Properties

Label 8026.2.a.a.1.1
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $1$
Dimension $71$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(1\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.33028 q^{3} +1.00000 q^{4} -2.81719 q^{5} -3.33028 q^{6} +2.39962 q^{7} +1.00000 q^{8} +8.09075 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.33028 q^{3} +1.00000 q^{4} -2.81719 q^{5} -3.33028 q^{6} +2.39962 q^{7} +1.00000 q^{8} +8.09075 q^{9} -2.81719 q^{10} +2.12115 q^{11} -3.33028 q^{12} +1.83076 q^{13} +2.39962 q^{14} +9.38202 q^{15} +1.00000 q^{16} -5.43896 q^{17} +8.09075 q^{18} -1.66187 q^{19} -2.81719 q^{20} -7.99140 q^{21} +2.12115 q^{22} +0.107282 q^{23} -3.33028 q^{24} +2.93656 q^{25} +1.83076 q^{26} -16.9536 q^{27} +2.39962 q^{28} -1.06042 q^{29} +9.38202 q^{30} +1.63639 q^{31} +1.00000 q^{32} -7.06402 q^{33} -5.43896 q^{34} -6.76018 q^{35} +8.09075 q^{36} +3.16634 q^{37} -1.66187 q^{38} -6.09694 q^{39} -2.81719 q^{40} -8.30191 q^{41} -7.99140 q^{42} +0.583384 q^{43} +2.12115 q^{44} -22.7932 q^{45} +0.107282 q^{46} -4.59473 q^{47} -3.33028 q^{48} -1.24183 q^{49} +2.93656 q^{50} +18.1132 q^{51} +1.83076 q^{52} +4.37480 q^{53} -16.9536 q^{54} -5.97569 q^{55} +2.39962 q^{56} +5.53448 q^{57} -1.06042 q^{58} -1.74148 q^{59} +9.38202 q^{60} +11.1464 q^{61} +1.63639 q^{62} +19.4147 q^{63} +1.00000 q^{64} -5.15760 q^{65} -7.06402 q^{66} +3.04992 q^{67} -5.43896 q^{68} -0.357278 q^{69} -6.76018 q^{70} -13.4515 q^{71} +8.09075 q^{72} +9.59142 q^{73} +3.16634 q^{74} -9.77956 q^{75} -1.66187 q^{76} +5.08996 q^{77} -6.09694 q^{78} +4.39928 q^{79} -2.81719 q^{80} +32.1879 q^{81} -8.30191 q^{82} -3.04167 q^{83} -7.99140 q^{84} +15.3226 q^{85} +0.583384 q^{86} +3.53150 q^{87} +2.12115 q^{88} +1.94847 q^{89} -22.7932 q^{90} +4.39313 q^{91} +0.107282 q^{92} -5.44963 q^{93} -4.59473 q^{94} +4.68180 q^{95} -3.33028 q^{96} +2.50969 q^{97} -1.24183 q^{98} +17.1617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.33028 −1.92274 −0.961368 0.275266i \(-0.911234\pi\)
−0.961368 + 0.275266i \(0.911234\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.81719 −1.25989 −0.629943 0.776641i \(-0.716922\pi\)
−0.629943 + 0.776641i \(0.716922\pi\)
\(6\) −3.33028 −1.35958
\(7\) 2.39962 0.906971 0.453485 0.891264i \(-0.350180\pi\)
0.453485 + 0.891264i \(0.350180\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.09075 2.69692
\(10\) −2.81719 −0.890874
\(11\) 2.12115 0.639551 0.319776 0.947493i \(-0.396392\pi\)
0.319776 + 0.947493i \(0.396392\pi\)
\(12\) −3.33028 −0.961368
\(13\) 1.83076 0.507762 0.253881 0.967235i \(-0.418293\pi\)
0.253881 + 0.967235i \(0.418293\pi\)
\(14\) 2.39962 0.641325
\(15\) 9.38202 2.42243
\(16\) 1.00000 0.250000
\(17\) −5.43896 −1.31914 −0.659571 0.751643i \(-0.729262\pi\)
−0.659571 + 0.751643i \(0.729262\pi\)
\(18\) 8.09075 1.90701
\(19\) −1.66187 −0.381259 −0.190629 0.981662i \(-0.561053\pi\)
−0.190629 + 0.981662i \(0.561053\pi\)
\(20\) −2.81719 −0.629943
\(21\) −7.99140 −1.74387
\(22\) 2.12115 0.452231
\(23\) 0.107282 0.0223698 0.0111849 0.999937i \(-0.496440\pi\)
0.0111849 + 0.999937i \(0.496440\pi\)
\(24\) −3.33028 −0.679790
\(25\) 2.93656 0.587312
\(26\) 1.83076 0.359042
\(27\) −16.9536 −3.26272
\(28\) 2.39962 0.453485
\(29\) −1.06042 −0.196915 −0.0984576 0.995141i \(-0.531391\pi\)
−0.0984576 + 0.995141i \(0.531391\pi\)
\(30\) 9.38202 1.71292
\(31\) 1.63639 0.293904 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(32\) 1.00000 0.176777
\(33\) −7.06402 −1.22969
\(34\) −5.43896 −0.932774
\(35\) −6.76018 −1.14268
\(36\) 8.09075 1.34846
\(37\) 3.16634 0.520543 0.260272 0.965535i \(-0.416188\pi\)
0.260272 + 0.965535i \(0.416188\pi\)
\(38\) −1.66187 −0.269591
\(39\) −6.09694 −0.976292
\(40\) −2.81719 −0.445437
\(41\) −8.30191 −1.29654 −0.648270 0.761411i \(-0.724507\pi\)
−0.648270 + 0.761411i \(0.724507\pi\)
\(42\) −7.99140 −1.23310
\(43\) 0.583384 0.0889653 0.0444826 0.999010i \(-0.485836\pi\)
0.0444826 + 0.999010i \(0.485836\pi\)
\(44\) 2.12115 0.319776
\(45\) −22.7932 −3.39780
\(46\) 0.107282 0.0158178
\(47\) −4.59473 −0.670210 −0.335105 0.942181i \(-0.608772\pi\)
−0.335105 + 0.942181i \(0.608772\pi\)
\(48\) −3.33028 −0.480684
\(49\) −1.24183 −0.177404
\(50\) 2.93656 0.415292
\(51\) 18.1132 2.53636
\(52\) 1.83076 0.253881
\(53\) 4.37480 0.600924 0.300462 0.953794i \(-0.402859\pi\)
0.300462 + 0.953794i \(0.402859\pi\)
\(54\) −16.9536 −2.30709
\(55\) −5.97569 −0.805761
\(56\) 2.39962 0.320663
\(57\) 5.53448 0.733060
\(58\) −1.06042 −0.139240
\(59\) −1.74148 −0.226721 −0.113360 0.993554i \(-0.536161\pi\)
−0.113360 + 0.993554i \(0.536161\pi\)
\(60\) 9.38202 1.21121
\(61\) 11.1464 1.42715 0.713573 0.700581i \(-0.247076\pi\)
0.713573 + 0.700581i \(0.247076\pi\)
\(62\) 1.63639 0.207822
\(63\) 19.4147 2.44602
\(64\) 1.00000 0.125000
\(65\) −5.15760 −0.639722
\(66\) −7.06402 −0.869521
\(67\) 3.04992 0.372607 0.186303 0.982492i \(-0.440349\pi\)
0.186303 + 0.982492i \(0.440349\pi\)
\(68\) −5.43896 −0.659571
\(69\) −0.357278 −0.0430112
\(70\) −6.76018 −0.807997
\(71\) −13.4515 −1.59639 −0.798197 0.602397i \(-0.794213\pi\)
−0.798197 + 0.602397i \(0.794213\pi\)
\(72\) 8.09075 0.953504
\(73\) 9.59142 1.12259 0.561295 0.827616i \(-0.310303\pi\)
0.561295 + 0.827616i \(0.310303\pi\)
\(74\) 3.16634 0.368080
\(75\) −9.77956 −1.12925
\(76\) −1.66187 −0.190629
\(77\) 5.08996 0.580054
\(78\) −6.09694 −0.690343
\(79\) 4.39928 0.494958 0.247479 0.968893i \(-0.420398\pi\)
0.247479 + 0.968893i \(0.420398\pi\)
\(80\) −2.81719 −0.314971
\(81\) 32.1879 3.57644
\(82\) −8.30191 −0.916792
\(83\) −3.04167 −0.333866 −0.166933 0.985968i \(-0.553386\pi\)
−0.166933 + 0.985968i \(0.553386\pi\)
\(84\) −7.99140 −0.871933
\(85\) 15.3226 1.66197
\(86\) 0.583384 0.0629079
\(87\) 3.53150 0.378616
\(88\) 2.12115 0.226115
\(89\) 1.94847 0.206538 0.103269 0.994653i \(-0.467070\pi\)
0.103269 + 0.994653i \(0.467070\pi\)
\(90\) −22.7932 −2.40261
\(91\) 4.39313 0.460525
\(92\) 0.107282 0.0111849
\(93\) −5.44963 −0.565100
\(94\) −4.59473 −0.473910
\(95\) 4.68180 0.480342
\(96\) −3.33028 −0.339895
\(97\) 2.50969 0.254820 0.127410 0.991850i \(-0.459334\pi\)
0.127410 + 0.991850i \(0.459334\pi\)
\(98\) −1.24183 −0.125443
\(99\) 17.1617 1.72482
\(100\) 2.93656 0.293656
\(101\) −4.29911 −0.427778 −0.213889 0.976858i \(-0.568613\pi\)
−0.213889 + 0.976858i \(0.568613\pi\)
\(102\) 18.1132 1.79348
\(103\) −12.3774 −1.21958 −0.609791 0.792563i \(-0.708746\pi\)
−0.609791 + 0.792563i \(0.708746\pi\)
\(104\) 1.83076 0.179521
\(105\) 22.5133 2.19707
\(106\) 4.37480 0.424918
\(107\) 12.2003 1.17945 0.589725 0.807604i \(-0.299236\pi\)
0.589725 + 0.807604i \(0.299236\pi\)
\(108\) −16.9536 −1.63136
\(109\) 4.56595 0.437339 0.218669 0.975799i \(-0.429828\pi\)
0.218669 + 0.975799i \(0.429828\pi\)
\(110\) −5.97569 −0.569759
\(111\) −10.5448 −1.00087
\(112\) 2.39962 0.226743
\(113\) −11.7742 −1.10762 −0.553811 0.832643i \(-0.686827\pi\)
−0.553811 + 0.832643i \(0.686827\pi\)
\(114\) 5.53448 0.518352
\(115\) −0.302233 −0.0281833
\(116\) −1.06042 −0.0984576
\(117\) 14.8122 1.36939
\(118\) −1.74148 −0.160316
\(119\) −13.0514 −1.19642
\(120\) 9.38202 0.856458
\(121\) −6.50072 −0.590974
\(122\) 11.1464 1.00914
\(123\) 27.6476 2.49290
\(124\) 1.63639 0.146952
\(125\) 5.81310 0.519940
\(126\) 19.4147 1.72960
\(127\) 6.13122 0.544058 0.272029 0.962289i \(-0.412305\pi\)
0.272029 + 0.962289i \(0.412305\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.94283 −0.171057
\(130\) −5.15760 −0.452352
\(131\) −7.47793 −0.653350 −0.326675 0.945137i \(-0.605928\pi\)
−0.326675 + 0.945137i \(0.605928\pi\)
\(132\) −7.06402 −0.614844
\(133\) −3.98785 −0.345791
\(134\) 3.04992 0.263473
\(135\) 47.7615 4.11066
\(136\) −5.43896 −0.466387
\(137\) 11.3372 0.968605 0.484302 0.874901i \(-0.339073\pi\)
0.484302 + 0.874901i \(0.339073\pi\)
\(138\) −0.357278 −0.0304135
\(139\) 15.5959 1.32283 0.661413 0.750022i \(-0.269957\pi\)
0.661413 + 0.750022i \(0.269957\pi\)
\(140\) −6.76018 −0.571340
\(141\) 15.3017 1.28864
\(142\) −13.4515 −1.12882
\(143\) 3.88332 0.324740
\(144\) 8.09075 0.674229
\(145\) 2.98741 0.248091
\(146\) 9.59142 0.793791
\(147\) 4.13563 0.341101
\(148\) 3.16634 0.260272
\(149\) −4.90109 −0.401513 −0.200756 0.979641i \(-0.564340\pi\)
−0.200756 + 0.979641i \(0.564340\pi\)
\(150\) −9.77956 −0.798498
\(151\) 7.85586 0.639301 0.319650 0.947536i \(-0.396435\pi\)
0.319650 + 0.947536i \(0.396435\pi\)
\(152\) −1.66187 −0.134795
\(153\) −44.0052 −3.55761
\(154\) 5.08996 0.410160
\(155\) −4.61002 −0.370286
\(156\) −6.09694 −0.488146
\(157\) −3.77124 −0.300977 −0.150489 0.988612i \(-0.548085\pi\)
−0.150489 + 0.988612i \(0.548085\pi\)
\(158\) 4.39928 0.349988
\(159\) −14.5693 −1.15542
\(160\) −2.81719 −0.222718
\(161\) 0.257435 0.0202887
\(162\) 32.1879 2.52892
\(163\) 4.91488 0.384963 0.192482 0.981301i \(-0.438346\pi\)
0.192482 + 0.981301i \(0.438346\pi\)
\(164\) −8.30191 −0.648270
\(165\) 19.9007 1.54927
\(166\) −3.04167 −0.236079
\(167\) −5.12739 −0.396770 −0.198385 0.980124i \(-0.563570\pi\)
−0.198385 + 0.980124i \(0.563570\pi\)
\(168\) −7.99140 −0.616550
\(169\) −9.64831 −0.742178
\(170\) 15.3226 1.17519
\(171\) −13.4458 −1.02822
\(172\) 0.583384 0.0444826
\(173\) −5.95165 −0.452496 −0.226248 0.974070i \(-0.572646\pi\)
−0.226248 + 0.974070i \(0.572646\pi\)
\(174\) 3.53150 0.267722
\(175\) 7.04663 0.532675
\(176\) 2.12115 0.159888
\(177\) 5.79960 0.435924
\(178\) 1.94847 0.146044
\(179\) −5.15343 −0.385186 −0.192593 0.981279i \(-0.561690\pi\)
−0.192593 + 0.981279i \(0.561690\pi\)
\(180\) −22.7932 −1.69890
\(181\) 7.73594 0.575008 0.287504 0.957779i \(-0.407175\pi\)
0.287504 + 0.957779i \(0.407175\pi\)
\(182\) 4.39313 0.325641
\(183\) −37.1205 −2.74402
\(184\) 0.107282 0.00790891
\(185\) −8.92018 −0.655825
\(186\) −5.44963 −0.399586
\(187\) −11.5369 −0.843658
\(188\) −4.59473 −0.335105
\(189\) −40.6822 −2.95919
\(190\) 4.68180 0.339653
\(191\) −23.6317 −1.70993 −0.854967 0.518683i \(-0.826422\pi\)
−0.854967 + 0.518683i \(0.826422\pi\)
\(192\) −3.33028 −0.240342
\(193\) −19.0384 −1.37042 −0.685208 0.728348i \(-0.740289\pi\)
−0.685208 + 0.728348i \(0.740289\pi\)
\(194\) 2.50969 0.180185
\(195\) 17.1763 1.23002
\(196\) −1.24183 −0.0887019
\(197\) −1.31035 −0.0933584 −0.0466792 0.998910i \(-0.514864\pi\)
−0.0466792 + 0.998910i \(0.514864\pi\)
\(198\) 17.1617 1.21963
\(199\) −22.0771 −1.56501 −0.782503 0.622647i \(-0.786057\pi\)
−0.782503 + 0.622647i \(0.786057\pi\)
\(200\) 2.93656 0.207646
\(201\) −10.1571 −0.716425
\(202\) −4.29911 −0.302485
\(203\) −2.54461 −0.178596
\(204\) 18.1132 1.26818
\(205\) 23.3880 1.63349
\(206\) −12.3774 −0.862374
\(207\) 0.867988 0.0603294
\(208\) 1.83076 0.126941
\(209\) −3.52507 −0.243834
\(210\) 22.5133 1.55356
\(211\) 20.6971 1.42485 0.712424 0.701749i \(-0.247597\pi\)
0.712424 + 0.701749i \(0.247597\pi\)
\(212\) 4.37480 0.300462
\(213\) 44.7971 3.06944
\(214\) 12.2003 0.833997
\(215\) −1.64350 −0.112086
\(216\) −16.9536 −1.15355
\(217\) 3.92671 0.266563
\(218\) 4.56595 0.309245
\(219\) −31.9421 −2.15845
\(220\) −5.97569 −0.402881
\(221\) −9.95744 −0.669810
\(222\) −10.5448 −0.707720
\(223\) 1.08779 0.0728437 0.0364219 0.999337i \(-0.488404\pi\)
0.0364219 + 0.999337i \(0.488404\pi\)
\(224\) 2.39962 0.160331
\(225\) 23.7590 1.58393
\(226\) −11.7742 −0.783207
\(227\) 25.9393 1.72165 0.860827 0.508897i \(-0.169947\pi\)
0.860827 + 0.508897i \(0.169947\pi\)
\(228\) 5.53448 0.366530
\(229\) −5.88492 −0.388887 −0.194443 0.980914i \(-0.562290\pi\)
−0.194443 + 0.980914i \(0.562290\pi\)
\(230\) −0.302233 −0.0199286
\(231\) −16.9510 −1.11529
\(232\) −1.06042 −0.0696201
\(233\) 20.1406 1.31945 0.659726 0.751506i \(-0.270672\pi\)
0.659726 + 0.751506i \(0.270672\pi\)
\(234\) 14.8122 0.968306
\(235\) 12.9442 0.844388
\(236\) −1.74148 −0.113360
\(237\) −14.6508 −0.951673
\(238\) −13.0514 −0.845999
\(239\) −6.42727 −0.415746 −0.207873 0.978156i \(-0.566654\pi\)
−0.207873 + 0.978156i \(0.566654\pi\)
\(240\) 9.38202 0.605607
\(241\) −23.2804 −1.49962 −0.749810 0.661653i \(-0.769855\pi\)
−0.749810 + 0.661653i \(0.769855\pi\)
\(242\) −6.50072 −0.417882
\(243\) −56.3339 −3.61382
\(244\) 11.1464 0.713573
\(245\) 3.49846 0.223508
\(246\) 27.6476 1.76275
\(247\) −3.04248 −0.193589
\(248\) 1.63639 0.103911
\(249\) 10.1296 0.641937
\(250\) 5.81310 0.367653
\(251\) −20.4566 −1.29121 −0.645605 0.763672i \(-0.723395\pi\)
−0.645605 + 0.763672i \(0.723395\pi\)
\(252\) 19.4147 1.22301
\(253\) 0.227561 0.0143066
\(254\) 6.13122 0.384707
\(255\) −51.0284 −3.19553
\(256\) 1.00000 0.0625000
\(257\) −10.6643 −0.665221 −0.332611 0.943064i \(-0.607929\pi\)
−0.332611 + 0.943064i \(0.607929\pi\)
\(258\) −1.94283 −0.120955
\(259\) 7.59801 0.472117
\(260\) −5.15760 −0.319861
\(261\) −8.57960 −0.531064
\(262\) −7.47793 −0.461988
\(263\) 8.64981 0.533370 0.266685 0.963784i \(-0.414072\pi\)
0.266685 + 0.963784i \(0.414072\pi\)
\(264\) −7.06402 −0.434760
\(265\) −12.3246 −0.757096
\(266\) −3.98785 −0.244511
\(267\) −6.48895 −0.397117
\(268\) 3.04992 0.186303
\(269\) −0.162261 −0.00989325 −0.00494662 0.999988i \(-0.501575\pi\)
−0.00494662 + 0.999988i \(0.501575\pi\)
\(270\) 47.7615 2.90667
\(271\) −7.00820 −0.425718 −0.212859 0.977083i \(-0.568277\pi\)
−0.212859 + 0.977083i \(0.568277\pi\)
\(272\) −5.43896 −0.329785
\(273\) −14.6303 −0.885469
\(274\) 11.3372 0.684907
\(275\) 6.22889 0.375616
\(276\) −0.357278 −0.0215056
\(277\) −25.3290 −1.52187 −0.760935 0.648829i \(-0.775259\pi\)
−0.760935 + 0.648829i \(0.775259\pi\)
\(278\) 15.5959 0.935379
\(279\) 13.2396 0.792635
\(280\) −6.76018 −0.403998
\(281\) −15.4832 −0.923653 −0.461826 0.886970i \(-0.652806\pi\)
−0.461826 + 0.886970i \(0.652806\pi\)
\(282\) 15.3017 0.911204
\(283\) −4.23467 −0.251725 −0.125862 0.992048i \(-0.540170\pi\)
−0.125862 + 0.992048i \(0.540170\pi\)
\(284\) −13.4515 −0.798197
\(285\) −15.5917 −0.923572
\(286\) 3.88332 0.229626
\(287\) −19.9214 −1.17592
\(288\) 8.09075 0.476752
\(289\) 12.5823 0.740134
\(290\) 2.98741 0.175427
\(291\) −8.35795 −0.489952
\(292\) 9.59142 0.561295
\(293\) 22.9981 1.34356 0.671782 0.740749i \(-0.265529\pi\)
0.671782 + 0.740749i \(0.265529\pi\)
\(294\) 4.13563 0.241195
\(295\) 4.90607 0.285642
\(296\) 3.16634 0.184040
\(297\) −35.9611 −2.08668
\(298\) −4.90109 −0.283912
\(299\) 0.196407 0.0113585
\(300\) −9.77956 −0.564623
\(301\) 1.39990 0.0806889
\(302\) 7.85586 0.452054
\(303\) 14.3172 0.822504
\(304\) −1.66187 −0.0953147
\(305\) −31.4014 −1.79804
\(306\) −44.0052 −2.51561
\(307\) 24.9753 1.42541 0.712707 0.701462i \(-0.247469\pi\)
0.712707 + 0.701462i \(0.247469\pi\)
\(308\) 5.08996 0.290027
\(309\) 41.2202 2.34493
\(310\) −4.61002 −0.261832
\(311\) −5.44604 −0.308816 −0.154408 0.988007i \(-0.549347\pi\)
−0.154408 + 0.988007i \(0.549347\pi\)
\(312\) −6.09694 −0.345172
\(313\) −27.5364 −1.55645 −0.778223 0.627987i \(-0.783879\pi\)
−0.778223 + 0.627987i \(0.783879\pi\)
\(314\) −3.77124 −0.212823
\(315\) −54.6949 −3.08171
\(316\) 4.39928 0.247479
\(317\) −26.2604 −1.47493 −0.737466 0.675384i \(-0.763978\pi\)
−0.737466 + 0.675384i \(0.763978\pi\)
\(318\) −14.5693 −0.817005
\(319\) −2.24931 −0.125937
\(320\) −2.81719 −0.157486
\(321\) −40.6304 −2.26777
\(322\) 0.257435 0.0143463
\(323\) 9.03883 0.502934
\(324\) 32.1879 1.78822
\(325\) 5.37614 0.298215
\(326\) 4.91488 0.272210
\(327\) −15.2059 −0.840887
\(328\) −8.30191 −0.458396
\(329\) −11.0256 −0.607861
\(330\) 19.9007 1.09550
\(331\) −20.6672 −1.13597 −0.567986 0.823038i \(-0.692277\pi\)
−0.567986 + 0.823038i \(0.692277\pi\)
\(332\) −3.04167 −0.166933
\(333\) 25.6180 1.40386
\(334\) −5.12739 −0.280558
\(335\) −8.59220 −0.469442
\(336\) −7.99140 −0.435966
\(337\) 10.1111 0.550787 0.275394 0.961332i \(-0.411192\pi\)
0.275394 + 0.961332i \(0.411192\pi\)
\(338\) −9.64831 −0.524799
\(339\) 39.2113 2.12966
\(340\) 15.3226 0.830984
\(341\) 3.47103 0.187967
\(342\) −13.4458 −0.727063
\(343\) −19.7772 −1.06787
\(344\) 0.583384 0.0314540
\(345\) 1.00652 0.0541891
\(346\) −5.95165 −0.319963
\(347\) 23.8158 1.27850 0.639249 0.768999i \(-0.279245\pi\)
0.639249 + 0.768999i \(0.279245\pi\)
\(348\) 3.53150 0.189308
\(349\) −11.5771 −0.619710 −0.309855 0.950784i \(-0.600280\pi\)
−0.309855 + 0.950784i \(0.600280\pi\)
\(350\) 7.04663 0.376658
\(351\) −31.0380 −1.65669
\(352\) 2.12115 0.113058
\(353\) 10.4598 0.556720 0.278360 0.960477i \(-0.410209\pi\)
0.278360 + 0.960477i \(0.410209\pi\)
\(354\) 5.79960 0.308245
\(355\) 37.8953 2.01127
\(356\) 1.94847 0.103269
\(357\) 43.4649 2.30041
\(358\) −5.15343 −0.272367
\(359\) 21.2970 1.12401 0.562007 0.827133i \(-0.310030\pi\)
0.562007 + 0.827133i \(0.310030\pi\)
\(360\) −22.7932 −1.20131
\(361\) −16.2382 −0.854642
\(362\) 7.73594 0.406592
\(363\) 21.6492 1.13629
\(364\) 4.39313 0.230263
\(365\) −27.0208 −1.41434
\(366\) −37.1205 −1.94032
\(367\) 5.65006 0.294931 0.147465 0.989067i \(-0.452888\pi\)
0.147465 + 0.989067i \(0.452888\pi\)
\(368\) 0.107282 0.00559244
\(369\) −67.1686 −3.49666
\(370\) −8.92018 −0.463738
\(371\) 10.4978 0.545021
\(372\) −5.44963 −0.282550
\(373\) −32.2999 −1.67243 −0.836214 0.548403i \(-0.815236\pi\)
−0.836214 + 0.548403i \(0.815236\pi\)
\(374\) −11.5369 −0.596557
\(375\) −19.3592 −0.999707
\(376\) −4.59473 −0.236955
\(377\) −1.94138 −0.0999861
\(378\) −40.6822 −2.09247
\(379\) −17.0409 −0.875334 −0.437667 0.899137i \(-0.644195\pi\)
−0.437667 + 0.899137i \(0.644195\pi\)
\(380\) 4.68180 0.240171
\(381\) −20.4187 −1.04608
\(382\) −23.6317 −1.20911
\(383\) −3.21939 −0.164503 −0.0822515 0.996612i \(-0.526211\pi\)
−0.0822515 + 0.996612i \(0.526211\pi\)
\(384\) −3.33028 −0.169947
\(385\) −14.3394 −0.730802
\(386\) −19.0384 −0.969030
\(387\) 4.72001 0.239932
\(388\) 2.50969 0.127410
\(389\) 3.82490 0.193930 0.0969651 0.995288i \(-0.469086\pi\)
0.0969651 + 0.995288i \(0.469086\pi\)
\(390\) 17.1763 0.869753
\(391\) −0.583500 −0.0295089
\(392\) −1.24183 −0.0627217
\(393\) 24.9036 1.25622
\(394\) −1.31035 −0.0660143
\(395\) −12.3936 −0.623590
\(396\) 17.1617 0.862408
\(397\) −7.26808 −0.364774 −0.182387 0.983227i \(-0.558382\pi\)
−0.182387 + 0.983227i \(0.558382\pi\)
\(398\) −22.0771 −1.10663
\(399\) 13.2806 0.664864
\(400\) 2.93656 0.146828
\(401\) −32.7088 −1.63340 −0.816700 0.577063i \(-0.804199\pi\)
−0.816700 + 0.577063i \(0.804199\pi\)
\(402\) −10.1571 −0.506589
\(403\) 2.99584 0.149233
\(404\) −4.29911 −0.213889
\(405\) −90.6795 −4.50590
\(406\) −2.54461 −0.126287
\(407\) 6.71629 0.332914
\(408\) 18.1132 0.896739
\(409\) 14.8357 0.733577 0.366789 0.930304i \(-0.380457\pi\)
0.366789 + 0.930304i \(0.380457\pi\)
\(410\) 23.3880 1.15505
\(411\) −37.7561 −1.86237
\(412\) −12.3774 −0.609791
\(413\) −4.17888 −0.205629
\(414\) 0.867988 0.0426593
\(415\) 8.56895 0.420633
\(416\) 1.83076 0.0897605
\(417\) −51.9386 −2.54345
\(418\) −3.52507 −0.172417
\(419\) −2.90261 −0.141802 −0.0709008 0.997483i \(-0.522587\pi\)
−0.0709008 + 0.997483i \(0.522587\pi\)
\(420\) 22.5133 1.09854
\(421\) −6.00890 −0.292856 −0.146428 0.989221i \(-0.546778\pi\)
−0.146428 + 0.989221i \(0.546778\pi\)
\(422\) 20.6971 1.00752
\(423\) −37.1748 −1.80750
\(424\) 4.37480 0.212459
\(425\) −15.9718 −0.774748
\(426\) 44.7971 2.17042
\(427\) 26.7470 1.29438
\(428\) 12.2003 0.589725
\(429\) −12.9325 −0.624389
\(430\) −1.64350 −0.0792568
\(431\) −1.07201 −0.0516369 −0.0258184 0.999667i \(-0.508219\pi\)
−0.0258184 + 0.999667i \(0.508219\pi\)
\(432\) −16.9536 −0.815680
\(433\) −5.71521 −0.274656 −0.137328 0.990526i \(-0.543851\pi\)
−0.137328 + 0.990526i \(0.543851\pi\)
\(434\) 3.92671 0.188488
\(435\) −9.94890 −0.477013
\(436\) 4.56595 0.218669
\(437\) −0.178288 −0.00852867
\(438\) −31.9421 −1.52625
\(439\) 22.8507 1.09060 0.545302 0.838240i \(-0.316415\pi\)
0.545302 + 0.838240i \(0.316415\pi\)
\(440\) −5.97569 −0.284880
\(441\) −10.0473 −0.478443
\(442\) −9.95744 −0.473627
\(443\) −21.3288 −1.01336 −0.506680 0.862134i \(-0.669127\pi\)
−0.506680 + 0.862134i \(0.669127\pi\)
\(444\) −10.5448 −0.500434
\(445\) −5.48921 −0.260214
\(446\) 1.08779 0.0515083
\(447\) 16.3220 0.772003
\(448\) 2.39962 0.113371
\(449\) −5.71138 −0.269537 −0.134768 0.990877i \(-0.543029\pi\)
−0.134768 + 0.990877i \(0.543029\pi\)
\(450\) 23.7590 1.12001
\(451\) −17.6096 −0.829204
\(452\) −11.7742 −0.553811
\(453\) −26.1622 −1.22921
\(454\) 25.9393 1.21739
\(455\) −12.3763 −0.580209
\(456\) 5.53448 0.259176
\(457\) −12.8557 −0.601364 −0.300682 0.953724i \(-0.597214\pi\)
−0.300682 + 0.953724i \(0.597214\pi\)
\(458\) −5.88492 −0.274984
\(459\) 92.2099 4.30399
\(460\) −0.302233 −0.0140917
\(461\) 10.3980 0.484284 0.242142 0.970241i \(-0.422150\pi\)
0.242142 + 0.970241i \(0.422150\pi\)
\(462\) −16.9510 −0.788630
\(463\) 34.5449 1.60544 0.802718 0.596359i \(-0.203387\pi\)
0.802718 + 0.596359i \(0.203387\pi\)
\(464\) −1.06042 −0.0492288
\(465\) 15.3526 0.711962
\(466\) 20.1406 0.932993
\(467\) −28.5935 −1.32315 −0.661574 0.749880i \(-0.730111\pi\)
−0.661574 + 0.749880i \(0.730111\pi\)
\(468\) 14.8122 0.684696
\(469\) 7.31865 0.337944
\(470\) 12.9442 0.597072
\(471\) 12.5593 0.578700
\(472\) −1.74148 −0.0801579
\(473\) 1.23745 0.0568978
\(474\) −14.6508 −0.672934
\(475\) −4.88017 −0.223918
\(476\) −13.0514 −0.598211
\(477\) 35.3954 1.62064
\(478\) −6.42727 −0.293977
\(479\) −22.0974 −1.00966 −0.504828 0.863220i \(-0.668444\pi\)
−0.504828 + 0.863220i \(0.668444\pi\)
\(480\) 9.38202 0.428229
\(481\) 5.79681 0.264312
\(482\) −23.2804 −1.06039
\(483\) −0.857330 −0.0390099
\(484\) −6.50072 −0.295487
\(485\) −7.07026 −0.321044
\(486\) −56.3339 −2.55536
\(487\) −1.51950 −0.0688550 −0.0344275 0.999407i \(-0.510961\pi\)
−0.0344275 + 0.999407i \(0.510961\pi\)
\(488\) 11.1464 0.504572
\(489\) −16.3679 −0.740183
\(490\) 3.49846 0.158044
\(491\) −13.3366 −0.601870 −0.300935 0.953645i \(-0.597299\pi\)
−0.300935 + 0.953645i \(0.597299\pi\)
\(492\) 27.6476 1.24645
\(493\) 5.76759 0.259759
\(494\) −3.04248 −0.136888
\(495\) −48.3478 −2.17307
\(496\) 1.63639 0.0734761
\(497\) −32.2784 −1.44788
\(498\) 10.1296 0.453918
\(499\) −14.9268 −0.668217 −0.334108 0.942535i \(-0.608435\pi\)
−0.334108 + 0.942535i \(0.608435\pi\)
\(500\) 5.81310 0.259970
\(501\) 17.0756 0.762883
\(502\) −20.4566 −0.913023
\(503\) 14.9924 0.668478 0.334239 0.942488i \(-0.391521\pi\)
0.334239 + 0.942488i \(0.391521\pi\)
\(504\) 19.4147 0.864800
\(505\) 12.1114 0.538951
\(506\) 0.227561 0.0101163
\(507\) 32.1315 1.42701
\(508\) 6.13122 0.272029
\(509\) 12.5006 0.554078 0.277039 0.960859i \(-0.410647\pi\)
0.277039 + 0.960859i \(0.410647\pi\)
\(510\) −51.0284 −2.25958
\(511\) 23.0158 1.01816
\(512\) 1.00000 0.0441942
\(513\) 28.1746 1.24394
\(514\) −10.6643 −0.470383
\(515\) 34.8695 1.53653
\(516\) −1.94283 −0.0855284
\(517\) −9.74611 −0.428634
\(518\) 7.59801 0.333837
\(519\) 19.8206 0.870030
\(520\) −5.15760 −0.226176
\(521\) 11.2046 0.490881 0.245441 0.969412i \(-0.421067\pi\)
0.245441 + 0.969412i \(0.421067\pi\)
\(522\) −8.57960 −0.375519
\(523\) −7.09647 −0.310307 −0.155153 0.987890i \(-0.549587\pi\)
−0.155153 + 0.987890i \(0.549587\pi\)
\(524\) −7.47793 −0.326675
\(525\) −23.4672 −1.02419
\(526\) 8.64981 0.377150
\(527\) −8.90026 −0.387701
\(528\) −7.06402 −0.307422
\(529\) −22.9885 −0.999500
\(530\) −12.3246 −0.535348
\(531\) −14.0898 −0.611447
\(532\) −3.98785 −0.172895
\(533\) −15.1988 −0.658334
\(534\) −6.48895 −0.280804
\(535\) −34.3706 −1.48597
\(536\) 3.04992 0.131736
\(537\) 17.1624 0.740610
\(538\) −0.162261 −0.00699558
\(539\) −2.63410 −0.113459
\(540\) 47.7615 2.05533
\(541\) 12.5010 0.537462 0.268731 0.963215i \(-0.413396\pi\)
0.268731 + 0.963215i \(0.413396\pi\)
\(542\) −7.00820 −0.301028
\(543\) −25.7628 −1.10559
\(544\) −5.43896 −0.233193
\(545\) −12.8632 −0.550997
\(546\) −14.6303 −0.626121
\(547\) −8.46523 −0.361947 −0.180973 0.983488i \(-0.557925\pi\)
−0.180973 + 0.983488i \(0.557925\pi\)
\(548\) 11.3372 0.484302
\(549\) 90.1824 3.84889
\(550\) 6.22889 0.265601
\(551\) 1.76228 0.0750757
\(552\) −0.357278 −0.0152067
\(553\) 10.5566 0.448912
\(554\) −25.3290 −1.07612
\(555\) 29.7067 1.26098
\(556\) 15.5959 0.661413
\(557\) 16.0164 0.678636 0.339318 0.940672i \(-0.389804\pi\)
0.339318 + 0.940672i \(0.389804\pi\)
\(558\) 13.2396 0.560478
\(559\) 1.06804 0.0451732
\(560\) −6.76018 −0.285670
\(561\) 38.4209 1.62213
\(562\) −15.4832 −0.653121
\(563\) −6.27071 −0.264279 −0.132140 0.991231i \(-0.542185\pi\)
−0.132140 + 0.991231i \(0.542185\pi\)
\(564\) 15.3017 0.644318
\(565\) 33.1701 1.39548
\(566\) −4.23467 −0.177996
\(567\) 77.2388 3.24372
\(568\) −13.4515 −0.564410
\(569\) −19.2558 −0.807243 −0.403622 0.914926i \(-0.632249\pi\)
−0.403622 + 0.914926i \(0.632249\pi\)
\(570\) −15.5917 −0.653064
\(571\) −30.6514 −1.28272 −0.641361 0.767239i \(-0.721630\pi\)
−0.641361 + 0.767239i \(0.721630\pi\)
\(572\) 3.88332 0.162370
\(573\) 78.7003 3.28775
\(574\) −19.9214 −0.831504
\(575\) 0.315039 0.0131380
\(576\) 8.09075 0.337114
\(577\) −38.0375 −1.58352 −0.791761 0.610831i \(-0.790836\pi\)
−0.791761 + 0.610831i \(0.790836\pi\)
\(578\) 12.5823 0.523354
\(579\) 63.4032 2.63495
\(580\) 2.98741 0.124045
\(581\) −7.29884 −0.302807
\(582\) −8.35795 −0.346448
\(583\) 9.27960 0.384322
\(584\) 9.59142 0.396896
\(585\) −41.7289 −1.72528
\(586\) 22.9981 0.950043
\(587\) 5.10878 0.210862 0.105431 0.994427i \(-0.466378\pi\)
0.105431 + 0.994427i \(0.466378\pi\)
\(588\) 4.13563 0.170550
\(589\) −2.71946 −0.112054
\(590\) 4.90607 0.201980
\(591\) 4.36382 0.179504
\(592\) 3.16634 0.130136
\(593\) −6.74429 −0.276955 −0.138477 0.990366i \(-0.544221\pi\)
−0.138477 + 0.990366i \(0.544221\pi\)
\(594\) −35.9611 −1.47550
\(595\) 36.7684 1.50736
\(596\) −4.90109 −0.200756
\(597\) 73.5230 3.00909
\(598\) 0.196407 0.00803168
\(599\) 10.4436 0.426714 0.213357 0.976974i \(-0.431560\pi\)
0.213357 + 0.976974i \(0.431560\pi\)
\(600\) −9.77956 −0.399249
\(601\) −13.7652 −0.561494 −0.280747 0.959782i \(-0.590582\pi\)
−0.280747 + 0.959782i \(0.590582\pi\)
\(602\) 1.39990 0.0570557
\(603\) 24.6761 1.00489
\(604\) 7.85586 0.319650
\(605\) 18.3138 0.744560
\(606\) 14.3172 0.581598
\(607\) 36.2438 1.47109 0.735546 0.677475i \(-0.236926\pi\)
0.735546 + 0.677475i \(0.236926\pi\)
\(608\) −1.66187 −0.0673976
\(609\) 8.47425 0.343394
\(610\) −31.4014 −1.27141
\(611\) −8.41185 −0.340307
\(612\) −44.0052 −1.77881
\(613\) −29.3978 −1.18737 −0.593684 0.804699i \(-0.702327\pi\)
−0.593684 + 0.804699i \(0.702327\pi\)
\(614\) 24.9753 1.00792
\(615\) −77.8887 −3.14077
\(616\) 5.08996 0.205080
\(617\) 21.8819 0.880932 0.440466 0.897769i \(-0.354813\pi\)
0.440466 + 0.897769i \(0.354813\pi\)
\(618\) 41.2202 1.65812
\(619\) −11.7419 −0.471948 −0.235974 0.971759i \(-0.575828\pi\)
−0.235974 + 0.971759i \(0.575828\pi\)
\(620\) −4.61002 −0.185143
\(621\) −1.81881 −0.0729863
\(622\) −5.44604 −0.218366
\(623\) 4.67559 0.187324
\(624\) −6.09694 −0.244073
\(625\) −31.0594 −1.24238
\(626\) −27.5364 −1.10057
\(627\) 11.7395 0.468829
\(628\) −3.77124 −0.150489
\(629\) −17.2216 −0.686670
\(630\) −54.6949 −2.17910
\(631\) 32.1677 1.28058 0.640289 0.768134i \(-0.278815\pi\)
0.640289 + 0.768134i \(0.278815\pi\)
\(632\) 4.39928 0.174994
\(633\) −68.9271 −2.73961
\(634\) −26.2604 −1.04293
\(635\) −17.2728 −0.685450
\(636\) −14.5693 −0.577710
\(637\) −2.27349 −0.0900789
\(638\) −2.24931 −0.0890512
\(639\) −108.832 −4.30534
\(640\) −2.81719 −0.111359
\(641\) 8.66215 0.342134 0.171067 0.985259i \(-0.445278\pi\)
0.171067 + 0.985259i \(0.445278\pi\)
\(642\) −40.6304 −1.60356
\(643\) 16.9542 0.668608 0.334304 0.942465i \(-0.391499\pi\)
0.334304 + 0.942465i \(0.391499\pi\)
\(644\) 0.257435 0.0101444
\(645\) 5.47333 0.215512
\(646\) 9.03883 0.355628
\(647\) −14.0414 −0.552026 −0.276013 0.961154i \(-0.589013\pi\)
−0.276013 + 0.961154i \(0.589013\pi\)
\(648\) 32.1879 1.26446
\(649\) −3.69393 −0.145000
\(650\) 5.37614 0.210870
\(651\) −13.0770 −0.512530
\(652\) 4.91488 0.192482
\(653\) −2.56636 −0.100429 −0.0502147 0.998738i \(-0.515991\pi\)
−0.0502147 + 0.998738i \(0.515991\pi\)
\(654\) −15.2059 −0.594597
\(655\) 21.0668 0.823146
\(656\) −8.30191 −0.324135
\(657\) 77.6017 3.02753
\(658\) −11.0256 −0.429823
\(659\) −6.74059 −0.262576 −0.131288 0.991344i \(-0.541911\pi\)
−0.131288 + 0.991344i \(0.541911\pi\)
\(660\) 19.9007 0.774633
\(661\) −8.67051 −0.337244 −0.168622 0.985681i \(-0.553932\pi\)
−0.168622 + 0.985681i \(0.553932\pi\)
\(662\) −20.6672 −0.803254
\(663\) 33.1610 1.28787
\(664\) −3.04167 −0.118040
\(665\) 11.2345 0.435657
\(666\) 25.6180 0.992679
\(667\) −0.113764 −0.00440495
\(668\) −5.12739 −0.198385
\(669\) −3.62264 −0.140059
\(670\) −8.59220 −0.331946
\(671\) 23.6431 0.912733
\(672\) −7.99140 −0.308275
\(673\) −39.9558 −1.54018 −0.770091 0.637934i \(-0.779789\pi\)
−0.770091 + 0.637934i \(0.779789\pi\)
\(674\) 10.1111 0.389466
\(675\) −49.7852 −1.91623
\(676\) −9.64831 −0.371089
\(677\) −42.7582 −1.64333 −0.821666 0.569969i \(-0.806955\pi\)
−0.821666 + 0.569969i \(0.806955\pi\)
\(678\) 39.2113 1.50590
\(679\) 6.02229 0.231114
\(680\) 15.3226 0.587594
\(681\) −86.3852 −3.31029
\(682\) 3.47103 0.132913
\(683\) 13.9559 0.534007 0.267004 0.963696i \(-0.413966\pi\)
0.267004 + 0.963696i \(0.413966\pi\)
\(684\) −13.4458 −0.514111
\(685\) −31.9391 −1.22033
\(686\) −19.7772 −0.755099
\(687\) 19.5984 0.747727
\(688\) 0.583384 0.0222413
\(689\) 8.00921 0.305127
\(690\) 1.00652 0.0383175
\(691\) −3.78684 −0.144058 −0.0720290 0.997403i \(-0.522947\pi\)
−0.0720290 + 0.997403i \(0.522947\pi\)
\(692\) −5.95165 −0.226248
\(693\) 41.1815 1.56436
\(694\) 23.8158 0.904035
\(695\) −43.9366 −1.66661
\(696\) 3.53150 0.133861
\(697\) 45.1537 1.71032
\(698\) −11.5771 −0.438201
\(699\) −67.0736 −2.53696
\(700\) 7.04663 0.266337
\(701\) 14.3234 0.540989 0.270494 0.962722i \(-0.412813\pi\)
0.270494 + 0.962722i \(0.412813\pi\)
\(702\) −31.0380 −1.17145
\(703\) −5.26204 −0.198462
\(704\) 2.12115 0.0799439
\(705\) −43.1078 −1.62354
\(706\) 10.4598 0.393661
\(707\) −10.3162 −0.387982
\(708\) 5.79960 0.217962
\(709\) 30.9629 1.16284 0.581419 0.813604i \(-0.302498\pi\)
0.581419 + 0.813604i \(0.302498\pi\)
\(710\) 37.8953 1.42219
\(711\) 35.5935 1.33486
\(712\) 1.94847 0.0730220
\(713\) 0.175555 0.00657457
\(714\) 43.4649 1.62663
\(715\) −10.9401 −0.409135
\(716\) −5.15343 −0.192593
\(717\) 21.4046 0.799369
\(718\) 21.2970 0.794797
\(719\) −24.6366 −0.918791 −0.459395 0.888232i \(-0.651934\pi\)
−0.459395 + 0.888232i \(0.651934\pi\)
\(720\) −22.7932 −0.849451
\(721\) −29.7010 −1.10612
\(722\) −16.2382 −0.604323
\(723\) 77.5301 2.88337
\(724\) 7.73594 0.287504
\(725\) −3.11399 −0.115651
\(726\) 21.6492 0.803477
\(727\) 28.7483 1.06622 0.533108 0.846047i \(-0.321024\pi\)
0.533108 + 0.846047i \(0.321024\pi\)
\(728\) 4.39313 0.162820
\(729\) 91.0438 3.37199
\(730\) −27.0208 −1.00009
\(731\) −3.17300 −0.117358
\(732\) −37.1205 −1.37201
\(733\) 12.2348 0.451904 0.225952 0.974138i \(-0.427451\pi\)
0.225952 + 0.974138i \(0.427451\pi\)
\(734\) 5.65006 0.208548
\(735\) −11.6508 −0.429748
\(736\) 0.107282 0.00395445
\(737\) 6.46934 0.238301
\(738\) −67.1686 −2.47251
\(739\) −51.7245 −1.90272 −0.951359 0.308085i \(-0.900312\pi\)
−0.951359 + 0.308085i \(0.900312\pi\)
\(740\) −8.92018 −0.327912
\(741\) 10.1323 0.372220
\(742\) 10.4978 0.385388
\(743\) 9.33473 0.342458 0.171229 0.985231i \(-0.445226\pi\)
0.171229 + 0.985231i \(0.445226\pi\)
\(744\) −5.44963 −0.199793
\(745\) 13.8073 0.505860
\(746\) −32.2999 −1.18259
\(747\) −24.6093 −0.900409
\(748\) −11.5369 −0.421829
\(749\) 29.2761 1.06973
\(750\) −19.3592 −0.706900
\(751\) −25.9816 −0.948081 −0.474040 0.880503i \(-0.657205\pi\)
−0.474040 + 0.880503i \(0.657205\pi\)
\(752\) −4.59473 −0.167552
\(753\) 68.1262 2.48266
\(754\) −1.94138 −0.0707009
\(755\) −22.1315 −0.805446
\(756\) −40.6822 −1.47960
\(757\) −5.54040 −0.201369 −0.100685 0.994918i \(-0.532103\pi\)
−0.100685 + 0.994918i \(0.532103\pi\)
\(758\) −17.0409 −0.618955
\(759\) −0.757840 −0.0275078
\(760\) 4.68180 0.169827
\(761\) 19.6930 0.713869 0.356934 0.934129i \(-0.383822\pi\)
0.356934 + 0.934129i \(0.383822\pi\)
\(762\) −20.4187 −0.739690
\(763\) 10.9565 0.396654
\(764\) −23.6317 −0.854967
\(765\) 123.971 4.48218
\(766\) −3.21939 −0.116321
\(767\) −3.18823 −0.115120
\(768\) −3.33028 −0.120171
\(769\) −4.14681 −0.149538 −0.0747689 0.997201i \(-0.523822\pi\)
−0.0747689 + 0.997201i \(0.523822\pi\)
\(770\) −14.3394 −0.516755
\(771\) 35.5151 1.27905
\(772\) −19.0384 −0.685208
\(773\) −9.06029 −0.325876 −0.162938 0.986636i \(-0.552097\pi\)
−0.162938 + 0.986636i \(0.552097\pi\)
\(774\) 4.72001 0.169657
\(775\) 4.80536 0.172614
\(776\) 2.50969 0.0900925
\(777\) −25.3035 −0.907757
\(778\) 3.82490 0.137129
\(779\) 13.7967 0.494317
\(780\) 17.1763 0.615008
\(781\) −28.5326 −1.02098
\(782\) −0.583500 −0.0208659
\(783\) 17.9780 0.642480
\(784\) −1.24183 −0.0443509
\(785\) 10.6243 0.379197
\(786\) 24.9036 0.888281
\(787\) 13.6413 0.486259 0.243129 0.969994i \(-0.421826\pi\)
0.243129 + 0.969994i \(0.421826\pi\)
\(788\) −1.31035 −0.0466792
\(789\) −28.8063 −1.02553
\(790\) −12.3936 −0.440945
\(791\) −28.2535 −1.00458
\(792\) 17.1617 0.609814
\(793\) 20.4063 0.724650
\(794\) −7.26808 −0.257934
\(795\) 41.0444 1.45570
\(796\) −22.0771 −0.782503
\(797\) −3.56460 −0.126265 −0.0631323 0.998005i \(-0.520109\pi\)
−0.0631323 + 0.998005i \(0.520109\pi\)
\(798\) 13.2806 0.470130
\(799\) 24.9905 0.884102
\(800\) 2.93656 0.103823
\(801\) 15.7646 0.557014
\(802\) −32.7088 −1.15499
\(803\) 20.3448 0.717954
\(804\) −10.1571 −0.358213
\(805\) −0.725244 −0.0255615
\(806\) 2.99584 0.105524
\(807\) 0.540375 0.0190221
\(808\) −4.29911 −0.151242
\(809\) −35.3274 −1.24204 −0.621022 0.783793i \(-0.713282\pi\)
−0.621022 + 0.783793i \(0.713282\pi\)
\(810\) −90.6795 −3.18615
\(811\) 27.0764 0.950780 0.475390 0.879775i \(-0.342307\pi\)
0.475390 + 0.879775i \(0.342307\pi\)
\(812\) −2.54461 −0.0892982
\(813\) 23.3392 0.818543
\(814\) 6.71629 0.235406
\(815\) −13.8462 −0.485010
\(816\) 18.1132 0.634090
\(817\) −0.969508 −0.0339188
\(818\) 14.8357 0.518717
\(819\) 35.5437 1.24200
\(820\) 23.3880 0.816746
\(821\) 2.97788 0.103929 0.0519643 0.998649i \(-0.483452\pi\)
0.0519643 + 0.998649i \(0.483452\pi\)
\(822\) −37.7561 −1.31690
\(823\) 6.28468 0.219070 0.109535 0.993983i \(-0.465064\pi\)
0.109535 + 0.993983i \(0.465064\pi\)
\(824\) −12.3774 −0.431187
\(825\) −20.7439 −0.722211
\(826\) −4.17888 −0.145402
\(827\) −56.0991 −1.95076 −0.975378 0.220541i \(-0.929218\pi\)
−0.975378 + 0.220541i \(0.929218\pi\)
\(828\) 0.867988 0.0301647
\(829\) −36.0773 −1.25302 −0.626508 0.779415i \(-0.715516\pi\)
−0.626508 + 0.779415i \(0.715516\pi\)
\(830\) 8.56895 0.297433
\(831\) 84.3524 2.92615
\(832\) 1.83076 0.0634703
\(833\) 6.75424 0.234021
\(834\) −51.9386 −1.79849
\(835\) 14.4448 0.499884
\(836\) −3.52507 −0.121917
\(837\) −27.7427 −0.958928
\(838\) −2.90261 −0.100269
\(839\) −0.301000 −0.0103917 −0.00519584 0.999987i \(-0.501654\pi\)
−0.00519584 + 0.999987i \(0.501654\pi\)
\(840\) 22.5133 0.776782
\(841\) −27.8755 −0.961224
\(842\) −6.00890 −0.207080
\(843\) 51.5635 1.77594
\(844\) 20.6971 0.712424
\(845\) 27.1811 0.935059
\(846\) −37.1748 −1.27809
\(847\) −15.5992 −0.535996
\(848\) 4.37480 0.150231
\(849\) 14.1026 0.484001
\(850\) −15.9718 −0.547829
\(851\) 0.339690 0.0116444
\(852\) 44.7971 1.53472
\(853\) 22.8861 0.783606 0.391803 0.920049i \(-0.371851\pi\)
0.391803 + 0.920049i \(0.371851\pi\)
\(854\) 26.7470 0.915264
\(855\) 37.8792 1.29544
\(856\) 12.2003 0.416998
\(857\) −11.1541 −0.381018 −0.190509 0.981685i \(-0.561014\pi\)
−0.190509 + 0.981685i \(0.561014\pi\)
\(858\) −12.9325 −0.441510
\(859\) 41.7654 1.42502 0.712508 0.701664i \(-0.247559\pi\)
0.712508 + 0.701664i \(0.247559\pi\)
\(860\) −1.64350 −0.0560430
\(861\) 66.3438 2.26099
\(862\) −1.07201 −0.0365128
\(863\) 26.6667 0.907743 0.453872 0.891067i \(-0.350042\pi\)
0.453872 + 0.891067i \(0.350042\pi\)
\(864\) −16.9536 −0.576773
\(865\) 16.7669 0.570093
\(866\) −5.71521 −0.194211
\(867\) −41.9025 −1.42308
\(868\) 3.92671 0.133281
\(869\) 9.33154 0.316551
\(870\) −9.94890 −0.337299
\(871\) 5.58368 0.189196
\(872\) 4.56595 0.154623
\(873\) 20.3052 0.687228
\(874\) −0.178288 −0.00603068
\(875\) 13.9492 0.471570
\(876\) −31.9421 −1.07922
\(877\) −27.7169 −0.935935 −0.467967 0.883746i \(-0.655014\pi\)
−0.467967 + 0.883746i \(0.655014\pi\)
\(878\) 22.8507 0.771174
\(879\) −76.5901 −2.58332
\(880\) −5.97569 −0.201440
\(881\) 0.0685907 0.00231088 0.00115544 0.999999i \(-0.499632\pi\)
0.00115544 + 0.999999i \(0.499632\pi\)
\(882\) −10.0473 −0.338310
\(883\) −7.30373 −0.245790 −0.122895 0.992420i \(-0.539218\pi\)
−0.122895 + 0.992420i \(0.539218\pi\)
\(884\) −9.95744 −0.334905
\(885\) −16.3386 −0.549215
\(886\) −21.3288 −0.716553
\(887\) 48.1931 1.61817 0.809083 0.587694i \(-0.199964\pi\)
0.809083 + 0.587694i \(0.199964\pi\)
\(888\) −10.5448 −0.353860
\(889\) 14.7126 0.493444
\(890\) −5.48921 −0.183999
\(891\) 68.2755 2.28731
\(892\) 1.08779 0.0364219
\(893\) 7.63583 0.255523
\(894\) 16.3220 0.545888
\(895\) 14.5182 0.485290
\(896\) 2.39962 0.0801657
\(897\) −0.654090 −0.0218394
\(898\) −5.71138 −0.190591
\(899\) −1.73526 −0.0578743
\(900\) 23.7590 0.791965
\(901\) −23.7943 −0.792704
\(902\) −17.6096 −0.586336
\(903\) −4.66206 −0.155144
\(904\) −11.7742 −0.391603
\(905\) −21.7936 −0.724445
\(906\) −26.1622 −0.869181
\(907\) 13.4155 0.445453 0.222726 0.974881i \(-0.428504\pi\)
0.222726 + 0.974881i \(0.428504\pi\)
\(908\) 25.9393 0.860827
\(909\) −34.7830 −1.15368
\(910\) −12.3763 −0.410270
\(911\) 51.3465 1.70119 0.850593 0.525825i \(-0.176243\pi\)
0.850593 + 0.525825i \(0.176243\pi\)
\(912\) 5.53448 0.183265
\(913\) −6.45183 −0.213525
\(914\) −12.8557 −0.425229
\(915\) 104.575 3.45716
\(916\) −5.88492 −0.194443
\(917\) −17.9442 −0.592569
\(918\) 92.2099 3.04338
\(919\) 46.9713 1.54944 0.774721 0.632304i \(-0.217890\pi\)
0.774721 + 0.632304i \(0.217890\pi\)
\(920\) −0.302233 −0.00996432
\(921\) −83.1746 −2.74069
\(922\) 10.3980 0.342441
\(923\) −24.6264 −0.810588
\(924\) −16.9510 −0.557646
\(925\) 9.29815 0.305721
\(926\) 34.5449 1.13521
\(927\) −100.142 −3.28911
\(928\) −1.06042 −0.0348100
\(929\) 41.3379 1.35625 0.678126 0.734946i \(-0.262792\pi\)
0.678126 + 0.734946i \(0.262792\pi\)
\(930\) 15.3526 0.503433
\(931\) 2.06375 0.0676367
\(932\) 20.1406 0.659726
\(933\) 18.1368 0.593773
\(934\) −28.5935 −0.935607
\(935\) 32.5015 1.06291
\(936\) 14.8122 0.484153
\(937\) −39.1541 −1.27911 −0.639554 0.768746i \(-0.720881\pi\)
−0.639554 + 0.768746i \(0.720881\pi\)
\(938\) 7.31865 0.238962
\(939\) 91.7037 2.99264
\(940\) 12.9442 0.422194
\(941\) −14.0427 −0.457780 −0.228890 0.973452i \(-0.573510\pi\)
−0.228890 + 0.973452i \(0.573510\pi\)
\(942\) 12.5593 0.409203
\(943\) −0.890642 −0.0290033
\(944\) −1.74148 −0.0566802
\(945\) 114.609 3.72824
\(946\) 1.23745 0.0402329
\(947\) 25.2671 0.821071 0.410536 0.911845i \(-0.365342\pi\)
0.410536 + 0.911845i \(0.365342\pi\)
\(948\) −14.6508 −0.475837
\(949\) 17.5596 0.570009
\(950\) −4.88017 −0.158334
\(951\) 87.4545 2.83591
\(952\) −13.0514 −0.422999
\(953\) −31.9366 −1.03453 −0.517264 0.855826i \(-0.673049\pi\)
−0.517264 + 0.855826i \(0.673049\pi\)
\(954\) 35.3954 1.14597
\(955\) 66.5751 2.15432
\(956\) −6.42727 −0.207873
\(957\) 7.49084 0.242144
\(958\) −22.0974 −0.713935
\(959\) 27.2050 0.878496
\(960\) 9.38202 0.302804
\(961\) −28.3222 −0.913620
\(962\) 5.79681 0.186897
\(963\) 98.7097 3.18087
\(964\) −23.2804 −0.749810
\(965\) 53.6348 1.72657
\(966\) −0.857330 −0.0275841
\(967\) 29.8448 0.959745 0.479873 0.877338i \(-0.340683\pi\)
0.479873 + 0.877338i \(0.340683\pi\)
\(968\) −6.50072 −0.208941
\(969\) −30.1018 −0.967010
\(970\) −7.07026 −0.227013
\(971\) −20.7398 −0.665573 −0.332787 0.943002i \(-0.607989\pi\)
−0.332787 + 0.943002i \(0.607989\pi\)
\(972\) −56.3339 −1.80691
\(973\) 37.4242 1.19976
\(974\) −1.51950 −0.0486878
\(975\) −17.9040 −0.573388
\(976\) 11.1464 0.356786
\(977\) 2.94798 0.0943144 0.0471572 0.998887i \(-0.484984\pi\)
0.0471572 + 0.998887i \(0.484984\pi\)
\(978\) −16.3679 −0.523388
\(979\) 4.13300 0.132091
\(980\) 3.49846 0.111754
\(981\) 36.9420 1.17947
\(982\) −13.3366 −0.425587
\(983\) −12.5555 −0.400457 −0.200228 0.979749i \(-0.564168\pi\)
−0.200228 + 0.979749i \(0.564168\pi\)
\(984\) 27.6476 0.881375
\(985\) 3.69150 0.117621
\(986\) 5.76759 0.183677
\(987\) 36.7183 1.16876
\(988\) −3.04248 −0.0967943
\(989\) 0.0625864 0.00199013
\(990\) −48.3478 −1.53659
\(991\) 31.8321 1.01118 0.505589 0.862774i \(-0.331275\pi\)
0.505589 + 0.862774i \(0.331275\pi\)
\(992\) 1.63639 0.0519554
\(993\) 68.8275 2.18418
\(994\) −32.2784 −1.02381
\(995\) 62.1955 1.97173
\(996\) 10.1296 0.320968
\(997\) −17.5521 −0.555879 −0.277940 0.960599i \(-0.589651\pi\)
−0.277940 + 0.960599i \(0.589651\pi\)
\(998\) −14.9268 −0.472501
\(999\) −53.6808 −1.69839
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 8026.2.a.a.1.1 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.a.1.1 71 1.1 even 1 trivial