Properties

Label 4010.2.a.n.1.13
Level $4010$
Weight $2$
Character 4010.1
Self dual yes
Analytic conductor $32.020$
Analytic rank $0$
Dimension $22$
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] = [4010,2,Mod(1,4010)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4010, 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("4010.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4010.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: \(32.0200112105\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 4010.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +0.822612 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.822612 q^{6} +0.710831 q^{7} +1.00000 q^{8} -2.32331 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +0.822612 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.822612 q^{6} +0.710831 q^{7} +1.00000 q^{8} -2.32331 q^{9} +1.00000 q^{10} -4.10210 q^{11} +0.822612 q^{12} +0.532365 q^{13} +0.710831 q^{14} +0.822612 q^{15} +1.00000 q^{16} +1.61575 q^{17} -2.32331 q^{18} +7.94642 q^{19} +1.00000 q^{20} +0.584738 q^{21} -4.10210 q^{22} +6.05858 q^{23} +0.822612 q^{24} +1.00000 q^{25} +0.532365 q^{26} -4.37902 q^{27} +0.710831 q^{28} -0.915588 q^{29} +0.822612 q^{30} -5.17569 q^{31} +1.00000 q^{32} -3.37444 q^{33} +1.61575 q^{34} +0.710831 q^{35} -2.32331 q^{36} +10.3629 q^{37} +7.94642 q^{38} +0.437930 q^{39} +1.00000 q^{40} +6.76575 q^{41} +0.584738 q^{42} +8.64895 q^{43} -4.10210 q^{44} -2.32331 q^{45} +6.05858 q^{46} -6.55629 q^{47} +0.822612 q^{48} -6.49472 q^{49} +1.00000 q^{50} +1.32913 q^{51} +0.532365 q^{52} +11.1024 q^{53} -4.37902 q^{54} -4.10210 q^{55} +0.710831 q^{56} +6.53682 q^{57} -0.915588 q^{58} -3.59674 q^{59} +0.822612 q^{60} +4.86048 q^{61} -5.17569 q^{62} -1.65148 q^{63} +1.00000 q^{64} +0.532365 q^{65} -3.37444 q^{66} +6.55325 q^{67} +1.61575 q^{68} +4.98386 q^{69} +0.710831 q^{70} +6.01123 q^{71} -2.32331 q^{72} +2.41097 q^{73} +10.3629 q^{74} +0.822612 q^{75} +7.94642 q^{76} -2.91590 q^{77} +0.437930 q^{78} -2.92286 q^{79} +1.00000 q^{80} +3.36770 q^{81} +6.76575 q^{82} +6.74323 q^{83} +0.584738 q^{84} +1.61575 q^{85} +8.64895 q^{86} -0.753174 q^{87} -4.10210 q^{88} -4.52594 q^{89} -2.32331 q^{90} +0.378422 q^{91} +6.05858 q^{92} -4.25758 q^{93} -6.55629 q^{94} +7.94642 q^{95} +0.822612 q^{96} +1.24039 q^{97} -6.49472 q^{98} +9.53045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.822612 0.474935 0.237468 0.971395i \(-0.423683\pi\)
0.237468 + 0.971395i \(0.423683\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 0.822612 0.335830
\(7\) 0.710831 0.268669 0.134334 0.990936i \(-0.457110\pi\)
0.134334 + 0.990936i \(0.457110\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.32331 −0.774437
\(10\) 1.00000 0.316228
\(11\) −4.10210 −1.23683 −0.618415 0.785852i \(-0.712225\pi\)
−0.618415 + 0.785852i \(0.712225\pi\)
\(12\) 0.822612 0.237468
\(13\) 0.532365 0.147652 0.0738258 0.997271i \(-0.476479\pi\)
0.0738258 + 0.997271i \(0.476479\pi\)
\(14\) 0.710831 0.189978
\(15\) 0.822612 0.212397
\(16\) 1.00000 0.250000
\(17\) 1.61575 0.391877 0.195938 0.980616i \(-0.437225\pi\)
0.195938 + 0.980616i \(0.437225\pi\)
\(18\) −2.32331 −0.547609
\(19\) 7.94642 1.82303 0.911517 0.411261i \(-0.134912\pi\)
0.911517 + 0.411261i \(0.134912\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.584738 0.127600
\(22\) −4.10210 −0.874571
\(23\) 6.05858 1.26330 0.631651 0.775253i \(-0.282378\pi\)
0.631651 + 0.775253i \(0.282378\pi\)
\(24\) 0.822612 0.167915
\(25\) 1.00000 0.200000
\(26\) 0.532365 0.104405
\(27\) −4.37902 −0.842742
\(28\) 0.710831 0.134334
\(29\) −0.915588 −0.170020 −0.0850102 0.996380i \(-0.527092\pi\)
−0.0850102 + 0.996380i \(0.527092\pi\)
\(30\) 0.822612 0.150188
\(31\) −5.17569 −0.929581 −0.464790 0.885421i \(-0.653870\pi\)
−0.464790 + 0.885421i \(0.653870\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.37444 −0.587414
\(34\) 1.61575 0.277099
\(35\) 0.710831 0.120152
\(36\) −2.32331 −0.387218
\(37\) 10.3629 1.70365 0.851827 0.523823i \(-0.175495\pi\)
0.851827 + 0.523823i \(0.175495\pi\)
\(38\) 7.94642 1.28908
\(39\) 0.437930 0.0701249
\(40\) 1.00000 0.158114
\(41\) 6.76575 1.05663 0.528317 0.849047i \(-0.322823\pi\)
0.528317 + 0.849047i \(0.322823\pi\)
\(42\) 0.584738 0.0902270
\(43\) 8.64895 1.31895 0.659476 0.751725i \(-0.270778\pi\)
0.659476 + 0.751725i \(0.270778\pi\)
\(44\) −4.10210 −0.618415
\(45\) −2.32331 −0.346339
\(46\) 6.05858 0.893289
\(47\) −6.55629 −0.956333 −0.478166 0.878269i \(-0.658698\pi\)
−0.478166 + 0.878269i \(0.658698\pi\)
\(48\) 0.822612 0.118734
\(49\) −6.49472 −0.927817
\(50\) 1.00000 0.141421
\(51\) 1.32913 0.186116
\(52\) 0.532365 0.0738258
\(53\) 11.1024 1.52503 0.762517 0.646968i \(-0.223963\pi\)
0.762517 + 0.646968i \(0.223963\pi\)
\(54\) −4.37902 −0.595909
\(55\) −4.10210 −0.553127
\(56\) 0.710831 0.0949888
\(57\) 6.53682 0.865823
\(58\) −0.915588 −0.120223
\(59\) −3.59674 −0.468255 −0.234128 0.972206i \(-0.575223\pi\)
−0.234128 + 0.972206i \(0.575223\pi\)
\(60\) 0.822612 0.106199
\(61\) 4.86048 0.622321 0.311160 0.950357i \(-0.399282\pi\)
0.311160 + 0.950357i \(0.399282\pi\)
\(62\) −5.17569 −0.657313
\(63\) −1.65148 −0.208067
\(64\) 1.00000 0.125000
\(65\) 0.532365 0.0660318
\(66\) −3.37444 −0.415365
\(67\) 6.55325 0.800607 0.400304 0.916383i \(-0.368905\pi\)
0.400304 + 0.916383i \(0.368905\pi\)
\(68\) 1.61575 0.195938
\(69\) 4.98386 0.599987
\(70\) 0.710831 0.0849606
\(71\) 6.01123 0.713402 0.356701 0.934219i \(-0.383902\pi\)
0.356701 + 0.934219i \(0.383902\pi\)
\(72\) −2.32331 −0.273805
\(73\) 2.41097 0.282182 0.141091 0.989997i \(-0.454939\pi\)
0.141091 + 0.989997i \(0.454939\pi\)
\(74\) 10.3629 1.20467
\(75\) 0.822612 0.0949870
\(76\) 7.94642 0.911517
\(77\) −2.91590 −0.332298
\(78\) 0.437930 0.0495858
\(79\) −2.92286 −0.328847 −0.164424 0.986390i \(-0.552576\pi\)
−0.164424 + 0.986390i \(0.552576\pi\)
\(80\) 1.00000 0.111803
\(81\) 3.36770 0.374189
\(82\) 6.76575 0.747153
\(83\) 6.74323 0.740166 0.370083 0.928999i \(-0.379329\pi\)
0.370083 + 0.928999i \(0.379329\pi\)
\(84\) 0.584738 0.0638002
\(85\) 1.61575 0.175253
\(86\) 8.64895 0.932640
\(87\) −0.753174 −0.0807487
\(88\) −4.10210 −0.437286
\(89\) −4.52594 −0.479748 −0.239874 0.970804i \(-0.577106\pi\)
−0.239874 + 0.970804i \(0.577106\pi\)
\(90\) −2.32331 −0.244898
\(91\) 0.378422 0.0396694
\(92\) 6.05858 0.631651
\(93\) −4.25758 −0.441491
\(94\) −6.55629 −0.676230
\(95\) 7.94642 0.815286
\(96\) 0.822612 0.0839575
\(97\) 1.24039 0.125943 0.0629714 0.998015i \(-0.479942\pi\)
0.0629714 + 0.998015i \(0.479942\pi\)
\(98\) −6.49472 −0.656066
\(99\) 9.53045 0.957847
\(100\) 1.00000 0.100000
\(101\) −5.27186 −0.524570 −0.262285 0.964990i \(-0.584476\pi\)
−0.262285 + 0.964990i \(0.584476\pi\)
\(102\) 1.32913 0.131604
\(103\) −14.3540 −1.41434 −0.707172 0.707041i \(-0.750029\pi\)
−0.707172 + 0.707041i \(0.750029\pi\)
\(104\) 0.532365 0.0522027
\(105\) 0.584738 0.0570646
\(106\) 11.1024 1.07836
\(107\) 4.23982 0.409879 0.204939 0.978775i \(-0.434300\pi\)
0.204939 + 0.978775i \(0.434300\pi\)
\(108\) −4.37902 −0.421371
\(109\) 0.0957383 0.00917007 0.00458503 0.999989i \(-0.498541\pi\)
0.00458503 + 0.999989i \(0.498541\pi\)
\(110\) −4.10210 −0.391120
\(111\) 8.52467 0.809126
\(112\) 0.710831 0.0671672
\(113\) −8.32289 −0.782952 −0.391476 0.920188i \(-0.628035\pi\)
−0.391476 + 0.920188i \(0.628035\pi\)
\(114\) 6.53682 0.612230
\(115\) 6.05858 0.564966
\(116\) −0.915588 −0.0850102
\(117\) −1.23685 −0.114347
\(118\) −3.59674 −0.331107
\(119\) 1.14852 0.105285
\(120\) 0.822612 0.0750938
\(121\) 5.82724 0.529749
\(122\) 4.86048 0.440047
\(123\) 5.56559 0.501832
\(124\) −5.17569 −0.464790
\(125\) 1.00000 0.0894427
\(126\) −1.65148 −0.147126
\(127\) 21.2892 1.88911 0.944556 0.328351i \(-0.106493\pi\)
0.944556 + 0.328351i \(0.106493\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.11473 0.626417
\(130\) 0.532365 0.0466915
\(131\) −10.8187 −0.945237 −0.472619 0.881267i \(-0.656691\pi\)
−0.472619 + 0.881267i \(0.656691\pi\)
\(132\) −3.37444 −0.293707
\(133\) 5.64857 0.489793
\(134\) 6.55325 0.566115
\(135\) −4.37902 −0.376886
\(136\) 1.61575 0.138549
\(137\) −19.9787 −1.70690 −0.853449 0.521177i \(-0.825493\pi\)
−0.853449 + 0.521177i \(0.825493\pi\)
\(138\) 4.98386 0.424255
\(139\) 11.4197 0.968606 0.484303 0.874900i \(-0.339073\pi\)
0.484303 + 0.874900i \(0.339073\pi\)
\(140\) 0.710831 0.0600762
\(141\) −5.39328 −0.454196
\(142\) 6.01123 0.504451
\(143\) −2.18382 −0.182620
\(144\) −2.32331 −0.193609
\(145\) −0.915588 −0.0760355
\(146\) 2.41097 0.199533
\(147\) −5.34263 −0.440653
\(148\) 10.3629 0.851827
\(149\) 2.02784 0.166128 0.0830638 0.996544i \(-0.473529\pi\)
0.0830638 + 0.996544i \(0.473529\pi\)
\(150\) 0.822612 0.0671660
\(151\) −7.18615 −0.584801 −0.292400 0.956296i \(-0.594454\pi\)
−0.292400 + 0.956296i \(0.594454\pi\)
\(152\) 7.94642 0.644540
\(153\) −3.75389 −0.303484
\(154\) −2.91590 −0.234970
\(155\) −5.17569 −0.415721
\(156\) 0.437930 0.0350625
\(157\) 12.0915 0.965004 0.482502 0.875895i \(-0.339728\pi\)
0.482502 + 0.875895i \(0.339728\pi\)
\(158\) −2.92286 −0.232530
\(159\) 9.13298 0.724292
\(160\) 1.00000 0.0790569
\(161\) 4.30663 0.339410
\(162\) 3.36770 0.264591
\(163\) 15.2159 1.19180 0.595900 0.803059i \(-0.296796\pi\)
0.595900 + 0.803059i \(0.296796\pi\)
\(164\) 6.76575 0.528317
\(165\) −3.37444 −0.262700
\(166\) 6.74323 0.523376
\(167\) 6.56868 0.508300 0.254150 0.967165i \(-0.418204\pi\)
0.254150 + 0.967165i \(0.418204\pi\)
\(168\) 0.584738 0.0451135
\(169\) −12.7166 −0.978199
\(170\) 1.61575 0.123922
\(171\) −18.4620 −1.41182
\(172\) 8.64895 0.659476
\(173\) 0.546744 0.0415682 0.0207841 0.999784i \(-0.493384\pi\)
0.0207841 + 0.999784i \(0.493384\pi\)
\(174\) −0.753174 −0.0570979
\(175\) 0.710831 0.0537338
\(176\) −4.10210 −0.309208
\(177\) −2.95872 −0.222391
\(178\) −4.52594 −0.339233
\(179\) −0.244179 −0.0182508 −0.00912541 0.999958i \(-0.502905\pi\)
−0.00912541 + 0.999958i \(0.502905\pi\)
\(180\) −2.32331 −0.173169
\(181\) −25.9979 −1.93241 −0.966204 0.257777i \(-0.917010\pi\)
−0.966204 + 0.257777i \(0.917010\pi\)
\(182\) 0.378422 0.0280505
\(183\) 3.99829 0.295562
\(184\) 6.05858 0.446645
\(185\) 10.3629 0.761898
\(186\) −4.25758 −0.312181
\(187\) −6.62797 −0.484685
\(188\) −6.55629 −0.478166
\(189\) −3.11274 −0.226419
\(190\) 7.94642 0.576494
\(191\) −17.9504 −1.29884 −0.649421 0.760429i \(-0.724989\pi\)
−0.649421 + 0.760429i \(0.724989\pi\)
\(192\) 0.822612 0.0593669
\(193\) −11.3687 −0.818336 −0.409168 0.912459i \(-0.634181\pi\)
−0.409168 + 0.912459i \(0.634181\pi\)
\(194\) 1.24039 0.0890550
\(195\) 0.437930 0.0313608
\(196\) −6.49472 −0.463909
\(197\) 2.14807 0.153044 0.0765219 0.997068i \(-0.475618\pi\)
0.0765219 + 0.997068i \(0.475618\pi\)
\(198\) 9.53045 0.677300
\(199\) −21.8261 −1.54721 −0.773607 0.633666i \(-0.781549\pi\)
−0.773607 + 0.633666i \(0.781549\pi\)
\(200\) 1.00000 0.0707107
\(201\) 5.39078 0.380236
\(202\) −5.27186 −0.370927
\(203\) −0.650829 −0.0456792
\(204\) 1.32913 0.0930580
\(205\) 6.76575 0.472541
\(206\) −14.3540 −1.00009
\(207\) −14.0760 −0.978347
\(208\) 0.532365 0.0369129
\(209\) −32.5970 −2.25478
\(210\) 0.584738 0.0403508
\(211\) −16.3783 −1.12753 −0.563765 0.825935i \(-0.690648\pi\)
−0.563765 + 0.825935i \(0.690648\pi\)
\(212\) 11.1024 0.762517
\(213\) 4.94491 0.338820
\(214\) 4.23982 0.289828
\(215\) 8.64895 0.589853
\(216\) −4.37902 −0.297954
\(217\) −3.67904 −0.249749
\(218\) 0.0957383 0.00648422
\(219\) 1.98329 0.134018
\(220\) −4.10210 −0.276564
\(221\) 0.860169 0.0578612
\(222\) 8.52467 0.572138
\(223\) −11.2538 −0.753607 −0.376803 0.926293i \(-0.622977\pi\)
−0.376803 + 0.926293i \(0.622977\pi\)
\(224\) 0.710831 0.0474944
\(225\) −2.32331 −0.154887
\(226\) −8.32289 −0.553631
\(227\) −24.0637 −1.59716 −0.798582 0.601887i \(-0.794416\pi\)
−0.798582 + 0.601887i \(0.794416\pi\)
\(228\) 6.53682 0.432912
\(229\) −6.06411 −0.400728 −0.200364 0.979722i \(-0.564212\pi\)
−0.200364 + 0.979722i \(0.564212\pi\)
\(230\) 6.05858 0.399491
\(231\) −2.39866 −0.157820
\(232\) −0.915588 −0.0601113
\(233\) −23.9664 −1.57009 −0.785046 0.619438i \(-0.787361\pi\)
−0.785046 + 0.619438i \(0.787361\pi\)
\(234\) −1.23685 −0.0808554
\(235\) −6.55629 −0.427685
\(236\) −3.59674 −0.234128
\(237\) −2.40438 −0.156181
\(238\) 1.14852 0.0744478
\(239\) 18.2283 1.17909 0.589545 0.807736i \(-0.299307\pi\)
0.589545 + 0.807736i \(0.299307\pi\)
\(240\) 0.822612 0.0530994
\(241\) 25.3760 1.63461 0.817307 0.576203i \(-0.195466\pi\)
0.817307 + 0.576203i \(0.195466\pi\)
\(242\) 5.82724 0.374589
\(243\) 15.9074 1.02046
\(244\) 4.86048 0.311160
\(245\) −6.49472 −0.414932
\(246\) 5.56559 0.354849
\(247\) 4.23040 0.269174
\(248\) −5.17569 −0.328656
\(249\) 5.54706 0.351531
\(250\) 1.00000 0.0632456
\(251\) −10.2898 −0.649489 −0.324745 0.945802i \(-0.605278\pi\)
−0.324745 + 0.945802i \(0.605278\pi\)
\(252\) −1.65148 −0.104034
\(253\) −24.8529 −1.56249
\(254\) 21.2892 1.33580
\(255\) 1.32913 0.0832336
\(256\) 1.00000 0.0625000
\(257\) 24.3401 1.51829 0.759145 0.650921i \(-0.225617\pi\)
0.759145 + 0.650921i \(0.225617\pi\)
\(258\) 7.11473 0.442944
\(259\) 7.36629 0.457719
\(260\) 0.532365 0.0330159
\(261\) 2.12719 0.131670
\(262\) −10.8187 −0.668384
\(263\) −24.2660 −1.49630 −0.748152 0.663527i \(-0.769059\pi\)
−0.748152 + 0.663527i \(0.769059\pi\)
\(264\) −3.37444 −0.207682
\(265\) 11.1024 0.682016
\(266\) 5.64857 0.346336
\(267\) −3.72309 −0.227849
\(268\) 6.55325 0.400304
\(269\) 29.0440 1.77084 0.885421 0.464790i \(-0.153870\pi\)
0.885421 + 0.464790i \(0.153870\pi\)
\(270\) −4.37902 −0.266499
\(271\) −4.26080 −0.258825 −0.129413 0.991591i \(-0.541309\pi\)
−0.129413 + 0.991591i \(0.541309\pi\)
\(272\) 1.61575 0.0979692
\(273\) 0.311294 0.0188404
\(274\) −19.9787 −1.20696
\(275\) −4.10210 −0.247366
\(276\) 4.98386 0.299993
\(277\) 32.2204 1.93594 0.967968 0.251075i \(-0.0807841\pi\)
0.967968 + 0.251075i \(0.0807841\pi\)
\(278\) 11.4197 0.684908
\(279\) 12.0247 0.719901
\(280\) 0.710831 0.0424803
\(281\) −12.8003 −0.763602 −0.381801 0.924244i \(-0.624696\pi\)
−0.381801 + 0.924244i \(0.624696\pi\)
\(282\) −5.39328 −0.321165
\(283\) −6.26449 −0.372385 −0.186193 0.982513i \(-0.559615\pi\)
−0.186193 + 0.982513i \(0.559615\pi\)
\(284\) 6.01123 0.356701
\(285\) 6.53682 0.387208
\(286\) −2.18382 −0.129132
\(287\) 4.80931 0.283885
\(288\) −2.32331 −0.136902
\(289\) −14.3894 −0.846433
\(290\) −0.915588 −0.0537652
\(291\) 1.02036 0.0598147
\(292\) 2.41097 0.141091
\(293\) 5.23184 0.305647 0.152824 0.988253i \(-0.451163\pi\)
0.152824 + 0.988253i \(0.451163\pi\)
\(294\) −5.34263 −0.311589
\(295\) −3.59674 −0.209410
\(296\) 10.3629 0.602333
\(297\) 17.9632 1.04233
\(298\) 2.02784 0.117470
\(299\) 3.22538 0.186528
\(300\) 0.822612 0.0474935
\(301\) 6.14794 0.354361
\(302\) −7.18615 −0.413517
\(303\) −4.33670 −0.249137
\(304\) 7.94642 0.455759
\(305\) 4.86048 0.278310
\(306\) −3.75389 −0.214595
\(307\) 21.0333 1.20044 0.600218 0.799837i \(-0.295081\pi\)
0.600218 + 0.799837i \(0.295081\pi\)
\(308\) −2.91590 −0.166149
\(309\) −11.8078 −0.671722
\(310\) −5.17569 −0.293959
\(311\) −23.6109 −1.33885 −0.669427 0.742878i \(-0.733460\pi\)
−0.669427 + 0.742878i \(0.733460\pi\)
\(312\) 0.437930 0.0247929
\(313\) 32.5188 1.83807 0.919037 0.394171i \(-0.128968\pi\)
0.919037 + 0.394171i \(0.128968\pi\)
\(314\) 12.0915 0.682361
\(315\) −1.65148 −0.0930504
\(316\) −2.92286 −0.164424
\(317\) −31.4667 −1.76735 −0.883674 0.468102i \(-0.844938\pi\)
−0.883674 + 0.468102i \(0.844938\pi\)
\(318\) 9.13298 0.512152
\(319\) 3.75584 0.210286
\(320\) 1.00000 0.0559017
\(321\) 3.48773 0.194666
\(322\) 4.30663 0.239999
\(323\) 12.8394 0.714405
\(324\) 3.36770 0.187094
\(325\) 0.532365 0.0295303
\(326\) 15.2159 0.842729
\(327\) 0.0787555 0.00435519
\(328\) 6.76575 0.373576
\(329\) −4.66041 −0.256937
\(330\) −3.37444 −0.185757
\(331\) −20.7862 −1.14251 −0.571257 0.820771i \(-0.693544\pi\)
−0.571257 + 0.820771i \(0.693544\pi\)
\(332\) 6.74323 0.370083
\(333\) −24.0763 −1.31937
\(334\) 6.56868 0.359422
\(335\) 6.55325 0.358042
\(336\) 0.584738 0.0319001
\(337\) 31.6652 1.72492 0.862458 0.506129i \(-0.168924\pi\)
0.862458 + 0.506129i \(0.168924\pi\)
\(338\) −12.7166 −0.691691
\(339\) −6.84651 −0.371851
\(340\) 1.61575 0.0876263
\(341\) 21.2312 1.14973
\(342\) −18.4620 −0.998311
\(343\) −9.59247 −0.517944
\(344\) 8.64895 0.466320
\(345\) 4.98386 0.268322
\(346\) 0.546744 0.0293931
\(347\) 26.5634 1.42600 0.713000 0.701164i \(-0.247336\pi\)
0.713000 + 0.701164i \(0.247336\pi\)
\(348\) −0.753174 −0.0403743
\(349\) −1.96010 −0.104922 −0.0524608 0.998623i \(-0.516706\pi\)
−0.0524608 + 0.998623i \(0.516706\pi\)
\(350\) 0.710831 0.0379955
\(351\) −2.33124 −0.124432
\(352\) −4.10210 −0.218643
\(353\) 3.30982 0.176164 0.0880821 0.996113i \(-0.471926\pi\)
0.0880821 + 0.996113i \(0.471926\pi\)
\(354\) −2.95872 −0.157254
\(355\) 6.01123 0.319043
\(356\) −4.52594 −0.239874
\(357\) 0.944790 0.0500036
\(358\) −0.244179 −0.0129053
\(359\) −17.1912 −0.907319 −0.453659 0.891175i \(-0.649882\pi\)
−0.453659 + 0.891175i \(0.649882\pi\)
\(360\) −2.32331 −0.122449
\(361\) 44.1457 2.32346
\(362\) −25.9979 −1.36642
\(363\) 4.79356 0.251597
\(364\) 0.378422 0.0198347
\(365\) 2.41097 0.126196
\(366\) 3.99829 0.208994
\(367\) 6.47995 0.338250 0.169125 0.985595i \(-0.445906\pi\)
0.169125 + 0.985595i \(0.445906\pi\)
\(368\) 6.05858 0.315825
\(369\) −15.7189 −0.818295
\(370\) 10.3629 0.538743
\(371\) 7.89194 0.409729
\(372\) −4.25758 −0.220745
\(373\) −7.55550 −0.391209 −0.195604 0.980683i \(-0.562667\pi\)
−0.195604 + 0.980683i \(0.562667\pi\)
\(374\) −6.62797 −0.342724
\(375\) 0.822612 0.0424795
\(376\) −6.55629 −0.338115
\(377\) −0.487427 −0.0251038
\(378\) −3.11274 −0.160102
\(379\) 23.0385 1.18341 0.591705 0.806155i \(-0.298455\pi\)
0.591705 + 0.806155i \(0.298455\pi\)
\(380\) 7.94642 0.407643
\(381\) 17.5128 0.897206
\(382\) −17.9504 −0.918421
\(383\) −26.2392 −1.34076 −0.670380 0.742018i \(-0.733869\pi\)
−0.670380 + 0.742018i \(0.733869\pi\)
\(384\) 0.822612 0.0419787
\(385\) −2.91590 −0.148608
\(386\) −11.3687 −0.578651
\(387\) −20.0942 −1.02144
\(388\) 1.24039 0.0629714
\(389\) −0.818755 −0.0415125 −0.0207563 0.999785i \(-0.506607\pi\)
−0.0207563 + 0.999785i \(0.506607\pi\)
\(390\) 0.437930 0.0221754
\(391\) 9.78915 0.495059
\(392\) −6.49472 −0.328033
\(393\) −8.89962 −0.448926
\(394\) 2.14807 0.108218
\(395\) −2.92286 −0.147065
\(396\) 9.53045 0.478923
\(397\) −36.6154 −1.83768 −0.918838 0.394636i \(-0.870871\pi\)
−0.918838 + 0.394636i \(0.870871\pi\)
\(398\) −21.8261 −1.09404
\(399\) 4.64658 0.232620
\(400\) 1.00000 0.0500000
\(401\) 1.00000 0.0499376
\(402\) 5.39078 0.268868
\(403\) −2.75536 −0.137254
\(404\) −5.27186 −0.262285
\(405\) 3.36770 0.167342
\(406\) −0.650829 −0.0323001
\(407\) −42.5098 −2.10713
\(408\) 1.32913 0.0658020
\(409\) 25.7798 1.27473 0.637365 0.770562i \(-0.280024\pi\)
0.637365 + 0.770562i \(0.280024\pi\)
\(410\) 6.76575 0.334137
\(411\) −16.4347 −0.810666
\(412\) −14.3540 −0.707172
\(413\) −2.55667 −0.125806
\(414\) −14.0760 −0.691796
\(415\) 6.74323 0.331012
\(416\) 0.532365 0.0261013
\(417\) 9.39398 0.460025
\(418\) −32.5970 −1.59437
\(419\) 32.2101 1.57357 0.786784 0.617228i \(-0.211744\pi\)
0.786784 + 0.617228i \(0.211744\pi\)
\(420\) 0.584738 0.0285323
\(421\) −25.7842 −1.25665 −0.628323 0.777952i \(-0.716258\pi\)
−0.628323 + 0.777952i \(0.716258\pi\)
\(422\) −16.3783 −0.797284
\(423\) 15.2323 0.740619
\(424\) 11.1024 0.539181
\(425\) 1.61575 0.0783753
\(426\) 4.94491 0.239582
\(427\) 3.45498 0.167198
\(428\) 4.23982 0.204939
\(429\) −1.79643 −0.0867326
\(430\) 8.64895 0.417089
\(431\) 12.3190 0.593387 0.296693 0.954973i \(-0.404116\pi\)
0.296693 + 0.954973i \(0.404116\pi\)
\(432\) −4.37902 −0.210686
\(433\) 21.2530 1.02135 0.510677 0.859773i \(-0.329395\pi\)
0.510677 + 0.859773i \(0.329395\pi\)
\(434\) −3.67904 −0.176600
\(435\) −0.753174 −0.0361119
\(436\) 0.0957383 0.00458503
\(437\) 48.1441 2.30304
\(438\) 1.98329 0.0947652
\(439\) −1.82146 −0.0869336 −0.0434668 0.999055i \(-0.513840\pi\)
−0.0434668 + 0.999055i \(0.513840\pi\)
\(440\) −4.10210 −0.195560
\(441\) 15.0892 0.718535
\(442\) 0.860169 0.0409140
\(443\) −7.80446 −0.370801 −0.185401 0.982663i \(-0.559358\pi\)
−0.185401 + 0.982663i \(0.559358\pi\)
\(444\) 8.52467 0.404563
\(445\) −4.52594 −0.214550
\(446\) −11.2538 −0.532881
\(447\) 1.66813 0.0788998
\(448\) 0.710831 0.0335836
\(449\) −19.1754 −0.904945 −0.452473 0.891778i \(-0.649458\pi\)
−0.452473 + 0.891778i \(0.649458\pi\)
\(450\) −2.32331 −0.109522
\(451\) −27.7538 −1.30688
\(452\) −8.32289 −0.391476
\(453\) −5.91142 −0.277743
\(454\) −24.0637 −1.12936
\(455\) 0.378422 0.0177407
\(456\) 6.53682 0.306115
\(457\) −7.66012 −0.358325 −0.179163 0.983819i \(-0.557339\pi\)
−0.179163 + 0.983819i \(0.557339\pi\)
\(458\) −6.06411 −0.283357
\(459\) −7.07539 −0.330251
\(460\) 6.05858 0.282483
\(461\) 13.1999 0.614782 0.307391 0.951583i \(-0.400544\pi\)
0.307391 + 0.951583i \(0.400544\pi\)
\(462\) −2.39866 −0.111596
\(463\) 36.9795 1.71858 0.859291 0.511487i \(-0.170905\pi\)
0.859291 + 0.511487i \(0.170905\pi\)
\(464\) −0.915588 −0.0425051
\(465\) −4.25758 −0.197441
\(466\) −23.9664 −1.11022
\(467\) −23.2934 −1.07789 −0.538945 0.842341i \(-0.681177\pi\)
−0.538945 + 0.842341i \(0.681177\pi\)
\(468\) −1.23685 −0.0571734
\(469\) 4.65826 0.215098
\(470\) −6.55629 −0.302419
\(471\) 9.94658 0.458314
\(472\) −3.59674 −0.165553
\(473\) −35.4789 −1.63132
\(474\) −2.40438 −0.110437
\(475\) 7.94642 0.364607
\(476\) 1.14852 0.0526425
\(477\) −25.7943 −1.18104
\(478\) 18.2283 0.833742
\(479\) 32.2728 1.47458 0.737291 0.675576i \(-0.236105\pi\)
0.737291 + 0.675576i \(0.236105\pi\)
\(480\) 0.822612 0.0375469
\(481\) 5.51686 0.251547
\(482\) 25.3760 1.15585
\(483\) 3.54268 0.161198
\(484\) 5.82724 0.264875
\(485\) 1.24039 0.0563233
\(486\) 15.9074 0.721573
\(487\) −28.7215 −1.30149 −0.650747 0.759294i \(-0.725544\pi\)
−0.650747 + 0.759294i \(0.725544\pi\)
\(488\) 4.86048 0.220024
\(489\) 12.5168 0.566027
\(490\) −6.49472 −0.293402
\(491\) 28.6061 1.29098 0.645488 0.763771i \(-0.276654\pi\)
0.645488 + 0.763771i \(0.276654\pi\)
\(492\) 5.56559 0.250916
\(493\) −1.47936 −0.0666271
\(494\) 4.23040 0.190335
\(495\) 9.53045 0.428362
\(496\) −5.17569 −0.232395
\(497\) 4.27297 0.191669
\(498\) 5.54706 0.248570
\(499\) −16.7561 −0.750104 −0.375052 0.927004i \(-0.622375\pi\)
−0.375052 + 0.927004i \(0.622375\pi\)
\(500\) 1.00000 0.0447214
\(501\) 5.40347 0.241409
\(502\) −10.2898 −0.459258
\(503\) −3.21247 −0.143237 −0.0716185 0.997432i \(-0.522816\pi\)
−0.0716185 + 0.997432i \(0.522816\pi\)
\(504\) −1.65148 −0.0735628
\(505\) −5.27186 −0.234595
\(506\) −24.8529 −1.10485
\(507\) −10.4608 −0.464581
\(508\) 21.2892 0.944556
\(509\) −36.8385 −1.63284 −0.816418 0.577461i \(-0.804044\pi\)
−0.816418 + 0.577461i \(0.804044\pi\)
\(510\) 1.32913 0.0588551
\(511\) 1.71379 0.0758136
\(512\) 1.00000 0.0441942
\(513\) −34.7975 −1.53635
\(514\) 24.3401 1.07359
\(515\) −14.3540 −0.632514
\(516\) 7.11473 0.313208
\(517\) 26.8946 1.18282
\(518\) 7.36629 0.323656
\(519\) 0.449758 0.0197422
\(520\) 0.532365 0.0233458
\(521\) 7.30885 0.320207 0.160103 0.987100i \(-0.448817\pi\)
0.160103 + 0.987100i \(0.448817\pi\)
\(522\) 2.12719 0.0931048
\(523\) −41.3007 −1.80595 −0.902977 0.429689i \(-0.858623\pi\)
−0.902977 + 0.429689i \(0.858623\pi\)
\(524\) −10.8187 −0.472619
\(525\) 0.584738 0.0255201
\(526\) −24.2660 −1.05805
\(527\) −8.36261 −0.364281
\(528\) −3.37444 −0.146854
\(529\) 13.7064 0.595932
\(530\) 11.1024 0.482258
\(531\) 8.35634 0.362634
\(532\) 5.64857 0.244896
\(533\) 3.60185 0.156014
\(534\) −3.72309 −0.161114
\(535\) 4.23982 0.183303
\(536\) 6.55325 0.283057
\(537\) −0.200865 −0.00866795
\(538\) 29.0440 1.25217
\(539\) 26.6420 1.14755
\(540\) −4.37902 −0.188443
\(541\) 29.4398 1.26571 0.632857 0.774269i \(-0.281882\pi\)
0.632857 + 0.774269i \(0.281882\pi\)
\(542\) −4.26080 −0.183017
\(543\) −21.3862 −0.917769
\(544\) 1.61575 0.0692747
\(545\) 0.0957383 0.00410098
\(546\) 0.311294 0.0133222
\(547\) 10.2809 0.439577 0.219789 0.975547i \(-0.429463\pi\)
0.219789 + 0.975547i \(0.429463\pi\)
\(548\) −19.9787 −0.853449
\(549\) −11.2924 −0.481948
\(550\) −4.10210 −0.174914
\(551\) −7.27565 −0.309953
\(552\) 4.98386 0.212127
\(553\) −2.07766 −0.0883510
\(554\) 32.2204 1.36891
\(555\) 8.52467 0.361852
\(556\) 11.4197 0.484303
\(557\) 6.92435 0.293394 0.146697 0.989181i \(-0.453136\pi\)
0.146697 + 0.989181i \(0.453136\pi\)
\(558\) 12.0247 0.509047
\(559\) 4.60440 0.194745
\(560\) 0.710831 0.0300381
\(561\) −5.45225 −0.230194
\(562\) −12.8003 −0.539948
\(563\) 2.14831 0.0905406 0.0452703 0.998975i \(-0.485585\pi\)
0.0452703 + 0.998975i \(0.485585\pi\)
\(564\) −5.39328 −0.227098
\(565\) −8.32289 −0.350147
\(566\) −6.26449 −0.263316
\(567\) 2.39386 0.100533
\(568\) 6.01123 0.252226
\(569\) 24.5084 1.02745 0.513724 0.857956i \(-0.328266\pi\)
0.513724 + 0.857956i \(0.328266\pi\)
\(570\) 6.53682 0.273797
\(571\) −28.5781 −1.19596 −0.597979 0.801512i \(-0.704029\pi\)
−0.597979 + 0.801512i \(0.704029\pi\)
\(572\) −2.18382 −0.0913099
\(573\) −14.7662 −0.616866
\(574\) 4.80931 0.200737
\(575\) 6.05858 0.252660
\(576\) −2.32331 −0.0968046
\(577\) 5.64780 0.235121 0.117561 0.993066i \(-0.462493\pi\)
0.117561 + 0.993066i \(0.462493\pi\)
\(578\) −14.3894 −0.598518
\(579\) −9.35202 −0.388657
\(580\) −0.915588 −0.0380177
\(581\) 4.79330 0.198860
\(582\) 1.02036 0.0422953
\(583\) −45.5432 −1.88621
\(584\) 2.41097 0.0997664
\(585\) −1.23685 −0.0511374
\(586\) 5.23184 0.216125
\(587\) 16.9563 0.699862 0.349931 0.936775i \(-0.386205\pi\)
0.349931 + 0.936775i \(0.386205\pi\)
\(588\) −5.34263 −0.220326
\(589\) −41.1282 −1.69466
\(590\) −3.59674 −0.148075
\(591\) 1.76703 0.0726859
\(592\) 10.3629 0.425914
\(593\) −35.7935 −1.46986 −0.734932 0.678141i \(-0.762786\pi\)
−0.734932 + 0.678141i \(0.762786\pi\)
\(594\) 17.9632 0.737038
\(595\) 1.14852 0.0470849
\(596\) 2.02784 0.0830638
\(597\) −17.9544 −0.734826
\(598\) 3.22538 0.131896
\(599\) 21.2640 0.868823 0.434411 0.900715i \(-0.356956\pi\)
0.434411 + 0.900715i \(0.356956\pi\)
\(600\) 0.822612 0.0335830
\(601\) −37.8926 −1.54567 −0.772837 0.634605i \(-0.781163\pi\)
−0.772837 + 0.634605i \(0.781163\pi\)
\(602\) 6.14794 0.250571
\(603\) −15.2252 −0.620019
\(604\) −7.18615 −0.292400
\(605\) 5.82724 0.236911
\(606\) −4.33670 −0.176166
\(607\) −29.5517 −1.19947 −0.599734 0.800199i \(-0.704727\pi\)
−0.599734 + 0.800199i \(0.704727\pi\)
\(608\) 7.94642 0.322270
\(609\) −0.535379 −0.0216947
\(610\) 4.86048 0.196795
\(611\) −3.49034 −0.141204
\(612\) −3.75389 −0.151742
\(613\) −23.3355 −0.942513 −0.471256 0.881996i \(-0.656199\pi\)
−0.471256 + 0.881996i \(0.656199\pi\)
\(614\) 21.0333 0.848836
\(615\) 5.56559 0.224426
\(616\) −2.91590 −0.117485
\(617\) 30.4230 1.22479 0.612393 0.790554i \(-0.290207\pi\)
0.612393 + 0.790554i \(0.290207\pi\)
\(618\) −11.8078 −0.474979
\(619\) −31.1594 −1.25240 −0.626200 0.779662i \(-0.715391\pi\)
−0.626200 + 0.779662i \(0.715391\pi\)
\(620\) −5.17569 −0.207861
\(621\) −26.5306 −1.06464
\(622\) −23.6109 −0.946712
\(623\) −3.21718 −0.128893
\(624\) 0.437930 0.0175312
\(625\) 1.00000 0.0400000
\(626\) 32.5188 1.29971
\(627\) −26.8147 −1.07088
\(628\) 12.0915 0.482502
\(629\) 16.7439 0.667623
\(630\) −1.65148 −0.0657966
\(631\) 14.5621 0.579707 0.289854 0.957071i \(-0.406393\pi\)
0.289854 + 0.957071i \(0.406393\pi\)
\(632\) −2.92286 −0.116265
\(633\) −13.4730 −0.535503
\(634\) −31.4667 −1.24970
\(635\) 21.2892 0.844836
\(636\) 9.13298 0.362146
\(637\) −3.45756 −0.136994
\(638\) 3.75584 0.148695
\(639\) −13.9659 −0.552484
\(640\) 1.00000 0.0395285
\(641\) −35.5487 −1.40409 −0.702044 0.712134i \(-0.747729\pi\)
−0.702044 + 0.712134i \(0.747729\pi\)
\(642\) 3.48773 0.137650
\(643\) −23.5931 −0.930420 −0.465210 0.885200i \(-0.654021\pi\)
−0.465210 + 0.885200i \(0.654021\pi\)
\(644\) 4.30663 0.169705
\(645\) 7.11473 0.280142
\(646\) 12.8394 0.505161
\(647\) 12.1817 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(648\) 3.36770 0.132296
\(649\) 14.7542 0.579153
\(650\) 0.532365 0.0208811
\(651\) −3.02642 −0.118615
\(652\) 15.2159 0.595900
\(653\) −1.86304 −0.0729063 −0.0364532 0.999335i \(-0.511606\pi\)
−0.0364532 + 0.999335i \(0.511606\pi\)
\(654\) 0.0787555 0.00307958
\(655\) −10.8187 −0.422723
\(656\) 6.76575 0.264158
\(657\) −5.60142 −0.218532
\(658\) −4.66041 −0.181682
\(659\) −48.1507 −1.87568 −0.937842 0.347062i \(-0.887179\pi\)
−0.937842 + 0.347062i \(0.887179\pi\)
\(660\) −3.37444 −0.131350
\(661\) −30.8392 −1.19950 −0.599752 0.800186i \(-0.704734\pi\)
−0.599752 + 0.800186i \(0.704734\pi\)
\(662\) −20.7862 −0.807880
\(663\) 0.707585 0.0274803
\(664\) 6.74323 0.261688
\(665\) 5.64857 0.219042
\(666\) −24.0763 −0.932937
\(667\) −5.54717 −0.214787
\(668\) 6.56868 0.254150
\(669\) −9.25747 −0.357914
\(670\) 6.55325 0.253174
\(671\) −19.9382 −0.769705
\(672\) 0.584738 0.0225568
\(673\) 29.5955 1.14082 0.570411 0.821359i \(-0.306784\pi\)
0.570411 + 0.821359i \(0.306784\pi\)
\(674\) 31.6652 1.21970
\(675\) −4.37902 −0.168548
\(676\) −12.7166 −0.489100
\(677\) −7.41223 −0.284875 −0.142438 0.989804i \(-0.545494\pi\)
−0.142438 + 0.989804i \(0.545494\pi\)
\(678\) −6.84651 −0.262939
\(679\) 0.881710 0.0338369
\(680\) 1.61575 0.0619612
\(681\) −19.7951 −0.758549
\(682\) 21.2312 0.812985
\(683\) −13.3379 −0.510359 −0.255180 0.966894i \(-0.582135\pi\)
−0.255180 + 0.966894i \(0.582135\pi\)
\(684\) −18.4620 −0.705912
\(685\) −19.9787 −0.763348
\(686\) −9.59247 −0.366242
\(687\) −4.98841 −0.190320
\(688\) 8.64895 0.329738
\(689\) 5.91054 0.225174
\(690\) 4.98386 0.189732
\(691\) −9.88208 −0.375932 −0.187966 0.982176i \(-0.560190\pi\)
−0.187966 + 0.982176i \(0.560190\pi\)
\(692\) 0.546744 0.0207841
\(693\) 6.77454 0.257344
\(694\) 26.5634 1.00833
\(695\) 11.4197 0.433174
\(696\) −0.753174 −0.0285490
\(697\) 10.9318 0.414070
\(698\) −1.96010 −0.0741908
\(699\) −19.7151 −0.745692
\(700\) 0.710831 0.0268669
\(701\) −6.23968 −0.235669 −0.117835 0.993033i \(-0.537595\pi\)
−0.117835 + 0.993033i \(0.537595\pi\)
\(702\) −2.33124 −0.0879868
\(703\) 82.3482 3.10582
\(704\) −4.10210 −0.154604
\(705\) −5.39328 −0.203123
\(706\) 3.30982 0.124567
\(707\) −3.74740 −0.140936
\(708\) −2.95872 −0.111195
\(709\) 39.8810 1.49776 0.748881 0.662704i \(-0.230591\pi\)
0.748881 + 0.662704i \(0.230591\pi\)
\(710\) 6.01123 0.225597
\(711\) 6.79070 0.254671
\(712\) −4.52594 −0.169617
\(713\) −31.3573 −1.17434
\(714\) 0.944790 0.0353579
\(715\) −2.18382 −0.0816701
\(716\) −0.244179 −0.00912541
\(717\) 14.9948 0.559991
\(718\) −17.1912 −0.641571
\(719\) 8.66995 0.323335 0.161667 0.986845i \(-0.448313\pi\)
0.161667 + 0.986845i \(0.448313\pi\)
\(720\) −2.32331 −0.0865846
\(721\) −10.2033 −0.379990
\(722\) 44.1457 1.64293
\(723\) 20.8746 0.776335
\(724\) −25.9979 −0.966204
\(725\) −0.915588 −0.0340041
\(726\) 4.79356 0.177906
\(727\) −31.1141 −1.15396 −0.576979 0.816759i \(-0.695769\pi\)
−0.576979 + 0.816759i \(0.695769\pi\)
\(728\) 0.378422 0.0140252
\(729\) 2.98249 0.110463
\(730\) 2.41097 0.0892338
\(731\) 13.9745 0.516867
\(732\) 3.99829 0.147781
\(733\) −10.6284 −0.392570 −0.196285 0.980547i \(-0.562888\pi\)
−0.196285 + 0.980547i \(0.562888\pi\)
\(734\) 6.47995 0.239179
\(735\) −5.34263 −0.197066
\(736\) 6.05858 0.223322
\(737\) −26.8821 −0.990215
\(738\) −15.7189 −0.578622
\(739\) 32.1897 1.18412 0.592059 0.805894i \(-0.298315\pi\)
0.592059 + 0.805894i \(0.298315\pi\)
\(740\) 10.3629 0.380949
\(741\) 3.47998 0.127840
\(742\) 7.89194 0.289722
\(743\) −40.4608 −1.48436 −0.742181 0.670200i \(-0.766208\pi\)
−0.742181 + 0.670200i \(0.766208\pi\)
\(744\) −4.25758 −0.156091
\(745\) 2.02784 0.0742945
\(746\) −7.55550 −0.276626
\(747\) −15.6666 −0.573211
\(748\) −6.62797 −0.242343
\(749\) 3.01380 0.110122
\(750\) 0.822612 0.0300375
\(751\) 27.5477 1.00523 0.502615 0.864510i \(-0.332371\pi\)
0.502615 + 0.864510i \(0.332371\pi\)
\(752\) −6.55629 −0.239083
\(753\) −8.46455 −0.308465
\(754\) −0.487427 −0.0177511
\(755\) −7.18615 −0.261531
\(756\) −3.11274 −0.113209
\(757\) 11.5209 0.418735 0.209368 0.977837i \(-0.432859\pi\)
0.209368 + 0.977837i \(0.432859\pi\)
\(758\) 23.0385 0.836797
\(759\) −20.4443 −0.742082
\(760\) 7.94642 0.288247
\(761\) 18.7715 0.680468 0.340234 0.940341i \(-0.389494\pi\)
0.340234 + 0.940341i \(0.389494\pi\)
\(762\) 17.5128 0.634420
\(763\) 0.0680538 0.00246371
\(764\) −17.9504 −0.649421
\(765\) −3.75389 −0.135722
\(766\) −26.2392 −0.948061
\(767\) −1.91478 −0.0691386
\(768\) 0.822612 0.0296834
\(769\) 45.0305 1.62384 0.811921 0.583767i \(-0.198422\pi\)
0.811921 + 0.583767i \(0.198422\pi\)
\(770\) −2.91590 −0.105082
\(771\) 20.0224 0.721090
\(772\) −11.3687 −0.409168
\(773\) 26.7052 0.960520 0.480260 0.877126i \(-0.340542\pi\)
0.480260 + 0.877126i \(0.340542\pi\)
\(774\) −20.0942 −0.722271
\(775\) −5.17569 −0.185916
\(776\) 1.24039 0.0445275
\(777\) 6.05960 0.217387
\(778\) −0.818755 −0.0293538
\(779\) 53.7636 1.92628
\(780\) 0.437930 0.0156804
\(781\) −24.6587 −0.882357
\(782\) 9.78915 0.350059
\(783\) 4.00938 0.143283
\(784\) −6.49472 −0.231954
\(785\) 12.0915 0.431563
\(786\) −8.89962 −0.317439
\(787\) 45.1456 1.60927 0.804634 0.593771i \(-0.202362\pi\)
0.804634 + 0.593771i \(0.202362\pi\)
\(788\) 2.14807 0.0765219
\(789\) −19.9615 −0.710648
\(790\) −2.92286 −0.103991
\(791\) −5.91617 −0.210355
\(792\) 9.53045 0.338650
\(793\) 2.58755 0.0918866
\(794\) −36.6154 −1.29943
\(795\) 9.13298 0.323913
\(796\) −21.8261 −0.773607
\(797\) 17.5910 0.623106 0.311553 0.950229i \(-0.399151\pi\)
0.311553 + 0.950229i \(0.399151\pi\)
\(798\) 4.64658 0.164487
\(799\) −10.5933 −0.374765
\(800\) 1.00000 0.0353553
\(801\) 10.5151 0.371535
\(802\) 1.00000 0.0353112
\(803\) −9.89003 −0.349011
\(804\) 5.39078 0.190118
\(805\) 4.30663 0.151789
\(806\) −2.75536 −0.0970533
\(807\) 23.8919 0.841035
\(808\) −5.27186 −0.185463
\(809\) −30.7415 −1.08081 −0.540407 0.841404i \(-0.681730\pi\)
−0.540407 + 0.841404i \(0.681730\pi\)
\(810\) 3.36770 0.118329
\(811\) 19.8606 0.697400 0.348700 0.937234i \(-0.386623\pi\)
0.348700 + 0.937234i \(0.386623\pi\)
\(812\) −0.650829 −0.0228396
\(813\) −3.50499 −0.122925
\(814\) −42.5098 −1.48997
\(815\) 15.2159 0.532989
\(816\) 1.32913 0.0465290
\(817\) 68.7282 2.40450
\(818\) 25.7798 0.901370
\(819\) −0.879191 −0.0307214
\(820\) 6.76575 0.236270
\(821\) 20.3088 0.708781 0.354391 0.935097i \(-0.384688\pi\)
0.354391 + 0.935097i \(0.384688\pi\)
\(822\) −16.4347 −0.573227
\(823\) −44.9814 −1.56795 −0.783977 0.620790i \(-0.786812\pi\)
−0.783977 + 0.620790i \(0.786812\pi\)
\(824\) −14.3540 −0.500046
\(825\) −3.37444 −0.117483
\(826\) −2.55667 −0.0889580
\(827\) −53.7445 −1.86888 −0.934439 0.356123i \(-0.884099\pi\)
−0.934439 + 0.356123i \(0.884099\pi\)
\(828\) −14.0760 −0.489174
\(829\) 21.5647 0.748973 0.374486 0.927232i \(-0.377819\pi\)
0.374486 + 0.927232i \(0.377819\pi\)
\(830\) 6.74323 0.234061
\(831\) 26.5049 0.919444
\(832\) 0.532365 0.0184564
\(833\) −10.4938 −0.363590
\(834\) 9.39398 0.325287
\(835\) 6.56868 0.227319
\(836\) −32.5970 −1.12739
\(837\) 22.6644 0.783397
\(838\) 32.2101 1.11268
\(839\) −31.8683 −1.10022 −0.550108 0.835094i \(-0.685413\pi\)
−0.550108 + 0.835094i \(0.685413\pi\)
\(840\) 0.584738 0.0201754
\(841\) −28.1617 −0.971093
\(842\) −25.7842 −0.888583
\(843\) −10.5297 −0.362662
\(844\) −16.3783 −0.563765
\(845\) −12.7166 −0.437464
\(846\) 15.2323 0.523697
\(847\) 4.14219 0.142327
\(848\) 11.1024 0.381258
\(849\) −5.15324 −0.176859
\(850\) 1.61575 0.0554197
\(851\) 62.7847 2.15223
\(852\) 4.94491 0.169410
\(853\) −0.143060 −0.00489829 −0.00244915 0.999997i \(-0.500780\pi\)
−0.00244915 + 0.999997i \(0.500780\pi\)
\(854\) 3.45498 0.118227
\(855\) −18.4620 −0.631387
\(856\) 4.23982 0.144914
\(857\) 51.9988 1.77625 0.888123 0.459605i \(-0.152009\pi\)
0.888123 + 0.459605i \(0.152009\pi\)
\(858\) −1.79643 −0.0613292
\(859\) −46.3058 −1.57993 −0.789967 0.613149i \(-0.789902\pi\)
−0.789967 + 0.613149i \(0.789902\pi\)
\(860\) 8.64895 0.294927
\(861\) 3.95619 0.134827
\(862\) 12.3190 0.419588
\(863\) −5.47632 −0.186416 −0.0932081 0.995647i \(-0.529712\pi\)
−0.0932081 + 0.995647i \(0.529712\pi\)
\(864\) −4.37902 −0.148977
\(865\) 0.546744 0.0185899
\(866\) 21.2530 0.722206
\(867\) −11.8369 −0.402001
\(868\) −3.67904 −0.124875
\(869\) 11.9899 0.406728
\(870\) −0.753174 −0.0255350
\(871\) 3.48872 0.118211
\(872\) 0.0957383 0.00324211
\(873\) −2.88182 −0.0975347
\(874\) 48.1441 1.62850
\(875\) 0.710831 0.0240305
\(876\) 1.98329 0.0670091
\(877\) −48.9770 −1.65384 −0.826919 0.562322i \(-0.809908\pi\)
−0.826919 + 0.562322i \(0.809908\pi\)
\(878\) −1.82146 −0.0614713
\(879\) 4.30377 0.145163
\(880\) −4.10210 −0.138282
\(881\) −1.07440 −0.0361976 −0.0180988 0.999836i \(-0.505761\pi\)
−0.0180988 + 0.999836i \(0.505761\pi\)
\(882\) 15.0892 0.508081
\(883\) −41.8301 −1.40769 −0.703847 0.710351i \(-0.748536\pi\)
−0.703847 + 0.710351i \(0.748536\pi\)
\(884\) 0.860169 0.0289306
\(885\) −2.95872 −0.0994563
\(886\) −7.80446 −0.262196
\(887\) −41.8468 −1.40508 −0.702539 0.711646i \(-0.747950\pi\)
−0.702539 + 0.711646i \(0.747950\pi\)
\(888\) 8.52467 0.286069
\(889\) 15.1330 0.507546
\(890\) −4.52594 −0.151710
\(891\) −13.8146 −0.462808
\(892\) −11.2538 −0.376803
\(893\) −52.0991 −1.74343
\(894\) 1.66813 0.0557906
\(895\) −0.244179 −0.00816201
\(896\) 0.710831 0.0237472
\(897\) 2.65323 0.0885889
\(898\) −19.1754 −0.639893
\(899\) 4.73880 0.158048
\(900\) −2.32331 −0.0774437
\(901\) 17.9387 0.597625
\(902\) −27.7538 −0.924101
\(903\) 5.05737 0.168299
\(904\) −8.32289 −0.276815
\(905\) −25.9979 −0.864199
\(906\) −5.91142 −0.196394
\(907\) 9.29471 0.308626 0.154313 0.988022i \(-0.450684\pi\)
0.154313 + 0.988022i \(0.450684\pi\)
\(908\) −24.0637 −0.798582
\(909\) 12.2482 0.406246
\(910\) 0.378422 0.0125446
\(911\) 5.80056 0.192181 0.0960905 0.995373i \(-0.469366\pi\)
0.0960905 + 0.995373i \(0.469366\pi\)
\(912\) 6.53682 0.216456
\(913\) −27.6614 −0.915459
\(914\) −7.66012 −0.253374
\(915\) 3.99829 0.132179
\(916\) −6.06411 −0.200364
\(917\) −7.69029 −0.253956
\(918\) −7.07539 −0.233523
\(919\) 22.2815 0.735000 0.367500 0.930023i \(-0.380214\pi\)
0.367500 + 0.930023i \(0.380214\pi\)
\(920\) 6.05858 0.199746
\(921\) 17.3023 0.570129
\(922\) 13.1999 0.434716
\(923\) 3.20017 0.105335
\(924\) −2.39866 −0.0789100
\(925\) 10.3629 0.340731
\(926\) 36.9795 1.21522
\(927\) 33.3489 1.09532
\(928\) −0.915588 −0.0300557
\(929\) −55.1248 −1.80859 −0.904294 0.426911i \(-0.859602\pi\)
−0.904294 + 0.426911i \(0.859602\pi\)
\(930\) −4.25758 −0.139612
\(931\) −51.6098 −1.69144
\(932\) −23.9664 −0.785046
\(933\) −19.4226 −0.635869
\(934\) −23.2934 −0.762183
\(935\) −6.62797 −0.216758
\(936\) −1.23685 −0.0404277
\(937\) 16.3385 0.533756 0.266878 0.963730i \(-0.414008\pi\)
0.266878 + 0.963730i \(0.414008\pi\)
\(938\) 4.65826 0.152097
\(939\) 26.7504 0.872966
\(940\) −6.55629 −0.213843
\(941\) −48.8585 −1.59274 −0.796371 0.604809i \(-0.793249\pi\)
−0.796371 + 0.604809i \(0.793249\pi\)
\(942\) 9.94658 0.324077
\(943\) 40.9909 1.33485
\(944\) −3.59674 −0.117064
\(945\) −3.11274 −0.101258
\(946\) −35.4789 −1.15352
\(947\) 45.2635 1.47086 0.735432 0.677598i \(-0.236979\pi\)
0.735432 + 0.677598i \(0.236979\pi\)
\(948\) −2.40438 −0.0780905
\(949\) 1.28351 0.0416646
\(950\) 7.94642 0.257816
\(951\) −25.8849 −0.839376
\(952\) 1.14852 0.0372239
\(953\) 43.3041 1.40276 0.701378 0.712789i \(-0.252568\pi\)
0.701378 + 0.712789i \(0.252568\pi\)
\(954\) −25.7943 −0.835123
\(955\) −17.9504 −0.580860
\(956\) 18.2283 0.589545
\(957\) 3.08960 0.0998724
\(958\) 32.2728 1.04269
\(959\) −14.2015 −0.458590
\(960\) 0.822612 0.0265497
\(961\) −4.21227 −0.135880
\(962\) 5.51686 0.177871
\(963\) −9.85042 −0.317425
\(964\) 25.3760 0.817307
\(965\) −11.3687 −0.365971
\(966\) 3.54268 0.113984
\(967\) 33.5978 1.08043 0.540216 0.841527i \(-0.318343\pi\)
0.540216 + 0.841527i \(0.318343\pi\)
\(968\) 5.82724 0.187295
\(969\) 10.5619 0.339296
\(970\) 1.24039 0.0398266
\(971\) −3.24372 −0.104096 −0.0520479 0.998645i \(-0.516575\pi\)
−0.0520479 + 0.998645i \(0.516575\pi\)
\(972\) 15.9074 0.510229
\(973\) 8.11748 0.260234
\(974\) −28.7215 −0.920296
\(975\) 0.437930 0.0140250
\(976\) 4.86048 0.155580
\(977\) −40.3001 −1.28931 −0.644657 0.764472i \(-0.723000\pi\)
−0.644657 + 0.764472i \(0.723000\pi\)
\(978\) 12.5168 0.400242
\(979\) 18.5658 0.593367
\(980\) −6.49472 −0.207466
\(981\) −0.222430 −0.00710164
\(982\) 28.6061 0.912857
\(983\) −4.73686 −0.151082 −0.0755412 0.997143i \(-0.524068\pi\)
−0.0755412 + 0.997143i \(0.524068\pi\)
\(984\) 5.56559 0.177425
\(985\) 2.14807 0.0684433
\(986\) −1.47936 −0.0471124
\(987\) −3.83371 −0.122028
\(988\) 4.23040 0.134587
\(989\) 52.4004 1.66624
\(990\) 9.53045 0.302898
\(991\) −49.7348 −1.57988 −0.789939 0.613186i \(-0.789888\pi\)
−0.789939 + 0.613186i \(0.789888\pi\)
\(992\) −5.17569 −0.164328
\(993\) −17.0990 −0.542620
\(994\) 4.27297 0.135530
\(995\) −21.8261 −0.691935
\(996\) 5.54706 0.175765
\(997\) −9.68842 −0.306835 −0.153418 0.988161i \(-0.549028\pi\)
−0.153418 + 0.988161i \(0.549028\pi\)
\(998\) −16.7561 −0.530404
\(999\) −45.3794 −1.43574
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 4010.2.a.n.1.13 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4010.2.a.n.1.13 22 1.1 even 1 trivial