Properties

Label 8006.2.a.d.1.12
Level $8006$
Weight $2$
Character 8006.1
Self dual yes
Analytic conductor $63.928$
Analytic rank $0$
Dimension $98$
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] = [8006,2,Mod(1,8006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8006, 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("8006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8006.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: \(63.9282318582\)
Analytic rank: \(0\)
Dimension: \(98\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.67018 q^{3} +1.00000 q^{4} +0.0387933 q^{5} -2.67018 q^{6} -0.245209 q^{7} +1.00000 q^{8} +4.12985 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.67018 q^{3} +1.00000 q^{4} +0.0387933 q^{5} -2.67018 q^{6} -0.245209 q^{7} +1.00000 q^{8} +4.12985 q^{9} +0.0387933 q^{10} +0.614227 q^{11} -2.67018 q^{12} +5.44648 q^{13} -0.245209 q^{14} -0.103585 q^{15} +1.00000 q^{16} +4.52679 q^{17} +4.12985 q^{18} +6.26006 q^{19} +0.0387933 q^{20} +0.654752 q^{21} +0.614227 q^{22} -5.73257 q^{23} -2.67018 q^{24} -4.99850 q^{25} +5.44648 q^{26} -3.01691 q^{27} -0.245209 q^{28} -3.88297 q^{29} -0.103585 q^{30} +2.99444 q^{31} +1.00000 q^{32} -1.64010 q^{33} +4.52679 q^{34} -0.00951248 q^{35} +4.12985 q^{36} +5.06219 q^{37} +6.26006 q^{38} -14.5431 q^{39} +0.0387933 q^{40} +7.74952 q^{41} +0.654752 q^{42} +6.14495 q^{43} +0.614227 q^{44} +0.160211 q^{45} -5.73257 q^{46} +13.2172 q^{47} -2.67018 q^{48} -6.93987 q^{49} -4.99850 q^{50} -12.0873 q^{51} +5.44648 q^{52} -10.8002 q^{53} -3.01691 q^{54} +0.0238279 q^{55} -0.245209 q^{56} -16.7155 q^{57} -3.88297 q^{58} +11.5393 q^{59} -0.103585 q^{60} -3.95778 q^{61} +2.99444 q^{62} -1.01268 q^{63} +1.00000 q^{64} +0.211287 q^{65} -1.64010 q^{66} +13.0393 q^{67} +4.52679 q^{68} +15.3070 q^{69} -0.00951248 q^{70} +3.91350 q^{71} +4.12985 q^{72} +8.12008 q^{73} +5.06219 q^{74} +13.3469 q^{75} +6.26006 q^{76} -0.150614 q^{77} -14.5431 q^{78} -12.9813 q^{79} +0.0387933 q^{80} -4.33388 q^{81} +7.74952 q^{82} -16.1098 q^{83} +0.654752 q^{84} +0.175609 q^{85} +6.14495 q^{86} +10.3682 q^{87} +0.614227 q^{88} -0.876082 q^{89} +0.160211 q^{90} -1.33553 q^{91} -5.73257 q^{92} -7.99568 q^{93} +13.2172 q^{94} +0.242849 q^{95} -2.67018 q^{96} -4.05879 q^{97} -6.93987 q^{98} +2.53667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 98 q + 98 q^{2} + 16 q^{3} + 98 q^{4} + 4 q^{5} + 16 q^{6} + 29 q^{7} + 98 q^{8} + 130 q^{9} + 4 q^{10} + 51 q^{11} + 16 q^{12} + 31 q^{13} + 29 q^{14} + 57 q^{15} + 98 q^{16} + 35 q^{17} + 130 q^{18} + 77 q^{19} + 4 q^{20} + 46 q^{21} + 51 q^{22} + 73 q^{23} + 16 q^{24} + 150 q^{25} + 31 q^{26} + 52 q^{27} + 29 q^{28} + 20 q^{29} + 57 q^{30} + 59 q^{31} + 98 q^{32} + 27 q^{33} + 35 q^{34} + 48 q^{35} + 130 q^{36} + 41 q^{37} + 77 q^{38} + 64 q^{39} + 4 q^{40} + 29 q^{41} + 46 q^{42} + 94 q^{43} + 51 q^{44} - 3 q^{45} + 73 q^{46} + 58 q^{47} + 16 q^{48} + 149 q^{49} + 150 q^{50} + 58 q^{51} + 31 q^{52} - 11 q^{53} + 52 q^{54} + 56 q^{55} + 29 q^{56} + 64 q^{57} + 20 q^{58} + 45 q^{59} + 57 q^{60} + 73 q^{61} + 59 q^{62} + 53 q^{63} + 98 q^{64} + 39 q^{65} + 27 q^{66} + 133 q^{67} + 35 q^{68} + 13 q^{69} + 48 q^{70} + 67 q^{71} + 130 q^{72} + 42 q^{73} + 41 q^{74} + 36 q^{75} + 77 q^{76} - 25 q^{77} + 64 q^{78} + 154 q^{79} + 4 q^{80} + 198 q^{81} + 29 q^{82} + 69 q^{83} + 46 q^{84} + 81 q^{85} + 94 q^{86} + 25 q^{87} + 51 q^{88} + 32 q^{89} - 3 q^{90} + 95 q^{91} + 73 q^{92} - 23 q^{93} + 58 q^{94} + 50 q^{95} + 16 q^{96} + 76 q^{97} + 149 q^{98} + 149 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.67018 −1.54163 −0.770814 0.637060i \(-0.780150\pi\)
−0.770814 + 0.637060i \(0.780150\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.0387933 0.0173489 0.00867445 0.999962i \(-0.497239\pi\)
0.00867445 + 0.999962i \(0.497239\pi\)
\(6\) −2.67018 −1.09010
\(7\) −0.245209 −0.0926803 −0.0463402 0.998926i \(-0.514756\pi\)
−0.0463402 + 0.998926i \(0.514756\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.12985 1.37662
\(10\) 0.0387933 0.0122675
\(11\) 0.614227 0.185196 0.0925982 0.995704i \(-0.470483\pi\)
0.0925982 + 0.995704i \(0.470483\pi\)
\(12\) −2.67018 −0.770814
\(13\) 5.44648 1.51058 0.755290 0.655390i \(-0.227496\pi\)
0.755290 + 0.655390i \(0.227496\pi\)
\(14\) −0.245209 −0.0655349
\(15\) −0.103585 −0.0267456
\(16\) 1.00000 0.250000
\(17\) 4.52679 1.09791 0.548954 0.835852i \(-0.315026\pi\)
0.548954 + 0.835852i \(0.315026\pi\)
\(18\) 4.12985 0.973416
\(19\) 6.26006 1.43616 0.718079 0.695962i \(-0.245022\pi\)
0.718079 + 0.695962i \(0.245022\pi\)
\(20\) 0.0387933 0.00867445
\(21\) 0.654752 0.142879
\(22\) 0.614227 0.130954
\(23\) −5.73257 −1.19532 −0.597662 0.801748i \(-0.703903\pi\)
−0.597662 + 0.801748i \(0.703903\pi\)
\(24\) −2.67018 −0.545048
\(25\) −4.99850 −0.999699
\(26\) 5.44648 1.06814
\(27\) −3.01691 −0.580604
\(28\) −0.245209 −0.0463402
\(29\) −3.88297 −0.721049 −0.360524 0.932750i \(-0.617402\pi\)
−0.360524 + 0.932750i \(0.617402\pi\)
\(30\) −0.103585 −0.0189120
\(31\) 2.99444 0.537817 0.268908 0.963166i \(-0.413337\pi\)
0.268908 + 0.963166i \(0.413337\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.64010 −0.285504
\(34\) 4.52679 0.776339
\(35\) −0.00951248 −0.00160790
\(36\) 4.12985 0.688309
\(37\) 5.06219 0.832219 0.416109 0.909315i \(-0.363393\pi\)
0.416109 + 0.909315i \(0.363393\pi\)
\(38\) 6.26006 1.01552
\(39\) −14.5431 −2.32875
\(40\) 0.0387933 0.00613376
\(41\) 7.74952 1.21027 0.605136 0.796122i \(-0.293119\pi\)
0.605136 + 0.796122i \(0.293119\pi\)
\(42\) 0.654752 0.101030
\(43\) 6.14495 0.937096 0.468548 0.883438i \(-0.344777\pi\)
0.468548 + 0.883438i \(0.344777\pi\)
\(44\) 0.614227 0.0925982
\(45\) 0.160211 0.0238828
\(46\) −5.73257 −0.845221
\(47\) 13.2172 1.92793 0.963967 0.266022i \(-0.0857094\pi\)
0.963967 + 0.266022i \(0.0857094\pi\)
\(48\) −2.67018 −0.385407
\(49\) −6.93987 −0.991410
\(50\) −4.99850 −0.706894
\(51\) −12.0873 −1.69257
\(52\) 5.44648 0.755290
\(53\) −10.8002 −1.48353 −0.741764 0.670661i \(-0.766010\pi\)
−0.741764 + 0.670661i \(0.766010\pi\)
\(54\) −3.01691 −0.410549
\(55\) 0.0238279 0.00321296
\(56\) −0.245209 −0.0327674
\(57\) −16.7155 −2.21402
\(58\) −3.88297 −0.509858
\(59\) 11.5393 1.50229 0.751144 0.660139i \(-0.229503\pi\)
0.751144 + 0.660139i \(0.229503\pi\)
\(60\) −0.103585 −0.0133728
\(61\) −3.95778 −0.506741 −0.253371 0.967369i \(-0.581539\pi\)
−0.253371 + 0.967369i \(0.581539\pi\)
\(62\) 2.99444 0.380294
\(63\) −1.01268 −0.127585
\(64\) 1.00000 0.125000
\(65\) 0.211287 0.0262069
\(66\) −1.64010 −0.201882
\(67\) 13.0393 1.59300 0.796502 0.604636i \(-0.206681\pi\)
0.796502 + 0.604636i \(0.206681\pi\)
\(68\) 4.52679 0.548954
\(69\) 15.3070 1.84274
\(70\) −0.00951248 −0.00113696
\(71\) 3.91350 0.464447 0.232224 0.972662i \(-0.425400\pi\)
0.232224 + 0.972662i \(0.425400\pi\)
\(72\) 4.12985 0.486708
\(73\) 8.12008 0.950383 0.475192 0.879882i \(-0.342379\pi\)
0.475192 + 0.879882i \(0.342379\pi\)
\(74\) 5.06219 0.588467
\(75\) 13.3469 1.54116
\(76\) 6.26006 0.718079
\(77\) −0.150614 −0.0171641
\(78\) −14.5431 −1.64668
\(79\) −12.9813 −1.46051 −0.730256 0.683173i \(-0.760599\pi\)
−0.730256 + 0.683173i \(0.760599\pi\)
\(80\) 0.0387933 0.00433723
\(81\) −4.33388 −0.481542
\(82\) 7.74952 0.855791
\(83\) −16.1098 −1.76828 −0.884139 0.467225i \(-0.845254\pi\)
−0.884139 + 0.467225i \(0.845254\pi\)
\(84\) 0.654752 0.0714393
\(85\) 0.175609 0.0190475
\(86\) 6.14495 0.662627
\(87\) 10.3682 1.11159
\(88\) 0.614227 0.0654768
\(89\) −0.876082 −0.0928645 −0.0464322 0.998921i \(-0.514785\pi\)
−0.0464322 + 0.998921i \(0.514785\pi\)
\(90\) 0.160211 0.0168877
\(91\) −1.33553 −0.140001
\(92\) −5.73257 −0.597662
\(93\) −7.99568 −0.829113
\(94\) 13.2172 1.36326
\(95\) 0.242849 0.0249158
\(96\) −2.67018 −0.272524
\(97\) −4.05879 −0.412107 −0.206054 0.978541i \(-0.566062\pi\)
−0.206054 + 0.978541i \(0.566062\pi\)
\(98\) −6.93987 −0.701033
\(99\) 2.53667 0.254945
\(100\) −4.99850 −0.499850
\(101\) −16.4040 −1.63226 −0.816130 0.577868i \(-0.803885\pi\)
−0.816130 + 0.577868i \(0.803885\pi\)
\(102\) −12.0873 −1.19683
\(103\) −10.2928 −1.01418 −0.507090 0.861893i \(-0.669279\pi\)
−0.507090 + 0.861893i \(0.669279\pi\)
\(104\) 5.44648 0.534071
\(105\) 0.0254000 0.00247879
\(106\) −10.8002 −1.04901
\(107\) −4.20498 −0.406511 −0.203256 0.979126i \(-0.565152\pi\)
−0.203256 + 0.979126i \(0.565152\pi\)
\(108\) −3.01691 −0.290302
\(109\) −9.55077 −0.914798 −0.457399 0.889262i \(-0.651219\pi\)
−0.457399 + 0.889262i \(0.651219\pi\)
\(110\) 0.0238279 0.00227190
\(111\) −13.5169 −1.28297
\(112\) −0.245209 −0.0231701
\(113\) −11.0791 −1.04223 −0.521116 0.853486i \(-0.674484\pi\)
−0.521116 + 0.853486i \(0.674484\pi\)
\(114\) −16.7155 −1.56555
\(115\) −0.222385 −0.0207376
\(116\) −3.88297 −0.360524
\(117\) 22.4931 2.07949
\(118\) 11.5393 1.06228
\(119\) −1.11001 −0.101755
\(120\) −0.103585 −0.00945598
\(121\) −10.6227 −0.965702
\(122\) −3.95778 −0.358320
\(123\) −20.6926 −1.86579
\(124\) 2.99444 0.268908
\(125\) −0.387875 −0.0346926
\(126\) −1.01268 −0.0902165
\(127\) 2.32324 0.206154 0.103077 0.994673i \(-0.467131\pi\)
0.103077 + 0.994673i \(0.467131\pi\)
\(128\) 1.00000 0.0883883
\(129\) −16.4081 −1.44465
\(130\) 0.211287 0.0185311
\(131\) 14.1634 1.23746 0.618732 0.785602i \(-0.287647\pi\)
0.618732 + 0.785602i \(0.287647\pi\)
\(132\) −1.64010 −0.142752
\(133\) −1.53502 −0.133104
\(134\) 13.0393 1.12642
\(135\) −0.117036 −0.0100728
\(136\) 4.52679 0.388169
\(137\) 1.99119 0.170119 0.0850594 0.996376i \(-0.472892\pi\)
0.0850594 + 0.996376i \(0.472892\pi\)
\(138\) 15.3070 1.30302
\(139\) 4.98502 0.422824 0.211412 0.977397i \(-0.432194\pi\)
0.211412 + 0.977397i \(0.432194\pi\)
\(140\) −0.00951248 −0.000803951 0
\(141\) −35.2924 −2.97216
\(142\) 3.91350 0.328414
\(143\) 3.34537 0.279754
\(144\) 4.12985 0.344154
\(145\) −0.150633 −0.0125094
\(146\) 8.12008 0.672023
\(147\) 18.5307 1.52839
\(148\) 5.06219 0.416109
\(149\) 10.3669 0.849290 0.424645 0.905360i \(-0.360399\pi\)
0.424645 + 0.905360i \(0.360399\pi\)
\(150\) 13.3469 1.08977
\(151\) 18.0604 1.46973 0.734866 0.678212i \(-0.237245\pi\)
0.734866 + 0.678212i \(0.237245\pi\)
\(152\) 6.26006 0.507758
\(153\) 18.6950 1.51140
\(154\) −0.150614 −0.0121368
\(155\) 0.116164 0.00933053
\(156\) −14.5431 −1.16438
\(157\) 2.96996 0.237028 0.118514 0.992952i \(-0.462187\pi\)
0.118514 + 0.992952i \(0.462187\pi\)
\(158\) −12.9813 −1.03274
\(159\) 28.8386 2.28705
\(160\) 0.0387933 0.00306688
\(161\) 1.40568 0.110783
\(162\) −4.33388 −0.340501
\(163\) 8.25223 0.646364 0.323182 0.946337i \(-0.395247\pi\)
0.323182 + 0.946337i \(0.395247\pi\)
\(164\) 7.74952 0.605136
\(165\) −0.0636248 −0.00495318
\(166\) −16.1098 −1.25036
\(167\) −7.38164 −0.571208 −0.285604 0.958348i \(-0.592194\pi\)
−0.285604 + 0.958348i \(0.592194\pi\)
\(168\) 0.654752 0.0505152
\(169\) 16.6641 1.28185
\(170\) 0.175609 0.0134686
\(171\) 25.8531 1.97704
\(172\) 6.14495 0.468548
\(173\) −10.5712 −0.803714 −0.401857 0.915702i \(-0.631635\pi\)
−0.401857 + 0.915702i \(0.631635\pi\)
\(174\) 10.3682 0.786012
\(175\) 1.22568 0.0926524
\(176\) 0.614227 0.0462991
\(177\) −30.8120 −2.31597
\(178\) −0.876082 −0.0656651
\(179\) 8.50968 0.636043 0.318022 0.948083i \(-0.396982\pi\)
0.318022 + 0.948083i \(0.396982\pi\)
\(180\) 0.160211 0.0119414
\(181\) 23.7885 1.76818 0.884092 0.467314i \(-0.154778\pi\)
0.884092 + 0.467314i \(0.154778\pi\)
\(182\) −1.33553 −0.0989957
\(183\) 10.5680 0.781207
\(184\) −5.73257 −0.422611
\(185\) 0.196379 0.0144381
\(186\) −7.99568 −0.586272
\(187\) 2.78048 0.203329
\(188\) 13.2172 0.963967
\(189\) 0.739773 0.0538106
\(190\) 0.242849 0.0176181
\(191\) −9.69339 −0.701389 −0.350695 0.936490i \(-0.614054\pi\)
−0.350695 + 0.936490i \(0.614054\pi\)
\(192\) −2.67018 −0.192704
\(193\) −12.9799 −0.934312 −0.467156 0.884175i \(-0.654721\pi\)
−0.467156 + 0.884175i \(0.654721\pi\)
\(194\) −4.05879 −0.291404
\(195\) −0.564174 −0.0404013
\(196\) −6.93987 −0.495705
\(197\) 7.79852 0.555622 0.277811 0.960636i \(-0.410391\pi\)
0.277811 + 0.960636i \(0.410391\pi\)
\(198\) 2.53667 0.180273
\(199\) −23.1244 −1.63924 −0.819621 0.572905i \(-0.805816\pi\)
−0.819621 + 0.572905i \(0.805816\pi\)
\(200\) −4.99850 −0.353447
\(201\) −34.8173 −2.45582
\(202\) −16.4040 −1.15418
\(203\) 0.952139 0.0668270
\(204\) −12.0873 −0.846284
\(205\) 0.300630 0.0209969
\(206\) −10.2928 −0.717133
\(207\) −23.6747 −1.64550
\(208\) 5.44648 0.377645
\(209\) 3.84510 0.265971
\(210\) 0.0254000 0.00175277
\(211\) 22.6794 1.56131 0.780657 0.624960i \(-0.214885\pi\)
0.780657 + 0.624960i \(0.214885\pi\)
\(212\) −10.8002 −0.741764
\(213\) −10.4497 −0.716005
\(214\) −4.20498 −0.287447
\(215\) 0.238383 0.0162576
\(216\) −3.01691 −0.205275
\(217\) −0.734263 −0.0498450
\(218\) −9.55077 −0.646860
\(219\) −21.6821 −1.46514
\(220\) 0.0238279 0.00160648
\(221\) 24.6551 1.65848
\(222\) −13.5169 −0.907198
\(223\) 11.2807 0.755413 0.377707 0.925925i \(-0.376713\pi\)
0.377707 + 0.925925i \(0.376713\pi\)
\(224\) −0.245209 −0.0163837
\(225\) −20.6430 −1.37620
\(226\) −11.0791 −0.736969
\(227\) 26.0937 1.73190 0.865951 0.500129i \(-0.166714\pi\)
0.865951 + 0.500129i \(0.166714\pi\)
\(228\) −16.7155 −1.10701
\(229\) 9.06761 0.599205 0.299602 0.954064i \(-0.403146\pi\)
0.299602 + 0.954064i \(0.403146\pi\)
\(230\) −0.222385 −0.0146637
\(231\) 0.402166 0.0264606
\(232\) −3.88297 −0.254929
\(233\) 17.1795 1.12547 0.562734 0.826638i \(-0.309750\pi\)
0.562734 + 0.826638i \(0.309750\pi\)
\(234\) 22.4931 1.47042
\(235\) 0.512741 0.0334475
\(236\) 11.5393 0.751144
\(237\) 34.6624 2.25157
\(238\) −1.11001 −0.0719513
\(239\) −11.7483 −0.759935 −0.379967 0.925000i \(-0.624065\pi\)
−0.379967 + 0.925000i \(0.624065\pi\)
\(240\) −0.103585 −0.00668639
\(241\) 9.55671 0.615602 0.307801 0.951451i \(-0.400407\pi\)
0.307801 + 0.951451i \(0.400407\pi\)
\(242\) −10.6227 −0.682855
\(243\) 20.6229 1.32296
\(244\) −3.95778 −0.253371
\(245\) −0.269221 −0.0171999
\(246\) −20.6926 −1.31931
\(247\) 34.0953 2.16943
\(248\) 2.99444 0.190147
\(249\) 43.0160 2.72603
\(250\) −0.387875 −0.0245314
\(251\) 3.22576 0.203608 0.101804 0.994804i \(-0.467538\pi\)
0.101804 + 0.994804i \(0.467538\pi\)
\(252\) −1.01268 −0.0637927
\(253\) −3.52110 −0.221370
\(254\) 2.32324 0.145773
\(255\) −0.468908 −0.0293642
\(256\) 1.00000 0.0625000
\(257\) 3.92975 0.245131 0.122566 0.992460i \(-0.460888\pi\)
0.122566 + 0.992460i \(0.460888\pi\)
\(258\) −16.4081 −1.02152
\(259\) −1.24129 −0.0771303
\(260\) 0.211287 0.0131035
\(261\) −16.0361 −0.992608
\(262\) 14.1634 0.875020
\(263\) 14.9787 0.923627 0.461814 0.886977i \(-0.347199\pi\)
0.461814 + 0.886977i \(0.347199\pi\)
\(264\) −1.64010 −0.100941
\(265\) −0.418977 −0.0257376
\(266\) −1.53502 −0.0941184
\(267\) 2.33929 0.143163
\(268\) 13.0393 0.796502
\(269\) −17.5697 −1.07124 −0.535622 0.844458i \(-0.679923\pi\)
−0.535622 + 0.844458i \(0.679923\pi\)
\(270\) −0.117036 −0.00712258
\(271\) 25.9833 1.57837 0.789186 0.614154i \(-0.210503\pi\)
0.789186 + 0.614154i \(0.210503\pi\)
\(272\) 4.52679 0.274477
\(273\) 3.56609 0.215830
\(274\) 1.99119 0.120292
\(275\) −3.07021 −0.185141
\(276\) 15.3070 0.921372
\(277\) −12.3616 −0.742735 −0.371368 0.928486i \(-0.621111\pi\)
−0.371368 + 0.928486i \(0.621111\pi\)
\(278\) 4.98502 0.298982
\(279\) 12.3666 0.740368
\(280\) −0.00951248 −0.000568479 0
\(281\) 19.5555 1.16658 0.583290 0.812264i \(-0.301765\pi\)
0.583290 + 0.812264i \(0.301765\pi\)
\(282\) −35.2924 −2.10163
\(283\) 6.32929 0.376237 0.188119 0.982146i \(-0.439761\pi\)
0.188119 + 0.982146i \(0.439761\pi\)
\(284\) 3.91350 0.232224
\(285\) −0.648449 −0.0384108
\(286\) 3.34537 0.197816
\(287\) −1.90025 −0.112168
\(288\) 4.12985 0.243354
\(289\) 3.49187 0.205404
\(290\) −0.150633 −0.00884549
\(291\) 10.8377 0.635317
\(292\) 8.12008 0.475192
\(293\) −23.6910 −1.38404 −0.692021 0.721878i \(-0.743279\pi\)
−0.692021 + 0.721878i \(0.743279\pi\)
\(294\) 18.5307 1.08073
\(295\) 0.447647 0.0260630
\(296\) 5.06219 0.294234
\(297\) −1.85307 −0.107526
\(298\) 10.3669 0.600539
\(299\) −31.2223 −1.80563
\(300\) 13.3469 0.770582
\(301\) −1.50680 −0.0868504
\(302\) 18.0604 1.03926
\(303\) 43.8017 2.51634
\(304\) 6.26006 0.359039
\(305\) −0.153535 −0.00879141
\(306\) 18.6950 1.06872
\(307\) 21.6283 1.23439 0.617197 0.786809i \(-0.288268\pi\)
0.617197 + 0.786809i \(0.288268\pi\)
\(308\) −0.150614 −0.00858203
\(309\) 27.4836 1.56349
\(310\) 0.116164 0.00659768
\(311\) −0.398441 −0.0225935 −0.0112968 0.999936i \(-0.503596\pi\)
−0.0112968 + 0.999936i \(0.503596\pi\)
\(312\) −14.5431 −0.823339
\(313\) 4.54967 0.257162 0.128581 0.991699i \(-0.458958\pi\)
0.128581 + 0.991699i \(0.458958\pi\)
\(314\) 2.96996 0.167604
\(315\) −0.0392851 −0.00221347
\(316\) −12.9813 −0.730256
\(317\) −27.8929 −1.56662 −0.783311 0.621630i \(-0.786471\pi\)
−0.783311 + 0.621630i \(0.786471\pi\)
\(318\) 28.8386 1.61719
\(319\) −2.38502 −0.133536
\(320\) 0.0387933 0.00216861
\(321\) 11.2281 0.626689
\(322\) 1.40568 0.0783354
\(323\) 28.3380 1.57677
\(324\) −4.33388 −0.240771
\(325\) −27.2242 −1.51013
\(326\) 8.25223 0.457049
\(327\) 25.5023 1.41028
\(328\) 7.74952 0.427895
\(329\) −3.24099 −0.178682
\(330\) −0.0636248 −0.00350243
\(331\) 15.1509 0.832767 0.416384 0.909189i \(-0.363297\pi\)
0.416384 + 0.909189i \(0.363297\pi\)
\(332\) −16.1098 −0.884139
\(333\) 20.9061 1.14565
\(334\) −7.38164 −0.403905
\(335\) 0.505838 0.0276369
\(336\) 0.654752 0.0357196
\(337\) 20.1118 1.09556 0.547780 0.836623i \(-0.315473\pi\)
0.547780 + 0.836623i \(0.315473\pi\)
\(338\) 16.6641 0.906408
\(339\) 29.5831 1.60673
\(340\) 0.175609 0.00952376
\(341\) 1.83926 0.0996017
\(342\) 25.8531 1.39798
\(343\) 3.41818 0.184565
\(344\) 6.14495 0.331314
\(345\) 0.593809 0.0319696
\(346\) −10.5712 −0.568312
\(347\) −24.3117 −1.30512 −0.652559 0.757738i \(-0.726305\pi\)
−0.652559 + 0.757738i \(0.726305\pi\)
\(348\) 10.3682 0.555795
\(349\) 8.10640 0.433926 0.216963 0.976180i \(-0.430385\pi\)
0.216963 + 0.976180i \(0.430385\pi\)
\(350\) 1.22568 0.0655152
\(351\) −16.4315 −0.877050
\(352\) 0.614227 0.0327384
\(353\) −20.3427 −1.08273 −0.541367 0.840787i \(-0.682093\pi\)
−0.541367 + 0.840787i \(0.682093\pi\)
\(354\) −30.8120 −1.63764
\(355\) 0.151818 0.00805765
\(356\) −0.876082 −0.0464322
\(357\) 2.96393 0.156868
\(358\) 8.50968 0.449750
\(359\) 26.7484 1.41173 0.705864 0.708347i \(-0.250559\pi\)
0.705864 + 0.708347i \(0.250559\pi\)
\(360\) 0.160211 0.00844385
\(361\) 20.1884 1.06255
\(362\) 23.7885 1.25029
\(363\) 28.3646 1.48875
\(364\) −1.33553 −0.0700006
\(365\) 0.315005 0.0164881
\(366\) 10.5680 0.552397
\(367\) 26.4394 1.38012 0.690062 0.723750i \(-0.257583\pi\)
0.690062 + 0.723750i \(0.257583\pi\)
\(368\) −5.73257 −0.298831
\(369\) 32.0044 1.66608
\(370\) 0.196379 0.0102093
\(371\) 2.64832 0.137494
\(372\) −7.99568 −0.414557
\(373\) −16.9400 −0.877119 −0.438560 0.898702i \(-0.644511\pi\)
−0.438560 + 0.898702i \(0.644511\pi\)
\(374\) 2.78048 0.143775
\(375\) 1.03570 0.0534831
\(376\) 13.2172 0.681628
\(377\) −21.1485 −1.08920
\(378\) 0.739773 0.0380498
\(379\) −37.2869 −1.91530 −0.957651 0.287932i \(-0.907032\pi\)
−0.957651 + 0.287932i \(0.907032\pi\)
\(380\) 0.242849 0.0124579
\(381\) −6.20346 −0.317813
\(382\) −9.69339 −0.495957
\(383\) −24.1208 −1.23252 −0.616258 0.787544i \(-0.711352\pi\)
−0.616258 + 0.787544i \(0.711352\pi\)
\(384\) −2.67018 −0.136262
\(385\) −0.00584282 −0.000297778 0
\(386\) −12.9799 −0.660658
\(387\) 25.3777 1.29002
\(388\) −4.05879 −0.206054
\(389\) 21.2138 1.07558 0.537792 0.843078i \(-0.319259\pi\)
0.537792 + 0.843078i \(0.319259\pi\)
\(390\) −0.564174 −0.0285681
\(391\) −25.9502 −1.31236
\(392\) −6.93987 −0.350516
\(393\) −37.8189 −1.90771
\(394\) 7.79852 0.392884
\(395\) −0.503588 −0.0253383
\(396\) 2.53667 0.127472
\(397\) 25.1165 1.26056 0.630281 0.776367i \(-0.282940\pi\)
0.630281 + 0.776367i \(0.282940\pi\)
\(398\) −23.1244 −1.15912
\(399\) 4.09879 0.205196
\(400\) −4.99850 −0.249925
\(401\) 23.0519 1.15116 0.575580 0.817746i \(-0.304777\pi\)
0.575580 + 0.817746i \(0.304777\pi\)
\(402\) −34.8173 −1.73653
\(403\) 16.3091 0.812415
\(404\) −16.4040 −0.816130
\(405\) −0.168125 −0.00835422
\(406\) 0.952139 0.0472538
\(407\) 3.10933 0.154124
\(408\) −12.0873 −0.598413
\(409\) −30.8180 −1.52385 −0.761926 0.647664i \(-0.775746\pi\)
−0.761926 + 0.647664i \(0.775746\pi\)
\(410\) 0.300630 0.0148470
\(411\) −5.31683 −0.262260
\(412\) −10.2928 −0.507090
\(413\) −2.82954 −0.139232
\(414\) −23.6747 −1.16355
\(415\) −0.624952 −0.0306777
\(416\) 5.44648 0.267036
\(417\) −13.3109 −0.651837
\(418\) 3.84510 0.188070
\(419\) −1.65891 −0.0810428 −0.0405214 0.999179i \(-0.512902\pi\)
−0.0405214 + 0.999179i \(0.512902\pi\)
\(420\) 0.0254000 0.00123939
\(421\) −9.64421 −0.470030 −0.235015 0.971992i \(-0.575514\pi\)
−0.235015 + 0.971992i \(0.575514\pi\)
\(422\) 22.6794 1.10402
\(423\) 54.5853 2.65403
\(424\) −10.8002 −0.524506
\(425\) −22.6272 −1.09758
\(426\) −10.4497 −0.506292
\(427\) 0.970483 0.0469649
\(428\) −4.20498 −0.203256
\(429\) −8.93275 −0.431277
\(430\) 0.238383 0.0114959
\(431\) 6.07992 0.292859 0.146430 0.989221i \(-0.453222\pi\)
0.146430 + 0.989221i \(0.453222\pi\)
\(432\) −3.01691 −0.145151
\(433\) 20.5245 0.986343 0.493172 0.869932i \(-0.335837\pi\)
0.493172 + 0.869932i \(0.335837\pi\)
\(434\) −0.734263 −0.0352457
\(435\) 0.402218 0.0192849
\(436\) −9.55077 −0.457399
\(437\) −35.8863 −1.71667
\(438\) −21.6821 −1.03601
\(439\) 4.24562 0.202633 0.101316 0.994854i \(-0.467695\pi\)
0.101316 + 0.994854i \(0.467695\pi\)
\(440\) 0.0238279 0.00113595
\(441\) −28.6606 −1.36479
\(442\) 24.6551 1.17272
\(443\) 25.2000 1.19729 0.598645 0.801014i \(-0.295706\pi\)
0.598645 + 0.801014i \(0.295706\pi\)
\(444\) −13.5169 −0.641486
\(445\) −0.0339861 −0.00161110
\(446\) 11.2807 0.534158
\(447\) −27.6815 −1.30929
\(448\) −0.245209 −0.0115850
\(449\) 19.0875 0.900796 0.450398 0.892828i \(-0.351282\pi\)
0.450398 + 0.892828i \(0.351282\pi\)
\(450\) −20.6430 −0.973123
\(451\) 4.75996 0.224138
\(452\) −11.0791 −0.521116
\(453\) −48.2244 −2.26578
\(454\) 26.0937 1.22464
\(455\) −0.0518095 −0.00242887
\(456\) −16.7155 −0.782775
\(457\) 28.5928 1.33752 0.668758 0.743480i \(-0.266826\pi\)
0.668758 + 0.743480i \(0.266826\pi\)
\(458\) 9.06761 0.423702
\(459\) −13.6569 −0.637450
\(460\) −0.222385 −0.0103688
\(461\) 8.59595 0.400354 0.200177 0.979760i \(-0.435848\pi\)
0.200177 + 0.979760i \(0.435848\pi\)
\(462\) 0.402166 0.0187105
\(463\) 23.6207 1.09775 0.548873 0.835906i \(-0.315057\pi\)
0.548873 + 0.835906i \(0.315057\pi\)
\(464\) −3.88297 −0.180262
\(465\) −0.310179 −0.0143842
\(466\) 17.1795 0.795826
\(467\) −16.0747 −0.743849 −0.371925 0.928263i \(-0.621302\pi\)
−0.371925 + 0.928263i \(0.621302\pi\)
\(468\) 22.4931 1.03975
\(469\) −3.19735 −0.147640
\(470\) 0.512741 0.0236510
\(471\) −7.93032 −0.365410
\(472\) 11.5393 0.531139
\(473\) 3.77440 0.173547
\(474\) 34.6624 1.59210
\(475\) −31.2909 −1.43573
\(476\) −1.11001 −0.0508773
\(477\) −44.6034 −2.04225
\(478\) −11.7483 −0.537355
\(479\) −4.74526 −0.216816 −0.108408 0.994106i \(-0.534575\pi\)
−0.108408 + 0.994106i \(0.534575\pi\)
\(480\) −0.103585 −0.00472799
\(481\) 27.5711 1.25713
\(482\) 9.55671 0.435296
\(483\) −3.75341 −0.170786
\(484\) −10.6227 −0.482851
\(485\) −0.157454 −0.00714961
\(486\) 20.6229 0.935476
\(487\) −9.08566 −0.411710 −0.205855 0.978582i \(-0.565998\pi\)
−0.205855 + 0.978582i \(0.565998\pi\)
\(488\) −3.95778 −0.179160
\(489\) −22.0349 −0.996454
\(490\) −0.269221 −0.0121622
\(491\) 6.41519 0.289513 0.144757 0.989467i \(-0.453760\pi\)
0.144757 + 0.989467i \(0.453760\pi\)
\(492\) −20.6926 −0.932894
\(493\) −17.5774 −0.791646
\(494\) 34.0953 1.53402
\(495\) 0.0984058 0.00442301
\(496\) 2.99444 0.134454
\(497\) −0.959626 −0.0430451
\(498\) 43.0160 1.92759
\(499\) −34.9687 −1.56541 −0.782707 0.622390i \(-0.786162\pi\)
−0.782707 + 0.622390i \(0.786162\pi\)
\(500\) −0.387875 −0.0173463
\(501\) 19.7103 0.880591
\(502\) 3.22576 0.143973
\(503\) 1.26728 0.0565054 0.0282527 0.999601i \(-0.491006\pi\)
0.0282527 + 0.999601i \(0.491006\pi\)
\(504\) −1.01268 −0.0451082
\(505\) −0.636366 −0.0283179
\(506\) −3.52110 −0.156532
\(507\) −44.4962 −1.97614
\(508\) 2.32324 0.103077
\(509\) −7.47595 −0.331366 −0.165683 0.986179i \(-0.552983\pi\)
−0.165683 + 0.986179i \(0.552983\pi\)
\(510\) −0.468908 −0.0207636
\(511\) −1.99112 −0.0880818
\(512\) 1.00000 0.0441942
\(513\) −18.8860 −0.833839
\(514\) 3.92975 0.173334
\(515\) −0.399292 −0.0175949
\(516\) −16.4081 −0.722327
\(517\) 8.11839 0.357047
\(518\) −1.24129 −0.0545393
\(519\) 28.2270 1.23903
\(520\) 0.211287 0.00926555
\(521\) 0.840534 0.0368245 0.0184122 0.999830i \(-0.494139\pi\)
0.0184122 + 0.999830i \(0.494139\pi\)
\(522\) −16.0361 −0.701880
\(523\) 14.4486 0.631792 0.315896 0.948794i \(-0.397695\pi\)
0.315896 + 0.948794i \(0.397695\pi\)
\(524\) 14.1634 0.618732
\(525\) −3.27277 −0.142836
\(526\) 14.9787 0.653103
\(527\) 13.5552 0.590474
\(528\) −1.64010 −0.0713760
\(529\) 9.86237 0.428799
\(530\) −0.418977 −0.0181992
\(531\) 47.6556 2.06807
\(532\) −1.53502 −0.0665518
\(533\) 42.2076 1.82821
\(534\) 2.33929 0.101231
\(535\) −0.163125 −0.00705252
\(536\) 13.0393 0.563212
\(537\) −22.7224 −0.980542
\(538\) −17.5697 −0.757484
\(539\) −4.26266 −0.183606
\(540\) −0.117036 −0.00503642
\(541\) −10.1803 −0.437684 −0.218842 0.975760i \(-0.570228\pi\)
−0.218842 + 0.975760i \(0.570228\pi\)
\(542\) 25.9833 1.11608
\(543\) −63.5195 −2.72588
\(544\) 4.52679 0.194085
\(545\) −0.370506 −0.0158707
\(546\) 3.56609 0.152615
\(547\) −29.4273 −1.25822 −0.629109 0.777317i \(-0.716580\pi\)
−0.629109 + 0.777317i \(0.716580\pi\)
\(548\) 1.99119 0.0850594
\(549\) −16.3450 −0.697589
\(550\) −3.07021 −0.130914
\(551\) −24.3076 −1.03554
\(552\) 15.3070 0.651509
\(553\) 3.18314 0.135361
\(554\) −12.3616 −0.525193
\(555\) −0.524367 −0.0222582
\(556\) 4.98502 0.211412
\(557\) 4.29434 0.181957 0.0909784 0.995853i \(-0.471001\pi\)
0.0909784 + 0.995853i \(0.471001\pi\)
\(558\) 12.3666 0.523519
\(559\) 33.4683 1.41556
\(560\) −0.00951248 −0.000401975 0
\(561\) −7.42438 −0.313457
\(562\) 19.5555 0.824897
\(563\) −7.70744 −0.324830 −0.162415 0.986723i \(-0.551928\pi\)
−0.162415 + 0.986723i \(0.551928\pi\)
\(564\) −35.2924 −1.48608
\(565\) −0.429794 −0.0180816
\(566\) 6.32929 0.266040
\(567\) 1.06271 0.0446294
\(568\) 3.91350 0.164207
\(569\) −32.9066 −1.37951 −0.689757 0.724040i \(-0.742283\pi\)
−0.689757 + 0.724040i \(0.742283\pi\)
\(570\) −0.648449 −0.0271606
\(571\) 33.9154 1.41931 0.709657 0.704547i \(-0.248850\pi\)
0.709657 + 0.704547i \(0.248850\pi\)
\(572\) 3.34537 0.139877
\(573\) 25.8831 1.08128
\(574\) −1.90025 −0.0793150
\(575\) 28.6542 1.19496
\(576\) 4.12985 0.172077
\(577\) 42.5789 1.77258 0.886291 0.463128i \(-0.153273\pi\)
0.886291 + 0.463128i \(0.153273\pi\)
\(578\) 3.49187 0.145242
\(579\) 34.6586 1.44036
\(580\) −0.150633 −0.00625470
\(581\) 3.95026 0.163884
\(582\) 10.8377 0.449237
\(583\) −6.63380 −0.274744
\(584\) 8.12008 0.336011
\(585\) 0.872584 0.0360769
\(586\) −23.6910 −0.978665
\(587\) −16.6455 −0.687034 −0.343517 0.939146i \(-0.611618\pi\)
−0.343517 + 0.939146i \(0.611618\pi\)
\(588\) 18.5307 0.764193
\(589\) 18.7454 0.772389
\(590\) 0.447647 0.0184294
\(591\) −20.8235 −0.856562
\(592\) 5.06219 0.208055
\(593\) 31.7189 1.30254 0.651270 0.758846i \(-0.274236\pi\)
0.651270 + 0.758846i \(0.274236\pi\)
\(594\) −1.85307 −0.0760323
\(595\) −0.0430610 −0.00176533
\(596\) 10.3669 0.424645
\(597\) 61.7462 2.52710
\(598\) −31.2223 −1.27678
\(599\) −8.33948 −0.340742 −0.170371 0.985380i \(-0.554497\pi\)
−0.170371 + 0.985380i \(0.554497\pi\)
\(600\) 13.3469 0.544884
\(601\) 40.0492 1.63364 0.816820 0.576893i \(-0.195735\pi\)
0.816820 + 0.576893i \(0.195735\pi\)
\(602\) −1.50680 −0.0614125
\(603\) 53.8504 2.19296
\(604\) 18.0604 0.734866
\(605\) −0.412091 −0.0167539
\(606\) 43.8017 1.77932
\(607\) −46.5892 −1.89100 −0.945498 0.325628i \(-0.894424\pi\)
−0.945498 + 0.325628i \(0.894424\pi\)
\(608\) 6.26006 0.253879
\(609\) −2.54238 −0.103022
\(610\) −0.153535 −0.00621646
\(611\) 71.9874 2.91230
\(612\) 18.6950 0.755700
\(613\) −20.3636 −0.822479 −0.411240 0.911527i \(-0.634904\pi\)
−0.411240 + 0.911527i \(0.634904\pi\)
\(614\) 21.6283 0.872848
\(615\) −0.802734 −0.0323694
\(616\) −0.150614 −0.00606841
\(617\) −4.26438 −0.171677 −0.0858387 0.996309i \(-0.527357\pi\)
−0.0858387 + 0.996309i \(0.527357\pi\)
\(618\) 27.4836 1.10555
\(619\) −32.4660 −1.30492 −0.652460 0.757823i \(-0.726263\pi\)
−0.652460 + 0.757823i \(0.726263\pi\)
\(620\) 0.116164 0.00466526
\(621\) 17.2946 0.694010
\(622\) −0.398441 −0.0159760
\(623\) 0.214823 0.00860671
\(624\) −14.5431 −0.582189
\(625\) 24.9774 0.999097
\(626\) 4.54967 0.181841
\(627\) −10.2671 −0.410029
\(628\) 2.96996 0.118514
\(629\) 22.9155 0.913700
\(630\) −0.0392851 −0.00156516
\(631\) 12.9019 0.513616 0.256808 0.966462i \(-0.417329\pi\)
0.256808 + 0.966462i \(0.417329\pi\)
\(632\) −12.9813 −0.516369
\(633\) −60.5580 −2.40697
\(634\) −27.8929 −1.10777
\(635\) 0.0901262 0.00357655
\(636\) 28.8386 1.14352
\(637\) −37.7979 −1.49761
\(638\) −2.38502 −0.0944240
\(639\) 16.1622 0.639366
\(640\) 0.0387933 0.00153344
\(641\) −4.86586 −0.192190 −0.0960949 0.995372i \(-0.530635\pi\)
−0.0960949 + 0.995372i \(0.530635\pi\)
\(642\) 11.2281 0.443136
\(643\) 2.11293 0.0833260 0.0416630 0.999132i \(-0.486734\pi\)
0.0416630 + 0.999132i \(0.486734\pi\)
\(644\) 1.40568 0.0553915
\(645\) −0.636525 −0.0250632
\(646\) 28.3380 1.11494
\(647\) −43.1312 −1.69566 −0.847831 0.530266i \(-0.822092\pi\)
−0.847831 + 0.530266i \(0.822092\pi\)
\(648\) −4.33388 −0.170251
\(649\) 7.08774 0.278218
\(650\) −27.2242 −1.06782
\(651\) 1.96061 0.0768425
\(652\) 8.25223 0.323182
\(653\) −14.8454 −0.580945 −0.290473 0.956883i \(-0.593813\pi\)
−0.290473 + 0.956883i \(0.593813\pi\)
\(654\) 25.5023 0.997217
\(655\) 0.549447 0.0214687
\(656\) 7.74952 0.302568
\(657\) 33.5347 1.30831
\(658\) −3.24099 −0.126347
\(659\) −30.7917 −1.19948 −0.599738 0.800196i \(-0.704729\pi\)
−0.599738 + 0.800196i \(0.704729\pi\)
\(660\) −0.0636248 −0.00247659
\(661\) −13.5504 −0.527049 −0.263525 0.964653i \(-0.584885\pi\)
−0.263525 + 0.964653i \(0.584885\pi\)
\(662\) 15.1509 0.588855
\(663\) −65.8335 −2.55676
\(664\) −16.1098 −0.625180
\(665\) −0.0595487 −0.00230920
\(666\) 20.9061 0.810095
\(667\) 22.2594 0.861887
\(668\) −7.38164 −0.285604
\(669\) −30.1216 −1.16457
\(670\) 0.505838 0.0195422
\(671\) −2.43097 −0.0938467
\(672\) 0.654752 0.0252576
\(673\) −8.10403 −0.312387 −0.156194 0.987726i \(-0.549922\pi\)
−0.156194 + 0.987726i \(0.549922\pi\)
\(674\) 20.1118 0.774678
\(675\) 15.0800 0.580429
\(676\) 16.6641 0.640927
\(677\) 16.9160 0.650134 0.325067 0.945691i \(-0.394613\pi\)
0.325067 + 0.945691i \(0.394613\pi\)
\(678\) 29.5831 1.13613
\(679\) 0.995252 0.0381942
\(680\) 0.175609 0.00673431
\(681\) −69.6749 −2.66995
\(682\) 1.83926 0.0704291
\(683\) 25.0868 0.959921 0.479960 0.877290i \(-0.340651\pi\)
0.479960 + 0.877290i \(0.340651\pi\)
\(684\) 25.8531 0.988520
\(685\) 0.0772449 0.00295137
\(686\) 3.41818 0.130507
\(687\) −24.2121 −0.923751
\(688\) 6.14495 0.234274
\(689\) −58.8233 −2.24099
\(690\) 0.593809 0.0226059
\(691\) −20.1568 −0.766803 −0.383401 0.923582i \(-0.625247\pi\)
−0.383401 + 0.923582i \(0.625247\pi\)
\(692\) −10.5712 −0.401857
\(693\) −0.622014 −0.0236284
\(694\) −24.3117 −0.922858
\(695\) 0.193386 0.00733553
\(696\) 10.3682 0.393006
\(697\) 35.0805 1.32877
\(698\) 8.10640 0.306832
\(699\) −45.8724 −1.73505
\(700\) 1.22568 0.0463262
\(701\) 48.7422 1.84097 0.920484 0.390780i \(-0.127795\pi\)
0.920484 + 0.390780i \(0.127795\pi\)
\(702\) −16.4315 −0.620168
\(703\) 31.6896 1.19520
\(704\) 0.614227 0.0231496
\(705\) −1.36911 −0.0515637
\(706\) −20.3427 −0.765608
\(707\) 4.02241 0.151278
\(708\) −30.8120 −1.15798
\(709\) 23.0709 0.866447 0.433223 0.901287i \(-0.357376\pi\)
0.433223 + 0.901287i \(0.357376\pi\)
\(710\) 0.151818 0.00569762
\(711\) −53.6109 −2.01057
\(712\) −0.876082 −0.0328326
\(713\) −17.1658 −0.642865
\(714\) 2.96393 0.110922
\(715\) 0.129778 0.00485343
\(716\) 8.50968 0.318022
\(717\) 31.3701 1.17154
\(718\) 26.7484 0.998243
\(719\) −10.8499 −0.404632 −0.202316 0.979320i \(-0.564847\pi\)
−0.202316 + 0.979320i \(0.564847\pi\)
\(720\) 0.160211 0.00597070
\(721\) 2.52389 0.0939944
\(722\) 20.1884 0.751335
\(723\) −25.5181 −0.949029
\(724\) 23.7885 0.884092
\(725\) 19.4090 0.720832
\(726\) 28.3646 1.05271
\(727\) −22.4701 −0.833371 −0.416686 0.909051i \(-0.636808\pi\)
−0.416686 + 0.909051i \(0.636808\pi\)
\(728\) −1.33553 −0.0494979
\(729\) −42.0653 −1.55797
\(730\) 0.315005 0.0116589
\(731\) 27.8169 1.02885
\(732\) 10.5680 0.390603
\(733\) −17.7389 −0.655201 −0.327600 0.944816i \(-0.606240\pi\)
−0.327600 + 0.944816i \(0.606240\pi\)
\(734\) 26.4394 0.975895
\(735\) 0.718867 0.0265158
\(736\) −5.73257 −0.211305
\(737\) 8.00909 0.295019
\(738\) 32.0044 1.17810
\(739\) 18.9612 0.697500 0.348750 0.937216i \(-0.386606\pi\)
0.348750 + 0.937216i \(0.386606\pi\)
\(740\) 0.196379 0.00721904
\(741\) −91.0405 −3.34446
\(742\) 2.64832 0.0972228
\(743\) −27.2233 −0.998727 −0.499364 0.866392i \(-0.666433\pi\)
−0.499364 + 0.866392i \(0.666433\pi\)
\(744\) −7.99568 −0.293136
\(745\) 0.402167 0.0147343
\(746\) −16.9400 −0.620217
\(747\) −66.5310 −2.43424
\(748\) 2.78048 0.101664
\(749\) 1.03110 0.0376756
\(750\) 1.03570 0.0378182
\(751\) −21.0078 −0.766585 −0.383292 0.923627i \(-0.625210\pi\)
−0.383292 + 0.923627i \(0.625210\pi\)
\(752\) 13.2172 0.481983
\(753\) −8.61336 −0.313888
\(754\) −21.1485 −0.770183
\(755\) 0.700622 0.0254982
\(756\) 0.739773 0.0269053
\(757\) −13.9970 −0.508729 −0.254364 0.967108i \(-0.581866\pi\)
−0.254364 + 0.967108i \(0.581866\pi\)
\(758\) −37.2869 −1.35432
\(759\) 9.40197 0.341270
\(760\) 0.242849 0.00880905
\(761\) 29.3070 1.06238 0.531188 0.847254i \(-0.321746\pi\)
0.531188 + 0.847254i \(0.321746\pi\)
\(762\) −6.20346 −0.224728
\(763\) 2.34194 0.0847837
\(764\) −9.69339 −0.350695
\(765\) 0.725241 0.0262211
\(766\) −24.1208 −0.871520
\(767\) 62.8485 2.26933
\(768\) −2.67018 −0.0963518
\(769\) 4.66718 0.168303 0.0841514 0.996453i \(-0.473182\pi\)
0.0841514 + 0.996453i \(0.473182\pi\)
\(770\) −0.00584282 −0.000210561 0
\(771\) −10.4931 −0.377901
\(772\) −12.9799 −0.467156
\(773\) 12.0542 0.433558 0.216779 0.976221i \(-0.430445\pi\)
0.216779 + 0.976221i \(0.430445\pi\)
\(774\) 25.3777 0.912184
\(775\) −14.9677 −0.537655
\(776\) −4.05879 −0.145702
\(777\) 3.31448 0.118906
\(778\) 21.2138 0.760553
\(779\) 48.5125 1.73814
\(780\) −0.564174 −0.0202007
\(781\) 2.40378 0.0860140
\(782\) −25.9502 −0.927976
\(783\) 11.7146 0.418644
\(784\) −6.93987 −0.247853
\(785\) 0.115215 0.00411218
\(786\) −37.8189 −1.34895
\(787\) 44.0561 1.57043 0.785215 0.619223i \(-0.212552\pi\)
0.785215 + 0.619223i \(0.212552\pi\)
\(788\) 7.79852 0.277811
\(789\) −39.9958 −1.42389
\(790\) −0.503588 −0.0179169
\(791\) 2.71669 0.0965944
\(792\) 2.53667 0.0901366
\(793\) −21.5559 −0.765474
\(794\) 25.1165 0.891352
\(795\) 1.11874 0.0396778
\(796\) −23.1244 −0.819621
\(797\) −7.00035 −0.247965 −0.123983 0.992284i \(-0.539567\pi\)
−0.123983 + 0.992284i \(0.539567\pi\)
\(798\) 4.09879 0.145096
\(799\) 59.8318 2.11670
\(800\) −4.99850 −0.176723
\(801\) −3.61809 −0.127839
\(802\) 23.0519 0.813992
\(803\) 4.98757 0.176008
\(804\) −34.8173 −1.22791
\(805\) 0.0545309 0.00192196
\(806\) 16.3091 0.574464
\(807\) 46.9143 1.65146
\(808\) −16.4040 −0.577091
\(809\) −21.2848 −0.748335 −0.374168 0.927361i \(-0.622072\pi\)
−0.374168 + 0.927361i \(0.622072\pi\)
\(810\) −0.168125 −0.00590733
\(811\) −3.97132 −0.139452 −0.0697260 0.997566i \(-0.522213\pi\)
−0.0697260 + 0.997566i \(0.522213\pi\)
\(812\) 0.952139 0.0334135
\(813\) −69.3800 −2.43326
\(814\) 3.10933 0.108982
\(815\) 0.320131 0.0112137
\(816\) −12.0873 −0.423142
\(817\) 38.4678 1.34582
\(818\) −30.8180 −1.07753
\(819\) −5.51552 −0.192728
\(820\) 0.300630 0.0104984
\(821\) 9.80769 0.342291 0.171145 0.985246i \(-0.445253\pi\)
0.171145 + 0.985246i \(0.445253\pi\)
\(822\) −5.31683 −0.185446
\(823\) −29.2818 −1.02070 −0.510349 0.859967i \(-0.670484\pi\)
−0.510349 + 0.859967i \(0.670484\pi\)
\(824\) −10.2928 −0.358567
\(825\) 8.19801 0.285418
\(826\) −2.82954 −0.0984522
\(827\) −15.6278 −0.543431 −0.271716 0.962378i \(-0.587591\pi\)
−0.271716 + 0.962378i \(0.587591\pi\)
\(828\) −23.6747 −0.822752
\(829\) −12.1408 −0.421667 −0.210833 0.977522i \(-0.567618\pi\)
−0.210833 + 0.977522i \(0.567618\pi\)
\(830\) −0.624952 −0.0216924
\(831\) 33.0076 1.14502
\(832\) 5.44648 0.188823
\(833\) −31.4154 −1.08848
\(834\) −13.3109 −0.460919
\(835\) −0.286358 −0.00990984
\(836\) 3.84510 0.132986
\(837\) −9.03394 −0.312259
\(838\) −1.65891 −0.0573059
\(839\) −3.99697 −0.137991 −0.0689953 0.997617i \(-0.521979\pi\)
−0.0689953 + 0.997617i \(0.521979\pi\)
\(840\) 0.0254000 0.000876383 0
\(841\) −13.9226 −0.480089
\(842\) −9.64421 −0.332361
\(843\) −52.2166 −1.79843
\(844\) 22.6794 0.780657
\(845\) 0.646456 0.0222388
\(846\) 54.5853 1.87668
\(847\) 2.60479 0.0895016
\(848\) −10.8002 −0.370882
\(849\) −16.9003 −0.580018
\(850\) −22.6272 −0.776105
\(851\) −29.0194 −0.994771
\(852\) −10.4497 −0.358002
\(853\) −8.45459 −0.289480 −0.144740 0.989470i \(-0.546235\pi\)
−0.144740 + 0.989470i \(0.546235\pi\)
\(854\) 0.970483 0.0332092
\(855\) 1.00293 0.0342995
\(856\) −4.20498 −0.143723
\(857\) 13.0534 0.445895 0.222948 0.974830i \(-0.428432\pi\)
0.222948 + 0.974830i \(0.428432\pi\)
\(858\) −8.93275 −0.304959
\(859\) 47.9735 1.63684 0.818418 0.574624i \(-0.194852\pi\)
0.818418 + 0.574624i \(0.194852\pi\)
\(860\) 0.238383 0.00812880
\(861\) 5.07401 0.172922
\(862\) 6.07992 0.207083
\(863\) 13.0411 0.443924 0.221962 0.975055i \(-0.428754\pi\)
0.221962 + 0.975055i \(0.428754\pi\)
\(864\) −3.01691 −0.102637
\(865\) −0.410092 −0.0139436
\(866\) 20.5245 0.697450
\(867\) −9.32390 −0.316656
\(868\) −0.734263 −0.0249225
\(869\) −7.97348 −0.270482
\(870\) 0.402218 0.0136365
\(871\) 71.0182 2.40636
\(872\) −9.55077 −0.323430
\(873\) −16.7622 −0.567314
\(874\) −35.8863 −1.21387
\(875\) 0.0951104 0.00321532
\(876\) −21.6821 −0.732569
\(877\) −17.9480 −0.606062 −0.303031 0.952981i \(-0.597999\pi\)
−0.303031 + 0.952981i \(0.597999\pi\)
\(878\) 4.24562 0.143283
\(879\) 63.2591 2.13368
\(880\) 0.0238279 0.000803239 0
\(881\) 35.8679 1.20842 0.604211 0.796825i \(-0.293489\pi\)
0.604211 + 0.796825i \(0.293489\pi\)
\(882\) −28.6606 −0.965054
\(883\) −5.14535 −0.173155 −0.0865773 0.996245i \(-0.527593\pi\)
−0.0865773 + 0.996245i \(0.527593\pi\)
\(884\) 24.6551 0.829240
\(885\) −1.19530 −0.0401795
\(886\) 25.2000 0.846612
\(887\) −11.8793 −0.398868 −0.199434 0.979911i \(-0.563910\pi\)
−0.199434 + 0.979911i \(0.563910\pi\)
\(888\) −13.5169 −0.453599
\(889\) −0.569679 −0.0191064
\(890\) −0.0339861 −0.00113922
\(891\) −2.66198 −0.0891798
\(892\) 11.2807 0.377707
\(893\) 82.7408 2.76882
\(894\) −27.6815 −0.925807
\(895\) 0.330119 0.0110346
\(896\) −0.245209 −0.00819186
\(897\) 83.3691 2.78361
\(898\) 19.0875 0.636959
\(899\) −11.6273 −0.387792
\(900\) −20.6430 −0.688102
\(901\) −48.8905 −1.62878
\(902\) 4.75996 0.158489
\(903\) 4.02342 0.133891
\(904\) −11.0791 −0.368485
\(905\) 0.922834 0.0306760
\(906\) −48.2244 −1.60215
\(907\) −16.3792 −0.543863 −0.271931 0.962317i \(-0.587662\pi\)
−0.271931 + 0.962317i \(0.587662\pi\)
\(908\) 26.0937 0.865951
\(909\) −67.7462 −2.24700
\(910\) −0.0518095 −0.00171747
\(911\) 12.1555 0.402730 0.201365 0.979516i \(-0.435462\pi\)
0.201365 + 0.979516i \(0.435462\pi\)
\(912\) −16.7155 −0.553505
\(913\) −9.89506 −0.327479
\(914\) 28.5928 0.945767
\(915\) 0.409967 0.0135531
\(916\) 9.06761 0.299602
\(917\) −3.47300 −0.114689
\(918\) −13.6569 −0.450746
\(919\) 12.2556 0.404275 0.202137 0.979357i \(-0.435211\pi\)
0.202137 + 0.979357i \(0.435211\pi\)
\(920\) −0.222385 −0.00733183
\(921\) −57.7515 −1.90298
\(922\) 8.59595 0.283093
\(923\) 21.3148 0.701585
\(924\) 0.402166 0.0132303
\(925\) −25.3033 −0.831968
\(926\) 23.6207 0.776224
\(927\) −42.5077 −1.39614
\(928\) −3.88297 −0.127465
\(929\) −29.0287 −0.952400 −0.476200 0.879337i \(-0.657986\pi\)
−0.476200 + 0.879337i \(0.657986\pi\)
\(930\) −0.310179 −0.0101712
\(931\) −43.4441 −1.42382
\(932\) 17.1795 0.562734
\(933\) 1.06391 0.0348308
\(934\) −16.0747 −0.525981
\(935\) 0.107864 0.00352753
\(936\) 22.4931 0.735211
\(937\) −11.9568 −0.390613 −0.195306 0.980742i \(-0.562570\pi\)
−0.195306 + 0.980742i \(0.562570\pi\)
\(938\) −3.19735 −0.104397
\(939\) −12.1484 −0.396449
\(940\) 0.512741 0.0167238
\(941\) 48.7480 1.58914 0.794569 0.607174i \(-0.207697\pi\)
0.794569 + 0.607174i \(0.207697\pi\)
\(942\) −7.93032 −0.258384
\(943\) −44.4246 −1.44667
\(944\) 11.5393 0.375572
\(945\) 0.0286983 0.000933554 0
\(946\) 3.77440 0.122716
\(947\) 44.7818 1.45521 0.727606 0.685995i \(-0.240633\pi\)
0.727606 + 0.685995i \(0.240633\pi\)
\(948\) 34.6624 1.12578
\(949\) 44.2258 1.43563
\(950\) −31.2909 −1.01521
\(951\) 74.4790 2.41515
\(952\) −1.11001 −0.0359757
\(953\) −4.49735 −0.145684 −0.0728418 0.997344i \(-0.523207\pi\)
−0.0728418 + 0.997344i \(0.523207\pi\)
\(954\) −44.6034 −1.44409
\(955\) −0.376039 −0.0121683
\(956\) −11.7483 −0.379967
\(957\) 6.36844 0.205862
\(958\) −4.74526 −0.153312
\(959\) −0.488258 −0.0157667
\(960\) −0.103585 −0.00334319
\(961\) −22.0334 −0.710753
\(962\) 27.5711 0.888928
\(963\) −17.3660 −0.559610
\(964\) 9.55671 0.307801
\(965\) −0.503533 −0.0162093
\(966\) −3.75341 −0.120764
\(967\) 40.2014 1.29279 0.646395 0.763003i \(-0.276276\pi\)
0.646395 + 0.763003i \(0.276276\pi\)
\(968\) −10.6227 −0.341427
\(969\) −75.6676 −2.43079
\(970\) −0.157454 −0.00505554
\(971\) 38.9525 1.25005 0.625023 0.780607i \(-0.285090\pi\)
0.625023 + 0.780607i \(0.285090\pi\)
\(972\) 20.6229 0.661481
\(973\) −1.22237 −0.0391875
\(974\) −9.08566 −0.291123
\(975\) 72.6934 2.32805
\(976\) −3.95778 −0.126685
\(977\) 11.2106 0.358657 0.179329 0.983789i \(-0.442607\pi\)
0.179329 + 0.983789i \(0.442607\pi\)
\(978\) −22.0349 −0.704599
\(979\) −0.538113 −0.0171982
\(980\) −0.269221 −0.00859994
\(981\) −39.4433 −1.25933
\(982\) 6.41519 0.204717
\(983\) −24.7558 −0.789587 −0.394793 0.918770i \(-0.629184\pi\)
−0.394793 + 0.918770i \(0.629184\pi\)
\(984\) −20.6926 −0.659656
\(985\) 0.302531 0.00963943
\(986\) −17.5774 −0.559778
\(987\) 8.65402 0.275460
\(988\) 34.0953 1.08472
\(989\) −35.2264 −1.12013
\(990\) 0.0984058 0.00312754
\(991\) −23.3731 −0.742473 −0.371236 0.928538i \(-0.621066\pi\)
−0.371236 + 0.928538i \(0.621066\pi\)
\(992\) 2.99444 0.0950734
\(993\) −40.4555 −1.28382
\(994\) −0.959626 −0.0304375
\(995\) −0.897071 −0.0284391
\(996\) 43.0160 1.36301
\(997\) −54.1021 −1.71343 −0.856716 0.515788i \(-0.827499\pi\)
−0.856716 + 0.515788i \(0.827499\pi\)
\(998\) −34.9687 −1.10692
\(999\) −15.2722 −0.483190
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 8006.2.a.d.1.12 98
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8006.2.a.d.1.12 98 1.1 even 1 trivial