Properties

Label 8045.2.a.c.1.18
Level $8045$
Weight $2$
Character 8045.1
Self dual yes
Analytic conductor $64.240$
Analytic rank $1$
Dimension $127$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8045,2,Mod(1,8045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8045, 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("8045.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8045 = 5 \cdot 1609 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8045.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: \(64.2396484261\)
Analytic rank: \(1\)
Dimension: \(127\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.26786 q^{2} -1.17957 q^{3} +3.14318 q^{4} +1.00000 q^{5} +2.67510 q^{6} +2.15242 q^{7} -2.59257 q^{8} -1.60862 q^{9} +O(q^{10})\) \(q-2.26786 q^{2} -1.17957 q^{3} +3.14318 q^{4} +1.00000 q^{5} +2.67510 q^{6} +2.15242 q^{7} -2.59257 q^{8} -1.60862 q^{9} -2.26786 q^{10} +2.67641 q^{11} -3.70760 q^{12} -0.871351 q^{13} -4.88139 q^{14} -1.17957 q^{15} -0.406787 q^{16} +1.87569 q^{17} +3.64811 q^{18} +2.38854 q^{19} +3.14318 q^{20} -2.53893 q^{21} -6.06972 q^{22} -6.26628 q^{23} +3.05811 q^{24} +1.00000 q^{25} +1.97610 q^{26} +5.43618 q^{27} +6.76545 q^{28} -4.67773 q^{29} +2.67510 q^{30} -1.14119 q^{31} +6.10767 q^{32} -3.15701 q^{33} -4.25379 q^{34} +2.15242 q^{35} -5.05617 q^{36} +4.20115 q^{37} -5.41687 q^{38} +1.02782 q^{39} -2.59257 q^{40} +3.21088 q^{41} +5.75793 q^{42} -6.74241 q^{43} +8.41243 q^{44} -1.60862 q^{45} +14.2110 q^{46} -3.44792 q^{47} +0.479833 q^{48} -2.36708 q^{49} -2.26786 q^{50} -2.21250 q^{51} -2.73881 q^{52} +2.67159 q^{53} -12.3285 q^{54} +2.67641 q^{55} -5.58029 q^{56} -2.81745 q^{57} +10.6084 q^{58} +10.8214 q^{59} -3.70760 q^{60} +8.70416 q^{61} +2.58806 q^{62} -3.46242 q^{63} -13.0377 q^{64} -0.871351 q^{65} +7.15965 q^{66} -4.63129 q^{67} +5.89562 q^{68} +7.39151 q^{69} -4.88139 q^{70} -8.76413 q^{71} +4.17044 q^{72} -7.75806 q^{73} -9.52762 q^{74} -1.17957 q^{75} +7.50760 q^{76} +5.76076 q^{77} -2.33095 q^{78} -1.66908 q^{79} -0.406787 q^{80} -1.58650 q^{81} -7.28181 q^{82} -3.48575 q^{83} -7.98031 q^{84} +1.87569 q^{85} +15.2908 q^{86} +5.51770 q^{87} -6.93877 q^{88} -1.89909 q^{89} +3.64811 q^{90} -1.87552 q^{91} -19.6960 q^{92} +1.34611 q^{93} +7.81940 q^{94} +2.38854 q^{95} -7.20442 q^{96} -11.7240 q^{97} +5.36820 q^{98} -4.30532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 127 q - 20 q^{2} - 31 q^{3} + 116 q^{4} + 127 q^{5} - 17 q^{6} - 63 q^{7} - 57 q^{8} + 122 q^{9} - 20 q^{10} - 32 q^{11} - 65 q^{12} - 49 q^{13} - 4 q^{14} - 31 q^{15} + 98 q^{16} - 53 q^{17} - 60 q^{18} - 126 q^{19} + 116 q^{20} - 24 q^{21} - 46 q^{22} - 121 q^{23} - 51 q^{24} + 127 q^{25} - 9 q^{26} - 112 q^{27} - 123 q^{28} - 6 q^{29} - 17 q^{30} - 54 q^{31} - 119 q^{32} - 57 q^{33} - 53 q^{34} - 63 q^{35} + 133 q^{36} - 61 q^{37} - 27 q^{38} - 33 q^{39} - 57 q^{40} - 8 q^{41} - 46 q^{42} - 208 q^{43} - 54 q^{44} + 122 q^{45} - 34 q^{46} - 116 q^{47} - 106 q^{48} + 110 q^{49} - 20 q^{50} - 54 q^{51} - 142 q^{52} - 60 q^{53} - 62 q^{54} - 32 q^{55} + 33 q^{56} - 56 q^{57} - 87 q^{58} - 53 q^{59} - 65 q^{60} - 76 q^{61} - 84 q^{62} - 215 q^{63} + 67 q^{64} - 49 q^{65} + 9 q^{66} - 145 q^{67} - 133 q^{68} + q^{69} - 4 q^{70} - 4 q^{71} - 167 q^{72} - 155 q^{73} - 14 q^{74} - 31 q^{75} - 199 q^{76} - 97 q^{77} - 24 q^{78} - 73 q^{79} + 98 q^{80} + 127 q^{81} - 69 q^{82} - 225 q^{83} - 59 q^{84} - 53 q^{85} + 30 q^{86} - 179 q^{87} - 119 q^{88} - 25 q^{89} - 60 q^{90} - 160 q^{91} - 188 q^{92} - 44 q^{93} - 32 q^{94} - 126 q^{95} - 43 q^{96} - 72 q^{97} - 111 q^{98} - 141 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26786 −1.60362 −0.801809 0.597581i \(-0.796129\pi\)
−0.801809 + 0.597581i \(0.796129\pi\)
\(3\) −1.17957 −0.681025 −0.340512 0.940240i \(-0.610601\pi\)
−0.340512 + 0.940240i \(0.610601\pi\)
\(4\) 3.14318 1.57159
\(5\) 1.00000 0.447214
\(6\) 2.67510 1.09210
\(7\) 2.15242 0.813539 0.406770 0.913531i \(-0.366655\pi\)
0.406770 + 0.913531i \(0.366655\pi\)
\(8\) −2.59257 −0.916610
\(9\) −1.60862 −0.536205
\(10\) −2.26786 −0.717160
\(11\) 2.67641 0.806968 0.403484 0.914987i \(-0.367799\pi\)
0.403484 + 0.914987i \(0.367799\pi\)
\(12\) −3.70760 −1.07029
\(13\) −0.871351 −0.241669 −0.120835 0.992673i \(-0.538557\pi\)
−0.120835 + 0.992673i \(0.538557\pi\)
\(14\) −4.88139 −1.30461
\(15\) −1.17957 −0.304563
\(16\) −0.406787 −0.101697
\(17\) 1.87569 0.454921 0.227461 0.973787i \(-0.426958\pi\)
0.227461 + 0.973787i \(0.426958\pi\)
\(18\) 3.64811 0.859868
\(19\) 2.38854 0.547968 0.273984 0.961734i \(-0.411658\pi\)
0.273984 + 0.961734i \(0.411658\pi\)
\(20\) 3.14318 0.702836
\(21\) −2.53893 −0.554040
\(22\) −6.06972 −1.29407
\(23\) −6.26628 −1.30661 −0.653305 0.757095i \(-0.726618\pi\)
−0.653305 + 0.757095i \(0.726618\pi\)
\(24\) 3.05811 0.624234
\(25\) 1.00000 0.200000
\(26\) 1.97610 0.387545
\(27\) 5.43618 1.04619
\(28\) 6.76545 1.27855
\(29\) −4.67773 −0.868632 −0.434316 0.900761i \(-0.643010\pi\)
−0.434316 + 0.900761i \(0.643010\pi\)
\(30\) 2.67510 0.488403
\(31\) −1.14119 −0.204964 −0.102482 0.994735i \(-0.532678\pi\)
−0.102482 + 0.994735i \(0.532678\pi\)
\(32\) 6.10767 1.07969
\(33\) −3.15701 −0.549565
\(34\) −4.25379 −0.729519
\(35\) 2.15242 0.363826
\(36\) −5.05617 −0.842695
\(37\) 4.20115 0.690665 0.345333 0.938480i \(-0.387766\pi\)
0.345333 + 0.938480i \(0.387766\pi\)
\(38\) −5.41687 −0.878732
\(39\) 1.02782 0.164583
\(40\) −2.59257 −0.409921
\(41\) 3.21088 0.501455 0.250727 0.968058i \(-0.419330\pi\)
0.250727 + 0.968058i \(0.419330\pi\)
\(42\) 5.75793 0.888468
\(43\) −6.74241 −1.02821 −0.514104 0.857728i \(-0.671876\pi\)
−0.514104 + 0.857728i \(0.671876\pi\)
\(44\) 8.41243 1.26822
\(45\) −1.60862 −0.239798
\(46\) 14.2110 2.09530
\(47\) −3.44792 −0.502931 −0.251466 0.967866i \(-0.580913\pi\)
−0.251466 + 0.967866i \(0.580913\pi\)
\(48\) 0.479833 0.0692580
\(49\) −2.36708 −0.338154
\(50\) −2.26786 −0.320724
\(51\) −2.21250 −0.309812
\(52\) −2.73881 −0.379805
\(53\) 2.67159 0.366971 0.183485 0.983022i \(-0.441262\pi\)
0.183485 + 0.983022i \(0.441262\pi\)
\(54\) −12.3285 −1.67769
\(55\) 2.67641 0.360887
\(56\) −5.58029 −0.745698
\(57\) −2.81745 −0.373180
\(58\) 10.6084 1.39295
\(59\) 10.8214 1.40882 0.704410 0.709793i \(-0.251212\pi\)
0.704410 + 0.709793i \(0.251212\pi\)
\(60\) −3.70760 −0.478649
\(61\) 8.70416 1.11445 0.557226 0.830361i \(-0.311866\pi\)
0.557226 + 0.830361i \(0.311866\pi\)
\(62\) 2.58806 0.328684
\(63\) −3.46242 −0.436224
\(64\) −13.0377 −1.62972
\(65\) −0.871351 −0.108078
\(66\) 7.15965 0.881292
\(67\) −4.63129 −0.565802 −0.282901 0.959149i \(-0.591297\pi\)
−0.282901 + 0.959149i \(0.591297\pi\)
\(68\) 5.89562 0.714949
\(69\) 7.39151 0.889834
\(70\) −4.88139 −0.583437
\(71\) −8.76413 −1.04011 −0.520056 0.854132i \(-0.674089\pi\)
−0.520056 + 0.854132i \(0.674089\pi\)
\(72\) 4.17044 0.491491
\(73\) −7.75806 −0.908012 −0.454006 0.890999i \(-0.650006\pi\)
−0.454006 + 0.890999i \(0.650006\pi\)
\(74\) −9.52762 −1.10756
\(75\) −1.17957 −0.136205
\(76\) 7.50760 0.861181
\(77\) 5.76076 0.656500
\(78\) −2.33095 −0.263928
\(79\) −1.66908 −0.187786 −0.0938928 0.995582i \(-0.529931\pi\)
−0.0938928 + 0.995582i \(0.529931\pi\)
\(80\) −0.406787 −0.0454802
\(81\) −1.58650 −0.176278
\(82\) −7.28181 −0.804142
\(83\) −3.48575 −0.382610 −0.191305 0.981531i \(-0.561272\pi\)
−0.191305 + 0.981531i \(0.561272\pi\)
\(84\) −7.98031 −0.870723
\(85\) 1.87569 0.203447
\(86\) 15.2908 1.64885
\(87\) 5.51770 0.591560
\(88\) −6.93877 −0.739675
\(89\) −1.89909 −0.201303 −0.100651 0.994922i \(-0.532093\pi\)
−0.100651 + 0.994922i \(0.532093\pi\)
\(90\) 3.64811 0.384545
\(91\) −1.87552 −0.196607
\(92\) −19.6960 −2.05345
\(93\) 1.34611 0.139585
\(94\) 7.81940 0.806509
\(95\) 2.38854 0.245059
\(96\) −7.20442 −0.735298
\(97\) −11.7240 −1.19039 −0.595196 0.803581i \(-0.702926\pi\)
−0.595196 + 0.803581i \(0.702926\pi\)
\(98\) 5.36820 0.542270
\(99\) −4.30532 −0.432701
\(100\) 3.14318 0.314318
\(101\) 5.78568 0.575696 0.287848 0.957676i \(-0.407060\pi\)
0.287848 + 0.957676i \(0.407060\pi\)
\(102\) 5.01764 0.496821
\(103\) −19.2652 −1.89826 −0.949129 0.314887i \(-0.898033\pi\)
−0.949129 + 0.314887i \(0.898033\pi\)
\(104\) 2.25904 0.221517
\(105\) −2.53893 −0.247774
\(106\) −6.05878 −0.588480
\(107\) 12.7793 1.23542 0.617709 0.786407i \(-0.288061\pi\)
0.617709 + 0.786407i \(0.288061\pi\)
\(108\) 17.0869 1.64419
\(109\) 12.8600 1.23177 0.615883 0.787838i \(-0.288799\pi\)
0.615883 + 0.787838i \(0.288799\pi\)
\(110\) −6.06972 −0.578725
\(111\) −4.95555 −0.470360
\(112\) −0.875577 −0.0827343
\(113\) −17.0935 −1.60802 −0.804008 0.594618i \(-0.797303\pi\)
−0.804008 + 0.594618i \(0.797303\pi\)
\(114\) 6.38957 0.598438
\(115\) −6.26628 −0.584334
\(116\) −14.7029 −1.36513
\(117\) 1.40167 0.129584
\(118\) −24.5413 −2.25921
\(119\) 4.03727 0.370096
\(120\) 3.05811 0.279166
\(121\) −3.83683 −0.348803
\(122\) −19.7398 −1.78716
\(123\) −3.78745 −0.341503
\(124\) −3.58697 −0.322119
\(125\) 1.00000 0.0894427
\(126\) 7.85228 0.699537
\(127\) 0.0825097 0.00732155 0.00366078 0.999993i \(-0.498835\pi\)
0.00366078 + 0.999993i \(0.498835\pi\)
\(128\) 17.3524 1.53375
\(129\) 7.95314 0.700235
\(130\) 1.97610 0.173315
\(131\) 14.3859 1.25690 0.628451 0.777849i \(-0.283689\pi\)
0.628451 + 0.777849i \(0.283689\pi\)
\(132\) −9.92305 −0.863690
\(133\) 5.14114 0.445794
\(134\) 10.5031 0.907330
\(135\) 5.43618 0.467872
\(136\) −4.86284 −0.416985
\(137\) 0.499890 0.0427085 0.0213542 0.999772i \(-0.493202\pi\)
0.0213542 + 0.999772i \(0.493202\pi\)
\(138\) −16.7629 −1.42695
\(139\) 2.29988 0.195073 0.0975367 0.995232i \(-0.468904\pi\)
0.0975367 + 0.995232i \(0.468904\pi\)
\(140\) 6.76545 0.571785
\(141\) 4.06706 0.342509
\(142\) 19.8758 1.66794
\(143\) −2.33209 −0.195019
\(144\) 0.654364 0.0545303
\(145\) −4.67773 −0.388464
\(146\) 17.5942 1.45610
\(147\) 2.79213 0.230291
\(148\) 13.2050 1.08544
\(149\) −19.1682 −1.57032 −0.785158 0.619295i \(-0.787418\pi\)
−0.785158 + 0.619295i \(0.787418\pi\)
\(150\) 2.67510 0.218421
\(151\) −23.8297 −1.93923 −0.969615 0.244636i \(-0.921332\pi\)
−0.969615 + 0.244636i \(0.921332\pi\)
\(152\) −6.19244 −0.502274
\(153\) −3.01726 −0.243931
\(154\) −13.0646 −1.05277
\(155\) −1.14119 −0.0916626
\(156\) 3.23062 0.258657
\(157\) −2.47485 −0.197515 −0.0987574 0.995112i \(-0.531487\pi\)
−0.0987574 + 0.995112i \(0.531487\pi\)
\(158\) 3.78522 0.301136
\(159\) −3.15132 −0.249916
\(160\) 6.10767 0.482853
\(161\) −13.4877 −1.06298
\(162\) 3.59797 0.282683
\(163\) 13.9411 1.09195 0.545977 0.837800i \(-0.316159\pi\)
0.545977 + 0.837800i \(0.316159\pi\)
\(164\) 10.0924 0.788081
\(165\) −3.15701 −0.245773
\(166\) 7.90517 0.613561
\(167\) −10.1364 −0.784377 −0.392188 0.919885i \(-0.628282\pi\)
−0.392188 + 0.919885i \(0.628282\pi\)
\(168\) 6.58234 0.507839
\(169\) −12.2407 −0.941596
\(170\) −4.25379 −0.326251
\(171\) −3.84224 −0.293824
\(172\) −21.1926 −1.61592
\(173\) 8.92803 0.678786 0.339393 0.940645i \(-0.389778\pi\)
0.339393 + 0.940645i \(0.389778\pi\)
\(174\) −12.5134 −0.948635
\(175\) 2.15242 0.162708
\(176\) −1.08873 −0.0820660
\(177\) −12.7645 −0.959441
\(178\) 4.30686 0.322813
\(179\) −7.71860 −0.576915 −0.288458 0.957493i \(-0.593142\pi\)
−0.288458 + 0.957493i \(0.593142\pi\)
\(180\) −5.05617 −0.376865
\(181\) −2.08498 −0.154976 −0.0774878 0.996993i \(-0.524690\pi\)
−0.0774878 + 0.996993i \(0.524690\pi\)
\(182\) 4.25340 0.315283
\(183\) −10.2672 −0.758970
\(184\) 16.2457 1.19765
\(185\) 4.20115 0.308875
\(186\) −3.05279 −0.223842
\(187\) 5.02011 0.367107
\(188\) −10.8374 −0.790401
\(189\) 11.7010 0.851119
\(190\) −5.41687 −0.392981
\(191\) −20.8169 −1.50626 −0.753129 0.657873i \(-0.771456\pi\)
−0.753129 + 0.657873i \(0.771456\pi\)
\(192\) 15.3789 1.10988
\(193\) −14.0844 −1.01382 −0.506909 0.862000i \(-0.669212\pi\)
−0.506909 + 0.862000i \(0.669212\pi\)
\(194\) 26.5884 1.90893
\(195\) 1.02782 0.0736037
\(196\) −7.44015 −0.531440
\(197\) −26.7784 −1.90788 −0.953942 0.299991i \(-0.903016\pi\)
−0.953942 + 0.299991i \(0.903016\pi\)
\(198\) 9.76385 0.693886
\(199\) 26.5851 1.88457 0.942284 0.334816i \(-0.108674\pi\)
0.942284 + 0.334816i \(0.108674\pi\)
\(200\) −2.59257 −0.183322
\(201\) 5.46293 0.385325
\(202\) −13.1211 −0.923197
\(203\) −10.0684 −0.706666
\(204\) −6.95429 −0.486898
\(205\) 3.21088 0.224257
\(206\) 43.6908 3.04408
\(207\) 10.0800 0.700612
\(208\) 0.354454 0.0245770
\(209\) 6.39271 0.442193
\(210\) 5.75793 0.397335
\(211\) −6.53514 −0.449898 −0.224949 0.974371i \(-0.572222\pi\)
−0.224949 + 0.974371i \(0.572222\pi\)
\(212\) 8.39727 0.576727
\(213\) 10.3379 0.708341
\(214\) −28.9815 −1.98114
\(215\) −6.74241 −0.459829
\(216\) −14.0937 −0.958952
\(217\) −2.45632 −0.166746
\(218\) −29.1647 −1.97528
\(219\) 9.15117 0.618379
\(220\) 8.41243 0.567166
\(221\) −1.63438 −0.109940
\(222\) 11.2385 0.754278
\(223\) −25.5269 −1.70941 −0.854703 0.519118i \(-0.826260\pi\)
−0.854703 + 0.519118i \(0.826260\pi\)
\(224\) 13.1463 0.878372
\(225\) −1.60862 −0.107241
\(226\) 38.7655 2.57864
\(227\) 18.7251 1.24283 0.621413 0.783483i \(-0.286559\pi\)
0.621413 + 0.783483i \(0.286559\pi\)
\(228\) −8.85574 −0.586486
\(229\) 6.77749 0.447869 0.223935 0.974604i \(-0.428110\pi\)
0.223935 + 0.974604i \(0.428110\pi\)
\(230\) 14.2110 0.937048
\(231\) −6.79522 −0.447093
\(232\) 12.1273 0.796197
\(233\) 18.7073 1.22556 0.612778 0.790255i \(-0.290052\pi\)
0.612778 + 0.790255i \(0.290052\pi\)
\(234\) −3.17879 −0.207804
\(235\) −3.44792 −0.224918
\(236\) 34.0134 2.21409
\(237\) 1.96879 0.127887
\(238\) −9.15596 −0.593492
\(239\) 17.9729 1.16257 0.581284 0.813701i \(-0.302551\pi\)
0.581284 + 0.813701i \(0.302551\pi\)
\(240\) 0.479833 0.0309731
\(241\) 8.93184 0.575350 0.287675 0.957728i \(-0.407118\pi\)
0.287675 + 0.957728i \(0.407118\pi\)
\(242\) 8.70138 0.559346
\(243\) −14.4372 −0.926144
\(244\) 27.3587 1.75146
\(245\) −2.36708 −0.151227
\(246\) 8.58940 0.547640
\(247\) −2.08126 −0.132427
\(248\) 2.95861 0.187872
\(249\) 4.11168 0.260567
\(250\) −2.26786 −0.143432
\(251\) 26.6149 1.67992 0.839959 0.542650i \(-0.182579\pi\)
0.839959 + 0.542650i \(0.182579\pi\)
\(252\) −10.8830 −0.685565
\(253\) −16.7711 −1.05439
\(254\) −0.187120 −0.0117410
\(255\) −2.21250 −0.138552
\(256\) −13.2773 −0.829832
\(257\) −29.3850 −1.83299 −0.916494 0.400049i \(-0.868993\pi\)
−0.916494 + 0.400049i \(0.868993\pi\)
\(258\) −18.0366 −1.12291
\(259\) 9.04266 0.561883
\(260\) −2.73881 −0.169854
\(261\) 7.52467 0.465765
\(262\) −32.6252 −2.01559
\(263\) −21.1468 −1.30397 −0.651985 0.758232i \(-0.726063\pi\)
−0.651985 + 0.758232i \(0.726063\pi\)
\(264\) 8.18476 0.503737
\(265\) 2.67159 0.164114
\(266\) −11.6594 −0.714883
\(267\) 2.24011 0.137092
\(268\) −14.5570 −0.889209
\(269\) 6.64167 0.404950 0.202475 0.979287i \(-0.435102\pi\)
0.202475 + 0.979287i \(0.435102\pi\)
\(270\) −12.3285 −0.750288
\(271\) 15.0187 0.912319 0.456160 0.889898i \(-0.349225\pi\)
0.456160 + 0.889898i \(0.349225\pi\)
\(272\) −0.763005 −0.0462640
\(273\) 2.21230 0.133895
\(274\) −1.13368 −0.0684880
\(275\) 2.67641 0.161394
\(276\) 23.2328 1.39845
\(277\) −9.85060 −0.591865 −0.295933 0.955209i \(-0.595630\pi\)
−0.295933 + 0.955209i \(0.595630\pi\)
\(278\) −5.21580 −0.312823
\(279\) 1.83574 0.109903
\(280\) −5.58029 −0.333486
\(281\) 27.2213 1.62389 0.811943 0.583736i \(-0.198410\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(282\) −9.22352 −0.549253
\(283\) −3.27407 −0.194623 −0.0973116 0.995254i \(-0.531024\pi\)
−0.0973116 + 0.995254i \(0.531024\pi\)
\(284\) −27.5472 −1.63463
\(285\) −2.81745 −0.166891
\(286\) 5.28885 0.312737
\(287\) 6.91116 0.407953
\(288\) −9.82489 −0.578937
\(289\) −13.4818 −0.793047
\(290\) 10.6084 0.622948
\(291\) 13.8293 0.810686
\(292\) −24.3850 −1.42702
\(293\) 13.1616 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(294\) −6.33216 −0.369299
\(295\) 10.8214 0.630043
\(296\) −10.8918 −0.633071
\(297\) 14.5495 0.844245
\(298\) 43.4707 2.51819
\(299\) 5.46013 0.315768
\(300\) −3.70760 −0.214058
\(301\) −14.5125 −0.836488
\(302\) 54.0423 3.10978
\(303\) −6.82461 −0.392063
\(304\) −0.971627 −0.0557266
\(305\) 8.70416 0.498398
\(306\) 6.84272 0.391172
\(307\) 27.9742 1.59657 0.798285 0.602279i \(-0.205741\pi\)
0.798285 + 0.602279i \(0.205741\pi\)
\(308\) 18.1071 1.03175
\(309\) 22.7247 1.29276
\(310\) 2.58806 0.146992
\(311\) 27.0616 1.53452 0.767261 0.641335i \(-0.221619\pi\)
0.767261 + 0.641335i \(0.221619\pi\)
\(312\) −2.66469 −0.150858
\(313\) −3.07038 −0.173548 −0.0867741 0.996228i \(-0.527656\pi\)
−0.0867741 + 0.996228i \(0.527656\pi\)
\(314\) 5.61261 0.316738
\(315\) −3.46242 −0.195085
\(316\) −5.24620 −0.295122
\(317\) 6.68029 0.375202 0.187601 0.982245i \(-0.439929\pi\)
0.187601 + 0.982245i \(0.439929\pi\)
\(318\) 7.14675 0.400770
\(319\) −12.5195 −0.700958
\(320\) −13.0377 −0.728832
\(321\) −15.0740 −0.841349
\(322\) 30.5881 1.70461
\(323\) 4.48015 0.249282
\(324\) −4.98667 −0.277037
\(325\) −0.871351 −0.0483339
\(326\) −31.6165 −1.75108
\(327\) −15.1693 −0.838863
\(328\) −8.32441 −0.459639
\(329\) −7.42138 −0.409154
\(330\) 7.15965 0.394126
\(331\) −5.37572 −0.295476 −0.147738 0.989027i \(-0.547199\pi\)
−0.147738 + 0.989027i \(0.547199\pi\)
\(332\) −10.9563 −0.601306
\(333\) −6.75805 −0.370339
\(334\) 22.9879 1.25784
\(335\) −4.63129 −0.253034
\(336\) 1.03280 0.0563441
\(337\) 8.61737 0.469418 0.234709 0.972066i \(-0.424586\pi\)
0.234709 + 0.972066i \(0.424586\pi\)
\(338\) 27.7603 1.50996
\(339\) 20.1629 1.09510
\(340\) 5.89562 0.319735
\(341\) −3.05429 −0.165399
\(342\) 8.71366 0.471181
\(343\) −20.1619 −1.08864
\(344\) 17.4802 0.942467
\(345\) 7.39151 0.397946
\(346\) −20.2475 −1.08851
\(347\) −35.2905 −1.89449 −0.947247 0.320505i \(-0.896148\pi\)
−0.947247 + 0.320505i \(0.896148\pi\)
\(348\) 17.3431 0.929689
\(349\) 8.71790 0.466659 0.233329 0.972398i \(-0.425038\pi\)
0.233329 + 0.972398i \(0.425038\pi\)
\(350\) −4.88139 −0.260921
\(351\) −4.73682 −0.252833
\(352\) 16.3466 0.871278
\(353\) −9.15282 −0.487155 −0.243578 0.969881i \(-0.578321\pi\)
−0.243578 + 0.969881i \(0.578321\pi\)
\(354\) 28.9481 1.53858
\(355\) −8.76413 −0.465152
\(356\) −5.96917 −0.316366
\(357\) −4.76224 −0.252044
\(358\) 17.5047 0.925151
\(359\) 27.5872 1.45600 0.727998 0.685579i \(-0.240451\pi\)
0.727998 + 0.685579i \(0.240451\pi\)
\(360\) 4.17044 0.219802
\(361\) −13.2949 −0.699731
\(362\) 4.72844 0.248522
\(363\) 4.52581 0.237543
\(364\) −5.89508 −0.308986
\(365\) −7.75806 −0.406075
\(366\) 23.2844 1.21710
\(367\) −6.96519 −0.363580 −0.181790 0.983337i \(-0.558189\pi\)
−0.181790 + 0.983337i \(0.558189\pi\)
\(368\) 2.54904 0.132878
\(369\) −5.16507 −0.268883
\(370\) −9.52762 −0.495317
\(371\) 5.75038 0.298545
\(372\) 4.23107 0.219371
\(373\) −1.22195 −0.0632701 −0.0316351 0.999499i \(-0.510071\pi\)
−0.0316351 + 0.999499i \(0.510071\pi\)
\(374\) −11.3849 −0.588699
\(375\) −1.17957 −0.0609127
\(376\) 8.93897 0.460992
\(377\) 4.07594 0.209922
\(378\) −26.5361 −1.36487
\(379\) −0.590855 −0.0303502 −0.0151751 0.999885i \(-0.504831\pi\)
−0.0151751 + 0.999885i \(0.504831\pi\)
\(380\) 7.50760 0.385132
\(381\) −0.0973259 −0.00498616
\(382\) 47.2098 2.41546
\(383\) 11.6682 0.596217 0.298109 0.954532i \(-0.403644\pi\)
0.298109 + 0.954532i \(0.403644\pi\)
\(384\) −20.4684 −1.04452
\(385\) 5.76076 0.293596
\(386\) 31.9414 1.62578
\(387\) 10.8460 0.551331
\(388\) −36.8506 −1.87081
\(389\) −20.7143 −1.05026 −0.525129 0.851023i \(-0.675983\pi\)
−0.525129 + 0.851023i \(0.675983\pi\)
\(390\) −2.33095 −0.118032
\(391\) −11.7536 −0.594404
\(392\) 6.13681 0.309956
\(393\) −16.9692 −0.855982
\(394\) 60.7297 3.05952
\(395\) −1.66908 −0.0839803
\(396\) −13.5324 −0.680028
\(397\) 10.2217 0.513013 0.256506 0.966543i \(-0.417429\pi\)
0.256506 + 0.966543i \(0.417429\pi\)
\(398\) −60.2912 −3.02212
\(399\) −6.06433 −0.303596
\(400\) −0.406787 −0.0203393
\(401\) −24.8160 −1.23925 −0.619626 0.784897i \(-0.712716\pi\)
−0.619626 + 0.784897i \(0.712716\pi\)
\(402\) −12.3891 −0.617914
\(403\) 0.994378 0.0495335
\(404\) 18.1854 0.904758
\(405\) −1.58650 −0.0788340
\(406\) 22.8338 1.13322
\(407\) 11.2440 0.557345
\(408\) 5.73606 0.283977
\(409\) 21.5935 1.06773 0.533866 0.845569i \(-0.320739\pi\)
0.533866 + 0.845569i \(0.320739\pi\)
\(410\) −7.28181 −0.359623
\(411\) −0.589655 −0.0290855
\(412\) −60.5540 −2.98328
\(413\) 23.2921 1.14613
\(414\) −22.8601 −1.12351
\(415\) −3.48575 −0.171109
\(416\) −5.32192 −0.260929
\(417\) −2.71287 −0.132850
\(418\) −14.4978 −0.709108
\(419\) 9.24921 0.451853 0.225927 0.974144i \(-0.427459\pi\)
0.225927 + 0.974144i \(0.427459\pi\)
\(420\) −7.98031 −0.389399
\(421\) 16.7295 0.815344 0.407672 0.913128i \(-0.366341\pi\)
0.407672 + 0.913128i \(0.366341\pi\)
\(422\) 14.8208 0.721464
\(423\) 5.54638 0.269674
\(424\) −6.92626 −0.336369
\(425\) 1.87569 0.0909842
\(426\) −23.4449 −1.13591
\(427\) 18.7350 0.906651
\(428\) 40.1675 1.94157
\(429\) 2.75087 0.132813
\(430\) 15.2908 0.737390
\(431\) 2.38773 0.115013 0.0575066 0.998345i \(-0.481685\pi\)
0.0575066 + 0.998345i \(0.481685\pi\)
\(432\) −2.21137 −0.106394
\(433\) −24.0579 −1.15615 −0.578074 0.815984i \(-0.696196\pi\)
−0.578074 + 0.815984i \(0.696196\pi\)
\(434\) 5.57059 0.267397
\(435\) 5.51770 0.264554
\(436\) 40.4213 1.93583
\(437\) −14.9673 −0.715981
\(438\) −20.7535 −0.991643
\(439\) −24.5456 −1.17150 −0.585748 0.810493i \(-0.699199\pi\)
−0.585748 + 0.810493i \(0.699199\pi\)
\(440\) −6.93877 −0.330793
\(441\) 3.80772 0.181320
\(442\) 3.70655 0.176302
\(443\) 27.4866 1.30593 0.652965 0.757388i \(-0.273525\pi\)
0.652965 + 0.757388i \(0.273525\pi\)
\(444\) −15.5762 −0.739213
\(445\) −1.89909 −0.0900254
\(446\) 57.8913 2.74123
\(447\) 22.6102 1.06942
\(448\) −28.0627 −1.32584
\(449\) 0.815687 0.0384946 0.0192473 0.999815i \(-0.493873\pi\)
0.0192473 + 0.999815i \(0.493873\pi\)
\(450\) 3.64811 0.171974
\(451\) 8.59363 0.404658
\(452\) −53.7278 −2.52714
\(453\) 28.1087 1.32066
\(454\) −42.4657 −1.99302
\(455\) −1.87552 −0.0879255
\(456\) 7.30442 0.342061
\(457\) 36.9412 1.72803 0.864017 0.503462i \(-0.167941\pi\)
0.864017 + 0.503462i \(0.167941\pi\)
\(458\) −15.3704 −0.718211
\(459\) 10.1966 0.475936
\(460\) −19.6960 −0.918333
\(461\) −20.5808 −0.958545 −0.479273 0.877666i \(-0.659099\pi\)
−0.479273 + 0.877666i \(0.659099\pi\)
\(462\) 15.4106 0.716966
\(463\) 26.8023 1.24561 0.622804 0.782378i \(-0.285993\pi\)
0.622804 + 0.782378i \(0.285993\pi\)
\(464\) 1.90284 0.0883370
\(465\) 1.34611 0.0624245
\(466\) −42.4255 −1.96532
\(467\) −14.5415 −0.672902 −0.336451 0.941701i \(-0.609227\pi\)
−0.336451 + 0.941701i \(0.609227\pi\)
\(468\) 4.40570 0.203653
\(469\) −9.96849 −0.460302
\(470\) 7.81940 0.360682
\(471\) 2.91926 0.134512
\(472\) −28.0551 −1.29134
\(473\) −18.0455 −0.829731
\(474\) −4.46494 −0.205081
\(475\) 2.38854 0.109594
\(476\) 12.6899 0.581639
\(477\) −4.29756 −0.196772
\(478\) −40.7599 −1.86431
\(479\) 16.1558 0.738176 0.369088 0.929394i \(-0.379670\pi\)
0.369088 + 0.929394i \(0.379670\pi\)
\(480\) −7.20442 −0.328835
\(481\) −3.66068 −0.166913
\(482\) −20.2561 −0.922642
\(483\) 15.9097 0.723914
\(484\) −12.0598 −0.548175
\(485\) −11.7240 −0.532359
\(486\) 32.7414 1.48518
\(487\) 13.5078 0.612098 0.306049 0.952016i \(-0.400993\pi\)
0.306049 + 0.952016i \(0.400993\pi\)
\(488\) −22.5661 −1.02152
\(489\) −16.4445 −0.743647
\(490\) 5.36820 0.242511
\(491\) 0.658614 0.0297228 0.0148614 0.999890i \(-0.495269\pi\)
0.0148614 + 0.999890i \(0.495269\pi\)
\(492\) −11.9046 −0.536703
\(493\) −8.77395 −0.395159
\(494\) 4.71999 0.212363
\(495\) −4.30532 −0.193510
\(496\) 0.464221 0.0208442
\(497\) −18.8641 −0.846171
\(498\) −9.32470 −0.417850
\(499\) −32.4550 −1.45289 −0.726443 0.687226i \(-0.758828\pi\)
−0.726443 + 0.687226i \(0.758828\pi\)
\(500\) 3.14318 0.140567
\(501\) 11.9566 0.534180
\(502\) −60.3588 −2.69395
\(503\) −1.91624 −0.0854411 −0.0427205 0.999087i \(-0.513603\pi\)
−0.0427205 + 0.999087i \(0.513603\pi\)
\(504\) 8.97655 0.399847
\(505\) 5.78568 0.257459
\(506\) 38.0346 1.69084
\(507\) 14.4388 0.641250
\(508\) 0.259343 0.0115065
\(509\) 30.6006 1.35635 0.678174 0.734902i \(-0.262772\pi\)
0.678174 + 0.734902i \(0.262772\pi\)
\(510\) 5.01764 0.222185
\(511\) −16.6986 −0.738703
\(512\) −4.59376 −0.203018
\(513\) 12.9845 0.573281
\(514\) 66.6411 2.93941
\(515\) −19.2652 −0.848927
\(516\) 24.9982 1.10048
\(517\) −9.22805 −0.405849
\(518\) −20.5075 −0.901046
\(519\) −10.5312 −0.462270
\(520\) 2.25904 0.0990652
\(521\) 6.69698 0.293400 0.146700 0.989181i \(-0.453135\pi\)
0.146700 + 0.989181i \(0.453135\pi\)
\(522\) −17.0649 −0.746909
\(523\) 12.7692 0.558358 0.279179 0.960239i \(-0.409938\pi\)
0.279179 + 0.960239i \(0.409938\pi\)
\(524\) 45.2175 1.97533
\(525\) −2.53893 −0.110808
\(526\) 47.9580 2.09107
\(527\) −2.14052 −0.0932424
\(528\) 1.28423 0.0558890
\(529\) 16.2663 0.707230
\(530\) −6.05878 −0.263176
\(531\) −17.4074 −0.755417
\(532\) 16.1595 0.700605
\(533\) −2.79780 −0.121186
\(534\) −5.08024 −0.219844
\(535\) 12.7793 0.552495
\(536\) 12.0069 0.518620
\(537\) 9.10462 0.392893
\(538\) −15.0624 −0.649385
\(539\) −6.33528 −0.272880
\(540\) 17.0869 0.735303
\(541\) 16.8445 0.724201 0.362101 0.932139i \(-0.382060\pi\)
0.362101 + 0.932139i \(0.382060\pi\)
\(542\) −34.0602 −1.46301
\(543\) 2.45938 0.105542
\(544\) 11.4561 0.491175
\(545\) 12.8600 0.550862
\(546\) −5.01718 −0.214716
\(547\) −40.7302 −1.74150 −0.870748 0.491729i \(-0.836365\pi\)
−0.870748 + 0.491729i \(0.836365\pi\)
\(548\) 1.57124 0.0671202
\(549\) −14.0016 −0.597576
\(550\) −6.06972 −0.258814
\(551\) −11.1729 −0.475983
\(552\) −19.1630 −0.815631
\(553\) −3.59255 −0.152771
\(554\) 22.3398 0.949125
\(555\) −4.95555 −0.210351
\(556\) 7.22894 0.306575
\(557\) −12.6720 −0.536929 −0.268465 0.963290i \(-0.586516\pi\)
−0.268465 + 0.963290i \(0.586516\pi\)
\(558\) −4.16319 −0.176242
\(559\) 5.87501 0.248486
\(560\) −0.875577 −0.0369999
\(561\) −5.92157 −0.250009
\(562\) −61.7340 −2.60409
\(563\) −21.7518 −0.916727 −0.458364 0.888765i \(-0.651564\pi\)
−0.458364 + 0.888765i \(0.651564\pi\)
\(564\) 12.7835 0.538283
\(565\) −17.0935 −0.719127
\(566\) 7.42512 0.312101
\(567\) −3.41483 −0.143409
\(568\) 22.7216 0.953376
\(569\) −19.8873 −0.833720 −0.416860 0.908971i \(-0.636869\pi\)
−0.416860 + 0.908971i \(0.636869\pi\)
\(570\) 6.38957 0.267630
\(571\) −6.68180 −0.279625 −0.139812 0.990178i \(-0.544650\pi\)
−0.139812 + 0.990178i \(0.544650\pi\)
\(572\) −7.33018 −0.306490
\(573\) 24.5550 1.02580
\(574\) −15.6735 −0.654201
\(575\) −6.26628 −0.261322
\(576\) 20.9727 0.873864
\(577\) −43.2384 −1.80004 −0.900020 0.435849i \(-0.856448\pi\)
−0.900020 + 0.435849i \(0.856448\pi\)
\(578\) 30.5748 1.27174
\(579\) 16.6135 0.690435
\(580\) −14.7029 −0.610506
\(581\) −7.50280 −0.311268
\(582\) −31.3628 −1.30003
\(583\) 7.15026 0.296133
\(584\) 20.1133 0.832293
\(585\) 1.40167 0.0579519
\(586\) −29.8487 −1.23304
\(587\) 14.9180 0.615731 0.307865 0.951430i \(-0.400385\pi\)
0.307865 + 0.951430i \(0.400385\pi\)
\(588\) 8.77618 0.361923
\(589\) −2.72578 −0.112314
\(590\) −24.5413 −1.01035
\(591\) 31.5870 1.29932
\(592\) −1.70897 −0.0702384
\(593\) 8.39461 0.344725 0.172363 0.985034i \(-0.444860\pi\)
0.172363 + 0.985034i \(0.444860\pi\)
\(594\) −32.9961 −1.35385
\(595\) 4.03727 0.165512
\(596\) −60.2489 −2.46789
\(597\) −31.3590 −1.28344
\(598\) −12.3828 −0.506371
\(599\) 15.0159 0.613532 0.306766 0.951785i \(-0.400753\pi\)
0.306766 + 0.951785i \(0.400753\pi\)
\(600\) 3.05811 0.124847
\(601\) −30.3220 −1.23686 −0.618431 0.785839i \(-0.712231\pi\)
−0.618431 + 0.785839i \(0.712231\pi\)
\(602\) 32.9123 1.34141
\(603\) 7.44997 0.303386
\(604\) −74.9009 −3.04767
\(605\) −3.83683 −0.155989
\(606\) 15.4772 0.628720
\(607\) −24.5095 −0.994808 −0.497404 0.867519i \(-0.665713\pi\)
−0.497404 + 0.867519i \(0.665713\pi\)
\(608\) 14.5884 0.591638
\(609\) 11.8764 0.481257
\(610\) −19.7398 −0.799241
\(611\) 3.00435 0.121543
\(612\) −9.48379 −0.383360
\(613\) −10.6258 −0.429171 −0.214585 0.976705i \(-0.568840\pi\)
−0.214585 + 0.976705i \(0.568840\pi\)
\(614\) −63.4415 −2.56029
\(615\) −3.78745 −0.152725
\(616\) −14.9352 −0.601755
\(617\) −0.813911 −0.0327668 −0.0163834 0.999866i \(-0.505215\pi\)
−0.0163834 + 0.999866i \(0.505215\pi\)
\(618\) −51.5363 −2.07309
\(619\) −23.0166 −0.925114 −0.462557 0.886589i \(-0.653068\pi\)
−0.462557 + 0.886589i \(0.653068\pi\)
\(620\) −3.58697 −0.144056
\(621\) −34.0647 −1.36697
\(622\) −61.3718 −2.46079
\(623\) −4.08764 −0.163768
\(624\) −0.418103 −0.0167375
\(625\) 1.00000 0.0400000
\(626\) 6.96319 0.278305
\(627\) −7.54064 −0.301144
\(628\) −7.77890 −0.310412
\(629\) 7.88005 0.314198
\(630\) 7.85228 0.312842
\(631\) −35.2879 −1.40479 −0.702394 0.711788i \(-0.747886\pi\)
−0.702394 + 0.711788i \(0.747886\pi\)
\(632\) 4.32719 0.172126
\(633\) 7.70866 0.306392
\(634\) −15.1499 −0.601681
\(635\) 0.0825097 0.00327430
\(636\) −9.90516 −0.392765
\(637\) 2.06256 0.0817215
\(638\) 28.3925 1.12407
\(639\) 14.0981 0.557713
\(640\) 17.3524 0.685914
\(641\) 33.2214 1.31217 0.656083 0.754689i \(-0.272212\pi\)
0.656083 + 0.754689i \(0.272212\pi\)
\(642\) 34.1857 1.34920
\(643\) 10.6624 0.420484 0.210242 0.977649i \(-0.432575\pi\)
0.210242 + 0.977649i \(0.432575\pi\)
\(644\) −42.3942 −1.67057
\(645\) 7.95314 0.313155
\(646\) −10.1603 −0.399754
\(647\) −27.5899 −1.08467 −0.542335 0.840162i \(-0.682460\pi\)
−0.542335 + 0.840162i \(0.682460\pi\)
\(648\) 4.11312 0.161578
\(649\) 28.9624 1.13687
\(650\) 1.97610 0.0775090
\(651\) 2.89740 0.113558
\(652\) 43.8195 1.71610
\(653\) 27.0599 1.05893 0.529467 0.848330i \(-0.322392\pi\)
0.529467 + 0.848330i \(0.322392\pi\)
\(654\) 34.4018 1.34522
\(655\) 14.3859 0.562104
\(656\) −1.30614 −0.0509963
\(657\) 12.4797 0.486881
\(658\) 16.8306 0.656127
\(659\) 4.50008 0.175298 0.0876492 0.996151i \(-0.472065\pi\)
0.0876492 + 0.996151i \(0.472065\pi\)
\(660\) −9.92305 −0.386254
\(661\) −23.2858 −0.905714 −0.452857 0.891583i \(-0.649595\pi\)
−0.452857 + 0.891583i \(0.649595\pi\)
\(662\) 12.1914 0.473831
\(663\) 1.92787 0.0748722
\(664\) 9.03702 0.350705
\(665\) 5.14114 0.199365
\(666\) 15.3263 0.593881
\(667\) 29.3119 1.13496
\(668\) −31.8605 −1.23272
\(669\) 30.1107 1.16415
\(670\) 10.5031 0.405770
\(671\) 23.2959 0.899328
\(672\) −15.5069 −0.598193
\(673\) −7.90601 −0.304754 −0.152377 0.988322i \(-0.548693\pi\)
−0.152377 + 0.988322i \(0.548693\pi\)
\(674\) −19.5430 −0.752767
\(675\) 5.43618 0.209239
\(676\) −38.4749 −1.47980
\(677\) 31.5502 1.21257 0.606287 0.795246i \(-0.292658\pi\)
0.606287 + 0.795246i \(0.292658\pi\)
\(678\) −45.7266 −1.75612
\(679\) −25.2350 −0.968430
\(680\) −4.86284 −0.186482
\(681\) −22.0875 −0.846395
\(682\) 6.92670 0.265237
\(683\) −32.0048 −1.22463 −0.612315 0.790614i \(-0.709762\pi\)
−0.612315 + 0.790614i \(0.709762\pi\)
\(684\) −12.0769 −0.461770
\(685\) 0.499890 0.0190998
\(686\) 45.7243 1.74576
\(687\) −7.99452 −0.305010
\(688\) 2.74273 0.104565
\(689\) −2.32789 −0.0886855
\(690\) −16.7629 −0.638153
\(691\) −52.1096 −1.98234 −0.991170 0.132594i \(-0.957669\pi\)
−0.991170 + 0.132594i \(0.957669\pi\)
\(692\) 28.0624 1.06677
\(693\) −9.26686 −0.352019
\(694\) 80.0339 3.03804
\(695\) 2.29988 0.0872395
\(696\) −14.3050 −0.542230
\(697\) 6.02260 0.228122
\(698\) −19.7710 −0.748342
\(699\) −22.0666 −0.834634
\(700\) 6.76545 0.255710
\(701\) 18.5657 0.701218 0.350609 0.936522i \(-0.385975\pi\)
0.350609 + 0.936522i \(0.385975\pi\)
\(702\) 10.7424 0.405447
\(703\) 10.0346 0.378463
\(704\) −34.8943 −1.31513
\(705\) 4.06706 0.153174
\(706\) 20.7573 0.781211
\(707\) 12.4532 0.468352
\(708\) −40.1212 −1.50785
\(709\) −27.5543 −1.03482 −0.517411 0.855737i \(-0.673104\pi\)
−0.517411 + 0.855737i \(0.673104\pi\)
\(710\) 19.8758 0.745926
\(711\) 2.68490 0.100692
\(712\) 4.92351 0.184516
\(713\) 7.15102 0.267808
\(714\) 10.8001 0.404183
\(715\) −2.33209 −0.0872153
\(716\) −24.2609 −0.906673
\(717\) −21.2002 −0.791737
\(718\) −62.5638 −2.33486
\(719\) 3.70636 0.138224 0.0691119 0.997609i \(-0.477983\pi\)
0.0691119 + 0.997609i \(0.477983\pi\)
\(720\) 0.654364 0.0243867
\(721\) −41.4669 −1.54431
\(722\) 30.1509 1.12210
\(723\) −10.5357 −0.391828
\(724\) −6.55347 −0.243558
\(725\) −4.67773 −0.173726
\(726\) −10.2639 −0.380929
\(727\) −24.7897 −0.919399 −0.459699 0.888075i \(-0.652043\pi\)
−0.459699 + 0.888075i \(0.652043\pi\)
\(728\) 4.86240 0.180212
\(729\) 21.7891 0.807005
\(730\) 17.5942 0.651190
\(731\) −12.6467 −0.467754
\(732\) −32.2715 −1.19279
\(733\) −48.2555 −1.78236 −0.891179 0.453651i \(-0.850121\pi\)
−0.891179 + 0.453651i \(0.850121\pi\)
\(734\) 15.7961 0.583043
\(735\) 2.79213 0.102989
\(736\) −38.2724 −1.41074
\(737\) −12.3952 −0.456584
\(738\) 11.7136 0.431185
\(739\) −1.74310 −0.0641210 −0.0320605 0.999486i \(-0.510207\pi\)
−0.0320605 + 0.999486i \(0.510207\pi\)
\(740\) 13.2050 0.485425
\(741\) 2.45499 0.0901862
\(742\) −13.0410 −0.478752
\(743\) 17.9667 0.659136 0.329568 0.944132i \(-0.393097\pi\)
0.329568 + 0.944132i \(0.393097\pi\)
\(744\) −3.48989 −0.127945
\(745\) −19.1682 −0.702267
\(746\) 2.77121 0.101461
\(747\) 5.60723 0.205158
\(748\) 15.7791 0.576941
\(749\) 27.5063 1.00506
\(750\) 2.67510 0.0976807
\(751\) −45.2066 −1.64961 −0.824805 0.565417i \(-0.808715\pi\)
−0.824805 + 0.565417i \(0.808715\pi\)
\(752\) 1.40257 0.0511465
\(753\) −31.3941 −1.14407
\(754\) −9.24366 −0.336634
\(755\) −23.8297 −0.867250
\(756\) 36.7782 1.33761
\(757\) −29.7522 −1.08136 −0.540682 0.841227i \(-0.681834\pi\)
−0.540682 + 0.841227i \(0.681834\pi\)
\(758\) 1.33998 0.0486701
\(759\) 19.7827 0.718067
\(760\) −6.19244 −0.224624
\(761\) −10.7823 −0.390857 −0.195428 0.980718i \(-0.562610\pi\)
−0.195428 + 0.980718i \(0.562610\pi\)
\(762\) 0.220721 0.00799589
\(763\) 27.6802 1.00209
\(764\) −65.4312 −2.36722
\(765\) −3.01726 −0.109089
\(766\) −26.4618 −0.956105
\(767\) −9.42920 −0.340469
\(768\) 15.6615 0.565136
\(769\) 27.5402 0.993123 0.496562 0.868001i \(-0.334596\pi\)
0.496562 + 0.868001i \(0.334596\pi\)
\(770\) −13.0646 −0.470815
\(771\) 34.6617 1.24831
\(772\) −44.2698 −1.59331
\(773\) 25.1433 0.904340 0.452170 0.891932i \(-0.350650\pi\)
0.452170 + 0.891932i \(0.350650\pi\)
\(774\) −24.5971 −0.884124
\(775\) −1.14119 −0.0409928
\(776\) 30.3952 1.09113
\(777\) −10.6664 −0.382656
\(778\) 46.9771 1.68421
\(779\) 7.66931 0.274781
\(780\) 3.23062 0.115675
\(781\) −23.4564 −0.839336
\(782\) 26.6555 0.953197
\(783\) −25.4290 −0.908757
\(784\) 0.962897 0.0343892
\(785\) −2.47485 −0.0883313
\(786\) 38.4837 1.37267
\(787\) −22.0217 −0.784990 −0.392495 0.919754i \(-0.628388\pi\)
−0.392495 + 0.919754i \(0.628388\pi\)
\(788\) −84.1694 −2.99841
\(789\) 24.9442 0.888035
\(790\) 3.78522 0.134672
\(791\) −36.7923 −1.30818
\(792\) 11.1618 0.396618
\(793\) −7.58438 −0.269329
\(794\) −23.1814 −0.822676
\(795\) −3.15132 −0.111766
\(796\) 83.5617 2.96177
\(797\) −8.79230 −0.311439 −0.155720 0.987801i \(-0.549770\pi\)
−0.155720 + 0.987801i \(0.549770\pi\)
\(798\) 13.7530 0.486853
\(799\) −6.46723 −0.228794
\(800\) 6.10767 0.215939
\(801\) 3.05491 0.107940
\(802\) 56.2792 1.98729
\(803\) −20.7637 −0.732737
\(804\) 17.1710 0.605573
\(805\) −13.4877 −0.475378
\(806\) −2.25511 −0.0794328
\(807\) −7.83431 −0.275781
\(808\) −14.9997 −0.527689
\(809\) −44.4529 −1.56288 −0.781441 0.623979i \(-0.785515\pi\)
−0.781441 + 0.623979i \(0.785515\pi\)
\(810\) 3.59797 0.126420
\(811\) 0.974230 0.0342098 0.0171049 0.999854i \(-0.494555\pi\)
0.0171049 + 0.999854i \(0.494555\pi\)
\(812\) −31.6469 −1.11059
\(813\) −17.7156 −0.621312
\(814\) −25.4998 −0.893768
\(815\) 13.9411 0.488336
\(816\) 0.900017 0.0315069
\(817\) −16.1045 −0.563426
\(818\) −48.9711 −1.71223
\(819\) 3.01698 0.105422
\(820\) 10.0924 0.352441
\(821\) −20.7121 −0.722859 −0.361429 0.932399i \(-0.617711\pi\)
−0.361429 + 0.932399i \(0.617711\pi\)
\(822\) 1.33725 0.0466420
\(823\) −56.3089 −1.96281 −0.981403 0.191958i \(-0.938516\pi\)
−0.981403 + 0.191958i \(0.938516\pi\)
\(824\) 49.9463 1.73996
\(825\) −3.15701 −0.109913
\(826\) −52.8232 −1.83795
\(827\) −53.8747 −1.87341 −0.936703 0.350125i \(-0.886139\pi\)
−0.936703 + 0.350125i \(0.886139\pi\)
\(828\) 31.6834 1.10107
\(829\) 31.5772 1.09672 0.548360 0.836242i \(-0.315252\pi\)
0.548360 + 0.836242i \(0.315252\pi\)
\(830\) 7.90517 0.274393
\(831\) 11.6195 0.403075
\(832\) 11.3605 0.393853
\(833\) −4.43990 −0.153833
\(834\) 6.15240 0.213040
\(835\) −10.1364 −0.350784
\(836\) 20.0934 0.694946
\(837\) −6.20372 −0.214432
\(838\) −20.9759 −0.724600
\(839\) 4.52828 0.156334 0.0781668 0.996940i \(-0.475093\pi\)
0.0781668 + 0.996940i \(0.475093\pi\)
\(840\) 6.58234 0.227112
\(841\) −7.11889 −0.245479
\(842\) −37.9401 −1.30750
\(843\) −32.1094 −1.10591
\(844\) −20.5411 −0.707055
\(845\) −12.2407 −0.421095
\(846\) −12.5784 −0.432455
\(847\) −8.25848 −0.283765
\(848\) −1.08677 −0.0373197
\(849\) 3.86199 0.132543
\(850\) −4.25379 −0.145904
\(851\) −26.3256 −0.902431
\(852\) 32.4939 1.11322
\(853\) 45.3894 1.55410 0.777051 0.629438i \(-0.216715\pi\)
0.777051 + 0.629438i \(0.216715\pi\)
\(854\) −42.4883 −1.45392
\(855\) −3.84224 −0.131402
\(856\) −33.1311 −1.13240
\(857\) 20.5039 0.700401 0.350201 0.936675i \(-0.386113\pi\)
0.350201 + 0.936675i \(0.386113\pi\)
\(858\) −6.23857 −0.212981
\(859\) −8.72936 −0.297842 −0.148921 0.988849i \(-0.547580\pi\)
−0.148921 + 0.988849i \(0.547580\pi\)
\(860\) −21.1926 −0.722662
\(861\) −8.15220 −0.277826
\(862\) −5.41504 −0.184437
\(863\) 4.08393 0.139019 0.0695094 0.997581i \(-0.477857\pi\)
0.0695094 + 0.997581i \(0.477857\pi\)
\(864\) 33.2024 1.12957
\(865\) 8.92803 0.303562
\(866\) 54.5599 1.85402
\(867\) 15.9027 0.540084
\(868\) −7.72066 −0.262056
\(869\) −4.46713 −0.151537
\(870\) −12.5134 −0.424243
\(871\) 4.03548 0.136737
\(872\) −33.3404 −1.12905
\(873\) 18.8594 0.638295
\(874\) 33.9436 1.14816
\(875\) 2.15242 0.0727651
\(876\) 28.7638 0.971837
\(877\) 27.5213 0.929330 0.464665 0.885487i \(-0.346175\pi\)
0.464665 + 0.885487i \(0.346175\pi\)
\(878\) 55.6659 1.87863
\(879\) −15.5251 −0.523647
\(880\) −1.08873 −0.0367010
\(881\) 4.35240 0.146636 0.0733180 0.997309i \(-0.476641\pi\)
0.0733180 + 0.997309i \(0.476641\pi\)
\(882\) −8.63538 −0.290768
\(883\) −47.5253 −1.59935 −0.799677 0.600430i \(-0.794996\pi\)
−0.799677 + 0.600430i \(0.794996\pi\)
\(884\) −5.13716 −0.172781
\(885\) −12.7645 −0.429075
\(886\) −62.3358 −2.09421
\(887\) 32.5618 1.09332 0.546658 0.837356i \(-0.315900\pi\)
0.546658 + 0.837356i \(0.315900\pi\)
\(888\) 12.8476 0.431137
\(889\) 0.177596 0.00595637
\(890\) 4.30686 0.144366
\(891\) −4.24614 −0.142251
\(892\) −80.2355 −2.68648
\(893\) −8.23550 −0.275590
\(894\) −51.2766 −1.71495
\(895\) −7.71860 −0.258004
\(896\) 37.3497 1.24777
\(897\) −6.44061 −0.215046
\(898\) −1.84986 −0.0617307
\(899\) 5.33818 0.178038
\(900\) −5.05617 −0.168539
\(901\) 5.01106 0.166943
\(902\) −19.4891 −0.648917
\(903\) 17.1185 0.569669
\(904\) 44.3159 1.47392
\(905\) −2.08498 −0.0693072
\(906\) −63.7466 −2.11784
\(907\) −54.8562 −1.82147 −0.910735 0.412991i \(-0.864484\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(908\) 58.8562 1.95321
\(909\) −9.30694 −0.308692
\(910\) 4.25340 0.140999
\(911\) −20.5620 −0.681248 −0.340624 0.940200i \(-0.610638\pi\)
−0.340624 + 0.940200i \(0.610638\pi\)
\(912\) 1.14610 0.0379512
\(913\) −9.32928 −0.308754
\(914\) −83.7773 −2.77111
\(915\) −10.2672 −0.339422
\(916\) 21.3029 0.703867
\(917\) 30.9646 1.02254
\(918\) −23.1244 −0.763219
\(919\) 15.6907 0.517588 0.258794 0.965932i \(-0.416675\pi\)
0.258794 + 0.965932i \(0.416675\pi\)
\(920\) 16.2457 0.535606
\(921\) −32.9975 −1.08730
\(922\) 46.6744 1.53714
\(923\) 7.63664 0.251363
\(924\) −21.3586 −0.702646
\(925\) 4.20115 0.138133
\(926\) −60.7838 −1.99748
\(927\) 30.9903 1.01786
\(928\) −28.5700 −0.937856
\(929\) 29.9859 0.983805 0.491903 0.870650i \(-0.336302\pi\)
0.491903 + 0.870650i \(0.336302\pi\)
\(930\) −3.05279 −0.100105
\(931\) −5.65386 −0.185298
\(932\) 58.8004 1.92607
\(933\) −31.9210 −1.04505
\(934\) 32.9781 1.07908
\(935\) 5.02011 0.164175
\(936\) −3.63392 −0.118778
\(937\) −23.8466 −0.779035 −0.389517 0.921019i \(-0.627358\pi\)
−0.389517 + 0.921019i \(0.627358\pi\)
\(938\) 22.6071 0.738149
\(939\) 3.62173 0.118191
\(940\) −10.8374 −0.353478
\(941\) −33.0287 −1.07671 −0.538353 0.842719i \(-0.680953\pi\)
−0.538353 + 0.842719i \(0.680953\pi\)
\(942\) −6.62047 −0.215706
\(943\) −20.1203 −0.655206
\(944\) −4.40198 −0.143272
\(945\) 11.7010 0.380632
\(946\) 40.9245 1.33057
\(947\) 48.5143 1.57650 0.788252 0.615353i \(-0.210986\pi\)
0.788252 + 0.615353i \(0.210986\pi\)
\(948\) 6.18826 0.200985
\(949\) 6.76000 0.219439
\(950\) −5.41687 −0.175746
\(951\) −7.87986 −0.255522
\(952\) −10.4669 −0.339234
\(953\) −36.2788 −1.17519 −0.587593 0.809157i \(-0.699924\pi\)
−0.587593 + 0.809157i \(0.699924\pi\)
\(954\) 9.74625 0.315546
\(955\) −20.8169 −0.673619
\(956\) 56.4919 1.82708
\(957\) 14.7676 0.477370
\(958\) −36.6390 −1.18375
\(959\) 1.07597 0.0347450
\(960\) 15.3789 0.496353
\(961\) −29.6977 −0.957990
\(962\) 8.30190 0.267664
\(963\) −20.5569 −0.662437
\(964\) 28.0744 0.904214
\(965\) −14.0844 −0.453393
\(966\) −36.0808 −1.16088
\(967\) 46.4911 1.49505 0.747527 0.664232i \(-0.231241\pi\)
0.747527 + 0.664232i \(0.231241\pi\)
\(968\) 9.94723 0.319716
\(969\) −5.28465 −0.169767
\(970\) 26.5884 0.853701
\(971\) −45.1256 −1.44815 −0.724074 0.689722i \(-0.757733\pi\)
−0.724074 + 0.689722i \(0.757733\pi\)
\(972\) −45.3786 −1.45552
\(973\) 4.95031 0.158700
\(974\) −30.6338 −0.981571
\(975\) 1.02782 0.0329166
\(976\) −3.54074 −0.113336
\(977\) 0.557065 0.0178221 0.00891104 0.999960i \(-0.497163\pi\)
0.00891104 + 0.999960i \(0.497163\pi\)
\(978\) 37.2938 1.19253
\(979\) −5.08274 −0.162445
\(980\) −7.44015 −0.237667
\(981\) −20.6868 −0.660480
\(982\) −1.49364 −0.0476640
\(983\) 59.9611 1.91246 0.956231 0.292611i \(-0.0945242\pi\)
0.956231 + 0.292611i \(0.0945242\pi\)
\(984\) 9.81922 0.313025
\(985\) −26.7784 −0.853232
\(986\) 19.8981 0.633684
\(987\) 8.75404 0.278644
\(988\) −6.54176 −0.208121
\(989\) 42.2499 1.34347
\(990\) 9.76385 0.310315
\(991\) −16.0026 −0.508338 −0.254169 0.967160i \(-0.581802\pi\)
−0.254169 + 0.967160i \(0.581802\pi\)
\(992\) −6.97001 −0.221298
\(993\) 6.34103 0.201227
\(994\) 42.7811 1.35693
\(995\) 26.5851 0.842804
\(996\) 12.9237 0.409504
\(997\) −23.9096 −0.757224 −0.378612 0.925555i \(-0.623599\pi\)
−0.378612 + 0.925555i \(0.623599\pi\)
\(998\) 73.6034 2.32987
\(999\) 22.8382 0.722570
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 8045.2.a.c.1.18 127
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8045.2.a.c.1.18 127 1.1 even 1 trivial