Properties

Label 8006.2.a.b.1.12
Level $8006$
Weight $2$
Character 8006.1
Self dual yes
Analytic conductor $63.928$
Analytic rank $1$
Dimension $75$
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] = [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: \(1\)
Dimension: \(75\)
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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.34883 q^{3} +1.00000 q^{4} +2.23352 q^{5} +2.34883 q^{6} +0.995037 q^{7} -1.00000 q^{8} +2.51700 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.34883 q^{3} +1.00000 q^{4} +2.23352 q^{5} +2.34883 q^{6} +0.995037 q^{7} -1.00000 q^{8} +2.51700 q^{9} -2.23352 q^{10} +5.14516 q^{11} -2.34883 q^{12} -3.84886 q^{13} -0.995037 q^{14} -5.24617 q^{15} +1.00000 q^{16} +1.71393 q^{17} -2.51700 q^{18} -7.38779 q^{19} +2.23352 q^{20} -2.33717 q^{21} -5.14516 q^{22} -2.20233 q^{23} +2.34883 q^{24} -0.0113665 q^{25} +3.84886 q^{26} +1.13449 q^{27} +0.995037 q^{28} -3.74508 q^{29} +5.24617 q^{30} +8.09676 q^{31} -1.00000 q^{32} -12.0851 q^{33} -1.71393 q^{34} +2.22244 q^{35} +2.51700 q^{36} +7.24334 q^{37} +7.38779 q^{38} +9.04032 q^{39} -2.23352 q^{40} +11.4099 q^{41} +2.33717 q^{42} +8.01588 q^{43} +5.14516 q^{44} +5.62177 q^{45} +2.20233 q^{46} -10.9483 q^{47} -2.34883 q^{48} -6.00990 q^{49} +0.0113665 q^{50} -4.02573 q^{51} -3.84886 q^{52} -8.67445 q^{53} -1.13449 q^{54} +11.4919 q^{55} -0.995037 q^{56} +17.3526 q^{57} +3.74508 q^{58} -9.49865 q^{59} -5.24617 q^{60} -8.32675 q^{61} -8.09676 q^{62} +2.50450 q^{63} +1.00000 q^{64} -8.59653 q^{65} +12.0851 q^{66} -3.71549 q^{67} +1.71393 q^{68} +5.17289 q^{69} -2.22244 q^{70} -6.29825 q^{71} -2.51700 q^{72} +8.73715 q^{73} -7.24334 q^{74} +0.0266980 q^{75} -7.38779 q^{76} +5.11963 q^{77} -9.04032 q^{78} -13.0345 q^{79} +2.23352 q^{80} -10.2157 q^{81} -11.4099 q^{82} +3.23651 q^{83} -2.33717 q^{84} +3.82810 q^{85} -8.01588 q^{86} +8.79654 q^{87} -5.14516 q^{88} -7.51185 q^{89} -5.62177 q^{90} -3.82976 q^{91} -2.20233 q^{92} -19.0179 q^{93} +10.9483 q^{94} -16.5008 q^{95} +2.34883 q^{96} -9.27019 q^{97} +6.00990 q^{98} +12.9504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 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
\(3\) −2.34883 −1.35610 −0.678048 0.735017i \(-0.737174\pi\)
−0.678048 + 0.735017i \(0.737174\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.23352 0.998863 0.499431 0.866353i \(-0.333542\pi\)
0.499431 + 0.866353i \(0.333542\pi\)
\(6\) 2.34883 0.958905
\(7\) 0.995037 0.376089 0.188044 0.982161i \(-0.439785\pi\)
0.188044 + 0.982161i \(0.439785\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.51700 0.838999
\(10\) −2.23352 −0.706303
\(11\) 5.14516 1.55133 0.775663 0.631148i \(-0.217416\pi\)
0.775663 + 0.631148i \(0.217416\pi\)
\(12\) −2.34883 −0.678048
\(13\) −3.84886 −1.06748 −0.533741 0.845648i \(-0.679214\pi\)
−0.533741 + 0.845648i \(0.679214\pi\)
\(14\) −0.995037 −0.265935
\(15\) −5.24617 −1.35455
\(16\) 1.00000 0.250000
\(17\) 1.71393 0.415689 0.207844 0.978162i \(-0.433355\pi\)
0.207844 + 0.978162i \(0.433355\pi\)
\(18\) −2.51700 −0.593262
\(19\) −7.38779 −1.69487 −0.847437 0.530895i \(-0.821856\pi\)
−0.847437 + 0.530895i \(0.821856\pi\)
\(20\) 2.23352 0.499431
\(21\) −2.33717 −0.510013
\(22\) −5.14516 −1.09695
\(23\) −2.20233 −0.459217 −0.229609 0.973283i \(-0.573745\pi\)
−0.229609 + 0.973283i \(0.573745\pi\)
\(24\) 2.34883 0.479453
\(25\) −0.0113665 −0.00227330
\(26\) 3.84886 0.754824
\(27\) 1.13449 0.218334
\(28\) 0.995037 0.188044
\(29\) −3.74508 −0.695443 −0.347722 0.937598i \(-0.613045\pi\)
−0.347722 + 0.937598i \(0.613045\pi\)
\(30\) 5.24617 0.957815
\(31\) 8.09676 1.45422 0.727111 0.686520i \(-0.240863\pi\)
0.727111 + 0.686520i \(0.240863\pi\)
\(32\) −1.00000 −0.176777
\(33\) −12.0851 −2.10375
\(34\) −1.71393 −0.293936
\(35\) 2.22244 0.375661
\(36\) 2.51700 0.419499
\(37\) 7.24334 1.19080 0.595399 0.803430i \(-0.296994\pi\)
0.595399 + 0.803430i \(0.296994\pi\)
\(38\) 7.38779 1.19846
\(39\) 9.04032 1.44761
\(40\) −2.23352 −0.353151
\(41\) 11.4099 1.78193 0.890964 0.454074i \(-0.150030\pi\)
0.890964 + 0.454074i \(0.150030\pi\)
\(42\) 2.33717 0.360633
\(43\) 8.01588 1.22241 0.611205 0.791472i \(-0.290685\pi\)
0.611205 + 0.791472i \(0.290685\pi\)
\(44\) 5.14516 0.775663
\(45\) 5.62177 0.838044
\(46\) 2.20233 0.324716
\(47\) −10.9483 −1.59697 −0.798484 0.602017i \(-0.794364\pi\)
−0.798484 + 0.602017i \(0.794364\pi\)
\(48\) −2.34883 −0.339024
\(49\) −6.00990 −0.858557
\(50\) 0.0113665 0.00160747
\(51\) −4.02573 −0.563714
\(52\) −3.84886 −0.533741
\(53\) −8.67445 −1.19153 −0.595763 0.803160i \(-0.703150\pi\)
−0.595763 + 0.803160i \(0.703150\pi\)
\(54\) −1.13449 −0.154385
\(55\) 11.4919 1.54956
\(56\) −0.995037 −0.132967
\(57\) 17.3526 2.29841
\(58\) 3.74508 0.491753
\(59\) −9.49865 −1.23662 −0.618310 0.785935i \(-0.712182\pi\)
−0.618310 + 0.785935i \(0.712182\pi\)
\(60\) −5.24617 −0.677277
\(61\) −8.32675 −1.06613 −0.533066 0.846074i \(-0.678960\pi\)
−0.533066 + 0.846074i \(0.678960\pi\)
\(62\) −8.09676 −1.02829
\(63\) 2.50450 0.315538
\(64\) 1.00000 0.125000
\(65\) −8.59653 −1.06627
\(66\) 12.0851 1.48757
\(67\) −3.71549 −0.453919 −0.226960 0.973904i \(-0.572879\pi\)
−0.226960 + 0.973904i \(0.572879\pi\)
\(68\) 1.71393 0.207844
\(69\) 5.17289 0.622743
\(70\) −2.22244 −0.265632
\(71\) −6.29825 −0.747465 −0.373733 0.927537i \(-0.621922\pi\)
−0.373733 + 0.927537i \(0.621922\pi\)
\(72\) −2.51700 −0.296631
\(73\) 8.73715 1.02261 0.511303 0.859400i \(-0.329163\pi\)
0.511303 + 0.859400i \(0.329163\pi\)
\(74\) −7.24334 −0.842021
\(75\) 0.0266980 0.00308282
\(76\) −7.38779 −0.847437
\(77\) 5.11963 0.583436
\(78\) −9.04032 −1.02361
\(79\) −13.0345 −1.46649 −0.733247 0.679963i \(-0.761996\pi\)
−0.733247 + 0.679963i \(0.761996\pi\)
\(80\) 2.23352 0.249716
\(81\) −10.2157 −1.13508
\(82\) −11.4099 −1.26001
\(83\) 3.23651 0.355253 0.177627 0.984098i \(-0.443158\pi\)
0.177627 + 0.984098i \(0.443158\pi\)
\(84\) −2.33717 −0.255006
\(85\) 3.82810 0.415216
\(86\) −8.01588 −0.864375
\(87\) 8.79654 0.943088
\(88\) −5.14516 −0.548476
\(89\) −7.51185 −0.796254 −0.398127 0.917330i \(-0.630340\pi\)
−0.398127 + 0.917330i \(0.630340\pi\)
\(90\) −5.62177 −0.592587
\(91\) −3.82976 −0.401468
\(92\) −2.20233 −0.229609
\(93\) −19.0179 −1.97207
\(94\) 10.9483 1.12923
\(95\) −16.5008 −1.69295
\(96\) 2.34883 0.239726
\(97\) −9.27019 −0.941245 −0.470623 0.882335i \(-0.655971\pi\)
−0.470623 + 0.882335i \(0.655971\pi\)
\(98\) 6.00990 0.607092
\(99\) 12.9504 1.30156
\(100\) −0.0113665 −0.00113665
\(101\) −9.58731 −0.953973 −0.476987 0.878911i \(-0.658271\pi\)
−0.476987 + 0.878911i \(0.658271\pi\)
\(102\) 4.02573 0.398606
\(103\) 9.85484 0.971027 0.485513 0.874229i \(-0.338633\pi\)
0.485513 + 0.874229i \(0.338633\pi\)
\(104\) 3.84886 0.377412
\(105\) −5.22013 −0.509433
\(106\) 8.67445 0.842537
\(107\) 8.30423 0.802800 0.401400 0.915903i \(-0.368524\pi\)
0.401400 + 0.915903i \(0.368524\pi\)
\(108\) 1.13449 0.109167
\(109\) −8.73192 −0.836366 −0.418183 0.908363i \(-0.637333\pi\)
−0.418183 + 0.908363i \(0.637333\pi\)
\(110\) −11.4919 −1.09570
\(111\) −17.0134 −1.61484
\(112\) 0.995037 0.0940221
\(113\) 20.4964 1.92814 0.964071 0.265643i \(-0.0855843\pi\)
0.964071 + 0.265643i \(0.0855843\pi\)
\(114\) −17.3526 −1.62522
\(115\) −4.91896 −0.458695
\(116\) −3.74508 −0.347722
\(117\) −9.68757 −0.895616
\(118\) 9.49865 0.874422
\(119\) 1.70542 0.156336
\(120\) 5.24617 0.478907
\(121\) 15.4727 1.40661
\(122\) 8.32675 0.753869
\(123\) −26.7999 −2.41647
\(124\) 8.09676 0.727111
\(125\) −11.1930 −1.00113
\(126\) −2.50450 −0.223119
\(127\) −11.6925 −1.03754 −0.518770 0.854914i \(-0.673610\pi\)
−0.518770 + 0.854914i \(0.673610\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −18.8279 −1.65771
\(130\) 8.59653 0.753966
\(131\) −1.34288 −0.117328 −0.0586639 0.998278i \(-0.518684\pi\)
−0.0586639 + 0.998278i \(0.518684\pi\)
\(132\) −12.0851 −1.05187
\(133\) −7.35112 −0.637423
\(134\) 3.71549 0.320970
\(135\) 2.53392 0.218085
\(136\) −1.71393 −0.146968
\(137\) −5.22331 −0.446257 −0.223129 0.974789i \(-0.571627\pi\)
−0.223129 + 0.974789i \(0.571627\pi\)
\(138\) −5.17289 −0.440346
\(139\) 12.6423 1.07230 0.536151 0.844122i \(-0.319878\pi\)
0.536151 + 0.844122i \(0.319878\pi\)
\(140\) 2.22244 0.187830
\(141\) 25.7156 2.16564
\(142\) 6.29825 0.528538
\(143\) −19.8030 −1.65601
\(144\) 2.51700 0.209750
\(145\) −8.36472 −0.694652
\(146\) −8.73715 −0.723092
\(147\) 14.1162 1.16429
\(148\) 7.24334 0.595399
\(149\) −7.49216 −0.613782 −0.306891 0.951745i \(-0.599289\pi\)
−0.306891 + 0.951745i \(0.599289\pi\)
\(150\) −0.0266980 −0.00217988
\(151\) −10.8580 −0.883608 −0.441804 0.897112i \(-0.645661\pi\)
−0.441804 + 0.897112i \(0.645661\pi\)
\(152\) 7.38779 0.599229
\(153\) 4.31395 0.348762
\(154\) −5.11963 −0.412551
\(155\) 18.0843 1.45257
\(156\) 9.04032 0.723805
\(157\) 10.8927 0.869332 0.434666 0.900592i \(-0.356866\pi\)
0.434666 + 0.900592i \(0.356866\pi\)
\(158\) 13.0345 1.03697
\(159\) 20.3748 1.61583
\(160\) −2.23352 −0.176576
\(161\) −2.19140 −0.172706
\(162\) 10.2157 0.802623
\(163\) −1.51117 −0.118364 −0.0591819 0.998247i \(-0.518849\pi\)
−0.0591819 + 0.998247i \(0.518849\pi\)
\(164\) 11.4099 0.890964
\(165\) −26.9924 −2.10135
\(166\) −3.23651 −0.251202
\(167\) 9.36815 0.724929 0.362465 0.931998i \(-0.381935\pi\)
0.362465 + 0.931998i \(0.381935\pi\)
\(168\) 2.33717 0.180317
\(169\) 1.81375 0.139519
\(170\) −3.82810 −0.293602
\(171\) −18.5950 −1.42200
\(172\) 8.01588 0.611205
\(173\) 0.294859 0.0224177 0.0112089 0.999937i \(-0.496432\pi\)
0.0112089 + 0.999937i \(0.496432\pi\)
\(174\) −8.79654 −0.666864
\(175\) −0.0113101 −0.000854962 0
\(176\) 5.14516 0.387831
\(177\) 22.3107 1.67698
\(178\) 7.51185 0.563037
\(179\) −12.7957 −0.956392 −0.478196 0.878253i \(-0.658709\pi\)
−0.478196 + 0.878253i \(0.658709\pi\)
\(180\) 5.62177 0.419022
\(181\) −9.17056 −0.681642 −0.340821 0.940128i \(-0.610705\pi\)
−0.340821 + 0.940128i \(0.610705\pi\)
\(182\) 3.82976 0.283881
\(183\) 19.5581 1.44578
\(184\) 2.20233 0.162358
\(185\) 16.1782 1.18944
\(186\) 19.0179 1.39446
\(187\) 8.81845 0.644869
\(188\) −10.9483 −0.798484
\(189\) 1.12886 0.0821128
\(190\) 16.5008 1.19709
\(191\) −10.0537 −0.727462 −0.363731 0.931504i \(-0.618497\pi\)
−0.363731 + 0.931504i \(0.618497\pi\)
\(192\) −2.34883 −0.169512
\(193\) 16.0777 1.15730 0.578651 0.815576i \(-0.303580\pi\)
0.578651 + 0.815576i \(0.303580\pi\)
\(194\) 9.27019 0.665561
\(195\) 20.1918 1.44596
\(196\) −6.00990 −0.429279
\(197\) 2.71892 0.193715 0.0968575 0.995298i \(-0.469121\pi\)
0.0968575 + 0.995298i \(0.469121\pi\)
\(198\) −12.9504 −0.920342
\(199\) 20.9881 1.48781 0.743903 0.668288i \(-0.232973\pi\)
0.743903 + 0.668288i \(0.232973\pi\)
\(200\) 0.0113665 0.000803733 0
\(201\) 8.72705 0.615559
\(202\) 9.58731 0.674561
\(203\) −3.72649 −0.261548
\(204\) −4.02573 −0.281857
\(205\) 25.4843 1.77990
\(206\) −9.85484 −0.686619
\(207\) −5.54325 −0.385283
\(208\) −3.84886 −0.266871
\(209\) −38.0114 −2.62930
\(210\) 5.22013 0.360223
\(211\) 13.5100 0.930064 0.465032 0.885294i \(-0.346043\pi\)
0.465032 + 0.885294i \(0.346043\pi\)
\(212\) −8.67445 −0.595763
\(213\) 14.7935 1.01364
\(214\) −8.30423 −0.567665
\(215\) 17.9037 1.22102
\(216\) −1.13449 −0.0771926
\(217\) 8.05658 0.546916
\(218\) 8.73192 0.591400
\(219\) −20.5221 −1.38675
\(220\) 11.4919 0.774780
\(221\) −6.59668 −0.443741
\(222\) 17.0134 1.14186
\(223\) −6.63393 −0.444241 −0.222120 0.975019i \(-0.571298\pi\)
−0.222120 + 0.975019i \(0.571298\pi\)
\(224\) −0.995037 −0.0664837
\(225\) −0.0286094 −0.00190730
\(226\) −20.4964 −1.36340
\(227\) −19.1777 −1.27287 −0.636435 0.771330i \(-0.719592\pi\)
−0.636435 + 0.771330i \(0.719592\pi\)
\(228\) 17.3526 1.14921
\(229\) −17.8995 −1.18283 −0.591417 0.806366i \(-0.701431\pi\)
−0.591417 + 0.806366i \(0.701431\pi\)
\(230\) 4.91896 0.324346
\(231\) −12.0251 −0.791195
\(232\) 3.74508 0.245876
\(233\) 15.5094 1.01606 0.508029 0.861340i \(-0.330374\pi\)
0.508029 + 0.861340i \(0.330374\pi\)
\(234\) 9.68757 0.633296
\(235\) −24.4532 −1.59515
\(236\) −9.49865 −0.618310
\(237\) 30.6158 1.98871
\(238\) −1.70542 −0.110546
\(239\) −2.07421 −0.134170 −0.0670849 0.997747i \(-0.521370\pi\)
−0.0670849 + 0.997747i \(0.521370\pi\)
\(240\) −5.24617 −0.338639
\(241\) −11.8031 −0.760306 −0.380153 0.924924i \(-0.624129\pi\)
−0.380153 + 0.924924i \(0.624129\pi\)
\(242\) −15.4727 −0.994623
\(243\) 20.5915 1.32094
\(244\) −8.32675 −0.533066
\(245\) −13.4233 −0.857581
\(246\) 26.7999 1.70870
\(247\) 28.4346 1.80925
\(248\) −8.09676 −0.514145
\(249\) −7.60201 −0.481758
\(250\) 11.1930 0.707908
\(251\) 28.9777 1.82906 0.914528 0.404523i \(-0.132563\pi\)
0.914528 + 0.404523i \(0.132563\pi\)
\(252\) 2.50450 0.157769
\(253\) −11.3313 −0.712395
\(254\) 11.6925 0.733652
\(255\) −8.99156 −0.563073
\(256\) 1.00000 0.0625000
\(257\) 20.1050 1.25412 0.627059 0.778972i \(-0.284259\pi\)
0.627059 + 0.778972i \(0.284259\pi\)
\(258\) 18.8279 1.17218
\(259\) 7.20739 0.447845
\(260\) −8.59653 −0.533134
\(261\) −9.42634 −0.583476
\(262\) 1.34288 0.0829632
\(263\) −0.370427 −0.0228415 −0.0114208 0.999935i \(-0.503635\pi\)
−0.0114208 + 0.999935i \(0.503635\pi\)
\(264\) 12.0851 0.743787
\(265\) −19.3746 −1.19017
\(266\) 7.35112 0.450726
\(267\) 17.6440 1.07980
\(268\) −3.71549 −0.226960
\(269\) −27.3825 −1.66954 −0.834770 0.550598i \(-0.814400\pi\)
−0.834770 + 0.550598i \(0.814400\pi\)
\(270\) −2.53392 −0.154210
\(271\) 19.0234 1.15559 0.577794 0.816183i \(-0.303914\pi\)
0.577794 + 0.816183i \(0.303914\pi\)
\(272\) 1.71393 0.103922
\(273\) 8.99545 0.544430
\(274\) 5.22331 0.315551
\(275\) −0.0584825 −0.00352663
\(276\) 5.17289 0.311372
\(277\) −18.3627 −1.10331 −0.551653 0.834074i \(-0.686003\pi\)
−0.551653 + 0.834074i \(0.686003\pi\)
\(278\) −12.6423 −0.758232
\(279\) 20.3795 1.22009
\(280\) −2.22244 −0.132816
\(281\) −27.6749 −1.65095 −0.825473 0.564442i \(-0.809091\pi\)
−0.825473 + 0.564442i \(0.809091\pi\)
\(282\) −25.7156 −1.53134
\(283\) 21.1856 1.25935 0.629677 0.776857i \(-0.283187\pi\)
0.629677 + 0.776857i \(0.283187\pi\)
\(284\) −6.29825 −0.373733
\(285\) 38.7576 2.29580
\(286\) 19.8030 1.17098
\(287\) 11.3533 0.670163
\(288\) −2.51700 −0.148315
\(289\) −14.0624 −0.827203
\(290\) 8.36472 0.491193
\(291\) 21.7741 1.27642
\(292\) 8.73715 0.511303
\(293\) −13.1598 −0.768806 −0.384403 0.923165i \(-0.625593\pi\)
−0.384403 + 0.923165i \(0.625593\pi\)
\(294\) −14.1162 −0.823275
\(295\) −21.2155 −1.23521
\(296\) −7.24334 −0.421010
\(297\) 5.83716 0.338706
\(298\) 7.49216 0.434009
\(299\) 8.47646 0.490206
\(300\) 0.0266980 0.00154141
\(301\) 7.97610 0.459735
\(302\) 10.8580 0.624805
\(303\) 22.5189 1.29368
\(304\) −7.38779 −0.423719
\(305\) −18.5980 −1.06492
\(306\) −4.31395 −0.246612
\(307\) 2.80861 0.160296 0.0801480 0.996783i \(-0.474461\pi\)
0.0801480 + 0.996783i \(0.474461\pi\)
\(308\) 5.11963 0.291718
\(309\) −23.1473 −1.31681
\(310\) −18.0843 −1.02712
\(311\) −13.4142 −0.760648 −0.380324 0.924853i \(-0.624187\pi\)
−0.380324 + 0.924853i \(0.624187\pi\)
\(312\) −9.04032 −0.511807
\(313\) 7.26667 0.410737 0.205368 0.978685i \(-0.434161\pi\)
0.205368 + 0.978685i \(0.434161\pi\)
\(314\) −10.8927 −0.614711
\(315\) 5.59387 0.315179
\(316\) −13.0345 −0.733247
\(317\) 2.98249 0.167513 0.0837567 0.996486i \(-0.473308\pi\)
0.0837567 + 0.996486i \(0.473308\pi\)
\(318\) −20.3748 −1.14256
\(319\) −19.2690 −1.07886
\(320\) 2.23352 0.124858
\(321\) −19.5052 −1.08867
\(322\) 2.19140 0.122122
\(323\) −12.6621 −0.704541
\(324\) −10.2157 −0.567540
\(325\) 0.0437481 0.00242671
\(326\) 1.51117 0.0836958
\(327\) 20.5098 1.13419
\(328\) −11.4099 −0.630007
\(329\) −10.8939 −0.600601
\(330\) 26.9924 1.48588
\(331\) 24.7285 1.35920 0.679600 0.733583i \(-0.262153\pi\)
0.679600 + 0.733583i \(0.262153\pi\)
\(332\) 3.23651 0.177627
\(333\) 18.2314 0.999077
\(334\) −9.36815 −0.512602
\(335\) −8.29864 −0.453403
\(336\) −2.33717 −0.127503
\(337\) 24.8604 1.35423 0.677117 0.735875i \(-0.263229\pi\)
0.677117 + 0.735875i \(0.263229\pi\)
\(338\) −1.81375 −0.0986551
\(339\) −48.1426 −2.61475
\(340\) 3.82810 0.207608
\(341\) 41.6592 2.25597
\(342\) 18.5950 1.00550
\(343\) −12.9453 −0.698982
\(344\) −8.01588 −0.432187
\(345\) 11.5538 0.622035
\(346\) −0.294859 −0.0158517
\(347\) −16.1853 −0.868872 −0.434436 0.900703i \(-0.643052\pi\)
−0.434436 + 0.900703i \(0.643052\pi\)
\(348\) 8.79654 0.471544
\(349\) −18.0334 −0.965308 −0.482654 0.875811i \(-0.660327\pi\)
−0.482654 + 0.875811i \(0.660327\pi\)
\(350\) 0.0113101 0.000604550 0
\(351\) −4.36651 −0.233067
\(352\) −5.14516 −0.274238
\(353\) −24.7218 −1.31581 −0.657904 0.753102i \(-0.728557\pi\)
−0.657904 + 0.753102i \(0.728557\pi\)
\(354\) −22.3107 −1.18580
\(355\) −14.0673 −0.746615
\(356\) −7.51185 −0.398127
\(357\) −4.00575 −0.212007
\(358\) 12.7957 0.676271
\(359\) 22.6756 1.19677 0.598385 0.801209i \(-0.295809\pi\)
0.598385 + 0.801209i \(0.295809\pi\)
\(360\) −5.62177 −0.296293
\(361\) 35.5794 1.87260
\(362\) 9.17056 0.481994
\(363\) −36.3427 −1.90750
\(364\) −3.82976 −0.200734
\(365\) 19.5147 1.02144
\(366\) −19.5581 −1.02232
\(367\) 9.01555 0.470608 0.235304 0.971922i \(-0.424391\pi\)
0.235304 + 0.971922i \(0.424391\pi\)
\(368\) −2.20233 −0.114804
\(369\) 28.7187 1.49503
\(370\) −16.1782 −0.841063
\(371\) −8.63139 −0.448120
\(372\) −19.0179 −0.986033
\(373\) −21.3928 −1.10768 −0.553838 0.832624i \(-0.686837\pi\)
−0.553838 + 0.832624i \(0.686837\pi\)
\(374\) −8.81845 −0.455991
\(375\) 26.2905 1.35763
\(376\) 10.9483 0.564613
\(377\) 14.4143 0.742374
\(378\) −1.12886 −0.0580625
\(379\) −11.9165 −0.612107 −0.306054 0.952014i \(-0.599009\pi\)
−0.306054 + 0.952014i \(0.599009\pi\)
\(380\) −16.5008 −0.846474
\(381\) 27.4636 1.40700
\(382\) 10.0537 0.514393
\(383\) −37.7910 −1.93103 −0.965515 0.260346i \(-0.916163\pi\)
−0.965515 + 0.260346i \(0.916163\pi\)
\(384\) 2.34883 0.119863
\(385\) 11.4348 0.582772
\(386\) −16.0777 −0.818335
\(387\) 20.1759 1.02560
\(388\) −9.27019 −0.470623
\(389\) −9.45255 −0.479263 −0.239632 0.970864i \(-0.577027\pi\)
−0.239632 + 0.970864i \(0.577027\pi\)
\(390\) −20.1918 −1.02245
\(391\) −3.77464 −0.190892
\(392\) 6.00990 0.303546
\(393\) 3.15419 0.159108
\(394\) −2.71892 −0.136977
\(395\) −29.1128 −1.46483
\(396\) 12.9504 0.650780
\(397\) 1.57937 0.0792663 0.0396332 0.999214i \(-0.487381\pi\)
0.0396332 + 0.999214i \(0.487381\pi\)
\(398\) −20.9881 −1.05204
\(399\) 17.2665 0.864407
\(400\) −0.0113665 −0.000568325 0
\(401\) 4.35142 0.217300 0.108650 0.994080i \(-0.465347\pi\)
0.108650 + 0.994080i \(0.465347\pi\)
\(402\) −8.72705 −0.435266
\(403\) −31.1633 −1.55236
\(404\) −9.58731 −0.476987
\(405\) −22.8171 −1.13379
\(406\) 3.72649 0.184943
\(407\) 37.2682 1.84731
\(408\) 4.02573 0.199303
\(409\) −30.4919 −1.50773 −0.753863 0.657031i \(-0.771812\pi\)
−0.753863 + 0.657031i \(0.771812\pi\)
\(410\) −25.4843 −1.25858
\(411\) 12.2687 0.605168
\(412\) 9.85484 0.485513
\(413\) −9.45151 −0.465078
\(414\) 5.54325 0.272436
\(415\) 7.22883 0.354849
\(416\) 3.84886 0.188706
\(417\) −29.6945 −1.45414
\(418\) 38.0114 1.85920
\(419\) 31.0210 1.51547 0.757736 0.652561i \(-0.226305\pi\)
0.757736 + 0.652561i \(0.226305\pi\)
\(420\) −5.22013 −0.254716
\(421\) −18.6987 −0.911317 −0.455659 0.890155i \(-0.650596\pi\)
−0.455659 + 0.890155i \(0.650596\pi\)
\(422\) −13.5100 −0.657654
\(423\) −27.5567 −1.33985
\(424\) 8.67445 0.421268
\(425\) −0.0194814 −0.000944986 0
\(426\) −14.7935 −0.716748
\(427\) −8.28543 −0.400960
\(428\) 8.30423 0.401400
\(429\) 46.5139 2.24571
\(430\) −17.9037 −0.863392
\(431\) −11.7880 −0.567806 −0.283903 0.958853i \(-0.591629\pi\)
−0.283903 + 0.958853i \(0.591629\pi\)
\(432\) 1.13449 0.0545834
\(433\) 6.35407 0.305357 0.152679 0.988276i \(-0.451210\pi\)
0.152679 + 0.988276i \(0.451210\pi\)
\(434\) −8.05658 −0.386728
\(435\) 19.6473 0.942016
\(436\) −8.73192 −0.418183
\(437\) 16.2703 0.778316
\(438\) 20.5221 0.980583
\(439\) 2.15788 0.102990 0.0514951 0.998673i \(-0.483601\pi\)
0.0514951 + 0.998673i \(0.483601\pi\)
\(440\) −11.4919 −0.547852
\(441\) −15.1269 −0.720328
\(442\) 6.59668 0.313772
\(443\) −31.7447 −1.50824 −0.754118 0.656739i \(-0.771935\pi\)
−0.754118 + 0.656739i \(0.771935\pi\)
\(444\) −17.0134 −0.807418
\(445\) −16.7779 −0.795349
\(446\) 6.63393 0.314126
\(447\) 17.5978 0.832347
\(448\) 0.995037 0.0470111
\(449\) −21.0383 −0.992859 −0.496430 0.868077i \(-0.665356\pi\)
−0.496430 + 0.868077i \(0.665356\pi\)
\(450\) 0.0286094 0.00134866
\(451\) 58.7058 2.76435
\(452\) 20.4964 0.964071
\(453\) 25.5035 1.19826
\(454\) 19.1777 0.900056
\(455\) −8.55387 −0.401011
\(456\) −17.3526 −0.812612
\(457\) −33.2982 −1.55762 −0.778811 0.627258i \(-0.784177\pi\)
−0.778811 + 0.627258i \(0.784177\pi\)
\(458\) 17.8995 0.836390
\(459\) 1.94444 0.0907588
\(460\) −4.91896 −0.229347
\(461\) 27.2173 1.26764 0.633818 0.773482i \(-0.281487\pi\)
0.633818 + 0.773482i \(0.281487\pi\)
\(462\) 12.0251 0.559460
\(463\) −17.4002 −0.808655 −0.404328 0.914614i \(-0.632494\pi\)
−0.404328 + 0.914614i \(0.632494\pi\)
\(464\) −3.74508 −0.173861
\(465\) −42.4770 −1.96982
\(466\) −15.5094 −0.718461
\(467\) 37.5732 1.73868 0.869341 0.494212i \(-0.164543\pi\)
0.869341 + 0.494212i \(0.164543\pi\)
\(468\) −9.68757 −0.447808
\(469\) −3.69705 −0.170714
\(470\) 24.4532 1.12794
\(471\) −25.5851 −1.17890
\(472\) 9.49865 0.437211
\(473\) 41.2430 1.89636
\(474\) −30.6158 −1.40623
\(475\) 0.0839733 0.00385296
\(476\) 1.70542 0.0781679
\(477\) −21.8335 −0.999689
\(478\) 2.07421 0.0948723
\(479\) 42.7897 1.95511 0.977555 0.210680i \(-0.0675678\pi\)
0.977555 + 0.210680i \(0.0675678\pi\)
\(480\) 5.24617 0.239454
\(481\) −27.8786 −1.27116
\(482\) 11.8031 0.537618
\(483\) 5.14722 0.234207
\(484\) 15.4727 0.703305
\(485\) −20.7052 −0.940175
\(486\) −20.5915 −0.934049
\(487\) 40.1808 1.82077 0.910384 0.413764i \(-0.135786\pi\)
0.910384 + 0.413764i \(0.135786\pi\)
\(488\) 8.32675 0.376934
\(489\) 3.54947 0.160513
\(490\) 13.4233 0.606401
\(491\) 19.8522 0.895915 0.447958 0.894055i \(-0.352152\pi\)
0.447958 + 0.894055i \(0.352152\pi\)
\(492\) −26.7999 −1.20823
\(493\) −6.41880 −0.289088
\(494\) −28.4346 −1.27933
\(495\) 28.9249 1.30008
\(496\) 8.09676 0.363555
\(497\) −6.26699 −0.281113
\(498\) 7.60201 0.340654
\(499\) 28.0755 1.25683 0.628416 0.777878i \(-0.283704\pi\)
0.628416 + 0.777878i \(0.283704\pi\)
\(500\) −11.1930 −0.500567
\(501\) −22.0042 −0.983074
\(502\) −28.9777 −1.29334
\(503\) 38.4524 1.71451 0.857253 0.514895i \(-0.172169\pi\)
0.857253 + 0.514895i \(0.172169\pi\)
\(504\) −2.50450 −0.111559
\(505\) −21.4135 −0.952888
\(506\) 11.3313 0.503739
\(507\) −4.26019 −0.189202
\(508\) −11.6925 −0.518770
\(509\) −29.3003 −1.29871 −0.649357 0.760483i \(-0.724962\pi\)
−0.649357 + 0.760483i \(0.724962\pi\)
\(510\) 8.99156 0.398153
\(511\) 8.69379 0.384591
\(512\) −1.00000 −0.0441942
\(513\) −8.38140 −0.370048
\(514\) −20.1050 −0.886795
\(515\) 22.0110 0.969922
\(516\) −18.8279 −0.828854
\(517\) −56.3306 −2.47742
\(518\) −7.20739 −0.316674
\(519\) −0.692573 −0.0304006
\(520\) 8.59653 0.376983
\(521\) −18.7152 −0.819929 −0.409965 0.912101i \(-0.634459\pi\)
−0.409965 + 0.912101i \(0.634459\pi\)
\(522\) 9.42634 0.412580
\(523\) 0.595583 0.0260430 0.0130215 0.999915i \(-0.495855\pi\)
0.0130215 + 0.999915i \(0.495855\pi\)
\(524\) −1.34288 −0.0586639
\(525\) 0.0265655 0.00115941
\(526\) 0.370427 0.0161514
\(527\) 13.8773 0.604504
\(528\) −12.0851 −0.525937
\(529\) −18.1497 −0.789120
\(530\) 19.3746 0.841578
\(531\) −23.9081 −1.03752
\(532\) −7.35112 −0.318712
\(533\) −43.9152 −1.90218
\(534\) −17.6440 −0.763533
\(535\) 18.5477 0.801887
\(536\) 3.71549 0.160485
\(537\) 30.0548 1.29696
\(538\) 27.3825 1.18054
\(539\) −30.9219 −1.33190
\(540\) 2.53392 0.109043
\(541\) −29.3256 −1.26080 −0.630402 0.776269i \(-0.717110\pi\)
−0.630402 + 0.776269i \(0.717110\pi\)
\(542\) −19.0234 −0.817124
\(543\) 21.5401 0.924373
\(544\) −1.71393 −0.0734841
\(545\) −19.5030 −0.835415
\(546\) −8.99545 −0.384970
\(547\) −11.7341 −0.501714 −0.250857 0.968024i \(-0.580712\pi\)
−0.250857 + 0.968024i \(0.580712\pi\)
\(548\) −5.22331 −0.223129
\(549\) −20.9584 −0.894483
\(550\) 0.0584825 0.00249370
\(551\) 27.6678 1.17869
\(552\) −5.17289 −0.220173
\(553\) −12.9698 −0.551532
\(554\) 18.3627 0.780155
\(555\) −37.9998 −1.61300
\(556\) 12.6423 0.536151
\(557\) −24.2803 −1.02879 −0.514395 0.857554i \(-0.671983\pi\)
−0.514395 + 0.857554i \(0.671983\pi\)
\(558\) −20.3795 −0.862734
\(559\) −30.8520 −1.30490
\(560\) 2.22244 0.0939152
\(561\) −20.7130 −0.874504
\(562\) 27.6749 1.16740
\(563\) −41.4899 −1.74859 −0.874295 0.485396i \(-0.838676\pi\)
−0.874295 + 0.485396i \(0.838676\pi\)
\(564\) 25.7156 1.08282
\(565\) 45.7793 1.92595
\(566\) −21.1856 −0.890497
\(567\) −10.1650 −0.426891
\(568\) 6.29825 0.264269
\(569\) 16.5791 0.695033 0.347517 0.937674i \(-0.387025\pi\)
0.347517 + 0.937674i \(0.387025\pi\)
\(570\) −38.7576 −1.62338
\(571\) −0.865552 −0.0362222 −0.0181111 0.999836i \(-0.505765\pi\)
−0.0181111 + 0.999836i \(0.505765\pi\)
\(572\) −19.8030 −0.828006
\(573\) 23.6145 0.986508
\(574\) −11.3533 −0.473877
\(575\) 0.0250328 0.00104394
\(576\) 2.51700 0.104875
\(577\) −6.50059 −0.270623 −0.135312 0.990803i \(-0.543204\pi\)
−0.135312 + 0.990803i \(0.543204\pi\)
\(578\) 14.0624 0.584921
\(579\) −37.7639 −1.56941
\(580\) −8.36472 −0.347326
\(581\) 3.22045 0.133607
\(582\) −21.7741 −0.902565
\(583\) −44.6314 −1.84845
\(584\) −8.73715 −0.361546
\(585\) −21.6374 −0.894598
\(586\) 13.1598 0.543628
\(587\) −37.3417 −1.54126 −0.770628 0.637285i \(-0.780057\pi\)
−0.770628 + 0.637285i \(0.780057\pi\)
\(588\) 14.1162 0.582143
\(589\) −59.8172 −2.46472
\(590\) 21.2155 0.873427
\(591\) −6.38627 −0.262696
\(592\) 7.24334 0.297699
\(593\) 30.1915 1.23981 0.619907 0.784675i \(-0.287170\pi\)
0.619907 + 0.784675i \(0.287170\pi\)
\(594\) −5.83716 −0.239502
\(595\) 3.80910 0.156158
\(596\) −7.49216 −0.306891
\(597\) −49.2974 −2.01761
\(598\) −8.47646 −0.346628
\(599\) −0.494951 −0.0202231 −0.0101116 0.999949i \(-0.503219\pi\)
−0.0101116 + 0.999949i \(0.503219\pi\)
\(600\) −0.0266980 −0.00108994
\(601\) −19.9566 −0.814048 −0.407024 0.913418i \(-0.633433\pi\)
−0.407024 + 0.913418i \(0.633433\pi\)
\(602\) −7.97610 −0.325082
\(603\) −9.35187 −0.380838
\(604\) −10.8580 −0.441804
\(605\) 34.5587 1.40501
\(606\) −22.5189 −0.914770
\(607\) −45.0130 −1.82702 −0.913510 0.406815i \(-0.866639\pi\)
−0.913510 + 0.406815i \(0.866639\pi\)
\(608\) 7.38779 0.299614
\(609\) 8.75288 0.354685
\(610\) 18.5980 0.753011
\(611\) 42.1383 1.70473
\(612\) 4.31395 0.174381
\(613\) −9.66995 −0.390566 −0.195283 0.980747i \(-0.562562\pi\)
−0.195283 + 0.980747i \(0.562562\pi\)
\(614\) −2.80861 −0.113346
\(615\) −59.8583 −2.41372
\(616\) −5.11963 −0.206276
\(617\) 24.0775 0.969323 0.484662 0.874702i \(-0.338943\pi\)
0.484662 + 0.874702i \(0.338943\pi\)
\(618\) 23.1473 0.931122
\(619\) 11.0834 0.445480 0.222740 0.974878i \(-0.428500\pi\)
0.222740 + 0.974878i \(0.428500\pi\)
\(620\) 18.0843 0.726284
\(621\) −2.49853 −0.100263
\(622\) 13.4142 0.537859
\(623\) −7.47457 −0.299462
\(624\) 9.04032 0.361902
\(625\) −24.9430 −0.997722
\(626\) −7.26667 −0.290435
\(627\) 89.2822 3.56559
\(628\) 10.8927 0.434666
\(629\) 12.4146 0.495001
\(630\) −5.59387 −0.222865
\(631\) −20.6835 −0.823396 −0.411698 0.911320i \(-0.635064\pi\)
−0.411698 + 0.911320i \(0.635064\pi\)
\(632\) 13.0345 0.518484
\(633\) −31.7326 −1.26126
\(634\) −2.98249 −0.118450
\(635\) −26.1155 −1.03636
\(636\) 20.3748 0.807913
\(637\) 23.1313 0.916495
\(638\) 19.2690 0.762868
\(639\) −15.8527 −0.627122
\(640\) −2.23352 −0.0882878
\(641\) 25.4843 1.00657 0.503285 0.864121i \(-0.332125\pi\)
0.503285 + 0.864121i \(0.332125\pi\)
\(642\) 19.5052 0.769809
\(643\) 26.7173 1.05363 0.526813 0.849981i \(-0.323387\pi\)
0.526813 + 0.849981i \(0.323387\pi\)
\(644\) −2.19140 −0.0863532
\(645\) −42.0527 −1.65582
\(646\) 12.6621 0.498185
\(647\) −14.1580 −0.556610 −0.278305 0.960493i \(-0.589773\pi\)
−0.278305 + 0.960493i \(0.589773\pi\)
\(648\) 10.2157 0.401311
\(649\) −48.8721 −1.91840
\(650\) −0.0437481 −0.00171594
\(651\) −18.9235 −0.741671
\(652\) −1.51117 −0.0591819
\(653\) −4.20829 −0.164683 −0.0823415 0.996604i \(-0.526240\pi\)
−0.0823415 + 0.996604i \(0.526240\pi\)
\(654\) −20.5098 −0.801996
\(655\) −2.99935 −0.117194
\(656\) 11.4099 0.445482
\(657\) 21.9914 0.857965
\(658\) 10.8939 0.424689
\(659\) 10.1760 0.396400 0.198200 0.980162i \(-0.436490\pi\)
0.198200 + 0.980162i \(0.436490\pi\)
\(660\) −26.9924 −1.05068
\(661\) −17.6388 −0.686068 −0.343034 0.939323i \(-0.611455\pi\)
−0.343034 + 0.939323i \(0.611455\pi\)
\(662\) −24.7285 −0.961100
\(663\) 15.4945 0.601755
\(664\) −3.23651 −0.125601
\(665\) −16.4189 −0.636698
\(666\) −18.2314 −0.706454
\(667\) 8.24789 0.319360
\(668\) 9.36815 0.362465
\(669\) 15.5820 0.602434
\(670\) 8.29864 0.320604
\(671\) −42.8425 −1.65392
\(672\) 2.33717 0.0901583
\(673\) −1.96373 −0.0756964 −0.0378482 0.999284i \(-0.512050\pi\)
−0.0378482 + 0.999284i \(0.512050\pi\)
\(674\) −24.8604 −0.957588
\(675\) −0.0128952 −0.000496338 0
\(676\) 1.81375 0.0697597
\(677\) 29.2002 1.12225 0.561126 0.827730i \(-0.310368\pi\)
0.561126 + 0.827730i \(0.310368\pi\)
\(678\) 48.1426 1.84891
\(679\) −9.22418 −0.353992
\(680\) −3.82810 −0.146801
\(681\) 45.0452 1.72614
\(682\) −41.6592 −1.59521
\(683\) 23.9120 0.914966 0.457483 0.889218i \(-0.348751\pi\)
0.457483 + 0.889218i \(0.348751\pi\)
\(684\) −18.5950 −0.710999
\(685\) −11.6664 −0.445750
\(686\) 12.9453 0.494255
\(687\) 42.0429 1.60404
\(688\) 8.01588 0.305603
\(689\) 33.3868 1.27193
\(690\) −11.5538 −0.439845
\(691\) −15.6254 −0.594417 −0.297209 0.954813i \(-0.596056\pi\)
−0.297209 + 0.954813i \(0.596056\pi\)
\(692\) 0.294859 0.0112089
\(693\) 12.8861 0.489502
\(694\) 16.1853 0.614385
\(695\) 28.2368 1.07108
\(696\) −8.79654 −0.333432
\(697\) 19.5558 0.740728
\(698\) 18.0334 0.682576
\(699\) −36.4290 −1.37787
\(700\) −0.0113101 −0.000427481 0
\(701\) −34.3225 −1.29634 −0.648172 0.761494i \(-0.724466\pi\)
−0.648172 + 0.761494i \(0.724466\pi\)
\(702\) 4.36651 0.164803
\(703\) −53.5122 −2.01825
\(704\) 5.14516 0.193916
\(705\) 57.4364 2.16318
\(706\) 24.7218 0.930416
\(707\) −9.53973 −0.358778
\(708\) 22.3107 0.838488
\(709\) 2.78977 0.104772 0.0523859 0.998627i \(-0.483317\pi\)
0.0523859 + 0.998627i \(0.483317\pi\)
\(710\) 14.0673 0.527937
\(711\) −32.8077 −1.23039
\(712\) 7.51185 0.281518
\(713\) −17.8317 −0.667804
\(714\) 4.00575 0.149911
\(715\) −44.2306 −1.65413
\(716\) −12.7957 −0.478196
\(717\) 4.87197 0.181947
\(718\) −22.6756 −0.846244
\(719\) −32.8736 −1.22598 −0.612989 0.790091i \(-0.710033\pi\)
−0.612989 + 0.790091i \(0.710033\pi\)
\(720\) 5.62177 0.209511
\(721\) 9.80593 0.365192
\(722\) −35.5794 −1.32413
\(723\) 27.7235 1.03105
\(724\) −9.17056 −0.340821
\(725\) 0.0425684 0.00158095
\(726\) 36.3427 1.34881
\(727\) −13.7935 −0.511572 −0.255786 0.966733i \(-0.582334\pi\)
−0.255786 + 0.966733i \(0.582334\pi\)
\(728\) 3.82976 0.141940
\(729\) −17.7187 −0.656249
\(730\) −19.5147 −0.722270
\(731\) 13.7387 0.508142
\(732\) 19.5581 0.722889
\(733\) 27.5268 1.01673 0.508363 0.861143i \(-0.330251\pi\)
0.508363 + 0.861143i \(0.330251\pi\)
\(734\) −9.01555 −0.332770
\(735\) 31.5289 1.16296
\(736\) 2.20233 0.0811789
\(737\) −19.1168 −0.704177
\(738\) −28.7187 −1.05715
\(739\) 16.5669 0.609422 0.304711 0.952445i \(-0.401440\pi\)
0.304711 + 0.952445i \(0.401440\pi\)
\(740\) 16.1782 0.594721
\(741\) −66.7880 −2.45352
\(742\) 8.63139 0.316868
\(743\) 21.4188 0.785781 0.392890 0.919585i \(-0.371475\pi\)
0.392890 + 0.919585i \(0.371475\pi\)
\(744\) 19.0179 0.697230
\(745\) −16.7339 −0.613084
\(746\) 21.3928 0.783246
\(747\) 8.14628 0.298057
\(748\) 8.81845 0.322434
\(749\) 8.26301 0.301924
\(750\) −26.2905 −0.959992
\(751\) −10.3607 −0.378068 −0.189034 0.981971i \(-0.560536\pi\)
−0.189034 + 0.981971i \(0.560536\pi\)
\(752\) −10.9483 −0.399242
\(753\) −68.0636 −2.48038
\(754\) −14.4143 −0.524937
\(755\) −24.2515 −0.882603
\(756\) 1.12886 0.0410564
\(757\) 16.3663 0.594845 0.297422 0.954746i \(-0.403873\pi\)
0.297422 + 0.954746i \(0.403873\pi\)
\(758\) 11.9165 0.432825
\(759\) 26.6154 0.966077
\(760\) 16.5008 0.598547
\(761\) 26.4737 0.959669 0.479835 0.877359i \(-0.340697\pi\)
0.479835 + 0.877359i \(0.340697\pi\)
\(762\) −27.4636 −0.994903
\(763\) −8.68858 −0.314548
\(764\) −10.0537 −0.363731
\(765\) 9.63532 0.348366
\(766\) 37.7910 1.36544
\(767\) 36.5590 1.32007
\(768\) −2.34883 −0.0847561
\(769\) −12.8384 −0.462965 −0.231482 0.972839i \(-0.574358\pi\)
−0.231482 + 0.972839i \(0.574358\pi\)
\(770\) −11.4348 −0.412082
\(771\) −47.2233 −1.70070
\(772\) 16.0777 0.578651
\(773\) −19.2624 −0.692819 −0.346410 0.938083i \(-0.612599\pi\)
−0.346410 + 0.938083i \(0.612599\pi\)
\(774\) −20.1759 −0.725209
\(775\) −0.0920319 −0.00330588
\(776\) 9.27019 0.332781
\(777\) −16.9289 −0.607322
\(778\) 9.45255 0.338890
\(779\) −84.2940 −3.02014
\(780\) 20.1918 0.722982
\(781\) −32.4055 −1.15956
\(782\) 3.77464 0.134981
\(783\) −4.24877 −0.151839
\(784\) −6.00990 −0.214639
\(785\) 24.3291 0.868344
\(786\) −3.15419 −0.112506
\(787\) 4.71235 0.167977 0.0839885 0.996467i \(-0.473234\pi\)
0.0839885 + 0.996467i \(0.473234\pi\)
\(788\) 2.71892 0.0968575
\(789\) 0.870071 0.0309753
\(790\) 29.1128 1.03579
\(791\) 20.3947 0.725153
\(792\) −12.9504 −0.460171
\(793\) 32.0485 1.13808
\(794\) −1.57937 −0.0560498
\(795\) 45.5076 1.61399
\(796\) 20.9881 0.743903
\(797\) 1.43465 0.0508181 0.0254090 0.999677i \(-0.491911\pi\)
0.0254090 + 0.999677i \(0.491911\pi\)
\(798\) −17.2665 −0.611228
\(799\) −18.7645 −0.663841
\(800\) 0.0113665 0.000401867 0
\(801\) −18.9073 −0.668056
\(802\) −4.35142 −0.153654
\(803\) 44.9541 1.58640
\(804\) 8.72705 0.307779
\(805\) −4.89454 −0.172510
\(806\) 31.1633 1.09768
\(807\) 64.3168 2.26406
\(808\) 9.58731 0.337280
\(809\) 46.9252 1.64980 0.824901 0.565277i \(-0.191231\pi\)
0.824901 + 0.565277i \(0.191231\pi\)
\(810\) 22.8171 0.801710
\(811\) −23.8180 −0.836362 −0.418181 0.908364i \(-0.637332\pi\)
−0.418181 + 0.908364i \(0.637332\pi\)
\(812\) −3.72649 −0.130774
\(813\) −44.6826 −1.56709
\(814\) −37.2682 −1.30625
\(815\) −3.37523 −0.118229
\(816\) −4.02573 −0.140929
\(817\) −59.2196 −2.07183
\(818\) 30.4919 1.06612
\(819\) −9.63949 −0.336831
\(820\) 25.4843 0.889951
\(821\) 1.20419 0.0420266 0.0210133 0.999779i \(-0.493311\pi\)
0.0210133 + 0.999779i \(0.493311\pi\)
\(822\) −12.2687 −0.427918
\(823\) 18.5327 0.646011 0.323006 0.946397i \(-0.395307\pi\)
0.323006 + 0.946397i \(0.395307\pi\)
\(824\) −9.85484 −0.343310
\(825\) 0.137365 0.00478245
\(826\) 9.45151 0.328860
\(827\) −9.34430 −0.324933 −0.162467 0.986714i \(-0.551945\pi\)
−0.162467 + 0.986714i \(0.551945\pi\)
\(828\) −5.54325 −0.192641
\(829\) −24.0958 −0.836883 −0.418441 0.908244i \(-0.637423\pi\)
−0.418441 + 0.908244i \(0.637423\pi\)
\(830\) −7.22883 −0.250916
\(831\) 43.1308 1.49619
\(832\) −3.84886 −0.133435
\(833\) −10.3005 −0.356893
\(834\) 29.6945 1.02824
\(835\) 20.9240 0.724105
\(836\) −38.0114 −1.31465
\(837\) 9.18573 0.317505
\(838\) −31.0210 −1.07160
\(839\) 12.9542 0.447230 0.223615 0.974678i \(-0.428214\pi\)
0.223615 + 0.974678i \(0.428214\pi\)
\(840\) 5.22013 0.180112
\(841\) −14.9744 −0.516359
\(842\) 18.6987 0.644399
\(843\) 65.0036 2.23884
\(844\) 13.5100 0.465032
\(845\) 4.05106 0.139361
\(846\) 27.5567 0.947419
\(847\) 15.3959 0.529010
\(848\) −8.67445 −0.297882
\(849\) −49.7613 −1.70781
\(850\) 0.0194814 0.000668206 0
\(851\) −15.9522 −0.546835
\(852\) 14.7935 0.506818
\(853\) −2.81402 −0.0963503 −0.0481751 0.998839i \(-0.515341\pi\)
−0.0481751 + 0.998839i \(0.515341\pi\)
\(854\) 8.28543 0.283521
\(855\) −41.5325 −1.42038
\(856\) −8.30423 −0.283833
\(857\) 2.63164 0.0898949 0.0449475 0.998989i \(-0.485688\pi\)
0.0449475 + 0.998989i \(0.485688\pi\)
\(858\) −46.5139 −1.58796
\(859\) −24.0385 −0.820183 −0.410091 0.912044i \(-0.634503\pi\)
−0.410091 + 0.912044i \(0.634503\pi\)
\(860\) 17.9037 0.610510
\(861\) −26.6669 −0.908805
\(862\) 11.7880 0.401499
\(863\) −1.06568 −0.0362762 −0.0181381 0.999835i \(-0.505774\pi\)
−0.0181381 + 0.999835i \(0.505774\pi\)
\(864\) −1.13449 −0.0385963
\(865\) 0.658575 0.0223922
\(866\) −6.35407 −0.215920
\(867\) 33.0303 1.12177
\(868\) 8.05658 0.273458
\(869\) −67.0645 −2.27501
\(870\) −19.6473 −0.666106
\(871\) 14.3004 0.484551
\(872\) 8.73192 0.295700
\(873\) −23.3330 −0.789704
\(874\) −16.2703 −0.550352
\(875\) −11.1375 −0.376515
\(876\) −20.5221 −0.693377
\(877\) −39.3923 −1.33018 −0.665091 0.746762i \(-0.731607\pi\)
−0.665091 + 0.746762i \(0.731607\pi\)
\(878\) −2.15788 −0.0728250
\(879\) 30.9102 1.04258
\(880\) 11.4919 0.387390
\(881\) 56.7603 1.91230 0.956152 0.292870i \(-0.0946105\pi\)
0.956152 + 0.292870i \(0.0946105\pi\)
\(882\) 15.1269 0.509349
\(883\) −32.0198 −1.07755 −0.538775 0.842450i \(-0.681113\pi\)
−0.538775 + 0.842450i \(0.681113\pi\)
\(884\) −6.59668 −0.221870
\(885\) 49.8315 1.67507
\(886\) 31.7447 1.06648
\(887\) −50.0266 −1.67973 −0.839864 0.542797i \(-0.817365\pi\)
−0.839864 + 0.542797i \(0.817365\pi\)
\(888\) 17.0134 0.570931
\(889\) −11.6345 −0.390207
\(890\) 16.7779 0.562397
\(891\) −52.5615 −1.76088
\(892\) −6.63393 −0.222120
\(893\) 80.8834 2.70666
\(894\) −17.5978 −0.588558
\(895\) −28.5794 −0.955304
\(896\) −0.995037 −0.0332418
\(897\) −19.9098 −0.664767
\(898\) 21.0383 0.702057
\(899\) −30.3230 −1.01133
\(900\) −0.0286094 −0.000953648 0
\(901\) −14.8674 −0.495304
\(902\) −58.7058 −1.95469
\(903\) −18.7345 −0.623445
\(904\) −20.4964 −0.681701
\(905\) −20.4827 −0.680867
\(906\) −25.5035 −0.847297
\(907\) −28.7556 −0.954814 −0.477407 0.878682i \(-0.658423\pi\)
−0.477407 + 0.878682i \(0.658423\pi\)
\(908\) −19.1777 −0.636435
\(909\) −24.1312 −0.800382
\(910\) 8.55387 0.283558
\(911\) 38.9709 1.29116 0.645582 0.763691i \(-0.276615\pi\)
0.645582 + 0.763691i \(0.276615\pi\)
\(912\) 17.3526 0.574604
\(913\) 16.6524 0.551113
\(914\) 33.2982 1.10141
\(915\) 43.6835 1.44413
\(916\) −17.8995 −0.591417
\(917\) −1.33621 −0.0441256
\(918\) −1.94444 −0.0641762
\(919\) −36.0484 −1.18913 −0.594563 0.804049i \(-0.702675\pi\)
−0.594563 + 0.804049i \(0.702675\pi\)
\(920\) 4.91896 0.162173
\(921\) −6.59695 −0.217377
\(922\) −27.2173 −0.896354
\(923\) 24.2411 0.797906
\(924\) −12.0251 −0.395598
\(925\) −0.0823314 −0.00270704
\(926\) 17.4002 0.571805
\(927\) 24.8046 0.814690
\(928\) 3.74508 0.122938
\(929\) −33.7157 −1.10618 −0.553088 0.833123i \(-0.686551\pi\)
−0.553088 + 0.833123i \(0.686551\pi\)
\(930\) 42.4770 1.39288
\(931\) 44.3999 1.45515
\(932\) 15.5094 0.508029
\(933\) 31.5076 1.03151
\(934\) −37.5732 −1.22943
\(935\) 19.6962 0.644135
\(936\) 9.68757 0.316648
\(937\) −41.2182 −1.34654 −0.673270 0.739397i \(-0.735111\pi\)
−0.673270 + 0.739397i \(0.735111\pi\)
\(938\) 3.69705 0.120713
\(939\) −17.0682 −0.556999
\(940\) −24.4532 −0.797575
\(941\) −57.3203 −1.86859 −0.934293 0.356505i \(-0.883968\pi\)
−0.934293 + 0.356505i \(0.883968\pi\)
\(942\) 25.5851 0.833607
\(943\) −25.1284 −0.818292
\(944\) −9.49865 −0.309155
\(945\) 2.52135 0.0820194
\(946\) −41.2430 −1.34093
\(947\) −20.6235 −0.670173 −0.335086 0.942187i \(-0.608765\pi\)
−0.335086 + 0.942187i \(0.608765\pi\)
\(948\) 30.6158 0.994354
\(949\) −33.6281 −1.09161
\(950\) −0.0839733 −0.00272445
\(951\) −7.00536 −0.227164
\(952\) −1.70542 −0.0552731
\(953\) −17.5106 −0.567225 −0.283613 0.958939i \(-0.591533\pi\)
−0.283613 + 0.958939i \(0.591533\pi\)
\(954\) 21.8335 0.706887
\(955\) −22.4552 −0.726634
\(956\) −2.07421 −0.0670849
\(957\) 45.2596 1.46304
\(958\) −42.7897 −1.38247
\(959\) −5.19738 −0.167832
\(960\) −5.24617 −0.169319
\(961\) 34.5576 1.11476
\(962\) 27.8786 0.898843
\(963\) 20.9017 0.673548
\(964\) −11.8031 −0.380153
\(965\) 35.9100 1.15598
\(966\) −5.14722 −0.165609
\(967\) −55.9622 −1.79962 −0.899812 0.436278i \(-0.856296\pi\)
−0.899812 + 0.436278i \(0.856296\pi\)
\(968\) −15.4727 −0.497312
\(969\) 29.7412 0.955425
\(970\) 20.7052 0.664804
\(971\) 10.0573 0.322755 0.161378 0.986893i \(-0.448406\pi\)
0.161378 + 0.986893i \(0.448406\pi\)
\(972\) 20.5915 0.660472
\(973\) 12.5795 0.403280
\(974\) −40.1808 −1.28748
\(975\) −0.102757 −0.00329085
\(976\) −8.32675 −0.266533
\(977\) −46.0128 −1.47208 −0.736040 0.676938i \(-0.763307\pi\)
−0.736040 + 0.676938i \(0.763307\pi\)
\(978\) −3.54947 −0.113500
\(979\) −38.6497 −1.23525
\(980\) −13.4233 −0.428790
\(981\) −21.9782 −0.701710
\(982\) −19.8522 −0.633508
\(983\) −10.1921 −0.325079 −0.162539 0.986702i \(-0.551968\pi\)
−0.162539 + 0.986702i \(0.551968\pi\)
\(984\) 26.7999 0.854350
\(985\) 6.07277 0.193495
\(986\) 6.41880 0.204416
\(987\) 25.5879 0.814473
\(988\) 28.4346 0.904625
\(989\) −17.6536 −0.561352
\(990\) −28.9249 −0.919295
\(991\) −28.2206 −0.896458 −0.448229 0.893919i \(-0.647945\pi\)
−0.448229 + 0.893919i \(0.647945\pi\)
\(992\) −8.09676 −0.257073
\(993\) −58.0830 −1.84321
\(994\) 6.26699 0.198777
\(995\) 46.8774 1.48611
\(996\) −7.60201 −0.240879
\(997\) 24.5981 0.779030 0.389515 0.921020i \(-0.372643\pi\)
0.389515 + 0.921020i \(0.372643\pi\)
\(998\) −28.0755 −0.888714
\(999\) 8.21753 0.259991
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.b.1.12 75
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8006.2.a.b.1.12 75 1.1 even 1 trivial