Properties

Label 8002.2.a.d.1.33
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $1$
Dimension $69$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, 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("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.33
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -0.671966 q^{3} +1.00000 q^{4} -3.60256 q^{5} -0.671966 q^{6} +0.00320310 q^{7} +1.00000 q^{8} -2.54846 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -0.671966 q^{3} +1.00000 q^{4} -3.60256 q^{5} -0.671966 q^{6} +0.00320310 q^{7} +1.00000 q^{8} -2.54846 q^{9} -3.60256 q^{10} +2.35705 q^{11} -0.671966 q^{12} -5.53956 q^{13} +0.00320310 q^{14} +2.42080 q^{15} +1.00000 q^{16} +0.517979 q^{17} -2.54846 q^{18} +6.37915 q^{19} -3.60256 q^{20} -0.00215238 q^{21} +2.35705 q^{22} +0.165673 q^{23} -0.671966 q^{24} +7.97845 q^{25} -5.53956 q^{26} +3.72838 q^{27} +0.00320310 q^{28} -0.662984 q^{29} +2.42080 q^{30} +9.38043 q^{31} +1.00000 q^{32} -1.58386 q^{33} +0.517979 q^{34} -0.0115394 q^{35} -2.54846 q^{36} +10.4690 q^{37} +6.37915 q^{38} +3.72240 q^{39} -3.60256 q^{40} -10.1097 q^{41} -0.00215238 q^{42} +5.22363 q^{43} +2.35705 q^{44} +9.18099 q^{45} +0.165673 q^{46} -8.34349 q^{47} -0.671966 q^{48} -6.99999 q^{49} +7.97845 q^{50} -0.348064 q^{51} -5.53956 q^{52} -3.30773 q^{53} +3.72838 q^{54} -8.49142 q^{55} +0.00320310 q^{56} -4.28657 q^{57} -0.662984 q^{58} -12.7440 q^{59} +2.42080 q^{60} +8.70514 q^{61} +9.38043 q^{62} -0.00816299 q^{63} +1.00000 q^{64} +19.9566 q^{65} -1.58386 q^{66} +6.01503 q^{67} +0.517979 q^{68} -0.111326 q^{69} -0.0115394 q^{70} +9.69955 q^{71} -2.54846 q^{72} -6.96842 q^{73} +10.4690 q^{74} -5.36125 q^{75} +6.37915 q^{76} +0.00754988 q^{77} +3.72240 q^{78} +0.137198 q^{79} -3.60256 q^{80} +5.14004 q^{81} -10.1097 q^{82} -9.96639 q^{83} -0.00215238 q^{84} -1.86605 q^{85} +5.22363 q^{86} +0.445503 q^{87} +2.35705 q^{88} -8.65440 q^{89} +9.18099 q^{90} -0.0177438 q^{91} +0.165673 q^{92} -6.30333 q^{93} -8.34349 q^{94} -22.9813 q^{95} -0.671966 q^{96} +17.4819 q^{97} -6.99999 q^{98} -6.00685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 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
\(3\) −0.671966 −0.387960 −0.193980 0.981006i \(-0.562140\pi\)
−0.193980 + 0.981006i \(0.562140\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.60256 −1.61111 −0.805557 0.592518i \(-0.798134\pi\)
−0.805557 + 0.592518i \(0.798134\pi\)
\(6\) −0.671966 −0.274329
\(7\) 0.00320310 0.00121066 0.000605330 1.00000i \(-0.499807\pi\)
0.000605330 1.00000i \(0.499807\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.54846 −0.849487
\(10\) −3.60256 −1.13923
\(11\) 2.35705 0.710677 0.355339 0.934738i \(-0.384366\pi\)
0.355339 + 0.934738i \(0.384366\pi\)
\(12\) −0.671966 −0.193980
\(13\) −5.53956 −1.53640 −0.768199 0.640211i \(-0.778847\pi\)
−0.768199 + 0.640211i \(0.778847\pi\)
\(14\) 0.00320310 0.000856066 0
\(15\) 2.42080 0.625048
\(16\) 1.00000 0.250000
\(17\) 0.517979 0.125628 0.0628142 0.998025i \(-0.479992\pi\)
0.0628142 + 0.998025i \(0.479992\pi\)
\(18\) −2.54846 −0.600678
\(19\) 6.37915 1.46348 0.731739 0.681585i \(-0.238709\pi\)
0.731739 + 0.681585i \(0.238709\pi\)
\(20\) −3.60256 −0.805557
\(21\) −0.00215238 −0.000469687 0
\(22\) 2.35705 0.502525
\(23\) 0.165673 0.0345451 0.0172726 0.999851i \(-0.494502\pi\)
0.0172726 + 0.999851i \(0.494502\pi\)
\(24\) −0.671966 −0.137165
\(25\) 7.97845 1.59569
\(26\) −5.53956 −1.08640
\(27\) 3.72838 0.717527
\(28\) 0.00320310 0.000605330 0
\(29\) −0.662984 −0.123113 −0.0615565 0.998104i \(-0.519606\pi\)
−0.0615565 + 0.998104i \(0.519606\pi\)
\(30\) 2.42080 0.441975
\(31\) 9.38043 1.68477 0.842387 0.538873i \(-0.181150\pi\)
0.842387 + 0.538873i \(0.181150\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.58386 −0.275714
\(34\) 0.517979 0.0888326
\(35\) −0.0115394 −0.00195051
\(36\) −2.54846 −0.424744
\(37\) 10.4690 1.72109 0.860547 0.509371i \(-0.170122\pi\)
0.860547 + 0.509371i \(0.170122\pi\)
\(38\) 6.37915 1.03483
\(39\) 3.72240 0.596061
\(40\) −3.60256 −0.569615
\(41\) −10.1097 −1.57888 −0.789438 0.613830i \(-0.789628\pi\)
−0.789438 + 0.613830i \(0.789628\pi\)
\(42\) −0.00215238 −0.000332119 0
\(43\) 5.22363 0.796596 0.398298 0.917256i \(-0.369601\pi\)
0.398298 + 0.917256i \(0.369601\pi\)
\(44\) 2.35705 0.355339
\(45\) 9.18099 1.36862
\(46\) 0.165673 0.0244271
\(47\) −8.34349 −1.21702 −0.608511 0.793545i \(-0.708233\pi\)
−0.608511 + 0.793545i \(0.708233\pi\)
\(48\) −0.671966 −0.0969900
\(49\) −6.99999 −0.999999
\(50\) 7.97845 1.12832
\(51\) −0.348064 −0.0487387
\(52\) −5.53956 −0.768199
\(53\) −3.30773 −0.454352 −0.227176 0.973854i \(-0.572949\pi\)
−0.227176 + 0.973854i \(0.572949\pi\)
\(54\) 3.72838 0.507368
\(55\) −8.49142 −1.14498
\(56\) 0.00320310 0.000428033 0
\(57\) −4.28657 −0.567770
\(58\) −0.662984 −0.0870540
\(59\) −12.7440 −1.65913 −0.829565 0.558410i \(-0.811412\pi\)
−0.829565 + 0.558410i \(0.811412\pi\)
\(60\) 2.42080 0.312524
\(61\) 8.70514 1.11458 0.557290 0.830318i \(-0.311841\pi\)
0.557290 + 0.830318i \(0.311841\pi\)
\(62\) 9.38043 1.19132
\(63\) −0.00816299 −0.00102844
\(64\) 1.00000 0.125000
\(65\) 19.9566 2.47531
\(66\) −1.58386 −0.194959
\(67\) 6.01503 0.734852 0.367426 0.930053i \(-0.380239\pi\)
0.367426 + 0.930053i \(0.380239\pi\)
\(68\) 0.517979 0.0628142
\(69\) −0.111326 −0.0134021
\(70\) −0.0115394 −0.00137922
\(71\) 9.69955 1.15112 0.575562 0.817758i \(-0.304783\pi\)
0.575562 + 0.817758i \(0.304783\pi\)
\(72\) −2.54846 −0.300339
\(73\) −6.96842 −0.815592 −0.407796 0.913073i \(-0.633703\pi\)
−0.407796 + 0.913073i \(0.633703\pi\)
\(74\) 10.4690 1.21700
\(75\) −5.36125 −0.619063
\(76\) 6.37915 0.731739
\(77\) 0.00754988 0.000860388 0
\(78\) 3.72240 0.421479
\(79\) 0.137198 0.0154360 0.00771802 0.999970i \(-0.497543\pi\)
0.00771802 + 0.999970i \(0.497543\pi\)
\(80\) −3.60256 −0.402779
\(81\) 5.14004 0.571116
\(82\) −10.1097 −1.11643
\(83\) −9.96639 −1.09395 −0.546977 0.837148i \(-0.684221\pi\)
−0.546977 + 0.837148i \(0.684221\pi\)
\(84\) −0.00215238 −0.000234844 0
\(85\) −1.86605 −0.202402
\(86\) 5.22363 0.563278
\(87\) 0.445503 0.0477629
\(88\) 2.35705 0.251262
\(89\) −8.65440 −0.917365 −0.458682 0.888600i \(-0.651678\pi\)
−0.458682 + 0.888600i \(0.651678\pi\)
\(90\) 9.18099 0.967761
\(91\) −0.0177438 −0.00186006
\(92\) 0.165673 0.0172726
\(93\) −6.30333 −0.653625
\(94\) −8.34349 −0.860565
\(95\) −22.9813 −2.35783
\(96\) −0.671966 −0.0685823
\(97\) 17.4819 1.77502 0.887510 0.460789i \(-0.152434\pi\)
0.887510 + 0.460789i \(0.152434\pi\)
\(98\) −6.99999 −0.707106
\(99\) −6.00685 −0.603711
\(100\) 7.97845 0.797845
\(101\) 14.1088 1.40388 0.701941 0.712235i \(-0.252317\pi\)
0.701941 + 0.712235i \(0.252317\pi\)
\(102\) −0.348064 −0.0344635
\(103\) −10.7738 −1.06158 −0.530789 0.847504i \(-0.678104\pi\)
−0.530789 + 0.847504i \(0.678104\pi\)
\(104\) −5.53956 −0.543199
\(105\) 0.00775407 0.000756720 0
\(106\) −3.30773 −0.321276
\(107\) −9.25256 −0.894479 −0.447239 0.894414i \(-0.647593\pi\)
−0.447239 + 0.894414i \(0.647593\pi\)
\(108\) 3.72838 0.358763
\(109\) 7.66927 0.734583 0.367291 0.930106i \(-0.380285\pi\)
0.367291 + 0.930106i \(0.380285\pi\)
\(110\) −8.49142 −0.809625
\(111\) −7.03482 −0.667715
\(112\) 0.00320310 0.000302665 0
\(113\) 6.17042 0.580464 0.290232 0.956956i \(-0.406268\pi\)
0.290232 + 0.956956i \(0.406268\pi\)
\(114\) −4.28657 −0.401474
\(115\) −0.596845 −0.0556561
\(116\) −0.662984 −0.0615565
\(117\) 14.1174 1.30515
\(118\) −12.7440 −1.17318
\(119\) 0.00165914 0.000152093 0
\(120\) 2.42080 0.220988
\(121\) −5.44431 −0.494938
\(122\) 8.70514 0.788126
\(123\) 6.79341 0.612541
\(124\) 9.38043 0.842387
\(125\) −10.7300 −0.959723
\(126\) −0.00816299 −0.000727217 0
\(127\) −15.6138 −1.38550 −0.692750 0.721178i \(-0.743601\pi\)
−0.692750 + 0.721178i \(0.743601\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.51010 −0.309047
\(130\) 19.9566 1.75031
\(131\) −9.21171 −0.804831 −0.402415 0.915457i \(-0.631829\pi\)
−0.402415 + 0.915457i \(0.631829\pi\)
\(132\) −1.58386 −0.137857
\(133\) 0.0204331 0.00177177
\(134\) 6.01503 0.519619
\(135\) −13.4317 −1.15602
\(136\) 0.517979 0.0444163
\(137\) −14.8483 −1.26857 −0.634286 0.773098i \(-0.718706\pi\)
−0.634286 + 0.773098i \(0.718706\pi\)
\(138\) −0.111326 −0.00947673
\(139\) −8.10001 −0.687034 −0.343517 0.939146i \(-0.611618\pi\)
−0.343517 + 0.939146i \(0.611618\pi\)
\(140\) −0.0115394 −0.000975255 0
\(141\) 5.60654 0.472156
\(142\) 9.69955 0.813968
\(143\) −13.0570 −1.09188
\(144\) −2.54846 −0.212372
\(145\) 2.38844 0.198349
\(146\) −6.96842 −0.576711
\(147\) 4.70376 0.387959
\(148\) 10.4690 0.860547
\(149\) −7.99537 −0.655007 −0.327503 0.944850i \(-0.606207\pi\)
−0.327503 + 0.944850i \(0.606207\pi\)
\(150\) −5.36125 −0.437744
\(151\) −20.5151 −1.66949 −0.834747 0.550633i \(-0.814386\pi\)
−0.834747 + 0.550633i \(0.814386\pi\)
\(152\) 6.37915 0.517417
\(153\) −1.32005 −0.106720
\(154\) 0.00754988 0.000608386 0
\(155\) −33.7936 −2.71436
\(156\) 3.72240 0.298031
\(157\) −22.6547 −1.80804 −0.904020 0.427491i \(-0.859398\pi\)
−0.904020 + 0.427491i \(0.859398\pi\)
\(158\) 0.137198 0.0109149
\(159\) 2.22269 0.176270
\(160\) −3.60256 −0.284807
\(161\) 0.000530666 0 4.18224e−5 0
\(162\) 5.14004 0.403840
\(163\) −22.1106 −1.73184 −0.865919 0.500183i \(-0.833266\pi\)
−0.865919 + 0.500183i \(0.833266\pi\)
\(164\) −10.1097 −0.789438
\(165\) 5.70594 0.444207
\(166\) −9.96639 −0.773542
\(167\) 19.4887 1.50808 0.754042 0.656826i \(-0.228101\pi\)
0.754042 + 0.656826i \(0.228101\pi\)
\(168\) −0.00215238 −0.000166060 0
\(169\) 17.6868 1.36052
\(170\) −1.86605 −0.143120
\(171\) −16.2570 −1.24321
\(172\) 5.22363 0.398298
\(173\) 9.37562 0.712815 0.356407 0.934331i \(-0.384002\pi\)
0.356407 + 0.934331i \(0.384002\pi\)
\(174\) 0.445503 0.0337735
\(175\) 0.0255558 0.00193184
\(176\) 2.35705 0.177669
\(177\) 8.56355 0.643676
\(178\) −8.65440 −0.648675
\(179\) 0.360173 0.0269206 0.0134603 0.999909i \(-0.495715\pi\)
0.0134603 + 0.999909i \(0.495715\pi\)
\(180\) 9.18099 0.684310
\(181\) −14.0808 −1.04662 −0.523309 0.852143i \(-0.675303\pi\)
−0.523309 + 0.852143i \(0.675303\pi\)
\(182\) −0.0177438 −0.00131526
\(183\) −5.84956 −0.432412
\(184\) 0.165673 0.0122135
\(185\) −37.7152 −2.77288
\(186\) −6.30333 −0.462182
\(187\) 1.22090 0.0892812
\(188\) −8.34349 −0.608511
\(189\) 0.0119424 0.000868681 0
\(190\) −22.9813 −1.66724
\(191\) −9.96640 −0.721143 −0.360572 0.932732i \(-0.617418\pi\)
−0.360572 + 0.932732i \(0.617418\pi\)
\(192\) −0.671966 −0.0484950
\(193\) 18.3471 1.32065 0.660327 0.750978i \(-0.270418\pi\)
0.660327 + 0.750978i \(0.270418\pi\)
\(194\) 17.4819 1.25513
\(195\) −13.4102 −0.960322
\(196\) −6.99999 −0.499999
\(197\) −18.8320 −1.34172 −0.670861 0.741583i \(-0.734075\pi\)
−0.670861 + 0.741583i \(0.734075\pi\)
\(198\) −6.00685 −0.426888
\(199\) −17.7025 −1.25490 −0.627450 0.778657i \(-0.715901\pi\)
−0.627450 + 0.778657i \(0.715901\pi\)
\(200\) 7.97845 0.564161
\(201\) −4.04189 −0.285093
\(202\) 14.1088 0.992694
\(203\) −0.00212361 −0.000149048 0
\(204\) −0.348064 −0.0243694
\(205\) 36.4210 2.54375
\(206\) −10.7738 −0.750650
\(207\) −0.422210 −0.0293456
\(208\) −5.53956 −0.384100
\(209\) 15.0360 1.04006
\(210\) 0.00775407 0.000535082 0
\(211\) 19.3268 1.33051 0.665257 0.746615i \(-0.268322\pi\)
0.665257 + 0.746615i \(0.268322\pi\)
\(212\) −3.30773 −0.227176
\(213\) −6.51777 −0.446590
\(214\) −9.25256 −0.632492
\(215\) −18.8184 −1.28341
\(216\) 3.72838 0.253684
\(217\) 0.0300465 0.00203969
\(218\) 7.66927 0.519429
\(219\) 4.68254 0.316417
\(220\) −8.49142 −0.572491
\(221\) −2.86938 −0.193015
\(222\) −7.03482 −0.472146
\(223\) 14.7486 0.987642 0.493821 0.869563i \(-0.335600\pi\)
0.493821 + 0.869563i \(0.335600\pi\)
\(224\) 0.00320310 0.000214016 0
\(225\) −20.3328 −1.35552
\(226\) 6.17042 0.410450
\(227\) 7.54663 0.500887 0.250444 0.968131i \(-0.419424\pi\)
0.250444 + 0.968131i \(0.419424\pi\)
\(228\) −4.28657 −0.283885
\(229\) −15.2598 −1.00839 −0.504197 0.863589i \(-0.668212\pi\)
−0.504197 + 0.863589i \(0.668212\pi\)
\(230\) −0.596845 −0.0393548
\(231\) −0.00507326 −0.000333796 0
\(232\) −0.662984 −0.0435270
\(233\) 4.01000 0.262704 0.131352 0.991336i \(-0.458068\pi\)
0.131352 + 0.991336i \(0.458068\pi\)
\(234\) 14.1174 0.922881
\(235\) 30.0579 1.96076
\(236\) −12.7440 −0.829565
\(237\) −0.0921927 −0.00598856
\(238\) 0.00165914 0.000107546 0
\(239\) 7.17759 0.464280 0.232140 0.972682i \(-0.425427\pi\)
0.232140 + 0.972682i \(0.425427\pi\)
\(240\) 2.42080 0.156262
\(241\) 13.8399 0.891506 0.445753 0.895156i \(-0.352936\pi\)
0.445753 + 0.895156i \(0.352936\pi\)
\(242\) −5.44431 −0.349974
\(243\) −14.6391 −0.939097
\(244\) 8.70514 0.557290
\(245\) 25.2179 1.61111
\(246\) 6.79341 0.433132
\(247\) −35.3377 −2.24848
\(248\) 9.38043 0.595658
\(249\) 6.69707 0.424410
\(250\) −10.7300 −0.678627
\(251\) 1.00600 0.0634984 0.0317492 0.999496i \(-0.489892\pi\)
0.0317492 + 0.999496i \(0.489892\pi\)
\(252\) −0.00816299 −0.000514220 0
\(253\) 0.390498 0.0245504
\(254\) −15.6138 −0.979697
\(255\) 1.25392 0.0785237
\(256\) 1.00000 0.0625000
\(257\) −15.2690 −0.952454 −0.476227 0.879322i \(-0.657996\pi\)
−0.476227 + 0.879322i \(0.657996\pi\)
\(258\) −3.51010 −0.218529
\(259\) 0.0335333 0.00208366
\(260\) 19.9566 1.23766
\(261\) 1.68959 0.104583
\(262\) −9.21171 −0.569101
\(263\) −2.79277 −0.172210 −0.0861048 0.996286i \(-0.527442\pi\)
−0.0861048 + 0.996286i \(0.527442\pi\)
\(264\) −1.58386 −0.0974797
\(265\) 11.9163 0.732013
\(266\) 0.0204331 0.00125283
\(267\) 5.81547 0.355901
\(268\) 6.01503 0.367426
\(269\) 2.65737 0.162023 0.0810114 0.996713i \(-0.474185\pi\)
0.0810114 + 0.996713i \(0.474185\pi\)
\(270\) −13.4317 −0.817428
\(271\) 20.1846 1.22612 0.613062 0.790034i \(-0.289937\pi\)
0.613062 + 0.790034i \(0.289937\pi\)
\(272\) 0.517979 0.0314071
\(273\) 0.0119232 0.000721627 0
\(274\) −14.8483 −0.897016
\(275\) 18.8056 1.13402
\(276\) −0.111326 −0.00670106
\(277\) 16.4138 0.986212 0.493106 0.869969i \(-0.335861\pi\)
0.493106 + 0.869969i \(0.335861\pi\)
\(278\) −8.10001 −0.485807
\(279\) −23.9057 −1.43119
\(280\) −0.0115394 −0.000689610 0
\(281\) 8.03318 0.479219 0.239610 0.970869i \(-0.422981\pi\)
0.239610 + 0.970869i \(0.422981\pi\)
\(282\) 5.60654 0.333865
\(283\) −3.61553 −0.214921 −0.107460 0.994209i \(-0.534272\pi\)
−0.107460 + 0.994209i \(0.534272\pi\)
\(284\) 9.69955 0.575562
\(285\) 15.4426 0.914743
\(286\) −13.0570 −0.772078
\(287\) −0.0323826 −0.00191148
\(288\) −2.54846 −0.150170
\(289\) −16.7317 −0.984218
\(290\) 2.38844 0.140254
\(291\) −11.7473 −0.688636
\(292\) −6.96842 −0.407796
\(293\) −30.8642 −1.80311 −0.901553 0.432669i \(-0.857572\pi\)
−0.901553 + 0.432669i \(0.857572\pi\)
\(294\) 4.70376 0.274329
\(295\) 45.9111 2.67305
\(296\) 10.4690 0.608499
\(297\) 8.78797 0.509930
\(298\) −7.99537 −0.463160
\(299\) −0.917754 −0.0530751
\(300\) −5.36125 −0.309532
\(301\) 0.0167318 0.000964406 0
\(302\) −20.5151 −1.18051
\(303\) −9.48066 −0.544650
\(304\) 6.37915 0.365869
\(305\) −31.3608 −1.79571
\(306\) −1.32005 −0.0754622
\(307\) 19.0538 1.08746 0.543728 0.839261i \(-0.317012\pi\)
0.543728 + 0.839261i \(0.317012\pi\)
\(308\) 0.00754988 0.000430194 0
\(309\) 7.23966 0.411850
\(310\) −33.7936 −1.91934
\(311\) 11.8968 0.674604 0.337302 0.941396i \(-0.390486\pi\)
0.337302 + 0.941396i \(0.390486\pi\)
\(312\) 3.72240 0.210739
\(313\) −32.2628 −1.82360 −0.911800 0.410636i \(-0.865307\pi\)
−0.911800 + 0.410636i \(0.865307\pi\)
\(314\) −22.6547 −1.27848
\(315\) 0.0294077 0.00165693
\(316\) 0.137198 0.00771802
\(317\) 11.4805 0.644807 0.322404 0.946602i \(-0.395509\pi\)
0.322404 + 0.946602i \(0.395509\pi\)
\(318\) 2.22269 0.124642
\(319\) −1.56269 −0.0874936
\(320\) −3.60256 −0.201389
\(321\) 6.21741 0.347022
\(322\) 0.000530666 0 2.95729e−5 0
\(323\) 3.30426 0.183854
\(324\) 5.14004 0.285558
\(325\) −44.1971 −2.45161
\(326\) −22.1106 −1.22460
\(327\) −5.15349 −0.284989
\(328\) −10.1097 −0.558217
\(329\) −0.0267251 −0.00147340
\(330\) 5.70594 0.314102
\(331\) −18.9411 −1.04110 −0.520549 0.853832i \(-0.674273\pi\)
−0.520549 + 0.853832i \(0.674273\pi\)
\(332\) −9.96639 −0.546977
\(333\) −26.6799 −1.46205
\(334\) 19.4887 1.06638
\(335\) −21.6695 −1.18393
\(336\) −0.00215238 −0.000117422 0
\(337\) 21.7910 1.18703 0.593515 0.804823i \(-0.297740\pi\)
0.593515 + 0.804823i \(0.297740\pi\)
\(338\) 17.6868 0.962034
\(339\) −4.14631 −0.225197
\(340\) −1.86605 −0.101201
\(341\) 22.1101 1.19733
\(342\) −16.2570 −0.879079
\(343\) −0.0448434 −0.00242132
\(344\) 5.22363 0.281639
\(345\) 0.401060 0.0215923
\(346\) 9.37562 0.504036
\(347\) −20.6062 −1.10620 −0.553099 0.833115i \(-0.686555\pi\)
−0.553099 + 0.833115i \(0.686555\pi\)
\(348\) 0.445503 0.0238814
\(349\) −2.04297 −0.109358 −0.0546788 0.998504i \(-0.517414\pi\)
−0.0546788 + 0.998504i \(0.517414\pi\)
\(350\) 0.0255558 0.00136601
\(351\) −20.6536 −1.10241
\(352\) 2.35705 0.125631
\(353\) −6.25826 −0.333094 −0.166547 0.986034i \(-0.553262\pi\)
−0.166547 + 0.986034i \(0.553262\pi\)
\(354\) 8.56355 0.455148
\(355\) −34.9432 −1.85459
\(356\) −8.65440 −0.458682
\(357\) −0.00111489 −5.90060e−5 0
\(358\) 0.360173 0.0190357
\(359\) −2.32159 −0.122529 −0.0612643 0.998122i \(-0.519513\pi\)
−0.0612643 + 0.998122i \(0.519513\pi\)
\(360\) 9.18099 0.483881
\(361\) 21.6936 1.14177
\(362\) −14.0808 −0.740071
\(363\) 3.65840 0.192016
\(364\) −0.0177438 −0.000930028 0
\(365\) 25.1042 1.31401
\(366\) −5.84956 −0.305761
\(367\) 34.7000 1.81133 0.905663 0.423999i \(-0.139374\pi\)
0.905663 + 0.423999i \(0.139374\pi\)
\(368\) 0.165673 0.00863628
\(369\) 25.7643 1.34124
\(370\) −37.7152 −1.96072
\(371\) −0.0105950 −0.000550066 0
\(372\) −6.30333 −0.326812
\(373\) 10.0646 0.521125 0.260562 0.965457i \(-0.416092\pi\)
0.260562 + 0.965457i \(0.416092\pi\)
\(374\) 1.22090 0.0631313
\(375\) 7.21022 0.372334
\(376\) −8.34349 −0.430283
\(377\) 3.67264 0.189151
\(378\) 0.0119424 0.000614250 0
\(379\) −1.70743 −0.0877048 −0.0438524 0.999038i \(-0.513963\pi\)
−0.0438524 + 0.999038i \(0.513963\pi\)
\(380\) −22.9813 −1.17891
\(381\) 10.4919 0.537519
\(382\) −9.96640 −0.509925
\(383\) −25.8225 −1.31947 −0.659734 0.751499i \(-0.729331\pi\)
−0.659734 + 0.751499i \(0.729331\pi\)
\(384\) −0.671966 −0.0342911
\(385\) −0.0271989 −0.00138618
\(386\) 18.3471 0.933843
\(387\) −13.3122 −0.676698
\(388\) 17.4819 0.887510
\(389\) −21.7658 −1.10357 −0.551786 0.833986i \(-0.686053\pi\)
−0.551786 + 0.833986i \(0.686053\pi\)
\(390\) −13.4102 −0.679050
\(391\) 0.0858148 0.00433984
\(392\) −6.99999 −0.353553
\(393\) 6.18996 0.312242
\(394\) −18.8320 −0.948741
\(395\) −0.494266 −0.0248692
\(396\) −6.00685 −0.301856
\(397\) −15.9100 −0.798502 −0.399251 0.916842i \(-0.630730\pi\)
−0.399251 + 0.916842i \(0.630730\pi\)
\(398\) −17.7025 −0.887348
\(399\) −0.0137303 −0.000687377 0
\(400\) 7.97845 0.398922
\(401\) 27.3375 1.36517 0.682586 0.730806i \(-0.260855\pi\)
0.682586 + 0.730806i \(0.260855\pi\)
\(402\) −4.04189 −0.201591
\(403\) −51.9635 −2.58848
\(404\) 14.1088 0.701941
\(405\) −18.5173 −0.920132
\(406\) −0.00212361 −0.000105393 0
\(407\) 24.6760 1.22314
\(408\) −0.348064 −0.0172317
\(409\) −1.77857 −0.0879444 −0.0439722 0.999033i \(-0.514001\pi\)
−0.0439722 + 0.999033i \(0.514001\pi\)
\(410\) 36.4210 1.79870
\(411\) 9.97753 0.492155
\(412\) −10.7738 −0.530789
\(413\) −0.0408204 −0.00200864
\(414\) −0.422210 −0.0207505
\(415\) 35.9045 1.76248
\(416\) −5.53956 −0.271599
\(417\) 5.44293 0.266542
\(418\) 15.0360 0.735434
\(419\) 33.0783 1.61598 0.807990 0.589196i \(-0.200555\pi\)
0.807990 + 0.589196i \(0.200555\pi\)
\(420\) 0.00775407 0.000378360 0
\(421\) 8.69390 0.423715 0.211857 0.977301i \(-0.432049\pi\)
0.211857 + 0.977301i \(0.432049\pi\)
\(422\) 19.3268 0.940815
\(423\) 21.2631 1.03385
\(424\) −3.30773 −0.160638
\(425\) 4.13267 0.200464
\(426\) −6.51777 −0.315787
\(427\) 0.0278835 0.00134938
\(428\) −9.25256 −0.447239
\(429\) 8.77388 0.423607
\(430\) −18.8184 −0.907506
\(431\) −9.39970 −0.452768 −0.226384 0.974038i \(-0.572690\pi\)
−0.226384 + 0.974038i \(0.572690\pi\)
\(432\) 3.72838 0.179382
\(433\) −10.4032 −0.499947 −0.249974 0.968253i \(-0.580422\pi\)
−0.249974 + 0.968253i \(0.580422\pi\)
\(434\) 0.0300465 0.00144228
\(435\) −1.60495 −0.0769515
\(436\) 7.66927 0.367291
\(437\) 1.05685 0.0505560
\(438\) 4.68254 0.223741
\(439\) −22.4008 −1.06913 −0.534566 0.845127i \(-0.679525\pi\)
−0.534566 + 0.845127i \(0.679525\pi\)
\(440\) −8.49142 −0.404812
\(441\) 17.8392 0.849486
\(442\) −2.86938 −0.136482
\(443\) 37.0228 1.75901 0.879504 0.475892i \(-0.157875\pi\)
0.879504 + 0.475892i \(0.157875\pi\)
\(444\) −7.03482 −0.333858
\(445\) 31.1780 1.47798
\(446\) 14.7486 0.698369
\(447\) 5.37262 0.254116
\(448\) 0.00320310 0.000151332 0
\(449\) −23.0335 −1.08702 −0.543509 0.839404i \(-0.682905\pi\)
−0.543509 + 0.839404i \(0.682905\pi\)
\(450\) −20.3328 −0.958496
\(451\) −23.8292 −1.12207
\(452\) 6.17042 0.290232
\(453\) 13.7855 0.647697
\(454\) 7.54663 0.354181
\(455\) 0.0639231 0.00299676
\(456\) −4.28657 −0.200737
\(457\) 15.5058 0.725333 0.362666 0.931919i \(-0.381866\pi\)
0.362666 + 0.931919i \(0.381866\pi\)
\(458\) −15.2598 −0.713043
\(459\) 1.93122 0.0901417
\(460\) −0.596845 −0.0278281
\(461\) 4.71579 0.219636 0.109818 0.993952i \(-0.464973\pi\)
0.109818 + 0.993952i \(0.464973\pi\)
\(462\) −0.00507326 −0.000236029 0
\(463\) 2.51673 0.116962 0.0584812 0.998289i \(-0.481374\pi\)
0.0584812 + 0.998289i \(0.481374\pi\)
\(464\) −0.662984 −0.0307782
\(465\) 22.7081 1.05306
\(466\) 4.01000 0.185760
\(467\) −23.6562 −1.09468 −0.547339 0.836911i \(-0.684359\pi\)
−0.547339 + 0.836911i \(0.684359\pi\)
\(468\) 14.1174 0.652576
\(469\) 0.0192668 0.000889656 0
\(470\) 30.0579 1.38647
\(471\) 15.2232 0.701447
\(472\) −12.7440 −0.586591
\(473\) 12.3124 0.566123
\(474\) −0.0921927 −0.00423455
\(475\) 50.8957 2.33525
\(476\) 0.00165914 7.60465e−5 0
\(477\) 8.42963 0.385966
\(478\) 7.17759 0.328296
\(479\) 5.55788 0.253946 0.126973 0.991906i \(-0.459474\pi\)
0.126973 + 0.991906i \(0.459474\pi\)
\(480\) 2.42080 0.110494
\(481\) −57.9937 −2.64429
\(482\) 13.8399 0.630390
\(483\) −0.000356590 0 −1.62254e−5 0
\(484\) −5.44431 −0.247469
\(485\) −62.9796 −2.85976
\(486\) −14.6391 −0.664042
\(487\) −33.0410 −1.49723 −0.748616 0.663004i \(-0.769281\pi\)
−0.748616 + 0.663004i \(0.769281\pi\)
\(488\) 8.70514 0.394063
\(489\) 14.8576 0.671884
\(490\) 25.2179 1.13923
\(491\) 9.44418 0.426210 0.213105 0.977029i \(-0.431642\pi\)
0.213105 + 0.977029i \(0.431642\pi\)
\(492\) 6.79341 0.306270
\(493\) −0.343412 −0.0154665
\(494\) −35.3377 −1.58992
\(495\) 21.6400 0.972648
\(496\) 9.38043 0.421194
\(497\) 0.0310687 0.00139362
\(498\) 6.69707 0.300103
\(499\) −31.4323 −1.40710 −0.703551 0.710644i \(-0.748404\pi\)
−0.703551 + 0.710644i \(0.748404\pi\)
\(500\) −10.7300 −0.479862
\(501\) −13.0958 −0.585076
\(502\) 1.00600 0.0449001
\(503\) 22.7101 1.01260 0.506298 0.862359i \(-0.331014\pi\)
0.506298 + 0.862359i \(0.331014\pi\)
\(504\) −0.00816299 −0.000363608 0
\(505\) −50.8279 −2.26181
\(506\) 0.390498 0.0173598
\(507\) −11.8849 −0.527828
\(508\) −15.6138 −0.692750
\(509\) −42.2922 −1.87457 −0.937283 0.348568i \(-0.886668\pi\)
−0.937283 + 0.348568i \(0.886668\pi\)
\(510\) 1.25392 0.0555246
\(511\) −0.0223206 −0.000987404 0
\(512\) 1.00000 0.0441942
\(513\) 23.7839 1.05008
\(514\) −15.2690 −0.673487
\(515\) 38.8134 1.71032
\(516\) −3.51010 −0.154524
\(517\) −19.6660 −0.864910
\(518\) 0.0335333 0.00147337
\(519\) −6.30010 −0.276544
\(520\) 19.9566 0.875156
\(521\) −7.63690 −0.334579 −0.167289 0.985908i \(-0.553501\pi\)
−0.167289 + 0.985908i \(0.553501\pi\)
\(522\) 1.68959 0.0739513
\(523\) −30.3552 −1.32734 −0.663670 0.748025i \(-0.731002\pi\)
−0.663670 + 0.748025i \(0.731002\pi\)
\(524\) −9.21171 −0.402415
\(525\) −0.0171726 −0.000749475 0
\(526\) −2.79277 −0.121771
\(527\) 4.85886 0.211655
\(528\) −1.58386 −0.0689286
\(529\) −22.9726 −0.998807
\(530\) 11.9163 0.517612
\(531\) 32.4777 1.40941
\(532\) 0.0204331 0.000885886 0
\(533\) 56.0036 2.42578
\(534\) 5.81547 0.251660
\(535\) 33.3329 1.44111
\(536\) 6.01503 0.259810
\(537\) −0.242024 −0.0104441
\(538\) 2.65737 0.114567
\(539\) −16.4993 −0.710676
\(540\) −13.4317 −0.578009
\(541\) 41.1438 1.76891 0.884456 0.466624i \(-0.154530\pi\)
0.884456 + 0.466624i \(0.154530\pi\)
\(542\) 20.1846 0.867001
\(543\) 9.46183 0.406046
\(544\) 0.517979 0.0222082
\(545\) −27.6290 −1.18350
\(546\) 0.0119232 0.000510267 0
\(547\) −22.0474 −0.942677 −0.471338 0.881952i \(-0.656229\pi\)
−0.471338 + 0.881952i \(0.656229\pi\)
\(548\) −14.8483 −0.634286
\(549\) −22.1847 −0.946821
\(550\) 18.8056 0.801873
\(551\) −4.22927 −0.180173
\(552\) −0.111326 −0.00473836
\(553\) 0.000439461 0 1.86878e−5 0
\(554\) 16.4138 0.697357
\(555\) 25.3434 1.07577
\(556\) −8.10001 −0.343517
\(557\) 12.8761 0.545578 0.272789 0.962074i \(-0.412054\pi\)
0.272789 + 0.962074i \(0.412054\pi\)
\(558\) −23.9057 −1.01201
\(559\) −28.9366 −1.22389
\(560\) −0.0115394 −0.000487628 0
\(561\) −0.820405 −0.0346375
\(562\) 8.03318 0.338859
\(563\) −21.6422 −0.912110 −0.456055 0.889952i \(-0.650738\pi\)
−0.456055 + 0.889952i \(0.650738\pi\)
\(564\) 5.60654 0.236078
\(565\) −22.2293 −0.935194
\(566\) −3.61553 −0.151972
\(567\) 0.0164641 0.000691427 0
\(568\) 9.69955 0.406984
\(569\) 3.87671 0.162520 0.0812600 0.996693i \(-0.474106\pi\)
0.0812600 + 0.996693i \(0.474106\pi\)
\(570\) 15.4426 0.646821
\(571\) 13.8813 0.580913 0.290456 0.956888i \(-0.406193\pi\)
0.290456 + 0.956888i \(0.406193\pi\)
\(572\) −13.0570 −0.545942
\(573\) 6.69708 0.279775
\(574\) −0.0323826 −0.00135162
\(575\) 1.32181 0.0551232
\(576\) −2.54846 −0.106186
\(577\) 3.99826 0.166450 0.0832249 0.996531i \(-0.473478\pi\)
0.0832249 + 0.996531i \(0.473478\pi\)
\(578\) −16.7317 −0.695947
\(579\) −12.3286 −0.512361
\(580\) 2.38844 0.0991745
\(581\) −0.0319234 −0.00132440
\(582\) −11.7473 −0.486939
\(583\) −7.79650 −0.322898
\(584\) −6.96842 −0.288355
\(585\) −50.8587 −2.10275
\(586\) −30.8642 −1.27499
\(587\) −33.3117 −1.37492 −0.687460 0.726223i \(-0.741274\pi\)
−0.687460 + 0.726223i \(0.741274\pi\)
\(588\) 4.70376 0.193980
\(589\) 59.8391 2.46563
\(590\) 45.9111 1.89013
\(591\) 12.6544 0.520534
\(592\) 10.4690 0.430273
\(593\) 26.2795 1.07917 0.539584 0.841931i \(-0.318581\pi\)
0.539584 + 0.841931i \(0.318581\pi\)
\(594\) 8.78797 0.360575
\(595\) −0.00597715 −0.000245039 0
\(596\) −7.99537 −0.327503
\(597\) 11.8955 0.486851
\(598\) −0.917754 −0.0375297
\(599\) 15.7522 0.643617 0.321808 0.946805i \(-0.395709\pi\)
0.321808 + 0.946805i \(0.395709\pi\)
\(600\) −5.36125 −0.218872
\(601\) −36.9363 −1.50666 −0.753331 0.657641i \(-0.771554\pi\)
−0.753331 + 0.657641i \(0.771554\pi\)
\(602\) 0.0167318 0.000681938 0
\(603\) −15.3291 −0.624248
\(604\) −20.5151 −0.834747
\(605\) 19.6135 0.797401
\(606\) −9.48066 −0.385126
\(607\) −32.3173 −1.31172 −0.655859 0.754883i \(-0.727693\pi\)
−0.655859 + 0.754883i \(0.727693\pi\)
\(608\) 6.37915 0.258709
\(609\) 0.00142699 5.78246e−5 0
\(610\) −31.3608 −1.26976
\(611\) 46.2193 1.86983
\(612\) −1.32005 −0.0533598
\(613\) −30.4679 −1.23059 −0.615294 0.788298i \(-0.710963\pi\)
−0.615294 + 0.788298i \(0.710963\pi\)
\(614\) 19.0538 0.768948
\(615\) −24.4737 −0.986873
\(616\) 0.00754988 0.000304193 0
\(617\) 33.2509 1.33863 0.669316 0.742978i \(-0.266587\pi\)
0.669316 + 0.742978i \(0.266587\pi\)
\(618\) 7.23966 0.291222
\(619\) −17.3282 −0.696479 −0.348240 0.937406i \(-0.613220\pi\)
−0.348240 + 0.937406i \(0.613220\pi\)
\(620\) −33.7936 −1.35718
\(621\) 0.617690 0.0247870
\(622\) 11.8968 0.477017
\(623\) −0.0277210 −0.00111062
\(624\) 3.72240 0.149015
\(625\) −1.23664 −0.0494656
\(626\) −32.2628 −1.28948
\(627\) −10.1037 −0.403502
\(628\) −22.6547 −0.904020
\(629\) 5.42272 0.216218
\(630\) 0.0294077 0.00117163
\(631\) −21.7063 −0.864114 −0.432057 0.901846i \(-0.642212\pi\)
−0.432057 + 0.901846i \(0.642212\pi\)
\(632\) 0.137198 0.00545746
\(633\) −12.9870 −0.516186
\(634\) 11.4805 0.455948
\(635\) 56.2497 2.23220
\(636\) 2.22269 0.0881352
\(637\) 38.7769 1.53640
\(638\) −1.56269 −0.0618673
\(639\) −24.7189 −0.977866
\(640\) −3.60256 −0.142404
\(641\) 16.3099 0.644201 0.322101 0.946705i \(-0.395611\pi\)
0.322101 + 0.946705i \(0.395611\pi\)
\(642\) 6.21741 0.245381
\(643\) −25.8929 −1.02112 −0.510558 0.859843i \(-0.670561\pi\)
−0.510558 + 0.859843i \(0.670561\pi\)
\(644\) 0.000530666 0 2.09112e−5 0
\(645\) 12.6454 0.497910
\(646\) 3.30426 0.130005
\(647\) −28.8063 −1.13249 −0.566245 0.824237i \(-0.691605\pi\)
−0.566245 + 0.824237i \(0.691605\pi\)
\(648\) 5.14004 0.201920
\(649\) −30.0383 −1.17911
\(650\) −44.1971 −1.73355
\(651\) −0.0201902 −0.000791317 0
\(652\) −22.1106 −0.865919
\(653\) −6.45010 −0.252412 −0.126206 0.992004i \(-0.540280\pi\)
−0.126206 + 0.992004i \(0.540280\pi\)
\(654\) −5.15349 −0.201517
\(655\) 33.1857 1.29667
\(656\) −10.1097 −0.394719
\(657\) 17.7588 0.692835
\(658\) −0.0267251 −0.00104185
\(659\) 3.70233 0.144222 0.0721112 0.997397i \(-0.477026\pi\)
0.0721112 + 0.997397i \(0.477026\pi\)
\(660\) 5.70594 0.222104
\(661\) 18.7570 0.729562 0.364781 0.931093i \(-0.381144\pi\)
0.364781 + 0.931093i \(0.381144\pi\)
\(662\) −18.9411 −0.736168
\(663\) 1.92812 0.0748821
\(664\) −9.96639 −0.386771
\(665\) −0.0736114 −0.00285453
\(666\) −26.6799 −1.03382
\(667\) −0.109838 −0.00425295
\(668\) 19.4887 0.754042
\(669\) −9.91059 −0.383166
\(670\) −21.6695 −0.837166
\(671\) 20.5185 0.792106
\(672\) −0.00215238 −8.30298e−5 0
\(673\) 3.54194 0.136532 0.0682659 0.997667i \(-0.478253\pi\)
0.0682659 + 0.997667i \(0.478253\pi\)
\(674\) 21.7910 0.839357
\(675\) 29.7467 1.14495
\(676\) 17.6868 0.680261
\(677\) −31.0465 −1.19321 −0.596606 0.802534i \(-0.703485\pi\)
−0.596606 + 0.802534i \(0.703485\pi\)
\(678\) −4.14631 −0.159238
\(679\) 0.0559964 0.00214894
\(680\) −1.86605 −0.0715598
\(681\) −5.07108 −0.194324
\(682\) 22.1101 0.846641
\(683\) −21.0820 −0.806680 −0.403340 0.915050i \(-0.632151\pi\)
−0.403340 + 0.915050i \(0.632151\pi\)
\(684\) −16.2570 −0.621603
\(685\) 53.4918 2.04382
\(686\) −0.0448434 −0.00171213
\(687\) 10.2541 0.391217
\(688\) 5.22363 0.199149
\(689\) 18.3234 0.698066
\(690\) 0.401060 0.0152681
\(691\) 2.52267 0.0959671 0.0479835 0.998848i \(-0.484721\pi\)
0.0479835 + 0.998848i \(0.484721\pi\)
\(692\) 9.37562 0.356407
\(693\) −0.0192406 −0.000730889 0
\(694\) −20.6062 −0.782201
\(695\) 29.1808 1.10689
\(696\) 0.445503 0.0168867
\(697\) −5.23663 −0.198352
\(698\) −2.04297 −0.0773276
\(699\) −2.69459 −0.101919
\(700\) 0.0255558 0.000965918 0
\(701\) 26.7602 1.01072 0.505359 0.862909i \(-0.331360\pi\)
0.505359 + 0.862909i \(0.331360\pi\)
\(702\) −20.6536 −0.779520
\(703\) 66.7833 2.51878
\(704\) 2.35705 0.0888347
\(705\) −20.1979 −0.760697
\(706\) −6.25826 −0.235533
\(707\) 0.0451921 0.00169962
\(708\) 8.56355 0.321838
\(709\) −4.06287 −0.152584 −0.0762921 0.997086i \(-0.524308\pi\)
−0.0762921 + 0.997086i \(0.524308\pi\)
\(710\) −34.9432 −1.31140
\(711\) −0.349645 −0.0131127
\(712\) −8.65440 −0.324337
\(713\) 1.55408 0.0582007
\(714\) −0.00111489 −4.17236e−5 0
\(715\) 47.0387 1.75915
\(716\) 0.360173 0.0134603
\(717\) −4.82310 −0.180122
\(718\) −2.32159 −0.0866408
\(719\) −20.3585 −0.759244 −0.379622 0.925142i \(-0.623946\pi\)
−0.379622 + 0.925142i \(0.623946\pi\)
\(720\) 9.18099 0.342155
\(721\) −0.0345098 −0.00128521
\(722\) 21.6936 0.807350
\(723\) −9.29994 −0.345868
\(724\) −14.0808 −0.523309
\(725\) −5.28958 −0.196450
\(726\) 3.65840 0.135776
\(727\) 10.6501 0.394989 0.197495 0.980304i \(-0.436719\pi\)
0.197495 + 0.980304i \(0.436719\pi\)
\(728\) −0.0177438 −0.000657629 0
\(729\) −5.58316 −0.206784
\(730\) 25.1042 0.929147
\(731\) 2.70573 0.100075
\(732\) −5.84956 −0.216206
\(733\) −12.9808 −0.479456 −0.239728 0.970840i \(-0.577058\pi\)
−0.239728 + 0.970840i \(0.577058\pi\)
\(734\) 34.7000 1.28080
\(735\) −16.9456 −0.625047
\(736\) 0.165673 0.00610677
\(737\) 14.1777 0.522243
\(738\) 25.7643 0.948397
\(739\) 1.18608 0.0436308 0.0218154 0.999762i \(-0.493055\pi\)
0.0218154 + 0.999762i \(0.493055\pi\)
\(740\) −37.7152 −1.38644
\(741\) 23.7457 0.872322
\(742\) −0.0105950 −0.000388955 0
\(743\) −32.8493 −1.20512 −0.602562 0.798072i \(-0.705853\pi\)
−0.602562 + 0.798072i \(0.705853\pi\)
\(744\) −6.30333 −0.231091
\(745\) 28.8038 1.05529
\(746\) 10.0646 0.368491
\(747\) 25.3990 0.929299
\(748\) 1.22090 0.0446406
\(749\) −0.0296369 −0.00108291
\(750\) 7.21022 0.263280
\(751\) −4.04124 −0.147467 −0.0737335 0.997278i \(-0.523491\pi\)
−0.0737335 + 0.997278i \(0.523491\pi\)
\(752\) −8.34349 −0.304256
\(753\) −0.676000 −0.0246348
\(754\) 3.67264 0.133750
\(755\) 73.9069 2.68975
\(756\) 0.0119424 0.000434340 0
\(757\) −33.6150 −1.22176 −0.610879 0.791724i \(-0.709184\pi\)
−0.610879 + 0.791724i \(0.709184\pi\)
\(758\) −1.70743 −0.0620166
\(759\) −0.262402 −0.00952458
\(760\) −22.9813 −0.833618
\(761\) 5.80307 0.210361 0.105181 0.994453i \(-0.466458\pi\)
0.105181 + 0.994453i \(0.466458\pi\)
\(762\) 10.4919 0.380083
\(763\) 0.0245655 0.000889330 0
\(764\) −9.96640 −0.360572
\(765\) 4.75556 0.171938
\(766\) −25.8225 −0.933005
\(767\) 70.5963 2.54909
\(768\) −0.671966 −0.0242475
\(769\) −9.59462 −0.345991 −0.172995 0.984923i \(-0.555345\pi\)
−0.172995 + 0.984923i \(0.555345\pi\)
\(770\) −0.0271989 −0.000980180 0
\(771\) 10.2603 0.369514
\(772\) 18.3471 0.660327
\(773\) 6.48372 0.233203 0.116602 0.993179i \(-0.462800\pi\)
0.116602 + 0.993179i \(0.462800\pi\)
\(774\) −13.3122 −0.478498
\(775\) 74.8412 2.68838
\(776\) 17.4819 0.627564
\(777\) −0.0225332 −0.000808376 0
\(778\) −21.7658 −0.780343
\(779\) −64.4916 −2.31065
\(780\) −13.4102 −0.480161
\(781\) 22.8623 0.818078
\(782\) 0.0858148 0.00306873
\(783\) −2.47185 −0.0883369
\(784\) −6.99999 −0.250000
\(785\) 81.6148 2.91296
\(786\) 6.18996 0.220788
\(787\) −28.7497 −1.02481 −0.512407 0.858742i \(-0.671246\pi\)
−0.512407 + 0.858742i \(0.671246\pi\)
\(788\) −18.8320 −0.670861
\(789\) 1.87665 0.0668104
\(790\) −0.494266 −0.0175852
\(791\) 0.0197645 0.000702744 0
\(792\) −6.00685 −0.213444
\(793\) −48.2227 −1.71244
\(794\) −15.9100 −0.564627
\(795\) −8.00736 −0.283992
\(796\) −17.7025 −0.627450
\(797\) −33.1793 −1.17527 −0.587635 0.809126i \(-0.699941\pi\)
−0.587635 + 0.809126i \(0.699941\pi\)
\(798\) −0.0137303 −0.000486049 0
\(799\) −4.32175 −0.152893
\(800\) 7.97845 0.282081
\(801\) 22.0554 0.779290
\(802\) 27.3375 0.965322
\(803\) −16.4249 −0.579623
\(804\) −4.04189 −0.142547
\(805\) −0.00191176 −6.73806e−5 0
\(806\) −51.9635 −1.83034
\(807\) −1.78566 −0.0628584
\(808\) 14.1088 0.496347
\(809\) −21.5104 −0.756265 −0.378132 0.925752i \(-0.623434\pi\)
−0.378132 + 0.925752i \(0.623434\pi\)
\(810\) −18.5173 −0.650632
\(811\) 26.4504 0.928800 0.464400 0.885626i \(-0.346270\pi\)
0.464400 + 0.885626i \(0.346270\pi\)
\(812\) −0.00212361 −7.45240e−5 0
\(813\) −13.5633 −0.475687
\(814\) 24.6760 0.864892
\(815\) 79.6549 2.79019
\(816\) −0.348064 −0.0121847
\(817\) 33.3223 1.16580
\(818\) −1.77857 −0.0621861
\(819\) 0.0452194 0.00158009
\(820\) 36.4210 1.27188
\(821\) −33.5884 −1.17224 −0.586122 0.810223i \(-0.699346\pi\)
−0.586122 + 0.810223i \(0.699346\pi\)
\(822\) 9.97753 0.348006
\(823\) 35.2370 1.22829 0.614143 0.789195i \(-0.289502\pi\)
0.614143 + 0.789195i \(0.289502\pi\)
\(824\) −10.7738 −0.375325
\(825\) −12.6367 −0.439954
\(826\) −0.0408204 −0.00142032
\(827\) −10.8491 −0.377260 −0.188630 0.982048i \(-0.560405\pi\)
−0.188630 + 0.982048i \(0.560405\pi\)
\(828\) −0.422210 −0.0146728
\(829\) −7.26722 −0.252401 −0.126201 0.992005i \(-0.540278\pi\)
−0.126201 + 0.992005i \(0.540278\pi\)
\(830\) 35.9045 1.24626
\(831\) −11.0295 −0.382611
\(832\) −5.53956 −0.192050
\(833\) −3.62585 −0.125628
\(834\) 5.44293 0.188473
\(835\) −70.2094 −2.42970
\(836\) 15.0360 0.520030
\(837\) 34.9738 1.20887
\(838\) 33.0783 1.14267
\(839\) 14.2921 0.493417 0.246709 0.969090i \(-0.420651\pi\)
0.246709 + 0.969090i \(0.420651\pi\)
\(840\) 0.00775407 0.000267541 0
\(841\) −28.5605 −0.984843
\(842\) 8.69390 0.299611
\(843\) −5.39803 −0.185918
\(844\) 19.3268 0.665257
\(845\) −63.7177 −2.19195
\(846\) 21.2631 0.731039
\(847\) −0.0174387 −0.000599201 0
\(848\) −3.30773 −0.113588
\(849\) 2.42951 0.0833806
\(850\) 4.13267 0.141749
\(851\) 1.73443 0.0594554
\(852\) −6.51777 −0.223295
\(853\) 1.05162 0.0360069 0.0180034 0.999838i \(-0.494269\pi\)
0.0180034 + 0.999838i \(0.494269\pi\)
\(854\) 0.0278835 0.000954153 0
\(855\) 58.5669 2.00295
\(856\) −9.25256 −0.316246
\(857\) −51.9264 −1.77377 −0.886886 0.461988i \(-0.847136\pi\)
−0.886886 + 0.461988i \(0.847136\pi\)
\(858\) 8.77388 0.299535
\(859\) 8.23630 0.281019 0.140510 0.990079i \(-0.455126\pi\)
0.140510 + 0.990079i \(0.455126\pi\)
\(860\) −18.8184 −0.641703
\(861\) 0.0217600 0.000741578 0
\(862\) −9.39970 −0.320155
\(863\) −9.17787 −0.312418 −0.156209 0.987724i \(-0.549927\pi\)
−0.156209 + 0.987724i \(0.549927\pi\)
\(864\) 3.72838 0.126842
\(865\) −33.7762 −1.14843
\(866\) −10.4032 −0.353516
\(867\) 11.2431 0.381837
\(868\) 0.0300465 0.00101984
\(869\) 0.323384 0.0109700
\(870\) −1.60495 −0.0544129
\(871\) −33.3206 −1.12903
\(872\) 7.66927 0.259714
\(873\) −44.5520 −1.50786
\(874\) 1.05685 0.0357485
\(875\) −0.0343694 −0.00116190
\(876\) 4.68254 0.158208
\(877\) −10.7179 −0.361918 −0.180959 0.983491i \(-0.557920\pi\)
−0.180959 + 0.983491i \(0.557920\pi\)
\(878\) −22.4008 −0.755990
\(879\) 20.7397 0.699533
\(880\) −8.49142 −0.286246
\(881\) 34.6970 1.16897 0.584487 0.811403i \(-0.301296\pi\)
0.584487 + 0.811403i \(0.301296\pi\)
\(882\) 17.8392 0.600677
\(883\) −30.8117 −1.03690 −0.518448 0.855109i \(-0.673490\pi\)
−0.518448 + 0.855109i \(0.673490\pi\)
\(884\) −2.86938 −0.0965076
\(885\) −30.8507 −1.03704
\(886\) 37.0228 1.24381
\(887\) −4.14407 −0.139144 −0.0695721 0.997577i \(-0.522163\pi\)
−0.0695721 + 0.997577i \(0.522163\pi\)
\(888\) −7.03482 −0.236073
\(889\) −0.0500126 −0.00167737
\(890\) 31.1780 1.04509
\(891\) 12.1153 0.405879
\(892\) 14.7486 0.493821
\(893\) −53.2244 −1.78109
\(894\) 5.37262 0.179687
\(895\) −1.29754 −0.0433721
\(896\) 0.00320310 0.000107008 0
\(897\) 0.616699 0.0205910
\(898\) −23.0335 −0.768637
\(899\) −6.21907 −0.207418
\(900\) −20.3328 −0.677759
\(901\) −1.71334 −0.0570795
\(902\) −23.8292 −0.793425
\(903\) −0.0112432 −0.000374151 0
\(904\) 6.17042 0.205225
\(905\) 50.7270 1.68622
\(906\) 13.7855 0.457991
\(907\) −40.2684 −1.33709 −0.668545 0.743672i \(-0.733083\pi\)
−0.668545 + 0.743672i \(0.733083\pi\)
\(908\) 7.54663 0.250444
\(909\) −35.9558 −1.19258
\(910\) 0.0639231 0.00211903
\(911\) 9.19510 0.304647 0.152324 0.988331i \(-0.451324\pi\)
0.152324 + 0.988331i \(0.451324\pi\)
\(912\) −4.28657 −0.141943
\(913\) −23.4913 −0.777448
\(914\) 15.5058 0.512888
\(915\) 21.0734 0.696665
\(916\) −15.2598 −0.504197
\(917\) −0.0295061 −0.000974376 0
\(918\) 1.93122 0.0637398
\(919\) 55.5879 1.83368 0.916838 0.399260i \(-0.130733\pi\)
0.916838 + 0.399260i \(0.130733\pi\)
\(920\) −0.596845 −0.0196774
\(921\) −12.8035 −0.421890
\(922\) 4.71579 0.155306
\(923\) −53.7313 −1.76859
\(924\) −0.00507326 −0.000166898 0
\(925\) 83.5264 2.74633
\(926\) 2.51673 0.0827048
\(927\) 27.4567 0.901798
\(928\) −0.662984 −0.0217635
\(929\) 46.2577 1.51767 0.758833 0.651285i \(-0.225770\pi\)
0.758833 + 0.651285i \(0.225770\pi\)
\(930\) 22.7081 0.744629
\(931\) −44.6540 −1.46348
\(932\) 4.01000 0.131352
\(933\) −7.99423 −0.261719
\(934\) −23.6562 −0.774055
\(935\) −4.39837 −0.143842
\(936\) 14.1174 0.461441
\(937\) 52.3222 1.70929 0.854646 0.519211i \(-0.173774\pi\)
0.854646 + 0.519211i \(0.173774\pi\)
\(938\) 0.0192668 0.000629082 0
\(939\) 21.6795 0.707483
\(940\) 30.0579 0.980381
\(941\) 20.8204 0.678727 0.339363 0.940655i \(-0.389788\pi\)
0.339363 + 0.940655i \(0.389788\pi\)
\(942\) 15.2232 0.495998
\(943\) −1.67491 −0.0545425
\(944\) −12.7440 −0.414783
\(945\) −0.0430232 −0.00139954
\(946\) 12.3124 0.400309
\(947\) 4.95633 0.161059 0.0805296 0.996752i \(-0.474339\pi\)
0.0805296 + 0.996752i \(0.474339\pi\)
\(948\) −0.0921927 −0.00299428
\(949\) 38.6020 1.25307
\(950\) 50.8957 1.65127
\(951\) −7.71448 −0.250159
\(952\) 0.00165914 5.37730e−5 0
\(953\) 12.1823 0.394622 0.197311 0.980341i \(-0.436779\pi\)
0.197311 + 0.980341i \(0.436779\pi\)
\(954\) 8.42963 0.272919
\(955\) 35.9046 1.16184
\(956\) 7.17759 0.232140
\(957\) 1.05007 0.0339440
\(958\) 5.55788 0.179567
\(959\) −0.0475605 −0.00153581
\(960\) 2.42080 0.0781310
\(961\) 56.9924 1.83846
\(962\) −57.9937 −1.86979
\(963\) 23.5798 0.759848
\(964\) 13.8399 0.445753
\(965\) −66.0966 −2.12772
\(966\) −0.000356590 0 −1.14731e−5 0
\(967\) 45.0624 1.44911 0.724555 0.689217i \(-0.242045\pi\)
0.724555 + 0.689217i \(0.242045\pi\)
\(968\) −5.44431 −0.174987
\(969\) −2.22035 −0.0713280
\(970\) −62.9796 −2.02215
\(971\) −53.5674 −1.71906 −0.859530 0.511085i \(-0.829244\pi\)
−0.859530 + 0.511085i \(0.829244\pi\)
\(972\) −14.6391 −0.469548
\(973\) −0.0259452 −0.000831764 0
\(974\) −33.0410 −1.05870
\(975\) 29.6990 0.951128
\(976\) 8.70514 0.278645
\(977\) −40.9825 −1.31115 −0.655573 0.755132i \(-0.727573\pi\)
−0.655573 + 0.755132i \(0.727573\pi\)
\(978\) 14.8576 0.475094
\(979\) −20.3989 −0.651951
\(980\) 25.2179 0.805556
\(981\) −19.5448 −0.624019
\(982\) 9.44418 0.301376
\(983\) −12.6994 −0.405047 −0.202524 0.979277i \(-0.564914\pi\)
−0.202524 + 0.979277i \(0.564914\pi\)
\(984\) 6.79341 0.216566
\(985\) 67.8433 2.16167
\(986\) −0.343412 −0.0109365
\(987\) 0.0179583 0.000571620 0
\(988\) −35.3377 −1.12424
\(989\) 0.865412 0.0275185
\(990\) 21.6400 0.687766
\(991\) −3.69875 −0.117495 −0.0587473 0.998273i \(-0.518711\pi\)
−0.0587473 + 0.998273i \(0.518711\pi\)
\(992\) 9.38043 0.297829
\(993\) 12.7278 0.403905
\(994\) 0.0310687 0.000985438 0
\(995\) 63.7745 2.02179
\(996\) 6.69707 0.212205
\(997\) 1.55814 0.0493468 0.0246734 0.999696i \(-0.492145\pi\)
0.0246734 + 0.999696i \(0.492145\pi\)
\(998\) −31.4323 −0.994972
\(999\) 39.0324 1.23493
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 8002.2.a.d.1.33 69
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.d.1.33 69 1.1 even 1 trivial