Properties

Label 4011.2.a.j.1.12
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $26$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.596587 q^{2} -1.00000 q^{3} -1.64408 q^{4} +4.06129 q^{5} +0.596587 q^{6} -1.00000 q^{7} +2.17401 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.596587 q^{2} -1.00000 q^{3} -1.64408 q^{4} +4.06129 q^{5} +0.596587 q^{6} -1.00000 q^{7} +2.17401 q^{8} +1.00000 q^{9} -2.42291 q^{10} -0.0366506 q^{11} +1.64408 q^{12} +5.73847 q^{13} +0.596587 q^{14} -4.06129 q^{15} +1.99118 q^{16} +3.28922 q^{17} -0.596587 q^{18} -0.844005 q^{19} -6.67711 q^{20} +1.00000 q^{21} +0.0218653 q^{22} -2.13704 q^{23} -2.17401 q^{24} +11.4941 q^{25} -3.42350 q^{26} -1.00000 q^{27} +1.64408 q^{28} +7.14777 q^{29} +2.42291 q^{30} +6.50937 q^{31} -5.53594 q^{32} +0.0366506 q^{33} -1.96231 q^{34} -4.06129 q^{35} -1.64408 q^{36} -10.4102 q^{37} +0.503522 q^{38} -5.73847 q^{39} +8.82930 q^{40} +10.9305 q^{41} -0.596587 q^{42} -4.01763 q^{43} +0.0602567 q^{44} +4.06129 q^{45} +1.27493 q^{46} +1.96344 q^{47} -1.99118 q^{48} +1.00000 q^{49} -6.85723 q^{50} -3.28922 q^{51} -9.43453 q^{52} +11.2481 q^{53} +0.596587 q^{54} -0.148849 q^{55} -2.17401 q^{56} +0.844005 q^{57} -4.26426 q^{58} -2.72011 q^{59} +6.67711 q^{60} -5.24229 q^{61} -3.88341 q^{62} -1.00000 q^{63} -0.679692 q^{64} +23.3056 q^{65} -0.0218653 q^{66} -5.39696 q^{67} -5.40776 q^{68} +2.13704 q^{69} +2.42291 q^{70} -11.4633 q^{71} +2.17401 q^{72} -5.56933 q^{73} +6.21061 q^{74} -11.4941 q^{75} +1.38761 q^{76} +0.0366506 q^{77} +3.42350 q^{78} +3.28461 q^{79} +8.08677 q^{80} +1.00000 q^{81} -6.52101 q^{82} +12.0518 q^{83} -1.64408 q^{84} +13.3585 q^{85} +2.39687 q^{86} -7.14777 q^{87} -0.0796790 q^{88} -9.93837 q^{89} -2.42291 q^{90} -5.73847 q^{91} +3.51347 q^{92} -6.50937 q^{93} -1.17136 q^{94} -3.42775 q^{95} +5.53594 q^{96} +12.7465 q^{97} -0.596587 q^{98} -0.0366506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.596587 −0.421851 −0.210925 0.977502i \(-0.567648\pi\)
−0.210925 + 0.977502i \(0.567648\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.64408 −0.822042
\(5\) 4.06129 1.81627 0.908133 0.418682i \(-0.137508\pi\)
0.908133 + 0.418682i \(0.137508\pi\)
\(6\) 0.596587 0.243556
\(7\) −1.00000 −0.377964
\(8\) 2.17401 0.768630
\(9\) 1.00000 0.333333
\(10\) −2.42291 −0.766193
\(11\) −0.0366506 −0.0110506 −0.00552529 0.999985i \(-0.501759\pi\)
−0.00552529 + 0.999985i \(0.501759\pi\)
\(12\) 1.64408 0.474606
\(13\) 5.73847 1.59157 0.795783 0.605582i \(-0.207060\pi\)
0.795783 + 0.605582i \(0.207060\pi\)
\(14\) 0.596587 0.159445
\(15\) −4.06129 −1.04862
\(16\) 1.99118 0.497795
\(17\) 3.28922 0.797753 0.398877 0.917005i \(-0.369400\pi\)
0.398877 + 0.917005i \(0.369400\pi\)
\(18\) −0.596587 −0.140617
\(19\) −0.844005 −0.193628 −0.0968140 0.995302i \(-0.530865\pi\)
−0.0968140 + 0.995302i \(0.530865\pi\)
\(20\) −6.67711 −1.49305
\(21\) 1.00000 0.218218
\(22\) 0.0218653 0.00466170
\(23\) −2.13704 −0.445603 −0.222801 0.974864i \(-0.571520\pi\)
−0.222801 + 0.974864i \(0.571520\pi\)
\(24\) −2.17401 −0.443769
\(25\) 11.4941 2.29882
\(26\) −3.42350 −0.671403
\(27\) −1.00000 −0.192450
\(28\) 1.64408 0.310703
\(29\) 7.14777 1.32731 0.663653 0.748040i \(-0.269005\pi\)
0.663653 + 0.748040i \(0.269005\pi\)
\(30\) 2.42291 0.442362
\(31\) 6.50937 1.16912 0.584559 0.811351i \(-0.301267\pi\)
0.584559 + 0.811351i \(0.301267\pi\)
\(32\) −5.53594 −0.978625
\(33\) 0.0366506 0.00638006
\(34\) −1.96231 −0.336533
\(35\) −4.06129 −0.686484
\(36\) −1.64408 −0.274014
\(37\) −10.4102 −1.71143 −0.855716 0.517446i \(-0.826883\pi\)
−0.855716 + 0.517446i \(0.826883\pi\)
\(38\) 0.503522 0.0816821
\(39\) −5.73847 −0.918891
\(40\) 8.82930 1.39604
\(41\) 10.9305 1.70706 0.853531 0.521042i \(-0.174456\pi\)
0.853531 + 0.521042i \(0.174456\pi\)
\(42\) −0.596587 −0.0920554
\(43\) −4.01763 −0.612683 −0.306342 0.951922i \(-0.599105\pi\)
−0.306342 + 0.951922i \(0.599105\pi\)
\(44\) 0.0602567 0.00908404
\(45\) 4.06129 0.605422
\(46\) 1.27493 0.187978
\(47\) 1.96344 0.286397 0.143198 0.989694i \(-0.454261\pi\)
0.143198 + 0.989694i \(0.454261\pi\)
\(48\) −1.99118 −0.287402
\(49\) 1.00000 0.142857
\(50\) −6.85723 −0.969759
\(51\) −3.28922 −0.460583
\(52\) −9.43453 −1.30833
\(53\) 11.2481 1.54505 0.772524 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(54\) 0.596587 0.0811852
\(55\) −0.148849 −0.0200708
\(56\) −2.17401 −0.290515
\(57\) 0.844005 0.111791
\(58\) −4.26426 −0.559925
\(59\) −2.72011 −0.354128 −0.177064 0.984199i \(-0.556660\pi\)
−0.177064 + 0.984199i \(0.556660\pi\)
\(60\) 6.67711 0.862011
\(61\) −5.24229 −0.671207 −0.335603 0.942003i \(-0.608940\pi\)
−0.335603 + 0.942003i \(0.608940\pi\)
\(62\) −3.88341 −0.493193
\(63\) −1.00000 −0.125988
\(64\) −0.679692 −0.0849615
\(65\) 23.3056 2.89071
\(66\) −0.0218653 −0.00269143
\(67\) −5.39696 −0.659343 −0.329672 0.944096i \(-0.606938\pi\)
−0.329672 + 0.944096i \(0.606938\pi\)
\(68\) −5.40776 −0.655787
\(69\) 2.13704 0.257269
\(70\) 2.42291 0.289594
\(71\) −11.4633 −1.36044 −0.680222 0.733006i \(-0.738116\pi\)
−0.680222 + 0.733006i \(0.738116\pi\)
\(72\) 2.17401 0.256210
\(73\) −5.56933 −0.651841 −0.325920 0.945397i \(-0.605674\pi\)
−0.325920 + 0.945397i \(0.605674\pi\)
\(74\) 6.21061 0.721968
\(75\) −11.4941 −1.32722
\(76\) 1.38761 0.159170
\(77\) 0.0366506 0.00417673
\(78\) 3.42350 0.387635
\(79\) 3.28461 0.369547 0.184774 0.982781i \(-0.440845\pi\)
0.184774 + 0.982781i \(0.440845\pi\)
\(80\) 8.08677 0.904128
\(81\) 1.00000 0.111111
\(82\) −6.52101 −0.720126
\(83\) 12.0518 1.32286 0.661430 0.750007i \(-0.269950\pi\)
0.661430 + 0.750007i \(0.269950\pi\)
\(84\) −1.64408 −0.179384
\(85\) 13.3585 1.44893
\(86\) 2.39687 0.258461
\(87\) −7.14777 −0.766321
\(88\) −0.0796790 −0.00849381
\(89\) −9.93837 −1.05347 −0.526733 0.850031i \(-0.676583\pi\)
−0.526733 + 0.850031i \(0.676583\pi\)
\(90\) −2.42291 −0.255398
\(91\) −5.73847 −0.601555
\(92\) 3.51347 0.366304
\(93\) −6.50937 −0.674991
\(94\) −1.17136 −0.120817
\(95\) −3.42775 −0.351680
\(96\) 5.53594 0.565009
\(97\) 12.7465 1.29422 0.647108 0.762398i \(-0.275978\pi\)
0.647108 + 0.762398i \(0.275978\pi\)
\(98\) −0.596587 −0.0602644
\(99\) −0.0366506 −0.00368353
\(100\) −18.8973 −1.88973
\(101\) 8.42052 0.837873 0.418936 0.908016i \(-0.362403\pi\)
0.418936 + 0.908016i \(0.362403\pi\)
\(102\) 1.96231 0.194297
\(103\) −8.41991 −0.829638 −0.414819 0.909904i \(-0.636155\pi\)
−0.414819 + 0.909904i \(0.636155\pi\)
\(104\) 12.4755 1.22332
\(105\) 4.06129 0.396342
\(106\) −6.71048 −0.651780
\(107\) −3.52936 −0.341196 −0.170598 0.985341i \(-0.554570\pi\)
−0.170598 + 0.985341i \(0.554570\pi\)
\(108\) 1.64408 0.158202
\(109\) −4.43885 −0.425165 −0.212582 0.977143i \(-0.568187\pi\)
−0.212582 + 0.977143i \(0.568187\pi\)
\(110\) 0.0888014 0.00846688
\(111\) 10.4102 0.988095
\(112\) −1.99118 −0.188149
\(113\) −13.4260 −1.26301 −0.631505 0.775372i \(-0.717562\pi\)
−0.631505 + 0.775372i \(0.717562\pi\)
\(114\) −0.503522 −0.0471592
\(115\) −8.67913 −0.809333
\(116\) −11.7515 −1.09110
\(117\) 5.73847 0.530522
\(118\) 1.62278 0.149389
\(119\) −3.28922 −0.301522
\(120\) −8.82930 −0.806002
\(121\) −10.9987 −0.999878
\(122\) 3.12748 0.283149
\(123\) −10.9305 −0.985573
\(124\) −10.7020 −0.961064
\(125\) 26.3745 2.35900
\(126\) 0.596587 0.0531482
\(127\) 1.64452 0.145928 0.0729638 0.997335i \(-0.476754\pi\)
0.0729638 + 0.997335i \(0.476754\pi\)
\(128\) 11.4774 1.01447
\(129\) 4.01763 0.353733
\(130\) −13.9038 −1.21945
\(131\) 20.1631 1.76166 0.880830 0.473432i \(-0.156985\pi\)
0.880830 + 0.473432i \(0.156985\pi\)
\(132\) −0.0602567 −0.00524468
\(133\) 0.844005 0.0731845
\(134\) 3.21975 0.278144
\(135\) −4.06129 −0.349540
\(136\) 7.15081 0.613177
\(137\) −7.27768 −0.621775 −0.310887 0.950447i \(-0.600626\pi\)
−0.310887 + 0.950447i \(0.600626\pi\)
\(138\) −1.27493 −0.108529
\(139\) −12.5015 −1.06036 −0.530181 0.847884i \(-0.677876\pi\)
−0.530181 + 0.847884i \(0.677876\pi\)
\(140\) 6.67711 0.564319
\(141\) −1.96344 −0.165351
\(142\) 6.83885 0.573904
\(143\) −0.210319 −0.0175877
\(144\) 1.99118 0.165932
\(145\) 29.0292 2.41074
\(146\) 3.32259 0.274980
\(147\) −1.00000 −0.0824786
\(148\) 17.1153 1.40687
\(149\) −17.4040 −1.42579 −0.712896 0.701270i \(-0.752617\pi\)
−0.712896 + 0.701270i \(0.752617\pi\)
\(150\) 6.85723 0.559891
\(151\) −12.6550 −1.02985 −0.514924 0.857236i \(-0.672180\pi\)
−0.514924 + 0.857236i \(0.672180\pi\)
\(152\) −1.83488 −0.148828
\(153\) 3.28922 0.265918
\(154\) −0.0218653 −0.00176196
\(155\) 26.4365 2.12343
\(156\) 9.43453 0.755367
\(157\) −8.35868 −0.667095 −0.333548 0.942733i \(-0.608246\pi\)
−0.333548 + 0.942733i \(0.608246\pi\)
\(158\) −1.95955 −0.155894
\(159\) −11.2481 −0.892034
\(160\) −22.4831 −1.77744
\(161\) 2.13704 0.168422
\(162\) −0.596587 −0.0468723
\(163\) −14.3097 −1.12082 −0.560410 0.828216i \(-0.689356\pi\)
−0.560410 + 0.828216i \(0.689356\pi\)
\(164\) −17.9707 −1.40328
\(165\) 0.148849 0.0115879
\(166\) −7.18997 −0.558050
\(167\) 8.50396 0.658056 0.329028 0.944320i \(-0.393279\pi\)
0.329028 + 0.944320i \(0.393279\pi\)
\(168\) 2.17401 0.167729
\(169\) 19.9300 1.53308
\(170\) −7.96950 −0.611233
\(171\) −0.844005 −0.0645427
\(172\) 6.60533 0.503651
\(173\) 8.94722 0.680245 0.340122 0.940381i \(-0.389532\pi\)
0.340122 + 0.940381i \(0.389532\pi\)
\(174\) 4.26426 0.323273
\(175\) −11.4941 −0.868873
\(176\) −0.0729780 −0.00550093
\(177\) 2.72011 0.204456
\(178\) 5.92910 0.444405
\(179\) 15.6746 1.17157 0.585786 0.810466i \(-0.300786\pi\)
0.585786 + 0.810466i \(0.300786\pi\)
\(180\) −6.67711 −0.497682
\(181\) 23.4932 1.74624 0.873119 0.487507i \(-0.162093\pi\)
0.873119 + 0.487507i \(0.162093\pi\)
\(182\) 3.42350 0.253766
\(183\) 5.24229 0.387521
\(184\) −4.64594 −0.342504
\(185\) −42.2790 −3.10841
\(186\) 3.88341 0.284745
\(187\) −0.120552 −0.00881564
\(188\) −3.22806 −0.235430
\(189\) 1.00000 0.0727393
\(190\) 2.04495 0.148356
\(191\) 1.00000 0.0723575
\(192\) 0.679692 0.0490526
\(193\) 13.5056 0.972155 0.486077 0.873916i \(-0.338427\pi\)
0.486077 + 0.873916i \(0.338427\pi\)
\(194\) −7.60442 −0.545966
\(195\) −23.3056 −1.66895
\(196\) −1.64408 −0.117435
\(197\) −7.82429 −0.557457 −0.278729 0.960370i \(-0.589913\pi\)
−0.278729 + 0.960370i \(0.589913\pi\)
\(198\) 0.0218653 0.00155390
\(199\) 24.9482 1.76853 0.884266 0.466984i \(-0.154659\pi\)
0.884266 + 0.466984i \(0.154659\pi\)
\(200\) 24.9883 1.76694
\(201\) 5.39696 0.380672
\(202\) −5.02357 −0.353457
\(203\) −7.14777 −0.501675
\(204\) 5.40776 0.378619
\(205\) 44.3921 3.10048
\(206\) 5.02321 0.349983
\(207\) −2.13704 −0.148534
\(208\) 11.4263 0.792273
\(209\) 0.0309333 0.00213970
\(210\) −2.42291 −0.167197
\(211\) 8.87133 0.610728 0.305364 0.952236i \(-0.401222\pi\)
0.305364 + 0.952236i \(0.401222\pi\)
\(212\) −18.4929 −1.27009
\(213\) 11.4633 0.785452
\(214\) 2.10557 0.143934
\(215\) −16.3168 −1.11280
\(216\) −2.17401 −0.147923
\(217\) −6.50937 −0.441885
\(218\) 2.64816 0.179356
\(219\) 5.56933 0.376341
\(220\) 0.244720 0.0164990
\(221\) 18.8751 1.26968
\(222\) −6.21061 −0.416829
\(223\) 4.09068 0.273932 0.136966 0.990576i \(-0.456265\pi\)
0.136966 + 0.990576i \(0.456265\pi\)
\(224\) 5.53594 0.369885
\(225\) 11.4941 0.766274
\(226\) 8.00976 0.532801
\(227\) −11.2615 −0.747451 −0.373725 0.927539i \(-0.621920\pi\)
−0.373725 + 0.927539i \(0.621920\pi\)
\(228\) −1.38761 −0.0918970
\(229\) −13.8576 −0.915737 −0.457868 0.889020i \(-0.651387\pi\)
−0.457868 + 0.889020i \(0.651387\pi\)
\(230\) 5.17786 0.341418
\(231\) −0.0366506 −0.00241143
\(232\) 15.5393 1.02021
\(233\) −2.61287 −0.171175 −0.0855873 0.996331i \(-0.527277\pi\)
−0.0855873 + 0.996331i \(0.527277\pi\)
\(234\) −3.42350 −0.223801
\(235\) 7.97410 0.520173
\(236\) 4.47209 0.291108
\(237\) −3.28461 −0.213358
\(238\) 1.96231 0.127197
\(239\) 2.39576 0.154969 0.0774845 0.996994i \(-0.475311\pi\)
0.0774845 + 0.996994i \(0.475311\pi\)
\(240\) −8.08677 −0.521999
\(241\) 1.09133 0.0702989 0.0351495 0.999382i \(-0.488809\pi\)
0.0351495 + 0.999382i \(0.488809\pi\)
\(242\) 6.56166 0.421799
\(243\) −1.00000 −0.0641500
\(244\) 8.61877 0.551760
\(245\) 4.06129 0.259467
\(246\) 6.52101 0.415765
\(247\) −4.84330 −0.308172
\(248\) 14.1515 0.898619
\(249\) −12.0518 −0.763754
\(250\) −15.7347 −0.995147
\(251\) 26.5495 1.67579 0.837896 0.545830i \(-0.183786\pi\)
0.837896 + 0.545830i \(0.183786\pi\)
\(252\) 1.64408 0.103568
\(253\) 0.0783237 0.00492417
\(254\) −0.981100 −0.0615597
\(255\) −13.3585 −0.836541
\(256\) −5.48787 −0.342992
\(257\) −27.5507 −1.71856 −0.859281 0.511503i \(-0.829089\pi\)
−0.859281 + 0.511503i \(0.829089\pi\)
\(258\) −2.39687 −0.149222
\(259\) 10.4102 0.646860
\(260\) −38.3164 −2.37628
\(261\) 7.14777 0.442436
\(262\) −12.0291 −0.743158
\(263\) −3.07677 −0.189722 −0.0948609 0.995491i \(-0.530241\pi\)
−0.0948609 + 0.995491i \(0.530241\pi\)
\(264\) 0.0796790 0.00490390
\(265\) 45.6819 2.80622
\(266\) −0.503522 −0.0308729
\(267\) 9.93837 0.608218
\(268\) 8.87305 0.542008
\(269\) −6.88448 −0.419754 −0.209877 0.977728i \(-0.567306\pi\)
−0.209877 + 0.977728i \(0.567306\pi\)
\(270\) 2.42291 0.147454
\(271\) 12.8477 0.780442 0.390221 0.920721i \(-0.372399\pi\)
0.390221 + 0.920721i \(0.372399\pi\)
\(272\) 6.54943 0.397118
\(273\) 5.73847 0.347308
\(274\) 4.34177 0.262296
\(275\) −0.421266 −0.0254033
\(276\) −3.51347 −0.211486
\(277\) −5.36962 −0.322629 −0.161314 0.986903i \(-0.551573\pi\)
−0.161314 + 0.986903i \(0.551573\pi\)
\(278\) 7.45823 0.447315
\(279\) 6.50937 0.389706
\(280\) −8.82930 −0.527652
\(281\) −10.8067 −0.644672 −0.322336 0.946625i \(-0.604468\pi\)
−0.322336 + 0.946625i \(0.604468\pi\)
\(282\) 1.17136 0.0697535
\(283\) 8.30846 0.493887 0.246943 0.969030i \(-0.420574\pi\)
0.246943 + 0.969030i \(0.420574\pi\)
\(284\) 18.8466 1.11834
\(285\) 3.42775 0.203042
\(286\) 0.125473 0.00741939
\(287\) −10.9305 −0.645209
\(288\) −5.53594 −0.326208
\(289\) −6.18102 −0.363590
\(290\) −17.3184 −1.01697
\(291\) −12.7465 −0.747216
\(292\) 9.15645 0.535841
\(293\) 30.6949 1.79321 0.896607 0.442827i \(-0.146024\pi\)
0.896607 + 0.442827i \(0.146024\pi\)
\(294\) 0.596587 0.0347937
\(295\) −11.0472 −0.643191
\(296\) −22.6320 −1.31546
\(297\) 0.0366506 0.00212669
\(298\) 10.3830 0.601471
\(299\) −12.2633 −0.709206
\(300\) 18.8973 1.09103
\(301\) 4.01763 0.231572
\(302\) 7.54980 0.434442
\(303\) −8.42052 −0.483746
\(304\) −1.68057 −0.0963870
\(305\) −21.2905 −1.21909
\(306\) −1.96231 −0.112178
\(307\) 29.7647 1.69876 0.849381 0.527780i \(-0.176976\pi\)
0.849381 + 0.527780i \(0.176976\pi\)
\(308\) −0.0602567 −0.00343345
\(309\) 8.41991 0.478992
\(310\) −15.7717 −0.895770
\(311\) −8.78746 −0.498291 −0.249146 0.968466i \(-0.580150\pi\)
−0.249146 + 0.968466i \(0.580150\pi\)
\(312\) −12.4755 −0.706287
\(313\) 23.8210 1.34644 0.673222 0.739440i \(-0.264910\pi\)
0.673222 + 0.739440i \(0.264910\pi\)
\(314\) 4.98668 0.281414
\(315\) −4.06129 −0.228828
\(316\) −5.40017 −0.303783
\(317\) −11.5055 −0.646215 −0.323107 0.946362i \(-0.604728\pi\)
−0.323107 + 0.946362i \(0.604728\pi\)
\(318\) 6.71048 0.376305
\(319\) −0.261970 −0.0146675
\(320\) −2.76043 −0.154313
\(321\) 3.52936 0.196990
\(322\) −1.27493 −0.0710489
\(323\) −2.77612 −0.154467
\(324\) −1.64408 −0.0913380
\(325\) 65.9586 3.65872
\(326\) 8.53696 0.472818
\(327\) 4.43885 0.245469
\(328\) 23.7631 1.31210
\(329\) −1.96344 −0.108248
\(330\) −0.0888014 −0.00488835
\(331\) −33.5885 −1.84619 −0.923096 0.384569i \(-0.874350\pi\)
−0.923096 + 0.384569i \(0.874350\pi\)
\(332\) −19.8142 −1.08745
\(333\) −10.4102 −0.570477
\(334\) −5.07335 −0.277601
\(335\) −21.9186 −1.19754
\(336\) 1.99118 0.108628
\(337\) −2.20891 −0.120327 −0.0601635 0.998189i \(-0.519162\pi\)
−0.0601635 + 0.998189i \(0.519162\pi\)
\(338\) −11.8900 −0.646731
\(339\) 13.4260 0.729199
\(340\) −21.9625 −1.19108
\(341\) −0.238573 −0.0129194
\(342\) 0.503522 0.0272274
\(343\) −1.00000 −0.0539949
\(344\) −8.73439 −0.470927
\(345\) 8.67913 0.467269
\(346\) −5.33780 −0.286962
\(347\) 28.3669 1.52281 0.761406 0.648275i \(-0.224509\pi\)
0.761406 + 0.648275i \(0.224509\pi\)
\(348\) 11.7515 0.629948
\(349\) −2.59706 −0.139018 −0.0695088 0.997581i \(-0.522143\pi\)
−0.0695088 + 0.997581i \(0.522143\pi\)
\(350\) 6.85723 0.366534
\(351\) −5.73847 −0.306297
\(352\) 0.202896 0.0108144
\(353\) −13.2413 −0.704763 −0.352382 0.935856i \(-0.614628\pi\)
−0.352382 + 0.935856i \(0.614628\pi\)
\(354\) −1.62278 −0.0862499
\(355\) −46.5558 −2.47093
\(356\) 16.3395 0.865993
\(357\) 3.28922 0.174084
\(358\) −9.35124 −0.494228
\(359\) 33.1025 1.74708 0.873541 0.486751i \(-0.161818\pi\)
0.873541 + 0.486751i \(0.161818\pi\)
\(360\) 8.82930 0.465345
\(361\) −18.2877 −0.962508
\(362\) −14.0158 −0.736652
\(363\) 10.9987 0.577280
\(364\) 9.43453 0.494504
\(365\) −22.6187 −1.18392
\(366\) −3.12748 −0.163476
\(367\) 16.0319 0.836857 0.418429 0.908250i \(-0.362581\pi\)
0.418429 + 0.908250i \(0.362581\pi\)
\(368\) −4.25522 −0.221819
\(369\) 10.9305 0.569021
\(370\) 25.2231 1.31129
\(371\) −11.2481 −0.583973
\(372\) 10.7020 0.554871
\(373\) 19.2805 0.998307 0.499153 0.866514i \(-0.333644\pi\)
0.499153 + 0.866514i \(0.333644\pi\)
\(374\) 0.0719198 0.00371888
\(375\) −26.3745 −1.36197
\(376\) 4.26854 0.220133
\(377\) 41.0172 2.11250
\(378\) −0.596587 −0.0306851
\(379\) 18.7562 0.963442 0.481721 0.876325i \(-0.340012\pi\)
0.481721 + 0.876325i \(0.340012\pi\)
\(380\) 5.63551 0.289096
\(381\) −1.64452 −0.0842514
\(382\) −0.596587 −0.0305240
\(383\) 16.0788 0.821589 0.410794 0.911728i \(-0.365251\pi\)
0.410794 + 0.911728i \(0.365251\pi\)
\(384\) −11.4774 −0.585702
\(385\) 0.148849 0.00758605
\(386\) −8.05727 −0.410104
\(387\) −4.01763 −0.204228
\(388\) −20.9564 −1.06390
\(389\) −19.8417 −1.00602 −0.503008 0.864282i \(-0.667773\pi\)
−0.503008 + 0.864282i \(0.667773\pi\)
\(390\) 13.9038 0.704047
\(391\) −7.02918 −0.355481
\(392\) 2.17401 0.109804
\(393\) −20.1631 −1.01710
\(394\) 4.66787 0.235164
\(395\) 13.3398 0.671196
\(396\) 0.0602567 0.00302801
\(397\) 11.3893 0.571613 0.285807 0.958287i \(-0.407739\pi\)
0.285807 + 0.958287i \(0.407739\pi\)
\(398\) −14.8838 −0.746056
\(399\) −0.844005 −0.0422531
\(400\) 22.8868 1.14434
\(401\) 38.1159 1.90342 0.951708 0.307005i \(-0.0993267\pi\)
0.951708 + 0.307005i \(0.0993267\pi\)
\(402\) −3.21975 −0.160587
\(403\) 37.3539 1.86073
\(404\) −13.8440 −0.688767
\(405\) 4.06129 0.201807
\(406\) 4.26426 0.211632
\(407\) 0.381542 0.0189123
\(408\) −7.15081 −0.354018
\(409\) 29.2086 1.44427 0.722136 0.691752i \(-0.243161\pi\)
0.722136 + 0.691752i \(0.243161\pi\)
\(410\) −26.4838 −1.30794
\(411\) 7.27768 0.358982
\(412\) 13.8430 0.681997
\(413\) 2.72011 0.133848
\(414\) 1.27493 0.0626593
\(415\) 48.9460 2.40267
\(416\) −31.7678 −1.55755
\(417\) 12.5015 0.612201
\(418\) −0.0184544 −0.000902635 0
\(419\) −1.82071 −0.0889475 −0.0444737 0.999011i \(-0.514161\pi\)
−0.0444737 + 0.999011i \(0.514161\pi\)
\(420\) −6.67711 −0.325809
\(421\) 5.80427 0.282883 0.141441 0.989947i \(-0.454826\pi\)
0.141441 + 0.989947i \(0.454826\pi\)
\(422\) −5.29252 −0.257636
\(423\) 1.96344 0.0954656
\(424\) 24.4536 1.18757
\(425\) 37.8067 1.83389
\(426\) −6.83885 −0.331344
\(427\) 5.24229 0.253692
\(428\) 5.80257 0.280478
\(429\) 0.210319 0.0101543
\(430\) 9.73438 0.469434
\(431\) −4.95352 −0.238603 −0.119301 0.992858i \(-0.538065\pi\)
−0.119301 + 0.992858i \(0.538065\pi\)
\(432\) −1.99118 −0.0958007
\(433\) 26.1195 1.25522 0.627612 0.778526i \(-0.284032\pi\)
0.627612 + 0.778526i \(0.284032\pi\)
\(434\) 3.88341 0.186410
\(435\) −29.0292 −1.39184
\(436\) 7.29785 0.349503
\(437\) 1.80367 0.0862812
\(438\) −3.32259 −0.158760
\(439\) 23.2695 1.11059 0.555295 0.831653i \(-0.312605\pi\)
0.555295 + 0.831653i \(0.312605\pi\)
\(440\) −0.323600 −0.0154270
\(441\) 1.00000 0.0476190
\(442\) −11.2606 −0.535614
\(443\) 9.99727 0.474985 0.237492 0.971389i \(-0.423675\pi\)
0.237492 + 0.971389i \(0.423675\pi\)
\(444\) −17.1153 −0.812256
\(445\) −40.3626 −1.91337
\(446\) −2.44044 −0.115558
\(447\) 17.4040 0.823181
\(448\) 0.679692 0.0321124
\(449\) −21.8543 −1.03137 −0.515684 0.856779i \(-0.672462\pi\)
−0.515684 + 0.856779i \(0.672462\pi\)
\(450\) −6.85723 −0.323253
\(451\) −0.400611 −0.0188640
\(452\) 22.0734 1.03825
\(453\) 12.6550 0.594583
\(454\) 6.71845 0.315313
\(455\) −23.3056 −1.09258
\(456\) 1.83488 0.0859260
\(457\) 10.1375 0.474211 0.237105 0.971484i \(-0.423801\pi\)
0.237105 + 0.971484i \(0.423801\pi\)
\(458\) 8.26727 0.386304
\(459\) −3.28922 −0.153528
\(460\) 14.2692 0.665306
\(461\) 26.8464 1.25036 0.625181 0.780480i \(-0.285025\pi\)
0.625181 + 0.780480i \(0.285025\pi\)
\(462\) 0.0218653 0.00101727
\(463\) −22.8400 −1.06146 −0.530731 0.847540i \(-0.678083\pi\)
−0.530731 + 0.847540i \(0.678083\pi\)
\(464\) 14.2325 0.660727
\(465\) −26.4365 −1.22596
\(466\) 1.55880 0.0722101
\(467\) 2.83717 0.131289 0.0656443 0.997843i \(-0.479090\pi\)
0.0656443 + 0.997843i \(0.479090\pi\)
\(468\) −9.43453 −0.436111
\(469\) 5.39696 0.249208
\(470\) −4.75724 −0.219435
\(471\) 8.35868 0.385147
\(472\) −5.91356 −0.272194
\(473\) 0.147249 0.00677051
\(474\) 1.95955 0.0900053
\(475\) −9.70108 −0.445116
\(476\) 5.40776 0.247864
\(477\) 11.2481 0.515016
\(478\) −1.42928 −0.0653738
\(479\) −6.85478 −0.313203 −0.156601 0.987662i \(-0.550054\pi\)
−0.156601 + 0.987662i \(0.550054\pi\)
\(480\) 22.4831 1.02621
\(481\) −59.7388 −2.72385
\(482\) −0.651075 −0.0296557
\(483\) −2.13704 −0.0972385
\(484\) 18.0827 0.821942
\(485\) 51.7675 2.35064
\(486\) 0.596587 0.0270617
\(487\) 31.0590 1.40742 0.703709 0.710488i \(-0.251526\pi\)
0.703709 + 0.710488i \(0.251526\pi\)
\(488\) −11.3968 −0.515910
\(489\) 14.3097 0.647105
\(490\) −2.42291 −0.109456
\(491\) −1.64485 −0.0742310 −0.0371155 0.999311i \(-0.511817\pi\)
−0.0371155 + 0.999311i \(0.511817\pi\)
\(492\) 17.9707 0.810182
\(493\) 23.5106 1.05886
\(494\) 2.88945 0.130002
\(495\) −0.148849 −0.00669026
\(496\) 12.9613 0.581981
\(497\) 11.4633 0.514199
\(498\) 7.18997 0.322190
\(499\) −33.7150 −1.50929 −0.754646 0.656133i \(-0.772191\pi\)
−0.754646 + 0.656133i \(0.772191\pi\)
\(500\) −43.3618 −1.93920
\(501\) −8.50396 −0.379929
\(502\) −15.8391 −0.706934
\(503\) −15.5582 −0.693705 −0.346852 0.937920i \(-0.612750\pi\)
−0.346852 + 0.937920i \(0.612750\pi\)
\(504\) −2.17401 −0.0968382
\(505\) 34.1982 1.52180
\(506\) −0.0467269 −0.00207726
\(507\) −19.9300 −0.885124
\(508\) −2.70373 −0.119959
\(509\) 4.26687 0.189126 0.0945628 0.995519i \(-0.469855\pi\)
0.0945628 + 0.995519i \(0.469855\pi\)
\(510\) 7.96950 0.352895
\(511\) 5.56933 0.246373
\(512\) −19.6808 −0.869775
\(513\) 0.844005 0.0372637
\(514\) 16.4364 0.724977
\(515\) −34.1957 −1.50684
\(516\) −6.60533 −0.290783
\(517\) −0.0719612 −0.00316485
\(518\) −6.21061 −0.272878
\(519\) −8.94722 −0.392739
\(520\) 50.6667 2.22188
\(521\) −30.6461 −1.34263 −0.671314 0.741173i \(-0.734270\pi\)
−0.671314 + 0.741173i \(0.734270\pi\)
\(522\) −4.26426 −0.186642
\(523\) 3.94602 0.172547 0.0862737 0.996271i \(-0.472504\pi\)
0.0862737 + 0.996271i \(0.472504\pi\)
\(524\) −33.1499 −1.44816
\(525\) 11.4941 0.501644
\(526\) 1.83556 0.0800343
\(527\) 21.4108 0.932668
\(528\) 0.0729780 0.00317596
\(529\) −18.4331 −0.801438
\(530\) −27.2532 −1.18381
\(531\) −2.72011 −0.118043
\(532\) −1.38761 −0.0601607
\(533\) 62.7245 2.71690
\(534\) −5.92910 −0.256577
\(535\) −14.3338 −0.619703
\(536\) −11.7331 −0.506791
\(537\) −15.6746 −0.676407
\(538\) 4.10719 0.177074
\(539\) −0.0366506 −0.00157865
\(540\) 6.67711 0.287337
\(541\) −43.0110 −1.84919 −0.924595 0.380952i \(-0.875596\pi\)
−0.924595 + 0.380952i \(0.875596\pi\)
\(542\) −7.66477 −0.329230
\(543\) −23.4932 −1.00819
\(544\) −18.2089 −0.780701
\(545\) −18.0275 −0.772212
\(546\) −3.42350 −0.146512
\(547\) −24.6409 −1.05357 −0.526784 0.849999i \(-0.676602\pi\)
−0.526784 + 0.849999i \(0.676602\pi\)
\(548\) 11.9651 0.511125
\(549\) −5.24229 −0.223736
\(550\) 0.251322 0.0107164
\(551\) −6.03275 −0.257004
\(552\) 4.64594 0.197745
\(553\) −3.28461 −0.139676
\(554\) 3.20344 0.136101
\(555\) 42.2790 1.79464
\(556\) 20.5535 0.871663
\(557\) −20.6836 −0.876391 −0.438196 0.898880i \(-0.644382\pi\)
−0.438196 + 0.898880i \(0.644382\pi\)
\(558\) −3.88341 −0.164398
\(559\) −23.0551 −0.975125
\(560\) −8.08677 −0.341728
\(561\) 0.120552 0.00508971
\(562\) 6.44712 0.271955
\(563\) −31.0927 −1.31040 −0.655201 0.755455i \(-0.727416\pi\)
−0.655201 + 0.755455i \(0.727416\pi\)
\(564\) 3.22806 0.135926
\(565\) −54.5268 −2.29396
\(566\) −4.95672 −0.208346
\(567\) −1.00000 −0.0419961
\(568\) −24.9214 −1.04568
\(569\) 2.11572 0.0886956 0.0443478 0.999016i \(-0.485879\pi\)
0.0443478 + 0.999016i \(0.485879\pi\)
\(570\) −2.04495 −0.0856536
\(571\) 25.8638 1.08236 0.541182 0.840905i \(-0.317977\pi\)
0.541182 + 0.840905i \(0.317977\pi\)
\(572\) 0.345781 0.0144578
\(573\) −1.00000 −0.0417756
\(574\) 6.52101 0.272182
\(575\) −24.5633 −1.02436
\(576\) −0.679692 −0.0283205
\(577\) 15.1456 0.630519 0.315259 0.949006i \(-0.397909\pi\)
0.315259 + 0.949006i \(0.397909\pi\)
\(578\) 3.68752 0.153381
\(579\) −13.5056 −0.561274
\(580\) −47.7264 −1.98173
\(581\) −12.0518 −0.499994
\(582\) 7.60442 0.315214
\(583\) −0.412251 −0.0170737
\(584\) −12.1078 −0.501024
\(585\) 23.3056 0.963568
\(586\) −18.3122 −0.756469
\(587\) −39.2402 −1.61961 −0.809807 0.586696i \(-0.800428\pi\)
−0.809807 + 0.586696i \(0.800428\pi\)
\(588\) 1.64408 0.0678009
\(589\) −5.49394 −0.226374
\(590\) 6.59060 0.271331
\(591\) 7.82429 0.321848
\(592\) −20.7286 −0.851942
\(593\) −0.156852 −0.00644115 −0.00322057 0.999995i \(-0.501025\pi\)
−0.00322057 + 0.999995i \(0.501025\pi\)
\(594\) −0.0218653 −0.000897144 0
\(595\) −13.3585 −0.547645
\(596\) 28.6136 1.17206
\(597\) −24.9482 −1.02106
\(598\) 7.31613 0.299179
\(599\) −28.8827 −1.18011 −0.590057 0.807362i \(-0.700895\pi\)
−0.590057 + 0.807362i \(0.700895\pi\)
\(600\) −24.9883 −1.02014
\(601\) −14.1337 −0.576526 −0.288263 0.957551i \(-0.593078\pi\)
−0.288263 + 0.957551i \(0.593078\pi\)
\(602\) −2.39687 −0.0976890
\(603\) −5.39696 −0.219781
\(604\) 20.8058 0.846578
\(605\) −44.6688 −1.81604
\(606\) 5.02357 0.204069
\(607\) −43.0094 −1.74570 −0.872850 0.487989i \(-0.837731\pi\)
−0.872850 + 0.487989i \(0.837731\pi\)
\(608\) 4.67236 0.189489
\(609\) 7.14777 0.289642
\(610\) 12.7016 0.514274
\(611\) 11.2671 0.455819
\(612\) −5.40776 −0.218596
\(613\) −16.3540 −0.660532 −0.330266 0.943888i \(-0.607138\pi\)
−0.330266 + 0.943888i \(0.607138\pi\)
\(614\) −17.7572 −0.716624
\(615\) −44.3921 −1.79006
\(616\) 0.0796790 0.00321036
\(617\) −33.4102 −1.34504 −0.672522 0.740077i \(-0.734789\pi\)
−0.672522 + 0.740077i \(0.734789\pi\)
\(618\) −5.02321 −0.202063
\(619\) 35.9494 1.44493 0.722464 0.691409i \(-0.243010\pi\)
0.722464 + 0.691409i \(0.243010\pi\)
\(620\) −43.4638 −1.74555
\(621\) 2.13704 0.0857563
\(622\) 5.24248 0.210204
\(623\) 9.93837 0.398172
\(624\) −11.4263 −0.457419
\(625\) 49.6439 1.98576
\(626\) −14.2113 −0.567999
\(627\) −0.0309333 −0.00123536
\(628\) 13.7424 0.548380
\(629\) −34.2415 −1.36530
\(630\) 2.42291 0.0965312
\(631\) −26.5993 −1.05890 −0.529452 0.848340i \(-0.677602\pi\)
−0.529452 + 0.848340i \(0.677602\pi\)
\(632\) 7.14078 0.284045
\(633\) −8.87133 −0.352604
\(634\) 6.86405 0.272606
\(635\) 6.67888 0.265043
\(636\) 18.4929 0.733290
\(637\) 5.73847 0.227366
\(638\) 0.156288 0.00618750
\(639\) −11.4633 −0.453481
\(640\) 46.6130 1.84254
\(641\) 34.1004 1.34688 0.673442 0.739240i \(-0.264815\pi\)
0.673442 + 0.739240i \(0.264815\pi\)
\(642\) −2.10557 −0.0831003
\(643\) 8.80594 0.347272 0.173636 0.984810i \(-0.444448\pi\)
0.173636 + 0.984810i \(0.444448\pi\)
\(644\) −3.51347 −0.138450
\(645\) 16.3168 0.642473
\(646\) 1.65620 0.0651622
\(647\) 10.6708 0.419513 0.209757 0.977754i \(-0.432733\pi\)
0.209757 + 0.977754i \(0.432733\pi\)
\(648\) 2.17401 0.0854033
\(649\) 0.0996938 0.00391332
\(650\) −39.3500 −1.54343
\(651\) 6.50937 0.255123
\(652\) 23.5263 0.921360
\(653\) −26.1605 −1.02374 −0.511870 0.859063i \(-0.671047\pi\)
−0.511870 + 0.859063i \(0.671047\pi\)
\(654\) −2.64816 −0.103551
\(655\) 81.8884 3.19964
\(656\) 21.7647 0.849767
\(657\) −5.56933 −0.217280
\(658\) 1.17136 0.0456644
\(659\) −37.8063 −1.47272 −0.736362 0.676588i \(-0.763458\pi\)
−0.736362 + 0.676588i \(0.763458\pi\)
\(660\) −0.244720 −0.00952572
\(661\) 13.3380 0.518790 0.259395 0.965771i \(-0.416477\pi\)
0.259395 + 0.965771i \(0.416477\pi\)
\(662\) 20.0385 0.778817
\(663\) −18.8751 −0.733048
\(664\) 26.2008 1.01679
\(665\) 3.42775 0.132922
\(666\) 6.21061 0.240656
\(667\) −15.2750 −0.591452
\(668\) −13.9812 −0.540950
\(669\) −4.09068 −0.158155
\(670\) 13.0764 0.505184
\(671\) 0.192133 0.00741723
\(672\) −5.53594 −0.213553
\(673\) −29.9320 −1.15379 −0.576897 0.816817i \(-0.695736\pi\)
−0.576897 + 0.816817i \(0.695736\pi\)
\(674\) 1.31781 0.0507600
\(675\) −11.4941 −0.442408
\(676\) −32.7667 −1.26026
\(677\) 20.5821 0.791034 0.395517 0.918459i \(-0.370565\pi\)
0.395517 + 0.918459i \(0.370565\pi\)
\(678\) −8.00976 −0.307613
\(679\) −12.7465 −0.489168
\(680\) 29.0415 1.11369
\(681\) 11.2615 0.431541
\(682\) 0.142329 0.00545007
\(683\) 3.86925 0.148053 0.0740264 0.997256i \(-0.476415\pi\)
0.0740264 + 0.997256i \(0.476415\pi\)
\(684\) 1.38761 0.0530568
\(685\) −29.5568 −1.12931
\(686\) 0.596587 0.0227778
\(687\) 13.8576 0.528701
\(688\) −7.99983 −0.304991
\(689\) 64.5470 2.45905
\(690\) −5.17786 −0.197118
\(691\) −38.8416 −1.47761 −0.738803 0.673922i \(-0.764608\pi\)
−0.738803 + 0.673922i \(0.764608\pi\)
\(692\) −14.7100 −0.559190
\(693\) 0.0366506 0.00139224
\(694\) −16.9233 −0.642399
\(695\) −50.7722 −1.92590
\(696\) −15.5393 −0.589017
\(697\) 35.9529 1.36181
\(698\) 1.54937 0.0586447
\(699\) 2.61287 0.0988277
\(700\) 18.8973 0.714250
\(701\) −29.6266 −1.11898 −0.559490 0.828837i \(-0.689003\pi\)
−0.559490 + 0.828837i \(0.689003\pi\)
\(702\) 3.42350 0.129212
\(703\) 8.78628 0.331381
\(704\) 0.0249111 0.000938874 0
\(705\) −7.97410 −0.300322
\(706\) 7.89958 0.297305
\(707\) −8.42052 −0.316686
\(708\) −4.47209 −0.168071
\(709\) 28.9486 1.08719 0.543593 0.839349i \(-0.317064\pi\)
0.543593 + 0.839349i \(0.317064\pi\)
\(710\) 27.7746 1.04236
\(711\) 3.28461 0.123182
\(712\) −21.6061 −0.809725
\(713\) −13.9108 −0.520962
\(714\) −1.96231 −0.0734375
\(715\) −0.854166 −0.0319440
\(716\) −25.7703 −0.963081
\(717\) −2.39576 −0.0894714
\(718\) −19.7485 −0.737008
\(719\) 18.1650 0.677439 0.338720 0.940887i \(-0.390006\pi\)
0.338720 + 0.940887i \(0.390006\pi\)
\(720\) 8.08677 0.301376
\(721\) 8.41991 0.313574
\(722\) 10.9102 0.406035
\(723\) −1.09133 −0.0405871
\(724\) −38.6249 −1.43548
\(725\) 82.1572 3.05124
\(726\) −6.56166 −0.243526
\(727\) 6.28106 0.232952 0.116476 0.993194i \(-0.462840\pi\)
0.116476 + 0.993194i \(0.462840\pi\)
\(728\) −12.4755 −0.462373
\(729\) 1.00000 0.0370370
\(730\) 13.4940 0.499436
\(731\) −13.2149 −0.488770
\(732\) −8.61877 −0.318559
\(733\) −4.43301 −0.163737 −0.0818685 0.996643i \(-0.526089\pi\)
−0.0818685 + 0.996643i \(0.526089\pi\)
\(734\) −9.56441 −0.353029
\(735\) −4.06129 −0.149803
\(736\) 11.8305 0.436078
\(737\) 0.197802 0.00728613
\(738\) −6.52101 −0.240042
\(739\) 41.9437 1.54292 0.771462 0.636276i \(-0.219526\pi\)
0.771462 + 0.636276i \(0.219526\pi\)
\(740\) 69.5102 2.55525
\(741\) 4.84330 0.177923
\(742\) 6.71048 0.246350
\(743\) 17.6244 0.646575 0.323287 0.946301i \(-0.395212\pi\)
0.323287 + 0.946301i \(0.395212\pi\)
\(744\) −14.1515 −0.518818
\(745\) −70.6828 −2.58962
\(746\) −11.5025 −0.421136
\(747\) 12.0518 0.440954
\(748\) 0.198198 0.00724683
\(749\) 3.52936 0.128960
\(750\) 15.7347 0.574549
\(751\) 12.1380 0.442921 0.221461 0.975169i \(-0.428918\pi\)
0.221461 + 0.975169i \(0.428918\pi\)
\(752\) 3.90956 0.142567
\(753\) −26.5495 −0.967519
\(754\) −24.4704 −0.891158
\(755\) −51.3956 −1.87048
\(756\) −1.64408 −0.0597948
\(757\) −30.4617 −1.10715 −0.553575 0.832800i \(-0.686737\pi\)
−0.553575 + 0.832800i \(0.686737\pi\)
\(758\) −11.1897 −0.406429
\(759\) −0.0783237 −0.00284297
\(760\) −7.45197 −0.270312
\(761\) −12.7952 −0.463824 −0.231912 0.972737i \(-0.574498\pi\)
−0.231912 + 0.972737i \(0.574498\pi\)
\(762\) 0.981100 0.0355415
\(763\) 4.43885 0.160697
\(764\) −1.64408 −0.0594809
\(765\) 13.3585 0.482977
\(766\) −9.59241 −0.346588
\(767\) −15.6093 −0.563618
\(768\) 5.48787 0.198026
\(769\) −7.30174 −0.263307 −0.131654 0.991296i \(-0.542029\pi\)
−0.131654 + 0.991296i \(0.542029\pi\)
\(770\) −0.0888014 −0.00320018
\(771\) 27.5507 0.992213
\(772\) −22.2044 −0.799152
\(773\) −39.0629 −1.40500 −0.702498 0.711685i \(-0.747932\pi\)
−0.702498 + 0.711685i \(0.747932\pi\)
\(774\) 2.39687 0.0861536
\(775\) 74.8194 2.68759
\(776\) 27.7112 0.994773
\(777\) −10.4102 −0.373465
\(778\) 11.8373 0.424388
\(779\) −9.22542 −0.330535
\(780\) 38.3164 1.37195
\(781\) 0.420137 0.0150337
\(782\) 4.19352 0.149960
\(783\) −7.14777 −0.255440
\(784\) 1.99118 0.0711136
\(785\) −33.9470 −1.21162
\(786\) 12.0291 0.429062
\(787\) −38.1559 −1.36011 −0.680056 0.733160i \(-0.738045\pi\)
−0.680056 + 0.733160i \(0.738045\pi\)
\(788\) 12.8638 0.458253
\(789\) 3.07677 0.109536
\(790\) −7.95833 −0.283145
\(791\) 13.4260 0.477373
\(792\) −0.0796790 −0.00283127
\(793\) −30.0827 −1.06827
\(794\) −6.79471 −0.241135
\(795\) −45.6819 −1.62017
\(796\) −41.0169 −1.45381
\(797\) −48.3879 −1.71399 −0.856994 0.515327i \(-0.827670\pi\)
−0.856994 + 0.515327i \(0.827670\pi\)
\(798\) 0.503522 0.0178245
\(799\) 6.45818 0.228474
\(800\) −63.6306 −2.24968
\(801\) −9.93837 −0.351155
\(802\) −22.7394 −0.802957
\(803\) 0.204120 0.00720322
\(804\) −8.87305 −0.312928
\(805\) 8.67913 0.305899
\(806\) −22.2848 −0.784949
\(807\) 6.88448 0.242345
\(808\) 18.3063 0.644014
\(809\) −9.39155 −0.330189 −0.165095 0.986278i \(-0.552793\pi\)
−0.165095 + 0.986278i \(0.552793\pi\)
\(810\) −2.42291 −0.0851325
\(811\) 9.09656 0.319423 0.159712 0.987164i \(-0.448944\pi\)
0.159712 + 0.987164i \(0.448944\pi\)
\(812\) 11.7515 0.412398
\(813\) −12.8477 −0.450589
\(814\) −0.227623 −0.00797817
\(815\) −58.1157 −2.03571
\(816\) −6.54943 −0.229276
\(817\) 3.39090 0.118633
\(818\) −17.4255 −0.609267
\(819\) −5.73847 −0.200518
\(820\) −72.9844 −2.54872
\(821\) −8.81763 −0.307737 −0.153869 0.988091i \(-0.549173\pi\)
−0.153869 + 0.988091i \(0.549173\pi\)
\(822\) −4.34177 −0.151437
\(823\) 42.8775 1.49462 0.747308 0.664477i \(-0.231346\pi\)
0.747308 + 0.664477i \(0.231346\pi\)
\(824\) −18.3050 −0.637685
\(825\) 0.421266 0.0146666
\(826\) −1.62278 −0.0564638
\(827\) 9.82786 0.341748 0.170874 0.985293i \(-0.445341\pi\)
0.170874 + 0.985293i \(0.445341\pi\)
\(828\) 3.51347 0.122101
\(829\) −2.90732 −0.100975 −0.0504876 0.998725i \(-0.516078\pi\)
−0.0504876 + 0.998725i \(0.516078\pi\)
\(830\) −29.2006 −1.01357
\(831\) 5.36962 0.186270
\(832\) −3.90039 −0.135222
\(833\) 3.28922 0.113965
\(834\) −7.45823 −0.258257
\(835\) 34.5371 1.19520
\(836\) −0.0508570 −0.00175892
\(837\) −6.50937 −0.224997
\(838\) 1.08621 0.0375226
\(839\) −2.75261 −0.0950308 −0.0475154 0.998871i \(-0.515130\pi\)
−0.0475154 + 0.998871i \(0.515130\pi\)
\(840\) 8.82930 0.304640
\(841\) 22.0906 0.761743
\(842\) −3.46275 −0.119334
\(843\) 10.8067 0.372202
\(844\) −14.5852 −0.502044
\(845\) 80.9417 2.78448
\(846\) −1.17136 −0.0402722
\(847\) 10.9987 0.377918
\(848\) 22.3970 0.769118
\(849\) −8.30846 −0.285146
\(850\) −22.5550 −0.773629
\(851\) 22.2470 0.762618
\(852\) −18.8466 −0.645675
\(853\) −35.9223 −1.22996 −0.614979 0.788544i \(-0.710835\pi\)
−0.614979 + 0.788544i \(0.710835\pi\)
\(854\) −3.12748 −0.107020
\(855\) −3.42775 −0.117227
\(856\) −7.67288 −0.262254
\(857\) −17.6768 −0.603828 −0.301914 0.953335i \(-0.597625\pi\)
−0.301914 + 0.953335i \(0.597625\pi\)
\(858\) −0.125473 −0.00428359
\(859\) −4.86891 −0.166125 −0.0830625 0.996544i \(-0.526470\pi\)
−0.0830625 + 0.996544i \(0.526470\pi\)
\(860\) 26.8262 0.914765
\(861\) 10.9305 0.372512
\(862\) 2.95521 0.100655
\(863\) 52.0150 1.77061 0.885305 0.465011i \(-0.153950\pi\)
0.885305 + 0.465011i \(0.153950\pi\)
\(864\) 5.53594 0.188336
\(865\) 36.3373 1.23550
\(866\) −15.5826 −0.529517
\(867\) 6.18102 0.209919
\(868\) 10.7020 0.363248
\(869\) −0.120383 −0.00408371
\(870\) 17.3184 0.587150
\(871\) −30.9703 −1.04939
\(872\) −9.65012 −0.326794
\(873\) 12.7465 0.431405
\(874\) −1.07605 −0.0363978
\(875\) −26.3745 −0.891620
\(876\) −9.15645 −0.309368
\(877\) 6.39599 0.215977 0.107989 0.994152i \(-0.465559\pi\)
0.107989 + 0.994152i \(0.465559\pi\)
\(878\) −13.8823 −0.468503
\(879\) −30.6949 −1.03531
\(880\) −0.296385 −0.00999114
\(881\) 44.6292 1.50359 0.751797 0.659394i \(-0.229187\pi\)
0.751797 + 0.659394i \(0.229187\pi\)
\(882\) −0.596587 −0.0200881
\(883\) −2.45544 −0.0826320 −0.0413160 0.999146i \(-0.513155\pi\)
−0.0413160 + 0.999146i \(0.513155\pi\)
\(884\) −31.0322 −1.04373
\(885\) 11.0472 0.371347
\(886\) −5.96424 −0.200373
\(887\) −7.52473 −0.252656 −0.126328 0.991989i \(-0.540319\pi\)
−0.126328 + 0.991989i \(0.540319\pi\)
\(888\) 22.6320 0.759479
\(889\) −1.64452 −0.0551555
\(890\) 24.0798 0.807157
\(891\) −0.0366506 −0.00122784
\(892\) −6.72542 −0.225184
\(893\) −1.65715 −0.0554544
\(894\) −10.3830 −0.347259
\(895\) 63.6590 2.12789
\(896\) −11.4774 −0.383432
\(897\) 12.2633 0.409460
\(898\) 13.0380 0.435084
\(899\) 46.5275 1.55178
\(900\) −18.8973 −0.629909
\(901\) 36.9976 1.23257
\(902\) 0.238999 0.00795781
\(903\) −4.01763 −0.133698
\(904\) −29.1882 −0.970787
\(905\) 95.4129 3.17163
\(906\) −7.54980 −0.250825
\(907\) 27.8467 0.924636 0.462318 0.886714i \(-0.347018\pi\)
0.462318 + 0.886714i \(0.347018\pi\)
\(908\) 18.5148 0.614436
\(909\) 8.42052 0.279291
\(910\) 13.9038 0.460907
\(911\) −30.2050 −1.00074 −0.500369 0.865812i \(-0.666802\pi\)
−0.500369 + 0.865812i \(0.666802\pi\)
\(912\) 1.68057 0.0556491
\(913\) −0.441707 −0.0146184
\(914\) −6.04788 −0.200046
\(915\) 21.2905 0.703842
\(916\) 22.7831 0.752774
\(917\) −20.1631 −0.665845
\(918\) 1.96231 0.0647658
\(919\) −1.03564 −0.0341627 −0.0170813 0.999854i \(-0.505437\pi\)
−0.0170813 + 0.999854i \(0.505437\pi\)
\(920\) −18.8685 −0.622077
\(921\) −29.7647 −0.980781
\(922\) −16.0162 −0.527466
\(923\) −65.7818 −2.16523
\(924\) 0.0602567 0.00198230
\(925\) −119.656 −3.93427
\(926\) 13.6260 0.447779
\(927\) −8.41991 −0.276546
\(928\) −39.5696 −1.29894
\(929\) −4.20876 −0.138085 −0.0690424 0.997614i \(-0.521994\pi\)
−0.0690424 + 0.997614i \(0.521994\pi\)
\(930\) 15.7717 0.517173
\(931\) −0.844005 −0.0276611
\(932\) 4.29577 0.140713
\(933\) 8.78746 0.287689
\(934\) −1.69262 −0.0553842
\(935\) −0.489597 −0.0160115
\(936\) 12.4755 0.407775
\(937\) −47.6812 −1.55768 −0.778838 0.627225i \(-0.784190\pi\)
−0.778838 + 0.627225i \(0.784190\pi\)
\(938\) −3.21975 −0.105129
\(939\) −23.8210 −0.777370
\(940\) −13.1101 −0.427604
\(941\) 10.4356 0.340191 0.170096 0.985428i \(-0.445592\pi\)
0.170096 + 0.985428i \(0.445592\pi\)
\(942\) −4.98668 −0.162475
\(943\) −23.3589 −0.760672
\(944\) −5.41623 −0.176283
\(945\) 4.06129 0.132114
\(946\) −0.0878467 −0.00285614
\(947\) 36.3005 1.17961 0.589803 0.807547i \(-0.299205\pi\)
0.589803 + 0.807547i \(0.299205\pi\)
\(948\) 5.40017 0.175389
\(949\) −31.9594 −1.03745
\(950\) 5.78754 0.187772
\(951\) 11.5055 0.373092
\(952\) −7.15081 −0.231759
\(953\) 37.0334 1.19963 0.599815 0.800138i \(-0.295241\pi\)
0.599815 + 0.800138i \(0.295241\pi\)
\(954\) −6.71048 −0.217260
\(955\) 4.06129 0.131420
\(956\) −3.93883 −0.127391
\(957\) 0.261970 0.00846829
\(958\) 4.08947 0.132125
\(959\) 7.27768 0.235009
\(960\) 2.76043 0.0890925
\(961\) 11.3720 0.366837
\(962\) 35.6394 1.14906
\(963\) −3.52936 −0.113732
\(964\) −1.79424 −0.0577887
\(965\) 54.8502 1.76569
\(966\) 1.27493 0.0410201
\(967\) −41.1212 −1.32237 −0.661185 0.750223i \(-0.729946\pi\)
−0.661185 + 0.750223i \(0.729946\pi\)
\(968\) −23.9112 −0.768536
\(969\) 2.77612 0.0891818
\(970\) −30.8838 −0.991619
\(971\) −27.8410 −0.893460 −0.446730 0.894669i \(-0.647411\pi\)
−0.446730 + 0.894669i \(0.647411\pi\)
\(972\) 1.64408 0.0527340
\(973\) 12.5015 0.400780
\(974\) −18.5294 −0.593720
\(975\) −65.9586 −2.11236
\(976\) −10.4384 −0.334123
\(977\) 31.0538 0.993499 0.496750 0.867894i \(-0.334527\pi\)
0.496750 + 0.867894i \(0.334527\pi\)
\(978\) −8.53696 −0.272982
\(979\) 0.364248 0.0116414
\(980\) −6.67711 −0.213292
\(981\) −4.43885 −0.141722
\(982\) 0.981295 0.0313144
\(983\) −16.0732 −0.512655 −0.256327 0.966590i \(-0.582513\pi\)
−0.256327 + 0.966590i \(0.582513\pi\)
\(984\) −23.7631 −0.757541
\(985\) −31.7767 −1.01249
\(986\) −14.0261 −0.446682
\(987\) 1.96344 0.0624969
\(988\) 7.96279 0.253330
\(989\) 8.58583 0.273013
\(990\) 0.0888014 0.00282229
\(991\) −35.6406 −1.13216 −0.566080 0.824350i \(-0.691541\pi\)
−0.566080 + 0.824350i \(0.691541\pi\)
\(992\) −36.0355 −1.14413
\(993\) 33.5885 1.06590
\(994\) −6.83885 −0.216915
\(995\) 101.322 3.21212
\(996\) 19.8142 0.627838
\(997\) 28.8499 0.913684 0.456842 0.889548i \(-0.348980\pi\)
0.456842 + 0.889548i \(0.348980\pi\)
\(998\) 20.1139 0.636696
\(999\) 10.4102 0.329365
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 4011.2.a.j.1.12 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.j.1.12 26 1.1 even 1 trivial