Properties

Label 8027.2.a.d.1.17
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 1.17
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)
 
\(f(q)\) \(=\) \(q-2.27388 q^{2} +0.787573 q^{3} +3.17053 q^{4} -4.28008 q^{5} -1.79085 q^{6} +1.25028 q^{7} -2.66164 q^{8} -2.37973 q^{9} +O(q^{10})\) \(q-2.27388 q^{2} +0.787573 q^{3} +3.17053 q^{4} -4.28008 q^{5} -1.79085 q^{6} +1.25028 q^{7} -2.66164 q^{8} -2.37973 q^{9} +9.73239 q^{10} +2.44033 q^{11} +2.49702 q^{12} +2.67145 q^{13} -2.84298 q^{14} -3.37088 q^{15} -0.288799 q^{16} +2.63677 q^{17} +5.41122 q^{18} -3.45020 q^{19} -13.5701 q^{20} +0.984684 q^{21} -5.54902 q^{22} -1.00000 q^{23} -2.09624 q^{24} +13.3191 q^{25} -6.07456 q^{26} -4.23693 q^{27} +3.96404 q^{28} +7.37128 q^{29} +7.66497 q^{30} -9.30618 q^{31} +5.97998 q^{32} +1.92194 q^{33} -5.99571 q^{34} -5.35129 q^{35} -7.54500 q^{36} -6.59241 q^{37} +7.84534 q^{38} +2.10396 q^{39} +11.3921 q^{40} +2.90291 q^{41} -2.23905 q^{42} -8.50068 q^{43} +7.73714 q^{44} +10.1854 q^{45} +2.27388 q^{46} +3.14677 q^{47} -0.227450 q^{48} -5.43681 q^{49} -30.2861 q^{50} +2.07665 q^{51} +8.46992 q^{52} +6.05340 q^{53} +9.63427 q^{54} -10.4448 q^{55} -3.32779 q^{56} -2.71728 q^{57} -16.7614 q^{58} +3.90287 q^{59} -10.6875 q^{60} +0.783546 q^{61} +21.1611 q^{62} -2.97532 q^{63} -13.0202 q^{64} -11.4340 q^{65} -4.37026 q^{66} +6.43593 q^{67} +8.35997 q^{68} -0.787573 q^{69} +12.1682 q^{70} +0.619609 q^{71} +6.33399 q^{72} +11.0559 q^{73} +14.9903 q^{74} +10.4898 q^{75} -10.9390 q^{76} +3.05109 q^{77} -4.78416 q^{78} -6.19070 q^{79} +1.23608 q^{80} +3.80229 q^{81} -6.60087 q^{82} -13.5113 q^{83} +3.12197 q^{84} -11.2856 q^{85} +19.3295 q^{86} +5.80542 q^{87} -6.49529 q^{88} -1.31530 q^{89} -23.1605 q^{90} +3.34006 q^{91} -3.17053 q^{92} -7.32930 q^{93} -7.15538 q^{94} +14.7671 q^{95} +4.70968 q^{96} +0.201416 q^{97} +12.3626 q^{98} -5.80732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27388 −1.60788 −0.803938 0.594713i \(-0.797266\pi\)
−0.803938 + 0.594713i \(0.797266\pi\)
\(3\) 0.787573 0.454706 0.227353 0.973812i \(-0.426993\pi\)
0.227353 + 0.973812i \(0.426993\pi\)
\(4\) 3.17053 1.58527
\(5\) −4.28008 −1.91411 −0.957056 0.289904i \(-0.906376\pi\)
−0.957056 + 0.289904i \(0.906376\pi\)
\(6\) −1.79085 −0.731110
\(7\) 1.25028 0.472560 0.236280 0.971685i \(-0.424072\pi\)
0.236280 + 0.971685i \(0.424072\pi\)
\(8\) −2.66164 −0.941034
\(9\) −2.37973 −0.793243
\(10\) 9.73239 3.07765
\(11\) 2.44033 0.735787 0.367894 0.929868i \(-0.380079\pi\)
0.367894 + 0.929868i \(0.380079\pi\)
\(12\) 2.49702 0.720829
\(13\) 2.67145 0.740928 0.370464 0.928847i \(-0.379199\pi\)
0.370464 + 0.928847i \(0.379199\pi\)
\(14\) −2.84298 −0.759818
\(15\) −3.37088 −0.870357
\(16\) −0.288799 −0.0721997
\(17\) 2.63677 0.639512 0.319756 0.947500i \(-0.396399\pi\)
0.319756 + 0.947500i \(0.396399\pi\)
\(18\) 5.41122 1.27544
\(19\) −3.45020 −0.791530 −0.395765 0.918352i \(-0.629520\pi\)
−0.395765 + 0.918352i \(0.629520\pi\)
\(20\) −13.5701 −3.03437
\(21\) 0.984684 0.214876
\(22\) −5.54902 −1.18305
\(23\) −1.00000 −0.208514
\(24\) −2.09624 −0.427893
\(25\) 13.3191 2.66382
\(26\) −6.07456 −1.19132
\(27\) −4.23693 −0.815398
\(28\) 3.96404 0.749133
\(29\) 7.37128 1.36881 0.684406 0.729101i \(-0.260062\pi\)
0.684406 + 0.729101i \(0.260062\pi\)
\(30\) 7.66497 1.39943
\(31\) −9.30618 −1.67144 −0.835719 0.549157i \(-0.814949\pi\)
−0.835719 + 0.549157i \(0.814949\pi\)
\(32\) 5.97998 1.05712
\(33\) 1.92194 0.334567
\(34\) −5.99571 −1.02826
\(35\) −5.35129 −0.904533
\(36\) −7.54500 −1.25750
\(37\) −6.59241 −1.08379 −0.541893 0.840448i \(-0.682292\pi\)
−0.541893 + 0.840448i \(0.682292\pi\)
\(38\) 7.84534 1.27268
\(39\) 2.10396 0.336904
\(40\) 11.3921 1.80124
\(41\) 2.90291 0.453358 0.226679 0.973969i \(-0.427213\pi\)
0.226679 + 0.973969i \(0.427213\pi\)
\(42\) −2.23905 −0.345494
\(43\) −8.50068 −1.29634 −0.648171 0.761495i \(-0.724466\pi\)
−0.648171 + 0.761495i \(0.724466\pi\)
\(44\) 7.73714 1.16642
\(45\) 10.1854 1.51835
\(46\) 2.27388 0.335265
\(47\) 3.14677 0.459004 0.229502 0.973308i \(-0.426290\pi\)
0.229502 + 0.973308i \(0.426290\pi\)
\(48\) −0.227450 −0.0328296
\(49\) −5.43681 −0.776687
\(50\) −30.2861 −4.28309
\(51\) 2.07665 0.290790
\(52\) 8.46992 1.17457
\(53\) 6.05340 0.831499 0.415750 0.909479i \(-0.363519\pi\)
0.415750 + 0.909479i \(0.363519\pi\)
\(54\) 9.63427 1.31106
\(55\) −10.4448 −1.40838
\(56\) −3.32779 −0.444695
\(57\) −2.71728 −0.359913
\(58\) −16.7614 −2.20088
\(59\) 3.90287 0.508110 0.254055 0.967190i \(-0.418236\pi\)
0.254055 + 0.967190i \(0.418236\pi\)
\(60\) −10.6875 −1.37975
\(61\) 0.783546 0.100323 0.0501614 0.998741i \(-0.484026\pi\)
0.0501614 + 0.998741i \(0.484026\pi\)
\(62\) 21.1611 2.68747
\(63\) −2.97532 −0.374855
\(64\) −13.0202 −1.62752
\(65\) −11.4340 −1.41822
\(66\) −4.37026 −0.537941
\(67\) 6.43593 0.786274 0.393137 0.919480i \(-0.371390\pi\)
0.393137 + 0.919480i \(0.371390\pi\)
\(68\) 8.35997 1.01380
\(69\) −0.787573 −0.0948127
\(70\) 12.1682 1.45438
\(71\) 0.619609 0.0735340 0.0367670 0.999324i \(-0.488294\pi\)
0.0367670 + 0.999324i \(0.488294\pi\)
\(72\) 6.33399 0.746468
\(73\) 11.0559 1.29400 0.647000 0.762490i \(-0.276023\pi\)
0.647000 + 0.762490i \(0.276023\pi\)
\(74\) 14.9903 1.74259
\(75\) 10.4898 1.21125
\(76\) −10.9390 −1.25478
\(77\) 3.05109 0.347704
\(78\) −4.78416 −0.541700
\(79\) −6.19070 −0.696508 −0.348254 0.937400i \(-0.613225\pi\)
−0.348254 + 0.937400i \(0.613225\pi\)
\(80\) 1.23608 0.138198
\(81\) 3.80229 0.422477
\(82\) −6.60087 −0.728944
\(83\) −13.5113 −1.48306 −0.741530 0.670919i \(-0.765900\pi\)
−0.741530 + 0.670919i \(0.765900\pi\)
\(84\) 3.12197 0.340635
\(85\) −11.2856 −1.22410
\(86\) 19.3295 2.08436
\(87\) 5.80542 0.622406
\(88\) −6.49529 −0.692400
\(89\) −1.31530 −0.139421 −0.0697107 0.997567i \(-0.522208\pi\)
−0.0697107 + 0.997567i \(0.522208\pi\)
\(90\) −23.1605 −2.44133
\(91\) 3.34006 0.350133
\(92\) −3.17053 −0.330551
\(93\) −7.32930 −0.760013
\(94\) −7.15538 −0.738022
\(95\) 14.7671 1.51508
\(96\) 4.70968 0.480679
\(97\) 0.201416 0.0204507 0.0102254 0.999948i \(-0.496745\pi\)
0.0102254 + 0.999948i \(0.496745\pi\)
\(98\) 12.3626 1.24882
\(99\) −5.80732 −0.583658
\(100\) 42.2286 4.22286
\(101\) −2.20421 −0.219327 −0.109664 0.993969i \(-0.534977\pi\)
−0.109664 + 0.993969i \(0.534977\pi\)
\(102\) −4.72206 −0.467553
\(103\) −6.69109 −0.659292 −0.329646 0.944105i \(-0.606929\pi\)
−0.329646 + 0.944105i \(0.606929\pi\)
\(104\) −7.11046 −0.697238
\(105\) −4.21453 −0.411296
\(106\) −13.7647 −1.33695
\(107\) 15.4984 1.49829 0.749145 0.662406i \(-0.230465\pi\)
0.749145 + 0.662406i \(0.230465\pi\)
\(108\) −13.4333 −1.29262
\(109\) 0.0936218 0.00896734 0.00448367 0.999990i \(-0.498573\pi\)
0.00448367 + 0.999990i \(0.498573\pi\)
\(110\) 23.7503 2.26450
\(111\) −5.19200 −0.492803
\(112\) −0.361079 −0.0341187
\(113\) −15.2000 −1.42990 −0.714948 0.699178i \(-0.753550\pi\)
−0.714948 + 0.699178i \(0.753550\pi\)
\(114\) 6.17878 0.578695
\(115\) 4.28008 0.399120
\(116\) 23.3709 2.16993
\(117\) −6.35733 −0.587736
\(118\) −8.87465 −0.816978
\(119\) 3.29670 0.302208
\(120\) 8.97208 0.819035
\(121\) −5.04479 −0.458617
\(122\) −1.78169 −0.161307
\(123\) 2.28625 0.206145
\(124\) −29.5055 −2.64967
\(125\) −35.6065 −3.18474
\(126\) 6.76552 0.602720
\(127\) 12.8681 1.14186 0.570928 0.821000i \(-0.306584\pi\)
0.570928 + 0.821000i \(0.306584\pi\)
\(128\) 17.6463 1.55973
\(129\) −6.69491 −0.589454
\(130\) 25.9996 2.28032
\(131\) −2.56745 −0.224319 −0.112160 0.993690i \(-0.535777\pi\)
−0.112160 + 0.993690i \(0.535777\pi\)
\(132\) 6.09356 0.530377
\(133\) −4.31370 −0.374045
\(134\) −14.6345 −1.26423
\(135\) 18.1344 1.56076
\(136\) −7.01816 −0.601802
\(137\) 1.71935 0.146894 0.0734470 0.997299i \(-0.476600\pi\)
0.0734470 + 0.997299i \(0.476600\pi\)
\(138\) 1.79085 0.152447
\(139\) 21.4823 1.82210 0.911051 0.412294i \(-0.135272\pi\)
0.911051 + 0.412294i \(0.135272\pi\)
\(140\) −16.9664 −1.43392
\(141\) 2.47831 0.208712
\(142\) −1.40892 −0.118234
\(143\) 6.51923 0.545165
\(144\) 0.687263 0.0572719
\(145\) −31.5497 −2.62006
\(146\) −25.1399 −2.08059
\(147\) −4.28188 −0.353164
\(148\) −20.9014 −1.71809
\(149\) 3.15103 0.258142 0.129071 0.991635i \(-0.458800\pi\)
0.129071 + 0.991635i \(0.458800\pi\)
\(150\) −23.8525 −1.94755
\(151\) 11.9695 0.974061 0.487031 0.873385i \(-0.338080\pi\)
0.487031 + 0.873385i \(0.338080\pi\)
\(152\) 9.18320 0.744856
\(153\) −6.27481 −0.507288
\(154\) −6.93781 −0.559064
\(155\) 39.8312 3.19932
\(156\) 6.67068 0.534082
\(157\) 16.0992 1.28485 0.642427 0.766347i \(-0.277928\pi\)
0.642427 + 0.766347i \(0.277928\pi\)
\(158\) 14.0769 1.11990
\(159\) 4.76750 0.378087
\(160\) −25.5948 −2.02345
\(161\) −1.25028 −0.0985356
\(162\) −8.64596 −0.679291
\(163\) −0.269021 −0.0210714 −0.0105357 0.999944i \(-0.503354\pi\)
−0.0105357 + 0.999944i \(0.503354\pi\)
\(164\) 9.20376 0.718693
\(165\) −8.22606 −0.640398
\(166\) 30.7231 2.38458
\(167\) 10.3717 0.802584 0.401292 0.915950i \(-0.368561\pi\)
0.401292 + 0.915950i \(0.368561\pi\)
\(168\) −2.62088 −0.202205
\(169\) −5.86334 −0.451026
\(170\) 25.6621 1.96820
\(171\) 8.21053 0.627875
\(172\) −26.9517 −2.05505
\(173\) 17.7835 1.35205 0.676026 0.736878i \(-0.263701\pi\)
0.676026 + 0.736878i \(0.263701\pi\)
\(174\) −13.2008 −1.00075
\(175\) 16.6526 1.25882
\(176\) −0.704765 −0.0531236
\(177\) 3.07379 0.231041
\(178\) 2.99083 0.224172
\(179\) 22.9220 1.71327 0.856634 0.515925i \(-0.172552\pi\)
0.856634 + 0.515925i \(0.172552\pi\)
\(180\) 32.2932 2.40700
\(181\) −19.5684 −1.45451 −0.727255 0.686367i \(-0.759204\pi\)
−0.727255 + 0.686367i \(0.759204\pi\)
\(182\) −7.59488 −0.562970
\(183\) 0.617100 0.0456173
\(184\) 2.66164 0.196219
\(185\) 28.2161 2.07449
\(186\) 16.6659 1.22201
\(187\) 6.43460 0.470544
\(188\) 9.97694 0.727643
\(189\) −5.29733 −0.385324
\(190\) −33.5787 −2.43605
\(191\) −16.5236 −1.19561 −0.597804 0.801642i \(-0.703960\pi\)
−0.597804 + 0.801642i \(0.703960\pi\)
\(192\) −10.2543 −0.740043
\(193\) −0.896292 −0.0645165 −0.0322583 0.999480i \(-0.510270\pi\)
−0.0322583 + 0.999480i \(0.510270\pi\)
\(194\) −0.457997 −0.0328823
\(195\) −9.00514 −0.644872
\(196\) −17.2376 −1.23125
\(197\) 5.69587 0.405814 0.202907 0.979198i \(-0.434961\pi\)
0.202907 + 0.979198i \(0.434961\pi\)
\(198\) 13.2052 0.938449
\(199\) −5.86630 −0.415851 −0.207926 0.978145i \(-0.566671\pi\)
−0.207926 + 0.978145i \(0.566671\pi\)
\(200\) −35.4507 −2.50675
\(201\) 5.06876 0.357523
\(202\) 5.01211 0.352651
\(203\) 9.21613 0.646846
\(204\) 6.58409 0.460978
\(205\) −12.4247 −0.867778
\(206\) 15.2147 1.06006
\(207\) 2.37973 0.165403
\(208\) −0.771513 −0.0534948
\(209\) −8.41962 −0.582397
\(210\) 9.58334 0.661313
\(211\) 11.7676 0.810116 0.405058 0.914291i \(-0.367251\pi\)
0.405058 + 0.914291i \(0.367251\pi\)
\(212\) 19.1925 1.31815
\(213\) 0.487987 0.0334363
\(214\) −35.2416 −2.40906
\(215\) 36.3836 2.48134
\(216\) 11.2772 0.767317
\(217\) −11.6353 −0.789855
\(218\) −0.212885 −0.0144184
\(219\) 8.70737 0.588389
\(220\) −33.1156 −2.23265
\(221\) 7.04402 0.473832
\(222\) 11.8060 0.792367
\(223\) 25.3383 1.69678 0.848390 0.529372i \(-0.177572\pi\)
0.848390 + 0.529372i \(0.177572\pi\)
\(224\) 7.47663 0.499554
\(225\) −31.6959 −2.11306
\(226\) 34.5630 2.29909
\(227\) −22.1634 −1.47104 −0.735519 0.677504i \(-0.763062\pi\)
−0.735519 + 0.677504i \(0.763062\pi\)
\(228\) −8.61523 −0.570557
\(229\) 0.975720 0.0644774 0.0322387 0.999480i \(-0.489736\pi\)
0.0322387 + 0.999480i \(0.489736\pi\)
\(230\) −9.73239 −0.641735
\(231\) 2.40295 0.158103
\(232\) −19.6197 −1.28810
\(233\) 21.7967 1.42795 0.713974 0.700172i \(-0.246893\pi\)
0.713974 + 0.700172i \(0.246893\pi\)
\(234\) 14.4558 0.945006
\(235\) −13.4684 −0.878585
\(236\) 12.3742 0.805489
\(237\) −4.87563 −0.316706
\(238\) −7.49629 −0.485912
\(239\) −25.1787 −1.62868 −0.814338 0.580391i \(-0.802900\pi\)
−0.814338 + 0.580391i \(0.802900\pi\)
\(240\) 0.973506 0.0628396
\(241\) −24.6809 −1.58984 −0.794919 0.606716i \(-0.792487\pi\)
−0.794919 + 0.606716i \(0.792487\pi\)
\(242\) 11.4712 0.737400
\(243\) 15.7054 1.00750
\(244\) 2.48426 0.159038
\(245\) 23.2700 1.48667
\(246\) −5.19867 −0.331455
\(247\) −9.21704 −0.586466
\(248\) 24.7697 1.57288
\(249\) −10.6412 −0.674356
\(250\) 80.9648 5.12067
\(251\) 28.2330 1.78205 0.891024 0.453956i \(-0.149988\pi\)
0.891024 + 0.453956i \(0.149988\pi\)
\(252\) −9.43334 −0.594244
\(253\) −2.44033 −0.153422
\(254\) −29.2604 −1.83596
\(255\) −8.88824 −0.556603
\(256\) −14.0853 −0.880331
\(257\) 14.8114 0.923912 0.461956 0.886903i \(-0.347148\pi\)
0.461956 + 0.886903i \(0.347148\pi\)
\(258\) 15.2234 0.947769
\(259\) −8.24234 −0.512154
\(260\) −36.2520 −2.24825
\(261\) −17.5416 −1.08580
\(262\) 5.83808 0.360678
\(263\) −16.3895 −1.01062 −0.505309 0.862939i \(-0.668621\pi\)
−0.505309 + 0.862939i \(0.668621\pi\)
\(264\) −5.11552 −0.314838
\(265\) −25.9091 −1.59158
\(266\) 9.80884 0.601419
\(267\) −1.03589 −0.0633957
\(268\) 20.4053 1.24645
\(269\) −24.4249 −1.48921 −0.744605 0.667505i \(-0.767362\pi\)
−0.744605 + 0.667505i \(0.767362\pi\)
\(270\) −41.2355 −2.50951
\(271\) −8.50273 −0.516504 −0.258252 0.966078i \(-0.583146\pi\)
−0.258252 + 0.966078i \(0.583146\pi\)
\(272\) −0.761498 −0.0461726
\(273\) 2.63054 0.159207
\(274\) −3.90960 −0.236187
\(275\) 32.5030 1.96001
\(276\) −2.49702 −0.150303
\(277\) −22.8741 −1.37437 −0.687186 0.726481i \(-0.741154\pi\)
−0.687186 + 0.726481i \(0.741154\pi\)
\(278\) −48.8481 −2.92971
\(279\) 22.1462 1.32586
\(280\) 14.2432 0.851196
\(281\) −10.3974 −0.620259 −0.310129 0.950694i \(-0.600372\pi\)
−0.310129 + 0.950694i \(0.600372\pi\)
\(282\) −5.63539 −0.335583
\(283\) −7.61323 −0.452559 −0.226280 0.974062i \(-0.572656\pi\)
−0.226280 + 0.974062i \(0.572656\pi\)
\(284\) 1.96449 0.116571
\(285\) 11.6302 0.688913
\(286\) −14.8239 −0.876558
\(287\) 3.62944 0.214239
\(288\) −14.2307 −0.838554
\(289\) −10.0474 −0.591025
\(290\) 71.7402 4.21273
\(291\) 0.158630 0.00929907
\(292\) 35.0532 2.05133
\(293\) 27.1230 1.58454 0.792270 0.610170i \(-0.208899\pi\)
0.792270 + 0.610170i \(0.208899\pi\)
\(294\) 9.73649 0.567844
\(295\) −16.7046 −0.972579
\(296\) 17.5467 1.01988
\(297\) −10.3395 −0.599959
\(298\) −7.16505 −0.415060
\(299\) −2.67145 −0.154494
\(300\) 33.2581 1.92016
\(301\) −10.6282 −0.612600
\(302\) −27.2171 −1.56617
\(303\) −1.73598 −0.0997293
\(304\) 0.996414 0.0571482
\(305\) −3.35364 −0.192029
\(306\) 14.2682 0.815656
\(307\) −19.8534 −1.13309 −0.566547 0.824029i \(-0.691721\pi\)
−0.566547 + 0.824029i \(0.691721\pi\)
\(308\) 9.67356 0.551202
\(309\) −5.26972 −0.299784
\(310\) −90.5714 −5.14411
\(311\) −6.48325 −0.367632 −0.183816 0.982961i \(-0.558845\pi\)
−0.183816 + 0.982961i \(0.558845\pi\)
\(312\) −5.60001 −0.317038
\(313\) −10.6090 −0.599656 −0.299828 0.953993i \(-0.596929\pi\)
−0.299828 + 0.953993i \(0.596929\pi\)
\(314\) −36.6076 −2.06588
\(315\) 12.7346 0.717514
\(316\) −19.6278 −1.10415
\(317\) −17.2767 −0.970356 −0.485178 0.874415i \(-0.661245\pi\)
−0.485178 + 0.874415i \(0.661245\pi\)
\(318\) −10.8407 −0.607917
\(319\) 17.9883 1.00715
\(320\) 55.7274 3.11526
\(321\) 12.2062 0.681281
\(322\) 2.84298 0.158433
\(323\) −9.09739 −0.506192
\(324\) 12.0553 0.669738
\(325\) 35.5814 1.97370
\(326\) 0.611722 0.0338802
\(327\) 0.0737340 0.00407750
\(328\) −7.72652 −0.426625
\(329\) 3.93434 0.216907
\(330\) 18.7051 1.02968
\(331\) −27.1881 −1.49439 −0.747196 0.664604i \(-0.768600\pi\)
−0.747196 + 0.664604i \(0.768600\pi\)
\(332\) −42.8381 −2.35104
\(333\) 15.6881 0.859705
\(334\) −23.5839 −1.29045
\(335\) −27.5463 −1.50502
\(336\) −0.284376 −0.0155140
\(337\) 4.48772 0.244462 0.122231 0.992502i \(-0.460995\pi\)
0.122231 + 0.992502i \(0.460995\pi\)
\(338\) 13.3325 0.725194
\(339\) −11.9711 −0.650182
\(340\) −35.7814 −1.94052
\(341\) −22.7101 −1.22982
\(342\) −18.6698 −1.00955
\(343\) −15.5495 −0.839591
\(344\) 22.6258 1.21990
\(345\) 3.37088 0.181482
\(346\) −40.4375 −2.17393
\(347\) 1.50060 0.0805564 0.0402782 0.999189i \(-0.487176\pi\)
0.0402782 + 0.999189i \(0.487176\pi\)
\(348\) 18.4063 0.986679
\(349\) −1.00000 −0.0535288
\(350\) −37.8659 −2.02402
\(351\) −11.3188 −0.604151
\(352\) 14.5931 0.777817
\(353\) 15.8373 0.842934 0.421467 0.906844i \(-0.361515\pi\)
0.421467 + 0.906844i \(0.361515\pi\)
\(354\) −6.98944 −0.371484
\(355\) −2.65198 −0.140752
\(356\) −4.17020 −0.221020
\(357\) 2.59639 0.137416
\(358\) −52.1218 −2.75472
\(359\) −25.7781 −1.36052 −0.680258 0.732972i \(-0.738132\pi\)
−0.680258 + 0.732972i \(0.738132\pi\)
\(360\) −27.1100 −1.42882
\(361\) −7.09614 −0.373481
\(362\) 44.4963 2.33867
\(363\) −3.97314 −0.208536
\(364\) 10.5897 0.555053
\(365\) −47.3204 −2.47686
\(366\) −1.40321 −0.0733470
\(367\) −9.60812 −0.501540 −0.250770 0.968047i \(-0.580684\pi\)
−0.250770 + 0.968047i \(0.580684\pi\)
\(368\) 0.288799 0.0150547
\(369\) −6.90814 −0.359623
\(370\) −64.1599 −3.33552
\(371\) 7.56843 0.392933
\(372\) −23.2378 −1.20482
\(373\) −0.209451 −0.0108450 −0.00542248 0.999985i \(-0.501726\pi\)
−0.00542248 + 0.999985i \(0.501726\pi\)
\(374\) −14.6315 −0.756577
\(375\) −28.0427 −1.44812
\(376\) −8.37559 −0.431938
\(377\) 19.6920 1.01419
\(378\) 12.0455 0.619554
\(379\) −18.0633 −0.927849 −0.463925 0.885875i \(-0.653559\pi\)
−0.463925 + 0.885875i \(0.653559\pi\)
\(380\) 46.8196 2.40180
\(381\) 10.1345 0.519208
\(382\) 37.5728 1.92239
\(383\) 19.0299 0.972384 0.486192 0.873852i \(-0.338386\pi\)
0.486192 + 0.873852i \(0.338386\pi\)
\(384\) 13.8978 0.709218
\(385\) −13.0589 −0.665543
\(386\) 2.03806 0.103735
\(387\) 20.2293 1.02831
\(388\) 0.638597 0.0324199
\(389\) 27.6343 1.40111 0.700556 0.713597i \(-0.252935\pi\)
0.700556 + 0.713597i \(0.252935\pi\)
\(390\) 20.4766 1.03687
\(391\) −2.63677 −0.133347
\(392\) 14.4709 0.730888
\(393\) −2.02206 −0.101999
\(394\) −12.9517 −0.652498
\(395\) 26.4967 1.33319
\(396\) −18.4123 −0.925252
\(397\) −34.8216 −1.74764 −0.873822 0.486245i \(-0.838366\pi\)
−0.873822 + 0.486245i \(0.838366\pi\)
\(398\) 13.3393 0.668637
\(399\) −3.39736 −0.170081
\(400\) −3.84655 −0.192327
\(401\) 21.5855 1.07793 0.538964 0.842329i \(-0.318816\pi\)
0.538964 + 0.842329i \(0.318816\pi\)
\(402\) −11.5258 −0.574853
\(403\) −24.8610 −1.23842
\(404\) −6.98852 −0.347692
\(405\) −16.2741 −0.808668
\(406\) −20.9564 −1.04005
\(407\) −16.0877 −0.797435
\(408\) −5.52731 −0.273643
\(409\) 23.6939 1.17159 0.585794 0.810460i \(-0.300783\pi\)
0.585794 + 0.810460i \(0.300783\pi\)
\(410\) 28.2523 1.39528
\(411\) 1.35411 0.0667935
\(412\) −21.2143 −1.04515
\(413\) 4.87966 0.240113
\(414\) −5.41122 −0.265947
\(415\) 57.8296 2.83874
\(416\) 15.9752 0.783251
\(417\) 16.9189 0.828520
\(418\) 19.1452 0.936423
\(419\) 16.6173 0.811808 0.405904 0.913916i \(-0.366957\pi\)
0.405904 + 0.913916i \(0.366957\pi\)
\(420\) −13.3623 −0.652013
\(421\) 8.12051 0.395769 0.197885 0.980225i \(-0.436593\pi\)
0.197885 + 0.980225i \(0.436593\pi\)
\(422\) −26.7582 −1.30257
\(423\) −7.48847 −0.364102
\(424\) −16.1120 −0.782469
\(425\) 35.1195 1.70354
\(426\) −1.10962 −0.0537615
\(427\) 0.979650 0.0474086
\(428\) 49.1382 2.37519
\(429\) 5.13437 0.247890
\(430\) −82.7320 −3.98969
\(431\) 10.8759 0.523873 0.261937 0.965085i \(-0.415639\pi\)
0.261937 + 0.965085i \(0.415639\pi\)
\(432\) 1.22362 0.0588715
\(433\) 35.2088 1.69203 0.846014 0.533161i \(-0.178996\pi\)
0.846014 + 0.533161i \(0.178996\pi\)
\(434\) 26.4573 1.26999
\(435\) −24.8477 −1.19135
\(436\) 0.296831 0.0142156
\(437\) 3.45020 0.165045
\(438\) −19.7995 −0.946057
\(439\) 25.8833 1.23534 0.617670 0.786437i \(-0.288077\pi\)
0.617670 + 0.786437i \(0.288077\pi\)
\(440\) 27.8004 1.32533
\(441\) 12.9381 0.616101
\(442\) −16.0172 −0.761863
\(443\) −35.1901 −1.67193 −0.835965 0.548782i \(-0.815092\pi\)
−0.835965 + 0.548782i \(0.815092\pi\)
\(444\) −16.4614 −0.781224
\(445\) 5.62959 0.266868
\(446\) −57.6163 −2.72821
\(447\) 2.48166 0.117379
\(448\) −16.2788 −0.769102
\(449\) −8.97668 −0.423636 −0.211818 0.977309i \(-0.567938\pi\)
−0.211818 + 0.977309i \(0.567938\pi\)
\(450\) 72.0726 3.39753
\(451\) 7.08406 0.333575
\(452\) −48.1921 −2.26676
\(453\) 9.42683 0.442911
\(454\) 50.3970 2.36525
\(455\) −14.2957 −0.670193
\(456\) 7.23244 0.338690
\(457\) −17.6964 −0.827803 −0.413902 0.910322i \(-0.635834\pi\)
−0.413902 + 0.910322i \(0.635834\pi\)
\(458\) −2.21867 −0.103672
\(459\) −11.1718 −0.521456
\(460\) 13.5701 0.632711
\(461\) −11.3698 −0.529542 −0.264771 0.964311i \(-0.585296\pi\)
−0.264771 + 0.964311i \(0.585296\pi\)
\(462\) −5.46403 −0.254210
\(463\) 33.8439 1.57286 0.786431 0.617679i \(-0.211927\pi\)
0.786431 + 0.617679i \(0.211927\pi\)
\(464\) −2.12882 −0.0988279
\(465\) 31.3700 1.45475
\(466\) −49.5630 −2.29596
\(467\) −4.76103 −0.220314 −0.110157 0.993914i \(-0.535135\pi\)
−0.110157 + 0.993914i \(0.535135\pi\)
\(468\) −20.1561 −0.931717
\(469\) 8.04669 0.371562
\(470\) 30.6256 1.41266
\(471\) 12.6793 0.584230
\(472\) −10.3880 −0.478149
\(473\) −20.7445 −0.953832
\(474\) 11.0866 0.509224
\(475\) −45.9536 −2.10849
\(476\) 10.4523 0.479079
\(477\) −14.4055 −0.659581
\(478\) 57.2534 2.61871
\(479\) −3.63253 −0.165975 −0.0829874 0.996551i \(-0.526446\pi\)
−0.0829874 + 0.996551i \(0.526446\pi\)
\(480\) −20.1578 −0.920074
\(481\) −17.6113 −0.803007
\(482\) 56.1214 2.55626
\(483\) −0.984684 −0.0448047
\(484\) −15.9947 −0.727030
\(485\) −0.862079 −0.0391450
\(486\) −35.7121 −1.61994
\(487\) 2.27769 0.103212 0.0516060 0.998668i \(-0.483566\pi\)
0.0516060 + 0.998668i \(0.483566\pi\)
\(488\) −2.08552 −0.0944071
\(489\) −0.211874 −0.00958127
\(490\) −52.9132 −2.39037
\(491\) −28.9331 −1.30573 −0.652866 0.757473i \(-0.726434\pi\)
−0.652866 + 0.757473i \(0.726434\pi\)
\(492\) 7.24864 0.326794
\(493\) 19.4364 0.875371
\(494\) 20.9584 0.942965
\(495\) 24.8558 1.11719
\(496\) 2.68761 0.120677
\(497\) 0.774682 0.0347493
\(498\) 24.1967 1.08428
\(499\) −26.9272 −1.20543 −0.602714 0.797957i \(-0.705914\pi\)
−0.602714 + 0.797957i \(0.705914\pi\)
\(500\) −112.891 −5.04866
\(501\) 8.16845 0.364939
\(502\) −64.1984 −2.86531
\(503\) −27.2625 −1.21558 −0.607788 0.794099i \(-0.707943\pi\)
−0.607788 + 0.794099i \(0.707943\pi\)
\(504\) 7.91924 0.352751
\(505\) 9.43421 0.419817
\(506\) 5.54902 0.246684
\(507\) −4.61781 −0.205084
\(508\) 40.7985 1.81014
\(509\) −18.0179 −0.798628 −0.399314 0.916814i \(-0.630752\pi\)
−0.399314 + 0.916814i \(0.630752\pi\)
\(510\) 20.2108 0.894949
\(511\) 13.8230 0.611493
\(512\) −3.26437 −0.144266
\(513\) 14.6182 0.645411
\(514\) −33.6794 −1.48554
\(515\) 28.6384 1.26196
\(516\) −21.2264 −0.934441
\(517\) 7.67916 0.337729
\(518\) 18.7421 0.823480
\(519\) 14.0058 0.614786
\(520\) 30.4334 1.33459
\(521\) −16.7772 −0.735024 −0.367512 0.930019i \(-0.619790\pi\)
−0.367512 + 0.930019i \(0.619790\pi\)
\(522\) 39.8876 1.74583
\(523\) −11.3706 −0.497200 −0.248600 0.968606i \(-0.579970\pi\)
−0.248600 + 0.968606i \(0.579970\pi\)
\(524\) −8.14018 −0.355606
\(525\) 13.1151 0.572391
\(526\) 37.2677 1.62495
\(527\) −24.5383 −1.06890
\(528\) −0.555054 −0.0241556
\(529\) 1.00000 0.0434783
\(530\) 58.9141 2.55907
\(531\) −9.28777 −0.403055
\(532\) −13.6767 −0.592961
\(533\) 7.75499 0.335906
\(534\) 2.35550 0.101932
\(535\) −66.3346 −2.86789
\(536\) −17.1302 −0.739910
\(537\) 18.0527 0.779033
\(538\) 55.5392 2.39447
\(539\) −13.2676 −0.571476
\(540\) 57.4957 2.47422
\(541\) −16.3138 −0.701384 −0.350692 0.936491i \(-0.614054\pi\)
−0.350692 + 0.936491i \(0.614054\pi\)
\(542\) 19.3342 0.830474
\(543\) −15.4116 −0.661374
\(544\) 15.7679 0.676042
\(545\) −0.400709 −0.0171645
\(546\) −5.98153 −0.255986
\(547\) −38.2131 −1.63387 −0.816937 0.576727i \(-0.804330\pi\)
−0.816937 + 0.576727i \(0.804330\pi\)
\(548\) 5.45125 0.232866
\(549\) −1.86463 −0.0795803
\(550\) −73.9080 −3.15145
\(551\) −25.4324 −1.08345
\(552\) 2.09624 0.0892219
\(553\) −7.74009 −0.329142
\(554\) 52.0130 2.20982
\(555\) 22.2222 0.943280
\(556\) 68.1102 2.88851
\(557\) −37.9355 −1.60738 −0.803688 0.595050i \(-0.797132\pi\)
−0.803688 + 0.595050i \(0.797132\pi\)
\(558\) −50.3577 −2.13181
\(559\) −22.7092 −0.960496
\(560\) 1.54545 0.0653070
\(561\) 5.06772 0.213959
\(562\) 23.6425 0.997299
\(563\) 27.1671 1.14496 0.572478 0.819920i \(-0.305982\pi\)
0.572478 + 0.819920i \(0.305982\pi\)
\(564\) 7.85757 0.330863
\(565\) 65.0572 2.73698
\(566\) 17.3116 0.727659
\(567\) 4.75392 0.199646
\(568\) −1.64918 −0.0691980
\(569\) 2.64363 0.110827 0.0554133 0.998464i \(-0.482352\pi\)
0.0554133 + 0.998464i \(0.482352\pi\)
\(570\) −26.4457 −1.10769
\(571\) 24.1686 1.01143 0.505713 0.862702i \(-0.331230\pi\)
0.505713 + 0.862702i \(0.331230\pi\)
\(572\) 20.6694 0.864231
\(573\) −13.0136 −0.543650
\(574\) −8.25291 −0.344470
\(575\) −13.3191 −0.555445
\(576\) 30.9845 1.29102
\(577\) −26.7917 −1.11535 −0.557676 0.830059i \(-0.688307\pi\)
−0.557676 + 0.830059i \(0.688307\pi\)
\(578\) 22.8466 0.950295
\(579\) −0.705896 −0.0293360
\(580\) −100.029 −4.15349
\(581\) −16.8929 −0.700835
\(582\) −0.360706 −0.0149518
\(583\) 14.7723 0.611806
\(584\) −29.4270 −1.21770
\(585\) 27.2099 1.12499
\(586\) −61.6744 −2.54775
\(587\) −21.7750 −0.898752 −0.449376 0.893343i \(-0.648354\pi\)
−0.449376 + 0.893343i \(0.648354\pi\)
\(588\) −13.5758 −0.559858
\(589\) 32.1081 1.32299
\(590\) 37.9842 1.56379
\(591\) 4.48591 0.184526
\(592\) 1.90388 0.0782490
\(593\) −17.0690 −0.700940 −0.350470 0.936574i \(-0.613978\pi\)
−0.350470 + 0.936574i \(0.613978\pi\)
\(594\) 23.5108 0.964660
\(595\) −14.1101 −0.578459
\(596\) 9.99042 0.409224
\(597\) −4.62014 −0.189090
\(598\) 6.07456 0.248407
\(599\) −37.5141 −1.53278 −0.766392 0.642373i \(-0.777950\pi\)
−0.766392 + 0.642373i \(0.777950\pi\)
\(600\) −27.9201 −1.13983
\(601\) −35.0311 −1.42895 −0.714474 0.699662i \(-0.753334\pi\)
−0.714474 + 0.699662i \(0.753334\pi\)
\(602\) 24.1673 0.984984
\(603\) −15.3158 −0.623706
\(604\) 37.9496 1.54415
\(605\) 21.5921 0.877845
\(606\) 3.94741 0.160352
\(607\) −33.6012 −1.36383 −0.681915 0.731431i \(-0.738853\pi\)
−0.681915 + 0.731431i \(0.738853\pi\)
\(608\) −20.6321 −0.836743
\(609\) 7.25838 0.294124
\(610\) 7.62578 0.308759
\(611\) 8.40646 0.340089
\(612\) −19.8945 −0.804186
\(613\) 16.5942 0.670234 0.335117 0.942177i \(-0.391224\pi\)
0.335117 + 0.942177i \(0.391224\pi\)
\(614\) 45.1443 1.82187
\(615\) −9.78536 −0.394584
\(616\) −8.12091 −0.327201
\(617\) 15.9693 0.642900 0.321450 0.946927i \(-0.395830\pi\)
0.321450 + 0.946927i \(0.395830\pi\)
\(618\) 11.9827 0.482015
\(619\) 19.4694 0.782542 0.391271 0.920275i \(-0.372035\pi\)
0.391271 + 0.920275i \(0.372035\pi\)
\(620\) 126.286 5.07177
\(621\) 4.23693 0.170022
\(622\) 14.7421 0.591106
\(623\) −1.64449 −0.0658850
\(624\) −0.607623 −0.0243244
\(625\) 85.8031 3.43212
\(626\) 24.1236 0.964173
\(627\) −6.63107 −0.264819
\(628\) 51.0429 2.03683
\(629\) −17.3827 −0.693093
\(630\) −28.9570 −1.15367
\(631\) 30.9048 1.23030 0.615151 0.788410i \(-0.289095\pi\)
0.615151 + 0.788410i \(0.289095\pi\)
\(632\) 16.4774 0.655438
\(633\) 9.26786 0.368364
\(634\) 39.2851 1.56021
\(635\) −55.0763 −2.18564
\(636\) 15.1155 0.599369
\(637\) −14.5242 −0.575469
\(638\) −40.9033 −1.61938
\(639\) −1.47450 −0.0583303
\(640\) −75.5278 −2.98550
\(641\) −13.7208 −0.541937 −0.270969 0.962588i \(-0.587344\pi\)
−0.270969 + 0.962588i \(0.587344\pi\)
\(642\) −27.7553 −1.09542
\(643\) 31.7679 1.25280 0.626402 0.779500i \(-0.284527\pi\)
0.626402 + 0.779500i \(0.284527\pi\)
\(644\) −3.96404 −0.156205
\(645\) 28.6548 1.12828
\(646\) 20.6864 0.813895
\(647\) −3.92509 −0.154311 −0.0771556 0.997019i \(-0.524584\pi\)
−0.0771556 + 0.997019i \(0.524584\pi\)
\(648\) −10.1204 −0.397565
\(649\) 9.52428 0.373861
\(650\) −80.9078 −3.17346
\(651\) −9.16365 −0.359152
\(652\) −0.852940 −0.0334037
\(653\) −28.6791 −1.12230 −0.561151 0.827714i \(-0.689641\pi\)
−0.561151 + 0.827714i \(0.689641\pi\)
\(654\) −0.167662 −0.00655611
\(655\) 10.9889 0.429372
\(656\) −0.838357 −0.0327324
\(657\) −26.3101 −1.02646
\(658\) −8.94621 −0.348760
\(659\) 38.8836 1.51469 0.757345 0.653015i \(-0.226496\pi\)
0.757345 + 0.653015i \(0.226496\pi\)
\(660\) −26.0810 −1.01520
\(661\) 27.5299 1.07079 0.535394 0.844602i \(-0.320163\pi\)
0.535394 + 0.844602i \(0.320163\pi\)
\(662\) 61.8224 2.40280
\(663\) 5.54768 0.215454
\(664\) 35.9624 1.39561
\(665\) 18.4630 0.715964
\(666\) −35.6730 −1.38230
\(667\) −7.37128 −0.285417
\(668\) 32.8837 1.27231
\(669\) 19.9558 0.771535
\(670\) 62.6370 2.41988
\(671\) 1.91211 0.0738162
\(672\) 5.88840 0.227150
\(673\) 7.96647 0.307085 0.153542 0.988142i \(-0.450932\pi\)
0.153542 + 0.988142i \(0.450932\pi\)
\(674\) −10.2045 −0.393064
\(675\) −56.4321 −2.17207
\(676\) −18.5899 −0.714996
\(677\) −8.55997 −0.328987 −0.164493 0.986378i \(-0.552599\pi\)
−0.164493 + 0.986378i \(0.552599\pi\)
\(678\) 27.2209 1.04541
\(679\) 0.251826 0.00966421
\(680\) 30.0383 1.15192
\(681\) −17.4553 −0.668889
\(682\) 51.6401 1.97740
\(683\) 13.7651 0.526705 0.263353 0.964700i \(-0.415172\pi\)
0.263353 + 0.964700i \(0.415172\pi\)
\(684\) 26.0317 0.995349
\(685\) −7.35896 −0.281171
\(686\) 35.3576 1.34996
\(687\) 0.768451 0.0293182
\(688\) 2.45499 0.0935956
\(689\) 16.1714 0.616081
\(690\) −7.66497 −0.291801
\(691\) 25.0605 0.953348 0.476674 0.879080i \(-0.341842\pi\)
0.476674 + 0.879080i \(0.341842\pi\)
\(692\) 56.3830 2.14336
\(693\) −7.26076 −0.275813
\(694\) −3.41218 −0.129525
\(695\) −91.9459 −3.48771
\(696\) −15.4520 −0.585705
\(697\) 7.65432 0.289928
\(698\) 2.27388 0.0860676
\(699\) 17.1665 0.649296
\(700\) 52.7975 1.99556
\(701\) −8.87842 −0.335333 −0.167667 0.985844i \(-0.553623\pi\)
−0.167667 + 0.985844i \(0.553623\pi\)
\(702\) 25.7375 0.971399
\(703\) 22.7451 0.857848
\(704\) −31.7735 −1.19751
\(705\) −10.6074 −0.399497
\(706\) −36.0121 −1.35533
\(707\) −2.75587 −0.103645
\(708\) 9.74556 0.366260
\(709\) −51.5176 −1.93479 −0.967393 0.253281i \(-0.918490\pi\)
−0.967393 + 0.253281i \(0.918490\pi\)
\(710\) 6.03028 0.226312
\(711\) 14.7322 0.552500
\(712\) 3.50086 0.131200
\(713\) 9.30618 0.348519
\(714\) −5.90388 −0.220947
\(715\) −27.9028 −1.04351
\(716\) 72.6748 2.71598
\(717\) −19.8301 −0.740568
\(718\) 58.6163 2.18754
\(719\) 34.8274 1.29884 0.649421 0.760429i \(-0.275011\pi\)
0.649421 + 0.760429i \(0.275011\pi\)
\(720\) −2.94154 −0.109625
\(721\) −8.36571 −0.311555
\(722\) 16.1358 0.600511
\(723\) −19.4380 −0.722908
\(724\) −62.0423 −2.30579
\(725\) 98.1788 3.64627
\(726\) 9.03445 0.335300
\(727\) 24.1001 0.893824 0.446912 0.894578i \(-0.352524\pi\)
0.446912 + 0.894578i \(0.352524\pi\)
\(728\) −8.89004 −0.329487
\(729\) 0.962255 0.0356391
\(730\) 107.601 3.98249
\(731\) −22.4144 −0.829026
\(732\) 1.95653 0.0723156
\(733\) −29.0018 −1.07121 −0.535604 0.844469i \(-0.679916\pi\)
−0.535604 + 0.844469i \(0.679916\pi\)
\(734\) 21.8477 0.806414
\(735\) 18.3268 0.675995
\(736\) −5.97998 −0.220425
\(737\) 15.7058 0.578530
\(738\) 15.7083 0.578230
\(739\) −36.0770 −1.32711 −0.663557 0.748126i \(-0.730954\pi\)
−0.663557 + 0.748126i \(0.730954\pi\)
\(740\) 89.4599 3.28861
\(741\) −7.25909 −0.266669
\(742\) −17.2097 −0.631788
\(743\) −20.1265 −0.738370 −0.369185 0.929356i \(-0.620363\pi\)
−0.369185 + 0.929356i \(0.620363\pi\)
\(744\) 19.5080 0.715197
\(745\) −13.4866 −0.494113
\(746\) 0.476267 0.0174374
\(747\) 32.1533 1.17643
\(748\) 20.4011 0.745938
\(749\) 19.3773 0.708032
\(750\) 63.7657 2.32840
\(751\) 39.9246 1.45687 0.728435 0.685115i \(-0.240248\pi\)
0.728435 + 0.685115i \(0.240248\pi\)
\(752\) −0.908785 −0.0331400
\(753\) 22.2355 0.810307
\(754\) −44.7773 −1.63069
\(755\) −51.2303 −1.86446
\(756\) −16.7954 −0.610841
\(757\) −43.2244 −1.57102 −0.785508 0.618851i \(-0.787598\pi\)
−0.785508 + 0.618851i \(0.787598\pi\)
\(758\) 41.0738 1.49187
\(759\) −1.92194 −0.0697619
\(760\) −39.3049 −1.42574
\(761\) −1.59654 −0.0578746 −0.0289373 0.999581i \(-0.509212\pi\)
−0.0289373 + 0.999581i \(0.509212\pi\)
\(762\) −23.0447 −0.834822
\(763\) 0.117053 0.00423761
\(764\) −52.3887 −1.89536
\(765\) 26.8567 0.971006
\(766\) −43.2718 −1.56347
\(767\) 10.4263 0.376473
\(768\) −11.0932 −0.400292
\(769\) 27.4309 0.989182 0.494591 0.869126i \(-0.335318\pi\)
0.494591 + 0.869126i \(0.335318\pi\)
\(770\) 29.6944 1.07011
\(771\) 11.6651 0.420108
\(772\) −2.84172 −0.102276
\(773\) 11.5095 0.413969 0.206984 0.978344i \(-0.433635\pi\)
0.206984 + 0.978344i \(0.433635\pi\)
\(774\) −45.9990 −1.65340
\(775\) −123.950 −4.45241
\(776\) −0.536099 −0.0192448
\(777\) −6.49144 −0.232879
\(778\) −62.8370 −2.25282
\(779\) −10.0156 −0.358847
\(780\) −28.5511 −1.02229
\(781\) 1.51205 0.0541054
\(782\) 5.99571 0.214406
\(783\) −31.2316 −1.11613
\(784\) 1.57014 0.0560766
\(785\) −68.9058 −2.45935
\(786\) 4.59791 0.164002
\(787\) 13.3807 0.476969 0.238485 0.971146i \(-0.423349\pi\)
0.238485 + 0.971146i \(0.423349\pi\)
\(788\) 18.0589 0.643323
\(789\) −12.9079 −0.459533
\(790\) −60.2503 −2.14361
\(791\) −19.0042 −0.675712
\(792\) 15.4570 0.549242
\(793\) 2.09321 0.0743320
\(794\) 79.1801 2.81000
\(795\) −20.4053 −0.723701
\(796\) −18.5993 −0.659235
\(797\) −34.4601 −1.22064 −0.610320 0.792155i \(-0.708959\pi\)
−0.610320 + 0.792155i \(0.708959\pi\)
\(798\) 7.72518 0.273468
\(799\) 8.29733 0.293538
\(800\) 79.6481 2.81598
\(801\) 3.13006 0.110595
\(802\) −49.0828 −1.73317
\(803\) 26.9802 0.952109
\(804\) 16.0707 0.566769
\(805\) 5.35129 0.188608
\(806\) 56.5310 1.99122
\(807\) −19.2364 −0.677153
\(808\) 5.86683 0.206394
\(809\) 18.4374 0.648223 0.324112 0.946019i \(-0.394935\pi\)
0.324112 + 0.946019i \(0.394935\pi\)
\(810\) 37.0054 1.30024
\(811\) 1.02712 0.0360672 0.0180336 0.999837i \(-0.494259\pi\)
0.0180336 + 0.999837i \(0.494259\pi\)
\(812\) 29.2200 1.02542
\(813\) −6.69652 −0.234857
\(814\) 36.5814 1.28218
\(815\) 1.15143 0.0403329
\(816\) −0.599735 −0.0209949
\(817\) 29.3290 1.02609
\(818\) −53.8771 −1.88377
\(819\) −7.94842 −0.277740
\(820\) −39.3929 −1.37566
\(821\) −8.34345 −0.291188 −0.145594 0.989344i \(-0.546509\pi\)
−0.145594 + 0.989344i \(0.546509\pi\)
\(822\) −3.07909 −0.107396
\(823\) −9.78040 −0.340923 −0.170462 0.985364i \(-0.554526\pi\)
−0.170462 + 0.985364i \(0.554526\pi\)
\(824\) 17.8093 0.620416
\(825\) 25.5985 0.891226
\(826\) −11.0958 −0.386071
\(827\) −23.1805 −0.806064 −0.403032 0.915186i \(-0.632044\pi\)
−0.403032 + 0.915186i \(0.632044\pi\)
\(828\) 7.54500 0.262207
\(829\) −46.2579 −1.60660 −0.803302 0.595572i \(-0.796925\pi\)
−0.803302 + 0.595572i \(0.796925\pi\)
\(830\) −131.498 −4.56435
\(831\) −18.0150 −0.624935
\(832\) −34.7828 −1.20588
\(833\) −14.3356 −0.496700
\(834\) −38.4714 −1.33216
\(835\) −44.3916 −1.53623
\(836\) −26.6947 −0.923254
\(837\) 39.4296 1.36289
\(838\) −37.7857 −1.30529
\(839\) −8.14768 −0.281289 −0.140645 0.990060i \(-0.544917\pi\)
−0.140645 + 0.990060i \(0.544917\pi\)
\(840\) 11.2176 0.387043
\(841\) 25.3357 0.873645
\(842\) −18.4651 −0.636348
\(843\) −8.18874 −0.282035
\(844\) 37.3096 1.28425
\(845\) 25.0956 0.863314
\(846\) 17.0279 0.585430
\(847\) −6.30738 −0.216724
\(848\) −1.74822 −0.0600340
\(849\) −5.99597 −0.205781
\(850\) −79.8575 −2.73909
\(851\) 6.59241 0.225985
\(852\) 1.54718 0.0530055
\(853\) −25.2300 −0.863859 −0.431930 0.901907i \(-0.642167\pi\)
−0.431930 + 0.901907i \(0.642167\pi\)
\(854\) −2.22761 −0.0762271
\(855\) −35.1418 −1.20182
\(856\) −41.2513 −1.40994
\(857\) −7.64134 −0.261023 −0.130512 0.991447i \(-0.541662\pi\)
−0.130512 + 0.991447i \(0.541662\pi\)
\(858\) −11.6749 −0.398576
\(859\) 26.3385 0.898658 0.449329 0.893366i \(-0.351663\pi\)
0.449329 + 0.893366i \(0.351663\pi\)
\(860\) 115.355 3.93359
\(861\) 2.85845 0.0974157
\(862\) −24.7305 −0.842324
\(863\) −44.3325 −1.50909 −0.754547 0.656246i \(-0.772144\pi\)
−0.754547 + 0.656246i \(0.772144\pi\)
\(864\) −25.3368 −0.861975
\(865\) −76.1147 −2.58798
\(866\) −80.0606 −2.72057
\(867\) −7.91308 −0.268742
\(868\) −36.8901 −1.25213
\(869\) −15.1073 −0.512482
\(870\) 56.5006 1.91555
\(871\) 17.1933 0.582572
\(872\) −0.249188 −0.00843857
\(873\) −0.479317 −0.0162224
\(874\) −7.84534 −0.265372
\(875\) −44.5179 −1.50498
\(876\) 27.6070 0.932753
\(877\) −21.9031 −0.739616 −0.369808 0.929108i \(-0.620577\pi\)
−0.369808 + 0.929108i \(0.620577\pi\)
\(878\) −58.8554 −1.98627
\(879\) 21.3613 0.720500
\(880\) 3.01645 0.101685
\(881\) 38.2893 1.29000 0.645000 0.764182i \(-0.276857\pi\)
0.645000 + 0.764182i \(0.276857\pi\)
\(882\) −29.4197 −0.990614
\(883\) −3.05985 −0.102972 −0.0514860 0.998674i \(-0.516396\pi\)
−0.0514860 + 0.998674i \(0.516396\pi\)
\(884\) 22.3333 0.751149
\(885\) −13.1561 −0.442237
\(886\) 80.0180 2.68826
\(887\) −7.29589 −0.244972 −0.122486 0.992470i \(-0.539087\pi\)
−0.122486 + 0.992470i \(0.539087\pi\)
\(888\) 13.8193 0.463744
\(889\) 16.0886 0.539595
\(890\) −12.8010 −0.429091
\(891\) 9.27885 0.310853
\(892\) 80.3359 2.68985
\(893\) −10.8570 −0.363315
\(894\) −5.64300 −0.188730
\(895\) −98.1079 −3.27939
\(896\) 22.0628 0.737066
\(897\) −2.10396 −0.0702493
\(898\) 20.4119 0.681154
\(899\) −68.5984 −2.28788
\(900\) −100.493 −3.34976
\(901\) 15.9615 0.531753
\(902\) −16.1083 −0.536348
\(903\) −8.37049 −0.278553
\(904\) 40.4570 1.34558
\(905\) 83.7545 2.78410
\(906\) −21.4355 −0.712146
\(907\) −38.2560 −1.27027 −0.635135 0.772401i \(-0.719056\pi\)
−0.635135 + 0.772401i \(0.719056\pi\)
\(908\) −70.2698 −2.33199
\(909\) 5.24542 0.173980
\(910\) 32.5067 1.07759
\(911\) 45.1729 1.49665 0.748323 0.663335i \(-0.230860\pi\)
0.748323 + 0.663335i \(0.230860\pi\)
\(912\) 0.784749 0.0259856
\(913\) −32.9721 −1.09122
\(914\) 40.2395 1.33100
\(915\) −2.64124 −0.0873167
\(916\) 3.09355 0.102214
\(917\) −3.21003 −0.106004
\(918\) 25.4034 0.838437
\(919\) −37.5627 −1.23908 −0.619539 0.784966i \(-0.712680\pi\)
−0.619539 + 0.784966i \(0.712680\pi\)
\(920\) −11.3921 −0.375585
\(921\) −15.6360 −0.515224
\(922\) 25.8535 0.851439
\(923\) 1.65526 0.0544834
\(924\) 7.61864 0.250635
\(925\) −87.8050 −2.88701
\(926\) −76.9571 −2.52897
\(927\) 15.9230 0.522979
\(928\) 44.0801 1.44700
\(929\) −45.7850 −1.50216 −0.751078 0.660214i \(-0.770466\pi\)
−0.751078 + 0.660214i \(0.770466\pi\)
\(930\) −71.3316 −2.33906
\(931\) 18.7581 0.614771
\(932\) 69.1070 2.26368
\(933\) −5.10604 −0.167164
\(934\) 10.8260 0.354238
\(935\) −27.5406 −0.900674
\(936\) 16.9210 0.553079
\(937\) −46.4090 −1.51612 −0.758059 0.652186i \(-0.773852\pi\)
−0.758059 + 0.652186i \(0.773852\pi\)
\(938\) −18.2972 −0.597425
\(939\) −8.35537 −0.272667
\(940\) −42.7021 −1.39279
\(941\) −44.1426 −1.43901 −0.719504 0.694489i \(-0.755631\pi\)
−0.719504 + 0.694489i \(0.755631\pi\)
\(942\) −28.8311 −0.939369
\(943\) −2.90291 −0.0945318
\(944\) −1.12714 −0.0366854
\(945\) 22.6730 0.737554
\(946\) 47.1704 1.53364
\(947\) 32.7680 1.06482 0.532408 0.846488i \(-0.321287\pi\)
0.532408 + 0.846488i \(0.321287\pi\)
\(948\) −15.4583 −0.502063
\(949\) 29.5354 0.958761
\(950\) 104.493 3.39020
\(951\) −13.6067 −0.441226
\(952\) −8.77464 −0.284388
\(953\) 24.9222 0.807310 0.403655 0.914911i \(-0.367740\pi\)
0.403655 + 0.914911i \(0.367740\pi\)
\(954\) 32.7563 1.06052
\(955\) 70.7226 2.28853
\(956\) −79.8299 −2.58188
\(957\) 14.1671 0.457959
\(958\) 8.25995 0.266867
\(959\) 2.14966 0.0694163
\(960\) 43.8894 1.41652
\(961\) 55.6049 1.79371
\(962\) 40.0460 1.29114
\(963\) −36.8821 −1.18851
\(964\) −78.2516 −2.52031
\(965\) 3.83621 0.123492
\(966\) 2.23905 0.0720404
\(967\) 29.7679 0.957272 0.478636 0.878013i \(-0.341131\pi\)
0.478636 + 0.878013i \(0.341131\pi\)
\(968\) 13.4274 0.431574
\(969\) −7.16486 −0.230169
\(970\) 1.96026 0.0629403
\(971\) −34.6957 −1.11344 −0.556718 0.830701i \(-0.687940\pi\)
−0.556718 + 0.830701i \(0.687940\pi\)
\(972\) 49.7944 1.59715
\(973\) 26.8588 0.861053
\(974\) −5.17920 −0.165952
\(975\) 28.0229 0.897452
\(976\) −0.226287 −0.00724328
\(977\) −32.1801 −1.02953 −0.514767 0.857330i \(-0.672121\pi\)
−0.514767 + 0.857330i \(0.672121\pi\)
\(978\) 0.481776 0.0154055
\(979\) −3.20976 −0.102585
\(980\) 73.7782 2.35676
\(981\) −0.222794 −0.00711328
\(982\) 65.7904 2.09946
\(983\) −2.63034 −0.0838948 −0.0419474 0.999120i \(-0.513356\pi\)
−0.0419474 + 0.999120i \(0.513356\pi\)
\(984\) −6.08520 −0.193989
\(985\) −24.3788 −0.776773
\(986\) −44.1960 −1.40749
\(987\) 3.09858 0.0986288
\(988\) −29.2229 −0.929704
\(989\) 8.50068 0.270306
\(990\) −56.5191 −1.79630
\(991\) 43.3282 1.37636 0.688182 0.725538i \(-0.258409\pi\)
0.688182 + 0.725538i \(0.258409\pi\)
\(992\) −55.6508 −1.76691
\(993\) −21.4126 −0.679508
\(994\) −1.76153 −0.0558725
\(995\) 25.1083 0.795986
\(996\) −33.7381 −1.06903
\(997\) 21.7317 0.688251 0.344126 0.938924i \(-0.388175\pi\)
0.344126 + 0.938924i \(0.388175\pi\)
\(998\) 61.2293 1.93818
\(999\) 27.9316 0.883716
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.1.17 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.d.1.17 149 1.1 even 1 trivial