Properties

Label 8003.2.a.b.1.12
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $1$
Dimension $153$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46809 q^{2} +2.55539 q^{3} +4.09144 q^{4} +0.103837 q^{5} -6.30691 q^{6} +0.172456 q^{7} -5.16186 q^{8} +3.53000 q^{9} +O(q^{10})\) \(q-2.46809 q^{2} +2.55539 q^{3} +4.09144 q^{4} +0.103837 q^{5} -6.30691 q^{6} +0.172456 q^{7} -5.16186 q^{8} +3.53000 q^{9} -0.256278 q^{10} +0.565880 q^{11} +10.4552 q^{12} +2.15838 q^{13} -0.425636 q^{14} +0.265343 q^{15} +4.55703 q^{16} -1.75558 q^{17} -8.71235 q^{18} -0.748607 q^{19} +0.424843 q^{20} +0.440692 q^{21} -1.39664 q^{22} +8.39148 q^{23} -13.1906 q^{24} -4.98922 q^{25} -5.32707 q^{26} +1.35437 q^{27} +0.705594 q^{28} -9.65832 q^{29} -0.654890 q^{30} -4.98087 q^{31} -0.923406 q^{32} +1.44604 q^{33} +4.33293 q^{34} +0.0179073 q^{35} +14.4428 q^{36} +5.47785 q^{37} +1.84763 q^{38} +5.51550 q^{39} -0.535992 q^{40} +4.50250 q^{41} -1.08766 q^{42} -12.4190 q^{43} +2.31527 q^{44} +0.366545 q^{45} -20.7109 q^{46} -7.34736 q^{47} +11.6450 q^{48} -6.97026 q^{49} +12.3138 q^{50} -4.48620 q^{51} +8.83090 q^{52} -1.00000 q^{53} -3.34270 q^{54} +0.0587592 q^{55} -0.890194 q^{56} -1.91298 q^{57} +23.8376 q^{58} -10.9196 q^{59} +1.08564 q^{60} -5.33209 q^{61} +12.2932 q^{62} +0.608770 q^{63} -6.83501 q^{64} +0.224120 q^{65} -3.56896 q^{66} -2.87403 q^{67} -7.18287 q^{68} +21.4435 q^{69} -0.0441967 q^{70} -0.701405 q^{71} -18.2214 q^{72} -5.45468 q^{73} -13.5198 q^{74} -12.7494 q^{75} -3.06288 q^{76} +0.0975894 q^{77} -13.6127 q^{78} +11.2134 q^{79} +0.473187 q^{80} -7.12908 q^{81} -11.1126 q^{82} -1.56654 q^{83} +1.80307 q^{84} -0.182294 q^{85} +30.6511 q^{86} -24.6808 q^{87} -2.92099 q^{88} -17.5104 q^{89} -0.904663 q^{90} +0.372226 q^{91} +34.3333 q^{92} -12.7281 q^{93} +18.1339 q^{94} -0.0777330 q^{95} -2.35966 q^{96} -1.77592 q^{97} +17.2032 q^{98} +1.99756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46809 −1.74520 −0.872600 0.488436i \(-0.837568\pi\)
−0.872600 + 0.488436i \(0.837568\pi\)
\(3\) 2.55539 1.47535 0.737677 0.675154i \(-0.235923\pi\)
0.737677 + 0.675154i \(0.235923\pi\)
\(4\) 4.09144 2.04572
\(5\) 0.103837 0.0464373 0.0232186 0.999730i \(-0.492609\pi\)
0.0232186 + 0.999730i \(0.492609\pi\)
\(6\) −6.30691 −2.57479
\(7\) 0.172456 0.0651822 0.0325911 0.999469i \(-0.489624\pi\)
0.0325911 + 0.999469i \(0.489624\pi\)
\(8\) −5.16186 −1.82499
\(9\) 3.53000 1.17667
\(10\) −0.256278 −0.0810423
\(11\) 0.565880 0.170619 0.0853096 0.996354i \(-0.472812\pi\)
0.0853096 + 0.996354i \(0.472812\pi\)
\(12\) 10.4552 3.01816
\(13\) 2.15838 0.598628 0.299314 0.954155i \(-0.403242\pi\)
0.299314 + 0.954155i \(0.403242\pi\)
\(14\) −0.425636 −0.113756
\(15\) 0.265343 0.0685114
\(16\) 4.55703 1.13926
\(17\) −1.75558 −0.425792 −0.212896 0.977075i \(-0.568289\pi\)
−0.212896 + 0.977075i \(0.568289\pi\)
\(18\) −8.71235 −2.05352
\(19\) −0.748607 −0.171742 −0.0858711 0.996306i \(-0.527367\pi\)
−0.0858711 + 0.996306i \(0.527367\pi\)
\(20\) 0.424843 0.0949977
\(21\) 0.440692 0.0961668
\(22\) −1.39664 −0.297765
\(23\) 8.39148 1.74975 0.874873 0.484353i \(-0.160945\pi\)
0.874873 + 0.484353i \(0.160945\pi\)
\(24\) −13.1906 −2.69251
\(25\) −4.98922 −0.997844
\(26\) −5.32707 −1.04472
\(27\) 1.35437 0.260648
\(28\) 0.705594 0.133345
\(29\) −9.65832 −1.79351 −0.896753 0.442532i \(-0.854080\pi\)
−0.896753 + 0.442532i \(0.854080\pi\)
\(30\) −0.654890 −0.119566
\(31\) −4.98087 −0.894591 −0.447296 0.894386i \(-0.647613\pi\)
−0.447296 + 0.894386i \(0.647613\pi\)
\(32\) −0.923406 −0.163237
\(33\) 1.44604 0.251724
\(34\) 4.33293 0.743091
\(35\) 0.0179073 0.00302688
\(36\) 14.4428 2.40714
\(37\) 5.47785 0.900553 0.450277 0.892889i \(-0.351325\pi\)
0.450277 + 0.892889i \(0.351325\pi\)
\(38\) 1.84763 0.299725
\(39\) 5.51550 0.883187
\(40\) −0.535992 −0.0847477
\(41\) 4.50250 0.703173 0.351586 0.936155i \(-0.385642\pi\)
0.351586 + 0.936155i \(0.385642\pi\)
\(42\) −1.08766 −0.167830
\(43\) −12.4190 −1.89388 −0.946940 0.321411i \(-0.895843\pi\)
−0.946940 + 0.321411i \(0.895843\pi\)
\(44\) 2.31527 0.349040
\(45\) 0.366545 0.0546413
\(46\) −20.7109 −3.05365
\(47\) −7.34736 −1.07172 −0.535861 0.844306i \(-0.680013\pi\)
−0.535861 + 0.844306i \(0.680013\pi\)
\(48\) 11.6450 1.68081
\(49\) −6.97026 −0.995751
\(50\) 12.3138 1.74144
\(51\) −4.48620 −0.628193
\(52\) 8.83090 1.22463
\(53\) −1.00000 −0.137361
\(54\) −3.34270 −0.454883
\(55\) 0.0587592 0.00792309
\(56\) −0.890194 −0.118957
\(57\) −1.91298 −0.253381
\(58\) 23.8376 3.13003
\(59\) −10.9196 −1.42161 −0.710807 0.703387i \(-0.751670\pi\)
−0.710807 + 0.703387i \(0.751670\pi\)
\(60\) 1.08564 0.140155
\(61\) −5.33209 −0.682704 −0.341352 0.939935i \(-0.610885\pi\)
−0.341352 + 0.939935i \(0.610885\pi\)
\(62\) 12.2932 1.56124
\(63\) 0.608770 0.0766979
\(64\) −6.83501 −0.854376
\(65\) 0.224120 0.0277986
\(66\) −3.56896 −0.439308
\(67\) −2.87403 −0.351118 −0.175559 0.984469i \(-0.556173\pi\)
−0.175559 + 0.984469i \(0.556173\pi\)
\(68\) −7.18287 −0.871051
\(69\) 21.4435 2.58149
\(70\) −0.0441967 −0.00528252
\(71\) −0.701405 −0.0832415 −0.0416207 0.999133i \(-0.513252\pi\)
−0.0416207 + 0.999133i \(0.513252\pi\)
\(72\) −18.2214 −2.14741
\(73\) −5.45468 −0.638421 −0.319211 0.947684i \(-0.603418\pi\)
−0.319211 + 0.947684i \(0.603418\pi\)
\(74\) −13.5198 −1.57165
\(75\) −12.7494 −1.47217
\(76\) −3.06288 −0.351337
\(77\) 0.0975894 0.0111213
\(78\) −13.6127 −1.54134
\(79\) 11.2134 1.26160 0.630802 0.775944i \(-0.282726\pi\)
0.630802 + 0.775944i \(0.282726\pi\)
\(80\) 0.473187 0.0529040
\(81\) −7.12908 −0.792120
\(82\) −11.1126 −1.22718
\(83\) −1.56654 −0.171950 −0.0859752 0.996297i \(-0.527401\pi\)
−0.0859752 + 0.996297i \(0.527401\pi\)
\(84\) 1.80307 0.196731
\(85\) −0.182294 −0.0197726
\(86\) 30.6511 3.30520
\(87\) −24.6808 −2.64606
\(88\) −2.92099 −0.311379
\(89\) −17.5104 −1.85610 −0.928048 0.372461i \(-0.878514\pi\)
−0.928048 + 0.372461i \(0.878514\pi\)
\(90\) −0.904663 −0.0953599
\(91\) 0.372226 0.0390199
\(92\) 34.3333 3.57949
\(93\) −12.7281 −1.31984
\(94\) 18.1339 1.87037
\(95\) −0.0777330 −0.00797524
\(96\) −2.35966 −0.240832
\(97\) −1.77592 −0.180317 −0.0901587 0.995927i \(-0.528737\pi\)
−0.0901587 + 0.995927i \(0.528737\pi\)
\(98\) 17.2032 1.73778
\(99\) 1.99756 0.200762
\(100\) −20.4131 −2.04131
\(101\) −5.49978 −0.547249 −0.273624 0.961837i \(-0.588223\pi\)
−0.273624 + 0.961837i \(0.588223\pi\)
\(102\) 11.0723 1.09632
\(103\) −10.2114 −1.00615 −0.503077 0.864241i \(-0.667799\pi\)
−0.503077 + 0.864241i \(0.667799\pi\)
\(104\) −11.1413 −1.09249
\(105\) 0.0457601 0.00446572
\(106\) 2.46809 0.239722
\(107\) −2.82827 −0.273419 −0.136709 0.990611i \(-0.543653\pi\)
−0.136709 + 0.990611i \(0.543653\pi\)
\(108\) 5.54132 0.533214
\(109\) 5.99163 0.573894 0.286947 0.957946i \(-0.407360\pi\)
0.286947 + 0.957946i \(0.407360\pi\)
\(110\) −0.145023 −0.0138274
\(111\) 13.9980 1.32863
\(112\) 0.785887 0.0742593
\(113\) 6.56301 0.617396 0.308698 0.951160i \(-0.400107\pi\)
0.308698 + 0.951160i \(0.400107\pi\)
\(114\) 4.72140 0.442200
\(115\) 0.871345 0.0812534
\(116\) −39.5165 −3.66901
\(117\) 7.61910 0.704386
\(118\) 26.9506 2.48100
\(119\) −0.302761 −0.0277540
\(120\) −1.36967 −0.125033
\(121\) −10.6798 −0.970889
\(122\) 13.1601 1.19146
\(123\) 11.5056 1.03743
\(124\) −20.3790 −1.83008
\(125\) −1.03725 −0.0927744
\(126\) −1.50250 −0.133853
\(127\) 2.18997 0.194329 0.0971644 0.995268i \(-0.469023\pi\)
0.0971644 + 0.995268i \(0.469023\pi\)
\(128\) 18.7162 1.65429
\(129\) −31.7353 −2.79414
\(130\) −0.553146 −0.0485141
\(131\) 9.16932 0.801127 0.400564 0.916269i \(-0.368814\pi\)
0.400564 + 0.916269i \(0.368814\pi\)
\(132\) 5.91640 0.514957
\(133\) −0.129102 −0.0111945
\(134\) 7.09334 0.612772
\(135\) 0.140633 0.0121038
\(136\) 9.06208 0.777067
\(137\) −7.13531 −0.609611 −0.304806 0.952415i \(-0.598591\pi\)
−0.304806 + 0.952415i \(0.598591\pi\)
\(138\) −52.9244 −4.50522
\(139\) 0.368786 0.0312800 0.0156400 0.999878i \(-0.495021\pi\)
0.0156400 + 0.999878i \(0.495021\pi\)
\(140\) 0.0732667 0.00619216
\(141\) −18.7753 −1.58117
\(142\) 1.73113 0.145273
\(143\) 1.22139 0.102137
\(144\) 16.0863 1.34053
\(145\) −1.00289 −0.0832855
\(146\) 13.4626 1.11417
\(147\) −17.8117 −1.46909
\(148\) 22.4123 1.84228
\(149\) 18.1013 1.48292 0.741458 0.670999i \(-0.234135\pi\)
0.741458 + 0.670999i \(0.234135\pi\)
\(150\) 31.4666 2.56923
\(151\) −1.00000 −0.0813788
\(152\) 3.86421 0.313429
\(153\) −6.19722 −0.501015
\(154\) −0.240859 −0.0194090
\(155\) −0.517198 −0.0415424
\(156\) 22.5664 1.80676
\(157\) 7.36224 0.587570 0.293785 0.955871i \(-0.405085\pi\)
0.293785 + 0.955871i \(0.405085\pi\)
\(158\) −27.6756 −2.20175
\(159\) −2.55539 −0.202655
\(160\) −0.0958836 −0.00758026
\(161\) 1.44716 0.114052
\(162\) 17.5952 1.38241
\(163\) 7.58431 0.594049 0.297025 0.954870i \(-0.404006\pi\)
0.297025 + 0.954870i \(0.404006\pi\)
\(164\) 18.4217 1.43850
\(165\) 0.150153 0.0116894
\(166\) 3.86636 0.300088
\(167\) 5.33856 0.413110 0.206555 0.978435i \(-0.433775\pi\)
0.206555 + 0.978435i \(0.433775\pi\)
\(168\) −2.27479 −0.175504
\(169\) −8.34139 −0.641645
\(170\) 0.449918 0.0345071
\(171\) −2.64259 −0.202084
\(172\) −50.8116 −3.87435
\(173\) 19.9931 1.52005 0.760023 0.649896i \(-0.225188\pi\)
0.760023 + 0.649896i \(0.225188\pi\)
\(174\) 60.9142 4.61789
\(175\) −0.860420 −0.0650417
\(176\) 2.57873 0.194379
\(177\) −27.9039 −2.09738
\(178\) 43.2171 3.23926
\(179\) 18.7362 1.40041 0.700204 0.713943i \(-0.253092\pi\)
0.700204 + 0.713943i \(0.253092\pi\)
\(180\) 1.49970 0.111781
\(181\) 22.3542 1.66157 0.830786 0.556591i \(-0.187891\pi\)
0.830786 + 0.556591i \(0.187891\pi\)
\(182\) −0.918685 −0.0680975
\(183\) −13.6256 −1.00723
\(184\) −43.3157 −3.19327
\(185\) 0.568803 0.0418192
\(186\) 31.4139 2.30338
\(187\) −0.993450 −0.0726482
\(188\) −30.0613 −2.19245
\(189\) 0.233569 0.0169896
\(190\) 0.191852 0.0139184
\(191\) −9.19731 −0.665494 −0.332747 0.943016i \(-0.607976\pi\)
−0.332747 + 0.943016i \(0.607976\pi\)
\(192\) −17.4661 −1.26051
\(193\) −6.37906 −0.459175 −0.229587 0.973288i \(-0.573738\pi\)
−0.229587 + 0.973288i \(0.573738\pi\)
\(194\) 4.38312 0.314690
\(195\) 0.572713 0.0410128
\(196\) −28.5184 −2.03703
\(197\) 17.2622 1.22988 0.614942 0.788573i \(-0.289180\pi\)
0.614942 + 0.788573i \(0.289180\pi\)
\(198\) −4.93015 −0.350370
\(199\) −5.00217 −0.354595 −0.177297 0.984157i \(-0.556735\pi\)
−0.177297 + 0.984157i \(0.556735\pi\)
\(200\) 25.7537 1.82106
\(201\) −7.34425 −0.518024
\(202\) 13.5739 0.955059
\(203\) −1.66564 −0.116905
\(204\) −18.3550 −1.28511
\(205\) 0.467526 0.0326534
\(206\) 25.2025 1.75594
\(207\) 29.6220 2.05887
\(208\) 9.83581 0.681990
\(209\) −0.423622 −0.0293025
\(210\) −0.112940 −0.00779358
\(211\) 5.51788 0.379866 0.189933 0.981797i \(-0.439173\pi\)
0.189933 + 0.981797i \(0.439173\pi\)
\(212\) −4.09144 −0.281002
\(213\) −1.79236 −0.122811
\(214\) 6.98040 0.477170
\(215\) −1.28955 −0.0879466
\(216\) −6.99106 −0.475681
\(217\) −0.858981 −0.0583115
\(218\) −14.7879 −1.00156
\(219\) −13.9388 −0.941897
\(220\) 0.240410 0.0162084
\(221\) −3.78922 −0.254891
\(222\) −34.5483 −2.31873
\(223\) −16.1960 −1.08456 −0.542281 0.840197i \(-0.682439\pi\)
−0.542281 + 0.840197i \(0.682439\pi\)
\(224\) −0.159247 −0.0106401
\(225\) −17.6120 −1.17413
\(226\) −16.1981 −1.07748
\(227\) 5.87661 0.390044 0.195022 0.980799i \(-0.437522\pi\)
0.195022 + 0.980799i \(0.437522\pi\)
\(228\) −7.82686 −0.518346
\(229\) −28.1971 −1.86331 −0.931657 0.363339i \(-0.881637\pi\)
−0.931657 + 0.363339i \(0.881637\pi\)
\(230\) −2.15055 −0.141803
\(231\) 0.249379 0.0164079
\(232\) 49.8549 3.27314
\(233\) 0.789484 0.0517208 0.0258604 0.999666i \(-0.491767\pi\)
0.0258604 + 0.999666i \(0.491767\pi\)
\(234\) −18.8046 −1.22929
\(235\) −0.762926 −0.0497678
\(236\) −44.6770 −2.90823
\(237\) 28.6545 1.86131
\(238\) 0.747240 0.0484364
\(239\) −11.4881 −0.743102 −0.371551 0.928412i \(-0.621174\pi\)
−0.371551 + 0.928412i \(0.621174\pi\)
\(240\) 1.20918 0.0780520
\(241\) −30.1872 −1.94453 −0.972265 0.233883i \(-0.924857\pi\)
−0.972265 + 0.233883i \(0.924857\pi\)
\(242\) 26.3586 1.69440
\(243\) −22.2807 −1.42931
\(244\) −21.8160 −1.39662
\(245\) −0.723770 −0.0462400
\(246\) −28.3969 −1.81052
\(247\) −1.61578 −0.102810
\(248\) 25.7106 1.63262
\(249\) −4.00313 −0.253688
\(250\) 2.56002 0.161910
\(251\) 5.43876 0.343291 0.171646 0.985159i \(-0.445092\pi\)
0.171646 + 0.985159i \(0.445092\pi\)
\(252\) 2.49075 0.156903
\(253\) 4.74857 0.298540
\(254\) −5.40504 −0.339143
\(255\) −0.465833 −0.0291716
\(256\) −32.5231 −2.03270
\(257\) 9.22605 0.575505 0.287753 0.957705i \(-0.407092\pi\)
0.287753 + 0.957705i \(0.407092\pi\)
\(258\) 78.3255 4.87634
\(259\) 0.944688 0.0587001
\(260\) 0.916973 0.0568683
\(261\) −34.0939 −2.11036
\(262\) −22.6307 −1.39813
\(263\) 24.9490 1.53842 0.769210 0.638996i \(-0.220650\pi\)
0.769210 + 0.638996i \(0.220650\pi\)
\(264\) −7.46427 −0.459394
\(265\) −0.103837 −0.00637865
\(266\) 0.318634 0.0195367
\(267\) −44.7458 −2.73840
\(268\) −11.7589 −0.718291
\(269\) −29.0691 −1.77238 −0.886189 0.463325i \(-0.846656\pi\)
−0.886189 + 0.463325i \(0.846656\pi\)
\(270\) −0.347095 −0.0211235
\(271\) −20.9946 −1.27533 −0.637664 0.770314i \(-0.720099\pi\)
−0.637664 + 0.770314i \(0.720099\pi\)
\(272\) −8.00024 −0.485086
\(273\) 0.951181 0.0575681
\(274\) 17.6106 1.06389
\(275\) −2.82330 −0.170251
\(276\) 87.7348 5.28102
\(277\) −3.30566 −0.198618 −0.0993090 0.995057i \(-0.531663\pi\)
−0.0993090 + 0.995057i \(0.531663\pi\)
\(278\) −0.910195 −0.0545899
\(279\) −17.5825 −1.05264
\(280\) −0.0924350 −0.00552405
\(281\) −3.12279 −0.186290 −0.0931451 0.995653i \(-0.529692\pi\)
−0.0931451 + 0.995653i \(0.529692\pi\)
\(282\) 46.3391 2.75946
\(283\) −8.77184 −0.521432 −0.260716 0.965416i \(-0.583959\pi\)
−0.260716 + 0.965416i \(0.583959\pi\)
\(284\) −2.86976 −0.170289
\(285\) −0.198638 −0.0117663
\(286\) −3.01448 −0.178250
\(287\) 0.776483 0.0458344
\(288\) −3.25963 −0.192075
\(289\) −13.9179 −0.818702
\(290\) 2.47522 0.145350
\(291\) −4.53817 −0.266032
\(292\) −22.3175 −1.30603
\(293\) 27.9322 1.63182 0.815908 0.578181i \(-0.196237\pi\)
0.815908 + 0.578181i \(0.196237\pi\)
\(294\) 43.9608 2.56385
\(295\) −1.13386 −0.0660159
\(296\) −28.2759 −1.64350
\(297\) 0.766410 0.0444716
\(298\) −44.6755 −2.58798
\(299\) 18.1120 1.04745
\(300\) −52.1634 −3.01166
\(301\) −2.14173 −0.123447
\(302\) 2.46809 0.142022
\(303\) −14.0541 −0.807386
\(304\) −3.41142 −0.195659
\(305\) −0.553668 −0.0317029
\(306\) 15.2953 0.874372
\(307\) −15.3704 −0.877233 −0.438617 0.898674i \(-0.644531\pi\)
−0.438617 + 0.898674i \(0.644531\pi\)
\(308\) 0.399282 0.0227512
\(309\) −26.0940 −1.48443
\(310\) 1.27649 0.0724997
\(311\) −5.31176 −0.301202 −0.150601 0.988595i \(-0.548121\pi\)
−0.150601 + 0.988595i \(0.548121\pi\)
\(312\) −28.4703 −1.61181
\(313\) 16.6482 0.941015 0.470507 0.882396i \(-0.344071\pi\)
0.470507 + 0.882396i \(0.344071\pi\)
\(314\) −18.1706 −1.02543
\(315\) 0.0632128 0.00356164
\(316\) 45.8789 2.58089
\(317\) 30.0316 1.68674 0.843372 0.537330i \(-0.180567\pi\)
0.843372 + 0.537330i \(0.180567\pi\)
\(318\) 6.30691 0.353674
\(319\) −5.46545 −0.306007
\(320\) −0.709726 −0.0396749
\(321\) −7.22732 −0.403389
\(322\) −3.57172 −0.199044
\(323\) 1.31424 0.0731264
\(324\) −29.1682 −1.62046
\(325\) −10.7686 −0.597337
\(326\) −18.7187 −1.03673
\(327\) 15.3109 0.846697
\(328\) −23.2413 −1.28329
\(329\) −1.26710 −0.0698572
\(330\) −0.370589 −0.0204003
\(331\) 21.7299 1.19438 0.597192 0.802098i \(-0.296283\pi\)
0.597192 + 0.802098i \(0.296283\pi\)
\(332\) −6.40942 −0.351763
\(333\) 19.3368 1.05965
\(334\) −13.1760 −0.720959
\(335\) −0.298430 −0.0163050
\(336\) 2.00824 0.109559
\(337\) −4.25708 −0.231898 −0.115949 0.993255i \(-0.536991\pi\)
−0.115949 + 0.993255i \(0.536991\pi\)
\(338\) 20.5873 1.11980
\(339\) 16.7710 0.910878
\(340\) −0.745847 −0.0404492
\(341\) −2.81858 −0.152634
\(342\) 6.52213 0.352676
\(343\) −2.40925 −0.130088
\(344\) 64.1052 3.45632
\(345\) 2.22662 0.119877
\(346\) −49.3446 −2.65278
\(347\) 6.29183 0.337763 0.168882 0.985636i \(-0.445984\pi\)
0.168882 + 0.985636i \(0.445984\pi\)
\(348\) −100.980 −5.41309
\(349\) 21.3005 1.14019 0.570094 0.821580i \(-0.306907\pi\)
0.570094 + 0.821580i \(0.306907\pi\)
\(350\) 2.12359 0.113511
\(351\) 2.92324 0.156031
\(352\) −0.522537 −0.0278513
\(353\) 5.35264 0.284892 0.142446 0.989803i \(-0.454503\pi\)
0.142446 + 0.989803i \(0.454503\pi\)
\(354\) 68.8691 3.66035
\(355\) −0.0728317 −0.00386551
\(356\) −71.6427 −3.79706
\(357\) −0.773671 −0.0409470
\(358\) −46.2425 −2.44399
\(359\) −1.38427 −0.0730591 −0.0365296 0.999333i \(-0.511630\pi\)
−0.0365296 + 0.999333i \(0.511630\pi\)
\(360\) −1.89205 −0.0997199
\(361\) −18.4396 −0.970505
\(362\) −55.1720 −2.89978
\(363\) −27.2910 −1.43240
\(364\) 1.52294 0.0798238
\(365\) −0.566396 −0.0296465
\(366\) 33.6290 1.75782
\(367\) 1.47682 0.0770891 0.0385446 0.999257i \(-0.487728\pi\)
0.0385446 + 0.999257i \(0.487728\pi\)
\(368\) 38.2402 1.99341
\(369\) 15.8939 0.827401
\(370\) −1.40385 −0.0729829
\(371\) −0.172456 −0.00895347
\(372\) −52.0761 −2.70002
\(373\) 4.07843 0.211173 0.105587 0.994410i \(-0.466328\pi\)
0.105587 + 0.994410i \(0.466328\pi\)
\(374\) 2.45192 0.126786
\(375\) −2.65057 −0.136875
\(376\) 37.9260 1.95589
\(377\) −20.8464 −1.07364
\(378\) −0.576468 −0.0296503
\(379\) −22.4684 −1.15413 −0.577063 0.816699i \(-0.695801\pi\)
−0.577063 + 0.816699i \(0.695801\pi\)
\(380\) −0.318040 −0.0163151
\(381\) 5.59623 0.286704
\(382\) 22.6998 1.16142
\(383\) −26.7557 −1.36715 −0.683577 0.729878i \(-0.739577\pi\)
−0.683577 + 0.729878i \(0.739577\pi\)
\(384\) 47.8271 2.44067
\(385\) 0.0101334 0.000516445 0
\(386\) 15.7441 0.801352
\(387\) −43.8391 −2.22847
\(388\) −7.26608 −0.368879
\(389\) 6.57256 0.333242 0.166621 0.986021i \(-0.446714\pi\)
0.166621 + 0.986021i \(0.446714\pi\)
\(390\) −1.41350 −0.0715755
\(391\) −14.7319 −0.745027
\(392\) 35.9795 1.81724
\(393\) 23.4312 1.18195
\(394\) −42.6047 −2.14639
\(395\) 1.16436 0.0585854
\(396\) 8.17290 0.410704
\(397\) −35.2687 −1.77008 −0.885042 0.465512i \(-0.845870\pi\)
−0.885042 + 0.465512i \(0.845870\pi\)
\(398\) 12.3458 0.618839
\(399\) −0.329905 −0.0165159
\(400\) −22.7360 −1.13680
\(401\) 28.6118 1.42880 0.714402 0.699736i \(-0.246699\pi\)
0.714402 + 0.699736i \(0.246699\pi\)
\(402\) 18.1262 0.904055
\(403\) −10.7506 −0.535527
\(404\) −22.5021 −1.11952
\(405\) −0.740261 −0.0367839
\(406\) 4.11093 0.204022
\(407\) 3.09981 0.153652
\(408\) 23.1571 1.14645
\(409\) 29.6125 1.46425 0.732123 0.681172i \(-0.238530\pi\)
0.732123 + 0.681172i \(0.238530\pi\)
\(410\) −1.15389 −0.0569867
\(411\) −18.2335 −0.899392
\(412\) −41.7792 −2.05831
\(413\) −1.88315 −0.0926640
\(414\) −73.1096 −3.59314
\(415\) −0.162665 −0.00798491
\(416\) −1.99306 −0.0977180
\(417\) 0.942391 0.0461491
\(418\) 1.04553 0.0511388
\(419\) −15.7929 −0.771534 −0.385767 0.922596i \(-0.626063\pi\)
−0.385767 + 0.922596i \(0.626063\pi\)
\(420\) 0.187225 0.00913563
\(421\) −3.93361 −0.191712 −0.0958562 0.995395i \(-0.530559\pi\)
−0.0958562 + 0.995395i \(0.530559\pi\)
\(422\) −13.6186 −0.662942
\(423\) −25.9362 −1.26106
\(424\) 5.16186 0.250682
\(425\) 8.75899 0.424873
\(426\) 4.42370 0.214329
\(427\) −0.919551 −0.0445002
\(428\) −11.5717 −0.559339
\(429\) 3.12111 0.150689
\(430\) 3.18272 0.153484
\(431\) 6.78334 0.326742 0.163371 0.986565i \(-0.447763\pi\)
0.163371 + 0.986565i \(0.447763\pi\)
\(432\) 6.17189 0.296945
\(433\) 20.4266 0.981642 0.490821 0.871260i \(-0.336697\pi\)
0.490821 + 0.871260i \(0.336697\pi\)
\(434\) 2.12004 0.101765
\(435\) −2.56277 −0.122876
\(436\) 24.5144 1.17403
\(437\) −6.28192 −0.300505
\(438\) 34.4022 1.64380
\(439\) 37.4414 1.78698 0.893489 0.449085i \(-0.148250\pi\)
0.893489 + 0.449085i \(0.148250\pi\)
\(440\) −0.303307 −0.0144596
\(441\) −24.6050 −1.17167
\(442\) 9.35212 0.444835
\(443\) −5.57274 −0.264769 −0.132385 0.991198i \(-0.542263\pi\)
−0.132385 + 0.991198i \(0.542263\pi\)
\(444\) 57.2722 2.71802
\(445\) −1.81822 −0.0861920
\(446\) 39.9730 1.89278
\(447\) 46.2558 2.18783
\(448\) −1.17874 −0.0556901
\(449\) 25.8083 1.21797 0.608984 0.793182i \(-0.291577\pi\)
0.608984 + 0.793182i \(0.291577\pi\)
\(450\) 43.4678 2.04909
\(451\) 2.54788 0.119975
\(452\) 26.8522 1.26302
\(453\) −2.55539 −0.120063
\(454\) −14.5040 −0.680705
\(455\) 0.0386508 0.00181198
\(456\) 9.87455 0.462418
\(457\) −30.8355 −1.44242 −0.721212 0.692714i \(-0.756415\pi\)
−0.721212 + 0.692714i \(0.756415\pi\)
\(458\) 69.5927 3.25185
\(459\) −2.37771 −0.110982
\(460\) 3.56506 0.166222
\(461\) −23.6309 −1.10060 −0.550301 0.834967i \(-0.685487\pi\)
−0.550301 + 0.834967i \(0.685487\pi\)
\(462\) −0.615488 −0.0286351
\(463\) 15.3530 0.713514 0.356757 0.934197i \(-0.383882\pi\)
0.356757 + 0.934197i \(0.383882\pi\)
\(464\) −44.0132 −2.04326
\(465\) −1.32164 −0.0612897
\(466\) −1.94851 −0.0902632
\(467\) −3.48787 −0.161399 −0.0806996 0.996738i \(-0.525715\pi\)
−0.0806996 + 0.996738i \(0.525715\pi\)
\(468\) 31.1731 1.44098
\(469\) −0.495643 −0.0228867
\(470\) 1.88297 0.0868548
\(471\) 18.8134 0.866874
\(472\) 56.3656 2.59444
\(473\) −7.02766 −0.323132
\(474\) −70.7218 −3.24836
\(475\) 3.73496 0.171372
\(476\) −1.23873 −0.0567771
\(477\) −3.53000 −0.161628
\(478\) 28.3536 1.29686
\(479\) −8.32025 −0.380162 −0.190081 0.981768i \(-0.560875\pi\)
−0.190081 + 0.981768i \(0.560875\pi\)
\(480\) −0.245020 −0.0111836
\(481\) 11.8233 0.539096
\(482\) 74.5046 3.39359
\(483\) 3.69806 0.168267
\(484\) −43.6957 −1.98617
\(485\) −0.184406 −0.00837345
\(486\) 54.9906 2.49442
\(487\) −41.6307 −1.88647 −0.943234 0.332130i \(-0.892233\pi\)
−0.943234 + 0.332130i \(0.892233\pi\)
\(488\) 27.5235 1.24593
\(489\) 19.3809 0.876433
\(490\) 1.78633 0.0806980
\(491\) 34.8173 1.57128 0.785640 0.618683i \(-0.212334\pi\)
0.785640 + 0.618683i \(0.212334\pi\)
\(492\) 47.0747 2.12229
\(493\) 16.9560 0.763660
\(494\) 3.98788 0.179423
\(495\) 0.207420 0.00932285
\(496\) −22.6980 −1.01917
\(497\) −0.120962 −0.00542587
\(498\) 9.88005 0.442736
\(499\) 10.9030 0.488087 0.244043 0.969764i \(-0.421526\pi\)
0.244043 + 0.969764i \(0.421526\pi\)
\(500\) −4.24385 −0.189791
\(501\) 13.6421 0.609483
\(502\) −13.4233 −0.599112
\(503\) −30.5987 −1.36433 −0.682164 0.731199i \(-0.738961\pi\)
−0.682164 + 0.731199i \(0.738961\pi\)
\(504\) −3.14239 −0.139973
\(505\) −0.571080 −0.0254127
\(506\) −11.7199 −0.521012
\(507\) −21.3155 −0.946653
\(508\) 8.96016 0.397543
\(509\) −6.49420 −0.287850 −0.143925 0.989589i \(-0.545972\pi\)
−0.143925 + 0.989589i \(0.545972\pi\)
\(510\) 1.14971 0.0509102
\(511\) −0.940691 −0.0416137
\(512\) 42.8375 1.89317
\(513\) −1.01389 −0.0447643
\(514\) −22.7707 −1.00437
\(515\) −1.06032 −0.0467231
\(516\) −129.843 −5.71604
\(517\) −4.15772 −0.182856
\(518\) −2.33157 −0.102443
\(519\) 51.0901 2.24261
\(520\) −1.15687 −0.0507323
\(521\) 4.74968 0.208087 0.104044 0.994573i \(-0.466822\pi\)
0.104044 + 0.994573i \(0.466822\pi\)
\(522\) 84.1467 3.68300
\(523\) −7.42721 −0.324769 −0.162385 0.986728i \(-0.551919\pi\)
−0.162385 + 0.986728i \(0.551919\pi\)
\(524\) 37.5158 1.63888
\(525\) −2.19871 −0.0959595
\(526\) −61.5762 −2.68485
\(527\) 8.74434 0.380909
\(528\) 6.58966 0.286778
\(529\) 47.4170 2.06161
\(530\) 0.256278 0.0111320
\(531\) −38.5463 −1.67277
\(532\) −0.528213 −0.0229009
\(533\) 9.71812 0.420939
\(534\) 110.436 4.77905
\(535\) −0.293678 −0.0126968
\(536\) 14.8353 0.640789
\(537\) 47.8782 2.06610
\(538\) 71.7451 3.09315
\(539\) −3.94433 −0.169894
\(540\) 0.575393 0.0247610
\(541\) 12.5831 0.540989 0.270495 0.962722i \(-0.412813\pi\)
0.270495 + 0.962722i \(0.412813\pi\)
\(542\) 51.8164 2.22570
\(543\) 57.1236 2.45141
\(544\) 1.62112 0.0695048
\(545\) 0.622152 0.0266501
\(546\) −2.34760 −0.100468
\(547\) 39.7652 1.70024 0.850119 0.526590i \(-0.176530\pi\)
0.850119 + 0.526590i \(0.176530\pi\)
\(548\) −29.1937 −1.24709
\(549\) −18.8223 −0.803316
\(550\) 6.96814 0.297123
\(551\) 7.23029 0.308021
\(552\) −110.688 −4.71121
\(553\) 1.93381 0.0822341
\(554\) 8.15866 0.346628
\(555\) 1.45351 0.0616981
\(556\) 1.50887 0.0639902
\(557\) −14.8826 −0.630597 −0.315299 0.948992i \(-0.602105\pi\)
−0.315299 + 0.948992i \(0.602105\pi\)
\(558\) 43.3951 1.83706
\(559\) −26.8049 −1.13373
\(560\) 0.0816040 0.00344840
\(561\) −2.53865 −0.107182
\(562\) 7.70732 0.325114
\(563\) 34.2066 1.44164 0.720818 0.693125i \(-0.243766\pi\)
0.720818 + 0.693125i \(0.243766\pi\)
\(564\) −76.8183 −3.23463
\(565\) 0.681483 0.0286702
\(566\) 21.6496 0.910002
\(567\) −1.22945 −0.0516321
\(568\) 3.62056 0.151915
\(569\) 22.8508 0.957953 0.478977 0.877828i \(-0.341008\pi\)
0.478977 + 0.877828i \(0.341008\pi\)
\(570\) 0.490256 0.0205345
\(571\) −3.11691 −0.130439 −0.0652194 0.997871i \(-0.520775\pi\)
−0.0652194 + 0.997871i \(0.520775\pi\)
\(572\) 4.99723 0.208945
\(573\) −23.5027 −0.981839
\(574\) −1.91643 −0.0799901
\(575\) −41.8669 −1.74597
\(576\) −24.1276 −1.00532
\(577\) −5.66766 −0.235948 −0.117974 0.993017i \(-0.537640\pi\)
−0.117974 + 0.993017i \(0.537640\pi\)
\(578\) 34.3506 1.42880
\(579\) −16.3010 −0.677445
\(580\) −4.10327 −0.170379
\(581\) −0.270160 −0.0112081
\(582\) 11.2006 0.464279
\(583\) −0.565880 −0.0234364
\(584\) 28.1563 1.16512
\(585\) 0.791143 0.0327098
\(586\) −68.9390 −2.84785
\(587\) −33.0590 −1.36449 −0.682245 0.731124i \(-0.738996\pi\)
−0.682245 + 0.731124i \(0.738996\pi\)
\(588\) −72.8756 −3.00534
\(589\) 3.72872 0.153639
\(590\) 2.79846 0.115211
\(591\) 44.1117 1.81451
\(592\) 24.9627 1.02596
\(593\) 3.24206 0.133135 0.0665677 0.997782i \(-0.478795\pi\)
0.0665677 + 0.997782i \(0.478795\pi\)
\(594\) −1.89156 −0.0776118
\(595\) −0.0314377 −0.00128882
\(596\) 74.0604 3.03363
\(597\) −12.7825 −0.523153
\(598\) −44.7020 −1.82800
\(599\) 15.6286 0.638566 0.319283 0.947659i \(-0.396558\pi\)
0.319283 + 0.947659i \(0.396558\pi\)
\(600\) 65.8106 2.68671
\(601\) 3.63163 0.148137 0.0740687 0.997253i \(-0.476402\pi\)
0.0740687 + 0.997253i \(0.476402\pi\)
\(602\) 5.28597 0.215440
\(603\) −10.1453 −0.413150
\(604\) −4.09144 −0.166479
\(605\) −1.10895 −0.0450854
\(606\) 34.6867 1.40905
\(607\) 16.0391 0.651008 0.325504 0.945541i \(-0.394466\pi\)
0.325504 + 0.945541i \(0.394466\pi\)
\(608\) 0.691268 0.0280346
\(609\) −4.25634 −0.172476
\(610\) 1.36650 0.0553279
\(611\) −15.8584 −0.641562
\(612\) −25.3556 −1.02494
\(613\) 43.2000 1.74483 0.872416 0.488765i \(-0.162552\pi\)
0.872416 + 0.488765i \(0.162552\pi\)
\(614\) 37.9354 1.53095
\(615\) 1.19471 0.0481753
\(616\) −0.503743 −0.0202964
\(617\) 43.9417 1.76903 0.884514 0.466514i \(-0.154490\pi\)
0.884514 + 0.466514i \(0.154490\pi\)
\(618\) 64.4021 2.59063
\(619\) 23.4850 0.943943 0.471971 0.881614i \(-0.343543\pi\)
0.471971 + 0.881614i \(0.343543\pi\)
\(620\) −2.11609 −0.0849841
\(621\) 11.3652 0.456068
\(622\) 13.1099 0.525658
\(623\) −3.01977 −0.120984
\(624\) 25.1343 1.00618
\(625\) 24.8384 0.993535
\(626\) −41.0893 −1.64226
\(627\) −1.08252 −0.0432316
\(628\) 30.1222 1.20201
\(629\) −9.61683 −0.383448
\(630\) −0.156015 −0.00621577
\(631\) 11.3374 0.451334 0.225667 0.974204i \(-0.427544\pi\)
0.225667 + 0.974204i \(0.427544\pi\)
\(632\) −57.8819 −2.30242
\(633\) 14.1003 0.560437
\(634\) −74.1206 −2.94371
\(635\) 0.227400 0.00902410
\(636\) −10.4552 −0.414577
\(637\) −15.0445 −0.596084
\(638\) 13.4892 0.534043
\(639\) −2.47596 −0.0979476
\(640\) 1.94343 0.0768209
\(641\) −14.0365 −0.554407 −0.277204 0.960811i \(-0.589408\pi\)
−0.277204 + 0.960811i \(0.589408\pi\)
\(642\) 17.8376 0.703995
\(643\) 6.22662 0.245554 0.122777 0.992434i \(-0.460820\pi\)
0.122777 + 0.992434i \(0.460820\pi\)
\(644\) 5.92098 0.233319
\(645\) −3.29530 −0.129752
\(646\) −3.24366 −0.127620
\(647\) −24.5682 −0.965874 −0.482937 0.875655i \(-0.660430\pi\)
−0.482937 + 0.875655i \(0.660430\pi\)
\(648\) 36.7993 1.44561
\(649\) −6.17920 −0.242555
\(650\) 26.5779 1.04247
\(651\) −2.19503 −0.0860300
\(652\) 31.0308 1.21526
\(653\) −36.7709 −1.43896 −0.719479 0.694515i \(-0.755619\pi\)
−0.719479 + 0.694515i \(0.755619\pi\)
\(654\) −37.7887 −1.47766
\(655\) 0.952114 0.0372022
\(656\) 20.5180 0.801094
\(657\) −19.2550 −0.751210
\(658\) 3.12730 0.121915
\(659\) −36.6585 −1.42801 −0.714006 0.700140i \(-0.753121\pi\)
−0.714006 + 0.700140i \(0.753121\pi\)
\(660\) 0.614341 0.0239132
\(661\) −44.6395 −1.73628 −0.868138 0.496322i \(-0.834684\pi\)
−0.868138 + 0.496322i \(0.834684\pi\)
\(662\) −53.6313 −2.08444
\(663\) −9.68293 −0.376054
\(664\) 8.08628 0.313809
\(665\) −0.0134055 −0.000519844 0
\(666\) −47.7250 −1.84930
\(667\) −81.0477 −3.13818
\(668\) 21.8424 0.845108
\(669\) −41.3869 −1.60011
\(670\) 0.736551 0.0284554
\(671\) −3.01732 −0.116482
\(672\) −0.406937 −0.0156980
\(673\) −35.7957 −1.37982 −0.689912 0.723894i \(-0.742351\pi\)
−0.689912 + 0.723894i \(0.742351\pi\)
\(674\) 10.5068 0.404708
\(675\) −6.75724 −0.260086
\(676\) −34.1283 −1.31263
\(677\) 15.5815 0.598845 0.299423 0.954121i \(-0.403206\pi\)
0.299423 + 0.954121i \(0.403206\pi\)
\(678\) −41.3924 −1.58966
\(679\) −0.306268 −0.0117535
\(680\) 0.940978 0.0360849
\(681\) 15.0170 0.575453
\(682\) 6.95649 0.266378
\(683\) −15.6392 −0.598419 −0.299210 0.954187i \(-0.596723\pi\)
−0.299210 + 0.954187i \(0.596723\pi\)
\(684\) −10.8120 −0.413407
\(685\) −0.740909 −0.0283087
\(686\) 5.94625 0.227029
\(687\) −72.0544 −2.74905
\(688\) −56.5937 −2.15761
\(689\) −2.15838 −0.0822278
\(690\) −5.49550 −0.209210
\(691\) 3.52011 0.133911 0.0669556 0.997756i \(-0.478671\pi\)
0.0669556 + 0.997756i \(0.478671\pi\)
\(692\) 81.8006 3.10959
\(693\) 0.344491 0.0130861
\(694\) −15.5288 −0.589464
\(695\) 0.0382936 0.00145256
\(696\) 127.399 4.82903
\(697\) −7.90452 −0.299405
\(698\) −52.5713 −1.98985
\(699\) 2.01744 0.0763065
\(700\) −3.52036 −0.133057
\(701\) −24.8486 −0.938519 −0.469259 0.883060i \(-0.655479\pi\)
−0.469259 + 0.883060i \(0.655479\pi\)
\(702\) −7.21481 −0.272306
\(703\) −4.10076 −0.154663
\(704\) −3.86780 −0.145773
\(705\) −1.94957 −0.0734252
\(706\) −13.2108 −0.497194
\(707\) −0.948470 −0.0356709
\(708\) −114.167 −4.29066
\(709\) 28.6154 1.07467 0.537337 0.843367i \(-0.319430\pi\)
0.537337 + 0.843367i \(0.319430\pi\)
\(710\) 0.179755 0.00674608
\(711\) 39.5833 1.48449
\(712\) 90.3861 3.38736
\(713\) −41.7969 −1.56531
\(714\) 1.90949 0.0714607
\(715\) 0.126825 0.00474298
\(716\) 76.6580 2.86484
\(717\) −29.3565 −1.09634
\(718\) 3.41650 0.127503
\(719\) 10.3163 0.384734 0.192367 0.981323i \(-0.438384\pi\)
0.192367 + 0.981323i \(0.438384\pi\)
\(720\) 1.67035 0.0622504
\(721\) −1.76101 −0.0655834
\(722\) 45.5105 1.69372
\(723\) −77.1400 −2.86887
\(724\) 91.4609 3.39912
\(725\) 48.1875 1.78964
\(726\) 67.3564 2.49983
\(727\) −38.9321 −1.44391 −0.721956 0.691939i \(-0.756757\pi\)
−0.721956 + 0.691939i \(0.756757\pi\)
\(728\) −1.92138 −0.0712110
\(729\) −35.5485 −1.31661
\(730\) 1.39791 0.0517391
\(731\) 21.8026 0.806398
\(732\) −55.7482 −2.06051
\(733\) −37.1857 −1.37349 −0.686743 0.726901i \(-0.740960\pi\)
−0.686743 + 0.726901i \(0.740960\pi\)
\(734\) −3.64491 −0.134536
\(735\) −1.84951 −0.0682203
\(736\) −7.74875 −0.285623
\(737\) −1.62635 −0.0599076
\(738\) −39.2274 −1.44398
\(739\) 25.1717 0.925958 0.462979 0.886369i \(-0.346781\pi\)
0.462979 + 0.886369i \(0.346781\pi\)
\(740\) 2.32723 0.0855505
\(741\) −4.12895 −0.151681
\(742\) 0.425636 0.0156256
\(743\) 40.6990 1.49310 0.746551 0.665328i \(-0.231708\pi\)
0.746551 + 0.665328i \(0.231708\pi\)
\(744\) 65.7005 2.40870
\(745\) 1.87958 0.0688625
\(746\) −10.0659 −0.368540
\(747\) −5.52991 −0.202329
\(748\) −4.06464 −0.148618
\(749\) −0.487751 −0.0178220
\(750\) 6.54184 0.238874
\(751\) −32.0099 −1.16806 −0.584028 0.811733i \(-0.698524\pi\)
−0.584028 + 0.811733i \(0.698524\pi\)
\(752\) −33.4821 −1.22097
\(753\) 13.8981 0.506476
\(754\) 51.4506 1.87372
\(755\) −0.103837 −0.00377901
\(756\) 0.955634 0.0347561
\(757\) 7.11054 0.258437 0.129219 0.991616i \(-0.458753\pi\)
0.129219 + 0.991616i \(0.458753\pi\)
\(758\) 55.4540 2.01418
\(759\) 12.1344 0.440452
\(760\) 0.401247 0.0145548
\(761\) 1.05467 0.0382318 0.0191159 0.999817i \(-0.493915\pi\)
0.0191159 + 0.999817i \(0.493915\pi\)
\(762\) −13.8120 −0.500355
\(763\) 1.03329 0.0374077
\(764\) −37.6303 −1.36142
\(765\) −0.643500 −0.0232658
\(766\) 66.0355 2.38596
\(767\) −23.5687 −0.851017
\(768\) −83.1092 −2.99895
\(769\) 8.41409 0.303420 0.151710 0.988425i \(-0.451522\pi\)
0.151710 + 0.988425i \(0.451522\pi\)
\(770\) −0.0250100 −0.000901299 0
\(771\) 23.5761 0.849074
\(772\) −26.0996 −0.939344
\(773\) −39.2847 −1.41297 −0.706485 0.707728i \(-0.749720\pi\)
−0.706485 + 0.707728i \(0.749720\pi\)
\(774\) 108.199 3.88912
\(775\) 24.8507 0.892662
\(776\) 9.16706 0.329078
\(777\) 2.41404 0.0866034
\(778\) −16.2216 −0.581574
\(779\) −3.37061 −0.120764
\(780\) 2.34322 0.0839008
\(781\) −0.396911 −0.0142026
\(782\) 36.3597 1.30022
\(783\) −13.0809 −0.467474
\(784\) −31.7637 −1.13442
\(785\) 0.764471 0.0272852
\(786\) −57.8301 −2.06273
\(787\) −9.17468 −0.327042 −0.163521 0.986540i \(-0.552285\pi\)
−0.163521 + 0.986540i \(0.552285\pi\)
\(788\) 70.6275 2.51600
\(789\) 63.7543 2.26971
\(790\) −2.87374 −0.102243
\(791\) 1.13183 0.0402433
\(792\) −10.3111 −0.366390
\(793\) −11.5087 −0.408686
\(794\) 87.0460 3.08915
\(795\) −0.265343 −0.00941076
\(796\) −20.4661 −0.725402
\(797\) 16.2878 0.576943 0.288471 0.957489i \(-0.406853\pi\)
0.288471 + 0.957489i \(0.406853\pi\)
\(798\) 0.814234 0.0288236
\(799\) 12.8989 0.456330
\(800\) 4.60707 0.162885
\(801\) −61.8117 −2.18401
\(802\) −70.6163 −2.49355
\(803\) −3.08669 −0.108927
\(804\) −30.0486 −1.05973
\(805\) 0.150269 0.00529628
\(806\) 26.5335 0.934601
\(807\) −74.2829 −2.61488
\(808\) 28.3891 0.998726
\(809\) 14.9443 0.525415 0.262707 0.964876i \(-0.415385\pi\)
0.262707 + 0.964876i \(0.415385\pi\)
\(810\) 1.82703 0.0641952
\(811\) −11.1121 −0.390197 −0.195099 0.980784i \(-0.562503\pi\)
−0.195099 + 0.980784i \(0.562503\pi\)
\(812\) −6.81486 −0.239155
\(813\) −53.6492 −1.88156
\(814\) −7.65059 −0.268153
\(815\) 0.787531 0.0275860
\(816\) −20.4437 −0.715673
\(817\) 9.29695 0.325259
\(818\) −73.0863 −2.55540
\(819\) 1.31396 0.0459135
\(820\) 1.91286 0.0667998
\(821\) −38.8092 −1.35445 −0.677226 0.735775i \(-0.736818\pi\)
−0.677226 + 0.735775i \(0.736818\pi\)
\(822\) 45.0018 1.56962
\(823\) 18.3597 0.639978 0.319989 0.947421i \(-0.396321\pi\)
0.319989 + 0.947421i \(0.396321\pi\)
\(824\) 52.7096 1.83623
\(825\) −7.21462 −0.251181
\(826\) 4.64779 0.161717
\(827\) 42.5891 1.48097 0.740485 0.672073i \(-0.234596\pi\)
0.740485 + 0.672073i \(0.234596\pi\)
\(828\) 121.197 4.21187
\(829\) 21.6893 0.753300 0.376650 0.926356i \(-0.377076\pi\)
0.376650 + 0.926356i \(0.377076\pi\)
\(830\) 0.401471 0.0139353
\(831\) −8.44725 −0.293032
\(832\) −14.7526 −0.511453
\(833\) 12.2369 0.423982
\(834\) −2.32590 −0.0805393
\(835\) 0.554339 0.0191837
\(836\) −1.73323 −0.0599449
\(837\) −6.74594 −0.233174
\(838\) 38.9783 1.34648
\(839\) −12.5533 −0.433389 −0.216695 0.976239i \(-0.569528\pi\)
−0.216695 + 0.976239i \(0.569528\pi\)
\(840\) −0.236207 −0.00814992
\(841\) 64.2832 2.21666
\(842\) 9.70848 0.334576
\(843\) −7.97994 −0.274844
\(844\) 22.5761 0.777101
\(845\) −0.866143 −0.0297962
\(846\) 64.0128 2.20080
\(847\) −1.84179 −0.0632847
\(848\) −4.55703 −0.156489
\(849\) −22.4154 −0.769296
\(850\) −21.6179 −0.741489
\(851\) 45.9673 1.57574
\(852\) −7.33335 −0.251236
\(853\) −0.196035 −0.00671211 −0.00335605 0.999994i \(-0.501068\pi\)
−0.00335605 + 0.999994i \(0.501068\pi\)
\(854\) 2.26953 0.0776617
\(855\) −0.274398 −0.00938421
\(856\) 14.5991 0.498988
\(857\) 48.2744 1.64902 0.824511 0.565846i \(-0.191450\pi\)
0.824511 + 0.565846i \(0.191450\pi\)
\(858\) −7.70317 −0.262982
\(859\) −19.8797 −0.678288 −0.339144 0.940734i \(-0.610137\pi\)
−0.339144 + 0.940734i \(0.610137\pi\)
\(860\) −5.27612 −0.179914
\(861\) 1.98422 0.0676219
\(862\) −16.7419 −0.570230
\(863\) 40.1220 1.36577 0.682884 0.730527i \(-0.260725\pi\)
0.682884 + 0.730527i \(0.260725\pi\)
\(864\) −1.25063 −0.0425474
\(865\) 2.07602 0.0705868
\(866\) −50.4147 −1.71316
\(867\) −35.5657 −1.20787
\(868\) −3.51447 −0.119289
\(869\) 6.34543 0.215254
\(870\) 6.32514 0.214442
\(871\) −6.20325 −0.210189
\(872\) −30.9280 −1.04735
\(873\) −6.26901 −0.212174
\(874\) 15.5043 0.524442
\(875\) −0.178880 −0.00604724
\(876\) −57.0299 −1.92686
\(877\) −50.6486 −1.71028 −0.855141 0.518396i \(-0.826530\pi\)
−0.855141 + 0.518396i \(0.826530\pi\)
\(878\) −92.4084 −3.11863
\(879\) 71.3776 2.40751
\(880\) 0.267767 0.00902643
\(881\) 5.50224 0.185375 0.0926875 0.995695i \(-0.470454\pi\)
0.0926875 + 0.995695i \(0.470454\pi\)
\(882\) 60.7274 2.04480
\(883\) 33.7443 1.13559 0.567793 0.823171i \(-0.307797\pi\)
0.567793 + 0.823171i \(0.307797\pi\)
\(884\) −15.5034 −0.521435
\(885\) −2.89745 −0.0973967
\(886\) 13.7540 0.462075
\(887\) −51.5124 −1.72962 −0.864809 0.502102i \(-0.832560\pi\)
−0.864809 + 0.502102i \(0.832560\pi\)
\(888\) −72.2559 −2.42475
\(889\) 0.377674 0.0126668
\(890\) 4.48753 0.150422
\(891\) −4.03420 −0.135151
\(892\) −66.2649 −2.21871
\(893\) 5.50028 0.184060
\(894\) −114.163 −3.81819
\(895\) 1.94551 0.0650311
\(896\) 3.22772 0.107831
\(897\) 46.2832 1.54535
\(898\) −63.6971 −2.12560
\(899\) 48.1069 1.60445
\(900\) −72.0584 −2.40195
\(901\) 1.75558 0.0584870
\(902\) −6.28838 −0.209380
\(903\) −5.47295 −0.182128
\(904\) −33.8774 −1.12674
\(905\) 2.32119 0.0771589
\(906\) 6.30691 0.209533
\(907\) 8.76393 0.291002 0.145501 0.989358i \(-0.453521\pi\)
0.145501 + 0.989358i \(0.453521\pi\)
\(908\) 24.0438 0.797922
\(909\) −19.4143 −0.643930
\(910\) −0.0953934 −0.00316226
\(911\) −0.877559 −0.0290748 −0.0145374 0.999894i \(-0.504628\pi\)
−0.0145374 + 0.999894i \(0.504628\pi\)
\(912\) −8.71751 −0.288666
\(913\) −0.886476 −0.0293381
\(914\) 76.1047 2.51732
\(915\) −1.41484 −0.0467730
\(916\) −115.367 −3.81182
\(917\) 1.58130 0.0522193
\(918\) 5.86838 0.193685
\(919\) 36.8190 1.21455 0.607274 0.794493i \(-0.292263\pi\)
0.607274 + 0.794493i \(0.292263\pi\)
\(920\) −4.49776 −0.148287
\(921\) −39.2772 −1.29423
\(922\) 58.3231 1.92077
\(923\) −1.51390 −0.0498306
\(924\) 1.02032 0.0335660
\(925\) −27.3302 −0.898611
\(926\) −37.8925 −1.24522
\(927\) −36.0461 −1.18391
\(928\) 8.91855 0.292766
\(929\) 2.49644 0.0819056 0.0409528 0.999161i \(-0.486961\pi\)
0.0409528 + 0.999161i \(0.486961\pi\)
\(930\) 3.26192 0.106963
\(931\) 5.21799 0.171013
\(932\) 3.23013 0.105806
\(933\) −13.5736 −0.444380
\(934\) 8.60835 0.281674
\(935\) −0.103157 −0.00337359
\(936\) −39.3287 −1.28550
\(937\) −41.8399 −1.36685 −0.683424 0.730022i \(-0.739510\pi\)
−0.683424 + 0.730022i \(0.739510\pi\)
\(938\) 1.22329 0.0399418
\(939\) 42.5427 1.38833
\(940\) −3.12147 −0.101811
\(941\) 4.01422 0.130860 0.0654300 0.997857i \(-0.479158\pi\)
0.0654300 + 0.997857i \(0.479158\pi\)
\(942\) −46.4330 −1.51287
\(943\) 37.7827 1.23037
\(944\) −49.7610 −1.61958
\(945\) 0.0242531 0.000788952 0
\(946\) 17.3449 0.563930
\(947\) −8.72438 −0.283504 −0.141752 0.989902i \(-0.545274\pi\)
−0.141752 + 0.989902i \(0.545274\pi\)
\(948\) 117.238 3.80773
\(949\) −11.7733 −0.382177
\(950\) −9.21821 −0.299078
\(951\) 76.7424 2.48854
\(952\) 1.56281 0.0506510
\(953\) −32.7943 −1.06231 −0.531156 0.847274i \(-0.678242\pi\)
−0.531156 + 0.847274i \(0.678242\pi\)
\(954\) 8.71235 0.282073
\(955\) −0.955020 −0.0309037
\(956\) −47.0029 −1.52018
\(957\) −13.9663 −0.451468
\(958\) 20.5351 0.663458
\(959\) −1.23053 −0.0397358
\(960\) −1.81362 −0.0585345
\(961\) −6.19090 −0.199707
\(962\) −29.1809 −0.940830
\(963\) −9.98379 −0.321723
\(964\) −123.509 −3.97797
\(965\) −0.662382 −0.0213228
\(966\) −9.12712 −0.293660
\(967\) −15.5792 −0.500993 −0.250496 0.968118i \(-0.580594\pi\)
−0.250496 + 0.968118i \(0.580594\pi\)
\(968\) 55.1276 1.77187
\(969\) 3.35840 0.107887
\(970\) 0.455130 0.0146133
\(971\) −2.27263 −0.0729320 −0.0364660 0.999335i \(-0.511610\pi\)
−0.0364660 + 0.999335i \(0.511610\pi\)
\(972\) −91.1601 −2.92396
\(973\) 0.0635993 0.00203890
\(974\) 102.748 3.29226
\(975\) −27.5180 −0.881283
\(976\) −24.2985 −0.777775
\(977\) −54.4600 −1.74233 −0.871166 0.490989i \(-0.836635\pi\)
−0.871166 + 0.490989i \(0.836635\pi\)
\(978\) −47.8336 −1.52955
\(979\) −9.90877 −0.316686
\(980\) −2.96126 −0.0945941
\(981\) 21.1505 0.675283
\(982\) −85.9319 −2.74220
\(983\) −42.0353 −1.34072 −0.670359 0.742037i \(-0.733860\pi\)
−0.670359 + 0.742037i \(0.733860\pi\)
\(984\) −59.3905 −1.89330
\(985\) 1.79246 0.0571124
\(986\) −41.8488 −1.33274
\(987\) −3.23792 −0.103064
\(988\) −6.61088 −0.210320
\(989\) −104.214 −3.31381
\(990\) −0.511931 −0.0162702
\(991\) −3.82361 −0.121461 −0.0607305 0.998154i \(-0.519343\pi\)
−0.0607305 + 0.998154i \(0.519343\pi\)
\(992\) 4.59937 0.146030
\(993\) 55.5283 1.76214
\(994\) 0.298543 0.00946922
\(995\) −0.519410 −0.0164664
\(996\) −16.3786 −0.518975
\(997\) −48.6594 −1.54106 −0.770529 0.637405i \(-0.780008\pi\)
−0.770529 + 0.637405i \(0.780008\pi\)
\(998\) −26.9096 −0.851809
\(999\) 7.41903 0.234728
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 8003.2.a.b.1.12 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.12 153 1.1 even 1 trivial