Properties

Label 8014.2.a.e.1.13
Level $8014$
Weight $2$
Character 8014.1
Self dual yes
Analytic conductor $63.992$
Analytic rank $0$
Dimension $91$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8014,2,Mod(1,8014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8014, 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("8014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8014 = 2 \cdot 4007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8014.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: \(63.9921121799\)
Analytic rank: \(0\)
Dimension: \(91\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 8014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.66657 q^{3} +1.00000 q^{4} +3.59792 q^{5} +2.66657 q^{6} +3.19859 q^{7} -1.00000 q^{8} +4.11059 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.66657 q^{3} +1.00000 q^{4} +3.59792 q^{5} +2.66657 q^{6} +3.19859 q^{7} -1.00000 q^{8} +4.11059 q^{9} -3.59792 q^{10} -1.32899 q^{11} -2.66657 q^{12} +2.26975 q^{13} -3.19859 q^{14} -9.59410 q^{15} +1.00000 q^{16} +6.09379 q^{17} -4.11059 q^{18} +4.87657 q^{19} +3.59792 q^{20} -8.52925 q^{21} +1.32899 q^{22} +7.31948 q^{23} +2.66657 q^{24} +7.94502 q^{25} -2.26975 q^{26} -2.96147 q^{27} +3.19859 q^{28} -5.39268 q^{29} +9.59410 q^{30} -2.70729 q^{31} -1.00000 q^{32} +3.54385 q^{33} -6.09379 q^{34} +11.5083 q^{35} +4.11059 q^{36} +2.13851 q^{37} -4.87657 q^{38} -6.05244 q^{39} -3.59792 q^{40} +4.41143 q^{41} +8.52925 q^{42} +1.02970 q^{43} -1.32899 q^{44} +14.7896 q^{45} -7.31948 q^{46} +6.69810 q^{47} -2.66657 q^{48} +3.23095 q^{49} -7.94502 q^{50} -16.2495 q^{51} +2.26975 q^{52} +6.02243 q^{53} +2.96147 q^{54} -4.78161 q^{55} -3.19859 q^{56} -13.0037 q^{57} +5.39268 q^{58} -4.11176 q^{59} -9.59410 q^{60} -4.38096 q^{61} +2.70729 q^{62} +13.1481 q^{63} +1.00000 q^{64} +8.16636 q^{65} -3.54385 q^{66} -6.73124 q^{67} +6.09379 q^{68} -19.5179 q^{69} -11.5083 q^{70} -4.54564 q^{71} -4.11059 q^{72} +10.2577 q^{73} -2.13851 q^{74} -21.1859 q^{75} +4.87657 q^{76} -4.25090 q^{77} +6.05244 q^{78} +5.60002 q^{79} +3.59792 q^{80} -4.43481 q^{81} -4.41143 q^{82} -0.675599 q^{83} -8.52925 q^{84} +21.9249 q^{85} -1.02970 q^{86} +14.3799 q^{87} +1.32899 q^{88} -1.83218 q^{89} -14.7896 q^{90} +7.25998 q^{91} +7.31948 q^{92} +7.21918 q^{93} -6.69810 q^{94} +17.5455 q^{95} +2.66657 q^{96} +13.9690 q^{97} -3.23095 q^{98} -5.46295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.66657 −1.53954 −0.769772 0.638319i \(-0.779630\pi\)
−0.769772 + 0.638319i \(0.779630\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.59792 1.60904 0.804519 0.593927i \(-0.202423\pi\)
0.804519 + 0.593927i \(0.202423\pi\)
\(6\) 2.66657 1.08862
\(7\) 3.19859 1.20895 0.604476 0.796623i \(-0.293383\pi\)
0.604476 + 0.796623i \(0.293383\pi\)
\(8\) −1.00000 −0.353553
\(9\) 4.11059 1.37020
\(10\) −3.59792 −1.13776
\(11\) −1.32899 −0.400706 −0.200353 0.979724i \(-0.564209\pi\)
−0.200353 + 0.979724i \(0.564209\pi\)
\(12\) −2.66657 −0.769772
\(13\) 2.26975 0.629514 0.314757 0.949172i \(-0.398077\pi\)
0.314757 + 0.949172i \(0.398077\pi\)
\(14\) −3.19859 −0.854858
\(15\) −9.59410 −2.47719
\(16\) 1.00000 0.250000
\(17\) 6.09379 1.47796 0.738980 0.673727i \(-0.235308\pi\)
0.738980 + 0.673727i \(0.235308\pi\)
\(18\) −4.11059 −0.968876
\(19\) 4.87657 1.11876 0.559381 0.828910i \(-0.311039\pi\)
0.559381 + 0.828910i \(0.311039\pi\)
\(20\) 3.59792 0.804519
\(21\) −8.52925 −1.86123
\(22\) 1.32899 0.283342
\(23\) 7.31948 1.52622 0.763109 0.646270i \(-0.223672\pi\)
0.763109 + 0.646270i \(0.223672\pi\)
\(24\) 2.66657 0.544311
\(25\) 7.94502 1.58900
\(26\) −2.26975 −0.445134
\(27\) −2.96147 −0.569935
\(28\) 3.19859 0.604476
\(29\) −5.39268 −1.00139 −0.500697 0.865622i \(-0.666923\pi\)
−0.500697 + 0.865622i \(0.666923\pi\)
\(30\) 9.59410 1.75163
\(31\) −2.70729 −0.486244 −0.243122 0.969996i \(-0.578172\pi\)
−0.243122 + 0.969996i \(0.578172\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.54385 0.616905
\(34\) −6.09379 −1.04508
\(35\) 11.5083 1.94525
\(36\) 4.11059 0.685099
\(37\) 2.13851 0.351568 0.175784 0.984429i \(-0.443754\pi\)
0.175784 + 0.984429i \(0.443754\pi\)
\(38\) −4.87657 −0.791085
\(39\) −6.05244 −0.969165
\(40\) −3.59792 −0.568881
\(41\) 4.41143 0.688950 0.344475 0.938796i \(-0.388057\pi\)
0.344475 + 0.938796i \(0.388057\pi\)
\(42\) 8.52925 1.31609
\(43\) 1.02970 0.157027 0.0785136 0.996913i \(-0.474983\pi\)
0.0785136 + 0.996913i \(0.474983\pi\)
\(44\) −1.32899 −0.200353
\(45\) 14.7896 2.20470
\(46\) −7.31948 −1.07920
\(47\) 6.69810 0.977018 0.488509 0.872559i \(-0.337541\pi\)
0.488509 + 0.872559i \(0.337541\pi\)
\(48\) −2.66657 −0.384886
\(49\) 3.23095 0.461564
\(50\) −7.94502 −1.12360
\(51\) −16.2495 −2.27539
\(52\) 2.26975 0.314757
\(53\) 6.02243 0.827244 0.413622 0.910449i \(-0.364264\pi\)
0.413622 + 0.910449i \(0.364264\pi\)
\(54\) 2.96147 0.403005
\(55\) −4.78161 −0.644752
\(56\) −3.19859 −0.427429
\(57\) −13.0037 −1.72239
\(58\) 5.39268 0.708093
\(59\) −4.11176 −0.535306 −0.267653 0.963515i \(-0.586248\pi\)
−0.267653 + 0.963515i \(0.586248\pi\)
\(60\) −9.59410 −1.23859
\(61\) −4.38096 −0.560924 −0.280462 0.959865i \(-0.590488\pi\)
−0.280462 + 0.959865i \(0.590488\pi\)
\(62\) 2.70729 0.343826
\(63\) 13.1481 1.65650
\(64\) 1.00000 0.125000
\(65\) 8.16636 1.01291
\(66\) −3.54385 −0.436218
\(67\) −6.73124 −0.822352 −0.411176 0.911556i \(-0.634882\pi\)
−0.411176 + 0.911556i \(0.634882\pi\)
\(68\) 6.09379 0.738980
\(69\) −19.5179 −2.34968
\(70\) −11.5083 −1.37550
\(71\) −4.54564 −0.539468 −0.269734 0.962935i \(-0.586936\pi\)
−0.269734 + 0.962935i \(0.586936\pi\)
\(72\) −4.11059 −0.484438
\(73\) 10.2577 1.20057 0.600286 0.799785i \(-0.295053\pi\)
0.600286 + 0.799785i \(0.295053\pi\)
\(74\) −2.13851 −0.248596
\(75\) −21.1859 −2.44634
\(76\) 4.87657 0.559381
\(77\) −4.25090 −0.484435
\(78\) 6.05244 0.685303
\(79\) 5.60002 0.630051 0.315026 0.949083i \(-0.397987\pi\)
0.315026 + 0.949083i \(0.397987\pi\)
\(80\) 3.59792 0.402260
\(81\) −4.43481 −0.492757
\(82\) −4.41143 −0.487161
\(83\) −0.675599 −0.0741566 −0.0370783 0.999312i \(-0.511805\pi\)
−0.0370783 + 0.999312i \(0.511805\pi\)
\(84\) −8.52925 −0.930617
\(85\) 21.9249 2.37809
\(86\) −1.02970 −0.111035
\(87\) 14.3799 1.54169
\(88\) 1.32899 0.141671
\(89\) −1.83218 −0.194211 −0.0971054 0.995274i \(-0.530958\pi\)
−0.0971054 + 0.995274i \(0.530958\pi\)
\(90\) −14.7896 −1.55896
\(91\) 7.25998 0.761052
\(92\) 7.31948 0.763109
\(93\) 7.21918 0.748594
\(94\) −6.69810 −0.690856
\(95\) 17.5455 1.80013
\(96\) 2.66657 0.272156
\(97\) 13.9690 1.41834 0.709170 0.705038i \(-0.249070\pi\)
0.709170 + 0.705038i \(0.249070\pi\)
\(98\) −3.23095 −0.326375
\(99\) −5.46295 −0.549047
\(100\) 7.94502 0.794502
\(101\) 10.6892 1.06361 0.531806 0.846866i \(-0.321514\pi\)
0.531806 + 0.846866i \(0.321514\pi\)
\(102\) 16.2495 1.60894
\(103\) 9.90004 0.975480 0.487740 0.872989i \(-0.337821\pi\)
0.487740 + 0.872989i \(0.337821\pi\)
\(104\) −2.26975 −0.222567
\(105\) −30.6875 −2.99480
\(106\) −6.02243 −0.584950
\(107\) −5.86232 −0.566732 −0.283366 0.959012i \(-0.591451\pi\)
−0.283366 + 0.959012i \(0.591451\pi\)
\(108\) −2.96147 −0.284968
\(109\) 18.2037 1.74360 0.871799 0.489863i \(-0.162953\pi\)
0.871799 + 0.489863i \(0.162953\pi\)
\(110\) 4.78161 0.455908
\(111\) −5.70248 −0.541255
\(112\) 3.19859 0.302238
\(113\) 10.4459 0.982670 0.491335 0.870971i \(-0.336509\pi\)
0.491335 + 0.870971i \(0.336509\pi\)
\(114\) 13.0037 1.21791
\(115\) 26.3349 2.45574
\(116\) −5.39268 −0.500697
\(117\) 9.33000 0.862559
\(118\) 4.11176 0.378518
\(119\) 19.4915 1.78678
\(120\) 9.59410 0.875817
\(121\) −9.23378 −0.839434
\(122\) 4.38096 0.396633
\(123\) −11.7634 −1.06067
\(124\) −2.70729 −0.243122
\(125\) 10.5959 0.947729
\(126\) −13.1481 −1.17132
\(127\) −11.4991 −1.02038 −0.510189 0.860063i \(-0.670424\pi\)
−0.510189 + 0.860063i \(0.670424\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.74576 −0.241750
\(130\) −8.16636 −0.716237
\(131\) −9.49369 −0.829467 −0.414734 0.909943i \(-0.636125\pi\)
−0.414734 + 0.909943i \(0.636125\pi\)
\(132\) 3.54385 0.308453
\(133\) 15.5981 1.35253
\(134\) 6.73124 0.581491
\(135\) −10.6551 −0.917047
\(136\) −6.09379 −0.522538
\(137\) 11.5333 0.985358 0.492679 0.870211i \(-0.336018\pi\)
0.492679 + 0.870211i \(0.336018\pi\)
\(138\) 19.5179 1.66147
\(139\) 19.6241 1.66449 0.832246 0.554407i \(-0.187055\pi\)
0.832246 + 0.554407i \(0.187055\pi\)
\(140\) 11.5083 0.972625
\(141\) −17.8609 −1.50416
\(142\) 4.54564 0.381462
\(143\) −3.01648 −0.252250
\(144\) 4.11059 0.342549
\(145\) −19.4024 −1.61128
\(146\) −10.2577 −0.848933
\(147\) −8.61555 −0.710599
\(148\) 2.13851 0.175784
\(149\) 6.55575 0.537068 0.268534 0.963270i \(-0.413461\pi\)
0.268534 + 0.963270i \(0.413461\pi\)
\(150\) 21.1859 1.72982
\(151\) −18.7026 −1.52200 −0.760998 0.648754i \(-0.775290\pi\)
−0.760998 + 0.648754i \(0.775290\pi\)
\(152\) −4.87657 −0.395542
\(153\) 25.0491 2.02510
\(154\) 4.25090 0.342547
\(155\) −9.74061 −0.782385
\(156\) −6.05244 −0.484583
\(157\) −16.5108 −1.31771 −0.658854 0.752271i \(-0.728958\pi\)
−0.658854 + 0.752271i \(0.728958\pi\)
\(158\) −5.60002 −0.445514
\(159\) −16.0592 −1.27358
\(160\) −3.59792 −0.284440
\(161\) 23.4120 1.84512
\(162\) 4.43481 0.348432
\(163\) −15.7314 −1.23218 −0.616089 0.787677i \(-0.711284\pi\)
−0.616089 + 0.787677i \(0.711284\pi\)
\(164\) 4.41143 0.344475
\(165\) 12.7505 0.992624
\(166\) 0.675599 0.0524367
\(167\) −19.1834 −1.48446 −0.742229 0.670146i \(-0.766231\pi\)
−0.742229 + 0.670146i \(0.766231\pi\)
\(168\) 8.52925 0.658046
\(169\) −7.84825 −0.603712
\(170\) −21.9249 −1.68157
\(171\) 20.0456 1.53293
\(172\) 1.02970 0.0785136
\(173\) −7.94282 −0.603882 −0.301941 0.953327i \(-0.597635\pi\)
−0.301941 + 0.953327i \(0.597635\pi\)
\(174\) −14.3799 −1.09014
\(175\) 25.4128 1.92103
\(176\) −1.32899 −0.100177
\(177\) 10.9643 0.824127
\(178\) 1.83218 0.137328
\(179\) −22.1103 −1.65260 −0.826302 0.563227i \(-0.809560\pi\)
−0.826302 + 0.563227i \(0.809560\pi\)
\(180\) 14.7896 1.10235
\(181\) −13.1737 −0.979191 −0.489595 0.871950i \(-0.662855\pi\)
−0.489595 + 0.871950i \(0.662855\pi\)
\(182\) −7.25998 −0.538145
\(183\) 11.6821 0.863568
\(184\) −7.31948 −0.539599
\(185\) 7.69417 0.565687
\(186\) −7.21918 −0.529336
\(187\) −8.09860 −0.592228
\(188\) 6.69810 0.488509
\(189\) −9.47251 −0.689024
\(190\) −17.5455 −1.27289
\(191\) 3.67683 0.266046 0.133023 0.991113i \(-0.457532\pi\)
0.133023 + 0.991113i \(0.457532\pi\)
\(192\) −2.66657 −0.192443
\(193\) −6.87538 −0.494901 −0.247450 0.968901i \(-0.579593\pi\)
−0.247450 + 0.968901i \(0.579593\pi\)
\(194\) −13.9690 −1.00292
\(195\) −21.7762 −1.55942
\(196\) 3.23095 0.230782
\(197\) 1.60178 0.114122 0.0570612 0.998371i \(-0.481827\pi\)
0.0570612 + 0.998371i \(0.481827\pi\)
\(198\) 5.46295 0.388235
\(199\) 1.18019 0.0836611 0.0418306 0.999125i \(-0.486681\pi\)
0.0418306 + 0.999125i \(0.486681\pi\)
\(200\) −7.94502 −0.561798
\(201\) 17.9493 1.26605
\(202\) −10.6892 −0.752087
\(203\) −17.2489 −1.21064
\(204\) −16.2495 −1.13769
\(205\) 15.8720 1.10855
\(206\) −9.90004 −0.689769
\(207\) 30.0874 2.09122
\(208\) 2.26975 0.157379
\(209\) −6.48093 −0.448295
\(210\) 30.6875 2.11764
\(211\) −21.3981 −1.47311 −0.736553 0.676379i \(-0.763548\pi\)
−0.736553 + 0.676379i \(0.763548\pi\)
\(212\) 6.02243 0.413622
\(213\) 12.1213 0.830535
\(214\) 5.86232 0.400740
\(215\) 3.70476 0.252663
\(216\) 2.96147 0.201502
\(217\) −8.65950 −0.587845
\(218\) −18.2037 −1.23291
\(219\) −27.3528 −1.84833
\(220\) −4.78161 −0.322376
\(221\) 13.8313 0.930397
\(222\) 5.70248 0.382725
\(223\) −23.5596 −1.57767 −0.788834 0.614606i \(-0.789315\pi\)
−0.788834 + 0.614606i \(0.789315\pi\)
\(224\) −3.19859 −0.213714
\(225\) 32.6587 2.17725
\(226\) −10.4459 −0.694852
\(227\) −14.6906 −0.975051 −0.487526 0.873109i \(-0.662100\pi\)
−0.487526 + 0.873109i \(0.662100\pi\)
\(228\) −13.0037 −0.861193
\(229\) −14.2127 −0.939201 −0.469600 0.882879i \(-0.655602\pi\)
−0.469600 + 0.882879i \(0.655602\pi\)
\(230\) −26.3349 −1.73647
\(231\) 11.3353 0.745809
\(232\) 5.39268 0.354046
\(233\) −23.9962 −1.57204 −0.786020 0.618201i \(-0.787862\pi\)
−0.786020 + 0.618201i \(0.787862\pi\)
\(234\) −9.33000 −0.609921
\(235\) 24.0992 1.57206
\(236\) −4.11176 −0.267653
\(237\) −14.9328 −0.969992
\(238\) −19.4915 −1.26345
\(239\) 24.6830 1.59661 0.798306 0.602252i \(-0.205730\pi\)
0.798306 + 0.602252i \(0.205730\pi\)
\(240\) −9.59410 −0.619296
\(241\) 16.5929 1.06884 0.534421 0.845218i \(-0.320530\pi\)
0.534421 + 0.845218i \(0.320530\pi\)
\(242\) 9.23378 0.593570
\(243\) 20.7101 1.32856
\(244\) −4.38096 −0.280462
\(245\) 11.6247 0.742674
\(246\) 11.7634 0.750006
\(247\) 11.0686 0.704277
\(248\) 2.70729 0.171913
\(249\) 1.80153 0.114167
\(250\) −10.5959 −0.670146
\(251\) 11.8700 0.749225 0.374612 0.927182i \(-0.377776\pi\)
0.374612 + 0.927182i \(0.377776\pi\)
\(252\) 13.1481 0.828251
\(253\) −9.72753 −0.611565
\(254\) 11.4991 0.721516
\(255\) −58.4644 −3.66118
\(256\) 1.00000 0.0625000
\(257\) 23.8871 1.49003 0.745017 0.667046i \(-0.232442\pi\)
0.745017 + 0.667046i \(0.232442\pi\)
\(258\) 2.74576 0.170943
\(259\) 6.84020 0.425029
\(260\) 8.16636 0.506456
\(261\) −22.1671 −1.37211
\(262\) 9.49369 0.586522
\(263\) 6.35171 0.391663 0.195832 0.980638i \(-0.437259\pi\)
0.195832 + 0.980638i \(0.437259\pi\)
\(264\) −3.54385 −0.218109
\(265\) 21.6682 1.33107
\(266\) −15.5981 −0.956383
\(267\) 4.88564 0.298996
\(268\) −6.73124 −0.411176
\(269\) 21.2676 1.29671 0.648354 0.761339i \(-0.275458\pi\)
0.648354 + 0.761339i \(0.275458\pi\)
\(270\) 10.6551 0.648450
\(271\) −25.0598 −1.52227 −0.761136 0.648592i \(-0.775358\pi\)
−0.761136 + 0.648592i \(0.775358\pi\)
\(272\) 6.09379 0.369490
\(273\) −19.3592 −1.17167
\(274\) −11.5333 −0.696753
\(275\) −10.5589 −0.636724
\(276\) −19.5179 −1.17484
\(277\) 1.28916 0.0774578 0.0387289 0.999250i \(-0.487669\pi\)
0.0387289 + 0.999250i \(0.487669\pi\)
\(278\) −19.6241 −1.17697
\(279\) −11.1286 −0.666250
\(280\) −11.5083 −0.687749
\(281\) −11.5384 −0.688321 −0.344160 0.938911i \(-0.611836\pi\)
−0.344160 + 0.938911i \(0.611836\pi\)
\(282\) 17.8609 1.06360
\(283\) −10.5119 −0.624870 −0.312435 0.949939i \(-0.601145\pi\)
−0.312435 + 0.949939i \(0.601145\pi\)
\(284\) −4.54564 −0.269734
\(285\) −46.7863 −2.77138
\(286\) 3.01648 0.178368
\(287\) 14.1103 0.832907
\(288\) −4.11059 −0.242219
\(289\) 20.1342 1.18437
\(290\) 19.4024 1.13935
\(291\) −37.2494 −2.18360
\(292\) 10.2577 0.600286
\(293\) −17.8079 −1.04035 −0.520175 0.854059i \(-0.674133\pi\)
−0.520175 + 0.854059i \(0.674133\pi\)
\(294\) 8.61555 0.502469
\(295\) −14.7938 −0.861327
\(296\) −2.13851 −0.124298
\(297\) 3.93577 0.228377
\(298\) −6.55575 −0.379764
\(299\) 16.6134 0.960776
\(300\) −21.1859 −1.22317
\(301\) 3.29357 0.189838
\(302\) 18.7026 1.07621
\(303\) −28.5034 −1.63748
\(304\) 4.87657 0.279691
\(305\) −15.7623 −0.902549
\(306\) −25.0491 −1.43196
\(307\) −20.8759 −1.19145 −0.595724 0.803189i \(-0.703135\pi\)
−0.595724 + 0.803189i \(0.703135\pi\)
\(308\) −4.25090 −0.242217
\(309\) −26.3991 −1.50179
\(310\) 9.74061 0.553230
\(311\) 20.5052 1.16274 0.581371 0.813639i \(-0.302517\pi\)
0.581371 + 0.813639i \(0.302517\pi\)
\(312\) 6.05244 0.342652
\(313\) −9.60209 −0.542742 −0.271371 0.962475i \(-0.587477\pi\)
−0.271371 + 0.962475i \(0.587477\pi\)
\(314\) 16.5108 0.931760
\(315\) 47.3057 2.66538
\(316\) 5.60002 0.315026
\(317\) −22.4659 −1.26181 −0.630905 0.775860i \(-0.717316\pi\)
−0.630905 + 0.775860i \(0.717316\pi\)
\(318\) 16.0592 0.900556
\(319\) 7.16683 0.401265
\(320\) 3.59792 0.201130
\(321\) 15.6323 0.872510
\(322\) −23.4120 −1.30470
\(323\) 29.7168 1.65349
\(324\) −4.43481 −0.246378
\(325\) 18.0332 1.00030
\(326\) 15.7314 0.871281
\(327\) −48.5414 −2.68435
\(328\) −4.41143 −0.243581
\(329\) 21.4244 1.18117
\(330\) −12.7505 −0.701891
\(331\) 12.3144 0.676863 0.338432 0.940991i \(-0.390104\pi\)
0.338432 + 0.940991i \(0.390104\pi\)
\(332\) −0.675599 −0.0370783
\(333\) 8.79053 0.481718
\(334\) 19.1834 1.04967
\(335\) −24.2185 −1.32320
\(336\) −8.52925 −0.465309
\(337\) −11.1065 −0.605007 −0.302503 0.953148i \(-0.597822\pi\)
−0.302503 + 0.953148i \(0.597822\pi\)
\(338\) 7.84825 0.426889
\(339\) −27.8548 −1.51286
\(340\) 21.9249 1.18905
\(341\) 3.59797 0.194841
\(342\) −20.0456 −1.08394
\(343\) −12.0556 −0.650943
\(344\) −1.02970 −0.0555175
\(345\) −70.2238 −3.78072
\(346\) 7.94282 0.427009
\(347\) −28.1726 −1.51239 −0.756194 0.654348i \(-0.772943\pi\)
−0.756194 + 0.654348i \(0.772943\pi\)
\(348\) 14.3799 0.770846
\(349\) 22.7155 1.21593 0.607967 0.793962i \(-0.291985\pi\)
0.607967 + 0.793962i \(0.291985\pi\)
\(350\) −25.4128 −1.35837
\(351\) −6.72178 −0.358782
\(352\) 1.32899 0.0708355
\(353\) 20.2776 1.07927 0.539634 0.841900i \(-0.318563\pi\)
0.539634 + 0.841900i \(0.318563\pi\)
\(354\) −10.9643 −0.582746
\(355\) −16.3548 −0.868025
\(356\) −1.83218 −0.0971054
\(357\) −51.9754 −2.75083
\(358\) 22.1103 1.16857
\(359\) 9.80334 0.517401 0.258700 0.965958i \(-0.416706\pi\)
0.258700 + 0.965958i \(0.416706\pi\)
\(360\) −14.7896 −0.779479
\(361\) 4.78098 0.251630
\(362\) 13.1737 0.692392
\(363\) 24.6225 1.29235
\(364\) 7.25998 0.380526
\(365\) 36.9063 1.93177
\(366\) −11.6821 −0.610635
\(367\) −24.6913 −1.28888 −0.644438 0.764656i \(-0.722909\pi\)
−0.644438 + 0.764656i \(0.722909\pi\)
\(368\) 7.31948 0.381554
\(369\) 18.1336 0.943997
\(370\) −7.69417 −0.400001
\(371\) 19.2632 1.00010
\(372\) 7.21918 0.374297
\(373\) −30.8849 −1.59916 −0.799580 0.600560i \(-0.794944\pi\)
−0.799580 + 0.600560i \(0.794944\pi\)
\(374\) 8.09860 0.418768
\(375\) −28.2548 −1.45907
\(376\) −6.69810 −0.345428
\(377\) −12.2400 −0.630392
\(378\) 9.47251 0.487214
\(379\) −0.433900 −0.0222879 −0.0111440 0.999938i \(-0.503547\pi\)
−0.0111440 + 0.999938i \(0.503547\pi\)
\(380\) 17.5455 0.900066
\(381\) 30.6631 1.57092
\(382\) −3.67683 −0.188123
\(383\) −11.0133 −0.562752 −0.281376 0.959598i \(-0.590791\pi\)
−0.281376 + 0.959598i \(0.590791\pi\)
\(384\) 2.66657 0.136078
\(385\) −15.2944 −0.779474
\(386\) 6.87538 0.349948
\(387\) 4.23266 0.215158
\(388\) 13.9690 0.709170
\(389\) −29.4374 −1.49254 −0.746269 0.665645i \(-0.768157\pi\)
−0.746269 + 0.665645i \(0.768157\pi\)
\(390\) 21.7762 1.10268
\(391\) 44.6033 2.25569
\(392\) −3.23095 −0.163188
\(393\) 25.3156 1.27700
\(394\) −1.60178 −0.0806967
\(395\) 20.1484 1.01378
\(396\) −5.46295 −0.274523
\(397\) 21.5567 1.08190 0.540950 0.841054i \(-0.318065\pi\)
0.540950 + 0.841054i \(0.318065\pi\)
\(398\) −1.18019 −0.0591574
\(399\) −41.5935 −2.08228
\(400\) 7.94502 0.397251
\(401\) −29.9435 −1.49531 −0.747654 0.664088i \(-0.768820\pi\)
−0.747654 + 0.664088i \(0.768820\pi\)
\(402\) −17.9493 −0.895231
\(403\) −6.14487 −0.306098
\(404\) 10.6892 0.531806
\(405\) −15.9561 −0.792864
\(406\) 17.2489 0.856050
\(407\) −2.84206 −0.140876
\(408\) 16.2495 0.804470
\(409\) 16.2936 0.805667 0.402834 0.915273i \(-0.368025\pi\)
0.402834 + 0.915273i \(0.368025\pi\)
\(410\) −15.8720 −0.783861
\(411\) −30.7544 −1.51700
\(412\) 9.90004 0.487740
\(413\) −13.1518 −0.647159
\(414\) −30.0874 −1.47871
\(415\) −2.43075 −0.119321
\(416\) −2.26975 −0.111283
\(417\) −52.3289 −2.56256
\(418\) 6.48093 0.316993
\(419\) −5.26824 −0.257371 −0.128685 0.991685i \(-0.541076\pi\)
−0.128685 + 0.991685i \(0.541076\pi\)
\(420\) −30.6875 −1.49740
\(421\) 3.59050 0.174990 0.0874952 0.996165i \(-0.472114\pi\)
0.0874952 + 0.996165i \(0.472114\pi\)
\(422\) 21.3981 1.04164
\(423\) 27.5331 1.33871
\(424\) −6.02243 −0.292475
\(425\) 48.4152 2.34848
\(426\) −12.1213 −0.587277
\(427\) −14.0129 −0.678131
\(428\) −5.86232 −0.283366
\(429\) 8.04364 0.388351
\(430\) −3.70476 −0.178660
\(431\) −1.15129 −0.0554559 −0.0277279 0.999616i \(-0.508827\pi\)
−0.0277279 + 0.999616i \(0.508827\pi\)
\(432\) −2.96147 −0.142484
\(433\) 16.7962 0.807174 0.403587 0.914941i \(-0.367763\pi\)
0.403587 + 0.914941i \(0.367763\pi\)
\(434\) 8.65950 0.415669
\(435\) 51.7379 2.48064
\(436\) 18.2037 0.871799
\(437\) 35.6940 1.70747
\(438\) 27.3528 1.30697
\(439\) −34.9034 −1.66585 −0.832923 0.553388i \(-0.813335\pi\)
−0.832923 + 0.553388i \(0.813335\pi\)
\(440\) 4.78161 0.227954
\(441\) 13.2811 0.632434
\(442\) −13.8313 −0.657890
\(443\) −0.622830 −0.0295916 −0.0147958 0.999891i \(-0.504710\pi\)
−0.0147958 + 0.999891i \(0.504710\pi\)
\(444\) −5.70248 −0.270627
\(445\) −6.59204 −0.312492
\(446\) 23.5596 1.11558
\(447\) −17.4813 −0.826839
\(448\) 3.19859 0.151119
\(449\) −1.56565 −0.0738878 −0.0369439 0.999317i \(-0.511762\pi\)
−0.0369439 + 0.999317i \(0.511762\pi\)
\(450\) −32.6587 −1.53955
\(451\) −5.86276 −0.276067
\(452\) 10.4459 0.491335
\(453\) 49.8718 2.34318
\(454\) 14.6906 0.689465
\(455\) 26.1208 1.22456
\(456\) 13.0037 0.608955
\(457\) −7.80596 −0.365147 −0.182574 0.983192i \(-0.558443\pi\)
−0.182574 + 0.983192i \(0.558443\pi\)
\(458\) 14.2127 0.664115
\(459\) −18.0466 −0.842341
\(460\) 26.3349 1.22787
\(461\) 32.5904 1.51789 0.758944 0.651156i \(-0.225716\pi\)
0.758944 + 0.651156i \(0.225716\pi\)
\(462\) −11.3353 −0.527366
\(463\) 1.65032 0.0766971 0.0383485 0.999264i \(-0.487790\pi\)
0.0383485 + 0.999264i \(0.487790\pi\)
\(464\) −5.39268 −0.250349
\(465\) 25.9740 1.20452
\(466\) 23.9962 1.11160
\(467\) −21.9615 −1.01626 −0.508128 0.861281i \(-0.669662\pi\)
−0.508128 + 0.861281i \(0.669662\pi\)
\(468\) 9.33000 0.431279
\(469\) −21.5305 −0.994184
\(470\) −24.0992 −1.11161
\(471\) 44.0273 2.02867
\(472\) 4.11176 0.189259
\(473\) −1.36846 −0.0629218
\(474\) 14.9328 0.685888
\(475\) 38.7445 1.77772
\(476\) 19.4915 0.893391
\(477\) 24.7557 1.13349
\(478\) −24.6830 −1.12898
\(479\) −8.67908 −0.396557 −0.198279 0.980146i \(-0.563535\pi\)
−0.198279 + 0.980146i \(0.563535\pi\)
\(480\) 9.59410 0.437909
\(481\) 4.85387 0.221317
\(482\) −16.5929 −0.755786
\(483\) −62.4297 −2.84065
\(484\) −9.23378 −0.419717
\(485\) 50.2594 2.28216
\(486\) −20.7101 −0.939431
\(487\) −21.4000 −0.969728 −0.484864 0.874590i \(-0.661131\pi\)
−0.484864 + 0.874590i \(0.661131\pi\)
\(488\) 4.38096 0.198317
\(489\) 41.9488 1.89699
\(490\) −11.6247 −0.525150
\(491\) 5.96869 0.269363 0.134682 0.990889i \(-0.456999\pi\)
0.134682 + 0.990889i \(0.456999\pi\)
\(492\) −11.7634 −0.530334
\(493\) −32.8618 −1.48002
\(494\) −11.0686 −0.497999
\(495\) −19.6552 −0.883437
\(496\) −2.70729 −0.121561
\(497\) −14.5396 −0.652191
\(498\) −1.80153 −0.0807286
\(499\) −16.9220 −0.757531 −0.378765 0.925493i \(-0.623651\pi\)
−0.378765 + 0.925493i \(0.623651\pi\)
\(500\) 10.5959 0.473865
\(501\) 51.1540 2.28539
\(502\) −11.8700 −0.529782
\(503\) 3.44928 0.153796 0.0768980 0.997039i \(-0.475498\pi\)
0.0768980 + 0.997039i \(0.475498\pi\)
\(504\) −13.1481 −0.585662
\(505\) 38.4587 1.71139
\(506\) 9.72753 0.432442
\(507\) 20.9279 0.929441
\(508\) −11.4991 −0.510189
\(509\) −28.5841 −1.26697 −0.633485 0.773755i \(-0.718376\pi\)
−0.633485 + 0.773755i \(0.718376\pi\)
\(510\) 58.4644 2.58885
\(511\) 32.8101 1.45143
\(512\) −1.00000 −0.0441942
\(513\) −14.4418 −0.637622
\(514\) −23.8871 −1.05361
\(515\) 35.6195 1.56958
\(516\) −2.74576 −0.120875
\(517\) −8.90172 −0.391497
\(518\) −6.84020 −0.300541
\(519\) 21.1801 0.929703
\(520\) −8.16636 −0.358119
\(521\) 34.4759 1.51042 0.755208 0.655485i \(-0.227536\pi\)
0.755208 + 0.655485i \(0.227536\pi\)
\(522\) 22.1671 0.970227
\(523\) 12.0464 0.526754 0.263377 0.964693i \(-0.415164\pi\)
0.263377 + 0.964693i \(0.415164\pi\)
\(524\) −9.49369 −0.414734
\(525\) −67.7650 −2.95751
\(526\) −6.35171 −0.276948
\(527\) −16.4977 −0.718649
\(528\) 3.54385 0.154226
\(529\) 30.5748 1.32934
\(530\) −21.6682 −0.941206
\(531\) −16.9018 −0.733475
\(532\) 15.5981 0.676265
\(533\) 10.0128 0.433704
\(534\) −4.88564 −0.211422
\(535\) −21.0922 −0.911894
\(536\) 6.73124 0.290745
\(537\) 58.9587 2.54426
\(538\) −21.2676 −0.916911
\(539\) −4.29391 −0.184952
\(540\) −10.6551 −0.458524
\(541\) −11.7617 −0.505676 −0.252838 0.967509i \(-0.581364\pi\)
−0.252838 + 0.967509i \(0.581364\pi\)
\(542\) 25.0598 1.07641
\(543\) 35.1285 1.50751
\(544\) −6.09379 −0.261269
\(545\) 65.4954 2.80552
\(546\) 19.3592 0.828499
\(547\) 36.6164 1.56560 0.782802 0.622270i \(-0.213790\pi\)
0.782802 + 0.622270i \(0.213790\pi\)
\(548\) 11.5333 0.492679
\(549\) −18.0083 −0.768577
\(550\) 10.5589 0.450232
\(551\) −26.2978 −1.12032
\(552\) 19.5179 0.830737
\(553\) 17.9121 0.761702
\(554\) −1.28916 −0.0547710
\(555\) −20.5170 −0.870900
\(556\) 19.6241 0.832246
\(557\) −39.4054 −1.66966 −0.834830 0.550509i \(-0.814434\pi\)
−0.834830 + 0.550509i \(0.814434\pi\)
\(558\) 11.1286 0.471110
\(559\) 2.33715 0.0988509
\(560\) 11.5083 0.486312
\(561\) 21.5955 0.911761
\(562\) 11.5384 0.486716
\(563\) 36.6532 1.54475 0.772375 0.635167i \(-0.219069\pi\)
0.772375 + 0.635167i \(0.219069\pi\)
\(564\) −17.8609 −0.752081
\(565\) 37.5836 1.58115
\(566\) 10.5119 0.441850
\(567\) −14.1851 −0.595719
\(568\) 4.54564 0.190731
\(569\) −21.0877 −0.884044 −0.442022 0.897004i \(-0.645739\pi\)
−0.442022 + 0.897004i \(0.645739\pi\)
\(570\) 46.7863 1.95966
\(571\) −16.8959 −0.707072 −0.353536 0.935421i \(-0.615021\pi\)
−0.353536 + 0.935421i \(0.615021\pi\)
\(572\) −3.01648 −0.126125
\(573\) −9.80453 −0.409590
\(574\) −14.1103 −0.588954
\(575\) 58.1534 2.42516
\(576\) 4.11059 0.171275
\(577\) 25.2493 1.05114 0.525571 0.850750i \(-0.323852\pi\)
0.525571 + 0.850750i \(0.323852\pi\)
\(578\) −20.1342 −0.837474
\(579\) 18.3337 0.761922
\(580\) −19.4024 −0.805641
\(581\) −2.16096 −0.0896518
\(582\) 37.2494 1.54404
\(583\) −8.00376 −0.331482
\(584\) −10.2577 −0.424466
\(585\) 33.5686 1.38789
\(586\) 17.8079 0.735639
\(587\) 15.1066 0.623516 0.311758 0.950161i \(-0.399082\pi\)
0.311758 + 0.950161i \(0.399082\pi\)
\(588\) −8.61555 −0.355299
\(589\) −13.2023 −0.543992
\(590\) 14.7938 0.609050
\(591\) −4.27127 −0.175696
\(592\) 2.13851 0.0878921
\(593\) −8.33602 −0.342319 −0.171160 0.985243i \(-0.554751\pi\)
−0.171160 + 0.985243i \(0.554751\pi\)
\(594\) −3.93577 −0.161487
\(595\) 70.1288 2.87500
\(596\) 6.55575 0.268534
\(597\) −3.14705 −0.128800
\(598\) −16.6134 −0.679371
\(599\) −3.67650 −0.150218 −0.0751088 0.997175i \(-0.523930\pi\)
−0.0751088 + 0.997175i \(0.523930\pi\)
\(600\) 21.1859 0.864912
\(601\) 33.5749 1.36955 0.684775 0.728755i \(-0.259901\pi\)
0.684775 + 0.728755i \(0.259901\pi\)
\(602\) −3.29357 −0.134236
\(603\) −27.6694 −1.12678
\(604\) −18.7026 −0.760998
\(605\) −33.2224 −1.35068
\(606\) 28.5034 1.15787
\(607\) 29.7699 1.20832 0.604162 0.796862i \(-0.293508\pi\)
0.604162 + 0.796862i \(0.293508\pi\)
\(608\) −4.87657 −0.197771
\(609\) 45.9955 1.86383
\(610\) 15.7623 0.638198
\(611\) 15.2030 0.615047
\(612\) 25.0491 1.01255
\(613\) −13.2420 −0.534839 −0.267420 0.963580i \(-0.586171\pi\)
−0.267420 + 0.963580i \(0.586171\pi\)
\(614\) 20.8759 0.842481
\(615\) −42.3237 −1.70666
\(616\) 4.25090 0.171273
\(617\) −0.201658 −0.00811845 −0.00405923 0.999992i \(-0.501292\pi\)
−0.00405923 + 0.999992i \(0.501292\pi\)
\(618\) 26.3991 1.06193
\(619\) −20.3442 −0.817702 −0.408851 0.912601i \(-0.634070\pi\)
−0.408851 + 0.912601i \(0.634070\pi\)
\(620\) −9.74061 −0.391193
\(621\) −21.6764 −0.869845
\(622\) −20.5052 −0.822182
\(623\) −5.86039 −0.234791
\(624\) −6.05244 −0.242291
\(625\) −1.60178 −0.0640712
\(626\) 9.60209 0.383777
\(627\) 17.2819 0.690171
\(628\) −16.5108 −0.658854
\(629\) 13.0316 0.519604
\(630\) −47.3057 −1.88470
\(631\) −34.8064 −1.38562 −0.692811 0.721119i \(-0.743628\pi\)
−0.692811 + 0.721119i \(0.743628\pi\)
\(632\) −5.60002 −0.222757
\(633\) 57.0595 2.26791
\(634\) 22.4659 0.892234
\(635\) −41.3727 −1.64183
\(636\) −16.0592 −0.636789
\(637\) 7.33344 0.290561
\(638\) −7.16683 −0.283737
\(639\) −18.6853 −0.739178
\(640\) −3.59792 −0.142220
\(641\) 31.0353 1.22582 0.612910 0.790153i \(-0.289999\pi\)
0.612910 + 0.790153i \(0.289999\pi\)
\(642\) −15.6323 −0.616957
\(643\) 19.7146 0.777470 0.388735 0.921350i \(-0.372912\pi\)
0.388735 + 0.921350i \(0.372912\pi\)
\(644\) 23.4120 0.922561
\(645\) −9.87901 −0.388986
\(646\) −29.7168 −1.16919
\(647\) 14.3874 0.565629 0.282814 0.959175i \(-0.408732\pi\)
0.282814 + 0.959175i \(0.408732\pi\)
\(648\) 4.43481 0.174216
\(649\) 5.46450 0.214500
\(650\) −18.0332 −0.707319
\(651\) 23.0912 0.905014
\(652\) −15.7314 −0.616089
\(653\) 5.24123 0.205105 0.102553 0.994728i \(-0.467299\pi\)
0.102553 + 0.994728i \(0.467299\pi\)
\(654\) 48.5414 1.89812
\(655\) −34.1575 −1.33464
\(656\) 4.41143 0.172237
\(657\) 42.1652 1.64502
\(658\) −21.4244 −0.835211
\(659\) −32.5676 −1.26865 −0.634327 0.773065i \(-0.718723\pi\)
−0.634327 + 0.773065i \(0.718723\pi\)
\(660\) 12.7505 0.496312
\(661\) 0.377381 0.0146784 0.00733922 0.999973i \(-0.497664\pi\)
0.00733922 + 0.999973i \(0.497664\pi\)
\(662\) −12.3144 −0.478614
\(663\) −36.8823 −1.43239
\(664\) 0.675599 0.0262183
\(665\) 56.1208 2.17627
\(666\) −8.79053 −0.340626
\(667\) −39.4716 −1.52835
\(668\) −19.1834 −0.742229
\(669\) 62.8233 2.42889
\(670\) 24.2185 0.935641
\(671\) 5.82226 0.224766
\(672\) 8.52925 0.329023
\(673\) 28.3516 1.09287 0.546437 0.837500i \(-0.315984\pi\)
0.546437 + 0.837500i \(0.315984\pi\)
\(674\) 11.1065 0.427805
\(675\) −23.5289 −0.905629
\(676\) −7.84825 −0.301856
\(677\) −5.49077 −0.211027 −0.105514 0.994418i \(-0.533649\pi\)
−0.105514 + 0.994418i \(0.533649\pi\)
\(678\) 27.8548 1.06976
\(679\) 44.6811 1.71470
\(680\) −21.9249 −0.840783
\(681\) 39.1736 1.50113
\(682\) −3.59797 −0.137773
\(683\) −21.3734 −0.817830 −0.408915 0.912573i \(-0.634093\pi\)
−0.408915 + 0.912573i \(0.634093\pi\)
\(684\) 20.0456 0.766463
\(685\) 41.4959 1.58548
\(686\) 12.0556 0.460286
\(687\) 37.8991 1.44594
\(688\) 1.02970 0.0392568
\(689\) 13.6694 0.520762
\(690\) 70.2238 2.67337
\(691\) −26.3952 −1.00412 −0.502061 0.864832i \(-0.667425\pi\)
−0.502061 + 0.864832i \(0.667425\pi\)
\(692\) −7.94282 −0.301941
\(693\) −17.4737 −0.663771
\(694\) 28.1726 1.06942
\(695\) 70.6058 2.67823
\(696\) −14.3799 −0.545070
\(697\) 26.8823 1.01824
\(698\) −22.7155 −0.859795
\(699\) 63.9874 2.42023
\(700\) 25.4128 0.960514
\(701\) 32.9856 1.24585 0.622925 0.782282i \(-0.285944\pi\)
0.622925 + 0.782282i \(0.285944\pi\)
\(702\) 6.72178 0.253697
\(703\) 10.4286 0.393322
\(704\) −1.32899 −0.0500883
\(705\) −64.2622 −2.42025
\(706\) −20.2776 −0.763157
\(707\) 34.1902 1.28585
\(708\) 10.9643 0.412064
\(709\) 7.39923 0.277884 0.138942 0.990301i \(-0.455630\pi\)
0.138942 + 0.990301i \(0.455630\pi\)
\(710\) 16.3548 0.613786
\(711\) 23.0194 0.863295
\(712\) 1.83218 0.0686639
\(713\) −19.8160 −0.742114
\(714\) 51.9754 1.94513
\(715\) −10.8530 −0.405880
\(716\) −22.1103 −0.826302
\(717\) −65.8190 −2.45806
\(718\) −9.80334 −0.365858
\(719\) −10.3170 −0.384761 −0.192380 0.981320i \(-0.561621\pi\)
−0.192380 + 0.981320i \(0.561621\pi\)
\(720\) 14.7896 0.551175
\(721\) 31.6661 1.17931
\(722\) −4.78098 −0.177930
\(723\) −44.2461 −1.64553
\(724\) −13.1737 −0.489595
\(725\) −42.8449 −1.59122
\(726\) −24.6225 −0.913827
\(727\) −18.4038 −0.682560 −0.341280 0.939962i \(-0.610860\pi\)
−0.341280 + 0.939962i \(0.610860\pi\)
\(728\) −7.25998 −0.269073
\(729\) −41.9206 −1.55261
\(730\) −36.9063 −1.36596
\(731\) 6.27475 0.232080
\(732\) 11.6821 0.431784
\(733\) 41.4006 1.52917 0.764583 0.644526i \(-0.222945\pi\)
0.764583 + 0.644526i \(0.222945\pi\)
\(734\) 24.6913 0.911373
\(735\) −30.9980 −1.14338
\(736\) −7.31948 −0.269800
\(737\) 8.94577 0.329522
\(738\) −18.1336 −0.667507
\(739\) 51.3016 1.88716 0.943580 0.331146i \(-0.107435\pi\)
0.943580 + 0.331146i \(0.107435\pi\)
\(740\) 7.69417 0.282843
\(741\) −29.5152 −1.08427
\(742\) −19.2632 −0.707176
\(743\) −14.1002 −0.517285 −0.258642 0.965973i \(-0.583275\pi\)
−0.258642 + 0.965973i \(0.583275\pi\)
\(744\) −7.21918 −0.264668
\(745\) 23.5870 0.864162
\(746\) 30.8849 1.13078
\(747\) −2.77711 −0.101609
\(748\) −8.09860 −0.296114
\(749\) −18.7511 −0.685152
\(750\) 28.2548 1.03172
\(751\) −29.0479 −1.05997 −0.529986 0.848006i \(-0.677803\pi\)
−0.529986 + 0.848006i \(0.677803\pi\)
\(752\) 6.69810 0.244254
\(753\) −31.6520 −1.15346
\(754\) 12.2400 0.445755
\(755\) −67.2905 −2.44895
\(756\) −9.47251 −0.344512
\(757\) −32.0960 −1.16655 −0.583275 0.812275i \(-0.698229\pi\)
−0.583275 + 0.812275i \(0.698229\pi\)
\(758\) 0.433900 0.0157600
\(759\) 25.9391 0.941531
\(760\) −17.5455 −0.636443
\(761\) 12.0267 0.435966 0.217983 0.975953i \(-0.430052\pi\)
0.217983 + 0.975953i \(0.430052\pi\)
\(762\) −30.6631 −1.11081
\(763\) 58.2261 2.10793
\(764\) 3.67683 0.133023
\(765\) 90.1245 3.25846
\(766\) 11.0133 0.397926
\(767\) −9.33266 −0.336983
\(768\) −2.66657 −0.0962215
\(769\) 1.27561 0.0459996 0.0229998 0.999735i \(-0.492678\pi\)
0.0229998 + 0.999735i \(0.492678\pi\)
\(770\) 15.2944 0.551171
\(771\) −63.6965 −2.29397
\(772\) −6.87538 −0.247450
\(773\) −19.8733 −0.714791 −0.357396 0.933953i \(-0.616335\pi\)
−0.357396 + 0.933953i \(0.616335\pi\)
\(774\) −4.23266 −0.152140
\(775\) −21.5095 −0.772643
\(776\) −13.9690 −0.501459
\(777\) −18.2399 −0.654351
\(778\) 29.4374 1.05538
\(779\) 21.5127 0.770772
\(780\) −21.7762 −0.779712
\(781\) 6.04112 0.216168
\(782\) −44.6033 −1.59501
\(783\) 15.9702 0.570730
\(784\) 3.23095 0.115391
\(785\) −59.4046 −2.12024
\(786\) −25.3156 −0.902977
\(787\) 19.6093 0.698995 0.349498 0.936937i \(-0.386352\pi\)
0.349498 + 0.936937i \(0.386352\pi\)
\(788\) 1.60178 0.0570612
\(789\) −16.9373 −0.602983
\(790\) −20.1484 −0.716848
\(791\) 33.4122 1.18800
\(792\) 5.46295 0.194117
\(793\) −9.94367 −0.353110
\(794\) −21.5567 −0.765019
\(795\) −57.7797 −2.04924
\(796\) 1.18019 0.0418306
\(797\) −38.1433 −1.35110 −0.675552 0.737312i \(-0.736095\pi\)
−0.675552 + 0.737312i \(0.736095\pi\)
\(798\) 41.5935 1.47239
\(799\) 40.8168 1.44399
\(800\) −7.94502 −0.280899
\(801\) −7.53134 −0.266107
\(802\) 29.9435 1.05734
\(803\) −13.6324 −0.481077
\(804\) 17.9493 0.633024
\(805\) 84.2344 2.96887
\(806\) 6.14487 0.216444
\(807\) −56.7115 −1.99634
\(808\) −10.6892 −0.376043
\(809\) 7.33870 0.258015 0.129007 0.991644i \(-0.458821\pi\)
0.129007 + 0.991644i \(0.458821\pi\)
\(810\) 15.9561 0.560640
\(811\) 36.8868 1.29527 0.647636 0.761950i \(-0.275758\pi\)
0.647636 + 0.761950i \(0.275758\pi\)
\(812\) −17.2489 −0.605319
\(813\) 66.8236 2.34361
\(814\) 2.84206 0.0996141
\(815\) −56.6003 −1.98262
\(816\) −16.2495 −0.568846
\(817\) 5.02139 0.175676
\(818\) −16.2936 −0.569693
\(819\) 29.8428 1.04279
\(820\) 15.8720 0.554273
\(821\) 4.01688 0.140190 0.0700950 0.997540i \(-0.477670\pi\)
0.0700950 + 0.997540i \(0.477670\pi\)
\(822\) 30.7544 1.07268
\(823\) 16.2283 0.565685 0.282842 0.959166i \(-0.408723\pi\)
0.282842 + 0.959166i \(0.408723\pi\)
\(824\) −9.90004 −0.344884
\(825\) 28.1560 0.980265
\(826\) 13.1518 0.457610
\(827\) 26.6985 0.928399 0.464199 0.885731i \(-0.346342\pi\)
0.464199 + 0.885731i \(0.346342\pi\)
\(828\) 30.0874 1.04561
\(829\) 10.3889 0.360822 0.180411 0.983591i \(-0.442257\pi\)
0.180411 + 0.983591i \(0.442257\pi\)
\(830\) 2.43075 0.0843726
\(831\) −3.43762 −0.119250
\(832\) 2.26975 0.0786893
\(833\) 19.6887 0.682174
\(834\) 52.3289 1.81200
\(835\) −69.0204 −2.38855
\(836\) −6.48093 −0.224148
\(837\) 8.01756 0.277127
\(838\) 5.26824 0.181988
\(839\) −49.2725 −1.70108 −0.850538 0.525913i \(-0.823724\pi\)
−0.850538 + 0.525913i \(0.823724\pi\)
\(840\) 30.6875 1.05882
\(841\) 0.0809489 0.00279134
\(842\) −3.59050 −0.123737
\(843\) 30.7678 1.05970
\(844\) −21.3981 −0.736553
\(845\) −28.2374 −0.971395
\(846\) −27.5331 −0.946609
\(847\) −29.5350 −1.01484
\(848\) 6.02243 0.206811
\(849\) 28.0308 0.962015
\(850\) −48.4152 −1.66063
\(851\) 15.6528 0.536569
\(852\) 12.1213 0.415268
\(853\) −44.4165 −1.52079 −0.760397 0.649459i \(-0.774995\pi\)
−0.760397 + 0.649459i \(0.774995\pi\)
\(854\) 14.0129 0.479511
\(855\) 72.1225 2.46654
\(856\) 5.86232 0.200370
\(857\) −9.19397 −0.314060 −0.157030 0.987594i \(-0.550192\pi\)
−0.157030 + 0.987594i \(0.550192\pi\)
\(858\) −8.04364 −0.274605
\(859\) 0.626342 0.0213705 0.0106853 0.999943i \(-0.496599\pi\)
0.0106853 + 0.999943i \(0.496599\pi\)
\(860\) 3.70476 0.126331
\(861\) −37.6262 −1.28230
\(862\) 1.15129 0.0392132
\(863\) 5.33294 0.181535 0.0907677 0.995872i \(-0.471068\pi\)
0.0907677 + 0.995872i \(0.471068\pi\)
\(864\) 2.96147 0.100751
\(865\) −28.5776 −0.971669
\(866\) −16.7962 −0.570758
\(867\) −53.6893 −1.82339
\(868\) −8.65950 −0.293923
\(869\) −7.44238 −0.252466
\(870\) −51.7379 −1.75408
\(871\) −15.2782 −0.517682
\(872\) −18.2037 −0.616455
\(873\) 57.4209 1.94340
\(874\) −35.6940 −1.20737
\(875\) 33.8920 1.14576
\(876\) −27.3528 −0.924167
\(877\) 33.6104 1.13494 0.567472 0.823393i \(-0.307922\pi\)
0.567472 + 0.823393i \(0.307922\pi\)
\(878\) 34.9034 1.17793
\(879\) 47.4861 1.60167
\(880\) −4.78161 −0.161188
\(881\) 14.0574 0.473607 0.236803 0.971558i \(-0.423900\pi\)
0.236803 + 0.971558i \(0.423900\pi\)
\(882\) −13.2811 −0.447198
\(883\) 0.648007 0.0218072 0.0109036 0.999941i \(-0.496529\pi\)
0.0109036 + 0.999941i \(0.496529\pi\)
\(884\) 13.8313 0.465199
\(885\) 39.4487 1.32605
\(886\) 0.622830 0.0209244
\(887\) 45.0985 1.51426 0.757129 0.653265i \(-0.226601\pi\)
0.757129 + 0.653265i \(0.226601\pi\)
\(888\) 5.70248 0.191363
\(889\) −36.7808 −1.23359
\(890\) 6.59204 0.220966
\(891\) 5.89383 0.197451
\(892\) −23.5596 −0.788834
\(893\) 32.6638 1.09305
\(894\) 17.4813 0.584664
\(895\) −79.5512 −2.65910
\(896\) −3.19859 −0.106857
\(897\) −44.3007 −1.47916
\(898\) 1.56565 0.0522466
\(899\) 14.5995 0.486922
\(900\) 32.6587 1.08862
\(901\) 36.6994 1.22263
\(902\) 5.86276 0.195209
\(903\) −8.78254 −0.292265
\(904\) −10.4459 −0.347426
\(905\) −47.3978 −1.57555
\(906\) −49.8718 −1.65688
\(907\) 40.0990 1.33147 0.665733 0.746190i \(-0.268119\pi\)
0.665733 + 0.746190i \(0.268119\pi\)
\(908\) −14.6906 −0.487526
\(909\) 43.9388 1.45736
\(910\) −26.1208 −0.865896
\(911\) 43.0149 1.42515 0.712574 0.701597i \(-0.247529\pi\)
0.712574 + 0.701597i \(0.247529\pi\)
\(912\) −13.0037 −0.430596
\(913\) 0.897866 0.0297150
\(914\) 7.80596 0.258198
\(915\) 42.0314 1.38951
\(916\) −14.2127 −0.469600
\(917\) −30.3664 −1.00279
\(918\) 18.0466 0.595625
\(919\) 29.5540 0.974895 0.487448 0.873152i \(-0.337928\pi\)
0.487448 + 0.873152i \(0.337928\pi\)
\(920\) −26.3349 −0.868236
\(921\) 55.6669 1.83429
\(922\) −32.5904 −1.07331
\(923\) −10.3174 −0.339603
\(924\) 11.3353 0.372904
\(925\) 16.9905 0.558643
\(926\) −1.65032 −0.0542330
\(927\) 40.6950 1.33660
\(928\) 5.39268 0.177023
\(929\) 0.891824 0.0292598 0.0146299 0.999893i \(-0.495343\pi\)
0.0146299 + 0.999893i \(0.495343\pi\)
\(930\) −25.9740 −0.851722
\(931\) 15.7560 0.516381
\(932\) −23.9962 −0.786020
\(933\) −54.6785 −1.79009
\(934\) 21.9615 0.718602
\(935\) −29.1381 −0.952917
\(936\) −9.33000 −0.304961
\(937\) −23.3613 −0.763180 −0.381590 0.924332i \(-0.624623\pi\)
−0.381590 + 0.924332i \(0.624623\pi\)
\(938\) 21.5305 0.702994
\(939\) 25.6046 0.835576
\(940\) 24.0992 0.786029
\(941\) −4.93692 −0.160939 −0.0804695 0.996757i \(-0.525642\pi\)
−0.0804695 + 0.996757i \(0.525642\pi\)
\(942\) −44.0273 −1.43449
\(943\) 32.2894 1.05149
\(944\) −4.11176 −0.133826
\(945\) −34.0813 −1.10867
\(946\) 1.36846 0.0444924
\(947\) 5.24835 0.170549 0.0852743 0.996358i \(-0.472823\pi\)
0.0852743 + 0.996358i \(0.472823\pi\)
\(948\) −14.9328 −0.484996
\(949\) 23.2824 0.755777
\(950\) −38.7445 −1.25704
\(951\) 59.9068 1.94261
\(952\) −19.4915 −0.631723
\(953\) −6.68845 −0.216660 −0.108330 0.994115i \(-0.534550\pi\)
−0.108330 + 0.994115i \(0.534550\pi\)
\(954\) −24.7557 −0.801496
\(955\) 13.2290 0.428079
\(956\) 24.6830 0.798306
\(957\) −19.1108 −0.617766
\(958\) 8.67908 0.280408
\(959\) 36.8903 1.19125
\(960\) −9.59410 −0.309648
\(961\) −23.6706 −0.763567
\(962\) −4.85387 −0.156495
\(963\) −24.0976 −0.776535
\(964\) 16.5929 0.534421
\(965\) −24.7371 −0.796314
\(966\) 62.4297 2.00864
\(967\) −14.3457 −0.461327 −0.230663 0.973034i \(-0.574090\pi\)
−0.230663 + 0.973034i \(0.574090\pi\)
\(968\) 9.23378 0.296785
\(969\) −79.2419 −2.54562
\(970\) −50.2594 −1.61373
\(971\) 47.4118 1.52152 0.760758 0.649035i \(-0.224827\pi\)
0.760758 + 0.649035i \(0.224827\pi\)
\(972\) 20.7101 0.664278
\(973\) 62.7692 2.01229
\(974\) 21.4000 0.685701
\(975\) −48.0867 −1.54001
\(976\) −4.38096 −0.140231
\(977\) 59.5117 1.90395 0.951974 0.306180i \(-0.0990511\pi\)
0.951974 + 0.306180i \(0.0990511\pi\)
\(978\) −41.9488 −1.34138
\(979\) 2.43495 0.0778215
\(980\) 11.6247 0.371337
\(981\) 74.8280 2.38907
\(982\) −5.96869 −0.190469
\(983\) 23.1944 0.739788 0.369894 0.929074i \(-0.379394\pi\)
0.369894 + 0.929074i \(0.379394\pi\)
\(984\) 11.7634 0.375003
\(985\) 5.76309 0.183627
\(986\) 32.8618 1.04653
\(987\) −57.1297 −1.81846
\(988\) 11.0686 0.352139
\(989\) 7.53684 0.239658
\(990\) 19.6552 0.624684
\(991\) −19.6101 −0.622936 −0.311468 0.950257i \(-0.600821\pi\)
−0.311468 + 0.950257i \(0.600821\pi\)
\(992\) 2.70729 0.0859566
\(993\) −32.8373 −1.04206
\(994\) 14.5396 0.461169
\(995\) 4.24621 0.134614
\(996\) 1.80153 0.0570837
\(997\) −13.7603 −0.435794 −0.217897 0.975972i \(-0.569920\pi\)
−0.217897 + 0.975972i \(0.569920\pi\)
\(998\) 16.9220 0.535655
\(999\) −6.33312 −0.200371
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 8014.2.a.e.1.13 91
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8014.2.a.e.1.13 91 1.1 even 1 trivial