Properties

Label 4018.2.a.bs.1.9
Level $4018$
Weight $2$
Character 4018.1
Self dual yes
Analytic conductor $32.084$
Analytic rank $0$
Dimension $10$
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] = [4018,2,Mod(1,4018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4018, 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("4018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.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: \(32.0838915322\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(0.553933\) of defining polynomial
Character \(\chi\) \(=\) 4018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.84461 q^{3} +1.00000 q^{4} +0.100034 q^{5} -2.84461 q^{6} -1.00000 q^{8} +5.09179 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.84461 q^{3} +1.00000 q^{4} +0.100034 q^{5} -2.84461 q^{6} -1.00000 q^{8} +5.09179 q^{9} -0.100034 q^{10} +5.49180 q^{11} +2.84461 q^{12} +2.00425 q^{13} +0.284559 q^{15} +1.00000 q^{16} -2.02518 q^{17} -5.09179 q^{18} +5.25933 q^{19} +0.100034 q^{20} -5.49180 q^{22} -0.177764 q^{23} -2.84461 q^{24} -4.98999 q^{25} -2.00425 q^{26} +5.95032 q^{27} +1.92418 q^{29} -0.284559 q^{30} -1.74323 q^{31} -1.00000 q^{32} +15.6220 q^{33} +2.02518 q^{34} +5.09179 q^{36} +0.296315 q^{37} -5.25933 q^{38} +5.70130 q^{39} -0.100034 q^{40} +1.00000 q^{41} -3.48995 q^{43} +5.49180 q^{44} +0.509354 q^{45} +0.177764 q^{46} +12.7178 q^{47} +2.84461 q^{48} +4.98999 q^{50} -5.76085 q^{51} +2.00425 q^{52} -0.522296 q^{53} -5.95032 q^{54} +0.549369 q^{55} +14.9607 q^{57} -1.92418 q^{58} -10.3189 q^{59} +0.284559 q^{60} +10.2472 q^{61} +1.74323 q^{62} +1.00000 q^{64} +0.200494 q^{65} -15.6220 q^{66} +7.52851 q^{67} -2.02518 q^{68} -0.505669 q^{69} +0.0873211 q^{71} -5.09179 q^{72} -7.69792 q^{73} -0.296315 q^{74} -14.1946 q^{75} +5.25933 q^{76} -5.70130 q^{78} -2.15620 q^{79} +0.100034 q^{80} +1.65095 q^{81} -1.00000 q^{82} -1.63342 q^{83} -0.202588 q^{85} +3.48995 q^{86} +5.47353 q^{87} -5.49180 q^{88} -6.70260 q^{89} -0.509354 q^{90} -0.177764 q^{92} -4.95879 q^{93} -12.7178 q^{94} +0.526114 q^{95} -2.84461 q^{96} -0.783908 q^{97} +27.9631 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} + 4 q^{3} + 10 q^{4} + 4 q^{5} - 4 q^{6} - 10 q^{8} + 10 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 20 q^{17} - 10 q^{18} + 4 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 16 q^{27} - 4 q^{29} - 4 q^{30} - 4 q^{31} - 10 q^{32} + 36 q^{33} - 20 q^{34} + 10 q^{36} - 16 q^{37} + 20 q^{39} - 4 q^{40} + 10 q^{41} - 8 q^{43} + 4 q^{44} + 4 q^{45} - 4 q^{46} + 24 q^{47} + 4 q^{48} - 6 q^{50} + 20 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{54} + 20 q^{55} - 4 q^{57} + 4 q^{58} + 4 q^{60} + 4 q^{62} + 10 q^{64} - 12 q^{65} - 36 q^{66} + 8 q^{67} + 20 q^{68} + 4 q^{71} - 10 q^{72} - 24 q^{73} + 16 q^{74} + 48 q^{75} - 20 q^{78} + 24 q^{79} + 4 q^{80} - 18 q^{81} - 10 q^{82} + 48 q^{83} + 8 q^{85} + 8 q^{86} + 4 q^{87} - 4 q^{88} + 20 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 24 q^{94} - 4 q^{95} - 4 q^{96} + 4 q^{97} + 32 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 2.84461 1.64233 0.821167 0.570687i \(-0.193323\pi\)
0.821167 + 0.570687i \(0.193323\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.100034 0.0447367 0.0223684 0.999750i \(-0.492879\pi\)
0.0223684 + 0.999750i \(0.492879\pi\)
\(6\) −2.84461 −1.16131
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 5.09179 1.69726
\(10\) −0.100034 −0.0316336
\(11\) 5.49180 1.65584 0.827921 0.560845i \(-0.189524\pi\)
0.827921 + 0.560845i \(0.189524\pi\)
\(12\) 2.84461 0.821167
\(13\) 2.00425 0.555878 0.277939 0.960599i \(-0.410349\pi\)
0.277939 + 0.960599i \(0.410349\pi\)
\(14\) 0 0
\(15\) 0.284559 0.0734727
\(16\) 1.00000 0.250000
\(17\) −2.02518 −0.491179 −0.245590 0.969374i \(-0.578982\pi\)
−0.245590 + 0.969374i \(0.578982\pi\)
\(18\) −5.09179 −1.20015
\(19\) 5.25933 1.20657 0.603287 0.797524i \(-0.293857\pi\)
0.603287 + 0.797524i \(0.293857\pi\)
\(20\) 0.100034 0.0223684
\(21\) 0 0
\(22\) −5.49180 −1.17086
\(23\) −0.177764 −0.0370663 −0.0185332 0.999828i \(-0.505900\pi\)
−0.0185332 + 0.999828i \(0.505900\pi\)
\(24\) −2.84461 −0.580653
\(25\) −4.98999 −0.997999
\(26\) −2.00425 −0.393065
\(27\) 5.95032 1.14514
\(28\) 0 0
\(29\) 1.92418 0.357311 0.178655 0.983912i \(-0.442825\pi\)
0.178655 + 0.983912i \(0.442825\pi\)
\(30\) −0.284559 −0.0519530
\(31\) −1.74323 −0.313093 −0.156546 0.987671i \(-0.550036\pi\)
−0.156546 + 0.987671i \(0.550036\pi\)
\(32\) −1.00000 −0.176777
\(33\) 15.6220 2.71945
\(34\) 2.02518 0.347316
\(35\) 0 0
\(36\) 5.09179 0.848632
\(37\) 0.296315 0.0487138 0.0243569 0.999703i \(-0.492246\pi\)
0.0243569 + 0.999703i \(0.492246\pi\)
\(38\) −5.25933 −0.853176
\(39\) 5.70130 0.912938
\(40\) −0.100034 −0.0158168
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −3.48995 −0.532213 −0.266106 0.963944i \(-0.585737\pi\)
−0.266106 + 0.963944i \(0.585737\pi\)
\(44\) 5.49180 0.827921
\(45\) 0.509354 0.0759300
\(46\) 0.177764 0.0262099
\(47\) 12.7178 1.85509 0.927543 0.373718i \(-0.121917\pi\)
0.927543 + 0.373718i \(0.121917\pi\)
\(48\) 2.84461 0.410584
\(49\) 0 0
\(50\) 4.98999 0.705692
\(51\) −5.76085 −0.806681
\(52\) 2.00425 0.277939
\(53\) −0.522296 −0.0717429 −0.0358714 0.999356i \(-0.511421\pi\)
−0.0358714 + 0.999356i \(0.511421\pi\)
\(54\) −5.95032 −0.809736
\(55\) 0.549369 0.0740769
\(56\) 0 0
\(57\) 14.9607 1.98160
\(58\) −1.92418 −0.252657
\(59\) −10.3189 −1.34341 −0.671703 0.740820i \(-0.734437\pi\)
−0.671703 + 0.740820i \(0.734437\pi\)
\(60\) 0.284559 0.0367363
\(61\) 10.2472 1.31202 0.656012 0.754751i \(-0.272242\pi\)
0.656012 + 0.754751i \(0.272242\pi\)
\(62\) 1.74323 0.221390
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.200494 0.0248682
\(66\) −15.6220 −1.92294
\(67\) 7.52851 0.919754 0.459877 0.887983i \(-0.347894\pi\)
0.459877 + 0.887983i \(0.347894\pi\)
\(68\) −2.02518 −0.245590
\(69\) −0.505669 −0.0608753
\(70\) 0 0
\(71\) 0.0873211 0.0103631 0.00518155 0.999987i \(-0.498351\pi\)
0.00518155 + 0.999987i \(0.498351\pi\)
\(72\) −5.09179 −0.600073
\(73\) −7.69792 −0.900974 −0.450487 0.892783i \(-0.648750\pi\)
−0.450487 + 0.892783i \(0.648750\pi\)
\(74\) −0.296315 −0.0344459
\(75\) −14.1946 −1.63905
\(76\) 5.25933 0.603287
\(77\) 0 0
\(78\) −5.70130 −0.645545
\(79\) −2.15620 −0.242591 −0.121295 0.992616i \(-0.538705\pi\)
−0.121295 + 0.992616i \(0.538705\pi\)
\(80\) 0.100034 0.0111842
\(81\) 1.65095 0.183439
\(82\) −1.00000 −0.110432
\(83\) −1.63342 −0.179291 −0.0896455 0.995974i \(-0.528573\pi\)
−0.0896455 + 0.995974i \(0.528573\pi\)
\(84\) 0 0
\(85\) −0.202588 −0.0219738
\(86\) 3.48995 0.376331
\(87\) 5.47353 0.586824
\(88\) −5.49180 −0.585428
\(89\) −6.70260 −0.710475 −0.355237 0.934776i \(-0.615600\pi\)
−0.355237 + 0.934776i \(0.615600\pi\)
\(90\) −0.509354 −0.0536906
\(91\) 0 0
\(92\) −0.177764 −0.0185332
\(93\) −4.95879 −0.514203
\(94\) −12.7178 −1.31174
\(95\) 0.526114 0.0539782
\(96\) −2.84461 −0.290326
\(97\) −0.783908 −0.0795938 −0.0397969 0.999208i \(-0.512671\pi\)
−0.0397969 + 0.999208i \(0.512671\pi\)
\(98\) 0 0
\(99\) 27.9631 2.81040
\(100\) −4.98999 −0.498999
\(101\) −9.35530 −0.930888 −0.465444 0.885077i \(-0.654105\pi\)
−0.465444 + 0.885077i \(0.654105\pi\)
\(102\) 5.76085 0.570410
\(103\) −3.51803 −0.346642 −0.173321 0.984865i \(-0.555450\pi\)
−0.173321 + 0.984865i \(0.555450\pi\)
\(104\) −2.00425 −0.196533
\(105\) 0 0
\(106\) 0.522296 0.0507299
\(107\) −20.6228 −1.99368 −0.996840 0.0794300i \(-0.974690\pi\)
−0.996840 + 0.0794300i \(0.974690\pi\)
\(108\) 5.95032 0.572570
\(109\) 9.45841 0.905951 0.452976 0.891523i \(-0.350362\pi\)
0.452976 + 0.891523i \(0.350362\pi\)
\(110\) −0.549369 −0.0523803
\(111\) 0.842898 0.0800044
\(112\) 0 0
\(113\) 19.7178 1.85490 0.927449 0.373951i \(-0.121997\pi\)
0.927449 + 0.373951i \(0.121997\pi\)
\(114\) −14.9607 −1.40120
\(115\) −0.0177825 −0.00165823
\(116\) 1.92418 0.178655
\(117\) 10.2052 0.943472
\(118\) 10.3189 0.949932
\(119\) 0 0
\(120\) −0.284559 −0.0259765
\(121\) 19.1599 1.74181
\(122\) −10.2472 −0.927740
\(123\) 2.84461 0.256490
\(124\) −1.74323 −0.156546
\(125\) −0.999343 −0.0893839
\(126\) 0 0
\(127\) −18.1085 −1.60687 −0.803436 0.595391i \(-0.796997\pi\)
−0.803436 + 0.595391i \(0.796997\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −9.92754 −0.874071
\(130\) −0.200494 −0.0175845
\(131\) 5.55912 0.485703 0.242851 0.970063i \(-0.421917\pi\)
0.242851 + 0.970063i \(0.421917\pi\)
\(132\) 15.6220 1.35972
\(133\) 0 0
\(134\) −7.52851 −0.650364
\(135\) 0.595237 0.0512298
\(136\) 2.02518 0.173658
\(137\) −1.42351 −0.121619 −0.0608093 0.998149i \(-0.519368\pi\)
−0.0608093 + 0.998149i \(0.519368\pi\)
\(138\) 0.505669 0.0430454
\(139\) −9.46170 −0.802531 −0.401265 0.915962i \(-0.631429\pi\)
−0.401265 + 0.915962i \(0.631429\pi\)
\(140\) 0 0
\(141\) 36.1772 3.04667
\(142\) −0.0873211 −0.00732783
\(143\) 11.0069 0.920446
\(144\) 5.09179 0.424316
\(145\) 0.192484 0.0159849
\(146\) 7.69792 0.637085
\(147\) 0 0
\(148\) 0.296315 0.0243569
\(149\) 1.81036 0.148310 0.0741551 0.997247i \(-0.476374\pi\)
0.0741551 + 0.997247i \(0.476374\pi\)
\(150\) 14.1946 1.15898
\(151\) −3.08499 −0.251053 −0.125526 0.992090i \(-0.540062\pi\)
−0.125526 + 0.992090i \(0.540062\pi\)
\(152\) −5.25933 −0.426588
\(153\) −10.3118 −0.833661
\(154\) 0 0
\(155\) −0.174383 −0.0140067
\(156\) 5.70130 0.456469
\(157\) 7.34951 0.586555 0.293278 0.956027i \(-0.405254\pi\)
0.293278 + 0.956027i \(0.405254\pi\)
\(158\) 2.15620 0.171538
\(159\) −1.48573 −0.117826
\(160\) −0.100034 −0.00790841
\(161\) 0 0
\(162\) −1.65095 −0.129711
\(163\) 3.24890 0.254473 0.127237 0.991872i \(-0.459389\pi\)
0.127237 + 0.991872i \(0.459389\pi\)
\(164\) 1.00000 0.0780869
\(165\) 1.56274 0.121659
\(166\) 1.63342 0.126778
\(167\) 22.7027 1.75679 0.878393 0.477939i \(-0.158616\pi\)
0.878393 + 0.477939i \(0.158616\pi\)
\(168\) 0 0
\(169\) −8.98299 −0.690999
\(170\) 0.202588 0.0155378
\(171\) 26.7794 2.04787
\(172\) −3.48995 −0.266106
\(173\) 18.8660 1.43436 0.717179 0.696889i \(-0.245433\pi\)
0.717179 + 0.696889i \(0.245433\pi\)
\(174\) −5.47353 −0.414947
\(175\) 0 0
\(176\) 5.49180 0.413960
\(177\) −29.3532 −2.20632
\(178\) 6.70260 0.502381
\(179\) −13.1779 −0.984965 −0.492482 0.870322i \(-0.663910\pi\)
−0.492482 + 0.870322i \(0.663910\pi\)
\(180\) 0.509354 0.0379650
\(181\) −11.4642 −0.852127 −0.426064 0.904693i \(-0.640100\pi\)
−0.426064 + 0.904693i \(0.640100\pi\)
\(182\) 0 0
\(183\) 29.1493 2.15478
\(184\) 0.177764 0.0131049
\(185\) 0.0296416 0.00217930
\(186\) 4.95879 0.363596
\(187\) −11.1219 −0.813315
\(188\) 12.7178 0.927543
\(189\) 0 0
\(190\) −0.526114 −0.0381683
\(191\) 11.5032 0.832340 0.416170 0.909287i \(-0.363372\pi\)
0.416170 + 0.909287i \(0.363372\pi\)
\(192\) 2.84461 0.205292
\(193\) −10.8671 −0.782232 −0.391116 0.920341i \(-0.627911\pi\)
−0.391116 + 0.920341i \(0.627911\pi\)
\(194\) 0.783908 0.0562813
\(195\) 0.570326 0.0408419
\(196\) 0 0
\(197\) 24.6123 1.75355 0.876777 0.480897i \(-0.159689\pi\)
0.876777 + 0.480897i \(0.159689\pi\)
\(198\) −27.9631 −1.98725
\(199\) 14.6903 1.04137 0.520685 0.853749i \(-0.325677\pi\)
0.520685 + 0.853749i \(0.325677\pi\)
\(200\) 4.98999 0.352846
\(201\) 21.4156 1.51054
\(202\) 9.35530 0.658237
\(203\) 0 0
\(204\) −5.76085 −0.403340
\(205\) 0.100034 0.00698670
\(206\) 3.51803 0.245113
\(207\) −0.905137 −0.0629113
\(208\) 2.00425 0.138970
\(209\) 28.8832 1.99789
\(210\) 0 0
\(211\) −4.10608 −0.282675 −0.141337 0.989962i \(-0.545140\pi\)
−0.141337 + 0.989962i \(0.545140\pi\)
\(212\) −0.522296 −0.0358714
\(213\) 0.248394 0.0170197
\(214\) 20.6228 1.40975
\(215\) −0.349115 −0.0238095
\(216\) −5.95032 −0.404868
\(217\) 0 0
\(218\) −9.45841 −0.640604
\(219\) −21.8976 −1.47970
\(220\) 0.549369 0.0370385
\(221\) −4.05897 −0.273036
\(222\) −0.842898 −0.0565716
\(223\) 3.97766 0.266364 0.133182 0.991092i \(-0.457481\pi\)
0.133182 + 0.991092i \(0.457481\pi\)
\(224\) 0 0
\(225\) −25.4080 −1.69387
\(226\) −19.7178 −1.31161
\(227\) 22.8040 1.51355 0.756777 0.653674i \(-0.226773\pi\)
0.756777 + 0.653674i \(0.226773\pi\)
\(228\) 14.9607 0.990799
\(229\) −20.3461 −1.34451 −0.672255 0.740320i \(-0.734674\pi\)
−0.672255 + 0.740320i \(0.734674\pi\)
\(230\) 0.0177825 0.00117254
\(231\) 0 0
\(232\) −1.92418 −0.126328
\(233\) 29.0821 1.90523 0.952614 0.304181i \(-0.0983827\pi\)
0.952614 + 0.304181i \(0.0983827\pi\)
\(234\) −10.2052 −0.667135
\(235\) 1.27222 0.0829905
\(236\) −10.3189 −0.671703
\(237\) −6.13353 −0.398415
\(238\) 0 0
\(239\) −17.3310 −1.12105 −0.560523 0.828139i \(-0.689400\pi\)
−0.560523 + 0.828139i \(0.689400\pi\)
\(240\) 0.284559 0.0183682
\(241\) −11.3155 −0.728897 −0.364448 0.931224i \(-0.618742\pi\)
−0.364448 + 0.931224i \(0.618742\pi\)
\(242\) −19.1599 −1.23165
\(243\) −13.1546 −0.843871
\(244\) 10.2472 0.656012
\(245\) 0 0
\(246\) −2.84461 −0.181366
\(247\) 10.5410 0.670708
\(248\) 1.74323 0.110695
\(249\) −4.64643 −0.294456
\(250\) 0.999343 0.0632040
\(251\) −21.4095 −1.35135 −0.675676 0.737198i \(-0.736148\pi\)
−0.675676 + 0.737198i \(0.736148\pi\)
\(252\) 0 0
\(253\) −0.976245 −0.0613760
\(254\) 18.1085 1.13623
\(255\) −0.576283 −0.0360883
\(256\) 1.00000 0.0625000
\(257\) 5.68866 0.354849 0.177424 0.984134i \(-0.443223\pi\)
0.177424 + 0.984134i \(0.443223\pi\)
\(258\) 9.92754 0.618062
\(259\) 0 0
\(260\) 0.200494 0.0124341
\(261\) 9.79751 0.606451
\(262\) −5.55912 −0.343444
\(263\) −13.9215 −0.858436 −0.429218 0.903201i \(-0.641211\pi\)
−0.429218 + 0.903201i \(0.641211\pi\)
\(264\) −15.6220 −0.961469
\(265\) −0.0522476 −0.00320954
\(266\) 0 0
\(267\) −19.0663 −1.16684
\(268\) 7.52851 0.459877
\(269\) 12.4410 0.758539 0.379270 0.925286i \(-0.376175\pi\)
0.379270 + 0.925286i \(0.376175\pi\)
\(270\) −0.595237 −0.0362249
\(271\) 10.3626 0.629481 0.314741 0.949178i \(-0.398082\pi\)
0.314741 + 0.949178i \(0.398082\pi\)
\(272\) −2.02518 −0.122795
\(273\) 0 0
\(274\) 1.42351 0.0859973
\(275\) −27.4041 −1.65253
\(276\) −0.505669 −0.0304377
\(277\) 4.84034 0.290828 0.145414 0.989371i \(-0.453549\pi\)
0.145414 + 0.989371i \(0.453549\pi\)
\(278\) 9.46170 0.567475
\(279\) −8.87614 −0.531401
\(280\) 0 0
\(281\) −29.0716 −1.73426 −0.867132 0.498079i \(-0.834039\pi\)
−0.867132 + 0.498079i \(0.834039\pi\)
\(282\) −36.1772 −2.15432
\(283\) 3.80733 0.226322 0.113161 0.993577i \(-0.463902\pi\)
0.113161 + 0.993577i \(0.463902\pi\)
\(284\) 0.0873211 0.00518155
\(285\) 1.49659 0.0886502
\(286\) −11.0069 −0.650854
\(287\) 0 0
\(288\) −5.09179 −0.300037
\(289\) −12.8986 −0.758743
\(290\) −0.192484 −0.0113030
\(291\) −2.22991 −0.130720
\(292\) −7.69792 −0.450487
\(293\) 21.2048 1.23880 0.619398 0.785077i \(-0.287377\pi\)
0.619398 + 0.785077i \(0.287377\pi\)
\(294\) 0 0
\(295\) −1.03224 −0.0600996
\(296\) −0.296315 −0.0172229
\(297\) 32.6780 1.89617
\(298\) −1.81036 −0.104871
\(299\) −0.356283 −0.0206044
\(300\) −14.1946 −0.819524
\(301\) 0 0
\(302\) 3.08499 0.177521
\(303\) −26.6122 −1.52883
\(304\) 5.25933 0.301643
\(305\) 1.02508 0.0586956
\(306\) 10.3118 0.589487
\(307\) 23.6483 1.34968 0.674840 0.737964i \(-0.264213\pi\)
0.674840 + 0.737964i \(0.264213\pi\)
\(308\) 0 0
\(309\) −10.0074 −0.569302
\(310\) 0.174383 0.00990426
\(311\) −4.53369 −0.257082 −0.128541 0.991704i \(-0.541029\pi\)
−0.128541 + 0.991704i \(0.541029\pi\)
\(312\) −5.70130 −0.322772
\(313\) −13.9532 −0.788681 −0.394340 0.918964i \(-0.629027\pi\)
−0.394340 + 0.918964i \(0.629027\pi\)
\(314\) −7.34951 −0.414757
\(315\) 0 0
\(316\) −2.15620 −0.121295
\(317\) −18.2179 −1.02322 −0.511610 0.859218i \(-0.670951\pi\)
−0.511610 + 0.859218i \(0.670951\pi\)
\(318\) 1.48573 0.0833154
\(319\) 10.5672 0.591650
\(320\) 0.100034 0.00559209
\(321\) −58.6638 −3.27429
\(322\) 0 0
\(323\) −10.6511 −0.592644
\(324\) 1.65095 0.0917196
\(325\) −10.0012 −0.554766
\(326\) −3.24890 −0.179940
\(327\) 26.9055 1.48788
\(328\) −1.00000 −0.0552158
\(329\) 0 0
\(330\) −1.56274 −0.0860260
\(331\) −9.32265 −0.512419 −0.256210 0.966621i \(-0.582474\pi\)
−0.256210 + 0.966621i \(0.582474\pi\)
\(332\) −1.63342 −0.0896455
\(333\) 1.50877 0.0826802
\(334\) −22.7027 −1.24224
\(335\) 0.753110 0.0411468
\(336\) 0 0
\(337\) −28.3634 −1.54505 −0.772525 0.634984i \(-0.781007\pi\)
−0.772525 + 0.634984i \(0.781007\pi\)
\(338\) 8.98299 0.488610
\(339\) 56.0895 3.04636
\(340\) −0.202588 −0.0109869
\(341\) −9.57346 −0.518432
\(342\) −26.7794 −1.44806
\(343\) 0 0
\(344\) 3.48995 0.188166
\(345\) −0.0505842 −0.00272336
\(346\) −18.8660 −1.01424
\(347\) 25.9901 1.39522 0.697612 0.716476i \(-0.254246\pi\)
0.697612 + 0.716476i \(0.254246\pi\)
\(348\) 5.47353 0.293412
\(349\) 6.07191 0.325022 0.162511 0.986707i \(-0.448041\pi\)
0.162511 + 0.986707i \(0.448041\pi\)
\(350\) 0 0
\(351\) 11.9259 0.636558
\(352\) −5.49180 −0.292714
\(353\) 8.90538 0.473986 0.236993 0.971511i \(-0.423838\pi\)
0.236993 + 0.971511i \(0.423838\pi\)
\(354\) 29.3532 1.56011
\(355\) 0.00873511 0.000463612 0
\(356\) −6.70260 −0.355237
\(357\) 0 0
\(358\) 13.1779 0.696475
\(359\) −22.2052 −1.17195 −0.585973 0.810331i \(-0.699288\pi\)
−0.585973 + 0.810331i \(0.699288\pi\)
\(360\) −0.509354 −0.0268453
\(361\) 8.66057 0.455819
\(362\) 11.4642 0.602545
\(363\) 54.5024 2.86063
\(364\) 0 0
\(365\) −0.770057 −0.0403066
\(366\) −29.1493 −1.52366
\(367\) −22.7662 −1.18839 −0.594193 0.804323i \(-0.702528\pi\)
−0.594193 + 0.804323i \(0.702528\pi\)
\(368\) −0.177764 −0.00926659
\(369\) 5.09179 0.265068
\(370\) −0.0296416 −0.00154100
\(371\) 0 0
\(372\) −4.95879 −0.257101
\(373\) 25.1403 1.30172 0.650859 0.759199i \(-0.274409\pi\)
0.650859 + 0.759199i \(0.274409\pi\)
\(374\) 11.1219 0.575101
\(375\) −2.84274 −0.146798
\(376\) −12.7178 −0.655872
\(377\) 3.85653 0.198621
\(378\) 0 0
\(379\) 11.7756 0.604874 0.302437 0.953169i \(-0.402200\pi\)
0.302437 + 0.953169i \(0.402200\pi\)
\(380\) 0.526114 0.0269891
\(381\) −51.5117 −2.63902
\(382\) −11.5032 −0.588553
\(383\) 32.1184 1.64117 0.820586 0.571522i \(-0.193647\pi\)
0.820586 + 0.571522i \(0.193647\pi\)
\(384\) −2.84461 −0.145163
\(385\) 0 0
\(386\) 10.8671 0.553122
\(387\) −17.7701 −0.903305
\(388\) −0.783908 −0.0397969
\(389\) −20.4285 −1.03576 −0.517882 0.855452i \(-0.673279\pi\)
−0.517882 + 0.855452i \(0.673279\pi\)
\(390\) −0.570326 −0.0288796
\(391\) 0.360005 0.0182062
\(392\) 0 0
\(393\) 15.8135 0.797687
\(394\) −24.6123 −1.23995
\(395\) −0.215694 −0.0108527
\(396\) 27.9631 1.40520
\(397\) 13.2034 0.662660 0.331330 0.943515i \(-0.392503\pi\)
0.331330 + 0.943515i \(0.392503\pi\)
\(398\) −14.6903 −0.736360
\(399\) 0 0
\(400\) −4.98999 −0.249500
\(401\) −6.19120 −0.309174 −0.154587 0.987979i \(-0.549405\pi\)
−0.154587 + 0.987979i \(0.549405\pi\)
\(402\) −21.4156 −1.06812
\(403\) −3.49386 −0.174041
\(404\) −9.35530 −0.465444
\(405\) 0.165152 0.00820647
\(406\) 0 0
\(407\) 1.62730 0.0806623
\(408\) 5.76085 0.285205
\(409\) −7.68619 −0.380058 −0.190029 0.981779i \(-0.560858\pi\)
−0.190029 + 0.981779i \(0.560858\pi\)
\(410\) −0.100034 −0.00494035
\(411\) −4.04932 −0.199738
\(412\) −3.51803 −0.173321
\(413\) 0 0
\(414\) 0.905137 0.0444850
\(415\) −0.163398 −0.00802089
\(416\) −2.00425 −0.0982663
\(417\) −26.9148 −1.31802
\(418\) −28.8832 −1.41272
\(419\) 5.34493 0.261117 0.130559 0.991441i \(-0.458323\pi\)
0.130559 + 0.991441i \(0.458323\pi\)
\(420\) 0 0
\(421\) 31.0458 1.51308 0.756539 0.653949i \(-0.226889\pi\)
0.756539 + 0.653949i \(0.226889\pi\)
\(422\) 4.10608 0.199881
\(423\) 64.7565 3.14857
\(424\) 0.522296 0.0253649
\(425\) 10.1057 0.490196
\(426\) −0.248394 −0.0120347
\(427\) 0 0
\(428\) −20.6228 −0.996840
\(429\) 31.3104 1.51168
\(430\) 0.349115 0.0168358
\(431\) −28.4490 −1.37034 −0.685170 0.728383i \(-0.740272\pi\)
−0.685170 + 0.728383i \(0.740272\pi\)
\(432\) 5.95032 0.286285
\(433\) 2.21499 0.106446 0.0532229 0.998583i \(-0.483051\pi\)
0.0532229 + 0.998583i \(0.483051\pi\)
\(434\) 0 0
\(435\) 0.547541 0.0262526
\(436\) 9.45841 0.452976
\(437\) −0.934919 −0.0447233
\(438\) 21.8976 1.04631
\(439\) −33.6220 −1.60469 −0.802346 0.596859i \(-0.796415\pi\)
−0.802346 + 0.596859i \(0.796415\pi\)
\(440\) −0.549369 −0.0261901
\(441\) 0 0
\(442\) 4.05897 0.193066
\(443\) 4.73115 0.224784 0.112392 0.993664i \(-0.464149\pi\)
0.112392 + 0.993664i \(0.464149\pi\)
\(444\) 0.842898 0.0400022
\(445\) −0.670491 −0.0317843
\(446\) −3.97766 −0.188348
\(447\) 5.14976 0.243575
\(448\) 0 0
\(449\) −19.0673 −0.899844 −0.449922 0.893068i \(-0.648548\pi\)
−0.449922 + 0.893068i \(0.648548\pi\)
\(450\) 25.4080 1.19774
\(451\) 5.49180 0.258599
\(452\) 19.7178 0.927449
\(453\) −8.77557 −0.412312
\(454\) −22.8040 −1.07024
\(455\) 0 0
\(456\) −14.9607 −0.700600
\(457\) −21.8939 −1.02415 −0.512076 0.858940i \(-0.671123\pi\)
−0.512076 + 0.858940i \(0.671123\pi\)
\(458\) 20.3461 0.950712
\(459\) −12.0505 −0.562469
\(460\) −0.0177825 −0.000829114 0
\(461\) 35.8923 1.67167 0.835836 0.548979i \(-0.184983\pi\)
0.835836 + 0.548979i \(0.184983\pi\)
\(462\) 0 0
\(463\) −17.2360 −0.801027 −0.400513 0.916291i \(-0.631168\pi\)
−0.400513 + 0.916291i \(0.631168\pi\)
\(464\) 1.92418 0.0893277
\(465\) −0.496050 −0.0230038
\(466\) −29.0821 −1.34720
\(467\) 32.8802 1.52152 0.760758 0.649036i \(-0.224828\pi\)
0.760758 + 0.649036i \(0.224828\pi\)
\(468\) 10.2052 0.471736
\(469\) 0 0
\(470\) −1.27222 −0.0586831
\(471\) 20.9065 0.963320
\(472\) 10.3189 0.474966
\(473\) −19.1661 −0.881259
\(474\) 6.13353 0.281722
\(475\) −26.2440 −1.20416
\(476\) 0 0
\(477\) −2.65942 −0.121767
\(478\) 17.3310 0.792700
\(479\) −25.1914 −1.15103 −0.575513 0.817793i \(-0.695198\pi\)
−0.575513 + 0.817793i \(0.695198\pi\)
\(480\) −0.284559 −0.0129883
\(481\) 0.593888 0.0270789
\(482\) 11.3155 0.515408
\(483\) 0 0
\(484\) 19.1599 0.870905
\(485\) −0.0784177 −0.00356077
\(486\) 13.1546 0.596707
\(487\) −31.1451 −1.41132 −0.705659 0.708552i \(-0.749349\pi\)
−0.705659 + 0.708552i \(0.749349\pi\)
\(488\) −10.2472 −0.463870
\(489\) 9.24184 0.417930
\(490\) 0 0
\(491\) −1.81906 −0.0820930 −0.0410465 0.999157i \(-0.513069\pi\)
−0.0410465 + 0.999157i \(0.513069\pi\)
\(492\) 2.84461 0.128245
\(493\) −3.89682 −0.175504
\(494\) −10.5410 −0.474262
\(495\) 2.79727 0.125728
\(496\) −1.74323 −0.0782732
\(497\) 0 0
\(498\) 4.64643 0.208212
\(499\) −1.22056 −0.0546398 −0.0273199 0.999627i \(-0.508697\pi\)
−0.0273199 + 0.999627i \(0.508697\pi\)
\(500\) −0.999343 −0.0446920
\(501\) 64.5802 2.88523
\(502\) 21.4095 0.955551
\(503\) −0.303892 −0.0135499 −0.00677493 0.999977i \(-0.502157\pi\)
−0.00677493 + 0.999977i \(0.502157\pi\)
\(504\) 0 0
\(505\) −0.935852 −0.0416449
\(506\) 0.976245 0.0433994
\(507\) −25.5531 −1.13485
\(508\) −18.1085 −0.803436
\(509\) 23.7535 1.05286 0.526429 0.850219i \(-0.323531\pi\)
0.526429 + 0.850219i \(0.323531\pi\)
\(510\) 0.576283 0.0255183
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 31.2947 1.38169
\(514\) −5.68866 −0.250916
\(515\) −0.351924 −0.0155076
\(516\) −9.92754 −0.437036
\(517\) 69.8438 3.07173
\(518\) 0 0
\(519\) 53.6664 2.35570
\(520\) −0.200494 −0.00879223
\(521\) −12.1542 −0.532486 −0.266243 0.963906i \(-0.585782\pi\)
−0.266243 + 0.963906i \(0.585782\pi\)
\(522\) −9.79751 −0.428825
\(523\) 28.3221 1.23844 0.619218 0.785219i \(-0.287450\pi\)
0.619218 + 0.785219i \(0.287450\pi\)
\(524\) 5.55912 0.242851
\(525\) 0 0
\(526\) 13.9215 0.607006
\(527\) 3.53035 0.153785
\(528\) 15.6220 0.679861
\(529\) −22.9684 −0.998626
\(530\) 0.0522476 0.00226949
\(531\) −52.5417 −2.28011
\(532\) 0 0
\(533\) 2.00425 0.0868136
\(534\) 19.0663 0.825078
\(535\) −2.06299 −0.0891908
\(536\) −7.52851 −0.325182
\(537\) −37.4860 −1.61764
\(538\) −12.4410 −0.536368
\(539\) 0 0
\(540\) 0.595237 0.0256149
\(541\) 30.8867 1.32792 0.663961 0.747768i \(-0.268874\pi\)
0.663961 + 0.747768i \(0.268874\pi\)
\(542\) −10.3626 −0.445110
\(543\) −32.6111 −1.39948
\(544\) 2.02518 0.0868291
\(545\) 0.946166 0.0405293
\(546\) 0 0
\(547\) −15.6662 −0.669839 −0.334920 0.942247i \(-0.608709\pi\)
−0.334920 + 0.942247i \(0.608709\pi\)
\(548\) −1.42351 −0.0608093
\(549\) 52.1767 2.22685
\(550\) 27.4041 1.16851
\(551\) 10.1199 0.431122
\(552\) 0.505669 0.0215227
\(553\) 0 0
\(554\) −4.84034 −0.205646
\(555\) 0.0843188 0.00357913
\(556\) −9.46170 −0.401265
\(557\) −23.0865 −0.978207 −0.489104 0.872226i \(-0.662676\pi\)
−0.489104 + 0.872226i \(0.662676\pi\)
\(558\) 8.87614 0.375757
\(559\) −6.99472 −0.295845
\(560\) 0 0
\(561\) −31.6375 −1.33574
\(562\) 29.0716 1.22631
\(563\) −5.20512 −0.219369 −0.109685 0.993966i \(-0.534984\pi\)
−0.109685 + 0.993966i \(0.534984\pi\)
\(564\) 36.1772 1.52334
\(565\) 1.97246 0.0829820
\(566\) −3.80733 −0.160034
\(567\) 0 0
\(568\) −0.0873211 −0.00366391
\(569\) −6.61422 −0.277283 −0.138641 0.990343i \(-0.544274\pi\)
−0.138641 + 0.990343i \(0.544274\pi\)
\(570\) −1.49659 −0.0626852
\(571\) −10.4373 −0.436788 −0.218394 0.975861i \(-0.570082\pi\)
−0.218394 + 0.975861i \(0.570082\pi\)
\(572\) 11.0069 0.460223
\(573\) 32.7220 1.36698
\(574\) 0 0
\(575\) 0.887041 0.0369922
\(576\) 5.09179 0.212158
\(577\) −44.8936 −1.86894 −0.934472 0.356037i \(-0.884128\pi\)
−0.934472 + 0.356037i \(0.884128\pi\)
\(578\) 12.8986 0.536512
\(579\) −30.9127 −1.28469
\(580\) 0.192484 0.00799246
\(581\) 0 0
\(582\) 2.22991 0.0924327
\(583\) −2.86835 −0.118795
\(584\) 7.69792 0.318542
\(585\) 1.02087 0.0422078
\(586\) −21.2048 −0.875961
\(587\) −4.58306 −0.189163 −0.0945816 0.995517i \(-0.530151\pi\)
−0.0945816 + 0.995517i \(0.530151\pi\)
\(588\) 0 0
\(589\) −9.16820 −0.377769
\(590\) 1.03224 0.0424968
\(591\) 70.0124 2.87992
\(592\) 0.296315 0.0121785
\(593\) 40.8080 1.67578 0.837891 0.545837i \(-0.183788\pi\)
0.837891 + 0.545837i \(0.183788\pi\)
\(594\) −32.6780 −1.34079
\(595\) 0 0
\(596\) 1.81036 0.0741551
\(597\) 41.7882 1.71028
\(598\) 0.356283 0.0145695
\(599\) −35.9219 −1.46773 −0.733865 0.679295i \(-0.762286\pi\)
−0.733865 + 0.679295i \(0.762286\pi\)
\(600\) 14.1946 0.579491
\(601\) 3.31498 0.135221 0.0676105 0.997712i \(-0.478462\pi\)
0.0676105 + 0.997712i \(0.478462\pi\)
\(602\) 0 0
\(603\) 38.3336 1.56106
\(604\) −3.08499 −0.125526
\(605\) 1.91665 0.0779229
\(606\) 26.6122 1.08105
\(607\) 46.0105 1.86751 0.933754 0.357916i \(-0.116513\pi\)
0.933754 + 0.357916i \(0.116513\pi\)
\(608\) −5.25933 −0.213294
\(609\) 0 0
\(610\) −1.02508 −0.0415041
\(611\) 25.4897 1.03120
\(612\) −10.3118 −0.416830
\(613\) 27.3935 1.10641 0.553206 0.833044i \(-0.313404\pi\)
0.553206 + 0.833044i \(0.313404\pi\)
\(614\) −23.6483 −0.954368
\(615\) 0.284559 0.0114745
\(616\) 0 0
\(617\) −11.8256 −0.476082 −0.238041 0.971255i \(-0.576505\pi\)
−0.238041 + 0.971255i \(0.576505\pi\)
\(618\) 10.0074 0.402557
\(619\) −30.5284 −1.22704 −0.613519 0.789680i \(-0.710247\pi\)
−0.613519 + 0.789680i \(0.710247\pi\)
\(620\) −0.174383 −0.00700337
\(621\) −1.05775 −0.0424461
\(622\) 4.53369 0.181784
\(623\) 0 0
\(624\) 5.70130 0.228234
\(625\) 24.8500 0.994000
\(626\) 13.9532 0.557682
\(627\) 82.1614 3.28121
\(628\) 7.34951 0.293278
\(629\) −0.600092 −0.0239272
\(630\) 0 0
\(631\) −10.4403 −0.415621 −0.207811 0.978169i \(-0.566634\pi\)
−0.207811 + 0.978169i \(0.566634\pi\)
\(632\) 2.15620 0.0857688
\(633\) −11.6802 −0.464246
\(634\) 18.2179 0.723525
\(635\) −1.81148 −0.0718862
\(636\) −1.48573 −0.0589129
\(637\) 0 0
\(638\) −10.5672 −0.418360
\(639\) 0.444621 0.0175889
\(640\) −0.100034 −0.00395421
\(641\) 16.2483 0.641771 0.320886 0.947118i \(-0.396019\pi\)
0.320886 + 0.947118i \(0.396019\pi\)
\(642\) 58.6638 2.31527
\(643\) −48.1432 −1.89858 −0.949292 0.314396i \(-0.898198\pi\)
−0.949292 + 0.314396i \(0.898198\pi\)
\(644\) 0 0
\(645\) −0.993095 −0.0391031
\(646\) 10.6511 0.419063
\(647\) 6.61217 0.259951 0.129976 0.991517i \(-0.458510\pi\)
0.129976 + 0.991517i \(0.458510\pi\)
\(648\) −1.65095 −0.0648555
\(649\) −56.6694 −2.22447
\(650\) 10.0012 0.392279
\(651\) 0 0
\(652\) 3.24890 0.127237
\(653\) 33.6484 1.31676 0.658381 0.752685i \(-0.271242\pi\)
0.658381 + 0.752685i \(0.271242\pi\)
\(654\) −26.9055 −1.05209
\(655\) 0.556104 0.0217288
\(656\) 1.00000 0.0390434
\(657\) −39.1962 −1.52919
\(658\) 0 0
\(659\) 26.5436 1.03399 0.516996 0.855988i \(-0.327050\pi\)
0.516996 + 0.855988i \(0.327050\pi\)
\(660\) 1.56274 0.0608296
\(661\) 22.9496 0.892635 0.446317 0.894875i \(-0.352735\pi\)
0.446317 + 0.894875i \(0.352735\pi\)
\(662\) 9.32265 0.362335
\(663\) −11.5462 −0.448416
\(664\) 1.63342 0.0633889
\(665\) 0 0
\(666\) −1.50877 −0.0584637
\(667\) −0.342049 −0.0132442
\(668\) 22.7027 0.878393
\(669\) 11.3149 0.437458
\(670\) −0.753110 −0.0290952
\(671\) 56.2758 2.17250
\(672\) 0 0
\(673\) 20.7757 0.800844 0.400422 0.916331i \(-0.368864\pi\)
0.400422 + 0.916331i \(0.368864\pi\)
\(674\) 28.3634 1.09252
\(675\) −29.6921 −1.14285
\(676\) −8.98299 −0.345500
\(677\) −35.0420 −1.34677 −0.673386 0.739291i \(-0.735161\pi\)
−0.673386 + 0.739291i \(0.735161\pi\)
\(678\) −56.0895 −2.15410
\(679\) 0 0
\(680\) 0.202588 0.00776890
\(681\) 64.8684 2.48576
\(682\) 9.57346 0.366587
\(683\) −25.1924 −0.963959 −0.481979 0.876183i \(-0.660082\pi\)
−0.481979 + 0.876183i \(0.660082\pi\)
\(684\) 26.7794 1.02394
\(685\) −0.142400 −0.00544082
\(686\) 0 0
\(687\) −57.8767 −2.20814
\(688\) −3.48995 −0.133053
\(689\) −1.04681 −0.0398803
\(690\) 0.0505842 0.00192571
\(691\) −11.8598 −0.451170 −0.225585 0.974224i \(-0.572429\pi\)
−0.225585 + 0.974224i \(0.572429\pi\)
\(692\) 18.8660 0.717179
\(693\) 0 0
\(694\) −25.9901 −0.986572
\(695\) −0.946495 −0.0359026
\(696\) −5.47353 −0.207474
\(697\) −2.02518 −0.0767093
\(698\) −6.07191 −0.229825
\(699\) 82.7270 3.12902
\(700\) 0 0
\(701\) −26.7864 −1.01171 −0.505853 0.862620i \(-0.668822\pi\)
−0.505853 + 0.862620i \(0.668822\pi\)
\(702\) −11.9259 −0.450115
\(703\) 1.55842 0.0587768
\(704\) 5.49180 0.206980
\(705\) 3.61896 0.136298
\(706\) −8.90538 −0.335159
\(707\) 0 0
\(708\) −29.3532 −1.10316
\(709\) 2.12837 0.0799325 0.0399663 0.999201i \(-0.487275\pi\)
0.0399663 + 0.999201i \(0.487275\pi\)
\(710\) −0.00873511 −0.000327823 0
\(711\) −10.9789 −0.411741
\(712\) 6.70260 0.251191
\(713\) 0.309883 0.0116052
\(714\) 0 0
\(715\) 1.10107 0.0411777
\(716\) −13.1779 −0.492482
\(717\) −49.2998 −1.84113
\(718\) 22.2052 0.828691
\(719\) −27.0515 −1.00885 −0.504426 0.863455i \(-0.668296\pi\)
−0.504426 + 0.863455i \(0.668296\pi\)
\(720\) 0.509354 0.0189825
\(721\) 0 0
\(722\) −8.66057 −0.322313
\(723\) −32.1882 −1.19709
\(724\) −11.4642 −0.426064
\(725\) −9.60163 −0.356596
\(726\) −54.5024 −2.02277
\(727\) −7.85211 −0.291219 −0.145609 0.989342i \(-0.546514\pi\)
−0.145609 + 0.989342i \(0.546514\pi\)
\(728\) 0 0
\(729\) −42.3727 −1.56936
\(730\) 0.770057 0.0285011
\(731\) 7.06779 0.261412
\(732\) 29.1493 1.07739
\(733\) −19.5270 −0.721247 −0.360624 0.932711i \(-0.617436\pi\)
−0.360624 + 0.932711i \(0.617436\pi\)
\(734\) 22.7662 0.840316
\(735\) 0 0
\(736\) 0.177764 0.00655247
\(737\) 41.3451 1.52297
\(738\) −5.09179 −0.187431
\(739\) 3.91797 0.144125 0.0720625 0.997400i \(-0.477042\pi\)
0.0720625 + 0.997400i \(0.477042\pi\)
\(740\) 0.0296416 0.00108965
\(741\) 29.9850 1.10153
\(742\) 0 0
\(743\) 41.6030 1.52627 0.763133 0.646241i \(-0.223660\pi\)
0.763133 + 0.646241i \(0.223660\pi\)
\(744\) 4.95879 0.181798
\(745\) 0.181098 0.00663492
\(746\) −25.1403 −0.920453
\(747\) −8.31702 −0.304304
\(748\) −11.1219 −0.406657
\(749\) 0 0
\(750\) 2.84274 0.103802
\(751\) −39.0167 −1.42374 −0.711869 0.702312i \(-0.752151\pi\)
−0.711869 + 0.702312i \(0.752151\pi\)
\(752\) 12.7178 0.463771
\(753\) −60.9015 −2.21937
\(754\) −3.85653 −0.140446
\(755\) −0.308605 −0.0112313
\(756\) 0 0
\(757\) −37.8068 −1.37411 −0.687055 0.726605i \(-0.741097\pi\)
−0.687055 + 0.726605i \(0.741097\pi\)
\(758\) −11.7756 −0.427710
\(759\) −2.77703 −0.100800
\(760\) −0.526114 −0.0190842
\(761\) 1.71848 0.0622949 0.0311475 0.999515i \(-0.490084\pi\)
0.0311475 + 0.999515i \(0.490084\pi\)
\(762\) 51.5117 1.86607
\(763\) 0 0
\(764\) 11.5032 0.416170
\(765\) −1.03154 −0.0372953
\(766\) −32.1184 −1.16048
\(767\) −20.6816 −0.746770
\(768\) 2.84461 0.102646
\(769\) −12.0903 −0.435988 −0.217994 0.975950i \(-0.569951\pi\)
−0.217994 + 0.975950i \(0.569951\pi\)
\(770\) 0 0
\(771\) 16.1820 0.582780
\(772\) −10.8671 −0.391116
\(773\) −43.1222 −1.55100 −0.775499 0.631349i \(-0.782502\pi\)
−0.775499 + 0.631349i \(0.782502\pi\)
\(774\) 17.7701 0.638733
\(775\) 8.69869 0.312466
\(776\) 0.783908 0.0281406
\(777\) 0 0
\(778\) 20.4285 0.732396
\(779\) 5.25933 0.188435
\(780\) 0.570326 0.0204209
\(781\) 0.479550 0.0171597
\(782\) −0.360005 −0.0128737
\(783\) 11.4495 0.409171
\(784\) 0 0
\(785\) 0.735204 0.0262406
\(786\) −15.8135 −0.564050
\(787\) −46.6990 −1.66464 −0.832321 0.554295i \(-0.812988\pi\)
−0.832321 + 0.554295i \(0.812988\pi\)
\(788\) 24.6123 0.876777
\(789\) −39.6012 −1.40984
\(790\) 0.215694 0.00767404
\(791\) 0 0
\(792\) −27.9631 −0.993626
\(793\) 20.5380 0.729325
\(794\) −13.2034 −0.468571
\(795\) −0.148624 −0.00527114
\(796\) 14.6903 0.520685
\(797\) 13.3684 0.473535 0.236767 0.971566i \(-0.423912\pi\)
0.236767 + 0.971566i \(0.423912\pi\)
\(798\) 0 0
\(799\) −25.7559 −0.911180
\(800\) 4.98999 0.176423
\(801\) −34.1282 −1.20586
\(802\) 6.19120 0.218619
\(803\) −42.2755 −1.49187
\(804\) 21.4156 0.755272
\(805\) 0 0
\(806\) 3.49386 0.123066
\(807\) 35.3897 1.24577
\(808\) 9.35530 0.329118
\(809\) 9.16465 0.322212 0.161106 0.986937i \(-0.448494\pi\)
0.161106 + 0.986937i \(0.448494\pi\)
\(810\) −0.165152 −0.00580285
\(811\) 13.7703 0.483542 0.241771 0.970333i \(-0.422272\pi\)
0.241771 + 0.970333i \(0.422272\pi\)
\(812\) 0 0
\(813\) 29.4774 1.03382
\(814\) −1.62730 −0.0570369
\(815\) 0.325001 0.0113843
\(816\) −5.76085 −0.201670
\(817\) −18.3548 −0.642153
\(818\) 7.68619 0.268741
\(819\) 0 0
\(820\) 0.100034 0.00349335
\(821\) 18.0395 0.629581 0.314791 0.949161i \(-0.398066\pi\)
0.314791 + 0.949161i \(0.398066\pi\)
\(822\) 4.04932 0.141236
\(823\) −50.5380 −1.76164 −0.880821 0.473449i \(-0.843009\pi\)
−0.880821 + 0.473449i \(0.843009\pi\)
\(824\) 3.51803 0.122556
\(825\) −77.9538 −2.71400
\(826\) 0 0
\(827\) −32.6901 −1.13675 −0.568373 0.822771i \(-0.692427\pi\)
−0.568373 + 0.822771i \(0.692427\pi\)
\(828\) −0.905137 −0.0314557
\(829\) −5.77411 −0.200543 −0.100272 0.994960i \(-0.531971\pi\)
−0.100272 + 0.994960i \(0.531971\pi\)
\(830\) 0.163398 0.00567163
\(831\) 13.7689 0.477637
\(832\) 2.00425 0.0694848
\(833\) 0 0
\(834\) 26.9148 0.931984
\(835\) 2.27105 0.0785929
\(836\) 28.8832 0.998947
\(837\) −10.3728 −0.358535
\(838\) −5.34493 −0.184638
\(839\) −16.1542 −0.557705 −0.278853 0.960334i \(-0.589954\pi\)
−0.278853 + 0.960334i \(0.589954\pi\)
\(840\) 0 0
\(841\) −25.2975 −0.872329
\(842\) −31.0458 −1.06991
\(843\) −82.6971 −2.84824
\(844\) −4.10608 −0.141337
\(845\) −0.898608 −0.0309131
\(846\) −64.7565 −2.22637
\(847\) 0 0
\(848\) −0.522296 −0.0179357
\(849\) 10.8304 0.371697
\(850\) −10.1057 −0.346621
\(851\) −0.0526740 −0.00180564
\(852\) 0.248394 0.00850985
\(853\) −51.3396 −1.75784 −0.878918 0.476974i \(-0.841734\pi\)
−0.878918 + 0.476974i \(0.841734\pi\)
\(854\) 0 0
\(855\) 2.67886 0.0916151
\(856\) 20.6228 0.704873
\(857\) −2.40688 −0.0822175 −0.0411088 0.999155i \(-0.513089\pi\)
−0.0411088 + 0.999155i \(0.513089\pi\)
\(858\) −31.3104 −1.06892
\(859\) 19.6567 0.670678 0.335339 0.942098i \(-0.391149\pi\)
0.335339 + 0.942098i \(0.391149\pi\)
\(860\) −0.349115 −0.0119047
\(861\) 0 0
\(862\) 28.4490 0.968977
\(863\) 11.4517 0.389820 0.194910 0.980821i \(-0.437559\pi\)
0.194910 + 0.980821i \(0.437559\pi\)
\(864\) −5.95032 −0.202434
\(865\) 1.88725 0.0641685
\(866\) −2.21499 −0.0752686
\(867\) −36.6915 −1.24611
\(868\) 0 0
\(869\) −11.8414 −0.401692
\(870\) −0.547541 −0.0185634
\(871\) 15.0890 0.511271
\(872\) −9.45841 −0.320302
\(873\) −3.99149 −0.135092
\(874\) 0.934919 0.0316241
\(875\) 0 0
\(876\) −21.8976 −0.739850
\(877\) 0.985999 0.0332948 0.0166474 0.999861i \(-0.494701\pi\)
0.0166474 + 0.999861i \(0.494701\pi\)
\(878\) 33.6220 1.13469
\(879\) 60.3193 2.03452
\(880\) 0.549369 0.0185192
\(881\) −34.6171 −1.16628 −0.583139 0.812372i \(-0.698176\pi\)
−0.583139 + 0.812372i \(0.698176\pi\)
\(882\) 0 0
\(883\) 33.2742 1.11977 0.559884 0.828571i \(-0.310846\pi\)
0.559884 + 0.828571i \(0.310846\pi\)
\(884\) −4.05897 −0.136518
\(885\) −2.93633 −0.0987037
\(886\) −4.73115 −0.158946
\(887\) 11.5309 0.387168 0.193584 0.981084i \(-0.437989\pi\)
0.193584 + 0.981084i \(0.437989\pi\)
\(888\) −0.842898 −0.0282858
\(889\) 0 0
\(890\) 0.670491 0.0224749
\(891\) 9.06671 0.303746
\(892\) 3.97766 0.133182
\(893\) 66.8872 2.23830
\(894\) −5.14976 −0.172234
\(895\) −1.31825 −0.0440641
\(896\) 0 0
\(897\) −1.01348 −0.0338393
\(898\) 19.0673 0.636286
\(899\) −3.35428 −0.111871
\(900\) −25.4080 −0.846933
\(901\) 1.05775 0.0352386
\(902\) −5.49180 −0.182857
\(903\) 0 0
\(904\) −19.7178 −0.655805
\(905\) −1.14681 −0.0381214
\(906\) 8.77557 0.291549
\(907\) −17.3966 −0.577644 −0.288822 0.957383i \(-0.593264\pi\)
−0.288822 + 0.957383i \(0.593264\pi\)
\(908\) 22.8040 0.756777
\(909\) −47.6352 −1.57996
\(910\) 0 0
\(911\) 54.3873 1.80193 0.900966 0.433889i \(-0.142859\pi\)
0.900966 + 0.433889i \(0.142859\pi\)
\(912\) 14.9607 0.495399
\(913\) −8.97041 −0.296877
\(914\) 21.8939 0.724184
\(915\) 2.91594 0.0963979
\(916\) −20.3461 −0.672255
\(917\) 0 0
\(918\) 12.0505 0.397726
\(919\) 17.4287 0.574919 0.287459 0.957793i \(-0.407189\pi\)
0.287459 + 0.957793i \(0.407189\pi\)
\(920\) 0.0177825 0.000586272 0
\(921\) 67.2701 2.21663
\(922\) −35.8923 −1.18205
\(923\) 0.175013 0.00576063
\(924\) 0 0
\(925\) −1.47861 −0.0486163
\(926\) 17.2360 0.566411
\(927\) −17.9131 −0.588343
\(928\) −1.92418 −0.0631642
\(929\) 37.0389 1.21521 0.607604 0.794240i \(-0.292131\pi\)
0.607604 + 0.794240i \(0.292131\pi\)
\(930\) 0.496050 0.0162661
\(931\) 0 0
\(932\) 29.0821 0.952614
\(933\) −12.8966 −0.422215
\(934\) −32.8802 −1.07587
\(935\) −1.11257 −0.0363851
\(936\) −10.2052 −0.333568
\(937\) −7.43914 −0.243026 −0.121513 0.992590i \(-0.538775\pi\)
−0.121513 + 0.992590i \(0.538775\pi\)
\(938\) 0 0
\(939\) −39.6913 −1.29528
\(940\) 1.27222 0.0414952
\(941\) 48.7109 1.58793 0.793966 0.607962i \(-0.208013\pi\)
0.793966 + 0.607962i \(0.208013\pi\)
\(942\) −20.9065 −0.681170
\(943\) −0.177764 −0.00578879
\(944\) −10.3189 −0.335852
\(945\) 0 0
\(946\) 19.1661 0.623144
\(947\) −25.7136 −0.835580 −0.417790 0.908544i \(-0.637195\pi\)
−0.417790 + 0.908544i \(0.637195\pi\)
\(948\) −6.13353 −0.199208
\(949\) −15.4285 −0.500832
\(950\) 26.2440 0.851469
\(951\) −51.8228 −1.68047
\(952\) 0 0
\(953\) 22.4560 0.727422 0.363711 0.931512i \(-0.381510\pi\)
0.363711 + 0.931512i \(0.381510\pi\)
\(954\) 2.65942 0.0861019
\(955\) 1.15071 0.0372362
\(956\) −17.3310 −0.560523
\(957\) 30.0596 0.971687
\(958\) 25.1914 0.813898
\(959\) 0 0
\(960\) 0.284559 0.00918409
\(961\) −27.9612 −0.901973
\(962\) −0.593888 −0.0191477
\(963\) −105.007 −3.38380
\(964\) −11.3155 −0.364448
\(965\) −1.08709 −0.0349945
\(966\) 0 0
\(967\) −42.3511 −1.36192 −0.680960 0.732320i \(-0.738437\pi\)
−0.680960 + 0.732320i \(0.738437\pi\)
\(968\) −19.1599 −0.615823
\(969\) −30.2982 −0.973320
\(970\) 0.0784177 0.00251784
\(971\) −33.3395 −1.06991 −0.534957 0.844879i \(-0.679672\pi\)
−0.534957 + 0.844879i \(0.679672\pi\)
\(972\) −13.1546 −0.421936
\(973\) 0 0
\(974\) 31.1451 0.997953
\(975\) −28.4494 −0.911111
\(976\) 10.2472 0.328006
\(977\) 50.5717 1.61793 0.808966 0.587855i \(-0.200028\pi\)
0.808966 + 0.587855i \(0.200028\pi\)
\(978\) −9.24184 −0.295521
\(979\) −36.8094 −1.17643
\(980\) 0 0
\(981\) 48.1602 1.53764
\(982\) 1.81906 0.0580485
\(983\) 16.7283 0.533551 0.266775 0.963759i \(-0.414042\pi\)
0.266775 + 0.963759i \(0.414042\pi\)
\(984\) −2.84461 −0.0906828
\(985\) 2.46208 0.0784483
\(986\) 3.89682 0.124100
\(987\) 0 0
\(988\) 10.5410 0.335354
\(989\) 0.620387 0.0197272
\(990\) −2.79727 −0.0889032
\(991\) −18.9987 −0.603513 −0.301756 0.953385i \(-0.597573\pi\)
−0.301756 + 0.953385i \(0.597573\pi\)
\(992\) 1.74323 0.0553475
\(993\) −26.5193 −0.841564
\(994\) 0 0
\(995\) 1.46954 0.0465875
\(996\) −4.64643 −0.147228
\(997\) −5.34619 −0.169316 −0.0846578 0.996410i \(-0.526980\pi\)
−0.0846578 + 0.996410i \(0.526980\pi\)
\(998\) 1.22056 0.0386362
\(999\) 1.76317 0.0557841
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 4018.2.a.bs.1.9 yes 10
7.6 odd 2 4018.2.a.br.1.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4018.2.a.br.1.2 10 7.6 odd 2
4018.2.a.bs.1.9 yes 10 1.1 even 1 trivial