Properties

Label 8281.2.a.cx.1.13
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8281,2,Mod(1,8281)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8281.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 637)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 8281.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.565505 q^{2} -3.09111 q^{3} -1.68020 q^{4} +1.80514 q^{5} +1.74804 q^{6} +2.08118 q^{8} +6.55499 q^{9} +O(q^{10})\) \(q-0.565505 q^{2} -3.09111 q^{3} -1.68020 q^{4} +1.80514 q^{5} +1.74804 q^{6} +2.08118 q^{8} +6.55499 q^{9} -1.02082 q^{10} +3.58433 q^{11} +5.19370 q^{12} -5.57989 q^{15} +2.18349 q^{16} -6.14919 q^{17} -3.70688 q^{18} -2.51075 q^{19} -3.03300 q^{20} -2.02696 q^{22} +4.13185 q^{23} -6.43315 q^{24} -1.74147 q^{25} -10.9889 q^{27} +5.11133 q^{29} +3.15546 q^{30} +4.55318 q^{31} -5.39713 q^{32} -11.0796 q^{33} +3.47740 q^{34} -11.0137 q^{36} +11.7215 q^{37} +1.41984 q^{38} +3.75681 q^{40} -1.86640 q^{41} -1.42314 q^{43} -6.02240 q^{44} +11.8327 q^{45} -2.33658 q^{46} +8.86595 q^{47} -6.74942 q^{48} +0.984810 q^{50} +19.0078 q^{51} +2.02920 q^{53} +6.21427 q^{54} +6.47021 q^{55} +7.76102 q^{57} -2.89049 q^{58} +9.10752 q^{59} +9.37536 q^{60} -5.47841 q^{61} -2.57485 q^{62} -1.31488 q^{64} +6.26555 q^{66} -7.02055 q^{67} +10.3319 q^{68} -12.7720 q^{69} +4.49410 q^{71} +13.6421 q^{72} +9.35564 q^{73} -6.62856 q^{74} +5.38308 q^{75} +4.21858 q^{76} +5.20970 q^{79} +3.94151 q^{80} +14.3029 q^{81} +1.05546 q^{82} +9.42491 q^{83} -11.1001 q^{85} +0.804791 q^{86} -15.7997 q^{87} +7.45961 q^{88} +0.355648 q^{89} -6.69144 q^{90} -6.94235 q^{92} -14.0744 q^{93} -5.01374 q^{94} -4.53226 q^{95} +16.6831 q^{96} +10.6035 q^{97} +23.4952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 40 q^{4} + 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 40 q^{4} + 56 q^{9} + 56 q^{16} - 16 q^{22} + 48 q^{23} + 40 q^{25} + 48 q^{29} + 48 q^{30} + 184 q^{36} + 24 q^{43} + 72 q^{53} - 32 q^{64} - 48 q^{74} + 96 q^{79} + 128 q^{81} + 112 q^{88} + 168 q^{92} + 168 q^{95}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.565505 −0.399873 −0.199936 0.979809i \(-0.564074\pi\)
−0.199936 + 0.979809i \(0.564074\pi\)
\(3\) −3.09111 −1.78466 −0.892328 0.451388i \(-0.850929\pi\)
−0.892328 + 0.451388i \(0.850929\pi\)
\(4\) −1.68020 −0.840102
\(5\) 1.80514 0.807283 0.403642 0.914917i \(-0.367744\pi\)
0.403642 + 0.914917i \(0.367744\pi\)
\(6\) 1.74804 0.713635
\(7\) 0 0
\(8\) 2.08118 0.735806
\(9\) 6.55499 2.18500
\(10\) −1.02082 −0.322811
\(11\) 3.58433 1.08072 0.540358 0.841436i \(-0.318289\pi\)
0.540358 + 0.841436i \(0.318289\pi\)
\(12\) 5.19370 1.49929
\(13\) 0 0
\(14\) 0 0
\(15\) −5.57989 −1.44072
\(16\) 2.18349 0.545873
\(17\) −6.14919 −1.49140 −0.745699 0.666283i \(-0.767884\pi\)
−0.745699 + 0.666283i \(0.767884\pi\)
\(18\) −3.70688 −0.873720
\(19\) −2.51075 −0.576006 −0.288003 0.957629i \(-0.592991\pi\)
−0.288003 + 0.957629i \(0.592991\pi\)
\(20\) −3.03300 −0.678200
\(21\) 0 0
\(22\) −2.02696 −0.432148
\(23\) 4.13185 0.861550 0.430775 0.902459i \(-0.358240\pi\)
0.430775 + 0.902459i \(0.358240\pi\)
\(24\) −6.43315 −1.31316
\(25\) −1.74147 −0.348294
\(26\) 0 0
\(27\) −10.9889 −2.11481
\(28\) 0 0
\(29\) 5.11133 0.949151 0.474576 0.880215i \(-0.342602\pi\)
0.474576 + 0.880215i \(0.342602\pi\)
\(30\) 3.15546 0.576106
\(31\) 4.55318 0.817775 0.408888 0.912585i \(-0.365917\pi\)
0.408888 + 0.912585i \(0.365917\pi\)
\(32\) −5.39713 −0.954086
\(33\) −11.0796 −1.92870
\(34\) 3.47740 0.596369
\(35\) 0 0
\(36\) −11.0137 −1.83562
\(37\) 11.7215 1.92700 0.963500 0.267708i \(-0.0862663\pi\)
0.963500 + 0.267708i \(0.0862663\pi\)
\(38\) 1.41984 0.230329
\(39\) 0 0
\(40\) 3.75681 0.594004
\(41\) −1.86640 −0.291483 −0.145742 0.989323i \(-0.546557\pi\)
−0.145742 + 0.989323i \(0.546557\pi\)
\(42\) 0 0
\(43\) −1.42314 −0.217026 −0.108513 0.994095i \(-0.534609\pi\)
−0.108513 + 0.994095i \(0.534609\pi\)
\(44\) −6.02240 −0.907911
\(45\) 11.8327 1.76391
\(46\) −2.33658 −0.344510
\(47\) 8.86595 1.29323 0.646616 0.762816i \(-0.276184\pi\)
0.646616 + 0.762816i \(0.276184\pi\)
\(48\) −6.74942 −0.974195
\(49\) 0 0
\(50\) 0.984810 0.139273
\(51\) 19.0078 2.66163
\(52\) 0 0
\(53\) 2.02920 0.278732 0.139366 0.990241i \(-0.455494\pi\)
0.139366 + 0.990241i \(0.455494\pi\)
\(54\) 6.21427 0.845655
\(55\) 6.47021 0.872443
\(56\) 0 0
\(57\) 7.76102 1.02797
\(58\) −2.89049 −0.379540
\(59\) 9.10752 1.18570 0.592849 0.805314i \(-0.298003\pi\)
0.592849 + 0.805314i \(0.298003\pi\)
\(60\) 9.37536 1.21035
\(61\) −5.47841 −0.701438 −0.350719 0.936481i \(-0.614063\pi\)
−0.350719 + 0.936481i \(0.614063\pi\)
\(62\) −2.57485 −0.327006
\(63\) 0 0
\(64\) −1.31488 −0.164360
\(65\) 0 0
\(66\) 6.26555 0.771236
\(67\) −7.02055 −0.857697 −0.428849 0.903376i \(-0.641081\pi\)
−0.428849 + 0.903376i \(0.641081\pi\)
\(68\) 10.3319 1.25293
\(69\) −12.7720 −1.53757
\(70\) 0 0
\(71\) 4.49410 0.533351 0.266676 0.963786i \(-0.414075\pi\)
0.266676 + 0.963786i \(0.414075\pi\)
\(72\) 13.6421 1.60773
\(73\) 9.35564 1.09499 0.547497 0.836807i \(-0.315581\pi\)
0.547497 + 0.836807i \(0.315581\pi\)
\(74\) −6.62856 −0.770555
\(75\) 5.38308 0.621584
\(76\) 4.21858 0.483904
\(77\) 0 0
\(78\) 0 0
\(79\) 5.20970 0.586137 0.293069 0.956091i \(-0.405324\pi\)
0.293069 + 0.956091i \(0.405324\pi\)
\(80\) 3.94151 0.440674
\(81\) 14.3029 1.58921
\(82\) 1.05546 0.116556
\(83\) 9.42491 1.03452 0.517259 0.855829i \(-0.326952\pi\)
0.517259 + 0.855829i \(0.326952\pi\)
\(84\) 0 0
\(85\) −11.1001 −1.20398
\(86\) 0.804791 0.0867829
\(87\) −15.7997 −1.69391
\(88\) 7.45961 0.795197
\(89\) 0.355648 0.0376986 0.0188493 0.999822i \(-0.494000\pi\)
0.0188493 + 0.999822i \(0.494000\pi\)
\(90\) −6.69144 −0.705340
\(91\) 0 0
\(92\) −6.94235 −0.723790
\(93\) −14.0744 −1.45945
\(94\) −5.01374 −0.517128
\(95\) −4.53226 −0.465000
\(96\) 16.6831 1.70272
\(97\) 10.6035 1.07663 0.538313 0.842745i \(-0.319062\pi\)
0.538313 + 0.842745i \(0.319062\pi\)
\(98\) 0 0
\(99\) 23.4952 2.36136
\(100\) 2.92602 0.292602
\(101\) 3.42508 0.340808 0.170404 0.985374i \(-0.445493\pi\)
0.170404 + 0.985374i \(0.445493\pi\)
\(102\) −10.7490 −1.06431
\(103\) −12.9558 −1.27658 −0.638288 0.769798i \(-0.720357\pi\)
−0.638288 + 0.769798i \(0.720357\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1.14752 −0.111457
\(107\) −18.1696 −1.75653 −0.878263 0.478179i \(-0.841297\pi\)
−0.878263 + 0.478179i \(0.841297\pi\)
\(108\) 18.4635 1.77666
\(109\) 13.9294 1.33420 0.667098 0.744970i \(-0.267536\pi\)
0.667098 + 0.744970i \(0.267536\pi\)
\(110\) −3.65894 −0.348866
\(111\) −36.2324 −3.43903
\(112\) 0 0
\(113\) −10.1281 −0.952770 −0.476385 0.879237i \(-0.658053\pi\)
−0.476385 + 0.879237i \(0.658053\pi\)
\(114\) −4.38890 −0.411058
\(115\) 7.45857 0.695515
\(116\) −8.58808 −0.797383
\(117\) 0 0
\(118\) −5.15035 −0.474128
\(119\) 0 0
\(120\) −11.6127 −1.06009
\(121\) 1.84739 0.167945
\(122\) 3.09807 0.280486
\(123\) 5.76927 0.520197
\(124\) −7.65027 −0.687014
\(125\) −12.1693 −1.08845
\(126\) 0 0
\(127\) 6.10219 0.541482 0.270741 0.962652i \(-0.412731\pi\)
0.270741 + 0.962652i \(0.412731\pi\)
\(128\) 11.5378 1.01981
\(129\) 4.39908 0.387317
\(130\) 0 0
\(131\) −5.97266 −0.521833 −0.260917 0.965361i \(-0.584025\pi\)
−0.260917 + 0.965361i \(0.584025\pi\)
\(132\) 18.6159 1.62031
\(133\) 0 0
\(134\) 3.97016 0.342970
\(135\) −19.8365 −1.70725
\(136\) −12.7975 −1.09738
\(137\) 3.60737 0.308198 0.154099 0.988055i \(-0.450753\pi\)
0.154099 + 0.988055i \(0.450753\pi\)
\(138\) 7.22265 0.614833
\(139\) −12.9167 −1.09558 −0.547789 0.836617i \(-0.684530\pi\)
−0.547789 + 0.836617i \(0.684530\pi\)
\(140\) 0 0
\(141\) −27.4057 −2.30797
\(142\) −2.54144 −0.213273
\(143\) 0 0
\(144\) 14.3128 1.19273
\(145\) 9.22668 0.766234
\(146\) −5.29067 −0.437859
\(147\) 0 0
\(148\) −19.6945 −1.61888
\(149\) 2.19416 0.179753 0.0898763 0.995953i \(-0.471353\pi\)
0.0898763 + 0.995953i \(0.471353\pi\)
\(150\) −3.04416 −0.248555
\(151\) 1.94893 0.158602 0.0793009 0.996851i \(-0.474731\pi\)
0.0793009 + 0.996851i \(0.474731\pi\)
\(152\) −5.22532 −0.423829
\(153\) −40.3078 −3.25870
\(154\) 0 0
\(155\) 8.21913 0.660176
\(156\) 0 0
\(157\) −18.3508 −1.46455 −0.732275 0.681009i \(-0.761541\pi\)
−0.732275 + 0.681009i \(0.761541\pi\)
\(158\) −2.94611 −0.234380
\(159\) −6.27248 −0.497440
\(160\) −9.74257 −0.770218
\(161\) 0 0
\(162\) −8.08836 −0.635482
\(163\) 22.0599 1.72786 0.863931 0.503611i \(-0.167996\pi\)
0.863931 + 0.503611i \(0.167996\pi\)
\(164\) 3.13594 0.244876
\(165\) −20.0002 −1.55701
\(166\) −5.32984 −0.413676
\(167\) −2.83878 −0.219672 −0.109836 0.993950i \(-0.535033\pi\)
−0.109836 + 0.993950i \(0.535033\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 6.27719 0.481439
\(171\) −16.4580 −1.25857
\(172\) 2.39116 0.182324
\(173\) 3.52822 0.268246 0.134123 0.990965i \(-0.457178\pi\)
0.134123 + 0.990965i \(0.457178\pi\)
\(174\) 8.93483 0.677347
\(175\) 0 0
\(176\) 7.82635 0.589933
\(177\) −28.1524 −2.11606
\(178\) −0.201121 −0.0150746
\(179\) −6.69470 −0.500385 −0.250193 0.968196i \(-0.580494\pi\)
−0.250193 + 0.968196i \(0.580494\pi\)
\(180\) −19.8813 −1.48186
\(181\) −12.5317 −0.931476 −0.465738 0.884923i \(-0.654211\pi\)
−0.465738 + 0.884923i \(0.654211\pi\)
\(182\) 0 0
\(183\) 16.9344 1.25183
\(184\) 8.59910 0.633934
\(185\) 21.1589 1.55563
\(186\) 7.95915 0.583593
\(187\) −22.0407 −1.61178
\(188\) −14.8966 −1.08645
\(189\) 0 0
\(190\) 2.56302 0.185941
\(191\) 3.03641 0.219707 0.109854 0.993948i \(-0.464962\pi\)
0.109854 + 0.993948i \(0.464962\pi\)
\(192\) 4.06444 0.293326
\(193\) −26.9449 −1.93954 −0.969769 0.244023i \(-0.921533\pi\)
−0.969769 + 0.244023i \(0.921533\pi\)
\(194\) −5.99635 −0.430513
\(195\) 0 0
\(196\) 0 0
\(197\) 9.29898 0.662525 0.331262 0.943539i \(-0.392525\pi\)
0.331262 + 0.943539i \(0.392525\pi\)
\(198\) −13.2867 −0.944242
\(199\) 17.3848 1.23238 0.616190 0.787598i \(-0.288676\pi\)
0.616190 + 0.787598i \(0.288676\pi\)
\(200\) −3.62430 −0.256277
\(201\) 21.7013 1.53069
\(202\) −1.93690 −0.136280
\(203\) 0 0
\(204\) −31.9370 −2.23604
\(205\) −3.36912 −0.235310
\(206\) 7.32659 0.510468
\(207\) 27.0842 1.88248
\(208\) 0 0
\(209\) −8.99936 −0.622499
\(210\) 0 0
\(211\) 21.8236 1.50240 0.751199 0.660075i \(-0.229476\pi\)
0.751199 + 0.660075i \(0.229476\pi\)
\(212\) −3.40947 −0.234163
\(213\) −13.8918 −0.951849
\(214\) 10.2750 0.702386
\(215\) −2.56896 −0.175202
\(216\) −22.8698 −1.55609
\(217\) 0 0
\(218\) −7.87716 −0.533508
\(219\) −28.9194 −1.95419
\(220\) −10.8713 −0.732941
\(221\) 0 0
\(222\) 20.4896 1.37517
\(223\) −1.91187 −0.128029 −0.0640143 0.997949i \(-0.520390\pi\)
−0.0640143 + 0.997949i \(0.520390\pi\)
\(224\) 0 0
\(225\) −11.4153 −0.761020
\(226\) 5.72749 0.380987
\(227\) −10.3347 −0.685939 −0.342969 0.939347i \(-0.611433\pi\)
−0.342969 + 0.939347i \(0.611433\pi\)
\(228\) −13.0401 −0.863602
\(229\) 6.10394 0.403360 0.201680 0.979451i \(-0.435360\pi\)
0.201680 + 0.979451i \(0.435360\pi\)
\(230\) −4.21786 −0.278118
\(231\) 0 0
\(232\) 10.6376 0.698391
\(233\) 7.12776 0.466955 0.233478 0.972362i \(-0.424989\pi\)
0.233478 + 0.972362i \(0.424989\pi\)
\(234\) 0 0
\(235\) 16.0043 1.04400
\(236\) −15.3025 −0.996107
\(237\) −16.1038 −1.04605
\(238\) 0 0
\(239\) 7.32349 0.473717 0.236859 0.971544i \(-0.423882\pi\)
0.236859 + 0.971544i \(0.423882\pi\)
\(240\) −12.1837 −0.786451
\(241\) −0.263098 −0.0169477 −0.00847383 0.999964i \(-0.502697\pi\)
−0.00847383 + 0.999964i \(0.502697\pi\)
\(242\) −1.04471 −0.0671566
\(243\) −11.2453 −0.721384
\(244\) 9.20484 0.589280
\(245\) 0 0
\(246\) −3.26255 −0.208013
\(247\) 0 0
\(248\) 9.47596 0.601724
\(249\) −29.1335 −1.84626
\(250\) 6.88180 0.435243
\(251\) −13.2819 −0.838347 −0.419173 0.907906i \(-0.637680\pi\)
−0.419173 + 0.907906i \(0.637680\pi\)
\(252\) 0 0
\(253\) 14.8099 0.931090
\(254\) −3.45082 −0.216524
\(255\) 34.3118 2.14869
\(256\) −3.89494 −0.243434
\(257\) −17.4144 −1.08628 −0.543139 0.839643i \(-0.682764\pi\)
−0.543139 + 0.839643i \(0.682764\pi\)
\(258\) −2.48770 −0.154878
\(259\) 0 0
\(260\) 0 0
\(261\) 33.5047 2.07389
\(262\) 3.37757 0.208667
\(263\) −12.7276 −0.784820 −0.392410 0.919790i \(-0.628359\pi\)
−0.392410 + 0.919790i \(0.628359\pi\)
\(264\) −23.0585 −1.41915
\(265\) 3.66299 0.225015
\(266\) 0 0
\(267\) −1.09935 −0.0672790
\(268\) 11.7960 0.720553
\(269\) −2.16163 −0.131797 −0.0658985 0.997826i \(-0.520991\pi\)
−0.0658985 + 0.997826i \(0.520991\pi\)
\(270\) 11.2176 0.682683
\(271\) −5.82966 −0.354127 −0.177063 0.984199i \(-0.556660\pi\)
−0.177063 + 0.984199i \(0.556660\pi\)
\(272\) −13.4267 −0.814113
\(273\) 0 0
\(274\) −2.03999 −0.123240
\(275\) −6.24199 −0.376406
\(276\) 21.4596 1.29172
\(277\) −11.6473 −0.699820 −0.349910 0.936783i \(-0.613788\pi\)
−0.349910 + 0.936783i \(0.613788\pi\)
\(278\) 7.30445 0.438092
\(279\) 29.8460 1.78684
\(280\) 0 0
\(281\) −24.7940 −1.47908 −0.739542 0.673110i \(-0.764958\pi\)
−0.739542 + 0.673110i \(0.764958\pi\)
\(282\) 15.4981 0.922896
\(283\) 15.1432 0.900172 0.450086 0.892985i \(-0.351393\pi\)
0.450086 + 0.892985i \(0.351393\pi\)
\(284\) −7.55100 −0.448069
\(285\) 14.0097 0.829865
\(286\) 0 0
\(287\) 0 0
\(288\) −35.3781 −2.08467
\(289\) 20.8125 1.22427
\(290\) −5.21773 −0.306396
\(291\) −32.7767 −1.92141
\(292\) −15.7194 −0.919907
\(293\) 24.9203 1.45586 0.727929 0.685652i \(-0.240483\pi\)
0.727929 + 0.685652i \(0.240483\pi\)
\(294\) 0 0
\(295\) 16.4404 0.957194
\(296\) 24.3945 1.41790
\(297\) −39.3877 −2.28551
\(298\) −1.24081 −0.0718782
\(299\) 0 0
\(300\) −9.04467 −0.522194
\(301\) 0 0
\(302\) −1.10213 −0.0634205
\(303\) −10.5873 −0.608225
\(304\) −5.48221 −0.314426
\(305\) −9.88930 −0.566259
\(306\) 22.7943 1.30306
\(307\) 3.90158 0.222675 0.111337 0.993783i \(-0.464487\pi\)
0.111337 + 0.993783i \(0.464487\pi\)
\(308\) 0 0
\(309\) 40.0479 2.27825
\(310\) −4.64796 −0.263986
\(311\) 19.7180 1.11810 0.559052 0.829132i \(-0.311165\pi\)
0.559052 + 0.829132i \(0.311165\pi\)
\(312\) 0 0
\(313\) 2.89235 0.163485 0.0817427 0.996653i \(-0.473951\pi\)
0.0817427 + 0.996653i \(0.473951\pi\)
\(314\) 10.3775 0.585633
\(315\) 0 0
\(316\) −8.75336 −0.492415
\(317\) −15.9537 −0.896046 −0.448023 0.894022i \(-0.647872\pi\)
−0.448023 + 0.894022i \(0.647872\pi\)
\(318\) 3.54712 0.198913
\(319\) 18.3207 1.02576
\(320\) −2.37354 −0.132685
\(321\) 56.1644 3.13479
\(322\) 0 0
\(323\) 15.4391 0.859054
\(324\) −24.0318 −1.33510
\(325\) 0 0
\(326\) −12.4750 −0.690924
\(327\) −43.0574 −2.38108
\(328\) −3.88431 −0.214475
\(329\) 0 0
\(330\) 11.3102 0.622606
\(331\) 3.82678 0.210339 0.105169 0.994454i \(-0.466462\pi\)
0.105169 + 0.994454i \(0.466462\pi\)
\(332\) −15.8358 −0.869101
\(333\) 76.8342 4.21049
\(334\) 1.60535 0.0878407
\(335\) −12.6731 −0.692405
\(336\) 0 0
\(337\) −9.78172 −0.532844 −0.266422 0.963856i \(-0.585842\pi\)
−0.266422 + 0.963856i \(0.585842\pi\)
\(338\) 0 0
\(339\) 31.3071 1.70037
\(340\) 18.6505 1.01147
\(341\) 16.3201 0.883782
\(342\) 9.30706 0.503268
\(343\) 0 0
\(344\) −2.96180 −0.159689
\(345\) −23.0553 −1.24126
\(346\) −1.99523 −0.107264
\(347\) 5.33403 0.286346 0.143173 0.989698i \(-0.454269\pi\)
0.143173 + 0.989698i \(0.454269\pi\)
\(348\) 26.5467 1.42305
\(349\) 14.7030 0.787032 0.393516 0.919318i \(-0.371259\pi\)
0.393516 + 0.919318i \(0.371259\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −19.3451 −1.03110
\(353\) −35.5173 −1.89039 −0.945196 0.326502i \(-0.894130\pi\)
−0.945196 + 0.326502i \(0.894130\pi\)
\(354\) 15.9203 0.846156
\(355\) 8.11248 0.430566
\(356\) −0.597560 −0.0316706
\(357\) 0 0
\(358\) 3.78589 0.200090
\(359\) 15.9147 0.839945 0.419972 0.907537i \(-0.362040\pi\)
0.419972 + 0.907537i \(0.362040\pi\)
\(360\) 24.6259 1.29790
\(361\) −12.6961 −0.668217
\(362\) 7.08676 0.372472
\(363\) −5.71051 −0.299724
\(364\) 0 0
\(365\) 16.8882 0.883971
\(366\) −9.57649 −0.500571
\(367\) −18.2446 −0.952361 −0.476181 0.879348i \(-0.657979\pi\)
−0.476181 + 0.879348i \(0.657979\pi\)
\(368\) 9.02186 0.470297
\(369\) −12.2343 −0.636890
\(370\) −11.9655 −0.622056
\(371\) 0 0
\(372\) 23.6479 1.22608
\(373\) −13.5744 −0.702856 −0.351428 0.936215i \(-0.614304\pi\)
−0.351428 + 0.936215i \(0.614304\pi\)
\(374\) 12.4641 0.644505
\(375\) 37.6167 1.94252
\(376\) 18.4516 0.951568
\(377\) 0 0
\(378\) 0 0
\(379\) 7.23572 0.371674 0.185837 0.982581i \(-0.440500\pi\)
0.185837 + 0.982581i \(0.440500\pi\)
\(380\) 7.61512 0.390648
\(381\) −18.8626 −0.966359
\(382\) −1.71711 −0.0878549
\(383\) −20.3464 −1.03965 −0.519827 0.854272i \(-0.674004\pi\)
−0.519827 + 0.854272i \(0.674004\pi\)
\(384\) −35.6647 −1.82001
\(385\) 0 0
\(386\) 15.2375 0.775569
\(387\) −9.32864 −0.474202
\(388\) −17.8161 −0.904475
\(389\) 2.48306 0.125896 0.0629481 0.998017i \(-0.479950\pi\)
0.0629481 + 0.998017i \(0.479950\pi\)
\(390\) 0 0
\(391\) −25.4075 −1.28491
\(392\) 0 0
\(393\) 18.4622 0.931293
\(394\) −5.25862 −0.264926
\(395\) 9.40424 0.473179
\(396\) −39.4767 −1.98378
\(397\) 10.7391 0.538980 0.269490 0.963003i \(-0.413145\pi\)
0.269490 + 0.963003i \(0.413145\pi\)
\(398\) −9.83122 −0.492795
\(399\) 0 0
\(400\) −3.80248 −0.190124
\(401\) 14.7540 0.736778 0.368389 0.929672i \(-0.379909\pi\)
0.368389 + 0.929672i \(0.379909\pi\)
\(402\) −12.2722 −0.612083
\(403\) 0 0
\(404\) −5.75483 −0.286313
\(405\) 25.8187 1.28294
\(406\) 0 0
\(407\) 42.0136 2.08254
\(408\) 39.5586 1.95844
\(409\) 6.34448 0.313714 0.156857 0.987621i \(-0.449864\pi\)
0.156857 + 0.987621i \(0.449864\pi\)
\(410\) 1.90526 0.0940939
\(411\) −11.1508 −0.550028
\(412\) 21.7684 1.07245
\(413\) 0 0
\(414\) −15.3163 −0.752754
\(415\) 17.0133 0.835150
\(416\) 0 0
\(417\) 39.9269 1.95523
\(418\) 5.08919 0.248920
\(419\) 18.0851 0.883513 0.441756 0.897135i \(-0.354356\pi\)
0.441756 + 0.897135i \(0.354356\pi\)
\(420\) 0 0
\(421\) 19.7043 0.960327 0.480164 0.877179i \(-0.340577\pi\)
0.480164 + 0.877179i \(0.340577\pi\)
\(422\) −12.3414 −0.600768
\(423\) 58.1162 2.82571
\(424\) 4.22312 0.205093
\(425\) 10.7086 0.519444
\(426\) 7.85587 0.380618
\(427\) 0 0
\(428\) 30.5287 1.47566
\(429\) 0 0
\(430\) 1.45276 0.0700584
\(431\) 10.5039 0.505953 0.252977 0.967472i \(-0.418590\pi\)
0.252977 + 0.967472i \(0.418590\pi\)
\(432\) −23.9941 −1.15442
\(433\) −9.11805 −0.438186 −0.219093 0.975704i \(-0.570310\pi\)
−0.219093 + 0.975704i \(0.570310\pi\)
\(434\) 0 0
\(435\) −28.5207 −1.36746
\(436\) −23.4043 −1.12086
\(437\) −10.3741 −0.496258
\(438\) 16.3541 0.781427
\(439\) 29.2801 1.39746 0.698731 0.715384i \(-0.253748\pi\)
0.698731 + 0.715384i \(0.253748\pi\)
\(440\) 13.4656 0.641949
\(441\) 0 0
\(442\) 0 0
\(443\) −26.7353 −1.27023 −0.635117 0.772416i \(-0.719048\pi\)
−0.635117 + 0.772416i \(0.719048\pi\)
\(444\) 60.8779 2.88914
\(445\) 0.641994 0.0304334
\(446\) 1.08118 0.0511951
\(447\) −6.78240 −0.320797
\(448\) 0 0
\(449\) 21.2155 1.00122 0.500611 0.865673i \(-0.333109\pi\)
0.500611 + 0.865673i \(0.333109\pi\)
\(450\) 6.45542 0.304311
\(451\) −6.68980 −0.315010
\(452\) 17.0172 0.800424
\(453\) −6.02437 −0.283050
\(454\) 5.84433 0.274288
\(455\) 0 0
\(456\) 16.1521 0.756389
\(457\) 14.6446 0.685046 0.342523 0.939509i \(-0.388718\pi\)
0.342523 + 0.939509i \(0.388718\pi\)
\(458\) −3.45181 −0.161293
\(459\) 67.5726 3.15402
\(460\) −12.5319 −0.584304
\(461\) −24.8946 −1.15946 −0.579729 0.814810i \(-0.696841\pi\)
−0.579729 + 0.814810i \(0.696841\pi\)
\(462\) 0 0
\(463\) 10.1069 0.469706 0.234853 0.972031i \(-0.424539\pi\)
0.234853 + 0.972031i \(0.424539\pi\)
\(464\) 11.1606 0.518116
\(465\) −25.4063 −1.17819
\(466\) −4.03079 −0.186723
\(467\) 11.4825 0.531346 0.265673 0.964063i \(-0.414406\pi\)
0.265673 + 0.964063i \(0.414406\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.05051 −0.417469
\(471\) 56.7243 2.61372
\(472\) 18.9543 0.872444
\(473\) −5.10099 −0.234544
\(474\) 9.10678 0.418288
\(475\) 4.37240 0.200619
\(476\) 0 0
\(477\) 13.3014 0.609028
\(478\) −4.14147 −0.189427
\(479\) 1.08116 0.0493997 0.0246998 0.999695i \(-0.492137\pi\)
0.0246998 + 0.999695i \(0.492137\pi\)
\(480\) 30.1154 1.37457
\(481\) 0 0
\(482\) 0.148784 0.00677691
\(483\) 0 0
\(484\) −3.10400 −0.141091
\(485\) 19.1409 0.869142
\(486\) 6.35926 0.288462
\(487\) 25.2677 1.14499 0.572493 0.819909i \(-0.305976\pi\)
0.572493 + 0.819909i \(0.305976\pi\)
\(488\) −11.4015 −0.516123
\(489\) −68.1895 −3.08364
\(490\) 0 0
\(491\) 41.7180 1.88271 0.941355 0.337419i \(-0.109554\pi\)
0.941355 + 0.337419i \(0.109554\pi\)
\(492\) −9.69354 −0.437019
\(493\) −31.4306 −1.41556
\(494\) 0 0
\(495\) 42.4122 1.90628
\(496\) 9.94183 0.446401
\(497\) 0 0
\(498\) 16.4751 0.738269
\(499\) 10.4684 0.468628 0.234314 0.972161i \(-0.424716\pi\)
0.234314 + 0.972161i \(0.424716\pi\)
\(500\) 20.4469 0.914413
\(501\) 8.77501 0.392038
\(502\) 7.51099 0.335232
\(503\) 2.57470 0.114800 0.0574001 0.998351i \(-0.481719\pi\)
0.0574001 + 0.998351i \(0.481719\pi\)
\(504\) 0 0
\(505\) 6.18275 0.275129
\(506\) −8.37508 −0.372318
\(507\) 0 0
\(508\) −10.2529 −0.454900
\(509\) −7.52681 −0.333620 −0.166810 0.985989i \(-0.553347\pi\)
−0.166810 + 0.985989i \(0.553347\pi\)
\(510\) −19.4035 −0.859202
\(511\) 0 0
\(512\) −20.8730 −0.922467
\(513\) 27.5903 1.21814
\(514\) 9.84792 0.434373
\(515\) −23.3871 −1.03056
\(516\) −7.39135 −0.325386
\(517\) 31.7785 1.39761
\(518\) 0 0
\(519\) −10.9061 −0.478726
\(520\) 0 0
\(521\) 0.0156677 0.000686413 0 0.000343207 1.00000i \(-0.499891\pi\)
0.000343207 1.00000i \(0.499891\pi\)
\(522\) −18.9471 −0.829292
\(523\) 24.0715 1.05257 0.526286 0.850308i \(-0.323584\pi\)
0.526286 + 0.850308i \(0.323584\pi\)
\(524\) 10.0353 0.438393
\(525\) 0 0
\(526\) 7.19755 0.313828
\(527\) −27.9984 −1.21963
\(528\) −24.1921 −1.05283
\(529\) −5.92781 −0.257731
\(530\) −2.07144 −0.0899775
\(531\) 59.6997 2.59075
\(532\) 0 0
\(533\) 0 0
\(534\) 0.621687 0.0269030
\(535\) −32.7987 −1.41801
\(536\) −14.6110 −0.631099
\(537\) 20.6941 0.893015
\(538\) 1.22241 0.0527020
\(539\) 0 0
\(540\) 33.3293 1.43426
\(541\) 37.7763 1.62413 0.812065 0.583567i \(-0.198344\pi\)
0.812065 + 0.583567i \(0.198344\pi\)
\(542\) 3.29671 0.141606
\(543\) 38.7370 1.66236
\(544\) 33.1879 1.42292
\(545\) 25.1445 1.07707
\(546\) 0 0
\(547\) 28.4925 1.21825 0.609126 0.793074i \(-0.291521\pi\)
0.609126 + 0.793074i \(0.291521\pi\)
\(548\) −6.06111 −0.258918
\(549\) −35.9109 −1.53264
\(550\) 3.52988 0.150515
\(551\) −12.8333 −0.546717
\(552\) −26.5808 −1.13135
\(553\) 0 0
\(554\) 6.58663 0.279839
\(555\) −65.4046 −2.77627
\(556\) 21.7026 0.920397
\(557\) −19.8646 −0.841692 −0.420846 0.907132i \(-0.638267\pi\)
−0.420846 + 0.907132i \(0.638267\pi\)
\(558\) −16.8781 −0.714507
\(559\) 0 0
\(560\) 0 0
\(561\) 68.1303 2.87646
\(562\) 14.0211 0.591445
\(563\) −15.5397 −0.654919 −0.327459 0.944865i \(-0.606192\pi\)
−0.327459 + 0.944865i \(0.606192\pi\)
\(564\) 46.0471 1.93893
\(565\) −18.2826 −0.769155
\(566\) −8.56358 −0.359954
\(567\) 0 0
\(568\) 9.35301 0.392443
\(569\) −31.1088 −1.30415 −0.652075 0.758154i \(-0.726101\pi\)
−0.652075 + 0.758154i \(0.726101\pi\)
\(570\) −7.92258 −0.331840
\(571\) −0.602653 −0.0252202 −0.0126101 0.999920i \(-0.504014\pi\)
−0.0126101 + 0.999920i \(0.504014\pi\)
\(572\) 0 0
\(573\) −9.38590 −0.392102
\(574\) 0 0
\(575\) −7.19549 −0.300073
\(576\) −8.61902 −0.359126
\(577\) 5.21634 0.217159 0.108580 0.994088i \(-0.465370\pi\)
0.108580 + 0.994088i \(0.465370\pi\)
\(578\) −11.7696 −0.489550
\(579\) 83.2899 3.46141
\(580\) −15.5027 −0.643714
\(581\) 0 0
\(582\) 18.5354 0.768318
\(583\) 7.27331 0.301230
\(584\) 19.4707 0.805704
\(585\) 0 0
\(586\) −14.0926 −0.582158
\(587\) −17.1895 −0.709487 −0.354743 0.934964i \(-0.615432\pi\)
−0.354743 + 0.934964i \(0.615432\pi\)
\(588\) 0 0
\(589\) −11.4319 −0.471044
\(590\) −9.29711 −0.382756
\(591\) −28.7442 −1.18238
\(592\) 25.5938 1.05190
\(593\) 10.6452 0.437147 0.218574 0.975820i \(-0.429860\pi\)
0.218574 + 0.975820i \(0.429860\pi\)
\(594\) 22.2740 0.913912
\(595\) 0 0
\(596\) −3.68664 −0.151011
\(597\) −53.7385 −2.19937
\(598\) 0 0
\(599\) 25.1472 1.02749 0.513744 0.857944i \(-0.328258\pi\)
0.513744 + 0.857944i \(0.328258\pi\)
\(600\) 11.2031 0.457366
\(601\) −3.24667 −0.132434 −0.0662172 0.997805i \(-0.521093\pi\)
−0.0662172 + 0.997805i \(0.521093\pi\)
\(602\) 0 0
\(603\) −46.0196 −1.87406
\(604\) −3.27460 −0.133242
\(605\) 3.33481 0.135579
\(606\) 5.98718 0.243213
\(607\) 17.1124 0.694572 0.347286 0.937759i \(-0.387103\pi\)
0.347286 + 0.937759i \(0.387103\pi\)
\(608\) 13.5509 0.549560
\(609\) 0 0
\(610\) 5.59245 0.226432
\(611\) 0 0
\(612\) 67.7254 2.73764
\(613\) −28.0427 −1.13264 −0.566318 0.824187i \(-0.691632\pi\)
−0.566318 + 0.824187i \(0.691632\pi\)
\(614\) −2.20636 −0.0890415
\(615\) 10.4143 0.419947
\(616\) 0 0
\(617\) −42.0926 −1.69459 −0.847293 0.531126i \(-0.821769\pi\)
−0.847293 + 0.531126i \(0.821769\pi\)
\(618\) −22.6473 −0.911009
\(619\) 27.1308 1.09048 0.545239 0.838280i \(-0.316439\pi\)
0.545239 + 0.838280i \(0.316439\pi\)
\(620\) −13.8098 −0.554615
\(621\) −45.4044 −1.82201
\(622\) −11.1506 −0.447099
\(623\) 0 0
\(624\) 0 0
\(625\) −13.2599 −0.530398
\(626\) −1.63564 −0.0653733
\(627\) 27.8180 1.11095
\(628\) 30.8330 1.23037
\(629\) −72.0776 −2.87392
\(630\) 0 0
\(631\) −16.0095 −0.637329 −0.318665 0.947868i \(-0.603234\pi\)
−0.318665 + 0.947868i \(0.603234\pi\)
\(632\) 10.8423 0.431284
\(633\) −67.4593 −2.68126
\(634\) 9.02188 0.358304
\(635\) 11.0153 0.437129
\(636\) 10.5390 0.417900
\(637\) 0 0
\(638\) −10.3604 −0.410174
\(639\) 29.4588 1.16537
\(640\) 20.8274 0.823275
\(641\) −14.6814 −0.579880 −0.289940 0.957045i \(-0.593635\pi\)
−0.289940 + 0.957045i \(0.593635\pi\)
\(642\) −31.7613 −1.25352
\(643\) 37.1435 1.46480 0.732399 0.680875i \(-0.238400\pi\)
0.732399 + 0.680875i \(0.238400\pi\)
\(644\) 0 0
\(645\) 7.94095 0.312675
\(646\) −8.73089 −0.343512
\(647\) 14.2284 0.559377 0.279689 0.960091i \(-0.409769\pi\)
0.279689 + 0.960091i \(0.409769\pi\)
\(648\) 29.7668 1.16935
\(649\) 32.6443 1.28140
\(650\) 0 0
\(651\) 0 0
\(652\) −37.0650 −1.45158
\(653\) −21.8455 −0.854880 −0.427440 0.904044i \(-0.640585\pi\)
−0.427440 + 0.904044i \(0.640585\pi\)
\(654\) 24.3492 0.952129
\(655\) −10.7815 −0.421267
\(656\) −4.07528 −0.159113
\(657\) 61.3261 2.39256
\(658\) 0 0
\(659\) 33.1051 1.28959 0.644796 0.764355i \(-0.276943\pi\)
0.644796 + 0.764355i \(0.276943\pi\)
\(660\) 33.6043 1.30805
\(661\) 23.3428 0.907930 0.453965 0.891020i \(-0.350009\pi\)
0.453965 + 0.891020i \(0.350009\pi\)
\(662\) −2.16406 −0.0841087
\(663\) 0 0
\(664\) 19.6149 0.761206
\(665\) 0 0
\(666\) −43.4501 −1.68366
\(667\) 21.1193 0.817741
\(668\) 4.76974 0.184547
\(669\) 5.90982 0.228487
\(670\) 7.16670 0.276874
\(671\) −19.6364 −0.758055
\(672\) 0 0
\(673\) −48.4847 −1.86895 −0.934474 0.356030i \(-0.884130\pi\)
−0.934474 + 0.356030i \(0.884130\pi\)
\(674\) 5.53162 0.213070
\(675\) 19.1368 0.736575
\(676\) 0 0
\(677\) −43.8976 −1.68712 −0.843560 0.537034i \(-0.819545\pi\)
−0.843560 + 0.537034i \(0.819545\pi\)
\(678\) −17.7043 −0.679930
\(679\) 0 0
\(680\) −23.1013 −0.885896
\(681\) 31.9458 1.22416
\(682\) −9.22909 −0.353400
\(683\) 44.9278 1.71912 0.859558 0.511039i \(-0.170739\pi\)
0.859558 + 0.511039i \(0.170739\pi\)
\(684\) 27.6527 1.05733
\(685\) 6.51180 0.248803
\(686\) 0 0
\(687\) −18.8680 −0.719859
\(688\) −3.10741 −0.118469
\(689\) 0 0
\(690\) 13.0379 0.496344
\(691\) −45.4493 −1.72897 −0.864486 0.502656i \(-0.832356\pi\)
−0.864486 + 0.502656i \(0.832356\pi\)
\(692\) −5.92813 −0.225354
\(693\) 0 0
\(694\) −3.01643 −0.114502
\(695\) −23.3164 −0.884441
\(696\) −32.8820 −1.24639
\(697\) 11.4769 0.434717
\(698\) −8.31461 −0.314713
\(699\) −22.0327 −0.833354
\(700\) 0 0
\(701\) −28.7914 −1.08744 −0.543718 0.839268i \(-0.682984\pi\)
−0.543718 + 0.839268i \(0.682984\pi\)
\(702\) 0 0
\(703\) −29.4298 −1.10996
\(704\) −4.71296 −0.177626
\(705\) −49.4711 −1.86319
\(706\) 20.0852 0.755916
\(707\) 0 0
\(708\) 47.3017 1.77771
\(709\) −17.3626 −0.652068 −0.326034 0.945358i \(-0.605712\pi\)
−0.326034 + 0.945358i \(0.605712\pi\)
\(710\) −4.58765 −0.172171
\(711\) 34.1495 1.28071
\(712\) 0.740165 0.0277389
\(713\) 18.8131 0.704554
\(714\) 0 0
\(715\) 0 0
\(716\) 11.2485 0.420374
\(717\) −22.6377 −0.845422
\(718\) −8.99984 −0.335871
\(719\) 9.98708 0.372455 0.186228 0.982507i \(-0.440374\pi\)
0.186228 + 0.982507i \(0.440374\pi\)
\(720\) 25.8365 0.962871
\(721\) 0 0
\(722\) 7.17972 0.267202
\(723\) 0.813267 0.0302457
\(724\) 21.0558 0.782534
\(725\) −8.90123 −0.330583
\(726\) 3.22932 0.119851
\(727\) −8.00409 −0.296855 −0.148428 0.988923i \(-0.547421\pi\)
−0.148428 + 0.988923i \(0.547421\pi\)
\(728\) 0 0
\(729\) −8.14827 −0.301788
\(730\) −9.55039 −0.353476
\(731\) 8.75114 0.323672
\(732\) −28.4532 −1.05166
\(733\) 44.8461 1.65643 0.828214 0.560412i \(-0.189357\pi\)
0.828214 + 0.560412i \(0.189357\pi\)
\(734\) 10.3174 0.380823
\(735\) 0 0
\(736\) −22.3001 −0.821993
\(737\) −25.1640 −0.926926
\(738\) 6.91854 0.254675
\(739\) −25.0756 −0.922421 −0.461210 0.887291i \(-0.652585\pi\)
−0.461210 + 0.887291i \(0.652585\pi\)
\(740\) −35.5513 −1.30689
\(741\) 0 0
\(742\) 0 0
\(743\) −18.4191 −0.675733 −0.337866 0.941194i \(-0.609705\pi\)
−0.337866 + 0.941194i \(0.609705\pi\)
\(744\) −29.2913 −1.07387
\(745\) 3.96077 0.145111
\(746\) 7.67639 0.281053
\(747\) 61.7802 2.26042
\(748\) 37.0329 1.35406
\(749\) 0 0
\(750\) −21.2724 −0.776760
\(751\) 11.6918 0.426638 0.213319 0.976983i \(-0.431573\pi\)
0.213319 + 0.976983i \(0.431573\pi\)
\(752\) 19.3587 0.705940
\(753\) 41.0559 1.49616
\(754\) 0 0
\(755\) 3.51810 0.128037
\(756\) 0 0
\(757\) 15.5490 0.565137 0.282569 0.959247i \(-0.408814\pi\)
0.282569 + 0.959247i \(0.408814\pi\)
\(758\) −4.09184 −0.148622
\(759\) −45.7791 −1.66168
\(760\) −9.43243 −0.342150
\(761\) −31.9505 −1.15821 −0.579103 0.815254i \(-0.696597\pi\)
−0.579103 + 0.815254i \(0.696597\pi\)
\(762\) 10.6669 0.386420
\(763\) 0 0
\(764\) −5.10179 −0.184576
\(765\) −72.7613 −2.63069
\(766\) 11.5060 0.415729
\(767\) 0 0
\(768\) 12.0397 0.434446
\(769\) 14.5302 0.523972 0.261986 0.965072i \(-0.415623\pi\)
0.261986 + 0.965072i \(0.415623\pi\)
\(770\) 0 0
\(771\) 53.8298 1.93863
\(772\) 45.2730 1.62941
\(773\) −42.1103 −1.51460 −0.757301 0.653066i \(-0.773482\pi\)
−0.757301 + 0.653066i \(0.773482\pi\)
\(774\) 5.27540 0.189620
\(775\) −7.92922 −0.284826
\(776\) 22.0678 0.792188
\(777\) 0 0
\(778\) −1.40418 −0.0503424
\(779\) 4.68608 0.167896
\(780\) 0 0
\(781\) 16.1083 0.576401
\(782\) 14.3681 0.513802
\(783\) −56.1678 −2.00727
\(784\) 0 0
\(785\) −33.1257 −1.18231
\(786\) −10.4405 −0.372399
\(787\) −6.09474 −0.217254 −0.108627 0.994083i \(-0.534645\pi\)
−0.108627 + 0.994083i \(0.534645\pi\)
\(788\) −15.6242 −0.556588
\(789\) 39.3426 1.40063
\(790\) −5.31815 −0.189211
\(791\) 0 0
\(792\) 48.8976 1.73750
\(793\) 0 0
\(794\) −6.07302 −0.215523
\(795\) −11.3227 −0.401575
\(796\) −29.2101 −1.03532
\(797\) 36.8038 1.30366 0.651830 0.758366i \(-0.274002\pi\)
0.651830 + 0.758366i \(0.274002\pi\)
\(798\) 0 0
\(799\) −54.5184 −1.92872
\(800\) 9.39893 0.332302
\(801\) 2.33127 0.0823712
\(802\) −8.34345 −0.294617
\(803\) 33.5337 1.18338
\(804\) −36.4627 −1.28594
\(805\) 0 0
\(806\) 0 0
\(807\) 6.68185 0.235212
\(808\) 7.12819 0.250769
\(809\) −8.73333 −0.307048 −0.153524 0.988145i \(-0.549062\pi\)
−0.153524 + 0.988145i \(0.549062\pi\)
\(810\) −14.6006 −0.513014
\(811\) 37.1024 1.30284 0.651421 0.758716i \(-0.274173\pi\)
0.651421 + 0.758716i \(0.274173\pi\)
\(812\) 0 0
\(813\) 18.0202 0.631995
\(814\) −23.7589 −0.832750
\(815\) 39.8211 1.39487
\(816\) 41.5035 1.45291
\(817\) 3.57314 0.125009
\(818\) −3.58784 −0.125446
\(819\) 0 0
\(820\) 5.66081 0.197684
\(821\) 42.1578 1.47132 0.735658 0.677353i \(-0.236873\pi\)
0.735658 + 0.677353i \(0.236873\pi\)
\(822\) 6.30583 0.219941
\(823\) −18.5452 −0.646445 −0.323223 0.946323i \(-0.604766\pi\)
−0.323223 + 0.946323i \(0.604766\pi\)
\(824\) −26.9633 −0.939312
\(825\) 19.2947 0.671756
\(826\) 0 0
\(827\) 12.5050 0.434841 0.217420 0.976078i \(-0.430236\pi\)
0.217420 + 0.976078i \(0.430236\pi\)
\(828\) −45.5070 −1.58148
\(829\) −45.7666 −1.58954 −0.794770 0.606911i \(-0.792409\pi\)
−0.794770 + 0.606911i \(0.792409\pi\)
\(830\) −9.62111 −0.333954
\(831\) 36.0032 1.24894
\(832\) 0 0
\(833\) 0 0
\(834\) −22.5789 −0.781843
\(835\) −5.12440 −0.177337
\(836\) 15.1208 0.522962
\(837\) −50.0343 −1.72944
\(838\) −10.2272 −0.353293
\(839\) 12.8196 0.442580 0.221290 0.975208i \(-0.428973\pi\)
0.221290 + 0.975208i \(0.428973\pi\)
\(840\) 0 0
\(841\) −2.87426 −0.0991124
\(842\) −11.1429 −0.384009
\(843\) 76.6410 2.63966
\(844\) −36.6681 −1.26217
\(845\) 0 0
\(846\) −32.8650 −1.12992
\(847\) 0 0
\(848\) 4.43074 0.152152
\(849\) −46.8095 −1.60650
\(850\) −6.05578 −0.207712
\(851\) 48.4314 1.66021
\(852\) 23.3410 0.799650
\(853\) −4.51954 −0.154746 −0.0773730 0.997002i \(-0.524653\pi\)
−0.0773730 + 0.997002i \(0.524653\pi\)
\(854\) 0 0
\(855\) −29.7089 −1.01602
\(856\) −37.8142 −1.29246
\(857\) 47.2746 1.61487 0.807435 0.589957i \(-0.200855\pi\)
0.807435 + 0.589957i \(0.200855\pi\)
\(858\) 0 0
\(859\) 48.0543 1.63959 0.819795 0.572657i \(-0.194087\pi\)
0.819795 + 0.572657i \(0.194087\pi\)
\(860\) 4.31638 0.147187
\(861\) 0 0
\(862\) −5.93999 −0.202317
\(863\) −27.5799 −0.938831 −0.469415 0.882977i \(-0.655535\pi\)
−0.469415 + 0.882977i \(0.655535\pi\)
\(864\) 59.3083 2.01771
\(865\) 6.36893 0.216550
\(866\) 5.15631 0.175218
\(867\) −64.3339 −2.18489
\(868\) 0 0
\(869\) 18.6733 0.633447
\(870\) 16.1286 0.546811
\(871\) 0 0
\(872\) 28.9895 0.981710
\(873\) 69.5060 2.35242
\(874\) 5.86659 0.198440
\(875\) 0 0
\(876\) 48.5904 1.64172
\(877\) 49.4487 1.66976 0.834882 0.550430i \(-0.185536\pi\)
0.834882 + 0.550430i \(0.185536\pi\)
\(878\) −16.5581 −0.558807
\(879\) −77.0315 −2.59821
\(880\) 14.1277 0.476243
\(881\) −1.23791 −0.0417061 −0.0208530 0.999783i \(-0.506638\pi\)
−0.0208530 + 0.999783i \(0.506638\pi\)
\(882\) 0 0
\(883\) 41.4537 1.39503 0.697514 0.716571i \(-0.254289\pi\)
0.697514 + 0.716571i \(0.254289\pi\)
\(884\) 0 0
\(885\) −50.8190 −1.70826
\(886\) 15.1190 0.507932
\(887\) −1.17172 −0.0393426 −0.0196713 0.999807i \(-0.506262\pi\)
−0.0196713 + 0.999807i \(0.506262\pi\)
\(888\) −75.4061 −2.53046
\(889\) 0 0
\(890\) −0.363051 −0.0121695
\(891\) 51.2662 1.71748
\(892\) 3.21234 0.107557
\(893\) −22.2602 −0.744910
\(894\) 3.83548 0.128278
\(895\) −12.0849 −0.403952
\(896\) 0 0
\(897\) 0 0
\(898\) −11.9975 −0.400361
\(899\) 23.2728 0.776192
\(900\) 19.1800 0.639335
\(901\) −12.4779 −0.415700
\(902\) 3.78312 0.125964
\(903\) 0 0
\(904\) −21.0783 −0.701054
\(905\) −22.6215 −0.751965
\(906\) 3.40681 0.113184
\(907\) −42.9537 −1.42625 −0.713127 0.701035i \(-0.752722\pi\)
−0.713127 + 0.701035i \(0.752722\pi\)
\(908\) 17.3644 0.576258
\(909\) 22.4513 0.744664
\(910\) 0 0
\(911\) 24.5412 0.813085 0.406543 0.913632i \(-0.366734\pi\)
0.406543 + 0.913632i \(0.366734\pi\)
\(912\) 16.9461 0.561142
\(913\) 33.7820 1.11802
\(914\) −8.28161 −0.273931
\(915\) 30.5689 1.01058
\(916\) −10.2559 −0.338863
\(917\) 0 0
\(918\) −38.2127 −1.26121
\(919\) 36.6615 1.20935 0.604675 0.796472i \(-0.293303\pi\)
0.604675 + 0.796472i \(0.293303\pi\)
\(920\) 15.5226 0.511765
\(921\) −12.0602 −0.397398
\(922\) 14.0780 0.463635
\(923\) 0 0
\(924\) 0 0
\(925\) −20.4126 −0.671162
\(926\) −5.71549 −0.187823
\(927\) −84.9253 −2.78931
\(928\) −27.5865 −0.905572
\(929\) 25.9653 0.851894 0.425947 0.904748i \(-0.359941\pi\)
0.425947 + 0.904748i \(0.359941\pi\)
\(930\) 14.3674 0.471125
\(931\) 0 0
\(932\) −11.9761 −0.392290
\(933\) −60.9506 −1.99543
\(934\) −6.49340 −0.212471
\(935\) −39.7865 −1.30116
\(936\) 0 0
\(937\) 11.8632 0.387554 0.193777 0.981046i \(-0.437926\pi\)
0.193777 + 0.981046i \(0.437926\pi\)
\(938\) 0 0
\(939\) −8.94059 −0.291765
\(940\) −26.8905 −0.877070
\(941\) −9.51954 −0.310328 −0.155164 0.987889i \(-0.549591\pi\)
−0.155164 + 0.987889i \(0.549591\pi\)
\(942\) −32.0779 −1.04515
\(943\) −7.71170 −0.251128
\(944\) 19.8862 0.647241
\(945\) 0 0
\(946\) 2.88464 0.0937876
\(947\) 42.5868 1.38388 0.691942 0.721953i \(-0.256755\pi\)
0.691942 + 0.721953i \(0.256755\pi\)
\(948\) 27.0576 0.878791
\(949\) 0 0
\(950\) −2.47261 −0.0802222
\(951\) 49.3146 1.59913
\(952\) 0 0
\(953\) 31.4390 1.01841 0.509204 0.860646i \(-0.329940\pi\)
0.509204 + 0.860646i \(0.329940\pi\)
\(954\) −7.52199 −0.243534
\(955\) 5.48115 0.177366
\(956\) −12.3050 −0.397971
\(957\) −56.6313 −1.83063
\(958\) −0.611404 −0.0197536
\(959\) 0 0
\(960\) 7.33689 0.236797
\(961\) −10.2686 −0.331244
\(962\) 0 0
\(963\) −119.102 −3.83800
\(964\) 0.442059 0.0142378
\(965\) −48.6394 −1.56576
\(966\) 0 0
\(967\) −6.05894 −0.194842 −0.0974212 0.995243i \(-0.531059\pi\)
−0.0974212 + 0.995243i \(0.531059\pi\)
\(968\) 3.84475 0.123575
\(969\) −47.7240 −1.53312
\(970\) −10.8243 −0.347546
\(971\) −43.4692 −1.39499 −0.697497 0.716588i \(-0.745703\pi\)
−0.697497 + 0.716588i \(0.745703\pi\)
\(972\) 18.8943 0.606036
\(973\) 0 0
\(974\) −14.2890 −0.457849
\(975\) 0 0
\(976\) −11.9621 −0.382896
\(977\) 28.8178 0.921964 0.460982 0.887409i \(-0.347497\pi\)
0.460982 + 0.887409i \(0.347497\pi\)
\(978\) 38.5615 1.23306
\(979\) 1.27476 0.0407414
\(980\) 0 0
\(981\) 91.3071 2.91521
\(982\) −23.5918 −0.752844
\(983\) 31.1850 0.994647 0.497323 0.867565i \(-0.334316\pi\)
0.497323 + 0.867565i \(0.334316\pi\)
\(984\) 12.0069 0.382765
\(985\) 16.7860 0.534845
\(986\) 17.7742 0.566044
\(987\) 0 0
\(988\) 0 0
\(989\) −5.88019 −0.186979
\(990\) −23.9843 −0.762271
\(991\) −62.1395 −1.97393 −0.986963 0.160946i \(-0.948546\pi\)
−0.986963 + 0.160946i \(0.948546\pi\)
\(992\) −24.5741 −0.780228
\(993\) −11.8290 −0.375382
\(994\) 0 0
\(995\) 31.3821 0.994879
\(996\) 48.9502 1.55105
\(997\) 17.3144 0.548351 0.274176 0.961680i \(-0.411595\pi\)
0.274176 + 0.961680i \(0.411595\pi\)
\(998\) −5.91991 −0.187392
\(999\) −128.806 −4.07524
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 8281.2.a.cx.1.13 32
7.6 odd 2 inner 8281.2.a.cx.1.14 32
13.6 odd 12 637.2.q.j.491.10 yes 32
13.11 odd 12 637.2.q.j.589.10 yes 32
13.12 even 2 inner 8281.2.a.cx.1.19 32
91.6 even 12 637.2.q.j.491.9 32
91.11 odd 12 637.2.u.j.30.7 32
91.19 even 12 637.2.u.j.361.8 32
91.24 even 12 637.2.u.j.30.8 32
91.32 odd 12 637.2.k.j.569.10 32
91.37 odd 12 637.2.k.j.459.8 32
91.45 even 12 637.2.k.j.569.9 32
91.58 odd 12 637.2.u.j.361.7 32
91.76 even 12 637.2.q.j.589.9 yes 32
91.89 even 12 637.2.k.j.459.7 32
91.90 odd 2 inner 8281.2.a.cx.1.20 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.k.j.459.7 32 91.89 even 12
637.2.k.j.459.8 32 91.37 odd 12
637.2.k.j.569.9 32 91.45 even 12
637.2.k.j.569.10 32 91.32 odd 12
637.2.q.j.491.9 32 91.6 even 12
637.2.q.j.491.10 yes 32 13.6 odd 12
637.2.q.j.589.9 yes 32 91.76 even 12
637.2.q.j.589.10 yes 32 13.11 odd 12
637.2.u.j.30.7 32 91.11 odd 12
637.2.u.j.30.8 32 91.24 even 12
637.2.u.j.361.7 32 91.58 odd 12
637.2.u.j.361.8 32 91.19 even 12
8281.2.a.cx.1.13 32 1.1 even 1 trivial
8281.2.a.cx.1.14 32 7.6 odd 2 inner
8281.2.a.cx.1.19 32 13.12 even 2 inner
8281.2.a.cx.1.20 32 91.90 odd 2 inner