Properties

Label 6034.2.a.p.1.1
Level $6034$
Weight $2$
Character 6034.1
Self dual yes
Analytic conductor $48.182$
Analytic rank $0$
Dimension $27$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.22794 q^{3} +1.00000 q^{4} +1.50843 q^{5} +3.22794 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.41957 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.22794 q^{3} +1.00000 q^{4} +1.50843 q^{5} +3.22794 q^{6} +1.00000 q^{7} -1.00000 q^{8} +7.41957 q^{9} -1.50843 q^{10} +2.69181 q^{11} -3.22794 q^{12} +2.34378 q^{13} -1.00000 q^{14} -4.86911 q^{15} +1.00000 q^{16} -1.99039 q^{17} -7.41957 q^{18} -3.26883 q^{19} +1.50843 q^{20} -3.22794 q^{21} -2.69181 q^{22} +5.95775 q^{23} +3.22794 q^{24} -2.72464 q^{25} -2.34378 q^{26} -14.2661 q^{27} +1.00000 q^{28} -7.07809 q^{29} +4.86911 q^{30} +9.75321 q^{31} -1.00000 q^{32} -8.68898 q^{33} +1.99039 q^{34} +1.50843 q^{35} +7.41957 q^{36} +2.88944 q^{37} +3.26883 q^{38} -7.56558 q^{39} -1.50843 q^{40} +8.32408 q^{41} +3.22794 q^{42} +3.75276 q^{43} +2.69181 q^{44} +11.1919 q^{45} -5.95775 q^{46} +8.78196 q^{47} -3.22794 q^{48} +1.00000 q^{49} +2.72464 q^{50} +6.42486 q^{51} +2.34378 q^{52} -3.37076 q^{53} +14.2661 q^{54} +4.06040 q^{55} -1.00000 q^{56} +10.5516 q^{57} +7.07809 q^{58} -0.771012 q^{59} -4.86911 q^{60} +11.1625 q^{61} -9.75321 q^{62} +7.41957 q^{63} +1.00000 q^{64} +3.53543 q^{65} +8.68898 q^{66} -1.49141 q^{67} -1.99039 q^{68} -19.2312 q^{69} -1.50843 q^{70} +14.9001 q^{71} -7.41957 q^{72} -12.1773 q^{73} -2.88944 q^{74} +8.79498 q^{75} -3.26883 q^{76} +2.69181 q^{77} +7.56558 q^{78} +2.71302 q^{79} +1.50843 q^{80} +23.7914 q^{81} -8.32408 q^{82} -7.89882 q^{83} -3.22794 q^{84} -3.00236 q^{85} -3.75276 q^{86} +22.8476 q^{87} -2.69181 q^{88} +10.1594 q^{89} -11.1919 q^{90} +2.34378 q^{91} +5.95775 q^{92} -31.4827 q^{93} -8.78196 q^{94} -4.93080 q^{95} +3.22794 q^{96} -12.8948 q^{97} -1.00000 q^{98} +19.9721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 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
\(3\) −3.22794 −1.86365 −0.931825 0.362908i \(-0.881784\pi\)
−0.931825 + 0.362908i \(0.881784\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.50843 0.674590 0.337295 0.941399i \(-0.390488\pi\)
0.337295 + 0.941399i \(0.390488\pi\)
\(6\) 3.22794 1.31780
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 7.41957 2.47319
\(10\) −1.50843 −0.477007
\(11\) 2.69181 0.811611 0.405805 0.913960i \(-0.366991\pi\)
0.405805 + 0.913960i \(0.366991\pi\)
\(12\) −3.22794 −0.931825
\(13\) 2.34378 0.650048 0.325024 0.945706i \(-0.394628\pi\)
0.325024 + 0.945706i \(0.394628\pi\)
\(14\) −1.00000 −0.267261
\(15\) −4.86911 −1.25720
\(16\) 1.00000 0.250000
\(17\) −1.99039 −0.482741 −0.241370 0.970433i \(-0.577597\pi\)
−0.241370 + 0.970433i \(0.577597\pi\)
\(18\) −7.41957 −1.74881
\(19\) −3.26883 −0.749922 −0.374961 0.927041i \(-0.622344\pi\)
−0.374961 + 0.927041i \(0.622344\pi\)
\(20\) 1.50843 0.337295
\(21\) −3.22794 −0.704393
\(22\) −2.69181 −0.573895
\(23\) 5.95775 1.24228 0.621139 0.783701i \(-0.286670\pi\)
0.621139 + 0.783701i \(0.286670\pi\)
\(24\) 3.22794 0.658900
\(25\) −2.72464 −0.544929
\(26\) −2.34378 −0.459653
\(27\) −14.2661 −2.74551
\(28\) 1.00000 0.188982
\(29\) −7.07809 −1.31437 −0.657184 0.753730i \(-0.728252\pi\)
−0.657184 + 0.753730i \(0.728252\pi\)
\(30\) 4.86911 0.888974
\(31\) 9.75321 1.75173 0.875864 0.482558i \(-0.160292\pi\)
0.875864 + 0.482558i \(0.160292\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.68898 −1.51256
\(34\) 1.99039 0.341349
\(35\) 1.50843 0.254971
\(36\) 7.41957 1.23660
\(37\) 2.88944 0.475021 0.237511 0.971385i \(-0.423669\pi\)
0.237511 + 0.971385i \(0.423669\pi\)
\(38\) 3.26883 0.530275
\(39\) −7.56558 −1.21146
\(40\) −1.50843 −0.238503
\(41\) 8.32408 1.30000 0.650001 0.759933i \(-0.274768\pi\)
0.650001 + 0.759933i \(0.274768\pi\)
\(42\) 3.22794 0.498081
\(43\) 3.75276 0.572290 0.286145 0.958186i \(-0.407626\pi\)
0.286145 + 0.958186i \(0.407626\pi\)
\(44\) 2.69181 0.405805
\(45\) 11.1919 1.66839
\(46\) −5.95775 −0.878423
\(47\) 8.78196 1.28098 0.640490 0.767966i \(-0.278731\pi\)
0.640490 + 0.767966i \(0.278731\pi\)
\(48\) −3.22794 −0.465913
\(49\) 1.00000 0.142857
\(50\) 2.72464 0.385323
\(51\) 6.42486 0.899660
\(52\) 2.34378 0.325024
\(53\) −3.37076 −0.463009 −0.231504 0.972834i \(-0.574365\pi\)
−0.231504 + 0.972834i \(0.574365\pi\)
\(54\) 14.2661 1.94137
\(55\) 4.06040 0.547504
\(56\) −1.00000 −0.133631
\(57\) 10.5516 1.39759
\(58\) 7.07809 0.929398
\(59\) −0.771012 −0.100377 −0.0501886 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(60\) −4.86911 −0.628599
\(61\) 11.1625 1.42922 0.714609 0.699524i \(-0.246605\pi\)
0.714609 + 0.699524i \(0.246605\pi\)
\(62\) −9.75321 −1.23866
\(63\) 7.41957 0.934778
\(64\) 1.00000 0.125000
\(65\) 3.53543 0.438516
\(66\) 8.68898 1.06954
\(67\) −1.49141 −0.182205 −0.0911025 0.995842i \(-0.529039\pi\)
−0.0911025 + 0.995842i \(0.529039\pi\)
\(68\) −1.99039 −0.241370
\(69\) −19.2312 −2.31517
\(70\) −1.50843 −0.180292
\(71\) 14.9001 1.76832 0.884160 0.467184i \(-0.154732\pi\)
0.884160 + 0.467184i \(0.154732\pi\)
\(72\) −7.41957 −0.874405
\(73\) −12.1773 −1.42524 −0.712620 0.701550i \(-0.752492\pi\)
−0.712620 + 0.701550i \(0.752492\pi\)
\(74\) −2.88944 −0.335891
\(75\) 8.79498 1.01556
\(76\) −3.26883 −0.374961
\(77\) 2.69181 0.306760
\(78\) 7.56558 0.856633
\(79\) 2.71302 0.305239 0.152619 0.988285i \(-0.451229\pi\)
0.152619 + 0.988285i \(0.451229\pi\)
\(80\) 1.50843 0.168647
\(81\) 23.7914 2.64348
\(82\) −8.32408 −0.919240
\(83\) −7.89882 −0.867008 −0.433504 0.901152i \(-0.642723\pi\)
−0.433504 + 0.901152i \(0.642723\pi\)
\(84\) −3.22794 −0.352197
\(85\) −3.00236 −0.325652
\(86\) −3.75276 −0.404670
\(87\) 22.8476 2.44952
\(88\) −2.69181 −0.286948
\(89\) 10.1594 1.07690 0.538449 0.842658i \(-0.319010\pi\)
0.538449 + 0.842658i \(0.319010\pi\)
\(90\) −11.1919 −1.17973
\(91\) 2.34378 0.245695
\(92\) 5.95775 0.621139
\(93\) −31.4827 −3.26461
\(94\) −8.78196 −0.905790
\(95\) −4.93080 −0.505889
\(96\) 3.22794 0.329450
\(97\) −12.8948 −1.30927 −0.654637 0.755944i \(-0.727178\pi\)
−0.654637 + 0.755944i \(0.727178\pi\)
\(98\) −1.00000 −0.101015
\(99\) 19.9721 2.00727
\(100\) −2.72464 −0.272464
\(101\) −15.7843 −1.57059 −0.785297 0.619119i \(-0.787490\pi\)
−0.785297 + 0.619119i \(0.787490\pi\)
\(102\) −6.42486 −0.636156
\(103\) −0.299389 −0.0294997 −0.0147498 0.999891i \(-0.504695\pi\)
−0.0147498 + 0.999891i \(0.504695\pi\)
\(104\) −2.34378 −0.229827
\(105\) −4.86911 −0.475176
\(106\) 3.37076 0.327397
\(107\) −0.402137 −0.0388760 −0.0194380 0.999811i \(-0.506188\pi\)
−0.0194380 + 0.999811i \(0.506188\pi\)
\(108\) −14.2661 −1.37276
\(109\) 12.5157 1.19878 0.599392 0.800456i \(-0.295409\pi\)
0.599392 + 0.800456i \(0.295409\pi\)
\(110\) −4.06040 −0.387144
\(111\) −9.32693 −0.885273
\(112\) 1.00000 0.0944911
\(113\) 13.0313 1.22588 0.612941 0.790129i \(-0.289986\pi\)
0.612941 + 0.790129i \(0.289986\pi\)
\(114\) −10.5516 −0.988247
\(115\) 8.98684 0.838027
\(116\) −7.07809 −0.657184
\(117\) 17.3899 1.60769
\(118\) 0.771012 0.0709774
\(119\) −1.99039 −0.182459
\(120\) 4.86911 0.444487
\(121\) −3.75417 −0.341288
\(122\) −11.1625 −1.01061
\(123\) −26.8696 −2.42275
\(124\) 9.75321 0.875864
\(125\) −11.6521 −1.04219
\(126\) −7.41957 −0.660988
\(127\) −7.23989 −0.642436 −0.321218 0.947005i \(-0.604092\pi\)
−0.321218 + 0.947005i \(0.604092\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.1137 −1.06655
\(130\) −3.53543 −0.310077
\(131\) −4.12405 −0.360320 −0.180160 0.983637i \(-0.557662\pi\)
−0.180160 + 0.983637i \(0.557662\pi\)
\(132\) −8.68898 −0.756279
\(133\) −3.26883 −0.283444
\(134\) 1.49141 0.128838
\(135\) −21.5194 −1.85209
\(136\) 1.99039 0.170675
\(137\) −3.14143 −0.268390 −0.134195 0.990955i \(-0.542845\pi\)
−0.134195 + 0.990955i \(0.542845\pi\)
\(138\) 19.2312 1.63707
\(139\) −3.62990 −0.307884 −0.153942 0.988080i \(-0.549197\pi\)
−0.153942 + 0.988080i \(0.549197\pi\)
\(140\) 1.50843 0.127485
\(141\) −28.3476 −2.38730
\(142\) −14.9001 −1.25039
\(143\) 6.30901 0.527586
\(144\) 7.41957 0.618298
\(145\) −10.6768 −0.886659
\(146\) 12.1773 1.00780
\(147\) −3.22794 −0.266236
\(148\) 2.88944 0.237511
\(149\) 10.4225 0.853842 0.426921 0.904289i \(-0.359598\pi\)
0.426921 + 0.904289i \(0.359598\pi\)
\(150\) −8.79498 −0.718107
\(151\) 14.6673 1.19361 0.596804 0.802387i \(-0.296437\pi\)
0.596804 + 0.802387i \(0.296437\pi\)
\(152\) 3.26883 0.265137
\(153\) −14.7679 −1.19391
\(154\) −2.69181 −0.216912
\(155\) 14.7120 1.18170
\(156\) −7.56558 −0.605731
\(157\) 7.59333 0.606013 0.303007 0.952988i \(-0.402010\pi\)
0.303007 + 0.952988i \(0.402010\pi\)
\(158\) −2.71302 −0.215837
\(159\) 10.8806 0.862887
\(160\) −1.50843 −0.119252
\(161\) 5.95775 0.469537
\(162\) −23.7914 −1.86923
\(163\) 6.15575 0.482155 0.241078 0.970506i \(-0.422499\pi\)
0.241078 + 0.970506i \(0.422499\pi\)
\(164\) 8.32408 0.650001
\(165\) −13.1067 −1.02036
\(166\) 7.89882 0.613068
\(167\) 13.7924 1.06729 0.533645 0.845709i \(-0.320822\pi\)
0.533645 + 0.845709i \(0.320822\pi\)
\(168\) 3.22794 0.249041
\(169\) −7.50669 −0.577437
\(170\) 3.00236 0.230271
\(171\) −24.2534 −1.85470
\(172\) 3.75276 0.286145
\(173\) −21.6024 −1.64240 −0.821201 0.570640i \(-0.806695\pi\)
−0.821201 + 0.570640i \(0.806695\pi\)
\(174\) −22.8476 −1.73207
\(175\) −2.72464 −0.205964
\(176\) 2.69181 0.202903
\(177\) 2.48878 0.187068
\(178\) −10.1594 −0.761482
\(179\) 5.76165 0.430646 0.215323 0.976543i \(-0.430920\pi\)
0.215323 + 0.976543i \(0.430920\pi\)
\(180\) 11.1919 0.834194
\(181\) −12.1495 −0.903062 −0.451531 0.892255i \(-0.649122\pi\)
−0.451531 + 0.892255i \(0.649122\pi\)
\(182\) −2.34378 −0.173733
\(183\) −36.0320 −2.66356
\(184\) −5.95775 −0.439211
\(185\) 4.35851 0.320444
\(186\) 31.4827 2.30843
\(187\) −5.35775 −0.391798
\(188\) 8.78196 0.640490
\(189\) −14.2661 −1.03771
\(190\) 4.93080 0.357718
\(191\) 3.57067 0.258365 0.129182 0.991621i \(-0.458765\pi\)
0.129182 + 0.991621i \(0.458765\pi\)
\(192\) −3.22794 −0.232956
\(193\) 1.06836 0.0769019 0.0384510 0.999260i \(-0.487758\pi\)
0.0384510 + 0.999260i \(0.487758\pi\)
\(194\) 12.8948 0.925796
\(195\) −11.4121 −0.817240
\(196\) 1.00000 0.0714286
\(197\) 0.859221 0.0612170 0.0306085 0.999531i \(-0.490255\pi\)
0.0306085 + 0.999531i \(0.490255\pi\)
\(198\) −19.9721 −1.41935
\(199\) −1.00002 −0.0708897 −0.0354448 0.999372i \(-0.511285\pi\)
−0.0354448 + 0.999372i \(0.511285\pi\)
\(200\) 2.72464 0.192661
\(201\) 4.81418 0.339566
\(202\) 15.7843 1.11058
\(203\) −7.07809 −0.496784
\(204\) 6.42486 0.449830
\(205\) 12.5563 0.876968
\(206\) 0.299389 0.0208594
\(207\) 44.2040 3.07239
\(208\) 2.34378 0.162512
\(209\) −8.79907 −0.608644
\(210\) 4.86911 0.336001
\(211\) 22.3911 1.54147 0.770733 0.637158i \(-0.219890\pi\)
0.770733 + 0.637158i \(0.219890\pi\)
\(212\) −3.37076 −0.231504
\(213\) −48.0967 −3.29553
\(214\) 0.402137 0.0274895
\(215\) 5.66076 0.386061
\(216\) 14.2661 0.970685
\(217\) 9.75321 0.662091
\(218\) −12.5157 −0.847668
\(219\) 39.3074 2.65615
\(220\) 4.06040 0.273752
\(221\) −4.66504 −0.313805
\(222\) 9.32693 0.625983
\(223\) −8.48735 −0.568355 −0.284178 0.958772i \(-0.591721\pi\)
−0.284178 + 0.958772i \(0.591721\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −20.2157 −1.34771
\(226\) −13.0313 −0.866829
\(227\) 24.5082 1.62666 0.813332 0.581800i \(-0.197651\pi\)
0.813332 + 0.581800i \(0.197651\pi\)
\(228\) 10.5516 0.698796
\(229\) −23.2995 −1.53967 −0.769837 0.638241i \(-0.779662\pi\)
−0.769837 + 0.638241i \(0.779662\pi\)
\(230\) −8.98684 −0.592575
\(231\) −8.68898 −0.571693
\(232\) 7.07809 0.464699
\(233\) −0.337960 −0.0221405 −0.0110703 0.999939i \(-0.503524\pi\)
−0.0110703 + 0.999939i \(0.503524\pi\)
\(234\) −17.3899 −1.13681
\(235\) 13.2470 0.864136
\(236\) −0.771012 −0.0501886
\(237\) −8.75747 −0.568859
\(238\) 1.99039 0.129018
\(239\) −30.5154 −1.97388 −0.986940 0.161088i \(-0.948500\pi\)
−0.986940 + 0.161088i \(0.948500\pi\)
\(240\) −4.86911 −0.314300
\(241\) −1.29495 −0.0834152 −0.0417076 0.999130i \(-0.513280\pi\)
−0.0417076 + 0.999130i \(0.513280\pi\)
\(242\) 3.75417 0.241327
\(243\) −33.9987 −2.18102
\(244\) 11.1625 0.714609
\(245\) 1.50843 0.0963699
\(246\) 26.8696 1.71314
\(247\) −7.66143 −0.487485
\(248\) −9.75321 −0.619329
\(249\) 25.4969 1.61580
\(250\) 11.6521 0.736942
\(251\) −24.5643 −1.55048 −0.775242 0.631665i \(-0.782372\pi\)
−0.775242 + 0.631665i \(0.782372\pi\)
\(252\) 7.41957 0.467389
\(253\) 16.0371 1.00825
\(254\) 7.23989 0.454271
\(255\) 9.69144 0.606901
\(256\) 1.00000 0.0625000
\(257\) −26.1892 −1.63364 −0.816819 0.576894i \(-0.804264\pi\)
−0.816819 + 0.576894i \(0.804264\pi\)
\(258\) 12.1137 0.754163
\(259\) 2.88944 0.179541
\(260\) 3.53543 0.219258
\(261\) −52.5164 −3.25068
\(262\) 4.12405 0.254785
\(263\) 0.277761 0.0171275 0.00856374 0.999963i \(-0.497274\pi\)
0.00856374 + 0.999963i \(0.497274\pi\)
\(264\) 8.68898 0.534770
\(265\) −5.08454 −0.312341
\(266\) 3.26883 0.200425
\(267\) −32.7940 −2.00696
\(268\) −1.49141 −0.0911025
\(269\) 25.1147 1.53127 0.765634 0.643276i \(-0.222425\pi\)
0.765634 + 0.643276i \(0.222425\pi\)
\(270\) 21.5194 1.30963
\(271\) −18.0708 −1.09772 −0.548862 0.835913i \(-0.684939\pi\)
−0.548862 + 0.835913i \(0.684939\pi\)
\(272\) −1.99039 −0.120685
\(273\) −7.56558 −0.457890
\(274\) 3.14143 0.189780
\(275\) −7.33422 −0.442270
\(276\) −19.2312 −1.15758
\(277\) 18.3269 1.10116 0.550580 0.834783i \(-0.314407\pi\)
0.550580 + 0.834783i \(0.314407\pi\)
\(278\) 3.62990 0.217707
\(279\) 72.3646 4.33236
\(280\) −1.50843 −0.0901458
\(281\) 11.1314 0.664041 0.332020 0.943272i \(-0.392270\pi\)
0.332020 + 0.943272i \(0.392270\pi\)
\(282\) 28.3476 1.68808
\(283\) −16.8138 −0.999478 −0.499739 0.866176i \(-0.666571\pi\)
−0.499739 + 0.866176i \(0.666571\pi\)
\(284\) 14.9001 0.884160
\(285\) 15.9163 0.942801
\(286\) −6.30901 −0.373060
\(287\) 8.32408 0.491355
\(288\) −7.41957 −0.437203
\(289\) −13.0383 −0.766961
\(290\) 10.6768 0.626962
\(291\) 41.6237 2.44003
\(292\) −12.1773 −0.712620
\(293\) −12.0673 −0.704981 −0.352490 0.935815i \(-0.614665\pi\)
−0.352490 + 0.935815i \(0.614665\pi\)
\(294\) 3.22794 0.188257
\(295\) −1.16302 −0.0677134
\(296\) −2.88944 −0.167945
\(297\) −38.4016 −2.22829
\(298\) −10.4225 −0.603758
\(299\) 13.9637 0.807540
\(300\) 8.79498 0.507778
\(301\) 3.75276 0.216305
\(302\) −14.6673 −0.844008
\(303\) 50.9506 2.92704
\(304\) −3.26883 −0.187480
\(305\) 16.8379 0.964136
\(306\) 14.7679 0.844222
\(307\) −10.1488 −0.579221 −0.289611 0.957145i \(-0.593526\pi\)
−0.289611 + 0.957145i \(0.593526\pi\)
\(308\) 2.69181 0.153380
\(309\) 0.966408 0.0549770
\(310\) −14.7120 −0.835586
\(311\) 2.91875 0.165507 0.0827536 0.996570i \(-0.473629\pi\)
0.0827536 + 0.996570i \(0.473629\pi\)
\(312\) 7.56558 0.428317
\(313\) 28.3749 1.60384 0.801921 0.597430i \(-0.203812\pi\)
0.801921 + 0.597430i \(0.203812\pi\)
\(314\) −7.59333 −0.428516
\(315\) 11.1919 0.630592
\(316\) 2.71302 0.152619
\(317\) 17.2455 0.968606 0.484303 0.874900i \(-0.339073\pi\)
0.484303 + 0.874900i \(0.339073\pi\)
\(318\) −10.8806 −0.610153
\(319\) −19.0528 −1.06675
\(320\) 1.50843 0.0843237
\(321\) 1.29807 0.0724513
\(322\) −5.95775 −0.332013
\(323\) 6.50626 0.362018
\(324\) 23.7914 1.32174
\(325\) −6.38597 −0.354230
\(326\) −6.15575 −0.340935
\(327\) −40.3998 −2.23411
\(328\) −8.32408 −0.459620
\(329\) 8.78196 0.484165
\(330\) 13.1067 0.721501
\(331\) 31.9632 1.75685 0.878427 0.477877i \(-0.158593\pi\)
0.878427 + 0.477877i \(0.158593\pi\)
\(332\) −7.89882 −0.433504
\(333\) 21.4384 1.17482
\(334\) −13.7924 −0.754688
\(335\) −2.24969 −0.122914
\(336\) −3.22794 −0.176098
\(337\) 18.6668 1.01684 0.508422 0.861108i \(-0.330229\pi\)
0.508422 + 0.861108i \(0.330229\pi\)
\(338\) 7.50669 0.408310
\(339\) −42.0642 −2.28461
\(340\) −3.00236 −0.162826
\(341\) 26.2538 1.42172
\(342\) 24.2534 1.31147
\(343\) 1.00000 0.0539949
\(344\) −3.75276 −0.202335
\(345\) −29.0090 −1.56179
\(346\) 21.6024 1.16135
\(347\) −10.9018 −0.585242 −0.292621 0.956229i \(-0.594527\pi\)
−0.292621 + 0.956229i \(0.594527\pi\)
\(348\) 22.8476 1.22476
\(349\) −28.8675 −1.54524 −0.772622 0.634866i \(-0.781055\pi\)
−0.772622 + 0.634866i \(0.781055\pi\)
\(350\) 2.72464 0.145638
\(351\) −33.4366 −1.78472
\(352\) −2.69181 −0.143474
\(353\) 15.6173 0.831224 0.415612 0.909542i \(-0.363567\pi\)
0.415612 + 0.909542i \(0.363567\pi\)
\(354\) −2.48878 −0.132277
\(355\) 22.4758 1.19289
\(356\) 10.1594 0.538449
\(357\) 6.42486 0.340040
\(358\) −5.76165 −0.304513
\(359\) 1.07679 0.0568310 0.0284155 0.999596i \(-0.490954\pi\)
0.0284155 + 0.999596i \(0.490954\pi\)
\(360\) −11.1919 −0.589865
\(361\) −8.31473 −0.437617
\(362\) 12.1495 0.638562
\(363\) 12.1182 0.636042
\(364\) 2.34378 0.122848
\(365\) −18.3685 −0.961452
\(366\) 36.0320 1.88342
\(367\) 2.73231 0.142625 0.0713127 0.997454i \(-0.477281\pi\)
0.0713127 + 0.997454i \(0.477281\pi\)
\(368\) 5.95775 0.310569
\(369\) 61.7611 3.21515
\(370\) −4.35851 −0.226588
\(371\) −3.37076 −0.175001
\(372\) −31.4827 −1.63230
\(373\) −31.8728 −1.65031 −0.825154 0.564907i \(-0.808912\pi\)
−0.825154 + 0.564907i \(0.808912\pi\)
\(374\) 5.35775 0.277043
\(375\) 37.6121 1.94228
\(376\) −8.78196 −0.452895
\(377\) −16.5895 −0.854402
\(378\) 14.2661 0.733769
\(379\) 33.5657 1.72415 0.862077 0.506777i \(-0.169163\pi\)
0.862077 + 0.506777i \(0.169163\pi\)
\(380\) −4.93080 −0.252945
\(381\) 23.3699 1.19728
\(382\) −3.57067 −0.182692
\(383\) 29.1282 1.48838 0.744190 0.667968i \(-0.232836\pi\)
0.744190 + 0.667968i \(0.232836\pi\)
\(384\) 3.22794 0.164725
\(385\) 4.06040 0.206937
\(386\) −1.06836 −0.0543779
\(387\) 27.8438 1.41538
\(388\) −12.8948 −0.654637
\(389\) 23.5239 1.19271 0.596355 0.802721i \(-0.296615\pi\)
0.596355 + 0.802721i \(0.296615\pi\)
\(390\) 11.4121 0.577876
\(391\) −11.8583 −0.599698
\(392\) −1.00000 −0.0505076
\(393\) 13.3122 0.671511
\(394\) −0.859221 −0.0432869
\(395\) 4.09240 0.205911
\(396\) 19.9721 1.00363
\(397\) −19.2102 −0.964131 −0.482065 0.876135i \(-0.660113\pi\)
−0.482065 + 0.876135i \(0.660113\pi\)
\(398\) 1.00002 0.0501266
\(399\) 10.5516 0.528240
\(400\) −2.72464 −0.136232
\(401\) 28.4563 1.42104 0.710521 0.703676i \(-0.248460\pi\)
0.710521 + 0.703676i \(0.248460\pi\)
\(402\) −4.81418 −0.240110
\(403\) 22.8594 1.13871
\(404\) −15.7843 −0.785297
\(405\) 35.8875 1.78327
\(406\) 7.07809 0.351279
\(407\) 7.77782 0.385532
\(408\) −6.42486 −0.318078
\(409\) 30.0035 1.48358 0.741789 0.670634i \(-0.233978\pi\)
0.741789 + 0.670634i \(0.233978\pi\)
\(410\) −12.5563 −0.620110
\(411\) 10.1403 0.500185
\(412\) −0.299389 −0.0147498
\(413\) −0.771012 −0.0379390
\(414\) −44.2040 −2.17251
\(415\) −11.9148 −0.584875
\(416\) −2.34378 −0.114913
\(417\) 11.7171 0.573788
\(418\) 8.79907 0.430377
\(419\) 8.81082 0.430437 0.215218 0.976566i \(-0.430954\pi\)
0.215218 + 0.976566i \(0.430954\pi\)
\(420\) −4.86911 −0.237588
\(421\) −12.3383 −0.601332 −0.300666 0.953730i \(-0.597209\pi\)
−0.300666 + 0.953730i \(0.597209\pi\)
\(422\) −22.3911 −1.08998
\(423\) 65.1584 3.16811
\(424\) 3.37076 0.163698
\(425\) 5.42311 0.263059
\(426\) 48.0967 2.33029
\(427\) 11.1625 0.540194
\(428\) −0.402137 −0.0194380
\(429\) −20.3651 −0.983236
\(430\) −5.66076 −0.272986
\(431\) −1.00000 −0.0481683
\(432\) −14.2661 −0.686378
\(433\) −33.2119 −1.59606 −0.798032 0.602615i \(-0.794125\pi\)
−0.798032 + 0.602615i \(0.794125\pi\)
\(434\) −9.75321 −0.468169
\(435\) 34.4640 1.65242
\(436\) 12.5157 0.599392
\(437\) −19.4749 −0.931611
\(438\) −39.3074 −1.87818
\(439\) 32.5701 1.55448 0.777242 0.629202i \(-0.216618\pi\)
0.777242 + 0.629202i \(0.216618\pi\)
\(440\) −4.06040 −0.193572
\(441\) 7.41957 0.353313
\(442\) 4.66504 0.221894
\(443\) 13.5122 0.641983 0.320992 0.947082i \(-0.395984\pi\)
0.320992 + 0.947082i \(0.395984\pi\)
\(444\) −9.32693 −0.442636
\(445\) 15.3248 0.726465
\(446\) 8.48735 0.401888
\(447\) −33.6431 −1.59126
\(448\) 1.00000 0.0472456
\(449\) −35.3651 −1.66898 −0.834491 0.551022i \(-0.814238\pi\)
−0.834491 + 0.551022i \(0.814238\pi\)
\(450\) 20.2157 0.952977
\(451\) 22.4068 1.05510
\(452\) 13.0313 0.612941
\(453\) −47.3451 −2.22447
\(454\) −24.5082 −1.15023
\(455\) 3.53543 0.165743
\(456\) −10.5516 −0.494123
\(457\) 17.9663 0.840429 0.420214 0.907425i \(-0.361955\pi\)
0.420214 + 0.907425i \(0.361955\pi\)
\(458\) 23.2995 1.08871
\(459\) 28.3951 1.32537
\(460\) 8.98684 0.419014
\(461\) 4.93636 0.229909 0.114954 0.993371i \(-0.463328\pi\)
0.114954 + 0.993371i \(0.463328\pi\)
\(462\) 8.68898 0.404248
\(463\) −26.3298 −1.22365 −0.611824 0.790994i \(-0.709564\pi\)
−0.611824 + 0.790994i \(0.709564\pi\)
\(464\) −7.07809 −0.328592
\(465\) −47.4894 −2.20227
\(466\) 0.337960 0.0156557
\(467\) −16.2673 −0.752763 −0.376381 0.926465i \(-0.622832\pi\)
−0.376381 + 0.926465i \(0.622832\pi\)
\(468\) 17.3899 0.803847
\(469\) −1.49141 −0.0688670
\(470\) −13.2470 −0.611036
\(471\) −24.5108 −1.12940
\(472\) 0.771012 0.0354887
\(473\) 10.1017 0.464477
\(474\) 8.75747 0.402244
\(475\) 8.90641 0.408654
\(476\) −1.99039 −0.0912295
\(477\) −25.0096 −1.14511
\(478\) 30.5154 1.39574
\(479\) −21.2767 −0.972156 −0.486078 0.873915i \(-0.661573\pi\)
−0.486078 + 0.873915i \(0.661573\pi\)
\(480\) 4.86911 0.222243
\(481\) 6.77222 0.308787
\(482\) 1.29495 0.0589835
\(483\) −19.2312 −0.875052
\(484\) −3.75417 −0.170644
\(485\) −19.4509 −0.883222
\(486\) 33.9987 1.54221
\(487\) 5.98714 0.271303 0.135652 0.990757i \(-0.456687\pi\)
0.135652 + 0.990757i \(0.456687\pi\)
\(488\) −11.1625 −0.505305
\(489\) −19.8704 −0.898569
\(490\) −1.50843 −0.0681438
\(491\) 36.4413 1.64457 0.822286 0.569075i \(-0.192699\pi\)
0.822286 + 0.569075i \(0.192699\pi\)
\(492\) −26.8696 −1.21137
\(493\) 14.0882 0.634499
\(494\) 7.66143 0.344704
\(495\) 30.1264 1.35408
\(496\) 9.75321 0.437932
\(497\) 14.9001 0.668362
\(498\) −25.4969 −1.14254
\(499\) 6.63243 0.296908 0.148454 0.988919i \(-0.452570\pi\)
0.148454 + 0.988919i \(0.452570\pi\)
\(500\) −11.6521 −0.521096
\(501\) −44.5211 −1.98905
\(502\) 24.5643 1.09636
\(503\) 42.5396 1.89675 0.948373 0.317156i \(-0.102728\pi\)
0.948373 + 0.317156i \(0.102728\pi\)
\(504\) −7.41957 −0.330494
\(505\) −23.8094 −1.05951
\(506\) −16.0371 −0.712937
\(507\) 24.2311 1.07614
\(508\) −7.23989 −0.321218
\(509\) −7.20298 −0.319266 −0.159633 0.987176i \(-0.551031\pi\)
−0.159633 + 0.987176i \(0.551031\pi\)
\(510\) −9.69144 −0.429144
\(511\) −12.1773 −0.538690
\(512\) −1.00000 −0.0441942
\(513\) 46.6335 2.05892
\(514\) 26.1892 1.15516
\(515\) −0.451607 −0.0199002
\(516\) −12.1137 −0.533274
\(517\) 23.6393 1.03966
\(518\) −2.88944 −0.126955
\(519\) 69.7312 3.06086
\(520\) −3.53543 −0.155039
\(521\) 24.9797 1.09438 0.547190 0.837009i \(-0.315698\pi\)
0.547190 + 0.837009i \(0.315698\pi\)
\(522\) 52.5164 2.29858
\(523\) 2.44361 0.106852 0.0534258 0.998572i \(-0.482986\pi\)
0.0534258 + 0.998572i \(0.482986\pi\)
\(524\) −4.12405 −0.180160
\(525\) 8.79498 0.383844
\(526\) −0.277761 −0.0121110
\(527\) −19.4127 −0.845631
\(528\) −8.68898 −0.378140
\(529\) 12.4948 0.543253
\(530\) 5.08454 0.220858
\(531\) −5.72058 −0.248252
\(532\) −3.26883 −0.141722
\(533\) 19.5098 0.845064
\(534\) 32.7940 1.41914
\(535\) −0.606595 −0.0262254
\(536\) 1.49141 0.0644192
\(537\) −18.5982 −0.802574
\(538\) −25.1147 −1.08277
\(539\) 2.69181 0.115944
\(540\) −21.5194 −0.926047
\(541\) −34.0698 −1.46478 −0.732388 0.680887i \(-0.761594\pi\)
−0.732388 + 0.680887i \(0.761594\pi\)
\(542\) 18.0708 0.776208
\(543\) 39.2177 1.68299
\(544\) 1.99039 0.0853373
\(545\) 18.8790 0.808687
\(546\) 7.56558 0.323777
\(547\) 9.86277 0.421702 0.210851 0.977518i \(-0.432377\pi\)
0.210851 + 0.977518i \(0.432377\pi\)
\(548\) −3.14143 −0.134195
\(549\) 82.8214 3.53473
\(550\) 7.33422 0.312732
\(551\) 23.1371 0.985673
\(552\) 19.2312 0.818536
\(553\) 2.71302 0.115369
\(554\) −18.3269 −0.778637
\(555\) −14.0690 −0.597196
\(556\) −3.62990 −0.153942
\(557\) 8.01471 0.339594 0.169797 0.985479i \(-0.445689\pi\)
0.169797 + 0.985479i \(0.445689\pi\)
\(558\) −72.3646 −3.06344
\(559\) 8.79564 0.372016
\(560\) 1.50843 0.0637427
\(561\) 17.2945 0.730174
\(562\) −11.1314 −0.469548
\(563\) −41.3772 −1.74384 −0.871920 0.489648i \(-0.837125\pi\)
−0.871920 + 0.489648i \(0.837125\pi\)
\(564\) −28.3476 −1.19365
\(565\) 19.6568 0.826967
\(566\) 16.8138 0.706738
\(567\) 23.7914 0.999143
\(568\) −14.9001 −0.625195
\(569\) 19.7446 0.827736 0.413868 0.910337i \(-0.364178\pi\)
0.413868 + 0.910337i \(0.364178\pi\)
\(570\) −15.9163 −0.666661
\(571\) 17.1819 0.719042 0.359521 0.933137i \(-0.382940\pi\)
0.359521 + 0.933137i \(0.382940\pi\)
\(572\) 6.30901 0.263793
\(573\) −11.5259 −0.481502
\(574\) −8.32408 −0.347440
\(575\) −16.2328 −0.676953
\(576\) 7.41957 0.309149
\(577\) 27.5181 1.14559 0.572797 0.819697i \(-0.305858\pi\)
0.572797 + 0.819697i \(0.305858\pi\)
\(578\) 13.0383 0.542323
\(579\) −3.44858 −0.143318
\(580\) −10.6768 −0.443329
\(581\) −7.89882 −0.327698
\(582\) −41.6237 −1.72536
\(583\) −9.07343 −0.375783
\(584\) 12.1773 0.503898
\(585\) 26.2314 1.08453
\(586\) 12.0673 0.498497
\(587\) 17.8475 0.736646 0.368323 0.929698i \(-0.379932\pi\)
0.368323 + 0.929698i \(0.379932\pi\)
\(588\) −3.22794 −0.133118
\(589\) −31.8816 −1.31366
\(590\) 1.16302 0.0478806
\(591\) −2.77351 −0.114087
\(592\) 2.88944 0.118755
\(593\) −31.4173 −1.29015 −0.645077 0.764117i \(-0.723175\pi\)
−0.645077 + 0.764117i \(0.723175\pi\)
\(594\) 38.4016 1.57564
\(595\) −3.00236 −0.123085
\(596\) 10.4225 0.426921
\(597\) 3.22801 0.132114
\(598\) −13.9637 −0.571017
\(599\) 40.9431 1.67289 0.836445 0.548051i \(-0.184630\pi\)
0.836445 + 0.548051i \(0.184630\pi\)
\(600\) −8.79498 −0.359054
\(601\) −11.0768 −0.451832 −0.225916 0.974147i \(-0.572538\pi\)
−0.225916 + 0.974147i \(0.572538\pi\)
\(602\) −3.75276 −0.152951
\(603\) −11.0656 −0.450628
\(604\) 14.6673 0.596804
\(605\) −5.66290 −0.230230
\(606\) −50.9506 −2.06973
\(607\) −9.89165 −0.401490 −0.200745 0.979644i \(-0.564336\pi\)
−0.200745 + 0.979644i \(0.564336\pi\)
\(608\) 3.26883 0.132569
\(609\) 22.8476 0.925832
\(610\) −16.8379 −0.681747
\(611\) 20.5830 0.832699
\(612\) −14.7679 −0.596955
\(613\) 4.41319 0.178247 0.0891235 0.996021i \(-0.471593\pi\)
0.0891235 + 0.996021i \(0.471593\pi\)
\(614\) 10.1488 0.409571
\(615\) −40.5308 −1.63436
\(616\) −2.69181 −0.108456
\(617\) −19.5141 −0.785606 −0.392803 0.919623i \(-0.628495\pi\)
−0.392803 + 0.919623i \(0.628495\pi\)
\(618\) −0.966408 −0.0388746
\(619\) −15.0744 −0.605892 −0.302946 0.953008i \(-0.597970\pi\)
−0.302946 + 0.953008i \(0.597970\pi\)
\(620\) 14.7120 0.590849
\(621\) −84.9939 −3.41069
\(622\) −2.91875 −0.117031
\(623\) 10.1594 0.407029
\(624\) −7.56558 −0.302866
\(625\) −3.95309 −0.158123
\(626\) −28.3749 −1.13409
\(627\) 28.4028 1.13430
\(628\) 7.59333 0.303007
\(629\) −5.75112 −0.229312
\(630\) −11.1919 −0.445896
\(631\) −19.6002 −0.780273 −0.390136 0.920757i \(-0.627572\pi\)
−0.390136 + 0.920757i \(0.627572\pi\)
\(632\) −2.71302 −0.107918
\(633\) −72.2770 −2.87275
\(634\) −17.2455 −0.684908
\(635\) −10.9209 −0.433381
\(636\) 10.8806 0.431443
\(637\) 2.34378 0.0928640
\(638\) 19.0528 0.754309
\(639\) 110.553 4.37339
\(640\) −1.50843 −0.0596259
\(641\) 21.8799 0.864203 0.432102 0.901825i \(-0.357772\pi\)
0.432102 + 0.901825i \(0.357772\pi\)
\(642\) −1.29807 −0.0512308
\(643\) −8.12830 −0.320549 −0.160274 0.987072i \(-0.551238\pi\)
−0.160274 + 0.987072i \(0.551238\pi\)
\(644\) 5.95775 0.234768
\(645\) −18.2726 −0.719482
\(646\) −6.50626 −0.255985
\(647\) −21.1450 −0.831295 −0.415648 0.909526i \(-0.636445\pi\)
−0.415648 + 0.909526i \(0.636445\pi\)
\(648\) −23.7914 −0.934613
\(649\) −2.07542 −0.0814672
\(650\) 6.38597 0.250478
\(651\) −31.4827 −1.23391
\(652\) 6.15575 0.241078
\(653\) 22.3846 0.875979 0.437989 0.898980i \(-0.355691\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(654\) 40.3998 1.57976
\(655\) −6.22084 −0.243068
\(656\) 8.32408 0.325001
\(657\) −90.3500 −3.52489
\(658\) −8.78196 −0.342356
\(659\) 24.2136 0.943228 0.471614 0.881805i \(-0.343671\pi\)
0.471614 + 0.881805i \(0.343671\pi\)
\(660\) −13.1067 −0.510178
\(661\) 29.3944 1.14331 0.571656 0.820494i \(-0.306301\pi\)
0.571656 + 0.820494i \(0.306301\pi\)
\(662\) −31.9632 −1.24228
\(663\) 15.0585 0.584822
\(664\) 7.89882 0.306534
\(665\) −4.93080 −0.191208
\(666\) −21.4384 −0.830722
\(667\) −42.1695 −1.63281
\(668\) 13.7924 0.533645
\(669\) 27.3966 1.05922
\(670\) 2.24969 0.0869130
\(671\) 30.0474 1.15997
\(672\) 3.22794 0.124520
\(673\) −43.0873 −1.66089 −0.830446 0.557099i \(-0.811914\pi\)
−0.830446 + 0.557099i \(0.811914\pi\)
\(674\) −18.6668 −0.719017
\(675\) 38.8701 1.49611
\(676\) −7.50669 −0.288719
\(677\) −22.7507 −0.874382 −0.437191 0.899369i \(-0.644027\pi\)
−0.437191 + 0.899369i \(0.644027\pi\)
\(678\) 42.0642 1.61547
\(679\) −12.8948 −0.494859
\(680\) 3.00236 0.115135
\(681\) −79.1108 −3.03153
\(682\) −26.2538 −1.00531
\(683\) 20.4017 0.780648 0.390324 0.920678i \(-0.372363\pi\)
0.390324 + 0.920678i \(0.372363\pi\)
\(684\) −24.2534 −0.927350
\(685\) −4.73861 −0.181053
\(686\) −1.00000 −0.0381802
\(687\) 75.2093 2.86941
\(688\) 3.75276 0.143072
\(689\) −7.90032 −0.300978
\(690\) 29.0090 1.10435
\(691\) 10.7276 0.408096 0.204048 0.978961i \(-0.434590\pi\)
0.204048 + 0.978961i \(0.434590\pi\)
\(692\) −21.6024 −0.821201
\(693\) 19.9721 0.758676
\(694\) 10.9018 0.413829
\(695\) −5.47544 −0.207695
\(696\) −22.8476 −0.866036
\(697\) −16.5682 −0.627564
\(698\) 28.8675 1.09265
\(699\) 1.09091 0.0412621
\(700\) −2.72464 −0.102982
\(701\) 44.5397 1.68224 0.841121 0.540847i \(-0.181896\pi\)
0.841121 + 0.540847i \(0.181896\pi\)
\(702\) 33.4366 1.26198
\(703\) −9.44510 −0.356229
\(704\) 2.69181 0.101451
\(705\) −42.7603 −1.61045
\(706\) −15.6173 −0.587764
\(707\) −15.7843 −0.593629
\(708\) 2.48878 0.0935340
\(709\) −4.98936 −0.187379 −0.0936896 0.995601i \(-0.529866\pi\)
−0.0936896 + 0.995601i \(0.529866\pi\)
\(710\) −22.4758 −0.843501
\(711\) 20.1295 0.754914
\(712\) −10.1594 −0.380741
\(713\) 58.1072 2.17613
\(714\) −6.42486 −0.240444
\(715\) 9.51669 0.355904
\(716\) 5.76165 0.215323
\(717\) 98.5019 3.67862
\(718\) −1.07679 −0.0401856
\(719\) −10.0762 −0.375778 −0.187889 0.982190i \(-0.560164\pi\)
−0.187889 + 0.982190i \(0.560164\pi\)
\(720\) 11.1919 0.417097
\(721\) −0.299389 −0.0111498
\(722\) 8.31473 0.309442
\(723\) 4.18002 0.155457
\(724\) −12.1495 −0.451531
\(725\) 19.2853 0.716237
\(726\) −12.1182 −0.449750
\(727\) −11.9306 −0.442482 −0.221241 0.975219i \(-0.571011\pi\)
−0.221241 + 0.975219i \(0.571011\pi\)
\(728\) −2.34378 −0.0868663
\(729\) 38.3715 1.42117
\(730\) 18.3685 0.679849
\(731\) −7.46945 −0.276268
\(732\) −36.0320 −1.33178
\(733\) 30.7298 1.13503 0.567516 0.823363i \(-0.307905\pi\)
0.567516 + 0.823363i \(0.307905\pi\)
\(734\) −2.73231 −0.100851
\(735\) −4.86911 −0.179600
\(736\) −5.95775 −0.219606
\(737\) −4.01459 −0.147879
\(738\) −61.7611 −2.27346
\(739\) −15.7916 −0.580902 −0.290451 0.956890i \(-0.593805\pi\)
−0.290451 + 0.956890i \(0.593805\pi\)
\(740\) 4.35851 0.160222
\(741\) 24.7306 0.908502
\(742\) 3.37076 0.123744
\(743\) 19.9736 0.732760 0.366380 0.930465i \(-0.380597\pi\)
0.366380 + 0.930465i \(0.380597\pi\)
\(744\) 31.4827 1.15421
\(745\) 15.7216 0.575993
\(746\) 31.8728 1.16694
\(747\) −58.6059 −2.14428
\(748\) −5.35775 −0.195899
\(749\) −0.402137 −0.0146938
\(750\) −37.6121 −1.37340
\(751\) −3.13621 −0.114442 −0.0572210 0.998362i \(-0.518224\pi\)
−0.0572210 + 0.998362i \(0.518224\pi\)
\(752\) 8.78196 0.320245
\(753\) 79.2919 2.88956
\(754\) 16.5895 0.604154
\(755\) 22.1246 0.805195
\(756\) −14.2661 −0.518853
\(757\) −13.0861 −0.475624 −0.237812 0.971311i \(-0.576430\pi\)
−0.237812 + 0.971311i \(0.576430\pi\)
\(758\) −33.5657 −1.21916
\(759\) −51.7668 −1.87902
\(760\) 4.93080 0.178859
\(761\) 20.9009 0.757658 0.378829 0.925467i \(-0.376327\pi\)
0.378829 + 0.925467i \(0.376327\pi\)
\(762\) −23.3699 −0.846602
\(763\) 12.5157 0.453098
\(764\) 3.57067 0.129182
\(765\) −22.2763 −0.805400
\(766\) −29.1282 −1.05244
\(767\) −1.80708 −0.0652500
\(768\) −3.22794 −0.116478
\(769\) 15.3750 0.554436 0.277218 0.960807i \(-0.410588\pi\)
0.277218 + 0.960807i \(0.410588\pi\)
\(770\) −4.06040 −0.146327
\(771\) 84.5371 3.04453
\(772\) 1.06836 0.0384510
\(773\) −0.368057 −0.0132381 −0.00661905 0.999978i \(-0.502107\pi\)
−0.00661905 + 0.999978i \(0.502107\pi\)
\(774\) −27.8438 −1.00083
\(775\) −26.5740 −0.954567
\(776\) 12.8948 0.462898
\(777\) −9.32693 −0.334602
\(778\) −23.5239 −0.843373
\(779\) −27.2100 −0.974900
\(780\) −11.4121 −0.408620
\(781\) 40.1083 1.43519
\(782\) 11.8583 0.424051
\(783\) 100.977 3.60861
\(784\) 1.00000 0.0357143
\(785\) 11.4540 0.408810
\(786\) −13.3122 −0.474830
\(787\) 17.1667 0.611928 0.305964 0.952043i \(-0.401021\pi\)
0.305964 + 0.952043i \(0.401021\pi\)
\(788\) 0.859221 0.0306085
\(789\) −0.896595 −0.0319196
\(790\) −4.09240 −0.145601
\(791\) 13.0313 0.463340
\(792\) −19.9721 −0.709676
\(793\) 26.1626 0.929061
\(794\) 19.2102 0.681744
\(795\) 16.4126 0.582094
\(796\) −1.00002 −0.0354448
\(797\) 45.2551 1.60302 0.801508 0.597984i \(-0.204031\pi\)
0.801508 + 0.597984i \(0.204031\pi\)
\(798\) −10.5516 −0.373522
\(799\) −17.4795 −0.618382
\(800\) 2.72464 0.0963307
\(801\) 75.3787 2.66338
\(802\) −28.4563 −1.00483
\(803\) −32.7788 −1.15674
\(804\) 4.81418 0.169783
\(805\) 8.98684 0.316745
\(806\) −22.8594 −0.805188
\(807\) −81.0686 −2.85375
\(808\) 15.7843 0.555289
\(809\) 6.78879 0.238681 0.119341 0.992853i \(-0.461922\pi\)
0.119341 + 0.992853i \(0.461922\pi\)
\(810\) −35.8875 −1.26096
\(811\) −0.0664774 −0.00233434 −0.00116717 0.999999i \(-0.500372\pi\)
−0.00116717 + 0.999999i \(0.500372\pi\)
\(812\) −7.07809 −0.248392
\(813\) 58.3314 2.04577
\(814\) −7.77782 −0.272612
\(815\) 9.28550 0.325257
\(816\) 6.42486 0.224915
\(817\) −12.2671 −0.429173
\(818\) −30.0035 −1.04905
\(819\) 17.3899 0.607651
\(820\) 12.5563 0.438484
\(821\) 6.30860 0.220172 0.110086 0.993922i \(-0.464887\pi\)
0.110086 + 0.993922i \(0.464887\pi\)
\(822\) −10.1403 −0.353684
\(823\) −12.2833 −0.428169 −0.214084 0.976815i \(-0.568677\pi\)
−0.214084 + 0.976815i \(0.568677\pi\)
\(824\) 0.299389 0.0104297
\(825\) 23.6744 0.824237
\(826\) 0.771012 0.0268269
\(827\) −20.1290 −0.699954 −0.349977 0.936758i \(-0.613811\pi\)
−0.349977 + 0.936758i \(0.613811\pi\)
\(828\) 44.2040 1.53619
\(829\) −16.0295 −0.556728 −0.278364 0.960476i \(-0.589792\pi\)
−0.278364 + 0.960476i \(0.589792\pi\)
\(830\) 11.9148 0.413569
\(831\) −59.1582 −2.05218
\(832\) 2.34378 0.0812560
\(833\) −1.99039 −0.0689630
\(834\) −11.7171 −0.405730
\(835\) 20.8049 0.719982
\(836\) −8.79907 −0.304322
\(837\) −139.140 −4.80939
\(838\) −8.81082 −0.304365
\(839\) 35.4121 1.22256 0.611280 0.791414i \(-0.290655\pi\)
0.611280 + 0.791414i \(0.290655\pi\)
\(840\) 4.86911 0.168000
\(841\) 21.0993 0.727562
\(842\) 12.3383 0.425206
\(843\) −35.9313 −1.23754
\(844\) 22.3911 0.770733
\(845\) −11.3233 −0.389533
\(846\) −65.1584 −2.24019
\(847\) −3.75417 −0.128995
\(848\) −3.37076 −0.115752
\(849\) 54.2740 1.86268
\(850\) −5.42311 −0.186011
\(851\) 17.2146 0.590108
\(852\) −48.0967 −1.64776
\(853\) 23.1897 0.794000 0.397000 0.917819i \(-0.370051\pi\)
0.397000 + 0.917819i \(0.370051\pi\)
\(854\) −11.1625 −0.381975
\(855\) −36.5844 −1.25116
\(856\) 0.402137 0.0137448
\(857\) 32.6339 1.11475 0.557377 0.830260i \(-0.311808\pi\)
0.557377 + 0.830260i \(0.311808\pi\)
\(858\) 20.3651 0.695253
\(859\) 51.3605 1.75240 0.876199 0.481950i \(-0.160071\pi\)
0.876199 + 0.481950i \(0.160071\pi\)
\(860\) 5.66076 0.193030
\(861\) −26.8696 −0.915713
\(862\) 1.00000 0.0340601
\(863\) −29.2470 −0.995579 −0.497789 0.867298i \(-0.665855\pi\)
−0.497789 + 0.867298i \(0.665855\pi\)
\(864\) 14.2661 0.485343
\(865\) −32.5857 −1.10795
\(866\) 33.2119 1.12859
\(867\) 42.0869 1.42935
\(868\) 9.75321 0.331045
\(869\) 7.30294 0.247735
\(870\) −34.4640 −1.16844
\(871\) −3.49554 −0.118442
\(872\) −12.5157 −0.423834
\(873\) −95.6743 −3.23808
\(874\) 19.4749 0.658748
\(875\) −11.6521 −0.393912
\(876\) 39.3074 1.32807
\(877\) −34.8175 −1.17571 −0.587853 0.808968i \(-0.700026\pi\)
−0.587853 + 0.808968i \(0.700026\pi\)
\(878\) −32.5701 −1.09919
\(879\) 38.9526 1.31384
\(880\) 4.06040 0.136876
\(881\) 50.2851 1.69415 0.847074 0.531475i \(-0.178362\pi\)
0.847074 + 0.531475i \(0.178362\pi\)
\(882\) −7.41957 −0.249830
\(883\) −27.8694 −0.937879 −0.468940 0.883230i \(-0.655364\pi\)
−0.468940 + 0.883230i \(0.655364\pi\)
\(884\) −4.66504 −0.156902
\(885\) 3.75414 0.126194
\(886\) −13.5122 −0.453951
\(887\) −2.43896 −0.0818923 −0.0409461 0.999161i \(-0.513037\pi\)
−0.0409461 + 0.999161i \(0.513037\pi\)
\(888\) 9.32693 0.312991
\(889\) −7.23989 −0.242818
\(890\) −15.3248 −0.513688
\(891\) 64.0418 2.14548
\(892\) −8.48735 −0.284178
\(893\) −28.7068 −0.960635
\(894\) 33.6431 1.12519
\(895\) 8.69104 0.290509
\(896\) −1.00000 −0.0334077
\(897\) −45.0738 −1.50497
\(898\) 35.3651 1.18015
\(899\) −69.0340 −2.30241
\(900\) −20.2157 −0.673857
\(901\) 6.70913 0.223513
\(902\) −22.4068 −0.746065
\(903\) −12.1137 −0.403117
\(904\) −13.0313 −0.433415
\(905\) −18.3266 −0.609196
\(906\) 47.3451 1.57294
\(907\) 20.2124 0.671140 0.335570 0.942015i \(-0.391071\pi\)
0.335570 + 0.942015i \(0.391071\pi\)
\(908\) 24.5082 0.813332
\(909\) −117.113 −3.88438
\(910\) −3.53543 −0.117198
\(911\) 20.5060 0.679394 0.339697 0.940535i \(-0.389675\pi\)
0.339697 + 0.940535i \(0.389675\pi\)
\(912\) 10.5516 0.349398
\(913\) −21.2621 −0.703673
\(914\) −17.9663 −0.594273
\(915\) −54.3517 −1.79681
\(916\) −23.2995 −0.769837
\(917\) −4.12405 −0.136188
\(918\) −28.3951 −0.937179
\(919\) 2.76912 0.0913448 0.0456724 0.998956i \(-0.485457\pi\)
0.0456724 + 0.998956i \(0.485457\pi\)
\(920\) −8.98684 −0.296287
\(921\) 32.7596 1.07947
\(922\) −4.93636 −0.162570
\(923\) 34.9227 1.14949
\(924\) −8.68898 −0.285847
\(925\) −7.87270 −0.258853
\(926\) 26.3298 0.865250
\(927\) −2.22134 −0.0729583
\(928\) 7.07809 0.232350
\(929\) 38.6933 1.26949 0.634743 0.772724i \(-0.281106\pi\)
0.634743 + 0.772724i \(0.281106\pi\)
\(930\) 47.4894 1.55724
\(931\) −3.26883 −0.107132
\(932\) −0.337960 −0.0110703
\(933\) −9.42154 −0.308447
\(934\) 16.2673 0.532284
\(935\) −8.08178 −0.264303
\(936\) −17.3899 −0.568405
\(937\) −47.2698 −1.54424 −0.772119 0.635478i \(-0.780803\pi\)
−0.772119 + 0.635478i \(0.780803\pi\)
\(938\) 1.49141 0.0486963
\(939\) −91.5922 −2.98900
\(940\) 13.2470 0.432068
\(941\) 43.8583 1.42974 0.714869 0.699258i \(-0.246486\pi\)
0.714869 + 0.699258i \(0.246486\pi\)
\(942\) 24.5108 0.798604
\(943\) 49.5928 1.61496
\(944\) −0.771012 −0.0250943
\(945\) −21.5194 −0.700026
\(946\) −10.1017 −0.328435
\(947\) −10.1254 −0.329032 −0.164516 0.986374i \(-0.552606\pi\)
−0.164516 + 0.986374i \(0.552606\pi\)
\(948\) −8.75747 −0.284429
\(949\) −28.5408 −0.926475
\(950\) −8.90641 −0.288962
\(951\) −55.6675 −1.80514
\(952\) 1.99039 0.0645090
\(953\) −18.5160 −0.599790 −0.299895 0.953972i \(-0.596952\pi\)
−0.299895 + 0.953972i \(0.596952\pi\)
\(954\) 25.0096 0.809715
\(955\) 5.38611 0.174290
\(956\) −30.5154 −0.986940
\(957\) 61.5014 1.98806
\(958\) 21.2767 0.687418
\(959\) −3.14143 −0.101442
\(960\) −4.86911 −0.157150
\(961\) 64.1251 2.06855
\(962\) −6.77222 −0.218345
\(963\) −2.98368 −0.0961479
\(964\) −1.29495 −0.0417076
\(965\) 1.61154 0.0518772
\(966\) 19.2312 0.618755
\(967\) −8.85459 −0.284744 −0.142372 0.989813i \(-0.545473\pi\)
−0.142372 + 0.989813i \(0.545473\pi\)
\(968\) 3.75417 0.120664
\(969\) −21.0018 −0.674675
\(970\) 19.4509 0.624532
\(971\) −34.8884 −1.11962 −0.559811 0.828620i \(-0.689126\pi\)
−0.559811 + 0.828620i \(0.689126\pi\)
\(972\) −33.9987 −1.09051
\(973\) −3.62990 −0.116369
\(974\) −5.98714 −0.191840
\(975\) 20.6135 0.660161
\(976\) 11.1625 0.357305
\(977\) 7.99558 0.255801 0.127901 0.991787i \(-0.459176\pi\)
0.127901 + 0.991787i \(0.459176\pi\)
\(978\) 19.8704 0.635384
\(979\) 27.3473 0.874022
\(980\) 1.50843 0.0481850
\(981\) 92.8609 2.96482
\(982\) −36.4413 −1.16289
\(983\) −43.1930 −1.37764 −0.688822 0.724931i \(-0.741872\pi\)
−0.688822 + 0.724931i \(0.741872\pi\)
\(984\) 26.8696 0.856571
\(985\) 1.29607 0.0412963
\(986\) −14.0882 −0.448658
\(987\) −28.3476 −0.902314
\(988\) −7.66143 −0.243743
\(989\) 22.3580 0.710943
\(990\) −30.1264 −0.957481
\(991\) 1.25519 0.0398723 0.0199362 0.999801i \(-0.493654\pi\)
0.0199362 + 0.999801i \(0.493654\pi\)
\(992\) −9.75321 −0.309665
\(993\) −103.175 −3.27416
\(994\) −14.9001 −0.472603
\(995\) −1.50846 −0.0478214
\(996\) 25.4969 0.807900
\(997\) −17.6419 −0.558725 −0.279362 0.960186i \(-0.590123\pi\)
−0.279362 + 0.960186i \(0.590123\pi\)
\(998\) −6.63243 −0.209946
\(999\) −41.2211 −1.30418
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 6034.2.a.p.1.1 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6034.2.a.p.1.1 27 1.1 even 1 trivial