Properties

Label 8026.2.a.c.1.4
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $0$
Dimension $86$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(0\)
Dimension: \(86\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.19050 q^{3} +1.00000 q^{4} -0.434778 q^{5} +3.19050 q^{6} +2.23469 q^{7} -1.00000 q^{8} +7.17932 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.19050 q^{3} +1.00000 q^{4} -0.434778 q^{5} +3.19050 q^{6} +2.23469 q^{7} -1.00000 q^{8} +7.17932 q^{9} +0.434778 q^{10} -0.690985 q^{11} -3.19050 q^{12} +4.85100 q^{13} -2.23469 q^{14} +1.38716 q^{15} +1.00000 q^{16} -1.67758 q^{17} -7.17932 q^{18} -6.17918 q^{19} -0.434778 q^{20} -7.12978 q^{21} +0.690985 q^{22} -0.601471 q^{23} +3.19050 q^{24} -4.81097 q^{25} -4.85100 q^{26} -13.3341 q^{27} +2.23469 q^{28} +0.669083 q^{29} -1.38716 q^{30} +4.81141 q^{31} -1.00000 q^{32} +2.20459 q^{33} +1.67758 q^{34} -0.971594 q^{35} +7.17932 q^{36} -9.68724 q^{37} +6.17918 q^{38} -15.4771 q^{39} +0.434778 q^{40} -0.204017 q^{41} +7.12978 q^{42} +5.09994 q^{43} -0.690985 q^{44} -3.12141 q^{45} +0.601471 q^{46} +4.45461 q^{47} -3.19050 q^{48} -2.00617 q^{49} +4.81097 q^{50} +5.35232 q^{51} +4.85100 q^{52} +11.4209 q^{53} +13.3341 q^{54} +0.300425 q^{55} -2.23469 q^{56} +19.7147 q^{57} -0.669083 q^{58} +13.4068 q^{59} +1.38716 q^{60} -2.80565 q^{61} -4.81141 q^{62} +16.0435 q^{63} +1.00000 q^{64} -2.10911 q^{65} -2.20459 q^{66} +6.27731 q^{67} -1.67758 q^{68} +1.91900 q^{69} +0.971594 q^{70} -5.15436 q^{71} -7.17932 q^{72} -0.0754243 q^{73} +9.68724 q^{74} +15.3494 q^{75} -6.17918 q^{76} -1.54413 q^{77} +15.4771 q^{78} +10.5721 q^{79} -0.434778 q^{80} +21.0047 q^{81} +0.204017 q^{82} +8.43670 q^{83} -7.12978 q^{84} +0.729375 q^{85} -5.09994 q^{86} -2.13471 q^{87} +0.690985 q^{88} -1.88869 q^{89} +3.12141 q^{90} +10.8405 q^{91} -0.601471 q^{92} -15.3508 q^{93} -4.45461 q^{94} +2.68657 q^{95} +3.19050 q^{96} -15.3399 q^{97} +2.00617 q^{98} -4.96080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −3.19050 −1.84204 −0.921019 0.389517i \(-0.872642\pi\)
−0.921019 + 0.389517i \(0.872642\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.434778 −0.194439 −0.0972194 0.995263i \(-0.530995\pi\)
−0.0972194 + 0.995263i \(0.530995\pi\)
\(6\) 3.19050 1.30252
\(7\) 2.23469 0.844632 0.422316 0.906449i \(-0.361217\pi\)
0.422316 + 0.906449i \(0.361217\pi\)
\(8\) −1.00000 −0.353553
\(9\) 7.17932 2.39311
\(10\) 0.434778 0.137489
\(11\) −0.690985 −0.208340 −0.104170 0.994560i \(-0.533219\pi\)
−0.104170 + 0.994560i \(0.533219\pi\)
\(12\) −3.19050 −0.921019
\(13\) 4.85100 1.34543 0.672713 0.739904i \(-0.265129\pi\)
0.672713 + 0.739904i \(0.265129\pi\)
\(14\) −2.23469 −0.597245
\(15\) 1.38716 0.358164
\(16\) 1.00000 0.250000
\(17\) −1.67758 −0.406872 −0.203436 0.979088i \(-0.565211\pi\)
−0.203436 + 0.979088i \(0.565211\pi\)
\(18\) −7.17932 −1.69218
\(19\) −6.17918 −1.41760 −0.708800 0.705409i \(-0.750763\pi\)
−0.708800 + 0.705409i \(0.750763\pi\)
\(20\) −0.434778 −0.0972194
\(21\) −7.12978 −1.55585
\(22\) 0.690985 0.147318
\(23\) −0.601471 −0.125415 −0.0627077 0.998032i \(-0.519974\pi\)
−0.0627077 + 0.998032i \(0.519974\pi\)
\(24\) 3.19050 0.651259
\(25\) −4.81097 −0.962194
\(26\) −4.85100 −0.951359
\(27\) −13.3341 −2.56616
\(28\) 2.23469 0.422316
\(29\) 0.669083 0.124246 0.0621228 0.998069i \(-0.480213\pi\)
0.0621228 + 0.998069i \(0.480213\pi\)
\(30\) −1.38716 −0.253260
\(31\) 4.81141 0.864155 0.432077 0.901836i \(-0.357781\pi\)
0.432077 + 0.901836i \(0.357781\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.20459 0.383770
\(34\) 1.67758 0.287702
\(35\) −0.971594 −0.164229
\(36\) 7.17932 1.19655
\(37\) −9.68724 −1.59257 −0.796286 0.604920i \(-0.793205\pi\)
−0.796286 + 0.604920i \(0.793205\pi\)
\(38\) 6.17918 1.00240
\(39\) −15.4771 −2.47833
\(40\) 0.434778 0.0687445
\(41\) −0.204017 −0.0318621 −0.0159310 0.999873i \(-0.505071\pi\)
−0.0159310 + 0.999873i \(0.505071\pi\)
\(42\) 7.12978 1.10015
\(43\) 5.09994 0.777733 0.388867 0.921294i \(-0.372867\pi\)
0.388867 + 0.921294i \(0.372867\pi\)
\(44\) −0.690985 −0.104170
\(45\) −3.12141 −0.465313
\(46\) 0.601471 0.0886820
\(47\) 4.45461 0.649772 0.324886 0.945753i \(-0.394674\pi\)
0.324886 + 0.945753i \(0.394674\pi\)
\(48\) −3.19050 −0.460510
\(49\) −2.00617 −0.286596
\(50\) 4.81097 0.680374
\(51\) 5.35232 0.749475
\(52\) 4.85100 0.672713
\(53\) 11.4209 1.56878 0.784388 0.620271i \(-0.212977\pi\)
0.784388 + 0.620271i \(0.212977\pi\)
\(54\) 13.3341 1.81455
\(55\) 0.300425 0.0405093
\(56\) −2.23469 −0.298623
\(57\) 19.7147 2.61128
\(58\) −0.669083 −0.0878549
\(59\) 13.4068 1.74541 0.872707 0.488245i \(-0.162363\pi\)
0.872707 + 0.488245i \(0.162363\pi\)
\(60\) 1.38716 0.179082
\(61\) −2.80565 −0.359227 −0.179613 0.983737i \(-0.557485\pi\)
−0.179613 + 0.983737i \(0.557485\pi\)
\(62\) −4.81141 −0.611050
\(63\) 16.0435 2.02130
\(64\) 1.00000 0.125000
\(65\) −2.10911 −0.261603
\(66\) −2.20459 −0.271366
\(67\) 6.27731 0.766895 0.383448 0.923563i \(-0.374737\pi\)
0.383448 + 0.923563i \(0.374737\pi\)
\(68\) −1.67758 −0.203436
\(69\) 1.91900 0.231020
\(70\) 0.971594 0.116128
\(71\) −5.15436 −0.611710 −0.305855 0.952078i \(-0.598942\pi\)
−0.305855 + 0.952078i \(0.598942\pi\)
\(72\) −7.17932 −0.846091
\(73\) −0.0754243 −0.00882775 −0.00441388 0.999990i \(-0.501405\pi\)
−0.00441388 + 0.999990i \(0.501405\pi\)
\(74\) 9.68724 1.12612
\(75\) 15.3494 1.77240
\(76\) −6.17918 −0.708800
\(77\) −1.54413 −0.175971
\(78\) 15.4771 1.75244
\(79\) 10.5721 1.18946 0.594728 0.803927i \(-0.297260\pi\)
0.594728 + 0.803927i \(0.297260\pi\)
\(80\) −0.434778 −0.0486097
\(81\) 21.0047 2.33385
\(82\) 0.204017 0.0225299
\(83\) 8.43670 0.926048 0.463024 0.886346i \(-0.346764\pi\)
0.463024 + 0.886346i \(0.346764\pi\)
\(84\) −7.12978 −0.777923
\(85\) 0.729375 0.0791118
\(86\) −5.09994 −0.549941
\(87\) −2.13471 −0.228865
\(88\) 0.690985 0.0736592
\(89\) −1.88869 −0.200200 −0.100100 0.994977i \(-0.531916\pi\)
−0.100100 + 0.994977i \(0.531916\pi\)
\(90\) 3.12141 0.329026
\(91\) 10.8405 1.13639
\(92\) −0.601471 −0.0627077
\(93\) −15.3508 −1.59181
\(94\) −4.45461 −0.459458
\(95\) 2.68657 0.275637
\(96\) 3.19050 0.325630
\(97\) −15.3399 −1.55753 −0.778766 0.627315i \(-0.784154\pi\)
−0.778766 + 0.627315i \(0.784154\pi\)
\(98\) 2.00617 0.202654
\(99\) −4.96080 −0.498579
\(100\) −4.81097 −0.481097
\(101\) −2.51366 −0.250118 −0.125059 0.992149i \(-0.539912\pi\)
−0.125059 + 0.992149i \(0.539912\pi\)
\(102\) −5.35232 −0.529959
\(103\) −18.1843 −1.79176 −0.895878 0.444299i \(-0.853453\pi\)
−0.895878 + 0.444299i \(0.853453\pi\)
\(104\) −4.85100 −0.475680
\(105\) 3.09987 0.302517
\(106\) −11.4209 −1.10929
\(107\) 3.01826 0.291786 0.145893 0.989300i \(-0.453395\pi\)
0.145893 + 0.989300i \(0.453395\pi\)
\(108\) −13.3341 −1.28308
\(109\) −2.62418 −0.251351 −0.125675 0.992071i \(-0.540110\pi\)
−0.125675 + 0.992071i \(0.540110\pi\)
\(110\) −0.300425 −0.0286444
\(111\) 30.9072 2.93358
\(112\) 2.23469 0.211158
\(113\) −3.89903 −0.366790 −0.183395 0.983039i \(-0.558709\pi\)
−0.183395 + 0.983039i \(0.558709\pi\)
\(114\) −19.7147 −1.84645
\(115\) 0.261507 0.0243856
\(116\) 0.669083 0.0621228
\(117\) 34.8269 3.21975
\(118\) −13.4068 −1.23419
\(119\) −3.74886 −0.343657
\(120\) −1.38716 −0.126630
\(121\) −10.5225 −0.956595
\(122\) 2.80565 0.254012
\(123\) 0.650917 0.0586912
\(124\) 4.81141 0.432077
\(125\) 4.26560 0.381527
\(126\) −16.0435 −1.42927
\(127\) −4.44903 −0.394788 −0.197394 0.980324i \(-0.563248\pi\)
−0.197394 + 0.980324i \(0.563248\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −16.2714 −1.43262
\(130\) 2.10911 0.184981
\(131\) 12.1312 1.05991 0.529954 0.848026i \(-0.322209\pi\)
0.529954 + 0.848026i \(0.322209\pi\)
\(132\) 2.20459 0.191885
\(133\) −13.8085 −1.19735
\(134\) −6.27731 −0.542277
\(135\) 5.79740 0.498960
\(136\) 1.67758 0.143851
\(137\) −17.6190 −1.50529 −0.752644 0.658427i \(-0.771222\pi\)
−0.752644 + 0.658427i \(0.771222\pi\)
\(138\) −1.91900 −0.163356
\(139\) 6.22339 0.527861 0.263931 0.964542i \(-0.414981\pi\)
0.263931 + 0.964542i \(0.414981\pi\)
\(140\) −0.971594 −0.0821147
\(141\) −14.2125 −1.19690
\(142\) 5.15436 0.432544
\(143\) −3.35197 −0.280306
\(144\) 7.17932 0.598277
\(145\) −0.290903 −0.0241582
\(146\) 0.0754243 0.00624216
\(147\) 6.40071 0.527922
\(148\) −9.68724 −0.796286
\(149\) 0.801116 0.0656300 0.0328150 0.999461i \(-0.489553\pi\)
0.0328150 + 0.999461i \(0.489553\pi\)
\(150\) −15.3494 −1.25327
\(151\) 7.68648 0.625517 0.312759 0.949833i \(-0.398747\pi\)
0.312759 + 0.949833i \(0.398747\pi\)
\(152\) 6.17918 0.501198
\(153\) −12.0439 −0.973689
\(154\) 1.54413 0.124430
\(155\) −2.09190 −0.168025
\(156\) −15.4771 −1.23916
\(157\) −13.7351 −1.09618 −0.548090 0.836419i \(-0.684645\pi\)
−0.548090 + 0.836419i \(0.684645\pi\)
\(158\) −10.5721 −0.841073
\(159\) −36.4383 −2.88975
\(160\) 0.434778 0.0343723
\(161\) −1.34410 −0.105930
\(162\) −21.0047 −1.65028
\(163\) 8.72923 0.683726 0.341863 0.939750i \(-0.388942\pi\)
0.341863 + 0.939750i \(0.388942\pi\)
\(164\) −0.204017 −0.0159310
\(165\) −0.958509 −0.0746198
\(166\) −8.43670 −0.654815
\(167\) 21.8834 1.69339 0.846693 0.532082i \(-0.178590\pi\)
0.846693 + 0.532082i \(0.178590\pi\)
\(168\) 7.12978 0.550074
\(169\) 10.5322 0.810169
\(170\) −0.729375 −0.0559405
\(171\) −44.3623 −3.39247
\(172\) 5.09994 0.388867
\(173\) 21.5724 1.64012 0.820060 0.572277i \(-0.193940\pi\)
0.820060 + 0.572277i \(0.193940\pi\)
\(174\) 2.13471 0.161832
\(175\) −10.7510 −0.812700
\(176\) −0.690985 −0.0520849
\(177\) −42.7744 −3.21512
\(178\) 1.88869 0.141563
\(179\) 20.1156 1.50351 0.751755 0.659442i \(-0.229207\pi\)
0.751755 + 0.659442i \(0.229207\pi\)
\(180\) −3.12141 −0.232656
\(181\) −6.25494 −0.464926 −0.232463 0.972605i \(-0.574678\pi\)
−0.232463 + 0.972605i \(0.574678\pi\)
\(182\) −10.8405 −0.803549
\(183\) 8.95144 0.661709
\(184\) 0.601471 0.0443410
\(185\) 4.21180 0.309658
\(186\) 15.3508 1.12558
\(187\) 1.15918 0.0847677
\(188\) 4.45461 0.324886
\(189\) −29.7976 −2.16746
\(190\) −2.68657 −0.194905
\(191\) 5.72799 0.414463 0.207232 0.978292i \(-0.433555\pi\)
0.207232 + 0.978292i \(0.433555\pi\)
\(192\) −3.19050 −0.230255
\(193\) 14.5513 1.04742 0.523712 0.851895i \(-0.324547\pi\)
0.523712 + 0.851895i \(0.324547\pi\)
\(194\) 15.3399 1.10134
\(195\) 6.72913 0.481883
\(196\) −2.00617 −0.143298
\(197\) 4.38440 0.312376 0.156188 0.987727i \(-0.450079\pi\)
0.156188 + 0.987727i \(0.450079\pi\)
\(198\) 4.96080 0.352549
\(199\) 2.04300 0.144825 0.0724123 0.997375i \(-0.476930\pi\)
0.0724123 + 0.997375i \(0.476930\pi\)
\(200\) 4.81097 0.340187
\(201\) −20.0278 −1.41265
\(202\) 2.51366 0.176860
\(203\) 1.49519 0.104942
\(204\) 5.35232 0.374737
\(205\) 0.0887021 0.00619523
\(206\) 18.1843 1.26696
\(207\) −4.31815 −0.300132
\(208\) 4.85100 0.336356
\(209\) 4.26972 0.295343
\(210\) −3.09987 −0.213912
\(211\) −2.47265 −0.170224 −0.0851120 0.996371i \(-0.527125\pi\)
−0.0851120 + 0.996371i \(0.527125\pi\)
\(212\) 11.4209 0.784388
\(213\) 16.4450 1.12679
\(214\) −3.01826 −0.206324
\(215\) −2.21734 −0.151222
\(216\) 13.3341 0.907273
\(217\) 10.7520 0.729893
\(218\) 2.62418 0.177732
\(219\) 0.240642 0.0162611
\(220\) 0.300425 0.0202547
\(221\) −8.13793 −0.547416
\(222\) −30.9072 −2.07435
\(223\) −19.9821 −1.33810 −0.669050 0.743218i \(-0.733299\pi\)
−0.669050 + 0.743218i \(0.733299\pi\)
\(224\) −2.23469 −0.149311
\(225\) −34.5395 −2.30263
\(226\) 3.89903 0.259359
\(227\) −1.66765 −0.110686 −0.0553428 0.998467i \(-0.517625\pi\)
−0.0553428 + 0.998467i \(0.517625\pi\)
\(228\) 19.7147 1.30564
\(229\) −18.4150 −1.21690 −0.608449 0.793593i \(-0.708208\pi\)
−0.608449 + 0.793593i \(0.708208\pi\)
\(230\) −0.261507 −0.0172432
\(231\) 4.92657 0.324144
\(232\) −0.669083 −0.0439275
\(233\) −14.5883 −0.955714 −0.477857 0.878438i \(-0.658586\pi\)
−0.477857 + 0.878438i \(0.658586\pi\)
\(234\) −34.8269 −2.27670
\(235\) −1.93677 −0.126341
\(236\) 13.4068 0.872707
\(237\) −33.7304 −2.19103
\(238\) 3.74886 0.243003
\(239\) −21.6769 −1.40216 −0.701080 0.713083i \(-0.747298\pi\)
−0.701080 + 0.713083i \(0.747298\pi\)
\(240\) 1.38716 0.0895410
\(241\) 14.0509 0.905096 0.452548 0.891740i \(-0.350515\pi\)
0.452548 + 0.891740i \(0.350515\pi\)
\(242\) 10.5225 0.676414
\(243\) −27.0131 −1.73289
\(244\) −2.80565 −0.179613
\(245\) 0.872241 0.0557255
\(246\) −0.650917 −0.0415009
\(247\) −29.9752 −1.90728
\(248\) −4.81141 −0.305525
\(249\) −26.9173 −1.70582
\(250\) −4.26560 −0.269780
\(251\) 19.0646 1.20335 0.601673 0.798743i \(-0.294501\pi\)
0.601673 + 0.798743i \(0.294501\pi\)
\(252\) 16.0435 1.01065
\(253\) 0.415607 0.0261290
\(254\) 4.44903 0.279157
\(255\) −2.32707 −0.145727
\(256\) 1.00000 0.0625000
\(257\) 4.62253 0.288346 0.144173 0.989553i \(-0.453948\pi\)
0.144173 + 0.989553i \(0.453948\pi\)
\(258\) 16.2714 1.01301
\(259\) −21.6479 −1.34514
\(260\) −2.10911 −0.130801
\(261\) 4.80356 0.297333
\(262\) −12.1312 −0.749468
\(263\) −21.6171 −1.33297 −0.666484 0.745519i \(-0.732201\pi\)
−0.666484 + 0.745519i \(0.732201\pi\)
\(264\) −2.20459 −0.135683
\(265\) −4.96554 −0.305031
\(266\) 13.8085 0.846655
\(267\) 6.02586 0.368777
\(268\) 6.27731 0.383448
\(269\) −15.4263 −0.940559 −0.470280 0.882518i \(-0.655847\pi\)
−0.470280 + 0.882518i \(0.655847\pi\)
\(270\) −5.79740 −0.352818
\(271\) 12.2999 0.747167 0.373584 0.927597i \(-0.378129\pi\)
0.373584 + 0.927597i \(0.378129\pi\)
\(272\) −1.67758 −0.101718
\(273\) −34.5866 −2.09327
\(274\) 17.6190 1.06440
\(275\) 3.32431 0.200463
\(276\) 1.91900 0.115510
\(277\) 23.9710 1.44028 0.720138 0.693831i \(-0.244079\pi\)
0.720138 + 0.693831i \(0.244079\pi\)
\(278\) −6.22339 −0.373254
\(279\) 34.5427 2.06801
\(280\) 0.971594 0.0580638
\(281\) 20.8408 1.24326 0.621629 0.783312i \(-0.286471\pi\)
0.621629 + 0.783312i \(0.286471\pi\)
\(282\) 14.2125 0.846339
\(283\) −2.23312 −0.132745 −0.0663726 0.997795i \(-0.521143\pi\)
−0.0663726 + 0.997795i \(0.521143\pi\)
\(284\) −5.15436 −0.305855
\(285\) −8.57153 −0.507733
\(286\) 3.35197 0.198206
\(287\) −0.455914 −0.0269117
\(288\) −7.17932 −0.423045
\(289\) −14.1857 −0.834455
\(290\) 0.290903 0.0170824
\(291\) 48.9420 2.86903
\(292\) −0.0754243 −0.00441388
\(293\) −4.57319 −0.267168 −0.133584 0.991037i \(-0.542649\pi\)
−0.133584 + 0.991037i \(0.542649\pi\)
\(294\) −6.40071 −0.373297
\(295\) −5.82898 −0.339376
\(296\) 9.68724 0.563059
\(297\) 9.21369 0.534632
\(298\) −0.801116 −0.0464074
\(299\) −2.91773 −0.168737
\(300\) 15.3494 0.886199
\(301\) 11.3968 0.656899
\(302\) −7.68648 −0.442307
\(303\) 8.01984 0.460728
\(304\) −6.17918 −0.354400
\(305\) 1.21984 0.0698476
\(306\) 12.0439 0.688502
\(307\) 5.08758 0.290363 0.145182 0.989405i \(-0.453623\pi\)
0.145182 + 0.989405i \(0.453623\pi\)
\(308\) −1.54413 −0.0879853
\(309\) 58.0172 3.30049
\(310\) 2.09190 0.118812
\(311\) 18.3559 1.04087 0.520433 0.853902i \(-0.325770\pi\)
0.520433 + 0.853902i \(0.325770\pi\)
\(312\) 15.4771 0.876220
\(313\) −11.1858 −0.632260 −0.316130 0.948716i \(-0.602384\pi\)
−0.316130 + 0.948716i \(0.602384\pi\)
\(314\) 13.7351 0.775117
\(315\) −6.97538 −0.393018
\(316\) 10.5721 0.594728
\(317\) −33.1048 −1.85935 −0.929675 0.368380i \(-0.879912\pi\)
−0.929675 + 0.368380i \(0.879912\pi\)
\(318\) 36.4383 2.04336
\(319\) −0.462326 −0.0258853
\(320\) −0.434778 −0.0243049
\(321\) −9.62976 −0.537481
\(322\) 1.34410 0.0749037
\(323\) 10.3661 0.576783
\(324\) 21.0047 1.16693
\(325\) −23.3380 −1.29456
\(326\) −8.72923 −0.483467
\(327\) 8.37246 0.462998
\(328\) 0.204017 0.0112649
\(329\) 9.95466 0.548818
\(330\) 0.958509 0.0527642
\(331\) −25.5319 −1.40336 −0.701679 0.712493i \(-0.747566\pi\)
−0.701679 + 0.712493i \(0.747566\pi\)
\(332\) 8.43670 0.463024
\(333\) −69.5478 −3.81119
\(334\) −21.8834 −1.19740
\(335\) −2.72924 −0.149114
\(336\) −7.12978 −0.388961
\(337\) 6.83133 0.372126 0.186063 0.982538i \(-0.440427\pi\)
0.186063 + 0.982538i \(0.440427\pi\)
\(338\) −10.5322 −0.572876
\(339\) 12.4399 0.675641
\(340\) 0.729375 0.0395559
\(341\) −3.32461 −0.180038
\(342\) 44.3623 2.39884
\(343\) −20.1260 −1.08670
\(344\) −5.09994 −0.274970
\(345\) −0.834338 −0.0449192
\(346\) −21.5724 −1.15974
\(347\) −22.3332 −1.19891 −0.599455 0.800408i \(-0.704616\pi\)
−0.599455 + 0.800408i \(0.704616\pi\)
\(348\) −2.13471 −0.114433
\(349\) 2.52858 0.135352 0.0676758 0.997707i \(-0.478442\pi\)
0.0676758 + 0.997707i \(0.478442\pi\)
\(350\) 10.7510 0.574665
\(351\) −64.6839 −3.45257
\(352\) 0.690985 0.0368296
\(353\) 26.1718 1.39298 0.696491 0.717565i \(-0.254744\pi\)
0.696491 + 0.717565i \(0.254744\pi\)
\(354\) 42.7744 2.27343
\(355\) 2.24100 0.118940
\(356\) −1.88869 −0.100100
\(357\) 11.9608 0.633030
\(358\) −20.1156 −1.06314
\(359\) 32.3652 1.70817 0.854084 0.520135i \(-0.174118\pi\)
0.854084 + 0.520135i \(0.174118\pi\)
\(360\) 3.12141 0.164513
\(361\) 19.1823 1.00959
\(362\) 6.25494 0.328752
\(363\) 33.5722 1.76208
\(364\) 10.8405 0.568195
\(365\) 0.0327929 0.00171646
\(366\) −8.95144 −0.467899
\(367\) −22.1576 −1.15662 −0.578310 0.815817i \(-0.696288\pi\)
−0.578310 + 0.815817i \(0.696288\pi\)
\(368\) −0.601471 −0.0313538
\(369\) −1.46470 −0.0762493
\(370\) −4.21180 −0.218961
\(371\) 25.5220 1.32504
\(372\) −15.3508 −0.795903
\(373\) 20.6328 1.06833 0.534164 0.845381i \(-0.320627\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(374\) −1.15918 −0.0599398
\(375\) −13.6094 −0.702787
\(376\) −4.45461 −0.229729
\(377\) 3.24572 0.167163
\(378\) 29.7976 1.53262
\(379\) −1.71081 −0.0878783 −0.0439392 0.999034i \(-0.513991\pi\)
−0.0439392 + 0.999034i \(0.513991\pi\)
\(380\) 2.68657 0.137818
\(381\) 14.1947 0.727215
\(382\) −5.72799 −0.293070
\(383\) −14.4585 −0.738794 −0.369397 0.929272i \(-0.620436\pi\)
−0.369397 + 0.929272i \(0.620436\pi\)
\(384\) 3.19050 0.162815
\(385\) 0.671357 0.0342155
\(386\) −14.5513 −0.740641
\(387\) 36.6141 1.86120
\(388\) −15.3399 −0.778766
\(389\) 36.0677 1.82870 0.914351 0.404922i \(-0.132701\pi\)
0.914351 + 0.404922i \(0.132701\pi\)
\(390\) −6.72913 −0.340743
\(391\) 1.00901 0.0510280
\(392\) 2.00617 0.101327
\(393\) −38.7046 −1.95239
\(394\) −4.38440 −0.220883
\(395\) −4.59653 −0.231277
\(396\) −4.96080 −0.249290
\(397\) 8.48096 0.425647 0.212824 0.977091i \(-0.431734\pi\)
0.212824 + 0.977091i \(0.431734\pi\)
\(398\) −2.04300 −0.102406
\(399\) 44.0562 2.20557
\(400\) −4.81097 −0.240548
\(401\) 21.6468 1.08099 0.540494 0.841348i \(-0.318237\pi\)
0.540494 + 0.841348i \(0.318237\pi\)
\(402\) 20.0278 0.998895
\(403\) 23.3402 1.16266
\(404\) −2.51366 −0.125059
\(405\) −9.13238 −0.453792
\(406\) −1.49519 −0.0742051
\(407\) 6.69373 0.331796
\(408\) −5.35232 −0.264979
\(409\) 13.6209 0.673510 0.336755 0.941592i \(-0.390671\pi\)
0.336755 + 0.941592i \(0.390671\pi\)
\(410\) −0.0887021 −0.00438069
\(411\) 56.2134 2.77280
\(412\) −18.1843 −0.895878
\(413\) 29.9599 1.47423
\(414\) 4.31815 0.212226
\(415\) −3.66810 −0.180060
\(416\) −4.85100 −0.237840
\(417\) −19.8558 −0.972341
\(418\) −4.26972 −0.208839
\(419\) −18.6525 −0.911233 −0.455616 0.890176i \(-0.650581\pi\)
−0.455616 + 0.890176i \(0.650581\pi\)
\(420\) 3.09987 0.151258
\(421\) 15.6150 0.761028 0.380514 0.924775i \(-0.375747\pi\)
0.380514 + 0.924775i \(0.375747\pi\)
\(422\) 2.47265 0.120367
\(423\) 31.9811 1.55497
\(424\) −11.4209 −0.554646
\(425\) 8.07077 0.391490
\(426\) −16.4450 −0.796763
\(427\) −6.26975 −0.303414
\(428\) 3.01826 0.145893
\(429\) 10.6945 0.516334
\(430\) 2.21734 0.106930
\(431\) 9.49407 0.457313 0.228657 0.973507i \(-0.426567\pi\)
0.228657 + 0.973507i \(0.426567\pi\)
\(432\) −13.3341 −0.641539
\(433\) −23.8845 −1.14782 −0.573908 0.818920i \(-0.694573\pi\)
−0.573908 + 0.818920i \(0.694573\pi\)
\(434\) −10.7520 −0.516112
\(435\) 0.928127 0.0445003
\(436\) −2.62418 −0.125675
\(437\) 3.71660 0.177789
\(438\) −0.240642 −0.0114983
\(439\) 25.0931 1.19763 0.598814 0.800888i \(-0.295639\pi\)
0.598814 + 0.800888i \(0.295639\pi\)
\(440\) −0.300425 −0.0143222
\(441\) −14.4030 −0.685856
\(442\) 8.13793 0.387082
\(443\) 9.65000 0.458485 0.229243 0.973369i \(-0.426375\pi\)
0.229243 + 0.973369i \(0.426375\pi\)
\(444\) 30.9072 1.46679
\(445\) 0.821160 0.0389267
\(446\) 19.9821 0.946179
\(447\) −2.55596 −0.120893
\(448\) 2.23469 0.105579
\(449\) −33.6196 −1.58661 −0.793303 0.608827i \(-0.791641\pi\)
−0.793303 + 0.608827i \(0.791641\pi\)
\(450\) 34.5395 1.62821
\(451\) 0.140973 0.00663814
\(452\) −3.89903 −0.183395
\(453\) −24.5238 −1.15223
\(454\) 1.66765 0.0782665
\(455\) −4.71320 −0.220958
\(456\) −19.7147 −0.923225
\(457\) 27.1743 1.27116 0.635581 0.772034i \(-0.280761\pi\)
0.635581 + 0.772034i \(0.280761\pi\)
\(458\) 18.4150 0.860477
\(459\) 22.3691 1.04410
\(460\) 0.261507 0.0121928
\(461\) 37.6724 1.75458 0.877290 0.479961i \(-0.159349\pi\)
0.877290 + 0.479961i \(0.159349\pi\)
\(462\) −4.92657 −0.229205
\(463\) −22.4542 −1.04353 −0.521767 0.853088i \(-0.674727\pi\)
−0.521767 + 0.853088i \(0.674727\pi\)
\(464\) 0.669083 0.0310614
\(465\) 6.67421 0.309509
\(466\) 14.5883 0.675792
\(467\) 13.9658 0.646260 0.323130 0.946355i \(-0.395265\pi\)
0.323130 + 0.946355i \(0.395265\pi\)
\(468\) 34.8269 1.60987
\(469\) 14.0278 0.647744
\(470\) 1.93677 0.0893365
\(471\) 43.8219 2.01921
\(472\) −13.4068 −0.617097
\(473\) −3.52398 −0.162033
\(474\) 33.7304 1.54929
\(475\) 29.7278 1.36401
\(476\) −3.74886 −0.171829
\(477\) 81.9940 3.75425
\(478\) 21.6769 0.991476
\(479\) −19.6348 −0.897137 −0.448569 0.893748i \(-0.648066\pi\)
−0.448569 + 0.893748i \(0.648066\pi\)
\(480\) −1.38716 −0.0633150
\(481\) −46.9928 −2.14269
\(482\) −14.0509 −0.640000
\(483\) 4.28835 0.195127
\(484\) −10.5225 −0.478297
\(485\) 6.66946 0.302845
\(486\) 27.0131 1.22534
\(487\) −28.1435 −1.27530 −0.637652 0.770324i \(-0.720094\pi\)
−0.637652 + 0.770324i \(0.720094\pi\)
\(488\) 2.80565 0.127006
\(489\) −27.8506 −1.25945
\(490\) −0.872241 −0.0394039
\(491\) −0.558892 −0.0252224 −0.0126112 0.999920i \(-0.504014\pi\)
−0.0126112 + 0.999920i \(0.504014\pi\)
\(492\) 0.650917 0.0293456
\(493\) −1.12244 −0.0505521
\(494\) 29.9752 1.34865
\(495\) 2.15685 0.0969432
\(496\) 4.81141 0.216039
\(497\) −11.5184 −0.516670
\(498\) 26.9173 1.20619
\(499\) 6.35830 0.284637 0.142318 0.989821i \(-0.454544\pi\)
0.142318 + 0.989821i \(0.454544\pi\)
\(500\) 4.26560 0.190763
\(501\) −69.8190 −3.11928
\(502\) −19.0646 −0.850894
\(503\) 34.8764 1.55506 0.777531 0.628844i \(-0.216472\pi\)
0.777531 + 0.628844i \(0.216472\pi\)
\(504\) −16.0435 −0.714636
\(505\) 1.09288 0.0486327
\(506\) −0.415607 −0.0184760
\(507\) −33.6030 −1.49236
\(508\) −4.44903 −0.197394
\(509\) −16.7908 −0.744239 −0.372119 0.928185i \(-0.621369\pi\)
−0.372119 + 0.928185i \(0.621369\pi\)
\(510\) 2.32707 0.103045
\(511\) −0.168550 −0.00745620
\(512\) −1.00000 −0.0441942
\(513\) 82.3940 3.63779
\(514\) −4.62253 −0.203891
\(515\) 7.90616 0.348387
\(516\) −16.2714 −0.716308
\(517\) −3.07807 −0.135373
\(518\) 21.6479 0.951156
\(519\) −68.8269 −3.02117
\(520\) 2.10911 0.0924906
\(521\) 3.88674 0.170281 0.0851406 0.996369i \(-0.472866\pi\)
0.0851406 + 0.996369i \(0.472866\pi\)
\(522\) −4.80356 −0.210246
\(523\) −12.5600 −0.549211 −0.274606 0.961557i \(-0.588547\pi\)
−0.274606 + 0.961557i \(0.588547\pi\)
\(524\) 12.1312 0.529954
\(525\) 34.3011 1.49702
\(526\) 21.6171 0.942551
\(527\) −8.07152 −0.351601
\(528\) 2.20459 0.0959425
\(529\) −22.6382 −0.984271
\(530\) 4.96554 0.215689
\(531\) 96.2515 4.17696
\(532\) −13.8085 −0.598676
\(533\) −0.989685 −0.0428680
\(534\) −6.02586 −0.260764
\(535\) −1.31227 −0.0567345
\(536\) −6.27731 −0.271138
\(537\) −64.1789 −2.76952
\(538\) 15.4263 0.665076
\(539\) 1.38624 0.0597094
\(540\) 5.79740 0.249480
\(541\) 39.9823 1.71897 0.859486 0.511160i \(-0.170784\pi\)
0.859486 + 0.511160i \(0.170784\pi\)
\(542\) −12.2999 −0.528327
\(543\) 19.9564 0.856412
\(544\) 1.67758 0.0719255
\(545\) 1.14094 0.0488724
\(546\) 34.5866 1.48017
\(547\) −16.1721 −0.691470 −0.345735 0.938332i \(-0.612370\pi\)
−0.345735 + 0.938332i \(0.612370\pi\)
\(548\) −17.6190 −0.752644
\(549\) −20.1427 −0.859668
\(550\) −3.32431 −0.141749
\(551\) −4.13438 −0.176131
\(552\) −1.91900 −0.0816779
\(553\) 23.6254 1.00465
\(554\) −23.9710 −1.01843
\(555\) −13.4378 −0.570402
\(556\) 6.22339 0.263931
\(557\) 8.29052 0.351281 0.175640 0.984454i \(-0.443800\pi\)
0.175640 + 0.984454i \(0.443800\pi\)
\(558\) −34.5427 −1.46231
\(559\) 24.7398 1.04638
\(560\) −0.971594 −0.0410573
\(561\) −3.69837 −0.156145
\(562\) −20.8408 −0.879115
\(563\) 15.0492 0.634250 0.317125 0.948384i \(-0.397282\pi\)
0.317125 + 0.948384i \(0.397282\pi\)
\(564\) −14.2125 −0.598452
\(565\) 1.69521 0.0713181
\(566\) 2.23312 0.0938651
\(567\) 46.9389 1.97125
\(568\) 5.15436 0.216272
\(569\) −19.2835 −0.808407 −0.404203 0.914669i \(-0.632451\pi\)
−0.404203 + 0.914669i \(0.632451\pi\)
\(570\) 8.57153 0.359022
\(571\) 9.82929 0.411343 0.205672 0.978621i \(-0.434062\pi\)
0.205672 + 0.978621i \(0.434062\pi\)
\(572\) −3.35197 −0.140153
\(573\) −18.2752 −0.763457
\(574\) 0.455914 0.0190295
\(575\) 2.89366 0.120674
\(576\) 7.17932 0.299138
\(577\) 35.0862 1.46066 0.730329 0.683096i \(-0.239367\pi\)
0.730329 + 0.683096i \(0.239367\pi\)
\(578\) 14.1857 0.590049
\(579\) −46.4259 −1.92940
\(580\) −0.290903 −0.0120791
\(581\) 18.8534 0.782170
\(582\) −48.9420 −2.02871
\(583\) −7.89164 −0.326838
\(584\) 0.0754243 0.00312108
\(585\) −15.1420 −0.626044
\(586\) 4.57319 0.188917
\(587\) −9.47018 −0.390876 −0.195438 0.980716i \(-0.562613\pi\)
−0.195438 + 0.980716i \(0.562613\pi\)
\(588\) 6.40071 0.263961
\(589\) −29.7306 −1.22503
\(590\) 5.82898 0.239975
\(591\) −13.9885 −0.575408
\(592\) −9.68724 −0.398143
\(593\) 7.68455 0.315567 0.157783 0.987474i \(-0.449565\pi\)
0.157783 + 0.987474i \(0.449565\pi\)
\(594\) −9.21369 −0.378042
\(595\) 1.62992 0.0668204
\(596\) 0.801116 0.0328150
\(597\) −6.51821 −0.266772
\(598\) 2.91773 0.119315
\(599\) 42.6494 1.74261 0.871303 0.490746i \(-0.163276\pi\)
0.871303 + 0.490746i \(0.163276\pi\)
\(600\) −15.3494 −0.626637
\(601\) −9.36300 −0.381925 −0.190962 0.981597i \(-0.561161\pi\)
−0.190962 + 0.981597i \(0.561161\pi\)
\(602\) −11.3968 −0.464498
\(603\) 45.0668 1.83526
\(604\) 7.68648 0.312759
\(605\) 4.57497 0.185999
\(606\) −8.01984 −0.325784
\(607\) −15.5118 −0.629603 −0.314802 0.949158i \(-0.601938\pi\)
−0.314802 + 0.949158i \(0.601938\pi\)
\(608\) 6.17918 0.250599
\(609\) −4.77041 −0.193307
\(610\) −1.21984 −0.0493897
\(611\) 21.6093 0.874219
\(612\) −12.0439 −0.486844
\(613\) 36.6250 1.47927 0.739634 0.673009i \(-0.234999\pi\)
0.739634 + 0.673009i \(0.234999\pi\)
\(614\) −5.08758 −0.205318
\(615\) −0.283005 −0.0114118
\(616\) 1.54413 0.0622150
\(617\) −31.1175 −1.25274 −0.626372 0.779524i \(-0.715461\pi\)
−0.626372 + 0.779524i \(0.715461\pi\)
\(618\) −58.0172 −2.33380
\(619\) 21.2455 0.853929 0.426965 0.904268i \(-0.359583\pi\)
0.426965 + 0.904268i \(0.359583\pi\)
\(620\) −2.09190 −0.0840126
\(621\) 8.02009 0.321835
\(622\) −18.3559 −0.736004
\(623\) −4.22062 −0.169096
\(624\) −15.4771 −0.619581
\(625\) 22.2002 0.888010
\(626\) 11.1858 0.447075
\(627\) −13.6226 −0.544033
\(628\) −13.7351 −0.548090
\(629\) 16.2511 0.647973
\(630\) 6.97538 0.277906
\(631\) −22.7666 −0.906324 −0.453162 0.891428i \(-0.649704\pi\)
−0.453162 + 0.891428i \(0.649704\pi\)
\(632\) −10.5721 −0.420536
\(633\) 7.88899 0.313559
\(634\) 33.1048 1.31476
\(635\) 1.93434 0.0767621
\(636\) −36.4383 −1.44487
\(637\) −9.73195 −0.385594
\(638\) 0.462326 0.0183037
\(639\) −37.0048 −1.46389
\(640\) 0.434778 0.0171861
\(641\) −14.4369 −0.570222 −0.285111 0.958495i \(-0.592030\pi\)
−0.285111 + 0.958495i \(0.592030\pi\)
\(642\) 9.62976 0.380056
\(643\) 5.96496 0.235235 0.117617 0.993059i \(-0.462474\pi\)
0.117617 + 0.993059i \(0.462474\pi\)
\(644\) −1.34410 −0.0529649
\(645\) 7.07445 0.278556
\(646\) −10.3661 −0.407847
\(647\) 25.6332 1.00775 0.503873 0.863778i \(-0.331908\pi\)
0.503873 + 0.863778i \(0.331908\pi\)
\(648\) −21.0047 −0.825142
\(649\) −9.26388 −0.363639
\(650\) 23.3380 0.915392
\(651\) −34.3043 −1.34449
\(652\) 8.72923 0.341863
\(653\) −9.64933 −0.377607 −0.188804 0.982015i \(-0.560461\pi\)
−0.188804 + 0.982015i \(0.560461\pi\)
\(654\) −8.37246 −0.327389
\(655\) −5.27438 −0.206087
\(656\) −0.204017 −0.00796552
\(657\) −0.541495 −0.0211257
\(658\) −9.95466 −0.388073
\(659\) −1.15673 −0.0450596 −0.0225298 0.999746i \(-0.507172\pi\)
−0.0225298 + 0.999746i \(0.507172\pi\)
\(660\) −0.958509 −0.0373099
\(661\) 20.4660 0.796037 0.398018 0.917377i \(-0.369698\pi\)
0.398018 + 0.917377i \(0.369698\pi\)
\(662\) 25.5319 0.992324
\(663\) 25.9641 1.00836
\(664\) −8.43670 −0.327408
\(665\) 6.00365 0.232812
\(666\) 69.5478 2.69492
\(667\) −0.402434 −0.0155823
\(668\) 21.8834 0.846693
\(669\) 63.7530 2.46483
\(670\) 2.72924 0.105440
\(671\) 1.93866 0.0748412
\(672\) 7.12978 0.275037
\(673\) −35.2819 −1.36002 −0.680010 0.733203i \(-0.738024\pi\)
−0.680010 + 0.733203i \(0.738024\pi\)
\(674\) −6.83133 −0.263133
\(675\) 64.1501 2.46914
\(676\) 10.5322 0.405084
\(677\) 3.26115 0.125336 0.0626681 0.998034i \(-0.480039\pi\)
0.0626681 + 0.998034i \(0.480039\pi\)
\(678\) −12.4399 −0.477750
\(679\) −34.2799 −1.31554
\(680\) −0.729375 −0.0279702
\(681\) 5.32063 0.203887
\(682\) 3.32461 0.127306
\(683\) −43.0908 −1.64882 −0.824412 0.565990i \(-0.808494\pi\)
−0.824412 + 0.565990i \(0.808494\pi\)
\(684\) −44.3623 −1.69624
\(685\) 7.66034 0.292687
\(686\) 20.1260 0.768413
\(687\) 58.7532 2.24157
\(688\) 5.09994 0.194433
\(689\) 55.4026 2.11067
\(690\) 0.834338 0.0317627
\(691\) −11.8968 −0.452575 −0.226288 0.974061i \(-0.572659\pi\)
−0.226288 + 0.974061i \(0.572659\pi\)
\(692\) 21.5724 0.820060
\(693\) −11.0858 −0.421116
\(694\) 22.3332 0.847758
\(695\) −2.70580 −0.102637
\(696\) 2.13471 0.0809161
\(697\) 0.342254 0.0129638
\(698\) −2.52858 −0.0957080
\(699\) 46.5442 1.76046
\(700\) −10.7510 −0.406350
\(701\) 17.1232 0.646733 0.323366 0.946274i \(-0.395185\pi\)
0.323366 + 0.946274i \(0.395185\pi\)
\(702\) 64.6839 2.44134
\(703\) 59.8592 2.25763
\(704\) −0.690985 −0.0260425
\(705\) 6.17927 0.232725
\(706\) −26.1718 −0.984987
\(707\) −5.61724 −0.211258
\(708\) −42.7744 −1.60756
\(709\) 19.9521 0.749315 0.374658 0.927163i \(-0.377760\pi\)
0.374658 + 0.927163i \(0.377760\pi\)
\(710\) −2.24100 −0.0841034
\(711\) 75.9006 2.84650
\(712\) 1.88869 0.0707815
\(713\) −2.89392 −0.108378
\(714\) −11.9608 −0.447620
\(715\) 1.45736 0.0545023
\(716\) 20.1156 0.751755
\(717\) 69.1601 2.58283
\(718\) −32.3652 −1.20786
\(719\) 27.2122 1.01485 0.507423 0.861697i \(-0.330598\pi\)
0.507423 + 0.861697i \(0.330598\pi\)
\(720\) −3.12141 −0.116328
\(721\) −40.6363 −1.51338
\(722\) −19.1823 −0.713890
\(723\) −44.8294 −1.66722
\(724\) −6.25494 −0.232463
\(725\) −3.21894 −0.119548
\(726\) −33.5722 −1.24598
\(727\) 40.3850 1.49780 0.748898 0.662685i \(-0.230583\pi\)
0.748898 + 0.662685i \(0.230583\pi\)
\(728\) −10.8405 −0.401774
\(729\) 23.1714 0.858199
\(730\) −0.0327929 −0.00121372
\(731\) −8.55554 −0.316438
\(732\) 8.95144 0.330855
\(733\) −0.722953 −0.0267029 −0.0133514 0.999911i \(-0.504250\pi\)
−0.0133514 + 0.999911i \(0.504250\pi\)
\(734\) 22.1576 0.817854
\(735\) −2.78289 −0.102648
\(736\) 0.601471 0.0221705
\(737\) −4.33752 −0.159775
\(738\) 1.46470 0.0539164
\(739\) 46.4468 1.70857 0.854287 0.519802i \(-0.173994\pi\)
0.854287 + 0.519802i \(0.173994\pi\)
\(740\) 4.21180 0.154829
\(741\) 95.6360 3.51328
\(742\) −25.5220 −0.936944
\(743\) 20.9873 0.769948 0.384974 0.922927i \(-0.374210\pi\)
0.384974 + 0.922927i \(0.374210\pi\)
\(744\) 15.3508 0.562789
\(745\) −0.348308 −0.0127610
\(746\) −20.6328 −0.755422
\(747\) 60.5698 2.21613
\(748\) 1.15918 0.0423838
\(749\) 6.74486 0.246452
\(750\) 13.6094 0.496945
\(751\) −27.5006 −1.00351 −0.501756 0.865009i \(-0.667313\pi\)
−0.501756 + 0.865009i \(0.667313\pi\)
\(752\) 4.45461 0.162443
\(753\) −60.8256 −2.21661
\(754\) −3.24572 −0.118202
\(755\) −3.34192 −0.121625
\(756\) −29.7976 −1.08373
\(757\) 42.3996 1.54104 0.770520 0.637416i \(-0.219997\pi\)
0.770520 + 0.637416i \(0.219997\pi\)
\(758\) 1.71081 0.0621393
\(759\) −1.32600 −0.0481306
\(760\) −2.68657 −0.0974523
\(761\) −52.8117 −1.91442 −0.957212 0.289387i \(-0.906549\pi\)
−0.957212 + 0.289387i \(0.906549\pi\)
\(762\) −14.1947 −0.514218
\(763\) −5.86422 −0.212299
\(764\) 5.72799 0.207232
\(765\) 5.23641 0.189323
\(766\) 14.4585 0.522406
\(767\) 65.0363 2.34832
\(768\) −3.19050 −0.115127
\(769\) 27.0390 0.975051 0.487526 0.873109i \(-0.337900\pi\)
0.487526 + 0.873109i \(0.337900\pi\)
\(770\) −0.671357 −0.0241940
\(771\) −14.7482 −0.531144
\(772\) 14.5513 0.523712
\(773\) −15.3813 −0.553228 −0.276614 0.960981i \(-0.589212\pi\)
−0.276614 + 0.960981i \(0.589212\pi\)
\(774\) −36.6141 −1.31607
\(775\) −23.1475 −0.831484
\(776\) 15.3399 0.550671
\(777\) 69.0679 2.47780
\(778\) −36.0677 −1.29309
\(779\) 1.26066 0.0451677
\(780\) 6.72913 0.240941
\(781\) 3.56158 0.127443
\(782\) −1.00901 −0.0360823
\(783\) −8.92165 −0.318834
\(784\) −2.00617 −0.0716491
\(785\) 5.97173 0.213140
\(786\) 38.7046 1.38055
\(787\) 5.19527 0.185191 0.0925957 0.995704i \(-0.470484\pi\)
0.0925957 + 0.995704i \(0.470484\pi\)
\(788\) 4.38440 0.156188
\(789\) 68.9695 2.45538
\(790\) 4.59653 0.163537
\(791\) −8.71310 −0.309802
\(792\) 4.96080 0.176274
\(793\) −13.6102 −0.483313
\(794\) −8.48096 −0.300978
\(795\) 15.8426 0.561879
\(796\) 2.04300 0.0724123
\(797\) −39.6371 −1.40402 −0.702009 0.712168i \(-0.747713\pi\)
−0.702009 + 0.712168i \(0.747713\pi\)
\(798\) −44.0562 −1.55957
\(799\) −7.47296 −0.264374
\(800\) 4.81097 0.170093
\(801\) −13.5595 −0.479100
\(802\) −21.6468 −0.764375
\(803\) 0.0521171 0.00183917
\(804\) −20.0278 −0.706325
\(805\) 0.584385 0.0205969
\(806\) −23.3402 −0.822122
\(807\) 49.2177 1.73255
\(808\) 2.51366 0.0884302
\(809\) 30.6616 1.07800 0.539002 0.842304i \(-0.318801\pi\)
0.539002 + 0.842304i \(0.318801\pi\)
\(810\) 9.13238 0.320879
\(811\) 28.7049 1.00797 0.503983 0.863714i \(-0.331867\pi\)
0.503983 + 0.863714i \(0.331867\pi\)
\(812\) 1.49519 0.0524709
\(813\) −39.2430 −1.37631
\(814\) −6.69373 −0.234615
\(815\) −3.79528 −0.132943
\(816\) 5.35232 0.187369
\(817\) −31.5134 −1.10252
\(818\) −13.6209 −0.476243
\(819\) 77.8272 2.71950
\(820\) 0.0887021 0.00309761
\(821\) −23.3443 −0.814722 −0.407361 0.913267i \(-0.633551\pi\)
−0.407361 + 0.913267i \(0.633551\pi\)
\(822\) −56.2134 −1.96067
\(823\) −11.5343 −0.402060 −0.201030 0.979585i \(-0.564429\pi\)
−0.201030 + 0.979585i \(0.564429\pi\)
\(824\) 18.1843 0.633482
\(825\) −10.6062 −0.369261
\(826\) −29.9599 −1.04244
\(827\) −23.5308 −0.818245 −0.409123 0.912479i \(-0.634165\pi\)
−0.409123 + 0.912479i \(0.634165\pi\)
\(828\) −4.31815 −0.150066
\(829\) 48.3032 1.67764 0.838820 0.544409i \(-0.183246\pi\)
0.838820 + 0.544409i \(0.183246\pi\)
\(830\) 3.66810 0.127322
\(831\) −76.4795 −2.65304
\(832\) 4.85100 0.168178
\(833\) 3.36551 0.116608
\(834\) 19.8558 0.687549
\(835\) −9.51442 −0.329260
\(836\) 4.26972 0.147671
\(837\) −64.1560 −2.21756
\(838\) 18.6525 0.644339
\(839\) 41.5932 1.43596 0.717978 0.696066i \(-0.245068\pi\)
0.717978 + 0.696066i \(0.245068\pi\)
\(840\) −3.09987 −0.106956
\(841\) −28.5523 −0.984563
\(842\) −15.6150 −0.538128
\(843\) −66.4926 −2.29013
\(844\) −2.47265 −0.0851120
\(845\) −4.57917 −0.157528
\(846\) −31.9811 −1.09953
\(847\) −23.5146 −0.807971
\(848\) 11.4209 0.392194
\(849\) 7.12478 0.244522
\(850\) −8.07077 −0.276825
\(851\) 5.82659 0.199733
\(852\) 16.4450 0.563396
\(853\) 7.87204 0.269534 0.134767 0.990877i \(-0.456971\pi\)
0.134767 + 0.990877i \(0.456971\pi\)
\(854\) 6.26975 0.214546
\(855\) 19.2878 0.659628
\(856\) −3.01826 −0.103162
\(857\) 48.9451 1.67193 0.835966 0.548781i \(-0.184908\pi\)
0.835966 + 0.548781i \(0.184908\pi\)
\(858\) −10.6945 −0.365103
\(859\) −1.78872 −0.0610302 −0.0305151 0.999534i \(-0.509715\pi\)
−0.0305151 + 0.999534i \(0.509715\pi\)
\(860\) −2.21734 −0.0756108
\(861\) 1.45459 0.0495725
\(862\) −9.49407 −0.323369
\(863\) −12.1851 −0.414787 −0.207394 0.978258i \(-0.566498\pi\)
−0.207394 + 0.978258i \(0.566498\pi\)
\(864\) 13.3341 0.453637
\(865\) −9.37922 −0.318903
\(866\) 23.8845 0.811629
\(867\) 45.2596 1.53710
\(868\) 10.7520 0.364947
\(869\) −7.30518 −0.247811
\(870\) −0.928127 −0.0314665
\(871\) 30.4512 1.03180
\(872\) 2.62418 0.0888659
\(873\) −110.130 −3.72734
\(874\) −3.71660 −0.125716
\(875\) 9.53228 0.322250
\(876\) 0.240642 0.00813053
\(877\) 8.80170 0.297212 0.148606 0.988896i \(-0.452521\pi\)
0.148606 + 0.988896i \(0.452521\pi\)
\(878\) −25.0931 −0.846851
\(879\) 14.5908 0.492135
\(880\) 0.300425 0.0101273
\(881\) 4.14156 0.139533 0.0697664 0.997563i \(-0.477775\pi\)
0.0697664 + 0.997563i \(0.477775\pi\)
\(882\) 14.4030 0.484973
\(883\) 46.6939 1.57137 0.785687 0.618625i \(-0.212310\pi\)
0.785687 + 0.618625i \(0.212310\pi\)
\(884\) −8.13793 −0.273708
\(885\) 18.5974 0.625144
\(886\) −9.65000 −0.324198
\(887\) 15.0022 0.503724 0.251862 0.967763i \(-0.418957\pi\)
0.251862 + 0.967763i \(0.418957\pi\)
\(888\) −30.9072 −1.03718
\(889\) −9.94220 −0.333451
\(890\) −0.821160 −0.0275253
\(891\) −14.5139 −0.486234
\(892\) −19.9821 −0.669050
\(893\) −27.5258 −0.921117
\(894\) 2.55596 0.0854842
\(895\) −8.74583 −0.292341
\(896\) −2.23469 −0.0746556
\(897\) 9.30904 0.310820
\(898\) 33.6196 1.12190
\(899\) 3.21923 0.107367
\(900\) −34.5395 −1.15132
\(901\) −19.1594 −0.638291
\(902\) −0.140973 −0.00469387
\(903\) −36.3614 −1.21003
\(904\) 3.89903 0.129680
\(905\) 2.71951 0.0903997
\(906\) 24.5238 0.814747
\(907\) 8.73615 0.290079 0.145040 0.989426i \(-0.453669\pi\)
0.145040 + 0.989426i \(0.453669\pi\)
\(908\) −1.66765 −0.0553428
\(909\) −18.0464 −0.598560
\(910\) 4.71320 0.156241
\(911\) 3.39763 0.112568 0.0562842 0.998415i \(-0.482075\pi\)
0.0562842 + 0.998415i \(0.482075\pi\)
\(912\) 19.7147 0.652819
\(913\) −5.82963 −0.192933
\(914\) −27.1743 −0.898847
\(915\) −3.89189 −0.128662
\(916\) −18.4150 −0.608449
\(917\) 27.1094 0.895232
\(918\) −22.3691 −0.738289
\(919\) 28.1388 0.928214 0.464107 0.885779i \(-0.346375\pi\)
0.464107 + 0.885779i \(0.346375\pi\)
\(920\) −0.261507 −0.00862161
\(921\) −16.2319 −0.534861
\(922\) −37.6724 −1.24067
\(923\) −25.0038 −0.823010
\(924\) 4.92657 0.162072
\(925\) 46.6050 1.53236
\(926\) 22.4542 0.737890
\(927\) −130.551 −4.28787
\(928\) −0.669083 −0.0219637
\(929\) 23.7268 0.778451 0.389225 0.921143i \(-0.372743\pi\)
0.389225 + 0.921143i \(0.372743\pi\)
\(930\) −6.67421 −0.218856
\(931\) 12.3965 0.406279
\(932\) −14.5883 −0.477857
\(933\) −58.5645 −1.91732
\(934\) −13.9658 −0.456975
\(935\) −0.503987 −0.0164821
\(936\) −34.8269 −1.13835
\(937\) 2.66814 0.0871645 0.0435822 0.999050i \(-0.486123\pi\)
0.0435822 + 0.999050i \(0.486123\pi\)
\(938\) −14.0278 −0.458024
\(939\) 35.6884 1.16465
\(940\) −1.93677 −0.0631704
\(941\) 14.1493 0.461254 0.230627 0.973042i \(-0.425922\pi\)
0.230627 + 0.973042i \(0.425922\pi\)
\(942\) −43.8219 −1.42780
\(943\) 0.122710 0.00399599
\(944\) 13.4068 0.436353
\(945\) 12.9554 0.421438
\(946\) 3.52398 0.114575
\(947\) −25.2469 −0.820413 −0.410207 0.911993i \(-0.634543\pi\)
−0.410207 + 0.911993i \(0.634543\pi\)
\(948\) −33.7304 −1.09551
\(949\) −0.365883 −0.0118771
\(950\) −29.7278 −0.964498
\(951\) 105.621 3.42500
\(952\) 3.74886 0.121501
\(953\) −31.4012 −1.01718 −0.508592 0.861008i \(-0.669834\pi\)
−0.508592 + 0.861008i \(0.669834\pi\)
\(954\) −81.9940 −2.65465
\(955\) −2.49041 −0.0805877
\(956\) −21.6769 −0.701080
\(957\) 1.47505 0.0476817
\(958\) 19.6348 0.634372
\(959\) −39.3728 −1.27142
\(960\) 1.38716 0.0447705
\(961\) −7.85032 −0.253236
\(962\) 46.9928 1.51511
\(963\) 21.6690 0.698274
\(964\) 14.0509 0.452548
\(965\) −6.32658 −0.203660
\(966\) −4.28835 −0.137976
\(967\) −8.01967 −0.257895 −0.128948 0.991651i \(-0.541160\pi\)
−0.128948 + 0.991651i \(0.541160\pi\)
\(968\) 10.5225 0.338207
\(969\) −33.0729 −1.06246
\(970\) −6.66946 −0.214143
\(971\) −27.5999 −0.885723 −0.442862 0.896590i \(-0.646037\pi\)
−0.442862 + 0.896590i \(0.646037\pi\)
\(972\) −27.0131 −0.866445
\(973\) 13.9073 0.445849
\(974\) 28.1435 0.901776
\(975\) 74.4600 2.38463
\(976\) −2.80565 −0.0898067
\(977\) 25.1886 0.805853 0.402927 0.915232i \(-0.367993\pi\)
0.402927 + 0.915232i \(0.367993\pi\)
\(978\) 27.8506 0.890565
\(979\) 1.30505 0.0417097
\(980\) 0.872241 0.0278627
\(981\) −18.8398 −0.601509
\(982\) 0.558892 0.0178349
\(983\) 32.2196 1.02764 0.513822 0.857897i \(-0.328229\pi\)
0.513822 + 0.857897i \(0.328229\pi\)
\(984\) −0.650917 −0.0207505
\(985\) −1.90624 −0.0607380
\(986\) 1.12244 0.0357457
\(987\) −31.7604 −1.01094
\(988\) −29.9752 −0.953638
\(989\) −3.06746 −0.0975397
\(990\) −2.15685 −0.0685492
\(991\) 26.3492 0.837010 0.418505 0.908215i \(-0.362554\pi\)
0.418505 + 0.908215i \(0.362554\pi\)
\(992\) −4.81141 −0.152762
\(993\) 81.4595 2.58504
\(994\) 11.5184 0.365341
\(995\) −0.888253 −0.0281595
\(996\) −26.9173 −0.852909
\(997\) −43.7618 −1.38595 −0.692975 0.720961i \(-0.743701\pi\)
−0.692975 + 0.720961i \(0.743701\pi\)
\(998\) −6.35830 −0.201268
\(999\) 129.171 4.08679
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 8026.2.a.c.1.4 86
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.c.1.4 86 1.1 even 1 trivial