Properties

Label 6002.2.a.a.1.11
Level $6002$
Weight $2$
Character 6002.1
Self dual yes
Analytic conductor $47.926$
Analytic rank $1$
Dimension $47$
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] = [6002,2,Mod(1,6002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6002, 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("6002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6002.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: \(47.9262112932\)
Analytic rank: \(1\)
Dimension: \(47\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 6002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.93355 q^{3} +1.00000 q^{4} +2.56764 q^{5} -1.93355 q^{6} +0.413652 q^{7} +1.00000 q^{8} +0.738635 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.93355 q^{3} +1.00000 q^{4} +2.56764 q^{5} -1.93355 q^{6} +0.413652 q^{7} +1.00000 q^{8} +0.738635 q^{9} +2.56764 q^{10} -4.92866 q^{11} -1.93355 q^{12} -4.75124 q^{13} +0.413652 q^{14} -4.96467 q^{15} +1.00000 q^{16} +2.77589 q^{17} +0.738635 q^{18} -3.30404 q^{19} +2.56764 q^{20} -0.799818 q^{21} -4.92866 q^{22} +8.30176 q^{23} -1.93355 q^{24} +1.59277 q^{25} -4.75124 q^{26} +4.37247 q^{27} +0.413652 q^{28} +1.61248 q^{29} -4.96467 q^{30} +4.91787 q^{31} +1.00000 q^{32} +9.52983 q^{33} +2.77589 q^{34} +1.06211 q^{35} +0.738635 q^{36} -3.63902 q^{37} -3.30404 q^{38} +9.18678 q^{39} +2.56764 q^{40} -6.36535 q^{41} -0.799818 q^{42} +1.72691 q^{43} -4.92866 q^{44} +1.89655 q^{45} +8.30176 q^{46} +9.71136 q^{47} -1.93355 q^{48} -6.82889 q^{49} +1.59277 q^{50} -5.36733 q^{51} -4.75124 q^{52} -0.605764 q^{53} +4.37247 q^{54} -12.6550 q^{55} +0.413652 q^{56} +6.38855 q^{57} +1.61248 q^{58} -9.89689 q^{59} -4.96467 q^{60} +0.612830 q^{61} +4.91787 q^{62} +0.305537 q^{63} +1.00000 q^{64} -12.1995 q^{65} +9.52983 q^{66} -5.34629 q^{67} +2.77589 q^{68} -16.0519 q^{69} +1.06211 q^{70} -3.67923 q^{71} +0.738635 q^{72} -5.61956 q^{73} -3.63902 q^{74} -3.07971 q^{75} -3.30404 q^{76} -2.03875 q^{77} +9.18678 q^{78} -6.22166 q^{79} +2.56764 q^{80} -10.6703 q^{81} -6.36535 q^{82} -2.42115 q^{83} -0.799818 q^{84} +7.12748 q^{85} +1.72691 q^{86} -3.11781 q^{87} -4.92866 q^{88} -14.5830 q^{89} +1.89655 q^{90} -1.96536 q^{91} +8.30176 q^{92} -9.50897 q^{93} +9.71136 q^{94} -8.48359 q^{95} -1.93355 q^{96} +11.2460 q^{97} -6.82889 q^{98} -3.64048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.93355 −1.11634 −0.558169 0.829727i \(-0.688496\pi\)
−0.558169 + 0.829727i \(0.688496\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.56764 1.14828 0.574142 0.818756i \(-0.305336\pi\)
0.574142 + 0.818756i \(0.305336\pi\)
\(6\) −1.93355 −0.789370
\(7\) 0.413652 0.156346 0.0781728 0.996940i \(-0.475091\pi\)
0.0781728 + 0.996940i \(0.475091\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.738635 0.246212
\(10\) 2.56764 0.811959
\(11\) −4.92866 −1.48605 −0.743023 0.669265i \(-0.766609\pi\)
−0.743023 + 0.669265i \(0.766609\pi\)
\(12\) −1.93355 −0.558169
\(13\) −4.75124 −1.31776 −0.658878 0.752249i \(-0.728969\pi\)
−0.658878 + 0.752249i \(0.728969\pi\)
\(14\) 0.413652 0.110553
\(15\) −4.96467 −1.28187
\(16\) 1.00000 0.250000
\(17\) 2.77589 0.673251 0.336626 0.941639i \(-0.390714\pi\)
0.336626 + 0.941639i \(0.390714\pi\)
\(18\) 0.738635 0.174098
\(19\) −3.30404 −0.757999 −0.379000 0.925397i \(-0.623732\pi\)
−0.379000 + 0.925397i \(0.623732\pi\)
\(20\) 2.56764 0.574142
\(21\) −0.799818 −0.174535
\(22\) −4.92866 −1.05079
\(23\) 8.30176 1.73104 0.865518 0.500878i \(-0.166990\pi\)
0.865518 + 0.500878i \(0.166990\pi\)
\(24\) −1.93355 −0.394685
\(25\) 1.59277 0.318554
\(26\) −4.75124 −0.931795
\(27\) 4.37247 0.841483
\(28\) 0.413652 0.0781728
\(29\) 1.61248 0.299430 0.149715 0.988729i \(-0.452164\pi\)
0.149715 + 0.988729i \(0.452164\pi\)
\(30\) −4.96467 −0.906421
\(31\) 4.91787 0.883276 0.441638 0.897193i \(-0.354398\pi\)
0.441638 + 0.897193i \(0.354398\pi\)
\(32\) 1.00000 0.176777
\(33\) 9.52983 1.65893
\(34\) 2.77589 0.476061
\(35\) 1.06211 0.179529
\(36\) 0.738635 0.123106
\(37\) −3.63902 −0.598251 −0.299126 0.954214i \(-0.596695\pi\)
−0.299126 + 0.954214i \(0.596695\pi\)
\(38\) −3.30404 −0.535986
\(39\) 9.18678 1.47106
\(40\) 2.56764 0.405979
\(41\) −6.36535 −0.994101 −0.497051 0.867722i \(-0.665584\pi\)
−0.497051 + 0.867722i \(0.665584\pi\)
\(42\) −0.799818 −0.123415
\(43\) 1.72691 0.263351 0.131676 0.991293i \(-0.457964\pi\)
0.131676 + 0.991293i \(0.457964\pi\)
\(44\) −4.92866 −0.743023
\(45\) 1.89655 0.282721
\(46\) 8.30176 1.22403
\(47\) 9.71136 1.41655 0.708274 0.705938i \(-0.249474\pi\)
0.708274 + 0.705938i \(0.249474\pi\)
\(48\) −1.93355 −0.279085
\(49\) −6.82889 −0.975556
\(50\) 1.59277 0.225252
\(51\) −5.36733 −0.751576
\(52\) −4.75124 −0.658878
\(53\) −0.605764 −0.0832081 −0.0416041 0.999134i \(-0.513247\pi\)
−0.0416041 + 0.999134i \(0.513247\pi\)
\(54\) 4.37247 0.595018
\(55\) −12.6550 −1.70640
\(56\) 0.413652 0.0552765
\(57\) 6.38855 0.846184
\(58\) 1.61248 0.211729
\(59\) −9.89689 −1.28846 −0.644232 0.764830i \(-0.722823\pi\)
−0.644232 + 0.764830i \(0.722823\pi\)
\(60\) −4.96467 −0.640936
\(61\) 0.612830 0.0784648 0.0392324 0.999230i \(-0.487509\pi\)
0.0392324 + 0.999230i \(0.487509\pi\)
\(62\) 4.91787 0.624570
\(63\) 0.305537 0.0384941
\(64\) 1.00000 0.125000
\(65\) −12.1995 −1.51316
\(66\) 9.52983 1.17304
\(67\) −5.34629 −0.653154 −0.326577 0.945171i \(-0.605895\pi\)
−0.326577 + 0.945171i \(0.605895\pi\)
\(68\) 2.77589 0.336626
\(69\) −16.0519 −1.93242
\(70\) 1.06211 0.126946
\(71\) −3.67923 −0.436644 −0.218322 0.975877i \(-0.570058\pi\)
−0.218322 + 0.975877i \(0.570058\pi\)
\(72\) 0.738635 0.0870489
\(73\) −5.61956 −0.657720 −0.328860 0.944379i \(-0.606664\pi\)
−0.328860 + 0.944379i \(0.606664\pi\)
\(74\) −3.63902 −0.423028
\(75\) −3.07971 −0.355614
\(76\) −3.30404 −0.379000
\(77\) −2.03875 −0.232337
\(78\) 9.18678 1.04020
\(79\) −6.22166 −0.699992 −0.349996 0.936751i \(-0.613817\pi\)
−0.349996 + 0.936751i \(0.613817\pi\)
\(80\) 2.56764 0.287071
\(81\) −10.6703 −1.18559
\(82\) −6.36535 −0.702936
\(83\) −2.42115 −0.265756 −0.132878 0.991132i \(-0.542422\pi\)
−0.132878 + 0.991132i \(0.542422\pi\)
\(84\) −0.799818 −0.0872673
\(85\) 7.12748 0.773083
\(86\) 1.72691 0.186217
\(87\) −3.11781 −0.334265
\(88\) −4.92866 −0.525397
\(89\) −14.5830 −1.54580 −0.772900 0.634528i \(-0.781194\pi\)
−0.772900 + 0.634528i \(0.781194\pi\)
\(90\) 1.89655 0.199914
\(91\) −1.96536 −0.206026
\(92\) 8.30176 0.865518
\(93\) −9.50897 −0.986035
\(94\) 9.71136 1.00165
\(95\) −8.48359 −0.870398
\(96\) −1.93355 −0.197343
\(97\) 11.2460 1.14186 0.570929 0.821000i \(-0.306583\pi\)
0.570929 + 0.821000i \(0.306583\pi\)
\(98\) −6.82889 −0.689822
\(99\) −3.64048 −0.365882
\(100\) 1.59277 0.159277
\(101\) −5.24995 −0.522390 −0.261195 0.965286i \(-0.584117\pi\)
−0.261195 + 0.965286i \(0.584117\pi\)
\(102\) −5.36733 −0.531445
\(103\) −1.90296 −0.187505 −0.0937523 0.995596i \(-0.529886\pi\)
−0.0937523 + 0.995596i \(0.529886\pi\)
\(104\) −4.75124 −0.465897
\(105\) −2.05365 −0.200415
\(106\) −0.605764 −0.0588370
\(107\) −18.1159 −1.75133 −0.875664 0.482922i \(-0.839576\pi\)
−0.875664 + 0.482922i \(0.839576\pi\)
\(108\) 4.37247 0.420742
\(109\) 2.69697 0.258323 0.129161 0.991624i \(-0.458772\pi\)
0.129161 + 0.991624i \(0.458772\pi\)
\(110\) −12.6550 −1.20661
\(111\) 7.03625 0.667851
\(112\) 0.413652 0.0390864
\(113\) −14.3092 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(114\) 6.38855 0.598342
\(115\) 21.3159 1.98772
\(116\) 1.61248 0.149715
\(117\) −3.50943 −0.324447
\(118\) −9.89689 −0.911082
\(119\) 1.14825 0.105260
\(120\) −4.96467 −0.453210
\(121\) 13.2917 1.20834
\(122\) 0.612830 0.0554830
\(123\) 12.3078 1.10975
\(124\) 4.91787 0.441638
\(125\) −8.74853 −0.782493
\(126\) 0.305537 0.0272194
\(127\) −9.03404 −0.801642 −0.400821 0.916156i \(-0.631275\pi\)
−0.400821 + 0.916156i \(0.631275\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.33907 −0.293989
\(130\) −12.1995 −1.06996
\(131\) −16.6184 −1.45195 −0.725977 0.687719i \(-0.758612\pi\)
−0.725977 + 0.687719i \(0.758612\pi\)
\(132\) 9.52983 0.829466
\(133\) −1.36672 −0.118510
\(134\) −5.34629 −0.461850
\(135\) 11.2269 0.966261
\(136\) 2.77589 0.238030
\(137\) 7.48957 0.639877 0.319939 0.947438i \(-0.396338\pi\)
0.319939 + 0.947438i \(0.396338\pi\)
\(138\) −16.0519 −1.36643
\(139\) 2.34644 0.199022 0.0995110 0.995036i \(-0.468272\pi\)
0.0995110 + 0.995036i \(0.468272\pi\)
\(140\) 1.06211 0.0897645
\(141\) −18.7774 −1.58135
\(142\) −3.67923 −0.308754
\(143\) 23.4172 1.95825
\(144\) 0.738635 0.0615529
\(145\) 4.14026 0.343830
\(146\) −5.61956 −0.465078
\(147\) 13.2040 1.08905
\(148\) −3.63902 −0.299126
\(149\) 2.01065 0.164719 0.0823593 0.996603i \(-0.473754\pi\)
0.0823593 + 0.996603i \(0.473754\pi\)
\(150\) −3.07971 −0.251457
\(151\) −1.86117 −0.151460 −0.0757299 0.997128i \(-0.524129\pi\)
−0.0757299 + 0.997128i \(0.524129\pi\)
\(152\) −3.30404 −0.267993
\(153\) 2.05037 0.165762
\(154\) −2.03875 −0.164287
\(155\) 12.6273 1.01425
\(156\) 9.18678 0.735531
\(157\) −11.3534 −0.906100 −0.453050 0.891485i \(-0.649664\pi\)
−0.453050 + 0.891485i \(0.649664\pi\)
\(158\) −6.22166 −0.494969
\(159\) 1.17128 0.0928884
\(160\) 2.56764 0.202990
\(161\) 3.43404 0.270640
\(162\) −10.6703 −0.838340
\(163\) 22.1221 1.73274 0.866370 0.499403i \(-0.166447\pi\)
0.866370 + 0.499403i \(0.166447\pi\)
\(164\) −6.36535 −0.497051
\(165\) 24.4692 1.90492
\(166\) −2.42115 −0.187918
\(167\) −13.5895 −1.05159 −0.525794 0.850612i \(-0.676232\pi\)
−0.525794 + 0.850612i \(0.676232\pi\)
\(168\) −0.799818 −0.0617073
\(169\) 9.57428 0.736483
\(170\) 7.12748 0.546652
\(171\) −2.44048 −0.186628
\(172\) 1.72691 0.131676
\(173\) 1.63376 0.124213 0.0621064 0.998070i \(-0.480218\pi\)
0.0621064 + 0.998070i \(0.480218\pi\)
\(174\) −3.11781 −0.236361
\(175\) 0.658853 0.0498046
\(176\) −4.92866 −0.371512
\(177\) 19.1362 1.43836
\(178\) −14.5830 −1.09305
\(179\) −3.35613 −0.250849 −0.125425 0.992103i \(-0.540029\pi\)
−0.125425 + 0.992103i \(0.540029\pi\)
\(180\) 1.89655 0.141360
\(181\) −13.6760 −1.01653 −0.508264 0.861201i \(-0.669713\pi\)
−0.508264 + 0.861201i \(0.669713\pi\)
\(182\) −1.96536 −0.145682
\(183\) −1.18494 −0.0875933
\(184\) 8.30176 0.612014
\(185\) −9.34369 −0.686962
\(186\) −9.50897 −0.697232
\(187\) −13.6814 −1.00048
\(188\) 9.71136 0.708274
\(189\) 1.80868 0.131562
\(190\) −8.48359 −0.615464
\(191\) −9.74651 −0.705233 −0.352616 0.935768i \(-0.614708\pi\)
−0.352616 + 0.935768i \(0.614708\pi\)
\(192\) −1.93355 −0.139542
\(193\) 14.2238 1.02385 0.511926 0.859030i \(-0.328932\pi\)
0.511926 + 0.859030i \(0.328932\pi\)
\(194\) 11.2460 0.807415
\(195\) 23.5883 1.68920
\(196\) −6.82889 −0.487778
\(197\) −14.3214 −1.02036 −0.510180 0.860067i \(-0.670421\pi\)
−0.510180 + 0.860067i \(0.670421\pi\)
\(198\) −3.64048 −0.258718
\(199\) 19.3170 1.36935 0.684673 0.728851i \(-0.259945\pi\)
0.684673 + 0.728851i \(0.259945\pi\)
\(200\) 1.59277 0.112626
\(201\) 10.3374 0.729141
\(202\) −5.24995 −0.369385
\(203\) 0.667004 0.0468145
\(204\) −5.36733 −0.375788
\(205\) −16.3439 −1.14151
\(206\) −1.90296 −0.132586
\(207\) 6.13196 0.426201
\(208\) −4.75124 −0.329439
\(209\) 16.2845 1.12642
\(210\) −2.05365 −0.141715
\(211\) −9.72587 −0.669556 −0.334778 0.942297i \(-0.608661\pi\)
−0.334778 + 0.942297i \(0.608661\pi\)
\(212\) −0.605764 −0.0416041
\(213\) 7.11399 0.487443
\(214\) −18.1159 −1.23838
\(215\) 4.43408 0.302402
\(216\) 4.37247 0.297509
\(217\) 2.03429 0.138096
\(218\) 2.69697 0.182662
\(219\) 10.8657 0.734238
\(220\) −12.6550 −0.853201
\(221\) −13.1889 −0.887182
\(222\) 7.03625 0.472242
\(223\) 12.8515 0.860597 0.430299 0.902687i \(-0.358408\pi\)
0.430299 + 0.902687i \(0.358408\pi\)
\(224\) 0.413652 0.0276383
\(225\) 1.17648 0.0784317
\(226\) −14.3092 −0.951835
\(227\) 20.7443 1.37685 0.688424 0.725308i \(-0.258303\pi\)
0.688424 + 0.725308i \(0.258303\pi\)
\(228\) 6.38855 0.423092
\(229\) −24.2219 −1.60063 −0.800313 0.599582i \(-0.795333\pi\)
−0.800313 + 0.599582i \(0.795333\pi\)
\(230\) 21.3159 1.40553
\(231\) 3.94203 0.259367
\(232\) 1.61248 0.105864
\(233\) −17.6446 −1.15593 −0.577967 0.816060i \(-0.696154\pi\)
−0.577967 + 0.816060i \(0.696154\pi\)
\(234\) −3.50943 −0.229419
\(235\) 24.9353 1.62660
\(236\) −9.89689 −0.644232
\(237\) 12.0299 0.781428
\(238\) 1.14825 0.0744300
\(239\) −8.87316 −0.573957 −0.286979 0.957937i \(-0.592651\pi\)
−0.286979 + 0.957937i \(0.592651\pi\)
\(240\) −4.96467 −0.320468
\(241\) −4.22672 −0.272267 −0.136133 0.990691i \(-0.543468\pi\)
−0.136133 + 0.990691i \(0.543468\pi\)
\(242\) 13.2917 0.854422
\(243\) 7.51423 0.482038
\(244\) 0.612830 0.0392324
\(245\) −17.5341 −1.12021
\(246\) 12.3078 0.784714
\(247\) 15.6983 0.998859
\(248\) 4.91787 0.312285
\(249\) 4.68144 0.296674
\(250\) −8.74853 −0.553306
\(251\) 23.0729 1.45635 0.728175 0.685391i \(-0.240369\pi\)
0.728175 + 0.685391i \(0.240369\pi\)
\(252\) 0.305537 0.0192471
\(253\) −40.9165 −2.57240
\(254\) −9.03404 −0.566846
\(255\) −13.7814 −0.863023
\(256\) 1.00000 0.0625000
\(257\) −3.78417 −0.236050 −0.118025 0.993011i \(-0.537656\pi\)
−0.118025 + 0.993011i \(0.537656\pi\)
\(258\) −3.33907 −0.207882
\(259\) −1.50529 −0.0935340
\(260\) −12.1995 −0.756579
\(261\) 1.19103 0.0737230
\(262\) −16.6184 −1.02669
\(263\) 10.2110 0.629636 0.314818 0.949152i \(-0.398057\pi\)
0.314818 + 0.949152i \(0.398057\pi\)
\(264\) 9.52983 0.586521
\(265\) −1.55538 −0.0955465
\(266\) −1.36672 −0.0837992
\(267\) 28.1971 1.72564
\(268\) −5.34629 −0.326577
\(269\) −30.2363 −1.84354 −0.921770 0.387736i \(-0.873257\pi\)
−0.921770 + 0.387736i \(0.873257\pi\)
\(270\) 11.2269 0.683250
\(271\) 15.6754 0.952214 0.476107 0.879387i \(-0.342048\pi\)
0.476107 + 0.879387i \(0.342048\pi\)
\(272\) 2.77589 0.168313
\(273\) 3.80013 0.229994
\(274\) 7.48957 0.452462
\(275\) −7.85023 −0.473386
\(276\) −16.0519 −0.966211
\(277\) 9.00319 0.540949 0.270474 0.962727i \(-0.412819\pi\)
0.270474 + 0.962727i \(0.412819\pi\)
\(278\) 2.34644 0.140730
\(279\) 3.63251 0.217473
\(280\) 1.06211 0.0634731
\(281\) 16.8358 1.00434 0.502171 0.864768i \(-0.332535\pi\)
0.502171 + 0.864768i \(0.332535\pi\)
\(282\) −18.7774 −1.11818
\(283\) −28.0035 −1.66463 −0.832316 0.554301i \(-0.812986\pi\)
−0.832316 + 0.554301i \(0.812986\pi\)
\(284\) −3.67923 −0.218322
\(285\) 16.4035 0.971659
\(286\) 23.4172 1.38469
\(287\) −2.63304 −0.155423
\(288\) 0.738635 0.0435245
\(289\) −9.29445 −0.546732
\(290\) 4.14026 0.243124
\(291\) −21.7447 −1.27470
\(292\) −5.61956 −0.328860
\(293\) 13.2870 0.776236 0.388118 0.921610i \(-0.373125\pi\)
0.388118 + 0.921610i \(0.373125\pi\)
\(294\) 13.2040 0.770075
\(295\) −25.4116 −1.47952
\(296\) −3.63902 −0.211514
\(297\) −21.5504 −1.25048
\(298\) 2.01065 0.116474
\(299\) −39.4436 −2.28108
\(300\) −3.07971 −0.177807
\(301\) 0.714339 0.0411738
\(302\) −1.86117 −0.107098
\(303\) 10.1511 0.583164
\(304\) −3.30404 −0.189500
\(305\) 1.57353 0.0900998
\(306\) 2.05037 0.117212
\(307\) 24.6758 1.40832 0.704162 0.710039i \(-0.251323\pi\)
0.704162 + 0.710039i \(0.251323\pi\)
\(308\) −2.03875 −0.116168
\(309\) 3.67948 0.209318
\(310\) 12.6273 0.717183
\(311\) 19.7793 1.12158 0.560790 0.827958i \(-0.310498\pi\)
0.560790 + 0.827958i \(0.310498\pi\)
\(312\) 9.18678 0.520099
\(313\) 11.4419 0.646734 0.323367 0.946274i \(-0.395185\pi\)
0.323367 + 0.946274i \(0.395185\pi\)
\(314\) −11.3534 −0.640710
\(315\) 0.784510 0.0442021
\(316\) −6.22166 −0.349996
\(317\) −4.06866 −0.228518 −0.114259 0.993451i \(-0.536449\pi\)
−0.114259 + 0.993451i \(0.536449\pi\)
\(318\) 1.17128 0.0656820
\(319\) −7.94735 −0.444966
\(320\) 2.56764 0.143535
\(321\) 35.0280 1.95507
\(322\) 3.43404 0.191371
\(323\) −9.17165 −0.510324
\(324\) −10.6703 −0.592796
\(325\) −7.56764 −0.419777
\(326\) 22.1221 1.22523
\(327\) −5.21473 −0.288375
\(328\) −6.36535 −0.351468
\(329\) 4.01712 0.221471
\(330\) 24.4692 1.34698
\(331\) −7.33817 −0.403342 −0.201671 0.979453i \(-0.564637\pi\)
−0.201671 + 0.979453i \(0.564637\pi\)
\(332\) −2.42115 −0.132878
\(333\) −2.68791 −0.147296
\(334\) −13.5895 −0.743585
\(335\) −13.7274 −0.750006
\(336\) −0.799818 −0.0436337
\(337\) −16.3019 −0.888022 −0.444011 0.896021i \(-0.646445\pi\)
−0.444011 + 0.896021i \(0.646445\pi\)
\(338\) 9.57428 0.520772
\(339\) 27.6677 1.50270
\(340\) 7.12748 0.386542
\(341\) −24.2385 −1.31259
\(342\) −2.44048 −0.131966
\(343\) −5.72035 −0.308870
\(344\) 1.72691 0.0931087
\(345\) −41.2155 −2.21897
\(346\) 1.63376 0.0878317
\(347\) 25.2580 1.35592 0.677960 0.735099i \(-0.262864\pi\)
0.677960 + 0.735099i \(0.262864\pi\)
\(348\) −3.11781 −0.167132
\(349\) −8.44865 −0.452246 −0.226123 0.974099i \(-0.572605\pi\)
−0.226123 + 0.974099i \(0.572605\pi\)
\(350\) 0.658853 0.0352171
\(351\) −20.7747 −1.10887
\(352\) −4.92866 −0.262698
\(353\) −7.06045 −0.375790 −0.187895 0.982189i \(-0.560166\pi\)
−0.187895 + 0.982189i \(0.560166\pi\)
\(354\) 19.1362 1.01708
\(355\) −9.44693 −0.501391
\(356\) −14.5830 −0.772900
\(357\) −2.22021 −0.117506
\(358\) −3.35613 −0.177377
\(359\) 13.4090 0.707702 0.353851 0.935302i \(-0.384872\pi\)
0.353851 + 0.935302i \(0.384872\pi\)
\(360\) 1.89655 0.0999568
\(361\) −8.08330 −0.425437
\(362\) −13.6760 −0.718794
\(363\) −25.7002 −1.34891
\(364\) −1.96536 −0.103013
\(365\) −14.4290 −0.755249
\(366\) −1.18494 −0.0619378
\(367\) 0.383791 0.0200337 0.0100169 0.999950i \(-0.496811\pi\)
0.0100169 + 0.999950i \(0.496811\pi\)
\(368\) 8.30176 0.432759
\(369\) −4.70167 −0.244759
\(370\) −9.34369 −0.485755
\(371\) −0.250575 −0.0130092
\(372\) −9.50897 −0.493017
\(373\) 25.6861 1.32997 0.664987 0.746855i \(-0.268437\pi\)
0.664987 + 0.746855i \(0.268437\pi\)
\(374\) −13.6814 −0.707448
\(375\) 16.9158 0.873527
\(376\) 9.71136 0.500825
\(377\) −7.66127 −0.394575
\(378\) 1.80868 0.0930285
\(379\) −9.41195 −0.483459 −0.241730 0.970344i \(-0.577715\pi\)
−0.241730 + 0.970344i \(0.577715\pi\)
\(380\) −8.48359 −0.435199
\(381\) 17.4678 0.894903
\(382\) −9.74651 −0.498675
\(383\) 27.7202 1.41644 0.708218 0.705994i \(-0.249499\pi\)
0.708218 + 0.705994i \(0.249499\pi\)
\(384\) −1.93355 −0.0986713
\(385\) −5.23477 −0.266789
\(386\) 14.2238 0.723972
\(387\) 1.27555 0.0648401
\(388\) 11.2460 0.570929
\(389\) −23.6989 −1.20158 −0.600790 0.799407i \(-0.705147\pi\)
−0.600790 + 0.799407i \(0.705147\pi\)
\(390\) 23.5883 1.19444
\(391\) 23.0447 1.16542
\(392\) −6.82889 −0.344911
\(393\) 32.1325 1.62087
\(394\) −14.3214 −0.721504
\(395\) −15.9750 −0.803789
\(396\) −3.64048 −0.182941
\(397\) −9.01291 −0.452345 −0.226172 0.974087i \(-0.572621\pi\)
−0.226172 + 0.974087i \(0.572621\pi\)
\(398\) 19.3170 0.968273
\(399\) 2.64263 0.132297
\(400\) 1.59277 0.0796386
\(401\) −36.5026 −1.82286 −0.911428 0.411460i \(-0.865019\pi\)
−0.911428 + 0.411460i \(0.865019\pi\)
\(402\) 10.3374 0.515580
\(403\) −23.3660 −1.16394
\(404\) −5.24995 −0.261195
\(405\) −27.3975 −1.36139
\(406\) 0.667004 0.0331029
\(407\) 17.9355 0.889029
\(408\) −5.36733 −0.265722
\(409\) −28.1491 −1.39188 −0.695942 0.718098i \(-0.745013\pi\)
−0.695942 + 0.718098i \(0.745013\pi\)
\(410\) −16.3439 −0.807169
\(411\) −14.4815 −0.714320
\(412\) −1.90296 −0.0937523
\(413\) −4.09386 −0.201446
\(414\) 6.13196 0.301370
\(415\) −6.21665 −0.305163
\(416\) −4.75124 −0.232949
\(417\) −4.53696 −0.222176
\(418\) 16.2845 0.796501
\(419\) −1.00405 −0.0490510 −0.0245255 0.999699i \(-0.507807\pi\)
−0.0245255 + 0.999699i \(0.507807\pi\)
\(420\) −2.05365 −0.100208
\(421\) −20.3510 −0.991847 −0.495924 0.868366i \(-0.665170\pi\)
−0.495924 + 0.868366i \(0.665170\pi\)
\(422\) −9.72587 −0.473448
\(423\) 7.17315 0.348770
\(424\) −0.605764 −0.0294185
\(425\) 4.42135 0.214467
\(426\) 7.11399 0.344674
\(427\) 0.253498 0.0122676
\(428\) −18.1159 −0.875664
\(429\) −45.2785 −2.18607
\(430\) 4.43408 0.213830
\(431\) 36.1827 1.74286 0.871429 0.490522i \(-0.163194\pi\)
0.871429 + 0.490522i \(0.163194\pi\)
\(432\) 4.37247 0.210371
\(433\) 23.3687 1.12303 0.561514 0.827467i \(-0.310219\pi\)
0.561514 + 0.827467i \(0.310219\pi\)
\(434\) 2.03429 0.0976488
\(435\) −8.00542 −0.383831
\(436\) 2.69697 0.129161
\(437\) −27.4294 −1.31212
\(438\) 10.8657 0.519185
\(439\) 23.1787 1.10626 0.553130 0.833095i \(-0.313433\pi\)
0.553130 + 0.833095i \(0.313433\pi\)
\(440\) −12.6550 −0.603304
\(441\) −5.04406 −0.240193
\(442\) −13.1889 −0.627332
\(443\) 7.14042 0.339252 0.169626 0.985509i \(-0.445744\pi\)
0.169626 + 0.985509i \(0.445744\pi\)
\(444\) 7.03625 0.333925
\(445\) −37.4440 −1.77502
\(446\) 12.8515 0.608534
\(447\) −3.88770 −0.183882
\(448\) 0.413652 0.0195432
\(449\) −33.7316 −1.59189 −0.795945 0.605368i \(-0.793026\pi\)
−0.795945 + 0.605368i \(0.793026\pi\)
\(450\) 1.17648 0.0554596
\(451\) 31.3727 1.47728
\(452\) −14.3092 −0.673049
\(453\) 3.59867 0.169080
\(454\) 20.7443 0.973579
\(455\) −5.04633 −0.236576
\(456\) 6.38855 0.299171
\(457\) 19.5946 0.916599 0.458299 0.888798i \(-0.348459\pi\)
0.458299 + 0.888798i \(0.348459\pi\)
\(458\) −24.2219 −1.13181
\(459\) 12.1375 0.566530
\(460\) 21.3159 0.993860
\(461\) 28.2593 1.31617 0.658084 0.752944i \(-0.271367\pi\)
0.658084 + 0.752944i \(0.271367\pi\)
\(462\) 3.94203 0.183400
\(463\) 22.6776 1.05392 0.526959 0.849890i \(-0.323332\pi\)
0.526959 + 0.849890i \(0.323332\pi\)
\(464\) 1.61248 0.0748574
\(465\) −24.4156 −1.13225
\(466\) −17.6446 −0.817368
\(467\) −40.1342 −1.85719 −0.928594 0.371097i \(-0.878982\pi\)
−0.928594 + 0.371097i \(0.878982\pi\)
\(468\) −3.50943 −0.162223
\(469\) −2.21150 −0.102118
\(470\) 24.9353 1.15018
\(471\) 21.9524 1.01151
\(472\) −9.89689 −0.455541
\(473\) −8.51134 −0.391352
\(474\) 12.0299 0.552553
\(475\) −5.26258 −0.241464
\(476\) 1.14825 0.0526300
\(477\) −0.447438 −0.0204868
\(478\) −8.87316 −0.405849
\(479\) −0.525069 −0.0239910 −0.0119955 0.999928i \(-0.503818\pi\)
−0.0119955 + 0.999928i \(0.503818\pi\)
\(480\) −4.96467 −0.226605
\(481\) 17.2899 0.788350
\(482\) −4.22672 −0.192522
\(483\) −6.63990 −0.302126
\(484\) 13.2917 0.604168
\(485\) 28.8756 1.31118
\(486\) 7.51423 0.340852
\(487\) −25.0558 −1.13539 −0.567694 0.823240i \(-0.692164\pi\)
−0.567694 + 0.823240i \(0.692164\pi\)
\(488\) 0.612830 0.0277415
\(489\) −42.7744 −1.93432
\(490\) −17.5341 −0.792111
\(491\) −17.7648 −0.801715 −0.400857 0.916140i \(-0.631288\pi\)
−0.400857 + 0.916140i \(0.631288\pi\)
\(492\) 12.3078 0.554877
\(493\) 4.47605 0.201591
\(494\) 15.6983 0.706300
\(495\) −9.34743 −0.420136
\(496\) 4.91787 0.220819
\(497\) −1.52192 −0.0682674
\(498\) 4.68144 0.209780
\(499\) 3.09140 0.138390 0.0691950 0.997603i \(-0.477957\pi\)
0.0691950 + 0.997603i \(0.477957\pi\)
\(500\) −8.74853 −0.391246
\(501\) 26.2761 1.17393
\(502\) 23.0729 1.02980
\(503\) −39.7743 −1.77345 −0.886725 0.462298i \(-0.847025\pi\)
−0.886725 + 0.462298i \(0.847025\pi\)
\(504\) 0.305537 0.0136097
\(505\) −13.4800 −0.599851
\(506\) −40.9165 −1.81896
\(507\) −18.5124 −0.822164
\(508\) −9.03404 −0.400821
\(509\) −18.2698 −0.809795 −0.404898 0.914362i \(-0.632693\pi\)
−0.404898 + 0.914362i \(0.632693\pi\)
\(510\) −13.7814 −0.610249
\(511\) −2.32454 −0.102832
\(512\) 1.00000 0.0441942
\(513\) −14.4468 −0.637844
\(514\) −3.78417 −0.166912
\(515\) −4.88612 −0.215308
\(516\) −3.33907 −0.146994
\(517\) −47.8640 −2.10506
\(518\) −1.50529 −0.0661385
\(519\) −3.15897 −0.138664
\(520\) −12.1995 −0.534982
\(521\) −1.09617 −0.0480243 −0.0240121 0.999712i \(-0.507644\pi\)
−0.0240121 + 0.999712i \(0.507644\pi\)
\(522\) 1.19103 0.0521300
\(523\) −29.1966 −1.27668 −0.638338 0.769756i \(-0.720378\pi\)
−0.638338 + 0.769756i \(0.720378\pi\)
\(524\) −16.6184 −0.725977
\(525\) −1.27393 −0.0555988
\(526\) 10.2110 0.445220
\(527\) 13.6515 0.594667
\(528\) 9.52983 0.414733
\(529\) 45.9191 1.99648
\(530\) −1.55538 −0.0675616
\(531\) −7.31018 −0.317235
\(532\) −1.36672 −0.0592550
\(533\) 30.2433 1.30998
\(534\) 28.1971 1.22021
\(535\) −46.5150 −2.01102
\(536\) −5.34629 −0.230925
\(537\) 6.48927 0.280033
\(538\) −30.2363 −1.30358
\(539\) 33.6573 1.44972
\(540\) 11.2269 0.483130
\(541\) 34.0157 1.46245 0.731224 0.682138i \(-0.238950\pi\)
0.731224 + 0.682138i \(0.238950\pi\)
\(542\) 15.6754 0.673317
\(543\) 26.4433 1.13479
\(544\) 2.77589 0.119015
\(545\) 6.92484 0.296627
\(546\) 3.80013 0.162630
\(547\) −11.7874 −0.503991 −0.251995 0.967728i \(-0.581087\pi\)
−0.251995 + 0.967728i \(0.581087\pi\)
\(548\) 7.48957 0.319939
\(549\) 0.452657 0.0193189
\(550\) −7.85023 −0.334735
\(551\) −5.32769 −0.226967
\(552\) −16.0519 −0.683214
\(553\) −2.57360 −0.109441
\(554\) 9.00319 0.382509
\(555\) 18.0665 0.766882
\(556\) 2.34644 0.0995110
\(557\) 0.0686557 0.00290904 0.00145452 0.999999i \(-0.499537\pi\)
0.00145452 + 0.999999i \(0.499537\pi\)
\(558\) 3.63251 0.153776
\(559\) −8.20495 −0.347033
\(560\) 1.06211 0.0448823
\(561\) 26.4537 1.11688
\(562\) 16.8358 0.710177
\(563\) 19.2633 0.811852 0.405926 0.913906i \(-0.366949\pi\)
0.405926 + 0.913906i \(0.366949\pi\)
\(564\) −18.7774 −0.790673
\(565\) −36.7409 −1.54570
\(566\) −28.0035 −1.17707
\(567\) −4.41380 −0.185362
\(568\) −3.67923 −0.154377
\(569\) −24.2099 −1.01493 −0.507466 0.861672i \(-0.669418\pi\)
−0.507466 + 0.861672i \(0.669418\pi\)
\(570\) 16.4035 0.687066
\(571\) 29.7908 1.24670 0.623352 0.781941i \(-0.285770\pi\)
0.623352 + 0.781941i \(0.285770\pi\)
\(572\) 23.4172 0.979124
\(573\) 18.8454 0.787278
\(574\) −2.63304 −0.109901
\(575\) 13.2228 0.551429
\(576\) 0.738635 0.0307764
\(577\) −30.5888 −1.27343 −0.636713 0.771101i \(-0.719707\pi\)
−0.636713 + 0.771101i \(0.719707\pi\)
\(578\) −9.29445 −0.386598
\(579\) −27.5025 −1.14296
\(580\) 4.14026 0.171915
\(581\) −1.00151 −0.0415498
\(582\) −21.7447 −0.901348
\(583\) 2.98561 0.123651
\(584\) −5.61956 −0.232539
\(585\) −9.01095 −0.372557
\(586\) 13.2870 0.548882
\(587\) 20.7049 0.854584 0.427292 0.904114i \(-0.359468\pi\)
0.427292 + 0.904114i \(0.359468\pi\)
\(588\) 13.2040 0.544525
\(589\) −16.2489 −0.669522
\(590\) −25.4116 −1.04618
\(591\) 27.6913 1.13907
\(592\) −3.63902 −0.149563
\(593\) 35.9861 1.47777 0.738885 0.673831i \(-0.235353\pi\)
0.738885 + 0.673831i \(0.235353\pi\)
\(594\) −21.5504 −0.884225
\(595\) 2.94829 0.120868
\(596\) 2.01065 0.0823593
\(597\) −37.3505 −1.52865
\(598\) −39.4436 −1.61297
\(599\) 21.4359 0.875846 0.437923 0.899012i \(-0.355714\pi\)
0.437923 + 0.899012i \(0.355714\pi\)
\(600\) −3.07971 −0.125729
\(601\) 44.3471 1.80896 0.904479 0.426519i \(-0.140260\pi\)
0.904479 + 0.426519i \(0.140260\pi\)
\(602\) 0.714339 0.0291143
\(603\) −3.94896 −0.160814
\(604\) −1.86117 −0.0757299
\(605\) 34.1283 1.38751
\(606\) 10.1511 0.412359
\(607\) 9.18367 0.372754 0.186377 0.982478i \(-0.440325\pi\)
0.186377 + 0.982478i \(0.440325\pi\)
\(608\) −3.30404 −0.133997
\(609\) −1.28969 −0.0522608
\(610\) 1.57353 0.0637102
\(611\) −46.1410 −1.86667
\(612\) 2.05037 0.0828811
\(613\) 30.5892 1.23549 0.617744 0.786380i \(-0.288047\pi\)
0.617744 + 0.786380i \(0.288047\pi\)
\(614\) 24.6758 0.995835
\(615\) 31.6019 1.27431
\(616\) −2.03875 −0.0821435
\(617\) 41.3796 1.66588 0.832939 0.553365i \(-0.186656\pi\)
0.832939 + 0.553365i \(0.186656\pi\)
\(618\) 3.67948 0.148011
\(619\) −34.0705 −1.36941 −0.684704 0.728821i \(-0.740069\pi\)
−0.684704 + 0.728821i \(0.740069\pi\)
\(620\) 12.6273 0.507125
\(621\) 36.2992 1.45664
\(622\) 19.7793 0.793077
\(623\) −6.03230 −0.241679
\(624\) 9.18678 0.367766
\(625\) −30.4269 −1.21708
\(626\) 11.4419 0.457310
\(627\) −31.4870 −1.25747
\(628\) −11.3534 −0.453050
\(629\) −10.1015 −0.402774
\(630\) 0.784510 0.0312556
\(631\) −20.1027 −0.800277 −0.400138 0.916455i \(-0.631038\pi\)
−0.400138 + 0.916455i \(0.631038\pi\)
\(632\) −6.22166 −0.247484
\(633\) 18.8055 0.747452
\(634\) −4.06866 −0.161587
\(635\) −23.1962 −0.920512
\(636\) 1.17128 0.0464442
\(637\) 32.4457 1.28555
\(638\) −7.94735 −0.314639
\(639\) −2.71761 −0.107507
\(640\) 2.56764 0.101495
\(641\) 17.1231 0.676323 0.338161 0.941088i \(-0.390195\pi\)
0.338161 + 0.941088i \(0.390195\pi\)
\(642\) 35.0280 1.38245
\(643\) −40.8807 −1.61218 −0.806088 0.591796i \(-0.798419\pi\)
−0.806088 + 0.591796i \(0.798419\pi\)
\(644\) 3.43404 0.135320
\(645\) −8.57353 −0.337582
\(646\) −9.17165 −0.360854
\(647\) 16.7157 0.657164 0.328582 0.944476i \(-0.393429\pi\)
0.328582 + 0.944476i \(0.393429\pi\)
\(648\) −10.6703 −0.419170
\(649\) 48.7784 1.91472
\(650\) −7.56764 −0.296827
\(651\) −3.93340 −0.154162
\(652\) 22.1221 0.866370
\(653\) 36.8297 1.44126 0.720629 0.693321i \(-0.243853\pi\)
0.720629 + 0.693321i \(0.243853\pi\)
\(654\) −5.21473 −0.203912
\(655\) −42.6700 −1.66725
\(656\) −6.36535 −0.248525
\(657\) −4.15080 −0.161938
\(658\) 4.01712 0.156604
\(659\) 30.6710 1.19477 0.597386 0.801954i \(-0.296206\pi\)
0.597386 + 0.801954i \(0.296206\pi\)
\(660\) 24.4692 0.952461
\(661\) 10.3495 0.402549 0.201275 0.979535i \(-0.435492\pi\)
0.201275 + 0.979535i \(0.435492\pi\)
\(662\) −7.33817 −0.285206
\(663\) 25.5015 0.990395
\(664\) −2.42115 −0.0939590
\(665\) −3.50925 −0.136083
\(666\) −2.68791 −0.104154
\(667\) 13.3864 0.518323
\(668\) −13.5895 −0.525794
\(669\) −24.8490 −0.960718
\(670\) −13.7274 −0.530334
\(671\) −3.02043 −0.116602
\(672\) −0.799818 −0.0308537
\(673\) −2.79597 −0.107777 −0.0538883 0.998547i \(-0.517161\pi\)
−0.0538883 + 0.998547i \(0.517161\pi\)
\(674\) −16.3019 −0.627926
\(675\) 6.96435 0.268058
\(676\) 9.57428 0.368241
\(677\) −8.22059 −0.315943 −0.157972 0.987444i \(-0.550495\pi\)
−0.157972 + 0.987444i \(0.550495\pi\)
\(678\) 27.6677 1.06257
\(679\) 4.65192 0.178524
\(680\) 7.12748 0.273326
\(681\) −40.1103 −1.53703
\(682\) −24.2385 −0.928141
\(683\) −4.45405 −0.170430 −0.0852148 0.996363i \(-0.527158\pi\)
−0.0852148 + 0.996363i \(0.527158\pi\)
\(684\) −2.44048 −0.0933141
\(685\) 19.2305 0.734760
\(686\) −5.72035 −0.218404
\(687\) 46.8343 1.78684
\(688\) 1.72691 0.0658378
\(689\) 2.87813 0.109648
\(690\) −41.2155 −1.56905
\(691\) 15.3478 0.583857 0.291928 0.956440i \(-0.405703\pi\)
0.291928 + 0.956440i \(0.405703\pi\)
\(692\) 1.63376 0.0621064
\(693\) −1.50589 −0.0572040
\(694\) 25.2580 0.958780
\(695\) 6.02480 0.228534
\(696\) −3.11781 −0.118180
\(697\) −17.6695 −0.669280
\(698\) −8.44865 −0.319786
\(699\) 34.1167 1.29041
\(700\) 0.658853 0.0249023
\(701\) 20.8173 0.786260 0.393130 0.919483i \(-0.371392\pi\)
0.393130 + 0.919483i \(0.371392\pi\)
\(702\) −20.7747 −0.784089
\(703\) 12.0235 0.453474
\(704\) −4.92866 −0.185756
\(705\) −48.2137 −1.81583
\(706\) −7.06045 −0.265724
\(707\) −2.17165 −0.0816734
\(708\) 19.1362 0.719181
\(709\) −42.0190 −1.57806 −0.789029 0.614356i \(-0.789416\pi\)
−0.789029 + 0.614356i \(0.789416\pi\)
\(710\) −9.44693 −0.354537
\(711\) −4.59554 −0.172346
\(712\) −14.5830 −0.546523
\(713\) 40.8270 1.52898
\(714\) −2.22021 −0.0830891
\(715\) 60.1270 2.24862
\(716\) −3.35613 −0.125425
\(717\) 17.1568 0.640731
\(718\) 13.4090 0.500421
\(719\) −3.15233 −0.117562 −0.0587810 0.998271i \(-0.518721\pi\)
−0.0587810 + 0.998271i \(0.518721\pi\)
\(720\) 1.89655 0.0706801
\(721\) −0.787164 −0.0293155
\(722\) −8.08330 −0.300829
\(723\) 8.17259 0.303942
\(724\) −13.6760 −0.508264
\(725\) 2.56831 0.0953845
\(726\) −25.7002 −0.953824
\(727\) 0.261421 0.00969557 0.00484779 0.999988i \(-0.498457\pi\)
0.00484779 + 0.999988i \(0.498457\pi\)
\(728\) −1.96536 −0.0728410
\(729\) 17.4818 0.647474
\(730\) −14.4290 −0.534042
\(731\) 4.79370 0.177301
\(732\) −1.18494 −0.0437966
\(733\) −45.3766 −1.67602 −0.838011 0.545653i \(-0.816282\pi\)
−0.838011 + 0.545653i \(0.816282\pi\)
\(734\) 0.383791 0.0141660
\(735\) 33.9032 1.25054
\(736\) 8.30176 0.306007
\(737\) 26.3501 0.970617
\(738\) −4.70167 −0.173071
\(739\) 19.7514 0.726567 0.363284 0.931679i \(-0.381656\pi\)
0.363284 + 0.931679i \(0.381656\pi\)
\(740\) −9.34369 −0.343481
\(741\) −30.3535 −1.11506
\(742\) −0.250575 −0.00919891
\(743\) −13.0237 −0.477793 −0.238896 0.971045i \(-0.576786\pi\)
−0.238896 + 0.971045i \(0.576786\pi\)
\(744\) −9.50897 −0.348616
\(745\) 5.16262 0.189144
\(746\) 25.6861 0.940434
\(747\) −1.78835 −0.0654322
\(748\) −13.6814 −0.500242
\(749\) −7.49366 −0.273812
\(750\) 16.9158 0.617677
\(751\) −20.6835 −0.754751 −0.377376 0.926060i \(-0.623173\pi\)
−0.377376 + 0.926060i \(0.623173\pi\)
\(752\) 9.71136 0.354137
\(753\) −44.6128 −1.62578
\(754\) −7.66127 −0.279007
\(755\) −4.77881 −0.173919
\(756\) 1.80868 0.0657811
\(757\) 18.8837 0.686340 0.343170 0.939273i \(-0.388499\pi\)
0.343170 + 0.939273i \(0.388499\pi\)
\(758\) −9.41195 −0.341857
\(759\) 79.1144 2.87167
\(760\) −8.48359 −0.307732
\(761\) 45.0144 1.63177 0.815885 0.578214i \(-0.196250\pi\)
0.815885 + 0.578214i \(0.196250\pi\)
\(762\) 17.4678 0.632792
\(763\) 1.11561 0.0403876
\(764\) −9.74651 −0.352616
\(765\) 5.26460 0.190342
\(766\) 27.7202 1.00157
\(767\) 47.0225 1.69788
\(768\) −1.93355 −0.0697712
\(769\) 31.4828 1.13530 0.567649 0.823271i \(-0.307853\pi\)
0.567649 + 0.823271i \(0.307853\pi\)
\(770\) −5.23477 −0.188648
\(771\) 7.31690 0.263512
\(772\) 14.2238 0.511926
\(773\) 20.6565 0.742963 0.371482 0.928440i \(-0.378850\pi\)
0.371482 + 0.928440i \(0.378850\pi\)
\(774\) 1.27555 0.0458488
\(775\) 7.83304 0.281371
\(776\) 11.2460 0.403707
\(777\) 2.91056 0.104416
\(778\) −23.6989 −0.849646
\(779\) 21.0314 0.753528
\(780\) 23.5883 0.844598
\(781\) 18.1337 0.648874
\(782\) 23.0447 0.824078
\(783\) 7.05052 0.251965
\(784\) −6.82889 −0.243889
\(785\) −29.1514 −1.04046
\(786\) 32.1325 1.14613
\(787\) −17.0863 −0.609060 −0.304530 0.952503i \(-0.598499\pi\)
−0.304530 + 0.952503i \(0.598499\pi\)
\(788\) −14.3214 −0.510180
\(789\) −19.7435 −0.702887
\(790\) −15.9750 −0.568365
\(791\) −5.91903 −0.210457
\(792\) −3.64048 −0.129359
\(793\) −2.91170 −0.103398
\(794\) −9.01291 −0.319856
\(795\) 3.00742 0.106662
\(796\) 19.3170 0.684673
\(797\) −16.8575 −0.597122 −0.298561 0.954391i \(-0.596507\pi\)
−0.298561 + 0.954391i \(0.596507\pi\)
\(798\) 2.64263 0.0935482
\(799\) 26.9576 0.953693
\(800\) 1.59277 0.0563130
\(801\) −10.7715 −0.380594
\(802\) −36.5026 −1.28895
\(803\) 27.6969 0.977403
\(804\) 10.3374 0.364570
\(805\) 8.81736 0.310771
\(806\) −23.3660 −0.823032
\(807\) 58.4636 2.05802
\(808\) −5.24995 −0.184693
\(809\) 48.2144 1.69513 0.847564 0.530693i \(-0.178068\pi\)
0.847564 + 0.530693i \(0.178068\pi\)
\(810\) −27.3975 −0.962651
\(811\) 48.9937 1.72040 0.860200 0.509956i \(-0.170338\pi\)
0.860200 + 0.509956i \(0.170338\pi\)
\(812\) 0.667004 0.0234073
\(813\) −30.3093 −1.06299
\(814\) 17.9355 0.628639
\(815\) 56.8017 1.98968
\(816\) −5.36733 −0.187894
\(817\) −5.70578 −0.199620
\(818\) −28.1491 −0.984211
\(819\) −1.45168 −0.0507259
\(820\) −16.3439 −0.570755
\(821\) 13.5893 0.474271 0.237136 0.971477i \(-0.423791\pi\)
0.237136 + 0.971477i \(0.423791\pi\)
\(822\) −14.4815 −0.505100
\(823\) −28.7843 −1.00336 −0.501679 0.865054i \(-0.667284\pi\)
−0.501679 + 0.865054i \(0.667284\pi\)
\(824\) −1.90296 −0.0662929
\(825\) 15.1788 0.528460
\(826\) −4.09386 −0.142444
\(827\) 13.4759 0.468603 0.234301 0.972164i \(-0.424720\pi\)
0.234301 + 0.972164i \(0.424720\pi\)
\(828\) 6.13196 0.213100
\(829\) −21.3585 −0.741812 −0.370906 0.928670i \(-0.620953\pi\)
−0.370906 + 0.928670i \(0.620953\pi\)
\(830\) −6.21665 −0.215783
\(831\) −17.4082 −0.603882
\(832\) −4.75124 −0.164720
\(833\) −18.9562 −0.656795
\(834\) −4.53696 −0.157102
\(835\) −34.8930 −1.20752
\(836\) 16.2845 0.563211
\(837\) 21.5033 0.743261
\(838\) −1.00405 −0.0346843
\(839\) −23.8230 −0.822461 −0.411231 0.911531i \(-0.634901\pi\)
−0.411231 + 0.911531i \(0.634901\pi\)
\(840\) −2.05365 −0.0708575
\(841\) −26.3999 −0.910342
\(842\) −20.3510 −0.701342
\(843\) −32.5530 −1.12119
\(844\) −9.72587 −0.334778
\(845\) 24.5833 0.845691
\(846\) 7.17315 0.246618
\(847\) 5.49813 0.188918
\(848\) −0.605764 −0.0208020
\(849\) 54.1462 1.85829
\(850\) 4.42135 0.151651
\(851\) −30.2103 −1.03559
\(852\) 7.11399 0.243721
\(853\) −49.1931 −1.68434 −0.842170 0.539212i \(-0.818722\pi\)
−0.842170 + 0.539212i \(0.818722\pi\)
\(854\) 0.253498 0.00867453
\(855\) −6.26627 −0.214302
\(856\) −18.1159 −0.619188
\(857\) 29.9945 1.02459 0.512296 0.858809i \(-0.328795\pi\)
0.512296 + 0.858809i \(0.328795\pi\)
\(858\) −45.2785 −1.54578
\(859\) −6.64819 −0.226833 −0.113417 0.993548i \(-0.536179\pi\)
−0.113417 + 0.993548i \(0.536179\pi\)
\(860\) 4.43408 0.151201
\(861\) 5.09113 0.173505
\(862\) 36.1827 1.23239
\(863\) −36.5616 −1.24457 −0.622285 0.782791i \(-0.713796\pi\)
−0.622285 + 0.782791i \(0.713796\pi\)
\(864\) 4.37247 0.148755
\(865\) 4.19492 0.142631
\(866\) 23.3687 0.794101
\(867\) 17.9713 0.610338
\(868\) 2.03429 0.0690482
\(869\) 30.6645 1.04022
\(870\) −8.00542 −0.271409
\(871\) 25.4015 0.860698
\(872\) 2.69697 0.0913308
\(873\) 8.30668 0.281138
\(874\) −27.4294 −0.927812
\(875\) −3.61885 −0.122339
\(876\) 10.8657 0.367119
\(877\) −48.8766 −1.65045 −0.825223 0.564806i \(-0.808951\pi\)
−0.825223 + 0.564806i \(0.808951\pi\)
\(878\) 23.1787 0.782244
\(879\) −25.6912 −0.866542
\(880\) −12.6550 −0.426601
\(881\) 45.4991 1.53290 0.766452 0.642302i \(-0.222020\pi\)
0.766452 + 0.642302i \(0.222020\pi\)
\(882\) −5.04406 −0.169842
\(883\) 42.8472 1.44192 0.720962 0.692975i \(-0.243700\pi\)
0.720962 + 0.692975i \(0.243700\pi\)
\(884\) −13.1889 −0.443591
\(885\) 49.1348 1.65165
\(886\) 7.14042 0.239887
\(887\) −25.6534 −0.861358 −0.430679 0.902505i \(-0.641726\pi\)
−0.430679 + 0.902505i \(0.641726\pi\)
\(888\) 7.03625 0.236121
\(889\) −3.73695 −0.125333
\(890\) −37.4440 −1.25513
\(891\) 52.5904 1.76184
\(892\) 12.8515 0.430299
\(893\) −32.0867 −1.07374
\(894\) −3.88770 −0.130024
\(895\) −8.61734 −0.288046
\(896\) 0.413652 0.0138191
\(897\) 76.2664 2.54646
\(898\) −33.7316 −1.12564
\(899\) 7.92995 0.264479
\(900\) 1.17648 0.0392159
\(901\) −1.68153 −0.0560200
\(902\) 31.3727 1.04460
\(903\) −1.38121 −0.0459639
\(904\) −14.3092 −0.475917
\(905\) −35.1150 −1.16726
\(906\) 3.59867 0.119558
\(907\) 22.7668 0.755958 0.377979 0.925814i \(-0.376619\pi\)
0.377979 + 0.925814i \(0.376619\pi\)
\(908\) 20.7443 0.688424
\(909\) −3.87780 −0.128618
\(910\) −5.04633 −0.167284
\(911\) −17.7160 −0.586958 −0.293479 0.955965i \(-0.594813\pi\)
−0.293479 + 0.955965i \(0.594813\pi\)
\(912\) 6.38855 0.211546
\(913\) 11.9330 0.394926
\(914\) 19.5946 0.648133
\(915\) −3.04250 −0.100582
\(916\) −24.2219 −0.800313
\(917\) −6.87422 −0.227007
\(918\) 12.1375 0.400597
\(919\) −40.9559 −1.35101 −0.675506 0.737354i \(-0.736075\pi\)
−0.675506 + 0.737354i \(0.736075\pi\)
\(920\) 21.3159 0.702765
\(921\) −47.7121 −1.57217
\(922\) 28.2593 0.930672
\(923\) 17.4809 0.575391
\(924\) 3.94203 0.129683
\(925\) −5.79613 −0.190575
\(926\) 22.6776 0.745233
\(927\) −1.40559 −0.0461658
\(928\) 1.61248 0.0529322
\(929\) −30.0806 −0.986913 −0.493457 0.869770i \(-0.664267\pi\)
−0.493457 + 0.869770i \(0.664267\pi\)
\(930\) −24.4156 −0.800619
\(931\) 22.5630 0.739471
\(932\) −17.6446 −0.577967
\(933\) −38.2443 −1.25206
\(934\) −40.1342 −1.31323
\(935\) −35.1289 −1.14884
\(936\) −3.50943 −0.114709
\(937\) 33.8861 1.10701 0.553505 0.832846i \(-0.313290\pi\)
0.553505 + 0.832846i \(0.313290\pi\)
\(938\) −2.21150 −0.0722082
\(939\) −22.1235 −0.721974
\(940\) 24.9353 0.813299
\(941\) 19.5372 0.636896 0.318448 0.947940i \(-0.396838\pi\)
0.318448 + 0.947940i \(0.396838\pi\)
\(942\) 21.9524 0.715249
\(943\) −52.8436 −1.72082
\(944\) −9.89689 −0.322116
\(945\) 4.64404 0.151071
\(946\) −8.51134 −0.276728
\(947\) −13.4623 −0.437467 −0.218734 0.975785i \(-0.570193\pi\)
−0.218734 + 0.975785i \(0.570193\pi\)
\(948\) 12.0299 0.390714
\(949\) 26.6999 0.866715
\(950\) −5.26258 −0.170741
\(951\) 7.86697 0.255104
\(952\) 1.14825 0.0372150
\(953\) −43.0656 −1.39503 −0.697516 0.716570i \(-0.745711\pi\)
−0.697516 + 0.716570i \(0.745711\pi\)
\(954\) −0.447438 −0.0144864
\(955\) −25.0255 −0.809807
\(956\) −8.87316 −0.286979
\(957\) 15.3666 0.496733
\(958\) −0.525069 −0.0169642
\(959\) 3.09808 0.100042
\(960\) −4.96467 −0.160234
\(961\) −6.81455 −0.219824
\(962\) 17.2899 0.557447
\(963\) −13.3810 −0.431197
\(964\) −4.22672 −0.136133
\(965\) 36.5216 1.17567
\(966\) −6.63990 −0.213635
\(967\) −23.2361 −0.747222 −0.373611 0.927585i \(-0.621880\pi\)
−0.373611 + 0.927585i \(0.621880\pi\)
\(968\) 13.2917 0.427211
\(969\) 17.7339 0.569695
\(970\) 28.8756 0.927141
\(971\) −55.8924 −1.79367 −0.896837 0.442362i \(-0.854141\pi\)
−0.896837 + 0.442362i \(0.854141\pi\)
\(972\) 7.51423 0.241019
\(973\) 0.970607 0.0311162
\(974\) −25.0558 −0.802841
\(975\) 14.6324 0.468613
\(976\) 0.612830 0.0196162
\(977\) −35.2286 −1.12706 −0.563531 0.826095i \(-0.690558\pi\)
−0.563531 + 0.826095i \(0.690558\pi\)
\(978\) −42.7744 −1.36777
\(979\) 71.8748 2.29713
\(980\) −17.5341 −0.560107
\(981\) 1.99207 0.0636020
\(982\) −17.7648 −0.566898
\(983\) −13.5401 −0.431864 −0.215932 0.976408i \(-0.569279\pi\)
−0.215932 + 0.976408i \(0.569279\pi\)
\(984\) 12.3078 0.392357
\(985\) −36.7723 −1.17166
\(986\) 4.47605 0.142547
\(987\) −7.76732 −0.247237
\(988\) 15.6983 0.499429
\(989\) 14.3364 0.455870
\(990\) −9.34743 −0.297081
\(991\) 6.04736 0.192101 0.0960503 0.995376i \(-0.469379\pi\)
0.0960503 + 0.995376i \(0.469379\pi\)
\(992\) 4.91787 0.156143
\(993\) 14.1888 0.450267
\(994\) −1.52192 −0.0482723
\(995\) 49.5991 1.57240
\(996\) 4.68144 0.148337
\(997\) 7.88141 0.249607 0.124803 0.992181i \(-0.460170\pi\)
0.124803 + 0.992181i \(0.460170\pi\)
\(998\) 3.09140 0.0978564
\(999\) −15.9115 −0.503418
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 6002.2.a.a.1.11 47
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6002.2.a.a.1.11 47 1.1 even 1 trivial