Properties

Label 2005.2.a.g.1.16
Level $2005$
Weight $2$
Character 2005.1
Self dual yes
Analytic conductor $16.010$
Analytic rank $0$
Dimension $37$
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] = [2005,2,Mod(1,2005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2005, 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("2005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.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: \(16.0100056053\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 2005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.0686864 q^{2} -2.29330 q^{3} -1.99528 q^{4} +1.00000 q^{5} -0.157518 q^{6} -2.03277 q^{7} -0.274422 q^{8} +2.25922 q^{9} +O(q^{10})\) \(q+0.0686864 q^{2} -2.29330 q^{3} -1.99528 q^{4} +1.00000 q^{5} -0.157518 q^{6} -2.03277 q^{7} -0.274422 q^{8} +2.25922 q^{9} +0.0686864 q^{10} +1.26389 q^{11} +4.57578 q^{12} -4.81535 q^{13} -0.139624 q^{14} -2.29330 q^{15} +3.97172 q^{16} -2.38909 q^{17} +0.155178 q^{18} -7.50921 q^{19} -1.99528 q^{20} +4.66175 q^{21} +0.0868118 q^{22} +4.71068 q^{23} +0.629331 q^{24} +1.00000 q^{25} -0.330749 q^{26} +1.69883 q^{27} +4.05595 q^{28} -7.82808 q^{29} -0.157518 q^{30} -10.0129 q^{31} +0.821646 q^{32} -2.89847 q^{33} -0.164098 q^{34} -2.03277 q^{35} -4.50778 q^{36} -1.21553 q^{37} -0.515781 q^{38} +11.0430 q^{39} -0.274422 q^{40} -5.30331 q^{41} +0.320199 q^{42} +11.1157 q^{43} -2.52181 q^{44} +2.25922 q^{45} +0.323560 q^{46} -1.14647 q^{47} -9.10833 q^{48} -2.86785 q^{49} +0.0686864 q^{50} +5.47889 q^{51} +9.60799 q^{52} -4.81033 q^{53} +0.116687 q^{54} +1.26389 q^{55} +0.557836 q^{56} +17.2209 q^{57} -0.537683 q^{58} -12.1261 q^{59} +4.57578 q^{60} +11.7159 q^{61} -0.687753 q^{62} -4.59247 q^{63} -7.88699 q^{64} -4.81535 q^{65} -0.199085 q^{66} +6.36635 q^{67} +4.76690 q^{68} -10.8030 q^{69} -0.139624 q^{70} +7.57731 q^{71} -0.619979 q^{72} +8.79484 q^{73} -0.0834902 q^{74} -2.29330 q^{75} +14.9830 q^{76} -2.56919 q^{77} +0.758507 q^{78} +7.66525 q^{79} +3.97172 q^{80} -10.6736 q^{81} -0.364265 q^{82} -0.963961 q^{83} -9.30150 q^{84} -2.38909 q^{85} +0.763498 q^{86} +17.9521 q^{87} -0.346838 q^{88} -4.66081 q^{89} +0.155178 q^{90} +9.78850 q^{91} -9.39913 q^{92} +22.9627 q^{93} -0.0787472 q^{94} -7.50921 q^{95} -1.88428 q^{96} -3.28704 q^{97} -0.196982 q^{98} +2.85540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0686864 0.0485686 0.0242843 0.999705i \(-0.492269\pi\)
0.0242843 + 0.999705i \(0.492269\pi\)
\(3\) −2.29330 −1.32404 −0.662018 0.749488i \(-0.730300\pi\)
−0.662018 + 0.749488i \(0.730300\pi\)
\(4\) −1.99528 −0.997641
\(5\) 1.00000 0.447214
\(6\) −0.157518 −0.0643067
\(7\) −2.03277 −0.768314 −0.384157 0.923268i \(-0.625508\pi\)
−0.384157 + 0.923268i \(0.625508\pi\)
\(8\) −0.274422 −0.0970227
\(9\) 2.25922 0.753073
\(10\) 0.0686864 0.0217206
\(11\) 1.26389 0.381076 0.190538 0.981680i \(-0.438977\pi\)
0.190538 + 0.981680i \(0.438977\pi\)
\(12\) 4.57578 1.32091
\(13\) −4.81535 −1.33554 −0.667769 0.744368i \(-0.732751\pi\)
−0.667769 + 0.744368i \(0.732751\pi\)
\(14\) −0.139624 −0.0373160
\(15\) −2.29330 −0.592127
\(16\) 3.97172 0.992929
\(17\) −2.38909 −0.579438 −0.289719 0.957112i \(-0.593562\pi\)
−0.289719 + 0.957112i \(0.593562\pi\)
\(18\) 0.155178 0.0365757
\(19\) −7.50921 −1.72273 −0.861365 0.507986i \(-0.830390\pi\)
−0.861365 + 0.507986i \(0.830390\pi\)
\(20\) −1.99528 −0.446159
\(21\) 4.66175 1.01728
\(22\) 0.0868118 0.0185083
\(23\) 4.71068 0.982244 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(24\) 0.629331 0.128462
\(25\) 1.00000 0.200000
\(26\) −0.330749 −0.0648653
\(27\) 1.69883 0.326940
\(28\) 4.05595 0.766502
\(29\) −7.82808 −1.45364 −0.726819 0.686829i \(-0.759002\pi\)
−0.726819 + 0.686829i \(0.759002\pi\)
\(30\) −0.157518 −0.0287588
\(31\) −10.0129 −1.79838 −0.899189 0.437561i \(-0.855843\pi\)
−0.899189 + 0.437561i \(0.855843\pi\)
\(32\) 0.821646 0.145248
\(33\) −2.89847 −0.504559
\(34\) −0.164098 −0.0281425
\(35\) −2.03277 −0.343601
\(36\) −4.50778 −0.751297
\(37\) −1.21553 −0.199831 −0.0999157 0.994996i \(-0.531857\pi\)
−0.0999157 + 0.994996i \(0.531857\pi\)
\(38\) −0.515781 −0.0836707
\(39\) 11.0430 1.76830
\(40\) −0.274422 −0.0433899
\(41\) −5.30331 −0.828238 −0.414119 0.910223i \(-0.635910\pi\)
−0.414119 + 0.910223i \(0.635910\pi\)
\(42\) 0.320199 0.0494077
\(43\) 11.1157 1.69513 0.847564 0.530693i \(-0.178068\pi\)
0.847564 + 0.530693i \(0.178068\pi\)
\(44\) −2.52181 −0.380177
\(45\) 2.25922 0.336785
\(46\) 0.323560 0.0477063
\(47\) −1.14647 −0.167230 −0.0836152 0.996498i \(-0.526647\pi\)
−0.0836152 + 0.996498i \(0.526647\pi\)
\(48\) −9.10833 −1.31467
\(49\) −2.86785 −0.409693
\(50\) 0.0686864 0.00971373
\(51\) 5.47889 0.767198
\(52\) 9.60799 1.33239
\(53\) −4.81033 −0.660749 −0.330375 0.943850i \(-0.607175\pi\)
−0.330375 + 0.943850i \(0.607175\pi\)
\(54\) 0.116687 0.0158790
\(55\) 1.26389 0.170422
\(56\) 0.557836 0.0745439
\(57\) 17.2209 2.28096
\(58\) −0.537683 −0.0706012
\(59\) −12.1261 −1.57868 −0.789341 0.613955i \(-0.789578\pi\)
−0.789341 + 0.613955i \(0.789578\pi\)
\(60\) 4.57578 0.590730
\(61\) 11.7159 1.50007 0.750035 0.661398i \(-0.230036\pi\)
0.750035 + 0.661398i \(0.230036\pi\)
\(62\) −0.687753 −0.0873448
\(63\) −4.59247 −0.578597
\(64\) −7.88699 −0.985874
\(65\) −4.81535 −0.597271
\(66\) −0.199085 −0.0245057
\(67\) 6.36635 0.777774 0.388887 0.921286i \(-0.372860\pi\)
0.388887 + 0.921286i \(0.372860\pi\)
\(68\) 4.76690 0.578071
\(69\) −10.8030 −1.30053
\(70\) −0.139624 −0.0166882
\(71\) 7.57731 0.899261 0.449630 0.893215i \(-0.351556\pi\)
0.449630 + 0.893215i \(0.351556\pi\)
\(72\) −0.619979 −0.0730652
\(73\) 8.79484 1.02936 0.514679 0.857383i \(-0.327911\pi\)
0.514679 + 0.857383i \(0.327911\pi\)
\(74\) −0.0834902 −0.00970554
\(75\) −2.29330 −0.264807
\(76\) 14.9830 1.71867
\(77\) −2.56919 −0.292786
\(78\) 0.758507 0.0858840
\(79\) 7.66525 0.862408 0.431204 0.902255i \(-0.358089\pi\)
0.431204 + 0.902255i \(0.358089\pi\)
\(80\) 3.97172 0.444051
\(81\) −10.6736 −1.18595
\(82\) −0.364265 −0.0402264
\(83\) −0.963961 −0.105808 −0.0529042 0.998600i \(-0.516848\pi\)
−0.0529042 + 0.998600i \(0.516848\pi\)
\(84\) −9.30150 −1.01488
\(85\) −2.38909 −0.259133
\(86\) 0.763498 0.0823301
\(87\) 17.9521 1.92467
\(88\) −0.346838 −0.0369730
\(89\) −4.66081 −0.494045 −0.247022 0.969010i \(-0.579452\pi\)
−0.247022 + 0.969010i \(0.579452\pi\)
\(90\) 0.155178 0.0163572
\(91\) 9.78850 1.02611
\(92\) −9.39913 −0.979927
\(93\) 22.9627 2.38112
\(94\) −0.0787472 −0.00812215
\(95\) −7.50921 −0.770428
\(96\) −1.88428 −0.192314
\(97\) −3.28704 −0.333748 −0.166874 0.985978i \(-0.553367\pi\)
−0.166874 + 0.985978i \(0.553367\pi\)
\(98\) −0.196982 −0.0198982
\(99\) 2.85540 0.286978
\(100\) −1.99528 −0.199528
\(101\) 0.173128 0.0172269 0.00861346 0.999963i \(-0.497258\pi\)
0.00861346 + 0.999963i \(0.497258\pi\)
\(102\) 0.376325 0.0372617
\(103\) 0.382084 0.0376479 0.0188239 0.999823i \(-0.494008\pi\)
0.0188239 + 0.999823i \(0.494008\pi\)
\(104\) 1.32144 0.129578
\(105\) 4.66175 0.454940
\(106\) −0.330404 −0.0320917
\(107\) 14.9058 1.44100 0.720501 0.693454i \(-0.243912\pi\)
0.720501 + 0.693454i \(0.243912\pi\)
\(108\) −3.38965 −0.326169
\(109\) 11.7215 1.12272 0.561358 0.827573i \(-0.310279\pi\)
0.561358 + 0.827573i \(0.310279\pi\)
\(110\) 0.0868118 0.00827718
\(111\) 2.78757 0.264584
\(112\) −8.07358 −0.762881
\(113\) 18.6465 1.75412 0.877060 0.480381i \(-0.159502\pi\)
0.877060 + 0.480381i \(0.159502\pi\)
\(114\) 1.18284 0.110783
\(115\) 4.71068 0.439273
\(116\) 15.6192 1.45021
\(117\) −10.8789 −1.00576
\(118\) −0.832898 −0.0766744
\(119\) 4.85646 0.445191
\(120\) 0.629331 0.0574498
\(121\) −9.40259 −0.854781
\(122\) 0.804725 0.0728564
\(123\) 12.1621 1.09662
\(124\) 19.9786 1.79414
\(125\) 1.00000 0.0894427
\(126\) −0.315440 −0.0281017
\(127\) 8.19546 0.727229 0.363615 0.931549i \(-0.381542\pi\)
0.363615 + 0.931549i \(0.381542\pi\)
\(128\) −2.18502 −0.193130
\(129\) −25.4916 −2.24441
\(130\) −0.330749 −0.0290086
\(131\) 9.86588 0.861986 0.430993 0.902355i \(-0.358163\pi\)
0.430993 + 0.902355i \(0.358163\pi\)
\(132\) 5.78326 0.503368
\(133\) 15.2645 1.32360
\(134\) 0.437282 0.0377754
\(135\) 1.69883 0.146212
\(136\) 0.655617 0.0562187
\(137\) 7.67423 0.655653 0.327827 0.944738i \(-0.393684\pi\)
0.327827 + 0.944738i \(0.393684\pi\)
\(138\) −0.742019 −0.0631648
\(139\) 0.743374 0.0630522 0.0315261 0.999503i \(-0.489963\pi\)
0.0315261 + 0.999503i \(0.489963\pi\)
\(140\) 4.05595 0.342790
\(141\) 2.62921 0.221419
\(142\) 0.520458 0.0436759
\(143\) −6.08606 −0.508942
\(144\) 8.97298 0.747748
\(145\) −7.82808 −0.650087
\(146\) 0.604086 0.0499945
\(147\) 6.57684 0.542449
\(148\) 2.42532 0.199360
\(149\) 13.1477 1.07710 0.538552 0.842592i \(-0.318971\pi\)
0.538552 + 0.842592i \(0.318971\pi\)
\(150\) −0.157518 −0.0128613
\(151\) 3.78434 0.307965 0.153983 0.988074i \(-0.450790\pi\)
0.153983 + 0.988074i \(0.450790\pi\)
\(152\) 2.06069 0.167144
\(153\) −5.39747 −0.436359
\(154\) −0.176468 −0.0142202
\(155\) −10.0129 −0.804259
\(156\) −22.0340 −1.76413
\(157\) −17.9124 −1.42957 −0.714784 0.699345i \(-0.753475\pi\)
−0.714784 + 0.699345i \(0.753475\pi\)
\(158\) 0.526498 0.0418860
\(159\) 11.0315 0.874856
\(160\) 0.821646 0.0649568
\(161\) −9.57572 −0.754672
\(162\) −0.733130 −0.0576002
\(163\) 19.8035 1.55113 0.775565 0.631268i \(-0.217465\pi\)
0.775565 + 0.631268i \(0.217465\pi\)
\(164\) 10.5816 0.826284
\(165\) −2.89847 −0.225645
\(166\) −0.0662110 −0.00513897
\(167\) −9.99112 −0.773136 −0.386568 0.922261i \(-0.626340\pi\)
−0.386568 + 0.922261i \(0.626340\pi\)
\(168\) −1.27928 −0.0986989
\(169\) 10.1876 0.783663
\(170\) −0.164098 −0.0125857
\(171\) −16.9649 −1.29734
\(172\) −22.1790 −1.69113
\(173\) −14.5582 −1.10684 −0.553421 0.832902i \(-0.686678\pi\)
−0.553421 + 0.832902i \(0.686678\pi\)
\(174\) 1.23307 0.0934786
\(175\) −2.03277 −0.153663
\(176\) 5.01980 0.378381
\(177\) 27.8087 2.09023
\(178\) −0.320134 −0.0239951
\(179\) −4.72802 −0.353389 −0.176694 0.984266i \(-0.556540\pi\)
−0.176694 + 0.984266i \(0.556540\pi\)
\(180\) −4.50778 −0.335990
\(181\) −4.53675 −0.337214 −0.168607 0.985683i \(-0.553927\pi\)
−0.168607 + 0.985683i \(0.553927\pi\)
\(182\) 0.672337 0.0498369
\(183\) −26.8681 −1.98615
\(184\) −1.29271 −0.0953000
\(185\) −1.21553 −0.0893673
\(186\) 1.57722 0.115648
\(187\) −3.01953 −0.220810
\(188\) 2.28754 0.166836
\(189\) −3.45333 −0.251193
\(190\) −0.515781 −0.0374187
\(191\) 20.8682 1.50997 0.754984 0.655743i \(-0.227644\pi\)
0.754984 + 0.655743i \(0.227644\pi\)
\(192\) 18.0872 1.30533
\(193\) −16.6824 −1.20082 −0.600411 0.799691i \(-0.704996\pi\)
−0.600411 + 0.799691i \(0.704996\pi\)
\(194\) −0.225775 −0.0162097
\(195\) 11.0430 0.790809
\(196\) 5.72217 0.408727
\(197\) −18.9546 −1.35046 −0.675229 0.737608i \(-0.735955\pi\)
−0.675229 + 0.737608i \(0.735955\pi\)
\(198\) 0.196127 0.0139381
\(199\) −10.4269 −0.739142 −0.369571 0.929202i \(-0.620495\pi\)
−0.369571 + 0.929202i \(0.620495\pi\)
\(200\) −0.274422 −0.0194045
\(201\) −14.5999 −1.02980
\(202\) 0.0118916 0.000836688 0
\(203\) 15.9127 1.11685
\(204\) −10.9319 −0.765388
\(205\) −5.30331 −0.370399
\(206\) 0.0262440 0.00182851
\(207\) 10.6425 0.739702
\(208\) −19.1252 −1.32609
\(209\) −9.49078 −0.656491
\(210\) 0.320199 0.0220958
\(211\) −2.66555 −0.183504 −0.0917519 0.995782i \(-0.529247\pi\)
−0.0917519 + 0.995782i \(0.529247\pi\)
\(212\) 9.59796 0.659190
\(213\) −17.3770 −1.19065
\(214\) 1.02383 0.0699875
\(215\) 11.1157 0.758085
\(216\) −0.466196 −0.0317206
\(217\) 20.3540 1.38172
\(218\) 0.805108 0.0545288
\(219\) −20.1692 −1.36291
\(220\) −2.52181 −0.170020
\(221\) 11.5043 0.773862
\(222\) 0.191468 0.0128505
\(223\) −2.25357 −0.150910 −0.0754550 0.997149i \(-0.524041\pi\)
−0.0754550 + 0.997149i \(0.524041\pi\)
\(224\) −1.67022 −0.111596
\(225\) 2.25922 0.150615
\(226\) 1.28076 0.0851952
\(227\) 23.5087 1.56033 0.780163 0.625576i \(-0.215136\pi\)
0.780163 + 0.625576i \(0.215136\pi\)
\(228\) −34.3605 −2.27558
\(229\) 22.5757 1.49185 0.745923 0.666032i \(-0.232009\pi\)
0.745923 + 0.666032i \(0.232009\pi\)
\(230\) 0.323560 0.0213349
\(231\) 5.89192 0.387660
\(232\) 2.14820 0.141036
\(233\) −21.1051 −1.38264 −0.691319 0.722550i \(-0.742970\pi\)
−0.691319 + 0.722550i \(0.742970\pi\)
\(234\) −0.747235 −0.0488483
\(235\) −1.14647 −0.0747877
\(236\) 24.1950 1.57496
\(237\) −17.5787 −1.14186
\(238\) 0.333573 0.0216223
\(239\) −18.4318 −1.19225 −0.596126 0.802891i \(-0.703294\pi\)
−0.596126 + 0.802891i \(0.703294\pi\)
\(240\) −9.10833 −0.587940
\(241\) 26.9333 1.73493 0.867463 0.497502i \(-0.165749\pi\)
0.867463 + 0.497502i \(0.165749\pi\)
\(242\) −0.645830 −0.0415156
\(243\) 19.3812 1.24331
\(244\) −23.3766 −1.49653
\(245\) −2.86785 −0.183220
\(246\) 0.835369 0.0532612
\(247\) 36.1595 2.30077
\(248\) 2.74777 0.174483
\(249\) 2.21065 0.140094
\(250\) 0.0686864 0.00434411
\(251\) 5.92164 0.373771 0.186885 0.982382i \(-0.440161\pi\)
0.186885 + 0.982382i \(0.440161\pi\)
\(252\) 9.16327 0.577232
\(253\) 5.95376 0.374310
\(254\) 0.562917 0.0353205
\(255\) 5.47889 0.343101
\(256\) 15.6239 0.976494
\(257\) −2.79072 −0.174080 −0.0870401 0.996205i \(-0.527741\pi\)
−0.0870401 + 0.996205i \(0.527741\pi\)
\(258\) −1.75093 −0.109008
\(259\) 2.47089 0.153533
\(260\) 9.60799 0.595862
\(261\) −17.6854 −1.09470
\(262\) 0.677652 0.0418655
\(263\) −2.32513 −0.143374 −0.0716869 0.997427i \(-0.522838\pi\)
−0.0716869 + 0.997427i \(0.522838\pi\)
\(264\) 0.795403 0.0489536
\(265\) −4.81033 −0.295496
\(266\) 1.04846 0.0642854
\(267\) 10.6886 0.654133
\(268\) −12.7027 −0.775939
\(269\) −7.98611 −0.486922 −0.243461 0.969911i \(-0.578283\pi\)
−0.243461 + 0.969911i \(0.578283\pi\)
\(270\) 0.116687 0.00710132
\(271\) 6.28776 0.381954 0.190977 0.981595i \(-0.438834\pi\)
0.190977 + 0.981595i \(0.438834\pi\)
\(272\) −9.48877 −0.575341
\(273\) −22.4479 −1.35861
\(274\) 0.527115 0.0318442
\(275\) 1.26389 0.0762152
\(276\) 21.5550 1.29746
\(277\) 26.1777 1.57287 0.786434 0.617674i \(-0.211925\pi\)
0.786434 + 0.617674i \(0.211925\pi\)
\(278\) 0.0510597 0.00306236
\(279\) −22.6214 −1.35431
\(280\) 0.557836 0.0333371
\(281\) −28.1138 −1.67713 −0.838566 0.544801i \(-0.816605\pi\)
−0.838566 + 0.544801i \(0.816605\pi\)
\(282\) 0.180591 0.0107540
\(283\) 11.7982 0.701331 0.350665 0.936501i \(-0.385955\pi\)
0.350665 + 0.936501i \(0.385955\pi\)
\(284\) −15.1189 −0.897140
\(285\) 17.2209 1.02008
\(286\) −0.418030 −0.0247186
\(287\) 10.7804 0.636347
\(288\) 1.85628 0.109382
\(289\) −11.2923 −0.664251
\(290\) −0.537683 −0.0315738
\(291\) 7.53817 0.441895
\(292\) −17.5482 −1.02693
\(293\) −10.0677 −0.588163 −0.294082 0.955780i \(-0.595014\pi\)
−0.294082 + 0.955780i \(0.595014\pi\)
\(294\) 0.451740 0.0263460
\(295\) −12.1261 −0.706008
\(296\) 0.333567 0.0193882
\(297\) 2.14713 0.124589
\(298\) 0.903071 0.0523135
\(299\) −22.6836 −1.31182
\(300\) 4.57578 0.264183
\(301\) −22.5956 −1.30239
\(302\) 0.259933 0.0149574
\(303\) −0.397035 −0.0228091
\(304\) −29.8244 −1.71055
\(305\) 11.7159 0.670852
\(306\) −0.370733 −0.0211934
\(307\) −12.8876 −0.735534 −0.367767 0.929918i \(-0.619878\pi\)
−0.367767 + 0.929918i \(0.619878\pi\)
\(308\) 5.12626 0.292096
\(309\) −0.876233 −0.0498472
\(310\) −0.687753 −0.0390618
\(311\) −12.9711 −0.735525 −0.367763 0.929920i \(-0.619876\pi\)
−0.367763 + 0.929920i \(0.619876\pi\)
\(312\) −3.03045 −0.171565
\(313\) −8.49231 −0.480014 −0.240007 0.970771i \(-0.577150\pi\)
−0.240007 + 0.970771i \(0.577150\pi\)
\(314\) −1.23034 −0.0694322
\(315\) −4.59247 −0.258756
\(316\) −15.2943 −0.860373
\(317\) 11.2023 0.629183 0.314592 0.949227i \(-0.398132\pi\)
0.314592 + 0.949227i \(0.398132\pi\)
\(318\) 0.757715 0.0424906
\(319\) −9.89381 −0.553947
\(320\) −7.88699 −0.440896
\(321\) −34.1835 −1.90794
\(322\) −0.657722 −0.0366534
\(323\) 17.9401 0.998216
\(324\) 21.2968 1.18316
\(325\) −4.81535 −0.267108
\(326\) 1.36023 0.0753363
\(327\) −26.8809 −1.48652
\(328\) 1.45534 0.0803579
\(329\) 2.33051 0.128485
\(330\) −0.199085 −0.0109593
\(331\) −13.3112 −0.731647 −0.365824 0.930684i \(-0.619213\pi\)
−0.365824 + 0.930684i \(0.619213\pi\)
\(332\) 1.92337 0.105559
\(333\) −2.74614 −0.150488
\(334\) −0.686254 −0.0375502
\(335\) 6.36635 0.347831
\(336\) 18.5151 1.01008
\(337\) −30.9921 −1.68825 −0.844123 0.536149i \(-0.819879\pi\)
−0.844123 + 0.536149i \(0.819879\pi\)
\(338\) 0.699751 0.0380614
\(339\) −42.7621 −2.32252
\(340\) 4.76690 0.258521
\(341\) −12.6552 −0.685319
\(342\) −1.16526 −0.0630101
\(343\) 20.0591 1.08309
\(344\) −3.05039 −0.164466
\(345\) −10.8030 −0.581614
\(346\) −0.999953 −0.0537578
\(347\) 15.5828 0.836528 0.418264 0.908326i \(-0.362639\pi\)
0.418264 + 0.908326i \(0.362639\pi\)
\(348\) −35.8196 −1.92013
\(349\) 2.73748 0.146534 0.0732671 0.997312i \(-0.476657\pi\)
0.0732671 + 0.997312i \(0.476657\pi\)
\(350\) −0.139624 −0.00746320
\(351\) −8.18047 −0.436641
\(352\) 1.03847 0.0553505
\(353\) −27.5367 −1.46563 −0.732815 0.680428i \(-0.761794\pi\)
−0.732815 + 0.680428i \(0.761794\pi\)
\(354\) 1.91008 0.101520
\(355\) 7.57731 0.402162
\(356\) 9.29963 0.492879
\(357\) −11.1373 −0.589449
\(358\) −0.324751 −0.0171636
\(359\) 17.8466 0.941906 0.470953 0.882158i \(-0.343910\pi\)
0.470953 + 0.882158i \(0.343910\pi\)
\(360\) −0.619979 −0.0326757
\(361\) 37.3882 1.96780
\(362\) −0.311613 −0.0163780
\(363\) 21.5630 1.13176
\(364\) −19.5308 −1.02369
\(365\) 8.79484 0.460343
\(366\) −1.84548 −0.0964645
\(367\) 7.65545 0.399611 0.199806 0.979836i \(-0.435969\pi\)
0.199806 + 0.979836i \(0.435969\pi\)
\(368\) 18.7095 0.975299
\(369\) −11.9813 −0.623724
\(370\) −0.0834902 −0.00434045
\(371\) 9.77828 0.507663
\(372\) −45.8170 −2.37550
\(373\) −0.560977 −0.0290463 −0.0145232 0.999895i \(-0.504623\pi\)
−0.0145232 + 0.999895i \(0.504623\pi\)
\(374\) −0.207401 −0.0107244
\(375\) −2.29330 −0.118425
\(376\) 0.314617 0.0162251
\(377\) 37.6950 1.94139
\(378\) −0.237197 −0.0122001
\(379\) −11.3575 −0.583397 −0.291699 0.956510i \(-0.594220\pi\)
−0.291699 + 0.956510i \(0.594220\pi\)
\(380\) 14.9830 0.768611
\(381\) −18.7946 −0.962879
\(382\) 1.43336 0.0733371
\(383\) −11.6322 −0.594378 −0.297189 0.954819i \(-0.596049\pi\)
−0.297189 + 0.954819i \(0.596049\pi\)
\(384\) 5.01091 0.255712
\(385\) −2.56919 −0.130938
\(386\) −1.14585 −0.0583223
\(387\) 25.1128 1.27656
\(388\) 6.55857 0.332961
\(389\) 2.60796 0.132229 0.0661144 0.997812i \(-0.478940\pi\)
0.0661144 + 0.997812i \(0.478940\pi\)
\(390\) 0.758507 0.0384085
\(391\) −11.2542 −0.569150
\(392\) 0.787001 0.0397495
\(393\) −22.6254 −1.14130
\(394\) −1.30192 −0.0655899
\(395\) 7.66525 0.385680
\(396\) −5.69732 −0.286301
\(397\) 8.66596 0.434932 0.217466 0.976068i \(-0.430221\pi\)
0.217466 + 0.976068i \(0.430221\pi\)
\(398\) −0.716185 −0.0358991
\(399\) −35.0060 −1.75249
\(400\) 3.97172 0.198586
\(401\) −1.00000 −0.0499376
\(402\) −1.00282 −0.0500160
\(403\) 48.2159 2.40180
\(404\) −0.345440 −0.0171863
\(405\) −10.6736 −0.530375
\(406\) 1.09299 0.0542439
\(407\) −1.53629 −0.0761510
\(408\) −1.50353 −0.0744356
\(409\) 17.1486 0.847945 0.423973 0.905675i \(-0.360635\pi\)
0.423973 + 0.905675i \(0.360635\pi\)
\(410\) −0.364265 −0.0179898
\(411\) −17.5993 −0.868109
\(412\) −0.762366 −0.0375591
\(413\) 24.6495 1.21292
\(414\) 0.730992 0.0359263
\(415\) −0.963961 −0.0473190
\(416\) −3.95652 −0.193984
\(417\) −1.70478 −0.0834834
\(418\) −0.651888 −0.0318849
\(419\) −2.89009 −0.141190 −0.0705951 0.997505i \(-0.522490\pi\)
−0.0705951 + 0.997505i \(0.522490\pi\)
\(420\) −9.30150 −0.453867
\(421\) −26.2090 −1.27735 −0.638675 0.769477i \(-0.720517\pi\)
−0.638675 + 0.769477i \(0.720517\pi\)
\(422\) −0.183087 −0.00891253
\(423\) −2.59013 −0.125937
\(424\) 1.32006 0.0641077
\(425\) −2.38909 −0.115888
\(426\) −1.19357 −0.0578285
\(427\) −23.8158 −1.15253
\(428\) −29.7414 −1.43760
\(429\) 13.9571 0.673857
\(430\) 0.763498 0.0368191
\(431\) −22.3806 −1.07803 −0.539017 0.842295i \(-0.681204\pi\)
−0.539017 + 0.842295i \(0.681204\pi\)
\(432\) 6.74728 0.324628
\(433\) 21.2078 1.01918 0.509591 0.860417i \(-0.329797\pi\)
0.509591 + 0.860417i \(0.329797\pi\)
\(434\) 1.39804 0.0671082
\(435\) 17.9521 0.860739
\(436\) −23.3877 −1.12007
\(437\) −35.3735 −1.69214
\(438\) −1.38535 −0.0661946
\(439\) −26.6625 −1.27253 −0.636265 0.771471i \(-0.719521\pi\)
−0.636265 + 0.771471i \(0.719521\pi\)
\(440\) −0.346838 −0.0165348
\(441\) −6.47911 −0.308529
\(442\) 0.790188 0.0375854
\(443\) −24.0130 −1.14089 −0.570446 0.821335i \(-0.693230\pi\)
−0.570446 + 0.821335i \(0.693230\pi\)
\(444\) −5.56198 −0.263960
\(445\) −4.66081 −0.220944
\(446\) −0.154789 −0.00732949
\(447\) −30.1517 −1.42613
\(448\) 16.0324 0.757461
\(449\) 21.4170 1.01073 0.505366 0.862905i \(-0.331357\pi\)
0.505366 + 0.862905i \(0.331357\pi\)
\(450\) 0.155178 0.00731515
\(451\) −6.70278 −0.315622
\(452\) −37.2051 −1.74998
\(453\) −8.67862 −0.407757
\(454\) 1.61473 0.0757829
\(455\) 9.78850 0.458892
\(456\) −4.72578 −0.221305
\(457\) 10.3582 0.484536 0.242268 0.970209i \(-0.422109\pi\)
0.242268 + 0.970209i \(0.422109\pi\)
\(458\) 1.55065 0.0724569
\(459\) −4.05865 −0.189442
\(460\) −9.39913 −0.438237
\(461\) 19.2891 0.898384 0.449192 0.893435i \(-0.351712\pi\)
0.449192 + 0.893435i \(0.351712\pi\)
\(462\) 0.404695 0.0188281
\(463\) −18.4897 −0.859290 −0.429645 0.902998i \(-0.641361\pi\)
−0.429645 + 0.902998i \(0.641361\pi\)
\(464\) −31.0909 −1.44336
\(465\) 22.9627 1.06487
\(466\) −1.44963 −0.0671528
\(467\) 34.2749 1.58605 0.793026 0.609188i \(-0.208504\pi\)
0.793026 + 0.609188i \(0.208504\pi\)
\(468\) 21.7065 1.00339
\(469\) −12.9413 −0.597575
\(470\) −0.0787472 −0.00363234
\(471\) 41.0786 1.89280
\(472\) 3.32766 0.153168
\(473\) 14.0490 0.645973
\(474\) −1.20742 −0.0554586
\(475\) −7.50921 −0.344546
\(476\) −9.69000 −0.444141
\(477\) −10.8676 −0.497592
\(478\) −1.26601 −0.0579061
\(479\) 28.6185 1.30761 0.653807 0.756661i \(-0.273171\pi\)
0.653807 + 0.756661i \(0.273171\pi\)
\(480\) −1.88428 −0.0860052
\(481\) 5.85319 0.266883
\(482\) 1.84995 0.0842630
\(483\) 21.9600 0.999214
\(484\) 18.7608 0.852765
\(485\) −3.28704 −0.149257
\(486\) 1.33123 0.0603857
\(487\) 38.3521 1.73790 0.868949 0.494902i \(-0.164796\pi\)
0.868949 + 0.494902i \(0.164796\pi\)
\(488\) −3.21510 −0.145541
\(489\) −45.4153 −2.05375
\(490\) −0.196982 −0.00889876
\(491\) 14.7490 0.665614 0.332807 0.942995i \(-0.392004\pi\)
0.332807 + 0.942995i \(0.392004\pi\)
\(492\) −24.2668 −1.09403
\(493\) 18.7020 0.842294
\(494\) 2.48367 0.111745
\(495\) 2.85540 0.128341
\(496\) −39.7686 −1.78566
\(497\) −15.4029 −0.690915
\(498\) 0.151842 0.00680419
\(499\) 19.7799 0.885468 0.442734 0.896653i \(-0.354009\pi\)
0.442734 + 0.896653i \(0.354009\pi\)
\(500\) −1.99528 −0.0892317
\(501\) 22.9126 1.02366
\(502\) 0.406736 0.0181535
\(503\) 6.51523 0.290500 0.145250 0.989395i \(-0.453601\pi\)
0.145250 + 0.989395i \(0.453601\pi\)
\(504\) 1.26027 0.0561370
\(505\) 0.173128 0.00770411
\(506\) 0.408943 0.0181797
\(507\) −23.3632 −1.03760
\(508\) −16.3523 −0.725514
\(509\) −21.9119 −0.971229 −0.485614 0.874173i \(-0.661404\pi\)
−0.485614 + 0.874173i \(0.661404\pi\)
\(510\) 0.376325 0.0166640
\(511\) −17.8779 −0.790871
\(512\) 5.44319 0.240557
\(513\) −12.7569 −0.563230
\(514\) −0.191684 −0.00845484
\(515\) 0.382084 0.0168366
\(516\) 50.8630 2.23912
\(517\) −1.44901 −0.0637275
\(518\) 0.169716 0.00745691
\(519\) 33.3864 1.46550
\(520\) 1.32144 0.0579488
\(521\) 41.9668 1.83860 0.919300 0.393558i \(-0.128756\pi\)
0.919300 + 0.393558i \(0.128756\pi\)
\(522\) −1.21474 −0.0531679
\(523\) −30.6394 −1.33977 −0.669883 0.742467i \(-0.733656\pi\)
−0.669883 + 0.742467i \(0.733656\pi\)
\(524\) −19.6852 −0.859953
\(525\) 4.66175 0.203455
\(526\) −0.159705 −0.00696347
\(527\) 23.9218 1.04205
\(528\) −11.5119 −0.500991
\(529\) −0.809511 −0.0351961
\(530\) −0.330404 −0.0143518
\(531\) −27.3955 −1.18886
\(532\) −30.4569 −1.32048
\(533\) 25.5373 1.10614
\(534\) 0.734164 0.0317704
\(535\) 14.9058 0.644436
\(536\) −1.74706 −0.0754617
\(537\) 10.8428 0.467900
\(538\) −0.548537 −0.0236491
\(539\) −3.62464 −0.156124
\(540\) −3.38965 −0.145867
\(541\) −17.7533 −0.763275 −0.381637 0.924312i \(-0.624640\pi\)
−0.381637 + 0.924312i \(0.624640\pi\)
\(542\) 0.431884 0.0185510
\(543\) 10.4041 0.446484
\(544\) −1.96298 −0.0841622
\(545\) 11.7215 0.502094
\(546\) −1.54187 −0.0659859
\(547\) 6.85761 0.293210 0.146605 0.989195i \(-0.453165\pi\)
0.146605 + 0.989195i \(0.453165\pi\)
\(548\) −15.3122 −0.654107
\(549\) 26.4688 1.12966
\(550\) 0.0868118 0.00370167
\(551\) 58.7827 2.50423
\(552\) 2.96458 0.126181
\(553\) −15.5817 −0.662600
\(554\) 1.79806 0.0763921
\(555\) 2.78757 0.118326
\(556\) −1.48324 −0.0629035
\(557\) −27.3532 −1.15899 −0.579496 0.814975i \(-0.696751\pi\)
−0.579496 + 0.814975i \(0.696751\pi\)
\(558\) −1.55379 −0.0657770
\(559\) −53.5260 −2.26391
\(560\) −8.07358 −0.341171
\(561\) 6.92469 0.292361
\(562\) −1.93104 −0.0814560
\(563\) 37.8474 1.59508 0.797539 0.603268i \(-0.206135\pi\)
0.797539 + 0.603268i \(0.206135\pi\)
\(564\) −5.24601 −0.220897
\(565\) 18.6465 0.784466
\(566\) 0.810377 0.0340627
\(567\) 21.6969 0.911185
\(568\) −2.07938 −0.0872487
\(569\) −5.48139 −0.229792 −0.114896 0.993378i \(-0.536653\pi\)
−0.114896 + 0.993378i \(0.536653\pi\)
\(570\) 1.18284 0.0495437
\(571\) −39.4038 −1.64900 −0.824499 0.565864i \(-0.808543\pi\)
−0.824499 + 0.565864i \(0.808543\pi\)
\(572\) 12.1434 0.507741
\(573\) −47.8570 −1.99925
\(574\) 0.740467 0.0309065
\(575\) 4.71068 0.196449
\(576\) −17.8185 −0.742435
\(577\) −10.1073 −0.420773 −0.210386 0.977618i \(-0.567472\pi\)
−0.210386 + 0.977618i \(0.567472\pi\)
\(578\) −0.775626 −0.0322618
\(579\) 38.2576 1.58993
\(580\) 15.6192 0.648553
\(581\) 1.95951 0.0812942
\(582\) 0.517770 0.0214622
\(583\) −6.07970 −0.251796
\(584\) −2.41350 −0.0998711
\(585\) −10.8789 −0.449789
\(586\) −0.691516 −0.0285663
\(587\) 10.8190 0.446550 0.223275 0.974756i \(-0.428325\pi\)
0.223275 + 0.974756i \(0.428325\pi\)
\(588\) −13.1227 −0.541169
\(589\) 75.1893 3.09812
\(590\) −0.832898 −0.0342899
\(591\) 43.4685 1.78806
\(592\) −4.82773 −0.198418
\(593\) 23.6934 0.972971 0.486485 0.873689i \(-0.338279\pi\)
0.486485 + 0.873689i \(0.338279\pi\)
\(594\) 0.147479 0.00605112
\(595\) 4.85646 0.199095
\(596\) −26.2334 −1.07456
\(597\) 23.9120 0.978651
\(598\) −1.55805 −0.0637136
\(599\) −3.11993 −0.127477 −0.0637384 0.997967i \(-0.520302\pi\)
−0.0637384 + 0.997967i \(0.520302\pi\)
\(600\) 0.629331 0.0256923
\(601\) 25.4983 1.04010 0.520048 0.854137i \(-0.325914\pi\)
0.520048 + 0.854137i \(0.325914\pi\)
\(602\) −1.55201 −0.0632554
\(603\) 14.3830 0.585720
\(604\) −7.55082 −0.307239
\(605\) −9.40259 −0.382270
\(606\) −0.0272709 −0.00110781
\(607\) 15.2032 0.617081 0.308540 0.951211i \(-0.400160\pi\)
0.308540 + 0.951211i \(0.400160\pi\)
\(608\) −6.16991 −0.250223
\(609\) −36.4925 −1.47875
\(610\) 0.804725 0.0325824
\(611\) 5.52067 0.223343
\(612\) 10.7695 0.435330
\(613\) −0.324285 −0.0130977 −0.00654887 0.999979i \(-0.502085\pi\)
−0.00654887 + 0.999979i \(0.502085\pi\)
\(614\) −0.885203 −0.0357239
\(615\) 12.1621 0.490422
\(616\) 0.705041 0.0284069
\(617\) 26.3365 1.06027 0.530133 0.847914i \(-0.322142\pi\)
0.530133 + 0.847914i \(0.322142\pi\)
\(618\) −0.0601853 −0.00242101
\(619\) 17.6193 0.708181 0.354090 0.935211i \(-0.384791\pi\)
0.354090 + 0.935211i \(0.384791\pi\)
\(620\) 19.9786 0.802362
\(621\) 8.00265 0.321135
\(622\) −0.890941 −0.0357235
\(623\) 9.47435 0.379582
\(624\) 43.8598 1.75580
\(625\) 1.00000 0.0400000
\(626\) −0.583307 −0.0233136
\(627\) 21.7652 0.869218
\(628\) 35.7404 1.42620
\(629\) 2.90400 0.115790
\(630\) −0.315440 −0.0125674
\(631\) −41.5355 −1.65350 −0.826752 0.562567i \(-0.809814\pi\)
−0.826752 + 0.562567i \(0.809814\pi\)
\(632\) −2.10351 −0.0836731
\(633\) 6.11289 0.242966
\(634\) 0.769445 0.0305586
\(635\) 8.19546 0.325227
\(636\) −22.0110 −0.872792
\(637\) 13.8097 0.547161
\(638\) −0.679570 −0.0269044
\(639\) 17.1188 0.677209
\(640\) −2.18502 −0.0863706
\(641\) −28.5960 −1.12947 −0.564737 0.825271i \(-0.691022\pi\)
−0.564737 + 0.825271i \(0.691022\pi\)
\(642\) −2.34795 −0.0926660
\(643\) 31.2100 1.23080 0.615402 0.788214i \(-0.288994\pi\)
0.615402 + 0.788214i \(0.288994\pi\)
\(644\) 19.1063 0.752892
\(645\) −25.4916 −1.00373
\(646\) 1.23224 0.0484820
\(647\) 41.9392 1.64880 0.824400 0.566007i \(-0.191513\pi\)
0.824400 + 0.566007i \(0.191513\pi\)
\(648\) 2.92906 0.115064
\(649\) −15.3260 −0.601598
\(650\) −0.330749 −0.0129731
\(651\) −46.6778 −1.82945
\(652\) −39.5136 −1.54747
\(653\) −3.98499 −0.155945 −0.0779724 0.996956i \(-0.524845\pi\)
−0.0779724 + 0.996956i \(0.524845\pi\)
\(654\) −1.84635 −0.0721981
\(655\) 9.86588 0.385492
\(656\) −21.0632 −0.822381
\(657\) 19.8695 0.775182
\(658\) 0.160075 0.00624036
\(659\) 29.7898 1.16044 0.580222 0.814458i \(-0.302966\pi\)
0.580222 + 0.814458i \(0.302966\pi\)
\(660\) 5.78326 0.225113
\(661\) −21.8127 −0.848416 −0.424208 0.905565i \(-0.639447\pi\)
−0.424208 + 0.905565i \(0.639447\pi\)
\(662\) −0.914296 −0.0355351
\(663\) −26.3828 −1.02462
\(664\) 0.264532 0.0102658
\(665\) 15.2645 0.591931
\(666\) −0.188623 −0.00730898
\(667\) −36.8756 −1.42783
\(668\) 19.9351 0.771312
\(669\) 5.16810 0.199810
\(670\) 0.437282 0.0168937
\(671\) 14.8076 0.571641
\(672\) 3.83031 0.147757
\(673\) −8.02898 −0.309495 −0.154747 0.987954i \(-0.549456\pi\)
−0.154747 + 0.987954i \(0.549456\pi\)
\(674\) −2.12874 −0.0819959
\(675\) 1.69883 0.0653881
\(676\) −20.3272 −0.781814
\(677\) 27.4427 1.05471 0.527355 0.849645i \(-0.323184\pi\)
0.527355 + 0.849645i \(0.323184\pi\)
\(678\) −2.93718 −0.112802
\(679\) 6.68179 0.256424
\(680\) 0.655617 0.0251418
\(681\) −53.9124 −2.06593
\(682\) −0.869242 −0.0332850
\(683\) −33.7349 −1.29083 −0.645414 0.763833i \(-0.723315\pi\)
−0.645414 + 0.763833i \(0.723315\pi\)
\(684\) 33.8499 1.29428
\(685\) 7.67423 0.293217
\(686\) 1.37779 0.0526041
\(687\) −51.7729 −1.97526
\(688\) 44.1484 1.68314
\(689\) 23.1634 0.882456
\(690\) −0.742019 −0.0282482
\(691\) −16.0490 −0.610531 −0.305266 0.952267i \(-0.598745\pi\)
−0.305266 + 0.952267i \(0.598745\pi\)
\(692\) 29.0478 1.10423
\(693\) −5.80436 −0.220489
\(694\) 1.07033 0.0406290
\(695\) 0.743374 0.0281978
\(696\) −4.92645 −0.186737
\(697\) 12.6701 0.479913
\(698\) 0.188028 0.00711696
\(699\) 48.4002 1.83066
\(700\) 4.05595 0.153300
\(701\) 1.59219 0.0601363 0.0300681 0.999548i \(-0.490428\pi\)
0.0300681 + 0.999548i \(0.490428\pi\)
\(702\) −0.561887 −0.0212071
\(703\) 9.12765 0.344256
\(704\) −9.96826 −0.375693
\(705\) 2.62921 0.0990216
\(706\) −1.89140 −0.0711837
\(707\) −0.351930 −0.0132357
\(708\) −55.4863 −2.08530
\(709\) −38.6350 −1.45097 −0.725484 0.688239i \(-0.758384\pi\)
−0.725484 + 0.688239i \(0.758384\pi\)
\(710\) 0.520458 0.0195324
\(711\) 17.3175 0.649456
\(712\) 1.27903 0.0479336
\(713\) −47.1678 −1.76645
\(714\) −0.764982 −0.0286287
\(715\) −6.08606 −0.227606
\(716\) 9.43373 0.352555
\(717\) 42.2696 1.57859
\(718\) 1.22582 0.0457471
\(719\) 31.5917 1.17817 0.589086 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(720\) 8.97298 0.334403
\(721\) −0.776689 −0.0289254
\(722\) 2.56806 0.0955734
\(723\) −61.7661 −2.29711
\(724\) 9.05210 0.336419
\(725\) −7.82808 −0.290728
\(726\) 1.48108 0.0549681
\(727\) −18.6686 −0.692380 −0.346190 0.938164i \(-0.612525\pi\)
−0.346190 + 0.938164i \(0.612525\pi\)
\(728\) −2.68618 −0.0995563
\(729\) −12.4262 −0.460229
\(730\) 0.604086 0.0223582
\(731\) −26.5564 −0.982222
\(732\) 53.6095 1.98146
\(733\) 50.2011 1.85422 0.927110 0.374790i \(-0.122285\pi\)
0.927110 + 0.374790i \(0.122285\pi\)
\(734\) 0.525826 0.0194086
\(735\) 6.57684 0.242590
\(736\) 3.87051 0.142669
\(737\) 8.04634 0.296391
\(738\) −0.822955 −0.0302934
\(739\) 14.4025 0.529804 0.264902 0.964275i \(-0.414660\pi\)
0.264902 + 0.964275i \(0.414660\pi\)
\(740\) 2.42532 0.0891565
\(741\) −82.9245 −3.04631
\(742\) 0.671635 0.0246565
\(743\) 28.7991 1.05654 0.528269 0.849077i \(-0.322841\pi\)
0.528269 + 0.849077i \(0.322841\pi\)
\(744\) −6.30145 −0.231023
\(745\) 13.1477 0.481696
\(746\) −0.0385315 −0.00141074
\(747\) −2.17780 −0.0796815
\(748\) 6.02482 0.220289
\(749\) −30.3001 −1.10714
\(750\) −0.157518 −0.00575176
\(751\) −10.6209 −0.387561 −0.193780 0.981045i \(-0.562075\pi\)
−0.193780 + 0.981045i \(0.562075\pi\)
\(752\) −4.55347 −0.166048
\(753\) −13.5801 −0.494886
\(754\) 2.58913 0.0942907
\(755\) 3.78434 0.137726
\(756\) 6.89037 0.250600
\(757\) −14.6026 −0.530740 −0.265370 0.964147i \(-0.585494\pi\)
−0.265370 + 0.964147i \(0.585494\pi\)
\(758\) −0.780108 −0.0283348
\(759\) −13.6538 −0.495600
\(760\) 2.06069 0.0747491
\(761\) 3.50797 0.127164 0.0635819 0.997977i \(-0.479748\pi\)
0.0635819 + 0.997977i \(0.479748\pi\)
\(762\) −1.29094 −0.0467657
\(763\) −23.8271 −0.862599
\(764\) −41.6379 −1.50641
\(765\) −5.39747 −0.195146
\(766\) −0.798975 −0.0288681
\(767\) 58.3914 2.10839
\(768\) −35.8303 −1.29291
\(769\) −42.2575 −1.52384 −0.761922 0.647669i \(-0.775744\pi\)
−0.761922 + 0.647669i \(0.775744\pi\)
\(770\) −0.176468 −0.00635948
\(771\) 6.39995 0.230489
\(772\) 33.2860 1.19799
\(773\) −35.0490 −1.26062 −0.630312 0.776342i \(-0.717073\pi\)
−0.630312 + 0.776342i \(0.717073\pi\)
\(774\) 1.72491 0.0620006
\(775\) −10.0129 −0.359676
\(776\) 0.902035 0.0323812
\(777\) −5.66648 −0.203284
\(778\) 0.179132 0.00642218
\(779\) 39.8237 1.42683
\(780\) −22.0340 −0.788943
\(781\) 9.57685 0.342687
\(782\) −0.773012 −0.0276428
\(783\) −13.2986 −0.475253
\(784\) −11.3903 −0.406796
\(785\) −17.9124 −0.639323
\(786\) −1.55406 −0.0554315
\(787\) −3.51929 −0.125449 −0.0627246 0.998031i \(-0.519979\pi\)
−0.0627246 + 0.998031i \(0.519979\pi\)
\(788\) 37.8197 1.34727
\(789\) 5.33222 0.189832
\(790\) 0.526498 0.0187320
\(791\) −37.9041 −1.34772
\(792\) −0.783583 −0.0278434
\(793\) −56.4163 −2.00340
\(794\) 0.595234 0.0211241
\(795\) 11.0315 0.391248
\(796\) 20.8046 0.737398
\(797\) −38.8055 −1.37456 −0.687281 0.726392i \(-0.741196\pi\)
−0.687281 + 0.726392i \(0.741196\pi\)
\(798\) −2.40444 −0.0851162
\(799\) 2.73902 0.0968996
\(800\) 0.821646 0.0290496
\(801\) −10.5298 −0.372052
\(802\) −0.0686864 −0.00242540
\(803\) 11.1157 0.392264
\(804\) 29.1310 1.02737
\(805\) −9.57572 −0.337500
\(806\) 3.31177 0.116652
\(807\) 18.3145 0.644702
\(808\) −0.0475102 −0.00167140
\(809\) −4.66124 −0.163881 −0.0819403 0.996637i \(-0.526112\pi\)
−0.0819403 + 0.996637i \(0.526112\pi\)
\(810\) −0.733130 −0.0257596
\(811\) 12.2621 0.430579 0.215289 0.976550i \(-0.430930\pi\)
0.215289 + 0.976550i \(0.430930\pi\)
\(812\) −31.7503 −1.11422
\(813\) −14.4197 −0.505721
\(814\) −0.105522 −0.00369855
\(815\) 19.8035 0.693686
\(816\) 21.7606 0.761773
\(817\) −83.4701 −2.92025
\(818\) 1.17788 0.0411835
\(819\) 22.1144 0.772738
\(820\) 10.5816 0.369525
\(821\) 23.8589 0.832683 0.416341 0.909208i \(-0.363312\pi\)
0.416341 + 0.909208i \(0.363312\pi\)
\(822\) −1.20883 −0.0421629
\(823\) −18.5900 −0.648008 −0.324004 0.946056i \(-0.605029\pi\)
−0.324004 + 0.946056i \(0.605029\pi\)
\(824\) −0.104852 −0.00365270
\(825\) −2.89847 −0.100912
\(826\) 1.69309 0.0589101
\(827\) 7.47569 0.259955 0.129978 0.991517i \(-0.458509\pi\)
0.129978 + 0.991517i \(0.458509\pi\)
\(828\) −21.2347 −0.737957
\(829\) 43.4384 1.50868 0.754338 0.656486i \(-0.227958\pi\)
0.754338 + 0.656486i \(0.227958\pi\)
\(830\) −0.0662110 −0.00229822
\(831\) −60.0334 −2.08254
\(832\) 37.9787 1.31667
\(833\) 6.85154 0.237392
\(834\) −0.117095 −0.00405468
\(835\) −9.99112 −0.345757
\(836\) 18.9368 0.654943
\(837\) −17.0103 −0.587962
\(838\) −0.198510 −0.00685742
\(839\) 1.10795 0.0382506 0.0191253 0.999817i \(-0.493912\pi\)
0.0191253 + 0.999817i \(0.493912\pi\)
\(840\) −1.27928 −0.0441395
\(841\) 32.2789 1.11307
\(842\) −1.80020 −0.0620392
\(843\) 64.4734 2.22058
\(844\) 5.31852 0.183071
\(845\) 10.1876 0.350465
\(846\) −0.177907 −0.00611657
\(847\) 19.1133 0.656741
\(848\) −19.1052 −0.656077
\(849\) −27.0568 −0.928587
\(850\) −0.164098 −0.00562851
\(851\) −5.72596 −0.196283
\(852\) 34.6721 1.18785
\(853\) 35.2400 1.20659 0.603297 0.797516i \(-0.293853\pi\)
0.603297 + 0.797516i \(0.293853\pi\)
\(854\) −1.63582 −0.0559766
\(855\) −16.9649 −0.580189
\(856\) −4.09048 −0.139810
\(857\) 19.6165 0.670088 0.335044 0.942202i \(-0.391249\pi\)
0.335044 + 0.942202i \(0.391249\pi\)
\(858\) 0.958667 0.0327283
\(859\) 18.2577 0.622946 0.311473 0.950255i \(-0.399178\pi\)
0.311473 + 0.950255i \(0.399178\pi\)
\(860\) −22.1790 −0.756296
\(861\) −24.7227 −0.842547
\(862\) −1.53724 −0.0523586
\(863\) −22.6540 −0.771150 −0.385575 0.922676i \(-0.625997\pi\)
−0.385575 + 0.922676i \(0.625997\pi\)
\(864\) 1.39584 0.0474874
\(865\) −14.5582 −0.494995
\(866\) 1.45669 0.0495003
\(867\) 25.8966 0.879493
\(868\) −40.6120 −1.37846
\(869\) 9.68800 0.328643
\(870\) 1.23307 0.0418049
\(871\) −30.6562 −1.03875
\(872\) −3.21663 −0.108929
\(873\) −7.42615 −0.251337
\(874\) −2.42968 −0.0821850
\(875\) −2.03277 −0.0687201
\(876\) 40.2432 1.35969
\(877\) −38.3278 −1.29424 −0.647118 0.762390i \(-0.724026\pi\)
−0.647118 + 0.762390i \(0.724026\pi\)
\(878\) −1.83135 −0.0618050
\(879\) 23.0883 0.778749
\(880\) 5.01980 0.169217
\(881\) 0.681458 0.0229589 0.0114795 0.999934i \(-0.496346\pi\)
0.0114795 + 0.999934i \(0.496346\pi\)
\(882\) −0.445027 −0.0149848
\(883\) 51.2132 1.72346 0.861730 0.507367i \(-0.169381\pi\)
0.861730 + 0.507367i \(0.169381\pi\)
\(884\) −22.9543 −0.772037
\(885\) 27.8087 0.934781
\(886\) −1.64937 −0.0554116
\(887\) −54.8540 −1.84182 −0.920908 0.389780i \(-0.872551\pi\)
−0.920908 + 0.389780i \(0.872551\pi\)
\(888\) −0.764969 −0.0256707
\(889\) −16.6595 −0.558741
\(890\) −0.320134 −0.0107309
\(891\) −13.4902 −0.451939
\(892\) 4.49650 0.150554
\(893\) 8.60911 0.288093
\(894\) −2.07101 −0.0692650
\(895\) −4.72802 −0.158040
\(896\) 4.44164 0.148385
\(897\) 52.0202 1.73690
\(898\) 1.47106 0.0490899
\(899\) 78.3822 2.61419
\(900\) −4.50778 −0.150259
\(901\) 11.4923 0.382863
\(902\) −0.460390 −0.0153293
\(903\) 51.8186 1.72441
\(904\) −5.11702 −0.170189
\(905\) −4.53675 −0.150807
\(906\) −0.596103 −0.0198042
\(907\) −54.0409 −1.79440 −0.897200 0.441625i \(-0.854402\pi\)
−0.897200 + 0.441625i \(0.854402\pi\)
\(908\) −46.9064 −1.55665
\(909\) 0.391135 0.0129731
\(910\) 0.672337 0.0222877
\(911\) 27.6933 0.917518 0.458759 0.888561i \(-0.348294\pi\)
0.458759 + 0.888561i \(0.348294\pi\)
\(912\) 68.3963 2.26483
\(913\) −1.21834 −0.0403211
\(914\) 0.711467 0.0235332
\(915\) −26.8681 −0.888233
\(916\) −45.0450 −1.48833
\(917\) −20.0551 −0.662276
\(918\) −0.278774 −0.00920093
\(919\) −6.18778 −0.204116 −0.102058 0.994778i \(-0.532543\pi\)
−0.102058 + 0.994778i \(0.532543\pi\)
\(920\) −1.29271 −0.0426195
\(921\) 29.5551 0.973874
\(922\) 1.32490 0.0436333
\(923\) −36.4874 −1.20100
\(924\) −11.7560 −0.386745
\(925\) −1.21553 −0.0399663
\(926\) −1.26999 −0.0417345
\(927\) 0.863212 0.0283516
\(928\) −6.43192 −0.211138
\(929\) 7.32688 0.240387 0.120194 0.992750i \(-0.461648\pi\)
0.120194 + 0.992750i \(0.461648\pi\)
\(930\) 1.57722 0.0517192
\(931\) 21.5353 0.705791
\(932\) 42.1105 1.37938
\(933\) 29.7467 0.973862
\(934\) 2.35422 0.0770324
\(935\) −3.01953 −0.0987493
\(936\) 2.98542 0.0975814
\(937\) −35.2493 −1.15155 −0.575773 0.817610i \(-0.695299\pi\)
−0.575773 + 0.817610i \(0.695299\pi\)
\(938\) −0.888893 −0.0290234
\(939\) 19.4754 0.635556
\(940\) 2.28754 0.0746113
\(941\) −41.0123 −1.33696 −0.668481 0.743729i \(-0.733055\pi\)
−0.668481 + 0.743729i \(0.733055\pi\)
\(942\) 2.82154 0.0919308
\(943\) −24.9822 −0.813532
\(944\) −48.1614 −1.56752
\(945\) −3.45333 −0.112337
\(946\) 0.964974 0.0313740
\(947\) 45.2788 1.47136 0.735681 0.677328i \(-0.236862\pi\)
0.735681 + 0.677328i \(0.236862\pi\)
\(948\) 35.0745 1.13917
\(949\) −42.3503 −1.37475
\(950\) −0.515781 −0.0167341
\(951\) −25.6902 −0.833061
\(952\) −1.33272 −0.0431936
\(953\) −9.34121 −0.302591 −0.151296 0.988489i \(-0.548345\pi\)
−0.151296 + 0.988489i \(0.548345\pi\)
\(954\) −0.746455 −0.0241674
\(955\) 20.8682 0.675278
\(956\) 36.7766 1.18944
\(957\) 22.6895 0.733446
\(958\) 1.96571 0.0635091
\(959\) −15.5999 −0.503748
\(960\) 18.0872 0.583763
\(961\) 69.2590 2.23416
\(962\) 0.402035 0.0129621
\(963\) 33.6756 1.08518
\(964\) −53.7395 −1.73083
\(965\) −16.6824 −0.537024
\(966\) 1.50835 0.0485305
\(967\) −5.58522 −0.179609 −0.0898043 0.995959i \(-0.528624\pi\)
−0.0898043 + 0.995959i \(0.528624\pi\)
\(968\) 2.58027 0.0829332
\(969\) −41.1421 −1.32167
\(970\) −0.225775 −0.00724920
\(971\) 6.65089 0.213437 0.106719 0.994289i \(-0.465966\pi\)
0.106719 + 0.994289i \(0.465966\pi\)
\(972\) −38.6710 −1.24037
\(973\) −1.51111 −0.0484439
\(974\) 2.63427 0.0844073
\(975\) 11.0430 0.353660
\(976\) 46.5323 1.48946
\(977\) 51.0852 1.63436 0.817180 0.576383i \(-0.195536\pi\)
0.817180 + 0.576383i \(0.195536\pi\)
\(978\) −3.11942 −0.0997480
\(979\) −5.89073 −0.188269
\(980\) 5.72217 0.182788
\(981\) 26.4814 0.845487
\(982\) 1.01306 0.0323280
\(983\) 13.6611 0.435722 0.217861 0.975980i \(-0.430092\pi\)
0.217861 + 0.975980i \(0.430092\pi\)
\(984\) −3.33754 −0.106397
\(985\) −18.9546 −0.603943
\(986\) 1.28457 0.0409091
\(987\) −5.34457 −0.170119
\(988\) −72.1484 −2.29535
\(989\) 52.3625 1.66503
\(990\) 0.196127 0.00623332
\(991\) −30.3668 −0.964632 −0.482316 0.875997i \(-0.660204\pi\)
−0.482316 + 0.875997i \(0.660204\pi\)
\(992\) −8.22710 −0.261211
\(993\) 30.5265 0.968728
\(994\) −1.05797 −0.0335568
\(995\) −10.4269 −0.330554
\(996\) −4.41087 −0.139764
\(997\) −41.6293 −1.31841 −0.659207 0.751962i \(-0.729108\pi\)
−0.659207 + 0.751962i \(0.729108\pi\)
\(998\) 1.35861 0.0430060
\(999\) −2.06498 −0.0653329
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 2005.2.a.g.1.16 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2005.2.a.g.1.16 37 1.1 even 1 trivial