Properties

Label 8005.2.a.f.1.9
Level $8005$
Weight $2$
Character 8005.1
Self dual yes
Analytic conductor $63.920$
Analytic rank $1$
Dimension $127$
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] = [8005,2,Mod(1,8005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8005, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8005.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: \(63.9202468180\)
Analytic rank: \(1\)
Dimension: \(127\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 8005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.51650 q^{2} +0.753102 q^{3} +4.33277 q^{4} -1.00000 q^{5} -1.89518 q^{6} +3.99606 q^{7} -5.87042 q^{8} -2.43284 q^{9} +O(q^{10})\) \(q-2.51650 q^{2} +0.753102 q^{3} +4.33277 q^{4} -1.00000 q^{5} -1.89518 q^{6} +3.99606 q^{7} -5.87042 q^{8} -2.43284 q^{9} +2.51650 q^{10} -2.93325 q^{11} +3.26302 q^{12} +2.05745 q^{13} -10.0561 q^{14} -0.753102 q^{15} +6.10737 q^{16} -5.01088 q^{17} +6.12223 q^{18} -0.166190 q^{19} -4.33277 q^{20} +3.00944 q^{21} +7.38152 q^{22} -5.55870 q^{23} -4.42103 q^{24} +1.00000 q^{25} -5.17757 q^{26} -4.09148 q^{27} +17.3140 q^{28} +5.25849 q^{29} +1.89518 q^{30} +0.0944094 q^{31} -3.62836 q^{32} -2.20904 q^{33} +12.6099 q^{34} -3.99606 q^{35} -10.5409 q^{36} -7.37787 q^{37} +0.418216 q^{38} +1.54947 q^{39} +5.87042 q^{40} +4.05592 q^{41} -7.57325 q^{42} +7.97811 q^{43} -12.7091 q^{44} +2.43284 q^{45} +13.9885 q^{46} +2.45961 q^{47} +4.59948 q^{48} +8.96846 q^{49} -2.51650 q^{50} -3.77370 q^{51} +8.91445 q^{52} +8.25694 q^{53} +10.2962 q^{54} +2.93325 q^{55} -23.4585 q^{56} -0.125158 q^{57} -13.2330 q^{58} +4.93979 q^{59} -3.26302 q^{60} +7.37984 q^{61} -0.237581 q^{62} -9.72175 q^{63} -3.08398 q^{64} -2.05745 q^{65} +5.55904 q^{66} +3.23307 q^{67} -21.7110 q^{68} -4.18627 q^{69} +10.0561 q^{70} -1.69878 q^{71} +14.2818 q^{72} -12.2421 q^{73} +18.5664 q^{74} +0.753102 q^{75} -0.720061 q^{76} -11.7214 q^{77} -3.89924 q^{78} +4.89167 q^{79} -6.10737 q^{80} +4.21720 q^{81} -10.2067 q^{82} +8.21795 q^{83} +13.0392 q^{84} +5.01088 q^{85} -20.0769 q^{86} +3.96018 q^{87} +17.2194 q^{88} -9.46497 q^{89} -6.12223 q^{90} +8.22168 q^{91} -24.0846 q^{92} +0.0711000 q^{93} -6.18961 q^{94} +0.166190 q^{95} -2.73252 q^{96} +18.4022 q^{97} -22.5691 q^{98} +7.13611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51650 −1.77943 −0.889717 0.456512i \(-0.849098\pi\)
−0.889717 + 0.456512i \(0.849098\pi\)
\(3\) 0.753102 0.434804 0.217402 0.976082i \(-0.430242\pi\)
0.217402 + 0.976082i \(0.430242\pi\)
\(4\) 4.33277 2.16639
\(5\) −1.00000 −0.447214
\(6\) −1.89518 −0.773705
\(7\) 3.99606 1.51037 0.755183 0.655513i \(-0.227548\pi\)
0.755183 + 0.655513i \(0.227548\pi\)
\(8\) −5.87042 −2.07551
\(9\) −2.43284 −0.810946
\(10\) 2.51650 0.795787
\(11\) −2.93325 −0.884407 −0.442204 0.896915i \(-0.645803\pi\)
−0.442204 + 0.896915i \(0.645803\pi\)
\(12\) 3.26302 0.941953
\(13\) 2.05745 0.570633 0.285317 0.958433i \(-0.407901\pi\)
0.285317 + 0.958433i \(0.407901\pi\)
\(14\) −10.0561 −2.68760
\(15\) −0.753102 −0.194450
\(16\) 6.10737 1.52684
\(17\) −5.01088 −1.21532 −0.607658 0.794199i \(-0.707891\pi\)
−0.607658 + 0.794199i \(0.707891\pi\)
\(18\) 6.12223 1.44302
\(19\) −0.166190 −0.0381265 −0.0190632 0.999818i \(-0.506068\pi\)
−0.0190632 + 0.999818i \(0.506068\pi\)
\(20\) −4.33277 −0.968837
\(21\) 3.00944 0.656713
\(22\) 7.38152 1.57374
\(23\) −5.55870 −1.15907 −0.579535 0.814947i \(-0.696766\pi\)
−0.579535 + 0.814947i \(0.696766\pi\)
\(24\) −4.42103 −0.902439
\(25\) 1.00000 0.200000
\(26\) −5.17757 −1.01540
\(27\) −4.09148 −0.787406
\(28\) 17.3140 3.27204
\(29\) 5.25849 0.976476 0.488238 0.872710i \(-0.337640\pi\)
0.488238 + 0.872710i \(0.337640\pi\)
\(30\) 1.89518 0.346011
\(31\) 0.0944094 0.0169564 0.00847822 0.999964i \(-0.497301\pi\)
0.00847822 + 0.999964i \(0.497301\pi\)
\(32\) −3.62836 −0.641409
\(33\) −2.20904 −0.384544
\(34\) 12.6099 2.16258
\(35\) −3.99606 −0.675457
\(36\) −10.5409 −1.75682
\(37\) −7.37787 −1.21292 −0.606458 0.795116i \(-0.707410\pi\)
−0.606458 + 0.795116i \(0.707410\pi\)
\(38\) 0.418216 0.0678436
\(39\) 1.54947 0.248114
\(40\) 5.87042 0.928195
\(41\) 4.05592 0.633428 0.316714 0.948521i \(-0.397420\pi\)
0.316714 + 0.948521i \(0.397420\pi\)
\(42\) −7.57325 −1.16858
\(43\) 7.97811 1.21665 0.608325 0.793688i \(-0.291842\pi\)
0.608325 + 0.793688i \(0.291842\pi\)
\(44\) −12.7091 −1.91597
\(45\) 2.43284 0.362666
\(46\) 13.9885 2.06249
\(47\) 2.45961 0.358771 0.179385 0.983779i \(-0.442589\pi\)
0.179385 + 0.983779i \(0.442589\pi\)
\(48\) 4.59948 0.663877
\(49\) 8.96846 1.28121
\(50\) −2.51650 −0.355887
\(51\) −3.77370 −0.528424
\(52\) 8.91445 1.23621
\(53\) 8.25694 1.13418 0.567089 0.823657i \(-0.308070\pi\)
0.567089 + 0.823657i \(0.308070\pi\)
\(54\) 10.2962 1.40114
\(55\) 2.93325 0.395519
\(56\) −23.4585 −3.13478
\(57\) −0.125158 −0.0165775
\(58\) −13.2330 −1.73758
\(59\) 4.93979 0.643106 0.321553 0.946892i \(-0.395795\pi\)
0.321553 + 0.946892i \(0.395795\pi\)
\(60\) −3.26302 −0.421254
\(61\) 7.37984 0.944892 0.472446 0.881360i \(-0.343371\pi\)
0.472446 + 0.881360i \(0.343371\pi\)
\(62\) −0.237581 −0.0301729
\(63\) −9.72175 −1.22483
\(64\) −3.08398 −0.385498
\(65\) −2.05745 −0.255195
\(66\) 5.55904 0.684270
\(67\) 3.23307 0.394982 0.197491 0.980305i \(-0.436721\pi\)
0.197491 + 0.980305i \(0.436721\pi\)
\(68\) −21.7110 −2.63284
\(69\) −4.18627 −0.503968
\(70\) 10.0561 1.20193
\(71\) −1.69878 −0.201608 −0.100804 0.994906i \(-0.532142\pi\)
−0.100804 + 0.994906i \(0.532142\pi\)
\(72\) 14.2818 1.68312
\(73\) −12.2421 −1.43283 −0.716414 0.697676i \(-0.754218\pi\)
−0.716414 + 0.697676i \(0.754218\pi\)
\(74\) 18.5664 2.15830
\(75\) 0.753102 0.0869608
\(76\) −0.720061 −0.0825967
\(77\) −11.7214 −1.33578
\(78\) −3.89924 −0.441502
\(79\) 4.89167 0.550356 0.275178 0.961393i \(-0.411263\pi\)
0.275178 + 0.961393i \(0.411263\pi\)
\(80\) −6.10737 −0.682825
\(81\) 4.21720 0.468578
\(82\) −10.2067 −1.12714
\(83\) 8.21795 0.902038 0.451019 0.892514i \(-0.351061\pi\)
0.451019 + 0.892514i \(0.351061\pi\)
\(84\) 13.0392 1.42270
\(85\) 5.01088 0.543506
\(86\) −20.0769 −2.16495
\(87\) 3.96018 0.424576
\(88\) 17.2194 1.83559
\(89\) −9.46497 −1.00329 −0.501643 0.865075i \(-0.667271\pi\)
−0.501643 + 0.865075i \(0.667271\pi\)
\(90\) −6.12223 −0.645340
\(91\) 8.22168 0.861866
\(92\) −24.0846 −2.51099
\(93\) 0.0711000 0.00737272
\(94\) −6.18961 −0.638409
\(95\) 0.166190 0.0170507
\(96\) −2.73252 −0.278887
\(97\) 18.4022 1.86846 0.934228 0.356675i \(-0.116090\pi\)
0.934228 + 0.356675i \(0.116090\pi\)
\(98\) −22.5691 −2.27983
\(99\) 7.13611 0.717206
\(100\) 4.33277 0.433277
\(101\) 7.52463 0.748729 0.374364 0.927282i \(-0.377861\pi\)
0.374364 + 0.927282i \(0.377861\pi\)
\(102\) 9.49653 0.940296
\(103\) −1.50301 −0.148096 −0.0740478 0.997255i \(-0.523592\pi\)
−0.0740478 + 0.997255i \(0.523592\pi\)
\(104\) −12.0781 −1.18435
\(105\) −3.00944 −0.293691
\(106\) −20.7786 −2.01819
\(107\) −5.06875 −0.490015 −0.245008 0.969521i \(-0.578790\pi\)
−0.245008 + 0.969521i \(0.578790\pi\)
\(108\) −17.7275 −1.70583
\(109\) 10.8875 1.04284 0.521418 0.853302i \(-0.325403\pi\)
0.521418 + 0.853302i \(0.325403\pi\)
\(110\) −7.38152 −0.703800
\(111\) −5.55630 −0.527380
\(112\) 24.4054 2.30609
\(113\) −2.91635 −0.274347 −0.137174 0.990547i \(-0.543802\pi\)
−0.137174 + 0.990547i \(0.543802\pi\)
\(114\) 0.314959 0.0294987
\(115\) 5.55870 0.518352
\(116\) 22.7838 2.11542
\(117\) −5.00543 −0.462753
\(118\) −12.4310 −1.14437
\(119\) −20.0237 −1.83557
\(120\) 4.42103 0.403583
\(121\) −2.39606 −0.217824
\(122\) −18.5714 −1.68137
\(123\) 3.05452 0.275417
\(124\) 0.409055 0.0367342
\(125\) −1.00000 −0.0894427
\(126\) 24.4648 2.17950
\(127\) −8.19089 −0.726824 −0.363412 0.931629i \(-0.618388\pi\)
−0.363412 + 0.931629i \(0.618388\pi\)
\(128\) 15.0176 1.32738
\(129\) 6.00833 0.529004
\(130\) 5.17757 0.454103
\(131\) −15.5734 −1.36066 −0.680329 0.732907i \(-0.738163\pi\)
−0.680329 + 0.732907i \(0.738163\pi\)
\(132\) −9.57125 −0.833070
\(133\) −0.664102 −0.0575850
\(134\) −8.13602 −0.702845
\(135\) 4.09148 0.352139
\(136\) 29.4160 2.52240
\(137\) −1.56824 −0.133984 −0.0669918 0.997754i \(-0.521340\pi\)
−0.0669918 + 0.997754i \(0.521340\pi\)
\(138\) 10.5348 0.896778
\(139\) −19.0766 −1.61806 −0.809029 0.587768i \(-0.800007\pi\)
−0.809029 + 0.587768i \(0.800007\pi\)
\(140\) −17.3140 −1.46330
\(141\) 1.85234 0.155995
\(142\) 4.27498 0.358749
\(143\) −6.03500 −0.504672
\(144\) −14.8582 −1.23819
\(145\) −5.25849 −0.436693
\(146\) 30.8072 2.54962
\(147\) 6.75417 0.557074
\(148\) −31.9667 −2.62764
\(149\) −11.0172 −0.902563 −0.451282 0.892382i \(-0.649033\pi\)
−0.451282 + 0.892382i \(0.649033\pi\)
\(150\) −1.89518 −0.154741
\(151\) −10.0933 −0.821378 −0.410689 0.911776i \(-0.634712\pi\)
−0.410689 + 0.911776i \(0.634712\pi\)
\(152\) 0.975602 0.0791318
\(153\) 12.1906 0.985555
\(154\) 29.4969 2.37693
\(155\) −0.0944094 −0.00758315
\(156\) 6.71350 0.537510
\(157\) 11.2029 0.894089 0.447045 0.894512i \(-0.352476\pi\)
0.447045 + 0.894512i \(0.352476\pi\)
\(158\) −12.3099 −0.979322
\(159\) 6.21832 0.493145
\(160\) 3.62836 0.286847
\(161\) −22.2129 −1.75062
\(162\) −10.6126 −0.833804
\(163\) −1.41195 −0.110592 −0.0552961 0.998470i \(-0.517610\pi\)
−0.0552961 + 0.998470i \(0.517610\pi\)
\(164\) 17.5734 1.37225
\(165\) 2.20904 0.171973
\(166\) −20.6805 −1.60512
\(167\) 2.91798 0.225800 0.112900 0.993606i \(-0.463986\pi\)
0.112900 + 0.993606i \(0.463986\pi\)
\(168\) −17.6667 −1.36301
\(169\) −8.76691 −0.674378
\(170\) −12.6099 −0.967133
\(171\) 0.404312 0.0309185
\(172\) 34.5673 2.63573
\(173\) −7.50937 −0.570927 −0.285464 0.958390i \(-0.592148\pi\)
−0.285464 + 0.958390i \(0.592148\pi\)
\(174\) −9.96579 −0.755505
\(175\) 3.99606 0.302073
\(176\) −17.9144 −1.35035
\(177\) 3.72017 0.279625
\(178\) 23.8186 1.78528
\(179\) −20.7665 −1.55216 −0.776080 0.630634i \(-0.782795\pi\)
−0.776080 + 0.630634i \(0.782795\pi\)
\(180\) 10.5409 0.785674
\(181\) 8.69763 0.646490 0.323245 0.946315i \(-0.395226\pi\)
0.323245 + 0.946315i \(0.395226\pi\)
\(182\) −20.6898 −1.53363
\(183\) 5.55778 0.410843
\(184\) 32.6319 2.40566
\(185\) 7.37787 0.542432
\(186\) −0.178923 −0.0131193
\(187\) 14.6981 1.07483
\(188\) 10.6569 0.777236
\(189\) −16.3498 −1.18927
\(190\) −0.418216 −0.0303406
\(191\) −0.397811 −0.0287846 −0.0143923 0.999896i \(-0.504581\pi\)
−0.0143923 + 0.999896i \(0.504581\pi\)
\(192\) −2.32255 −0.167616
\(193\) −23.6175 −1.70002 −0.850012 0.526763i \(-0.823405\pi\)
−0.850012 + 0.526763i \(0.823405\pi\)
\(194\) −46.3090 −3.32480
\(195\) −1.54947 −0.110960
\(196\) 38.8583 2.77559
\(197\) −16.3979 −1.16831 −0.584153 0.811644i \(-0.698573\pi\)
−0.584153 + 0.811644i \(0.698573\pi\)
\(198\) −17.9580 −1.27622
\(199\) −2.20919 −0.156605 −0.0783027 0.996930i \(-0.524950\pi\)
−0.0783027 + 0.996930i \(0.524950\pi\)
\(200\) −5.87042 −0.415101
\(201\) 2.43483 0.171740
\(202\) −18.9357 −1.33231
\(203\) 21.0132 1.47484
\(204\) −16.3506 −1.14477
\(205\) −4.05592 −0.283278
\(206\) 3.78232 0.263527
\(207\) 13.5234 0.939942
\(208\) 12.5656 0.871268
\(209\) 0.487475 0.0337193
\(210\) 7.57325 0.522604
\(211\) −21.4320 −1.47544 −0.737720 0.675107i \(-0.764097\pi\)
−0.737720 + 0.675107i \(0.764097\pi\)
\(212\) 35.7754 2.45707
\(213\) −1.27936 −0.0876601
\(214\) 12.7555 0.871949
\(215\) −7.97811 −0.544102
\(216\) 24.0187 1.63427
\(217\) 0.377265 0.0256104
\(218\) −27.3984 −1.85566
\(219\) −9.21954 −0.622999
\(220\) 12.7091 0.856847
\(221\) −10.3096 −0.693500
\(222\) 13.9824 0.938438
\(223\) 22.0336 1.47548 0.737739 0.675086i \(-0.235894\pi\)
0.737739 + 0.675086i \(0.235894\pi\)
\(224\) −14.4991 −0.968763
\(225\) −2.43284 −0.162189
\(226\) 7.33900 0.488183
\(227\) −13.2707 −0.880810 −0.440405 0.897799i \(-0.645165\pi\)
−0.440405 + 0.897799i \(0.645165\pi\)
\(228\) −0.542280 −0.0359134
\(229\) −18.6307 −1.23115 −0.615576 0.788078i \(-0.711077\pi\)
−0.615576 + 0.788078i \(0.711077\pi\)
\(230\) −13.9885 −0.922373
\(231\) −8.82743 −0.580802
\(232\) −30.8695 −2.02668
\(233\) 12.4126 0.813174 0.406587 0.913612i \(-0.366719\pi\)
0.406587 + 0.913612i \(0.366719\pi\)
\(234\) 12.5962 0.823438
\(235\) −2.45961 −0.160447
\(236\) 21.4030 1.39322
\(237\) 3.68393 0.239297
\(238\) 50.3898 3.26628
\(239\) −15.6207 −1.01042 −0.505210 0.862997i \(-0.668585\pi\)
−0.505210 + 0.862997i \(0.668585\pi\)
\(240\) −4.59948 −0.296895
\(241\) 12.3797 0.797449 0.398724 0.917071i \(-0.369453\pi\)
0.398724 + 0.917071i \(0.369453\pi\)
\(242\) 6.02969 0.387603
\(243\) 15.4504 0.991146
\(244\) 31.9752 2.04700
\(245\) −8.96846 −0.572974
\(246\) −7.68671 −0.490087
\(247\) −0.341926 −0.0217562
\(248\) −0.554223 −0.0351932
\(249\) 6.18896 0.392209
\(250\) 2.51650 0.159157
\(251\) −4.49831 −0.283930 −0.141965 0.989872i \(-0.545342\pi\)
−0.141965 + 0.989872i \(0.545342\pi\)
\(252\) −42.1221 −2.65344
\(253\) 16.3051 1.02509
\(254\) 20.6124 1.29334
\(255\) 3.77370 0.236319
\(256\) −31.6237 −1.97648
\(257\) −23.6484 −1.47515 −0.737573 0.675267i \(-0.764028\pi\)
−0.737573 + 0.675267i \(0.764028\pi\)
\(258\) −15.1200 −0.941328
\(259\) −29.4824 −1.83195
\(260\) −8.91445 −0.552851
\(261\) −12.7930 −0.791869
\(262\) 39.1906 2.42120
\(263\) −29.8265 −1.83918 −0.919591 0.392877i \(-0.871480\pi\)
−0.919591 + 0.392877i \(0.871480\pi\)
\(264\) 12.9680 0.798123
\(265\) −8.25694 −0.507220
\(266\) 1.67121 0.102469
\(267\) −7.12809 −0.436232
\(268\) 14.0082 0.855685
\(269\) 10.8485 0.661447 0.330724 0.943728i \(-0.392707\pi\)
0.330724 + 0.943728i \(0.392707\pi\)
\(270\) −10.2962 −0.626608
\(271\) −19.2702 −1.17058 −0.585291 0.810823i \(-0.699020\pi\)
−0.585291 + 0.810823i \(0.699020\pi\)
\(272\) −30.6033 −1.85560
\(273\) 6.19176 0.374743
\(274\) 3.94647 0.238415
\(275\) −2.93325 −0.176881
\(276\) −18.1382 −1.09179
\(277\) −10.9023 −0.655058 −0.327529 0.944841i \(-0.606216\pi\)
−0.327529 + 0.944841i \(0.606216\pi\)
\(278\) 48.0063 2.87923
\(279\) −0.229683 −0.0137507
\(280\) 23.4585 1.40192
\(281\) −17.7515 −1.05896 −0.529482 0.848321i \(-0.677614\pi\)
−0.529482 + 0.848321i \(0.677614\pi\)
\(282\) −4.66141 −0.277583
\(283\) 8.34685 0.496169 0.248085 0.968738i \(-0.420199\pi\)
0.248085 + 0.968738i \(0.420199\pi\)
\(284\) −7.36044 −0.436761
\(285\) 0.125158 0.00741370
\(286\) 15.1871 0.898031
\(287\) 16.2077 0.956709
\(288\) 8.82720 0.520148
\(289\) 8.10889 0.476994
\(290\) 13.2330 0.777067
\(291\) 13.8587 0.812412
\(292\) −53.0422 −3.10406
\(293\) 3.98033 0.232533 0.116267 0.993218i \(-0.462907\pi\)
0.116267 + 0.993218i \(0.462907\pi\)
\(294\) −16.9969 −0.991277
\(295\) −4.93979 −0.287606
\(296\) 43.3112 2.51741
\(297\) 12.0013 0.696388
\(298\) 27.7248 1.60605
\(299\) −11.4367 −0.661404
\(300\) 3.26302 0.188391
\(301\) 31.8810 1.83759
\(302\) 25.3997 1.46159
\(303\) 5.66682 0.325550
\(304\) −1.01498 −0.0582132
\(305\) −7.37984 −0.422568
\(306\) −30.6778 −1.75373
\(307\) −12.1070 −0.690982 −0.345491 0.938422i \(-0.612288\pi\)
−0.345491 + 0.938422i \(0.612288\pi\)
\(308\) −50.7862 −2.89381
\(309\) −1.13192 −0.0643926
\(310\) 0.237581 0.0134937
\(311\) −3.74541 −0.212383 −0.106191 0.994346i \(-0.533866\pi\)
−0.106191 + 0.994346i \(0.533866\pi\)
\(312\) −9.09604 −0.514962
\(313\) −1.79610 −0.101521 −0.0507607 0.998711i \(-0.516165\pi\)
−0.0507607 + 0.998711i \(0.516165\pi\)
\(314\) −28.1921 −1.59097
\(315\) 9.72175 0.547759
\(316\) 21.1945 1.19228
\(317\) −1.74388 −0.0979463 −0.0489732 0.998800i \(-0.515595\pi\)
−0.0489732 + 0.998800i \(0.515595\pi\)
\(318\) −15.6484 −0.877519
\(319\) −15.4244 −0.863603
\(320\) 3.08398 0.172400
\(321\) −3.81729 −0.213060
\(322\) 55.8987 3.11511
\(323\) 0.832755 0.0463357
\(324\) 18.2722 1.01512
\(325\) 2.05745 0.114127
\(326\) 3.55316 0.196792
\(327\) 8.19942 0.453429
\(328\) −23.8100 −1.31468
\(329\) 9.82874 0.541876
\(330\) −5.55904 −0.306015
\(331\) 5.32362 0.292613 0.146306 0.989239i \(-0.453261\pi\)
0.146306 + 0.989239i \(0.453261\pi\)
\(332\) 35.6065 1.95416
\(333\) 17.9492 0.983608
\(334\) −7.34309 −0.401796
\(335\) −3.23307 −0.176642
\(336\) 18.3798 1.00270
\(337\) 1.73739 0.0946417 0.0473208 0.998880i \(-0.484932\pi\)
0.0473208 + 0.998880i \(0.484932\pi\)
\(338\) 22.0619 1.20001
\(339\) −2.19631 −0.119287
\(340\) 21.7110 1.17744
\(341\) −0.276926 −0.0149964
\(342\) −1.01745 −0.0550174
\(343\) 7.86607 0.424728
\(344\) −46.8349 −2.52517
\(345\) 4.18627 0.225381
\(346\) 18.8973 1.01593
\(347\) 17.4519 0.936869 0.468435 0.883498i \(-0.344818\pi\)
0.468435 + 0.883498i \(0.344818\pi\)
\(348\) 17.1586 0.919795
\(349\) −22.4777 −1.20320 −0.601601 0.798797i \(-0.705470\pi\)
−0.601601 + 0.798797i \(0.705470\pi\)
\(350\) −10.0561 −0.537520
\(351\) −8.41801 −0.449320
\(352\) 10.6429 0.567267
\(353\) 18.8829 1.00504 0.502518 0.864567i \(-0.332407\pi\)
0.502518 + 0.864567i \(0.332407\pi\)
\(354\) −9.36181 −0.497575
\(355\) 1.69878 0.0901620
\(356\) −41.0096 −2.17350
\(357\) −15.0799 −0.798115
\(358\) 52.2589 2.76197
\(359\) −4.32684 −0.228362 −0.114181 0.993460i \(-0.536424\pi\)
−0.114181 + 0.993460i \(0.536424\pi\)
\(360\) −14.2818 −0.752716
\(361\) −18.9724 −0.998546
\(362\) −21.8876 −1.15039
\(363\) −1.80448 −0.0947106
\(364\) 35.6227 1.86713
\(365\) 12.2421 0.640780
\(366\) −13.9861 −0.731067
\(367\) −14.6523 −0.764844 −0.382422 0.923988i \(-0.624910\pi\)
−0.382422 + 0.923988i \(0.624910\pi\)
\(368\) −33.9491 −1.76972
\(369\) −9.86739 −0.513676
\(370\) −18.5664 −0.965222
\(371\) 32.9952 1.71302
\(372\) 0.308060 0.0159722
\(373\) −1.20013 −0.0621403 −0.0310701 0.999517i \(-0.509892\pi\)
−0.0310701 + 0.999517i \(0.509892\pi\)
\(374\) −36.9879 −1.91260
\(375\) −0.753102 −0.0388900
\(376\) −14.4389 −0.744632
\(377\) 10.8191 0.557210
\(378\) 41.1443 2.11623
\(379\) 20.8052 1.06869 0.534346 0.845266i \(-0.320558\pi\)
0.534346 + 0.845266i \(0.320558\pi\)
\(380\) 0.720061 0.0369384
\(381\) −6.16858 −0.316026
\(382\) 1.00109 0.0512202
\(383\) −6.69396 −0.342045 −0.171023 0.985267i \(-0.554707\pi\)
−0.171023 + 0.985267i \(0.554707\pi\)
\(384\) 11.3098 0.577149
\(385\) 11.7214 0.597379
\(386\) 59.4334 3.02508
\(387\) −19.4094 −0.986637
\(388\) 79.7324 4.04780
\(389\) 33.4831 1.69766 0.848830 0.528666i \(-0.177308\pi\)
0.848830 + 0.528666i \(0.177308\pi\)
\(390\) 3.89924 0.197446
\(391\) 27.8540 1.40864
\(392\) −52.6486 −2.65916
\(393\) −11.7284 −0.591619
\(394\) 41.2654 2.07892
\(395\) −4.89167 −0.246127
\(396\) 30.9191 1.55375
\(397\) −21.2884 −1.06843 −0.534216 0.845348i \(-0.679393\pi\)
−0.534216 + 0.845348i \(0.679393\pi\)
\(398\) 5.55943 0.278669
\(399\) −0.500137 −0.0250382
\(400\) 6.10737 0.305369
\(401\) −24.0840 −1.20270 −0.601350 0.798986i \(-0.705370\pi\)
−0.601350 + 0.798986i \(0.705370\pi\)
\(402\) −6.12726 −0.305600
\(403\) 0.194242 0.00967591
\(404\) 32.6025 1.62204
\(405\) −4.21720 −0.209555
\(406\) −52.8797 −2.62438
\(407\) 21.6411 1.07271
\(408\) 22.1532 1.09675
\(409\) −22.8579 −1.13025 −0.565126 0.825005i \(-0.691172\pi\)
−0.565126 + 0.825005i \(0.691172\pi\)
\(410\) 10.2067 0.504074
\(411\) −1.18104 −0.0582566
\(412\) −6.51219 −0.320832
\(413\) 19.7397 0.971327
\(414\) −34.0317 −1.67257
\(415\) −8.21795 −0.403403
\(416\) −7.46516 −0.366009
\(417\) −14.3667 −0.703538
\(418\) −1.22673 −0.0600014
\(419\) 7.91441 0.386644 0.193322 0.981135i \(-0.438074\pi\)
0.193322 + 0.981135i \(0.438074\pi\)
\(420\) −13.0392 −0.636249
\(421\) −28.7996 −1.40361 −0.701804 0.712370i \(-0.747622\pi\)
−0.701804 + 0.712370i \(0.747622\pi\)
\(422\) 53.9336 2.62545
\(423\) −5.98383 −0.290944
\(424\) −48.4717 −2.35399
\(425\) −5.01088 −0.243063
\(426\) 3.21950 0.155985
\(427\) 29.4903 1.42713
\(428\) −21.9618 −1.06156
\(429\) −4.54498 −0.219434
\(430\) 20.0769 0.968194
\(431\) −7.13540 −0.343700 −0.171850 0.985123i \(-0.554974\pi\)
−0.171850 + 0.985123i \(0.554974\pi\)
\(432\) −24.9882 −1.20225
\(433\) 25.3279 1.21718 0.608589 0.793485i \(-0.291736\pi\)
0.608589 + 0.793485i \(0.291736\pi\)
\(434\) −0.949388 −0.0455721
\(435\) −3.96018 −0.189876
\(436\) 47.1731 2.25918
\(437\) 0.923798 0.0441913
\(438\) 23.2010 1.10859
\(439\) −12.0492 −0.575075 −0.287538 0.957769i \(-0.592837\pi\)
−0.287538 + 0.957769i \(0.592837\pi\)
\(440\) −17.2194 −0.820903
\(441\) −21.8188 −1.03899
\(442\) 25.9442 1.23404
\(443\) 4.96577 0.235931 0.117965 0.993018i \(-0.462363\pi\)
0.117965 + 0.993018i \(0.462363\pi\)
\(444\) −24.0742 −1.14251
\(445\) 9.46497 0.448683
\(446\) −55.4475 −2.62552
\(447\) −8.29707 −0.392438
\(448\) −12.3238 −0.582243
\(449\) 16.4040 0.774155 0.387077 0.922047i \(-0.373485\pi\)
0.387077 + 0.922047i \(0.373485\pi\)
\(450\) 6.12223 0.288605
\(451\) −11.8970 −0.560209
\(452\) −12.6359 −0.594342
\(453\) −7.60126 −0.357138
\(454\) 33.3958 1.56734
\(455\) −8.22168 −0.385438
\(456\) 0.734729 0.0344068
\(457\) 31.5273 1.47479 0.737393 0.675464i \(-0.236056\pi\)
0.737393 + 0.675464i \(0.236056\pi\)
\(458\) 46.8842 2.19075
\(459\) 20.5019 0.956948
\(460\) 24.0846 1.12295
\(461\) 2.39850 0.111709 0.0558547 0.998439i \(-0.482212\pi\)
0.0558547 + 0.998439i \(0.482212\pi\)
\(462\) 22.2142 1.03350
\(463\) −21.0691 −0.979165 −0.489582 0.871957i \(-0.662851\pi\)
−0.489582 + 0.871957i \(0.662851\pi\)
\(464\) 32.1155 1.49093
\(465\) −0.0711000 −0.00329718
\(466\) −31.2362 −1.44699
\(467\) 19.1836 0.887709 0.443855 0.896099i \(-0.353611\pi\)
0.443855 + 0.896099i \(0.353611\pi\)
\(468\) −21.6874 −1.00250
\(469\) 12.9195 0.596568
\(470\) 6.18961 0.285505
\(471\) 8.43694 0.388754
\(472\) −28.9987 −1.33477
\(473\) −23.4018 −1.07601
\(474\) −9.27060 −0.425813
\(475\) −0.166190 −0.00762530
\(476\) −86.7583 −3.97656
\(477\) −20.0878 −0.919756
\(478\) 39.3095 1.79798
\(479\) 3.48238 0.159114 0.0795569 0.996830i \(-0.474649\pi\)
0.0795569 + 0.996830i \(0.474649\pi\)
\(480\) 2.73252 0.124722
\(481\) −15.1796 −0.692130
\(482\) −31.1536 −1.41901
\(483\) −16.7286 −0.761177
\(484\) −10.3816 −0.471890
\(485\) −18.4022 −0.835599
\(486\) −38.8810 −1.76368
\(487\) 9.07055 0.411026 0.205513 0.978654i \(-0.434114\pi\)
0.205513 + 0.978654i \(0.434114\pi\)
\(488\) −43.3228 −1.96113
\(489\) −1.06334 −0.0480859
\(490\) 22.5691 1.01957
\(491\) −26.6063 −1.20073 −0.600364 0.799727i \(-0.704977\pi\)
−0.600364 + 0.799727i \(0.704977\pi\)
\(492\) 13.2346 0.596660
\(493\) −26.3496 −1.18673
\(494\) 0.860457 0.0387138
\(495\) −7.13611 −0.320744
\(496\) 0.576593 0.0258898
\(497\) −6.78843 −0.304503
\(498\) −15.5745 −0.697911
\(499\) −25.3493 −1.13479 −0.567396 0.823445i \(-0.692049\pi\)
−0.567396 + 0.823445i \(0.692049\pi\)
\(500\) −4.33277 −0.193767
\(501\) 2.19753 0.0981786
\(502\) 11.3200 0.505236
\(503\) −14.6855 −0.654794 −0.327397 0.944887i \(-0.606172\pi\)
−0.327397 + 0.944887i \(0.606172\pi\)
\(504\) 57.0708 2.54213
\(505\) −7.52463 −0.334842
\(506\) −41.0317 −1.82408
\(507\) −6.60238 −0.293222
\(508\) −35.4893 −1.57458
\(509\) 5.78678 0.256495 0.128247 0.991742i \(-0.459065\pi\)
0.128247 + 0.991742i \(0.459065\pi\)
\(510\) −9.49653 −0.420513
\(511\) −48.9200 −2.16410
\(512\) 49.5460 2.18964
\(513\) 0.679961 0.0300210
\(514\) 59.5112 2.62493
\(515\) 1.50301 0.0662304
\(516\) 26.0327 1.14603
\(517\) −7.21464 −0.317300
\(518\) 74.1925 3.25983
\(519\) −5.65533 −0.248241
\(520\) 12.0781 0.529659
\(521\) −39.6468 −1.73696 −0.868478 0.495727i \(-0.834902\pi\)
−0.868478 + 0.495727i \(0.834902\pi\)
\(522\) 32.1937 1.40908
\(523\) 16.3443 0.714686 0.357343 0.933973i \(-0.383683\pi\)
0.357343 + 0.933973i \(0.383683\pi\)
\(524\) −67.4762 −2.94771
\(525\) 3.00944 0.131343
\(526\) 75.0584 3.27270
\(527\) −0.473074 −0.0206074
\(528\) −13.4914 −0.587138
\(529\) 7.89918 0.343443
\(530\) 20.7786 0.902564
\(531\) −12.0177 −0.521524
\(532\) −2.87740 −0.124751
\(533\) 8.34484 0.361455
\(534\) 17.9378 0.776247
\(535\) 5.06875 0.219141
\(536\) −18.9795 −0.819789
\(537\) −15.6393 −0.674886
\(538\) −27.3003 −1.17700
\(539\) −26.3067 −1.13311
\(540\) 17.7275 0.762869
\(541\) 28.8949 1.24229 0.621144 0.783696i \(-0.286668\pi\)
0.621144 + 0.783696i \(0.286668\pi\)
\(542\) 48.4935 2.08298
\(543\) 6.55021 0.281096
\(544\) 18.1813 0.779515
\(545\) −10.8875 −0.466370
\(546\) −15.5816 −0.666830
\(547\) 34.4502 1.47299 0.736493 0.676445i \(-0.236480\pi\)
0.736493 + 0.676445i \(0.236480\pi\)
\(548\) −6.79482 −0.290260
\(549\) −17.9539 −0.766256
\(550\) 7.38152 0.314749
\(551\) −0.873905 −0.0372296
\(552\) 24.5752 1.04599
\(553\) 19.5474 0.831239
\(554\) 27.4357 1.16563
\(555\) 5.55630 0.235852
\(556\) −82.6547 −3.50534
\(557\) −37.2548 −1.57854 −0.789268 0.614048i \(-0.789540\pi\)
−0.789268 + 0.614048i \(0.789540\pi\)
\(558\) 0.577997 0.0244685
\(559\) 16.4145 0.694261
\(560\) −24.4054 −1.03132
\(561\) 11.0692 0.467342
\(562\) 44.6716 1.88436
\(563\) 10.2636 0.432558 0.216279 0.976332i \(-0.430608\pi\)
0.216279 + 0.976332i \(0.430608\pi\)
\(564\) 8.02576 0.337945
\(565\) 2.91635 0.122692
\(566\) −21.0049 −0.882900
\(567\) 16.8522 0.707725
\(568\) 9.97257 0.418440
\(569\) 24.6216 1.03219 0.516095 0.856532i \(-0.327385\pi\)
0.516095 + 0.856532i \(0.327385\pi\)
\(570\) −0.314959 −0.0131922
\(571\) −1.75610 −0.0734905 −0.0367452 0.999325i \(-0.511699\pi\)
−0.0367452 + 0.999325i \(0.511699\pi\)
\(572\) −26.1483 −1.09332
\(573\) −0.299592 −0.0125156
\(574\) −40.7866 −1.70240
\(575\) −5.55870 −0.231814
\(576\) 7.50283 0.312618
\(577\) −43.3354 −1.80407 −0.902037 0.431658i \(-0.857929\pi\)
−0.902037 + 0.431658i \(0.857929\pi\)
\(578\) −20.4060 −0.848779
\(579\) −17.7864 −0.739177
\(580\) −22.7838 −0.946047
\(581\) 32.8394 1.36241
\(582\) −34.8755 −1.44563
\(583\) −24.2196 −1.00307
\(584\) 71.8662 2.97384
\(585\) 5.00543 0.206949
\(586\) −10.0165 −0.413778
\(587\) 21.2092 0.875397 0.437698 0.899122i \(-0.355794\pi\)
0.437698 + 0.899122i \(0.355794\pi\)
\(588\) 29.2643 1.20684
\(589\) −0.0156899 −0.000646489 0
\(590\) 12.4310 0.511776
\(591\) −12.3493 −0.507984
\(592\) −45.0594 −1.85193
\(593\) 35.8639 1.47276 0.736378 0.676571i \(-0.236535\pi\)
0.736378 + 0.676571i \(0.236535\pi\)
\(594\) −30.2013 −1.23918
\(595\) 20.0237 0.820893
\(596\) −47.7350 −1.95530
\(597\) −1.66375 −0.0680926
\(598\) 28.7806 1.17692
\(599\) 41.4774 1.69472 0.847361 0.531018i \(-0.178190\pi\)
0.847361 + 0.531018i \(0.178190\pi\)
\(600\) −4.42103 −0.180488
\(601\) 19.6940 0.803334 0.401667 0.915786i \(-0.368431\pi\)
0.401667 + 0.915786i \(0.368431\pi\)
\(602\) −80.2284 −3.26987
\(603\) −7.86553 −0.320309
\(604\) −43.7318 −1.77942
\(605\) 2.39606 0.0974137
\(606\) −14.2605 −0.579295
\(607\) 1.75836 0.0713695 0.0356848 0.999363i \(-0.488639\pi\)
0.0356848 + 0.999363i \(0.488639\pi\)
\(608\) 0.602995 0.0244547
\(609\) 15.8251 0.641265
\(610\) 18.5714 0.751933
\(611\) 5.06052 0.204727
\(612\) 52.8193 2.13509
\(613\) 16.5802 0.669670 0.334835 0.942277i \(-0.391319\pi\)
0.334835 + 0.942277i \(0.391319\pi\)
\(614\) 30.4672 1.22956
\(615\) −3.05452 −0.123170
\(616\) 68.8097 2.77242
\(617\) 12.2308 0.492392 0.246196 0.969220i \(-0.420819\pi\)
0.246196 + 0.969220i \(0.420819\pi\)
\(618\) 2.84847 0.114582
\(619\) 21.0497 0.846061 0.423030 0.906115i \(-0.360966\pi\)
0.423030 + 0.906115i \(0.360966\pi\)
\(620\) −0.409055 −0.0164280
\(621\) 22.7433 0.912659
\(622\) 9.42532 0.377921
\(623\) −37.8226 −1.51533
\(624\) 9.46318 0.378831
\(625\) 1.00000 0.0400000
\(626\) 4.51988 0.180651
\(627\) 0.367119 0.0146613
\(628\) 48.5396 1.93694
\(629\) 36.9696 1.47408
\(630\) −24.4648 −0.974700
\(631\) −12.1107 −0.482120 −0.241060 0.970510i \(-0.577495\pi\)
−0.241060 + 0.970510i \(0.577495\pi\)
\(632\) −28.7162 −1.14227
\(633\) −16.1405 −0.641527
\(634\) 4.38849 0.174289
\(635\) 8.19089 0.325046
\(636\) 26.9426 1.06834
\(637\) 18.4521 0.731100
\(638\) 38.8156 1.53672
\(639\) 4.13286 0.163493
\(640\) −15.0176 −0.593621
\(641\) 12.0727 0.476844 0.238422 0.971162i \(-0.423370\pi\)
0.238422 + 0.971162i \(0.423370\pi\)
\(642\) 9.60621 0.379127
\(643\) 4.59818 0.181335 0.0906674 0.995881i \(-0.471100\pi\)
0.0906674 + 0.995881i \(0.471100\pi\)
\(644\) −96.2434 −3.79252
\(645\) −6.00833 −0.236578
\(646\) −2.09563 −0.0824514
\(647\) 22.5734 0.887454 0.443727 0.896162i \(-0.353656\pi\)
0.443727 + 0.896162i \(0.353656\pi\)
\(648\) −24.7568 −0.972538
\(649\) −14.4896 −0.568768
\(650\) −5.17757 −0.203081
\(651\) 0.284119 0.0111355
\(652\) −6.11764 −0.239585
\(653\) −26.5754 −1.03998 −0.519988 0.854173i \(-0.674064\pi\)
−0.519988 + 0.854173i \(0.674064\pi\)
\(654\) −20.6338 −0.806847
\(655\) 15.5734 0.608505
\(656\) 24.7710 0.967145
\(657\) 29.7830 1.16194
\(658\) −24.7340 −0.964232
\(659\) 45.8432 1.78580 0.892899 0.450256i \(-0.148667\pi\)
0.892899 + 0.450256i \(0.148667\pi\)
\(660\) 9.57125 0.372560
\(661\) −8.43433 −0.328058 −0.164029 0.986456i \(-0.552449\pi\)
−0.164029 + 0.986456i \(0.552449\pi\)
\(662\) −13.3969 −0.520685
\(663\) −7.76420 −0.301537
\(664\) −48.2428 −1.87219
\(665\) 0.664102 0.0257528
\(666\) −45.1691 −1.75027
\(667\) −29.2304 −1.13180
\(668\) 12.6429 0.489169
\(669\) 16.5935 0.641543
\(670\) 8.13602 0.314322
\(671\) −21.6469 −0.835669
\(672\) −10.9193 −0.421222
\(673\) −3.27540 −0.126258 −0.0631288 0.998005i \(-0.520108\pi\)
−0.0631288 + 0.998005i \(0.520108\pi\)
\(674\) −4.37214 −0.168409
\(675\) −4.09148 −0.157481
\(676\) −37.9850 −1.46096
\(677\) 46.5928 1.79071 0.895353 0.445356i \(-0.146923\pi\)
0.895353 + 0.445356i \(0.146923\pi\)
\(678\) 5.52702 0.212264
\(679\) 73.5361 2.82206
\(680\) −29.4160 −1.12805
\(681\) −9.99423 −0.382980
\(682\) 0.696885 0.0266851
\(683\) −18.1601 −0.694879 −0.347439 0.937702i \(-0.612949\pi\)
−0.347439 + 0.937702i \(0.612949\pi\)
\(684\) 1.75179 0.0669814
\(685\) 1.56824 0.0599193
\(686\) −19.7950 −0.755776
\(687\) −14.0308 −0.535310
\(688\) 48.7253 1.85763
\(689\) 16.9882 0.647199
\(690\) −10.5348 −0.401051
\(691\) −39.9667 −1.52041 −0.760203 0.649685i \(-0.774901\pi\)
−0.760203 + 0.649685i \(0.774901\pi\)
\(692\) −32.5364 −1.23685
\(693\) 28.5163 1.08324
\(694\) −43.9178 −1.66710
\(695\) 19.0766 0.723618
\(696\) −23.2479 −0.881210
\(697\) −20.3237 −0.769816
\(698\) 56.5651 2.14102
\(699\) 9.34793 0.353571
\(700\) 17.3140 0.654408
\(701\) −40.5683 −1.53225 −0.766123 0.642694i \(-0.777817\pi\)
−0.766123 + 0.642694i \(0.777817\pi\)
\(702\) 21.1839 0.799536
\(703\) 1.22613 0.0462442
\(704\) 9.04608 0.340937
\(705\) −1.85234 −0.0697631
\(706\) −47.5188 −1.78839
\(707\) 30.0688 1.13086
\(708\) 16.1187 0.605776
\(709\) −32.3272 −1.21407 −0.607037 0.794674i \(-0.707642\pi\)
−0.607037 + 0.794674i \(0.707642\pi\)
\(710\) −4.27498 −0.160437
\(711\) −11.9006 −0.446309
\(712\) 55.5634 2.08233
\(713\) −0.524794 −0.0196537
\(714\) 37.9486 1.42019
\(715\) 6.03500 0.225696
\(716\) −89.9765 −3.36258
\(717\) −11.7640 −0.439334
\(718\) 10.8885 0.406355
\(719\) −22.5771 −0.841983 −0.420992 0.907065i \(-0.638318\pi\)
−0.420992 + 0.907065i \(0.638318\pi\)
\(720\) 14.8582 0.553734
\(721\) −6.00610 −0.223679
\(722\) 47.7440 1.77685
\(723\) 9.32321 0.346734
\(724\) 37.6849 1.40055
\(725\) 5.25849 0.195295
\(726\) 4.54097 0.168531
\(727\) 38.4524 1.42612 0.713059 0.701104i \(-0.247309\pi\)
0.713059 + 0.701104i \(0.247309\pi\)
\(728\) −48.2647 −1.78881
\(729\) −1.01585 −0.0376241
\(730\) −30.8072 −1.14023
\(731\) −39.9773 −1.47861
\(732\) 24.0806 0.890044
\(733\) 46.6025 1.72130 0.860652 0.509194i \(-0.170057\pi\)
0.860652 + 0.509194i \(0.170057\pi\)
\(734\) 36.8725 1.36099
\(735\) −6.75417 −0.249131
\(736\) 20.1690 0.743438
\(737\) −9.48340 −0.349325
\(738\) 24.8313 0.914052
\(739\) 23.0438 0.847681 0.423841 0.905737i \(-0.360682\pi\)
0.423841 + 0.905737i \(0.360682\pi\)
\(740\) 31.9667 1.17512
\(741\) −0.257506 −0.00945970
\(742\) −83.0324 −3.04821
\(743\) 19.3194 0.708760 0.354380 0.935102i \(-0.384692\pi\)
0.354380 + 0.935102i \(0.384692\pi\)
\(744\) −0.417387 −0.0153021
\(745\) 11.0172 0.403638
\(746\) 3.02012 0.110575
\(747\) −19.9929 −0.731503
\(748\) 63.6837 2.32851
\(749\) −20.2550 −0.740102
\(750\) 1.89518 0.0692023
\(751\) −46.3090 −1.68984 −0.844920 0.534893i \(-0.820352\pi\)
−0.844920 + 0.534893i \(0.820352\pi\)
\(752\) 15.0217 0.547787
\(753\) −3.38768 −0.123454
\(754\) −27.2262 −0.991519
\(755\) 10.0933 0.367331
\(756\) −70.8399 −2.57642
\(757\) −36.9789 −1.34402 −0.672011 0.740541i \(-0.734569\pi\)
−0.672011 + 0.740541i \(0.734569\pi\)
\(758\) −52.3564 −1.90167
\(759\) 12.2794 0.445713
\(760\) −0.975602 −0.0353888
\(761\) −30.0375 −1.08886 −0.544429 0.838807i \(-0.683254\pi\)
−0.544429 + 0.838807i \(0.683254\pi\)
\(762\) 15.5232 0.562347
\(763\) 43.5071 1.57506
\(764\) −1.72362 −0.0623585
\(765\) −12.1906 −0.440754
\(766\) 16.8454 0.608647
\(767\) 10.1634 0.366978
\(768\) −23.8159 −0.859382
\(769\) −49.3885 −1.78100 −0.890498 0.454987i \(-0.849644\pi\)
−0.890498 + 0.454987i \(0.849644\pi\)
\(770\) −29.4969 −1.06300
\(771\) −17.8097 −0.641399
\(772\) −102.329 −3.68291
\(773\) −2.37992 −0.0855996 −0.0427998 0.999084i \(-0.513628\pi\)
−0.0427998 + 0.999084i \(0.513628\pi\)
\(774\) 48.8438 1.75566
\(775\) 0.0944094 0.00339129
\(776\) −108.028 −3.87800
\(777\) −22.2033 −0.796538
\(778\) −84.2602 −3.02087
\(779\) −0.674051 −0.0241504
\(780\) −6.71350 −0.240382
\(781\) 4.98295 0.178304
\(782\) −70.0945 −2.50658
\(783\) −21.5150 −0.768884
\(784\) 54.7737 1.95620
\(785\) −11.2029 −0.399849
\(786\) 29.5145 1.05275
\(787\) −26.1423 −0.931871 −0.465935 0.884819i \(-0.654282\pi\)
−0.465935 + 0.884819i \(0.654282\pi\)
\(788\) −71.0486 −2.53100
\(789\) −22.4624 −0.799683
\(790\) 12.3099 0.437966
\(791\) −11.6539 −0.414365
\(792\) −41.8920 −1.48857
\(793\) 15.1836 0.539187
\(794\) 53.5722 1.90120
\(795\) −6.21832 −0.220541
\(796\) −9.57192 −0.339268
\(797\) −29.4977 −1.04486 −0.522431 0.852681i \(-0.674975\pi\)
−0.522431 + 0.852681i \(0.674975\pi\)
\(798\) 1.25860 0.0445538
\(799\) −12.3248 −0.436020
\(800\) −3.62836 −0.128282
\(801\) 23.0267 0.813610
\(802\) 60.6075 2.14012
\(803\) 35.9091 1.26720
\(804\) 10.5496 0.372055
\(805\) 22.2129 0.782901
\(806\) −0.488811 −0.0172176
\(807\) 8.17006 0.287600
\(808\) −44.1728 −1.55399
\(809\) −2.41340 −0.0848507 −0.0424254 0.999100i \(-0.513508\pi\)
−0.0424254 + 0.999100i \(0.513508\pi\)
\(810\) 10.6126 0.372889
\(811\) −17.9036 −0.628682 −0.314341 0.949310i \(-0.601784\pi\)
−0.314341 + 0.949310i \(0.601784\pi\)
\(812\) 91.0454 3.19507
\(813\) −14.5125 −0.508974
\(814\) −54.4599 −1.90882
\(815\) 1.41195 0.0494583
\(816\) −23.0474 −0.806821
\(817\) −1.32588 −0.0463866
\(818\) 57.5220 2.01121
\(819\) −20.0020 −0.698926
\(820\) −17.5734 −0.613689
\(821\) −44.1546 −1.54100 −0.770502 0.637437i \(-0.779995\pi\)
−0.770502 + 0.637437i \(0.779995\pi\)
\(822\) 2.97210 0.103664
\(823\) −43.2535 −1.50772 −0.753862 0.657033i \(-0.771811\pi\)
−0.753862 + 0.657033i \(0.771811\pi\)
\(824\) 8.82328 0.307374
\(825\) −2.20904 −0.0769088
\(826\) −49.6749 −1.72841
\(827\) 11.0394 0.383876 0.191938 0.981407i \(-0.438523\pi\)
0.191938 + 0.981407i \(0.438523\pi\)
\(828\) 58.5939 2.03628
\(829\) −41.4653 −1.44015 −0.720075 0.693896i \(-0.755893\pi\)
−0.720075 + 0.693896i \(0.755893\pi\)
\(830\) 20.6805 0.717830
\(831\) −8.21057 −0.284822
\(832\) −6.34513 −0.219978
\(833\) −44.9398 −1.55707
\(834\) 36.1537 1.25190
\(835\) −2.91798 −0.100981
\(836\) 2.11212 0.0730491
\(837\) −0.386275 −0.0133516
\(838\) −19.9166 −0.688008
\(839\) 35.7175 1.23310 0.616552 0.787314i \(-0.288529\pi\)
0.616552 + 0.787314i \(0.288529\pi\)
\(840\) 17.6667 0.609558
\(841\) −1.34833 −0.0464941
\(842\) 72.4743 2.49763
\(843\) −13.3687 −0.460442
\(844\) −92.8600 −3.19637
\(845\) 8.76691 0.301591
\(846\) 15.0583 0.517715
\(847\) −9.57479 −0.328994
\(848\) 50.4282 1.73171
\(849\) 6.28604 0.215736
\(850\) 12.6099 0.432515
\(851\) 41.0114 1.40585
\(852\) −5.54316 −0.189906
\(853\) −34.4609 −1.17992 −0.589959 0.807433i \(-0.700856\pi\)
−0.589959 + 0.807433i \(0.700856\pi\)
\(854\) −74.2122 −2.53949
\(855\) −0.404312 −0.0138272
\(856\) 29.7557 1.01703
\(857\) 7.94566 0.271419 0.135709 0.990749i \(-0.456669\pi\)
0.135709 + 0.990749i \(0.456669\pi\)
\(858\) 11.4374 0.390468
\(859\) −13.7030 −0.467541 −0.233771 0.972292i \(-0.575106\pi\)
−0.233771 + 0.972292i \(0.575106\pi\)
\(860\) −34.5673 −1.17874
\(861\) 12.2060 0.415981
\(862\) 17.9562 0.611592
\(863\) 11.8714 0.404109 0.202054 0.979374i \(-0.435238\pi\)
0.202054 + 0.979374i \(0.435238\pi\)
\(864\) 14.8454 0.505049
\(865\) 7.50937 0.255326
\(866\) −63.7375 −2.16589
\(867\) 6.10683 0.207399
\(868\) 1.63460 0.0554821
\(869\) −14.3485 −0.486739
\(870\) 9.96579 0.337872
\(871\) 6.65188 0.225390
\(872\) −63.9143 −2.16441
\(873\) −44.7695 −1.51522
\(874\) −2.32474 −0.0786354
\(875\) −3.99606 −0.135091
\(876\) −39.9462 −1.34966
\(877\) 55.0907 1.86028 0.930140 0.367205i \(-0.119685\pi\)
0.930140 + 0.367205i \(0.119685\pi\)
\(878\) 30.3217 1.02331
\(879\) 2.99759 0.101106
\(880\) 17.9144 0.603895
\(881\) 37.5632 1.26554 0.632768 0.774342i \(-0.281919\pi\)
0.632768 + 0.774342i \(0.281919\pi\)
\(882\) 54.9070 1.84881
\(883\) 31.4013 1.05674 0.528368 0.849015i \(-0.322804\pi\)
0.528368 + 0.849015i \(0.322804\pi\)
\(884\) −44.6692 −1.50239
\(885\) −3.72017 −0.125052
\(886\) −12.4964 −0.419823
\(887\) −41.8321 −1.40459 −0.702293 0.711888i \(-0.747840\pi\)
−0.702293 + 0.711888i \(0.747840\pi\)
\(888\) 32.6178 1.09458
\(889\) −32.7312 −1.09777
\(890\) −23.8186 −0.798401
\(891\) −12.3701 −0.414414
\(892\) 95.4665 3.19645
\(893\) −0.408761 −0.0136787
\(894\) 20.8796 0.698318
\(895\) 20.7665 0.694147
\(896\) 60.0110 2.00483
\(897\) −8.61304 −0.287581
\(898\) −41.2808 −1.37756
\(899\) 0.496451 0.0165576
\(900\) −10.5409 −0.351364
\(901\) −41.3745 −1.37838
\(902\) 29.9388 0.996854
\(903\) 24.0096 0.798990
\(904\) 17.1202 0.569410
\(905\) −8.69763 −0.289119
\(906\) 19.1286 0.635504
\(907\) −14.4937 −0.481254 −0.240627 0.970618i \(-0.577353\pi\)
−0.240627 + 0.970618i \(0.577353\pi\)
\(908\) −57.4991 −1.90818
\(909\) −18.3062 −0.607178
\(910\) 20.6898 0.685862
\(911\) 1.14461 0.0379226 0.0189613 0.999820i \(-0.493964\pi\)
0.0189613 + 0.999820i \(0.493964\pi\)
\(912\) −0.764385 −0.0253113
\(913\) −24.1053 −0.797769
\(914\) −79.3385 −2.62429
\(915\) −5.55778 −0.183734
\(916\) −80.7226 −2.66715
\(917\) −62.2323 −2.05509
\(918\) −51.5931 −1.70283
\(919\) −24.1791 −0.797596 −0.398798 0.917039i \(-0.630573\pi\)
−0.398798 + 0.917039i \(0.630573\pi\)
\(920\) −32.6319 −1.07584
\(921\) −9.11779 −0.300442
\(922\) −6.03583 −0.198780
\(923\) −3.49516 −0.115044
\(924\) −38.2472 −1.25824
\(925\) −7.37787 −0.242583
\(926\) 53.0204 1.74236
\(927\) 3.65657 0.120098
\(928\) −19.0797 −0.626321
\(929\) −12.9899 −0.426184 −0.213092 0.977032i \(-0.568353\pi\)
−0.213092 + 0.977032i \(0.568353\pi\)
\(930\) 0.178923 0.00586712
\(931\) −1.49046 −0.0488480
\(932\) 53.7808 1.76165
\(933\) −2.82068 −0.0923448
\(934\) −48.2754 −1.57962
\(935\) −14.6981 −0.480681
\(936\) 29.3840 0.960447
\(937\) −35.6713 −1.16533 −0.582664 0.812713i \(-0.697990\pi\)
−0.582664 + 0.812713i \(0.697990\pi\)
\(938\) −32.5120 −1.06155
\(939\) −1.35265 −0.0441419
\(940\) −10.6569 −0.347591
\(941\) −50.3647 −1.64184 −0.820922 0.571041i \(-0.806540\pi\)
−0.820922 + 0.571041i \(0.806540\pi\)
\(942\) −21.2316 −0.691761
\(943\) −22.5457 −0.734188
\(944\) 30.1692 0.981922
\(945\) 16.3498 0.531859
\(946\) 58.8905 1.91470
\(947\) −0.334759 −0.0108782 −0.00543911 0.999985i \(-0.501731\pi\)
−0.00543911 + 0.999985i \(0.501731\pi\)
\(948\) 15.9616 0.518409
\(949\) −25.1874 −0.817619
\(950\) 0.418216 0.0135687
\(951\) −1.31332 −0.0425874
\(952\) 117.548 3.80975
\(953\) 3.28444 0.106393 0.0531967 0.998584i \(-0.483059\pi\)
0.0531967 + 0.998584i \(0.483059\pi\)
\(954\) 50.5509 1.63665
\(955\) 0.397811 0.0128728
\(956\) −67.6810 −2.18896
\(957\) −11.6162 −0.375498
\(958\) −8.76340 −0.283133
\(959\) −6.26677 −0.202364
\(960\) 2.32255 0.0749601
\(961\) −30.9911 −0.999712
\(962\) 38.1994 1.23160
\(963\) 12.3315 0.397375
\(964\) 53.6386 1.72758
\(965\) 23.6175 0.760274
\(966\) 42.0975 1.35446
\(967\) −44.6783 −1.43676 −0.718379 0.695652i \(-0.755116\pi\)
−0.718379 + 0.695652i \(0.755116\pi\)
\(968\) 14.0659 0.452095
\(969\) 0.627150 0.0201470
\(970\) 46.3090 1.48689
\(971\) 13.5657 0.435343 0.217671 0.976022i \(-0.430154\pi\)
0.217671 + 0.976022i \(0.430154\pi\)
\(972\) 66.9432 2.14720
\(973\) −76.2313 −2.44386
\(974\) −22.8260 −0.731393
\(975\) 1.54947 0.0496227
\(976\) 45.0714 1.44270
\(977\) −2.71231 −0.0867745 −0.0433872 0.999058i \(-0.513815\pi\)
−0.0433872 + 0.999058i \(0.513815\pi\)
\(978\) 2.67590 0.0855658
\(979\) 27.7631 0.887313
\(980\) −38.8583 −1.24128
\(981\) −26.4876 −0.845682
\(982\) 66.9548 2.13661
\(983\) 55.4615 1.76895 0.884473 0.466591i \(-0.154518\pi\)
0.884473 + 0.466591i \(0.154518\pi\)
\(984\) −17.9313 −0.571630
\(985\) 16.3979 0.522482
\(986\) 66.3088 2.11170
\(987\) 7.40204 0.235610
\(988\) −1.48149 −0.0471324
\(989\) −44.3479 −1.41018
\(990\) 17.9580 0.570743
\(991\) 22.7289 0.722007 0.361004 0.932564i \(-0.382434\pi\)
0.361004 + 0.932564i \(0.382434\pi\)
\(992\) −0.342551 −0.0108760
\(993\) 4.00923 0.127229
\(994\) 17.0831 0.541842
\(995\) 2.20919 0.0700360
\(996\) 26.8154 0.849677
\(997\) −16.7659 −0.530982 −0.265491 0.964113i \(-0.585534\pi\)
−0.265491 + 0.964113i \(0.585534\pi\)
\(998\) 63.7916 2.01929
\(999\) 30.1864 0.955057
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 8005.2.a.f.1.9 127
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8005.2.a.f.1.9 127 1.1 even 1 trivial