Properties

Label 6005.2.a.g.1.17
Level $6005$
Weight $2$
Character 6005.1
Self dual yes
Analytic conductor $47.950$
Analytic rank $0$
Dimension $113$
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] = [6005,2,Mod(1,6005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6005, 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("6005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6005 = 5 \cdot 1201 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6005.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: \(47.9501664138\)
Analytic rank: \(0\)
Dimension: \(113\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 6005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.18171 q^{2} +2.09909 q^{3} +2.75987 q^{4} -1.00000 q^{5} -4.57961 q^{6} -2.68153 q^{7} -1.65781 q^{8} +1.40617 q^{9} +O(q^{10})\) \(q-2.18171 q^{2} +2.09909 q^{3} +2.75987 q^{4} -1.00000 q^{5} -4.57961 q^{6} -2.68153 q^{7} -1.65781 q^{8} +1.40617 q^{9} +2.18171 q^{10} +0.412490 q^{11} +5.79321 q^{12} +1.83522 q^{13} +5.85033 q^{14} -2.09909 q^{15} -1.90287 q^{16} +0.163414 q^{17} -3.06786 q^{18} +7.14152 q^{19} -2.75987 q^{20} -5.62877 q^{21} -0.899935 q^{22} -5.22422 q^{23} -3.47990 q^{24} +1.00000 q^{25} -4.00392 q^{26} -3.34559 q^{27} -7.40067 q^{28} +9.21346 q^{29} +4.57961 q^{30} -10.6409 q^{31} +7.46713 q^{32} +0.865853 q^{33} -0.356523 q^{34} +2.68153 q^{35} +3.88085 q^{36} +1.57980 q^{37} -15.5807 q^{38} +3.85229 q^{39} +1.65781 q^{40} +7.59348 q^{41} +12.2804 q^{42} -9.07160 q^{43} +1.13842 q^{44} -1.40617 q^{45} +11.3977 q^{46} -1.76996 q^{47} -3.99428 q^{48} +0.190616 q^{49} -2.18171 q^{50} +0.343021 q^{51} +5.06496 q^{52} -3.12694 q^{53} +7.29911 q^{54} -0.412490 q^{55} +4.44548 q^{56} +14.9907 q^{57} -20.1011 q^{58} +5.64814 q^{59} -5.79321 q^{60} +12.9160 q^{61} +23.2154 q^{62} -3.77069 q^{63} -12.4854 q^{64} -1.83522 q^{65} -1.88904 q^{66} +9.28256 q^{67} +0.451002 q^{68} -10.9661 q^{69} -5.85033 q^{70} -10.2797 q^{71} -2.33117 q^{72} +8.34284 q^{73} -3.44667 q^{74} +2.09909 q^{75} +19.7096 q^{76} -1.10611 q^{77} -8.40458 q^{78} +7.62559 q^{79} +1.90287 q^{80} -11.2412 q^{81} -16.5668 q^{82} +0.362022 q^{83} -15.5347 q^{84} -0.163414 q^{85} +19.7916 q^{86} +19.3399 q^{87} -0.683831 q^{88} -11.2820 q^{89} +3.06786 q^{90} -4.92120 q^{91} -14.4181 q^{92} -22.3362 q^{93} +3.86154 q^{94} -7.14152 q^{95} +15.6742 q^{96} -4.67679 q^{97} -0.415869 q^{98} +0.580032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.18171 −1.54270 −0.771352 0.636409i \(-0.780419\pi\)
−0.771352 + 0.636409i \(0.780419\pi\)
\(3\) 2.09909 1.21191 0.605955 0.795499i \(-0.292791\pi\)
0.605955 + 0.795499i \(0.292791\pi\)
\(4\) 2.75987 1.37993
\(5\) −1.00000 −0.447214
\(6\) −4.57961 −1.86962
\(7\) −2.68153 −1.01352 −0.506762 0.862086i \(-0.669158\pi\)
−0.506762 + 0.862086i \(0.669158\pi\)
\(8\) −1.65781 −0.586125
\(9\) 1.40617 0.468724
\(10\) 2.18171 0.689918
\(11\) 0.412490 0.124370 0.0621852 0.998065i \(-0.480193\pi\)
0.0621852 + 0.998065i \(0.480193\pi\)
\(12\) 5.79321 1.67235
\(13\) 1.83522 0.508998 0.254499 0.967073i \(-0.418089\pi\)
0.254499 + 0.967073i \(0.418089\pi\)
\(14\) 5.85033 1.56357
\(15\) −2.09909 −0.541982
\(16\) −1.90287 −0.475716
\(17\) 0.163414 0.0396338 0.0198169 0.999804i \(-0.493692\pi\)
0.0198169 + 0.999804i \(0.493692\pi\)
\(18\) −3.06786 −0.723102
\(19\) 7.14152 1.63838 0.819188 0.573525i \(-0.194425\pi\)
0.819188 + 0.573525i \(0.194425\pi\)
\(20\) −2.75987 −0.617125
\(21\) −5.62877 −1.22830
\(22\) −0.899935 −0.191867
\(23\) −5.22422 −1.08932 −0.544662 0.838655i \(-0.683342\pi\)
−0.544662 + 0.838655i \(0.683342\pi\)
\(24\) −3.47990 −0.710331
\(25\) 1.00000 0.200000
\(26\) −4.00392 −0.785233
\(27\) −3.34559 −0.643858
\(28\) −7.40067 −1.39860
\(29\) 9.21346 1.71090 0.855448 0.517888i \(-0.173282\pi\)
0.855448 + 0.517888i \(0.173282\pi\)
\(30\) 4.57961 0.836118
\(31\) −10.6409 −1.91117 −0.955583 0.294722i \(-0.904773\pi\)
−0.955583 + 0.294722i \(0.904773\pi\)
\(32\) 7.46713 1.32001
\(33\) 0.865853 0.150726
\(34\) −0.356523 −0.0611431
\(35\) 2.68153 0.453262
\(36\) 3.88085 0.646808
\(37\) 1.57980 0.259718 0.129859 0.991532i \(-0.458548\pi\)
0.129859 + 0.991532i \(0.458548\pi\)
\(38\) −15.5807 −2.52753
\(39\) 3.85229 0.616860
\(40\) 1.65781 0.262123
\(41\) 7.59348 1.18590 0.592951 0.805239i \(-0.297963\pi\)
0.592951 + 0.805239i \(0.297963\pi\)
\(42\) 12.2804 1.89490
\(43\) −9.07160 −1.38341 −0.691703 0.722182i \(-0.743139\pi\)
−0.691703 + 0.722182i \(0.743139\pi\)
\(44\) 1.13842 0.171623
\(45\) −1.40617 −0.209620
\(46\) 11.3977 1.68050
\(47\) −1.76996 −0.258175 −0.129087 0.991633i \(-0.541205\pi\)
−0.129087 + 0.991633i \(0.541205\pi\)
\(48\) −3.99428 −0.576525
\(49\) 0.190616 0.0272309
\(50\) −2.18171 −0.308541
\(51\) 0.343021 0.0480325
\(52\) 5.06496 0.702384
\(53\) −3.12694 −0.429519 −0.214759 0.976667i \(-0.568897\pi\)
−0.214759 + 0.976667i \(0.568897\pi\)
\(54\) 7.29911 0.993283
\(55\) −0.412490 −0.0556202
\(56\) 4.44548 0.594052
\(57\) 14.9907 1.98556
\(58\) −20.1011 −2.63941
\(59\) 5.64814 0.735325 0.367663 0.929959i \(-0.380158\pi\)
0.367663 + 0.929959i \(0.380158\pi\)
\(60\) −5.79321 −0.747900
\(61\) 12.9160 1.65372 0.826862 0.562404i \(-0.190124\pi\)
0.826862 + 0.562404i \(0.190124\pi\)
\(62\) 23.2154 2.94836
\(63\) −3.77069 −0.475063
\(64\) −12.4854 −1.56067
\(65\) −1.83522 −0.227631
\(66\) −1.88904 −0.232525
\(67\) 9.28256 1.13405 0.567023 0.823702i \(-0.308095\pi\)
0.567023 + 0.823702i \(0.308095\pi\)
\(68\) 0.451002 0.0546920
\(69\) −10.9661 −1.32016
\(70\) −5.85033 −0.699248
\(71\) −10.2797 −1.21998 −0.609991 0.792409i \(-0.708827\pi\)
−0.609991 + 0.792409i \(0.708827\pi\)
\(72\) −2.33117 −0.274731
\(73\) 8.34284 0.976456 0.488228 0.872716i \(-0.337644\pi\)
0.488228 + 0.872716i \(0.337644\pi\)
\(74\) −3.44667 −0.400668
\(75\) 2.09909 0.242382
\(76\) 19.7096 2.26085
\(77\) −1.10611 −0.126052
\(78\) −8.40458 −0.951632
\(79\) 7.62559 0.857946 0.428973 0.903317i \(-0.358875\pi\)
0.428973 + 0.903317i \(0.358875\pi\)
\(80\) 1.90287 0.212747
\(81\) −11.2412 −1.24902
\(82\) −16.5668 −1.82950
\(83\) 0.362022 0.0397371 0.0198685 0.999803i \(-0.493675\pi\)
0.0198685 + 0.999803i \(0.493675\pi\)
\(84\) −15.5347 −1.69497
\(85\) −0.163414 −0.0177248
\(86\) 19.7916 2.13418
\(87\) 19.3399 2.07345
\(88\) −0.683831 −0.0728967
\(89\) −11.2820 −1.19589 −0.597944 0.801538i \(-0.704015\pi\)
−0.597944 + 0.801538i \(0.704015\pi\)
\(90\) 3.06786 0.323381
\(91\) −4.92120 −0.515882
\(92\) −14.4181 −1.50320
\(93\) −22.3362 −2.31616
\(94\) 3.86154 0.398287
\(95\) −7.14152 −0.732704
\(96\) 15.6742 1.59974
\(97\) −4.67679 −0.474857 −0.237428 0.971405i \(-0.576304\pi\)
−0.237428 + 0.971405i \(0.576304\pi\)
\(98\) −0.415869 −0.0420091
\(99\) 0.580032 0.0582954
\(100\) 2.75987 0.275987
\(101\) −6.74742 −0.671393 −0.335697 0.941970i \(-0.608972\pi\)
−0.335697 + 0.941970i \(0.608972\pi\)
\(102\) −0.748373 −0.0740999
\(103\) 15.0154 1.47951 0.739755 0.672877i \(-0.234941\pi\)
0.739755 + 0.672877i \(0.234941\pi\)
\(104\) −3.04245 −0.298337
\(105\) 5.62877 0.549312
\(106\) 6.82209 0.662620
\(107\) −4.82653 −0.466598 −0.233299 0.972405i \(-0.574952\pi\)
−0.233299 + 0.972405i \(0.574952\pi\)
\(108\) −9.23338 −0.888482
\(109\) 5.54853 0.531453 0.265726 0.964048i \(-0.414388\pi\)
0.265726 + 0.964048i \(0.414388\pi\)
\(110\) 0.899935 0.0858054
\(111\) 3.31614 0.314754
\(112\) 5.10260 0.482150
\(113\) 7.99808 0.752396 0.376198 0.926539i \(-0.377231\pi\)
0.376198 + 0.926539i \(0.377231\pi\)
\(114\) −32.7053 −3.06313
\(115\) 5.22422 0.487161
\(116\) 25.4279 2.36092
\(117\) 2.58063 0.238580
\(118\) −12.3226 −1.13439
\(119\) −0.438200 −0.0401698
\(120\) 3.47990 0.317670
\(121\) −10.8299 −0.984532
\(122\) −28.1790 −2.55121
\(123\) 15.9394 1.43721
\(124\) −29.3675 −2.63728
\(125\) −1.00000 −0.0894427
\(126\) 8.22657 0.732881
\(127\) −6.13550 −0.544438 −0.272219 0.962235i \(-0.587757\pi\)
−0.272219 + 0.962235i \(0.587757\pi\)
\(128\) 12.3053 1.08764
\(129\) −19.0421 −1.67656
\(130\) 4.00392 0.351167
\(131\) 0.575780 0.0503061 0.0251530 0.999684i \(-0.491993\pi\)
0.0251530 + 0.999684i \(0.491993\pi\)
\(132\) 2.38964 0.207991
\(133\) −19.1502 −1.66053
\(134\) −20.2519 −1.74950
\(135\) 3.34559 0.287942
\(136\) −0.270910 −0.0232303
\(137\) −10.5516 −0.901482 −0.450741 0.892655i \(-0.648840\pi\)
−0.450741 + 0.892655i \(0.648840\pi\)
\(138\) 23.9249 2.03662
\(139\) 12.2636 1.04019 0.520093 0.854110i \(-0.325897\pi\)
0.520093 + 0.854110i \(0.325897\pi\)
\(140\) 7.40067 0.625471
\(141\) −3.71530 −0.312884
\(142\) 22.4274 1.88207
\(143\) 0.757010 0.0633043
\(144\) −2.67576 −0.222980
\(145\) −9.21346 −0.765136
\(146\) −18.2017 −1.50638
\(147\) 0.400120 0.0330013
\(148\) 4.36004 0.358393
\(149\) −15.6300 −1.28046 −0.640228 0.768185i \(-0.721160\pi\)
−0.640228 + 0.768185i \(0.721160\pi\)
\(150\) −4.57961 −0.373923
\(151\) 15.7045 1.27802 0.639008 0.769200i \(-0.279345\pi\)
0.639008 + 0.769200i \(0.279345\pi\)
\(152\) −11.8393 −0.960294
\(153\) 0.229788 0.0185773
\(154\) 2.41320 0.194462
\(155\) 10.6409 0.854700
\(156\) 10.6318 0.851226
\(157\) −14.0678 −1.12273 −0.561364 0.827569i \(-0.689723\pi\)
−0.561364 + 0.827569i \(0.689723\pi\)
\(158\) −16.6369 −1.32356
\(159\) −6.56373 −0.520538
\(160\) −7.46713 −0.590328
\(161\) 14.0089 1.10406
\(162\) 24.5251 1.92687
\(163\) 23.4405 1.83600 0.918001 0.396578i \(-0.129803\pi\)
0.918001 + 0.396578i \(0.129803\pi\)
\(164\) 20.9570 1.63647
\(165\) −0.865853 −0.0674066
\(166\) −0.789828 −0.0613025
\(167\) 20.0398 1.55073 0.775364 0.631515i \(-0.217566\pi\)
0.775364 + 0.631515i \(0.217566\pi\)
\(168\) 9.33145 0.719937
\(169\) −9.63197 −0.740921
\(170\) 0.356523 0.0273440
\(171\) 10.0422 0.767946
\(172\) −25.0364 −1.90901
\(173\) −1.17842 −0.0895934 −0.0447967 0.998996i \(-0.514264\pi\)
−0.0447967 + 0.998996i \(0.514264\pi\)
\(174\) −42.1940 −3.19872
\(175\) −2.68153 −0.202705
\(176\) −0.784913 −0.0591651
\(177\) 11.8559 0.891147
\(178\) 24.6140 1.84490
\(179\) 25.7489 1.92456 0.962281 0.272057i \(-0.0877040\pi\)
0.962281 + 0.272057i \(0.0877040\pi\)
\(180\) −3.88085 −0.289261
\(181\) 10.0896 0.749951 0.374976 0.927035i \(-0.377651\pi\)
0.374976 + 0.927035i \(0.377651\pi\)
\(182\) 10.7366 0.795853
\(183\) 27.1118 2.00416
\(184\) 8.66077 0.638481
\(185\) −1.57980 −0.116149
\(186\) 48.7312 3.57315
\(187\) 0.0674067 0.00492927
\(188\) −4.88485 −0.356264
\(189\) 8.97130 0.652566
\(190\) 15.5807 1.13034
\(191\) 0.850433 0.0615352 0.0307676 0.999527i \(-0.490205\pi\)
0.0307676 + 0.999527i \(0.490205\pi\)
\(192\) −26.2080 −1.89140
\(193\) −9.89347 −0.712148 −0.356074 0.934458i \(-0.615885\pi\)
−0.356074 + 0.934458i \(0.615885\pi\)
\(194\) 10.2034 0.732563
\(195\) −3.85229 −0.275868
\(196\) 0.526075 0.0375768
\(197\) −3.85789 −0.274863 −0.137431 0.990511i \(-0.543885\pi\)
−0.137431 + 0.990511i \(0.543885\pi\)
\(198\) −1.26546 −0.0899325
\(199\) 15.0938 1.06997 0.534985 0.844861i \(-0.320317\pi\)
0.534985 + 0.844861i \(0.320317\pi\)
\(200\) −1.65781 −0.117225
\(201\) 19.4849 1.37436
\(202\) 14.7209 1.03576
\(203\) −24.7062 −1.73403
\(204\) 0.946692 0.0662817
\(205\) −7.59348 −0.530352
\(206\) −32.7592 −2.28244
\(207\) −7.34614 −0.510592
\(208\) −3.49218 −0.242139
\(209\) 2.94580 0.203766
\(210\) −12.2804 −0.847426
\(211\) −0.645352 −0.0444279 −0.0222139 0.999753i \(-0.507071\pi\)
−0.0222139 + 0.999753i \(0.507071\pi\)
\(212\) −8.62995 −0.592708
\(213\) −21.5781 −1.47851
\(214\) 10.5301 0.719823
\(215\) 9.07160 0.618678
\(216\) 5.54636 0.377382
\(217\) 28.5340 1.93701
\(218\) −12.1053 −0.819874
\(219\) 17.5124 1.18338
\(220\) −1.13842 −0.0767521
\(221\) 0.299901 0.0201735
\(222\) −7.23487 −0.485573
\(223\) −7.35555 −0.492564 −0.246282 0.969198i \(-0.579209\pi\)
−0.246282 + 0.969198i \(0.579209\pi\)
\(224\) −20.0234 −1.33787
\(225\) 1.40617 0.0937448
\(226\) −17.4495 −1.16072
\(227\) 10.3846 0.689252 0.344626 0.938740i \(-0.388006\pi\)
0.344626 + 0.938740i \(0.388006\pi\)
\(228\) 41.3723 2.73995
\(229\) 21.5471 1.42387 0.711937 0.702243i \(-0.247818\pi\)
0.711937 + 0.702243i \(0.247818\pi\)
\(230\) −11.3977 −0.751545
\(231\) −2.32181 −0.152764
\(232\) −15.2742 −1.00280
\(233\) −1.63338 −0.107006 −0.0535032 0.998568i \(-0.517039\pi\)
−0.0535032 + 0.998568i \(0.517039\pi\)
\(234\) −5.63020 −0.368058
\(235\) 1.76996 0.115459
\(236\) 15.5881 1.01470
\(237\) 16.0068 1.03975
\(238\) 0.956027 0.0619700
\(239\) −7.92983 −0.512938 −0.256469 0.966552i \(-0.582559\pi\)
−0.256469 + 0.966552i \(0.582559\pi\)
\(240\) 3.99428 0.257830
\(241\) 23.5440 1.51660 0.758301 0.651905i \(-0.226030\pi\)
0.758301 + 0.651905i \(0.226030\pi\)
\(242\) 23.6276 1.51884
\(243\) −13.5595 −0.869842
\(244\) 35.6465 2.28203
\(245\) −0.190616 −0.0121780
\(246\) −34.7751 −2.21718
\(247\) 13.1062 0.833931
\(248\) 17.6407 1.12018
\(249\) 0.759916 0.0481577
\(250\) 2.18171 0.137984
\(251\) 31.2993 1.97559 0.987796 0.155756i \(-0.0497813\pi\)
0.987796 + 0.155756i \(0.0497813\pi\)
\(252\) −10.4066 −0.655555
\(253\) −2.15494 −0.135480
\(254\) 13.3859 0.839906
\(255\) −0.343021 −0.0214808
\(256\) −1.87579 −0.117237
\(257\) 13.7076 0.855058 0.427529 0.904002i \(-0.359384\pi\)
0.427529 + 0.904002i \(0.359384\pi\)
\(258\) 41.5444 2.58644
\(259\) −4.23629 −0.263230
\(260\) −5.06496 −0.314116
\(261\) 12.9557 0.801938
\(262\) −1.25619 −0.0776074
\(263\) 2.12966 0.131320 0.0656602 0.997842i \(-0.479085\pi\)
0.0656602 + 0.997842i \(0.479085\pi\)
\(264\) −1.43542 −0.0883441
\(265\) 3.12694 0.192087
\(266\) 41.7802 2.56171
\(267\) −23.6819 −1.44931
\(268\) 25.6186 1.56491
\(269\) 4.65888 0.284057 0.142028 0.989863i \(-0.454638\pi\)
0.142028 + 0.989863i \(0.454638\pi\)
\(270\) −7.29911 −0.444210
\(271\) 12.4820 0.758226 0.379113 0.925350i \(-0.376229\pi\)
0.379113 + 0.925350i \(0.376229\pi\)
\(272\) −0.310955 −0.0188544
\(273\) −10.3300 −0.625202
\(274\) 23.0205 1.39072
\(275\) 0.412490 0.0248741
\(276\) −30.2650 −1.82174
\(277\) 4.72817 0.284088 0.142044 0.989860i \(-0.454633\pi\)
0.142044 + 0.989860i \(0.454633\pi\)
\(278\) −26.7556 −1.60470
\(279\) −14.9630 −0.895809
\(280\) −4.44548 −0.265668
\(281\) −8.04840 −0.480127 −0.240064 0.970757i \(-0.577168\pi\)
−0.240064 + 0.970757i \(0.577168\pi\)
\(282\) 8.10571 0.482688
\(283\) 17.8203 1.05931 0.529653 0.848214i \(-0.322322\pi\)
0.529653 + 0.848214i \(0.322322\pi\)
\(284\) −28.3707 −1.68349
\(285\) −14.9907 −0.887971
\(286\) −1.65158 −0.0976598
\(287\) −20.3622 −1.20194
\(288\) 10.5001 0.618722
\(289\) −16.9733 −0.998429
\(290\) 20.1011 1.18038
\(291\) −9.81700 −0.575483
\(292\) 23.0251 1.34744
\(293\) −10.4735 −0.611867 −0.305933 0.952053i \(-0.598968\pi\)
−0.305933 + 0.952053i \(0.598968\pi\)
\(294\) −0.872946 −0.0509113
\(295\) −5.64814 −0.328847
\(296\) −2.61902 −0.152227
\(297\) −1.38002 −0.0800770
\(298\) 34.1001 1.97536
\(299\) −9.58758 −0.554464
\(300\) 5.79321 0.334471
\(301\) 24.3258 1.40212
\(302\) −34.2628 −1.97160
\(303\) −14.1634 −0.813667
\(304\) −13.5893 −0.779402
\(305\) −12.9160 −0.739568
\(306\) −0.501332 −0.0286592
\(307\) 8.10659 0.462668 0.231334 0.972874i \(-0.425691\pi\)
0.231334 + 0.972874i \(0.425691\pi\)
\(308\) −3.05271 −0.173944
\(309\) 31.5186 1.79303
\(310\) −23.2154 −1.31855
\(311\) 10.3454 0.586634 0.293317 0.956015i \(-0.405241\pi\)
0.293317 + 0.956015i \(0.405241\pi\)
\(312\) −6.38637 −0.361557
\(313\) 16.5124 0.933338 0.466669 0.884432i \(-0.345454\pi\)
0.466669 + 0.884432i \(0.345454\pi\)
\(314\) 30.6918 1.73204
\(315\) 3.77069 0.212455
\(316\) 21.0456 1.18391
\(317\) −7.75811 −0.435739 −0.217869 0.975978i \(-0.569911\pi\)
−0.217869 + 0.975978i \(0.569911\pi\)
\(318\) 14.3202 0.803035
\(319\) 3.80046 0.212785
\(320\) 12.4854 0.697955
\(321\) −10.1313 −0.565475
\(322\) −30.5634 −1.70323
\(323\) 1.16702 0.0649350
\(324\) −31.0242 −1.72357
\(325\) 1.83522 0.101800
\(326\) −51.1404 −2.83241
\(327\) 11.6469 0.644073
\(328\) −12.5886 −0.695087
\(329\) 4.74620 0.261666
\(330\) 1.88904 0.103988
\(331\) 7.26729 0.399446 0.199723 0.979852i \(-0.435996\pi\)
0.199723 + 0.979852i \(0.435996\pi\)
\(332\) 0.999133 0.0548345
\(333\) 2.22147 0.121736
\(334\) −43.7211 −2.39231
\(335\) −9.28256 −0.507160
\(336\) 10.7108 0.584322
\(337\) 22.5005 1.22568 0.612839 0.790208i \(-0.290027\pi\)
0.612839 + 0.790208i \(0.290027\pi\)
\(338\) 21.0142 1.14302
\(339\) 16.7887 0.911836
\(340\) −0.451002 −0.0244590
\(341\) −4.38928 −0.237693
\(342\) −21.9092 −1.18471
\(343\) 18.2596 0.985925
\(344\) 15.0390 0.810849
\(345\) 10.9661 0.590395
\(346\) 2.57097 0.138216
\(347\) −4.15850 −0.223240 −0.111620 0.993751i \(-0.535604\pi\)
−0.111620 + 0.993751i \(0.535604\pi\)
\(348\) 53.3755 2.86123
\(349\) 23.7678 1.27226 0.636132 0.771581i \(-0.280534\pi\)
0.636132 + 0.771581i \(0.280534\pi\)
\(350\) 5.85033 0.312713
\(351\) −6.13989 −0.327723
\(352\) 3.08012 0.164171
\(353\) −15.5948 −0.830025 −0.415012 0.909816i \(-0.636223\pi\)
−0.415012 + 0.909816i \(0.636223\pi\)
\(354\) −25.8663 −1.37478
\(355\) 10.2797 0.545592
\(356\) −31.1368 −1.65025
\(357\) −0.919821 −0.0486821
\(358\) −56.1767 −2.96903
\(359\) −12.1179 −0.639561 −0.319780 0.947492i \(-0.603609\pi\)
−0.319780 + 0.947492i \(0.603609\pi\)
\(360\) 2.33117 0.122863
\(361\) 32.0012 1.68428
\(362\) −22.0125 −1.15695
\(363\) −22.7328 −1.19316
\(364\) −13.5819 −0.711883
\(365\) −8.34284 −0.436684
\(366\) −59.1502 −3.09183
\(367\) −5.55057 −0.289738 −0.144869 0.989451i \(-0.546276\pi\)
−0.144869 + 0.989451i \(0.546276\pi\)
\(368\) 9.94098 0.518210
\(369\) 10.6777 0.555861
\(370\) 3.44667 0.179184
\(371\) 8.38500 0.435328
\(372\) −61.6451 −3.19615
\(373\) −13.8265 −0.715908 −0.357954 0.933739i \(-0.616526\pi\)
−0.357954 + 0.933739i \(0.616526\pi\)
\(374\) −0.147062 −0.00760440
\(375\) −2.09909 −0.108396
\(376\) 2.93426 0.151323
\(377\) 16.9087 0.870844
\(378\) −19.5728 −1.00672
\(379\) −0.771167 −0.0396122 −0.0198061 0.999804i \(-0.506305\pi\)
−0.0198061 + 0.999804i \(0.506305\pi\)
\(380\) −19.7096 −1.01108
\(381\) −12.8790 −0.659809
\(382\) −1.85540 −0.0949305
\(383\) −11.5295 −0.589130 −0.294565 0.955631i \(-0.595175\pi\)
−0.294565 + 0.955631i \(0.595175\pi\)
\(384\) 25.8299 1.31813
\(385\) 1.10611 0.0563724
\(386\) 21.5847 1.09863
\(387\) −12.7562 −0.648435
\(388\) −12.9073 −0.655271
\(389\) −8.62762 −0.437437 −0.218719 0.975788i \(-0.570188\pi\)
−0.218719 + 0.975788i \(0.570188\pi\)
\(390\) 8.40458 0.425583
\(391\) −0.853711 −0.0431740
\(392\) −0.316006 −0.0159607
\(393\) 1.20861 0.0609664
\(394\) 8.41680 0.424032
\(395\) −7.62559 −0.383685
\(396\) 1.60081 0.0804438
\(397\) −26.2096 −1.31542 −0.657712 0.753269i \(-0.728476\pi\)
−0.657712 + 0.753269i \(0.728476\pi\)
\(398\) −32.9303 −1.65065
\(399\) −40.1980 −2.01242
\(400\) −1.90287 −0.0951433
\(401\) 8.37489 0.418222 0.209111 0.977892i \(-0.432943\pi\)
0.209111 + 0.977892i \(0.432943\pi\)
\(402\) −42.5105 −2.12023
\(403\) −19.5284 −0.972780
\(404\) −18.6220 −0.926478
\(405\) 11.2412 0.558580
\(406\) 53.9018 2.67510
\(407\) 0.651653 0.0323012
\(408\) −0.568664 −0.0281531
\(409\) 21.2094 1.04874 0.524368 0.851492i \(-0.324302\pi\)
0.524368 + 0.851492i \(0.324302\pi\)
\(410\) 16.5668 0.818175
\(411\) −22.1487 −1.09251
\(412\) 41.4405 2.04163
\(413\) −15.1457 −0.745270
\(414\) 16.0272 0.787693
\(415\) −0.362022 −0.0177710
\(416\) 13.7038 0.671885
\(417\) 25.7424 1.26061
\(418\) −6.42690 −0.314350
\(419\) 14.2591 0.696604 0.348302 0.937382i \(-0.386758\pi\)
0.348302 + 0.937382i \(0.386758\pi\)
\(420\) 15.5347 0.758014
\(421\) −6.51538 −0.317540 −0.158770 0.987316i \(-0.550753\pi\)
−0.158770 + 0.987316i \(0.550753\pi\)
\(422\) 1.40797 0.0685390
\(423\) −2.48886 −0.121013
\(424\) 5.18389 0.251752
\(425\) 0.163414 0.00792675
\(426\) 47.0772 2.28090
\(427\) −34.6347 −1.67609
\(428\) −13.3206 −0.643875
\(429\) 1.58903 0.0767191
\(430\) −19.7916 −0.954437
\(431\) −10.7471 −0.517670 −0.258835 0.965922i \(-0.583339\pi\)
−0.258835 + 0.965922i \(0.583339\pi\)
\(432\) 6.36620 0.306294
\(433\) 4.83537 0.232373 0.116187 0.993227i \(-0.462933\pi\)
0.116187 + 0.993227i \(0.462933\pi\)
\(434\) −62.2529 −2.98824
\(435\) −19.3399 −0.927276
\(436\) 15.3132 0.733370
\(437\) −37.3088 −1.78472
\(438\) −38.2069 −1.82560
\(439\) −11.5831 −0.552831 −0.276416 0.961038i \(-0.589147\pi\)
−0.276416 + 0.961038i \(0.589147\pi\)
\(440\) 0.683831 0.0326004
\(441\) 0.268039 0.0127638
\(442\) −0.654297 −0.0311218
\(443\) −5.34739 −0.254062 −0.127031 0.991899i \(-0.540545\pi\)
−0.127031 + 0.991899i \(0.540545\pi\)
\(444\) 9.15212 0.434340
\(445\) 11.2820 0.534817
\(446\) 16.0477 0.759880
\(447\) −32.8087 −1.55180
\(448\) 33.4800 1.58178
\(449\) 17.0683 0.805503 0.402752 0.915309i \(-0.368054\pi\)
0.402752 + 0.915309i \(0.368054\pi\)
\(450\) −3.06786 −0.144620
\(451\) 3.13223 0.147491
\(452\) 22.0736 1.03826
\(453\) 32.9652 1.54884
\(454\) −22.6563 −1.06331
\(455\) 4.92120 0.230709
\(456\) −24.8517 −1.16379
\(457\) −40.2217 −1.88149 −0.940745 0.339114i \(-0.889873\pi\)
−0.940745 + 0.339114i \(0.889873\pi\)
\(458\) −47.0096 −2.19662
\(459\) −0.546716 −0.0255185
\(460\) 14.4181 0.672250
\(461\) 13.4737 0.627535 0.313768 0.949500i \(-0.398409\pi\)
0.313768 + 0.949500i \(0.398409\pi\)
\(462\) 5.06553 0.235670
\(463\) 11.1515 0.518253 0.259127 0.965843i \(-0.416565\pi\)
0.259127 + 0.965843i \(0.416565\pi\)
\(464\) −17.5320 −0.813902
\(465\) 22.3362 1.03582
\(466\) 3.56357 0.165079
\(467\) 26.1996 1.21237 0.606186 0.795323i \(-0.292699\pi\)
0.606186 + 0.795323i \(0.292699\pi\)
\(468\) 7.12221 0.329224
\(469\) −24.8915 −1.14938
\(470\) −3.86154 −0.178119
\(471\) −29.5295 −1.36065
\(472\) −9.36356 −0.430993
\(473\) −3.74194 −0.172055
\(474\) −34.9222 −1.60403
\(475\) 7.14152 0.327675
\(476\) −1.20938 −0.0554316
\(477\) −4.39702 −0.201326
\(478\) 17.3006 0.791311
\(479\) 14.7105 0.672140 0.336070 0.941837i \(-0.390902\pi\)
0.336070 + 0.941837i \(0.390902\pi\)
\(480\) −15.6742 −0.715424
\(481\) 2.89928 0.132196
\(482\) −51.3662 −2.33967
\(483\) 29.4059 1.33802
\(484\) −29.8890 −1.35859
\(485\) 4.67679 0.212362
\(486\) 29.5829 1.34191
\(487\) −5.28058 −0.239286 −0.119643 0.992817i \(-0.538175\pi\)
−0.119643 + 0.992817i \(0.538175\pi\)
\(488\) −21.4123 −0.969290
\(489\) 49.2037 2.22507
\(490\) 0.415869 0.0187871
\(491\) 12.1477 0.548217 0.274108 0.961699i \(-0.411617\pi\)
0.274108 + 0.961699i \(0.411617\pi\)
\(492\) 43.9906 1.98325
\(493\) 1.50561 0.0678093
\(494\) −28.5941 −1.28651
\(495\) −0.580032 −0.0260705
\(496\) 20.2482 0.909173
\(497\) 27.5655 1.23648
\(498\) −1.65792 −0.0742931
\(499\) 20.6552 0.924653 0.462327 0.886710i \(-0.347015\pi\)
0.462327 + 0.886710i \(0.347015\pi\)
\(500\) −2.75987 −0.123425
\(501\) 42.0653 1.87934
\(502\) −68.2860 −3.04775
\(503\) −2.23118 −0.0994833 −0.0497417 0.998762i \(-0.515840\pi\)
−0.0497417 + 0.998762i \(0.515840\pi\)
\(504\) 6.25110 0.278446
\(505\) 6.74742 0.300256
\(506\) 4.70145 0.209005
\(507\) −20.2184 −0.897929
\(508\) −16.9332 −0.751288
\(509\) −33.8303 −1.49950 −0.749751 0.661720i \(-0.769827\pi\)
−0.749751 + 0.661720i \(0.769827\pi\)
\(510\) 0.748373 0.0331385
\(511\) −22.3716 −0.989661
\(512\) −20.5181 −0.906782
\(513\) −23.8926 −1.05488
\(514\) −29.9061 −1.31910
\(515\) −15.0154 −0.661657
\(516\) −52.5536 −2.31355
\(517\) −0.730090 −0.0321093
\(518\) 9.24236 0.406086
\(519\) −2.47360 −0.108579
\(520\) 3.04245 0.133420
\(521\) 15.4443 0.676626 0.338313 0.941034i \(-0.390144\pi\)
0.338313 + 0.941034i \(0.390144\pi\)
\(522\) −28.2656 −1.23715
\(523\) 15.1533 0.662609 0.331305 0.943524i \(-0.392511\pi\)
0.331305 + 0.943524i \(0.392511\pi\)
\(524\) 1.58908 0.0694191
\(525\) −5.62877 −0.245660
\(526\) −4.64630 −0.202588
\(527\) −1.73888 −0.0757467
\(528\) −1.64760 −0.0717027
\(529\) 4.29244 0.186628
\(530\) −6.82209 −0.296333
\(531\) 7.94225 0.344664
\(532\) −52.8520 −2.29143
\(533\) 13.9357 0.603622
\(534\) 51.6670 2.23585
\(535\) 4.82653 0.208669
\(536\) −15.3887 −0.664692
\(537\) 54.0492 2.33239
\(538\) −10.1643 −0.438215
\(539\) 0.0786272 0.00338671
\(540\) 9.23338 0.397341
\(541\) 14.8129 0.636857 0.318428 0.947947i \(-0.396845\pi\)
0.318428 + 0.947947i \(0.396845\pi\)
\(542\) −27.2321 −1.16972
\(543\) 21.1789 0.908873
\(544\) 1.22023 0.0523171
\(545\) −5.54853 −0.237673
\(546\) 22.5372 0.964501
\(547\) 3.51714 0.150382 0.0751910 0.997169i \(-0.476043\pi\)
0.0751910 + 0.997169i \(0.476043\pi\)
\(548\) −29.1210 −1.24399
\(549\) 18.1621 0.775140
\(550\) −0.899935 −0.0383733
\(551\) 65.7981 2.80309
\(552\) 18.1797 0.773781
\(553\) −20.4483 −0.869549
\(554\) −10.3155 −0.438263
\(555\) −3.31614 −0.140762
\(556\) 33.8459 1.43539
\(557\) 8.07874 0.342307 0.171154 0.985244i \(-0.445251\pi\)
0.171154 + 0.985244i \(0.445251\pi\)
\(558\) 32.6449 1.38197
\(559\) −16.6484 −0.704151
\(560\) −5.10260 −0.215624
\(561\) 0.141493 0.00597383
\(562\) 17.5593 0.740694
\(563\) 20.1854 0.850715 0.425357 0.905025i \(-0.360148\pi\)
0.425357 + 0.905025i \(0.360148\pi\)
\(564\) −10.2537 −0.431760
\(565\) −7.99808 −0.336482
\(566\) −38.8787 −1.63420
\(567\) 30.1436 1.26591
\(568\) 17.0419 0.715062
\(569\) 13.3507 0.559690 0.279845 0.960045i \(-0.409717\pi\)
0.279845 + 0.960045i \(0.409717\pi\)
\(570\) 32.7053 1.36988
\(571\) 35.1768 1.47210 0.736052 0.676925i \(-0.236688\pi\)
0.736052 + 0.676925i \(0.236688\pi\)
\(572\) 2.08925 0.0873558
\(573\) 1.78513 0.0745750
\(574\) 44.4244 1.85424
\(575\) −5.22422 −0.217865
\(576\) −17.5566 −0.731525
\(577\) 2.88165 0.119965 0.0599823 0.998199i \(-0.480896\pi\)
0.0599823 + 0.998199i \(0.480896\pi\)
\(578\) 37.0308 1.54028
\(579\) −20.7673 −0.863058
\(580\) −25.4279 −1.05584
\(581\) −0.970774 −0.0402745
\(582\) 21.4179 0.887800
\(583\) −1.28983 −0.0534194
\(584\) −13.8309 −0.572325
\(585\) −2.58063 −0.106696
\(586\) 22.8501 0.943929
\(587\) −15.3878 −0.635122 −0.317561 0.948238i \(-0.602864\pi\)
−0.317561 + 0.948238i \(0.602864\pi\)
\(588\) 1.10428 0.0455396
\(589\) −75.9923 −3.13121
\(590\) 12.3226 0.507314
\(591\) −8.09804 −0.333109
\(592\) −3.00615 −0.123552
\(593\) −28.9773 −1.18995 −0.594977 0.803742i \(-0.702839\pi\)
−0.594977 + 0.803742i \(0.702839\pi\)
\(594\) 3.01081 0.123535
\(595\) 0.438200 0.0179645
\(596\) −43.1366 −1.76694
\(597\) 31.6832 1.29671
\(598\) 20.9173 0.855374
\(599\) 10.3313 0.422125 0.211062 0.977473i \(-0.432308\pi\)
0.211062 + 0.977473i \(0.432308\pi\)
\(600\) −3.47990 −0.142066
\(601\) 27.5913 1.12547 0.562737 0.826636i \(-0.309748\pi\)
0.562737 + 0.826636i \(0.309748\pi\)
\(602\) −53.0719 −2.16305
\(603\) 13.0529 0.531554
\(604\) 43.3424 1.76358
\(605\) 10.8299 0.440296
\(606\) 30.9005 1.25525
\(607\) 40.1345 1.62901 0.814505 0.580156i \(-0.197008\pi\)
0.814505 + 0.580156i \(0.197008\pi\)
\(608\) 53.3266 2.16268
\(609\) −51.8605 −2.10149
\(610\) 28.1790 1.14093
\(611\) −3.24826 −0.131411
\(612\) 0.634185 0.0256354
\(613\) 8.72394 0.352357 0.176178 0.984358i \(-0.443626\pi\)
0.176178 + 0.984358i \(0.443626\pi\)
\(614\) −17.6862 −0.713759
\(615\) −15.9394 −0.642738
\(616\) 1.83372 0.0738825
\(617\) 16.3340 0.657582 0.328791 0.944403i \(-0.393359\pi\)
0.328791 + 0.944403i \(0.393359\pi\)
\(618\) −68.7645 −2.76612
\(619\) −31.2311 −1.25528 −0.627641 0.778503i \(-0.715980\pi\)
−0.627641 + 0.778503i \(0.715980\pi\)
\(620\) 29.3675 1.17943
\(621\) 17.4781 0.701371
\(622\) −22.5707 −0.905003
\(623\) 30.2530 1.21206
\(624\) −7.33039 −0.293450
\(625\) 1.00000 0.0400000
\(626\) −36.0254 −1.43986
\(627\) 6.18350 0.246945
\(628\) −38.8251 −1.54929
\(629\) 0.258162 0.0102936
\(630\) −8.22657 −0.327754
\(631\) −15.0017 −0.597210 −0.298605 0.954377i \(-0.596521\pi\)
−0.298605 + 0.954377i \(0.596521\pi\)
\(632\) −12.6418 −0.502864
\(633\) −1.35465 −0.0538425
\(634\) 16.9260 0.672216
\(635\) 6.13550 0.243480
\(636\) −18.1150 −0.718308
\(637\) 0.349822 0.0138605
\(638\) −8.29151 −0.328264
\(639\) −14.4551 −0.571834
\(640\) −12.3053 −0.486409
\(641\) 15.9636 0.630523 0.315261 0.949005i \(-0.397908\pi\)
0.315261 + 0.949005i \(0.397908\pi\)
\(642\) 22.1036 0.872360
\(643\) −16.5047 −0.650881 −0.325440 0.945563i \(-0.605513\pi\)
−0.325440 + 0.945563i \(0.605513\pi\)
\(644\) 38.6627 1.52353
\(645\) 19.0421 0.749781
\(646\) −2.54611 −0.100175
\(647\) 25.5197 1.00328 0.501642 0.865075i \(-0.332729\pi\)
0.501642 + 0.865075i \(0.332729\pi\)
\(648\) 18.6358 0.732083
\(649\) 2.32980 0.0914527
\(650\) −4.00392 −0.157047
\(651\) 59.8953 2.34748
\(652\) 64.6927 2.53356
\(653\) 16.3131 0.638383 0.319191 0.947690i \(-0.396589\pi\)
0.319191 + 0.947690i \(0.396589\pi\)
\(654\) −25.4101 −0.993613
\(655\) −0.575780 −0.0224976
\(656\) −14.4494 −0.564153
\(657\) 11.7315 0.457688
\(658\) −10.3548 −0.403674
\(659\) 9.11201 0.354954 0.177477 0.984125i \(-0.443207\pi\)
0.177477 + 0.984125i \(0.443207\pi\)
\(660\) −2.38964 −0.0930166
\(661\) 24.9480 0.970363 0.485182 0.874413i \(-0.338753\pi\)
0.485182 + 0.874413i \(0.338753\pi\)
\(662\) −15.8551 −0.616227
\(663\) 0.629518 0.0244485
\(664\) −0.600165 −0.0232909
\(665\) 19.1502 0.742613
\(666\) −4.84661 −0.187802
\(667\) −48.1331 −1.86372
\(668\) 55.3072 2.13990
\(669\) −15.4399 −0.596943
\(670\) 20.2519 0.782398
\(671\) 5.32772 0.205674
\(672\) −42.0308 −1.62137
\(673\) 14.6152 0.563375 0.281687 0.959506i \(-0.409106\pi\)
0.281687 + 0.959506i \(0.409106\pi\)
\(674\) −49.0895 −1.89086
\(675\) −3.34559 −0.128772
\(676\) −26.5830 −1.02242
\(677\) −21.5771 −0.829274 −0.414637 0.909987i \(-0.636092\pi\)
−0.414637 + 0.909987i \(0.636092\pi\)
\(678\) −36.6281 −1.40669
\(679\) 12.5410 0.481279
\(680\) 0.270910 0.0103889
\(681\) 21.7983 0.835311
\(682\) 9.57614 0.366689
\(683\) −0.513188 −0.0196366 −0.00981829 0.999952i \(-0.503125\pi\)
−0.00981829 + 0.999952i \(0.503125\pi\)
\(684\) 27.7151 1.05971
\(685\) 10.5516 0.403155
\(686\) −39.8372 −1.52099
\(687\) 45.2293 1.72561
\(688\) 17.2620 0.658109
\(689\) −5.73863 −0.218624
\(690\) −23.9249 −0.910804
\(691\) 2.16319 0.0822917 0.0411459 0.999153i \(-0.486899\pi\)
0.0411459 + 0.999153i \(0.486899\pi\)
\(692\) −3.25228 −0.123633
\(693\) −1.55537 −0.0590838
\(694\) 9.07266 0.344393
\(695\) −12.2636 −0.465185
\(696\) −32.0619 −1.21530
\(697\) 1.24088 0.0470018
\(698\) −51.8546 −1.96272
\(699\) −3.42861 −0.129682
\(700\) −7.40067 −0.279719
\(701\) −35.7695 −1.35100 −0.675498 0.737361i \(-0.736072\pi\)
−0.675498 + 0.737361i \(0.736072\pi\)
\(702\) 13.3955 0.505579
\(703\) 11.2822 0.425515
\(704\) −5.15010 −0.194102
\(705\) 3.71530 0.139926
\(706\) 34.0233 1.28048
\(707\) 18.0934 0.680473
\(708\) 32.7208 1.22972
\(709\) −25.0734 −0.941650 −0.470825 0.882227i \(-0.656044\pi\)
−0.470825 + 0.882227i \(0.656044\pi\)
\(710\) −22.4274 −0.841687
\(711\) 10.7229 0.402140
\(712\) 18.7034 0.700940
\(713\) 55.5905 2.08188
\(714\) 2.00679 0.0751021
\(715\) −0.757010 −0.0283106
\(716\) 71.0635 2.65577
\(717\) −16.6454 −0.621634
\(718\) 26.4379 0.986652
\(719\) −3.84664 −0.143456 −0.0717278 0.997424i \(-0.522851\pi\)
−0.0717278 + 0.997424i \(0.522851\pi\)
\(720\) 2.67576 0.0997195
\(721\) −40.2642 −1.49952
\(722\) −69.8175 −2.59834
\(723\) 49.4209 1.83798
\(724\) 27.8459 1.03488
\(725\) 9.21346 0.342179
\(726\) 49.5965 1.84070
\(727\) 14.9477 0.554381 0.277190 0.960815i \(-0.410597\pi\)
0.277190 + 0.960815i \(0.410597\pi\)
\(728\) 8.15843 0.302371
\(729\) 5.26100 0.194852
\(730\) 18.2017 0.673674
\(731\) −1.48243 −0.0548296
\(732\) 74.8251 2.76561
\(733\) −15.8984 −0.587222 −0.293611 0.955925i \(-0.594857\pi\)
−0.293611 + 0.955925i \(0.594857\pi\)
\(734\) 12.1098 0.446979
\(735\) −0.400120 −0.0147586
\(736\) −39.0099 −1.43792
\(737\) 3.82896 0.141042
\(738\) −23.2957 −0.857528
\(739\) 36.0121 1.32473 0.662363 0.749183i \(-0.269554\pi\)
0.662363 + 0.749183i \(0.269554\pi\)
\(740\) −4.36004 −0.160278
\(741\) 27.5112 1.01065
\(742\) −18.2937 −0.671581
\(743\) −26.0522 −0.955763 −0.477882 0.878424i \(-0.658595\pi\)
−0.477882 + 0.878424i \(0.658595\pi\)
\(744\) 37.0293 1.35756
\(745\) 15.6300 0.572637
\(746\) 30.1654 1.10443
\(747\) 0.509065 0.0186257
\(748\) 0.186034 0.00680206
\(749\) 12.9425 0.472909
\(750\) 4.57961 0.167224
\(751\) 1.75278 0.0639600 0.0319800 0.999489i \(-0.489819\pi\)
0.0319800 + 0.999489i \(0.489819\pi\)
\(752\) 3.36799 0.122818
\(753\) 65.6999 2.39424
\(754\) −36.8900 −1.34345
\(755\) −15.7045 −0.571546
\(756\) 24.7596 0.900498
\(757\) −15.8250 −0.575171 −0.287586 0.957755i \(-0.592853\pi\)
−0.287586 + 0.957755i \(0.592853\pi\)
\(758\) 1.68247 0.0611099
\(759\) −4.52340 −0.164189
\(760\) 11.8393 0.429456
\(761\) −36.0339 −1.30623 −0.653113 0.757260i \(-0.726537\pi\)
−0.653113 + 0.757260i \(0.726537\pi\)
\(762\) 28.0982 1.01789
\(763\) −14.8786 −0.538640
\(764\) 2.34708 0.0849145
\(765\) −0.229788 −0.00830802
\(766\) 25.1541 0.908853
\(767\) 10.3656 0.374279
\(768\) −3.93745 −0.142080
\(769\) 30.4982 1.09979 0.549896 0.835233i \(-0.314667\pi\)
0.549896 + 0.835233i \(0.314667\pi\)
\(770\) −2.41320 −0.0869658
\(771\) 28.7735 1.03625
\(772\) −27.3047 −0.982717
\(773\) −2.03719 −0.0732725 −0.0366362 0.999329i \(-0.511664\pi\)
−0.0366362 + 0.999329i \(0.511664\pi\)
\(774\) 27.8304 1.00034
\(775\) −10.6409 −0.382233
\(776\) 7.75325 0.278325
\(777\) −8.89234 −0.319011
\(778\) 18.8230 0.674836
\(779\) 54.2289 1.94295
\(780\) −10.6318 −0.380680
\(781\) −4.24029 −0.151730
\(782\) 1.86255 0.0666047
\(783\) −30.8244 −1.10158
\(784\) −0.362717 −0.0129542
\(785\) 14.0678 0.502100
\(786\) −2.63684 −0.0940531
\(787\) 8.41615 0.300003 0.150002 0.988686i \(-0.452072\pi\)
0.150002 + 0.988686i \(0.452072\pi\)
\(788\) −10.6473 −0.379293
\(789\) 4.47034 0.159148
\(790\) 16.6369 0.591913
\(791\) −21.4471 −0.762572
\(792\) −0.961584 −0.0341684
\(793\) 23.7037 0.841743
\(794\) 57.1819 2.02931
\(795\) 6.56373 0.232792
\(796\) 41.6569 1.47649
\(797\) −34.6815 −1.22848 −0.614240 0.789119i \(-0.710537\pi\)
−0.614240 + 0.789119i \(0.710537\pi\)
\(798\) 87.7004 3.10456
\(799\) −0.289236 −0.0102324
\(800\) 7.46713 0.264003
\(801\) −15.8644 −0.560541
\(802\) −18.2716 −0.645192
\(803\) 3.44134 0.121442
\(804\) 53.7758 1.89653
\(805\) −14.0089 −0.493749
\(806\) 42.6054 1.50071
\(807\) 9.77939 0.344251
\(808\) 11.1860 0.393520
\(809\) 33.1397 1.16513 0.582565 0.812784i \(-0.302049\pi\)
0.582565 + 0.812784i \(0.302049\pi\)
\(810\) −24.5251 −0.861723
\(811\) 51.2766 1.80057 0.900283 0.435305i \(-0.143359\pi\)
0.900283 + 0.435305i \(0.143359\pi\)
\(812\) −68.1858 −2.39285
\(813\) 26.2008 0.918901
\(814\) −1.42172 −0.0498312
\(815\) −23.4405 −0.821085
\(816\) −0.652722 −0.0228499
\(817\) −64.7850 −2.26654
\(818\) −46.2727 −1.61789
\(819\) −6.92005 −0.241806
\(820\) −20.9570 −0.731850
\(821\) −45.7128 −1.59539 −0.797694 0.603063i \(-0.793947\pi\)
−0.797694 + 0.603063i \(0.793947\pi\)
\(822\) 48.3221 1.68543
\(823\) 0.890322 0.0310347 0.0155173 0.999880i \(-0.495060\pi\)
0.0155173 + 0.999880i \(0.495060\pi\)
\(824\) −24.8927 −0.867178
\(825\) 0.865853 0.0301451
\(826\) 33.0435 1.14973
\(827\) −40.4417 −1.40629 −0.703147 0.711044i \(-0.748223\pi\)
−0.703147 + 0.711044i \(0.748223\pi\)
\(828\) −20.2744 −0.704584
\(829\) 19.8894 0.690786 0.345393 0.938458i \(-0.387746\pi\)
0.345393 + 0.938458i \(0.387746\pi\)
\(830\) 0.789828 0.0274153
\(831\) 9.92484 0.344289
\(832\) −22.9134 −0.794381
\(833\) 0.0311494 0.00107926
\(834\) −56.1625 −1.94475
\(835\) −20.0398 −0.693507
\(836\) 8.13003 0.281183
\(837\) 35.6001 1.23052
\(838\) −31.1093 −1.07465
\(839\) −34.5482 −1.19274 −0.596368 0.802711i \(-0.703390\pi\)
−0.596368 + 0.802711i \(0.703390\pi\)
\(840\) −9.33145 −0.321966
\(841\) 55.8879 1.92717
\(842\) 14.2147 0.489870
\(843\) −16.8943 −0.581871
\(844\) −1.78109 −0.0613075
\(845\) 9.63197 0.331350
\(846\) 5.42998 0.186687
\(847\) 29.0406 0.997847
\(848\) 5.95015 0.204329
\(849\) 37.4064 1.28378
\(850\) −0.356523 −0.0122286
\(851\) −8.25323 −0.282917
\(852\) −59.5527 −2.04024
\(853\) −30.5568 −1.04625 −0.523123 0.852257i \(-0.675233\pi\)
−0.523123 + 0.852257i \(0.675233\pi\)
\(854\) 75.5629 2.58571
\(855\) −10.0422 −0.343436
\(856\) 8.00149 0.273485
\(857\) 46.2745 1.58071 0.790354 0.612651i \(-0.209897\pi\)
0.790354 + 0.612651i \(0.209897\pi\)
\(858\) −3.46681 −0.118355
\(859\) −21.5525 −0.735361 −0.367681 0.929952i \(-0.619848\pi\)
−0.367681 + 0.929952i \(0.619848\pi\)
\(860\) 25.0364 0.853735
\(861\) −42.7420 −1.45664
\(862\) 23.4471 0.798611
\(863\) −16.6225 −0.565837 −0.282919 0.959144i \(-0.591303\pi\)
−0.282919 + 0.959144i \(0.591303\pi\)
\(864\) −24.9819 −0.849903
\(865\) 1.17842 0.0400674
\(866\) −10.5494 −0.358483
\(867\) −35.6284 −1.21001
\(868\) 78.7500 2.67295
\(869\) 3.14548 0.106703
\(870\) 42.1940 1.43051
\(871\) 17.0355 0.577227
\(872\) −9.19842 −0.311498
\(873\) −6.57638 −0.222577
\(874\) 81.3971 2.75330
\(875\) 2.68153 0.0906523
\(876\) 48.3318 1.63298
\(877\) 27.2412 0.919869 0.459934 0.887953i \(-0.347873\pi\)
0.459934 + 0.887953i \(0.347873\pi\)
\(878\) 25.2710 0.852855
\(879\) −21.9847 −0.741527
\(880\) 0.784913 0.0264594
\(881\) −3.58110 −0.120650 −0.0603251 0.998179i \(-0.519214\pi\)
−0.0603251 + 0.998179i \(0.519214\pi\)
\(882\) −0.584783 −0.0196907
\(883\) 49.8593 1.67790 0.838949 0.544209i \(-0.183170\pi\)
0.838949 + 0.544209i \(0.183170\pi\)
\(884\) 0.827687 0.0278381
\(885\) −11.8559 −0.398533
\(886\) 11.6665 0.391943
\(887\) 33.5973 1.12809 0.564043 0.825745i \(-0.309245\pi\)
0.564043 + 0.825745i \(0.309245\pi\)
\(888\) −5.49754 −0.184485
\(889\) 16.4525 0.551801
\(890\) −24.6140 −0.825064
\(891\) −4.63688 −0.155341
\(892\) −20.3003 −0.679706
\(893\) −12.6402 −0.422987
\(894\) 71.5791 2.39396
\(895\) −25.7489 −0.860690
\(896\) −32.9970 −1.10235
\(897\) −20.1252 −0.671960
\(898\) −37.2381 −1.24265
\(899\) −98.0397 −3.26981
\(900\) 3.88085 0.129362
\(901\) −0.510987 −0.0170234
\(902\) −6.83363 −0.227535
\(903\) 51.0620 1.69924
\(904\) −13.2593 −0.440998
\(905\) −10.0896 −0.335389
\(906\) −71.9205 −2.38940
\(907\) −14.8891 −0.494383 −0.247191 0.968967i \(-0.579508\pi\)
−0.247191 + 0.968967i \(0.579508\pi\)
\(908\) 28.6602 0.951123
\(909\) −9.48803 −0.314698
\(910\) −10.7366 −0.355916
\(911\) 13.2749 0.439818 0.219909 0.975520i \(-0.429424\pi\)
0.219909 + 0.975520i \(0.429424\pi\)
\(912\) −28.5252 −0.944565
\(913\) 0.149331 0.00494212
\(914\) 87.7521 2.90258
\(915\) −27.1118 −0.896290
\(916\) 59.4672 1.96485
\(917\) −1.54397 −0.0509864
\(918\) 1.19278 0.0393675
\(919\) 12.6882 0.418544 0.209272 0.977857i \(-0.432891\pi\)
0.209272 + 0.977857i \(0.432891\pi\)
\(920\) −8.66077 −0.285537
\(921\) 17.0164 0.560711
\(922\) −29.3958 −0.968100
\(923\) −18.8656 −0.620968
\(924\) −6.40790 −0.210804
\(925\) 1.57980 0.0519436
\(926\) −24.3293 −0.799511
\(927\) 21.1142 0.693481
\(928\) 68.7981 2.25841
\(929\) −55.8616 −1.83276 −0.916380 0.400309i \(-0.868903\pi\)
−0.916380 + 0.400309i \(0.868903\pi\)
\(930\) −48.7312 −1.59796
\(931\) 1.36129 0.0446144
\(932\) −4.50792 −0.147662
\(933\) 21.7159 0.710947
\(934\) −57.1599 −1.87033
\(935\) −0.0674067 −0.00220444
\(936\) −4.27821 −0.139838
\(937\) −9.92086 −0.324100 −0.162050 0.986783i \(-0.551811\pi\)
−0.162050 + 0.986783i \(0.551811\pi\)
\(938\) 54.3060 1.77316
\(939\) 34.6611 1.13112
\(940\) 4.88485 0.159326
\(941\) 32.8606 1.07123 0.535613 0.844464i \(-0.320081\pi\)
0.535613 + 0.844464i \(0.320081\pi\)
\(942\) 64.4248 2.09907
\(943\) −39.6700 −1.29183
\(944\) −10.7477 −0.349806
\(945\) −8.97130 −0.291836
\(946\) 8.16385 0.265430
\(947\) 57.3764 1.86448 0.932242 0.361836i \(-0.117850\pi\)
0.932242 + 0.361836i \(0.117850\pi\)
\(948\) 44.1766 1.43479
\(949\) 15.3109 0.497014
\(950\) −15.5807 −0.505506
\(951\) −16.2850 −0.528076
\(952\) 0.726454 0.0235445
\(953\) −30.7280 −0.995378 −0.497689 0.867356i \(-0.665818\pi\)
−0.497689 + 0.867356i \(0.665818\pi\)
\(954\) 9.59303 0.310586
\(955\) −0.850433 −0.0275194
\(956\) −21.8853 −0.707820
\(957\) 7.97750 0.257876
\(958\) −32.0941 −1.03691
\(959\) 28.2944 0.913674
\(960\) 26.2080 0.845858
\(961\) 82.2292 2.65256
\(962\) −6.32540 −0.203939
\(963\) −6.78693 −0.218706
\(964\) 64.9783 2.09281
\(965\) 9.89347 0.318482
\(966\) −64.1553 −2.06416
\(967\) 39.2555 1.26237 0.631185 0.775632i \(-0.282569\pi\)
0.631185 + 0.775632i \(0.282569\pi\)
\(968\) 17.9539 0.577059
\(969\) 2.44969 0.0786953
\(970\) −10.2034 −0.327612
\(971\) 50.8234 1.63100 0.815500 0.578757i \(-0.196462\pi\)
0.815500 + 0.578757i \(0.196462\pi\)
\(972\) −37.4224 −1.20033
\(973\) −32.8852 −1.05425
\(974\) 11.5207 0.369147
\(975\) 3.85229 0.123372
\(976\) −24.5774 −0.786704
\(977\) −29.7903 −0.953075 −0.476537 0.879154i \(-0.658108\pi\)
−0.476537 + 0.879154i \(0.658108\pi\)
\(978\) −107.348 −3.43262
\(979\) −4.65370 −0.148733
\(980\) −0.526075 −0.0168048
\(981\) 7.80218 0.249105
\(982\) −26.5027 −0.845736
\(983\) −28.1487 −0.897804 −0.448902 0.893581i \(-0.648185\pi\)
−0.448902 + 0.893581i \(0.648185\pi\)
\(984\) −26.4245 −0.842383
\(985\) 3.85789 0.122922
\(986\) −3.28481 −0.104610
\(987\) 9.96269 0.317116
\(988\) 36.1715 1.15077
\(989\) 47.3920 1.50698
\(990\) 1.26546 0.0402190
\(991\) −40.1637 −1.27584 −0.637921 0.770102i \(-0.720206\pi\)
−0.637921 + 0.770102i \(0.720206\pi\)
\(992\) −79.4572 −2.52277
\(993\) 15.2547 0.484093
\(994\) −60.1399 −1.90752
\(995\) −15.0938 −0.478505
\(996\) 2.09727 0.0664545
\(997\) 40.2155 1.27364 0.636819 0.771013i \(-0.280250\pi\)
0.636819 + 0.771013i \(0.280250\pi\)
\(998\) −45.0637 −1.42647
\(999\) −5.28536 −0.167221
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 6005.2.a.g.1.17 113
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6005.2.a.g.1.17 113 1.1 even 1 trivial