Properties

Label 8281.2.a.bf.1.3
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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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: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 169)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.445042\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q+0.801938 q^{2} +2.24698 q^{3} -1.35690 q^{4} -0.246980 q^{5} +1.80194 q^{6} -2.69202 q^{8} +2.04892 q^{9} +O(q^{10})\) \(q+0.801938 q^{2} +2.24698 q^{3} -1.35690 q^{4} -0.246980 q^{5} +1.80194 q^{6} -2.69202 q^{8} +2.04892 q^{9} -0.198062 q^{10} -4.24698 q^{11} -3.04892 q^{12} -0.554958 q^{15} +0.554958 q^{16} -2.15883 q^{17} +1.64310 q^{18} +0.0881460 q^{19} +0.335126 q^{20} -3.40581 q^{22} +1.49396 q^{23} -6.04892 q^{24} -4.93900 q^{25} -2.13706 q^{27} +4.63102 q^{29} -0.445042 q^{30} +6.63102 q^{31} +5.82908 q^{32} -9.54288 q^{33} -1.73125 q^{34} -2.78017 q^{36} +5.69202 q^{37} +0.0706876 q^{38} +0.664874 q^{40} +11.5918 q^{41} -0.295897 q^{43} +5.76271 q^{44} -0.506041 q^{45} +1.19806 q^{46} +7.35690 q^{47} +1.24698 q^{48} -3.96077 q^{50} -4.85086 q^{51} -10.3937 q^{53} -1.71379 q^{54} +1.04892 q^{55} +0.198062 q^{57} +3.71379 q^{58} +6.78017 q^{59} +0.753020 q^{60} -3.47219 q^{61} +5.31767 q^{62} +3.56465 q^{64} -7.65279 q^{66} +7.67994 q^{67} +2.92931 q^{68} +3.35690 q^{69} -8.66487 q^{71} -5.51573 q^{72} -6.73556 q^{73} +4.56465 q^{74} -11.0978 q^{75} -0.119605 q^{76} +9.97046 q^{79} -0.137063 q^{80} -10.9487 q^{81} +9.29590 q^{82} -1.60925 q^{83} +0.533188 q^{85} -0.237291 q^{86} +10.4058 q^{87} +11.4330 q^{88} +2.88471 q^{89} -0.405813 q^{90} -2.02715 q^{92} +14.8998 q^{93} +5.89977 q^{94} -0.0217703 q^{95} +13.0978 q^{96} +8.05861 q^{97} -8.70171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{2} + 2 q^{3} + 4 q^{5} + q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{2} + 2 q^{3} + 4 q^{5} + q^{6} - 3 q^{8} - 3 q^{9} - 5 q^{10} - 8 q^{11} - 2 q^{15} + 2 q^{16} + 2 q^{17} + 9 q^{18} + 4 q^{19} + 3 q^{22} - 5 q^{23} - 9 q^{24} - 5 q^{25} - q^{27} - q^{29} - q^{30} + 5 q^{31} + 7 q^{32} - 10 q^{33} - 13 q^{34} - 7 q^{36} + 12 q^{37} - 12 q^{38} + 3 q^{40} + 7 q^{41} + 13 q^{43} - 11 q^{45} + 8 q^{46} + 18 q^{47} - q^{48} + q^{50} - q^{51} + q^{53} + 3 q^{54} - 6 q^{55} + 5 q^{57} + 3 q^{58} + 19 q^{59} + 7 q^{60} - 4 q^{61} - q^{62} - 11 q^{64} - 5 q^{66} - q^{67} + 21 q^{68} + 6 q^{69} - 27 q^{71} - 4 q^{72} - 9 q^{73} - 8 q^{74} - 15 q^{75} + 21 q^{76} - 5 q^{79} + 5 q^{80} - q^{81} + 14 q^{82} + 7 q^{83} + 5 q^{85} - 18 q^{86} + 18 q^{87} + 15 q^{88} + 11 q^{89} + 12 q^{90} + 22 q^{93} - 5 q^{94} + 3 q^{95} + 21 q^{96} - 7 q^{97} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.801938 0.567056 0.283528 0.958964i \(-0.408495\pi\)
0.283528 + 0.958964i \(0.408495\pi\)
\(3\) 2.24698 1.29729 0.648647 0.761089i \(-0.275335\pi\)
0.648647 + 0.761089i \(0.275335\pi\)
\(4\) −1.35690 −0.678448
\(5\) −0.246980 −0.110453 −0.0552263 0.998474i \(-0.517588\pi\)
−0.0552263 + 0.998474i \(0.517588\pi\)
\(6\) 1.80194 0.735638
\(7\) 0 0
\(8\) −2.69202 −0.951773
\(9\) 2.04892 0.682972
\(10\) −0.198062 −0.0626328
\(11\) −4.24698 −1.28051 −0.640256 0.768161i \(-0.721172\pi\)
−0.640256 + 0.768161i \(0.721172\pi\)
\(12\) −3.04892 −0.880147
\(13\) 0 0
\(14\) 0 0
\(15\) −0.554958 −0.143290
\(16\) 0.554958 0.138740
\(17\) −2.15883 −0.523594 −0.261797 0.965123i \(-0.584315\pi\)
−0.261797 + 0.965123i \(0.584315\pi\)
\(18\) 1.64310 0.387283
\(19\) 0.0881460 0.0202221 0.0101110 0.999949i \(-0.496782\pi\)
0.0101110 + 0.999949i \(0.496782\pi\)
\(20\) 0.335126 0.0749364
\(21\) 0 0
\(22\) −3.40581 −0.726122
\(23\) 1.49396 0.311512 0.155756 0.987796i \(-0.450219\pi\)
0.155756 + 0.987796i \(0.450219\pi\)
\(24\) −6.04892 −1.23473
\(25\) −4.93900 −0.987800
\(26\) 0 0
\(27\) −2.13706 −0.411278
\(28\) 0 0
\(29\) 4.63102 0.859959 0.429980 0.902839i \(-0.358521\pi\)
0.429980 + 0.902839i \(0.358521\pi\)
\(30\) −0.445042 −0.0812532
\(31\) 6.63102 1.19097 0.595483 0.803368i \(-0.296961\pi\)
0.595483 + 0.803368i \(0.296961\pi\)
\(32\) 5.82908 1.03045
\(33\) −9.54288 −1.66120
\(34\) −1.73125 −0.296907
\(35\) 0 0
\(36\) −2.78017 −0.463361
\(37\) 5.69202 0.935763 0.467881 0.883791i \(-0.345017\pi\)
0.467881 + 0.883791i \(0.345017\pi\)
\(38\) 0.0706876 0.0114670
\(39\) 0 0
\(40\) 0.664874 0.105126
\(41\) 11.5918 1.81033 0.905167 0.425056i \(-0.139746\pi\)
0.905167 + 0.425056i \(0.139746\pi\)
\(42\) 0 0
\(43\) −0.295897 −0.0451239 −0.0225619 0.999745i \(-0.507182\pi\)
−0.0225619 + 0.999745i \(0.507182\pi\)
\(44\) 5.76271 0.868761
\(45\) −0.506041 −0.0754361
\(46\) 1.19806 0.176645
\(47\) 7.35690 1.07311 0.536557 0.843864i \(-0.319725\pi\)
0.536557 + 0.843864i \(0.319725\pi\)
\(48\) 1.24698 0.179986
\(49\) 0 0
\(50\) −3.96077 −0.560138
\(51\) −4.85086 −0.679256
\(52\) 0 0
\(53\) −10.3937 −1.42769 −0.713844 0.700304i \(-0.753048\pi\)
−0.713844 + 0.700304i \(0.753048\pi\)
\(54\) −1.71379 −0.233218
\(55\) 1.04892 0.141436
\(56\) 0 0
\(57\) 0.198062 0.0262340
\(58\) 3.71379 0.487645
\(59\) 6.78017 0.882703 0.441351 0.897334i \(-0.354499\pi\)
0.441351 + 0.897334i \(0.354499\pi\)
\(60\) 0.753020 0.0972145
\(61\) −3.47219 −0.444568 −0.222284 0.974982i \(-0.571351\pi\)
−0.222284 + 0.974982i \(0.571351\pi\)
\(62\) 5.31767 0.675344
\(63\) 0 0
\(64\) 3.56465 0.445581
\(65\) 0 0
\(66\) −7.65279 −0.941994
\(67\) 7.67994 0.938254 0.469127 0.883131i \(-0.344569\pi\)
0.469127 + 0.883131i \(0.344569\pi\)
\(68\) 2.92931 0.355231
\(69\) 3.35690 0.404123
\(70\) 0 0
\(71\) −8.66487 −1.02833 −0.514166 0.857691i \(-0.671898\pi\)
−0.514166 + 0.857691i \(0.671898\pi\)
\(72\) −5.51573 −0.650035
\(73\) −6.73556 −0.788338 −0.394169 0.919038i \(-0.628968\pi\)
−0.394169 + 0.919038i \(0.628968\pi\)
\(74\) 4.56465 0.530629
\(75\) −11.0978 −1.28147
\(76\) −0.119605 −0.0137196
\(77\) 0 0
\(78\) 0 0
\(79\) 9.97046 1.12176 0.560882 0.827896i \(-0.310462\pi\)
0.560882 + 0.827896i \(0.310462\pi\)
\(80\) −0.137063 −0.0153241
\(81\) −10.9487 −1.21652
\(82\) 9.29590 1.02656
\(83\) −1.60925 −0.176638 −0.0883192 0.996092i \(-0.528150\pi\)
−0.0883192 + 0.996092i \(0.528150\pi\)
\(84\) 0 0
\(85\) 0.533188 0.0578323
\(86\) −0.237291 −0.0255877
\(87\) 10.4058 1.11562
\(88\) 11.4330 1.21876
\(89\) 2.88471 0.305778 0.152889 0.988243i \(-0.451142\pi\)
0.152889 + 0.988243i \(0.451142\pi\)
\(90\) −0.405813 −0.0427765
\(91\) 0 0
\(92\) −2.02715 −0.211345
\(93\) 14.8998 1.54503
\(94\) 5.89977 0.608515
\(95\) −0.0217703 −0.00223358
\(96\) 13.0978 1.33679
\(97\) 8.05861 0.818227 0.409114 0.912483i \(-0.365838\pi\)
0.409114 + 0.912483i \(0.365838\pi\)
\(98\) 0 0
\(99\) −8.70171 −0.874555
\(100\) 6.70171 0.670171
\(101\) 13.3545 1.32882 0.664411 0.747367i \(-0.268682\pi\)
0.664411 + 0.747367i \(0.268682\pi\)
\(102\) −3.89008 −0.385176
\(103\) −1.36227 −0.134229 −0.0671144 0.997745i \(-0.521379\pi\)
−0.0671144 + 0.997745i \(0.521379\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −8.33513 −0.809579
\(107\) 3.26875 0.316002 0.158001 0.987439i \(-0.449495\pi\)
0.158001 + 0.987439i \(0.449495\pi\)
\(108\) 2.89977 0.279031
\(109\) 15.7017 1.50395 0.751976 0.659191i \(-0.229101\pi\)
0.751976 + 0.659191i \(0.229101\pi\)
\(110\) 0.841166 0.0802021
\(111\) 12.7899 1.21396
\(112\) 0 0
\(113\) 12.0489 1.13347 0.566733 0.823901i \(-0.308207\pi\)
0.566733 + 0.823901i \(0.308207\pi\)
\(114\) 0.158834 0.0148761
\(115\) −0.368977 −0.0344073
\(116\) −6.28382 −0.583438
\(117\) 0 0
\(118\) 5.43727 0.500541
\(119\) 0 0
\(120\) 1.49396 0.136379
\(121\) 7.03684 0.639712
\(122\) −2.78448 −0.252095
\(123\) 26.0465 2.34854
\(124\) −8.99761 −0.808009
\(125\) 2.45473 0.219558
\(126\) 0 0
\(127\) −9.80731 −0.870258 −0.435129 0.900368i \(-0.643297\pi\)
−0.435129 + 0.900368i \(0.643297\pi\)
\(128\) −8.79954 −0.777777
\(129\) −0.664874 −0.0585389
\(130\) 0 0
\(131\) 6.57673 0.574611 0.287306 0.957839i \(-0.407240\pi\)
0.287306 + 0.957839i \(0.407240\pi\)
\(132\) 12.9487 1.12704
\(133\) 0 0
\(134\) 6.15883 0.532042
\(135\) 0.527811 0.0454267
\(136\) 5.81163 0.498343
\(137\) 6.21983 0.531396 0.265698 0.964056i \(-0.414398\pi\)
0.265698 + 0.964056i \(0.414398\pi\)
\(138\) 2.69202 0.229160
\(139\) 14.7071 1.24744 0.623719 0.781648i \(-0.285621\pi\)
0.623719 + 0.781648i \(0.285621\pi\)
\(140\) 0 0
\(141\) 16.5308 1.39214
\(142\) −6.94869 −0.583121
\(143\) 0 0
\(144\) 1.13706 0.0947553
\(145\) −1.14377 −0.0949848
\(146\) −5.40150 −0.447031
\(147\) 0 0
\(148\) −7.72348 −0.634866
\(149\) 4.33513 0.355147 0.177574 0.984108i \(-0.443175\pi\)
0.177574 + 0.984108i \(0.443175\pi\)
\(150\) −8.89977 −0.726663
\(151\) 3.94438 0.320989 0.160494 0.987037i \(-0.448691\pi\)
0.160494 + 0.987037i \(0.448691\pi\)
\(152\) −0.237291 −0.0192468
\(153\) −4.42327 −0.357600
\(154\) 0 0
\(155\) −1.63773 −0.131545
\(156\) 0 0
\(157\) −4.45473 −0.355526 −0.177763 0.984073i \(-0.556886\pi\)
−0.177763 + 0.984073i \(0.556886\pi\)
\(158\) 7.99569 0.636103
\(159\) −23.3545 −1.85213
\(160\) −1.43967 −0.113816
\(161\) 0 0
\(162\) −8.78017 −0.689835
\(163\) 16.1588 1.26566 0.632829 0.774292i \(-0.281894\pi\)
0.632829 + 0.774292i \(0.281894\pi\)
\(164\) −15.7289 −1.22822
\(165\) 2.35690 0.183484
\(166\) −1.29052 −0.100164
\(167\) −16.1172 −1.24719 −0.623594 0.781749i \(-0.714328\pi\)
−0.623594 + 0.781749i \(0.714328\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0.427583 0.0327942
\(171\) 0.180604 0.0138111
\(172\) 0.401501 0.0306142
\(173\) 21.5362 1.63736 0.818682 0.574247i \(-0.194705\pi\)
0.818682 + 0.574247i \(0.194705\pi\)
\(174\) 8.34481 0.632619
\(175\) 0 0
\(176\) −2.35690 −0.177658
\(177\) 15.2349 1.14513
\(178\) 2.31336 0.173393
\(179\) 11.4330 0.854540 0.427270 0.904124i \(-0.359475\pi\)
0.427270 + 0.904124i \(0.359475\pi\)
\(180\) 0.686645 0.0511795
\(181\) −20.9705 −1.55872 −0.779361 0.626575i \(-0.784456\pi\)
−0.779361 + 0.626575i \(0.784456\pi\)
\(182\) 0 0
\(183\) −7.80194 −0.576736
\(184\) −4.02177 −0.296489
\(185\) −1.40581 −0.103357
\(186\) 11.9487 0.876120
\(187\) 9.16852 0.670469
\(188\) −9.98254 −0.728052
\(189\) 0 0
\(190\) −0.0174584 −0.00126657
\(191\) −14.4373 −1.04464 −0.522322 0.852748i \(-0.674934\pi\)
−0.522322 + 0.852748i \(0.674934\pi\)
\(192\) 8.00969 0.578049
\(193\) −13.5797 −0.977489 −0.488745 0.872427i \(-0.662545\pi\)
−0.488745 + 0.872427i \(0.662545\pi\)
\(194\) 6.46250 0.463980
\(195\) 0 0
\(196\) 0 0
\(197\) −0.560335 −0.0399222 −0.0199611 0.999801i \(-0.506354\pi\)
−0.0199611 + 0.999801i \(0.506354\pi\)
\(198\) −6.97823 −0.495921
\(199\) −11.4916 −0.814616 −0.407308 0.913291i \(-0.633532\pi\)
−0.407308 + 0.913291i \(0.633532\pi\)
\(200\) 13.2959 0.940162
\(201\) 17.2567 1.21719
\(202\) 10.7095 0.753516
\(203\) 0 0
\(204\) 6.58211 0.460840
\(205\) −2.86294 −0.199956
\(206\) −1.09246 −0.0761151
\(207\) 3.06100 0.212754
\(208\) 0 0
\(209\) −0.374354 −0.0258946
\(210\) 0 0
\(211\) 8.78448 0.604748 0.302374 0.953189i \(-0.402221\pi\)
0.302374 + 0.953189i \(0.402221\pi\)
\(212\) 14.1032 0.968613
\(213\) −19.4698 −1.33405
\(214\) 2.62133 0.179191
\(215\) 0.0730805 0.00498405
\(216\) 5.75302 0.391443
\(217\) 0 0
\(218\) 12.5918 0.852824
\(219\) −15.1347 −1.02271
\(220\) −1.42327 −0.0959570
\(221\) 0 0
\(222\) 10.2567 0.688383
\(223\) 2.25906 0.151278 0.0756390 0.997135i \(-0.475900\pi\)
0.0756390 + 0.997135i \(0.475900\pi\)
\(224\) 0 0
\(225\) −10.1196 −0.674640
\(226\) 9.66248 0.642739
\(227\) 6.96615 0.462359 0.231180 0.972911i \(-0.425741\pi\)
0.231180 + 0.972911i \(0.425741\pi\)
\(228\) −0.268750 −0.0177984
\(229\) 24.1739 1.59746 0.798728 0.601692i \(-0.205507\pi\)
0.798728 + 0.601692i \(0.205507\pi\)
\(230\) −0.295897 −0.0195109
\(231\) 0 0
\(232\) −12.4668 −0.818486
\(233\) −3.06100 −0.200533 −0.100266 0.994961i \(-0.531969\pi\)
−0.100266 + 0.994961i \(0.531969\pi\)
\(234\) 0 0
\(235\) −1.81700 −0.118528
\(236\) −9.19998 −0.598868
\(237\) 22.4034 1.45526
\(238\) 0 0
\(239\) −25.1468 −1.62661 −0.813304 0.581839i \(-0.802333\pi\)
−0.813304 + 0.581839i \(0.802333\pi\)
\(240\) −0.307979 −0.0198799
\(241\) 20.2664 1.30547 0.652735 0.757586i \(-0.273621\pi\)
0.652735 + 0.757586i \(0.273621\pi\)
\(242\) 5.64310 0.362752
\(243\) −18.1903 −1.16691
\(244\) 4.71140 0.301616
\(245\) 0 0
\(246\) 20.8877 1.33175
\(247\) 0 0
\(248\) −17.8509 −1.13353
\(249\) −3.61596 −0.229152
\(250\) 1.96854 0.124501
\(251\) 23.7211 1.49726 0.748631 0.662987i \(-0.230712\pi\)
0.748631 + 0.662987i \(0.230712\pi\)
\(252\) 0 0
\(253\) −6.34481 −0.398895
\(254\) −7.86486 −0.493485
\(255\) 1.19806 0.0750256
\(256\) −14.1860 −0.886624
\(257\) −14.2241 −0.887278 −0.443639 0.896206i \(-0.646313\pi\)
−0.443639 + 0.896206i \(0.646313\pi\)
\(258\) −0.533188 −0.0331948
\(259\) 0 0
\(260\) 0 0
\(261\) 9.48858 0.587329
\(262\) 5.27413 0.325837
\(263\) −17.0954 −1.05415 −0.527075 0.849819i \(-0.676711\pi\)
−0.527075 + 0.849819i \(0.676711\pi\)
\(264\) 25.6896 1.58109
\(265\) 2.56704 0.157692
\(266\) 0 0
\(267\) 6.48188 0.396684
\(268\) −10.4209 −0.636556
\(269\) 6.46681 0.394288 0.197144 0.980374i \(-0.436833\pi\)
0.197144 + 0.980374i \(0.436833\pi\)
\(270\) 0.423272 0.0257595
\(271\) −6.44803 −0.391690 −0.195845 0.980635i \(-0.562745\pi\)
−0.195845 + 0.980635i \(0.562745\pi\)
\(272\) −1.19806 −0.0726432
\(273\) 0 0
\(274\) 4.98792 0.301331
\(275\) 20.9758 1.26489
\(276\) −4.55496 −0.274176
\(277\) 13.4601 0.808739 0.404370 0.914596i \(-0.367491\pi\)
0.404370 + 0.914596i \(0.367491\pi\)
\(278\) 11.7942 0.707367
\(279\) 13.5864 0.813398
\(280\) 0 0
\(281\) 5.03684 0.300472 0.150236 0.988650i \(-0.451997\pi\)
0.150236 + 0.988650i \(0.451997\pi\)
\(282\) 13.2567 0.789423
\(283\) −22.1280 −1.31537 −0.657686 0.753293i \(-0.728464\pi\)
−0.657686 + 0.753293i \(0.728464\pi\)
\(284\) 11.7573 0.697669
\(285\) −0.0489173 −0.00289761
\(286\) 0 0
\(287\) 0 0
\(288\) 11.9433 0.703766
\(289\) −12.3394 −0.725849
\(290\) −0.917231 −0.0538616
\(291\) 18.1075 1.06148
\(292\) 9.13946 0.534846
\(293\) −14.9463 −0.873172 −0.436586 0.899663i \(-0.643813\pi\)
−0.436586 + 0.899663i \(0.643813\pi\)
\(294\) 0 0
\(295\) −1.67456 −0.0974968
\(296\) −15.3230 −0.890634
\(297\) 9.07606 0.526647
\(298\) 3.47650 0.201388
\(299\) 0 0
\(300\) 15.0586 0.869409
\(301\) 0 0
\(302\) 3.16315 0.182019
\(303\) 30.0073 1.72387
\(304\) 0.0489173 0.00280560
\(305\) 0.857560 0.0491037
\(306\) −3.54719 −0.202779
\(307\) −19.1293 −1.09177 −0.545883 0.837861i \(-0.683806\pi\)
−0.545883 + 0.837861i \(0.683806\pi\)
\(308\) 0 0
\(309\) −3.06100 −0.174134
\(310\) −1.31336 −0.0745936
\(311\) 0.269815 0.0152998 0.00764990 0.999971i \(-0.497565\pi\)
0.00764990 + 0.999971i \(0.497565\pi\)
\(312\) 0 0
\(313\) 23.3937 1.32229 0.661146 0.750257i \(-0.270070\pi\)
0.661146 + 0.750257i \(0.270070\pi\)
\(314\) −3.57242 −0.201603
\(315\) 0 0
\(316\) −13.5289 −0.761059
\(317\) −13.9952 −0.786050 −0.393025 0.919528i \(-0.628571\pi\)
−0.393025 + 0.919528i \(0.628571\pi\)
\(318\) −18.7289 −1.05026
\(319\) −19.6679 −1.10119
\(320\) −0.880395 −0.0492156
\(321\) 7.34481 0.409948
\(322\) 0 0
\(323\) −0.190293 −0.0105882
\(324\) 14.8562 0.825346
\(325\) 0 0
\(326\) 12.9584 0.717698
\(327\) 35.2814 1.95107
\(328\) −31.2054 −1.72303
\(329\) 0 0
\(330\) 1.89008 0.104046
\(331\) 17.8213 0.979548 0.489774 0.871849i \(-0.337079\pi\)
0.489774 + 0.871849i \(0.337079\pi\)
\(332\) 2.18359 0.119840
\(333\) 11.6625 0.639100
\(334\) −12.9250 −0.707225
\(335\) −1.89679 −0.103633
\(336\) 0 0
\(337\) −27.8485 −1.51700 −0.758501 0.651672i \(-0.774068\pi\)
−0.758501 + 0.651672i \(0.774068\pi\)
\(338\) 0 0
\(339\) 27.0737 1.47044
\(340\) −0.723480 −0.0392362
\(341\) −28.1618 −1.52505
\(342\) 0.144833 0.00783167
\(343\) 0 0
\(344\) 0.796561 0.0429477
\(345\) −0.829085 −0.0446364
\(346\) 17.2707 0.928477
\(347\) 1.50365 0.0807200 0.0403600 0.999185i \(-0.487150\pi\)
0.0403600 + 0.999185i \(0.487150\pi\)
\(348\) −14.1196 −0.756890
\(349\) 14.1860 0.759358 0.379679 0.925118i \(-0.376034\pi\)
0.379679 + 0.925118i \(0.376034\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −24.7560 −1.31950
\(353\) 7.16852 0.381542 0.190771 0.981635i \(-0.438901\pi\)
0.190771 + 0.981635i \(0.438901\pi\)
\(354\) 12.2174 0.649350
\(355\) 2.14005 0.113582
\(356\) −3.91425 −0.207455
\(357\) 0 0
\(358\) 9.16852 0.484571
\(359\) 19.8853 1.04951 0.524753 0.851255i \(-0.324158\pi\)
0.524753 + 0.851255i \(0.324158\pi\)
\(360\) 1.36227 0.0717981
\(361\) −18.9922 −0.999591
\(362\) −16.8170 −0.883882
\(363\) 15.8116 0.829895
\(364\) 0 0
\(365\) 1.66355 0.0870740
\(366\) −6.25667 −0.327041
\(367\) −1.08383 −0.0565757 −0.0282878 0.999600i \(-0.509006\pi\)
−0.0282878 + 0.999600i \(0.509006\pi\)
\(368\) 0.829085 0.0432190
\(369\) 23.7506 1.23641
\(370\) −1.12737 −0.0586094
\(371\) 0 0
\(372\) −20.2174 −1.04823
\(373\) −6.13036 −0.317418 −0.158709 0.987325i \(-0.550733\pi\)
−0.158709 + 0.987325i \(0.550733\pi\)
\(374\) 7.35258 0.380193
\(375\) 5.51573 0.284831
\(376\) −19.8049 −1.02136
\(377\) 0 0
\(378\) 0 0
\(379\) −2.40880 −0.123732 −0.0618658 0.998084i \(-0.519705\pi\)
−0.0618658 + 0.998084i \(0.519705\pi\)
\(380\) 0.0295400 0.00151537
\(381\) −22.0368 −1.12898
\(382\) −11.5778 −0.592371
\(383\) 30.3913 1.55292 0.776462 0.630164i \(-0.217012\pi\)
0.776462 + 0.630164i \(0.217012\pi\)
\(384\) −19.7724 −1.00901
\(385\) 0 0
\(386\) −10.8901 −0.554291
\(387\) −0.606268 −0.0308184
\(388\) −10.9347 −0.555125
\(389\) −15.9409 −0.808237 −0.404118 0.914707i \(-0.632422\pi\)
−0.404118 + 0.914707i \(0.632422\pi\)
\(390\) 0 0
\(391\) −3.22521 −0.163106
\(392\) 0 0
\(393\) 14.7778 0.745440
\(394\) −0.449354 −0.0226381
\(395\) −2.46250 −0.123902
\(396\) 11.8073 0.593340
\(397\) −16.9148 −0.848931 −0.424466 0.905444i \(-0.639538\pi\)
−0.424466 + 0.905444i \(0.639538\pi\)
\(398\) −9.21552 −0.461932
\(399\) 0 0
\(400\) −2.74094 −0.137047
\(401\) 26.6625 1.33146 0.665730 0.746192i \(-0.268120\pi\)
0.665730 + 0.746192i \(0.268120\pi\)
\(402\) 13.8388 0.690215
\(403\) 0 0
\(404\) −18.1207 −0.901537
\(405\) 2.70410 0.134368
\(406\) 0 0
\(407\) −24.1739 −1.19826
\(408\) 13.0586 0.646497
\(409\) −28.5163 −1.41004 −0.705021 0.709187i \(-0.749062\pi\)
−0.705021 + 0.709187i \(0.749062\pi\)
\(410\) −2.29590 −0.113386
\(411\) 13.9758 0.689377
\(412\) 1.84846 0.0910672
\(413\) 0 0
\(414\) 2.45473 0.120643
\(415\) 0.397452 0.0195102
\(416\) 0 0
\(417\) 33.0465 1.61830
\(418\) −0.300209 −0.0146837
\(419\) 29.6093 1.44651 0.723253 0.690583i \(-0.242646\pi\)
0.723253 + 0.690583i \(0.242646\pi\)
\(420\) 0 0
\(421\) −11.6606 −0.568301 −0.284151 0.958780i \(-0.591712\pi\)
−0.284151 + 0.958780i \(0.591712\pi\)
\(422\) 7.04461 0.342926
\(423\) 15.0737 0.732907
\(424\) 27.9801 1.35884
\(425\) 10.6625 0.517206
\(426\) −15.6136 −0.756480
\(427\) 0 0
\(428\) −4.43535 −0.214391
\(429\) 0 0
\(430\) 0.0586060 0.00282623
\(431\) 4.34913 0.209490 0.104745 0.994499i \(-0.466597\pi\)
0.104745 + 0.994499i \(0.466597\pi\)
\(432\) −1.18598 −0.0570605
\(433\) 14.3884 0.691460 0.345730 0.938334i \(-0.387631\pi\)
0.345730 + 0.938334i \(0.387631\pi\)
\(434\) 0 0
\(435\) −2.57002 −0.123223
\(436\) −21.3056 −1.02035
\(437\) 0.131687 0.00629942
\(438\) −12.1371 −0.579931
\(439\) 20.2325 0.965645 0.482822 0.875718i \(-0.339612\pi\)
0.482822 + 0.875718i \(0.339612\pi\)
\(440\) −2.82371 −0.134615
\(441\) 0 0
\(442\) 0 0
\(443\) 8.12200 0.385888 0.192944 0.981210i \(-0.438196\pi\)
0.192944 + 0.981210i \(0.438196\pi\)
\(444\) −17.3545 −0.823608
\(445\) −0.712464 −0.0337740
\(446\) 1.81163 0.0857830
\(447\) 9.74094 0.460731
\(448\) 0 0
\(449\) 12.4916 0.589513 0.294757 0.955572i \(-0.404761\pi\)
0.294757 + 0.955572i \(0.404761\pi\)
\(450\) −8.11529 −0.382559
\(451\) −49.2301 −2.31816
\(452\) −16.3491 −0.768998
\(453\) 8.86294 0.416417
\(454\) 5.58642 0.262184
\(455\) 0 0
\(456\) −0.533188 −0.0249688
\(457\) 5.98121 0.279789 0.139895 0.990166i \(-0.455324\pi\)
0.139895 + 0.990166i \(0.455324\pi\)
\(458\) 19.3860 0.905847
\(459\) 4.61356 0.215343
\(460\) 0.500664 0.0233436
\(461\) 2.05669 0.0957895 0.0478947 0.998852i \(-0.484749\pi\)
0.0478947 + 0.998852i \(0.484749\pi\)
\(462\) 0 0
\(463\) −8.44935 −0.392675 −0.196337 0.980536i \(-0.562905\pi\)
−0.196337 + 0.980536i \(0.562905\pi\)
\(464\) 2.57002 0.119310
\(465\) −3.67994 −0.170653
\(466\) −2.45473 −0.113713
\(467\) −33.5139 −1.55084 −0.775420 0.631446i \(-0.782462\pi\)
−0.775420 + 0.631446i \(0.782462\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.45712 −0.0672121
\(471\) −10.0097 −0.461222
\(472\) −18.2524 −0.840133
\(473\) 1.25667 0.0577817
\(474\) 17.9661 0.825213
\(475\) −0.435353 −0.0199754
\(476\) 0 0
\(477\) −21.2959 −0.975072
\(478\) −20.1661 −0.922377
\(479\) 24.7313 1.13000 0.565000 0.825091i \(-0.308876\pi\)
0.565000 + 0.825091i \(0.308876\pi\)
\(480\) −3.23490 −0.147652
\(481\) 0 0
\(482\) 16.2524 0.740275
\(483\) 0 0
\(484\) −9.54825 −0.434012
\(485\) −1.99031 −0.0903754
\(486\) −14.5875 −0.661702
\(487\) −37.7555 −1.71087 −0.855433 0.517913i \(-0.826709\pi\)
−0.855433 + 0.517913i \(0.826709\pi\)
\(488\) 9.34721 0.423128
\(489\) 36.3086 1.64193
\(490\) 0 0
\(491\) 31.3110 1.41304 0.706522 0.707691i \(-0.250263\pi\)
0.706522 + 0.707691i \(0.250263\pi\)
\(492\) −35.3424 −1.59336
\(493\) −9.99761 −0.450270
\(494\) 0 0
\(495\) 2.14914 0.0965969
\(496\) 3.67994 0.165234
\(497\) 0 0
\(498\) −2.89977 −0.129942
\(499\) 21.4873 0.961902 0.480951 0.876748i \(-0.340292\pi\)
0.480951 + 0.876748i \(0.340292\pi\)
\(500\) −3.33081 −0.148959
\(501\) −36.2150 −1.61797
\(502\) 19.0228 0.849031
\(503\) −37.5924 −1.67616 −0.838081 0.545546i \(-0.816322\pi\)
−0.838081 + 0.545546i \(0.816322\pi\)
\(504\) 0 0
\(505\) −3.29829 −0.146772
\(506\) −5.08815 −0.226196
\(507\) 0 0
\(508\) 13.3075 0.590425
\(509\) 17.1075 0.758278 0.379139 0.925340i \(-0.376220\pi\)
0.379139 + 0.925340i \(0.376220\pi\)
\(510\) 0.960771 0.0425437
\(511\) 0 0
\(512\) 6.22282 0.275012
\(513\) −0.188374 −0.00831690
\(514\) −11.4069 −0.503136
\(515\) 0.336454 0.0148259
\(516\) 0.902165 0.0397156
\(517\) −31.2446 −1.37414
\(518\) 0 0
\(519\) 48.3913 2.12414
\(520\) 0 0
\(521\) 19.8465 0.869493 0.434746 0.900553i \(-0.356838\pi\)
0.434746 + 0.900553i \(0.356838\pi\)
\(522\) 7.60925 0.333048
\(523\) 11.4300 0.499798 0.249899 0.968272i \(-0.419603\pi\)
0.249899 + 0.968272i \(0.419603\pi\)
\(524\) −8.92394 −0.389844
\(525\) 0 0
\(526\) −13.7095 −0.597762
\(527\) −14.3153 −0.623583
\(528\) −5.29590 −0.230474
\(529\) −20.7681 −0.902960
\(530\) 2.05861 0.0894201
\(531\) 13.8920 0.602862
\(532\) 0 0
\(533\) 0 0
\(534\) 5.19806 0.224942
\(535\) −0.807315 −0.0349033
\(536\) −20.6746 −0.893005
\(537\) 25.6896 1.10859
\(538\) 5.18598 0.223584
\(539\) 0 0
\(540\) −0.716185 −0.0308197
\(541\) 16.1884 0.695993 0.347996 0.937496i \(-0.386862\pi\)
0.347996 + 0.937496i \(0.386862\pi\)
\(542\) −5.17092 −0.222110
\(543\) −47.1202 −2.02212
\(544\) −12.5840 −0.539536
\(545\) −3.87800 −0.166115
\(546\) 0 0
\(547\) 5.33081 0.227929 0.113965 0.993485i \(-0.463645\pi\)
0.113965 + 0.993485i \(0.463645\pi\)
\(548\) −8.43967 −0.360525
\(549\) −7.11423 −0.303628
\(550\) 16.8213 0.717263
\(551\) 0.408206 0.0173902
\(552\) −9.03684 −0.384633
\(553\) 0 0
\(554\) 10.7942 0.458600
\(555\) −3.15883 −0.134085
\(556\) −19.9560 −0.846322
\(557\) 7.39075 0.313156 0.156578 0.987666i \(-0.449954\pi\)
0.156578 + 0.987666i \(0.449954\pi\)
\(558\) 10.8955 0.461242
\(559\) 0 0
\(560\) 0 0
\(561\) 20.6015 0.869795
\(562\) 4.03923 0.170385
\(563\) 9.47889 0.399488 0.199744 0.979848i \(-0.435989\pi\)
0.199744 + 0.979848i \(0.435989\pi\)
\(564\) −22.4306 −0.944497
\(565\) −2.97584 −0.125194
\(566\) −17.7453 −0.745889
\(567\) 0 0
\(568\) 23.3260 0.978738
\(569\) −10.1438 −0.425249 −0.212624 0.977134i \(-0.568201\pi\)
−0.212624 + 0.977134i \(0.568201\pi\)
\(570\) −0.0392287 −0.00164311
\(571\) −14.0925 −0.589751 −0.294876 0.955536i \(-0.595278\pi\)
−0.294876 + 0.955536i \(0.595278\pi\)
\(572\) 0 0
\(573\) −32.4403 −1.35521
\(574\) 0 0
\(575\) −7.37867 −0.307712
\(576\) 7.30367 0.304319
\(577\) −25.1545 −1.04720 −0.523598 0.851965i \(-0.675411\pi\)
−0.523598 + 0.851965i \(0.675411\pi\)
\(578\) −9.89546 −0.411597
\(579\) −30.5133 −1.26809
\(580\) 1.55197 0.0644422
\(581\) 0 0
\(582\) 14.5211 0.601919
\(583\) 44.1420 1.82817
\(584\) 18.1323 0.750319
\(585\) 0 0
\(586\) −11.9860 −0.495137
\(587\) −43.8353 −1.80928 −0.904639 0.426180i \(-0.859859\pi\)
−0.904639 + 0.426180i \(0.859859\pi\)
\(588\) 0 0
\(589\) 0.584498 0.0240838
\(590\) −1.34290 −0.0552861
\(591\) −1.25906 −0.0517909
\(592\) 3.15883 0.129827
\(593\) 24.9965 1.02648 0.513242 0.858244i \(-0.328444\pi\)
0.513242 + 0.858244i \(0.328444\pi\)
\(594\) 7.27844 0.298638
\(595\) 0 0
\(596\) −5.88231 −0.240949
\(597\) −25.8213 −1.05680
\(598\) 0 0
\(599\) −6.24027 −0.254971 −0.127485 0.991840i \(-0.540691\pi\)
−0.127485 + 0.991840i \(0.540691\pi\)
\(600\) 29.8756 1.21967
\(601\) −6.32975 −0.258196 −0.129098 0.991632i \(-0.541208\pi\)
−0.129098 + 0.991632i \(0.541208\pi\)
\(602\) 0 0
\(603\) 15.7356 0.640802
\(604\) −5.35211 −0.217774
\(605\) −1.73795 −0.0706579
\(606\) 24.0640 0.977532
\(607\) 43.6480 1.77162 0.885809 0.464050i \(-0.153604\pi\)
0.885809 + 0.464050i \(0.153604\pi\)
\(608\) 0.513811 0.0208378
\(609\) 0 0
\(610\) 0.687710 0.0278445
\(611\) 0 0
\(612\) 6.00192 0.242613
\(613\) −25.9541 −1.04827 −0.524137 0.851634i \(-0.675612\pi\)
−0.524137 + 0.851634i \(0.675612\pi\)
\(614\) −15.3405 −0.619092
\(615\) −6.43296 −0.259402
\(616\) 0 0
\(617\) 45.9396 1.84946 0.924729 0.380626i \(-0.124291\pi\)
0.924729 + 0.380626i \(0.124291\pi\)
\(618\) −2.45473 −0.0987437
\(619\) −6.73556 −0.270725 −0.135363 0.990796i \(-0.543220\pi\)
−0.135363 + 0.990796i \(0.543220\pi\)
\(620\) 2.22223 0.0892467
\(621\) −3.19269 −0.128118
\(622\) 0.216375 0.00867583
\(623\) 0 0
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) 18.7603 0.749813
\(627\) −0.841166 −0.0335930
\(628\) 6.04461 0.241206
\(629\) −12.2881 −0.489960
\(630\) 0 0
\(631\) 45.0998 1.79539 0.897696 0.440614i \(-0.145239\pi\)
0.897696 + 0.440614i \(0.145239\pi\)
\(632\) −26.8407 −1.06767
\(633\) 19.7385 0.784537
\(634\) −11.2233 −0.445734
\(635\) 2.42221 0.0961223
\(636\) 31.6896 1.25658
\(637\) 0 0
\(638\) −15.7724 −0.624435
\(639\) −17.7536 −0.702322
\(640\) 2.17331 0.0859075
\(641\) 32.5821 1.28692 0.643458 0.765482i \(-0.277499\pi\)
0.643458 + 0.765482i \(0.277499\pi\)
\(642\) 5.89008 0.232463
\(643\) −25.5754 −1.00860 −0.504298 0.863530i \(-0.668249\pi\)
−0.504298 + 0.863530i \(0.668249\pi\)
\(644\) 0 0
\(645\) 0.164210 0.00646578
\(646\) −0.152603 −0.00600408
\(647\) 30.1715 1.18616 0.593082 0.805142i \(-0.297911\pi\)
0.593082 + 0.805142i \(0.297911\pi\)
\(648\) 29.4741 1.15785
\(649\) −28.7952 −1.13031
\(650\) 0 0
\(651\) 0 0
\(652\) −21.9259 −0.858683
\(653\) 36.9028 1.44412 0.722058 0.691832i \(-0.243196\pi\)
0.722058 + 0.691832i \(0.243196\pi\)
\(654\) 28.2935 1.10636
\(655\) −1.62432 −0.0634673
\(656\) 6.43296 0.251165
\(657\) −13.8006 −0.538413
\(658\) 0 0
\(659\) 23.6866 0.922701 0.461350 0.887218i \(-0.347365\pi\)
0.461350 + 0.887218i \(0.347365\pi\)
\(660\) −3.19806 −0.124484
\(661\) 31.7590 1.23528 0.617641 0.786460i \(-0.288089\pi\)
0.617641 + 0.786460i \(0.288089\pi\)
\(662\) 14.2916 0.555458
\(663\) 0 0
\(664\) 4.33214 0.168120
\(665\) 0 0
\(666\) 9.35258 0.362405
\(667\) 6.91856 0.267888
\(668\) 21.8694 0.846152
\(669\) 5.07606 0.196252
\(670\) −1.52111 −0.0587655
\(671\) 14.7463 0.569275
\(672\) 0 0
\(673\) −7.50232 −0.289193 −0.144597 0.989491i \(-0.546188\pi\)
−0.144597 + 0.989491i \(0.546188\pi\)
\(674\) −22.3327 −0.860225
\(675\) 10.5550 0.406261
\(676\) 0 0
\(677\) 35.0315 1.34637 0.673184 0.739475i \(-0.264926\pi\)
0.673184 + 0.739475i \(0.264926\pi\)
\(678\) 21.7114 0.833821
\(679\) 0 0
\(680\) −1.43535 −0.0550433
\(681\) 15.6528 0.599816
\(682\) −22.5840 −0.864787
\(683\) −24.0834 −0.921524 −0.460762 0.887524i \(-0.652424\pi\)
−0.460762 + 0.887524i \(0.652424\pi\)
\(684\) −0.245061 −0.00937013
\(685\) −1.53617 −0.0586941
\(686\) 0 0
\(687\) 54.3183 2.07237
\(688\) −0.164210 −0.00626046
\(689\) 0 0
\(690\) −0.664874 −0.0253113
\(691\) −2.01447 −0.0766342 −0.0383171 0.999266i \(-0.512200\pi\)
−0.0383171 + 0.999266i \(0.512200\pi\)
\(692\) −29.2223 −1.11087
\(693\) 0 0
\(694\) 1.20583 0.0457728
\(695\) −3.63235 −0.137783
\(696\) −28.0127 −1.06182
\(697\) −25.0248 −0.947880
\(698\) 11.3763 0.430598
\(699\) −6.87800 −0.260150
\(700\) 0 0
\(701\) −48.8189 −1.84387 −0.921933 0.387350i \(-0.873390\pi\)
−0.921933 + 0.387350i \(0.873390\pi\)
\(702\) 0 0
\(703\) 0.501729 0.0189231
\(704\) −15.1390 −0.570572
\(705\) −4.08277 −0.153766
\(706\) 5.74871 0.216355
\(707\) 0 0
\(708\) −20.6722 −0.776908
\(709\) −20.8060 −0.781385 −0.390693 0.920521i \(-0.627764\pi\)
−0.390693 + 0.920521i \(0.627764\pi\)
\(710\) 1.71618 0.0644073
\(711\) 20.4286 0.766134
\(712\) −7.76569 −0.291032
\(713\) 9.90648 0.371000
\(714\) 0 0
\(715\) 0 0
\(716\) −15.5133 −0.579761
\(717\) −56.5042 −2.11019
\(718\) 15.9468 0.595128
\(719\) −21.4306 −0.799225 −0.399613 0.916684i \(-0.630855\pi\)
−0.399613 + 0.916684i \(0.630855\pi\)
\(720\) −0.280831 −0.0104660
\(721\) 0 0
\(722\) −15.2306 −0.566824
\(723\) 45.5381 1.69358
\(724\) 28.4547 1.05751
\(725\) −22.8726 −0.849468
\(726\) 12.6799 0.470597
\(727\) −13.4862 −0.500175 −0.250088 0.968223i \(-0.580459\pi\)
−0.250088 + 0.968223i \(0.580459\pi\)
\(728\) 0 0
\(729\) −8.02715 −0.297302
\(730\) 1.33406 0.0493758
\(731\) 0.638792 0.0236266
\(732\) 10.5864 0.391285
\(733\) 43.5424 1.60828 0.804138 0.594443i \(-0.202627\pi\)
0.804138 + 0.594443i \(0.202627\pi\)
\(734\) −0.869167 −0.0320816
\(735\) 0 0
\(736\) 8.70841 0.320996
\(737\) −32.6165 −1.20145
\(738\) 19.0465 0.701112
\(739\) 20.0543 0.737709 0.368855 0.929487i \(-0.379750\pi\)
0.368855 + 0.929487i \(0.379750\pi\)
\(740\) 1.90754 0.0701226
\(741\) 0 0
\(742\) 0 0
\(743\) −33.1685 −1.21684 −0.608418 0.793617i \(-0.708195\pi\)
−0.608418 + 0.793617i \(0.708195\pi\)
\(744\) −40.1105 −1.47052
\(745\) −1.07069 −0.0392270
\(746\) −4.91617 −0.179994
\(747\) −3.29722 −0.120639
\(748\) −12.4407 −0.454878
\(749\) 0 0
\(750\) 4.42327 0.161515
\(751\) 39.2814 1.43340 0.716700 0.697382i \(-0.245652\pi\)
0.716700 + 0.697382i \(0.245652\pi\)
\(752\) 4.08277 0.148883
\(753\) 53.3008 1.94239
\(754\) 0 0
\(755\) −0.974181 −0.0354541
\(756\) 0 0
\(757\) −46.6426 −1.69526 −0.847628 0.530592i \(-0.821970\pi\)
−0.847628 + 0.530592i \(0.821970\pi\)
\(758\) −1.93171 −0.0701627
\(759\) −14.2567 −0.517484
\(760\) 0.0586060 0.00212586
\(761\) 21.8984 0.793818 0.396909 0.917858i \(-0.370083\pi\)
0.396909 + 0.917858i \(0.370083\pi\)
\(762\) −17.6722 −0.640195
\(763\) 0 0
\(764\) 19.5899 0.708737
\(765\) 1.09246 0.0394979
\(766\) 24.3720 0.880595
\(767\) 0 0
\(768\) −31.8756 −1.15021
\(769\) −46.7096 −1.68439 −0.842196 0.539172i \(-0.818737\pi\)
−0.842196 + 0.539172i \(0.818737\pi\)
\(770\) 0 0
\(771\) −31.9614 −1.15106
\(772\) 18.4263 0.663175
\(773\) 30.2416 1.08771 0.543857 0.839178i \(-0.316963\pi\)
0.543857 + 0.839178i \(0.316963\pi\)
\(774\) −0.486189 −0.0174757
\(775\) −32.7506 −1.17644
\(776\) −21.6939 −0.778767
\(777\) 0 0
\(778\) −12.7836 −0.458315
\(779\) 1.02177 0.0366087
\(780\) 0 0
\(781\) 36.7995 1.31679
\(782\) −2.58642 −0.0924901
\(783\) −9.89679 −0.353682
\(784\) 0 0
\(785\) 1.10023 0.0392688
\(786\) 11.8509 0.422706
\(787\) −28.7023 −1.02313 −0.511563 0.859246i \(-0.670933\pi\)
−0.511563 + 0.859246i \(0.670933\pi\)
\(788\) 0.760316 0.0270851
\(789\) −38.4131 −1.36754
\(790\) −1.97477 −0.0702592
\(791\) 0 0
\(792\) 23.4252 0.832378
\(793\) 0 0
\(794\) −13.5646 −0.481391
\(795\) 5.76809 0.204573
\(796\) 15.5929 0.552674
\(797\) 18.5418 0.656785 0.328392 0.944541i \(-0.393493\pi\)
0.328392 + 0.944541i \(0.393493\pi\)
\(798\) 0 0
\(799\) −15.8823 −0.561876
\(800\) −28.7899 −1.01788
\(801\) 5.91053 0.208838
\(802\) 21.3817 0.755012
\(803\) 28.6058 1.00948
\(804\) −23.4155 −0.825801
\(805\) 0 0
\(806\) 0 0
\(807\) 14.5308 0.511508
\(808\) −35.9506 −1.26474
\(809\) −10.0677 −0.353962 −0.176981 0.984214i \(-0.556633\pi\)
−0.176981 + 0.984214i \(0.556633\pi\)
\(810\) 2.16852 0.0761941
\(811\) 10.0285 0.352147 0.176074 0.984377i \(-0.443660\pi\)
0.176074 + 0.984377i \(0.443660\pi\)
\(812\) 0 0
\(813\) −14.4886 −0.508137
\(814\) −19.3860 −0.679478
\(815\) −3.99090 −0.139795
\(816\) −2.69202 −0.0942396
\(817\) −0.0260821 −0.000912498 0
\(818\) −22.8683 −0.799572
\(819\) 0 0
\(820\) 3.88471 0.135660
\(821\) −26.1704 −0.913355 −0.456677 0.889632i \(-0.650961\pi\)
−0.456677 + 0.889632i \(0.650961\pi\)
\(822\) 11.2078 0.390915
\(823\) 1.82238 0.0635242 0.0317621 0.999495i \(-0.489888\pi\)
0.0317621 + 0.999495i \(0.489888\pi\)
\(824\) 3.66727 0.127755
\(825\) 47.1323 1.64094
\(826\) 0 0
\(827\) −32.2941 −1.12298 −0.561488 0.827485i \(-0.689771\pi\)
−0.561488 + 0.827485i \(0.689771\pi\)
\(828\) −4.15346 −0.144343
\(829\) −15.1002 −0.524453 −0.262226 0.965006i \(-0.584457\pi\)
−0.262226 + 0.965006i \(0.584457\pi\)
\(830\) 0.318732 0.0110634
\(831\) 30.2446 1.04917
\(832\) 0 0
\(833\) 0 0
\(834\) 26.5013 0.917663
\(835\) 3.98062 0.137755
\(836\) 0.507960 0.0175682
\(837\) −14.1709 −0.489818
\(838\) 23.7448 0.820250
\(839\) 32.9965 1.13917 0.569584 0.821933i \(-0.307104\pi\)
0.569584 + 0.821933i \(0.307104\pi\)
\(840\) 0 0
\(841\) −7.55363 −0.260470
\(842\) −9.35105 −0.322258
\(843\) 11.3177 0.389801
\(844\) −11.9196 −0.410290
\(845\) 0 0
\(846\) 12.0881 0.415599
\(847\) 0 0
\(848\) −5.76809 −0.198077
\(849\) −49.7211 −1.70642
\(850\) 8.55065 0.293285
\(851\) 8.50365 0.291501
\(852\) 26.4185 0.905082
\(853\) 37.7802 1.29357 0.646784 0.762673i \(-0.276113\pi\)
0.646784 + 0.762673i \(0.276113\pi\)
\(854\) 0 0
\(855\) −0.0446055 −0.00152547
\(856\) −8.79954 −0.300762
\(857\) −27.3623 −0.934677 −0.467339 0.884078i \(-0.654787\pi\)
−0.467339 + 0.884078i \(0.654787\pi\)
\(858\) 0 0
\(859\) 20.0629 0.684538 0.342269 0.939602i \(-0.388805\pi\)
0.342269 + 0.939602i \(0.388805\pi\)
\(860\) −0.0991626 −0.00338142
\(861\) 0 0
\(862\) 3.48773 0.118792
\(863\) −6.14483 −0.209173 −0.104586 0.994516i \(-0.533352\pi\)
−0.104586 + 0.994516i \(0.533352\pi\)
\(864\) −12.4571 −0.423800
\(865\) −5.31900 −0.180851
\(866\) 11.5386 0.392096
\(867\) −27.7265 −0.941640
\(868\) 0 0
\(869\) −42.3443 −1.43643
\(870\) −2.06100 −0.0698744
\(871\) 0 0
\(872\) −42.2693 −1.43142
\(873\) 16.5114 0.558827
\(874\) 0.105604 0.00357212
\(875\) 0 0
\(876\) 20.5362 0.693853
\(877\) −13.5077 −0.456123 −0.228061 0.973647i \(-0.573239\pi\)
−0.228061 + 0.973647i \(0.573239\pi\)
\(878\) 16.2252 0.547574
\(879\) −33.5840 −1.13276
\(880\) 0.582105 0.0196228
\(881\) 5.23431 0.176348 0.0881741 0.996105i \(-0.471897\pi\)
0.0881741 + 0.996105i \(0.471897\pi\)
\(882\) 0 0
\(883\) −4.57301 −0.153894 −0.0769470 0.997035i \(-0.524517\pi\)
−0.0769470 + 0.997035i \(0.524517\pi\)
\(884\) 0 0
\(885\) −3.76271 −0.126482
\(886\) 6.51334 0.218820
\(887\) 1.64071 0.0550897 0.0275448 0.999621i \(-0.491231\pi\)
0.0275448 + 0.999621i \(0.491231\pi\)
\(888\) −34.4306 −1.15541
\(889\) 0 0
\(890\) −0.571352 −0.0191517
\(891\) 46.4989 1.55777
\(892\) −3.06531 −0.102634
\(893\) 0.648481 0.0217006
\(894\) 7.81163 0.261260
\(895\) −2.82371 −0.0943861
\(896\) 0 0
\(897\) 0 0
\(898\) 10.0175 0.334287
\(899\) 30.7084 1.02418
\(900\) 13.7313 0.457708
\(901\) 22.4383 0.747529
\(902\) −39.4795 −1.31452
\(903\) 0 0
\(904\) −32.4359 −1.07880
\(905\) 5.17928 0.172165
\(906\) 7.10752 0.236132
\(907\) 8.10215 0.269027 0.134514 0.990912i \(-0.457053\pi\)
0.134514 + 0.990912i \(0.457053\pi\)
\(908\) −9.45234 −0.313687
\(909\) 27.3623 0.907549
\(910\) 0 0
\(911\) −9.18119 −0.304187 −0.152093 0.988366i \(-0.548601\pi\)
−0.152093 + 0.988366i \(0.548601\pi\)
\(912\) 0.109916 0.00363969
\(913\) 6.83446 0.226188
\(914\) 4.79656 0.158656
\(915\) 1.92692 0.0637020
\(916\) −32.8015 −1.08379
\(917\) 0 0
\(918\) 3.69979 0.122111
\(919\) 27.5036 0.907262 0.453631 0.891190i \(-0.350128\pi\)
0.453631 + 0.891190i \(0.350128\pi\)
\(920\) 0.993295 0.0327480
\(921\) −42.9831 −1.41634
\(922\) 1.64933 0.0543180
\(923\) 0 0
\(924\) 0 0
\(925\) −28.1129 −0.924346
\(926\) −6.77586 −0.222668
\(927\) −2.79118 −0.0916745
\(928\) 26.9946 0.886142
\(929\) −24.2131 −0.794407 −0.397203 0.917731i \(-0.630019\pi\)
−0.397203 + 0.917731i \(0.630019\pi\)
\(930\) −2.95108 −0.0967698
\(931\) 0 0
\(932\) 4.15346 0.136051
\(933\) 0.606268 0.0198483
\(934\) −26.8761 −0.879412
\(935\) −2.26444 −0.0740550
\(936\) 0 0
\(937\) −11.1830 −0.365333 −0.182666 0.983175i \(-0.558473\pi\)
−0.182666 + 0.983175i \(0.558473\pi\)
\(938\) 0 0
\(939\) 52.5652 1.71540
\(940\) 2.46548 0.0804152
\(941\) 15.9638 0.520404 0.260202 0.965554i \(-0.416211\pi\)
0.260202 + 0.965554i \(0.416211\pi\)
\(942\) −8.02715 −0.261539
\(943\) 17.3177 0.563941
\(944\) 3.76271 0.122466
\(945\) 0 0
\(946\) 1.00777 0.0327654
\(947\) 6.51466 0.211698 0.105849 0.994382i \(-0.466244\pi\)
0.105849 + 0.994382i \(0.466244\pi\)
\(948\) −30.3991 −0.987317
\(949\) 0 0
\(950\) −0.349126 −0.0113271
\(951\) −31.4470 −1.01974
\(952\) 0 0
\(953\) 47.6469 1.54344 0.771718 0.635965i \(-0.219398\pi\)
0.771718 + 0.635965i \(0.219398\pi\)
\(954\) −17.0780 −0.552920
\(955\) 3.56571 0.115384
\(956\) 34.1215 1.10357
\(957\) −44.1933 −1.42857
\(958\) 19.8329 0.640773
\(959\) 0 0
\(960\) −1.97823 −0.0638471
\(961\) 12.9705 0.418402
\(962\) 0 0
\(963\) 6.69740 0.215821
\(964\) −27.4993 −0.885694
\(965\) 3.35391 0.107966
\(966\) 0 0
\(967\) −43.8122 −1.40891 −0.704453 0.709751i \(-0.748808\pi\)
−0.704453 + 0.709751i \(0.748808\pi\)
\(968\) −18.9433 −0.608861
\(969\) −0.427583 −0.0137360
\(970\) −1.59611 −0.0512479
\(971\) −4.29483 −0.137828 −0.0689139 0.997623i \(-0.521953\pi\)
−0.0689139 + 0.997623i \(0.521953\pi\)
\(972\) 24.6823 0.791686
\(973\) 0 0
\(974\) −30.2776 −0.970156
\(975\) 0 0
\(976\) −1.92692 −0.0616792
\(977\) 26.8019 0.857470 0.428735 0.903430i \(-0.358959\pi\)
0.428735 + 0.903430i \(0.358959\pi\)
\(978\) 29.1172 0.931066
\(979\) −12.2513 −0.391553
\(980\) 0 0
\(981\) 32.1715 1.02716
\(982\) 25.1094 0.801275
\(983\) −27.2495 −0.869124 −0.434562 0.900642i \(-0.643097\pi\)
−0.434562 + 0.900642i \(0.643097\pi\)
\(984\) −70.1178 −2.23527
\(985\) 0.138391 0.00440951
\(986\) −8.01746 −0.255328
\(987\) 0 0
\(988\) 0 0
\(989\) −0.442058 −0.0140566
\(990\) 1.72348 0.0547758
\(991\) 24.3889 0.774740 0.387370 0.921924i \(-0.373384\pi\)
0.387370 + 0.921924i \(0.373384\pi\)
\(992\) 38.6528 1.22723
\(993\) 40.0441 1.27076
\(994\) 0 0
\(995\) 2.83818 0.0899764
\(996\) 4.90648 0.155468
\(997\) −31.3207 −0.991935 −0.495967 0.868341i \(-0.665186\pi\)
−0.495967 + 0.868341i \(0.665186\pi\)
\(998\) 17.2314 0.545452
\(999\) −12.1642 −0.384859
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.bf.1.3 3
7.6 odd 2 169.2.a.b.1.3 3
13.12 even 2 8281.2.a.bj.1.1 3
21.20 even 2 1521.2.a.r.1.1 3
28.27 even 2 2704.2.a.z.1.3 3
35.34 odd 2 4225.2.a.bg.1.1 3
91.6 even 12 169.2.e.b.23.2 12
91.20 even 12 169.2.e.b.23.5 12
91.34 even 4 169.2.b.b.168.5 6
91.41 even 12 169.2.e.b.147.5 12
91.48 odd 6 169.2.c.c.146.1 6
91.55 odd 6 169.2.c.c.22.1 6
91.62 odd 6 169.2.c.b.22.3 6
91.69 odd 6 169.2.c.b.146.3 6
91.76 even 12 169.2.e.b.147.2 12
91.83 even 4 169.2.b.b.168.2 6
91.90 odd 2 169.2.a.c.1.1 yes 3
273.83 odd 4 1521.2.b.l.1351.5 6
273.125 odd 4 1521.2.b.l.1351.2 6
273.272 even 2 1521.2.a.o.1.3 3
364.83 odd 4 2704.2.f.o.337.5 6
364.307 odd 4 2704.2.f.o.337.6 6
364.363 even 2 2704.2.a.ba.1.3 3
455.454 odd 2 4225.2.a.bb.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.a.b.1.3 3 7.6 odd 2
169.2.a.c.1.1 yes 3 91.90 odd 2
169.2.b.b.168.2 6 91.83 even 4
169.2.b.b.168.5 6 91.34 even 4
169.2.c.b.22.3 6 91.62 odd 6
169.2.c.b.146.3 6 91.69 odd 6
169.2.c.c.22.1 6 91.55 odd 6
169.2.c.c.146.1 6 91.48 odd 6
169.2.e.b.23.2 12 91.6 even 12
169.2.e.b.23.5 12 91.20 even 12
169.2.e.b.147.2 12 91.76 even 12
169.2.e.b.147.5 12 91.41 even 12
1521.2.a.o.1.3 3 273.272 even 2
1521.2.a.r.1.1 3 21.20 even 2
1521.2.b.l.1351.2 6 273.125 odd 4
1521.2.b.l.1351.5 6 273.83 odd 4
2704.2.a.z.1.3 3 28.27 even 2
2704.2.a.ba.1.3 3 364.363 even 2
2704.2.f.o.337.5 6 364.83 odd 4
2704.2.f.o.337.6 6 364.307 odd 4
4225.2.a.bb.1.3 3 455.454 odd 2
4225.2.a.bg.1.1 3 35.34 odd 2
8281.2.a.bf.1.3 3 1.1 even 1 trivial
8281.2.a.bj.1.1 3 13.12 even 2