Properties

Label 6014.2.a.l.1.20
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $38$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.173832 q^{3} +1.00000 q^{4} -1.31890 q^{5} +0.173832 q^{6} -4.23696 q^{7} -1.00000 q^{8} -2.96978 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.173832 q^{3} +1.00000 q^{4} -1.31890 q^{5} +0.173832 q^{6} -4.23696 q^{7} -1.00000 q^{8} -2.96978 q^{9} +1.31890 q^{10} -3.61787 q^{11} -0.173832 q^{12} +3.62079 q^{13} +4.23696 q^{14} +0.229266 q^{15} +1.00000 q^{16} +6.39360 q^{17} +2.96978 q^{18} -6.69433 q^{19} -1.31890 q^{20} +0.736518 q^{21} +3.61787 q^{22} -9.21759 q^{23} +0.173832 q^{24} -3.26051 q^{25} -3.62079 q^{26} +1.03774 q^{27} -4.23696 q^{28} -6.74803 q^{29} -0.229266 q^{30} +1.00000 q^{31} -1.00000 q^{32} +0.628900 q^{33} -6.39360 q^{34} +5.58811 q^{35} -2.96978 q^{36} +10.0326 q^{37} +6.69433 q^{38} -0.629408 q^{39} +1.31890 q^{40} -8.49568 q^{41} -0.736518 q^{42} -12.1935 q^{43} -3.61787 q^{44} +3.91684 q^{45} +9.21759 q^{46} +1.87213 q^{47} -0.173832 q^{48} +10.9518 q^{49} +3.26051 q^{50} -1.11141 q^{51} +3.62079 q^{52} -6.92618 q^{53} -1.03774 q^{54} +4.77159 q^{55} +4.23696 q^{56} +1.16369 q^{57} +6.74803 q^{58} -12.6522 q^{59} +0.229266 q^{60} -6.60424 q^{61} -1.00000 q^{62} +12.5828 q^{63} +1.00000 q^{64} -4.77544 q^{65} -0.628900 q^{66} -4.94181 q^{67} +6.39360 q^{68} +1.60231 q^{69} -5.58811 q^{70} -2.79897 q^{71} +2.96978 q^{72} +0.608398 q^{73} -10.0326 q^{74} +0.566780 q^{75} -6.69433 q^{76} +15.3287 q^{77} +0.629408 q^{78} -14.7478 q^{79} -1.31890 q^{80} +8.72896 q^{81} +8.49568 q^{82} -14.4747 q^{83} +0.736518 q^{84} -8.43250 q^{85} +12.1935 q^{86} +1.17302 q^{87} +3.61787 q^{88} +13.4900 q^{89} -3.91684 q^{90} -15.3411 q^{91} -9.21759 q^{92} -0.173832 q^{93} -1.87213 q^{94} +8.82913 q^{95} +0.173832 q^{96} -1.00000 q^{97} -10.9518 q^{98} +10.7443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 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
\(3\) −0.173832 −0.100362 −0.0501809 0.998740i \(-0.515980\pi\)
−0.0501809 + 0.998740i \(0.515980\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.31890 −0.589829 −0.294914 0.955524i \(-0.595291\pi\)
−0.294914 + 0.955524i \(0.595291\pi\)
\(6\) 0.173832 0.0709665
\(7\) −4.23696 −1.60142 −0.800710 0.599053i \(-0.795544\pi\)
−0.800710 + 0.599053i \(0.795544\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.96978 −0.989927
\(10\) 1.31890 0.417072
\(11\) −3.61787 −1.09083 −0.545414 0.838167i \(-0.683628\pi\)
−0.545414 + 0.838167i \(0.683628\pi\)
\(12\) −0.173832 −0.0501809
\(13\) 3.62079 1.00423 0.502113 0.864802i \(-0.332556\pi\)
0.502113 + 0.864802i \(0.332556\pi\)
\(14\) 4.23696 1.13237
\(15\) 0.229266 0.0591963
\(16\) 1.00000 0.250000
\(17\) 6.39360 1.55068 0.775338 0.631546i \(-0.217579\pi\)
0.775338 + 0.631546i \(0.217579\pi\)
\(18\) 2.96978 0.699984
\(19\) −6.69433 −1.53578 −0.767892 0.640579i \(-0.778694\pi\)
−0.767892 + 0.640579i \(0.778694\pi\)
\(20\) −1.31890 −0.294914
\(21\) 0.736518 0.160721
\(22\) 3.61787 0.771332
\(23\) −9.21759 −1.92200 −0.961000 0.276548i \(-0.910809\pi\)
−0.961000 + 0.276548i \(0.910809\pi\)
\(24\) 0.173832 0.0354833
\(25\) −3.26051 −0.652102
\(26\) −3.62079 −0.710094
\(27\) 1.03774 0.199713
\(28\) −4.23696 −0.800710
\(29\) −6.74803 −1.25308 −0.626539 0.779390i \(-0.715529\pi\)
−0.626539 + 0.779390i \(0.715529\pi\)
\(30\) −0.229266 −0.0418581
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) 0.628900 0.109478
\(34\) −6.39360 −1.09649
\(35\) 5.58811 0.944563
\(36\) −2.96978 −0.494964
\(37\) 10.0326 1.64935 0.824676 0.565605i \(-0.191357\pi\)
0.824676 + 0.565605i \(0.191357\pi\)
\(38\) 6.69433 1.08596
\(39\) −0.629408 −0.100786
\(40\) 1.31890 0.208536
\(41\) −8.49568 −1.32680 −0.663401 0.748264i \(-0.730888\pi\)
−0.663401 + 0.748264i \(0.730888\pi\)
\(42\) −0.736518 −0.113647
\(43\) −12.1935 −1.85949 −0.929746 0.368202i \(-0.879974\pi\)
−0.929746 + 0.368202i \(0.879974\pi\)
\(44\) −3.61787 −0.545414
\(45\) 3.91684 0.583888
\(46\) 9.21759 1.35906
\(47\) 1.87213 0.273078 0.136539 0.990635i \(-0.456402\pi\)
0.136539 + 0.990635i \(0.456402\pi\)
\(48\) −0.173832 −0.0250905
\(49\) 10.9518 1.56454
\(50\) 3.26051 0.461106
\(51\) −1.11141 −0.155629
\(52\) 3.62079 0.502113
\(53\) −6.92618 −0.951384 −0.475692 0.879612i \(-0.657802\pi\)
−0.475692 + 0.879612i \(0.657802\pi\)
\(54\) −1.03774 −0.141218
\(55\) 4.77159 0.643402
\(56\) 4.23696 0.566187
\(57\) 1.16369 0.154134
\(58\) 6.74803 0.886059
\(59\) −12.6522 −1.64718 −0.823590 0.567186i \(-0.808032\pi\)
−0.823590 + 0.567186i \(0.808032\pi\)
\(60\) 0.229266 0.0295982
\(61\) −6.60424 −0.845587 −0.422793 0.906226i \(-0.638950\pi\)
−0.422793 + 0.906226i \(0.638950\pi\)
\(62\) −1.00000 −0.127000
\(63\) 12.5828 1.58529
\(64\) 1.00000 0.125000
\(65\) −4.77544 −0.592321
\(66\) −0.628900 −0.0774123
\(67\) −4.94181 −0.603739 −0.301869 0.953349i \(-0.597611\pi\)
−0.301869 + 0.953349i \(0.597611\pi\)
\(68\) 6.39360 0.775338
\(69\) 1.60231 0.192895
\(70\) −5.58811 −0.667907
\(71\) −2.79897 −0.332176 −0.166088 0.986111i \(-0.553114\pi\)
−0.166088 + 0.986111i \(0.553114\pi\)
\(72\) 2.96978 0.349992
\(73\) 0.608398 0.0712076 0.0356038 0.999366i \(-0.488665\pi\)
0.0356038 + 0.999366i \(0.488665\pi\)
\(74\) −10.0326 −1.16627
\(75\) 0.566780 0.0654462
\(76\) −6.69433 −0.767892
\(77\) 15.3287 1.74687
\(78\) 0.629408 0.0712664
\(79\) −14.7478 −1.65926 −0.829631 0.558312i \(-0.811449\pi\)
−0.829631 + 0.558312i \(0.811449\pi\)
\(80\) −1.31890 −0.147457
\(81\) 8.72896 0.969884
\(82\) 8.49568 0.938191
\(83\) −14.4747 −1.58881 −0.794403 0.607391i \(-0.792216\pi\)
−0.794403 + 0.607391i \(0.792216\pi\)
\(84\) 0.736518 0.0803607
\(85\) −8.43250 −0.914633
\(86\) 12.1935 1.31486
\(87\) 1.17302 0.125761
\(88\) 3.61787 0.385666
\(89\) 13.4900 1.42994 0.714970 0.699155i \(-0.246440\pi\)
0.714970 + 0.699155i \(0.246440\pi\)
\(90\) −3.91684 −0.412871
\(91\) −15.3411 −1.60819
\(92\) −9.21759 −0.961000
\(93\) −0.173832 −0.0180255
\(94\) −1.87213 −0.193096
\(95\) 8.82913 0.905850
\(96\) 0.173832 0.0177416
\(97\) −1.00000 −0.101535
\(98\) −10.9518 −1.10630
\(99\) 10.7443 1.07984
\(100\) −3.26051 −0.326051
\(101\) −13.9642 −1.38949 −0.694743 0.719258i \(-0.744482\pi\)
−0.694743 + 0.719258i \(0.744482\pi\)
\(102\) 1.11141 0.110046
\(103\) 2.32597 0.229184 0.114592 0.993413i \(-0.463444\pi\)
0.114592 + 0.993413i \(0.463444\pi\)
\(104\) −3.62079 −0.355047
\(105\) −0.971391 −0.0947981
\(106\) 6.92618 0.672730
\(107\) −12.6743 −1.22527 −0.612635 0.790366i \(-0.709890\pi\)
−0.612635 + 0.790366i \(0.709890\pi\)
\(108\) 1.03774 0.0998564
\(109\) −18.1590 −1.73932 −0.869658 0.493655i \(-0.835661\pi\)
−0.869658 + 0.493655i \(0.835661\pi\)
\(110\) −4.77159 −0.454954
\(111\) −1.74399 −0.165532
\(112\) −4.23696 −0.400355
\(113\) 13.0026 1.22318 0.611591 0.791174i \(-0.290530\pi\)
0.611591 + 0.791174i \(0.290530\pi\)
\(114\) −1.16369 −0.108989
\(115\) 12.1571 1.13365
\(116\) −6.74803 −0.626539
\(117\) −10.7529 −0.994110
\(118\) 12.6522 1.16473
\(119\) −27.0894 −2.48328
\(120\) −0.229266 −0.0209291
\(121\) 2.08896 0.189906
\(122\) 6.60424 0.597920
\(123\) 1.47682 0.133160
\(124\) 1.00000 0.0898027
\(125\) 10.8948 0.974457
\(126\) −12.5828 −1.12097
\(127\) 8.34281 0.740305 0.370152 0.928971i \(-0.379306\pi\)
0.370152 + 0.928971i \(0.379306\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 2.11962 0.186622
\(130\) 4.77544 0.418834
\(131\) 15.3536 1.34145 0.670727 0.741705i \(-0.265982\pi\)
0.670727 + 0.741705i \(0.265982\pi\)
\(132\) 0.628900 0.0547388
\(133\) 28.3636 2.45943
\(134\) 4.94181 0.426908
\(135\) −1.36867 −0.117796
\(136\) −6.39360 −0.548247
\(137\) 5.54086 0.473387 0.236694 0.971584i \(-0.423936\pi\)
0.236694 + 0.971584i \(0.423936\pi\)
\(138\) −1.60231 −0.136398
\(139\) 6.11248 0.518454 0.259227 0.965816i \(-0.416532\pi\)
0.259227 + 0.965816i \(0.416532\pi\)
\(140\) 5.58811 0.472282
\(141\) −0.325436 −0.0274066
\(142\) 2.79897 0.234884
\(143\) −13.0995 −1.09544
\(144\) −2.96978 −0.247482
\(145\) 8.89995 0.739101
\(146\) −0.608398 −0.0503514
\(147\) −1.90377 −0.157021
\(148\) 10.0326 0.824676
\(149\) −4.93241 −0.404078 −0.202039 0.979377i \(-0.564757\pi\)
−0.202039 + 0.979377i \(0.564757\pi\)
\(150\) −0.566780 −0.0462774
\(151\) −0.674030 −0.0548518 −0.0274259 0.999624i \(-0.508731\pi\)
−0.0274259 + 0.999624i \(0.508731\pi\)
\(152\) 6.69433 0.542982
\(153\) −18.9876 −1.53506
\(154\) −15.3287 −1.23523
\(155\) −1.31890 −0.105936
\(156\) −0.629408 −0.0503929
\(157\) 11.6883 0.932830 0.466415 0.884566i \(-0.345545\pi\)
0.466415 + 0.884566i \(0.345545\pi\)
\(158\) 14.7478 1.17328
\(159\) 1.20399 0.0954826
\(160\) 1.31890 0.104268
\(161\) 39.0545 3.07793
\(162\) −8.72896 −0.685812
\(163\) 11.1027 0.869630 0.434815 0.900520i \(-0.356814\pi\)
0.434815 + 0.900520i \(0.356814\pi\)
\(164\) −8.49568 −0.663401
\(165\) −0.829455 −0.0645730
\(166\) 14.4747 1.12346
\(167\) −9.06043 −0.701117 −0.350558 0.936541i \(-0.614008\pi\)
−0.350558 + 0.936541i \(0.614008\pi\)
\(168\) −0.736518 −0.0568236
\(169\) 0.110086 0.00846817
\(170\) 8.43250 0.646743
\(171\) 19.8807 1.52032
\(172\) −12.1935 −0.929746
\(173\) −12.6604 −0.962555 −0.481277 0.876568i \(-0.659827\pi\)
−0.481277 + 0.876568i \(0.659827\pi\)
\(174\) −1.17302 −0.0889265
\(175\) 13.8146 1.04429
\(176\) −3.61787 −0.272707
\(177\) 2.19936 0.165314
\(178\) −13.4900 −1.01112
\(179\) 9.89983 0.739948 0.369974 0.929042i \(-0.379367\pi\)
0.369974 + 0.929042i \(0.379367\pi\)
\(180\) 3.91684 0.291944
\(181\) −4.97321 −0.369655 −0.184828 0.982771i \(-0.559173\pi\)
−0.184828 + 0.982771i \(0.559173\pi\)
\(182\) 15.3411 1.13716
\(183\) 1.14803 0.0848647
\(184\) 9.21759 0.679530
\(185\) −13.2320 −0.972836
\(186\) 0.173832 0.0127460
\(187\) −23.1312 −1.69152
\(188\) 1.87213 0.136539
\(189\) −4.39685 −0.319824
\(190\) −8.82913 −0.640532
\(191\) 9.19255 0.665150 0.332575 0.943077i \(-0.392083\pi\)
0.332575 + 0.943077i \(0.392083\pi\)
\(192\) −0.173832 −0.0125452
\(193\) 3.43888 0.247536 0.123768 0.992311i \(-0.460502\pi\)
0.123768 + 0.992311i \(0.460502\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0.830124 0.0594464
\(196\) 10.9518 0.782272
\(197\) 23.5917 1.68084 0.840419 0.541938i \(-0.182309\pi\)
0.840419 + 0.541938i \(0.182309\pi\)
\(198\) −10.7443 −0.763563
\(199\) 3.42905 0.243079 0.121540 0.992587i \(-0.461217\pi\)
0.121540 + 0.992587i \(0.461217\pi\)
\(200\) 3.26051 0.230553
\(201\) 0.859045 0.0605923
\(202\) 13.9642 0.982515
\(203\) 28.5911 2.00670
\(204\) −1.11141 −0.0778144
\(205\) 11.2049 0.782586
\(206\) −2.32597 −0.162058
\(207\) 27.3742 1.90264
\(208\) 3.62079 0.251056
\(209\) 24.2192 1.67528
\(210\) 0.971391 0.0670324
\(211\) 6.88052 0.473674 0.236837 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(212\) −6.92618 −0.475692
\(213\) 0.486550 0.0333378
\(214\) 12.6743 0.866396
\(215\) 16.0820 1.09678
\(216\) −1.03774 −0.0706091
\(217\) −4.23696 −0.287623
\(218\) 18.1590 1.22988
\(219\) −0.105759 −0.00714653
\(220\) 4.77159 0.321701
\(221\) 23.1499 1.55723
\(222\) 1.74399 0.117049
\(223\) 4.06475 0.272196 0.136098 0.990695i \(-0.456544\pi\)
0.136098 + 0.990695i \(0.456544\pi\)
\(224\) 4.23696 0.283094
\(225\) 9.68301 0.645534
\(226\) −13.0026 −0.864921
\(227\) 0.866799 0.0575315 0.0287657 0.999586i \(-0.490842\pi\)
0.0287657 + 0.999586i \(0.490842\pi\)
\(228\) 1.16369 0.0770671
\(229\) 15.1554 1.00150 0.500748 0.865593i \(-0.333059\pi\)
0.500748 + 0.865593i \(0.333059\pi\)
\(230\) −12.1571 −0.801612
\(231\) −2.66462 −0.175319
\(232\) 6.74803 0.443030
\(233\) 5.38639 0.352874 0.176437 0.984312i \(-0.443543\pi\)
0.176437 + 0.984312i \(0.443543\pi\)
\(234\) 10.7529 0.702942
\(235\) −2.46915 −0.161069
\(236\) −12.6522 −0.823590
\(237\) 2.56364 0.166527
\(238\) 27.0894 1.75595
\(239\) −17.6518 −1.14180 −0.570901 0.821019i \(-0.693406\pi\)
−0.570901 + 0.821019i \(0.693406\pi\)
\(240\) 0.229266 0.0147991
\(241\) −3.92400 −0.252767 −0.126383 0.991981i \(-0.540337\pi\)
−0.126383 + 0.991981i \(0.540337\pi\)
\(242\) −2.08896 −0.134284
\(243\) −4.63058 −0.297052
\(244\) −6.60424 −0.422793
\(245\) −14.4443 −0.922813
\(246\) −1.47682 −0.0941586
\(247\) −24.2387 −1.54227
\(248\) −1.00000 −0.0635001
\(249\) 2.51617 0.159456
\(250\) −10.8948 −0.689045
\(251\) −27.8382 −1.75713 −0.878567 0.477619i \(-0.841500\pi\)
−0.878567 + 0.477619i \(0.841500\pi\)
\(252\) 12.5828 0.792644
\(253\) 33.3480 2.09657
\(254\) −8.34281 −0.523474
\(255\) 1.46584 0.0917943
\(256\) 1.00000 0.0625000
\(257\) 1.99512 0.124452 0.0622262 0.998062i \(-0.480180\pi\)
0.0622262 + 0.998062i \(0.480180\pi\)
\(258\) −2.11962 −0.131962
\(259\) −42.5078 −2.64131
\(260\) −4.77544 −0.296160
\(261\) 20.0402 1.24046
\(262\) −15.3536 −0.948551
\(263\) 2.99842 0.184890 0.0924451 0.995718i \(-0.470532\pi\)
0.0924451 + 0.995718i \(0.470532\pi\)
\(264\) −0.628900 −0.0387061
\(265\) 9.13491 0.561153
\(266\) −28.3636 −1.73908
\(267\) −2.34500 −0.143511
\(268\) −4.94181 −0.301869
\(269\) 4.42303 0.269677 0.134838 0.990868i \(-0.456948\pi\)
0.134838 + 0.990868i \(0.456948\pi\)
\(270\) 1.36867 0.0832946
\(271\) 27.8927 1.69436 0.847181 0.531304i \(-0.178298\pi\)
0.847181 + 0.531304i \(0.178298\pi\)
\(272\) 6.39360 0.387669
\(273\) 2.66677 0.161400
\(274\) −5.54086 −0.334735
\(275\) 11.7961 0.711331
\(276\) 1.60231 0.0964477
\(277\) −8.08413 −0.485728 −0.242864 0.970060i \(-0.578087\pi\)
−0.242864 + 0.970060i \(0.578087\pi\)
\(278\) −6.11248 −0.366602
\(279\) −2.96978 −0.177796
\(280\) −5.58811 −0.333953
\(281\) −32.6934 −1.95032 −0.975162 0.221494i \(-0.928907\pi\)
−0.975162 + 0.221494i \(0.928907\pi\)
\(282\) 0.325436 0.0193794
\(283\) −7.15089 −0.425076 −0.212538 0.977153i \(-0.568173\pi\)
−0.212538 + 0.977153i \(0.568173\pi\)
\(284\) −2.79897 −0.166088
\(285\) −1.53478 −0.0909127
\(286\) 13.0995 0.774591
\(287\) 35.9958 2.12477
\(288\) 2.96978 0.174996
\(289\) 23.8781 1.40460
\(290\) −8.89995 −0.522623
\(291\) 0.173832 0.0101902
\(292\) 0.608398 0.0356038
\(293\) −0.212267 −0.0124008 −0.00620039 0.999981i \(-0.501974\pi\)
−0.00620039 + 0.999981i \(0.501974\pi\)
\(294\) 1.90377 0.111030
\(295\) 16.6870 0.971554
\(296\) −10.0326 −0.583134
\(297\) −3.75440 −0.217852
\(298\) 4.93241 0.285727
\(299\) −33.3749 −1.93012
\(300\) 0.566780 0.0327231
\(301\) 51.6633 2.97783
\(302\) 0.674030 0.0387861
\(303\) 2.42741 0.139451
\(304\) −6.69433 −0.383946
\(305\) 8.71032 0.498751
\(306\) 18.9876 1.08545
\(307\) −7.50586 −0.428382 −0.214191 0.976792i \(-0.568711\pi\)
−0.214191 + 0.976792i \(0.568711\pi\)
\(308\) 15.3287 0.873437
\(309\) −0.404327 −0.0230014
\(310\) 1.31890 0.0749083
\(311\) −26.5197 −1.50379 −0.751897 0.659281i \(-0.770861\pi\)
−0.751897 + 0.659281i \(0.770861\pi\)
\(312\) 0.629408 0.0356332
\(313\) −16.5080 −0.933086 −0.466543 0.884499i \(-0.654501\pi\)
−0.466543 + 0.884499i \(0.654501\pi\)
\(314\) −11.6883 −0.659611
\(315\) −16.5955 −0.935049
\(316\) −14.7478 −0.829631
\(317\) 6.43940 0.361673 0.180836 0.983513i \(-0.442120\pi\)
0.180836 + 0.983513i \(0.442120\pi\)
\(318\) −1.20399 −0.0675164
\(319\) 24.4135 1.36689
\(320\) −1.31890 −0.0737286
\(321\) 2.20319 0.122970
\(322\) −39.0545 −2.17642
\(323\) −42.8009 −2.38150
\(324\) 8.72896 0.484942
\(325\) −11.8056 −0.654857
\(326\) −11.1027 −0.614921
\(327\) 3.15661 0.174561
\(328\) 8.49568 0.469095
\(329\) −7.93214 −0.437313
\(330\) 0.829455 0.0456600
\(331\) 16.8284 0.924974 0.462487 0.886626i \(-0.346957\pi\)
0.462487 + 0.886626i \(0.346957\pi\)
\(332\) −14.4747 −0.794403
\(333\) −29.7947 −1.63274
\(334\) 9.06043 0.495764
\(335\) 6.51774 0.356102
\(336\) 0.736518 0.0401804
\(337\) −27.0110 −1.47138 −0.735691 0.677318i \(-0.763142\pi\)
−0.735691 + 0.677318i \(0.763142\pi\)
\(338\) −0.110086 −0.00598790
\(339\) −2.26027 −0.122761
\(340\) −8.43250 −0.457317
\(341\) −3.61787 −0.195918
\(342\) −19.8807 −1.07503
\(343\) −16.7436 −0.904071
\(344\) 12.1935 0.657430
\(345\) −2.11328 −0.113775
\(346\) 12.6604 0.680629
\(347\) 9.78225 0.525138 0.262569 0.964913i \(-0.415430\pi\)
0.262569 + 0.964913i \(0.415430\pi\)
\(348\) 1.17302 0.0628806
\(349\) −22.8126 −1.22113 −0.610565 0.791966i \(-0.709058\pi\)
−0.610565 + 0.791966i \(0.709058\pi\)
\(350\) −13.8146 −0.738424
\(351\) 3.75743 0.200557
\(352\) 3.61787 0.192833
\(353\) 3.05550 0.162628 0.0813140 0.996689i \(-0.474088\pi\)
0.0813140 + 0.996689i \(0.474088\pi\)
\(354\) −2.19936 −0.116895
\(355\) 3.69155 0.195927
\(356\) 13.4900 0.714970
\(357\) 4.70900 0.249227
\(358\) −9.89983 −0.523222
\(359\) 31.3452 1.65434 0.827168 0.561954i \(-0.189950\pi\)
0.827168 + 0.561954i \(0.189950\pi\)
\(360\) −3.91684 −0.206435
\(361\) 25.8140 1.35863
\(362\) 4.97321 0.261386
\(363\) −0.363128 −0.0190593
\(364\) −15.3411 −0.804093
\(365\) −0.802415 −0.0420003
\(366\) −1.14803 −0.0600084
\(367\) 0.529997 0.0276656 0.0138328 0.999904i \(-0.495597\pi\)
0.0138328 + 0.999904i \(0.495597\pi\)
\(368\) −9.21759 −0.480500
\(369\) 25.2303 1.31344
\(370\) 13.2320 0.687899
\(371\) 29.3459 1.52356
\(372\) −0.173832 −0.00901276
\(373\) −23.4992 −1.21674 −0.608371 0.793652i \(-0.708177\pi\)
−0.608371 + 0.793652i \(0.708177\pi\)
\(374\) 23.1312 1.19609
\(375\) −1.89386 −0.0977983
\(376\) −1.87213 −0.0965478
\(377\) −24.4332 −1.25837
\(378\) 4.39685 0.226150
\(379\) −19.6438 −1.00904 −0.504518 0.863401i \(-0.668330\pi\)
−0.504518 + 0.863401i \(0.668330\pi\)
\(380\) 8.82913 0.452925
\(381\) −1.45025 −0.0742983
\(382\) −9.19255 −0.470332
\(383\) −9.46299 −0.483536 −0.241768 0.970334i \(-0.577727\pi\)
−0.241768 + 0.970334i \(0.577727\pi\)
\(384\) 0.173832 0.00887082
\(385\) −20.2170 −1.03036
\(386\) −3.43888 −0.175034
\(387\) 36.2121 1.84076
\(388\) −1.00000 −0.0507673
\(389\) 31.2880 1.58637 0.793183 0.608983i \(-0.208422\pi\)
0.793183 + 0.608983i \(0.208422\pi\)
\(390\) −0.830124 −0.0420350
\(391\) −58.9336 −2.98040
\(392\) −10.9518 −0.553150
\(393\) −2.66895 −0.134631
\(394\) −23.5917 −1.18853
\(395\) 19.4509 0.978680
\(396\) 10.7443 0.539920
\(397\) 3.82153 0.191797 0.0958985 0.995391i \(-0.469428\pi\)
0.0958985 + 0.995391i \(0.469428\pi\)
\(398\) −3.42905 −0.171883
\(399\) −4.93049 −0.246833
\(400\) −3.26051 −0.163026
\(401\) −12.8041 −0.639408 −0.319704 0.947518i \(-0.603583\pi\)
−0.319704 + 0.947518i \(0.603583\pi\)
\(402\) −0.859045 −0.0428452
\(403\) 3.62079 0.180364
\(404\) −13.9642 −0.694743
\(405\) −11.5126 −0.572065
\(406\) −28.5911 −1.41895
\(407\) −36.2967 −1.79916
\(408\) 1.11141 0.0550231
\(409\) −21.2957 −1.05300 −0.526502 0.850174i \(-0.676497\pi\)
−0.526502 + 0.850174i \(0.676497\pi\)
\(410\) −11.2049 −0.553372
\(411\) −0.963177 −0.0475100
\(412\) 2.32597 0.114592
\(413\) 53.6069 2.63782
\(414\) −27.3742 −1.34537
\(415\) 19.0907 0.937124
\(416\) −3.62079 −0.177524
\(417\) −1.06254 −0.0520330
\(418\) −24.2192 −1.18460
\(419\) 4.03517 0.197131 0.0985654 0.995131i \(-0.468575\pi\)
0.0985654 + 0.995131i \(0.468575\pi\)
\(420\) −0.971391 −0.0473990
\(421\) 7.42421 0.361834 0.180917 0.983498i \(-0.442093\pi\)
0.180917 + 0.983498i \(0.442093\pi\)
\(422\) −6.88052 −0.334938
\(423\) −5.55982 −0.270328
\(424\) 6.92618 0.336365
\(425\) −20.8464 −1.01120
\(426\) −0.486550 −0.0235734
\(427\) 27.9819 1.35414
\(428\) −12.6743 −0.612635
\(429\) 2.27711 0.109940
\(430\) −16.0820 −0.775542
\(431\) 11.4262 0.550380 0.275190 0.961390i \(-0.411259\pi\)
0.275190 + 0.961390i \(0.411259\pi\)
\(432\) 1.03774 0.0499282
\(433\) −20.6999 −0.994773 −0.497386 0.867529i \(-0.665707\pi\)
−0.497386 + 0.867529i \(0.665707\pi\)
\(434\) 4.23696 0.203380
\(435\) −1.54709 −0.0741775
\(436\) −18.1590 −0.869658
\(437\) 61.7056 2.95178
\(438\) 0.105759 0.00505336
\(439\) 12.7594 0.608974 0.304487 0.952517i \(-0.401515\pi\)
0.304487 + 0.952517i \(0.401515\pi\)
\(440\) −4.77159 −0.227477
\(441\) −32.5245 −1.54878
\(442\) −23.1499 −1.10113
\(443\) −13.3180 −0.632757 −0.316379 0.948633i \(-0.602467\pi\)
−0.316379 + 0.948633i \(0.602467\pi\)
\(444\) −1.74399 −0.0827660
\(445\) −17.7920 −0.843420
\(446\) −4.06475 −0.192471
\(447\) 0.857409 0.0405541
\(448\) −4.23696 −0.200177
\(449\) −24.1592 −1.14014 −0.570072 0.821594i \(-0.693085\pi\)
−0.570072 + 0.821594i \(0.693085\pi\)
\(450\) −9.68301 −0.456461
\(451\) 30.7362 1.44731
\(452\) 13.0026 0.611591
\(453\) 0.117168 0.00550502
\(454\) −0.866799 −0.0406809
\(455\) 20.2333 0.948554
\(456\) −1.16369 −0.0544947
\(457\) 23.1157 1.08131 0.540653 0.841246i \(-0.318177\pi\)
0.540653 + 0.841246i \(0.318177\pi\)
\(458\) −15.1554 −0.708164
\(459\) 6.63488 0.309690
\(460\) 12.1571 0.566825
\(461\) −15.7824 −0.735059 −0.367529 0.930012i \(-0.619796\pi\)
−0.367529 + 0.930012i \(0.619796\pi\)
\(462\) 2.66462 0.123970
\(463\) 11.8773 0.551984 0.275992 0.961160i \(-0.410994\pi\)
0.275992 + 0.961160i \(0.410994\pi\)
\(464\) −6.74803 −0.313269
\(465\) 0.229266 0.0106320
\(466\) −5.38639 −0.249520
\(467\) −27.1256 −1.25522 −0.627611 0.778527i \(-0.715967\pi\)
−0.627611 + 0.778527i \(0.715967\pi\)
\(468\) −10.7529 −0.497055
\(469\) 20.9383 0.966839
\(470\) 2.46915 0.113893
\(471\) −2.03180 −0.0936206
\(472\) 12.6522 0.582366
\(473\) 44.1145 2.02839
\(474\) −2.56364 −0.117752
\(475\) 21.8269 1.00149
\(476\) −27.0894 −1.24164
\(477\) 20.5692 0.941801
\(478\) 17.6518 0.807376
\(479\) 16.3194 0.745652 0.372826 0.927901i \(-0.378389\pi\)
0.372826 + 0.927901i \(0.378389\pi\)
\(480\) −0.229266 −0.0104645
\(481\) 36.3260 1.65632
\(482\) 3.92400 0.178733
\(483\) −6.78892 −0.308907
\(484\) 2.08896 0.0949529
\(485\) 1.31890 0.0598880
\(486\) 4.63058 0.210048
\(487\) 14.9165 0.675931 0.337966 0.941158i \(-0.390261\pi\)
0.337966 + 0.941158i \(0.390261\pi\)
\(488\) 6.60424 0.298960
\(489\) −1.93000 −0.0872777
\(490\) 14.4443 0.652527
\(491\) −16.6762 −0.752585 −0.376292 0.926501i \(-0.622801\pi\)
−0.376292 + 0.926501i \(0.622801\pi\)
\(492\) 1.47682 0.0665802
\(493\) −43.1442 −1.94312
\(494\) 24.2387 1.09055
\(495\) −14.1706 −0.636921
\(496\) 1.00000 0.0449013
\(497\) 11.8591 0.531953
\(498\) −2.51617 −0.112752
\(499\) 31.1702 1.39537 0.697686 0.716404i \(-0.254213\pi\)
0.697686 + 0.716404i \(0.254213\pi\)
\(500\) 10.8948 0.487229
\(501\) 1.57499 0.0703654
\(502\) 27.8382 1.24248
\(503\) 4.86875 0.217087 0.108543 0.994092i \(-0.465381\pi\)
0.108543 + 0.994092i \(0.465381\pi\)
\(504\) −12.5828 −0.560484
\(505\) 18.4173 0.819558
\(506\) −33.3480 −1.48250
\(507\) −0.0191365 −0.000849881 0
\(508\) 8.34281 0.370152
\(509\) −1.43778 −0.0637286 −0.0318643 0.999492i \(-0.510144\pi\)
−0.0318643 + 0.999492i \(0.510144\pi\)
\(510\) −1.46584 −0.0649084
\(511\) −2.57776 −0.114033
\(512\) −1.00000 −0.0441942
\(513\) −6.94696 −0.306716
\(514\) −1.99512 −0.0880011
\(515\) −3.06771 −0.135179
\(516\) 2.11962 0.0933110
\(517\) −6.77312 −0.297881
\(518\) 42.5078 1.86768
\(519\) 2.20079 0.0966038
\(520\) 4.77544 0.209417
\(521\) −39.4832 −1.72979 −0.864896 0.501951i \(-0.832616\pi\)
−0.864896 + 0.501951i \(0.832616\pi\)
\(522\) −20.0402 −0.877134
\(523\) 37.3384 1.63270 0.816348 0.577560i \(-0.195995\pi\)
0.816348 + 0.577560i \(0.195995\pi\)
\(524\) 15.3536 0.670727
\(525\) −2.40142 −0.104807
\(526\) −2.99842 −0.130737
\(527\) 6.39360 0.278510
\(528\) 0.628900 0.0273694
\(529\) 61.9639 2.69408
\(530\) −9.13491 −0.396795
\(531\) 37.5744 1.63059
\(532\) 28.3636 1.22972
\(533\) −30.7610 −1.33241
\(534\) 2.34500 0.101478
\(535\) 16.7161 0.722699
\(536\) 4.94181 0.213454
\(537\) −1.72091 −0.0742626
\(538\) −4.42303 −0.190690
\(539\) −39.6222 −1.70665
\(540\) −1.36867 −0.0588982
\(541\) −12.4064 −0.533393 −0.266697 0.963781i \(-0.585932\pi\)
−0.266697 + 0.963781i \(0.585932\pi\)
\(542\) −27.8927 −1.19810
\(543\) 0.864501 0.0370993
\(544\) −6.39360 −0.274123
\(545\) 23.9498 1.02590
\(546\) −2.66677 −0.114127
\(547\) 24.6365 1.05338 0.526690 0.850057i \(-0.323433\pi\)
0.526690 + 0.850057i \(0.323433\pi\)
\(548\) 5.54086 0.236694
\(549\) 19.6132 0.837070
\(550\) −11.7961 −0.502987
\(551\) 45.1735 1.92446
\(552\) −1.60231 −0.0681988
\(553\) 62.4860 2.65717
\(554\) 8.08413 0.343462
\(555\) 2.30014 0.0976356
\(556\) 6.11248 0.259227
\(557\) −21.7501 −0.921580 −0.460790 0.887509i \(-0.652434\pi\)
−0.460790 + 0.887509i \(0.652434\pi\)
\(558\) 2.96978 0.125721
\(559\) −44.1501 −1.86735
\(560\) 5.58811 0.236141
\(561\) 4.02094 0.169764
\(562\) 32.6934 1.37909
\(563\) −25.3959 −1.07031 −0.535154 0.844754i \(-0.679747\pi\)
−0.535154 + 0.844754i \(0.679747\pi\)
\(564\) −0.325436 −0.0137033
\(565\) −17.1491 −0.721468
\(566\) 7.15089 0.300574
\(567\) −36.9842 −1.55319
\(568\) 2.79897 0.117442
\(569\) −22.3151 −0.935497 −0.467749 0.883862i \(-0.654935\pi\)
−0.467749 + 0.883862i \(0.654935\pi\)
\(570\) 1.53478 0.0642850
\(571\) 25.2273 1.05573 0.527866 0.849328i \(-0.322992\pi\)
0.527866 + 0.849328i \(0.322992\pi\)
\(572\) −13.0995 −0.547718
\(573\) −1.59796 −0.0667557
\(574\) −35.9958 −1.50244
\(575\) 30.0540 1.25334
\(576\) −2.96978 −0.123741
\(577\) −39.4406 −1.64193 −0.820967 0.570975i \(-0.806565\pi\)
−0.820967 + 0.570975i \(0.806565\pi\)
\(578\) −23.8781 −0.993200
\(579\) −0.597786 −0.0248432
\(580\) 8.89995 0.369550
\(581\) 61.3288 2.54435
\(582\) −0.173832 −0.00720556
\(583\) 25.0580 1.03780
\(584\) −0.608398 −0.0251757
\(585\) 14.1820 0.586355
\(586\) 0.212267 0.00876867
\(587\) −27.7266 −1.14440 −0.572200 0.820114i \(-0.693910\pi\)
−0.572200 + 0.820114i \(0.693910\pi\)
\(588\) −1.90377 −0.0785103
\(589\) −6.69433 −0.275835
\(590\) −16.6870 −0.686992
\(591\) −4.10098 −0.168692
\(592\) 10.0326 0.412338
\(593\) 8.88644 0.364922 0.182461 0.983213i \(-0.441594\pi\)
0.182461 + 0.983213i \(0.441594\pi\)
\(594\) 3.75440 0.154045
\(595\) 35.7282 1.46471
\(596\) −4.93241 −0.202039
\(597\) −0.596079 −0.0243959
\(598\) 33.3749 1.36480
\(599\) −28.1985 −1.15216 −0.576079 0.817394i \(-0.695418\pi\)
−0.576079 + 0.817394i \(0.695418\pi\)
\(600\) −0.566780 −0.0231387
\(601\) 33.4749 1.36547 0.682736 0.730665i \(-0.260790\pi\)
0.682736 + 0.730665i \(0.260790\pi\)
\(602\) −51.6633 −2.10564
\(603\) 14.6761 0.597658
\(604\) −0.674030 −0.0274259
\(605\) −2.75513 −0.112012
\(606\) −2.42741 −0.0986070
\(607\) −23.2609 −0.944132 −0.472066 0.881563i \(-0.656492\pi\)
−0.472066 + 0.881563i \(0.656492\pi\)
\(608\) 6.69433 0.271491
\(609\) −4.97004 −0.201396
\(610\) −8.71032 −0.352671
\(611\) 6.77858 0.274232
\(612\) −18.9876 −0.767528
\(613\) 24.3093 0.981845 0.490922 0.871203i \(-0.336660\pi\)
0.490922 + 0.871203i \(0.336660\pi\)
\(614\) 7.50586 0.302912
\(615\) −1.94777 −0.0785418
\(616\) −15.3287 −0.617613
\(617\) 10.9593 0.441205 0.220602 0.975364i \(-0.429198\pi\)
0.220602 + 0.975364i \(0.429198\pi\)
\(618\) 0.404327 0.0162644
\(619\) 35.1657 1.41343 0.706714 0.707499i \(-0.250177\pi\)
0.706714 + 0.707499i \(0.250177\pi\)
\(620\) −1.31890 −0.0529682
\(621\) −9.56544 −0.383848
\(622\) 26.5197 1.06334
\(623\) −57.1567 −2.28993
\(624\) −0.629408 −0.0251965
\(625\) 1.93348 0.0773392
\(626\) 16.5080 0.659791
\(627\) −4.21007 −0.168134
\(628\) 11.6883 0.466415
\(629\) 64.1446 2.55761
\(630\) 16.5955 0.661179
\(631\) 1.14073 0.0454117 0.0227059 0.999742i \(-0.492772\pi\)
0.0227059 + 0.999742i \(0.492772\pi\)
\(632\) 14.7478 0.586638
\(633\) −1.19605 −0.0475388
\(634\) −6.43940 −0.255741
\(635\) −11.0033 −0.436653
\(636\) 1.20399 0.0477413
\(637\) 39.6541 1.57115
\(638\) −24.4135 −0.966538
\(639\) 8.31232 0.328830
\(640\) 1.31890 0.0521340
\(641\) −36.2581 −1.43211 −0.716055 0.698044i \(-0.754054\pi\)
−0.716055 + 0.698044i \(0.754054\pi\)
\(642\) −2.20319 −0.0869531
\(643\) 14.2857 0.563374 0.281687 0.959506i \(-0.409106\pi\)
0.281687 + 0.959506i \(0.409106\pi\)
\(644\) 39.0545 1.53896
\(645\) −2.79556 −0.110075
\(646\) 42.8009 1.68398
\(647\) 28.9194 1.13694 0.568470 0.822704i \(-0.307536\pi\)
0.568470 + 0.822704i \(0.307536\pi\)
\(648\) −8.72896 −0.342906
\(649\) 45.7741 1.79679
\(650\) 11.8056 0.463054
\(651\) 0.736518 0.0288664
\(652\) 11.1027 0.434815
\(653\) −45.5471 −1.78239 −0.891197 0.453616i \(-0.850134\pi\)
−0.891197 + 0.453616i \(0.850134\pi\)
\(654\) −3.15661 −0.123433
\(655\) −20.2499 −0.791228
\(656\) −8.49568 −0.331701
\(657\) −1.80681 −0.0704904
\(658\) 7.93214 0.309227
\(659\) 43.4631 1.69308 0.846541 0.532324i \(-0.178681\pi\)
0.846541 + 0.532324i \(0.178681\pi\)
\(660\) −0.829455 −0.0322865
\(661\) −17.5186 −0.681396 −0.340698 0.940173i \(-0.610663\pi\)
−0.340698 + 0.940173i \(0.610663\pi\)
\(662\) −16.8284 −0.654056
\(663\) −4.02418 −0.156286
\(664\) 14.4747 0.561728
\(665\) −37.4086 −1.45065
\(666\) 29.7947 1.15452
\(667\) 62.2005 2.40841
\(668\) −9.06043 −0.350558
\(669\) −0.706582 −0.0273180
\(670\) −6.51774 −0.251802
\(671\) 23.8933 0.922390
\(672\) −0.736518 −0.0284118
\(673\) −29.5198 −1.13790 −0.568952 0.822371i \(-0.692651\pi\)
−0.568952 + 0.822371i \(0.692651\pi\)
\(674\) 27.0110 1.04042
\(675\) −3.38356 −0.130233
\(676\) 0.110086 0.00423408
\(677\) −44.2751 −1.70163 −0.850815 0.525465i \(-0.823891\pi\)
−0.850815 + 0.525465i \(0.823891\pi\)
\(678\) 2.26027 0.0868051
\(679\) 4.23696 0.162599
\(680\) 8.43250 0.323372
\(681\) −0.150677 −0.00577397
\(682\) 3.61787 0.138535
\(683\) −21.3490 −0.816898 −0.408449 0.912781i \(-0.633930\pi\)
−0.408449 + 0.912781i \(0.633930\pi\)
\(684\) 19.8807 0.760158
\(685\) −7.30782 −0.279217
\(686\) 16.7436 0.639275
\(687\) −2.63449 −0.100512
\(688\) −12.1935 −0.464873
\(689\) −25.0782 −0.955403
\(690\) 2.11328 0.0804513
\(691\) 14.9082 0.567135 0.283567 0.958952i \(-0.408482\pi\)
0.283567 + 0.958952i \(0.408482\pi\)
\(692\) −12.6604 −0.481277
\(693\) −45.5230 −1.72928
\(694\) −9.78225 −0.371329
\(695\) −8.06174 −0.305799
\(696\) −1.17302 −0.0444633
\(697\) −54.3180 −2.05744
\(698\) 22.8126 0.863470
\(699\) −0.936326 −0.0354151
\(700\) 13.8146 0.522144
\(701\) −43.5750 −1.64580 −0.822902 0.568184i \(-0.807646\pi\)
−0.822902 + 0.568184i \(0.807646\pi\)
\(702\) −3.75743 −0.141815
\(703\) −67.1617 −2.53305
\(704\) −3.61787 −0.136354
\(705\) 0.429216 0.0161652
\(706\) −3.05550 −0.114995
\(707\) 59.1655 2.22515
\(708\) 2.19936 0.0826570
\(709\) 6.08427 0.228499 0.114250 0.993452i \(-0.463554\pi\)
0.114250 + 0.993452i \(0.463554\pi\)
\(710\) −3.69155 −0.138541
\(711\) 43.7979 1.64255
\(712\) −13.4900 −0.505560
\(713\) −9.21759 −0.345201
\(714\) −4.70900 −0.176230
\(715\) 17.2769 0.646120
\(716\) 9.89983 0.369974
\(717\) 3.06845 0.114593
\(718\) −31.3452 −1.16979
\(719\) −5.71962 −0.213306 −0.106653 0.994296i \(-0.534013\pi\)
−0.106653 + 0.994296i \(0.534013\pi\)
\(720\) 3.91684 0.145972
\(721\) −9.85502 −0.367020
\(722\) −25.8140 −0.960699
\(723\) 0.682115 0.0253681
\(724\) −4.97321 −0.184828
\(725\) 22.0020 0.817134
\(726\) 0.363128 0.0134770
\(727\) 8.17750 0.303287 0.151643 0.988435i \(-0.451543\pi\)
0.151643 + 0.988435i \(0.451543\pi\)
\(728\) 15.3411 0.568579
\(729\) −25.3819 −0.940071
\(730\) 0.802415 0.0296987
\(731\) −77.9604 −2.88347
\(732\) 1.14803 0.0424323
\(733\) −37.5681 −1.38761 −0.693805 0.720163i \(-0.744067\pi\)
−0.693805 + 0.720163i \(0.744067\pi\)
\(734\) −0.529997 −0.0195625
\(735\) 2.51088 0.0926152
\(736\) 9.21759 0.339765
\(737\) 17.8788 0.658575
\(738\) −25.2303 −0.928741
\(739\) 14.9091 0.548441 0.274220 0.961667i \(-0.411580\pi\)
0.274220 + 0.961667i \(0.411580\pi\)
\(740\) −13.2320 −0.486418
\(741\) 4.21346 0.154785
\(742\) −29.3459 −1.07732
\(743\) −23.6468 −0.867516 −0.433758 0.901029i \(-0.642813\pi\)
−0.433758 + 0.901029i \(0.642813\pi\)
\(744\) 0.173832 0.00637298
\(745\) 6.50534 0.238337
\(746\) 23.4992 0.860367
\(747\) 42.9868 1.57280
\(748\) −23.1312 −0.845760
\(749\) 53.7004 1.96217
\(750\) 1.89386 0.0691539
\(751\) −41.4838 −1.51377 −0.756883 0.653551i \(-0.773279\pi\)
−0.756883 + 0.653551i \(0.773279\pi\)
\(752\) 1.87213 0.0682696
\(753\) 4.83917 0.176349
\(754\) 24.4332 0.889803
\(755\) 0.888976 0.0323531
\(756\) −4.39685 −0.159912
\(757\) 9.85862 0.358318 0.179159 0.983820i \(-0.442662\pi\)
0.179159 + 0.983820i \(0.442662\pi\)
\(758\) 19.6438 0.713496
\(759\) −5.79695 −0.210416
\(760\) −8.82913 −0.320266
\(761\) 11.4352 0.414526 0.207263 0.978285i \(-0.433544\pi\)
0.207263 + 0.978285i \(0.433544\pi\)
\(762\) 1.45025 0.0525369
\(763\) 76.9389 2.78537
\(764\) 9.19255 0.332575
\(765\) 25.0427 0.905421
\(766\) 9.46299 0.341912
\(767\) −45.8110 −1.65414
\(768\) −0.173832 −0.00627262
\(769\) −11.0578 −0.398754 −0.199377 0.979923i \(-0.563892\pi\)
−0.199377 + 0.979923i \(0.563892\pi\)
\(770\) 20.2170 0.728572
\(771\) −0.346816 −0.0124903
\(772\) 3.43888 0.123768
\(773\) −38.2248 −1.37485 −0.687426 0.726255i \(-0.741259\pi\)
−0.687426 + 0.726255i \(0.741259\pi\)
\(774\) −36.2121 −1.30162
\(775\) −3.26051 −0.117121
\(776\) 1.00000 0.0358979
\(777\) 7.38921 0.265086
\(778\) −31.2880 −1.12173
\(779\) 56.8729 2.03768
\(780\) 0.830124 0.0297232
\(781\) 10.1263 0.362347
\(782\) 58.9336 2.10746
\(783\) −7.00268 −0.250256
\(784\) 10.9518 0.391136
\(785\) −15.4157 −0.550210
\(786\) 2.66895 0.0951983
\(787\) 43.0967 1.53623 0.768116 0.640311i \(-0.221195\pi\)
0.768116 + 0.640311i \(0.221195\pi\)
\(788\) 23.5917 0.840419
\(789\) −0.521220 −0.0185559
\(790\) −19.4509 −0.692031
\(791\) −55.0915 −1.95883
\(792\) −10.7443 −0.381781
\(793\) −23.9126 −0.849160
\(794\) −3.82153 −0.135621
\(795\) −1.58794 −0.0563184
\(796\) 3.42905 0.121540
\(797\) −0.876194 −0.0310364 −0.0155182 0.999880i \(-0.504940\pi\)
−0.0155182 + 0.999880i \(0.504940\pi\)
\(798\) 4.93049 0.174538
\(799\) 11.9697 0.423456
\(800\) 3.26051 0.115276
\(801\) −40.0625 −1.41554
\(802\) 12.8041 0.452130
\(803\) −2.20110 −0.0776753
\(804\) 0.859045 0.0302962
\(805\) −51.5089 −1.81545
\(806\) −3.62079 −0.127537
\(807\) −0.768863 −0.0270653
\(808\) 13.9642 0.491257
\(809\) −29.1068 −1.02334 −0.511671 0.859181i \(-0.670973\pi\)
−0.511671 + 0.859181i \(0.670973\pi\)
\(810\) 11.5126 0.404511
\(811\) −52.0320 −1.82709 −0.913545 0.406738i \(-0.866666\pi\)
−0.913545 + 0.406738i \(0.866666\pi\)
\(812\) 28.5911 1.00335
\(813\) −4.84864 −0.170049
\(814\) 36.2967 1.27220
\(815\) −14.6433 −0.512933
\(816\) −1.11141 −0.0389072
\(817\) 81.6273 2.85578
\(818\) 21.2957 0.744587
\(819\) 45.5598 1.59199
\(820\) 11.2049 0.391293
\(821\) 2.04825 0.0714843 0.0357421 0.999361i \(-0.488620\pi\)
0.0357421 + 0.999361i \(0.488620\pi\)
\(822\) 0.963177 0.0335947
\(823\) 4.36551 0.152172 0.0760861 0.997101i \(-0.475758\pi\)
0.0760861 + 0.997101i \(0.475758\pi\)
\(824\) −2.32597 −0.0810289
\(825\) −2.05054 −0.0713905
\(826\) −53.6069 −1.86522
\(827\) −8.08686 −0.281208 −0.140604 0.990066i \(-0.544904\pi\)
−0.140604 + 0.990066i \(0.544904\pi\)
\(828\) 27.3742 0.951320
\(829\) −16.9502 −0.588705 −0.294352 0.955697i \(-0.595104\pi\)
−0.294352 + 0.955697i \(0.595104\pi\)
\(830\) −19.0907 −0.662647
\(831\) 1.40528 0.0487486
\(832\) 3.62079 0.125528
\(833\) 70.0215 2.42610
\(834\) 1.06254 0.0367929
\(835\) 11.9498 0.413539
\(836\) 24.2192 0.837638
\(837\) 1.03774 0.0358695
\(838\) −4.03517 −0.139393
\(839\) −31.3851 −1.08354 −0.541768 0.840528i \(-0.682245\pi\)
−0.541768 + 0.840528i \(0.682245\pi\)
\(840\) 0.971391 0.0335162
\(841\) 16.5359 0.570202
\(842\) −7.42421 −0.255855
\(843\) 5.68315 0.195738
\(844\) 6.88052 0.236837
\(845\) −0.145192 −0.00499477
\(846\) 5.55982 0.191151
\(847\) −8.85085 −0.304119
\(848\) −6.92618 −0.237846
\(849\) 1.24305 0.0426615
\(850\) 20.8464 0.715026
\(851\) −92.4766 −3.17006
\(852\) 0.486550 0.0166689
\(853\) 24.3909 0.835127 0.417564 0.908648i \(-0.362884\pi\)
0.417564 + 0.908648i \(0.362884\pi\)
\(854\) −27.9819 −0.957521
\(855\) −26.2206 −0.896725
\(856\) 12.6743 0.433198
\(857\) 6.00163 0.205012 0.102506 0.994732i \(-0.467314\pi\)
0.102506 + 0.994732i \(0.467314\pi\)
\(858\) −2.27711 −0.0777394
\(859\) 55.9301 1.90831 0.954156 0.299310i \(-0.0967566\pi\)
0.954156 + 0.299310i \(0.0967566\pi\)
\(860\) 16.0820 0.548391
\(861\) −6.25722 −0.213246
\(862\) −11.4262 −0.389177
\(863\) 19.5488 0.665449 0.332725 0.943024i \(-0.392032\pi\)
0.332725 + 0.943024i \(0.392032\pi\)
\(864\) −1.03774 −0.0353046
\(865\) 16.6978 0.567742
\(866\) 20.6999 0.703411
\(867\) −4.15078 −0.140968
\(868\) −4.23696 −0.143812
\(869\) 53.3557 1.80997
\(870\) 1.54709 0.0524514
\(871\) −17.8932 −0.606290
\(872\) 18.1590 0.614941
\(873\) 2.96978 0.100512
\(874\) −61.7056 −2.08722
\(875\) −46.1606 −1.56051
\(876\) −0.105759 −0.00357326
\(877\) −11.9413 −0.403228 −0.201614 0.979465i \(-0.564619\pi\)
−0.201614 + 0.979465i \(0.564619\pi\)
\(878\) −12.7594 −0.430610
\(879\) 0.0368988 0.00124456
\(880\) 4.77159 0.160850
\(881\) −45.4310 −1.53061 −0.765304 0.643669i \(-0.777412\pi\)
−0.765304 + 0.643669i \(0.777412\pi\)
\(882\) 32.5245 1.09516
\(883\) 22.5467 0.758757 0.379378 0.925242i \(-0.376138\pi\)
0.379378 + 0.925242i \(0.376138\pi\)
\(884\) 23.1499 0.778614
\(885\) −2.90073 −0.0975069
\(886\) 13.3180 0.447427
\(887\) −22.4420 −0.753530 −0.376765 0.926309i \(-0.622964\pi\)
−0.376765 + 0.926309i \(0.622964\pi\)
\(888\) 1.74399 0.0585244
\(889\) −35.3481 −1.18554
\(890\) 17.7920 0.596388
\(891\) −31.5802 −1.05798
\(892\) 4.06475 0.136098
\(893\) −12.5327 −0.419389
\(894\) −0.857409 −0.0286761
\(895\) −13.0569 −0.436443
\(896\) 4.23696 0.141547
\(897\) 5.80162 0.193710
\(898\) 24.1592 0.806204
\(899\) −6.74803 −0.225059
\(900\) 9.68301 0.322767
\(901\) −44.2832 −1.47529
\(902\) −30.7362 −1.02340
\(903\) −8.98073 −0.298860
\(904\) −13.0026 −0.432460
\(905\) 6.55915 0.218033
\(906\) −0.117168 −0.00389264
\(907\) −11.1784 −0.371171 −0.185586 0.982628i \(-0.559418\pi\)
−0.185586 + 0.982628i \(0.559418\pi\)
\(908\) 0.866799 0.0287657
\(909\) 41.4705 1.37549
\(910\) −20.2333 −0.670729
\(911\) 18.0496 0.598011 0.299006 0.954251i \(-0.403345\pi\)
0.299006 + 0.954251i \(0.403345\pi\)
\(912\) 1.16369 0.0385335
\(913\) 52.3676 1.73311
\(914\) −23.1157 −0.764599
\(915\) −1.51413 −0.0500556
\(916\) 15.1554 0.500748
\(917\) −65.0527 −2.14823
\(918\) −6.63488 −0.218984
\(919\) 46.3061 1.52750 0.763749 0.645514i \(-0.223357\pi\)
0.763749 + 0.645514i \(0.223357\pi\)
\(920\) −12.1571 −0.400806
\(921\) 1.30476 0.0429932
\(922\) 15.7824 0.519765
\(923\) −10.1345 −0.333580
\(924\) −2.66462 −0.0876597
\(925\) −32.7115 −1.07555
\(926\) −11.8773 −0.390312
\(927\) −6.90761 −0.226876
\(928\) 6.74803 0.221515
\(929\) 37.4875 1.22993 0.614963 0.788556i \(-0.289171\pi\)
0.614963 + 0.788556i \(0.289171\pi\)
\(930\) −0.229266 −0.00751794
\(931\) −73.3150 −2.40280
\(932\) 5.38639 0.176437
\(933\) 4.60996 0.150923
\(934\) 27.1256 0.887576
\(935\) 30.5077 0.997708
\(936\) 10.7529 0.351471
\(937\) −39.8737 −1.30262 −0.651309 0.758812i \(-0.725780\pi\)
−0.651309 + 0.758812i \(0.725780\pi\)
\(938\) −20.9383 −0.683658
\(939\) 2.86961 0.0936462
\(940\) −2.46915 −0.0805347
\(941\) −0.123850 −0.00403740 −0.00201870 0.999998i \(-0.500643\pi\)
−0.00201870 + 0.999998i \(0.500643\pi\)
\(942\) 2.03180 0.0661998
\(943\) 78.3097 2.55011
\(944\) −12.6522 −0.411795
\(945\) 5.79900 0.188641
\(946\) −44.1145 −1.43429
\(947\) −33.0353 −1.07350 −0.536751 0.843741i \(-0.680349\pi\)
−0.536751 + 0.843741i \(0.680349\pi\)
\(948\) 2.56364 0.0832633
\(949\) 2.20288 0.0715085
\(950\) −21.8269 −0.708159
\(951\) −1.11937 −0.0362981
\(952\) 27.0894 0.877973
\(953\) 45.1825 1.46361 0.731803 0.681516i \(-0.238679\pi\)
0.731803 + 0.681516i \(0.238679\pi\)
\(954\) −20.5692 −0.665954
\(955\) −12.1240 −0.392324
\(956\) −17.6518 −0.570901
\(957\) −4.24384 −0.137184
\(958\) −16.3194 −0.527256
\(959\) −23.4764 −0.758091
\(960\) 0.229266 0.00739954
\(961\) 1.00000 0.0322581
\(962\) −36.3260 −1.17120
\(963\) 37.6399 1.21293
\(964\) −3.92400 −0.126383
\(965\) −4.53553 −0.146004
\(966\) 6.78892 0.218430
\(967\) 15.5107 0.498789 0.249395 0.968402i \(-0.419768\pi\)
0.249395 + 0.968402i \(0.419768\pi\)
\(968\) −2.08896 −0.0671418
\(969\) 7.44015 0.239012
\(970\) −1.31890 −0.0423472
\(971\) 11.5909 0.371969 0.185985 0.982553i \(-0.440453\pi\)
0.185985 + 0.982553i \(0.440453\pi\)
\(972\) −4.63058 −0.148526
\(973\) −25.8983 −0.830262
\(974\) −14.9165 −0.477955
\(975\) 2.05219 0.0657227
\(976\) −6.60424 −0.211397
\(977\) 43.9247 1.40527 0.702637 0.711548i \(-0.252006\pi\)
0.702637 + 0.711548i \(0.252006\pi\)
\(978\) 1.93000 0.0617147
\(979\) −48.8051 −1.55982
\(980\) −14.4443 −0.461406
\(981\) 53.9283 1.72180
\(982\) 16.6762 0.532158
\(983\) 41.1580 1.31274 0.656368 0.754441i \(-0.272092\pi\)
0.656368 + 0.754441i \(0.272092\pi\)
\(984\) −1.47682 −0.0470793
\(985\) −31.1150 −0.991406
\(986\) 43.1442 1.37399
\(987\) 1.37886 0.0438895
\(988\) −24.2387 −0.771137
\(989\) 112.395 3.57394
\(990\) 14.1706 0.450371
\(991\) −10.7951 −0.342919 −0.171459 0.985191i \(-0.554848\pi\)
−0.171459 + 0.985191i \(0.554848\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −2.92532 −0.0928321
\(994\) −11.8591 −0.376148
\(995\) −4.52257 −0.143375
\(996\) 2.51617 0.0797278
\(997\) −33.1731 −1.05060 −0.525301 0.850917i \(-0.676047\pi\)
−0.525301 + 0.850917i \(0.676047\pi\)
\(998\) −31.1702 −0.986677
\(999\) 10.4112 0.329397
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 6014.2.a.l.1.20 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.l.1.20 38 1.1 even 1 trivial