Properties

Label 6041.2.a.d.1.9
Level $6041$
Weight $2$
Character 6041.1
Self dual yes
Analytic conductor $48.238$
Analytic rank $1$
Dimension $101$
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] = [6041,2,Mod(1,6041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6041, 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("6041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.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: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.41440 q^{2} +0.0560859 q^{3} +3.82935 q^{4} +0.0819711 q^{5} -0.135414 q^{6} -1.00000 q^{7} -4.41678 q^{8} -2.99685 q^{9} +O(q^{10})\) \(q-2.41440 q^{2} +0.0560859 q^{3} +3.82935 q^{4} +0.0819711 q^{5} -0.135414 q^{6} -1.00000 q^{7} -4.41678 q^{8} -2.99685 q^{9} -0.197911 q^{10} +3.15377 q^{11} +0.214772 q^{12} +4.29773 q^{13} +2.41440 q^{14} +0.00459743 q^{15} +3.00520 q^{16} -0.551630 q^{17} +7.23562 q^{18} +1.49915 q^{19} +0.313896 q^{20} -0.0560859 q^{21} -7.61448 q^{22} +8.04809 q^{23} -0.247719 q^{24} -4.99328 q^{25} -10.3765 q^{26} -0.336339 q^{27} -3.82935 q^{28} -4.31245 q^{29} -0.0111000 q^{30} +1.10509 q^{31} +1.57780 q^{32} +0.176882 q^{33} +1.33186 q^{34} -0.0819711 q^{35} -11.4760 q^{36} +0.672899 q^{37} -3.61956 q^{38} +0.241042 q^{39} -0.362048 q^{40} -10.1240 q^{41} +0.135414 q^{42} -9.67718 q^{43} +12.0769 q^{44} -0.245656 q^{45} -19.4313 q^{46} -10.9562 q^{47} +0.168549 q^{48} +1.00000 q^{49} +12.0558 q^{50} -0.0309387 q^{51} +16.4575 q^{52} -9.48952 q^{53} +0.812058 q^{54} +0.258518 q^{55} +4.41678 q^{56} +0.0840813 q^{57} +10.4120 q^{58} +13.0712 q^{59} +0.0176051 q^{60} +10.3213 q^{61} -2.66813 q^{62} +2.99685 q^{63} -9.81984 q^{64} +0.352290 q^{65} -0.427065 q^{66} -6.59342 q^{67} -2.11238 q^{68} +0.451384 q^{69} +0.197911 q^{70} +4.97738 q^{71} +13.2364 q^{72} -1.21658 q^{73} -1.62465 q^{74} -0.280053 q^{75} +5.74077 q^{76} -3.15377 q^{77} -0.581973 q^{78} -11.9439 q^{79} +0.246339 q^{80} +8.97170 q^{81} +24.4434 q^{82} +1.13422 q^{83} -0.214772 q^{84} -0.0452177 q^{85} +23.3646 q^{86} -0.241868 q^{87} -13.9295 q^{88} -6.27688 q^{89} +0.593112 q^{90} -4.29773 q^{91} +30.8189 q^{92} +0.0619799 q^{93} +26.4527 q^{94} +0.122887 q^{95} +0.0884924 q^{96} -1.10396 q^{97} -2.41440 q^{98} -9.45140 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41440 −1.70724 −0.853621 0.520895i \(-0.825598\pi\)
−0.853621 + 0.520895i \(0.825598\pi\)
\(3\) 0.0560859 0.0323812 0.0161906 0.999869i \(-0.494846\pi\)
0.0161906 + 0.999869i \(0.494846\pi\)
\(4\) 3.82935 1.91467
\(5\) 0.0819711 0.0366586 0.0183293 0.999832i \(-0.494165\pi\)
0.0183293 + 0.999832i \(0.494165\pi\)
\(6\) −0.135414 −0.0552826
\(7\) −1.00000 −0.377964
\(8\) −4.41678 −1.56157
\(9\) −2.99685 −0.998951
\(10\) −0.197911 −0.0625851
\(11\) 3.15377 0.950899 0.475449 0.879743i \(-0.342286\pi\)
0.475449 + 0.879743i \(0.342286\pi\)
\(12\) 0.214772 0.0619994
\(13\) 4.29773 1.19198 0.595988 0.802993i \(-0.296761\pi\)
0.595988 + 0.802993i \(0.296761\pi\)
\(14\) 2.41440 0.645277
\(15\) 0.00459743 0.00118705
\(16\) 3.00520 0.751299
\(17\) −0.551630 −0.133790 −0.0668949 0.997760i \(-0.521309\pi\)
−0.0668949 + 0.997760i \(0.521309\pi\)
\(18\) 7.23562 1.70545
\(19\) 1.49915 0.343929 0.171964 0.985103i \(-0.444989\pi\)
0.171964 + 0.985103i \(0.444989\pi\)
\(20\) 0.313896 0.0701892
\(21\) −0.0560859 −0.0122389
\(22\) −7.61448 −1.62341
\(23\) 8.04809 1.67814 0.839071 0.544022i \(-0.183099\pi\)
0.839071 + 0.544022i \(0.183099\pi\)
\(24\) −0.247719 −0.0505654
\(25\) −4.99328 −0.998656
\(26\) −10.3765 −2.03499
\(27\) −0.336339 −0.0647285
\(28\) −3.82935 −0.723678
\(29\) −4.31245 −0.800803 −0.400401 0.916340i \(-0.631129\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(30\) −0.0111000 −0.00202658
\(31\) 1.10509 0.198480 0.0992398 0.995064i \(-0.468359\pi\)
0.0992398 + 0.995064i \(0.468359\pi\)
\(32\) 1.57780 0.278918
\(33\) 0.176882 0.0307913
\(34\) 1.33186 0.228412
\(35\) −0.0819711 −0.0138556
\(36\) −11.4760 −1.91267
\(37\) 0.672899 0.110624 0.0553119 0.998469i \(-0.482385\pi\)
0.0553119 + 0.998469i \(0.482385\pi\)
\(38\) −3.61956 −0.587170
\(39\) 0.241042 0.0385976
\(40\) −0.362048 −0.0572449
\(41\) −10.1240 −1.58110 −0.790552 0.612395i \(-0.790206\pi\)
−0.790552 + 0.612395i \(0.790206\pi\)
\(42\) 0.135414 0.0208948
\(43\) −9.67718 −1.47576 −0.737878 0.674934i \(-0.764172\pi\)
−0.737878 + 0.674934i \(0.764172\pi\)
\(44\) 12.0769 1.82066
\(45\) −0.245656 −0.0366202
\(46\) −19.4313 −2.86499
\(47\) −10.9562 −1.59813 −0.799063 0.601247i \(-0.794671\pi\)
−0.799063 + 0.601247i \(0.794671\pi\)
\(48\) 0.168549 0.0243280
\(49\) 1.00000 0.142857
\(50\) 12.0558 1.70495
\(51\) −0.0309387 −0.00433228
\(52\) 16.4575 2.28224
\(53\) −9.48952 −1.30349 −0.651743 0.758440i \(-0.725962\pi\)
−0.651743 + 0.758440i \(0.725962\pi\)
\(54\) 0.812058 0.110507
\(55\) 0.258518 0.0348586
\(56\) 4.41678 0.590217
\(57\) 0.0840813 0.0111368
\(58\) 10.4120 1.36716
\(59\) 13.0712 1.70173 0.850866 0.525383i \(-0.176078\pi\)
0.850866 + 0.525383i \(0.176078\pi\)
\(60\) 0.0176051 0.00227281
\(61\) 10.3213 1.32150 0.660751 0.750605i \(-0.270238\pi\)
0.660751 + 0.750605i \(0.270238\pi\)
\(62\) −2.66813 −0.338853
\(63\) 2.99685 0.377568
\(64\) −9.81984 −1.22748
\(65\) 0.352290 0.0436962
\(66\) −0.427065 −0.0525681
\(67\) −6.59342 −0.805515 −0.402757 0.915307i \(-0.631948\pi\)
−0.402757 + 0.915307i \(0.631948\pi\)
\(68\) −2.11238 −0.256164
\(69\) 0.451384 0.0543403
\(70\) 0.197911 0.0236549
\(71\) 4.97738 0.590706 0.295353 0.955388i \(-0.404563\pi\)
0.295353 + 0.955388i \(0.404563\pi\)
\(72\) 13.2364 1.55993
\(73\) −1.21658 −0.142390 −0.0711949 0.997462i \(-0.522681\pi\)
−0.0711949 + 0.997462i \(0.522681\pi\)
\(74\) −1.62465 −0.188862
\(75\) −0.280053 −0.0323377
\(76\) 5.74077 0.658511
\(77\) −3.15377 −0.359406
\(78\) −0.581973 −0.0658955
\(79\) −11.9439 −1.34379 −0.671896 0.740645i \(-0.734520\pi\)
−0.671896 + 0.740645i \(0.734520\pi\)
\(80\) 0.246339 0.0275416
\(81\) 8.97170 0.996855
\(82\) 24.4434 2.69933
\(83\) 1.13422 0.124496 0.0622482 0.998061i \(-0.480173\pi\)
0.0622482 + 0.998061i \(0.480173\pi\)
\(84\) −0.214772 −0.0234336
\(85\) −0.0452177 −0.00490455
\(86\) 23.3646 2.51947
\(87\) −0.241868 −0.0259310
\(88\) −13.9295 −1.48489
\(89\) −6.27688 −0.665348 −0.332674 0.943042i \(-0.607951\pi\)
−0.332674 + 0.943042i \(0.607951\pi\)
\(90\) 0.593112 0.0625195
\(91\) −4.29773 −0.450524
\(92\) 30.8189 3.21309
\(93\) 0.0619799 0.00642701
\(94\) 26.4527 2.72839
\(95\) 0.122887 0.0126080
\(96\) 0.0884924 0.00903172
\(97\) −1.10396 −0.112091 −0.0560453 0.998428i \(-0.517849\pi\)
−0.0560453 + 0.998428i \(0.517849\pi\)
\(98\) −2.41440 −0.243892
\(99\) −9.45140 −0.949902
\(100\) −19.1210 −1.91210
\(101\) 8.62256 0.857976 0.428988 0.903310i \(-0.358870\pi\)
0.428988 + 0.903310i \(0.358870\pi\)
\(102\) 0.0746984 0.00739625
\(103\) 14.2294 1.40207 0.701033 0.713128i \(-0.252722\pi\)
0.701033 + 0.713128i \(0.252722\pi\)
\(104\) −18.9821 −1.86135
\(105\) −0.00459743 −0.000448663 0
\(106\) 22.9115 2.22537
\(107\) 7.21146 0.697159 0.348579 0.937279i \(-0.386664\pi\)
0.348579 + 0.937279i \(0.386664\pi\)
\(108\) −1.28796 −0.123934
\(109\) −7.16991 −0.686753 −0.343376 0.939198i \(-0.611571\pi\)
−0.343376 + 0.939198i \(0.611571\pi\)
\(110\) −0.624168 −0.0595121
\(111\) 0.0377401 0.00358214
\(112\) −3.00520 −0.283964
\(113\) −2.22752 −0.209548 −0.104774 0.994496i \(-0.533412\pi\)
−0.104774 + 0.994496i \(0.533412\pi\)
\(114\) −0.203006 −0.0190133
\(115\) 0.659711 0.0615183
\(116\) −16.5139 −1.53328
\(117\) −12.8797 −1.19073
\(118\) −31.5593 −2.90527
\(119\) 0.551630 0.0505678
\(120\) −0.0203058 −0.00185366
\(121\) −1.05371 −0.0957918
\(122\) −24.9197 −2.25612
\(123\) −0.567814 −0.0511981
\(124\) 4.23176 0.380024
\(125\) −0.819160 −0.0732679
\(126\) −7.23562 −0.644600
\(127\) 17.1362 1.52059 0.760295 0.649578i \(-0.225054\pi\)
0.760295 + 0.649578i \(0.225054\pi\)
\(128\) 20.5535 1.81669
\(129\) −0.542753 −0.0477868
\(130\) −0.850570 −0.0745999
\(131\) 6.79906 0.594037 0.297018 0.954872i \(-0.404008\pi\)
0.297018 + 0.954872i \(0.404008\pi\)
\(132\) 0.677343 0.0589552
\(133\) −1.49915 −0.129993
\(134\) 15.9192 1.37521
\(135\) −0.0275701 −0.00237286
\(136\) 2.43643 0.208922
\(137\) −15.8412 −1.35340 −0.676702 0.736257i \(-0.736591\pi\)
−0.676702 + 0.736257i \(0.736591\pi\)
\(138\) −1.08982 −0.0927720
\(139\) −21.3759 −1.81308 −0.906539 0.422122i \(-0.861285\pi\)
−0.906539 + 0.422122i \(0.861285\pi\)
\(140\) −0.313896 −0.0265290
\(141\) −0.614489 −0.0517493
\(142\) −12.0174 −1.00848
\(143\) 13.5541 1.13345
\(144\) −9.00614 −0.750511
\(145\) −0.353497 −0.0293563
\(146\) 2.93731 0.243094
\(147\) 0.0560859 0.00462589
\(148\) 2.57676 0.211809
\(149\) 20.5007 1.67948 0.839741 0.542987i \(-0.182707\pi\)
0.839741 + 0.542987i \(0.182707\pi\)
\(150\) 0.676160 0.0552083
\(151\) −10.6366 −0.865593 −0.432796 0.901492i \(-0.642473\pi\)
−0.432796 + 0.901492i \(0.642473\pi\)
\(152\) −6.62142 −0.537068
\(153\) 1.65315 0.133650
\(154\) 7.61448 0.613593
\(155\) 0.0905853 0.00727599
\(156\) 0.923033 0.0739018
\(157\) −8.37693 −0.668552 −0.334276 0.942475i \(-0.608492\pi\)
−0.334276 + 0.942475i \(0.608492\pi\)
\(158\) 28.8374 2.29418
\(159\) −0.532229 −0.0422085
\(160\) 0.129334 0.0102248
\(161\) −8.04809 −0.634278
\(162\) −21.6613 −1.70187
\(163\) −1.95682 −0.153270 −0.0766349 0.997059i \(-0.524418\pi\)
−0.0766349 + 0.997059i \(0.524418\pi\)
\(164\) −38.7683 −3.02730
\(165\) 0.0144992 0.00112876
\(166\) −2.73846 −0.212546
\(167\) 14.8763 1.15116 0.575580 0.817745i \(-0.304776\pi\)
0.575580 + 0.817745i \(0.304776\pi\)
\(168\) 0.247719 0.0191119
\(169\) 5.47048 0.420806
\(170\) 0.109174 0.00837325
\(171\) −4.49274 −0.343568
\(172\) −37.0573 −2.82559
\(173\) 1.13517 0.0863052 0.0431526 0.999068i \(-0.486260\pi\)
0.0431526 + 0.999068i \(0.486260\pi\)
\(174\) 0.583967 0.0442704
\(175\) 4.99328 0.377457
\(176\) 9.47771 0.714409
\(177\) 0.733113 0.0551041
\(178\) 15.1549 1.13591
\(179\) 10.9609 0.819256 0.409628 0.912253i \(-0.365659\pi\)
0.409628 + 0.912253i \(0.365659\pi\)
\(180\) −0.940700 −0.0701156
\(181\) −15.4773 −1.15042 −0.575210 0.818005i \(-0.695080\pi\)
−0.575210 + 0.818005i \(0.695080\pi\)
\(182\) 10.3765 0.769154
\(183\) 0.578877 0.0427918
\(184\) −35.5466 −2.62053
\(185\) 0.0551583 0.00405532
\(186\) −0.149644 −0.0109725
\(187\) −1.73972 −0.127221
\(188\) −41.9551 −3.05989
\(189\) 0.336339 0.0244651
\(190\) −0.296699 −0.0215248
\(191\) −1.92433 −0.139240 −0.0696198 0.997574i \(-0.522179\pi\)
−0.0696198 + 0.997574i \(0.522179\pi\)
\(192\) −0.550755 −0.0397473
\(193\) −15.6916 −1.12951 −0.564754 0.825259i \(-0.691029\pi\)
−0.564754 + 0.825259i \(0.691029\pi\)
\(194\) 2.66542 0.191366
\(195\) 0.0197585 0.00141493
\(196\) 3.82935 0.273525
\(197\) −9.76693 −0.695865 −0.347932 0.937520i \(-0.613116\pi\)
−0.347932 + 0.937520i \(0.613116\pi\)
\(198\) 22.8195 1.62171
\(199\) 0.135391 0.00959761 0.00479880 0.999988i \(-0.498472\pi\)
0.00479880 + 0.999988i \(0.498472\pi\)
\(200\) 22.0542 1.55947
\(201\) −0.369798 −0.0260836
\(202\) −20.8183 −1.46477
\(203\) 4.31245 0.302675
\(204\) −0.118475 −0.00829490
\(205\) −0.829876 −0.0579611
\(206\) −34.3556 −2.39367
\(207\) −24.1189 −1.67638
\(208\) 12.9155 0.895530
\(209\) 4.72799 0.327042
\(210\) 0.0111000 0.000765976 0
\(211\) 0.819139 0.0563919 0.0281959 0.999602i \(-0.491024\pi\)
0.0281959 + 0.999602i \(0.491024\pi\)
\(212\) −36.3387 −2.49575
\(213\) 0.279161 0.0191278
\(214\) −17.4114 −1.19022
\(215\) −0.793249 −0.0540992
\(216\) 1.48554 0.101078
\(217\) −1.10509 −0.0750183
\(218\) 17.3111 1.17245
\(219\) −0.0682329 −0.00461075
\(220\) 0.989956 0.0667428
\(221\) −2.37076 −0.159474
\(222\) −0.0911199 −0.00611557
\(223\) 9.55532 0.639872 0.319936 0.947439i \(-0.396339\pi\)
0.319936 + 0.947439i \(0.396339\pi\)
\(224\) −1.57780 −0.105421
\(225\) 14.9641 0.997609
\(226\) 5.37814 0.357749
\(227\) −29.7144 −1.97222 −0.986108 0.166103i \(-0.946882\pi\)
−0.986108 + 0.166103i \(0.946882\pi\)
\(228\) 0.321976 0.0213234
\(229\) 24.0175 1.58712 0.793561 0.608490i \(-0.208224\pi\)
0.793561 + 0.608490i \(0.208224\pi\)
\(230\) −1.59281 −0.105027
\(231\) −0.176882 −0.0116380
\(232\) 19.0472 1.25051
\(233\) −5.08403 −0.333066 −0.166533 0.986036i \(-0.553257\pi\)
−0.166533 + 0.986036i \(0.553257\pi\)
\(234\) 31.0967 2.03286
\(235\) −0.898092 −0.0585851
\(236\) 50.0543 3.25826
\(237\) −0.669884 −0.0435137
\(238\) −1.33186 −0.0863315
\(239\) −7.01350 −0.453666 −0.226833 0.973934i \(-0.572837\pi\)
−0.226833 + 0.973934i \(0.572837\pi\)
\(240\) 0.0138162 0.000891830 0
\(241\) −18.7569 −1.20824 −0.604120 0.796894i \(-0.706475\pi\)
−0.604120 + 0.796894i \(0.706475\pi\)
\(242\) 2.54408 0.163540
\(243\) 1.51220 0.0970079
\(244\) 39.5237 2.53024
\(245\) 0.0819711 0.00523694
\(246\) 1.37093 0.0874075
\(247\) 6.44295 0.409955
\(248\) −4.88093 −0.309939
\(249\) 0.0636136 0.00403135
\(250\) 1.97778 0.125086
\(251\) −26.5570 −1.67626 −0.838130 0.545470i \(-0.816351\pi\)
−0.838130 + 0.545470i \(0.816351\pi\)
\(252\) 11.4760 0.722919
\(253\) 25.3818 1.59574
\(254\) −41.3736 −2.59601
\(255\) −0.00253608 −0.000158815 0
\(256\) −29.9847 −1.87404
\(257\) 15.1895 0.947498 0.473749 0.880660i \(-0.342900\pi\)
0.473749 + 0.880660i \(0.342900\pi\)
\(258\) 1.31043 0.0815836
\(259\) −0.672899 −0.0418119
\(260\) 1.34904 0.0836639
\(261\) 12.9238 0.799963
\(262\) −16.4157 −1.01416
\(263\) 28.1462 1.73557 0.867785 0.496939i \(-0.165543\pi\)
0.867785 + 0.496939i \(0.165543\pi\)
\(264\) −0.781250 −0.0480826
\(265\) −0.777867 −0.0477840
\(266\) 3.61956 0.221929
\(267\) −0.352045 −0.0215448
\(268\) −25.2485 −1.54230
\(269\) −5.63250 −0.343420 −0.171710 0.985148i \(-0.554929\pi\)
−0.171710 + 0.985148i \(0.554929\pi\)
\(270\) 0.0665653 0.00405104
\(271\) −14.0654 −0.854413 −0.427207 0.904154i \(-0.640502\pi\)
−0.427207 + 0.904154i \(0.640502\pi\)
\(272\) −1.65776 −0.100516
\(273\) −0.241042 −0.0145885
\(274\) 38.2470 2.31059
\(275\) −15.7477 −0.949621
\(276\) 1.72851 0.104044
\(277\) 3.44564 0.207029 0.103514 0.994628i \(-0.466991\pi\)
0.103514 + 0.994628i \(0.466991\pi\)
\(278\) 51.6100 3.09536
\(279\) −3.31179 −0.198272
\(280\) 0.362048 0.0216365
\(281\) −2.96343 −0.176783 −0.0883916 0.996086i \(-0.528173\pi\)
−0.0883916 + 0.996086i \(0.528173\pi\)
\(282\) 1.48362 0.0883485
\(283\) 29.6443 1.76217 0.881085 0.472959i \(-0.156814\pi\)
0.881085 + 0.472959i \(0.156814\pi\)
\(284\) 19.0601 1.13101
\(285\) 0.00689224 0.000408261 0
\(286\) −32.7250 −1.93507
\(287\) 10.1240 0.597601
\(288\) −4.72844 −0.278626
\(289\) −16.6957 −0.982100
\(290\) 0.853484 0.0501183
\(291\) −0.0619168 −0.00362963
\(292\) −4.65870 −0.272630
\(293\) −5.71006 −0.333585 −0.166793 0.985992i \(-0.553341\pi\)
−0.166793 + 0.985992i \(0.553341\pi\)
\(294\) −0.135414 −0.00789751
\(295\) 1.07147 0.0623831
\(296\) −2.97204 −0.172747
\(297\) −1.06074 −0.0615502
\(298\) −49.4970 −2.86728
\(299\) 34.5885 2.00030
\(300\) −1.07242 −0.0619161
\(301\) 9.67718 0.557783
\(302\) 25.6810 1.47778
\(303\) 0.483604 0.0277823
\(304\) 4.50524 0.258393
\(305\) 0.846045 0.0484444
\(306\) −3.99138 −0.228172
\(307\) 9.48632 0.541413 0.270706 0.962662i \(-0.412743\pi\)
0.270706 + 0.962662i \(0.412743\pi\)
\(308\) −12.0769 −0.688145
\(309\) 0.798070 0.0454006
\(310\) −0.218710 −0.0124219
\(311\) −17.1321 −0.971474 −0.485737 0.874105i \(-0.661449\pi\)
−0.485737 + 0.874105i \(0.661449\pi\)
\(312\) −1.06463 −0.0602728
\(313\) −21.4207 −1.21077 −0.605385 0.795933i \(-0.706981\pi\)
−0.605385 + 0.795933i \(0.706981\pi\)
\(314\) 20.2253 1.14138
\(315\) 0.245656 0.0138411
\(316\) −45.7373 −2.57292
\(317\) −1.31458 −0.0738340 −0.0369170 0.999318i \(-0.511754\pi\)
−0.0369170 + 0.999318i \(0.511754\pi\)
\(318\) 1.28501 0.0720600
\(319\) −13.6005 −0.761482
\(320\) −0.804943 −0.0449977
\(321\) 0.404462 0.0225748
\(322\) 19.4313 1.08287
\(323\) −0.826977 −0.0460142
\(324\) 34.3557 1.90865
\(325\) −21.4598 −1.19037
\(326\) 4.72455 0.261669
\(327\) −0.402131 −0.0222379
\(328\) 44.7155 2.46900
\(329\) 10.9562 0.604035
\(330\) −0.0350070 −0.00192707
\(331\) −6.00091 −0.329840 −0.164920 0.986307i \(-0.552737\pi\)
−0.164920 + 0.986307i \(0.552737\pi\)
\(332\) 4.34331 0.238370
\(333\) −2.01658 −0.110508
\(334\) −35.9173 −1.96531
\(335\) −0.540470 −0.0295291
\(336\) −0.168549 −0.00919511
\(337\) −28.9489 −1.57695 −0.788475 0.615067i \(-0.789129\pi\)
−0.788475 + 0.615067i \(0.789129\pi\)
\(338\) −13.2079 −0.718417
\(339\) −0.124933 −0.00678542
\(340\) −0.173154 −0.00939061
\(341\) 3.48520 0.188734
\(342\) 10.8473 0.586554
\(343\) −1.00000 −0.0539949
\(344\) 42.7420 2.30449
\(345\) 0.0370005 0.00199204
\(346\) −2.74075 −0.147344
\(347\) 22.5157 1.20871 0.604354 0.796716i \(-0.293431\pi\)
0.604354 + 0.796716i \(0.293431\pi\)
\(348\) −0.926196 −0.0496493
\(349\) 5.94338 0.318142 0.159071 0.987267i \(-0.449150\pi\)
0.159071 + 0.987267i \(0.449150\pi\)
\(350\) −12.0558 −0.644409
\(351\) −1.44549 −0.0771548
\(352\) 4.97603 0.265223
\(353\) 7.95562 0.423435 0.211718 0.977331i \(-0.432094\pi\)
0.211718 + 0.977331i \(0.432094\pi\)
\(354\) −1.77003 −0.0940761
\(355\) 0.408001 0.0216545
\(356\) −24.0364 −1.27392
\(357\) 0.0309387 0.00163745
\(358\) −26.4640 −1.39867
\(359\) 33.8130 1.78458 0.892291 0.451460i \(-0.149097\pi\)
0.892291 + 0.451460i \(0.149097\pi\)
\(360\) 1.08501 0.0571848
\(361\) −16.7525 −0.881713
\(362\) 37.3685 1.96405
\(363\) −0.0590983 −0.00310186
\(364\) −16.4575 −0.862607
\(365\) −0.0997243 −0.00521981
\(366\) −1.39764 −0.0730560
\(367\) 20.0561 1.04692 0.523460 0.852050i \(-0.324641\pi\)
0.523460 + 0.852050i \(0.324641\pi\)
\(368\) 24.1861 1.26079
\(369\) 30.3402 1.57945
\(370\) −0.133174 −0.00692340
\(371\) 9.48952 0.492672
\(372\) 0.237342 0.0123056
\(373\) −31.4212 −1.62693 −0.813463 0.581617i \(-0.802420\pi\)
−0.813463 + 0.581617i \(0.802420\pi\)
\(374\) 4.20038 0.217196
\(375\) −0.0459434 −0.00237251
\(376\) 48.3911 2.49558
\(377\) −18.5338 −0.954537
\(378\) −0.812058 −0.0417678
\(379\) −3.80824 −0.195616 −0.0978081 0.995205i \(-0.531183\pi\)
−0.0978081 + 0.995205i \(0.531183\pi\)
\(380\) 0.470577 0.0241401
\(381\) 0.961098 0.0492385
\(382\) 4.64611 0.237716
\(383\) 22.8584 1.16801 0.584004 0.811751i \(-0.301485\pi\)
0.584004 + 0.811751i \(0.301485\pi\)
\(384\) 1.15276 0.0588265
\(385\) −0.258518 −0.0131753
\(386\) 37.8859 1.92834
\(387\) 29.0011 1.47421
\(388\) −4.22746 −0.214617
\(389\) −6.78685 −0.344107 −0.172054 0.985088i \(-0.555040\pi\)
−0.172054 + 0.985088i \(0.555040\pi\)
\(390\) −0.0477050 −0.00241564
\(391\) −4.43956 −0.224518
\(392\) −4.41678 −0.223081
\(393\) 0.381331 0.0192356
\(394\) 23.5813 1.18801
\(395\) −0.979054 −0.0492616
\(396\) −36.1927 −1.81875
\(397\) −19.4657 −0.976955 −0.488478 0.872576i \(-0.662448\pi\)
−0.488478 + 0.872576i \(0.662448\pi\)
\(398\) −0.326888 −0.0163854
\(399\) −0.0840813 −0.00420933
\(400\) −15.0058 −0.750289
\(401\) 34.5712 1.72641 0.863203 0.504857i \(-0.168455\pi\)
0.863203 + 0.504857i \(0.168455\pi\)
\(402\) 0.892842 0.0445309
\(403\) 4.74937 0.236583
\(404\) 33.0187 1.64274
\(405\) 0.735420 0.0365433
\(406\) −10.4120 −0.516739
\(407\) 2.12217 0.105192
\(408\) 0.136649 0.00676514
\(409\) 26.9808 1.33411 0.667057 0.745007i \(-0.267554\pi\)
0.667057 + 0.745007i \(0.267554\pi\)
\(410\) 2.00366 0.0989535
\(411\) −0.888467 −0.0438249
\(412\) 54.4894 2.68450
\(413\) −13.0712 −0.643194
\(414\) 58.2329 2.86199
\(415\) 0.0929730 0.00456387
\(416\) 6.78096 0.332464
\(417\) −1.19889 −0.0587097
\(418\) −11.4153 −0.558339
\(419\) −19.4415 −0.949779 −0.474889 0.880046i \(-0.657512\pi\)
−0.474889 + 0.880046i \(0.657512\pi\)
\(420\) −0.0176051 −0.000859042 0
\(421\) −13.4138 −0.653748 −0.326874 0.945068i \(-0.605995\pi\)
−0.326874 + 0.945068i \(0.605995\pi\)
\(422\) −1.97773 −0.0962745
\(423\) 32.8341 1.59645
\(424\) 41.9131 2.03548
\(425\) 2.75444 0.133610
\(426\) −0.674007 −0.0326557
\(427\) −10.3213 −0.499481
\(428\) 27.6152 1.33483
\(429\) 0.760192 0.0367024
\(430\) 1.91522 0.0923603
\(431\) 2.07220 0.0998145 0.0499073 0.998754i \(-0.484107\pi\)
0.0499073 + 0.998754i \(0.484107\pi\)
\(432\) −1.01076 −0.0486304
\(433\) 11.0911 0.533003 0.266502 0.963834i \(-0.414132\pi\)
0.266502 + 0.963834i \(0.414132\pi\)
\(434\) 2.66813 0.128074
\(435\) −0.0198262 −0.000950593 0
\(436\) −27.4561 −1.31491
\(437\) 12.0653 0.577162
\(438\) 0.164742 0.00787167
\(439\) −29.7983 −1.42220 −0.711098 0.703093i \(-0.751802\pi\)
−0.711098 + 0.703093i \(0.751802\pi\)
\(440\) −1.14182 −0.0544341
\(441\) −2.99685 −0.142707
\(442\) 5.72396 0.272261
\(443\) 38.2754 1.81852 0.909259 0.416231i \(-0.136649\pi\)
0.909259 + 0.416231i \(0.136649\pi\)
\(444\) 0.144520 0.00685862
\(445\) −0.514523 −0.0243907
\(446\) −23.0704 −1.09242
\(447\) 1.14980 0.0543837
\(448\) 9.81984 0.463944
\(449\) −13.6143 −0.642498 −0.321249 0.946995i \(-0.604103\pi\)
−0.321249 + 0.946995i \(0.604103\pi\)
\(450\) −36.1295 −1.70316
\(451\) −31.9288 −1.50347
\(452\) −8.52996 −0.401216
\(453\) −0.596562 −0.0280289
\(454\) 71.7427 3.36705
\(455\) −0.352290 −0.0165156
\(456\) −0.371368 −0.0173909
\(457\) −13.2829 −0.621349 −0.310675 0.950516i \(-0.600555\pi\)
−0.310675 + 0.950516i \(0.600555\pi\)
\(458\) −57.9880 −2.70960
\(459\) 0.185535 0.00866002
\(460\) 2.52626 0.117788
\(461\) −25.1599 −1.17181 −0.585907 0.810378i \(-0.699262\pi\)
−0.585907 + 0.810378i \(0.699262\pi\)
\(462\) 0.427065 0.0198689
\(463\) −24.1655 −1.12306 −0.561532 0.827455i \(-0.689788\pi\)
−0.561532 + 0.827455i \(0.689788\pi\)
\(464\) −12.9598 −0.601642
\(465\) 0.00508056 0.000235605 0
\(466\) 12.2749 0.568624
\(467\) 18.5509 0.858435 0.429217 0.903201i \(-0.358789\pi\)
0.429217 + 0.903201i \(0.358789\pi\)
\(468\) −49.3207 −2.27985
\(469\) 6.59342 0.304456
\(470\) 2.16836 0.100019
\(471\) −0.469828 −0.0216485
\(472\) −57.7328 −2.65737
\(473\) −30.5196 −1.40329
\(474\) 1.61737 0.0742883
\(475\) −7.48568 −0.343467
\(476\) 2.11238 0.0968208
\(477\) 28.4387 1.30212
\(478\) 16.9334 0.774517
\(479\) −37.6934 −1.72226 −0.861129 0.508387i \(-0.830242\pi\)
−0.861129 + 0.508387i \(0.830242\pi\)
\(480\) 0.00725382 0.000331090 0
\(481\) 2.89194 0.131861
\(482\) 45.2868 2.06276
\(483\) −0.451384 −0.0205387
\(484\) −4.03502 −0.183410
\(485\) −0.0904932 −0.00410908
\(486\) −3.65107 −0.165616
\(487\) −37.2945 −1.68997 −0.844987 0.534786i \(-0.820392\pi\)
−0.844987 + 0.534786i \(0.820392\pi\)
\(488\) −45.5867 −2.06361
\(489\) −0.109750 −0.00496306
\(490\) −0.197911 −0.00894073
\(491\) −10.2577 −0.462922 −0.231461 0.972844i \(-0.574351\pi\)
−0.231461 + 0.972844i \(0.574351\pi\)
\(492\) −2.17436 −0.0980276
\(493\) 2.37888 0.107139
\(494\) −15.5559 −0.699892
\(495\) −0.774742 −0.0348221
\(496\) 3.32101 0.149118
\(497\) −4.97738 −0.223266
\(498\) −0.153589 −0.00688248
\(499\) −18.9967 −0.850408 −0.425204 0.905098i \(-0.639798\pi\)
−0.425204 + 0.905098i \(0.639798\pi\)
\(500\) −3.13685 −0.140284
\(501\) 0.834350 0.0372760
\(502\) 64.1192 2.86178
\(503\) 31.0533 1.38460 0.692300 0.721610i \(-0.256598\pi\)
0.692300 + 0.721610i \(0.256598\pi\)
\(504\) −13.2364 −0.589598
\(505\) 0.706801 0.0314522
\(506\) −61.2820 −2.72432
\(507\) 0.306817 0.0136262
\(508\) 65.6203 2.91143
\(509\) −0.858249 −0.0380412 −0.0190206 0.999819i \(-0.506055\pi\)
−0.0190206 + 0.999819i \(0.506055\pi\)
\(510\) 0.00612311 0.000271136 0
\(511\) 1.21658 0.0538183
\(512\) 31.2882 1.38275
\(513\) −0.504223 −0.0222620
\(514\) −36.6737 −1.61761
\(515\) 1.16640 0.0513978
\(516\) −2.07839 −0.0914960
\(517\) −34.5534 −1.51966
\(518\) 1.62465 0.0713830
\(519\) 0.0636669 0.00279467
\(520\) −1.55599 −0.0682345
\(521\) −9.48521 −0.415555 −0.207777 0.978176i \(-0.566623\pi\)
−0.207777 + 0.978176i \(0.566623\pi\)
\(522\) −31.2033 −1.36573
\(523\) −27.8802 −1.21912 −0.609559 0.792741i \(-0.708653\pi\)
−0.609559 + 0.792741i \(0.708653\pi\)
\(524\) 26.0359 1.13739
\(525\) 0.280053 0.0122225
\(526\) −67.9564 −2.96304
\(527\) −0.609599 −0.0265546
\(528\) 0.531566 0.0231334
\(529\) 41.7717 1.81616
\(530\) 1.87808 0.0815788
\(531\) −39.1726 −1.69995
\(532\) −5.74077 −0.248894
\(533\) −43.5102 −1.88464
\(534\) 0.849978 0.0367822
\(535\) 0.591132 0.0255569
\(536\) 29.1217 1.25787
\(537\) 0.614752 0.0265285
\(538\) 13.5991 0.586300
\(539\) 3.15377 0.135843
\(540\) −0.105575 −0.00454324
\(541\) 1.66474 0.0715726 0.0357863 0.999359i \(-0.488606\pi\)
0.0357863 + 0.999359i \(0.488606\pi\)
\(542\) 33.9596 1.45869
\(543\) −0.868060 −0.0372520
\(544\) −0.870362 −0.0373165
\(545\) −0.587726 −0.0251754
\(546\) 0.581973 0.0249061
\(547\) −6.97421 −0.298196 −0.149098 0.988822i \(-0.547637\pi\)
−0.149098 + 0.988822i \(0.547637\pi\)
\(548\) −60.6614 −2.59132
\(549\) −30.9313 −1.32012
\(550\) 38.0213 1.62123
\(551\) −6.46502 −0.275419
\(552\) −1.99366 −0.0848560
\(553\) 11.9439 0.507906
\(554\) −8.31918 −0.353448
\(555\) 0.00309360 0.000131316 0
\(556\) −81.8556 −3.47145
\(557\) −14.1799 −0.600824 −0.300412 0.953810i \(-0.597124\pi\)
−0.300412 + 0.953810i \(0.597124\pi\)
\(558\) 7.99599 0.338497
\(559\) −41.5899 −1.75907
\(560\) −0.246339 −0.0104097
\(561\) −0.0975735 −0.00411956
\(562\) 7.15491 0.301812
\(563\) 32.4036 1.36565 0.682825 0.730582i \(-0.260751\pi\)
0.682825 + 0.730582i \(0.260751\pi\)
\(564\) −2.35309 −0.0990829
\(565\) −0.182593 −0.00768173
\(566\) −71.5732 −3.00845
\(567\) −8.97170 −0.376776
\(568\) −21.9840 −0.922427
\(569\) 6.88989 0.288839 0.144420 0.989517i \(-0.453868\pi\)
0.144420 + 0.989517i \(0.453868\pi\)
\(570\) −0.0166406 −0.000697000 0
\(571\) −45.3534 −1.89798 −0.948991 0.315303i \(-0.897894\pi\)
−0.948991 + 0.315303i \(0.897894\pi\)
\(572\) 51.9032 2.17018
\(573\) −0.107928 −0.00450875
\(574\) −24.4434 −1.02025
\(575\) −40.1864 −1.67589
\(576\) 29.4286 1.22619
\(577\) −11.5503 −0.480847 −0.240423 0.970668i \(-0.577286\pi\)
−0.240423 + 0.970668i \(0.577286\pi\)
\(578\) 40.3102 1.67668
\(579\) −0.880079 −0.0365748
\(580\) −1.35366 −0.0562077
\(581\) −1.13422 −0.0470552
\(582\) 0.149492 0.00619665
\(583\) −29.9278 −1.23948
\(584\) 5.37336 0.222351
\(585\) −1.05576 −0.0436503
\(586\) 13.7864 0.569510
\(587\) −24.4168 −1.00779 −0.503895 0.863765i \(-0.668100\pi\)
−0.503895 + 0.863765i \(0.668100\pi\)
\(588\) 0.214772 0.00885706
\(589\) 1.65669 0.0682629
\(590\) −2.58695 −0.106503
\(591\) −0.547787 −0.0225329
\(592\) 2.02219 0.0831116
\(593\) −0.958541 −0.0393626 −0.0196813 0.999806i \(-0.506265\pi\)
−0.0196813 + 0.999806i \(0.506265\pi\)
\(594\) 2.56105 0.105081
\(595\) 0.0452177 0.00185375
\(596\) 78.5042 3.21566
\(597\) 0.00759352 0.000310782 0
\(598\) −83.5106 −3.41500
\(599\) −27.6161 −1.12836 −0.564182 0.825651i \(-0.690808\pi\)
−0.564182 + 0.825651i \(0.690808\pi\)
\(600\) 1.23693 0.0504975
\(601\) −9.10119 −0.371245 −0.185623 0.982621i \(-0.559430\pi\)
−0.185623 + 0.982621i \(0.559430\pi\)
\(602\) −23.3646 −0.952271
\(603\) 19.7595 0.804670
\(604\) −40.7311 −1.65733
\(605\) −0.0863738 −0.00351159
\(606\) −1.16762 −0.0474311
\(607\) 11.2104 0.455015 0.227508 0.973776i \(-0.426942\pi\)
0.227508 + 0.973776i \(0.426942\pi\)
\(608\) 2.36536 0.0959281
\(609\) 0.241868 0.00980098
\(610\) −2.04269 −0.0827063
\(611\) −47.0868 −1.90493
\(612\) 6.33050 0.255895
\(613\) −37.2292 −1.50367 −0.751837 0.659349i \(-0.770832\pi\)
−0.751837 + 0.659349i \(0.770832\pi\)
\(614\) −22.9038 −0.924322
\(615\) −0.0465444 −0.00187685
\(616\) 13.9295 0.561236
\(617\) 24.4563 0.984574 0.492287 0.870433i \(-0.336161\pi\)
0.492287 + 0.870433i \(0.336161\pi\)
\(618\) −1.92686 −0.0775098
\(619\) −25.6117 −1.02942 −0.514711 0.857364i \(-0.672101\pi\)
−0.514711 + 0.857364i \(0.672101\pi\)
\(620\) 0.346882 0.0139311
\(621\) −2.70689 −0.108624
\(622\) 41.3639 1.65854
\(623\) 6.27688 0.251478
\(624\) 0.724379 0.0289984
\(625\) 24.8993 0.995970
\(626\) 51.7182 2.06708
\(627\) 0.265173 0.0105900
\(628\) −32.0781 −1.28006
\(629\) −0.371191 −0.0148004
\(630\) −0.593112 −0.0236301
\(631\) 7.07244 0.281549 0.140775 0.990042i \(-0.455041\pi\)
0.140775 + 0.990042i \(0.455041\pi\)
\(632\) 52.7535 2.09842
\(633\) 0.0459422 0.00182604
\(634\) 3.17392 0.126052
\(635\) 1.40467 0.0557427
\(636\) −2.03809 −0.0808154
\(637\) 4.29773 0.170282
\(638\) 32.8371 1.30003
\(639\) −14.9165 −0.590086
\(640\) 1.68479 0.0665972
\(641\) −49.0316 −1.93663 −0.968317 0.249726i \(-0.919659\pi\)
−0.968317 + 0.249726i \(0.919659\pi\)
\(642\) −0.976534 −0.0385407
\(643\) −48.7332 −1.92185 −0.960924 0.276812i \(-0.910722\pi\)
−0.960924 + 0.276812i \(0.910722\pi\)
\(644\) −30.8189 −1.21444
\(645\) −0.0444901 −0.00175180
\(646\) 1.99666 0.0785574
\(647\) −20.2375 −0.795617 −0.397809 0.917468i \(-0.630229\pi\)
−0.397809 + 0.917468i \(0.630229\pi\)
\(648\) −39.6260 −1.55666
\(649\) 41.2238 1.61817
\(650\) 51.8125 2.03226
\(651\) −0.0619799 −0.00242918
\(652\) −7.49333 −0.293462
\(653\) 23.1701 0.906715 0.453357 0.891329i \(-0.350226\pi\)
0.453357 + 0.891329i \(0.350226\pi\)
\(654\) 0.970906 0.0379654
\(655\) 0.557327 0.0217766
\(656\) −30.4246 −1.18788
\(657\) 3.64591 0.142240
\(658\) −26.4527 −1.03123
\(659\) −42.9127 −1.67164 −0.835820 0.549003i \(-0.815008\pi\)
−0.835820 + 0.549003i \(0.815008\pi\)
\(660\) 0.0555226 0.00216121
\(661\) 4.68953 0.182402 0.0912009 0.995833i \(-0.470929\pi\)
0.0912009 + 0.995833i \(0.470929\pi\)
\(662\) 14.4886 0.563116
\(663\) −0.132966 −0.00516397
\(664\) −5.00959 −0.194410
\(665\) −0.122887 −0.00476536
\(666\) 4.86884 0.188664
\(667\) −34.7070 −1.34386
\(668\) 56.9664 2.20410
\(669\) 0.535919 0.0207198
\(670\) 1.30491 0.0504132
\(671\) 32.5509 1.25661
\(672\) −0.0884924 −0.00341367
\(673\) 29.2236 1.12649 0.563243 0.826291i \(-0.309553\pi\)
0.563243 + 0.826291i \(0.309553\pi\)
\(674\) 69.8945 2.69223
\(675\) 1.67944 0.0646415
\(676\) 20.9483 0.805706
\(677\) −29.6696 −1.14029 −0.570147 0.821543i \(-0.693114\pi\)
−0.570147 + 0.821543i \(0.693114\pi\)
\(678\) 0.301638 0.0115843
\(679\) 1.10396 0.0423663
\(680\) 0.199717 0.00765878
\(681\) −1.66656 −0.0638628
\(682\) −8.41467 −0.322215
\(683\) −11.2066 −0.428807 −0.214404 0.976745i \(-0.568781\pi\)
−0.214404 + 0.976745i \(0.568781\pi\)
\(684\) −17.2042 −0.657821
\(685\) −1.29852 −0.0496139
\(686\) 2.41440 0.0921824
\(687\) 1.34704 0.0513930
\(688\) −29.0818 −1.10873
\(689\) −40.7834 −1.55372
\(690\) −0.0893341 −0.00340089
\(691\) 13.8607 0.527287 0.263643 0.964620i \(-0.415076\pi\)
0.263643 + 0.964620i \(0.415076\pi\)
\(692\) 4.34695 0.165246
\(693\) 9.45140 0.359029
\(694\) −54.3621 −2.06356
\(695\) −1.75220 −0.0664649
\(696\) 1.06828 0.0404929
\(697\) 5.58470 0.211536
\(698\) −14.3497 −0.543145
\(699\) −0.285142 −0.0107851
\(700\) 19.1210 0.722706
\(701\) −27.7333 −1.04747 −0.523737 0.851880i \(-0.675462\pi\)
−0.523737 + 0.851880i \(0.675462\pi\)
\(702\) 3.49001 0.131722
\(703\) 1.00878 0.0380467
\(704\) −30.9696 −1.16721
\(705\) −0.0503703 −0.00189706
\(706\) −19.2081 −0.722906
\(707\) −8.62256 −0.324285
\(708\) 2.80734 0.105506
\(709\) 2.99495 0.112478 0.0562388 0.998417i \(-0.482089\pi\)
0.0562388 + 0.998417i \(0.482089\pi\)
\(710\) −0.985079 −0.0369694
\(711\) 35.7941 1.34238
\(712\) 27.7236 1.03899
\(713\) 8.89384 0.333077
\(714\) −0.0746984 −0.00279552
\(715\) 1.11104 0.0415506
\(716\) 41.9731 1.56861
\(717\) −0.393359 −0.0146902
\(718\) −81.6383 −3.04671
\(719\) 18.6326 0.694877 0.347438 0.937703i \(-0.387052\pi\)
0.347438 + 0.937703i \(0.387052\pi\)
\(720\) −0.738243 −0.0275127
\(721\) −14.2294 −0.529931
\(722\) 40.4474 1.50530
\(723\) −1.05200 −0.0391243
\(724\) −59.2680 −2.20268
\(725\) 21.5333 0.799727
\(726\) 0.142687 0.00529562
\(727\) −8.40706 −0.311801 −0.155900 0.987773i \(-0.549828\pi\)
−0.155900 + 0.987773i \(0.549828\pi\)
\(728\) 18.9821 0.703524
\(729\) −26.8303 −0.993714
\(730\) 0.240775 0.00891148
\(731\) 5.33822 0.197441
\(732\) 2.21672 0.0819323
\(733\) 26.4109 0.975508 0.487754 0.872981i \(-0.337816\pi\)
0.487754 + 0.872981i \(0.337816\pi\)
\(734\) −48.4236 −1.78735
\(735\) 0.00459743 0.000169579 0
\(736\) 12.6983 0.468065
\(737\) −20.7942 −0.765963
\(738\) −73.2534 −2.69650
\(739\) −42.4791 −1.56262 −0.781310 0.624144i \(-0.785448\pi\)
−0.781310 + 0.624144i \(0.785448\pi\)
\(740\) 0.211220 0.00776460
\(741\) 0.361359 0.0132748
\(742\) −22.9115 −0.841109
\(743\) 16.5269 0.606314 0.303157 0.952941i \(-0.401959\pi\)
0.303157 + 0.952941i \(0.401959\pi\)
\(744\) −0.273751 −0.0100362
\(745\) 1.68047 0.0615675
\(746\) 75.8633 2.77755
\(747\) −3.39908 −0.124366
\(748\) −6.66197 −0.243586
\(749\) −7.21146 −0.263501
\(750\) 0.110926 0.00405044
\(751\) −27.3920 −0.999548 −0.499774 0.866156i \(-0.666584\pi\)
−0.499774 + 0.866156i \(0.666584\pi\)
\(752\) −32.9255 −1.20067
\(753\) −1.48947 −0.0542794
\(754\) 44.7480 1.62963
\(755\) −0.871893 −0.0317314
\(756\) 1.28796 0.0468426
\(757\) 54.5074 1.98111 0.990553 0.137127i \(-0.0437869\pi\)
0.990553 + 0.137127i \(0.0437869\pi\)
\(758\) 9.19463 0.333964
\(759\) 1.42356 0.0516721
\(760\) −0.542765 −0.0196882
\(761\) −7.88285 −0.285753 −0.142876 0.989741i \(-0.545635\pi\)
−0.142876 + 0.989741i \(0.545635\pi\)
\(762\) −2.32048 −0.0840621
\(763\) 7.16991 0.259568
\(764\) −7.36892 −0.266598
\(765\) 0.135511 0.00489941
\(766\) −55.1893 −1.99407
\(767\) 56.1767 2.02842
\(768\) −1.68172 −0.0606837
\(769\) 10.8798 0.392336 0.196168 0.980570i \(-0.437150\pi\)
0.196168 + 0.980570i \(0.437150\pi\)
\(770\) 0.624168 0.0224934
\(771\) 0.851920 0.0306811
\(772\) −60.0886 −2.16264
\(773\) 41.0549 1.47664 0.738321 0.674450i \(-0.235619\pi\)
0.738321 + 0.674450i \(0.235619\pi\)
\(774\) −70.0204 −2.51683
\(775\) −5.51801 −0.198213
\(776\) 4.87597 0.175037
\(777\) −0.0377401 −0.00135392
\(778\) 16.3862 0.587474
\(779\) −15.1774 −0.543788
\(780\) 0.0756621 0.00270914
\(781\) 15.6975 0.561701
\(782\) 10.7189 0.383307
\(783\) 1.45045 0.0518347
\(784\) 3.00520 0.107328
\(785\) −0.686666 −0.0245082
\(786\) −0.920688 −0.0328399
\(787\) −21.4170 −0.763434 −0.381717 0.924279i \(-0.624667\pi\)
−0.381717 + 0.924279i \(0.624667\pi\)
\(788\) −37.4009 −1.33235
\(789\) 1.57861 0.0561999
\(790\) 2.36383 0.0841014
\(791\) 2.22752 0.0792017
\(792\) 41.7447 1.48334
\(793\) 44.3580 1.57520
\(794\) 46.9981 1.66790
\(795\) −0.0436274 −0.00154730
\(796\) 0.518459 0.0183763
\(797\) −4.20032 −0.148783 −0.0743914 0.997229i \(-0.523701\pi\)
−0.0743914 + 0.997229i \(0.523701\pi\)
\(798\) 0.203006 0.00718634
\(799\) 6.04377 0.213813
\(800\) −7.87840 −0.278544
\(801\) 18.8109 0.664651
\(802\) −83.4689 −2.94739
\(803\) −3.83681 −0.135398
\(804\) −1.41609 −0.0499415
\(805\) −0.659711 −0.0232517
\(806\) −11.4669 −0.403904
\(807\) −0.315904 −0.0111203
\(808\) −38.0839 −1.33979
\(809\) −50.8669 −1.78838 −0.894192 0.447683i \(-0.852249\pi\)
−0.894192 + 0.447683i \(0.852249\pi\)
\(810\) −1.77560 −0.0623883
\(811\) −26.5180 −0.931173 −0.465587 0.885002i \(-0.654157\pi\)
−0.465587 + 0.885002i \(0.654157\pi\)
\(812\) 16.5139 0.579524
\(813\) −0.788872 −0.0276669
\(814\) −5.12378 −0.179588
\(815\) −0.160403 −0.00561866
\(816\) −0.0929767 −0.00325484
\(817\) −14.5076 −0.507555
\(818\) −65.1425 −2.27765
\(819\) 12.8797 0.450052
\(820\) −3.17788 −0.110976
\(821\) −35.3221 −1.23275 −0.616376 0.787452i \(-0.711400\pi\)
−0.616376 + 0.787452i \(0.711400\pi\)
\(822\) 2.14512 0.0748196
\(823\) 27.6666 0.964399 0.482199 0.876061i \(-0.339838\pi\)
0.482199 + 0.876061i \(0.339838\pi\)
\(824\) −62.8482 −2.18942
\(825\) −0.883223 −0.0307499
\(826\) 31.5593 1.09809
\(827\) −20.6867 −0.719347 −0.359674 0.933078i \(-0.617112\pi\)
−0.359674 + 0.933078i \(0.617112\pi\)
\(828\) −92.3598 −3.20972
\(829\) 37.6166 1.30648 0.653240 0.757151i \(-0.273409\pi\)
0.653240 + 0.757151i \(0.273409\pi\)
\(830\) −0.224474 −0.00779162
\(831\) 0.193252 0.00670384
\(832\) −42.2030 −1.46313
\(833\) −0.551630 −0.0191128
\(834\) 2.89459 0.100232
\(835\) 1.21943 0.0421999
\(836\) 18.1051 0.626178
\(837\) −0.371684 −0.0128473
\(838\) 46.9396 1.62150
\(839\) 14.5068 0.500832 0.250416 0.968138i \(-0.419433\pi\)
0.250416 + 0.968138i \(0.419433\pi\)
\(840\) 0.0203058 0.000700617 0
\(841\) −10.4027 −0.358715
\(842\) 32.3863 1.11610
\(843\) −0.166206 −0.00572445
\(844\) 3.13677 0.107972
\(845\) 0.448421 0.0154262
\(846\) −79.2749 −2.72553
\(847\) 1.05371 0.0362059
\(848\) −28.5179 −0.979308
\(849\) 1.66263 0.0570612
\(850\) −6.65034 −0.228105
\(851\) 5.41555 0.185643
\(852\) 1.06900 0.0366234
\(853\) −12.1159 −0.414841 −0.207421 0.978252i \(-0.566507\pi\)
−0.207421 + 0.978252i \(0.566507\pi\)
\(854\) 24.9197 0.852734
\(855\) −0.368275 −0.0125947
\(856\) −31.8514 −1.08866
\(857\) 1.88506 0.0643923 0.0321961 0.999482i \(-0.489750\pi\)
0.0321961 + 0.999482i \(0.489750\pi\)
\(858\) −1.83541 −0.0626599
\(859\) −49.6659 −1.69458 −0.847290 0.531131i \(-0.821767\pi\)
−0.847290 + 0.531131i \(0.821767\pi\)
\(860\) −3.03763 −0.103582
\(861\) 0.567814 0.0193511
\(862\) −5.00314 −0.170407
\(863\) −1.00000 −0.0340404
\(864\) −0.530676 −0.0180540
\(865\) 0.0930510 0.00316383
\(866\) −26.7784 −0.909965
\(867\) −0.936394 −0.0318016
\(868\) −4.23176 −0.143635
\(869\) −37.6683 −1.27781
\(870\) 0.0478684 0.00162289
\(871\) −28.3368 −0.960154
\(872\) 31.6679 1.07241
\(873\) 3.30842 0.111973
\(874\) −29.1305 −0.985354
\(875\) 0.819160 0.0276927
\(876\) −0.261287 −0.00882809
\(877\) 31.9024 1.07727 0.538634 0.842540i \(-0.318941\pi\)
0.538634 + 0.842540i \(0.318941\pi\)
\(878\) 71.9451 2.42803
\(879\) −0.320254 −0.0108019
\(880\) 0.776899 0.0261892
\(881\) 26.8097 0.903243 0.451622 0.892210i \(-0.350846\pi\)
0.451622 + 0.892210i \(0.350846\pi\)
\(882\) 7.23562 0.243636
\(883\) 40.4759 1.36212 0.681061 0.732227i \(-0.261519\pi\)
0.681061 + 0.732227i \(0.261519\pi\)
\(884\) −9.07844 −0.305341
\(885\) 0.0600941 0.00202004
\(886\) −92.4122 −3.10465
\(887\) 9.09625 0.305422 0.152711 0.988271i \(-0.451200\pi\)
0.152711 + 0.988271i \(0.451200\pi\)
\(888\) −0.166690 −0.00559375
\(889\) −17.1362 −0.574729
\(890\) 1.24227 0.0416409
\(891\) 28.2947 0.947908
\(892\) 36.5906 1.22514
\(893\) −16.4250 −0.549642
\(894\) −2.77608 −0.0928461
\(895\) 0.898477 0.0300328
\(896\) −20.5535 −0.686643
\(897\) 1.93993 0.0647723
\(898\) 32.8704 1.09690
\(899\) −4.76564 −0.158943
\(900\) 57.3028 1.91009
\(901\) 5.23470 0.174393
\(902\) 77.0891 2.56679
\(903\) 0.542753 0.0180617
\(904\) 9.83848 0.327223
\(905\) −1.26869 −0.0421728
\(906\) 1.44034 0.0478522
\(907\) 18.1566 0.602880 0.301440 0.953485i \(-0.402533\pi\)
0.301440 + 0.953485i \(0.402533\pi\)
\(908\) −113.787 −3.77615
\(909\) −25.8405 −0.857077
\(910\) 0.850570 0.0281961
\(911\) −3.22155 −0.106735 −0.0533674 0.998575i \(-0.516995\pi\)
−0.0533674 + 0.998575i \(0.516995\pi\)
\(912\) 0.252681 0.00836710
\(913\) 3.57706 0.118384
\(914\) 32.0704 1.06079
\(915\) 0.0474512 0.00156869
\(916\) 91.9714 3.03882
\(917\) −6.79906 −0.224525
\(918\) −0.447956 −0.0147847
\(919\) 21.9632 0.724500 0.362250 0.932081i \(-0.382009\pi\)
0.362250 + 0.932081i \(0.382009\pi\)
\(920\) −2.91380 −0.0960650
\(921\) 0.532049 0.0175316
\(922\) 60.7462 2.00057
\(923\) 21.3914 0.704107
\(924\) −0.677343 −0.0222830
\(925\) −3.35997 −0.110475
\(926\) 58.3452 1.91734
\(927\) −42.6435 −1.40060
\(928\) −6.80419 −0.223359
\(929\) 43.0635 1.41287 0.706434 0.707778i \(-0.250302\pi\)
0.706434 + 0.707778i \(0.250302\pi\)
\(930\) −0.0122665 −0.000402235 0
\(931\) 1.49915 0.0491327
\(932\) −19.4685 −0.637712
\(933\) −0.960871 −0.0314575
\(934\) −44.7894 −1.46556
\(935\) −0.142606 −0.00466373
\(936\) 56.8866 1.85940
\(937\) −49.0340 −1.60187 −0.800936 0.598750i \(-0.795664\pi\)
−0.800936 + 0.598750i \(0.795664\pi\)
\(938\) −15.9192 −0.519780
\(939\) −1.20140 −0.0392062
\(940\) −3.43911 −0.112171
\(941\) 17.6625 0.575781 0.287890 0.957663i \(-0.407046\pi\)
0.287890 + 0.957663i \(0.407046\pi\)
\(942\) 1.13435 0.0369592
\(943\) −81.4789 −2.65332
\(944\) 39.2817 1.27851
\(945\) 0.0275701 0.000896855 0
\(946\) 73.6867 2.39576
\(947\) −23.6183 −0.767493 −0.383747 0.923438i \(-0.625366\pi\)
−0.383747 + 0.923438i \(0.625366\pi\)
\(948\) −2.56522 −0.0833144
\(949\) −5.22853 −0.169725
\(950\) 18.0735 0.586381
\(951\) −0.0737293 −0.00239084
\(952\) −2.43643 −0.0789650
\(953\) 26.0428 0.843609 0.421804 0.906687i \(-0.361397\pi\)
0.421804 + 0.906687i \(0.361397\pi\)
\(954\) −68.6626 −2.22303
\(955\) −0.157739 −0.00510433
\(956\) −26.8571 −0.868621
\(957\) −0.762797 −0.0246577
\(958\) 91.0072 2.94031
\(959\) 15.8412 0.511538
\(960\) −0.0451460 −0.00145708
\(961\) −29.7788 −0.960606
\(962\) −6.98230 −0.225118
\(963\) −21.6117 −0.696428
\(964\) −71.8267 −2.31338
\(965\) −1.28626 −0.0414062
\(966\) 1.08982 0.0350645
\(967\) 58.4964 1.88112 0.940559 0.339630i \(-0.110302\pi\)
0.940559 + 0.339630i \(0.110302\pi\)
\(968\) 4.65400 0.149585
\(969\) −0.0463817 −0.00149000
\(970\) 0.218487 0.00701520
\(971\) 21.7832 0.699055 0.349528 0.936926i \(-0.386342\pi\)
0.349528 + 0.936926i \(0.386342\pi\)
\(972\) 5.79075 0.185738
\(973\) 21.3759 0.685279
\(974\) 90.0440 2.88519
\(975\) −1.20359 −0.0385458
\(976\) 31.0174 0.992843
\(977\) −33.2853 −1.06489 −0.532446 0.846464i \(-0.678727\pi\)
−0.532446 + 0.846464i \(0.678727\pi\)
\(978\) 0.264981 0.00847315
\(979\) −19.7959 −0.632679
\(980\) 0.313896 0.0100270
\(981\) 21.4872 0.686033
\(982\) 24.7662 0.790320
\(983\) −51.0697 −1.62887 −0.814435 0.580255i \(-0.802953\pi\)
−0.814435 + 0.580255i \(0.802953\pi\)
\(984\) 2.50791 0.0799492
\(985\) −0.800606 −0.0255094
\(986\) −5.74357 −0.182913
\(987\) 0.614489 0.0195594
\(988\) 24.6723 0.784930
\(989\) −77.8828 −2.47653
\(990\) 1.87054 0.0594497
\(991\) 32.1226 1.02041 0.510205 0.860053i \(-0.329570\pi\)
0.510205 + 0.860053i \(0.329570\pi\)
\(992\) 1.74361 0.0553596
\(993\) −0.336566 −0.0106806
\(994\) 12.0174 0.381169
\(995\) 0.0110981 0.000351835 0
\(996\) 0.243598 0.00771871
\(997\) 6.92242 0.219235 0.109618 0.993974i \(-0.465037\pi\)
0.109618 + 0.993974i \(0.465037\pi\)
\(998\) 45.8656 1.45185
\(999\) −0.226322 −0.00716052
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 6041.2.a.d.1.9 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6041.2.a.d.1.9 101 1.1 even 1 trivial