425\) −19.1920 −0.930951
\(426\) −10.3116 −0.499599
\(427\) 1.41072 0.0682695
\(428\) 7.67997 0.371225
\(429\) 0 0
\(430\) 0.193142 0.00931414
\(431\) −21.4490 −1.03316 −0.516582 0.856238i \(-0.672796\pi\)
−0.516582 + 0.856238i \(0.672796\pi\)
\(432\) −5.65567 −0.272108
\(433\) −7.85455 −0.377466 −0.188733 0.982028i \(-0.560438\pi\)
−0.188733 + 0.982028i \(0.560438\pi\)
\(434\) 8.90089 0.427257
\(435\) −0.273833 −0.0131293
\(436\) −11.1198 −0.532540
\(437\) 3.57498 0.171014
\(438\) 6.96297 0.332704
\(439\) −0.650885 −0.0310650 −0.0155325 0.999879i \(-0.504944\pi\)
−0.0155325 + 0.999879i \(0.504944\pi\)
\(440\) 0 0
\(441\) 5.71502 0.272144
\(442\) −5.46410 −0.259901
\(443\) 4.53815 0.215614 0.107807 0.994172i \(-0.465617\pi\)
0.107807 + 0.994172i \(0.465617\pi\)
\(444\) −0.267949 −0.0127163
\(445\) −1.13517 −0.0538124
\(446\) 7.01450 0.332146
\(447\) 22.8250 1.07958
\(448\) 1.00000 0.0472456
\(449\) 37.3091 1.76073 0.880363 0.474300i \(-0.157299\pi\)
0.880363 + 0.474300i \(0.157299\pi\)
\(450\) −4.67613 −0.220435
\(451\) 0 0
\(452\) −7.33180 −0.344859
\(453\) −1.30340 −0.0612390
\(454\) 2.63089 0.123474
\(455\) −0.420912 −0.0197326
\(456\) 1.43091 0.0670084
\(457\) −21.3693 −0.999614 −0.499807 0.866137i \(-0.666596\pi\)
−0.499807 + 0.866137i \(0.666596\pi\)
\(458\) 4.43961 0.207449
\(459\) −22.1098 −1.03200
\(460\) 1.07658 0.0501958
\(461\) 9.44157 0.439738 0.219869 0.975529i \(-0.429437\pi\)
0.219869 + 0.975529i \(0.429437\pi\)
\(462\) 0 0
\(463\) −15.4976 −0.720233 −0.360117 0.932907i \(-0.617263\pi\)
−0.360117 + 0.932907i \(0.617263\pi\)
\(464\) 0.635480 0.0295014
\(465\) 3.83546 0.177865
\(466\) 15.4482 0.715625
\(467\) −5.81733 −0.269194 −0.134597 0.990900i \(-0.542974\pi\)
−0.134597 + 0.990900i \(0.542974\pi\)
\(468\) −1.33133 −0.0615406
\(469\) 8.14454 0.376080
\(470\) −2.27383 −0.104884
\(471\) 20.7264 0.955020
\(472\) −0.502705 −0.0231389
\(473\) 0 0
\(474\) 8.20429 0.376836
\(475\) 4.90931 0.225255
\(476\) 3.90931 0.179183
\(477\) 0.875644 0.0400930
\(478\) 13.1489 0.601414
\(479\) 24.8407 1.13500 0.567501 0.823373i \(-0.307910\pi\)
0.567501 + 0.823373i \(0.307910\pi\)
\(480\) 0.430908 0.0196682
\(481\) −0.261733 −0.0119340
\(482\) 16.1545 0.735819
\(483\) −5.11546 −0.232762
\(484\) 0 0
\(485\) 0.477735 0.0216928
\(486\) −9.47587 −0.429834
\(487\) −10.5918 −0.479961 −0.239980 0.970778i \(-0.577141\pi\)
−0.239980 + 0.970778i \(0.577141\pi\)
\(488\) −1.41072 −0.0638603
\(489\) −21.0864 −0.953559
\(490\) −1.80686 −0.0816255
\(491\) 38.6077 1.74234 0.871170 0.490981i \(-0.163362\pi\)
0.871170 + 0.490981i \(0.163362\pi\)
\(492\) −11.4889 −0.517959
\(493\) 2.48429 0.111887
\(494\) 1.39771 0.0628861
\(495\) 0 0
\(496\) −8.90089 −0.399662
\(497\) 7.20634 0.323249
\(498\) −21.3423 −0.956370
\(499\) 4.54198 0.203327 0.101663 0.994819i \(-0.467584\pi\)
0.101663 + 0.994819i \(0.467584\pi\)
\(500\) 2.98412 0.133454
\(501\) −23.6068 −1.05467
\(502\) −4.74683 −0.211861
\(503\) 34.6954 1.54699 0.773496 0.633801i \(-0.218506\pi\)
0.773496 + 0.633801i \(0.218506\pi\)
\(504\) 0.952503 0.0424278
\(505\) 2.06208 0.0917614
\(506\) 0 0
\(507\) −15.8064 −0.701986
\(508\) −4.07816 −0.180939
\(509\) 25.2232 1.11800 0.558999 0.829168i \(-0.311186\pi\)
0.558999 + 0.829168i \(0.311186\pi\)
\(510\) 1.68455 0.0745933
\(511\) −4.86612 −0.215265
\(512\) −1.00000 −0.0441942
\(513\) 5.65567 0.249704
\(514\) −20.6804 −0.912175
\(515\) −1.56785 −0.0690879
\(516\) 0.917732 0.0404009
\(517\) 0 0
\(518\) 0.187258 0.00822765
\(519\) 7.26384 0.318847
\(520\) 0.420912 0.0184582
\(521\) −2.72459 −0.119366 −0.0596832 0.998217i \(-0.519009\pi\)
−0.0596832 + 0.998217i \(0.519009\pi\)
\(522\) 0.605296 0.0264931
\(523\) −22.7787 −0.996044 −0.498022 0.867164i \(-0.665940\pi\)
−0.498022 + 0.867164i \(0.665940\pi\)
\(524\) −6.73636 −0.294279
\(525\) −7.02477 −0.306586
\(526\) 16.2184 0.707155
\(527\) −34.7964 −1.51575
\(528\) 0 0
\(529\) −10.2195 −0.444328
\(530\) −0.276843 −0.0120253
\(531\) −0.478828 −0.0207793
\(532\) −1.00000 −0.0433555
\(533\) −11.2224 −0.486094
\(534\) −5.39388 −0.233416
\(535\) −2.31277 −0.0999897
\(536\) −8.14454 −0.351791
\(537\) 6.09725 0.263116
\(538\) 1.93074 0.0832401
\(539\) 0 0
\(540\) 1.70316 0.0732925
\(541\) 12.8536 0.552619 0.276310 0.961069i \(-0.410889\pi\)
0.276310 + 0.961069i \(0.410889\pi\)
\(542\) 4.51475 0.193925
\(543\) −16.1445 −0.692829
\(544\) −3.90931 −0.167610
\(545\) 3.34864 0.143440
\(546\) −2.00000 −0.0855921
\(547\) 31.7903 1.35926 0.679628 0.733557i \(-0.262141\pi\)
0.679628 + 0.733557i \(0.262141\pi\)
\(548\) −21.0107 −0.897531
\(549\) −1.34372 −0.0573484
\(550\) 0 0
\(551\) −0.635480 −0.0270723
\(552\) 5.11546 0.217728
\(553\) −5.73363 −0.243819
\(554\) 12.6071 0.535623
\(555\) 0.0806910 0.00342514
\(556\) −1.30272 −0.0552476
\(557\) −3.20457 −0.135782 −0.0678910 0.997693i \(-0.521627\pi\)
−0.0678910 + 0.997693i \(0.521627\pi\)
\(558\) −8.47813 −0.358908
\(559\) 0.896443 0.0379155
\(560\) −0.301143 −0.0127256
\(561\) 0 0
\(562\) −13.3200 −0.561872
\(563\) −0.824315 −0.0347407 −0.0173704 0.999849i \(-0.505529\pi\)
−0.0173704 + 0.999849i \(0.505529\pi\)
\(564\) −10.8043 −0.454944
\(565\) 2.20792 0.0928879
\(566\) −24.5772 −1.03306
\(567\) −5.23523 −0.219859
\(568\) −7.20634 −0.302371
\(569\) −16.0832 −0.674244 −0.337122 0.941461i \(-0.609453\pi\)
−0.337122 + 0.941461i \(0.609453\pi\)
\(570\) −0.430908 −0.0180487
\(571\) −26.7916 −1.12119 −0.560597 0.828089i \(-0.689428\pi\)
−0.560597 + 0.828089i \(0.689428\pi\)
\(572\) 0 0
\(573\) −0.709328 −0.0296326
\(574\) 8.02908 0.335127
\(575\) 17.5507 0.731914
\(576\) −0.952503 −0.0396876
\(577\) 19.2616 0.801870 0.400935 0.916106i \(-0.368685\pi\)
0.400935 + 0.916106i \(0.368685\pi\)
\(578\) 1.71727 0.0714291
\(579\) 27.6191 1.14781
\(580\) −0.191370 −0.00794622
\(581\) 14.9152 0.618787
\(582\) 2.27000 0.0940946
\(583\) 0 0
\(584\) 4.86612 0.201362
\(585\) 0.400920 0.0165760
\(586\) 6.95839 0.287448
\(587\) −38.6661 −1.59592 −0.797961 0.602709i \(-0.794088\pi\)
−0.797961 + 0.602709i \(0.794088\pi\)
\(588\) −8.58545 −0.354058
\(589\) 8.90089 0.366755
\(590\) 0.151386 0.00623246
\(591\) 32.8523 1.35136
\(592\) −0.187258 −0.00769626
\(593\) 38.0454 1.56234 0.781169 0.624319i \(-0.214623\pi\)
0.781169 + 0.624319i \(0.214623\pi\)
\(594\) 0 0
\(595\) −1.17726 −0.0482630
\(596\) 15.9514 0.653395
\(597\) −35.1447 −1.43838
\(598\) 4.99679 0.204334
\(599\) 31.7240 1.29621 0.648104 0.761552i \(-0.275562\pi\)
0.648104 + 0.761552i \(0.275562\pi\)
\(600\) 7.02477 0.286785
\(601\) −47.9295 −1.95508 −0.977542 0.210739i \(-0.932413\pi\)
−0.977542 + 0.210739i \(0.932413\pi\)
\(602\) −0.641364 −0.0261400
\(603\) −7.75770 −0.315918
\(604\) −0.910890 −0.0370636
\(605\) 0 0
\(606\) 9.79816 0.398023
\(607\) 35.2950 1.43258 0.716289 0.697803i \(-0.245839\pi\)
0.716289 + 0.697803i \(0.245839\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0.909313 0.0368472
\(610\) 0.424829 0.0172008
\(611\) −10.5537 −0.426956
\(612\) −3.72363 −0.150519
\(613\) −16.4588 −0.664763 −0.332381 0.943145i \(-0.607852\pi\)
−0.332381 + 0.943145i \(0.607852\pi\)
\(614\) −11.0608 −0.446379
\(615\) 3.45979 0.139512
\(616\) 0 0
\(617\) 19.0456 0.766748 0.383374 0.923593i \(-0.374762\pi\)
0.383374 + 0.923593i \(0.374762\pi\)
\(618\) −7.44980 −0.299675
\(619\) −15.5372 −0.624492 −0.312246 0.950001i \(-0.601081\pi\)
−0.312246 + 0.950001i \(0.601081\pi\)
\(620\) 2.68044 0.107649
\(621\) 20.2189 0.811356
\(622\) −25.7857 −1.03391
\(623\) 3.76955 0.151024
\(624\) 2.00000 0.0800641
\(625\) 23.6479 0.945917
\(626\) 17.3016 0.691512
\(627\) 0 0
\(628\) 14.4848 0.578005
\(629\) −0.732051 −0.0291888
\(630\) −0.286840 −0.0114280
\(631\) −17.1545 −0.682908 −0.341454 0.939898i \(-0.610919\pi\)
−0.341454 + 0.939898i \(0.610919\pi\)
\(632\) 5.73363 0.228071
\(633\) −18.6477 −0.741180
\(634\) 11.8272 0.469720
\(635\) 1.22811 0.0487360
\(636\) −1.31545 −0.0521608
\(637\) −8.38628 −0.332277
\(638\) 0 0
\(639\) −6.86406 −0.271538
\(640\) 0.301143 0.0119037
\(641\) 3.65547 0.144382 0.0721912 0.997391i \(-0.477001\pi\)
0.0721912 + 0.997391i \(0.477001\pi\)
\(642\) −10.9893 −0.433714
\(643\) 47.9841 1.89231 0.946154 0.323716i \(-0.104932\pi\)
0.946154 + 0.323716i \(0.104932\pi\)
\(644\) −3.57498 −0.140874
\(645\) −0.276369 −0.0108820
\(646\) 3.90931 0.153810
\(647\) −44.3431 −1.74331 −0.871654 0.490121i \(-0.836953\pi\)
−0.871654 + 0.490121i \(0.836953\pi\)
\(648\) 5.23523 0.205659
\(649\) 0 0
\(650\) 6.86182 0.269143
\(651\) −12.7364 −0.499177
\(652\) −14.7364 −0.577120
\(653\) −36.1754 −1.41565 −0.707826 0.706386i \(-0.750324\pi\)
−0.707826 + 0.706386i \(0.750324\pi\)
\(654\) 15.9114 0.622184
\(655\) 2.02861 0.0792642
\(656\) −8.02908 −0.313483
\(657\) 4.63500 0.180828
\(658\) 7.55068 0.294356
\(659\) −27.7848 −1.08234 −0.541171 0.840912i \(-0.682019\pi\)
−0.541171 + 0.840912i \(0.682019\pi\)
\(660\) 0 0
\(661\) −15.1358 −0.588716 −0.294358 0.955695i \(-0.595106\pi\)
−0.294358 + 0.955695i \(0.595106\pi\)
\(662\) 21.1398 0.821620
\(663\) 7.81863 0.303650
\(664\) −14.9152 −0.578822
\(665\) 0.301143 0.0116778
\(666\) −0.178364 −0.00691146
\(667\) −2.27182 −0.0879654
\(668\) −16.4978 −0.638318
\(669\) −10.0371 −0.388057
\(670\) 2.45267 0.0947550
\(671\) 0 0
\(672\) −1.43091 −0.0551985
\(673\) 2.79968 0.107920 0.0539598 0.998543i \(-0.482816\pi\)
0.0539598 + 0.998543i \(0.482816\pi\)
\(674\) −3.64725 −0.140487
\(675\) 27.7654 1.06869
\(676\) −11.0464 −0.424861
\(677\) 0.584013 0.0224455 0.0112227 0.999937i \(-0.496428\pi\)
0.0112227 + 0.999937i \(0.496428\pi\)
\(678\) 10.4911 0.402909
\(679\) −1.58641 −0.0608807
\(680\) 1.17726 0.0451459
\(681\) −3.76457 −0.144258
\(682\) 0 0
\(683\) 5.43455 0.207947 0.103974 0.994580i \(-0.466844\pi\)
0.103974 + 0.994580i \(0.466844\pi\)
\(684\) 0.952503 0.0364199
\(685\) 6.32721 0.241750
\(686\) 13.0000 0.496342
\(687\) −6.35267 −0.242369
\(688\) 0.641364 0.0244518
\(689\) −1.28493 −0.0489520
\(690\) −1.54049 −0.0586453
\(691\) −2.27124 −0.0864020 −0.0432010 0.999066i \(-0.513756\pi\)
−0.0432010 + 0.999066i \(0.513756\pi\)
\(692\) 5.07638 0.192975
\(693\) 0 0
\(694\) −5.70933 −0.216723
\(695\) 0.392305 0.0148810
\(696\) −0.909313 −0.0344674
\(697\) −31.3882 −1.18891
\(698\) −7.82910 −0.296336
\(699\) −22.1050 −0.836087
\(700\) −4.90931 −0.185555
\(701\) −25.4477 −0.961145 −0.480572 0.876955i \(-0.659571\pi\)
−0.480572 + 0.876955i \(0.659571\pi\)
\(702\) 7.90501 0.298355
\(703\) 0.187258 0.00706258
\(704\) 0 0
\(705\) 3.25365 0.122539
\(706\) −3.13708 −0.118066
\(707\) −6.84751 −0.257527
\(708\) 0.719324 0.0270338
\(709\) −10.9778 −0.412278 −0.206139 0.978523i \(-0.566090\pi\)
−0.206139 + 0.978523i \(0.566090\pi\)
\(710\) 2.17014 0.0814439
\(711\) 5.46130 0.204815
\(712\) −3.76955 −0.141270
\(713\) 31.8205 1.19169
\(714\) −5.59387 −0.209345
\(715\) 0 0
\(716\) 4.26111 0.159245
\(717\) −18.8148 −0.702651
\(718\) 9.10566 0.339820
\(719\) −32.1855 −1.20032 −0.600158 0.799882i \(-0.704896\pi\)
−0.600158 + 0.799882i \(0.704896\pi\)
\(720\) 0.286840 0.0106899
\(721\) 5.20634 0.193894
\(722\) −1.00000 −0.0372161
\(723\) −23.1157 −0.859681
\(724\) −11.2827 −0.419319
\(725\) −3.11977 −0.115865
\(726\) 0 0
\(727\) 47.1057 1.74705 0.873526 0.486778i \(-0.161828\pi\)
0.873526 + 0.486778i \(0.161828\pi\)
\(728\) −1.39771 −0.0518027
\(729\) 29.2648 1.08388
\(730\) −1.46540 −0.0542368
\(731\) 2.50729 0.0927355
\(732\) 2.01861 0.0746100
\(733\) −39.3132 −1.45207 −0.726033 0.687660i \(-0.758638\pi\)
−0.726033 + 0.687660i \(0.758638\pi\)
\(734\) −1.30291 −0.0480915
\(735\) 2.58545 0.0953657
\(736\) 3.57498 0.131775
\(737\) 0 0
\(738\) −7.64772 −0.281517
\(739\) 29.1248 1.07137 0.535687 0.844417i \(-0.320053\pi\)
0.535687 + 0.844417i \(0.320053\pi\)
\(740\) 0.0563915 0.00207299
\(741\) −2.00000 −0.0734718
\(742\) 0.919309 0.0337489
\(743\) 16.7650 0.615047 0.307523 0.951540i \(-0.400500\pi\)
0.307523 + 0.951540i \(0.400500\pi\)
\(744\) 12.7364 0.466938
\(745\) −4.80365 −0.175992
\(746\) 0.845461 0.0309545
\(747\) −14.2068 −0.519798
\(748\) 0 0
\(749\) 7.67997 0.280620
\(750\) −4.27000 −0.155918
\(751\) 19.0714 0.695927 0.347964 0.937508i \(-0.386873\pi\)
0.347964 + 0.937508i \(0.386873\pi\)
\(752\) −7.55068 −0.275345
\(753\) 6.79227 0.247524
\(754\) −0.888219 −0.0323470
\(755\) 0.274308 0.00998309
\(756\) −5.65567 −0.205695
\(757\) −51.1070 −1.85752 −0.928759 0.370685i \(-0.879123\pi\)
−0.928759 + 0.370685i \(0.879123\pi\)
\(758\) 16.4689 0.598177
\(759\) 0 0
\(760\) −0.301143 −0.0109236
\(761\) 13.0980 0.474802 0.237401 0.971412i \(-0.423704\pi\)
0.237401 + 0.971412i \(0.423704\pi\)
\(762\) 5.83546 0.211397
\(763\) −11.1198 −0.402563
\(764\) −0.495719 −0.0179345
\(765\) 1.12135 0.0405423
\(766\) −14.8014 −0.534798
\(767\) 0.702637 0.0253708
\(768\) 1.43091 0.0516334
\(769\) 23.8480 0.859980 0.429990 0.902834i \(-0.358517\pi\)
0.429990 + 0.902834i \(0.358517\pi\)
\(770\) 0 0
\(771\) 29.5918 1.06572
\(772\) 19.3018 0.694687
\(773\) −15.1475 −0.544817 −0.272408 0.962182i \(-0.587820\pi\)
−0.272408 + 0.962182i \(0.587820\pi\)
\(774\) 0.610901 0.0219584
\(775\) 43.6973 1.56965
\(776\) 1.58641 0.0569487
\(777\) −0.267949 −0.00961262
\(778\) 3.91931 0.140514
\(779\) 8.02908 0.287672
\(780\) −0.602286 −0.0215653
\(781\) 0 0
\(782\) 13.9757 0.499770
\(783\) −3.59406 −0.128441
\(784\) −6.00000 −0.214286
\(785\) −4.36198 −0.155686
\(786\) 9.63911 0.343816
\(787\) −10.5856 −0.377335 −0.188668 0.982041i \(-0.560417\pi\)
−0.188668 + 0.982041i \(0.560417\pi\)
\(788\) 22.9591 0.817883
\(789\) −23.2070 −0.826192
\(790\) −1.72664 −0.0614312
\(791\) −7.33180 −0.260689
\(792\) 0 0
\(793\) 1.97178 0.0700201
\(794\) −12.9082 −0.458095
\(795\) 0.396137 0.0140495
\(796\) −24.5611 −0.870547
\(797\) −31.4937 −1.11556 −0.557781 0.829988i \(-0.688347\pi\)
−0.557781 + 0.829988i \(0.688347\pi\)
\(798\) 1.43091 0.0506536
\(799\) −29.5180 −1.04427
\(800\) 4.90931 0.173570
\(801\) −3.59051 −0.126864
\(802\) 2.53413 0.0894831
\(803\) 0 0
\(804\) 11.6541 0.411008
\(805\) 1.07658 0.0379444
\(806\) 12.4409 0.438212
\(807\) −2.76271 −0.0972520
\(808\) 6.84751 0.240895
\(809\) 4.29264 0.150921 0.0754606 0.997149i \(-0.475957\pi\)
0.0754606 + 0.997149i \(0.475957\pi\)
\(810\) −1.57655 −0.0553944
\(811\) 45.3464 1.59233 0.796163 0.605082i \(-0.206860\pi\)
0.796163 + 0.605082i \(0.206860\pi\)
\(812\) 0.635480 0.0223010
\(813\) −6.46019 −0.226569
\(814\) 0 0
\(815\) 4.43775 0.155448
\(816\) 5.59387 0.195824
\(817\) −0.641364 −0.0224385
\(818\) 28.3472 0.991138
\(819\) −1.33133 −0.0465203
\(820\) 2.41790 0.0844368
\(821\) −26.1744 −0.913492 −0.456746 0.889597i \(-0.650985\pi\)
−0.456746 + 0.889597i \(0.650985\pi\)
\(822\) 30.0643 1.04861
\(823\) −42.1604 −1.46962 −0.734810 0.678273i \(-0.762729\pi\)
−0.734810 + 0.678273i \(0.762729\pi\)
\(824\) −5.20634 −0.181372
\(825\) 0 0
\(826\) −0.502705 −0.0174913
\(827\) 29.8252 1.03712 0.518562 0.855040i \(-0.326468\pi\)
0.518562 + 0.855040i \(0.326468\pi\)
\(828\) 3.40517 0.118338
\(829\) −27.5800 −0.957894 −0.478947 0.877844i \(-0.658981\pi\)
−0.478947 + 0.877844i \(0.658981\pi\)
\(830\) 4.49161 0.155906
\(831\) −18.0396 −0.625785
\(832\) 1.39771 0.0484570
\(833\) −23.4559 −0.812698
\(834\) 1.86407 0.0645475
\(835\) 4.96819 0.171931
\(836\) 0 0
\(837\) 50.3405 1.74002
\(838\) 1.82561 0.0630647
\(839\) −38.6032 −1.33273 −0.666364 0.745626i \(-0.732150\pi\)
−0.666364 + 0.745626i \(0.732150\pi\)
\(840\) 0.430908 0.0148677
\(841\) −28.5962 −0.986075
\(842\) −24.0238 −0.827915
\(843\) 19.0597 0.656452
\(844\) −13.0321 −0.448583
\(845\) 3.32654 0.114437
\(846\) −7.19204 −0.247267
\(847\) 0 0
\(848\) −0.919309 −0.0315692
\(849\) 35.1677 1.20695
\(850\) 19.1920 0.658282
\(851\) 0.669444 0.0229482
\(852\) 10.3116 0.353270
\(853\) 30.2567 1.03597 0.517985 0.855390i \(-0.326682\pi\)
0.517985 + 0.855390i \(0.326682\pi\)
\(854\) −1.41072 −0.0482739
\(855\) −0.286840 −0.00980970
\(856\) −7.67997 −0.262496
\(857\) −10.1668 −0.347291 −0.173645 0.984808i \(-0.555555\pi\)
−0.173645 + 0.984808i \(0.555555\pi\)
\(858\) 0 0
\(859\) −6.90568 −0.235619 −0.117809 0.993036i \(-0.537587\pi\)
−0.117809 + 0.993036i \(0.537587\pi\)
\(860\) −0.193142 −0.00658609
\(861\) −11.4889 −0.391540
\(862\) 21.4490 0.730557
\(863\) 49.7723 1.69427 0.847134 0.531379i \(-0.178326\pi\)
0.847134 + 0.531379i \(0.178326\pi\)
\(864\) 5.65567 0.192410
\(865\) −1.52872 −0.0519779
\(866\) 7.85455 0.266908
\(867\) −2.45726 −0.0834529
\(868\) −8.90089 −0.302116
\(869\) 0 0
\(870\) 0.273833 0.00928381
\(871\) 11.3837 0.385723
\(872\) 11.1198 0.376563
\(873\) 1.51106 0.0511415
\(874\) −3.57498 −0.120925
\(875\) 2.98412 0.100882
\(876\) −6.96297 −0.235257
\(877\) 46.3334 1.56457 0.782284 0.622922i \(-0.214054\pi\)
0.782284 + 0.622922i \(0.214054\pi\)
\(878\) 0.650885 0.0219663
\(879\) −9.95681 −0.335835
\(880\) 0 0
\(881\) 19.6804 0.663051 0.331525 0.943446i \(-0.392437\pi\)
0.331525 + 0.943446i \(0.392437\pi\)
\(882\) −5.71502 −0.192435
\(883\) 34.0283 1.14514 0.572572 0.819854i \(-0.305946\pi\)
0.572572 + 0.819854i \(0.305946\pi\)
\(884\) 5.46410 0.183778
\(885\) −0.216619 −0.00728158
\(886\) −4.53815 −0.152462
\(887\) 1.87463 0.0629438 0.0314719 0.999505i \(-0.489981\pi\)
0.0314719 + 0.999505i \(0.489981\pi\)
\(888\) 0.267949 0.00899179
\(889\) −4.07816 −0.136777
\(890\) 1.13517 0.0380511
\(891\) 0 0
\(892\) −7.01450 −0.234863
\(893\) 7.55068 0.252674
\(894\) −22.8250 −0.763382
\(895\) −1.28320 −0.0428927
\(896\) −1.00000 −0.0334077
\(897\) −7.14995 −0.238730
\(898\) −37.3091 −1.24502
\(899\) −5.65634 −0.188649
\(900\) 4.67613 0.155871
\(901\) −3.59387 −0.119729
\(902\) 0 0
\(903\) 0.917732 0.0305402
\(904\) 7.33180 0.243852
\(905\) 3.39771 0.112944
\(906\) 1.30340 0.0433025
\(907\) 56.5072 1.87629 0.938145 0.346242i \(-0.112542\pi\)
0.938145 + 0.346242i \(0.112542\pi\)
\(908\) −2.63089 −0.0873092
\(909\) 6.52227 0.216330
\(910\) 0.420912 0.0139531
\(911\) 34.8858 1.15582 0.577909 0.816101i \(-0.303869\pi\)
0.577909 + 0.816101i \(0.303869\pi\)
\(912\) −1.43091 −0.0473821
\(913\) 0 0
\(914\) 21.3693 0.706834
\(915\) −0.607890 −0.0200962
\(916\) −4.43961 −0.146689
\(917\) −6.73636 −0.222454
\(918\) 22.1098 0.729731
\(919\) 27.5658 0.909312 0.454656 0.890667i \(-0.349762\pi\)
0.454656 + 0.890667i \(0.349762\pi\)
\(920\) −1.07658 −0.0354938
\(921\) 15.8270 0.521519
\(922\) −9.44157 −0.310942
\(923\) 10.0724 0.331537
\(924\) 0 0
\(925\) 0.919309 0.0302267
\(926\) 15.4976 0.509282
\(927\) −4.95906 −0.162877
\(928\) −0.635480 −0.0208606
\(929\) −56.1027 −1.84067 −0.920335 0.391131i \(-0.872084\pi\)
−0.920335 + 0.391131i \(0.872084\pi\)
\(930\) −3.83546 −0.125770
\(931\) 6.00000 0.196642
\(932\) −15.4482 −0.506023
\(933\) 36.8970 1.20795
\(934\) 5.81733 0.190349
\(935\) 0 0
\(936\) 1.33133 0.0435158
\(937\) 29.4082 0.960725 0.480363 0.877070i \(-0.340505\pi\)
0.480363 + 0.877070i \(0.340505\pi\)
\(938\) −8.14454 −0.265929
\(939\) −24.7570 −0.807915
\(940\) 2.27383 0.0741643
\(941\) −50.0127 −1.63037 −0.815184 0.579202i \(-0.803364\pi\)
−0.815184 + 0.579202i \(0.803364\pi\)
\(942\) −20.7264 −0.675301
\(943\) 28.7038 0.934724
\(944\) 0.502705 0.0163616
\(945\) 1.70316 0.0554039
\(946\) 0 0
\(947\) 20.5117 0.666542 0.333271 0.942831i \(-0.391848\pi\)
0.333271 + 0.942831i \(0.391848\pi\)
\(948\) −8.20429 −0.266463
\(949\) −6.80145 −0.220784
\(950\) −4.90931 −0.159279
\(951\) −16.9237 −0.548788
\(952\) −3.90931 −0.126702
\(953\) −12.2473 −0.396729 −0.198364 0.980128i \(-0.563563\pi\)
−0.198364 + 0.980128i \(0.563563\pi\)
\(954\) −0.875644 −0.0283500
\(955\) 0.149282 0.00483066
\(956\) −13.1489 −0.425264
\(957\) 0 0
\(958\) −24.8407 −0.802567
\(959\) −21.0107 −0.678470
\(960\) −0.430908 −0.0139075
\(961\) 48.2259 1.55567
\(962\) 0.261733 0.00843862
\(963\) −7.31519 −0.235729
\(964\) −16.1545 −0.520303
\(965\) −5.81261 −0.187114
\(966\) 5.11546 0.164587
\(967\) 14.7363 0.473889 0.236945 0.971523i \(-0.423854\pi\)
0.236945 + 0.971523i \(0.423854\pi\)
\(968\) 0 0
\(969\) −5.59387 −0.179701
\(970\) −0.477735 −0.0153391
\(971\) 16.1716 0.518970 0.259485 0.965747i \(-0.416447\pi\)
0.259485 + 0.965747i \(0.416447\pi\)
\(972\) 9.47587 0.303939
\(973\) −1.30272 −0.0417633
\(974\) 10.5918 0.339384
\(975\) −9.81863 −0.314448
\(976\) 1.41072 0.0451561
\(977\) 13.4473 0.430216 0.215108 0.976590i \(-0.430990\pi\)
0.215108 + 0.976590i \(0.430990\pi\)
\(978\) 21.0864 0.674268
\(979\) 0 0
\(980\) 1.80686 0.0577180
\(981\) 10.5916 0.338164
\(982\) −38.6077 −1.23202
\(983\) 22.9399 0.731669 0.365834 0.930680i \(-0.380784\pi\)
0.365834 + 0.930680i \(0.380784\pi\)
\(984\) 11.4889 0.366252
\(985\) −6.91396 −0.220297
\(986\) −2.48429 −0.0791159
\(987\) −10.8043 −0.343905
\(988\) −1.39771 −0.0444672
\(989\) −2.29286 −0.0729087
\(990\) 0 0
\(991\) −9.97222 −0.316778 −0.158389 0.987377i \(-0.550630\pi\)
−0.158389 + 0.987377i \(0.550630\pi\)
\(992\) 8.90089 0.282604
\(993\) −30.2490 −0.959925
\(994\) −7.20634 −0.228571
\(995\) 7.39642 0.234482
\(996\) 21.3423 0.676256
\(997\) −47.9311 −1.51799 −0.758997 0.651094i \(-0.774310\pi\)
−0.758997 + 0.651094i \(0.774310\pi\)
\(998\) −4.54198 −0.143774
\(999\) 1.05907 0.0335075
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 4598.2.a.bq.1.4 4
11.10 odd 2 4598.2.a.bt.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.bq.1.4 4 1.1 even 1 trivial
4598.2.a.bt.1.4 yes 4 11.10 odd 2