Properties

Label 8007.2.a.f.1.27
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.390980 q^{2} -1.00000 q^{3} -1.84713 q^{4} +3.91390 q^{5} -0.390980 q^{6} +2.71351 q^{7} -1.50415 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.390980 q^{2} -1.00000 q^{3} -1.84713 q^{4} +3.91390 q^{5} -0.390980 q^{6} +2.71351 q^{7} -1.50415 q^{8} +1.00000 q^{9} +1.53026 q^{10} -5.03642 q^{11} +1.84713 q^{12} -2.69008 q^{13} +1.06093 q^{14} -3.91390 q^{15} +3.10618 q^{16} -1.00000 q^{17} +0.390980 q^{18} -4.89634 q^{19} -7.22950 q^{20} -2.71351 q^{21} -1.96914 q^{22} +3.69816 q^{23} +1.50415 q^{24} +10.3186 q^{25} -1.05177 q^{26} -1.00000 q^{27} -5.01222 q^{28} +0.627384 q^{29} -1.53026 q^{30} +2.22657 q^{31} +4.22276 q^{32} +5.03642 q^{33} -0.390980 q^{34} +10.6204 q^{35} -1.84713 q^{36} -4.11141 q^{37} -1.91437 q^{38} +2.69008 q^{39} -5.88710 q^{40} -3.46252 q^{41} -1.06093 q^{42} +10.0757 q^{43} +9.30295 q^{44} +3.91390 q^{45} +1.44590 q^{46} -7.23632 q^{47} -3.10618 q^{48} +0.363126 q^{49} +4.03438 q^{50} +1.00000 q^{51} +4.96893 q^{52} -0.926864 q^{53} -0.390980 q^{54} -19.7121 q^{55} -4.08153 q^{56} +4.89634 q^{57} +0.245295 q^{58} +0.268502 q^{59} +7.22950 q^{60} -2.95056 q^{61} +0.870546 q^{62} +2.71351 q^{63} -4.56134 q^{64} -10.5287 q^{65} +1.96914 q^{66} +11.4515 q^{67} +1.84713 q^{68} -3.69816 q^{69} +4.15236 q^{70} -4.07057 q^{71} -1.50415 q^{72} -12.2324 q^{73} -1.60748 q^{74} -10.3186 q^{75} +9.04419 q^{76} -13.6664 q^{77} +1.05177 q^{78} -13.1141 q^{79} +12.1573 q^{80} +1.00000 q^{81} -1.35377 q^{82} +12.0126 q^{83} +5.01222 q^{84} -3.91390 q^{85} +3.93939 q^{86} -0.627384 q^{87} +7.57555 q^{88} +2.79877 q^{89} +1.53026 q^{90} -7.29954 q^{91} -6.83100 q^{92} -2.22657 q^{93} -2.82926 q^{94} -19.1638 q^{95} -4.22276 q^{96} -11.8418 q^{97} +0.141975 q^{98} -5.03642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.390980 0.276464 0.138232 0.990400i \(-0.455858\pi\)
0.138232 + 0.990400i \(0.455858\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.84713 −0.923567
\(5\) 3.91390 1.75035 0.875175 0.483806i \(-0.160746\pi\)
0.875175 + 0.483806i \(0.160746\pi\)
\(6\) −0.390980 −0.159617
\(7\) 2.71351 1.02561 0.512805 0.858505i \(-0.328606\pi\)
0.512805 + 0.858505i \(0.328606\pi\)
\(8\) −1.50415 −0.531798
\(9\) 1.00000 0.333333
\(10\) 1.53026 0.483910
\(11\) −5.03642 −1.51854 −0.759269 0.650777i \(-0.774443\pi\)
−0.759269 + 0.650777i \(0.774443\pi\)
\(12\) 1.84713 0.533222
\(13\) −2.69008 −0.746093 −0.373046 0.927813i \(-0.621687\pi\)
−0.373046 + 0.927813i \(0.621687\pi\)
\(14\) 1.06093 0.283545
\(15\) −3.91390 −1.01057
\(16\) 3.10618 0.776544
\(17\) −1.00000 −0.242536
\(18\) 0.390980 0.0921548
\(19\) −4.89634 −1.12330 −0.561648 0.827376i \(-0.689833\pi\)
−0.561648 + 0.827376i \(0.689833\pi\)
\(20\) −7.22950 −1.61657
\(21\) −2.71351 −0.592136
\(22\) −1.96914 −0.419822
\(23\) 3.69816 0.771119 0.385560 0.922683i \(-0.374008\pi\)
0.385560 + 0.922683i \(0.374008\pi\)
\(24\) 1.50415 0.307034
\(25\) 10.3186 2.06373
\(26\) −1.05177 −0.206268
\(27\) −1.00000 −0.192450
\(28\) −5.01222 −0.947220
\(29\) 0.627384 0.116502 0.0582512 0.998302i \(-0.481448\pi\)
0.0582512 + 0.998302i \(0.481448\pi\)
\(30\) −1.53026 −0.279385
\(31\) 2.22657 0.399905 0.199952 0.979806i \(-0.435921\pi\)
0.199952 + 0.979806i \(0.435921\pi\)
\(32\) 4.22276 0.746485
\(33\) 5.03642 0.876729
\(34\) −0.390980 −0.0670525
\(35\) 10.6204 1.79518
\(36\) −1.84713 −0.307856
\(37\) −4.11141 −0.675911 −0.337956 0.941162i \(-0.609735\pi\)
−0.337956 + 0.941162i \(0.609735\pi\)
\(38\) −1.91437 −0.310552
\(39\) 2.69008 0.430757
\(40\) −5.88710 −0.930833
\(41\) −3.46252 −0.540754 −0.270377 0.962754i \(-0.587148\pi\)
−0.270377 + 0.962754i \(0.587148\pi\)
\(42\) −1.06093 −0.163705
\(43\) 10.0757 1.53653 0.768265 0.640132i \(-0.221120\pi\)
0.768265 + 0.640132i \(0.221120\pi\)
\(44\) 9.30295 1.40247
\(45\) 3.91390 0.583450
\(46\) 1.44590 0.213187
\(47\) −7.23632 −1.05553 −0.527763 0.849392i \(-0.676969\pi\)
−0.527763 + 0.849392i \(0.676969\pi\)
\(48\) −3.10618 −0.448338
\(49\) 0.363126 0.0518751
\(50\) 4.03438 0.570547
\(51\) 1.00000 0.140028
\(52\) 4.96893 0.689067
\(53\) −0.926864 −0.127315 −0.0636573 0.997972i \(-0.520276\pi\)
−0.0636573 + 0.997972i \(0.520276\pi\)
\(54\) −0.390980 −0.0532056
\(55\) −19.7121 −2.65797
\(56\) −4.08153 −0.545417
\(57\) 4.89634 0.648536
\(58\) 0.245295 0.0322088
\(59\) 0.268502 0.0349560 0.0174780 0.999847i \(-0.494436\pi\)
0.0174780 + 0.999847i \(0.494436\pi\)
\(60\) 7.22950 0.933325
\(61\) −2.95056 −0.377780 −0.188890 0.981998i \(-0.560489\pi\)
−0.188890 + 0.981998i \(0.560489\pi\)
\(62\) 0.870546 0.110559
\(63\) 2.71351 0.341870
\(64\) −4.56134 −0.570168
\(65\) −10.5287 −1.30592
\(66\) 1.96914 0.242384
\(67\) 11.4515 1.39902 0.699509 0.714624i \(-0.253402\pi\)
0.699509 + 0.714624i \(0.253402\pi\)
\(68\) 1.84713 0.223998
\(69\) −3.69816 −0.445206
\(70\) 4.15236 0.496302
\(71\) −4.07057 −0.483088 −0.241544 0.970390i \(-0.577654\pi\)
−0.241544 + 0.970390i \(0.577654\pi\)
\(72\) −1.50415 −0.177266
\(73\) −12.2324 −1.43169 −0.715845 0.698260i \(-0.753958\pi\)
−0.715845 + 0.698260i \(0.753958\pi\)
\(74\) −1.60748 −0.186865
\(75\) −10.3186 −1.19149
\(76\) 9.04419 1.03744
\(77\) −13.6664 −1.55743
\(78\) 1.05177 0.119089
\(79\) −13.1141 −1.47545 −0.737723 0.675103i \(-0.764099\pi\)
−0.737723 + 0.675103i \(0.764099\pi\)
\(80\) 12.1573 1.35922
\(81\) 1.00000 0.111111
\(82\) −1.35377 −0.149499
\(83\) 12.0126 1.31856 0.659280 0.751898i \(-0.270861\pi\)
0.659280 + 0.751898i \(0.270861\pi\)
\(84\) 5.01222 0.546878
\(85\) −3.91390 −0.424522
\(86\) 3.93939 0.424796
\(87\) −0.627384 −0.0672627
\(88\) 7.57555 0.807556
\(89\) 2.79877 0.296669 0.148335 0.988937i \(-0.452609\pi\)
0.148335 + 0.988937i \(0.452609\pi\)
\(90\) 1.53026 0.161303
\(91\) −7.29954 −0.765200
\(92\) −6.83100 −0.712180
\(93\) −2.22657 −0.230885
\(94\) −2.82926 −0.291815
\(95\) −19.1638 −1.96616
\(96\) −4.22276 −0.430983
\(97\) −11.8418 −1.20235 −0.601175 0.799118i \(-0.705300\pi\)
−0.601175 + 0.799118i \(0.705300\pi\)
\(98\) 0.141975 0.0143416
\(99\) −5.03642 −0.506179
\(100\) −19.0599 −1.90599
\(101\) −18.3679 −1.82768 −0.913839 0.406077i \(-0.866897\pi\)
−0.913839 + 0.406077i \(0.866897\pi\)
\(102\) 0.390980 0.0387128
\(103\) −6.88240 −0.678143 −0.339071 0.940761i \(-0.610113\pi\)
−0.339071 + 0.940761i \(0.610113\pi\)
\(104\) 4.04628 0.396771
\(105\) −10.6204 −1.03645
\(106\) −0.362385 −0.0351980
\(107\) 8.90217 0.860606 0.430303 0.902685i \(-0.358407\pi\)
0.430303 + 0.902685i \(0.358407\pi\)
\(108\) 1.84713 0.177741
\(109\) −7.57002 −0.725076 −0.362538 0.931969i \(-0.618090\pi\)
−0.362538 + 0.931969i \(0.618090\pi\)
\(110\) −7.70702 −0.734835
\(111\) 4.11141 0.390237
\(112\) 8.42863 0.796431
\(113\) 6.73057 0.633159 0.316579 0.948566i \(-0.397466\pi\)
0.316579 + 0.948566i \(0.397466\pi\)
\(114\) 1.91437 0.179297
\(115\) 14.4742 1.34973
\(116\) −1.15886 −0.107598
\(117\) −2.69008 −0.248698
\(118\) 0.104979 0.00966409
\(119\) −2.71351 −0.248747
\(120\) 5.88710 0.537417
\(121\) 14.3656 1.30596
\(122\) −1.15361 −0.104443
\(123\) 3.46252 0.312205
\(124\) −4.11278 −0.369339
\(125\) 20.8166 1.86189
\(126\) 1.06093 0.0945149
\(127\) 7.85630 0.697134 0.348567 0.937284i \(-0.386668\pi\)
0.348567 + 0.937284i \(0.386668\pi\)
\(128\) −10.2289 −0.904116
\(129\) −10.0757 −0.887116
\(130\) −4.11651 −0.361041
\(131\) −0.368603 −0.0322050 −0.0161025 0.999870i \(-0.505126\pi\)
−0.0161025 + 0.999870i \(0.505126\pi\)
\(132\) −9.30295 −0.809718
\(133\) −13.2862 −1.15206
\(134\) 4.47729 0.386779
\(135\) −3.91390 −0.336855
\(136\) 1.50415 0.128980
\(137\) −14.3166 −1.22315 −0.611574 0.791187i \(-0.709463\pi\)
−0.611574 + 0.791187i \(0.709463\pi\)
\(138\) −1.44590 −0.123084
\(139\) −21.0100 −1.78204 −0.891021 0.453962i \(-0.850010\pi\)
−0.891021 + 0.453962i \(0.850010\pi\)
\(140\) −19.6173 −1.65797
\(141\) 7.23632 0.609408
\(142\) −1.59151 −0.133557
\(143\) 13.5484 1.13297
\(144\) 3.10618 0.258848
\(145\) 2.45552 0.203920
\(146\) −4.78261 −0.395811
\(147\) −0.363126 −0.0299501
\(148\) 7.59432 0.624249
\(149\) 10.1025 0.827626 0.413813 0.910362i \(-0.364197\pi\)
0.413813 + 0.910362i \(0.364197\pi\)
\(150\) −4.03438 −0.329405
\(151\) 0.503267 0.0409553 0.0204776 0.999790i \(-0.493481\pi\)
0.0204776 + 0.999790i \(0.493481\pi\)
\(152\) 7.36483 0.597367
\(153\) −1.00000 −0.0808452
\(154\) −5.34328 −0.430573
\(155\) 8.71460 0.699973
\(156\) −4.96893 −0.397833
\(157\) −1.00000 −0.0798087
\(158\) −5.12733 −0.407908
\(159\) 0.926864 0.0735051
\(160\) 16.5275 1.30661
\(161\) 10.0350 0.790867
\(162\) 0.390980 0.0307183
\(163\) −14.5475 −1.13945 −0.569724 0.821836i \(-0.692950\pi\)
−0.569724 + 0.821836i \(0.692950\pi\)
\(164\) 6.39574 0.499423
\(165\) 19.7121 1.53458
\(166\) 4.69670 0.364535
\(167\) −16.3017 −1.26146 −0.630731 0.776002i \(-0.717245\pi\)
−0.630731 + 0.776002i \(0.717245\pi\)
\(168\) 4.08153 0.314897
\(169\) −5.76349 −0.443346
\(170\) −1.53026 −0.117365
\(171\) −4.89634 −0.374432
\(172\) −18.6112 −1.41909
\(173\) 18.7711 1.42714 0.713569 0.700585i \(-0.247077\pi\)
0.713569 + 0.700585i \(0.247077\pi\)
\(174\) −0.245295 −0.0185957
\(175\) 27.9997 2.11658
\(176\) −15.6440 −1.17921
\(177\) −0.268502 −0.0201818
\(178\) 1.09426 0.0820186
\(179\) −17.3903 −1.29981 −0.649907 0.760014i \(-0.725192\pi\)
−0.649907 + 0.760014i \(0.725192\pi\)
\(180\) −7.22950 −0.538855
\(181\) 0.951024 0.0706891 0.0353445 0.999375i \(-0.488747\pi\)
0.0353445 + 0.999375i \(0.488747\pi\)
\(182\) −2.85397 −0.211551
\(183\) 2.95056 0.218112
\(184\) −5.56259 −0.410080
\(185\) −16.0916 −1.18308
\(186\) −0.870546 −0.0638315
\(187\) 5.03642 0.368300
\(188\) 13.3665 0.974849
\(189\) −2.71351 −0.197379
\(190\) −7.49265 −0.543574
\(191\) −25.5087 −1.84575 −0.922874 0.385102i \(-0.874166\pi\)
−0.922874 + 0.385102i \(0.874166\pi\)
\(192\) 4.56134 0.329186
\(193\) 12.5600 0.904087 0.452043 0.891996i \(-0.350695\pi\)
0.452043 + 0.891996i \(0.350695\pi\)
\(194\) −4.62989 −0.332407
\(195\) 10.5287 0.753975
\(196\) −0.670743 −0.0479102
\(197\) 2.66907 0.190163 0.0950817 0.995469i \(-0.469689\pi\)
0.0950817 + 0.995469i \(0.469689\pi\)
\(198\) −1.96914 −0.139941
\(199\) 8.32187 0.589922 0.294961 0.955509i \(-0.404693\pi\)
0.294961 + 0.955509i \(0.404693\pi\)
\(200\) −15.5208 −1.09749
\(201\) −11.4515 −0.807724
\(202\) −7.18149 −0.505288
\(203\) 1.70241 0.119486
\(204\) −1.84713 −0.129325
\(205\) −13.5520 −0.946510
\(206\) −2.69088 −0.187482
\(207\) 3.69816 0.257040
\(208\) −8.35585 −0.579374
\(209\) 24.6600 1.70577
\(210\) −4.15236 −0.286540
\(211\) −9.85334 −0.678332 −0.339166 0.940727i \(-0.610145\pi\)
−0.339166 + 0.940727i \(0.610145\pi\)
\(212\) 1.71204 0.117584
\(213\) 4.07057 0.278911
\(214\) 3.48057 0.237927
\(215\) 39.4353 2.68946
\(216\) 1.50415 0.102345
\(217\) 6.04183 0.410146
\(218\) −2.95972 −0.200458
\(219\) 12.2324 0.826586
\(220\) 36.4108 2.45482
\(221\) 2.69008 0.180954
\(222\) 1.60748 0.107887
\(223\) 24.2147 1.62153 0.810767 0.585368i \(-0.199050\pi\)
0.810767 + 0.585368i \(0.199050\pi\)
\(224\) 11.4585 0.765602
\(225\) 10.3186 0.687909
\(226\) 2.63152 0.175046
\(227\) 8.04202 0.533767 0.266884 0.963729i \(-0.414006\pi\)
0.266884 + 0.963729i \(0.414006\pi\)
\(228\) −9.04419 −0.598966
\(229\) 16.1158 1.06496 0.532482 0.846441i \(-0.321259\pi\)
0.532482 + 0.846441i \(0.321259\pi\)
\(230\) 5.65913 0.373152
\(231\) 13.6664 0.899181
\(232\) −0.943681 −0.0619557
\(233\) −16.3553 −1.07147 −0.535736 0.844385i \(-0.679966\pi\)
−0.535736 + 0.844385i \(0.679966\pi\)
\(234\) −1.05177 −0.0687560
\(235\) −28.3223 −1.84754
\(236\) −0.495959 −0.0322842
\(237\) 13.1141 0.851849
\(238\) −1.06093 −0.0687697
\(239\) 25.1365 1.62595 0.812973 0.582302i \(-0.197848\pi\)
0.812973 + 0.582302i \(0.197848\pi\)
\(240\) −12.1573 −0.784748
\(241\) −15.1972 −0.978938 −0.489469 0.872021i \(-0.662809\pi\)
−0.489469 + 0.872021i \(0.662809\pi\)
\(242\) 5.61664 0.361051
\(243\) −1.00000 −0.0641500
\(244\) 5.45008 0.348906
\(245\) 1.42124 0.0907997
\(246\) 1.35377 0.0863135
\(247\) 13.1715 0.838083
\(248\) −3.34911 −0.212669
\(249\) −12.0126 −0.761271
\(250\) 8.13887 0.514747
\(251\) 6.79441 0.428859 0.214430 0.976739i \(-0.431211\pi\)
0.214430 + 0.976739i \(0.431211\pi\)
\(252\) −5.01222 −0.315740
\(253\) −18.6255 −1.17097
\(254\) 3.07166 0.192733
\(255\) 3.91390 0.245098
\(256\) 5.12339 0.320212
\(257\) 2.97235 0.185410 0.0927051 0.995694i \(-0.470449\pi\)
0.0927051 + 0.995694i \(0.470449\pi\)
\(258\) −3.93939 −0.245256
\(259\) −11.1563 −0.693221
\(260\) 19.4479 1.20611
\(261\) 0.627384 0.0388341
\(262\) −0.144117 −0.00890355
\(263\) −11.9656 −0.737830 −0.368915 0.929463i \(-0.620271\pi\)
−0.368915 + 0.929463i \(0.620271\pi\)
\(264\) −7.57555 −0.466243
\(265\) −3.62766 −0.222845
\(266\) −5.19466 −0.318505
\(267\) −2.79877 −0.171282
\(268\) −21.1524 −1.29209
\(269\) −25.5460 −1.55757 −0.778783 0.627294i \(-0.784163\pi\)
−0.778783 + 0.627294i \(0.784163\pi\)
\(270\) −1.53026 −0.0931285
\(271\) 23.9568 1.45527 0.727635 0.685965i \(-0.240620\pi\)
0.727635 + 0.685965i \(0.240620\pi\)
\(272\) −3.10618 −0.188340
\(273\) 7.29954 0.441788
\(274\) −5.59749 −0.338157
\(275\) −51.9690 −3.13385
\(276\) 6.83100 0.411178
\(277\) 21.8448 1.31252 0.656262 0.754533i \(-0.272136\pi\)
0.656262 + 0.754533i \(0.272136\pi\)
\(278\) −8.21447 −0.492671
\(279\) 2.22657 0.133302
\(280\) −15.9747 −0.954671
\(281\) −13.1790 −0.786192 −0.393096 0.919498i \(-0.628596\pi\)
−0.393096 + 0.919498i \(0.628596\pi\)
\(282\) 2.82926 0.168480
\(283\) −17.8527 −1.06123 −0.530617 0.847612i \(-0.678040\pi\)
−0.530617 + 0.847612i \(0.678040\pi\)
\(284\) 7.51889 0.446164
\(285\) 19.1638 1.13516
\(286\) 5.29713 0.313226
\(287\) −9.39557 −0.554603
\(288\) 4.22276 0.248828
\(289\) 1.00000 0.0588235
\(290\) 0.960059 0.0563766
\(291\) 11.8418 0.694177
\(292\) 22.5948 1.32226
\(293\) −14.5044 −0.847353 −0.423677 0.905813i \(-0.639261\pi\)
−0.423677 + 0.905813i \(0.639261\pi\)
\(294\) −0.141975 −0.00828015
\(295\) 1.05089 0.0611852
\(296\) 6.18418 0.359448
\(297\) 5.03642 0.292243
\(298\) 3.94986 0.228809
\(299\) −9.94832 −0.575326
\(300\) 19.0599 1.10042
\(301\) 27.3405 1.57588
\(302\) 0.196767 0.0113227
\(303\) 18.3679 1.05521
\(304\) −15.2089 −0.872289
\(305\) −11.5482 −0.661248
\(306\) −0.390980 −0.0223508
\(307\) 31.5035 1.79800 0.899000 0.437949i \(-0.144295\pi\)
0.899000 + 0.437949i \(0.144295\pi\)
\(308\) 25.2436 1.43839
\(309\) 6.88240 0.391526
\(310\) 3.40723 0.193518
\(311\) −2.25888 −0.128090 −0.0640448 0.997947i \(-0.520400\pi\)
−0.0640448 + 0.997947i \(0.520400\pi\)
\(312\) −4.04628 −0.229076
\(313\) −25.5127 −1.44206 −0.721032 0.692902i \(-0.756332\pi\)
−0.721032 + 0.692902i \(0.756332\pi\)
\(314\) −0.390980 −0.0220643
\(315\) 10.6204 0.598392
\(316\) 24.2234 1.36267
\(317\) −20.5528 −1.15436 −0.577180 0.816617i \(-0.695847\pi\)
−0.577180 + 0.816617i \(0.695847\pi\)
\(318\) 0.362385 0.0203215
\(319\) −3.15977 −0.176913
\(320\) −17.8526 −0.997993
\(321\) −8.90217 −0.496871
\(322\) 3.92347 0.218647
\(323\) 4.89634 0.272439
\(324\) −1.84713 −0.102619
\(325\) −27.7579 −1.53973
\(326\) −5.68778 −0.315017
\(327\) 7.57002 0.418623
\(328\) 5.20815 0.287572
\(329\) −19.6358 −1.08256
\(330\) 7.70702 0.424257
\(331\) −5.22816 −0.287366 −0.143683 0.989624i \(-0.545895\pi\)
−0.143683 + 0.989624i \(0.545895\pi\)
\(332\) −22.1890 −1.21778
\(333\) −4.11141 −0.225304
\(334\) −6.37362 −0.348749
\(335\) 44.8199 2.44877
\(336\) −8.42863 −0.459820
\(337\) 19.6234 1.06896 0.534478 0.845182i \(-0.320508\pi\)
0.534478 + 0.845182i \(0.320508\pi\)
\(338\) −2.25341 −0.122569
\(339\) −6.73057 −0.365554
\(340\) 7.22950 0.392075
\(341\) −11.2140 −0.607271
\(342\) −1.91437 −0.103517
\(343\) −18.0092 −0.972406
\(344\) −15.1554 −0.817123
\(345\) −14.4742 −0.779266
\(346\) 7.33911 0.394553
\(347\) −9.67098 −0.519166 −0.259583 0.965721i \(-0.583585\pi\)
−0.259583 + 0.965721i \(0.583585\pi\)
\(348\) 1.15886 0.0621216
\(349\) −8.50332 −0.455172 −0.227586 0.973758i \(-0.573083\pi\)
−0.227586 + 0.973758i \(0.573083\pi\)
\(350\) 10.9473 0.585158
\(351\) 2.69008 0.143586
\(352\) −21.2676 −1.13357
\(353\) −13.4112 −0.713806 −0.356903 0.934141i \(-0.616167\pi\)
−0.356903 + 0.934141i \(0.616167\pi\)
\(354\) −0.104979 −0.00557956
\(355\) −15.9318 −0.845573
\(356\) −5.16971 −0.273994
\(357\) 2.71351 0.143614
\(358\) −6.79927 −0.359352
\(359\) −16.1583 −0.852802 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(360\) −5.88710 −0.310278
\(361\) 4.97411 0.261795
\(362\) 0.371831 0.0195430
\(363\) −14.3656 −0.753996
\(364\) 13.4832 0.706714
\(365\) −47.8763 −2.50596
\(366\) 1.15361 0.0603001
\(367\) −2.09072 −0.109135 −0.0545674 0.998510i \(-0.517378\pi\)
−0.0545674 + 0.998510i \(0.517378\pi\)
\(368\) 11.4871 0.598808
\(369\) −3.46252 −0.180251
\(370\) −6.29151 −0.327080
\(371\) −2.51505 −0.130575
\(372\) 4.11278 0.213238
\(373\) −14.5443 −0.753075 −0.376538 0.926401i \(-0.622885\pi\)
−0.376538 + 0.926401i \(0.622885\pi\)
\(374\) 1.96914 0.101822
\(375\) −20.8166 −1.07496
\(376\) 10.8845 0.561327
\(377\) −1.68771 −0.0869215
\(378\) −1.06093 −0.0545682
\(379\) 12.5409 0.644181 0.322091 0.946709i \(-0.395614\pi\)
0.322091 + 0.946709i \(0.395614\pi\)
\(380\) 35.3981 1.81588
\(381\) −7.85630 −0.402491
\(382\) −9.97340 −0.510284
\(383\) 33.8549 1.72990 0.864951 0.501856i \(-0.167349\pi\)
0.864951 + 0.501856i \(0.167349\pi\)
\(384\) 10.2289 0.521992
\(385\) −53.4888 −2.72604
\(386\) 4.91070 0.249948
\(387\) 10.0757 0.512176
\(388\) 21.8733 1.11045
\(389\) −34.4262 −1.74548 −0.872740 0.488186i \(-0.837659\pi\)
−0.872740 + 0.488186i \(0.837659\pi\)
\(390\) 4.11651 0.208447
\(391\) −3.69816 −0.187024
\(392\) −0.546197 −0.0275871
\(393\) 0.368603 0.0185936
\(394\) 1.04355 0.0525734
\(395\) −51.3271 −2.58255
\(396\) 9.30295 0.467491
\(397\) −12.9328 −0.649078 −0.324539 0.945872i \(-0.605209\pi\)
−0.324539 + 0.945872i \(0.605209\pi\)
\(398\) 3.25368 0.163092
\(399\) 13.2862 0.665144
\(400\) 32.0515 1.60257
\(401\) 13.0276 0.650566 0.325283 0.945617i \(-0.394540\pi\)
0.325283 + 0.945617i \(0.394540\pi\)
\(402\) −4.47729 −0.223307
\(403\) −5.98965 −0.298366
\(404\) 33.9281 1.68798
\(405\) 3.91390 0.194483
\(406\) 0.665609 0.0330336
\(407\) 20.7068 1.02640
\(408\) −1.50415 −0.0744666
\(409\) −28.1191 −1.39040 −0.695200 0.718817i \(-0.744684\pi\)
−0.695200 + 0.718817i \(0.744684\pi\)
\(410\) −5.29854 −0.261676
\(411\) 14.3166 0.706185
\(412\) 12.7127 0.626311
\(413\) 0.728582 0.0358512
\(414\) 1.44590 0.0710623
\(415\) 47.0163 2.30794
\(416\) −11.3595 −0.556947
\(417\) 21.0100 1.02886
\(418\) 9.64157 0.471585
\(419\) 14.6967 0.717980 0.358990 0.933341i \(-0.383121\pi\)
0.358990 + 0.933341i \(0.383121\pi\)
\(420\) 19.6173 0.957227
\(421\) −30.7408 −1.49821 −0.749107 0.662449i \(-0.769517\pi\)
−0.749107 + 0.662449i \(0.769517\pi\)
\(422\) −3.85246 −0.187535
\(423\) −7.23632 −0.351842
\(424\) 1.39414 0.0677056
\(425\) −10.3186 −0.500527
\(426\) 1.59151 0.0771089
\(427\) −8.00637 −0.387455
\(428\) −16.4435 −0.794827
\(429\) −13.5484 −0.654121
\(430\) 15.4184 0.743541
\(431\) 23.6442 1.13890 0.569451 0.822025i \(-0.307156\pi\)
0.569451 + 0.822025i \(0.307156\pi\)
\(432\) −3.10618 −0.149446
\(433\) 9.03598 0.434242 0.217121 0.976145i \(-0.430333\pi\)
0.217121 + 0.976145i \(0.430333\pi\)
\(434\) 2.36223 0.113391
\(435\) −2.45552 −0.117733
\(436\) 13.9828 0.669657
\(437\) −18.1074 −0.866196
\(438\) 4.78261 0.228522
\(439\) −3.12261 −0.149034 −0.0745170 0.997220i \(-0.523741\pi\)
−0.0745170 + 0.997220i \(0.523741\pi\)
\(440\) 29.6499 1.41351
\(441\) 0.363126 0.0172917
\(442\) 1.05177 0.0500274
\(443\) −18.1452 −0.862106 −0.431053 0.902327i \(-0.641858\pi\)
−0.431053 + 0.902327i \(0.641858\pi\)
\(444\) −7.59432 −0.360411
\(445\) 10.9541 0.519275
\(446\) 9.46745 0.448297
\(447\) −10.1025 −0.477830
\(448\) −12.3772 −0.584769
\(449\) −16.5972 −0.783269 −0.391634 0.920121i \(-0.628090\pi\)
−0.391634 + 0.920121i \(0.628090\pi\)
\(450\) 4.03438 0.190182
\(451\) 17.4387 0.821156
\(452\) −12.4323 −0.584765
\(453\) −0.503267 −0.0236455
\(454\) 3.14427 0.147568
\(455\) −28.5697 −1.33937
\(456\) −7.36483 −0.344890
\(457\) −3.14747 −0.147233 −0.0736163 0.997287i \(-0.523454\pi\)
−0.0736163 + 0.997287i \(0.523454\pi\)
\(458\) 6.30097 0.294425
\(459\) 1.00000 0.0466760
\(460\) −26.7358 −1.24657
\(461\) 19.8597 0.924957 0.462478 0.886631i \(-0.346960\pi\)
0.462478 + 0.886631i \(0.346960\pi\)
\(462\) 5.34328 0.248592
\(463\) 18.2132 0.846438 0.423219 0.906027i \(-0.360900\pi\)
0.423219 + 0.906027i \(0.360900\pi\)
\(464\) 1.94877 0.0904692
\(465\) −8.71460 −0.404130
\(466\) −6.39460 −0.296224
\(467\) 8.44237 0.390666 0.195333 0.980737i \(-0.437421\pi\)
0.195333 + 0.980737i \(0.437421\pi\)
\(468\) 4.96893 0.229689
\(469\) 31.0736 1.43485
\(470\) −11.0734 −0.510779
\(471\) 1.00000 0.0460776
\(472\) −0.403868 −0.0185895
\(473\) −50.7455 −2.33328
\(474\) 5.12733 0.235506
\(475\) −50.5235 −2.31818
\(476\) 5.01222 0.229735
\(477\) −0.926864 −0.0424382
\(478\) 9.82787 0.449516
\(479\) −27.0597 −1.23639 −0.618195 0.786025i \(-0.712136\pi\)
−0.618195 + 0.786025i \(0.712136\pi\)
\(480\) −16.5275 −0.754372
\(481\) 11.0600 0.504292
\(482\) −5.94180 −0.270642
\(483\) −10.0350 −0.456607
\(484\) −26.5351 −1.20614
\(485\) −46.3475 −2.10453
\(486\) −0.390980 −0.0177352
\(487\) −30.8115 −1.39620 −0.698101 0.715999i \(-0.745971\pi\)
−0.698101 + 0.715999i \(0.745971\pi\)
\(488\) 4.43809 0.200903
\(489\) 14.5475 0.657861
\(490\) 0.555676 0.0251029
\(491\) −37.9651 −1.71334 −0.856672 0.515862i \(-0.827472\pi\)
−0.856672 + 0.515862i \(0.827472\pi\)
\(492\) −6.39574 −0.288342
\(493\) −0.627384 −0.0282560
\(494\) 5.14980 0.231700
\(495\) −19.7121 −0.885991
\(496\) 6.91613 0.310544
\(497\) −11.0455 −0.495459
\(498\) −4.69670 −0.210464
\(499\) −1.11532 −0.0499286 −0.0249643 0.999688i \(-0.507947\pi\)
−0.0249643 + 0.999688i \(0.507947\pi\)
\(500\) −38.4511 −1.71958
\(501\) 16.3017 0.728305
\(502\) 2.65648 0.118564
\(503\) 28.7185 1.28049 0.640247 0.768169i \(-0.278832\pi\)
0.640247 + 0.768169i \(0.278832\pi\)
\(504\) −4.08153 −0.181806
\(505\) −71.8903 −3.19908
\(506\) −7.28219 −0.323733
\(507\) 5.76349 0.255966
\(508\) −14.5116 −0.643850
\(509\) −1.10663 −0.0490505 −0.0245252 0.999699i \(-0.507807\pi\)
−0.0245252 + 0.999699i \(0.507807\pi\)
\(510\) 1.53026 0.0677609
\(511\) −33.1926 −1.46835
\(512\) 22.4610 0.992643
\(513\) 4.89634 0.216179
\(514\) 1.16213 0.0512594
\(515\) −26.9370 −1.18699
\(516\) 18.6112 0.819311
\(517\) 36.4452 1.60286
\(518\) −4.36190 −0.191651
\(519\) −18.7711 −0.823959
\(520\) 15.8368 0.694488
\(521\) −8.89276 −0.389599 −0.194800 0.980843i \(-0.562406\pi\)
−0.194800 + 0.980843i \(0.562406\pi\)
\(522\) 0.245295 0.0107363
\(523\) −29.5908 −1.29392 −0.646959 0.762525i \(-0.723959\pi\)
−0.646959 + 0.762525i \(0.723959\pi\)
\(524\) 0.680860 0.0297435
\(525\) −27.9997 −1.22201
\(526\) −4.67831 −0.203984
\(527\) −2.22657 −0.0969911
\(528\) 15.6440 0.680818
\(529\) −9.32363 −0.405375
\(530\) −1.41834 −0.0616088
\(531\) 0.268502 0.0116520
\(532\) 24.5415 1.06401
\(533\) 9.31443 0.403453
\(534\) −1.09426 −0.0473534
\(535\) 34.8422 1.50636
\(536\) −17.2247 −0.743995
\(537\) 17.3903 0.750448
\(538\) −9.98796 −0.430612
\(539\) −1.82886 −0.0787744
\(540\) 7.22950 0.311108
\(541\) 27.9717 1.20260 0.601298 0.799025i \(-0.294650\pi\)
0.601298 + 0.799025i \(0.294650\pi\)
\(542\) 9.36661 0.402330
\(543\) −0.951024 −0.0408124
\(544\) −4.22276 −0.181049
\(545\) −29.6283 −1.26914
\(546\) 2.85397 0.122139
\(547\) −6.33546 −0.270885 −0.135442 0.990785i \(-0.543246\pi\)
−0.135442 + 0.990785i \(0.543246\pi\)
\(548\) 26.4446 1.12966
\(549\) −2.95056 −0.125927
\(550\) −20.3188 −0.866398
\(551\) −3.07188 −0.130867
\(552\) 5.56259 0.236760
\(553\) −35.5851 −1.51323
\(554\) 8.54086 0.362866
\(555\) 16.0916 0.683052
\(556\) 38.8082 1.64584
\(557\) 9.51901 0.403333 0.201667 0.979454i \(-0.435364\pi\)
0.201667 + 0.979454i \(0.435364\pi\)
\(558\) 0.870546 0.0368531
\(559\) −27.1044 −1.14639
\(560\) 32.9889 1.39403
\(561\) −5.03642 −0.212638
\(562\) −5.15271 −0.217354
\(563\) 24.6388 1.03840 0.519201 0.854652i \(-0.326230\pi\)
0.519201 + 0.854652i \(0.326230\pi\)
\(564\) −13.3665 −0.562830
\(565\) 26.3428 1.10825
\(566\) −6.98005 −0.293393
\(567\) 2.71351 0.113957
\(568\) 6.12275 0.256905
\(569\) −34.8417 −1.46064 −0.730320 0.683106i \(-0.760629\pi\)
−0.730320 + 0.683106i \(0.760629\pi\)
\(570\) 7.49265 0.313833
\(571\) −31.1425 −1.30327 −0.651637 0.758531i \(-0.725917\pi\)
−0.651637 + 0.758531i \(0.725917\pi\)
\(572\) −25.0256 −1.04637
\(573\) 25.5087 1.06564
\(574\) −3.67348 −0.153328
\(575\) 38.1599 1.59138
\(576\) −4.56134 −0.190056
\(577\) 24.5020 1.02003 0.510016 0.860165i \(-0.329639\pi\)
0.510016 + 0.860165i \(0.329639\pi\)
\(578\) 0.390980 0.0162626
\(579\) −12.5600 −0.521975
\(580\) −4.53568 −0.188334
\(581\) 32.5964 1.35233
\(582\) 4.62989 0.191915
\(583\) 4.66808 0.193332
\(584\) 18.3993 0.761370
\(585\) −10.5287 −0.435308
\(586\) −5.67091 −0.234263
\(587\) 10.4206 0.430106 0.215053 0.976602i \(-0.431008\pi\)
0.215053 + 0.976602i \(0.431008\pi\)
\(588\) 0.670743 0.0276610
\(589\) −10.9021 −0.449212
\(590\) 0.410877 0.0169155
\(591\) −2.66907 −0.109791
\(592\) −12.7708 −0.524875
\(593\) 0.863996 0.0354801 0.0177400 0.999843i \(-0.494353\pi\)
0.0177400 + 0.999843i \(0.494353\pi\)
\(594\) 1.96914 0.0807948
\(595\) −10.6204 −0.435394
\(596\) −18.6606 −0.764368
\(597\) −8.32187 −0.340592
\(598\) −3.88959 −0.159057
\(599\) 15.4502 0.631277 0.315639 0.948879i \(-0.397781\pi\)
0.315639 + 0.948879i \(0.397781\pi\)
\(600\) 15.5208 0.633634
\(601\) 2.71877 0.110901 0.0554505 0.998461i \(-0.482340\pi\)
0.0554505 + 0.998461i \(0.482340\pi\)
\(602\) 10.6896 0.435675
\(603\) 11.4515 0.466339
\(604\) −0.929602 −0.0378250
\(605\) 56.2254 2.28589
\(606\) 7.18149 0.291728
\(607\) −4.92228 −0.199789 −0.0998947 0.994998i \(-0.531851\pi\)
−0.0998947 + 0.994998i \(0.531851\pi\)
\(608\) −20.6760 −0.838524
\(609\) −1.70241 −0.0689852
\(610\) −4.51511 −0.182812
\(611\) 19.4663 0.787520
\(612\) 1.84713 0.0746660
\(613\) −45.0334 −1.81888 −0.909440 0.415835i \(-0.863489\pi\)
−0.909440 + 0.415835i \(0.863489\pi\)
\(614\) 12.3172 0.497083
\(615\) 13.5520 0.546468
\(616\) 20.5563 0.828237
\(617\) 7.28965 0.293470 0.146735 0.989176i \(-0.453124\pi\)
0.146735 + 0.989176i \(0.453124\pi\)
\(618\) 2.69088 0.108243
\(619\) 35.8709 1.44177 0.720886 0.693054i \(-0.243735\pi\)
0.720886 + 0.693054i \(0.243735\pi\)
\(620\) −16.0970 −0.646472
\(621\) −3.69816 −0.148402
\(622\) −0.883178 −0.0354122
\(623\) 7.59450 0.304267
\(624\) 8.35585 0.334502
\(625\) 29.8810 1.19524
\(626\) −9.97495 −0.398679
\(627\) −24.6600 −0.984826
\(628\) 1.84713 0.0737087
\(629\) 4.11141 0.163933
\(630\) 4.15236 0.165434
\(631\) −5.46917 −0.217724 −0.108862 0.994057i \(-0.534721\pi\)
−0.108862 + 0.994057i \(0.534721\pi\)
\(632\) 19.7255 0.784639
\(633\) 9.85334 0.391635
\(634\) −8.03573 −0.319140
\(635\) 30.7488 1.22023
\(636\) −1.71204 −0.0678869
\(637\) −0.976837 −0.0387037
\(638\) −1.23541 −0.0489102
\(639\) −4.07057 −0.161029
\(640\) −40.0349 −1.58252
\(641\) −9.80582 −0.387307 −0.193653 0.981070i \(-0.562034\pi\)
−0.193653 + 0.981070i \(0.562034\pi\)
\(642\) −3.48057 −0.137367
\(643\) −0.935603 −0.0368966 −0.0184483 0.999830i \(-0.505873\pi\)
−0.0184483 + 0.999830i \(0.505873\pi\)
\(644\) −18.5360 −0.730419
\(645\) −39.4353 −1.55276
\(646\) 1.91437 0.0753198
\(647\) 34.9678 1.37473 0.687363 0.726315i \(-0.258768\pi\)
0.687363 + 0.726315i \(0.258768\pi\)
\(648\) −1.50415 −0.0590887
\(649\) −1.35229 −0.0530820
\(650\) −10.8528 −0.425681
\(651\) −6.04183 −0.236798
\(652\) 26.8712 1.05236
\(653\) 9.78767 0.383021 0.191510 0.981491i \(-0.438661\pi\)
0.191510 + 0.981491i \(0.438661\pi\)
\(654\) 2.95972 0.115734
\(655\) −1.44268 −0.0563701
\(656\) −10.7552 −0.419920
\(657\) −12.2324 −0.477230
\(658\) −7.67721 −0.299289
\(659\) 27.2614 1.06196 0.530978 0.847386i \(-0.321825\pi\)
0.530978 + 0.847386i \(0.321825\pi\)
\(660\) −36.4108 −1.41729
\(661\) −29.7500 −1.15714 −0.578571 0.815632i \(-0.696389\pi\)
−0.578571 + 0.815632i \(0.696389\pi\)
\(662\) −2.04410 −0.0794464
\(663\) −2.69008 −0.104474
\(664\) −18.0689 −0.701207
\(665\) −52.0011 −2.01652
\(666\) −1.60748 −0.0622885
\(667\) 2.32017 0.0898372
\(668\) 30.1114 1.16504
\(669\) −24.2147 −0.936194
\(670\) 17.5237 0.676998
\(671\) 14.8603 0.573674
\(672\) −11.4585 −0.442021
\(673\) 8.44710 0.325612 0.162806 0.986658i \(-0.447946\pi\)
0.162806 + 0.986658i \(0.447946\pi\)
\(674\) 7.67236 0.295528
\(675\) −10.3186 −0.397164
\(676\) 10.6459 0.409460
\(677\) 44.8786 1.72482 0.862412 0.506207i \(-0.168953\pi\)
0.862412 + 0.506207i \(0.168953\pi\)
\(678\) −2.63152 −0.101063
\(679\) −32.1327 −1.23314
\(680\) 5.88710 0.225760
\(681\) −8.04202 −0.308171
\(682\) −4.38444 −0.167889
\(683\) −20.4485 −0.782442 −0.391221 0.920297i \(-0.627947\pi\)
−0.391221 + 0.920297i \(0.627947\pi\)
\(684\) 9.04419 0.345813
\(685\) −56.0337 −2.14094
\(686\) −7.04124 −0.268836
\(687\) −16.1158 −0.614858
\(688\) 31.2969 1.19318
\(689\) 2.49333 0.0949885
\(690\) −5.65913 −0.215439
\(691\) −12.8532 −0.488960 −0.244480 0.969654i \(-0.578617\pi\)
−0.244480 + 0.969654i \(0.578617\pi\)
\(692\) −34.6727 −1.31806
\(693\) −13.6664 −0.519143
\(694\) −3.78116 −0.143531
\(695\) −82.2309 −3.11920
\(696\) 0.943681 0.0357701
\(697\) 3.46252 0.131152
\(698\) −3.32463 −0.125839
\(699\) 16.3553 0.618615
\(700\) −51.7192 −1.95480
\(701\) 19.0313 0.718804 0.359402 0.933183i \(-0.382981\pi\)
0.359402 + 0.933183i \(0.382981\pi\)
\(702\) 1.05177 0.0396963
\(703\) 20.1308 0.759249
\(704\) 22.9728 0.865821
\(705\) 28.3223 1.06668
\(706\) −5.24351 −0.197342
\(707\) −49.8415 −1.87448
\(708\) 0.495959 0.0186393
\(709\) −28.1634 −1.05770 −0.528850 0.848715i \(-0.677377\pi\)
−0.528850 + 0.848715i \(0.677377\pi\)
\(710\) −6.22901 −0.233771
\(711\) −13.1141 −0.491815
\(712\) −4.20978 −0.157768
\(713\) 8.23422 0.308374
\(714\) 1.06093 0.0397042
\(715\) 53.0269 1.98310
\(716\) 32.1223 1.20047
\(717\) −25.1365 −0.938740
\(718\) −6.31757 −0.235770
\(719\) −29.6726 −1.10660 −0.553300 0.832982i \(-0.686632\pi\)
−0.553300 + 0.832982i \(0.686632\pi\)
\(720\) 12.1573 0.453075
\(721\) −18.6754 −0.695510
\(722\) 1.94478 0.0723771
\(723\) 15.1972 0.565190
\(724\) −1.75667 −0.0652861
\(725\) 6.47375 0.240429
\(726\) −5.61664 −0.208453
\(727\) 47.0603 1.74537 0.872685 0.488283i \(-0.162377\pi\)
0.872685 + 0.488283i \(0.162377\pi\)
\(728\) 10.9796 0.406932
\(729\) 1.00000 0.0370370
\(730\) −18.7187 −0.692808
\(731\) −10.0757 −0.372663
\(732\) −5.45008 −0.201441
\(733\) −12.7425 −0.470656 −0.235328 0.971916i \(-0.575616\pi\)
−0.235328 + 0.971916i \(0.575616\pi\)
\(734\) −0.817430 −0.0301719
\(735\) −1.42124 −0.0524232
\(736\) 15.6164 0.575629
\(737\) −57.6744 −2.12446
\(738\) −1.35377 −0.0498331
\(739\) −4.08206 −0.150161 −0.0750804 0.997177i \(-0.523921\pi\)
−0.0750804 + 0.997177i \(0.523921\pi\)
\(740\) 29.7234 1.09266
\(741\) −13.1715 −0.483868
\(742\) −0.983335 −0.0360994
\(743\) −45.7473 −1.67831 −0.839154 0.543894i \(-0.816949\pi\)
−0.839154 + 0.543894i \(0.816949\pi\)
\(744\) 3.34911 0.122784
\(745\) 39.5400 1.44864
\(746\) −5.68653 −0.208199
\(747\) 12.0126 0.439520
\(748\) −9.30295 −0.340150
\(749\) 24.1561 0.882645
\(750\) −8.13887 −0.297190
\(751\) 10.1158 0.369130 0.184565 0.982820i \(-0.440912\pi\)
0.184565 + 0.982820i \(0.440912\pi\)
\(752\) −22.4773 −0.819663
\(753\) −6.79441 −0.247602
\(754\) −0.659861 −0.0240307
\(755\) 1.96974 0.0716861
\(756\) 5.01222 0.182293
\(757\) −44.3243 −1.61100 −0.805498 0.592599i \(-0.798102\pi\)
−0.805498 + 0.592599i \(0.798102\pi\)
\(758\) 4.90323 0.178093
\(759\) 18.6255 0.676062
\(760\) 28.8252 1.04560
\(761\) −4.31678 −0.156483 −0.0782417 0.996934i \(-0.524931\pi\)
−0.0782417 + 0.996934i \(0.524931\pi\)
\(762\) −3.07166 −0.111274
\(763\) −20.5413 −0.743645
\(764\) 47.1181 1.70467
\(765\) −3.91390 −0.141507
\(766\) 13.2366 0.478257
\(767\) −0.722291 −0.0260804
\(768\) −5.12339 −0.184874
\(769\) −40.1856 −1.44913 −0.724565 0.689206i \(-0.757959\pi\)
−0.724565 + 0.689206i \(0.757959\pi\)
\(770\) −20.9131 −0.753654
\(771\) −2.97235 −0.107047
\(772\) −23.2000 −0.834985
\(773\) −41.6002 −1.49625 −0.748127 0.663555i \(-0.769047\pi\)
−0.748127 + 0.663555i \(0.769047\pi\)
\(774\) 3.93939 0.141599
\(775\) 22.9752 0.825294
\(776\) 17.8118 0.639407
\(777\) 11.1563 0.400231
\(778\) −13.4600 −0.482563
\(779\) 16.9537 0.607428
\(780\) −19.4479 −0.696347
\(781\) 20.5011 0.733587
\(782\) −1.44590 −0.0517055
\(783\) −0.627384 −0.0224209
\(784\) 1.12793 0.0402833
\(785\) −3.91390 −0.139693
\(786\) 0.144117 0.00514047
\(787\) −4.67893 −0.166786 −0.0833930 0.996517i \(-0.526576\pi\)
−0.0833930 + 0.996517i \(0.526576\pi\)
\(788\) −4.93013 −0.175629
\(789\) 11.9656 0.425987
\(790\) −20.0679 −0.713983
\(791\) 18.2635 0.649374
\(792\) 7.57555 0.269185
\(793\) 7.93723 0.281859
\(794\) −5.05646 −0.179447
\(795\) 3.62766 0.128660
\(796\) −15.3716 −0.544833
\(797\) 27.8694 0.987185 0.493592 0.869693i \(-0.335683\pi\)
0.493592 + 0.869693i \(0.335683\pi\)
\(798\) 5.19466 0.183889
\(799\) 7.23632 0.256003
\(800\) 43.5731 1.54054
\(801\) 2.79877 0.0988898
\(802\) 5.09352 0.179858
\(803\) 61.6073 2.17408
\(804\) 21.1524 0.745987
\(805\) 39.2759 1.38429
\(806\) −2.34183 −0.0824876
\(807\) 25.5460 0.899261
\(808\) 27.6282 0.971956
\(809\) −22.4890 −0.790670 −0.395335 0.918537i \(-0.629371\pi\)
−0.395335 + 0.918537i \(0.629371\pi\)
\(810\) 1.53026 0.0537677
\(811\) 28.3476 0.995420 0.497710 0.867343i \(-0.334174\pi\)
0.497710 + 0.867343i \(0.334174\pi\)
\(812\) −3.14459 −0.110353
\(813\) −23.9568 −0.840200
\(814\) 8.09593 0.283762
\(815\) −56.9375 −1.99443
\(816\) 3.10618 0.108738
\(817\) −49.3340 −1.72598
\(818\) −10.9940 −0.384396
\(819\) −7.29954 −0.255067
\(820\) 25.0323 0.874165
\(821\) 21.4621 0.749031 0.374515 0.927221i \(-0.377809\pi\)
0.374515 + 0.927221i \(0.377809\pi\)
\(822\) 5.59749 0.195235
\(823\) 16.2167 0.565279 0.282639 0.959226i \(-0.408790\pi\)
0.282639 + 0.959226i \(0.408790\pi\)
\(824\) 10.3522 0.360635
\(825\) 51.9690 1.80933
\(826\) 0.284861 0.00991158
\(827\) 44.8546 1.55975 0.779874 0.625936i \(-0.215283\pi\)
0.779874 + 0.625936i \(0.215283\pi\)
\(828\) −6.83100 −0.237393
\(829\) 12.0470 0.418409 0.209204 0.977872i \(-0.432913\pi\)
0.209204 + 0.977872i \(0.432913\pi\)
\(830\) 18.3824 0.638064
\(831\) −21.8448 −0.757786
\(832\) 12.2704 0.425398
\(833\) −0.363126 −0.0125816
\(834\) 8.21447 0.284444
\(835\) −63.8031 −2.20800
\(836\) −45.5504 −1.57539
\(837\) −2.22657 −0.0769617
\(838\) 5.74611 0.198496
\(839\) −6.52612 −0.225307 −0.112653 0.993634i \(-0.535935\pi\)
−0.112653 + 0.993634i \(0.535935\pi\)
\(840\) 15.9747 0.551180
\(841\) −28.6064 −0.986427
\(842\) −12.0190 −0.414203
\(843\) 13.1790 0.453908
\(844\) 18.2005 0.626486
\(845\) −22.5577 −0.776010
\(846\) −2.82926 −0.0972718
\(847\) 38.9810 1.33940
\(848\) −2.87900 −0.0988654
\(849\) 17.8527 0.612703
\(850\) −4.03438 −0.138378
\(851\) −15.2046 −0.521208
\(852\) −7.51889 −0.257593
\(853\) 22.5464 0.771975 0.385988 0.922504i \(-0.373861\pi\)
0.385988 + 0.922504i \(0.373861\pi\)
\(854\) −3.13033 −0.107118
\(855\) −19.1638 −0.655388
\(856\) −13.3902 −0.457668
\(857\) 33.3447 1.13903 0.569516 0.821980i \(-0.307131\pi\)
0.569516 + 0.821980i \(0.307131\pi\)
\(858\) −5.29713 −0.180841
\(859\) 2.66269 0.0908498 0.0454249 0.998968i \(-0.485536\pi\)
0.0454249 + 0.998968i \(0.485536\pi\)
\(860\) −72.8423 −2.48390
\(861\) 9.39557 0.320200
\(862\) 9.24441 0.314866
\(863\) −35.0239 −1.19223 −0.596114 0.802900i \(-0.703290\pi\)
−0.596114 + 0.802900i \(0.703290\pi\)
\(864\) −4.22276 −0.143661
\(865\) 73.4682 2.49799
\(866\) 3.53289 0.120052
\(867\) −1.00000 −0.0339618
\(868\) −11.1601 −0.378798
\(869\) 66.0479 2.24052
\(870\) −0.960059 −0.0325491
\(871\) −30.8053 −1.04380
\(872\) 11.3865 0.385594
\(873\) −11.8418 −0.400783
\(874\) −7.07964 −0.239472
\(875\) 56.4860 1.90958
\(876\) −22.5948 −0.763408
\(877\) 4.94513 0.166985 0.0834927 0.996508i \(-0.473392\pi\)
0.0834927 + 0.996508i \(0.473392\pi\)
\(878\) −1.22088 −0.0412026
\(879\) 14.5044 0.489220
\(880\) −61.2292 −2.06403
\(881\) −19.2954 −0.650080 −0.325040 0.945700i \(-0.605378\pi\)
−0.325040 + 0.945700i \(0.605378\pi\)
\(882\) 0.141975 0.00478055
\(883\) 53.6574 1.80572 0.902858 0.429940i \(-0.141465\pi\)
0.902858 + 0.429940i \(0.141465\pi\)
\(884\) −4.96893 −0.167123
\(885\) −1.05089 −0.0353253
\(886\) −7.09442 −0.238342
\(887\) 34.5970 1.16165 0.580827 0.814027i \(-0.302729\pi\)
0.580827 + 0.814027i \(0.302729\pi\)
\(888\) −6.18418 −0.207527
\(889\) 21.3181 0.714987
\(890\) 4.28284 0.143561
\(891\) −5.03642 −0.168726
\(892\) −44.7278 −1.49760
\(893\) 35.4315 1.18567
\(894\) −3.94986 −0.132103
\(895\) −68.0641 −2.27513
\(896\) −27.7562 −0.927270
\(897\) 9.94832 0.332165
\(898\) −6.48916 −0.216546
\(899\) 1.39692 0.0465898
\(900\) −19.0599 −0.635330
\(901\) 0.926864 0.0308783
\(902\) 6.81818 0.227021
\(903\) −27.3405 −0.909834
\(904\) −10.1238 −0.336713
\(905\) 3.72222 0.123731
\(906\) −0.196767 −0.00653715
\(907\) 3.96175 0.131548 0.0657739 0.997835i \(-0.479048\pi\)
0.0657739 + 0.997835i \(0.479048\pi\)
\(908\) −14.8547 −0.492970
\(909\) −18.3679 −0.609226
\(910\) −11.1702 −0.370288
\(911\) 36.9384 1.22382 0.611912 0.790926i \(-0.290401\pi\)
0.611912 + 0.790926i \(0.290401\pi\)
\(912\) 15.2089 0.503617
\(913\) −60.5008 −2.00228
\(914\) −1.23060 −0.0407046
\(915\) 11.5482 0.381772
\(916\) −29.7681 −0.983567
\(917\) −1.00021 −0.0330298
\(918\) 0.390980 0.0129043
\(919\) 5.40711 0.178364 0.0891821 0.996015i \(-0.471575\pi\)
0.0891821 + 0.996015i \(0.471575\pi\)
\(920\) −21.7714 −0.717783
\(921\) −31.5035 −1.03808
\(922\) 7.76473 0.255718
\(923\) 10.9501 0.360428
\(924\) −25.2436 −0.830455
\(925\) −42.4241 −1.39490
\(926\) 7.12098 0.234010
\(927\) −6.88240 −0.226048
\(928\) 2.64929 0.0869672
\(929\) −1.13541 −0.0372515 −0.0186257 0.999827i \(-0.505929\pi\)
−0.0186257 + 0.999827i \(0.505929\pi\)
\(930\) −3.40723 −0.111728
\(931\) −1.77799 −0.0582712
\(932\) 30.2105 0.989577
\(933\) 2.25888 0.0739526
\(934\) 3.30080 0.108005
\(935\) 19.7121 0.644653
\(936\) 4.04628 0.132257
\(937\) 13.5583 0.442929 0.221464 0.975168i \(-0.428916\pi\)
0.221464 + 0.975168i \(0.428916\pi\)
\(938\) 12.1492 0.396684
\(939\) 25.5127 0.832575
\(940\) 52.3150 1.70633
\(941\) −5.52485 −0.180105 −0.0900525 0.995937i \(-0.528703\pi\)
−0.0900525 + 0.995937i \(0.528703\pi\)
\(942\) 0.390980 0.0127388
\(943\) −12.8049 −0.416986
\(944\) 0.834015 0.0271449
\(945\) −10.6204 −0.345482
\(946\) −19.8405 −0.645069
\(947\) −6.86093 −0.222950 −0.111475 0.993767i \(-0.535558\pi\)
−0.111475 + 0.993767i \(0.535558\pi\)
\(948\) −24.2234 −0.786740
\(949\) 32.9060 1.06817
\(950\) −19.7537 −0.640894
\(951\) 20.5528 0.666470
\(952\) 4.08153 0.132283
\(953\) −12.1796 −0.394537 −0.197269 0.980349i \(-0.563207\pi\)
−0.197269 + 0.980349i \(0.563207\pi\)
\(954\) −0.362385 −0.0117327
\(955\) −99.8387 −3.23071
\(956\) −46.4305 −1.50167
\(957\) 3.15977 0.102141
\(958\) −10.5798 −0.341818
\(959\) −38.8481 −1.25447
\(960\) 17.8526 0.576191
\(961\) −26.0424 −0.840076
\(962\) 4.32423 0.139419
\(963\) 8.90217 0.286869
\(964\) 28.0713 0.904116
\(965\) 49.1585 1.58247
\(966\) −3.92347 −0.126236
\(967\) 58.8927 1.89386 0.946930 0.321439i \(-0.104167\pi\)
0.946930 + 0.321439i \(0.104167\pi\)
\(968\) −21.6080 −0.694507
\(969\) −4.89634 −0.157293
\(970\) −18.1209 −0.581828
\(971\) 30.9759 0.994063 0.497032 0.867732i \(-0.334423\pi\)
0.497032 + 0.867732i \(0.334423\pi\)
\(972\) 1.84713 0.0592469
\(973\) −57.0107 −1.82768
\(974\) −12.0467 −0.386000
\(975\) 27.7579 0.888964
\(976\) −9.16496 −0.293363
\(977\) 4.33188 0.138589 0.0692945 0.997596i \(-0.477925\pi\)
0.0692945 + 0.997596i \(0.477925\pi\)
\(978\) 5.68778 0.181875
\(979\) −14.0958 −0.450504
\(980\) −2.62522 −0.0838596
\(981\) −7.57002 −0.241692
\(982\) −14.8436 −0.473679
\(983\) −42.4941 −1.35535 −0.677675 0.735361i \(-0.737012\pi\)
−0.677675 + 0.735361i \(0.737012\pi\)
\(984\) −5.20815 −0.166030
\(985\) 10.4465 0.332853
\(986\) −0.245295 −0.00781177
\(987\) 19.6358 0.625015
\(988\) −24.3296 −0.774027
\(989\) 37.2615 1.18485
\(990\) −7.70702 −0.244945
\(991\) −20.6176 −0.654941 −0.327471 0.944861i \(-0.606196\pi\)
−0.327471 + 0.944861i \(0.606196\pi\)
\(992\) 9.40228 0.298523
\(993\) 5.22816 0.165911
\(994\) −4.31858 −0.136977
\(995\) 32.5710 1.03257
\(996\) 22.1890 0.703085
\(997\) 34.9737 1.10763 0.553814 0.832640i \(-0.313172\pi\)
0.553814 + 0.832640i \(0.313172\pi\)
\(998\) −0.436068 −0.0138035
\(999\) 4.11141 0.130079
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 8007.2.a.f.1.27 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.27 48 1.1 even 1 trivial