Properties

Label 6039.2.a.c.1.10
Level $6039$
Weight $2$
Character 6039.1
Self dual yes
Analytic conductor $48.222$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6039,2,Mod(1,6039)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6039.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6039.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: \(48.2216577807\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 66x^{7} - 125x^{6} - 115x^{5} + 227x^{4} + 40x^{3} - 129x^{2} + 26x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2013)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.05394\) of defining polynomial
Character \(\chi\) \(=\) 6039.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.05394 q^{2} +2.21866 q^{4} +0.0248942 q^{5} +1.52855 q^{7} +0.449108 q^{8} +O(q^{10})\) \(q+2.05394 q^{2} +2.21866 q^{4} +0.0248942 q^{5} +1.52855 q^{7} +0.449108 q^{8} +0.0511312 q^{10} -1.00000 q^{11} -2.02531 q^{13} +3.13954 q^{14} -3.51487 q^{16} -4.80386 q^{17} -3.29218 q^{19} +0.0552317 q^{20} -2.05394 q^{22} +1.24741 q^{23} -4.99938 q^{25} -4.15986 q^{26} +3.39132 q^{28} +8.92727 q^{29} +5.62645 q^{31} -8.11755 q^{32} -9.86683 q^{34} +0.0380520 q^{35} -6.88845 q^{37} -6.76194 q^{38} +0.0111802 q^{40} -8.93150 q^{41} -6.34956 q^{43} -2.21866 q^{44} +2.56209 q^{46} -4.19274 q^{47} -4.66354 q^{49} -10.2684 q^{50} -4.49347 q^{52} +3.56791 q^{53} -0.0248942 q^{55} +0.686483 q^{56} +18.3360 q^{58} -1.96110 q^{59} +1.00000 q^{61} +11.5564 q^{62} -9.64318 q^{64} -0.0504185 q^{65} -2.12656 q^{67} -10.6581 q^{68} +0.0781565 q^{70} -8.06823 q^{71} +0.798991 q^{73} -14.1484 q^{74} -7.30423 q^{76} -1.52855 q^{77} -0.406283 q^{79} -0.0875001 q^{80} -18.3447 q^{82} +1.36890 q^{83} -0.119588 q^{85} -13.0416 q^{86} -0.449108 q^{88} +8.42620 q^{89} -3.09579 q^{91} +2.76757 q^{92} -8.61163 q^{94} -0.0819564 q^{95} +15.8144 q^{97} -9.57862 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 2 q^{2} + 10 q^{4} + q^{5} - 11 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 2 q^{2} + 10 q^{4} + q^{5} - 11 q^{7} + 3 q^{8} - 8 q^{10} - 11 q^{11} - 13 q^{13} - 5 q^{14} + 4 q^{16} + 13 q^{17} - 12 q^{19} + 7 q^{20} - 2 q^{22} + 3 q^{23} + 12 q^{25} - 12 q^{26} - 13 q^{28} - 2 q^{29} + q^{31} + 23 q^{32} - 14 q^{34} + 4 q^{35} - 14 q^{37} + 8 q^{38} - 34 q^{40} - 3 q^{41} - 21 q^{43} - 10 q^{44} - 12 q^{46} + 16 q^{47} - 18 q^{49} + 13 q^{50} - 33 q^{52} - q^{55} - 16 q^{56} - 17 q^{58} - 3 q^{59} + 11 q^{61} + 21 q^{62} - 7 q^{64} + q^{65} - 24 q^{67} - 2 q^{68} + 4 q^{70} - 7 q^{71} - 42 q^{73} + 16 q^{74} - 13 q^{76} + 11 q^{77} - 11 q^{79} - 42 q^{80} - 38 q^{82} + 34 q^{83} - 14 q^{85} - 42 q^{86} - 3 q^{88} - 29 q^{89} + 9 q^{91} - 42 q^{92} - 33 q^{94} + 31 q^{95} - 45 q^{97} + 33 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.05394 1.45235 0.726176 0.687508i \(-0.241296\pi\)
0.726176 + 0.687508i \(0.241296\pi\)
\(3\) 0 0
\(4\) 2.21866 1.10933
\(5\) 0.0248942 0.0111330 0.00556652 0.999985i \(-0.498228\pi\)
0.00556652 + 0.999985i \(0.498228\pi\)
\(6\) 0 0
\(7\) 1.52855 0.577737 0.288868 0.957369i \(-0.406721\pi\)
0.288868 + 0.957369i \(0.406721\pi\)
\(8\) 0.449108 0.158784
\(9\) 0 0
\(10\) 0.0511312 0.0161691
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −2.02531 −0.561720 −0.280860 0.959749i \(-0.590620\pi\)
−0.280860 + 0.959749i \(0.590620\pi\)
\(14\) 3.13954 0.839078
\(15\) 0 0
\(16\) −3.51487 −0.878719
\(17\) −4.80386 −1.16511 −0.582554 0.812792i \(-0.697947\pi\)
−0.582554 + 0.812792i \(0.697947\pi\)
\(18\) 0 0
\(19\) −3.29218 −0.755279 −0.377639 0.925953i \(-0.623264\pi\)
−0.377639 + 0.925953i \(0.623264\pi\)
\(20\) 0.0552317 0.0123502
\(21\) 0 0
\(22\) −2.05394 −0.437901
\(23\) 1.24741 0.260102 0.130051 0.991507i \(-0.458486\pi\)
0.130051 + 0.991507i \(0.458486\pi\)
\(24\) 0 0
\(25\) −4.99938 −0.999876
\(26\) −4.15986 −0.815816
\(27\) 0 0
\(28\) 3.39132 0.640900
\(29\) 8.92727 1.65775 0.828876 0.559433i \(-0.188981\pi\)
0.828876 + 0.559433i \(0.188981\pi\)
\(30\) 0 0
\(31\) 5.62645 1.01054 0.505270 0.862961i \(-0.331393\pi\)
0.505270 + 0.862961i \(0.331393\pi\)
\(32\) −8.11755 −1.43499
\(33\) 0 0
\(34\) −9.86683 −1.69215
\(35\) 0.0380520 0.00643197
\(36\) 0 0
\(37\) −6.88845 −1.13245 −0.566227 0.824249i \(-0.691597\pi\)
−0.566227 + 0.824249i \(0.691597\pi\)
\(38\) −6.76194 −1.09693
\(39\) 0 0
\(40\) 0.0111802 0.00176774
\(41\) −8.93150 −1.39487 −0.697433 0.716650i \(-0.745674\pi\)
−0.697433 + 0.716650i \(0.745674\pi\)
\(42\) 0 0
\(43\) −6.34956 −0.968298 −0.484149 0.874986i \(-0.660871\pi\)
−0.484149 + 0.874986i \(0.660871\pi\)
\(44\) −2.21866 −0.334475
\(45\) 0 0
\(46\) 2.56209 0.377760
\(47\) −4.19274 −0.611574 −0.305787 0.952100i \(-0.598920\pi\)
−0.305787 + 0.952100i \(0.598920\pi\)
\(48\) 0 0
\(49\) −4.66354 −0.666220
\(50\) −10.2684 −1.45217
\(51\) 0 0
\(52\) −4.49347 −0.623132
\(53\) 3.56791 0.490090 0.245045 0.969512i \(-0.421197\pi\)
0.245045 + 0.969512i \(0.421197\pi\)
\(54\) 0 0
\(55\) −0.0248942 −0.00335674
\(56\) 0.686483 0.0917352
\(57\) 0 0
\(58\) 18.3360 2.40764
\(59\) −1.96110 −0.255314 −0.127657 0.991818i \(-0.540746\pi\)
−0.127657 + 0.991818i \(0.540746\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) 11.5564 1.46766
\(63\) 0 0
\(64\) −9.64318 −1.20540
\(65\) −0.0504185 −0.00625365
\(66\) 0 0
\(67\) −2.12656 −0.259801 −0.129900 0.991527i \(-0.541466\pi\)
−0.129900 + 0.991527i \(0.541466\pi\)
\(68\) −10.6581 −1.29249
\(69\) 0 0
\(70\) 0.0781565 0.00934148
\(71\) −8.06823 −0.957523 −0.478761 0.877945i \(-0.658914\pi\)
−0.478761 + 0.877945i \(0.658914\pi\)
\(72\) 0 0
\(73\) 0.798991 0.0935148 0.0467574 0.998906i \(-0.485111\pi\)
0.0467574 + 0.998906i \(0.485111\pi\)
\(74\) −14.1484 −1.64472
\(75\) 0 0
\(76\) −7.30423 −0.837852
\(77\) −1.52855 −0.174194
\(78\) 0 0
\(79\) −0.406283 −0.0457104 −0.0228552 0.999739i \(-0.507276\pi\)
−0.0228552 + 0.999739i \(0.507276\pi\)
\(80\) −0.0875001 −0.00978281
\(81\) 0 0
\(82\) −18.3447 −2.02584
\(83\) 1.36890 0.150256 0.0751279 0.997174i \(-0.476063\pi\)
0.0751279 + 0.997174i \(0.476063\pi\)
\(84\) 0 0
\(85\) −0.119588 −0.0129712
\(86\) −13.0416 −1.40631
\(87\) 0 0
\(88\) −0.449108 −0.0478751
\(89\) 8.42620 0.893175 0.446588 0.894740i \(-0.352639\pi\)
0.446588 + 0.894740i \(0.352639\pi\)
\(90\) 0 0
\(91\) −3.09579 −0.324527
\(92\) 2.76757 0.288539
\(93\) 0 0
\(94\) −8.61163 −0.888221
\(95\) −0.0819564 −0.00840854
\(96\) 0 0
\(97\) 15.8144 1.60571 0.802854 0.596176i \(-0.203314\pi\)
0.802854 + 0.596176i \(0.203314\pi\)
\(98\) −9.57862 −0.967586
\(99\) 0 0
\(100\) −11.0919 −1.10919
\(101\) −2.04802 −0.203785 −0.101893 0.994795i \(-0.532490\pi\)
−0.101893 + 0.994795i \(0.532490\pi\)
\(102\) 0 0
\(103\) −3.41108 −0.336103 −0.168052 0.985778i \(-0.553748\pi\)
−0.168052 + 0.985778i \(0.553748\pi\)
\(104\) −0.909584 −0.0891920
\(105\) 0 0
\(106\) 7.32826 0.711784
\(107\) 13.6931 1.32376 0.661880 0.749610i \(-0.269759\pi\)
0.661880 + 0.749610i \(0.269759\pi\)
\(108\) 0 0
\(109\) 0.997758 0.0955679 0.0477840 0.998858i \(-0.484784\pi\)
0.0477840 + 0.998858i \(0.484784\pi\)
\(110\) −0.0511312 −0.00487517
\(111\) 0 0
\(112\) −5.37266 −0.507668
\(113\) −11.2280 −1.05624 −0.528122 0.849168i \(-0.677104\pi\)
−0.528122 + 0.849168i \(0.677104\pi\)
\(114\) 0 0
\(115\) 0.0310532 0.00289573
\(116\) 19.8065 1.83899
\(117\) 0 0
\(118\) −4.02798 −0.370806
\(119\) −7.34294 −0.673126
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 2.05394 0.185955
\(123\) 0 0
\(124\) 12.4832 1.12102
\(125\) −0.248927 −0.0222647
\(126\) 0 0
\(127\) −21.3177 −1.89164 −0.945819 0.324695i \(-0.894738\pi\)
−0.945819 + 0.324695i \(0.894738\pi\)
\(128\) −3.57139 −0.315669
\(129\) 0 0
\(130\) −0.103557 −0.00908251
\(131\) 2.47278 0.216048 0.108024 0.994148i \(-0.465548\pi\)
0.108024 + 0.994148i \(0.465548\pi\)
\(132\) 0 0
\(133\) −5.03226 −0.436352
\(134\) −4.36782 −0.377322
\(135\) 0 0
\(136\) −2.15745 −0.185000
\(137\) 3.40578 0.290975 0.145488 0.989360i \(-0.453525\pi\)
0.145488 + 0.989360i \(0.453525\pi\)
\(138\) 0 0
\(139\) −20.0352 −1.69936 −0.849682 0.527295i \(-0.823206\pi\)
−0.849682 + 0.527295i \(0.823206\pi\)
\(140\) 0.0844244 0.00713516
\(141\) 0 0
\(142\) −16.5716 −1.39066
\(143\) 2.02531 0.169365
\(144\) 0 0
\(145\) 0.222237 0.0184558
\(146\) 1.64108 0.135817
\(147\) 0 0
\(148\) −15.2831 −1.25626
\(149\) −9.57828 −0.784683 −0.392341 0.919820i \(-0.628335\pi\)
−0.392341 + 0.919820i \(0.628335\pi\)
\(150\) 0 0
\(151\) 5.18531 0.421974 0.210987 0.977489i \(-0.432332\pi\)
0.210987 + 0.977489i \(0.432332\pi\)
\(152\) −1.47855 −0.119926
\(153\) 0 0
\(154\) −3.13954 −0.252992
\(155\) 0.140066 0.0112504
\(156\) 0 0
\(157\) −14.0899 −1.12450 −0.562248 0.826969i \(-0.690063\pi\)
−0.562248 + 0.826969i \(0.690063\pi\)
\(158\) −0.834480 −0.0663877
\(159\) 0 0
\(160\) −0.202080 −0.0159758
\(161\) 1.90672 0.150271
\(162\) 0 0
\(163\) −8.28468 −0.648906 −0.324453 0.945902i \(-0.605180\pi\)
−0.324453 + 0.945902i \(0.605180\pi\)
\(164\) −19.8159 −1.54736
\(165\) 0 0
\(166\) 2.81163 0.218225
\(167\) 1.28807 0.0996742 0.0498371 0.998757i \(-0.484130\pi\)
0.0498371 + 0.998757i \(0.484130\pi\)
\(168\) 0 0
\(169\) −8.89811 −0.684470
\(170\) −0.245627 −0.0188387
\(171\) 0 0
\(172\) −14.0875 −1.07416
\(173\) 9.44976 0.718452 0.359226 0.933251i \(-0.383041\pi\)
0.359226 + 0.933251i \(0.383041\pi\)
\(174\) 0 0
\(175\) −7.64179 −0.577665
\(176\) 3.51487 0.264944
\(177\) 0 0
\(178\) 17.3069 1.29721
\(179\) 2.21840 0.165811 0.0829057 0.996557i \(-0.473580\pi\)
0.0829057 + 0.996557i \(0.473580\pi\)
\(180\) 0 0
\(181\) 2.94663 0.219021 0.109511 0.993986i \(-0.465072\pi\)
0.109511 + 0.993986i \(0.465072\pi\)
\(182\) −6.35855 −0.471327
\(183\) 0 0
\(184\) 0.560220 0.0413000
\(185\) −0.171483 −0.0126076
\(186\) 0 0
\(187\) 4.80386 0.351293
\(188\) −9.30226 −0.678437
\(189\) 0 0
\(190\) −0.168333 −0.0122122
\(191\) 16.3873 1.18574 0.592870 0.805298i \(-0.297995\pi\)
0.592870 + 0.805298i \(0.297995\pi\)
\(192\) 0 0
\(193\) 6.43974 0.463543 0.231771 0.972770i \(-0.425548\pi\)
0.231771 + 0.972770i \(0.425548\pi\)
\(194\) 32.4817 2.33205
\(195\) 0 0
\(196\) −10.3468 −0.739057
\(197\) 11.9244 0.849576 0.424788 0.905293i \(-0.360349\pi\)
0.424788 + 0.905293i \(0.360349\pi\)
\(198\) 0 0
\(199\) 1.99146 0.141171 0.0705853 0.997506i \(-0.477513\pi\)
0.0705853 + 0.997506i \(0.477513\pi\)
\(200\) −2.24526 −0.158764
\(201\) 0 0
\(202\) −4.20650 −0.295968
\(203\) 13.6458 0.957744
\(204\) 0 0
\(205\) −0.222343 −0.0155291
\(206\) −7.00613 −0.488140
\(207\) 0 0
\(208\) 7.11871 0.493594
\(209\) 3.29218 0.227725
\(210\) 0 0
\(211\) −0.541369 −0.0372694 −0.0186347 0.999826i \(-0.505932\pi\)
−0.0186347 + 0.999826i \(0.505932\pi\)
\(212\) 7.91597 0.543671
\(213\) 0 0
\(214\) 28.1247 1.92257
\(215\) −0.158067 −0.0107801
\(216\) 0 0
\(217\) 8.60030 0.583827
\(218\) 2.04933 0.138798
\(219\) 0 0
\(220\) −0.0552317 −0.00372372
\(221\) 9.72932 0.654465
\(222\) 0 0
\(223\) −13.3029 −0.890826 −0.445413 0.895325i \(-0.646943\pi\)
−0.445413 + 0.895325i \(0.646943\pi\)
\(224\) −12.4081 −0.829049
\(225\) 0 0
\(226\) −23.0617 −1.53404
\(227\) 6.94528 0.460974 0.230487 0.973075i \(-0.425968\pi\)
0.230487 + 0.973075i \(0.425968\pi\)
\(228\) 0 0
\(229\) 18.1019 1.19621 0.598105 0.801418i \(-0.295921\pi\)
0.598105 + 0.801418i \(0.295921\pi\)
\(230\) 0.0637813 0.00420561
\(231\) 0 0
\(232\) 4.00931 0.263224
\(233\) 8.79705 0.576314 0.288157 0.957583i \(-0.406957\pi\)
0.288157 + 0.957583i \(0.406957\pi\)
\(234\) 0 0
\(235\) −0.104375 −0.00680868
\(236\) −4.35102 −0.283227
\(237\) 0 0
\(238\) −15.0819 −0.977616
\(239\) 2.68814 0.173881 0.0869407 0.996213i \(-0.472291\pi\)
0.0869407 + 0.996213i \(0.472291\pi\)
\(240\) 0 0
\(241\) 15.9889 1.02993 0.514967 0.857210i \(-0.327804\pi\)
0.514967 + 0.857210i \(0.327804\pi\)
\(242\) 2.05394 0.132032
\(243\) 0 0
\(244\) 2.21866 0.142035
\(245\) −0.116095 −0.00741705
\(246\) 0 0
\(247\) 6.66770 0.424255
\(248\) 2.52688 0.160457
\(249\) 0 0
\(250\) −0.511280 −0.0323362
\(251\) 7.34500 0.463612 0.231806 0.972762i \(-0.425537\pi\)
0.231806 + 0.972762i \(0.425537\pi\)
\(252\) 0 0
\(253\) −1.24741 −0.0784237
\(254\) −43.7852 −2.74733
\(255\) 0 0
\(256\) 11.9509 0.746934
\(257\) 18.7759 1.17121 0.585604 0.810597i \(-0.300857\pi\)
0.585604 + 0.810597i \(0.300857\pi\)
\(258\) 0 0
\(259\) −10.5293 −0.654260
\(260\) −0.111861 −0.00693735
\(261\) 0 0
\(262\) 5.07893 0.313777
\(263\) 12.4646 0.768600 0.384300 0.923208i \(-0.374443\pi\)
0.384300 + 0.923208i \(0.374443\pi\)
\(264\) 0 0
\(265\) 0.0888203 0.00545619
\(266\) −10.3359 −0.633738
\(267\) 0 0
\(268\) −4.71811 −0.288204
\(269\) −16.3747 −0.998385 −0.499192 0.866491i \(-0.666370\pi\)
−0.499192 + 0.866491i \(0.666370\pi\)
\(270\) 0 0
\(271\) −8.56788 −0.520461 −0.260231 0.965546i \(-0.583799\pi\)
−0.260231 + 0.965546i \(0.583799\pi\)
\(272\) 16.8850 1.02380
\(273\) 0 0
\(274\) 6.99525 0.422598
\(275\) 4.99938 0.301474
\(276\) 0 0
\(277\) −30.0553 −1.80585 −0.902923 0.429803i \(-0.858583\pi\)
−0.902923 + 0.429803i \(0.858583\pi\)
\(278\) −41.1511 −2.46808
\(279\) 0 0
\(280\) 0.0170895 0.00102129
\(281\) 19.5195 1.16444 0.582218 0.813033i \(-0.302185\pi\)
0.582218 + 0.813033i \(0.302185\pi\)
\(282\) 0 0
\(283\) −24.5866 −1.46152 −0.730762 0.682632i \(-0.760835\pi\)
−0.730762 + 0.682632i \(0.760835\pi\)
\(284\) −17.9006 −1.06221
\(285\) 0 0
\(286\) 4.15986 0.245978
\(287\) −13.6522 −0.805865
\(288\) 0 0
\(289\) 6.07711 0.357477
\(290\) 0.456461 0.0268043
\(291\) 0 0
\(292\) 1.77269 0.103739
\(293\) 8.52124 0.497816 0.248908 0.968527i \(-0.419928\pi\)
0.248908 + 0.968527i \(0.419928\pi\)
\(294\) 0 0
\(295\) −0.0488201 −0.00284242
\(296\) −3.09366 −0.179815
\(297\) 0 0
\(298\) −19.6732 −1.13964
\(299\) −2.52638 −0.146105
\(300\) 0 0
\(301\) −9.70560 −0.559422
\(302\) 10.6503 0.612856
\(303\) 0 0
\(304\) 11.5716 0.663678
\(305\) 0.0248942 0.00142544
\(306\) 0 0
\(307\) 6.29270 0.359143 0.179572 0.983745i \(-0.442529\pi\)
0.179572 + 0.983745i \(0.442529\pi\)
\(308\) −3.39132 −0.193239
\(309\) 0 0
\(310\) 0.287687 0.0163395
\(311\) −32.0080 −1.81500 −0.907502 0.420047i \(-0.862014\pi\)
−0.907502 + 0.420047i \(0.862014\pi\)
\(312\) 0 0
\(313\) −4.08898 −0.231123 −0.115561 0.993300i \(-0.536867\pi\)
−0.115561 + 0.993300i \(0.536867\pi\)
\(314\) −28.9398 −1.63316
\(315\) 0 0
\(316\) −0.901403 −0.0507079
\(317\) −17.3234 −0.972981 −0.486491 0.873686i \(-0.661723\pi\)
−0.486491 + 0.873686i \(0.661723\pi\)
\(318\) 0 0
\(319\) −8.92727 −0.499831
\(320\) −0.240059 −0.0134197
\(321\) 0 0
\(322\) 3.91628 0.218246
\(323\) 15.8152 0.879981
\(324\) 0 0
\(325\) 10.1253 0.561651
\(326\) −17.0162 −0.942440
\(327\) 0 0
\(328\) −4.01121 −0.221482
\(329\) −6.40881 −0.353329
\(330\) 0 0
\(331\) −8.06729 −0.443419 −0.221709 0.975113i \(-0.571164\pi\)
−0.221709 + 0.975113i \(0.571164\pi\)
\(332\) 3.03711 0.166683
\(333\) 0 0
\(334\) 2.64562 0.144762
\(335\) −0.0529391 −0.00289237
\(336\) 0 0
\(337\) −22.1813 −1.20829 −0.604146 0.796874i \(-0.706486\pi\)
−0.604146 + 0.796874i \(0.706486\pi\)
\(338\) −18.2762 −0.994092
\(339\) 0 0
\(340\) −0.265326 −0.0143893
\(341\) −5.62645 −0.304689
\(342\) 0 0
\(343\) −17.8283 −0.962637
\(344\) −2.85164 −0.153750
\(345\) 0 0
\(346\) 19.4092 1.04345
\(347\) −0.647734 −0.0347722 −0.0173861 0.999849i \(-0.505534\pi\)
−0.0173861 + 0.999849i \(0.505534\pi\)
\(348\) 0 0
\(349\) −9.79589 −0.524362 −0.262181 0.965019i \(-0.584442\pi\)
−0.262181 + 0.965019i \(0.584442\pi\)
\(350\) −15.6958 −0.838974
\(351\) 0 0
\(352\) 8.11755 0.432667
\(353\) 27.1957 1.44748 0.723740 0.690073i \(-0.242422\pi\)
0.723740 + 0.690073i \(0.242422\pi\)
\(354\) 0 0
\(355\) −0.200852 −0.0106601
\(356\) 18.6948 0.990825
\(357\) 0 0
\(358\) 4.55646 0.240817
\(359\) 17.1339 0.904292 0.452146 0.891944i \(-0.350659\pi\)
0.452146 + 0.891944i \(0.350659\pi\)
\(360\) 0 0
\(361\) −8.16153 −0.429554
\(362\) 6.05220 0.318096
\(363\) 0 0
\(364\) −6.86849 −0.360007
\(365\) 0.0198903 0.00104110
\(366\) 0 0
\(367\) 24.5299 1.28045 0.640226 0.768187i \(-0.278841\pi\)
0.640226 + 0.768187i \(0.278841\pi\)
\(368\) −4.38447 −0.228557
\(369\) 0 0
\(370\) −0.352214 −0.0183108
\(371\) 5.45372 0.283143
\(372\) 0 0
\(373\) −7.77613 −0.402633 −0.201316 0.979526i \(-0.564522\pi\)
−0.201316 + 0.979526i \(0.564522\pi\)
\(374\) 9.86683 0.510202
\(375\) 0 0
\(376\) −1.88299 −0.0971080
\(377\) −18.0805 −0.931193
\(378\) 0 0
\(379\) −26.8315 −1.37824 −0.689121 0.724646i \(-0.742003\pi\)
−0.689121 + 0.724646i \(0.742003\pi\)
\(380\) −0.181833 −0.00932784
\(381\) 0 0
\(382\) 33.6584 1.72211
\(383\) 1.73648 0.0887299 0.0443650 0.999015i \(-0.485874\pi\)
0.0443650 + 0.999015i \(0.485874\pi\)
\(384\) 0 0
\(385\) −0.0380520 −0.00193931
\(386\) 13.2268 0.673228
\(387\) 0 0
\(388\) 35.0867 1.78126
\(389\) −30.1018 −1.52622 −0.763112 0.646267i \(-0.776329\pi\)
−0.763112 + 0.646267i \(0.776329\pi\)
\(390\) 0 0
\(391\) −5.99237 −0.303047
\(392\) −2.09443 −0.105785
\(393\) 0 0
\(394\) 24.4919 1.23388
\(395\) −0.0101141 −0.000508896 0
\(396\) 0 0
\(397\) 18.5205 0.929516 0.464758 0.885438i \(-0.346141\pi\)
0.464758 + 0.885438i \(0.346141\pi\)
\(398\) 4.09033 0.205030
\(399\) 0 0
\(400\) 17.5722 0.878610
\(401\) −11.5890 −0.578728 −0.289364 0.957219i \(-0.593444\pi\)
−0.289364 + 0.957219i \(0.593444\pi\)
\(402\) 0 0
\(403\) −11.3953 −0.567641
\(404\) −4.54385 −0.226065
\(405\) 0 0
\(406\) 28.0275 1.39098
\(407\) 6.88845 0.341448
\(408\) 0 0
\(409\) 1.09585 0.0541861 0.0270930 0.999633i \(-0.491375\pi\)
0.0270930 + 0.999633i \(0.491375\pi\)
\(410\) −0.456678 −0.0225537
\(411\) 0 0
\(412\) −7.56801 −0.372849
\(413\) −2.99764 −0.147504
\(414\) 0 0
\(415\) 0.0340776 0.00167280
\(416\) 16.4406 0.806065
\(417\) 0 0
\(418\) 6.76194 0.330737
\(419\) −13.1872 −0.644237 −0.322118 0.946699i \(-0.604395\pi\)
−0.322118 + 0.946699i \(0.604395\pi\)
\(420\) 0 0
\(421\) 21.5730 1.05140 0.525702 0.850669i \(-0.323803\pi\)
0.525702 + 0.850669i \(0.323803\pi\)
\(422\) −1.11194 −0.0541283
\(423\) 0 0
\(424\) 1.60238 0.0778183
\(425\) 24.0163 1.16496
\(426\) 0 0
\(427\) 1.52855 0.0739716
\(428\) 30.3803 1.46848
\(429\) 0 0
\(430\) −0.324660 −0.0156565
\(431\) −30.9425 −1.49045 −0.745225 0.666813i \(-0.767658\pi\)
−0.745225 + 0.666813i \(0.767658\pi\)
\(432\) 0 0
\(433\) 12.9300 0.621375 0.310687 0.950512i \(-0.399441\pi\)
0.310687 + 0.950512i \(0.399441\pi\)
\(434\) 17.6645 0.847922
\(435\) 0 0
\(436\) 2.21368 0.106016
\(437\) −4.10669 −0.196450
\(438\) 0 0
\(439\) 0.331483 0.0158208 0.00791041 0.999969i \(-0.497482\pi\)
0.00791041 + 0.999969i \(0.497482\pi\)
\(440\) −0.0111802 −0.000532995 0
\(441\) 0 0
\(442\) 19.9834 0.950514
\(443\) −29.5889 −1.40581 −0.702905 0.711284i \(-0.748114\pi\)
−0.702905 + 0.711284i \(0.748114\pi\)
\(444\) 0 0
\(445\) 0.209764 0.00994375
\(446\) −27.3232 −1.29379
\(447\) 0 0
\(448\) −14.7401 −0.696403
\(449\) −11.4457 −0.540155 −0.270078 0.962839i \(-0.587049\pi\)
−0.270078 + 0.962839i \(0.587049\pi\)
\(450\) 0 0
\(451\) 8.93150 0.420568
\(452\) −24.9112 −1.17172
\(453\) 0 0
\(454\) 14.2652 0.669497
\(455\) −0.0770672 −0.00361297
\(456\) 0 0
\(457\) 24.4054 1.14164 0.570818 0.821076i \(-0.306626\pi\)
0.570818 + 0.821076i \(0.306626\pi\)
\(458\) 37.1802 1.73732
\(459\) 0 0
\(460\) 0.0688964 0.00321231
\(461\) −15.4119 −0.717805 −0.358902 0.933375i \(-0.616849\pi\)
−0.358902 + 0.933375i \(0.616849\pi\)
\(462\) 0 0
\(463\) 37.2404 1.73071 0.865354 0.501161i \(-0.167094\pi\)
0.865354 + 0.501161i \(0.167094\pi\)
\(464\) −31.3782 −1.45670
\(465\) 0 0
\(466\) 18.0686 0.837011
\(467\) −0.981164 −0.0454028 −0.0227014 0.999742i \(-0.507227\pi\)
−0.0227014 + 0.999742i \(0.507227\pi\)
\(468\) 0 0
\(469\) −3.25055 −0.150096
\(470\) −0.214380 −0.00988860
\(471\) 0 0
\(472\) −0.880748 −0.0405397
\(473\) 6.34956 0.291953
\(474\) 0 0
\(475\) 16.4589 0.755185
\(476\) −16.2915 −0.746718
\(477\) 0 0
\(478\) 5.52127 0.252537
\(479\) 13.9754 0.638551 0.319275 0.947662i \(-0.396561\pi\)
0.319275 + 0.947662i \(0.396561\pi\)
\(480\) 0 0
\(481\) 13.9512 0.636122
\(482\) 32.8402 1.49583
\(483\) 0 0
\(484\) 2.21866 0.100848
\(485\) 0.393687 0.0178764
\(486\) 0 0
\(487\) −40.3289 −1.82748 −0.913739 0.406302i \(-0.866818\pi\)
−0.913739 + 0.406302i \(0.866818\pi\)
\(488\) 0.449108 0.0203302
\(489\) 0 0
\(490\) −0.238452 −0.0107722
\(491\) 33.6200 1.51725 0.758624 0.651528i \(-0.225872\pi\)
0.758624 + 0.651528i \(0.225872\pi\)
\(492\) 0 0
\(493\) −42.8854 −1.93146
\(494\) 13.6950 0.616168
\(495\) 0 0
\(496\) −19.7763 −0.887981
\(497\) −12.3327 −0.553196
\(498\) 0 0
\(499\) 15.1473 0.678084 0.339042 0.940771i \(-0.389897\pi\)
0.339042 + 0.940771i \(0.389897\pi\)
\(500\) −0.552283 −0.0246989
\(501\) 0 0
\(502\) 15.0862 0.673328
\(503\) 4.36125 0.194458 0.0972292 0.995262i \(-0.469002\pi\)
0.0972292 + 0.995262i \(0.469002\pi\)
\(504\) 0 0
\(505\) −0.0509838 −0.00226875
\(506\) −2.56209 −0.113899
\(507\) 0 0
\(508\) −47.2966 −2.09845
\(509\) −35.0017 −1.55142 −0.775711 0.631088i \(-0.782609\pi\)
−0.775711 + 0.631088i \(0.782609\pi\)
\(510\) 0 0
\(511\) 1.22130 0.0540270
\(512\) 31.6893 1.40048
\(513\) 0 0
\(514\) 38.5645 1.70101
\(515\) −0.0849161 −0.00374185
\(516\) 0 0
\(517\) 4.19274 0.184397
\(518\) −21.6266 −0.950217
\(519\) 0 0
\(520\) −0.0226434 −0.000992978 0
\(521\) 2.82818 0.123905 0.0619525 0.998079i \(-0.480267\pi\)
0.0619525 + 0.998079i \(0.480267\pi\)
\(522\) 0 0
\(523\) 20.0491 0.876685 0.438343 0.898808i \(-0.355566\pi\)
0.438343 + 0.898808i \(0.355566\pi\)
\(524\) 5.48625 0.239668
\(525\) 0 0
\(526\) 25.6015 1.11628
\(527\) −27.0287 −1.17739
\(528\) 0 0
\(529\) −21.4440 −0.932347
\(530\) 0.182431 0.00792431
\(531\) 0 0
\(532\) −11.1649 −0.484058
\(533\) 18.0891 0.783524
\(534\) 0 0
\(535\) 0.340879 0.0147375
\(536\) −0.955055 −0.0412521
\(537\) 0 0
\(538\) −33.6327 −1.45001
\(539\) 4.66354 0.200873
\(540\) 0 0
\(541\) −8.48400 −0.364756 −0.182378 0.983229i \(-0.558379\pi\)
−0.182378 + 0.983229i \(0.558379\pi\)
\(542\) −17.5979 −0.755894
\(543\) 0 0
\(544\) 38.9956 1.67192
\(545\) 0.0248384 0.00106396
\(546\) 0 0
\(547\) 12.2600 0.524200 0.262100 0.965041i \(-0.415585\pi\)
0.262100 + 0.965041i \(0.415585\pi\)
\(548\) 7.55625 0.322787
\(549\) 0 0
\(550\) 10.2684 0.437847
\(551\) −29.3902 −1.25206
\(552\) 0 0
\(553\) −0.621023 −0.0264086
\(554\) −61.7316 −2.62272
\(555\) 0 0
\(556\) −44.4513 −1.88515
\(557\) 41.7817 1.77035 0.885173 0.465262i \(-0.154040\pi\)
0.885173 + 0.465262i \(0.154040\pi\)
\(558\) 0 0
\(559\) 12.8598 0.543913
\(560\) −0.133748 −0.00565189
\(561\) 0 0
\(562\) 40.0918 1.69117
\(563\) 26.3634 1.11108 0.555542 0.831489i \(-0.312511\pi\)
0.555542 + 0.831489i \(0.312511\pi\)
\(564\) 0 0
\(565\) −0.279513 −0.0117592
\(566\) −50.4994 −2.12265
\(567\) 0 0
\(568\) −3.62351 −0.152039
\(569\) −24.4218 −1.02381 −0.511907 0.859041i \(-0.671061\pi\)
−0.511907 + 0.859041i \(0.671061\pi\)
\(570\) 0 0
\(571\) 26.8587 1.12400 0.562001 0.827137i \(-0.310032\pi\)
0.562001 + 0.827137i \(0.310032\pi\)
\(572\) 4.49347 0.187881
\(573\) 0 0
\(574\) −28.0408 −1.17040
\(575\) −6.23625 −0.260070
\(576\) 0 0
\(577\) −11.6001 −0.482918 −0.241459 0.970411i \(-0.577626\pi\)
−0.241459 + 0.970411i \(0.577626\pi\)
\(578\) 12.4820 0.519182
\(579\) 0 0
\(580\) 0.493068 0.0204736
\(581\) 2.09242 0.0868084
\(582\) 0 0
\(583\) −3.56791 −0.147768
\(584\) 0.358833 0.0148486
\(585\) 0 0
\(586\) 17.5021 0.723004
\(587\) 46.5397 1.92090 0.960450 0.278453i \(-0.0898217\pi\)
0.960450 + 0.278453i \(0.0898217\pi\)
\(588\) 0 0
\(589\) −18.5233 −0.763240
\(590\) −0.100274 −0.00412819
\(591\) 0 0
\(592\) 24.2120 0.995108
\(593\) 44.6499 1.83355 0.916776 0.399401i \(-0.130782\pi\)
0.916776 + 0.399401i \(0.130782\pi\)
\(594\) 0 0
\(595\) −0.182797 −0.00749393
\(596\) −21.2509 −0.870471
\(597\) 0 0
\(598\) −5.18903 −0.212195
\(599\) 6.40412 0.261665 0.130833 0.991404i \(-0.458235\pi\)
0.130833 + 0.991404i \(0.458235\pi\)
\(600\) 0 0
\(601\) 5.94428 0.242472 0.121236 0.992624i \(-0.461314\pi\)
0.121236 + 0.992624i \(0.461314\pi\)
\(602\) −19.9347 −0.812478
\(603\) 0 0
\(604\) 11.5044 0.468108
\(605\) 0.0248942 0.00101209
\(606\) 0 0
\(607\) −7.84406 −0.318380 −0.159190 0.987248i \(-0.550888\pi\)
−0.159190 + 0.987248i \(0.550888\pi\)
\(608\) 26.7245 1.08382
\(609\) 0 0
\(610\) 0.0511312 0.00207024
\(611\) 8.49161 0.343534
\(612\) 0 0
\(613\) 24.7279 0.998749 0.499374 0.866386i \(-0.333563\pi\)
0.499374 + 0.866386i \(0.333563\pi\)
\(614\) 12.9248 0.521603
\(615\) 0 0
\(616\) −0.686483 −0.0276592
\(617\) 19.4795 0.784217 0.392108 0.919919i \(-0.371746\pi\)
0.392108 + 0.919919i \(0.371746\pi\)
\(618\) 0 0
\(619\) 29.5947 1.18951 0.594755 0.803907i \(-0.297249\pi\)
0.594755 + 0.803907i \(0.297249\pi\)
\(620\) 0.310759 0.0124804
\(621\) 0 0
\(622\) −65.7423 −2.63603
\(623\) 12.8798 0.516020
\(624\) 0 0
\(625\) 24.9907 0.999628
\(626\) −8.39850 −0.335672
\(627\) 0 0
\(628\) −31.2606 −1.24744
\(629\) 33.0912 1.31943
\(630\) 0 0
\(631\) −29.6873 −1.18183 −0.590917 0.806733i \(-0.701234\pi\)
−0.590917 + 0.806733i \(0.701234\pi\)
\(632\) −0.182465 −0.00725807
\(633\) 0 0
\(634\) −35.5813 −1.41311
\(635\) −0.530687 −0.0210597
\(636\) 0 0
\(637\) 9.44512 0.374229
\(638\) −18.3360 −0.725931
\(639\) 0 0
\(640\) −0.0889070 −0.00351436
\(641\) −17.3957 −0.687087 −0.343544 0.939137i \(-0.611627\pi\)
−0.343544 + 0.939137i \(0.611627\pi\)
\(642\) 0 0
\(643\) 29.6750 1.17027 0.585133 0.810937i \(-0.301042\pi\)
0.585133 + 0.810937i \(0.301042\pi\)
\(644\) 4.23036 0.166699
\(645\) 0 0
\(646\) 32.4834 1.27804
\(647\) 30.7044 1.20711 0.603557 0.797320i \(-0.293750\pi\)
0.603557 + 0.797320i \(0.293750\pi\)
\(648\) 0 0
\(649\) 1.96110 0.0769800
\(650\) 20.7967 0.815715
\(651\) 0 0
\(652\) −18.3809 −0.719850
\(653\) −19.0430 −0.745212 −0.372606 0.927990i \(-0.621536\pi\)
−0.372606 + 0.927990i \(0.621536\pi\)
\(654\) 0 0
\(655\) 0.0615579 0.00240526
\(656\) 31.3931 1.22569
\(657\) 0 0
\(658\) −13.1633 −0.513158
\(659\) 18.7844 0.731738 0.365869 0.930666i \(-0.380772\pi\)
0.365869 + 0.930666i \(0.380772\pi\)
\(660\) 0 0
\(661\) −24.5103 −0.953340 −0.476670 0.879082i \(-0.658156\pi\)
−0.476670 + 0.879082i \(0.658156\pi\)
\(662\) −16.5697 −0.644000
\(663\) 0 0
\(664\) 0.614782 0.0238582
\(665\) −0.125274 −0.00485793
\(666\) 0 0
\(667\) 11.1359 0.431185
\(668\) 2.85780 0.110571
\(669\) 0 0
\(670\) −0.108733 −0.00420074
\(671\) −1.00000 −0.0386046
\(672\) 0 0
\(673\) −31.7336 −1.22324 −0.611620 0.791152i \(-0.709482\pi\)
−0.611620 + 0.791152i \(0.709482\pi\)
\(674\) −45.5590 −1.75487
\(675\) 0 0
\(676\) −19.7419 −0.759303
\(677\) −0.989479 −0.0380288 −0.0190144 0.999819i \(-0.506053\pi\)
−0.0190144 + 0.999819i \(0.506053\pi\)
\(678\) 0 0
\(679\) 24.1730 0.927676
\(680\) −0.0537081 −0.00205961
\(681\) 0 0
\(682\) −11.5564 −0.442517
\(683\) −9.17009 −0.350884 −0.175442 0.984490i \(-0.556135\pi\)
−0.175442 + 0.984490i \(0.556135\pi\)
\(684\) 0 0
\(685\) 0.0847841 0.00323944
\(686\) −36.6182 −1.39809
\(687\) 0 0
\(688\) 22.3179 0.850862
\(689\) −7.22613 −0.275294
\(690\) 0 0
\(691\) −26.4465 −1.00607 −0.503037 0.864265i \(-0.667784\pi\)
−0.503037 + 0.864265i \(0.667784\pi\)
\(692\) 20.9658 0.796999
\(693\) 0 0
\(694\) −1.33041 −0.0505015
\(695\) −0.498761 −0.0189191
\(696\) 0 0
\(697\) 42.9057 1.62517
\(698\) −20.1201 −0.761559
\(699\) 0 0
\(700\) −16.9545 −0.640821
\(701\) −0.0832491 −0.00314428 −0.00157214 0.999999i \(-0.500500\pi\)
−0.00157214 + 0.999999i \(0.500500\pi\)
\(702\) 0 0
\(703\) 22.6780 0.855318
\(704\) 9.64318 0.363441
\(705\) 0 0
\(706\) 55.8582 2.10225
\(707\) −3.13049 −0.117734
\(708\) 0 0
\(709\) 1.21742 0.0457212 0.0228606 0.999739i \(-0.492723\pi\)
0.0228606 + 0.999739i \(0.492723\pi\)
\(710\) −0.412538 −0.0154823
\(711\) 0 0
\(712\) 3.78427 0.141822
\(713\) 7.01847 0.262844
\(714\) 0 0
\(715\) 0.0504185 0.00188555
\(716\) 4.92188 0.183939
\(717\) 0 0
\(718\) 35.1919 1.31335
\(719\) 32.6735 1.21852 0.609259 0.792972i \(-0.291467\pi\)
0.609259 + 0.792972i \(0.291467\pi\)
\(720\) 0 0
\(721\) −5.21399 −0.194179
\(722\) −16.7633 −0.623864
\(723\) 0 0
\(724\) 6.53757 0.242967
\(725\) −44.6308 −1.65755
\(726\) 0 0
\(727\) −49.4836 −1.83525 −0.917623 0.397452i \(-0.869895\pi\)
−0.917623 + 0.397452i \(0.869895\pi\)
\(728\) −1.39034 −0.0515295
\(729\) 0 0
\(730\) 0.0408534 0.00151205
\(731\) 30.5024 1.12817
\(732\) 0 0
\(733\) −49.9962 −1.84665 −0.923326 0.384017i \(-0.874540\pi\)
−0.923326 + 0.384017i \(0.874540\pi\)
\(734\) 50.3829 1.85967
\(735\) 0 0
\(736\) −10.1259 −0.373245
\(737\) 2.12656 0.0783328
\(738\) 0 0
\(739\) −23.1840 −0.852837 −0.426418 0.904526i \(-0.640225\pi\)
−0.426418 + 0.904526i \(0.640225\pi\)
\(740\) −0.380461 −0.0139860
\(741\) 0 0
\(742\) 11.2016 0.411224
\(743\) −10.5448 −0.386853 −0.193426 0.981115i \(-0.561960\pi\)
−0.193426 + 0.981115i \(0.561960\pi\)
\(744\) 0 0
\(745\) −0.238444 −0.00873590
\(746\) −15.9717 −0.584764
\(747\) 0 0
\(748\) 10.6581 0.389700
\(749\) 20.9305 0.764785
\(750\) 0 0
\(751\) 6.78220 0.247486 0.123743 0.992314i \(-0.460510\pi\)
0.123743 + 0.992314i \(0.460510\pi\)
\(752\) 14.7370 0.537402
\(753\) 0 0
\(754\) −37.1362 −1.35242
\(755\) 0.129084 0.00469786
\(756\) 0 0
\(757\) 16.8134 0.611092 0.305546 0.952177i \(-0.401161\pi\)
0.305546 + 0.952177i \(0.401161\pi\)
\(758\) −55.1102 −2.00169
\(759\) 0 0
\(760\) −0.0368073 −0.00133514
\(761\) −18.3728 −0.666013 −0.333006 0.942925i \(-0.608063\pi\)
−0.333006 + 0.942925i \(0.608063\pi\)
\(762\) 0 0
\(763\) 1.52512 0.0552131
\(764\) 36.3577 1.31538
\(765\) 0 0
\(766\) 3.56662 0.128867
\(767\) 3.97184 0.143415
\(768\) 0 0
\(769\) 8.84361 0.318909 0.159454 0.987205i \(-0.449026\pi\)
0.159454 + 0.987205i \(0.449026\pi\)
\(770\) −0.0781565 −0.00281656
\(771\) 0 0
\(772\) 14.2876 0.514221
\(773\) −2.74567 −0.0987550 −0.0493775 0.998780i \(-0.515724\pi\)
−0.0493775 + 0.998780i \(0.515724\pi\)
\(774\) 0 0
\(775\) −28.1288 −1.01042
\(776\) 7.10237 0.254960
\(777\) 0 0
\(778\) −61.8273 −2.21661
\(779\) 29.4041 1.05351
\(780\) 0 0
\(781\) 8.06823 0.288704
\(782\) −12.3079 −0.440131
\(783\) 0 0
\(784\) 16.3918 0.585420
\(785\) −0.350757 −0.0125191
\(786\) 0 0
\(787\) 23.6507 0.843056 0.421528 0.906815i \(-0.361494\pi\)
0.421528 + 0.906815i \(0.361494\pi\)
\(788\) 26.4561 0.942459
\(789\) 0 0
\(790\) −0.0207737 −0.000739096 0
\(791\) −17.1626 −0.610232
\(792\) 0 0
\(793\) −2.02531 −0.0719209
\(794\) 38.0399 1.34999
\(795\) 0 0
\(796\) 4.41836 0.156605
\(797\) −14.1914 −0.502685 −0.251343 0.967898i \(-0.580872\pi\)
−0.251343 + 0.967898i \(0.580872\pi\)
\(798\) 0 0
\(799\) 20.1414 0.712550
\(800\) 40.5827 1.43482
\(801\) 0 0
\(802\) −23.8031 −0.840518
\(803\) −0.798991 −0.0281958
\(804\) 0 0
\(805\) 0.0474663 0.00167297
\(806\) −23.4053 −0.824415
\(807\) 0 0
\(808\) −0.919781 −0.0323578
\(809\) 32.5252 1.14353 0.571763 0.820419i \(-0.306260\pi\)
0.571763 + 0.820419i \(0.306260\pi\)
\(810\) 0 0
\(811\) −28.5530 −1.00263 −0.501315 0.865265i \(-0.667150\pi\)
−0.501315 + 0.865265i \(0.667150\pi\)
\(812\) 30.2753 1.06245
\(813\) 0 0
\(814\) 14.1484 0.495902
\(815\) −0.206241 −0.00722429
\(816\) 0 0
\(817\) 20.9039 0.731335
\(818\) 2.25080 0.0786973
\(819\) 0 0
\(820\) −0.493302 −0.0172269
\(821\) −32.0523 −1.11863 −0.559317 0.828954i \(-0.688937\pi\)
−0.559317 + 0.828954i \(0.688937\pi\)
\(822\) 0 0
\(823\) −11.2285 −0.391401 −0.195701 0.980664i \(-0.562698\pi\)
−0.195701 + 0.980664i \(0.562698\pi\)
\(824\) −1.53194 −0.0533677
\(825\) 0 0
\(826\) −6.15697 −0.214228
\(827\) 21.6816 0.753942 0.376971 0.926225i \(-0.376966\pi\)
0.376971 + 0.926225i \(0.376966\pi\)
\(828\) 0 0
\(829\) 25.4695 0.884593 0.442297 0.896869i \(-0.354164\pi\)
0.442297 + 0.896869i \(0.354164\pi\)
\(830\) 0.0699932 0.00242950
\(831\) 0 0
\(832\) 19.5304 0.677096
\(833\) 22.4030 0.776218
\(834\) 0 0
\(835\) 0.0320656 0.00110968
\(836\) 7.30423 0.252622
\(837\) 0 0
\(838\) −27.0857 −0.935659
\(839\) 30.6806 1.05921 0.529606 0.848244i \(-0.322340\pi\)
0.529606 + 0.848244i \(0.322340\pi\)
\(840\) 0 0
\(841\) 50.6961 1.74814
\(842\) 44.3096 1.52701
\(843\) 0 0
\(844\) −1.20111 −0.0413440
\(845\) −0.221512 −0.00762023
\(846\) 0 0
\(847\) 1.52855 0.0525215
\(848\) −12.5408 −0.430651
\(849\) 0 0
\(850\) 49.3281 1.69194
\(851\) −8.59269 −0.294554
\(852\) 0 0
\(853\) 34.6407 1.18608 0.593038 0.805175i \(-0.297928\pi\)
0.593038 + 0.805175i \(0.297928\pi\)
\(854\) 3.13954 0.107433
\(855\) 0 0
\(856\) 6.14967 0.210192
\(857\) 11.2033 0.382697 0.191349 0.981522i \(-0.438714\pi\)
0.191349 + 0.981522i \(0.438714\pi\)
\(858\) 0 0
\(859\) −9.97945 −0.340494 −0.170247 0.985401i \(-0.554457\pi\)
−0.170247 + 0.985401i \(0.554457\pi\)
\(860\) −0.350697 −0.0119587
\(861\) 0 0
\(862\) −63.5540 −2.16466
\(863\) −23.7258 −0.807635 −0.403818 0.914840i \(-0.632317\pi\)
−0.403818 + 0.914840i \(0.632317\pi\)
\(864\) 0 0
\(865\) 0.235244 0.00799855
\(866\) 26.5573 0.902455
\(867\) 0 0
\(868\) 19.0811 0.647656
\(869\) 0.406283 0.0137822
\(870\) 0 0
\(871\) 4.30695 0.145935
\(872\) 0.448101 0.0151746
\(873\) 0 0
\(874\) −8.43488 −0.285314
\(875\) −0.380497 −0.0128631
\(876\) 0 0
\(877\) 41.5832 1.40417 0.702083 0.712095i \(-0.252253\pi\)
0.702083 + 0.712095i \(0.252253\pi\)
\(878\) 0.680845 0.0229774
\(879\) 0 0
\(880\) 0.0875001 0.00294963
\(881\) −39.2012 −1.32072 −0.660362 0.750948i \(-0.729597\pi\)
−0.660362 + 0.750948i \(0.729597\pi\)
\(882\) 0 0
\(883\) −50.8271 −1.71047 −0.855235 0.518241i \(-0.826587\pi\)
−0.855235 + 0.518241i \(0.826587\pi\)
\(884\) 21.5860 0.726016
\(885\) 0 0
\(886\) −60.7737 −2.04173
\(887\) 47.9367 1.60956 0.804779 0.593575i \(-0.202284\pi\)
0.804779 + 0.593575i \(0.202284\pi\)
\(888\) 0 0
\(889\) −32.5851 −1.09287
\(890\) 0.430841 0.0144418
\(891\) 0 0
\(892\) −29.5145 −0.988218
\(893\) 13.8033 0.461909
\(894\) 0 0
\(895\) 0.0552255 0.00184598
\(896\) −5.45905 −0.182374
\(897\) 0 0
\(898\) −23.5087 −0.784496
\(899\) 50.2288 1.67523
\(900\) 0 0
\(901\) −17.1398 −0.571008
\(902\) 18.3447 0.610813
\(903\) 0 0
\(904\) −5.04260 −0.167714
\(905\) 0.0733541 0.00243837
\(906\) 0 0
\(907\) 46.9393 1.55859 0.779297 0.626655i \(-0.215577\pi\)
0.779297 + 0.626655i \(0.215577\pi\)
\(908\) 15.4092 0.511372
\(909\) 0 0
\(910\) −0.158291 −0.00524730
\(911\) 33.9584 1.12509 0.562546 0.826766i \(-0.309822\pi\)
0.562546 + 0.826766i \(0.309822\pi\)
\(912\) 0 0
\(913\) −1.36890 −0.0453038
\(914\) 50.1272 1.65806
\(915\) 0 0
\(916\) 40.1620 1.32699
\(917\) 3.77976 0.124819
\(918\) 0 0
\(919\) −48.4841 −1.59934 −0.799671 0.600438i \(-0.794993\pi\)
−0.799671 + 0.600438i \(0.794993\pi\)
\(920\) 0.0139462 0.000459794 0
\(921\) 0 0
\(922\) −31.6551 −1.04251
\(923\) 16.3407 0.537860
\(924\) 0 0
\(925\) 34.4380 1.13231
\(926\) 76.4894 2.51360
\(927\) 0 0
\(928\) −72.4675 −2.37886
\(929\) 10.2315 0.335685 0.167842 0.985814i \(-0.446320\pi\)
0.167842 + 0.985814i \(0.446320\pi\)
\(930\) 0 0
\(931\) 15.3532 0.503182
\(932\) 19.5176 0.639322
\(933\) 0 0
\(934\) −2.01525 −0.0659409
\(935\) 0.119588 0.00391096
\(936\) 0 0
\(937\) −38.9700 −1.27309 −0.636547 0.771238i \(-0.719638\pi\)
−0.636547 + 0.771238i \(0.719638\pi\)
\(938\) −6.67642 −0.217993
\(939\) 0 0
\(940\) −0.231572 −0.00755306
\(941\) −40.7968 −1.32994 −0.664969 0.746871i \(-0.731555\pi\)
−0.664969 + 0.746871i \(0.731555\pi\)
\(942\) 0 0
\(943\) −11.1412 −0.362807
\(944\) 6.89303 0.224349
\(945\) 0 0
\(946\) 13.0416 0.424019
\(947\) −35.3399 −1.14839 −0.574196 0.818718i \(-0.694685\pi\)
−0.574196 + 0.818718i \(0.694685\pi\)
\(948\) 0 0
\(949\) −1.61821 −0.0525292
\(950\) 33.8055 1.09680
\(951\) 0 0
\(952\) −3.29777 −0.106881
\(953\) −34.0800 −1.10396 −0.551979 0.833858i \(-0.686127\pi\)
−0.551979 + 0.833858i \(0.686127\pi\)
\(954\) 0 0
\(955\) 0.407948 0.0132009
\(956\) 5.96406 0.192892
\(957\) 0 0
\(958\) 28.7045 0.927401
\(959\) 5.20589 0.168107
\(960\) 0 0
\(961\) 0.656951 0.0211920
\(962\) 28.6550 0.923874
\(963\) 0 0
\(964\) 35.4739 1.14254
\(965\) 0.160312 0.00516064
\(966\) 0 0
\(967\) −8.97996 −0.288776 −0.144388 0.989521i \(-0.546121\pi\)
−0.144388 + 0.989521i \(0.546121\pi\)
\(968\) 0.449108 0.0144349
\(969\) 0 0
\(970\) 0.808608 0.0259628
\(971\) 26.8795 0.862604 0.431302 0.902208i \(-0.358054\pi\)
0.431302 + 0.902208i \(0.358054\pi\)
\(972\) 0 0
\(973\) −30.6248 −0.981786
\(974\) −82.8331 −2.65414
\(975\) 0 0
\(976\) −3.51487 −0.112508
\(977\) 30.1502 0.964590 0.482295 0.876009i \(-0.339803\pi\)
0.482295 + 0.876009i \(0.339803\pi\)
\(978\) 0 0
\(979\) −8.42620 −0.269302
\(980\) −0.257575 −0.00822795
\(981\) 0 0
\(982\) 69.0533 2.20358
\(983\) 15.9793 0.509660 0.254830 0.966986i \(-0.417980\pi\)
0.254830 + 0.966986i \(0.417980\pi\)
\(984\) 0 0
\(985\) 0.296848 0.00945836
\(986\) −88.0838 −2.80516
\(987\) 0 0
\(988\) 14.7933 0.470639
\(989\) −7.92047 −0.251856
\(990\) 0 0
\(991\) −42.4827 −1.34951 −0.674754 0.738043i \(-0.735750\pi\)
−0.674754 + 0.738043i \(0.735750\pi\)
\(992\) −45.6730 −1.45012
\(993\) 0 0
\(994\) −25.3305 −0.803436
\(995\) 0.0495758 0.00157166
\(996\) 0 0
\(997\) −2.14096 −0.0678049 −0.0339025 0.999425i \(-0.510794\pi\)
−0.0339025 + 0.999425i \(0.510794\pi\)
\(998\) 31.1115 0.984817
\(999\) 0 0
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 6039.2.a.c.1.10 11
3.2 odd 2 2013.2.a.b.1.2 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.2.a.b.1.2 11 3.2 odd 2
6039.2.a.c.1.10 11 1.1 even 1 trivial