Properties

Label 6018.2.a.s.1.4
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $8$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, 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("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.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: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(3.92135\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03120 q^{5} +1.00000 q^{6} -2.85327 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.03120 q^{5} +1.00000 q^{6} -2.85327 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.03120 q^{10} -4.15019 q^{11} -1.00000 q^{12} +2.83799 q^{13} +2.85327 q^{14} +1.03120 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -2.04690 q^{19} -1.03120 q^{20} +2.85327 q^{21} +4.15019 q^{22} +7.42217 q^{23} +1.00000 q^{24} -3.93662 q^{25} -2.83799 q^{26} -1.00000 q^{27} -2.85327 q^{28} -9.72983 q^{29} -1.03120 q^{30} +8.92011 q^{31} -1.00000 q^{32} +4.15019 q^{33} +1.00000 q^{34} +2.94230 q^{35} +1.00000 q^{36} -4.78182 q^{37} +2.04690 q^{38} -2.83799 q^{39} +1.03120 q^{40} -1.47977 q^{41} -2.85327 q^{42} +0.900717 q^{43} -4.15019 q^{44} -1.03120 q^{45} -7.42217 q^{46} -11.7184 q^{47} -1.00000 q^{48} +1.14113 q^{49} +3.93662 q^{50} +1.00000 q^{51} +2.83799 q^{52} -0.396211 q^{53} +1.00000 q^{54} +4.27969 q^{55} +2.85327 q^{56} +2.04690 q^{57} +9.72983 q^{58} +1.00000 q^{59} +1.03120 q^{60} +5.11471 q^{61} -8.92011 q^{62} -2.85327 q^{63} +1.00000 q^{64} -2.92654 q^{65} -4.15019 q^{66} -11.5926 q^{67} -1.00000 q^{68} -7.42217 q^{69} -2.94230 q^{70} -15.8105 q^{71} -1.00000 q^{72} -14.8648 q^{73} +4.78182 q^{74} +3.93662 q^{75} -2.04690 q^{76} +11.8416 q^{77} +2.83799 q^{78} +9.87378 q^{79} -1.03120 q^{80} +1.00000 q^{81} +1.47977 q^{82} -4.49553 q^{83} +2.85327 q^{84} +1.03120 q^{85} -0.900717 q^{86} +9.72983 q^{87} +4.15019 q^{88} +10.4285 q^{89} +1.03120 q^{90} -8.09755 q^{91} +7.42217 q^{92} -8.92011 q^{93} +11.7184 q^{94} +2.11077 q^{95} +1.00000 q^{96} +9.26422 q^{97} -1.14113 q^{98} -4.15019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} - 8 q^{3} + 8 q^{4} - q^{5} + 8 q^{6} + 6 q^{7} - 8 q^{8} + 8 q^{9} + q^{10} - 8 q^{12} + 6 q^{13} - 6 q^{14} + q^{15} + 8 q^{16} - 8 q^{17} - 8 q^{18} - 7 q^{19} - q^{20} - 6 q^{21} - 5 q^{23} + 8 q^{24} + 9 q^{25} - 6 q^{26} - 8 q^{27} + 6 q^{28} - 15 q^{29} - q^{30} + 21 q^{31} - 8 q^{32} + 8 q^{34} - 2 q^{35} + 8 q^{36} + 7 q^{37} + 7 q^{38} - 6 q^{39} + q^{40} - q^{41} + 6 q^{42} + 14 q^{43} - q^{45} + 5 q^{46} - 8 q^{47} - 8 q^{48} + 2 q^{49} - 9 q^{50} + 8 q^{51} + 6 q^{52} + 8 q^{53} + 8 q^{54} + 24 q^{55} - 6 q^{56} + 7 q^{57} + 15 q^{58} + 8 q^{59} + q^{60} - 21 q^{62} + 6 q^{63} + 8 q^{64} + 6 q^{65} + 15 q^{67} - 8 q^{68} + 5 q^{69} + 2 q^{70} - 22 q^{71} - 8 q^{72} + 13 q^{73} - 7 q^{74} - 9 q^{75} - 7 q^{76} - 6 q^{77} + 6 q^{78} + 26 q^{79} - q^{80} + 8 q^{81} + q^{82} + 30 q^{83} - 6 q^{84} + q^{85} - 14 q^{86} + 15 q^{87} - 6 q^{89} + q^{90} + 3 q^{91} - 5 q^{92} - 21 q^{93} + 8 q^{94} + 37 q^{95} + 8 q^{96} + 23 q^{97} - 2 q^{98}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.03120 −0.461168 −0.230584 0.973052i \(-0.574064\pi\)
−0.230584 + 0.973052i \(0.574064\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.85327 −1.07843 −0.539217 0.842167i \(-0.681280\pi\)
−0.539217 + 0.842167i \(0.681280\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.03120 0.326095
\(11\) −4.15019 −1.25133 −0.625665 0.780092i \(-0.715172\pi\)
−0.625665 + 0.780092i \(0.715172\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.83799 0.787117 0.393559 0.919300i \(-0.371244\pi\)
0.393559 + 0.919300i \(0.371244\pi\)
\(14\) 2.85327 0.762567
\(15\) 1.03120 0.266255
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) −2.04690 −0.469591 −0.234795 0.972045i \(-0.575442\pi\)
−0.234795 + 0.972045i \(0.575442\pi\)
\(20\) −1.03120 −0.230584
\(21\) 2.85327 0.622634
\(22\) 4.15019 0.884824
\(23\) 7.42217 1.54763 0.773814 0.633412i \(-0.218346\pi\)
0.773814 + 0.633412i \(0.218346\pi\)
\(24\) 1.00000 0.204124
\(25\) −3.93662 −0.787324
\(26\) −2.83799 −0.556576
\(27\) −1.00000 −0.192450
\(28\) −2.85327 −0.539217
\(29\) −9.72983 −1.80678 −0.903392 0.428817i \(-0.858931\pi\)
−0.903392 + 0.428817i \(0.858931\pi\)
\(30\) −1.03120 −0.188271
\(31\) 8.92011 1.60210 0.801049 0.598599i \(-0.204276\pi\)
0.801049 + 0.598599i \(0.204276\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.15019 0.722456
\(34\) 1.00000 0.171499
\(35\) 2.94230 0.497339
\(36\) 1.00000 0.166667
\(37\) −4.78182 −0.786126 −0.393063 0.919511i \(-0.628585\pi\)
−0.393063 + 0.919511i \(0.628585\pi\)
\(38\) 2.04690 0.332051
\(39\) −2.83799 −0.454442
\(40\) 1.03120 0.163047
\(41\) −1.47977 −0.231101 −0.115551 0.993302i \(-0.536863\pi\)
−0.115551 + 0.993302i \(0.536863\pi\)
\(42\) −2.85327 −0.440269
\(43\) 0.900717 0.137358 0.0686790 0.997639i \(-0.478122\pi\)
0.0686790 + 0.997639i \(0.478122\pi\)
\(44\) −4.15019 −0.625665
\(45\) −1.03120 −0.153723
\(46\) −7.42217 −1.09434
\(47\) −11.7184 −1.70931 −0.854655 0.519196i \(-0.826231\pi\)
−0.854655 + 0.519196i \(0.826231\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.14113 0.163018
\(50\) 3.93662 0.556722
\(51\) 1.00000 0.140028
\(52\) 2.83799 0.393559
\(53\) −0.396211 −0.0544238 −0.0272119 0.999630i \(-0.508663\pi\)
−0.0272119 + 0.999630i \(0.508663\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.27969 0.577073
\(56\) 2.85327 0.381284
\(57\) 2.04690 0.271118
\(58\) 9.72983 1.27759
\(59\) 1.00000 0.130189
\(60\) 1.03120 0.133128
\(61\) 5.11471 0.654872 0.327436 0.944873i \(-0.393815\pi\)
0.327436 + 0.944873i \(0.393815\pi\)
\(62\) −8.92011 −1.13285
\(63\) −2.85327 −0.359478
\(64\) 1.00000 0.125000
\(65\) −2.92654 −0.362993
\(66\) −4.15019 −0.510854
\(67\) −11.5926 −1.41626 −0.708130 0.706083i \(-0.750461\pi\)
−0.708130 + 0.706083i \(0.750461\pi\)
\(68\) −1.00000 −0.121268
\(69\) −7.42217 −0.893524
\(70\) −2.94230 −0.351672
\(71\) −15.8105 −1.87636 −0.938182 0.346144i \(-0.887491\pi\)
−0.938182 + 0.346144i \(0.887491\pi\)
\(72\) −1.00000 −0.117851
\(73\) −14.8648 −1.73979 −0.869896 0.493236i \(-0.835814\pi\)
−0.869896 + 0.493236i \(0.835814\pi\)
\(74\) 4.78182 0.555875
\(75\) 3.93662 0.454562
\(76\) −2.04690 −0.234795
\(77\) 11.8416 1.34948
\(78\) 2.83799 0.321339
\(79\) 9.87378 1.11089 0.555444 0.831554i \(-0.312548\pi\)
0.555444 + 0.831554i \(0.312548\pi\)
\(80\) −1.03120 −0.115292
\(81\) 1.00000 0.111111
\(82\) 1.47977 0.163413
\(83\) −4.49553 −0.493449 −0.246724 0.969086i \(-0.579354\pi\)
−0.246724 + 0.969086i \(0.579354\pi\)
\(84\) 2.85327 0.311317
\(85\) 1.03120 0.111850
\(86\) −0.900717 −0.0971268
\(87\) 9.72983 1.04315
\(88\) 4.15019 0.442412
\(89\) 10.4285 1.10542 0.552711 0.833373i \(-0.313594\pi\)
0.552711 + 0.833373i \(0.313594\pi\)
\(90\) 1.03120 0.108698
\(91\) −8.09755 −0.848853
\(92\) 7.42217 0.773814
\(93\) −8.92011 −0.924972
\(94\) 11.7184 1.20866
\(95\) 2.11077 0.216560
\(96\) 1.00000 0.102062
\(97\) 9.26422 0.940639 0.470319 0.882496i \(-0.344139\pi\)
0.470319 + 0.882496i \(0.344139\pi\)
\(98\) −1.14113 −0.115271
\(99\) −4.15019 −0.417110
\(100\) −3.93662 −0.393662
\(101\) −18.8205 −1.87271 −0.936356 0.351053i \(-0.885824\pi\)
−0.936356 + 0.351053i \(0.885824\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −4.20239 −0.414074 −0.207037 0.978333i \(-0.566382\pi\)
−0.207037 + 0.978333i \(0.566382\pi\)
\(104\) −2.83799 −0.278288
\(105\) −2.94230 −0.287139
\(106\) 0.396211 0.0384834
\(107\) 5.99395 0.579457 0.289728 0.957109i \(-0.406435\pi\)
0.289728 + 0.957109i \(0.406435\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −10.3925 −0.995417 −0.497709 0.867344i \(-0.665825\pi\)
−0.497709 + 0.867344i \(0.665825\pi\)
\(110\) −4.27969 −0.408053
\(111\) 4.78182 0.453870
\(112\) −2.85327 −0.269608
\(113\) 15.8258 1.48877 0.744384 0.667752i \(-0.232743\pi\)
0.744384 + 0.667752i \(0.232743\pi\)
\(114\) −2.04690 −0.191710
\(115\) −7.65376 −0.713717
\(116\) −9.72983 −0.903392
\(117\) 2.83799 0.262372
\(118\) −1.00000 −0.0920575
\(119\) 2.85327 0.261558
\(120\) −1.03120 −0.0941355
\(121\) 6.22411 0.565828
\(122\) −5.11471 −0.463064
\(123\) 1.47977 0.133426
\(124\) 8.92011 0.801049
\(125\) 9.21547 0.824257
\(126\) 2.85327 0.254189
\(127\) −10.4413 −0.926515 −0.463257 0.886224i \(-0.653319\pi\)
−0.463257 + 0.886224i \(0.653319\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.900717 −0.0793037
\(130\) 2.92654 0.256675
\(131\) 13.9696 1.22053 0.610264 0.792198i \(-0.291063\pi\)
0.610264 + 0.792198i \(0.291063\pi\)
\(132\) 4.15019 0.361228
\(133\) 5.84035 0.506423
\(134\) 11.5926 1.00145
\(135\) 1.03120 0.0887518
\(136\) 1.00000 0.0857493
\(137\) −21.2201 −1.81296 −0.906479 0.422250i \(-0.861240\pi\)
−0.906479 + 0.422250i \(0.861240\pi\)
\(138\) 7.42217 0.631817
\(139\) 0.195248 0.0165607 0.00828037 0.999966i \(-0.497364\pi\)
0.00828037 + 0.999966i \(0.497364\pi\)
\(140\) 2.94230 0.248669
\(141\) 11.7184 0.986871
\(142\) 15.8105 1.32679
\(143\) −11.7782 −0.984944
\(144\) 1.00000 0.0833333
\(145\) 10.0334 0.833230
\(146\) 14.8648 1.23022
\(147\) −1.14113 −0.0941186
\(148\) −4.78182 −0.393063
\(149\) −14.4831 −1.18650 −0.593251 0.805017i \(-0.702156\pi\)
−0.593251 + 0.805017i \(0.702156\pi\)
\(150\) −3.93662 −0.321424
\(151\) 23.7118 1.92964 0.964821 0.262908i \(-0.0846814\pi\)
0.964821 + 0.262908i \(0.0846814\pi\)
\(152\) 2.04690 0.166025
\(153\) −1.00000 −0.0808452
\(154\) −11.8416 −0.954224
\(155\) −9.19844 −0.738836
\(156\) −2.83799 −0.227221
\(157\) 2.87240 0.229242 0.114621 0.993409i \(-0.463435\pi\)
0.114621 + 0.993409i \(0.463435\pi\)
\(158\) −9.87378 −0.785516
\(159\) 0.396211 0.0314216
\(160\) 1.03120 0.0815237
\(161\) −21.1774 −1.66901
\(162\) −1.00000 −0.0785674
\(163\) 20.9048 1.63739 0.818694 0.574229i \(-0.194698\pi\)
0.818694 + 0.574229i \(0.194698\pi\)
\(164\) −1.47977 −0.115551
\(165\) −4.27969 −0.333174
\(166\) 4.49553 0.348921
\(167\) 11.9527 0.924930 0.462465 0.886638i \(-0.346965\pi\)
0.462465 + 0.886638i \(0.346965\pi\)
\(168\) −2.85327 −0.220134
\(169\) −4.94580 −0.380446
\(170\) −1.03120 −0.0790896
\(171\) −2.04690 −0.156530
\(172\) 0.900717 0.0686790
\(173\) 13.3211 1.01278 0.506392 0.862303i \(-0.330979\pi\)
0.506392 + 0.862303i \(0.330979\pi\)
\(174\) −9.72983 −0.737616
\(175\) 11.2322 0.849077
\(176\) −4.15019 −0.312833
\(177\) −1.00000 −0.0751646
\(178\) −10.4285 −0.781651
\(179\) 1.96370 0.146774 0.0733870 0.997304i \(-0.476619\pi\)
0.0733870 + 0.997304i \(0.476619\pi\)
\(180\) −1.03120 −0.0768613
\(181\) 5.25021 0.390245 0.195122 0.980779i \(-0.437490\pi\)
0.195122 + 0.980779i \(0.437490\pi\)
\(182\) 8.09755 0.600230
\(183\) −5.11471 −0.378091
\(184\) −7.42217 −0.547169
\(185\) 4.93103 0.362536
\(186\) 8.92011 0.654054
\(187\) 4.15019 0.303492
\(188\) −11.7184 −0.854655
\(189\) 2.85327 0.207545
\(190\) −2.11077 −0.153131
\(191\) −12.5699 −0.909529 −0.454764 0.890612i \(-0.650277\pi\)
−0.454764 + 0.890612i \(0.650277\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 24.5408 1.76649 0.883243 0.468916i \(-0.155355\pi\)
0.883243 + 0.468916i \(0.155355\pi\)
\(194\) −9.26422 −0.665132
\(195\) 2.92654 0.209574
\(196\) 1.14113 0.0815091
\(197\) −21.5354 −1.53434 −0.767169 0.641446i \(-0.778335\pi\)
−0.767169 + 0.641446i \(0.778335\pi\)
\(198\) 4.15019 0.294941
\(199\) 13.3601 0.947072 0.473536 0.880774i \(-0.342977\pi\)
0.473536 + 0.880774i \(0.342977\pi\)
\(200\) 3.93662 0.278361
\(201\) 11.5926 0.817678
\(202\) 18.8205 1.32421
\(203\) 27.7618 1.94849
\(204\) 1.00000 0.0700140
\(205\) 1.52594 0.106576
\(206\) 4.20239 0.292795
\(207\) 7.42217 0.515876
\(208\) 2.83799 0.196779
\(209\) 8.49503 0.587614
\(210\) 2.94230 0.203038
\(211\) −14.2367 −0.980097 −0.490049 0.871695i \(-0.663021\pi\)
−0.490049 + 0.871695i \(0.663021\pi\)
\(212\) −0.396211 −0.0272119
\(213\) 15.8105 1.08332
\(214\) −5.99395 −0.409738
\(215\) −0.928822 −0.0633451
\(216\) 1.00000 0.0680414
\(217\) −25.4514 −1.72776
\(218\) 10.3925 0.703866
\(219\) 14.8648 1.00447
\(220\) 4.27969 0.288537
\(221\) −2.83799 −0.190904
\(222\) −4.78182 −0.320935
\(223\) 13.2331 0.886151 0.443075 0.896484i \(-0.353887\pi\)
0.443075 + 0.896484i \(0.353887\pi\)
\(224\) 2.85327 0.190642
\(225\) −3.93662 −0.262441
\(226\) −15.8258 −1.05272
\(227\) 6.46192 0.428893 0.214446 0.976736i \(-0.431205\pi\)
0.214446 + 0.976736i \(0.431205\pi\)
\(228\) 2.04690 0.135559
\(229\) 3.06685 0.202663 0.101332 0.994853i \(-0.467690\pi\)
0.101332 + 0.994853i \(0.467690\pi\)
\(230\) 7.65376 0.504674
\(231\) −11.8416 −0.779121
\(232\) 9.72983 0.638794
\(233\) 8.04281 0.526902 0.263451 0.964673i \(-0.415139\pi\)
0.263451 + 0.964673i \(0.415139\pi\)
\(234\) −2.83799 −0.185525
\(235\) 12.0841 0.788279
\(236\) 1.00000 0.0650945
\(237\) −9.87378 −0.641371
\(238\) −2.85327 −0.184950
\(239\) −16.3115 −1.05510 −0.527550 0.849524i \(-0.676889\pi\)
−0.527550 + 0.849524i \(0.676889\pi\)
\(240\) 1.03120 0.0665638
\(241\) 17.8390 1.14911 0.574556 0.818465i \(-0.305175\pi\)
0.574556 + 0.818465i \(0.305175\pi\)
\(242\) −6.22411 −0.400101
\(243\) −1.00000 −0.0641500
\(244\) 5.11471 0.327436
\(245\) −1.17673 −0.0751788
\(246\) −1.47977 −0.0943466
\(247\) −5.80908 −0.369623
\(248\) −8.92011 −0.566427
\(249\) 4.49553 0.284893
\(250\) −9.21547 −0.582837
\(251\) −22.1576 −1.39857 −0.699286 0.714842i \(-0.746499\pi\)
−0.699286 + 0.714842i \(0.746499\pi\)
\(252\) −2.85327 −0.179739
\(253\) −30.8034 −1.93660
\(254\) 10.4413 0.655145
\(255\) −1.03120 −0.0645764
\(256\) 1.00000 0.0625000
\(257\) −5.50481 −0.343381 −0.171690 0.985151i \(-0.554923\pi\)
−0.171690 + 0.985151i \(0.554923\pi\)
\(258\) 0.900717 0.0560762
\(259\) 13.6438 0.847785
\(260\) −2.92654 −0.181497
\(261\) −9.72983 −0.602261
\(262\) −13.9696 −0.863043
\(263\) 18.3990 1.13453 0.567266 0.823535i \(-0.308001\pi\)
0.567266 + 0.823535i \(0.308001\pi\)
\(264\) −4.15019 −0.255427
\(265\) 0.408574 0.0250985
\(266\) −5.84035 −0.358095
\(267\) −10.4285 −0.638215
\(268\) −11.5926 −0.708130
\(269\) −18.3949 −1.12156 −0.560780 0.827965i \(-0.689499\pi\)
−0.560780 + 0.827965i \(0.689499\pi\)
\(270\) −1.03120 −0.0627570
\(271\) 16.0260 0.973507 0.486754 0.873539i \(-0.338181\pi\)
0.486754 + 0.873539i \(0.338181\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 8.09755 0.490086
\(274\) 21.2201 1.28196
\(275\) 16.3377 0.985203
\(276\) −7.42217 −0.446762
\(277\) −13.7057 −0.823493 −0.411747 0.911298i \(-0.635081\pi\)
−0.411747 + 0.911298i \(0.635081\pi\)
\(278\) −0.195248 −0.0117102
\(279\) 8.92011 0.534033
\(280\) −2.94230 −0.175836
\(281\) −7.42920 −0.443189 −0.221594 0.975139i \(-0.571126\pi\)
−0.221594 + 0.975139i \(0.571126\pi\)
\(282\) −11.7184 −0.697823
\(283\) −4.43689 −0.263746 −0.131873 0.991267i \(-0.542099\pi\)
−0.131873 + 0.991267i \(0.542099\pi\)
\(284\) −15.8105 −0.938182
\(285\) −2.11077 −0.125031
\(286\) 11.7782 0.696461
\(287\) 4.22217 0.249227
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −10.0334 −0.589183
\(291\) −9.26422 −0.543078
\(292\) −14.8648 −0.869896
\(293\) 27.1947 1.58873 0.794365 0.607440i \(-0.207804\pi\)
0.794365 + 0.607440i \(0.207804\pi\)
\(294\) 1.14113 0.0665519
\(295\) −1.03120 −0.0600389
\(296\) 4.78182 0.277938
\(297\) 4.15019 0.240819
\(298\) 14.4831 0.838984
\(299\) 21.0640 1.21817
\(300\) 3.93662 0.227281
\(301\) −2.56999 −0.148131
\(302\) −23.7118 −1.36446
\(303\) 18.8205 1.08121
\(304\) −2.04690 −0.117398
\(305\) −5.27431 −0.302006
\(306\) 1.00000 0.0571662
\(307\) 8.18518 0.467153 0.233577 0.972338i \(-0.424957\pi\)
0.233577 + 0.972338i \(0.424957\pi\)
\(308\) 11.8416 0.674738
\(309\) 4.20239 0.239066
\(310\) 9.19844 0.522436
\(311\) 18.1124 1.02706 0.513530 0.858072i \(-0.328338\pi\)
0.513530 + 0.858072i \(0.328338\pi\)
\(312\) 2.83799 0.160670
\(313\) −22.5547 −1.27487 −0.637434 0.770505i \(-0.720004\pi\)
−0.637434 + 0.770505i \(0.720004\pi\)
\(314\) −2.87240 −0.162099
\(315\) 2.94230 0.165780
\(316\) 9.87378 0.555444
\(317\) −13.9298 −0.782376 −0.391188 0.920311i \(-0.627936\pi\)
−0.391188 + 0.920311i \(0.627936\pi\)
\(318\) −0.396211 −0.0222184
\(319\) 40.3807 2.26088
\(320\) −1.03120 −0.0576460
\(321\) −5.99395 −0.334550
\(322\) 21.1774 1.18017
\(323\) 2.04690 0.113893
\(324\) 1.00000 0.0555556
\(325\) −11.1721 −0.619716
\(326\) −20.9048 −1.15781
\(327\) 10.3925 0.574705
\(328\) 1.47977 0.0817066
\(329\) 33.4358 1.84338
\(330\) 4.27969 0.235589
\(331\) 8.91532 0.490030 0.245015 0.969519i \(-0.421207\pi\)
0.245015 + 0.969519i \(0.421207\pi\)
\(332\) −4.49553 −0.246724
\(333\) −4.78182 −0.262042
\(334\) −11.9527 −0.654024
\(335\) 11.9543 0.653133
\(336\) 2.85327 0.155658
\(337\) 18.5601 1.01103 0.505517 0.862817i \(-0.331302\pi\)
0.505517 + 0.862817i \(0.331302\pi\)
\(338\) 4.94580 0.269016
\(339\) −15.8258 −0.859541
\(340\) 1.03120 0.0559248
\(341\) −37.0202 −2.00475
\(342\) 2.04690 0.110684
\(343\) 16.7169 0.902629
\(344\) −0.900717 −0.0485634
\(345\) 7.65376 0.412065
\(346\) −13.3211 −0.716147
\(347\) 28.3802 1.52353 0.761764 0.647855i \(-0.224334\pi\)
0.761764 + 0.647855i \(0.224334\pi\)
\(348\) 9.72983 0.521573
\(349\) −0.411099 −0.0220056 −0.0110028 0.999939i \(-0.503502\pi\)
−0.0110028 + 0.999939i \(0.503502\pi\)
\(350\) −11.2322 −0.600388
\(351\) −2.83799 −0.151481
\(352\) 4.15019 0.221206
\(353\) 11.4830 0.611176 0.305588 0.952164i \(-0.401147\pi\)
0.305588 + 0.952164i \(0.401147\pi\)
\(354\) 1.00000 0.0531494
\(355\) 16.3038 0.865318
\(356\) 10.4285 0.552711
\(357\) −2.85327 −0.151011
\(358\) −1.96370 −0.103785
\(359\) 6.07107 0.320419 0.160209 0.987083i \(-0.448783\pi\)
0.160209 + 0.987083i \(0.448783\pi\)
\(360\) 1.03120 0.0543492
\(361\) −14.8102 −0.779484
\(362\) −5.25021 −0.275945
\(363\) −6.22411 −0.326681
\(364\) −8.09755 −0.424427
\(365\) 15.3286 0.802336
\(366\) 5.11471 0.267350
\(367\) 4.70200 0.245443 0.122721 0.992441i \(-0.460838\pi\)
0.122721 + 0.992441i \(0.460838\pi\)
\(368\) 7.42217 0.386907
\(369\) −1.47977 −0.0770337
\(370\) −4.93103 −0.256352
\(371\) 1.13050 0.0586924
\(372\) −8.92011 −0.462486
\(373\) 28.6835 1.48517 0.742587 0.669749i \(-0.233598\pi\)
0.742587 + 0.669749i \(0.233598\pi\)
\(374\) −4.15019 −0.214601
\(375\) −9.21547 −0.475885
\(376\) 11.7184 0.604332
\(377\) −27.6132 −1.42215
\(378\) −2.85327 −0.146756
\(379\) −1.44882 −0.0744207 −0.0372103 0.999307i \(-0.511847\pi\)
−0.0372103 + 0.999307i \(0.511847\pi\)
\(380\) 2.11077 0.108280
\(381\) 10.4413 0.534923
\(382\) 12.5699 0.643134
\(383\) −24.9862 −1.27673 −0.638366 0.769733i \(-0.720390\pi\)
−0.638366 + 0.769733i \(0.720390\pi\)
\(384\) 1.00000 0.0510310
\(385\) −12.2111 −0.622335
\(386\) −24.5408 −1.24909
\(387\) 0.900717 0.0457860
\(388\) 9.26422 0.470319
\(389\) 22.6642 1.14912 0.574560 0.818462i \(-0.305173\pi\)
0.574560 + 0.818462i \(0.305173\pi\)
\(390\) −2.92654 −0.148191
\(391\) −7.42217 −0.375355
\(392\) −1.14113 −0.0576356
\(393\) −13.9696 −0.704672
\(394\) 21.5354 1.08494
\(395\) −10.1819 −0.512306
\(396\) −4.15019 −0.208555
\(397\) −30.5327 −1.53239 −0.766196 0.642607i \(-0.777853\pi\)
−0.766196 + 0.642607i \(0.777853\pi\)
\(398\) −13.3601 −0.669681
\(399\) −5.84035 −0.292383
\(400\) −3.93662 −0.196831
\(401\) −17.8910 −0.893433 −0.446717 0.894676i \(-0.647407\pi\)
−0.446717 + 0.894676i \(0.647407\pi\)
\(402\) −11.5926 −0.578185
\(403\) 25.3152 1.26104
\(404\) −18.8205 −0.936356
\(405\) −1.03120 −0.0512409
\(406\) −27.7618 −1.37779
\(407\) 19.8455 0.983704
\(408\) −1.00000 −0.0495074
\(409\) −15.1451 −0.748879 −0.374439 0.927251i \(-0.622165\pi\)
−0.374439 + 0.927251i \(0.622165\pi\)
\(410\) −1.52594 −0.0753609
\(411\) 21.2201 1.04671
\(412\) −4.20239 −0.207037
\(413\) −2.85327 −0.140400
\(414\) −7.42217 −0.364780
\(415\) 4.63581 0.227563
\(416\) −2.83799 −0.139144
\(417\) −0.195248 −0.00956135
\(418\) −8.49503 −0.415506
\(419\) −9.60013 −0.468997 −0.234499 0.972116i \(-0.575345\pi\)
−0.234499 + 0.972116i \(0.575345\pi\)
\(420\) −2.94230 −0.143569
\(421\) −19.7712 −0.963589 −0.481794 0.876284i \(-0.660015\pi\)
−0.481794 + 0.876284i \(0.660015\pi\)
\(422\) 14.2367 0.693033
\(423\) −11.7184 −0.569770
\(424\) 0.396211 0.0192417
\(425\) 3.93662 0.190954
\(426\) −15.8105 −0.766022
\(427\) −14.5936 −0.706236
\(428\) 5.99395 0.289728
\(429\) 11.7782 0.568658
\(430\) 0.928822 0.0447918
\(431\) −1.01173 −0.0487334 −0.0243667 0.999703i \(-0.507757\pi\)
−0.0243667 + 0.999703i \(0.507757\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 6.61470 0.317882 0.158941 0.987288i \(-0.449192\pi\)
0.158941 + 0.987288i \(0.449192\pi\)
\(434\) 25.4514 1.22171
\(435\) −10.0334 −0.481066
\(436\) −10.3925 −0.497709
\(437\) −15.1924 −0.726753
\(438\) −14.8648 −0.710267
\(439\) 2.17249 0.103687 0.0518436 0.998655i \(-0.483490\pi\)
0.0518436 + 0.998655i \(0.483490\pi\)
\(440\) −4.27969 −0.204026
\(441\) 1.14113 0.0543394
\(442\) 2.83799 0.134989
\(443\) −16.4903 −0.783479 −0.391739 0.920076i \(-0.628127\pi\)
−0.391739 + 0.920076i \(0.628127\pi\)
\(444\) 4.78182 0.226935
\(445\) −10.7539 −0.509785
\(446\) −13.2331 −0.626603
\(447\) 14.4831 0.685027
\(448\) −2.85327 −0.134804
\(449\) 33.2089 1.56722 0.783612 0.621250i \(-0.213375\pi\)
0.783612 + 0.621250i \(0.213375\pi\)
\(450\) 3.93662 0.185574
\(451\) 6.14133 0.289184
\(452\) 15.8258 0.744384
\(453\) −23.7118 −1.11408
\(454\) −6.46192 −0.303273
\(455\) 8.35021 0.391464
\(456\) −2.04690 −0.0958549
\(457\) −4.22666 −0.197715 −0.0988574 0.995102i \(-0.531519\pi\)
−0.0988574 + 0.995102i \(0.531519\pi\)
\(458\) −3.06685 −0.143305
\(459\) 1.00000 0.0466760
\(460\) −7.65376 −0.356858
\(461\) 30.0219 1.39826 0.699130 0.714994i \(-0.253571\pi\)
0.699130 + 0.714994i \(0.253571\pi\)
\(462\) 11.8416 0.550921
\(463\) 11.2614 0.523363 0.261681 0.965154i \(-0.415723\pi\)
0.261681 + 0.965154i \(0.415723\pi\)
\(464\) −9.72983 −0.451696
\(465\) 9.19844 0.426567
\(466\) −8.04281 −0.372576
\(467\) 21.2014 0.981085 0.490542 0.871417i \(-0.336799\pi\)
0.490542 + 0.871417i \(0.336799\pi\)
\(468\) 2.83799 0.131186
\(469\) 33.0767 1.52734
\(470\) −12.0841 −0.557397
\(471\) −2.87240 −0.132353
\(472\) −1.00000 −0.0460287
\(473\) −3.73815 −0.171880
\(474\) 9.87378 0.453518
\(475\) 8.05787 0.369720
\(476\) 2.85327 0.130779
\(477\) −0.396211 −0.0181413
\(478\) 16.3115 0.746068
\(479\) −17.0838 −0.780579 −0.390290 0.920692i \(-0.627625\pi\)
−0.390290 + 0.920692i \(0.627625\pi\)
\(480\) −1.03120 −0.0470677
\(481\) −13.5708 −0.618774
\(482\) −17.8390 −0.812545
\(483\) 21.1774 0.963606
\(484\) 6.22411 0.282914
\(485\) −9.55329 −0.433792
\(486\) 1.00000 0.0453609
\(487\) 22.8872 1.03712 0.518559 0.855042i \(-0.326469\pi\)
0.518559 + 0.855042i \(0.326469\pi\)
\(488\) −5.11471 −0.231532
\(489\) −20.9048 −0.945347
\(490\) 1.17673 0.0531594
\(491\) −13.2217 −0.596685 −0.298343 0.954459i \(-0.596434\pi\)
−0.298343 + 0.954459i \(0.596434\pi\)
\(492\) 1.47977 0.0667131
\(493\) 9.72983 0.438209
\(494\) 5.80908 0.261363
\(495\) 4.27969 0.192358
\(496\) 8.92011 0.400525
\(497\) 45.1116 2.02353
\(498\) −4.49553 −0.201450
\(499\) 17.8300 0.798181 0.399091 0.916911i \(-0.369326\pi\)
0.399091 + 0.916911i \(0.369326\pi\)
\(500\) 9.21547 0.412128
\(501\) −11.9527 −0.534008
\(502\) 22.1576 0.988940
\(503\) 10.5689 0.471243 0.235621 0.971845i \(-0.424288\pi\)
0.235621 + 0.971845i \(0.424288\pi\)
\(504\) 2.85327 0.127095
\(505\) 19.4078 0.863634
\(506\) 30.8034 1.36938
\(507\) 4.94580 0.219651
\(508\) −10.4413 −0.463257
\(509\) −35.6227 −1.57895 −0.789473 0.613785i \(-0.789646\pi\)
−0.789473 + 0.613785i \(0.789646\pi\)
\(510\) 1.03120 0.0456624
\(511\) 42.4132 1.87625
\(512\) −1.00000 −0.0441942
\(513\) 2.04690 0.0903728
\(514\) 5.50481 0.242807
\(515\) 4.33352 0.190958
\(516\) −0.900717 −0.0396519
\(517\) 48.6338 2.13891
\(518\) −13.6438 −0.599474
\(519\) −13.3211 −0.584731
\(520\) 2.92654 0.128337
\(521\) 29.8750 1.30885 0.654424 0.756128i \(-0.272911\pi\)
0.654424 + 0.756128i \(0.272911\pi\)
\(522\) 9.72983 0.425863
\(523\) 35.1099 1.53525 0.767625 0.640899i \(-0.221438\pi\)
0.767625 + 0.640899i \(0.221438\pi\)
\(524\) 13.9696 0.610264
\(525\) −11.2322 −0.490215
\(526\) −18.3990 −0.802235
\(527\) −8.92011 −0.388566
\(528\) 4.15019 0.180614
\(529\) 32.0886 1.39515
\(530\) −0.408574 −0.0177473
\(531\) 1.00000 0.0433963
\(532\) 5.84035 0.253211
\(533\) −4.19957 −0.181904
\(534\) 10.4285 0.451286
\(535\) −6.18098 −0.267227
\(536\) 11.5926 0.500723
\(537\) −1.96370 −0.0847400
\(538\) 18.3949 0.793063
\(539\) −4.73590 −0.203990
\(540\) 1.03120 0.0443759
\(541\) 5.15896 0.221801 0.110901 0.993832i \(-0.464627\pi\)
0.110901 + 0.993832i \(0.464627\pi\)
\(542\) −16.0260 −0.688374
\(543\) −5.25021 −0.225308
\(544\) 1.00000 0.0428746
\(545\) 10.7167 0.459055
\(546\) −8.09755 −0.346543
\(547\) 6.05215 0.258771 0.129386 0.991594i \(-0.458700\pi\)
0.129386 + 0.991594i \(0.458700\pi\)
\(548\) −21.2201 −0.906479
\(549\) 5.11471 0.218291
\(550\) −16.3377 −0.696644
\(551\) 19.9160 0.848449
\(552\) 7.42217 0.315908
\(553\) −28.1725 −1.19802
\(554\) 13.7057 0.582298
\(555\) −4.93103 −0.209310
\(556\) 0.195248 0.00828037
\(557\) −0.641625 −0.0271865 −0.0135933 0.999908i \(-0.504327\pi\)
−0.0135933 + 0.999908i \(0.504327\pi\)
\(558\) −8.92011 −0.377618
\(559\) 2.55623 0.108117
\(560\) 2.94230 0.124335
\(561\) −4.15019 −0.175221
\(562\) 7.42920 0.313382
\(563\) 39.4104 1.66095 0.830476 0.557055i \(-0.188069\pi\)
0.830476 + 0.557055i \(0.188069\pi\)
\(564\) 11.7184 0.493435
\(565\) −16.3196 −0.686572
\(566\) 4.43689 0.186496
\(567\) −2.85327 −0.119826
\(568\) 15.8105 0.663395
\(569\) 34.6319 1.45185 0.725923 0.687776i \(-0.241413\pi\)
0.725923 + 0.687776i \(0.241413\pi\)
\(570\) 2.11077 0.0884104
\(571\) 29.4151 1.23099 0.615493 0.788143i \(-0.288957\pi\)
0.615493 + 0.788143i \(0.288957\pi\)
\(572\) −11.7782 −0.492472
\(573\) 12.5699 0.525117
\(574\) −4.22217 −0.176230
\(575\) −29.2183 −1.21849
\(576\) 1.00000 0.0416667
\(577\) −22.8470 −0.951133 −0.475566 0.879680i \(-0.657757\pi\)
−0.475566 + 0.879680i \(0.657757\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −24.5408 −1.01988
\(580\) 10.0334 0.416615
\(581\) 12.8270 0.532152
\(582\) 9.26422 0.384014
\(583\) 1.64435 0.0681021
\(584\) 14.8648 0.615109
\(585\) −2.92654 −0.120998
\(586\) −27.1947 −1.12340
\(587\) −3.81976 −0.157658 −0.0788292 0.996888i \(-0.525118\pi\)
−0.0788292 + 0.996888i \(0.525118\pi\)
\(588\) −1.14113 −0.0470593
\(589\) −18.2586 −0.752331
\(590\) 1.03120 0.0424539
\(591\) 21.5354 0.885850
\(592\) −4.78182 −0.196532
\(593\) −4.48418 −0.184143 −0.0920717 0.995752i \(-0.529349\pi\)
−0.0920717 + 0.995752i \(0.529349\pi\)
\(594\) −4.15019 −0.170285
\(595\) −2.94230 −0.120622
\(596\) −14.4831 −0.593251
\(597\) −13.3601 −0.546792
\(598\) −21.0640 −0.861373
\(599\) −21.1277 −0.863255 −0.431627 0.902052i \(-0.642060\pi\)
−0.431627 + 0.902052i \(0.642060\pi\)
\(600\) −3.93662 −0.160712
\(601\) −11.3490 −0.462936 −0.231468 0.972843i \(-0.574353\pi\)
−0.231468 + 0.972843i \(0.574353\pi\)
\(602\) 2.56999 0.104745
\(603\) −11.5926 −0.472086
\(604\) 23.7118 0.964821
\(605\) −6.41832 −0.260942
\(606\) −18.8205 −0.764531
\(607\) 39.5281 1.60440 0.802198 0.597059i \(-0.203664\pi\)
0.802198 + 0.597059i \(0.203664\pi\)
\(608\) 2.04690 0.0830127
\(609\) −27.7618 −1.12496
\(610\) 5.27431 0.213550
\(611\) −33.2568 −1.34543
\(612\) −1.00000 −0.0404226
\(613\) 18.5275 0.748317 0.374159 0.927365i \(-0.377932\pi\)
0.374159 + 0.927365i \(0.377932\pi\)
\(614\) −8.18518 −0.330327
\(615\) −1.52594 −0.0615319
\(616\) −11.8416 −0.477112
\(617\) −12.8821 −0.518614 −0.259307 0.965795i \(-0.583494\pi\)
−0.259307 + 0.965795i \(0.583494\pi\)
\(618\) −4.20239 −0.169045
\(619\) 7.43248 0.298737 0.149368 0.988782i \(-0.452276\pi\)
0.149368 + 0.988782i \(0.452276\pi\)
\(620\) −9.19844 −0.369418
\(621\) −7.42217 −0.297841
\(622\) −18.1124 −0.726241
\(623\) −29.7553 −1.19212
\(624\) −2.83799 −0.113611
\(625\) 10.1801 0.407204
\(626\) 22.5547 0.901468
\(627\) −8.49503 −0.339259
\(628\) 2.87240 0.114621
\(629\) 4.78182 0.190664
\(630\) −2.94230 −0.117224
\(631\) 23.5434 0.937247 0.468624 0.883398i \(-0.344750\pi\)
0.468624 + 0.883398i \(0.344750\pi\)
\(632\) −9.87378 −0.392758
\(633\) 14.2367 0.565859
\(634\) 13.9298 0.553223
\(635\) 10.7671 0.427279
\(636\) 0.396211 0.0157108
\(637\) 3.23851 0.128314
\(638\) −40.3807 −1.59869
\(639\) −15.8105 −0.625454
\(640\) 1.03120 0.0407619
\(641\) −7.93734 −0.313506 −0.156753 0.987638i \(-0.550103\pi\)
−0.156753 + 0.987638i \(0.550103\pi\)
\(642\) 5.99395 0.236562
\(643\) 10.7247 0.422941 0.211471 0.977384i \(-0.432175\pi\)
0.211471 + 0.977384i \(0.432175\pi\)
\(644\) −21.1774 −0.834507
\(645\) 0.928822 0.0365723
\(646\) −2.04690 −0.0805342
\(647\) 40.7598 1.60243 0.801216 0.598375i \(-0.204187\pi\)
0.801216 + 0.598375i \(0.204187\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −4.15019 −0.162909
\(650\) 11.1721 0.438206
\(651\) 25.4514 0.997520
\(652\) 20.9048 0.818694
\(653\) 10.9227 0.427439 0.213719 0.976895i \(-0.431442\pi\)
0.213719 + 0.976895i \(0.431442\pi\)
\(654\) −10.3925 −0.406377
\(655\) −14.4055 −0.562868
\(656\) −1.47977 −0.0577753
\(657\) −14.8648 −0.579930
\(658\) −33.4358 −1.30346
\(659\) −22.5972 −0.880261 −0.440131 0.897934i \(-0.645068\pi\)
−0.440131 + 0.897934i \(0.645068\pi\)
\(660\) −4.27969 −0.166587
\(661\) −1.14472 −0.0445245 −0.0222622 0.999752i \(-0.507087\pi\)
−0.0222622 + 0.999752i \(0.507087\pi\)
\(662\) −8.91532 −0.346504
\(663\) 2.83799 0.110218
\(664\) 4.49553 0.174461
\(665\) −6.02258 −0.233546
\(666\) 4.78182 0.185292
\(667\) −72.2164 −2.79623
\(668\) 11.9527 0.462465
\(669\) −13.2331 −0.511619
\(670\) −11.9543 −0.461835
\(671\) −21.2271 −0.819461
\(672\) −2.85327 −0.110067
\(673\) −12.8522 −0.495415 −0.247707 0.968835i \(-0.579677\pi\)
−0.247707 + 0.968835i \(0.579677\pi\)
\(674\) −18.5601 −0.714908
\(675\) 3.93662 0.151521
\(676\) −4.94580 −0.190223
\(677\) −34.2655 −1.31693 −0.658465 0.752611i \(-0.728794\pi\)
−0.658465 + 0.752611i \(0.728794\pi\)
\(678\) 15.8258 0.607787
\(679\) −26.4333 −1.01442
\(680\) −1.03120 −0.0395448
\(681\) −6.46192 −0.247621
\(682\) 37.0202 1.41758
\(683\) 2.53827 0.0971242 0.0485621 0.998820i \(-0.484536\pi\)
0.0485621 + 0.998820i \(0.484536\pi\)
\(684\) −2.04690 −0.0782652
\(685\) 21.8823 0.836078
\(686\) −16.7169 −0.638255
\(687\) −3.06685 −0.117008
\(688\) 0.900717 0.0343395
\(689\) −1.12444 −0.0428379
\(690\) −7.65376 −0.291374
\(691\) 38.5062 1.46485 0.732423 0.680850i \(-0.238389\pi\)
0.732423 + 0.680850i \(0.238389\pi\)
\(692\) 13.3211 0.506392
\(693\) 11.8416 0.449826
\(694\) −28.3802 −1.07730
\(695\) −0.201341 −0.00763728
\(696\) −9.72983 −0.368808
\(697\) 1.47977 0.0560502
\(698\) 0.411099 0.0155603
\(699\) −8.04281 −0.304207
\(700\) 11.2322 0.424538
\(701\) 1.11309 0.0420409 0.0210205 0.999779i \(-0.493308\pi\)
0.0210205 + 0.999779i \(0.493308\pi\)
\(702\) 2.83799 0.107113
\(703\) 9.78791 0.369158
\(704\) −4.15019 −0.156416
\(705\) −12.0841 −0.455113
\(706\) −11.4830 −0.432167
\(707\) 53.6999 2.01959
\(708\) −1.00000 −0.0375823
\(709\) −18.5538 −0.696802 −0.348401 0.937346i \(-0.613275\pi\)
−0.348401 + 0.937346i \(0.613275\pi\)
\(710\) −16.3038 −0.611872
\(711\) 9.87378 0.370296
\(712\) −10.4285 −0.390825
\(713\) 66.2065 2.47945
\(714\) 2.85327 0.106781
\(715\) 12.1457 0.454224
\(716\) 1.96370 0.0733870
\(717\) 16.3115 0.609162
\(718\) −6.07107 −0.226570
\(719\) −4.27977 −0.159609 −0.0798043 0.996811i \(-0.525430\pi\)
−0.0798043 + 0.996811i \(0.525430\pi\)
\(720\) −1.03120 −0.0384307
\(721\) 11.9905 0.446551
\(722\) 14.8102 0.551179
\(723\) −17.8390 −0.663440
\(724\) 5.25021 0.195122
\(725\) 38.3026 1.42252
\(726\) 6.22411 0.230998
\(727\) −5.07131 −0.188084 −0.0940422 0.995568i \(-0.529979\pi\)
−0.0940422 + 0.995568i \(0.529979\pi\)
\(728\) 8.09755 0.300115
\(729\) 1.00000 0.0370370
\(730\) −15.3286 −0.567337
\(731\) −0.900717 −0.0333142
\(732\) −5.11471 −0.189045
\(733\) −4.89485 −0.180795 −0.0903976 0.995906i \(-0.528814\pi\)
−0.0903976 + 0.995906i \(0.528814\pi\)
\(734\) −4.70200 −0.173554
\(735\) 1.17673 0.0434045
\(736\) −7.42217 −0.273585
\(737\) 48.1115 1.77221
\(738\) 1.47977 0.0544711
\(739\) −38.3700 −1.41146 −0.705732 0.708479i \(-0.749382\pi\)
−0.705732 + 0.708479i \(0.749382\pi\)
\(740\) 4.93103 0.181268
\(741\) 5.80908 0.213402
\(742\) −1.13050 −0.0415018
\(743\) −9.94179 −0.364729 −0.182364 0.983231i \(-0.558375\pi\)
−0.182364 + 0.983231i \(0.558375\pi\)
\(744\) 8.92011 0.327027
\(745\) 14.9350 0.547177
\(746\) −28.6835 −1.05018
\(747\) −4.49553 −0.164483
\(748\) 4.15019 0.151746
\(749\) −17.1023 −0.624906
\(750\) 9.21547 0.336501
\(751\) 16.4626 0.600729 0.300365 0.953824i \(-0.402892\pi\)
0.300365 + 0.953824i \(0.402892\pi\)
\(752\) −11.7184 −0.427328
\(753\) 22.1576 0.807466
\(754\) 27.6132 1.00561
\(755\) −24.4517 −0.889889
\(756\) 2.85327 0.103772
\(757\) 2.38610 0.0867243 0.0433622 0.999059i \(-0.486193\pi\)
0.0433622 + 0.999059i \(0.486193\pi\)
\(758\) 1.44882 0.0526234
\(759\) 30.8034 1.11809
\(760\) −2.11077 −0.0765656
\(761\) −16.0025 −0.580091 −0.290045 0.957013i \(-0.593670\pi\)
−0.290045 + 0.957013i \(0.593670\pi\)
\(762\) −10.4413 −0.378248
\(763\) 29.6525 1.07349
\(764\) −12.5699 −0.454764
\(765\) 1.03120 0.0372832
\(766\) 24.9862 0.902786
\(767\) 2.83799 0.102474
\(768\) −1.00000 −0.0360844
\(769\) 26.4893 0.955229 0.477615 0.878569i \(-0.341502\pi\)
0.477615 + 0.878569i \(0.341502\pi\)
\(770\) 12.2111 0.440057
\(771\) 5.50481 0.198251
\(772\) 24.5408 0.883243
\(773\) 46.4652 1.67124 0.835618 0.549311i \(-0.185110\pi\)
0.835618 + 0.549311i \(0.185110\pi\)
\(774\) −0.900717 −0.0323756
\(775\) −35.1151 −1.26137
\(776\) −9.26422 −0.332566
\(777\) −13.6438 −0.489469
\(778\) −22.6642 −0.812551
\(779\) 3.02894 0.108523
\(780\) 2.92654 0.104787
\(781\) 65.6167 2.34795
\(782\) 7.42217 0.265416
\(783\) 9.72983 0.347716
\(784\) 1.14113 0.0407546
\(785\) −2.96202 −0.105719
\(786\) 13.9696 0.498278
\(787\) 10.7835 0.384389 0.192195 0.981357i \(-0.438439\pi\)
0.192195 + 0.981357i \(0.438439\pi\)
\(788\) −21.5354 −0.767169
\(789\) −18.3990 −0.655022
\(790\) 10.1819 0.362255
\(791\) −45.1553 −1.60554
\(792\) 4.15019 0.147471
\(793\) 14.5155 0.515461
\(794\) 30.5327 1.08356
\(795\) −0.408574 −0.0144906
\(796\) 13.3601 0.473536
\(797\) −2.90504 −0.102902 −0.0514510 0.998676i \(-0.516385\pi\)
−0.0514510 + 0.998676i \(0.516385\pi\)
\(798\) 5.84035 0.206746
\(799\) 11.7184 0.414569
\(800\) 3.93662 0.139181
\(801\) 10.4285 0.368474
\(802\) 17.8910 0.631753
\(803\) 61.6917 2.17705
\(804\) 11.5926 0.408839
\(805\) 21.8382 0.769696
\(806\) −25.3152 −0.891689
\(807\) 18.3949 0.647533
\(808\) 18.8205 0.662103
\(809\) 14.3462 0.504386 0.252193 0.967677i \(-0.418848\pi\)
0.252193 + 0.967677i \(0.418848\pi\)
\(810\) 1.03120 0.0362328
\(811\) 40.0121 1.40501 0.702507 0.711677i \(-0.252064\pi\)
0.702507 + 0.711677i \(0.252064\pi\)
\(812\) 27.7618 0.974247
\(813\) −16.0260 −0.562055
\(814\) −19.8455 −0.695584
\(815\) −21.5571 −0.755111
\(816\) 1.00000 0.0350070
\(817\) −1.84368 −0.0645021
\(818\) 15.1451 0.529537
\(819\) −8.09755 −0.282951
\(820\) 1.52594 0.0532882
\(821\) 2.35122 0.0820581 0.0410290 0.999158i \(-0.486936\pi\)
0.0410290 + 0.999158i \(0.486936\pi\)
\(822\) −21.2201 −0.740137
\(823\) −8.96315 −0.312436 −0.156218 0.987723i \(-0.549930\pi\)
−0.156218 + 0.987723i \(0.549930\pi\)
\(824\) 4.20239 0.146397
\(825\) −16.3377 −0.568807
\(826\) 2.85327 0.0992778
\(827\) −31.0802 −1.08076 −0.540381 0.841420i \(-0.681720\pi\)
−0.540381 + 0.841420i \(0.681720\pi\)
\(828\) 7.42217 0.257938
\(829\) −31.2205 −1.08433 −0.542167 0.840271i \(-0.682396\pi\)
−0.542167 + 0.840271i \(0.682396\pi\)
\(830\) −4.63581 −0.160911
\(831\) 13.7057 0.475444
\(832\) 2.83799 0.0983897
\(833\) −1.14113 −0.0395377
\(834\) 0.195248 0.00676090
\(835\) −12.3257 −0.426548
\(836\) 8.49503 0.293807
\(837\) −8.92011 −0.308324
\(838\) 9.60013 0.331631
\(839\) −52.3257 −1.80648 −0.903241 0.429134i \(-0.858819\pi\)
−0.903241 + 0.429134i \(0.858819\pi\)
\(840\) 2.94230 0.101519
\(841\) 65.6695 2.26447
\(842\) 19.7712 0.681360
\(843\) 7.42920 0.255875
\(844\) −14.2367 −0.490049
\(845\) 5.10013 0.175450
\(846\) 11.7184 0.402888
\(847\) −17.7590 −0.610208
\(848\) −0.396211 −0.0136059
\(849\) 4.43689 0.152274
\(850\) −3.93662 −0.135025
\(851\) −35.4915 −1.21663
\(852\) 15.8105 0.541659
\(853\) −25.1915 −0.862542 −0.431271 0.902222i \(-0.641935\pi\)
−0.431271 + 0.902222i \(0.641935\pi\)
\(854\) 14.5936 0.499384
\(855\) 2.11077 0.0721868
\(856\) −5.99395 −0.204869
\(857\) 20.1661 0.688862 0.344431 0.938812i \(-0.388072\pi\)
0.344431 + 0.938812i \(0.388072\pi\)
\(858\) −11.7782 −0.402102
\(859\) −18.8529 −0.643254 −0.321627 0.946867i \(-0.604230\pi\)
−0.321627 + 0.946867i \(0.604230\pi\)
\(860\) −0.928822 −0.0316726
\(861\) −4.22217 −0.143891
\(862\) 1.01173 0.0344597
\(863\) 15.1503 0.515721 0.257860 0.966182i \(-0.416983\pi\)
0.257860 + 0.966182i \(0.416983\pi\)
\(864\) 1.00000 0.0340207
\(865\) −13.7368 −0.467064
\(866\) −6.61470 −0.224777
\(867\) −1.00000 −0.0339618
\(868\) −25.4514 −0.863878
\(869\) −40.9781 −1.39009
\(870\) 10.0334 0.340165
\(871\) −32.8996 −1.11476
\(872\) 10.3925 0.351933
\(873\) 9.26422 0.313546
\(874\) 15.1924 0.513892
\(875\) −26.2942 −0.888906
\(876\) 14.8648 0.502235
\(877\) 46.1047 1.55684 0.778422 0.627742i \(-0.216021\pi\)
0.778422 + 0.627742i \(0.216021\pi\)
\(878\) −2.17249 −0.0733180
\(879\) −27.1947 −0.917254
\(880\) 4.27969 0.144268
\(881\) −8.00830 −0.269806 −0.134903 0.990859i \(-0.543072\pi\)
−0.134903 + 0.990859i \(0.543072\pi\)
\(882\) −1.14113 −0.0384238
\(883\) 46.4484 1.56311 0.781557 0.623834i \(-0.214426\pi\)
0.781557 + 0.623834i \(0.214426\pi\)
\(884\) −2.83799 −0.0954520
\(885\) 1.03120 0.0346635
\(886\) 16.4903 0.554003
\(887\) 11.6316 0.390552 0.195276 0.980748i \(-0.437440\pi\)
0.195276 + 0.980748i \(0.437440\pi\)
\(888\) −4.78182 −0.160467
\(889\) 29.7918 0.999184
\(890\) 10.7539 0.360472
\(891\) −4.15019 −0.139037
\(892\) 13.2331 0.443075
\(893\) 23.9865 0.802677
\(894\) −14.4831 −0.484388
\(895\) −2.02497 −0.0676874
\(896\) 2.85327 0.0953209
\(897\) −21.0640 −0.703308
\(898\) −33.2089 −1.10820
\(899\) −86.7911 −2.89464
\(900\) −3.93662 −0.131221
\(901\) 0.396211 0.0131997
\(902\) −6.14133 −0.204484
\(903\) 2.56999 0.0855238
\(904\) −15.8258 −0.526359
\(905\) −5.41403 −0.179968
\(906\) 23.7118 0.787773
\(907\) 26.1930 0.869723 0.434862 0.900497i \(-0.356797\pi\)
0.434862 + 0.900497i \(0.356797\pi\)
\(908\) 6.46192 0.214446
\(909\) −18.8205 −0.624237
\(910\) −8.35021 −0.276807
\(911\) 3.08448 0.102194 0.0510968 0.998694i \(-0.483728\pi\)
0.0510968 + 0.998694i \(0.483728\pi\)
\(912\) 2.04690 0.0677796
\(913\) 18.6573 0.617468
\(914\) 4.22666 0.139805
\(915\) 5.27431 0.174363
\(916\) 3.06685 0.101332
\(917\) −39.8589 −1.31626
\(918\) −1.00000 −0.0330049
\(919\) −54.6821 −1.80380 −0.901899 0.431948i \(-0.857826\pi\)
−0.901899 + 0.431948i \(0.857826\pi\)
\(920\) 7.65376 0.252337
\(921\) −8.18518 −0.269711
\(922\) −30.0219 −0.988719
\(923\) −44.8701 −1.47692
\(924\) −11.8416 −0.389560
\(925\) 18.8242 0.618936
\(926\) −11.2614 −0.370073
\(927\) −4.20239 −0.138025
\(928\) 9.72983 0.319397
\(929\) −0.283339 −0.00929607 −0.00464803 0.999989i \(-0.501480\pi\)
−0.00464803 + 0.999989i \(0.501480\pi\)
\(930\) −9.19844 −0.301629
\(931\) −2.33577 −0.0765519
\(932\) 8.04281 0.263451
\(933\) −18.1124 −0.592973
\(934\) −21.2014 −0.693732
\(935\) −4.27969 −0.139961
\(936\) −2.83799 −0.0927627
\(937\) 19.3764 0.632998 0.316499 0.948593i \(-0.397493\pi\)
0.316499 + 0.948593i \(0.397493\pi\)
\(938\) −33.0767 −1.07999
\(939\) 22.5547 0.736046
\(940\) 12.0841 0.394140
\(941\) −32.1218 −1.04714 −0.523571 0.851982i \(-0.675400\pi\)
−0.523571 + 0.851982i \(0.675400\pi\)
\(942\) 2.87240 0.0935878
\(943\) −10.9831 −0.357659
\(944\) 1.00000 0.0325472
\(945\) −2.94230 −0.0957129
\(946\) 3.73815 0.121538
\(947\) −51.6508 −1.67843 −0.839213 0.543803i \(-0.816984\pi\)
−0.839213 + 0.543803i \(0.816984\pi\)
\(948\) −9.87378 −0.320686
\(949\) −42.1861 −1.36942
\(950\) −8.05787 −0.261432
\(951\) 13.9298 0.451705
\(952\) −2.85327 −0.0924749
\(953\) −36.1579 −1.17127 −0.585634 0.810576i \(-0.699154\pi\)
−0.585634 + 0.810576i \(0.699154\pi\)
\(954\) 0.396211 0.0128278
\(955\) 12.9622 0.419446
\(956\) −16.3115 −0.527550
\(957\) −40.3807 −1.30532
\(958\) 17.0838 0.551953
\(959\) 60.5467 1.95516
\(960\) 1.03120 0.0332819
\(961\) 48.5683 1.56672
\(962\) 13.5708 0.437539
\(963\) 5.99395 0.193152
\(964\) 17.8390 0.574556
\(965\) −25.3065 −0.814647
\(966\) −21.1774 −0.681372
\(967\) −22.6614 −0.728742 −0.364371 0.931254i \(-0.618716\pi\)
−0.364371 + 0.931254i \(0.618716\pi\)
\(968\) −6.22411 −0.200051
\(969\) −2.04690 −0.0657559
\(970\) 9.55329 0.306738
\(971\) 24.8841 0.798568 0.399284 0.916827i \(-0.369259\pi\)
0.399284 + 0.916827i \(0.369259\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −0.557095 −0.0178597
\(974\) −22.8872 −0.733353
\(975\) 11.1721 0.357793
\(976\) 5.11471 0.163718
\(977\) 7.67116 0.245422 0.122711 0.992442i \(-0.460841\pi\)
0.122711 + 0.992442i \(0.460841\pi\)
\(978\) 20.9048 0.668461
\(979\) −43.2804 −1.38325
\(980\) −1.17673 −0.0375894
\(981\) −10.3925 −0.331806
\(982\) 13.2217 0.421920
\(983\) 36.1355 1.15254 0.576271 0.817259i \(-0.304507\pi\)
0.576271 + 0.817259i \(0.304507\pi\)
\(984\) −1.47977 −0.0471733
\(985\) 22.2074 0.707587
\(986\) −9.72983 −0.309861
\(987\) −33.4358 −1.06427
\(988\) −5.80908 −0.184812
\(989\) 6.68527 0.212579
\(990\) −4.27969 −0.136018
\(991\) 34.1460 1.08468 0.542342 0.840158i \(-0.317538\pi\)
0.542342 + 0.840158i \(0.317538\pi\)
\(992\) −8.92011 −0.283214
\(993\) −8.91532 −0.282919
\(994\) −45.1116 −1.43085
\(995\) −13.7770 −0.436759
\(996\) 4.49553 0.142446
\(997\) 16.2682 0.515220 0.257610 0.966249i \(-0.417065\pi\)
0.257610 + 0.966249i \(0.417065\pi\)
\(998\) −17.8300 −0.564399
\(999\) 4.78182 0.151290
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 6018.2.a.s.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.s.1.4 8 1.1 even 1 trivial