Properties

Label 4026.2.a.q.1.4
Level $4026$
Weight $2$
Character 4026.1
Self dual yes
Analytic conductor $32.148$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4026,2,Mod(1,4026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4026, 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("4026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.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: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.6809.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 5x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.29041\) of defining polynomial
Character \(\chi\) \(=\) 4026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.29041 q^{5} +1.00000 q^{6} -0.955570 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.29041 q^{5} +1.00000 q^{6} -0.955570 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.29041 q^{10} -1.00000 q^{11} -1.00000 q^{12} +2.11919 q^{13} +0.955570 q^{14} -2.29041 q^{15} +1.00000 q^{16} +4.97299 q^{17} -1.00000 q^{18} +7.95360 q^{19} +2.29041 q^{20} +0.955570 q^{21} +1.00000 q^{22} +7.11919 q^{23} +1.00000 q^{24} +0.245981 q^{25} -2.11919 q^{26} -1.00000 q^{27} -0.955570 q^{28} -6.92856 q^{29} +2.29041 q^{30} +7.11721 q^{31} -1.00000 q^{32} +1.00000 q^{33} -4.97299 q^{34} -2.18865 q^{35} +1.00000 q^{36} -10.7379 q^{37} -7.95360 q^{38} -2.11919 q^{39} -2.29041 q^{40} +7.66968 q^{41} -0.955570 q^{42} -3.54400 q^{43} -1.00000 q^{44} +2.29041 q^{45} -7.11919 q^{46} -5.59372 q^{47} -1.00000 q^{48} -6.08689 q^{49} -0.245981 q^{50} -4.97299 q^{51} +2.11919 q^{52} +8.21368 q^{53} +1.00000 q^{54} -2.29041 q^{55} +0.955570 q^{56} -7.95360 q^{57} +6.92856 q^{58} +4.62525 q^{59} -2.29041 q^{60} +1.00000 q^{61} -7.11721 q^{62} -0.955570 q^{63} +1.00000 q^{64} +4.85381 q^{65} -1.00000 q^{66} +12.3059 q^{67} +4.97299 q^{68} -7.11919 q^{69} +2.18865 q^{70} -4.85183 q^{71} -1.00000 q^{72} -9.48633 q^{73} +10.7379 q^{74} -0.245981 q^{75} +7.95360 q^{76} +0.955570 q^{77} +2.11919 q^{78} +6.68822 q^{79} +2.29041 q^{80} +1.00000 q^{81} -7.66968 q^{82} -1.24401 q^{83} +0.955570 q^{84} +11.3902 q^{85} +3.54400 q^{86} +6.92856 q^{87} +1.00000 q^{88} -6.29041 q^{89} -2.29041 q^{90} -2.02503 q^{91} +7.11919 q^{92} -7.11721 q^{93} +5.59372 q^{94} +18.2170 q^{95} +1.00000 q^{96} -4.37166 q^{97} +6.08689 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{12} - 4 q^{13} + 2 q^{14} + 4 q^{16} - q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{21} + 4 q^{22} + 16 q^{23} + 4 q^{24} - 10 q^{25} + 4 q^{26} - 4 q^{27} - 2 q^{28} - 5 q^{29} - 10 q^{31} - 4 q^{32} + 4 q^{33} + q^{34} + 7 q^{35} + 4 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{41} - 2 q^{42} - 8 q^{43} - 4 q^{44} - 16 q^{46} - 7 q^{47} - 4 q^{48} - 2 q^{49} + 10 q^{50} + q^{51} - 4 q^{52} + 12 q^{53} + 4 q^{54} + 2 q^{56} - 4 q^{57} + 5 q^{58} + 2 q^{59} + 4 q^{61} + 10 q^{62} - 2 q^{63} + 4 q^{64} + 11 q^{65} - 4 q^{66} - 5 q^{67} - q^{68} - 16 q^{69} - 7 q^{70} + 15 q^{71} - 4 q^{72} - 28 q^{73} + 10 q^{74} + 10 q^{75} + 4 q^{76} + 2 q^{77} - 4 q^{78} + 3 q^{79} + 4 q^{81} - 16 q^{82} + 32 q^{83} + 2 q^{84} + 17 q^{85} + 8 q^{86} + 5 q^{87} + 4 q^{88} - 16 q^{89} - 3 q^{91} + 16 q^{92} + 10 q^{93} + 7 q^{94} + 15 q^{95} + 4 q^{96} + 2 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 2.29041 1.02430 0.512151 0.858895i \(-0.328849\pi\)
0.512151 + 0.858895i \(0.328849\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.955570 −0.361172 −0.180586 0.983559i \(-0.557799\pi\)
−0.180586 + 0.983559i \(0.557799\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.29041 −0.724291
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) 2.11919 0.587757 0.293878 0.955843i \(-0.405054\pi\)
0.293878 + 0.955843i \(0.405054\pi\)
\(14\) 0.955570 0.255387
\(15\) −2.29041 −0.591381
\(16\) 1.00000 0.250000
\(17\) 4.97299 1.20613 0.603064 0.797693i \(-0.293946\pi\)
0.603064 + 0.797693i \(0.293946\pi\)
\(18\) −1.00000 −0.235702
\(19\) 7.95360 1.82468 0.912340 0.409433i \(-0.134274\pi\)
0.912340 + 0.409433i \(0.134274\pi\)
\(20\) 2.29041 0.512151
\(21\) 0.955570 0.208523
\(22\) 1.00000 0.213201
\(23\) 7.11919 1.48445 0.742227 0.670149i \(-0.233770\pi\)
0.742227 + 0.670149i \(0.233770\pi\)
\(24\) 1.00000 0.204124
\(25\) 0.245981 0.0491962
\(26\) −2.11919 −0.415607
\(27\) −1.00000 −0.192450
\(28\) −0.955570 −0.180586
\(29\) −6.92856 −1.28660 −0.643301 0.765613i \(-0.722436\pi\)
−0.643301 + 0.765613i \(0.722436\pi\)
\(30\) 2.29041 0.418170
\(31\) 7.11721 1.27829 0.639145 0.769087i \(-0.279289\pi\)
0.639145 + 0.769087i \(0.279289\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) −4.97299 −0.852861
\(35\) −2.18865 −0.369949
\(36\) 1.00000 0.166667
\(37\) −10.7379 −1.76531 −0.882653 0.470024i \(-0.844245\pi\)
−0.882653 + 0.470024i \(0.844245\pi\)
\(38\) −7.95360 −1.29024
\(39\) −2.11919 −0.339341
\(40\) −2.29041 −0.362146
\(41\) 7.66968 1.19780 0.598901 0.800823i \(-0.295604\pi\)
0.598901 + 0.800823i \(0.295604\pi\)
\(42\) −0.955570 −0.147448
\(43\) −3.54400 −0.540455 −0.270227 0.962797i \(-0.587099\pi\)
−0.270227 + 0.962797i \(0.587099\pi\)
\(44\) −1.00000 −0.150756
\(45\) 2.29041 0.341434
\(46\) −7.11919 −1.04967
\(47\) −5.59372 −0.815929 −0.407964 0.912998i \(-0.633761\pi\)
−0.407964 + 0.912998i \(0.633761\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.08689 −0.869555
\(50\) −0.245981 −0.0347869
\(51\) −4.97299 −0.696358
\(52\) 2.11919 0.293878
\(53\) 8.21368 1.12824 0.564118 0.825694i \(-0.309216\pi\)
0.564118 + 0.825694i \(0.309216\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.29041 −0.308839
\(56\) 0.955570 0.127693
\(57\) −7.95360 −1.05348
\(58\) 6.92856 0.909765
\(59\) 4.62525 0.602156 0.301078 0.953599i \(-0.402653\pi\)
0.301078 + 0.953599i \(0.402653\pi\)
\(60\) −2.29041 −0.295691
\(61\) 1.00000 0.128037
\(62\) −7.11721 −0.903887
\(63\) −0.955570 −0.120391
\(64\) 1.00000 0.125000
\(65\) 4.85381 0.602041
\(66\) −1.00000 −0.123091
\(67\) 12.3059 1.50340 0.751700 0.659505i \(-0.229234\pi\)
0.751700 + 0.659505i \(0.229234\pi\)
\(68\) 4.97299 0.603064
\(69\) −7.11919 −0.857049
\(70\) 2.18865 0.261593
\(71\) −4.85183 −0.575807 −0.287903 0.957659i \(-0.592958\pi\)
−0.287903 + 0.957659i \(0.592958\pi\)
\(72\) −1.00000 −0.117851
\(73\) −9.48633 −1.11029 −0.555145 0.831753i \(-0.687337\pi\)
−0.555145 + 0.831753i \(0.687337\pi\)
\(74\) 10.7379 1.24826
\(75\) −0.245981 −0.0284034
\(76\) 7.95360 0.912340
\(77\) 0.955570 0.108897
\(78\) 2.11919 0.239951
\(79\) 6.68822 0.752483 0.376242 0.926522i \(-0.377216\pi\)
0.376242 + 0.926522i \(0.377216\pi\)
\(80\) 2.29041 0.256076
\(81\) 1.00000 0.111111
\(82\) −7.66968 −0.846975
\(83\) −1.24401 −0.136547 −0.0682737 0.997667i \(-0.521749\pi\)
−0.0682737 + 0.997667i \(0.521749\pi\)
\(84\) 0.955570 0.104261
\(85\) 11.3902 1.23544
\(86\) 3.54400 0.382159
\(87\) 6.92856 0.742820
\(88\) 1.00000 0.106600
\(89\) −6.29041 −0.666782 −0.333391 0.942789i \(-0.608193\pi\)
−0.333391 + 0.942789i \(0.608193\pi\)
\(90\) −2.29041 −0.241430
\(91\) −2.02503 −0.212281
\(92\) 7.11919 0.742227
\(93\) −7.11721 −0.738021
\(94\) 5.59372 0.576949
\(95\) 18.2170 1.86902
\(96\) 1.00000 0.102062
\(97\) −4.37166 −0.443875 −0.221938 0.975061i \(-0.571238\pi\)
−0.221938 + 0.975061i \(0.571238\pi\)
\(98\) 6.08689 0.614868
\(99\) −1.00000 −0.100504
\(100\) 0.245981 0.0245981
\(101\) 17.8704 1.77817 0.889084 0.457744i \(-0.151342\pi\)
0.889084 + 0.457744i \(0.151342\pi\)
\(102\) 4.97299 0.492400
\(103\) 6.09868 0.600920 0.300460 0.953794i \(-0.402860\pi\)
0.300460 + 0.953794i \(0.402860\pi\)
\(104\) −2.11919 −0.207803
\(105\) 2.18865 0.213590
\(106\) −8.21368 −0.797783
\(107\) −16.4577 −1.59102 −0.795512 0.605937i \(-0.792798\pi\)
−0.795512 + 0.605937i \(0.792798\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 6.53528 0.625966 0.312983 0.949759i \(-0.398672\pi\)
0.312983 + 0.949759i \(0.398672\pi\)
\(110\) 2.29041 0.218382
\(111\) 10.7379 1.01920
\(112\) −0.955570 −0.0902929
\(113\) −6.67079 −0.627535 −0.313768 0.949500i \(-0.601591\pi\)
−0.313768 + 0.949500i \(0.601591\pi\)
\(114\) 7.95360 0.744923
\(115\) 16.3059 1.52053
\(116\) −6.92856 −0.643301
\(117\) 2.11919 0.195919
\(118\) −4.62525 −0.425789
\(119\) −4.75205 −0.435619
\(120\) 2.29041 0.209085
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −7.66968 −0.691552
\(124\) 7.11721 0.639145
\(125\) −10.8887 −0.973911
\(126\) 0.955570 0.0851290
\(127\) 9.31544 0.826612 0.413306 0.910592i \(-0.364374\pi\)
0.413306 + 0.910592i \(0.364374\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.54400 0.312032
\(130\) −4.85381 −0.425707
\(131\) 6.88611 0.601642 0.300821 0.953681i \(-0.402739\pi\)
0.300821 + 0.953681i \(0.402739\pi\)
\(132\) 1.00000 0.0870388
\(133\) −7.60022 −0.659023
\(134\) −12.3059 −1.06306
\(135\) −2.29041 −0.197127
\(136\) −4.97299 −0.426431
\(137\) 12.8841 1.10077 0.550383 0.834912i \(-0.314482\pi\)
0.550383 + 0.834912i \(0.314482\pi\)
\(138\) 7.11919 0.606025
\(139\) −0.407623 −0.0345742 −0.0172871 0.999851i \(-0.505503\pi\)
−0.0172871 + 0.999851i \(0.505503\pi\)
\(140\) −2.18865 −0.184975
\(141\) 5.59372 0.471077
\(142\) 4.85183 0.407157
\(143\) −2.11919 −0.177215
\(144\) 1.00000 0.0833333
\(145\) −15.8693 −1.31787
\(146\) 9.48633 0.785094
\(147\) 6.08689 0.502038
\(148\) −10.7379 −0.882653
\(149\) −6.54169 −0.535916 −0.267958 0.963431i \(-0.586349\pi\)
−0.267958 + 0.963431i \(0.586349\pi\)
\(150\) 0.245981 0.0200842
\(151\) −23.2854 −1.89493 −0.947467 0.319852i \(-0.896367\pi\)
−0.947467 + 0.319852i \(0.896367\pi\)
\(152\) −7.95360 −0.645122
\(153\) 4.97299 0.402043
\(154\) −0.955570 −0.0770020
\(155\) 16.3013 1.30936
\(156\) −2.11919 −0.169671
\(157\) −19.0675 −1.52175 −0.760876 0.648898i \(-0.775230\pi\)
−0.760876 + 0.648898i \(0.775230\pi\)
\(158\) −6.68822 −0.532086
\(159\) −8.21368 −0.651387
\(160\) −2.29041 −0.181073
\(161\) −6.80288 −0.536142
\(162\) −1.00000 −0.0785674
\(163\) 14.3786 1.12622 0.563111 0.826381i \(-0.309604\pi\)
0.563111 + 0.826381i \(0.309604\pi\)
\(164\) 7.66968 0.598901
\(165\) 2.29041 0.178308
\(166\) 1.24401 0.0965537
\(167\) −9.78237 −0.756983 −0.378491 0.925605i \(-0.623557\pi\)
−0.378491 + 0.925605i \(0.623557\pi\)
\(168\) −0.955570 −0.0737238
\(169\) −8.50905 −0.654542
\(170\) −11.3902 −0.873588
\(171\) 7.95360 0.608227
\(172\) −3.54400 −0.270227
\(173\) 9.17089 0.697250 0.348625 0.937262i \(-0.386649\pi\)
0.348625 + 0.937262i \(0.386649\pi\)
\(174\) −6.92856 −0.525253
\(175\) −0.235052 −0.0177683
\(176\) −1.00000 −0.0753778
\(177\) −4.62525 −0.347655
\(178\) 6.29041 0.471486
\(179\) 9.93222 0.742369 0.371185 0.928559i \(-0.378952\pi\)
0.371185 + 0.928559i \(0.378952\pi\)
\(180\) 2.29041 0.170717
\(181\) 6.05093 0.449762 0.224881 0.974386i \(-0.427801\pi\)
0.224881 + 0.974386i \(0.427801\pi\)
\(182\) 2.02503 0.150105
\(183\) −1.00000 −0.0739221
\(184\) −7.11919 −0.524833
\(185\) −24.5943 −1.80821
\(186\) 7.11721 0.521859
\(187\) −4.97299 −0.363661
\(188\) −5.59372 −0.407964
\(189\) 0.955570 0.0695075
\(190\) −18.2170 −1.32160
\(191\) 19.3685 1.40145 0.700727 0.713429i \(-0.252859\pi\)
0.700727 + 0.713429i \(0.252859\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −0.00563344 −0.000405504 0 −0.000202752 1.00000i \(-0.500065\pi\)
−0.000202752 1.00000i \(0.500065\pi\)
\(194\) 4.37166 0.313867
\(195\) −4.85381 −0.347588
\(196\) −6.08689 −0.434778
\(197\) −2.81665 −0.200678 −0.100339 0.994953i \(-0.531993\pi\)
−0.100339 + 0.994953i \(0.531993\pi\)
\(198\) 1.00000 0.0710669
\(199\) −5.67941 −0.402603 −0.201301 0.979529i \(-0.564517\pi\)
−0.201301 + 0.979529i \(0.564517\pi\)
\(200\) −0.245981 −0.0173935
\(201\) −12.3059 −0.867988
\(202\) −17.8704 −1.25735
\(203\) 6.62073 0.464684
\(204\) −4.97299 −0.348179
\(205\) 17.5667 1.22691
\(206\) −6.09868 −0.424915
\(207\) 7.11919 0.494818
\(208\) 2.11919 0.146939
\(209\) −7.95360 −0.550162
\(210\) −2.18865 −0.151031
\(211\) 25.9408 1.78584 0.892921 0.450214i \(-0.148652\pi\)
0.892921 + 0.450214i \(0.148652\pi\)
\(212\) 8.21368 0.564118
\(213\) 4.85183 0.332442
\(214\) 16.4577 1.12502
\(215\) −8.11721 −0.553589
\(216\) 1.00000 0.0680414
\(217\) −6.80100 −0.461682
\(218\) −6.53528 −0.442625
\(219\) 9.48633 0.641027
\(220\) −2.29041 −0.154419
\(221\) 10.5387 0.708910
\(222\) −10.7379 −0.720684
\(223\) −13.9319 −0.932948 −0.466474 0.884535i \(-0.654476\pi\)
−0.466474 + 0.884535i \(0.654476\pi\)
\(224\) 0.955570 0.0638467
\(225\) 0.245981 0.0163987
\(226\) 6.67079 0.443735
\(227\) 26.5355 1.76122 0.880612 0.473837i \(-0.157131\pi\)
0.880612 + 0.473837i \(0.157131\pi\)
\(228\) −7.95360 −0.526740
\(229\) −20.9876 −1.38690 −0.693449 0.720505i \(-0.743910\pi\)
−0.693449 + 0.720505i \(0.743910\pi\)
\(230\) −16.3059 −1.07518
\(231\) −0.955570 −0.0628719
\(232\) 6.92856 0.454883
\(233\) 27.3573 1.79223 0.896117 0.443817i \(-0.146376\pi\)
0.896117 + 0.443817i \(0.146376\pi\)
\(234\) −2.11919 −0.138536
\(235\) −12.8119 −0.835758
\(236\) 4.62525 0.301078
\(237\) −6.68822 −0.434446
\(238\) 4.75205 0.308029
\(239\) 15.5679 1.00700 0.503502 0.863994i \(-0.332044\pi\)
0.503502 + 0.863994i \(0.332044\pi\)
\(240\) −2.29041 −0.147845
\(241\) −19.3688 −1.24766 −0.623828 0.781562i \(-0.714423\pi\)
−0.623828 + 0.781562i \(0.714423\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 1.00000 0.0640184
\(245\) −13.9415 −0.890688
\(246\) 7.66968 0.489001
\(247\) 16.8552 1.07247
\(248\) −7.11721 −0.451943
\(249\) 1.24401 0.0788357
\(250\) 10.8887 0.688659
\(251\) −1.85183 −0.116887 −0.0584434 0.998291i \(-0.518614\pi\)
−0.0584434 + 0.998291i \(0.518614\pi\)
\(252\) −0.955570 −0.0601953
\(253\) −7.11919 −0.447579
\(254\) −9.31544 −0.584503
\(255\) −11.3902 −0.713282
\(256\) 1.00000 0.0625000
\(257\) 29.4287 1.83571 0.917856 0.396913i \(-0.129919\pi\)
0.917856 + 0.396913i \(0.129919\pi\)
\(258\) −3.54400 −0.220640
\(259\) 10.2609 0.637579
\(260\) 4.85381 0.301020
\(261\) −6.92856 −0.428867
\(262\) −6.88611 −0.425425
\(263\) 30.8588 1.90284 0.951418 0.307902i \(-0.0996270\pi\)
0.951418 + 0.307902i \(0.0996270\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 18.8127 1.15565
\(266\) 7.60022 0.465999
\(267\) 6.29041 0.384967
\(268\) 12.3059 0.751700
\(269\) −1.87321 −0.114211 −0.0571057 0.998368i \(-0.518187\pi\)
−0.0571057 + 0.998368i \(0.518187\pi\)
\(270\) 2.29041 0.139390
\(271\) −29.1719 −1.77207 −0.886035 0.463619i \(-0.846551\pi\)
−0.886035 + 0.463619i \(0.846551\pi\)
\(272\) 4.97299 0.301532
\(273\) 2.02503 0.122560
\(274\) −12.8841 −0.778359
\(275\) −0.245981 −0.0148332
\(276\) −7.11919 −0.428525
\(277\) −15.3837 −0.924317 −0.462159 0.886797i \(-0.652925\pi\)
−0.462159 + 0.886797i \(0.652925\pi\)
\(278\) 0.407623 0.0244476
\(279\) 7.11721 0.426096
\(280\) 2.18865 0.130797
\(281\) 23.6753 1.41235 0.706175 0.708037i \(-0.250419\pi\)
0.706175 + 0.708037i \(0.250419\pi\)
\(282\) −5.59372 −0.333101
\(283\) 7.17969 0.426788 0.213394 0.976966i \(-0.431548\pi\)
0.213394 + 0.976966i \(0.431548\pi\)
\(284\) −4.85183 −0.287903
\(285\) −18.2170 −1.07908
\(286\) 2.11919 0.125310
\(287\) −7.32892 −0.432612
\(288\) −1.00000 −0.0589256
\(289\) 7.73067 0.454745
\(290\) 15.8693 0.931875
\(291\) 4.37166 0.256271
\(292\) −9.48633 −0.555145
\(293\) 14.8090 0.865153 0.432577 0.901597i \(-0.357604\pi\)
0.432577 + 0.901597i \(0.357604\pi\)
\(294\) −6.08689 −0.354994
\(295\) 10.5937 0.616790
\(296\) 10.7379 0.624130
\(297\) 1.00000 0.0580259
\(298\) 6.54169 0.378950
\(299\) 15.0869 0.872497
\(300\) −0.245981 −0.0142017
\(301\) 3.38654 0.195197
\(302\) 23.2854 1.33992
\(303\) −17.8704 −1.02663
\(304\) 7.95360 0.456170
\(305\) 2.29041 0.131149
\(306\) −4.97299 −0.284287
\(307\) 18.6245 1.06296 0.531478 0.847072i \(-0.321637\pi\)
0.531478 + 0.847072i \(0.321637\pi\)
\(308\) 0.955570 0.0544487
\(309\) −6.09868 −0.346942
\(310\) −16.3013 −0.925854
\(311\) 4.09647 0.232289 0.116145 0.993232i \(-0.462946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(312\) 2.11919 0.119975
\(313\) −19.5465 −1.10484 −0.552418 0.833567i \(-0.686295\pi\)
−0.552418 + 0.833567i \(0.686295\pi\)
\(314\) 19.0675 1.07604
\(315\) −2.18865 −0.123316
\(316\) 6.68822 0.376242
\(317\) −7.28921 −0.409403 −0.204701 0.978824i \(-0.565622\pi\)
−0.204701 + 0.978824i \(0.565622\pi\)
\(318\) 8.21368 0.460600
\(319\) 6.92856 0.387925
\(320\) 2.29041 0.128038
\(321\) 16.4577 0.918578
\(322\) 6.80288 0.379110
\(323\) 39.5532 2.20080
\(324\) 1.00000 0.0555556
\(325\) 0.521279 0.0289154
\(326\) −14.3786 −0.796359
\(327\) −6.53528 −0.361402
\(328\) −7.66968 −0.423487
\(329\) 5.34520 0.294690
\(330\) −2.29041 −0.126083
\(331\) 12.2209 0.671724 0.335862 0.941911i \(-0.390972\pi\)
0.335862 + 0.941911i \(0.390972\pi\)
\(332\) −1.24401 −0.0682737
\(333\) −10.7379 −0.588436
\(334\) 9.78237 0.535268
\(335\) 28.1855 1.53994
\(336\) 0.955570 0.0521306
\(337\) −15.3770 −0.837636 −0.418818 0.908070i \(-0.637556\pi\)
−0.418818 + 0.908070i \(0.637556\pi\)
\(338\) 8.50905 0.462831
\(339\) 6.67079 0.362308
\(340\) 11.3902 0.617720
\(341\) −7.11721 −0.385419
\(342\) −7.95360 −0.430081
\(343\) 12.5054 0.675230
\(344\) 3.54400 0.191080
\(345\) −16.3059 −0.877878
\(346\) −9.17089 −0.493030
\(347\) 20.4399 1.09727 0.548636 0.836061i \(-0.315147\pi\)
0.548636 + 0.836061i \(0.315147\pi\)
\(348\) 6.92856 0.371410
\(349\) 19.9050 1.06549 0.532744 0.846276i \(-0.321161\pi\)
0.532744 + 0.846276i \(0.321161\pi\)
\(350\) 0.235052 0.0125641
\(351\) −2.11919 −0.113114
\(352\) 1.00000 0.0533002
\(353\) −26.1923 −1.39408 −0.697038 0.717034i \(-0.745499\pi\)
−0.697038 + 0.717034i \(0.745499\pi\)
\(354\) 4.62525 0.245829
\(355\) −11.1127 −0.589800
\(356\) −6.29041 −0.333391
\(357\) 4.75205 0.251505
\(358\) −9.93222 −0.524934
\(359\) 29.1045 1.53608 0.768040 0.640402i \(-0.221232\pi\)
0.768040 + 0.640402i \(0.221232\pi\)
\(360\) −2.29041 −0.120715
\(361\) 44.2597 2.32946
\(362\) −6.05093 −0.318030
\(363\) −1.00000 −0.0524864
\(364\) −2.02503 −0.106140
\(365\) −21.7276 −1.13727
\(366\) 1.00000 0.0522708
\(367\) 8.26229 0.431288 0.215644 0.976472i \(-0.430815\pi\)
0.215644 + 0.976472i \(0.430815\pi\)
\(368\) 7.11919 0.371113
\(369\) 7.66968 0.399268
\(370\) 24.5943 1.27860
\(371\) −7.84875 −0.407487
\(372\) −7.11721 −0.369010
\(373\) −24.0005 −1.24270 −0.621349 0.783534i \(-0.713415\pi\)
−0.621349 + 0.783534i \(0.713415\pi\)
\(374\) 4.97299 0.257147
\(375\) 10.8887 0.562288
\(376\) 5.59372 0.288474
\(377\) −14.6829 −0.756209
\(378\) −0.955570 −0.0491492
\(379\) −12.3500 −0.634374 −0.317187 0.948363i \(-0.602738\pi\)
−0.317187 + 0.948363i \(0.602738\pi\)
\(380\) 18.2170 0.934512
\(381\) −9.31544 −0.477245
\(382\) −19.3685 −0.990978
\(383\) −30.4079 −1.55377 −0.776884 0.629643i \(-0.783201\pi\)
−0.776884 + 0.629643i \(0.783201\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.18865 0.111544
\(386\) 0.00563344 0.000286734 0
\(387\) −3.54400 −0.180152
\(388\) −4.37166 −0.221938
\(389\) −24.1891 −1.22644 −0.613219 0.789913i \(-0.710126\pi\)
−0.613219 + 0.789913i \(0.710126\pi\)
\(390\) 4.85381 0.245782
\(391\) 35.4037 1.79044
\(392\) 6.08689 0.307434
\(393\) −6.88611 −0.347358
\(394\) 2.81665 0.141901
\(395\) 15.3188 0.770771
\(396\) −1.00000 −0.0502519
\(397\) 21.8667 1.09746 0.548729 0.836000i \(-0.315112\pi\)
0.548729 + 0.836000i \(0.315112\pi\)
\(398\) 5.67941 0.284683
\(399\) 7.60022 0.380487
\(400\) 0.245981 0.0122990
\(401\) 11.0868 0.553648 0.276824 0.960921i \(-0.410718\pi\)
0.276824 + 0.960921i \(0.410718\pi\)
\(402\) 12.3059 0.613761
\(403\) 15.0827 0.751323
\(404\) 17.8704 0.889084
\(405\) 2.29041 0.113811
\(406\) −6.62073 −0.328581
\(407\) 10.7379 0.532260
\(408\) 4.97299 0.246200
\(409\) 6.66232 0.329431 0.164715 0.986341i \(-0.447329\pi\)
0.164715 + 0.986341i \(0.447329\pi\)
\(410\) −17.5667 −0.867558
\(411\) −12.8841 −0.635527
\(412\) 6.09868 0.300460
\(413\) −4.41975 −0.217482
\(414\) −7.11919 −0.349889
\(415\) −2.84929 −0.139866
\(416\) −2.11919 −0.103902
\(417\) 0.407623 0.0199614
\(418\) 7.95360 0.389023
\(419\) 16.5348 0.807776 0.403888 0.914809i \(-0.367659\pi\)
0.403888 + 0.914809i \(0.367659\pi\)
\(420\) 2.18865 0.106795
\(421\) 20.0115 0.975301 0.487650 0.873039i \(-0.337854\pi\)
0.487650 + 0.873039i \(0.337854\pi\)
\(422\) −25.9408 −1.26278
\(423\) −5.59372 −0.271976
\(424\) −8.21368 −0.398892
\(425\) 1.22326 0.0593369
\(426\) −4.85183 −0.235072
\(427\) −0.955570 −0.0462433
\(428\) −16.4577 −0.795512
\(429\) 2.11919 0.102315
\(430\) 8.11721 0.391447
\(431\) 1.25411 0.0604085 0.0302042 0.999544i \(-0.490384\pi\)
0.0302042 + 0.999544i \(0.490384\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −18.6548 −0.896493 −0.448246 0.893910i \(-0.647951\pi\)
−0.448246 + 0.893910i \(0.647951\pi\)
\(434\) 6.80100 0.326458
\(435\) 15.8693 0.760873
\(436\) 6.53528 0.312983
\(437\) 56.6231 2.70865
\(438\) −9.48633 −0.453274
\(439\) 11.2330 0.536121 0.268061 0.963402i \(-0.413617\pi\)
0.268061 + 0.963402i \(0.413617\pi\)
\(440\) 2.29041 0.109191
\(441\) −6.08689 −0.289852
\(442\) −10.5387 −0.501275
\(443\) −39.3617 −1.87013 −0.935066 0.354475i \(-0.884660\pi\)
−0.935066 + 0.354475i \(0.884660\pi\)
\(444\) 10.7379 0.509600
\(445\) −14.4076 −0.682987
\(446\) 13.9319 0.659694
\(447\) 6.54169 0.309411
\(448\) −0.955570 −0.0451464
\(449\) 7.53196 0.355455 0.177728 0.984080i \(-0.443125\pi\)
0.177728 + 0.984080i \(0.443125\pi\)
\(450\) −0.245981 −0.0115956
\(451\) −7.66968 −0.361151
\(452\) −6.67079 −0.313768
\(453\) 23.2854 1.09404
\(454\) −26.5355 −1.24537
\(455\) −4.63815 −0.217440
\(456\) 7.95360 0.372461
\(457\) 3.25494 0.152259 0.0761297 0.997098i \(-0.475744\pi\)
0.0761297 + 0.997098i \(0.475744\pi\)
\(458\) 20.9876 0.980685
\(459\) −4.97299 −0.232119
\(460\) 16.3059 0.760265
\(461\) −10.6567 −0.496332 −0.248166 0.968718i \(-0.579828\pi\)
−0.248166 + 0.968718i \(0.579828\pi\)
\(462\) 0.955570 0.0444571
\(463\) −26.9484 −1.25240 −0.626200 0.779662i \(-0.715391\pi\)
−0.626200 + 0.779662i \(0.715391\pi\)
\(464\) −6.92856 −0.321651
\(465\) −16.3013 −0.755957
\(466\) −27.3573 −1.26730
\(467\) −36.6878 −1.69771 −0.848855 0.528626i \(-0.822708\pi\)
−0.848855 + 0.528626i \(0.822708\pi\)
\(468\) 2.11919 0.0979594
\(469\) −11.7591 −0.542985
\(470\) 12.8119 0.590970
\(471\) 19.0675 0.878583
\(472\) −4.62525 −0.212894
\(473\) 3.54400 0.162953
\(474\) 6.68822 0.307200
\(475\) 1.95643 0.0897673
\(476\) −4.75205 −0.217810
\(477\) 8.21368 0.376079
\(478\) −15.5679 −0.712060
\(479\) 37.7824 1.72632 0.863160 0.504930i \(-0.168482\pi\)
0.863160 + 0.504930i \(0.168482\pi\)
\(480\) 2.29041 0.104542
\(481\) −22.7557 −1.03757
\(482\) 19.3688 0.882226
\(483\) 6.80288 0.309542
\(484\) 1.00000 0.0454545
\(485\) −10.0129 −0.454662
\(486\) 1.00000 0.0453609
\(487\) −29.7214 −1.34681 −0.673403 0.739275i \(-0.735168\pi\)
−0.673403 + 0.739275i \(0.735168\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −14.3786 −0.650225
\(490\) 13.9415 0.629811
\(491\) 1.92302 0.0867846 0.0433923 0.999058i \(-0.486183\pi\)
0.0433923 + 0.999058i \(0.486183\pi\)
\(492\) −7.66968 −0.345776
\(493\) −34.4557 −1.55181
\(494\) −16.8552 −0.758349
\(495\) −2.29041 −0.102946
\(496\) 7.11721 0.319572
\(497\) 4.63627 0.207965
\(498\) −1.24401 −0.0557453
\(499\) 7.49173 0.335376 0.167688 0.985840i \(-0.446370\pi\)
0.167688 + 0.985840i \(0.446370\pi\)
\(500\) −10.8887 −0.486956
\(501\) 9.78237 0.437044
\(502\) 1.85183 0.0826514
\(503\) 20.4948 0.913820 0.456910 0.889513i \(-0.348956\pi\)
0.456910 + 0.889513i \(0.348956\pi\)
\(504\) 0.955570 0.0425645
\(505\) 40.9305 1.82138
\(506\) 7.11919 0.316486
\(507\) 8.50905 0.377900
\(508\) 9.31544 0.413306
\(509\) 13.9642 0.618952 0.309476 0.950907i \(-0.399846\pi\)
0.309476 + 0.950907i \(0.399846\pi\)
\(510\) 11.3902 0.504366
\(511\) 9.06485 0.401005
\(512\) −1.00000 −0.0441942
\(513\) −7.95360 −0.351160
\(514\) −29.4287 −1.29804
\(515\) 13.9685 0.615524
\(516\) 3.54400 0.156016
\(517\) 5.59372 0.246012
\(518\) −10.2609 −0.450836
\(519\) −9.17089 −0.402557
\(520\) −4.85381 −0.212854
\(521\) 24.1931 1.05992 0.529959 0.848023i \(-0.322207\pi\)
0.529959 + 0.848023i \(0.322207\pi\)
\(522\) 6.92856 0.303255
\(523\) −2.36594 −0.103455 −0.0517277 0.998661i \(-0.516473\pi\)
−0.0517277 + 0.998661i \(0.516473\pi\)
\(524\) 6.88611 0.300821
\(525\) 0.235052 0.0102585
\(526\) −30.8588 −1.34551
\(527\) 35.3939 1.54178
\(528\) 1.00000 0.0435194
\(529\) 27.6828 1.20360
\(530\) −18.8127 −0.817171
\(531\) 4.62525 0.200719
\(532\) −7.60022 −0.329511
\(533\) 16.2535 0.704017
\(534\) −6.29041 −0.272213
\(535\) −37.6949 −1.62969
\(536\) −12.3059 −0.531532
\(537\) −9.93222 −0.428607
\(538\) 1.87321 0.0807596
\(539\) 6.08689 0.262181
\(540\) −2.29041 −0.0985636
\(541\) 3.12328 0.134280 0.0671402 0.997744i \(-0.478613\pi\)
0.0671402 + 0.997744i \(0.478613\pi\)
\(542\) 29.1719 1.25304
\(543\) −6.05093 −0.259670
\(544\) −4.97299 −0.213215
\(545\) 14.9685 0.641179
\(546\) −2.02503 −0.0866634
\(547\) −20.0242 −0.856171 −0.428086 0.903738i \(-0.640812\pi\)
−0.428086 + 0.903738i \(0.640812\pi\)
\(548\) 12.8841 0.550383
\(549\) 1.00000 0.0426790
\(550\) 0.245981 0.0104887
\(551\) −55.1070 −2.34764
\(552\) 7.11919 0.303013
\(553\) −6.39106 −0.271776
\(554\) 15.3837 0.653591
\(555\) 24.5943 1.04397
\(556\) −0.407623 −0.0172871
\(557\) 29.0440 1.23064 0.615318 0.788279i \(-0.289028\pi\)
0.615318 + 0.788279i \(0.289028\pi\)
\(558\) −7.11721 −0.301296
\(559\) −7.51040 −0.317656
\(560\) −2.18865 −0.0924873
\(561\) 4.97299 0.209960
\(562\) −23.6753 −0.998683
\(563\) −33.0798 −1.39415 −0.697073 0.717000i \(-0.745515\pi\)
−0.697073 + 0.717000i \(0.745515\pi\)
\(564\) 5.59372 0.235538
\(565\) −15.2789 −0.642786
\(566\) −7.17969 −0.301785
\(567\) −0.955570 −0.0401302
\(568\) 4.85183 0.203578
\(569\) −38.4897 −1.61357 −0.806786 0.590844i \(-0.798795\pi\)
−0.806786 + 0.590844i \(0.798795\pi\)
\(570\) 18.2170 0.763026
\(571\) 14.9702 0.626482 0.313241 0.949674i \(-0.398585\pi\)
0.313241 + 0.949674i \(0.398585\pi\)
\(572\) −2.11919 −0.0886076
\(573\) −19.3685 −0.809130
\(574\) 7.32892 0.305903
\(575\) 1.75118 0.0730294
\(576\) 1.00000 0.0416667
\(577\) −26.9110 −1.12032 −0.560161 0.828384i \(-0.689261\pi\)
−0.560161 + 0.828384i \(0.689261\pi\)
\(578\) −7.73067 −0.321554
\(579\) 0.00563344 0.000234118 0
\(580\) −15.8693 −0.658935
\(581\) 1.18874 0.0493171
\(582\) −4.37166 −0.181211
\(583\) −8.21368 −0.340176
\(584\) 9.48633 0.392547
\(585\) 4.85381 0.200680
\(586\) −14.8090 −0.611756
\(587\) 8.62130 0.355839 0.177920 0.984045i \(-0.443063\pi\)
0.177920 + 0.984045i \(0.443063\pi\)
\(588\) 6.08689 0.251019
\(589\) 56.6074 2.33247
\(590\) −10.5937 −0.436137
\(591\) 2.81665 0.115861
\(592\) −10.7379 −0.441327
\(593\) 17.9932 0.738893 0.369446 0.929252i \(-0.379547\pi\)
0.369446 + 0.929252i \(0.379547\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −10.8841 −0.446206
\(596\) −6.54169 −0.267958
\(597\) 5.67941 0.232443
\(598\) −15.0869 −0.616949
\(599\) −7.62275 −0.311457 −0.155729 0.987800i \(-0.549773\pi\)
−0.155729 + 0.987800i \(0.549773\pi\)
\(600\) 0.245981 0.0100421
\(601\) 23.9940 0.978735 0.489368 0.872078i \(-0.337228\pi\)
0.489368 + 0.872078i \(0.337228\pi\)
\(602\) −3.38654 −0.138025
\(603\) 12.3059 0.501133
\(604\) −23.2854 −0.947467
\(605\) 2.29041 0.0931184
\(606\) 17.8704 0.725934
\(607\) 46.4708 1.88619 0.943096 0.332520i \(-0.107899\pi\)
0.943096 + 0.332520i \(0.107899\pi\)
\(608\) −7.95360 −0.322561
\(609\) −6.62073 −0.268286
\(610\) −2.29041 −0.0927360
\(611\) −11.8541 −0.479567
\(612\) 4.97299 0.201021
\(613\) 19.3828 0.782866 0.391433 0.920207i \(-0.371980\pi\)
0.391433 + 0.920207i \(0.371980\pi\)
\(614\) −18.6245 −0.751623
\(615\) −17.5667 −0.708358
\(616\) −0.955570 −0.0385010
\(617\) 30.1621 1.21428 0.607141 0.794594i \(-0.292316\pi\)
0.607141 + 0.794594i \(0.292316\pi\)
\(618\) 6.09868 0.245325
\(619\) −8.45291 −0.339751 −0.169876 0.985466i \(-0.554337\pi\)
−0.169876 + 0.985466i \(0.554337\pi\)
\(620\) 16.3013 0.654678
\(621\) −7.11919 −0.285683
\(622\) −4.09647 −0.164253
\(623\) 6.01093 0.240823
\(624\) −2.11919 −0.0848354
\(625\) −26.1694 −1.04678
\(626\) 19.5465 0.781237
\(627\) 7.95360 0.317636
\(628\) −19.0675 −0.760876
\(629\) −53.3997 −2.12919
\(630\) 2.18865 0.0871978
\(631\) 19.3634 0.770846 0.385423 0.922740i \(-0.374056\pi\)
0.385423 + 0.922740i \(0.374056\pi\)
\(632\) −6.68822 −0.266043
\(633\) −25.9408 −1.03106
\(634\) 7.28921 0.289492
\(635\) 21.3362 0.846701
\(636\) −8.21368 −0.325694
\(637\) −12.8992 −0.511087
\(638\) −6.92856 −0.274304
\(639\) −4.85183 −0.191936
\(640\) −2.29041 −0.0905364
\(641\) 10.1198 0.399706 0.199853 0.979826i \(-0.435953\pi\)
0.199853 + 0.979826i \(0.435953\pi\)
\(642\) −16.4577 −0.649533
\(643\) 20.7190 0.817076 0.408538 0.912741i \(-0.366039\pi\)
0.408538 + 0.912741i \(0.366039\pi\)
\(644\) −6.80288 −0.268071
\(645\) 8.11721 0.319615
\(646\) −39.5532 −1.55620
\(647\) −37.3438 −1.46814 −0.734069 0.679075i \(-0.762381\pi\)
−0.734069 + 0.679075i \(0.762381\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −4.62525 −0.181557
\(650\) −0.521279 −0.0204463
\(651\) 6.80100 0.266552
\(652\) 14.3786 0.563111
\(653\) 21.0253 0.822783 0.411391 0.911459i \(-0.365043\pi\)
0.411391 + 0.911459i \(0.365043\pi\)
\(654\) 6.53528 0.255550
\(655\) 15.7720 0.616264
\(656\) 7.66968 0.299451
\(657\) −9.48633 −0.370097
\(658\) −5.34520 −0.208377
\(659\) 22.4802 0.875703 0.437852 0.899047i \(-0.355740\pi\)
0.437852 + 0.899047i \(0.355740\pi\)
\(660\) 2.29041 0.0891541
\(661\) 23.9508 0.931580 0.465790 0.884895i \(-0.345770\pi\)
0.465790 + 0.884895i \(0.345770\pi\)
\(662\) −12.2209 −0.474981
\(663\) −10.5387 −0.409289
\(664\) 1.24401 0.0482768
\(665\) −17.4076 −0.675039
\(666\) 10.7379 0.416087
\(667\) −49.3257 −1.90990
\(668\) −9.78237 −0.378491
\(669\) 13.9319 0.538638
\(670\) −28.1855 −1.08890
\(671\) −1.00000 −0.0386046
\(672\) −0.955570 −0.0368619
\(673\) −0.0441412 −0.00170152 −0.000850760 1.00000i \(-0.500271\pi\)
−0.000850760 1.00000i \(0.500271\pi\)
\(674\) 15.3770 0.592298
\(675\) −0.245981 −0.00946781
\(676\) −8.50905 −0.327271
\(677\) −13.9598 −0.536517 −0.268258 0.963347i \(-0.586448\pi\)
−0.268258 + 0.963347i \(0.586448\pi\)
\(678\) −6.67079 −0.256190
\(679\) 4.17743 0.160315
\(680\) −11.3902 −0.436794
\(681\) −26.5355 −1.01684
\(682\) 7.11721 0.272532
\(683\) −34.4615 −1.31863 −0.659317 0.751865i \(-0.729154\pi\)
−0.659317 + 0.751865i \(0.729154\pi\)
\(684\) 7.95360 0.304113
\(685\) 29.5100 1.12752
\(686\) −12.5054 −0.477460
\(687\) 20.9876 0.800726
\(688\) −3.54400 −0.135114
\(689\) 17.4063 0.663128
\(690\) 16.3059 0.620754
\(691\) −30.3959 −1.15632 −0.578158 0.815925i \(-0.696228\pi\)
−0.578158 + 0.815925i \(0.696228\pi\)
\(692\) 9.17089 0.348625
\(693\) 0.955570 0.0362991
\(694\) −20.4399 −0.775889
\(695\) −0.933625 −0.0354144
\(696\) −6.92856 −0.262627
\(697\) 38.1413 1.44470
\(698\) −19.9050 −0.753414
\(699\) −27.3573 −1.03475
\(700\) −0.235052 −0.00888413
\(701\) 15.7658 0.595466 0.297733 0.954649i \(-0.403769\pi\)
0.297733 + 0.954649i \(0.403769\pi\)
\(702\) 2.11919 0.0799835
\(703\) −85.4053 −3.22112
\(704\) −1.00000 −0.0376889
\(705\) 12.8119 0.482525
\(706\) 26.1923 0.985760
\(707\) −17.0764 −0.642224
\(708\) −4.62525 −0.173828
\(709\) 30.8310 1.15788 0.578941 0.815369i \(-0.303466\pi\)
0.578941 + 0.815369i \(0.303466\pi\)
\(710\) 11.1127 0.417052
\(711\) 6.68822 0.250828
\(712\) 6.29041 0.235743
\(713\) 50.6688 1.89756
\(714\) −4.75205 −0.177841
\(715\) −4.85381 −0.181522
\(716\) 9.93222 0.371185
\(717\) −15.5679 −0.581395
\(718\) −29.1045 −1.08617
\(719\) −25.2408 −0.941324 −0.470662 0.882314i \(-0.655985\pi\)
−0.470662 + 0.882314i \(0.655985\pi\)
\(720\) 2.29041 0.0853586
\(721\) −5.82771 −0.217035
\(722\) −44.2597 −1.64718
\(723\) 19.3688 0.720334
\(724\) 6.05093 0.224881
\(725\) −1.70429 −0.0632959
\(726\) 1.00000 0.0371135
\(727\) −17.9477 −0.665644 −0.332822 0.942990i \(-0.608001\pi\)
−0.332822 + 0.942990i \(0.608001\pi\)
\(728\) 2.02503 0.0750527
\(729\) 1.00000 0.0370370
\(730\) 21.7276 0.804174
\(731\) −17.6243 −0.651858
\(732\) −1.00000 −0.0369611
\(733\) −41.0507 −1.51624 −0.758122 0.652113i \(-0.773883\pi\)
−0.758122 + 0.652113i \(0.773883\pi\)
\(734\) −8.26229 −0.304967
\(735\) 13.9415 0.514239
\(736\) −7.11919 −0.262417
\(737\) −12.3059 −0.453292
\(738\) −7.66968 −0.282325
\(739\) −14.1410 −0.520187 −0.260093 0.965583i \(-0.583753\pi\)
−0.260093 + 0.965583i \(0.583753\pi\)
\(740\) −24.5943 −0.904104
\(741\) −16.8552 −0.619190
\(742\) 7.84875 0.288137
\(743\) 11.3843 0.417649 0.208824 0.977953i \(-0.433036\pi\)
0.208824 + 0.977953i \(0.433036\pi\)
\(744\) 7.11721 0.260930
\(745\) −14.9831 −0.548940
\(746\) 24.0005 0.878720
\(747\) −1.24401 −0.0455158
\(748\) −4.97299 −0.181831
\(749\) 15.7265 0.574633
\(750\) −10.8887 −0.397598
\(751\) 2.99596 0.109324 0.0546621 0.998505i \(-0.482592\pi\)
0.0546621 + 0.998505i \(0.482592\pi\)
\(752\) −5.59372 −0.203982
\(753\) 1.85183 0.0674846
\(754\) 14.6829 0.534720
\(755\) −53.3330 −1.94099
\(756\) 0.955570 0.0347538
\(757\) −33.5931 −1.22096 −0.610481 0.792031i \(-0.709024\pi\)
−0.610481 + 0.792031i \(0.709024\pi\)
\(758\) 12.3500 0.448570
\(759\) 7.11919 0.258410
\(760\) −18.2170 −0.660800
\(761\) −4.80683 −0.174247 −0.0871237 0.996197i \(-0.527768\pi\)
−0.0871237 + 0.996197i \(0.527768\pi\)
\(762\) 9.31544 0.337463
\(763\) −6.24492 −0.226081
\(764\) 19.3685 0.700727
\(765\) 11.3902 0.411814
\(766\) 30.4079 1.09868
\(767\) 9.80177 0.353921
\(768\) −1.00000 −0.0360844
\(769\) −34.5793 −1.24696 −0.623481 0.781838i \(-0.714282\pi\)
−0.623481 + 0.781838i \(0.714282\pi\)
\(770\) −2.18865 −0.0788734
\(771\) −29.4287 −1.05985
\(772\) −0.00563344 −0.000202752 0
\(773\) 12.5207 0.450340 0.225170 0.974320i \(-0.427706\pi\)
0.225170 + 0.974320i \(0.427706\pi\)
\(774\) 3.54400 0.127386
\(775\) 1.75070 0.0628869
\(776\) 4.37166 0.156934
\(777\) −10.2609 −0.368106
\(778\) 24.1891 0.867222
\(779\) 61.0015 2.18561
\(780\) −4.85381 −0.173794
\(781\) 4.85183 0.173612
\(782\) −35.4037 −1.26603
\(783\) 6.92856 0.247607
\(784\) −6.08689 −0.217389
\(785\) −43.6724 −1.55873
\(786\) 6.88611 0.245619
\(787\) 15.9069 0.567021 0.283511 0.958969i \(-0.408501\pi\)
0.283511 + 0.958969i \(0.408501\pi\)
\(788\) −2.81665 −0.100339
\(789\) −30.8588 −1.09860
\(790\) −15.3188 −0.545017
\(791\) 6.37441 0.226648
\(792\) 1.00000 0.0355335
\(793\) 2.11919 0.0752545
\(794\) −21.8667 −0.776021
\(795\) −18.8127 −0.667218
\(796\) −5.67941 −0.201301
\(797\) −54.7388 −1.93895 −0.969473 0.245198i \(-0.921147\pi\)
−0.969473 + 0.245198i \(0.921147\pi\)
\(798\) −7.60022 −0.269045
\(799\) −27.8176 −0.984114
\(800\) −0.245981 −0.00869674
\(801\) −6.29041 −0.222261
\(802\) −11.0868 −0.391488
\(803\) 9.48633 0.334765
\(804\) −12.3059 −0.433994
\(805\) −15.5814 −0.549172
\(806\) −15.0827 −0.531266
\(807\) 1.87321 0.0659400
\(808\) −17.8704 −0.628677
\(809\) −35.5247 −1.24898 −0.624492 0.781031i \(-0.714694\pi\)
−0.624492 + 0.781031i \(0.714694\pi\)
\(810\) −2.29041 −0.0804768
\(811\) 11.4903 0.403478 0.201739 0.979439i \(-0.435341\pi\)
0.201739 + 0.979439i \(0.435341\pi\)
\(812\) 6.62073 0.232342
\(813\) 29.1719 1.02310
\(814\) −10.7379 −0.376365
\(815\) 32.9330 1.15359
\(816\) −4.97299 −0.174090
\(817\) −28.1875 −0.986157
\(818\) −6.66232 −0.232943
\(819\) −2.02503 −0.0707603
\(820\) 17.5667 0.613456
\(821\) −18.9077 −0.659884 −0.329942 0.944001i \(-0.607029\pi\)
−0.329942 + 0.944001i \(0.607029\pi\)
\(822\) 12.8841 0.449386
\(823\) −20.2629 −0.706320 −0.353160 0.935563i \(-0.614893\pi\)
−0.353160 + 0.935563i \(0.614893\pi\)
\(824\) −6.09868 −0.212457
\(825\) 0.245981 0.00856395
\(826\) 4.41975 0.153783
\(827\) 30.9597 1.07657 0.538287 0.842761i \(-0.319071\pi\)
0.538287 + 0.842761i \(0.319071\pi\)
\(828\) 7.11919 0.247409
\(829\) 3.63686 0.126313 0.0631566 0.998004i \(-0.479883\pi\)
0.0631566 + 0.998004i \(0.479883\pi\)
\(830\) 2.84929 0.0989002
\(831\) 15.3837 0.533655
\(832\) 2.11919 0.0734696
\(833\) −30.2700 −1.04879
\(834\) −0.407623 −0.0141148
\(835\) −22.4056 −0.775379
\(836\) −7.95360 −0.275081
\(837\) −7.11721 −0.246007
\(838\) −16.5348 −0.571184
\(839\) −19.3922 −0.669492 −0.334746 0.942308i \(-0.608651\pi\)
−0.334746 + 0.942308i \(0.608651\pi\)
\(840\) −2.18865 −0.0755155
\(841\) 19.0050 0.655345
\(842\) −20.0115 −0.689642
\(843\) −23.6753 −0.815421
\(844\) 25.9408 0.892921
\(845\) −19.4892 −0.670449
\(846\) 5.59372 0.192316
\(847\) −0.955570 −0.0328338
\(848\) 8.21368 0.282059
\(849\) −7.17969 −0.246406
\(850\) −1.22326 −0.0419575
\(851\) −76.4454 −2.62052
\(852\) 4.85183 0.166221
\(853\) 17.6487 0.604282 0.302141 0.953263i \(-0.402299\pi\)
0.302141 + 0.953263i \(0.402299\pi\)
\(854\) 0.955570 0.0326989
\(855\) 18.2170 0.623008
\(856\) 16.4577 0.562512
\(857\) −36.9544 −1.26234 −0.631169 0.775645i \(-0.717425\pi\)
−0.631169 + 0.775645i \(0.717425\pi\)
\(858\) −2.11919 −0.0723478
\(859\) 34.9450 1.19231 0.596154 0.802870i \(-0.296695\pi\)
0.596154 + 0.802870i \(0.296695\pi\)
\(860\) −8.11721 −0.276795
\(861\) 7.32892 0.249769
\(862\) −1.25411 −0.0427152
\(863\) 12.2622 0.417410 0.208705 0.977979i \(-0.433075\pi\)
0.208705 + 0.977979i \(0.433075\pi\)
\(864\) 1.00000 0.0340207
\(865\) 21.0051 0.714195
\(866\) 18.6548 0.633916
\(867\) −7.73067 −0.262547
\(868\) −6.80100 −0.230841
\(869\) −6.68822 −0.226882
\(870\) −15.8693 −0.538018
\(871\) 26.0784 0.883633
\(872\) −6.53528 −0.221312
\(873\) −4.37166 −0.147958
\(874\) −56.6231 −1.91531
\(875\) 10.4049 0.351749
\(876\) 9.48633 0.320513
\(877\) 11.7653 0.397285 0.198642 0.980072i \(-0.436347\pi\)
0.198642 + 0.980072i \(0.436347\pi\)
\(878\) −11.2330 −0.379095
\(879\) −14.8090 −0.499497
\(880\) −2.29041 −0.0772097
\(881\) −9.14296 −0.308034 −0.154017 0.988068i \(-0.549221\pi\)
−0.154017 + 0.988068i \(0.549221\pi\)
\(882\) 6.08689 0.204956
\(883\) −34.9399 −1.17582 −0.587911 0.808926i \(-0.700049\pi\)
−0.587911 + 0.808926i \(0.700049\pi\)
\(884\) 10.5387 0.354455
\(885\) −10.5937 −0.356104
\(886\) 39.3617 1.32238
\(887\) −42.2945 −1.42011 −0.710054 0.704147i \(-0.751330\pi\)
−0.710054 + 0.704147i \(0.751330\pi\)
\(888\) −10.7379 −0.360342
\(889\) −8.90156 −0.298549
\(890\) 14.4076 0.482945
\(891\) −1.00000 −0.0335013
\(892\) −13.9319 −0.466474
\(893\) −44.4902 −1.48881
\(894\) −6.54169 −0.218787
\(895\) 22.7489 0.760411
\(896\) 0.955570 0.0319234
\(897\) −15.0869 −0.503736
\(898\) −7.53196 −0.251345
\(899\) −49.3121 −1.64465
\(900\) 0.245981 0.00819936
\(901\) 40.8466 1.36080
\(902\) 7.66968 0.255372
\(903\) −3.38654 −0.112697
\(904\) 6.67079 0.221867
\(905\) 13.8591 0.460692
\(906\) −23.2854 −0.773604
\(907\) 25.1262 0.834301 0.417150 0.908837i \(-0.363029\pi\)
0.417150 + 0.908837i \(0.363029\pi\)
\(908\) 26.5355 0.880612
\(909\) 17.8704 0.592723
\(910\) 4.63815 0.153753
\(911\) 38.5060 1.27576 0.637881 0.770135i \(-0.279811\pi\)
0.637881 + 0.770135i \(0.279811\pi\)
\(912\) −7.95360 −0.263370
\(913\) 1.24401 0.0411706
\(914\) −3.25494 −0.107664
\(915\) −2.29041 −0.0757186
\(916\) −20.9876 −0.693449
\(917\) −6.58016 −0.217296
\(918\) 4.97299 0.164133
\(919\) 45.5184 1.50151 0.750757 0.660578i \(-0.229689\pi\)
0.750757 + 0.660578i \(0.229689\pi\)
\(920\) −16.3059 −0.537588
\(921\) −18.6245 −0.613697
\(922\) 10.6567 0.350959
\(923\) −10.2819 −0.338434
\(924\) −0.955570 −0.0314360
\(925\) −2.64133 −0.0868463
\(926\) 26.9484 0.885581
\(927\) 6.09868 0.200307
\(928\) 6.92856 0.227441
\(929\) 32.5812 1.06895 0.534477 0.845183i \(-0.320509\pi\)
0.534477 + 0.845183i \(0.320509\pi\)
\(930\) 16.3013 0.534542
\(931\) −48.4126 −1.58666
\(932\) 27.3573 0.896117
\(933\) −4.09647 −0.134112
\(934\) 36.6878 1.20046
\(935\) −11.3902 −0.372499
\(936\) −2.11919 −0.0692678
\(937\) 20.5672 0.671901 0.335951 0.941880i \(-0.390942\pi\)
0.335951 + 0.941880i \(0.390942\pi\)
\(938\) 11.7591 0.383949
\(939\) 19.5465 0.637877
\(940\) −12.8119 −0.417879
\(941\) 6.21893 0.202731 0.101366 0.994849i \(-0.467679\pi\)
0.101366 + 0.994849i \(0.467679\pi\)
\(942\) −19.0675 −0.621252
\(943\) 54.6019 1.77808
\(944\) 4.62525 0.150539
\(945\) 2.18865 0.0711967
\(946\) −3.54400 −0.115225
\(947\) −31.9775 −1.03913 −0.519565 0.854431i \(-0.673906\pi\)
−0.519565 + 0.854431i \(0.673906\pi\)
\(948\) −6.68822 −0.217223
\(949\) −20.1033 −0.652581
\(950\) −1.95643 −0.0634750
\(951\) 7.28921 0.236369
\(952\) 4.75205 0.154015
\(953\) 6.81968 0.220911 0.110456 0.993881i \(-0.464769\pi\)
0.110456 + 0.993881i \(0.464769\pi\)
\(954\) −8.21368 −0.265928
\(955\) 44.3618 1.43551
\(956\) 15.5679 0.503502
\(957\) −6.92856 −0.223969
\(958\) −37.7824 −1.22069
\(959\) −12.3117 −0.397565
\(960\) −2.29041 −0.0739227
\(961\) 19.6547 0.634023
\(962\) 22.7557 0.733673
\(963\) −16.4577 −0.530342
\(964\) −19.3688 −0.623828
\(965\) −0.0129029 −0.000415359 0
\(966\) −6.80288 −0.218879
\(967\) −32.2662 −1.03761 −0.518806 0.854892i \(-0.673623\pi\)
−0.518806 + 0.854892i \(0.673623\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −39.5532 −1.27063
\(970\) 10.0129 0.321495
\(971\) −14.3665 −0.461043 −0.230522 0.973067i \(-0.574043\pi\)
−0.230522 + 0.973067i \(0.574043\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0.389513 0.0124872
\(974\) 29.7214 0.952336
\(975\) −0.521279 −0.0166943
\(976\) 1.00000 0.0320092
\(977\) −13.8643 −0.443557 −0.221778 0.975097i \(-0.571186\pi\)
−0.221778 + 0.975097i \(0.571186\pi\)
\(978\) 14.3786 0.459778
\(979\) 6.29041 0.201042
\(980\) −13.9415 −0.445344
\(981\) 6.53528 0.208655
\(982\) −1.92302 −0.0613660
\(983\) 22.0561 0.703480 0.351740 0.936098i \(-0.385590\pi\)
0.351740 + 0.936098i \(0.385590\pi\)
\(984\) 7.66968 0.244500
\(985\) −6.45128 −0.205555
\(986\) 34.4557 1.09729
\(987\) −5.34520 −0.170139
\(988\) 16.8552 0.536234
\(989\) −25.2304 −0.802280
\(990\) 2.29041 0.0727940
\(991\) 36.7000 1.16581 0.582906 0.812539i \(-0.301915\pi\)
0.582906 + 0.812539i \(0.301915\pi\)
\(992\) −7.11721 −0.225972
\(993\) −12.2209 −0.387820
\(994\) −4.63627 −0.147053
\(995\) −13.0082 −0.412387
\(996\) 1.24401 0.0394179
\(997\) −22.7669 −0.721036 −0.360518 0.932752i \(-0.617400\pi\)
−0.360518 + 0.932752i \(0.617400\pi\)
\(998\) −7.49173 −0.237146
\(999\) 10.7379 0.339733
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 4026.2.a.q.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.q.1.4 4 1.1 even 1 trivial