Properties

Label 4006.2.a.g.1.26
Level $4006$
Weight $2$
Character 4006.1
Self dual yes
Analytic conductor $31.988$
Analytic rank $1$
Dimension $40$
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] = [4006,2,Mod(1,4006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4006, 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("4006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4006.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: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) \(=\) 4006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.32011 q^{3} +1.00000 q^{4} +2.16506 q^{5} -1.32011 q^{6} -2.98980 q^{7} -1.00000 q^{8} -1.25732 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.32011 q^{3} +1.00000 q^{4} +2.16506 q^{5} -1.32011 q^{6} -2.98980 q^{7} -1.00000 q^{8} -1.25732 q^{9} -2.16506 q^{10} +2.12624 q^{11} +1.32011 q^{12} +2.25829 q^{13} +2.98980 q^{14} +2.85811 q^{15} +1.00000 q^{16} +1.94651 q^{17} +1.25732 q^{18} -4.50586 q^{19} +2.16506 q^{20} -3.94685 q^{21} -2.12624 q^{22} -2.25316 q^{23} -1.32011 q^{24} -0.312513 q^{25} -2.25829 q^{26} -5.62011 q^{27} -2.98980 q^{28} -3.38241 q^{29} -2.85811 q^{30} -6.92035 q^{31} -1.00000 q^{32} +2.80686 q^{33} -1.94651 q^{34} -6.47309 q^{35} -1.25732 q^{36} -2.51819 q^{37} +4.50586 q^{38} +2.98119 q^{39} -2.16506 q^{40} -2.47696 q^{41} +3.94685 q^{42} -5.35666 q^{43} +2.12624 q^{44} -2.72217 q^{45} +2.25316 q^{46} +2.67325 q^{47} +1.32011 q^{48} +1.93889 q^{49} +0.312513 q^{50} +2.56961 q^{51} +2.25829 q^{52} -7.74916 q^{53} +5.62011 q^{54} +4.60343 q^{55} +2.98980 q^{56} -5.94822 q^{57} +3.38241 q^{58} +8.45119 q^{59} +2.85811 q^{60} -7.65002 q^{61} +6.92035 q^{62} +3.75913 q^{63} +1.00000 q^{64} +4.88934 q^{65} -2.80686 q^{66} +0.113844 q^{67} +1.94651 q^{68} -2.97441 q^{69} +6.47309 q^{70} +5.80999 q^{71} +1.25732 q^{72} -3.14947 q^{73} +2.51819 q^{74} -0.412551 q^{75} -4.50586 q^{76} -6.35702 q^{77} -2.98119 q^{78} +13.9186 q^{79} +2.16506 q^{80} -3.64719 q^{81} +2.47696 q^{82} +8.08512 q^{83} -3.94685 q^{84} +4.21432 q^{85} +5.35666 q^{86} -4.46515 q^{87} -2.12624 q^{88} -9.85193 q^{89} +2.72217 q^{90} -6.75184 q^{91} -2.25316 q^{92} -9.13560 q^{93} -2.67325 q^{94} -9.75547 q^{95} -1.32011 q^{96} -15.6858 q^{97} -1.93889 q^{98} -2.67336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 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
\(3\) 1.32011 0.762164 0.381082 0.924541i \(-0.375552\pi\)
0.381082 + 0.924541i \(0.375552\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.16506 0.968244 0.484122 0.875000i \(-0.339139\pi\)
0.484122 + 0.875000i \(0.339139\pi\)
\(6\) −1.32011 −0.538931
\(7\) −2.98980 −1.13004 −0.565019 0.825078i \(-0.691131\pi\)
−0.565019 + 0.825078i \(0.691131\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.25732 −0.419106
\(10\) −2.16506 −0.684652
\(11\) 2.12624 0.641085 0.320543 0.947234i \(-0.396135\pi\)
0.320543 + 0.947234i \(0.396135\pi\)
\(12\) 1.32011 0.381082
\(13\) 2.25829 0.626337 0.313169 0.949698i \(-0.398609\pi\)
0.313169 + 0.949698i \(0.398609\pi\)
\(14\) 2.98980 0.799057
\(15\) 2.85811 0.737961
\(16\) 1.00000 0.250000
\(17\) 1.94651 0.472099 0.236050 0.971741i \(-0.424147\pi\)
0.236050 + 0.971741i \(0.424147\pi\)
\(18\) 1.25732 0.296353
\(19\) −4.50586 −1.03372 −0.516858 0.856071i \(-0.672898\pi\)
−0.516858 + 0.856071i \(0.672898\pi\)
\(20\) 2.16506 0.484122
\(21\) −3.94685 −0.861274
\(22\) −2.12624 −0.453316
\(23\) −2.25316 −0.469815 −0.234908 0.972018i \(-0.575479\pi\)
−0.234908 + 0.972018i \(0.575479\pi\)
\(24\) −1.32011 −0.269466
\(25\) −0.312513 −0.0625027
\(26\) −2.25829 −0.442887
\(27\) −5.62011 −1.08159
\(28\) −2.98980 −0.565019
\(29\) −3.38241 −0.628099 −0.314049 0.949407i \(-0.601686\pi\)
−0.314049 + 0.949407i \(0.601686\pi\)
\(30\) −2.85811 −0.521817
\(31\) −6.92035 −1.24293 −0.621466 0.783441i \(-0.713463\pi\)
−0.621466 + 0.783441i \(0.713463\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.80686 0.488612
\(34\) −1.94651 −0.333824
\(35\) −6.47309 −1.09415
\(36\) −1.25732 −0.209553
\(37\) −2.51819 −0.413988 −0.206994 0.978342i \(-0.566368\pi\)
−0.206994 + 0.978342i \(0.566368\pi\)
\(38\) 4.50586 0.730947
\(39\) 2.98119 0.477372
\(40\) −2.16506 −0.342326
\(41\) −2.47696 −0.386836 −0.193418 0.981116i \(-0.561957\pi\)
−0.193418 + 0.981116i \(0.561957\pi\)
\(42\) 3.94685 0.609012
\(43\) −5.35666 −0.816884 −0.408442 0.912784i \(-0.633928\pi\)
−0.408442 + 0.912784i \(0.633928\pi\)
\(44\) 2.12624 0.320543
\(45\) −2.72217 −0.405797
\(46\) 2.25316 0.332210
\(47\) 2.67325 0.389934 0.194967 0.980810i \(-0.437540\pi\)
0.194967 + 0.980810i \(0.437540\pi\)
\(48\) 1.32011 0.190541
\(49\) 1.93889 0.276985
\(50\) 0.312513 0.0441961
\(51\) 2.56961 0.359817
\(52\) 2.25829 0.313169
\(53\) −7.74916 −1.06443 −0.532214 0.846610i \(-0.678640\pi\)
−0.532214 + 0.846610i \(0.678640\pi\)
\(54\) 5.62011 0.764801
\(55\) 4.60343 0.620727
\(56\) 2.98980 0.399529
\(57\) −5.94822 −0.787861
\(58\) 3.38241 0.444133
\(59\) 8.45119 1.10025 0.550126 0.835082i \(-0.314580\pi\)
0.550126 + 0.835082i \(0.314580\pi\)
\(60\) 2.85811 0.368980
\(61\) −7.65002 −0.979484 −0.489742 0.871867i \(-0.662909\pi\)
−0.489742 + 0.871867i \(0.662909\pi\)
\(62\) 6.92035 0.878886
\(63\) 3.75913 0.473606
\(64\) 1.00000 0.125000
\(65\) 4.88934 0.606448
\(66\) −2.80686 −0.345501
\(67\) 0.113844 0.0139083 0.00695413 0.999976i \(-0.497786\pi\)
0.00695413 + 0.999976i \(0.497786\pi\)
\(68\) 1.94651 0.236050
\(69\) −2.97441 −0.358076
\(70\) 6.47309 0.773683
\(71\) 5.80999 0.689519 0.344759 0.938691i \(-0.387960\pi\)
0.344759 + 0.938691i \(0.387960\pi\)
\(72\) 1.25732 0.148176
\(73\) −3.14947 −0.368617 −0.184309 0.982868i \(-0.559005\pi\)
−0.184309 + 0.982868i \(0.559005\pi\)
\(74\) 2.51819 0.292734
\(75\) −0.412551 −0.0476373
\(76\) −4.50586 −0.516858
\(77\) −6.35702 −0.724450
\(78\) −2.98119 −0.337553
\(79\) 13.9186 1.56597 0.782984 0.622041i \(-0.213696\pi\)
0.782984 + 0.622041i \(0.213696\pi\)
\(80\) 2.16506 0.242061
\(81\) −3.64719 −0.405243
\(82\) 2.47696 0.273535
\(83\) 8.08512 0.887457 0.443728 0.896161i \(-0.353655\pi\)
0.443728 + 0.896161i \(0.353655\pi\)
\(84\) −3.94685 −0.430637
\(85\) 4.21432 0.457107
\(86\) 5.35666 0.577624
\(87\) −4.46515 −0.478714
\(88\) −2.12624 −0.226658
\(89\) −9.85193 −1.04430 −0.522151 0.852853i \(-0.674870\pi\)
−0.522151 + 0.852853i \(0.674870\pi\)
\(90\) 2.72217 0.286942
\(91\) −6.75184 −0.707785
\(92\) −2.25316 −0.234908
\(93\) −9.13560 −0.947318
\(94\) −2.67325 −0.275725
\(95\) −9.75547 −1.00089
\(96\) −1.32011 −0.134733
\(97\) −15.6858 −1.59265 −0.796325 0.604869i \(-0.793225\pi\)
−0.796325 + 0.604869i \(0.793225\pi\)
\(98\) −1.93889 −0.195858
\(99\) −2.67336 −0.268683
\(100\) −0.312513 −0.0312513
\(101\) −1.42458 −0.141751 −0.0708753 0.997485i \(-0.522579\pi\)
−0.0708753 + 0.997485i \(0.522579\pi\)
\(102\) −2.56961 −0.254429
\(103\) −2.09945 −0.206865 −0.103433 0.994636i \(-0.532983\pi\)
−0.103433 + 0.994636i \(0.532983\pi\)
\(104\) −2.25829 −0.221444
\(105\) −8.54517 −0.833923
\(106\) 7.74916 0.752665
\(107\) 13.0021 1.25696 0.628481 0.777825i \(-0.283677\pi\)
0.628481 + 0.777825i \(0.283677\pi\)
\(108\) −5.62011 −0.540796
\(109\) −0.917102 −0.0878425 −0.0439212 0.999035i \(-0.513985\pi\)
−0.0439212 + 0.999035i \(0.513985\pi\)
\(110\) −4.60343 −0.438920
\(111\) −3.32428 −0.315527
\(112\) −2.98980 −0.282509
\(113\) 17.1610 1.61437 0.807187 0.590296i \(-0.200989\pi\)
0.807187 + 0.590296i \(0.200989\pi\)
\(114\) 5.94822 0.557102
\(115\) −4.87822 −0.454896
\(116\) −3.38241 −0.314049
\(117\) −2.83939 −0.262502
\(118\) −8.45119 −0.777995
\(119\) −5.81969 −0.533490
\(120\) −2.85811 −0.260909
\(121\) −6.47911 −0.589010
\(122\) 7.65002 0.692600
\(123\) −3.26985 −0.294833
\(124\) −6.92035 −0.621466
\(125\) −11.5019 −1.02876
\(126\) −3.75913 −0.334890
\(127\) −4.05230 −0.359584 −0.179792 0.983705i \(-0.557542\pi\)
−0.179792 + 0.983705i \(0.557542\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.07137 −0.622599
\(130\) −4.88934 −0.428823
\(131\) −16.2720 −1.42169 −0.710844 0.703349i \(-0.751687\pi\)
−0.710844 + 0.703349i \(0.751687\pi\)
\(132\) 2.80686 0.244306
\(133\) 13.4716 1.16814
\(134\) −0.113844 −0.00983462
\(135\) −12.1679 −1.04724
\(136\) −1.94651 −0.166912
\(137\) 2.45826 0.210023 0.105012 0.994471i \(-0.466512\pi\)
0.105012 + 0.994471i \(0.466512\pi\)
\(138\) 2.97441 0.253198
\(139\) 16.3074 1.38318 0.691588 0.722293i \(-0.256912\pi\)
0.691588 + 0.722293i \(0.256912\pi\)
\(140\) −6.47309 −0.547076
\(141\) 3.52897 0.297193
\(142\) −5.80999 −0.487564
\(143\) 4.80167 0.401536
\(144\) −1.25732 −0.104777
\(145\) −7.32313 −0.608153
\(146\) 3.14947 0.260652
\(147\) 2.55955 0.211108
\(148\) −2.51819 −0.206994
\(149\) −16.1736 −1.32499 −0.662497 0.749065i \(-0.730503\pi\)
−0.662497 + 0.749065i \(0.730503\pi\)
\(150\) 0.412551 0.0336846
\(151\) 14.1346 1.15026 0.575130 0.818062i \(-0.304951\pi\)
0.575130 + 0.818062i \(0.304951\pi\)
\(152\) 4.50586 0.365474
\(153\) −2.44739 −0.197860
\(154\) 6.35702 0.512264
\(155\) −14.9830 −1.20346
\(156\) 2.98119 0.238686
\(157\) −21.3423 −1.70330 −0.851651 0.524109i \(-0.824398\pi\)
−0.851651 + 0.524109i \(0.824398\pi\)
\(158\) −13.9186 −1.10731
\(159\) −10.2297 −0.811269
\(160\) −2.16506 −0.171163
\(161\) 6.73648 0.530909
\(162\) 3.64719 0.286550
\(163\) −13.4852 −1.05624 −0.528120 0.849170i \(-0.677103\pi\)
−0.528120 + 0.849170i \(0.677103\pi\)
\(164\) −2.47696 −0.193418
\(165\) 6.07702 0.473096
\(166\) −8.08512 −0.627527
\(167\) −4.72981 −0.366004 −0.183002 0.983113i \(-0.558581\pi\)
−0.183002 + 0.983113i \(0.558581\pi\)
\(168\) 3.94685 0.304506
\(169\) −7.90012 −0.607701
\(170\) −4.21432 −0.323224
\(171\) 5.66531 0.433237
\(172\) −5.35666 −0.408442
\(173\) −0.678924 −0.0516176 −0.0258088 0.999667i \(-0.508216\pi\)
−0.0258088 + 0.999667i \(0.508216\pi\)
\(174\) 4.46515 0.338502
\(175\) 0.934352 0.0706304
\(176\) 2.12624 0.160271
\(177\) 11.1565 0.838572
\(178\) 9.85193 0.738434
\(179\) 4.62412 0.345623 0.172811 0.984955i \(-0.444715\pi\)
0.172811 + 0.984955i \(0.444715\pi\)
\(180\) −2.72217 −0.202899
\(181\) −20.9925 −1.56036 −0.780181 0.625554i \(-0.784873\pi\)
−0.780181 + 0.625554i \(0.784873\pi\)
\(182\) 6.75184 0.500479
\(183\) −10.0988 −0.746527
\(184\) 2.25316 0.166105
\(185\) −5.45204 −0.400842
\(186\) 9.13560 0.669855
\(187\) 4.13875 0.302656
\(188\) 2.67325 0.194967
\(189\) 16.8030 1.22224
\(190\) 9.75547 0.707736
\(191\) 17.6068 1.27398 0.636992 0.770871i \(-0.280179\pi\)
0.636992 + 0.770871i \(0.280179\pi\)
\(192\) 1.32011 0.0952705
\(193\) 2.55233 0.183721 0.0918603 0.995772i \(-0.470719\pi\)
0.0918603 + 0.995772i \(0.470719\pi\)
\(194\) 15.6858 1.12617
\(195\) 6.45445 0.462212
\(196\) 1.93889 0.138492
\(197\) −12.9771 −0.924577 −0.462289 0.886729i \(-0.652972\pi\)
−0.462289 + 0.886729i \(0.652972\pi\)
\(198\) 2.67336 0.189987
\(199\) 16.5052 1.17002 0.585012 0.811025i \(-0.301090\pi\)
0.585012 + 0.811025i \(0.301090\pi\)
\(200\) 0.312513 0.0220980
\(201\) 0.150286 0.0106004
\(202\) 1.42458 0.100233
\(203\) 10.1127 0.709775
\(204\) 2.56961 0.179908
\(205\) −5.36277 −0.374552
\(206\) 2.09945 0.146276
\(207\) 2.83294 0.196903
\(208\) 2.25829 0.156584
\(209\) −9.58054 −0.662700
\(210\) 8.54517 0.589673
\(211\) −11.7135 −0.806388 −0.403194 0.915114i \(-0.632100\pi\)
−0.403194 + 0.915114i \(0.632100\pi\)
\(212\) −7.74916 −0.532214
\(213\) 7.66980 0.525526
\(214\) −13.0021 −0.888807
\(215\) −11.5975 −0.790943
\(216\) 5.62011 0.382400
\(217\) 20.6905 1.40456
\(218\) 0.917102 0.0621140
\(219\) −4.15763 −0.280947
\(220\) 4.60343 0.310364
\(221\) 4.39580 0.295693
\(222\) 3.32428 0.223111
\(223\) 0.245128 0.0164150 0.00820751 0.999966i \(-0.497387\pi\)
0.00820751 + 0.999966i \(0.497387\pi\)
\(224\) 2.98980 0.199764
\(225\) 0.392929 0.0261953
\(226\) −17.1610 −1.14153
\(227\) −18.4937 −1.22747 −0.613735 0.789512i \(-0.710334\pi\)
−0.613735 + 0.789512i \(0.710334\pi\)
\(228\) −5.94822 −0.393930
\(229\) 17.8858 1.18193 0.590964 0.806698i \(-0.298748\pi\)
0.590964 + 0.806698i \(0.298748\pi\)
\(230\) 4.87822 0.321660
\(231\) −8.39195 −0.552150
\(232\) 3.38241 0.222066
\(233\) 22.0406 1.44393 0.721963 0.691932i \(-0.243240\pi\)
0.721963 + 0.691932i \(0.243240\pi\)
\(234\) 2.83939 0.185617
\(235\) 5.78775 0.377551
\(236\) 8.45119 0.550126
\(237\) 18.3741 1.19352
\(238\) 5.81969 0.377234
\(239\) 12.0738 0.780987 0.390493 0.920606i \(-0.372304\pi\)
0.390493 + 0.920606i \(0.372304\pi\)
\(240\) 2.85811 0.184490
\(241\) −0.147118 −0.00947672 −0.00473836 0.999989i \(-0.501508\pi\)
−0.00473836 + 0.999989i \(0.501508\pi\)
\(242\) 6.47911 0.416493
\(243\) 12.0457 0.772730
\(244\) −7.65002 −0.489742
\(245\) 4.19782 0.268189
\(246\) 3.26985 0.208478
\(247\) −10.1756 −0.647455
\(248\) 6.92035 0.439443
\(249\) 10.6732 0.676388
\(250\) 11.5019 0.727445
\(251\) −25.4806 −1.60832 −0.804160 0.594413i \(-0.797385\pi\)
−0.804160 + 0.594413i \(0.797385\pi\)
\(252\) 3.75913 0.236803
\(253\) −4.79075 −0.301192
\(254\) 4.05230 0.254264
\(255\) 5.56335 0.348391
\(256\) 1.00000 0.0625000
\(257\) 21.7969 1.35965 0.679827 0.733372i \(-0.262055\pi\)
0.679827 + 0.733372i \(0.262055\pi\)
\(258\) 7.07137 0.440244
\(259\) 7.52889 0.467822
\(260\) 4.88934 0.303224
\(261\) 4.25278 0.263240
\(262\) 16.2720 1.00529
\(263\) −18.4250 −1.13613 −0.568067 0.822983i \(-0.692308\pi\)
−0.568067 + 0.822983i \(0.692308\pi\)
\(264\) −2.80686 −0.172750
\(265\) −16.7774 −1.03063
\(266\) −13.4716 −0.825998
\(267\) −13.0056 −0.795930
\(268\) 0.113844 0.00695413
\(269\) 17.1292 1.04439 0.522194 0.852827i \(-0.325114\pi\)
0.522194 + 0.852827i \(0.325114\pi\)
\(270\) 12.1679 0.740514
\(271\) 9.28318 0.563913 0.281957 0.959427i \(-0.409017\pi\)
0.281957 + 0.959427i \(0.409017\pi\)
\(272\) 1.94651 0.118025
\(273\) −8.91314 −0.539448
\(274\) −2.45826 −0.148509
\(275\) −0.664478 −0.0400695
\(276\) −2.97441 −0.179038
\(277\) 2.86014 0.171849 0.0859244 0.996302i \(-0.472616\pi\)
0.0859244 + 0.996302i \(0.472616\pi\)
\(278\) −16.3074 −0.978052
\(279\) 8.70109 0.520921
\(280\) 6.47309 0.386841
\(281\) 22.8730 1.36449 0.682244 0.731124i \(-0.261004\pi\)
0.682244 + 0.731124i \(0.261004\pi\)
\(282\) −3.52897 −0.210147
\(283\) −18.7531 −1.11475 −0.557377 0.830260i \(-0.688192\pi\)
−0.557377 + 0.830260i \(0.688192\pi\)
\(284\) 5.80999 0.344759
\(285\) −12.8783 −0.762842
\(286\) −4.80167 −0.283929
\(287\) 7.40561 0.437140
\(288\) 1.25732 0.0740882
\(289\) −13.2111 −0.777122
\(290\) 7.32313 0.430029
\(291\) −20.7069 −1.21386
\(292\) −3.14947 −0.184309
\(293\) −16.6418 −0.972224 −0.486112 0.873897i \(-0.661585\pi\)
−0.486112 + 0.873897i \(0.661585\pi\)
\(294\) −2.55955 −0.149276
\(295\) 18.2973 1.06531
\(296\) 2.51819 0.146367
\(297\) −11.9497 −0.693392
\(298\) 16.1736 0.936912
\(299\) −5.08828 −0.294263
\(300\) −0.412551 −0.0238186
\(301\) 16.0153 0.923109
\(302\) −14.1346 −0.813357
\(303\) −1.88059 −0.108037
\(304\) −4.50586 −0.258429
\(305\) −16.5627 −0.948380
\(306\) 2.44739 0.139908
\(307\) 14.4535 0.824904 0.412452 0.910979i \(-0.364672\pi\)
0.412452 + 0.910979i \(0.364672\pi\)
\(308\) −6.35702 −0.362225
\(309\) −2.77150 −0.157665
\(310\) 14.9830 0.850976
\(311\) −21.4694 −1.21742 −0.608709 0.793394i \(-0.708312\pi\)
−0.608709 + 0.793394i \(0.708312\pi\)
\(312\) −2.98119 −0.168776
\(313\) −2.02552 −0.114489 −0.0572446 0.998360i \(-0.518232\pi\)
−0.0572446 + 0.998360i \(0.518232\pi\)
\(314\) 21.3423 1.20442
\(315\) 8.13875 0.458566
\(316\) 13.9186 0.782984
\(317\) 28.9400 1.62543 0.812715 0.582661i \(-0.197989\pi\)
0.812715 + 0.582661i \(0.197989\pi\)
\(318\) 10.2297 0.573654
\(319\) −7.19182 −0.402665
\(320\) 2.16506 0.121031
\(321\) 17.1642 0.958011
\(322\) −6.73648 −0.375409
\(323\) −8.77073 −0.488016
\(324\) −3.64719 −0.202622
\(325\) −0.705746 −0.0391478
\(326\) 13.4852 0.746874
\(327\) −1.21067 −0.0669504
\(328\) 2.47696 0.136767
\(329\) −7.99248 −0.440640
\(330\) −6.07702 −0.334529
\(331\) 0.897068 0.0493073 0.0246537 0.999696i \(-0.492152\pi\)
0.0246537 + 0.999696i \(0.492152\pi\)
\(332\) 8.08512 0.443728
\(333\) 3.16617 0.173505
\(334\) 4.72981 0.258804
\(335\) 0.246479 0.0134666
\(336\) −3.94685 −0.215318
\(337\) 6.59167 0.359071 0.179536 0.983751i \(-0.442540\pi\)
0.179536 + 0.983751i \(0.442540\pi\)
\(338\) 7.90012 0.429710
\(339\) 22.6544 1.23042
\(340\) 4.21432 0.228554
\(341\) −14.7143 −0.796825
\(342\) −5.66531 −0.306345
\(343\) 15.1317 0.817034
\(344\) 5.35666 0.288812
\(345\) −6.43977 −0.346705
\(346\) 0.678924 0.0364992
\(347\) −10.9168 −0.586043 −0.293022 0.956106i \(-0.594661\pi\)
−0.293022 + 0.956106i \(0.594661\pi\)
\(348\) −4.46515 −0.239357
\(349\) −21.5336 −1.15267 −0.576334 0.817214i \(-0.695517\pi\)
−0.576334 + 0.817214i \(0.695517\pi\)
\(350\) −0.934352 −0.0499432
\(351\) −12.6919 −0.677441
\(352\) −2.12624 −0.113329
\(353\) −28.6488 −1.52482 −0.762411 0.647094i \(-0.775984\pi\)
−0.762411 + 0.647094i \(0.775984\pi\)
\(354\) −11.1565 −0.592960
\(355\) 12.5790 0.667623
\(356\) −9.85193 −0.522151
\(357\) −7.68260 −0.406606
\(358\) −4.62412 −0.244392
\(359\) −34.1295 −1.80129 −0.900644 0.434558i \(-0.856904\pi\)
−0.900644 + 0.434558i \(0.856904\pi\)
\(360\) 2.72217 0.143471
\(361\) 1.30280 0.0685685
\(362\) 20.9925 1.10334
\(363\) −8.55311 −0.448922
\(364\) −6.75184 −0.353892
\(365\) −6.81879 −0.356912
\(366\) 10.0988 0.527875
\(367\) 7.10430 0.370842 0.185421 0.982659i \(-0.440635\pi\)
0.185421 + 0.982659i \(0.440635\pi\)
\(368\) −2.25316 −0.117454
\(369\) 3.11433 0.162126
\(370\) 5.45204 0.283438
\(371\) 23.1684 1.20284
\(372\) −9.13560 −0.473659
\(373\) −30.3597 −1.57197 −0.785983 0.618249i \(-0.787842\pi\)
−0.785983 + 0.618249i \(0.787842\pi\)
\(374\) −4.13875 −0.214010
\(375\) −15.1837 −0.784085
\(376\) −2.67325 −0.137862
\(377\) −7.63848 −0.393402
\(378\) −16.8030 −0.864253
\(379\) 6.33979 0.325653 0.162827 0.986655i \(-0.447939\pi\)
0.162827 + 0.986655i \(0.447939\pi\)
\(380\) −9.75547 −0.500445
\(381\) −5.34947 −0.274062
\(382\) −17.6068 −0.900842
\(383\) 13.3979 0.684600 0.342300 0.939591i \(-0.388794\pi\)
0.342300 + 0.939591i \(0.388794\pi\)
\(384\) −1.32011 −0.0673664
\(385\) −13.7633 −0.701445
\(386\) −2.55233 −0.129910
\(387\) 6.73504 0.342361
\(388\) −15.6858 −0.796325
\(389\) −16.0931 −0.815953 −0.407976 0.912993i \(-0.633765\pi\)
−0.407976 + 0.912993i \(0.633765\pi\)
\(390\) −6.45445 −0.326834
\(391\) −4.38580 −0.221799
\(392\) −1.93889 −0.0979289
\(393\) −21.4807 −1.08356
\(394\) 12.9771 0.653775
\(395\) 30.1347 1.51624
\(396\) −2.67336 −0.134341
\(397\) 4.16939 0.209256 0.104628 0.994511i \(-0.466635\pi\)
0.104628 + 0.994511i \(0.466635\pi\)
\(398\) −16.5052 −0.827332
\(399\) 17.7840 0.890312
\(400\) −0.312513 −0.0156257
\(401\) −30.2228 −1.50925 −0.754627 0.656154i \(-0.772182\pi\)
−0.754627 + 0.656154i \(0.772182\pi\)
\(402\) −0.150286 −0.00749559
\(403\) −15.6282 −0.778495
\(404\) −1.42458 −0.0708753
\(405\) −7.89639 −0.392375
\(406\) −10.1127 −0.501887
\(407\) −5.35428 −0.265402
\(408\) −2.56961 −0.127214
\(409\) 11.3240 0.559936 0.279968 0.960009i \(-0.409676\pi\)
0.279968 + 0.960009i \(0.409676\pi\)
\(410\) 5.36277 0.264848
\(411\) 3.24516 0.160072
\(412\) −2.09945 −0.103433
\(413\) −25.2674 −1.24333
\(414\) −2.83294 −0.139231
\(415\) 17.5048 0.859275
\(416\) −2.25829 −0.110722
\(417\) 21.5275 1.05421
\(418\) 9.58054 0.468599
\(419\) −24.0175 −1.17333 −0.586665 0.809829i \(-0.699560\pi\)
−0.586665 + 0.809829i \(0.699560\pi\)
\(420\) −8.54517 −0.416962
\(421\) 3.70463 0.180553 0.0902763 0.995917i \(-0.471225\pi\)
0.0902763 + 0.995917i \(0.471225\pi\)
\(422\) 11.7135 0.570203
\(423\) −3.36113 −0.163424
\(424\) 7.74916 0.376332
\(425\) −0.608312 −0.0295075
\(426\) −7.66980 −0.371603
\(427\) 22.8720 1.10685
\(428\) 13.0021 0.628481
\(429\) 6.33871 0.306036
\(430\) 11.5975 0.559281
\(431\) −7.26122 −0.349761 −0.174880 0.984590i \(-0.555954\pi\)
−0.174880 + 0.984590i \(0.555954\pi\)
\(432\) −5.62011 −0.270398
\(433\) 19.3649 0.930617 0.465309 0.885148i \(-0.345943\pi\)
0.465309 + 0.885148i \(0.345943\pi\)
\(434\) −20.6905 −0.993174
\(435\) −9.66731 −0.463512
\(436\) −0.917102 −0.0439212
\(437\) 10.1524 0.485656
\(438\) 4.15763 0.198659
\(439\) 7.22422 0.344793 0.172397 0.985028i \(-0.444849\pi\)
0.172397 + 0.985028i \(0.444849\pi\)
\(440\) −4.60343 −0.219460
\(441\) −2.43781 −0.116086
\(442\) −4.39580 −0.209087
\(443\) 25.4666 1.20995 0.604977 0.796243i \(-0.293182\pi\)
0.604977 + 0.796243i \(0.293182\pi\)
\(444\) −3.32428 −0.157763
\(445\) −21.3300 −1.01114
\(446\) −0.245128 −0.0116072
\(447\) −21.3509 −1.00986
\(448\) −2.98980 −0.141255
\(449\) 9.85257 0.464971 0.232486 0.972600i \(-0.425314\pi\)
0.232486 + 0.972600i \(0.425314\pi\)
\(450\) −0.392929 −0.0185229
\(451\) −5.26661 −0.247995
\(452\) 17.1610 0.807187
\(453\) 18.6592 0.876687
\(454\) 18.4937 0.867953
\(455\) −14.6181 −0.685309
\(456\) 5.94822 0.278551
\(457\) −15.4524 −0.722835 −0.361417 0.932404i \(-0.617707\pi\)
−0.361417 + 0.932404i \(0.617707\pi\)
\(458\) −17.8858 −0.835749
\(459\) −10.9396 −0.510618
\(460\) −4.87822 −0.227448
\(461\) 4.28239 0.199451 0.0997254 0.995015i \(-0.468204\pi\)
0.0997254 + 0.995015i \(0.468204\pi\)
\(462\) 8.39195 0.390429
\(463\) 15.4021 0.715798 0.357899 0.933760i \(-0.383493\pi\)
0.357899 + 0.933760i \(0.383493\pi\)
\(464\) −3.38241 −0.157025
\(465\) −19.7791 −0.917235
\(466\) −22.0406 −1.02101
\(467\) 1.92711 0.0891762 0.0445881 0.999005i \(-0.485802\pi\)
0.0445881 + 0.999005i \(0.485802\pi\)
\(468\) −2.83939 −0.131251
\(469\) −0.340370 −0.0157168
\(470\) −5.78775 −0.266969
\(471\) −28.1741 −1.29820
\(472\) −8.45119 −0.388998
\(473\) −11.3895 −0.523692
\(474\) −18.3741 −0.843949
\(475\) 1.40814 0.0646100
\(476\) −5.81969 −0.266745
\(477\) 9.74316 0.446109
\(478\) −12.0738 −0.552241
\(479\) 14.1139 0.644881 0.322441 0.946590i \(-0.395497\pi\)
0.322441 + 0.946590i \(0.395497\pi\)
\(480\) −2.85811 −0.130454
\(481\) −5.68681 −0.259296
\(482\) 0.147118 0.00670105
\(483\) 8.89287 0.404640
\(484\) −6.47911 −0.294505
\(485\) −33.9607 −1.54207
\(486\) −12.0457 −0.546402
\(487\) −20.0385 −0.908031 −0.454016 0.890994i \(-0.650009\pi\)
−0.454016 + 0.890994i \(0.650009\pi\)
\(488\) 7.65002 0.346300
\(489\) −17.8019 −0.805028
\(490\) −4.19782 −0.189638
\(491\) 16.3461 0.737690 0.368845 0.929491i \(-0.379753\pi\)
0.368845 + 0.929491i \(0.379753\pi\)
\(492\) −3.26985 −0.147416
\(493\) −6.58392 −0.296525
\(494\) 10.1756 0.457820
\(495\) −5.78799 −0.260151
\(496\) −6.92035 −0.310733
\(497\) −17.3707 −0.779182
\(498\) −10.6732 −0.478278
\(499\) 21.2430 0.950966 0.475483 0.879725i \(-0.342273\pi\)
0.475483 + 0.879725i \(0.342273\pi\)
\(500\) −11.5019 −0.514381
\(501\) −6.24386 −0.278955
\(502\) 25.4806 1.13725
\(503\) −29.4391 −1.31262 −0.656312 0.754490i \(-0.727885\pi\)
−0.656312 + 0.754490i \(0.727885\pi\)
\(504\) −3.75913 −0.167445
\(505\) −3.08429 −0.137249
\(506\) 4.79075 0.212975
\(507\) −10.4290 −0.463168
\(508\) −4.05230 −0.179792
\(509\) −18.0171 −0.798593 −0.399297 0.916822i \(-0.630746\pi\)
−0.399297 + 0.916822i \(0.630746\pi\)
\(510\) −5.56335 −0.246349
\(511\) 9.41628 0.416552
\(512\) −1.00000 −0.0441942
\(513\) 25.3235 1.11806
\(514\) −21.7969 −0.961421
\(515\) −4.54544 −0.200296
\(516\) −7.07137 −0.311300
\(517\) 5.68397 0.249981
\(518\) −7.52889 −0.330800
\(519\) −0.896251 −0.0393411
\(520\) −4.88934 −0.214412
\(521\) 5.93413 0.259979 0.129990 0.991515i \(-0.458506\pi\)
0.129990 + 0.991515i \(0.458506\pi\)
\(522\) −4.25278 −0.186139
\(523\) 30.2412 1.32236 0.661178 0.750229i \(-0.270057\pi\)
0.661178 + 0.750229i \(0.270057\pi\)
\(524\) −16.2720 −0.710844
\(525\) 1.23344 0.0538319
\(526\) 18.4250 0.803368
\(527\) −13.4706 −0.586787
\(528\) 2.80686 0.122153
\(529\) −17.9233 −0.779273
\(530\) 16.7774 0.728763
\(531\) −10.6258 −0.461123
\(532\) 13.4716 0.584069
\(533\) −5.59370 −0.242290
\(534\) 13.0056 0.562807
\(535\) 28.1504 1.21705
\(536\) −0.113844 −0.00491731
\(537\) 6.10433 0.263421
\(538\) −17.1292 −0.738494
\(539\) 4.12255 0.177571
\(540\) −12.1679 −0.523622
\(541\) −23.9300 −1.02883 −0.514416 0.857541i \(-0.671991\pi\)
−0.514416 + 0.857541i \(0.671991\pi\)
\(542\) −9.28318 −0.398747
\(543\) −27.7124 −1.18925
\(544\) −1.94651 −0.0834561
\(545\) −1.98558 −0.0850530
\(546\) 8.91314 0.381447
\(547\) 9.37236 0.400733 0.200367 0.979721i \(-0.435787\pi\)
0.200367 + 0.979721i \(0.435787\pi\)
\(548\) 2.45826 0.105012
\(549\) 9.61851 0.410508
\(550\) 0.664478 0.0283334
\(551\) 15.2407 0.649276
\(552\) 2.97441 0.126599
\(553\) −41.6139 −1.76960
\(554\) −2.86014 −0.121516
\(555\) −7.19727 −0.305507
\(556\) 16.3074 0.691588
\(557\) 30.0225 1.27209 0.636047 0.771650i \(-0.280568\pi\)
0.636047 + 0.771650i \(0.280568\pi\)
\(558\) −8.70109 −0.368347
\(559\) −12.0969 −0.511645
\(560\) −6.47309 −0.273538
\(561\) 5.46359 0.230673
\(562\) −22.8730 −0.964839
\(563\) −14.3485 −0.604716 −0.302358 0.953194i \(-0.597774\pi\)
−0.302358 + 0.953194i \(0.597774\pi\)
\(564\) 3.52897 0.148597
\(565\) 37.1547 1.56311
\(566\) 18.7531 0.788250
\(567\) 10.9044 0.457940
\(568\) −5.80999 −0.243782
\(569\) 4.37504 0.183411 0.0917056 0.995786i \(-0.470768\pi\)
0.0917056 + 0.995786i \(0.470768\pi\)
\(570\) 12.8783 0.539411
\(571\) 44.4888 1.86180 0.930898 0.365279i \(-0.119026\pi\)
0.930898 + 0.365279i \(0.119026\pi\)
\(572\) 4.80167 0.200768
\(573\) 23.2428 0.970984
\(574\) −7.40561 −0.309104
\(575\) 0.704141 0.0293647
\(576\) −1.25732 −0.0523883
\(577\) −6.51332 −0.271153 −0.135576 0.990767i \(-0.543289\pi\)
−0.135576 + 0.990767i \(0.543289\pi\)
\(578\) 13.2111 0.549509
\(579\) 3.36935 0.140025
\(580\) −7.32313 −0.304077
\(581\) −24.1729 −1.00286
\(582\) 20.7069 0.858329
\(583\) −16.4766 −0.682389
\(584\) 3.14947 0.130326
\(585\) −6.14746 −0.254166
\(586\) 16.6418 0.687466
\(587\) 13.7882 0.569099 0.284550 0.958661i \(-0.408156\pi\)
0.284550 + 0.958661i \(0.408156\pi\)
\(588\) 2.55955 0.105554
\(589\) 31.1822 1.28484
\(590\) −18.2973 −0.753290
\(591\) −17.1311 −0.704679
\(592\) −2.51819 −0.103497
\(593\) 20.8586 0.856560 0.428280 0.903646i \(-0.359120\pi\)
0.428280 + 0.903646i \(0.359120\pi\)
\(594\) 11.9497 0.490302
\(595\) −12.6000 −0.516548
\(596\) −16.1736 −0.662497
\(597\) 21.7886 0.891750
\(598\) 5.08828 0.208075
\(599\) 3.66284 0.149660 0.0748298 0.997196i \(-0.476159\pi\)
0.0748298 + 0.997196i \(0.476159\pi\)
\(600\) 0.412551 0.0168423
\(601\) −12.8882 −0.525721 −0.262860 0.964834i \(-0.584666\pi\)
−0.262860 + 0.964834i \(0.584666\pi\)
\(602\) −16.0153 −0.652737
\(603\) −0.143138 −0.00582904
\(604\) 14.1346 0.575130
\(605\) −14.0277 −0.570306
\(606\) 1.88059 0.0763938
\(607\) 38.2100 1.55090 0.775448 0.631411i \(-0.217524\pi\)
0.775448 + 0.631411i \(0.217524\pi\)
\(608\) 4.50586 0.182737
\(609\) 13.3499 0.540965
\(610\) 16.5627 0.670606
\(611\) 6.03698 0.244230
\(612\) −2.44739 −0.0989299
\(613\) 44.6251 1.80239 0.901195 0.433413i \(-0.142691\pi\)
0.901195 + 0.433413i \(0.142691\pi\)
\(614\) −14.4535 −0.583295
\(615\) −7.07943 −0.285470
\(616\) 6.35702 0.256132
\(617\) −17.5453 −0.706347 −0.353174 0.935558i \(-0.614898\pi\)
−0.353174 + 0.935558i \(0.614898\pi\)
\(618\) 2.77150 0.111486
\(619\) 38.3689 1.54218 0.771089 0.636727i \(-0.219712\pi\)
0.771089 + 0.636727i \(0.219712\pi\)
\(620\) −14.9830 −0.601731
\(621\) 12.6630 0.508148
\(622\) 21.4694 0.860844
\(623\) 29.4553 1.18010
\(624\) 2.98119 0.119343
\(625\) −23.3398 −0.933591
\(626\) 2.02552 0.0809561
\(627\) −12.6473 −0.505086
\(628\) −21.3423 −0.851651
\(629\) −4.90170 −0.195443
\(630\) −8.13875 −0.324255
\(631\) −13.2877 −0.528976 −0.264488 0.964389i \(-0.585203\pi\)
−0.264488 + 0.964389i \(0.585203\pi\)
\(632\) −13.9186 −0.553654
\(633\) −15.4630 −0.614600
\(634\) −28.9400 −1.14935
\(635\) −8.77348 −0.348165
\(636\) −10.2297 −0.405634
\(637\) 4.37859 0.173486
\(638\) 7.19182 0.284727
\(639\) −7.30501 −0.288982
\(640\) −2.16506 −0.0855815
\(641\) −33.1174 −1.30806 −0.654030 0.756469i \(-0.726923\pi\)
−0.654030 + 0.756469i \(0.726923\pi\)
\(642\) −17.1642 −0.677416
\(643\) 28.5513 1.12595 0.562977 0.826473i \(-0.309656\pi\)
0.562977 + 0.826473i \(0.309656\pi\)
\(644\) 6.73648 0.265455
\(645\) −15.3099 −0.602828
\(646\) 8.77073 0.345080
\(647\) −1.08764 −0.0427594 −0.0213797 0.999771i \(-0.506806\pi\)
−0.0213797 + 0.999771i \(0.506806\pi\)
\(648\) 3.64719 0.143275
\(649\) 17.9693 0.705355
\(650\) 0.705746 0.0276817
\(651\) 27.3136 1.07050
\(652\) −13.4852 −0.528120
\(653\) 21.8427 0.854771 0.427385 0.904070i \(-0.359435\pi\)
0.427385 + 0.904070i \(0.359435\pi\)
\(654\) 1.21067 0.0473410
\(655\) −35.2298 −1.37654
\(656\) −2.47696 −0.0967091
\(657\) 3.95989 0.154490
\(658\) 7.99248 0.311579
\(659\) 18.8299 0.733507 0.366753 0.930318i \(-0.380469\pi\)
0.366753 + 0.930318i \(0.380469\pi\)
\(660\) 6.07702 0.236548
\(661\) −42.8016 −1.66479 −0.832395 0.554183i \(-0.813031\pi\)
−0.832395 + 0.554183i \(0.813031\pi\)
\(662\) −0.897068 −0.0348656
\(663\) 5.80292 0.225367
\(664\) −8.08512 −0.313763
\(665\) 29.1669 1.13104
\(666\) −3.16617 −0.122687
\(667\) 7.62111 0.295090
\(668\) −4.72981 −0.183002
\(669\) 0.323596 0.0125109
\(670\) −0.246479 −0.00952231
\(671\) −16.2658 −0.627933
\(672\) 3.94685 0.152253
\(673\) 4.63281 0.178582 0.0892908 0.996006i \(-0.471540\pi\)
0.0892908 + 0.996006i \(0.471540\pi\)
\(674\) −6.59167 −0.253902
\(675\) 1.75636 0.0676024
\(676\) −7.90012 −0.303851
\(677\) 28.1674 1.08256 0.541280 0.840843i \(-0.317940\pi\)
0.541280 + 0.840843i \(0.317940\pi\)
\(678\) −22.6544 −0.870037
\(679\) 46.8973 1.79975
\(680\) −4.21432 −0.161612
\(681\) −24.4137 −0.935533
\(682\) 14.7143 0.563440
\(683\) −22.0673 −0.844381 −0.422190 0.906507i \(-0.638739\pi\)
−0.422190 + 0.906507i \(0.638739\pi\)
\(684\) 5.66531 0.216618
\(685\) 5.32228 0.203354
\(686\) −15.1317 −0.577730
\(687\) 23.6112 0.900823
\(688\) −5.35666 −0.204221
\(689\) −17.4999 −0.666691
\(690\) 6.43977 0.245158
\(691\) −29.2271 −1.11185 −0.555926 0.831232i \(-0.687636\pi\)
−0.555926 + 0.831232i \(0.687636\pi\)
\(692\) −0.678924 −0.0258088
\(693\) 7.99281 0.303622
\(694\) 10.9168 0.414395
\(695\) 35.3065 1.33925
\(696\) 4.46515 0.169251
\(697\) −4.82144 −0.182625
\(698\) 21.5336 0.815059
\(699\) 29.0959 1.10051
\(700\) 0.934352 0.0353152
\(701\) −12.5663 −0.474622 −0.237311 0.971434i \(-0.576266\pi\)
−0.237311 + 0.971434i \(0.576266\pi\)
\(702\) 12.6919 0.479023
\(703\) 11.3466 0.427946
\(704\) 2.12624 0.0801356
\(705\) 7.64044 0.287756
\(706\) 28.6488 1.07821
\(707\) 4.25919 0.160183
\(708\) 11.1565 0.419286
\(709\) 42.0306 1.57849 0.789247 0.614076i \(-0.210471\pi\)
0.789247 + 0.614076i \(0.210471\pi\)
\(710\) −12.5790 −0.472081
\(711\) −17.5002 −0.656308
\(712\) 9.85193 0.369217
\(713\) 15.5926 0.583949
\(714\) 7.68260 0.287514
\(715\) 10.3959 0.388785
\(716\) 4.62412 0.172811
\(717\) 15.9386 0.595240
\(718\) 34.1295 1.27370
\(719\) −51.4835 −1.92001 −0.960006 0.279980i \(-0.909672\pi\)
−0.960006 + 0.279980i \(0.909672\pi\)
\(720\) −2.72217 −0.101449
\(721\) 6.27694 0.233766
\(722\) −1.30280 −0.0484852
\(723\) −0.194212 −0.00722281
\(724\) −20.9925 −0.780181
\(725\) 1.05705 0.0392578
\(726\) 8.55311 0.317436
\(727\) −17.0735 −0.633220 −0.316610 0.948556i \(-0.602545\pi\)
−0.316610 + 0.948556i \(0.602545\pi\)
\(728\) 6.75184 0.250240
\(729\) 26.8431 0.994190
\(730\) 6.81879 0.252375
\(731\) −10.4268 −0.385650
\(732\) −10.0988 −0.373264
\(733\) 38.9649 1.43920 0.719601 0.694387i \(-0.244325\pi\)
0.719601 + 0.694387i \(0.244325\pi\)
\(734\) −7.10430 −0.262225
\(735\) 5.54157 0.204404
\(736\) 2.25316 0.0830524
\(737\) 0.242059 0.00891637
\(738\) −3.11433 −0.114640
\(739\) 36.0084 1.32459 0.662295 0.749243i \(-0.269583\pi\)
0.662295 + 0.749243i \(0.269583\pi\)
\(740\) −5.45204 −0.200421
\(741\) −13.4328 −0.493467
\(742\) −23.1684 −0.850539
\(743\) 20.1384 0.738807 0.369404 0.929269i \(-0.379562\pi\)
0.369404 + 0.929269i \(0.379562\pi\)
\(744\) 9.13560 0.334927
\(745\) −35.0168 −1.28292
\(746\) 30.3597 1.11155
\(747\) −10.1656 −0.371939
\(748\) 4.13875 0.151328
\(749\) −38.8737 −1.42041
\(750\) 15.1837 0.554432
\(751\) −4.64736 −0.169585 −0.0847924 0.996399i \(-0.527023\pi\)
−0.0847924 + 0.996399i \(0.527023\pi\)
\(752\) 2.67325 0.0974834
\(753\) −33.6371 −1.22580
\(754\) 7.63848 0.278177
\(755\) 30.6024 1.11373
\(756\) 16.8030 0.611119
\(757\) 15.3542 0.558056 0.279028 0.960283i \(-0.409988\pi\)
0.279028 + 0.960283i \(0.409988\pi\)
\(758\) −6.33979 −0.230272
\(759\) −6.32430 −0.229557
\(760\) 9.75547 0.353868
\(761\) −16.6942 −0.605166 −0.302583 0.953123i \(-0.597849\pi\)
−0.302583 + 0.953123i \(0.597849\pi\)
\(762\) 5.34947 0.193791
\(763\) 2.74195 0.0992653
\(764\) 17.6068 0.636992
\(765\) −5.29875 −0.191577
\(766\) −13.3979 −0.484085
\(767\) 19.0853 0.689129
\(768\) 1.32011 0.0476352
\(769\) 7.45227 0.268736 0.134368 0.990932i \(-0.457100\pi\)
0.134368 + 0.990932i \(0.457100\pi\)
\(770\) 13.7633 0.495996
\(771\) 28.7742 1.03628
\(772\) 2.55233 0.0918603
\(773\) 15.6868 0.564215 0.282108 0.959383i \(-0.408966\pi\)
0.282108 + 0.959383i \(0.408966\pi\)
\(774\) −6.73504 −0.242086
\(775\) 2.16270 0.0776866
\(776\) 15.6858 0.563087
\(777\) 9.93893 0.356557
\(778\) 16.0931 0.576966
\(779\) 11.1608 0.399879
\(780\) 6.45445 0.231106
\(781\) 12.3534 0.442040
\(782\) 4.38580 0.156836
\(783\) 19.0096 0.679346
\(784\) 1.93889 0.0692462
\(785\) −46.2074 −1.64921
\(786\) 21.4807 0.766192
\(787\) −41.3291 −1.47322 −0.736611 0.676317i \(-0.763575\pi\)
−0.736611 + 0.676317i \(0.763575\pi\)
\(788\) −12.9771 −0.462289
\(789\) −24.3229 −0.865920
\(790\) −30.1347 −1.07214
\(791\) −51.3080 −1.82430
\(792\) 2.67336 0.0949937
\(793\) −17.2760 −0.613488
\(794\) −4.16939 −0.147966
\(795\) −22.1479 −0.785506
\(796\) 16.5052 0.585012
\(797\) −50.3649 −1.78402 −0.892008 0.452021i \(-0.850703\pi\)
−0.892008 + 0.452021i \(0.850703\pi\)
\(798\) −17.7840 −0.629546
\(799\) 5.20352 0.184087
\(800\) 0.312513 0.0110490
\(801\) 12.3870 0.437674
\(802\) 30.2228 1.06720
\(803\) −6.69652 −0.236315
\(804\) 0.150286 0.00530018
\(805\) 14.5849 0.514050
\(806\) 15.6282 0.550479
\(807\) 22.6124 0.795994
\(808\) 1.42458 0.0501164
\(809\) 55.1186 1.93787 0.968933 0.247324i \(-0.0795512\pi\)
0.968933 + 0.247324i \(0.0795512\pi\)
\(810\) 7.89639 0.277451
\(811\) 2.90379 0.101966 0.0509830 0.998700i \(-0.483765\pi\)
0.0509830 + 0.998700i \(0.483765\pi\)
\(812\) 10.1127 0.354888
\(813\) 12.2548 0.429794
\(814\) 5.35428 0.187667
\(815\) −29.1962 −1.02270
\(816\) 2.56961 0.0899542
\(817\) 24.1364 0.844426
\(818\) −11.3240 −0.395935
\(819\) 8.48921 0.296637
\(820\) −5.36277 −0.187276
\(821\) 4.44201 0.155027 0.0775136 0.996991i \(-0.475302\pi\)
0.0775136 + 0.996991i \(0.475302\pi\)
\(822\) −3.24516 −0.113188
\(823\) 0.174912 0.00609705 0.00304852 0.999995i \(-0.499030\pi\)
0.00304852 + 0.999995i \(0.499030\pi\)
\(824\) 2.09945 0.0731379
\(825\) −0.877182 −0.0305395
\(826\) 25.2674 0.879164
\(827\) −6.21409 −0.216085 −0.108043 0.994146i \(-0.534458\pi\)
−0.108043 + 0.994146i \(0.534458\pi\)
\(828\) 2.83294 0.0984513
\(829\) −15.7564 −0.547244 −0.273622 0.961837i \(-0.588222\pi\)
−0.273622 + 0.961837i \(0.588222\pi\)
\(830\) −17.5048 −0.607599
\(831\) 3.77568 0.130977
\(832\) 2.25829 0.0782922
\(833\) 3.77409 0.130764
\(834\) −21.5275 −0.745436
\(835\) −10.2403 −0.354381
\(836\) −9.58054 −0.331350
\(837\) 38.8932 1.34434
\(838\) 24.0175 0.829670
\(839\) −48.2103 −1.66440 −0.832202 0.554472i \(-0.812920\pi\)
−0.832202 + 0.554472i \(0.812920\pi\)
\(840\) 8.54517 0.294836
\(841\) −17.5593 −0.605492
\(842\) −3.70463 −0.127670
\(843\) 30.1948 1.03996
\(844\) −11.7135 −0.403194
\(845\) −17.1042 −0.588404
\(846\) 3.36113 0.115558
\(847\) 19.3712 0.665603
\(848\) −7.74916 −0.266107
\(849\) −24.7560 −0.849624
\(850\) 0.608312 0.0208649
\(851\) 5.67388 0.194498
\(852\) 7.66980 0.262763
\(853\) 49.3341 1.68917 0.844583 0.535424i \(-0.179848\pi\)
0.844583 + 0.535424i \(0.179848\pi\)
\(854\) −22.8720 −0.782664
\(855\) 12.2657 0.419479
\(856\) −13.0021 −0.444403
\(857\) 35.4657 1.21148 0.605742 0.795661i \(-0.292876\pi\)
0.605742 + 0.795661i \(0.292876\pi\)
\(858\) −6.33871 −0.216400
\(859\) −23.7784 −0.811309 −0.405655 0.914026i \(-0.632956\pi\)
−0.405655 + 0.914026i \(0.632956\pi\)
\(860\) −11.5975 −0.395471
\(861\) 9.77620 0.333172
\(862\) 7.26122 0.247318
\(863\) −18.7622 −0.638673 −0.319336 0.947641i \(-0.603460\pi\)
−0.319336 + 0.947641i \(0.603460\pi\)
\(864\) 5.62011 0.191200
\(865\) −1.46991 −0.0499785
\(866\) −19.3649 −0.658046
\(867\) −17.4400 −0.592295
\(868\) 20.6905 0.702280
\(869\) 29.5943 1.00392
\(870\) 9.66731 0.327753
\(871\) 0.257093 0.00871126
\(872\) 0.917102 0.0310570
\(873\) 19.7220 0.667490
\(874\) −10.1524 −0.343410
\(875\) 34.3884 1.16254
\(876\) −4.15763 −0.140473
\(877\) 31.2812 1.05629 0.528146 0.849154i \(-0.322887\pi\)
0.528146 + 0.849154i \(0.322887\pi\)
\(878\) −7.22422 −0.243806
\(879\) −21.9689 −0.740994
\(880\) 4.60343 0.155182
\(881\) 41.1348 1.38587 0.692934 0.721001i \(-0.256318\pi\)
0.692934 + 0.721001i \(0.256318\pi\)
\(882\) 2.43781 0.0820853
\(883\) −9.90735 −0.333409 −0.166704 0.986007i \(-0.553313\pi\)
−0.166704 + 0.986007i \(0.553313\pi\)
\(884\) 4.39580 0.147847
\(885\) 24.1544 0.811943
\(886\) −25.4666 −0.855567
\(887\) −10.1703 −0.341484 −0.170742 0.985316i \(-0.554616\pi\)
−0.170742 + 0.985316i \(0.554616\pi\)
\(888\) 3.32428 0.111556
\(889\) 12.1156 0.406343
\(890\) 21.3300 0.714984
\(891\) −7.75480 −0.259795
\(892\) 0.245128 0.00820751
\(893\) −12.0453 −0.403081
\(894\) 21.3509 0.714080
\(895\) 10.0115 0.334647
\(896\) 2.98980 0.0998822
\(897\) −6.71707 −0.224277
\(898\) −9.85257 −0.328784
\(899\) 23.4075 0.780684
\(900\) 0.392929 0.0130976
\(901\) −15.0838 −0.502516
\(902\) 5.26661 0.175359
\(903\) 21.1420 0.703560
\(904\) −17.1610 −0.570767
\(905\) −45.4501 −1.51081
\(906\) −18.6592 −0.619911
\(907\) 18.2885 0.607258 0.303629 0.952790i \(-0.401802\pi\)
0.303629 + 0.952790i \(0.401802\pi\)
\(908\) −18.4937 −0.613735
\(909\) 1.79115 0.0594086
\(910\) 14.6181 0.484586
\(911\) −31.1506 −1.03207 −0.516033 0.856569i \(-0.672592\pi\)
−0.516033 + 0.856569i \(0.672592\pi\)
\(912\) −5.94822 −0.196965
\(913\) 17.1909 0.568935
\(914\) 15.4524 0.511121
\(915\) −21.8646 −0.722821
\(916\) 17.8858 0.590964
\(917\) 48.6499 1.60656
\(918\) 10.9396 0.361062
\(919\) −24.3536 −0.803353 −0.401676 0.915782i \(-0.631572\pi\)
−0.401676 + 0.915782i \(0.631572\pi\)
\(920\) 4.87822 0.160830
\(921\) 19.0801 0.628712
\(922\) −4.28239 −0.141033
\(923\) 13.1207 0.431872
\(924\) −8.39195 −0.276075
\(925\) 0.786969 0.0258754
\(926\) −15.4021 −0.506145
\(927\) 2.63968 0.0866986
\(928\) 3.38241 0.111033
\(929\) −41.4128 −1.35871 −0.679355 0.733810i \(-0.737740\pi\)
−0.679355 + 0.733810i \(0.737740\pi\)
\(930\) 19.7791 0.648583
\(931\) −8.73639 −0.286324
\(932\) 22.0406 0.721963
\(933\) −28.3419 −0.927872
\(934\) −1.92711 −0.0630571
\(935\) 8.96065 0.293045
\(936\) 2.83939 0.0928085
\(937\) 20.8122 0.679904 0.339952 0.940443i \(-0.389589\pi\)
0.339952 + 0.940443i \(0.389589\pi\)
\(938\) 0.340370 0.0111135
\(939\) −2.67390 −0.0872596
\(940\) 5.78775 0.188776
\(941\) −30.2940 −0.987555 −0.493778 0.869588i \(-0.664384\pi\)
−0.493778 + 0.869588i \(0.664384\pi\)
\(942\) 28.1741 0.917963
\(943\) 5.58098 0.181742
\(944\) 8.45119 0.275063
\(945\) 36.3795 1.18343
\(946\) 11.3895 0.370306
\(947\) 53.3704 1.73431 0.867153 0.498042i \(-0.165947\pi\)
0.867153 + 0.498042i \(0.165947\pi\)
\(948\) 18.3741 0.596762
\(949\) −7.11242 −0.230879
\(950\) −1.40814 −0.0456862
\(951\) 38.2038 1.23884
\(952\) 5.81969 0.188617
\(953\) 37.1666 1.20395 0.601973 0.798517i \(-0.294382\pi\)
0.601973 + 0.798517i \(0.294382\pi\)
\(954\) −9.74316 −0.315447
\(955\) 38.1198 1.23353
\(956\) 12.0738 0.390493
\(957\) −9.49397 −0.306896
\(958\) −14.1139 −0.456000
\(959\) −7.34970 −0.237334
\(960\) 2.85811 0.0922451
\(961\) 16.8913 0.544880
\(962\) 5.68681 0.183350
\(963\) −16.3478 −0.526801
\(964\) −0.147118 −0.00473836
\(965\) 5.52595 0.177886
\(966\) −8.89287 −0.286123
\(967\) 23.8872 0.768161 0.384080 0.923300i \(-0.374519\pi\)
0.384080 + 0.923300i \(0.374519\pi\)
\(968\) 6.47911 0.208246
\(969\) −11.5783 −0.371948
\(970\) 33.9607 1.09041
\(971\) −48.1383 −1.54483 −0.772417 0.635116i \(-0.780952\pi\)
−0.772417 + 0.635116i \(0.780952\pi\)
\(972\) 12.0457 0.386365
\(973\) −48.7558 −1.56304
\(974\) 20.0385 0.642075
\(975\) −0.931660 −0.0298370
\(976\) −7.65002 −0.244871
\(977\) 13.3321 0.426531 0.213266 0.976994i \(-0.431590\pi\)
0.213266 + 0.976994i \(0.431590\pi\)
\(978\) 17.8019 0.569240
\(979\) −20.9476 −0.669487
\(980\) 4.19782 0.134095
\(981\) 1.15309 0.0368153
\(982\) −16.3461 −0.521626
\(983\) −46.9158 −1.49638 −0.748192 0.663483i \(-0.769078\pi\)
−0.748192 + 0.663483i \(0.769078\pi\)
\(984\) 3.26985 0.104239
\(985\) −28.0961 −0.895217
\(986\) 6.58392 0.209675
\(987\) −10.5509 −0.335840
\(988\) −10.1756 −0.323727
\(989\) 12.0694 0.383785
\(990\) 5.78799 0.183954
\(991\) 5.15628 0.163795 0.0818973 0.996641i \(-0.473902\pi\)
0.0818973 + 0.996641i \(0.473902\pi\)
\(992\) 6.92035 0.219721
\(993\) 1.18423 0.0375803
\(994\) 17.3707 0.550965
\(995\) 35.7348 1.13287
\(996\) 10.6732 0.338194
\(997\) 4.46240 0.141326 0.0706628 0.997500i \(-0.477489\pi\)
0.0706628 + 0.997500i \(0.477489\pi\)
\(998\) −21.2430 −0.672434
\(999\) 14.1525 0.447766
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 4006.2.a.g.1.26 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.26 40 1.1 even 1 trivial