Properties

Label 6022.2.a.b.1.19
Level $6022$
Weight $2$
Character 6022.1
Self dual yes
Analytic conductor $48.086$
Analytic rank $1$
Dimension $54$
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] = [6022,2,Mod(1,6022)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6022.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6022 = 2 \cdot 3011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6022.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0859120972\)
Analytic rank: \(1\)
Dimension: \(54\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 6022.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.52904 q^{3} +1.00000 q^{4} -3.77354 q^{5} -1.52904 q^{6} +0.908453 q^{7} +1.00000 q^{8} -0.662042 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.52904 q^{3} +1.00000 q^{4} -3.77354 q^{5} -1.52904 q^{6} +0.908453 q^{7} +1.00000 q^{8} -0.662042 q^{9} -3.77354 q^{10} -2.19947 q^{11} -1.52904 q^{12} -1.27619 q^{13} +0.908453 q^{14} +5.76988 q^{15} +1.00000 q^{16} +0.0603416 q^{17} -0.662042 q^{18} +4.24736 q^{19} -3.77354 q^{20} -1.38906 q^{21} -2.19947 q^{22} -1.92041 q^{23} -1.52904 q^{24} +9.23957 q^{25} -1.27619 q^{26} +5.59940 q^{27} +0.908453 q^{28} +9.79145 q^{29} +5.76988 q^{30} +7.27484 q^{31} +1.00000 q^{32} +3.36308 q^{33} +0.0603416 q^{34} -3.42808 q^{35} -0.662042 q^{36} -6.02467 q^{37} +4.24736 q^{38} +1.95135 q^{39} -3.77354 q^{40} -4.25253 q^{41} -1.38906 q^{42} +12.3544 q^{43} -2.19947 q^{44} +2.49824 q^{45} -1.92041 q^{46} -5.29910 q^{47} -1.52904 q^{48} -6.17471 q^{49} +9.23957 q^{50} -0.0922646 q^{51} -1.27619 q^{52} -1.73521 q^{53} +5.59940 q^{54} +8.29980 q^{55} +0.908453 q^{56} -6.49438 q^{57} +9.79145 q^{58} -5.60111 q^{59} +5.76988 q^{60} -5.24714 q^{61} +7.27484 q^{62} -0.601434 q^{63} +1.00000 q^{64} +4.81577 q^{65} +3.36308 q^{66} -0.803318 q^{67} +0.0603416 q^{68} +2.93638 q^{69} -3.42808 q^{70} -4.81511 q^{71} -0.662042 q^{72} +2.23818 q^{73} -6.02467 q^{74} -14.1277 q^{75} +4.24736 q^{76} -1.99812 q^{77} +1.95135 q^{78} +8.73390 q^{79} -3.77354 q^{80} -6.57558 q^{81} -4.25253 q^{82} +1.24574 q^{83} -1.38906 q^{84} -0.227701 q^{85} +12.3544 q^{86} -14.9715 q^{87} -2.19947 q^{88} -3.82706 q^{89} +2.49824 q^{90} -1.15936 q^{91} -1.92041 q^{92} -11.1235 q^{93} -5.29910 q^{94} -16.0276 q^{95} -1.52904 q^{96} +4.34112 q^{97} -6.17471 q^{98} +1.45614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.52904 −0.882791 −0.441395 0.897313i \(-0.645516\pi\)
−0.441395 + 0.897313i \(0.645516\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.77354 −1.68758 −0.843788 0.536676i \(-0.819680\pi\)
−0.843788 + 0.536676i \(0.819680\pi\)
\(6\) −1.52904 −0.624227
\(7\) 0.908453 0.343363 0.171682 0.985153i \(-0.445080\pi\)
0.171682 + 0.985153i \(0.445080\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.662042 −0.220681
\(10\) −3.77354 −1.19330
\(11\) −2.19947 −0.663167 −0.331583 0.943426i \(-0.607583\pi\)
−0.331583 + 0.943426i \(0.607583\pi\)
\(12\) −1.52904 −0.441395
\(13\) −1.27619 −0.353953 −0.176976 0.984215i \(-0.556632\pi\)
−0.176976 + 0.984215i \(0.556632\pi\)
\(14\) 0.908453 0.242794
\(15\) 5.76988 1.48978
\(16\) 1.00000 0.250000
\(17\) 0.0603416 0.0146350 0.00731749 0.999973i \(-0.497671\pi\)
0.00731749 + 0.999973i \(0.497671\pi\)
\(18\) −0.662042 −0.156045
\(19\) 4.24736 0.974411 0.487206 0.873287i \(-0.338016\pi\)
0.487206 + 0.873287i \(0.338016\pi\)
\(20\) −3.77354 −0.843788
\(21\) −1.38906 −0.303118
\(22\) −2.19947 −0.468930
\(23\) −1.92041 −0.400432 −0.200216 0.979752i \(-0.564164\pi\)
−0.200216 + 0.979752i \(0.564164\pi\)
\(24\) −1.52904 −0.312114
\(25\) 9.23957 1.84791
\(26\) −1.27619 −0.250282
\(27\) 5.59940 1.07761
\(28\) 0.908453 0.171682
\(29\) 9.79145 1.81823 0.909114 0.416548i \(-0.136760\pi\)
0.909114 + 0.416548i \(0.136760\pi\)
\(30\) 5.76988 1.05343
\(31\) 7.27484 1.30660 0.653300 0.757099i \(-0.273384\pi\)
0.653300 + 0.757099i \(0.273384\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.36308 0.585437
\(34\) 0.0603416 0.0103485
\(35\) −3.42808 −0.579451
\(36\) −0.662042 −0.110340
\(37\) −6.02467 −0.990450 −0.495225 0.868765i \(-0.664914\pi\)
−0.495225 + 0.868765i \(0.664914\pi\)
\(38\) 4.24736 0.689013
\(39\) 1.95135 0.312466
\(40\) −3.77354 −0.596648
\(41\) −4.25253 −0.664133 −0.332067 0.943256i \(-0.607746\pi\)
−0.332067 + 0.943256i \(0.607746\pi\)
\(42\) −1.38906 −0.214337
\(43\) 12.3544 1.88403 0.942017 0.335565i \(-0.108927\pi\)
0.942017 + 0.335565i \(0.108927\pi\)
\(44\) −2.19947 −0.331583
\(45\) 2.49824 0.372415
\(46\) −1.92041 −0.283149
\(47\) −5.29910 −0.772953 −0.386476 0.922299i \(-0.626308\pi\)
−0.386476 + 0.922299i \(0.626308\pi\)
\(48\) −1.52904 −0.220698
\(49\) −6.17471 −0.882102
\(50\) 9.23957 1.30667
\(51\) −0.0922646 −0.0129196
\(52\) −1.27619 −0.176976
\(53\) −1.73521 −0.238350 −0.119175 0.992873i \(-0.538025\pi\)
−0.119175 + 0.992873i \(0.538025\pi\)
\(54\) 5.59940 0.761982
\(55\) 8.29980 1.11914
\(56\) 0.908453 0.121397
\(57\) −6.49438 −0.860201
\(58\) 9.79145 1.28568
\(59\) −5.60111 −0.729202 −0.364601 0.931164i \(-0.618795\pi\)
−0.364601 + 0.931164i \(0.618795\pi\)
\(60\) 5.76988 0.744888
\(61\) −5.24714 −0.671828 −0.335914 0.941893i \(-0.609045\pi\)
−0.335914 + 0.941893i \(0.609045\pi\)
\(62\) 7.27484 0.923906
\(63\) −0.601434 −0.0757736
\(64\) 1.00000 0.125000
\(65\) 4.81577 0.597322
\(66\) 3.36308 0.413967
\(67\) −0.803318 −0.0981410 −0.0490705 0.998795i \(-0.515626\pi\)
−0.0490705 + 0.998795i \(0.515626\pi\)
\(68\) 0.0603416 0.00731749
\(69\) 2.93638 0.353498
\(70\) −3.42808 −0.409734
\(71\) −4.81511 −0.571448 −0.285724 0.958312i \(-0.592234\pi\)
−0.285724 + 0.958312i \(0.592234\pi\)
\(72\) −0.662042 −0.0780224
\(73\) 2.23818 0.261959 0.130980 0.991385i \(-0.458188\pi\)
0.130980 + 0.991385i \(0.458188\pi\)
\(74\) −6.02467 −0.700354
\(75\) −14.1277 −1.63132
\(76\) 4.24736 0.487206
\(77\) −1.99812 −0.227707
\(78\) 1.95135 0.220947
\(79\) 8.73390 0.982640 0.491320 0.870979i \(-0.336515\pi\)
0.491320 + 0.870979i \(0.336515\pi\)
\(80\) −3.77354 −0.421894
\(81\) −6.57558 −0.730619
\(82\) −4.25253 −0.469613
\(83\) 1.24574 0.136738 0.0683689 0.997660i \(-0.478221\pi\)
0.0683689 + 0.997660i \(0.478221\pi\)
\(84\) −1.38906 −0.151559
\(85\) −0.227701 −0.0246977
\(86\) 12.3544 1.33221
\(87\) −14.9715 −1.60511
\(88\) −2.19947 −0.234465
\(89\) −3.82706 −0.405667 −0.202834 0.979213i \(-0.565015\pi\)
−0.202834 + 0.979213i \(0.565015\pi\)
\(90\) 2.49824 0.263337
\(91\) −1.15936 −0.121534
\(92\) −1.92041 −0.200216
\(93\) −11.1235 −1.15345
\(94\) −5.29910 −0.546560
\(95\) −16.0276 −1.64439
\(96\) −1.52904 −0.156057
\(97\) 4.34112 0.440774 0.220387 0.975412i \(-0.429268\pi\)
0.220387 + 0.975412i \(0.429268\pi\)
\(98\) −6.17471 −0.623740
\(99\) 1.45614 0.146348
\(100\) 9.23957 0.923957
\(101\) −10.2852 −1.02342 −0.511708 0.859159i \(-0.670987\pi\)
−0.511708 + 0.859159i \(0.670987\pi\)
\(102\) −0.0922646 −0.00913555
\(103\) −6.32214 −0.622939 −0.311469 0.950256i \(-0.600821\pi\)
−0.311469 + 0.950256i \(0.600821\pi\)
\(104\) −1.27619 −0.125141
\(105\) 5.24167 0.511534
\(106\) −1.73521 −0.168539
\(107\) −0.853040 −0.0824665 −0.0412332 0.999150i \(-0.513129\pi\)
−0.0412332 + 0.999150i \(0.513129\pi\)
\(108\) 5.59940 0.538803
\(109\) −5.91086 −0.566158 −0.283079 0.959097i \(-0.591356\pi\)
−0.283079 + 0.959097i \(0.591356\pi\)
\(110\) 8.29980 0.791354
\(111\) 9.21196 0.874360
\(112\) 0.908453 0.0858408
\(113\) 7.51312 0.706775 0.353387 0.935477i \(-0.385030\pi\)
0.353387 + 0.935477i \(0.385030\pi\)
\(114\) −6.49438 −0.608254
\(115\) 7.24672 0.675760
\(116\) 9.79145 0.909114
\(117\) 0.844894 0.0781105
\(118\) −5.60111 −0.515624
\(119\) 0.0548175 0.00502511
\(120\) 5.76988 0.526716
\(121\) −6.16231 −0.560210
\(122\) −5.24714 −0.475054
\(123\) 6.50228 0.586291
\(124\) 7.27484 0.653300
\(125\) −15.9982 −1.43092
\(126\) −0.601434 −0.0535800
\(127\) −8.02104 −0.711752 −0.355876 0.934533i \(-0.615818\pi\)
−0.355876 + 0.934533i \(0.615818\pi\)
\(128\) 1.00000 0.0883883
\(129\) −18.8904 −1.66321
\(130\) 4.81577 0.422371
\(131\) −16.6949 −1.45864 −0.729320 0.684172i \(-0.760164\pi\)
−0.729320 + 0.684172i \(0.760164\pi\)
\(132\) 3.36308 0.292719
\(133\) 3.85853 0.334577
\(134\) −0.803318 −0.0693961
\(135\) −21.1295 −1.81854
\(136\) 0.0603416 0.00517425
\(137\) −18.5136 −1.58172 −0.790862 0.611995i \(-0.790367\pi\)
−0.790862 + 0.611995i \(0.790367\pi\)
\(138\) 2.93638 0.249961
\(139\) 5.05033 0.428364 0.214182 0.976794i \(-0.431292\pi\)
0.214182 + 0.976794i \(0.431292\pi\)
\(140\) −3.42808 −0.289726
\(141\) 8.10252 0.682356
\(142\) −4.81511 −0.404075
\(143\) 2.80696 0.234730
\(144\) −0.662042 −0.0551702
\(145\) −36.9484 −3.06840
\(146\) 2.23818 0.185233
\(147\) 9.44137 0.778711
\(148\) −6.02467 −0.495225
\(149\) 5.04022 0.412911 0.206455 0.978456i \(-0.433807\pi\)
0.206455 + 0.978456i \(0.433807\pi\)
\(150\) −14.1277 −1.15352
\(151\) 10.1333 0.824632 0.412316 0.911041i \(-0.364720\pi\)
0.412316 + 0.911041i \(0.364720\pi\)
\(152\) 4.24736 0.344506
\(153\) −0.0399486 −0.00322966
\(154\) −1.99812 −0.161013
\(155\) −27.4519 −2.20499
\(156\) 1.95135 0.156233
\(157\) −0.534403 −0.0426500 −0.0213250 0.999773i \(-0.506788\pi\)
−0.0213250 + 0.999773i \(0.506788\pi\)
\(158\) 8.73390 0.694831
\(159\) 2.65321 0.210413
\(160\) −3.77354 −0.298324
\(161\) −1.74460 −0.137494
\(162\) −6.57558 −0.516626
\(163\) −7.96805 −0.624106 −0.312053 0.950065i \(-0.601017\pi\)
−0.312053 + 0.950065i \(0.601017\pi\)
\(164\) −4.25253 −0.332067
\(165\) −12.6907 −0.987970
\(166\) 1.24574 0.0966882
\(167\) −12.9722 −1.00382 −0.501911 0.864919i \(-0.667369\pi\)
−0.501911 + 0.864919i \(0.667369\pi\)
\(168\) −1.38906 −0.107168
\(169\) −11.3713 −0.874717
\(170\) −0.227701 −0.0174639
\(171\) −2.81193 −0.215034
\(172\) 12.3544 0.942017
\(173\) 3.44804 0.262149 0.131075 0.991373i \(-0.458157\pi\)
0.131075 + 0.991373i \(0.458157\pi\)
\(174\) −14.9715 −1.13499
\(175\) 8.39372 0.634506
\(176\) −2.19947 −0.165792
\(177\) 8.56431 0.643733
\(178\) −3.82706 −0.286850
\(179\) 23.3164 1.74275 0.871374 0.490619i \(-0.163229\pi\)
0.871374 + 0.490619i \(0.163229\pi\)
\(180\) 2.49824 0.186208
\(181\) 5.03003 0.373879 0.186940 0.982371i \(-0.440143\pi\)
0.186940 + 0.982371i \(0.440143\pi\)
\(182\) −1.15936 −0.0859377
\(183\) 8.02308 0.593083
\(184\) −1.92041 −0.141574
\(185\) 22.7343 1.67146
\(186\) −11.1235 −0.815616
\(187\) −0.132720 −0.00970543
\(188\) −5.29910 −0.386476
\(189\) 5.08680 0.370010
\(190\) −16.0276 −1.16276
\(191\) 11.7699 0.851640 0.425820 0.904808i \(-0.359986\pi\)
0.425820 + 0.904808i \(0.359986\pi\)
\(192\) −1.52904 −0.110349
\(193\) −13.0136 −0.936740 −0.468370 0.883532i \(-0.655159\pi\)
−0.468370 + 0.883532i \(0.655159\pi\)
\(194\) 4.34112 0.311675
\(195\) −7.36349 −0.527311
\(196\) −6.17471 −0.441051
\(197\) 17.3836 1.23853 0.619263 0.785183i \(-0.287431\pi\)
0.619263 + 0.785183i \(0.287431\pi\)
\(198\) 1.45614 0.103484
\(199\) 17.6285 1.24965 0.624825 0.780765i \(-0.285170\pi\)
0.624825 + 0.780765i \(0.285170\pi\)
\(200\) 9.23957 0.653336
\(201\) 1.22830 0.0866379
\(202\) −10.2852 −0.723664
\(203\) 8.89508 0.624312
\(204\) −0.0922646 −0.00645981
\(205\) 16.0471 1.12078
\(206\) −6.32214 −0.440484
\(207\) 1.27139 0.0883677
\(208\) −1.27619 −0.0884882
\(209\) −9.34196 −0.646197
\(210\) 5.24167 0.361709
\(211\) 9.47712 0.652432 0.326216 0.945295i \(-0.394226\pi\)
0.326216 + 0.945295i \(0.394226\pi\)
\(212\) −1.73521 −0.119175
\(213\) 7.36248 0.504469
\(214\) −0.853040 −0.0583126
\(215\) −46.6199 −3.17945
\(216\) 5.59940 0.380991
\(217\) 6.60886 0.448638
\(218\) −5.91086 −0.400334
\(219\) −3.42227 −0.231255
\(220\) 8.29980 0.559572
\(221\) −0.0770076 −0.00518009
\(222\) 9.21196 0.618266
\(223\) 25.6987 1.72091 0.860455 0.509527i \(-0.170180\pi\)
0.860455 + 0.509527i \(0.170180\pi\)
\(224\) 0.908453 0.0606986
\(225\) −6.11698 −0.407799
\(226\) 7.51312 0.499765
\(227\) −22.5818 −1.49881 −0.749404 0.662113i \(-0.769660\pi\)
−0.749404 + 0.662113i \(0.769660\pi\)
\(228\) −6.49438 −0.430101
\(229\) −3.19706 −0.211268 −0.105634 0.994405i \(-0.533687\pi\)
−0.105634 + 0.994405i \(0.533687\pi\)
\(230\) 7.24672 0.477835
\(231\) 3.05520 0.201018
\(232\) 9.79145 0.642840
\(233\) −9.21154 −0.603468 −0.301734 0.953392i \(-0.597565\pi\)
−0.301734 + 0.953392i \(0.597565\pi\)
\(234\) 0.844894 0.0552325
\(235\) 19.9963 1.30442
\(236\) −5.60111 −0.364601
\(237\) −13.3545 −0.867465
\(238\) 0.0548175 0.00355329
\(239\) −18.4190 −1.19143 −0.595714 0.803197i \(-0.703131\pi\)
−0.595714 + 0.803197i \(0.703131\pi\)
\(240\) 5.76988 0.372444
\(241\) −18.5921 −1.19762 −0.598810 0.800891i \(-0.704360\pi\)
−0.598810 + 0.800891i \(0.704360\pi\)
\(242\) −6.16231 −0.396128
\(243\) −6.74390 −0.432621
\(244\) −5.24714 −0.335914
\(245\) 23.3005 1.48861
\(246\) 6.50228 0.414570
\(247\) −5.42046 −0.344895
\(248\) 7.27484 0.461953
\(249\) −1.90478 −0.120711
\(250\) −15.9982 −1.01181
\(251\) 21.8270 1.37771 0.688853 0.724901i \(-0.258114\pi\)
0.688853 + 0.724901i \(0.258114\pi\)
\(252\) −0.601434 −0.0378868
\(253\) 4.22389 0.265553
\(254\) −8.02104 −0.503285
\(255\) 0.348164 0.0218029
\(256\) 1.00000 0.0625000
\(257\) −22.7083 −1.41650 −0.708251 0.705961i \(-0.750515\pi\)
−0.708251 + 0.705961i \(0.750515\pi\)
\(258\) −18.8904 −1.17607
\(259\) −5.47314 −0.340084
\(260\) 4.81577 0.298661
\(261\) −6.48235 −0.401247
\(262\) −16.6949 −1.03141
\(263\) −15.0907 −0.930530 −0.465265 0.885172i \(-0.654041\pi\)
−0.465265 + 0.885172i \(0.654041\pi\)
\(264\) 3.36308 0.206983
\(265\) 6.54789 0.402234
\(266\) 3.85853 0.236582
\(267\) 5.85172 0.358119
\(268\) −0.803318 −0.0490705
\(269\) −5.69049 −0.346955 −0.173478 0.984838i \(-0.555500\pi\)
−0.173478 + 0.984838i \(0.555500\pi\)
\(270\) −21.1295 −1.28590
\(271\) −22.5694 −1.37099 −0.685496 0.728076i \(-0.740415\pi\)
−0.685496 + 0.728076i \(0.740415\pi\)
\(272\) 0.0603416 0.00365875
\(273\) 1.77271 0.107289
\(274\) −18.5136 −1.11845
\(275\) −20.3222 −1.22547
\(276\) 2.93638 0.176749
\(277\) −10.7753 −0.647422 −0.323711 0.946156i \(-0.604931\pi\)
−0.323711 + 0.946156i \(0.604931\pi\)
\(278\) 5.05033 0.302899
\(279\) −4.81625 −0.288341
\(280\) −3.42808 −0.204867
\(281\) 4.44325 0.265062 0.132531 0.991179i \(-0.457690\pi\)
0.132531 + 0.991179i \(0.457690\pi\)
\(282\) 8.10252 0.482498
\(283\) −17.7140 −1.05299 −0.526494 0.850179i \(-0.676494\pi\)
−0.526494 + 0.850179i \(0.676494\pi\)
\(284\) −4.81511 −0.285724
\(285\) 24.5068 1.45166
\(286\) 2.80696 0.165979
\(287\) −3.86322 −0.228039
\(288\) −0.662042 −0.0390112
\(289\) −16.9964 −0.999786
\(290\) −36.9484 −2.16968
\(291\) −6.63775 −0.389112
\(292\) 2.23818 0.130980
\(293\) −16.7408 −0.978010 −0.489005 0.872281i \(-0.662640\pi\)
−0.489005 + 0.872281i \(0.662640\pi\)
\(294\) 9.44137 0.550632
\(295\) 21.1360 1.23058
\(296\) −6.02467 −0.350177
\(297\) −12.3157 −0.714632
\(298\) 5.04022 0.291972
\(299\) 2.45081 0.141734
\(300\) −14.1277 −0.815661
\(301\) 11.2234 0.646908
\(302\) 10.1333 0.583103
\(303\) 15.7265 0.903462
\(304\) 4.24736 0.243603
\(305\) 19.8003 1.13376
\(306\) −0.0399486 −0.00228371
\(307\) 8.62774 0.492411 0.246206 0.969218i \(-0.420816\pi\)
0.246206 + 0.969218i \(0.420816\pi\)
\(308\) −1.99812 −0.113853
\(309\) 9.66679 0.549924
\(310\) −27.4519 −1.55916
\(311\) −7.71915 −0.437713 −0.218856 0.975757i \(-0.570233\pi\)
−0.218856 + 0.975757i \(0.570233\pi\)
\(312\) 1.95135 0.110473
\(313\) 15.5017 0.876206 0.438103 0.898925i \(-0.355651\pi\)
0.438103 + 0.898925i \(0.355651\pi\)
\(314\) −0.534403 −0.0301581
\(315\) 2.26953 0.127874
\(316\) 8.73390 0.491320
\(317\) 18.5157 1.03995 0.519974 0.854182i \(-0.325942\pi\)
0.519974 + 0.854182i \(0.325942\pi\)
\(318\) 2.65321 0.148784
\(319\) −21.5361 −1.20579
\(320\) −3.77354 −0.210947
\(321\) 1.30433 0.0728006
\(322\) −1.74460 −0.0972227
\(323\) 0.256292 0.0142605
\(324\) −6.57558 −0.365310
\(325\) −11.7915 −0.654074
\(326\) −7.96805 −0.441309
\(327\) 9.03794 0.499799
\(328\) −4.25253 −0.234807
\(329\) −4.81398 −0.265403
\(330\) −12.6907 −0.698600
\(331\) 12.0588 0.662809 0.331405 0.943489i \(-0.392478\pi\)
0.331405 + 0.943489i \(0.392478\pi\)
\(332\) 1.24574 0.0683689
\(333\) 3.98859 0.218573
\(334\) −12.9722 −0.709809
\(335\) 3.03135 0.165620
\(336\) −1.38906 −0.0757794
\(337\) 0.332736 0.0181253 0.00906265 0.999959i \(-0.497115\pi\)
0.00906265 + 0.999959i \(0.497115\pi\)
\(338\) −11.3713 −0.618519
\(339\) −11.4878 −0.623934
\(340\) −0.227701 −0.0123488
\(341\) −16.0008 −0.866494
\(342\) −2.81193 −0.152052
\(343\) −11.9686 −0.646244
\(344\) 12.3544 0.666107
\(345\) −11.0805 −0.596555
\(346\) 3.44804 0.185368
\(347\) −7.20839 −0.386967 −0.193483 0.981104i \(-0.561979\pi\)
−0.193483 + 0.981104i \(0.561979\pi\)
\(348\) −14.9715 −0.802557
\(349\) 18.5322 0.992007 0.496003 0.868321i \(-0.334800\pi\)
0.496003 + 0.868321i \(0.334800\pi\)
\(350\) 8.39372 0.448663
\(351\) −7.14593 −0.381421
\(352\) −2.19947 −0.117232
\(353\) −1.12923 −0.0601030 −0.0300515 0.999548i \(-0.509567\pi\)
−0.0300515 + 0.999548i \(0.509567\pi\)
\(354\) 8.56431 0.455188
\(355\) 18.1700 0.964362
\(356\) −3.82706 −0.202834
\(357\) −0.0838181 −0.00443612
\(358\) 23.3164 1.23231
\(359\) −8.06913 −0.425872 −0.212936 0.977066i \(-0.568303\pi\)
−0.212936 + 0.977066i \(0.568303\pi\)
\(360\) 2.49824 0.131669
\(361\) −0.959936 −0.0505230
\(362\) 5.03003 0.264372
\(363\) 9.42241 0.494548
\(364\) −1.15936 −0.0607671
\(365\) −8.44586 −0.442077
\(366\) 8.02308 0.419373
\(367\) −25.6227 −1.33750 −0.668748 0.743489i \(-0.733170\pi\)
−0.668748 + 0.743489i \(0.733170\pi\)
\(368\) −1.92041 −0.100108
\(369\) 2.81535 0.146561
\(370\) 22.7343 1.18190
\(371\) −1.57636 −0.0818405
\(372\) −11.1235 −0.576727
\(373\) −23.6666 −1.22541 −0.612706 0.790311i \(-0.709919\pi\)
−0.612706 + 0.790311i \(0.709919\pi\)
\(374\) −0.132720 −0.00686278
\(375\) 24.4618 1.26320
\(376\) −5.29910 −0.273280
\(377\) −12.4958 −0.643566
\(378\) 5.08680 0.261637
\(379\) 16.3583 0.840268 0.420134 0.907462i \(-0.361983\pi\)
0.420134 + 0.907462i \(0.361983\pi\)
\(380\) −16.0276 −0.822197
\(381\) 12.2645 0.628328
\(382\) 11.7699 0.602200
\(383\) 10.7888 0.551281 0.275640 0.961261i \(-0.411110\pi\)
0.275640 + 0.961261i \(0.411110\pi\)
\(384\) −1.52904 −0.0780284
\(385\) 7.53998 0.384273
\(386\) −13.0136 −0.662375
\(387\) −8.17915 −0.415770
\(388\) 4.34112 0.220387
\(389\) −7.82434 −0.396710 −0.198355 0.980130i \(-0.563560\pi\)
−0.198355 + 0.980130i \(0.563560\pi\)
\(390\) −7.36349 −0.372865
\(391\) −0.115880 −0.00586032
\(392\) −6.17471 −0.311870
\(393\) 25.5272 1.28767
\(394\) 17.3836 0.875771
\(395\) −32.9577 −1.65828
\(396\) 1.45614 0.0731740
\(397\) 1.81287 0.0909856 0.0454928 0.998965i \(-0.485514\pi\)
0.0454928 + 0.998965i \(0.485514\pi\)
\(398\) 17.6285 0.883636
\(399\) −5.89984 −0.295361
\(400\) 9.23957 0.461979
\(401\) 6.36350 0.317778 0.158889 0.987296i \(-0.449209\pi\)
0.158889 + 0.987296i \(0.449209\pi\)
\(402\) 1.22830 0.0612623
\(403\) −9.28412 −0.462475
\(404\) −10.2852 −0.511708
\(405\) 24.8132 1.23298
\(406\) 8.89508 0.441455
\(407\) 13.2511 0.656834
\(408\) −0.0922646 −0.00456778
\(409\) 18.0756 0.893778 0.446889 0.894589i \(-0.352532\pi\)
0.446889 + 0.894589i \(0.352532\pi\)
\(410\) 16.0471 0.792508
\(411\) 28.3080 1.39633
\(412\) −6.32214 −0.311469
\(413\) −5.08835 −0.250381
\(414\) 1.27139 0.0624854
\(415\) −4.70084 −0.230755
\(416\) −1.27619 −0.0625706
\(417\) −7.72215 −0.378155
\(418\) −9.34196 −0.456930
\(419\) −18.7947 −0.918183 −0.459092 0.888389i \(-0.651825\pi\)
−0.459092 + 0.888389i \(0.651825\pi\)
\(420\) 5.24167 0.255767
\(421\) −22.2817 −1.08594 −0.542971 0.839751i \(-0.682701\pi\)
−0.542971 + 0.839751i \(0.682701\pi\)
\(422\) 9.47712 0.461339
\(423\) 3.50822 0.170576
\(424\) −1.73521 −0.0842694
\(425\) 0.557530 0.0270442
\(426\) 7.36248 0.356713
\(427\) −4.76678 −0.230681
\(428\) −0.853040 −0.0412332
\(429\) −4.29195 −0.207217
\(430\) −46.6199 −2.24821
\(431\) 28.3379 1.36499 0.682495 0.730890i \(-0.260895\pi\)
0.682495 + 0.730890i \(0.260895\pi\)
\(432\) 5.59940 0.269401
\(433\) −30.3557 −1.45880 −0.729401 0.684087i \(-0.760201\pi\)
−0.729401 + 0.684087i \(0.760201\pi\)
\(434\) 6.60886 0.317235
\(435\) 56.4955 2.70875
\(436\) −5.91086 −0.283079
\(437\) −8.15666 −0.390186
\(438\) −3.42227 −0.163522
\(439\) −21.7396 −1.03757 −0.518787 0.854904i \(-0.673616\pi\)
−0.518787 + 0.854904i \(0.673616\pi\)
\(440\) 8.29980 0.395677
\(441\) 4.08792 0.194663
\(442\) −0.0770076 −0.00366288
\(443\) −6.34107 −0.301273 −0.150637 0.988589i \(-0.548132\pi\)
−0.150637 + 0.988589i \(0.548132\pi\)
\(444\) 9.21196 0.437180
\(445\) 14.4415 0.684595
\(446\) 25.6987 1.21687
\(447\) −7.70669 −0.364514
\(448\) 0.908453 0.0429204
\(449\) −17.0265 −0.803531 −0.401765 0.915743i \(-0.631603\pi\)
−0.401765 + 0.915743i \(0.631603\pi\)
\(450\) −6.11698 −0.288357
\(451\) 9.35333 0.440431
\(452\) 7.51312 0.353387
\(453\) −15.4941 −0.727978
\(454\) −22.5818 −1.05982
\(455\) 4.37490 0.205098
\(456\) −6.49438 −0.304127
\(457\) 21.1408 0.988923 0.494462 0.869199i \(-0.335365\pi\)
0.494462 + 0.869199i \(0.335365\pi\)
\(458\) −3.19706 −0.149389
\(459\) 0.337877 0.0157707
\(460\) 7.24672 0.337880
\(461\) 39.8194 1.85457 0.927287 0.374351i \(-0.122135\pi\)
0.927287 + 0.374351i \(0.122135\pi\)
\(462\) 3.05520 0.142141
\(463\) −18.1193 −0.842077 −0.421038 0.907043i \(-0.638334\pi\)
−0.421038 + 0.907043i \(0.638334\pi\)
\(464\) 9.79145 0.454557
\(465\) 41.9750 1.94654
\(466\) −9.21154 −0.426716
\(467\) 14.9161 0.690237 0.345118 0.938559i \(-0.387839\pi\)
0.345118 + 0.938559i \(0.387839\pi\)
\(468\) 0.844894 0.0390552
\(469\) −0.729777 −0.0336980
\(470\) 19.9963 0.922362
\(471\) 0.817122 0.0376510
\(472\) −5.60111 −0.257812
\(473\) −27.1733 −1.24943
\(474\) −13.3545 −0.613391
\(475\) 39.2438 1.80063
\(476\) 0.0548175 0.00251256
\(477\) 1.14878 0.0525992
\(478\) −18.4190 −0.842467
\(479\) 9.18330 0.419596 0.209798 0.977745i \(-0.432719\pi\)
0.209798 + 0.977745i \(0.432719\pi\)
\(480\) 5.76988 0.263358
\(481\) 7.68866 0.350573
\(482\) −18.5921 −0.846845
\(483\) 2.66756 0.121378
\(484\) −6.16231 −0.280105
\(485\) −16.3814 −0.743841
\(486\) −6.74390 −0.305910
\(487\) 24.2431 1.09856 0.549280 0.835638i \(-0.314902\pi\)
0.549280 + 0.835638i \(0.314902\pi\)
\(488\) −5.24714 −0.237527
\(489\) 12.1835 0.550955
\(490\) 23.3005 1.05261
\(491\) −16.3967 −0.739971 −0.369985 0.929038i \(-0.620637\pi\)
−0.369985 + 0.929038i \(0.620637\pi\)
\(492\) 6.50228 0.293145
\(493\) 0.590832 0.0266097
\(494\) −5.42046 −0.243878
\(495\) −5.49481 −0.246973
\(496\) 7.27484 0.326650
\(497\) −4.37430 −0.196214
\(498\) −1.90478 −0.0853554
\(499\) −2.03407 −0.0910576 −0.0455288 0.998963i \(-0.514497\pi\)
−0.0455288 + 0.998963i \(0.514497\pi\)
\(500\) −15.9982 −0.715460
\(501\) 19.8350 0.886164
\(502\) 21.8270 0.974186
\(503\) −5.30342 −0.236468 −0.118234 0.992986i \(-0.537723\pi\)
−0.118234 + 0.992986i \(0.537723\pi\)
\(504\) −0.601434 −0.0267900
\(505\) 38.8116 1.72709
\(506\) 4.22389 0.187775
\(507\) 17.3872 0.772192
\(508\) −8.02104 −0.355876
\(509\) −22.5760 −1.00066 −0.500331 0.865834i \(-0.666788\pi\)
−0.500331 + 0.865834i \(0.666788\pi\)
\(510\) 0.348164 0.0154169
\(511\) 2.03328 0.0899472
\(512\) 1.00000 0.0441942
\(513\) 23.7827 1.05003
\(514\) −22.7083 −1.00162
\(515\) 23.8568 1.05126
\(516\) −18.8904 −0.831604
\(517\) 11.6552 0.512596
\(518\) −5.47314 −0.240476
\(519\) −5.27218 −0.231423
\(520\) 4.81577 0.211185
\(521\) −26.6847 −1.16908 −0.584540 0.811365i \(-0.698725\pi\)
−0.584540 + 0.811365i \(0.698725\pi\)
\(522\) −6.48235 −0.283725
\(523\) −35.3765 −1.54691 −0.773454 0.633853i \(-0.781472\pi\)
−0.773454 + 0.633853i \(0.781472\pi\)
\(524\) −16.6949 −0.729320
\(525\) −12.8343 −0.560136
\(526\) −15.0907 −0.657984
\(527\) 0.438976 0.0191221
\(528\) 3.36308 0.146359
\(529\) −19.3120 −0.839654
\(530\) 6.54789 0.284422
\(531\) 3.70817 0.160921
\(532\) 3.85853 0.167288
\(533\) 5.42705 0.235072
\(534\) 5.85172 0.253229
\(535\) 3.21898 0.139168
\(536\) −0.803318 −0.0346981
\(537\) −35.6516 −1.53848
\(538\) −5.69049 −0.245334
\(539\) 13.5811 0.584980
\(540\) −21.1295 −0.909271
\(541\) −36.1096 −1.55247 −0.776237 0.630441i \(-0.782874\pi\)
−0.776237 + 0.630441i \(0.782874\pi\)
\(542\) −22.5694 −0.969438
\(543\) −7.69111 −0.330057
\(544\) 0.0603416 0.00258712
\(545\) 22.3049 0.955435
\(546\) 1.77271 0.0758650
\(547\) 12.6531 0.541007 0.270503 0.962719i \(-0.412810\pi\)
0.270503 + 0.962719i \(0.412810\pi\)
\(548\) −18.5136 −0.790862
\(549\) 3.47383 0.148259
\(550\) −20.3222 −0.866542
\(551\) 41.5878 1.77170
\(552\) 2.93638 0.124980
\(553\) 7.93434 0.337402
\(554\) −10.7753 −0.457797
\(555\) −34.7617 −1.47555
\(556\) 5.05033 0.214182
\(557\) 21.4239 0.907761 0.453881 0.891063i \(-0.350039\pi\)
0.453881 + 0.891063i \(0.350039\pi\)
\(558\) −4.81625 −0.203888
\(559\) −15.7667 −0.666859
\(560\) −3.42808 −0.144863
\(561\) 0.202934 0.00856786
\(562\) 4.44325 0.187427
\(563\) −37.7516 −1.59104 −0.795519 0.605928i \(-0.792802\pi\)
−0.795519 + 0.605928i \(0.792802\pi\)
\(564\) 8.10252 0.341178
\(565\) −28.3510 −1.19274
\(566\) −17.7140 −0.744574
\(567\) −5.97360 −0.250868
\(568\) −4.81511 −0.202037
\(569\) −5.82436 −0.244170 −0.122085 0.992520i \(-0.538958\pi\)
−0.122085 + 0.992520i \(0.538958\pi\)
\(570\) 24.5068 1.02648
\(571\) 13.9771 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(572\) 2.80696 0.117365
\(573\) −17.9966 −0.751820
\(574\) −3.86322 −0.161248
\(575\) −17.7437 −0.739965
\(576\) −0.662042 −0.0275851
\(577\) −24.8095 −1.03283 −0.516416 0.856338i \(-0.672734\pi\)
−0.516416 + 0.856338i \(0.672734\pi\)
\(578\) −16.9964 −0.706955
\(579\) 19.8983 0.826946
\(580\) −36.9484 −1.53420
\(581\) 1.13170 0.0469507
\(582\) −6.63775 −0.275143
\(583\) 3.81656 0.158066
\(584\) 2.23818 0.0926166
\(585\) −3.18824 −0.131817
\(586\) −16.7408 −0.691558
\(587\) 26.6909 1.10165 0.550825 0.834621i \(-0.314313\pi\)
0.550825 + 0.834621i \(0.314313\pi\)
\(588\) 9.44137 0.389356
\(589\) 30.8989 1.27317
\(590\) 21.1360 0.870155
\(591\) −26.5801 −1.09336
\(592\) −6.02467 −0.247613
\(593\) 13.3126 0.546684 0.273342 0.961917i \(-0.411871\pi\)
0.273342 + 0.961917i \(0.411871\pi\)
\(594\) −12.3157 −0.505321
\(595\) −0.206856 −0.00848026
\(596\) 5.04022 0.206455
\(597\) −26.9546 −1.10318
\(598\) 2.45081 0.100221
\(599\) 20.3987 0.833470 0.416735 0.909028i \(-0.363174\pi\)
0.416735 + 0.909028i \(0.363174\pi\)
\(600\) −14.1277 −0.576759
\(601\) −31.4856 −1.28432 −0.642162 0.766569i \(-0.721963\pi\)
−0.642162 + 0.766569i \(0.721963\pi\)
\(602\) 11.2234 0.457433
\(603\) 0.531830 0.0216578
\(604\) 10.1333 0.412316
\(605\) 23.2537 0.945397
\(606\) 15.7265 0.638844
\(607\) 10.4307 0.423370 0.211685 0.977338i \(-0.432105\pi\)
0.211685 + 0.977338i \(0.432105\pi\)
\(608\) 4.24736 0.172253
\(609\) −13.6009 −0.551137
\(610\) 19.8003 0.801690
\(611\) 6.76268 0.273589
\(612\) −0.0399486 −0.00161483
\(613\) 24.2024 0.977527 0.488764 0.872416i \(-0.337448\pi\)
0.488764 + 0.872416i \(0.337448\pi\)
\(614\) 8.62774 0.348187
\(615\) −24.5366 −0.989411
\(616\) −1.99812 −0.0805065
\(617\) −21.4118 −0.862008 −0.431004 0.902350i \(-0.641841\pi\)
−0.431004 + 0.902350i \(0.641841\pi\)
\(618\) 9.66679 0.388855
\(619\) −12.1478 −0.488261 −0.244131 0.969742i \(-0.578503\pi\)
−0.244131 + 0.969742i \(0.578503\pi\)
\(620\) −27.4519 −1.10249
\(621\) −10.7531 −0.431508
\(622\) −7.71915 −0.309510
\(623\) −3.47670 −0.139291
\(624\) 1.95135 0.0781165
\(625\) 14.1718 0.566873
\(626\) 15.5017 0.619571
\(627\) 14.2842 0.570457
\(628\) −0.534403 −0.0213250
\(629\) −0.363538 −0.0144952
\(630\) 2.26953 0.0904204
\(631\) 12.7341 0.506937 0.253469 0.967344i \(-0.418429\pi\)
0.253469 + 0.967344i \(0.418429\pi\)
\(632\) 8.73390 0.347416
\(633\) −14.4909 −0.575961
\(634\) 18.5157 0.735354
\(635\) 30.2677 1.20114
\(636\) 2.65321 0.105207
\(637\) 7.88014 0.312222
\(638\) −21.5361 −0.852620
\(639\) 3.18780 0.126107
\(640\) −3.77354 −0.149162
\(641\) 11.7600 0.464494 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(642\) 1.30433 0.0514778
\(643\) −10.5960 −0.417866 −0.208933 0.977930i \(-0.566999\pi\)
−0.208933 + 0.977930i \(0.566999\pi\)
\(644\) −1.74460 −0.0687469
\(645\) 71.2836 2.80679
\(646\) 0.256292 0.0100837
\(647\) −49.6333 −1.95129 −0.975643 0.219366i \(-0.929601\pi\)
−0.975643 + 0.219366i \(0.929601\pi\)
\(648\) −6.57558 −0.258313
\(649\) 12.3195 0.483582
\(650\) −11.7915 −0.462500
\(651\) −10.1052 −0.396054
\(652\) −7.96805 −0.312053
\(653\) 19.2194 0.752112 0.376056 0.926597i \(-0.377280\pi\)
0.376056 + 0.926597i \(0.377280\pi\)
\(654\) 9.03794 0.353411
\(655\) 62.9988 2.46157
\(656\) −4.25253 −0.166033
\(657\) −1.48177 −0.0578094
\(658\) −4.81398 −0.187669
\(659\) −43.4523 −1.69266 −0.846331 0.532657i \(-0.821193\pi\)
−0.846331 + 0.532657i \(0.821193\pi\)
\(660\) −12.6907 −0.493985
\(661\) −34.7821 −1.35287 −0.676434 0.736503i \(-0.736476\pi\)
−0.676434 + 0.736503i \(0.736476\pi\)
\(662\) 12.0588 0.468677
\(663\) 0.117748 0.00457294
\(664\) 1.24574 0.0483441
\(665\) −14.5603 −0.564624
\(666\) 3.98859 0.154555
\(667\) −18.8036 −0.728077
\(668\) −12.9722 −0.501911
\(669\) −39.2942 −1.51920
\(670\) 3.03135 0.117111
\(671\) 11.5410 0.445534
\(672\) −1.38906 −0.0535841
\(673\) 45.6657 1.76028 0.880141 0.474712i \(-0.157448\pi\)
0.880141 + 0.474712i \(0.157448\pi\)
\(674\) 0.332736 0.0128165
\(675\) 51.7361 1.99132
\(676\) −11.3713 −0.437359
\(677\) −0.957601 −0.0368036 −0.0184018 0.999831i \(-0.505858\pi\)
−0.0184018 + 0.999831i \(0.505858\pi\)
\(678\) −11.4878 −0.441188
\(679\) 3.94371 0.151346
\(680\) −0.227701 −0.00873194
\(681\) 34.5285 1.32313
\(682\) −16.0008 −0.612704
\(683\) 15.8152 0.605152 0.302576 0.953125i \(-0.402153\pi\)
0.302576 + 0.953125i \(0.402153\pi\)
\(684\) −2.81193 −0.107517
\(685\) 69.8617 2.66928
\(686\) −11.9686 −0.456964
\(687\) 4.88843 0.186505
\(688\) 12.3544 0.471009
\(689\) 2.21447 0.0843646
\(690\) −11.0805 −0.421828
\(691\) 41.4021 1.57501 0.787504 0.616309i \(-0.211373\pi\)
0.787504 + 0.616309i \(0.211373\pi\)
\(692\) 3.44804 0.131075
\(693\) 1.32284 0.0502505
\(694\) −7.20839 −0.273627
\(695\) −19.0576 −0.722896
\(696\) −14.9715 −0.567494
\(697\) −0.256604 −0.00971958
\(698\) 18.5322 0.701455
\(699\) 14.0848 0.532736
\(700\) 8.39372 0.317253
\(701\) −35.0104 −1.32233 −0.661163 0.750243i \(-0.729937\pi\)
−0.661163 + 0.750243i \(0.729937\pi\)
\(702\) −7.14593 −0.269706
\(703\) −25.5890 −0.965106
\(704\) −2.19947 −0.0828958
\(705\) −30.5752 −1.15153
\(706\) −1.12923 −0.0424992
\(707\) −9.34363 −0.351403
\(708\) 8.56431 0.321866
\(709\) 17.9260 0.673224 0.336612 0.941643i \(-0.390719\pi\)
0.336612 + 0.941643i \(0.390719\pi\)
\(710\) 18.1700 0.681907
\(711\) −5.78220 −0.216850
\(712\) −3.82706 −0.143425
\(713\) −13.9707 −0.523205
\(714\) −0.0838181 −0.00313681
\(715\) −10.5922 −0.396124
\(716\) 23.3164 0.871374
\(717\) 28.1634 1.05178
\(718\) −8.06913 −0.301137
\(719\) −35.1556 −1.31108 −0.655541 0.755160i \(-0.727559\pi\)
−0.655541 + 0.755160i \(0.727559\pi\)
\(720\) 2.49824 0.0931038
\(721\) −5.74337 −0.213894
\(722\) −0.959936 −0.0357251
\(723\) 28.4280 1.05725
\(724\) 5.03003 0.186940
\(725\) 90.4688 3.35993
\(726\) 9.42241 0.349698
\(727\) −17.9918 −0.667279 −0.333639 0.942701i \(-0.608277\pi\)
−0.333639 + 0.942701i \(0.608277\pi\)
\(728\) −1.15936 −0.0429689
\(729\) 30.0384 1.11253
\(730\) −8.44586 −0.312595
\(731\) 0.745486 0.0275728
\(732\) 8.02308 0.296542
\(733\) 12.1596 0.449125 0.224563 0.974460i \(-0.427905\pi\)
0.224563 + 0.974460i \(0.427905\pi\)
\(734\) −25.6227 −0.945753
\(735\) −35.6274 −1.31413
\(736\) −1.92041 −0.0707871
\(737\) 1.76688 0.0650838
\(738\) 2.81535 0.103635
\(739\) 32.1446 1.18246 0.591229 0.806504i \(-0.298643\pi\)
0.591229 + 0.806504i \(0.298643\pi\)
\(740\) 22.7343 0.835730
\(741\) 8.28809 0.304471
\(742\) −1.57636 −0.0578700
\(743\) −46.8272 −1.71792 −0.858961 0.512041i \(-0.828889\pi\)
−0.858961 + 0.512041i \(0.828889\pi\)
\(744\) −11.1235 −0.407808
\(745\) −19.0194 −0.696819
\(746\) −23.6666 −0.866497
\(747\) −0.824732 −0.0301754
\(748\) −0.132720 −0.00485272
\(749\) −0.774947 −0.0283159
\(750\) 24.4618 0.893219
\(751\) 27.2361 0.993859 0.496929 0.867791i \(-0.334461\pi\)
0.496929 + 0.867791i \(0.334461\pi\)
\(752\) −5.29910 −0.193238
\(753\) −33.3743 −1.21623
\(754\) −12.4958 −0.455070
\(755\) −38.2382 −1.39163
\(756\) 5.08680 0.185005
\(757\) 45.1707 1.64176 0.820878 0.571104i \(-0.193485\pi\)
0.820878 + 0.571104i \(0.193485\pi\)
\(758\) 16.3583 0.594159
\(759\) −6.45848 −0.234428
\(760\) −16.0276 −0.581381
\(761\) 11.5698 0.419406 0.209703 0.977765i \(-0.432750\pi\)
0.209703 + 0.977765i \(0.432750\pi\)
\(762\) 12.2645 0.444295
\(763\) −5.36974 −0.194398
\(764\) 11.7699 0.425820
\(765\) 0.150748 0.00545029
\(766\) 10.7888 0.389814
\(767\) 7.14810 0.258103
\(768\) −1.52904 −0.0551744
\(769\) −0.637726 −0.0229970 −0.0114985 0.999934i \(-0.503660\pi\)
−0.0114985 + 0.999934i \(0.503660\pi\)
\(770\) 7.53998 0.271722
\(771\) 34.7218 1.25047
\(772\) −13.0136 −0.468370
\(773\) −32.1925 −1.15788 −0.578942 0.815369i \(-0.696534\pi\)
−0.578942 + 0.815369i \(0.696534\pi\)
\(774\) −8.17915 −0.293994
\(775\) 67.2164 2.41449
\(776\) 4.34112 0.155837
\(777\) 8.36863 0.300223
\(778\) −7.82434 −0.280516
\(779\) −18.0620 −0.647139
\(780\) −7.36349 −0.263655
\(781\) 10.5907 0.378965
\(782\) −0.115880 −0.00414387
\(783\) 54.8263 1.95933
\(784\) −6.17471 −0.220525
\(785\) 2.01659 0.0719751
\(786\) 25.5272 0.910523
\(787\) −10.8708 −0.387504 −0.193752 0.981051i \(-0.562066\pi\)
−0.193752 + 0.981051i \(0.562066\pi\)
\(788\) 17.3836 0.619263
\(789\) 23.0742 0.821463
\(790\) −32.9577 −1.17258
\(791\) 6.82532 0.242680
\(792\) 1.45614 0.0517418
\(793\) 6.69637 0.237795
\(794\) 1.81287 0.0643365
\(795\) −10.0120 −0.355088
\(796\) 17.6285 0.624825
\(797\) 16.5443 0.586028 0.293014 0.956108i \(-0.405342\pi\)
0.293014 + 0.956108i \(0.405342\pi\)
\(798\) −5.89984 −0.208852
\(799\) −0.319756 −0.0113122
\(800\) 9.23957 0.326668
\(801\) 2.53367 0.0895229
\(802\) 6.36350 0.224703
\(803\) −4.92283 −0.173723
\(804\) 1.22830 0.0433190
\(805\) 6.58331 0.232031
\(806\) −9.28412 −0.327019
\(807\) 8.70098 0.306289
\(808\) −10.2852 −0.361832
\(809\) 34.8306 1.22458 0.612290 0.790633i \(-0.290249\pi\)
0.612290 + 0.790633i \(0.290249\pi\)
\(810\) 24.8132 0.871846
\(811\) −30.3987 −1.06744 −0.533721 0.845661i \(-0.679207\pi\)
−0.533721 + 0.845661i \(0.679207\pi\)
\(812\) 8.89508 0.312156
\(813\) 34.5094 1.21030
\(814\) 13.2511 0.464451
\(815\) 30.0677 1.05323
\(816\) −0.0922646 −0.00322991
\(817\) 52.4737 1.83582
\(818\) 18.0756 0.631997
\(819\) 0.767547 0.0268203
\(820\) 16.0471 0.560388
\(821\) 35.3608 1.23410 0.617050 0.786924i \(-0.288328\pi\)
0.617050 + 0.786924i \(0.288328\pi\)
\(822\) 28.3080 0.987355
\(823\) 10.0750 0.351192 0.175596 0.984462i \(-0.443815\pi\)
0.175596 + 0.984462i \(0.443815\pi\)
\(824\) −6.32214 −0.220242
\(825\) 31.0734 1.08184
\(826\) −5.08835 −0.177046
\(827\) −4.31639 −0.150096 −0.0750479 0.997180i \(-0.523911\pi\)
−0.0750479 + 0.997180i \(0.523911\pi\)
\(828\) 1.27139 0.0441838
\(829\) −21.1360 −0.734083 −0.367041 0.930205i \(-0.619629\pi\)
−0.367041 + 0.930205i \(0.619629\pi\)
\(830\) −4.70084 −0.163169
\(831\) 16.4758 0.571538
\(832\) −1.27619 −0.0442441
\(833\) −0.372592 −0.0129095
\(834\) −7.72215 −0.267396
\(835\) 48.9512 1.69403
\(836\) −9.34196 −0.323098
\(837\) 40.7348 1.40800
\(838\) −18.7947 −0.649254
\(839\) −29.2828 −1.01096 −0.505478 0.862840i \(-0.668684\pi\)
−0.505478 + 0.862840i \(0.668684\pi\)
\(840\) 5.24167 0.180855
\(841\) 66.8726 2.30595
\(842\) −22.2817 −0.767877
\(843\) −6.79391 −0.233995
\(844\) 9.47712 0.326216
\(845\) 42.9101 1.47615
\(846\) 3.50822 0.120615
\(847\) −5.59817 −0.192355
\(848\) −1.73521 −0.0595875
\(849\) 27.0854 0.929567
\(850\) 0.557530 0.0191231
\(851\) 11.5698 0.396608
\(852\) 7.36248 0.252234
\(853\) 24.6755 0.844874 0.422437 0.906392i \(-0.361175\pi\)
0.422437 + 0.906392i \(0.361175\pi\)
\(854\) −4.76678 −0.163116
\(855\) 10.6109 0.362886
\(856\) −0.853040 −0.0291563
\(857\) 38.6637 1.32073 0.660364 0.750946i \(-0.270402\pi\)
0.660364 + 0.750946i \(0.270402\pi\)
\(858\) −4.29195 −0.146525
\(859\) 13.7469 0.469040 0.234520 0.972111i \(-0.424648\pi\)
0.234520 + 0.972111i \(0.424648\pi\)
\(860\) −46.6199 −1.58973
\(861\) 5.90702 0.201311
\(862\) 28.3379 0.965194
\(863\) −13.2484 −0.450982 −0.225491 0.974245i \(-0.572399\pi\)
−0.225491 + 0.974245i \(0.572399\pi\)
\(864\) 5.59940 0.190496
\(865\) −13.0113 −0.442397
\(866\) −30.3557 −1.03153
\(867\) 25.9881 0.882602
\(868\) 6.60886 0.224319
\(869\) −19.2100 −0.651654
\(870\) 56.4955 1.91538
\(871\) 1.02519 0.0347373
\(872\) −5.91086 −0.200167
\(873\) −2.87401 −0.0972704
\(874\) −8.15666 −0.275903
\(875\) −14.5336 −0.491325
\(876\) −3.42227 −0.115628
\(877\) 43.6137 1.47273 0.736366 0.676584i \(-0.236540\pi\)
0.736366 + 0.676584i \(0.236540\pi\)
\(878\) −21.7396 −0.733675
\(879\) 25.5974 0.863378
\(880\) 8.29980 0.279786
\(881\) 37.7943 1.27332 0.636660 0.771144i \(-0.280315\pi\)
0.636660 + 0.771144i \(0.280315\pi\)
\(882\) 4.08792 0.137647
\(883\) −32.2356 −1.08481 −0.542407 0.840116i \(-0.682487\pi\)
−0.542407 + 0.840116i \(0.682487\pi\)
\(884\) −0.0770076 −0.00259005
\(885\) −32.3177 −1.08635
\(886\) −6.34107 −0.213032
\(887\) 18.9140 0.635069 0.317535 0.948247i \(-0.397145\pi\)
0.317535 + 0.948247i \(0.397145\pi\)
\(888\) 9.21196 0.309133
\(889\) −7.28674 −0.244390
\(890\) 14.4415 0.484081
\(891\) 14.4628 0.484522
\(892\) 25.6987 0.860455
\(893\) −22.5072 −0.753174
\(894\) −7.70669 −0.257750
\(895\) −87.9852 −2.94102
\(896\) 0.908453 0.0303493
\(897\) −3.74739 −0.125122
\(898\) −17.0265 −0.568182
\(899\) 71.2313 2.37570
\(900\) −6.11698 −0.203899
\(901\) −0.104705 −0.00348825
\(902\) 9.35333 0.311432
\(903\) −17.1611 −0.571084
\(904\) 7.51312 0.249883
\(905\) −18.9810 −0.630950
\(906\) −15.4941 −0.514758
\(907\) −10.2967 −0.341896 −0.170948 0.985280i \(-0.554683\pi\)
−0.170948 + 0.985280i \(0.554683\pi\)
\(908\) −22.5818 −0.749404
\(909\) 6.80923 0.225848
\(910\) 4.37490 0.145026
\(911\) 10.3128 0.341678 0.170839 0.985299i \(-0.445352\pi\)
0.170839 + 0.985299i \(0.445352\pi\)
\(912\) −6.49438 −0.215050
\(913\) −2.73997 −0.0906799
\(914\) 21.1408 0.699274
\(915\) −30.2754 −1.00087
\(916\) −3.19706 −0.105634
\(917\) −15.1665 −0.500843
\(918\) 0.337877 0.0111516
\(919\) 22.7858 0.751635 0.375817 0.926694i \(-0.377362\pi\)
0.375817 + 0.926694i \(0.377362\pi\)
\(920\) 7.24672 0.238917
\(921\) −13.1921 −0.434696
\(922\) 39.8194 1.31138
\(923\) 6.14501 0.202266
\(924\) 3.05520 0.100509
\(925\) −55.6654 −1.83027
\(926\) −18.1193 −0.595438
\(927\) 4.18552 0.137470
\(928\) 9.79145 0.321420
\(929\) 9.89839 0.324756 0.162378 0.986729i \(-0.448084\pi\)
0.162378 + 0.986729i \(0.448084\pi\)
\(930\) 41.9750 1.37641
\(931\) −26.2262 −0.859530
\(932\) −9.21154 −0.301734
\(933\) 11.8029 0.386409
\(934\) 14.9161 0.488071
\(935\) 0.500823 0.0163787
\(936\) 0.844894 0.0276162
\(937\) −43.5402 −1.42240 −0.711199 0.702991i \(-0.751847\pi\)
−0.711199 + 0.702991i \(0.751847\pi\)
\(938\) −0.729777 −0.0238281
\(939\) −23.7026 −0.773506
\(940\) 19.9963 0.652209
\(941\) 51.7914 1.68835 0.844176 0.536067i \(-0.180090\pi\)
0.844176 + 0.536067i \(0.180090\pi\)
\(942\) 0.817122 0.0266233
\(943\) 8.16658 0.265941
\(944\) −5.60111 −0.182301
\(945\) −19.1952 −0.624420
\(946\) −27.1733 −0.883479
\(947\) 12.0036 0.390064 0.195032 0.980797i \(-0.437519\pi\)
0.195032 + 0.980797i \(0.437519\pi\)
\(948\) −13.3545 −0.433733
\(949\) −2.85636 −0.0927213
\(950\) 39.2438 1.27324
\(951\) −28.3113 −0.918056
\(952\) 0.0548175 0.00177665
\(953\) −11.5510 −0.374173 −0.187086 0.982343i \(-0.559904\pi\)
−0.187086 + 0.982343i \(0.559904\pi\)
\(954\) 1.14878 0.0371932
\(955\) −44.4141 −1.43721
\(956\) −18.4190 −0.595714
\(957\) 32.9294 1.06446
\(958\) 9.18330 0.296699
\(959\) −16.8187 −0.543105
\(960\) 5.76988 0.186222
\(961\) 21.9234 0.707205
\(962\) 7.68866 0.247892
\(963\) 0.564748 0.0181988
\(964\) −18.5921 −0.598810
\(965\) 49.1073 1.58082
\(966\) 2.66756 0.0858273
\(967\) −14.4846 −0.465793 −0.232896 0.972502i \(-0.574820\pi\)
−0.232896 + 0.972502i \(0.574820\pi\)
\(968\) −6.16231 −0.198064
\(969\) −0.391881 −0.0125890
\(970\) −16.3814 −0.525975
\(971\) −43.2229 −1.38709 −0.693545 0.720413i \(-0.743952\pi\)
−0.693545 + 0.720413i \(0.743952\pi\)
\(972\) −6.74390 −0.216311
\(973\) 4.58799 0.147084
\(974\) 24.2431 0.776800
\(975\) 18.0296 0.577411
\(976\) −5.24714 −0.167957
\(977\) 4.26551 0.136466 0.0682328 0.997669i \(-0.478264\pi\)
0.0682328 + 0.997669i \(0.478264\pi\)
\(978\) 12.1835 0.389584
\(979\) 8.41752 0.269025
\(980\) 23.3005 0.744307
\(981\) 3.91324 0.124940
\(982\) −16.3967 −0.523238
\(983\) 12.5647 0.400752 0.200376 0.979719i \(-0.435784\pi\)
0.200376 + 0.979719i \(0.435784\pi\)
\(984\) 6.50228 0.207285
\(985\) −65.5975 −2.09011
\(986\) 0.590832 0.0188159
\(987\) 7.36076 0.234296
\(988\) −5.42046 −0.172448
\(989\) −23.7255 −0.754428
\(990\) −5.49481 −0.174637
\(991\) −29.5747 −0.939471 −0.469735 0.882807i \(-0.655651\pi\)
−0.469735 + 0.882807i \(0.655651\pi\)
\(992\) 7.27484 0.230977
\(993\) −18.4383 −0.585122
\(994\) −4.37430 −0.138744
\(995\) −66.5217 −2.10888
\(996\) −1.90478 −0.0603554
\(997\) 13.6944 0.433705 0.216852 0.976204i \(-0.430421\pi\)
0.216852 + 0.976204i \(0.430421\pi\)
\(998\) −2.03407 −0.0643875
\(999\) −33.7346 −1.06731
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 6022.2.a.b.1.19 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6022.2.a.b.1.19 54 1.1 even 1 trivial