Properties

Label 6010.2.a.f.1.2
Level $6010$
Weight $2$
Character 6010.1
Self dual yes
Analytic conductor $47.990$
Analytic rank $1$
Dimension $22$
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] = [6010,2,Mod(1,6010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6010, 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("6010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6010.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: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 6010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.13304 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.13304 q^{6} -3.32735 q^{7} +1.00000 q^{8} +6.81597 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.13304 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.13304 q^{6} -3.32735 q^{7} +1.00000 q^{8} +6.81597 q^{9} -1.00000 q^{10} -2.28351 q^{11} -3.13304 q^{12} -5.71900 q^{13} -3.32735 q^{14} +3.13304 q^{15} +1.00000 q^{16} -2.86619 q^{17} +6.81597 q^{18} +7.01791 q^{19} -1.00000 q^{20} +10.4247 q^{21} -2.28351 q^{22} +5.35441 q^{23} -3.13304 q^{24} +1.00000 q^{25} -5.71900 q^{26} -11.9556 q^{27} -3.32735 q^{28} +7.71402 q^{29} +3.13304 q^{30} +5.44874 q^{31} +1.00000 q^{32} +7.15433 q^{33} -2.86619 q^{34} +3.32735 q^{35} +6.81597 q^{36} +2.29615 q^{37} +7.01791 q^{38} +17.9179 q^{39} -1.00000 q^{40} -5.44074 q^{41} +10.4247 q^{42} -5.84523 q^{43} -2.28351 q^{44} -6.81597 q^{45} +5.35441 q^{46} -6.79959 q^{47} -3.13304 q^{48} +4.07127 q^{49} +1.00000 q^{50} +8.97991 q^{51} -5.71900 q^{52} +4.78179 q^{53} -11.9556 q^{54} +2.28351 q^{55} -3.32735 q^{56} -21.9874 q^{57} +7.71402 q^{58} +12.6266 q^{59} +3.13304 q^{60} +4.57895 q^{61} +5.44874 q^{62} -22.6791 q^{63} +1.00000 q^{64} +5.71900 q^{65} +7.15433 q^{66} -1.95789 q^{67} -2.86619 q^{68} -16.7756 q^{69} +3.32735 q^{70} +4.10993 q^{71} +6.81597 q^{72} -5.81595 q^{73} +2.29615 q^{74} -3.13304 q^{75} +7.01791 q^{76} +7.59804 q^{77} +17.9179 q^{78} +6.18394 q^{79} -1.00000 q^{80} +17.0095 q^{81} -5.44074 q^{82} +4.12859 q^{83} +10.4247 q^{84} +2.86619 q^{85} -5.84523 q^{86} -24.1684 q^{87} -2.28351 q^{88} -16.4434 q^{89} -6.81597 q^{90} +19.0291 q^{91} +5.35441 q^{92} -17.0711 q^{93} -6.79959 q^{94} -7.01791 q^{95} -3.13304 q^{96} -5.84681 q^{97} +4.07127 q^{98} -15.5643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 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
\(3\) −3.13304 −1.80886 −0.904432 0.426618i \(-0.859705\pi\)
−0.904432 + 0.426618i \(0.859705\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −3.13304 −1.27906
\(7\) −3.32735 −1.25762 −0.628810 0.777559i \(-0.716458\pi\)
−0.628810 + 0.777559i \(0.716458\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.81597 2.27199
\(10\) −1.00000 −0.316228
\(11\) −2.28351 −0.688504 −0.344252 0.938877i \(-0.611867\pi\)
−0.344252 + 0.938877i \(0.611867\pi\)
\(12\) −3.13304 −0.904432
\(13\) −5.71900 −1.58617 −0.793083 0.609114i \(-0.791525\pi\)
−0.793083 + 0.609114i \(0.791525\pi\)
\(14\) −3.32735 −0.889272
\(15\) 3.13304 0.808949
\(16\) 1.00000 0.250000
\(17\) −2.86619 −0.695154 −0.347577 0.937651i \(-0.612996\pi\)
−0.347577 + 0.937651i \(0.612996\pi\)
\(18\) 6.81597 1.60654
\(19\) 7.01791 1.61002 0.805010 0.593262i \(-0.202160\pi\)
0.805010 + 0.593262i \(0.202160\pi\)
\(20\) −1.00000 −0.223607
\(21\) 10.4247 2.27486
\(22\) −2.28351 −0.486846
\(23\) 5.35441 1.11647 0.558236 0.829682i \(-0.311478\pi\)
0.558236 + 0.829682i \(0.311478\pi\)
\(24\) −3.13304 −0.639530
\(25\) 1.00000 0.200000
\(26\) −5.71900 −1.12159
\(27\) −11.9556 −2.30085
\(28\) −3.32735 −0.628810
\(29\) 7.71402 1.43246 0.716229 0.697866i \(-0.245867\pi\)
0.716229 + 0.697866i \(0.245867\pi\)
\(30\) 3.13304 0.572013
\(31\) 5.44874 0.978622 0.489311 0.872109i \(-0.337248\pi\)
0.489311 + 0.872109i \(0.337248\pi\)
\(32\) 1.00000 0.176777
\(33\) 7.15433 1.24541
\(34\) −2.86619 −0.491548
\(35\) 3.32735 0.562425
\(36\) 6.81597 1.13599
\(37\) 2.29615 0.377484 0.188742 0.982027i \(-0.439559\pi\)
0.188742 + 0.982027i \(0.439559\pi\)
\(38\) 7.01791 1.13846
\(39\) 17.9179 2.86916
\(40\) −1.00000 −0.158114
\(41\) −5.44074 −0.849700 −0.424850 0.905264i \(-0.639673\pi\)
−0.424850 + 0.905264i \(0.639673\pi\)
\(42\) 10.4247 1.60857
\(43\) −5.84523 −0.891389 −0.445694 0.895185i \(-0.647043\pi\)
−0.445694 + 0.895185i \(0.647043\pi\)
\(44\) −2.28351 −0.344252
\(45\) −6.81597 −1.01606
\(46\) 5.35441 0.789465
\(47\) −6.79959 −0.991823 −0.495911 0.868373i \(-0.665166\pi\)
−0.495911 + 0.868373i \(0.665166\pi\)
\(48\) −3.13304 −0.452216
\(49\) 4.07127 0.581610
\(50\) 1.00000 0.141421
\(51\) 8.97991 1.25744
\(52\) −5.71900 −0.793083
\(53\) 4.78179 0.656829 0.328414 0.944534i \(-0.393486\pi\)
0.328414 + 0.944534i \(0.393486\pi\)
\(54\) −11.9556 −1.62695
\(55\) 2.28351 0.307908
\(56\) −3.32735 −0.444636
\(57\) −21.9874 −2.91231
\(58\) 7.71402 1.01290
\(59\) 12.6266 1.64385 0.821925 0.569596i \(-0.192900\pi\)
0.821925 + 0.569596i \(0.192900\pi\)
\(60\) 3.13304 0.404474
\(61\) 4.57895 0.586275 0.293137 0.956070i \(-0.405301\pi\)
0.293137 + 0.956070i \(0.405301\pi\)
\(62\) 5.44874 0.691990
\(63\) −22.6791 −2.85730
\(64\) 1.00000 0.125000
\(65\) 5.71900 0.709355
\(66\) 7.15433 0.880638
\(67\) −1.95789 −0.239194 −0.119597 0.992822i \(-0.538160\pi\)
−0.119597 + 0.992822i \(0.538160\pi\)
\(68\) −2.86619 −0.347577
\(69\) −16.7756 −2.01955
\(70\) 3.32735 0.397695
\(71\) 4.10993 0.487759 0.243879 0.969806i \(-0.421580\pi\)
0.243879 + 0.969806i \(0.421580\pi\)
\(72\) 6.81597 0.803269
\(73\) −5.81595 −0.680705 −0.340353 0.940298i \(-0.610546\pi\)
−0.340353 + 0.940298i \(0.610546\pi\)
\(74\) 2.29615 0.266922
\(75\) −3.13304 −0.361773
\(76\) 7.01791 0.805010
\(77\) 7.59804 0.865877
\(78\) 17.9179 2.02880
\(79\) 6.18394 0.695747 0.347874 0.937541i \(-0.386904\pi\)
0.347874 + 0.937541i \(0.386904\pi\)
\(80\) −1.00000 −0.111803
\(81\) 17.0095 1.88994
\(82\) −5.44074 −0.600829
\(83\) 4.12859 0.453172 0.226586 0.973991i \(-0.427244\pi\)
0.226586 + 0.973991i \(0.427244\pi\)
\(84\) 10.4247 1.13743
\(85\) 2.86619 0.310882
\(86\) −5.84523 −0.630307
\(87\) −24.1684 −2.59112
\(88\) −2.28351 −0.243423
\(89\) −16.4434 −1.74300 −0.871500 0.490395i \(-0.836853\pi\)
−0.871500 + 0.490395i \(0.836853\pi\)
\(90\) −6.81597 −0.718466
\(91\) 19.0291 1.99479
\(92\) 5.35441 0.558236
\(93\) −17.0711 −1.77019
\(94\) −6.79959 −0.701325
\(95\) −7.01791 −0.720022
\(96\) −3.13304 −0.319765
\(97\) −5.84681 −0.593653 −0.296827 0.954931i \(-0.595928\pi\)
−0.296827 + 0.954931i \(0.595928\pi\)
\(98\) 4.07127 0.411260
\(99\) −15.5643 −1.56427
\(100\) 1.00000 0.100000
\(101\) −12.4032 −1.23417 −0.617083 0.786898i \(-0.711686\pi\)
−0.617083 + 0.786898i \(0.711686\pi\)
\(102\) 8.97991 0.889144
\(103\) 11.1019 1.09390 0.546950 0.837165i \(-0.315789\pi\)
0.546950 + 0.837165i \(0.315789\pi\)
\(104\) −5.71900 −0.560794
\(105\) −10.4247 −1.01735
\(106\) 4.78179 0.464448
\(107\) 5.54492 0.536048 0.268024 0.963412i \(-0.413629\pi\)
0.268024 + 0.963412i \(0.413629\pi\)
\(108\) −11.9556 −1.15043
\(109\) −3.08254 −0.295254 −0.147627 0.989043i \(-0.547163\pi\)
−0.147627 + 0.989043i \(0.547163\pi\)
\(110\) 2.28351 0.217724
\(111\) −7.19393 −0.682818
\(112\) −3.32735 −0.314405
\(113\) 14.1167 1.32799 0.663995 0.747737i \(-0.268860\pi\)
0.663995 + 0.747737i \(0.268860\pi\)
\(114\) −21.9874 −2.05931
\(115\) −5.35441 −0.499301
\(116\) 7.71402 0.716229
\(117\) −38.9805 −3.60375
\(118\) 12.6266 1.16238
\(119\) 9.53684 0.874240
\(120\) 3.13304 0.286006
\(121\) −5.78559 −0.525963
\(122\) 4.57895 0.414559
\(123\) 17.0461 1.53699
\(124\) 5.44874 0.489311
\(125\) −1.00000 −0.0894427
\(126\) −22.6791 −2.02042
\(127\) −7.80540 −0.692617 −0.346309 0.938121i \(-0.612565\pi\)
−0.346309 + 0.938121i \(0.612565\pi\)
\(128\) 1.00000 0.0883883
\(129\) 18.3134 1.61240
\(130\) 5.71900 0.501590
\(131\) −14.3412 −1.25300 −0.626498 0.779423i \(-0.715512\pi\)
−0.626498 + 0.779423i \(0.715512\pi\)
\(132\) 7.15433 0.622705
\(133\) −23.3511 −2.02479
\(134\) −1.95789 −0.169136
\(135\) 11.9556 1.02897
\(136\) −2.86619 −0.245774
\(137\) 5.65409 0.483062 0.241531 0.970393i \(-0.422351\pi\)
0.241531 + 0.970393i \(0.422351\pi\)
\(138\) −16.7756 −1.42803
\(139\) −14.1896 −1.20355 −0.601773 0.798667i \(-0.705539\pi\)
−0.601773 + 0.798667i \(0.705539\pi\)
\(140\) 3.32735 0.281213
\(141\) 21.3034 1.79407
\(142\) 4.10993 0.344897
\(143\) 13.0594 1.09208
\(144\) 6.81597 0.567997
\(145\) −7.71402 −0.640614
\(146\) −5.81595 −0.481331
\(147\) −12.7555 −1.05205
\(148\) 2.29615 0.188742
\(149\) −14.2981 −1.17135 −0.585675 0.810546i \(-0.699170\pi\)
−0.585675 + 0.810546i \(0.699170\pi\)
\(150\) −3.13304 −0.255812
\(151\) 2.17667 0.177135 0.0885675 0.996070i \(-0.471771\pi\)
0.0885675 + 0.996070i \(0.471771\pi\)
\(152\) 7.01791 0.569228
\(153\) −19.5359 −1.57938
\(154\) 7.59804 0.612267
\(155\) −5.44874 −0.437653
\(156\) 17.9179 1.43458
\(157\) 4.36210 0.348133 0.174067 0.984734i \(-0.444309\pi\)
0.174067 + 0.984734i \(0.444309\pi\)
\(158\) 6.18394 0.491968
\(159\) −14.9815 −1.18811
\(160\) −1.00000 −0.0790569
\(161\) −17.8160 −1.40410
\(162\) 17.0095 1.33639
\(163\) 17.5782 1.37683 0.688414 0.725318i \(-0.258307\pi\)
0.688414 + 0.725318i \(0.258307\pi\)
\(164\) −5.44074 −0.424850
\(165\) −7.15433 −0.556964
\(166\) 4.12859 0.320441
\(167\) 15.3337 1.18656 0.593279 0.804997i \(-0.297833\pi\)
0.593279 + 0.804997i \(0.297833\pi\)
\(168\) 10.4247 0.804286
\(169\) 19.7070 1.51592
\(170\) 2.86619 0.219827
\(171\) 47.8338 3.65795
\(172\) −5.84523 −0.445694
\(173\) 1.04475 0.0794310 0.0397155 0.999211i \(-0.487355\pi\)
0.0397155 + 0.999211i \(0.487355\pi\)
\(174\) −24.1684 −1.83220
\(175\) −3.32735 −0.251524
\(176\) −2.28351 −0.172126
\(177\) −39.5598 −2.97350
\(178\) −16.4434 −1.23249
\(179\) 6.91419 0.516791 0.258396 0.966039i \(-0.416806\pi\)
0.258396 + 0.966039i \(0.416806\pi\)
\(180\) −6.81597 −0.508032
\(181\) 1.62026 0.120433 0.0602167 0.998185i \(-0.480821\pi\)
0.0602167 + 0.998185i \(0.480821\pi\)
\(182\) 19.0291 1.41053
\(183\) −14.3461 −1.06049
\(184\) 5.35441 0.394732
\(185\) −2.29615 −0.168816
\(186\) −17.0711 −1.25172
\(187\) 6.54498 0.478616
\(188\) −6.79959 −0.495911
\(189\) 39.7805 2.89360
\(190\) −7.01791 −0.509133
\(191\) −22.0018 −1.59199 −0.795996 0.605302i \(-0.793052\pi\)
−0.795996 + 0.605302i \(0.793052\pi\)
\(192\) −3.13304 −0.226108
\(193\) −1.66682 −0.119981 −0.0599903 0.998199i \(-0.519107\pi\)
−0.0599903 + 0.998199i \(0.519107\pi\)
\(194\) −5.84681 −0.419776
\(195\) −17.9179 −1.28313
\(196\) 4.07127 0.290805
\(197\) 14.4823 1.03182 0.515911 0.856642i \(-0.327454\pi\)
0.515911 + 0.856642i \(0.327454\pi\)
\(198\) −15.5643 −1.10611
\(199\) −6.58139 −0.466542 −0.233271 0.972412i \(-0.574943\pi\)
−0.233271 + 0.972412i \(0.574943\pi\)
\(200\) 1.00000 0.0707107
\(201\) 6.13416 0.432670
\(202\) −12.4032 −0.872688
\(203\) −25.6673 −1.80149
\(204\) 8.97991 0.628720
\(205\) 5.44074 0.379997
\(206\) 11.1019 0.773504
\(207\) 36.4955 2.53661
\(208\) −5.71900 −0.396541
\(209\) −16.0255 −1.10850
\(210\) −10.4247 −0.719375
\(211\) −20.5347 −1.41366 −0.706832 0.707381i \(-0.749876\pi\)
−0.706832 + 0.707381i \(0.749876\pi\)
\(212\) 4.78179 0.328414
\(213\) −12.8766 −0.882289
\(214\) 5.54492 0.379043
\(215\) 5.84523 0.398641
\(216\) −11.9556 −0.813475
\(217\) −18.1299 −1.23074
\(218\) −3.08254 −0.208776
\(219\) 18.2216 1.23130
\(220\) 2.28351 0.153954
\(221\) 16.3918 1.10263
\(222\) −7.19393 −0.482825
\(223\) 4.44359 0.297565 0.148782 0.988870i \(-0.452465\pi\)
0.148782 + 0.988870i \(0.452465\pi\)
\(224\) −3.32735 −0.222318
\(225\) 6.81597 0.454398
\(226\) 14.1167 0.939031
\(227\) −13.4043 −0.889673 −0.444836 0.895612i \(-0.646738\pi\)
−0.444836 + 0.895612i \(0.646738\pi\)
\(228\) −21.9874 −1.45615
\(229\) −20.5573 −1.35846 −0.679231 0.733925i \(-0.737687\pi\)
−0.679231 + 0.733925i \(0.737687\pi\)
\(230\) −5.35441 −0.353059
\(231\) −23.8050 −1.56625
\(232\) 7.71402 0.506450
\(233\) −24.1978 −1.58525 −0.792626 0.609708i \(-0.791287\pi\)
−0.792626 + 0.609708i \(0.791287\pi\)
\(234\) −38.9805 −2.54824
\(235\) 6.79959 0.443557
\(236\) 12.6266 0.821925
\(237\) −19.3745 −1.25851
\(238\) 9.53684 0.618181
\(239\) −14.5154 −0.938926 −0.469463 0.882952i \(-0.655552\pi\)
−0.469463 + 0.882952i \(0.655552\pi\)
\(240\) 3.13304 0.202237
\(241\) 18.5561 1.19530 0.597652 0.801756i \(-0.296101\pi\)
0.597652 + 0.801756i \(0.296101\pi\)
\(242\) −5.78559 −0.371912
\(243\) −17.4247 −1.11780
\(244\) 4.57895 0.293137
\(245\) −4.07127 −0.260104
\(246\) 17.0461 1.08682
\(247\) −40.1354 −2.55376
\(248\) 5.44874 0.345995
\(249\) −12.9351 −0.819727
\(250\) −1.00000 −0.0632456
\(251\) 25.3790 1.60191 0.800955 0.598724i \(-0.204325\pi\)
0.800955 + 0.598724i \(0.204325\pi\)
\(252\) −22.6791 −1.42865
\(253\) −12.2268 −0.768695
\(254\) −7.80540 −0.489754
\(255\) −8.97991 −0.562344
\(256\) 1.00000 0.0625000
\(257\) −4.41001 −0.275089 −0.137544 0.990496i \(-0.543921\pi\)
−0.137544 + 0.990496i \(0.543921\pi\)
\(258\) 18.3134 1.14014
\(259\) −7.64009 −0.474732
\(260\) 5.71900 0.354677
\(261\) 52.5785 3.25453
\(262\) −14.3412 −0.886002
\(263\) 5.99193 0.369478 0.184739 0.982788i \(-0.440856\pi\)
0.184739 + 0.982788i \(0.440856\pi\)
\(264\) 7.15433 0.440319
\(265\) −4.78179 −0.293743
\(266\) −23.3511 −1.43175
\(267\) 51.5180 3.15285
\(268\) −1.95789 −0.119597
\(269\) 8.90076 0.542689 0.271345 0.962482i \(-0.412532\pi\)
0.271345 + 0.962482i \(0.412532\pi\)
\(270\) 11.9556 0.727594
\(271\) −32.0806 −1.94876 −0.974379 0.224914i \(-0.927790\pi\)
−0.974379 + 0.224914i \(0.927790\pi\)
\(272\) −2.86619 −0.173789
\(273\) −59.6191 −3.60831
\(274\) 5.65409 0.341576
\(275\) −2.28351 −0.137701
\(276\) −16.7756 −1.00977
\(277\) 1.74567 0.104887 0.0524436 0.998624i \(-0.483299\pi\)
0.0524436 + 0.998624i \(0.483299\pi\)
\(278\) −14.1896 −0.851036
\(279\) 37.1384 2.22342
\(280\) 3.32735 0.198847
\(281\) −28.8021 −1.71819 −0.859093 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(282\) 21.3034 1.26860
\(283\) 15.7280 0.934933 0.467467 0.884011i \(-0.345167\pi\)
0.467467 + 0.884011i \(0.345167\pi\)
\(284\) 4.10993 0.243879
\(285\) 21.9874 1.30242
\(286\) 13.0594 0.772218
\(287\) 18.1032 1.06860
\(288\) 6.81597 0.401635
\(289\) −8.78493 −0.516761
\(290\) −7.71402 −0.452983
\(291\) 18.3183 1.07384
\(292\) −5.81595 −0.340353
\(293\) −29.8634 −1.74464 −0.872320 0.488936i \(-0.837385\pi\)
−0.872320 + 0.488936i \(0.837385\pi\)
\(294\) −12.7555 −0.743914
\(295\) −12.6266 −0.735152
\(296\) 2.29615 0.133461
\(297\) 27.3007 1.58415
\(298\) −14.2981 −0.828269
\(299\) −30.6219 −1.77091
\(300\) −3.13304 −0.180886
\(301\) 19.4491 1.12103
\(302\) 2.17667 0.125253
\(303\) 38.8599 2.23244
\(304\) 7.01791 0.402505
\(305\) −4.57895 −0.262190
\(306\) −19.5359 −1.11679
\(307\) 32.5376 1.85702 0.928510 0.371307i \(-0.121090\pi\)
0.928510 + 0.371307i \(0.121090\pi\)
\(308\) 7.59804 0.432938
\(309\) −34.7826 −1.97872
\(310\) −5.44874 −0.309468
\(311\) 17.6527 1.00099 0.500495 0.865739i \(-0.333151\pi\)
0.500495 + 0.865739i \(0.333151\pi\)
\(312\) 17.9179 1.01440
\(313\) 13.2919 0.751301 0.375650 0.926761i \(-0.377419\pi\)
0.375650 + 0.926761i \(0.377419\pi\)
\(314\) 4.36210 0.246167
\(315\) 22.6791 1.27782
\(316\) 6.18394 0.347874
\(317\) 32.2538 1.81155 0.905777 0.423754i \(-0.139288\pi\)
0.905777 + 0.423754i \(0.139288\pi\)
\(318\) −14.9815 −0.840124
\(319\) −17.6150 −0.986252
\(320\) −1.00000 −0.0559017
\(321\) −17.3725 −0.969637
\(322\) −17.8160 −0.992847
\(323\) −20.1147 −1.11921
\(324\) 17.0095 0.944972
\(325\) −5.71900 −0.317233
\(326\) 17.5782 0.973564
\(327\) 9.65773 0.534073
\(328\) −5.44074 −0.300414
\(329\) 22.6246 1.24734
\(330\) −7.15433 −0.393833
\(331\) 13.8549 0.761535 0.380767 0.924671i \(-0.375660\pi\)
0.380767 + 0.924671i \(0.375660\pi\)
\(332\) 4.12859 0.226586
\(333\) 15.6505 0.857640
\(334\) 15.3337 0.839024
\(335\) 1.95789 0.106971
\(336\) 10.4247 0.568716
\(337\) −16.1211 −0.878174 −0.439087 0.898445i \(-0.644698\pi\)
−0.439087 + 0.898445i \(0.644698\pi\)
\(338\) 19.7070 1.07192
\(339\) −44.2283 −2.40215
\(340\) 2.86619 0.155441
\(341\) −12.4422 −0.673785
\(342\) 47.8338 2.58656
\(343\) 9.74492 0.526176
\(344\) −5.84523 −0.315154
\(345\) 16.7756 0.903168
\(346\) 1.04475 0.0561662
\(347\) −19.8396 −1.06505 −0.532523 0.846415i \(-0.678756\pi\)
−0.532523 + 0.846415i \(0.678756\pi\)
\(348\) −24.1684 −1.29556
\(349\) −6.98979 −0.374155 −0.187077 0.982345i \(-0.559901\pi\)
−0.187077 + 0.982345i \(0.559901\pi\)
\(350\) −3.32735 −0.177854
\(351\) 68.3740 3.64954
\(352\) −2.28351 −0.121711
\(353\) −35.8141 −1.90619 −0.953097 0.302665i \(-0.902124\pi\)
−0.953097 + 0.302665i \(0.902124\pi\)
\(354\) −39.5598 −2.10258
\(355\) −4.10993 −0.218132
\(356\) −16.4434 −0.871500
\(357\) −29.8793 −1.58138
\(358\) 6.91419 0.365427
\(359\) 8.32788 0.439528 0.219764 0.975553i \(-0.429471\pi\)
0.219764 + 0.975553i \(0.429471\pi\)
\(360\) −6.81597 −0.359233
\(361\) 30.2511 1.59216
\(362\) 1.62026 0.0851592
\(363\) 18.1265 0.951395
\(364\) 19.0291 0.997397
\(365\) 5.81595 0.304421
\(366\) −14.3461 −0.749880
\(367\) −16.5165 −0.862154 −0.431077 0.902315i \(-0.641866\pi\)
−0.431077 + 0.902315i \(0.641866\pi\)
\(368\) 5.35441 0.279118
\(369\) −37.0839 −1.93051
\(370\) −2.29615 −0.119371
\(371\) −15.9107 −0.826042
\(372\) −17.0711 −0.885097
\(373\) −23.4075 −1.21199 −0.605997 0.795467i \(-0.707226\pi\)
−0.605997 + 0.795467i \(0.707226\pi\)
\(374\) 6.54498 0.338433
\(375\) 3.13304 0.161790
\(376\) −6.79959 −0.350662
\(377\) −44.1165 −2.27211
\(378\) 39.7805 2.04609
\(379\) 3.29299 0.169150 0.0845748 0.996417i \(-0.473047\pi\)
0.0845748 + 0.996417i \(0.473047\pi\)
\(380\) −7.01791 −0.360011
\(381\) 24.4547 1.25285
\(382\) −22.0018 −1.12571
\(383\) 27.5083 1.40561 0.702805 0.711382i \(-0.251931\pi\)
0.702805 + 0.711382i \(0.251931\pi\)
\(384\) −3.13304 −0.159882
\(385\) −7.59804 −0.387232
\(386\) −1.66682 −0.0848390
\(387\) −39.8409 −2.02523
\(388\) −5.84681 −0.296827
\(389\) −4.63597 −0.235053 −0.117526 0.993070i \(-0.537496\pi\)
−0.117526 + 0.993070i \(0.537496\pi\)
\(390\) −17.9179 −0.907307
\(391\) −15.3468 −0.776120
\(392\) 4.07127 0.205630
\(393\) 44.9316 2.26650
\(394\) 14.4823 0.729608
\(395\) −6.18394 −0.311148
\(396\) −15.5643 −0.782136
\(397\) −30.8511 −1.54837 −0.774187 0.632957i \(-0.781841\pi\)
−0.774187 + 0.632957i \(0.781841\pi\)
\(398\) −6.58139 −0.329895
\(399\) 73.1599 3.66258
\(400\) 1.00000 0.0500000
\(401\) −5.81994 −0.290634 −0.145317 0.989385i \(-0.546420\pi\)
−0.145317 + 0.989385i \(0.546420\pi\)
\(402\) 6.13416 0.305944
\(403\) −31.1613 −1.55226
\(404\) −12.4032 −0.617083
\(405\) −17.0095 −0.845209
\(406\) −25.6673 −1.27384
\(407\) −5.24327 −0.259899
\(408\) 8.97991 0.444572
\(409\) −35.4794 −1.75435 −0.877173 0.480175i \(-0.840573\pi\)
−0.877173 + 0.480175i \(0.840573\pi\)
\(410\) 5.44074 0.268699
\(411\) −17.7145 −0.873793
\(412\) 11.1019 0.546950
\(413\) −42.0133 −2.06734
\(414\) 36.4955 1.79366
\(415\) −4.12859 −0.202665
\(416\) −5.71900 −0.280397
\(417\) 44.4567 2.17705
\(418\) −16.0255 −0.783831
\(419\) −5.20695 −0.254376 −0.127188 0.991879i \(-0.540595\pi\)
−0.127188 + 0.991879i \(0.540595\pi\)
\(420\) −10.4247 −0.508675
\(421\) 16.9532 0.826250 0.413125 0.910674i \(-0.364437\pi\)
0.413125 + 0.910674i \(0.364437\pi\)
\(422\) −20.5347 −0.999612
\(423\) −46.3458 −2.25341
\(424\) 4.78179 0.232224
\(425\) −2.86619 −0.139031
\(426\) −12.8766 −0.623873
\(427\) −15.2358 −0.737311
\(428\) 5.54492 0.268024
\(429\) −40.9156 −1.97543
\(430\) 5.84523 0.281882
\(431\) −25.6428 −1.23517 −0.617586 0.786504i \(-0.711889\pi\)
−0.617586 + 0.786504i \(0.711889\pi\)
\(432\) −11.9556 −0.575214
\(433\) −0.0124318 −0.000597433 0 −0.000298717 1.00000i \(-0.500095\pi\)
−0.000298717 1.00000i \(0.500095\pi\)
\(434\) −18.1299 −0.870262
\(435\) 24.1684 1.15878
\(436\) −3.08254 −0.147627
\(437\) 37.5768 1.79754
\(438\) 18.2216 0.870663
\(439\) −24.1016 −1.15031 −0.575154 0.818045i \(-0.695058\pi\)
−0.575154 + 0.818045i \(0.695058\pi\)
\(440\) 2.28351 0.108862
\(441\) 27.7496 1.32141
\(442\) 16.3918 0.779677
\(443\) −25.9745 −1.23409 −0.617043 0.786929i \(-0.711670\pi\)
−0.617043 + 0.786929i \(0.711670\pi\)
\(444\) −7.19393 −0.341409
\(445\) 16.4434 0.779494
\(446\) 4.44359 0.210410
\(447\) 44.7967 2.11881
\(448\) −3.32735 −0.157203
\(449\) −5.64460 −0.266385 −0.133193 0.991090i \(-0.542523\pi\)
−0.133193 + 0.991090i \(0.542523\pi\)
\(450\) 6.81597 0.321308
\(451\) 12.4240 0.585022
\(452\) 14.1167 0.663995
\(453\) −6.81961 −0.320413
\(454\) −13.4043 −0.629094
\(455\) −19.0291 −0.892099
\(456\) −21.9874 −1.02966
\(457\) −20.2448 −0.947010 −0.473505 0.880791i \(-0.657011\pi\)
−0.473505 + 0.880791i \(0.657011\pi\)
\(458\) −20.5573 −0.960578
\(459\) 34.2670 1.59945
\(460\) −5.35441 −0.249651
\(461\) −8.98189 −0.418328 −0.209164 0.977881i \(-0.567074\pi\)
−0.209164 + 0.977881i \(0.567074\pi\)
\(462\) −23.8050 −1.10751
\(463\) 13.7804 0.640428 0.320214 0.947345i \(-0.396245\pi\)
0.320214 + 0.947345i \(0.396245\pi\)
\(464\) 7.71402 0.358114
\(465\) 17.0711 0.791655
\(466\) −24.1978 −1.12094
\(467\) 21.2600 0.983794 0.491897 0.870653i \(-0.336304\pi\)
0.491897 + 0.870653i \(0.336304\pi\)
\(468\) −38.9805 −1.80187
\(469\) 6.51459 0.300816
\(470\) 6.79959 0.313642
\(471\) −13.6666 −0.629726
\(472\) 12.6266 0.581189
\(473\) 13.3476 0.613725
\(474\) −19.3745 −0.889902
\(475\) 7.01791 0.322004
\(476\) 9.53684 0.437120
\(477\) 32.5925 1.49231
\(478\) −14.5154 −0.663921
\(479\) 0.670853 0.0306521 0.0153260 0.999883i \(-0.495121\pi\)
0.0153260 + 0.999883i \(0.495121\pi\)
\(480\) 3.13304 0.143003
\(481\) −13.1317 −0.598753
\(482\) 18.5561 0.845207
\(483\) 55.8183 2.53982
\(484\) −5.78559 −0.262981
\(485\) 5.84681 0.265490
\(486\) −17.4247 −0.790402
\(487\) −0.120064 −0.00544063 −0.00272032 0.999996i \(-0.500866\pi\)
−0.00272032 + 0.999996i \(0.500866\pi\)
\(488\) 4.57895 0.207279
\(489\) −55.0732 −2.49049
\(490\) −4.07127 −0.183921
\(491\) −15.2734 −0.689280 −0.344640 0.938735i \(-0.611999\pi\)
−0.344640 + 0.938735i \(0.611999\pi\)
\(492\) 17.0461 0.768496
\(493\) −22.1099 −0.995779
\(494\) −40.1354 −1.80578
\(495\) 15.5643 0.699564
\(496\) 5.44874 0.244656
\(497\) −13.6752 −0.613415
\(498\) −12.9351 −0.579634
\(499\) −43.2431 −1.93583 −0.967914 0.251280i \(-0.919149\pi\)
−0.967914 + 0.251280i \(0.919149\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −48.0412 −2.14632
\(502\) 25.3790 1.13272
\(503\) −41.3190 −1.84232 −0.921161 0.389181i \(-0.872758\pi\)
−0.921161 + 0.389181i \(0.872758\pi\)
\(504\) −22.6791 −1.01021
\(505\) 12.4032 0.551936
\(506\) −12.2268 −0.543550
\(507\) −61.7428 −2.74209
\(508\) −7.80540 −0.346309
\(509\) 24.0420 1.06564 0.532822 0.846227i \(-0.321132\pi\)
0.532822 + 0.846227i \(0.321132\pi\)
\(510\) −8.97991 −0.397637
\(511\) 19.3517 0.856069
\(512\) 1.00000 0.0441942
\(513\) −83.9033 −3.70442
\(514\) −4.41001 −0.194517
\(515\) −11.1019 −0.489207
\(516\) 18.3134 0.806200
\(517\) 15.5269 0.682874
\(518\) −7.64009 −0.335686
\(519\) −3.27325 −0.143680
\(520\) 5.71900 0.250795
\(521\) −2.59240 −0.113575 −0.0567876 0.998386i \(-0.518086\pi\)
−0.0567876 + 0.998386i \(0.518086\pi\)
\(522\) 52.5785 2.30130
\(523\) −26.7581 −1.17005 −0.585025 0.811015i \(-0.698915\pi\)
−0.585025 + 0.811015i \(0.698915\pi\)
\(524\) −14.3412 −0.626498
\(525\) 10.4247 0.454973
\(526\) 5.99193 0.261260
\(527\) −15.6171 −0.680293
\(528\) 7.15433 0.311352
\(529\) 5.66972 0.246510
\(530\) −4.78179 −0.207708
\(531\) 86.0628 3.73481
\(532\) −23.3511 −1.01240
\(533\) 31.1156 1.34777
\(534\) 51.5180 2.22940
\(535\) −5.54492 −0.239728
\(536\) −1.95789 −0.0845680
\(537\) −21.6625 −0.934805
\(538\) 8.90076 0.383739
\(539\) −9.29678 −0.400441
\(540\) 11.9556 0.514487
\(541\) −5.82473 −0.250425 −0.125212 0.992130i \(-0.539961\pi\)
−0.125212 + 0.992130i \(0.539961\pi\)
\(542\) −32.0806 −1.37798
\(543\) −5.07636 −0.217847
\(544\) −2.86619 −0.122887
\(545\) 3.08254 0.132041
\(546\) −59.6191 −2.55146
\(547\) 26.4717 1.13185 0.565925 0.824457i \(-0.308519\pi\)
0.565925 + 0.824457i \(0.308519\pi\)
\(548\) 5.65409 0.241531
\(549\) 31.2100 1.33201
\(550\) −2.28351 −0.0973691
\(551\) 54.1363 2.30628
\(552\) −16.7756 −0.714017
\(553\) −20.5761 −0.874986
\(554\) 1.74567 0.0741665
\(555\) 7.19393 0.305366
\(556\) −14.1896 −0.601773
\(557\) 15.1208 0.640690 0.320345 0.947301i \(-0.396201\pi\)
0.320345 + 0.947301i \(0.396201\pi\)
\(558\) 37.1384 1.57219
\(559\) 33.4289 1.41389
\(560\) 3.32735 0.140606
\(561\) −20.5057 −0.865752
\(562\) −28.8021 −1.21494
\(563\) −13.6335 −0.574582 −0.287291 0.957843i \(-0.592755\pi\)
−0.287291 + 0.957843i \(0.592755\pi\)
\(564\) 21.3034 0.897036
\(565\) −14.1167 −0.593895
\(566\) 15.7280 0.661098
\(567\) −56.5966 −2.37683
\(568\) 4.10993 0.172449
\(569\) −0.398579 −0.0167093 −0.00835465 0.999965i \(-0.502659\pi\)
−0.00835465 + 0.999965i \(0.502659\pi\)
\(570\) 21.9874 0.920952
\(571\) −17.2304 −0.721069 −0.360535 0.932746i \(-0.617406\pi\)
−0.360535 + 0.932746i \(0.617406\pi\)
\(572\) 13.0594 0.546040
\(573\) 68.9325 2.87970
\(574\) 18.1032 0.755615
\(575\) 5.35441 0.223294
\(576\) 6.81597 0.283999
\(577\) 27.8512 1.15946 0.579729 0.814809i \(-0.303158\pi\)
0.579729 + 0.814809i \(0.303158\pi\)
\(578\) −8.78493 −0.365405
\(579\) 5.22223 0.217028
\(580\) −7.71402 −0.320307
\(581\) −13.7373 −0.569919
\(582\) 18.3183 0.759318
\(583\) −10.9193 −0.452229
\(584\) −5.81595 −0.240666
\(585\) 38.9805 1.61165
\(586\) −29.8634 −1.23365
\(587\) 32.5195 1.34222 0.671112 0.741356i \(-0.265817\pi\)
0.671112 + 0.741356i \(0.265817\pi\)
\(588\) −12.7555 −0.526027
\(589\) 38.2388 1.57560
\(590\) −12.6266 −0.519831
\(591\) −45.3737 −1.86643
\(592\) 2.29615 0.0943711
\(593\) −40.6760 −1.67037 −0.835183 0.549973i \(-0.814638\pi\)
−0.835183 + 0.549973i \(0.814638\pi\)
\(594\) 27.3007 1.12016
\(595\) −9.53684 −0.390972
\(596\) −14.2981 −0.585675
\(597\) 20.6198 0.843911
\(598\) −30.6219 −1.25222
\(599\) 25.9105 1.05868 0.529338 0.848411i \(-0.322440\pi\)
0.529338 + 0.848411i \(0.322440\pi\)
\(600\) −3.13304 −0.127906
\(601\) 1.00000 0.0407909
\(602\) 19.4491 0.792687
\(603\) −13.3449 −0.543447
\(604\) 2.17667 0.0885675
\(605\) 5.78559 0.235218
\(606\) 38.8599 1.57857
\(607\) 11.0759 0.449558 0.224779 0.974410i \(-0.427834\pi\)
0.224779 + 0.974410i \(0.427834\pi\)
\(608\) 7.01791 0.284614
\(609\) 80.4166 3.25865
\(610\) −4.57895 −0.185396
\(611\) 38.8869 1.57319
\(612\) −19.5359 −0.789691
\(613\) −42.3475 −1.71040 −0.855200 0.518298i \(-0.826566\pi\)
−0.855200 + 0.518298i \(0.826566\pi\)
\(614\) 32.5376 1.31311
\(615\) −17.0461 −0.687364
\(616\) 7.59804 0.306134
\(617\) −15.0284 −0.605020 −0.302510 0.953146i \(-0.597824\pi\)
−0.302510 + 0.953146i \(0.597824\pi\)
\(618\) −34.7826 −1.39916
\(619\) 32.7880 1.31786 0.658931 0.752203i \(-0.271009\pi\)
0.658931 + 0.752203i \(0.271009\pi\)
\(620\) −5.44874 −0.218827
\(621\) −64.0151 −2.56884
\(622\) 17.6527 0.707807
\(623\) 54.7131 2.19203
\(624\) 17.9179 0.717289
\(625\) 1.00000 0.0400000
\(626\) 13.2919 0.531250
\(627\) 50.2085 2.00513
\(628\) 4.36210 0.174067
\(629\) −6.58121 −0.262410
\(630\) 22.6791 0.903558
\(631\) 22.0176 0.876507 0.438253 0.898851i \(-0.355597\pi\)
0.438253 + 0.898851i \(0.355597\pi\)
\(632\) 6.18394 0.245984
\(633\) 64.3360 2.55713
\(634\) 32.2538 1.28096
\(635\) 7.80540 0.309748
\(636\) −14.9815 −0.594057
\(637\) −23.2836 −0.922530
\(638\) −17.6150 −0.697386
\(639\) 28.0131 1.10818
\(640\) −1.00000 −0.0395285
\(641\) 4.43149 0.175033 0.0875167 0.996163i \(-0.472107\pi\)
0.0875167 + 0.996163i \(0.472107\pi\)
\(642\) −17.3725 −0.685637
\(643\) 22.6179 0.891961 0.445981 0.895043i \(-0.352855\pi\)
0.445981 + 0.895043i \(0.352855\pi\)
\(644\) −17.8160 −0.702049
\(645\) −18.3134 −0.721088
\(646\) −20.1147 −0.791402
\(647\) 22.5137 0.885105 0.442552 0.896743i \(-0.354073\pi\)
0.442552 + 0.896743i \(0.354073\pi\)
\(648\) 17.0095 0.668196
\(649\) −28.8331 −1.13180
\(650\) −5.71900 −0.224318
\(651\) 56.8017 2.22623
\(652\) 17.5782 0.688414
\(653\) 22.1426 0.866508 0.433254 0.901272i \(-0.357365\pi\)
0.433254 + 0.901272i \(0.357365\pi\)
\(654\) 9.65773 0.377647
\(655\) 14.3412 0.560357
\(656\) −5.44074 −0.212425
\(657\) −39.6413 −1.54655
\(658\) 22.6246 0.882000
\(659\) 39.1211 1.52394 0.761972 0.647610i \(-0.224231\pi\)
0.761972 + 0.647610i \(0.224231\pi\)
\(660\) −7.15433 −0.278482
\(661\) 15.4960 0.602726 0.301363 0.953510i \(-0.402558\pi\)
0.301363 + 0.953510i \(0.402558\pi\)
\(662\) 13.8549 0.538486
\(663\) −51.3561 −1.99451
\(664\) 4.12859 0.160221
\(665\) 23.3511 0.905515
\(666\) 15.6505 0.606443
\(667\) 41.3040 1.59930
\(668\) 15.3337 0.593279
\(669\) −13.9220 −0.538254
\(670\) 1.95789 0.0756399
\(671\) −10.4561 −0.403652
\(672\) 10.4247 0.402143
\(673\) 42.3649 1.63305 0.816523 0.577313i \(-0.195899\pi\)
0.816523 + 0.577313i \(0.195899\pi\)
\(674\) −16.1211 −0.620963
\(675\) −11.9556 −0.460171
\(676\) 19.7070 0.757960
\(677\) 17.2004 0.661064 0.330532 0.943795i \(-0.392772\pi\)
0.330532 + 0.943795i \(0.392772\pi\)
\(678\) −44.2283 −1.69858
\(679\) 19.4544 0.746591
\(680\) 2.86619 0.109914
\(681\) 41.9962 1.60930
\(682\) −12.4422 −0.476438
\(683\) 19.2386 0.736145 0.368073 0.929797i \(-0.380018\pi\)
0.368073 + 0.929797i \(0.380018\pi\)
\(684\) 47.8338 1.82897
\(685\) −5.65409 −0.216032
\(686\) 9.74492 0.372063
\(687\) 64.4068 2.45727
\(688\) −5.84523 −0.222847
\(689\) −27.3470 −1.04184
\(690\) 16.7756 0.638636
\(691\) −8.28888 −0.315324 −0.157662 0.987493i \(-0.550396\pi\)
−0.157662 + 0.987493i \(0.550396\pi\)
\(692\) 1.04475 0.0397155
\(693\) 51.7880 1.96726
\(694\) −19.8396 −0.753102
\(695\) 14.1896 0.538243
\(696\) −24.1684 −0.916099
\(697\) 15.5942 0.590673
\(698\) −6.98979 −0.264567
\(699\) 75.8128 2.86750
\(700\) −3.32735 −0.125762
\(701\) −9.28449 −0.350670 −0.175335 0.984509i \(-0.556101\pi\)
−0.175335 + 0.984509i \(0.556101\pi\)
\(702\) 68.3740 2.58061
\(703\) 16.1142 0.607757
\(704\) −2.28351 −0.0860630
\(705\) −21.3034 −0.802334
\(706\) −35.8141 −1.34788
\(707\) 41.2699 1.55211
\(708\) −39.5598 −1.48675
\(709\) 51.4294 1.93147 0.965736 0.259528i \(-0.0835670\pi\)
0.965736 + 0.259528i \(0.0835670\pi\)
\(710\) −4.10993 −0.154243
\(711\) 42.1495 1.58073
\(712\) −16.4434 −0.616244
\(713\) 29.1748 1.09260
\(714\) −29.8793 −1.11821
\(715\) −13.0594 −0.488393
\(716\) 6.91419 0.258396
\(717\) 45.4775 1.69839
\(718\) 8.32788 0.310794
\(719\) −0.355781 −0.0132684 −0.00663420 0.999978i \(-0.502112\pi\)
−0.00663420 + 0.999978i \(0.502112\pi\)
\(720\) −6.81597 −0.254016
\(721\) −36.9398 −1.37571
\(722\) 30.2511 1.12583
\(723\) −58.1371 −2.16214
\(724\) 1.62026 0.0602167
\(725\) 7.71402 0.286491
\(726\) 18.1265 0.672738
\(727\) −28.8880 −1.07140 −0.535698 0.844410i \(-0.679951\pi\)
−0.535698 + 0.844410i \(0.679951\pi\)
\(728\) 19.0291 0.705266
\(729\) 3.56396 0.131998
\(730\) 5.81595 0.215258
\(731\) 16.7536 0.619653
\(732\) −14.3461 −0.530246
\(733\) 24.5263 0.905901 0.452951 0.891536i \(-0.350371\pi\)
0.452951 + 0.891536i \(0.350371\pi\)
\(734\) −16.5165 −0.609635
\(735\) 12.7555 0.470493
\(736\) 5.35441 0.197366
\(737\) 4.47086 0.164686
\(738\) −37.0839 −1.36508
\(739\) 24.4832 0.900627 0.450314 0.892870i \(-0.351312\pi\)
0.450314 + 0.892870i \(0.351312\pi\)
\(740\) −2.29615 −0.0844081
\(741\) 125.746 4.61940
\(742\) −15.9107 −0.584100
\(743\) 28.9324 1.06143 0.530713 0.847552i \(-0.321924\pi\)
0.530713 + 0.847552i \(0.321924\pi\)
\(744\) −17.0711 −0.625858
\(745\) 14.2981 0.523843
\(746\) −23.4075 −0.857009
\(747\) 28.1404 1.02960
\(748\) 6.54498 0.239308
\(749\) −18.4499 −0.674145
\(750\) 3.13304 0.114403
\(751\) −22.9311 −0.836769 −0.418384 0.908270i \(-0.637403\pi\)
−0.418384 + 0.908270i \(0.637403\pi\)
\(752\) −6.79959 −0.247956
\(753\) −79.5137 −2.89764
\(754\) −44.1165 −1.60663
\(755\) −2.17667 −0.0792172
\(756\) 39.7805 1.44680
\(757\) −7.74385 −0.281455 −0.140728 0.990048i \(-0.544944\pi\)
−0.140728 + 0.990048i \(0.544944\pi\)
\(758\) 3.29299 0.119607
\(759\) 38.3072 1.39046
\(760\) −7.01791 −0.254566
\(761\) −7.60887 −0.275821 −0.137911 0.990445i \(-0.544039\pi\)
−0.137911 + 0.990445i \(0.544039\pi\)
\(762\) 24.4547 0.885899
\(763\) 10.2567 0.371317
\(764\) −22.0018 −0.795996
\(765\) 19.5359 0.706321
\(766\) 27.5083 0.993917
\(767\) −72.2118 −2.60742
\(768\) −3.13304 −0.113054
\(769\) −54.7236 −1.97338 −0.986692 0.162600i \(-0.948012\pi\)
−0.986692 + 0.162600i \(0.948012\pi\)
\(770\) −7.59804 −0.273814
\(771\) 13.8168 0.497599
\(772\) −1.66682 −0.0599903
\(773\) −4.96234 −0.178483 −0.0892414 0.996010i \(-0.528444\pi\)
−0.0892414 + 0.996010i \(0.528444\pi\)
\(774\) −39.8409 −1.43205
\(775\) 5.44874 0.195724
\(776\) −5.84681 −0.209888
\(777\) 23.9368 0.858726
\(778\) −4.63597 −0.166208
\(779\) −38.1826 −1.36803
\(780\) −17.9179 −0.641563
\(781\) −9.38506 −0.335824
\(782\) −15.3468 −0.548800
\(783\) −92.2256 −3.29588
\(784\) 4.07127 0.145402
\(785\) −4.36210 −0.155690
\(786\) 44.9316 1.60266
\(787\) 11.2463 0.400887 0.200444 0.979705i \(-0.435762\pi\)
0.200444 + 0.979705i \(0.435762\pi\)
\(788\) 14.4823 0.515911
\(789\) −18.7730 −0.668336
\(790\) −6.18394 −0.220015
\(791\) −46.9713 −1.67011
\(792\) −15.5643 −0.553054
\(793\) −26.1870 −0.929929
\(794\) −30.8511 −1.09487
\(795\) 14.9815 0.531341
\(796\) −6.58139 −0.233271
\(797\) −2.65747 −0.0941324 −0.0470662 0.998892i \(-0.514987\pi\)
−0.0470662 + 0.998892i \(0.514987\pi\)
\(798\) 73.1599 2.58983
\(799\) 19.4890 0.689470
\(800\) 1.00000 0.0353553
\(801\) −112.078 −3.96008
\(802\) −5.81994 −0.205509
\(803\) 13.2808 0.468668
\(804\) 6.13416 0.216335
\(805\) 17.8160 0.627932
\(806\) −31.1613 −1.09761
\(807\) −27.8865 −0.981651
\(808\) −12.4032 −0.436344
\(809\) 40.8239 1.43529 0.717645 0.696409i \(-0.245220\pi\)
0.717645 + 0.696409i \(0.245220\pi\)
\(810\) −17.0095 −0.597653
\(811\) 2.40839 0.0845701 0.0422850 0.999106i \(-0.486536\pi\)
0.0422850 + 0.999106i \(0.486536\pi\)
\(812\) −25.6673 −0.900744
\(813\) 100.510 3.52504
\(814\) −5.24327 −0.183777
\(815\) −17.5782 −0.615736
\(816\) 8.97991 0.314360
\(817\) −41.0213 −1.43515
\(818\) −35.4794 −1.24051
\(819\) 129.702 4.53215
\(820\) 5.44074 0.189999
\(821\) −41.9781 −1.46505 −0.732523 0.680742i \(-0.761657\pi\)
−0.732523 + 0.680742i \(0.761657\pi\)
\(822\) −17.7145 −0.617865
\(823\) −48.3360 −1.68489 −0.842443 0.538785i \(-0.818884\pi\)
−0.842443 + 0.538785i \(0.818884\pi\)
\(824\) 11.1019 0.386752
\(825\) 7.15433 0.249082
\(826\) −42.0133 −1.46183
\(827\) −12.2376 −0.425545 −0.212772 0.977102i \(-0.568249\pi\)
−0.212772 + 0.977102i \(0.568249\pi\)
\(828\) 36.4955 1.26831
\(829\) 43.1833 1.49982 0.749909 0.661541i \(-0.230097\pi\)
0.749909 + 0.661541i \(0.230097\pi\)
\(830\) −4.12859 −0.143306
\(831\) −5.46927 −0.189727
\(832\) −5.71900 −0.198271
\(833\) −11.6690 −0.404309
\(834\) 44.4567 1.53941
\(835\) −15.3337 −0.530645
\(836\) −16.0255 −0.554252
\(837\) −65.1429 −2.25167
\(838\) −5.20695 −0.179871
\(839\) −17.7217 −0.611821 −0.305911 0.952060i \(-0.598961\pi\)
−0.305911 + 0.952060i \(0.598961\pi\)
\(840\) −10.4247 −0.359688
\(841\) 30.5061 1.05193
\(842\) 16.9532 0.584247
\(843\) 90.2381 3.10797
\(844\) −20.5347 −0.706832
\(845\) −19.7070 −0.677940
\(846\) −46.3458 −1.59340
\(847\) 19.2507 0.661461
\(848\) 4.78179 0.164207
\(849\) −49.2766 −1.69117
\(850\) −2.86619 −0.0983097
\(851\) 12.2945 0.421451
\(852\) −12.8766 −0.441145
\(853\) −22.9308 −0.785134 −0.392567 0.919723i \(-0.628413\pi\)
−0.392567 + 0.919723i \(0.628413\pi\)
\(854\) −15.2358 −0.521358
\(855\) −47.8338 −1.63588
\(856\) 5.54492 0.189521
\(857\) −10.3690 −0.354197 −0.177099 0.984193i \(-0.556671\pi\)
−0.177099 + 0.984193i \(0.556671\pi\)
\(858\) −40.9156 −1.39684
\(859\) 4.79487 0.163599 0.0817994 0.996649i \(-0.473933\pi\)
0.0817994 + 0.996649i \(0.473933\pi\)
\(860\) 5.84523 0.199321
\(861\) −56.7183 −1.93295
\(862\) −25.6428 −0.873398
\(863\) −41.3420 −1.40730 −0.703649 0.710547i \(-0.748447\pi\)
−0.703649 + 0.710547i \(0.748447\pi\)
\(864\) −11.9556 −0.406737
\(865\) −1.04475 −0.0355226
\(866\) −0.0124318 −0.000422449 0
\(867\) 27.5236 0.934750
\(868\) −18.1299 −0.615368
\(869\) −14.1211 −0.479025
\(870\) 24.1684 0.819384
\(871\) 11.1972 0.379402
\(872\) −3.08254 −0.104388
\(873\) −39.8516 −1.34877
\(874\) 37.5768 1.27105
\(875\) 3.32735 0.112485
\(876\) 18.2216 0.615651
\(877\) −33.1687 −1.12003 −0.560013 0.828484i \(-0.689204\pi\)
−0.560013 + 0.828484i \(0.689204\pi\)
\(878\) −24.1016 −0.813391
\(879\) 93.5634 3.15581
\(880\) 2.28351 0.0769771
\(881\) 55.3045 1.86326 0.931628 0.363414i \(-0.118389\pi\)
0.931628 + 0.363414i \(0.118389\pi\)
\(882\) 27.7496 0.934379
\(883\) 37.0462 1.24671 0.623353 0.781941i \(-0.285770\pi\)
0.623353 + 0.781941i \(0.285770\pi\)
\(884\) 16.3918 0.551315
\(885\) 39.5598 1.32979
\(886\) −25.9745 −0.872631
\(887\) 15.4659 0.519293 0.259647 0.965704i \(-0.416394\pi\)
0.259647 + 0.965704i \(0.416394\pi\)
\(888\) −7.19393 −0.241413
\(889\) 25.9713 0.871050
\(890\) 16.4434 0.551185
\(891\) −38.8413 −1.30123
\(892\) 4.44359 0.148782
\(893\) −47.7189 −1.59685
\(894\) 44.7967 1.49823
\(895\) −6.91419 −0.231116
\(896\) −3.32735 −0.111159
\(897\) 95.9397 3.20333
\(898\) −5.64460 −0.188363
\(899\) 42.0317 1.40183
\(900\) 6.81597 0.227199
\(901\) −13.7055 −0.456597
\(902\) 12.4240 0.413673
\(903\) −60.9350 −2.02779
\(904\) 14.1167 0.469515
\(905\) −1.62026 −0.0538594
\(906\) −6.81961 −0.226566
\(907\) 41.4891 1.37762 0.688811 0.724941i \(-0.258133\pi\)
0.688811 + 0.724941i \(0.258133\pi\)
\(908\) −13.4043 −0.444836
\(909\) −84.5400 −2.80401
\(910\) −19.0291 −0.630809
\(911\) −44.6851 −1.48048 −0.740241 0.672341i \(-0.765289\pi\)
−0.740241 + 0.672341i \(0.765289\pi\)
\(912\) −21.9874 −0.728076
\(913\) −9.42768 −0.312011
\(914\) −20.2448 −0.669637
\(915\) 14.3461 0.474266
\(916\) −20.5573 −0.679231
\(917\) 47.7182 1.57579
\(918\) 34.2670 1.13098
\(919\) −22.0227 −0.726462 −0.363231 0.931699i \(-0.618326\pi\)
−0.363231 + 0.931699i \(0.618326\pi\)
\(920\) −5.35441 −0.176530
\(921\) −101.942 −3.35910
\(922\) −8.98189 −0.295803
\(923\) −23.5047 −0.773666
\(924\) −23.8050 −0.783126
\(925\) 2.29615 0.0754969
\(926\) 13.7804 0.452851
\(927\) 75.6700 2.48533
\(928\) 7.71402 0.253225
\(929\) 38.0273 1.24763 0.623817 0.781570i \(-0.285581\pi\)
0.623817 + 0.781570i \(0.285581\pi\)
\(930\) 17.0711 0.559785
\(931\) 28.5718 0.936403
\(932\) −24.1978 −0.792626
\(933\) −55.3066 −1.81066
\(934\) 21.2600 0.695647
\(935\) −6.54498 −0.214044
\(936\) −38.9805 −1.27412
\(937\) −30.6324 −1.00072 −0.500358 0.865818i \(-0.666798\pi\)
−0.500358 + 0.865818i \(0.666798\pi\)
\(938\) 6.51459 0.212709
\(939\) −41.6440 −1.35900
\(940\) 6.79959 0.221778
\(941\) −14.6502 −0.477584 −0.238792 0.971071i \(-0.576751\pi\)
−0.238792 + 0.971071i \(0.576751\pi\)
\(942\) −13.6666 −0.445283
\(943\) −29.1319 −0.948666
\(944\) 12.6266 0.410962
\(945\) −39.7805 −1.29406
\(946\) 13.3476 0.433969
\(947\) −6.59175 −0.214203 −0.107102 0.994248i \(-0.534157\pi\)
−0.107102 + 0.994248i \(0.534157\pi\)
\(948\) −19.3745 −0.629256
\(949\) 33.2614 1.07971
\(950\) 7.01791 0.227691
\(951\) −101.053 −3.27686
\(952\) 9.53684 0.309091
\(953\) 49.1037 1.59062 0.795312 0.606201i \(-0.207307\pi\)
0.795312 + 0.606201i \(0.207307\pi\)
\(954\) 32.5925 1.05522
\(955\) 22.0018 0.711961
\(956\) −14.5154 −0.469463
\(957\) 55.1887 1.78400
\(958\) 0.670853 0.0216743
\(959\) −18.8131 −0.607508
\(960\) 3.13304 0.101119
\(961\) −1.31125 −0.0422984
\(962\) −13.1317 −0.423382
\(963\) 37.7940 1.21789
\(964\) 18.5561 0.597652
\(965\) 1.66682 0.0536569
\(966\) 55.8183 1.79593
\(967\) 25.2387 0.811622 0.405811 0.913957i \(-0.366989\pi\)
0.405811 + 0.913957i \(0.366989\pi\)
\(968\) −5.78559 −0.185956
\(969\) 63.0202 2.02450
\(970\) 5.84681 0.187730
\(971\) 50.5542 1.62236 0.811181 0.584795i \(-0.198825\pi\)
0.811181 + 0.584795i \(0.198825\pi\)
\(972\) −17.4247 −0.558898
\(973\) 47.2138 1.51361
\(974\) −0.120064 −0.00384711
\(975\) 17.9179 0.573831
\(976\) 4.57895 0.146569
\(977\) −13.9373 −0.445895 −0.222947 0.974830i \(-0.571568\pi\)
−0.222947 + 0.974830i \(0.571568\pi\)
\(978\) −55.0732 −1.76105
\(979\) 37.5487 1.20006
\(980\) −4.07127 −0.130052
\(981\) −21.0105 −0.670813
\(982\) −15.2734 −0.487395
\(983\) −7.96064 −0.253905 −0.126952 0.991909i \(-0.540520\pi\)
−0.126952 + 0.991909i \(0.540520\pi\)
\(984\) 17.0461 0.543409
\(985\) −14.4823 −0.461445
\(986\) −22.1099 −0.704122
\(987\) −70.8840 −2.25626
\(988\) −40.1354 −1.27688
\(989\) −31.2977 −0.995211
\(990\) 15.5643 0.494666
\(991\) 46.1623 1.46639 0.733196 0.680017i \(-0.238028\pi\)
0.733196 + 0.680017i \(0.238028\pi\)
\(992\) 5.44874 0.172998
\(993\) −43.4081 −1.37751
\(994\) −13.6752 −0.433750
\(995\) 6.58139 0.208644
\(996\) −12.9351 −0.409863
\(997\) 29.6707 0.939681 0.469840 0.882751i \(-0.344311\pi\)
0.469840 + 0.882751i \(0.344311\pi\)
\(998\) −43.2431 −1.36884
\(999\) −27.4518 −0.868537
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 6010.2.a.f.1.2 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6010.2.a.f.1.2 22 1.1 even 1 trivial