Properties

Label 2001.2.a.l.1.4
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $0$
Dimension $11$
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] = [2001,2,Mod(1,2001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("2001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.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: \(15.9780654445\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.05971\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.05971 q^{2} -1.00000 q^{3} -0.877023 q^{4} -1.30384 q^{5} +1.05971 q^{6} +0.720797 q^{7} +3.04880 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.05971 q^{2} -1.00000 q^{3} -0.877023 q^{4} -1.30384 q^{5} +1.05971 q^{6} +0.720797 q^{7} +3.04880 q^{8} +1.00000 q^{9} +1.38169 q^{10} +4.26781 q^{11} +0.877023 q^{12} +6.49237 q^{13} -0.763833 q^{14} +1.30384 q^{15} -1.47678 q^{16} +1.60761 q^{17} -1.05971 q^{18} +0.0676063 q^{19} +1.14350 q^{20} -0.720797 q^{21} -4.52262 q^{22} +1.00000 q^{23} -3.04880 q^{24} -3.30000 q^{25} -6.88000 q^{26} -1.00000 q^{27} -0.632156 q^{28} -1.00000 q^{29} -1.38169 q^{30} -3.80124 q^{31} -4.53264 q^{32} -4.26781 q^{33} -1.70359 q^{34} -0.939804 q^{35} -0.877023 q^{36} -3.80081 q^{37} -0.0716428 q^{38} -6.49237 q^{39} -3.97515 q^{40} -0.467762 q^{41} +0.763833 q^{42} +0.971410 q^{43} -3.74296 q^{44} -1.30384 q^{45} -1.05971 q^{46} +7.97915 q^{47} +1.47678 q^{48} -6.48045 q^{49} +3.49703 q^{50} -1.60761 q^{51} -5.69396 q^{52} +13.3791 q^{53} +1.05971 q^{54} -5.56454 q^{55} +2.19756 q^{56} -0.0676063 q^{57} +1.05971 q^{58} -4.90374 q^{59} -1.14350 q^{60} +7.29114 q^{61} +4.02820 q^{62} +0.720797 q^{63} +7.75683 q^{64} -8.46502 q^{65} +4.52262 q^{66} +13.6988 q^{67} -1.40991 q^{68} -1.00000 q^{69} +0.995916 q^{70} -0.843676 q^{71} +3.04880 q^{72} -3.56146 q^{73} +4.02774 q^{74} +3.30000 q^{75} -0.0592923 q^{76} +3.07622 q^{77} +6.88000 q^{78} +3.50616 q^{79} +1.92549 q^{80} +1.00000 q^{81} +0.495690 q^{82} -8.90808 q^{83} +0.632156 q^{84} -2.09606 q^{85} -1.02941 q^{86} +1.00000 q^{87} +13.0117 q^{88} +15.1294 q^{89} +1.38169 q^{90} +4.67968 q^{91} -0.877023 q^{92} +3.80124 q^{93} -8.45555 q^{94} -0.0881479 q^{95} +4.53264 q^{96} +0.847630 q^{97} +6.86737 q^{98} +4.26781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.05971 −0.749325 −0.374663 0.927161i \(-0.622241\pi\)
−0.374663 + 0.927161i \(0.622241\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.877023 −0.438512
\(5\) −1.30384 −0.583095 −0.291548 0.956556i \(-0.594170\pi\)
−0.291548 + 0.956556i \(0.594170\pi\)
\(6\) 1.05971 0.432623
\(7\) 0.720797 0.272436 0.136218 0.990679i \(-0.456505\pi\)
0.136218 + 0.990679i \(0.456505\pi\)
\(8\) 3.04880 1.07791
\(9\) 1.00000 0.333333
\(10\) 1.38169 0.436928
\(11\) 4.26781 1.28679 0.643396 0.765534i \(-0.277525\pi\)
0.643396 + 0.765534i \(0.277525\pi\)
\(12\) 0.877023 0.253175
\(13\) 6.49237 1.80066 0.900330 0.435208i \(-0.143325\pi\)
0.900330 + 0.435208i \(0.143325\pi\)
\(14\) −0.763833 −0.204143
\(15\) 1.30384 0.336650
\(16\) −1.47678 −0.369196
\(17\) 1.60761 0.389902 0.194951 0.980813i \(-0.437545\pi\)
0.194951 + 0.980813i \(0.437545\pi\)
\(18\) −1.05971 −0.249775
\(19\) 0.0676063 0.0155100 0.00775498 0.999970i \(-0.497531\pi\)
0.00775498 + 0.999970i \(0.497531\pi\)
\(20\) 1.14350 0.255694
\(21\) −0.720797 −0.157291
\(22\) −4.52262 −0.964226
\(23\) 1.00000 0.208514
\(24\) −3.04880 −0.622333
\(25\) −3.30000 −0.660000
\(26\) −6.88000 −1.34928
\(27\) −1.00000 −0.192450
\(28\) −0.632156 −0.119466
\(29\) −1.00000 −0.185695
\(30\) −1.38169 −0.252260
\(31\) −3.80124 −0.682723 −0.341362 0.939932i \(-0.610888\pi\)
−0.341362 + 0.939932i \(0.610888\pi\)
\(32\) −4.53264 −0.801265
\(33\) −4.26781 −0.742930
\(34\) −1.70359 −0.292163
\(35\) −0.939804 −0.158856
\(36\) −0.877023 −0.146171
\(37\) −3.80081 −0.624849 −0.312425 0.949943i \(-0.601141\pi\)
−0.312425 + 0.949943i \(0.601141\pi\)
\(38\) −0.0716428 −0.0116220
\(39\) −6.49237 −1.03961
\(40\) −3.97515 −0.628526
\(41\) −0.467762 −0.0730521 −0.0365261 0.999333i \(-0.511629\pi\)
−0.0365261 + 0.999333i \(0.511629\pi\)
\(42\) 0.763833 0.117862
\(43\) 0.971410 0.148139 0.0740693 0.997253i \(-0.476401\pi\)
0.0740693 + 0.997253i \(0.476401\pi\)
\(44\) −3.74296 −0.564273
\(45\) −1.30384 −0.194365
\(46\) −1.05971 −0.156245
\(47\) 7.97915 1.16388 0.581939 0.813232i \(-0.302294\pi\)
0.581939 + 0.813232i \(0.302294\pi\)
\(48\) 1.47678 0.213155
\(49\) −6.48045 −0.925779
\(50\) 3.49703 0.494555
\(51\) −1.60761 −0.225110
\(52\) −5.69396 −0.789610
\(53\) 13.3791 1.83776 0.918881 0.394535i \(-0.129094\pi\)
0.918881 + 0.394535i \(0.129094\pi\)
\(54\) 1.05971 0.144208
\(55\) −5.56454 −0.750322
\(56\) 2.19756 0.293662
\(57\) −0.0676063 −0.00895468
\(58\) 1.05971 0.139146
\(59\) −4.90374 −0.638413 −0.319206 0.947685i \(-0.603416\pi\)
−0.319206 + 0.947685i \(0.603416\pi\)
\(60\) −1.14350 −0.147625
\(61\) 7.29114 0.933534 0.466767 0.884380i \(-0.345419\pi\)
0.466767 + 0.884380i \(0.345419\pi\)
\(62\) 4.02820 0.511582
\(63\) 0.720797 0.0908119
\(64\) 7.75683 0.969604
\(65\) −8.46502 −1.04996
\(66\) 4.52262 0.556696
\(67\) 13.6988 1.67358 0.836788 0.547526i \(-0.184430\pi\)
0.836788 + 0.547526i \(0.184430\pi\)
\(68\) −1.40991 −0.170977
\(69\) −1.00000 −0.120386
\(70\) 0.995916 0.119035
\(71\) −0.843676 −0.100126 −0.0500630 0.998746i \(-0.515942\pi\)
−0.0500630 + 0.998746i \(0.515942\pi\)
\(72\) 3.04880 0.359304
\(73\) −3.56146 −0.416837 −0.208419 0.978040i \(-0.566832\pi\)
−0.208419 + 0.978040i \(0.566832\pi\)
\(74\) 4.02774 0.468215
\(75\) 3.30000 0.381051
\(76\) −0.0592923 −0.00680130
\(77\) 3.07622 0.350568
\(78\) 6.88000 0.779007
\(79\) 3.50616 0.394474 0.197237 0.980356i \(-0.436803\pi\)
0.197237 + 0.980356i \(0.436803\pi\)
\(80\) 1.92549 0.215276
\(81\) 1.00000 0.111111
\(82\) 0.495690 0.0547398
\(83\) −8.90808 −0.977789 −0.488894 0.872343i \(-0.662600\pi\)
−0.488894 + 0.872343i \(0.662600\pi\)
\(84\) 0.632156 0.0689738
\(85\) −2.09606 −0.227350
\(86\) −1.02941 −0.111004
\(87\) 1.00000 0.107211
\(88\) 13.0117 1.38705
\(89\) 15.1294 1.60371 0.801856 0.597517i \(-0.203846\pi\)
0.801856 + 0.597517i \(0.203846\pi\)
\(90\) 1.38169 0.145643
\(91\) 4.67968 0.490564
\(92\) −0.877023 −0.0914360
\(93\) 3.80124 0.394170
\(94\) −8.45555 −0.872124
\(95\) −0.0881479 −0.00904378
\(96\) 4.53264 0.462611
\(97\) 0.847630 0.0860637 0.0430319 0.999074i \(-0.486298\pi\)
0.0430319 + 0.999074i \(0.486298\pi\)
\(98\) 6.86737 0.693709
\(99\) 4.26781 0.428931
\(100\) 2.89418 0.289418
\(101\) −4.21499 −0.419407 −0.209704 0.977765i \(-0.567250\pi\)
−0.209704 + 0.977765i \(0.567250\pi\)
\(102\) 1.70359 0.168681
\(103\) −3.25548 −0.320772 −0.160386 0.987054i \(-0.551274\pi\)
−0.160386 + 0.987054i \(0.551274\pi\)
\(104\) 19.7939 1.94095
\(105\) 0.939804 0.0917155
\(106\) −14.1779 −1.37708
\(107\) 9.91828 0.958836 0.479418 0.877587i \(-0.340848\pi\)
0.479418 + 0.877587i \(0.340848\pi\)
\(108\) 0.877023 0.0843916
\(109\) −14.9445 −1.43142 −0.715711 0.698396i \(-0.753897\pi\)
−0.715711 + 0.698396i \(0.753897\pi\)
\(110\) 5.89677 0.562235
\(111\) 3.80081 0.360757
\(112\) −1.06446 −0.100582
\(113\) 9.05430 0.851757 0.425879 0.904780i \(-0.359965\pi\)
0.425879 + 0.904780i \(0.359965\pi\)
\(114\) 0.0716428 0.00670997
\(115\) −1.30384 −0.121584
\(116\) 0.877023 0.0814296
\(117\) 6.49237 0.600220
\(118\) 5.19653 0.478379
\(119\) 1.15876 0.106223
\(120\) 3.97515 0.362880
\(121\) 7.21416 0.655833
\(122\) −7.72646 −0.699521
\(123\) 0.467762 0.0421767
\(124\) 3.33378 0.299382
\(125\) 10.8219 0.967938
\(126\) −0.763833 −0.0680476
\(127\) −16.8234 −1.49284 −0.746420 0.665476i \(-0.768229\pi\)
−0.746420 + 0.665476i \(0.768229\pi\)
\(128\) 0.845320 0.0747164
\(129\) −0.971410 −0.0855279
\(130\) 8.97043 0.786759
\(131\) 20.0112 1.74838 0.874192 0.485581i \(-0.161392\pi\)
0.874192 + 0.485581i \(0.161392\pi\)
\(132\) 3.74296 0.325783
\(133\) 0.0487304 0.00422547
\(134\) −14.5167 −1.25405
\(135\) 1.30384 0.112217
\(136\) 4.90127 0.420280
\(137\) −17.5827 −1.50219 −0.751097 0.660192i \(-0.770475\pi\)
−0.751097 + 0.660192i \(0.770475\pi\)
\(138\) 1.05971 0.0902082
\(139\) −11.2785 −0.956634 −0.478317 0.878187i \(-0.658753\pi\)
−0.478317 + 0.878187i \(0.658753\pi\)
\(140\) 0.824230 0.0696602
\(141\) −7.97915 −0.671966
\(142\) 0.894049 0.0750269
\(143\) 27.7082 2.31707
\(144\) −1.47678 −0.123065
\(145\) 1.30384 0.108278
\(146\) 3.77410 0.312347
\(147\) 6.48045 0.534499
\(148\) 3.33340 0.274004
\(149\) 8.68520 0.711519 0.355760 0.934578i \(-0.384222\pi\)
0.355760 + 0.934578i \(0.384222\pi\)
\(150\) −3.49703 −0.285531
\(151\) −3.77830 −0.307474 −0.153737 0.988112i \(-0.549131\pi\)
−0.153737 + 0.988112i \(0.549131\pi\)
\(152\) 0.206118 0.0167184
\(153\) 1.60761 0.129967
\(154\) −3.25989 −0.262689
\(155\) 4.95621 0.398093
\(156\) 5.69396 0.455882
\(157\) −22.4357 −1.79056 −0.895280 0.445503i \(-0.853025\pi\)
−0.895280 + 0.445503i \(0.853025\pi\)
\(158\) −3.71550 −0.295589
\(159\) −13.3791 −1.06103
\(160\) 5.90984 0.467214
\(161\) 0.720797 0.0568068
\(162\) −1.05971 −0.0832584
\(163\) 9.58430 0.750701 0.375350 0.926883i \(-0.377522\pi\)
0.375350 + 0.926883i \(0.377522\pi\)
\(164\) 0.410238 0.0320342
\(165\) 5.56454 0.433199
\(166\) 9.43994 0.732682
\(167\) −22.7911 −1.76363 −0.881816 0.471594i \(-0.843679\pi\)
−0.881816 + 0.471594i \(0.843679\pi\)
\(168\) −2.19756 −0.169546
\(169\) 29.1509 2.24238
\(170\) 2.22121 0.170359
\(171\) 0.0676063 0.00516999
\(172\) −0.851949 −0.0649605
\(173\) 3.11958 0.237177 0.118589 0.992943i \(-0.462163\pi\)
0.118589 + 0.992943i \(0.462163\pi\)
\(174\) −1.05971 −0.0803361
\(175\) −2.37863 −0.179808
\(176\) −6.30262 −0.475078
\(177\) 4.90374 0.368588
\(178\) −16.0327 −1.20170
\(179\) −4.43515 −0.331499 −0.165749 0.986168i \(-0.553004\pi\)
−0.165749 + 0.986168i \(0.553004\pi\)
\(180\) 1.14350 0.0852313
\(181\) 7.57878 0.563326 0.281663 0.959513i \(-0.409114\pi\)
0.281663 + 0.959513i \(0.409114\pi\)
\(182\) −4.95909 −0.367592
\(183\) −7.29114 −0.538976
\(184\) 3.04880 0.224760
\(185\) 4.95565 0.364347
\(186\) −4.02820 −0.295362
\(187\) 6.86095 0.501722
\(188\) −6.99790 −0.510374
\(189\) −0.720797 −0.0524303
\(190\) 0.0934108 0.00677673
\(191\) 23.8728 1.72738 0.863688 0.504026i \(-0.168149\pi\)
0.863688 + 0.504026i \(0.168149\pi\)
\(192\) −7.75683 −0.559801
\(193\) −23.7901 −1.71245 −0.856224 0.516605i \(-0.827196\pi\)
−0.856224 + 0.516605i \(0.827196\pi\)
\(194\) −0.898238 −0.0644897
\(195\) 8.46502 0.606192
\(196\) 5.68351 0.405965
\(197\) 10.2899 0.733125 0.366562 0.930393i \(-0.380535\pi\)
0.366562 + 0.930393i \(0.380535\pi\)
\(198\) −4.52262 −0.321409
\(199\) 6.69895 0.474876 0.237438 0.971403i \(-0.423692\pi\)
0.237438 + 0.971403i \(0.423692\pi\)
\(200\) −10.0610 −0.711423
\(201\) −13.6988 −0.966240
\(202\) 4.46665 0.314273
\(203\) −0.720797 −0.0505900
\(204\) 1.40991 0.0987133
\(205\) 0.609887 0.0425964
\(206\) 3.44986 0.240363
\(207\) 1.00000 0.0695048
\(208\) −9.58783 −0.664796
\(209\) 0.288531 0.0199581
\(210\) −0.995916 −0.0687247
\(211\) 19.4730 1.34058 0.670288 0.742101i \(-0.266170\pi\)
0.670288 + 0.742101i \(0.266170\pi\)
\(212\) −11.7338 −0.805880
\(213\) 0.843676 0.0578077
\(214\) −10.5105 −0.718480
\(215\) −1.26656 −0.0863789
\(216\) −3.04880 −0.207444
\(217\) −2.73992 −0.185998
\(218\) 15.8368 1.07260
\(219\) 3.56146 0.240661
\(220\) 4.88023 0.329025
\(221\) 10.4372 0.702081
\(222\) −4.02774 −0.270324
\(223\) 5.45268 0.365138 0.182569 0.983193i \(-0.441559\pi\)
0.182569 + 0.983193i \(0.441559\pi\)
\(224\) −3.26711 −0.218293
\(225\) −3.30000 −0.220000
\(226\) −9.59490 −0.638243
\(227\) 12.7976 0.849407 0.424704 0.905332i \(-0.360378\pi\)
0.424704 + 0.905332i \(0.360378\pi\)
\(228\) 0.0592923 0.00392673
\(229\) −17.9481 −1.18604 −0.593021 0.805187i \(-0.702065\pi\)
−0.593021 + 0.805187i \(0.702065\pi\)
\(230\) 1.38169 0.0911058
\(231\) −3.07622 −0.202400
\(232\) −3.04880 −0.200163
\(233\) 24.8070 1.62516 0.812579 0.582851i \(-0.198063\pi\)
0.812579 + 0.582851i \(0.198063\pi\)
\(234\) −6.88000 −0.449760
\(235\) −10.4035 −0.678652
\(236\) 4.30070 0.279952
\(237\) −3.50616 −0.227750
\(238\) −1.22794 −0.0795957
\(239\) 6.47432 0.418789 0.209394 0.977831i \(-0.432851\pi\)
0.209394 + 0.977831i \(0.432851\pi\)
\(240\) −1.92549 −0.124290
\(241\) −1.06870 −0.0688413 −0.0344207 0.999407i \(-0.510959\pi\)
−0.0344207 + 0.999407i \(0.510959\pi\)
\(242\) −7.64489 −0.491432
\(243\) −1.00000 −0.0641500
\(244\) −6.39450 −0.409366
\(245\) 8.44948 0.539817
\(246\) −0.495690 −0.0316040
\(247\) 0.438925 0.0279282
\(248\) −11.5892 −0.735916
\(249\) 8.90808 0.564526
\(250\) −11.4680 −0.725300
\(251\) −10.6611 −0.672920 −0.336460 0.941698i \(-0.609230\pi\)
−0.336460 + 0.941698i \(0.609230\pi\)
\(252\) −0.632156 −0.0398221
\(253\) 4.26781 0.268315
\(254\) 17.8279 1.11862
\(255\) 2.09606 0.131261
\(256\) −16.4095 −1.02559
\(257\) 26.4765 1.65156 0.825781 0.563991i \(-0.190735\pi\)
0.825781 + 0.563991i \(0.190735\pi\)
\(258\) 1.02941 0.0640882
\(259\) −2.73961 −0.170231
\(260\) 7.42402 0.460418
\(261\) −1.00000 −0.0618984
\(262\) −21.2059 −1.31011
\(263\) 3.04107 0.187520 0.0937602 0.995595i \(-0.470111\pi\)
0.0937602 + 0.995595i \(0.470111\pi\)
\(264\) −13.0117 −0.800814
\(265\) −17.4442 −1.07159
\(266\) −0.0516399 −0.00316625
\(267\) −15.1294 −0.925904
\(268\) −12.0142 −0.733883
\(269\) −30.1319 −1.83718 −0.918589 0.395215i \(-0.870670\pi\)
−0.918589 + 0.395215i \(0.870670\pi\)
\(270\) −1.38169 −0.0840868
\(271\) 18.0654 1.09740 0.548699 0.836020i \(-0.315123\pi\)
0.548699 + 0.836020i \(0.315123\pi\)
\(272\) −2.37409 −0.143950
\(273\) −4.67968 −0.283227
\(274\) 18.6325 1.12563
\(275\) −14.0838 −0.849283
\(276\) 0.877023 0.0527906
\(277\) 15.0741 0.905712 0.452856 0.891584i \(-0.350405\pi\)
0.452856 + 0.891584i \(0.350405\pi\)
\(278\) 11.9519 0.716830
\(279\) −3.80124 −0.227574
\(280\) −2.86527 −0.171233
\(281\) 17.4085 1.03850 0.519252 0.854621i \(-0.326211\pi\)
0.519252 + 0.854621i \(0.326211\pi\)
\(282\) 8.45555 0.503521
\(283\) 27.6295 1.64240 0.821202 0.570638i \(-0.193304\pi\)
0.821202 + 0.570638i \(0.193304\pi\)
\(284\) 0.739924 0.0439064
\(285\) 0.0881479 0.00522143
\(286\) −29.3625 −1.73624
\(287\) −0.337161 −0.0199020
\(288\) −4.53264 −0.267088
\(289\) −14.4156 −0.847977
\(290\) −1.38169 −0.0811355
\(291\) −0.847630 −0.0496889
\(292\) 3.12348 0.182788
\(293\) 9.65321 0.563946 0.281973 0.959422i \(-0.409011\pi\)
0.281973 + 0.959422i \(0.409011\pi\)
\(294\) −6.86737 −0.400513
\(295\) 6.39370 0.372256
\(296\) −11.5879 −0.673533
\(297\) −4.26781 −0.247643
\(298\) −9.20376 −0.533159
\(299\) 6.49237 0.375464
\(300\) −2.89418 −0.167095
\(301\) 0.700189 0.0403582
\(302\) 4.00389 0.230398
\(303\) 4.21499 0.242145
\(304\) −0.0998399 −0.00572621
\(305\) −9.50648 −0.544339
\(306\) −1.70359 −0.0973878
\(307\) 23.4872 1.34048 0.670242 0.742143i \(-0.266190\pi\)
0.670242 + 0.742143i \(0.266190\pi\)
\(308\) −2.69792 −0.153728
\(309\) 3.25548 0.185198
\(310\) −5.25213 −0.298301
\(311\) 10.2227 0.579679 0.289839 0.957075i \(-0.406398\pi\)
0.289839 + 0.957075i \(0.406398\pi\)
\(312\) −19.7939 −1.12061
\(313\) 4.95500 0.280073 0.140036 0.990146i \(-0.455278\pi\)
0.140036 + 0.990146i \(0.455278\pi\)
\(314\) 23.7752 1.34171
\(315\) −0.939804 −0.0529520
\(316\) −3.07498 −0.172981
\(317\) 6.20695 0.348617 0.174309 0.984691i \(-0.444231\pi\)
0.174309 + 0.984691i \(0.444231\pi\)
\(318\) 14.1779 0.795058
\(319\) −4.26781 −0.238951
\(320\) −10.1137 −0.565372
\(321\) −9.91828 −0.553584
\(322\) −0.763833 −0.0425667
\(323\) 0.108684 0.00604736
\(324\) −0.877023 −0.0487235
\(325\) −21.4248 −1.18844
\(326\) −10.1565 −0.562519
\(327\) 14.9445 0.826432
\(328\) −1.42611 −0.0787439
\(329\) 5.75135 0.317082
\(330\) −5.89677 −0.324607
\(331\) 4.70041 0.258358 0.129179 0.991621i \(-0.458766\pi\)
0.129179 + 0.991621i \(0.458766\pi\)
\(332\) 7.81259 0.428772
\(333\) −3.80081 −0.208283
\(334\) 24.1519 1.32153
\(335\) −17.8611 −0.975855
\(336\) 1.06446 0.0580711
\(337\) −9.18682 −0.500438 −0.250219 0.968189i \(-0.580503\pi\)
−0.250219 + 0.968189i \(0.580503\pi\)
\(338\) −30.8914 −1.68027
\(339\) −9.05430 −0.491762
\(340\) 1.83830 0.0996956
\(341\) −16.2230 −0.878523
\(342\) −0.0716428 −0.00387400
\(343\) −9.71667 −0.524651
\(344\) 2.96163 0.159681
\(345\) 1.30384 0.0701964
\(346\) −3.30584 −0.177723
\(347\) −19.5451 −1.04923 −0.524617 0.851339i \(-0.675791\pi\)
−0.524617 + 0.851339i \(0.675791\pi\)
\(348\) −0.877023 −0.0470134
\(349\) 35.7643 1.91442 0.957209 0.289398i \(-0.0934551\pi\)
0.957209 + 0.289398i \(0.0934551\pi\)
\(350\) 2.52065 0.134734
\(351\) −6.49237 −0.346537
\(352\) −19.3444 −1.03106
\(353\) 17.5958 0.936532 0.468266 0.883588i \(-0.344879\pi\)
0.468266 + 0.883588i \(0.344879\pi\)
\(354\) −5.19653 −0.276192
\(355\) 1.10002 0.0583830
\(356\) −13.2688 −0.703246
\(357\) −1.15876 −0.0613280
\(358\) 4.69995 0.248400
\(359\) 5.45515 0.287912 0.143956 0.989584i \(-0.454018\pi\)
0.143956 + 0.989584i \(0.454018\pi\)
\(360\) −3.97515 −0.209509
\(361\) −18.9954 −0.999759
\(362\) −8.03128 −0.422115
\(363\) −7.21416 −0.378645
\(364\) −4.10419 −0.215118
\(365\) 4.64358 0.243056
\(366\) 7.72646 0.403869
\(367\) 7.87986 0.411326 0.205663 0.978623i \(-0.434065\pi\)
0.205663 + 0.978623i \(0.434065\pi\)
\(368\) −1.47678 −0.0769827
\(369\) −0.467762 −0.0243507
\(370\) −5.25153 −0.273014
\(371\) 9.64362 0.500672
\(372\) −3.33378 −0.172848
\(373\) −12.3211 −0.637961 −0.318980 0.947761i \(-0.603340\pi\)
−0.318980 + 0.947761i \(0.603340\pi\)
\(374\) −7.27059 −0.375953
\(375\) −10.8219 −0.558839
\(376\) 24.3268 1.25456
\(377\) −6.49237 −0.334374
\(378\) 0.763833 0.0392873
\(379\) 21.0221 1.07983 0.539916 0.841719i \(-0.318456\pi\)
0.539916 + 0.841719i \(0.318456\pi\)
\(380\) 0.0773078 0.00396580
\(381\) 16.8234 0.861891
\(382\) −25.2982 −1.29437
\(383\) −26.7325 −1.36597 −0.682983 0.730434i \(-0.739318\pi\)
−0.682983 + 0.730434i \(0.739318\pi\)
\(384\) −0.845320 −0.0431375
\(385\) −4.01090 −0.204414
\(386\) 25.2105 1.28318
\(387\) 0.971410 0.0493795
\(388\) −0.743391 −0.0377400
\(389\) 18.2034 0.922949 0.461474 0.887154i \(-0.347321\pi\)
0.461474 + 0.887154i \(0.347321\pi\)
\(390\) −8.97043 −0.454235
\(391\) 1.60761 0.0813002
\(392\) −19.7576 −0.997909
\(393\) −20.0112 −1.00943
\(394\) −10.9043 −0.549349
\(395\) −4.57147 −0.230016
\(396\) −3.74296 −0.188091
\(397\) −14.9475 −0.750193 −0.375096 0.926986i \(-0.622390\pi\)
−0.375096 + 0.926986i \(0.622390\pi\)
\(398\) −7.09892 −0.355837
\(399\) −0.0487304 −0.00243957
\(400\) 4.87339 0.243669
\(401\) 5.93728 0.296494 0.148247 0.988950i \(-0.452637\pi\)
0.148247 + 0.988950i \(0.452637\pi\)
\(402\) 14.5167 0.724028
\(403\) −24.6791 −1.22935
\(404\) 3.69665 0.183915
\(405\) −1.30384 −0.0647884
\(406\) 0.763833 0.0379084
\(407\) −16.2211 −0.804051
\(408\) −4.90127 −0.242649
\(409\) 28.1625 1.39255 0.696274 0.717776i \(-0.254840\pi\)
0.696274 + 0.717776i \(0.254840\pi\)
\(410\) −0.646301 −0.0319185
\(411\) 17.5827 0.867292
\(412\) 2.85514 0.140662
\(413\) −3.53460 −0.173926
\(414\) −1.05971 −0.0520817
\(415\) 11.6147 0.570144
\(416\) −29.4276 −1.44281
\(417\) 11.2785 0.552313
\(418\) −0.305758 −0.0149551
\(419\) −15.7587 −0.769862 −0.384931 0.922945i \(-0.625775\pi\)
−0.384931 + 0.922945i \(0.625775\pi\)
\(420\) −0.824230 −0.0402183
\(421\) −37.5081 −1.82803 −0.914017 0.405676i \(-0.867036\pi\)
−0.914017 + 0.405676i \(0.867036\pi\)
\(422\) −20.6357 −1.00453
\(423\) 7.97915 0.387959
\(424\) 40.7902 1.98095
\(425\) −5.30510 −0.257335
\(426\) −0.894049 −0.0433168
\(427\) 5.25543 0.254328
\(428\) −8.69856 −0.420461
\(429\) −27.7082 −1.33776
\(430\) 1.34218 0.0647259
\(431\) 10.7335 0.517013 0.258507 0.966009i \(-0.416770\pi\)
0.258507 + 0.966009i \(0.416770\pi\)
\(432\) 1.47678 0.0710518
\(433\) 29.9000 1.43690 0.718452 0.695576i \(-0.244851\pi\)
0.718452 + 0.695576i \(0.244851\pi\)
\(434\) 2.90351 0.139373
\(435\) −1.30384 −0.0625144
\(436\) 13.1067 0.627696
\(437\) 0.0676063 0.00323405
\(438\) −3.77410 −0.180333
\(439\) 27.6423 1.31930 0.659648 0.751575i \(-0.270705\pi\)
0.659648 + 0.751575i \(0.270705\pi\)
\(440\) −16.9652 −0.808782
\(441\) −6.48045 −0.308593
\(442\) −11.0603 −0.526087
\(443\) 16.5336 0.785534 0.392767 0.919638i \(-0.371518\pi\)
0.392767 + 0.919638i \(0.371518\pi\)
\(444\) −3.33340 −0.158196
\(445\) −19.7263 −0.935117
\(446\) −5.77823 −0.273607
\(447\) −8.68520 −0.410796
\(448\) 5.59110 0.264155
\(449\) 15.6126 0.736805 0.368403 0.929666i \(-0.379905\pi\)
0.368403 + 0.929666i \(0.379905\pi\)
\(450\) 3.49703 0.164852
\(451\) −1.99632 −0.0940029
\(452\) −7.94084 −0.373506
\(453\) 3.77830 0.177520
\(454\) −13.5617 −0.636482
\(455\) −6.10156 −0.286045
\(456\) −0.206118 −0.00965237
\(457\) −39.1168 −1.82981 −0.914903 0.403674i \(-0.867733\pi\)
−0.914903 + 0.403674i \(0.867733\pi\)
\(458\) 19.0197 0.888731
\(459\) −1.60761 −0.0750366
\(460\) 1.14350 0.0533159
\(461\) 27.3047 1.27171 0.635854 0.771810i \(-0.280648\pi\)
0.635854 + 0.771810i \(0.280648\pi\)
\(462\) 3.25989 0.151664
\(463\) 25.1953 1.17093 0.585463 0.810699i \(-0.300913\pi\)
0.585463 + 0.810699i \(0.300913\pi\)
\(464\) 1.47678 0.0685580
\(465\) −4.95621 −0.229839
\(466\) −26.2881 −1.21777
\(467\) 10.5362 0.487556 0.243778 0.969831i \(-0.421613\pi\)
0.243778 + 0.969831i \(0.421613\pi\)
\(468\) −5.69396 −0.263203
\(469\) 9.87407 0.455942
\(470\) 11.0247 0.508531
\(471\) 22.4357 1.03378
\(472\) −14.9505 −0.688154
\(473\) 4.14579 0.190624
\(474\) 3.71550 0.170658
\(475\) −0.223101 −0.0102366
\(476\) −1.01626 −0.0465801
\(477\) 13.3791 0.612587
\(478\) −6.86087 −0.313809
\(479\) 22.6259 1.03380 0.516902 0.856045i \(-0.327085\pi\)
0.516902 + 0.856045i \(0.327085\pi\)
\(480\) −5.90984 −0.269746
\(481\) −24.6763 −1.12514
\(482\) 1.13251 0.0515845
\(483\) −0.720797 −0.0327974
\(484\) −6.32699 −0.287590
\(485\) −1.10517 −0.0501834
\(486\) 1.05971 0.0480692
\(487\) −1.33179 −0.0603490 −0.0301745 0.999545i \(-0.509606\pi\)
−0.0301745 + 0.999545i \(0.509606\pi\)
\(488\) 22.2292 1.00627
\(489\) −9.58430 −0.433417
\(490\) −8.95396 −0.404499
\(491\) −37.5483 −1.69453 −0.847265 0.531170i \(-0.821753\pi\)
−0.847265 + 0.531170i \(0.821753\pi\)
\(492\) −0.410238 −0.0184950
\(493\) −1.60761 −0.0724030
\(494\) −0.465132 −0.0209273
\(495\) −5.56454 −0.250107
\(496\) 5.61361 0.252059
\(497\) −0.608119 −0.0272779
\(498\) −9.43994 −0.423014
\(499\) −34.2219 −1.53198 −0.765992 0.642850i \(-0.777752\pi\)
−0.765992 + 0.642850i \(0.777752\pi\)
\(500\) −9.49104 −0.424452
\(501\) 22.7911 1.01823
\(502\) 11.2976 0.504236
\(503\) 28.4032 1.26643 0.633217 0.773974i \(-0.281734\pi\)
0.633217 + 0.773974i \(0.281734\pi\)
\(504\) 2.19756 0.0978873
\(505\) 5.49568 0.244554
\(506\) −4.52262 −0.201055
\(507\) −29.1509 −1.29464
\(508\) 14.7546 0.654627
\(509\) −6.08138 −0.269553 −0.134776 0.990876i \(-0.543032\pi\)
−0.134776 + 0.990876i \(0.543032\pi\)
\(510\) −2.22121 −0.0983568
\(511\) −2.56709 −0.113561
\(512\) 15.6986 0.693785
\(513\) −0.0676063 −0.00298489
\(514\) −28.0573 −1.23756
\(515\) 4.24463 0.187041
\(516\) 0.851949 0.0375050
\(517\) 34.0535 1.49767
\(518\) 2.90318 0.127559
\(519\) −3.11958 −0.136934
\(520\) −25.8081 −1.13176
\(521\) −38.6489 −1.69324 −0.846619 0.532200i \(-0.821366\pi\)
−0.846619 + 0.532200i \(0.821366\pi\)
\(522\) 1.05971 0.0463821
\(523\) 2.97908 0.130266 0.0651331 0.997877i \(-0.479253\pi\)
0.0651331 + 0.997877i \(0.479253\pi\)
\(524\) −17.5503 −0.766686
\(525\) 2.37863 0.103812
\(526\) −3.22264 −0.140514
\(527\) −6.11090 −0.266195
\(528\) 6.30262 0.274287
\(529\) 1.00000 0.0434783
\(530\) 18.4857 0.802970
\(531\) −4.90374 −0.212804
\(532\) −0.0427377 −0.00185292
\(533\) −3.03688 −0.131542
\(534\) 16.0327 0.693803
\(535\) −12.9319 −0.559093
\(536\) 41.7649 1.80397
\(537\) 4.43515 0.191391
\(538\) 31.9310 1.37664
\(539\) −27.6573 −1.19128
\(540\) −1.14350 −0.0492083
\(541\) 26.1703 1.12515 0.562574 0.826747i \(-0.309811\pi\)
0.562574 + 0.826747i \(0.309811\pi\)
\(542\) −19.1441 −0.822308
\(543\) −7.57878 −0.325237
\(544\) −7.28670 −0.312415
\(545\) 19.4852 0.834656
\(546\) 4.95909 0.212229
\(547\) 11.0205 0.471204 0.235602 0.971850i \(-0.424294\pi\)
0.235602 + 0.971850i \(0.424294\pi\)
\(548\) 15.4205 0.658729
\(549\) 7.29114 0.311178
\(550\) 14.9246 0.636389
\(551\) −0.0676063 −0.00288013
\(552\) −3.04880 −0.129765
\(553\) 2.52723 0.107469
\(554\) −15.9741 −0.678673
\(555\) −4.95565 −0.210356
\(556\) 9.89155 0.419495
\(557\) −26.2157 −1.11080 −0.555398 0.831585i \(-0.687434\pi\)
−0.555398 + 0.831585i \(0.687434\pi\)
\(558\) 4.02820 0.170527
\(559\) 6.30675 0.266747
\(560\) 1.38789 0.0586489
\(561\) −6.86095 −0.289670
\(562\) −18.4479 −0.778177
\(563\) −39.8761 −1.68058 −0.840288 0.542140i \(-0.817614\pi\)
−0.840288 + 0.542140i \(0.817614\pi\)
\(564\) 6.99790 0.294665
\(565\) −11.8054 −0.496656
\(566\) −29.2791 −1.23069
\(567\) 0.720797 0.0302706
\(568\) −2.57220 −0.107927
\(569\) −15.2160 −0.637886 −0.318943 0.947774i \(-0.603328\pi\)
−0.318943 + 0.947774i \(0.603328\pi\)
\(570\) −0.0934108 −0.00391255
\(571\) −11.9807 −0.501377 −0.250688 0.968068i \(-0.580657\pi\)
−0.250688 + 0.968068i \(0.580657\pi\)
\(572\) −24.3007 −1.01606
\(573\) −23.8728 −0.997301
\(574\) 0.357292 0.0149131
\(575\) −3.30000 −0.137620
\(576\) 7.75683 0.323201
\(577\) −21.5518 −0.897212 −0.448606 0.893730i \(-0.648079\pi\)
−0.448606 + 0.893730i \(0.648079\pi\)
\(578\) 15.2763 0.635410
\(579\) 23.7901 0.988682
\(580\) −1.14350 −0.0474812
\(581\) −6.42092 −0.266384
\(582\) 0.898238 0.0372332
\(583\) 57.0994 2.36482
\(584\) −10.8582 −0.449314
\(585\) −8.46502 −0.349985
\(586\) −10.2296 −0.422579
\(587\) −21.9895 −0.907604 −0.453802 0.891102i \(-0.649933\pi\)
−0.453802 + 0.891102i \(0.649933\pi\)
\(588\) −5.68351 −0.234384
\(589\) −0.256988 −0.0105890
\(590\) −6.77544 −0.278940
\(591\) −10.2899 −0.423270
\(592\) 5.61297 0.230692
\(593\) −18.0058 −0.739411 −0.369706 0.929149i \(-0.620541\pi\)
−0.369706 + 0.929149i \(0.620541\pi\)
\(594\) 4.52262 0.185565
\(595\) −1.51084 −0.0619382
\(596\) −7.61712 −0.312009
\(597\) −6.69895 −0.274170
\(598\) −6.88000 −0.281344
\(599\) 42.1452 1.72201 0.861004 0.508599i \(-0.169836\pi\)
0.861004 + 0.508599i \(0.169836\pi\)
\(600\) 10.0610 0.410740
\(601\) −1.18690 −0.0484145 −0.0242073 0.999707i \(-0.507706\pi\)
−0.0242073 + 0.999707i \(0.507706\pi\)
\(602\) −0.741995 −0.0302414
\(603\) 13.6988 0.557859
\(604\) 3.31366 0.134831
\(605\) −9.40612 −0.382413
\(606\) −4.46665 −0.181445
\(607\) −21.2693 −0.863296 −0.431648 0.902042i \(-0.642068\pi\)
−0.431648 + 0.902042i \(0.642068\pi\)
\(608\) −0.306435 −0.0124276
\(609\) 0.720797 0.0292082
\(610\) 10.0741 0.407887
\(611\) 51.8036 2.09575
\(612\) −1.40991 −0.0569922
\(613\) 3.41464 0.137916 0.0689580 0.997620i \(-0.478033\pi\)
0.0689580 + 0.997620i \(0.478033\pi\)
\(614\) −24.8895 −1.00446
\(615\) −0.609887 −0.0245930
\(616\) 9.37878 0.377882
\(617\) −3.56041 −0.143337 −0.0716684 0.997429i \(-0.522832\pi\)
−0.0716684 + 0.997429i \(0.522832\pi\)
\(618\) −3.44986 −0.138774
\(619\) −19.6807 −0.791033 −0.395516 0.918459i \(-0.629434\pi\)
−0.395516 + 0.918459i \(0.629434\pi\)
\(620\) −4.34671 −0.174568
\(621\) −1.00000 −0.0401286
\(622\) −10.8331 −0.434368
\(623\) 10.9052 0.436908
\(624\) 9.58783 0.383820
\(625\) 2.39000 0.0956000
\(626\) −5.25084 −0.209866
\(627\) −0.288531 −0.0115228
\(628\) 19.6766 0.785182
\(629\) −6.11021 −0.243630
\(630\) 0.995916 0.0396783
\(631\) −39.8399 −1.58600 −0.793000 0.609221i \(-0.791482\pi\)
−0.793000 + 0.609221i \(0.791482\pi\)
\(632\) 10.6896 0.425208
\(633\) −19.4730 −0.773982
\(634\) −6.57755 −0.261228
\(635\) 21.9351 0.870467
\(636\) 11.7338 0.465275
\(637\) −42.0735 −1.66701
\(638\) 4.52262 0.179052
\(639\) −0.843676 −0.0333753
\(640\) −1.10216 −0.0435668
\(641\) 5.19938 0.205363 0.102682 0.994714i \(-0.467258\pi\)
0.102682 + 0.994714i \(0.467258\pi\)
\(642\) 10.5105 0.414815
\(643\) −9.54077 −0.376251 −0.188126 0.982145i \(-0.560241\pi\)
−0.188126 + 0.982145i \(0.560241\pi\)
\(644\) −0.632156 −0.0249104
\(645\) 1.26656 0.0498709
\(646\) −0.115173 −0.00453144
\(647\) −38.0573 −1.49619 −0.748093 0.663594i \(-0.769030\pi\)
−0.748093 + 0.663594i \(0.769030\pi\)
\(648\) 3.04880 0.119768
\(649\) −20.9282 −0.821505
\(650\) 22.7040 0.890525
\(651\) 2.73992 0.107386
\(652\) −8.40566 −0.329191
\(653\) −7.10248 −0.277942 −0.138971 0.990296i \(-0.544379\pi\)
−0.138971 + 0.990296i \(0.544379\pi\)
\(654\) −15.8368 −0.619267
\(655\) −26.0914 −1.01947
\(656\) 0.690783 0.0269706
\(657\) −3.56146 −0.138946
\(658\) −6.09474 −0.237598
\(659\) 17.2293 0.671157 0.335579 0.942012i \(-0.391068\pi\)
0.335579 + 0.942012i \(0.391068\pi\)
\(660\) −4.88023 −0.189963
\(661\) 6.28912 0.244618 0.122309 0.992492i \(-0.460970\pi\)
0.122309 + 0.992492i \(0.460970\pi\)
\(662\) −4.98105 −0.193594
\(663\) −10.4372 −0.405346
\(664\) −27.1589 −1.05397
\(665\) −0.0635367 −0.00246385
\(666\) 4.02774 0.156072
\(667\) −1.00000 −0.0387202
\(668\) 19.9884 0.773373
\(669\) −5.45268 −0.210813
\(670\) 18.9275 0.731233
\(671\) 31.1172 1.20126
\(672\) 3.26711 0.126032
\(673\) −33.1852 −1.27920 −0.639598 0.768709i \(-0.720899\pi\)
−0.639598 + 0.768709i \(0.720899\pi\)
\(674\) 9.73533 0.374991
\(675\) 3.30000 0.127017
\(676\) −25.5660 −0.983308
\(677\) −27.3019 −1.04930 −0.524649 0.851318i \(-0.675804\pi\)
−0.524649 + 0.851318i \(0.675804\pi\)
\(678\) 9.59490 0.368490
\(679\) 0.610969 0.0234468
\(680\) −6.39047 −0.245063
\(681\) −12.7976 −0.490405
\(682\) 17.1916 0.658299
\(683\) −5.32782 −0.203863 −0.101932 0.994791i \(-0.532502\pi\)
−0.101932 + 0.994791i \(0.532502\pi\)
\(684\) −0.0592923 −0.00226710
\(685\) 22.9251 0.875922
\(686\) 10.2968 0.393134
\(687\) 17.9481 0.684762
\(688\) −1.43456 −0.0546922
\(689\) 86.8621 3.30918
\(690\) −1.38169 −0.0525999
\(691\) −2.75150 −0.104672 −0.0523360 0.998630i \(-0.516667\pi\)
−0.0523360 + 0.998630i \(0.516667\pi\)
\(692\) −2.73594 −0.104005
\(693\) 3.07622 0.116856
\(694\) 20.7120 0.786217
\(695\) 14.7054 0.557808
\(696\) 3.04880 0.115564
\(697\) −0.751977 −0.0284832
\(698\) −37.8996 −1.43452
\(699\) −24.8070 −0.938285
\(700\) 2.08611 0.0788477
\(701\) −37.4534 −1.41460 −0.707298 0.706916i \(-0.750086\pi\)
−0.707298 + 0.706916i \(0.750086\pi\)
\(702\) 6.88000 0.259669
\(703\) −0.256959 −0.00969139
\(704\) 33.1047 1.24768
\(705\) 10.4035 0.391820
\(706\) −18.6464 −0.701767
\(707\) −3.03815 −0.114262
\(708\) −4.30070 −0.161630
\(709\) 29.7909 1.11882 0.559411 0.828891i \(-0.311028\pi\)
0.559411 + 0.828891i \(0.311028\pi\)
\(710\) −1.16570 −0.0437478
\(711\) 3.50616 0.131491
\(712\) 46.1265 1.72866
\(713\) −3.80124 −0.142358
\(714\) 1.22794 0.0459546
\(715\) −36.1270 −1.35107
\(716\) 3.88973 0.145366
\(717\) −6.47432 −0.241788
\(718\) −5.78086 −0.215740
\(719\) −2.28034 −0.0850422 −0.0425211 0.999096i \(-0.513539\pi\)
−0.0425211 + 0.999096i \(0.513539\pi\)
\(720\) 1.92549 0.0717588
\(721\) −2.34654 −0.0873898
\(722\) 20.1296 0.749145
\(723\) 1.06870 0.0397455
\(724\) −6.64677 −0.247025
\(725\) 3.30000 0.122559
\(726\) 7.64489 0.283729
\(727\) 17.1529 0.636164 0.318082 0.948063i \(-0.396961\pi\)
0.318082 + 0.948063i \(0.396961\pi\)
\(728\) 14.2674 0.528785
\(729\) 1.00000 0.0370370
\(730\) −4.92082 −0.182128
\(731\) 1.56164 0.0577595
\(732\) 6.39450 0.236347
\(733\) 7.35753 0.271757 0.135878 0.990726i \(-0.456614\pi\)
0.135878 + 0.990726i \(0.456614\pi\)
\(734\) −8.35034 −0.308217
\(735\) −8.44948 −0.311664
\(736\) −4.53264 −0.167075
\(737\) 58.4639 2.15354
\(738\) 0.495690 0.0182466
\(739\) 24.1145 0.887067 0.443534 0.896258i \(-0.353725\pi\)
0.443534 + 0.896258i \(0.353725\pi\)
\(740\) −4.34622 −0.159770
\(741\) −0.438925 −0.0161243
\(742\) −10.2194 −0.375166
\(743\) 3.82636 0.140376 0.0701878 0.997534i \(-0.477640\pi\)
0.0701878 + 0.997534i \(0.477640\pi\)
\(744\) 11.5892 0.424881
\(745\) −11.3241 −0.414883
\(746\) 13.0567 0.478040
\(747\) −8.90808 −0.325930
\(748\) −6.01721 −0.220011
\(749\) 7.14906 0.261221
\(750\) 11.4680 0.418752
\(751\) 19.0615 0.695564 0.347782 0.937575i \(-0.386935\pi\)
0.347782 + 0.937575i \(0.386935\pi\)
\(752\) −11.7835 −0.429699
\(753\) 10.6611 0.388511
\(754\) 6.88000 0.250555
\(755\) 4.92630 0.179286
\(756\) 0.632156 0.0229913
\(757\) 46.5969 1.69359 0.846797 0.531916i \(-0.178528\pi\)
0.846797 + 0.531916i \(0.178528\pi\)
\(758\) −22.2772 −0.809146
\(759\) −4.26781 −0.154912
\(760\) −0.268745 −0.00974841
\(761\) −13.6355 −0.494288 −0.247144 0.968979i \(-0.579492\pi\)
−0.247144 + 0.968979i \(0.579492\pi\)
\(762\) −17.8279 −0.645837
\(763\) −10.7719 −0.389971
\(764\) −20.9370 −0.757475
\(765\) −2.09606 −0.0757833
\(766\) 28.3286 1.02355
\(767\) −31.8369 −1.14956
\(768\) 16.4095 0.592125
\(769\) −7.50359 −0.270586 −0.135293 0.990806i \(-0.543198\pi\)
−0.135293 + 0.990806i \(0.543198\pi\)
\(770\) 4.25038 0.153173
\(771\) −26.4765 −0.953529
\(772\) 20.8645 0.750929
\(773\) −54.1536 −1.94777 −0.973885 0.227043i \(-0.927094\pi\)
−0.973885 + 0.227043i \(0.927094\pi\)
\(774\) −1.02941 −0.0370013
\(775\) 12.5441 0.450597
\(776\) 2.58425 0.0927692
\(777\) 2.73961 0.0982830
\(778\) −19.2902 −0.691589
\(779\) −0.0316237 −0.00113304
\(780\) −7.42402 −0.265822
\(781\) −3.60065 −0.128841
\(782\) −1.70359 −0.0609203
\(783\) 1.00000 0.0357371
\(784\) 9.57022 0.341794
\(785\) 29.2525 1.04407
\(786\) 21.2059 0.756391
\(787\) −29.3341 −1.04565 −0.522823 0.852441i \(-0.675121\pi\)
−0.522823 + 0.852441i \(0.675121\pi\)
\(788\) −9.02448 −0.321484
\(789\) −3.04107 −0.108265
\(790\) 4.84442 0.172357
\(791\) 6.52632 0.232049
\(792\) 13.0117 0.462350
\(793\) 47.3368 1.68098
\(794\) 15.8399 0.562139
\(795\) 17.4442 0.618683
\(796\) −5.87514 −0.208239
\(797\) −26.7775 −0.948507 −0.474253 0.880388i \(-0.657282\pi\)
−0.474253 + 0.880388i \(0.657282\pi\)
\(798\) 0.0516399 0.00182803
\(799\) 12.8273 0.453798
\(800\) 14.9577 0.528835
\(801\) 15.1294 0.534571
\(802\) −6.29177 −0.222170
\(803\) −15.1996 −0.536383
\(804\) 12.0142 0.423708
\(805\) −0.939804 −0.0331237
\(806\) 26.1526 0.921185
\(807\) 30.1319 1.06069
\(808\) −12.8507 −0.452085
\(809\) 44.6884 1.57116 0.785579 0.618761i \(-0.212365\pi\)
0.785579 + 0.618761i \(0.212365\pi\)
\(810\) 1.38169 0.0485476
\(811\) 44.3620 1.55776 0.778880 0.627174i \(-0.215788\pi\)
0.778880 + 0.627174i \(0.215788\pi\)
\(812\) 0.632156 0.0221843
\(813\) −18.0654 −0.633583
\(814\) 17.1896 0.602496
\(815\) −12.4964 −0.437730
\(816\) 2.37409 0.0831097
\(817\) 0.0656735 0.00229762
\(818\) −29.8440 −1.04347
\(819\) 4.67968 0.163521
\(820\) −0.534885 −0.0186790
\(821\) −21.3612 −0.745510 −0.372755 0.927930i \(-0.621587\pi\)
−0.372755 + 0.927930i \(0.621587\pi\)
\(822\) −18.6325 −0.649884
\(823\) 16.2985 0.568131 0.284065 0.958805i \(-0.408317\pi\)
0.284065 + 0.958805i \(0.408317\pi\)
\(824\) −9.92532 −0.345765
\(825\) 14.0838 0.490334
\(826\) 3.74564 0.130327
\(827\) 5.01177 0.174276 0.0871381 0.996196i \(-0.472228\pi\)
0.0871381 + 0.996196i \(0.472228\pi\)
\(828\) −0.877023 −0.0304787
\(829\) −19.5777 −0.679962 −0.339981 0.940432i \(-0.610421\pi\)
−0.339981 + 0.940432i \(0.610421\pi\)
\(830\) −12.3082 −0.427223
\(831\) −15.0741 −0.522913
\(832\) 50.3602 1.74593
\(833\) −10.4180 −0.360963
\(834\) −11.9519 −0.413862
\(835\) 29.7160 1.02837
\(836\) −0.253048 −0.00875185
\(837\) 3.80124 0.131390
\(838\) 16.6996 0.576877
\(839\) 43.9097 1.51593 0.757965 0.652295i \(-0.226194\pi\)
0.757965 + 0.652295i \(0.226194\pi\)
\(840\) 2.86527 0.0988613
\(841\) 1.00000 0.0344828
\(842\) 39.7476 1.36979
\(843\) −17.4085 −0.599581
\(844\) −17.0783 −0.587859
\(845\) −38.0081 −1.30752
\(846\) −8.45555 −0.290708
\(847\) 5.19995 0.178672
\(848\) −19.7580 −0.678494
\(849\) −27.6295 −0.948242
\(850\) 5.62185 0.192828
\(851\) −3.80081 −0.130290
\(852\) −0.739924 −0.0253494
\(853\) 26.4519 0.905696 0.452848 0.891588i \(-0.350408\pi\)
0.452848 + 0.891588i \(0.350408\pi\)
\(854\) −5.56921 −0.190574
\(855\) −0.0881479 −0.00301459
\(856\) 30.2388 1.03354
\(857\) −26.0097 −0.888475 −0.444238 0.895909i \(-0.646525\pi\)
−0.444238 + 0.895909i \(0.646525\pi\)
\(858\) 29.3625 1.00242
\(859\) 12.0451 0.410973 0.205486 0.978660i \(-0.434122\pi\)
0.205486 + 0.978660i \(0.434122\pi\)
\(860\) 1.11081 0.0378782
\(861\) 0.337161 0.0114904
\(862\) −11.3743 −0.387411
\(863\) −26.1020 −0.888523 −0.444262 0.895897i \(-0.646534\pi\)
−0.444262 + 0.895897i \(0.646534\pi\)
\(864\) 4.53264 0.154204
\(865\) −4.06743 −0.138297
\(866\) −31.6853 −1.07671
\(867\) 14.4156 0.489579
\(868\) 2.40298 0.0815623
\(869\) 14.9636 0.507606
\(870\) 1.38169 0.0468436
\(871\) 88.9378 3.01354
\(872\) −45.5628 −1.54295
\(873\) 0.847630 0.0286879
\(874\) −0.0716428 −0.00242336
\(875\) 7.80038 0.263701
\(876\) −3.12348 −0.105533
\(877\) −7.72870 −0.260980 −0.130490 0.991450i \(-0.541655\pi\)
−0.130490 + 0.991450i \(0.541655\pi\)
\(878\) −29.2927 −0.988582
\(879\) −9.65321 −0.325595
\(880\) 8.21762 0.277016
\(881\) −14.2550 −0.480262 −0.240131 0.970741i \(-0.577190\pi\)
−0.240131 + 0.970741i \(0.577190\pi\)
\(882\) 6.86737 0.231236
\(883\) 18.3998 0.619203 0.309601 0.950866i \(-0.399804\pi\)
0.309601 + 0.950866i \(0.399804\pi\)
\(884\) −9.15365 −0.307871
\(885\) −6.39370 −0.214922
\(886\) −17.5207 −0.588621
\(887\) 0.871823 0.0292730 0.0146365 0.999893i \(-0.495341\pi\)
0.0146365 + 0.999893i \(0.495341\pi\)
\(888\) 11.5879 0.388865
\(889\) −12.1263 −0.406703
\(890\) 20.9041 0.700707
\(891\) 4.26781 0.142977
\(892\) −4.78212 −0.160117
\(893\) 0.539441 0.0180517
\(894\) 9.20376 0.307820
\(895\) 5.78273 0.193295
\(896\) 0.609304 0.0203554
\(897\) −6.49237 −0.216774
\(898\) −16.5448 −0.552107
\(899\) 3.80124 0.126779
\(900\) 2.89418 0.0964726
\(901\) 21.5083 0.716547
\(902\) 2.11551 0.0704387
\(903\) −0.700189 −0.0233008
\(904\) 27.6048 0.918120
\(905\) −9.88152 −0.328473
\(906\) −4.00389 −0.133020
\(907\) 55.9890 1.85908 0.929542 0.368716i \(-0.120202\pi\)
0.929542 + 0.368716i \(0.120202\pi\)
\(908\) −11.2238 −0.372475
\(909\) −4.21499 −0.139802
\(910\) 6.46586 0.214341
\(911\) 53.4421 1.77061 0.885307 0.465007i \(-0.153948\pi\)
0.885307 + 0.465007i \(0.153948\pi\)
\(912\) 0.0998399 0.00330603
\(913\) −38.0179 −1.25821
\(914\) 41.4523 1.37112
\(915\) 9.50648 0.314274
\(916\) 15.7409 0.520093
\(917\) 14.4240 0.476322
\(918\) 1.70359 0.0562269
\(919\) 42.9636 1.41724 0.708619 0.705591i \(-0.249319\pi\)
0.708619 + 0.705591i \(0.249319\pi\)
\(920\) −3.97515 −0.131057
\(921\) −23.4872 −0.773929
\(922\) −28.9350 −0.952922
\(923\) −5.47746 −0.180293
\(924\) 2.69792 0.0887550
\(925\) 12.5427 0.412400
\(926\) −26.6996 −0.877404
\(927\) −3.25548 −0.106924
\(928\) 4.53264 0.148791
\(929\) 12.0253 0.394537 0.197269 0.980349i \(-0.436793\pi\)
0.197269 + 0.980349i \(0.436793\pi\)
\(930\) 5.25213 0.172224
\(931\) −0.438120 −0.0143588
\(932\) −21.7563 −0.712651
\(933\) −10.2227 −0.334678
\(934\) −11.1652 −0.365338
\(935\) −8.94559 −0.292552
\(936\) 19.7939 0.646985
\(937\) −30.0372 −0.981274 −0.490637 0.871364i \(-0.663236\pi\)
−0.490637 + 0.871364i \(0.663236\pi\)
\(938\) −10.4636 −0.341649
\(939\) −4.95500 −0.161700
\(940\) 9.12415 0.297597
\(941\) 19.6719 0.641286 0.320643 0.947200i \(-0.396101\pi\)
0.320643 + 0.947200i \(0.396101\pi\)
\(942\) −23.7752 −0.774638
\(943\) −0.467762 −0.0152324
\(944\) 7.24177 0.235699
\(945\) 0.939804 0.0305718
\(946\) −4.39332 −0.142839
\(947\) −18.8653 −0.613041 −0.306520 0.951864i \(-0.599165\pi\)
−0.306520 + 0.951864i \(0.599165\pi\)
\(948\) 3.07498 0.0998708
\(949\) −23.1223 −0.750582
\(950\) 0.236421 0.00767052
\(951\) −6.20695 −0.201274
\(952\) 3.53282 0.114499
\(953\) −33.1756 −1.07466 −0.537331 0.843371i \(-0.680568\pi\)
−0.537331 + 0.843371i \(0.680568\pi\)
\(954\) −14.1779 −0.459027
\(955\) −31.1263 −1.00722
\(956\) −5.67813 −0.183644
\(957\) 4.26781 0.137959
\(958\) −23.9768 −0.774655
\(959\) −12.6736 −0.409251
\(960\) 10.1137 0.326417
\(961\) −16.5506 −0.533889
\(962\) 26.1496 0.843097
\(963\) 9.91828 0.319612
\(964\) 0.937279 0.0301877
\(965\) 31.0185 0.998520
\(966\) 0.763833 0.0245759
\(967\) −41.8683 −1.34640 −0.673198 0.739463i \(-0.735080\pi\)
−0.673198 + 0.739463i \(0.735080\pi\)
\(968\) 21.9945 0.706931
\(969\) −0.108684 −0.00349145
\(970\) 1.17116 0.0376037
\(971\) 24.2057 0.776799 0.388400 0.921491i \(-0.373028\pi\)
0.388400 + 0.921491i \(0.373028\pi\)
\(972\) 0.877023 0.0281305
\(973\) −8.12954 −0.260621
\(974\) 1.41130 0.0452210
\(975\) 21.4248 0.686144
\(976\) −10.7674 −0.344657
\(977\) 11.7282 0.375218 0.187609 0.982244i \(-0.439926\pi\)
0.187609 + 0.982244i \(0.439926\pi\)
\(978\) 10.1565 0.324770
\(979\) 64.5693 2.06364
\(980\) −7.41039 −0.236716
\(981\) −14.9445 −0.477141
\(982\) 39.7902 1.26975
\(983\) −1.37537 −0.0438675 −0.0219338 0.999759i \(-0.506982\pi\)
−0.0219338 + 0.999759i \(0.506982\pi\)
\(984\) 1.42611 0.0454628
\(985\) −13.4164 −0.427482
\(986\) 1.70359 0.0542534
\(987\) −5.75135 −0.183067
\(988\) −0.384948 −0.0122468
\(989\) 0.971410 0.0308890
\(990\) 5.89677 0.187412
\(991\) 60.9345 1.93565 0.967824 0.251629i \(-0.0809662\pi\)
0.967824 + 0.251629i \(0.0809662\pi\)
\(992\) 17.2297 0.547042
\(993\) −4.70041 −0.149163
\(994\) 0.644428 0.0204400
\(995\) −8.73436 −0.276898
\(996\) −7.81259 −0.247551
\(997\) −9.78792 −0.309986 −0.154993 0.987916i \(-0.549536\pi\)
−0.154993 + 0.987916i \(0.549536\pi\)
\(998\) 36.2652 1.14795
\(999\) 3.80081 0.120252
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 2001.2.a.l.1.4 11
3.2 odd 2 6003.2.a.m.1.8 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.4 11 1.1 even 1 trivial
6003.2.a.m.1.8 11 3.2 odd 2