Properties

Label 4006.2.a.g.1.40
Level $4006$
Weight $2$
Character 4006.1
Self dual yes
Analytic conductor $31.988$
Analytic rank $1$
Dimension $40$
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] = [4006,2,Mod(1,4006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4006, 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("4006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4006.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: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.40
Character \(\chi\) \(=\) 4006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.27981 q^{3} +1.00000 q^{4} -1.91132 q^{5} -3.27981 q^{6} +1.09804 q^{7} -1.00000 q^{8} +7.75714 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.27981 q^{3} +1.00000 q^{4} -1.91132 q^{5} -3.27981 q^{6} +1.09804 q^{7} -1.00000 q^{8} +7.75714 q^{9} +1.91132 q^{10} -3.44938 q^{11} +3.27981 q^{12} -2.45581 q^{13} -1.09804 q^{14} -6.26877 q^{15} +1.00000 q^{16} -5.97426 q^{17} -7.75714 q^{18} -1.07537 q^{19} -1.91132 q^{20} +3.60137 q^{21} +3.44938 q^{22} -5.86835 q^{23} -3.27981 q^{24} -1.34685 q^{25} +2.45581 q^{26} +15.6025 q^{27} +1.09804 q^{28} -1.05773 q^{29} +6.26877 q^{30} -0.801680 q^{31} -1.00000 q^{32} -11.3133 q^{33} +5.97426 q^{34} -2.09871 q^{35} +7.75714 q^{36} +11.0412 q^{37} +1.07537 q^{38} -8.05460 q^{39} +1.91132 q^{40} -1.22406 q^{41} -3.60137 q^{42} +4.23670 q^{43} -3.44938 q^{44} -14.8264 q^{45} +5.86835 q^{46} -2.09540 q^{47} +3.27981 q^{48} -5.79430 q^{49} +1.34685 q^{50} -19.5944 q^{51} -2.45581 q^{52} -13.0772 q^{53} -15.6025 q^{54} +6.59288 q^{55} -1.09804 q^{56} -3.52701 q^{57} +1.05773 q^{58} -4.64292 q^{59} -6.26877 q^{60} +9.17375 q^{61} +0.801680 q^{62} +8.51768 q^{63} +1.00000 q^{64} +4.69385 q^{65} +11.3133 q^{66} -7.02213 q^{67} -5.97426 q^{68} -19.2471 q^{69} +2.09871 q^{70} -7.43171 q^{71} -7.75714 q^{72} -10.8441 q^{73} -11.0412 q^{74} -4.41742 q^{75} -1.07537 q^{76} -3.78758 q^{77} +8.05460 q^{78} -2.91328 q^{79} -1.91132 q^{80} +27.9018 q^{81} +1.22406 q^{82} -11.0335 q^{83} +3.60137 q^{84} +11.4187 q^{85} -4.23670 q^{86} -3.46914 q^{87} +3.44938 q^{88} +3.10254 q^{89} +14.8264 q^{90} -2.69659 q^{91} -5.86835 q^{92} -2.62936 q^{93} +2.09540 q^{94} +2.05538 q^{95} -3.27981 q^{96} +2.04540 q^{97} +5.79430 q^{98} -26.7574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 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
\(3\) 3.27981 1.89360 0.946799 0.321825i \(-0.104296\pi\)
0.946799 + 0.321825i \(0.104296\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.91132 −0.854769 −0.427384 0.904070i \(-0.640565\pi\)
−0.427384 + 0.904070i \(0.640565\pi\)
\(6\) −3.27981 −1.33898
\(7\) 1.09804 0.415022 0.207511 0.978233i \(-0.433464\pi\)
0.207511 + 0.978233i \(0.433464\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.75714 2.58571
\(10\) 1.91132 0.604413
\(11\) −3.44938 −1.04003 −0.520014 0.854158i \(-0.674073\pi\)
−0.520014 + 0.854158i \(0.674073\pi\)
\(12\) 3.27981 0.946799
\(13\) −2.45581 −0.681120 −0.340560 0.940223i \(-0.610617\pi\)
−0.340560 + 0.940223i \(0.610617\pi\)
\(14\) −1.09804 −0.293465
\(15\) −6.26877 −1.61859
\(16\) 1.00000 0.250000
\(17\) −5.97426 −1.44897 −0.724485 0.689290i \(-0.757923\pi\)
−0.724485 + 0.689290i \(0.757923\pi\)
\(18\) −7.75714 −1.82838
\(19\) −1.07537 −0.246707 −0.123354 0.992363i \(-0.539365\pi\)
−0.123354 + 0.992363i \(0.539365\pi\)
\(20\) −1.91132 −0.427384
\(21\) 3.60137 0.785884
\(22\) 3.44938 0.735411
\(23\) −5.86835 −1.22364 −0.611818 0.790999i \(-0.709561\pi\)
−0.611818 + 0.790999i \(0.709561\pi\)
\(24\) −3.27981 −0.669488
\(25\) −1.34685 −0.269371
\(26\) 2.45581 0.481625
\(27\) 15.6025 3.00270
\(28\) 1.09804 0.207511
\(29\) −1.05773 −0.196415 −0.0982074 0.995166i \(-0.531311\pi\)
−0.0982074 + 0.995166i \(0.531311\pi\)
\(30\) 6.26877 1.14451
\(31\) −0.801680 −0.143986 −0.0719930 0.997405i \(-0.522936\pi\)
−0.0719930 + 0.997405i \(0.522936\pi\)
\(32\) −1.00000 −0.176777
\(33\) −11.3133 −1.96940
\(34\) 5.97426 1.02458
\(35\) −2.09871 −0.354748
\(36\) 7.75714 1.29286
\(37\) 11.0412 1.81516 0.907581 0.419877i \(-0.137927\pi\)
0.907581 + 0.419877i \(0.137927\pi\)
\(38\) 1.07537 0.174448
\(39\) −8.05460 −1.28977
\(40\) 1.91132 0.302206
\(41\) −1.22406 −0.191167 −0.0955834 0.995421i \(-0.530472\pi\)
−0.0955834 + 0.995421i \(0.530472\pi\)
\(42\) −3.60137 −0.555704
\(43\) 4.23670 0.646091 0.323045 0.946383i \(-0.395293\pi\)
0.323045 + 0.946383i \(0.395293\pi\)
\(44\) −3.44938 −0.520014
\(45\) −14.8264 −2.21019
\(46\) 5.86835 0.865241
\(47\) −2.09540 −0.305646 −0.152823 0.988254i \(-0.548836\pi\)
−0.152823 + 0.988254i \(0.548836\pi\)
\(48\) 3.27981 0.473400
\(49\) −5.79430 −0.827757
\(50\) 1.34685 0.190474
\(51\) −19.5944 −2.74377
\(52\) −2.45581 −0.340560
\(53\) −13.0772 −1.79629 −0.898144 0.439702i \(-0.855084\pi\)
−0.898144 + 0.439702i \(0.855084\pi\)
\(54\) −15.6025 −2.12323
\(55\) 6.59288 0.888984
\(56\) −1.09804 −0.146732
\(57\) −3.52701 −0.467164
\(58\) 1.05773 0.138886
\(59\) −4.64292 −0.604457 −0.302228 0.953236i \(-0.597730\pi\)
−0.302228 + 0.953236i \(0.597730\pi\)
\(60\) −6.26877 −0.809294
\(61\) 9.17375 1.17458 0.587289 0.809377i \(-0.300195\pi\)
0.587289 + 0.809377i \(0.300195\pi\)
\(62\) 0.801680 0.101813
\(63\) 8.51768 1.07313
\(64\) 1.00000 0.125000
\(65\) 4.69385 0.582200
\(66\) 11.3133 1.39257
\(67\) −7.02213 −0.857890 −0.428945 0.903331i \(-0.641115\pi\)
−0.428945 + 0.903331i \(0.641115\pi\)
\(68\) −5.97426 −0.724485
\(69\) −19.2471 −2.31707
\(70\) 2.09871 0.250844
\(71\) −7.43171 −0.881982 −0.440991 0.897511i \(-0.645373\pi\)
−0.440991 + 0.897511i \(0.645373\pi\)
\(72\) −7.75714 −0.914188
\(73\) −10.8441 −1.26921 −0.634603 0.772838i \(-0.718836\pi\)
−0.634603 + 0.772838i \(0.718836\pi\)
\(74\) −11.0412 −1.28351
\(75\) −4.41742 −0.510080
\(76\) −1.07537 −0.123354
\(77\) −3.78758 −0.431634
\(78\) 8.05460 0.912004
\(79\) −2.91328 −0.327770 −0.163885 0.986479i \(-0.552403\pi\)
−0.163885 + 0.986479i \(0.552403\pi\)
\(80\) −1.91132 −0.213692
\(81\) 27.9018 3.10020
\(82\) 1.22406 0.135175
\(83\) −11.0335 −1.21109 −0.605544 0.795811i \(-0.707045\pi\)
−0.605544 + 0.795811i \(0.707045\pi\)
\(84\) 3.60137 0.392942
\(85\) 11.4187 1.23853
\(86\) −4.23670 −0.456855
\(87\) −3.46914 −0.371931
\(88\) 3.44938 0.367706
\(89\) 3.10254 0.328869 0.164435 0.986388i \(-0.447420\pi\)
0.164435 + 0.986388i \(0.447420\pi\)
\(90\) 14.8264 1.56284
\(91\) −2.69659 −0.282680
\(92\) −5.86835 −0.611818
\(93\) −2.62936 −0.272652
\(94\) 2.09540 0.216124
\(95\) 2.05538 0.210878
\(96\) −3.27981 −0.334744
\(97\) 2.04540 0.207678 0.103839 0.994594i \(-0.466887\pi\)
0.103839 + 0.994594i \(0.466887\pi\)
\(98\) 5.79430 0.585313
\(99\) −26.7574 −2.68922
\(100\) −1.34685 −0.134685
\(101\) −3.98337 −0.396360 −0.198180 0.980166i \(-0.563503\pi\)
−0.198180 + 0.980166i \(0.563503\pi\)
\(102\) 19.5944 1.94014
\(103\) −8.36098 −0.823831 −0.411916 0.911222i \(-0.635140\pi\)
−0.411916 + 0.911222i \(0.635140\pi\)
\(104\) 2.45581 0.240812
\(105\) −6.88338 −0.671749
\(106\) 13.0772 1.27017
\(107\) 17.1374 1.65673 0.828367 0.560186i \(-0.189270\pi\)
0.828367 + 0.560186i \(0.189270\pi\)
\(108\) 15.6025 1.50135
\(109\) −17.6410 −1.68970 −0.844849 0.535004i \(-0.820310\pi\)
−0.844849 + 0.535004i \(0.820310\pi\)
\(110\) −6.59288 −0.628606
\(111\) 36.2130 3.43719
\(112\) 1.09804 0.103755
\(113\) 10.3617 0.974746 0.487373 0.873194i \(-0.337955\pi\)
0.487373 + 0.873194i \(0.337955\pi\)
\(114\) 3.52701 0.330335
\(115\) 11.2163 1.04593
\(116\) −1.05773 −0.0982074
\(117\) −19.0501 −1.76118
\(118\) 4.64292 0.427415
\(119\) −6.56000 −0.601354
\(120\) 6.26877 0.572257
\(121\) 0.898254 0.0816595
\(122\) −9.17375 −0.830552
\(123\) −4.01470 −0.361993
\(124\) −0.801680 −0.0719930
\(125\) 12.1309 1.08502
\(126\) −8.51768 −0.758816
\(127\) 11.5199 1.02222 0.511112 0.859514i \(-0.329234\pi\)
0.511112 + 0.859514i \(0.329234\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 13.8956 1.22344
\(130\) −4.69385 −0.411678
\(131\) 16.2852 1.42284 0.711420 0.702767i \(-0.248052\pi\)
0.711420 + 0.702767i \(0.248052\pi\)
\(132\) −11.3133 −0.984698
\(133\) −1.18081 −0.102389
\(134\) 7.02213 0.606620
\(135\) −29.8214 −2.56662
\(136\) 5.97426 0.512289
\(137\) 1.52041 0.129897 0.0649487 0.997889i \(-0.479312\pi\)
0.0649487 + 0.997889i \(0.479312\pi\)
\(138\) 19.2471 1.63842
\(139\) 19.7483 1.67503 0.837515 0.546414i \(-0.184007\pi\)
0.837515 + 0.546414i \(0.184007\pi\)
\(140\) −2.09871 −0.177374
\(141\) −6.87252 −0.578771
\(142\) 7.43171 0.623656
\(143\) 8.47105 0.708385
\(144\) 7.75714 0.646428
\(145\) 2.02165 0.167889
\(146\) 10.8441 0.897464
\(147\) −19.0042 −1.56744
\(148\) 11.0412 0.907581
\(149\) 16.3947 1.34311 0.671554 0.740956i \(-0.265627\pi\)
0.671554 + 0.740956i \(0.265627\pi\)
\(150\) 4.41742 0.360681
\(151\) −5.05534 −0.411398 −0.205699 0.978615i \(-0.565947\pi\)
−0.205699 + 0.978615i \(0.565947\pi\)
\(152\) 1.07537 0.0872242
\(153\) −46.3432 −3.74662
\(154\) 3.78758 0.305212
\(155\) 1.53227 0.123075
\(156\) −8.05460 −0.644884
\(157\) −8.49219 −0.677751 −0.338875 0.940831i \(-0.610046\pi\)
−0.338875 + 0.940831i \(0.610046\pi\)
\(158\) 2.91328 0.231768
\(159\) −42.8906 −3.40145
\(160\) 1.91132 0.151103
\(161\) −6.44371 −0.507835
\(162\) −27.9018 −2.19217
\(163\) −6.78097 −0.531127 −0.265563 0.964093i \(-0.585558\pi\)
−0.265563 + 0.964093i \(0.585558\pi\)
\(164\) −1.22406 −0.0955834
\(165\) 21.6234 1.68338
\(166\) 11.0335 0.856369
\(167\) 12.2107 0.944895 0.472447 0.881359i \(-0.343371\pi\)
0.472447 + 0.881359i \(0.343371\pi\)
\(168\) −3.60137 −0.277852
\(169\) −6.96898 −0.536075
\(170\) −11.4187 −0.875776
\(171\) −8.34181 −0.637914
\(172\) 4.23670 0.323045
\(173\) −25.2030 −1.91615 −0.958074 0.286522i \(-0.907501\pi\)
−0.958074 + 0.286522i \(0.907501\pi\)
\(174\) 3.46914 0.262995
\(175\) −1.47890 −0.111795
\(176\) −3.44938 −0.260007
\(177\) −15.2279 −1.14460
\(178\) −3.10254 −0.232546
\(179\) 0.0966408 0.00722327 0.00361163 0.999993i \(-0.498850\pi\)
0.00361163 + 0.999993i \(0.498850\pi\)
\(180\) −14.8264 −1.10509
\(181\) −13.5853 −1.00979 −0.504895 0.863181i \(-0.668469\pi\)
−0.504895 + 0.863181i \(0.668469\pi\)
\(182\) 2.69659 0.199885
\(183\) 30.0881 2.22418
\(184\) 5.86835 0.432620
\(185\) −21.1033 −1.55154
\(186\) 2.62936 0.192794
\(187\) 20.6075 1.50697
\(188\) −2.09540 −0.152823
\(189\) 17.1322 1.24619
\(190\) −2.05538 −0.149113
\(191\) −6.59808 −0.477420 −0.238710 0.971091i \(-0.576725\pi\)
−0.238710 + 0.971091i \(0.576725\pi\)
\(192\) 3.27981 0.236700
\(193\) 18.1038 1.30314 0.651569 0.758590i \(-0.274111\pi\)
0.651569 + 0.758590i \(0.274111\pi\)
\(194\) −2.04540 −0.146851
\(195\) 15.3949 1.10245
\(196\) −5.79430 −0.413878
\(197\) −19.5243 −1.39105 −0.695523 0.718503i \(-0.744827\pi\)
−0.695523 + 0.718503i \(0.744827\pi\)
\(198\) 26.7574 1.90156
\(199\) −8.31380 −0.589350 −0.294675 0.955598i \(-0.595211\pi\)
−0.294675 + 0.955598i \(0.595211\pi\)
\(200\) 1.34685 0.0952369
\(201\) −23.0312 −1.62450
\(202\) 3.98337 0.280269
\(203\) −1.16143 −0.0815164
\(204\) −19.5944 −1.37188
\(205\) 2.33958 0.163403
\(206\) 8.36098 0.582537
\(207\) −45.5216 −3.16397
\(208\) −2.45581 −0.170280
\(209\) 3.70937 0.256583
\(210\) 6.88338 0.474998
\(211\) −10.8425 −0.746431 −0.373215 0.927745i \(-0.621745\pi\)
−0.373215 + 0.927745i \(0.621745\pi\)
\(212\) −13.0772 −0.898144
\(213\) −24.3746 −1.67012
\(214\) −17.1374 −1.17149
\(215\) −8.09770 −0.552258
\(216\) −15.6025 −1.06162
\(217\) −0.880280 −0.0597573
\(218\) 17.6410 1.19480
\(219\) −35.5666 −2.40337
\(220\) 6.59288 0.444492
\(221\) 14.6717 0.986924
\(222\) −36.2130 −2.43046
\(223\) −1.51293 −0.101313 −0.0506567 0.998716i \(-0.516131\pi\)
−0.0506567 + 0.998716i \(0.516131\pi\)
\(224\) −1.09804 −0.0733662
\(225\) −10.4477 −0.696515
\(226\) −10.3617 −0.689250
\(227\) 10.8934 0.723019 0.361510 0.932368i \(-0.382261\pi\)
0.361510 + 0.932368i \(0.382261\pi\)
\(228\) −3.52701 −0.233582
\(229\) −7.10403 −0.469447 −0.234724 0.972062i \(-0.575419\pi\)
−0.234724 + 0.972062i \(0.575419\pi\)
\(230\) −11.2163 −0.739581
\(231\) −12.4225 −0.817342
\(232\) 1.05773 0.0694431
\(233\) 29.5080 1.93314 0.966568 0.256410i \(-0.0825397\pi\)
0.966568 + 0.256410i \(0.0825397\pi\)
\(234\) 19.0501 1.24534
\(235\) 4.00499 0.261257
\(236\) −4.64292 −0.302228
\(237\) −9.55500 −0.620664
\(238\) 6.56000 0.425222
\(239\) 4.21162 0.272427 0.136214 0.990679i \(-0.456507\pi\)
0.136214 + 0.990679i \(0.456507\pi\)
\(240\) −6.26877 −0.404647
\(241\) 19.4162 1.25071 0.625355 0.780341i \(-0.284954\pi\)
0.625355 + 0.780341i \(0.284954\pi\)
\(242\) −0.898254 −0.0577420
\(243\) 44.7051 2.86783
\(244\) 9.17375 0.587289
\(245\) 11.0748 0.707541
\(246\) 4.01470 0.255968
\(247\) 2.64091 0.168037
\(248\) 0.801680 0.0509067
\(249\) −36.1879 −2.29332
\(250\) −12.1309 −0.767224
\(251\) 6.06301 0.382694 0.191347 0.981522i \(-0.438714\pi\)
0.191347 + 0.981522i \(0.438714\pi\)
\(252\) 8.51768 0.536564
\(253\) 20.2422 1.27262
\(254\) −11.5199 −0.722821
\(255\) 37.4512 2.34529
\(256\) 1.00000 0.0625000
\(257\) −4.25432 −0.265377 −0.132689 0.991158i \(-0.542361\pi\)
−0.132689 + 0.991158i \(0.542361\pi\)
\(258\) −13.8956 −0.865100
\(259\) 12.1237 0.753332
\(260\) 4.69385 0.291100
\(261\) −8.20493 −0.507872
\(262\) −16.2852 −1.00610
\(263\) −12.7094 −0.783696 −0.391848 0.920030i \(-0.628164\pi\)
−0.391848 + 0.920030i \(0.628164\pi\)
\(264\) 11.3133 0.696287
\(265\) 24.9947 1.53541
\(266\) 1.18081 0.0723999
\(267\) 10.1758 0.622746
\(268\) −7.02213 −0.428945
\(269\) 8.03286 0.489772 0.244886 0.969552i \(-0.421249\pi\)
0.244886 + 0.969552i \(0.421249\pi\)
\(270\) 29.8214 1.81487
\(271\) −17.8576 −1.08477 −0.542385 0.840130i \(-0.682479\pi\)
−0.542385 + 0.840130i \(0.682479\pi\)
\(272\) −5.97426 −0.362243
\(273\) −8.84431 −0.535282
\(274\) −1.52041 −0.0918513
\(275\) 4.64581 0.280153
\(276\) −19.2471 −1.15854
\(277\) 29.7703 1.78873 0.894363 0.447341i \(-0.147629\pi\)
0.894363 + 0.447341i \(0.147629\pi\)
\(278\) −19.7483 −1.18443
\(279\) −6.21874 −0.372306
\(280\) 2.09871 0.125422
\(281\) −7.91897 −0.472406 −0.236203 0.971704i \(-0.575903\pi\)
−0.236203 + 0.971704i \(0.575903\pi\)
\(282\) 6.87252 0.409253
\(283\) 28.2406 1.67873 0.839365 0.543568i \(-0.182927\pi\)
0.839365 + 0.543568i \(0.182927\pi\)
\(284\) −7.43171 −0.440991
\(285\) 6.74125 0.399317
\(286\) −8.47105 −0.500904
\(287\) −1.34408 −0.0793384
\(288\) −7.75714 −0.457094
\(289\) 18.6918 1.09952
\(290\) −2.02165 −0.118716
\(291\) 6.70851 0.393260
\(292\) −10.8441 −0.634603
\(293\) −17.5694 −1.02641 −0.513207 0.858265i \(-0.671543\pi\)
−0.513207 + 0.858265i \(0.671543\pi\)
\(294\) 19.0042 1.10835
\(295\) 8.87411 0.516670
\(296\) −11.0412 −0.641757
\(297\) −53.8191 −3.12290
\(298\) −16.3947 −0.949721
\(299\) 14.4116 0.833443
\(300\) −4.41742 −0.255040
\(301\) 4.65209 0.268142
\(302\) 5.05534 0.290902
\(303\) −13.0647 −0.750546
\(304\) −1.07537 −0.0616768
\(305\) −17.5340 −1.00399
\(306\) 46.3432 2.64926
\(307\) 4.50149 0.256914 0.128457 0.991715i \(-0.458998\pi\)
0.128457 + 0.991715i \(0.458998\pi\)
\(308\) −3.78758 −0.215817
\(309\) −27.4224 −1.56001
\(310\) −1.53227 −0.0870269
\(311\) −13.2750 −0.752754 −0.376377 0.926467i \(-0.622830\pi\)
−0.376377 + 0.926467i \(0.622830\pi\)
\(312\) 8.05460 0.456002
\(313\) 18.2654 1.03242 0.516212 0.856461i \(-0.327342\pi\)
0.516212 + 0.856461i \(0.327342\pi\)
\(314\) 8.49219 0.479242
\(315\) −16.2800 −0.917275
\(316\) −2.91328 −0.163885
\(317\) −4.82884 −0.271215 −0.135607 0.990763i \(-0.543299\pi\)
−0.135607 + 0.990763i \(0.543299\pi\)
\(318\) 42.8906 2.40519
\(319\) 3.64850 0.204277
\(320\) −1.91132 −0.106846
\(321\) 56.2074 3.13719
\(322\) 6.44371 0.359094
\(323\) 6.42455 0.357472
\(324\) 27.9018 1.55010
\(325\) 3.30762 0.183474
\(326\) 6.78097 0.375563
\(327\) −57.8590 −3.19961
\(328\) 1.22406 0.0675877
\(329\) −2.30085 −0.126850
\(330\) −21.6234 −1.19033
\(331\) −19.8008 −1.08835 −0.544176 0.838971i \(-0.683158\pi\)
−0.544176 + 0.838971i \(0.683158\pi\)
\(332\) −11.0335 −0.605544
\(333\) 85.6482 4.69349
\(334\) −12.2107 −0.668142
\(335\) 13.4215 0.733297
\(336\) 3.60137 0.196471
\(337\) 13.4066 0.730305 0.365153 0.930948i \(-0.381017\pi\)
0.365153 + 0.930948i \(0.381017\pi\)
\(338\) 6.96898 0.379062
\(339\) 33.9844 1.84578
\(340\) 11.4187 0.619267
\(341\) 2.76530 0.149750
\(342\) 8.34181 0.451073
\(343\) −14.0487 −0.758559
\(344\) −4.23670 −0.228428
\(345\) 36.7873 1.98056
\(346\) 25.2030 1.35492
\(347\) −6.21002 −0.333371 −0.166686 0.986010i \(-0.553307\pi\)
−0.166686 + 0.986010i \(0.553307\pi\)
\(348\) −3.46914 −0.185965
\(349\) −3.71651 −0.198940 −0.0994701 0.995041i \(-0.531715\pi\)
−0.0994701 + 0.995041i \(0.531715\pi\)
\(350\) 1.47890 0.0790507
\(351\) −38.3169 −2.04520
\(352\) 3.44938 0.183853
\(353\) 1.59932 0.0851232 0.0425616 0.999094i \(-0.486448\pi\)
0.0425616 + 0.999094i \(0.486448\pi\)
\(354\) 15.2279 0.809353
\(355\) 14.2044 0.753891
\(356\) 3.10254 0.164435
\(357\) −21.5155 −1.13872
\(358\) −0.0966408 −0.00510762
\(359\) −13.9365 −0.735543 −0.367771 0.929916i \(-0.619879\pi\)
−0.367771 + 0.929916i \(0.619879\pi\)
\(360\) 14.8264 0.781419
\(361\) −17.8436 −0.939136
\(362\) 13.5853 0.714029
\(363\) 2.94610 0.154630
\(364\) −2.69659 −0.141340
\(365\) 20.7266 1.08488
\(366\) −30.0881 −1.57273
\(367\) −26.7668 −1.39722 −0.698608 0.715505i \(-0.746197\pi\)
−0.698608 + 0.715505i \(0.746197\pi\)
\(368\) −5.86835 −0.305909
\(369\) −9.49524 −0.494303
\(370\) 21.1033 1.09711
\(371\) −14.3593 −0.745498
\(372\) −2.62936 −0.136326
\(373\) 26.4820 1.37119 0.685593 0.727985i \(-0.259543\pi\)
0.685593 + 0.727985i \(0.259543\pi\)
\(374\) −20.6075 −1.06559
\(375\) 39.7869 2.05459
\(376\) 2.09540 0.108062
\(377\) 2.59758 0.133782
\(378\) −17.1322 −0.881187
\(379\) −20.3489 −1.04525 −0.522627 0.852561i \(-0.675048\pi\)
−0.522627 + 0.852561i \(0.675048\pi\)
\(380\) 2.05538 0.105439
\(381\) 37.7830 1.93568
\(382\) 6.59808 0.337587
\(383\) 8.44791 0.431668 0.215834 0.976430i \(-0.430753\pi\)
0.215834 + 0.976430i \(0.430753\pi\)
\(384\) −3.27981 −0.167372
\(385\) 7.23927 0.368948
\(386\) −18.1038 −0.921457
\(387\) 32.8647 1.67061
\(388\) 2.04540 0.103839
\(389\) 28.8520 1.46285 0.731427 0.681920i \(-0.238855\pi\)
0.731427 + 0.681920i \(0.238855\pi\)
\(390\) −15.3949 −0.779552
\(391\) 35.0590 1.77301
\(392\) 5.79430 0.292656
\(393\) 53.4122 2.69429
\(394\) 19.5243 0.983619
\(395\) 5.56821 0.280167
\(396\) −26.7574 −1.34461
\(397\) −10.2395 −0.513905 −0.256953 0.966424i \(-0.582718\pi\)
−0.256953 + 0.966424i \(0.582718\pi\)
\(398\) 8.31380 0.416733
\(399\) −3.87282 −0.193883
\(400\) −1.34685 −0.0673427
\(401\) −29.9424 −1.49525 −0.747625 0.664121i \(-0.768806\pi\)
−0.747625 + 0.664121i \(0.768806\pi\)
\(402\) 23.0312 1.14869
\(403\) 1.96878 0.0980718
\(404\) −3.98337 −0.198180
\(405\) −53.3293 −2.64995
\(406\) 1.16143 0.0576408
\(407\) −38.0854 −1.88782
\(408\) 19.5944 0.970069
\(409\) −7.40367 −0.366088 −0.183044 0.983105i \(-0.558595\pi\)
−0.183044 + 0.983105i \(0.558595\pi\)
\(410\) −2.33958 −0.115544
\(411\) 4.98665 0.245973
\(412\) −8.36098 −0.411916
\(413\) −5.09813 −0.250863
\(414\) 45.5216 2.23726
\(415\) 21.0886 1.03520
\(416\) 2.45581 0.120406
\(417\) 64.7707 3.17184
\(418\) −3.70937 −0.181431
\(419\) 4.67884 0.228576 0.114288 0.993448i \(-0.463541\pi\)
0.114288 + 0.993448i \(0.463541\pi\)
\(420\) −6.88338 −0.335875
\(421\) 1.46039 0.0711752 0.0355876 0.999367i \(-0.488670\pi\)
0.0355876 + 0.999367i \(0.488670\pi\)
\(422\) 10.8425 0.527806
\(423\) −16.2543 −0.790313
\(424\) 13.0772 0.635084
\(425\) 8.04645 0.390310
\(426\) 24.3746 1.18095
\(427\) 10.0732 0.487475
\(428\) 17.1374 0.828367
\(429\) 27.7834 1.34140
\(430\) 8.09770 0.390506
\(431\) −24.5944 −1.18467 −0.592336 0.805691i \(-0.701794\pi\)
−0.592336 + 0.805691i \(0.701794\pi\)
\(432\) 15.6025 0.750676
\(433\) 13.4899 0.648284 0.324142 0.946008i \(-0.394924\pi\)
0.324142 + 0.946008i \(0.394924\pi\)
\(434\) 0.880280 0.0422548
\(435\) 6.63064 0.317915
\(436\) −17.6410 −0.844849
\(437\) 6.31066 0.301880
\(438\) 35.5666 1.69944
\(439\) −28.2774 −1.34961 −0.674804 0.737997i \(-0.735772\pi\)
−0.674804 + 0.737997i \(0.735772\pi\)
\(440\) −6.59288 −0.314303
\(441\) −44.9472 −2.14034
\(442\) −14.6717 −0.697860
\(443\) 17.9594 0.853278 0.426639 0.904422i \(-0.359698\pi\)
0.426639 + 0.904422i \(0.359698\pi\)
\(444\) 36.2130 1.71859
\(445\) −5.92996 −0.281107
\(446\) 1.51293 0.0716394
\(447\) 53.7715 2.54331
\(448\) 1.09804 0.0518777
\(449\) 32.7174 1.54403 0.772014 0.635605i \(-0.219249\pi\)
0.772014 + 0.635605i \(0.219249\pi\)
\(450\) 10.4477 0.492511
\(451\) 4.22227 0.198819
\(452\) 10.3617 0.487373
\(453\) −16.5805 −0.779022
\(454\) −10.8934 −0.511252
\(455\) 5.15405 0.241626
\(456\) 3.52701 0.165168
\(457\) −40.8658 −1.91162 −0.955811 0.293981i \(-0.905020\pi\)
−0.955811 + 0.293981i \(0.905020\pi\)
\(458\) 7.10403 0.331949
\(459\) −93.2134 −4.35083
\(460\) 11.2163 0.522963
\(461\) 7.24778 0.337563 0.168781 0.985654i \(-0.446017\pi\)
0.168781 + 0.985654i \(0.446017\pi\)
\(462\) 12.4225 0.577948
\(463\) −26.8102 −1.24597 −0.622987 0.782232i \(-0.714081\pi\)
−0.622987 + 0.782232i \(0.714081\pi\)
\(464\) −1.05773 −0.0491037
\(465\) 5.02554 0.233054
\(466\) −29.5080 −1.36693
\(467\) −40.4222 −1.87052 −0.935258 0.353966i \(-0.884833\pi\)
−0.935258 + 0.353966i \(0.884833\pi\)
\(468\) −19.0501 −0.880591
\(469\) −7.71061 −0.356043
\(470\) −4.00499 −0.184736
\(471\) −27.8528 −1.28339
\(472\) 4.64292 0.213708
\(473\) −14.6140 −0.671953
\(474\) 9.55500 0.438876
\(475\) 1.44837 0.0664557
\(476\) −6.56000 −0.300677
\(477\) −101.441 −4.64469
\(478\) −4.21162 −0.192635
\(479\) −42.7351 −1.95262 −0.976308 0.216384i \(-0.930574\pi\)
−0.976308 + 0.216384i \(0.930574\pi\)
\(480\) 6.26877 0.286129
\(481\) −27.1151 −1.23634
\(482\) −19.4162 −0.884385
\(483\) −21.1341 −0.961636
\(484\) 0.898254 0.0408297
\(485\) −3.90941 −0.177517
\(486\) −44.7051 −2.02786
\(487\) 29.2596 1.32588 0.662939 0.748673i \(-0.269309\pi\)
0.662939 + 0.748673i \(0.269309\pi\)
\(488\) −9.17375 −0.415276
\(489\) −22.2403 −1.00574
\(490\) −11.0748 −0.500307
\(491\) −2.36499 −0.106730 −0.0533652 0.998575i \(-0.516995\pi\)
−0.0533652 + 0.998575i \(0.516995\pi\)
\(492\) −4.01470 −0.180997
\(493\) 6.31913 0.284599
\(494\) −2.64091 −0.118820
\(495\) 51.1419 2.29866
\(496\) −0.801680 −0.0359965
\(497\) −8.16035 −0.366042
\(498\) 36.1879 1.62162
\(499\) 27.2837 1.22138 0.610692 0.791868i \(-0.290891\pi\)
0.610692 + 0.791868i \(0.290891\pi\)
\(500\) 12.1309 0.542509
\(501\) 40.0489 1.78925
\(502\) −6.06301 −0.270606
\(503\) 10.8000 0.481550 0.240775 0.970581i \(-0.422598\pi\)
0.240775 + 0.970581i \(0.422598\pi\)
\(504\) −8.51768 −0.379408
\(505\) 7.61349 0.338796
\(506\) −20.2422 −0.899875
\(507\) −22.8569 −1.01511
\(508\) 11.5199 0.511112
\(509\) −8.32214 −0.368872 −0.184436 0.982844i \(-0.559046\pi\)
−0.184436 + 0.982844i \(0.559046\pi\)
\(510\) −37.4512 −1.65837
\(511\) −11.9073 −0.526748
\(512\) −1.00000 −0.0441942
\(513\) −16.7785 −0.740789
\(514\) 4.25432 0.187650
\(515\) 15.9805 0.704185
\(516\) 13.8956 0.611718
\(517\) 7.22785 0.317881
\(518\) −12.1237 −0.532686
\(519\) −82.6609 −3.62841
\(520\) −4.69385 −0.205839
\(521\) 6.05714 0.265368 0.132684 0.991158i \(-0.457640\pi\)
0.132684 + 0.991158i \(0.457640\pi\)
\(522\) 8.20493 0.359120
\(523\) 11.0178 0.481775 0.240887 0.970553i \(-0.422562\pi\)
0.240887 + 0.970553i \(0.422562\pi\)
\(524\) 16.2852 0.711420
\(525\) −4.85052 −0.211694
\(526\) 12.7094 0.554157
\(527\) 4.78944 0.208631
\(528\) −11.3133 −0.492349
\(529\) 11.4375 0.497283
\(530\) −24.9947 −1.08570
\(531\) −36.0158 −1.56295
\(532\) −1.18081 −0.0511944
\(533\) 3.00608 0.130208
\(534\) −10.1758 −0.440348
\(535\) −32.7551 −1.41612
\(536\) 7.02213 0.303310
\(537\) 0.316963 0.0136780
\(538\) −8.03286 −0.346321
\(539\) 19.9868 0.860891
\(540\) −29.8214 −1.28331
\(541\) −21.1166 −0.907874 −0.453937 0.891034i \(-0.649981\pi\)
−0.453937 + 0.891034i \(0.649981\pi\)
\(542\) 17.8576 0.767049
\(543\) −44.5573 −1.91214
\(544\) 5.97426 0.256144
\(545\) 33.7176 1.44430
\(546\) 8.84431 0.378501
\(547\) 17.3197 0.740537 0.370268 0.928925i \(-0.379266\pi\)
0.370268 + 0.928925i \(0.379266\pi\)
\(548\) 1.52041 0.0649487
\(549\) 71.1621 3.03712
\(550\) −4.64581 −0.198098
\(551\) 1.13745 0.0484570
\(552\) 19.2471 0.819209
\(553\) −3.19891 −0.136032
\(554\) −29.7703 −1.26482
\(555\) −69.2147 −2.93800
\(556\) 19.7483 0.837515
\(557\) −2.45081 −0.103844 −0.0519221 0.998651i \(-0.516535\pi\)
−0.0519221 + 0.998651i \(0.516535\pi\)
\(558\) 6.21874 0.263260
\(559\) −10.4046 −0.440066
\(560\) −2.09871 −0.0886869
\(561\) 67.5887 2.85360
\(562\) 7.91897 0.334042
\(563\) −6.66243 −0.280788 −0.140394 0.990096i \(-0.544837\pi\)
−0.140394 + 0.990096i \(0.544837\pi\)
\(564\) −6.87252 −0.289385
\(565\) −19.8045 −0.833183
\(566\) −28.2406 −1.18704
\(567\) 30.6374 1.28665
\(568\) 7.43171 0.311828
\(569\) 20.2085 0.847183 0.423591 0.905853i \(-0.360769\pi\)
0.423591 + 0.905853i \(0.360769\pi\)
\(570\) −6.74125 −0.282360
\(571\) 32.9979 1.38092 0.690459 0.723371i \(-0.257408\pi\)
0.690459 + 0.723371i \(0.257408\pi\)
\(572\) 8.47105 0.354192
\(573\) −21.6404 −0.904042
\(574\) 1.34408 0.0561007
\(575\) 7.90380 0.329611
\(576\) 7.75714 0.323214
\(577\) −5.58644 −0.232567 −0.116283 0.993216i \(-0.537098\pi\)
−0.116283 + 0.993216i \(0.537098\pi\)
\(578\) −18.6918 −0.777476
\(579\) 59.3769 2.46762
\(580\) 2.02165 0.0839446
\(581\) −12.1153 −0.502628
\(582\) −6.70851 −0.278077
\(583\) 45.1082 1.86819
\(584\) 10.8441 0.448732
\(585\) 36.4108 1.50540
\(586\) 17.5694 0.725784
\(587\) 24.8405 1.02528 0.512638 0.858605i \(-0.328668\pi\)
0.512638 + 0.858605i \(0.328668\pi\)
\(588\) −19.0042 −0.783720
\(589\) 0.862104 0.0355224
\(590\) −8.87411 −0.365341
\(591\) −64.0359 −2.63408
\(592\) 11.0412 0.453791
\(593\) 26.3962 1.08396 0.541981 0.840390i \(-0.317674\pi\)
0.541981 + 0.840390i \(0.317674\pi\)
\(594\) 53.8191 2.20822
\(595\) 12.5383 0.514019
\(596\) 16.3947 0.671554
\(597\) −27.2677 −1.11599
\(598\) −14.4116 −0.589333
\(599\) −23.6993 −0.968327 −0.484163 0.874978i \(-0.660876\pi\)
−0.484163 + 0.874978i \(0.660876\pi\)
\(600\) 4.41742 0.180340
\(601\) 32.7696 1.33670 0.668351 0.743846i \(-0.267001\pi\)
0.668351 + 0.743846i \(0.267001\pi\)
\(602\) −4.65209 −0.189605
\(603\) −54.4717 −2.21826
\(604\) −5.05534 −0.205699
\(605\) −1.71685 −0.0698000
\(606\) 13.0647 0.530716
\(607\) 21.8414 0.886516 0.443258 0.896394i \(-0.353823\pi\)
0.443258 + 0.896394i \(0.353823\pi\)
\(608\) 1.07537 0.0436121
\(609\) −3.80927 −0.154359
\(610\) 17.5340 0.709930
\(611\) 5.14592 0.208182
\(612\) −46.3432 −1.87331
\(613\) −15.6341 −0.631453 −0.315727 0.948850i \(-0.602248\pi\)
−0.315727 + 0.948850i \(0.602248\pi\)
\(614\) −4.50149 −0.181666
\(615\) 7.67337 0.309420
\(616\) 3.78758 0.152606
\(617\) 6.89977 0.277774 0.138887 0.990308i \(-0.455647\pi\)
0.138887 + 0.990308i \(0.455647\pi\)
\(618\) 27.4224 1.10309
\(619\) −10.3880 −0.417530 −0.208765 0.977966i \(-0.566944\pi\)
−0.208765 + 0.977966i \(0.566944\pi\)
\(620\) 1.53227 0.0615373
\(621\) −91.5610 −3.67421
\(622\) 13.2750 0.532277
\(623\) 3.40673 0.136488
\(624\) −8.05460 −0.322442
\(625\) −16.4517 −0.658069
\(626\) −18.2654 −0.730033
\(627\) 12.1660 0.485864
\(628\) −8.49219 −0.338875
\(629\) −65.9630 −2.63012
\(630\) 16.2800 0.648612
\(631\) 3.66725 0.145991 0.0729954 0.997332i \(-0.476744\pi\)
0.0729954 + 0.997332i \(0.476744\pi\)
\(632\) 2.91328 0.115884
\(633\) −35.5614 −1.41344
\(634\) 4.82884 0.191778
\(635\) −22.0182 −0.873764
\(636\) −42.8906 −1.70072
\(637\) 14.2297 0.563802
\(638\) −3.64850 −0.144446
\(639\) −57.6489 −2.28055
\(640\) 1.91132 0.0755516
\(641\) 17.2995 0.683291 0.341645 0.939829i \(-0.389016\pi\)
0.341645 + 0.939829i \(0.389016\pi\)
\(642\) −56.2074 −2.21833
\(643\) 15.4977 0.611171 0.305585 0.952165i \(-0.401148\pi\)
0.305585 + 0.952165i \(0.401148\pi\)
\(644\) −6.44371 −0.253918
\(645\) −26.5589 −1.04576
\(646\) −6.42455 −0.252771
\(647\) 35.1070 1.38020 0.690099 0.723715i \(-0.257567\pi\)
0.690099 + 0.723715i \(0.257567\pi\)
\(648\) −27.9018 −1.09609
\(649\) 16.0152 0.628652
\(650\) −3.30762 −0.129736
\(651\) −2.88715 −0.113156
\(652\) −6.78097 −0.265563
\(653\) −14.7734 −0.578126 −0.289063 0.957310i \(-0.593344\pi\)
−0.289063 + 0.957310i \(0.593344\pi\)
\(654\) 57.8590 2.26247
\(655\) −31.1262 −1.21620
\(656\) −1.22406 −0.0477917
\(657\) −84.1192 −3.28180
\(658\) 2.30085 0.0896963
\(659\) 5.35530 0.208613 0.104306 0.994545i \(-0.466738\pi\)
0.104306 + 0.994545i \(0.466738\pi\)
\(660\) 21.6234 0.841689
\(661\) 19.0949 0.742704 0.371352 0.928492i \(-0.378894\pi\)
0.371352 + 0.928492i \(0.378894\pi\)
\(662\) 19.8008 0.769581
\(663\) 48.1203 1.86884
\(664\) 11.0335 0.428185
\(665\) 2.25690 0.0875188
\(666\) −85.6482 −3.31880
\(667\) 6.20711 0.240340
\(668\) 12.2107 0.472447
\(669\) −4.96212 −0.191847
\(670\) −13.4215 −0.518519
\(671\) −31.6438 −1.22159
\(672\) −3.60137 −0.138926
\(673\) −20.0851 −0.774224 −0.387112 0.922033i \(-0.626527\pi\)
−0.387112 + 0.922033i \(0.626527\pi\)
\(674\) −13.4066 −0.516404
\(675\) −21.0143 −0.808840
\(676\) −6.96898 −0.268038
\(677\) −25.4361 −0.977590 −0.488795 0.872399i \(-0.662563\pi\)
−0.488795 + 0.872399i \(0.662563\pi\)
\(678\) −33.9844 −1.30516
\(679\) 2.24594 0.0861911
\(680\) −11.4187 −0.437888
\(681\) 35.7282 1.36911
\(682\) −2.76530 −0.105889
\(683\) −48.3779 −1.85113 −0.925564 0.378592i \(-0.876408\pi\)
−0.925564 + 0.378592i \(0.876408\pi\)
\(684\) −8.34181 −0.318957
\(685\) −2.90599 −0.111032
\(686\) 14.0487 0.536382
\(687\) −23.2999 −0.888945
\(688\) 4.23670 0.161523
\(689\) 32.1151 1.22349
\(690\) −36.7873 −1.40047
\(691\) −35.7633 −1.36050 −0.680249 0.732981i \(-0.738128\pi\)
−0.680249 + 0.732981i \(0.738128\pi\)
\(692\) −25.2030 −0.958074
\(693\) −29.3808 −1.11608
\(694\) 6.21002 0.235729
\(695\) −37.7454 −1.43176
\(696\) 3.46914 0.131497
\(697\) 7.31288 0.276995
\(698\) 3.71651 0.140672
\(699\) 96.7807 3.66058
\(700\) −1.47890 −0.0558973
\(701\) −11.3880 −0.430119 −0.215060 0.976601i \(-0.568995\pi\)
−0.215060 + 0.976601i \(0.568995\pi\)
\(702\) 38.3169 1.44618
\(703\) −11.8734 −0.447814
\(704\) −3.44938 −0.130004
\(705\) 13.1356 0.494715
\(706\) −1.59932 −0.0601912
\(707\) −4.37391 −0.164498
\(708\) −15.2279 −0.572299
\(709\) 34.0180 1.27757 0.638786 0.769384i \(-0.279437\pi\)
0.638786 + 0.769384i \(0.279437\pi\)
\(710\) −14.2044 −0.533081
\(711\) −22.5987 −0.847518
\(712\) −3.10254 −0.116273
\(713\) 4.70454 0.176186
\(714\) 21.5155 0.805199
\(715\) −16.1909 −0.605505
\(716\) 0.0966408 0.00361163
\(717\) 13.8133 0.515868
\(718\) 13.9365 0.520107
\(719\) 30.1708 1.12518 0.562590 0.826736i \(-0.309805\pi\)
0.562590 + 0.826736i \(0.309805\pi\)
\(720\) −14.8264 −0.552547
\(721\) −9.18072 −0.341908
\(722\) 17.8436 0.664069
\(723\) 63.6815 2.36834
\(724\) −13.5853 −0.504895
\(725\) 1.42460 0.0529084
\(726\) −2.94610 −0.109340
\(727\) −0.182495 −0.00676835 −0.00338418 0.999994i \(-0.501077\pi\)
−0.00338418 + 0.999994i \(0.501077\pi\)
\(728\) 2.69659 0.0999424
\(729\) 62.9186 2.33032
\(730\) −20.7266 −0.767124
\(731\) −25.3112 −0.936167
\(732\) 30.0881 1.11209
\(733\) −2.60018 −0.0960400 −0.0480200 0.998846i \(-0.515291\pi\)
−0.0480200 + 0.998846i \(0.515291\pi\)
\(734\) 26.7668 0.987981
\(735\) 36.3231 1.33980
\(736\) 5.86835 0.216310
\(737\) 24.2220 0.892230
\(738\) 9.49524 0.349525
\(739\) 3.26112 0.119962 0.0599812 0.998200i \(-0.480896\pi\)
0.0599812 + 0.998200i \(0.480896\pi\)
\(740\) −21.1033 −0.775772
\(741\) 8.66169 0.318195
\(742\) 14.3593 0.527147
\(743\) 18.9160 0.693962 0.346981 0.937872i \(-0.387207\pi\)
0.346981 + 0.937872i \(0.387207\pi\)
\(744\) 2.62936 0.0963969
\(745\) −31.3356 −1.14805
\(746\) −26.4820 −0.969575
\(747\) −85.5888 −3.13153
\(748\) 20.6075 0.753486
\(749\) 18.8176 0.687581
\(750\) −39.7869 −1.45281
\(751\) 1.60561 0.0585894 0.0292947 0.999571i \(-0.490674\pi\)
0.0292947 + 0.999571i \(0.490674\pi\)
\(752\) −2.09540 −0.0764115
\(753\) 19.8855 0.724669
\(754\) −2.59758 −0.0945982
\(755\) 9.66238 0.351650
\(756\) 17.1322 0.623094
\(757\) −48.9088 −1.77762 −0.888810 0.458275i \(-0.848467\pi\)
−0.888810 + 0.458275i \(0.848467\pi\)
\(758\) 20.3489 0.739107
\(759\) 66.3905 2.40982
\(760\) −2.05538 −0.0745565
\(761\) 38.1912 1.38443 0.692214 0.721692i \(-0.256635\pi\)
0.692214 + 0.721692i \(0.256635\pi\)
\(762\) −37.7830 −1.36873
\(763\) −19.3706 −0.701261
\(764\) −6.59808 −0.238710
\(765\) 88.5767 3.20250
\(766\) −8.44791 −0.305236
\(767\) 11.4021 0.411708
\(768\) 3.27981 0.118350
\(769\) 39.5368 1.42573 0.712867 0.701299i \(-0.247396\pi\)
0.712867 + 0.701299i \(0.247396\pi\)
\(770\) −7.23927 −0.260885
\(771\) −13.9534 −0.502518
\(772\) 18.1038 0.651569
\(773\) −41.0489 −1.47643 −0.738213 0.674568i \(-0.764330\pi\)
−0.738213 + 0.674568i \(0.764330\pi\)
\(774\) −32.8647 −1.18130
\(775\) 1.07975 0.0387856
\(776\) −2.04540 −0.0734254
\(777\) 39.7635 1.42651
\(778\) −28.8520 −1.03439
\(779\) 1.31632 0.0471622
\(780\) 15.3949 0.551227
\(781\) 25.6348 0.917287
\(782\) −35.0590 −1.25371
\(783\) −16.5032 −0.589776
\(784\) −5.79430 −0.206939
\(785\) 16.2313 0.579320
\(786\) −53.4122 −1.90515
\(787\) −52.0171 −1.85421 −0.927105 0.374802i \(-0.877711\pi\)
−0.927105 + 0.374802i \(0.877711\pi\)
\(788\) −19.5243 −0.695523
\(789\) −41.6845 −1.48401
\(790\) −5.56821 −0.198108
\(791\) 11.3776 0.404541
\(792\) 26.7574 0.950781
\(793\) −22.5290 −0.800029
\(794\) 10.2395 0.363386
\(795\) 81.9777 2.90745
\(796\) −8.31380 −0.294675
\(797\) −43.7229 −1.54874 −0.774372 0.632730i \(-0.781934\pi\)
−0.774372 + 0.632730i \(0.781934\pi\)
\(798\) 3.87282 0.137096
\(799\) 12.5185 0.442872
\(800\) 1.34685 0.0476184
\(801\) 24.0669 0.850361
\(802\) 29.9424 1.05730
\(803\) 37.4055 1.32001
\(804\) −23.0312 −0.812249
\(805\) 12.3160 0.434082
\(806\) −1.96878 −0.0693472
\(807\) 26.3462 0.927431
\(808\) 3.98337 0.140134
\(809\) 45.6733 1.60579 0.802895 0.596121i \(-0.203292\pi\)
0.802895 + 0.596121i \(0.203292\pi\)
\(810\) 53.3293 1.87380
\(811\) −33.4049 −1.17300 −0.586502 0.809948i \(-0.699495\pi\)
−0.586502 + 0.809948i \(0.699495\pi\)
\(812\) −1.16143 −0.0407582
\(813\) −58.5694 −2.05412
\(814\) 38.0854 1.33489
\(815\) 12.9606 0.453990
\(816\) −19.5944 −0.685942
\(817\) −4.55603 −0.159395
\(818\) 7.40367 0.258863
\(819\) −20.9178 −0.730929
\(820\) 2.33958 0.0817017
\(821\) 23.1612 0.808331 0.404165 0.914686i \(-0.367562\pi\)
0.404165 + 0.914686i \(0.367562\pi\)
\(822\) −4.98665 −0.173929
\(823\) 15.2517 0.531642 0.265821 0.964022i \(-0.414357\pi\)
0.265821 + 0.964022i \(0.414357\pi\)
\(824\) 8.36098 0.291268
\(825\) 15.2374 0.530497
\(826\) 5.09813 0.177387
\(827\) −30.2522 −1.05197 −0.525986 0.850493i \(-0.676304\pi\)
−0.525986 + 0.850493i \(0.676304\pi\)
\(828\) −45.5216 −1.58199
\(829\) 33.0136 1.14661 0.573304 0.819342i \(-0.305661\pi\)
0.573304 + 0.819342i \(0.305661\pi\)
\(830\) −21.0886 −0.731998
\(831\) 97.6410 3.38713
\(832\) −2.45581 −0.0851400
\(833\) 34.6167 1.19940
\(834\) −64.7707 −2.24283
\(835\) −23.3386 −0.807666
\(836\) 3.70937 0.128291
\(837\) −12.5082 −0.432347
\(838\) −4.67884 −0.161628
\(839\) 6.06219 0.209290 0.104645 0.994510i \(-0.466629\pi\)
0.104645 + 0.994510i \(0.466629\pi\)
\(840\) 6.88338 0.237499
\(841\) −27.8812 −0.961421
\(842\) −1.46039 −0.0503284
\(843\) −25.9727 −0.894547
\(844\) −10.8425 −0.373215
\(845\) 13.3200 0.458220
\(846\) 16.2543 0.558836
\(847\) 0.986323 0.0338905
\(848\) −13.0772 −0.449072
\(849\) 92.6238 3.17884
\(850\) −8.04645 −0.275991
\(851\) −64.7936 −2.22110
\(852\) −24.3746 −0.835060
\(853\) 2.88607 0.0988170 0.0494085 0.998779i \(-0.484266\pi\)
0.0494085 + 0.998779i \(0.484266\pi\)
\(854\) −10.0732 −0.344697
\(855\) 15.9439 0.545269
\(856\) −17.1374 −0.585744
\(857\) 19.8724 0.678829 0.339414 0.940637i \(-0.389771\pi\)
0.339414 + 0.940637i \(0.389771\pi\)
\(858\) −27.7834 −0.948510
\(859\) −16.4754 −0.562134 −0.281067 0.959688i \(-0.590688\pi\)
−0.281067 + 0.959688i \(0.590688\pi\)
\(860\) −8.09770 −0.276129
\(861\) −4.40832 −0.150235
\(862\) 24.5944 0.837689
\(863\) −1.94990 −0.0663754 −0.0331877 0.999449i \(-0.510566\pi\)
−0.0331877 + 0.999449i \(0.510566\pi\)
\(864\) −15.6025 −0.530808
\(865\) 48.1710 1.63786
\(866\) −13.4899 −0.458406
\(867\) 61.3055 2.08204
\(868\) −0.880280 −0.0298786
\(869\) 10.0490 0.340890
\(870\) −6.63064 −0.224800
\(871\) 17.2450 0.584326
\(872\) 17.6410 0.597399
\(873\) 15.8664 0.536997
\(874\) −6.31066 −0.213461
\(875\) 13.3202 0.450306
\(876\) −35.5666 −1.20168
\(877\) 46.5008 1.57022 0.785111 0.619355i \(-0.212606\pi\)
0.785111 + 0.619355i \(0.212606\pi\)
\(878\) 28.2774 0.954317
\(879\) −57.6242 −1.94361
\(880\) 6.59288 0.222246
\(881\) 21.2602 0.716274 0.358137 0.933669i \(-0.383412\pi\)
0.358137 + 0.933669i \(0.383412\pi\)
\(882\) 44.9472 1.51345
\(883\) 8.18177 0.275339 0.137669 0.990478i \(-0.456039\pi\)
0.137669 + 0.990478i \(0.456039\pi\)
\(884\) 14.6717 0.493462
\(885\) 29.1054 0.978366
\(886\) −17.9594 −0.603359
\(887\) 36.7954 1.23547 0.617734 0.786387i \(-0.288051\pi\)
0.617734 + 0.786387i \(0.288051\pi\)
\(888\) −36.2130 −1.21523
\(889\) 12.6493 0.424245
\(890\) 5.92996 0.198773
\(891\) −96.2441 −3.22430
\(892\) −1.51293 −0.0506567
\(893\) 2.25334 0.0754051
\(894\) −53.7715 −1.79839
\(895\) −0.184711 −0.00617422
\(896\) −1.09804 −0.0366831
\(897\) 47.2672 1.57821
\(898\) −32.7174 −1.09179
\(899\) 0.847958 0.0282810
\(900\) −10.4477 −0.348258
\(901\) 78.1264 2.60277
\(902\) −4.22227 −0.140586
\(903\) 15.2579 0.507753
\(904\) −10.3617 −0.344625
\(905\) 25.9659 0.863137
\(906\) 16.5805 0.550852
\(907\) −55.2478 −1.83447 −0.917236 0.398343i \(-0.869585\pi\)
−0.917236 + 0.398343i \(0.869585\pi\)
\(908\) 10.8934 0.361510
\(909\) −30.8995 −1.02487
\(910\) −5.15405 −0.170855
\(911\) −29.3886 −0.973689 −0.486844 0.873489i \(-0.661852\pi\)
−0.486844 + 0.873489i \(0.661852\pi\)
\(912\) −3.52701 −0.116791
\(913\) 38.0589 1.25957
\(914\) 40.8658 1.35172
\(915\) −57.5081 −1.90116
\(916\) −7.10403 −0.234724
\(917\) 17.8818 0.590510
\(918\) 93.2134 3.07650
\(919\) 40.5393 1.33727 0.668635 0.743591i \(-0.266879\pi\)
0.668635 + 0.743591i \(0.266879\pi\)
\(920\) −11.2163 −0.369790
\(921\) 14.7640 0.486492
\(922\) −7.24778 −0.238693
\(923\) 18.2509 0.600736
\(924\) −12.4225 −0.408671
\(925\) −14.8709 −0.488951
\(926\) 26.8102 0.881037
\(927\) −64.8573 −2.13019
\(928\) 1.05773 0.0347216
\(929\) −31.7618 −1.04207 −0.521036 0.853535i \(-0.674454\pi\)
−0.521036 + 0.853535i \(0.674454\pi\)
\(930\) −5.02554 −0.164794
\(931\) 6.23103 0.204214
\(932\) 29.5080 0.966568
\(933\) −43.5393 −1.42541
\(934\) 40.4222 1.32266
\(935\) −39.3876 −1.28811
\(936\) 19.0501 0.622672
\(937\) 7.68717 0.251129 0.125564 0.992085i \(-0.459926\pi\)
0.125564 + 0.992085i \(0.459926\pi\)
\(938\) 7.71061 0.251760
\(939\) 59.9071 1.95499
\(940\) 4.00499 0.130628
\(941\) −40.2010 −1.31051 −0.655257 0.755406i \(-0.727440\pi\)
−0.655257 + 0.755406i \(0.727440\pi\)
\(942\) 27.8528 0.907492
\(943\) 7.18324 0.233918
\(944\) −4.64292 −0.151114
\(945\) −32.7452 −1.06520
\(946\) 14.6140 0.475143
\(947\) 4.60833 0.149751 0.0748753 0.997193i \(-0.476144\pi\)
0.0748753 + 0.997193i \(0.476144\pi\)
\(948\) −9.55500 −0.310332
\(949\) 26.6311 0.864482
\(950\) −1.44837 −0.0469913
\(951\) −15.8377 −0.513572
\(952\) 6.56000 0.212611
\(953\) 16.6350 0.538860 0.269430 0.963020i \(-0.413165\pi\)
0.269430 + 0.963020i \(0.413165\pi\)
\(954\) 101.441 3.28429
\(955\) 12.6110 0.408084
\(956\) 4.21162 0.136214
\(957\) 11.9664 0.386819
\(958\) 42.7351 1.38071
\(959\) 1.66948 0.0539102
\(960\) −6.26877 −0.202324
\(961\) −30.3573 −0.979268
\(962\) 27.1151 0.874227
\(963\) 132.937 4.28384
\(964\) 19.4162 0.625355
\(965\) −34.6021 −1.11388
\(966\) 21.1341 0.679979
\(967\) 57.5053 1.84924 0.924622 0.380885i \(-0.124381\pi\)
0.924622 + 0.380885i \(0.124381\pi\)
\(968\) −0.898254 −0.0288710
\(969\) 21.0713 0.676908
\(970\) 3.90941 0.125524
\(971\) 2.47546 0.0794413 0.0397206 0.999211i \(-0.487353\pi\)
0.0397206 + 0.999211i \(0.487353\pi\)
\(972\) 44.7051 1.43392
\(973\) 21.6845 0.695174
\(974\) −29.2596 −0.937537
\(975\) 10.8484 0.347426
\(976\) 9.17375 0.293645
\(977\) −55.9403 −1.78969 −0.894845 0.446377i \(-0.852714\pi\)
−0.894845 + 0.446377i \(0.852714\pi\)
\(978\) 22.2403 0.711166
\(979\) −10.7019 −0.342033
\(980\) 11.0748 0.353770
\(981\) −136.843 −4.36908
\(982\) 2.36499 0.0754698
\(983\) 5.66670 0.180740 0.0903698 0.995908i \(-0.471195\pi\)
0.0903698 + 0.995908i \(0.471195\pi\)
\(984\) 4.01470 0.127984
\(985\) 37.3171 1.18902
\(986\) −6.31913 −0.201242
\(987\) −7.54633 −0.240202
\(988\) 2.64091 0.0840187
\(989\) −24.8624 −0.790580
\(990\) −51.1419 −1.62540
\(991\) 17.9190 0.569216 0.284608 0.958644i \(-0.408137\pi\)
0.284608 + 0.958644i \(0.408137\pi\)
\(992\) 0.801680 0.0254534
\(993\) −64.9429 −2.06090
\(994\) 8.16035 0.258831
\(995\) 15.8903 0.503758
\(996\) −36.1879 −1.14666
\(997\) 30.1813 0.955852 0.477926 0.878400i \(-0.341389\pi\)
0.477926 + 0.878400i \(0.341389\pi\)
\(998\) −27.2837 −0.863649
\(999\) 172.270 5.45040
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 4006.2.a.g.1.40 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.40 40 1.1 even 1 trivial