Properties

Label 6022.2.a.e.1.1
Level $6022$
Weight $2$
Character 6022.1
Self dual yes
Analytic conductor $48.086$
Analytic rank $0$
Dimension $68$
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] = [6022,2,Mod(1,6022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6022 = 2 \cdot 3011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6022.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: \(48.0859120972\)
Analytic rank: \(0\)
Dimension: \(68\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6022.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.35476 q^{3} +1.00000 q^{4} -3.57894 q^{5} -3.35476 q^{6} +1.79257 q^{7} +1.00000 q^{8} +8.25439 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.35476 q^{3} +1.00000 q^{4} -3.57894 q^{5} -3.35476 q^{6} +1.79257 q^{7} +1.00000 q^{8} +8.25439 q^{9} -3.57894 q^{10} -1.09193 q^{11} -3.35476 q^{12} +3.65827 q^{13} +1.79257 q^{14} +12.0065 q^{15} +1.00000 q^{16} +8.01652 q^{17} +8.25439 q^{18} +6.30514 q^{19} -3.57894 q^{20} -6.01365 q^{21} -1.09193 q^{22} +6.33291 q^{23} -3.35476 q^{24} +7.80879 q^{25} +3.65827 q^{26} -17.6272 q^{27} +1.79257 q^{28} -4.69220 q^{29} +12.0065 q^{30} +3.58165 q^{31} +1.00000 q^{32} +3.66317 q^{33} +8.01652 q^{34} -6.41551 q^{35} +8.25439 q^{36} -7.64723 q^{37} +6.30514 q^{38} -12.2726 q^{39} -3.57894 q^{40} +4.32902 q^{41} -6.01365 q^{42} -4.16493 q^{43} -1.09193 q^{44} -29.5419 q^{45} +6.33291 q^{46} -0.819644 q^{47} -3.35476 q^{48} -3.78668 q^{49} +7.80879 q^{50} -26.8935 q^{51} +3.65827 q^{52} +9.26718 q^{53} -17.6272 q^{54} +3.90797 q^{55} +1.79257 q^{56} -21.1522 q^{57} -4.69220 q^{58} +7.26145 q^{59} +12.0065 q^{60} -4.09228 q^{61} +3.58165 q^{62} +14.7966 q^{63} +1.00000 q^{64} -13.0927 q^{65} +3.66317 q^{66} +1.21956 q^{67} +8.01652 q^{68} -21.2454 q^{69} -6.41551 q^{70} +7.85175 q^{71} +8.25439 q^{72} -4.15959 q^{73} -7.64723 q^{74} -26.1966 q^{75} +6.30514 q^{76} -1.95737 q^{77} -12.2726 q^{78} -3.31384 q^{79} -3.57894 q^{80} +34.3718 q^{81} +4.32902 q^{82} +0.00149686 q^{83} -6.01365 q^{84} -28.6906 q^{85} -4.16493 q^{86} +15.7412 q^{87} -1.09193 q^{88} +0.505484 q^{89} -29.5419 q^{90} +6.55771 q^{91} +6.33291 q^{92} -12.0156 q^{93} -0.819644 q^{94} -22.5657 q^{95} -3.35476 q^{96} +13.1705 q^{97} -3.78668 q^{98} -9.01325 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 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
\(3\) −3.35476 −1.93687 −0.968435 0.249268i \(-0.919810\pi\)
−0.968435 + 0.249268i \(0.919810\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.57894 −1.60055 −0.800275 0.599634i \(-0.795313\pi\)
−0.800275 + 0.599634i \(0.795313\pi\)
\(6\) −3.35476 −1.36957
\(7\) 1.79257 0.677530 0.338765 0.940871i \(-0.389991\pi\)
0.338765 + 0.940871i \(0.389991\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.25439 2.75146
\(10\) −3.57894 −1.13176
\(11\) −1.09193 −0.329231 −0.164615 0.986358i \(-0.552638\pi\)
−0.164615 + 0.986358i \(0.552638\pi\)
\(12\) −3.35476 −0.968435
\(13\) 3.65827 1.01462 0.507310 0.861764i \(-0.330640\pi\)
0.507310 + 0.861764i \(0.330640\pi\)
\(14\) 1.79257 0.479086
\(15\) 12.0065 3.10005
\(16\) 1.00000 0.250000
\(17\) 8.01652 1.94429 0.972146 0.234376i \(-0.0753046\pi\)
0.972146 + 0.234376i \(0.0753046\pi\)
\(18\) 8.25439 1.94558
\(19\) 6.30514 1.44650 0.723249 0.690588i \(-0.242648\pi\)
0.723249 + 0.690588i \(0.242648\pi\)
\(20\) −3.57894 −0.800275
\(21\) −6.01365 −1.31229
\(22\) −1.09193 −0.232801
\(23\) 6.33291 1.32050 0.660251 0.751045i \(-0.270450\pi\)
0.660251 + 0.751045i \(0.270450\pi\)
\(24\) −3.35476 −0.684787
\(25\) 7.80879 1.56176
\(26\) 3.65827 0.717445
\(27\) −17.6272 −3.39235
\(28\) 1.79257 0.338765
\(29\) −4.69220 −0.871319 −0.435659 0.900112i \(-0.643485\pi\)
−0.435659 + 0.900112i \(0.643485\pi\)
\(30\) 12.0065 2.19207
\(31\) 3.58165 0.643284 0.321642 0.946861i \(-0.395765\pi\)
0.321642 + 0.946861i \(0.395765\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.66317 0.637677
\(34\) 8.01652 1.37482
\(35\) −6.41551 −1.08442
\(36\) 8.25439 1.37573
\(37\) −7.64723 −1.25720 −0.628599 0.777730i \(-0.716371\pi\)
−0.628599 + 0.777730i \(0.716371\pi\)
\(38\) 6.30514 1.02283
\(39\) −12.2726 −1.96519
\(40\) −3.57894 −0.565880
\(41\) 4.32902 0.676079 0.338039 0.941132i \(-0.390236\pi\)
0.338039 + 0.941132i \(0.390236\pi\)
\(42\) −6.01365 −0.927927
\(43\) −4.16493 −0.635145 −0.317573 0.948234i \(-0.602868\pi\)
−0.317573 + 0.948234i \(0.602868\pi\)
\(44\) −1.09193 −0.164615
\(45\) −29.5419 −4.40385
\(46\) 6.33291 0.933736
\(47\) −0.819644 −0.119557 −0.0597786 0.998212i \(-0.519039\pi\)
−0.0597786 + 0.998212i \(0.519039\pi\)
\(48\) −3.35476 −0.484217
\(49\) −3.78668 −0.540954
\(50\) 7.80879 1.10433
\(51\) −26.8935 −3.76584
\(52\) 3.65827 0.507310
\(53\) 9.26718 1.27295 0.636473 0.771299i \(-0.280393\pi\)
0.636473 + 0.771299i \(0.280393\pi\)
\(54\) −17.6272 −2.39876
\(55\) 3.90797 0.526950
\(56\) 1.79257 0.239543
\(57\) −21.1522 −2.80168
\(58\) −4.69220 −0.616115
\(59\) 7.26145 0.945361 0.472680 0.881234i \(-0.343287\pi\)
0.472680 + 0.881234i \(0.343287\pi\)
\(60\) 12.0065 1.55003
\(61\) −4.09228 −0.523962 −0.261981 0.965073i \(-0.584376\pi\)
−0.261981 + 0.965073i \(0.584376\pi\)
\(62\) 3.58165 0.454870
\(63\) 14.7966 1.86420
\(64\) 1.00000 0.125000
\(65\) −13.0927 −1.62395
\(66\) 3.66317 0.450906
\(67\) 1.21956 0.148993 0.0744966 0.997221i \(-0.476265\pi\)
0.0744966 + 0.997221i \(0.476265\pi\)
\(68\) 8.01652 0.972146
\(69\) −21.2454 −2.55764
\(70\) −6.41551 −0.766800
\(71\) 7.85175 0.931832 0.465916 0.884829i \(-0.345725\pi\)
0.465916 + 0.884829i \(0.345725\pi\)
\(72\) 8.25439 0.972789
\(73\) −4.15959 −0.486844 −0.243422 0.969921i \(-0.578270\pi\)
−0.243422 + 0.969921i \(0.578270\pi\)
\(74\) −7.64723 −0.888973
\(75\) −26.1966 −3.02492
\(76\) 6.30514 0.723249
\(77\) −1.95737 −0.223064
\(78\) −12.2726 −1.38960
\(79\) −3.31384 −0.372836 −0.186418 0.982470i \(-0.559688\pi\)
−0.186418 + 0.982470i \(0.559688\pi\)
\(80\) −3.57894 −0.400137
\(81\) 34.3718 3.81908
\(82\) 4.32902 0.478060
\(83\) 0.00149686 0.000164301 0 8.21506e−5 1.00000i \(-0.499974\pi\)
8.21506e−5 1.00000i \(0.499974\pi\)
\(84\) −6.01365 −0.656143
\(85\) −28.6906 −3.11194
\(86\) −4.16493 −0.449115
\(87\) 15.7412 1.68763
\(88\) −1.09193 −0.116401
\(89\) 0.505484 0.0535812 0.0267906 0.999641i \(-0.491471\pi\)
0.0267906 + 0.999641i \(0.491471\pi\)
\(90\) −29.5419 −3.11399
\(91\) 6.55771 0.687435
\(92\) 6.33291 0.660251
\(93\) −12.0156 −1.24596
\(94\) −0.819644 −0.0845398
\(95\) −22.5657 −2.31519
\(96\) −3.35476 −0.342393
\(97\) 13.1705 1.33726 0.668631 0.743595i \(-0.266881\pi\)
0.668631 + 0.743595i \(0.266881\pi\)
\(98\) −3.78668 −0.382512
\(99\) −9.01325 −0.905866
\(100\) 7.80879 0.780879
\(101\) 0.00889696 0.000885281 0 0.000442641 1.00000i \(-0.499859\pi\)
0.000442641 1.00000i \(0.499859\pi\)
\(102\) −26.8935 −2.66285
\(103\) −5.70849 −0.562474 −0.281237 0.959638i \(-0.590745\pi\)
−0.281237 + 0.959638i \(0.590745\pi\)
\(104\) 3.65827 0.358722
\(105\) 21.5225 2.10038
\(106\) 9.26718 0.900108
\(107\) 10.4291 1.00822 0.504108 0.863641i \(-0.331821\pi\)
0.504108 + 0.863641i \(0.331821\pi\)
\(108\) −17.6272 −1.69618
\(109\) 11.1233 1.06542 0.532708 0.846299i \(-0.321174\pi\)
0.532708 + 0.846299i \(0.321174\pi\)
\(110\) 3.90797 0.372610
\(111\) 25.6546 2.43503
\(112\) 1.79257 0.169382
\(113\) −14.6343 −1.37668 −0.688338 0.725390i \(-0.741659\pi\)
−0.688338 + 0.725390i \(0.741659\pi\)
\(114\) −21.1522 −1.98108
\(115\) −22.6651 −2.11353
\(116\) −4.69220 −0.435659
\(117\) 30.1967 2.79169
\(118\) 7.26145 0.668471
\(119\) 14.3702 1.31732
\(120\) 12.0065 1.09603
\(121\) −9.80768 −0.891607
\(122\) −4.09228 −0.370497
\(123\) −14.5228 −1.30948
\(124\) 3.58165 0.321642
\(125\) −10.0525 −0.899120
\(126\) 14.7966 1.31819
\(127\) −6.72888 −0.597092 −0.298546 0.954395i \(-0.596502\pi\)
−0.298546 + 0.954395i \(0.596502\pi\)
\(128\) 1.00000 0.0883883
\(129\) 13.9723 1.23019
\(130\) −13.0927 −1.14831
\(131\) 13.8913 1.21369 0.606844 0.794821i \(-0.292435\pi\)
0.606844 + 0.794821i \(0.292435\pi\)
\(132\) 3.66317 0.318838
\(133\) 11.3024 0.980045
\(134\) 1.21956 0.105354
\(135\) 63.0866 5.42963
\(136\) 8.01652 0.687411
\(137\) 13.3834 1.14342 0.571711 0.820455i \(-0.306280\pi\)
0.571711 + 0.820455i \(0.306280\pi\)
\(138\) −21.2454 −1.80853
\(139\) 2.97490 0.252328 0.126164 0.992009i \(-0.459733\pi\)
0.126164 + 0.992009i \(0.459733\pi\)
\(140\) −6.41551 −0.542210
\(141\) 2.74970 0.231567
\(142\) 7.85175 0.658905
\(143\) −3.99459 −0.334044
\(144\) 8.25439 0.687866
\(145\) 16.7931 1.39459
\(146\) −4.15959 −0.344251
\(147\) 12.7034 1.04776
\(148\) −7.64723 −0.628599
\(149\) −15.3432 −1.25697 −0.628483 0.777823i \(-0.716324\pi\)
−0.628483 + 0.777823i \(0.716324\pi\)
\(150\) −26.1966 −2.13894
\(151\) 5.99985 0.488261 0.244130 0.969742i \(-0.421497\pi\)
0.244130 + 0.969742i \(0.421497\pi\)
\(152\) 6.30514 0.511414
\(153\) 66.1715 5.34965
\(154\) −1.95737 −0.157730
\(155\) −12.8185 −1.02961
\(156\) −12.2726 −0.982593
\(157\) −14.8361 −1.18405 −0.592023 0.805921i \(-0.701671\pi\)
−0.592023 + 0.805921i \(0.701671\pi\)
\(158\) −3.31384 −0.263635
\(159\) −31.0891 −2.46553
\(160\) −3.57894 −0.282940
\(161\) 11.3522 0.894680
\(162\) 34.3718 2.70050
\(163\) −11.8622 −0.929119 −0.464560 0.885542i \(-0.653787\pi\)
−0.464560 + 0.885542i \(0.653787\pi\)
\(164\) 4.32902 0.338039
\(165\) −13.1103 −1.02063
\(166\) 0.00149686 0.000116179 0
\(167\) −2.37796 −0.184012 −0.0920060 0.995758i \(-0.529328\pi\)
−0.0920060 + 0.995758i \(0.529328\pi\)
\(168\) −6.01365 −0.463963
\(169\) 0.382907 0.0294544
\(170\) −28.6906 −2.20047
\(171\) 52.0450 3.97998
\(172\) −4.16493 −0.317573
\(173\) 6.73048 0.511709 0.255854 0.966715i \(-0.417643\pi\)
0.255854 + 0.966715i \(0.417643\pi\)
\(174\) 15.7412 1.19333
\(175\) 13.9978 1.05814
\(176\) −1.09193 −0.0823077
\(177\) −24.3604 −1.83104
\(178\) 0.505484 0.0378877
\(179\) 7.86388 0.587774 0.293887 0.955840i \(-0.405051\pi\)
0.293887 + 0.955840i \(0.405051\pi\)
\(180\) −29.5419 −2.20193
\(181\) −16.1105 −1.19749 −0.598743 0.800941i \(-0.704333\pi\)
−0.598743 + 0.800941i \(0.704333\pi\)
\(182\) 6.55771 0.486090
\(183\) 13.7286 1.01485
\(184\) 6.33291 0.466868
\(185\) 27.3690 2.01221
\(186\) −12.0156 −0.881024
\(187\) −8.75352 −0.640121
\(188\) −0.819644 −0.0597786
\(189\) −31.5981 −2.29842
\(190\) −22.5657 −1.63709
\(191\) 25.2272 1.82537 0.912686 0.408661i \(-0.134004\pi\)
0.912686 + 0.408661i \(0.134004\pi\)
\(192\) −3.35476 −0.242109
\(193\) −10.7465 −0.773553 −0.386776 0.922174i \(-0.626411\pi\)
−0.386776 + 0.922174i \(0.626411\pi\)
\(194\) 13.1705 0.945586
\(195\) 43.9228 3.14538
\(196\) −3.78668 −0.270477
\(197\) −0.178585 −0.0127236 −0.00636182 0.999980i \(-0.502025\pi\)
−0.00636182 + 0.999980i \(0.502025\pi\)
\(198\) −9.01325 −0.640544
\(199\) 7.22038 0.511839 0.255919 0.966698i \(-0.417622\pi\)
0.255919 + 0.966698i \(0.417622\pi\)
\(200\) 7.80879 0.552165
\(201\) −4.09133 −0.288580
\(202\) 0.00889696 0.000625988 0
\(203\) −8.41111 −0.590344
\(204\) −26.8935 −1.88292
\(205\) −15.4933 −1.08210
\(206\) −5.70849 −0.397729
\(207\) 52.2743 3.63331
\(208\) 3.65827 0.253655
\(209\) −6.88480 −0.476231
\(210\) 21.5225 1.48519
\(211\) −22.8969 −1.57629 −0.788145 0.615489i \(-0.788958\pi\)
−0.788145 + 0.615489i \(0.788958\pi\)
\(212\) 9.26718 0.636473
\(213\) −26.3407 −1.80484
\(214\) 10.4291 0.712917
\(215\) 14.9060 1.01658
\(216\) −17.6272 −1.19938
\(217\) 6.42038 0.435844
\(218\) 11.1233 0.753363
\(219\) 13.9544 0.942953
\(220\) 3.90797 0.263475
\(221\) 29.3266 1.97272
\(222\) 25.6546 1.72182
\(223\) 17.9641 1.20296 0.601481 0.798887i \(-0.294577\pi\)
0.601481 + 0.798887i \(0.294577\pi\)
\(224\) 1.79257 0.119771
\(225\) 64.4567 4.29712
\(226\) −14.6343 −0.973456
\(227\) 27.6520 1.83533 0.917664 0.397358i \(-0.130073\pi\)
0.917664 + 0.397358i \(0.130073\pi\)
\(228\) −21.1522 −1.40084
\(229\) 18.4296 1.21786 0.608930 0.793224i \(-0.291599\pi\)
0.608930 + 0.793224i \(0.291599\pi\)
\(230\) −22.6651 −1.49449
\(231\) 6.56651 0.432045
\(232\) −4.69220 −0.308058
\(233\) −17.2596 −1.13071 −0.565357 0.824847i \(-0.691261\pi\)
−0.565357 + 0.824847i \(0.691261\pi\)
\(234\) 30.1967 1.97402
\(235\) 2.93345 0.191357
\(236\) 7.26145 0.472680
\(237\) 11.1171 0.722135
\(238\) 14.3702 0.931483
\(239\) −23.7782 −1.53808 −0.769041 0.639200i \(-0.779266\pi\)
−0.769041 + 0.639200i \(0.779266\pi\)
\(240\) 12.0065 0.775014
\(241\) −29.4282 −1.89564 −0.947820 0.318807i \(-0.896718\pi\)
−0.947820 + 0.318807i \(0.896718\pi\)
\(242\) −9.80768 −0.630461
\(243\) −62.4273 −4.00471
\(244\) −4.09228 −0.261981
\(245\) 13.5523 0.865823
\(246\) −14.5228 −0.925939
\(247\) 23.0659 1.46765
\(248\) 3.58165 0.227435
\(249\) −0.00502158 −0.000318230 0
\(250\) −10.0525 −0.635774
\(251\) 29.9729 1.89187 0.945936 0.324355i \(-0.105147\pi\)
0.945936 + 0.324355i \(0.105147\pi\)
\(252\) 14.7966 0.932099
\(253\) −6.91512 −0.434750
\(254\) −6.72888 −0.422208
\(255\) 96.2500 6.02741
\(256\) 1.00000 0.0625000
\(257\) 8.70097 0.542752 0.271376 0.962473i \(-0.412521\pi\)
0.271376 + 0.962473i \(0.412521\pi\)
\(258\) 13.9723 0.869878
\(259\) −13.7082 −0.851788
\(260\) −13.0927 −0.811975
\(261\) −38.7312 −2.39740
\(262\) 13.8913 0.858208
\(263\) −19.5655 −1.20646 −0.603230 0.797567i \(-0.706120\pi\)
−0.603230 + 0.797567i \(0.706120\pi\)
\(264\) 3.66317 0.225453
\(265\) −33.1667 −2.03741
\(266\) 11.3024 0.692996
\(267\) −1.69578 −0.103780
\(268\) 1.21956 0.0744966
\(269\) 9.34653 0.569868 0.284934 0.958547i \(-0.408028\pi\)
0.284934 + 0.958547i \(0.408028\pi\)
\(270\) 63.0866 3.83933
\(271\) 13.2398 0.804259 0.402129 0.915583i \(-0.368270\pi\)
0.402129 + 0.915583i \(0.368270\pi\)
\(272\) 8.01652 0.486073
\(273\) −21.9995 −1.33147
\(274\) 13.3834 0.808522
\(275\) −8.52668 −0.514178
\(276\) −21.2454 −1.27882
\(277\) 11.5887 0.696299 0.348150 0.937439i \(-0.386810\pi\)
0.348150 + 0.937439i \(0.386810\pi\)
\(278\) 2.97490 0.178423
\(279\) 29.5643 1.76997
\(280\) −6.41551 −0.383400
\(281\) −10.0446 −0.599209 −0.299605 0.954063i \(-0.596855\pi\)
−0.299605 + 0.954063i \(0.596855\pi\)
\(282\) 2.74970 0.163742
\(283\) −25.5327 −1.51776 −0.758879 0.651231i \(-0.774253\pi\)
−0.758879 + 0.651231i \(0.774253\pi\)
\(284\) 7.85175 0.465916
\(285\) 75.7024 4.48422
\(286\) −3.99459 −0.236205
\(287\) 7.76008 0.458063
\(288\) 8.25439 0.486394
\(289\) 47.2646 2.78027
\(290\) 16.7931 0.986123
\(291\) −44.1838 −2.59010
\(292\) −4.15959 −0.243422
\(293\) 20.2283 1.18175 0.590876 0.806763i \(-0.298782\pi\)
0.590876 + 0.806763i \(0.298782\pi\)
\(294\) 12.7034 0.740876
\(295\) −25.9883 −1.51310
\(296\) −7.64723 −0.444486
\(297\) 19.2477 1.11687
\(298\) −15.3432 −0.888810
\(299\) 23.1675 1.33981
\(300\) −26.1966 −1.51246
\(301\) −7.46594 −0.430330
\(302\) 5.99985 0.345253
\(303\) −0.0298471 −0.00171467
\(304\) 6.30514 0.361624
\(305\) 14.6460 0.838627
\(306\) 66.1715 3.78277
\(307\) 25.0653 1.43055 0.715275 0.698843i \(-0.246301\pi\)
0.715275 + 0.698843i \(0.246301\pi\)
\(308\) −1.95737 −0.111532
\(309\) 19.1506 1.08944
\(310\) −12.8185 −0.728042
\(311\) −23.4401 −1.32917 −0.664583 0.747215i \(-0.731391\pi\)
−0.664583 + 0.747215i \(0.731391\pi\)
\(312\) −12.2726 −0.694799
\(313\) −6.05460 −0.342226 −0.171113 0.985251i \(-0.554736\pi\)
−0.171113 + 0.985251i \(0.554736\pi\)
\(314\) −14.8361 −0.837247
\(315\) −52.9561 −2.98374
\(316\) −3.31384 −0.186418
\(317\) −15.0739 −0.846637 −0.423318 0.905981i \(-0.639135\pi\)
−0.423318 + 0.905981i \(0.639135\pi\)
\(318\) −31.0891 −1.74339
\(319\) 5.12357 0.286865
\(320\) −3.57894 −0.200069
\(321\) −34.9870 −1.95278
\(322\) 11.3522 0.632634
\(323\) 50.5453 2.81241
\(324\) 34.3718 1.90954
\(325\) 28.5666 1.58459
\(326\) −11.8622 −0.656987
\(327\) −37.3159 −2.06357
\(328\) 4.32902 0.239030
\(329\) −1.46927 −0.0810036
\(330\) −13.1103 −0.721697
\(331\) −13.3559 −0.734108 −0.367054 0.930200i \(-0.619634\pi\)
−0.367054 + 0.930200i \(0.619634\pi\)
\(332\) 0.00149686 8.21506e−5 0
\(333\) −63.1232 −3.45913
\(334\) −2.37796 −0.130116
\(335\) −4.36473 −0.238471
\(336\) −6.01365 −0.328072
\(337\) 6.84980 0.373132 0.186566 0.982442i \(-0.440264\pi\)
0.186566 + 0.982442i \(0.440264\pi\)
\(338\) 0.382907 0.0208274
\(339\) 49.0944 2.66644
\(340\) −28.6906 −1.55597
\(341\) −3.91093 −0.211789
\(342\) 52.0450 2.81427
\(343\) −19.3359 −1.04404
\(344\) −4.16493 −0.224558
\(345\) 76.0358 4.09363
\(346\) 6.73048 0.361833
\(347\) −11.8184 −0.634446 −0.317223 0.948351i \(-0.602750\pi\)
−0.317223 + 0.948351i \(0.602750\pi\)
\(348\) 15.7412 0.843815
\(349\) −11.7736 −0.630225 −0.315113 0.949054i \(-0.602042\pi\)
−0.315113 + 0.949054i \(0.602042\pi\)
\(350\) 13.9978 0.748216
\(351\) −64.4849 −3.44195
\(352\) −1.09193 −0.0582003
\(353\) −15.9335 −0.848053 −0.424026 0.905650i \(-0.639384\pi\)
−0.424026 + 0.905650i \(0.639384\pi\)
\(354\) −24.3604 −1.29474
\(355\) −28.1009 −1.49144
\(356\) 0.505484 0.0267906
\(357\) −48.2086 −2.55147
\(358\) 7.86388 0.415619
\(359\) −26.9345 −1.42155 −0.710775 0.703420i \(-0.751655\pi\)
−0.710775 + 0.703420i \(0.751655\pi\)
\(360\) −29.5419 −1.55700
\(361\) 20.7548 1.09236
\(362\) −16.1105 −0.846751
\(363\) 32.9024 1.72693
\(364\) 6.55771 0.343718
\(365\) 14.8869 0.779217
\(366\) 13.7286 0.717605
\(367\) −13.8265 −0.721736 −0.360868 0.932617i \(-0.617520\pi\)
−0.360868 + 0.932617i \(0.617520\pi\)
\(368\) 6.33291 0.330126
\(369\) 35.7334 1.86021
\(370\) 27.3690 1.42284
\(371\) 16.6121 0.862458
\(372\) −12.0156 −0.622978
\(373\) −10.4072 −0.538867 −0.269433 0.963019i \(-0.586836\pi\)
−0.269433 + 0.963019i \(0.586836\pi\)
\(374\) −8.75352 −0.452634
\(375\) 33.7236 1.74148
\(376\) −0.819644 −0.0422699
\(377\) −17.1653 −0.884058
\(378\) −31.5981 −1.62523
\(379\) −7.07875 −0.363611 −0.181806 0.983335i \(-0.558194\pi\)
−0.181806 + 0.983335i \(0.558194\pi\)
\(380\) −22.5657 −1.15760
\(381\) 22.5738 1.15649
\(382\) 25.2272 1.29073
\(383\) −8.21579 −0.419807 −0.209904 0.977722i \(-0.567315\pi\)
−0.209904 + 0.977722i \(0.567315\pi\)
\(384\) −3.35476 −0.171197
\(385\) 7.00532 0.357024
\(386\) −10.7465 −0.546984
\(387\) −34.3789 −1.74758
\(388\) 13.1705 0.668631
\(389\) −6.36587 −0.322762 −0.161381 0.986892i \(-0.551595\pi\)
−0.161381 + 0.986892i \(0.551595\pi\)
\(390\) 43.9228 2.22412
\(391\) 50.7679 2.56744
\(392\) −3.78668 −0.191256
\(393\) −46.6019 −2.35076
\(394\) −0.178585 −0.00899697
\(395\) 11.8600 0.596743
\(396\) −9.01325 −0.452933
\(397\) −6.79701 −0.341132 −0.170566 0.985346i \(-0.554560\pi\)
−0.170566 + 0.985346i \(0.554560\pi\)
\(398\) 7.22038 0.361925
\(399\) −37.9169 −1.89822
\(400\) 7.80879 0.390439
\(401\) 36.0616 1.80083 0.900415 0.435033i \(-0.143263\pi\)
0.900415 + 0.435033i \(0.143263\pi\)
\(402\) −4.09133 −0.204057
\(403\) 13.1026 0.652689
\(404\) 0.00889696 0.000442641 0
\(405\) −123.014 −6.11263
\(406\) −8.41111 −0.417436
\(407\) 8.35028 0.413908
\(408\) −26.8935 −1.33143
\(409\) −31.9276 −1.57872 −0.789358 0.613933i \(-0.789586\pi\)
−0.789358 + 0.613933i \(0.789586\pi\)
\(410\) −15.4933 −0.765158
\(411\) −44.8981 −2.21466
\(412\) −5.70849 −0.281237
\(413\) 13.0167 0.640510
\(414\) 52.2743 2.56914
\(415\) −0.00535715 −0.000262972 0
\(416\) 3.65827 0.179361
\(417\) −9.98008 −0.488727
\(418\) −6.88480 −0.336746
\(419\) 2.92692 0.142989 0.0714946 0.997441i \(-0.477223\pi\)
0.0714946 + 0.997441i \(0.477223\pi\)
\(420\) 21.5225 1.05019
\(421\) −2.31229 −0.112694 −0.0563470 0.998411i \(-0.517945\pi\)
−0.0563470 + 0.998411i \(0.517945\pi\)
\(422\) −22.8969 −1.11461
\(423\) −6.76566 −0.328957
\(424\) 9.26718 0.450054
\(425\) 62.5993 3.03651
\(426\) −26.3407 −1.27621
\(427\) −7.33571 −0.355000
\(428\) 10.4291 0.504108
\(429\) 13.4009 0.647000
\(430\) 14.9060 0.718831
\(431\) −27.3341 −1.31664 −0.658318 0.752740i \(-0.728732\pi\)
−0.658318 + 0.752740i \(0.728732\pi\)
\(432\) −17.6272 −0.848089
\(433\) 38.7803 1.86366 0.931832 0.362891i \(-0.118210\pi\)
0.931832 + 0.362891i \(0.118210\pi\)
\(434\) 6.42038 0.308188
\(435\) −56.3366 −2.70114
\(436\) 11.1233 0.532708
\(437\) 39.9299 1.91010
\(438\) 13.9544 0.666768
\(439\) 3.11143 0.148500 0.0742501 0.997240i \(-0.476344\pi\)
0.0742501 + 0.997240i \(0.476344\pi\)
\(440\) 3.90797 0.186305
\(441\) −31.2567 −1.48841
\(442\) 29.3266 1.39492
\(443\) −8.04748 −0.382347 −0.191174 0.981556i \(-0.561229\pi\)
−0.191174 + 0.981556i \(0.561229\pi\)
\(444\) 25.6546 1.21751
\(445\) −1.80910 −0.0857594
\(446\) 17.9641 0.850623
\(447\) 51.4728 2.43458
\(448\) 1.79257 0.0846912
\(449\) −18.1602 −0.857031 −0.428515 0.903535i \(-0.640963\pi\)
−0.428515 + 0.903535i \(0.640963\pi\)
\(450\) 64.4567 3.03852
\(451\) −4.72700 −0.222586
\(452\) −14.6343 −0.688338
\(453\) −20.1280 −0.945698
\(454\) 27.6520 1.29777
\(455\) −23.4696 −1.10027
\(456\) −21.1522 −0.990542
\(457\) 15.1244 0.707491 0.353745 0.935342i \(-0.384908\pi\)
0.353745 + 0.935342i \(0.384908\pi\)
\(458\) 18.4296 0.861158
\(459\) −141.309 −6.59573
\(460\) −22.6651 −1.05676
\(461\) 17.6429 0.821711 0.410855 0.911701i \(-0.365230\pi\)
0.410855 + 0.911701i \(0.365230\pi\)
\(462\) 6.56651 0.305502
\(463\) 34.6719 1.61134 0.805670 0.592364i \(-0.201805\pi\)
0.805670 + 0.592364i \(0.201805\pi\)
\(464\) −4.69220 −0.217830
\(465\) 43.0030 1.99421
\(466\) −17.2596 −0.799535
\(467\) 18.1834 0.841426 0.420713 0.907194i \(-0.361780\pi\)
0.420713 + 0.907194i \(0.361780\pi\)
\(468\) 30.1967 1.39584
\(469\) 2.18616 0.100947
\(470\) 2.93345 0.135310
\(471\) 49.7714 2.29334
\(472\) 7.26145 0.334235
\(473\) 4.54783 0.209109
\(474\) 11.1171 0.510627
\(475\) 49.2355 2.25908
\(476\) 14.3702 0.658658
\(477\) 76.4949 3.50246
\(478\) −23.7782 −1.08759
\(479\) 31.7302 1.44979 0.724894 0.688860i \(-0.241889\pi\)
0.724894 + 0.688860i \(0.241889\pi\)
\(480\) 12.0065 0.548017
\(481\) −27.9756 −1.27558
\(482\) −29.4282 −1.34042
\(483\) −38.0839 −1.73288
\(484\) −9.80768 −0.445804
\(485\) −47.1364 −2.14035
\(486\) −62.4273 −2.83176
\(487\) 29.8048 1.35058 0.675291 0.737551i \(-0.264018\pi\)
0.675291 + 0.737551i \(0.264018\pi\)
\(488\) −4.09228 −0.185249
\(489\) 39.7948 1.79958
\(490\) 13.5523 0.612229
\(491\) 41.6480 1.87955 0.939774 0.341796i \(-0.111035\pi\)
0.939774 + 0.341796i \(0.111035\pi\)
\(492\) −14.5228 −0.654738
\(493\) −37.6151 −1.69410
\(494\) 23.0659 1.03778
\(495\) 32.2579 1.44988
\(496\) 3.58165 0.160821
\(497\) 14.0749 0.631344
\(498\) −0.00502158 −0.000225023 0
\(499\) 33.2866 1.49011 0.745056 0.667002i \(-0.232423\pi\)
0.745056 + 0.667002i \(0.232423\pi\)
\(500\) −10.0525 −0.449560
\(501\) 7.97748 0.356407
\(502\) 29.9729 1.33775
\(503\) 34.1045 1.52065 0.760323 0.649546i \(-0.225041\pi\)
0.760323 + 0.649546i \(0.225041\pi\)
\(504\) 14.7966 0.659093
\(505\) −0.0318417 −0.00141694
\(506\) −6.91512 −0.307415
\(507\) −1.28456 −0.0570493
\(508\) −6.72888 −0.298546
\(509\) −12.8444 −0.569317 −0.284658 0.958629i \(-0.591880\pi\)
−0.284658 + 0.958629i \(0.591880\pi\)
\(510\) 96.2500 4.26202
\(511\) −7.45639 −0.329851
\(512\) 1.00000 0.0441942
\(513\) −111.142 −4.90703
\(514\) 8.70097 0.383783
\(515\) 20.4303 0.900267
\(516\) 13.9723 0.615097
\(517\) 0.894997 0.0393619
\(518\) −13.7082 −0.602305
\(519\) −22.5791 −0.991113
\(520\) −13.0927 −0.574153
\(521\) −2.37323 −0.103973 −0.0519865 0.998648i \(-0.516555\pi\)
−0.0519865 + 0.998648i \(0.516555\pi\)
\(522\) −38.7312 −1.69522
\(523\) 42.1621 1.84362 0.921810 0.387643i \(-0.126711\pi\)
0.921810 + 0.387643i \(0.126711\pi\)
\(524\) 13.8913 0.606844
\(525\) −46.9593 −2.04947
\(526\) −19.5655 −0.853096
\(527\) 28.7124 1.25073
\(528\) 3.66317 0.159419
\(529\) 17.1057 0.743728
\(530\) −33.1667 −1.44067
\(531\) 59.9389 2.60112
\(532\) 11.3024 0.490022
\(533\) 15.8367 0.685963
\(534\) −1.69578 −0.0733834
\(535\) −37.3250 −1.61370
\(536\) 1.21956 0.0526771
\(537\) −26.3814 −1.13844
\(538\) 9.34653 0.402957
\(539\) 4.13480 0.178099
\(540\) 63.0866 2.71481
\(541\) 20.6984 0.889894 0.444947 0.895557i \(-0.353223\pi\)
0.444947 + 0.895557i \(0.353223\pi\)
\(542\) 13.2398 0.568697
\(543\) 54.0469 2.31938
\(544\) 8.01652 0.343706
\(545\) −39.8095 −1.70525
\(546\) −21.9995 −0.941493
\(547\) −15.2034 −0.650050 −0.325025 0.945705i \(-0.605373\pi\)
−0.325025 + 0.945705i \(0.605373\pi\)
\(548\) 13.3834 0.571711
\(549\) −33.7792 −1.44166
\(550\) −8.52668 −0.363579
\(551\) −29.5849 −1.26036
\(552\) −21.2454 −0.904263
\(553\) −5.94031 −0.252608
\(554\) 11.5887 0.492358
\(555\) −91.8162 −3.89738
\(556\) 2.97490 0.126164
\(557\) −3.49715 −0.148179 −0.0740895 0.997252i \(-0.523605\pi\)
−0.0740895 + 0.997252i \(0.523605\pi\)
\(558\) 29.5643 1.25156
\(559\) −15.2364 −0.644431
\(560\) −6.41551 −0.271105
\(561\) 29.3659 1.23983
\(562\) −10.0446 −0.423705
\(563\) 15.2490 0.642667 0.321333 0.946966i \(-0.395869\pi\)
0.321333 + 0.946966i \(0.395869\pi\)
\(564\) 2.74970 0.115783
\(565\) 52.3751 2.20344
\(566\) −25.5327 −1.07322
\(567\) 61.6139 2.58754
\(568\) 7.85175 0.329452
\(569\) 24.6859 1.03489 0.517444 0.855717i \(-0.326884\pi\)
0.517444 + 0.855717i \(0.326884\pi\)
\(570\) 75.7024 3.17082
\(571\) −26.7686 −1.12023 −0.560115 0.828415i \(-0.689243\pi\)
−0.560115 + 0.828415i \(0.689243\pi\)
\(572\) −3.99459 −0.167022
\(573\) −84.6309 −3.53551
\(574\) 7.76008 0.323900
\(575\) 49.4523 2.06230
\(576\) 8.25439 0.343933
\(577\) 9.74406 0.405650 0.202825 0.979215i \(-0.434988\pi\)
0.202825 + 0.979215i \(0.434988\pi\)
\(578\) 47.2646 1.96595
\(579\) 36.0520 1.49827
\(580\) 16.7931 0.697294
\(581\) 0.00268323 0.000111319 0
\(582\) −44.1838 −1.83148
\(583\) −10.1192 −0.419093
\(584\) −4.15959 −0.172125
\(585\) −108.072 −4.46824
\(586\) 20.2283 0.835624
\(587\) 10.1759 0.420005 0.210002 0.977701i \(-0.432653\pi\)
0.210002 + 0.977701i \(0.432653\pi\)
\(588\) 12.7034 0.523878
\(589\) 22.5828 0.930508
\(590\) −25.9883 −1.06992
\(591\) 0.599109 0.0246440
\(592\) −7.64723 −0.314299
\(593\) −5.11337 −0.209981 −0.104990 0.994473i \(-0.533481\pi\)
−0.104990 + 0.994473i \(0.533481\pi\)
\(594\) 19.2477 0.789744
\(595\) −51.4301 −2.10843
\(596\) −15.3432 −0.628483
\(597\) −24.2226 −0.991365
\(598\) 23.1675 0.947388
\(599\) −46.5323 −1.90126 −0.950629 0.310331i \(-0.899560\pi\)
−0.950629 + 0.310331i \(0.899560\pi\)
\(600\) −26.1966 −1.06947
\(601\) 19.4266 0.792430 0.396215 0.918158i \(-0.370324\pi\)
0.396215 + 0.918158i \(0.370324\pi\)
\(602\) −7.46594 −0.304289
\(603\) 10.0667 0.409949
\(604\) 5.99985 0.244130
\(605\) 35.1011 1.42706
\(606\) −0.0298471 −0.00121246
\(607\) −1.07284 −0.0435453 −0.0217727 0.999763i \(-0.506931\pi\)
−0.0217727 + 0.999763i \(0.506931\pi\)
\(608\) 6.30514 0.255707
\(609\) 28.2172 1.14342
\(610\) 14.6460 0.592999
\(611\) −2.99847 −0.121305
\(612\) 66.1715 2.67482
\(613\) 16.8203 0.679365 0.339683 0.940540i \(-0.389680\pi\)
0.339683 + 0.940540i \(0.389680\pi\)
\(614\) 25.0653 1.01155
\(615\) 51.9761 2.09588
\(616\) −1.95737 −0.0788649
\(617\) 4.90973 0.197658 0.0988291 0.995104i \(-0.468490\pi\)
0.0988291 + 0.995104i \(0.468490\pi\)
\(618\) 19.1506 0.770349
\(619\) −32.2378 −1.29574 −0.647872 0.761749i \(-0.724341\pi\)
−0.647872 + 0.761749i \(0.724341\pi\)
\(620\) −12.8185 −0.514804
\(621\) −111.631 −4.47961
\(622\) −23.4401 −0.939862
\(623\) 0.906118 0.0363029
\(624\) −12.2726 −0.491297
\(625\) −3.06679 −0.122672
\(626\) −6.05460 −0.241991
\(627\) 23.0968 0.922398
\(628\) −14.8361 −0.592023
\(629\) −61.3042 −2.44436
\(630\) −52.9561 −2.10982
\(631\) −41.6581 −1.65838 −0.829192 0.558964i \(-0.811199\pi\)
−0.829192 + 0.558964i \(0.811199\pi\)
\(632\) −3.31384 −0.131818
\(633\) 76.8137 3.05307
\(634\) −15.0739 −0.598662
\(635\) 24.0822 0.955675
\(636\) −31.0891 −1.23276
\(637\) −13.8527 −0.548863
\(638\) 5.12357 0.202844
\(639\) 64.8114 2.56390
\(640\) −3.57894 −0.141470
\(641\) 39.5295 1.56132 0.780660 0.624956i \(-0.214883\pi\)
0.780660 + 0.624956i \(0.214883\pi\)
\(642\) −34.9870 −1.38083
\(643\) 7.44453 0.293584 0.146792 0.989167i \(-0.453105\pi\)
0.146792 + 0.989167i \(0.453105\pi\)
\(644\) 11.3522 0.447340
\(645\) −50.0060 −1.96898
\(646\) 50.5453 1.98868
\(647\) 44.3770 1.74464 0.872321 0.488934i \(-0.162614\pi\)
0.872321 + 0.488934i \(0.162614\pi\)
\(648\) 34.3718 1.35025
\(649\) −7.92903 −0.311242
\(650\) 28.5666 1.12047
\(651\) −21.5388 −0.844172
\(652\) −11.8622 −0.464560
\(653\) 44.4547 1.73965 0.869823 0.493364i \(-0.164233\pi\)
0.869823 + 0.493364i \(0.164233\pi\)
\(654\) −37.3159 −1.45917
\(655\) −49.7161 −1.94257
\(656\) 4.32902 0.169020
\(657\) −34.3349 −1.33953
\(658\) −1.46927 −0.0572782
\(659\) −27.2924 −1.06316 −0.531580 0.847008i \(-0.678401\pi\)
−0.531580 + 0.847008i \(0.678401\pi\)
\(660\) −13.1103 −0.510317
\(661\) 11.0815 0.431020 0.215510 0.976502i \(-0.430859\pi\)
0.215510 + 0.976502i \(0.430859\pi\)
\(662\) −13.3559 −0.519093
\(663\) −98.3835 −3.82090
\(664\) 0.00149686 5.80893e−5 0
\(665\) −40.4507 −1.56861
\(666\) −63.1232 −2.44598
\(667\) −29.7152 −1.15058
\(668\) −2.37796 −0.0920060
\(669\) −60.2650 −2.32998
\(670\) −4.36473 −0.168624
\(671\) 4.46850 0.172504
\(672\) −6.01365 −0.231982
\(673\) 9.89588 0.381458 0.190729 0.981643i \(-0.438915\pi\)
0.190729 + 0.981643i \(0.438915\pi\)
\(674\) 6.84980 0.263844
\(675\) −137.647 −5.29803
\(676\) 0.382907 0.0147272
\(677\) 32.2116 1.23799 0.618995 0.785395i \(-0.287540\pi\)
0.618995 + 0.785395i \(0.287540\pi\)
\(678\) 49.0944 1.88546
\(679\) 23.6091 0.906034
\(680\) −28.6906 −1.10024
\(681\) −92.7657 −3.55479
\(682\) −3.91093 −0.149757
\(683\) −21.1526 −0.809384 −0.404692 0.914453i \(-0.632621\pi\)
−0.404692 + 0.914453i \(0.632621\pi\)
\(684\) 52.0450 1.98999
\(685\) −47.8984 −1.83010
\(686\) −19.3359 −0.738249
\(687\) −61.8267 −2.35884
\(688\) −4.16493 −0.158786
\(689\) 33.9018 1.29156
\(690\) 76.0358 2.89463
\(691\) 44.7002 1.70047 0.850237 0.526399i \(-0.176458\pi\)
0.850237 + 0.526399i \(0.176458\pi\)
\(692\) 6.73048 0.255854
\(693\) −16.1569 −0.613751
\(694\) −11.8184 −0.448621
\(695\) −10.6470 −0.403864
\(696\) 15.7412 0.596667
\(697\) 34.7036 1.31449
\(698\) −11.7736 −0.445637
\(699\) 57.9017 2.19004
\(700\) 13.9978 0.529068
\(701\) −39.2007 −1.48059 −0.740295 0.672282i \(-0.765314\pi\)
−0.740295 + 0.672282i \(0.765314\pi\)
\(702\) −64.4849 −2.43383
\(703\) −48.2169 −1.81853
\(704\) −1.09193 −0.0411538
\(705\) −9.84102 −0.370634
\(706\) −15.9335 −0.599664
\(707\) 0.0159485 0.000599804 0
\(708\) −24.3604 −0.915520
\(709\) −33.3399 −1.25211 −0.626053 0.779780i \(-0.715331\pi\)
−0.626053 + 0.779780i \(0.715331\pi\)
\(710\) −28.1009 −1.05461
\(711\) −27.3537 −1.02585
\(712\) 0.505484 0.0189438
\(713\) 22.6823 0.849458
\(714\) −48.2086 −1.80416
\(715\) 14.2964 0.534654
\(716\) 7.86388 0.293887
\(717\) 79.7699 2.97906
\(718\) −26.9345 −1.00519
\(719\) −22.5955 −0.842671 −0.421335 0.906905i \(-0.638438\pi\)
−0.421335 + 0.906905i \(0.638438\pi\)
\(720\) −29.5419 −1.10096
\(721\) −10.2329 −0.381093
\(722\) 20.7548 0.772412
\(723\) 98.7246 3.67161
\(724\) −16.1105 −0.598743
\(725\) −36.6403 −1.36079
\(726\) 32.9024 1.22112
\(727\) −21.2009 −0.786299 −0.393150 0.919474i \(-0.628615\pi\)
−0.393150 + 0.919474i \(0.628615\pi\)
\(728\) 6.55771 0.243045
\(729\) 106.313 3.93752
\(730\) 14.8869 0.550990
\(731\) −33.3882 −1.23491
\(732\) 13.7286 0.507423
\(733\) −28.1566 −1.03999 −0.519994 0.854170i \(-0.674066\pi\)
−0.519994 + 0.854170i \(0.674066\pi\)
\(734\) −13.8265 −0.510345
\(735\) −45.4646 −1.67699
\(736\) 6.33291 0.233434
\(737\) −1.33168 −0.0490531
\(738\) 35.7334 1.31536
\(739\) 5.41197 0.199083 0.0995413 0.995033i \(-0.468262\pi\)
0.0995413 + 0.995033i \(0.468262\pi\)
\(740\) 27.3690 1.00610
\(741\) −77.3804 −2.84264
\(742\) 16.6121 0.609850
\(743\) 37.2075 1.36501 0.682506 0.730880i \(-0.260890\pi\)
0.682506 + 0.730880i \(0.260890\pi\)
\(744\) −12.0156 −0.440512
\(745\) 54.9125 2.01184
\(746\) −10.4072 −0.381036
\(747\) 0.0123556 0.000452069 0
\(748\) −8.75352 −0.320060
\(749\) 18.6949 0.683096
\(750\) 33.7236 1.23141
\(751\) 11.9385 0.435642 0.217821 0.975989i \(-0.430105\pi\)
0.217821 + 0.975989i \(0.430105\pi\)
\(752\) −0.819644 −0.0298893
\(753\) −100.552 −3.66431
\(754\) −17.1653 −0.625123
\(755\) −21.4731 −0.781486
\(756\) −31.5981 −1.14921
\(757\) −24.6086 −0.894413 −0.447206 0.894431i \(-0.647581\pi\)
−0.447206 + 0.894431i \(0.647581\pi\)
\(758\) −7.07875 −0.257112
\(759\) 23.1986 0.842054
\(760\) −22.5657 −0.818543
\(761\) −41.2530 −1.49542 −0.747710 0.664026i \(-0.768846\pi\)
−0.747710 + 0.664026i \(0.768846\pi\)
\(762\) 22.5738 0.817761
\(763\) 19.9393 0.721851
\(764\) 25.2272 0.912686
\(765\) −236.824 −8.56237
\(766\) −8.21579 −0.296849
\(767\) 26.5643 0.959182
\(768\) −3.35476 −0.121054
\(769\) −35.6929 −1.28712 −0.643559 0.765396i \(-0.722543\pi\)
−0.643559 + 0.765396i \(0.722543\pi\)
\(770\) 7.00532 0.252454
\(771\) −29.1896 −1.05124
\(772\) −10.7465 −0.386776
\(773\) 4.37312 0.157290 0.0786452 0.996903i \(-0.474941\pi\)
0.0786452 + 0.996903i \(0.474941\pi\)
\(774\) −34.3789 −1.23572
\(775\) 27.9684 1.00465
\(776\) 13.1705 0.472793
\(777\) 45.9878 1.64980
\(778\) −6.36587 −0.228227
\(779\) 27.2950 0.977946
\(780\) 43.9228 1.57269
\(781\) −8.57360 −0.306788
\(782\) 50.7679 1.81546
\(783\) 82.7102 2.95582
\(784\) −3.78668 −0.135238
\(785\) 53.0973 1.89512
\(786\) −46.6019 −1.66224
\(787\) −23.6548 −0.843201 −0.421601 0.906782i \(-0.638532\pi\)
−0.421601 + 0.906782i \(0.638532\pi\)
\(788\) −0.178585 −0.00636182
\(789\) 65.6375 2.33676
\(790\) 11.8600 0.421961
\(791\) −26.2330 −0.932738
\(792\) −9.01325 −0.320272
\(793\) −14.9706 −0.531623
\(794\) −6.79701 −0.241217
\(795\) 111.266 3.94620
\(796\) 7.22038 0.255919
\(797\) −30.9024 −1.09462 −0.547309 0.836930i \(-0.684348\pi\)
−0.547309 + 0.836930i \(0.684348\pi\)
\(798\) −37.9169 −1.34224
\(799\) −6.57069 −0.232454
\(800\) 7.80879 0.276082
\(801\) 4.17246 0.147427
\(802\) 36.0616 1.27338
\(803\) 4.54201 0.160284
\(804\) −4.09133 −0.144290
\(805\) −40.6288 −1.43198
\(806\) 13.1026 0.461521
\(807\) −31.3553 −1.10376
\(808\) 0.00889696 0.000312994 0
\(809\) −37.2697 −1.31033 −0.655167 0.755484i \(-0.727402\pi\)
−0.655167 + 0.755484i \(0.727402\pi\)
\(810\) −123.014 −4.32228
\(811\) −6.47371 −0.227323 −0.113661 0.993520i \(-0.536258\pi\)
−0.113661 + 0.993520i \(0.536258\pi\)
\(812\) −8.41111 −0.295172
\(813\) −44.4162 −1.55774
\(814\) 8.35028 0.292677
\(815\) 42.4541 1.48710
\(816\) −26.8935 −0.941460
\(817\) −26.2604 −0.918736
\(818\) −31.9276 −1.11632
\(819\) 54.1299 1.89145
\(820\) −15.4933 −0.541048
\(821\) −27.0955 −0.945640 −0.472820 0.881159i \(-0.656764\pi\)
−0.472820 + 0.881159i \(0.656764\pi\)
\(822\) −44.8981 −1.56600
\(823\) 15.8182 0.551388 0.275694 0.961245i \(-0.411092\pi\)
0.275694 + 0.961245i \(0.411092\pi\)
\(824\) −5.70849 −0.198865
\(825\) 28.6049 0.995896
\(826\) 13.0167 0.452909
\(827\) 47.7220 1.65945 0.829727 0.558169i \(-0.188496\pi\)
0.829727 + 0.558169i \(0.188496\pi\)
\(828\) 52.2743 1.81666
\(829\) 11.3202 0.393168 0.196584 0.980487i \(-0.437015\pi\)
0.196584 + 0.980487i \(0.437015\pi\)
\(830\) −0.00535715 −0.000185949 0
\(831\) −38.8774 −1.34864
\(832\) 3.65827 0.126828
\(833\) −30.3560 −1.05177
\(834\) −9.98008 −0.345582
\(835\) 8.51057 0.294520
\(836\) −6.88480 −0.238116
\(837\) −63.1345 −2.18225
\(838\) 2.92692 0.101109
\(839\) 42.5039 1.46740 0.733698 0.679475i \(-0.237793\pi\)
0.733698 + 0.679475i \(0.237793\pi\)
\(840\) 21.5225 0.742596
\(841\) −6.98331 −0.240804
\(842\) −2.31229 −0.0796866
\(843\) 33.6971 1.16059
\(844\) −22.8969 −0.788145
\(845\) −1.37040 −0.0471432
\(846\) −6.76566 −0.232608
\(847\) −17.5810 −0.604090
\(848\) 9.26718 0.318236
\(849\) 85.6558 2.93970
\(850\) 62.5993 2.14714
\(851\) −48.4292 −1.66013
\(852\) −26.3407 −0.902418
\(853\) −2.98116 −0.102073 −0.0510364 0.998697i \(-0.516252\pi\)
−0.0510364 + 0.998697i \(0.516252\pi\)
\(854\) −7.33571 −0.251023
\(855\) −186.266 −6.37016
\(856\) 10.4291 0.356458
\(857\) −50.5479 −1.72668 −0.863341 0.504621i \(-0.831632\pi\)
−0.863341 + 0.504621i \(0.831632\pi\)
\(858\) 13.4009 0.457498
\(859\) 16.4483 0.561209 0.280604 0.959824i \(-0.409465\pi\)
0.280604 + 0.959824i \(0.409465\pi\)
\(860\) 14.9060 0.508291
\(861\) −26.0332 −0.887209
\(862\) −27.3341 −0.931002
\(863\) −22.5662 −0.768162 −0.384081 0.923299i \(-0.625482\pi\)
−0.384081 + 0.923299i \(0.625482\pi\)
\(864\) −17.6272 −0.599689
\(865\) −24.0880 −0.819015
\(866\) 38.7803 1.31781
\(867\) −158.561 −5.38502
\(868\) 6.42038 0.217922
\(869\) 3.61850 0.122749
\(870\) −56.3366 −1.90999
\(871\) 4.46148 0.151172
\(872\) 11.1233 0.376682
\(873\) 108.714 3.67942
\(874\) 39.9299 1.35065
\(875\) −18.0198 −0.609180
\(876\) 13.9544 0.471476
\(877\) −29.4453 −0.994297 −0.497149 0.867665i \(-0.665620\pi\)
−0.497149 + 0.867665i \(0.665620\pi\)
\(878\) 3.11143 0.105006
\(879\) −67.8611 −2.28890
\(880\) 3.90797 0.131737
\(881\) −32.7795 −1.10437 −0.552184 0.833722i \(-0.686205\pi\)
−0.552184 + 0.833722i \(0.686205\pi\)
\(882\) −31.2567 −1.05247
\(883\) 18.7679 0.631589 0.315794 0.948828i \(-0.397729\pi\)
0.315794 + 0.948828i \(0.397729\pi\)
\(884\) 29.3266 0.986359
\(885\) 87.1843 2.93067
\(886\) −8.04748 −0.270360
\(887\) 14.9446 0.501791 0.250895 0.968014i \(-0.419275\pi\)
0.250895 + 0.968014i \(0.419275\pi\)
\(888\) 25.6546 0.860912
\(889\) −12.0620 −0.404547
\(890\) −1.80910 −0.0606410
\(891\) −37.5317 −1.25736
\(892\) 17.9641 0.601481
\(893\) −5.16796 −0.172939
\(894\) 51.4728 1.72151
\(895\) −28.1443 −0.940761
\(896\) 1.79257 0.0598857
\(897\) −77.7212 −2.59503
\(898\) −18.1602 −0.606012
\(899\) −16.8058 −0.560505
\(900\) 64.4567 2.14856
\(901\) 74.2906 2.47498
\(902\) −4.72700 −0.157392
\(903\) 25.0464 0.833492
\(904\) −14.6343 −0.486728
\(905\) 57.6586 1.91664
\(906\) −20.1280 −0.668709
\(907\) 33.8155 1.12282 0.561412 0.827536i \(-0.310258\pi\)
0.561412 + 0.827536i \(0.310258\pi\)
\(908\) 27.6520 0.917664
\(909\) 0.0734390 0.00243582
\(910\) −23.4696 −0.778011
\(911\) −16.1929 −0.536495 −0.268248 0.963350i \(-0.586444\pi\)
−0.268248 + 0.963350i \(0.586444\pi\)
\(912\) −21.1522 −0.700419
\(913\) −0.00163447 −5.40930e−5 0
\(914\) 15.1244 0.500271
\(915\) −49.1337 −1.62431
\(916\) 18.4296 0.608930
\(917\) 24.9012 0.822310
\(918\) −141.309 −4.66388
\(919\) 58.8771 1.94218 0.971089 0.238719i \(-0.0767274\pi\)
0.971089 + 0.238719i \(0.0767274\pi\)
\(920\) −22.6651 −0.747245
\(921\) −84.0878 −2.77079
\(922\) 17.6429 0.581037
\(923\) 28.7238 0.945455
\(924\) 6.56651 0.216022
\(925\) −59.7156 −1.96344
\(926\) 34.6719 1.13939
\(927\) −47.1201 −1.54763
\(928\) −4.69220 −0.154029
\(929\) −24.4774 −0.803077 −0.401538 0.915842i \(-0.631524\pi\)
−0.401538 + 0.915842i \(0.631524\pi\)
\(930\) 43.0030 1.41012
\(931\) −23.8755 −0.782488
\(932\) −17.2596 −0.565357
\(933\) 78.6358 2.57442
\(934\) 18.1834 0.594978
\(935\) 31.3283 1.02454
\(936\) 30.1967 0.987011
\(937\) −41.7380 −1.36352 −0.681761 0.731575i \(-0.738786\pi\)
−0.681761 + 0.731575i \(0.738786\pi\)
\(938\) 2.18616 0.0713805
\(939\) 20.3117 0.662848
\(940\) 2.93345 0.0956787
\(941\) −25.6956 −0.837653 −0.418826 0.908066i \(-0.637558\pi\)
−0.418826 + 0.908066i \(0.637558\pi\)
\(942\) 49.7714 1.62164
\(943\) 27.4153 0.892764
\(944\) 7.26145 0.236340
\(945\) 113.087 3.67873
\(946\) 4.54783 0.147863
\(947\) 46.7596 1.51948 0.759742 0.650225i \(-0.225325\pi\)
0.759742 + 0.650225i \(0.225325\pi\)
\(948\) 11.1171 0.361068
\(949\) −15.2169 −0.493962
\(950\) 49.2355 1.59741
\(951\) 50.5694 1.63982
\(952\) 14.3702 0.465741
\(953\) 16.1464 0.523035 0.261517 0.965199i \(-0.415777\pi\)
0.261517 + 0.965199i \(0.415777\pi\)
\(954\) 76.4949 2.47661
\(955\) −90.2864 −2.92160
\(956\) −23.7782 −0.769041
\(957\) −17.1883 −0.555620
\(958\) 31.7302 1.02515
\(959\) 23.9908 0.774703
\(960\) 12.0065 0.387507
\(961\) −18.1718 −0.586186
\(962\) −27.9756 −0.901970
\(963\) 86.0856 2.77407
\(964\) −29.4282 −0.947820
\(965\) 38.4612 1.23811
\(966\) −38.0839 −1.22533
\(967\) 53.0340 1.70546 0.852729 0.522354i \(-0.174946\pi\)
0.852729 + 0.522354i \(0.174946\pi\)
\(968\) −9.80768 −0.315231
\(969\) −169.567 −5.44728
\(970\) −47.1364 −1.51346
\(971\) 25.9193 0.831791 0.415896 0.909412i \(-0.363468\pi\)
0.415896 + 0.909412i \(0.363468\pi\)
\(972\) −62.4273 −2.00236
\(973\) 5.33274 0.170960
\(974\) 29.8048 0.955006
\(975\) −95.8340 −3.06914
\(976\) −4.09228 −0.130991
\(977\) −36.3226 −1.16206 −0.581032 0.813881i \(-0.697351\pi\)
−0.581032 + 0.813881i \(0.697351\pi\)
\(978\) 39.7948 1.27250
\(979\) −0.551956 −0.0176406
\(980\) 13.5523 0.432911
\(981\) 91.8158 2.93145
\(982\) 41.6480 1.32904
\(983\) −11.0279 −0.351735 −0.175867 0.984414i \(-0.556273\pi\)
−0.175867 + 0.984414i \(0.556273\pi\)
\(984\) −14.5228 −0.462970
\(985\) 0.639144 0.0203648
\(986\) −37.6151 −1.19791
\(987\) 4.92905 0.156893
\(988\) 23.0659 0.733823
\(989\) −26.3761 −0.838711
\(990\) 32.2579 1.02522
\(991\) −58.0320 −1.84345 −0.921724 0.387847i \(-0.873219\pi\)
−0.921724 + 0.387847i \(0.873219\pi\)
\(992\) 3.58165 0.113718
\(993\) 44.8059 1.42187
\(994\) 14.0749 0.446427
\(995\) −25.8413 −0.819223
\(996\) −0.00502158 −0.000159115 0
\(997\) −40.5670 −1.28477 −0.642385 0.766382i \(-0.722055\pi\)
−0.642385 + 0.766382i \(0.722055\pi\)
\(998\) 33.2866 1.05367
\(999\) 134.799 4.26486
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 6022.2.a.e.1.1 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6022.2.a.e.1.1 68 1.1 even 1 trivial