Properties

Label 6038.2.a.e.1.4
Level $6038$
Weight $2$
Character 6038.1
Self dual yes
Analytic conductor $48.214$
Analytic rank $0$
Dimension $70$
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] = [6038,2,Mod(1,6038)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6038, 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("6038.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6038.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: \(48.2136727404\)
Analytic rank: \(0\)
Dimension: \(70\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6038.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.93737 q^{3} +1.00000 q^{4} -3.45627 q^{5} -2.93737 q^{6} +2.34218 q^{7} +1.00000 q^{8} +5.62815 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.93737 q^{3} +1.00000 q^{4} -3.45627 q^{5} -2.93737 q^{6} +2.34218 q^{7} +1.00000 q^{8} +5.62815 q^{9} -3.45627 q^{10} -0.656795 q^{11} -2.93737 q^{12} +2.18567 q^{13} +2.34218 q^{14} +10.1524 q^{15} +1.00000 q^{16} +5.83197 q^{17} +5.62815 q^{18} +1.72800 q^{19} -3.45627 q^{20} -6.87986 q^{21} -0.656795 q^{22} -2.54416 q^{23} -2.93737 q^{24} +6.94580 q^{25} +2.18567 q^{26} -7.71987 q^{27} +2.34218 q^{28} -0.470989 q^{29} +10.1524 q^{30} +7.36041 q^{31} +1.00000 q^{32} +1.92925 q^{33} +5.83197 q^{34} -8.09521 q^{35} +5.62815 q^{36} -4.86352 q^{37} +1.72800 q^{38} -6.42013 q^{39} -3.45627 q^{40} +8.72477 q^{41} -6.87986 q^{42} +2.91867 q^{43} -0.656795 q^{44} -19.4524 q^{45} -2.54416 q^{46} -6.33452 q^{47} -2.93737 q^{48} -1.51418 q^{49} +6.94580 q^{50} -17.1307 q^{51} +2.18567 q^{52} -12.0542 q^{53} -7.71987 q^{54} +2.27006 q^{55} +2.34218 q^{56} -5.07577 q^{57} -0.470989 q^{58} -8.19890 q^{59} +10.1524 q^{60} -14.6553 q^{61} +7.36041 q^{62} +13.1822 q^{63} +1.00000 q^{64} -7.55427 q^{65} +1.92925 q^{66} +10.6610 q^{67} +5.83197 q^{68} +7.47314 q^{69} -8.09521 q^{70} -2.15041 q^{71} +5.62815 q^{72} +6.44525 q^{73} -4.86352 q^{74} -20.4024 q^{75} +1.72800 q^{76} -1.53833 q^{77} -6.42013 q^{78} +10.8656 q^{79} -3.45627 q^{80} +5.79166 q^{81} +8.72477 q^{82} -2.43535 q^{83} -6.87986 q^{84} -20.1569 q^{85} +2.91867 q^{86} +1.38347 q^{87} -0.656795 q^{88} -10.8482 q^{89} -19.4524 q^{90} +5.11924 q^{91} -2.54416 q^{92} -21.6203 q^{93} -6.33452 q^{94} -5.97243 q^{95} -2.93737 q^{96} +8.27674 q^{97} -1.51418 q^{98} -3.69654 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 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
\(3\) −2.93737 −1.69589 −0.847946 0.530082i \(-0.822161\pi\)
−0.847946 + 0.530082i \(0.822161\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.45627 −1.54569 −0.772845 0.634594i \(-0.781167\pi\)
−0.772845 + 0.634594i \(0.781167\pi\)
\(6\) −2.93737 −1.19918
\(7\) 2.34218 0.885262 0.442631 0.896704i \(-0.354045\pi\)
0.442631 + 0.896704i \(0.354045\pi\)
\(8\) 1.00000 0.353553
\(9\) 5.62815 1.87605
\(10\) −3.45627 −1.09297
\(11\) −0.656795 −0.198031 −0.0990156 0.995086i \(-0.531569\pi\)
−0.0990156 + 0.995086i \(0.531569\pi\)
\(12\) −2.93737 −0.847946
\(13\) 2.18567 0.606197 0.303098 0.952959i \(-0.401979\pi\)
0.303098 + 0.952959i \(0.401979\pi\)
\(14\) 2.34218 0.625975
\(15\) 10.1524 2.62133
\(16\) 1.00000 0.250000
\(17\) 5.83197 1.41446 0.707231 0.706983i \(-0.249944\pi\)
0.707231 + 0.706983i \(0.249944\pi\)
\(18\) 5.62815 1.32657
\(19\) 1.72800 0.396430 0.198215 0.980159i \(-0.436486\pi\)
0.198215 + 0.980159i \(0.436486\pi\)
\(20\) −3.45627 −0.772845
\(21\) −6.87986 −1.50131
\(22\) −0.656795 −0.140029
\(23\) −2.54416 −0.530494 −0.265247 0.964181i \(-0.585453\pi\)
−0.265247 + 0.964181i \(0.585453\pi\)
\(24\) −2.93737 −0.599589
\(25\) 6.94580 1.38916
\(26\) 2.18567 0.428646
\(27\) −7.71987 −1.48569
\(28\) 2.34218 0.442631
\(29\) −0.470989 −0.0874604 −0.0437302 0.999043i \(-0.513924\pi\)
−0.0437302 + 0.999043i \(0.513924\pi\)
\(30\) 10.1524 1.85356
\(31\) 7.36041 1.32197 0.660984 0.750400i \(-0.270139\pi\)
0.660984 + 0.750400i \(0.270139\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.92925 0.335840
\(34\) 5.83197 1.00018
\(35\) −8.09521 −1.36834
\(36\) 5.62815 0.938026
\(37\) −4.86352 −0.799558 −0.399779 0.916612i \(-0.630913\pi\)
−0.399779 + 0.916612i \(0.630913\pi\)
\(38\) 1.72800 0.280318
\(39\) −6.42013 −1.02804
\(40\) −3.45627 −0.546484
\(41\) 8.72477 1.36258 0.681290 0.732013i \(-0.261419\pi\)
0.681290 + 0.732013i \(0.261419\pi\)
\(42\) −6.87986 −1.06159
\(43\) 2.91867 0.445093 0.222546 0.974922i \(-0.428563\pi\)
0.222546 + 0.974922i \(0.428563\pi\)
\(44\) −0.656795 −0.0990156
\(45\) −19.4524 −2.89980
\(46\) −2.54416 −0.375116
\(47\) −6.33452 −0.923984 −0.461992 0.886884i \(-0.652865\pi\)
−0.461992 + 0.886884i \(0.652865\pi\)
\(48\) −2.93737 −0.423973
\(49\) −1.51418 −0.216312
\(50\) 6.94580 0.982285
\(51\) −17.1307 −2.39877
\(52\) 2.18567 0.303098
\(53\) −12.0542 −1.65578 −0.827888 0.560894i \(-0.810457\pi\)
−0.827888 + 0.560894i \(0.810457\pi\)
\(54\) −7.71987 −1.05054
\(55\) 2.27006 0.306095
\(56\) 2.34218 0.312987
\(57\) −5.07577 −0.672303
\(58\) −0.470989 −0.0618439
\(59\) −8.19890 −1.06741 −0.533703 0.845672i \(-0.679200\pi\)
−0.533703 + 0.845672i \(0.679200\pi\)
\(60\) 10.1524 1.31066
\(61\) −14.6553 −1.87642 −0.938208 0.346073i \(-0.887515\pi\)
−0.938208 + 0.346073i \(0.887515\pi\)
\(62\) 7.36041 0.934773
\(63\) 13.1822 1.66080
\(64\) 1.00000 0.125000
\(65\) −7.55427 −0.936992
\(66\) 1.92925 0.237474
\(67\) 10.6610 1.30245 0.651225 0.758885i \(-0.274255\pi\)
0.651225 + 0.758885i \(0.274255\pi\)
\(68\) 5.83197 0.707231
\(69\) 7.47314 0.899660
\(70\) −8.09521 −0.967563
\(71\) −2.15041 −0.255207 −0.127603 0.991825i \(-0.540728\pi\)
−0.127603 + 0.991825i \(0.540728\pi\)
\(72\) 5.62815 0.663284
\(73\) 6.44525 0.754359 0.377179 0.926140i \(-0.376894\pi\)
0.377179 + 0.926140i \(0.376894\pi\)
\(74\) −4.86352 −0.565373
\(75\) −20.4024 −2.35587
\(76\) 1.72800 0.198215
\(77\) −1.53833 −0.175309
\(78\) −6.42013 −0.726937
\(79\) 10.8656 1.22248 0.611240 0.791445i \(-0.290671\pi\)
0.611240 + 0.791445i \(0.290671\pi\)
\(80\) −3.45627 −0.386423
\(81\) 5.79166 0.643518
\(82\) 8.72477 0.963490
\(83\) −2.43535 −0.267314 −0.133657 0.991028i \(-0.542672\pi\)
−0.133657 + 0.991028i \(0.542672\pi\)
\(84\) −6.87986 −0.750654
\(85\) −20.1569 −2.18632
\(86\) 2.91867 0.314728
\(87\) 1.38347 0.148323
\(88\) −0.656795 −0.0700146
\(89\) −10.8482 −1.14990 −0.574952 0.818187i \(-0.694979\pi\)
−0.574952 + 0.818187i \(0.694979\pi\)
\(90\) −19.4524 −2.05047
\(91\) 5.11924 0.536643
\(92\) −2.54416 −0.265247
\(93\) −21.6203 −2.24192
\(94\) −6.33452 −0.653355
\(95\) −5.97243 −0.612758
\(96\) −2.93737 −0.299794
\(97\) 8.27674 0.840375 0.420188 0.907437i \(-0.361964\pi\)
0.420188 + 0.907437i \(0.361964\pi\)
\(98\) −1.51418 −0.152955
\(99\) −3.69654 −0.371517
\(100\) 6.94580 0.694580
\(101\) 18.4330 1.83415 0.917075 0.398715i \(-0.130544\pi\)
0.917075 + 0.398715i \(0.130544\pi\)
\(102\) −17.1307 −1.69619
\(103\) 8.72607 0.859805 0.429902 0.902875i \(-0.358548\pi\)
0.429902 + 0.902875i \(0.358548\pi\)
\(104\) 2.18567 0.214323
\(105\) 23.7787 2.32056
\(106\) −12.0542 −1.17081
\(107\) 8.38135 0.810256 0.405128 0.914260i \(-0.367227\pi\)
0.405128 + 0.914260i \(0.367227\pi\)
\(108\) −7.71987 −0.742845
\(109\) 15.2202 1.45783 0.728915 0.684604i \(-0.240025\pi\)
0.728915 + 0.684604i \(0.240025\pi\)
\(110\) 2.27006 0.216442
\(111\) 14.2860 1.35596
\(112\) 2.34218 0.221315
\(113\) 14.5126 1.36523 0.682614 0.730779i \(-0.260843\pi\)
0.682614 + 0.730779i \(0.260843\pi\)
\(114\) −5.07577 −0.475390
\(115\) 8.79330 0.819979
\(116\) −0.470989 −0.0437302
\(117\) 12.3013 1.13726
\(118\) −8.19890 −0.754770
\(119\) 13.6595 1.25217
\(120\) 10.1524 0.926779
\(121\) −10.5686 −0.960784
\(122\) −14.6553 −1.32683
\(123\) −25.6279 −2.31079
\(124\) 7.36041 0.660984
\(125\) −6.72521 −0.601521
\(126\) 13.1822 1.17436
\(127\) −11.5680 −1.02650 −0.513249 0.858240i \(-0.671558\pi\)
−0.513249 + 0.858240i \(0.671558\pi\)
\(128\) 1.00000 0.0883883
\(129\) −8.57321 −0.754829
\(130\) −7.55427 −0.662554
\(131\) −6.72344 −0.587430 −0.293715 0.955893i \(-0.594892\pi\)
−0.293715 + 0.955893i \(0.594892\pi\)
\(132\) 1.92925 0.167920
\(133\) 4.04729 0.350944
\(134\) 10.6610 0.920972
\(135\) 26.6819 2.29642
\(136\) 5.83197 0.500088
\(137\) −4.65670 −0.397849 −0.198924 0.980015i \(-0.563745\pi\)
−0.198924 + 0.980015i \(0.563745\pi\)
\(138\) 7.47314 0.636156
\(139\) 5.37841 0.456191 0.228096 0.973639i \(-0.426750\pi\)
0.228096 + 0.973639i \(0.426750\pi\)
\(140\) −8.09521 −0.684171
\(141\) 18.6068 1.56698
\(142\) −2.15041 −0.180458
\(143\) −1.43554 −0.120046
\(144\) 5.62815 0.469013
\(145\) 1.62786 0.135187
\(146\) 6.44525 0.533412
\(147\) 4.44771 0.366841
\(148\) −4.86352 −0.399779
\(149\) −17.8551 −1.46275 −0.731374 0.681976i \(-0.761121\pi\)
−0.731374 + 0.681976i \(0.761121\pi\)
\(150\) −20.4024 −1.66585
\(151\) 14.8705 1.21014 0.605071 0.796171i \(-0.293145\pi\)
0.605071 + 0.796171i \(0.293145\pi\)
\(152\) 1.72800 0.140159
\(153\) 32.8233 2.65360
\(154\) −1.53833 −0.123962
\(155\) −25.4396 −2.04335
\(156\) −6.42013 −0.514022
\(157\) 7.61667 0.607877 0.303938 0.952692i \(-0.401698\pi\)
0.303938 + 0.952692i \(0.401698\pi\)
\(158\) 10.8656 0.864424
\(159\) 35.4077 2.80802
\(160\) −3.45627 −0.273242
\(161\) −5.95888 −0.469626
\(162\) 5.79166 0.455036
\(163\) −3.99369 −0.312810 −0.156405 0.987693i \(-0.549990\pi\)
−0.156405 + 0.987693i \(0.549990\pi\)
\(164\) 8.72477 0.681290
\(165\) −6.66801 −0.519104
\(166\) −2.43535 −0.189020
\(167\) −20.5551 −1.59060 −0.795299 0.606218i \(-0.792686\pi\)
−0.795299 + 0.606218i \(0.792686\pi\)
\(168\) −6.87986 −0.530793
\(169\) −8.22284 −0.632526
\(170\) −20.1569 −1.54596
\(171\) 9.72544 0.743723
\(172\) 2.91867 0.222546
\(173\) 19.2480 1.46340 0.731699 0.681628i \(-0.238728\pi\)
0.731699 + 0.681628i \(0.238728\pi\)
\(174\) 1.38347 0.104881
\(175\) 16.2683 1.22977
\(176\) −0.656795 −0.0495078
\(177\) 24.0832 1.81021
\(178\) −10.8482 −0.813105
\(179\) 11.9834 0.895680 0.447840 0.894114i \(-0.352193\pi\)
0.447840 + 0.894114i \(0.352193\pi\)
\(180\) −19.4524 −1.44990
\(181\) −22.1192 −1.64410 −0.822052 0.569412i \(-0.807171\pi\)
−0.822052 + 0.569412i \(0.807171\pi\)
\(182\) 5.11924 0.379464
\(183\) 43.0480 3.18220
\(184\) −2.54416 −0.187558
\(185\) 16.8096 1.23587
\(186\) −21.6203 −1.58527
\(187\) −3.83041 −0.280107
\(188\) −6.33452 −0.461992
\(189\) −18.0813 −1.31522
\(190\) −5.97243 −0.433286
\(191\) −13.9667 −1.01060 −0.505299 0.862945i \(-0.668618\pi\)
−0.505299 + 0.862945i \(0.668618\pi\)
\(192\) −2.93737 −0.211987
\(193\) −6.62364 −0.476780 −0.238390 0.971169i \(-0.576620\pi\)
−0.238390 + 0.971169i \(0.576620\pi\)
\(194\) 8.27674 0.594235
\(195\) 22.1897 1.58904
\(196\) −1.51418 −0.108156
\(197\) −9.12796 −0.650340 −0.325170 0.945655i \(-0.605422\pi\)
−0.325170 + 0.945655i \(0.605422\pi\)
\(198\) −3.69654 −0.262702
\(199\) 2.28989 0.162326 0.0811629 0.996701i \(-0.474137\pi\)
0.0811629 + 0.996701i \(0.474137\pi\)
\(200\) 6.94580 0.491142
\(201\) −31.3154 −2.20882
\(202\) 18.4330 1.29694
\(203\) −1.10314 −0.0774254
\(204\) −17.1307 −1.19939
\(205\) −30.1552 −2.10613
\(206\) 8.72607 0.607974
\(207\) −14.3189 −0.995234
\(208\) 2.18567 0.151549
\(209\) −1.13494 −0.0785055
\(210\) 23.7787 1.64088
\(211\) 9.98014 0.687061 0.343531 0.939141i \(-0.388377\pi\)
0.343531 + 0.939141i \(0.388377\pi\)
\(212\) −12.0542 −0.827888
\(213\) 6.31656 0.432803
\(214\) 8.38135 0.572938
\(215\) −10.0877 −0.687976
\(216\) −7.71987 −0.525270
\(217\) 17.2394 1.17029
\(218\) 15.2202 1.03084
\(219\) −18.9321 −1.27931
\(220\) 2.27006 0.153047
\(221\) 12.7468 0.857442
\(222\) 14.2860 0.958811
\(223\) 12.7627 0.854656 0.427328 0.904097i \(-0.359455\pi\)
0.427328 + 0.904097i \(0.359455\pi\)
\(224\) 2.34218 0.156494
\(225\) 39.0920 2.60614
\(226\) 14.5126 0.965362
\(227\) 2.90519 0.192824 0.0964121 0.995342i \(-0.469263\pi\)
0.0964121 + 0.995342i \(0.469263\pi\)
\(228\) −5.07577 −0.336151
\(229\) 2.08724 0.137929 0.0689643 0.997619i \(-0.478031\pi\)
0.0689643 + 0.997619i \(0.478031\pi\)
\(230\) 8.79330 0.579813
\(231\) 4.51866 0.297306
\(232\) −0.470989 −0.0309219
\(233\) 4.84432 0.317362 0.158681 0.987330i \(-0.449276\pi\)
0.158681 + 0.987330i \(0.449276\pi\)
\(234\) 12.3013 0.804161
\(235\) 21.8938 1.42819
\(236\) −8.19890 −0.533703
\(237\) −31.9164 −2.07319
\(238\) 13.6595 0.885417
\(239\) −17.4412 −1.12818 −0.564090 0.825713i \(-0.690773\pi\)
−0.564090 + 0.825713i \(0.690773\pi\)
\(240\) 10.1524 0.655331
\(241\) 24.0619 1.54996 0.774981 0.631984i \(-0.217759\pi\)
0.774981 + 0.631984i \(0.217759\pi\)
\(242\) −10.5686 −0.679377
\(243\) 6.14735 0.394352
\(244\) −14.6553 −0.938208
\(245\) 5.23342 0.334351
\(246\) −25.6279 −1.63398
\(247\) 3.77684 0.240315
\(248\) 7.36041 0.467386
\(249\) 7.15353 0.453337
\(250\) −6.72521 −0.425340
\(251\) 23.6182 1.49077 0.745385 0.666634i \(-0.232266\pi\)
0.745385 + 0.666634i \(0.232266\pi\)
\(252\) 13.1822 0.830398
\(253\) 1.67099 0.105054
\(254\) −11.5680 −0.725843
\(255\) 59.2082 3.70776
\(256\) 1.00000 0.0625000
\(257\) 17.5055 1.09197 0.545983 0.837796i \(-0.316156\pi\)
0.545983 + 0.837796i \(0.316156\pi\)
\(258\) −8.57321 −0.533745
\(259\) −11.3913 −0.707818
\(260\) −7.55427 −0.468496
\(261\) −2.65080 −0.164080
\(262\) −6.72344 −0.415376
\(263\) −8.91082 −0.549465 −0.274732 0.961521i \(-0.588589\pi\)
−0.274732 + 0.961521i \(0.588589\pi\)
\(264\) 1.92925 0.118737
\(265\) 41.6627 2.55932
\(266\) 4.04729 0.248155
\(267\) 31.8651 1.95011
\(268\) 10.6610 0.651225
\(269\) 28.9927 1.76772 0.883858 0.467755i \(-0.154937\pi\)
0.883858 + 0.467755i \(0.154937\pi\)
\(270\) 26.6819 1.62381
\(271\) 9.15317 0.556016 0.278008 0.960579i \(-0.410326\pi\)
0.278008 + 0.960579i \(0.410326\pi\)
\(272\) 5.83197 0.353615
\(273\) −15.0371 −0.910088
\(274\) −4.65670 −0.281322
\(275\) −4.56197 −0.275097
\(276\) 7.47314 0.449830
\(277\) −19.9289 −1.19741 −0.598705 0.800970i \(-0.704318\pi\)
−0.598705 + 0.800970i \(0.704318\pi\)
\(278\) 5.37841 0.322576
\(279\) 41.4255 2.48008
\(280\) −8.09521 −0.483782
\(281\) 25.8846 1.54414 0.772072 0.635535i \(-0.219221\pi\)
0.772072 + 0.635535i \(0.219221\pi\)
\(282\) 18.6068 1.10802
\(283\) 32.2342 1.91613 0.958063 0.286559i \(-0.0925113\pi\)
0.958063 + 0.286559i \(0.0925113\pi\)
\(284\) −2.15041 −0.127603
\(285\) 17.5432 1.03917
\(286\) −1.43554 −0.0848852
\(287\) 20.4350 1.20624
\(288\) 5.62815 0.331642
\(289\) 17.0119 1.00070
\(290\) 1.62786 0.0955915
\(291\) −24.3119 −1.42519
\(292\) 6.44525 0.377179
\(293\) 4.39700 0.256875 0.128438 0.991718i \(-0.459004\pi\)
0.128438 + 0.991718i \(0.459004\pi\)
\(294\) 4.44771 0.259396
\(295\) 28.3376 1.64988
\(296\) −4.86352 −0.282686
\(297\) 5.07037 0.294213
\(298\) −17.8551 −1.03432
\(299\) −5.56070 −0.321583
\(300\) −20.4024 −1.17793
\(301\) 6.83605 0.394024
\(302\) 14.8705 0.855700
\(303\) −54.1445 −3.11052
\(304\) 1.72800 0.0991075
\(305\) 50.6526 2.90036
\(306\) 32.8233 1.87638
\(307\) −14.0069 −0.799416 −0.399708 0.916642i \(-0.630889\pi\)
−0.399708 + 0.916642i \(0.630889\pi\)
\(308\) −1.53833 −0.0876547
\(309\) −25.6317 −1.45814
\(310\) −25.4396 −1.44487
\(311\) 31.7035 1.79774 0.898871 0.438213i \(-0.144388\pi\)
0.898871 + 0.438213i \(0.144388\pi\)
\(312\) −6.42013 −0.363468
\(313\) 3.81305 0.215526 0.107763 0.994177i \(-0.465631\pi\)
0.107763 + 0.994177i \(0.465631\pi\)
\(314\) 7.61667 0.429834
\(315\) −45.5611 −2.56708
\(316\) 10.8656 0.611240
\(317\) −2.62533 −0.147453 −0.0737265 0.997278i \(-0.523489\pi\)
−0.0737265 + 0.997278i \(0.523489\pi\)
\(318\) 35.4077 1.98557
\(319\) 0.309343 0.0173199
\(320\) −3.45627 −0.193211
\(321\) −24.6192 −1.37411
\(322\) −5.95888 −0.332076
\(323\) 10.0776 0.560735
\(324\) 5.79166 0.321759
\(325\) 15.1812 0.842104
\(326\) −3.99369 −0.221190
\(327\) −44.7074 −2.47232
\(328\) 8.72477 0.481745
\(329\) −14.8366 −0.817968
\(330\) −6.66801 −0.367062
\(331\) 23.9944 1.31885 0.659425 0.751770i \(-0.270800\pi\)
0.659425 + 0.751770i \(0.270800\pi\)
\(332\) −2.43535 −0.133657
\(333\) −27.3726 −1.50001
\(334\) −20.5551 −1.12472
\(335\) −36.8473 −2.01319
\(336\) −6.87986 −0.375327
\(337\) −15.7215 −0.856405 −0.428203 0.903683i \(-0.640853\pi\)
−0.428203 + 0.903683i \(0.640853\pi\)
\(338\) −8.22284 −0.447263
\(339\) −42.6288 −2.31528
\(340\) −20.1569 −1.09316
\(341\) −4.83428 −0.261791
\(342\) 9.72544 0.525892
\(343\) −19.9418 −1.07675
\(344\) 2.91867 0.157364
\(345\) −25.8292 −1.39060
\(346\) 19.2480 1.03478
\(347\) 11.6722 0.626596 0.313298 0.949655i \(-0.398566\pi\)
0.313298 + 0.949655i \(0.398566\pi\)
\(348\) 1.38347 0.0741617
\(349\) 3.37470 0.180643 0.0903217 0.995913i \(-0.471210\pi\)
0.0903217 + 0.995913i \(0.471210\pi\)
\(350\) 16.2683 0.869579
\(351\) −16.8731 −0.900620
\(352\) −0.656795 −0.0350073
\(353\) −9.97235 −0.530775 −0.265387 0.964142i \(-0.585500\pi\)
−0.265387 + 0.964142i \(0.585500\pi\)
\(354\) 24.0832 1.28001
\(355\) 7.43240 0.394471
\(356\) −10.8482 −0.574952
\(357\) −40.1232 −2.12354
\(358\) 11.9834 0.633341
\(359\) 4.48256 0.236580 0.118290 0.992979i \(-0.462259\pi\)
0.118290 + 0.992979i \(0.462259\pi\)
\(360\) −19.4524 −1.02523
\(361\) −16.0140 −0.842843
\(362\) −22.1192 −1.16256
\(363\) 31.0440 1.62939
\(364\) 5.11924 0.268321
\(365\) −22.2765 −1.16601
\(366\) 43.0480 2.25015
\(367\) −12.7562 −0.665870 −0.332935 0.942950i \(-0.608039\pi\)
−0.332935 + 0.942950i \(0.608039\pi\)
\(368\) −2.54416 −0.132623
\(369\) 49.1044 2.55627
\(370\) 16.8096 0.873891
\(371\) −28.2332 −1.46579
\(372\) −21.6203 −1.12096
\(373\) 8.66272 0.448539 0.224269 0.974527i \(-0.428000\pi\)
0.224269 + 0.974527i \(0.428000\pi\)
\(374\) −3.83041 −0.198066
\(375\) 19.7545 1.02012
\(376\) −6.33452 −0.326678
\(377\) −1.02943 −0.0530182
\(378\) −18.0813 −0.930004
\(379\) −5.69401 −0.292482 −0.146241 0.989249i \(-0.546717\pi\)
−0.146241 + 0.989249i \(0.546717\pi\)
\(380\) −5.97243 −0.306379
\(381\) 33.9796 1.74083
\(382\) −13.9667 −0.714600
\(383\) 32.1072 1.64060 0.820300 0.571934i \(-0.193807\pi\)
0.820300 + 0.571934i \(0.193807\pi\)
\(384\) −2.93737 −0.149897
\(385\) 5.31690 0.270974
\(386\) −6.62364 −0.337135
\(387\) 16.4267 0.835017
\(388\) 8.27674 0.420188
\(389\) −28.0029 −1.41980 −0.709902 0.704301i \(-0.751261\pi\)
−0.709902 + 0.704301i \(0.751261\pi\)
\(390\) 22.1897 1.12362
\(391\) −14.8375 −0.750363
\(392\) −1.51418 −0.0764777
\(393\) 19.7493 0.996218
\(394\) −9.12796 −0.459860
\(395\) −37.5546 −1.88958
\(396\) −3.69654 −0.185758
\(397\) 11.5059 0.577462 0.288731 0.957410i \(-0.406767\pi\)
0.288731 + 0.957410i \(0.406767\pi\)
\(398\) 2.28989 0.114782
\(399\) −11.8884 −0.595164
\(400\) 6.94580 0.347290
\(401\) −4.18547 −0.209013 −0.104506 0.994524i \(-0.533326\pi\)
−0.104506 + 0.994524i \(0.533326\pi\)
\(402\) −31.3154 −1.56187
\(403\) 16.0874 0.801373
\(404\) 18.4330 0.917075
\(405\) −20.0175 −0.994679
\(406\) −1.10314 −0.0547480
\(407\) 3.19434 0.158337
\(408\) −17.1307 −0.848095
\(409\) 34.4497 1.70343 0.851713 0.524008i \(-0.175564\pi\)
0.851713 + 0.524008i \(0.175564\pi\)
\(410\) −30.1552 −1.48926
\(411\) 13.6785 0.674709
\(412\) 8.72607 0.429902
\(413\) −19.2033 −0.944934
\(414\) −14.3189 −0.703736
\(415\) 8.41723 0.413186
\(416\) 2.18567 0.107161
\(417\) −15.7984 −0.773651
\(418\) −1.13494 −0.0555118
\(419\) −18.3632 −0.897101 −0.448551 0.893757i \(-0.648060\pi\)
−0.448551 + 0.893757i \(0.648060\pi\)
\(420\) 23.7787 1.16028
\(421\) 2.40129 0.117032 0.0585158 0.998286i \(-0.481363\pi\)
0.0585158 + 0.998286i \(0.481363\pi\)
\(422\) 9.98014 0.485826
\(423\) −35.6516 −1.73344
\(424\) −12.0542 −0.585405
\(425\) 40.5077 1.96491
\(426\) 6.31656 0.306038
\(427\) −34.3253 −1.66112
\(428\) 8.38135 0.405128
\(429\) 4.21671 0.203585
\(430\) −10.0877 −0.486472
\(431\) 23.4929 1.13162 0.565808 0.824537i \(-0.308564\pi\)
0.565808 + 0.824537i \(0.308564\pi\)
\(432\) −7.71987 −0.371422
\(433\) 18.9816 0.912197 0.456099 0.889929i \(-0.349246\pi\)
0.456099 + 0.889929i \(0.349246\pi\)
\(434\) 17.2394 0.827519
\(435\) −4.78164 −0.229262
\(436\) 15.2202 0.728915
\(437\) −4.39630 −0.210304
\(438\) −18.9321 −0.904610
\(439\) −5.98493 −0.285645 −0.142823 0.989748i \(-0.545618\pi\)
−0.142823 + 0.989748i \(0.545618\pi\)
\(440\) 2.27006 0.108221
\(441\) −8.52205 −0.405812
\(442\) 12.7468 0.606303
\(443\) 19.9090 0.945906 0.472953 0.881088i \(-0.343188\pi\)
0.472953 + 0.881088i \(0.343188\pi\)
\(444\) 14.2860 0.677982
\(445\) 37.4942 1.77740
\(446\) 12.7627 0.604333
\(447\) 52.4471 2.48066
\(448\) 2.34218 0.110658
\(449\) 6.38575 0.301362 0.150681 0.988582i \(-0.451853\pi\)
0.150681 + 0.988582i \(0.451853\pi\)
\(450\) 39.0920 1.84282
\(451\) −5.73039 −0.269833
\(452\) 14.5126 0.682614
\(453\) −43.6801 −2.05227
\(454\) 2.90519 0.136347
\(455\) −17.6935 −0.829484
\(456\) −5.07577 −0.237695
\(457\) −24.4654 −1.14444 −0.572221 0.820099i \(-0.693918\pi\)
−0.572221 + 0.820099i \(0.693918\pi\)
\(458\) 2.08724 0.0975303
\(459\) −45.0221 −2.10145
\(460\) 8.79330 0.409990
\(461\) −0.238585 −0.0111120 −0.00555602 0.999985i \(-0.501769\pi\)
−0.00555602 + 0.999985i \(0.501769\pi\)
\(462\) 4.51866 0.210227
\(463\) −1.83537 −0.0852969 −0.0426485 0.999090i \(-0.513580\pi\)
−0.0426485 + 0.999090i \(0.513580\pi\)
\(464\) −0.470989 −0.0218651
\(465\) 74.7254 3.46531
\(466\) 4.84432 0.224409
\(467\) −0.102036 −0.00472164 −0.00236082 0.999997i \(-0.500751\pi\)
−0.00236082 + 0.999997i \(0.500751\pi\)
\(468\) 12.3013 0.568628
\(469\) 24.9700 1.15301
\(470\) 21.8938 1.00989
\(471\) −22.3730 −1.03089
\(472\) −8.19890 −0.377385
\(473\) −1.91697 −0.0881422
\(474\) −31.9164 −1.46597
\(475\) 12.0023 0.550705
\(476\) 13.6595 0.626084
\(477\) −67.8430 −3.10632
\(478\) −17.4412 −0.797744
\(479\) −18.6033 −0.850008 −0.425004 0.905192i \(-0.639727\pi\)
−0.425004 + 0.905192i \(0.639727\pi\)
\(480\) 10.1524 0.463389
\(481\) −10.6301 −0.484689
\(482\) 24.0619 1.09599
\(483\) 17.5035 0.796435
\(484\) −10.5686 −0.480392
\(485\) −28.6066 −1.29896
\(486\) 6.14735 0.278849
\(487\) 3.46285 0.156917 0.0784584 0.996917i \(-0.475000\pi\)
0.0784584 + 0.996917i \(0.475000\pi\)
\(488\) −14.6553 −0.663413
\(489\) 11.7309 0.530491
\(490\) 5.23342 0.236422
\(491\) −15.0131 −0.677532 −0.338766 0.940871i \(-0.610010\pi\)
−0.338766 + 0.940871i \(0.610010\pi\)
\(492\) −25.6279 −1.15540
\(493\) −2.74679 −0.123709
\(494\) 3.77684 0.169928
\(495\) 12.7763 0.574250
\(496\) 7.36041 0.330492
\(497\) −5.03665 −0.225925
\(498\) 7.15353 0.320557
\(499\) −3.92722 −0.175806 −0.0879032 0.996129i \(-0.528017\pi\)
−0.0879032 + 0.996129i \(0.528017\pi\)
\(500\) −6.72521 −0.300761
\(501\) 60.3778 2.69748
\(502\) 23.6182 1.05413
\(503\) 43.1056 1.92198 0.960991 0.276579i \(-0.0892007\pi\)
0.960991 + 0.276579i \(0.0892007\pi\)
\(504\) 13.1822 0.587180
\(505\) −63.7093 −2.83503
\(506\) 1.67099 0.0742846
\(507\) 24.1535 1.07270
\(508\) −11.5680 −0.513249
\(509\) −28.5067 −1.26354 −0.631769 0.775157i \(-0.717671\pi\)
−0.631769 + 0.775157i \(0.717671\pi\)
\(510\) 59.2082 2.62179
\(511\) 15.0959 0.667805
\(512\) 1.00000 0.0441942
\(513\) −13.3399 −0.588972
\(514\) 17.5055 0.772136
\(515\) −30.1596 −1.32899
\(516\) −8.57321 −0.377415
\(517\) 4.16048 0.182978
\(518\) −11.3913 −0.500503
\(519\) −56.5385 −2.48177
\(520\) −7.55427 −0.331277
\(521\) 20.0442 0.878153 0.439077 0.898450i \(-0.355306\pi\)
0.439077 + 0.898450i \(0.355306\pi\)
\(522\) −2.65080 −0.116022
\(523\) 15.6380 0.683800 0.341900 0.939736i \(-0.388930\pi\)
0.341900 + 0.939736i \(0.388930\pi\)
\(524\) −6.72344 −0.293715
\(525\) −47.7861 −2.08556
\(526\) −8.91082 −0.388530
\(527\) 42.9257 1.86987
\(528\) 1.92925 0.0839599
\(529\) −16.5273 −0.718576
\(530\) 41.6627 1.80971
\(531\) −46.1447 −2.00251
\(532\) 4.04729 0.175472
\(533\) 19.0695 0.825992
\(534\) 31.8651 1.37894
\(535\) −28.9682 −1.25241
\(536\) 10.6610 0.460486
\(537\) −35.1996 −1.51898
\(538\) 28.9927 1.24996
\(539\) 0.994507 0.0428364
\(540\) 26.6819 1.14821
\(541\) 18.2496 0.784610 0.392305 0.919835i \(-0.371678\pi\)
0.392305 + 0.919835i \(0.371678\pi\)
\(542\) 9.15317 0.393162
\(543\) 64.9722 2.78823
\(544\) 5.83197 0.250044
\(545\) −52.6051 −2.25335
\(546\) −15.0371 −0.643530
\(547\) 34.0979 1.45792 0.728961 0.684556i \(-0.240004\pi\)
0.728961 + 0.684556i \(0.240004\pi\)
\(548\) −4.65670 −0.198924
\(549\) −82.4821 −3.52025
\(550\) −4.56197 −0.194523
\(551\) −0.813868 −0.0346719
\(552\) 7.47314 0.318078
\(553\) 25.4493 1.08221
\(554\) −19.9289 −0.846697
\(555\) −49.3762 −2.09590
\(556\) 5.37841 0.228096
\(557\) −24.3055 −1.02986 −0.514929 0.857233i \(-0.672182\pi\)
−0.514929 + 0.857233i \(0.672182\pi\)
\(558\) 41.4255 1.75368
\(559\) 6.37925 0.269814
\(560\) −8.09521 −0.342085
\(561\) 11.2513 0.475032
\(562\) 25.8846 1.09187
\(563\) 20.9132 0.881386 0.440693 0.897658i \(-0.354733\pi\)
0.440693 + 0.897658i \(0.354733\pi\)
\(564\) 18.6068 0.783489
\(565\) −50.1594 −2.11022
\(566\) 32.2342 1.35491
\(567\) 13.5651 0.569682
\(568\) −2.15041 −0.0902292
\(569\) 18.3885 0.770885 0.385442 0.922732i \(-0.374049\pi\)
0.385442 + 0.922732i \(0.374049\pi\)
\(570\) 17.5432 0.734806
\(571\) −4.13329 −0.172973 −0.0864863 0.996253i \(-0.527564\pi\)
−0.0864863 + 0.996253i \(0.527564\pi\)
\(572\) −1.43554 −0.0600229
\(573\) 41.0255 1.71386
\(574\) 20.4350 0.852941
\(575\) −17.6712 −0.736941
\(576\) 5.62815 0.234506
\(577\) 0.0386552 0.00160924 0.000804618 1.00000i \(-0.499744\pi\)
0.000804618 1.00000i \(0.499744\pi\)
\(578\) 17.0119 0.707603
\(579\) 19.4561 0.808568
\(580\) 1.62786 0.0675934
\(581\) −5.70404 −0.236643
\(582\) −24.3119 −1.00776
\(583\) 7.91715 0.327895
\(584\) 6.44525 0.266706
\(585\) −42.5166 −1.75785
\(586\) 4.39700 0.181638
\(587\) 39.1374 1.61537 0.807687 0.589612i \(-0.200719\pi\)
0.807687 + 0.589612i \(0.200719\pi\)
\(588\) 4.44771 0.183421
\(589\) 12.7188 0.524068
\(590\) 28.3376 1.16664
\(591\) 26.8122 1.10291
\(592\) −4.86352 −0.199889
\(593\) 18.4599 0.758057 0.379028 0.925385i \(-0.376258\pi\)
0.379028 + 0.925385i \(0.376258\pi\)
\(594\) 5.07037 0.208040
\(595\) −47.2111 −1.93547
\(596\) −17.8551 −0.731374
\(597\) −6.72625 −0.275287
\(598\) −5.56070 −0.227394
\(599\) −29.2823 −1.19644 −0.598221 0.801331i \(-0.704125\pi\)
−0.598221 + 0.801331i \(0.704125\pi\)
\(600\) −20.4024 −0.832925
\(601\) 7.08242 0.288898 0.144449 0.989512i \(-0.453859\pi\)
0.144449 + 0.989512i \(0.453859\pi\)
\(602\) 6.83605 0.278617
\(603\) 60.0018 2.44346
\(604\) 14.8705 0.605071
\(605\) 36.5280 1.48507
\(606\) −54.1445 −2.19947
\(607\) −18.9946 −0.770967 −0.385484 0.922715i \(-0.625965\pi\)
−0.385484 + 0.922715i \(0.625965\pi\)
\(608\) 1.72800 0.0700796
\(609\) 3.24034 0.131305
\(610\) 50.6526 2.05086
\(611\) −13.8452 −0.560116
\(612\) 32.8233 1.32680
\(613\) 6.63738 0.268081 0.134041 0.990976i \(-0.457205\pi\)
0.134041 + 0.990976i \(0.457205\pi\)
\(614\) −14.0069 −0.565273
\(615\) 88.5770 3.57177
\(616\) −1.53833 −0.0619812
\(617\) 38.3917 1.54559 0.772796 0.634654i \(-0.218858\pi\)
0.772796 + 0.634654i \(0.218858\pi\)
\(618\) −25.6317 −1.03106
\(619\) 8.07832 0.324695 0.162348 0.986734i \(-0.448093\pi\)
0.162348 + 0.986734i \(0.448093\pi\)
\(620\) −25.4396 −1.02168
\(621\) 19.6406 0.788149
\(622\) 31.7035 1.27120
\(623\) −25.4084 −1.01797
\(624\) −6.42013 −0.257011
\(625\) −11.4849 −0.459394
\(626\) 3.81305 0.152400
\(627\) 3.33374 0.133137
\(628\) 7.61667 0.303938
\(629\) −28.3639 −1.13094
\(630\) −45.5611 −1.81520
\(631\) 8.63352 0.343695 0.171848 0.985124i \(-0.445026\pi\)
0.171848 + 0.985124i \(0.445026\pi\)
\(632\) 10.8656 0.432212
\(633\) −29.3154 −1.16518
\(634\) −2.62533 −0.104265
\(635\) 39.9823 1.58665
\(636\) 35.4077 1.40401
\(637\) −3.30950 −0.131127
\(638\) 0.309343 0.0122470
\(639\) −12.1028 −0.478781
\(640\) −3.45627 −0.136621
\(641\) −15.9103 −0.628421 −0.314210 0.949353i \(-0.601740\pi\)
−0.314210 + 0.949353i \(0.601740\pi\)
\(642\) −24.6192 −0.971641
\(643\) −7.85935 −0.309942 −0.154971 0.987919i \(-0.549528\pi\)
−0.154971 + 0.987919i \(0.549528\pi\)
\(644\) −5.95888 −0.234813
\(645\) 29.6313 1.16673
\(646\) 10.0776 0.396500
\(647\) −25.9792 −1.02135 −0.510675 0.859774i \(-0.670604\pi\)
−0.510675 + 0.859774i \(0.670604\pi\)
\(648\) 5.79166 0.227518
\(649\) 5.38500 0.211380
\(650\) 15.1812 0.595458
\(651\) −50.6386 −1.98468
\(652\) −3.99369 −0.156405
\(653\) −12.2098 −0.477807 −0.238903 0.971043i \(-0.576788\pi\)
−0.238903 + 0.971043i \(0.576788\pi\)
\(654\) −44.7074 −1.74820
\(655\) 23.2380 0.907985
\(656\) 8.72477 0.340645
\(657\) 36.2748 1.41522
\(658\) −14.8366 −0.578391
\(659\) −21.1041 −0.822099 −0.411050 0.911613i \(-0.634838\pi\)
−0.411050 + 0.911613i \(0.634838\pi\)
\(660\) −6.66801 −0.259552
\(661\) −46.6871 −1.81592 −0.907959 0.419059i \(-0.862360\pi\)
−0.907959 + 0.419059i \(0.862360\pi\)
\(662\) 23.9944 0.932568
\(663\) −37.4421 −1.45413
\(664\) −2.43535 −0.0945099
\(665\) −13.9885 −0.542452
\(666\) −27.3726 −1.06067
\(667\) 1.19827 0.0463972
\(668\) −20.5551 −0.795299
\(669\) −37.4889 −1.44940
\(670\) −36.8473 −1.42354
\(671\) 9.62551 0.371589
\(672\) −6.87986 −0.265396
\(673\) −44.0678 −1.69869 −0.849345 0.527838i \(-0.823003\pi\)
−0.849345 + 0.527838i \(0.823003\pi\)
\(674\) −15.7215 −0.605570
\(675\) −53.6207 −2.06386
\(676\) −8.22284 −0.316263
\(677\) −27.3116 −1.04967 −0.524836 0.851203i \(-0.675873\pi\)
−0.524836 + 0.851203i \(0.675873\pi\)
\(678\) −42.6288 −1.63715
\(679\) 19.3856 0.743952
\(680\) −20.1569 −0.772981
\(681\) −8.53362 −0.327009
\(682\) −4.83428 −0.185114
\(683\) −10.5043 −0.401937 −0.200968 0.979598i \(-0.564409\pi\)
−0.200968 + 0.979598i \(0.564409\pi\)
\(684\) 9.72544 0.371862
\(685\) 16.0948 0.614951
\(686\) −19.9418 −0.761380
\(687\) −6.13100 −0.233912
\(688\) 2.91867 0.111273
\(689\) −26.3466 −1.00373
\(690\) −25.8292 −0.983300
\(691\) 9.12533 0.347144 0.173572 0.984821i \(-0.444469\pi\)
0.173572 + 0.984821i \(0.444469\pi\)
\(692\) 19.2480 0.731699
\(693\) −8.65798 −0.328889
\(694\) 11.6722 0.443070
\(695\) −18.5892 −0.705130
\(696\) 1.38347 0.0524403
\(697\) 50.8827 1.92732
\(698\) 3.37470 0.127734
\(699\) −14.2296 −0.538211
\(700\) 16.2683 0.614885
\(701\) −34.7665 −1.31311 −0.656556 0.754277i \(-0.727988\pi\)
−0.656556 + 0.754277i \(0.727988\pi\)
\(702\) −16.8731 −0.636834
\(703\) −8.40416 −0.316969
\(704\) −0.656795 −0.0247539
\(705\) −64.3102 −2.42206
\(706\) −9.97235 −0.375314
\(707\) 43.1734 1.62370
\(708\) 24.0832 0.905103
\(709\) 38.6532 1.45165 0.725825 0.687879i \(-0.241458\pi\)
0.725825 + 0.687879i \(0.241458\pi\)
\(710\) 7.43240 0.278933
\(711\) 61.1535 2.29343
\(712\) −10.8482 −0.406552
\(713\) −18.7260 −0.701296
\(714\) −40.1232 −1.50157
\(715\) 4.96161 0.185554
\(716\) 11.9834 0.447840
\(717\) 51.2314 1.91327
\(718\) 4.48256 0.167288
\(719\) −41.5614 −1.54998 −0.774989 0.631975i \(-0.782244\pi\)
−0.774989 + 0.631975i \(0.782244\pi\)
\(720\) −19.4524 −0.724949
\(721\) 20.4380 0.761152
\(722\) −16.0140 −0.595980
\(723\) −70.6787 −2.62857
\(724\) −22.1192 −0.822052
\(725\) −3.27139 −0.121497
\(726\) 31.0440 1.15215
\(727\) 21.2684 0.788801 0.394400 0.918939i \(-0.370952\pi\)
0.394400 + 0.918939i \(0.370952\pi\)
\(728\) 5.11924 0.189732
\(729\) −35.4320 −1.31230
\(730\) −22.2765 −0.824491
\(731\) 17.0216 0.629567
\(732\) 43.0480 1.59110
\(733\) −14.4927 −0.535299 −0.267650 0.963516i \(-0.586247\pi\)
−0.267650 + 0.963516i \(0.586247\pi\)
\(734\) −12.7562 −0.470841
\(735\) −15.3725 −0.567023
\(736\) −2.54416 −0.0937789
\(737\) −7.00210 −0.257926
\(738\) 49.1044 1.80756
\(739\) 8.29924 0.305292 0.152646 0.988281i \(-0.451221\pi\)
0.152646 + 0.988281i \(0.451221\pi\)
\(740\) 16.8096 0.617935
\(741\) −11.0940 −0.407548
\(742\) −28.2332 −1.03647
\(743\) 52.9087 1.94103 0.970516 0.241036i \(-0.0774873\pi\)
0.970516 + 0.241036i \(0.0774873\pi\)
\(744\) −21.6203 −0.792637
\(745\) 61.7121 2.26096
\(746\) 8.66272 0.317165
\(747\) −13.7065 −0.501496
\(748\) −3.83041 −0.140054
\(749\) 19.6307 0.717289
\(750\) 19.7545 0.721331
\(751\) 33.4170 1.21940 0.609702 0.792631i \(-0.291289\pi\)
0.609702 + 0.792631i \(0.291289\pi\)
\(752\) −6.33452 −0.230996
\(753\) −69.3756 −2.52819
\(754\) −1.02943 −0.0374895
\(755\) −51.3964 −1.87051
\(756\) −18.0813 −0.657612
\(757\) −41.8525 −1.52116 −0.760578 0.649247i \(-0.775084\pi\)
−0.760578 + 0.649247i \(0.775084\pi\)
\(758\) −5.69401 −0.206816
\(759\) −4.90832 −0.178161
\(760\) −5.97243 −0.216643
\(761\) 15.3238 0.555488 0.277744 0.960655i \(-0.410413\pi\)
0.277744 + 0.960655i \(0.410413\pi\)
\(762\) 33.9796 1.23095
\(763\) 35.6485 1.29056
\(764\) −13.9667 −0.505299
\(765\) −113.446 −4.10165
\(766\) 32.1072 1.16008
\(767\) −17.9201 −0.647058
\(768\) −2.93737 −0.105993
\(769\) −38.5588 −1.39047 −0.695234 0.718784i \(-0.744699\pi\)
−0.695234 + 0.718784i \(0.744699\pi\)
\(770\) 5.31690 0.191608
\(771\) −51.4203 −1.85186
\(772\) −6.62364 −0.238390
\(773\) −17.6953 −0.636456 −0.318228 0.948014i \(-0.603088\pi\)
−0.318228 + 0.948014i \(0.603088\pi\)
\(774\) 16.4267 0.590446
\(775\) 51.1239 1.83643
\(776\) 8.27674 0.297118
\(777\) 33.4603 1.20038
\(778\) −28.0029 −1.00395
\(779\) 15.0764 0.540168
\(780\) 22.1897 0.794519
\(781\) 1.41238 0.0505389
\(782\) −14.8375 −0.530587
\(783\) 3.63597 0.129939
\(784\) −1.51418 −0.0540779
\(785\) −26.3253 −0.939589
\(786\) 19.7493 0.704433
\(787\) 29.7056 1.05889 0.529446 0.848344i \(-0.322400\pi\)
0.529446 + 0.848344i \(0.322400\pi\)
\(788\) −9.12796 −0.325170
\(789\) 26.1744 0.931833
\(790\) −37.5546 −1.33613
\(791\) 33.9911 1.20858
\(792\) −3.69654 −0.131351
\(793\) −32.0316 −1.13748
\(794\) 11.5059 0.408327
\(795\) −122.379 −4.34033
\(796\) 2.28989 0.0811629
\(797\) 15.3006 0.541976 0.270988 0.962583i \(-0.412650\pi\)
0.270988 + 0.962583i \(0.412650\pi\)
\(798\) −11.8884 −0.420844
\(799\) −36.9427 −1.30694
\(800\) 6.94580 0.245571
\(801\) −61.0552 −2.15728
\(802\) −4.18547 −0.147794
\(803\) −4.23321 −0.149387
\(804\) −31.3154 −1.10441
\(805\) 20.5955 0.725896
\(806\) 16.0874 0.566656
\(807\) −85.1624 −2.99786
\(808\) 18.4330 0.648470
\(809\) 4.58106 0.161061 0.0805307 0.996752i \(-0.474338\pi\)
0.0805307 + 0.996752i \(0.474338\pi\)
\(810\) −20.0175 −0.703344
\(811\) −18.4837 −0.649049 −0.324524 0.945877i \(-0.605204\pi\)
−0.324524 + 0.945877i \(0.605204\pi\)
\(812\) −1.10314 −0.0387127
\(813\) −26.8863 −0.942943
\(814\) 3.19434 0.111961
\(815\) 13.8033 0.483507
\(816\) −17.1307 −0.599694
\(817\) 5.04345 0.176448
\(818\) 34.4497 1.20450
\(819\) 28.8119 1.00677
\(820\) −30.1552 −1.05306
\(821\) −1.57384 −0.0549274 −0.0274637 0.999623i \(-0.508743\pi\)
−0.0274637 + 0.999623i \(0.508743\pi\)
\(822\) 13.6785 0.477091
\(823\) −11.1197 −0.387609 −0.193805 0.981040i \(-0.562083\pi\)
−0.193805 + 0.981040i \(0.562083\pi\)
\(824\) 8.72607 0.303987
\(825\) 13.4002 0.466535
\(826\) −19.2033 −0.668169
\(827\) −2.55863 −0.0889724 −0.0444862 0.999010i \(-0.514165\pi\)
−0.0444862 + 0.999010i \(0.514165\pi\)
\(828\) −14.3189 −0.497617
\(829\) 1.40191 0.0486902 0.0243451 0.999704i \(-0.492250\pi\)
0.0243451 + 0.999704i \(0.492250\pi\)
\(830\) 8.41723 0.292166
\(831\) 58.5385 2.03068
\(832\) 2.18567 0.0757746
\(833\) −8.83067 −0.305964
\(834\) −15.7984 −0.547054
\(835\) 71.0438 2.45857
\(836\) −1.13494 −0.0392527
\(837\) −56.8214 −1.96403
\(838\) −18.3632 −0.634346
\(839\) −35.0322 −1.20944 −0.604722 0.796436i \(-0.706716\pi\)
−0.604722 + 0.796436i \(0.706716\pi\)
\(840\) 23.7787 0.820442
\(841\) −28.7782 −0.992351
\(842\) 2.40129 0.0827539
\(843\) −76.0326 −2.61870
\(844\) 9.98014 0.343531
\(845\) 28.4203 0.977689
\(846\) −35.6516 −1.22573
\(847\) −24.7536 −0.850545
\(848\) −12.0542 −0.413944
\(849\) −94.6839 −3.24954
\(850\) 40.5077 1.38940
\(851\) 12.3736 0.424160
\(852\) 6.31656 0.216402
\(853\) 30.3635 1.03963 0.519814 0.854279i \(-0.326001\pi\)
0.519814 + 0.854279i \(0.326001\pi\)
\(854\) −34.3253 −1.17459
\(855\) −33.6138 −1.14957
\(856\) 8.38135 0.286469
\(857\) −55.5795 −1.89856 −0.949280 0.314433i \(-0.898186\pi\)
−0.949280 + 0.314433i \(0.898186\pi\)
\(858\) 4.21671 0.143956
\(859\) 9.56023 0.326191 0.163095 0.986610i \(-0.447852\pi\)
0.163095 + 0.986610i \(0.447852\pi\)
\(860\) −10.0877 −0.343988
\(861\) −60.0252 −2.04565
\(862\) 23.4929 0.800173
\(863\) −22.8250 −0.776973 −0.388487 0.921454i \(-0.627002\pi\)
−0.388487 + 0.921454i \(0.627002\pi\)
\(864\) −7.71987 −0.262635
\(865\) −66.5263 −2.26196
\(866\) 18.9816 0.645021
\(867\) −49.9704 −1.69708
\(868\) 17.2394 0.585144
\(869\) −7.13650 −0.242089
\(870\) −4.78164 −0.162113
\(871\) 23.3015 0.789541
\(872\) 15.2202 0.515421
\(873\) 46.5828 1.57659
\(874\) −4.39630 −0.148707
\(875\) −15.7517 −0.532504
\(876\) −18.9321 −0.639656
\(877\) 42.3655 1.43058 0.715291 0.698827i \(-0.246294\pi\)
0.715291 + 0.698827i \(0.246294\pi\)
\(878\) −5.98493 −0.201982
\(879\) −12.9156 −0.435633
\(880\) 2.27006 0.0765237
\(881\) 20.9401 0.705490 0.352745 0.935720i \(-0.385248\pi\)
0.352745 + 0.935720i \(0.385248\pi\)
\(882\) −8.52205 −0.286952
\(883\) 24.3357 0.818961 0.409480 0.912319i \(-0.365710\pi\)
0.409480 + 0.912319i \(0.365710\pi\)
\(884\) 12.7468 0.428721
\(885\) −83.2381 −2.79802
\(886\) 19.9090 0.668857
\(887\) −6.73701 −0.226207 −0.113103 0.993583i \(-0.536079\pi\)
−0.113103 + 0.993583i \(0.536079\pi\)
\(888\) 14.2860 0.479406
\(889\) −27.0945 −0.908719
\(890\) 37.4942 1.25681
\(891\) −3.80393 −0.127437
\(892\) 12.7627 0.427328
\(893\) −10.9460 −0.366295
\(894\) 52.4471 1.75409
\(895\) −41.4178 −1.38444
\(896\) 2.34218 0.0782468
\(897\) 16.3338 0.545371
\(898\) 6.38575 0.213095
\(899\) −3.46667 −0.115620
\(900\) 39.0920 1.30307
\(901\) −70.2999 −2.34203
\(902\) −5.73039 −0.190801
\(903\) −20.0800 −0.668222
\(904\) 14.5126 0.482681
\(905\) 76.4498 2.54128
\(906\) −43.6801 −1.45117
\(907\) 27.9050 0.926571 0.463285 0.886209i \(-0.346670\pi\)
0.463285 + 0.886209i \(0.346670\pi\)
\(908\) 2.90519 0.0964121
\(909\) 103.744 3.44096
\(910\) −17.6935 −0.586533
\(911\) 12.9143 0.427870 0.213935 0.976848i \(-0.431372\pi\)
0.213935 + 0.976848i \(0.431372\pi\)
\(912\) −5.07577 −0.168076
\(913\) 1.59953 0.0529366
\(914\) −24.4654 −0.809243
\(915\) −148.785 −4.91870
\(916\) 2.08724 0.0689643
\(917\) −15.7475 −0.520029
\(918\) −45.0221 −1.48595
\(919\) 32.5572 1.07396 0.536981 0.843594i \(-0.319565\pi\)
0.536981 + 0.843594i \(0.319565\pi\)
\(920\) 8.79330 0.289906
\(921\) 41.1435 1.35572
\(922\) −0.238585 −0.00785739
\(923\) −4.70009 −0.154705
\(924\) 4.51866 0.148653
\(925\) −33.7810 −1.11071
\(926\) −1.83537 −0.0603140
\(927\) 49.1116 1.61304
\(928\) −0.470989 −0.0154610
\(929\) −34.7541 −1.14024 −0.570122 0.821560i \(-0.693104\pi\)
−0.570122 + 0.821560i \(0.693104\pi\)
\(930\) 74.7254 2.45034
\(931\) −2.61650 −0.0857524
\(932\) 4.84432 0.158681
\(933\) −93.1251 −3.04878
\(934\) −0.102036 −0.00333871
\(935\) 13.2389 0.432959
\(936\) 12.3013 0.402081
\(937\) −17.1286 −0.559566 −0.279783 0.960063i \(-0.590263\pi\)
−0.279783 + 0.960063i \(0.590263\pi\)
\(938\) 24.9700 0.815301
\(939\) −11.2003 −0.365509
\(940\) 21.8938 0.714097
\(941\) 32.4308 1.05721 0.528607 0.848866i \(-0.322714\pi\)
0.528607 + 0.848866i \(0.322714\pi\)
\(942\) −22.3730 −0.728952
\(943\) −22.1972 −0.722841
\(944\) −8.19890 −0.266851
\(945\) 62.4940 2.03293
\(946\) −1.91697 −0.0623260
\(947\) 60.2748 1.95867 0.979333 0.202253i \(-0.0648265\pi\)
0.979333 + 0.202253i \(0.0648265\pi\)
\(948\) −31.9164 −1.03660
\(949\) 14.0872 0.457290
\(950\) 12.0023 0.389407
\(951\) 7.71156 0.250065
\(952\) 13.6595 0.442708
\(953\) −35.6405 −1.15451 −0.577254 0.816565i \(-0.695876\pi\)
−0.577254 + 0.816565i \(0.695876\pi\)
\(954\) −67.8430 −2.19650
\(955\) 48.2728 1.56207
\(956\) −17.4412 −0.564090
\(957\) −0.908656 −0.0293727
\(958\) −18.6033 −0.601046
\(959\) −10.9068 −0.352200
\(960\) 10.1524 0.327666
\(961\) 23.1756 0.747601
\(962\) −10.6301 −0.342727
\(963\) 47.1716 1.52008
\(964\) 24.0619 0.774981
\(965\) 22.8931 0.736955
\(966\) 17.5035 0.563165
\(967\) 23.1386 0.744086 0.372043 0.928215i \(-0.378657\pi\)
0.372043 + 0.928215i \(0.378657\pi\)
\(968\) −10.5686 −0.339688
\(969\) −29.6018 −0.950946
\(970\) −28.6066 −0.918504
\(971\) 1.44238 0.0462881 0.0231440 0.999732i \(-0.492632\pi\)
0.0231440 + 0.999732i \(0.492632\pi\)
\(972\) 6.14735 0.197176
\(973\) 12.5972 0.403848
\(974\) 3.46285 0.110957
\(975\) −44.5930 −1.42812
\(976\) −14.6553 −0.469104
\(977\) −24.0426 −0.769190 −0.384595 0.923085i \(-0.625659\pi\)
−0.384595 + 0.923085i \(0.625659\pi\)
\(978\) 11.7309 0.375114
\(979\) 7.12502 0.227717
\(980\) 5.23342 0.167175
\(981\) 85.6616 2.73496
\(982\) −15.0131 −0.479088
\(983\) −10.3359 −0.329664 −0.164832 0.986322i \(-0.552708\pi\)
−0.164832 + 0.986322i \(0.552708\pi\)
\(984\) −25.6279 −0.816988
\(985\) 31.5487 1.00523
\(986\) −2.74679 −0.0874758
\(987\) 43.5806 1.38719
\(988\) 3.77684 0.120157
\(989\) −7.42556 −0.236119
\(990\) 12.7763 0.406056
\(991\) 45.1795 1.43517 0.717587 0.696469i \(-0.245247\pi\)
0.717587 + 0.696469i \(0.245247\pi\)
\(992\) 7.36041 0.233693
\(993\) −70.4804 −2.23663
\(994\) −5.03665 −0.159753
\(995\) −7.91447 −0.250905
\(996\) 7.15353 0.226668
\(997\) 25.2300 0.799041 0.399521 0.916724i \(-0.369177\pi\)
0.399521 + 0.916724i \(0.369177\pi\)
\(998\) −3.92722 −0.124314
\(999\) 37.5457 1.18789
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 6038.2.a.e.1.4 70
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6038.2.a.e.1.4 70 1.1 even 1 trivial