Properties

Label 8047.2.a.c.1.18
Level $8047$
Weight $2$
Character 8047.1
Self dual yes
Analytic conductor $64.256$
Analytic rank $1$
Dimension $151$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8047,2,Mod(1,8047)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8047, 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("8047.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8047 = 13 \cdot 619 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8047.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: \(64.2556185065\)
Analytic rank: \(1\)
Dimension: \(151\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8047.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.30742 q^{2} -2.51530 q^{3} +3.32419 q^{4} -4.19325 q^{5} +5.80386 q^{6} +2.00418 q^{7} -3.05546 q^{8} +3.32673 q^{9} +O(q^{10})\) \(q-2.30742 q^{2} -2.51530 q^{3} +3.32419 q^{4} -4.19325 q^{5} +5.80386 q^{6} +2.00418 q^{7} -3.05546 q^{8} +3.32673 q^{9} +9.67559 q^{10} +4.40006 q^{11} -8.36134 q^{12} -1.00000 q^{13} -4.62449 q^{14} +10.5473 q^{15} +0.401859 q^{16} +0.837810 q^{17} -7.67618 q^{18} +2.59581 q^{19} -13.9392 q^{20} -5.04112 q^{21} -10.1528 q^{22} -5.88386 q^{23} +7.68541 q^{24} +12.5834 q^{25} +2.30742 q^{26} -0.821837 q^{27} +6.66228 q^{28} +6.24966 q^{29} -24.3370 q^{30} +5.84018 q^{31} +5.18367 q^{32} -11.0675 q^{33} -1.93318 q^{34} -8.40403 q^{35} +11.0587 q^{36} -9.01297 q^{37} -5.98962 q^{38} +2.51530 q^{39} +12.8123 q^{40} +2.59430 q^{41} +11.6320 q^{42} +6.27715 q^{43} +14.6266 q^{44} -13.9498 q^{45} +13.5765 q^{46} -1.11510 q^{47} -1.01080 q^{48} -2.98326 q^{49} -29.0351 q^{50} -2.10734 q^{51} -3.32419 q^{52} -6.18217 q^{53} +1.89632 q^{54} -18.4506 q^{55} -6.12370 q^{56} -6.52923 q^{57} -14.4206 q^{58} -4.91759 q^{59} +35.0612 q^{60} +11.9123 q^{61} -13.4758 q^{62} +6.66738 q^{63} -12.7646 q^{64} +4.19325 q^{65} +25.5373 q^{66} -1.37117 q^{67} +2.78504 q^{68} +14.7997 q^{69} +19.3916 q^{70} +7.30611 q^{71} -10.1647 q^{72} -5.14693 q^{73} +20.7967 q^{74} -31.6509 q^{75} +8.62895 q^{76} +8.81852 q^{77} -5.80386 q^{78} -11.6248 q^{79} -1.68510 q^{80} -7.91304 q^{81} -5.98615 q^{82} -12.7465 q^{83} -16.7576 q^{84} -3.51315 q^{85} -14.4840 q^{86} -15.7198 q^{87} -13.4442 q^{88} -15.8100 q^{89} +32.1881 q^{90} -2.00418 q^{91} -19.5591 q^{92} -14.6898 q^{93} +2.57301 q^{94} -10.8849 q^{95} -13.0385 q^{96} -15.2479 q^{97} +6.88363 q^{98} +14.6378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30742 −1.63159 −0.815796 0.578339i \(-0.803701\pi\)
−0.815796 + 0.578339i \(0.803701\pi\)
\(3\) −2.51530 −1.45221 −0.726105 0.687584i \(-0.758671\pi\)
−0.726105 + 0.687584i \(0.758671\pi\)
\(4\) 3.32419 1.66209
\(5\) −4.19325 −1.87528 −0.937639 0.347609i \(-0.886994\pi\)
−0.937639 + 0.347609i \(0.886994\pi\)
\(6\) 5.80386 2.36941
\(7\) 2.00418 0.757509 0.378755 0.925497i \(-0.376352\pi\)
0.378755 + 0.925497i \(0.376352\pi\)
\(8\) −3.05546 −1.08027
\(9\) 3.32673 1.10891
\(10\) 9.67559 3.05969
\(11\) 4.40006 1.32667 0.663335 0.748323i \(-0.269141\pi\)
0.663335 + 0.748323i \(0.269141\pi\)
\(12\) −8.36134 −2.41371
\(13\) −1.00000 −0.277350
\(14\) −4.62449 −1.23595
\(15\) 10.5473 2.72330
\(16\) 0.401859 0.100465
\(17\) 0.837810 0.203199 0.101599 0.994825i \(-0.467604\pi\)
0.101599 + 0.994825i \(0.467604\pi\)
\(18\) −7.67618 −1.80929
\(19\) 2.59581 0.595519 0.297759 0.954641i \(-0.403761\pi\)
0.297759 + 0.954641i \(0.403761\pi\)
\(20\) −13.9392 −3.11689
\(21\) −5.04112 −1.10006
\(22\) −10.1528 −2.16458
\(23\) −5.88386 −1.22687 −0.613435 0.789745i \(-0.710213\pi\)
−0.613435 + 0.789745i \(0.710213\pi\)
\(24\) 7.68541 1.56878
\(25\) 12.5834 2.51667
\(26\) 2.30742 0.452522
\(27\) −0.821837 −0.158163
\(28\) 6.66228 1.25905
\(29\) 6.24966 1.16053 0.580267 0.814427i \(-0.302948\pi\)
0.580267 + 0.814427i \(0.302948\pi\)
\(30\) −24.3370 −4.44331
\(31\) 5.84018 1.04893 0.524464 0.851433i \(-0.324266\pi\)
0.524464 + 0.851433i \(0.324266\pi\)
\(32\) 5.18367 0.916352
\(33\) −11.0675 −1.92660
\(34\) −1.93318 −0.331538
\(35\) −8.40403 −1.42054
\(36\) 11.0587 1.84312
\(37\) −9.01297 −1.48172 −0.740861 0.671658i \(-0.765582\pi\)
−0.740861 + 0.671658i \(0.765582\pi\)
\(38\) −5.98962 −0.971644
\(39\) 2.51530 0.402770
\(40\) 12.8123 2.02581
\(41\) 2.59430 0.405162 0.202581 0.979265i \(-0.435067\pi\)
0.202581 + 0.979265i \(0.435067\pi\)
\(42\) 11.6320 1.79485
\(43\) 6.27715 0.957256 0.478628 0.878018i \(-0.341134\pi\)
0.478628 + 0.878018i \(0.341134\pi\)
\(44\) 14.6266 2.20505
\(45\) −13.9498 −2.07952
\(46\) 13.5765 2.00175
\(47\) −1.11510 −0.162655 −0.0813273 0.996687i \(-0.525916\pi\)
−0.0813273 + 0.996687i \(0.525916\pi\)
\(48\) −1.01080 −0.145896
\(49\) −2.98326 −0.426180
\(50\) −29.0351 −4.10618
\(51\) −2.10734 −0.295087
\(52\) −3.32419 −0.460982
\(53\) −6.18217 −0.849186 −0.424593 0.905384i \(-0.639583\pi\)
−0.424593 + 0.905384i \(0.639583\pi\)
\(54\) 1.89632 0.258057
\(55\) −18.4506 −2.48787
\(56\) −6.12370 −0.818314
\(57\) −6.52923 −0.864818
\(58\) −14.4206 −1.89352
\(59\) −4.91759 −0.640216 −0.320108 0.947381i \(-0.603719\pi\)
−0.320108 + 0.947381i \(0.603719\pi\)
\(60\) 35.0612 4.52638
\(61\) 11.9123 1.52521 0.762604 0.646866i \(-0.223921\pi\)
0.762604 + 0.646866i \(0.223921\pi\)
\(62\) −13.4758 −1.71142
\(63\) 6.66738 0.840011
\(64\) −12.7646 −1.59558
\(65\) 4.19325 0.520109
\(66\) 25.5373 3.14343
\(67\) −1.37117 −0.167516 −0.0837578 0.996486i \(-0.526692\pi\)
−0.0837578 + 0.996486i \(0.526692\pi\)
\(68\) 2.78504 0.337736
\(69\) 14.7997 1.78167
\(70\) 19.3916 2.31774
\(71\) 7.30611 0.867076 0.433538 0.901135i \(-0.357265\pi\)
0.433538 + 0.901135i \(0.357265\pi\)
\(72\) −10.1647 −1.19792
\(73\) −5.14693 −0.602402 −0.301201 0.953561i \(-0.597388\pi\)
−0.301201 + 0.953561i \(0.597388\pi\)
\(74\) 20.7967 2.41757
\(75\) −31.6509 −3.65473
\(76\) 8.62895 0.989809
\(77\) 8.81852 1.00496
\(78\) −5.80386 −0.657157
\(79\) −11.6248 −1.30789 −0.653947 0.756540i \(-0.726888\pi\)
−0.653947 + 0.756540i \(0.726888\pi\)
\(80\) −1.68510 −0.188399
\(81\) −7.91304 −0.879227
\(82\) −5.98615 −0.661060
\(83\) −12.7465 −1.39911 −0.699557 0.714577i \(-0.746619\pi\)
−0.699557 + 0.714577i \(0.746619\pi\)
\(84\) −16.7576 −1.82841
\(85\) −3.51315 −0.381054
\(86\) −14.4840 −1.56185
\(87\) −15.7198 −1.68534
\(88\) −13.4442 −1.43316
\(89\) −15.8100 −1.67585 −0.837927 0.545783i \(-0.816232\pi\)
−0.837927 + 0.545783i \(0.816232\pi\)
\(90\) 32.1881 3.39293
\(91\) −2.00418 −0.210095
\(92\) −19.5591 −2.03918
\(93\) −14.6898 −1.52326
\(94\) 2.57301 0.265386
\(95\) −10.8849 −1.11676
\(96\) −13.0385 −1.33073
\(97\) −15.2479 −1.54819 −0.774096 0.633068i \(-0.781795\pi\)
−0.774096 + 0.633068i \(0.781795\pi\)
\(98\) 6.88363 0.695352
\(99\) 14.6378 1.47116
\(100\) 41.8295 4.18295
\(101\) −16.0749 −1.59951 −0.799757 0.600324i \(-0.795038\pi\)
−0.799757 + 0.600324i \(0.795038\pi\)
\(102\) 4.86253 0.481462
\(103\) −1.59614 −0.157272 −0.0786360 0.996903i \(-0.525056\pi\)
−0.0786360 + 0.996903i \(0.525056\pi\)
\(104\) 3.05546 0.299613
\(105\) 21.1387 2.06292
\(106\) 14.2649 1.38553
\(107\) −0.938871 −0.0907641 −0.0453821 0.998970i \(-0.514451\pi\)
−0.0453821 + 0.998970i \(0.514451\pi\)
\(108\) −2.73194 −0.262881
\(109\) 19.4836 1.86619 0.933096 0.359627i \(-0.117096\pi\)
0.933096 + 0.359627i \(0.117096\pi\)
\(110\) 42.5732 4.05920
\(111\) 22.6703 2.15177
\(112\) 0.805398 0.0761030
\(113\) −2.27989 −0.214474 −0.107237 0.994233i \(-0.534200\pi\)
−0.107237 + 0.994233i \(0.534200\pi\)
\(114\) 15.0657 1.41103
\(115\) 24.6725 2.30072
\(116\) 20.7751 1.92892
\(117\) −3.32673 −0.307557
\(118\) 11.3470 1.04457
\(119\) 1.67912 0.153925
\(120\) −32.2268 −2.94189
\(121\) 8.36056 0.760051
\(122\) −27.4866 −2.48852
\(123\) −6.52545 −0.588380
\(124\) 19.4139 1.74342
\(125\) −31.7989 −2.84418
\(126\) −15.3844 −1.37056
\(127\) 4.10817 0.364541 0.182271 0.983248i \(-0.441655\pi\)
0.182271 + 0.983248i \(0.441655\pi\)
\(128\) 19.0860 1.68698
\(129\) −15.7889 −1.39014
\(130\) −9.67559 −0.848606
\(131\) −20.6051 −1.80027 −0.900136 0.435608i \(-0.856533\pi\)
−0.900136 + 0.435608i \(0.856533\pi\)
\(132\) −36.7904 −3.20219
\(133\) 5.20246 0.451111
\(134\) 3.16387 0.273317
\(135\) 3.44617 0.296599
\(136\) −2.55990 −0.219509
\(137\) 13.7361 1.17355 0.586775 0.809750i \(-0.300397\pi\)
0.586775 + 0.809750i \(0.300397\pi\)
\(138\) −34.1491 −2.90696
\(139\) 17.8883 1.51726 0.758631 0.651521i \(-0.225869\pi\)
0.758631 + 0.651521i \(0.225869\pi\)
\(140\) −27.9366 −2.36107
\(141\) 2.80482 0.236209
\(142\) −16.8583 −1.41472
\(143\) −4.40006 −0.367952
\(144\) 1.33688 0.111407
\(145\) −26.2064 −2.17632
\(146\) 11.8761 0.982875
\(147\) 7.50379 0.618902
\(148\) −29.9608 −2.46276
\(149\) 21.9430 1.79764 0.898819 0.438320i \(-0.144426\pi\)
0.898819 + 0.438320i \(0.144426\pi\)
\(150\) 73.0320 5.96304
\(151\) −0.607759 −0.0494587 −0.0247294 0.999694i \(-0.507872\pi\)
−0.0247294 + 0.999694i \(0.507872\pi\)
\(152\) −7.93139 −0.643321
\(153\) 2.78717 0.225329
\(154\) −20.3480 −1.63969
\(155\) −24.4894 −1.96703
\(156\) 8.36134 0.669443
\(157\) 19.4281 1.55053 0.775266 0.631635i \(-0.217616\pi\)
0.775266 + 0.631635i \(0.217616\pi\)
\(158\) 26.8234 2.13395
\(159\) 15.5500 1.23320
\(160\) −21.7364 −1.71842
\(161\) −11.7923 −0.929366
\(162\) 18.2587 1.43454
\(163\) −0.334974 −0.0262372 −0.0131186 0.999914i \(-0.504176\pi\)
−0.0131186 + 0.999914i \(0.504176\pi\)
\(164\) 8.62396 0.673418
\(165\) 46.4087 3.61291
\(166\) 29.4116 2.28278
\(167\) 1.75686 0.135950 0.0679749 0.997687i \(-0.478346\pi\)
0.0679749 + 0.997687i \(0.478346\pi\)
\(168\) 15.4029 1.18836
\(169\) 1.00000 0.0769231
\(170\) 8.10631 0.621726
\(171\) 8.63556 0.660378
\(172\) 20.8664 1.59105
\(173\) 9.19355 0.698973 0.349486 0.936941i \(-0.386356\pi\)
0.349486 + 0.936941i \(0.386356\pi\)
\(174\) 36.2721 2.74978
\(175\) 25.2193 1.90640
\(176\) 1.76821 0.133283
\(177\) 12.3692 0.929728
\(178\) 36.4803 2.73431
\(179\) −23.9686 −1.79150 −0.895748 0.444562i \(-0.853359\pi\)
−0.895748 + 0.444562i \(0.853359\pi\)
\(180\) −46.3719 −3.45636
\(181\) −3.26090 −0.242381 −0.121190 0.992629i \(-0.538671\pi\)
−0.121190 + 0.992629i \(0.538671\pi\)
\(182\) 4.62449 0.342790
\(183\) −29.9629 −2.21492
\(184\) 17.9779 1.32535
\(185\) 37.7936 2.77864
\(186\) 33.8956 2.48534
\(187\) 3.68642 0.269578
\(188\) −3.70682 −0.270347
\(189\) −1.64711 −0.119810
\(190\) 25.1160 1.82210
\(191\) −17.4760 −1.26452 −0.632261 0.774756i \(-0.717873\pi\)
−0.632261 + 0.774756i \(0.717873\pi\)
\(192\) 32.1069 2.31711
\(193\) 26.3480 1.89657 0.948285 0.317419i \(-0.102816\pi\)
0.948285 + 0.317419i \(0.102816\pi\)
\(194\) 35.1834 2.52602
\(195\) −10.5473 −0.755307
\(196\) −9.91692 −0.708351
\(197\) −21.9987 −1.56735 −0.783673 0.621174i \(-0.786656\pi\)
−0.783673 + 0.621174i \(0.786656\pi\)
\(198\) −33.7757 −2.40033
\(199\) 27.0569 1.91802 0.959008 0.283379i \(-0.0914555\pi\)
0.959008 + 0.283379i \(0.0914555\pi\)
\(200\) −38.4480 −2.71868
\(201\) 3.44891 0.243268
\(202\) 37.0916 2.60975
\(203\) 12.5255 0.879114
\(204\) −7.00521 −0.490463
\(205\) −10.8786 −0.759792
\(206\) 3.68296 0.256604
\(207\) −19.5741 −1.36049
\(208\) −0.401859 −0.0278639
\(209\) 11.4217 0.790056
\(210\) −48.7758 −3.36585
\(211\) 16.4545 1.13278 0.566388 0.824139i \(-0.308340\pi\)
0.566388 + 0.824139i \(0.308340\pi\)
\(212\) −20.5507 −1.41143
\(213\) −18.3771 −1.25918
\(214\) 2.16637 0.148090
\(215\) −26.3216 −1.79512
\(216\) 2.51109 0.170858
\(217\) 11.7048 0.794572
\(218\) −44.9569 −3.04487
\(219\) 12.9461 0.874814
\(220\) −61.3332 −4.13508
\(221\) −0.837810 −0.0563572
\(222\) −52.3099 −3.51081
\(223\) −6.80781 −0.455885 −0.227942 0.973675i \(-0.573200\pi\)
−0.227942 + 0.973675i \(0.573200\pi\)
\(224\) 10.3890 0.694145
\(225\) 41.8615 2.79077
\(226\) 5.26067 0.349935
\(227\) 2.76864 0.183761 0.0918804 0.995770i \(-0.470712\pi\)
0.0918804 + 0.995770i \(0.470712\pi\)
\(228\) −21.7044 −1.43741
\(229\) 16.6874 1.10273 0.551366 0.834264i \(-0.314107\pi\)
0.551366 + 0.834264i \(0.314107\pi\)
\(230\) −56.9299 −3.75384
\(231\) −22.1812 −1.45942
\(232\) −19.0956 −1.25369
\(233\) 22.5749 1.47893 0.739464 0.673196i \(-0.235079\pi\)
0.739464 + 0.673196i \(0.235079\pi\)
\(234\) 7.67618 0.501807
\(235\) 4.67591 0.305023
\(236\) −16.3470 −1.06410
\(237\) 29.2399 1.89934
\(238\) −3.87444 −0.251143
\(239\) −7.73348 −0.500237 −0.250119 0.968215i \(-0.580470\pi\)
−0.250119 + 0.968215i \(0.580470\pi\)
\(240\) 4.23852 0.273595
\(241\) 1.37304 0.0884450 0.0442225 0.999022i \(-0.485919\pi\)
0.0442225 + 0.999022i \(0.485919\pi\)
\(242\) −19.2913 −1.24009
\(243\) 22.3692 1.43498
\(244\) 39.5986 2.53504
\(245\) 12.5096 0.799206
\(246\) 15.0570 0.959997
\(247\) −2.59581 −0.165167
\(248\) −17.8445 −1.13312
\(249\) 32.0614 2.03181
\(250\) 73.3735 4.64055
\(251\) −6.34159 −0.400278 −0.200139 0.979768i \(-0.564139\pi\)
−0.200139 + 0.979768i \(0.564139\pi\)
\(252\) 22.1636 1.39618
\(253\) −25.8894 −1.62765
\(254\) −9.47928 −0.594783
\(255\) 8.83662 0.553371
\(256\) −18.5102 −1.15689
\(257\) −27.3339 −1.70504 −0.852522 0.522691i \(-0.824928\pi\)
−0.852522 + 0.522691i \(0.824928\pi\)
\(258\) 36.4316 2.26814
\(259\) −18.0636 −1.12242
\(260\) 13.9392 0.864470
\(261\) 20.7910 1.28693
\(262\) 47.5445 2.93731
\(263\) 0.297471 0.0183429 0.00917143 0.999958i \(-0.497081\pi\)
0.00917143 + 0.999958i \(0.497081\pi\)
\(264\) 33.8163 2.08125
\(265\) 25.9234 1.59246
\(266\) −12.0043 −0.736029
\(267\) 39.7668 2.43369
\(268\) −4.55804 −0.278427
\(269\) 29.5888 1.80406 0.902029 0.431675i \(-0.142077\pi\)
0.902029 + 0.431675i \(0.142077\pi\)
\(270\) −7.95176 −0.483929
\(271\) 2.59118 0.157403 0.0787014 0.996898i \(-0.474923\pi\)
0.0787014 + 0.996898i \(0.474923\pi\)
\(272\) 0.336682 0.0204143
\(273\) 5.04112 0.305102
\(274\) −31.6949 −1.91476
\(275\) 55.3676 3.33879
\(276\) 49.1970 2.96131
\(277\) 2.04608 0.122937 0.0614685 0.998109i \(-0.480422\pi\)
0.0614685 + 0.998109i \(0.480422\pi\)
\(278\) −41.2757 −2.47555
\(279\) 19.4287 1.16317
\(280\) 25.6782 1.53457
\(281\) −32.6588 −1.94826 −0.974130 0.225988i \(-0.927439\pi\)
−0.974130 + 0.225988i \(0.927439\pi\)
\(282\) −6.47190 −0.385396
\(283\) −4.86333 −0.289095 −0.144547 0.989498i \(-0.546173\pi\)
−0.144547 + 0.989498i \(0.546173\pi\)
\(284\) 24.2869 1.44116
\(285\) 27.3787 1.62177
\(286\) 10.1528 0.600347
\(287\) 5.19946 0.306914
\(288\) 17.2447 1.01615
\(289\) −16.2981 −0.958710
\(290\) 60.4692 3.55087
\(291\) 38.3531 2.24830
\(292\) −17.1094 −1.00125
\(293\) 10.0381 0.586432 0.293216 0.956046i \(-0.405274\pi\)
0.293216 + 0.956046i \(0.405274\pi\)
\(294\) −17.3144 −1.00980
\(295\) 20.6207 1.20058
\(296\) 27.5388 1.60066
\(297\) −3.61613 −0.209829
\(298\) −50.6317 −2.93301
\(299\) 5.88386 0.340273
\(300\) −105.214 −6.07451
\(301\) 12.5805 0.725130
\(302\) 1.40236 0.0806965
\(303\) 40.4332 2.32283
\(304\) 1.04315 0.0598287
\(305\) −49.9511 −2.86019
\(306\) −6.43118 −0.367646
\(307\) 24.1594 1.37885 0.689426 0.724356i \(-0.257863\pi\)
0.689426 + 0.724356i \(0.257863\pi\)
\(308\) 29.3144 1.67035
\(309\) 4.01476 0.228392
\(310\) 56.5072 3.20940
\(311\) −13.5451 −0.768072 −0.384036 0.923318i \(-0.625466\pi\)
−0.384036 + 0.923318i \(0.625466\pi\)
\(312\) −7.68541 −0.435101
\(313\) −14.6200 −0.826374 −0.413187 0.910646i \(-0.635584\pi\)
−0.413187 + 0.910646i \(0.635584\pi\)
\(314\) −44.8288 −2.52984
\(315\) −27.9580 −1.57525
\(316\) −38.6431 −2.17385
\(317\) 14.0975 0.791792 0.395896 0.918295i \(-0.370434\pi\)
0.395896 + 0.918295i \(0.370434\pi\)
\(318\) −35.8804 −2.01207
\(319\) 27.4989 1.53964
\(320\) 53.5253 2.99215
\(321\) 2.36154 0.131808
\(322\) 27.2099 1.51635
\(323\) 2.17479 0.121009
\(324\) −26.3044 −1.46136
\(325\) −12.5834 −0.697999
\(326\) 0.772927 0.0428085
\(327\) −49.0072 −2.71010
\(328\) −7.92680 −0.437684
\(329\) −2.23487 −0.123212
\(330\) −107.084 −5.89480
\(331\) −19.3268 −1.06230 −0.531148 0.847279i \(-0.678239\pi\)
−0.531148 + 0.847279i \(0.678239\pi\)
\(332\) −42.3719 −2.32546
\(333\) −29.9837 −1.64310
\(334\) −4.05381 −0.221815
\(335\) 5.74968 0.314138
\(336\) −2.02582 −0.110517
\(337\) 16.1962 0.882262 0.441131 0.897443i \(-0.354577\pi\)
0.441131 + 0.897443i \(0.354577\pi\)
\(338\) −2.30742 −0.125507
\(339\) 5.73462 0.311462
\(340\) −11.6784 −0.633349
\(341\) 25.6972 1.39158
\(342\) −19.9259 −1.07747
\(343\) −20.0083 −1.08034
\(344\) −19.1796 −1.03409
\(345\) −62.0588 −3.34113
\(346\) −21.2134 −1.14044
\(347\) −19.7790 −1.06179 −0.530897 0.847436i \(-0.678145\pi\)
−0.530897 + 0.847436i \(0.678145\pi\)
\(348\) −52.2555 −2.80119
\(349\) −24.1406 −1.29222 −0.646109 0.763245i \(-0.723605\pi\)
−0.646109 + 0.763245i \(0.723605\pi\)
\(350\) −58.1916 −3.11047
\(351\) 0.821837 0.0438664
\(352\) 22.8085 1.21570
\(353\) 12.2551 0.652272 0.326136 0.945323i \(-0.394253\pi\)
0.326136 + 0.945323i \(0.394253\pi\)
\(354\) −28.5410 −1.51694
\(355\) −30.6364 −1.62601
\(356\) −52.5553 −2.78543
\(357\) −4.22350 −0.223531
\(358\) 55.3056 2.92299
\(359\) −7.02540 −0.370786 −0.185393 0.982664i \(-0.559356\pi\)
−0.185393 + 0.982664i \(0.559356\pi\)
\(360\) 42.6232 2.24644
\(361\) −12.2618 −0.645357
\(362\) 7.52427 0.395467
\(363\) −21.0293 −1.10375
\(364\) −6.66228 −0.349198
\(365\) 21.5824 1.12967
\(366\) 69.1370 3.61385
\(367\) −33.9945 −1.77450 −0.887250 0.461289i \(-0.847387\pi\)
−0.887250 + 0.461289i \(0.847387\pi\)
\(368\) −2.36448 −0.123257
\(369\) 8.63056 0.449289
\(370\) −87.2058 −4.53361
\(371\) −12.3902 −0.643266
\(372\) −48.8317 −2.53181
\(373\) −4.97998 −0.257853 −0.128927 0.991654i \(-0.541153\pi\)
−0.128927 + 0.991654i \(0.541153\pi\)
\(374\) −8.50611 −0.439841
\(375\) 79.9838 4.13035
\(376\) 3.40716 0.175711
\(377\) −6.24966 −0.321874
\(378\) 3.80057 0.195480
\(379\) 22.4150 1.15138 0.575690 0.817668i \(-0.304734\pi\)
0.575690 + 0.817668i \(0.304734\pi\)
\(380\) −36.1834 −1.85617
\(381\) −10.3333 −0.529390
\(382\) 40.3246 2.06318
\(383\) −30.2749 −1.54697 −0.773487 0.633812i \(-0.781489\pi\)
−0.773487 + 0.633812i \(0.781489\pi\)
\(384\) −48.0071 −2.44985
\(385\) −36.9783 −1.88459
\(386\) −60.7959 −3.09443
\(387\) 20.8824 1.06151
\(388\) −50.6870 −2.57324
\(389\) −9.64014 −0.488774 −0.244387 0.969678i \(-0.578587\pi\)
−0.244387 + 0.969678i \(0.578587\pi\)
\(390\) 24.3370 1.23235
\(391\) −4.92956 −0.249299
\(392\) 9.11524 0.460389
\(393\) 51.8279 2.61437
\(394\) 50.7603 2.55727
\(395\) 48.7458 2.45267
\(396\) 48.6590 2.44521
\(397\) −26.0762 −1.30873 −0.654363 0.756180i \(-0.727063\pi\)
−0.654363 + 0.756180i \(0.727063\pi\)
\(398\) −62.4318 −3.12942
\(399\) −13.0858 −0.655107
\(400\) 5.05674 0.252837
\(401\) 36.0830 1.80190 0.900950 0.433924i \(-0.142871\pi\)
0.900950 + 0.433924i \(0.142871\pi\)
\(402\) −7.95809 −0.396914
\(403\) −5.84018 −0.290920
\(404\) −53.4361 −2.65854
\(405\) 33.1814 1.64880
\(406\) −28.9015 −1.43436
\(407\) −39.6576 −1.96576
\(408\) 6.43891 0.318774
\(409\) −31.8928 −1.57700 −0.788498 0.615037i \(-0.789141\pi\)
−0.788498 + 0.615037i \(0.789141\pi\)
\(410\) 25.1014 1.23967
\(411\) −34.5503 −1.70424
\(412\) −5.30586 −0.261401
\(413\) −9.85575 −0.484970
\(414\) 45.1656 2.21977
\(415\) 53.4494 2.62373
\(416\) −5.18367 −0.254150
\(417\) −44.9943 −2.20338
\(418\) −26.3547 −1.28905
\(419\) 14.1428 0.690923 0.345462 0.938433i \(-0.387722\pi\)
0.345462 + 0.938433i \(0.387722\pi\)
\(420\) 70.2689 3.42877
\(421\) 5.07246 0.247217 0.123608 0.992331i \(-0.460553\pi\)
0.123608 + 0.992331i \(0.460553\pi\)
\(422\) −37.9675 −1.84823
\(423\) −3.70966 −0.180370
\(424\) 18.8894 0.917350
\(425\) 10.5425 0.511384
\(426\) 42.4036 2.05446
\(427\) 23.8743 1.15536
\(428\) −3.12099 −0.150859
\(429\) 11.0675 0.534343
\(430\) 60.7351 2.92891
\(431\) 16.8209 0.810233 0.405116 0.914265i \(-0.367231\pi\)
0.405116 + 0.914265i \(0.367231\pi\)
\(432\) −0.330262 −0.0158898
\(433\) 15.9238 0.765249 0.382624 0.923904i \(-0.375020\pi\)
0.382624 + 0.923904i \(0.375020\pi\)
\(434\) −27.0079 −1.29642
\(435\) 65.9170 3.16048
\(436\) 64.7673 3.10179
\(437\) −15.2734 −0.730624
\(438\) −29.8720 −1.42734
\(439\) −17.3955 −0.830244 −0.415122 0.909766i \(-0.636261\pi\)
−0.415122 + 0.909766i \(0.636261\pi\)
\(440\) 56.3750 2.68757
\(441\) −9.92451 −0.472596
\(442\) 1.93318 0.0919520
\(443\) −14.0738 −0.668664 −0.334332 0.942455i \(-0.608511\pi\)
−0.334332 + 0.942455i \(0.608511\pi\)
\(444\) 75.3604 3.57645
\(445\) 66.2952 3.14269
\(446\) 15.7085 0.743818
\(447\) −55.1932 −2.61055
\(448\) −25.5826 −1.20866
\(449\) −19.3251 −0.912007 −0.456003 0.889978i \(-0.650720\pi\)
−0.456003 + 0.889978i \(0.650720\pi\)
\(450\) −96.5921 −4.55339
\(451\) 11.4151 0.537516
\(452\) −7.57880 −0.356477
\(453\) 1.52870 0.0718244
\(454\) −6.38841 −0.299823
\(455\) 8.40403 0.393987
\(456\) 19.9498 0.934236
\(457\) 13.0933 0.612477 0.306238 0.951955i \(-0.400930\pi\)
0.306238 + 0.951955i \(0.400930\pi\)
\(458\) −38.5047 −1.79921
\(459\) −0.688543 −0.0321384
\(460\) 82.0161 3.82402
\(461\) 17.4314 0.811861 0.405930 0.913904i \(-0.366948\pi\)
0.405930 + 0.913904i \(0.366948\pi\)
\(462\) 51.1814 2.38118
\(463\) −15.9368 −0.740644 −0.370322 0.928903i \(-0.620753\pi\)
−0.370322 + 0.928903i \(0.620753\pi\)
\(464\) 2.51148 0.116593
\(465\) 61.5981 2.85654
\(466\) −52.0897 −2.41301
\(467\) 31.3594 1.45114 0.725569 0.688149i \(-0.241576\pi\)
0.725569 + 0.688149i \(0.241576\pi\)
\(468\) −11.0587 −0.511189
\(469\) −2.74808 −0.126895
\(470\) −10.7893 −0.497673
\(471\) −48.8675 −2.25170
\(472\) 15.0255 0.691606
\(473\) 27.6198 1.26996
\(474\) −67.4688 −3.09894
\(475\) 32.6639 1.49872
\(476\) 5.58172 0.255838
\(477\) −20.5664 −0.941672
\(478\) 17.8444 0.816183
\(479\) −5.29035 −0.241722 −0.120861 0.992669i \(-0.538566\pi\)
−0.120861 + 0.992669i \(0.538566\pi\)
\(480\) 54.6736 2.49550
\(481\) 9.01297 0.410956
\(482\) −3.16817 −0.144306
\(483\) 29.6612 1.34963
\(484\) 27.7921 1.26328
\(485\) 63.9384 2.90329
\(486\) −51.6151 −2.34131
\(487\) −28.7874 −1.30448 −0.652240 0.758012i \(-0.726171\pi\)
−0.652240 + 0.758012i \(0.726171\pi\)
\(488\) −36.3975 −1.64764
\(489\) 0.842561 0.0381019
\(490\) −28.8648 −1.30398
\(491\) 9.24466 0.417205 0.208603 0.978000i \(-0.433108\pi\)
0.208603 + 0.978000i \(0.433108\pi\)
\(492\) −21.6918 −0.977944
\(493\) 5.23603 0.235819
\(494\) 5.98962 0.269486
\(495\) −61.3802 −2.75883
\(496\) 2.34693 0.105380
\(497\) 14.6428 0.656818
\(498\) −73.9790 −3.31508
\(499\) 0.659907 0.0295415 0.0147708 0.999891i \(-0.495298\pi\)
0.0147708 + 0.999891i \(0.495298\pi\)
\(500\) −105.706 −4.72730
\(501\) −4.41903 −0.197428
\(502\) 14.6327 0.653090
\(503\) 12.6755 0.565170 0.282585 0.959242i \(-0.408808\pi\)
0.282585 + 0.959242i \(0.408808\pi\)
\(504\) −20.3719 −0.907438
\(505\) 67.4061 2.99953
\(506\) 59.7377 2.65566
\(507\) −2.51530 −0.111708
\(508\) 13.6563 0.605902
\(509\) 10.8954 0.482931 0.241466 0.970409i \(-0.422372\pi\)
0.241466 + 0.970409i \(0.422372\pi\)
\(510\) −20.3898 −0.902876
\(511\) −10.3154 −0.456325
\(512\) 4.53884 0.200590
\(513\) −2.13333 −0.0941888
\(514\) 63.0709 2.78194
\(515\) 6.69300 0.294929
\(516\) −52.4853 −2.31054
\(517\) −4.90653 −0.215789
\(518\) 41.6804 1.83133
\(519\) −23.1245 −1.01505
\(520\) −12.8123 −0.561858
\(521\) 6.30000 0.276008 0.138004 0.990432i \(-0.455931\pi\)
0.138004 + 0.990432i \(0.455931\pi\)
\(522\) −47.9735 −2.09974
\(523\) −4.69048 −0.205100 −0.102550 0.994728i \(-0.532700\pi\)
−0.102550 + 0.994728i \(0.532700\pi\)
\(524\) −68.4951 −2.99222
\(525\) −63.4342 −2.76849
\(526\) −0.686391 −0.0299281
\(527\) 4.89296 0.213141
\(528\) −4.44757 −0.193556
\(529\) 11.6198 0.505211
\(530\) −59.8161 −2.59825
\(531\) −16.3595 −0.709943
\(532\) 17.2940 0.749789
\(533\) −2.59430 −0.112372
\(534\) −91.7588 −3.97079
\(535\) 3.93692 0.170208
\(536\) 4.18957 0.180962
\(537\) 60.2882 2.60163
\(538\) −68.2737 −2.94349
\(539\) −13.1265 −0.565400
\(540\) 11.4557 0.492975
\(541\) 9.11956 0.392081 0.196040 0.980596i \(-0.437192\pi\)
0.196040 + 0.980596i \(0.437192\pi\)
\(542\) −5.97893 −0.256817
\(543\) 8.20214 0.351988
\(544\) 4.34293 0.186202
\(545\) −81.6997 −3.49963
\(546\) −11.6320 −0.497803
\(547\) 16.9628 0.725275 0.362638 0.931930i \(-0.381876\pi\)
0.362638 + 0.931930i \(0.381876\pi\)
\(548\) 45.6613 1.95055
\(549\) 39.6289 1.69132
\(550\) −127.756 −5.44754
\(551\) 16.2229 0.691119
\(552\) −45.2199 −1.92469
\(553\) −23.2983 −0.990742
\(554\) −4.72117 −0.200583
\(555\) −95.0623 −4.03517
\(556\) 59.4640 2.52183
\(557\) 0.459805 0.0194825 0.00974127 0.999953i \(-0.496899\pi\)
0.00974127 + 0.999953i \(0.496899\pi\)
\(558\) −44.8303 −1.89782
\(559\) −6.27715 −0.265495
\(560\) −3.37724 −0.142714
\(561\) −9.27245 −0.391483
\(562\) 75.3576 3.17877
\(563\) 14.8643 0.626458 0.313229 0.949678i \(-0.398589\pi\)
0.313229 + 0.949678i \(0.398589\pi\)
\(564\) 9.32376 0.392601
\(565\) 9.56016 0.402199
\(566\) 11.2217 0.471685
\(567\) −15.8592 −0.666022
\(568\) −22.3236 −0.936676
\(569\) 31.3976 1.31626 0.658128 0.752906i \(-0.271349\pi\)
0.658128 + 0.752906i \(0.271349\pi\)
\(570\) −63.1742 −2.64608
\(571\) −15.3776 −0.643534 −0.321767 0.946819i \(-0.604277\pi\)
−0.321767 + 0.946819i \(0.604277\pi\)
\(572\) −14.6266 −0.611571
\(573\) 43.9575 1.83635
\(574\) −11.9973 −0.500759
\(575\) −74.0387 −3.08763
\(576\) −42.4645 −1.76935
\(577\) −32.4485 −1.35085 −0.675424 0.737429i \(-0.736039\pi\)
−0.675424 + 0.737429i \(0.736039\pi\)
\(578\) 37.6065 1.56422
\(579\) −66.2731 −2.75422
\(580\) −87.1151 −3.61726
\(581\) −25.5464 −1.05984
\(582\) −88.4967 −3.66831
\(583\) −27.2019 −1.12659
\(584\) 15.7262 0.650757
\(585\) 13.9498 0.576755
\(586\) −23.1621 −0.956818
\(587\) −15.1447 −0.625088 −0.312544 0.949903i \(-0.601181\pi\)
−0.312544 + 0.949903i \(0.601181\pi\)
\(588\) 24.9440 1.02867
\(589\) 15.1600 0.624656
\(590\) −47.5806 −1.95886
\(591\) 55.3334 2.27611
\(592\) −3.62194 −0.148861
\(593\) −35.3234 −1.45056 −0.725279 0.688455i \(-0.758289\pi\)
−0.725279 + 0.688455i \(0.758289\pi\)
\(594\) 8.34394 0.342356
\(595\) −7.04098 −0.288652
\(596\) 72.9426 2.98785
\(597\) −68.0563 −2.78536
\(598\) −13.5765 −0.555186
\(599\) 26.5482 1.08473 0.542364 0.840143i \(-0.317529\pi\)
0.542364 + 0.840143i \(0.317529\pi\)
\(600\) 96.7082 3.94810
\(601\) 13.0158 0.530924 0.265462 0.964121i \(-0.414476\pi\)
0.265462 + 0.964121i \(0.414476\pi\)
\(602\) −29.0286 −1.18312
\(603\) −4.56153 −0.185760
\(604\) −2.02031 −0.0822051
\(605\) −35.0579 −1.42531
\(606\) −93.2965 −3.78991
\(607\) 29.0374 1.17859 0.589297 0.807917i \(-0.299405\pi\)
0.589297 + 0.807917i \(0.299405\pi\)
\(608\) 13.4558 0.545705
\(609\) −31.5053 −1.27666
\(610\) 115.258 4.66667
\(611\) 1.11510 0.0451123
\(612\) 9.26509 0.374519
\(613\) 11.8500 0.478617 0.239308 0.970944i \(-0.423079\pi\)
0.239308 + 0.970944i \(0.423079\pi\)
\(614\) −55.7460 −2.24973
\(615\) 27.3629 1.10338
\(616\) −26.9447 −1.08563
\(617\) 37.5497 1.51169 0.755847 0.654749i \(-0.227225\pi\)
0.755847 + 0.654749i \(0.227225\pi\)
\(618\) −9.26374 −0.372642
\(619\) −1.00000 −0.0401934
\(620\) −81.4073 −3.26939
\(621\) 4.83557 0.194045
\(622\) 31.2542 1.25318
\(623\) −31.6860 −1.26947
\(624\) 1.01080 0.0404642
\(625\) 70.4240 2.81696
\(626\) 33.7346 1.34831
\(627\) −28.7290 −1.14733
\(628\) 64.5827 2.57713
\(629\) −7.55115 −0.301084
\(630\) 64.5108 2.57017
\(631\) 7.06177 0.281125 0.140562 0.990072i \(-0.455109\pi\)
0.140562 + 0.990072i \(0.455109\pi\)
\(632\) 35.5192 1.41288
\(633\) −41.3880 −1.64503
\(634\) −32.5288 −1.29188
\(635\) −17.2266 −0.683616
\(636\) 51.6912 2.04969
\(637\) 2.98326 0.118201
\(638\) −63.4516 −2.51207
\(639\) 24.3055 0.961511
\(640\) −80.0325 −3.16356
\(641\) 48.5922 1.91928 0.959638 0.281237i \(-0.0907446\pi\)
0.959638 + 0.281237i \(0.0907446\pi\)
\(642\) −5.44907 −0.215058
\(643\) −22.8077 −0.899450 −0.449725 0.893167i \(-0.648478\pi\)
−0.449725 + 0.893167i \(0.648478\pi\)
\(644\) −39.1999 −1.54469
\(645\) 66.2068 2.60689
\(646\) −5.01816 −0.197437
\(647\) 39.8494 1.56664 0.783320 0.621619i \(-0.213525\pi\)
0.783320 + 0.621619i \(0.213525\pi\)
\(648\) 24.1780 0.949802
\(649\) −21.6377 −0.849355
\(650\) 29.0351 1.13885
\(651\) −29.4410 −1.15389
\(652\) −1.11352 −0.0436087
\(653\) 21.9504 0.858987 0.429494 0.903070i \(-0.358692\pi\)
0.429494 + 0.903070i \(0.358692\pi\)
\(654\) 113.080 4.42178
\(655\) 86.4022 3.37601
\(656\) 1.04254 0.0407045
\(657\) −17.1225 −0.668011
\(658\) 5.15679 0.201032
\(659\) 49.2922 1.92015 0.960076 0.279740i \(-0.0902483\pi\)
0.960076 + 0.279740i \(0.0902483\pi\)
\(660\) 154.271 6.00501
\(661\) −31.3296 −1.21858 −0.609290 0.792948i \(-0.708545\pi\)
−0.609290 + 0.792948i \(0.708545\pi\)
\(662\) 44.5951 1.73324
\(663\) 2.10734 0.0818424
\(664\) 38.9466 1.51142
\(665\) −21.8152 −0.845959
\(666\) 69.1851 2.68087
\(667\) −36.7722 −1.42382
\(668\) 5.84013 0.225961
\(669\) 17.1237 0.662040
\(670\) −13.2669 −0.512546
\(671\) 52.4147 2.02345
\(672\) −26.1315 −1.00804
\(673\) −23.0839 −0.889821 −0.444910 0.895575i \(-0.646764\pi\)
−0.444910 + 0.895575i \(0.646764\pi\)
\(674\) −37.3714 −1.43949
\(675\) −10.3415 −0.398043
\(676\) 3.32419 0.127853
\(677\) −18.4307 −0.708351 −0.354175 0.935179i \(-0.615238\pi\)
−0.354175 + 0.935179i \(0.615238\pi\)
\(678\) −13.2322 −0.508178
\(679\) −30.5596 −1.17277
\(680\) 10.7343 0.411641
\(681\) −6.96395 −0.266859
\(682\) −59.2942 −2.27049
\(683\) 10.4717 0.400689 0.200345 0.979725i \(-0.435794\pi\)
0.200345 + 0.979725i \(0.435794\pi\)
\(684\) 28.7062 1.09761
\(685\) −57.5988 −2.20074
\(686\) 46.1675 1.76268
\(687\) −41.9737 −1.60140
\(688\) 2.52253 0.0961705
\(689\) 6.18217 0.235522
\(690\) 143.196 5.45137
\(691\) −48.1953 −1.83344 −0.916718 0.399535i \(-0.869172\pi\)
−0.916718 + 0.399535i \(0.869172\pi\)
\(692\) 30.5611 1.16176
\(693\) 29.3369 1.11442
\(694\) 45.6386 1.73242
\(695\) −75.0099 −2.84529
\(696\) 48.0312 1.82062
\(697\) 2.17353 0.0823285
\(698\) 55.7026 2.10837
\(699\) −56.7826 −2.14771
\(700\) 83.8338 3.16862
\(701\) 3.42573 0.129388 0.0646941 0.997905i \(-0.479393\pi\)
0.0646941 + 0.997905i \(0.479393\pi\)
\(702\) −1.89632 −0.0715721
\(703\) −23.3959 −0.882393
\(704\) −56.1651 −2.11680
\(705\) −11.7613 −0.442957
\(706\) −28.2776 −1.06424
\(707\) −32.2170 −1.21165
\(708\) 41.1177 1.54530
\(709\) 26.2834 0.987093 0.493546 0.869719i \(-0.335700\pi\)
0.493546 + 0.869719i \(0.335700\pi\)
\(710\) 70.6910 2.65299
\(711\) −38.6727 −1.45034
\(712\) 48.3068 1.81037
\(713\) −34.3628 −1.28690
\(714\) 9.74539 0.364712
\(715\) 18.4506 0.690012
\(716\) −79.6761 −2.97764
\(717\) 19.4520 0.726449
\(718\) 16.2106 0.604972
\(719\) 1.00578 0.0375094 0.0187547 0.999824i \(-0.494030\pi\)
0.0187547 + 0.999824i \(0.494030\pi\)
\(720\) −5.60587 −0.208918
\(721\) −3.19895 −0.119135
\(722\) 28.2931 1.05296
\(723\) −3.45360 −0.128441
\(724\) −10.8398 −0.402860
\(725\) 78.6417 2.92068
\(726\) 48.5235 1.80088
\(727\) 15.7201 0.583027 0.291513 0.956567i \(-0.405841\pi\)
0.291513 + 0.956567i \(0.405841\pi\)
\(728\) 6.12370 0.226959
\(729\) −32.5261 −1.20467
\(730\) −49.7996 −1.84317
\(731\) 5.25905 0.194513
\(732\) −99.6024 −3.68141
\(733\) −41.8845 −1.54704 −0.773519 0.633773i \(-0.781506\pi\)
−0.773519 + 0.633773i \(0.781506\pi\)
\(734\) 78.4397 2.89526
\(735\) −31.4653 −1.16061
\(736\) −30.5000 −1.12424
\(737\) −6.03325 −0.222238
\(738\) −19.9143 −0.733057
\(739\) −33.1751 −1.22036 −0.610182 0.792261i \(-0.708904\pi\)
−0.610182 + 0.792261i \(0.708904\pi\)
\(740\) 125.633 4.61837
\(741\) 6.52923 0.239857
\(742\) 28.5894 1.04955
\(743\) −28.3361 −1.03955 −0.519775 0.854303i \(-0.673984\pi\)
−0.519775 + 0.854303i \(0.673984\pi\)
\(744\) 44.8842 1.64553
\(745\) −92.0124 −3.37107
\(746\) 11.4909 0.420712
\(747\) −42.4043 −1.55149
\(748\) 12.2544 0.448063
\(749\) −1.88167 −0.0687547
\(750\) −184.556 −6.73904
\(751\) −29.2251 −1.06644 −0.533220 0.845977i \(-0.679018\pi\)
−0.533220 + 0.845977i \(0.679018\pi\)
\(752\) −0.448115 −0.0163411
\(753\) 15.9510 0.581287
\(754\) 14.4206 0.525167
\(755\) 2.54849 0.0927489
\(756\) −5.47530 −0.199135
\(757\) −3.60291 −0.130950 −0.0654750 0.997854i \(-0.520856\pi\)
−0.0654750 + 0.997854i \(0.520856\pi\)
\(758\) −51.7207 −1.87858
\(759\) 65.1195 2.36369
\(760\) 33.2583 1.20641
\(761\) −19.0691 −0.691253 −0.345626 0.938372i \(-0.612334\pi\)
−0.345626 + 0.938372i \(0.612334\pi\)
\(762\) 23.8432 0.863749
\(763\) 39.0487 1.41366
\(764\) −58.0937 −2.10175
\(765\) −11.6873 −0.422556
\(766\) 69.8569 2.52403
\(767\) 4.91759 0.177564
\(768\) 46.5588 1.68004
\(769\) 3.33850 0.120389 0.0601947 0.998187i \(-0.480828\pi\)
0.0601947 + 0.998187i \(0.480828\pi\)
\(770\) 85.3244 3.07488
\(771\) 68.7531 2.47608
\(772\) 87.5858 3.15228
\(773\) −24.8408 −0.893461 −0.446730 0.894669i \(-0.647412\pi\)
−0.446730 + 0.894669i \(0.647412\pi\)
\(774\) −48.1845 −1.73196
\(775\) 73.4891 2.63981
\(776\) 46.5895 1.67246
\(777\) 45.4354 1.62999
\(778\) 22.2438 0.797481
\(779\) 6.73431 0.241282
\(780\) −35.0612 −1.25539
\(781\) 32.1474 1.15032
\(782\) 11.3746 0.406754
\(783\) −5.13620 −0.183553
\(784\) −1.19885 −0.0428161
\(785\) −81.4670 −2.90768
\(786\) −119.589 −4.26559
\(787\) −28.3371 −1.01011 −0.505054 0.863088i \(-0.668527\pi\)
−0.505054 + 0.863088i \(0.668527\pi\)
\(788\) −73.1280 −2.60508
\(789\) −0.748230 −0.0266377
\(790\) −112.477 −4.00176
\(791\) −4.56932 −0.162466
\(792\) −44.7254 −1.58925
\(793\) −11.9123 −0.423017
\(794\) 60.1687 2.13531
\(795\) −65.2051 −2.31259
\(796\) 89.9424 3.18792
\(797\) 23.9952 0.849954 0.424977 0.905204i \(-0.360282\pi\)
0.424977 + 0.905204i \(0.360282\pi\)
\(798\) 30.1944 1.06887
\(799\) −0.934245 −0.0330512
\(800\) 65.2279 2.30616
\(801\) −52.5956 −1.85837
\(802\) −83.2587 −2.93997
\(803\) −22.6468 −0.799189
\(804\) 11.4648 0.404334
\(805\) 49.4482 1.74282
\(806\) 13.4758 0.474663
\(807\) −74.4246 −2.61987
\(808\) 49.1163 1.72791
\(809\) −9.66366 −0.339756 −0.169878 0.985465i \(-0.554337\pi\)
−0.169878 + 0.985465i \(0.554337\pi\)
\(810\) −76.5634 −2.69016
\(811\) −23.4690 −0.824109 −0.412055 0.911159i \(-0.635189\pi\)
−0.412055 + 0.911159i \(0.635189\pi\)
\(812\) 41.6370 1.46117
\(813\) −6.51758 −0.228582
\(814\) 91.5068 3.20731
\(815\) 1.40463 0.0492021
\(816\) −0.846855 −0.0296459
\(817\) 16.2943 0.570064
\(818\) 73.5901 2.57302
\(819\) −6.66738 −0.232977
\(820\) −36.1624 −1.26285
\(821\) −0.117516 −0.00410135 −0.00205068 0.999998i \(-0.500653\pi\)
−0.00205068 + 0.999998i \(0.500653\pi\)
\(822\) 79.7221 2.78063
\(823\) −18.1813 −0.633759 −0.316880 0.948466i \(-0.602635\pi\)
−0.316880 + 0.948466i \(0.602635\pi\)
\(824\) 4.87694 0.169896
\(825\) −139.266 −4.84862
\(826\) 22.7414 0.791273
\(827\) −54.8879 −1.90864 −0.954319 0.298789i \(-0.903417\pi\)
−0.954319 + 0.298789i \(0.903417\pi\)
\(828\) −65.0679 −2.26127
\(829\) 15.8018 0.548819 0.274409 0.961613i \(-0.411518\pi\)
0.274409 + 0.961613i \(0.411518\pi\)
\(830\) −123.330 −4.28086
\(831\) −5.14651 −0.178530
\(832\) 12.7646 0.442534
\(833\) −2.49940 −0.0865992
\(834\) 103.821 3.59502
\(835\) −7.36695 −0.254944
\(836\) 37.9679 1.31315
\(837\) −4.79968 −0.165901
\(838\) −32.6335 −1.12731
\(839\) 2.26113 0.0780630 0.0390315 0.999238i \(-0.487573\pi\)
0.0390315 + 0.999238i \(0.487573\pi\)
\(840\) −64.5884 −2.22851
\(841\) 10.0583 0.346837
\(842\) −11.7043 −0.403357
\(843\) 82.1467 2.82928
\(844\) 54.6979 1.88278
\(845\) −4.19325 −0.144252
\(846\) 8.55974 0.294290
\(847\) 16.7561 0.575745
\(848\) −2.48436 −0.0853133
\(849\) 12.2327 0.419826
\(850\) −24.3259 −0.834371
\(851\) 53.0311 1.81788
\(852\) −61.0889 −2.09287
\(853\) −0.161949 −0.00554503 −0.00277251 0.999996i \(-0.500883\pi\)
−0.00277251 + 0.999996i \(0.500883\pi\)
\(854\) −55.0881 −1.88508
\(855\) −36.2111 −1.23839
\(856\) 2.86869 0.0980497
\(857\) −3.34887 −0.114395 −0.0571976 0.998363i \(-0.518217\pi\)
−0.0571976 + 0.998363i \(0.518217\pi\)
\(858\) −25.5373 −0.871830
\(859\) 22.6702 0.773497 0.386749 0.922185i \(-0.373598\pi\)
0.386749 + 0.922185i \(0.373598\pi\)
\(860\) −87.4982 −2.98366
\(861\) −13.0782 −0.445704
\(862\) −38.8128 −1.32197
\(863\) 14.7355 0.501604 0.250802 0.968038i \(-0.419306\pi\)
0.250802 + 0.968038i \(0.419306\pi\)
\(864\) −4.26013 −0.144933
\(865\) −38.5509 −1.31077
\(866\) −36.7429 −1.24857
\(867\) 40.9945 1.39225
\(868\) 38.9089 1.32065
\(869\) −51.1500 −1.73514
\(870\) −152.098 −5.15661
\(871\) 1.37117 0.0464605
\(872\) −59.5315 −2.01599
\(873\) −50.7258 −1.71681
\(874\) 35.2421 1.19208
\(875\) −63.7308 −2.15449
\(876\) 43.0352 1.45402
\(877\) −13.4780 −0.455120 −0.227560 0.973764i \(-0.573075\pi\)
−0.227560 + 0.973764i \(0.573075\pi\)
\(878\) 40.1388 1.35462
\(879\) −25.2488 −0.851622
\(880\) −7.41453 −0.249944
\(881\) −30.3003 −1.02084 −0.510422 0.859924i \(-0.670511\pi\)
−0.510422 + 0.859924i \(0.670511\pi\)
\(882\) 22.9000 0.771084
\(883\) 31.8695 1.07249 0.536246 0.844061i \(-0.319842\pi\)
0.536246 + 0.844061i \(0.319842\pi\)
\(884\) −2.78504 −0.0936710
\(885\) −51.8673 −1.74350
\(886\) 32.4741 1.09099
\(887\) 14.0184 0.470692 0.235346 0.971912i \(-0.424378\pi\)
0.235346 + 0.971912i \(0.424378\pi\)
\(888\) −69.2683 −2.32449
\(889\) 8.23352 0.276143
\(890\) −152.971 −5.12759
\(891\) −34.8179 −1.16644
\(892\) −22.6305 −0.757724
\(893\) −2.89459 −0.0968639
\(894\) 127.354 4.25935
\(895\) 100.506 3.35955
\(896\) 38.2518 1.27790
\(897\) −14.7997 −0.494147
\(898\) 44.5911 1.48802
\(899\) 36.4992 1.21732
\(900\) 139.156 4.63852
\(901\) −5.17948 −0.172554
\(902\) −26.3394 −0.877008
\(903\) −31.6438 −1.05304
\(904\) 6.96613 0.231690
\(905\) 13.6738 0.454531
\(906\) −3.52735 −0.117188
\(907\) 11.4493 0.380169 0.190085 0.981768i \(-0.439124\pi\)
0.190085 + 0.981768i \(0.439124\pi\)
\(908\) 9.20347 0.305428
\(909\) −53.4770 −1.77372
\(910\) −19.3916 −0.642827
\(911\) 4.89970 0.162334 0.0811672 0.996701i \(-0.474135\pi\)
0.0811672 + 0.996701i \(0.474135\pi\)
\(912\) −2.62383 −0.0868837
\(913\) −56.0856 −1.85616
\(914\) −30.2117 −0.999313
\(915\) 125.642 4.15359
\(916\) 55.4719 1.83284
\(917\) −41.2963 −1.36372
\(918\) 1.58876 0.0524368
\(919\) 1.67117 0.0551267 0.0275633 0.999620i \(-0.491225\pi\)
0.0275633 + 0.999620i \(0.491225\pi\)
\(920\) −75.3860 −2.48540
\(921\) −60.7682 −2.00238
\(922\) −40.2215 −1.32463
\(923\) −7.30611 −0.240484
\(924\) −73.7346 −2.42569
\(925\) −113.413 −3.72901
\(926\) 36.7728 1.20843
\(927\) −5.30992 −0.174401
\(928\) 32.3962 1.06346
\(929\) −42.5355 −1.39555 −0.697773 0.716319i \(-0.745825\pi\)
−0.697773 + 0.716319i \(0.745825\pi\)
\(930\) −142.133 −4.66071
\(931\) −7.74396 −0.253798
\(932\) 75.0432 2.45812
\(933\) 34.0700 1.11540
\(934\) −72.3593 −2.36767
\(935\) −15.4581 −0.505533
\(936\) 10.1647 0.332244
\(937\) 0.952489 0.0311164 0.0155582 0.999879i \(-0.495047\pi\)
0.0155582 + 0.999879i \(0.495047\pi\)
\(938\) 6.34098 0.207040
\(939\) 36.7738 1.20007
\(940\) 15.5436 0.506977
\(941\) −4.21856 −0.137521 −0.0687606 0.997633i \(-0.521904\pi\)
−0.0687606 + 0.997633i \(0.521904\pi\)
\(942\) 112.758 3.67385
\(943\) −15.2645 −0.497082
\(944\) −1.97618 −0.0643192
\(945\) 6.90674 0.224676
\(946\) −63.7306 −2.07206
\(947\) −1.82244 −0.0592212 −0.0296106 0.999562i \(-0.509427\pi\)
−0.0296106 + 0.999562i \(0.509427\pi\)
\(948\) 97.1991 3.15688
\(949\) 5.14693 0.167076
\(950\) −75.3695 −2.44531
\(951\) −35.4593 −1.14985
\(952\) −5.13050 −0.166280
\(953\) −5.69949 −0.184625 −0.0923124 0.995730i \(-0.529426\pi\)
−0.0923124 + 0.995730i \(0.529426\pi\)
\(954\) 47.4554 1.53643
\(955\) 73.2814 2.37133
\(956\) −25.7076 −0.831442
\(957\) −69.1680 −2.23588
\(958\) 12.2071 0.394392
\(959\) 27.5296 0.888976
\(960\) −134.632 −4.34523
\(961\) 3.10773 0.100249
\(962\) −20.7967 −0.670513
\(963\) −3.12338 −0.100649
\(964\) 4.56423 0.147004
\(965\) −110.484 −3.55660
\(966\) −68.4410 −2.20205
\(967\) 46.0581 1.48113 0.740564 0.671986i \(-0.234558\pi\)
0.740564 + 0.671986i \(0.234558\pi\)
\(968\) −25.5454 −0.821060
\(969\) −5.47026 −0.175730
\(970\) −147.533 −4.73699
\(971\) −22.5596 −0.723972 −0.361986 0.932183i \(-0.617901\pi\)
−0.361986 + 0.932183i \(0.617901\pi\)
\(972\) 74.3594 2.38508
\(973\) 35.8513 1.14934
\(974\) 66.4246 2.12838
\(975\) 31.6509 1.01364
\(976\) 4.78705 0.153230
\(977\) −48.7202 −1.55870 −0.779349 0.626590i \(-0.784450\pi\)
−0.779349 + 0.626590i \(0.784450\pi\)
\(978\) −1.94414 −0.0621668
\(979\) −69.5649 −2.22330
\(980\) 41.5841 1.32836
\(981\) 64.8168 2.06944
\(982\) −21.3313 −0.680709
\(983\) −60.9557 −1.94419 −0.972093 0.234597i \(-0.924623\pi\)
−0.972093 + 0.234597i \(0.924623\pi\)
\(984\) 19.9383 0.635609
\(985\) 92.2462 2.93921
\(986\) −12.0817 −0.384760
\(987\) 5.62137 0.178930
\(988\) −8.62895 −0.274524
\(989\) −36.9339 −1.17443
\(990\) 141.630 4.50129
\(991\) 29.1645 0.926442 0.463221 0.886243i \(-0.346694\pi\)
0.463221 + 0.886243i \(0.346694\pi\)
\(992\) 30.2736 0.961187
\(993\) 48.6127 1.54268
\(994\) −33.7870 −1.07166
\(995\) −113.457 −3.59681
\(996\) 106.578 3.37705
\(997\) 41.4988 1.31428 0.657140 0.753768i \(-0.271766\pi\)
0.657140 + 0.753768i \(0.271766\pi\)
\(998\) −1.52268 −0.0481997
\(999\) 7.40718 0.234353
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 8047.2.a.c.1.18 151
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8047.2.a.c.1.18 151 1.1 even 1 trivial