Properties

Label 6033.2.a.c.1.7
Level $6033$
Weight $2$
Character 6033.1
Self dual yes
Analytic conductor $48.174$
Analytic rank $0$
Dimension $82$
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] = [6033,2,Mod(1,6033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6033, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6033 = 3 \cdot 2011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6033.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: \(48.1737475394\)
Analytic rank: \(0\)
Dimension: \(82\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.42144 q^{2} -1.00000 q^{3} +3.86336 q^{4} +1.61348 q^{5} +2.42144 q^{6} -0.957963 q^{7} -4.51200 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.42144 q^{2} -1.00000 q^{3} +3.86336 q^{4} +1.61348 q^{5} +2.42144 q^{6} -0.957963 q^{7} -4.51200 q^{8} +1.00000 q^{9} -3.90694 q^{10} +4.96714 q^{11} -3.86336 q^{12} +6.60137 q^{13} +2.31965 q^{14} -1.61348 q^{15} +3.19882 q^{16} -2.48372 q^{17} -2.42144 q^{18} -1.70780 q^{19} +6.23345 q^{20} +0.957963 q^{21} -12.0276 q^{22} +0.0237908 q^{23} +4.51200 q^{24} -2.39668 q^{25} -15.9848 q^{26} -1.00000 q^{27} -3.70096 q^{28} -5.14557 q^{29} +3.90694 q^{30} -2.01254 q^{31} +1.27827 q^{32} -4.96714 q^{33} +6.01417 q^{34} -1.54566 q^{35} +3.86336 q^{36} +0.922557 q^{37} +4.13534 q^{38} -6.60137 q^{39} -7.28003 q^{40} +9.18372 q^{41} -2.31965 q^{42} +7.22362 q^{43} +19.1898 q^{44} +1.61348 q^{45} -0.0576079 q^{46} +1.75920 q^{47} -3.19882 q^{48} -6.08231 q^{49} +5.80341 q^{50} +2.48372 q^{51} +25.5034 q^{52} +3.75167 q^{53} +2.42144 q^{54} +8.01438 q^{55} +4.32233 q^{56} +1.70780 q^{57} +12.4597 q^{58} +4.70218 q^{59} -6.23345 q^{60} -10.3653 q^{61} +4.87324 q^{62} -0.957963 q^{63} -9.49289 q^{64} +10.6512 q^{65} +12.0276 q^{66} +13.8015 q^{67} -9.59549 q^{68} -0.0237908 q^{69} +3.74271 q^{70} +5.39446 q^{71} -4.51200 q^{72} +4.67594 q^{73} -2.23391 q^{74} +2.39668 q^{75} -6.59785 q^{76} -4.75834 q^{77} +15.9848 q^{78} +1.17576 q^{79} +5.16123 q^{80} +1.00000 q^{81} -22.2378 q^{82} -17.1010 q^{83} +3.70096 q^{84} -4.00743 q^{85} -17.4915 q^{86} +5.14557 q^{87} -22.4117 q^{88} +4.29441 q^{89} -3.90694 q^{90} -6.32387 q^{91} +0.0919123 q^{92} +2.01254 q^{93} -4.25979 q^{94} -2.75551 q^{95} -1.27827 q^{96} -4.58146 q^{97} +14.7279 q^{98} +4.96714 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42144 −1.71221 −0.856107 0.516798i \(-0.827124\pi\)
−0.856107 + 0.516798i \(0.827124\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.86336 1.93168
\(5\) 1.61348 0.721571 0.360785 0.932649i \(-0.382509\pi\)
0.360785 + 0.932649i \(0.382509\pi\)
\(6\) 2.42144 0.988548
\(7\) −0.957963 −0.362076 −0.181038 0.983476i \(-0.557946\pi\)
−0.181038 + 0.983476i \(0.557946\pi\)
\(8\) −4.51200 −1.59523
\(9\) 1.00000 0.333333
\(10\) −3.90694 −1.23548
\(11\) 4.96714 1.49765 0.748824 0.662769i \(-0.230619\pi\)
0.748824 + 0.662769i \(0.230619\pi\)
\(12\) −3.86336 −1.11526
\(13\) 6.60137 1.83089 0.915445 0.402443i \(-0.131839\pi\)
0.915445 + 0.402443i \(0.131839\pi\)
\(14\) 2.31965 0.619952
\(15\) −1.61348 −0.416599
\(16\) 3.19882 0.799704
\(17\) −2.48372 −0.602390 −0.301195 0.953563i \(-0.597385\pi\)
−0.301195 + 0.953563i \(0.597385\pi\)
\(18\) −2.42144 −0.570738
\(19\) −1.70780 −0.391797 −0.195898 0.980624i \(-0.562762\pi\)
−0.195898 + 0.980624i \(0.562762\pi\)
\(20\) 6.23345 1.39384
\(21\) 0.957963 0.209045
\(22\) −12.0276 −2.56430
\(23\) 0.0237908 0.00496072 0.00248036 0.999997i \(-0.499210\pi\)
0.00248036 + 0.999997i \(0.499210\pi\)
\(24\) 4.51200 0.921009
\(25\) −2.39668 −0.479336
\(26\) −15.9848 −3.13488
\(27\) −1.00000 −0.192450
\(28\) −3.70096 −0.699415
\(29\) −5.14557 −0.955508 −0.477754 0.878494i \(-0.658549\pi\)
−0.477754 + 0.878494i \(0.658549\pi\)
\(30\) 3.90694 0.713307
\(31\) −2.01254 −0.361463 −0.180731 0.983532i \(-0.557846\pi\)
−0.180731 + 0.983532i \(0.557846\pi\)
\(32\) 1.27827 0.225969
\(33\) −4.96714 −0.864668
\(34\) 6.01417 1.03142
\(35\) −1.54566 −0.261263
\(36\) 3.86336 0.643893
\(37\) 0.922557 0.151667 0.0758337 0.997120i \(-0.475838\pi\)
0.0758337 + 0.997120i \(0.475838\pi\)
\(38\) 4.13534 0.670840
\(39\) −6.60137 −1.05706
\(40\) −7.28003 −1.15107
\(41\) 9.18372 1.43426 0.717128 0.696941i \(-0.245456\pi\)
0.717128 + 0.696941i \(0.245456\pi\)
\(42\) −2.31965 −0.357929
\(43\) 7.22362 1.10159 0.550796 0.834640i \(-0.314324\pi\)
0.550796 + 0.834640i \(0.314324\pi\)
\(44\) 19.1898 2.89298
\(45\) 1.61348 0.240524
\(46\) −0.0576079 −0.00849382
\(47\) 1.75920 0.256606 0.128303 0.991735i \(-0.459047\pi\)
0.128303 + 0.991735i \(0.459047\pi\)
\(48\) −3.19882 −0.461710
\(49\) −6.08231 −0.868901
\(50\) 5.80341 0.820726
\(51\) 2.48372 0.347790
\(52\) 25.5034 3.53669
\(53\) 3.75167 0.515331 0.257666 0.966234i \(-0.417047\pi\)
0.257666 + 0.966234i \(0.417047\pi\)
\(54\) 2.42144 0.329516
\(55\) 8.01438 1.08066
\(56\) 4.32233 0.577596
\(57\) 1.70780 0.226204
\(58\) 12.4597 1.63603
\(59\) 4.70218 0.612172 0.306086 0.952004i \(-0.400980\pi\)
0.306086 + 0.952004i \(0.400980\pi\)
\(60\) −6.23345 −0.804735
\(61\) −10.3653 −1.32714 −0.663570 0.748114i \(-0.730960\pi\)
−0.663570 + 0.748114i \(0.730960\pi\)
\(62\) 4.87324 0.618902
\(63\) −0.957963 −0.120692
\(64\) −9.49289 −1.18661
\(65\) 10.6512 1.32112
\(66\) 12.0276 1.48050
\(67\) 13.8015 1.68612 0.843058 0.537822i \(-0.180753\pi\)
0.843058 + 0.537822i \(0.180753\pi\)
\(68\) −9.59549 −1.16362
\(69\) −0.0237908 −0.00286407
\(70\) 3.74271 0.447339
\(71\) 5.39446 0.640205 0.320102 0.947383i \(-0.396283\pi\)
0.320102 + 0.947383i \(0.396283\pi\)
\(72\) −4.51200 −0.531745
\(73\) 4.67594 0.547277 0.273639 0.961833i \(-0.411773\pi\)
0.273639 + 0.961833i \(0.411773\pi\)
\(74\) −2.23391 −0.259687
\(75\) 2.39668 0.276745
\(76\) −6.59785 −0.756825
\(77\) −4.75834 −0.542263
\(78\) 15.9848 1.80992
\(79\) 1.17576 0.132283 0.0661417 0.997810i \(-0.478931\pi\)
0.0661417 + 0.997810i \(0.478931\pi\)
\(80\) 5.16123 0.577043
\(81\) 1.00000 0.111111
\(82\) −22.2378 −2.45575
\(83\) −17.1010 −1.87708 −0.938538 0.345175i \(-0.887820\pi\)
−0.938538 + 0.345175i \(0.887820\pi\)
\(84\) 3.70096 0.403807
\(85\) −4.00743 −0.434667
\(86\) −17.4915 −1.88616
\(87\) 5.14557 0.551663
\(88\) −22.4117 −2.38910
\(89\) 4.29441 0.455207 0.227603 0.973754i \(-0.426911\pi\)
0.227603 + 0.973754i \(0.426911\pi\)
\(90\) −3.90694 −0.411828
\(91\) −6.32387 −0.662922
\(92\) 0.0919123 0.00958252
\(93\) 2.01254 0.208691
\(94\) −4.25979 −0.439364
\(95\) −2.75551 −0.282709
\(96\) −1.27827 −0.130463
\(97\) −4.58146 −0.465177 −0.232588 0.972575i \(-0.574719\pi\)
−0.232588 + 0.972575i \(0.574719\pi\)
\(98\) 14.7279 1.48774
\(99\) 4.96714 0.499216
\(100\) −9.25923 −0.925923
\(101\) 5.82248 0.579359 0.289679 0.957124i \(-0.406451\pi\)
0.289679 + 0.957124i \(0.406451\pi\)
\(102\) −6.01417 −0.595491
\(103\) 2.68653 0.264711 0.132356 0.991202i \(-0.457746\pi\)
0.132356 + 0.991202i \(0.457746\pi\)
\(104\) −29.7854 −2.92070
\(105\) 1.54566 0.150841
\(106\) −9.08443 −0.882358
\(107\) 10.6391 1.02852 0.514259 0.857635i \(-0.328067\pi\)
0.514259 + 0.857635i \(0.328067\pi\)
\(108\) −3.86336 −0.371752
\(109\) 1.51029 0.144660 0.0723299 0.997381i \(-0.476957\pi\)
0.0723299 + 0.997381i \(0.476957\pi\)
\(110\) −19.4063 −1.85032
\(111\) −0.922557 −0.0875652
\(112\) −3.06435 −0.289554
\(113\) 12.7433 1.19879 0.599395 0.800454i \(-0.295408\pi\)
0.599395 + 0.800454i \(0.295408\pi\)
\(114\) −4.13534 −0.387310
\(115\) 0.0383860 0.00357951
\(116\) −19.8792 −1.84573
\(117\) 6.60137 0.610297
\(118\) −11.3860 −1.04817
\(119\) 2.37931 0.218111
\(120\) 7.28003 0.664573
\(121\) 13.6725 1.24295
\(122\) 25.0989 2.27235
\(123\) −9.18372 −0.828068
\(124\) −7.77516 −0.698230
\(125\) −11.9344 −1.06745
\(126\) 2.31965 0.206651
\(127\) −2.81709 −0.249976 −0.124988 0.992158i \(-0.539889\pi\)
−0.124988 + 0.992158i \(0.539889\pi\)
\(128\) 20.4299 1.80576
\(129\) −7.22362 −0.636004
\(130\) −25.7912 −2.26203
\(131\) 21.5539 1.88317 0.941587 0.336770i \(-0.109335\pi\)
0.941587 + 0.336770i \(0.109335\pi\)
\(132\) −19.1898 −1.67026
\(133\) 1.63601 0.141860
\(134\) −33.4194 −2.88699
\(135\) −1.61348 −0.138866
\(136\) 11.2065 0.960953
\(137\) 8.68182 0.741738 0.370869 0.928685i \(-0.379060\pi\)
0.370869 + 0.928685i \(0.379060\pi\)
\(138\) 0.0576079 0.00490391
\(139\) −18.7505 −1.59039 −0.795197 0.606351i \(-0.792633\pi\)
−0.795197 + 0.606351i \(0.792633\pi\)
\(140\) −5.97142 −0.504677
\(141\) −1.75920 −0.148151
\(142\) −13.0623 −1.09617
\(143\) 32.7899 2.74203
\(144\) 3.19882 0.266568
\(145\) −8.30227 −0.689466
\(146\) −11.3225 −0.937056
\(147\) 6.08231 0.501660
\(148\) 3.56417 0.292973
\(149\) 18.2742 1.49708 0.748539 0.663091i \(-0.230756\pi\)
0.748539 + 0.663091i \(0.230756\pi\)
\(150\) −5.80341 −0.473846
\(151\) −2.19947 −0.178990 −0.0894952 0.995987i \(-0.528525\pi\)
−0.0894952 + 0.995987i \(0.528525\pi\)
\(152\) 7.70561 0.625008
\(153\) −2.48372 −0.200797
\(154\) 11.5220 0.928470
\(155\) −3.24719 −0.260821
\(156\) −25.5034 −2.04191
\(157\) 9.57699 0.764327 0.382164 0.924095i \(-0.375179\pi\)
0.382164 + 0.924095i \(0.375179\pi\)
\(158\) −2.84703 −0.226497
\(159\) −3.75167 −0.297527
\(160\) 2.06247 0.163052
\(161\) −0.0227907 −0.00179616
\(162\) −2.42144 −0.190246
\(163\) −3.83487 −0.300370 −0.150185 0.988658i \(-0.547987\pi\)
−0.150185 + 0.988658i \(0.547987\pi\)
\(164\) 35.4800 2.77052
\(165\) −8.01438 −0.623919
\(166\) 41.4090 3.21396
\(167\) −4.05802 −0.314019 −0.157009 0.987597i \(-0.550185\pi\)
−0.157009 + 0.987597i \(0.550185\pi\)
\(168\) −4.32233 −0.333475
\(169\) 30.5781 2.35216
\(170\) 9.70374 0.744243
\(171\) −1.70780 −0.130599
\(172\) 27.9074 2.12792
\(173\) −3.16297 −0.240476 −0.120238 0.992745i \(-0.538366\pi\)
−0.120238 + 0.992745i \(0.538366\pi\)
\(174\) −12.4597 −0.944565
\(175\) 2.29593 0.173556
\(176\) 15.8890 1.19768
\(177\) −4.70218 −0.353438
\(178\) −10.3986 −0.779411
\(179\) −10.4284 −0.779458 −0.389729 0.920930i \(-0.627431\pi\)
−0.389729 + 0.920930i \(0.627431\pi\)
\(180\) 6.23345 0.464614
\(181\) −19.5701 −1.45463 −0.727317 0.686302i \(-0.759233\pi\)
−0.727317 + 0.686302i \(0.759233\pi\)
\(182\) 15.3129 1.13506
\(183\) 10.3653 0.766225
\(184\) −0.107344 −0.00791351
\(185\) 1.48853 0.109439
\(186\) −4.87324 −0.357323
\(187\) −12.3370 −0.902168
\(188\) 6.79641 0.495679
\(189\) 0.957963 0.0696816
\(190\) 6.67228 0.484058
\(191\) 15.8707 1.14836 0.574181 0.818729i \(-0.305321\pi\)
0.574181 + 0.818729i \(0.305321\pi\)
\(192\) 9.49289 0.685090
\(193\) −24.2289 −1.74403 −0.872017 0.489476i \(-0.837188\pi\)
−0.872017 + 0.489476i \(0.837188\pi\)
\(194\) 11.0937 0.796482
\(195\) −10.6512 −0.762747
\(196\) −23.4981 −1.67844
\(197\) 6.89095 0.490960 0.245480 0.969402i \(-0.421054\pi\)
0.245480 + 0.969402i \(0.421054\pi\)
\(198\) −12.0276 −0.854765
\(199\) −20.4711 −1.45116 −0.725580 0.688138i \(-0.758428\pi\)
−0.725580 + 0.688138i \(0.758428\pi\)
\(200\) 10.8138 0.764653
\(201\) −13.8015 −0.973480
\(202\) −14.0988 −0.991986
\(203\) 4.92927 0.345967
\(204\) 9.59549 0.671819
\(205\) 14.8178 1.03492
\(206\) −6.50526 −0.453243
\(207\) 0.0237908 0.00165357
\(208\) 21.1166 1.46417
\(209\) −8.48289 −0.586774
\(210\) −3.74271 −0.258271
\(211\) 9.26658 0.637937 0.318969 0.947765i \(-0.396664\pi\)
0.318969 + 0.947765i \(0.396664\pi\)
\(212\) 14.4940 0.995455
\(213\) −5.39446 −0.369622
\(214\) −25.7618 −1.76104
\(215\) 11.6552 0.794876
\(216\) 4.51200 0.307003
\(217\) 1.92794 0.130877
\(218\) −3.65708 −0.247689
\(219\) −4.67594 −0.315971
\(220\) 30.9624 2.08749
\(221\) −16.3959 −1.10291
\(222\) 2.23391 0.149930
\(223\) 26.5273 1.77640 0.888199 0.459458i \(-0.151956\pi\)
0.888199 + 0.459458i \(0.151956\pi\)
\(224\) −1.22454 −0.0818178
\(225\) −2.39668 −0.159779
\(226\) −30.8571 −2.05258
\(227\) 6.40963 0.425422 0.212711 0.977115i \(-0.431771\pi\)
0.212711 + 0.977115i \(0.431771\pi\)
\(228\) 6.59785 0.436953
\(229\) 20.9395 1.38372 0.691859 0.722032i \(-0.256792\pi\)
0.691859 + 0.722032i \(0.256792\pi\)
\(230\) −0.0929492 −0.00612889
\(231\) 4.75834 0.313075
\(232\) 23.2168 1.52426
\(233\) −13.5153 −0.885416 −0.442708 0.896666i \(-0.645982\pi\)
−0.442708 + 0.896666i \(0.645982\pi\)
\(234\) −15.9848 −1.04496
\(235\) 2.83843 0.185159
\(236\) 18.1662 1.18252
\(237\) −1.17576 −0.0763738
\(238\) −5.76135 −0.373453
\(239\) −7.51812 −0.486306 −0.243153 0.969988i \(-0.578182\pi\)
−0.243153 + 0.969988i \(0.578182\pi\)
\(240\) −5.16123 −0.333156
\(241\) −13.4155 −0.864169 −0.432084 0.901833i \(-0.642222\pi\)
−0.432084 + 0.901833i \(0.642222\pi\)
\(242\) −33.1070 −2.12820
\(243\) −1.00000 −0.0641500
\(244\) −40.0449 −2.56361
\(245\) −9.81368 −0.626973
\(246\) 22.2378 1.41783
\(247\) −11.2738 −0.717337
\(248\) 9.08059 0.576618
\(249\) 17.1010 1.08373
\(250\) 28.8984 1.82770
\(251\) −24.0858 −1.52028 −0.760141 0.649759i \(-0.774870\pi\)
−0.760141 + 0.649759i \(0.774870\pi\)
\(252\) −3.70096 −0.233138
\(253\) 0.118172 0.00742941
\(254\) 6.82140 0.428012
\(255\) 4.00743 0.250955
\(256\) −30.4839 −1.90525
\(257\) −15.0582 −0.939307 −0.469654 0.882851i \(-0.655621\pi\)
−0.469654 + 0.882851i \(0.655621\pi\)
\(258\) 17.4915 1.08898
\(259\) −0.883776 −0.0549151
\(260\) 41.1493 2.55197
\(261\) −5.14557 −0.318503
\(262\) −52.1914 −3.22440
\(263\) 27.2371 1.67951 0.839754 0.542967i \(-0.182699\pi\)
0.839754 + 0.542967i \(0.182699\pi\)
\(264\) 22.4117 1.37935
\(265\) 6.05325 0.371848
\(266\) −3.96150 −0.242895
\(267\) −4.29441 −0.262814
\(268\) 53.3200 3.25704
\(269\) −9.03426 −0.550829 −0.275414 0.961326i \(-0.588815\pi\)
−0.275414 + 0.961326i \(0.588815\pi\)
\(270\) 3.90694 0.237769
\(271\) −10.6330 −0.645908 −0.322954 0.946415i \(-0.604676\pi\)
−0.322954 + 0.946415i \(0.604676\pi\)
\(272\) −7.94496 −0.481734
\(273\) 6.32387 0.382738
\(274\) −21.0225 −1.27001
\(275\) −11.9046 −0.717877
\(276\) −0.0919123 −0.00553247
\(277\) −16.4006 −0.985417 −0.492708 0.870195i \(-0.663993\pi\)
−0.492708 + 0.870195i \(0.663993\pi\)
\(278\) 45.4031 2.72310
\(279\) −2.01254 −0.120488
\(280\) 6.97400 0.416776
\(281\) 9.43465 0.562824 0.281412 0.959587i \(-0.409197\pi\)
0.281412 + 0.959587i \(0.409197\pi\)
\(282\) 4.25979 0.253667
\(283\) 28.4391 1.69053 0.845266 0.534346i \(-0.179442\pi\)
0.845266 + 0.534346i \(0.179442\pi\)
\(284\) 20.8407 1.23667
\(285\) 2.75551 0.163222
\(286\) −79.3987 −4.69494
\(287\) −8.79767 −0.519310
\(288\) 1.27827 0.0753228
\(289\) −10.8311 −0.637126
\(290\) 20.1034 1.18051
\(291\) 4.58146 0.268570
\(292\) 18.0648 1.05716
\(293\) 19.9400 1.16491 0.582454 0.812863i \(-0.302092\pi\)
0.582454 + 0.812863i \(0.302092\pi\)
\(294\) −14.7279 −0.858950
\(295\) 7.58688 0.441725
\(296\) −4.16258 −0.241945
\(297\) −4.96714 −0.288223
\(298\) −44.2497 −2.56332
\(299\) 0.157052 0.00908253
\(300\) 9.25923 0.534582
\(301\) −6.91996 −0.398860
\(302\) 5.32588 0.306470
\(303\) −5.82248 −0.334493
\(304\) −5.46295 −0.313322
\(305\) −16.7242 −0.957626
\(306\) 6.01417 0.343807
\(307\) −5.84888 −0.333813 −0.166907 0.985973i \(-0.553378\pi\)
−0.166907 + 0.985973i \(0.553378\pi\)
\(308\) −18.3832 −1.04748
\(309\) −2.68653 −0.152831
\(310\) 7.86288 0.446581
\(311\) −30.6160 −1.73607 −0.868037 0.496499i \(-0.834618\pi\)
−0.868037 + 0.496499i \(0.834618\pi\)
\(312\) 29.7854 1.68627
\(313\) 7.93216 0.448352 0.224176 0.974549i \(-0.428031\pi\)
0.224176 + 0.974549i \(0.428031\pi\)
\(314\) −23.1901 −1.30869
\(315\) −1.54566 −0.0870878
\(316\) 4.54238 0.255529
\(317\) 10.7324 0.602794 0.301397 0.953499i \(-0.402547\pi\)
0.301397 + 0.953499i \(0.402547\pi\)
\(318\) 9.08443 0.509430
\(319\) −25.5587 −1.43101
\(320\) −15.3166 −0.856224
\(321\) −10.6391 −0.593815
\(322\) 0.0551862 0.00307541
\(323\) 4.24170 0.236014
\(324\) 3.86336 0.214631
\(325\) −15.8214 −0.877612
\(326\) 9.28589 0.514298
\(327\) −1.51029 −0.0835194
\(328\) −41.4370 −2.28797
\(329\) −1.68525 −0.0929107
\(330\) 19.4063 1.06828
\(331\) 32.9905 1.81332 0.906661 0.421860i \(-0.138623\pi\)
0.906661 + 0.421860i \(0.138623\pi\)
\(332\) −66.0672 −3.62591
\(333\) 0.922557 0.0505558
\(334\) 9.82624 0.537668
\(335\) 22.2684 1.21665
\(336\) 3.06435 0.167174
\(337\) −31.1729 −1.69810 −0.849048 0.528316i \(-0.822824\pi\)
−0.849048 + 0.528316i \(0.822824\pi\)
\(338\) −74.0429 −4.02740
\(339\) −12.7433 −0.692121
\(340\) −15.4821 −0.839637
\(341\) −9.99656 −0.541344
\(342\) 4.13534 0.223613
\(343\) 12.5324 0.676684
\(344\) −32.5930 −1.75730
\(345\) −0.0383860 −0.00206663
\(346\) 7.65893 0.411746
\(347\) 26.2290 1.40805 0.704023 0.710177i \(-0.251385\pi\)
0.704023 + 0.710177i \(0.251385\pi\)
\(348\) 19.8792 1.06564
\(349\) −12.8802 −0.689461 −0.344731 0.938702i \(-0.612030\pi\)
−0.344731 + 0.938702i \(0.612030\pi\)
\(350\) −5.55945 −0.297165
\(351\) −6.60137 −0.352355
\(352\) 6.34935 0.338421
\(353\) 10.3508 0.550916 0.275458 0.961313i \(-0.411170\pi\)
0.275458 + 0.961313i \(0.411170\pi\)
\(354\) 11.3860 0.605161
\(355\) 8.70386 0.461953
\(356\) 16.5908 0.879313
\(357\) −2.37931 −0.125926
\(358\) 25.2518 1.33460
\(359\) 14.9176 0.787323 0.393661 0.919256i \(-0.371208\pi\)
0.393661 + 0.919256i \(0.371208\pi\)
\(360\) −7.28003 −0.383691
\(361\) −16.0834 −0.846495
\(362\) 47.3878 2.49065
\(363\) −13.6725 −0.717618
\(364\) −24.4314 −1.28055
\(365\) 7.54454 0.394899
\(366\) −25.0989 −1.31194
\(367\) −29.6456 −1.54749 −0.773745 0.633498i \(-0.781619\pi\)
−0.773745 + 0.633498i \(0.781619\pi\)
\(368\) 0.0761023 0.00396711
\(369\) 9.18372 0.478085
\(370\) −3.60438 −0.187383
\(371\) −3.59396 −0.186589
\(372\) 7.77516 0.403123
\(373\) 31.4667 1.62928 0.814642 0.579964i \(-0.196933\pi\)
0.814642 + 0.579964i \(0.196933\pi\)
\(374\) 29.8732 1.54471
\(375\) 11.9344 0.616290
\(376\) −7.93751 −0.409346
\(377\) −33.9678 −1.74943
\(378\) −2.31965 −0.119310
\(379\) −15.2183 −0.781713 −0.390857 0.920452i \(-0.627821\pi\)
−0.390857 + 0.920452i \(0.627821\pi\)
\(380\) −10.6455 −0.546103
\(381\) 2.81709 0.144324
\(382\) −38.4298 −1.96624
\(383\) 31.9739 1.63379 0.816896 0.576785i \(-0.195693\pi\)
0.816896 + 0.576785i \(0.195693\pi\)
\(384\) −20.4299 −1.04256
\(385\) −7.67748 −0.391281
\(386\) 58.6687 2.98616
\(387\) 7.22362 0.367197
\(388\) −17.6998 −0.898572
\(389\) 4.30499 0.218271 0.109136 0.994027i \(-0.465192\pi\)
0.109136 + 0.994027i \(0.465192\pi\)
\(390\) 25.7912 1.30599
\(391\) −0.0590895 −0.00298829
\(392\) 27.4434 1.38610
\(393\) −21.5539 −1.08725
\(394\) −16.6860 −0.840628
\(395\) 1.89707 0.0954518
\(396\) 19.1898 0.964325
\(397\) −2.29107 −0.114986 −0.0574928 0.998346i \(-0.518311\pi\)
−0.0574928 + 0.998346i \(0.518311\pi\)
\(398\) 49.5695 2.48470
\(399\) −1.63601 −0.0819030
\(400\) −7.66654 −0.383327
\(401\) −28.3611 −1.41629 −0.708143 0.706069i \(-0.750467\pi\)
−0.708143 + 0.706069i \(0.750467\pi\)
\(402\) 33.4194 1.66681
\(403\) −13.2855 −0.661799
\(404\) 22.4943 1.11913
\(405\) 1.61348 0.0801745
\(406\) −11.9359 −0.592369
\(407\) 4.58247 0.227144
\(408\) −11.2065 −0.554806
\(409\) 0.444555 0.0219818 0.0109909 0.999940i \(-0.496501\pi\)
0.0109909 + 0.999940i \(0.496501\pi\)
\(410\) −35.8803 −1.77200
\(411\) −8.68182 −0.428243
\(412\) 10.3790 0.511337
\(413\) −4.50452 −0.221653
\(414\) −0.0576079 −0.00283127
\(415\) −27.5921 −1.35444
\(416\) 8.43834 0.413724
\(417\) 18.7505 0.918215
\(418\) 20.5408 1.00468
\(419\) −23.3583 −1.14113 −0.570565 0.821253i \(-0.693276\pi\)
−0.570565 + 0.821253i \(0.693276\pi\)
\(420\) 5.97142 0.291375
\(421\) 5.22449 0.254626 0.127313 0.991863i \(-0.459365\pi\)
0.127313 + 0.991863i \(0.459365\pi\)
\(422\) −22.4384 −1.09229
\(423\) 1.75920 0.0855352
\(424\) −16.9275 −0.822074
\(425\) 5.95268 0.288747
\(426\) 13.0623 0.632873
\(427\) 9.92958 0.480526
\(428\) 41.1025 1.98677
\(429\) −32.7899 −1.58311
\(430\) −28.2223 −1.36100
\(431\) 31.6031 1.52227 0.761135 0.648593i \(-0.224642\pi\)
0.761135 + 0.648593i \(0.224642\pi\)
\(432\) −3.19882 −0.153903
\(433\) −20.1063 −0.966248 −0.483124 0.875552i \(-0.660498\pi\)
−0.483124 + 0.875552i \(0.660498\pi\)
\(434\) −4.66839 −0.224090
\(435\) 8.30227 0.398064
\(436\) 5.83480 0.279436
\(437\) −0.0406299 −0.00194359
\(438\) 11.3225 0.541010
\(439\) −19.4198 −0.926858 −0.463429 0.886134i \(-0.653381\pi\)
−0.463429 + 0.886134i \(0.653381\pi\)
\(440\) −36.1609 −1.72390
\(441\) −6.08231 −0.289634
\(442\) 39.7017 1.88842
\(443\) 25.4266 1.20806 0.604028 0.796963i \(-0.293561\pi\)
0.604028 + 0.796963i \(0.293561\pi\)
\(444\) −3.56417 −0.169148
\(445\) 6.92895 0.328464
\(446\) −64.2342 −3.04158
\(447\) −18.2742 −0.864338
\(448\) 9.09384 0.429644
\(449\) −18.2866 −0.862997 −0.431499 0.902114i \(-0.642015\pi\)
−0.431499 + 0.902114i \(0.642015\pi\)
\(450\) 5.80341 0.273575
\(451\) 45.6168 2.14801
\(452\) 49.2320 2.31568
\(453\) 2.19947 0.103340
\(454\) −15.5205 −0.728414
\(455\) −10.2034 −0.478345
\(456\) −7.70561 −0.360848
\(457\) −22.6083 −1.05757 −0.528785 0.848756i \(-0.677352\pi\)
−0.528785 + 0.848756i \(0.677352\pi\)
\(458\) −50.7036 −2.36922
\(459\) 2.48372 0.115930
\(460\) 0.148299 0.00691446
\(461\) −9.11367 −0.424466 −0.212233 0.977219i \(-0.568074\pi\)
−0.212233 + 0.977219i \(0.568074\pi\)
\(462\) −11.5220 −0.536052
\(463\) 13.9641 0.648966 0.324483 0.945891i \(-0.394810\pi\)
0.324483 + 0.945891i \(0.394810\pi\)
\(464\) −16.4597 −0.764124
\(465\) 3.24719 0.150585
\(466\) 32.7264 1.51602
\(467\) 25.2799 1.16981 0.584907 0.811100i \(-0.301131\pi\)
0.584907 + 0.811100i \(0.301131\pi\)
\(468\) 25.5034 1.17890
\(469\) −13.2213 −0.610503
\(470\) −6.87309 −0.317032
\(471\) −9.57699 −0.441285
\(472\) −21.2163 −0.976558
\(473\) 35.8807 1.64980
\(474\) 2.84703 0.130768
\(475\) 4.09306 0.187802
\(476\) 9.19213 0.421320
\(477\) 3.75167 0.171777
\(478\) 18.2046 0.832661
\(479\) 13.6265 0.622613 0.311306 0.950310i \(-0.399233\pi\)
0.311306 + 0.950310i \(0.399233\pi\)
\(480\) −2.06247 −0.0941382
\(481\) 6.09014 0.277686
\(482\) 32.4848 1.47964
\(483\) 0.0227907 0.00103701
\(484\) 52.8216 2.40098
\(485\) −7.39209 −0.335658
\(486\) 2.42144 0.109839
\(487\) 25.6166 1.16080 0.580400 0.814332i \(-0.302896\pi\)
0.580400 + 0.814332i \(0.302896\pi\)
\(488\) 46.7683 2.11710
\(489\) 3.83487 0.173419
\(490\) 23.7632 1.07351
\(491\) 26.8885 1.21346 0.606730 0.794908i \(-0.292481\pi\)
0.606730 + 0.794908i \(0.292481\pi\)
\(492\) −35.4800 −1.59956
\(493\) 12.7801 0.575588
\(494\) 27.2989 1.22823
\(495\) 8.01438 0.360220
\(496\) −6.43775 −0.289064
\(497\) −5.16769 −0.231803
\(498\) −41.4090 −1.85558
\(499\) 7.47479 0.334618 0.167309 0.985905i \(-0.446492\pi\)
0.167309 + 0.985905i \(0.446492\pi\)
\(500\) −46.1069 −2.06196
\(501\) 4.05802 0.181299
\(502\) 58.3222 2.60305
\(503\) −32.1006 −1.43130 −0.715648 0.698461i \(-0.753869\pi\)
−0.715648 + 0.698461i \(0.753869\pi\)
\(504\) 4.32233 0.192532
\(505\) 9.39446 0.418048
\(506\) −0.286146 −0.0127207
\(507\) −30.5781 −1.35802
\(508\) −10.8834 −0.482873
\(509\) 26.0521 1.15474 0.577369 0.816483i \(-0.304079\pi\)
0.577369 + 0.816483i \(0.304079\pi\)
\(510\) −9.70374 −0.429689
\(511\) −4.47938 −0.198156
\(512\) 32.9551 1.45642
\(513\) 1.70780 0.0754013
\(514\) 36.4626 1.60830
\(515\) 4.33466 0.191008
\(516\) −27.9074 −1.22856
\(517\) 8.73818 0.384305
\(518\) 2.14001 0.0940265
\(519\) 3.16297 0.138839
\(520\) −48.0582 −2.10749
\(521\) 7.77855 0.340784 0.170392 0.985376i \(-0.445497\pi\)
0.170392 + 0.985376i \(0.445497\pi\)
\(522\) 12.4597 0.545345
\(523\) 25.0355 1.09472 0.547362 0.836896i \(-0.315632\pi\)
0.547362 + 0.836896i \(0.315632\pi\)
\(524\) 83.2705 3.63769
\(525\) −2.29593 −0.100203
\(526\) −65.9528 −2.87568
\(527\) 4.99858 0.217742
\(528\) −15.8890 −0.691479
\(529\) −22.9994 −0.999975
\(530\) −14.6576 −0.636683
\(531\) 4.70218 0.204057
\(532\) 6.32050 0.274028
\(533\) 60.6251 2.62597
\(534\) 10.3986 0.449993
\(535\) 17.1659 0.742148
\(536\) −62.2722 −2.68975
\(537\) 10.4284 0.450020
\(538\) 21.8759 0.943137
\(539\) −30.2116 −1.30131
\(540\) −6.23345 −0.268245
\(541\) 22.0380 0.947488 0.473744 0.880663i \(-0.342902\pi\)
0.473744 + 0.880663i \(0.342902\pi\)
\(542\) 25.7471 1.10593
\(543\) 19.5701 0.839833
\(544\) −3.17486 −0.136121
\(545\) 2.43683 0.104382
\(546\) −15.3129 −0.655330
\(547\) −25.8946 −1.10717 −0.553586 0.832792i \(-0.686741\pi\)
−0.553586 + 0.832792i \(0.686741\pi\)
\(548\) 33.5410 1.43280
\(549\) −10.3653 −0.442380
\(550\) 28.8263 1.22916
\(551\) 8.78761 0.374365
\(552\) 0.107344 0.00456887
\(553\) −1.12634 −0.0478966
\(554\) 39.7130 1.68724
\(555\) −1.48853 −0.0631845
\(556\) −72.4398 −3.07213
\(557\) 28.1511 1.19280 0.596400 0.802687i \(-0.296597\pi\)
0.596400 + 0.802687i \(0.296597\pi\)
\(558\) 4.87324 0.206301
\(559\) 47.6858 2.01689
\(560\) −4.94427 −0.208934
\(561\) 12.3370 0.520867
\(562\) −22.8454 −0.963676
\(563\) 17.4970 0.737409 0.368705 0.929547i \(-0.379801\pi\)
0.368705 + 0.929547i \(0.379801\pi\)
\(564\) −6.79641 −0.286181
\(565\) 20.5611 0.865011
\(566\) −68.8636 −2.89455
\(567\) −0.957963 −0.0402307
\(568\) −24.3398 −1.02128
\(569\) −39.9250 −1.67374 −0.836872 0.547398i \(-0.815618\pi\)
−0.836872 + 0.547398i \(0.815618\pi\)
\(570\) −6.67228 −0.279471
\(571\) 19.5354 0.817532 0.408766 0.912639i \(-0.365959\pi\)
0.408766 + 0.912639i \(0.365959\pi\)
\(572\) 126.679 5.29672
\(573\) −15.8707 −0.663007
\(574\) 21.3030 0.889170
\(575\) −0.0570189 −0.00237785
\(576\) −9.49289 −0.395537
\(577\) −1.78291 −0.0742236 −0.0371118 0.999311i \(-0.511816\pi\)
−0.0371118 + 0.999311i \(0.511816\pi\)
\(578\) 26.2269 1.09090
\(579\) 24.2289 1.00692
\(580\) −32.0747 −1.33183
\(581\) 16.3821 0.679645
\(582\) −11.0937 −0.459849
\(583\) 18.6351 0.771785
\(584\) −21.0979 −0.873036
\(585\) 10.6512 0.440372
\(586\) −48.2835 −1.99457
\(587\) 36.9682 1.52584 0.762920 0.646493i \(-0.223765\pi\)
0.762920 + 0.646493i \(0.223765\pi\)
\(588\) 23.4981 0.969046
\(589\) 3.43702 0.141620
\(590\) −18.3712 −0.756329
\(591\) −6.89095 −0.283456
\(592\) 2.95109 0.121289
\(593\) −28.6103 −1.17489 −0.587443 0.809266i \(-0.699865\pi\)
−0.587443 + 0.809266i \(0.699865\pi\)
\(594\) 12.0276 0.493499
\(595\) 3.83897 0.157382
\(596\) 70.5996 2.89187
\(597\) 20.4711 0.837827
\(598\) −0.380291 −0.0155512
\(599\) −47.7663 −1.95168 −0.975840 0.218488i \(-0.929888\pi\)
−0.975840 + 0.218488i \(0.929888\pi\)
\(600\) −10.8138 −0.441473
\(601\) −3.36864 −0.137410 −0.0687049 0.997637i \(-0.521887\pi\)
−0.0687049 + 0.997637i \(0.521887\pi\)
\(602\) 16.7563 0.682934
\(603\) 13.8015 0.562039
\(604\) −8.49734 −0.345752
\(605\) 22.0602 0.896876
\(606\) 14.0988 0.572723
\(607\) 13.7141 0.556640 0.278320 0.960488i \(-0.410222\pi\)
0.278320 + 0.960488i \(0.410222\pi\)
\(608\) −2.18303 −0.0885337
\(609\) −4.92927 −0.199744
\(610\) 40.4966 1.63966
\(611\) 11.6131 0.469817
\(612\) −9.59549 −0.387875
\(613\) 30.1698 1.21854 0.609272 0.792961i \(-0.291462\pi\)
0.609272 + 0.792961i \(0.291462\pi\)
\(614\) 14.1627 0.571560
\(615\) −14.8178 −0.597510
\(616\) 21.4696 0.865036
\(617\) 29.8768 1.20279 0.601397 0.798951i \(-0.294611\pi\)
0.601397 + 0.798951i \(0.294611\pi\)
\(618\) 6.50526 0.261680
\(619\) 31.8033 1.27828 0.639141 0.769090i \(-0.279290\pi\)
0.639141 + 0.769090i \(0.279290\pi\)
\(620\) −12.5451 −0.503822
\(621\) −0.0237908 −0.000954691 0
\(622\) 74.1347 2.97253
\(623\) −4.11389 −0.164819
\(624\) −21.1166 −0.845340
\(625\) −7.27252 −0.290901
\(626\) −19.2072 −0.767675
\(627\) 8.48289 0.338774
\(628\) 36.9994 1.47643
\(629\) −2.29137 −0.0913629
\(630\) 3.74271 0.149113
\(631\) 30.3041 1.20639 0.603193 0.797595i \(-0.293895\pi\)
0.603193 + 0.797595i \(0.293895\pi\)
\(632\) −5.30503 −0.211023
\(633\) −9.26658 −0.368313
\(634\) −25.9879 −1.03211
\(635\) −4.54531 −0.180375
\(636\) −14.4940 −0.574726
\(637\) −40.1515 −1.59086
\(638\) 61.8889 2.45020
\(639\) 5.39446 0.213402
\(640\) 32.9632 1.30299
\(641\) −38.4368 −1.51816 −0.759081 0.650996i \(-0.774351\pi\)
−0.759081 + 0.650996i \(0.774351\pi\)
\(642\) 25.7618 1.01674
\(643\) 22.5934 0.890997 0.445498 0.895283i \(-0.353026\pi\)
0.445498 + 0.895283i \(0.353026\pi\)
\(644\) −0.0880486 −0.00346960
\(645\) −11.6552 −0.458922
\(646\) −10.2710 −0.404107
\(647\) 0.440884 0.0173329 0.00866647 0.999962i \(-0.497241\pi\)
0.00866647 + 0.999962i \(0.497241\pi\)
\(648\) −4.51200 −0.177248
\(649\) 23.3564 0.916819
\(650\) 38.3104 1.50266
\(651\) −1.92794 −0.0755619
\(652\) −14.8155 −0.580219
\(653\) −41.6110 −1.62836 −0.814182 0.580609i \(-0.802814\pi\)
−0.814182 + 0.580609i \(0.802814\pi\)
\(654\) 3.65708 0.143003
\(655\) 34.7768 1.35884
\(656\) 29.3771 1.14698
\(657\) 4.67594 0.182426
\(658\) 4.08072 0.159083
\(659\) 13.9094 0.541833 0.270916 0.962603i \(-0.412673\pi\)
0.270916 + 0.962603i \(0.412673\pi\)
\(660\) −30.9624 −1.20521
\(661\) 37.0319 1.44037 0.720186 0.693781i \(-0.244056\pi\)
0.720186 + 0.693781i \(0.244056\pi\)
\(662\) −79.8844 −3.10480
\(663\) 16.3959 0.636765
\(664\) 77.1597 2.99438
\(665\) 2.63967 0.102362
\(666\) −2.23391 −0.0865624
\(667\) −0.122417 −0.00474001
\(668\) −15.6776 −0.606584
\(669\) −26.5273 −1.02560
\(670\) −53.9215 −2.08317
\(671\) −51.4859 −1.98759
\(672\) 1.22454 0.0472375
\(673\) −2.45981 −0.0948186 −0.0474093 0.998876i \(-0.515097\pi\)
−0.0474093 + 0.998876i \(0.515097\pi\)
\(674\) 75.4832 2.90750
\(675\) 2.39668 0.0922483
\(676\) 118.134 4.54361
\(677\) −24.9543 −0.959074 −0.479537 0.877522i \(-0.659195\pi\)
−0.479537 + 0.877522i \(0.659195\pi\)
\(678\) 30.8571 1.18506
\(679\) 4.38887 0.168429
\(680\) 18.0815 0.693395
\(681\) −6.40963 −0.245617
\(682\) 24.2061 0.926898
\(683\) −1.52721 −0.0584370 −0.0292185 0.999573i \(-0.509302\pi\)
−0.0292185 + 0.999573i \(0.509302\pi\)
\(684\) −6.59785 −0.252275
\(685\) 14.0080 0.535216
\(686\) −30.3463 −1.15863
\(687\) −20.9395 −0.798890
\(688\) 23.1070 0.880948
\(689\) 24.7661 0.943515
\(690\) 0.0929492 0.00353851
\(691\) −14.0182 −0.533277 −0.266638 0.963797i \(-0.585913\pi\)
−0.266638 + 0.963797i \(0.585913\pi\)
\(692\) −12.2197 −0.464522
\(693\) −4.75834 −0.180754
\(694\) −63.5118 −2.41088
\(695\) −30.2535 −1.14758
\(696\) −23.2168 −0.880031
\(697\) −22.8098 −0.863982
\(698\) 31.1886 1.18051
\(699\) 13.5153 0.511195
\(700\) 8.87001 0.335255
\(701\) 5.05638 0.190977 0.0954884 0.995431i \(-0.469559\pi\)
0.0954884 + 0.995431i \(0.469559\pi\)
\(702\) 15.9848 0.603307
\(703\) −1.57554 −0.0594228
\(704\) −47.1525 −1.77713
\(705\) −2.83843 −0.106902
\(706\) −25.0637 −0.943287
\(707\) −5.57772 −0.209772
\(708\) −18.1662 −0.682728
\(709\) 34.9209 1.31148 0.655740 0.754987i \(-0.272357\pi\)
0.655740 + 0.754987i \(0.272357\pi\)
\(710\) −21.0758 −0.790962
\(711\) 1.17576 0.0440945
\(712\) −19.3764 −0.726161
\(713\) −0.0478799 −0.00179312
\(714\) 5.76135 0.215613
\(715\) 52.9059 1.97857
\(716\) −40.2888 −1.50566
\(717\) 7.51812 0.280769
\(718\) −36.1221 −1.34807
\(719\) −41.5889 −1.55100 −0.775501 0.631346i \(-0.782503\pi\)
−0.775501 + 0.631346i \(0.782503\pi\)
\(720\) 5.16123 0.192348
\(721\) −2.57359 −0.0958457
\(722\) 38.9450 1.44938
\(723\) 13.4155 0.498928
\(724\) −75.6063 −2.80989
\(725\) 12.3323 0.458009
\(726\) 33.1070 1.22872
\(727\) −15.3774 −0.570318 −0.285159 0.958480i \(-0.592046\pi\)
−0.285159 + 0.958480i \(0.592046\pi\)
\(728\) 28.5333 1.05752
\(729\) 1.00000 0.0370370
\(730\) −18.2686 −0.676152
\(731\) −17.9414 −0.663588
\(732\) 40.0449 1.48010
\(733\) 21.1324 0.780542 0.390271 0.920700i \(-0.372381\pi\)
0.390271 + 0.920700i \(0.372381\pi\)
\(734\) 71.7850 2.64963
\(735\) 9.81368 0.361983
\(736\) 0.0304111 0.00112097
\(737\) 68.5537 2.52521
\(738\) −22.2378 −0.818585
\(739\) −32.0807 −1.18011 −0.590054 0.807364i \(-0.700893\pi\)
−0.590054 + 0.807364i \(0.700893\pi\)
\(740\) 5.75072 0.211400
\(741\) 11.2738 0.414155
\(742\) 8.70255 0.319481
\(743\) 15.5713 0.571254 0.285627 0.958341i \(-0.407798\pi\)
0.285627 + 0.958341i \(0.407798\pi\)
\(744\) −9.08059 −0.332911
\(745\) 29.4850 1.08025
\(746\) −76.1947 −2.78968
\(747\) −17.1010 −0.625692
\(748\) −47.6621 −1.74270
\(749\) −10.1918 −0.372402
\(750\) −28.8984 −1.05522
\(751\) 13.9185 0.507893 0.253947 0.967218i \(-0.418271\pi\)
0.253947 + 0.967218i \(0.418271\pi\)
\(752\) 5.62736 0.205209
\(753\) 24.0858 0.877735
\(754\) 82.2509 2.99540
\(755\) −3.54880 −0.129154
\(756\) 3.70096 0.134602
\(757\) 25.5963 0.930312 0.465156 0.885229i \(-0.345998\pi\)
0.465156 + 0.885229i \(0.345998\pi\)
\(758\) 36.8502 1.33846
\(759\) −0.118172 −0.00428937
\(760\) 12.4329 0.450987
\(761\) 30.8106 1.11688 0.558442 0.829543i \(-0.311399\pi\)
0.558442 + 0.829543i \(0.311399\pi\)
\(762\) −6.82140 −0.247113
\(763\) −1.44681 −0.0523779
\(764\) 61.3141 2.21827
\(765\) −4.00743 −0.144889
\(766\) −77.4229 −2.79740
\(767\) 31.0408 1.12082
\(768\) 30.4839 1.09999
\(769\) 13.5562 0.488847 0.244424 0.969669i \(-0.421401\pi\)
0.244424 + 0.969669i \(0.421401\pi\)
\(770\) 18.5905 0.669957
\(771\) 15.0582 0.542309
\(772\) −93.6049 −3.36891
\(773\) 3.90499 0.140453 0.0702263 0.997531i \(-0.477628\pi\)
0.0702263 + 0.997531i \(0.477628\pi\)
\(774\) −17.4915 −0.628721
\(775\) 4.82342 0.173262
\(776\) 20.6716 0.742066
\(777\) 0.883776 0.0317053
\(778\) −10.4243 −0.373728
\(779\) −15.6840 −0.561937
\(780\) −41.1493 −1.47338
\(781\) 26.7950 0.958801
\(782\) 0.143082 0.00511659
\(783\) 5.14557 0.183888
\(784\) −19.4562 −0.694864
\(785\) 15.4523 0.551516
\(786\) 52.1914 1.86161
\(787\) −2.72751 −0.0972254 −0.0486127 0.998818i \(-0.515480\pi\)
−0.0486127 + 0.998818i \(0.515480\pi\)
\(788\) 26.6222 0.948376
\(789\) −27.2371 −0.969665
\(790\) −4.59363 −0.163434
\(791\) −12.2076 −0.434053
\(792\) −22.4117 −0.796367
\(793\) −68.4252 −2.42985
\(794\) 5.54769 0.196880
\(795\) −6.05325 −0.214686
\(796\) −79.0873 −2.80317
\(797\) −42.3180 −1.49898 −0.749491 0.662015i \(-0.769702\pi\)
−0.749491 + 0.662015i \(0.769702\pi\)
\(798\) 3.96150 0.140236
\(799\) −4.36935 −0.154577
\(800\) −3.06361 −0.108315
\(801\) 4.29441 0.151736
\(802\) 68.6746 2.42499
\(803\) 23.2260 0.819629
\(804\) −53.3200 −1.88045
\(805\) −0.0367723 −0.00129605
\(806\) 32.1701 1.13314
\(807\) 9.03426 0.318021
\(808\) −26.2711 −0.924213
\(809\) 23.9958 0.843647 0.421824 0.906678i \(-0.361390\pi\)
0.421824 + 0.906678i \(0.361390\pi\)
\(810\) −3.90694 −0.137276
\(811\) 9.77499 0.343246 0.171623 0.985163i \(-0.445099\pi\)
0.171623 + 0.985163i \(0.445099\pi\)
\(812\) 19.0435 0.668296
\(813\) 10.6330 0.372915
\(814\) −11.0962 −0.388920
\(815\) −6.18749 −0.216738
\(816\) 7.94496 0.278129
\(817\) −12.3365 −0.431600
\(818\) −1.07646 −0.0376376
\(819\) −6.32387 −0.220974
\(820\) 57.2463 1.99913
\(821\) −13.4645 −0.469916 −0.234958 0.972006i \(-0.575495\pi\)
−0.234958 + 0.972006i \(0.575495\pi\)
\(822\) 21.0225 0.733243
\(823\) 28.0814 0.978857 0.489429 0.872043i \(-0.337205\pi\)
0.489429 + 0.872043i \(0.337205\pi\)
\(824\) −12.1216 −0.422277
\(825\) 11.9046 0.414466
\(826\) 10.9074 0.379517
\(827\) 12.2920 0.427435 0.213717 0.976896i \(-0.431443\pi\)
0.213717 + 0.976896i \(0.431443\pi\)
\(828\) 0.0919123 0.00319417
\(829\) −1.64799 −0.0572370 −0.0286185 0.999590i \(-0.509111\pi\)
−0.0286185 + 0.999590i \(0.509111\pi\)
\(830\) 66.8126 2.31910
\(831\) 16.4006 0.568931
\(832\) −62.6661 −2.17255
\(833\) 15.1067 0.523417
\(834\) −45.4031 −1.57218
\(835\) −6.54754 −0.226587
\(836\) −32.7724 −1.13346
\(837\) 2.01254 0.0695636
\(838\) 56.5607 1.95386
\(839\) 14.6464 0.505650 0.252825 0.967512i \(-0.418640\pi\)
0.252825 + 0.967512i \(0.418640\pi\)
\(840\) −6.97400 −0.240626
\(841\) −2.52313 −0.0870046
\(842\) −12.6508 −0.435974
\(843\) −9.43465 −0.324947
\(844\) 35.8001 1.23229
\(845\) 49.3371 1.69725
\(846\) −4.25979 −0.146455
\(847\) −13.0977 −0.450043
\(848\) 12.0009 0.412113
\(849\) −28.4391 −0.976029
\(850\) −14.4140 −0.494397
\(851\) 0.0219483 0.000752379 0
\(852\) −20.8407 −0.713992
\(853\) 4.53653 0.155328 0.0776639 0.996980i \(-0.475254\pi\)
0.0776639 + 0.996980i \(0.475254\pi\)
\(854\) −24.0439 −0.822764
\(855\) −2.75551 −0.0942363
\(856\) −48.0035 −1.64073
\(857\) 41.1667 1.40623 0.703114 0.711077i \(-0.251792\pi\)
0.703114 + 0.711077i \(0.251792\pi\)
\(858\) 79.3987 2.71063
\(859\) 50.1858 1.71232 0.856158 0.516714i \(-0.172845\pi\)
0.856158 + 0.516714i \(0.172845\pi\)
\(860\) 45.0281 1.53545
\(861\) 8.79767 0.299824
\(862\) −76.5250 −2.60645
\(863\) −3.71230 −0.126368 −0.0631841 0.998002i \(-0.520126\pi\)
−0.0631841 + 0.998002i \(0.520126\pi\)
\(864\) −1.27827 −0.0434877
\(865\) −5.10339 −0.173520
\(866\) 48.6862 1.65442
\(867\) 10.8311 0.367845
\(868\) 7.44832 0.252813
\(869\) 5.84016 0.198114
\(870\) −20.1034 −0.681570
\(871\) 91.1085 3.08709
\(872\) −6.81445 −0.230766
\(873\) −4.58146 −0.155059
\(874\) 0.0983828 0.00332785
\(875\) 11.4327 0.386496
\(876\) −18.0648 −0.610354
\(877\) −49.0483 −1.65624 −0.828122 0.560548i \(-0.810591\pi\)
−0.828122 + 0.560548i \(0.810591\pi\)
\(878\) 47.0239 1.58698
\(879\) −19.9400 −0.672560
\(880\) 25.6365 0.864208
\(881\) 43.0972 1.45198 0.725991 0.687705i \(-0.241382\pi\)
0.725991 + 0.687705i \(0.241382\pi\)
\(882\) 14.7279 0.495915
\(883\) 36.4929 1.22808 0.614042 0.789274i \(-0.289543\pi\)
0.614042 + 0.789274i \(0.289543\pi\)
\(884\) −63.3433 −2.13047
\(885\) −7.58688 −0.255030
\(886\) −61.5690 −2.06845
\(887\) −9.98684 −0.335325 −0.167663 0.985844i \(-0.553622\pi\)
−0.167663 + 0.985844i \(0.553622\pi\)
\(888\) 4.16258 0.139687
\(889\) 2.69866 0.0905103
\(890\) −16.7780 −0.562400
\(891\) 4.96714 0.166405
\(892\) 102.484 3.43143
\(893\) −3.00436 −0.100537
\(894\) 44.2497 1.47993
\(895\) −16.8261 −0.562434
\(896\) −19.5711 −0.653824
\(897\) −0.157052 −0.00524380
\(898\) 44.2798 1.47764
\(899\) 10.3557 0.345381
\(900\) −9.25923 −0.308641
\(901\) −9.31808 −0.310430
\(902\) −110.458 −3.67786
\(903\) 6.91996 0.230282
\(904\) −57.4978 −1.91235
\(905\) −31.5760 −1.04962
\(906\) −5.32588 −0.176940
\(907\) −48.0432 −1.59525 −0.797624 0.603155i \(-0.793910\pi\)
−0.797624 + 0.603155i \(0.793910\pi\)
\(908\) 24.7627 0.821779
\(909\) 5.82248 0.193120
\(910\) 24.7070 0.819029
\(911\) −46.6180 −1.54452 −0.772261 0.635305i \(-0.780874\pi\)
−0.772261 + 0.635305i \(0.780874\pi\)
\(912\) 5.46295 0.180896
\(913\) −84.9429 −2.81120
\(914\) 54.7445 1.81079
\(915\) 16.7242 0.552885
\(916\) 80.8966 2.67290
\(917\) −20.6479 −0.681852
\(918\) −6.01417 −0.198497
\(919\) 42.2503 1.39371 0.696855 0.717212i \(-0.254582\pi\)
0.696855 + 0.717212i \(0.254582\pi\)
\(920\) −0.173198 −0.00571015
\(921\) 5.84888 0.192727
\(922\) 22.0682 0.726777
\(923\) 35.6108 1.17214
\(924\) 18.3832 0.604761
\(925\) −2.21107 −0.0726997
\(926\) −33.8132 −1.11117
\(927\) 2.68653 0.0882371
\(928\) −6.57743 −0.215915
\(929\) 6.96846 0.228628 0.114314 0.993445i \(-0.463533\pi\)
0.114314 + 0.993445i \(0.463533\pi\)
\(930\) −7.86288 −0.257834
\(931\) 10.3874 0.340433
\(932\) −52.2144 −1.71034
\(933\) 30.6160 1.00232
\(934\) −61.2137 −2.00297
\(935\) −19.9055 −0.650978
\(936\) −29.7854 −0.973566
\(937\) −12.7551 −0.416690 −0.208345 0.978055i \(-0.566808\pi\)
−0.208345 + 0.978055i \(0.566808\pi\)
\(938\) 32.0145 1.04531
\(939\) −7.93216 −0.258856
\(940\) 10.9659 0.357668
\(941\) 31.5941 1.02994 0.514969 0.857209i \(-0.327803\pi\)
0.514969 + 0.857209i \(0.327803\pi\)
\(942\) 23.1901 0.755574
\(943\) 0.218488 0.00711494
\(944\) 15.0414 0.489557
\(945\) 1.54566 0.0502802
\(946\) −86.8829 −2.82481
\(947\) 25.1084 0.815915 0.407957 0.913001i \(-0.366241\pi\)
0.407957 + 0.913001i \(0.366241\pi\)
\(948\) −4.54238 −0.147530
\(949\) 30.8676 1.00200
\(950\) −9.91108 −0.321558
\(951\) −10.7324 −0.348023
\(952\) −10.7355 −0.347938
\(953\) 14.4020 0.466526 0.233263 0.972414i \(-0.425060\pi\)
0.233263 + 0.972414i \(0.425060\pi\)
\(954\) −9.08443 −0.294119
\(955\) 25.6070 0.828624
\(956\) −29.0452 −0.939388
\(957\) 25.5587 0.826197
\(958\) −32.9958 −1.06605
\(959\) −8.31687 −0.268566
\(960\) 15.3166 0.494341
\(961\) −26.9497 −0.869345
\(962\) −14.7469 −0.475459
\(963\) 10.6391 0.342839
\(964\) −51.8289 −1.66930
\(965\) −39.0928 −1.25844
\(966\) −0.0551862 −0.00177559
\(967\) −7.70633 −0.247819 −0.123909 0.992294i \(-0.539543\pi\)
−0.123909 + 0.992294i \(0.539543\pi\)
\(968\) −61.6902 −1.98280
\(969\) −4.24170 −0.136263
\(970\) 17.8995 0.574718
\(971\) −19.5480 −0.627326 −0.313663 0.949534i \(-0.601556\pi\)
−0.313663 + 0.949534i \(0.601556\pi\)
\(972\) −3.86336 −0.123917
\(973\) 17.9623 0.575844
\(974\) −62.0290 −1.98754
\(975\) 15.8214 0.506689
\(976\) −33.1567 −1.06132
\(977\) 15.7430 0.503664 0.251832 0.967771i \(-0.418967\pi\)
0.251832 + 0.967771i \(0.418967\pi\)
\(978\) −9.28589 −0.296930
\(979\) 21.3309 0.681739
\(980\) −37.9138 −1.21111
\(981\) 1.51029 0.0482199
\(982\) −65.1087 −2.07770
\(983\) −48.6284 −1.55100 −0.775502 0.631345i \(-0.782503\pi\)
−0.775502 + 0.631345i \(0.782503\pi\)
\(984\) 41.4370 1.32096
\(985\) 11.1184 0.354262
\(986\) −30.9463 −0.985531
\(987\) 1.68525 0.0536420
\(988\) −43.5548 −1.38566
\(989\) 0.171856 0.00546469
\(990\) −19.4063 −0.616773
\(991\) −41.7164 −1.32516 −0.662582 0.748989i \(-0.730539\pi\)
−0.662582 + 0.748989i \(0.730539\pi\)
\(992\) −2.57257 −0.0816792
\(993\) −32.9905 −1.04692
\(994\) 12.5132 0.396896
\(995\) −33.0298 −1.04711
\(996\) 66.0672 2.09342
\(997\) −47.0553 −1.49026 −0.745128 0.666922i \(-0.767611\pi\)
−0.745128 + 0.666922i \(0.767611\pi\)
\(998\) −18.0997 −0.572937
\(999\) −0.922557 −0.0291884
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 6033.2.a.c.1.7 82
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6033.2.a.c.1.7 82 1.1 even 1 trivial