Properties

Label 4334.2.a.g.1.20
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +2.26689 q^{3} +1.00000 q^{4} -4.31390 q^{5} +2.26689 q^{6} +1.45520 q^{7} +1.00000 q^{8} +2.13877 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +2.26689 q^{3} +1.00000 q^{4} -4.31390 q^{5} +2.26689 q^{6} +1.45520 q^{7} +1.00000 q^{8} +2.13877 q^{9} -4.31390 q^{10} +1.00000 q^{11} +2.26689 q^{12} +5.78539 q^{13} +1.45520 q^{14} -9.77913 q^{15} +1.00000 q^{16} +3.84797 q^{17} +2.13877 q^{18} -4.96345 q^{19} -4.31390 q^{20} +3.29878 q^{21} +1.00000 q^{22} -2.20643 q^{23} +2.26689 q^{24} +13.6098 q^{25} +5.78539 q^{26} -1.95230 q^{27} +1.45520 q^{28} +0.634230 q^{29} -9.77913 q^{30} +5.25012 q^{31} +1.00000 q^{32} +2.26689 q^{33} +3.84797 q^{34} -6.27760 q^{35} +2.13877 q^{36} +2.91592 q^{37} -4.96345 q^{38} +13.1148 q^{39} -4.31390 q^{40} -5.56125 q^{41} +3.29878 q^{42} +1.21278 q^{43} +1.00000 q^{44} -9.22647 q^{45} -2.20643 q^{46} -4.07168 q^{47} +2.26689 q^{48} -4.88239 q^{49} +13.6098 q^{50} +8.72291 q^{51} +5.78539 q^{52} -5.37607 q^{53} -1.95230 q^{54} -4.31390 q^{55} +1.45520 q^{56} -11.2516 q^{57} +0.634230 q^{58} +15.1544 q^{59} -9.77913 q^{60} +12.8293 q^{61} +5.25012 q^{62} +3.11235 q^{63} +1.00000 q^{64} -24.9576 q^{65} +2.26689 q^{66} +11.6941 q^{67} +3.84797 q^{68} -5.00172 q^{69} -6.27760 q^{70} +4.92023 q^{71} +2.13877 q^{72} +16.7710 q^{73} +2.91592 q^{74} +30.8518 q^{75} -4.96345 q^{76} +1.45520 q^{77} +13.1148 q^{78} +4.21494 q^{79} -4.31390 q^{80} -10.8420 q^{81} -5.56125 q^{82} -4.59201 q^{83} +3.29878 q^{84} -16.5998 q^{85} +1.21278 q^{86} +1.43773 q^{87} +1.00000 q^{88} +6.56639 q^{89} -9.22647 q^{90} +8.41891 q^{91} -2.20643 q^{92} +11.9014 q^{93} -4.07168 q^{94} +21.4118 q^{95} +2.26689 q^{96} -1.64673 q^{97} -4.88239 q^{98} +2.13877 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 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
\(3\) 2.26689 1.30879 0.654394 0.756154i \(-0.272924\pi\)
0.654394 + 0.756154i \(0.272924\pi\)
\(4\) 1.00000 0.500000
\(5\) −4.31390 −1.92924 −0.964618 0.263650i \(-0.915074\pi\)
−0.964618 + 0.263650i \(0.915074\pi\)
\(6\) 2.26689 0.925453
\(7\) 1.45520 0.550014 0.275007 0.961442i \(-0.411320\pi\)
0.275007 + 0.961442i \(0.411320\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.13877 0.712925
\(10\) −4.31390 −1.36418
\(11\) 1.00000 0.301511
\(12\) 2.26689 0.654394
\(13\) 5.78539 1.60458 0.802289 0.596935i \(-0.203615\pi\)
0.802289 + 0.596935i \(0.203615\pi\)
\(14\) 1.45520 0.388919
\(15\) −9.77913 −2.52496
\(16\) 1.00000 0.250000
\(17\) 3.84797 0.933270 0.466635 0.884450i \(-0.345466\pi\)
0.466635 + 0.884450i \(0.345466\pi\)
\(18\) 2.13877 0.504114
\(19\) −4.96345 −1.13869 −0.569346 0.822098i \(-0.692804\pi\)
−0.569346 + 0.822098i \(0.692804\pi\)
\(20\) −4.31390 −0.964618
\(21\) 3.29878 0.719852
\(22\) 1.00000 0.213201
\(23\) −2.20643 −0.460072 −0.230036 0.973182i \(-0.573884\pi\)
−0.230036 + 0.973182i \(0.573884\pi\)
\(24\) 2.26689 0.462726
\(25\) 13.6098 2.72196
\(26\) 5.78539 1.13461
\(27\) −1.95230 −0.375721
\(28\) 1.45520 0.275007
\(29\) 0.634230 0.117774 0.0588868 0.998265i \(-0.481245\pi\)
0.0588868 + 0.998265i \(0.481245\pi\)
\(30\) −9.77913 −1.78542
\(31\) 5.25012 0.942950 0.471475 0.881880i \(-0.343722\pi\)
0.471475 + 0.881880i \(0.343722\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.26689 0.394614
\(34\) 3.84797 0.659922
\(35\) −6.27760 −1.06111
\(36\) 2.13877 0.356462
\(37\) 2.91592 0.479374 0.239687 0.970850i \(-0.422955\pi\)
0.239687 + 0.970850i \(0.422955\pi\)
\(38\) −4.96345 −0.805178
\(39\) 13.1148 2.10005
\(40\) −4.31390 −0.682088
\(41\) −5.56125 −0.868522 −0.434261 0.900787i \(-0.642990\pi\)
−0.434261 + 0.900787i \(0.642990\pi\)
\(42\) 3.29878 0.509012
\(43\) 1.21278 0.184947 0.0924736 0.995715i \(-0.470523\pi\)
0.0924736 + 0.995715i \(0.470523\pi\)
\(44\) 1.00000 0.150756
\(45\) −9.22647 −1.37540
\(46\) −2.20643 −0.325320
\(47\) −4.07168 −0.593916 −0.296958 0.954890i \(-0.595972\pi\)
−0.296958 + 0.954890i \(0.595972\pi\)
\(48\) 2.26689 0.327197
\(49\) −4.88239 −0.697484
\(50\) 13.6098 1.92471
\(51\) 8.72291 1.22145
\(52\) 5.78539 0.802289
\(53\) −5.37607 −0.738460 −0.369230 0.929338i \(-0.620379\pi\)
−0.369230 + 0.929338i \(0.620379\pi\)
\(54\) −1.95230 −0.265675
\(55\) −4.31390 −0.581687
\(56\) 1.45520 0.194459
\(57\) −11.2516 −1.49031
\(58\) 0.634230 0.0832784
\(59\) 15.1544 1.97294 0.986469 0.163946i \(-0.0524223\pi\)
0.986469 + 0.163946i \(0.0524223\pi\)
\(60\) −9.77913 −1.26248
\(61\) 12.8293 1.64262 0.821311 0.570480i \(-0.193243\pi\)
0.821311 + 0.570480i \(0.193243\pi\)
\(62\) 5.25012 0.666766
\(63\) 3.11235 0.392119
\(64\) 1.00000 0.125000
\(65\) −24.9576 −3.09561
\(66\) 2.26689 0.279034
\(67\) 11.6941 1.42866 0.714329 0.699810i \(-0.246732\pi\)
0.714329 + 0.699810i \(0.246732\pi\)
\(68\) 3.84797 0.466635
\(69\) −5.00172 −0.602136
\(70\) −6.27760 −0.750317
\(71\) 4.92023 0.583924 0.291962 0.956430i \(-0.405692\pi\)
0.291962 + 0.956430i \(0.405692\pi\)
\(72\) 2.13877 0.252057
\(73\) 16.7710 1.96290 0.981448 0.191729i \(-0.0614094\pi\)
0.981448 + 0.191729i \(0.0614094\pi\)
\(74\) 2.91592 0.338969
\(75\) 30.8518 3.56246
\(76\) −4.96345 −0.569346
\(77\) 1.45520 0.165836
\(78\) 13.1148 1.48496
\(79\) 4.21494 0.474218 0.237109 0.971483i \(-0.423800\pi\)
0.237109 + 0.971483i \(0.423800\pi\)
\(80\) −4.31390 −0.482309
\(81\) −10.8420 −1.20466
\(82\) −5.56125 −0.614138
\(83\) −4.59201 −0.504039 −0.252019 0.967722i \(-0.581095\pi\)
−0.252019 + 0.967722i \(0.581095\pi\)
\(84\) 3.29878 0.359926
\(85\) −16.5998 −1.80050
\(86\) 1.21278 0.130777
\(87\) 1.43773 0.154140
\(88\) 1.00000 0.106600
\(89\) 6.56639 0.696036 0.348018 0.937488i \(-0.386855\pi\)
0.348018 + 0.937488i \(0.386855\pi\)
\(90\) −9.22647 −0.972555
\(91\) 8.41891 0.882541
\(92\) −2.20643 −0.230036
\(93\) 11.9014 1.23412
\(94\) −4.07168 −0.419962
\(95\) 21.4118 2.19681
\(96\) 2.26689 0.231363
\(97\) −1.64673 −0.167200 −0.0835998 0.996499i \(-0.526642\pi\)
−0.0835998 + 0.996499i \(0.526642\pi\)
\(98\) −4.88239 −0.493196
\(99\) 2.13877 0.214955
\(100\) 13.6098 1.36098
\(101\) 2.12355 0.211301 0.105650 0.994403i \(-0.466308\pi\)
0.105650 + 0.994403i \(0.466308\pi\)
\(102\) 8.72291 0.863697
\(103\) −6.81012 −0.671021 −0.335510 0.942037i \(-0.608909\pi\)
−0.335510 + 0.942037i \(0.608909\pi\)
\(104\) 5.78539 0.567304
\(105\) −14.2306 −1.38876
\(106\) −5.37607 −0.522170
\(107\) 4.19419 0.405468 0.202734 0.979234i \(-0.435017\pi\)
0.202734 + 0.979234i \(0.435017\pi\)
\(108\) −1.95230 −0.187860
\(109\) 10.4686 1.00271 0.501354 0.865242i \(-0.332835\pi\)
0.501354 + 0.865242i \(0.332835\pi\)
\(110\) −4.31390 −0.411315
\(111\) 6.61006 0.627399
\(112\) 1.45520 0.137504
\(113\) −18.0135 −1.69457 −0.847285 0.531138i \(-0.821765\pi\)
−0.847285 + 0.531138i \(0.821765\pi\)
\(114\) −11.2516 −1.05381
\(115\) 9.51831 0.887587
\(116\) 0.634230 0.0588868
\(117\) 12.3736 1.14394
\(118\) 15.1544 1.39508
\(119\) 5.59957 0.513312
\(120\) −9.77913 −0.892709
\(121\) 1.00000 0.0909091
\(122\) 12.8293 1.16151
\(123\) −12.6067 −1.13671
\(124\) 5.25012 0.471475
\(125\) −37.1418 −3.32206
\(126\) 3.11235 0.277270
\(127\) 12.4888 1.10820 0.554100 0.832450i \(-0.313063\pi\)
0.554100 + 0.832450i \(0.313063\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.74923 0.242057
\(130\) −24.9576 −2.18893
\(131\) 3.47476 0.303591 0.151796 0.988412i \(-0.451494\pi\)
0.151796 + 0.988412i \(0.451494\pi\)
\(132\) 2.26689 0.197307
\(133\) −7.22281 −0.626297
\(134\) 11.6941 1.01021
\(135\) 8.42204 0.724854
\(136\) 3.84797 0.329961
\(137\) −4.01709 −0.343203 −0.171602 0.985166i \(-0.554894\pi\)
−0.171602 + 0.985166i \(0.554894\pi\)
\(138\) −5.00172 −0.425775
\(139\) −5.28021 −0.447862 −0.223931 0.974605i \(-0.571889\pi\)
−0.223931 + 0.974605i \(0.571889\pi\)
\(140\) −6.27760 −0.530554
\(141\) −9.23005 −0.777310
\(142\) 4.92023 0.412897
\(143\) 5.78539 0.483799
\(144\) 2.13877 0.178231
\(145\) −2.73601 −0.227213
\(146\) 16.7710 1.38798
\(147\) −11.0678 −0.912859
\(148\) 2.91592 0.239687
\(149\) 2.22890 0.182598 0.0912992 0.995824i \(-0.470898\pi\)
0.0912992 + 0.995824i \(0.470898\pi\)
\(150\) 30.8518 2.51904
\(151\) 14.5914 1.18743 0.593716 0.804675i \(-0.297660\pi\)
0.593716 + 0.804675i \(0.297660\pi\)
\(152\) −4.96345 −0.402589
\(153\) 8.22994 0.665351
\(154\) 1.45520 0.117263
\(155\) −22.6485 −1.81917
\(156\) 13.1148 1.05003
\(157\) 1.69825 0.135535 0.0677674 0.997701i \(-0.478412\pi\)
0.0677674 + 0.997701i \(0.478412\pi\)
\(158\) 4.21494 0.335323
\(159\) −12.1869 −0.966487
\(160\) −4.31390 −0.341044
\(161\) −3.21079 −0.253046
\(162\) −10.8420 −0.851825
\(163\) −22.7432 −1.78138 −0.890691 0.454609i \(-0.849779\pi\)
−0.890691 + 0.454609i \(0.849779\pi\)
\(164\) −5.56125 −0.434261
\(165\) −9.77913 −0.761304
\(166\) −4.59201 −0.356409
\(167\) 1.19080 0.0921470 0.0460735 0.998938i \(-0.485329\pi\)
0.0460735 + 0.998938i \(0.485329\pi\)
\(168\) 3.29878 0.254506
\(169\) 20.4708 1.57467
\(170\) −16.5998 −1.27315
\(171\) −10.6157 −0.811802
\(172\) 1.21278 0.0924736
\(173\) 17.4792 1.32892 0.664458 0.747326i \(-0.268662\pi\)
0.664458 + 0.747326i \(0.268662\pi\)
\(174\) 1.43773 0.108994
\(175\) 19.8050 1.49711
\(176\) 1.00000 0.0753778
\(177\) 34.3534 2.58216
\(178\) 6.56639 0.492172
\(179\) −16.6632 −1.24547 −0.622733 0.782434i \(-0.713978\pi\)
−0.622733 + 0.782434i \(0.713978\pi\)
\(180\) −9.22647 −0.687700
\(181\) −24.0436 −1.78715 −0.893573 0.448919i \(-0.851809\pi\)
−0.893573 + 0.448919i \(0.851809\pi\)
\(182\) 8.41891 0.624051
\(183\) 29.0825 2.14984
\(184\) −2.20643 −0.162660
\(185\) −12.5790 −0.924826
\(186\) 11.9014 0.872655
\(187\) 3.84797 0.281392
\(188\) −4.07168 −0.296958
\(189\) −2.84099 −0.206652
\(190\) 21.4118 1.55338
\(191\) 16.7007 1.20842 0.604210 0.796825i \(-0.293489\pi\)
0.604210 + 0.796825i \(0.293489\pi\)
\(192\) 2.26689 0.163598
\(193\) −3.90861 −0.281348 −0.140674 0.990056i \(-0.544927\pi\)
−0.140674 + 0.990056i \(0.544927\pi\)
\(194\) −1.64673 −0.118228
\(195\) −56.5761 −4.05150
\(196\) −4.88239 −0.348742
\(197\) 1.00000 0.0712470
\(198\) 2.13877 0.151996
\(199\) −6.01298 −0.426249 −0.213124 0.977025i \(-0.568364\pi\)
−0.213124 + 0.977025i \(0.568364\pi\)
\(200\) 13.6098 0.962356
\(201\) 26.5091 1.86981
\(202\) 2.12355 0.149412
\(203\) 0.922932 0.0647771
\(204\) 8.72291 0.610726
\(205\) 23.9907 1.67558
\(206\) −6.81012 −0.474483
\(207\) −4.71905 −0.327997
\(208\) 5.78539 0.401145
\(209\) −4.96345 −0.343329
\(210\) −14.2306 −0.982005
\(211\) −11.5594 −0.795779 −0.397889 0.917433i \(-0.630257\pi\)
−0.397889 + 0.917433i \(0.630257\pi\)
\(212\) −5.37607 −0.369230
\(213\) 11.1536 0.764233
\(214\) 4.19419 0.286709
\(215\) −5.23182 −0.356807
\(216\) −1.95230 −0.132837
\(217\) 7.63998 0.518636
\(218\) 10.4686 0.709022
\(219\) 38.0179 2.56901
\(220\) −4.31390 −0.290843
\(221\) 22.2620 1.49751
\(222\) 6.61006 0.443638
\(223\) −21.3160 −1.42743 −0.713713 0.700438i \(-0.752988\pi\)
−0.713713 + 0.700438i \(0.752988\pi\)
\(224\) 1.45520 0.0972297
\(225\) 29.1082 1.94055
\(226\) −18.0135 −1.19824
\(227\) −11.1150 −0.737726 −0.368863 0.929484i \(-0.620253\pi\)
−0.368863 + 0.929484i \(0.620253\pi\)
\(228\) −11.2516 −0.745154
\(229\) −25.1307 −1.66069 −0.830343 0.557253i \(-0.811855\pi\)
−0.830343 + 0.557253i \(0.811855\pi\)
\(230\) 9.51831 0.627619
\(231\) 3.29878 0.217043
\(232\) 0.634230 0.0416392
\(233\) −8.50901 −0.557444 −0.278722 0.960372i \(-0.589911\pi\)
−0.278722 + 0.960372i \(0.589911\pi\)
\(234\) 12.3736 0.808891
\(235\) 17.5649 1.14581
\(236\) 15.1544 0.986469
\(237\) 9.55479 0.620651
\(238\) 5.59957 0.362966
\(239\) 18.9076 1.22303 0.611514 0.791234i \(-0.290561\pi\)
0.611514 + 0.791234i \(0.290561\pi\)
\(240\) −9.77913 −0.631240
\(241\) 1.93068 0.124366 0.0621830 0.998065i \(-0.480194\pi\)
0.0621830 + 0.998065i \(0.480194\pi\)
\(242\) 1.00000 0.0642824
\(243\) −18.7206 −1.20093
\(244\) 12.8293 0.821311
\(245\) 21.0622 1.34561
\(246\) −12.6067 −0.803776
\(247\) −28.7155 −1.82712
\(248\) 5.25012 0.333383
\(249\) −10.4096 −0.659680
\(250\) −37.1418 −2.34905
\(251\) 8.94751 0.564762 0.282381 0.959302i \(-0.408876\pi\)
0.282381 + 0.959302i \(0.408876\pi\)
\(252\) 3.11235 0.196059
\(253\) −2.20643 −0.138717
\(254\) 12.4888 0.783615
\(255\) −37.6298 −2.35647
\(256\) 1.00000 0.0625000
\(257\) −7.42717 −0.463294 −0.231647 0.972800i \(-0.574411\pi\)
−0.231647 + 0.972800i \(0.574411\pi\)
\(258\) 2.74923 0.171160
\(259\) 4.24325 0.263663
\(260\) −24.9576 −1.54781
\(261\) 1.35647 0.0839636
\(262\) 3.47476 0.214672
\(263\) −4.07400 −0.251214 −0.125607 0.992080i \(-0.540088\pi\)
−0.125607 + 0.992080i \(0.540088\pi\)
\(264\) 2.26689 0.139517
\(265\) 23.1919 1.42466
\(266\) −7.22281 −0.442859
\(267\) 14.8853 0.910963
\(268\) 11.6941 0.714329
\(269\) 12.8855 0.785645 0.392823 0.919614i \(-0.371499\pi\)
0.392823 + 0.919614i \(0.371499\pi\)
\(270\) 8.42204 0.512549
\(271\) −1.31221 −0.0797108 −0.0398554 0.999205i \(-0.512690\pi\)
−0.0398554 + 0.999205i \(0.512690\pi\)
\(272\) 3.84797 0.233318
\(273\) 19.0847 1.15506
\(274\) −4.01709 −0.242681
\(275\) 13.6098 0.820700
\(276\) −5.00172 −0.301068
\(277\) 4.52523 0.271895 0.135947 0.990716i \(-0.456592\pi\)
0.135947 + 0.990716i \(0.456592\pi\)
\(278\) −5.28021 −0.316686
\(279\) 11.2288 0.672252
\(280\) −6.27760 −0.375158
\(281\) −30.2456 −1.80430 −0.902151 0.431420i \(-0.858013\pi\)
−0.902151 + 0.431420i \(0.858013\pi\)
\(282\) −9.23005 −0.549641
\(283\) 9.95702 0.591884 0.295942 0.955206i \(-0.404367\pi\)
0.295942 + 0.955206i \(0.404367\pi\)
\(284\) 4.92023 0.291962
\(285\) 48.5382 2.87516
\(286\) 5.78539 0.342097
\(287\) −8.09274 −0.477699
\(288\) 2.13877 0.126028
\(289\) −2.19312 −0.129007
\(290\) −2.73601 −0.160664
\(291\) −3.73294 −0.218829
\(292\) 16.7710 0.981448
\(293\) −0.204412 −0.0119419 −0.00597095 0.999982i \(-0.501901\pi\)
−0.00597095 + 0.999982i \(0.501901\pi\)
\(294\) −11.0678 −0.645489
\(295\) −65.3748 −3.80627
\(296\) 2.91592 0.169484
\(297\) −1.95230 −0.113284
\(298\) 2.22890 0.129117
\(299\) −12.7650 −0.738221
\(300\) 30.8518 1.78123
\(301\) 1.76484 0.101724
\(302\) 14.5914 0.839641
\(303\) 4.81384 0.276548
\(304\) −4.96345 −0.284673
\(305\) −55.3443 −3.16901
\(306\) 8.22994 0.470474
\(307\) 5.99190 0.341976 0.170988 0.985273i \(-0.445304\pi\)
0.170988 + 0.985273i \(0.445304\pi\)
\(308\) 1.45520 0.0829178
\(309\) −15.4378 −0.878224
\(310\) −22.6485 −1.28635
\(311\) 29.6779 1.68288 0.841441 0.540349i \(-0.181708\pi\)
0.841441 + 0.540349i \(0.181708\pi\)
\(312\) 13.1148 0.742481
\(313\) −2.08952 −0.118106 −0.0590532 0.998255i \(-0.518808\pi\)
−0.0590532 + 0.998255i \(0.518808\pi\)
\(314\) 1.69825 0.0958375
\(315\) −13.4264 −0.756490
\(316\) 4.21494 0.237109
\(317\) 30.7875 1.72920 0.864598 0.502464i \(-0.167573\pi\)
0.864598 + 0.502464i \(0.167573\pi\)
\(318\) −12.1869 −0.683410
\(319\) 0.634230 0.0355100
\(320\) −4.31390 −0.241155
\(321\) 9.50775 0.530671
\(322\) −3.21079 −0.178931
\(323\) −19.0992 −1.06271
\(324\) −10.8420 −0.602332
\(325\) 78.7379 4.36759
\(326\) −22.7432 −1.25963
\(327\) 23.7311 1.31233
\(328\) −5.56125 −0.307069
\(329\) −5.92512 −0.326662
\(330\) −9.77913 −0.538324
\(331\) −25.5382 −1.40371 −0.701853 0.712322i \(-0.747644\pi\)
−0.701853 + 0.712322i \(0.747644\pi\)
\(332\) −4.59201 −0.252019
\(333\) 6.23649 0.341758
\(334\) 1.19080 0.0651578
\(335\) −50.4471 −2.75622
\(336\) 3.29878 0.179963
\(337\) −0.00855933 −0.000466257 0 −0.000233128 1.00000i \(-0.500074\pi\)
−0.000233128 1.00000i \(0.500074\pi\)
\(338\) 20.4708 1.11346
\(339\) −40.8346 −2.21783
\(340\) −16.5998 −0.900250
\(341\) 5.25012 0.284310
\(342\) −10.6157 −0.574031
\(343\) −17.2913 −0.933641
\(344\) 1.21278 0.0653887
\(345\) 21.5769 1.16166
\(346\) 17.4792 0.939685
\(347\) −25.4319 −1.36525 −0.682627 0.730767i \(-0.739163\pi\)
−0.682627 + 0.730767i \(0.739163\pi\)
\(348\) 1.43773 0.0770702
\(349\) 4.87428 0.260914 0.130457 0.991454i \(-0.458356\pi\)
0.130457 + 0.991454i \(0.458356\pi\)
\(350\) 19.8050 1.05862
\(351\) −11.2948 −0.602873
\(352\) 1.00000 0.0533002
\(353\) −13.5161 −0.719391 −0.359696 0.933070i \(-0.617119\pi\)
−0.359696 + 0.933070i \(0.617119\pi\)
\(354\) 34.3534 1.82586
\(355\) −21.2254 −1.12653
\(356\) 6.56639 0.348018
\(357\) 12.6936 0.671816
\(358\) −16.6632 −0.880677
\(359\) 17.8409 0.941607 0.470803 0.882238i \(-0.343964\pi\)
0.470803 + 0.882238i \(0.343964\pi\)
\(360\) −9.22647 −0.486278
\(361\) 5.63581 0.296622
\(362\) −24.0436 −1.26370
\(363\) 2.26689 0.118981
\(364\) 8.41891 0.441271
\(365\) −72.3485 −3.78689
\(366\) 29.0825 1.52017
\(367\) −0.856582 −0.0447132 −0.0223566 0.999750i \(-0.507117\pi\)
−0.0223566 + 0.999750i \(0.507117\pi\)
\(368\) −2.20643 −0.115018
\(369\) −11.8943 −0.619191
\(370\) −12.5790 −0.653951
\(371\) −7.82326 −0.406164
\(372\) 11.9014 0.617060
\(373\) −21.9814 −1.13815 −0.569077 0.822284i \(-0.692699\pi\)
−0.569077 + 0.822284i \(0.692699\pi\)
\(374\) 3.84797 0.198974
\(375\) −84.1961 −4.34787
\(376\) −4.07168 −0.209981
\(377\) 3.66927 0.188977
\(378\) −2.84099 −0.146125
\(379\) −10.5077 −0.539744 −0.269872 0.962896i \(-0.586981\pi\)
−0.269872 + 0.962896i \(0.586981\pi\)
\(380\) 21.4118 1.09840
\(381\) 28.3106 1.45040
\(382\) 16.7007 0.854482
\(383\) −29.0826 −1.48605 −0.743026 0.669263i \(-0.766610\pi\)
−0.743026 + 0.669263i \(0.766610\pi\)
\(384\) 2.26689 0.115682
\(385\) −6.27760 −0.319936
\(386\) −3.90861 −0.198943
\(387\) 2.59386 0.131853
\(388\) −1.64673 −0.0835998
\(389\) −12.5211 −0.634846 −0.317423 0.948284i \(-0.602817\pi\)
−0.317423 + 0.948284i \(0.602817\pi\)
\(390\) −56.5761 −2.86484
\(391\) −8.49027 −0.429371
\(392\) −4.88239 −0.246598
\(393\) 7.87689 0.397337
\(394\) 1.00000 0.0503793
\(395\) −18.1829 −0.914879
\(396\) 2.13877 0.107477
\(397\) −1.48312 −0.0744354 −0.0372177 0.999307i \(-0.511850\pi\)
−0.0372177 + 0.999307i \(0.511850\pi\)
\(398\) −6.01298 −0.301403
\(399\) −16.3733 −0.819690
\(400\) 13.6098 0.680489
\(401\) −20.3461 −1.01604 −0.508018 0.861347i \(-0.669622\pi\)
−0.508018 + 0.861347i \(0.669622\pi\)
\(402\) 26.5091 1.32216
\(403\) 30.3740 1.51304
\(404\) 2.12355 0.105650
\(405\) 46.7712 2.32408
\(406\) 0.922932 0.0458043
\(407\) 2.91592 0.144537
\(408\) 8.72291 0.431849
\(409\) −33.7304 −1.66786 −0.833929 0.551871i \(-0.813914\pi\)
−0.833929 + 0.551871i \(0.813914\pi\)
\(410\) 23.9907 1.18482
\(411\) −9.10629 −0.449180
\(412\) −6.81012 −0.335510
\(413\) 22.0527 1.08514
\(414\) −4.71905 −0.231929
\(415\) 19.8095 0.972410
\(416\) 5.78539 0.283652
\(417\) −11.9696 −0.586156
\(418\) −4.96345 −0.242770
\(419\) −13.6430 −0.666505 −0.333253 0.942838i \(-0.608146\pi\)
−0.333253 + 0.942838i \(0.608146\pi\)
\(420\) −14.2306 −0.694382
\(421\) 1.96082 0.0955646 0.0477823 0.998858i \(-0.484785\pi\)
0.0477823 + 0.998858i \(0.484785\pi\)
\(422\) −11.5594 −0.562700
\(423\) −8.70841 −0.423418
\(424\) −5.37607 −0.261085
\(425\) 52.3700 2.54032
\(426\) 11.1536 0.540394
\(427\) 18.6692 0.903466
\(428\) 4.19419 0.202734
\(429\) 13.1148 0.633190
\(430\) −5.23182 −0.252301
\(431\) −39.2100 −1.88868 −0.944339 0.328973i \(-0.893298\pi\)
−0.944339 + 0.328973i \(0.893298\pi\)
\(432\) −1.95230 −0.0939301
\(433\) 1.79869 0.0864395 0.0432198 0.999066i \(-0.486238\pi\)
0.0432198 + 0.999066i \(0.486238\pi\)
\(434\) 7.63998 0.366731
\(435\) −6.20222 −0.297374
\(436\) 10.4686 0.501354
\(437\) 10.9515 0.523880
\(438\) 38.0179 1.81657
\(439\) −18.5939 −0.887439 −0.443719 0.896166i \(-0.646341\pi\)
−0.443719 + 0.896166i \(0.646341\pi\)
\(440\) −4.31390 −0.205657
\(441\) −10.4423 −0.497254
\(442\) 22.2620 1.05890
\(443\) 14.9630 0.710912 0.355456 0.934693i \(-0.384326\pi\)
0.355456 + 0.934693i \(0.384326\pi\)
\(444\) 6.61006 0.313699
\(445\) −28.3268 −1.34282
\(446\) −21.3160 −1.00934
\(447\) 5.05266 0.238983
\(448\) 1.45520 0.0687518
\(449\) 4.22845 0.199553 0.0997764 0.995010i \(-0.468187\pi\)
0.0997764 + 0.995010i \(0.468187\pi\)
\(450\) 29.1082 1.37218
\(451\) −5.56125 −0.261869
\(452\) −18.0135 −0.847285
\(453\) 33.0771 1.55410
\(454\) −11.1150 −0.521651
\(455\) −36.3184 −1.70263
\(456\) −11.2516 −0.526903
\(457\) 14.5478 0.680519 0.340259 0.940332i \(-0.389485\pi\)
0.340259 + 0.940332i \(0.389485\pi\)
\(458\) −25.1307 −1.17428
\(459\) −7.51240 −0.350649
\(460\) 9.51831 0.443794
\(461\) 25.1335 1.17058 0.585291 0.810823i \(-0.300980\pi\)
0.585291 + 0.810823i \(0.300980\pi\)
\(462\) 3.29878 0.153473
\(463\) −11.4002 −0.529812 −0.264906 0.964274i \(-0.585341\pi\)
−0.264906 + 0.964274i \(0.585341\pi\)
\(464\) 0.634230 0.0294434
\(465\) −51.3416 −2.38091
\(466\) −8.50901 −0.394172
\(467\) 9.45646 0.437593 0.218796 0.975771i \(-0.429787\pi\)
0.218796 + 0.975771i \(0.429787\pi\)
\(468\) 12.3736 0.571972
\(469\) 17.0172 0.785783
\(470\) 17.5649 0.810207
\(471\) 3.84973 0.177386
\(472\) 15.1544 0.697539
\(473\) 1.21278 0.0557637
\(474\) 9.55479 0.438866
\(475\) −67.5514 −3.09947
\(476\) 5.59957 0.256656
\(477\) −11.4982 −0.526466
\(478\) 18.9076 0.864811
\(479\) −28.4335 −1.29916 −0.649580 0.760294i \(-0.725055\pi\)
−0.649580 + 0.760294i \(0.725055\pi\)
\(480\) −9.77913 −0.446354
\(481\) 16.8697 0.769194
\(482\) 1.93068 0.0879400
\(483\) −7.27851 −0.331184
\(484\) 1.00000 0.0454545
\(485\) 7.10382 0.322568
\(486\) −18.7206 −0.849184
\(487\) −10.1848 −0.461516 −0.230758 0.973011i \(-0.574121\pi\)
−0.230758 + 0.973011i \(0.574121\pi\)
\(488\) 12.8293 0.580755
\(489\) −51.5562 −2.33145
\(490\) 21.0622 0.951492
\(491\) 20.8722 0.941951 0.470975 0.882146i \(-0.343902\pi\)
0.470975 + 0.882146i \(0.343902\pi\)
\(492\) −12.6067 −0.568355
\(493\) 2.44050 0.109914
\(494\) −28.7155 −1.29197
\(495\) −9.22647 −0.414699
\(496\) 5.25012 0.235737
\(497\) 7.15993 0.321167
\(498\) −10.4096 −0.466464
\(499\) 25.4661 1.14002 0.570010 0.821638i \(-0.306939\pi\)
0.570010 + 0.821638i \(0.306939\pi\)
\(500\) −37.1418 −1.66103
\(501\) 2.69941 0.120601
\(502\) 8.94751 0.399347
\(503\) −23.8748 −1.06453 −0.532263 0.846579i \(-0.678658\pi\)
−0.532263 + 0.846579i \(0.678658\pi\)
\(504\) 3.11235 0.138635
\(505\) −9.16077 −0.407649
\(506\) −2.20643 −0.0980876
\(507\) 46.4049 2.06091
\(508\) 12.4888 0.554100
\(509\) −10.8474 −0.480801 −0.240401 0.970674i \(-0.577279\pi\)
−0.240401 + 0.970674i \(0.577279\pi\)
\(510\) −37.6298 −1.66628
\(511\) 24.4052 1.07962
\(512\) 1.00000 0.0441942
\(513\) 9.69014 0.427830
\(514\) −7.42717 −0.327599
\(515\) 29.3782 1.29456
\(516\) 2.74923 0.121028
\(517\) −4.07168 −0.179072
\(518\) 4.24325 0.186438
\(519\) 39.6233 1.73927
\(520\) −24.9576 −1.09446
\(521\) 0.434079 0.0190174 0.00950868 0.999955i \(-0.496973\pi\)
0.00950868 + 0.999955i \(0.496973\pi\)
\(522\) 1.35647 0.0593713
\(523\) 17.3608 0.759137 0.379568 0.925164i \(-0.376073\pi\)
0.379568 + 0.925164i \(0.376073\pi\)
\(524\) 3.47476 0.151796
\(525\) 44.8956 1.95940
\(526\) −4.07400 −0.177635
\(527\) 20.2023 0.880027
\(528\) 2.26689 0.0986536
\(529\) −18.1317 −0.788334
\(530\) 23.1919 1.00739
\(531\) 32.4119 1.40656
\(532\) −7.22281 −0.313149
\(533\) −32.1740 −1.39361
\(534\) 14.8853 0.644148
\(535\) −18.0933 −0.782243
\(536\) 11.6941 0.505107
\(537\) −37.7736 −1.63005
\(538\) 12.8855 0.555535
\(539\) −4.88239 −0.210299
\(540\) 8.42204 0.362427
\(541\) −30.1307 −1.29542 −0.647709 0.761887i \(-0.724273\pi\)
−0.647709 + 0.761887i \(0.724273\pi\)
\(542\) −1.31221 −0.0563641
\(543\) −54.5041 −2.33899
\(544\) 3.84797 0.164980
\(545\) −45.1605 −1.93446
\(546\) 19.0847 0.816750
\(547\) −17.1020 −0.731227 −0.365614 0.930767i \(-0.619141\pi\)
−0.365614 + 0.930767i \(0.619141\pi\)
\(548\) −4.01709 −0.171602
\(549\) 27.4390 1.17107
\(550\) 13.6098 0.580323
\(551\) −3.14797 −0.134108
\(552\) −5.00172 −0.212887
\(553\) 6.13359 0.260827
\(554\) 4.52523 0.192259
\(555\) −28.5152 −1.21040
\(556\) −5.28021 −0.223931
\(557\) −15.0213 −0.636475 −0.318237 0.948011i \(-0.603091\pi\)
−0.318237 + 0.948011i \(0.603091\pi\)
\(558\) 11.2288 0.475354
\(559\) 7.01641 0.296762
\(560\) −6.27760 −0.265277
\(561\) 8.72291 0.368282
\(562\) −30.2456 −1.27583
\(563\) 4.90766 0.206833 0.103417 0.994638i \(-0.467023\pi\)
0.103417 + 0.994638i \(0.467023\pi\)
\(564\) −9.23005 −0.388655
\(565\) 77.7087 3.26923
\(566\) 9.95702 0.418525
\(567\) −15.7772 −0.662582
\(568\) 4.92023 0.206448
\(569\) 20.6479 0.865605 0.432803 0.901489i \(-0.357525\pi\)
0.432803 + 0.901489i \(0.357525\pi\)
\(570\) 48.5382 2.03304
\(571\) −24.0233 −1.00535 −0.502673 0.864477i \(-0.667650\pi\)
−0.502673 + 0.864477i \(0.667650\pi\)
\(572\) 5.78539 0.241899
\(573\) 37.8586 1.58157
\(574\) −8.09274 −0.337785
\(575\) −30.0290 −1.25229
\(576\) 2.13877 0.0891156
\(577\) 2.40841 0.100264 0.0501318 0.998743i \(-0.484036\pi\)
0.0501318 + 0.998743i \(0.484036\pi\)
\(578\) −2.19312 −0.0912216
\(579\) −8.86038 −0.368225
\(580\) −2.73601 −0.113606
\(581\) −6.68230 −0.277229
\(582\) −3.73294 −0.154735
\(583\) −5.37607 −0.222654
\(584\) 16.7710 0.693988
\(585\) −53.3787 −2.20694
\(586\) −0.204412 −0.00844419
\(587\) 43.6735 1.80260 0.901298 0.433199i \(-0.142615\pi\)
0.901298 + 0.433199i \(0.142615\pi\)
\(588\) −11.0678 −0.456429
\(589\) −26.0587 −1.07373
\(590\) −65.3748 −2.69144
\(591\) 2.26689 0.0932472
\(592\) 2.91592 0.119844
\(593\) −45.1466 −1.85395 −0.926974 0.375126i \(-0.877599\pi\)
−0.926974 + 0.375126i \(0.877599\pi\)
\(594\) −1.95230 −0.0801039
\(595\) −24.1560 −0.990300
\(596\) 2.22890 0.0912992
\(597\) −13.6307 −0.557869
\(598\) −12.7650 −0.522001
\(599\) 32.3828 1.32313 0.661563 0.749890i \(-0.269894\pi\)
0.661563 + 0.749890i \(0.269894\pi\)
\(600\) 30.8518 1.25952
\(601\) 10.2594 0.418490 0.209245 0.977863i \(-0.432899\pi\)
0.209245 + 0.977863i \(0.432899\pi\)
\(602\) 1.76484 0.0719294
\(603\) 25.0110 1.01853
\(604\) 14.5914 0.593716
\(605\) −4.31390 −0.175385
\(606\) 4.81384 0.195549
\(607\) 9.92230 0.402734 0.201367 0.979516i \(-0.435462\pi\)
0.201367 + 0.979516i \(0.435462\pi\)
\(608\) −4.96345 −0.201294
\(609\) 2.09218 0.0847795
\(610\) −55.3443 −2.24083
\(611\) −23.5563 −0.952986
\(612\) 8.22994 0.332676
\(613\) 41.2583 1.66641 0.833204 0.552966i \(-0.186504\pi\)
0.833204 + 0.552966i \(0.186504\pi\)
\(614\) 5.99190 0.241813
\(615\) 54.3842 2.19298
\(616\) 1.45520 0.0586317
\(617\) 8.35400 0.336319 0.168160 0.985760i \(-0.446218\pi\)
0.168160 + 0.985760i \(0.446218\pi\)
\(618\) −15.4378 −0.620998
\(619\) 46.5618 1.87148 0.935739 0.352694i \(-0.114734\pi\)
0.935739 + 0.352694i \(0.114734\pi\)
\(620\) −22.6485 −0.909587
\(621\) 4.30761 0.172858
\(622\) 29.6779 1.18998
\(623\) 9.55542 0.382830
\(624\) 13.1148 0.525013
\(625\) 92.1771 3.68708
\(626\) −2.08952 −0.0835139
\(627\) −11.2516 −0.449344
\(628\) 1.69825 0.0677674
\(629\) 11.2204 0.447386
\(630\) −13.4264 −0.534919
\(631\) 13.1496 0.523477 0.261738 0.965139i \(-0.415704\pi\)
0.261738 + 0.965139i \(0.415704\pi\)
\(632\) 4.21494 0.167661
\(633\) −26.2037 −1.04151
\(634\) 30.7875 1.22273
\(635\) −53.8754 −2.13798
\(636\) −12.1869 −0.483244
\(637\) −28.2465 −1.11917
\(638\) 0.634230 0.0251094
\(639\) 10.5233 0.416294
\(640\) −4.31390 −0.170522
\(641\) −43.3331 −1.71155 −0.855777 0.517346i \(-0.826920\pi\)
−0.855777 + 0.517346i \(0.826920\pi\)
\(642\) 9.50775 0.375241
\(643\) 35.5339 1.40132 0.700660 0.713496i \(-0.252889\pi\)
0.700660 + 0.713496i \(0.252889\pi\)
\(644\) −3.21079 −0.126523
\(645\) −11.8599 −0.466984
\(646\) −19.0992 −0.751448
\(647\) 1.39887 0.0549952 0.0274976 0.999622i \(-0.491246\pi\)
0.0274976 + 0.999622i \(0.491246\pi\)
\(648\) −10.8420 −0.425913
\(649\) 15.1544 0.594863
\(650\) 78.7379 3.08835
\(651\) 17.3190 0.678784
\(652\) −22.7432 −0.890691
\(653\) −45.6792 −1.78756 −0.893782 0.448502i \(-0.851958\pi\)
−0.893782 + 0.448502i \(0.851958\pi\)
\(654\) 23.7311 0.927960
\(655\) −14.9898 −0.585700
\(656\) −5.56125 −0.217130
\(657\) 35.8694 1.39940
\(658\) −5.92512 −0.230985
\(659\) −16.8162 −0.655064 −0.327532 0.944840i \(-0.606217\pi\)
−0.327532 + 0.944840i \(0.606217\pi\)
\(660\) −9.77913 −0.380652
\(661\) −5.46832 −0.212693 −0.106347 0.994329i \(-0.533915\pi\)
−0.106347 + 0.994329i \(0.533915\pi\)
\(662\) −25.5382 −0.992570
\(663\) 50.4655 1.95992
\(664\) −4.59201 −0.178205
\(665\) 31.1585 1.20828
\(666\) 6.23649 0.241659
\(667\) −1.39938 −0.0541843
\(668\) 1.19080 0.0460735
\(669\) −48.3210 −1.86820
\(670\) −50.4471 −1.94894
\(671\) 12.8293 0.495269
\(672\) 3.29878 0.127253
\(673\) 40.1697 1.54843 0.774214 0.632923i \(-0.218145\pi\)
0.774214 + 0.632923i \(0.218145\pi\)
\(674\) −0.00855933 −0.000329693 0
\(675\) −26.5704 −1.02269
\(676\) 20.4708 0.787337
\(677\) −29.6833 −1.14082 −0.570411 0.821359i \(-0.693216\pi\)
−0.570411 + 0.821359i \(0.693216\pi\)
\(678\) −40.8346 −1.56824
\(679\) −2.39632 −0.0919622
\(680\) −16.5998 −0.636573
\(681\) −25.1963 −0.965526
\(682\) 5.25012 0.201038
\(683\) −23.5916 −0.902707 −0.451354 0.892345i \(-0.649059\pi\)
−0.451354 + 0.892345i \(0.649059\pi\)
\(684\) −10.6157 −0.405901
\(685\) 17.3293 0.662120
\(686\) −17.2913 −0.660184
\(687\) −56.9685 −2.17348
\(688\) 1.21278 0.0462368
\(689\) −31.1027 −1.18492
\(690\) 21.5769 0.821420
\(691\) −28.6987 −1.09175 −0.545874 0.837867i \(-0.683802\pi\)
−0.545874 + 0.837867i \(0.683802\pi\)
\(692\) 17.4792 0.664458
\(693\) 3.11235 0.118228
\(694\) −25.4319 −0.965380
\(695\) 22.7783 0.864031
\(696\) 1.43773 0.0544969
\(697\) −21.3995 −0.810566
\(698\) 4.87428 0.184494
\(699\) −19.2890 −0.729575
\(700\) 19.8050 0.748557
\(701\) −37.6729 −1.42288 −0.711442 0.702745i \(-0.751958\pi\)
−0.711442 + 0.702745i \(0.751958\pi\)
\(702\) −11.2948 −0.426296
\(703\) −14.4730 −0.545860
\(704\) 1.00000 0.0376889
\(705\) 39.8175 1.49962
\(706\) −13.5161 −0.508686
\(707\) 3.09019 0.116218
\(708\) 34.3534 1.29108
\(709\) −45.2100 −1.69790 −0.848949 0.528475i \(-0.822764\pi\)
−0.848949 + 0.528475i \(0.822764\pi\)
\(710\) −21.2254 −0.796576
\(711\) 9.01481 0.338082
\(712\) 6.56639 0.246086
\(713\) −11.5840 −0.433825
\(714\) 12.6936 0.475046
\(715\) −24.9576 −0.933362
\(716\) −16.6632 −0.622733
\(717\) 42.8613 1.60068
\(718\) 17.8409 0.665816
\(719\) 5.75749 0.214718 0.107359 0.994220i \(-0.465761\pi\)
0.107359 + 0.994220i \(0.465761\pi\)
\(720\) −9.22647 −0.343850
\(721\) −9.91009 −0.369071
\(722\) 5.63581 0.209743
\(723\) 4.37663 0.162769
\(724\) −24.0436 −0.893573
\(725\) 8.63172 0.320574
\(726\) 2.26689 0.0841320
\(727\) 30.2814 1.12308 0.561538 0.827451i \(-0.310210\pi\)
0.561538 + 0.827451i \(0.310210\pi\)
\(728\) 8.41891 0.312025
\(729\) −9.91159 −0.367096
\(730\) −72.3485 −2.67774
\(731\) 4.66674 0.172606
\(732\) 29.0825 1.07492
\(733\) 24.4091 0.901572 0.450786 0.892632i \(-0.351144\pi\)
0.450786 + 0.892632i \(0.351144\pi\)
\(734\) −0.856582 −0.0316170
\(735\) 47.7455 1.76112
\(736\) −2.20643 −0.0813300
\(737\) 11.6941 0.430757
\(738\) −11.8943 −0.437834
\(739\) −48.9157 −1.79939 −0.899696 0.436517i \(-0.856212\pi\)
−0.899696 + 0.436517i \(0.856212\pi\)
\(740\) −12.5790 −0.462413
\(741\) −65.0947 −2.39132
\(742\) −7.82326 −0.287201
\(743\) −31.3745 −1.15102 −0.575510 0.817795i \(-0.695196\pi\)
−0.575510 + 0.817795i \(0.695196\pi\)
\(744\) 11.9014 0.436328
\(745\) −9.61526 −0.352276
\(746\) −21.9814 −0.804796
\(747\) −9.82128 −0.359342
\(748\) 3.84797 0.140696
\(749\) 6.10339 0.223013
\(750\) −84.1961 −3.07441
\(751\) 7.64485 0.278965 0.139482 0.990225i \(-0.455456\pi\)
0.139482 + 0.990225i \(0.455456\pi\)
\(752\) −4.07168 −0.148479
\(753\) 20.2830 0.739153
\(754\) 3.66927 0.133627
\(755\) −62.9459 −2.29084
\(756\) −2.84099 −0.103326
\(757\) 31.3139 1.13812 0.569062 0.822295i \(-0.307306\pi\)
0.569062 + 0.822295i \(0.307306\pi\)
\(758\) −10.5077 −0.381657
\(759\) −5.00172 −0.181551
\(760\) 21.4118 0.776689
\(761\) −32.4940 −1.17791 −0.588953 0.808167i \(-0.700460\pi\)
−0.588953 + 0.808167i \(0.700460\pi\)
\(762\) 28.3106 1.02559
\(763\) 15.2339 0.551504
\(764\) 16.7007 0.604210
\(765\) −35.5032 −1.28362
\(766\) −29.0826 −1.05080
\(767\) 87.6743 3.16574
\(768\) 2.26689 0.0817992
\(769\) 19.8357 0.715292 0.357646 0.933857i \(-0.383579\pi\)
0.357646 + 0.933857i \(0.383579\pi\)
\(770\) −6.27760 −0.226229
\(771\) −16.8366 −0.606354
\(772\) −3.90861 −0.140674
\(773\) 43.3541 1.55934 0.779669 0.626192i \(-0.215387\pi\)
0.779669 + 0.626192i \(0.215387\pi\)
\(774\) 2.59386 0.0932344
\(775\) 71.4530 2.56667
\(776\) −1.64673 −0.0591140
\(777\) 9.61896 0.345078
\(778\) −12.5211 −0.448904
\(779\) 27.6030 0.988980
\(780\) −56.5761 −2.02575
\(781\) 4.92023 0.176060
\(782\) −8.49027 −0.303611
\(783\) −1.23821 −0.0442499
\(784\) −4.88239 −0.174371
\(785\) −7.32607 −0.261479
\(786\) 7.87689 0.280959
\(787\) 47.1570 1.68097 0.840484 0.541837i \(-0.182271\pi\)
0.840484 + 0.541837i \(0.182271\pi\)
\(788\) 1.00000 0.0356235
\(789\) −9.23530 −0.328785
\(790\) −18.1829 −0.646917
\(791\) −26.2133 −0.932038
\(792\) 2.13877 0.0759980
\(793\) 74.2225 2.63572
\(794\) −1.48312 −0.0526338
\(795\) 52.5733 1.86458
\(796\) −6.01298 −0.213124
\(797\) 34.9366 1.23752 0.618759 0.785581i \(-0.287636\pi\)
0.618759 + 0.785581i \(0.287636\pi\)
\(798\) −16.3733 −0.579609
\(799\) −15.6677 −0.554284
\(800\) 13.6098 0.481178
\(801\) 14.0440 0.496221
\(802\) −20.3461 −0.718446
\(803\) 16.7710 0.591835
\(804\) 26.5091 0.934905
\(805\) 13.8511 0.488186
\(806\) 30.3740 1.06988
\(807\) 29.2101 1.02824
\(808\) 2.12355 0.0747061
\(809\) 27.7986 0.977348 0.488674 0.872467i \(-0.337481\pi\)
0.488674 + 0.872467i \(0.337481\pi\)
\(810\) 46.7712 1.64337
\(811\) 26.8405 0.942496 0.471248 0.882001i \(-0.343804\pi\)
0.471248 + 0.882001i \(0.343804\pi\)
\(812\) 0.922932 0.0323886
\(813\) −2.97462 −0.104325
\(814\) 2.91592 0.102203
\(815\) 98.1119 3.43671
\(816\) 8.72291 0.305363
\(817\) −6.01957 −0.210598
\(818\) −33.7304 −1.17935
\(819\) 18.0061 0.629186
\(820\) 23.9907 0.837792
\(821\) 52.7522 1.84106 0.920531 0.390668i \(-0.127756\pi\)
0.920531 + 0.390668i \(0.127756\pi\)
\(822\) −9.10629 −0.317618
\(823\) 48.4851 1.69008 0.845042 0.534700i \(-0.179575\pi\)
0.845042 + 0.534700i \(0.179575\pi\)
\(824\) −6.81012 −0.237242
\(825\) 30.8518 1.07412
\(826\) 22.0527 0.767313
\(827\) −9.75721 −0.339292 −0.169646 0.985505i \(-0.554262\pi\)
−0.169646 + 0.985505i \(0.554262\pi\)
\(828\) −4.71905 −0.163998
\(829\) 53.5979 1.86153 0.930766 0.365615i \(-0.119141\pi\)
0.930766 + 0.365615i \(0.119141\pi\)
\(830\) 19.8095 0.687598
\(831\) 10.2582 0.355853
\(832\) 5.78539 0.200572
\(833\) −18.7873 −0.650941
\(834\) −11.9696 −0.414475
\(835\) −5.13701 −0.177773
\(836\) −4.96345 −0.171664
\(837\) −10.2498 −0.354286
\(838\) −13.6430 −0.471290
\(839\) 36.7945 1.27029 0.635143 0.772394i \(-0.280941\pi\)
0.635143 + 0.772394i \(0.280941\pi\)
\(840\) −14.2306 −0.491002
\(841\) −28.5978 −0.986129
\(842\) 1.96082 0.0675743
\(843\) −68.5634 −2.36145
\(844\) −11.5594 −0.397889
\(845\) −88.3089 −3.03792
\(846\) −8.70841 −0.299401
\(847\) 1.45520 0.0500013
\(848\) −5.37607 −0.184615
\(849\) 22.5714 0.774650
\(850\) 52.3700 1.79628
\(851\) −6.43376 −0.220547
\(852\) 11.1536 0.382116
\(853\) −0.761804 −0.0260837 −0.0130418 0.999915i \(-0.504151\pi\)
−0.0130418 + 0.999915i \(0.504151\pi\)
\(854\) 18.6692 0.638847
\(855\) 45.7951 1.56616
\(856\) 4.19419 0.143354
\(857\) 10.8886 0.371948 0.185974 0.982555i \(-0.440456\pi\)
0.185974 + 0.982555i \(0.440456\pi\)
\(858\) 13.1148 0.447733
\(859\) 28.6007 0.975844 0.487922 0.872887i \(-0.337755\pi\)
0.487922 + 0.872887i \(0.337755\pi\)
\(860\) −5.23182 −0.178403
\(861\) −18.3453 −0.625207
\(862\) −39.2100 −1.33550
\(863\) −3.78122 −0.128714 −0.0643572 0.997927i \(-0.520500\pi\)
−0.0643572 + 0.997927i \(0.520500\pi\)
\(864\) −1.95230 −0.0664186
\(865\) −75.4034 −2.56379
\(866\) 1.79869 0.0611220
\(867\) −4.97155 −0.168843
\(868\) 7.63998 0.259318
\(869\) 4.21494 0.142982
\(870\) −6.20222 −0.210275
\(871\) 67.6548 2.29240
\(872\) 10.4686 0.354511
\(873\) −3.52197 −0.119201
\(874\) 10.9515 0.370439
\(875\) −54.0487 −1.82718
\(876\) 38.0179 1.28451
\(877\) 28.8019 0.972570 0.486285 0.873800i \(-0.338352\pi\)
0.486285 + 0.873800i \(0.338352\pi\)
\(878\) −18.5939 −0.627514
\(879\) −0.463379 −0.0156294
\(880\) −4.31390 −0.145422
\(881\) −14.1829 −0.477832 −0.238916 0.971040i \(-0.576792\pi\)
−0.238916 + 0.971040i \(0.576792\pi\)
\(882\) −10.4423 −0.351612
\(883\) −25.9406 −0.872972 −0.436486 0.899711i \(-0.643777\pi\)
−0.436486 + 0.899711i \(0.643777\pi\)
\(884\) 22.2620 0.748753
\(885\) −148.197 −4.98159
\(886\) 14.9630 0.502691
\(887\) −1.39317 −0.0467781 −0.0233890 0.999726i \(-0.507446\pi\)
−0.0233890 + 0.999726i \(0.507446\pi\)
\(888\) 6.61006 0.221819
\(889\) 18.1737 0.609525
\(890\) −28.3268 −0.949516
\(891\) −10.8420 −0.363220
\(892\) −21.3160 −0.713713
\(893\) 20.2096 0.676288
\(894\) 5.05266 0.168986
\(895\) 71.8834 2.40280
\(896\) 1.45520 0.0486149
\(897\) −28.9369 −0.966175
\(898\) 4.22845 0.141105
\(899\) 3.32978 0.111054
\(900\) 29.1082 0.970275
\(901\) −20.6870 −0.689183
\(902\) −5.56125 −0.185169
\(903\) 4.00069 0.133135
\(904\) −18.0135 −0.599121
\(905\) 103.722 3.44783
\(906\) 33.0771 1.09891
\(907\) 20.3460 0.675578 0.337789 0.941222i \(-0.390321\pi\)
0.337789 + 0.941222i \(0.390321\pi\)
\(908\) −11.1150 −0.368863
\(909\) 4.54178 0.150641
\(910\) −36.3184 −1.20394
\(911\) −51.3026 −1.69973 −0.849866 0.526999i \(-0.823317\pi\)
−0.849866 + 0.526999i \(0.823317\pi\)
\(912\) −11.2516 −0.372577
\(913\) −4.59201 −0.151973
\(914\) 14.5478 0.481199
\(915\) −125.459 −4.14756
\(916\) −25.1307 −0.830343
\(917\) 5.05648 0.166980
\(918\) −7.51240 −0.247946
\(919\) −31.8043 −1.04913 −0.524563 0.851372i \(-0.675771\pi\)
−0.524563 + 0.851372i \(0.675771\pi\)
\(920\) 9.51831 0.313810
\(921\) 13.5830 0.447574
\(922\) 25.1335 0.827727
\(923\) 28.4655 0.936952
\(924\) 3.29878 0.108522
\(925\) 39.6850 1.30484
\(926\) −11.4002 −0.374633
\(927\) −14.5653 −0.478387
\(928\) 0.634230 0.0208196
\(929\) 27.2976 0.895606 0.447803 0.894132i \(-0.352207\pi\)
0.447803 + 0.894132i \(0.352207\pi\)
\(930\) −51.3416 −1.68356
\(931\) 24.2335 0.794220
\(932\) −8.50901 −0.278722
\(933\) 67.2765 2.20253
\(934\) 9.45646 0.309425
\(935\) −16.5998 −0.542871
\(936\) 12.3736 0.404445
\(937\) −8.70177 −0.284274 −0.142137 0.989847i \(-0.545397\pi\)
−0.142137 + 0.989847i \(0.545397\pi\)
\(938\) 17.0172 0.555632
\(939\) −4.73670 −0.154576
\(940\) 17.5649 0.572903
\(941\) 27.1491 0.885036 0.442518 0.896760i \(-0.354085\pi\)
0.442518 + 0.896760i \(0.354085\pi\)
\(942\) 3.84973 0.125431
\(943\) 12.2705 0.399582
\(944\) 15.1544 0.493235
\(945\) 12.2558 0.398680
\(946\) 1.21278 0.0394309
\(947\) 4.20252 0.136564 0.0682818 0.997666i \(-0.478248\pi\)
0.0682818 + 0.997666i \(0.478248\pi\)
\(948\) 9.55479 0.310325
\(949\) 97.0267 3.14962
\(950\) −67.5514 −2.19166
\(951\) 69.7917 2.26315
\(952\) 5.59957 0.181483
\(953\) −14.9812 −0.485290 −0.242645 0.970115i \(-0.578015\pi\)
−0.242645 + 0.970115i \(0.578015\pi\)
\(954\) −11.4982 −0.372268
\(955\) −72.0453 −2.33133
\(956\) 18.9076 0.611514
\(957\) 1.43773 0.0464751
\(958\) −28.4335 −0.918644
\(959\) −5.84567 −0.188767
\(960\) −9.77913 −0.315620
\(961\) −3.43622 −0.110846
\(962\) 16.8697 0.543902
\(963\) 8.97043 0.289068
\(964\) 1.93068 0.0621830
\(965\) 16.8614 0.542787
\(966\) −7.27851 −0.234182
\(967\) 35.7060 1.14823 0.574114 0.818776i \(-0.305347\pi\)
0.574114 + 0.818776i \(0.305347\pi\)
\(968\) 1.00000 0.0321412
\(969\) −43.2957 −1.39086
\(970\) 7.10382 0.228090
\(971\) −43.2921 −1.38931 −0.694655 0.719343i \(-0.744443\pi\)
−0.694655 + 0.719343i \(0.744443\pi\)
\(972\) −18.7206 −0.600464
\(973\) −7.68377 −0.246330
\(974\) −10.1848 −0.326341
\(975\) 178.490 5.71625
\(976\) 12.8293 0.410656
\(977\) 18.7437 0.599664 0.299832 0.953992i \(-0.403069\pi\)
0.299832 + 0.953992i \(0.403069\pi\)
\(978\) −51.5562 −1.64859
\(979\) 6.56639 0.209863
\(980\) 21.0622 0.672806
\(981\) 22.3899 0.714856
\(982\) 20.8722 0.666060
\(983\) 18.4010 0.586900 0.293450 0.955974i \(-0.405197\pi\)
0.293450 + 0.955974i \(0.405197\pi\)
\(984\) −12.6067 −0.401888
\(985\) −4.31390 −0.137452
\(986\) 2.44050 0.0777213
\(987\) −13.4316 −0.427532
\(988\) −28.7155 −0.913561
\(989\) −2.67591 −0.0850890
\(990\) −9.22647 −0.293236
\(991\) −0.361599 −0.0114866 −0.00574329 0.999984i \(-0.501828\pi\)
−0.00574329 + 0.999984i \(0.501828\pi\)
\(992\) 5.25012 0.166692
\(993\) −57.8922 −1.83715
\(994\) 7.15993 0.227099
\(995\) 25.9394 0.822334
\(996\) −10.4096 −0.329840
\(997\) −61.1462 −1.93652 −0.968260 0.249944i \(-0.919588\pi\)
−0.968260 + 0.249944i \(0.919588\pi\)
\(998\) 25.4661 0.806116
\(999\) −5.69275 −0.180111
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 4334.2.a.g.1.20 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.g.1.20 26 1.1 even 1 trivial