Properties

Label 8041.2.a.h.1.10
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $1$
Dimension $74$
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] = [8041,2,Mod(1,8041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8041, 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("8041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8041 = 11 \cdot 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8041.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: \(64.2077082653\)
Analytic rank: \(1\)
Dimension: \(74\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 8041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.34491 q^{2} -2.19404 q^{3} +3.49862 q^{4} +1.59097 q^{5} +5.14484 q^{6} -2.37576 q^{7} -3.51413 q^{8} +1.81381 q^{9} +O(q^{10})\) \(q-2.34491 q^{2} -2.19404 q^{3} +3.49862 q^{4} +1.59097 q^{5} +5.14484 q^{6} -2.37576 q^{7} -3.51413 q^{8} +1.81381 q^{9} -3.73069 q^{10} -1.00000 q^{11} -7.67611 q^{12} -5.53511 q^{13} +5.57096 q^{14} -3.49066 q^{15} +1.24310 q^{16} -1.00000 q^{17} -4.25324 q^{18} -1.91161 q^{19} +5.56620 q^{20} +5.21252 q^{21} +2.34491 q^{22} -0.773032 q^{23} +7.71015 q^{24} -2.46881 q^{25} +12.9794 q^{26} +2.60254 q^{27} -8.31190 q^{28} -9.38899 q^{29} +8.18529 q^{30} -4.00423 q^{31} +4.11331 q^{32} +2.19404 q^{33} +2.34491 q^{34} -3.77977 q^{35} +6.34585 q^{36} +9.93142 q^{37} +4.48256 q^{38} +12.1443 q^{39} -5.59089 q^{40} -1.96661 q^{41} -12.2229 q^{42} -1.00000 q^{43} -3.49862 q^{44} +2.88573 q^{45} +1.81269 q^{46} +9.42033 q^{47} -2.72741 q^{48} -1.35574 q^{49} +5.78914 q^{50} +2.19404 q^{51} -19.3652 q^{52} +12.4080 q^{53} -6.10273 q^{54} -1.59097 q^{55} +8.34875 q^{56} +4.19415 q^{57} +22.0164 q^{58} +10.4087 q^{59} -12.2125 q^{60} +4.26777 q^{61} +9.38958 q^{62} -4.30920 q^{63} -12.1315 q^{64} -8.80621 q^{65} -5.14484 q^{66} +12.6223 q^{67} -3.49862 q^{68} +1.69606 q^{69} +8.86324 q^{70} +2.28947 q^{71} -6.37398 q^{72} +6.33403 q^{73} -23.2883 q^{74} +5.41667 q^{75} -6.68799 q^{76} +2.37576 q^{77} -28.4772 q^{78} -6.22362 q^{79} +1.97773 q^{80} -11.1515 q^{81} +4.61153 q^{82} -8.00954 q^{83} +18.2366 q^{84} -1.59097 q^{85} +2.34491 q^{86} +20.5998 q^{87} +3.51413 q^{88} +16.2151 q^{89} -6.76678 q^{90} +13.1501 q^{91} -2.70454 q^{92} +8.78545 q^{93} -22.0899 q^{94} -3.04132 q^{95} -9.02476 q^{96} -0.975893 q^{97} +3.17910 q^{98} -1.81381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34491 −1.65810 −0.829052 0.559171i \(-0.811119\pi\)
−0.829052 + 0.559171i \(0.811119\pi\)
\(3\) −2.19404 −1.26673 −0.633365 0.773853i \(-0.718327\pi\)
−0.633365 + 0.773853i \(0.718327\pi\)
\(4\) 3.49862 1.74931
\(5\) 1.59097 0.711504 0.355752 0.934580i \(-0.384225\pi\)
0.355752 + 0.934580i \(0.384225\pi\)
\(6\) 5.14484 2.10037
\(7\) −2.37576 −0.897955 −0.448977 0.893543i \(-0.648212\pi\)
−0.448977 + 0.893543i \(0.648212\pi\)
\(8\) −3.51413 −1.24243
\(9\) 1.81381 0.604605
\(10\) −3.73069 −1.17975
\(11\) −1.00000 −0.301511
\(12\) −7.67611 −2.21590
\(13\) −5.53511 −1.53516 −0.767582 0.640951i \(-0.778540\pi\)
−0.767582 + 0.640951i \(0.778540\pi\)
\(14\) 5.57096 1.48890
\(15\) −3.49066 −0.901284
\(16\) 1.24310 0.310775
\(17\) −1.00000 −0.242536
\(18\) −4.25324 −1.00250
\(19\) −1.91161 −0.438553 −0.219277 0.975663i \(-0.570370\pi\)
−0.219277 + 0.975663i \(0.570370\pi\)
\(20\) 5.56620 1.24464
\(21\) 5.21252 1.13747
\(22\) 2.34491 0.499937
\(23\) −0.773032 −0.161188 −0.0805942 0.996747i \(-0.525682\pi\)
−0.0805942 + 0.996747i \(0.525682\pi\)
\(24\) 7.71015 1.57383
\(25\) −2.46881 −0.493762
\(26\) 12.9794 2.54546
\(27\) 2.60254 0.500859
\(28\) −8.31190 −1.57080
\(29\) −9.38899 −1.74349 −0.871745 0.489959i \(-0.837012\pi\)
−0.871745 + 0.489959i \(0.837012\pi\)
\(30\) 8.18529 1.49442
\(31\) −4.00423 −0.719181 −0.359591 0.933110i \(-0.617084\pi\)
−0.359591 + 0.933110i \(0.617084\pi\)
\(32\) 4.11331 0.727137
\(33\) 2.19404 0.381933
\(34\) 2.34491 0.402149
\(35\) −3.77977 −0.638898
\(36\) 6.34585 1.05764
\(37\) 9.93142 1.63272 0.816358 0.577546i \(-0.195990\pi\)
0.816358 + 0.577546i \(0.195990\pi\)
\(38\) 4.48256 0.727167
\(39\) 12.1443 1.94464
\(40\) −5.59089 −0.883997
\(41\) −1.96661 −0.307133 −0.153566 0.988138i \(-0.549076\pi\)
−0.153566 + 0.988138i \(0.549076\pi\)
\(42\) −12.2229 −1.88604
\(43\) −1.00000 −0.152499
\(44\) −3.49862 −0.527437
\(45\) 2.88573 0.430179
\(46\) 1.81269 0.267267
\(47\) 9.42033 1.37410 0.687048 0.726612i \(-0.258906\pi\)
0.687048 + 0.726612i \(0.258906\pi\)
\(48\) −2.72741 −0.393668
\(49\) −1.35574 −0.193677
\(50\) 5.78914 0.818709
\(51\) 2.19404 0.307227
\(52\) −19.3652 −2.68548
\(53\) 12.4080 1.70436 0.852182 0.523246i \(-0.175279\pi\)
0.852182 + 0.523246i \(0.175279\pi\)
\(54\) −6.10273 −0.830476
\(55\) −1.59097 −0.214527
\(56\) 8.34875 1.11565
\(57\) 4.19415 0.555528
\(58\) 22.0164 2.89089
\(59\) 10.4087 1.35510 0.677549 0.735477i \(-0.263042\pi\)
0.677549 + 0.735477i \(0.263042\pi\)
\(60\) −12.2125 −1.57662
\(61\) 4.26777 0.546432 0.273216 0.961953i \(-0.411913\pi\)
0.273216 + 0.961953i \(0.411913\pi\)
\(62\) 9.38958 1.19248
\(63\) −4.30920 −0.542908
\(64\) −12.1315 −1.51644
\(65\) −8.80621 −1.09228
\(66\) −5.14484 −0.633285
\(67\) 12.6223 1.54205 0.771027 0.636803i \(-0.219743\pi\)
0.771027 + 0.636803i \(0.219743\pi\)
\(68\) −3.49862 −0.424270
\(69\) 1.69606 0.204182
\(70\) 8.86324 1.05936
\(71\) 2.28947 0.271710 0.135855 0.990729i \(-0.456622\pi\)
0.135855 + 0.990729i \(0.456622\pi\)
\(72\) −6.37398 −0.751181
\(73\) 6.33403 0.741342 0.370671 0.928764i \(-0.379128\pi\)
0.370671 + 0.928764i \(0.379128\pi\)
\(74\) −23.2883 −2.70721
\(75\) 5.41667 0.625463
\(76\) −6.68799 −0.767165
\(77\) 2.37576 0.270744
\(78\) −28.4772 −3.22441
\(79\) −6.22362 −0.700212 −0.350106 0.936710i \(-0.613855\pi\)
−0.350106 + 0.936710i \(0.613855\pi\)
\(80\) 1.97773 0.221117
\(81\) −11.1515 −1.23906
\(82\) 4.61153 0.509258
\(83\) −8.00954 −0.879161 −0.439581 0.898203i \(-0.644873\pi\)
−0.439581 + 0.898203i \(0.644873\pi\)
\(84\) 18.2366 1.98978
\(85\) −1.59097 −0.172565
\(86\) 2.34491 0.252859
\(87\) 20.5998 2.20853
\(88\) 3.51413 0.374608
\(89\) 16.2151 1.71879 0.859396 0.511310i \(-0.170840\pi\)
0.859396 + 0.511310i \(0.170840\pi\)
\(90\) −6.76678 −0.713281
\(91\) 13.1501 1.37851
\(92\) −2.70454 −0.281968
\(93\) 8.78545 0.911008
\(94\) −22.0899 −2.27840
\(95\) −3.04132 −0.312032
\(96\) −9.02476 −0.921086
\(97\) −0.975893 −0.0990870 −0.0495435 0.998772i \(-0.515777\pi\)
−0.0495435 + 0.998772i \(0.515777\pi\)
\(98\) 3.17910 0.321137
\(99\) −1.81381 −0.182295
\(100\) −8.63742 −0.863742
\(101\) 16.0598 1.59801 0.799007 0.601322i \(-0.205359\pi\)
0.799007 + 0.601322i \(0.205359\pi\)
\(102\) −5.14484 −0.509415
\(103\) −15.6825 −1.54524 −0.772620 0.634869i \(-0.781054\pi\)
−0.772620 + 0.634869i \(0.781054\pi\)
\(104\) 19.4511 1.90734
\(105\) 8.29298 0.809312
\(106\) −29.0956 −2.82601
\(107\) −11.1554 −1.07843 −0.539217 0.842167i \(-0.681280\pi\)
−0.539217 + 0.842167i \(0.681280\pi\)
\(108\) 9.10530 0.876157
\(109\) 9.34647 0.895229 0.447615 0.894227i \(-0.352274\pi\)
0.447615 + 0.894227i \(0.352274\pi\)
\(110\) 3.73069 0.355707
\(111\) −21.7899 −2.06821
\(112\) −2.95331 −0.279062
\(113\) 10.2119 0.960652 0.480326 0.877090i \(-0.340518\pi\)
0.480326 + 0.877090i \(0.340518\pi\)
\(114\) −9.83491 −0.921124
\(115\) −1.22987 −0.114686
\(116\) −32.8485 −3.04991
\(117\) −10.0397 −0.928167
\(118\) −24.4075 −2.24689
\(119\) 2.37576 0.217786
\(120\) 12.2666 1.11978
\(121\) 1.00000 0.0909091
\(122\) −10.0076 −0.906042
\(123\) 4.31482 0.389054
\(124\) −14.0093 −1.25807
\(125\) −11.8827 −1.06282
\(126\) 10.1047 0.900197
\(127\) 15.6960 1.39280 0.696398 0.717656i \(-0.254785\pi\)
0.696398 + 0.717656i \(0.254785\pi\)
\(128\) 20.2208 1.78728
\(129\) 2.19404 0.193175
\(130\) 20.6498 1.81111
\(131\) 19.7724 1.72752 0.863760 0.503904i \(-0.168103\pi\)
0.863760 + 0.503904i \(0.168103\pi\)
\(132\) 7.67611 0.668120
\(133\) 4.54153 0.393801
\(134\) −29.5981 −2.55689
\(135\) 4.14057 0.356363
\(136\) 3.51413 0.301334
\(137\) −0.240622 −0.0205578 −0.0102789 0.999947i \(-0.503272\pi\)
−0.0102789 + 0.999947i \(0.503272\pi\)
\(138\) −3.97712 −0.338555
\(139\) −8.31531 −0.705295 −0.352648 0.935756i \(-0.614719\pi\)
−0.352648 + 0.935756i \(0.614719\pi\)
\(140\) −13.2240 −1.11763
\(141\) −20.6686 −1.74061
\(142\) −5.36860 −0.450523
\(143\) 5.53511 0.462869
\(144\) 2.25475 0.187896
\(145\) −14.9376 −1.24050
\(146\) −14.8527 −1.22922
\(147\) 2.97455 0.245337
\(148\) 34.7463 2.85613
\(149\) −16.0036 −1.31107 −0.655533 0.755167i \(-0.727556\pi\)
−0.655533 + 0.755167i \(0.727556\pi\)
\(150\) −12.7016 −1.03708
\(151\) −7.21937 −0.587504 −0.293752 0.955882i \(-0.594904\pi\)
−0.293752 + 0.955882i \(0.594904\pi\)
\(152\) 6.71765 0.544873
\(153\) −1.81381 −0.146638
\(154\) −5.57096 −0.448921
\(155\) −6.37062 −0.511700
\(156\) 42.4881 3.40177
\(157\) 0.315637 0.0251906 0.0125953 0.999921i \(-0.495991\pi\)
0.0125953 + 0.999921i \(0.495991\pi\)
\(158\) 14.5939 1.16103
\(159\) −27.2236 −2.15897
\(160\) 6.54415 0.517361
\(161\) 1.83654 0.144740
\(162\) 26.1494 2.05449
\(163\) −13.3783 −1.04787 −0.523936 0.851758i \(-0.675537\pi\)
−0.523936 + 0.851758i \(0.675537\pi\)
\(164\) −6.88042 −0.537270
\(165\) 3.49066 0.271747
\(166\) 18.7817 1.45774
\(167\) 0.808183 0.0625391 0.0312695 0.999511i \(-0.490045\pi\)
0.0312695 + 0.999511i \(0.490045\pi\)
\(168\) −18.3175 −1.41323
\(169\) 17.6375 1.35673
\(170\) 3.73069 0.286131
\(171\) −3.46730 −0.265151
\(172\) −3.49862 −0.266767
\(173\) −13.1291 −0.998189 −0.499095 0.866547i \(-0.666334\pi\)
−0.499095 + 0.866547i \(0.666334\pi\)
\(174\) −48.3048 −3.66198
\(175\) 5.86531 0.443376
\(176\) −1.24310 −0.0937021
\(177\) −22.8371 −1.71654
\(178\) −38.0229 −2.84994
\(179\) −18.2225 −1.36201 −0.681006 0.732278i \(-0.738457\pi\)
−0.681006 + 0.732278i \(0.738457\pi\)
\(180\) 10.0961 0.752516
\(181\) −2.66599 −0.198162 −0.0990808 0.995079i \(-0.531590\pi\)
−0.0990808 + 0.995079i \(0.531590\pi\)
\(182\) −30.8359 −2.28571
\(183\) −9.36367 −0.692182
\(184\) 2.71654 0.200266
\(185\) 15.8006 1.16168
\(186\) −20.6011 −1.51055
\(187\) 1.00000 0.0731272
\(188\) 32.9582 2.40372
\(189\) −6.18302 −0.449749
\(190\) 7.13162 0.517382
\(191\) −6.94712 −0.502676 −0.251338 0.967899i \(-0.580871\pi\)
−0.251338 + 0.967899i \(0.580871\pi\)
\(192\) 26.6171 1.92092
\(193\) 25.0618 1.80399 0.901994 0.431748i \(-0.142103\pi\)
0.901994 + 0.431748i \(0.142103\pi\)
\(194\) 2.28839 0.164297
\(195\) 19.3212 1.38362
\(196\) −4.74323 −0.338802
\(197\) 4.84872 0.345457 0.172729 0.984969i \(-0.444742\pi\)
0.172729 + 0.984969i \(0.444742\pi\)
\(198\) 4.25324 0.302264
\(199\) 4.56775 0.323799 0.161899 0.986807i \(-0.448238\pi\)
0.161899 + 0.986807i \(0.448238\pi\)
\(200\) 8.67572 0.613466
\(201\) −27.6937 −1.95337
\(202\) −37.6589 −2.64967
\(203\) 22.3060 1.56558
\(204\) 7.67611 0.537435
\(205\) −3.12882 −0.218526
\(206\) 36.7740 2.56217
\(207\) −1.40214 −0.0974552
\(208\) −6.88069 −0.477090
\(209\) 1.91161 0.132229
\(210\) −19.4463 −1.34192
\(211\) −22.0323 −1.51677 −0.758384 0.651808i \(-0.774011\pi\)
−0.758384 + 0.651808i \(0.774011\pi\)
\(212\) 43.4107 2.98146
\(213\) −5.02318 −0.344183
\(214\) 26.1585 1.78816
\(215\) −1.59097 −0.108503
\(216\) −9.14567 −0.622284
\(217\) 9.51311 0.645792
\(218\) −21.9167 −1.48438
\(219\) −13.8971 −0.939080
\(220\) −5.56620 −0.375273
\(221\) 5.53511 0.372332
\(222\) 51.0955 3.42931
\(223\) −16.6504 −1.11500 −0.557498 0.830178i \(-0.688239\pi\)
−0.557498 + 0.830178i \(0.688239\pi\)
\(224\) −9.77225 −0.652936
\(225\) −4.47796 −0.298531
\(226\) −23.9459 −1.59286
\(227\) −11.9907 −0.795850 −0.397925 0.917418i \(-0.630270\pi\)
−0.397925 + 0.917418i \(0.630270\pi\)
\(228\) 14.6737 0.971791
\(229\) −19.6798 −1.30048 −0.650238 0.759731i \(-0.725331\pi\)
−0.650238 + 0.759731i \(0.725331\pi\)
\(230\) 2.88394 0.190162
\(231\) −5.21252 −0.342959
\(232\) 32.9941 2.16617
\(233\) −7.11002 −0.465793 −0.232896 0.972502i \(-0.574820\pi\)
−0.232896 + 0.972502i \(0.574820\pi\)
\(234\) 23.5421 1.53900
\(235\) 14.9875 0.977676
\(236\) 36.4161 2.37049
\(237\) 13.6549 0.886980
\(238\) −5.57096 −0.361112
\(239\) 17.9261 1.15955 0.579773 0.814778i \(-0.303141\pi\)
0.579773 + 0.814778i \(0.303141\pi\)
\(240\) −4.33923 −0.280096
\(241\) −0.335908 −0.0216378 −0.0108189 0.999941i \(-0.503444\pi\)
−0.0108189 + 0.999941i \(0.503444\pi\)
\(242\) −2.34491 −0.150737
\(243\) 16.6593 1.06869
\(244\) 14.9313 0.955879
\(245\) −2.15695 −0.137802
\(246\) −10.1179 −0.645093
\(247\) 10.5810 0.673251
\(248\) 14.0714 0.893535
\(249\) 17.5733 1.11366
\(250\) 27.8638 1.76226
\(251\) −8.79768 −0.555304 −0.277652 0.960682i \(-0.589556\pi\)
−0.277652 + 0.960682i \(0.589556\pi\)
\(252\) −15.0762 −0.949714
\(253\) 0.773032 0.0486001
\(254\) −36.8058 −2.30940
\(255\) 3.49066 0.218593
\(256\) −23.1530 −1.44706
\(257\) 13.3127 0.830422 0.415211 0.909725i \(-0.363708\pi\)
0.415211 + 0.909725i \(0.363708\pi\)
\(258\) −5.14484 −0.320303
\(259\) −23.5947 −1.46610
\(260\) −30.8096 −1.91073
\(261\) −17.0299 −1.05412
\(262\) −46.3645 −2.86441
\(263\) 1.27144 0.0784001 0.0392000 0.999231i \(-0.487519\pi\)
0.0392000 + 0.999231i \(0.487519\pi\)
\(264\) −7.71015 −0.474527
\(265\) 19.7407 1.21266
\(266\) −10.6495 −0.652963
\(267\) −35.5765 −2.17725
\(268\) 44.1605 2.69753
\(269\) −9.93394 −0.605683 −0.302841 0.953041i \(-0.597935\pi\)
−0.302841 + 0.953041i \(0.597935\pi\)
\(270\) −9.70927 −0.590887
\(271\) 23.1776 1.40794 0.703970 0.710229i \(-0.251409\pi\)
0.703970 + 0.710229i \(0.251409\pi\)
\(272\) −1.24310 −0.0753739
\(273\) −28.8519 −1.74620
\(274\) 0.564239 0.0340869
\(275\) 2.46881 0.148875
\(276\) 5.93388 0.357178
\(277\) 9.30533 0.559103 0.279552 0.960131i \(-0.409814\pi\)
0.279552 + 0.960131i \(0.409814\pi\)
\(278\) 19.4987 1.16945
\(279\) −7.26293 −0.434820
\(280\) 13.2826 0.793789
\(281\) 14.6979 0.876801 0.438400 0.898780i \(-0.355545\pi\)
0.438400 + 0.898780i \(0.355545\pi\)
\(282\) 48.4661 2.88611
\(283\) 1.00619 0.0598119 0.0299060 0.999553i \(-0.490479\pi\)
0.0299060 + 0.999553i \(0.490479\pi\)
\(284\) 8.00997 0.475304
\(285\) 6.67277 0.395261
\(286\) −12.9794 −0.767486
\(287\) 4.67220 0.275791
\(288\) 7.46077 0.439630
\(289\) 1.00000 0.0588235
\(290\) 35.0274 2.05688
\(291\) 2.14115 0.125516
\(292\) 22.1603 1.29684
\(293\) −15.9111 −0.929537 −0.464769 0.885432i \(-0.653862\pi\)
−0.464769 + 0.885432i \(0.653862\pi\)
\(294\) −6.97507 −0.406794
\(295\) 16.5600 0.964158
\(296\) −34.9003 −2.02854
\(297\) −2.60254 −0.151015
\(298\) 37.5270 2.17388
\(299\) 4.27882 0.247450
\(300\) 18.9509 1.09413
\(301\) 2.37576 0.136937
\(302\) 16.9288 0.974143
\(303\) −35.2359 −2.02425
\(304\) −2.37632 −0.136291
\(305\) 6.78991 0.388789
\(306\) 4.25324 0.243141
\(307\) 28.4272 1.62243 0.811214 0.584749i \(-0.198807\pi\)
0.811214 + 0.584749i \(0.198807\pi\)
\(308\) 8.31190 0.473614
\(309\) 34.4080 1.95740
\(310\) 14.9386 0.848453
\(311\) 11.0735 0.627920 0.313960 0.949436i \(-0.398344\pi\)
0.313960 + 0.949436i \(0.398344\pi\)
\(312\) −42.6765 −2.41608
\(313\) 5.04811 0.285336 0.142668 0.989771i \(-0.454432\pi\)
0.142668 + 0.989771i \(0.454432\pi\)
\(314\) −0.740142 −0.0417686
\(315\) −6.85581 −0.386281
\(316\) −21.7741 −1.22489
\(317\) 10.4228 0.585405 0.292702 0.956204i \(-0.405445\pi\)
0.292702 + 0.956204i \(0.405445\pi\)
\(318\) 63.8369 3.57979
\(319\) 9.38899 0.525682
\(320\) −19.3009 −1.07896
\(321\) 24.4754 1.36609
\(322\) −4.30653 −0.239994
\(323\) 1.91161 0.106365
\(324\) −39.0149 −2.16750
\(325\) 13.6651 0.758005
\(326\) 31.3710 1.73748
\(327\) −20.5065 −1.13401
\(328\) 6.91093 0.381592
\(329\) −22.3805 −1.23388
\(330\) −8.18529 −0.450585
\(331\) 6.71947 0.369336 0.184668 0.982801i \(-0.440879\pi\)
0.184668 + 0.982801i \(0.440879\pi\)
\(332\) −28.0223 −1.53793
\(333\) 18.0138 0.987148
\(334\) −1.89512 −0.103696
\(335\) 20.0816 1.09718
\(336\) 6.47968 0.353496
\(337\) 26.3681 1.43636 0.718181 0.695857i \(-0.244975\pi\)
0.718181 + 0.695857i \(0.244975\pi\)
\(338\) −41.3583 −2.24960
\(339\) −22.4053 −1.21689
\(340\) −5.56620 −0.301870
\(341\) 4.00423 0.216841
\(342\) 8.13053 0.439649
\(343\) 19.8513 1.07187
\(344\) 3.51413 0.189469
\(345\) 2.69839 0.145276
\(346\) 30.7867 1.65510
\(347\) 1.93372 0.103808 0.0519038 0.998652i \(-0.483471\pi\)
0.0519038 + 0.998652i \(0.483471\pi\)
\(348\) 72.0709 3.86341
\(349\) 3.93316 0.210537 0.105269 0.994444i \(-0.466430\pi\)
0.105269 + 0.994444i \(0.466430\pi\)
\(350\) −13.7536 −0.735163
\(351\) −14.4053 −0.768901
\(352\) −4.11331 −0.219240
\(353\) 18.0015 0.958122 0.479061 0.877782i \(-0.340977\pi\)
0.479061 + 0.877782i \(0.340977\pi\)
\(354\) 53.5511 2.84621
\(355\) 3.64248 0.193323
\(356\) 56.7303 3.00670
\(357\) −5.21252 −0.275876
\(358\) 42.7301 2.25836
\(359\) −21.5735 −1.13861 −0.569304 0.822127i \(-0.692787\pi\)
−0.569304 + 0.822127i \(0.692787\pi\)
\(360\) −10.1408 −0.534469
\(361\) −15.3458 −0.807671
\(362\) 6.25152 0.328573
\(363\) −2.19404 −0.115157
\(364\) 46.0073 2.41144
\(365\) 10.0773 0.527468
\(366\) 21.9570 1.14771
\(367\) 17.2403 0.899936 0.449968 0.893045i \(-0.351435\pi\)
0.449968 + 0.893045i \(0.351435\pi\)
\(368\) −0.960955 −0.0500932
\(369\) −3.56706 −0.185694
\(370\) −37.0511 −1.92619
\(371\) −29.4784 −1.53044
\(372\) 30.7369 1.59364
\(373\) 2.79102 0.144514 0.0722569 0.997386i \(-0.476980\pi\)
0.0722569 + 0.997386i \(0.476980\pi\)
\(374\) −2.34491 −0.121253
\(375\) 26.0710 1.34630
\(376\) −33.1043 −1.70722
\(377\) 51.9691 2.67654
\(378\) 14.4987 0.745730
\(379\) 18.5682 0.953783 0.476891 0.878962i \(-0.341764\pi\)
0.476891 + 0.878962i \(0.341764\pi\)
\(380\) −10.6404 −0.545841
\(381\) −34.4377 −1.76430
\(382\) 16.2904 0.833489
\(383\) −18.6607 −0.953515 −0.476757 0.879035i \(-0.658188\pi\)
−0.476757 + 0.879035i \(0.658188\pi\)
\(384\) −44.3653 −2.26401
\(385\) 3.77977 0.192635
\(386\) −58.7678 −2.99120
\(387\) −1.81381 −0.0922014
\(388\) −3.41428 −0.173334
\(389\) −2.55867 −0.129730 −0.0648648 0.997894i \(-0.520662\pi\)
−0.0648648 + 0.997894i \(0.520662\pi\)
\(390\) −45.3065 −2.29418
\(391\) 0.773032 0.0390939
\(392\) 4.76426 0.240631
\(393\) −43.3814 −2.18830
\(394\) −11.3698 −0.572804
\(395\) −9.90161 −0.498204
\(396\) −6.34585 −0.318891
\(397\) −7.60085 −0.381476 −0.190738 0.981641i \(-0.561088\pi\)
−0.190738 + 0.981641i \(0.561088\pi\)
\(398\) −10.7110 −0.536892
\(399\) −9.96431 −0.498839
\(400\) −3.06897 −0.153449
\(401\) 11.5518 0.576868 0.288434 0.957500i \(-0.406865\pi\)
0.288434 + 0.957500i \(0.406865\pi\)
\(402\) 64.9394 3.23888
\(403\) 22.1639 1.10406
\(404\) 56.1873 2.79542
\(405\) −17.7418 −0.881595
\(406\) −52.3057 −2.59589
\(407\) −9.93142 −0.492282
\(408\) −7.71015 −0.381709
\(409\) −23.4594 −1.15999 −0.579997 0.814619i \(-0.696946\pi\)
−0.579997 + 0.814619i \(0.696946\pi\)
\(410\) 7.33681 0.362339
\(411\) 0.527935 0.0260411
\(412\) −54.8670 −2.70310
\(413\) −24.7286 −1.21682
\(414\) 3.28789 0.161591
\(415\) −12.7430 −0.625527
\(416\) −22.7676 −1.11627
\(417\) 18.2441 0.893418
\(418\) −4.48256 −0.219249
\(419\) −36.5491 −1.78554 −0.892770 0.450513i \(-0.851241\pi\)
−0.892770 + 0.450513i \(0.851241\pi\)
\(420\) 29.0140 1.41574
\(421\) 17.7712 0.866117 0.433058 0.901366i \(-0.357434\pi\)
0.433058 + 0.901366i \(0.357434\pi\)
\(422\) 51.6639 2.51496
\(423\) 17.0867 0.830785
\(424\) −43.6032 −2.11756
\(425\) 2.46881 0.119755
\(426\) 11.7789 0.570691
\(427\) −10.1392 −0.490672
\(428\) −39.0286 −1.88652
\(429\) −12.1443 −0.586330
\(430\) 3.73069 0.179910
\(431\) −27.1863 −1.30952 −0.654759 0.755838i \(-0.727230\pi\)
−0.654759 + 0.755838i \(0.727230\pi\)
\(432\) 3.23521 0.155654
\(433\) 15.6651 0.752816 0.376408 0.926454i \(-0.377159\pi\)
0.376408 + 0.926454i \(0.377159\pi\)
\(434\) −22.3074 −1.07079
\(435\) 32.7737 1.57138
\(436\) 32.6997 1.56603
\(437\) 1.47773 0.0706896
\(438\) 32.5875 1.55709
\(439\) −6.47146 −0.308866 −0.154433 0.988003i \(-0.549355\pi\)
−0.154433 + 0.988003i \(0.549355\pi\)
\(440\) 5.59089 0.266535
\(441\) −2.45906 −0.117098
\(442\) −12.9794 −0.617365
\(443\) 1.96090 0.0931651 0.0465825 0.998914i \(-0.485167\pi\)
0.0465825 + 0.998914i \(0.485167\pi\)
\(444\) −76.2347 −3.61794
\(445\) 25.7977 1.22293
\(446\) 39.0439 1.84878
\(447\) 35.1125 1.66077
\(448\) 28.8217 1.36170
\(449\) −20.2192 −0.954204 −0.477102 0.878848i \(-0.658313\pi\)
−0.477102 + 0.878848i \(0.658313\pi\)
\(450\) 10.5004 0.494995
\(451\) 1.96661 0.0926040
\(452\) 35.7274 1.68048
\(453\) 15.8396 0.744209
\(454\) 28.1171 1.31960
\(455\) 20.9215 0.980814
\(456\) −14.7388 −0.690207
\(457\) −27.3829 −1.28092 −0.640459 0.767992i \(-0.721256\pi\)
−0.640459 + 0.767992i \(0.721256\pi\)
\(458\) 46.1474 2.15632
\(459\) −2.60254 −0.121476
\(460\) −4.30285 −0.200622
\(461\) 1.61879 0.0753946 0.0376973 0.999289i \(-0.487998\pi\)
0.0376973 + 0.999289i \(0.487998\pi\)
\(462\) 12.2229 0.568662
\(463\) 28.9366 1.34480 0.672399 0.740189i \(-0.265264\pi\)
0.672399 + 0.740189i \(0.265264\pi\)
\(464\) −11.6714 −0.541833
\(465\) 13.9774 0.648186
\(466\) 16.6724 0.772333
\(467\) 9.71543 0.449577 0.224788 0.974408i \(-0.427831\pi\)
0.224788 + 0.974408i \(0.427831\pi\)
\(468\) −35.1250 −1.62365
\(469\) −29.9875 −1.38469
\(470\) −35.1443 −1.62109
\(471\) −0.692520 −0.0319097
\(472\) −36.5776 −1.68362
\(473\) 1.00000 0.0459800
\(474\) −32.0195 −1.47071
\(475\) 4.71940 0.216541
\(476\) 8.31190 0.380975
\(477\) 22.5057 1.03047
\(478\) −42.0353 −1.92265
\(479\) −2.14941 −0.0982091 −0.0491046 0.998794i \(-0.515637\pi\)
−0.0491046 + 0.998794i \(0.515637\pi\)
\(480\) −14.3581 −0.655356
\(481\) −54.9715 −2.50649
\(482\) 0.787676 0.0358777
\(483\) −4.02945 −0.183346
\(484\) 3.49862 0.159028
\(485\) −1.55262 −0.0705008
\(486\) −39.0645 −1.77200
\(487\) −24.3608 −1.10389 −0.551946 0.833880i \(-0.686115\pi\)
−0.551946 + 0.833880i \(0.686115\pi\)
\(488\) −14.9975 −0.678906
\(489\) 29.3526 1.32737
\(490\) 5.05786 0.228491
\(491\) −38.3450 −1.73048 −0.865242 0.501355i \(-0.832835\pi\)
−0.865242 + 0.501355i \(0.832835\pi\)
\(492\) 15.0959 0.680576
\(493\) 9.38899 0.422859
\(494\) −24.8115 −1.11632
\(495\) −2.88573 −0.129704
\(496\) −4.97765 −0.223503
\(497\) −5.43923 −0.243983
\(498\) −41.2078 −1.84656
\(499\) −11.4766 −0.513762 −0.256881 0.966443i \(-0.582695\pi\)
−0.256881 + 0.966443i \(0.582695\pi\)
\(500\) −41.5729 −1.85920
\(501\) −1.77319 −0.0792201
\(502\) 20.6298 0.920752
\(503\) −4.05706 −0.180895 −0.0904477 0.995901i \(-0.528830\pi\)
−0.0904477 + 0.995901i \(0.528830\pi\)
\(504\) 15.1431 0.674527
\(505\) 25.5507 1.13699
\(506\) −1.81269 −0.0805840
\(507\) −38.6973 −1.71861
\(508\) 54.9144 2.43643
\(509\) −11.6767 −0.517562 −0.258781 0.965936i \(-0.583321\pi\)
−0.258781 + 0.965936i \(0.583321\pi\)
\(510\) −8.18529 −0.362451
\(511\) −15.0482 −0.665691
\(512\) 13.8501 0.612092
\(513\) −4.97504 −0.219653
\(514\) −31.2171 −1.37693
\(515\) −24.9504 −1.09944
\(516\) 7.67611 0.337922
\(517\) −9.42033 −0.414306
\(518\) 55.3276 2.43095
\(519\) 28.8058 1.26444
\(520\) 30.9462 1.35708
\(521\) −7.47951 −0.327683 −0.163842 0.986487i \(-0.552389\pi\)
−0.163842 + 0.986487i \(0.552389\pi\)
\(522\) 39.9336 1.74785
\(523\) −6.58250 −0.287833 −0.143916 0.989590i \(-0.545970\pi\)
−0.143916 + 0.989590i \(0.545970\pi\)
\(524\) 69.1760 3.02197
\(525\) −12.8687 −0.561637
\(526\) −2.98141 −0.129995
\(527\) 4.00423 0.174427
\(528\) 2.72741 0.118695
\(529\) −22.4024 −0.974018
\(530\) −46.2902 −2.01072
\(531\) 18.8795 0.819299
\(532\) 15.8891 0.688880
\(533\) 10.8854 0.471499
\(534\) 83.4238 3.61010
\(535\) −17.7480 −0.767311
\(536\) −44.3563 −1.91590
\(537\) 39.9809 1.72530
\(538\) 23.2942 1.00429
\(539\) 1.35574 0.0583960
\(540\) 14.4863 0.623390
\(541\) 39.1193 1.68187 0.840936 0.541135i \(-0.182005\pi\)
0.840936 + 0.541135i \(0.182005\pi\)
\(542\) −54.3495 −2.33451
\(543\) 5.84930 0.251017
\(544\) −4.11331 −0.176357
\(545\) 14.8700 0.636959
\(546\) 67.6552 2.89538
\(547\) −7.97157 −0.340840 −0.170420 0.985372i \(-0.554512\pi\)
−0.170420 + 0.985372i \(0.554512\pi\)
\(548\) −0.841846 −0.0359619
\(549\) 7.74095 0.330376
\(550\) −5.78914 −0.246850
\(551\) 17.9481 0.764613
\(552\) −5.96019 −0.253683
\(553\) 14.7859 0.628759
\(554\) −21.8202 −0.927051
\(555\) −34.6672 −1.47154
\(556\) −29.0921 −1.23378
\(557\) 34.1259 1.44596 0.722981 0.690867i \(-0.242771\pi\)
0.722981 + 0.690867i \(0.242771\pi\)
\(558\) 17.0309 0.720978
\(559\) 5.53511 0.234110
\(560\) −4.69863 −0.198553
\(561\) −2.19404 −0.0926325
\(562\) −34.4652 −1.45383
\(563\) −23.7317 −1.00017 −0.500086 0.865975i \(-0.666698\pi\)
−0.500086 + 0.865975i \(0.666698\pi\)
\(564\) −72.3115 −3.04487
\(565\) 16.2468 0.683508
\(566\) −2.35943 −0.0991744
\(567\) 26.4934 1.11262
\(568\) −8.04549 −0.337581
\(569\) 8.43984 0.353816 0.176908 0.984227i \(-0.443390\pi\)
0.176908 + 0.984227i \(0.443390\pi\)
\(570\) −15.6471 −0.655384
\(571\) −3.10617 −0.129989 −0.0649947 0.997886i \(-0.520703\pi\)
−0.0649947 + 0.997886i \(0.520703\pi\)
\(572\) 19.3652 0.809702
\(573\) 15.2423 0.636755
\(574\) −10.9559 −0.457291
\(575\) 1.90847 0.0795886
\(576\) −22.0044 −0.916849
\(577\) 31.9577 1.33042 0.665208 0.746658i \(-0.268343\pi\)
0.665208 + 0.746658i \(0.268343\pi\)
\(578\) −2.34491 −0.0975355
\(579\) −54.9866 −2.28517
\(580\) −52.2610 −2.17002
\(581\) 19.0288 0.789447
\(582\) −5.02081 −0.208119
\(583\) −12.4080 −0.513885
\(584\) −22.2586 −0.921068
\(585\) −15.9728 −0.660395
\(586\) 37.3102 1.54127
\(587\) 2.13224 0.0880071 0.0440036 0.999031i \(-0.485989\pi\)
0.0440036 + 0.999031i \(0.485989\pi\)
\(588\) 10.4068 0.429171
\(589\) 7.65453 0.315399
\(590\) −38.8317 −1.59867
\(591\) −10.6383 −0.437601
\(592\) 12.3457 0.507407
\(593\) −23.1831 −0.952016 −0.476008 0.879441i \(-0.657917\pi\)
−0.476008 + 0.879441i \(0.657917\pi\)
\(594\) 6.10273 0.250398
\(595\) 3.77977 0.154956
\(596\) −55.9905 −2.29346
\(597\) −10.0218 −0.410166
\(598\) −10.0335 −0.410299
\(599\) −40.5055 −1.65501 −0.827504 0.561459i \(-0.810240\pi\)
−0.827504 + 0.561459i \(0.810240\pi\)
\(600\) −19.0349 −0.777096
\(601\) −12.6775 −0.517125 −0.258562 0.965995i \(-0.583249\pi\)
−0.258562 + 0.965995i \(0.583249\pi\)
\(602\) −5.57096 −0.227055
\(603\) 22.8944 0.932333
\(604\) −25.2578 −1.02773
\(605\) 1.59097 0.0646822
\(606\) 82.6252 3.35642
\(607\) −13.2614 −0.538264 −0.269132 0.963103i \(-0.586737\pi\)
−0.269132 + 0.963103i \(0.586737\pi\)
\(608\) −7.86303 −0.318888
\(609\) −48.9403 −1.98316
\(610\) −15.9217 −0.644653
\(611\) −52.1426 −2.10946
\(612\) −6.34585 −0.256516
\(613\) −6.99889 −0.282683 −0.141341 0.989961i \(-0.545142\pi\)
−0.141341 + 0.989961i \(0.545142\pi\)
\(614\) −66.6594 −2.69016
\(615\) 6.86476 0.276814
\(616\) −8.34875 −0.336381
\(617\) 41.0936 1.65437 0.827183 0.561933i \(-0.189942\pi\)
0.827183 + 0.561933i \(0.189942\pi\)
\(618\) −80.6837 −3.24557
\(619\) 9.84611 0.395749 0.197874 0.980227i \(-0.436596\pi\)
0.197874 + 0.980227i \(0.436596\pi\)
\(620\) −22.2884 −0.895122
\(621\) −2.01185 −0.0807326
\(622\) −25.9664 −1.04116
\(623\) −38.5232 −1.54340
\(624\) 15.0965 0.604344
\(625\) −6.56093 −0.262437
\(626\) −11.8374 −0.473117
\(627\) −4.19415 −0.167498
\(628\) 1.10429 0.0440661
\(629\) −9.93142 −0.395992
\(630\) 16.0763 0.640494
\(631\) 10.8018 0.430012 0.215006 0.976613i \(-0.431023\pi\)
0.215006 + 0.976613i \(0.431023\pi\)
\(632\) 21.8706 0.869967
\(633\) 48.3398 1.92133
\(634\) −24.4406 −0.970662
\(635\) 24.9719 0.990980
\(636\) −95.2449 −3.77670
\(637\) 7.50419 0.297327
\(638\) −22.0164 −0.871636
\(639\) 4.15267 0.164277
\(640\) 32.1707 1.27166
\(641\) −27.5400 −1.08776 −0.543882 0.839162i \(-0.683046\pi\)
−0.543882 + 0.839162i \(0.683046\pi\)
\(642\) −57.3928 −2.26511
\(643\) −3.11124 −0.122695 −0.0613477 0.998116i \(-0.519540\pi\)
−0.0613477 + 0.998116i \(0.519540\pi\)
\(644\) 6.42536 0.253195
\(645\) 3.49066 0.137444
\(646\) −4.48256 −0.176364
\(647\) −6.50985 −0.255929 −0.127964 0.991779i \(-0.540844\pi\)
−0.127964 + 0.991779i \(0.540844\pi\)
\(648\) 39.1879 1.53945
\(649\) −10.4087 −0.408578
\(650\) −32.0436 −1.25685
\(651\) −20.8722 −0.818044
\(652\) −46.8057 −1.83305
\(653\) −31.6499 −1.23856 −0.619279 0.785171i \(-0.712575\pi\)
−0.619279 + 0.785171i \(0.712575\pi\)
\(654\) 48.0860 1.88031
\(655\) 31.4573 1.22914
\(656\) −2.44469 −0.0954491
\(657\) 11.4887 0.448219
\(658\) 52.4803 2.04590
\(659\) −3.45044 −0.134410 −0.0672050 0.997739i \(-0.521408\pi\)
−0.0672050 + 0.997739i \(0.521408\pi\)
\(660\) 12.2125 0.475370
\(661\) −8.39294 −0.326448 −0.163224 0.986589i \(-0.552189\pi\)
−0.163224 + 0.986589i \(0.552189\pi\)
\(662\) −15.7566 −0.612397
\(663\) −12.1443 −0.471644
\(664\) 28.1466 1.09230
\(665\) 7.22545 0.280191
\(666\) −42.2407 −1.63679
\(667\) 7.25799 0.281030
\(668\) 2.82752 0.109400
\(669\) 36.5318 1.41240
\(670\) −47.0897 −1.81923
\(671\) −4.26777 −0.164756
\(672\) 21.4407 0.827093
\(673\) −25.3909 −0.978746 −0.489373 0.872075i \(-0.662774\pi\)
−0.489373 + 0.872075i \(0.662774\pi\)
\(674\) −61.8309 −2.38164
\(675\) −6.42517 −0.247305
\(676\) 61.7068 2.37334
\(677\) −24.3815 −0.937056 −0.468528 0.883449i \(-0.655216\pi\)
−0.468528 + 0.883449i \(0.655216\pi\)
\(678\) 52.5384 2.01772
\(679\) 2.31849 0.0889756
\(680\) 5.59089 0.214401
\(681\) 26.3081 1.00813
\(682\) −9.38958 −0.359545
\(683\) −18.9799 −0.726244 −0.363122 0.931742i \(-0.618289\pi\)
−0.363122 + 0.931742i \(0.618289\pi\)
\(684\) −12.1308 −0.463832
\(685\) −0.382823 −0.0146269
\(686\) −46.5495 −1.77727
\(687\) 43.1782 1.64735
\(688\) −1.24310 −0.0473927
\(689\) −68.6794 −2.61648
\(690\) −6.32749 −0.240883
\(691\) −22.1346 −0.842039 −0.421019 0.907052i \(-0.638328\pi\)
−0.421019 + 0.907052i \(0.638328\pi\)
\(692\) −45.9338 −1.74614
\(693\) 4.30920 0.163693
\(694\) −4.53441 −0.172124
\(695\) −13.2294 −0.501820
\(696\) −72.3905 −2.74395
\(697\) 1.96661 0.0744906
\(698\) −9.22291 −0.349092
\(699\) 15.5997 0.590034
\(700\) 20.5205 0.775602
\(701\) 17.5944 0.664533 0.332266 0.943186i \(-0.392187\pi\)
0.332266 + 0.943186i \(0.392187\pi\)
\(702\) 33.7793 1.27492
\(703\) −18.9850 −0.716033
\(704\) 12.1315 0.457225
\(705\) −32.8831 −1.23845
\(706\) −42.2119 −1.58867
\(707\) −38.1544 −1.43494
\(708\) −79.8984 −3.00277
\(709\) 39.5337 1.48472 0.742359 0.670002i \(-0.233707\pi\)
0.742359 + 0.670002i \(0.233707\pi\)
\(710\) −8.54129 −0.320549
\(711\) −11.2885 −0.423352
\(712\) −56.9819 −2.13549
\(713\) 3.09540 0.115924
\(714\) 12.2229 0.457431
\(715\) 8.80621 0.329333
\(716\) −63.7535 −2.38258
\(717\) −39.3307 −1.46883
\(718\) 50.5881 1.88793
\(719\) −13.0362 −0.486170 −0.243085 0.970005i \(-0.578159\pi\)
−0.243085 + 0.970005i \(0.578159\pi\)
\(720\) 3.58724 0.133689
\(721\) 37.2578 1.38755
\(722\) 35.9845 1.33920
\(723\) 0.736997 0.0274092
\(724\) −9.32729 −0.346646
\(725\) 23.1796 0.860869
\(726\) 5.14484 0.190943
\(727\) −49.4313 −1.83330 −0.916652 0.399686i \(-0.869119\pi\)
−0.916652 + 0.399686i \(0.869119\pi\)
\(728\) −46.2113 −1.71270
\(729\) −3.09656 −0.114687
\(730\) −23.6303 −0.874596
\(731\) 1.00000 0.0369863
\(732\) −32.7599 −1.21084
\(733\) 47.3777 1.74994 0.874968 0.484180i \(-0.160882\pi\)
0.874968 + 0.484180i \(0.160882\pi\)
\(734\) −40.4270 −1.49219
\(735\) 4.73243 0.174558
\(736\) −3.17972 −0.117206
\(737\) −12.6223 −0.464947
\(738\) 8.36446 0.307900
\(739\) 24.6277 0.905944 0.452972 0.891525i \(-0.350364\pi\)
0.452972 + 0.891525i \(0.350364\pi\)
\(740\) 55.2803 2.03215
\(741\) −23.2151 −0.852827
\(742\) 69.1243 2.53763
\(743\) 11.4594 0.420404 0.210202 0.977658i \(-0.432588\pi\)
0.210202 + 0.977658i \(0.432588\pi\)
\(744\) −30.8732 −1.13187
\(745\) −25.4613 −0.932828
\(746\) −6.54471 −0.239619
\(747\) −14.5278 −0.531545
\(748\) 3.49862 0.127922
\(749\) 26.5026 0.968386
\(750\) −61.1343 −2.23231
\(751\) 15.0548 0.549358 0.274679 0.961536i \(-0.411428\pi\)
0.274679 + 0.961536i \(0.411428\pi\)
\(752\) 11.7104 0.427034
\(753\) 19.3025 0.703421
\(754\) −121.863 −4.43799
\(755\) −11.4858 −0.418012
\(756\) −21.6320 −0.786750
\(757\) 10.5360 0.382936 0.191468 0.981499i \(-0.438675\pi\)
0.191468 + 0.981499i \(0.438675\pi\)
\(758\) −43.5407 −1.58147
\(759\) −1.69606 −0.0615632
\(760\) 10.6876 0.387680
\(761\) 44.6574 1.61883 0.809414 0.587238i \(-0.199785\pi\)
0.809414 + 0.587238i \(0.199785\pi\)
\(762\) 80.7534 2.92539
\(763\) −22.2050 −0.803875
\(764\) −24.3053 −0.879336
\(765\) −2.88573 −0.104334
\(766\) 43.7576 1.58103
\(767\) −57.6134 −2.08030
\(768\) 50.7985 1.83303
\(769\) −20.6666 −0.745255 −0.372627 0.927981i \(-0.621543\pi\)
−0.372627 + 0.927981i \(0.621543\pi\)
\(770\) −8.86324 −0.319409
\(771\) −29.2086 −1.05192
\(772\) 87.6817 3.15573
\(773\) −33.2310 −1.19524 −0.597619 0.801781i \(-0.703886\pi\)
−0.597619 + 0.801781i \(0.703886\pi\)
\(774\) 4.25324 0.152879
\(775\) 9.88568 0.355104
\(776\) 3.42942 0.123109
\(777\) 51.7678 1.85716
\(778\) 5.99986 0.215105
\(779\) 3.75939 0.134694
\(780\) 67.5974 2.42038
\(781\) −2.28947 −0.0819236
\(782\) −1.81269 −0.0648218
\(783\) −24.4352 −0.873243
\(784\) −1.68532 −0.0601900
\(785\) 0.502170 0.0179232
\(786\) 101.726 3.62843
\(787\) 53.8411 1.91923 0.959614 0.281321i \(-0.0907726\pi\)
0.959614 + 0.281321i \(0.0907726\pi\)
\(788\) 16.9638 0.604312
\(789\) −2.78958 −0.0993117
\(790\) 23.2184 0.826074
\(791\) −24.2610 −0.862622
\(792\) 6.37398 0.226490
\(793\) −23.6226 −0.838863
\(794\) 17.8233 0.632526
\(795\) −43.3119 −1.53611
\(796\) 15.9808 0.566425
\(797\) −7.55164 −0.267493 −0.133746 0.991016i \(-0.542701\pi\)
−0.133746 + 0.991016i \(0.542701\pi\)
\(798\) 23.3654 0.827128
\(799\) −9.42033 −0.333267
\(800\) −10.1550 −0.359032
\(801\) 29.4111 1.03919
\(802\) −27.0879 −0.956508
\(803\) −6.33403 −0.223523
\(804\) −96.8898 −3.41704
\(805\) 2.92189 0.102983
\(806\) −51.9724 −1.83065
\(807\) 21.7955 0.767237
\(808\) −56.4364 −1.98543
\(809\) 11.2585 0.395827 0.197913 0.980219i \(-0.436583\pi\)
0.197913 + 0.980219i \(0.436583\pi\)
\(810\) 41.6029 1.46178
\(811\) 3.90203 0.137019 0.0685093 0.997650i \(-0.478176\pi\)
0.0685093 + 0.997650i \(0.478176\pi\)
\(812\) 78.0403 2.73868
\(813\) −50.8527 −1.78348
\(814\) 23.2883 0.816255
\(815\) −21.2846 −0.745566
\(816\) 2.72741 0.0954784
\(817\) 1.91161 0.0668787
\(818\) 55.0103 1.92339
\(819\) 23.8519 0.833452
\(820\) −10.9465 −0.382270
\(821\) 46.7461 1.63145 0.815726 0.578439i \(-0.196338\pi\)
0.815726 + 0.578439i \(0.196338\pi\)
\(822\) −1.23796 −0.0431789
\(823\) 7.82455 0.272747 0.136373 0.990658i \(-0.456455\pi\)
0.136373 + 0.990658i \(0.456455\pi\)
\(824\) 55.1103 1.91986
\(825\) −5.41667 −0.188584
\(826\) 57.9865 2.01761
\(827\) −19.0899 −0.663822 −0.331911 0.943311i \(-0.607693\pi\)
−0.331911 + 0.943311i \(0.607693\pi\)
\(828\) −4.90554 −0.170479
\(829\) 10.9501 0.380313 0.190157 0.981754i \(-0.439100\pi\)
0.190157 + 0.981754i \(0.439100\pi\)
\(830\) 29.8811 1.03719
\(831\) −20.4163 −0.708233
\(832\) 67.1495 2.32799
\(833\) 1.35574 0.0469737
\(834\) −42.7809 −1.48138
\(835\) 1.28580 0.0444968
\(836\) 6.68799 0.231309
\(837\) −10.4212 −0.360208
\(838\) 85.7044 2.96061
\(839\) 19.0202 0.656652 0.328326 0.944565i \(-0.393516\pi\)
0.328326 + 0.944565i \(0.393516\pi\)
\(840\) −29.1426 −1.00552
\(841\) 59.1530 2.03976
\(842\) −41.6720 −1.43611
\(843\) −32.2477 −1.11067
\(844\) −77.0827 −2.65330
\(845\) 28.0607 0.965318
\(846\) −40.0669 −1.37753
\(847\) −2.37576 −0.0816322
\(848\) 15.4243 0.529673
\(849\) −2.20763 −0.0757655
\(850\) −5.78914 −0.198566
\(851\) −7.67731 −0.263175
\(852\) −17.5742 −0.602082
\(853\) 15.2365 0.521688 0.260844 0.965381i \(-0.415999\pi\)
0.260844 + 0.965381i \(0.415999\pi\)
\(854\) 23.7756 0.813585
\(855\) −5.51638 −0.188656
\(856\) 39.2016 1.33988
\(857\) −31.9983 −1.09304 −0.546521 0.837445i \(-0.684048\pi\)
−0.546521 + 0.837445i \(0.684048\pi\)
\(858\) 28.4772 0.972197
\(859\) −3.00700 −0.102597 −0.0512987 0.998683i \(-0.516336\pi\)
−0.0512987 + 0.998683i \(0.516336\pi\)
\(860\) −5.56620 −0.189806
\(861\) −10.2510 −0.349353
\(862\) 63.7495 2.17132
\(863\) 9.92154 0.337733 0.168867 0.985639i \(-0.445989\pi\)
0.168867 + 0.985639i \(0.445989\pi\)
\(864\) 10.7050 0.364193
\(865\) −20.8881 −0.710216
\(866\) −36.7333 −1.24825
\(867\) −2.19404 −0.0745135
\(868\) 33.2828 1.12969
\(869\) 6.22362 0.211122
\(870\) −76.8515 −2.60551
\(871\) −69.8656 −2.36730
\(872\) −32.8447 −1.11226
\(873\) −1.77009 −0.0599085
\(874\) −3.46516 −0.117211
\(875\) 28.2304 0.954362
\(876\) −48.6207 −1.64274
\(877\) −17.9276 −0.605373 −0.302687 0.953090i \(-0.597884\pi\)
−0.302687 + 0.953090i \(0.597884\pi\)
\(878\) 15.1750 0.512132
\(879\) 34.9096 1.17747
\(880\) −1.97773 −0.0666694
\(881\) −39.9023 −1.34434 −0.672171 0.740396i \(-0.734638\pi\)
−0.672171 + 0.740396i \(0.734638\pi\)
\(882\) 5.76629 0.194161
\(883\) −3.65112 −0.122870 −0.0614350 0.998111i \(-0.519568\pi\)
−0.0614350 + 0.998111i \(0.519568\pi\)
\(884\) 19.3652 0.651324
\(885\) −36.3332 −1.22133
\(886\) −4.59814 −0.154477
\(887\) 18.7593 0.629874 0.314937 0.949113i \(-0.398017\pi\)
0.314937 + 0.949113i \(0.398017\pi\)
\(888\) 76.5728 2.56961
\(889\) −37.2900 −1.25067
\(890\) −60.4934 −2.02774
\(891\) 11.1515 0.373590
\(892\) −58.2536 −1.95047
\(893\) −18.0080 −0.602615
\(894\) −82.3358 −2.75372
\(895\) −28.9915 −0.969077
\(896\) −48.0399 −1.60490
\(897\) −9.38790 −0.313453
\(898\) 47.4123 1.58217
\(899\) 37.5957 1.25389
\(900\) −15.6667 −0.522223
\(901\) −12.4080 −0.413369
\(902\) −4.61153 −0.153547
\(903\) −5.21252 −0.173462
\(904\) −35.8859 −1.19355
\(905\) −4.24152 −0.140993
\(906\) −37.1425 −1.23398
\(907\) 4.63897 0.154034 0.0770172 0.997030i \(-0.475460\pi\)
0.0770172 + 0.997030i \(0.475460\pi\)
\(908\) −41.9509 −1.39219
\(909\) 29.1296 0.966167
\(910\) −49.0590 −1.62629
\(911\) −56.9117 −1.88557 −0.942784 0.333403i \(-0.891803\pi\)
−0.942784 + 0.333403i \(0.891803\pi\)
\(912\) 5.21374 0.172644
\(913\) 8.00954 0.265077
\(914\) 64.2106 2.12390
\(915\) −14.8973 −0.492491
\(916\) −68.8520 −2.27494
\(917\) −46.9745 −1.55123
\(918\) 6.10273 0.201420
\(919\) 41.4529 1.36740 0.683702 0.729761i \(-0.260369\pi\)
0.683702 + 0.729761i \(0.260369\pi\)
\(920\) 4.32193 0.142490
\(921\) −62.3705 −2.05518
\(922\) −3.79592 −0.125012
\(923\) −12.6725 −0.417119
\(924\) −18.2366 −0.599941
\(925\) −24.5188 −0.806173
\(926\) −67.8538 −2.22982
\(927\) −28.4451 −0.934259
\(928\) −38.6198 −1.26776
\(929\) 57.4720 1.88559 0.942797 0.333368i \(-0.108185\pi\)
0.942797 + 0.333368i \(0.108185\pi\)
\(930\) −32.7758 −1.07476
\(931\) 2.59165 0.0849379
\(932\) −24.8752 −0.814816
\(933\) −24.2957 −0.795405
\(934\) −22.7818 −0.745445
\(935\) 1.59097 0.0520303
\(936\) 35.2807 1.15319
\(937\) 22.6074 0.738550 0.369275 0.929320i \(-0.379606\pi\)
0.369275 + 0.929320i \(0.379606\pi\)
\(938\) 70.3181 2.29597
\(939\) −11.0758 −0.361444
\(940\) 52.4355 1.71026
\(941\) −49.7955 −1.62329 −0.811643 0.584154i \(-0.801426\pi\)
−0.811643 + 0.584154i \(0.801426\pi\)
\(942\) 1.62390 0.0529095
\(943\) 1.52025 0.0495062
\(944\) 12.9390 0.421130
\(945\) −9.83701 −0.319998
\(946\) −2.34491 −0.0762397
\(947\) −39.6830 −1.28953 −0.644763 0.764383i \(-0.723044\pi\)
−0.644763 + 0.764383i \(0.723044\pi\)
\(948\) 47.7732 1.55160
\(949\) −35.0595 −1.13808
\(950\) −11.0666 −0.359047
\(951\) −22.8681 −0.741550
\(952\) −8.34875 −0.270585
\(953\) −10.6711 −0.345671 −0.172836 0.984951i \(-0.555293\pi\)
−0.172836 + 0.984951i \(0.555293\pi\)
\(954\) −52.7740 −1.70862
\(955\) −11.0527 −0.357656
\(956\) 62.7168 2.02841
\(957\) −20.5998 −0.665897
\(958\) 5.04018 0.162841
\(959\) 0.571662 0.0184599
\(960\) 42.3471 1.36675
\(961\) −14.9661 −0.482778
\(962\) 128.903 4.15602
\(963\) −20.2339 −0.652027
\(964\) −1.17522 −0.0378511
\(965\) 39.8726 1.28355
\(966\) 9.44871 0.304007
\(967\) −28.8159 −0.926656 −0.463328 0.886187i \(-0.653345\pi\)
−0.463328 + 0.886187i \(0.653345\pi\)
\(968\) −3.51413 −0.112949
\(969\) −4.19415 −0.134735
\(970\) 3.64076 0.116898
\(971\) 33.1467 1.06373 0.531864 0.846830i \(-0.321492\pi\)
0.531864 + 0.846830i \(0.321492\pi\)
\(972\) 58.2844 1.86947
\(973\) 19.7552 0.633323
\(974\) 57.1239 1.83037
\(975\) −29.9819 −0.960188
\(976\) 5.30526 0.169817
\(977\) 4.84326 0.154950 0.0774749 0.996994i \(-0.475314\pi\)
0.0774749 + 0.996994i \(0.475314\pi\)
\(978\) −68.8294 −2.20092
\(979\) −16.2151 −0.518235
\(980\) −7.54634 −0.241059
\(981\) 16.9528 0.541260
\(982\) 89.9156 2.86932
\(983\) 33.9439 1.08264 0.541321 0.840816i \(-0.317924\pi\)
0.541321 + 0.840816i \(0.317924\pi\)
\(984\) −15.1629 −0.483374
\(985\) 7.71418 0.245794
\(986\) −22.0164 −0.701144
\(987\) 49.1037 1.56299
\(988\) 37.0188 1.17772
\(989\) 0.773032 0.0245810
\(990\) 6.76678 0.215062
\(991\) −40.6334 −1.29076 −0.645382 0.763860i \(-0.723302\pi\)
−0.645382 + 0.763860i \(0.723302\pi\)
\(992\) −16.4706 −0.522943
\(993\) −14.7428 −0.467849
\(994\) 12.7545 0.404549
\(995\) 7.26715 0.230384
\(996\) 61.4821 1.94814
\(997\) −43.5337 −1.37873 −0.689364 0.724415i \(-0.742110\pi\)
−0.689364 + 0.724415i \(0.742110\pi\)
\(998\) 26.9116 0.851872
\(999\) 25.8469 0.817760
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 8041.2.a.h.1.10 74
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.h.1.10 74 1.1 even 1 trivial