Properties

Label 4011.2.a.l.1.2
Level $4011$
Weight $2$
Character 4011.1
Self dual yes
Analytic conductor $32.028$
Analytic rank $0$
Dimension $28$
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] = [4011,2,Mod(1,4011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4011.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: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 4011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.75611 q^{2} -1.00000 q^{3} +5.59616 q^{4} -2.11611 q^{5} +2.75611 q^{6} +1.00000 q^{7} -9.91144 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.75611 q^{2} -1.00000 q^{3} +5.59616 q^{4} -2.11611 q^{5} +2.75611 q^{6} +1.00000 q^{7} -9.91144 q^{8} +1.00000 q^{9} +5.83224 q^{10} -2.18663 q^{11} -5.59616 q^{12} -3.28792 q^{13} -2.75611 q^{14} +2.11611 q^{15} +16.1247 q^{16} +4.46735 q^{17} -2.75611 q^{18} +3.35498 q^{19} -11.8421 q^{20} -1.00000 q^{21} +6.02661 q^{22} -9.54424 q^{23} +9.91144 q^{24} -0.522072 q^{25} +9.06188 q^{26} -1.00000 q^{27} +5.59616 q^{28} +8.29783 q^{29} -5.83224 q^{30} -8.23902 q^{31} -24.6187 q^{32} +2.18663 q^{33} -12.3125 q^{34} -2.11611 q^{35} +5.59616 q^{36} +9.18971 q^{37} -9.24669 q^{38} +3.28792 q^{39} +20.9737 q^{40} +2.51603 q^{41} +2.75611 q^{42} -0.997412 q^{43} -12.2368 q^{44} -2.11611 q^{45} +26.3050 q^{46} -4.66122 q^{47} -16.1247 q^{48} +1.00000 q^{49} +1.43889 q^{50} -4.46735 q^{51} -18.3997 q^{52} -10.9605 q^{53} +2.75611 q^{54} +4.62716 q^{55} -9.91144 q^{56} -3.35498 q^{57} -22.8698 q^{58} -8.79911 q^{59} +11.8421 q^{60} -6.53065 q^{61} +22.7077 q^{62} +1.00000 q^{63} +35.6025 q^{64} +6.95761 q^{65} -6.02661 q^{66} -12.9550 q^{67} +25.0000 q^{68} +9.54424 q^{69} +5.83224 q^{70} +3.16272 q^{71} -9.91144 q^{72} +12.3345 q^{73} -25.3279 q^{74} +0.522072 q^{75} +18.7750 q^{76} -2.18663 q^{77} -9.06188 q^{78} +15.3503 q^{79} -34.1217 q^{80} +1.00000 q^{81} -6.93446 q^{82} +14.1553 q^{83} -5.59616 q^{84} -9.45341 q^{85} +2.74898 q^{86} -8.29783 q^{87} +21.6727 q^{88} +3.19891 q^{89} +5.83224 q^{90} -3.28792 q^{91} -53.4111 q^{92} +8.23902 q^{93} +12.8469 q^{94} -7.09950 q^{95} +24.6187 q^{96} +1.77027 q^{97} -2.75611 q^{98} -2.18663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75611 −1.94887 −0.974433 0.224677i \(-0.927867\pi\)
−0.974433 + 0.224677i \(0.927867\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.59616 2.79808
\(5\) −2.11611 −0.946354 −0.473177 0.880967i \(-0.656893\pi\)
−0.473177 + 0.880967i \(0.656893\pi\)
\(6\) 2.75611 1.12518
\(7\) 1.00000 0.377964
\(8\) −9.91144 −3.50422
\(9\) 1.00000 0.333333
\(10\) 5.83224 1.84432
\(11\) −2.18663 −0.659295 −0.329648 0.944104i \(-0.606930\pi\)
−0.329648 + 0.944104i \(0.606930\pi\)
\(12\) −5.59616 −1.61547
\(13\) −3.28792 −0.911905 −0.455953 0.890004i \(-0.650701\pi\)
−0.455953 + 0.890004i \(0.650701\pi\)
\(14\) −2.75611 −0.736602
\(15\) 2.11611 0.546378
\(16\) 16.1247 4.03118
\(17\) 4.46735 1.08349 0.541746 0.840542i \(-0.317764\pi\)
0.541746 + 0.840542i \(0.317764\pi\)
\(18\) −2.75611 −0.649622
\(19\) 3.35498 0.769684 0.384842 0.922982i \(-0.374256\pi\)
0.384842 + 0.922982i \(0.374256\pi\)
\(20\) −11.8421 −2.64798
\(21\) −1.00000 −0.218218
\(22\) 6.02661 1.28488
\(23\) −9.54424 −1.99011 −0.995056 0.0993165i \(-0.968334\pi\)
−0.995056 + 0.0993165i \(0.968334\pi\)
\(24\) 9.91144 2.02316
\(25\) −0.522072 −0.104414
\(26\) 9.06188 1.77718
\(27\) −1.00000 −0.192450
\(28\) 5.59616 1.05758
\(29\) 8.29783 1.54087 0.770434 0.637520i \(-0.220040\pi\)
0.770434 + 0.637520i \(0.220040\pi\)
\(30\) −5.83224 −1.06482
\(31\) −8.23902 −1.47977 −0.739886 0.672732i \(-0.765121\pi\)
−0.739886 + 0.672732i \(0.765121\pi\)
\(32\) −24.6187 −4.35201
\(33\) 2.18663 0.380644
\(34\) −12.3125 −2.11158
\(35\) −2.11611 −0.357688
\(36\) 5.59616 0.932694
\(37\) 9.18971 1.51078 0.755389 0.655276i \(-0.227448\pi\)
0.755389 + 0.655276i \(0.227448\pi\)
\(38\) −9.24669 −1.50001
\(39\) 3.28792 0.526489
\(40\) 20.9737 3.31623
\(41\) 2.51603 0.392938 0.196469 0.980510i \(-0.437053\pi\)
0.196469 + 0.980510i \(0.437053\pi\)
\(42\) 2.75611 0.425278
\(43\) −0.997412 −0.152104 −0.0760519 0.997104i \(-0.524231\pi\)
−0.0760519 + 0.997104i \(0.524231\pi\)
\(44\) −12.2368 −1.84476
\(45\) −2.11611 −0.315451
\(46\) 26.3050 3.87846
\(47\) −4.66122 −0.679909 −0.339954 0.940442i \(-0.610412\pi\)
−0.339954 + 0.940442i \(0.610412\pi\)
\(48\) −16.1247 −2.32740
\(49\) 1.00000 0.142857
\(50\) 1.43889 0.203490
\(51\) −4.46735 −0.625554
\(52\) −18.3997 −2.55158
\(53\) −10.9605 −1.50554 −0.752770 0.658284i \(-0.771283\pi\)
−0.752770 + 0.658284i \(0.771283\pi\)
\(54\) 2.75611 0.375060
\(55\) 4.62716 0.623926
\(56\) −9.91144 −1.32447
\(57\) −3.35498 −0.444377
\(58\) −22.8698 −3.00295
\(59\) −8.79911 −1.14555 −0.572773 0.819714i \(-0.694133\pi\)
−0.572773 + 0.819714i \(0.694133\pi\)
\(60\) 11.8421 1.52881
\(61\) −6.53065 −0.836164 −0.418082 0.908409i \(-0.637298\pi\)
−0.418082 + 0.908409i \(0.637298\pi\)
\(62\) 22.7077 2.88388
\(63\) 1.00000 0.125988
\(64\) 35.6025 4.45031
\(65\) 6.95761 0.862985
\(66\) −6.02661 −0.741825
\(67\) −12.9550 −1.58271 −0.791354 0.611358i \(-0.790623\pi\)
−0.791354 + 0.611358i \(0.790623\pi\)
\(68\) 25.0000 3.03170
\(69\) 9.54424 1.14899
\(70\) 5.83224 0.697087
\(71\) 3.16272 0.375345 0.187673 0.982232i \(-0.439906\pi\)
0.187673 + 0.982232i \(0.439906\pi\)
\(72\) −9.91144 −1.16807
\(73\) 12.3345 1.44364 0.721822 0.692079i \(-0.243305\pi\)
0.721822 + 0.692079i \(0.243305\pi\)
\(74\) −25.3279 −2.94431
\(75\) 0.522072 0.0602837
\(76\) 18.7750 2.15364
\(77\) −2.18663 −0.249190
\(78\) −9.06188 −1.02606
\(79\) 15.3503 1.72704 0.863521 0.504313i \(-0.168254\pi\)
0.863521 + 0.504313i \(0.168254\pi\)
\(80\) −34.1217 −3.81492
\(81\) 1.00000 0.111111
\(82\) −6.93446 −0.765783
\(83\) 14.1553 1.55375 0.776873 0.629657i \(-0.216805\pi\)
0.776873 + 0.629657i \(0.216805\pi\)
\(84\) −5.59616 −0.610592
\(85\) −9.45341 −1.02537
\(86\) 2.74898 0.296430
\(87\) −8.29783 −0.889620
\(88\) 21.6727 2.31032
\(89\) 3.19891 0.339084 0.169542 0.985523i \(-0.445771\pi\)
0.169542 + 0.985523i \(0.445771\pi\)
\(90\) 5.83224 0.614773
\(91\) −3.28792 −0.344668
\(92\) −53.4111 −5.56850
\(93\) 8.23902 0.854347
\(94\) 12.8469 1.32505
\(95\) −7.09950 −0.728393
\(96\) 24.6187 2.51263
\(97\) 1.77027 0.179744 0.0898720 0.995953i \(-0.471354\pi\)
0.0898720 + 0.995953i \(0.471354\pi\)
\(98\) −2.75611 −0.278410
\(99\) −2.18663 −0.219765
\(100\) −2.92160 −0.292160
\(101\) −11.6006 −1.15430 −0.577152 0.816637i \(-0.695836\pi\)
−0.577152 + 0.816637i \(0.695836\pi\)
\(102\) 12.3125 1.21912
\(103\) −11.1441 −1.09806 −0.549030 0.835803i \(-0.685003\pi\)
−0.549030 + 0.835803i \(0.685003\pi\)
\(104\) 32.5880 3.19552
\(105\) 2.11611 0.206511
\(106\) 30.2084 2.93410
\(107\) −8.51950 −0.823611 −0.411806 0.911272i \(-0.635102\pi\)
−0.411806 + 0.911272i \(0.635102\pi\)
\(108\) −5.59616 −0.538491
\(109\) 12.1672 1.16541 0.582703 0.812685i \(-0.301995\pi\)
0.582703 + 0.812685i \(0.301995\pi\)
\(110\) −12.7530 −1.21595
\(111\) −9.18971 −0.872249
\(112\) 16.1247 1.52364
\(113\) 1.00573 0.0946110 0.0473055 0.998880i \(-0.484937\pi\)
0.0473055 + 0.998880i \(0.484937\pi\)
\(114\) 9.24669 0.866032
\(115\) 20.1967 1.88335
\(116\) 46.4360 4.31147
\(117\) −3.28792 −0.303968
\(118\) 24.2514 2.23252
\(119\) 4.46735 0.409521
\(120\) −20.9737 −1.91463
\(121\) −6.21863 −0.565330
\(122\) 17.9992 1.62957
\(123\) −2.51603 −0.226863
\(124\) −46.1069 −4.14052
\(125\) 11.6853 1.04517
\(126\) −2.75611 −0.245534
\(127\) −20.2374 −1.79578 −0.897888 0.440224i \(-0.854899\pi\)
−0.897888 + 0.440224i \(0.854899\pi\)
\(128\) −48.8871 −4.32105
\(129\) 0.997412 0.0878172
\(130\) −19.1760 −1.68184
\(131\) 6.57730 0.574661 0.287331 0.957831i \(-0.407232\pi\)
0.287331 + 0.957831i \(0.407232\pi\)
\(132\) 12.2368 1.06507
\(133\) 3.35498 0.290913
\(134\) 35.7055 3.08449
\(135\) 2.11611 0.182126
\(136\) −44.2778 −3.79679
\(137\) −11.5417 −0.986072 −0.493036 0.870009i \(-0.664113\pi\)
−0.493036 + 0.870009i \(0.664113\pi\)
\(138\) −26.3050 −2.23923
\(139\) −4.37972 −0.371483 −0.185741 0.982599i \(-0.559469\pi\)
−0.185741 + 0.982599i \(0.559469\pi\)
\(140\) −11.8421 −1.00084
\(141\) 4.66122 0.392546
\(142\) −8.71681 −0.731498
\(143\) 7.18948 0.601215
\(144\) 16.1247 1.34373
\(145\) −17.5591 −1.45821
\(146\) −33.9953 −2.81347
\(147\) −1.00000 −0.0824786
\(148\) 51.4271 4.22728
\(149\) 21.7290 1.78011 0.890053 0.455857i \(-0.150667\pi\)
0.890053 + 0.455857i \(0.150667\pi\)
\(150\) −1.43889 −0.117485
\(151\) −11.5335 −0.938583 −0.469291 0.883043i \(-0.655491\pi\)
−0.469291 + 0.883043i \(0.655491\pi\)
\(152\) −33.2526 −2.69714
\(153\) 4.46735 0.361164
\(154\) 6.02661 0.485638
\(155\) 17.4347 1.40039
\(156\) 18.3997 1.47316
\(157\) 10.7752 0.859956 0.429978 0.902839i \(-0.358521\pi\)
0.429978 + 0.902839i \(0.358521\pi\)
\(158\) −42.3071 −3.36577
\(159\) 10.9605 0.869224
\(160\) 52.0959 4.11854
\(161\) −9.54424 −0.752192
\(162\) −2.75611 −0.216541
\(163\) −4.59452 −0.359870 −0.179935 0.983678i \(-0.557589\pi\)
−0.179935 + 0.983678i \(0.557589\pi\)
\(164\) 14.0801 1.09947
\(165\) −4.62716 −0.360224
\(166\) −39.0136 −3.02805
\(167\) 16.7510 1.29623 0.648116 0.761541i \(-0.275557\pi\)
0.648116 + 0.761541i \(0.275557\pi\)
\(168\) 9.91144 0.764684
\(169\) −2.18958 −0.168429
\(170\) 26.0547 1.99830
\(171\) 3.35498 0.256561
\(172\) −5.58168 −0.425599
\(173\) −10.6292 −0.808122 −0.404061 0.914732i \(-0.632402\pi\)
−0.404061 + 0.914732i \(0.632402\pi\)
\(174\) 22.8698 1.73375
\(175\) −0.522072 −0.0394650
\(176\) −35.2589 −2.65774
\(177\) 8.79911 0.661382
\(178\) −8.81655 −0.660829
\(179\) −19.0567 −1.42436 −0.712182 0.701995i \(-0.752293\pi\)
−0.712182 + 0.701995i \(0.752293\pi\)
\(180\) −11.8421 −0.882658
\(181\) 13.1844 0.979992 0.489996 0.871725i \(-0.336998\pi\)
0.489996 + 0.871725i \(0.336998\pi\)
\(182\) 9.06188 0.671711
\(183\) 6.53065 0.482760
\(184\) 94.5971 6.97379
\(185\) −19.4464 −1.42973
\(186\) −22.7077 −1.66501
\(187\) −9.76846 −0.714341
\(188\) −26.0850 −1.90244
\(189\) −1.00000 −0.0727393
\(190\) 19.5670 1.41954
\(191\) −1.00000 −0.0723575
\(192\) −35.6025 −2.56939
\(193\) −11.2526 −0.809978 −0.404989 0.914321i \(-0.632725\pi\)
−0.404989 + 0.914321i \(0.632725\pi\)
\(194\) −4.87907 −0.350297
\(195\) −6.95761 −0.498245
\(196\) 5.59616 0.399726
\(197\) 1.88628 0.134392 0.0671960 0.997740i \(-0.478595\pi\)
0.0671960 + 0.997740i \(0.478595\pi\)
\(198\) 6.02661 0.428293
\(199\) −4.43674 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(200\) 5.17449 0.365891
\(201\) 12.9550 0.913777
\(202\) 31.9726 2.24958
\(203\) 8.29783 0.582393
\(204\) −25.0000 −1.75035
\(205\) −5.32420 −0.371858
\(206\) 30.7144 2.13997
\(207\) −9.54424 −0.663371
\(208\) −53.0168 −3.67605
\(209\) −7.33611 −0.507449
\(210\) −5.83224 −0.402463
\(211\) −21.0358 −1.44816 −0.724082 0.689714i \(-0.757736\pi\)
−0.724082 + 0.689714i \(0.757736\pi\)
\(212\) −61.3367 −4.21262
\(213\) −3.16272 −0.216706
\(214\) 23.4807 1.60511
\(215\) 2.11063 0.143944
\(216\) 9.91144 0.674388
\(217\) −8.23902 −0.559301
\(218\) −33.5342 −2.27122
\(219\) −12.3345 −0.833488
\(220\) 25.8944 1.74580
\(221\) −14.6883 −0.988041
\(222\) 25.3279 1.69990
\(223\) 0.748847 0.0501465 0.0250733 0.999686i \(-0.492018\pi\)
0.0250733 + 0.999686i \(0.492018\pi\)
\(224\) −24.6187 −1.64491
\(225\) −0.522072 −0.0348048
\(226\) −2.77190 −0.184384
\(227\) 15.5627 1.03293 0.516467 0.856307i \(-0.327247\pi\)
0.516467 + 0.856307i \(0.327247\pi\)
\(228\) −18.7750 −1.24340
\(229\) 0.522483 0.0345266 0.0172633 0.999851i \(-0.494505\pi\)
0.0172633 + 0.999851i \(0.494505\pi\)
\(230\) −55.6643 −3.67040
\(231\) 2.18663 0.143870
\(232\) −82.2434 −5.39954
\(233\) 10.4341 0.683558 0.341779 0.939780i \(-0.388971\pi\)
0.341779 + 0.939780i \(0.388971\pi\)
\(234\) 9.06188 0.592394
\(235\) 9.86366 0.643434
\(236\) −49.2413 −3.20533
\(237\) −15.3503 −0.997108
\(238\) −12.3125 −0.798102
\(239\) −10.9384 −0.707548 −0.353774 0.935331i \(-0.615102\pi\)
−0.353774 + 0.935331i \(0.615102\pi\)
\(240\) 34.1217 2.20255
\(241\) −23.2504 −1.49769 −0.748844 0.662747i \(-0.769391\pi\)
−0.748844 + 0.662747i \(0.769391\pi\)
\(242\) 17.1392 1.10175
\(243\) −1.00000 −0.0641500
\(244\) −36.5466 −2.33966
\(245\) −2.11611 −0.135193
\(246\) 6.93446 0.442125
\(247\) −11.0309 −0.701879
\(248\) 81.6606 5.18545
\(249\) −14.1553 −0.897056
\(250\) −32.2061 −2.03689
\(251\) −16.0351 −1.01213 −0.506063 0.862496i \(-0.668900\pi\)
−0.506063 + 0.862496i \(0.668900\pi\)
\(252\) 5.59616 0.352525
\(253\) 20.8698 1.31207
\(254\) 55.7765 3.49973
\(255\) 9.45341 0.591995
\(256\) 63.5335 3.97084
\(257\) −13.3950 −0.835559 −0.417779 0.908549i \(-0.637191\pi\)
−0.417779 + 0.908549i \(0.637191\pi\)
\(258\) −2.74898 −0.171144
\(259\) 9.18971 0.571021
\(260\) 38.9359 2.41470
\(261\) 8.29783 0.513623
\(262\) −18.1278 −1.11994
\(263\) 23.0822 1.42331 0.711655 0.702529i \(-0.247946\pi\)
0.711655 + 0.702529i \(0.247946\pi\)
\(264\) −21.6727 −1.33386
\(265\) 23.1936 1.42477
\(266\) −9.24669 −0.566951
\(267\) −3.19891 −0.195770
\(268\) −72.4984 −4.42855
\(269\) 17.1973 1.04854 0.524269 0.851553i \(-0.324339\pi\)
0.524269 + 0.851553i \(0.324339\pi\)
\(270\) −5.83224 −0.354939
\(271\) 16.8486 1.02348 0.511741 0.859140i \(-0.329001\pi\)
0.511741 + 0.859140i \(0.329001\pi\)
\(272\) 72.0348 4.36775
\(273\) 3.28792 0.198994
\(274\) 31.8102 1.92172
\(275\) 1.14158 0.0688399
\(276\) 53.4111 3.21497
\(277\) 21.0004 1.26179 0.630895 0.775868i \(-0.282688\pi\)
0.630895 + 0.775868i \(0.282688\pi\)
\(278\) 12.0710 0.723970
\(279\) −8.23902 −0.493257
\(280\) 20.9737 1.25342
\(281\) 4.70943 0.280941 0.140471 0.990085i \(-0.455138\pi\)
0.140471 + 0.990085i \(0.455138\pi\)
\(282\) −12.8469 −0.765019
\(283\) 2.32384 0.138138 0.0690689 0.997612i \(-0.477997\pi\)
0.0690689 + 0.997612i \(0.477997\pi\)
\(284\) 17.6991 1.05025
\(285\) 7.09950 0.420538
\(286\) −19.8150 −1.17169
\(287\) 2.51603 0.148517
\(288\) −24.6187 −1.45067
\(289\) 2.95721 0.173953
\(290\) 48.3949 2.84185
\(291\) −1.77027 −0.103775
\(292\) 69.0259 4.03943
\(293\) 15.4114 0.900344 0.450172 0.892942i \(-0.351363\pi\)
0.450172 + 0.892942i \(0.351363\pi\)
\(294\) 2.75611 0.160740
\(295\) 18.6199 1.08409
\(296\) −91.0832 −5.29410
\(297\) 2.18663 0.126881
\(298\) −59.8875 −3.46919
\(299\) 31.3807 1.81479
\(300\) 2.92160 0.168679
\(301\) −0.997412 −0.0574899
\(302\) 31.7876 1.82917
\(303\) 11.6006 0.666438
\(304\) 54.0980 3.10274
\(305\) 13.8196 0.791307
\(306\) −12.3125 −0.703860
\(307\) −8.63781 −0.492986 −0.246493 0.969145i \(-0.579278\pi\)
−0.246493 + 0.969145i \(0.579278\pi\)
\(308\) −12.2368 −0.697254
\(309\) 11.1441 0.633965
\(310\) −48.0520 −2.72917
\(311\) 16.3592 0.927645 0.463822 0.885928i \(-0.346478\pi\)
0.463822 + 0.885928i \(0.346478\pi\)
\(312\) −32.5880 −1.84493
\(313\) −13.9498 −0.788490 −0.394245 0.919005i \(-0.628994\pi\)
−0.394245 + 0.919005i \(0.628994\pi\)
\(314\) −29.6977 −1.67594
\(315\) −2.11611 −0.119229
\(316\) 85.9027 4.83240
\(317\) 3.09494 0.173829 0.0869146 0.996216i \(-0.472299\pi\)
0.0869146 + 0.996216i \(0.472299\pi\)
\(318\) −30.2084 −1.69400
\(319\) −18.1443 −1.01589
\(320\) −75.3388 −4.21157
\(321\) 8.51950 0.475512
\(322\) 26.3050 1.46592
\(323\) 14.9878 0.833946
\(324\) 5.59616 0.310898
\(325\) 1.71653 0.0952161
\(326\) 12.6630 0.701339
\(327\) −12.1672 −0.672848
\(328\) −24.9375 −1.37694
\(329\) −4.66122 −0.256981
\(330\) 12.7530 0.702029
\(331\) 21.1056 1.16007 0.580034 0.814592i \(-0.303039\pi\)
0.580034 + 0.814592i \(0.303039\pi\)
\(332\) 79.2154 4.34751
\(333\) 9.18971 0.503593
\(334\) −46.1677 −2.52618
\(335\) 27.4143 1.49780
\(336\) −16.1247 −0.879676
\(337\) −11.4890 −0.625848 −0.312924 0.949778i \(-0.601309\pi\)
−0.312924 + 0.949778i \(0.601309\pi\)
\(338\) 6.03473 0.328246
\(339\) −1.00573 −0.0546237
\(340\) −52.9028 −2.86906
\(341\) 18.0157 0.975607
\(342\) −9.24669 −0.500004
\(343\) 1.00000 0.0539949
\(344\) 9.88578 0.533006
\(345\) −20.1967 −1.08735
\(346\) 29.2952 1.57492
\(347\) 12.4995 0.671009 0.335505 0.942039i \(-0.391093\pi\)
0.335505 + 0.942039i \(0.391093\pi\)
\(348\) −46.4360 −2.48923
\(349\) 20.6103 1.10325 0.551623 0.834093i \(-0.314009\pi\)
0.551623 + 0.834093i \(0.314009\pi\)
\(350\) 1.43889 0.0769119
\(351\) 3.28792 0.175496
\(352\) 53.8321 2.86926
\(353\) −27.9988 −1.49023 −0.745114 0.666937i \(-0.767605\pi\)
−0.745114 + 0.666937i \(0.767605\pi\)
\(354\) −24.2514 −1.28894
\(355\) −6.69266 −0.355210
\(356\) 17.9016 0.948784
\(357\) −4.46735 −0.236437
\(358\) 52.5224 2.77589
\(359\) 15.2709 0.805969 0.402984 0.915207i \(-0.367973\pi\)
0.402984 + 0.915207i \(0.367973\pi\)
\(360\) 20.9737 1.10541
\(361\) −7.74414 −0.407586
\(362\) −36.3378 −1.90987
\(363\) 6.21863 0.326393
\(364\) −18.3997 −0.964408
\(365\) −26.1012 −1.36620
\(366\) −17.9992 −0.940834
\(367\) 6.35567 0.331763 0.165882 0.986146i \(-0.446953\pi\)
0.165882 + 0.986146i \(0.446953\pi\)
\(368\) −153.898 −8.02250
\(369\) 2.51603 0.130979
\(370\) 53.5966 2.78636
\(371\) −10.9605 −0.569040
\(372\) 46.1069 2.39053
\(373\) −9.44285 −0.488932 −0.244466 0.969658i \(-0.578613\pi\)
−0.244466 + 0.969658i \(0.578613\pi\)
\(374\) 26.9230 1.39215
\(375\) −11.6853 −0.603427
\(376\) 46.1994 2.38255
\(377\) −27.2826 −1.40512
\(378\) 2.75611 0.141759
\(379\) 24.2886 1.24762 0.623810 0.781576i \(-0.285584\pi\)
0.623810 + 0.781576i \(0.285584\pi\)
\(380\) −39.7300 −2.03810
\(381\) 20.2374 1.03679
\(382\) 2.75611 0.141015
\(383\) 28.9024 1.47684 0.738422 0.674338i \(-0.235571\pi\)
0.738422 + 0.674338i \(0.235571\pi\)
\(384\) 48.8871 2.49476
\(385\) 4.62716 0.235822
\(386\) 31.0134 1.57854
\(387\) −0.997412 −0.0507013
\(388\) 9.90674 0.502938
\(389\) 27.3709 1.38776 0.693880 0.720091i \(-0.255900\pi\)
0.693880 + 0.720091i \(0.255900\pi\)
\(390\) 19.1760 0.971012
\(391\) −42.6375 −2.15627
\(392\) −9.91144 −0.500603
\(393\) −6.57730 −0.331781
\(394\) −5.19881 −0.261912
\(395\) −32.4829 −1.63439
\(396\) −12.2368 −0.614921
\(397\) −28.2806 −1.41936 −0.709681 0.704523i \(-0.751161\pi\)
−0.709681 + 0.704523i \(0.751161\pi\)
\(398\) 12.2282 0.612943
\(399\) −3.35498 −0.167959
\(400\) −8.41827 −0.420914
\(401\) −6.18517 −0.308873 −0.154436 0.988003i \(-0.549356\pi\)
−0.154436 + 0.988003i \(0.549356\pi\)
\(402\) −35.7055 −1.78083
\(403\) 27.0893 1.34941
\(404\) −64.9189 −3.22984
\(405\) −2.11611 −0.105150
\(406\) −22.8698 −1.13501
\(407\) −20.0945 −0.996049
\(408\) 44.2778 2.19208
\(409\) 36.8706 1.82313 0.911567 0.411151i \(-0.134873\pi\)
0.911567 + 0.411151i \(0.134873\pi\)
\(410\) 14.6741 0.724702
\(411\) 11.5417 0.569309
\(412\) −62.3642 −3.07246
\(413\) −8.79911 −0.432976
\(414\) 26.3050 1.29282
\(415\) −29.9542 −1.47039
\(416\) 80.9443 3.96862
\(417\) 4.37972 0.214476
\(418\) 20.2191 0.988951
\(419\) −4.46489 −0.218124 −0.109062 0.994035i \(-0.534785\pi\)
−0.109062 + 0.994035i \(0.534785\pi\)
\(420\) 11.8421 0.577836
\(421\) 14.6840 0.715653 0.357826 0.933788i \(-0.383518\pi\)
0.357826 + 0.933788i \(0.383518\pi\)
\(422\) 57.9771 2.82228
\(423\) −4.66122 −0.226636
\(424\) 108.634 5.27574
\(425\) −2.33228 −0.113132
\(426\) 8.71681 0.422331
\(427\) −6.53065 −0.316040
\(428\) −47.6765 −2.30453
\(429\) −7.18948 −0.347111
\(430\) −5.81715 −0.280528
\(431\) 6.71719 0.323556 0.161778 0.986827i \(-0.448277\pi\)
0.161778 + 0.986827i \(0.448277\pi\)
\(432\) −16.1247 −0.775801
\(433\) 29.0923 1.39809 0.699043 0.715080i \(-0.253610\pi\)
0.699043 + 0.715080i \(0.253610\pi\)
\(434\) 22.7077 1.09000
\(435\) 17.5591 0.841896
\(436\) 68.0896 3.26090
\(437\) −32.0207 −1.53176
\(438\) 33.9953 1.62436
\(439\) 22.6122 1.07922 0.539610 0.841915i \(-0.318572\pi\)
0.539610 + 0.841915i \(0.318572\pi\)
\(440\) −45.8618 −2.18638
\(441\) 1.00000 0.0476190
\(442\) 40.4826 1.92556
\(443\) 20.4059 0.969513 0.484756 0.874649i \(-0.338908\pi\)
0.484756 + 0.874649i \(0.338908\pi\)
\(444\) −51.4271 −2.44062
\(445\) −6.76925 −0.320893
\(446\) −2.06391 −0.0977289
\(447\) −21.7290 −1.02774
\(448\) 35.6025 1.68206
\(449\) 27.1454 1.28107 0.640536 0.767928i \(-0.278712\pi\)
0.640536 + 0.767928i \(0.278712\pi\)
\(450\) 1.43889 0.0678300
\(451\) −5.50164 −0.259062
\(452\) 5.62822 0.264729
\(453\) 11.5335 0.541891
\(454\) −42.8927 −2.01305
\(455\) 6.95761 0.326178
\(456\) 33.2526 1.55720
\(457\) −14.8386 −0.694120 −0.347060 0.937843i \(-0.612820\pi\)
−0.347060 + 0.937843i \(0.612820\pi\)
\(458\) −1.44002 −0.0672878
\(459\) −4.46735 −0.208518
\(460\) 113.024 5.26977
\(461\) 27.6469 1.28765 0.643823 0.765175i \(-0.277347\pi\)
0.643823 + 0.765175i \(0.277347\pi\)
\(462\) −6.02661 −0.280383
\(463\) 22.4006 1.04105 0.520523 0.853848i \(-0.325737\pi\)
0.520523 + 0.853848i \(0.325737\pi\)
\(464\) 133.800 6.21152
\(465\) −17.4347 −0.808514
\(466\) −28.7574 −1.33216
\(467\) −30.0050 −1.38846 −0.694232 0.719751i \(-0.744256\pi\)
−0.694232 + 0.719751i \(0.744256\pi\)
\(468\) −18.3997 −0.850528
\(469\) −12.9550 −0.598207
\(470\) −27.1854 −1.25397
\(471\) −10.7752 −0.496496
\(472\) 87.2118 4.01425
\(473\) 2.18097 0.100281
\(474\) 42.3071 1.94323
\(475\) −1.75154 −0.0803662
\(476\) 25.0000 1.14587
\(477\) −10.9605 −0.501846
\(478\) 30.1476 1.37892
\(479\) 27.7495 1.26791 0.633954 0.773370i \(-0.281431\pi\)
0.633954 + 0.773370i \(0.281431\pi\)
\(480\) −52.0959 −2.37784
\(481\) −30.2150 −1.37769
\(482\) 64.0806 2.91879
\(483\) 9.54424 0.434278
\(484\) −34.8005 −1.58184
\(485\) −3.74609 −0.170101
\(486\) 2.75611 0.125020
\(487\) 22.7088 1.02903 0.514517 0.857480i \(-0.327971\pi\)
0.514517 + 0.857480i \(0.327971\pi\)
\(488\) 64.7281 2.93010
\(489\) 4.59452 0.207771
\(490\) 5.83224 0.263474
\(491\) 21.1753 0.955629 0.477815 0.878461i \(-0.341429\pi\)
0.477815 + 0.878461i \(0.341429\pi\)
\(492\) −14.0801 −0.634780
\(493\) 37.0693 1.66952
\(494\) 30.4024 1.36787
\(495\) 4.62716 0.207975
\(496\) −132.852 −5.96523
\(497\) 3.16272 0.141867
\(498\) 39.0136 1.74824
\(499\) 22.9663 1.02811 0.514057 0.857756i \(-0.328142\pi\)
0.514057 + 0.857756i \(0.328142\pi\)
\(500\) 65.3930 2.92446
\(501\) −16.7510 −0.748380
\(502\) 44.1946 1.97250
\(503\) 28.2489 1.25956 0.629779 0.776774i \(-0.283145\pi\)
0.629779 + 0.776774i \(0.283145\pi\)
\(504\) −9.91144 −0.441490
\(505\) 24.5482 1.09238
\(506\) −57.5195 −2.55705
\(507\) 2.18958 0.0972427
\(508\) −113.252 −5.02473
\(509\) 13.8796 0.615204 0.307602 0.951515i \(-0.400474\pi\)
0.307602 + 0.951515i \(0.400474\pi\)
\(510\) −26.0547 −1.15372
\(511\) 12.3345 0.545646
\(512\) −77.3312 −3.41759
\(513\) −3.35498 −0.148126
\(514\) 36.9182 1.62839
\(515\) 23.5821 1.03915
\(516\) 5.58168 0.245720
\(517\) 10.1924 0.448261
\(518\) −25.3279 −1.11284
\(519\) 10.6292 0.466569
\(520\) −68.9599 −3.02409
\(521\) 8.69891 0.381106 0.190553 0.981677i \(-0.438972\pi\)
0.190553 + 0.981677i \(0.438972\pi\)
\(522\) −22.8698 −1.00098
\(523\) 4.21749 0.184418 0.0922090 0.995740i \(-0.470607\pi\)
0.0922090 + 0.995740i \(0.470607\pi\)
\(524\) 36.8076 1.60795
\(525\) 0.522072 0.0227851
\(526\) −63.6172 −2.77384
\(527\) −36.8066 −1.60332
\(528\) 35.2589 1.53445
\(529\) 68.0925 2.96054
\(530\) −63.9243 −2.77669
\(531\) −8.79911 −0.381849
\(532\) 18.7750 0.813999
\(533\) −8.27250 −0.358322
\(534\) 8.81655 0.381530
\(535\) 18.0282 0.779428
\(536\) 128.403 5.54616
\(537\) 19.0567 0.822356
\(538\) −47.3977 −2.04346
\(539\) −2.18663 −0.0941850
\(540\) 11.8421 0.509603
\(541\) −37.6038 −1.61671 −0.808356 0.588694i \(-0.799642\pi\)
−0.808356 + 0.588694i \(0.799642\pi\)
\(542\) −46.4368 −1.99463
\(543\) −13.1844 −0.565799
\(544\) −109.980 −4.71537
\(545\) −25.7471 −1.10289
\(546\) −9.06188 −0.387813
\(547\) 27.0576 1.15690 0.578449 0.815719i \(-0.303658\pi\)
0.578449 + 0.815719i \(0.303658\pi\)
\(548\) −64.5891 −2.75911
\(549\) −6.53065 −0.278721
\(550\) −3.14633 −0.134160
\(551\) 27.8390 1.18598
\(552\) −94.5971 −4.02632
\(553\) 15.3503 0.652761
\(554\) −57.8794 −2.45906
\(555\) 19.4464 0.825456
\(556\) −24.5096 −1.03944
\(557\) −7.29845 −0.309245 −0.154623 0.987974i \(-0.549416\pi\)
−0.154623 + 0.987974i \(0.549416\pi\)
\(558\) 22.7077 0.961293
\(559\) 3.27941 0.138704
\(560\) −34.1217 −1.44191
\(561\) 9.76846 0.412425
\(562\) −12.9797 −0.547517
\(563\) 4.33188 0.182567 0.0912836 0.995825i \(-0.470903\pi\)
0.0912836 + 0.995825i \(0.470903\pi\)
\(564\) 26.0850 1.09837
\(565\) −2.12823 −0.0895355
\(566\) −6.40476 −0.269212
\(567\) 1.00000 0.0419961
\(568\) −31.3471 −1.31529
\(569\) −31.9664 −1.34010 −0.670052 0.742315i \(-0.733728\pi\)
−0.670052 + 0.742315i \(0.733728\pi\)
\(570\) −19.5670 −0.819573
\(571\) 4.09939 0.171554 0.0857772 0.996314i \(-0.472663\pi\)
0.0857772 + 0.996314i \(0.472663\pi\)
\(572\) 40.2335 1.68225
\(573\) 1.00000 0.0417756
\(574\) −6.93446 −0.289439
\(575\) 4.98278 0.207796
\(576\) 35.6025 1.48344
\(577\) −16.9228 −0.704506 −0.352253 0.935905i \(-0.614584\pi\)
−0.352253 + 0.935905i \(0.614584\pi\)
\(578\) −8.15040 −0.339012
\(579\) 11.2526 0.467641
\(580\) −98.2637 −4.08018
\(581\) 14.1553 0.587261
\(582\) 4.87907 0.202244
\(583\) 23.9666 0.992595
\(584\) −122.253 −5.05885
\(585\) 6.95761 0.287662
\(586\) −42.4756 −1.75465
\(587\) 33.9789 1.40246 0.701230 0.712936i \(-0.252635\pi\)
0.701230 + 0.712936i \(0.252635\pi\)
\(588\) −5.59616 −0.230782
\(589\) −27.6417 −1.13896
\(590\) −51.3186 −2.11275
\(591\) −1.88628 −0.0775913
\(592\) 148.181 6.09022
\(593\) −16.3383 −0.670934 −0.335467 0.942052i \(-0.608894\pi\)
−0.335467 + 0.942052i \(0.608894\pi\)
\(594\) −6.02661 −0.247275
\(595\) −9.45341 −0.387552
\(596\) 121.599 4.98088
\(597\) 4.43674 0.181584
\(598\) −86.4888 −3.53679
\(599\) −23.1694 −0.946676 −0.473338 0.880881i \(-0.656951\pi\)
−0.473338 + 0.880881i \(0.656951\pi\)
\(600\) −5.17449 −0.211248
\(601\) 19.7009 0.803616 0.401808 0.915724i \(-0.368382\pi\)
0.401808 + 0.915724i \(0.368382\pi\)
\(602\) 2.74898 0.112040
\(603\) −12.9550 −0.527569
\(604\) −64.5433 −2.62623
\(605\) 13.1593 0.535002
\(606\) −31.9726 −1.29880
\(607\) −0.246448 −0.0100030 −0.00500151 0.999987i \(-0.501592\pi\)
−0.00500151 + 0.999987i \(0.501592\pi\)
\(608\) −82.5951 −3.34967
\(609\) −8.29783 −0.336245
\(610\) −38.0884 −1.54215
\(611\) 15.3257 0.620012
\(612\) 25.0000 1.01057
\(613\) −0.975068 −0.0393826 −0.0196913 0.999806i \(-0.506268\pi\)
−0.0196913 + 0.999806i \(0.506268\pi\)
\(614\) 23.8068 0.960763
\(615\) 5.32420 0.214692
\(616\) 21.6727 0.873218
\(617\) 4.85140 0.195310 0.0976551 0.995220i \(-0.468866\pi\)
0.0976551 + 0.995220i \(0.468866\pi\)
\(618\) −30.7144 −1.23551
\(619\) 31.0996 1.25000 0.624999 0.780625i \(-0.285099\pi\)
0.624999 + 0.780625i \(0.285099\pi\)
\(620\) 97.5674 3.91840
\(621\) 9.54424 0.382997
\(622\) −45.0878 −1.80786
\(623\) 3.19891 0.128162
\(624\) 53.0168 2.12237
\(625\) −22.1171 −0.884683
\(626\) 38.4473 1.53666
\(627\) 7.33611 0.292976
\(628\) 60.2999 2.40623
\(629\) 41.0536 1.63692
\(630\) 5.83224 0.232362
\(631\) 11.8055 0.469970 0.234985 0.971999i \(-0.424496\pi\)
0.234985 + 0.971999i \(0.424496\pi\)
\(632\) −152.143 −6.05194
\(633\) 21.0358 0.836098
\(634\) −8.53001 −0.338770
\(635\) 42.8245 1.69944
\(636\) 61.3367 2.43216
\(637\) −3.28792 −0.130272
\(638\) 50.0078 1.97983
\(639\) 3.16272 0.125115
\(640\) 103.451 4.08924
\(641\) −28.5668 −1.12832 −0.564160 0.825665i \(-0.690800\pi\)
−0.564160 + 0.825665i \(0.690800\pi\)
\(642\) −23.4807 −0.926710
\(643\) −41.9476 −1.65425 −0.827125 0.562018i \(-0.810025\pi\)
−0.827125 + 0.562018i \(0.810025\pi\)
\(644\) −53.4111 −2.10469
\(645\) −2.11063 −0.0831061
\(646\) −41.3082 −1.62525
\(647\) 6.49160 0.255211 0.127606 0.991825i \(-0.459271\pi\)
0.127606 + 0.991825i \(0.459271\pi\)
\(648\) −9.91144 −0.389358
\(649\) 19.2404 0.755253
\(650\) −4.73096 −0.185563
\(651\) 8.23902 0.322913
\(652\) −25.7117 −1.00695
\(653\) 43.1943 1.69032 0.845162 0.534510i \(-0.179504\pi\)
0.845162 + 0.534510i \(0.179504\pi\)
\(654\) 33.5342 1.31129
\(655\) −13.9183 −0.543833
\(656\) 40.5703 1.58400
\(657\) 12.3345 0.481215
\(658\) 12.8469 0.500823
\(659\) 3.79415 0.147799 0.0738996 0.997266i \(-0.476456\pi\)
0.0738996 + 0.997266i \(0.476456\pi\)
\(660\) −25.8944 −1.00794
\(661\) 18.8678 0.733873 0.366937 0.930246i \(-0.380407\pi\)
0.366937 + 0.930246i \(0.380407\pi\)
\(662\) −58.1694 −2.26082
\(663\) 14.6883 0.570446
\(664\) −140.299 −5.44467
\(665\) −7.09950 −0.275307
\(666\) −25.3279 −0.981436
\(667\) −79.1965 −3.06650
\(668\) 93.7414 3.62696
\(669\) −0.748847 −0.0289521
\(670\) −75.5569 −2.91902
\(671\) 14.2801 0.551279
\(672\) 24.6187 0.949687
\(673\) −19.9481 −0.768942 −0.384471 0.923137i \(-0.625616\pi\)
−0.384471 + 0.923137i \(0.625616\pi\)
\(674\) 31.6651 1.21969
\(675\) 0.522072 0.0200946
\(676\) −12.2532 −0.471279
\(677\) 23.5173 0.903842 0.451921 0.892058i \(-0.350739\pi\)
0.451921 + 0.892058i \(0.350739\pi\)
\(678\) 2.77190 0.106454
\(679\) 1.77027 0.0679368
\(680\) 93.6969 3.59311
\(681\) −15.5627 −0.596365
\(682\) −49.6534 −1.90133
\(683\) 2.22738 0.0852284 0.0426142 0.999092i \(-0.486431\pi\)
0.0426142 + 0.999092i \(0.486431\pi\)
\(684\) 18.7750 0.717880
\(685\) 24.4235 0.933173
\(686\) −2.75611 −0.105229
\(687\) −0.522483 −0.0199340
\(688\) −16.0830 −0.613158
\(689\) 36.0372 1.37291
\(690\) 55.6643 2.11911
\(691\) 36.2540 1.37917 0.689584 0.724206i \(-0.257793\pi\)
0.689584 + 0.724206i \(0.257793\pi\)
\(692\) −59.4827 −2.26119
\(693\) −2.18663 −0.0830634
\(694\) −34.4501 −1.30771
\(695\) 9.26797 0.351554
\(696\) 82.2434 3.11743
\(697\) 11.2400 0.425745
\(698\) −56.8044 −2.15008
\(699\) −10.4341 −0.394652
\(700\) −2.92160 −0.110426
\(701\) −25.6133 −0.967401 −0.483700 0.875234i \(-0.660708\pi\)
−0.483700 + 0.875234i \(0.660708\pi\)
\(702\) −9.06188 −0.342019
\(703\) 30.8312 1.16282
\(704\) −77.8496 −2.93407
\(705\) −9.86366 −0.371487
\(706\) 77.1680 2.90426
\(707\) −11.6006 −0.436286
\(708\) 49.2413 1.85060
\(709\) 29.3825 1.10348 0.551741 0.834015i \(-0.313964\pi\)
0.551741 + 0.834015i \(0.313964\pi\)
\(710\) 18.4457 0.692256
\(711\) 15.3503 0.575681
\(712\) −31.7058 −1.18822
\(713\) 78.6352 2.94491
\(714\) 12.3125 0.460785
\(715\) −15.2137 −0.568962
\(716\) −106.644 −3.98548
\(717\) 10.9384 0.408503
\(718\) −42.0884 −1.57073
\(719\) −31.9567 −1.19179 −0.595893 0.803064i \(-0.703202\pi\)
−0.595893 + 0.803064i \(0.703202\pi\)
\(720\) −34.1217 −1.27164
\(721\) −11.1441 −0.415028
\(722\) 21.3437 0.794332
\(723\) 23.2504 0.864690
\(724\) 73.7823 2.74210
\(725\) −4.33207 −0.160889
\(726\) −17.1392 −0.636097
\(727\) −10.1572 −0.376708 −0.188354 0.982101i \(-0.560315\pi\)
−0.188354 + 0.982101i \(0.560315\pi\)
\(728\) 32.5880 1.20779
\(729\) 1.00000 0.0370370
\(730\) 71.9378 2.66254
\(731\) −4.45579 −0.164803
\(732\) 36.5466 1.35080
\(733\) 10.9492 0.404419 0.202210 0.979342i \(-0.435188\pi\)
0.202210 + 0.979342i \(0.435188\pi\)
\(734\) −17.5169 −0.646562
\(735\) 2.11611 0.0780539
\(736\) 234.967 8.66099
\(737\) 28.3279 1.04347
\(738\) −6.93446 −0.255261
\(739\) −31.9795 −1.17638 −0.588192 0.808721i \(-0.700160\pi\)
−0.588192 + 0.808721i \(0.700160\pi\)
\(740\) −108.826 −4.00051
\(741\) 11.0309 0.405230
\(742\) 30.2084 1.10898
\(743\) −38.1901 −1.40106 −0.700530 0.713623i \(-0.747053\pi\)
−0.700530 + 0.713623i \(0.747053\pi\)
\(744\) −81.6606 −2.99382
\(745\) −45.9809 −1.68461
\(746\) 26.0256 0.952863
\(747\) 14.1553 0.517916
\(748\) −54.6659 −1.99878
\(749\) −8.51950 −0.311296
\(750\) 32.2061 1.17600
\(751\) −2.92633 −0.106783 −0.0533916 0.998574i \(-0.517003\pi\)
−0.0533916 + 0.998574i \(0.517003\pi\)
\(752\) −75.1609 −2.74084
\(753\) 16.0351 0.584351
\(754\) 75.1939 2.73840
\(755\) 24.4062 0.888231
\(756\) −5.59616 −0.203531
\(757\) 18.6454 0.677678 0.338839 0.940844i \(-0.389966\pi\)
0.338839 + 0.940844i \(0.389966\pi\)
\(758\) −66.9420 −2.43144
\(759\) −20.8698 −0.757525
\(760\) 70.3663 2.55245
\(761\) 18.0874 0.655669 0.327835 0.944735i \(-0.393681\pi\)
0.327835 + 0.944735i \(0.393681\pi\)
\(762\) −55.7765 −2.02057
\(763\) 12.1672 0.440482
\(764\) −5.59616 −0.202462
\(765\) −9.45341 −0.341789
\(766\) −79.6584 −2.87817
\(767\) 28.9308 1.04463
\(768\) −63.5335 −2.29257
\(769\) −28.1402 −1.01476 −0.507381 0.861722i \(-0.669386\pi\)
−0.507381 + 0.861722i \(0.669386\pi\)
\(770\) −12.7530 −0.459586
\(771\) 13.3950 0.482410
\(772\) −62.9713 −2.26639
\(773\) −23.5799 −0.848109 −0.424055 0.905637i \(-0.639394\pi\)
−0.424055 + 0.905637i \(0.639394\pi\)
\(774\) 2.74898 0.0988100
\(775\) 4.30137 0.154510
\(776\) −17.5459 −0.629863
\(777\) −9.18971 −0.329679
\(778\) −75.4373 −2.70456
\(779\) 8.44122 0.302438
\(780\) −38.9359 −1.39413
\(781\) −6.91570 −0.247463
\(782\) 117.514 4.20228
\(783\) −8.29783 −0.296540
\(784\) 16.1247 0.575883
\(785\) −22.8016 −0.813823
\(786\) 18.1278 0.646596
\(787\) 25.1308 0.895818 0.447909 0.894079i \(-0.352169\pi\)
0.447909 + 0.894079i \(0.352169\pi\)
\(788\) 10.5559 0.376040
\(789\) −23.0822 −0.821749
\(790\) 89.5266 3.18521
\(791\) 1.00573 0.0357596
\(792\) 21.6727 0.770106
\(793\) 21.4723 0.762502
\(794\) 77.9445 2.76615
\(795\) −23.1936 −0.822593
\(796\) −24.8287 −0.880032
\(797\) 50.6636 1.79460 0.897299 0.441423i \(-0.145526\pi\)
0.897299 + 0.441423i \(0.145526\pi\)
\(798\) 9.24669 0.327329
\(799\) −20.8233 −0.736675
\(800\) 12.8527 0.454413
\(801\) 3.19891 0.113028
\(802\) 17.0470 0.601952
\(803\) −26.9710 −0.951787
\(804\) 72.4984 2.55682
\(805\) 20.1967 0.711839
\(806\) −74.6611 −2.62982
\(807\) −17.1973 −0.605374
\(808\) 114.979 4.04494
\(809\) −31.8629 −1.12024 −0.560120 0.828411i \(-0.689245\pi\)
−0.560120 + 0.828411i \(0.689245\pi\)
\(810\) 5.83224 0.204924
\(811\) 22.1827 0.778940 0.389470 0.921039i \(-0.372658\pi\)
0.389470 + 0.921039i \(0.372658\pi\)
\(812\) 46.4360 1.62958
\(813\) −16.8486 −0.590908
\(814\) 55.3828 1.94117
\(815\) 9.72251 0.340565
\(816\) −72.0348 −2.52172
\(817\) −3.34629 −0.117072
\(818\) −101.620 −3.55305
\(819\) −3.28792 −0.114889
\(820\) −29.7951 −1.04049
\(821\) 3.32613 0.116083 0.0580414 0.998314i \(-0.481514\pi\)
0.0580414 + 0.998314i \(0.481514\pi\)
\(822\) −31.8102 −1.10951
\(823\) −45.2666 −1.57789 −0.788947 0.614461i \(-0.789373\pi\)
−0.788947 + 0.614461i \(0.789373\pi\)
\(824\) 110.454 3.84785
\(825\) −1.14158 −0.0397448
\(826\) 24.2514 0.843813
\(827\) 12.6262 0.439056 0.219528 0.975606i \(-0.429548\pi\)
0.219528 + 0.975606i \(0.429548\pi\)
\(828\) −53.4111 −1.85617
\(829\) −18.4456 −0.640642 −0.320321 0.947309i \(-0.603791\pi\)
−0.320321 + 0.947309i \(0.603791\pi\)
\(830\) 82.5572 2.86560
\(831\) −21.0004 −0.728495
\(832\) −117.058 −4.05826
\(833\) 4.46735 0.154784
\(834\) −12.0710 −0.417984
\(835\) −35.4470 −1.22669
\(836\) −41.0540 −1.41988
\(837\) 8.23902 0.284782
\(838\) 12.3057 0.425095
\(839\) 32.2901 1.11478 0.557389 0.830251i \(-0.311803\pi\)
0.557389 + 0.830251i \(0.311803\pi\)
\(840\) −20.9737 −0.723662
\(841\) 39.8539 1.37427
\(842\) −40.4707 −1.39471
\(843\) −4.70943 −0.162201
\(844\) −117.720 −4.05208
\(845\) 4.63340 0.159394
\(846\) 12.8469 0.441684
\(847\) −6.21863 −0.213675
\(848\) −176.735 −6.06910
\(849\) −2.32384 −0.0797538
\(850\) 6.42803 0.220480
\(851\) −87.7088 −3.00662
\(852\) −17.6991 −0.606360
\(853\) 40.5710 1.38912 0.694562 0.719433i \(-0.255598\pi\)
0.694562 + 0.719433i \(0.255598\pi\)
\(854\) 17.9992 0.615921
\(855\) −7.09950 −0.242798
\(856\) 84.4405 2.88612
\(857\) −10.9171 −0.372923 −0.186461 0.982462i \(-0.559702\pi\)
−0.186461 + 0.982462i \(0.559702\pi\)
\(858\) 19.8150 0.676474
\(859\) 29.2631 0.998443 0.499221 0.866475i \(-0.333619\pi\)
0.499221 + 0.866475i \(0.333619\pi\)
\(860\) 11.8115 0.402767
\(861\) −2.51603 −0.0857461
\(862\) −18.5134 −0.630567
\(863\) −9.14629 −0.311343 −0.155672 0.987809i \(-0.549754\pi\)
−0.155672 + 0.987809i \(0.549754\pi\)
\(864\) 24.6187 0.837545
\(865\) 22.4925 0.764769
\(866\) −80.1816 −2.72468
\(867\) −2.95721 −0.100432
\(868\) −46.1069 −1.56497
\(869\) −33.5655 −1.13863
\(870\) −48.3949 −1.64074
\(871\) 42.5951 1.44328
\(872\) −120.594 −4.08384
\(873\) 1.77027 0.0599147
\(874\) 88.2527 2.98519
\(875\) 11.6853 0.395036
\(876\) −69.0259 −2.33217
\(877\) 27.4597 0.927247 0.463624 0.886032i \(-0.346549\pi\)
0.463624 + 0.886032i \(0.346549\pi\)
\(878\) −62.3217 −2.10326
\(879\) −15.4114 −0.519814
\(880\) 74.6117 2.51516
\(881\) −8.62776 −0.290677 −0.145338 0.989382i \(-0.546427\pi\)
−0.145338 + 0.989382i \(0.546427\pi\)
\(882\) −2.75611 −0.0928032
\(883\) −30.6920 −1.03287 −0.516434 0.856327i \(-0.672741\pi\)
−0.516434 + 0.856327i \(0.672741\pi\)
\(884\) −82.1981 −2.76462
\(885\) −18.6199 −0.625901
\(886\) −56.2409 −1.88945
\(887\) 12.4362 0.417566 0.208783 0.977962i \(-0.433050\pi\)
0.208783 + 0.977962i \(0.433050\pi\)
\(888\) 91.0832 3.05655
\(889\) −20.2374 −0.678739
\(890\) 18.6568 0.625378
\(891\) −2.18663 −0.0732550
\(892\) 4.19067 0.140314
\(893\) −15.6383 −0.523315
\(894\) 59.8875 2.00294
\(895\) 40.3261 1.34795
\(896\) −48.8871 −1.63320
\(897\) −31.3807 −1.04777
\(898\) −74.8159 −2.49664
\(899\) −68.3660 −2.28013
\(900\) −2.92160 −0.0973867
\(901\) −48.9643 −1.63124
\(902\) 15.1631 0.504877
\(903\) 0.997412 0.0331918
\(904\) −9.96822 −0.331538
\(905\) −27.8998 −0.927419
\(906\) −31.7876 −1.05607
\(907\) −30.8690 −1.02499 −0.512494 0.858691i \(-0.671278\pi\)
−0.512494 + 0.858691i \(0.671278\pi\)
\(908\) 87.0916 2.89024
\(909\) −11.6006 −0.384768
\(910\) −19.1760 −0.635677
\(911\) −4.15241 −0.137575 −0.0687877 0.997631i \(-0.521913\pi\)
−0.0687877 + 0.997631i \(0.521913\pi\)
\(912\) −54.0980 −1.79137
\(913\) −30.9525 −1.02438
\(914\) 40.8969 1.35275
\(915\) −13.8196 −0.456861
\(916\) 2.92390 0.0966084
\(917\) 6.57730 0.217201
\(918\) 12.3125 0.406374
\(919\) −48.2362 −1.59116 −0.795582 0.605846i \(-0.792835\pi\)
−0.795582 + 0.605846i \(0.792835\pi\)
\(920\) −200.178 −6.59968
\(921\) 8.63781 0.284625
\(922\) −76.1981 −2.50945
\(923\) −10.3988 −0.342279
\(924\) 12.2368 0.402560
\(925\) −4.79769 −0.157747
\(926\) −61.7387 −2.02886
\(927\) −11.1441 −0.366020
\(928\) −204.282 −6.70587
\(929\) −36.6577 −1.20270 −0.601350 0.798986i \(-0.705370\pi\)
−0.601350 + 0.798986i \(0.705370\pi\)
\(930\) 48.0520 1.57569
\(931\) 3.35498 0.109955
\(932\) 58.3907 1.91265
\(933\) −16.3592 −0.535576
\(934\) 82.6971 2.70593
\(935\) 20.6712 0.676019
\(936\) 32.5880 1.06517
\(937\) 16.6817 0.544967 0.272483 0.962160i \(-0.412155\pi\)
0.272483 + 0.962160i \(0.412155\pi\)
\(938\) 35.7055 1.16583
\(939\) 13.9498 0.455235
\(940\) 55.1987 1.80038
\(941\) 32.4898 1.05914 0.529569 0.848267i \(-0.322354\pi\)
0.529569 + 0.848267i \(0.322354\pi\)
\(942\) 29.6977 0.967604
\(943\) −24.0136 −0.781990
\(944\) −141.883 −4.61791
\(945\) 2.11611 0.0688371
\(946\) −6.01102 −0.195435
\(947\) −14.4960 −0.471056 −0.235528 0.971868i \(-0.575682\pi\)
−0.235528 + 0.971868i \(0.575682\pi\)
\(948\) −85.9027 −2.78999
\(949\) −40.5548 −1.31647
\(950\) 4.82744 0.156623
\(951\) −3.09494 −0.100360
\(952\) −44.2778 −1.43505
\(953\) 8.71306 0.282244 0.141122 0.989992i \(-0.454929\pi\)
0.141122 + 0.989992i \(0.454929\pi\)
\(954\) 30.2084 0.978032
\(955\) 2.11611 0.0684758
\(956\) −61.2133 −1.97978
\(957\) 18.1443 0.586522
\(958\) −76.4809 −2.47099
\(959\) −11.5417 −0.372700
\(960\) 75.3388 2.43155
\(961\) 36.8815 1.18973
\(962\) 83.2761 2.68493
\(963\) −8.51950 −0.274537
\(964\) −130.113 −4.19065
\(965\) 23.8117 0.766526
\(966\) −26.3050 −0.846350
\(967\) 40.9388 1.31650 0.658252 0.752798i \(-0.271296\pi\)
0.658252 + 0.752798i \(0.271296\pi\)
\(968\) 61.6355 1.98104
\(969\) −14.9878 −0.481479
\(970\) 10.3247 0.331505
\(971\) −17.1882 −0.551595 −0.275798 0.961216i \(-0.588942\pi\)
−0.275798 + 0.961216i \(0.588942\pi\)
\(972\) −5.59616 −0.179497
\(973\) −4.37972 −0.140407
\(974\) −62.5880 −2.00545
\(975\) −1.71653 −0.0549730
\(976\) −105.305 −3.37073
\(977\) 45.0128 1.44009 0.720043 0.693929i \(-0.244122\pi\)
0.720043 + 0.693929i \(0.244122\pi\)
\(978\) −12.6630 −0.404918
\(979\) −6.99484 −0.223556
\(980\) −11.8421 −0.378282
\(981\) 12.1672 0.388469
\(982\) −58.3616 −1.86239
\(983\) 2.46244 0.0785397 0.0392699 0.999229i \(-0.487497\pi\)
0.0392699 + 0.999229i \(0.487497\pi\)
\(984\) 24.9375 0.794977
\(985\) −3.99158 −0.127182
\(986\) −102.167 −3.25367
\(987\) 4.66122 0.148368
\(988\) −61.7307 −1.96391
\(989\) 9.51954 0.302704
\(990\) −12.7530 −0.405317
\(991\) −17.5912 −0.558803 −0.279401 0.960174i \(-0.590136\pi\)
−0.279401 + 0.960174i \(0.590136\pi\)
\(992\) 202.834 6.43998
\(993\) −21.1056 −0.669766
\(994\) −8.71681 −0.276480
\(995\) 9.38865 0.297640
\(996\) −79.2154 −2.51004
\(997\) 54.0681 1.71235 0.856177 0.516683i \(-0.172833\pi\)
0.856177 + 0.516683i \(0.172833\pi\)
\(998\) −63.2978 −2.00366
\(999\) −9.18971 −0.290750
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 4011.2.a.l.1.2 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4011.2.a.l.1.2 28 1.1 even 1 trivial