Properties

Label 6001.2.a.a.1.20
Level $6001$
Weight $2$
Character 6001.1
Self dual yes
Analytic conductor $47.918$
Analytic rank $1$
Dimension $113$
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] = [6001,2,Mod(1,6001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6001 = 17 \cdot 353 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6001.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: \(47.9182262530\)
Analytic rank: \(1\)
Dimension: \(113\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 6001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.09226 q^{2} +2.92082 q^{3} +2.37755 q^{4} -1.12068 q^{5} -6.11112 q^{6} -1.50686 q^{7} -0.789928 q^{8} +5.53120 q^{9} +O(q^{10})\) \(q-2.09226 q^{2} +2.92082 q^{3} +2.37755 q^{4} -1.12068 q^{5} -6.11112 q^{6} -1.50686 q^{7} -0.789928 q^{8} +5.53120 q^{9} +2.34475 q^{10} +2.91595 q^{11} +6.94439 q^{12} +2.05981 q^{13} +3.15274 q^{14} -3.27330 q^{15} -3.10236 q^{16} -1.00000 q^{17} -11.5727 q^{18} -4.71794 q^{19} -2.66446 q^{20} -4.40127 q^{21} -6.10092 q^{22} -3.53888 q^{23} -2.30724 q^{24} -3.74408 q^{25} -4.30967 q^{26} +7.39319 q^{27} -3.58263 q^{28} -7.98982 q^{29} +6.84859 q^{30} +1.63173 q^{31} +8.07080 q^{32} +8.51697 q^{33} +2.09226 q^{34} +1.68870 q^{35} +13.1507 q^{36} +4.82817 q^{37} +9.87114 q^{38} +6.01635 q^{39} +0.885254 q^{40} +6.18730 q^{41} +9.20860 q^{42} +3.96664 q^{43} +6.93281 q^{44} -6.19869 q^{45} +7.40425 q^{46} -6.74019 q^{47} -9.06145 q^{48} -4.72937 q^{49} +7.83359 q^{50} -2.92082 q^{51} +4.89731 q^{52} -7.29570 q^{53} -15.4685 q^{54} -3.26784 q^{55} +1.19031 q^{56} -13.7802 q^{57} +16.7168 q^{58} +13.3308 q^{59} -7.78243 q^{60} -8.67070 q^{61} -3.41400 q^{62} -8.33475 q^{63} -10.6815 q^{64} -2.30839 q^{65} -17.8197 q^{66} +2.10029 q^{67} -2.37755 q^{68} -10.3364 q^{69} -3.53321 q^{70} -10.5667 q^{71} -4.36925 q^{72} -4.60744 q^{73} -10.1018 q^{74} -10.9358 q^{75} -11.2171 q^{76} -4.39393 q^{77} -12.5878 q^{78} +3.40285 q^{79} +3.47675 q^{80} +5.00058 q^{81} -12.9454 q^{82} -1.33273 q^{83} -10.4642 q^{84} +1.12068 q^{85} -8.29923 q^{86} -23.3368 q^{87} -2.30339 q^{88} -11.1870 q^{89} +12.9693 q^{90} -3.10385 q^{91} -8.41385 q^{92} +4.76600 q^{93} +14.1022 q^{94} +5.28728 q^{95} +23.5734 q^{96} -13.1324 q^{97} +9.89507 q^{98} +16.1287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09226 −1.47945 −0.739725 0.672909i \(-0.765045\pi\)
−0.739725 + 0.672909i \(0.765045\pi\)
\(3\) 2.92082 1.68634 0.843169 0.537649i \(-0.180687\pi\)
0.843169 + 0.537649i \(0.180687\pi\)
\(4\) 2.37755 1.18877
\(5\) −1.12068 −0.501182 −0.250591 0.968093i \(-0.580625\pi\)
−0.250591 + 0.968093i \(0.580625\pi\)
\(6\) −6.11112 −2.49485
\(7\) −1.50686 −0.569540 −0.284770 0.958596i \(-0.591917\pi\)
−0.284770 + 0.958596i \(0.591917\pi\)
\(8\) −0.789928 −0.279282
\(9\) 5.53120 1.84373
\(10\) 2.34475 0.741474
\(11\) 2.91595 0.879192 0.439596 0.898196i \(-0.355122\pi\)
0.439596 + 0.898196i \(0.355122\pi\)
\(12\) 6.94439 2.00467
\(13\) 2.05981 0.571290 0.285645 0.958336i \(-0.407792\pi\)
0.285645 + 0.958336i \(0.407792\pi\)
\(14\) 3.15274 0.842606
\(15\) −3.27330 −0.845162
\(16\) −3.10236 −0.775591
\(17\) −1.00000 −0.242536
\(18\) −11.5727 −2.72771
\(19\) −4.71794 −1.08237 −0.541184 0.840904i \(-0.682024\pi\)
−0.541184 + 0.840904i \(0.682024\pi\)
\(20\) −2.66446 −0.595792
\(21\) −4.40127 −0.960436
\(22\) −6.10092 −1.30072
\(23\) −3.53888 −0.737907 −0.368954 0.929448i \(-0.620284\pi\)
−0.368954 + 0.929448i \(0.620284\pi\)
\(24\) −2.30724 −0.470963
\(25\) −3.74408 −0.748816
\(26\) −4.30967 −0.845195
\(27\) 7.39319 1.42282
\(28\) −3.58263 −0.677054
\(29\) −7.98982 −1.48367 −0.741836 0.670581i \(-0.766045\pi\)
−0.741836 + 0.670581i \(0.766045\pi\)
\(30\) 6.84859 1.25038
\(31\) 1.63173 0.293068 0.146534 0.989206i \(-0.453188\pi\)
0.146534 + 0.989206i \(0.453188\pi\)
\(32\) 8.07080 1.42673
\(33\) 8.51697 1.48261
\(34\) 2.09226 0.358819
\(35\) 1.68870 0.285443
\(36\) 13.1507 2.19178
\(37\) 4.82817 0.793746 0.396873 0.917874i \(-0.370095\pi\)
0.396873 + 0.917874i \(0.370095\pi\)
\(38\) 9.87114 1.60131
\(39\) 6.01635 0.963387
\(40\) 0.885254 0.139971
\(41\) 6.18730 0.966294 0.483147 0.875539i \(-0.339494\pi\)
0.483147 + 0.875539i \(0.339494\pi\)
\(42\) 9.20860 1.42092
\(43\) 3.96664 0.604907 0.302453 0.953164i \(-0.402194\pi\)
0.302453 + 0.953164i \(0.402194\pi\)
\(44\) 6.93281 1.04516
\(45\) −6.19869 −0.924047
\(46\) 7.40425 1.09170
\(47\) −6.74019 −0.983158 −0.491579 0.870833i \(-0.663580\pi\)
−0.491579 + 0.870833i \(0.663580\pi\)
\(48\) −9.06145 −1.30791
\(49\) −4.72937 −0.675625
\(50\) 7.83359 1.10784
\(51\) −2.92082 −0.408997
\(52\) 4.89731 0.679134
\(53\) −7.29570 −1.00214 −0.501071 0.865406i \(-0.667060\pi\)
−0.501071 + 0.865406i \(0.667060\pi\)
\(54\) −15.4685 −2.10499
\(55\) −3.26784 −0.440635
\(56\) 1.19031 0.159062
\(57\) −13.7802 −1.82524
\(58\) 16.7168 2.19502
\(59\) 13.3308 1.73552 0.867761 0.496982i \(-0.165558\pi\)
0.867761 + 0.496982i \(0.165558\pi\)
\(60\) −7.78243 −1.00471
\(61\) −8.67070 −1.11017 −0.555084 0.831794i \(-0.687314\pi\)
−0.555084 + 0.831794i \(0.687314\pi\)
\(62\) −3.41400 −0.433579
\(63\) −8.33475 −1.05008
\(64\) −10.6815 −1.33519
\(65\) −2.30839 −0.286320
\(66\) −17.8197 −2.19345
\(67\) 2.10029 0.256591 0.128295 0.991736i \(-0.459049\pi\)
0.128295 + 0.991736i \(0.459049\pi\)
\(68\) −2.37755 −0.288320
\(69\) −10.3364 −1.24436
\(70\) −3.53321 −0.422299
\(71\) −10.5667 −1.25404 −0.627019 0.779004i \(-0.715725\pi\)
−0.627019 + 0.779004i \(0.715725\pi\)
\(72\) −4.36925 −0.514921
\(73\) −4.60744 −0.539261 −0.269630 0.962964i \(-0.586901\pi\)
−0.269630 + 0.962964i \(0.586901\pi\)
\(74\) −10.1018 −1.17431
\(75\) −10.9358 −1.26276
\(76\) −11.2171 −1.28669
\(77\) −4.39393 −0.500735
\(78\) −12.5878 −1.42528
\(79\) 3.40285 0.382850 0.191425 0.981507i \(-0.438689\pi\)
0.191425 + 0.981507i \(0.438689\pi\)
\(80\) 3.47675 0.388712
\(81\) 5.00058 0.555620
\(82\) −12.9454 −1.42958
\(83\) −1.33273 −0.146286 −0.0731429 0.997321i \(-0.523303\pi\)
−0.0731429 + 0.997321i \(0.523303\pi\)
\(84\) −10.4642 −1.14174
\(85\) 1.12068 0.121555
\(86\) −8.29923 −0.894929
\(87\) −23.3368 −2.50197
\(88\) −2.30339 −0.245542
\(89\) −11.1870 −1.18582 −0.592911 0.805268i \(-0.702021\pi\)
−0.592911 + 0.805268i \(0.702021\pi\)
\(90\) 12.9693 1.36708
\(91\) −3.10385 −0.325372
\(92\) −8.41385 −0.877205
\(93\) 4.76600 0.494211
\(94\) 14.1022 1.45453
\(95\) 5.28728 0.542464
\(96\) 23.5734 2.40595
\(97\) −13.1324 −1.33339 −0.666696 0.745329i \(-0.732292\pi\)
−0.666696 + 0.745329i \(0.732292\pi\)
\(98\) 9.89507 0.999553
\(99\) 16.1287 1.62100
\(100\) −8.90173 −0.890173
\(101\) −4.54060 −0.451807 −0.225903 0.974150i \(-0.572533\pi\)
−0.225903 + 0.974150i \(0.572533\pi\)
\(102\) 6.11112 0.605091
\(103\) 1.54723 0.152453 0.0762267 0.997091i \(-0.475713\pi\)
0.0762267 + 0.997091i \(0.475713\pi\)
\(104\) −1.62710 −0.159551
\(105\) 4.93241 0.481353
\(106\) 15.2645 1.48262
\(107\) −16.6699 −1.61154 −0.805771 0.592227i \(-0.798249\pi\)
−0.805771 + 0.592227i \(0.798249\pi\)
\(108\) 17.5777 1.69141
\(109\) −10.4819 −1.00398 −0.501991 0.864873i \(-0.667399\pi\)
−0.501991 + 0.864873i \(0.667399\pi\)
\(110\) 6.83717 0.651898
\(111\) 14.1022 1.33852
\(112\) 4.67483 0.441730
\(113\) 2.20891 0.207797 0.103899 0.994588i \(-0.466868\pi\)
0.103899 + 0.994588i \(0.466868\pi\)
\(114\) 28.8318 2.70035
\(115\) 3.96594 0.369826
\(116\) −18.9962 −1.76375
\(117\) 11.3932 1.05331
\(118\) −27.8915 −2.56762
\(119\) 1.50686 0.138134
\(120\) 2.58567 0.236038
\(121\) −2.49724 −0.227021
\(122\) 18.1413 1.64244
\(123\) 18.0720 1.62950
\(124\) 3.87952 0.348391
\(125\) 9.79930 0.876476
\(126\) 17.4385 1.55354
\(127\) −4.30706 −0.382190 −0.191095 0.981572i \(-0.561204\pi\)
−0.191095 + 0.981572i \(0.561204\pi\)
\(128\) 6.20682 0.548611
\(129\) 11.5858 1.02008
\(130\) 4.82975 0.423597
\(131\) 15.1256 1.32153 0.660764 0.750593i \(-0.270232\pi\)
0.660764 + 0.750593i \(0.270232\pi\)
\(132\) 20.2495 1.76249
\(133\) 7.10927 0.616452
\(134\) −4.39434 −0.379613
\(135\) −8.28538 −0.713092
\(136\) 0.789928 0.0677358
\(137\) 7.59385 0.648786 0.324393 0.945922i \(-0.394840\pi\)
0.324393 + 0.945922i \(0.394840\pi\)
\(138\) 21.6265 1.84097
\(139\) 18.4518 1.56506 0.782531 0.622611i \(-0.213928\pi\)
0.782531 + 0.622611i \(0.213928\pi\)
\(140\) 4.01498 0.339327
\(141\) −19.6869 −1.65794
\(142\) 22.1083 1.85529
\(143\) 6.00632 0.502273
\(144\) −17.1598 −1.42998
\(145\) 8.95401 0.743590
\(146\) 9.63997 0.797809
\(147\) −13.8137 −1.13933
\(148\) 11.4792 0.943584
\(149\) −19.4594 −1.59418 −0.797089 0.603862i \(-0.793628\pi\)
−0.797089 + 0.603862i \(0.793628\pi\)
\(150\) 22.8805 1.86819
\(151\) 10.1222 0.823734 0.411867 0.911244i \(-0.364877\pi\)
0.411867 + 0.911244i \(0.364877\pi\)
\(152\) 3.72683 0.302286
\(153\) −5.53120 −0.447171
\(154\) 9.19324 0.740812
\(155\) −1.82864 −0.146880
\(156\) 14.3042 1.14525
\(157\) 7.17830 0.572891 0.286445 0.958097i \(-0.407526\pi\)
0.286445 + 0.958097i \(0.407526\pi\)
\(158\) −7.11964 −0.566408
\(159\) −21.3094 −1.68995
\(160\) −9.04476 −0.715051
\(161\) 5.33260 0.420267
\(162\) −10.4625 −0.822013
\(163\) −20.1790 −1.58054 −0.790269 0.612760i \(-0.790059\pi\)
−0.790269 + 0.612760i \(0.790059\pi\)
\(164\) 14.7106 1.14871
\(165\) −9.54478 −0.743060
\(166\) 2.78841 0.216423
\(167\) 9.37290 0.725297 0.362648 0.931926i \(-0.381873\pi\)
0.362648 + 0.931926i \(0.381873\pi\)
\(168\) 3.47669 0.268232
\(169\) −8.75716 −0.673628
\(170\) −2.34475 −0.179834
\(171\) −26.0958 −1.99560
\(172\) 9.43087 0.719097
\(173\) 5.30304 0.403182 0.201591 0.979470i \(-0.435389\pi\)
0.201591 + 0.979470i \(0.435389\pi\)
\(174\) 48.8267 3.70154
\(175\) 5.64181 0.426481
\(176\) −9.04633 −0.681893
\(177\) 38.9369 2.92668
\(178\) 23.4061 1.75436
\(179\) −1.67012 −0.124831 −0.0624153 0.998050i \(-0.519880\pi\)
−0.0624153 + 0.998050i \(0.519880\pi\)
\(180\) −14.7377 −1.09848
\(181\) 24.2813 1.80482 0.902408 0.430882i \(-0.141797\pi\)
0.902408 + 0.430882i \(0.141797\pi\)
\(182\) 6.49406 0.481372
\(183\) −25.3256 −1.87212
\(184\) 2.79546 0.206084
\(185\) −5.41082 −0.397811
\(186\) −9.97170 −0.731160
\(187\) −2.91595 −0.213235
\(188\) −16.0251 −1.16875
\(189\) −11.1405 −0.810352
\(190\) −11.0624 −0.802548
\(191\) 3.63498 0.263018 0.131509 0.991315i \(-0.458018\pi\)
0.131509 + 0.991315i \(0.458018\pi\)
\(192\) −31.1987 −2.25157
\(193\) −19.6443 −1.41403 −0.707014 0.707199i \(-0.749958\pi\)
−0.707014 + 0.707199i \(0.749958\pi\)
\(194\) 27.4764 1.97269
\(195\) −6.74239 −0.482833
\(196\) −11.2443 −0.803165
\(197\) −16.6592 −1.18692 −0.593459 0.804864i \(-0.702238\pi\)
−0.593459 + 0.804864i \(0.702238\pi\)
\(198\) −33.7454 −2.39818
\(199\) −9.05940 −0.642204 −0.321102 0.947045i \(-0.604053\pi\)
−0.321102 + 0.947045i \(0.604053\pi\)
\(200\) 2.95755 0.209131
\(201\) 6.13456 0.432699
\(202\) 9.50011 0.668426
\(203\) 12.0395 0.845010
\(204\) −6.94439 −0.486205
\(205\) −6.93397 −0.484290
\(206\) −3.23721 −0.225547
\(207\) −19.5742 −1.36050
\(208\) −6.39029 −0.443087
\(209\) −13.7573 −0.951610
\(210\) −10.3199 −0.712139
\(211\) 26.2273 1.80556 0.902782 0.430099i \(-0.141522\pi\)
0.902782 + 0.430099i \(0.141522\pi\)
\(212\) −17.3459 −1.19132
\(213\) −30.8635 −2.11473
\(214\) 34.8778 2.38420
\(215\) −4.44532 −0.303168
\(216\) −5.84009 −0.397367
\(217\) −2.45879 −0.166914
\(218\) 21.9308 1.48534
\(219\) −13.4575 −0.909375
\(220\) −7.76944 −0.523816
\(221\) −2.05981 −0.138558
\(222\) −29.5055 −1.98028
\(223\) 22.5006 1.50675 0.753375 0.657591i \(-0.228425\pi\)
0.753375 + 0.657591i \(0.228425\pi\)
\(224\) −12.1616 −0.812579
\(225\) −20.7093 −1.38062
\(226\) −4.62162 −0.307425
\(227\) −2.82082 −0.187224 −0.0936120 0.995609i \(-0.529841\pi\)
−0.0936120 + 0.995609i \(0.529841\pi\)
\(228\) −32.7632 −2.16980
\(229\) 7.50404 0.495881 0.247940 0.968775i \(-0.420246\pi\)
0.247940 + 0.968775i \(0.420246\pi\)
\(230\) −8.29778 −0.547139
\(231\) −12.8339 −0.844408
\(232\) 6.31138 0.414362
\(233\) 25.0945 1.64399 0.821996 0.569493i \(-0.192860\pi\)
0.821996 + 0.569493i \(0.192860\pi\)
\(234\) −23.8376 −1.55831
\(235\) 7.55358 0.492741
\(236\) 31.6946 2.06314
\(237\) 9.93911 0.645615
\(238\) −3.15274 −0.204362
\(239\) −22.1072 −1.42999 −0.714997 0.699127i \(-0.753572\pi\)
−0.714997 + 0.699127i \(0.753572\pi\)
\(240\) 10.1550 0.655500
\(241\) 0.581873 0.0374818 0.0187409 0.999824i \(-0.494034\pi\)
0.0187409 + 0.999824i \(0.494034\pi\)
\(242\) 5.22486 0.335867
\(243\) −7.57375 −0.485856
\(244\) −20.6150 −1.31974
\(245\) 5.30010 0.338611
\(246\) −37.8113 −2.41076
\(247\) −9.71807 −0.618346
\(248\) −1.28895 −0.0818484
\(249\) −3.89266 −0.246687
\(250\) −20.5027 −1.29670
\(251\) −8.94918 −0.564867 −0.282434 0.959287i \(-0.591142\pi\)
−0.282434 + 0.959287i \(0.591142\pi\)
\(252\) −19.8163 −1.24831
\(253\) −10.3192 −0.648762
\(254\) 9.01148 0.565431
\(255\) 3.27330 0.204982
\(256\) 8.37668 0.523542
\(257\) 3.11937 0.194581 0.0972906 0.995256i \(-0.468982\pi\)
0.0972906 + 0.995256i \(0.468982\pi\)
\(258\) −24.2406 −1.50915
\(259\) −7.27537 −0.452070
\(260\) −5.48830 −0.340370
\(261\) −44.1933 −2.73550
\(262\) −31.6466 −1.95514
\(263\) 2.45658 0.151479 0.0757397 0.997128i \(-0.475868\pi\)
0.0757397 + 0.997128i \(0.475868\pi\)
\(264\) −6.72779 −0.414067
\(265\) 8.17613 0.502255
\(266\) −14.8744 −0.912010
\(267\) −32.6753 −1.99970
\(268\) 4.99353 0.305028
\(269\) −24.8873 −1.51740 −0.758701 0.651439i \(-0.774166\pi\)
−0.758701 + 0.651439i \(0.774166\pi\)
\(270\) 17.3352 1.05498
\(271\) 5.07021 0.307993 0.153997 0.988071i \(-0.450785\pi\)
0.153997 + 0.988071i \(0.450785\pi\)
\(272\) 3.10236 0.188108
\(273\) −9.06580 −0.548687
\(274\) −15.8883 −0.959847
\(275\) −10.9176 −0.658353
\(276\) −24.5754 −1.47926
\(277\) 4.25681 0.255767 0.127883 0.991789i \(-0.459182\pi\)
0.127883 + 0.991789i \(0.459182\pi\)
\(278\) −38.6060 −2.31543
\(279\) 9.02543 0.540338
\(280\) −1.33395 −0.0797190
\(281\) 20.3334 1.21299 0.606494 0.795088i \(-0.292576\pi\)
0.606494 + 0.795088i \(0.292576\pi\)
\(282\) 41.1901 2.45283
\(283\) 22.4162 1.33251 0.666253 0.745726i \(-0.267897\pi\)
0.666253 + 0.745726i \(0.267897\pi\)
\(284\) −25.1228 −1.49077
\(285\) 15.4432 0.914777
\(286\) −12.5668 −0.743089
\(287\) −9.32340 −0.550343
\(288\) 44.6412 2.63051
\(289\) 1.00000 0.0588235
\(290\) −18.7341 −1.10010
\(291\) −38.3574 −2.24855
\(292\) −10.9544 −0.641059
\(293\) −29.6747 −1.73361 −0.866807 0.498644i \(-0.833831\pi\)
−0.866807 + 0.498644i \(0.833831\pi\)
\(294\) 28.9017 1.68558
\(295\) −14.9395 −0.869813
\(296\) −3.81390 −0.221679
\(297\) 21.5582 1.25093
\(298\) 40.7142 2.35851
\(299\) −7.28943 −0.421559
\(300\) −26.0004 −1.50113
\(301\) −5.97717 −0.344518
\(302\) −21.1783 −1.21867
\(303\) −13.2623 −0.761899
\(304\) 14.6367 0.839475
\(305\) 9.71705 0.556397
\(306\) 11.5727 0.661568
\(307\) −29.6246 −1.69076 −0.845381 0.534163i \(-0.820627\pi\)
−0.845381 + 0.534163i \(0.820627\pi\)
\(308\) −10.4468 −0.595260
\(309\) 4.51919 0.257088
\(310\) 3.82600 0.217302
\(311\) 0.336416 0.0190764 0.00953821 0.999955i \(-0.496964\pi\)
0.00953821 + 0.999955i \(0.496964\pi\)
\(312\) −4.75248 −0.269056
\(313\) 23.5306 1.33003 0.665014 0.746831i \(-0.268426\pi\)
0.665014 + 0.746831i \(0.268426\pi\)
\(314\) −15.0189 −0.847564
\(315\) 9.34056 0.526281
\(316\) 8.09043 0.455122
\(317\) −30.6356 −1.72067 −0.860335 0.509729i \(-0.829745\pi\)
−0.860335 + 0.509729i \(0.829745\pi\)
\(318\) 44.5849 2.50019
\(319\) −23.2979 −1.30443
\(320\) 11.9705 0.669171
\(321\) −48.6899 −2.71760
\(322\) −11.1572 −0.621765
\(323\) 4.71794 0.262513
\(324\) 11.8891 0.660507
\(325\) −7.71211 −0.427791
\(326\) 42.2196 2.33833
\(327\) −30.6157 −1.69305
\(328\) −4.88752 −0.269868
\(329\) 10.1565 0.559948
\(330\) 19.9701 1.09932
\(331\) 24.0344 1.32105 0.660524 0.750805i \(-0.270334\pi\)
0.660524 + 0.750805i \(0.270334\pi\)
\(332\) −3.16862 −0.173901
\(333\) 26.7056 1.46346
\(334\) −19.6105 −1.07304
\(335\) −2.35374 −0.128599
\(336\) 13.6543 0.744905
\(337\) −21.5952 −1.17636 −0.588182 0.808729i \(-0.700156\pi\)
−0.588182 + 0.808729i \(0.700156\pi\)
\(338\) 18.3223 0.996599
\(339\) 6.45184 0.350416
\(340\) 2.66446 0.144501
\(341\) 4.75805 0.257663
\(342\) 54.5993 2.95239
\(343\) 17.6745 0.954335
\(344\) −3.13336 −0.168939
\(345\) 11.5838 0.623651
\(346\) −11.0953 −0.596489
\(347\) −4.64292 −0.249245 −0.124623 0.992204i \(-0.539772\pi\)
−0.124623 + 0.992204i \(0.539772\pi\)
\(348\) −55.4844 −2.97428
\(349\) 0.514772 0.0275551 0.0137776 0.999905i \(-0.495614\pi\)
0.0137776 + 0.999905i \(0.495614\pi\)
\(350\) −11.8041 −0.630957
\(351\) 15.2286 0.812842
\(352\) 23.5341 1.25437
\(353\) −1.00000 −0.0532246
\(354\) −81.4661 −4.32987
\(355\) 11.8419 0.628501
\(356\) −26.5977 −1.40967
\(357\) 4.40127 0.232940
\(358\) 3.49433 0.184681
\(359\) 35.6011 1.87896 0.939478 0.342610i \(-0.111311\pi\)
0.939478 + 0.342610i \(0.111311\pi\)
\(360\) 4.89652 0.258069
\(361\) 3.25891 0.171522
\(362\) −50.8028 −2.67014
\(363\) −7.29398 −0.382835
\(364\) −7.37956 −0.386794
\(365\) 5.16346 0.270268
\(366\) 52.9876 2.76971
\(367\) −3.37188 −0.176011 −0.0880054 0.996120i \(-0.528049\pi\)
−0.0880054 + 0.996120i \(0.528049\pi\)
\(368\) 10.9789 0.572314
\(369\) 34.2232 1.78159
\(370\) 11.3208 0.588542
\(371\) 10.9936 0.570759
\(372\) 11.3314 0.587505
\(373\) 27.8269 1.44082 0.720412 0.693546i \(-0.243953\pi\)
0.720412 + 0.693546i \(0.243953\pi\)
\(374\) 6.10092 0.315471
\(375\) 28.6220 1.47803
\(376\) 5.32427 0.274578
\(377\) −16.4575 −0.847607
\(378\) 23.3088 1.19888
\(379\) −17.7981 −0.914227 −0.457114 0.889408i \(-0.651117\pi\)
−0.457114 + 0.889408i \(0.651117\pi\)
\(380\) 12.5708 0.644867
\(381\) −12.5801 −0.644501
\(382\) −7.60532 −0.389122
\(383\) −33.1229 −1.69250 −0.846251 0.532785i \(-0.821146\pi\)
−0.846251 + 0.532785i \(0.821146\pi\)
\(384\) 18.1290 0.925143
\(385\) 4.92418 0.250959
\(386\) 41.1010 2.09199
\(387\) 21.9403 1.11529
\(388\) −31.2229 −1.58510
\(389\) −9.24216 −0.468596 −0.234298 0.972165i \(-0.575279\pi\)
−0.234298 + 0.972165i \(0.575279\pi\)
\(390\) 14.1068 0.714327
\(391\) 3.53888 0.178969
\(392\) 3.73586 0.188690
\(393\) 44.1792 2.22854
\(394\) 34.8553 1.75599
\(395\) −3.81349 −0.191878
\(396\) 38.3468 1.92700
\(397\) 14.0389 0.704595 0.352297 0.935888i \(-0.385401\pi\)
0.352297 + 0.935888i \(0.385401\pi\)
\(398\) 18.9546 0.950109
\(399\) 20.7649 1.03955
\(400\) 11.6155 0.580775
\(401\) 6.15096 0.307164 0.153582 0.988136i \(-0.450919\pi\)
0.153582 + 0.988136i \(0.450919\pi\)
\(402\) −12.8351 −0.640156
\(403\) 3.36106 0.167426
\(404\) −10.7955 −0.537096
\(405\) −5.60404 −0.278467
\(406\) −25.1898 −1.25015
\(407\) 14.0787 0.697855
\(408\) 2.30724 0.114225
\(409\) 8.60550 0.425514 0.212757 0.977105i \(-0.431756\pi\)
0.212757 + 0.977105i \(0.431756\pi\)
\(410\) 14.5077 0.716482
\(411\) 22.1803 1.09407
\(412\) 3.67862 0.181233
\(413\) −20.0876 −0.988449
\(414\) 40.9544 2.01280
\(415\) 1.49356 0.0733158
\(416\) 16.6244 0.815076
\(417\) 53.8945 2.63922
\(418\) 28.7838 1.40786
\(419\) −1.64627 −0.0804257 −0.0402129 0.999191i \(-0.512804\pi\)
−0.0402129 + 0.999191i \(0.512804\pi\)
\(420\) 11.7270 0.572220
\(421\) −13.5816 −0.661926 −0.330963 0.943644i \(-0.607373\pi\)
−0.330963 + 0.943644i \(0.607373\pi\)
\(422\) −54.8743 −2.67124
\(423\) −37.2814 −1.81268
\(424\) 5.76308 0.279880
\(425\) 3.74408 0.181615
\(426\) 64.5744 3.12864
\(427\) 13.0655 0.632285
\(428\) −39.6335 −1.91576
\(429\) 17.5434 0.847002
\(430\) 9.30077 0.448523
\(431\) −1.75410 −0.0844918 −0.0422459 0.999107i \(-0.513451\pi\)
−0.0422459 + 0.999107i \(0.513451\pi\)
\(432\) −22.9363 −1.10353
\(433\) 21.4367 1.03018 0.515092 0.857135i \(-0.327758\pi\)
0.515092 + 0.857135i \(0.327758\pi\)
\(434\) 5.14443 0.246940
\(435\) 26.1531 1.25394
\(436\) −24.9212 −1.19351
\(437\) 16.6962 0.798687
\(438\) 28.1566 1.34538
\(439\) −32.2632 −1.53984 −0.769919 0.638141i \(-0.779704\pi\)
−0.769919 + 0.638141i \(0.779704\pi\)
\(440\) 2.58136 0.123061
\(441\) −26.1591 −1.24567
\(442\) 4.30967 0.204990
\(443\) −33.4587 −1.58967 −0.794834 0.606826i \(-0.792442\pi\)
−0.794834 + 0.606826i \(0.792442\pi\)
\(444\) 33.5287 1.59120
\(445\) 12.5370 0.594313
\(446\) −47.0770 −2.22916
\(447\) −56.8375 −2.68832
\(448\) 16.0955 0.760441
\(449\) −22.1528 −1.04545 −0.522727 0.852500i \(-0.675085\pi\)
−0.522727 + 0.852500i \(0.675085\pi\)
\(450\) 43.3292 2.04256
\(451\) 18.0419 0.849558
\(452\) 5.25179 0.247024
\(453\) 29.5652 1.38909
\(454\) 5.90188 0.276989
\(455\) 3.47842 0.163071
\(456\) 10.8854 0.509756
\(457\) −3.69841 −0.173004 −0.0865021 0.996252i \(-0.527569\pi\)
−0.0865021 + 0.996252i \(0.527569\pi\)
\(458\) −15.7004 −0.733631
\(459\) −7.39319 −0.345084
\(460\) 9.42922 0.439639
\(461\) −0.428070 −0.0199372 −0.00996861 0.999950i \(-0.503173\pi\)
−0.00996861 + 0.999950i \(0.503173\pi\)
\(462\) 26.8518 1.24926
\(463\) −20.3406 −0.945307 −0.472654 0.881248i \(-0.656704\pi\)
−0.472654 + 0.881248i \(0.656704\pi\)
\(464\) 24.7873 1.15072
\(465\) −5.34114 −0.247690
\(466\) −52.5041 −2.43221
\(467\) −31.7998 −1.47152 −0.735760 0.677243i \(-0.763175\pi\)
−0.735760 + 0.677243i \(0.763175\pi\)
\(468\) 27.0880 1.25214
\(469\) −3.16484 −0.146139
\(470\) −15.8041 −0.728987
\(471\) 20.9665 0.966087
\(472\) −10.5304 −0.484699
\(473\) 11.5665 0.531829
\(474\) −20.7952 −0.955155
\(475\) 17.6643 0.810495
\(476\) 3.58263 0.164210
\(477\) −40.3540 −1.84768
\(478\) 46.2539 2.11561
\(479\) −24.6985 −1.12850 −0.564251 0.825603i \(-0.690835\pi\)
−0.564251 + 0.825603i \(0.690835\pi\)
\(480\) −26.4181 −1.20582
\(481\) 9.94513 0.453459
\(482\) −1.21743 −0.0554524
\(483\) 15.5756 0.708713
\(484\) −5.93730 −0.269877
\(485\) 14.7172 0.668273
\(486\) 15.8462 0.718800
\(487\) 0.972038 0.0440473 0.0220236 0.999757i \(-0.492989\pi\)
0.0220236 + 0.999757i \(0.492989\pi\)
\(488\) 6.84922 0.310050
\(489\) −58.9392 −2.66532
\(490\) −11.0892 −0.500958
\(491\) −28.5399 −1.28799 −0.643995 0.765030i \(-0.722724\pi\)
−0.643995 + 0.765030i \(0.722724\pi\)
\(492\) 42.9671 1.93711
\(493\) 7.98982 0.359843
\(494\) 20.3327 0.914812
\(495\) −18.0751 −0.812414
\(496\) −5.06222 −0.227300
\(497\) 15.9225 0.714224
\(498\) 8.14445 0.364962
\(499\) −33.3035 −1.49087 −0.745435 0.666578i \(-0.767758\pi\)
−0.745435 + 0.666578i \(0.767758\pi\)
\(500\) 23.2983 1.04193
\(501\) 27.3766 1.22310
\(502\) 18.7240 0.835693
\(503\) 4.22601 0.188429 0.0942143 0.995552i \(-0.469966\pi\)
0.0942143 + 0.995552i \(0.469966\pi\)
\(504\) 6.58385 0.293268
\(505\) 5.08855 0.226438
\(506\) 21.5904 0.959811
\(507\) −25.5781 −1.13596
\(508\) −10.2402 −0.454337
\(509\) −29.4232 −1.30416 −0.652080 0.758150i \(-0.726104\pi\)
−0.652080 + 0.758150i \(0.726104\pi\)
\(510\) −6.84859 −0.303261
\(511\) 6.94277 0.307130
\(512\) −29.9398 −1.32317
\(513\) −34.8806 −1.54002
\(514\) −6.52653 −0.287873
\(515\) −1.73395 −0.0764069
\(516\) 27.5459 1.21264
\(517\) −19.6541 −0.864385
\(518\) 15.2220 0.668815
\(519\) 15.4892 0.679902
\(520\) 1.82346 0.0799640
\(521\) −39.3172 −1.72252 −0.861260 0.508165i \(-0.830324\pi\)
−0.861260 + 0.508165i \(0.830324\pi\)
\(522\) 92.4638 4.04703
\(523\) 38.4232 1.68013 0.840064 0.542487i \(-0.182517\pi\)
0.840064 + 0.542487i \(0.182517\pi\)
\(524\) 35.9618 1.57100
\(525\) 16.4787 0.719190
\(526\) −5.13981 −0.224106
\(527\) −1.63173 −0.0710793
\(528\) −26.4227 −1.14990
\(529\) −10.4763 −0.455493
\(530\) −17.1066 −0.743062
\(531\) 73.7353 3.19984
\(532\) 16.9026 0.732822
\(533\) 12.7447 0.552034
\(534\) 68.3652 2.95845
\(535\) 18.6816 0.807676
\(536\) −1.65907 −0.0716611
\(537\) −4.87813 −0.210507
\(538\) 52.0706 2.24492
\(539\) −13.7906 −0.594004
\(540\) −19.6989 −0.847705
\(541\) −15.5468 −0.668408 −0.334204 0.942501i \(-0.608467\pi\)
−0.334204 + 0.942501i \(0.608467\pi\)
\(542\) −10.6082 −0.455661
\(543\) 70.9214 3.04353
\(544\) −8.07080 −0.346033
\(545\) 11.7468 0.503178
\(546\) 18.9680 0.811756
\(547\) 32.1816 1.37599 0.687994 0.725717i \(-0.258492\pi\)
0.687994 + 0.725717i \(0.258492\pi\)
\(548\) 18.0547 0.771260
\(549\) −47.9594 −2.04686
\(550\) 22.8424 0.974001
\(551\) 37.6954 1.60588
\(552\) 8.16504 0.347527
\(553\) −5.12762 −0.218048
\(554\) −8.90635 −0.378394
\(555\) −15.8040 −0.670844
\(556\) 43.8701 1.86051
\(557\) −8.19439 −0.347207 −0.173604 0.984816i \(-0.555541\pi\)
−0.173604 + 0.984816i \(0.555541\pi\)
\(558\) −18.8835 −0.799404
\(559\) 8.17054 0.345577
\(560\) −5.23897 −0.221387
\(561\) −8.51697 −0.359587
\(562\) −42.5427 −1.79455
\(563\) 14.7296 0.620779 0.310390 0.950609i \(-0.399540\pi\)
0.310390 + 0.950609i \(0.399540\pi\)
\(564\) −46.8066 −1.97091
\(565\) −2.47548 −0.104144
\(566\) −46.9005 −1.97138
\(567\) −7.53518 −0.316448
\(568\) 8.34693 0.350230
\(569\) 17.0456 0.714588 0.357294 0.933992i \(-0.383699\pi\)
0.357294 + 0.933992i \(0.383699\pi\)
\(570\) −32.3112 −1.35337
\(571\) 14.3775 0.601681 0.300840 0.953675i \(-0.402733\pi\)
0.300840 + 0.953675i \(0.402733\pi\)
\(572\) 14.2803 0.597090
\(573\) 10.6171 0.443537
\(574\) 19.5070 0.814205
\(575\) 13.2499 0.552557
\(576\) −59.0814 −2.46173
\(577\) 28.8467 1.20090 0.600451 0.799661i \(-0.294988\pi\)
0.600451 + 0.799661i \(0.294988\pi\)
\(578\) −2.09226 −0.0870265
\(579\) −57.3775 −2.38453
\(580\) 21.2886 0.883960
\(581\) 2.00823 0.0833156
\(582\) 80.2536 3.32662
\(583\) −21.2739 −0.881075
\(584\) 3.63955 0.150606
\(585\) −12.7682 −0.527898
\(586\) 62.0871 2.56479
\(587\) −1.87269 −0.0772942 −0.0386471 0.999253i \(-0.512305\pi\)
−0.0386471 + 0.999253i \(0.512305\pi\)
\(588\) −32.8426 −1.35441
\(589\) −7.69840 −0.317207
\(590\) 31.2574 1.28684
\(591\) −48.6585 −2.00154
\(592\) −14.9787 −0.615622
\(593\) 35.0188 1.43805 0.719025 0.694984i \(-0.244589\pi\)
0.719025 + 0.694984i \(0.244589\pi\)
\(594\) −45.1053 −1.85069
\(595\) −1.68870 −0.0692301
\(596\) −46.2657 −1.89512
\(597\) −26.4609 −1.08297
\(598\) 15.2514 0.623675
\(599\) −42.0083 −1.71641 −0.858207 0.513304i \(-0.828421\pi\)
−0.858207 + 0.513304i \(0.828421\pi\)
\(600\) 8.63849 0.352665
\(601\) −20.8721 −0.851392 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(602\) 12.5058 0.509698
\(603\) 11.6171 0.473085
\(604\) 24.0661 0.979234
\(605\) 2.79860 0.113779
\(606\) 27.7481 1.12719
\(607\) −20.8316 −0.845529 −0.422764 0.906240i \(-0.638940\pi\)
−0.422764 + 0.906240i \(0.638940\pi\)
\(608\) −38.0775 −1.54425
\(609\) 35.1654 1.42497
\(610\) −20.3306 −0.823162
\(611\) −13.8835 −0.561668
\(612\) −13.1507 −0.531585
\(613\) −7.37783 −0.297988 −0.148994 0.988838i \(-0.547603\pi\)
−0.148994 + 0.988838i \(0.547603\pi\)
\(614\) 61.9822 2.50140
\(615\) −20.2529 −0.816676
\(616\) 3.47089 0.139846
\(617\) −12.2365 −0.492622 −0.246311 0.969191i \(-0.579218\pi\)
−0.246311 + 0.969191i \(0.579218\pi\)
\(618\) −9.45532 −0.380349
\(619\) 39.0435 1.56929 0.784645 0.619946i \(-0.212845\pi\)
0.784645 + 0.619946i \(0.212845\pi\)
\(620\) −4.34769 −0.174607
\(621\) −26.1636 −1.04991
\(622\) −0.703870 −0.0282226
\(623\) 16.8573 0.675372
\(624\) −18.6649 −0.747194
\(625\) 7.73856 0.309542
\(626\) −49.2321 −1.96771
\(627\) −40.1825 −1.60474
\(628\) 17.0668 0.681038
\(629\) −4.82817 −0.192512
\(630\) −19.5429 −0.778607
\(631\) −7.60087 −0.302586 −0.151293 0.988489i \(-0.548344\pi\)
−0.151293 + 0.988489i \(0.548344\pi\)
\(632\) −2.68800 −0.106923
\(633\) 76.6053 3.04479
\(634\) 64.0977 2.54565
\(635\) 4.82682 0.191547
\(636\) −50.6642 −2.00897
\(637\) −9.74163 −0.385977
\(638\) 48.7453 1.92984
\(639\) −58.4466 −2.31211
\(640\) −6.95585 −0.274954
\(641\) 6.77343 0.267534 0.133767 0.991013i \(-0.457293\pi\)
0.133767 + 0.991013i \(0.457293\pi\)
\(642\) 101.872 4.02056
\(643\) −40.0262 −1.57848 −0.789239 0.614086i \(-0.789525\pi\)
−0.789239 + 0.614086i \(0.789525\pi\)
\(644\) 12.6785 0.499603
\(645\) −12.9840 −0.511244
\(646\) −9.87114 −0.388375
\(647\) 36.5553 1.43714 0.718568 0.695456i \(-0.244798\pi\)
0.718568 + 0.695456i \(0.244798\pi\)
\(648\) −3.95010 −0.155175
\(649\) 38.8719 1.52586
\(650\) 16.1357 0.632896
\(651\) −7.18169 −0.281473
\(652\) −47.9765 −1.87890
\(653\) −32.7511 −1.28165 −0.640824 0.767688i \(-0.721407\pi\)
−0.640824 + 0.767688i \(0.721407\pi\)
\(654\) 64.0560 2.50479
\(655\) −16.9509 −0.662327
\(656\) −19.1953 −0.749449
\(657\) −25.4847 −0.994253
\(658\) −21.2501 −0.828415
\(659\) −18.2769 −0.711968 −0.355984 0.934492i \(-0.615854\pi\)
−0.355984 + 0.934492i \(0.615854\pi\)
\(660\) −22.6932 −0.883330
\(661\) 38.4989 1.49743 0.748717 0.662890i \(-0.230670\pi\)
0.748717 + 0.662890i \(0.230670\pi\)
\(662\) −50.2861 −1.95443
\(663\) −6.01635 −0.233656
\(664\) 1.05276 0.0408549
\(665\) −7.96720 −0.308955
\(666\) −55.8750 −2.16511
\(667\) 28.2750 1.09481
\(668\) 22.2845 0.862214
\(669\) 65.7202 2.54089
\(670\) 4.92464 0.190255
\(671\) −25.2833 −0.976052
\(672\) −35.5218 −1.37028
\(673\) 25.6733 0.989631 0.494816 0.868998i \(-0.335236\pi\)
0.494816 + 0.868998i \(0.335236\pi\)
\(674\) 45.1827 1.74037
\(675\) −27.6807 −1.06543
\(676\) −20.8206 −0.800791
\(677\) −27.7345 −1.06592 −0.532962 0.846139i \(-0.678921\pi\)
−0.532962 + 0.846139i \(0.678921\pi\)
\(678\) −13.4989 −0.518423
\(679\) 19.7887 0.759420
\(680\) −0.885254 −0.0339480
\(681\) −8.23910 −0.315723
\(682\) −9.95506 −0.381199
\(683\) 1.38165 0.0528672 0.0264336 0.999651i \(-0.491585\pi\)
0.0264336 + 0.999651i \(0.491585\pi\)
\(684\) −62.0441 −2.37232
\(685\) −8.51025 −0.325160
\(686\) −36.9797 −1.41189
\(687\) 21.9180 0.836222
\(688\) −12.3059 −0.469160
\(689\) −15.0278 −0.572513
\(690\) −24.2363 −0.922661
\(691\) 6.55838 0.249492 0.124746 0.992189i \(-0.460188\pi\)
0.124746 + 0.992189i \(0.460188\pi\)
\(692\) 12.6082 0.479293
\(693\) −24.3037 −0.923222
\(694\) 9.71420 0.368746
\(695\) −20.6785 −0.784381
\(696\) 18.4344 0.698755
\(697\) −6.18730 −0.234361
\(698\) −1.07704 −0.0407664
\(699\) 73.2964 2.77233
\(700\) 13.4137 0.506989
\(701\) −7.67620 −0.289926 −0.144963 0.989437i \(-0.546306\pi\)
−0.144963 + 0.989437i \(0.546306\pi\)
\(702\) −31.8622 −1.20256
\(703\) −22.7790 −0.859125
\(704\) −31.1467 −1.17388
\(705\) 22.0627 0.830928
\(706\) 2.09226 0.0787432
\(707\) 6.84205 0.257322
\(708\) 92.5743 3.47916
\(709\) −7.36959 −0.276771 −0.138385 0.990378i \(-0.544191\pi\)
−0.138385 + 0.990378i \(0.544191\pi\)
\(710\) −24.7763 −0.929836
\(711\) 18.8218 0.705874
\(712\) 8.83694 0.331178
\(713\) −5.77450 −0.216257
\(714\) −9.20860 −0.344623
\(715\) −6.73114 −0.251731
\(716\) −3.97079 −0.148395
\(717\) −64.5711 −2.41145
\(718\) −74.4868 −2.77982
\(719\) 18.2251 0.679681 0.339841 0.940483i \(-0.389627\pi\)
0.339841 + 0.940483i \(0.389627\pi\)
\(720\) 19.2306 0.716682
\(721\) −2.33146 −0.0868283
\(722\) −6.81849 −0.253758
\(723\) 1.69955 0.0632069
\(724\) 57.7300 2.14552
\(725\) 29.9145 1.11100
\(726\) 15.2609 0.566385
\(727\) −17.0251 −0.631427 −0.315714 0.948855i \(-0.602244\pi\)
−0.315714 + 0.948855i \(0.602244\pi\)
\(728\) 2.45182 0.0908705
\(729\) −37.1233 −1.37494
\(730\) −10.8033 −0.399848
\(731\) −3.96664 −0.146711
\(732\) −60.2127 −2.22553
\(733\) −3.67794 −0.135848 −0.0679239 0.997691i \(-0.521638\pi\)
−0.0679239 + 0.997691i \(0.521638\pi\)
\(734\) 7.05485 0.260399
\(735\) 15.4807 0.571012
\(736\) −28.5616 −1.05279
\(737\) 6.12433 0.225593
\(738\) −71.6038 −2.63577
\(739\) −16.2366 −0.597271 −0.298636 0.954367i \(-0.596532\pi\)
−0.298636 + 0.954367i \(0.596532\pi\)
\(740\) −12.8645 −0.472908
\(741\) −28.3848 −1.04274
\(742\) −23.0015 −0.844410
\(743\) −8.90710 −0.326770 −0.163385 0.986562i \(-0.552241\pi\)
−0.163385 + 0.986562i \(0.552241\pi\)
\(744\) −3.76479 −0.138024
\(745\) 21.8077 0.798974
\(746\) −58.2212 −2.13163
\(747\) −7.37158 −0.269712
\(748\) −6.93281 −0.253489
\(749\) 25.1192 0.917837
\(750\) −59.8846 −2.18668
\(751\) −38.4571 −1.40332 −0.701660 0.712512i \(-0.747557\pi\)
−0.701660 + 0.712512i \(0.747557\pi\)
\(752\) 20.9105 0.762528
\(753\) −26.1390 −0.952557
\(754\) 34.4334 1.25399
\(755\) −11.3437 −0.412841
\(756\) −26.4871 −0.963326
\(757\) −12.7584 −0.463713 −0.231857 0.972750i \(-0.574480\pi\)
−0.231857 + 0.972750i \(0.574480\pi\)
\(758\) 37.2382 1.35255
\(759\) −30.1405 −1.09403
\(760\) −4.17657 −0.151500
\(761\) −28.0723 −1.01762 −0.508810 0.860879i \(-0.669914\pi\)
−0.508810 + 0.860879i \(0.669914\pi\)
\(762\) 26.3209 0.953507
\(763\) 15.7947 0.571808
\(764\) 8.64234 0.312669
\(765\) 6.19869 0.224114
\(766\) 69.3017 2.50397
\(767\) 27.4590 0.991486
\(768\) 24.4668 0.882869
\(769\) 0.902768 0.0325546 0.0162773 0.999868i \(-0.494819\pi\)
0.0162773 + 0.999868i \(0.494819\pi\)
\(770\) −10.3027 −0.371282
\(771\) 9.11113 0.328129
\(772\) −46.7053 −1.68096
\(773\) 41.0431 1.47622 0.738109 0.674682i \(-0.235719\pi\)
0.738109 + 0.674682i \(0.235719\pi\)
\(774\) −45.9047 −1.65001
\(775\) −6.10933 −0.219454
\(776\) 10.3736 0.372392
\(777\) −21.2501 −0.762342
\(778\) 19.3370 0.693265
\(779\) −29.1913 −1.04589
\(780\) −16.0304 −0.573979
\(781\) −30.8120 −1.10254
\(782\) −7.40425 −0.264775
\(783\) −59.0702 −2.11100
\(784\) 14.6722 0.524008
\(785\) −8.04456 −0.287123
\(786\) −92.4342 −3.29702
\(787\) 53.8797 1.92060 0.960302 0.278962i \(-0.0899903\pi\)
0.960302 + 0.278962i \(0.0899903\pi\)
\(788\) −39.6080 −1.41098
\(789\) 7.17525 0.255446
\(790\) 7.97882 0.283874
\(791\) −3.32852 −0.118349
\(792\) −12.7405 −0.452714
\(793\) −17.8600 −0.634228
\(794\) −29.3731 −1.04241
\(795\) 23.8810 0.846972
\(796\) −21.5392 −0.763435
\(797\) 17.6188 0.624091 0.312046 0.950067i \(-0.398986\pi\)
0.312046 + 0.950067i \(0.398986\pi\)
\(798\) −43.4456 −1.53796
\(799\) 6.74019 0.238451
\(800\) −30.2177 −1.06836
\(801\) −61.8776 −2.18634
\(802\) −12.8694 −0.454435
\(803\) −13.4351 −0.474114
\(804\) 14.5852 0.514381
\(805\) −5.97612 −0.210631
\(806\) −7.03221 −0.247699
\(807\) −72.6912 −2.55885
\(808\) 3.58675 0.126181
\(809\) 51.8905 1.82437 0.912186 0.409775i \(-0.134393\pi\)
0.912186 + 0.409775i \(0.134393\pi\)
\(810\) 11.7251 0.411978
\(811\) 15.5937 0.547568 0.273784 0.961791i \(-0.411725\pi\)
0.273784 + 0.961791i \(0.411725\pi\)
\(812\) 28.6246 1.00453
\(813\) 14.8092 0.519381
\(814\) −29.4563 −1.03244
\(815\) 22.6141 0.792138
\(816\) 9.06145 0.317214
\(817\) −18.7143 −0.654732
\(818\) −18.0049 −0.629528
\(819\) −17.1680 −0.599900
\(820\) −16.4858 −0.575711
\(821\) −23.9770 −0.836803 −0.418401 0.908262i \(-0.637409\pi\)
−0.418401 + 0.908262i \(0.637409\pi\)
\(822\) −46.4069 −1.61863
\(823\) −27.2545 −0.950033 −0.475017 0.879977i \(-0.657558\pi\)
−0.475017 + 0.879977i \(0.657558\pi\)
\(824\) −1.22220 −0.0425774
\(825\) −31.8882 −1.11021
\(826\) 42.0286 1.46236
\(827\) −46.3252 −1.61089 −0.805443 0.592674i \(-0.798072\pi\)
−0.805443 + 0.592674i \(0.798072\pi\)
\(828\) −46.5387 −1.61733
\(829\) 28.6879 0.996374 0.498187 0.867070i \(-0.333999\pi\)
0.498187 + 0.867070i \(0.333999\pi\)
\(830\) −3.12491 −0.108467
\(831\) 12.4334 0.431309
\(832\) −22.0019 −0.762778
\(833\) 4.72937 0.163863
\(834\) −112.761 −3.90460
\(835\) −10.5040 −0.363506
\(836\) −32.7086 −1.13125
\(837\) 12.0637 0.416982
\(838\) 3.44443 0.118986
\(839\) 1.94919 0.0672934 0.0336467 0.999434i \(-0.489288\pi\)
0.0336467 + 0.999434i \(0.489288\pi\)
\(840\) −3.89624 −0.134433
\(841\) 34.8372 1.20128
\(842\) 28.4162 0.979286
\(843\) 59.3902 2.04551
\(844\) 62.3567 2.14641
\(845\) 9.81396 0.337610
\(846\) 78.0023 2.68177
\(847\) 3.76299 0.129298
\(848\) 22.6339 0.777251
\(849\) 65.4738 2.24705
\(850\) −7.83359 −0.268690
\(851\) −17.0863 −0.585711
\(852\) −73.3794 −2.51394
\(853\) −7.34974 −0.251650 −0.125825 0.992052i \(-0.540158\pi\)
−0.125825 + 0.992052i \(0.540158\pi\)
\(854\) −27.3365 −0.935435
\(855\) 29.2450 1.00016
\(856\) 13.1680 0.450074
\(857\) 27.9071 0.953287 0.476644 0.879097i \(-0.341853\pi\)
0.476644 + 0.879097i \(0.341853\pi\)
\(858\) −36.7053 −1.25310
\(859\) 14.5279 0.495686 0.247843 0.968800i \(-0.420278\pi\)
0.247843 + 0.968800i \(0.420278\pi\)
\(860\) −10.5690 −0.360399
\(861\) −27.2320 −0.928064
\(862\) 3.67002 0.125001
\(863\) −22.4172 −0.763089 −0.381544 0.924350i \(-0.624608\pi\)
−0.381544 + 0.924350i \(0.624608\pi\)
\(864\) 59.6690 2.02998
\(865\) −5.94300 −0.202068
\(866\) −44.8512 −1.52411
\(867\) 2.92082 0.0991963
\(868\) −5.84589 −0.198423
\(869\) 9.92253 0.336599
\(870\) −54.7190 −1.85515
\(871\) 4.32620 0.146588
\(872\) 8.27993 0.280394
\(873\) −72.6379 −2.45842
\(874\) −34.9328 −1.18162
\(875\) −14.7662 −0.499188
\(876\) −31.9959 −1.08104
\(877\) 34.9189 1.17913 0.589564 0.807722i \(-0.299300\pi\)
0.589564 + 0.807722i \(0.299300\pi\)
\(878\) 67.5030 2.27812
\(879\) −86.6745 −2.92346
\(880\) 10.1380 0.341753
\(881\) −48.8077 −1.64437 −0.822187 0.569217i \(-0.807246\pi\)
−0.822187 + 0.569217i \(0.807246\pi\)
\(882\) 54.7316 1.84291
\(883\) 18.5946 0.625757 0.312879 0.949793i \(-0.398707\pi\)
0.312879 + 0.949793i \(0.398707\pi\)
\(884\) −4.89731 −0.164714
\(885\) −43.6357 −1.46680
\(886\) 70.0042 2.35184
\(887\) 4.39004 0.147403 0.0737016 0.997280i \(-0.476519\pi\)
0.0737016 + 0.997280i \(0.476519\pi\)
\(888\) −11.1397 −0.373825
\(889\) 6.49013 0.217672
\(890\) −26.2307 −0.879256
\(891\) 14.5815 0.488497
\(892\) 53.4962 1.79118
\(893\) 31.7998 1.06414
\(894\) 118.919 3.97724
\(895\) 1.87167 0.0625629
\(896\) −9.35282 −0.312456
\(897\) −21.2911 −0.710890
\(898\) 46.3493 1.54670
\(899\) −13.0372 −0.434816
\(900\) −49.2373 −1.64124
\(901\) 7.29570 0.243055
\(902\) −37.7483 −1.25688
\(903\) −17.4582 −0.580974
\(904\) −1.74488 −0.0580339
\(905\) −27.2115 −0.904542
\(906\) −61.8580 −2.05510
\(907\) 49.8365 1.65480 0.827398 0.561616i \(-0.189820\pi\)
0.827398 + 0.561616i \(0.189820\pi\)
\(908\) −6.70662 −0.222567
\(909\) −25.1150 −0.833011
\(910\) −7.27775 −0.241255
\(911\) 40.5300 1.34282 0.671409 0.741087i \(-0.265690\pi\)
0.671409 + 0.741087i \(0.265690\pi\)
\(912\) 42.7513 1.41564
\(913\) −3.88617 −0.128613
\(914\) 7.73802 0.255951
\(915\) 28.3818 0.938273
\(916\) 17.8412 0.589490
\(917\) −22.7922 −0.752663
\(918\) 15.4685 0.510535
\(919\) −9.71693 −0.320532 −0.160266 0.987074i \(-0.551235\pi\)
−0.160266 + 0.987074i \(0.551235\pi\)
\(920\) −3.13281 −0.103286
\(921\) −86.5280 −2.85120
\(922\) 0.895634 0.0294961
\(923\) −21.7655 −0.716419
\(924\) −30.5132 −1.00381
\(925\) −18.0771 −0.594370
\(926\) 42.5578 1.39854
\(927\) 8.55806 0.281083
\(928\) −64.4842 −2.11680
\(929\) −50.6367 −1.66134 −0.830669 0.556767i \(-0.812042\pi\)
−0.830669 + 0.556767i \(0.812042\pi\)
\(930\) 11.1751 0.366445
\(931\) 22.3129 0.731275
\(932\) 59.6633 1.95434
\(933\) 0.982612 0.0321693
\(934\) 66.5334 2.17704
\(935\) 3.26784 0.106870
\(936\) −8.99984 −0.294169
\(937\) 40.4166 1.32035 0.660177 0.751110i \(-0.270481\pi\)
0.660177 + 0.751110i \(0.270481\pi\)
\(938\) 6.62166 0.216205
\(939\) 68.7287 2.24288
\(940\) 17.9590 0.585758
\(941\) −21.1536 −0.689589 −0.344795 0.938678i \(-0.612051\pi\)
−0.344795 + 0.938678i \(0.612051\pi\)
\(942\) −43.8674 −1.42928
\(943\) −21.8961 −0.713036
\(944\) −41.3570 −1.34605
\(945\) 12.4849 0.406134
\(946\) −24.2002 −0.786815
\(947\) 21.2570 0.690761 0.345380 0.938463i \(-0.387750\pi\)
0.345380 + 0.938463i \(0.387750\pi\)
\(948\) 23.6307 0.767490
\(949\) −9.49048 −0.308074
\(950\) −36.9584 −1.19909
\(951\) −89.4813 −2.90163
\(952\) −1.19031 −0.0385782
\(953\) 3.38315 0.109591 0.0547955 0.998498i \(-0.482549\pi\)
0.0547955 + 0.998498i \(0.482549\pi\)
\(954\) 84.4310 2.73355
\(955\) −4.07364 −0.131820
\(956\) −52.5609 −1.69994
\(957\) −68.0491 −2.19971
\(958\) 51.6756 1.66956
\(959\) −11.4429 −0.369509
\(960\) 34.9637 1.12845
\(961\) −28.3375 −0.914111
\(962\) −20.8078 −0.670870
\(963\) −92.2047 −2.97125
\(964\) 1.38343 0.0445573
\(965\) 22.0149 0.708686
\(966\) −32.5881 −1.04851
\(967\) −31.4204 −1.01041 −0.505206 0.862999i \(-0.668583\pi\)
−0.505206 + 0.862999i \(0.668583\pi\)
\(968\) 1.97264 0.0634029
\(969\) 13.7802 0.442685
\(970\) −30.7922 −0.988677
\(971\) 23.2615 0.746496 0.373248 0.927732i \(-0.378244\pi\)
0.373248 + 0.927732i \(0.378244\pi\)
\(972\) −18.0070 −0.577573
\(973\) −27.8043 −0.891365
\(974\) −2.03376 −0.0651657
\(975\) −22.5257 −0.721400
\(976\) 26.8996 0.861036
\(977\) 29.5856 0.946526 0.473263 0.880921i \(-0.343076\pi\)
0.473263 + 0.880921i \(0.343076\pi\)
\(978\) 123.316 3.94321
\(979\) −32.6208 −1.04256
\(980\) 12.6012 0.402532
\(981\) −57.9774 −1.85108
\(982\) 59.7129 1.90552
\(983\) −24.6121 −0.785005 −0.392503 0.919751i \(-0.628391\pi\)
−0.392503 + 0.919751i \(0.628391\pi\)
\(984\) −14.2756 −0.455089
\(985\) 18.6696 0.594862
\(986\) −16.7168 −0.532370
\(987\) 29.6654 0.944261
\(988\) −23.1052 −0.735074
\(989\) −14.0374 −0.446365
\(990\) 37.8177 1.20193
\(991\) 53.8035 1.70913 0.854563 0.519348i \(-0.173825\pi\)
0.854563 + 0.519348i \(0.173825\pi\)
\(992\) 13.1694 0.418128
\(993\) 70.2001 2.22773
\(994\) −33.3141 −1.05666
\(995\) 10.1527 0.321861
\(996\) −9.25498 −0.293255
\(997\) −15.2141 −0.481834 −0.240917 0.970546i \(-0.577448\pi\)
−0.240917 + 0.970546i \(0.577448\pi\)
\(998\) 69.6796 2.20567
\(999\) 35.6956 1.12936
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 6001.2.a.a.1.20 113
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.a.1.20 113 1.1 even 1 trivial