Properties

Label 6002.2.a.a.1.14
Level $6002$
Weight $2$
Character 6002.1
Self dual yes
Analytic conductor $47.926$
Analytic rank $1$
Dimension $47$
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] = [6002,2,Mod(1,6002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6002, 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("6002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6002.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: \(47.9262112932\)
Analytic rank: \(1\)
Dimension: \(47\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.60528 q^{3} +1.00000 q^{4} +1.61064 q^{5} -1.60528 q^{6} -2.90280 q^{7} +1.00000 q^{8} -0.423077 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.60528 q^{3} +1.00000 q^{4} +1.61064 q^{5} -1.60528 q^{6} -2.90280 q^{7} +1.00000 q^{8} -0.423077 q^{9} +1.61064 q^{10} +0.613143 q^{11} -1.60528 q^{12} +5.17210 q^{13} -2.90280 q^{14} -2.58553 q^{15} +1.00000 q^{16} -2.85314 q^{17} -0.423077 q^{18} -2.15783 q^{19} +1.61064 q^{20} +4.65981 q^{21} +0.613143 q^{22} +6.80112 q^{23} -1.60528 q^{24} -2.40583 q^{25} +5.17210 q^{26} +5.49500 q^{27} -2.90280 q^{28} -8.18878 q^{29} -2.58553 q^{30} -5.91754 q^{31} +1.00000 q^{32} -0.984265 q^{33} -2.85314 q^{34} -4.67538 q^{35} -0.423077 q^{36} -4.25115 q^{37} -2.15783 q^{38} -8.30266 q^{39} +1.61064 q^{40} -4.79864 q^{41} +4.65981 q^{42} +2.35920 q^{43} +0.613143 q^{44} -0.681425 q^{45} +6.80112 q^{46} +5.37760 q^{47} -1.60528 q^{48} +1.42627 q^{49} -2.40583 q^{50} +4.58008 q^{51} +5.17210 q^{52} -2.42943 q^{53} +5.49500 q^{54} +0.987553 q^{55} -2.90280 q^{56} +3.46392 q^{57} -8.18878 q^{58} +1.10964 q^{59} -2.58553 q^{60} +6.36668 q^{61} -5.91754 q^{62} +1.22811 q^{63} +1.00000 q^{64} +8.33040 q^{65} -0.984265 q^{66} +9.58442 q^{67} -2.85314 q^{68} -10.9177 q^{69} -4.67538 q^{70} -4.11233 q^{71} -0.423077 q^{72} -1.09065 q^{73} -4.25115 q^{74} +3.86203 q^{75} -2.15783 q^{76} -1.77983 q^{77} -8.30266 q^{78} -6.18755 q^{79} +1.61064 q^{80} -7.55178 q^{81} -4.79864 q^{82} -3.24919 q^{83} +4.65981 q^{84} -4.59538 q^{85} +2.35920 q^{86} +13.1453 q^{87} +0.613143 q^{88} -6.20320 q^{89} -0.681425 q^{90} -15.0136 q^{91} +6.80112 q^{92} +9.49931 q^{93} +5.37760 q^{94} -3.47549 q^{95} -1.60528 q^{96} +3.83804 q^{97} +1.42627 q^{98} -0.259406 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 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
\(3\) −1.60528 −0.926809 −0.463404 0.886147i \(-0.653372\pi\)
−0.463404 + 0.886147i \(0.653372\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.61064 0.720301 0.360151 0.932894i \(-0.382725\pi\)
0.360151 + 0.932894i \(0.382725\pi\)
\(6\) −1.60528 −0.655353
\(7\) −2.90280 −1.09716 −0.548578 0.836099i \(-0.684831\pi\)
−0.548578 + 0.836099i \(0.684831\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.423077 −0.141026
\(10\) 1.61064 0.509330
\(11\) 0.613143 0.184869 0.0924347 0.995719i \(-0.470535\pi\)
0.0924347 + 0.995719i \(0.470535\pi\)
\(12\) −1.60528 −0.463404
\(13\) 5.17210 1.43448 0.717241 0.696825i \(-0.245405\pi\)
0.717241 + 0.696825i \(0.245405\pi\)
\(14\) −2.90280 −0.775807
\(15\) −2.58553 −0.667581
\(16\) 1.00000 0.250000
\(17\) −2.85314 −0.691987 −0.345993 0.938237i \(-0.612458\pi\)
−0.345993 + 0.938237i \(0.612458\pi\)
\(18\) −0.423077 −0.0997201
\(19\) −2.15783 −0.495040 −0.247520 0.968883i \(-0.579616\pi\)
−0.247520 + 0.968883i \(0.579616\pi\)
\(20\) 1.61064 0.360151
\(21\) 4.65981 1.01685
\(22\) 0.613143 0.130722
\(23\) 6.80112 1.41813 0.709066 0.705142i \(-0.249117\pi\)
0.709066 + 0.705142i \(0.249117\pi\)
\(24\) −1.60528 −0.327676
\(25\) −2.40583 −0.481166
\(26\) 5.17210 1.01433
\(27\) 5.49500 1.05751
\(28\) −2.90280 −0.548578
\(29\) −8.18878 −1.52062 −0.760309 0.649561i \(-0.774953\pi\)
−0.760309 + 0.649561i \(0.774953\pi\)
\(30\) −2.58553 −0.472051
\(31\) −5.91754 −1.06282 −0.531411 0.847114i \(-0.678338\pi\)
−0.531411 + 0.847114i \(0.678338\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.984265 −0.171339
\(34\) −2.85314 −0.489309
\(35\) −4.67538 −0.790283
\(36\) −0.423077 −0.0705128
\(37\) −4.25115 −0.698885 −0.349443 0.936958i \(-0.613629\pi\)
−0.349443 + 0.936958i \(0.613629\pi\)
\(38\) −2.15783 −0.350046
\(39\) −8.30266 −1.32949
\(40\) 1.61064 0.254665
\(41\) −4.79864 −0.749422 −0.374711 0.927142i \(-0.622258\pi\)
−0.374711 + 0.927142i \(0.622258\pi\)
\(42\) 4.65981 0.719025
\(43\) 2.35920 0.359774 0.179887 0.983687i \(-0.442427\pi\)
0.179887 + 0.983687i \(0.442427\pi\)
\(44\) 0.613143 0.0924347
\(45\) −0.681425 −0.101581
\(46\) 6.80112 1.00277
\(47\) 5.37760 0.784404 0.392202 0.919879i \(-0.371713\pi\)
0.392202 + 0.919879i \(0.371713\pi\)
\(48\) −1.60528 −0.231702
\(49\) 1.42627 0.203753
\(50\) −2.40583 −0.340236
\(51\) 4.58008 0.641340
\(52\) 5.17210 0.717241
\(53\) −2.42943 −0.333707 −0.166854 0.985982i \(-0.553361\pi\)
−0.166854 + 0.985982i \(0.553361\pi\)
\(54\) 5.49500 0.747774
\(55\) 0.987553 0.133162
\(56\) −2.90280 −0.387903
\(57\) 3.46392 0.458807
\(58\) −8.18878 −1.07524
\(59\) 1.10964 0.144463 0.0722314 0.997388i \(-0.476988\pi\)
0.0722314 + 0.997388i \(0.476988\pi\)
\(60\) −2.58553 −0.333791
\(61\) 6.36668 0.815170 0.407585 0.913167i \(-0.366371\pi\)
0.407585 + 0.913167i \(0.366371\pi\)
\(62\) −5.91754 −0.751528
\(63\) 1.22811 0.154727
\(64\) 1.00000 0.125000
\(65\) 8.33040 1.03326
\(66\) −0.984265 −0.121155
\(67\) 9.58442 1.17092 0.585461 0.810700i \(-0.300913\pi\)
0.585461 + 0.810700i \(0.300913\pi\)
\(68\) −2.85314 −0.345993
\(69\) −10.9177 −1.31434
\(70\) −4.67538 −0.558815
\(71\) −4.11233 −0.488044 −0.244022 0.969770i \(-0.578467\pi\)
−0.244022 + 0.969770i \(0.578467\pi\)
\(72\) −0.423077 −0.0498601
\(73\) −1.09065 −0.127651 −0.0638257 0.997961i \(-0.520330\pi\)
−0.0638257 + 0.997961i \(0.520330\pi\)
\(74\) −4.25115 −0.494186
\(75\) 3.86203 0.445949
\(76\) −2.15783 −0.247520
\(77\) −1.77983 −0.202831
\(78\) −8.30266 −0.940092
\(79\) −6.18755 −0.696154 −0.348077 0.937466i \(-0.613165\pi\)
−0.348077 + 0.937466i \(0.613165\pi\)
\(80\) 1.61064 0.180075
\(81\) −7.55178 −0.839086
\(82\) −4.79864 −0.529921
\(83\) −3.24919 −0.356645 −0.178322 0.983972i \(-0.557067\pi\)
−0.178322 + 0.983972i \(0.557067\pi\)
\(84\) 4.65981 0.508427
\(85\) −4.59538 −0.498439
\(86\) 2.35920 0.254399
\(87\) 13.1453 1.40932
\(88\) 0.613143 0.0653612
\(89\) −6.20320 −0.657538 −0.328769 0.944410i \(-0.606634\pi\)
−0.328769 + 0.944410i \(0.606634\pi\)
\(90\) −0.681425 −0.0718285
\(91\) −15.0136 −1.57385
\(92\) 6.80112 0.709066
\(93\) 9.49931 0.985032
\(94\) 5.37760 0.554657
\(95\) −3.47549 −0.356578
\(96\) −1.60528 −0.163838
\(97\) 3.83804 0.389694 0.194847 0.980834i \(-0.437579\pi\)
0.194847 + 0.980834i \(0.437579\pi\)
\(98\) 1.42627 0.144075
\(99\) −0.259406 −0.0260713
\(100\) −2.40583 −0.240583
\(101\) −1.06912 −0.106381 −0.0531907 0.998584i \(-0.516939\pi\)
−0.0531907 + 0.998584i \(0.516939\pi\)
\(102\) 4.58008 0.453496
\(103\) −14.8502 −1.46324 −0.731618 0.681715i \(-0.761235\pi\)
−0.731618 + 0.681715i \(0.761235\pi\)
\(104\) 5.17210 0.507166
\(105\) 7.50529 0.732441
\(106\) −2.42943 −0.235967
\(107\) 16.1974 1.56586 0.782929 0.622111i \(-0.213725\pi\)
0.782929 + 0.622111i \(0.213725\pi\)
\(108\) 5.49500 0.528756
\(109\) 10.4020 0.996331 0.498166 0.867082i \(-0.334007\pi\)
0.498166 + 0.867082i \(0.334007\pi\)
\(110\) 0.987553 0.0941595
\(111\) 6.82429 0.647733
\(112\) −2.90280 −0.274289
\(113\) −4.47004 −0.420506 −0.210253 0.977647i \(-0.567429\pi\)
−0.210253 + 0.977647i \(0.567429\pi\)
\(114\) 3.46392 0.324426
\(115\) 10.9542 1.02148
\(116\) −8.18878 −0.760309
\(117\) −2.18819 −0.202299
\(118\) 1.10964 0.102151
\(119\) 8.28209 0.759218
\(120\) −2.58553 −0.236026
\(121\) −10.6241 −0.965823
\(122\) 6.36668 0.576413
\(123\) 7.70316 0.694571
\(124\) −5.91754 −0.531411
\(125\) −11.9281 −1.06689
\(126\) 1.22811 0.109409
\(127\) 4.96090 0.440209 0.220104 0.975476i \(-0.429360\pi\)
0.220104 + 0.975476i \(0.429360\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.78717 −0.333442
\(130\) 8.33040 0.730624
\(131\) −11.7767 −1.02894 −0.514468 0.857510i \(-0.672010\pi\)
−0.514468 + 0.857510i \(0.672010\pi\)
\(132\) −0.984265 −0.0856693
\(133\) 6.26375 0.543136
\(134\) 9.58442 0.827967
\(135\) 8.85047 0.761727
\(136\) −2.85314 −0.244654
\(137\) −4.65592 −0.397783 −0.198891 0.980022i \(-0.563734\pi\)
−0.198891 + 0.980022i \(0.563734\pi\)
\(138\) −10.9177 −0.929376
\(139\) −20.3902 −1.72947 −0.864737 0.502225i \(-0.832515\pi\)
−0.864737 + 0.502225i \(0.832515\pi\)
\(140\) −4.67538 −0.395142
\(141\) −8.63256 −0.726993
\(142\) −4.11233 −0.345099
\(143\) 3.17123 0.265192
\(144\) −0.423077 −0.0352564
\(145\) −13.1892 −1.09530
\(146\) −1.09065 −0.0902632
\(147\) −2.28956 −0.188840
\(148\) −4.25115 −0.349443
\(149\) −12.6933 −1.03988 −0.519938 0.854204i \(-0.674045\pi\)
−0.519938 + 0.854204i \(0.674045\pi\)
\(150\) 3.86203 0.315334
\(151\) −21.3037 −1.73367 −0.866834 0.498598i \(-0.833849\pi\)
−0.866834 + 0.498598i \(0.833849\pi\)
\(152\) −2.15783 −0.175023
\(153\) 1.20709 0.0975878
\(154\) −1.77983 −0.143423
\(155\) −9.53104 −0.765552
\(156\) −8.30266 −0.664745
\(157\) −4.94059 −0.394302 −0.197151 0.980373i \(-0.563169\pi\)
−0.197151 + 0.980373i \(0.563169\pi\)
\(158\) −6.18755 −0.492255
\(159\) 3.89991 0.309283
\(160\) 1.61064 0.127332
\(161\) −19.7423 −1.55591
\(162\) −7.55178 −0.593324
\(163\) −14.0732 −1.10230 −0.551149 0.834407i \(-0.685810\pi\)
−0.551149 + 0.834407i \(0.685810\pi\)
\(164\) −4.79864 −0.374711
\(165\) −1.58530 −0.123415
\(166\) −3.24919 −0.252186
\(167\) 14.1468 1.09471 0.547356 0.836900i \(-0.315635\pi\)
0.547356 + 0.836900i \(0.315635\pi\)
\(168\) 4.65981 0.359512
\(169\) 13.7506 1.05774
\(170\) −4.59538 −0.352450
\(171\) 0.912927 0.0698132
\(172\) 2.35920 0.179887
\(173\) −10.9244 −0.830564 −0.415282 0.909693i \(-0.636317\pi\)
−0.415282 + 0.909693i \(0.636317\pi\)
\(174\) 13.1453 0.996542
\(175\) 6.98366 0.527915
\(176\) 0.613143 0.0462174
\(177\) −1.78128 −0.133889
\(178\) −6.20320 −0.464950
\(179\) −13.6406 −1.01955 −0.509773 0.860309i \(-0.670271\pi\)
−0.509773 + 0.860309i \(0.670271\pi\)
\(180\) −0.681425 −0.0507904
\(181\) −11.1492 −0.828716 −0.414358 0.910114i \(-0.635994\pi\)
−0.414358 + 0.910114i \(0.635994\pi\)
\(182\) −15.0136 −1.11288
\(183\) −10.2203 −0.755507
\(184\) 6.80112 0.501385
\(185\) −6.84708 −0.503408
\(186\) 9.49931 0.696523
\(187\) −1.74938 −0.127927
\(188\) 5.37760 0.392202
\(189\) −15.9509 −1.16026
\(190\) −3.47549 −0.252138
\(191\) −1.19781 −0.0866707 −0.0433353 0.999061i \(-0.513798\pi\)
−0.0433353 + 0.999061i \(0.513798\pi\)
\(192\) −1.60528 −0.115851
\(193\) −15.3062 −1.10177 −0.550884 0.834582i \(-0.685709\pi\)
−0.550884 + 0.834582i \(0.685709\pi\)
\(194\) 3.83804 0.275555
\(195\) −13.3726 −0.957633
\(196\) 1.42627 0.101876
\(197\) 11.8758 0.846112 0.423056 0.906103i \(-0.360957\pi\)
0.423056 + 0.906103i \(0.360957\pi\)
\(198\) −0.259406 −0.0184352
\(199\) 11.3550 0.804933 0.402467 0.915435i \(-0.368153\pi\)
0.402467 + 0.915435i \(0.368153\pi\)
\(200\) −2.40583 −0.170118
\(201\) −15.3857 −1.08522
\(202\) −1.06912 −0.0752230
\(203\) 23.7704 1.66836
\(204\) 4.58008 0.320670
\(205\) −7.72890 −0.539809
\(206\) −14.8502 −1.03466
\(207\) −2.87739 −0.199993
\(208\) 5.17210 0.358620
\(209\) −1.32306 −0.0915177
\(210\) 7.50529 0.517914
\(211\) 25.4028 1.74880 0.874401 0.485203i \(-0.161254\pi\)
0.874401 + 0.485203i \(0.161254\pi\)
\(212\) −2.42943 −0.166854
\(213\) 6.60144 0.452323
\(214\) 16.1974 1.10723
\(215\) 3.79982 0.259146
\(216\) 5.49500 0.373887
\(217\) 17.1775 1.16608
\(218\) 10.4020 0.704513
\(219\) 1.75081 0.118308
\(220\) 0.987553 0.0665808
\(221\) −14.7567 −0.992643
\(222\) 6.82429 0.458016
\(223\) −0.685057 −0.0458748 −0.0229374 0.999737i \(-0.507302\pi\)
−0.0229374 + 0.999737i \(0.507302\pi\)
\(224\) −2.90280 −0.193952
\(225\) 1.01785 0.0678567
\(226\) −4.47004 −0.297342
\(227\) −15.0151 −0.996585 −0.498293 0.867009i \(-0.666039\pi\)
−0.498293 + 0.867009i \(0.666039\pi\)
\(228\) 3.46392 0.229404
\(229\) 8.40883 0.555671 0.277836 0.960629i \(-0.410383\pi\)
0.277836 + 0.960629i \(0.410383\pi\)
\(230\) 10.9542 0.722297
\(231\) 2.85713 0.187985
\(232\) −8.18878 −0.537620
\(233\) −25.6289 −1.67900 −0.839501 0.543358i \(-0.817153\pi\)
−0.839501 + 0.543358i \(0.817153\pi\)
\(234\) −2.18819 −0.143047
\(235\) 8.66139 0.565007
\(236\) 1.10964 0.0722314
\(237\) 9.93275 0.645201
\(238\) 8.28209 0.536848
\(239\) 8.44585 0.546317 0.273158 0.961969i \(-0.411932\pi\)
0.273158 + 0.961969i \(0.411932\pi\)
\(240\) −2.58553 −0.166895
\(241\) −3.39704 −0.218823 −0.109411 0.993997i \(-0.534897\pi\)
−0.109411 + 0.993997i \(0.534897\pi\)
\(242\) −10.6241 −0.682940
\(243\) −4.36227 −0.279840
\(244\) 6.36668 0.407585
\(245\) 2.29721 0.146763
\(246\) 7.70316 0.491136
\(247\) −11.1605 −0.710126
\(248\) −5.91754 −0.375764
\(249\) 5.21586 0.330542
\(250\) −11.9281 −0.754402
\(251\) 24.4826 1.54533 0.772664 0.634815i \(-0.218924\pi\)
0.772664 + 0.634815i \(0.218924\pi\)
\(252\) 1.22811 0.0773636
\(253\) 4.17006 0.262169
\(254\) 4.96090 0.311275
\(255\) 7.37687 0.461958
\(256\) 1.00000 0.0625000
\(257\) −28.4841 −1.77679 −0.888393 0.459083i \(-0.848178\pi\)
−0.888393 + 0.459083i \(0.848178\pi\)
\(258\) −3.78717 −0.235779
\(259\) 12.3403 0.766787
\(260\) 8.33040 0.516629
\(261\) 3.46448 0.214446
\(262\) −11.7767 −0.727567
\(263\) −7.29287 −0.449697 −0.224849 0.974394i \(-0.572189\pi\)
−0.224849 + 0.974394i \(0.572189\pi\)
\(264\) −0.984265 −0.0605773
\(265\) −3.91294 −0.240370
\(266\) 6.26375 0.384055
\(267\) 9.95788 0.609412
\(268\) 9.58442 0.585461
\(269\) 13.1350 0.800858 0.400429 0.916328i \(-0.368861\pi\)
0.400429 + 0.916328i \(0.368861\pi\)
\(270\) 8.85047 0.538623
\(271\) −6.14537 −0.373304 −0.186652 0.982426i \(-0.559764\pi\)
−0.186652 + 0.982426i \(0.559764\pi\)
\(272\) −2.85314 −0.172997
\(273\) 24.1010 1.45866
\(274\) −4.65592 −0.281275
\(275\) −1.47512 −0.0889530
\(276\) −10.9177 −0.657168
\(277\) 10.7915 0.648400 0.324200 0.945989i \(-0.394905\pi\)
0.324200 + 0.945989i \(0.394905\pi\)
\(278\) −20.3902 −1.22292
\(279\) 2.50357 0.149885
\(280\) −4.67538 −0.279407
\(281\) −21.2837 −1.26968 −0.634839 0.772645i \(-0.718933\pi\)
−0.634839 + 0.772645i \(0.718933\pi\)
\(282\) −8.63256 −0.514061
\(283\) 9.37486 0.557278 0.278639 0.960396i \(-0.410117\pi\)
0.278639 + 0.960396i \(0.410117\pi\)
\(284\) −4.11233 −0.244022
\(285\) 5.57913 0.330479
\(286\) 3.17123 0.187519
\(287\) 13.9295 0.822233
\(288\) −0.423077 −0.0249300
\(289\) −8.85962 −0.521154
\(290\) −13.1892 −0.774496
\(291\) −6.16113 −0.361172
\(292\) −1.09065 −0.0638257
\(293\) −9.99871 −0.584131 −0.292065 0.956398i \(-0.594342\pi\)
−0.292065 + 0.956398i \(0.594342\pi\)
\(294\) −2.28956 −0.133530
\(295\) 1.78723 0.104057
\(296\) −4.25115 −0.247093
\(297\) 3.36922 0.195502
\(298\) −12.6933 −0.735303
\(299\) 35.1761 2.03428
\(300\) 3.86203 0.222975
\(301\) −6.84829 −0.394729
\(302\) −21.3037 −1.22589
\(303\) 1.71624 0.0985951
\(304\) −2.15783 −0.123760
\(305\) 10.2545 0.587168
\(306\) 1.20709 0.0690050
\(307\) 20.1444 1.14970 0.574851 0.818258i \(-0.305060\pi\)
0.574851 + 0.818258i \(0.305060\pi\)
\(308\) −1.77983 −0.101415
\(309\) 23.8388 1.35614
\(310\) −9.53104 −0.541327
\(311\) −4.42643 −0.251000 −0.125500 0.992094i \(-0.540053\pi\)
−0.125500 + 0.992094i \(0.540053\pi\)
\(312\) −8.30266 −0.470046
\(313\) −14.6136 −0.826010 −0.413005 0.910729i \(-0.635521\pi\)
−0.413005 + 0.910729i \(0.635521\pi\)
\(314\) −4.94059 −0.278813
\(315\) 1.97804 0.111450
\(316\) −6.18755 −0.348077
\(317\) 7.70700 0.432868 0.216434 0.976297i \(-0.430557\pi\)
0.216434 + 0.976297i \(0.430557\pi\)
\(318\) 3.89991 0.218696
\(319\) −5.02089 −0.281116
\(320\) 1.61064 0.0900376
\(321\) −26.0013 −1.45125
\(322\) −19.7423 −1.10020
\(323\) 6.15658 0.342561
\(324\) −7.55178 −0.419543
\(325\) −12.4432 −0.690224
\(326\) −14.0732 −0.779442
\(327\) −16.6981 −0.923409
\(328\) −4.79864 −0.264961
\(329\) −15.6101 −0.860614
\(330\) −1.58530 −0.0872679
\(331\) −13.5935 −0.747169 −0.373584 0.927596i \(-0.621871\pi\)
−0.373584 + 0.927596i \(0.621871\pi\)
\(332\) −3.24919 −0.178322
\(333\) 1.79856 0.0985607
\(334\) 14.1468 0.774078
\(335\) 15.4371 0.843417
\(336\) 4.65981 0.254214
\(337\) 7.20994 0.392751 0.196375 0.980529i \(-0.437083\pi\)
0.196375 + 0.980529i \(0.437083\pi\)
\(338\) 13.7506 0.747934
\(339\) 7.17566 0.389728
\(340\) −4.59538 −0.249219
\(341\) −3.62830 −0.196483
\(342\) 0.912927 0.0493654
\(343\) 16.1794 0.873608
\(344\) 2.35920 0.127199
\(345\) −17.5845 −0.946718
\(346\) −10.9244 −0.587298
\(347\) 9.99912 0.536781 0.268390 0.963310i \(-0.413508\pi\)
0.268390 + 0.963310i \(0.413508\pi\)
\(348\) 13.1453 0.704661
\(349\) 20.8433 1.11572 0.557859 0.829936i \(-0.311623\pi\)
0.557859 + 0.829936i \(0.311623\pi\)
\(350\) 6.98366 0.373292
\(351\) 28.4207 1.51698
\(352\) 0.613143 0.0326806
\(353\) −7.01615 −0.373432 −0.186716 0.982414i \(-0.559784\pi\)
−0.186716 + 0.982414i \(0.559784\pi\)
\(354\) −1.78128 −0.0946740
\(355\) −6.62350 −0.351539
\(356\) −6.20320 −0.328769
\(357\) −13.2951 −0.703650
\(358\) −13.6406 −0.720928
\(359\) −27.0092 −1.42549 −0.712746 0.701422i \(-0.752549\pi\)
−0.712746 + 0.701422i \(0.752549\pi\)
\(360\) −0.681425 −0.0359143
\(361\) −14.3438 −0.754936
\(362\) −11.1492 −0.585991
\(363\) 17.0546 0.895133
\(364\) −15.0136 −0.786926
\(365\) −1.75665 −0.0919475
\(366\) −10.2203 −0.534224
\(367\) −24.2512 −1.26590 −0.632951 0.774192i \(-0.718157\pi\)
−0.632951 + 0.774192i \(0.718157\pi\)
\(368\) 6.80112 0.354533
\(369\) 2.03019 0.105688
\(370\) −6.84708 −0.355963
\(371\) 7.05215 0.366129
\(372\) 9.49931 0.492516
\(373\) −36.4166 −1.88558 −0.942789 0.333390i \(-0.891807\pi\)
−0.942789 + 0.333390i \(0.891807\pi\)
\(374\) −1.74938 −0.0904582
\(375\) 19.1480 0.988799
\(376\) 5.37760 0.277329
\(377\) −42.3532 −2.18130
\(378\) −15.9509 −0.820426
\(379\) 27.9204 1.43417 0.717087 0.696984i \(-0.245475\pi\)
0.717087 + 0.696984i \(0.245475\pi\)
\(380\) −3.47549 −0.178289
\(381\) −7.96364 −0.407989
\(382\) −1.19781 −0.0612854
\(383\) −32.6657 −1.66914 −0.834570 0.550902i \(-0.814284\pi\)
−0.834570 + 0.550902i \(0.814284\pi\)
\(384\) −1.60528 −0.0819191
\(385\) −2.86667 −0.146099
\(386\) −15.3062 −0.779068
\(387\) −0.998122 −0.0507374
\(388\) 3.83804 0.194847
\(389\) 26.0544 1.32101 0.660505 0.750822i \(-0.270342\pi\)
0.660505 + 0.750822i \(0.270342\pi\)
\(390\) −13.3726 −0.677149
\(391\) −19.4045 −0.981328
\(392\) 1.42627 0.0720375
\(393\) 18.9049 0.953626
\(394\) 11.8758 0.598292
\(395\) −9.96593 −0.501440
\(396\) −0.259406 −0.0130357
\(397\) −9.13473 −0.458459 −0.229230 0.973372i \(-0.573621\pi\)
−0.229230 + 0.973372i \(0.573621\pi\)
\(398\) 11.3550 0.569174
\(399\) −10.0551 −0.503383
\(400\) −2.40583 −0.120292
\(401\) −12.5481 −0.626623 −0.313312 0.949650i \(-0.601438\pi\)
−0.313312 + 0.949650i \(0.601438\pi\)
\(402\) −15.3857 −0.767367
\(403\) −30.6061 −1.52460
\(404\) −1.06912 −0.0531907
\(405\) −12.1632 −0.604395
\(406\) 23.7704 1.17971
\(407\) −2.60656 −0.129202
\(408\) 4.58008 0.226748
\(409\) 19.3480 0.956696 0.478348 0.878170i \(-0.341236\pi\)
0.478348 + 0.878170i \(0.341236\pi\)
\(410\) −7.72890 −0.381703
\(411\) 7.47406 0.368668
\(412\) −14.8502 −0.731618
\(413\) −3.22107 −0.158498
\(414\) −2.87739 −0.141416
\(415\) −5.23328 −0.256892
\(416\) 5.17210 0.253583
\(417\) 32.7320 1.60289
\(418\) −1.32306 −0.0647128
\(419\) −1.07450 −0.0524927 −0.0262464 0.999656i \(-0.508355\pi\)
−0.0262464 + 0.999656i \(0.508355\pi\)
\(420\) 7.50529 0.366221
\(421\) −5.64351 −0.275048 −0.137524 0.990498i \(-0.543914\pi\)
−0.137524 + 0.990498i \(0.543914\pi\)
\(422\) 25.4028 1.23659
\(423\) −2.27514 −0.110621
\(424\) −2.42943 −0.117983
\(425\) 6.86416 0.332961
\(426\) 6.60144 0.319841
\(427\) −18.4812 −0.894370
\(428\) 16.1974 0.782929
\(429\) −5.09072 −0.245782
\(430\) 3.79982 0.183244
\(431\) 22.9508 1.10550 0.552750 0.833347i \(-0.313579\pi\)
0.552750 + 0.833347i \(0.313579\pi\)
\(432\) 5.49500 0.264378
\(433\) 0.363609 0.0174739 0.00873696 0.999962i \(-0.497219\pi\)
0.00873696 + 0.999962i \(0.497219\pi\)
\(434\) 17.1775 0.824545
\(435\) 21.1724 1.01514
\(436\) 10.4020 0.498166
\(437\) −14.6756 −0.702031
\(438\) 1.75081 0.0836567
\(439\) −1.56165 −0.0745333 −0.0372666 0.999305i \(-0.511865\pi\)
−0.0372666 + 0.999305i \(0.511865\pi\)
\(440\) 0.987553 0.0470798
\(441\) −0.603422 −0.0287344
\(442\) −14.7567 −0.701904
\(443\) 17.7606 0.843831 0.421915 0.906635i \(-0.361358\pi\)
0.421915 + 0.906635i \(0.361358\pi\)
\(444\) 6.82429 0.323866
\(445\) −9.99114 −0.473626
\(446\) −0.685057 −0.0324384
\(447\) 20.3763 0.963766
\(448\) −2.90280 −0.137145
\(449\) −23.4349 −1.10596 −0.552982 0.833193i \(-0.686510\pi\)
−0.552982 + 0.833193i \(0.686510\pi\)
\(450\) 1.01785 0.0479820
\(451\) −2.94225 −0.138545
\(452\) −4.47004 −0.210253
\(453\) 34.1983 1.60678
\(454\) −15.0151 −0.704692
\(455\) −24.1815 −1.13365
\(456\) 3.46392 0.162213
\(457\) −21.6662 −1.01350 −0.506750 0.862093i \(-0.669153\pi\)
−0.506750 + 0.862093i \(0.669153\pi\)
\(458\) 8.40883 0.392919
\(459\) −15.6780 −0.731785
\(460\) 10.9542 0.510741
\(461\) −13.0752 −0.608974 −0.304487 0.952516i \(-0.598485\pi\)
−0.304487 + 0.952516i \(0.598485\pi\)
\(462\) 2.85713 0.132926
\(463\) 20.6552 0.959927 0.479963 0.877288i \(-0.340650\pi\)
0.479963 + 0.877288i \(0.340650\pi\)
\(464\) −8.18878 −0.380155
\(465\) 15.3000 0.709520
\(466\) −25.6289 −1.18723
\(467\) 28.3332 1.31111 0.655553 0.755149i \(-0.272436\pi\)
0.655553 + 0.755149i \(0.272436\pi\)
\(468\) −2.18819 −0.101149
\(469\) −27.8217 −1.28469
\(470\) 8.66139 0.399520
\(471\) 7.93102 0.365442
\(472\) 1.10964 0.0510753
\(473\) 1.44652 0.0665113
\(474\) 9.93275 0.456226
\(475\) 5.19137 0.238196
\(476\) 8.28209 0.379609
\(477\) 1.02783 0.0470613
\(478\) 8.44585 0.386304
\(479\) −18.8996 −0.863546 −0.431773 0.901982i \(-0.642112\pi\)
−0.431773 + 0.901982i \(0.642112\pi\)
\(480\) −2.58553 −0.118013
\(481\) −21.9874 −1.00254
\(482\) −3.39704 −0.154731
\(483\) 31.6919 1.44203
\(484\) −10.6241 −0.482912
\(485\) 6.18171 0.280697
\(486\) −4.36227 −0.197877
\(487\) −12.7492 −0.577721 −0.288861 0.957371i \(-0.593276\pi\)
−0.288861 + 0.957371i \(0.593276\pi\)
\(488\) 6.36668 0.288206
\(489\) 22.5914 1.02162
\(490\) 2.29721 0.103777
\(491\) −10.8195 −0.488276 −0.244138 0.969741i \(-0.578505\pi\)
−0.244138 + 0.969741i \(0.578505\pi\)
\(492\) 7.70316 0.347285
\(493\) 23.3637 1.05225
\(494\) −11.1605 −0.502135
\(495\) −0.417811 −0.0187792
\(496\) −5.91754 −0.265705
\(497\) 11.9373 0.535461
\(498\) 5.21586 0.233728
\(499\) 35.9161 1.60782 0.803912 0.594748i \(-0.202748\pi\)
0.803912 + 0.594748i \(0.202748\pi\)
\(500\) −11.9281 −0.533443
\(501\) −22.7096 −1.01459
\(502\) 24.4826 1.09271
\(503\) −4.54899 −0.202830 −0.101415 0.994844i \(-0.532337\pi\)
−0.101415 + 0.994844i \(0.532337\pi\)
\(504\) 1.22811 0.0547043
\(505\) −1.72197 −0.0766266
\(506\) 4.17006 0.185382
\(507\) −22.0736 −0.980321
\(508\) 4.96090 0.220104
\(509\) 22.9769 1.01843 0.509217 0.860638i \(-0.329935\pi\)
0.509217 + 0.860638i \(0.329935\pi\)
\(510\) 7.37687 0.326653
\(511\) 3.16596 0.140054
\(512\) 1.00000 0.0441942
\(513\) −11.8573 −0.523511
\(514\) −28.4841 −1.25638
\(515\) −23.9184 −1.05397
\(516\) −3.78717 −0.166721
\(517\) 3.29724 0.145012
\(518\) 12.3403 0.542200
\(519\) 17.5367 0.769774
\(520\) 8.33040 0.365312
\(521\) 29.6392 1.29852 0.649259 0.760567i \(-0.275079\pi\)
0.649259 + 0.760567i \(0.275079\pi\)
\(522\) 3.46448 0.151636
\(523\) 2.26804 0.0991743 0.0495871 0.998770i \(-0.484209\pi\)
0.0495871 + 0.998770i \(0.484209\pi\)
\(524\) −11.7767 −0.514468
\(525\) −11.2107 −0.489276
\(526\) −7.29287 −0.317984
\(527\) 16.8835 0.735459
\(528\) −0.984265 −0.0428347
\(529\) 23.2552 1.01110
\(530\) −3.91294 −0.169967
\(531\) −0.469462 −0.0203729
\(532\) 6.26375 0.271568
\(533\) −24.8190 −1.07503
\(534\) 9.95788 0.430920
\(535\) 26.0882 1.12789
\(536\) 9.58442 0.413984
\(537\) 21.8970 0.944924
\(538\) 13.1350 0.566292
\(539\) 0.874507 0.0376677
\(540\) 8.85047 0.380864
\(541\) −34.9925 −1.50445 −0.752223 0.658909i \(-0.771018\pi\)
−0.752223 + 0.658909i \(0.771018\pi\)
\(542\) −6.14537 −0.263966
\(543\) 17.8976 0.768061
\(544\) −2.85314 −0.122327
\(545\) 16.7539 0.717659
\(546\) 24.1010 1.03143
\(547\) 28.0256 1.19829 0.599144 0.800641i \(-0.295508\pi\)
0.599144 + 0.800641i \(0.295508\pi\)
\(548\) −4.65592 −0.198891
\(549\) −2.69360 −0.114960
\(550\) −1.47512 −0.0628992
\(551\) 17.6700 0.752767
\(552\) −10.9177 −0.464688
\(553\) 17.9612 0.763790
\(554\) 10.7915 0.458488
\(555\) 10.9915 0.466563
\(556\) −20.3902 −0.864737
\(557\) 27.9829 1.18567 0.592836 0.805323i \(-0.298008\pi\)
0.592836 + 0.805323i \(0.298008\pi\)
\(558\) 2.50357 0.105985
\(559\) 12.2020 0.516090
\(560\) −4.67538 −0.197571
\(561\) 2.80824 0.118564
\(562\) −21.2837 −0.897798
\(563\) 16.8376 0.709619 0.354810 0.934939i \(-0.384546\pi\)
0.354810 + 0.934939i \(0.384546\pi\)
\(564\) −8.63256 −0.363496
\(565\) −7.19963 −0.302891
\(566\) 9.37486 0.394055
\(567\) 21.9213 0.920609
\(568\) −4.11233 −0.172550
\(569\) −13.5294 −0.567181 −0.283591 0.958945i \(-0.591526\pi\)
−0.283591 + 0.958945i \(0.591526\pi\)
\(570\) 5.57913 0.233684
\(571\) −1.44675 −0.0605446 −0.0302723 0.999542i \(-0.509637\pi\)
−0.0302723 + 0.999542i \(0.509637\pi\)
\(572\) 3.17123 0.132596
\(573\) 1.92282 0.0803271
\(574\) 13.9295 0.581407
\(575\) −16.3623 −0.682357
\(576\) −0.423077 −0.0176282
\(577\) 11.4814 0.477975 0.238988 0.971023i \(-0.423184\pi\)
0.238988 + 0.971023i \(0.423184\pi\)
\(578\) −8.85962 −0.368512
\(579\) 24.5708 1.02113
\(580\) −13.1892 −0.547652
\(581\) 9.43176 0.391295
\(582\) −6.16113 −0.255387
\(583\) −1.48958 −0.0616923
\(584\) −1.09065 −0.0451316
\(585\) −3.52440 −0.145716
\(586\) −9.99871 −0.413043
\(587\) −2.72740 −0.112572 −0.0562860 0.998415i \(-0.517926\pi\)
−0.0562860 + 0.998415i \(0.517926\pi\)
\(588\) −2.28956 −0.0944200
\(589\) 12.7690 0.526139
\(590\) 1.78723 0.0735792
\(591\) −19.0639 −0.784184
\(592\) −4.25115 −0.174721
\(593\) 10.0423 0.412387 0.206194 0.978511i \(-0.433892\pi\)
0.206194 + 0.978511i \(0.433892\pi\)
\(594\) 3.36922 0.138241
\(595\) 13.3395 0.546866
\(596\) −12.6933 −0.519938
\(597\) −18.2279 −0.746019
\(598\) 35.1761 1.43846
\(599\) 7.34230 0.299998 0.149999 0.988686i \(-0.452073\pi\)
0.149999 + 0.988686i \(0.452073\pi\)
\(600\) 3.86203 0.157667
\(601\) 40.5772 1.65518 0.827589 0.561334i \(-0.189712\pi\)
0.827589 + 0.561334i \(0.189712\pi\)
\(602\) −6.84829 −0.279115
\(603\) −4.05494 −0.165130
\(604\) −21.3037 −0.866834
\(605\) −17.1116 −0.695684
\(606\) 1.71624 0.0697173
\(607\) −35.6343 −1.44635 −0.723175 0.690664i \(-0.757318\pi\)
−0.723175 + 0.690664i \(0.757318\pi\)
\(608\) −2.15783 −0.0875115
\(609\) −38.1582 −1.54625
\(610\) 10.2545 0.415191
\(611\) 27.8135 1.12521
\(612\) 1.20709 0.0487939
\(613\) −11.7896 −0.476179 −0.238089 0.971243i \(-0.576521\pi\)
−0.238089 + 0.971243i \(0.576521\pi\)
\(614\) 20.1444 0.812963
\(615\) 12.4070 0.500300
\(616\) −1.77983 −0.0717115
\(617\) 6.84209 0.275452 0.137726 0.990470i \(-0.456021\pi\)
0.137726 + 0.990470i \(0.456021\pi\)
\(618\) 23.8388 0.958936
\(619\) −13.6702 −0.549452 −0.274726 0.961523i \(-0.588587\pi\)
−0.274726 + 0.961523i \(0.588587\pi\)
\(620\) −9.53104 −0.382776
\(621\) 37.3721 1.49969
\(622\) −4.42643 −0.177484
\(623\) 18.0067 0.721423
\(624\) −8.30266 −0.332373
\(625\) −7.18281 −0.287313
\(626\) −14.6136 −0.584077
\(627\) 2.12388 0.0848194
\(628\) −4.94059 −0.197151
\(629\) 12.1291 0.483619
\(630\) 1.97804 0.0788071
\(631\) 18.6938 0.744187 0.372094 0.928195i \(-0.378640\pi\)
0.372094 + 0.928195i \(0.378640\pi\)
\(632\) −6.18755 −0.246127
\(633\) −40.7786 −1.62081
\(634\) 7.70700 0.306084
\(635\) 7.99024 0.317083
\(636\) 3.89991 0.154641
\(637\) 7.37681 0.292280
\(638\) −5.02089 −0.198779
\(639\) 1.73983 0.0688267
\(640\) 1.61064 0.0636662
\(641\) −23.1132 −0.912915 −0.456457 0.889745i \(-0.650882\pi\)
−0.456457 + 0.889745i \(0.650882\pi\)
\(642\) −26.0013 −1.02619
\(643\) −27.2569 −1.07491 −0.537454 0.843293i \(-0.680614\pi\)
−0.537454 + 0.843293i \(0.680614\pi\)
\(644\) −19.7423 −0.777956
\(645\) −6.09978 −0.240179
\(646\) 6.15658 0.242227
\(647\) −38.4786 −1.51275 −0.756374 0.654139i \(-0.773031\pi\)
−0.756374 + 0.654139i \(0.773031\pi\)
\(648\) −7.55178 −0.296662
\(649\) 0.680367 0.0267067
\(650\) −12.4432 −0.488062
\(651\) −27.5746 −1.08074
\(652\) −14.0732 −0.551149
\(653\) −3.54866 −0.138870 −0.0694349 0.997586i \(-0.522120\pi\)
−0.0694349 + 0.997586i \(0.522120\pi\)
\(654\) −16.6981 −0.652949
\(655\) −18.9681 −0.741143
\(656\) −4.79864 −0.187356
\(657\) 0.461430 0.0180021
\(658\) −15.6101 −0.608546
\(659\) 5.33248 0.207724 0.103862 0.994592i \(-0.466880\pi\)
0.103862 + 0.994592i \(0.466880\pi\)
\(660\) −1.58530 −0.0617077
\(661\) −36.9767 −1.43823 −0.719113 0.694893i \(-0.755452\pi\)
−0.719113 + 0.694893i \(0.755452\pi\)
\(662\) −13.5935 −0.528328
\(663\) 23.6886 0.919990
\(664\) −3.24919 −0.126093
\(665\) 10.0887 0.391222
\(666\) 1.79856 0.0696929
\(667\) −55.6929 −2.15644
\(668\) 14.1468 0.547356
\(669\) 1.09971 0.0425172
\(670\) 15.4371 0.596386
\(671\) 3.90369 0.150700
\(672\) 4.65981 0.179756
\(673\) 33.6190 1.29592 0.647960 0.761675i \(-0.275623\pi\)
0.647960 + 0.761675i \(0.275623\pi\)
\(674\) 7.20994 0.277717
\(675\) −13.2200 −0.508839
\(676\) 13.7506 0.528869
\(677\) 17.2853 0.664329 0.332164 0.943222i \(-0.392221\pi\)
0.332164 + 0.943222i \(0.392221\pi\)
\(678\) 7.17566 0.275580
\(679\) −11.1411 −0.427555
\(680\) −4.59538 −0.176225
\(681\) 24.1034 0.923644
\(682\) −3.62830 −0.138935
\(683\) 15.8935 0.608149 0.304075 0.952648i \(-0.401653\pi\)
0.304075 + 0.952648i \(0.401653\pi\)
\(684\) 0.912927 0.0349066
\(685\) −7.49903 −0.286523
\(686\) 16.1794 0.617734
\(687\) −13.4985 −0.515001
\(688\) 2.35920 0.0899436
\(689\) −12.5652 −0.478697
\(690\) −17.5845 −0.669431
\(691\) 52.1085 1.98230 0.991150 0.132743i \(-0.0423786\pi\)
0.991150 + 0.132743i \(0.0423786\pi\)
\(692\) −10.9244 −0.415282
\(693\) 0.753006 0.0286043
\(694\) 9.99912 0.379561
\(695\) −32.8413 −1.24574
\(696\) 13.1453 0.498271
\(697\) 13.6912 0.518590
\(698\) 20.8433 0.788932
\(699\) 41.1415 1.55611
\(700\) 6.98366 0.263957
\(701\) −31.7666 −1.19981 −0.599903 0.800073i \(-0.704794\pi\)
−0.599903 + 0.800073i \(0.704794\pi\)
\(702\) 28.4207 1.07267
\(703\) 9.17326 0.345976
\(704\) 0.613143 0.0231087
\(705\) −13.9040 −0.523654
\(706\) −7.01615 −0.264056
\(707\) 3.10344 0.116717
\(708\) −1.78128 −0.0669447
\(709\) 13.1374 0.493385 0.246693 0.969094i \(-0.420656\pi\)
0.246693 + 0.969094i \(0.420656\pi\)
\(710\) −6.62350 −0.248575
\(711\) 2.61781 0.0981754
\(712\) −6.20320 −0.232475
\(713\) −40.2459 −1.50722
\(714\) −13.2951 −0.497556
\(715\) 5.10772 0.191018
\(716\) −13.6406 −0.509773
\(717\) −13.5580 −0.506331
\(718\) −27.0092 −1.00797
\(719\) 47.4367 1.76909 0.884546 0.466454i \(-0.154469\pi\)
0.884546 + 0.466454i \(0.154469\pi\)
\(720\) −0.681425 −0.0253952
\(721\) 43.1073 1.60540
\(722\) −14.3438 −0.533820
\(723\) 5.45320 0.202807
\(724\) −11.1492 −0.414358
\(725\) 19.7008 0.731671
\(726\) 17.0546 0.632955
\(727\) −30.8221 −1.14313 −0.571564 0.820558i \(-0.693663\pi\)
−0.571564 + 0.820558i \(0.693663\pi\)
\(728\) −15.0136 −0.556441
\(729\) 29.6580 1.09844
\(730\) −1.75665 −0.0650167
\(731\) −6.73111 −0.248959
\(732\) −10.2203 −0.377754
\(733\) −3.36484 −0.124283 −0.0621416 0.998067i \(-0.519793\pi\)
−0.0621416 + 0.998067i \(0.519793\pi\)
\(734\) −24.2512 −0.895128
\(735\) −3.68767 −0.136022
\(736\) 6.80112 0.250693
\(737\) 5.87661 0.216468
\(738\) 2.03019 0.0747325
\(739\) −32.1841 −1.18391 −0.591955 0.805971i \(-0.701644\pi\)
−0.591955 + 0.805971i \(0.701644\pi\)
\(740\) −6.84708 −0.251704
\(741\) 17.9157 0.658151
\(742\) 7.05215 0.258893
\(743\) 33.2602 1.22020 0.610099 0.792325i \(-0.291130\pi\)
0.610099 + 0.792325i \(0.291130\pi\)
\(744\) 9.49931 0.348262
\(745\) −20.4444 −0.749023
\(746\) −36.4166 −1.33331
\(747\) 1.37466 0.0502960
\(748\) −1.74938 −0.0639636
\(749\) −47.0178 −1.71799
\(750\) 19.1480 0.699186
\(751\) 0.749297 0.0273422 0.0136711 0.999907i \(-0.495648\pi\)
0.0136711 + 0.999907i \(0.495648\pi\)
\(752\) 5.37760 0.196101
\(753\) −39.3014 −1.43222
\(754\) −42.3532 −1.54241
\(755\) −34.3126 −1.24876
\(756\) −15.9509 −0.580128
\(757\) 34.8482 1.26658 0.633290 0.773915i \(-0.281704\pi\)
0.633290 + 0.773915i \(0.281704\pi\)
\(758\) 27.9204 1.01411
\(759\) −6.69411 −0.242981
\(760\) −3.47549 −0.126069
\(761\) 11.8636 0.430053 0.215027 0.976608i \(-0.431016\pi\)
0.215027 + 0.976608i \(0.431016\pi\)
\(762\) −7.96364 −0.288492
\(763\) −30.1950 −1.09313
\(764\) −1.19781 −0.0433353
\(765\) 1.94420 0.0702926
\(766\) −32.6657 −1.18026
\(767\) 5.73916 0.207229
\(768\) −1.60528 −0.0579255
\(769\) 15.6706 0.565097 0.282549 0.959253i \(-0.408820\pi\)
0.282549 + 0.959253i \(0.408820\pi\)
\(770\) −2.86667 −0.103308
\(771\) 45.7249 1.64674
\(772\) −15.3062 −0.550884
\(773\) −23.8886 −0.859212 −0.429606 0.903016i \(-0.641348\pi\)
−0.429606 + 0.903016i \(0.641348\pi\)
\(774\) −0.998122 −0.0358767
\(775\) 14.2366 0.511394
\(776\) 3.83804 0.137778
\(777\) −19.8096 −0.710664
\(778\) 26.0544 0.934095
\(779\) 10.3546 0.370994
\(780\) −13.3726 −0.478817
\(781\) −2.52145 −0.0902244
\(782\) −19.4045 −0.693904
\(783\) −44.9973 −1.60807
\(784\) 1.42627 0.0509382
\(785\) −7.95752 −0.284016
\(786\) 18.9049 0.674316
\(787\) 15.8142 0.563714 0.281857 0.959456i \(-0.409050\pi\)
0.281857 + 0.959456i \(0.409050\pi\)
\(788\) 11.8758 0.423056
\(789\) 11.7071 0.416784
\(790\) −9.96593 −0.354572
\(791\) 12.9756 0.461361
\(792\) −0.259406 −0.00921760
\(793\) 32.9291 1.16935
\(794\) −9.13473 −0.324180
\(795\) 6.28136 0.222777
\(796\) 11.3550 0.402467
\(797\) 17.8895 0.633679 0.316840 0.948479i \(-0.397378\pi\)
0.316840 + 0.948479i \(0.397378\pi\)
\(798\) −10.0551 −0.355946
\(799\) −15.3430 −0.542797
\(800\) −2.40583 −0.0850590
\(801\) 2.62443 0.0927297
\(802\) −12.5481 −0.443090
\(803\) −0.668727 −0.0235989
\(804\) −15.3857 −0.542611
\(805\) −31.7978 −1.12073
\(806\) −30.6061 −1.07805
\(807\) −21.0854 −0.742242
\(808\) −1.06912 −0.0376115
\(809\) 35.8976 1.26209 0.631047 0.775745i \(-0.282626\pi\)
0.631047 + 0.775745i \(0.282626\pi\)
\(810\) −12.1632 −0.427372
\(811\) −6.17127 −0.216703 −0.108351 0.994113i \(-0.534557\pi\)
−0.108351 + 0.994113i \(0.534557\pi\)
\(812\) 23.7704 0.834179
\(813\) 9.86503 0.345982
\(814\) −2.60656 −0.0913600
\(815\) −22.6669 −0.793986
\(816\) 4.58008 0.160335
\(817\) −5.09074 −0.178103
\(818\) 19.3480 0.676486
\(819\) 6.35190 0.221953
\(820\) −7.72890 −0.269905
\(821\) −19.8132 −0.691484 −0.345742 0.938330i \(-0.612373\pi\)
−0.345742 + 0.938330i \(0.612373\pi\)
\(822\) 7.47406 0.260688
\(823\) 42.6614 1.48708 0.743542 0.668689i \(-0.233144\pi\)
0.743542 + 0.668689i \(0.233144\pi\)
\(824\) −14.8502 −0.517332
\(825\) 2.36798 0.0824424
\(826\) −3.22107 −0.112075
\(827\) 45.7757 1.59178 0.795889 0.605443i \(-0.207004\pi\)
0.795889 + 0.605443i \(0.207004\pi\)
\(828\) −2.87739 −0.0999964
\(829\) −34.1301 −1.18539 −0.592693 0.805428i \(-0.701935\pi\)
−0.592693 + 0.805428i \(0.701935\pi\)
\(830\) −5.23328 −0.181650
\(831\) −17.3234 −0.600943
\(832\) 5.17210 0.179310
\(833\) −4.06934 −0.140994
\(834\) 32.7320 1.13342
\(835\) 22.7854 0.788522
\(836\) −1.32306 −0.0457589
\(837\) −32.5169 −1.12395
\(838\) −1.07450 −0.0371180
\(839\) −55.3500 −1.91089 −0.955447 0.295162i \(-0.904626\pi\)
−0.955447 + 0.295162i \(0.904626\pi\)
\(840\) 7.50529 0.258957
\(841\) 38.0562 1.31228
\(842\) −5.64351 −0.194488
\(843\) 34.1663 1.17675
\(844\) 25.4028 0.874401
\(845\) 22.1473 0.761890
\(846\) −2.27514 −0.0782209
\(847\) 30.8396 1.05966
\(848\) −2.42943 −0.0834269
\(849\) −15.0493 −0.516490
\(850\) 6.86416 0.235439
\(851\) −28.9126 −0.991111
\(852\) 6.60144 0.226162
\(853\) 20.2567 0.693576 0.346788 0.937944i \(-0.387272\pi\)
0.346788 + 0.937944i \(0.387272\pi\)
\(854\) −18.4812 −0.632415
\(855\) 1.47040 0.0502866
\(856\) 16.1974 0.553615
\(857\) 32.3309 1.10440 0.552202 0.833711i \(-0.313788\pi\)
0.552202 + 0.833711i \(0.313788\pi\)
\(858\) −5.09072 −0.173794
\(859\) 4.78636 0.163309 0.0816543 0.996661i \(-0.473980\pi\)
0.0816543 + 0.996661i \(0.473980\pi\)
\(860\) 3.79982 0.129573
\(861\) −22.3608 −0.762053
\(862\) 22.9508 0.781706
\(863\) −3.49398 −0.118936 −0.0594682 0.998230i \(-0.518941\pi\)
−0.0594682 + 0.998230i \(0.518941\pi\)
\(864\) 5.49500 0.186944
\(865\) −17.5952 −0.598256
\(866\) 0.363609 0.0123559
\(867\) 14.2222 0.483010
\(868\) 17.1775 0.583041
\(869\) −3.79385 −0.128698
\(870\) 21.1724 0.717810
\(871\) 49.5715 1.67967
\(872\) 10.4020 0.352256
\(873\) −1.62378 −0.0549568
\(874\) −14.6756 −0.496411
\(875\) 34.6251 1.17054
\(876\) 1.75081 0.0591542
\(877\) 18.7186 0.632083 0.316041 0.948745i \(-0.397646\pi\)
0.316041 + 0.948745i \(0.397646\pi\)
\(878\) −1.56165 −0.0527030
\(879\) 16.0507 0.541378
\(880\) 0.987553 0.0332904
\(881\) −14.0115 −0.472059 −0.236030 0.971746i \(-0.575846\pi\)
−0.236030 + 0.971746i \(0.575846\pi\)
\(882\) −0.603422 −0.0203183
\(883\) 40.6697 1.36864 0.684321 0.729181i \(-0.260099\pi\)
0.684321 + 0.729181i \(0.260099\pi\)
\(884\) −14.7567 −0.496321
\(885\) −2.86901 −0.0964406
\(886\) 17.7606 0.596678
\(887\) −34.9929 −1.17495 −0.587473 0.809244i \(-0.699877\pi\)
−0.587473 + 0.809244i \(0.699877\pi\)
\(888\) 6.82429 0.229008
\(889\) −14.4005 −0.482978
\(890\) −9.99114 −0.334904
\(891\) −4.63032 −0.155121
\(892\) −0.685057 −0.0229374
\(893\) −11.6039 −0.388311
\(894\) 20.3763 0.681485
\(895\) −21.9701 −0.734380
\(896\) −2.90280 −0.0969759
\(897\) −56.4674 −1.88539
\(898\) −23.4349 −0.782034
\(899\) 48.4575 1.61615
\(900\) 1.01785 0.0339284
\(901\) 6.93148 0.230921
\(902\) −2.94225 −0.0979663
\(903\) 10.9934 0.365838
\(904\) −4.47004 −0.148671
\(905\) −17.9574 −0.596925
\(906\) 34.1983 1.13616
\(907\) −35.5327 −1.17984 −0.589922 0.807460i \(-0.700841\pi\)
−0.589922 + 0.807460i \(0.700841\pi\)
\(908\) −15.0151 −0.498293
\(909\) 0.452319 0.0150025
\(910\) −24.1815 −0.801609
\(911\) −49.1174 −1.62733 −0.813666 0.581333i \(-0.802531\pi\)
−0.813666 + 0.581333i \(0.802531\pi\)
\(912\) 3.46392 0.114702
\(913\) −1.99222 −0.0659327
\(914\) −21.6662 −0.716653
\(915\) −16.4613 −0.544193
\(916\) 8.40883 0.277836
\(917\) 34.1855 1.12890
\(918\) −15.6780 −0.517450
\(919\) 23.4462 0.773420 0.386710 0.922201i \(-0.373611\pi\)
0.386710 + 0.922201i \(0.373611\pi\)
\(920\) 10.9542 0.361148
\(921\) −32.3374 −1.06555
\(922\) −13.0752 −0.430610
\(923\) −21.2694 −0.700090
\(924\) 2.85713 0.0939927
\(925\) 10.2276 0.336280
\(926\) 20.6552 0.678771
\(927\) 6.28278 0.206354
\(928\) −8.18878 −0.268810
\(929\) −2.97924 −0.0977456 −0.0488728 0.998805i \(-0.515563\pi\)
−0.0488728 + 0.998805i \(0.515563\pi\)
\(930\) 15.3000 0.501706
\(931\) −3.07765 −0.100866
\(932\) −25.6289 −0.839501
\(933\) 7.10566 0.232629
\(934\) 28.3332 0.927092
\(935\) −2.81762 −0.0921461
\(936\) −2.18819 −0.0715234
\(937\) 59.1944 1.93380 0.966898 0.255163i \(-0.0821291\pi\)
0.966898 + 0.255163i \(0.0821291\pi\)
\(938\) −27.8217 −0.908410
\(939\) 23.4589 0.765554
\(940\) 8.66139 0.282504
\(941\) 7.58648 0.247312 0.123656 0.992325i \(-0.460538\pi\)
0.123656 + 0.992325i \(0.460538\pi\)
\(942\) 7.93102 0.258407
\(943\) −32.6361 −1.06278
\(944\) 1.10964 0.0361157
\(945\) −25.6912 −0.835734
\(946\) 1.44652 0.0470306
\(947\) −3.45331 −0.112218 −0.0561088 0.998425i \(-0.517869\pi\)
−0.0561088 + 0.998425i \(0.517869\pi\)
\(948\) 9.93275 0.322601
\(949\) −5.64097 −0.183114
\(950\) 5.19137 0.168430
\(951\) −12.3719 −0.401186
\(952\) 8.28209 0.268424
\(953\) −30.3400 −0.982808 −0.491404 0.870932i \(-0.663516\pi\)
−0.491404 + 0.870932i \(0.663516\pi\)
\(954\) 1.02783 0.0332773
\(955\) −1.92925 −0.0624290
\(956\) 8.44585 0.273158
\(957\) 8.05994 0.260541
\(958\) −18.8996 −0.610619
\(959\) 13.5152 0.436430
\(960\) −2.58553 −0.0834477
\(961\) 4.01729 0.129590
\(962\) −21.9874 −0.708901
\(963\) −6.85273 −0.220826
\(964\) −3.39704 −0.109411
\(965\) −24.6529 −0.793605
\(966\) 31.6919 1.01967
\(967\) −43.9810 −1.41433 −0.707166 0.707048i \(-0.750027\pi\)
−0.707166 + 0.707048i \(0.750027\pi\)
\(968\) −10.6241 −0.341470
\(969\) −9.88303 −0.317489
\(970\) 6.18171 0.198483
\(971\) 48.1984 1.54676 0.773380 0.633943i \(-0.218565\pi\)
0.773380 + 0.633943i \(0.218565\pi\)
\(972\) −4.36227 −0.139920
\(973\) 59.1887 1.89750
\(974\) −12.7492 −0.408511
\(975\) 19.9748 0.639706
\(976\) 6.36668 0.203793
\(977\) 0.822113 0.0263017 0.0131509 0.999914i \(-0.495814\pi\)
0.0131509 + 0.999914i \(0.495814\pi\)
\(978\) 22.5914 0.722394
\(979\) −3.80345 −0.121559
\(980\) 2.29721 0.0733817
\(981\) −4.40085 −0.140508
\(982\) −10.8195 −0.345263
\(983\) −21.3221 −0.680070 −0.340035 0.940413i \(-0.610439\pi\)
−0.340035 + 0.940413i \(0.610439\pi\)
\(984\) 7.70316 0.245568
\(985\) 19.1276 0.609456
\(986\) 23.3637 0.744052
\(987\) 25.0586 0.797625
\(988\) −11.1605 −0.355063
\(989\) 16.0452 0.510207
\(990\) −0.417811 −0.0132789
\(991\) 9.59233 0.304710 0.152355 0.988326i \(-0.451314\pi\)
0.152355 + 0.988326i \(0.451314\pi\)
\(992\) −5.91754 −0.187882
\(993\) 21.8214 0.692482
\(994\) 11.9373 0.378628
\(995\) 18.2888 0.579794
\(996\) 5.21586 0.165271
\(997\) 42.4252 1.34362 0.671809 0.740724i \(-0.265517\pi\)
0.671809 + 0.740724i \(0.265517\pi\)
\(998\) 35.9161 1.13690
\(999\) −23.3601 −0.739080
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 6002.2.a.a.1.14 47
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6002.2.a.a.1.14 47 1.1 even 1 trivial