Properties

Label 8041.2.a.c.1.5
Level $8041$
Weight $2$
Character 8041.1
Self dual yes
Analytic conductor $64.208$
Analytic rank $1$
Dimension $60$
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: \(60\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
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)
 
\(f(q)\) \(=\) \(q-2.51152 q^{2} -1.72847 q^{3} +4.30774 q^{4} -3.07277 q^{5} +4.34109 q^{6} -4.07006 q^{7} -5.79593 q^{8} -0.0123937 q^{9} +O(q^{10})\) \(q-2.51152 q^{2} -1.72847 q^{3} +4.30774 q^{4} -3.07277 q^{5} +4.34109 q^{6} -4.07006 q^{7} -5.79593 q^{8} -0.0123937 q^{9} +7.71734 q^{10} +1.00000 q^{11} -7.44579 q^{12} +0.957676 q^{13} +10.2220 q^{14} +5.31120 q^{15} +5.94112 q^{16} +1.00000 q^{17} +0.0311271 q^{18} -5.04648 q^{19} -13.2367 q^{20} +7.03497 q^{21} -2.51152 q^{22} +1.39295 q^{23} +10.0181 q^{24} +4.44194 q^{25} -2.40522 q^{26} +5.20683 q^{27} -17.5327 q^{28} -8.87402 q^{29} -13.3392 q^{30} -0.871366 q^{31} -3.32939 q^{32} -1.72847 q^{33} -2.51152 q^{34} +12.5064 q^{35} -0.0533890 q^{36} -3.42882 q^{37} +12.6743 q^{38} -1.65531 q^{39} +17.8096 q^{40} -4.61354 q^{41} -17.6685 q^{42} -1.00000 q^{43} +4.30774 q^{44} +0.0380832 q^{45} -3.49842 q^{46} -10.9923 q^{47} -10.2690 q^{48} +9.56537 q^{49} -11.1560 q^{50} -1.72847 q^{51} +4.12542 q^{52} +7.25851 q^{53} -13.0771 q^{54} -3.07277 q^{55} +23.5898 q^{56} +8.72268 q^{57} +22.2873 q^{58} -9.48152 q^{59} +22.8792 q^{60} -6.63668 q^{61} +2.18845 q^{62} +0.0504433 q^{63} -3.52041 q^{64} -2.94272 q^{65} +4.34109 q^{66} -7.78213 q^{67} +4.30774 q^{68} -2.40767 q^{69} -31.4100 q^{70} -14.6845 q^{71} +0.0718332 q^{72} +15.3747 q^{73} +8.61155 q^{74} -7.67776 q^{75} -21.7389 q^{76} -4.07006 q^{77} +4.15735 q^{78} +14.9013 q^{79} -18.2557 q^{80} -8.96267 q^{81} +11.5870 q^{82} -7.35421 q^{83} +30.3048 q^{84} -3.07277 q^{85} +2.51152 q^{86} +15.3385 q^{87} -5.79593 q^{88} +6.13495 q^{89} -0.0956467 q^{90} -3.89780 q^{91} +6.00046 q^{92} +1.50613 q^{93} +27.6073 q^{94} +15.5067 q^{95} +5.75474 q^{96} -14.7119 q^{97} -24.0236 q^{98} -0.0123937 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51152 −1.77591 −0.887957 0.459927i \(-0.847876\pi\)
−0.887957 + 0.459927i \(0.847876\pi\)
\(3\) −1.72847 −0.997932 −0.498966 0.866621i \(-0.666287\pi\)
−0.498966 + 0.866621i \(0.666287\pi\)
\(4\) 4.30774 2.15387
\(5\) −3.07277 −1.37419 −0.687093 0.726569i \(-0.741114\pi\)
−0.687093 + 0.726569i \(0.741114\pi\)
\(6\) 4.34109 1.77224
\(7\) −4.07006 −1.53834 −0.769169 0.639046i \(-0.779329\pi\)
−0.769169 + 0.639046i \(0.779329\pi\)
\(8\) −5.79593 −2.04917
\(9\) −0.0123937 −0.00413125
\(10\) 7.71734 2.44044
\(11\) 1.00000 0.301511
\(12\) −7.44579 −2.14941
\(13\) 0.957676 0.265612 0.132806 0.991142i \(-0.457601\pi\)
0.132806 + 0.991142i \(0.457601\pi\)
\(14\) 10.2220 2.73195
\(15\) 5.31120 1.37134
\(16\) 5.94112 1.48528
\(17\) 1.00000 0.242536
\(18\) 0.0311271 0.00733674
\(19\) −5.04648 −1.15774 −0.578871 0.815419i \(-0.696506\pi\)
−0.578871 + 0.815419i \(0.696506\pi\)
\(20\) −13.2367 −2.95982
\(21\) 7.03497 1.53516
\(22\) −2.51152 −0.535458
\(23\) 1.39295 0.290450 0.145225 0.989399i \(-0.453609\pi\)
0.145225 + 0.989399i \(0.453609\pi\)
\(24\) 10.0181 2.04493
\(25\) 4.44194 0.888388
\(26\) −2.40522 −0.471703
\(27\) 5.20683 1.00205
\(28\) −17.5327 −3.31338
\(29\) −8.87402 −1.64786 −0.823932 0.566688i \(-0.808225\pi\)
−0.823932 + 0.566688i \(0.808225\pi\)
\(30\) −13.3392 −2.43539
\(31\) −0.871366 −0.156502 −0.0782509 0.996934i \(-0.524934\pi\)
−0.0782509 + 0.996934i \(0.524934\pi\)
\(32\) −3.32939 −0.588558
\(33\) −1.72847 −0.300888
\(34\) −2.51152 −0.430722
\(35\) 12.5064 2.11396
\(36\) −0.0533890 −0.00889816
\(37\) −3.42882 −0.563694 −0.281847 0.959459i \(-0.590947\pi\)
−0.281847 + 0.959459i \(0.590947\pi\)
\(38\) 12.6743 2.05605
\(39\) −1.65531 −0.265062
\(40\) 17.8096 2.81594
\(41\) −4.61354 −0.720513 −0.360257 0.932853i \(-0.617311\pi\)
−0.360257 + 0.932853i \(0.617311\pi\)
\(42\) −17.6685 −2.72630
\(43\) −1.00000 −0.152499
\(44\) 4.30774 0.649416
\(45\) 0.0380832 0.00567710
\(46\) −3.49842 −0.515814
\(47\) −10.9923 −1.60339 −0.801695 0.597734i \(-0.796068\pi\)
−0.801695 + 0.597734i \(0.796068\pi\)
\(48\) −10.2690 −1.48221
\(49\) 9.56537 1.36648
\(50\) −11.1560 −1.57770
\(51\) −1.72847 −0.242034
\(52\) 4.12542 0.572092
\(53\) 7.25851 0.997034 0.498517 0.866880i \(-0.333878\pi\)
0.498517 + 0.866880i \(0.333878\pi\)
\(54\) −13.0771 −1.77956
\(55\) −3.07277 −0.414333
\(56\) 23.5898 3.15231
\(57\) 8.72268 1.15535
\(58\) 22.2873 2.92647
\(59\) −9.48152 −1.23439 −0.617194 0.786811i \(-0.711731\pi\)
−0.617194 + 0.786811i \(0.711731\pi\)
\(60\) 22.8792 2.95370
\(61\) −6.63668 −0.849740 −0.424870 0.905254i \(-0.639680\pi\)
−0.424870 + 0.905254i \(0.639680\pi\)
\(62\) 2.18845 0.277934
\(63\) 0.0504433 0.00635525
\(64\) −3.52041 −0.440052
\(65\) −2.94272 −0.365000
\(66\) 4.34109 0.534351
\(67\) −7.78213 −0.950738 −0.475369 0.879786i \(-0.657686\pi\)
−0.475369 + 0.879786i \(0.657686\pi\)
\(68\) 4.30774 0.522390
\(69\) −2.40767 −0.289849
\(70\) −31.4100 −3.75421
\(71\) −14.6845 −1.74273 −0.871366 0.490634i \(-0.836765\pi\)
−0.871366 + 0.490634i \(0.836765\pi\)
\(72\) 0.0718332 0.00846563
\(73\) 15.3747 1.79947 0.899735 0.436436i \(-0.143760\pi\)
0.899735 + 0.436436i \(0.143760\pi\)
\(74\) 8.61155 1.00107
\(75\) −7.67776 −0.886551
\(76\) −21.7389 −2.49362
\(77\) −4.07006 −0.463826
\(78\) 4.15735 0.470728
\(79\) 14.9013 1.67653 0.838264 0.545264i \(-0.183571\pi\)
0.838264 + 0.545264i \(0.183571\pi\)
\(80\) −18.2557 −2.04105
\(81\) −8.96267 −0.995852
\(82\) 11.5870 1.27957
\(83\) −7.35421 −0.807229 −0.403615 0.914929i \(-0.632246\pi\)
−0.403615 + 0.914929i \(0.632246\pi\)
\(84\) 30.3048 3.30652
\(85\) −3.07277 −0.333289
\(86\) 2.51152 0.270824
\(87\) 15.3385 1.64446
\(88\) −5.79593 −0.617848
\(89\) 6.13495 0.650303 0.325152 0.945662i \(-0.394585\pi\)
0.325152 + 0.945662i \(0.394585\pi\)
\(90\) −0.0956467 −0.0100820
\(91\) −3.89780 −0.408600
\(92\) 6.00046 0.625591
\(93\) 1.50613 0.156178
\(94\) 27.6073 2.84748
\(95\) 15.5067 1.59095
\(96\) 5.75474 0.587341
\(97\) −14.7119 −1.49377 −0.746884 0.664955i \(-0.768451\pi\)
−0.746884 + 0.664955i \(0.768451\pi\)
\(98\) −24.0236 −2.42675
\(99\) −0.0123937 −0.00124562
\(100\) 19.1347 1.91347
\(101\) 2.71656 0.270308 0.135154 0.990825i \(-0.456847\pi\)
0.135154 + 0.990825i \(0.456847\pi\)
\(102\) 4.34109 0.429832
\(103\) 12.2332 1.20538 0.602688 0.797977i \(-0.294096\pi\)
0.602688 + 0.797977i \(0.294096\pi\)
\(104\) −5.55062 −0.544283
\(105\) −21.6169 −2.10959
\(106\) −18.2299 −1.77065
\(107\) 7.02095 0.678741 0.339370 0.940653i \(-0.389786\pi\)
0.339370 + 0.940653i \(0.389786\pi\)
\(108\) 22.4296 2.15829
\(109\) 18.5287 1.77473 0.887365 0.461068i \(-0.152534\pi\)
0.887365 + 0.461068i \(0.152534\pi\)
\(110\) 7.71734 0.735819
\(111\) 5.92661 0.562529
\(112\) −24.1807 −2.28486
\(113\) 18.9369 1.78143 0.890717 0.454559i \(-0.150203\pi\)
0.890717 + 0.454559i \(0.150203\pi\)
\(114\) −21.9072 −2.05180
\(115\) −4.28022 −0.399132
\(116\) −38.2270 −3.54928
\(117\) −0.0118692 −0.00109731
\(118\) 23.8130 2.19217
\(119\) −4.07006 −0.373102
\(120\) −30.7833 −2.81012
\(121\) 1.00000 0.0909091
\(122\) 16.6682 1.50906
\(123\) 7.97435 0.719023
\(124\) −3.75361 −0.337084
\(125\) 1.71479 0.153376
\(126\) −0.126689 −0.0112864
\(127\) 3.76221 0.333843 0.166921 0.985970i \(-0.446617\pi\)
0.166921 + 0.985970i \(0.446617\pi\)
\(128\) 15.5004 1.37005
\(129\) 1.72847 0.152183
\(130\) 7.39071 0.648208
\(131\) 11.3225 0.989255 0.494628 0.869105i \(-0.335304\pi\)
0.494628 + 0.869105i \(0.335304\pi\)
\(132\) −7.44579 −0.648073
\(133\) 20.5395 1.78100
\(134\) 19.5450 1.68843
\(135\) −15.9994 −1.37701
\(136\) −5.79593 −0.496997
\(137\) −18.1406 −1.54986 −0.774928 0.632049i \(-0.782214\pi\)
−0.774928 + 0.632049i \(0.782214\pi\)
\(138\) 6.04691 0.514747
\(139\) 9.66277 0.819585 0.409793 0.912179i \(-0.365601\pi\)
0.409793 + 0.912179i \(0.365601\pi\)
\(140\) 53.8741 4.55320
\(141\) 18.9998 1.60007
\(142\) 36.8805 3.09494
\(143\) 0.957676 0.0800849
\(144\) −0.0736327 −0.00613606
\(145\) 27.2679 2.26447
\(146\) −38.6138 −3.19570
\(147\) −16.5334 −1.36366
\(148\) −14.7704 −1.21412
\(149\) 2.68124 0.219656 0.109828 0.993951i \(-0.464970\pi\)
0.109828 + 0.993951i \(0.464970\pi\)
\(150\) 19.2828 1.57444
\(151\) −12.9334 −1.05250 −0.526252 0.850329i \(-0.676403\pi\)
−0.526252 + 0.850329i \(0.676403\pi\)
\(152\) 29.2490 2.37241
\(153\) −0.0123937 −0.00100197
\(154\) 10.2220 0.823715
\(155\) 2.67751 0.215063
\(156\) −7.13065 −0.570909
\(157\) 16.1200 1.28652 0.643258 0.765649i \(-0.277582\pi\)
0.643258 + 0.765649i \(0.277582\pi\)
\(158\) −37.4249 −2.97737
\(159\) −12.5461 −0.994972
\(160\) 10.2304 0.808788
\(161\) −5.66938 −0.446810
\(162\) 22.5099 1.76855
\(163\) 19.1671 1.50128 0.750640 0.660711i \(-0.229745\pi\)
0.750640 + 0.660711i \(0.229745\pi\)
\(164\) −19.8739 −1.55189
\(165\) 5.31120 0.413476
\(166\) 18.4703 1.43357
\(167\) 3.03783 0.235074 0.117537 0.993068i \(-0.462500\pi\)
0.117537 + 0.993068i \(0.462500\pi\)
\(168\) −40.7742 −3.14580
\(169\) −12.0829 −0.929450
\(170\) 7.71734 0.591893
\(171\) 0.0625447 0.00478292
\(172\) −4.30774 −0.328462
\(173\) 15.2981 1.16310 0.581548 0.813512i \(-0.302447\pi\)
0.581548 + 0.813512i \(0.302447\pi\)
\(174\) −38.5229 −2.92041
\(175\) −18.0790 −1.36664
\(176\) 5.94112 0.447829
\(177\) 16.3885 1.23184
\(178\) −15.4080 −1.15488
\(179\) −10.3322 −0.772262 −0.386131 0.922444i \(-0.626189\pi\)
−0.386131 + 0.922444i \(0.626189\pi\)
\(180\) 0.164052 0.0122277
\(181\) −11.6949 −0.869273 −0.434636 0.900606i \(-0.643123\pi\)
−0.434636 + 0.900606i \(0.643123\pi\)
\(182\) 9.78940 0.725638
\(183\) 11.4713 0.847983
\(184\) −8.07343 −0.595181
\(185\) 10.5360 0.774621
\(186\) −3.78267 −0.277359
\(187\) 1.00000 0.0731272
\(188\) −47.3519 −3.45349
\(189\) −21.1921 −1.54150
\(190\) −38.9454 −2.82539
\(191\) −6.45239 −0.466879 −0.233439 0.972371i \(-0.574998\pi\)
−0.233439 + 0.972371i \(0.574998\pi\)
\(192\) 6.08493 0.439142
\(193\) 1.10464 0.0795134 0.0397567 0.999209i \(-0.487342\pi\)
0.0397567 + 0.999209i \(0.487342\pi\)
\(194\) 36.9493 2.65280
\(195\) 5.08641 0.364245
\(196\) 41.2051 2.94322
\(197\) −12.0890 −0.861303 −0.430652 0.902518i \(-0.641716\pi\)
−0.430652 + 0.902518i \(0.641716\pi\)
\(198\) 0.0311271 0.00221211
\(199\) 22.8358 1.61878 0.809392 0.587269i \(-0.199797\pi\)
0.809392 + 0.587269i \(0.199797\pi\)
\(200\) −25.7452 −1.82046
\(201\) 13.4512 0.948772
\(202\) −6.82269 −0.480043
\(203\) 36.1178 2.53497
\(204\) −7.44579 −0.521310
\(205\) 14.1764 0.990119
\(206\) −30.7240 −2.14064
\(207\) −0.0172639 −0.00119992
\(208\) 5.68967 0.394507
\(209\) −5.04648 −0.349072
\(210\) 54.2912 3.74645
\(211\) 0.490257 0.0337507 0.0168753 0.999858i \(-0.494628\pi\)
0.0168753 + 0.999858i \(0.494628\pi\)
\(212\) 31.2678 2.14748
\(213\) 25.3817 1.73913
\(214\) −17.6333 −1.20538
\(215\) 3.07277 0.209561
\(216\) −30.1784 −2.05338
\(217\) 3.54651 0.240753
\(218\) −46.5353 −3.15177
\(219\) −26.5747 −1.79575
\(220\) −13.2367 −0.892418
\(221\) 0.957676 0.0644203
\(222\) −14.8848 −0.999002
\(223\) 12.0925 0.809774 0.404887 0.914367i \(-0.367311\pi\)
0.404887 + 0.914367i \(0.367311\pi\)
\(224\) 13.5508 0.905400
\(225\) −0.0550523 −0.00367015
\(226\) −47.5604 −3.16367
\(227\) 0.839075 0.0556914 0.0278457 0.999612i \(-0.491135\pi\)
0.0278457 + 0.999612i \(0.491135\pi\)
\(228\) 37.5750 2.48847
\(229\) 16.7714 1.10828 0.554142 0.832422i \(-0.313047\pi\)
0.554142 + 0.832422i \(0.313047\pi\)
\(230\) 10.7499 0.708824
\(231\) 7.03497 0.462867
\(232\) 51.4332 3.37675
\(233\) −0.502200 −0.0329002 −0.0164501 0.999865i \(-0.505236\pi\)
−0.0164501 + 0.999865i \(0.505236\pi\)
\(234\) 0.0298097 0.00194872
\(235\) 33.7768 2.20336
\(236\) −40.8439 −2.65871
\(237\) −25.7565 −1.67306
\(238\) 10.2220 0.662596
\(239\) −18.0172 −1.16543 −0.582717 0.812675i \(-0.698010\pi\)
−0.582717 + 0.812675i \(0.698010\pi\)
\(240\) 31.5544 2.03683
\(241\) −29.2086 −1.88149 −0.940747 0.339110i \(-0.889874\pi\)
−0.940747 + 0.339110i \(0.889874\pi\)
\(242\) −2.51152 −0.161447
\(243\) −0.128799 −0.00826244
\(244\) −28.5891 −1.83023
\(245\) −29.3922 −1.87780
\(246\) −20.0278 −1.27692
\(247\) −4.83289 −0.307509
\(248\) 5.05037 0.320699
\(249\) 12.7115 0.805560
\(250\) −4.30674 −0.272382
\(251\) 11.2257 0.708563 0.354281 0.935139i \(-0.384726\pi\)
0.354281 + 0.935139i \(0.384726\pi\)
\(252\) 0.217296 0.0136884
\(253\) 1.39295 0.0875740
\(254\) −9.44888 −0.592875
\(255\) 5.31120 0.332600
\(256\) −31.8887 −1.99304
\(257\) −9.25154 −0.577095 −0.288548 0.957466i \(-0.593172\pi\)
−0.288548 + 0.957466i \(0.593172\pi\)
\(258\) −4.34109 −0.270264
\(259\) 13.9555 0.867152
\(260\) −12.6765 −0.786161
\(261\) 0.109982 0.00680774
\(262\) −28.4368 −1.75683
\(263\) −15.0524 −0.928169 −0.464084 0.885791i \(-0.653617\pi\)
−0.464084 + 0.885791i \(0.653617\pi\)
\(264\) 10.0181 0.616570
\(265\) −22.3038 −1.37011
\(266\) −51.5853 −3.16290
\(267\) −10.6041 −0.648959
\(268\) −33.5234 −2.04776
\(269\) −11.6076 −0.707726 −0.353863 0.935297i \(-0.615132\pi\)
−0.353863 + 0.935297i \(0.615132\pi\)
\(270\) 40.1829 2.44545
\(271\) −4.93739 −0.299925 −0.149962 0.988692i \(-0.547915\pi\)
−0.149962 + 0.988692i \(0.547915\pi\)
\(272\) 5.94112 0.360233
\(273\) 6.73722 0.407755
\(274\) 45.5605 2.75241
\(275\) 4.44194 0.267859
\(276\) −10.3716 −0.624297
\(277\) 22.6927 1.36347 0.681736 0.731598i \(-0.261225\pi\)
0.681736 + 0.731598i \(0.261225\pi\)
\(278\) −24.2682 −1.45551
\(279\) 0.0107995 0.000646548 0
\(280\) −72.4860 −4.33187
\(281\) 19.8526 1.18431 0.592154 0.805825i \(-0.298278\pi\)
0.592154 + 0.805825i \(0.298278\pi\)
\(282\) −47.7184 −2.84159
\(283\) 0.844338 0.0501907 0.0250953 0.999685i \(-0.492011\pi\)
0.0250953 + 0.999685i \(0.492011\pi\)
\(284\) −63.2570 −3.75361
\(285\) −26.8028 −1.58766
\(286\) −2.40522 −0.142224
\(287\) 18.7774 1.10839
\(288\) 0.0412635 0.00243148
\(289\) 1.00000 0.0588235
\(290\) −68.4838 −4.02151
\(291\) 25.4291 1.49068
\(292\) 66.2301 3.87582
\(293\) −4.64842 −0.271563 −0.135782 0.990739i \(-0.543355\pi\)
−0.135782 + 0.990739i \(0.543355\pi\)
\(294\) 41.5241 2.42173
\(295\) 29.1346 1.69628
\(296\) 19.8732 1.15511
\(297\) 5.20683 0.302131
\(298\) −6.73400 −0.390090
\(299\) 1.33399 0.0771469
\(300\) −33.0738 −1.90951
\(301\) 4.07006 0.234594
\(302\) 32.4825 1.86916
\(303\) −4.69549 −0.269749
\(304\) −29.9817 −1.71957
\(305\) 20.3930 1.16770
\(306\) 0.0311271 0.00177942
\(307\) 30.7201 1.75329 0.876643 0.481141i \(-0.159777\pi\)
0.876643 + 0.481141i \(0.159777\pi\)
\(308\) −17.5327 −0.999020
\(309\) −21.1448 −1.20288
\(310\) −6.72462 −0.381933
\(311\) 33.5002 1.89962 0.949811 0.312824i \(-0.101275\pi\)
0.949811 + 0.312824i \(0.101275\pi\)
\(312\) 9.59408 0.543158
\(313\) −20.1237 −1.13746 −0.568728 0.822525i \(-0.692564\pi\)
−0.568728 + 0.822525i \(0.692564\pi\)
\(314\) −40.4857 −2.28474
\(315\) −0.155001 −0.00873330
\(316\) 64.1909 3.61102
\(317\) 27.0592 1.51979 0.759897 0.650044i \(-0.225249\pi\)
0.759897 + 0.650044i \(0.225249\pi\)
\(318\) 31.5098 1.76698
\(319\) −8.87402 −0.496850
\(320\) 10.8174 0.604713
\(321\) −12.1355 −0.677337
\(322\) 14.2388 0.793496
\(323\) −5.04648 −0.280793
\(324\) −38.6088 −2.14493
\(325\) 4.25394 0.235966
\(326\) −48.1385 −2.66614
\(327\) −32.0263 −1.77106
\(328\) 26.7397 1.47645
\(329\) 44.7392 2.46655
\(330\) −13.3392 −0.734298
\(331\) 10.6370 0.584661 0.292331 0.956317i \(-0.405569\pi\)
0.292331 + 0.956317i \(0.405569\pi\)
\(332\) −31.6800 −1.73867
\(333\) 0.0424959 0.00232876
\(334\) −7.62956 −0.417471
\(335\) 23.9127 1.30649
\(336\) 41.7956 2.28014
\(337\) 16.9782 0.924862 0.462431 0.886655i \(-0.346977\pi\)
0.462431 + 0.886655i \(0.346977\pi\)
\(338\) 30.3463 1.65062
\(339\) −32.7318 −1.77775
\(340\) −13.2367 −0.717861
\(341\) −0.871366 −0.0471871
\(342\) −0.157082 −0.00849404
\(343\) −10.4412 −0.563772
\(344\) 5.79593 0.312495
\(345\) 7.39822 0.398307
\(346\) −38.4216 −2.06556
\(347\) −27.1297 −1.45640 −0.728200 0.685365i \(-0.759643\pi\)
−0.728200 + 0.685365i \(0.759643\pi\)
\(348\) 66.0741 3.54194
\(349\) 20.6834 1.10715 0.553577 0.832798i \(-0.313262\pi\)
0.553577 + 0.832798i \(0.313262\pi\)
\(350\) 45.4057 2.42703
\(351\) 4.98646 0.266157
\(352\) −3.32939 −0.177457
\(353\) 7.45407 0.396740 0.198370 0.980127i \(-0.436435\pi\)
0.198370 + 0.980127i \(0.436435\pi\)
\(354\) −41.1601 −2.18763
\(355\) 45.1222 2.39484
\(356\) 26.4277 1.40067
\(357\) 7.03497 0.372330
\(358\) 25.9494 1.37147
\(359\) 33.0111 1.74226 0.871129 0.491054i \(-0.163388\pi\)
0.871129 + 0.491054i \(0.163388\pi\)
\(360\) −0.220727 −0.0116333
\(361\) 6.46693 0.340365
\(362\) 29.3719 1.54375
\(363\) −1.72847 −0.0907211
\(364\) −16.7907 −0.880071
\(365\) −47.2429 −2.47281
\(366\) −28.8104 −1.50594
\(367\) 24.3527 1.27120 0.635601 0.772017i \(-0.280752\pi\)
0.635601 + 0.772017i \(0.280752\pi\)
\(368\) 8.27567 0.431399
\(369\) 0.0571790 0.00297662
\(370\) −26.4613 −1.37566
\(371\) −29.5426 −1.53377
\(372\) 6.48800 0.336387
\(373\) −32.0815 −1.66112 −0.830559 0.556931i \(-0.811979\pi\)
−0.830559 + 0.556931i \(0.811979\pi\)
\(374\) −2.51152 −0.129868
\(375\) −2.96397 −0.153058
\(376\) 63.7105 3.28562
\(377\) −8.49844 −0.437692
\(378\) 53.2244 2.73757
\(379\) −28.9196 −1.48550 −0.742751 0.669568i \(-0.766479\pi\)
−0.742751 + 0.669568i \(0.766479\pi\)
\(380\) 66.7987 3.42670
\(381\) −6.50287 −0.333152
\(382\) 16.2053 0.829136
\(383\) −27.2853 −1.39421 −0.697107 0.716967i \(-0.745530\pi\)
−0.697107 + 0.716967i \(0.745530\pi\)
\(384\) −26.7919 −1.36722
\(385\) 12.5064 0.637384
\(386\) −2.77432 −0.141209
\(387\) 0.0123937 0.000630009 0
\(388\) −63.3750 −3.21738
\(389\) −18.4624 −0.936082 −0.468041 0.883707i \(-0.655040\pi\)
−0.468041 + 0.883707i \(0.655040\pi\)
\(390\) −12.7746 −0.646868
\(391\) 1.39295 0.0704445
\(392\) −55.4402 −2.80015
\(393\) −19.5707 −0.987210
\(394\) 30.3617 1.52960
\(395\) −45.7884 −2.30386
\(396\) −0.0533890 −0.00268290
\(397\) 30.3957 1.52551 0.762757 0.646685i \(-0.223845\pi\)
0.762757 + 0.646685i \(0.223845\pi\)
\(398\) −57.3525 −2.87482
\(399\) −35.5018 −1.77731
\(400\) 26.3901 1.31950
\(401\) −6.42102 −0.320650 −0.160325 0.987064i \(-0.551254\pi\)
−0.160325 + 0.987064i \(0.551254\pi\)
\(402\) −33.7829 −1.68494
\(403\) −0.834486 −0.0415687
\(404\) 11.7022 0.582207
\(405\) 27.5402 1.36849
\(406\) −90.7106 −4.50189
\(407\) −3.42882 −0.169960
\(408\) 10.0181 0.495969
\(409\) 5.19743 0.256996 0.128498 0.991710i \(-0.458984\pi\)
0.128498 + 0.991710i \(0.458984\pi\)
\(410\) −35.6042 −1.75837
\(411\) 31.3555 1.54665
\(412\) 52.6975 2.59622
\(413\) 38.5903 1.89891
\(414\) 0.0433585 0.00213096
\(415\) 22.5978 1.10928
\(416\) −3.18847 −0.156328
\(417\) −16.7018 −0.817890
\(418\) 12.6743 0.619922
\(419\) −10.3251 −0.504412 −0.252206 0.967674i \(-0.581156\pi\)
−0.252206 + 0.967674i \(0.581156\pi\)
\(420\) −93.1198 −4.54378
\(421\) 7.72873 0.376675 0.188338 0.982104i \(-0.439690\pi\)
0.188338 + 0.982104i \(0.439690\pi\)
\(422\) −1.23129 −0.0599382
\(423\) 0.136236 0.00662400
\(424\) −42.0698 −2.04309
\(425\) 4.44194 0.215466
\(426\) −63.7468 −3.08854
\(427\) 27.0117 1.30719
\(428\) 30.2444 1.46192
\(429\) −1.65531 −0.0799193
\(430\) −7.71734 −0.372163
\(431\) −5.61361 −0.270398 −0.135199 0.990818i \(-0.543167\pi\)
−0.135199 + 0.990818i \(0.543167\pi\)
\(432\) 30.9344 1.48833
\(433\) 13.4380 0.645789 0.322894 0.946435i \(-0.395344\pi\)
0.322894 + 0.946435i \(0.395344\pi\)
\(434\) −8.90713 −0.427556
\(435\) −47.1317 −2.25979
\(436\) 79.8168 3.82253
\(437\) −7.02948 −0.336266
\(438\) 66.7428 3.18910
\(439\) −19.8752 −0.948591 −0.474295 0.880366i \(-0.657297\pi\)
−0.474295 + 0.880366i \(0.657297\pi\)
\(440\) 17.8096 0.849038
\(441\) −0.118551 −0.00564527
\(442\) −2.40522 −0.114405
\(443\) −6.44799 −0.306353 −0.153177 0.988199i \(-0.548950\pi\)
−0.153177 + 0.988199i \(0.548950\pi\)
\(444\) 25.5303 1.21161
\(445\) −18.8513 −0.893638
\(446\) −30.3706 −1.43809
\(447\) −4.63445 −0.219202
\(448\) 14.3283 0.676948
\(449\) 9.15718 0.432154 0.216077 0.976376i \(-0.430674\pi\)
0.216077 + 0.976376i \(0.430674\pi\)
\(450\) 0.138265 0.00651787
\(451\) −4.61354 −0.217243
\(452\) 81.5751 3.83697
\(453\) 22.3550 1.05033
\(454\) −2.10736 −0.0989031
\(455\) 11.9770 0.561493
\(456\) −50.5560 −2.36750
\(457\) 29.6428 1.38663 0.693316 0.720633i \(-0.256149\pi\)
0.693316 + 0.720633i \(0.256149\pi\)
\(458\) −42.1217 −1.96822
\(459\) 5.20683 0.243034
\(460\) −18.4380 −0.859678
\(461\) 1.73615 0.0808604 0.0404302 0.999182i \(-0.487127\pi\)
0.0404302 + 0.999182i \(0.487127\pi\)
\(462\) −17.6685 −0.822012
\(463\) 10.4156 0.484054 0.242027 0.970269i \(-0.422188\pi\)
0.242027 + 0.970269i \(0.422188\pi\)
\(464\) −52.7216 −2.44754
\(465\) −4.62799 −0.214618
\(466\) 1.26129 0.0584279
\(467\) −11.6323 −0.538277 −0.269139 0.963101i \(-0.586739\pi\)
−0.269139 + 0.963101i \(0.586739\pi\)
\(468\) −0.0511293 −0.00236345
\(469\) 31.6737 1.46256
\(470\) −84.8311 −3.91297
\(471\) −27.8629 −1.28386
\(472\) 54.9542 2.52947
\(473\) −1.00000 −0.0459800
\(474\) 64.6879 2.97121
\(475\) −22.4161 −1.02852
\(476\) −17.5327 −0.803612
\(477\) −0.0899602 −0.00411899
\(478\) 45.2505 2.06971
\(479\) −36.0123 −1.64544 −0.822722 0.568444i \(-0.807545\pi\)
−0.822722 + 0.568444i \(0.807545\pi\)
\(480\) −17.6830 −0.807116
\(481\) −3.28370 −0.149724
\(482\) 73.3581 3.34137
\(483\) 9.79935 0.445886
\(484\) 4.30774 0.195806
\(485\) 45.2064 2.05271
\(486\) 0.323481 0.0146734
\(487\) 4.95570 0.224564 0.112282 0.993676i \(-0.464184\pi\)
0.112282 + 0.993676i \(0.464184\pi\)
\(488\) 38.4657 1.74126
\(489\) −33.1297 −1.49818
\(490\) 73.8192 3.33481
\(491\) −27.7067 −1.25039 −0.625193 0.780470i \(-0.714980\pi\)
−0.625193 + 0.780470i \(0.714980\pi\)
\(492\) 34.3514 1.54868
\(493\) −8.87402 −0.399666
\(494\) 12.1379 0.546110
\(495\) 0.0380832 0.00171171
\(496\) −5.17689 −0.232449
\(497\) 59.7668 2.68091
\(498\) −31.9253 −1.43061
\(499\) 19.4068 0.868767 0.434384 0.900728i \(-0.356966\pi\)
0.434384 + 0.900728i \(0.356966\pi\)
\(500\) 7.38687 0.330351
\(501\) −5.25079 −0.234588
\(502\) −28.1937 −1.25835
\(503\) 40.7164 1.81545 0.907727 0.419560i \(-0.137816\pi\)
0.907727 + 0.419560i \(0.137816\pi\)
\(504\) −0.292365 −0.0130230
\(505\) −8.34737 −0.371453
\(506\) −3.49842 −0.155524
\(507\) 20.8848 0.927529
\(508\) 16.2066 0.719053
\(509\) −14.7463 −0.653617 −0.326809 0.945091i \(-0.605973\pi\)
−0.326809 + 0.945091i \(0.605973\pi\)
\(510\) −13.3392 −0.590669
\(511\) −62.5758 −2.76819
\(512\) 49.0883 2.16942
\(513\) −26.2761 −1.16012
\(514\) 23.2354 1.02487
\(515\) −37.5900 −1.65641
\(516\) 7.44579 0.327783
\(517\) −10.9923 −0.483440
\(518\) −35.0495 −1.53999
\(519\) −26.4424 −1.16069
\(520\) 17.0558 0.747946
\(521\) 36.4465 1.59675 0.798374 0.602161i \(-0.205694\pi\)
0.798374 + 0.602161i \(0.205694\pi\)
\(522\) −0.276223 −0.0120900
\(523\) 40.0022 1.74917 0.874587 0.484868i \(-0.161132\pi\)
0.874587 + 0.484868i \(0.161132\pi\)
\(524\) 48.7745 2.13073
\(525\) 31.2489 1.36381
\(526\) 37.8043 1.64835
\(527\) −0.871366 −0.0379573
\(528\) −10.2690 −0.446903
\(529\) −21.0597 −0.915639
\(530\) 56.0164 2.43320
\(531\) 0.117512 0.00509957
\(532\) 88.4785 3.83603
\(533\) −4.41827 −0.191377
\(534\) 26.6323 1.15249
\(535\) −21.5738 −0.932716
\(536\) 45.1046 1.94822
\(537\) 17.8588 0.770665
\(538\) 29.1526 1.25686
\(539\) 9.56537 0.412010
\(540\) −68.9212 −2.96590
\(541\) 16.1137 0.692780 0.346390 0.938091i \(-0.387407\pi\)
0.346390 + 0.938091i \(0.387407\pi\)
\(542\) 12.4003 0.532641
\(543\) 20.2142 0.867476
\(544\) −3.32939 −0.142746
\(545\) −56.9346 −2.43881
\(546\) −16.9207 −0.724138
\(547\) 15.6845 0.670620 0.335310 0.942108i \(-0.391159\pi\)
0.335310 + 0.942108i \(0.391159\pi\)
\(548\) −78.1450 −3.33819
\(549\) 0.0822533 0.00351049
\(550\) −11.1560 −0.475694
\(551\) 44.7826 1.90780
\(552\) 13.9547 0.593950
\(553\) −60.6492 −2.57907
\(554\) −56.9932 −2.42141
\(555\) −18.2111 −0.773019
\(556\) 41.6246 1.76528
\(557\) −11.5455 −0.489198 −0.244599 0.969624i \(-0.578656\pi\)
−0.244599 + 0.969624i \(0.578656\pi\)
\(558\) −0.0271231 −0.00114821
\(559\) −0.957676 −0.0405054
\(560\) 74.3018 3.13982
\(561\) −1.72847 −0.0729760
\(562\) −49.8603 −2.10323
\(563\) −26.3085 −1.10877 −0.554385 0.832260i \(-0.687047\pi\)
−0.554385 + 0.832260i \(0.687047\pi\)
\(564\) 81.8462 3.44635
\(565\) −58.1888 −2.44802
\(566\) −2.12057 −0.0891343
\(567\) 36.4786 1.53196
\(568\) 85.1104 3.57115
\(569\) −20.0636 −0.841109 −0.420554 0.907267i \(-0.638164\pi\)
−0.420554 + 0.907267i \(0.638164\pi\)
\(570\) 67.3158 2.81955
\(571\) 13.2226 0.553351 0.276675 0.960963i \(-0.410767\pi\)
0.276675 + 0.960963i \(0.410767\pi\)
\(572\) 4.12542 0.172492
\(573\) 11.1528 0.465913
\(574\) −47.1597 −1.96841
\(575\) 6.18740 0.258032
\(576\) 0.0436311 0.00181796
\(577\) −4.43110 −0.184469 −0.0922345 0.995737i \(-0.529401\pi\)
−0.0922345 + 0.995737i \(0.529401\pi\)
\(578\) −2.51152 −0.104465
\(579\) −1.90933 −0.0793490
\(580\) 117.463 4.87738
\(581\) 29.9321 1.24179
\(582\) −63.8656 −2.64732
\(583\) 7.25851 0.300617
\(584\) −89.1105 −3.68742
\(585\) 0.0364713 0.00150790
\(586\) 11.6746 0.482273
\(587\) −30.1011 −1.24241 −0.621203 0.783650i \(-0.713356\pi\)
−0.621203 + 0.783650i \(0.713356\pi\)
\(588\) −71.2217 −2.93713
\(589\) 4.39733 0.181189
\(590\) −73.1721 −3.01245
\(591\) 20.8954 0.859522
\(592\) −20.3710 −0.837244
\(593\) 34.6151 1.42147 0.710736 0.703459i \(-0.248362\pi\)
0.710736 + 0.703459i \(0.248362\pi\)
\(594\) −13.0771 −0.536558
\(595\) 12.5064 0.512711
\(596\) 11.5501 0.473110
\(597\) −39.4709 −1.61544
\(598\) −3.35035 −0.137006
\(599\) −9.78730 −0.399898 −0.199949 0.979806i \(-0.564078\pi\)
−0.199949 + 0.979806i \(0.564078\pi\)
\(600\) 44.4997 1.81669
\(601\) −8.32684 −0.339659 −0.169829 0.985473i \(-0.554322\pi\)
−0.169829 + 0.985473i \(0.554322\pi\)
\(602\) −10.2220 −0.416619
\(603\) 0.0964497 0.00392774
\(604\) −55.7136 −2.26696
\(605\) −3.07277 −0.124926
\(606\) 11.7928 0.479050
\(607\) 14.8722 0.603644 0.301822 0.953364i \(-0.402405\pi\)
0.301822 + 0.953364i \(0.402405\pi\)
\(608\) 16.8017 0.681398
\(609\) −62.4285 −2.52973
\(610\) −51.2175 −2.07374
\(611\) −10.5270 −0.425879
\(612\) −0.0533890 −0.00215812
\(613\) −18.1248 −0.732054 −0.366027 0.930604i \(-0.619282\pi\)
−0.366027 + 0.930604i \(0.619282\pi\)
\(614\) −77.1541 −3.11369
\(615\) −24.5034 −0.988072
\(616\) 23.5898 0.950458
\(617\) −9.31026 −0.374817 −0.187409 0.982282i \(-0.560009\pi\)
−0.187409 + 0.982282i \(0.560009\pi\)
\(618\) 53.1055 2.13622
\(619\) 20.6673 0.830687 0.415343 0.909665i \(-0.363661\pi\)
0.415343 + 0.909665i \(0.363661\pi\)
\(620\) 11.5340 0.463217
\(621\) 7.25285 0.291047
\(622\) −84.1365 −3.37356
\(623\) −24.9696 −1.00039
\(624\) −9.83441 −0.393692
\(625\) −27.4789 −1.09915
\(626\) 50.5410 2.02002
\(627\) 8.72268 0.348350
\(628\) 69.4408 2.77099
\(629\) −3.42882 −0.136716
\(630\) 0.389287 0.0155096
\(631\) −30.7411 −1.22379 −0.611893 0.790941i \(-0.709592\pi\)
−0.611893 + 0.790941i \(0.709592\pi\)
\(632\) −86.3669 −3.43549
\(633\) −0.847394 −0.0336809
\(634\) −67.9596 −2.69902
\(635\) −11.5604 −0.458762
\(636\) −54.0454 −2.14304
\(637\) 9.16053 0.362953
\(638\) 22.2873 0.882362
\(639\) 0.181996 0.00719966
\(640\) −47.6291 −1.88271
\(641\) 25.0640 0.989968 0.494984 0.868902i \(-0.335174\pi\)
0.494984 + 0.868902i \(0.335174\pi\)
\(642\) 30.4785 1.20289
\(643\) 21.8511 0.861724 0.430862 0.902418i \(-0.358210\pi\)
0.430862 + 0.902418i \(0.358210\pi\)
\(644\) −24.4222 −0.962370
\(645\) −5.31120 −0.209128
\(646\) 12.6743 0.498665
\(647\) −39.4577 −1.55124 −0.775622 0.631198i \(-0.782564\pi\)
−0.775622 + 0.631198i \(0.782564\pi\)
\(648\) 51.9469 2.04067
\(649\) −9.48152 −0.372182
\(650\) −10.6839 −0.419055
\(651\) −6.13003 −0.240255
\(652\) 82.5666 3.23356
\(653\) −29.8903 −1.16970 −0.584850 0.811142i \(-0.698846\pi\)
−0.584850 + 0.811142i \(0.698846\pi\)
\(654\) 80.4348 3.14525
\(655\) −34.7916 −1.35942
\(656\) −27.4096 −1.07016
\(657\) −0.190550 −0.00743406
\(658\) −112.363 −4.38038
\(659\) 38.9056 1.51555 0.757774 0.652517i \(-0.226287\pi\)
0.757774 + 0.652517i \(0.226287\pi\)
\(660\) 22.8792 0.890573
\(661\) 13.8252 0.537736 0.268868 0.963177i \(-0.413350\pi\)
0.268868 + 0.963177i \(0.413350\pi\)
\(662\) −26.7150 −1.03831
\(663\) −1.65531 −0.0642871
\(664\) 42.6245 1.65415
\(665\) −63.1131 −2.44742
\(666\) −0.106729 −0.00413568
\(667\) −12.3611 −0.478622
\(668\) 13.0862 0.506319
\(669\) −20.9015 −0.808099
\(670\) −60.0573 −2.32022
\(671\) −6.63668 −0.256206
\(672\) −23.4221 −0.903528
\(673\) 51.0698 1.96860 0.984299 0.176511i \(-0.0564813\pi\)
0.984299 + 0.176511i \(0.0564813\pi\)
\(674\) −42.6411 −1.64247
\(675\) 23.1284 0.890214
\(676\) −52.0498 −2.00191
\(677\) 1.76712 0.0679161 0.0339580 0.999423i \(-0.489189\pi\)
0.0339580 + 0.999423i \(0.489189\pi\)
\(678\) 82.2067 3.15713
\(679\) 59.8783 2.29792
\(680\) 17.8096 0.682966
\(681\) −1.45032 −0.0555762
\(682\) 2.18845 0.0838002
\(683\) 2.31279 0.0884966 0.0442483 0.999021i \(-0.485911\pi\)
0.0442483 + 0.999021i \(0.485911\pi\)
\(684\) 0.269426 0.0103018
\(685\) 55.7420 2.12979
\(686\) 26.2233 1.00121
\(687\) −28.9888 −1.10599
\(688\) −5.94112 −0.226503
\(689\) 6.95131 0.264824
\(690\) −18.5808 −0.707359
\(691\) 2.51007 0.0954875 0.0477438 0.998860i \(-0.484797\pi\)
0.0477438 + 0.998860i \(0.484797\pi\)
\(692\) 65.9003 2.50515
\(693\) 0.0504433 0.00191618
\(694\) 68.1369 2.58644
\(695\) −29.6915 −1.12626
\(696\) −88.9007 −3.36977
\(697\) −4.61354 −0.174750
\(698\) −51.9467 −1.96621
\(699\) 0.868037 0.0328322
\(700\) −77.8794 −2.94356
\(701\) 22.4762 0.848913 0.424457 0.905448i \(-0.360465\pi\)
0.424457 + 0.905448i \(0.360465\pi\)
\(702\) −12.5236 −0.472672
\(703\) 17.3035 0.652612
\(704\) −3.52041 −0.132681
\(705\) −58.3822 −2.19880
\(706\) −18.7210 −0.704576
\(707\) −11.0565 −0.415824
\(708\) 70.5974 2.65321
\(709\) −35.5549 −1.33529 −0.667646 0.744479i \(-0.732698\pi\)
−0.667646 + 0.744479i \(0.732698\pi\)
\(710\) −113.325 −4.25302
\(711\) −0.184683 −0.00692615
\(712\) −35.5577 −1.33258
\(713\) −1.21377 −0.0454560
\(714\) −17.6685 −0.661226
\(715\) −2.94272 −0.110052
\(716\) −44.5082 −1.66335
\(717\) 31.1421 1.16302
\(718\) −82.9080 −3.09410
\(719\) −24.1014 −0.898830 −0.449415 0.893323i \(-0.648368\pi\)
−0.449415 + 0.893323i \(0.648368\pi\)
\(720\) 0.226257 0.00843209
\(721\) −49.7900 −1.85428
\(722\) −16.2418 −0.604458
\(723\) 50.4862 1.87760
\(724\) −50.3784 −1.87230
\(725\) −39.4179 −1.46394
\(726\) 4.34109 0.161113
\(727\) −31.0090 −1.15006 −0.575031 0.818132i \(-0.695010\pi\)
−0.575031 + 0.818132i \(0.695010\pi\)
\(728\) 22.5913 0.837291
\(729\) 27.1106 1.00410
\(730\) 118.652 4.39149
\(731\) −1.00000 −0.0369863
\(732\) 49.4153 1.82644
\(733\) −53.2069 −1.96524 −0.982620 0.185628i \(-0.940568\pi\)
−0.982620 + 0.185628i \(0.940568\pi\)
\(734\) −61.1624 −2.25755
\(735\) 50.8036 1.87392
\(736\) −4.63766 −0.170947
\(737\) −7.78213 −0.286658
\(738\) −0.143606 −0.00528622
\(739\) 35.7246 1.31415 0.657076 0.753824i \(-0.271793\pi\)
0.657076 + 0.753824i \(0.271793\pi\)
\(740\) 45.3862 1.66843
\(741\) 8.35350 0.306874
\(742\) 74.1968 2.72385
\(743\) −44.3788 −1.62810 −0.814051 0.580794i \(-0.802742\pi\)
−0.814051 + 0.580794i \(0.802742\pi\)
\(744\) −8.72941 −0.320036
\(745\) −8.23885 −0.301848
\(746\) 80.5734 2.95000
\(747\) 0.0911462 0.00333486
\(748\) 4.30774 0.157506
\(749\) −28.5757 −1.04413
\(750\) 7.44406 0.271819
\(751\) −53.7911 −1.96287 −0.981433 0.191806i \(-0.938566\pi\)
−0.981433 + 0.191806i \(0.938566\pi\)
\(752\) −65.3064 −2.38148
\(753\) −19.4034 −0.707098
\(754\) 21.3440 0.777303
\(755\) 39.7414 1.44634
\(756\) −91.2900 −3.32018
\(757\) −13.5792 −0.493544 −0.246772 0.969074i \(-0.579370\pi\)
−0.246772 + 0.969074i \(0.579370\pi\)
\(758\) 72.6322 2.63812
\(759\) −2.40767 −0.0873929
\(760\) −89.8756 −3.26013
\(761\) 33.2124 1.20395 0.601975 0.798515i \(-0.294381\pi\)
0.601975 + 0.798515i \(0.294381\pi\)
\(762\) 16.3321 0.591649
\(763\) −75.4130 −2.73013
\(764\) −27.7952 −1.00559
\(765\) 0.0380832 0.00137690
\(766\) 68.5276 2.47600
\(767\) −9.08023 −0.327868
\(768\) 55.1186 1.98892
\(769\) 5.48535 0.197807 0.0989035 0.995097i \(-0.468466\pi\)
0.0989035 + 0.995097i \(0.468466\pi\)
\(770\) −31.4100 −1.13194
\(771\) 15.9910 0.575902
\(772\) 4.75848 0.171261
\(773\) 25.4863 0.916677 0.458338 0.888778i \(-0.348445\pi\)
0.458338 + 0.888778i \(0.348445\pi\)
\(774\) −0.0311271 −0.00111884
\(775\) −3.87055 −0.139034
\(776\) 85.2691 3.06098
\(777\) −24.1216 −0.865359
\(778\) 46.3687 1.66240
\(779\) 23.2821 0.834168
\(780\) 21.9109 0.784536
\(781\) −14.6845 −0.525453
\(782\) −3.49842 −0.125103
\(783\) −46.2055 −1.65125
\(784\) 56.8290 2.02961
\(785\) −49.5332 −1.76791
\(786\) 49.1521 1.75320
\(787\) 36.7552 1.31018 0.655090 0.755551i \(-0.272631\pi\)
0.655090 + 0.755551i \(0.272631\pi\)
\(788\) −52.0761 −1.85513
\(789\) 26.0176 0.926249
\(790\) 114.998 4.09146
\(791\) −77.0743 −2.74044
\(792\) 0.0718332 0.00255248
\(793\) −6.35579 −0.225701
\(794\) −76.3393 −2.70918
\(795\) 38.5514 1.36728
\(796\) 98.3704 3.48665
\(797\) 8.07288 0.285956 0.142978 0.989726i \(-0.454332\pi\)
0.142978 + 0.989726i \(0.454332\pi\)
\(798\) 89.1635 3.15635
\(799\) −10.9923 −0.388879
\(800\) −14.7889 −0.522868
\(801\) −0.0760350 −0.00268656
\(802\) 16.1265 0.569447
\(803\) 15.3747 0.542561
\(804\) 57.9441 2.04353
\(805\) 17.4207 0.614000
\(806\) 2.09583 0.0738224
\(807\) 20.0633 0.706262
\(808\) −15.7450 −0.553906
\(809\) −29.7142 −1.04469 −0.522347 0.852733i \(-0.674944\pi\)
−0.522347 + 0.852733i \(0.674944\pi\)
\(810\) −69.1679 −2.43031
\(811\) −18.7036 −0.656771 −0.328385 0.944544i \(-0.606504\pi\)
−0.328385 + 0.944544i \(0.606504\pi\)
\(812\) 155.586 5.46000
\(813\) 8.53412 0.299305
\(814\) 8.61155 0.301835
\(815\) −58.8961 −2.06304
\(816\) −10.2690 −0.359488
\(817\) 5.04648 0.176554
\(818\) −13.0535 −0.456403
\(819\) 0.0483083 0.00168803
\(820\) 61.0680 2.13259
\(821\) −13.7431 −0.479639 −0.239819 0.970818i \(-0.577088\pi\)
−0.239819 + 0.970818i \(0.577088\pi\)
\(822\) −78.7500 −2.74672
\(823\) −18.6551 −0.650276 −0.325138 0.945667i \(-0.605411\pi\)
−0.325138 + 0.945667i \(0.605411\pi\)
\(824\) −70.9029 −2.47002
\(825\) −7.67776 −0.267305
\(826\) −96.9204 −3.37229
\(827\) 17.3331 0.602730 0.301365 0.953509i \(-0.402558\pi\)
0.301365 + 0.953509i \(0.402558\pi\)
\(828\) −0.0743681 −0.00258447
\(829\) −9.87328 −0.342913 −0.171457 0.985192i \(-0.554847\pi\)
−0.171457 + 0.985192i \(0.554847\pi\)
\(830\) −56.7549 −1.96999
\(831\) −39.2236 −1.36065
\(832\) −3.37142 −0.116883
\(833\) 9.56537 0.331420
\(834\) 41.9469 1.45250
\(835\) −9.33455 −0.323036
\(836\) −21.7389 −0.751855
\(837\) −4.53705 −0.156823
\(838\) 25.9316 0.895792
\(839\) −10.8840 −0.375757 −0.187878 0.982192i \(-0.560161\pi\)
−0.187878 + 0.982192i \(0.560161\pi\)
\(840\) 125.290 4.32291
\(841\) 49.7483 1.71546
\(842\) −19.4109 −0.668943
\(843\) −34.3147 −1.18186
\(844\) 2.11190 0.0726945
\(845\) 37.1279 1.27724
\(846\) −0.342158 −0.0117636
\(847\) −4.07006 −0.139849
\(848\) 43.1237 1.48087
\(849\) −1.45941 −0.0500869
\(850\) −11.1560 −0.382648
\(851\) −4.77617 −0.163725
\(852\) 109.338 3.74585
\(853\) −25.2059 −0.863032 −0.431516 0.902105i \(-0.642021\pi\)
−0.431516 + 0.902105i \(0.642021\pi\)
\(854\) −67.8404 −2.32145
\(855\) −0.192186 −0.00657262
\(856\) −40.6929 −1.39085
\(857\) 5.71204 0.195119 0.0975597 0.995230i \(-0.468896\pi\)
0.0975597 + 0.995230i \(0.468896\pi\)
\(858\) 4.15735 0.141930
\(859\) 34.0504 1.16178 0.580892 0.813981i \(-0.302704\pi\)
0.580892 + 0.813981i \(0.302704\pi\)
\(860\) 13.2367 0.451368
\(861\) −32.4561 −1.10610
\(862\) 14.0987 0.480203
\(863\) 0.247807 0.00843545 0.00421773 0.999991i \(-0.498657\pi\)
0.00421773 + 0.999991i \(0.498657\pi\)
\(864\) −17.3355 −0.589767
\(865\) −47.0077 −1.59831
\(866\) −33.7498 −1.14686
\(867\) −1.72847 −0.0587019
\(868\) 15.2774 0.518549
\(869\) 14.9013 0.505492
\(870\) 118.372 4.01319
\(871\) −7.45276 −0.252527
\(872\) −107.391 −3.63672
\(873\) 0.182336 0.00617112
\(874\) 17.6547 0.597179
\(875\) −6.97930 −0.235943
\(876\) −114.477 −3.86781
\(877\) 12.9801 0.438306 0.219153 0.975690i \(-0.429671\pi\)
0.219153 + 0.975690i \(0.429671\pi\)
\(878\) 49.9169 1.68461
\(879\) 8.03465 0.271002
\(880\) −18.2557 −0.615400
\(881\) −12.2860 −0.413927 −0.206963 0.978349i \(-0.566358\pi\)
−0.206963 + 0.978349i \(0.566358\pi\)
\(882\) 0.297743 0.0100255
\(883\) −17.6559 −0.594169 −0.297085 0.954851i \(-0.596014\pi\)
−0.297085 + 0.954851i \(0.596014\pi\)
\(884\) 4.12542 0.138753
\(885\) −50.3582 −1.69277
\(886\) 16.1943 0.544057
\(887\) 2.88101 0.0967349 0.0483674 0.998830i \(-0.484598\pi\)
0.0483674 + 0.998830i \(0.484598\pi\)
\(888\) −34.3502 −1.15272
\(889\) −15.3124 −0.513562
\(890\) 47.3455 1.58702
\(891\) −8.96267 −0.300261
\(892\) 52.0913 1.74415
\(893\) 55.4723 1.85631
\(894\) 11.6395 0.389283
\(895\) 31.7484 1.06123
\(896\) −63.0874 −2.10760
\(897\) −2.30577 −0.0769873
\(898\) −22.9984 −0.767468
\(899\) 7.73252 0.257894
\(900\) −0.237151 −0.00790502
\(901\) 7.25851 0.241816
\(902\) 11.5870 0.385805
\(903\) −7.03497 −0.234109
\(904\) −109.757 −3.65046
\(905\) 35.9357 1.19454
\(906\) −56.1450 −1.86529
\(907\) −33.5907 −1.11536 −0.557681 0.830056i \(-0.688309\pi\)
−0.557681 + 0.830056i \(0.688309\pi\)
\(908\) 3.61452 0.119952
\(909\) −0.0336683 −0.00111671
\(910\) −30.0806 −0.997162
\(911\) −53.4280 −1.77015 −0.885075 0.465449i \(-0.845893\pi\)
−0.885075 + 0.465449i \(0.845893\pi\)
\(912\) 51.8225 1.71601
\(913\) −7.35421 −0.243389
\(914\) −74.4486 −2.46254
\(915\) −35.2487 −1.16529
\(916\) 72.2466 2.38710
\(917\) −46.0834 −1.52181
\(918\) −13.0771 −0.431607
\(919\) −21.0869 −0.695593 −0.347796 0.937570i \(-0.613070\pi\)
−0.347796 + 0.937570i \(0.613070\pi\)
\(920\) 24.8078 0.817890
\(921\) −53.0987 −1.74966
\(922\) −4.36037 −0.143601
\(923\) −14.0630 −0.462890
\(924\) 30.3048 0.996955
\(925\) −15.2306 −0.500779
\(926\) −26.1590 −0.859638
\(927\) −0.151616 −0.00497971
\(928\) 29.5450 0.969864
\(929\) 54.5513 1.78977 0.894885 0.446297i \(-0.147257\pi\)
0.894885 + 0.446297i \(0.147257\pi\)
\(930\) 11.6233 0.381143
\(931\) −48.2714 −1.58203
\(932\) −2.16334 −0.0708627
\(933\) −57.9041 −1.89569
\(934\) 29.2147 0.955934
\(935\) −3.07277 −0.100490
\(936\) 0.0687930 0.00224857
\(937\) 42.6946 1.39477 0.697386 0.716696i \(-0.254346\pi\)
0.697386 + 0.716696i \(0.254346\pi\)
\(938\) −79.5492 −2.59737
\(939\) 34.7831 1.13510
\(940\) 145.502 4.74574
\(941\) −40.4869 −1.31984 −0.659918 0.751338i \(-0.729409\pi\)
−0.659918 + 0.751338i \(0.729409\pi\)
\(942\) 69.9784 2.28002
\(943\) −6.42642 −0.209273
\(944\) −56.3308 −1.83341
\(945\) 65.1185 2.11831
\(946\) 2.51152 0.0816566
\(947\) 41.8258 1.35915 0.679577 0.733604i \(-0.262163\pi\)
0.679577 + 0.733604i \(0.262163\pi\)
\(948\) −110.952 −3.60355
\(949\) 14.7240 0.477960
\(950\) 56.2986 1.82657
\(951\) −46.7709 −1.51665
\(952\) 23.5898 0.764548
\(953\) 42.1410 1.36508 0.682541 0.730847i \(-0.260875\pi\)
0.682541 + 0.730847i \(0.260875\pi\)
\(954\) 0.225937 0.00731497
\(955\) 19.8267 0.641578
\(956\) −77.6132 −2.51019
\(957\) 15.3385 0.495823
\(958\) 90.4456 2.92216
\(959\) 73.8333 2.38420
\(960\) −18.6976 −0.603463
\(961\) −30.2407 −0.975507
\(962\) 8.24707 0.265896
\(963\) −0.0870158 −0.00280405
\(964\) −125.823 −4.05249
\(965\) −3.39430 −0.109266
\(966\) −24.6113 −0.791855
\(967\) −40.4434 −1.30057 −0.650287 0.759689i \(-0.725351\pi\)
−0.650287 + 0.759689i \(0.725351\pi\)
\(968\) −5.79593 −0.186288
\(969\) 8.72268 0.280213
\(970\) −113.537 −3.64544
\(971\) −32.2416 −1.03468 −0.517341 0.855780i \(-0.673078\pi\)
−0.517341 + 0.855780i \(0.673078\pi\)
\(972\) −0.554831 −0.0177962
\(973\) −39.3280 −1.26080
\(974\) −12.4463 −0.398806
\(975\) −7.35281 −0.235478
\(976\) −39.4293 −1.26210
\(977\) −47.1595 −1.50876 −0.754382 0.656435i \(-0.772063\pi\)
−0.754382 + 0.656435i \(0.772063\pi\)
\(978\) 83.2059 2.66063
\(979\) 6.13495 0.196074
\(980\) −126.614 −4.04453
\(981\) −0.229640 −0.00733185
\(982\) 69.5859 2.22058
\(983\) 21.0037 0.669914 0.334957 0.942233i \(-0.391278\pi\)
0.334957 + 0.942233i \(0.391278\pi\)
\(984\) −46.2188 −1.47340
\(985\) 37.1467 1.18359
\(986\) 22.2873 0.709772
\(987\) −77.3304 −2.46145
\(988\) −20.8188 −0.662335
\(989\) −1.39295 −0.0442932
\(990\) −0.0956467 −0.00303985
\(991\) −24.0947 −0.765392 −0.382696 0.923874i \(-0.625004\pi\)
−0.382696 + 0.923874i \(0.625004\pi\)
\(992\) 2.90111 0.0921104
\(993\) −18.3857 −0.583452
\(994\) −150.106 −4.76106
\(995\) −70.1691 −2.22451
\(996\) 54.7579 1.73507
\(997\) 42.9102 1.35898 0.679490 0.733685i \(-0.262201\pi\)
0.679490 + 0.733685i \(0.262201\pi\)
\(998\) −48.7406 −1.54286
\(999\) −17.8533 −0.564853
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.c.1.5 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8041.2.a.c.1.5 60 1.1 even 1 trivial