Properties

Label 4011.2.a.m.1.17
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $29$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.830058 q^{2} +1.00000 q^{3} -1.31100 q^{4} -1.52882 q^{5} +0.830058 q^{6} -1.00000 q^{7} -2.74832 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.830058 q^{2} +1.00000 q^{3} -1.31100 q^{4} -1.52882 q^{5} +0.830058 q^{6} -1.00000 q^{7} -2.74832 q^{8} +1.00000 q^{9} -1.26901 q^{10} +4.02473 q^{11} -1.31100 q^{12} +6.14463 q^{13} -0.830058 q^{14} -1.52882 q^{15} +0.340740 q^{16} -3.32216 q^{17} +0.830058 q^{18} +2.48074 q^{19} +2.00429 q^{20} -1.00000 q^{21} +3.34076 q^{22} -2.89647 q^{23} -2.74832 q^{24} -2.66271 q^{25} +5.10040 q^{26} +1.00000 q^{27} +1.31100 q^{28} -10.4514 q^{29} -1.26901 q^{30} -5.02164 q^{31} +5.77948 q^{32} +4.02473 q^{33} -2.75758 q^{34} +1.52882 q^{35} -1.31100 q^{36} -6.55237 q^{37} +2.05916 q^{38} +6.14463 q^{39} +4.20169 q^{40} +11.1902 q^{41} -0.830058 q^{42} +4.15694 q^{43} -5.27644 q^{44} -1.52882 q^{45} -2.40424 q^{46} +13.4200 q^{47} +0.340740 q^{48} +1.00000 q^{49} -2.21021 q^{50} -3.32216 q^{51} -8.05563 q^{52} +8.05843 q^{53} +0.830058 q^{54} -6.15309 q^{55} +2.74832 q^{56} +2.48074 q^{57} -8.67522 q^{58} +13.5392 q^{59} +2.00429 q^{60} +0.535440 q^{61} -4.16825 q^{62} -1.00000 q^{63} +4.11582 q^{64} -9.39402 q^{65} +3.34076 q^{66} -3.24185 q^{67} +4.35537 q^{68} -2.89647 q^{69} +1.26901 q^{70} +4.25971 q^{71} -2.74832 q^{72} -8.90203 q^{73} -5.43885 q^{74} -2.66271 q^{75} -3.25227 q^{76} -4.02473 q^{77} +5.10040 q^{78} +16.1767 q^{79} -0.520930 q^{80} +1.00000 q^{81} +9.28847 q^{82} +13.7237 q^{83} +1.31100 q^{84} +5.07898 q^{85} +3.45050 q^{86} -10.4514 q^{87} -11.0613 q^{88} -14.1315 q^{89} -1.26901 q^{90} -6.14463 q^{91} +3.79729 q^{92} -5.02164 q^{93} +11.1394 q^{94} -3.79261 q^{95} +5.77948 q^{96} -4.30960 q^{97} +0.830058 q^{98} +4.02473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.830058 0.586939 0.293470 0.955968i \(-0.405190\pi\)
0.293470 + 0.955968i \(0.405190\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.31100 −0.655502
\(5\) −1.52882 −0.683709 −0.341854 0.939753i \(-0.611055\pi\)
−0.341854 + 0.939753i \(0.611055\pi\)
\(6\) 0.830058 0.338870
\(7\) −1.00000 −0.377964
\(8\) −2.74832 −0.971679
\(9\) 1.00000 0.333333
\(10\) −1.26901 −0.401296
\(11\) 4.02473 1.21350 0.606751 0.794892i \(-0.292472\pi\)
0.606751 + 0.794892i \(0.292472\pi\)
\(12\) −1.31100 −0.378454
\(13\) 6.14463 1.70421 0.852107 0.523368i \(-0.175325\pi\)
0.852107 + 0.523368i \(0.175325\pi\)
\(14\) −0.830058 −0.221842
\(15\) −1.52882 −0.394739
\(16\) 0.340740 0.0851851
\(17\) −3.32216 −0.805742 −0.402871 0.915257i \(-0.631988\pi\)
−0.402871 + 0.915257i \(0.631988\pi\)
\(18\) 0.830058 0.195646
\(19\) 2.48074 0.569122 0.284561 0.958658i \(-0.408152\pi\)
0.284561 + 0.958658i \(0.408152\pi\)
\(20\) 2.00429 0.448172
\(21\) −1.00000 −0.218218
\(22\) 3.34076 0.712253
\(23\) −2.89647 −0.603957 −0.301978 0.953315i \(-0.597647\pi\)
−0.301978 + 0.953315i \(0.597647\pi\)
\(24\) −2.74832 −0.560999
\(25\) −2.66271 −0.532543
\(26\) 5.10040 1.00027
\(27\) 1.00000 0.192450
\(28\) 1.31100 0.247757
\(29\) −10.4514 −1.94077 −0.970384 0.241570i \(-0.922338\pi\)
−0.970384 + 0.241570i \(0.922338\pi\)
\(30\) −1.26901 −0.231688
\(31\) −5.02164 −0.901914 −0.450957 0.892546i \(-0.648917\pi\)
−0.450957 + 0.892546i \(0.648917\pi\)
\(32\) 5.77948 1.02168
\(33\) 4.02473 0.700616
\(34\) −2.75758 −0.472922
\(35\) 1.52882 0.258418
\(36\) −1.31100 −0.218501
\(37\) −6.55237 −1.07720 −0.538602 0.842560i \(-0.681047\pi\)
−0.538602 + 0.842560i \(0.681047\pi\)
\(38\) 2.05916 0.334040
\(39\) 6.14463 0.983928
\(40\) 4.20169 0.664346
\(41\) 11.1902 1.74761 0.873804 0.486278i \(-0.161646\pi\)
0.873804 + 0.486278i \(0.161646\pi\)
\(42\) −0.830058 −0.128081
\(43\) 4.15694 0.633928 0.316964 0.948438i \(-0.397337\pi\)
0.316964 + 0.948438i \(0.397337\pi\)
\(44\) −5.27644 −0.795454
\(45\) −1.52882 −0.227903
\(46\) −2.40424 −0.354486
\(47\) 13.4200 1.95751 0.978756 0.205030i \(-0.0657293\pi\)
0.978756 + 0.205030i \(0.0657293\pi\)
\(48\) 0.340740 0.0491816
\(49\) 1.00000 0.142857
\(50\) −2.21021 −0.312570
\(51\) −3.32216 −0.465195
\(52\) −8.05563 −1.11712
\(53\) 8.05843 1.10691 0.553455 0.832879i \(-0.313309\pi\)
0.553455 + 0.832879i \(0.313309\pi\)
\(54\) 0.830058 0.112957
\(55\) −6.15309 −0.829682
\(56\) 2.74832 0.367260
\(57\) 2.48074 0.328583
\(58\) −8.67522 −1.13911
\(59\) 13.5392 1.76265 0.881326 0.472509i \(-0.156652\pi\)
0.881326 + 0.472509i \(0.156652\pi\)
\(60\) 2.00429 0.258752
\(61\) 0.535440 0.0685561 0.0342780 0.999412i \(-0.489087\pi\)
0.0342780 + 0.999412i \(0.489087\pi\)
\(62\) −4.16825 −0.529369
\(63\) −1.00000 −0.125988
\(64\) 4.11582 0.514478
\(65\) −9.39402 −1.16519
\(66\) 3.34076 0.411219
\(67\) −3.24185 −0.396055 −0.198028 0.980196i \(-0.563454\pi\)
−0.198028 + 0.980196i \(0.563454\pi\)
\(68\) 4.35537 0.528166
\(69\) −2.89647 −0.348694
\(70\) 1.26901 0.151675
\(71\) 4.25971 0.505535 0.252767 0.967527i \(-0.418659\pi\)
0.252767 + 0.967527i \(0.418659\pi\)
\(72\) −2.74832 −0.323893
\(73\) −8.90203 −1.04190 −0.520952 0.853586i \(-0.674423\pi\)
−0.520952 + 0.853586i \(0.674423\pi\)
\(74\) −5.43885 −0.632253
\(75\) −2.66271 −0.307464
\(76\) −3.25227 −0.373060
\(77\) −4.02473 −0.458661
\(78\) 5.10040 0.577506
\(79\) 16.1767 1.82002 0.910009 0.414589i \(-0.136075\pi\)
0.910009 + 0.414589i \(0.136075\pi\)
\(80\) −0.520930 −0.0582418
\(81\) 1.00000 0.111111
\(82\) 9.28847 1.02574
\(83\) 13.7237 1.50637 0.753184 0.657810i \(-0.228517\pi\)
0.753184 + 0.657810i \(0.228517\pi\)
\(84\) 1.31100 0.143042
\(85\) 5.07898 0.550893
\(86\) 3.45050 0.372077
\(87\) −10.4514 −1.12050
\(88\) −11.0613 −1.17914
\(89\) −14.1315 −1.49794 −0.748970 0.662604i \(-0.769451\pi\)
−0.748970 + 0.662604i \(0.769451\pi\)
\(90\) −1.26901 −0.133765
\(91\) −6.14463 −0.644132
\(92\) 3.79729 0.395895
\(93\) −5.02164 −0.520720
\(94\) 11.1394 1.14894
\(95\) −3.79261 −0.389113
\(96\) 5.77948 0.589866
\(97\) −4.30960 −0.437574 −0.218787 0.975773i \(-0.570210\pi\)
−0.218787 + 0.975773i \(0.570210\pi\)
\(98\) 0.830058 0.0838485
\(99\) 4.02473 0.404501
\(100\) 3.49083 0.349083
\(101\) 4.31759 0.429616 0.214808 0.976656i \(-0.431087\pi\)
0.214808 + 0.976656i \(0.431087\pi\)
\(102\) −2.75758 −0.273042
\(103\) 9.58633 0.944569 0.472285 0.881446i \(-0.343429\pi\)
0.472285 + 0.881446i \(0.343429\pi\)
\(104\) −16.8874 −1.65595
\(105\) 1.52882 0.149197
\(106\) 6.68896 0.649690
\(107\) 1.00532 0.0971884 0.0485942 0.998819i \(-0.484526\pi\)
0.0485942 + 0.998819i \(0.484526\pi\)
\(108\) −1.31100 −0.126151
\(109\) 19.3708 1.85539 0.927694 0.373341i \(-0.121788\pi\)
0.927694 + 0.373341i \(0.121788\pi\)
\(110\) −5.10742 −0.486973
\(111\) −6.55237 −0.621924
\(112\) −0.340740 −0.0321969
\(113\) 7.36650 0.692982 0.346491 0.938053i \(-0.387373\pi\)
0.346491 + 0.938053i \(0.387373\pi\)
\(114\) 2.05916 0.192858
\(115\) 4.42818 0.412930
\(116\) 13.7018 1.27218
\(117\) 6.14463 0.568071
\(118\) 11.2383 1.03457
\(119\) 3.32216 0.304542
\(120\) 4.20169 0.383560
\(121\) 5.19848 0.472589
\(122\) 0.444446 0.0402383
\(123\) 11.1902 1.00898
\(124\) 6.58339 0.591206
\(125\) 11.7149 1.04781
\(126\) −0.830058 −0.0739474
\(127\) 13.7820 1.22295 0.611476 0.791263i \(-0.290576\pi\)
0.611476 + 0.791263i \(0.290576\pi\)
\(128\) −8.14259 −0.719711
\(129\) 4.15694 0.365999
\(130\) −7.79758 −0.683893
\(131\) −13.4714 −1.17700 −0.588499 0.808498i \(-0.700281\pi\)
−0.588499 + 0.808498i \(0.700281\pi\)
\(132\) −5.27644 −0.459255
\(133\) −2.48074 −0.215108
\(134\) −2.69092 −0.232460
\(135\) −1.52882 −0.131580
\(136\) 9.13037 0.782923
\(137\) −18.8074 −1.60683 −0.803413 0.595423i \(-0.796985\pi\)
−0.803413 + 0.595423i \(0.796985\pi\)
\(138\) −2.40424 −0.204663
\(139\) −7.09584 −0.601861 −0.300930 0.953646i \(-0.597297\pi\)
−0.300930 + 0.953646i \(0.597297\pi\)
\(140\) −2.00429 −0.169393
\(141\) 13.4200 1.13017
\(142\) 3.53581 0.296718
\(143\) 24.7305 2.06807
\(144\) 0.340740 0.0283950
\(145\) 15.9782 1.32692
\(146\) −7.38920 −0.611534
\(147\) 1.00000 0.0824786
\(148\) 8.59019 0.706109
\(149\) 21.9661 1.79953 0.899766 0.436373i \(-0.143737\pi\)
0.899766 + 0.436373i \(0.143737\pi\)
\(150\) −2.21021 −0.180463
\(151\) −12.5399 −1.02048 −0.510241 0.860032i \(-0.670444\pi\)
−0.510241 + 0.860032i \(0.670444\pi\)
\(152\) −6.81789 −0.553004
\(153\) −3.32216 −0.268581
\(154\) −3.34076 −0.269206
\(155\) 7.67718 0.616646
\(156\) −8.05563 −0.644967
\(157\) 0.792324 0.0632343 0.0316172 0.999500i \(-0.489934\pi\)
0.0316172 + 0.999500i \(0.489934\pi\)
\(158\) 13.4276 1.06824
\(159\) 8.05843 0.639075
\(160\) −8.83578 −0.698530
\(161\) 2.89647 0.228274
\(162\) 0.830058 0.0652155
\(163\) 21.1577 1.65720 0.828599 0.559842i \(-0.189138\pi\)
0.828599 + 0.559842i \(0.189138\pi\)
\(164\) −14.6703 −1.14556
\(165\) −6.15309 −0.479017
\(166\) 11.3914 0.884147
\(167\) 21.0658 1.63012 0.815059 0.579378i \(-0.196705\pi\)
0.815059 + 0.579378i \(0.196705\pi\)
\(168\) 2.74832 0.212038
\(169\) 24.7565 1.90434
\(170\) 4.21585 0.323341
\(171\) 2.48074 0.189707
\(172\) −5.44977 −0.415541
\(173\) 7.57553 0.575957 0.287978 0.957637i \(-0.407017\pi\)
0.287978 + 0.957637i \(0.407017\pi\)
\(174\) −8.67522 −0.657667
\(175\) 2.66271 0.201282
\(176\) 1.37139 0.103372
\(177\) 13.5392 1.01767
\(178\) −11.7300 −0.879200
\(179\) −5.01295 −0.374685 −0.187343 0.982295i \(-0.559987\pi\)
−0.187343 + 0.982295i \(0.559987\pi\)
\(180\) 2.00429 0.149391
\(181\) 4.19182 0.311575 0.155788 0.987791i \(-0.450208\pi\)
0.155788 + 0.987791i \(0.450208\pi\)
\(182\) −5.10040 −0.378067
\(183\) 0.535440 0.0395809
\(184\) 7.96045 0.586852
\(185\) 10.0174 0.736493
\(186\) −4.16825 −0.305631
\(187\) −13.3708 −0.977770
\(188\) −17.5937 −1.28315
\(189\) −1.00000 −0.0727393
\(190\) −3.14808 −0.228386
\(191\) −1.00000 −0.0723575
\(192\) 4.11582 0.297034
\(193\) −1.04418 −0.0751618 −0.0375809 0.999294i \(-0.511965\pi\)
−0.0375809 + 0.999294i \(0.511965\pi\)
\(194\) −3.57722 −0.256829
\(195\) −9.39402 −0.672720
\(196\) −1.31100 −0.0936432
\(197\) −7.51328 −0.535299 −0.267649 0.963516i \(-0.586247\pi\)
−0.267649 + 0.963516i \(0.586247\pi\)
\(198\) 3.34076 0.237418
\(199\) 3.41954 0.242405 0.121202 0.992628i \(-0.461325\pi\)
0.121202 + 0.992628i \(0.461325\pi\)
\(200\) 7.31800 0.517461
\(201\) −3.24185 −0.228663
\(202\) 3.58385 0.252158
\(203\) 10.4514 0.733541
\(204\) 4.35537 0.304937
\(205\) −17.1077 −1.19486
\(206\) 7.95721 0.554405
\(207\) −2.89647 −0.201319
\(208\) 2.09372 0.145174
\(209\) 9.98433 0.690631
\(210\) 1.26901 0.0875699
\(211\) −23.8431 −1.64143 −0.820715 0.571338i \(-0.806425\pi\)
−0.820715 + 0.571338i \(0.806425\pi\)
\(212\) −10.5646 −0.725582
\(213\) 4.25971 0.291871
\(214\) 0.834478 0.0570437
\(215\) −6.35522 −0.433422
\(216\) −2.74832 −0.187000
\(217\) 5.02164 0.340891
\(218\) 16.0789 1.08900
\(219\) −8.90203 −0.601543
\(220\) 8.06673 0.543859
\(221\) −20.4134 −1.37316
\(222\) −5.43885 −0.365032
\(223\) −19.3056 −1.29280 −0.646401 0.762998i \(-0.723726\pi\)
−0.646401 + 0.762998i \(0.723726\pi\)
\(224\) −5.77948 −0.386158
\(225\) −2.66271 −0.177514
\(226\) 6.11462 0.406738
\(227\) −20.6127 −1.36812 −0.684058 0.729428i \(-0.739786\pi\)
−0.684058 + 0.729428i \(0.739786\pi\)
\(228\) −3.25227 −0.215387
\(229\) −10.0822 −0.666250 −0.333125 0.942883i \(-0.608103\pi\)
−0.333125 + 0.942883i \(0.608103\pi\)
\(230\) 3.67565 0.242365
\(231\) −4.02473 −0.264808
\(232\) 28.7237 1.88580
\(233\) 22.0942 1.44744 0.723719 0.690094i \(-0.242431\pi\)
0.723719 + 0.690094i \(0.242431\pi\)
\(234\) 5.10040 0.333423
\(235\) −20.5168 −1.33837
\(236\) −17.7499 −1.15542
\(237\) 16.1767 1.05079
\(238\) 2.75758 0.178748
\(239\) 1.69534 0.109662 0.0548311 0.998496i \(-0.482538\pi\)
0.0548311 + 0.998496i \(0.482538\pi\)
\(240\) −0.520930 −0.0336259
\(241\) 2.45933 0.158419 0.0792096 0.996858i \(-0.474760\pi\)
0.0792096 + 0.996858i \(0.474760\pi\)
\(242\) 4.31504 0.277381
\(243\) 1.00000 0.0641500
\(244\) −0.701964 −0.0449387
\(245\) −1.52882 −0.0976727
\(246\) 9.28847 0.592212
\(247\) 15.2432 0.969905
\(248\) 13.8011 0.876371
\(249\) 13.7237 0.869702
\(250\) 9.72404 0.615002
\(251\) 12.0568 0.761018 0.380509 0.924777i \(-0.375749\pi\)
0.380509 + 0.924777i \(0.375749\pi\)
\(252\) 1.31100 0.0825855
\(253\) −11.6575 −0.732903
\(254\) 11.4398 0.717799
\(255\) 5.07898 0.318058
\(256\) −14.9905 −0.936905
\(257\) 9.62851 0.600610 0.300305 0.953843i \(-0.402911\pi\)
0.300305 + 0.953843i \(0.402911\pi\)
\(258\) 3.45050 0.214819
\(259\) 6.55237 0.407145
\(260\) 12.3156 0.763781
\(261\) −10.4514 −0.646922
\(262\) −11.1820 −0.690827
\(263\) 19.3325 1.19210 0.596048 0.802949i \(-0.296737\pi\)
0.596048 + 0.802949i \(0.296737\pi\)
\(264\) −11.0613 −0.680774
\(265\) −12.3199 −0.756805
\(266\) −2.05916 −0.126255
\(267\) −14.1315 −0.864836
\(268\) 4.25008 0.259615
\(269\) −13.3998 −0.816997 −0.408499 0.912759i \(-0.633948\pi\)
−0.408499 + 0.912759i \(0.633948\pi\)
\(270\) −1.26901 −0.0772294
\(271\) 14.5707 0.885106 0.442553 0.896742i \(-0.354073\pi\)
0.442553 + 0.896742i \(0.354073\pi\)
\(272\) −1.13199 −0.0686372
\(273\) −6.14463 −0.371890
\(274\) −15.6112 −0.943109
\(275\) −10.7167 −0.646242
\(276\) 3.79729 0.228570
\(277\) 1.22840 0.0738073 0.0369037 0.999319i \(-0.488251\pi\)
0.0369037 + 0.999319i \(0.488251\pi\)
\(278\) −5.88995 −0.353256
\(279\) −5.02164 −0.300638
\(280\) −4.20169 −0.251099
\(281\) −8.52086 −0.508312 −0.254156 0.967163i \(-0.581798\pi\)
−0.254156 + 0.967163i \(0.581798\pi\)
\(282\) 11.1394 0.663341
\(283\) 12.5808 0.747851 0.373926 0.927459i \(-0.378012\pi\)
0.373926 + 0.927459i \(0.378012\pi\)
\(284\) −5.58450 −0.331379
\(285\) −3.79261 −0.224655
\(286\) 20.5277 1.21383
\(287\) −11.1902 −0.660534
\(288\) 5.77948 0.340559
\(289\) −5.96325 −0.350780
\(290\) 13.2628 0.778821
\(291\) −4.30960 −0.252633
\(292\) 11.6706 0.682970
\(293\) −12.1071 −0.707306 −0.353653 0.935377i \(-0.615061\pi\)
−0.353653 + 0.935377i \(0.615061\pi\)
\(294\) 0.830058 0.0484099
\(295\) −20.6990 −1.20514
\(296\) 18.0081 1.04670
\(297\) 4.02473 0.233539
\(298\) 18.2331 1.05622
\(299\) −17.7978 −1.02927
\(300\) 3.49083 0.201543
\(301\) −4.15694 −0.239602
\(302\) −10.4088 −0.598961
\(303\) 4.31759 0.248039
\(304\) 0.845289 0.0484807
\(305\) −0.818591 −0.0468724
\(306\) −2.75758 −0.157641
\(307\) −19.8703 −1.13406 −0.567028 0.823698i \(-0.691907\pi\)
−0.567028 + 0.823698i \(0.691907\pi\)
\(308\) 5.27644 0.300653
\(309\) 9.58633 0.545347
\(310\) 6.37250 0.361934
\(311\) 31.9589 1.81222 0.906112 0.423037i \(-0.139036\pi\)
0.906112 + 0.423037i \(0.139036\pi\)
\(312\) −16.8874 −0.956063
\(313\) −7.83387 −0.442797 −0.221398 0.975183i \(-0.571062\pi\)
−0.221398 + 0.975183i \(0.571062\pi\)
\(314\) 0.657675 0.0371147
\(315\) 1.52882 0.0861392
\(316\) −21.2077 −1.19303
\(317\) −9.12873 −0.512720 −0.256360 0.966581i \(-0.582523\pi\)
−0.256360 + 0.966581i \(0.582523\pi\)
\(318\) 6.68896 0.375099
\(319\) −42.0639 −2.35513
\(320\) −6.29235 −0.351753
\(321\) 1.00532 0.0561118
\(322\) 2.40424 0.133983
\(323\) −8.24143 −0.458565
\(324\) −1.31100 −0.0728336
\(325\) −16.3614 −0.907566
\(326\) 17.5621 0.972675
\(327\) 19.3708 1.07121
\(328\) −30.7542 −1.69812
\(329\) −13.4200 −0.739870
\(330\) −5.10742 −0.281154
\(331\) −20.1555 −1.10785 −0.553924 0.832567i \(-0.686870\pi\)
−0.553924 + 0.832567i \(0.686870\pi\)
\(332\) −17.9918 −0.987428
\(333\) −6.55237 −0.359068
\(334\) 17.4858 0.956780
\(335\) 4.95620 0.270786
\(336\) −0.340740 −0.0185889
\(337\) −1.18462 −0.0645303 −0.0322652 0.999479i \(-0.510272\pi\)
−0.0322652 + 0.999479i \(0.510272\pi\)
\(338\) 20.5493 1.11773
\(339\) 7.36650 0.400093
\(340\) −6.65857 −0.361111
\(341\) −20.2108 −1.09447
\(342\) 2.05916 0.111347
\(343\) −1.00000 −0.0539949
\(344\) −11.4246 −0.615975
\(345\) 4.42818 0.238405
\(346\) 6.28812 0.338052
\(347\) 18.2669 0.980620 0.490310 0.871548i \(-0.336884\pi\)
0.490310 + 0.871548i \(0.336884\pi\)
\(348\) 13.7018 0.734492
\(349\) 31.1707 1.66853 0.834265 0.551364i \(-0.185893\pi\)
0.834265 + 0.551364i \(0.185893\pi\)
\(350\) 2.21021 0.118140
\(351\) 6.14463 0.327976
\(352\) 23.2609 1.23981
\(353\) −28.9747 −1.54217 −0.771085 0.636733i \(-0.780286\pi\)
−0.771085 + 0.636733i \(0.780286\pi\)
\(354\) 11.2383 0.597309
\(355\) −6.51233 −0.345638
\(356\) 18.5265 0.981903
\(357\) 3.32216 0.175827
\(358\) −4.16103 −0.219918
\(359\) −10.0633 −0.531119 −0.265560 0.964094i \(-0.585557\pi\)
−0.265560 + 0.964094i \(0.585557\pi\)
\(360\) 4.20169 0.221449
\(361\) −12.8459 −0.676101
\(362\) 3.47945 0.182876
\(363\) 5.19848 0.272850
\(364\) 8.05563 0.422230
\(365\) 13.6096 0.712358
\(366\) 0.444446 0.0232316
\(367\) −18.6218 −0.972051 −0.486025 0.873945i \(-0.661554\pi\)
−0.486025 + 0.873945i \(0.661554\pi\)
\(368\) −0.986945 −0.0514481
\(369\) 11.1902 0.582536
\(370\) 8.31501 0.432277
\(371\) −8.05843 −0.418373
\(372\) 6.58339 0.341333
\(373\) −7.15580 −0.370513 −0.185257 0.982690i \(-0.559312\pi\)
−0.185257 + 0.982690i \(0.559312\pi\)
\(374\) −11.0985 −0.573892
\(375\) 11.7149 0.604955
\(376\) −36.8826 −1.90207
\(377\) −64.2197 −3.30748
\(378\) −0.830058 −0.0426936
\(379\) 2.52006 0.129447 0.0647233 0.997903i \(-0.479384\pi\)
0.0647233 + 0.997903i \(0.479384\pi\)
\(380\) 4.97212 0.255065
\(381\) 13.7820 0.706072
\(382\) −0.830058 −0.0424694
\(383\) 8.77635 0.448451 0.224225 0.974537i \(-0.428015\pi\)
0.224225 + 0.974537i \(0.428015\pi\)
\(384\) −8.14259 −0.415525
\(385\) 6.15309 0.313590
\(386\) −0.866730 −0.0441154
\(387\) 4.15694 0.211309
\(388\) 5.64991 0.286831
\(389\) 24.4274 1.23852 0.619259 0.785187i \(-0.287433\pi\)
0.619259 + 0.785187i \(0.287433\pi\)
\(390\) −7.79758 −0.394846
\(391\) 9.62255 0.486633
\(392\) −2.74832 −0.138811
\(393\) −13.4714 −0.679541
\(394\) −6.23645 −0.314188
\(395\) −24.7312 −1.24436
\(396\) −5.27644 −0.265151
\(397\) −5.65483 −0.283808 −0.141904 0.989880i \(-0.545322\pi\)
−0.141904 + 0.989880i \(0.545322\pi\)
\(398\) 2.83842 0.142277
\(399\) −2.48074 −0.124193
\(400\) −0.907294 −0.0453647
\(401\) 6.29687 0.314450 0.157225 0.987563i \(-0.449745\pi\)
0.157225 + 0.987563i \(0.449745\pi\)
\(402\) −2.69092 −0.134211
\(403\) −30.8561 −1.53705
\(404\) −5.66037 −0.281614
\(405\) −1.52882 −0.0759676
\(406\) 8.67522 0.430544
\(407\) −26.3716 −1.30719
\(408\) 9.13037 0.452021
\(409\) −21.8882 −1.08230 −0.541151 0.840925i \(-0.682011\pi\)
−0.541151 + 0.840925i \(0.682011\pi\)
\(410\) −14.2004 −0.701308
\(411\) −18.8074 −0.927701
\(412\) −12.5677 −0.619167
\(413\) −13.5392 −0.666220
\(414\) −2.40424 −0.118162
\(415\) −20.9810 −1.02992
\(416\) 35.5128 1.74116
\(417\) −7.09584 −0.347485
\(418\) 8.28757 0.405358
\(419\) −16.4271 −0.802518 −0.401259 0.915965i \(-0.631427\pi\)
−0.401259 + 0.915965i \(0.631427\pi\)
\(420\) −2.00429 −0.0977992
\(421\) −4.73970 −0.230999 −0.115500 0.993308i \(-0.536847\pi\)
−0.115500 + 0.993308i \(0.536847\pi\)
\(422\) −19.7912 −0.963420
\(423\) 13.4200 0.652504
\(424\) −22.1472 −1.07556
\(425\) 8.84596 0.429092
\(426\) 3.53581 0.171310
\(427\) −0.535440 −0.0259118
\(428\) −1.31799 −0.0637072
\(429\) 24.7305 1.19400
\(430\) −5.27520 −0.254393
\(431\) 6.28780 0.302873 0.151436 0.988467i \(-0.451610\pi\)
0.151436 + 0.988467i \(0.451610\pi\)
\(432\) 0.340740 0.0163939
\(433\) 14.8514 0.713711 0.356855 0.934160i \(-0.383849\pi\)
0.356855 + 0.934160i \(0.383849\pi\)
\(434\) 4.16825 0.200083
\(435\) 15.9782 0.766097
\(436\) −25.3952 −1.21621
\(437\) −7.18541 −0.343725
\(438\) −7.38920 −0.353069
\(439\) 7.21505 0.344355 0.172178 0.985066i \(-0.444920\pi\)
0.172178 + 0.985066i \(0.444920\pi\)
\(440\) 16.9107 0.806185
\(441\) 1.00000 0.0476190
\(442\) −16.9443 −0.805960
\(443\) 18.5395 0.880840 0.440420 0.897792i \(-0.354830\pi\)
0.440420 + 0.897792i \(0.354830\pi\)
\(444\) 8.59019 0.407672
\(445\) 21.6046 1.02415
\(446\) −16.0248 −0.758796
\(447\) 21.9661 1.03896
\(448\) −4.11582 −0.194454
\(449\) 30.9615 1.46116 0.730582 0.682825i \(-0.239249\pi\)
0.730582 + 0.682825i \(0.239249\pi\)
\(450\) −2.21021 −0.104190
\(451\) 45.0374 2.12073
\(452\) −9.65751 −0.454251
\(453\) −12.5399 −0.589175
\(454\) −17.1098 −0.803001
\(455\) 9.39402 0.440399
\(456\) −6.81789 −0.319277
\(457\) −3.30691 −0.154691 −0.0773453 0.997004i \(-0.524644\pi\)
−0.0773453 + 0.997004i \(0.524644\pi\)
\(458\) −8.36880 −0.391048
\(459\) −3.32216 −0.155065
\(460\) −5.80537 −0.270677
\(461\) 6.32803 0.294726 0.147363 0.989083i \(-0.452922\pi\)
0.147363 + 0.989083i \(0.452922\pi\)
\(462\) −3.34076 −0.155426
\(463\) 8.22463 0.382231 0.191116 0.981568i \(-0.438789\pi\)
0.191116 + 0.981568i \(0.438789\pi\)
\(464\) −3.56120 −0.165324
\(465\) 7.67718 0.356021
\(466\) 18.3395 0.849559
\(467\) −14.2979 −0.661627 −0.330814 0.943696i \(-0.607323\pi\)
−0.330814 + 0.943696i \(0.607323\pi\)
\(468\) −8.05563 −0.372372
\(469\) 3.24185 0.149695
\(470\) −17.0301 −0.785541
\(471\) 0.792324 0.0365084
\(472\) −37.2101 −1.71273
\(473\) 16.7306 0.769274
\(474\) 13.4276 0.616749
\(475\) −6.60551 −0.303081
\(476\) −4.35537 −0.199628
\(477\) 8.05843 0.368970
\(478\) 1.40723 0.0643651
\(479\) 24.5915 1.12361 0.561806 0.827269i \(-0.310107\pi\)
0.561806 + 0.827269i \(0.310107\pi\)
\(480\) −8.83578 −0.403296
\(481\) −40.2619 −1.83578
\(482\) 2.04138 0.0929824
\(483\) 2.89647 0.131794
\(484\) −6.81523 −0.309783
\(485\) 6.58860 0.299173
\(486\) 0.830058 0.0376522
\(487\) 3.43732 0.155760 0.0778799 0.996963i \(-0.475185\pi\)
0.0778799 + 0.996963i \(0.475185\pi\)
\(488\) −1.47156 −0.0666145
\(489\) 21.1577 0.956784
\(490\) −1.26901 −0.0573279
\(491\) 30.9198 1.39539 0.697696 0.716394i \(-0.254209\pi\)
0.697696 + 0.716394i \(0.254209\pi\)
\(492\) −14.6703 −0.661390
\(493\) 34.7211 1.56376
\(494\) 12.6528 0.569275
\(495\) −6.15309 −0.276561
\(496\) −1.71108 −0.0768296
\(497\) −4.25971 −0.191074
\(498\) 11.3914 0.510463
\(499\) −19.7248 −0.883004 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(500\) −15.3583 −0.686843
\(501\) 21.0658 0.941149
\(502\) 10.0078 0.446671
\(503\) −30.1407 −1.34391 −0.671953 0.740594i \(-0.734544\pi\)
−0.671953 + 0.740594i \(0.734544\pi\)
\(504\) 2.74832 0.122420
\(505\) −6.60081 −0.293732
\(506\) −9.67643 −0.430170
\(507\) 24.7565 1.09947
\(508\) −18.0682 −0.801648
\(509\) 11.6522 0.516476 0.258238 0.966081i \(-0.416858\pi\)
0.258238 + 0.966081i \(0.416858\pi\)
\(510\) 4.21585 0.186681
\(511\) 8.90203 0.393803
\(512\) 3.84223 0.169804
\(513\) 2.48074 0.109528
\(514\) 7.99222 0.352522
\(515\) −14.6558 −0.645810
\(516\) −5.44977 −0.239913
\(517\) 54.0120 2.37545
\(518\) 5.43885 0.238969
\(519\) 7.57553 0.332529
\(520\) 25.8178 1.13219
\(521\) −26.9870 −1.18232 −0.591162 0.806553i \(-0.701330\pi\)
−0.591162 + 0.806553i \(0.701330\pi\)
\(522\) −8.67522 −0.379704
\(523\) −24.8392 −1.08614 −0.543071 0.839687i \(-0.682738\pi\)
−0.543071 + 0.839687i \(0.682738\pi\)
\(524\) 17.6610 0.771525
\(525\) 2.66271 0.116210
\(526\) 16.0471 0.699688
\(527\) 16.6827 0.726710
\(528\) 1.37139 0.0596820
\(529\) −14.6104 −0.635236
\(530\) −10.2262 −0.444198
\(531\) 13.5392 0.587550
\(532\) 3.25227 0.141004
\(533\) 68.7593 2.97830
\(534\) −11.7300 −0.507607
\(535\) −1.53696 −0.0664486
\(536\) 8.90966 0.384839
\(537\) −5.01295 −0.216325
\(538\) −11.1226 −0.479528
\(539\) 4.02473 0.173358
\(540\) 2.00429 0.0862508
\(541\) −5.80003 −0.249363 −0.124681 0.992197i \(-0.539791\pi\)
−0.124681 + 0.992197i \(0.539791\pi\)
\(542\) 12.0945 0.519504
\(543\) 4.19182 0.179888
\(544\) −19.2004 −0.823209
\(545\) −29.6145 −1.26855
\(546\) −5.10040 −0.218277
\(547\) 37.7702 1.61494 0.807468 0.589911i \(-0.200837\pi\)
0.807468 + 0.589911i \(0.200837\pi\)
\(548\) 24.6566 1.05328
\(549\) 0.535440 0.0228520
\(550\) −8.89549 −0.379305
\(551\) −25.9271 −1.10453
\(552\) 7.96045 0.338819
\(553\) −16.1767 −0.687902
\(554\) 1.01964 0.0433204
\(555\) 10.0174 0.425215
\(556\) 9.30267 0.394521
\(557\) −36.1075 −1.52992 −0.764962 0.644075i \(-0.777242\pi\)
−0.764962 + 0.644075i \(0.777242\pi\)
\(558\) −4.16825 −0.176456
\(559\) 25.5429 1.08035
\(560\) 0.520930 0.0220133
\(561\) −13.3708 −0.564516
\(562\) −7.07281 −0.298348
\(563\) −7.63693 −0.321858 −0.160929 0.986966i \(-0.551449\pi\)
−0.160929 + 0.986966i \(0.551449\pi\)
\(564\) −17.5937 −0.740829
\(565\) −11.2620 −0.473798
\(566\) 10.4428 0.438943
\(567\) −1.00000 −0.0419961
\(568\) −11.7071 −0.491218
\(569\) −19.4874 −0.816953 −0.408477 0.912769i \(-0.633940\pi\)
−0.408477 + 0.912769i \(0.633940\pi\)
\(570\) −3.14808 −0.131859
\(571\) −35.7402 −1.49568 −0.747839 0.663880i \(-0.768909\pi\)
−0.747839 + 0.663880i \(0.768909\pi\)
\(572\) −32.4218 −1.35562
\(573\) −1.00000 −0.0417756
\(574\) −9.28847 −0.387693
\(575\) 7.71248 0.321633
\(576\) 4.11582 0.171493
\(577\) −23.2704 −0.968759 −0.484380 0.874858i \(-0.660955\pi\)
−0.484380 + 0.874858i \(0.660955\pi\)
\(578\) −4.94984 −0.205886
\(579\) −1.04418 −0.0433947
\(580\) −20.9475 −0.869798
\(581\) −13.7237 −0.569354
\(582\) −3.57722 −0.148281
\(583\) 32.4330 1.34324
\(584\) 24.4657 1.01240
\(585\) −9.39402 −0.388395
\(586\) −10.0496 −0.415146
\(587\) 13.4787 0.556327 0.278164 0.960534i \(-0.410274\pi\)
0.278164 + 0.960534i \(0.410274\pi\)
\(588\) −1.31100 −0.0540649
\(589\) −12.4574 −0.513298
\(590\) −17.1813 −0.707344
\(591\) −7.51328 −0.309055
\(592\) −2.23266 −0.0917617
\(593\) 18.4944 0.759475 0.379738 0.925094i \(-0.376014\pi\)
0.379738 + 0.925094i \(0.376014\pi\)
\(594\) 3.34076 0.137073
\(595\) −5.07898 −0.208218
\(596\) −28.7976 −1.17960
\(597\) 3.41954 0.139953
\(598\) −14.7732 −0.604120
\(599\) −19.2852 −0.787971 −0.393986 0.919117i \(-0.628904\pi\)
−0.393986 + 0.919117i \(0.628904\pi\)
\(600\) 7.31800 0.298756
\(601\) 14.9518 0.609897 0.304948 0.952369i \(-0.401361\pi\)
0.304948 + 0.952369i \(0.401361\pi\)
\(602\) −3.45050 −0.140632
\(603\) −3.24185 −0.132018
\(604\) 16.4398 0.668928
\(605\) −7.94754 −0.323113
\(606\) 3.58385 0.145584
\(607\) −15.7161 −0.637895 −0.318948 0.947772i \(-0.603329\pi\)
−0.318948 + 0.947772i \(0.603329\pi\)
\(608\) 14.3374 0.581459
\(609\) 10.4514 0.423510
\(610\) −0.679478 −0.0275113
\(611\) 82.4610 3.33602
\(612\) 4.35537 0.176055
\(613\) 28.4145 1.14765 0.573825 0.818978i \(-0.305459\pi\)
0.573825 + 0.818978i \(0.305459\pi\)
\(614\) −16.4935 −0.665622
\(615\) −17.1077 −0.689850
\(616\) 11.0613 0.445671
\(617\) −11.1635 −0.449426 −0.224713 0.974425i \(-0.572145\pi\)
−0.224713 + 0.974425i \(0.572145\pi\)
\(618\) 7.95721 0.320086
\(619\) −27.2446 −1.09505 −0.547526 0.836788i \(-0.684430\pi\)
−0.547526 + 0.836788i \(0.684430\pi\)
\(620\) −10.0648 −0.404213
\(621\) −2.89647 −0.116231
\(622\) 26.5278 1.06367
\(623\) 14.1315 0.566168
\(624\) 2.09372 0.0838160
\(625\) −4.59640 −0.183856
\(626\) −6.50257 −0.259895
\(627\) 9.98433 0.398736
\(628\) −1.03874 −0.0414502
\(629\) 21.7680 0.867948
\(630\) 1.26901 0.0505585
\(631\) 23.1155 0.920215 0.460108 0.887863i \(-0.347811\pi\)
0.460108 + 0.887863i \(0.347811\pi\)
\(632\) −44.4587 −1.76847
\(633\) −23.8431 −0.947680
\(634\) −7.57737 −0.300936
\(635\) −21.0701 −0.836143
\(636\) −10.5646 −0.418915
\(637\) 6.14463 0.243459
\(638\) −34.9155 −1.38232
\(639\) 4.25971 0.168512
\(640\) 12.4486 0.492072
\(641\) 15.6032 0.616289 0.308144 0.951340i \(-0.400292\pi\)
0.308144 + 0.951340i \(0.400292\pi\)
\(642\) 0.834478 0.0329342
\(643\) −35.0952 −1.38402 −0.692009 0.721889i \(-0.743274\pi\)
−0.692009 + 0.721889i \(0.743274\pi\)
\(644\) −3.79729 −0.149634
\(645\) −6.35522 −0.250236
\(646\) −6.84086 −0.269150
\(647\) 26.7307 1.05089 0.525447 0.850827i \(-0.323898\pi\)
0.525447 + 0.850827i \(0.323898\pi\)
\(648\) −2.74832 −0.107964
\(649\) 54.4916 2.13898
\(650\) −13.5809 −0.532686
\(651\) 5.02164 0.196814
\(652\) −27.7378 −1.08630
\(653\) −12.1361 −0.474922 −0.237461 0.971397i \(-0.576315\pi\)
−0.237461 + 0.971397i \(0.576315\pi\)
\(654\) 16.0789 0.628735
\(655\) 20.5953 0.804724
\(656\) 3.81294 0.148870
\(657\) −8.90203 −0.347301
\(658\) −11.1394 −0.434259
\(659\) −3.45960 −0.134767 −0.0673834 0.997727i \(-0.521465\pi\)
−0.0673834 + 0.997727i \(0.521465\pi\)
\(660\) 8.06673 0.313997
\(661\) 31.4619 1.22373 0.611864 0.790963i \(-0.290420\pi\)
0.611864 + 0.790963i \(0.290420\pi\)
\(662\) −16.7303 −0.650240
\(663\) −20.4134 −0.792792
\(664\) −37.7171 −1.46371
\(665\) 3.79261 0.147071
\(666\) −5.43885 −0.210751
\(667\) 30.2721 1.17214
\(668\) −27.6173 −1.06855
\(669\) −19.3056 −0.746399
\(670\) 4.11394 0.158935
\(671\) 2.15500 0.0831930
\(672\) −5.77948 −0.222948
\(673\) 20.6902 0.797548 0.398774 0.917049i \(-0.369436\pi\)
0.398774 + 0.917049i \(0.369436\pi\)
\(674\) −0.983302 −0.0378754
\(675\) −2.66271 −0.102488
\(676\) −32.4558 −1.24830
\(677\) −16.3774 −0.629436 −0.314718 0.949185i \(-0.601910\pi\)
−0.314718 + 0.949185i \(0.601910\pi\)
\(678\) 6.11462 0.234831
\(679\) 4.30960 0.165387
\(680\) −13.9587 −0.535291
\(681\) −20.6127 −0.789882
\(682\) −16.7761 −0.642390
\(683\) −42.5224 −1.62707 −0.813536 0.581514i \(-0.802461\pi\)
−0.813536 + 0.581514i \(0.802461\pi\)
\(684\) −3.25227 −0.124353
\(685\) 28.7531 1.09860
\(686\) −0.830058 −0.0316918
\(687\) −10.0822 −0.384659
\(688\) 1.41644 0.0540012
\(689\) 49.5161 1.88641
\(690\) 3.67565 0.139930
\(691\) −27.0097 −1.02750 −0.513748 0.857941i \(-0.671743\pi\)
−0.513748 + 0.857941i \(0.671743\pi\)
\(692\) −9.93155 −0.377541
\(693\) −4.02473 −0.152887
\(694\) 15.1626 0.575565
\(695\) 10.8482 0.411497
\(696\) 28.7237 1.08877
\(697\) −37.1755 −1.40812
\(698\) 25.8735 0.979326
\(699\) 22.0942 0.835679
\(700\) −3.49083 −0.131941
\(701\) 26.1459 0.987516 0.493758 0.869599i \(-0.335623\pi\)
0.493758 + 0.869599i \(0.335623\pi\)
\(702\) 5.10040 0.192502
\(703\) −16.2548 −0.613060
\(704\) 16.5651 0.624321
\(705\) −20.5168 −0.772707
\(706\) −24.0507 −0.905160
\(707\) −4.31759 −0.162380
\(708\) −17.7499 −0.667083
\(709\) 44.2270 1.66098 0.830489 0.557034i \(-0.188061\pi\)
0.830489 + 0.557034i \(0.188061\pi\)
\(710\) −5.40561 −0.202869
\(711\) 16.1767 0.606673
\(712\) 38.8381 1.45552
\(713\) 14.5451 0.544717
\(714\) 2.75758 0.103200
\(715\) −37.8084 −1.41396
\(716\) 6.57199 0.245607
\(717\) 1.69534 0.0633135
\(718\) −8.35310 −0.311735
\(719\) −7.43310 −0.277208 −0.138604 0.990348i \(-0.544262\pi\)
−0.138604 + 0.990348i \(0.544262\pi\)
\(720\) −0.520930 −0.0194139
\(721\) −9.58633 −0.357014
\(722\) −10.6628 −0.396830
\(723\) 2.45933 0.0914633
\(724\) −5.49549 −0.204238
\(725\) 27.8289 1.03354
\(726\) 4.31504 0.160146
\(727\) 5.28684 0.196078 0.0980390 0.995183i \(-0.468743\pi\)
0.0980390 + 0.995183i \(0.468743\pi\)
\(728\) 16.8874 0.625890
\(729\) 1.00000 0.0370370
\(730\) 11.2967 0.418111
\(731\) −13.8100 −0.510783
\(732\) −0.701964 −0.0259453
\(733\) −35.3919 −1.30723 −0.653615 0.756827i \(-0.726748\pi\)
−0.653615 + 0.756827i \(0.726748\pi\)
\(734\) −15.4572 −0.570535
\(735\) −1.52882 −0.0563913
\(736\) −16.7401 −0.617049
\(737\) −13.0476 −0.480614
\(738\) 9.28847 0.341913
\(739\) −15.0899 −0.555091 −0.277545 0.960713i \(-0.589521\pi\)
−0.277545 + 0.960713i \(0.589521\pi\)
\(740\) −13.1328 −0.482773
\(741\) 15.2432 0.559975
\(742\) −6.68896 −0.245560
\(743\) −30.5071 −1.11920 −0.559599 0.828763i \(-0.689045\pi\)
−0.559599 + 0.828763i \(0.689045\pi\)
\(744\) 13.8011 0.505973
\(745\) −33.5822 −1.23036
\(746\) −5.93973 −0.217469
\(747\) 13.7237 0.502123
\(748\) 17.5292 0.640931
\(749\) −1.00532 −0.0367338
\(750\) 9.72404 0.355072
\(751\) 35.5975 1.29897 0.649486 0.760374i \(-0.274984\pi\)
0.649486 + 0.760374i \(0.274984\pi\)
\(752\) 4.57274 0.166751
\(753\) 12.0568 0.439374
\(754\) −53.3060 −1.94129
\(755\) 19.1712 0.697712
\(756\) 1.31100 0.0476808
\(757\) −24.8284 −0.902405 −0.451203 0.892422i \(-0.649005\pi\)
−0.451203 + 0.892422i \(0.649005\pi\)
\(758\) 2.09179 0.0759773
\(759\) −11.6575 −0.423142
\(760\) 10.4233 0.378093
\(761\) 15.2657 0.553383 0.276691 0.960959i \(-0.410762\pi\)
0.276691 + 0.960959i \(0.410762\pi\)
\(762\) 11.4398 0.414421
\(763\) −19.3708 −0.701271
\(764\) 1.31100 0.0474305
\(765\) 5.07898 0.183631
\(766\) 7.28488 0.263213
\(767\) 83.1932 3.00393
\(768\) −14.9905 −0.540922
\(769\) −15.5419 −0.560456 −0.280228 0.959933i \(-0.590410\pi\)
−0.280228 + 0.959933i \(0.590410\pi\)
\(770\) 5.10742 0.184059
\(771\) 9.62851 0.346762
\(772\) 1.36893 0.0492687
\(773\) −44.9287 −1.61597 −0.807986 0.589202i \(-0.799442\pi\)
−0.807986 + 0.589202i \(0.799442\pi\)
\(774\) 3.45050 0.124026
\(775\) 13.3712 0.480307
\(776\) 11.8442 0.425182
\(777\) 6.55237 0.235065
\(778\) 20.2761 0.726935
\(779\) 27.7599 0.994602
\(780\) 12.3156 0.440969
\(781\) 17.1442 0.613468
\(782\) 7.98727 0.285624
\(783\) −10.4514 −0.373501
\(784\) 0.340740 0.0121693
\(785\) −1.21132 −0.0432339
\(786\) −11.1820 −0.398849
\(787\) −42.5175 −1.51559 −0.757793 0.652495i \(-0.773722\pi\)
−0.757793 + 0.652495i \(0.773722\pi\)
\(788\) 9.84994 0.350889
\(789\) 19.3325 0.688257
\(790\) −20.5283 −0.730365
\(791\) −7.36650 −0.261923
\(792\) −11.0613 −0.393045
\(793\) 3.29008 0.116834
\(794\) −4.69383 −0.166578
\(795\) −12.3199 −0.436941
\(796\) −4.48303 −0.158897
\(797\) −26.6049 −0.942395 −0.471198 0.882028i \(-0.656178\pi\)
−0.471198 + 0.882028i \(0.656178\pi\)
\(798\) −2.05916 −0.0728935
\(799\) −44.5835 −1.57725
\(800\) −15.3891 −0.544087
\(801\) −14.1315 −0.499314
\(802\) 5.22676 0.184563
\(803\) −35.8283 −1.26435
\(804\) 4.25008 0.149889
\(805\) −4.42818 −0.156073
\(806\) −25.6124 −0.902157
\(807\) −13.3998 −0.471694
\(808\) −11.8661 −0.417449
\(809\) −2.82324 −0.0992598 −0.0496299 0.998768i \(-0.515804\pi\)
−0.0496299 + 0.998768i \(0.515804\pi\)
\(810\) −1.26901 −0.0445884
\(811\) −0.309319 −0.0108617 −0.00543084 0.999985i \(-0.501729\pi\)
−0.00543084 + 0.999985i \(0.501729\pi\)
\(812\) −13.7018 −0.480838
\(813\) 14.5707 0.511016
\(814\) −21.8899 −0.767241
\(815\) −32.3463 −1.13304
\(816\) −1.13199 −0.0396277
\(817\) 10.3123 0.360782
\(818\) −18.1685 −0.635246
\(819\) −6.14463 −0.214711
\(820\) 22.4283 0.783230
\(821\) −16.8078 −0.586596 −0.293298 0.956021i \(-0.594753\pi\)
−0.293298 + 0.956021i \(0.594753\pi\)
\(822\) −15.6112 −0.544504
\(823\) −30.6401 −1.06805 −0.534023 0.845470i \(-0.679320\pi\)
−0.534023 + 0.845470i \(0.679320\pi\)
\(824\) −26.3464 −0.917819
\(825\) −10.7167 −0.373108
\(826\) −11.2383 −0.391031
\(827\) 23.2923 0.809954 0.404977 0.914327i \(-0.367279\pi\)
0.404977 + 0.914327i \(0.367279\pi\)
\(828\) 3.79729 0.131965
\(829\) −21.1253 −0.733712 −0.366856 0.930278i \(-0.619566\pi\)
−0.366856 + 0.930278i \(0.619566\pi\)
\(830\) −17.4154 −0.604499
\(831\) 1.22840 0.0426127
\(832\) 25.2902 0.876780
\(833\) −3.32216 −0.115106
\(834\) −5.88995 −0.203952
\(835\) −32.2057 −1.11453
\(836\) −13.0895 −0.452710
\(837\) −5.02164 −0.173573
\(838\) −13.6355 −0.471029
\(839\) 45.6767 1.57693 0.788467 0.615077i \(-0.210875\pi\)
0.788467 + 0.615077i \(0.210875\pi\)
\(840\) −4.20169 −0.144972
\(841\) 80.2307 2.76658
\(842\) −3.93423 −0.135582
\(843\) −8.52086 −0.293474
\(844\) 31.2585 1.07596
\(845\) −37.8481 −1.30202
\(846\) 11.1394 0.382980
\(847\) −5.19848 −0.178622
\(848\) 2.74583 0.0942923
\(849\) 12.5808 0.431772
\(850\) 7.34266 0.251851
\(851\) 18.9788 0.650584
\(852\) −5.58450 −0.191322
\(853\) 5.09505 0.174451 0.0872256 0.996189i \(-0.472200\pi\)
0.0872256 + 0.996189i \(0.472200\pi\)
\(854\) −0.444446 −0.0152086
\(855\) −3.79261 −0.129704
\(856\) −2.76296 −0.0944360
\(857\) 30.7087 1.04899 0.524495 0.851414i \(-0.324254\pi\)
0.524495 + 0.851414i \(0.324254\pi\)
\(858\) 20.5277 0.700805
\(859\) −17.7177 −0.604520 −0.302260 0.953225i \(-0.597741\pi\)
−0.302260 + 0.953225i \(0.597741\pi\)
\(860\) 8.33171 0.284109
\(861\) −11.1902 −0.381359
\(862\) 5.21924 0.177768
\(863\) 11.6399 0.396228 0.198114 0.980179i \(-0.436518\pi\)
0.198114 + 0.980179i \(0.436518\pi\)
\(864\) 5.77948 0.196622
\(865\) −11.5816 −0.393787
\(866\) 12.3275 0.418905
\(867\) −5.96325 −0.202523
\(868\) −6.58339 −0.223455
\(869\) 65.1068 2.20860
\(870\) 13.2628 0.449653
\(871\) −19.9200 −0.674963
\(872\) −53.2373 −1.80284
\(873\) −4.30960 −0.145858
\(874\) −5.96430 −0.201746
\(875\) −11.7149 −0.396036
\(876\) 11.6706 0.394313
\(877\) −17.2143 −0.581284 −0.290642 0.956832i \(-0.593869\pi\)
−0.290642 + 0.956832i \(0.593869\pi\)
\(878\) 5.98891 0.202116
\(879\) −12.1071 −0.408363
\(880\) −2.09661 −0.0706766
\(881\) 25.8814 0.871967 0.435984 0.899955i \(-0.356401\pi\)
0.435984 + 0.899955i \(0.356401\pi\)
\(882\) 0.830058 0.0279495
\(883\) 37.9449 1.27695 0.638473 0.769644i \(-0.279566\pi\)
0.638473 + 0.769644i \(0.279566\pi\)
\(884\) 26.7621 0.900107
\(885\) −20.6990 −0.695788
\(886\) 15.3889 0.517000
\(887\) 32.4685 1.09019 0.545093 0.838376i \(-0.316495\pi\)
0.545093 + 0.838376i \(0.316495\pi\)
\(888\) 18.0081 0.604311
\(889\) −13.7820 −0.462232
\(890\) 17.9330 0.601117
\(891\) 4.02473 0.134834
\(892\) 25.3098 0.847434
\(893\) 33.2916 1.11406
\(894\) 18.2331 0.609807
\(895\) 7.66389 0.256175
\(896\) 8.14259 0.272025
\(897\) −17.7978 −0.594250
\(898\) 25.6998 0.857615
\(899\) 52.4829 1.75040
\(900\) 3.49083 0.116361
\(901\) −26.7714 −0.891885
\(902\) 37.3836 1.24474
\(903\) −4.15694 −0.138334
\(904\) −20.2455 −0.673356
\(905\) −6.40853 −0.213027
\(906\) −10.4088 −0.345810
\(907\) −47.3887 −1.57352 −0.786758 0.617262i \(-0.788242\pi\)
−0.786758 + 0.617262i \(0.788242\pi\)
\(908\) 27.0234 0.896803
\(909\) 4.31759 0.143205
\(910\) 7.79758 0.258487
\(911\) −20.1287 −0.666894 −0.333447 0.942769i \(-0.608212\pi\)
−0.333447 + 0.942769i \(0.608212\pi\)
\(912\) 0.845289 0.0279903
\(913\) 55.2341 1.82798
\(914\) −2.74492 −0.0907940
\(915\) −0.818591 −0.0270618
\(916\) 13.2178 0.436728
\(917\) 13.4714 0.444864
\(918\) −2.75758 −0.0910138
\(919\) 36.1807 1.19349 0.596745 0.802431i \(-0.296460\pi\)
0.596745 + 0.802431i \(0.296460\pi\)
\(920\) −12.1701 −0.401236
\(921\) −19.8703 −0.654748
\(922\) 5.25263 0.172986
\(923\) 26.1743 0.861539
\(924\) 5.27644 0.173582
\(925\) 17.4471 0.573657
\(926\) 6.82692 0.224346
\(927\) 9.58633 0.314856
\(928\) −60.4034 −1.98284
\(929\) 26.7688 0.878254 0.439127 0.898425i \(-0.355288\pi\)
0.439127 + 0.898425i \(0.355288\pi\)
\(930\) 6.37250 0.208963
\(931\) 2.48074 0.0813031
\(932\) −28.9656 −0.948799
\(933\) 31.9589 1.04629
\(934\) −11.8681 −0.388335
\(935\) 20.4415 0.668510
\(936\) −16.8874 −0.551983
\(937\) 12.7471 0.416429 0.208215 0.978083i \(-0.433235\pi\)
0.208215 + 0.978083i \(0.433235\pi\)
\(938\) 2.69092 0.0878618
\(939\) −7.83387 −0.255649
\(940\) 26.8976 0.877303
\(941\) 2.38970 0.0779020 0.0389510 0.999241i \(-0.487598\pi\)
0.0389510 + 0.999241i \(0.487598\pi\)
\(942\) 0.657675 0.0214282
\(943\) −32.4120 −1.05548
\(944\) 4.61334 0.150152
\(945\) 1.52882 0.0497325
\(946\) 13.8874 0.451517
\(947\) 8.47809 0.275501 0.137751 0.990467i \(-0.456013\pi\)
0.137751 + 0.990467i \(0.456013\pi\)
\(948\) −21.2077 −0.688794
\(949\) −54.6997 −1.77563
\(950\) −5.48295 −0.177890
\(951\) −9.12873 −0.296019
\(952\) −9.13037 −0.295917
\(953\) 42.8298 1.38739 0.693696 0.720268i \(-0.255981\pi\)
0.693696 + 0.720268i \(0.255981\pi\)
\(954\) 6.68896 0.216563
\(955\) 1.52882 0.0494714
\(956\) −2.22259 −0.0718838
\(957\) −42.0639 −1.35973
\(958\) 20.4123 0.659492
\(959\) 18.8074 0.607323
\(960\) −6.29235 −0.203085
\(961\) −5.78311 −0.186552
\(962\) −33.4197 −1.07749
\(963\) 1.00532 0.0323961
\(964\) −3.22419 −0.103844
\(965\) 1.59636 0.0513888
\(966\) 2.40424 0.0773552
\(967\) 39.8967 1.28299 0.641496 0.767126i \(-0.278314\pi\)
0.641496 + 0.767126i \(0.278314\pi\)
\(968\) −14.2871 −0.459205
\(969\) −8.24143 −0.264753
\(970\) 5.46892 0.175596
\(971\) 38.3321 1.23014 0.615069 0.788474i \(-0.289128\pi\)
0.615069 + 0.788474i \(0.289128\pi\)
\(972\) −1.31100 −0.0420505
\(973\) 7.09584 0.227482
\(974\) 2.85317 0.0914215
\(975\) −16.3614 −0.523984
\(976\) 0.182446 0.00583996
\(977\) 29.8406 0.954685 0.477342 0.878717i \(-0.341600\pi\)
0.477342 + 0.878717i \(0.341600\pi\)
\(978\) 17.5621 0.561574
\(979\) −56.8757 −1.81776
\(980\) 2.00429 0.0640246
\(981\) 19.3708 0.618463
\(982\) 25.6652 0.819011
\(983\) 22.2442 0.709478 0.354739 0.934965i \(-0.384570\pi\)
0.354739 + 0.934965i \(0.384570\pi\)
\(984\) −30.7542 −0.980407
\(985\) 11.4864 0.365988
\(986\) 28.8205 0.917831
\(987\) −13.4200 −0.427164
\(988\) −19.9840 −0.635775
\(989\) −12.0405 −0.382865
\(990\) −5.10742 −0.162324
\(991\) −9.37819 −0.297908 −0.148954 0.988844i \(-0.547591\pi\)
−0.148954 + 0.988844i \(0.547591\pi\)
\(992\) −29.0225 −0.921465
\(993\) −20.1555 −0.639617
\(994\) −3.53581 −0.112149
\(995\) −5.22786 −0.165734
\(996\) −17.9918 −0.570092
\(997\) −8.22451 −0.260473 −0.130236 0.991483i \(-0.541574\pi\)
−0.130236 + 0.991483i \(0.541574\pi\)
\(998\) −16.3727 −0.518270
\(999\) −6.55237 −0.207308
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 4011.2.a.m.1.17 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.m.1.17 29 1.1 even 1 trivial