Properties

Label 8027.2.a.d.1.6
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $149$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60291 q^{2} +2.78039 q^{3} +4.77512 q^{4} -1.36371 q^{5} -7.23709 q^{6} -4.03414 q^{7} -7.22339 q^{8} +4.73056 q^{9} +O(q^{10})\) \(q-2.60291 q^{2} +2.78039 q^{3} +4.77512 q^{4} -1.36371 q^{5} -7.23709 q^{6} -4.03414 q^{7} -7.22339 q^{8} +4.73056 q^{9} +3.54962 q^{10} -3.33382 q^{11} +13.2767 q^{12} +3.04561 q^{13} +10.5005 q^{14} -3.79165 q^{15} +9.25157 q^{16} +0.158916 q^{17} -12.3132 q^{18} -4.36044 q^{19} -6.51190 q^{20} -11.2165 q^{21} +8.67763 q^{22} -1.00000 q^{23} -20.0838 q^{24} -3.14029 q^{25} -7.92743 q^{26} +4.81163 q^{27} -19.2635 q^{28} +7.56463 q^{29} +9.86931 q^{30} +8.19797 q^{31} -9.63419 q^{32} -9.26932 q^{33} -0.413643 q^{34} +5.50141 q^{35} +22.5890 q^{36} -6.78196 q^{37} +11.3498 q^{38} +8.46797 q^{39} +9.85063 q^{40} +6.49295 q^{41} +29.1955 q^{42} +4.80654 q^{43} -15.9194 q^{44} -6.45112 q^{45} +2.60291 q^{46} +10.2963 q^{47} +25.7230 q^{48} +9.27430 q^{49} +8.17388 q^{50} +0.441847 q^{51} +14.5431 q^{52} -0.354937 q^{53} -12.5242 q^{54} +4.54637 q^{55} +29.1402 q^{56} -12.1237 q^{57} -19.6900 q^{58} +14.2564 q^{59} -18.1056 q^{60} +8.78484 q^{61} -21.3386 q^{62} -19.0838 q^{63} +6.57376 q^{64} -4.15333 q^{65} +24.1272 q^{66} -15.5705 q^{67} +0.758842 q^{68} -2.78039 q^{69} -14.3197 q^{70} -12.1475 q^{71} -34.1707 q^{72} -1.66239 q^{73} +17.6528 q^{74} -8.73122 q^{75} -20.8216 q^{76} +13.4491 q^{77} -22.0413 q^{78} +16.4330 q^{79} -12.6165 q^{80} -0.813484 q^{81} -16.9005 q^{82} +4.08140 q^{83} -53.5601 q^{84} -0.216715 q^{85} -12.5110 q^{86} +21.0326 q^{87} +24.0815 q^{88} -2.58156 q^{89} +16.7917 q^{90} -12.2864 q^{91} -4.77512 q^{92} +22.7935 q^{93} -26.8003 q^{94} +5.94638 q^{95} -26.7868 q^{96} -12.3407 q^{97} -24.1401 q^{98} -15.7708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60291 −1.84053 −0.920267 0.391292i \(-0.872028\pi\)
−0.920267 + 0.391292i \(0.872028\pi\)
\(3\) 2.78039 1.60526 0.802629 0.596479i \(-0.203434\pi\)
0.802629 + 0.596479i \(0.203434\pi\)
\(4\) 4.77512 2.38756
\(5\) −1.36371 −0.609871 −0.304935 0.952373i \(-0.598635\pi\)
−0.304935 + 0.952373i \(0.598635\pi\)
\(6\) −7.23709 −2.95453
\(7\) −4.03414 −1.52476 −0.762381 0.647128i \(-0.775970\pi\)
−0.762381 + 0.647128i \(0.775970\pi\)
\(8\) −7.22339 −2.55385
\(9\) 4.73056 1.57685
\(10\) 3.54962 1.12249
\(11\) −3.33382 −1.00518 −0.502592 0.864523i \(-0.667620\pi\)
−0.502592 + 0.864523i \(0.667620\pi\)
\(12\) 13.2767 3.83265
\(13\) 3.04561 0.844699 0.422350 0.906433i \(-0.361205\pi\)
0.422350 + 0.906433i \(0.361205\pi\)
\(14\) 10.5005 2.80638
\(15\) −3.79165 −0.979000
\(16\) 9.25157 2.31289
\(17\) 0.158916 0.0385427 0.0192714 0.999814i \(-0.493865\pi\)
0.0192714 + 0.999814i \(0.493865\pi\)
\(18\) −12.3132 −2.90225
\(19\) −4.36044 −1.00035 −0.500176 0.865924i \(-0.666732\pi\)
−0.500176 + 0.865924i \(0.666732\pi\)
\(20\) −6.51190 −1.45610
\(21\) −11.2165 −2.44764
\(22\) 8.67763 1.85008
\(23\) −1.00000 −0.208514
\(24\) −20.0838 −4.09960
\(25\) −3.14029 −0.628058
\(26\) −7.92743 −1.55470
\(27\) 4.81163 0.925998
\(28\) −19.2635 −3.64047
\(29\) 7.56463 1.40472 0.702358 0.711824i \(-0.252131\pi\)
0.702358 + 0.711824i \(0.252131\pi\)
\(30\) 9.86931 1.80188
\(31\) 8.19797 1.47240 0.736199 0.676765i \(-0.236619\pi\)
0.736199 + 0.676765i \(0.236619\pi\)
\(32\) −9.63419 −1.70310
\(33\) −9.26932 −1.61358
\(34\) −0.413643 −0.0709391
\(35\) 5.50141 0.929908
\(36\) 22.5890 3.76484
\(37\) −6.78196 −1.11495 −0.557474 0.830194i \(-0.688229\pi\)
−0.557474 + 0.830194i \(0.688229\pi\)
\(38\) 11.3498 1.84118
\(39\) 8.46797 1.35596
\(40\) 9.85063 1.55752
\(41\) 6.49295 1.01403 0.507014 0.861938i \(-0.330749\pi\)
0.507014 + 0.861938i \(0.330749\pi\)
\(42\) 29.1955 4.50496
\(43\) 4.80654 0.732990 0.366495 0.930420i \(-0.380558\pi\)
0.366495 + 0.930420i \(0.380558\pi\)
\(44\) −15.9194 −2.39994
\(45\) −6.45112 −0.961677
\(46\) 2.60291 0.383778
\(47\) 10.2963 1.50187 0.750935 0.660376i \(-0.229603\pi\)
0.750935 + 0.660376i \(0.229603\pi\)
\(48\) 25.7230 3.71279
\(49\) 9.27430 1.32490
\(50\) 8.17388 1.15596
\(51\) 0.441847 0.0618710
\(52\) 14.5431 2.01677
\(53\) −0.354937 −0.0487543 −0.0243771 0.999703i \(-0.507760\pi\)
−0.0243771 + 0.999703i \(0.507760\pi\)
\(54\) −12.5242 −1.70433
\(55\) 4.54637 0.613033
\(56\) 29.1402 3.89402
\(57\) −12.1237 −1.60582
\(58\) −19.6900 −2.58543
\(59\) 14.2564 1.85602 0.928011 0.372554i \(-0.121518\pi\)
0.928011 + 0.372554i \(0.121518\pi\)
\(60\) −18.1056 −2.33742
\(61\) 8.78484 1.12478 0.562392 0.826871i \(-0.309881\pi\)
0.562392 + 0.826871i \(0.309881\pi\)
\(62\) −21.3386 −2.71000
\(63\) −19.0838 −2.40433
\(64\) 6.57376 0.821720
\(65\) −4.15333 −0.515157
\(66\) 24.1272 2.96985
\(67\) −15.5705 −1.90224 −0.951121 0.308818i \(-0.900067\pi\)
−0.951121 + 0.308818i \(0.900067\pi\)
\(68\) 0.758842 0.0920231
\(69\) −2.78039 −0.334719
\(70\) −14.3197 −1.71153
\(71\) −12.1475 −1.44164 −0.720821 0.693121i \(-0.756235\pi\)
−0.720821 + 0.693121i \(0.756235\pi\)
\(72\) −34.1707 −4.02705
\(73\) −1.66239 −0.194569 −0.0972843 0.995257i \(-0.531016\pi\)
−0.0972843 + 0.995257i \(0.531016\pi\)
\(74\) 17.6528 2.05210
\(75\) −8.73122 −1.00819
\(76\) −20.8216 −2.38840
\(77\) 13.4491 1.53267
\(78\) −22.0413 −2.49569
\(79\) 16.4330 1.84886 0.924431 0.381350i \(-0.124541\pi\)
0.924431 + 0.381350i \(0.124541\pi\)
\(80\) −12.6165 −1.41057
\(81\) −0.813484 −0.0903871
\(82\) −16.9005 −1.86635
\(83\) 4.08140 0.447992 0.223996 0.974590i \(-0.428090\pi\)
0.223996 + 0.974590i \(0.428090\pi\)
\(84\) −53.5601 −5.84389
\(85\) −0.216715 −0.0235061
\(86\) −12.5110 −1.34909
\(87\) 21.0326 2.25493
\(88\) 24.0815 2.56710
\(89\) −2.58156 −0.273645 −0.136822 0.990596i \(-0.543689\pi\)
−0.136822 + 0.990596i \(0.543689\pi\)
\(90\) 16.7917 1.77000
\(91\) −12.2864 −1.28797
\(92\) −4.77512 −0.497841
\(93\) 22.7935 2.36358
\(94\) −26.8003 −2.76424
\(95\) 5.94638 0.610086
\(96\) −26.7868 −2.73391
\(97\) −12.3407 −1.25301 −0.626503 0.779419i \(-0.715515\pi\)
−0.626503 + 0.779419i \(0.715515\pi\)
\(98\) −24.1401 −2.43852
\(99\) −15.7708 −1.58503
\(100\) −14.9953 −1.49953
\(101\) −11.5044 −1.14473 −0.572366 0.819998i \(-0.693974\pi\)
−0.572366 + 0.819998i \(0.693974\pi\)
\(102\) −1.15009 −0.113876
\(103\) −1.39858 −0.137806 −0.0689031 0.997623i \(-0.521950\pi\)
−0.0689031 + 0.997623i \(0.521950\pi\)
\(104\) −21.9996 −2.15724
\(105\) 15.2961 1.49274
\(106\) 0.923867 0.0897339
\(107\) 7.25864 0.701720 0.350860 0.936428i \(-0.385889\pi\)
0.350860 + 0.936428i \(0.385889\pi\)
\(108\) 22.9761 2.21088
\(109\) −12.7326 −1.21956 −0.609780 0.792570i \(-0.708742\pi\)
−0.609780 + 0.792570i \(0.708742\pi\)
\(110\) −11.8338 −1.12831
\(111\) −18.8565 −1.78978
\(112\) −37.3221 −3.52661
\(113\) −4.83065 −0.454429 −0.227215 0.973845i \(-0.572962\pi\)
−0.227215 + 0.973845i \(0.572962\pi\)
\(114\) 31.5569 2.95557
\(115\) 1.36371 0.127167
\(116\) 36.1220 3.35385
\(117\) 14.4074 1.33197
\(118\) −37.1080 −3.41607
\(119\) −0.641088 −0.0587685
\(120\) 27.3886 2.50022
\(121\) 0.114364 0.0103967
\(122\) −22.8661 −2.07020
\(123\) 18.0529 1.62778
\(124\) 39.1463 3.51544
\(125\) 11.1010 0.992905
\(126\) 49.6732 4.42524
\(127\) −17.2237 −1.52836 −0.764178 0.645006i \(-0.776855\pi\)
−0.764178 + 0.645006i \(0.776855\pi\)
\(128\) 2.15749 0.190697
\(129\) 13.3640 1.17664
\(130\) 10.8107 0.948164
\(131\) −5.41863 −0.473428 −0.236714 0.971579i \(-0.576070\pi\)
−0.236714 + 0.971579i \(0.576070\pi\)
\(132\) −44.2622 −3.85253
\(133\) 17.5906 1.52530
\(134\) 40.5286 3.50114
\(135\) −6.56168 −0.564739
\(136\) −1.14791 −0.0984325
\(137\) −11.6743 −0.997404 −0.498702 0.866774i \(-0.666190\pi\)
−0.498702 + 0.866774i \(0.666190\pi\)
\(138\) 7.23709 0.616062
\(139\) 10.9603 0.929641 0.464821 0.885405i \(-0.346119\pi\)
0.464821 + 0.885405i \(0.346119\pi\)
\(140\) 26.2699 2.22021
\(141\) 28.6277 2.41089
\(142\) 31.6188 2.65339
\(143\) −10.1535 −0.849079
\(144\) 43.7651 3.64709
\(145\) −10.3160 −0.856695
\(146\) 4.32706 0.358110
\(147\) 25.7862 2.12681
\(148\) −32.3847 −2.66201
\(149\) 10.6443 0.872014 0.436007 0.899943i \(-0.356392\pi\)
0.436007 + 0.899943i \(0.356392\pi\)
\(150\) 22.7266 1.85562
\(151\) −13.0362 −1.06087 −0.530434 0.847726i \(-0.677971\pi\)
−0.530434 + 0.847726i \(0.677971\pi\)
\(152\) 31.4971 2.55476
\(153\) 0.751760 0.0607762
\(154\) −35.0068 −2.82093
\(155\) −11.1797 −0.897973
\(156\) 40.4356 3.23744
\(157\) 11.0360 0.880767 0.440383 0.897810i \(-0.354843\pi\)
0.440383 + 0.897810i \(0.354843\pi\)
\(158\) −42.7737 −3.40289
\(159\) −0.986862 −0.0782632
\(160\) 13.1383 1.03867
\(161\) 4.03414 0.317935
\(162\) 2.11742 0.166360
\(163\) −17.5860 −1.37744 −0.688721 0.725026i \(-0.741828\pi\)
−0.688721 + 0.725026i \(0.741828\pi\)
\(164\) 31.0046 2.42106
\(165\) 12.6407 0.984076
\(166\) −10.6235 −0.824544
\(167\) −9.30364 −0.719937 −0.359969 0.932964i \(-0.617213\pi\)
−0.359969 + 0.932964i \(0.617213\pi\)
\(168\) 81.0210 6.25091
\(169\) −3.72429 −0.286484
\(170\) 0.564090 0.0432637
\(171\) −20.6273 −1.57741
\(172\) 22.9518 1.75006
\(173\) −18.9570 −1.44127 −0.720636 0.693313i \(-0.756150\pi\)
−0.720636 + 0.693313i \(0.756150\pi\)
\(174\) −54.7459 −4.15028
\(175\) 12.6684 0.957639
\(176\) −30.8431 −2.32488
\(177\) 39.6382 2.97939
\(178\) 6.71956 0.503653
\(179\) 15.2536 1.14010 0.570052 0.821609i \(-0.306923\pi\)
0.570052 + 0.821609i \(0.306923\pi\)
\(180\) −30.8049 −2.29606
\(181\) −20.9167 −1.55473 −0.777364 0.629051i \(-0.783444\pi\)
−0.777364 + 0.629051i \(0.783444\pi\)
\(182\) 31.9804 2.37054
\(183\) 24.4253 1.80557
\(184\) 7.22339 0.532516
\(185\) 9.24865 0.679974
\(186\) −59.3295 −4.35025
\(187\) −0.529796 −0.0387426
\(188\) 49.1661 3.58581
\(189\) −19.4108 −1.41193
\(190\) −15.4779 −1.12288
\(191\) −14.1508 −1.02392 −0.511959 0.859010i \(-0.671080\pi\)
−0.511959 + 0.859010i \(0.671080\pi\)
\(192\) 18.2776 1.31907
\(193\) −12.5103 −0.900510 −0.450255 0.892900i \(-0.648667\pi\)
−0.450255 + 0.892900i \(0.648667\pi\)
\(194\) 32.1217 2.30620
\(195\) −11.5479 −0.826960
\(196\) 44.2860 3.16328
\(197\) 18.1564 1.29359 0.646794 0.762665i \(-0.276109\pi\)
0.646794 + 0.762665i \(0.276109\pi\)
\(198\) 41.0500 2.91730
\(199\) −27.2662 −1.93285 −0.966425 0.256949i \(-0.917283\pi\)
−0.966425 + 0.256949i \(0.917283\pi\)
\(200\) 22.6835 1.60397
\(201\) −43.2921 −3.05359
\(202\) 29.9449 2.10692
\(203\) −30.5168 −2.14186
\(204\) 2.10988 0.147721
\(205\) −8.85452 −0.618426
\(206\) 3.64038 0.253637
\(207\) −4.73056 −0.328797
\(208\) 28.1766 1.95370
\(209\) 14.5369 1.00554
\(210\) −39.8142 −2.74744
\(211\) 23.1335 1.59257 0.796287 0.604919i \(-0.206795\pi\)
0.796287 + 0.604919i \(0.206795\pi\)
\(212\) −1.69487 −0.116404
\(213\) −33.7747 −2.31421
\(214\) −18.8936 −1.29154
\(215\) −6.55473 −0.447029
\(216\) −34.7563 −2.36487
\(217\) −33.0718 −2.24506
\(218\) 33.1417 2.24464
\(219\) −4.62210 −0.312333
\(220\) 21.7095 1.46365
\(221\) 0.483995 0.0325570
\(222\) 49.0817 3.29415
\(223\) −23.6814 −1.58583 −0.792913 0.609335i \(-0.791437\pi\)
−0.792913 + 0.609335i \(0.791437\pi\)
\(224\) 38.8657 2.59682
\(225\) −14.8553 −0.990355
\(226\) 12.5737 0.836392
\(227\) 25.6706 1.70382 0.851910 0.523688i \(-0.175444\pi\)
0.851910 + 0.523688i \(0.175444\pi\)
\(228\) −57.8922 −3.83401
\(229\) 10.5015 0.693959 0.346979 0.937873i \(-0.387207\pi\)
0.346979 + 0.937873i \(0.387207\pi\)
\(230\) −3.54962 −0.234055
\(231\) 37.3937 2.46033
\(232\) −54.6423 −3.58744
\(233\) −20.7921 −1.36214 −0.681069 0.732220i \(-0.738484\pi\)
−0.681069 + 0.732220i \(0.738484\pi\)
\(234\) −37.5012 −2.45153
\(235\) −14.0412 −0.915946
\(236\) 68.0760 4.43137
\(237\) 45.6902 2.96790
\(238\) 1.66869 0.108165
\(239\) −29.0262 −1.87755 −0.938774 0.344535i \(-0.888037\pi\)
−0.938774 + 0.344535i \(0.888037\pi\)
\(240\) −35.0787 −2.26432
\(241\) 6.23083 0.401363 0.200681 0.979657i \(-0.435684\pi\)
0.200681 + 0.979657i \(0.435684\pi\)
\(242\) −0.297678 −0.0191355
\(243\) −16.6967 −1.07109
\(244\) 41.9487 2.68549
\(245\) −12.6475 −0.808018
\(246\) −46.9901 −2.99598
\(247\) −13.2802 −0.844997
\(248\) −59.2171 −3.76029
\(249\) 11.3479 0.719143
\(250\) −28.8949 −1.82747
\(251\) −0.600486 −0.0379024 −0.0189512 0.999820i \(-0.506033\pi\)
−0.0189512 + 0.999820i \(0.506033\pi\)
\(252\) −91.1273 −5.74048
\(253\) 3.33382 0.209596
\(254\) 44.8317 2.81299
\(255\) −0.602553 −0.0377333
\(256\) −18.7633 −1.17270
\(257\) 8.60111 0.536523 0.268261 0.963346i \(-0.413551\pi\)
0.268261 + 0.963346i \(0.413551\pi\)
\(258\) −34.7853 −2.16564
\(259\) 27.3594 1.70003
\(260\) −19.8327 −1.22997
\(261\) 35.7849 2.21503
\(262\) 14.1042 0.871360
\(263\) −26.6833 −1.64536 −0.822682 0.568502i \(-0.807523\pi\)
−0.822682 + 0.568502i \(0.807523\pi\)
\(264\) 66.9559 4.12085
\(265\) 0.484031 0.0297338
\(266\) −45.7868 −2.80737
\(267\) −7.17774 −0.439271
\(268\) −74.3512 −4.54172
\(269\) −10.8196 −0.659686 −0.329843 0.944036i \(-0.606996\pi\)
−0.329843 + 0.944036i \(0.606996\pi\)
\(270\) 17.0794 1.03942
\(271\) −10.5213 −0.639124 −0.319562 0.947565i \(-0.603536\pi\)
−0.319562 + 0.947565i \(0.603536\pi\)
\(272\) 1.47022 0.0891451
\(273\) −34.1610 −2.06752
\(274\) 30.3871 1.83575
\(275\) 10.4692 0.631314
\(276\) −13.2767 −0.799164
\(277\) −8.23535 −0.494814 −0.247407 0.968912i \(-0.579578\pi\)
−0.247407 + 0.968912i \(0.579578\pi\)
\(278\) −28.5287 −1.71104
\(279\) 38.7810 2.32176
\(280\) −39.7388 −2.37485
\(281\) −6.44166 −0.384277 −0.192139 0.981368i \(-0.561542\pi\)
−0.192139 + 0.981368i \(0.561542\pi\)
\(282\) −74.5153 −4.43732
\(283\) 6.90455 0.410433 0.205216 0.978717i \(-0.434210\pi\)
0.205216 + 0.978717i \(0.434210\pi\)
\(284\) −58.0058 −3.44201
\(285\) 16.5333 0.979345
\(286\) 26.4286 1.56276
\(287\) −26.1935 −1.54615
\(288\) −45.5751 −2.68554
\(289\) −16.9747 −0.998514
\(290\) 26.8515 1.57678
\(291\) −34.3119 −2.01140
\(292\) −7.93814 −0.464545
\(293\) 4.43221 0.258933 0.129466 0.991584i \(-0.458674\pi\)
0.129466 + 0.991584i \(0.458674\pi\)
\(294\) −67.1190 −3.91446
\(295\) −19.4416 −1.13193
\(296\) 48.9888 2.84741
\(297\) −16.0411 −0.930800
\(298\) −27.7061 −1.60497
\(299\) −3.04561 −0.176132
\(300\) −41.6927 −2.40713
\(301\) −19.3902 −1.11764
\(302\) 33.9319 1.95256
\(303\) −31.9867 −1.83759
\(304\) −40.3409 −2.31371
\(305\) −11.9800 −0.685973
\(306\) −1.95676 −0.111861
\(307\) −32.1297 −1.83374 −0.916870 0.399185i \(-0.869293\pi\)
−0.916870 + 0.399185i \(0.869293\pi\)
\(308\) 64.2212 3.65934
\(309\) −3.88860 −0.221215
\(310\) 29.0996 1.65275
\(311\) −10.9159 −0.618984 −0.309492 0.950902i \(-0.600159\pi\)
−0.309492 + 0.950902i \(0.600159\pi\)
\(312\) −61.1674 −3.46292
\(313\) 9.80624 0.554282 0.277141 0.960829i \(-0.410613\pi\)
0.277141 + 0.960829i \(0.410613\pi\)
\(314\) −28.7256 −1.62108
\(315\) 26.0247 1.46633
\(316\) 78.4698 4.41427
\(317\) −19.0524 −1.07009 −0.535044 0.844824i \(-0.679705\pi\)
−0.535044 + 0.844824i \(0.679705\pi\)
\(318\) 2.56871 0.144046
\(319\) −25.2191 −1.41200
\(320\) −8.96472 −0.501143
\(321\) 20.1818 1.12644
\(322\) −10.5005 −0.585170
\(323\) −0.692942 −0.0385563
\(324\) −3.88449 −0.215805
\(325\) −9.56408 −0.530520
\(326\) 45.7747 2.53523
\(327\) −35.4015 −1.95771
\(328\) −46.9011 −2.58968
\(329\) −41.5367 −2.28999
\(330\) −32.9025 −1.81122
\(331\) 8.08544 0.444416 0.222208 0.974999i \(-0.428674\pi\)
0.222208 + 0.974999i \(0.428674\pi\)
\(332\) 19.4892 1.06961
\(333\) −32.0825 −1.75811
\(334\) 24.2165 1.32507
\(335\) 21.2337 1.16012
\(336\) −103.770 −5.66112
\(337\) −2.15213 −0.117234 −0.0586170 0.998281i \(-0.518669\pi\)
−0.0586170 + 0.998281i \(0.518669\pi\)
\(338\) 9.69397 0.527283
\(339\) −13.4311 −0.729476
\(340\) −1.03484 −0.0561222
\(341\) −27.3306 −1.48003
\(342\) 53.6910 2.90327
\(343\) −9.17486 −0.495396
\(344\) −34.7195 −1.87195
\(345\) 3.79165 0.204136
\(346\) 49.3433 2.65271
\(347\) 30.9474 1.66135 0.830673 0.556761i \(-0.187956\pi\)
0.830673 + 0.556761i \(0.187956\pi\)
\(348\) 100.433 5.38379
\(349\) −1.00000 −0.0535288
\(350\) −32.9746 −1.76257
\(351\) 14.6543 0.782190
\(352\) 32.1187 1.71193
\(353\) 32.9297 1.75267 0.876337 0.481699i \(-0.159980\pi\)
0.876337 + 0.481699i \(0.159980\pi\)
\(354\) −103.175 −5.48367
\(355\) 16.5657 0.879215
\(356\) −12.3273 −0.653344
\(357\) −1.78247 −0.0943386
\(358\) −39.7036 −2.09840
\(359\) 10.5393 0.556245 0.278123 0.960546i \(-0.410288\pi\)
0.278123 + 0.960546i \(0.410288\pi\)
\(360\) 46.5990 2.45598
\(361\) 0.0134087 0.000705721 0
\(362\) 54.4443 2.86153
\(363\) 0.317976 0.0166894
\(364\) −58.6691 −3.07510
\(365\) 2.26703 0.118662
\(366\) −63.5767 −3.32321
\(367\) 24.2005 1.26325 0.631627 0.775272i \(-0.282387\pi\)
0.631627 + 0.775272i \(0.282387\pi\)
\(368\) −9.25157 −0.482271
\(369\) 30.7153 1.59897
\(370\) −24.0734 −1.25151
\(371\) 1.43186 0.0743387
\(372\) 108.842 5.64319
\(373\) 11.0453 0.571905 0.285953 0.958244i \(-0.407690\pi\)
0.285953 + 0.958244i \(0.407690\pi\)
\(374\) 1.37901 0.0713070
\(375\) 30.8651 1.59387
\(376\) −74.3742 −3.83556
\(377\) 23.0389 1.18656
\(378\) 50.5245 2.59870
\(379\) −24.3895 −1.25281 −0.626403 0.779499i \(-0.715474\pi\)
−0.626403 + 0.779499i \(0.715474\pi\)
\(380\) 28.3947 1.45662
\(381\) −47.8885 −2.45340
\(382\) 36.8333 1.88456
\(383\) 18.0641 0.923030 0.461515 0.887132i \(-0.347306\pi\)
0.461515 + 0.887132i \(0.347306\pi\)
\(384\) 5.99867 0.306118
\(385\) −18.3407 −0.934729
\(386\) 32.5631 1.65742
\(387\) 22.7376 1.15582
\(388\) −58.9283 −2.99163
\(389\) 21.4135 1.08571 0.542854 0.839827i \(-0.317344\pi\)
0.542854 + 0.839827i \(0.317344\pi\)
\(390\) 30.0580 1.52205
\(391\) −0.158916 −0.00803671
\(392\) −66.9919 −3.38360
\(393\) −15.0659 −0.759974
\(394\) −47.2593 −2.38089
\(395\) −22.4099 −1.12757
\(396\) −75.3077 −3.78436
\(397\) −11.9097 −0.597733 −0.298867 0.954295i \(-0.596609\pi\)
−0.298867 + 0.954295i \(0.596609\pi\)
\(398\) 70.9714 3.55747
\(399\) 48.9088 2.44850
\(400\) −29.0526 −1.45263
\(401\) −18.6728 −0.932474 −0.466237 0.884660i \(-0.654391\pi\)
−0.466237 + 0.884660i \(0.654391\pi\)
\(402\) 112.685 5.62023
\(403\) 24.9678 1.24373
\(404\) −54.9350 −2.73312
\(405\) 1.10936 0.0551244
\(406\) 79.4324 3.94216
\(407\) 22.6099 1.12073
\(408\) −3.19164 −0.158010
\(409\) 24.2432 1.19875 0.599376 0.800468i \(-0.295416\pi\)
0.599376 + 0.800468i \(0.295416\pi\)
\(410\) 23.0475 1.13823
\(411\) −32.4591 −1.60109
\(412\) −6.67840 −0.329021
\(413\) −57.5122 −2.82999
\(414\) 12.3132 0.605161
\(415\) −5.56586 −0.273217
\(416\) −29.3419 −1.43861
\(417\) 30.4739 1.49231
\(418\) −37.8382 −1.85073
\(419\) −30.4515 −1.48765 −0.743826 0.668373i \(-0.766991\pi\)
−0.743826 + 0.668373i \(0.766991\pi\)
\(420\) 73.0406 3.56402
\(421\) 1.41765 0.0690921 0.0345460 0.999403i \(-0.489001\pi\)
0.0345460 + 0.999403i \(0.489001\pi\)
\(422\) −60.2143 −2.93119
\(423\) 48.7073 2.36823
\(424\) 2.56385 0.124511
\(425\) −0.499041 −0.0242070
\(426\) 87.9125 4.25938
\(427\) −35.4393 −1.71503
\(428\) 34.6609 1.67540
\(429\) −28.2307 −1.36299
\(430\) 17.0614 0.822772
\(431\) 7.08869 0.341450 0.170725 0.985319i \(-0.445389\pi\)
0.170725 + 0.985319i \(0.445389\pi\)
\(432\) 44.5151 2.14173
\(433\) 0.387898 0.0186412 0.00932059 0.999957i \(-0.497033\pi\)
0.00932059 + 0.999957i \(0.497033\pi\)
\(434\) 86.0827 4.13210
\(435\) −28.6824 −1.37522
\(436\) −60.7997 −2.91178
\(437\) 4.36044 0.208588
\(438\) 12.0309 0.574859
\(439\) −37.6565 −1.79725 −0.898624 0.438719i \(-0.855432\pi\)
−0.898624 + 0.438719i \(0.855432\pi\)
\(440\) −32.8402 −1.56560
\(441\) 43.8726 2.08917
\(442\) −1.25979 −0.0599222
\(443\) −13.5551 −0.644020 −0.322010 0.946736i \(-0.604358\pi\)
−0.322010 + 0.946736i \(0.604358\pi\)
\(444\) −90.0421 −4.27321
\(445\) 3.52051 0.166888
\(446\) 61.6406 2.91877
\(447\) 29.5953 1.39981
\(448\) −26.5195 −1.25293
\(449\) −3.82446 −0.180487 −0.0902437 0.995920i \(-0.528765\pi\)
−0.0902437 + 0.995920i \(0.528765\pi\)
\(450\) 38.6670 1.82278
\(451\) −21.6463 −1.01929
\(452\) −23.0670 −1.08498
\(453\) −36.2456 −1.70297
\(454\) −66.8183 −3.13594
\(455\) 16.7551 0.785492
\(456\) 87.5743 4.10104
\(457\) −16.9428 −0.792552 −0.396276 0.918131i \(-0.629698\pi\)
−0.396276 + 0.918131i \(0.629698\pi\)
\(458\) −27.3344 −1.27725
\(459\) 0.764643 0.0356905
\(460\) 6.51190 0.303619
\(461\) −15.4883 −0.721361 −0.360681 0.932689i \(-0.617456\pi\)
−0.360681 + 0.932689i \(0.617456\pi\)
\(462\) −97.3324 −4.52832
\(463\) 21.4330 0.996076 0.498038 0.867155i \(-0.334054\pi\)
0.498038 + 0.867155i \(0.334054\pi\)
\(464\) 69.9847 3.24896
\(465\) −31.0838 −1.44148
\(466\) 54.1200 2.50706
\(467\) −13.2395 −0.612653 −0.306326 0.951927i \(-0.599100\pi\)
−0.306326 + 0.951927i \(0.599100\pi\)
\(468\) 68.7972 3.18015
\(469\) 62.8137 2.90047
\(470\) 36.5479 1.68583
\(471\) 30.6843 1.41386
\(472\) −102.979 −4.74001
\(473\) −16.0241 −0.736790
\(474\) −118.927 −5.46252
\(475\) 13.6930 0.628279
\(476\) −3.06128 −0.140313
\(477\) −1.67905 −0.0768784
\(478\) 75.5524 3.45569
\(479\) 16.3784 0.748348 0.374174 0.927358i \(-0.377926\pi\)
0.374174 + 0.927358i \(0.377926\pi\)
\(480\) 36.5295 1.66733
\(481\) −20.6552 −0.941795
\(482\) −16.2183 −0.738722
\(483\) 11.2165 0.510368
\(484\) 0.546101 0.0248228
\(485\) 16.8291 0.764172
\(486\) 43.4599 1.97138
\(487\) 18.7581 0.850008 0.425004 0.905191i \(-0.360273\pi\)
0.425004 + 0.905191i \(0.360273\pi\)
\(488\) −63.4564 −2.87254
\(489\) −48.8959 −2.21115
\(490\) 32.9202 1.48718
\(491\) 26.8223 1.21047 0.605236 0.796046i \(-0.293079\pi\)
0.605236 + 0.796046i \(0.293079\pi\)
\(492\) 86.2050 3.88642
\(493\) 1.20214 0.0541416
\(494\) 34.5670 1.55525
\(495\) 21.5069 0.966663
\(496\) 75.8441 3.40550
\(497\) 49.0047 2.19816
\(498\) −29.5375 −1.32361
\(499\) 21.7496 0.973646 0.486823 0.873501i \(-0.338156\pi\)
0.486823 + 0.873501i \(0.338156\pi\)
\(500\) 53.0087 2.37062
\(501\) −25.8677 −1.15569
\(502\) 1.56301 0.0697606
\(503\) 16.1677 0.720881 0.360441 0.932782i \(-0.382626\pi\)
0.360441 + 0.932782i \(0.382626\pi\)
\(504\) 137.849 6.14030
\(505\) 15.6887 0.698138
\(506\) −8.67763 −0.385768
\(507\) −10.3550 −0.459880
\(508\) −82.2453 −3.64904
\(509\) −42.0955 −1.86585 −0.932925 0.360071i \(-0.882753\pi\)
−0.932925 + 0.360071i \(0.882753\pi\)
\(510\) 1.56839 0.0694494
\(511\) 6.70634 0.296671
\(512\) 44.5241 1.96770
\(513\) −20.9808 −0.926325
\(514\) −22.3879 −0.987488
\(515\) 1.90726 0.0840440
\(516\) 63.8149 2.80930
\(517\) −34.3260 −1.50966
\(518\) −71.2140 −3.12896
\(519\) −52.7078 −2.31361
\(520\) 30.0011 1.31564
\(521\) −10.3470 −0.453310 −0.226655 0.973975i \(-0.572779\pi\)
−0.226655 + 0.973975i \(0.572779\pi\)
\(522\) −93.1448 −4.07684
\(523\) −26.6023 −1.16324 −0.581618 0.813462i \(-0.697580\pi\)
−0.581618 + 0.813462i \(0.697580\pi\)
\(524\) −25.8746 −1.13034
\(525\) 35.2230 1.53726
\(526\) 69.4542 3.02835
\(527\) 1.30279 0.0567502
\(528\) −85.7557 −3.73204
\(529\) 1.00000 0.0434783
\(530\) −1.25989 −0.0547261
\(531\) 67.4406 2.92667
\(532\) 83.9974 3.64175
\(533\) 19.7750 0.856549
\(534\) 18.6830 0.808492
\(535\) −9.89870 −0.427958
\(536\) 112.472 4.85805
\(537\) 42.4108 1.83016
\(538\) 28.1625 1.21417
\(539\) −30.9189 −1.33177
\(540\) −31.3328 −1.34835
\(541\) 23.2865 1.00116 0.500582 0.865689i \(-0.333119\pi\)
0.500582 + 0.865689i \(0.333119\pi\)
\(542\) 27.3860 1.17633
\(543\) −58.1566 −2.49574
\(544\) −1.53102 −0.0656421
\(545\) 17.3636 0.743774
\(546\) 88.9179 3.80533
\(547\) 15.5491 0.664830 0.332415 0.943133i \(-0.392137\pi\)
0.332415 + 0.943133i \(0.392137\pi\)
\(548\) −55.7463 −2.38136
\(549\) 41.5572 1.77362
\(550\) −27.2502 −1.16195
\(551\) −32.9851 −1.40521
\(552\) 20.0838 0.854825
\(553\) −66.2932 −2.81907
\(554\) 21.4358 0.910722
\(555\) 25.7148 1.09153
\(556\) 52.3369 2.21958
\(557\) 21.9668 0.930762 0.465381 0.885110i \(-0.345917\pi\)
0.465381 + 0.885110i \(0.345917\pi\)
\(558\) −100.943 −4.27327
\(559\) 14.6388 0.619156
\(560\) 50.8967 2.15078
\(561\) −1.47304 −0.0621918
\(562\) 16.7670 0.707275
\(563\) 1.00084 0.0421803 0.0210901 0.999778i \(-0.493286\pi\)
0.0210901 + 0.999778i \(0.493286\pi\)
\(564\) 136.701 5.75615
\(565\) 6.58762 0.277143
\(566\) −17.9719 −0.755415
\(567\) 3.28171 0.137819
\(568\) 87.7461 3.68174
\(569\) −25.8517 −1.08376 −0.541880 0.840456i \(-0.682287\pi\)
−0.541880 + 0.840456i \(0.682287\pi\)
\(570\) −43.0345 −1.80252
\(571\) 36.8534 1.54227 0.771133 0.636675i \(-0.219691\pi\)
0.771133 + 0.636675i \(0.219691\pi\)
\(572\) −48.4843 −2.02723
\(573\) −39.3448 −1.64365
\(574\) 68.1792 2.84574
\(575\) 3.14029 0.130959
\(576\) 31.0976 1.29573
\(577\) −4.33062 −0.180286 −0.0901429 0.995929i \(-0.528732\pi\)
−0.0901429 + 0.995929i \(0.528732\pi\)
\(578\) 44.1837 1.83780
\(579\) −34.7835 −1.44555
\(580\) −49.2601 −2.04541
\(581\) −16.4650 −0.683081
\(582\) 89.3107 3.70205
\(583\) 1.18330 0.0490071
\(584\) 12.0081 0.496900
\(585\) −19.6476 −0.812327
\(586\) −11.5366 −0.476574
\(587\) 14.2394 0.587722 0.293861 0.955848i \(-0.405060\pi\)
0.293861 + 0.955848i \(0.405060\pi\)
\(588\) 123.132 5.07788
\(589\) −35.7467 −1.47292
\(590\) 50.6047 2.08336
\(591\) 50.4818 2.07654
\(592\) −62.7438 −2.57875
\(593\) 30.8143 1.26539 0.632695 0.774401i \(-0.281949\pi\)
0.632695 + 0.774401i \(0.281949\pi\)
\(594\) 41.7535 1.71317
\(595\) 0.874260 0.0358412
\(596\) 50.8278 2.08199
\(597\) −75.8106 −3.10272
\(598\) 7.92743 0.324177
\(599\) −5.87754 −0.240150 −0.120075 0.992765i \(-0.538313\pi\)
−0.120075 + 0.992765i \(0.538313\pi\)
\(600\) 63.0690 2.57478
\(601\) −19.6502 −0.801549 −0.400775 0.916177i \(-0.631259\pi\)
−0.400775 + 0.916177i \(0.631259\pi\)
\(602\) 50.4710 2.05704
\(603\) −73.6573 −2.99956
\(604\) −62.2494 −2.53289
\(605\) −0.155959 −0.00634064
\(606\) 83.2585 3.38215
\(607\) 15.0478 0.610771 0.305386 0.952229i \(-0.401215\pi\)
0.305386 + 0.952229i \(0.401215\pi\)
\(608\) 42.0093 1.70370
\(609\) −84.8485 −3.43824
\(610\) 31.1828 1.26256
\(611\) 31.3585 1.26863
\(612\) 3.58975 0.145107
\(613\) −48.5970 −1.96282 −0.981408 0.191935i \(-0.938524\pi\)
−0.981408 + 0.191935i \(0.938524\pi\)
\(614\) 83.6307 3.37506
\(615\) −24.6190 −0.992734
\(616\) −97.1482 −3.91421
\(617\) −11.6449 −0.468807 −0.234404 0.972139i \(-0.575314\pi\)
−0.234404 + 0.972139i \(0.575314\pi\)
\(618\) 10.1217 0.407153
\(619\) 28.7361 1.15500 0.577500 0.816391i \(-0.304028\pi\)
0.577500 + 0.816391i \(0.304028\pi\)
\(620\) −53.3843 −2.14397
\(621\) −4.81163 −0.193084
\(622\) 28.4131 1.13926
\(623\) 10.4144 0.417244
\(624\) 78.3420 3.13619
\(625\) 0.562852 0.0225141
\(626\) −25.5247 −1.02017
\(627\) 40.4183 1.61415
\(628\) 52.6982 2.10289
\(629\) −1.07776 −0.0429731
\(630\) −67.7400 −2.69883
\(631\) 28.5390 1.13612 0.568060 0.822987i \(-0.307694\pi\)
0.568060 + 0.822987i \(0.307694\pi\)
\(632\) −118.702 −4.72172
\(633\) 64.3200 2.55649
\(634\) 49.5916 1.96953
\(635\) 23.4882 0.932099
\(636\) −4.71239 −0.186858
\(637\) 28.2459 1.11914
\(638\) 65.6430 2.59883
\(639\) −57.4644 −2.27326
\(640\) −2.94220 −0.116301
\(641\) −48.3855 −1.91111 −0.955556 0.294811i \(-0.904743\pi\)
−0.955556 + 0.294811i \(0.904743\pi\)
\(642\) −52.5315 −2.07325
\(643\) −36.9845 −1.45853 −0.729263 0.684233i \(-0.760137\pi\)
−0.729263 + 0.684233i \(0.760137\pi\)
\(644\) 19.2635 0.759090
\(645\) −18.2247 −0.717597
\(646\) 1.80366 0.0709642
\(647\) −10.3514 −0.406954 −0.203477 0.979080i \(-0.565224\pi\)
−0.203477 + 0.979080i \(0.565224\pi\)
\(648\) 5.87611 0.230835
\(649\) −47.5282 −1.86564
\(650\) 24.8944 0.976439
\(651\) −91.9524 −3.60390
\(652\) −83.9754 −3.28873
\(653\) 18.0082 0.704715 0.352358 0.935865i \(-0.385380\pi\)
0.352358 + 0.935865i \(0.385380\pi\)
\(654\) 92.1469 3.60323
\(655\) 7.38946 0.288730
\(656\) 60.0700 2.34534
\(657\) −7.86406 −0.306806
\(658\) 108.116 4.21481
\(659\) 31.4918 1.22675 0.613373 0.789793i \(-0.289812\pi\)
0.613373 + 0.789793i \(0.289812\pi\)
\(660\) 60.3608 2.34954
\(661\) 18.2788 0.710965 0.355482 0.934683i \(-0.384317\pi\)
0.355482 + 0.934683i \(0.384317\pi\)
\(662\) −21.0457 −0.817963
\(663\) 1.34569 0.0522624
\(664\) −29.4816 −1.14411
\(665\) −23.9885 −0.930236
\(666\) 83.5077 3.23586
\(667\) −7.56463 −0.292904
\(668\) −44.4260 −1.71890
\(669\) −65.8436 −2.54566
\(670\) −55.2694 −2.13524
\(671\) −29.2871 −1.13062
\(672\) 108.062 4.16857
\(673\) −36.1959 −1.39525 −0.697625 0.716463i \(-0.745760\pi\)
−0.697625 + 0.716463i \(0.745760\pi\)
\(674\) 5.60179 0.215773
\(675\) −15.1099 −0.581580
\(676\) −17.7839 −0.683997
\(677\) −4.34341 −0.166931 −0.0834653 0.996511i \(-0.526599\pi\)
−0.0834653 + 0.996511i \(0.526599\pi\)
\(678\) 34.9599 1.34262
\(679\) 49.7841 1.91054
\(680\) 1.56542 0.0600311
\(681\) 71.3744 2.73507
\(682\) 71.1389 2.72405
\(683\) 11.0265 0.421917 0.210958 0.977495i \(-0.432342\pi\)
0.210958 + 0.977495i \(0.432342\pi\)
\(684\) −98.4980 −3.76616
\(685\) 15.9204 0.608287
\(686\) 23.8813 0.911793
\(687\) 29.1982 1.11398
\(688\) 44.4680 1.69533
\(689\) −1.08100 −0.0411827
\(690\) −9.86931 −0.375718
\(691\) −24.8647 −0.945897 −0.472948 0.881090i \(-0.656810\pi\)
−0.472948 + 0.881090i \(0.656810\pi\)
\(692\) −90.5220 −3.44113
\(693\) 63.6218 2.41679
\(694\) −80.5533 −3.05776
\(695\) −14.9467 −0.566961
\(696\) −151.927 −5.75877
\(697\) 1.03183 0.0390834
\(698\) 2.60291 0.0985215
\(699\) −57.8102 −2.18658
\(700\) 60.4930 2.28642
\(701\) 15.2705 0.576758 0.288379 0.957516i \(-0.406884\pi\)
0.288379 + 0.957516i \(0.406884\pi\)
\(702\) −38.1438 −1.43965
\(703\) 29.5723 1.11534
\(704\) −21.9157 −0.825980
\(705\) −39.0400 −1.47033
\(706\) −85.7131 −3.22585
\(707\) 46.4104 1.74544
\(708\) 189.278 7.11349
\(709\) 0.0323175 0.00121371 0.000606856 1.00000i \(-0.499807\pi\)
0.000606856 1.00000i \(0.499807\pi\)
\(710\) −43.1189 −1.61822
\(711\) 77.7375 2.91538
\(712\) 18.6476 0.698849
\(713\) −8.19797 −0.307016
\(714\) 4.63962 0.173633
\(715\) 13.8465 0.517828
\(716\) 72.8376 2.72207
\(717\) −80.7040 −3.01395
\(718\) −27.4329 −1.02379
\(719\) 14.5959 0.544334 0.272167 0.962250i \(-0.412260\pi\)
0.272167 + 0.962250i \(0.412260\pi\)
\(720\) −59.6830 −2.22425
\(721\) 5.64207 0.210122
\(722\) −0.0349016 −0.00129890
\(723\) 17.3241 0.644291
\(724\) −99.8800 −3.71201
\(725\) −23.7551 −0.882243
\(726\) −0.827661 −0.0307174
\(727\) −9.96456 −0.369565 −0.184783 0.982779i \(-0.559158\pi\)
−0.184783 + 0.982779i \(0.559158\pi\)
\(728\) 88.7495 3.28928
\(729\) −43.9828 −1.62899
\(730\) −5.90086 −0.218401
\(731\) 0.763834 0.0282514
\(732\) 116.634 4.31091
\(733\) −38.6023 −1.42581 −0.712904 0.701262i \(-0.752620\pi\)
−0.712904 + 0.701262i \(0.752620\pi\)
\(734\) −62.9916 −2.32506
\(735\) −35.1649 −1.29708
\(736\) 9.63419 0.355121
\(737\) 51.9093 1.91211
\(738\) −79.9490 −2.94296
\(739\) 34.4926 1.26883 0.634415 0.772993i \(-0.281241\pi\)
0.634415 + 0.772993i \(0.281241\pi\)
\(740\) 44.1634 1.62348
\(741\) −36.9240 −1.35644
\(742\) −3.72701 −0.136823
\(743\) −9.18695 −0.337036 −0.168518 0.985699i \(-0.553898\pi\)
−0.168518 + 0.985699i \(0.553898\pi\)
\(744\) −164.647 −6.03624
\(745\) −14.5158 −0.531816
\(746\) −28.7499 −1.05261
\(747\) 19.3073 0.706418
\(748\) −2.52984 −0.0925003
\(749\) −29.2824 −1.06996
\(750\) −80.3391 −2.93357
\(751\) 10.7256 0.391383 0.195692 0.980665i \(-0.437305\pi\)
0.195692 + 0.980665i \(0.437305\pi\)
\(752\) 95.2569 3.47366
\(753\) −1.66959 −0.0608431
\(754\) −59.9681 −2.18391
\(755\) 17.7776 0.646993
\(756\) −92.6890 −3.37106
\(757\) 46.7619 1.69959 0.849794 0.527114i \(-0.176726\pi\)
0.849794 + 0.527114i \(0.176726\pi\)
\(758\) 63.4837 2.30583
\(759\) 9.26932 0.336455
\(760\) −42.9530 −1.55807
\(761\) 48.5597 1.76029 0.880145 0.474706i \(-0.157445\pi\)
0.880145 + 0.474706i \(0.157445\pi\)
\(762\) 124.649 4.51557
\(763\) 51.3651 1.85954
\(764\) −67.5720 −2.44467
\(765\) −1.02518 −0.0370656
\(766\) −47.0191 −1.69887
\(767\) 43.4193 1.56778
\(768\) −52.1692 −1.88249
\(769\) 14.0526 0.506749 0.253374 0.967368i \(-0.418460\pi\)
0.253374 + 0.967368i \(0.418460\pi\)
\(770\) 47.7392 1.72040
\(771\) 23.9144 0.861258
\(772\) −59.7382 −2.15002
\(773\) −5.34611 −0.192286 −0.0961431 0.995368i \(-0.530651\pi\)
−0.0961431 + 0.995368i \(0.530651\pi\)
\(774\) −59.1839 −2.12732
\(775\) −25.7440 −0.924751
\(776\) 89.1416 3.20000
\(777\) 76.0698 2.72899
\(778\) −55.7374 −1.99828
\(779\) −28.3121 −1.01439
\(780\) −55.1425 −1.97442
\(781\) 40.4976 1.44912
\(782\) 0.413643 0.0147918
\(783\) 36.3982 1.30076
\(784\) 85.8018 3.06435
\(785\) −15.0499 −0.537154
\(786\) 39.2151 1.39876
\(787\) 38.8629 1.38531 0.692657 0.721268i \(-0.256440\pi\)
0.692657 + 0.721268i \(0.256440\pi\)
\(788\) 86.6989 3.08852
\(789\) −74.1900 −2.64123
\(790\) 58.3310 2.07532
\(791\) 19.4875 0.692897
\(792\) 113.919 4.04793
\(793\) 26.7552 0.950104
\(794\) 31.0000 1.10015
\(795\) 1.34580 0.0477304
\(796\) −130.200 −4.61480
\(797\) −13.6058 −0.481941 −0.240970 0.970533i \(-0.577466\pi\)
−0.240970 + 0.970533i \(0.577466\pi\)
\(798\) −127.305 −4.50655
\(799\) 1.63624 0.0578861
\(800\) 30.2541 1.06964
\(801\) −12.2122 −0.431498
\(802\) 48.6035 1.71625
\(803\) 5.54213 0.195577
\(804\) −206.725 −7.29064
\(805\) −5.50141 −0.193899
\(806\) −64.9888 −2.28913
\(807\) −30.0828 −1.05897
\(808\) 83.1009 2.92348
\(809\) 31.0235 1.09073 0.545365 0.838199i \(-0.316391\pi\)
0.545365 + 0.838199i \(0.316391\pi\)
\(810\) −2.88755 −0.101458
\(811\) −2.81553 −0.0988666 −0.0494333 0.998777i \(-0.515742\pi\)
−0.0494333 + 0.998777i \(0.515742\pi\)
\(812\) −145.721 −5.11382
\(813\) −29.2533 −1.02596
\(814\) −58.8513 −2.06274
\(815\) 23.9823 0.840062
\(816\) 4.08778 0.143101
\(817\) −20.9586 −0.733248
\(818\) −63.1029 −2.20634
\(819\) −58.1216 −2.03093
\(820\) −42.2814 −1.47653
\(821\) −17.1795 −0.599570 −0.299785 0.954007i \(-0.596915\pi\)
−0.299785 + 0.954007i \(0.596915\pi\)
\(822\) 84.4881 2.94686
\(823\) 43.4035 1.51295 0.756476 0.654021i \(-0.226919\pi\)
0.756476 + 0.654021i \(0.226919\pi\)
\(824\) 10.1025 0.351937
\(825\) 29.1083 1.01342
\(826\) 149.699 5.20869
\(827\) −18.8788 −0.656480 −0.328240 0.944594i \(-0.606455\pi\)
−0.328240 + 0.944594i \(0.606455\pi\)
\(828\) −22.5890 −0.785023
\(829\) 17.9676 0.624041 0.312020 0.950075i \(-0.398994\pi\)
0.312020 + 0.950075i \(0.398994\pi\)
\(830\) 14.4874 0.502865
\(831\) −22.8975 −0.794304
\(832\) 20.0211 0.694106
\(833\) 1.47383 0.0510653
\(834\) −79.3208 −2.74665
\(835\) 12.6875 0.439069
\(836\) 69.4156 2.40079
\(837\) 39.4456 1.36344
\(838\) 79.2624 2.73807
\(839\) −20.8917 −0.721260 −0.360630 0.932709i \(-0.617438\pi\)
−0.360630 + 0.932709i \(0.617438\pi\)
\(840\) −110.489 −3.81225
\(841\) 28.2236 0.973228
\(842\) −3.69001 −0.127166
\(843\) −17.9103 −0.616864
\(844\) 110.465 3.80237
\(845\) 5.07886 0.174718
\(846\) −126.780 −4.35880
\(847\) −0.461359 −0.0158525
\(848\) −3.28372 −0.112763
\(849\) 19.1973 0.658850
\(850\) 1.29896 0.0445539
\(851\) 6.78196 0.232483
\(852\) −161.279 −5.52531
\(853\) −2.02790 −0.0694341 −0.0347170 0.999397i \(-0.511053\pi\)
−0.0347170 + 0.999397i \(0.511053\pi\)
\(854\) 92.2452 3.15657
\(855\) 28.1297 0.962016
\(856\) −52.4320 −1.79209
\(857\) −6.01004 −0.205299 −0.102649 0.994718i \(-0.532732\pi\)
−0.102649 + 0.994718i \(0.532732\pi\)
\(858\) 73.4819 2.50863
\(859\) −14.1592 −0.483107 −0.241553 0.970388i \(-0.577657\pi\)
−0.241553 + 0.970388i \(0.577657\pi\)
\(860\) −31.2997 −1.06731
\(861\) −72.8281 −2.48197
\(862\) −18.4512 −0.628451
\(863\) −18.1308 −0.617181 −0.308591 0.951195i \(-0.599857\pi\)
−0.308591 + 0.951195i \(0.599857\pi\)
\(864\) −46.3561 −1.57707
\(865\) 25.8519 0.878990
\(866\) −1.00966 −0.0343097
\(867\) −47.1964 −1.60287
\(868\) −157.922 −5.36022
\(869\) −54.7848 −1.85845
\(870\) 74.6577 2.53113
\(871\) −47.4217 −1.60682
\(872\) 91.9725 3.11458
\(873\) −58.3783 −1.97581
\(874\) −11.3498 −0.383913
\(875\) −44.7831 −1.51394
\(876\) −22.0711 −0.745714
\(877\) −8.74218 −0.295203 −0.147601 0.989047i \(-0.547155\pi\)
−0.147601 + 0.989047i \(0.547155\pi\)
\(878\) 98.0165 3.30789
\(879\) 12.3233 0.415654
\(880\) 42.0611 1.41788
\(881\) −28.9335 −0.974793 −0.487397 0.873181i \(-0.662053\pi\)
−0.487397 + 0.873181i \(0.662053\pi\)
\(882\) −114.196 −3.84519
\(883\) 32.1090 1.08055 0.540277 0.841487i \(-0.318319\pi\)
0.540277 + 0.841487i \(0.318319\pi\)
\(884\) 2.31113 0.0777319
\(885\) −54.0552 −1.81704
\(886\) 35.2826 1.18534
\(887\) −29.2805 −0.983144 −0.491572 0.870837i \(-0.663577\pi\)
−0.491572 + 0.870837i \(0.663577\pi\)
\(888\) 136.208 4.57084
\(889\) 69.4828 2.33038
\(890\) −9.16355 −0.307163
\(891\) 2.71201 0.0908557
\(892\) −113.082 −3.78626
\(893\) −44.8964 −1.50240
\(894\) −77.0337 −2.57639
\(895\) −20.8015 −0.695316
\(896\) −8.70363 −0.290768
\(897\) −8.46797 −0.282737
\(898\) 9.95471 0.332193
\(899\) 62.0146 2.06830
\(900\) −70.9360 −2.36453
\(901\) −0.0564050 −0.00187912
\(902\) 56.3434 1.87603
\(903\) −53.9124 −1.79409
\(904\) 34.8937 1.16055
\(905\) 28.5244 0.948183
\(906\) 94.3440 3.13437
\(907\) −33.4901 −1.11202 −0.556010 0.831176i \(-0.687668\pi\)
−0.556010 + 0.831176i \(0.687668\pi\)
\(908\) 122.581 4.06798
\(909\) −54.4223 −1.80507
\(910\) −43.6120 −1.44572
\(911\) −3.23737 −0.107259 −0.0536294 0.998561i \(-0.517079\pi\)
−0.0536294 + 0.998561i \(0.517079\pi\)
\(912\) −112.163 −3.71410
\(913\) −13.6067 −0.450315
\(914\) 44.1006 1.45872
\(915\) −33.3091 −1.10116
\(916\) 50.1460 1.65687
\(917\) 21.8595 0.721865
\(918\) −1.99030 −0.0656895
\(919\) −15.0331 −0.495897 −0.247949 0.968773i \(-0.579756\pi\)
−0.247949 + 0.968773i \(0.579756\pi\)
\(920\) −9.85063 −0.324766
\(921\) −89.3331 −2.94363
\(922\) 40.3146 1.32769
\(923\) −36.9965 −1.21775
\(924\) 178.560 5.87419
\(925\) 21.2973 0.700252
\(926\) −55.7881 −1.83331
\(927\) −6.61607 −0.217300
\(928\) −72.8791 −2.39237
\(929\) 24.2943 0.797069 0.398534 0.917153i \(-0.369519\pi\)
0.398534 + 0.917153i \(0.369519\pi\)
\(930\) 80.9083 2.65309
\(931\) −40.4400 −1.32537
\(932\) −99.2850 −3.25219
\(933\) −30.3504 −0.993628
\(934\) 34.4613 1.12761
\(935\) 0.722490 0.0236280
\(936\) −104.070 −3.40165
\(937\) −31.9099 −1.04245 −0.521225 0.853419i \(-0.674525\pi\)
−0.521225 + 0.853419i \(0.674525\pi\)
\(938\) −163.498 −5.33841
\(939\) 27.2652 0.889765
\(940\) −67.0484 −2.18688
\(941\) −47.3623 −1.54397 −0.771983 0.635643i \(-0.780735\pi\)
−0.771983 + 0.635643i \(0.780735\pi\)
\(942\) −79.8684 −2.60225
\(943\) −6.49295 −0.211440
\(944\) 131.894 4.29278
\(945\) 26.4707 0.861093
\(946\) 41.7093 1.35609
\(947\) −13.4565 −0.437278 −0.218639 0.975806i \(-0.570162\pi\)
−0.218639 + 0.975806i \(0.570162\pi\)
\(948\) 218.177 7.08604
\(949\) −5.06300 −0.164352
\(950\) −35.6417 −1.15637
\(951\) −52.9730 −1.71777
\(952\) 4.63083 0.150086
\(953\) 45.5210 1.47457 0.737286 0.675581i \(-0.236107\pi\)
0.737286 + 0.675581i \(0.236107\pi\)
\(954\) 4.37041 0.141497
\(955\) 19.2977 0.624458
\(956\) −138.604 −4.48276
\(957\) −70.1189 −2.26662
\(958\) −42.6315 −1.37736
\(959\) 47.0958 1.52080
\(960\) −24.9254 −0.804464
\(961\) 36.2067 1.16796
\(962\) 53.7635 1.73341
\(963\) 34.3374 1.10651
\(964\) 29.7530 0.958279
\(965\) 17.0604 0.549195
\(966\) −29.1955 −0.939349
\(967\) −51.4672 −1.65507 −0.827537 0.561411i \(-0.810259\pi\)
−0.827537 + 0.561411i \(0.810259\pi\)
\(968\) −0.826094 −0.0265517
\(969\) −1.92665 −0.0618928
\(970\) −43.8047 −1.40648
\(971\) 43.6587 1.40107 0.700537 0.713617i \(-0.252944\pi\)
0.700537 + 0.713617i \(0.252944\pi\)
\(972\) −79.7288 −2.55730
\(973\) −44.2154 −1.41748
\(974\) −48.8255 −1.56447
\(975\) −26.5919 −0.851621
\(976\) 81.2736 2.60150
\(977\) 3.77898 0.120900 0.0604502 0.998171i \(-0.480746\pi\)
0.0604502 + 0.998171i \(0.480746\pi\)
\(978\) 127.272 4.06970
\(979\) 8.60646 0.275064
\(980\) −60.3933 −1.92919
\(981\) −60.2323 −1.92307
\(982\) −69.8159 −2.22792
\(983\) −12.8855 −0.410984 −0.205492 0.978659i \(-0.565879\pi\)
−0.205492 + 0.978659i \(0.565879\pi\)
\(984\) −130.403 −4.15711
\(985\) −24.7601 −0.788921
\(986\) −3.12905 −0.0996494
\(987\) −115.488 −3.67603
\(988\) −63.4145 −2.01748
\(989\) −4.80654 −0.152839
\(990\) −55.9804 −1.77918
\(991\) −6.94849 −0.220726 −0.110363 0.993891i \(-0.535201\pi\)
−0.110363 + 0.993891i \(0.535201\pi\)
\(992\) −78.9808 −2.50764
\(993\) 22.4807 0.713402
\(994\) −127.555 −4.04579
\(995\) 37.1833 1.17879
\(996\) 54.1875 1.71700
\(997\) −61.2404 −1.93950 −0.969751 0.244096i \(-0.921509\pi\)
−0.969751 + 0.244096i \(0.921509\pi\)
\(998\) −56.6122 −1.79203
\(999\) −32.6323 −1.03244
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 8027.2.a.d.1.6 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.d.1.6 149 1.1 even 1 trivial