Properties

Label 8002.2.a.f.1.15
Level $8002$
Weight $2$
Character 8002.1
Self dual yes
Analytic conductor $63.896$
Analytic rank $1$
Dimension $89$
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] = [8002,2,Mod(1,8002)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8002, 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("8002.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8002.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: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(89\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 8002.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.39406 q^{3} +1.00000 q^{4} +3.62374 q^{5} +2.39406 q^{6} -4.52806 q^{7} -1.00000 q^{8} +2.73150 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.39406 q^{3} +1.00000 q^{4} +3.62374 q^{5} +2.39406 q^{6} -4.52806 q^{7} -1.00000 q^{8} +2.73150 q^{9} -3.62374 q^{10} +2.26084 q^{11} -2.39406 q^{12} +4.69364 q^{13} +4.52806 q^{14} -8.67544 q^{15} +1.00000 q^{16} +3.55658 q^{17} -2.73150 q^{18} -3.26930 q^{19} +3.62374 q^{20} +10.8404 q^{21} -2.26084 q^{22} +0.716528 q^{23} +2.39406 q^{24} +8.13152 q^{25} -4.69364 q^{26} +0.642799 q^{27} -4.52806 q^{28} -0.534178 q^{29} +8.67544 q^{30} -1.14211 q^{31} -1.00000 q^{32} -5.41258 q^{33} -3.55658 q^{34} -16.4085 q^{35} +2.73150 q^{36} -10.8724 q^{37} +3.26930 q^{38} -11.2368 q^{39} -3.62374 q^{40} -1.11139 q^{41} -10.8404 q^{42} -10.6887 q^{43} +2.26084 q^{44} +9.89826 q^{45} -0.716528 q^{46} -9.03883 q^{47} -2.39406 q^{48} +13.5034 q^{49} -8.13152 q^{50} -8.51465 q^{51} +4.69364 q^{52} -4.68525 q^{53} -0.642799 q^{54} +8.19271 q^{55} +4.52806 q^{56} +7.82689 q^{57} +0.534178 q^{58} +12.6910 q^{59} -8.67544 q^{60} +3.60034 q^{61} +1.14211 q^{62} -12.3684 q^{63} +1.00000 q^{64} +17.0086 q^{65} +5.41258 q^{66} -1.78990 q^{67} +3.55658 q^{68} -1.71541 q^{69} +16.4085 q^{70} -5.04234 q^{71} -2.73150 q^{72} -2.10107 q^{73} +10.8724 q^{74} -19.4673 q^{75} -3.26930 q^{76} -10.2372 q^{77} +11.2368 q^{78} -3.34115 q^{79} +3.62374 q^{80} -9.73340 q^{81} +1.11139 q^{82} +13.3227 q^{83} +10.8404 q^{84} +12.8881 q^{85} +10.6887 q^{86} +1.27885 q^{87} -2.26084 q^{88} -12.8692 q^{89} -9.89826 q^{90} -21.2531 q^{91} +0.716528 q^{92} +2.73428 q^{93} +9.03883 q^{94} -11.8471 q^{95} +2.39406 q^{96} +0.0981843 q^{97} -13.5034 q^{98} +6.17549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9} + 18 q^{10} - 26 q^{11} - 12 q^{12} + 2 q^{13} + 27 q^{14} - 21 q^{15} + 89 q^{16} - 60 q^{17} - 95 q^{18} + q^{19} - 18 q^{20} - 6 q^{21} + 26 q^{22} - 45 q^{23} + 12 q^{24} + 107 q^{25} - 2 q^{26} - 45 q^{27} - 27 q^{28} - 18 q^{29} + 21 q^{30} - 38 q^{31} - 89 q^{32} - 29 q^{33} + 60 q^{34} - 47 q^{35} + 95 q^{36} - 15 q^{37} - q^{38} - 38 q^{39} + 18 q^{40} - 50 q^{41} + 6 q^{42} - 15 q^{43} - 26 q^{44} - 35 q^{45} + 45 q^{46} - 121 q^{47} - 12 q^{48} + 132 q^{49} - 107 q^{50} + 6 q^{51} + 2 q^{52} - 46 q^{53} + 45 q^{54} - 37 q^{55} + 27 q^{56} - 42 q^{57} + 18 q^{58} - 34 q^{59} - 21 q^{60} + 41 q^{61} + 38 q^{62} - 131 q^{63} + 89 q^{64} - 57 q^{65} + 29 q^{66} - 11 q^{67} - 60 q^{68} + 15 q^{69} + 47 q^{70} - 66 q^{71} - 95 q^{72} - 47 q^{73} + 15 q^{74} - 46 q^{75} + q^{76} - 106 q^{77} + 38 q^{78} - 51 q^{79} - 18 q^{80} + 113 q^{81} + 50 q^{82} - 141 q^{83} - 6 q^{84} - 7 q^{85} + 15 q^{86} - 110 q^{87} + 26 q^{88} - 30 q^{89} + 35 q^{90} + 37 q^{91} - 45 q^{92} - 44 q^{93} + 121 q^{94} - 98 q^{95} + 12 q^{96} + 3 q^{97} - 132 q^{98} - 71 q^{99}+O(q^{100}) \) 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
\(3\) −2.39406 −1.38221 −0.691104 0.722755i \(-0.742875\pi\)
−0.691104 + 0.722755i \(0.742875\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.62374 1.62059 0.810294 0.586024i \(-0.199308\pi\)
0.810294 + 0.586024i \(0.199308\pi\)
\(6\) 2.39406 0.977369
\(7\) −4.52806 −1.71145 −0.855724 0.517433i \(-0.826888\pi\)
−0.855724 + 0.517433i \(0.826888\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.73150 0.910501
\(10\) −3.62374 −1.14593
\(11\) 2.26084 0.681669 0.340835 0.940123i \(-0.389290\pi\)
0.340835 + 0.940123i \(0.389290\pi\)
\(12\) −2.39406 −0.691104
\(13\) 4.69364 1.30178 0.650891 0.759171i \(-0.274395\pi\)
0.650891 + 0.759171i \(0.274395\pi\)
\(14\) 4.52806 1.21018
\(15\) −8.67544 −2.23999
\(16\) 1.00000 0.250000
\(17\) 3.55658 0.862597 0.431299 0.902209i \(-0.358056\pi\)
0.431299 + 0.902209i \(0.358056\pi\)
\(18\) −2.73150 −0.643821
\(19\) −3.26930 −0.750029 −0.375014 0.927019i \(-0.622362\pi\)
−0.375014 + 0.927019i \(0.622362\pi\)
\(20\) 3.62374 0.810294
\(21\) 10.8404 2.36558
\(22\) −2.26084 −0.482013
\(23\) 0.716528 0.149406 0.0747032 0.997206i \(-0.476199\pi\)
0.0747032 + 0.997206i \(0.476199\pi\)
\(24\) 2.39406 0.488685
\(25\) 8.13152 1.62630
\(26\) −4.69364 −0.920499
\(27\) 0.642799 0.123707
\(28\) −4.52806 −0.855724
\(29\) −0.534178 −0.0991944 −0.0495972 0.998769i \(-0.515794\pi\)
−0.0495972 + 0.998769i \(0.515794\pi\)
\(30\) 8.67544 1.58391
\(31\) −1.14211 −0.205130 −0.102565 0.994726i \(-0.532705\pi\)
−0.102565 + 0.994726i \(0.532705\pi\)
\(32\) −1.00000 −0.176777
\(33\) −5.41258 −0.942209
\(34\) −3.55658 −0.609949
\(35\) −16.4085 −2.77355
\(36\) 2.73150 0.455250
\(37\) −10.8724 −1.78741 −0.893706 0.448654i \(-0.851904\pi\)
−0.893706 + 0.448654i \(0.851904\pi\)
\(38\) 3.26930 0.530351
\(39\) −11.2368 −1.79934
\(40\) −3.62374 −0.572964
\(41\) −1.11139 −0.173569 −0.0867847 0.996227i \(-0.527659\pi\)
−0.0867847 + 0.996227i \(0.527659\pi\)
\(42\) −10.8404 −1.67272
\(43\) −10.6887 −1.63001 −0.815005 0.579454i \(-0.803266\pi\)
−0.815005 + 0.579454i \(0.803266\pi\)
\(44\) 2.26084 0.340835
\(45\) 9.89826 1.47555
\(46\) −0.716528 −0.105646
\(47\) −9.03883 −1.31845 −0.659225 0.751946i \(-0.729115\pi\)
−0.659225 + 0.751946i \(0.729115\pi\)
\(48\) −2.39406 −0.345552
\(49\) 13.5034 1.92905
\(50\) −8.13152 −1.14997
\(51\) −8.51465 −1.19229
\(52\) 4.69364 0.650891
\(53\) −4.68525 −0.643569 −0.321784 0.946813i \(-0.604283\pi\)
−0.321784 + 0.946813i \(0.604283\pi\)
\(54\) −0.642799 −0.0874738
\(55\) 8.19271 1.10470
\(56\) 4.52806 0.605088
\(57\) 7.82689 1.03670
\(58\) 0.534178 0.0701410
\(59\) 12.6910 1.65222 0.826112 0.563506i \(-0.190548\pi\)
0.826112 + 0.563506i \(0.190548\pi\)
\(60\) −8.67544 −1.11999
\(61\) 3.60034 0.460977 0.230488 0.973075i \(-0.425968\pi\)
0.230488 + 0.973075i \(0.425968\pi\)
\(62\) 1.14211 0.145049
\(63\) −12.3684 −1.55827
\(64\) 1.00000 0.125000
\(65\) 17.0086 2.10965
\(66\) 5.41258 0.666242
\(67\) −1.78990 −0.218671 −0.109336 0.994005i \(-0.534872\pi\)
−0.109336 + 0.994005i \(0.534872\pi\)
\(68\) 3.55658 0.431299
\(69\) −1.71541 −0.206511
\(70\) 16.4085 1.96120
\(71\) −5.04234 −0.598415 −0.299208 0.954188i \(-0.596722\pi\)
−0.299208 + 0.954188i \(0.596722\pi\)
\(72\) −2.73150 −0.321911
\(73\) −2.10107 −0.245911 −0.122956 0.992412i \(-0.539237\pi\)
−0.122956 + 0.992412i \(0.539237\pi\)
\(74\) 10.8724 1.26389
\(75\) −19.4673 −2.24789
\(76\) −3.26930 −0.375014
\(77\) −10.2372 −1.16664
\(78\) 11.2368 1.27232
\(79\) −3.34115 −0.375909 −0.187954 0.982178i \(-0.560186\pi\)
−0.187954 + 0.982178i \(0.560186\pi\)
\(80\) 3.62374 0.405147
\(81\) −9.73340 −1.08149
\(82\) 1.11139 0.122732
\(83\) 13.3227 1.46235 0.731176 0.682189i \(-0.238972\pi\)
0.731176 + 0.682189i \(0.238972\pi\)
\(84\) 10.8404 1.18279
\(85\) 12.8881 1.39791
\(86\) 10.6887 1.15259
\(87\) 1.27885 0.137107
\(88\) −2.26084 −0.241006
\(89\) −12.8692 −1.36414 −0.682068 0.731288i \(-0.738919\pi\)
−0.682068 + 0.731288i \(0.738919\pi\)
\(90\) −9.89826 −1.04337
\(91\) −21.2531 −2.22793
\(92\) 0.716528 0.0747032
\(93\) 2.73428 0.283532
\(94\) 9.03883 0.932284
\(95\) −11.8471 −1.21549
\(96\) 2.39406 0.244342
\(97\) 0.0981843 0.00996910 0.00498455 0.999988i \(-0.498413\pi\)
0.00498455 + 0.999988i \(0.498413\pi\)
\(98\) −13.5034 −1.36405
\(99\) 6.17549 0.620660
\(100\) 8.13152 0.813152
\(101\) 14.2187 1.41481 0.707406 0.706808i \(-0.249865\pi\)
0.707406 + 0.706808i \(0.249865\pi\)
\(102\) 8.51465 0.843076
\(103\) −17.2899 −1.70362 −0.851812 0.523848i \(-0.824496\pi\)
−0.851812 + 0.523848i \(0.824496\pi\)
\(104\) −4.69364 −0.460250
\(105\) 39.2830 3.83363
\(106\) 4.68525 0.455072
\(107\) 11.2384 1.08646 0.543229 0.839585i \(-0.317202\pi\)
0.543229 + 0.839585i \(0.317202\pi\)
\(108\) 0.642799 0.0618533
\(109\) −1.44304 −0.138218 −0.0691091 0.997609i \(-0.522016\pi\)
−0.0691091 + 0.997609i \(0.522016\pi\)
\(110\) −8.19271 −0.781144
\(111\) 26.0291 2.47058
\(112\) −4.52806 −0.427862
\(113\) 6.87791 0.647020 0.323510 0.946225i \(-0.395137\pi\)
0.323510 + 0.946225i \(0.395137\pi\)
\(114\) −7.82689 −0.733055
\(115\) 2.59651 0.242126
\(116\) −0.534178 −0.0495972
\(117\) 12.8207 1.18527
\(118\) −12.6910 −1.16830
\(119\) −16.1044 −1.47629
\(120\) 8.67544 0.791956
\(121\) −5.88860 −0.535327
\(122\) −3.60034 −0.325960
\(123\) 2.66072 0.239909
\(124\) −1.14211 −0.102565
\(125\) 11.3478 1.01498
\(126\) 12.3684 1.10187
\(127\) −9.27798 −0.823288 −0.411644 0.911345i \(-0.635045\pi\)
−0.411644 + 0.911345i \(0.635045\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 25.5893 2.25301
\(130\) −17.0086 −1.49175
\(131\) −1.62186 −0.141703 −0.0708513 0.997487i \(-0.522572\pi\)
−0.0708513 + 0.997487i \(0.522572\pi\)
\(132\) −5.41258 −0.471105
\(133\) 14.8036 1.28364
\(134\) 1.78990 0.154624
\(135\) 2.32934 0.200477
\(136\) −3.55658 −0.304974
\(137\) 13.8541 1.18363 0.591817 0.806073i \(-0.298411\pi\)
0.591817 + 0.806073i \(0.298411\pi\)
\(138\) 1.71541 0.146025
\(139\) 6.13120 0.520041 0.260021 0.965603i \(-0.416271\pi\)
0.260021 + 0.965603i \(0.416271\pi\)
\(140\) −16.4085 −1.38678
\(141\) 21.6395 1.82237
\(142\) 5.04234 0.423143
\(143\) 10.6116 0.887385
\(144\) 2.73150 0.227625
\(145\) −1.93572 −0.160753
\(146\) 2.10107 0.173886
\(147\) −32.3278 −2.66635
\(148\) −10.8724 −0.893706
\(149\) −19.9991 −1.63839 −0.819197 0.573512i \(-0.805580\pi\)
−0.819197 + 0.573512i \(0.805580\pi\)
\(150\) 19.4673 1.58950
\(151\) −6.38314 −0.519452 −0.259726 0.965682i \(-0.583632\pi\)
−0.259726 + 0.965682i \(0.583632\pi\)
\(152\) 3.26930 0.265175
\(153\) 9.71481 0.785396
\(154\) 10.2372 0.824940
\(155\) −4.13873 −0.332431
\(156\) −11.2368 −0.899668
\(157\) −12.8240 −1.02347 −0.511735 0.859143i \(-0.670997\pi\)
−0.511735 + 0.859143i \(0.670997\pi\)
\(158\) 3.34115 0.265808
\(159\) 11.2168 0.889547
\(160\) −3.62374 −0.286482
\(161\) −3.24449 −0.255701
\(162\) 9.73340 0.764728
\(163\) −14.6654 −1.14869 −0.574343 0.818615i \(-0.694742\pi\)
−0.574343 + 0.818615i \(0.694742\pi\)
\(164\) −1.11139 −0.0867847
\(165\) −19.6138 −1.52693
\(166\) −13.3227 −1.03404
\(167\) 14.2266 1.10089 0.550443 0.834873i \(-0.314459\pi\)
0.550443 + 0.834873i \(0.314459\pi\)
\(168\) −10.8404 −0.836358
\(169\) 9.03029 0.694638
\(170\) −12.8881 −0.988475
\(171\) −8.93010 −0.682902
\(172\) −10.6887 −0.815005
\(173\) −4.18903 −0.318486 −0.159243 0.987239i \(-0.550905\pi\)
−0.159243 + 0.987239i \(0.550905\pi\)
\(174\) −1.27885 −0.0969495
\(175\) −36.8200 −2.78333
\(176\) 2.26084 0.170417
\(177\) −30.3829 −2.28372
\(178\) 12.8692 0.964590
\(179\) 18.4418 1.37840 0.689202 0.724569i \(-0.257961\pi\)
0.689202 + 0.724569i \(0.257961\pi\)
\(180\) 9.89826 0.737773
\(181\) −4.43507 −0.329656 −0.164828 0.986322i \(-0.552707\pi\)
−0.164828 + 0.986322i \(0.552707\pi\)
\(182\) 21.2531 1.57539
\(183\) −8.61942 −0.637166
\(184\) −0.716528 −0.0528232
\(185\) −39.3988 −2.89666
\(186\) −2.73428 −0.200487
\(187\) 8.04086 0.588006
\(188\) −9.03883 −0.659225
\(189\) −2.91063 −0.211717
\(190\) 11.8471 0.859479
\(191\) 14.7216 1.06522 0.532610 0.846361i \(-0.321211\pi\)
0.532610 + 0.846361i \(0.321211\pi\)
\(192\) −2.39406 −0.172776
\(193\) 19.3196 1.39066 0.695329 0.718691i \(-0.255259\pi\)
0.695329 + 0.718691i \(0.255259\pi\)
\(194\) −0.0981843 −0.00704922
\(195\) −40.7194 −2.91598
\(196\) 13.5034 0.964526
\(197\) −24.2286 −1.72621 −0.863107 0.505021i \(-0.831485\pi\)
−0.863107 + 0.505021i \(0.831485\pi\)
\(198\) −6.17549 −0.438873
\(199\) 0.365447 0.0259059 0.0129529 0.999916i \(-0.495877\pi\)
0.0129529 + 0.999916i \(0.495877\pi\)
\(200\) −8.13152 −0.574985
\(201\) 4.28513 0.302249
\(202\) −14.2187 −1.00042
\(203\) 2.41879 0.169766
\(204\) −8.51465 −0.596145
\(205\) −4.02738 −0.281284
\(206\) 17.2899 1.20464
\(207\) 1.95720 0.136035
\(208\) 4.69364 0.325446
\(209\) −7.39137 −0.511272
\(210\) −39.2830 −2.71078
\(211\) −11.2593 −0.775120 −0.387560 0.921844i \(-0.626682\pi\)
−0.387560 + 0.921844i \(0.626682\pi\)
\(212\) −4.68525 −0.321784
\(213\) 12.0716 0.827135
\(214\) −11.2384 −0.768242
\(215\) −38.7331 −2.64157
\(216\) −0.642799 −0.0437369
\(217\) 5.17157 0.351069
\(218\) 1.44304 0.0977350
\(219\) 5.03007 0.339901
\(220\) 8.19271 0.552352
\(221\) 16.6933 1.12291
\(222\) −26.0291 −1.74696
\(223\) −12.7748 −0.855461 −0.427731 0.903906i \(-0.640687\pi\)
−0.427731 + 0.903906i \(0.640687\pi\)
\(224\) 4.52806 0.302544
\(225\) 22.2113 1.48075
\(226\) −6.87791 −0.457512
\(227\) 18.6882 1.24038 0.620191 0.784451i \(-0.287055\pi\)
0.620191 + 0.784451i \(0.287055\pi\)
\(228\) 7.82689 0.518348
\(229\) 11.3690 0.751283 0.375642 0.926765i \(-0.377422\pi\)
0.375642 + 0.926765i \(0.377422\pi\)
\(230\) −2.59651 −0.171209
\(231\) 24.5085 1.61254
\(232\) 0.534178 0.0350705
\(233\) −24.7164 −1.61922 −0.809612 0.586965i \(-0.800323\pi\)
−0.809612 + 0.586965i \(0.800323\pi\)
\(234\) −12.8207 −0.838115
\(235\) −32.7544 −2.13666
\(236\) 12.6910 0.826112
\(237\) 7.99890 0.519584
\(238\) 16.1044 1.04389
\(239\) 7.14402 0.462108 0.231054 0.972941i \(-0.425783\pi\)
0.231054 + 0.972941i \(0.425783\pi\)
\(240\) −8.67544 −0.559997
\(241\) 9.92812 0.639527 0.319763 0.947497i \(-0.396397\pi\)
0.319763 + 0.947497i \(0.396397\pi\)
\(242\) 5.88860 0.378533
\(243\) 21.3739 1.37114
\(244\) 3.60034 0.230488
\(245\) 48.9328 3.12620
\(246\) −2.66072 −0.169641
\(247\) −15.3449 −0.976375
\(248\) 1.14211 0.0725243
\(249\) −31.8952 −2.02127
\(250\) −11.3478 −0.717699
\(251\) 14.1361 0.892262 0.446131 0.894968i \(-0.352802\pi\)
0.446131 + 0.894968i \(0.352802\pi\)
\(252\) −12.3684 −0.779137
\(253\) 1.61996 0.101846
\(254\) 9.27798 0.582152
\(255\) −30.8549 −1.93221
\(256\) 1.00000 0.0625000
\(257\) 19.0786 1.19009 0.595044 0.803693i \(-0.297135\pi\)
0.595044 + 0.803693i \(0.297135\pi\)
\(258\) −25.5893 −1.59312
\(259\) 49.2309 3.05906
\(260\) 17.0086 1.05483
\(261\) −1.45911 −0.0903165
\(262\) 1.62186 0.100199
\(263\) −31.2966 −1.92983 −0.964915 0.262564i \(-0.915432\pi\)
−0.964915 + 0.262564i \(0.915432\pi\)
\(264\) 5.41258 0.333121
\(265\) −16.9782 −1.04296
\(266\) −14.8036 −0.907667
\(267\) 30.8097 1.88552
\(268\) −1.78990 −0.109336
\(269\) 4.49940 0.274333 0.137167 0.990548i \(-0.456200\pi\)
0.137167 + 0.990548i \(0.456200\pi\)
\(270\) −2.32934 −0.141759
\(271\) −13.7538 −0.835484 −0.417742 0.908566i \(-0.637178\pi\)
−0.417742 + 0.908566i \(0.637178\pi\)
\(272\) 3.55658 0.215649
\(273\) 50.8812 3.07947
\(274\) −13.8541 −0.836955
\(275\) 18.3841 1.10860
\(276\) −1.71541 −0.103255
\(277\) −11.0106 −0.661561 −0.330781 0.943708i \(-0.607312\pi\)
−0.330781 + 0.943708i \(0.607312\pi\)
\(278\) −6.13120 −0.367725
\(279\) −3.11969 −0.186771
\(280\) 16.4085 0.980598
\(281\) 30.8707 1.84159 0.920797 0.390042i \(-0.127540\pi\)
0.920797 + 0.390042i \(0.127540\pi\)
\(282\) −21.6395 −1.28861
\(283\) 2.08025 0.123658 0.0618290 0.998087i \(-0.480307\pi\)
0.0618290 + 0.998087i \(0.480307\pi\)
\(284\) −5.04234 −0.299208
\(285\) 28.3626 1.68006
\(286\) −10.6116 −0.627476
\(287\) 5.03243 0.297055
\(288\) −2.73150 −0.160955
\(289\) −4.35074 −0.255926
\(290\) 1.93572 0.113670
\(291\) −0.235059 −0.0137794
\(292\) −2.10107 −0.122956
\(293\) −8.00119 −0.467434 −0.233717 0.972305i \(-0.575089\pi\)
−0.233717 + 0.972305i \(0.575089\pi\)
\(294\) 32.3278 1.88540
\(295\) 45.9888 2.67757
\(296\) 10.8724 0.631945
\(297\) 1.45327 0.0843270
\(298\) 19.9991 1.15852
\(299\) 3.36313 0.194495
\(300\) −19.4673 −1.12395
\(301\) 48.3991 2.78968
\(302\) 6.38314 0.367308
\(303\) −34.0403 −1.95556
\(304\) −3.26930 −0.187507
\(305\) 13.0467 0.747053
\(306\) −9.71481 −0.555359
\(307\) −24.1519 −1.37842 −0.689210 0.724561i \(-0.742042\pi\)
−0.689210 + 0.724561i \(0.742042\pi\)
\(308\) −10.2372 −0.583321
\(309\) 41.3930 2.35476
\(310\) 4.13873 0.235064
\(311\) 12.5984 0.714391 0.357195 0.934030i \(-0.383733\pi\)
0.357195 + 0.934030i \(0.383733\pi\)
\(312\) 11.2368 0.636161
\(313\) 19.9674 1.12863 0.564313 0.825561i \(-0.309141\pi\)
0.564313 + 0.825561i \(0.309141\pi\)
\(314\) 12.8240 0.723703
\(315\) −44.8200 −2.52532
\(316\) −3.34115 −0.187954
\(317\) 1.53264 0.0860815 0.0430407 0.999073i \(-0.486295\pi\)
0.0430407 + 0.999073i \(0.486295\pi\)
\(318\) −11.2168 −0.629004
\(319\) −1.20769 −0.0676177
\(320\) 3.62374 0.202573
\(321\) −26.9054 −1.50171
\(322\) 3.24449 0.180808
\(323\) −11.6275 −0.646973
\(324\) −9.73340 −0.540745
\(325\) 38.1664 2.11709
\(326\) 14.6654 0.812243
\(327\) 3.45472 0.191046
\(328\) 1.11139 0.0613661
\(329\) 40.9284 2.25646
\(330\) 19.6138 1.07970
\(331\) −10.4917 −0.576676 −0.288338 0.957529i \(-0.593103\pi\)
−0.288338 + 0.957529i \(0.593103\pi\)
\(332\) 13.3227 0.731176
\(333\) −29.6980 −1.62744
\(334\) −14.2266 −0.778444
\(335\) −6.48615 −0.354376
\(336\) 10.8404 0.591394
\(337\) −23.2031 −1.26395 −0.631976 0.774988i \(-0.717756\pi\)
−0.631976 + 0.774988i \(0.717756\pi\)
\(338\) −9.03029 −0.491183
\(339\) −16.4661 −0.894316
\(340\) 12.8881 0.698957
\(341\) −2.58214 −0.139831
\(342\) 8.93010 0.482885
\(343\) −29.4477 −1.59003
\(344\) 10.6887 0.576295
\(345\) −6.21620 −0.334669
\(346\) 4.18903 0.225203
\(347\) 3.54059 0.190069 0.0950344 0.995474i \(-0.469704\pi\)
0.0950344 + 0.995474i \(0.469704\pi\)
\(348\) 1.27885 0.0685537
\(349\) −32.6885 −1.74978 −0.874888 0.484326i \(-0.839065\pi\)
−0.874888 + 0.484326i \(0.839065\pi\)
\(350\) 36.8200 1.96811
\(351\) 3.01707 0.161039
\(352\) −2.26084 −0.120503
\(353\) 20.9819 1.11675 0.558377 0.829587i \(-0.311424\pi\)
0.558377 + 0.829587i \(0.311424\pi\)
\(354\) 30.3829 1.61483
\(355\) −18.2721 −0.969784
\(356\) −12.8692 −0.682068
\(357\) 38.5549 2.04054
\(358\) −18.4418 −0.974679
\(359\) 32.3869 1.70932 0.854658 0.519191i \(-0.173767\pi\)
0.854658 + 0.519191i \(0.173767\pi\)
\(360\) −9.89826 −0.521684
\(361\) −8.31168 −0.437457
\(362\) 4.43507 0.233102
\(363\) 14.0976 0.739934
\(364\) −21.2531 −1.11397
\(365\) −7.61373 −0.398521
\(366\) 8.61942 0.450544
\(367\) −21.3339 −1.11362 −0.556809 0.830640i \(-0.687975\pi\)
−0.556809 + 0.830640i \(0.687975\pi\)
\(368\) 0.716528 0.0373516
\(369\) −3.03576 −0.158035
\(370\) 39.3988 2.04825
\(371\) 21.2151 1.10143
\(372\) 2.73428 0.141766
\(373\) −8.68720 −0.449806 −0.224903 0.974381i \(-0.572207\pi\)
−0.224903 + 0.974381i \(0.572207\pi\)
\(374\) −8.04086 −0.415783
\(375\) −27.1673 −1.40291
\(376\) 9.03883 0.466142
\(377\) −2.50724 −0.129130
\(378\) 2.91063 0.149707
\(379\) −7.77342 −0.399294 −0.199647 0.979868i \(-0.563980\pi\)
−0.199647 + 0.979868i \(0.563980\pi\)
\(380\) −11.8471 −0.607744
\(381\) 22.2120 1.13796
\(382\) −14.7216 −0.753225
\(383\) 31.5159 1.61039 0.805193 0.593013i \(-0.202062\pi\)
0.805193 + 0.593013i \(0.202062\pi\)
\(384\) 2.39406 0.122171
\(385\) −37.0971 −1.89064
\(386\) −19.3196 −0.983344
\(387\) −29.1962 −1.48412
\(388\) 0.0981843 0.00498455
\(389\) −17.4550 −0.885006 −0.442503 0.896767i \(-0.645909\pi\)
−0.442503 + 0.896767i \(0.645909\pi\)
\(390\) 40.7194 2.06191
\(391\) 2.54839 0.128878
\(392\) −13.5034 −0.682023
\(393\) 3.88283 0.195863
\(394\) 24.2286 1.22062
\(395\) −12.1075 −0.609193
\(396\) 6.17549 0.310330
\(397\) −20.1859 −1.01310 −0.506550 0.862211i \(-0.669079\pi\)
−0.506550 + 0.862211i \(0.669079\pi\)
\(398\) −0.365447 −0.0183182
\(399\) −35.4406 −1.77425
\(400\) 8.13152 0.406576
\(401\) −30.9339 −1.54477 −0.772383 0.635157i \(-0.780935\pi\)
−0.772383 + 0.635157i \(0.780935\pi\)
\(402\) −4.28513 −0.213723
\(403\) −5.36068 −0.267034
\(404\) 14.2187 0.707406
\(405\) −35.2714 −1.75265
\(406\) −2.41879 −0.120043
\(407\) −24.5808 −1.21842
\(408\) 8.51465 0.421538
\(409\) 20.7917 1.02808 0.514041 0.857765i \(-0.328148\pi\)
0.514041 + 0.857765i \(0.328148\pi\)
\(410\) 4.02738 0.198898
\(411\) −33.1674 −1.63603
\(412\) −17.2899 −0.851812
\(413\) −57.4656 −2.82770
\(414\) −1.95720 −0.0961910
\(415\) 48.2779 2.36987
\(416\) −4.69364 −0.230125
\(417\) −14.6784 −0.718805
\(418\) 7.39137 0.361524
\(419\) 30.4461 1.48739 0.743694 0.668520i \(-0.233072\pi\)
0.743694 + 0.668520i \(0.233072\pi\)
\(420\) 39.2830 1.91681
\(421\) −13.9994 −0.682289 −0.341145 0.940011i \(-0.610815\pi\)
−0.341145 + 0.940011i \(0.610815\pi\)
\(422\) 11.2593 0.548093
\(423\) −24.6896 −1.20045
\(424\) 4.68525 0.227536
\(425\) 28.9204 1.40285
\(426\) −12.0716 −0.584873
\(427\) −16.3026 −0.788937
\(428\) 11.2384 0.543229
\(429\) −25.4047 −1.22655
\(430\) 38.7331 1.86787
\(431\) −27.9060 −1.34419 −0.672093 0.740467i \(-0.734605\pi\)
−0.672093 + 0.740467i \(0.734605\pi\)
\(432\) 0.642799 0.0309267
\(433\) 12.0911 0.581059 0.290530 0.956866i \(-0.406169\pi\)
0.290530 + 0.956866i \(0.406169\pi\)
\(434\) −5.17157 −0.248243
\(435\) 4.63423 0.222194
\(436\) −1.44304 −0.0691091
\(437\) −2.34255 −0.112059
\(438\) −5.03007 −0.240346
\(439\) 14.8967 0.710980 0.355490 0.934680i \(-0.384314\pi\)
0.355490 + 0.934680i \(0.384314\pi\)
\(440\) −8.19271 −0.390572
\(441\) 36.8845 1.75640
\(442\) −16.6933 −0.794020
\(443\) −27.9427 −1.32760 −0.663798 0.747912i \(-0.731057\pi\)
−0.663798 + 0.747912i \(0.731057\pi\)
\(444\) 26.0291 1.23529
\(445\) −46.6348 −2.21070
\(446\) 12.7748 0.604902
\(447\) 47.8791 2.26460
\(448\) −4.52806 −0.213931
\(449\) 24.5693 1.15950 0.579749 0.814795i \(-0.303151\pi\)
0.579749 + 0.814795i \(0.303151\pi\)
\(450\) −22.2113 −1.04705
\(451\) −2.51267 −0.118317
\(452\) 6.87791 0.323510
\(453\) 15.2816 0.717992
\(454\) −18.6882 −0.877083
\(455\) −77.0159 −3.61056
\(456\) −7.82689 −0.366528
\(457\) −9.00593 −0.421280 −0.210640 0.977564i \(-0.567555\pi\)
−0.210640 + 0.977564i \(0.567555\pi\)
\(458\) −11.3690 −0.531238
\(459\) 2.28617 0.106709
\(460\) 2.59651 0.121063
\(461\) −24.8496 −1.15736 −0.578681 0.815554i \(-0.696432\pi\)
−0.578681 + 0.815554i \(0.696432\pi\)
\(462\) −24.5085 −1.14024
\(463\) 1.19650 0.0556060 0.0278030 0.999613i \(-0.491149\pi\)
0.0278030 + 0.999613i \(0.491149\pi\)
\(464\) −0.534178 −0.0247986
\(465\) 9.90834 0.459488
\(466\) 24.7164 1.14496
\(467\) 5.50533 0.254756 0.127378 0.991854i \(-0.459344\pi\)
0.127378 + 0.991854i \(0.459344\pi\)
\(468\) 12.8207 0.592637
\(469\) 8.10479 0.374245
\(470\) 32.7544 1.51085
\(471\) 30.7015 1.41465
\(472\) −12.6910 −0.584149
\(473\) −24.1654 −1.11113
\(474\) −7.99890 −0.367402
\(475\) −26.5844 −1.21977
\(476\) −16.1044 −0.738145
\(477\) −12.7978 −0.585970
\(478\) −7.14402 −0.326760
\(479\) 8.58037 0.392047 0.196024 0.980599i \(-0.437197\pi\)
0.196024 + 0.980599i \(0.437197\pi\)
\(480\) 8.67544 0.395978
\(481\) −51.0312 −2.32682
\(482\) −9.92812 −0.452214
\(483\) 7.76748 0.353433
\(484\) −5.88860 −0.267664
\(485\) 0.355795 0.0161558
\(486\) −21.3739 −0.969540
\(487\) 6.92054 0.313600 0.156800 0.987630i \(-0.449882\pi\)
0.156800 + 0.987630i \(0.449882\pi\)
\(488\) −3.60034 −0.162980
\(489\) 35.1099 1.58772
\(490\) −48.9328 −2.21056
\(491\) −32.7740 −1.47907 −0.739536 0.673117i \(-0.764955\pi\)
−0.739536 + 0.673117i \(0.764955\pi\)
\(492\) 2.66072 0.119955
\(493\) −1.89985 −0.0855648
\(494\) 15.3449 0.690401
\(495\) 22.3784 1.00583
\(496\) −1.14211 −0.0512824
\(497\) 22.8320 1.02416
\(498\) 31.8952 1.42926
\(499\) −19.5945 −0.877172 −0.438586 0.898689i \(-0.644521\pi\)
−0.438586 + 0.898689i \(0.644521\pi\)
\(500\) 11.3478 0.507490
\(501\) −34.0592 −1.52165
\(502\) −14.1361 −0.630924
\(503\) −22.8431 −1.01852 −0.509261 0.860612i \(-0.670081\pi\)
−0.509261 + 0.860612i \(0.670081\pi\)
\(504\) 12.3684 0.550933
\(505\) 51.5248 2.29283
\(506\) −1.61996 −0.0720158
\(507\) −21.6190 −0.960134
\(508\) −9.27798 −0.411644
\(509\) −9.89769 −0.438707 −0.219354 0.975645i \(-0.570395\pi\)
−0.219354 + 0.975645i \(0.570395\pi\)
\(510\) 30.8549 1.36628
\(511\) 9.51377 0.420864
\(512\) −1.00000 −0.0441942
\(513\) −2.10150 −0.0927836
\(514\) −19.0786 −0.841519
\(515\) −62.6541 −2.76087
\(516\) 25.5893 1.12651
\(517\) −20.4354 −0.898746
\(518\) −49.2309 −2.16308
\(519\) 10.0288 0.440214
\(520\) −17.0086 −0.745875
\(521\) −10.7629 −0.471529 −0.235765 0.971810i \(-0.575759\pi\)
−0.235765 + 0.971810i \(0.575759\pi\)
\(522\) 1.45911 0.0638634
\(523\) −0.766585 −0.0335204 −0.0167602 0.999860i \(-0.505335\pi\)
−0.0167602 + 0.999860i \(0.505335\pi\)
\(524\) −1.62186 −0.0708513
\(525\) 88.1492 3.84715
\(526\) 31.2966 1.36460
\(527\) −4.06202 −0.176944
\(528\) −5.41258 −0.235552
\(529\) −22.4866 −0.977678
\(530\) 16.9782 0.737484
\(531\) 34.6654 1.50435
\(532\) 14.8036 0.641818
\(533\) −5.21645 −0.225950
\(534\) −30.8097 −1.33327
\(535\) 40.7251 1.76070
\(536\) 1.78990 0.0773120
\(537\) −44.1507 −1.90524
\(538\) −4.49940 −0.193983
\(539\) 30.5290 1.31498
\(540\) 2.32934 0.100239
\(541\) 22.4906 0.966947 0.483473 0.875359i \(-0.339375\pi\)
0.483473 + 0.875359i \(0.339375\pi\)
\(542\) 13.7538 0.590776
\(543\) 10.6178 0.455653
\(544\) −3.55658 −0.152487
\(545\) −5.22921 −0.223995
\(546\) −50.8812 −2.17751
\(547\) −7.74802 −0.331282 −0.165641 0.986186i \(-0.552969\pi\)
−0.165641 + 0.986186i \(0.552969\pi\)
\(548\) 13.8541 0.591817
\(549\) 9.83435 0.419720
\(550\) −18.3841 −0.783899
\(551\) 1.74639 0.0743986
\(552\) 1.71541 0.0730126
\(553\) 15.1289 0.643348
\(554\) 11.0106 0.467794
\(555\) 94.3229 4.00378
\(556\) 6.13120 0.260021
\(557\) −30.6954 −1.30061 −0.650303 0.759675i \(-0.725358\pi\)
−0.650303 + 0.759675i \(0.725358\pi\)
\(558\) 3.11969 0.132067
\(559\) −50.1689 −2.12192
\(560\) −16.4085 −0.693388
\(561\) −19.2503 −0.812747
\(562\) −30.8707 −1.30220
\(563\) −3.54795 −0.149528 −0.0747641 0.997201i \(-0.523820\pi\)
−0.0747641 + 0.997201i \(0.523820\pi\)
\(564\) 21.6395 0.911186
\(565\) 24.9238 1.04855
\(566\) −2.08025 −0.0874394
\(567\) 44.0735 1.85091
\(568\) 5.04234 0.211572
\(569\) 42.1066 1.76520 0.882601 0.470123i \(-0.155790\pi\)
0.882601 + 0.470123i \(0.155790\pi\)
\(570\) −28.3626 −1.18798
\(571\) −25.3353 −1.06025 −0.530124 0.847920i \(-0.677855\pi\)
−0.530124 + 0.847920i \(0.677855\pi\)
\(572\) 10.6116 0.443693
\(573\) −35.2444 −1.47236
\(574\) −5.03243 −0.210050
\(575\) 5.82646 0.242980
\(576\) 2.73150 0.113813
\(577\) −29.6274 −1.23341 −0.616703 0.787196i \(-0.711532\pi\)
−0.616703 + 0.787196i \(0.711532\pi\)
\(578\) 4.35074 0.180967
\(579\) −46.2523 −1.92218
\(580\) −1.93572 −0.0803766
\(581\) −60.3258 −2.50274
\(582\) 0.235059 0.00974349
\(583\) −10.5926 −0.438701
\(584\) 2.10107 0.0869428
\(585\) 46.4589 1.92084
\(586\) 8.00119 0.330526
\(587\) −5.10598 −0.210746 −0.105373 0.994433i \(-0.533604\pi\)
−0.105373 + 0.994433i \(0.533604\pi\)
\(588\) −32.3278 −1.33318
\(589\) 3.73391 0.153853
\(590\) −45.9888 −1.89333
\(591\) 58.0045 2.38599
\(592\) −10.8724 −0.446853
\(593\) 3.49206 0.143402 0.0717009 0.997426i \(-0.477157\pi\)
0.0717009 + 0.997426i \(0.477157\pi\)
\(594\) −1.45327 −0.0596282
\(595\) −58.3583 −2.39246
\(596\) −19.9991 −0.819197
\(597\) −0.874901 −0.0358073
\(598\) −3.36313 −0.137529
\(599\) 28.4802 1.16367 0.581835 0.813307i \(-0.302335\pi\)
0.581835 + 0.813307i \(0.302335\pi\)
\(600\) 19.4673 0.794749
\(601\) −38.5141 −1.57102 −0.785512 0.618847i \(-0.787600\pi\)
−0.785512 + 0.618847i \(0.787600\pi\)
\(602\) −48.3991 −1.97260
\(603\) −4.88912 −0.199100
\(604\) −6.38314 −0.259726
\(605\) −21.3388 −0.867544
\(606\) 34.0403 1.38279
\(607\) −29.4426 −1.19504 −0.597519 0.801855i \(-0.703847\pi\)
−0.597519 + 0.801855i \(0.703847\pi\)
\(608\) 3.26930 0.132588
\(609\) −5.79072 −0.234652
\(610\) −13.0467 −0.528246
\(611\) −42.4251 −1.71633
\(612\) 9.71481 0.392698
\(613\) 29.5501 1.19352 0.596759 0.802421i \(-0.296455\pi\)
0.596759 + 0.802421i \(0.296455\pi\)
\(614\) 24.1519 0.974691
\(615\) 9.64177 0.388794
\(616\) 10.2372 0.412470
\(617\) 18.7791 0.756019 0.378009 0.925802i \(-0.376609\pi\)
0.378009 + 0.925802i \(0.376609\pi\)
\(618\) −41.3930 −1.66507
\(619\) 36.6843 1.47447 0.737234 0.675637i \(-0.236131\pi\)
0.737234 + 0.675637i \(0.236131\pi\)
\(620\) −4.13873 −0.166215
\(621\) 0.460583 0.0184826
\(622\) −12.5984 −0.505151
\(623\) 58.2728 2.33465
\(624\) −11.2368 −0.449834
\(625\) 0.463985 0.0185594
\(626\) −19.9674 −0.798059
\(627\) 17.6953 0.706684
\(628\) −12.8240 −0.511735
\(629\) −38.6686 −1.54182
\(630\) 44.8200 1.78567
\(631\) −30.5770 −1.21725 −0.608625 0.793458i \(-0.708278\pi\)
−0.608625 + 0.793458i \(0.708278\pi\)
\(632\) 3.34115 0.132904
\(633\) 26.9553 1.07138
\(634\) −1.53264 −0.0608688
\(635\) −33.6210 −1.33421
\(636\) 11.2168 0.444773
\(637\) 63.3800 2.51121
\(638\) 1.20769 0.0478130
\(639\) −13.7732 −0.544858
\(640\) −3.62374 −0.143241
\(641\) 14.5656 0.575305 0.287653 0.957735i \(-0.407125\pi\)
0.287653 + 0.957735i \(0.407125\pi\)
\(642\) 26.9054 1.06187
\(643\) 36.1814 1.42686 0.713428 0.700728i \(-0.247141\pi\)
0.713428 + 0.700728i \(0.247141\pi\)
\(644\) −3.24449 −0.127851
\(645\) 92.7291 3.65120
\(646\) 11.6275 0.457479
\(647\) −45.1311 −1.77429 −0.887144 0.461493i \(-0.847314\pi\)
−0.887144 + 0.461493i \(0.847314\pi\)
\(648\) 9.73340 0.382364
\(649\) 28.6923 1.12627
\(650\) −38.1664 −1.49701
\(651\) −12.3810 −0.485250
\(652\) −14.6654 −0.574343
\(653\) −5.37003 −0.210146 −0.105073 0.994465i \(-0.533508\pi\)
−0.105073 + 0.994465i \(0.533508\pi\)
\(654\) −3.45472 −0.135090
\(655\) −5.87721 −0.229642
\(656\) −1.11139 −0.0433924
\(657\) −5.73907 −0.223902
\(658\) −40.9284 −1.59556
\(659\) 5.88129 0.229102 0.114551 0.993417i \(-0.463457\pi\)
0.114551 + 0.993417i \(0.463457\pi\)
\(660\) −19.6138 −0.763466
\(661\) −19.0357 −0.740402 −0.370201 0.928952i \(-0.620711\pi\)
−0.370201 + 0.928952i \(0.620711\pi\)
\(662\) 10.4917 0.407772
\(663\) −39.9647 −1.55210
\(664\) −13.3227 −0.517019
\(665\) 53.6445 2.08024
\(666\) 29.6980 1.15077
\(667\) −0.382754 −0.0148203
\(668\) 14.2266 0.550443
\(669\) 30.5835 1.18243
\(670\) 6.48615 0.250582
\(671\) 8.13980 0.314234
\(672\) −10.8404 −0.418179
\(673\) 8.65779 0.333733 0.166867 0.985979i \(-0.446635\pi\)
0.166867 + 0.985979i \(0.446635\pi\)
\(674\) 23.2031 0.893749
\(675\) 5.22693 0.201185
\(676\) 9.03029 0.347319
\(677\) −10.2663 −0.394566 −0.197283 0.980347i \(-0.563212\pi\)
−0.197283 + 0.980347i \(0.563212\pi\)
\(678\) 16.4661 0.632377
\(679\) −0.444585 −0.0170616
\(680\) −12.8881 −0.494237
\(681\) −44.7407 −1.71447
\(682\) 2.58214 0.0988752
\(683\) −31.8049 −1.21698 −0.608490 0.793561i \(-0.708225\pi\)
−0.608490 + 0.793561i \(0.708225\pi\)
\(684\) −8.93010 −0.341451
\(685\) 50.2036 1.91818
\(686\) 29.4477 1.12432
\(687\) −27.2180 −1.03843
\(688\) −10.6887 −0.407502
\(689\) −21.9909 −0.837787
\(690\) 6.21620 0.236647
\(691\) −2.89440 −0.110108 −0.0550541 0.998483i \(-0.517533\pi\)
−0.0550541 + 0.998483i \(0.517533\pi\)
\(692\) −4.18903 −0.159243
\(693\) −27.9630 −1.06223
\(694\) −3.54059 −0.134399
\(695\) 22.2179 0.842772
\(696\) −1.27885 −0.0484748
\(697\) −3.95274 −0.149721
\(698\) 32.6885 1.23728
\(699\) 59.1724 2.23811
\(700\) −36.8200 −1.39167
\(701\) 27.8401 1.05151 0.525753 0.850637i \(-0.323784\pi\)
0.525753 + 0.850637i \(0.323784\pi\)
\(702\) −3.01707 −0.113872
\(703\) 35.5451 1.34061
\(704\) 2.26084 0.0852087
\(705\) 78.4159 2.95331
\(706\) −20.9819 −0.789665
\(707\) −64.3831 −2.42138
\(708\) −30.3829 −1.14186
\(709\) −17.3183 −0.650402 −0.325201 0.945645i \(-0.605432\pi\)
−0.325201 + 0.945645i \(0.605432\pi\)
\(710\) 18.2721 0.685741
\(711\) −9.12636 −0.342265
\(712\) 12.8692 0.482295
\(713\) −0.818357 −0.0306477
\(714\) −38.5549 −1.44288
\(715\) 38.4537 1.43809
\(716\) 18.4418 0.689202
\(717\) −17.1032 −0.638730
\(718\) −32.3869 −1.20867
\(719\) 3.79195 0.141416 0.0707080 0.997497i \(-0.477474\pi\)
0.0707080 + 0.997497i \(0.477474\pi\)
\(720\) 9.89826 0.368886
\(721\) 78.2897 2.91566
\(722\) 8.31168 0.309329
\(723\) −23.7685 −0.883959
\(724\) −4.43507 −0.164828
\(725\) −4.34368 −0.161320
\(726\) −14.0976 −0.523212
\(727\) 3.60482 0.133695 0.0668477 0.997763i \(-0.478706\pi\)
0.0668477 + 0.997763i \(0.478706\pi\)
\(728\) 21.2531 0.787693
\(729\) −21.9701 −0.813708
\(730\) 7.61373 0.281797
\(731\) −38.0152 −1.40604
\(732\) −8.61942 −0.318583
\(733\) 10.4879 0.387379 0.193690 0.981063i \(-0.437954\pi\)
0.193690 + 0.981063i \(0.437954\pi\)
\(734\) 21.3339 0.787447
\(735\) −117.148 −4.32106
\(736\) −0.716528 −0.0264116
\(737\) −4.04668 −0.149062
\(738\) 3.03576 0.111748
\(739\) −42.9737 −1.58081 −0.790407 0.612582i \(-0.790131\pi\)
−0.790407 + 0.612582i \(0.790131\pi\)
\(740\) −39.3988 −1.44833
\(741\) 36.7366 1.34955
\(742\) −21.2151 −0.778832
\(743\) −47.9697 −1.75984 −0.879918 0.475125i \(-0.842403\pi\)
−0.879918 + 0.475125i \(0.842403\pi\)
\(744\) −2.73428 −0.100244
\(745\) −72.4718 −2.65516
\(746\) 8.68720 0.318061
\(747\) 36.3909 1.33147
\(748\) 8.04086 0.294003
\(749\) −50.8882 −1.85942
\(750\) 27.1673 0.992010
\(751\) −20.3145 −0.741288 −0.370644 0.928775i \(-0.620863\pi\)
−0.370644 + 0.928775i \(0.620863\pi\)
\(752\) −9.03883 −0.329612
\(753\) −33.8426 −1.23329
\(754\) 2.50724 0.0913083
\(755\) −23.1309 −0.841818
\(756\) −2.91063 −0.105859
\(757\) −49.1717 −1.78718 −0.893588 0.448888i \(-0.851820\pi\)
−0.893588 + 0.448888i \(0.851820\pi\)
\(758\) 7.77342 0.282343
\(759\) −3.87827 −0.140772
\(760\) 11.8471 0.429740
\(761\) 42.8577 1.55359 0.776795 0.629754i \(-0.216844\pi\)
0.776795 + 0.629754i \(0.216844\pi\)
\(762\) −22.2120 −0.804656
\(763\) 6.53418 0.236553
\(764\) 14.7216 0.532610
\(765\) 35.2040 1.27280
\(766\) −31.5159 −1.13871
\(767\) 59.5669 2.15084
\(768\) −2.39406 −0.0863880
\(769\) −11.8690 −0.428008 −0.214004 0.976833i \(-0.568651\pi\)
−0.214004 + 0.976833i \(0.568651\pi\)
\(770\) 37.0971 1.33689
\(771\) −45.6751 −1.64495
\(772\) 19.3196 0.695329
\(773\) −19.0584 −0.685483 −0.342741 0.939430i \(-0.611355\pi\)
−0.342741 + 0.939430i \(0.611355\pi\)
\(774\) 29.1962 1.04943
\(775\) −9.28712 −0.333603
\(776\) −0.0981843 −0.00352461
\(777\) −117.862 −4.22826
\(778\) 17.4550 0.625794
\(779\) 3.63346 0.130182
\(780\) −40.7194 −1.45799
\(781\) −11.3999 −0.407921
\(782\) −2.54839 −0.0911302
\(783\) −0.343369 −0.0122710
\(784\) 13.5034 0.482263
\(785\) −46.4711 −1.65862
\(786\) −3.88283 −0.138496
\(787\) 18.7130 0.667048 0.333524 0.942742i \(-0.391762\pi\)
0.333524 + 0.942742i \(0.391762\pi\)
\(788\) −24.2286 −0.863107
\(789\) 74.9257 2.66743
\(790\) 12.1075 0.430765
\(791\) −31.1436 −1.10734
\(792\) −6.17549 −0.219437
\(793\) 16.8987 0.600091
\(794\) 20.1859 0.716370
\(795\) 40.6466 1.44159
\(796\) 0.365447 0.0129529
\(797\) −40.9899 −1.45194 −0.725968 0.687729i \(-0.758608\pi\)
−0.725968 + 0.687729i \(0.758608\pi\)
\(798\) 35.4406 1.25459
\(799\) −32.1473 −1.13729
\(800\) −8.13152 −0.287493
\(801\) −35.1524 −1.24205
\(802\) 30.9339 1.09231
\(803\) −4.75018 −0.167630
\(804\) 4.28513 0.151125
\(805\) −11.7572 −0.414386
\(806\) 5.36068 0.188822
\(807\) −10.7718 −0.379186
\(808\) −14.2187 −0.500211
\(809\) −16.0225 −0.563321 −0.281660 0.959514i \(-0.590885\pi\)
−0.281660 + 0.959514i \(0.590885\pi\)
\(810\) 35.2714 1.23931
\(811\) 21.8834 0.768432 0.384216 0.923243i \(-0.374472\pi\)
0.384216 + 0.923243i \(0.374472\pi\)
\(812\) 2.41879 0.0848830
\(813\) 32.9274 1.15481
\(814\) 24.5808 0.861555
\(815\) −53.1438 −1.86155
\(816\) −8.51465 −0.298072
\(817\) 34.9445 1.22255
\(818\) −20.7917 −0.726964
\(819\) −58.0530 −2.02853
\(820\) −4.02738 −0.140642
\(821\) −40.6855 −1.41993 −0.709966 0.704236i \(-0.751290\pi\)
−0.709966 + 0.704236i \(0.751290\pi\)
\(822\) 33.1674 1.15685
\(823\) −28.6666 −0.999254 −0.499627 0.866241i \(-0.666530\pi\)
−0.499627 + 0.866241i \(0.666530\pi\)
\(824\) 17.2899 0.602322
\(825\) −44.0125 −1.53232
\(826\) 57.4656 1.99948
\(827\) −9.37183 −0.325890 −0.162945 0.986635i \(-0.552099\pi\)
−0.162945 + 0.986635i \(0.552099\pi\)
\(828\) 1.95720 0.0680173
\(829\) −3.33811 −0.115937 −0.0579687 0.998318i \(-0.518462\pi\)
−0.0579687 + 0.998318i \(0.518462\pi\)
\(830\) −48.2779 −1.67575
\(831\) 26.3599 0.914416
\(832\) 4.69364 0.162723
\(833\) 48.0258 1.66400
\(834\) 14.6784 0.508272
\(835\) 51.5535 1.78408
\(836\) −7.39137 −0.255636
\(837\) −0.734149 −0.0253759
\(838\) −30.4461 −1.05174
\(839\) 38.3835 1.32514 0.662572 0.748998i \(-0.269465\pi\)
0.662572 + 0.748998i \(0.269465\pi\)
\(840\) −39.2830 −1.35539
\(841\) −28.7147 −0.990160
\(842\) 13.9994 0.482451
\(843\) −73.9063 −2.54547
\(844\) −11.2593 −0.387560
\(845\) 32.7235 1.12572
\(846\) 24.6896 0.848846
\(847\) 26.6640 0.916184
\(848\) −4.68525 −0.160892
\(849\) −4.98023 −0.170921
\(850\) −28.9204 −0.991961
\(851\) −7.79038 −0.267051
\(852\) 12.0716 0.413567
\(853\) −48.6331 −1.66516 −0.832582 0.553901i \(-0.813138\pi\)
−0.832582 + 0.553901i \(0.813138\pi\)
\(854\) 16.3026 0.557863
\(855\) −32.3604 −1.10670
\(856\) −11.2384 −0.384121
\(857\) 11.9410 0.407898 0.203949 0.978982i \(-0.434622\pi\)
0.203949 + 0.978982i \(0.434622\pi\)
\(858\) 25.4047 0.867303
\(859\) −11.2099 −0.382476 −0.191238 0.981544i \(-0.561250\pi\)
−0.191238 + 0.981544i \(0.561250\pi\)
\(860\) −38.7331 −1.32079
\(861\) −12.0479 −0.410592
\(862\) 27.9060 0.950483
\(863\) 43.0231 1.46452 0.732261 0.681024i \(-0.238465\pi\)
0.732261 + 0.681024i \(0.238465\pi\)
\(864\) −0.642799 −0.0218685
\(865\) −15.1800 −0.516134
\(866\) −12.0911 −0.410871
\(867\) 10.4159 0.353743
\(868\) 5.17157 0.175534
\(869\) −7.55381 −0.256245
\(870\) −4.63423 −0.157115
\(871\) −8.40116 −0.284663
\(872\) 1.44304 0.0488675
\(873\) 0.268190 0.00907687
\(874\) 2.34255 0.0792378
\(875\) −51.3836 −1.73708
\(876\) 5.03007 0.169950
\(877\) 42.5092 1.43543 0.717716 0.696336i \(-0.245187\pi\)
0.717716 + 0.696336i \(0.245187\pi\)
\(878\) −14.8967 −0.502738
\(879\) 19.1553 0.646092
\(880\) 8.19271 0.276176
\(881\) −19.1034 −0.643610 −0.321805 0.946806i \(-0.604290\pi\)
−0.321805 + 0.946806i \(0.604290\pi\)
\(882\) −36.8845 −1.24197
\(883\) 56.3436 1.89611 0.948057 0.318100i \(-0.103045\pi\)
0.948057 + 0.318100i \(0.103045\pi\)
\(884\) 16.6933 0.561457
\(885\) −110.100 −3.70097
\(886\) 27.9427 0.938752
\(887\) −20.0143 −0.672013 −0.336006 0.941860i \(-0.609076\pi\)
−0.336006 + 0.941860i \(0.609076\pi\)
\(888\) −26.0291 −0.873480
\(889\) 42.0113 1.40901
\(890\) 46.6348 1.56320
\(891\) −22.0057 −0.737218
\(892\) −12.7748 −0.427731
\(893\) 29.5507 0.988875
\(894\) −47.8791 −1.60132
\(895\) 66.8283 2.23382
\(896\) 4.52806 0.151272
\(897\) −8.05152 −0.268832
\(898\) −24.5693 −0.819889
\(899\) 0.610092 0.0203477
\(900\) 22.2113 0.740375
\(901\) −16.6635 −0.555141
\(902\) 2.51267 0.0836627
\(903\) −115.870 −3.85591
\(904\) −6.87791 −0.228756
\(905\) −16.0715 −0.534236
\(906\) −15.2816 −0.507697
\(907\) 45.2561 1.50270 0.751352 0.659901i \(-0.229402\pi\)
0.751352 + 0.659901i \(0.229402\pi\)
\(908\) 18.6882 0.620191
\(909\) 38.8384 1.28819
\(910\) 77.0159 2.55305
\(911\) 13.3220 0.441376 0.220688 0.975344i \(-0.429170\pi\)
0.220688 + 0.975344i \(0.429170\pi\)
\(912\) 7.82689 0.259174
\(913\) 30.1204 0.996840
\(914\) 9.00593 0.297890
\(915\) −31.2346 −1.03258
\(916\) 11.3690 0.375642
\(917\) 7.34389 0.242517
\(918\) −2.28617 −0.0754547
\(919\) 18.5089 0.610553 0.305277 0.952264i \(-0.401251\pi\)
0.305277 + 0.952264i \(0.401251\pi\)
\(920\) −2.59651 −0.0856045
\(921\) 57.8209 1.90526
\(922\) 24.8496 0.818379
\(923\) −23.6669 −0.779007
\(924\) 24.5085 0.806271
\(925\) −88.4091 −2.90687
\(926\) −1.19650 −0.0393194
\(927\) −47.2274 −1.55115
\(928\) 0.534178 0.0175353
\(929\) 29.0552 0.953270 0.476635 0.879101i \(-0.341856\pi\)
0.476635 + 0.879101i \(0.341856\pi\)
\(930\) −9.90834 −0.324907
\(931\) −44.1466 −1.44685
\(932\) −24.7164 −0.809612
\(933\) −30.1613 −0.987437
\(934\) −5.50533 −0.180140
\(935\) 29.1380 0.952915
\(936\) −12.8207 −0.419058
\(937\) 2.93807 0.0959826 0.0479913 0.998848i \(-0.484718\pi\)
0.0479913 + 0.998848i \(0.484718\pi\)
\(938\) −8.10479 −0.264631
\(939\) −47.8031 −1.56000
\(940\) −32.7544 −1.06833
\(941\) 53.4754 1.74325 0.871624 0.490176i \(-0.163067\pi\)
0.871624 + 0.490176i \(0.163067\pi\)
\(942\) −30.7015 −1.00031
\(943\) −0.796340 −0.0259324
\(944\) 12.6910 0.413056
\(945\) −10.5474 −0.343107
\(946\) 24.1654 0.785686
\(947\) −39.3678 −1.27928 −0.639641 0.768674i \(-0.720917\pi\)
−0.639641 + 0.768674i \(0.720917\pi\)
\(948\) 7.99890 0.259792
\(949\) −9.86166 −0.320123
\(950\) 26.5844 0.862511
\(951\) −3.66922 −0.118983
\(952\) 16.1044 0.521947
\(953\) −22.3747 −0.724789 −0.362394 0.932025i \(-0.618041\pi\)
−0.362394 + 0.932025i \(0.618041\pi\)
\(954\) 12.7978 0.414343
\(955\) 53.3474 1.72628
\(956\) 7.14402 0.231054
\(957\) 2.89128 0.0934618
\(958\) −8.58037 −0.277219
\(959\) −62.7321 −2.02573
\(960\) −8.67544 −0.279999
\(961\) −29.6956 −0.957922
\(962\) 51.0312 1.64531
\(963\) 30.6977 0.989221
\(964\) 9.92812 0.319763
\(965\) 70.0094 2.25368
\(966\) −7.76748 −0.249915
\(967\) −40.5707 −1.30467 −0.652334 0.757932i \(-0.726210\pi\)
−0.652334 + 0.757932i \(0.726210\pi\)
\(968\) 5.88860 0.189267
\(969\) 27.8370 0.894252
\(970\) −0.355795 −0.0114239
\(971\) −14.0961 −0.452366 −0.226183 0.974085i \(-0.572625\pi\)
−0.226183 + 0.974085i \(0.572625\pi\)
\(972\) 21.3739 0.685568
\(973\) −27.7625 −0.890023
\(974\) −6.92054 −0.221749
\(975\) −91.3726 −2.92626
\(976\) 3.60034 0.115244
\(977\) −45.9679 −1.47064 −0.735321 0.677719i \(-0.762969\pi\)
−0.735321 + 0.677719i \(0.762969\pi\)
\(978\) −35.1099 −1.12269
\(979\) −29.0953 −0.929890
\(980\) 48.9328 1.56310
\(981\) −3.94167 −0.125848
\(982\) 32.7740 1.04586
\(983\) −22.4337 −0.715523 −0.357762 0.933813i \(-0.616460\pi\)
−0.357762 + 0.933813i \(0.616460\pi\)
\(984\) −2.66072 −0.0848207
\(985\) −87.7981 −2.79748
\(986\) 1.89985 0.0605035
\(987\) −97.9849 −3.11889
\(988\) −15.3449 −0.488187
\(989\) −7.65875 −0.243534
\(990\) −22.3784 −0.711232
\(991\) −14.4829 −0.460064 −0.230032 0.973183i \(-0.573883\pi\)
−0.230032 + 0.973183i \(0.573883\pi\)
\(992\) 1.14211 0.0362622
\(993\) 25.1177 0.797087
\(994\) −22.8320 −0.724188
\(995\) 1.32429 0.0419827
\(996\) −31.8952 −1.01064
\(997\) −0.0104048 −0.000329524 0 −0.000164762 1.00000i \(-0.500052\pi\)
−0.000164762 1.00000i \(0.500052\pi\)
\(998\) 19.5945 0.620254
\(999\) −6.98876 −0.221115
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 8002.2.a.f.1.15 89
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8002.2.a.f.1.15 89 1.1 even 1 trivial