Properties

Label 4021.2.a.b.1.13
Level $4021$
Weight $2$
Character 4021.1
Self dual yes
Analytic conductor $32.108$
Analytic rank $1$
Dimension $151$
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] = [4021,2,Mod(1,4021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4021, 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("4021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4021 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4021.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: \(32.1078466528\)
Analytic rank: \(1\)
Dimension: \(151\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 4021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.43685 q^{2} -1.07161 q^{3} +3.93825 q^{4} +2.02983 q^{5} +2.61136 q^{6} +3.59143 q^{7} -4.72324 q^{8} -1.85165 q^{9} +O(q^{10})\) \(q-2.43685 q^{2} -1.07161 q^{3} +3.93825 q^{4} +2.02983 q^{5} +2.61136 q^{6} +3.59143 q^{7} -4.72324 q^{8} -1.85165 q^{9} -4.94641 q^{10} -0.699000 q^{11} -4.22028 q^{12} -5.57852 q^{13} -8.75178 q^{14} -2.17520 q^{15} +3.63334 q^{16} -0.0570413 q^{17} +4.51219 q^{18} +1.27541 q^{19} +7.99400 q^{20} -3.84862 q^{21} +1.70336 q^{22} +1.59342 q^{23} +5.06149 q^{24} -0.879774 q^{25} +13.5940 q^{26} +5.19909 q^{27} +14.1440 q^{28} -9.25685 q^{29} +5.30063 q^{30} +10.2053 q^{31} +0.592565 q^{32} +0.749057 q^{33} +0.139001 q^{34} +7.29000 q^{35} -7.29226 q^{36} -3.73274 q^{37} -3.10798 q^{38} +5.97801 q^{39} -9.58740 q^{40} +7.29221 q^{41} +9.37852 q^{42} +9.81419 q^{43} -2.75284 q^{44} -3.75854 q^{45} -3.88293 q^{46} -12.3638 q^{47} -3.89353 q^{48} +5.89835 q^{49} +2.14388 q^{50} +0.0611261 q^{51} -21.9696 q^{52} -5.71490 q^{53} -12.6694 q^{54} -1.41885 q^{55} -16.9632 q^{56} -1.36674 q^{57} +22.5576 q^{58} +7.29092 q^{59} -8.56647 q^{60} -15.5050 q^{61} -24.8688 q^{62} -6.65005 q^{63} -8.71068 q^{64} -11.3235 q^{65} -1.82534 q^{66} +13.7342 q^{67} -0.224643 q^{68} -1.70753 q^{69} -17.7647 q^{70} -12.3668 q^{71} +8.74578 q^{72} -4.43873 q^{73} +9.09615 q^{74} +0.942777 q^{75} +5.02288 q^{76} -2.51041 q^{77} -14.5675 q^{78} +3.28843 q^{79} +7.37508 q^{80} -0.0164646 q^{81} -17.7700 q^{82} +3.69258 q^{83} -15.1568 q^{84} -0.115784 q^{85} -23.9157 q^{86} +9.91975 q^{87} +3.30155 q^{88} +5.62527 q^{89} +9.15900 q^{90} -20.0349 q^{91} +6.27530 q^{92} -10.9361 q^{93} +30.1288 q^{94} +2.58887 q^{95} -0.635000 q^{96} -10.5580 q^{97} -14.3734 q^{98} +1.29430 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43685 −1.72312 −0.861558 0.507659i \(-0.830511\pi\)
−0.861558 + 0.507659i \(0.830511\pi\)
\(3\) −1.07161 −0.618696 −0.309348 0.950949i \(-0.600111\pi\)
−0.309348 + 0.950949i \(0.600111\pi\)
\(4\) 3.93825 1.96913
\(5\) 2.02983 0.907769 0.453885 0.891060i \(-0.350038\pi\)
0.453885 + 0.891060i \(0.350038\pi\)
\(6\) 2.61136 1.06608
\(7\) 3.59143 1.35743 0.678716 0.734401i \(-0.262537\pi\)
0.678716 + 0.734401i \(0.262537\pi\)
\(8\) −4.72324 −1.66992
\(9\) −1.85165 −0.617216
\(10\) −4.94641 −1.56419
\(11\) −0.699000 −0.210757 −0.105378 0.994432i \(-0.533605\pi\)
−0.105378 + 0.994432i \(0.533605\pi\)
\(12\) −4.22028 −1.21829
\(13\) −5.57852 −1.54720 −0.773602 0.633672i \(-0.781547\pi\)
−0.773602 + 0.633672i \(0.781547\pi\)
\(14\) −8.75178 −2.33901
\(15\) −2.17520 −0.561633
\(16\) 3.63334 0.908335
\(17\) −0.0570413 −0.0138345 −0.00691727 0.999976i \(-0.502202\pi\)
−0.00691727 + 0.999976i \(0.502202\pi\)
\(18\) 4.51219 1.06353
\(19\) 1.27541 0.292599 0.146299 0.989240i \(-0.453264\pi\)
0.146299 + 0.989240i \(0.453264\pi\)
\(20\) 7.99400 1.78751
\(21\) −3.84862 −0.839837
\(22\) 1.70336 0.363158
\(23\) 1.59342 0.332251 0.166126 0.986105i \(-0.446874\pi\)
0.166126 + 0.986105i \(0.446874\pi\)
\(24\) 5.06149 1.03317
\(25\) −0.879774 −0.175955
\(26\) 13.5940 2.66601
\(27\) 5.19909 1.00056
\(28\) 14.1440 2.67296
\(29\) −9.25685 −1.71895 −0.859477 0.511175i \(-0.829210\pi\)
−0.859477 + 0.511175i \(0.829210\pi\)
\(30\) 5.30063 0.967759
\(31\) 10.2053 1.83293 0.916463 0.400120i \(-0.131031\pi\)
0.916463 + 0.400120i \(0.131031\pi\)
\(32\) 0.592565 0.104752
\(33\) 0.749057 0.130394
\(34\) 0.139001 0.0238385
\(35\) 7.29000 1.23223
\(36\) −7.29226 −1.21538
\(37\) −3.73274 −0.613659 −0.306830 0.951764i \(-0.599268\pi\)
−0.306830 + 0.951764i \(0.599268\pi\)
\(38\) −3.10798 −0.504181
\(39\) 5.97801 0.957248
\(40\) −9.58740 −1.51590
\(41\) 7.29221 1.13885 0.569426 0.822043i \(-0.307166\pi\)
0.569426 + 0.822043i \(0.307166\pi\)
\(42\) 9.37852 1.44714
\(43\) 9.81419 1.49665 0.748325 0.663332i \(-0.230858\pi\)
0.748325 + 0.663332i \(0.230858\pi\)
\(44\) −2.75284 −0.415006
\(45\) −3.75854 −0.560289
\(46\) −3.88293 −0.572507
\(47\) −12.3638 −1.80345 −0.901725 0.432311i \(-0.857698\pi\)
−0.901725 + 0.432311i \(0.857698\pi\)
\(48\) −3.89353 −0.561983
\(49\) 5.89835 0.842621
\(50\) 2.14388 0.303191
\(51\) 0.0611261 0.00855937
\(52\) −21.9696 −3.04664
\(53\) −5.71490 −0.785002 −0.392501 0.919752i \(-0.628390\pi\)
−0.392501 + 0.919752i \(0.628390\pi\)
\(54\) −12.6694 −1.72409
\(55\) −1.41885 −0.191318
\(56\) −16.9632 −2.26680
\(57\) −1.36674 −0.181030
\(58\) 22.5576 2.96195
\(59\) 7.29092 0.949197 0.474598 0.880203i \(-0.342593\pi\)
0.474598 + 0.880203i \(0.342593\pi\)
\(60\) −8.56647 −1.10593
\(61\) −15.5050 −1.98522 −0.992608 0.121362i \(-0.961274\pi\)
−0.992608 + 0.121362i \(0.961274\pi\)
\(62\) −24.8688 −3.15834
\(63\) −6.65005 −0.837828
\(64\) −8.71068 −1.08883
\(65\) −11.3235 −1.40450
\(66\) −1.82534 −0.224684
\(67\) 13.7342 1.67790 0.838952 0.544206i \(-0.183169\pi\)
0.838952 + 0.544206i \(0.183169\pi\)
\(68\) −0.224643 −0.0272420
\(69\) −1.70753 −0.205562
\(70\) −17.7647 −2.12328
\(71\) −12.3668 −1.46766 −0.733832 0.679331i \(-0.762270\pi\)
−0.733832 + 0.679331i \(0.762270\pi\)
\(72\) 8.74578 1.03070
\(73\) −4.43873 −0.519514 −0.259757 0.965674i \(-0.583642\pi\)
−0.259757 + 0.965674i \(0.583642\pi\)
\(74\) 9.09615 1.05741
\(75\) 0.942777 0.108863
\(76\) 5.02288 0.576164
\(77\) −2.51041 −0.286088
\(78\) −14.5675 −1.64945
\(79\) 3.28843 0.369977 0.184989 0.982741i \(-0.440775\pi\)
0.184989 + 0.982741i \(0.440775\pi\)
\(80\) 7.37508 0.824559
\(81\) −0.0164646 −0.00182941
\(82\) −17.7700 −1.96237
\(83\) 3.69258 0.405313 0.202656 0.979250i \(-0.435043\pi\)
0.202656 + 0.979250i \(0.435043\pi\)
\(84\) −15.1568 −1.65375
\(85\) −0.115784 −0.0125586
\(86\) −23.9157 −2.57890
\(87\) 9.91975 1.06351
\(88\) 3.30155 0.351946
\(89\) 5.62527 0.596277 0.298139 0.954523i \(-0.403634\pi\)
0.298139 + 0.954523i \(0.403634\pi\)
\(90\) 9.15900 0.965443
\(91\) −20.0349 −2.10022
\(92\) 6.27530 0.654245
\(93\) −10.9361 −1.13402
\(94\) 30.1288 3.10755
\(95\) 2.58887 0.265612
\(96\) −0.635000 −0.0648094
\(97\) −10.5580 −1.07200 −0.535999 0.844219i \(-0.680065\pi\)
−0.535999 + 0.844219i \(0.680065\pi\)
\(98\) −14.3734 −1.45193
\(99\) 1.29430 0.130082
\(100\) −3.46477 −0.346477
\(101\) −3.15445 −0.313879 −0.156940 0.987608i \(-0.550163\pi\)
−0.156940 + 0.987608i \(0.550163\pi\)
\(102\) −0.148955 −0.0147488
\(103\) −6.76343 −0.666421 −0.333210 0.942853i \(-0.608132\pi\)
−0.333210 + 0.942853i \(0.608132\pi\)
\(104\) 26.3487 2.58370
\(105\) −7.81206 −0.762379
\(106\) 13.9264 1.35265
\(107\) −9.15365 −0.884916 −0.442458 0.896789i \(-0.645893\pi\)
−0.442458 + 0.896789i \(0.645893\pi\)
\(108\) 20.4753 1.97024
\(109\) −0.816517 −0.0782082 −0.0391041 0.999235i \(-0.512450\pi\)
−0.0391041 + 0.999235i \(0.512450\pi\)
\(110\) 3.45754 0.329664
\(111\) 4.00005 0.379668
\(112\) 13.0489 1.23300
\(113\) 4.55559 0.428554 0.214277 0.976773i \(-0.431260\pi\)
0.214277 + 0.976773i \(0.431260\pi\)
\(114\) 3.33055 0.311935
\(115\) 3.23438 0.301607
\(116\) −36.4558 −3.38484
\(117\) 10.3295 0.954958
\(118\) −17.7669 −1.63558
\(119\) −0.204860 −0.0187794
\(120\) 10.2740 0.937881
\(121\) −10.5114 −0.955582
\(122\) 37.7835 3.42076
\(123\) −7.81442 −0.704603
\(124\) 40.1911 3.60926
\(125\) −11.9350 −1.06750
\(126\) 16.2052 1.44367
\(127\) 20.3524 1.80598 0.902990 0.429661i \(-0.141367\pi\)
0.902990 + 0.429661i \(0.141367\pi\)
\(128\) 20.0415 1.77144
\(129\) −10.5170 −0.925971
\(130\) 27.5937 2.42012
\(131\) 0.0553331 0.00483448 0.00241724 0.999997i \(-0.499231\pi\)
0.00241724 + 0.999997i \(0.499231\pi\)
\(132\) 2.94998 0.256763
\(133\) 4.58054 0.397183
\(134\) −33.4683 −2.89122
\(135\) 10.5533 0.908282
\(136\) 0.269420 0.0231026
\(137\) −13.0531 −1.11520 −0.557601 0.830109i \(-0.688278\pi\)
−0.557601 + 0.830109i \(0.688278\pi\)
\(138\) 4.16100 0.354208
\(139\) −21.7655 −1.84613 −0.923064 0.384647i \(-0.874323\pi\)
−0.923064 + 0.384647i \(0.874323\pi\)
\(140\) 28.7099 2.42643
\(141\) 13.2492 1.11579
\(142\) 30.1360 2.52895
\(143\) 3.89939 0.326083
\(144\) −6.72767 −0.560639
\(145\) −18.7899 −1.56041
\(146\) 10.8165 0.895182
\(147\) −6.32074 −0.521326
\(148\) −14.7005 −1.20837
\(149\) −7.22958 −0.592270 −0.296135 0.955146i \(-0.595698\pi\)
−0.296135 + 0.955146i \(0.595698\pi\)
\(150\) −2.29741 −0.187583
\(151\) 2.37832 0.193545 0.0967725 0.995307i \(-0.469148\pi\)
0.0967725 + 0.995307i \(0.469148\pi\)
\(152\) −6.02406 −0.488616
\(153\) 0.105620 0.00853889
\(154\) 6.11750 0.492962
\(155\) 20.7151 1.66387
\(156\) 23.5429 1.88494
\(157\) 18.5647 1.48162 0.740812 0.671712i \(-0.234441\pi\)
0.740812 + 0.671712i \(0.234441\pi\)
\(158\) −8.01342 −0.637513
\(159\) 6.12416 0.485678
\(160\) 1.20281 0.0950903
\(161\) 5.72265 0.451008
\(162\) 0.0401219 0.00315228
\(163\) −5.19637 −0.407011 −0.203506 0.979074i \(-0.565234\pi\)
−0.203506 + 0.979074i \(0.565234\pi\)
\(164\) 28.7186 2.24254
\(165\) 1.52046 0.118368
\(166\) −8.99827 −0.698401
\(167\) 1.99829 0.154632 0.0773160 0.997007i \(-0.475365\pi\)
0.0773160 + 0.997007i \(0.475365\pi\)
\(168\) 18.1780 1.40246
\(169\) 18.1199 1.39384
\(170\) 0.282149 0.0216399
\(171\) −2.36161 −0.180596
\(172\) 38.6508 2.94709
\(173\) 2.75559 0.209504 0.104752 0.994498i \(-0.466595\pi\)
0.104752 + 0.994498i \(0.466595\pi\)
\(174\) −24.1730 −1.83255
\(175\) −3.15964 −0.238847
\(176\) −2.53971 −0.191438
\(177\) −7.81304 −0.587264
\(178\) −13.7080 −1.02745
\(179\) −22.6072 −1.68974 −0.844869 0.534973i \(-0.820322\pi\)
−0.844869 + 0.534973i \(0.820322\pi\)
\(180\) −14.8021 −1.10328
\(181\) 14.0374 1.04339 0.521696 0.853131i \(-0.325299\pi\)
0.521696 + 0.853131i \(0.325299\pi\)
\(182\) 48.8220 3.61893
\(183\) 16.6154 1.22825
\(184\) −7.52611 −0.554832
\(185\) −7.57685 −0.557061
\(186\) 26.6497 1.95405
\(187\) 0.0398719 0.00291572
\(188\) −48.6919 −3.55122
\(189\) 18.6721 1.35820
\(190\) −6.30869 −0.457680
\(191\) −9.00097 −0.651287 −0.325644 0.945493i \(-0.605581\pi\)
−0.325644 + 0.945493i \(0.605581\pi\)
\(192\) 9.33447 0.673657
\(193\) −10.8034 −0.777643 −0.388822 0.921313i \(-0.627118\pi\)
−0.388822 + 0.921313i \(0.627118\pi\)
\(194\) 25.7282 1.84718
\(195\) 12.1344 0.868961
\(196\) 23.2292 1.65923
\(197\) −4.68851 −0.334042 −0.167021 0.985953i \(-0.553415\pi\)
−0.167021 + 0.985953i \(0.553415\pi\)
\(198\) −3.15402 −0.224147
\(199\) 8.19977 0.581266 0.290633 0.956835i \(-0.406134\pi\)
0.290633 + 0.956835i \(0.406134\pi\)
\(200\) 4.15539 0.293830
\(201\) −14.7178 −1.03811
\(202\) 7.68693 0.540850
\(203\) −33.2453 −2.33336
\(204\) 0.240730 0.0168545
\(205\) 14.8020 1.03381
\(206\) 16.4815 1.14832
\(207\) −2.95045 −0.205071
\(208\) −20.2687 −1.40538
\(209\) −0.891511 −0.0616671
\(210\) 19.0368 1.31367
\(211\) 13.9709 0.961798 0.480899 0.876776i \(-0.340310\pi\)
0.480899 + 0.876776i \(0.340310\pi\)
\(212\) −22.5067 −1.54577
\(213\) 13.2524 0.908037
\(214\) 22.3061 1.52481
\(215\) 19.9212 1.35861
\(216\) −24.5565 −1.67086
\(217\) 36.6516 2.48807
\(218\) 1.98973 0.134762
\(219\) 4.75659 0.321421
\(220\) −5.58781 −0.376730
\(221\) 0.318206 0.0214049
\(222\) −9.74755 −0.654213
\(223\) 3.31724 0.222139 0.111069 0.993813i \(-0.464572\pi\)
0.111069 + 0.993813i \(0.464572\pi\)
\(224\) 2.12815 0.142193
\(225\) 1.62903 0.108602
\(226\) −11.1013 −0.738448
\(227\) −2.29259 −0.152165 −0.0760824 0.997102i \(-0.524241\pi\)
−0.0760824 + 0.997102i \(0.524241\pi\)
\(228\) −5.38258 −0.356470
\(229\) −9.01852 −0.595960 −0.297980 0.954572i \(-0.596313\pi\)
−0.297980 + 0.954572i \(0.596313\pi\)
\(230\) −7.88171 −0.519704
\(231\) 2.69019 0.177001
\(232\) 43.7223 2.87051
\(233\) −7.80223 −0.511141 −0.255571 0.966790i \(-0.582263\pi\)
−0.255571 + 0.966790i \(0.582263\pi\)
\(234\) −25.1714 −1.64550
\(235\) −25.0965 −1.63712
\(236\) 28.7135 1.86909
\(237\) −3.52392 −0.228903
\(238\) 0.499213 0.0323592
\(239\) 19.7301 1.27624 0.638119 0.769938i \(-0.279713\pi\)
0.638119 + 0.769938i \(0.279713\pi\)
\(240\) −7.90323 −0.510151
\(241\) −14.0580 −0.905557 −0.452779 0.891623i \(-0.649567\pi\)
−0.452779 + 0.891623i \(0.649567\pi\)
\(242\) 25.6147 1.64658
\(243\) −15.5796 −0.999433
\(244\) −61.0628 −3.90914
\(245\) 11.9727 0.764906
\(246\) 19.0426 1.21411
\(247\) −7.11489 −0.452710
\(248\) −48.2021 −3.06084
\(249\) −3.95701 −0.250765
\(250\) 29.0838 1.83942
\(251\) −15.1627 −0.957063 −0.478532 0.878070i \(-0.658831\pi\)
−0.478532 + 0.878070i \(0.658831\pi\)
\(252\) −26.1896 −1.64979
\(253\) −1.11380 −0.0700241
\(254\) −49.5957 −3.11191
\(255\) 0.124076 0.00776994
\(256\) −31.4169 −1.96355
\(257\) 8.80216 0.549063 0.274532 0.961578i \(-0.411477\pi\)
0.274532 + 0.961578i \(0.411477\pi\)
\(258\) 25.6284 1.59556
\(259\) −13.4059 −0.833001
\(260\) −44.5947 −2.76565
\(261\) 17.1404 1.06096
\(262\) −0.134839 −0.00833036
\(263\) −17.7323 −1.09342 −0.546710 0.837322i \(-0.684120\pi\)
−0.546710 + 0.837322i \(0.684120\pi\)
\(264\) −3.53798 −0.217748
\(265\) −11.6003 −0.712601
\(266\) −11.1621 −0.684392
\(267\) −6.02811 −0.368914
\(268\) 54.0889 3.30401
\(269\) −27.1110 −1.65299 −0.826493 0.562948i \(-0.809667\pi\)
−0.826493 + 0.562948i \(0.809667\pi\)
\(270\) −25.7168 −1.56507
\(271\) 15.9858 0.971065 0.485533 0.874219i \(-0.338626\pi\)
0.485533 + 0.874219i \(0.338626\pi\)
\(272\) −0.207250 −0.0125664
\(273\) 21.4696 1.29940
\(274\) 31.8085 1.92162
\(275\) 0.614962 0.0370836
\(276\) −6.72468 −0.404778
\(277\) −12.1369 −0.729237 −0.364619 0.931157i \(-0.618801\pi\)
−0.364619 + 0.931157i \(0.618801\pi\)
\(278\) 53.0394 3.18109
\(279\) −18.8966 −1.13131
\(280\) −34.4324 −2.05773
\(281\) −23.6536 −1.41106 −0.705529 0.708681i \(-0.749291\pi\)
−0.705529 + 0.708681i \(0.749291\pi\)
\(282\) −32.2864 −1.92263
\(283\) −2.95925 −0.175909 −0.0879546 0.996124i \(-0.528033\pi\)
−0.0879546 + 0.996124i \(0.528033\pi\)
\(284\) −48.7034 −2.89002
\(285\) −2.77426 −0.164333
\(286\) −9.50224 −0.561879
\(287\) 26.1894 1.54591
\(288\) −1.09722 −0.0646543
\(289\) −16.9967 −0.999809
\(290\) 45.7881 2.68877
\(291\) 11.3140 0.663240
\(292\) −17.4808 −1.02299
\(293\) −16.6100 −0.970366 −0.485183 0.874413i \(-0.661247\pi\)
−0.485183 + 0.874413i \(0.661247\pi\)
\(294\) 15.4027 0.898305
\(295\) 14.7994 0.861651
\(296\) 17.6307 1.02476
\(297\) −3.63416 −0.210875
\(298\) 17.6174 1.02055
\(299\) −8.88893 −0.514060
\(300\) 3.71290 0.214364
\(301\) 35.2469 2.03160
\(302\) −5.79562 −0.333500
\(303\) 3.38035 0.194196
\(304\) 4.63399 0.265778
\(305\) −31.4727 −1.80212
\(306\) −0.257381 −0.0147135
\(307\) −4.42029 −0.252279 −0.126140 0.992012i \(-0.540259\pi\)
−0.126140 + 0.992012i \(0.540259\pi\)
\(308\) −9.88663 −0.563343
\(309\) 7.24778 0.412312
\(310\) −50.4796 −2.86705
\(311\) −21.9982 −1.24740 −0.623701 0.781663i \(-0.714372\pi\)
−0.623701 + 0.781663i \(0.714372\pi\)
\(312\) −28.2356 −1.59853
\(313\) 3.60533 0.203785 0.101893 0.994795i \(-0.467510\pi\)
0.101893 + 0.994795i \(0.467510\pi\)
\(314\) −45.2395 −2.55301
\(315\) −13.4985 −0.760555
\(316\) 12.9507 0.728532
\(317\) 0.623785 0.0350352 0.0175176 0.999847i \(-0.494424\pi\)
0.0175176 + 0.999847i \(0.494424\pi\)
\(318\) −14.9237 −0.836879
\(319\) 6.47054 0.362281
\(320\) −17.6812 −0.988411
\(321\) 9.80916 0.547494
\(322\) −13.9453 −0.777139
\(323\) −0.0727509 −0.00404797
\(324\) −0.0648420 −0.00360233
\(325\) 4.90784 0.272238
\(326\) 12.6628 0.701327
\(327\) 0.874990 0.0483871
\(328\) −34.4429 −1.90179
\(329\) −44.4038 −2.44806
\(330\) −3.70514 −0.203961
\(331\) 11.3026 0.621247 0.310623 0.950533i \(-0.399462\pi\)
0.310623 + 0.950533i \(0.399462\pi\)
\(332\) 14.5423 0.798113
\(333\) 6.91172 0.378760
\(334\) −4.86953 −0.266449
\(335\) 27.8782 1.52315
\(336\) −13.9833 −0.762854
\(337\) 21.3269 1.16175 0.580876 0.813992i \(-0.302710\pi\)
0.580876 + 0.813992i \(0.302710\pi\)
\(338\) −44.1556 −2.40175
\(339\) −4.88183 −0.265145
\(340\) −0.455988 −0.0247294
\(341\) −7.13351 −0.386301
\(342\) 5.75489 0.311189
\(343\) −3.95650 −0.213631
\(344\) −46.3548 −2.49928
\(345\) −3.46600 −0.186603
\(346\) −6.71498 −0.360999
\(347\) 26.6198 1.42902 0.714512 0.699623i \(-0.246649\pi\)
0.714512 + 0.699623i \(0.246649\pi\)
\(348\) 39.0665 2.09418
\(349\) 10.1568 0.543683 0.271841 0.962342i \(-0.412367\pi\)
0.271841 + 0.962342i \(0.412367\pi\)
\(350\) 7.69959 0.411560
\(351\) −29.0032 −1.54808
\(352\) −0.414203 −0.0220771
\(353\) −2.09661 −0.111591 −0.0557955 0.998442i \(-0.517770\pi\)
−0.0557955 + 0.998442i \(0.517770\pi\)
\(354\) 19.0392 1.01192
\(355\) −25.1025 −1.33230
\(356\) 22.1537 1.17415
\(357\) 0.219530 0.0116188
\(358\) 55.0903 2.91162
\(359\) 7.28312 0.384388 0.192194 0.981357i \(-0.438440\pi\)
0.192194 + 0.981357i \(0.438440\pi\)
\(360\) 17.7525 0.935638
\(361\) −17.3733 −0.914386
\(362\) −34.2071 −1.79789
\(363\) 11.2641 0.591214
\(364\) −78.9024 −4.13561
\(365\) −9.00988 −0.471598
\(366\) −40.4893 −2.11641
\(367\) 26.9252 1.40549 0.702743 0.711444i \(-0.251958\pi\)
0.702743 + 0.711444i \(0.251958\pi\)
\(368\) 5.78944 0.301795
\(369\) −13.5026 −0.702917
\(370\) 18.4637 0.959881
\(371\) −20.5247 −1.06559
\(372\) −43.0693 −2.23304
\(373\) 30.5207 1.58030 0.790152 0.612911i \(-0.210002\pi\)
0.790152 + 0.612911i \(0.210002\pi\)
\(374\) −0.0971619 −0.00502412
\(375\) 12.7897 0.660455
\(376\) 58.3974 3.01161
\(377\) 51.6395 2.65957
\(378\) −45.5013 −2.34033
\(379\) −25.8030 −1.32541 −0.662706 0.748880i \(-0.730592\pi\)
−0.662706 + 0.748880i \(0.730592\pi\)
\(380\) 10.1956 0.523024
\(381\) −21.8099 −1.11735
\(382\) 21.9340 1.12224
\(383\) −35.7225 −1.82533 −0.912667 0.408705i \(-0.865981\pi\)
−0.912667 + 0.408705i \(0.865981\pi\)
\(384\) −21.4767 −1.09598
\(385\) −5.09571 −0.259702
\(386\) 26.3262 1.33997
\(387\) −18.1724 −0.923756
\(388\) −41.5799 −2.11090
\(389\) −13.9922 −0.709434 −0.354717 0.934974i \(-0.615423\pi\)
−0.354717 + 0.934974i \(0.615423\pi\)
\(390\) −29.5697 −1.49732
\(391\) −0.0908907 −0.00459654
\(392\) −27.8593 −1.40711
\(393\) −0.0592956 −0.00299107
\(394\) 11.4252 0.575594
\(395\) 6.67496 0.335854
\(396\) 5.09729 0.256148
\(397\) 10.3643 0.520171 0.260086 0.965586i \(-0.416249\pi\)
0.260086 + 0.965586i \(0.416249\pi\)
\(398\) −19.9816 −1.00159
\(399\) −4.90856 −0.245735
\(400\) −3.19652 −0.159826
\(401\) 3.61257 0.180403 0.0902015 0.995924i \(-0.471249\pi\)
0.0902015 + 0.995924i \(0.471249\pi\)
\(402\) 35.8651 1.78879
\(403\) −56.9305 −2.83591
\(404\) −12.4230 −0.618068
\(405\) −0.0334205 −0.00166068
\(406\) 81.0139 4.02065
\(407\) 2.60919 0.129333
\(408\) −0.288714 −0.0142935
\(409\) 5.25608 0.259896 0.129948 0.991521i \(-0.458519\pi\)
0.129948 + 0.991521i \(0.458519\pi\)
\(410\) −36.0702 −1.78138
\(411\) 13.9879 0.689971
\(412\) −26.6361 −1.31227
\(413\) 26.1848 1.28847
\(414\) 7.18982 0.353360
\(415\) 7.49532 0.367931
\(416\) −3.30564 −0.162072
\(417\) 23.3242 1.14219
\(418\) 2.17248 0.106260
\(419\) 5.70977 0.278940 0.139470 0.990226i \(-0.455460\pi\)
0.139470 + 0.990226i \(0.455460\pi\)
\(420\) −30.7659 −1.50122
\(421\) 5.04277 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(422\) −34.0451 −1.65729
\(423\) 22.8934 1.11312
\(424\) 26.9929 1.31089
\(425\) 0.0501834 0.00243425
\(426\) −32.2941 −1.56465
\(427\) −55.6852 −2.69480
\(428\) −36.0494 −1.74251
\(429\) −4.17863 −0.201746
\(430\) −48.5450 −2.34105
\(431\) −10.4867 −0.505126 −0.252563 0.967581i \(-0.581273\pi\)
−0.252563 + 0.967581i \(0.581273\pi\)
\(432\) 18.8901 0.908848
\(433\) 27.0552 1.30019 0.650096 0.759852i \(-0.274729\pi\)
0.650096 + 0.759852i \(0.274729\pi\)
\(434\) −89.3145 −4.28724
\(435\) 20.1354 0.965421
\(436\) −3.21565 −0.154002
\(437\) 2.03226 0.0972162
\(438\) −11.5911 −0.553845
\(439\) −3.14513 −0.150109 −0.0750545 0.997179i \(-0.523913\pi\)
−0.0750545 + 0.997179i \(0.523913\pi\)
\(440\) 6.70160 0.319486
\(441\) −10.9217 −0.520079
\(442\) −0.775422 −0.0368830
\(443\) −3.13688 −0.149038 −0.0745188 0.997220i \(-0.523742\pi\)
−0.0745188 + 0.997220i \(0.523742\pi\)
\(444\) 15.7532 0.747615
\(445\) 11.4184 0.541282
\(446\) −8.08362 −0.382770
\(447\) 7.74731 0.366435
\(448\) −31.2838 −1.47802
\(449\) 5.70852 0.269402 0.134701 0.990886i \(-0.456993\pi\)
0.134701 + 0.990886i \(0.456993\pi\)
\(450\) −3.96971 −0.187134
\(451\) −5.09726 −0.240020
\(452\) 17.9411 0.843878
\(453\) −2.54864 −0.119745
\(454\) 5.58671 0.262197
\(455\) −40.6674 −1.90652
\(456\) 6.45546 0.302305
\(457\) −10.3278 −0.483114 −0.241557 0.970387i \(-0.577658\pi\)
−0.241557 + 0.970387i \(0.577658\pi\)
\(458\) 21.9768 1.02691
\(459\) −0.296562 −0.0138424
\(460\) 12.7378 0.593903
\(461\) −22.5154 −1.04865 −0.524324 0.851519i \(-0.675682\pi\)
−0.524324 + 0.851519i \(0.675682\pi\)
\(462\) −6.55559 −0.304994
\(463\) 15.8379 0.736050 0.368025 0.929816i \(-0.380034\pi\)
0.368025 + 0.929816i \(0.380034\pi\)
\(464\) −33.6333 −1.56139
\(465\) −22.1985 −1.02943
\(466\) 19.0129 0.880756
\(467\) −37.2193 −1.72230 −0.861151 0.508349i \(-0.830256\pi\)
−0.861151 + 0.508349i \(0.830256\pi\)
\(468\) 40.6800 1.88043
\(469\) 49.3255 2.27764
\(470\) 61.1565 2.82094
\(471\) −19.8942 −0.916675
\(472\) −34.4368 −1.58508
\(473\) −6.86012 −0.315429
\(474\) 8.58728 0.394427
\(475\) −1.12207 −0.0514842
\(476\) −0.806789 −0.0369791
\(477\) 10.5820 0.484516
\(478\) −48.0795 −2.19910
\(479\) 27.6531 1.26350 0.631751 0.775171i \(-0.282336\pi\)
0.631751 + 0.775171i \(0.282336\pi\)
\(480\) −1.28894 −0.0588320
\(481\) 20.8232 0.949456
\(482\) 34.2574 1.56038
\(483\) −6.13247 −0.279037
\(484\) −41.3966 −1.88166
\(485\) −21.4309 −0.973127
\(486\) 37.9652 1.72214
\(487\) −1.24369 −0.0563568 −0.0281784 0.999603i \(-0.508971\pi\)
−0.0281784 + 0.999603i \(0.508971\pi\)
\(488\) 73.2341 3.31515
\(489\) 5.56850 0.251816
\(490\) −29.1756 −1.31802
\(491\) 3.45145 0.155762 0.0778810 0.996963i \(-0.475185\pi\)
0.0778810 + 0.996963i \(0.475185\pi\)
\(492\) −30.7752 −1.38745
\(493\) 0.528022 0.0237809
\(494\) 17.3380 0.780071
\(495\) 2.62722 0.118085
\(496\) 37.0793 1.66491
\(497\) −44.4143 −1.99225
\(498\) 9.64266 0.432098
\(499\) 30.5598 1.36805 0.684023 0.729460i \(-0.260229\pi\)
0.684023 + 0.729460i \(0.260229\pi\)
\(500\) −47.0029 −2.10204
\(501\) −2.14139 −0.0956702
\(502\) 36.9494 1.64913
\(503\) −5.09930 −0.227366 −0.113683 0.993517i \(-0.536265\pi\)
−0.113683 + 0.993517i \(0.536265\pi\)
\(504\) 31.4098 1.39910
\(505\) −6.40300 −0.284930
\(506\) 2.71417 0.120660
\(507\) −19.4175 −0.862363
\(508\) 80.1528 3.55621
\(509\) −20.3945 −0.903969 −0.451985 0.892026i \(-0.649284\pi\)
−0.451985 + 0.892026i \(0.649284\pi\)
\(510\) −0.302355 −0.0133885
\(511\) −15.9414 −0.705204
\(512\) 36.4753 1.61200
\(513\) 6.63096 0.292764
\(514\) −21.4496 −0.946100
\(515\) −13.7286 −0.604956
\(516\) −41.4187 −1.82335
\(517\) 8.64232 0.380089
\(518\) 32.6682 1.43536
\(519\) −2.95293 −0.129619
\(520\) 53.4835 2.34541
\(521\) 37.2724 1.63293 0.816467 0.577392i \(-0.195929\pi\)
0.816467 + 0.577392i \(0.195929\pi\)
\(522\) −41.7687 −1.82816
\(523\) −35.1765 −1.53816 −0.769080 0.639152i \(-0.779285\pi\)
−0.769080 + 0.639152i \(0.779285\pi\)
\(524\) 0.217916 0.00951970
\(525\) 3.38591 0.147773
\(526\) 43.2110 1.88409
\(527\) −0.582123 −0.0253577
\(528\) 2.72158 0.118442
\(529\) −20.4610 −0.889609
\(530\) 28.2682 1.22789
\(531\) −13.5002 −0.585859
\(532\) 18.0393 0.782104
\(533\) −40.6798 −1.76204
\(534\) 14.6896 0.635682
\(535\) −18.5804 −0.803300
\(536\) −64.8701 −2.80196
\(537\) 24.2261 1.04543
\(538\) 66.0655 2.84828
\(539\) −4.12295 −0.177588
\(540\) 41.5615 1.78852
\(541\) −42.1942 −1.81407 −0.907036 0.421053i \(-0.861661\pi\)
−0.907036 + 0.421053i \(0.861661\pi\)
\(542\) −38.9549 −1.67326
\(543\) −15.0427 −0.645543
\(544\) −0.0338006 −0.00144919
\(545\) −1.65739 −0.0709950
\(546\) −52.3183 −2.23902
\(547\) 22.7832 0.974141 0.487070 0.873363i \(-0.338066\pi\)
0.487070 + 0.873363i \(0.338066\pi\)
\(548\) −51.4064 −2.19597
\(549\) 28.7098 1.22531
\(550\) −1.49857 −0.0638994
\(551\) −11.8063 −0.502963
\(552\) 8.06508 0.343272
\(553\) 11.8102 0.502219
\(554\) 29.5759 1.25656
\(555\) 8.11945 0.344651
\(556\) −85.7182 −3.63526
\(557\) 24.6271 1.04348 0.521741 0.853104i \(-0.325283\pi\)
0.521741 + 0.853104i \(0.325283\pi\)
\(558\) 46.0483 1.94938
\(559\) −54.7487 −2.31562
\(560\) 26.4871 1.11928
\(561\) −0.0427272 −0.00180394
\(562\) 57.6405 2.43142
\(563\) −21.2483 −0.895509 −0.447755 0.894156i \(-0.647776\pi\)
−0.447755 + 0.894156i \(0.647776\pi\)
\(564\) 52.1789 2.19713
\(565\) 9.24710 0.389028
\(566\) 7.21126 0.303112
\(567\) −0.0591316 −0.00248329
\(568\) 58.4112 2.45088
\(569\) 13.6503 0.572251 0.286125 0.958192i \(-0.407633\pi\)
0.286125 + 0.958192i \(0.407633\pi\)
\(570\) 6.76047 0.283165
\(571\) −0.986146 −0.0412689 −0.0206345 0.999787i \(-0.506569\pi\)
−0.0206345 + 0.999787i \(0.506569\pi\)
\(572\) 15.3568 0.642100
\(573\) 9.64555 0.402949
\(574\) −63.8198 −2.66379
\(575\) −1.40185 −0.0584612
\(576\) 16.1291 0.672046
\(577\) −30.9051 −1.28660 −0.643298 0.765616i \(-0.722434\pi\)
−0.643298 + 0.765616i \(0.722434\pi\)
\(578\) 41.4186 1.72279
\(579\) 11.5770 0.481124
\(580\) −73.9993 −3.07265
\(581\) 13.2616 0.550185
\(582\) −27.5706 −1.14284
\(583\) 3.99472 0.165444
\(584\) 20.9652 0.867545
\(585\) 20.9671 0.866882
\(586\) 40.4761 1.67205
\(587\) −5.00514 −0.206584 −0.103292 0.994651i \(-0.532938\pi\)
−0.103292 + 0.994651i \(0.532938\pi\)
\(588\) −24.8927 −1.02656
\(589\) 13.0159 0.536312
\(590\) −36.0638 −1.48473
\(591\) 5.02426 0.206671
\(592\) −13.5623 −0.557408
\(593\) 27.1705 1.11576 0.557880 0.829922i \(-0.311615\pi\)
0.557880 + 0.829922i \(0.311615\pi\)
\(594\) 8.85592 0.363363
\(595\) −0.415831 −0.0170474
\(596\) −28.4719 −1.16626
\(597\) −8.78698 −0.359627
\(598\) 21.6610 0.885785
\(599\) −16.0618 −0.656268 −0.328134 0.944631i \(-0.606420\pi\)
−0.328134 + 0.944631i \(0.606420\pi\)
\(600\) −4.45297 −0.181792
\(601\) −29.5441 −1.20513 −0.602564 0.798071i \(-0.705854\pi\)
−0.602564 + 0.798071i \(0.705854\pi\)
\(602\) −85.8916 −3.50068
\(603\) −25.4309 −1.03563
\(604\) 9.36643 0.381115
\(605\) −21.3364 −0.867448
\(606\) −8.23741 −0.334622
\(607\) 38.1337 1.54780 0.773900 0.633308i \(-0.218303\pi\)
0.773900 + 0.633308i \(0.218303\pi\)
\(608\) 0.755762 0.0306502
\(609\) 35.6261 1.44364
\(610\) 76.6942 3.10526
\(611\) 68.9719 2.79030
\(612\) 0.415960 0.0168142
\(613\) −11.7360 −0.474012 −0.237006 0.971508i \(-0.576166\pi\)
−0.237006 + 0.971508i \(0.576166\pi\)
\(614\) 10.7716 0.434706
\(615\) −15.8620 −0.639617
\(616\) 11.8573 0.477743
\(617\) −15.2634 −0.614483 −0.307242 0.951632i \(-0.599406\pi\)
−0.307242 + 0.951632i \(0.599406\pi\)
\(618\) −17.6618 −0.710460
\(619\) −18.7830 −0.754952 −0.377476 0.926019i \(-0.623208\pi\)
−0.377476 + 0.926019i \(0.623208\pi\)
\(620\) 81.5812 3.27638
\(621\) 8.28433 0.332439
\(622\) 53.6063 2.14942
\(623\) 20.2027 0.809406
\(624\) 21.7202 0.869503
\(625\) −19.8271 −0.793085
\(626\) −8.78567 −0.351146
\(627\) 0.955354 0.0381532
\(628\) 73.1125 2.91751
\(629\) 0.212920 0.00848970
\(630\) 32.8939 1.31052
\(631\) −46.1200 −1.83601 −0.918005 0.396569i \(-0.870201\pi\)
−0.918005 + 0.396569i \(0.870201\pi\)
\(632\) −15.5321 −0.617832
\(633\) −14.9714 −0.595060
\(634\) −1.52007 −0.0603698
\(635\) 41.3119 1.63941
\(636\) 24.1185 0.956361
\(637\) −32.9041 −1.30371
\(638\) −15.7678 −0.624251
\(639\) 22.8989 0.905865
\(640\) 40.6809 1.60806
\(641\) 9.91182 0.391493 0.195747 0.980654i \(-0.437287\pi\)
0.195747 + 0.980654i \(0.437287\pi\)
\(642\) −23.9035 −0.943395
\(643\) −15.0888 −0.595043 −0.297522 0.954715i \(-0.596160\pi\)
−0.297522 + 0.954715i \(0.596160\pi\)
\(644\) 22.5373 0.888093
\(645\) −21.3478 −0.840568
\(646\) 0.177283 0.00697512
\(647\) 33.4370 1.31454 0.657272 0.753654i \(-0.271710\pi\)
0.657272 + 0.753654i \(0.271710\pi\)
\(648\) 0.0777665 0.00305496
\(649\) −5.09635 −0.200049
\(650\) −11.9597 −0.469098
\(651\) −39.2763 −1.53936
\(652\) −20.4646 −0.801457
\(653\) −44.3877 −1.73702 −0.868512 0.495669i \(-0.834923\pi\)
−0.868512 + 0.495669i \(0.834923\pi\)
\(654\) −2.13222 −0.0833765
\(655\) 0.112317 0.00438859
\(656\) 26.4951 1.03446
\(657\) 8.21895 0.320652
\(658\) 108.206 4.21829
\(659\) −45.5212 −1.77325 −0.886626 0.462486i \(-0.846957\pi\)
−0.886626 + 0.462486i \(0.846957\pi\)
\(660\) 5.98797 0.233081
\(661\) −7.82259 −0.304264 −0.152132 0.988360i \(-0.548614\pi\)
−0.152132 + 0.988360i \(0.548614\pi\)
\(662\) −27.5428 −1.07048
\(663\) −0.340994 −0.0132431
\(664\) −17.4409 −0.676840
\(665\) 9.29773 0.360550
\(666\) −16.8429 −0.652647
\(667\) −14.7500 −0.571124
\(668\) 7.86976 0.304490
\(669\) −3.55479 −0.137436
\(670\) −67.9351 −2.62456
\(671\) 10.8380 0.418397
\(672\) −2.28056 −0.0879743
\(673\) −11.7259 −0.452000 −0.226000 0.974127i \(-0.572565\pi\)
−0.226000 + 0.974127i \(0.572565\pi\)
\(674\) −51.9706 −2.00183
\(675\) −4.57402 −0.176054
\(676\) 71.3609 2.74465
\(677\) −24.5974 −0.945355 −0.472678 0.881235i \(-0.656712\pi\)
−0.472678 + 0.881235i \(0.656712\pi\)
\(678\) 11.8963 0.456875
\(679\) −37.9181 −1.45516
\(680\) 0.546878 0.0209718
\(681\) 2.45677 0.0941437
\(682\) 17.3833 0.665641
\(683\) 28.9165 1.10646 0.553230 0.833028i \(-0.313395\pi\)
0.553230 + 0.833028i \(0.313395\pi\)
\(684\) −9.30060 −0.355617
\(685\) −26.4956 −1.01235
\(686\) 9.64142 0.368111
\(687\) 9.66435 0.368718
\(688\) 35.6583 1.35946
\(689\) 31.8807 1.21456
\(690\) 8.44614 0.321539
\(691\) −50.4019 −1.91738 −0.958689 0.284456i \(-0.908187\pi\)
−0.958689 + 0.284456i \(0.908187\pi\)
\(692\) 10.8522 0.412540
\(693\) 4.64839 0.176578
\(694\) −64.8685 −2.46238
\(695\) −44.1804 −1.67586
\(696\) −46.8534 −1.77597
\(697\) −0.415957 −0.0157555
\(698\) −24.7507 −0.936828
\(699\) 8.36097 0.316241
\(700\) −12.4435 −0.470320
\(701\) 2.12343 0.0802007 0.0401003 0.999196i \(-0.487232\pi\)
0.0401003 + 0.999196i \(0.487232\pi\)
\(702\) 70.6766 2.66752
\(703\) −4.76077 −0.179556
\(704\) 6.08877 0.229479
\(705\) 26.8937 1.01288
\(706\) 5.10912 0.192284
\(707\) −11.3290 −0.426070
\(708\) −30.7697 −1.15640
\(709\) 22.9837 0.863170 0.431585 0.902072i \(-0.357954\pi\)
0.431585 + 0.902072i \(0.357954\pi\)
\(710\) 61.1710 2.29571
\(711\) −6.08901 −0.228356
\(712\) −26.5695 −0.995735
\(713\) 16.2613 0.608992
\(714\) −0.534963 −0.0200205
\(715\) 7.91511 0.296008
\(716\) −89.0328 −3.32731
\(717\) −21.1431 −0.789602
\(718\) −17.7479 −0.662345
\(719\) −19.1718 −0.714987 −0.357494 0.933916i \(-0.616369\pi\)
−0.357494 + 0.933916i \(0.616369\pi\)
\(720\) −13.6560 −0.508931
\(721\) −24.2904 −0.904620
\(722\) 42.3363 1.57559
\(723\) 15.0648 0.560264
\(724\) 55.2829 2.05457
\(725\) 8.14393 0.302458
\(726\) −27.4491 −1.01873
\(727\) 10.2018 0.378366 0.189183 0.981942i \(-0.439416\pi\)
0.189183 + 0.981942i \(0.439416\pi\)
\(728\) 94.6295 3.50720
\(729\) 16.7447 0.620174
\(730\) 21.9557 0.812619
\(731\) −0.559814 −0.0207055
\(732\) 65.4356 2.41857
\(733\) −33.7170 −1.24536 −0.622682 0.782475i \(-0.713957\pi\)
−0.622682 + 0.782475i \(0.713957\pi\)
\(734\) −65.6129 −2.42182
\(735\) −12.8301 −0.473244
\(736\) 0.944205 0.0348038
\(737\) −9.60023 −0.353629
\(738\) 32.9038 1.21121
\(739\) −25.8951 −0.952567 −0.476283 0.879292i \(-0.658016\pi\)
−0.476283 + 0.879292i \(0.658016\pi\)
\(740\) −29.8396 −1.09692
\(741\) 7.62441 0.280090
\(742\) 50.0156 1.83613
\(743\) 47.8074 1.75388 0.876941 0.480598i \(-0.159580\pi\)
0.876941 + 0.480598i \(0.159580\pi\)
\(744\) 51.6540 1.89373
\(745\) −14.6748 −0.537645
\(746\) −74.3746 −2.72305
\(747\) −6.83735 −0.250165
\(748\) 0.157026 0.00574142
\(749\) −32.8746 −1.20121
\(750\) −31.1665 −1.13804
\(751\) 18.9193 0.690376 0.345188 0.938534i \(-0.387815\pi\)
0.345188 + 0.938534i \(0.387815\pi\)
\(752\) −44.9220 −1.63814
\(753\) 16.2486 0.592131
\(754\) −125.838 −4.58275
\(755\) 4.82759 0.175694
\(756\) 73.5356 2.67446
\(757\) 43.6512 1.58653 0.793265 0.608876i \(-0.208379\pi\)
0.793265 + 0.608876i \(0.208379\pi\)
\(758\) 62.8781 2.28384
\(759\) 1.19356 0.0433236
\(760\) −12.2278 −0.443551
\(761\) −20.7315 −0.751516 −0.375758 0.926718i \(-0.622618\pi\)
−0.375758 + 0.926718i \(0.622618\pi\)
\(762\) 53.1474 1.92533
\(763\) −2.93246 −0.106162
\(764\) −35.4481 −1.28247
\(765\) 0.214392 0.00775135
\(766\) 87.0504 3.14526
\(767\) −40.6725 −1.46860
\(768\) 33.6667 1.21484
\(769\) −44.5445 −1.60632 −0.803158 0.595766i \(-0.796849\pi\)
−0.803158 + 0.595766i \(0.796849\pi\)
\(770\) 12.4175 0.447496
\(771\) −9.43250 −0.339703
\(772\) −42.5464 −1.53128
\(773\) 7.53079 0.270864 0.135432 0.990787i \(-0.456758\pi\)
0.135432 + 0.990787i \(0.456758\pi\)
\(774\) 44.2835 1.59174
\(775\) −8.97836 −0.322512
\(776\) 49.8678 1.79015
\(777\) 14.3659 0.515374
\(778\) 34.0970 1.22244
\(779\) 9.30054 0.333227
\(780\) 47.7883 1.71109
\(781\) 8.64436 0.309320
\(782\) 0.221487 0.00792037
\(783\) −48.1271 −1.71992
\(784\) 21.4307 0.765383
\(785\) 37.6833 1.34497
\(786\) 0.144495 0.00515396
\(787\) 38.8712 1.38561 0.692805 0.721125i \(-0.256375\pi\)
0.692805 + 0.721125i \(0.256375\pi\)
\(788\) −18.4645 −0.657772
\(789\) 19.0021 0.676494
\(790\) −16.2659 −0.578715
\(791\) 16.3611 0.581733
\(792\) −6.11330 −0.217227
\(793\) 86.4952 3.07153
\(794\) −25.2564 −0.896316
\(795\) 12.4310 0.440883
\(796\) 32.2928 1.14459
\(797\) −11.0465 −0.391287 −0.195644 0.980675i \(-0.562680\pi\)
−0.195644 + 0.980675i \(0.562680\pi\)
\(798\) 11.9614 0.423430
\(799\) 0.705249 0.0249499
\(800\) −0.521323 −0.0184316
\(801\) −10.4160 −0.368032
\(802\) −8.80330 −0.310855
\(803\) 3.10267 0.109491
\(804\) −57.9624 −2.04417
\(805\) 11.6160 0.409411
\(806\) 138.731 4.88660
\(807\) 29.0525 1.02269
\(808\) 14.8992 0.524153
\(809\) −2.35835 −0.0829152 −0.0414576 0.999140i \(-0.513200\pi\)
−0.0414576 + 0.999140i \(0.513200\pi\)
\(810\) 0.0814409 0.00286154
\(811\) −50.5944 −1.77661 −0.888305 0.459255i \(-0.848116\pi\)
−0.888305 + 0.459255i \(0.848116\pi\)
\(812\) −130.928 −4.59469
\(813\) −17.1305 −0.600794
\(814\) −6.35821 −0.222855
\(815\) −10.5478 −0.369472
\(816\) 0.222092 0.00777478
\(817\) 12.5171 0.437918
\(818\) −12.8083 −0.447832
\(819\) 37.0975 1.29629
\(820\) 58.2939 2.03571
\(821\) 12.0978 0.422215 0.211108 0.977463i \(-0.432293\pi\)
0.211108 + 0.977463i \(0.432293\pi\)
\(822\) −34.0864 −1.18890
\(823\) 46.0771 1.60615 0.803074 0.595880i \(-0.203196\pi\)
0.803074 + 0.595880i \(0.203196\pi\)
\(824\) 31.9453 1.11287
\(825\) −0.659001 −0.0229435
\(826\) −63.8085 −2.22018
\(827\) 18.6727 0.649312 0.324656 0.945832i \(-0.394751\pi\)
0.324656 + 0.945832i \(0.394751\pi\)
\(828\) −11.6196 −0.403810
\(829\) −14.3860 −0.499645 −0.249823 0.968292i \(-0.580372\pi\)
−0.249823 + 0.968292i \(0.580372\pi\)
\(830\) −18.2650 −0.633987
\(831\) 13.0061 0.451176
\(832\) 48.5927 1.68465
\(833\) −0.336449 −0.0116573
\(834\) −56.8377 −1.96813
\(835\) 4.05619 0.140370
\(836\) −3.51100 −0.121430
\(837\) 53.0582 1.83396
\(838\) −13.9139 −0.480646
\(839\) −25.7863 −0.890244 −0.445122 0.895470i \(-0.646840\pi\)
−0.445122 + 0.895470i \(0.646840\pi\)
\(840\) 36.8982 1.27311
\(841\) 56.6892 1.95480
\(842\) −12.2885 −0.423490
\(843\) 25.3475 0.873016
\(844\) 55.0211 1.89390
\(845\) 36.7804 1.26529
\(846\) −55.7880 −1.91803
\(847\) −37.7509 −1.29714
\(848\) −20.7642 −0.713045
\(849\) 3.17117 0.108834
\(850\) −0.122290 −0.00419450
\(851\) −5.94783 −0.203889
\(852\) 52.1912 1.78804
\(853\) 34.3691 1.17678 0.588388 0.808578i \(-0.299763\pi\)
0.588388 + 0.808578i \(0.299763\pi\)
\(854\) 135.697 4.64345
\(855\) −4.79367 −0.163940
\(856\) 43.2349 1.47774
\(857\) 38.1880 1.30448 0.652238 0.758014i \(-0.273830\pi\)
0.652238 + 0.758014i \(0.273830\pi\)
\(858\) 10.1827 0.347632
\(859\) 55.7453 1.90200 0.951002 0.309184i \(-0.100056\pi\)
0.951002 + 0.309184i \(0.100056\pi\)
\(860\) 78.4547 2.67528
\(861\) −28.0649 −0.956450
\(862\) 25.5545 0.870390
\(863\) 28.2678 0.962247 0.481124 0.876653i \(-0.340229\pi\)
0.481124 + 0.876653i \(0.340229\pi\)
\(864\) 3.08079 0.104811
\(865\) 5.59340 0.190181
\(866\) −65.9296 −2.24038
\(867\) 18.2139 0.618577
\(868\) 144.343 4.89933
\(869\) −2.29861 −0.0779751
\(870\) −49.0671 −1.66353
\(871\) −76.6167 −2.59606
\(872\) 3.85661 0.130601
\(873\) 19.5496 0.661654
\(874\) −4.95232 −0.167515
\(875\) −42.8636 −1.44905
\(876\) 18.7327 0.632919
\(877\) −39.4428 −1.33189 −0.665945 0.746001i \(-0.731972\pi\)
−0.665945 + 0.746001i \(0.731972\pi\)
\(878\) 7.66423 0.258655
\(879\) 17.7995 0.600361
\(880\) −5.15518 −0.173781
\(881\) −51.9652 −1.75075 −0.875375 0.483444i \(-0.839386\pi\)
−0.875375 + 0.483444i \(0.839386\pi\)
\(882\) 26.6145 0.896156
\(883\) 38.4928 1.29538 0.647692 0.761902i \(-0.275734\pi\)
0.647692 + 0.761902i \(0.275734\pi\)
\(884\) 1.25318 0.0421489
\(885\) −15.8592 −0.533100
\(886\) 7.64411 0.256809
\(887\) 54.7458 1.83819 0.919093 0.394041i \(-0.128923\pi\)
0.919093 + 0.394041i \(0.128923\pi\)
\(888\) −18.8932 −0.634015
\(889\) 73.0940 2.45150
\(890\) −27.8249 −0.932692
\(891\) 0.0115088 0.000385559 0
\(892\) 13.0641 0.437419
\(893\) −15.7689 −0.527687
\(894\) −18.8791 −0.631410
\(895\) −45.8888 −1.53389
\(896\) 71.9776 2.40460
\(897\) 9.52549 0.318047
\(898\) −13.9108 −0.464210
\(899\) −94.4689 −3.15071
\(900\) 6.41554 0.213851
\(901\) 0.325985 0.0108601
\(902\) 12.4213 0.413583
\(903\) −37.7711 −1.25694
\(904\) −21.5172 −0.715651
\(905\) 28.4936 0.947160
\(906\) 6.21065 0.206335
\(907\) 8.22837 0.273219 0.136609 0.990625i \(-0.456380\pi\)
0.136609 + 0.990625i \(0.456380\pi\)
\(908\) −9.02882 −0.299632
\(909\) 5.84092 0.193731
\(910\) 99.1006 3.28515
\(911\) −8.57553 −0.284120 −0.142060 0.989858i \(-0.545373\pi\)
−0.142060 + 0.989858i \(0.545373\pi\)
\(912\) −4.96585 −0.164436
\(913\) −2.58111 −0.0854223
\(914\) 25.1673 0.832461
\(915\) 33.7265 1.11496
\(916\) −35.5172 −1.17352
\(917\) 0.198725 0.00656247
\(918\) 0.722679 0.0238520
\(919\) 19.2320 0.634404 0.317202 0.948358i \(-0.397257\pi\)
0.317202 + 0.948358i \(0.397257\pi\)
\(920\) −15.2768 −0.503660
\(921\) 4.73684 0.156084
\(922\) 54.8668 1.80694
\(923\) 68.9882 2.27077
\(924\) 10.5946 0.348538
\(925\) 3.28397 0.107976
\(926\) −38.5947 −1.26830
\(927\) 12.5235 0.411325
\(928\) −5.48528 −0.180063
\(929\) −37.2500 −1.22213 −0.611067 0.791579i \(-0.709259\pi\)
−0.611067 + 0.791579i \(0.709259\pi\)
\(930\) 54.0945 1.77383
\(931\) 7.52280 0.246550
\(932\) −30.7272 −1.00650
\(933\) 23.5735 0.771762
\(934\) 90.6979 2.96773
\(935\) 0.0809333 0.00264680
\(936\) −48.7885 −1.59470
\(937\) 30.2830 0.989303 0.494652 0.869091i \(-0.335296\pi\)
0.494652 + 0.869091i \(0.335296\pi\)
\(938\) −120.199 −3.92464
\(939\) −3.86352 −0.126081
\(940\) −98.8365 −3.22369
\(941\) 9.51868 0.310300 0.155150 0.987891i \(-0.450414\pi\)
0.155150 + 0.987891i \(0.450414\pi\)
\(942\) 48.4792 1.57954
\(943\) 11.6196 0.378385
\(944\) 26.4904 0.862189
\(945\) 37.9013 1.23293
\(946\) 16.7171 0.543520
\(947\) 9.06861 0.294690 0.147345 0.989085i \(-0.452927\pi\)
0.147345 + 0.989085i \(0.452927\pi\)
\(948\) −13.8781 −0.450740
\(949\) 24.7615 0.803793
\(950\) 2.73432 0.0887132
\(951\) −0.668455 −0.0216762
\(952\) 0.967602 0.0313602
\(953\) −23.6680 −0.766680 −0.383340 0.923607i \(-0.625226\pi\)
−0.383340 + 0.923607i \(0.625226\pi\)
\(954\) −25.7867 −0.834876
\(955\) −18.2705 −0.591219
\(956\) 77.7023 2.51307
\(957\) −6.93391 −0.224141
\(958\) −67.3865 −2.17716
\(959\) −46.8793 −1.51381
\(960\) 18.9474 0.611525
\(961\) 73.1481 2.35962
\(962\) −50.7431 −1.63602
\(963\) 16.9493 0.546184
\(964\) −55.3641 −1.78316
\(965\) −21.9290 −0.705920
\(966\) 14.9439 0.480813
\(967\) 12.1322 0.390147 0.195073 0.980789i \(-0.437506\pi\)
0.195073 + 0.980789i \(0.437506\pi\)
\(968\) 49.6479 1.59574
\(969\) 0.0779608 0.00250446
\(970\) 52.2239 1.67681
\(971\) 10.1344 0.325229 0.162615 0.986690i \(-0.448007\pi\)
0.162615 + 0.986690i \(0.448007\pi\)
\(972\) −61.3565 −1.96801
\(973\) −78.1693 −2.50599
\(974\) 3.03068 0.0971093
\(975\) −5.25930 −0.168433
\(976\) −56.3351 −1.80324
\(977\) −3.98483 −0.127486 −0.0637430 0.997966i \(-0.520304\pi\)
−0.0637430 + 0.997966i \(0.520304\pi\)
\(978\) −13.5696 −0.433908
\(979\) −3.93207 −0.125669
\(980\) 47.1514 1.50620
\(981\) 1.51190 0.0482713
\(982\) −8.41069 −0.268396
\(983\) −24.2374 −0.773053 −0.386526 0.922278i \(-0.626325\pi\)
−0.386526 + 0.922278i \(0.626325\pi\)
\(984\) 36.9094 1.17663
\(985\) −9.51689 −0.303233
\(986\) −1.28671 −0.0409773
\(987\) 47.5836 1.51460
\(988\) −28.0203 −0.891443
\(989\) 15.6381 0.497264
\(990\) −6.40214 −0.203473
\(991\) 36.8311 1.16998 0.584990 0.811041i \(-0.301098\pi\)
0.584990 + 0.811041i \(0.301098\pi\)
\(992\) 6.04730 0.192002
\(993\) −12.1120 −0.384363
\(994\) 108.231 3.43288
\(995\) 16.6442 0.527656
\(996\) −15.5837 −0.493789
\(997\) −61.1628 −1.93705 −0.968523 0.248924i \(-0.919923\pi\)
−0.968523 + 0.248924i \(0.919923\pi\)
\(998\) −74.4699 −2.35730
\(999\) −19.4069 −0.614006
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 4021.2.a.b.1.13 151
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4021.2.a.b.1.13 151 1.1 even 1 trivial