Properties

Label 983.2.a.b.1.5
Level $983$
Weight $2$
Character 983.1
Self dual yes
Analytic conductor $7.849$
Analytic rank $0$
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] = [983,2,Mod(1,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, 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("983.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 983.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: \(7.84929451869\)
Analytic rank: \(0\)
Dimension: \(54\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 983.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.42129 q^{2} +0.803744 q^{3} +3.86265 q^{4} +3.28925 q^{5} -1.94610 q^{6} +3.29937 q^{7} -4.51003 q^{8} -2.35400 q^{9} +O(q^{10})\) \(q-2.42129 q^{2} +0.803744 q^{3} +3.86265 q^{4} +3.28925 q^{5} -1.94610 q^{6} +3.29937 q^{7} -4.51003 q^{8} -2.35400 q^{9} -7.96423 q^{10} +6.14409 q^{11} +3.10459 q^{12} +1.33980 q^{13} -7.98873 q^{14} +2.64372 q^{15} +3.19479 q^{16} -1.21072 q^{17} +5.69971 q^{18} +2.94674 q^{19} +12.7052 q^{20} +2.65185 q^{21} -14.8766 q^{22} +6.73380 q^{23} -3.62491 q^{24} +5.81917 q^{25} -3.24404 q^{26} -4.30324 q^{27} +12.7443 q^{28} -9.21882 q^{29} -6.40121 q^{30} +8.05855 q^{31} +1.28454 q^{32} +4.93828 q^{33} +2.93151 q^{34} +10.8524 q^{35} -9.09267 q^{36} -7.06873 q^{37} -7.13492 q^{38} +1.07685 q^{39} -14.8346 q^{40} -11.2443 q^{41} -6.42089 q^{42} +3.36362 q^{43} +23.7325 q^{44} -7.74288 q^{45} -16.3045 q^{46} -9.40914 q^{47} +2.56779 q^{48} +3.88582 q^{49} -14.0899 q^{50} -0.973110 q^{51} +5.17517 q^{52} -9.27055 q^{53} +10.4194 q^{54} +20.2094 q^{55} -14.8802 q^{56} +2.36842 q^{57} +22.3214 q^{58} -1.86338 q^{59} +10.2118 q^{60} +3.12115 q^{61} -19.5121 q^{62} -7.76669 q^{63} -9.49983 q^{64} +4.40693 q^{65} -11.9570 q^{66} -14.6369 q^{67} -4.67660 q^{68} +5.41225 q^{69} -26.2769 q^{70} -16.2584 q^{71} +10.6166 q^{72} +0.808970 q^{73} +17.1155 q^{74} +4.67712 q^{75} +11.3822 q^{76} +20.2716 q^{77} -2.60738 q^{78} +0.804882 q^{79} +10.5085 q^{80} +3.60328 q^{81} +27.2256 q^{82} +11.0360 q^{83} +10.2432 q^{84} -3.98237 q^{85} -8.14431 q^{86} -7.40957 q^{87} -27.7100 q^{88} -2.88249 q^{89} +18.7478 q^{90} +4.42048 q^{91} +26.0103 q^{92} +6.47701 q^{93} +22.7823 q^{94} +9.69256 q^{95} +1.03245 q^{96} +8.89616 q^{97} -9.40870 q^{98} -14.4632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42129 −1.71211 −0.856056 0.516883i \(-0.827092\pi\)
−0.856056 + 0.516883i \(0.827092\pi\)
\(3\) 0.803744 0.464042 0.232021 0.972711i \(-0.425466\pi\)
0.232021 + 0.972711i \(0.425466\pi\)
\(4\) 3.86265 1.93133
\(5\) 3.28925 1.47100 0.735499 0.677526i \(-0.236948\pi\)
0.735499 + 0.677526i \(0.236948\pi\)
\(6\) −1.94610 −0.794492
\(7\) 3.29937 1.24704 0.623522 0.781806i \(-0.285701\pi\)
0.623522 + 0.781806i \(0.285701\pi\)
\(8\) −4.51003 −1.59454
\(9\) −2.35400 −0.784665
\(10\) −7.96423 −2.51851
\(11\) 6.14409 1.85251 0.926256 0.376894i \(-0.123008\pi\)
0.926256 + 0.376894i \(0.123008\pi\)
\(12\) 3.10459 0.896217
\(13\) 1.33980 0.371593 0.185796 0.982588i \(-0.440513\pi\)
0.185796 + 0.982588i \(0.440513\pi\)
\(14\) −7.98873 −2.13508
\(15\) 2.64372 0.682604
\(16\) 3.19479 0.798697
\(17\) −1.21072 −0.293643 −0.146822 0.989163i \(-0.546904\pi\)
−0.146822 + 0.989163i \(0.546904\pi\)
\(18\) 5.69971 1.34343
\(19\) 2.94674 0.676028 0.338014 0.941141i \(-0.390245\pi\)
0.338014 + 0.941141i \(0.390245\pi\)
\(20\) 12.7052 2.84098
\(21\) 2.65185 0.578680
\(22\) −14.8766 −3.17171
\(23\) 6.73380 1.40409 0.702047 0.712131i \(-0.252270\pi\)
0.702047 + 0.712131i \(0.252270\pi\)
\(24\) −3.62491 −0.739931
\(25\) 5.81917 1.16383
\(26\) −3.24404 −0.636209
\(27\) −4.30324 −0.828159
\(28\) 12.7443 2.40845
\(29\) −9.21882 −1.71189 −0.855946 0.517066i \(-0.827024\pi\)
−0.855946 + 0.517066i \(0.827024\pi\)
\(30\) −6.40121 −1.16870
\(31\) 8.05855 1.44736 0.723679 0.690136i \(-0.242450\pi\)
0.723679 + 0.690136i \(0.242450\pi\)
\(32\) 1.28454 0.227078
\(33\) 4.93828 0.859644
\(34\) 2.93151 0.502750
\(35\) 10.8524 1.83440
\(36\) −9.09267 −1.51544
\(37\) −7.06873 −1.16209 −0.581046 0.813870i \(-0.697356\pi\)
−0.581046 + 0.813870i \(0.697356\pi\)
\(38\) −7.13492 −1.15744
\(39\) 1.07685 0.172435
\(40\) −14.8346 −2.34556
\(41\) −11.2443 −1.75606 −0.878029 0.478607i \(-0.841142\pi\)
−0.878029 + 0.478607i \(0.841142\pi\)
\(42\) −6.42089 −0.990765
\(43\) 3.36362 0.512947 0.256474 0.966551i \(-0.417439\pi\)
0.256474 + 0.966551i \(0.417439\pi\)
\(44\) 23.7325 3.57781
\(45\) −7.74288 −1.15424
\(46\) −16.3045 −2.40397
\(47\) −9.40914 −1.37246 −0.686232 0.727382i \(-0.740737\pi\)
−0.686232 + 0.727382i \(0.740737\pi\)
\(48\) 2.56779 0.370629
\(49\) 3.88582 0.555117
\(50\) −14.0899 −1.99261
\(51\) −0.973110 −0.136263
\(52\) 5.17517 0.717668
\(53\) −9.27055 −1.27341 −0.636704 0.771109i \(-0.719703\pi\)
−0.636704 + 0.771109i \(0.719703\pi\)
\(54\) 10.4194 1.41790
\(55\) 20.2094 2.72504
\(56\) −14.8802 −1.98846
\(57\) 2.36842 0.313706
\(58\) 22.3214 2.93095
\(59\) −1.86338 −0.242592 −0.121296 0.992616i \(-0.538705\pi\)
−0.121296 + 0.992616i \(0.538705\pi\)
\(60\) 10.2118 1.31833
\(61\) 3.12115 0.399623 0.199811 0.979834i \(-0.435967\pi\)
0.199811 + 0.979834i \(0.435967\pi\)
\(62\) −19.5121 −2.47804
\(63\) −7.76669 −0.978511
\(64\) −9.49983 −1.18748
\(65\) 4.40693 0.546612
\(66\) −11.9570 −1.47181
\(67\) −14.6369 −1.78818 −0.894091 0.447885i \(-0.852177\pi\)
−0.894091 + 0.447885i \(0.852177\pi\)
\(68\) −4.67660 −0.567121
\(69\) 5.41225 0.651558
\(70\) −26.2769 −3.14069
\(71\) −16.2584 −1.92951 −0.964757 0.263142i \(-0.915241\pi\)
−0.964757 + 0.263142i \(0.915241\pi\)
\(72\) 10.6166 1.25118
\(73\) 0.808970 0.0946828 0.0473414 0.998879i \(-0.484925\pi\)
0.0473414 + 0.998879i \(0.484925\pi\)
\(74\) 17.1155 1.98963
\(75\) 4.67712 0.540067
\(76\) 11.3822 1.30563
\(77\) 20.2716 2.31016
\(78\) −2.60738 −0.295227
\(79\) 0.804882 0.0905563 0.0452781 0.998974i \(-0.485583\pi\)
0.0452781 + 0.998974i \(0.485583\pi\)
\(80\) 10.5085 1.17488
\(81\) 3.60328 0.400364
\(82\) 27.2256 3.00657
\(83\) 11.0360 1.21136 0.605680 0.795709i \(-0.292901\pi\)
0.605680 + 0.795709i \(0.292901\pi\)
\(84\) 10.2432 1.11762
\(85\) −3.98237 −0.431948
\(86\) −8.14431 −0.878223
\(87\) −7.40957 −0.794389
\(88\) −27.7100 −2.95390
\(89\) −2.88249 −0.305544 −0.152772 0.988261i \(-0.548820\pi\)
−0.152772 + 0.988261i \(0.548820\pi\)
\(90\) 18.7478 1.97619
\(91\) 4.42048 0.463392
\(92\) 26.0103 2.71176
\(93\) 6.47701 0.671635
\(94\) 22.7823 2.34981
\(95\) 9.69256 0.994436
\(96\) 1.03245 0.105373
\(97\) 8.89616 0.903268 0.451634 0.892203i \(-0.350841\pi\)
0.451634 + 0.892203i \(0.350841\pi\)
\(98\) −9.40870 −0.950422
\(99\) −14.4632 −1.45360
\(100\) 22.4774 2.24774
\(101\) 5.30180 0.527549 0.263775 0.964584i \(-0.415032\pi\)
0.263775 + 0.964584i \(0.415032\pi\)
\(102\) 2.35618 0.233297
\(103\) 7.45869 0.734927 0.367463 0.930038i \(-0.380226\pi\)
0.367463 + 0.930038i \(0.380226\pi\)
\(104\) −6.04253 −0.592518
\(105\) 8.72259 0.851237
\(106\) 22.4467 2.18022
\(107\) 6.18674 0.598094 0.299047 0.954238i \(-0.403331\pi\)
0.299047 + 0.954238i \(0.403331\pi\)
\(108\) −16.6219 −1.59945
\(109\) 6.29568 0.603017 0.301508 0.953464i \(-0.402510\pi\)
0.301508 + 0.953464i \(0.402510\pi\)
\(110\) −48.9330 −4.66558
\(111\) −5.68145 −0.539260
\(112\) 10.5408 0.996009
\(113\) −15.0787 −1.41849 −0.709244 0.704963i \(-0.750963\pi\)
−0.709244 + 0.704963i \(0.750963\pi\)
\(114\) −5.73465 −0.537099
\(115\) 22.1491 2.06542
\(116\) −35.6091 −3.30622
\(117\) −3.15388 −0.291576
\(118\) 4.51179 0.415344
\(119\) −3.99461 −0.366186
\(120\) −11.9232 −1.08844
\(121\) 26.7498 2.43180
\(122\) −7.55722 −0.684199
\(123\) −9.03751 −0.814885
\(124\) 31.1274 2.79532
\(125\) 2.69444 0.240998
\(126\) 18.8054 1.67532
\(127\) 8.43191 0.748211 0.374105 0.927386i \(-0.377950\pi\)
0.374105 + 0.927386i \(0.377950\pi\)
\(128\) 20.4328 1.80602
\(129\) 2.70349 0.238029
\(130\) −10.6705 −0.935861
\(131\) −20.3969 −1.78208 −0.891041 0.453923i \(-0.850024\pi\)
−0.891041 + 0.453923i \(0.850024\pi\)
\(132\) 19.0749 1.66025
\(133\) 9.72237 0.843037
\(134\) 35.4402 3.06157
\(135\) −14.1544 −1.21822
\(136\) 5.46039 0.468224
\(137\) 5.36786 0.458607 0.229304 0.973355i \(-0.426355\pi\)
0.229304 + 0.973355i \(0.426355\pi\)
\(138\) −13.1046 −1.11554
\(139\) −12.7662 −1.08282 −0.541409 0.840759i \(-0.682109\pi\)
−0.541409 + 0.840759i \(0.682109\pi\)
\(140\) 41.9192 3.54282
\(141\) −7.56254 −0.636881
\(142\) 39.3663 3.30354
\(143\) 8.23184 0.688381
\(144\) −7.52052 −0.626710
\(145\) −30.3230 −2.51819
\(146\) −1.95875 −0.162107
\(147\) 3.12320 0.257597
\(148\) −27.3041 −2.24438
\(149\) −9.43354 −0.772826 −0.386413 0.922326i \(-0.626286\pi\)
−0.386413 + 0.922326i \(0.626286\pi\)
\(150\) −11.3247 −0.924656
\(151\) −1.65838 −0.134957 −0.0674785 0.997721i \(-0.521495\pi\)
−0.0674785 + 0.997721i \(0.521495\pi\)
\(152\) −13.2899 −1.07795
\(153\) 2.85003 0.230412
\(154\) −49.0835 −3.95526
\(155\) 26.5066 2.12906
\(156\) 4.15952 0.333028
\(157\) 10.3429 0.825451 0.412726 0.910855i \(-0.364577\pi\)
0.412726 + 0.910855i \(0.364577\pi\)
\(158\) −1.94885 −0.155042
\(159\) −7.45115 −0.590914
\(160\) 4.22519 0.334030
\(161\) 22.2173 1.75097
\(162\) −8.72459 −0.685469
\(163\) −2.74614 −0.215095 −0.107547 0.994200i \(-0.534300\pi\)
−0.107547 + 0.994200i \(0.534300\pi\)
\(164\) −43.4327 −3.39152
\(165\) 16.2432 1.26453
\(166\) −26.7214 −2.07398
\(167\) 16.9268 1.30983 0.654916 0.755702i \(-0.272704\pi\)
0.654916 + 0.755702i \(0.272704\pi\)
\(168\) −11.9599 −0.922726
\(169\) −11.2049 −0.861919
\(170\) 9.64247 0.739544
\(171\) −6.93661 −0.530456
\(172\) 12.9925 0.990669
\(173\) 17.3079 1.31590 0.657950 0.753062i \(-0.271424\pi\)
0.657950 + 0.753062i \(0.271424\pi\)
\(174\) 17.9407 1.36008
\(175\) 19.1996 1.45135
\(176\) 19.6291 1.47960
\(177\) −1.49768 −0.112573
\(178\) 6.97936 0.523125
\(179\) 6.41225 0.479274 0.239637 0.970863i \(-0.422972\pi\)
0.239637 + 0.970863i \(0.422972\pi\)
\(180\) −29.9081 −2.22922
\(181\) 5.30566 0.394366 0.197183 0.980367i \(-0.436821\pi\)
0.197183 + 0.980367i \(0.436821\pi\)
\(182\) −10.7033 −0.793380
\(183\) 2.50861 0.185442
\(184\) −30.3696 −2.23888
\(185\) −23.2508 −1.70944
\(186\) −15.6827 −1.14991
\(187\) −7.43878 −0.543978
\(188\) −36.3443 −2.65068
\(189\) −14.1980 −1.03275
\(190\) −23.4685 −1.70259
\(191\) 6.66755 0.482447 0.241223 0.970470i \(-0.422451\pi\)
0.241223 + 0.970470i \(0.422451\pi\)
\(192\) −7.63543 −0.551040
\(193\) 17.2573 1.24221 0.621104 0.783728i \(-0.286684\pi\)
0.621104 + 0.783728i \(0.286684\pi\)
\(194\) −21.5402 −1.54650
\(195\) 3.54204 0.253651
\(196\) 15.0096 1.07211
\(197\) −21.1512 −1.50696 −0.753481 0.657470i \(-0.771627\pi\)
−0.753481 + 0.657470i \(0.771627\pi\)
\(198\) 35.0195 2.48873
\(199\) −5.65771 −0.401065 −0.200532 0.979687i \(-0.564267\pi\)
−0.200532 + 0.979687i \(0.564267\pi\)
\(200\) −26.2446 −1.85577
\(201\) −11.7643 −0.829791
\(202\) −12.8372 −0.903223
\(203\) −30.4163 −2.13480
\(204\) −3.75879 −0.263168
\(205\) −36.9852 −2.58316
\(206\) −18.0597 −1.25828
\(207\) −15.8513 −1.10174
\(208\) 4.28037 0.296790
\(209\) 18.1050 1.25235
\(210\) −21.1199 −1.45741
\(211\) −15.9055 −1.09498 −0.547488 0.836813i \(-0.684416\pi\)
−0.547488 + 0.836813i \(0.684416\pi\)
\(212\) −35.8089 −2.45937
\(213\) −13.0676 −0.895375
\(214\) −14.9799 −1.02400
\(215\) 11.0638 0.754544
\(216\) 19.4077 1.32053
\(217\) 26.5881 1.80492
\(218\) −15.2437 −1.03243
\(219\) 0.650205 0.0439368
\(220\) 78.0621 5.26295
\(221\) −1.62212 −0.109116
\(222\) 13.7565 0.923273
\(223\) 12.1633 0.814513 0.407256 0.913314i \(-0.366486\pi\)
0.407256 + 0.913314i \(0.366486\pi\)
\(224\) 4.23818 0.283176
\(225\) −13.6983 −0.913219
\(226\) 36.5100 2.42861
\(227\) 2.24524 0.149022 0.0745110 0.997220i \(-0.476260\pi\)
0.0745110 + 0.997220i \(0.476260\pi\)
\(228\) 9.14841 0.605868
\(229\) 2.30927 0.152601 0.0763005 0.997085i \(-0.475689\pi\)
0.0763005 + 0.997085i \(0.475689\pi\)
\(230\) −53.6295 −3.53623
\(231\) 16.2932 1.07201
\(232\) 41.5771 2.72967
\(233\) 16.5492 1.08417 0.542086 0.840323i \(-0.317635\pi\)
0.542086 + 0.840323i \(0.317635\pi\)
\(234\) 7.63646 0.499211
\(235\) −30.9490 −2.01889
\(236\) −7.19760 −0.468524
\(237\) 0.646919 0.0420219
\(238\) 9.67213 0.626951
\(239\) −1.64872 −0.106647 −0.0533234 0.998577i \(-0.516981\pi\)
−0.0533234 + 0.998577i \(0.516981\pi\)
\(240\) 8.44611 0.545194
\(241\) −23.7503 −1.52989 −0.764945 0.644096i \(-0.777234\pi\)
−0.764945 + 0.644096i \(0.777234\pi\)
\(242\) −64.7692 −4.16352
\(243\) 15.8058 1.01395
\(244\) 12.0559 0.771802
\(245\) 12.7814 0.816575
\(246\) 21.8824 1.39517
\(247\) 3.94803 0.251207
\(248\) −36.3443 −2.30787
\(249\) 8.87013 0.562121
\(250\) −6.52404 −0.412616
\(251\) 26.1399 1.64993 0.824967 0.565181i \(-0.191194\pi\)
0.824967 + 0.565181i \(0.191194\pi\)
\(252\) −30.0000 −1.88983
\(253\) 41.3730 2.60110
\(254\) −20.4161 −1.28102
\(255\) −3.20080 −0.200442
\(256\) −30.4740 −1.90463
\(257\) −12.3353 −0.769456 −0.384728 0.923030i \(-0.625705\pi\)
−0.384728 + 0.923030i \(0.625705\pi\)
\(258\) −6.54594 −0.407532
\(259\) −23.3223 −1.44918
\(260\) 17.0224 1.05569
\(261\) 21.7011 1.34326
\(262\) 49.3868 3.05112
\(263\) −9.11640 −0.562141 −0.281071 0.959687i \(-0.590690\pi\)
−0.281071 + 0.959687i \(0.590690\pi\)
\(264\) −22.2718 −1.37073
\(265\) −30.4931 −1.87318
\(266\) −23.5407 −1.44337
\(267\) −2.31679 −0.141785
\(268\) −56.5373 −3.45356
\(269\) 9.01140 0.549434 0.274717 0.961525i \(-0.411416\pi\)
0.274717 + 0.961525i \(0.411416\pi\)
\(270\) 34.2720 2.08573
\(271\) −3.07864 −0.187014 −0.0935070 0.995619i \(-0.529808\pi\)
−0.0935070 + 0.995619i \(0.529808\pi\)
\(272\) −3.86800 −0.234532
\(273\) 3.55294 0.215034
\(274\) −12.9972 −0.785187
\(275\) 35.7535 2.15602
\(276\) 20.9056 1.25837
\(277\) 17.9366 1.07771 0.538853 0.842400i \(-0.318858\pi\)
0.538853 + 0.842400i \(0.318858\pi\)
\(278\) 30.9108 1.85391
\(279\) −18.9698 −1.13569
\(280\) −48.9448 −2.92501
\(281\) −12.1412 −0.724281 −0.362141 0.932123i \(-0.617954\pi\)
−0.362141 + 0.932123i \(0.617954\pi\)
\(282\) 18.3111 1.09041
\(283\) 22.6686 1.34751 0.673755 0.738954i \(-0.264680\pi\)
0.673755 + 0.738954i \(0.264680\pi\)
\(284\) −62.8005 −3.72652
\(285\) 7.79034 0.461460
\(286\) −19.9317 −1.17858
\(287\) −37.0989 −2.18988
\(288\) −3.02381 −0.178180
\(289\) −15.5342 −0.913774
\(290\) 73.4208 4.31142
\(291\) 7.15023 0.419154
\(292\) 3.12477 0.182863
\(293\) −5.07419 −0.296438 −0.148219 0.988955i \(-0.547354\pi\)
−0.148219 + 0.988955i \(0.547354\pi\)
\(294\) −7.56218 −0.441036
\(295\) −6.12913 −0.356852
\(296\) 31.8802 1.85300
\(297\) −26.4395 −1.53418
\(298\) 22.8414 1.32316
\(299\) 9.02192 0.521751
\(300\) 18.0661 1.04305
\(301\) 11.0978 0.639668
\(302\) 4.01542 0.231061
\(303\) 4.26129 0.244805
\(304\) 9.41421 0.539942
\(305\) 10.2663 0.587844
\(306\) −6.90076 −0.394490
\(307\) −19.3639 −1.10515 −0.552577 0.833462i \(-0.686356\pi\)
−0.552577 + 0.833462i \(0.686356\pi\)
\(308\) 78.3022 4.46168
\(309\) 5.99488 0.341037
\(310\) −64.1802 −3.64519
\(311\) −13.2713 −0.752546 −0.376273 0.926509i \(-0.622795\pi\)
−0.376273 + 0.926509i \(0.622795\pi\)
\(312\) −4.85664 −0.274953
\(313\) −19.1230 −1.08089 −0.540447 0.841378i \(-0.681745\pi\)
−0.540447 + 0.841378i \(0.681745\pi\)
\(314\) −25.0431 −1.41326
\(315\) −25.5466 −1.43939
\(316\) 3.10898 0.174894
\(317\) 13.6712 0.767849 0.383924 0.923365i \(-0.374572\pi\)
0.383924 + 0.923365i \(0.374572\pi\)
\(318\) 18.0414 1.01171
\(319\) −56.6412 −3.17130
\(320\) −31.2473 −1.74678
\(321\) 4.97255 0.277541
\(322\) −53.7945 −2.99785
\(323\) −3.56768 −0.198511
\(324\) 13.9182 0.773235
\(325\) 7.79650 0.432472
\(326\) 6.64922 0.368266
\(327\) 5.06011 0.279825
\(328\) 50.7119 2.80010
\(329\) −31.0442 −1.71152
\(330\) −39.3296 −2.16502
\(331\) 18.5842 1.02148 0.510741 0.859734i \(-0.329371\pi\)
0.510741 + 0.859734i \(0.329371\pi\)
\(332\) 42.6283 2.33953
\(333\) 16.6398 0.911854
\(334\) −40.9846 −2.24258
\(335\) −48.1444 −2.63041
\(336\) 8.47209 0.462190
\(337\) 31.1121 1.69479 0.847393 0.530966i \(-0.178171\pi\)
0.847393 + 0.530966i \(0.178171\pi\)
\(338\) 27.1304 1.47570
\(339\) −12.1194 −0.658238
\(340\) −15.3825 −0.834233
\(341\) 49.5125 2.68125
\(342\) 16.7956 0.908200
\(343\) −10.2748 −0.554789
\(344\) −15.1700 −0.817913
\(345\) 17.8022 0.958440
\(346\) −41.9076 −2.25297
\(347\) 6.38552 0.342793 0.171396 0.985202i \(-0.445172\pi\)
0.171396 + 0.985202i \(0.445172\pi\)
\(348\) −28.6206 −1.53423
\(349\) 28.4885 1.52495 0.762477 0.647015i \(-0.223983\pi\)
0.762477 + 0.647015i \(0.223983\pi\)
\(350\) −46.4877 −2.48487
\(351\) −5.76547 −0.307738
\(352\) 7.89236 0.420664
\(353\) −7.94868 −0.423065 −0.211533 0.977371i \(-0.567845\pi\)
−0.211533 + 0.977371i \(0.567845\pi\)
\(354\) 3.62633 0.192737
\(355\) −53.4779 −2.83831
\(356\) −11.1341 −0.590105
\(357\) −3.21065 −0.169925
\(358\) −15.5259 −0.820570
\(359\) 5.61107 0.296141 0.148071 0.988977i \(-0.452694\pi\)
0.148071 + 0.988977i \(0.452694\pi\)
\(360\) 34.9206 1.84048
\(361\) −10.3167 −0.542986
\(362\) −12.8465 −0.675199
\(363\) 21.5000 1.12846
\(364\) 17.0748 0.894962
\(365\) 2.66090 0.139278
\(366\) −6.07407 −0.317497
\(367\) −13.6352 −0.711751 −0.355875 0.934533i \(-0.615817\pi\)
−0.355875 + 0.934533i \(0.615817\pi\)
\(368\) 21.5130 1.12145
\(369\) 26.4689 1.37792
\(370\) 56.2971 2.92674
\(371\) −30.5869 −1.58799
\(372\) 25.0185 1.29715
\(373\) −18.3438 −0.949804 −0.474902 0.880039i \(-0.657516\pi\)
−0.474902 + 0.880039i \(0.657516\pi\)
\(374\) 18.0115 0.931351
\(375\) 2.16564 0.111833
\(376\) 42.4355 2.18844
\(377\) −12.3513 −0.636127
\(378\) 34.3774 1.76818
\(379\) 24.4662 1.25674 0.628371 0.777914i \(-0.283722\pi\)
0.628371 + 0.777914i \(0.283722\pi\)
\(380\) 37.4390 1.92058
\(381\) 6.77710 0.347201
\(382\) −16.1441 −0.826003
\(383\) 27.6006 1.41033 0.705163 0.709045i \(-0.250874\pi\)
0.705163 + 0.709045i \(0.250874\pi\)
\(384\) 16.4227 0.838069
\(385\) 66.6784 3.39824
\(386\) −41.7850 −2.12680
\(387\) −7.91795 −0.402492
\(388\) 34.3628 1.74451
\(389\) −15.7915 −0.800659 −0.400329 0.916371i \(-0.631104\pi\)
−0.400329 + 0.916371i \(0.631104\pi\)
\(390\) −8.57632 −0.434279
\(391\) −8.15275 −0.412302
\(392\) −17.5251 −0.885154
\(393\) −16.3939 −0.826961
\(394\) 51.2133 2.58009
\(395\) 2.64746 0.133208
\(396\) −55.8662 −2.80738
\(397\) 8.54584 0.428903 0.214452 0.976735i \(-0.431204\pi\)
0.214452 + 0.976735i \(0.431204\pi\)
\(398\) 13.6990 0.686668
\(399\) 7.81430 0.391204
\(400\) 18.5910 0.929550
\(401\) −22.1699 −1.10711 −0.553555 0.832813i \(-0.686729\pi\)
−0.553555 + 0.832813i \(0.686729\pi\)
\(402\) 28.4849 1.42070
\(403\) 10.7968 0.537828
\(404\) 20.4790 1.01887
\(405\) 11.8521 0.588935
\(406\) 73.6466 3.65502
\(407\) −43.4309 −2.15279
\(408\) 4.38876 0.217276
\(409\) 4.50609 0.222812 0.111406 0.993775i \(-0.464465\pi\)
0.111406 + 0.993775i \(0.464465\pi\)
\(410\) 89.5519 4.42265
\(411\) 4.31438 0.212813
\(412\) 28.8103 1.41938
\(413\) −6.14798 −0.302522
\(414\) 38.3807 1.88631
\(415\) 36.3002 1.78191
\(416\) 1.72103 0.0843804
\(417\) −10.2608 −0.502473
\(418\) −43.8376 −2.14417
\(419\) −7.62431 −0.372472 −0.186236 0.982505i \(-0.559629\pi\)
−0.186236 + 0.982505i \(0.559629\pi\)
\(420\) 33.6923 1.64402
\(421\) 1.89700 0.0924543 0.0462271 0.998931i \(-0.485280\pi\)
0.0462271 + 0.998931i \(0.485280\pi\)
\(422\) 38.5117 1.87472
\(423\) 22.1491 1.07693
\(424\) 41.8104 2.03049
\(425\) −7.04539 −0.341752
\(426\) 31.6404 1.53298
\(427\) 10.2978 0.498347
\(428\) 23.8972 1.15512
\(429\) 6.61629 0.319438
\(430\) −26.7887 −1.29186
\(431\) 25.4036 1.22365 0.611824 0.790994i \(-0.290436\pi\)
0.611824 + 0.790994i \(0.290436\pi\)
\(432\) −13.7479 −0.661448
\(433\) −24.9618 −1.19959 −0.599793 0.800155i \(-0.704750\pi\)
−0.599793 + 0.800155i \(0.704750\pi\)
\(434\) −64.3776 −3.09022
\(435\) −24.3719 −1.16854
\(436\) 24.3180 1.16462
\(437\) 19.8427 0.949207
\(438\) −1.57434 −0.0752247
\(439\) 7.59473 0.362476 0.181238 0.983439i \(-0.441989\pi\)
0.181238 + 0.983439i \(0.441989\pi\)
\(440\) −91.1452 −4.34518
\(441\) −9.14720 −0.435581
\(442\) 3.92763 0.186818
\(443\) −2.20249 −0.104644 −0.0523218 0.998630i \(-0.516662\pi\)
−0.0523218 + 0.998630i \(0.516662\pi\)
\(444\) −21.9455 −1.04149
\(445\) −9.48124 −0.449454
\(446\) −29.4508 −1.39454
\(447\) −7.58215 −0.358624
\(448\) −31.3434 −1.48084
\(449\) 14.5271 0.685575 0.342788 0.939413i \(-0.388629\pi\)
0.342788 + 0.939413i \(0.388629\pi\)
\(450\) 33.1676 1.56353
\(451\) −69.0858 −3.25312
\(452\) −58.2439 −2.73956
\(453\) −1.33291 −0.0626257
\(454\) −5.43639 −0.255142
\(455\) 14.5401 0.681649
\(456\) −10.6817 −0.500215
\(457\) 16.7787 0.784874 0.392437 0.919779i \(-0.371632\pi\)
0.392437 + 0.919779i \(0.371632\pi\)
\(458\) −5.59142 −0.261270
\(459\) 5.21003 0.243183
\(460\) 85.5545 3.98900
\(461\) 10.9469 0.509849 0.254925 0.966961i \(-0.417949\pi\)
0.254925 + 0.966961i \(0.417949\pi\)
\(462\) −39.4505 −1.83541
\(463\) 13.0103 0.604642 0.302321 0.953206i \(-0.402239\pi\)
0.302321 + 0.953206i \(0.402239\pi\)
\(464\) −29.4522 −1.36728
\(465\) 21.3045 0.987973
\(466\) −40.0703 −1.85622
\(467\) 6.05147 0.280028 0.140014 0.990149i \(-0.455285\pi\)
0.140014 + 0.990149i \(0.455285\pi\)
\(468\) −12.1823 −0.563129
\(469\) −48.2925 −2.22994
\(470\) 74.9366 3.45657
\(471\) 8.31302 0.383044
\(472\) 8.40391 0.386821
\(473\) 20.6664 0.950242
\(474\) −1.56638 −0.0719462
\(475\) 17.1476 0.786784
\(476\) −15.4298 −0.707224
\(477\) 21.8228 0.999198
\(478\) 3.99203 0.182591
\(479\) −1.27446 −0.0582317 −0.0291159 0.999576i \(-0.509269\pi\)
−0.0291159 + 0.999576i \(0.509269\pi\)
\(480\) 3.39597 0.155004
\(481\) −9.47067 −0.431825
\(482\) 57.5063 2.61934
\(483\) 17.8570 0.812521
\(484\) 103.325 4.69661
\(485\) 29.2617 1.32870
\(486\) −38.2706 −1.73599
\(487\) 1.09275 0.0495174 0.0247587 0.999693i \(-0.492118\pi\)
0.0247587 + 0.999693i \(0.492118\pi\)
\(488\) −14.0765 −0.637213
\(489\) −2.20720 −0.0998129
\(490\) −30.9476 −1.39807
\(491\) 7.14892 0.322626 0.161313 0.986903i \(-0.448427\pi\)
0.161313 + 0.986903i \(0.448427\pi\)
\(492\) −34.9088 −1.57381
\(493\) 11.1614 0.502685
\(494\) −9.55934 −0.430095
\(495\) −47.5730 −2.13825
\(496\) 25.7454 1.15600
\(497\) −53.6423 −2.40619
\(498\) −21.4772 −0.962415
\(499\) −9.58772 −0.429205 −0.214603 0.976701i \(-0.568846\pi\)
−0.214603 + 0.976701i \(0.568846\pi\)
\(500\) 10.4077 0.465447
\(501\) 13.6048 0.607817
\(502\) −63.2923 −2.82487
\(503\) 1.43629 0.0640409 0.0320205 0.999487i \(-0.489806\pi\)
0.0320205 + 0.999487i \(0.489806\pi\)
\(504\) 35.0280 1.56027
\(505\) 17.4390 0.776023
\(506\) −100.176 −4.45338
\(507\) −9.00591 −0.399966
\(508\) 32.5695 1.44504
\(509\) −12.9579 −0.574350 −0.287175 0.957878i \(-0.592716\pi\)
−0.287175 + 0.957878i \(0.592716\pi\)
\(510\) 7.75008 0.343179
\(511\) 2.66909 0.118073
\(512\) 32.9210 1.45492
\(513\) −12.6805 −0.559859
\(514\) 29.8674 1.31739
\(515\) 24.5335 1.08108
\(516\) 10.4427 0.459712
\(517\) −57.8106 −2.54251
\(518\) 56.4702 2.48116
\(519\) 13.9112 0.610632
\(520\) −19.8754 −0.871593
\(521\) −6.60279 −0.289274 −0.144637 0.989485i \(-0.546201\pi\)
−0.144637 + 0.989485i \(0.546201\pi\)
\(522\) −52.5446 −2.29981
\(523\) 23.2758 1.01778 0.508890 0.860832i \(-0.330056\pi\)
0.508890 + 0.860832i \(0.330056\pi\)
\(524\) −78.7860 −3.44178
\(525\) 15.4315 0.673487
\(526\) 22.0735 0.962449
\(527\) −9.75666 −0.425007
\(528\) 15.7767 0.686595
\(529\) 22.3440 0.971478
\(530\) 73.8328 3.20709
\(531\) 4.38639 0.190353
\(532\) 37.5542 1.62818
\(533\) −15.0650 −0.652539
\(534\) 5.60962 0.242752
\(535\) 20.3497 0.879795
\(536\) 66.0128 2.85132
\(537\) 5.15381 0.222403
\(538\) −21.8192 −0.940693
\(539\) 23.8748 1.02836
\(540\) −54.6737 −2.35278
\(541\) −0.834327 −0.0358705 −0.0179353 0.999839i \(-0.505709\pi\)
−0.0179353 + 0.999839i \(0.505709\pi\)
\(542\) 7.45428 0.320189
\(543\) 4.26439 0.183003
\(544\) −1.55523 −0.0666798
\(545\) 20.7081 0.887036
\(546\) −8.60270 −0.368161
\(547\) −0.150874 −0.00645091 −0.00322545 0.999995i \(-0.501027\pi\)
−0.00322545 + 0.999995i \(0.501027\pi\)
\(548\) 20.7342 0.885720
\(549\) −7.34718 −0.313570
\(550\) −86.5696 −3.69134
\(551\) −27.1655 −1.15729
\(552\) −24.4094 −1.03893
\(553\) 2.65560 0.112928
\(554\) −43.4297 −1.84515
\(555\) −18.6877 −0.793250
\(556\) −49.3116 −2.09128
\(557\) −24.3484 −1.03168 −0.515838 0.856686i \(-0.672519\pi\)
−0.515838 + 0.856686i \(0.672519\pi\)
\(558\) 45.9314 1.94443
\(559\) 4.50657 0.190608
\(560\) 34.6712 1.46513
\(561\) −5.97888 −0.252428
\(562\) 29.3973 1.24005
\(563\) 23.9303 1.00854 0.504271 0.863545i \(-0.331761\pi\)
0.504271 + 0.863545i \(0.331761\pi\)
\(564\) −29.2115 −1.23003
\(565\) −49.5977 −2.08659
\(566\) −54.8874 −2.30709
\(567\) 11.8885 0.499272
\(568\) 73.3257 3.07668
\(569\) −31.7158 −1.32959 −0.664797 0.747024i \(-0.731482\pi\)
−0.664797 + 0.747024i \(0.731482\pi\)
\(570\) −18.8627 −0.790071
\(571\) −12.8077 −0.535983 −0.267992 0.963421i \(-0.586360\pi\)
−0.267992 + 0.963421i \(0.586360\pi\)
\(572\) 31.7967 1.32949
\(573\) 5.35900 0.223876
\(574\) 89.8273 3.74932
\(575\) 39.1851 1.63413
\(576\) 22.3626 0.931773
\(577\) −38.4001 −1.59862 −0.799309 0.600921i \(-0.794801\pi\)
−0.799309 + 0.600921i \(0.794801\pi\)
\(578\) 37.6127 1.56448
\(579\) 13.8705 0.576437
\(580\) −117.127 −4.86344
\(581\) 36.4118 1.51062
\(582\) −17.3128 −0.717639
\(583\) −56.9591 −2.35900
\(584\) −3.64848 −0.150975
\(585\) −10.3739 −0.428908
\(586\) 12.2861 0.507534
\(587\) −32.6561 −1.34786 −0.673932 0.738794i \(-0.735396\pi\)
−0.673932 + 0.738794i \(0.735396\pi\)
\(588\) 12.0639 0.497505
\(589\) 23.7465 0.978456
\(590\) 14.8404 0.610970
\(591\) −17.0002 −0.699293
\(592\) −22.5831 −0.928160
\(593\) 14.3464 0.589137 0.294569 0.955630i \(-0.404824\pi\)
0.294569 + 0.955630i \(0.404824\pi\)
\(594\) 64.0178 2.62668
\(595\) −13.1393 −0.538658
\(596\) −36.4385 −1.49258
\(597\) −4.54735 −0.186111
\(598\) −21.8447 −0.893296
\(599\) −3.28237 −0.134114 −0.0670570 0.997749i \(-0.521361\pi\)
−0.0670570 + 0.997749i \(0.521361\pi\)
\(600\) −21.0940 −0.861157
\(601\) 15.8292 0.645686 0.322843 0.946453i \(-0.395361\pi\)
0.322843 + 0.946453i \(0.395361\pi\)
\(602\) −26.8711 −1.09518
\(603\) 34.4552 1.40312
\(604\) −6.40574 −0.260646
\(605\) 87.9869 3.57718
\(606\) −10.3178 −0.419133
\(607\) 33.3281 1.35275 0.676373 0.736559i \(-0.263551\pi\)
0.676373 + 0.736559i \(0.263551\pi\)
\(608\) 3.78522 0.153511
\(609\) −24.4469 −0.990638
\(610\) −24.8576 −1.00645
\(611\) −12.6063 −0.509998
\(612\) 11.0087 0.445000
\(613\) 25.1970 1.01770 0.508848 0.860857i \(-0.330072\pi\)
0.508848 + 0.860857i \(0.330072\pi\)
\(614\) 46.8856 1.89215
\(615\) −29.7266 −1.19869
\(616\) −91.4255 −3.68364
\(617\) −23.1096 −0.930356 −0.465178 0.885217i \(-0.654010\pi\)
−0.465178 + 0.885217i \(0.654010\pi\)
\(618\) −14.5154 −0.583893
\(619\) −27.8661 −1.12003 −0.560017 0.828481i \(-0.689206\pi\)
−0.560017 + 0.828481i \(0.689206\pi\)
\(620\) 102.386 4.11191
\(621\) −28.9772 −1.16281
\(622\) 32.1337 1.28844
\(623\) −9.51040 −0.381026
\(624\) 3.44032 0.137723
\(625\) −20.2331 −0.809325
\(626\) 46.3023 1.85061
\(627\) 14.5518 0.581144
\(628\) 39.9509 1.59422
\(629\) 8.55827 0.341240
\(630\) 61.8558 2.46439
\(631\) −41.4360 −1.64954 −0.824770 0.565469i \(-0.808695\pi\)
−0.824770 + 0.565469i \(0.808695\pi\)
\(632\) −3.63004 −0.144395
\(633\) −12.7839 −0.508115
\(634\) −33.1019 −1.31464
\(635\) 27.7347 1.10062
\(636\) −28.7812 −1.14125
\(637\) 5.20621 0.206277
\(638\) 137.145 5.42962
\(639\) 38.2721 1.51402
\(640\) 67.2085 2.65665
\(641\) −16.1050 −0.636107 −0.318054 0.948073i \(-0.603029\pi\)
−0.318054 + 0.948073i \(0.603029\pi\)
\(642\) −12.0400 −0.475181
\(643\) −0.458480 −0.0180807 −0.00904034 0.999959i \(-0.502878\pi\)
−0.00904034 + 0.999959i \(0.502878\pi\)
\(644\) 85.8176 3.38169
\(645\) 8.89246 0.350140
\(646\) 8.63840 0.339873
\(647\) −36.3681 −1.42978 −0.714890 0.699237i \(-0.753523\pi\)
−0.714890 + 0.699237i \(0.753523\pi\)
\(648\) −16.2509 −0.638396
\(649\) −11.4488 −0.449404
\(650\) −18.8776 −0.740441
\(651\) 21.3700 0.837558
\(652\) −10.6074 −0.415418
\(653\) −32.2652 −1.26263 −0.631317 0.775525i \(-0.717485\pi\)
−0.631317 + 0.775525i \(0.717485\pi\)
\(654\) −12.2520 −0.479092
\(655\) −67.0904 −2.62144
\(656\) −35.9230 −1.40256
\(657\) −1.90431 −0.0742943
\(658\) 75.1671 2.93032
\(659\) 32.6197 1.27068 0.635341 0.772232i \(-0.280859\pi\)
0.635341 + 0.772232i \(0.280859\pi\)
\(660\) 62.7420 2.44223
\(661\) −37.7214 −1.46719 −0.733596 0.679586i \(-0.762159\pi\)
−0.733596 + 0.679586i \(0.762159\pi\)
\(662\) −44.9979 −1.74889
\(663\) −1.30377 −0.0506343
\(664\) −49.7727 −1.93156
\(665\) 31.9793 1.24010
\(666\) −40.2897 −1.56120
\(667\) −62.0776 −2.40366
\(668\) 65.3822 2.52971
\(669\) 9.77616 0.377968
\(670\) 116.572 4.50356
\(671\) 19.1766 0.740306
\(672\) 3.40641 0.131405
\(673\) −7.79588 −0.300509 −0.150255 0.988647i \(-0.548009\pi\)
−0.150255 + 0.988647i \(0.548009\pi\)
\(674\) −75.3315 −2.90166
\(675\) −25.0413 −0.963839
\(676\) −43.2808 −1.66465
\(677\) 14.2574 0.547955 0.273977 0.961736i \(-0.411661\pi\)
0.273977 + 0.961736i \(0.411661\pi\)
\(678\) 29.3447 1.12698
\(679\) 29.3517 1.12641
\(680\) 17.9606 0.688757
\(681\) 1.80460 0.0691525
\(682\) −119.884 −4.59060
\(683\) 21.4229 0.819725 0.409863 0.912147i \(-0.365577\pi\)
0.409863 + 0.912147i \(0.365577\pi\)
\(684\) −26.7937 −1.02448
\(685\) 17.6562 0.674610
\(686\) 24.8784 0.949860
\(687\) 1.85606 0.0708132
\(688\) 10.7461 0.409690
\(689\) −12.4207 −0.473189
\(690\) −43.1044 −1.64096
\(691\) −30.9626 −1.17787 −0.588936 0.808180i \(-0.700453\pi\)
−0.588936 + 0.808180i \(0.700453\pi\)
\(692\) 66.8546 2.54143
\(693\) −47.7193 −1.81270
\(694\) −15.4612 −0.586899
\(695\) −41.9913 −1.59282
\(696\) 33.4174 1.26668
\(697\) 13.6137 0.515655
\(698\) −68.9790 −2.61089
\(699\) 13.3013 0.503101
\(700\) 74.1613 2.80303
\(701\) −16.0964 −0.607951 −0.303976 0.952680i \(-0.598314\pi\)
−0.303976 + 0.952680i \(0.598314\pi\)
\(702\) 13.9599 0.526882
\(703\) −20.8297 −0.785608
\(704\) −58.3678 −2.19982
\(705\) −24.8751 −0.936850
\(706\) 19.2461 0.724335
\(707\) 17.4926 0.657877
\(708\) −5.78503 −0.217415
\(709\) −19.3427 −0.726432 −0.363216 0.931705i \(-0.618321\pi\)
−0.363216 + 0.931705i \(0.618321\pi\)
\(710\) 129.486 4.85950
\(711\) −1.89469 −0.0710563
\(712\) 13.0001 0.487200
\(713\) 54.2646 2.03223
\(714\) 7.77391 0.290931
\(715\) 27.0766 1.01261
\(716\) 24.7683 0.925635
\(717\) −1.32515 −0.0494886
\(718\) −13.5860 −0.507027
\(719\) −3.42701 −0.127806 −0.0639030 0.997956i \(-0.520355\pi\)
−0.0639030 + 0.997956i \(0.520355\pi\)
\(720\) −24.7369 −0.921888
\(721\) 24.6090 0.916485
\(722\) 24.9798 0.929652
\(723\) −19.0891 −0.709933
\(724\) 20.4939 0.761650
\(725\) −53.6458 −1.99236
\(726\) −52.0578 −1.93205
\(727\) 30.6237 1.13577 0.567886 0.823108i \(-0.307762\pi\)
0.567886 + 0.823108i \(0.307762\pi\)
\(728\) −19.9365 −0.738896
\(729\) 1.89401 0.0701486
\(730\) −6.44283 −0.238460
\(731\) −4.07241 −0.150623
\(732\) 9.68989 0.358149
\(733\) 3.39721 0.125479 0.0627394 0.998030i \(-0.480016\pi\)
0.0627394 + 0.998030i \(0.480016\pi\)
\(734\) 33.0147 1.21860
\(735\) 10.2730 0.378925
\(736\) 8.64986 0.318838
\(737\) −89.9304 −3.31263
\(738\) −64.0890 −2.35915
\(739\) −35.9271 −1.32160 −0.660800 0.750562i \(-0.729783\pi\)
−0.660800 + 0.750562i \(0.729783\pi\)
\(740\) −89.8099 −3.30148
\(741\) 3.17321 0.116571
\(742\) 74.0599 2.71882
\(743\) −32.3705 −1.18756 −0.593780 0.804627i \(-0.702365\pi\)
−0.593780 + 0.804627i \(0.702365\pi\)
\(744\) −29.2115 −1.07095
\(745\) −31.0293 −1.13682
\(746\) 44.4156 1.62617
\(747\) −25.9787 −0.950511
\(748\) −28.7334 −1.05060
\(749\) 20.4123 0.745850
\(750\) −5.24366 −0.191471
\(751\) −6.53721 −0.238546 −0.119273 0.992861i \(-0.538056\pi\)
−0.119273 + 0.992861i \(0.538056\pi\)
\(752\) −30.0602 −1.09618
\(753\) 21.0098 0.765639
\(754\) 29.9062 1.08912
\(755\) −5.45482 −0.198521
\(756\) −54.8419 −1.99458
\(757\) −20.6167 −0.749326 −0.374663 0.927161i \(-0.622242\pi\)
−0.374663 + 0.927161i \(0.622242\pi\)
\(758\) −59.2397 −2.15168
\(759\) 33.2533 1.20702
\(760\) −43.7137 −1.58566
\(761\) 10.8207 0.392249 0.196124 0.980579i \(-0.437164\pi\)
0.196124 + 0.980579i \(0.437164\pi\)
\(762\) −16.4093 −0.594447
\(763\) 20.7717 0.751988
\(764\) 25.7544 0.931763
\(765\) 9.37447 0.338935
\(766\) −66.8292 −2.41464
\(767\) −2.49656 −0.0901454
\(768\) −24.4933 −0.883827
\(769\) −9.55581 −0.344591 −0.172296 0.985045i \(-0.555118\pi\)
−0.172296 + 0.985045i \(0.555118\pi\)
\(770\) −161.448 −5.81817
\(771\) −9.91444 −0.357060
\(772\) 66.6590 2.39911
\(773\) 4.47482 0.160948 0.0804741 0.996757i \(-0.474357\pi\)
0.0804741 + 0.996757i \(0.474357\pi\)
\(774\) 19.1717 0.689111
\(775\) 46.8941 1.68448
\(776\) −40.1219 −1.44029
\(777\) −18.7452 −0.672480
\(778\) 38.2357 1.37082
\(779\) −33.1339 −1.18715
\(780\) 13.6817 0.489883
\(781\) −99.8929 −3.57445
\(782\) 19.7402 0.705908
\(783\) 39.6708 1.41772
\(784\) 12.4144 0.443370
\(785\) 34.0203 1.21424
\(786\) 39.6943 1.41585
\(787\) 14.3480 0.511452 0.255726 0.966749i \(-0.417686\pi\)
0.255726 + 0.966749i \(0.417686\pi\)
\(788\) −81.6998 −2.91044
\(789\) −7.32726 −0.260857
\(790\) −6.41027 −0.228067
\(791\) −49.7503 −1.76892
\(792\) 65.2293 2.31782
\(793\) 4.18171 0.148497
\(794\) −20.6920 −0.734331
\(795\) −24.5087 −0.869233
\(796\) −21.8538 −0.774587
\(797\) 20.0333 0.709617 0.354809 0.934939i \(-0.384546\pi\)
0.354809 + 0.934939i \(0.384546\pi\)
\(798\) −18.9207 −0.669786
\(799\) 11.3919 0.403015
\(800\) 7.47498 0.264280
\(801\) 6.78538 0.239749
\(802\) 53.6797 1.89550
\(803\) 4.97038 0.175401
\(804\) −45.4415 −1.60260
\(805\) 73.0781 2.57567
\(806\) −26.1423 −0.920822
\(807\) 7.24286 0.254961
\(808\) −23.9113 −0.841196
\(809\) 14.3152 0.503295 0.251647 0.967819i \(-0.419028\pi\)
0.251647 + 0.967819i \(0.419028\pi\)
\(810\) −28.6974 −1.00832
\(811\) 24.0754 0.845402 0.422701 0.906269i \(-0.361082\pi\)
0.422701 + 0.906269i \(0.361082\pi\)
\(812\) −117.487 −4.12300
\(813\) −2.47444 −0.0867823
\(814\) 105.159 3.68582
\(815\) −9.03276 −0.316404
\(816\) −3.10888 −0.108833
\(817\) 9.91172 0.346767
\(818\) −10.9106 −0.381479
\(819\) −10.4058 −0.363608
\(820\) −142.861 −4.98892
\(821\) 6.50109 0.226889 0.113445 0.993544i \(-0.463812\pi\)
0.113445 + 0.993544i \(0.463812\pi\)
\(822\) −10.4464 −0.364359
\(823\) 44.6737 1.55723 0.778614 0.627503i \(-0.215923\pi\)
0.778614 + 0.627503i \(0.215923\pi\)
\(824\) −33.6389 −1.17187
\(825\) 28.7367 1.00048
\(826\) 14.8861 0.517952
\(827\) 51.2060 1.78061 0.890303 0.455369i \(-0.150493\pi\)
0.890303 + 0.455369i \(0.150493\pi\)
\(828\) −61.2282 −2.12783
\(829\) −15.0751 −0.523581 −0.261790 0.965125i \(-0.584313\pi\)
−0.261790 + 0.965125i \(0.584313\pi\)
\(830\) −87.8934 −3.05082
\(831\) 14.4164 0.500101
\(832\) −12.7279 −0.441259
\(833\) −4.70464 −0.163006
\(834\) 24.8444 0.860290
\(835\) 55.6763 1.92676
\(836\) 69.9335 2.41870
\(837\) −34.6779 −1.19864
\(838\) 18.4607 0.637713
\(839\) −31.1054 −1.07388 −0.536939 0.843621i \(-0.680419\pi\)
−0.536939 + 0.843621i \(0.680419\pi\)
\(840\) −39.3391 −1.35733
\(841\) 55.9866 1.93057
\(842\) −4.59320 −0.158292
\(843\) −9.75839 −0.336097
\(844\) −61.4373 −2.11476
\(845\) −36.8559 −1.26788
\(846\) −53.6294 −1.84382
\(847\) 88.2575 3.03256
\(848\) −29.6174 −1.01707
\(849\) 18.2198 0.625301
\(850\) 17.0589 0.585117
\(851\) −47.5994 −1.63169
\(852\) −50.4755 −1.72926
\(853\) 47.7800 1.63596 0.817978 0.575250i \(-0.195095\pi\)
0.817978 + 0.575250i \(0.195095\pi\)
\(854\) −24.9340 −0.853225
\(855\) −22.8163 −0.780299
\(856\) −27.9024 −0.953683
\(857\) −8.56877 −0.292704 −0.146352 0.989233i \(-0.546753\pi\)
−0.146352 + 0.989233i \(0.546753\pi\)
\(858\) −16.0200 −0.546913
\(859\) −2.51035 −0.0856520 −0.0428260 0.999083i \(-0.513636\pi\)
−0.0428260 + 0.999083i \(0.513636\pi\)
\(860\) 42.7356 1.45727
\(861\) −29.8181 −1.01620
\(862\) −61.5095 −2.09502
\(863\) 48.3935 1.64733 0.823666 0.567075i \(-0.191925\pi\)
0.823666 + 0.567075i \(0.191925\pi\)
\(864\) −5.52771 −0.188056
\(865\) 56.9302 1.93568
\(866\) 60.4397 2.05383
\(867\) −12.4855 −0.424029
\(868\) 102.701 3.48589
\(869\) 4.94527 0.167757
\(870\) 59.0116 2.00068
\(871\) −19.6105 −0.664476
\(872\) −28.3937 −0.961532
\(873\) −20.9415 −0.708763
\(874\) −48.0451 −1.62515
\(875\) 8.88996 0.300535
\(876\) 2.51152 0.0848563
\(877\) −19.4485 −0.656731 −0.328365 0.944551i \(-0.606498\pi\)
−0.328365 + 0.944551i \(0.606498\pi\)
\(878\) −18.3890 −0.620600
\(879\) −4.07835 −0.137559
\(880\) 64.5649 2.17648
\(881\) 52.0215 1.75265 0.876325 0.481721i \(-0.159988\pi\)
0.876325 + 0.481721i \(0.159988\pi\)
\(882\) 22.1480 0.745763
\(883\) 22.6883 0.763522 0.381761 0.924261i \(-0.375318\pi\)
0.381761 + 0.924261i \(0.375318\pi\)
\(884\) −6.26569 −0.210738
\(885\) −4.92625 −0.165594
\(886\) 5.33288 0.179162
\(887\) −7.55308 −0.253608 −0.126804 0.991928i \(-0.540472\pi\)
−0.126804 + 0.991928i \(0.540472\pi\)
\(888\) 25.6235 0.859869
\(889\) 27.8200 0.933051
\(890\) 22.9569 0.769515
\(891\) 22.1389 0.741680
\(892\) 46.9825 1.57309
\(893\) −27.7263 −0.927825
\(894\) 18.3586 0.614004
\(895\) 21.0915 0.705011
\(896\) 67.4152 2.25218
\(897\) 7.25132 0.242114
\(898\) −35.1743 −1.17378
\(899\) −74.2903 −2.47772
\(900\) −52.9118 −1.76373
\(901\) 11.2240 0.373927
\(902\) 167.277 5.56971
\(903\) 8.91981 0.296833
\(904\) 68.0055 2.26183
\(905\) 17.4516 0.580112
\(906\) 3.22737 0.107222
\(907\) 41.6658 1.38349 0.691746 0.722141i \(-0.256842\pi\)
0.691746 + 0.722141i \(0.256842\pi\)
\(908\) 8.67260 0.287810
\(909\) −12.4804 −0.413949
\(910\) −35.2058 −1.16706
\(911\) 19.7433 0.654126 0.327063 0.945003i \(-0.393941\pi\)
0.327063 + 0.945003i \(0.393941\pi\)
\(912\) 7.56661 0.250556
\(913\) 67.8062 2.24406
\(914\) −40.6261 −1.34379
\(915\) 8.25144 0.272784
\(916\) 8.91992 0.294722
\(917\) −67.2967 −2.22233
\(918\) −12.6150 −0.416357
\(919\) −20.2294 −0.667307 −0.333653 0.942696i \(-0.608282\pi\)
−0.333653 + 0.942696i \(0.608282\pi\)
\(920\) −99.8933 −3.29338
\(921\) −15.5636 −0.512838
\(922\) −26.5057 −0.872919
\(923\) −21.7829 −0.716994
\(924\) 62.9349 2.07041
\(925\) −41.1341 −1.35248
\(926\) −31.5019 −1.03522
\(927\) −17.5577 −0.576671
\(928\) −11.8420 −0.388732
\(929\) 36.8216 1.20808 0.604038 0.796955i \(-0.293557\pi\)
0.604038 + 0.796955i \(0.293557\pi\)
\(930\) −51.5845 −1.69152
\(931\) 11.4505 0.375275
\(932\) 63.9237 2.09389
\(933\) −10.6667 −0.349213
\(934\) −14.6524 −0.479440
\(935\) −24.4680 −0.800190
\(936\) 14.2241 0.464928
\(937\) −5.09128 −0.166325 −0.0831624 0.996536i \(-0.526502\pi\)
−0.0831624 + 0.996536i \(0.526502\pi\)
\(938\) 116.930 3.81791
\(939\) −15.3700 −0.501580
\(940\) −119.545 −3.89914
\(941\) 16.2549 0.529895 0.264948 0.964263i \(-0.414645\pi\)
0.264948 + 0.964263i \(0.414645\pi\)
\(942\) −20.1283 −0.655814
\(943\) −75.7166 −2.46567
\(944\) −5.95311 −0.193757
\(945\) −46.7007 −1.51917
\(946\) −50.0394 −1.62692
\(947\) 40.0445 1.30127 0.650635 0.759391i \(-0.274503\pi\)
0.650635 + 0.759391i \(0.274503\pi\)
\(948\) 2.49882 0.0811580
\(949\) 1.08386 0.0351834
\(950\) −41.5193 −1.34706
\(951\) 10.9881 0.356314
\(952\) 18.0158 0.583896
\(953\) 21.4494 0.694813 0.347407 0.937715i \(-0.387062\pi\)
0.347407 + 0.937715i \(0.387062\pi\)
\(954\) −52.8394 −1.71074
\(955\) 21.9312 0.709678
\(956\) −6.36844 −0.205970
\(957\) −45.5251 −1.47162
\(958\) 3.08585 0.0996992
\(959\) 17.7105 0.571903
\(960\) −25.1149 −0.810578
\(961\) 33.9402 1.09485
\(962\) 22.9313 0.739333
\(963\) −14.5636 −0.469304
\(964\) −91.7391 −2.95472
\(965\) 56.7636 1.82729
\(966\) −43.2370 −1.39113
\(967\) 53.0430 1.70575 0.852874 0.522116i \(-0.174857\pi\)
0.852874 + 0.522116i \(0.174857\pi\)
\(968\) −120.643 −3.87760
\(969\) −2.86750 −0.0921175
\(970\) −70.8511 −2.27489
\(971\) 30.5076 0.979035 0.489518 0.871993i \(-0.337173\pi\)
0.489518 + 0.871993i \(0.337173\pi\)
\(972\) 61.0525 1.95826
\(973\) −42.1205 −1.35032
\(974\) −2.64588 −0.0847794
\(975\) 6.26640 0.200685
\(976\) 9.97142 0.319177
\(977\) 14.8942 0.476506 0.238253 0.971203i \(-0.423425\pi\)
0.238253 + 0.971203i \(0.423425\pi\)
\(978\) 5.34427 0.170891
\(979\) −17.7103 −0.566024
\(980\) 49.3702 1.57707
\(981\) −14.8200 −0.473166
\(982\) −17.3096 −0.552372
\(983\) 1.00000 0.0318950
\(984\) 40.7594 1.29936
\(985\) −69.5716 −2.21674
\(986\) −27.0251 −0.860653
\(987\) −24.9516 −0.794218
\(988\) 15.2499 0.485164
\(989\) 22.6499 0.720226
\(990\) 115.188 3.66091
\(991\) −22.8058 −0.724450 −0.362225 0.932091i \(-0.617983\pi\)
−0.362225 + 0.932091i \(0.617983\pi\)
\(992\) 10.3516 0.328663
\(993\) 14.9370 0.474011
\(994\) 129.884 4.11966
\(995\) −18.6096 −0.589965
\(996\) 34.2622 1.08564
\(997\) 22.6404 0.717029 0.358514 0.933524i \(-0.383283\pi\)
0.358514 + 0.933524i \(0.383283\pi\)
\(998\) 23.2147 0.734847
\(999\) 30.4185 0.962398
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 983.2.a.b.1.5 54
3.2 odd 2 8847.2.a.g.1.50 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.2.a.b.1.5 54 1.1 even 1 trivial
8847.2.a.g.1.50 54 3.2 odd 2