Properties

Label 8027.2.a.c.1.20
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $143$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(143\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.30190 q^{2} +0.450462 q^{3} +3.29874 q^{4} -0.676454 q^{5} -1.03692 q^{6} +2.59801 q^{7} -2.98957 q^{8} -2.79708 q^{9} +O(q^{10})\) \(q-2.30190 q^{2} +0.450462 q^{3} +3.29874 q^{4} -0.676454 q^{5} -1.03692 q^{6} +2.59801 q^{7} -2.98957 q^{8} -2.79708 q^{9} +1.55713 q^{10} -0.532065 q^{11} +1.48596 q^{12} +0.729873 q^{13} -5.98035 q^{14} -0.304717 q^{15} +0.284200 q^{16} +5.25909 q^{17} +6.43860 q^{18} +7.16390 q^{19} -2.23145 q^{20} +1.17030 q^{21} +1.22476 q^{22} +1.00000 q^{23} -1.34669 q^{24} -4.54241 q^{25} -1.68009 q^{26} -2.61137 q^{27} +8.57015 q^{28} -2.03287 q^{29} +0.701428 q^{30} -5.72890 q^{31} +5.32493 q^{32} -0.239675 q^{33} -12.1059 q^{34} -1.75743 q^{35} -9.22685 q^{36} -2.86077 q^{37} -16.4906 q^{38} +0.328780 q^{39} +2.02230 q^{40} +9.47383 q^{41} -2.69392 q^{42} -2.30599 q^{43} -1.75514 q^{44} +1.89210 q^{45} -2.30190 q^{46} -9.97423 q^{47} +0.128021 q^{48} -0.250360 q^{49} +10.4562 q^{50} +2.36902 q^{51} +2.40766 q^{52} -0.217009 q^{53} +6.01110 q^{54} +0.359917 q^{55} -7.76691 q^{56} +3.22707 q^{57} +4.67947 q^{58} -9.30020 q^{59} -1.00518 q^{60} -12.0722 q^{61} +13.1874 q^{62} -7.26684 q^{63} -12.8259 q^{64} -0.493726 q^{65} +0.551707 q^{66} -11.4418 q^{67} +17.3484 q^{68} +0.450462 q^{69} +4.04543 q^{70} +8.16300 q^{71} +8.36207 q^{72} -8.03668 q^{73} +6.58520 q^{74} -2.04618 q^{75} +23.6318 q^{76} -1.38231 q^{77} -0.756818 q^{78} +6.16246 q^{79} -0.192249 q^{80} +7.21493 q^{81} -21.8078 q^{82} -1.85525 q^{83} +3.86053 q^{84} -3.55754 q^{85} +5.30816 q^{86} -0.915733 q^{87} +1.59064 q^{88} +12.2675 q^{89} -4.35542 q^{90} +1.89621 q^{91} +3.29874 q^{92} -2.58065 q^{93} +22.9597 q^{94} -4.84605 q^{95} +2.39868 q^{96} +6.62865 q^{97} +0.576303 q^{98} +1.48823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30190 −1.62769 −0.813844 0.581083i \(-0.802629\pi\)
−0.813844 + 0.581083i \(0.802629\pi\)
\(3\) 0.450462 0.260074 0.130037 0.991509i \(-0.458490\pi\)
0.130037 + 0.991509i \(0.458490\pi\)
\(4\) 3.29874 1.64937
\(5\) −0.676454 −0.302520 −0.151260 0.988494i \(-0.548333\pi\)
−0.151260 + 0.988494i \(0.548333\pi\)
\(6\) −1.03692 −0.423320
\(7\) 2.59801 0.981954 0.490977 0.871172i \(-0.336640\pi\)
0.490977 + 0.871172i \(0.336640\pi\)
\(8\) −2.98957 −1.05697
\(9\) −2.79708 −0.932361
\(10\) 1.55713 0.492408
\(11\) −0.532065 −0.160424 −0.0802118 0.996778i \(-0.525560\pi\)
−0.0802118 + 0.996778i \(0.525560\pi\)
\(12\) 1.48596 0.428959
\(13\) 0.729873 0.202430 0.101215 0.994865i \(-0.467727\pi\)
0.101215 + 0.994865i \(0.467727\pi\)
\(14\) −5.98035 −1.59832
\(15\) −0.304717 −0.0786776
\(16\) 0.284200 0.0710501
\(17\) 5.25909 1.27552 0.637759 0.770236i \(-0.279862\pi\)
0.637759 + 0.770236i \(0.279862\pi\)
\(18\) 6.43860 1.51759
\(19\) 7.16390 1.64351 0.821756 0.569839i \(-0.192995\pi\)
0.821756 + 0.569839i \(0.192995\pi\)
\(20\) −2.23145 −0.498967
\(21\) 1.17030 0.255381
\(22\) 1.22476 0.261119
\(23\) 1.00000 0.208514
\(24\) −1.34669 −0.274891
\(25\) −4.54241 −0.908482
\(26\) −1.68009 −0.329493
\(27\) −2.61137 −0.502558
\(28\) 8.57015 1.61961
\(29\) −2.03287 −0.377495 −0.188748 0.982026i \(-0.560443\pi\)
−0.188748 + 0.982026i \(0.560443\pi\)
\(30\) 0.701428 0.128063
\(31\) −5.72890 −1.02894 −0.514471 0.857508i \(-0.672012\pi\)
−0.514471 + 0.857508i \(0.672012\pi\)
\(32\) 5.32493 0.941324
\(33\) −0.239675 −0.0417220
\(34\) −12.1059 −2.07614
\(35\) −1.75743 −0.297060
\(36\) −9.22685 −1.53781
\(37\) −2.86077 −0.470307 −0.235154 0.971958i \(-0.575559\pi\)
−0.235154 + 0.971958i \(0.575559\pi\)
\(38\) −16.4906 −2.67513
\(39\) 0.328780 0.0526469
\(40\) 2.02230 0.319754
\(41\) 9.47383 1.47956 0.739782 0.672847i \(-0.234929\pi\)
0.739782 + 0.672847i \(0.234929\pi\)
\(42\) −2.69392 −0.415681
\(43\) −2.30599 −0.351660 −0.175830 0.984421i \(-0.556261\pi\)
−0.175830 + 0.984421i \(0.556261\pi\)
\(44\) −1.75514 −0.264598
\(45\) 1.89210 0.282058
\(46\) −2.30190 −0.339396
\(47\) −9.97423 −1.45489 −0.727446 0.686165i \(-0.759293\pi\)
−0.727446 + 0.686165i \(0.759293\pi\)
\(48\) 0.128021 0.0184783
\(49\) −0.250360 −0.0357657
\(50\) 10.4562 1.47873
\(51\) 2.36902 0.331729
\(52\) 2.40766 0.333882
\(53\) −0.217009 −0.0298085 −0.0149043 0.999889i \(-0.504744\pi\)
−0.0149043 + 0.999889i \(0.504744\pi\)
\(54\) 6.01110 0.818007
\(55\) 0.359917 0.0485313
\(56\) −7.76691 −1.03790
\(57\) 3.22707 0.427435
\(58\) 4.67947 0.614445
\(59\) −9.30020 −1.21078 −0.605391 0.795928i \(-0.706983\pi\)
−0.605391 + 0.795928i \(0.706983\pi\)
\(60\) −1.00518 −0.129768
\(61\) −12.0722 −1.54568 −0.772841 0.634600i \(-0.781165\pi\)
−0.772841 + 0.634600i \(0.781165\pi\)
\(62\) 13.1874 1.67480
\(63\) −7.26684 −0.915536
\(64\) −12.8259 −1.60323
\(65\) −0.493726 −0.0612391
\(66\) 0.551707 0.0679105
\(67\) −11.4418 −1.39783 −0.698917 0.715203i \(-0.746334\pi\)
−0.698917 + 0.715203i \(0.746334\pi\)
\(68\) 17.3484 2.10380
\(69\) 0.450462 0.0542293
\(70\) 4.04543 0.483522
\(71\) 8.16300 0.968769 0.484385 0.874855i \(-0.339044\pi\)
0.484385 + 0.874855i \(0.339044\pi\)
\(72\) 8.36207 0.985479
\(73\) −8.03668 −0.940622 −0.470311 0.882501i \(-0.655858\pi\)
−0.470311 + 0.882501i \(0.655858\pi\)
\(74\) 6.58520 0.765514
\(75\) −2.04618 −0.236273
\(76\) 23.6318 2.71076
\(77\) −1.38231 −0.157529
\(78\) −0.756818 −0.0856928
\(79\) 6.16246 0.693330 0.346665 0.937989i \(-0.387314\pi\)
0.346665 + 0.937989i \(0.387314\pi\)
\(80\) −0.192249 −0.0214941
\(81\) 7.21493 0.801659
\(82\) −21.8078 −2.40827
\(83\) −1.85525 −0.203640 −0.101820 0.994803i \(-0.532467\pi\)
−0.101820 + 0.994803i \(0.532467\pi\)
\(84\) 3.86053 0.421218
\(85\) −3.55754 −0.385869
\(86\) 5.30816 0.572393
\(87\) −0.915733 −0.0981768
\(88\) 1.59064 0.169563
\(89\) 12.2675 1.30036 0.650179 0.759781i \(-0.274694\pi\)
0.650179 + 0.759781i \(0.274694\pi\)
\(90\) −4.35542 −0.459102
\(91\) 1.89621 0.198777
\(92\) 3.29874 0.343917
\(93\) −2.58065 −0.267601
\(94\) 22.9597 2.36811
\(95\) −4.84605 −0.497195
\(96\) 2.39868 0.244814
\(97\) 6.62865 0.673038 0.336519 0.941677i \(-0.390750\pi\)
0.336519 + 0.941677i \(0.390750\pi\)
\(98\) 0.576303 0.0582154
\(99\) 1.48823 0.149573
\(100\) −14.9842 −1.49842
\(101\) −10.9290 −1.08748 −0.543738 0.839255i \(-0.682992\pi\)
−0.543738 + 0.839255i \(0.682992\pi\)
\(102\) −5.45325 −0.539952
\(103\) 16.5985 1.63550 0.817750 0.575574i \(-0.195221\pi\)
0.817750 + 0.575574i \(0.195221\pi\)
\(104\) −2.18200 −0.213963
\(105\) −0.791657 −0.0772578
\(106\) 0.499533 0.0485190
\(107\) 10.4331 1.00860 0.504302 0.863528i \(-0.331750\pi\)
0.504302 + 0.863528i \(0.331750\pi\)
\(108\) −8.61422 −0.828903
\(109\) −18.4203 −1.76435 −0.882174 0.470923i \(-0.843921\pi\)
−0.882174 + 0.470923i \(0.843921\pi\)
\(110\) −0.828494 −0.0789938
\(111\) −1.28867 −0.122315
\(112\) 0.738355 0.0697680
\(113\) −8.54331 −0.803687 −0.401843 0.915708i \(-0.631630\pi\)
−0.401843 + 0.915708i \(0.631630\pi\)
\(114\) −7.42838 −0.695732
\(115\) −0.676454 −0.0630797
\(116\) −6.70592 −0.622629
\(117\) −2.04152 −0.188738
\(118\) 21.4081 1.97078
\(119\) 13.6632 1.25250
\(120\) 0.910972 0.0831599
\(121\) −10.7169 −0.974264
\(122\) 27.7889 2.51589
\(123\) 4.26760 0.384797
\(124\) −18.8982 −1.69710
\(125\) 6.45500 0.577353
\(126\) 16.7275 1.49021
\(127\) −1.87428 −0.166315 −0.0831575 0.996536i \(-0.526500\pi\)
−0.0831575 + 0.996536i \(0.526500\pi\)
\(128\) 18.8740 1.66824
\(129\) −1.03876 −0.0914578
\(130\) 1.13651 0.0996782
\(131\) −3.19986 −0.279573 −0.139787 0.990182i \(-0.544642\pi\)
−0.139787 + 0.990182i \(0.544642\pi\)
\(132\) −0.790625 −0.0688151
\(133\) 18.6119 1.61385
\(134\) 26.3378 2.27524
\(135\) 1.76647 0.152034
\(136\) −15.7224 −1.34818
\(137\) 17.2803 1.47636 0.738179 0.674605i \(-0.235686\pi\)
0.738179 + 0.674605i \(0.235686\pi\)
\(138\) −1.03692 −0.0882683
\(139\) −13.2952 −1.12769 −0.563843 0.825882i \(-0.690678\pi\)
−0.563843 + 0.825882i \(0.690678\pi\)
\(140\) −5.79731 −0.489962
\(141\) −4.49301 −0.378380
\(142\) −18.7904 −1.57685
\(143\) −0.388339 −0.0324746
\(144\) −0.794932 −0.0662444
\(145\) 1.37515 0.114200
\(146\) 18.4996 1.53104
\(147\) −0.112778 −0.00930174
\(148\) −9.43693 −0.775711
\(149\) −10.9380 −0.896076 −0.448038 0.894015i \(-0.647877\pi\)
−0.448038 + 0.894015i \(0.647877\pi\)
\(150\) 4.71011 0.384579
\(151\) 7.20621 0.586433 0.293216 0.956046i \(-0.405274\pi\)
0.293216 + 0.956046i \(0.405274\pi\)
\(152\) −21.4170 −1.73715
\(153\) −14.7101 −1.18924
\(154\) 3.18193 0.256407
\(155\) 3.87534 0.311275
\(156\) 1.08456 0.0868342
\(157\) −12.0129 −0.958733 −0.479367 0.877615i \(-0.659134\pi\)
−0.479367 + 0.877615i \(0.659134\pi\)
\(158\) −14.1854 −1.12853
\(159\) −0.0977544 −0.00775243
\(160\) −3.60207 −0.284769
\(161\) 2.59801 0.204752
\(162\) −16.6080 −1.30485
\(163\) 2.76599 0.216649 0.108325 0.994116i \(-0.465451\pi\)
0.108325 + 0.994116i \(0.465451\pi\)
\(164\) 31.2517 2.44035
\(165\) 0.162129 0.0126217
\(166\) 4.27059 0.331462
\(167\) 1.56285 0.120937 0.0604685 0.998170i \(-0.480741\pi\)
0.0604685 + 0.998170i \(0.480741\pi\)
\(168\) −3.49870 −0.269930
\(169\) −12.4673 −0.959022
\(170\) 8.18909 0.628075
\(171\) −20.0380 −1.53235
\(172\) −7.60686 −0.580018
\(173\) 12.9134 0.981785 0.490892 0.871220i \(-0.336671\pi\)
0.490892 + 0.871220i \(0.336671\pi\)
\(174\) 2.10792 0.159801
\(175\) −11.8012 −0.892088
\(176\) −0.151213 −0.0113981
\(177\) −4.18938 −0.314893
\(178\) −28.2387 −2.11658
\(179\) 3.84425 0.287333 0.143666 0.989626i \(-0.454111\pi\)
0.143666 + 0.989626i \(0.454111\pi\)
\(180\) 6.24154 0.465217
\(181\) −20.0182 −1.48794 −0.743971 0.668212i \(-0.767060\pi\)
−0.743971 + 0.668212i \(0.767060\pi\)
\(182\) −4.36489 −0.323547
\(183\) −5.43805 −0.401992
\(184\) −2.98957 −0.220394
\(185\) 1.93518 0.142277
\(186\) 5.94040 0.435571
\(187\) −2.79818 −0.204623
\(188\) −32.9024 −2.39965
\(189\) −6.78435 −0.493489
\(190\) 11.1551 0.809278
\(191\) −25.6972 −1.85938 −0.929692 0.368337i \(-0.879927\pi\)
−0.929692 + 0.368337i \(0.879927\pi\)
\(192\) −5.77756 −0.416959
\(193\) 11.6595 0.839270 0.419635 0.907693i \(-0.362158\pi\)
0.419635 + 0.907693i \(0.362158\pi\)
\(194\) −15.2585 −1.09550
\(195\) −0.222405 −0.0159267
\(196\) −0.825871 −0.0589908
\(197\) 5.06007 0.360515 0.180257 0.983619i \(-0.442307\pi\)
0.180257 + 0.983619i \(0.442307\pi\)
\(198\) −3.42575 −0.243458
\(199\) 3.06102 0.216990 0.108495 0.994097i \(-0.465397\pi\)
0.108495 + 0.994097i \(0.465397\pi\)
\(200\) 13.5798 0.960239
\(201\) −5.15408 −0.363541
\(202\) 25.1575 1.77007
\(203\) −5.28142 −0.370683
\(204\) 7.81478 0.547144
\(205\) −6.40862 −0.447597
\(206\) −38.2081 −2.66208
\(207\) −2.79708 −0.194411
\(208\) 0.207430 0.0143827
\(209\) −3.81166 −0.263658
\(210\) 1.82231 0.125752
\(211\) −12.6479 −0.870716 −0.435358 0.900257i \(-0.643378\pi\)
−0.435358 + 0.900257i \(0.643378\pi\)
\(212\) −0.715857 −0.0491652
\(213\) 3.67712 0.251952
\(214\) −24.0159 −1.64169
\(215\) 1.55990 0.106384
\(216\) 7.80685 0.531189
\(217\) −14.8837 −1.01037
\(218\) 42.4018 2.87181
\(219\) −3.62022 −0.244632
\(220\) 1.18727 0.0800460
\(221\) 3.83847 0.258203
\(222\) 2.96638 0.199091
\(223\) 7.22817 0.484034 0.242017 0.970272i \(-0.422191\pi\)
0.242017 + 0.970272i \(0.422191\pi\)
\(224\) 13.8342 0.924337
\(225\) 12.7055 0.847033
\(226\) 19.6658 1.30815
\(227\) 20.3368 1.34980 0.674899 0.737910i \(-0.264187\pi\)
0.674899 + 0.737910i \(0.264187\pi\)
\(228\) 10.6453 0.704999
\(229\) −2.09707 −0.138578 −0.0692891 0.997597i \(-0.522073\pi\)
−0.0692891 + 0.997597i \(0.522073\pi\)
\(230\) 1.55713 0.102674
\(231\) −0.622677 −0.0409691
\(232\) 6.07741 0.399002
\(233\) −18.0222 −1.18067 −0.590337 0.807157i \(-0.701005\pi\)
−0.590337 + 0.807157i \(0.701005\pi\)
\(234\) 4.69936 0.307207
\(235\) 6.74711 0.440133
\(236\) −30.6789 −1.99703
\(237\) 2.77595 0.180317
\(238\) −31.4512 −2.03868
\(239\) −1.23873 −0.0801269 −0.0400635 0.999197i \(-0.512756\pi\)
−0.0400635 + 0.999197i \(0.512756\pi\)
\(240\) −0.0866007 −0.00559005
\(241\) 18.7225 1.20602 0.603011 0.797733i \(-0.293967\pi\)
0.603011 + 0.797733i \(0.293967\pi\)
\(242\) 24.6692 1.58580
\(243\) 11.0842 0.711049
\(244\) −39.8229 −2.54940
\(245\) 0.169357 0.0108198
\(246\) −9.82359 −0.626329
\(247\) 5.22874 0.332697
\(248\) 17.1269 1.08756
\(249\) −0.835718 −0.0529615
\(250\) −14.8588 −0.939751
\(251\) 16.1000 1.01622 0.508111 0.861291i \(-0.330344\pi\)
0.508111 + 0.861291i \(0.330344\pi\)
\(252\) −23.9714 −1.51006
\(253\) −0.532065 −0.0334506
\(254\) 4.31439 0.270709
\(255\) −1.60254 −0.100355
\(256\) −17.7942 −1.11214
\(257\) 15.0426 0.938334 0.469167 0.883109i \(-0.344554\pi\)
0.469167 + 0.883109i \(0.344554\pi\)
\(258\) 2.39112 0.148865
\(259\) −7.43229 −0.461820
\(260\) −1.62867 −0.101006
\(261\) 5.68612 0.351962
\(262\) 7.36576 0.455058
\(263\) −17.1549 −1.05782 −0.528910 0.848678i \(-0.677399\pi\)
−0.528910 + 0.848678i \(0.677399\pi\)
\(264\) 0.716524 0.0440990
\(265\) 0.146797 0.00901766
\(266\) −42.8427 −2.62685
\(267\) 5.52607 0.338190
\(268\) −37.7434 −2.30555
\(269\) 8.67351 0.528834 0.264417 0.964409i \(-0.414821\pi\)
0.264417 + 0.964409i \(0.414821\pi\)
\(270\) −4.06624 −0.247463
\(271\) 4.90192 0.297771 0.148885 0.988854i \(-0.452431\pi\)
0.148885 + 0.988854i \(0.452431\pi\)
\(272\) 1.49464 0.0906256
\(273\) 0.854173 0.0516969
\(274\) −39.7776 −2.40305
\(275\) 2.41686 0.145742
\(276\) 1.48596 0.0894441
\(277\) 9.46268 0.568557 0.284279 0.958742i \(-0.408246\pi\)
0.284279 + 0.958742i \(0.408246\pi\)
\(278\) 30.6042 1.83552
\(279\) 16.0242 0.959345
\(280\) 5.25396 0.313984
\(281\) −26.3523 −1.57204 −0.786022 0.618198i \(-0.787863\pi\)
−0.786022 + 0.618198i \(0.787863\pi\)
\(282\) 10.3425 0.615885
\(283\) −15.5302 −0.923172 −0.461586 0.887096i \(-0.652719\pi\)
−0.461586 + 0.887096i \(0.652719\pi\)
\(284\) 26.9276 1.59786
\(285\) −2.18296 −0.129308
\(286\) 0.893918 0.0528585
\(287\) 24.6131 1.45286
\(288\) −14.8943 −0.877654
\(289\) 10.6581 0.626945
\(290\) −3.16545 −0.185882
\(291\) 2.98596 0.175040
\(292\) −26.5109 −1.55143
\(293\) −26.5973 −1.55383 −0.776915 0.629605i \(-0.783217\pi\)
−0.776915 + 0.629605i \(0.783217\pi\)
\(294\) 0.259603 0.0151403
\(295\) 6.29116 0.366285
\(296\) 8.55245 0.497101
\(297\) 1.38942 0.0806221
\(298\) 25.1782 1.45853
\(299\) 0.729873 0.0422096
\(300\) −6.74982 −0.389701
\(301\) −5.99098 −0.345314
\(302\) −16.5880 −0.954530
\(303\) −4.92310 −0.282825
\(304\) 2.03598 0.116772
\(305\) 8.16627 0.467599
\(306\) 33.8612 1.93572
\(307\) −17.2748 −0.985923 −0.492962 0.870051i \(-0.664086\pi\)
−0.492962 + 0.870051i \(0.664086\pi\)
\(308\) −4.55987 −0.259823
\(309\) 7.47700 0.425352
\(310\) −8.92064 −0.506658
\(311\) −3.83308 −0.217354 −0.108677 0.994077i \(-0.534661\pi\)
−0.108677 + 0.994077i \(0.534661\pi\)
\(312\) −0.982909 −0.0556463
\(313\) 3.35058 0.189386 0.0946930 0.995507i \(-0.469813\pi\)
0.0946930 + 0.995507i \(0.469813\pi\)
\(314\) 27.6525 1.56052
\(315\) 4.91569 0.276968
\(316\) 20.3283 1.14356
\(317\) 1.11245 0.0624817 0.0312408 0.999512i \(-0.490054\pi\)
0.0312408 + 0.999512i \(0.490054\pi\)
\(318\) 0.225021 0.0126185
\(319\) 1.08162 0.0605591
\(320\) 8.67610 0.485009
\(321\) 4.69970 0.262312
\(322\) −5.98035 −0.333272
\(323\) 37.6756 2.09633
\(324\) 23.8002 1.32223
\(325\) −3.31538 −0.183904
\(326\) −6.36703 −0.352637
\(327\) −8.29766 −0.458862
\(328\) −28.3226 −1.56386
\(329\) −25.9131 −1.42864
\(330\) −0.373205 −0.0205443
\(331\) 2.25969 0.124204 0.0621018 0.998070i \(-0.480220\pi\)
0.0621018 + 0.998070i \(0.480220\pi\)
\(332\) −6.11998 −0.335877
\(333\) 8.00181 0.438496
\(334\) −3.59753 −0.196848
\(335\) 7.73983 0.422872
\(336\) 0.332601 0.0181449
\(337\) 18.1162 0.986850 0.493425 0.869788i \(-0.335745\pi\)
0.493425 + 0.869788i \(0.335745\pi\)
\(338\) 28.6984 1.56099
\(339\) −3.84844 −0.209018
\(340\) −11.7354 −0.636441
\(341\) 3.04815 0.165066
\(342\) 46.1255 2.49418
\(343\) −18.8365 −1.01707
\(344\) 6.89391 0.371695
\(345\) −0.304717 −0.0164054
\(346\) −29.7253 −1.59804
\(347\) −23.5290 −1.26310 −0.631552 0.775334i \(-0.717582\pi\)
−0.631552 + 0.775334i \(0.717582\pi\)
\(348\) −3.02076 −0.161930
\(349\) 1.00000 0.0535288
\(350\) 27.1652 1.45204
\(351\) −1.90596 −0.101733
\(352\) −2.83321 −0.151010
\(353\) 14.6673 0.780662 0.390331 0.920675i \(-0.372361\pi\)
0.390331 + 0.920675i \(0.372361\pi\)
\(354\) 9.64354 0.512548
\(355\) −5.52189 −0.293072
\(356\) 40.4674 2.14477
\(357\) 6.15473 0.325743
\(358\) −8.84908 −0.467688
\(359\) −7.09296 −0.374352 −0.187176 0.982326i \(-0.559933\pi\)
−0.187176 + 0.982326i \(0.559933\pi\)
\(360\) −5.65656 −0.298127
\(361\) 32.3215 1.70113
\(362\) 46.0799 2.42191
\(363\) −4.82756 −0.253381
\(364\) 6.25512 0.327857
\(365\) 5.43645 0.284557
\(366\) 12.5178 0.654318
\(367\) −34.1665 −1.78348 −0.891739 0.452550i \(-0.850514\pi\)
−0.891739 + 0.452550i \(0.850514\pi\)
\(368\) 0.284200 0.0148150
\(369\) −26.4991 −1.37949
\(370\) −4.45459 −0.231583
\(371\) −0.563791 −0.0292706
\(372\) −8.51290 −0.441373
\(373\) 19.4167 1.00536 0.502679 0.864473i \(-0.332348\pi\)
0.502679 + 0.864473i \(0.332348\pi\)
\(374\) 6.44112 0.333062
\(375\) 2.90773 0.150155
\(376\) 29.8186 1.53778
\(377\) −1.48374 −0.0764165
\(378\) 15.6169 0.803246
\(379\) 5.78176 0.296989 0.148495 0.988913i \(-0.452557\pi\)
0.148495 + 0.988913i \(0.452557\pi\)
\(380\) −15.9859 −0.820058
\(381\) −0.844290 −0.0432543
\(382\) 59.1524 3.02650
\(383\) −7.60060 −0.388372 −0.194186 0.980965i \(-0.562207\pi\)
−0.194186 + 0.980965i \(0.562207\pi\)
\(384\) 8.50200 0.433866
\(385\) 0.935068 0.0476555
\(386\) −26.8390 −1.36607
\(387\) 6.45005 0.327875
\(388\) 21.8662 1.11009
\(389\) −18.8645 −0.956467 −0.478233 0.878233i \(-0.658723\pi\)
−0.478233 + 0.878233i \(0.658723\pi\)
\(390\) 0.511953 0.0259237
\(391\) 5.25909 0.265964
\(392\) 0.748467 0.0378033
\(393\) −1.44142 −0.0727098
\(394\) −11.6478 −0.586806
\(395\) −4.16862 −0.209746
\(396\) 4.90928 0.246701
\(397\) −1.67839 −0.0842359 −0.0421180 0.999113i \(-0.513411\pi\)
−0.0421180 + 0.999113i \(0.513411\pi\)
\(398\) −7.04616 −0.353192
\(399\) 8.38394 0.419722
\(400\) −1.29095 −0.0645477
\(401\) 7.75110 0.387071 0.193536 0.981093i \(-0.438004\pi\)
0.193536 + 0.981093i \(0.438004\pi\)
\(402\) 11.8642 0.591731
\(403\) −4.18137 −0.208289
\(404\) −36.0519 −1.79365
\(405\) −4.88057 −0.242518
\(406\) 12.1573 0.603357
\(407\) 1.52211 0.0754484
\(408\) −7.08235 −0.350628
\(409\) 21.1155 1.04409 0.522047 0.852917i \(-0.325169\pi\)
0.522047 + 0.852917i \(0.325169\pi\)
\(410\) 14.7520 0.728549
\(411\) 7.78413 0.383963
\(412\) 54.7542 2.69754
\(413\) −24.1620 −1.18893
\(414\) 6.43860 0.316440
\(415\) 1.25499 0.0616050
\(416\) 3.88652 0.190552
\(417\) −5.98899 −0.293282
\(418\) 8.77406 0.429153
\(419\) −7.75518 −0.378866 −0.189433 0.981894i \(-0.560665\pi\)
−0.189433 + 0.981894i \(0.560665\pi\)
\(420\) −2.61147 −0.127427
\(421\) −2.97097 −0.144796 −0.0723982 0.997376i \(-0.523065\pi\)
−0.0723982 + 0.997376i \(0.523065\pi\)
\(422\) 29.1142 1.41725
\(423\) 27.8988 1.35648
\(424\) 0.648763 0.0315067
\(425\) −23.8890 −1.15878
\(426\) −8.46436 −0.410099
\(427\) −31.3636 −1.51779
\(428\) 34.4160 1.66356
\(429\) −0.174932 −0.00844580
\(430\) −3.59073 −0.173160
\(431\) 37.5503 1.80873 0.904367 0.426755i \(-0.140343\pi\)
0.904367 + 0.426755i \(0.140343\pi\)
\(432\) −0.742151 −0.0357068
\(433\) 22.5975 1.08597 0.542984 0.839743i \(-0.317294\pi\)
0.542984 + 0.839743i \(0.317294\pi\)
\(434\) 34.2608 1.64457
\(435\) 0.619451 0.0297004
\(436\) −60.7639 −2.91006
\(437\) 7.16390 0.342696
\(438\) 8.33338 0.398184
\(439\) 3.47082 0.165653 0.0828265 0.996564i \(-0.473605\pi\)
0.0828265 + 0.996564i \(0.473605\pi\)
\(440\) −1.07600 −0.0512961
\(441\) 0.700277 0.0333465
\(442\) −8.83577 −0.420275
\(443\) 28.8446 1.37045 0.685223 0.728333i \(-0.259705\pi\)
0.685223 + 0.728333i \(0.259705\pi\)
\(444\) −4.25098 −0.201742
\(445\) −8.29844 −0.393384
\(446\) −16.6385 −0.787856
\(447\) −4.92715 −0.233046
\(448\) −33.3217 −1.57430
\(449\) 35.5161 1.67611 0.838053 0.545588i \(-0.183694\pi\)
0.838053 + 0.545588i \(0.183694\pi\)
\(450\) −29.2468 −1.37871
\(451\) −5.04069 −0.237357
\(452\) −28.1821 −1.32558
\(453\) 3.24612 0.152516
\(454\) −46.8132 −2.19705
\(455\) −1.28270 −0.0601340
\(456\) −9.64753 −0.451787
\(457\) 2.67908 0.125322 0.0626610 0.998035i \(-0.480041\pi\)
0.0626610 + 0.998035i \(0.480041\pi\)
\(458\) 4.82724 0.225562
\(459\) −13.7334 −0.641021
\(460\) −2.23145 −0.104042
\(461\) −6.34928 −0.295715 −0.147858 0.989009i \(-0.547238\pi\)
−0.147858 + 0.989009i \(0.547238\pi\)
\(462\) 1.43334 0.0666850
\(463\) −39.6465 −1.84253 −0.921264 0.388938i \(-0.872842\pi\)
−0.921264 + 0.388938i \(0.872842\pi\)
\(464\) −0.577744 −0.0268211
\(465\) 1.74569 0.0809546
\(466\) 41.4853 1.92177
\(467\) 37.2245 1.72254 0.861272 0.508145i \(-0.169669\pi\)
0.861272 + 0.508145i \(0.169669\pi\)
\(468\) −6.73443 −0.311299
\(469\) −29.7258 −1.37261
\(470\) −15.5312 −0.716400
\(471\) −5.41135 −0.249342
\(472\) 27.8035 1.27976
\(473\) 1.22694 0.0564146
\(474\) −6.38996 −0.293501
\(475\) −32.5414 −1.49310
\(476\) 45.0712 2.06583
\(477\) 0.606993 0.0277923
\(478\) 2.85144 0.130422
\(479\) −3.93541 −0.179814 −0.0899068 0.995950i \(-0.528657\pi\)
−0.0899068 + 0.995950i \(0.528657\pi\)
\(480\) −1.62260 −0.0740611
\(481\) −2.08800 −0.0952044
\(482\) −43.0973 −1.96303
\(483\) 1.17030 0.0532507
\(484\) −35.3523 −1.60692
\(485\) −4.48398 −0.203607
\(486\) −25.5146 −1.15737
\(487\) −36.3550 −1.64740 −0.823701 0.567024i \(-0.808095\pi\)
−0.823701 + 0.567024i \(0.808095\pi\)
\(488\) 36.0905 1.63374
\(489\) 1.24597 0.0563449
\(490\) −0.389843 −0.0176113
\(491\) −43.1950 −1.94936 −0.974681 0.223601i \(-0.928219\pi\)
−0.974681 + 0.223601i \(0.928219\pi\)
\(492\) 14.0777 0.634672
\(493\) −10.6911 −0.481502
\(494\) −12.0360 −0.541526
\(495\) −1.00672 −0.0452487
\(496\) −1.62816 −0.0731064
\(497\) 21.2075 0.951287
\(498\) 1.92374 0.0862048
\(499\) −22.0846 −0.988641 −0.494320 0.869280i \(-0.664583\pi\)
−0.494320 + 0.869280i \(0.664583\pi\)
\(500\) 21.2934 0.952269
\(501\) 0.704005 0.0314526
\(502\) −37.0606 −1.65409
\(503\) 36.5671 1.63045 0.815223 0.579147i \(-0.196614\pi\)
0.815223 + 0.579147i \(0.196614\pi\)
\(504\) 21.7247 0.967695
\(505\) 7.39297 0.328983
\(506\) 1.22476 0.0544472
\(507\) −5.61604 −0.249417
\(508\) −6.18274 −0.274315
\(509\) −9.53790 −0.422760 −0.211380 0.977404i \(-0.567796\pi\)
−0.211380 + 0.977404i \(0.567796\pi\)
\(510\) 3.68887 0.163346
\(511\) −20.8793 −0.923648
\(512\) 3.21262 0.141979
\(513\) −18.7076 −0.825960
\(514\) −34.6266 −1.52732
\(515\) −11.2281 −0.494771
\(516\) −3.42660 −0.150848
\(517\) 5.30694 0.233399
\(518\) 17.1084 0.751700
\(519\) 5.81698 0.255337
\(520\) 1.47603 0.0647280
\(521\) −38.1601 −1.67183 −0.835913 0.548862i \(-0.815061\pi\)
−0.835913 + 0.548862i \(0.815061\pi\)
\(522\) −13.0889 −0.572884
\(523\) −24.7989 −1.08438 −0.542190 0.840256i \(-0.682405\pi\)
−0.542190 + 0.840256i \(0.682405\pi\)
\(524\) −10.5555 −0.461119
\(525\) −5.31600 −0.232009
\(526\) 39.4890 1.72180
\(527\) −30.1288 −1.31243
\(528\) −0.0681157 −0.00296436
\(529\) 1.00000 0.0434783
\(530\) −0.337911 −0.0146779
\(531\) 26.0134 1.12889
\(532\) 61.3957 2.66184
\(533\) 6.91469 0.299509
\(534\) −12.7204 −0.550467
\(535\) −7.05750 −0.305122
\(536\) 34.2059 1.47747
\(537\) 1.73169 0.0747279
\(538\) −19.9656 −0.860776
\(539\) 0.133208 0.00573766
\(540\) 5.82712 0.250759
\(541\) −25.0101 −1.07527 −0.537633 0.843179i \(-0.680681\pi\)
−0.537633 + 0.843179i \(0.680681\pi\)
\(542\) −11.2837 −0.484678
\(543\) −9.01745 −0.386976
\(544\) 28.0043 1.20067
\(545\) 12.4605 0.533750
\(546\) −1.96622 −0.0841464
\(547\) −21.0696 −0.900873 −0.450437 0.892808i \(-0.648732\pi\)
−0.450437 + 0.892808i \(0.648732\pi\)
\(548\) 57.0033 2.43506
\(549\) 33.7668 1.44113
\(550\) −5.56336 −0.237222
\(551\) −14.5633 −0.620418
\(552\) −1.34669 −0.0573188
\(553\) 16.0101 0.680819
\(554\) −21.7821 −0.925434
\(555\) 0.871725 0.0370027
\(556\) −43.8574 −1.85997
\(557\) 35.8969 1.52100 0.760501 0.649337i \(-0.224954\pi\)
0.760501 + 0.649337i \(0.224954\pi\)
\(558\) −36.8861 −1.56151
\(559\) −1.68308 −0.0711867
\(560\) −0.499463 −0.0211062
\(561\) −1.26047 −0.0532172
\(562\) 60.6602 2.55880
\(563\) −20.6084 −0.868540 −0.434270 0.900783i \(-0.642994\pi\)
−0.434270 + 0.900783i \(0.642994\pi\)
\(564\) −14.8213 −0.624088
\(565\) 5.77916 0.243131
\(566\) 35.7488 1.50264
\(567\) 18.7444 0.787192
\(568\) −24.4038 −1.02396
\(569\) 47.6202 1.99634 0.998172 0.0604411i \(-0.0192507\pi\)
0.998172 + 0.0604411i \(0.0192507\pi\)
\(570\) 5.02496 0.210472
\(571\) −4.18551 −0.175158 −0.0875791 0.996158i \(-0.527913\pi\)
−0.0875791 + 0.996158i \(0.527913\pi\)
\(572\) −1.28103 −0.0535626
\(573\) −11.5756 −0.483578
\(574\) −56.6568 −2.36481
\(575\) −4.54241 −0.189432
\(576\) 35.8750 1.49479
\(577\) 45.4693 1.89291 0.946457 0.322831i \(-0.104635\pi\)
0.946457 + 0.322831i \(0.104635\pi\)
\(578\) −24.5338 −1.02047
\(579\) 5.25217 0.218273
\(580\) 4.53625 0.188358
\(581\) −4.81994 −0.199965
\(582\) −6.87337 −0.284910
\(583\) 0.115463 0.00478198
\(584\) 24.0262 0.994210
\(585\) 1.38099 0.0570970
\(586\) 61.2243 2.52915
\(587\) −40.6615 −1.67828 −0.839140 0.543915i \(-0.816941\pi\)
−0.839140 + 0.543915i \(0.816941\pi\)
\(588\) −0.372024 −0.0153420
\(589\) −41.0413 −1.69108
\(590\) −14.4816 −0.596198
\(591\) 2.27937 0.0937607
\(592\) −0.813031 −0.0334154
\(593\) 9.23175 0.379103 0.189551 0.981871i \(-0.439297\pi\)
0.189551 + 0.981871i \(0.439297\pi\)
\(594\) −3.19829 −0.131228
\(595\) −9.24250 −0.378906
\(596\) −36.0816 −1.47796
\(597\) 1.37887 0.0564336
\(598\) −1.68009 −0.0687041
\(599\) −12.1800 −0.497661 −0.248830 0.968547i \(-0.580046\pi\)
−0.248830 + 0.968547i \(0.580046\pi\)
\(600\) 6.11720 0.249734
\(601\) −1.82296 −0.0743600 −0.0371800 0.999309i \(-0.511837\pi\)
−0.0371800 + 0.999309i \(0.511837\pi\)
\(602\) 13.7906 0.562064
\(603\) 32.0036 1.30329
\(604\) 23.7714 0.967244
\(605\) 7.24950 0.294734
\(606\) 11.3325 0.460351
\(607\) −18.2677 −0.741464 −0.370732 0.928740i \(-0.620893\pi\)
−0.370732 + 0.928740i \(0.620893\pi\)
\(608\) 38.1473 1.54708
\(609\) −2.37908 −0.0964052
\(610\) −18.7979 −0.761106
\(611\) −7.27992 −0.294514
\(612\) −48.5249 −1.96150
\(613\) −11.0989 −0.448280 −0.224140 0.974557i \(-0.571957\pi\)
−0.224140 + 0.974557i \(0.571957\pi\)
\(614\) 39.7648 1.60478
\(615\) −2.88684 −0.116409
\(616\) 4.13250 0.166503
\(617\) −43.5771 −1.75435 −0.877173 0.480174i \(-0.840573\pi\)
−0.877173 + 0.480174i \(0.840573\pi\)
\(618\) −17.2113 −0.692340
\(619\) −15.1405 −0.608547 −0.304274 0.952585i \(-0.598414\pi\)
−0.304274 + 0.952585i \(0.598414\pi\)
\(620\) 12.7837 0.513407
\(621\) −2.61137 −0.104791
\(622\) 8.82336 0.353784
\(623\) 31.8712 1.27689
\(624\) 0.0934394 0.00374057
\(625\) 18.3455 0.733821
\(626\) −7.71270 −0.308261
\(627\) −1.71701 −0.0685707
\(628\) −39.6274 −1.58131
\(629\) −15.0450 −0.599885
\(630\) −11.3154 −0.450817
\(631\) 7.89231 0.314188 0.157094 0.987584i \(-0.449787\pi\)
0.157094 + 0.987584i \(0.449787\pi\)
\(632\) −18.4231 −0.732830
\(633\) −5.69739 −0.226451
\(634\) −2.56076 −0.101701
\(635\) 1.26786 0.0503136
\(636\) −0.322466 −0.0127866
\(637\) −0.182731 −0.00724005
\(638\) −2.48978 −0.0985714
\(639\) −22.8326 −0.903243
\(640\) −12.7674 −0.504675
\(641\) −34.6711 −1.36943 −0.684714 0.728812i \(-0.740073\pi\)
−0.684714 + 0.728812i \(0.740073\pi\)
\(642\) −10.8182 −0.426962
\(643\) −36.8908 −1.45483 −0.727416 0.686197i \(-0.759279\pi\)
−0.727416 + 0.686197i \(0.759279\pi\)
\(644\) 8.57015 0.337711
\(645\) 0.702675 0.0276678
\(646\) −86.7255 −3.41217
\(647\) 19.4703 0.765455 0.382727 0.923861i \(-0.374985\pi\)
0.382727 + 0.923861i \(0.374985\pi\)
\(648\) −21.5695 −0.847330
\(649\) 4.94831 0.194238
\(650\) 7.63167 0.299339
\(651\) −6.70455 −0.262772
\(652\) 9.12428 0.357334
\(653\) 2.57892 0.100921 0.0504606 0.998726i \(-0.483931\pi\)
0.0504606 + 0.998726i \(0.483931\pi\)
\(654\) 19.1004 0.746884
\(655\) 2.16456 0.0845764
\(656\) 2.69247 0.105123
\(657\) 22.4793 0.876999
\(658\) 59.6494 2.32538
\(659\) 4.90585 0.191105 0.0955524 0.995424i \(-0.469538\pi\)
0.0955524 + 0.995424i \(0.469538\pi\)
\(660\) 0.534822 0.0208179
\(661\) 33.3328 1.29650 0.648248 0.761429i \(-0.275502\pi\)
0.648248 + 0.761429i \(0.275502\pi\)
\(662\) −5.20157 −0.202165
\(663\) 1.72908 0.0671521
\(664\) 5.54638 0.215241
\(665\) −12.5901 −0.488223
\(666\) −18.4194 −0.713735
\(667\) −2.03287 −0.0787132
\(668\) 5.15544 0.199470
\(669\) 3.25602 0.125885
\(670\) −17.8163 −0.688304
\(671\) 6.42317 0.247964
\(672\) 6.23178 0.240396
\(673\) 8.76446 0.337845 0.168923 0.985629i \(-0.445971\pi\)
0.168923 + 0.985629i \(0.445971\pi\)
\(674\) −41.7016 −1.60628
\(675\) 11.8619 0.456565
\(676\) −41.1263 −1.58178
\(677\) −16.0614 −0.617291 −0.308645 0.951177i \(-0.599876\pi\)
−0.308645 + 0.951177i \(0.599876\pi\)
\(678\) 8.85871 0.340217
\(679\) 17.2213 0.660892
\(680\) 10.6355 0.407852
\(681\) 9.16094 0.351048
\(682\) −7.01652 −0.268677
\(683\) 27.3422 1.04622 0.523109 0.852266i \(-0.324772\pi\)
0.523109 + 0.852266i \(0.324772\pi\)
\(684\) −66.1003 −2.52741
\(685\) −11.6893 −0.446627
\(686\) 43.3597 1.65548
\(687\) −0.944650 −0.0360407
\(688\) −0.655364 −0.0249855
\(689\) −0.158389 −0.00603414
\(690\) 0.701428 0.0267029
\(691\) −19.3882 −0.737562 −0.368781 0.929516i \(-0.620225\pi\)
−0.368781 + 0.929516i \(0.620225\pi\)
\(692\) 42.5978 1.61933
\(693\) 3.86643 0.146874
\(694\) 54.1614 2.05594
\(695\) 8.99361 0.341147
\(696\) 2.73764 0.103770
\(697\) 49.8238 1.88721
\(698\) −2.30190 −0.0871282
\(699\) −8.11832 −0.307063
\(700\) −38.9291 −1.47138
\(701\) −47.5515 −1.79599 −0.897997 0.440001i \(-0.854978\pi\)
−0.897997 + 0.440001i \(0.854978\pi\)
\(702\) 4.38734 0.165589
\(703\) −20.4943 −0.772956
\(704\) 6.82418 0.257196
\(705\) 3.03932 0.114467
\(706\) −33.7627 −1.27067
\(707\) −28.3936 −1.06785
\(708\) −13.8197 −0.519376
\(709\) 40.2461 1.51147 0.755737 0.654875i \(-0.227279\pi\)
0.755737 + 0.654875i \(0.227279\pi\)
\(710\) 12.7108 0.477029
\(711\) −17.2369 −0.646435
\(712\) −36.6746 −1.37444
\(713\) −5.72890 −0.214549
\(714\) −14.1676 −0.530208
\(715\) 0.262694 0.00982420
\(716\) 12.6812 0.473918
\(717\) −0.558002 −0.0208390
\(718\) 16.3273 0.609328
\(719\) −6.19770 −0.231135 −0.115568 0.993300i \(-0.536869\pi\)
−0.115568 + 0.993300i \(0.536869\pi\)
\(720\) 0.537736 0.0200402
\(721\) 43.1231 1.60599
\(722\) −74.4009 −2.76891
\(723\) 8.43378 0.313656
\(724\) −66.0349 −2.45417
\(725\) 9.23415 0.342948
\(726\) 11.1126 0.412426
\(727\) −20.4663 −0.759053 −0.379527 0.925181i \(-0.623913\pi\)
−0.379527 + 0.925181i \(0.623913\pi\)
\(728\) −5.66886 −0.210102
\(729\) −16.6518 −0.616733
\(730\) −12.5141 −0.463169
\(731\) −12.1274 −0.448549
\(732\) −17.9387 −0.663034
\(733\) 26.2574 0.969837 0.484919 0.874559i \(-0.338849\pi\)
0.484919 + 0.874559i \(0.338849\pi\)
\(734\) 78.6479 2.90295
\(735\) 0.0762889 0.00281396
\(736\) 5.32493 0.196280
\(737\) 6.08776 0.224245
\(738\) 60.9983 2.24538
\(739\) 39.3874 1.44889 0.724445 0.689333i \(-0.242096\pi\)
0.724445 + 0.689333i \(0.242096\pi\)
\(740\) 6.38365 0.234668
\(741\) 2.35535 0.0865259
\(742\) 1.29779 0.0476434
\(743\) −44.1735 −1.62057 −0.810284 0.586037i \(-0.800687\pi\)
−0.810284 + 0.586037i \(0.800687\pi\)
\(744\) 7.71503 0.282847
\(745\) 7.39906 0.271080
\(746\) −44.6952 −1.63641
\(747\) 5.18928 0.189866
\(748\) −9.23046 −0.337499
\(749\) 27.1052 0.990402
\(750\) −6.69331 −0.244405
\(751\) 41.6869 1.52118 0.760588 0.649235i \(-0.224911\pi\)
0.760588 + 0.649235i \(0.224911\pi\)
\(752\) −2.83468 −0.103370
\(753\) 7.25244 0.264294
\(754\) 3.41542 0.124382
\(755\) −4.87467 −0.177407
\(756\) −22.3798 −0.813945
\(757\) 9.54400 0.346883 0.173441 0.984844i \(-0.444511\pi\)
0.173441 + 0.984844i \(0.444511\pi\)
\(758\) −13.3090 −0.483406
\(759\) −0.239675 −0.00869965
\(760\) 14.4876 0.525520
\(761\) 11.6267 0.421466 0.210733 0.977544i \(-0.432415\pi\)
0.210733 + 0.977544i \(0.432415\pi\)
\(762\) 1.94347 0.0704045
\(763\) −47.8562 −1.73251
\(764\) −84.7684 −3.06681
\(765\) 9.95073 0.359769
\(766\) 17.4958 0.632149
\(767\) −6.78796 −0.245099
\(768\) −8.01563 −0.289239
\(769\) −47.2710 −1.70464 −0.852318 0.523023i \(-0.824804\pi\)
−0.852318 + 0.523023i \(0.824804\pi\)
\(770\) −2.15243 −0.0775683
\(771\) 6.77614 0.244037
\(772\) 38.4617 1.38427
\(773\) −25.4283 −0.914593 −0.457297 0.889314i \(-0.651182\pi\)
−0.457297 + 0.889314i \(0.651182\pi\)
\(774\) −14.8474 −0.533678
\(775\) 26.0230 0.934774
\(776\) −19.8168 −0.711381
\(777\) −3.34797 −0.120108
\(778\) 43.4241 1.55683
\(779\) 67.8696 2.43168
\(780\) −0.733655 −0.0262691
\(781\) −4.34324 −0.155413
\(782\) −12.1059 −0.432906
\(783\) 5.30858 0.189713
\(784\) −0.0711523 −0.00254116
\(785\) 8.12618 0.290036
\(786\) 3.31799 0.118349
\(787\) −12.1955 −0.434722 −0.217361 0.976091i \(-0.569745\pi\)
−0.217361 + 0.976091i \(0.569745\pi\)
\(788\) 16.6918 0.594622
\(789\) −7.72765 −0.275112
\(790\) 9.59574 0.341401
\(791\) −22.1956 −0.789184
\(792\) −4.44916 −0.158094
\(793\) −8.81114 −0.312893
\(794\) 3.86348 0.137110
\(795\) 0.0661264 0.00234526
\(796\) 10.0975 0.357897
\(797\) −26.2616 −0.930232 −0.465116 0.885250i \(-0.653987\pi\)
−0.465116 + 0.885250i \(0.653987\pi\)
\(798\) −19.2990 −0.683177
\(799\) −52.4554 −1.85574
\(800\) −24.1880 −0.855175
\(801\) −34.3134 −1.21240
\(802\) −17.8422 −0.630031
\(803\) 4.27603 0.150898
\(804\) −17.0020 −0.599613
\(805\) −1.75743 −0.0619414
\(806\) 9.62509 0.339029
\(807\) 3.90709 0.137536
\(808\) 32.6730 1.14943
\(809\) −23.3633 −0.821408 −0.410704 0.911769i \(-0.634717\pi\)
−0.410704 + 0.911769i \(0.634717\pi\)
\(810\) 11.2346 0.394743
\(811\) 31.0247 1.08942 0.544712 0.838623i \(-0.316639\pi\)
0.544712 + 0.838623i \(0.316639\pi\)
\(812\) −17.4220 −0.611393
\(813\) 2.20813 0.0774425
\(814\) −3.50375 −0.122806
\(815\) −1.87107 −0.0655406
\(816\) 0.673277 0.0235694
\(817\) −16.5199 −0.577958
\(818\) −48.6057 −1.69946
\(819\) −5.30387 −0.185332
\(820\) −21.1403 −0.738253
\(821\) 30.2399 1.05538 0.527689 0.849437i \(-0.323059\pi\)
0.527689 + 0.849437i \(0.323059\pi\)
\(822\) −17.9183 −0.624972
\(823\) −29.6483 −1.03347 −0.516737 0.856144i \(-0.672853\pi\)
−0.516737 + 0.856144i \(0.672853\pi\)
\(824\) −49.6223 −1.72868
\(825\) 1.08870 0.0379037
\(826\) 55.6184 1.93521
\(827\) 0.638474 0.0222019 0.0111010 0.999938i \(-0.496466\pi\)
0.0111010 + 0.999938i \(0.496466\pi\)
\(828\) −9.22685 −0.320655
\(829\) 29.4268 1.02204 0.511018 0.859570i \(-0.329268\pi\)
0.511018 + 0.859570i \(0.329268\pi\)
\(830\) −2.88886 −0.100274
\(831\) 4.26258 0.147867
\(832\) −9.36124 −0.324543
\(833\) −1.31667 −0.0456197
\(834\) 13.7860 0.477372
\(835\) −1.05720 −0.0365858
\(836\) −12.5737 −0.434870
\(837\) 14.9603 0.517102
\(838\) 17.8516 0.616675
\(839\) −52.5348 −1.81370 −0.906851 0.421452i \(-0.861521\pi\)
−0.906851 + 0.421452i \(0.861521\pi\)
\(840\) 2.36671 0.0816593
\(841\) −24.8674 −0.857497
\(842\) 6.83888 0.235683
\(843\) −11.8707 −0.408848
\(844\) −41.7221 −1.43613
\(845\) 8.43355 0.290123
\(846\) −64.2201 −2.20793
\(847\) −27.8426 −0.956683
\(848\) −0.0616741 −0.00211790
\(849\) −6.99574 −0.240093
\(850\) 54.9900 1.88614
\(851\) −2.86077 −0.0980659
\(852\) 12.1299 0.415562
\(853\) −2.68199 −0.0918294 −0.0459147 0.998945i \(-0.514620\pi\)
−0.0459147 + 0.998945i \(0.514620\pi\)
\(854\) 72.1957 2.47049
\(855\) 13.5548 0.463565
\(856\) −31.1904 −1.06606
\(857\) −11.6838 −0.399111 −0.199556 0.979887i \(-0.563950\pi\)
−0.199556 + 0.979887i \(0.563950\pi\)
\(858\) 0.402676 0.0137471
\(859\) 4.29914 0.146685 0.0733424 0.997307i \(-0.476633\pi\)
0.0733424 + 0.997307i \(0.476633\pi\)
\(860\) 5.14570 0.175467
\(861\) 11.0873 0.377853
\(862\) −86.4370 −2.94406
\(863\) −40.9437 −1.39374 −0.696870 0.717197i \(-0.745425\pi\)
−0.696870 + 0.717197i \(0.745425\pi\)
\(864\) −13.9053 −0.473069
\(865\) −8.73530 −0.297009
\(866\) −52.0172 −1.76762
\(867\) 4.80105 0.163052
\(868\) −49.0975 −1.66648
\(869\) −3.27882 −0.111227
\(870\) −1.42591 −0.0483430
\(871\) −8.35103 −0.282964
\(872\) 55.0688 1.86487
\(873\) −18.5409 −0.627514
\(874\) −16.4906 −0.557802
\(875\) 16.7701 0.566934
\(876\) −11.9422 −0.403488
\(877\) 15.8310 0.534576 0.267288 0.963617i \(-0.413872\pi\)
0.267288 + 0.963617i \(0.413872\pi\)
\(878\) −7.98947 −0.269632
\(879\) −11.9811 −0.404112
\(880\) 0.102289 0.00344815
\(881\) 16.2842 0.548629 0.274315 0.961640i \(-0.411549\pi\)
0.274315 + 0.961640i \(0.411549\pi\)
\(882\) −1.61197 −0.0542778
\(883\) 36.9930 1.24491 0.622457 0.782654i \(-0.286135\pi\)
0.622457 + 0.782654i \(0.286135\pi\)
\(884\) 12.6621 0.425873
\(885\) 2.83393 0.0952614
\(886\) −66.3973 −2.23066
\(887\) −24.7479 −0.830955 −0.415477 0.909604i \(-0.636385\pi\)
−0.415477 + 0.909604i \(0.636385\pi\)
\(888\) 3.85256 0.129283
\(889\) −4.86938 −0.163314
\(890\) 19.1022 0.640306
\(891\) −3.83881 −0.128605
\(892\) 23.8438 0.798351
\(893\) −71.4544 −2.39113
\(894\) 11.3418 0.379327
\(895\) −2.60046 −0.0869238
\(896\) 49.0347 1.63813
\(897\) 0.328780 0.0109776
\(898\) −81.7544 −2.72818
\(899\) 11.6461 0.388420
\(900\) 41.9121 1.39707
\(901\) −1.14127 −0.0380213
\(902\) 11.6032 0.386343
\(903\) −2.69871 −0.0898074
\(904\) 25.5408 0.849474
\(905\) 13.5414 0.450132
\(906\) −7.47225 −0.248249
\(907\) −23.6237 −0.784412 −0.392206 0.919877i \(-0.628288\pi\)
−0.392206 + 0.919877i \(0.628288\pi\)
\(908\) 67.0857 2.22632
\(909\) 30.5694 1.01392
\(910\) 2.95265 0.0978794
\(911\) −44.0244 −1.45859 −0.729297 0.684197i \(-0.760153\pi\)
−0.729297 + 0.684197i \(0.760153\pi\)
\(912\) 0.917134 0.0303693
\(913\) 0.987111 0.0326686
\(914\) −6.16697 −0.203985
\(915\) 3.67859 0.121611
\(916\) −6.91769 −0.228567
\(917\) −8.31326 −0.274528
\(918\) 31.6129 1.04338
\(919\) −5.00612 −0.165137 −0.0825683 0.996585i \(-0.526312\pi\)
−0.0825683 + 0.996585i \(0.526312\pi\)
\(920\) 2.02230 0.0666734
\(921\) −7.78163 −0.256413
\(922\) 14.6154 0.481333
\(923\) 5.95795 0.196108
\(924\) −2.05405 −0.0675733
\(925\) 12.9948 0.427266
\(926\) 91.2622 2.99906
\(927\) −46.4274 −1.52488
\(928\) −10.8249 −0.355345
\(929\) 23.4320 0.768778 0.384389 0.923171i \(-0.374412\pi\)
0.384389 + 0.923171i \(0.374412\pi\)
\(930\) −4.01841 −0.131769
\(931\) −1.79355 −0.0587813
\(932\) −59.4505 −1.94737
\(933\) −1.72666 −0.0565282
\(934\) −85.6870 −2.80376
\(935\) 1.89284 0.0619025
\(936\) 6.10324 0.199491
\(937\) −49.4856 −1.61662 −0.808312 0.588755i \(-0.799618\pi\)
−0.808312 + 0.588755i \(0.799618\pi\)
\(938\) 68.4258 2.23418
\(939\) 1.50931 0.0492544
\(940\) 22.2570 0.725942
\(941\) −3.88524 −0.126655 −0.0633277 0.997993i \(-0.520171\pi\)
−0.0633277 + 0.997993i \(0.520171\pi\)
\(942\) 12.4564 0.405851
\(943\) 9.47383 0.308510
\(944\) −2.64312 −0.0860262
\(945\) 4.58930 0.149290
\(946\) −2.82428 −0.0918254
\(947\) 44.5798 1.44865 0.724325 0.689459i \(-0.242152\pi\)
0.724325 + 0.689459i \(0.242152\pi\)
\(948\) 9.15714 0.297410
\(949\) −5.86575 −0.190410
\(950\) 74.9070 2.43030
\(951\) 0.501119 0.0162499
\(952\) −40.8469 −1.32386
\(953\) −42.7096 −1.38350 −0.691750 0.722137i \(-0.743160\pi\)
−0.691750 + 0.722137i \(0.743160\pi\)
\(954\) −1.39724 −0.0452372
\(955\) 17.3830 0.562500
\(956\) −4.08625 −0.132159
\(957\) 0.487229 0.0157499
\(958\) 9.05892 0.292681
\(959\) 44.8944 1.44972
\(960\) 3.90826 0.126138
\(961\) 1.82032 0.0587199
\(962\) 4.80636 0.154963
\(963\) −29.1822 −0.940383
\(964\) 61.7607 1.98918
\(965\) −7.88713 −0.253896
\(966\) −2.69392 −0.0866755
\(967\) −53.1748 −1.70999 −0.854993 0.518639i \(-0.826439\pi\)
−0.854993 + 0.518639i \(0.826439\pi\)
\(968\) 32.0389 1.02977
\(969\) 16.9714 0.545201
\(970\) 10.3217 0.331409
\(971\) 30.7375 0.986415 0.493207 0.869912i \(-0.335824\pi\)
0.493207 + 0.869912i \(0.335824\pi\)
\(972\) 36.5637 1.17278
\(973\) −34.5411 −1.10734
\(974\) 83.6855 2.68146
\(975\) −1.49345 −0.0478288
\(976\) −3.43091 −0.109821
\(977\) −38.4939 −1.23153 −0.615764 0.787930i \(-0.711153\pi\)
−0.615764 + 0.787930i \(0.711153\pi\)
\(978\) −2.86811 −0.0917119
\(979\) −6.52713 −0.208608
\(980\) 0.558664 0.0178459
\(981\) 51.5232 1.64501
\(982\) 99.4304 3.17295
\(983\) −17.0256 −0.543034 −0.271517 0.962434i \(-0.587525\pi\)
−0.271517 + 0.962434i \(0.587525\pi\)
\(984\) −12.7583 −0.406719
\(985\) −3.42291 −0.109063
\(986\) 24.6098 0.783735
\(987\) −11.6729 −0.371552
\(988\) 17.2482 0.548740
\(989\) −2.30599 −0.0733263
\(990\) 2.31737 0.0736507
\(991\) −0.579966 −0.0184232 −0.00921161 0.999958i \(-0.502932\pi\)
−0.00921161 + 0.999958i \(0.502932\pi\)
\(992\) −30.5060 −0.968567
\(993\) 1.01790 0.0323022
\(994\) −48.8176 −1.54840
\(995\) −2.07064 −0.0656438
\(996\) −2.75682 −0.0873531
\(997\) −16.9796 −0.537749 −0.268875 0.963175i \(-0.586652\pi\)
−0.268875 + 0.963175i \(0.586652\pi\)
\(998\) 50.8364 1.60920
\(999\) 7.47051 0.236357
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8027.2.a.c.1.20 143
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.c.1.20 143 1.1 even 1 trivial