Properties

Label 1441.2.a.c.1.17
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $1$
Dimension $23$
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] = [1441,2,Mod(1,1441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1441, 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("1441.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.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: \(11.5064429313\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 1441.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.714474 q^{2} +2.60520 q^{3} -1.48953 q^{4} -0.266226 q^{5} +1.86135 q^{6} -4.25119 q^{7} -2.49318 q^{8} +3.78706 q^{9} +O(q^{10})\) \(q+0.714474 q^{2} +2.60520 q^{3} -1.48953 q^{4} -0.266226 q^{5} +1.86135 q^{6} -4.25119 q^{7} -2.49318 q^{8} +3.78706 q^{9} -0.190211 q^{10} +1.00000 q^{11} -3.88052 q^{12} -1.98481 q^{13} -3.03736 q^{14} -0.693572 q^{15} +1.19775 q^{16} -2.40857 q^{17} +2.70576 q^{18} -3.84156 q^{19} +0.396551 q^{20} -11.0752 q^{21} +0.714474 q^{22} -4.84360 q^{23} -6.49522 q^{24} -4.92912 q^{25} -1.41809 q^{26} +2.05045 q^{27} +6.33227 q^{28} +7.38740 q^{29} -0.495539 q^{30} -7.56343 q^{31} +5.84211 q^{32} +2.60520 q^{33} -1.72086 q^{34} +1.13178 q^{35} -5.64093 q^{36} +7.68404 q^{37} -2.74469 q^{38} -5.17081 q^{39} +0.663748 q^{40} +3.36181 q^{41} -7.91294 q^{42} -6.49093 q^{43} -1.48953 q^{44} -1.00821 q^{45} -3.46063 q^{46} -7.86384 q^{47} +3.12037 q^{48} +11.0726 q^{49} -3.52173 q^{50} -6.27479 q^{51} +2.95642 q^{52} +2.59581 q^{53} +1.46500 q^{54} -0.266226 q^{55} +10.5990 q^{56} -10.0080 q^{57} +5.27810 q^{58} +9.89990 q^{59} +1.03309 q^{60} -13.9195 q^{61} -5.40387 q^{62} -16.0995 q^{63} +1.77854 q^{64} +0.528407 q^{65} +1.86135 q^{66} +2.88224 q^{67} +3.58762 q^{68} -12.6186 q^{69} +0.808625 q^{70} -2.24673 q^{71} -9.44181 q^{72} -1.68777 q^{73} +5.49005 q^{74} -12.8413 q^{75} +5.72211 q^{76} -4.25119 q^{77} -3.69441 q^{78} -1.28914 q^{79} -0.318871 q^{80} -6.01934 q^{81} +2.40192 q^{82} -8.11186 q^{83} +16.4968 q^{84} +0.641223 q^{85} -4.63760 q^{86} +19.2457 q^{87} -2.49318 q^{88} +6.17174 q^{89} -0.720343 q^{90} +8.43779 q^{91} +7.21468 q^{92} -19.7043 q^{93} -5.61850 q^{94} +1.02272 q^{95} +15.2199 q^{96} +10.5173 q^{97} +7.91110 q^{98} +3.78706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.714474 0.505209 0.252605 0.967570i \(-0.418713\pi\)
0.252605 + 0.967570i \(0.418713\pi\)
\(3\) 2.60520 1.50411 0.752056 0.659099i \(-0.229062\pi\)
0.752056 + 0.659099i \(0.229062\pi\)
\(4\) −1.48953 −0.744764
\(5\) −0.266226 −0.119060 −0.0595299 0.998227i \(-0.518960\pi\)
−0.0595299 + 0.998227i \(0.518960\pi\)
\(6\) 1.86135 0.759891
\(7\) −4.25119 −1.60680 −0.803400 0.595440i \(-0.796978\pi\)
−0.803400 + 0.595440i \(0.796978\pi\)
\(8\) −2.49318 −0.881471
\(9\) 3.78706 1.26235
\(10\) −0.190211 −0.0601501
\(11\) 1.00000 0.301511
\(12\) −3.88052 −1.12021
\(13\) −1.98481 −0.550486 −0.275243 0.961375i \(-0.588758\pi\)
−0.275243 + 0.961375i \(0.588758\pi\)
\(14\) −3.03736 −0.811770
\(15\) −0.693572 −0.179079
\(16\) 1.19775 0.299437
\(17\) −2.40857 −0.584163 −0.292081 0.956393i \(-0.594348\pi\)
−0.292081 + 0.956393i \(0.594348\pi\)
\(18\) 2.70576 0.637753
\(19\) −3.84156 −0.881314 −0.440657 0.897676i \(-0.645254\pi\)
−0.440657 + 0.897676i \(0.645254\pi\)
\(20\) 0.396551 0.0886715
\(21\) −11.0752 −2.41681
\(22\) 0.714474 0.152326
\(23\) −4.84360 −1.00996 −0.504981 0.863131i \(-0.668500\pi\)
−0.504981 + 0.863131i \(0.668500\pi\)
\(24\) −6.49522 −1.32583
\(25\) −4.92912 −0.985825
\(26\) −1.41809 −0.278111
\(27\) 2.05045 0.394610
\(28\) 6.33227 1.19669
\(29\) 7.38740 1.37181 0.685903 0.727693i \(-0.259407\pi\)
0.685903 + 0.727693i \(0.259407\pi\)
\(30\) −0.495539 −0.0904726
\(31\) −7.56343 −1.35843 −0.679216 0.733938i \(-0.737680\pi\)
−0.679216 + 0.733938i \(0.737680\pi\)
\(32\) 5.84211 1.03275
\(33\) 2.60520 0.453507
\(34\) −1.72086 −0.295124
\(35\) 1.13178 0.191305
\(36\) −5.64093 −0.940156
\(37\) 7.68404 1.26325 0.631624 0.775275i \(-0.282389\pi\)
0.631624 + 0.775275i \(0.282389\pi\)
\(38\) −2.74469 −0.445248
\(39\) −5.17081 −0.827993
\(40\) 0.663748 0.104948
\(41\) 3.36181 0.525026 0.262513 0.964928i \(-0.415449\pi\)
0.262513 + 0.964928i \(0.415449\pi\)
\(42\) −7.91294 −1.22099
\(43\) −6.49093 −0.989857 −0.494928 0.868934i \(-0.664806\pi\)
−0.494928 + 0.868934i \(0.664806\pi\)
\(44\) −1.48953 −0.224555
\(45\) −1.00821 −0.150296
\(46\) −3.46063 −0.510242
\(47\) −7.86384 −1.14706 −0.573529 0.819185i \(-0.694426\pi\)
−0.573529 + 0.819185i \(0.694426\pi\)
\(48\) 3.12037 0.450386
\(49\) 11.0726 1.58180
\(50\) −3.52173 −0.498048
\(51\) −6.27479 −0.878647
\(52\) 2.95642 0.409982
\(53\) 2.59581 0.356563 0.178281 0.983980i \(-0.442946\pi\)
0.178281 + 0.983980i \(0.442946\pi\)
\(54\) 1.46500 0.199361
\(55\) −0.266226 −0.0358979
\(56\) 10.5990 1.41635
\(57\) −10.0080 −1.32560
\(58\) 5.27810 0.693049
\(59\) 9.89990 1.28886 0.644428 0.764665i \(-0.277095\pi\)
0.644428 + 0.764665i \(0.277095\pi\)
\(60\) 1.03309 0.133372
\(61\) −13.9195 −1.78221 −0.891105 0.453798i \(-0.850069\pi\)
−0.891105 + 0.453798i \(0.850069\pi\)
\(62\) −5.40387 −0.686293
\(63\) −16.0995 −2.02835
\(64\) 1.77854 0.222317
\(65\) 0.528407 0.0655408
\(66\) 1.86135 0.229116
\(67\) 2.88224 0.352121 0.176061 0.984379i \(-0.443665\pi\)
0.176061 + 0.984379i \(0.443665\pi\)
\(68\) 3.58762 0.435063
\(69\) −12.6186 −1.51910
\(70\) 0.808625 0.0966492
\(71\) −2.24673 −0.266638 −0.133319 0.991073i \(-0.542563\pi\)
−0.133319 + 0.991073i \(0.542563\pi\)
\(72\) −9.44181 −1.11273
\(73\) −1.68777 −0.197539 −0.0987695 0.995110i \(-0.531491\pi\)
−0.0987695 + 0.995110i \(0.531491\pi\)
\(74\) 5.49005 0.638205
\(75\) −12.8413 −1.48279
\(76\) 5.72211 0.656371
\(77\) −4.25119 −0.484468
\(78\) −3.69441 −0.418310
\(79\) −1.28914 −0.145039 −0.0725195 0.997367i \(-0.523104\pi\)
−0.0725195 + 0.997367i \(0.523104\pi\)
\(80\) −0.318871 −0.0356509
\(81\) −6.01934 −0.668816
\(82\) 2.40192 0.265248
\(83\) −8.11186 −0.890392 −0.445196 0.895433i \(-0.646866\pi\)
−0.445196 + 0.895433i \(0.646866\pi\)
\(84\) 16.4968 1.79995
\(85\) 0.641223 0.0695504
\(86\) −4.63760 −0.500085
\(87\) 19.2457 2.06335
\(88\) −2.49318 −0.265773
\(89\) 6.17174 0.654204 0.327102 0.944989i \(-0.393928\pi\)
0.327102 + 0.944989i \(0.393928\pi\)
\(90\) −0.720343 −0.0759308
\(91\) 8.43779 0.884521
\(92\) 7.21468 0.752183
\(93\) −19.7043 −2.04324
\(94\) −5.61850 −0.579504
\(95\) 1.02272 0.104929
\(96\) 15.2199 1.55337
\(97\) 10.5173 1.06787 0.533934 0.845526i \(-0.320713\pi\)
0.533934 + 0.845526i \(0.320713\pi\)
\(98\) 7.91110 0.799142
\(99\) 3.78706 0.380614
\(100\) 7.34206 0.734206
\(101\) 13.7609 1.36926 0.684631 0.728889i \(-0.259963\pi\)
0.684631 + 0.728889i \(0.259963\pi\)
\(102\) −4.48317 −0.443900
\(103\) 3.27857 0.323047 0.161524 0.986869i \(-0.448359\pi\)
0.161524 + 0.986869i \(0.448359\pi\)
\(104\) 4.94847 0.485237
\(105\) 2.94851 0.287745
\(106\) 1.85464 0.180139
\(107\) 2.86062 0.276547 0.138273 0.990394i \(-0.455845\pi\)
0.138273 + 0.990394i \(0.455845\pi\)
\(108\) −3.05421 −0.293891
\(109\) −11.3437 −1.08653 −0.543264 0.839562i \(-0.682812\pi\)
−0.543264 + 0.839562i \(0.682812\pi\)
\(110\) −0.190211 −0.0181360
\(111\) 20.0185 1.90007
\(112\) −5.09185 −0.481135
\(113\) 2.47478 0.232807 0.116404 0.993202i \(-0.462863\pi\)
0.116404 + 0.993202i \(0.462863\pi\)
\(114\) −7.15047 −0.669703
\(115\) 1.28949 0.120246
\(116\) −11.0037 −1.02167
\(117\) −7.51658 −0.694908
\(118\) 7.07322 0.651142
\(119\) 10.2393 0.938633
\(120\) 1.72920 0.157853
\(121\) 1.00000 0.0909091
\(122\) −9.94512 −0.900389
\(123\) 8.75817 0.789698
\(124\) 11.2659 1.01171
\(125\) 2.64339 0.236432
\(126\) −11.5027 −1.02474
\(127\) −18.9979 −1.68579 −0.842895 0.538078i \(-0.819151\pi\)
−0.842895 + 0.538078i \(0.819151\pi\)
\(128\) −10.4135 −0.920432
\(129\) −16.9102 −1.48886
\(130\) 0.377533 0.0331118
\(131\) 1.00000 0.0873704
\(132\) −3.88052 −0.337756
\(133\) 16.3312 1.41610
\(134\) 2.05928 0.177895
\(135\) −0.545884 −0.0469822
\(136\) 6.00498 0.514922
\(137\) 21.4642 1.83381 0.916904 0.399107i \(-0.130680\pi\)
0.916904 + 0.399107i \(0.130680\pi\)
\(138\) −9.01562 −0.767461
\(139\) 4.21451 0.357470 0.178735 0.983897i \(-0.442800\pi\)
0.178735 + 0.983897i \(0.442800\pi\)
\(140\) −1.68581 −0.142477
\(141\) −20.4869 −1.72530
\(142\) −1.60523 −0.134708
\(143\) −1.98481 −0.165978
\(144\) 4.53594 0.377995
\(145\) −1.96672 −0.163327
\(146\) −1.20587 −0.0997985
\(147\) 28.8464 2.37921
\(148\) −11.4456 −0.940822
\(149\) −12.0843 −0.989983 −0.494991 0.868898i \(-0.664829\pi\)
−0.494991 + 0.868898i \(0.664829\pi\)
\(150\) −9.17481 −0.749120
\(151\) −16.6533 −1.35522 −0.677612 0.735420i \(-0.736985\pi\)
−0.677612 + 0.735420i \(0.736985\pi\)
\(152\) 9.57768 0.776852
\(153\) −9.12139 −0.737420
\(154\) −3.03736 −0.244758
\(155\) 2.01358 0.161735
\(156\) 7.70207 0.616659
\(157\) 18.0718 1.44228 0.721142 0.692787i \(-0.243617\pi\)
0.721142 + 0.692787i \(0.243617\pi\)
\(158\) −0.921053 −0.0732751
\(159\) 6.76261 0.536310
\(160\) −1.55532 −0.122959
\(161\) 20.5911 1.62281
\(162\) −4.30066 −0.337892
\(163\) 9.04640 0.708569 0.354284 0.935138i \(-0.384725\pi\)
0.354284 + 0.935138i \(0.384725\pi\)
\(164\) −5.00750 −0.391020
\(165\) −0.693572 −0.0539945
\(166\) −5.79571 −0.449834
\(167\) 8.80777 0.681565 0.340783 0.940142i \(-0.389308\pi\)
0.340783 + 0.940142i \(0.389308\pi\)
\(168\) 27.6124 2.13034
\(169\) −9.06055 −0.696965
\(170\) 0.458137 0.0351375
\(171\) −14.5482 −1.11253
\(172\) 9.66841 0.737209
\(173\) −4.77384 −0.362949 −0.181474 0.983396i \(-0.558087\pi\)
−0.181474 + 0.983396i \(0.558087\pi\)
\(174\) 13.7505 1.04242
\(175\) 20.9547 1.58402
\(176\) 1.19775 0.0902835
\(177\) 25.7912 1.93859
\(178\) 4.40955 0.330510
\(179\) −9.33183 −0.697493 −0.348747 0.937217i \(-0.613393\pi\)
−0.348747 + 0.937217i \(0.613393\pi\)
\(180\) 1.50176 0.111935
\(181\) −9.65106 −0.717358 −0.358679 0.933461i \(-0.616773\pi\)
−0.358679 + 0.933461i \(0.616773\pi\)
\(182\) 6.02858 0.446868
\(183\) −36.2631 −2.68064
\(184\) 12.0760 0.890251
\(185\) −2.04569 −0.150402
\(186\) −14.0782 −1.03226
\(187\) −2.40857 −0.176132
\(188\) 11.7134 0.854287
\(189\) −8.71688 −0.634059
\(190\) 0.730709 0.0530112
\(191\) 21.3649 1.54591 0.772956 0.634459i \(-0.218777\pi\)
0.772956 + 0.634459i \(0.218777\pi\)
\(192\) 4.63345 0.334391
\(193\) −1.97627 −0.142255 −0.0711275 0.997467i \(-0.522660\pi\)
−0.0711275 + 0.997467i \(0.522660\pi\)
\(194\) 7.51433 0.539497
\(195\) 1.37660 0.0985807
\(196\) −16.4930 −1.17807
\(197\) 1.08589 0.0773661 0.0386831 0.999252i \(-0.487684\pi\)
0.0386831 + 0.999252i \(0.487684\pi\)
\(198\) 2.70576 0.192290
\(199\) −2.84707 −0.201823 −0.100912 0.994895i \(-0.532176\pi\)
−0.100912 + 0.994895i \(0.532176\pi\)
\(200\) 12.2892 0.868976
\(201\) 7.50880 0.529630
\(202\) 9.83182 0.691764
\(203\) −31.4053 −2.20422
\(204\) 9.34648 0.654384
\(205\) −0.895000 −0.0625095
\(206\) 2.34245 0.163206
\(207\) −18.3430 −1.27493
\(208\) −2.37729 −0.164836
\(209\) −3.84156 −0.265726
\(210\) 2.10663 0.145371
\(211\) −12.4333 −0.855945 −0.427972 0.903792i \(-0.640772\pi\)
−0.427972 + 0.903792i \(0.640772\pi\)
\(212\) −3.86654 −0.265555
\(213\) −5.85317 −0.401053
\(214\) 2.04384 0.139714
\(215\) 1.72805 0.117852
\(216\) −5.11214 −0.347837
\(217\) 32.1536 2.18273
\(218\) −8.10477 −0.548924
\(219\) −4.39699 −0.297121
\(220\) 0.396551 0.0267355
\(221\) 4.78053 0.321574
\(222\) 14.3027 0.959932
\(223\) −3.20148 −0.214387 −0.107194 0.994238i \(-0.534186\pi\)
−0.107194 + 0.994238i \(0.534186\pi\)
\(224\) −24.8359 −1.65942
\(225\) −18.6669 −1.24446
\(226\) 1.76816 0.117616
\(227\) 16.9260 1.12342 0.561708 0.827336i \(-0.310144\pi\)
0.561708 + 0.827336i \(0.310144\pi\)
\(228\) 14.9072 0.987255
\(229\) −11.5175 −0.761101 −0.380550 0.924760i \(-0.624265\pi\)
−0.380550 + 0.924760i \(0.624265\pi\)
\(230\) 0.921309 0.0607493
\(231\) −11.0752 −0.728695
\(232\) −18.4181 −1.20921
\(233\) 11.5699 0.757970 0.378985 0.925403i \(-0.376273\pi\)
0.378985 + 0.925403i \(0.376273\pi\)
\(234\) −5.37040 −0.351074
\(235\) 2.09356 0.136569
\(236\) −14.7462 −0.959894
\(237\) −3.35845 −0.218155
\(238\) 7.31569 0.474206
\(239\) −6.83651 −0.442217 −0.221109 0.975249i \(-0.570968\pi\)
−0.221109 + 0.975249i \(0.570968\pi\)
\(240\) −0.830723 −0.0536229
\(241\) −23.7835 −1.53203 −0.766016 0.642822i \(-0.777764\pi\)
−0.766016 + 0.642822i \(0.777764\pi\)
\(242\) 0.714474 0.0459281
\(243\) −21.8330 −1.40058
\(244\) 20.7335 1.32733
\(245\) −2.94782 −0.188329
\(246\) 6.25748 0.398963
\(247\) 7.62475 0.485151
\(248\) 18.8570 1.19742
\(249\) −21.1330 −1.33925
\(250\) 1.88863 0.119448
\(251\) −17.6289 −1.11273 −0.556363 0.830939i \(-0.687804\pi\)
−0.556363 + 0.830939i \(0.687804\pi\)
\(252\) 23.9807 1.51064
\(253\) −4.84360 −0.304515
\(254\) −13.5735 −0.851677
\(255\) 1.67051 0.104612
\(256\) −10.9973 −0.687328
\(257\) 21.6333 1.34945 0.674723 0.738071i \(-0.264263\pi\)
0.674723 + 0.738071i \(0.264263\pi\)
\(258\) −12.0819 −0.752184
\(259\) −32.6663 −2.02979
\(260\) −0.787076 −0.0488124
\(261\) 27.9766 1.73171
\(262\) 0.714474 0.0441403
\(263\) 2.30575 0.142179 0.0710893 0.997470i \(-0.477352\pi\)
0.0710893 + 0.997470i \(0.477352\pi\)
\(264\) −6.49522 −0.399753
\(265\) −0.691073 −0.0424523
\(266\) 11.6682 0.715424
\(267\) 16.0786 0.983996
\(268\) −4.29317 −0.262247
\(269\) −8.27886 −0.504771 −0.252386 0.967627i \(-0.581215\pi\)
−0.252386 + 0.967627i \(0.581215\pi\)
\(270\) −0.390020 −0.0237359
\(271\) −11.6606 −0.708330 −0.354165 0.935183i \(-0.615235\pi\)
−0.354165 + 0.935183i \(0.615235\pi\)
\(272\) −2.88485 −0.174920
\(273\) 21.9821 1.33042
\(274\) 15.3356 0.926457
\(275\) −4.92912 −0.297237
\(276\) 18.7957 1.13137
\(277\) −18.2078 −1.09400 −0.546999 0.837133i \(-0.684230\pi\)
−0.546999 + 0.837133i \(0.684230\pi\)
\(278\) 3.01116 0.180597
\(279\) −28.6432 −1.71482
\(280\) −2.82172 −0.168630
\(281\) −9.98596 −0.595712 −0.297856 0.954611i \(-0.596272\pi\)
−0.297856 + 0.954611i \(0.596272\pi\)
\(282\) −14.6373 −0.871640
\(283\) 11.1669 0.663806 0.331903 0.943313i \(-0.392309\pi\)
0.331903 + 0.943313i \(0.392309\pi\)
\(284\) 3.34656 0.198582
\(285\) 2.66440 0.157825
\(286\) −1.41809 −0.0838535
\(287\) −14.2917 −0.843611
\(288\) 22.1244 1.30369
\(289\) −11.1988 −0.658754
\(290\) −1.40517 −0.0825143
\(291\) 27.3996 1.60619
\(292\) 2.51399 0.147120
\(293\) −19.6074 −1.14548 −0.572738 0.819738i \(-0.694119\pi\)
−0.572738 + 0.819738i \(0.694119\pi\)
\(294\) 20.6100 1.20200
\(295\) −2.63561 −0.153451
\(296\) −19.1577 −1.11352
\(297\) 2.05045 0.118979
\(298\) −8.63390 −0.500148
\(299\) 9.61361 0.555970
\(300\) 19.1275 1.10433
\(301\) 27.5942 1.59050
\(302\) −11.8983 −0.684672
\(303\) 35.8499 2.05953
\(304\) −4.60121 −0.263898
\(305\) 3.70573 0.212190
\(306\) −6.51699 −0.372552
\(307\) 23.8034 1.35853 0.679266 0.733893i \(-0.262298\pi\)
0.679266 + 0.733893i \(0.262298\pi\)
\(308\) 6.33227 0.360814
\(309\) 8.54133 0.485899
\(310\) 1.43865 0.0817099
\(311\) −24.9116 −1.41261 −0.706304 0.707909i \(-0.749639\pi\)
−0.706304 + 0.707909i \(0.749639\pi\)
\(312\) 12.8917 0.729851
\(313\) 21.1283 1.19424 0.597120 0.802152i \(-0.296311\pi\)
0.597120 + 0.802152i \(0.296311\pi\)
\(314\) 12.9118 0.728655
\(315\) 4.28611 0.241495
\(316\) 1.92020 0.108020
\(317\) −22.2781 −1.25126 −0.625631 0.780119i \(-0.715158\pi\)
−0.625631 + 0.780119i \(0.715158\pi\)
\(318\) 4.83171 0.270949
\(319\) 7.38740 0.413615
\(320\) −0.473494 −0.0264691
\(321\) 7.45249 0.415958
\(322\) 14.7118 0.819856
\(323\) 9.25265 0.514831
\(324\) 8.96598 0.498110
\(325\) 9.78335 0.542683
\(326\) 6.46341 0.357975
\(327\) −29.5526 −1.63426
\(328\) −8.38157 −0.462795
\(329\) 33.4307 1.84309
\(330\) −0.495539 −0.0272785
\(331\) −24.2164 −1.33105 −0.665527 0.746373i \(-0.731793\pi\)
−0.665527 + 0.746373i \(0.731793\pi\)
\(332\) 12.0828 0.663132
\(333\) 29.0999 1.59467
\(334\) 6.29292 0.344333
\(335\) −0.767326 −0.0419235
\(336\) −13.2653 −0.723681
\(337\) 20.2912 1.10533 0.552666 0.833403i \(-0.313610\pi\)
0.552666 + 0.833403i \(0.313610\pi\)
\(338\) −6.47352 −0.352113
\(339\) 6.44729 0.350169
\(340\) −0.955119 −0.0517986
\(341\) −7.56343 −0.409583
\(342\) −10.3943 −0.562061
\(343\) −17.3135 −0.934844
\(344\) 16.1830 0.872530
\(345\) 3.35939 0.180863
\(346\) −3.41079 −0.183365
\(347\) 1.03831 0.0557395 0.0278697 0.999612i \(-0.491128\pi\)
0.0278697 + 0.999612i \(0.491128\pi\)
\(348\) −28.6669 −1.53671
\(349\) 11.6628 0.624297 0.312148 0.950033i \(-0.398951\pi\)
0.312148 + 0.950033i \(0.398951\pi\)
\(350\) 14.9715 0.800263
\(351\) −4.06975 −0.217227
\(352\) 5.84211 0.311385
\(353\) 3.76830 0.200567 0.100283 0.994959i \(-0.468025\pi\)
0.100283 + 0.994959i \(0.468025\pi\)
\(354\) 18.4271 0.979391
\(355\) 0.598137 0.0317458
\(356\) −9.19298 −0.487227
\(357\) 26.6753 1.41181
\(358\) −6.66734 −0.352380
\(359\) −19.5949 −1.03418 −0.517090 0.855931i \(-0.672985\pi\)
−0.517090 + 0.855931i \(0.672985\pi\)
\(360\) 2.51366 0.132481
\(361\) −4.24242 −0.223286
\(362\) −6.89543 −0.362416
\(363\) 2.60520 0.136737
\(364\) −12.5683 −0.658759
\(365\) 0.449329 0.0235190
\(366\) −25.9090 −1.35429
\(367\) 29.8625 1.55881 0.779405 0.626521i \(-0.215522\pi\)
0.779405 + 0.626521i \(0.215522\pi\)
\(368\) −5.80141 −0.302419
\(369\) 12.7314 0.662769
\(370\) −1.46159 −0.0759846
\(371\) −11.0353 −0.572925
\(372\) 29.3500 1.52173
\(373\) −24.5808 −1.27275 −0.636373 0.771381i \(-0.719566\pi\)
−0.636373 + 0.771381i \(0.719566\pi\)
\(374\) −1.72086 −0.0889834
\(375\) 6.88656 0.355620
\(376\) 19.6059 1.01110
\(377\) −14.6626 −0.755160
\(378\) −6.22798 −0.320333
\(379\) −27.5041 −1.41279 −0.706395 0.707818i \(-0.749680\pi\)
−0.706395 + 0.707818i \(0.749680\pi\)
\(380\) −1.52337 −0.0781474
\(381\) −49.4933 −2.53562
\(382\) 15.2647 0.781009
\(383\) −12.8012 −0.654113 −0.327057 0.945005i \(-0.606057\pi\)
−0.327057 + 0.945005i \(0.606057\pi\)
\(384\) −27.1292 −1.38443
\(385\) 1.13178 0.0576807
\(386\) −1.41199 −0.0718685
\(387\) −24.5815 −1.24955
\(388\) −15.6658 −0.795310
\(389\) 26.4465 1.34089 0.670445 0.741959i \(-0.266103\pi\)
0.670445 + 0.741959i \(0.266103\pi\)
\(390\) 0.983548 0.0498039
\(391\) 11.6661 0.589982
\(392\) −27.6060 −1.39431
\(393\) 2.60520 0.131415
\(394\) 0.775836 0.0390861
\(395\) 0.343201 0.0172683
\(396\) −5.64093 −0.283468
\(397\) −9.72895 −0.488282 −0.244141 0.969740i \(-0.578506\pi\)
−0.244141 + 0.969740i \(0.578506\pi\)
\(398\) −2.03416 −0.101963
\(399\) 42.5460 2.12997
\(400\) −5.90384 −0.295192
\(401\) −20.1705 −1.00727 −0.503634 0.863917i \(-0.668004\pi\)
−0.503634 + 0.863917i \(0.668004\pi\)
\(402\) 5.36484 0.267574
\(403\) 15.0119 0.747798
\(404\) −20.4973 −1.01978
\(405\) 1.60251 0.0796292
\(406\) −22.4382 −1.11359
\(407\) 7.68404 0.380884
\(408\) 15.6442 0.774501
\(409\) −36.3003 −1.79493 −0.897467 0.441081i \(-0.854595\pi\)
−0.897467 + 0.441081i \(0.854595\pi\)
\(410\) −0.639454 −0.0315804
\(411\) 55.9185 2.75825
\(412\) −4.88352 −0.240594
\(413\) −42.0864 −2.07093
\(414\) −13.1056 −0.644106
\(415\) 2.15959 0.106010
\(416\) −11.5955 −0.568514
\(417\) 10.9796 0.537675
\(418\) −2.74469 −0.134247
\(419\) 33.8065 1.65156 0.825779 0.563994i \(-0.190736\pi\)
0.825779 + 0.563994i \(0.190736\pi\)
\(420\) −4.39188 −0.214302
\(421\) 18.2031 0.887164 0.443582 0.896234i \(-0.353707\pi\)
0.443582 + 0.896234i \(0.353707\pi\)
\(422\) −8.88327 −0.432431
\(423\) −29.7808 −1.44799
\(424\) −6.47182 −0.314299
\(425\) 11.8721 0.575882
\(426\) −4.18194 −0.202616
\(427\) 59.1745 2.86365
\(428\) −4.26098 −0.205962
\(429\) −5.17081 −0.249649
\(430\) 1.23465 0.0595400
\(431\) −22.8935 −1.10274 −0.551371 0.834260i \(-0.685895\pi\)
−0.551371 + 0.834260i \(0.685895\pi\)
\(432\) 2.45593 0.118161
\(433\) 10.7709 0.517619 0.258809 0.965928i \(-0.416670\pi\)
0.258809 + 0.965928i \(0.416670\pi\)
\(434\) 22.9729 1.10273
\(435\) −5.12369 −0.245662
\(436\) 16.8967 0.809207
\(437\) 18.6070 0.890093
\(438\) −3.14153 −0.150108
\(439\) 36.5458 1.74424 0.872119 0.489294i \(-0.162745\pi\)
0.872119 + 0.489294i \(0.162745\pi\)
\(440\) 0.663748 0.0316429
\(441\) 41.9328 1.99680
\(442\) 3.41557 0.162462
\(443\) −22.2850 −1.05879 −0.529395 0.848375i \(-0.677581\pi\)
−0.529395 + 0.848375i \(0.677581\pi\)
\(444\) −29.8180 −1.41510
\(445\) −1.64308 −0.0778894
\(446\) −2.28738 −0.108310
\(447\) −31.4820 −1.48905
\(448\) −7.56091 −0.357220
\(449\) −28.5134 −1.34563 −0.672815 0.739810i \(-0.734915\pi\)
−0.672815 + 0.739810i \(0.734915\pi\)
\(450\) −13.3370 −0.628713
\(451\) 3.36181 0.158301
\(452\) −3.68625 −0.173387
\(453\) −43.3851 −2.03841
\(454\) 12.0932 0.567560
\(455\) −2.24636 −0.105311
\(456\) 24.9518 1.16847
\(457\) 41.2473 1.92947 0.964733 0.263229i \(-0.0847874\pi\)
0.964733 + 0.263229i \(0.0847874\pi\)
\(458\) −8.22898 −0.384515
\(459\) −4.93865 −0.230517
\(460\) −1.92074 −0.0895548
\(461\) 2.54139 0.118364 0.0591822 0.998247i \(-0.481151\pi\)
0.0591822 + 0.998247i \(0.481151\pi\)
\(462\) −7.91294 −0.368143
\(463\) 4.86610 0.226147 0.113074 0.993587i \(-0.463930\pi\)
0.113074 + 0.993587i \(0.463930\pi\)
\(464\) 8.84824 0.410769
\(465\) 5.24578 0.243267
\(466\) 8.26640 0.382934
\(467\) −23.3242 −1.07932 −0.539659 0.841884i \(-0.681447\pi\)
−0.539659 + 0.841884i \(0.681447\pi\)
\(468\) 11.1962 0.517542
\(469\) −12.2529 −0.565788
\(470\) 1.49579 0.0689957
\(471\) 47.0806 2.16936
\(472\) −24.6822 −1.13609
\(473\) −6.49093 −0.298453
\(474\) −2.39953 −0.110214
\(475\) 18.9355 0.868821
\(476\) −15.2517 −0.699060
\(477\) 9.83051 0.450108
\(478\) −4.88451 −0.223412
\(479\) −14.5582 −0.665183 −0.332591 0.943071i \(-0.607923\pi\)
−0.332591 + 0.943071i \(0.607923\pi\)
\(480\) −4.05192 −0.184944
\(481\) −15.2513 −0.695401
\(482\) −16.9927 −0.773996
\(483\) 53.6439 2.44088
\(484\) −1.48953 −0.0677058
\(485\) −2.79998 −0.127140
\(486\) −15.5991 −0.707588
\(487\) 11.8275 0.535954 0.267977 0.963425i \(-0.413645\pi\)
0.267977 + 0.963425i \(0.413645\pi\)
\(488\) 34.7038 1.57097
\(489\) 23.5677 1.06577
\(490\) −2.10614 −0.0951458
\(491\) −14.3248 −0.646468 −0.323234 0.946319i \(-0.604770\pi\)
−0.323234 + 0.946319i \(0.604770\pi\)
\(492\) −13.0455 −0.588138
\(493\) −17.7930 −0.801358
\(494\) 5.44768 0.245103
\(495\) −1.00821 −0.0453159
\(496\) −9.05908 −0.406765
\(497\) 9.55127 0.428433
\(498\) −15.0990 −0.676601
\(499\) −1.55205 −0.0694791 −0.0347396 0.999396i \(-0.511060\pi\)
−0.0347396 + 0.999396i \(0.511060\pi\)
\(500\) −3.93740 −0.176086
\(501\) 22.9460 1.02515
\(502\) −12.5954 −0.562160
\(503\) 18.8718 0.841451 0.420726 0.907188i \(-0.361775\pi\)
0.420726 + 0.907188i \(0.361775\pi\)
\(504\) 40.1390 1.78793
\(505\) −3.66352 −0.163024
\(506\) −3.46063 −0.153844
\(507\) −23.6045 −1.04831
\(508\) 28.2979 1.25552
\(509\) 26.1357 1.15844 0.579222 0.815170i \(-0.303356\pi\)
0.579222 + 0.815170i \(0.303356\pi\)
\(510\) 1.19354 0.0528507
\(511\) 7.17505 0.317406
\(512\) 12.9698 0.573187
\(513\) −7.87694 −0.347776
\(514\) 15.4564 0.681752
\(515\) −0.872841 −0.0384619
\(516\) 25.1881 1.10885
\(517\) −7.86384 −0.345851
\(518\) −23.3392 −1.02547
\(519\) −12.4368 −0.545916
\(520\) −1.31741 −0.0577723
\(521\) −19.2406 −0.842946 −0.421473 0.906841i \(-0.638487\pi\)
−0.421473 + 0.906841i \(0.638487\pi\)
\(522\) 19.9885 0.874873
\(523\) 42.4943 1.85815 0.929073 0.369897i \(-0.120607\pi\)
0.929073 + 0.369897i \(0.120607\pi\)
\(524\) −1.48953 −0.0650703
\(525\) 54.5910 2.38255
\(526\) 1.64740 0.0718300
\(527\) 18.2170 0.793546
\(528\) 3.12037 0.135797
\(529\) 0.460505 0.0200220
\(530\) −0.493754 −0.0214473
\(531\) 37.4915 1.62699
\(532\) −24.3258 −1.05466
\(533\) −6.67253 −0.289019
\(534\) 11.4878 0.497124
\(535\) −0.761572 −0.0329256
\(536\) −7.18592 −0.310385
\(537\) −24.3113 −1.04911
\(538\) −5.91503 −0.255015
\(539\) 11.0726 0.476932
\(540\) 0.813110 0.0349907
\(541\) −17.9628 −0.772280 −0.386140 0.922440i \(-0.626192\pi\)
−0.386140 + 0.922440i \(0.626192\pi\)
\(542\) −8.33118 −0.357855
\(543\) −25.1429 −1.07899
\(544\) −14.0711 −0.603294
\(545\) 3.01999 0.129362
\(546\) 15.7056 0.672140
\(547\) 12.4288 0.531419 0.265709 0.964053i \(-0.414394\pi\)
0.265709 + 0.964053i \(0.414394\pi\)
\(548\) −31.9715 −1.36575
\(549\) −52.7140 −2.24978
\(550\) −3.52173 −0.150167
\(551\) −28.3791 −1.20899
\(552\) 31.4603 1.33904
\(553\) 5.48036 0.233049
\(554\) −13.0090 −0.552698
\(555\) −5.32943 −0.226222
\(556\) −6.27763 −0.266231
\(557\) −22.8075 −0.966386 −0.483193 0.875514i \(-0.660523\pi\)
−0.483193 + 0.875514i \(0.660523\pi\)
\(558\) −20.4648 −0.866344
\(559\) 12.8832 0.544902
\(560\) 1.35558 0.0572838
\(561\) −6.27479 −0.264922
\(562\) −7.13470 −0.300959
\(563\) 28.9191 1.21879 0.609397 0.792865i \(-0.291412\pi\)
0.609397 + 0.792865i \(0.291412\pi\)
\(564\) 30.5157 1.28494
\(565\) −0.658850 −0.0277180
\(566\) 7.97849 0.335361
\(567\) 25.5894 1.07465
\(568\) 5.60149 0.235033
\(569\) −33.0466 −1.38539 −0.692693 0.721232i \(-0.743576\pi\)
−0.692693 + 0.721232i \(0.743576\pi\)
\(570\) 1.90364 0.0797348
\(571\) −7.45509 −0.311986 −0.155993 0.987758i \(-0.549858\pi\)
−0.155993 + 0.987758i \(0.549858\pi\)
\(572\) 2.95642 0.123614
\(573\) 55.6599 2.32523
\(574\) −10.2110 −0.426200
\(575\) 23.8747 0.995645
\(576\) 6.73544 0.280643
\(577\) −30.8478 −1.28421 −0.642105 0.766617i \(-0.721939\pi\)
−0.642105 + 0.766617i \(0.721939\pi\)
\(578\) −8.00126 −0.332808
\(579\) −5.14857 −0.213967
\(580\) 2.92948 0.121640
\(581\) 34.4851 1.43068
\(582\) 19.5763 0.811464
\(583\) 2.59581 0.107508
\(584\) 4.20792 0.174125
\(585\) 2.00111 0.0827357
\(586\) −14.0090 −0.578705
\(587\) 18.9140 0.780663 0.390332 0.920674i \(-0.372360\pi\)
0.390332 + 0.920674i \(0.372360\pi\)
\(588\) −42.9675 −1.77195
\(589\) 29.0554 1.19721
\(590\) −1.88307 −0.0775249
\(591\) 2.82895 0.116367
\(592\) 9.20354 0.378263
\(593\) 3.62157 0.148720 0.0743600 0.997231i \(-0.476309\pi\)
0.0743600 + 0.997231i \(0.476309\pi\)
\(594\) 1.46500 0.0601095
\(595\) −2.72596 −0.111753
\(596\) 17.9999 0.737303
\(597\) −7.41718 −0.303565
\(598\) 6.86867 0.280881
\(599\) 23.1218 0.944731 0.472366 0.881403i \(-0.343400\pi\)
0.472366 + 0.881403i \(0.343400\pi\)
\(600\) 32.0157 1.30704
\(601\) 31.8636 1.29974 0.649872 0.760044i \(-0.274823\pi\)
0.649872 + 0.760044i \(0.274823\pi\)
\(602\) 19.7153 0.803536
\(603\) 10.9152 0.444502
\(604\) 24.8055 1.00932
\(605\) −0.266226 −0.0108236
\(606\) 25.6138 1.04049
\(607\) 1.26037 0.0511567 0.0255784 0.999673i \(-0.491857\pi\)
0.0255784 + 0.999673i \(0.491857\pi\)
\(608\) −22.4428 −0.910176
\(609\) −81.8170 −3.31539
\(610\) 2.64765 0.107200
\(611\) 15.6082 0.631440
\(612\) 13.5866 0.549204
\(613\) −46.8958 −1.89410 −0.947052 0.321081i \(-0.895954\pi\)
−0.947052 + 0.321081i \(0.895954\pi\)
\(614\) 17.0069 0.686342
\(615\) −2.33165 −0.0940213
\(616\) 10.5990 0.427045
\(617\) 3.67254 0.147851 0.0739253 0.997264i \(-0.476447\pi\)
0.0739253 + 0.997264i \(0.476447\pi\)
\(618\) 6.10255 0.245481
\(619\) 0.370412 0.0148881 0.00744405 0.999972i \(-0.497630\pi\)
0.00744405 + 0.999972i \(0.497630\pi\)
\(620\) −2.99929 −0.120454
\(621\) −9.93159 −0.398541
\(622\) −17.7987 −0.713662
\(623\) −26.2373 −1.05117
\(624\) −6.19332 −0.247931
\(625\) 23.9419 0.957675
\(626\) 15.0956 0.603341
\(627\) −10.0080 −0.399682
\(628\) −26.9184 −1.07416
\(629\) −18.5075 −0.737943
\(630\) 3.06231 0.122006
\(631\) 4.35362 0.173315 0.0866574 0.996238i \(-0.472381\pi\)
0.0866574 + 0.996238i \(0.472381\pi\)
\(632\) 3.21404 0.127848
\(633\) −32.3913 −1.28744
\(634\) −15.9171 −0.632149
\(635\) 5.05773 0.200710
\(636\) −10.0731 −0.399424
\(637\) −21.9770 −0.870761
\(638\) 5.27810 0.208962
\(639\) −8.50850 −0.336591
\(640\) 2.77234 0.109587
\(641\) 39.9828 1.57922 0.789612 0.613606i \(-0.210282\pi\)
0.789612 + 0.613606i \(0.210282\pi\)
\(642\) 5.32461 0.210146
\(643\) −3.38648 −0.133550 −0.0667749 0.997768i \(-0.521271\pi\)
−0.0667749 + 0.997768i \(0.521271\pi\)
\(644\) −30.6710 −1.20861
\(645\) 4.50192 0.177263
\(646\) 6.61077 0.260097
\(647\) −28.0366 −1.10223 −0.551116 0.834429i \(-0.685798\pi\)
−0.551116 + 0.834429i \(0.685798\pi\)
\(648\) 15.0073 0.589542
\(649\) 9.89990 0.388605
\(650\) 6.98995 0.274168
\(651\) 83.7666 3.28307
\(652\) −13.4749 −0.527716
\(653\) −39.0063 −1.52644 −0.763218 0.646141i \(-0.776382\pi\)
−0.763218 + 0.646141i \(0.776382\pi\)
\(654\) −21.1145 −0.825644
\(655\) −0.266226 −0.0104023
\(656\) 4.02659 0.157212
\(657\) −6.39170 −0.249364
\(658\) 23.8853 0.931147
\(659\) −4.52931 −0.176437 −0.0882184 0.996101i \(-0.528117\pi\)
−0.0882184 + 0.996101i \(0.528117\pi\)
\(660\) 1.03309 0.0402131
\(661\) −0.350350 −0.0136270 −0.00681351 0.999977i \(-0.502169\pi\)
−0.00681351 + 0.999977i \(0.502169\pi\)
\(662\) −17.3020 −0.672461
\(663\) 12.4542 0.483683
\(664\) 20.2243 0.784855
\(665\) −4.34779 −0.168600
\(666\) 20.7911 0.805641
\(667\) −35.7817 −1.38547
\(668\) −13.1194 −0.507605
\(669\) −8.34050 −0.322462
\(670\) −0.548235 −0.0211801
\(671\) −13.9195 −0.537356
\(672\) −64.7025 −2.49595
\(673\) −51.6049 −1.98922 −0.994611 0.103681i \(-0.966938\pi\)
−0.994611 + 0.103681i \(0.966938\pi\)
\(674\) 14.4975 0.558424
\(675\) −10.1069 −0.389016
\(676\) 13.4959 0.519074
\(677\) −29.7237 −1.14238 −0.571188 0.820820i \(-0.693517\pi\)
−0.571188 + 0.820820i \(0.693517\pi\)
\(678\) 4.60642 0.176908
\(679\) −44.7110 −1.71585
\(680\) −1.59868 −0.0613066
\(681\) 44.0955 1.68974
\(682\) −5.40387 −0.206925
\(683\) 31.8490 1.21867 0.609335 0.792913i \(-0.291437\pi\)
0.609335 + 0.792913i \(0.291437\pi\)
\(684\) 21.6700 0.828572
\(685\) −5.71432 −0.218333
\(686\) −12.3701 −0.472292
\(687\) −30.0055 −1.14478
\(688\) −7.77448 −0.296399
\(689\) −5.15219 −0.196283
\(690\) 2.40019 0.0913738
\(691\) −48.1853 −1.83306 −0.916528 0.399971i \(-0.869020\pi\)
−0.916528 + 0.399971i \(0.869020\pi\)
\(692\) 7.11077 0.270311
\(693\) −16.0995 −0.611571
\(694\) 0.741846 0.0281601
\(695\) −1.12201 −0.0425603
\(696\) −47.9828 −1.81878
\(697\) −8.09713 −0.306701
\(698\) 8.33278 0.315400
\(699\) 30.1419 1.14007
\(700\) −31.2125 −1.17972
\(701\) 18.3989 0.694918 0.347459 0.937695i \(-0.387045\pi\)
0.347459 + 0.937695i \(0.387045\pi\)
\(702\) −2.90773 −0.109745
\(703\) −29.5187 −1.11332
\(704\) 1.77854 0.0670312
\(705\) 5.45413 0.205415
\(706\) 2.69235 0.101328
\(707\) −58.5003 −2.20013
\(708\) −38.4167 −1.44379
\(709\) 4.91804 0.184701 0.0923505 0.995727i \(-0.470562\pi\)
0.0923505 + 0.995727i \(0.470562\pi\)
\(710\) 0.427353 0.0160383
\(711\) −4.88204 −0.183091
\(712\) −15.3872 −0.576661
\(713\) 36.6343 1.37196
\(714\) 19.0588 0.713259
\(715\) 0.528407 0.0197613
\(716\) 13.9000 0.519468
\(717\) −17.8105 −0.665144
\(718\) −14.0000 −0.522477
\(719\) −30.6686 −1.14375 −0.571873 0.820342i \(-0.693783\pi\)
−0.571873 + 0.820342i \(0.693783\pi\)
\(720\) −1.20759 −0.0450041
\(721\) −13.9378 −0.519072
\(722\) −3.03110 −0.112806
\(723\) −61.9608 −2.30435
\(724\) 14.3755 0.534262
\(725\) −36.4134 −1.35236
\(726\) 1.86135 0.0690810
\(727\) −25.9818 −0.963610 −0.481805 0.876278i \(-0.660019\pi\)
−0.481805 + 0.876278i \(0.660019\pi\)
\(728\) −21.0369 −0.779679
\(729\) −38.8212 −1.43782
\(730\) 0.321034 0.0118820
\(731\) 15.6338 0.578238
\(732\) 54.0148 1.99645
\(733\) 12.5535 0.463676 0.231838 0.972754i \(-0.425526\pi\)
0.231838 + 0.972754i \(0.425526\pi\)
\(734\) 21.3360 0.787525
\(735\) −7.67966 −0.283269
\(736\) −28.2969 −1.04304
\(737\) 2.88224 0.106169
\(738\) 9.09623 0.334837
\(739\) 34.5797 1.27203 0.636017 0.771675i \(-0.280581\pi\)
0.636017 + 0.771675i \(0.280581\pi\)
\(740\) 3.04711 0.112014
\(741\) 19.8640 0.729722
\(742\) −7.88444 −0.289447
\(743\) −53.7937 −1.97350 −0.986749 0.162254i \(-0.948124\pi\)
−0.986749 + 0.162254i \(0.948124\pi\)
\(744\) 49.1262 1.80105
\(745\) 3.21715 0.117867
\(746\) −17.5623 −0.643003
\(747\) −30.7201 −1.12399
\(748\) 3.58762 0.131177
\(749\) −12.1611 −0.444355
\(750\) 4.92027 0.179663
\(751\) 8.65830 0.315946 0.157973 0.987443i \(-0.449504\pi\)
0.157973 + 0.987443i \(0.449504\pi\)
\(752\) −9.41888 −0.343471
\(753\) −45.9268 −1.67367
\(754\) −10.4760 −0.381514
\(755\) 4.43353 0.161353
\(756\) 12.9840 0.472224
\(757\) 38.9883 1.41705 0.708527 0.705684i \(-0.249360\pi\)
0.708527 + 0.705684i \(0.249360\pi\)
\(758\) −19.6509 −0.713754
\(759\) −12.6186 −0.458025
\(760\) −2.54983 −0.0924920
\(761\) −11.7092 −0.424458 −0.212229 0.977220i \(-0.568072\pi\)
−0.212229 + 0.977220i \(0.568072\pi\)
\(762\) −35.3617 −1.28102
\(763\) 48.2242 1.74583
\(764\) −31.8237 −1.15134
\(765\) 2.42835 0.0877972
\(766\) −9.14615 −0.330464
\(767\) −19.6494 −0.709498
\(768\) −28.6500 −1.03382
\(769\) 31.3179 1.12935 0.564676 0.825313i \(-0.309001\pi\)
0.564676 + 0.825313i \(0.309001\pi\)
\(770\) 0.808625 0.0291408
\(771\) 56.3589 2.02972
\(772\) 2.94371 0.105946
\(773\) −33.1955 −1.19396 −0.596980 0.802256i \(-0.703633\pi\)
−0.596980 + 0.802256i \(0.703633\pi\)
\(774\) −17.5629 −0.631284
\(775\) 37.2811 1.33918
\(776\) −26.2214 −0.941295
\(777\) −85.1023 −3.05303
\(778\) 18.8953 0.677430
\(779\) −12.9146 −0.462713
\(780\) −2.05049 −0.0734193
\(781\) −2.24673 −0.0803942
\(782\) 8.33515 0.298064
\(783\) 15.1475 0.541329
\(784\) 13.2622 0.473650
\(785\) −4.81118 −0.171718
\(786\) 1.86135 0.0663920
\(787\) −22.0869 −0.787311 −0.393656 0.919258i \(-0.628790\pi\)
−0.393656 + 0.919258i \(0.628790\pi\)
\(788\) −1.61746 −0.0576195
\(789\) 6.00694 0.213853
\(790\) 0.245208 0.00872412
\(791\) −10.5208 −0.374075
\(792\) −9.44181 −0.335500
\(793\) 27.6275 0.981081
\(794\) −6.95108 −0.246685
\(795\) −1.80038 −0.0638530
\(796\) 4.24079 0.150311
\(797\) −15.1330 −0.536038 −0.268019 0.963414i \(-0.586369\pi\)
−0.268019 + 0.963414i \(0.586369\pi\)
\(798\) 30.3980 1.07608
\(799\) 18.9406 0.670069
\(800\) −28.7965 −1.01811
\(801\) 23.3728 0.825837
\(802\) −14.4113 −0.508881
\(803\) −1.68777 −0.0595602
\(804\) −11.1846 −0.394449
\(805\) −5.48188 −0.193211
\(806\) 10.7256 0.377795
\(807\) −21.5681 −0.759233
\(808\) −34.3084 −1.20697
\(809\) −1.66364 −0.0584904 −0.0292452 0.999572i \(-0.509310\pi\)
−0.0292452 + 0.999572i \(0.509310\pi\)
\(810\) 1.14495 0.0402294
\(811\) −29.3003 −1.02887 −0.514436 0.857529i \(-0.671999\pi\)
−0.514436 + 0.857529i \(0.671999\pi\)
\(812\) 46.7790 1.64162
\(813\) −30.3782 −1.06541
\(814\) 5.49005 0.192426
\(815\) −2.40839 −0.0843621
\(816\) −7.51561 −0.263099
\(817\) 24.9353 0.872375
\(818\) −25.9356 −0.906817
\(819\) 31.9544 1.11658
\(820\) 1.33313 0.0465548
\(821\) 7.42566 0.259157 0.129579 0.991569i \(-0.458638\pi\)
0.129579 + 0.991569i \(0.458638\pi\)
\(822\) 39.9523 1.39350
\(823\) 54.3346 1.89399 0.946993 0.321254i \(-0.104104\pi\)
0.946993 + 0.321254i \(0.104104\pi\)
\(824\) −8.17405 −0.284757
\(825\) −12.8413 −0.447078
\(826\) −30.0696 −1.04626
\(827\) −24.3212 −0.845730 −0.422865 0.906193i \(-0.638975\pi\)
−0.422865 + 0.906193i \(0.638975\pi\)
\(828\) 27.3225 0.949521
\(829\) −14.6214 −0.507821 −0.253910 0.967228i \(-0.581717\pi\)
−0.253910 + 0.967228i \(0.581717\pi\)
\(830\) 1.54297 0.0535572
\(831\) −47.4349 −1.64550
\(832\) −3.53006 −0.122383
\(833\) −26.6692 −0.924032
\(834\) 7.84466 0.271638
\(835\) −2.34486 −0.0811471
\(836\) 5.72211 0.197903
\(837\) −15.5085 −0.536051
\(838\) 24.1539 0.834382
\(839\) −32.5592 −1.12407 −0.562034 0.827114i \(-0.689981\pi\)
−0.562034 + 0.827114i \(0.689981\pi\)
\(840\) −7.35114 −0.253639
\(841\) 25.5737 0.881852
\(842\) 13.0056 0.448204
\(843\) −26.0154 −0.896018
\(844\) 18.5198 0.637476
\(845\) 2.41215 0.0829806
\(846\) −21.2776 −0.731540
\(847\) −4.25119 −0.146073
\(848\) 3.10913 0.106768
\(849\) 29.0921 0.998439
\(850\) 8.48231 0.290941
\(851\) −37.2185 −1.27583
\(852\) 8.71846 0.298690
\(853\) −40.7002 −1.39355 −0.696773 0.717291i \(-0.745382\pi\)
−0.696773 + 0.717291i \(0.745382\pi\)
\(854\) 42.2786 1.44674
\(855\) 3.87312 0.132458
\(856\) −7.13203 −0.243768
\(857\) 46.5073 1.58866 0.794330 0.607486i \(-0.207822\pi\)
0.794330 + 0.607486i \(0.207822\pi\)
\(858\) −3.69441 −0.126125
\(859\) −2.91381 −0.0994178 −0.0497089 0.998764i \(-0.515829\pi\)
−0.0497089 + 0.998764i \(0.515829\pi\)
\(860\) −2.57398 −0.0877721
\(861\) −37.2327 −1.26889
\(862\) −16.3568 −0.557115
\(863\) −2.91705 −0.0992975 −0.0496488 0.998767i \(-0.515810\pi\)
−0.0496488 + 0.998767i \(0.515810\pi\)
\(864\) 11.9790 0.407533
\(865\) 1.27092 0.0432126
\(866\) 7.69556 0.261506
\(867\) −29.1751 −0.990840
\(868\) −47.8937 −1.62562
\(869\) −1.28914 −0.0437309
\(870\) −3.66074 −0.124111
\(871\) −5.72068 −0.193838
\(872\) 28.2818 0.957743
\(873\) 39.8296 1.34803
\(874\) 13.2942 0.449683
\(875\) −11.2376 −0.379899
\(876\) 6.54943 0.221285
\(877\) 30.6741 1.03579 0.517896 0.855444i \(-0.326715\pi\)
0.517896 + 0.855444i \(0.326715\pi\)
\(878\) 26.1110 0.881205
\(879\) −51.0812 −1.72293
\(880\) −0.318871 −0.0107491
\(881\) 11.6939 0.393976 0.196988 0.980406i \(-0.436884\pi\)
0.196988 + 0.980406i \(0.436884\pi\)
\(882\) 29.9598 1.00880
\(883\) −26.5476 −0.893399 −0.446699 0.894684i \(-0.647401\pi\)
−0.446699 + 0.894684i \(0.647401\pi\)
\(884\) −7.12074 −0.239496
\(885\) −6.86629 −0.230808
\(886\) −15.9220 −0.534910
\(887\) 17.0043 0.570947 0.285473 0.958387i \(-0.407849\pi\)
0.285473 + 0.958387i \(0.407849\pi\)
\(888\) −49.9095 −1.67485
\(889\) 80.7637 2.70873
\(890\) −1.17394 −0.0393504
\(891\) −6.01934 −0.201656
\(892\) 4.76870 0.159668
\(893\) 30.2094 1.01092
\(894\) −22.4930 −0.752279
\(895\) 2.48437 0.0830435
\(896\) 44.2698 1.47895
\(897\) 25.0454 0.836241
\(898\) −20.3721 −0.679825
\(899\) −55.8741 −1.86351
\(900\) 27.8049 0.926829
\(901\) −6.25219 −0.208291
\(902\) 2.40192 0.0799752
\(903\) 71.8883 2.39229
\(904\) −6.17005 −0.205213
\(905\) 2.56936 0.0854085
\(906\) −30.9975 −1.02982
\(907\) 29.5835 0.982304 0.491152 0.871074i \(-0.336576\pi\)
0.491152 + 0.871074i \(0.336576\pi\)
\(908\) −25.2117 −0.836680
\(909\) 52.1135 1.72849
\(910\) −1.60496 −0.0532040
\(911\) −28.2406 −0.935654 −0.467827 0.883820i \(-0.654963\pi\)
−0.467827 + 0.883820i \(0.654963\pi\)
\(912\) −11.9871 −0.396932
\(913\) −8.11186 −0.268463
\(914\) 29.4701 0.974784
\(915\) 9.65417 0.319157
\(916\) 17.1557 0.566840
\(917\) −4.25119 −0.140387
\(918\) −3.52854 −0.116459
\(919\) 38.4904 1.26968 0.634841 0.772643i \(-0.281066\pi\)
0.634841 + 0.772643i \(0.281066\pi\)
\(920\) −3.21493 −0.105993
\(921\) 62.0126 2.04338
\(922\) 1.81576 0.0597988
\(923\) 4.45932 0.146780
\(924\) 16.4968 0.542705
\(925\) −37.8756 −1.24534
\(926\) 3.47670 0.114252
\(927\) 12.4162 0.407800
\(928\) 43.1580 1.41673
\(929\) −27.9687 −0.917623 −0.458812 0.888534i \(-0.651725\pi\)
−0.458812 + 0.888534i \(0.651725\pi\)
\(930\) 3.74797 0.122901
\(931\) −42.5362 −1.39407
\(932\) −17.2337 −0.564509
\(933\) −64.8997 −2.12472
\(934\) −16.6646 −0.545281
\(935\) 0.641223 0.0209702
\(936\) 18.7402 0.612541
\(937\) 19.5560 0.638867 0.319434 0.947609i \(-0.396507\pi\)
0.319434 + 0.947609i \(0.396507\pi\)
\(938\) −8.75441 −0.285841
\(939\) 55.0434 1.79627
\(940\) −3.11841 −0.101711
\(941\) 16.1475 0.526393 0.263196 0.964742i \(-0.415223\pi\)
0.263196 + 0.964742i \(0.415223\pi\)
\(942\) 33.6378 1.09598
\(943\) −16.2833 −0.530256
\(944\) 11.8576 0.385931
\(945\) 2.32066 0.0754910
\(946\) −4.63760 −0.150781
\(947\) −26.2944 −0.854454 −0.427227 0.904144i \(-0.640509\pi\)
−0.427227 + 0.904144i \(0.640509\pi\)
\(948\) 5.00251 0.162474
\(949\) 3.34990 0.108742
\(950\) 13.5289 0.438936
\(951\) −58.0388 −1.88204
\(952\) −25.5283 −0.827377
\(953\) 58.3380 1.88975 0.944876 0.327428i \(-0.106182\pi\)
0.944876 + 0.327428i \(0.106182\pi\)
\(954\) 7.02364 0.227399
\(955\) −5.68790 −0.184056
\(956\) 10.1832 0.329347
\(957\) 19.2457 0.622124
\(958\) −10.4015 −0.336056
\(959\) −91.2483 −2.94656
\(960\) −1.23354 −0.0398125
\(961\) 26.2055 0.845340
\(962\) −10.8967 −0.351323
\(963\) 10.8334 0.349100
\(964\) 35.4262 1.14100
\(965\) 0.526134 0.0169369
\(966\) 38.3272 1.23316
\(967\) 25.0975 0.807083 0.403541 0.914961i \(-0.367779\pi\)
0.403541 + 0.914961i \(0.367779\pi\)
\(968\) −2.49318 −0.0801337
\(969\) 24.1050 0.774364
\(970\) −2.00051 −0.0642325
\(971\) −53.2720 −1.70958 −0.854790 0.518974i \(-0.826314\pi\)
−0.854790 + 0.518974i \(0.826314\pi\)
\(972\) 32.5208 1.04310
\(973\) −17.9167 −0.574383
\(974\) 8.45042 0.270769
\(975\) 25.4876 0.816256
\(976\) −16.6720 −0.533659
\(977\) 51.6324 1.65187 0.825933 0.563768i \(-0.190649\pi\)
0.825933 + 0.563768i \(0.190649\pi\)
\(978\) 16.8385 0.538435
\(979\) 6.17174 0.197250
\(980\) 4.39086 0.140261
\(981\) −42.9593 −1.37158
\(982\) −10.2347 −0.326602
\(983\) 19.9166 0.635242 0.317621 0.948218i \(-0.397116\pi\)
0.317621 + 0.948218i \(0.397116\pi\)
\(984\) −21.8357 −0.696096
\(985\) −0.289091 −0.00921120
\(986\) −12.7127 −0.404854
\(987\) 87.0936 2.77222
\(988\) −11.3573 −0.361323
\(989\) 31.4395 0.999717
\(990\) −0.720343 −0.0228940
\(991\) −32.4303 −1.03018 −0.515092 0.857135i \(-0.672242\pi\)
−0.515092 + 0.857135i \(0.672242\pi\)
\(992\) −44.1864 −1.40292
\(993\) −63.0886 −2.00206
\(994\) 6.82413 0.216448
\(995\) 0.757964 0.0240291
\(996\) 31.4782 0.997425
\(997\) −13.8957 −0.440082 −0.220041 0.975491i \(-0.570619\pi\)
−0.220041 + 0.975491i \(0.570619\pi\)
\(998\) −1.10890 −0.0351015
\(999\) 15.7558 0.498491
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 1441.2.a.c.1.17 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.c.1.17 23 1.1 even 1 trivial