Properties

Label 8018.2.a.g.1.7
Level $8018$
Weight $2$
Character 8018.1
Self dual yes
Analytic conductor $64.024$
Analytic rank $1$
Dimension $34$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, 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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.37210 q^{3} +1.00000 q^{4} -2.30761 q^{5} +2.37210 q^{6} +0.129234 q^{7} -1.00000 q^{8} +2.62686 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.37210 q^{3} +1.00000 q^{4} -2.30761 q^{5} +2.37210 q^{6} +0.129234 q^{7} -1.00000 q^{8} +2.62686 q^{9} +2.30761 q^{10} +5.58164 q^{11} -2.37210 q^{12} +2.97992 q^{13} -0.129234 q^{14} +5.47389 q^{15} +1.00000 q^{16} -0.801585 q^{17} -2.62686 q^{18} +1.00000 q^{19} -2.30761 q^{20} -0.306555 q^{21} -5.58164 q^{22} -0.622860 q^{23} +2.37210 q^{24} +0.325080 q^{25} -2.97992 q^{26} +0.885125 q^{27} +0.129234 q^{28} -2.21051 q^{29} -5.47389 q^{30} +1.01037 q^{31} -1.00000 q^{32} -13.2402 q^{33} +0.801585 q^{34} -0.298221 q^{35} +2.62686 q^{36} -5.12381 q^{37} -1.00000 q^{38} -7.06866 q^{39} +2.30761 q^{40} -10.1635 q^{41} +0.306555 q^{42} -2.32824 q^{43} +5.58164 q^{44} -6.06178 q^{45} +0.622860 q^{46} +11.3413 q^{47} -2.37210 q^{48} -6.98330 q^{49} -0.325080 q^{50} +1.90144 q^{51} +2.97992 q^{52} -2.55489 q^{53} -0.885125 q^{54} -12.8803 q^{55} -0.129234 q^{56} -2.37210 q^{57} +2.21051 q^{58} +8.14745 q^{59} +5.47389 q^{60} -12.4457 q^{61} -1.01037 q^{62} +0.339479 q^{63} +1.00000 q^{64} -6.87650 q^{65} +13.2402 q^{66} +3.73408 q^{67} -0.801585 q^{68} +1.47749 q^{69} +0.298221 q^{70} +4.94171 q^{71} -2.62686 q^{72} +0.583139 q^{73} +5.12381 q^{74} -0.771123 q^{75} +1.00000 q^{76} +0.721336 q^{77} +7.06866 q^{78} -2.00030 q^{79} -2.30761 q^{80} -9.98019 q^{81} +10.1635 q^{82} -17.2842 q^{83} -0.306555 q^{84} +1.84975 q^{85} +2.32824 q^{86} +5.24354 q^{87} -5.58164 q^{88} +13.0624 q^{89} +6.06178 q^{90} +0.385106 q^{91} -0.622860 q^{92} -2.39669 q^{93} -11.3413 q^{94} -2.30761 q^{95} +2.37210 q^{96} +1.54557 q^{97} +6.98330 q^{98} +14.6622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(3\) −2.37210 −1.36953 −0.684766 0.728763i \(-0.740096\pi\)
−0.684766 + 0.728763i \(0.740096\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.30761 −1.03200 −0.515998 0.856590i \(-0.672579\pi\)
−0.515998 + 0.856590i \(0.672579\pi\)
\(6\) 2.37210 0.968406
\(7\) 0.129234 0.0488457 0.0244229 0.999702i \(-0.492225\pi\)
0.0244229 + 0.999702i \(0.492225\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.62686 0.875620
\(10\) 2.30761 0.729731
\(11\) 5.58164 1.68293 0.841464 0.540312i \(-0.181694\pi\)
0.841464 + 0.540312i \(0.181694\pi\)
\(12\) −2.37210 −0.684766
\(13\) 2.97992 0.826480 0.413240 0.910622i \(-0.364397\pi\)
0.413240 + 0.910622i \(0.364397\pi\)
\(14\) −0.129234 −0.0345391
\(15\) 5.47389 1.41335
\(16\) 1.00000 0.250000
\(17\) −0.801585 −0.194413 −0.0972065 0.995264i \(-0.530991\pi\)
−0.0972065 + 0.995264i \(0.530991\pi\)
\(18\) −2.62686 −0.619157
\(19\) 1.00000 0.229416
\(20\) −2.30761 −0.515998
\(21\) −0.306555 −0.0668958
\(22\) −5.58164 −1.19001
\(23\) −0.622860 −0.129875 −0.0649376 0.997889i \(-0.520685\pi\)
−0.0649376 + 0.997889i \(0.520685\pi\)
\(24\) 2.37210 0.484203
\(25\) 0.325080 0.0650161
\(26\) −2.97992 −0.584410
\(27\) 0.885125 0.170342
\(28\) 0.129234 0.0244229
\(29\) −2.21051 −0.410481 −0.205240 0.978712i \(-0.565798\pi\)
−0.205240 + 0.978712i \(0.565798\pi\)
\(30\) −5.47389 −0.999391
\(31\) 1.01037 0.181467 0.0907337 0.995875i \(-0.471079\pi\)
0.0907337 + 0.995875i \(0.471079\pi\)
\(32\) −1.00000 −0.176777
\(33\) −13.2402 −2.30483
\(34\) 0.801585 0.137471
\(35\) −0.298221 −0.0504086
\(36\) 2.62686 0.437810
\(37\) −5.12381 −0.842350 −0.421175 0.906979i \(-0.638382\pi\)
−0.421175 + 0.906979i \(0.638382\pi\)
\(38\) −1.00000 −0.162221
\(39\) −7.06866 −1.13189
\(40\) 2.30761 0.364866
\(41\) −10.1635 −1.58728 −0.793638 0.608390i \(-0.791816\pi\)
−0.793638 + 0.608390i \(0.791816\pi\)
\(42\) 0.306555 0.0473025
\(43\) −2.32824 −0.355054 −0.177527 0.984116i \(-0.556810\pi\)
−0.177527 + 0.984116i \(0.556810\pi\)
\(44\) 5.58164 0.841464
\(45\) −6.06178 −0.903637
\(46\) 0.622860 0.0918357
\(47\) 11.3413 1.65430 0.827150 0.561981i \(-0.189961\pi\)
0.827150 + 0.561981i \(0.189961\pi\)
\(48\) −2.37210 −0.342383
\(49\) −6.98330 −0.997614
\(50\) −0.325080 −0.0459733
\(51\) 1.90144 0.266255
\(52\) 2.97992 0.413240
\(53\) −2.55489 −0.350942 −0.175471 0.984485i \(-0.556145\pi\)
−0.175471 + 0.984485i \(0.556145\pi\)
\(54\) −0.885125 −0.120450
\(55\) −12.8803 −1.73678
\(56\) −0.129234 −0.0172696
\(57\) −2.37210 −0.314192
\(58\) 2.21051 0.290254
\(59\) 8.14745 1.06071 0.530354 0.847776i \(-0.322059\pi\)
0.530354 + 0.847776i \(0.322059\pi\)
\(60\) 5.47389 0.706676
\(61\) −12.4457 −1.59351 −0.796756 0.604301i \(-0.793453\pi\)
−0.796756 + 0.604301i \(0.793453\pi\)
\(62\) −1.01037 −0.128317
\(63\) 0.339479 0.0427703
\(64\) 1.00000 0.125000
\(65\) −6.87650 −0.852925
\(66\) 13.2402 1.62976
\(67\) 3.73408 0.456191 0.228095 0.973639i \(-0.426750\pi\)
0.228095 + 0.973639i \(0.426750\pi\)
\(68\) −0.801585 −0.0972065
\(69\) 1.47749 0.177868
\(70\) 0.298221 0.0356443
\(71\) 4.94171 0.586473 0.293237 0.956040i \(-0.405268\pi\)
0.293237 + 0.956040i \(0.405268\pi\)
\(72\) −2.62686 −0.309578
\(73\) 0.583139 0.0682513 0.0341256 0.999418i \(-0.489135\pi\)
0.0341256 + 0.999418i \(0.489135\pi\)
\(74\) 5.12381 0.595631
\(75\) −0.771123 −0.0890416
\(76\) 1.00000 0.114708
\(77\) 0.721336 0.0822039
\(78\) 7.06866 0.800369
\(79\) −2.00030 −0.225051 −0.112525 0.993649i \(-0.535894\pi\)
−0.112525 + 0.993649i \(0.535894\pi\)
\(80\) −2.30761 −0.257999
\(81\) −9.98019 −1.10891
\(82\) 10.1635 1.12237
\(83\) −17.2842 −1.89719 −0.948594 0.316496i \(-0.897494\pi\)
−0.948594 + 0.316496i \(0.897494\pi\)
\(84\) −0.306555 −0.0334479
\(85\) 1.84975 0.200633
\(86\) 2.32824 0.251061
\(87\) 5.24354 0.562167
\(88\) −5.58164 −0.595005
\(89\) 13.0624 1.38462 0.692308 0.721602i \(-0.256594\pi\)
0.692308 + 0.721602i \(0.256594\pi\)
\(90\) 6.06178 0.638968
\(91\) 0.385106 0.0403700
\(92\) −0.622860 −0.0649376
\(93\) −2.39669 −0.248526
\(94\) −11.3413 −1.16977
\(95\) −2.30761 −0.236756
\(96\) 2.37210 0.242101
\(97\) 1.54557 0.156929 0.0784645 0.996917i \(-0.474998\pi\)
0.0784645 + 0.996917i \(0.474998\pi\)
\(98\) 6.98330 0.705420
\(99\) 14.6622 1.47361
\(100\) 0.325080 0.0325080
\(101\) 5.15007 0.512451 0.256226 0.966617i \(-0.417521\pi\)
0.256226 + 0.966617i \(0.417521\pi\)
\(102\) −1.90144 −0.188271
\(103\) 10.8934 1.07335 0.536677 0.843788i \(-0.319679\pi\)
0.536677 + 0.843788i \(0.319679\pi\)
\(104\) −2.97992 −0.292205
\(105\) 0.707411 0.0690362
\(106\) 2.55489 0.248153
\(107\) −15.6812 −1.51596 −0.757980 0.652278i \(-0.773814\pi\)
−0.757980 + 0.652278i \(0.773814\pi\)
\(108\) 0.885125 0.0851712
\(109\) 1.52087 0.145672 0.0728362 0.997344i \(-0.476795\pi\)
0.0728362 + 0.997344i \(0.476795\pi\)
\(110\) 12.8803 1.22809
\(111\) 12.1542 1.15363
\(112\) 0.129234 0.0122114
\(113\) 9.94313 0.935371 0.467685 0.883895i \(-0.345088\pi\)
0.467685 + 0.883895i \(0.345088\pi\)
\(114\) 2.37210 0.222168
\(115\) 1.43732 0.134031
\(116\) −2.21051 −0.205240
\(117\) 7.82783 0.723683
\(118\) −8.14745 −0.750034
\(119\) −0.103592 −0.00949624
\(120\) −5.47389 −0.499696
\(121\) 20.1547 1.83225
\(122\) 12.4457 1.12678
\(123\) 24.1089 2.17383
\(124\) 1.01037 0.0907337
\(125\) 10.7879 0.964900
\(126\) −0.339479 −0.0302432
\(127\) −11.4861 −1.01923 −0.509614 0.860403i \(-0.670212\pi\)
−0.509614 + 0.860403i \(0.670212\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.52283 0.486258
\(130\) 6.87650 0.603109
\(131\) −17.2685 −1.50876 −0.754378 0.656440i \(-0.772062\pi\)
−0.754378 + 0.656440i \(0.772062\pi\)
\(132\) −13.2402 −1.15241
\(133\) 0.129234 0.0112060
\(134\) −3.73408 −0.322576
\(135\) −2.04253 −0.175793
\(136\) 0.801585 0.0687354
\(137\) 7.83325 0.669240 0.334620 0.942353i \(-0.391392\pi\)
0.334620 + 0.942353i \(0.391392\pi\)
\(138\) −1.47749 −0.125772
\(139\) 19.6350 1.66542 0.832710 0.553709i \(-0.186788\pi\)
0.832710 + 0.553709i \(0.186788\pi\)
\(140\) −0.298221 −0.0252043
\(141\) −26.9027 −2.26562
\(142\) −4.94171 −0.414699
\(143\) 16.6328 1.39091
\(144\) 2.62686 0.218905
\(145\) 5.10099 0.423614
\(146\) −0.583139 −0.0482609
\(147\) 16.5651 1.36627
\(148\) −5.12381 −0.421175
\(149\) 0.281926 0.0230963 0.0115481 0.999933i \(-0.496324\pi\)
0.0115481 + 0.999933i \(0.496324\pi\)
\(150\) 0.771123 0.0629619
\(151\) 5.05857 0.411660 0.205830 0.978588i \(-0.434011\pi\)
0.205830 + 0.978588i \(0.434011\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −2.10565 −0.170232
\(154\) −0.721336 −0.0581269
\(155\) −2.33154 −0.187274
\(156\) −7.06866 −0.565946
\(157\) −14.6778 −1.17142 −0.585708 0.810522i \(-0.699183\pi\)
−0.585708 + 0.810522i \(0.699183\pi\)
\(158\) 2.00030 0.159135
\(159\) 6.06046 0.480626
\(160\) 2.30761 0.182433
\(161\) −0.0804944 −0.00634385
\(162\) 9.98019 0.784117
\(163\) 4.94513 0.387332 0.193666 0.981067i \(-0.437962\pi\)
0.193666 + 0.981067i \(0.437962\pi\)
\(164\) −10.1635 −0.793638
\(165\) 30.5533 2.37857
\(166\) 17.2842 1.34151
\(167\) 0.0773168 0.00598295 0.00299148 0.999996i \(-0.499048\pi\)
0.00299148 + 0.999996i \(0.499048\pi\)
\(168\) 0.306555 0.0236512
\(169\) −4.12009 −0.316930
\(170\) −1.84975 −0.141869
\(171\) 2.62686 0.200881
\(172\) −2.32824 −0.177527
\(173\) 15.0036 1.14070 0.570349 0.821402i \(-0.306808\pi\)
0.570349 + 0.821402i \(0.306808\pi\)
\(174\) −5.24354 −0.397512
\(175\) 0.0420113 0.00317576
\(176\) 5.58164 0.420732
\(177\) −19.3266 −1.45267
\(178\) −13.0624 −0.979072
\(179\) 17.6441 1.31878 0.659392 0.751800i \(-0.270814\pi\)
0.659392 + 0.751800i \(0.270814\pi\)
\(180\) −6.06178 −0.451818
\(181\) 20.5425 1.52691 0.763454 0.645862i \(-0.223502\pi\)
0.763454 + 0.645862i \(0.223502\pi\)
\(182\) −0.385106 −0.0285459
\(183\) 29.5225 2.18237
\(184\) 0.622860 0.0459178
\(185\) 11.8238 0.869302
\(186\) 2.39669 0.175734
\(187\) −4.47416 −0.327183
\(188\) 11.3413 0.827150
\(189\) 0.114388 0.00832049
\(190\) 2.30761 0.167412
\(191\) 3.51326 0.254211 0.127105 0.991889i \(-0.459431\pi\)
0.127105 + 0.991889i \(0.459431\pi\)
\(192\) −2.37210 −0.171192
\(193\) −25.2223 −1.81554 −0.907770 0.419469i \(-0.862216\pi\)
−0.907770 + 0.419469i \(0.862216\pi\)
\(194\) −1.54557 −0.110966
\(195\) 16.3117 1.16811
\(196\) −6.98330 −0.498807
\(197\) −21.7650 −1.55069 −0.775345 0.631538i \(-0.782424\pi\)
−0.775345 + 0.631538i \(0.782424\pi\)
\(198\) −14.6622 −1.04200
\(199\) −12.0030 −0.850869 −0.425435 0.904989i \(-0.639879\pi\)
−0.425435 + 0.904989i \(0.639879\pi\)
\(200\) −0.325080 −0.0229866
\(201\) −8.85762 −0.624768
\(202\) −5.15007 −0.362358
\(203\) −0.285672 −0.0200502
\(204\) 1.90144 0.133127
\(205\) 23.4535 1.63806
\(206\) −10.8934 −0.758976
\(207\) −1.63617 −0.113721
\(208\) 2.97992 0.206620
\(209\) 5.58164 0.386090
\(210\) −0.707411 −0.0488160
\(211\) 1.00000 0.0688428
\(212\) −2.55489 −0.175471
\(213\) −11.7222 −0.803194
\(214\) 15.6812 1.07195
\(215\) 5.37269 0.366414
\(216\) −0.885125 −0.0602251
\(217\) 0.130573 0.00886391
\(218\) −1.52087 −0.103006
\(219\) −1.38326 −0.0934724
\(220\) −12.8803 −0.868388
\(221\) −2.38866 −0.160679
\(222\) −12.1542 −0.815737
\(223\) −21.9021 −1.46667 −0.733337 0.679865i \(-0.762038\pi\)
−0.733337 + 0.679865i \(0.762038\pi\)
\(224\) −0.129234 −0.00863478
\(225\) 0.853941 0.0569294
\(226\) −9.94313 −0.661407
\(227\) −18.3678 −1.21911 −0.609556 0.792743i \(-0.708652\pi\)
−0.609556 + 0.792743i \(0.708652\pi\)
\(228\) −2.37210 −0.157096
\(229\) −25.1732 −1.66349 −0.831745 0.555158i \(-0.812658\pi\)
−0.831745 + 0.555158i \(0.812658\pi\)
\(230\) −1.43732 −0.0947741
\(231\) −1.71108 −0.112581
\(232\) 2.21051 0.145127
\(233\) 11.4777 0.751929 0.375964 0.926634i \(-0.377312\pi\)
0.375964 + 0.926634i \(0.377312\pi\)
\(234\) −7.82783 −0.511721
\(235\) −26.1714 −1.70723
\(236\) 8.14745 0.530354
\(237\) 4.74490 0.308215
\(238\) 0.103592 0.00671486
\(239\) 7.31317 0.473050 0.236525 0.971625i \(-0.423991\pi\)
0.236525 + 0.971625i \(0.423991\pi\)
\(240\) 5.47389 0.353338
\(241\) 24.2493 1.56204 0.781018 0.624508i \(-0.214701\pi\)
0.781018 + 0.624508i \(0.214701\pi\)
\(242\) −20.1547 −1.29560
\(243\) 21.0186 1.34835
\(244\) −12.4457 −0.796756
\(245\) 16.1148 1.02953
\(246\) −24.1089 −1.53713
\(247\) 2.97992 0.189608
\(248\) −1.01037 −0.0641584
\(249\) 40.9999 2.59826
\(250\) −10.7879 −0.682287
\(251\) 9.33387 0.589149 0.294574 0.955629i \(-0.404822\pi\)
0.294574 + 0.955629i \(0.404822\pi\)
\(252\) 0.339479 0.0213851
\(253\) −3.47658 −0.218571
\(254\) 11.4861 0.720703
\(255\) −4.38779 −0.274774
\(256\) 1.00000 0.0625000
\(257\) −11.4864 −0.716500 −0.358250 0.933626i \(-0.616626\pi\)
−0.358250 + 0.933626i \(0.616626\pi\)
\(258\) −5.52283 −0.343836
\(259\) −0.662169 −0.0411452
\(260\) −6.87650 −0.426462
\(261\) −5.80669 −0.359425
\(262\) 17.2685 1.06685
\(263\) 22.6393 1.39600 0.697999 0.716098i \(-0.254074\pi\)
0.697999 + 0.716098i \(0.254074\pi\)
\(264\) 13.2402 0.814879
\(265\) 5.89571 0.362170
\(266\) −0.129234 −0.00792382
\(267\) −30.9854 −1.89628
\(268\) 3.73408 0.228095
\(269\) 12.7878 0.779687 0.389843 0.920881i \(-0.372529\pi\)
0.389843 + 0.920881i \(0.372529\pi\)
\(270\) 2.04253 0.124304
\(271\) −14.2202 −0.863818 −0.431909 0.901917i \(-0.642160\pi\)
−0.431909 + 0.901917i \(0.642160\pi\)
\(272\) −0.801585 −0.0486032
\(273\) −0.913509 −0.0552881
\(274\) −7.83325 −0.473224
\(275\) 1.81448 0.109417
\(276\) 1.47749 0.0889342
\(277\) −1.20237 −0.0722435 −0.0361217 0.999347i \(-0.511500\pi\)
−0.0361217 + 0.999347i \(0.511500\pi\)
\(278\) −19.6350 −1.17763
\(279\) 2.65410 0.158897
\(280\) 0.298221 0.0178221
\(281\) 18.9818 1.13236 0.566179 0.824283i \(-0.308421\pi\)
0.566179 + 0.824283i \(0.308421\pi\)
\(282\) 26.9027 1.60203
\(283\) −9.36990 −0.556983 −0.278491 0.960439i \(-0.589834\pi\)
−0.278491 + 0.960439i \(0.589834\pi\)
\(284\) 4.94171 0.293237
\(285\) 5.47389 0.324245
\(286\) −16.6328 −0.983520
\(287\) −1.31347 −0.0775317
\(288\) −2.62686 −0.154789
\(289\) −16.3575 −0.962204
\(290\) −5.10099 −0.299541
\(291\) −3.66625 −0.214919
\(292\) 0.583139 0.0341256
\(293\) 27.4042 1.60097 0.800484 0.599354i \(-0.204576\pi\)
0.800484 + 0.599354i \(0.204576\pi\)
\(294\) −16.5651 −0.966095
\(295\) −18.8012 −1.09465
\(296\) 5.12381 0.297816
\(297\) 4.94045 0.286674
\(298\) −0.281926 −0.0163315
\(299\) −1.85607 −0.107339
\(300\) −0.771123 −0.0445208
\(301\) −0.300887 −0.0173429
\(302\) −5.05857 −0.291088
\(303\) −12.2165 −0.701819
\(304\) 1.00000 0.0573539
\(305\) 28.7199 1.64450
\(306\) 2.10565 0.120372
\(307\) −14.3611 −0.819629 −0.409814 0.912169i \(-0.634407\pi\)
−0.409814 + 0.912169i \(0.634407\pi\)
\(308\) 0.721336 0.0411019
\(309\) −25.8401 −1.46999
\(310\) 2.33154 0.132422
\(311\) −5.93100 −0.336316 −0.168158 0.985760i \(-0.553782\pi\)
−0.168158 + 0.985760i \(0.553782\pi\)
\(312\) 7.06866 0.400184
\(313\) −16.2381 −0.917834 −0.458917 0.888479i \(-0.651763\pi\)
−0.458917 + 0.888479i \(0.651763\pi\)
\(314\) 14.6778 0.828316
\(315\) −0.783386 −0.0441388
\(316\) −2.00030 −0.112525
\(317\) −24.7840 −1.39201 −0.696005 0.718037i \(-0.745041\pi\)
−0.696005 + 0.718037i \(0.745041\pi\)
\(318\) −6.06046 −0.339854
\(319\) −12.3383 −0.690810
\(320\) −2.30761 −0.129000
\(321\) 37.1974 2.07616
\(322\) 0.0804944 0.00448578
\(323\) −0.801585 −0.0446014
\(324\) −9.98019 −0.554455
\(325\) 0.968713 0.0537345
\(326\) −4.94513 −0.273885
\(327\) −3.60765 −0.199503
\(328\) 10.1635 0.561187
\(329\) 1.46568 0.0808055
\(330\) −30.5533 −1.68190
\(331\) 4.86006 0.267133 0.133566 0.991040i \(-0.457357\pi\)
0.133566 + 0.991040i \(0.457357\pi\)
\(332\) −17.2842 −0.948594
\(333\) −13.4595 −0.737579
\(334\) −0.0773168 −0.00423059
\(335\) −8.61682 −0.470787
\(336\) −0.306555 −0.0167240
\(337\) −21.8159 −1.18839 −0.594195 0.804321i \(-0.702529\pi\)
−0.594195 + 0.804321i \(0.702529\pi\)
\(338\) 4.12009 0.224103
\(339\) −23.5861 −1.28102
\(340\) 1.84975 0.100317
\(341\) 5.63951 0.305397
\(342\) −2.62686 −0.142044
\(343\) −1.80711 −0.0975749
\(344\) 2.32824 0.125531
\(345\) −3.40947 −0.183560
\(346\) −15.0036 −0.806596
\(347\) 3.29941 0.177122 0.0885609 0.996071i \(-0.471773\pi\)
0.0885609 + 0.996071i \(0.471773\pi\)
\(348\) 5.24354 0.281083
\(349\) 21.8699 1.17067 0.585336 0.810791i \(-0.300963\pi\)
0.585336 + 0.810791i \(0.300963\pi\)
\(350\) −0.0420113 −0.00224560
\(351\) 2.63760 0.140785
\(352\) −5.58164 −0.297503
\(353\) −19.7130 −1.04922 −0.524610 0.851343i \(-0.675789\pi\)
−0.524610 + 0.851343i \(0.675789\pi\)
\(354\) 19.3266 1.02720
\(355\) −11.4036 −0.605238
\(356\) 13.0624 0.692308
\(357\) 0.245730 0.0130054
\(358\) −17.6441 −0.932521
\(359\) 10.4907 0.553676 0.276838 0.960917i \(-0.410713\pi\)
0.276838 + 0.960917i \(0.410713\pi\)
\(360\) 6.06178 0.319484
\(361\) 1.00000 0.0526316
\(362\) −20.5425 −1.07969
\(363\) −47.8091 −2.50933
\(364\) 0.385106 0.0201850
\(365\) −1.34566 −0.0704351
\(366\) −29.5225 −1.54317
\(367\) 9.60866 0.501568 0.250784 0.968043i \(-0.419312\pi\)
0.250784 + 0.968043i \(0.419312\pi\)
\(368\) −0.622860 −0.0324688
\(369\) −26.6982 −1.38985
\(370\) −11.8238 −0.614689
\(371\) −0.330178 −0.0171420
\(372\) −2.39669 −0.124263
\(373\) 8.01561 0.415032 0.207516 0.978232i \(-0.433462\pi\)
0.207516 + 0.978232i \(0.433462\pi\)
\(374\) 4.47416 0.231353
\(375\) −25.5900 −1.32146
\(376\) −11.3413 −0.584883
\(377\) −6.58713 −0.339254
\(378\) −0.114388 −0.00588348
\(379\) −1.12368 −0.0577197 −0.0288599 0.999583i \(-0.509188\pi\)
−0.0288599 + 0.999583i \(0.509188\pi\)
\(380\) −2.30761 −0.118378
\(381\) 27.2462 1.39587
\(382\) −3.51326 −0.179754
\(383\) −32.8370 −1.67789 −0.838945 0.544216i \(-0.816827\pi\)
−0.838945 + 0.544216i \(0.816827\pi\)
\(384\) 2.37210 0.121051
\(385\) −1.66456 −0.0848341
\(386\) 25.2223 1.28378
\(387\) −6.11597 −0.310892
\(388\) 1.54557 0.0784645
\(389\) 15.4191 0.781780 0.390890 0.920437i \(-0.372167\pi\)
0.390890 + 0.920437i \(0.372167\pi\)
\(390\) −16.3117 −0.825977
\(391\) 0.499275 0.0252494
\(392\) 6.98330 0.352710
\(393\) 40.9626 2.06629
\(394\) 21.7650 1.09650
\(395\) 4.61591 0.232252
\(396\) 14.6622 0.736803
\(397\) 11.8721 0.595844 0.297922 0.954590i \(-0.403706\pi\)
0.297922 + 0.954590i \(0.403706\pi\)
\(398\) 12.0030 0.601656
\(399\) −0.306555 −0.0153470
\(400\) 0.325080 0.0162540
\(401\) 3.78310 0.188919 0.0944595 0.995529i \(-0.469888\pi\)
0.0944595 + 0.995529i \(0.469888\pi\)
\(402\) 8.85762 0.441778
\(403\) 3.01081 0.149979
\(404\) 5.15007 0.256226
\(405\) 23.0304 1.14439
\(406\) 0.285672 0.0141776
\(407\) −28.5993 −1.41762
\(408\) −1.90144 −0.0941353
\(409\) 4.53713 0.224347 0.112173 0.993689i \(-0.464219\pi\)
0.112173 + 0.993689i \(0.464219\pi\)
\(410\) −23.4535 −1.15829
\(411\) −18.5813 −0.916546
\(412\) 10.8934 0.536677
\(413\) 1.05292 0.0518110
\(414\) 1.63617 0.0804132
\(415\) 39.8853 1.95789
\(416\) −2.97992 −0.146102
\(417\) −46.5762 −2.28085
\(418\) −5.58164 −0.273007
\(419\) −37.3366 −1.82401 −0.912007 0.410175i \(-0.865468\pi\)
−0.912007 + 0.410175i \(0.865468\pi\)
\(420\) 0.707411 0.0345181
\(421\) 9.85092 0.480105 0.240052 0.970760i \(-0.422835\pi\)
0.240052 + 0.970760i \(0.422835\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 29.7920 1.44854
\(424\) 2.55489 0.124077
\(425\) −0.260580 −0.0126400
\(426\) 11.7222 0.567944
\(427\) −1.60841 −0.0778363
\(428\) −15.6812 −0.757980
\(429\) −39.4548 −1.90489
\(430\) −5.37269 −0.259094
\(431\) 10.2991 0.496092 0.248046 0.968748i \(-0.420212\pi\)
0.248046 + 0.968748i \(0.420212\pi\)
\(432\) 0.885125 0.0425856
\(433\) −38.9898 −1.87373 −0.936865 0.349691i \(-0.886287\pi\)
−0.936865 + 0.349691i \(0.886287\pi\)
\(434\) −0.130573 −0.00626773
\(435\) −12.1001 −0.580154
\(436\) 1.52087 0.0728362
\(437\) −0.622860 −0.0297954
\(438\) 1.38326 0.0660949
\(439\) −7.31729 −0.349235 −0.174618 0.984636i \(-0.555869\pi\)
−0.174618 + 0.984636i \(0.555869\pi\)
\(440\) 12.8803 0.614043
\(441\) −18.3442 −0.873531
\(442\) 2.38866 0.113617
\(443\) −11.9408 −0.567324 −0.283662 0.958924i \(-0.591549\pi\)
−0.283662 + 0.958924i \(0.591549\pi\)
\(444\) 12.1542 0.576813
\(445\) −30.1431 −1.42892
\(446\) 21.9021 1.03710
\(447\) −0.668757 −0.0316311
\(448\) 0.129234 0.00610571
\(449\) 4.60064 0.217118 0.108559 0.994090i \(-0.465376\pi\)
0.108559 + 0.994090i \(0.465376\pi\)
\(450\) −0.853941 −0.0402551
\(451\) −56.7292 −2.67127
\(452\) 9.94313 0.467685
\(453\) −11.9994 −0.563782
\(454\) 18.3678 0.862042
\(455\) −0.888675 −0.0416617
\(456\) 2.37210 0.111084
\(457\) 1.03784 0.0485481 0.0242740 0.999705i \(-0.492273\pi\)
0.0242740 + 0.999705i \(0.492273\pi\)
\(458\) 25.1732 1.17627
\(459\) −0.709503 −0.0331168
\(460\) 1.43732 0.0670154
\(461\) −7.79244 −0.362930 −0.181465 0.983397i \(-0.558084\pi\)
−0.181465 + 0.983397i \(0.558084\pi\)
\(462\) 1.71108 0.0796067
\(463\) −32.5424 −1.51237 −0.756187 0.654355i \(-0.772940\pi\)
−0.756187 + 0.654355i \(0.772940\pi\)
\(464\) −2.21051 −0.102620
\(465\) 5.53064 0.256477
\(466\) −11.4777 −0.531694
\(467\) 0.107350 0.00496756 0.00248378 0.999997i \(-0.499209\pi\)
0.00248378 + 0.999997i \(0.499209\pi\)
\(468\) 7.82783 0.361841
\(469\) 0.482569 0.0222830
\(470\) 26.1714 1.20719
\(471\) 34.8172 1.60429
\(472\) −8.14745 −0.375017
\(473\) −12.9954 −0.597530
\(474\) −4.74490 −0.217941
\(475\) 0.325080 0.0149157
\(476\) −0.103592 −0.00474812
\(477\) −6.71135 −0.307292
\(478\) −7.31317 −0.334497
\(479\) 3.45727 0.157966 0.0789832 0.996876i \(-0.474833\pi\)
0.0789832 + 0.996876i \(0.474833\pi\)
\(480\) −5.47389 −0.249848
\(481\) −15.2685 −0.696186
\(482\) −24.2493 −1.10453
\(483\) 0.190941 0.00868811
\(484\) 20.1547 0.916125
\(485\) −3.56658 −0.161950
\(486\) −21.0186 −0.953424
\(487\) −19.0364 −0.862620 −0.431310 0.902204i \(-0.641948\pi\)
−0.431310 + 0.902204i \(0.641948\pi\)
\(488\) 12.4457 0.563392
\(489\) −11.7303 −0.530464
\(490\) −16.1148 −0.727990
\(491\) 34.7226 1.56701 0.783504 0.621387i \(-0.213431\pi\)
0.783504 + 0.621387i \(0.213431\pi\)
\(492\) 24.1089 1.08691
\(493\) 1.77191 0.0798028
\(494\) −2.97992 −0.134073
\(495\) −33.8347 −1.52076
\(496\) 1.01037 0.0453669
\(497\) 0.638635 0.0286467
\(498\) −40.9999 −1.83725
\(499\) 38.9035 1.74156 0.870779 0.491674i \(-0.163615\pi\)
0.870779 + 0.491674i \(0.163615\pi\)
\(500\) 10.7879 0.482450
\(501\) −0.183403 −0.00819385
\(502\) −9.33387 −0.416591
\(503\) −28.0907 −1.25250 −0.626251 0.779622i \(-0.715411\pi\)
−0.626251 + 0.779622i \(0.715411\pi\)
\(504\) −0.339479 −0.0151216
\(505\) −11.8844 −0.528848
\(506\) 3.47658 0.154553
\(507\) 9.77327 0.434046
\(508\) −11.4861 −0.509614
\(509\) 23.8570 1.05744 0.528722 0.848795i \(-0.322671\pi\)
0.528722 + 0.848795i \(0.322671\pi\)
\(510\) 4.38779 0.194295
\(511\) 0.0753612 0.00333378
\(512\) −1.00000 −0.0441942
\(513\) 0.885125 0.0390792
\(514\) 11.4864 0.506642
\(515\) −25.1376 −1.10770
\(516\) 5.52283 0.243129
\(517\) 63.3031 2.78407
\(518\) 0.662169 0.0290940
\(519\) −35.5899 −1.56222
\(520\) 6.87650 0.301554
\(521\) 40.6734 1.78193 0.890967 0.454068i \(-0.150028\pi\)
0.890967 + 0.454068i \(0.150028\pi\)
\(522\) 5.80669 0.254152
\(523\) 15.6487 0.684272 0.342136 0.939650i \(-0.388850\pi\)
0.342136 + 0.939650i \(0.388850\pi\)
\(524\) −17.2685 −0.754378
\(525\) −0.0996550 −0.00434930
\(526\) −22.6393 −0.987120
\(527\) −0.809896 −0.0352796
\(528\) −13.2402 −0.576207
\(529\) −22.6120 −0.983132
\(530\) −5.89571 −0.256093
\(531\) 21.4022 0.928777
\(532\) 0.129234 0.00560299
\(533\) −30.2865 −1.31185
\(534\) 30.9854 1.34087
\(535\) 36.1862 1.56446
\(536\) −3.73408 −0.161288
\(537\) −41.8536 −1.80612
\(538\) −12.7878 −0.551322
\(539\) −38.9783 −1.67891
\(540\) −2.04253 −0.0878963
\(541\) −18.1414 −0.779959 −0.389979 0.920824i \(-0.627518\pi\)
−0.389979 + 0.920824i \(0.627518\pi\)
\(542\) 14.2202 0.610811
\(543\) −48.7288 −2.09115
\(544\) 0.801585 0.0343677
\(545\) −3.50957 −0.150333
\(546\) 0.913509 0.0390946
\(547\) 8.19147 0.350242 0.175121 0.984547i \(-0.443968\pi\)
0.175121 + 0.984547i \(0.443968\pi\)
\(548\) 7.83325 0.334620
\(549\) −32.6932 −1.39531
\(550\) −1.81448 −0.0773698
\(551\) −2.21051 −0.0941707
\(552\) −1.47749 −0.0628860
\(553\) −0.258506 −0.0109928
\(554\) 1.20237 0.0510838
\(555\) −28.0472 −1.19054
\(556\) 19.6350 0.832710
\(557\) −31.2483 −1.32403 −0.662016 0.749490i \(-0.730299\pi\)
−0.662016 + 0.749490i \(0.730299\pi\)
\(558\) −2.65410 −0.112357
\(559\) −6.93798 −0.293445
\(560\) −0.298221 −0.0126021
\(561\) 10.6132 0.448088
\(562\) −18.9818 −0.800697
\(563\) 38.3130 1.61470 0.807351 0.590072i \(-0.200901\pi\)
0.807351 + 0.590072i \(0.200901\pi\)
\(564\) −26.9027 −1.13281
\(565\) −22.9449 −0.965299
\(566\) 9.36990 0.393846
\(567\) −1.28978 −0.0541655
\(568\) −4.94171 −0.207350
\(569\) −28.7008 −1.20320 −0.601600 0.798797i \(-0.705470\pi\)
−0.601600 + 0.798797i \(0.705470\pi\)
\(570\) −5.47389 −0.229276
\(571\) 23.5432 0.985251 0.492626 0.870241i \(-0.336037\pi\)
0.492626 + 0.870241i \(0.336037\pi\)
\(572\) 16.6328 0.695454
\(573\) −8.33382 −0.348150
\(574\) 1.31347 0.0548232
\(575\) −0.202479 −0.00844398
\(576\) 2.62686 0.109453
\(577\) 18.9958 0.790804 0.395402 0.918508i \(-0.370605\pi\)
0.395402 + 0.918508i \(0.370605\pi\)
\(578\) 16.3575 0.680381
\(579\) 59.8298 2.48644
\(580\) 5.10099 0.211807
\(581\) −2.23370 −0.0926695
\(582\) 3.66625 0.151971
\(583\) −14.2605 −0.590610
\(584\) −0.583139 −0.0241305
\(585\) −18.0636 −0.746838
\(586\) −27.4042 −1.13206
\(587\) 0.812759 0.0335462 0.0167731 0.999859i \(-0.494661\pi\)
0.0167731 + 0.999859i \(0.494661\pi\)
\(588\) 16.5651 0.683133
\(589\) 1.01037 0.0416315
\(590\) 18.8012 0.774032
\(591\) 51.6287 2.12372
\(592\) −5.12381 −0.210587
\(593\) 42.2880 1.73656 0.868279 0.496076i \(-0.165226\pi\)
0.868279 + 0.496076i \(0.165226\pi\)
\(594\) −4.94045 −0.202709
\(595\) 0.239050 0.00980009
\(596\) 0.281926 0.0115481
\(597\) 28.4723 1.16529
\(598\) 1.85607 0.0759004
\(599\) −40.5198 −1.65559 −0.827796 0.561029i \(-0.810406\pi\)
−0.827796 + 0.561029i \(0.810406\pi\)
\(600\) 0.771123 0.0314810
\(601\) −7.54494 −0.307765 −0.153882 0.988089i \(-0.549178\pi\)
−0.153882 + 0.988089i \(0.549178\pi\)
\(602\) 0.300887 0.0122633
\(603\) 9.80891 0.399450
\(604\) 5.05857 0.205830
\(605\) −46.5094 −1.89087
\(606\) 12.2165 0.496261
\(607\) 15.5292 0.630309 0.315155 0.949040i \(-0.397944\pi\)
0.315155 + 0.949040i \(0.397944\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0.677642 0.0274594
\(610\) −28.7199 −1.16284
\(611\) 33.7962 1.36725
\(612\) −2.10565 −0.0851160
\(613\) 30.3832 1.22717 0.613583 0.789630i \(-0.289727\pi\)
0.613583 + 0.789630i \(0.289727\pi\)
\(614\) 14.3611 0.579565
\(615\) −55.6341 −2.24338
\(616\) −0.721336 −0.0290635
\(617\) −10.1528 −0.408738 −0.204369 0.978894i \(-0.565514\pi\)
−0.204369 + 0.978894i \(0.565514\pi\)
\(618\) 25.8401 1.03944
\(619\) −33.6293 −1.35168 −0.675838 0.737050i \(-0.736218\pi\)
−0.675838 + 0.737050i \(0.736218\pi\)
\(620\) −2.33154 −0.0936368
\(621\) −0.551309 −0.0221233
\(622\) 5.93100 0.237812
\(623\) 1.68811 0.0676326
\(624\) −7.06866 −0.282973
\(625\) −26.5197 −1.06079
\(626\) 16.2381 0.649007
\(627\) −13.2402 −0.528763
\(628\) −14.6778 −0.585708
\(629\) 4.10717 0.163764
\(630\) 0.783386 0.0312108
\(631\) −30.0336 −1.19562 −0.597809 0.801639i \(-0.703962\pi\)
−0.597809 + 0.801639i \(0.703962\pi\)
\(632\) 2.00030 0.0795675
\(633\) −2.37210 −0.0942825
\(634\) 24.7840 0.984300
\(635\) 26.5055 1.05184
\(636\) 6.06046 0.240313
\(637\) −20.8097 −0.824509
\(638\) 12.3383 0.488476
\(639\) 12.9812 0.513528
\(640\) 2.30761 0.0912164
\(641\) 23.6455 0.933942 0.466971 0.884273i \(-0.345345\pi\)
0.466971 + 0.884273i \(0.345345\pi\)
\(642\) −37.1974 −1.46806
\(643\) −17.9992 −0.709821 −0.354911 0.934900i \(-0.615489\pi\)
−0.354911 + 0.934900i \(0.615489\pi\)
\(644\) −0.0804944 −0.00317192
\(645\) −12.7446 −0.501816
\(646\) 0.801585 0.0315380
\(647\) −4.73165 −0.186020 −0.0930102 0.995665i \(-0.529649\pi\)
−0.0930102 + 0.995665i \(0.529649\pi\)
\(648\) 9.98019 0.392059
\(649\) 45.4762 1.78510
\(650\) −0.968713 −0.0379960
\(651\) −0.309733 −0.0121394
\(652\) 4.94513 0.193666
\(653\) −32.9607 −1.28985 −0.644925 0.764246i \(-0.723112\pi\)
−0.644925 + 0.764246i \(0.723112\pi\)
\(654\) 3.60765 0.141070
\(655\) 39.8490 1.55703
\(656\) −10.1635 −0.396819
\(657\) 1.53183 0.0597622
\(658\) −1.46568 −0.0571381
\(659\) 33.7736 1.31563 0.657817 0.753178i \(-0.271480\pi\)
0.657817 + 0.753178i \(0.271480\pi\)
\(660\) 30.5533 1.18929
\(661\) −43.2002 −1.68029 −0.840146 0.542361i \(-0.817531\pi\)
−0.840146 + 0.542361i \(0.817531\pi\)
\(662\) −4.86006 −0.188892
\(663\) 5.66614 0.220055
\(664\) 17.2842 0.670757
\(665\) −0.298221 −0.0115645
\(666\) 13.4595 0.521547
\(667\) 1.37684 0.0533113
\(668\) 0.0773168 0.00299148
\(669\) 51.9540 2.00866
\(670\) 8.61682 0.332897
\(671\) −69.4676 −2.68177
\(672\) 0.306555 0.0118256
\(673\) −40.9130 −1.57708 −0.788539 0.614984i \(-0.789162\pi\)
−0.788539 + 0.614984i \(0.789162\pi\)
\(674\) 21.8159 0.840318
\(675\) 0.287737 0.0110750
\(676\) −4.12009 −0.158465
\(677\) −29.1685 −1.12104 −0.560518 0.828142i \(-0.689398\pi\)
−0.560518 + 0.828142i \(0.689398\pi\)
\(678\) 23.5861 0.905819
\(679\) 0.199740 0.00766531
\(680\) −1.84975 −0.0709346
\(681\) 43.5702 1.66961
\(682\) −5.63951 −0.215948
\(683\) −31.2307 −1.19501 −0.597505 0.801865i \(-0.703841\pi\)
−0.597505 + 0.801865i \(0.703841\pi\)
\(684\) 2.62686 0.100441
\(685\) −18.0761 −0.690653
\(686\) 1.80711 0.0689959
\(687\) 59.7133 2.27820
\(688\) −2.32824 −0.0887635
\(689\) −7.61337 −0.290046
\(690\) 3.40947 0.129796
\(691\) 7.72699 0.293949 0.146974 0.989140i \(-0.453047\pi\)
0.146974 + 0.989140i \(0.453047\pi\)
\(692\) 15.0036 0.570349
\(693\) 1.89485 0.0719794
\(694\) −3.29941 −0.125244
\(695\) −45.3100 −1.71871
\(696\) −5.24354 −0.198756
\(697\) 8.14694 0.308587
\(698\) −21.8699 −0.827790
\(699\) −27.2262 −1.02979
\(700\) 0.0420113 0.00158788
\(701\) −1.85902 −0.0702144 −0.0351072 0.999384i \(-0.511177\pi\)
−0.0351072 + 0.999384i \(0.511177\pi\)
\(702\) −2.63760 −0.0995497
\(703\) −5.12381 −0.193248
\(704\) 5.58164 0.210366
\(705\) 62.0811 2.33811
\(706\) 19.7130 0.741910
\(707\) 0.665562 0.0250311
\(708\) −19.3266 −0.726337
\(709\) −5.51880 −0.207263 −0.103631 0.994616i \(-0.533046\pi\)
−0.103631 + 0.994616i \(0.533046\pi\)
\(710\) 11.4036 0.427968
\(711\) −5.25450 −0.197059
\(712\) −13.0624 −0.489536
\(713\) −0.629317 −0.0235681
\(714\) −0.245730 −0.00919622
\(715\) −38.3822 −1.43541
\(716\) 17.6441 0.659392
\(717\) −17.3476 −0.647857
\(718\) −10.4907 −0.391508
\(719\) 6.11637 0.228102 0.114051 0.993475i \(-0.463617\pi\)
0.114051 + 0.993475i \(0.463617\pi\)
\(720\) −6.06178 −0.225909
\(721\) 1.40779 0.0524287
\(722\) −1.00000 −0.0372161
\(723\) −57.5218 −2.13926
\(724\) 20.5425 0.763454
\(725\) −0.718592 −0.0266878
\(726\) 47.8091 1.77436
\(727\) 3.99503 0.148167 0.0740836 0.997252i \(-0.476397\pi\)
0.0740836 + 0.997252i \(0.476397\pi\)
\(728\) −0.385106 −0.0142730
\(729\) −19.9177 −0.737694
\(730\) 1.34566 0.0498051
\(731\) 1.86629 0.0690271
\(732\) 29.5225 1.09118
\(733\) 19.0468 0.703508 0.351754 0.936092i \(-0.385585\pi\)
0.351754 + 0.936092i \(0.385585\pi\)
\(734\) −9.60866 −0.354662
\(735\) −38.2258 −1.40998
\(736\) 0.622860 0.0229589
\(737\) 20.8423 0.767737
\(738\) 26.6982 0.982773
\(739\) −11.5377 −0.424421 −0.212210 0.977224i \(-0.568066\pi\)
−0.212210 + 0.977224i \(0.568066\pi\)
\(740\) 11.8238 0.434651
\(741\) −7.06866 −0.259674
\(742\) 0.330178 0.0121212
\(743\) 18.4628 0.677333 0.338666 0.940907i \(-0.390024\pi\)
0.338666 + 0.940907i \(0.390024\pi\)
\(744\) 2.39669 0.0878671
\(745\) −0.650576 −0.0238353
\(746\) −8.01561 −0.293472
\(747\) −45.4032 −1.66122
\(748\) −4.47416 −0.163592
\(749\) −2.02654 −0.0740481
\(750\) 25.5900 0.934415
\(751\) 52.2066 1.90505 0.952523 0.304468i \(-0.0984787\pi\)
0.952523 + 0.304468i \(0.0984787\pi\)
\(752\) 11.3413 0.413575
\(753\) −22.1409 −0.806859
\(754\) 6.58713 0.239889
\(755\) −11.6732 −0.424832
\(756\) 0.114388 0.00416025
\(757\) −26.8635 −0.976371 −0.488185 0.872740i \(-0.662341\pi\)
−0.488185 + 0.872740i \(0.662341\pi\)
\(758\) 1.12368 0.0408140
\(759\) 8.24680 0.299340
\(760\) 2.30761 0.0837059
\(761\) 47.5802 1.72478 0.862391 0.506243i \(-0.168966\pi\)
0.862391 + 0.506243i \(0.168966\pi\)
\(762\) −27.2462 −0.987027
\(763\) 0.196547 0.00711548
\(764\) 3.51326 0.127105
\(765\) 4.85903 0.175679
\(766\) 32.8370 1.18645
\(767\) 24.2787 0.876654
\(768\) −2.37210 −0.0855958
\(769\) −24.1209 −0.869824 −0.434912 0.900473i \(-0.643220\pi\)
−0.434912 + 0.900473i \(0.643220\pi\)
\(770\) 1.66456 0.0599868
\(771\) 27.2468 0.981270
\(772\) −25.2223 −0.907770
\(773\) −12.5397 −0.451022 −0.225511 0.974241i \(-0.572405\pi\)
−0.225511 + 0.974241i \(0.572405\pi\)
\(774\) 6.11597 0.219834
\(775\) 0.328451 0.0117983
\(776\) −1.54557 −0.0554828
\(777\) 1.57073 0.0563497
\(778\) −15.4191 −0.552802
\(779\) −10.1635 −0.364146
\(780\) 16.3117 0.584054
\(781\) 27.5829 0.986993
\(782\) −0.499275 −0.0178540
\(783\) −1.95657 −0.0699222
\(784\) −6.98330 −0.249404
\(785\) 33.8707 1.20890
\(786\) −40.9626 −1.46109
\(787\) 33.4332 1.19177 0.595883 0.803072i \(-0.296802\pi\)
0.595883 + 0.803072i \(0.296802\pi\)
\(788\) −21.7650 −0.775345
\(789\) −53.7027 −1.91187
\(790\) −4.61591 −0.164227
\(791\) 1.28499 0.0456889
\(792\) −14.6622 −0.520999
\(793\) −37.0873 −1.31701
\(794\) −11.8721 −0.421326
\(795\) −13.9852 −0.496004
\(796\) −12.0030 −0.425435
\(797\) 13.7999 0.488818 0.244409 0.969672i \(-0.421406\pi\)
0.244409 + 0.969672i \(0.421406\pi\)
\(798\) 0.306555 0.0108519
\(799\) −9.09103 −0.321617
\(800\) −0.325080 −0.0114933
\(801\) 34.3132 1.21240
\(802\) −3.78310 −0.133586
\(803\) 3.25487 0.114862
\(804\) −8.85762 −0.312384
\(805\) 0.185750 0.00654683
\(806\) −3.01081 −0.106051
\(807\) −30.3340 −1.06781
\(808\) −5.15007 −0.181179
\(809\) −56.4095 −1.98325 −0.991626 0.129143i \(-0.958777\pi\)
−0.991626 + 0.129143i \(0.958777\pi\)
\(810\) −23.0304 −0.809206
\(811\) −14.2172 −0.499234 −0.249617 0.968345i \(-0.580305\pi\)
−0.249617 + 0.968345i \(0.580305\pi\)
\(812\) −0.285672 −0.0100251
\(813\) 33.7318 1.18303
\(814\) 28.5993 1.00241
\(815\) −11.4114 −0.399726
\(816\) 1.90144 0.0665637
\(817\) −2.32824 −0.0814549
\(818\) −4.53713 −0.158637
\(819\) 1.01162 0.0353488
\(820\) 23.4535 0.819032
\(821\) −24.1925 −0.844323 −0.422161 0.906521i \(-0.638728\pi\)
−0.422161 + 0.906521i \(0.638728\pi\)
\(822\) 18.5813 0.648096
\(823\) 17.0192 0.593253 0.296627 0.954994i \(-0.404138\pi\)
0.296627 + 0.954994i \(0.404138\pi\)
\(824\) −10.8934 −0.379488
\(825\) −4.30413 −0.149851
\(826\) −1.05292 −0.0366359
\(827\) −50.4370 −1.75387 −0.876934 0.480611i \(-0.840415\pi\)
−0.876934 + 0.480611i \(0.840415\pi\)
\(828\) −1.63617 −0.0568607
\(829\) 34.8686 1.21104 0.605518 0.795832i \(-0.292966\pi\)
0.605518 + 0.795832i \(0.292966\pi\)
\(830\) −39.8853 −1.38444
\(831\) 2.85214 0.0989398
\(832\) 2.97992 0.103310
\(833\) 5.59771 0.193949
\(834\) 46.5762 1.61280
\(835\) −0.178417 −0.00617439
\(836\) 5.58164 0.193045
\(837\) 0.894301 0.0309116
\(838\) 37.3366 1.28977
\(839\) −28.8383 −0.995609 −0.497804 0.867289i \(-0.665860\pi\)
−0.497804 + 0.867289i \(0.665860\pi\)
\(840\) −0.707411 −0.0244080
\(841\) −24.1137 −0.831506
\(842\) −9.85092 −0.339485
\(843\) −45.0266 −1.55080
\(844\) 1.00000 0.0344214
\(845\) 9.50758 0.327071
\(846\) −29.7920 −1.02427
\(847\) 2.60467 0.0894976
\(848\) −2.55489 −0.0877354
\(849\) 22.2263 0.762806
\(850\) 0.260580 0.00893781
\(851\) 3.19142 0.109400
\(852\) −11.7222 −0.401597
\(853\) 13.4926 0.461977 0.230988 0.972956i \(-0.425804\pi\)
0.230988 + 0.972956i \(0.425804\pi\)
\(854\) 1.60841 0.0550386
\(855\) −6.06178 −0.207308
\(856\) 15.6812 0.535973
\(857\) 24.2814 0.829437 0.414718 0.909950i \(-0.363880\pi\)
0.414718 + 0.909950i \(0.363880\pi\)
\(858\) 39.4548 1.34696
\(859\) 16.3125 0.556574 0.278287 0.960498i \(-0.410233\pi\)
0.278287 + 0.960498i \(0.410233\pi\)
\(860\) 5.37269 0.183207
\(861\) 3.11568 0.106182
\(862\) −10.2991 −0.350790
\(863\) −36.8429 −1.25415 −0.627074 0.778960i \(-0.715748\pi\)
−0.627074 + 0.778960i \(0.715748\pi\)
\(864\) −0.885125 −0.0301126
\(865\) −34.6224 −1.17720
\(866\) 38.9898 1.32493
\(867\) 38.8015 1.31777
\(868\) 0.130573 0.00443195
\(869\) −11.1649 −0.378745
\(870\) 12.1001 0.410231
\(871\) 11.1273 0.377033
\(872\) −1.52087 −0.0515030
\(873\) 4.06000 0.137410
\(874\) 0.622860 0.0210685
\(875\) 1.39416 0.0471312
\(876\) −1.38326 −0.0467362
\(877\) −47.6415 −1.60874 −0.804370 0.594128i \(-0.797497\pi\)
−0.804370 + 0.594128i \(0.797497\pi\)
\(878\) 7.31729 0.246946
\(879\) −65.0054 −2.19258
\(880\) −12.8803 −0.434194
\(881\) −50.6020 −1.70483 −0.852413 0.522870i \(-0.824861\pi\)
−0.852413 + 0.522870i \(0.824861\pi\)
\(882\) 18.3442 0.617680
\(883\) −26.1128 −0.878765 −0.439382 0.898300i \(-0.644803\pi\)
−0.439382 + 0.898300i \(0.644803\pi\)
\(884\) −2.38866 −0.0803393
\(885\) 44.5982 1.49915
\(886\) 11.9408 0.401159
\(887\) 33.8581 1.13685 0.568423 0.822737i \(-0.307554\pi\)
0.568423 + 0.822737i \(0.307554\pi\)
\(888\) −12.1542 −0.407868
\(889\) −1.48439 −0.0497849
\(890\) 30.1431 1.01040
\(891\) −55.7058 −1.86622
\(892\) −21.9021 −0.733337
\(893\) 11.3413 0.379522
\(894\) 0.668757 0.0223666
\(895\) −40.7158 −1.36098
\(896\) −0.129234 −0.00431739
\(897\) 4.40279 0.147005
\(898\) −4.60064 −0.153525
\(899\) −2.23342 −0.0744889
\(900\) 0.853941 0.0284647
\(901\) 2.04797 0.0682276
\(902\) 56.7292 1.88888
\(903\) 0.713735 0.0237516
\(904\) −9.94313 −0.330703
\(905\) −47.4041 −1.57576
\(906\) 11.9994 0.398654
\(907\) −54.7679 −1.81854 −0.909270 0.416207i \(-0.863359\pi\)
−0.909270 + 0.416207i \(0.863359\pi\)
\(908\) −18.3678 −0.609556
\(909\) 13.5285 0.448713
\(910\) 0.888675 0.0294593
\(911\) 0.808514 0.0267873 0.0133936 0.999910i \(-0.495737\pi\)
0.0133936 + 0.999910i \(0.495737\pi\)
\(912\) −2.37210 −0.0785481
\(913\) −96.4743 −3.19283
\(914\) −1.03784 −0.0343287
\(915\) −68.1266 −2.25220
\(916\) −25.1732 −0.831745
\(917\) −2.23167 −0.0736963
\(918\) 0.709503 0.0234171
\(919\) −22.2345 −0.733449 −0.366725 0.930330i \(-0.619521\pi\)
−0.366725 + 0.930330i \(0.619521\pi\)
\(920\) −1.43732 −0.0473870
\(921\) 34.0659 1.12251
\(922\) 7.79244 0.256630
\(923\) 14.7259 0.484709
\(924\) −1.71108 −0.0562904
\(925\) −1.66565 −0.0547663
\(926\) 32.5424 1.06941
\(927\) 28.6153 0.939850
\(928\) 2.21051 0.0725634
\(929\) 8.67844 0.284730 0.142365 0.989814i \(-0.454529\pi\)
0.142365 + 0.989814i \(0.454529\pi\)
\(930\) −5.53064 −0.181357
\(931\) −6.98330 −0.228868
\(932\) 11.4777 0.375964
\(933\) 14.0689 0.460596
\(934\) −0.107350 −0.00351259
\(935\) 10.3246 0.337652
\(936\) −7.82783 −0.255861
\(937\) −38.8362 −1.26872 −0.634362 0.773036i \(-0.718737\pi\)
−0.634362 + 0.773036i \(0.718737\pi\)
\(938\) −0.482569 −0.0157564
\(939\) 38.5185 1.25700
\(940\) −26.1714 −0.853615
\(941\) 14.9926 0.488746 0.244373 0.969681i \(-0.421418\pi\)
0.244373 + 0.969681i \(0.421418\pi\)
\(942\) −34.8172 −1.13441
\(943\) 6.33045 0.206148
\(944\) 8.14745 0.265177
\(945\) −0.263963 −0.00858672
\(946\) 12.9954 0.422518
\(947\) −39.7491 −1.29167 −0.645837 0.763476i \(-0.723491\pi\)
−0.645837 + 0.763476i \(0.723491\pi\)
\(948\) 4.74490 0.154107
\(949\) 1.73771 0.0564083
\(950\) −0.325080 −0.0105470
\(951\) 58.7902 1.90640
\(952\) 0.103592 0.00335743
\(953\) 11.1609 0.361536 0.180768 0.983526i \(-0.442142\pi\)
0.180768 + 0.983526i \(0.442142\pi\)
\(954\) 6.71135 0.217288
\(955\) −8.10726 −0.262345
\(956\) 7.31317 0.236525
\(957\) 29.2676 0.946087
\(958\) −3.45727 −0.111699
\(959\) 1.01232 0.0326895
\(960\) 5.47389 0.176669
\(961\) −29.9792 −0.967070
\(962\) 15.2685 0.492278
\(963\) −41.1923 −1.32740
\(964\) 24.2493 0.781018
\(965\) 58.2033 1.87363
\(966\) −0.190941 −0.00614342
\(967\) −46.8485 −1.50654 −0.753272 0.657709i \(-0.771526\pi\)
−0.753272 + 0.657709i \(0.771526\pi\)
\(968\) −20.1547 −0.647798
\(969\) 1.90144 0.0610831
\(970\) 3.56658 0.114516
\(971\) −0.952180 −0.0305569 −0.0152785 0.999883i \(-0.504863\pi\)
−0.0152785 + 0.999883i \(0.504863\pi\)
\(972\) 21.0186 0.674173
\(973\) 2.53750 0.0813486
\(974\) 19.0364 0.609965
\(975\) −2.29788 −0.0735912
\(976\) −12.4457 −0.398378
\(977\) 35.9822 1.15117 0.575587 0.817741i \(-0.304774\pi\)
0.575587 + 0.817741i \(0.304774\pi\)
\(978\) 11.7303 0.375095
\(979\) 72.9099 2.33021
\(980\) 16.1148 0.514767
\(981\) 3.99510 0.127554
\(982\) −34.7226 −1.10804
\(983\) −1.18236 −0.0377113 −0.0188557 0.999822i \(-0.506002\pi\)
−0.0188557 + 0.999822i \(0.506002\pi\)
\(984\) −24.1089 −0.768564
\(985\) 50.2251 1.60031
\(986\) −1.77191 −0.0564291
\(987\) −3.47674 −0.110666
\(988\) 2.97992 0.0948038
\(989\) 1.45017 0.0461127
\(990\) 33.8347 1.07534
\(991\) −36.0652 −1.14565 −0.572825 0.819678i \(-0.694152\pi\)
−0.572825 + 0.819678i \(0.694152\pi\)
\(992\) −1.01037 −0.0320792
\(993\) −11.5285 −0.365847
\(994\) −0.638635 −0.0202563
\(995\) 27.6983 0.878094
\(996\) 40.9999 1.29913
\(997\) 33.6365 1.06528 0.532640 0.846342i \(-0.321200\pi\)
0.532640 + 0.846342i \(0.321200\pi\)
\(998\) −38.9035 −1.23147
\(999\) −4.53521 −0.143488
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 8018.2.a.g.1.7 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8018.2.a.g.1.7 34 1.1 even 1 trivial