Properties

Label 6014.2.a.f.1.13
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $22$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(22\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.253397 q^{3} +1.00000 q^{4} -0.480250 q^{5} -0.253397 q^{6} +2.09789 q^{7} -1.00000 q^{8} -2.93579 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.253397 q^{3} +1.00000 q^{4} -0.480250 q^{5} -0.253397 q^{6} +2.09789 q^{7} -1.00000 q^{8} -2.93579 q^{9} +0.480250 q^{10} -0.665471 q^{11} +0.253397 q^{12} +2.39046 q^{13} -2.09789 q^{14} -0.121694 q^{15} +1.00000 q^{16} -3.40960 q^{17} +2.93579 q^{18} -1.80607 q^{19} -0.480250 q^{20} +0.531600 q^{21} +0.665471 q^{22} +7.76002 q^{23} -0.253397 q^{24} -4.76936 q^{25} -2.39046 q^{26} -1.50411 q^{27} +2.09789 q^{28} -4.82413 q^{29} +0.121694 q^{30} +1.00000 q^{31} -1.00000 q^{32} -0.168629 q^{33} +3.40960 q^{34} -1.00751 q^{35} -2.93579 q^{36} +5.29145 q^{37} +1.80607 q^{38} +0.605737 q^{39} +0.480250 q^{40} +6.01318 q^{41} -0.531600 q^{42} -3.79195 q^{43} -0.665471 q^{44} +1.40991 q^{45} -7.76002 q^{46} +7.00498 q^{47} +0.253397 q^{48} -2.59886 q^{49} +4.76936 q^{50} -0.863985 q^{51} +2.39046 q^{52} -1.21348 q^{53} +1.50411 q^{54} +0.319592 q^{55} -2.09789 q^{56} -0.457653 q^{57} +4.82413 q^{58} +8.41980 q^{59} -0.121694 q^{60} -4.49726 q^{61} -1.00000 q^{62} -6.15897 q^{63} +1.00000 q^{64} -1.14802 q^{65} +0.168629 q^{66} -15.5489 q^{67} -3.40960 q^{68} +1.96637 q^{69} +1.00751 q^{70} -12.1087 q^{71} +2.93579 q^{72} -1.77532 q^{73} -5.29145 q^{74} -1.20854 q^{75} -1.80607 q^{76} -1.39609 q^{77} -0.605737 q^{78} -9.47170 q^{79} -0.480250 q^{80} +8.42623 q^{81} -6.01318 q^{82} -6.01881 q^{83} +0.531600 q^{84} +1.63746 q^{85} +3.79195 q^{86} -1.22242 q^{87} +0.665471 q^{88} +14.3028 q^{89} -1.40991 q^{90} +5.01493 q^{91} +7.76002 q^{92} +0.253397 q^{93} -7.00498 q^{94} +0.867364 q^{95} -0.253397 q^{96} +1.00000 q^{97} +2.59886 q^{98} +1.95368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 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
\(3\) 0.253397 0.146299 0.0731495 0.997321i \(-0.476695\pi\)
0.0731495 + 0.997321i \(0.476695\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.480250 −0.214774 −0.107387 0.994217i \(-0.534248\pi\)
−0.107387 + 0.994217i \(0.534248\pi\)
\(6\) −0.253397 −0.103449
\(7\) 2.09789 0.792928 0.396464 0.918050i \(-0.370237\pi\)
0.396464 + 0.918050i \(0.370237\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.93579 −0.978597
\(10\) 0.480250 0.151868
\(11\) −0.665471 −0.200647 −0.100324 0.994955i \(-0.531988\pi\)
−0.100324 + 0.994955i \(0.531988\pi\)
\(12\) 0.253397 0.0731495
\(13\) 2.39046 0.662995 0.331497 0.943456i \(-0.392446\pi\)
0.331497 + 0.943456i \(0.392446\pi\)
\(14\) −2.09789 −0.560685
\(15\) −0.121694 −0.0314213
\(16\) 1.00000 0.250000
\(17\) −3.40960 −0.826951 −0.413475 0.910515i \(-0.635685\pi\)
−0.413475 + 0.910515i \(0.635685\pi\)
\(18\) 2.93579 0.691972
\(19\) −1.80607 −0.414341 −0.207170 0.978305i \(-0.566425\pi\)
−0.207170 + 0.978305i \(0.566425\pi\)
\(20\) −0.480250 −0.107387
\(21\) 0.531600 0.116005
\(22\) 0.665471 0.141879
\(23\) 7.76002 1.61808 0.809038 0.587757i \(-0.199989\pi\)
0.809038 + 0.587757i \(0.199989\pi\)
\(24\) −0.253397 −0.0517245
\(25\) −4.76936 −0.953872
\(26\) −2.39046 −0.468808
\(27\) −1.50411 −0.289467
\(28\) 2.09789 0.396464
\(29\) −4.82413 −0.895818 −0.447909 0.894079i \(-0.647831\pi\)
−0.447909 + 0.894079i \(0.647831\pi\)
\(30\) 0.121694 0.0222182
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) −0.168629 −0.0293545
\(34\) 3.40960 0.584742
\(35\) −1.00751 −0.170300
\(36\) −2.93579 −0.489298
\(37\) 5.29145 0.869909 0.434954 0.900453i \(-0.356765\pi\)
0.434954 + 0.900453i \(0.356765\pi\)
\(38\) 1.80607 0.292983
\(39\) 0.605737 0.0969955
\(40\) 0.480250 0.0759341
\(41\) 6.01318 0.939101 0.469550 0.882906i \(-0.344416\pi\)
0.469550 + 0.882906i \(0.344416\pi\)
\(42\) −0.531600 −0.0820277
\(43\) −3.79195 −0.578266 −0.289133 0.957289i \(-0.593367\pi\)
−0.289133 + 0.957289i \(0.593367\pi\)
\(44\) −0.665471 −0.100324
\(45\) 1.40991 0.210177
\(46\) −7.76002 −1.14415
\(47\) 7.00498 1.02178 0.510891 0.859646i \(-0.329316\pi\)
0.510891 + 0.859646i \(0.329316\pi\)
\(48\) 0.253397 0.0365748
\(49\) −2.59886 −0.371265
\(50\) 4.76936 0.674489
\(51\) −0.863985 −0.120982
\(52\) 2.39046 0.331497
\(53\) −1.21348 −0.166684 −0.0833422 0.996521i \(-0.526559\pi\)
−0.0833422 + 0.996521i \(0.526559\pi\)
\(54\) 1.50411 0.204684
\(55\) 0.319592 0.0430938
\(56\) −2.09789 −0.280342
\(57\) −0.457653 −0.0606177
\(58\) 4.82413 0.633439
\(59\) 8.41980 1.09617 0.548083 0.836424i \(-0.315358\pi\)
0.548083 + 0.836424i \(0.315358\pi\)
\(60\) −0.121694 −0.0157106
\(61\) −4.49726 −0.575815 −0.287908 0.957658i \(-0.592960\pi\)
−0.287908 + 0.957658i \(0.592960\pi\)
\(62\) −1.00000 −0.127000
\(63\) −6.15897 −0.775957
\(64\) 1.00000 0.125000
\(65\) −1.14802 −0.142394
\(66\) 0.168629 0.0207568
\(67\) −15.5489 −1.89960 −0.949801 0.312854i \(-0.898715\pi\)
−0.949801 + 0.312854i \(0.898715\pi\)
\(68\) −3.40960 −0.413475
\(69\) 1.96637 0.236723
\(70\) 1.00751 0.120421
\(71\) −12.1087 −1.43704 −0.718518 0.695508i \(-0.755179\pi\)
−0.718518 + 0.695508i \(0.755179\pi\)
\(72\) 2.93579 0.345986
\(73\) −1.77532 −0.207785 −0.103893 0.994589i \(-0.533130\pi\)
−0.103893 + 0.994589i \(0.533130\pi\)
\(74\) −5.29145 −0.615118
\(75\) −1.20854 −0.139551
\(76\) −1.80607 −0.207170
\(77\) −1.39609 −0.159099
\(78\) −0.605737 −0.0685862
\(79\) −9.47170 −1.06565 −0.532824 0.846226i \(-0.678869\pi\)
−0.532824 + 0.846226i \(0.678869\pi\)
\(80\) −0.480250 −0.0536935
\(81\) 8.42623 0.936248
\(82\) −6.01318 −0.664044
\(83\) −6.01881 −0.660650 −0.330325 0.943867i \(-0.607158\pi\)
−0.330325 + 0.943867i \(0.607158\pi\)
\(84\) 0.531600 0.0580023
\(85\) 1.63746 0.177608
\(86\) 3.79195 0.408896
\(87\) −1.22242 −0.131057
\(88\) 0.665471 0.0709395
\(89\) 14.3028 1.51610 0.758049 0.652198i \(-0.226153\pi\)
0.758049 + 0.652198i \(0.226153\pi\)
\(90\) −1.40991 −0.148618
\(91\) 5.01493 0.525707
\(92\) 7.76002 0.809038
\(93\) 0.253397 0.0262761
\(94\) −7.00498 −0.722508
\(95\) 0.867364 0.0889897
\(96\) −0.253397 −0.0258623
\(97\) 1.00000 0.101535
\(98\) 2.59886 0.262524
\(99\) 1.95368 0.196353
\(100\) −4.76936 −0.476936
\(101\) 16.3076 1.62267 0.811333 0.584584i \(-0.198742\pi\)
0.811333 + 0.584584i \(0.198742\pi\)
\(102\) 0.863985 0.0855473
\(103\) −4.25960 −0.419711 −0.209855 0.977732i \(-0.567299\pi\)
−0.209855 + 0.977732i \(0.567299\pi\)
\(104\) −2.39046 −0.234404
\(105\) −0.255301 −0.0249148
\(106\) 1.21348 0.117864
\(107\) −16.8783 −1.63169 −0.815844 0.578272i \(-0.803727\pi\)
−0.815844 + 0.578272i \(0.803727\pi\)
\(108\) −1.50411 −0.144733
\(109\) 9.71703 0.930723 0.465361 0.885121i \(-0.345924\pi\)
0.465361 + 0.885121i \(0.345924\pi\)
\(110\) −0.319592 −0.0304719
\(111\) 1.34084 0.127267
\(112\) 2.09789 0.198232
\(113\) −8.10723 −0.762664 −0.381332 0.924438i \(-0.624535\pi\)
−0.381332 + 0.924438i \(0.624535\pi\)
\(114\) 0.457653 0.0428632
\(115\) −3.72675 −0.347521
\(116\) −4.82413 −0.447909
\(117\) −7.01789 −0.648804
\(118\) −8.41980 −0.775106
\(119\) −7.15298 −0.655712
\(120\) 0.121694 0.0111091
\(121\) −10.5571 −0.959741
\(122\) 4.49726 0.407163
\(123\) 1.52372 0.137390
\(124\) 1.00000 0.0898027
\(125\) 4.69173 0.419641
\(126\) 6.15897 0.548684
\(127\) −14.5625 −1.29221 −0.646107 0.763247i \(-0.723604\pi\)
−0.646107 + 0.763247i \(0.723604\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.960870 −0.0845998
\(130\) 1.14802 0.100688
\(131\) 13.9631 1.21996 0.609982 0.792416i \(-0.291177\pi\)
0.609982 + 0.792416i \(0.291177\pi\)
\(132\) −0.168629 −0.0146772
\(133\) −3.78894 −0.328542
\(134\) 15.5489 1.34322
\(135\) 0.722350 0.0621700
\(136\) 3.40960 0.292371
\(137\) 9.13671 0.780602 0.390301 0.920687i \(-0.372371\pi\)
0.390301 + 0.920687i \(0.372371\pi\)
\(138\) −1.96637 −0.167388
\(139\) −1.94326 −0.164825 −0.0824125 0.996598i \(-0.526262\pi\)
−0.0824125 + 0.996598i \(0.526262\pi\)
\(140\) −1.00751 −0.0851502
\(141\) 1.77504 0.149486
\(142\) 12.1087 1.01614
\(143\) −1.59078 −0.133028
\(144\) −2.93579 −0.244649
\(145\) 2.31679 0.192399
\(146\) 1.77532 0.146926
\(147\) −0.658543 −0.0543157
\(148\) 5.29145 0.434954
\(149\) −17.7125 −1.45106 −0.725532 0.688189i \(-0.758406\pi\)
−0.725532 + 0.688189i \(0.758406\pi\)
\(150\) 1.20854 0.0986772
\(151\) −9.88828 −0.804697 −0.402348 0.915487i \(-0.631806\pi\)
−0.402348 + 0.915487i \(0.631806\pi\)
\(152\) 1.80607 0.146492
\(153\) 10.0099 0.809251
\(154\) 1.39609 0.112500
\(155\) −0.480250 −0.0385746
\(156\) 0.605737 0.0484978
\(157\) −8.35754 −0.667004 −0.333502 0.942749i \(-0.608230\pi\)
−0.333502 + 0.942749i \(0.608230\pi\)
\(158\) 9.47170 0.753528
\(159\) −0.307493 −0.0243858
\(160\) 0.480250 0.0379671
\(161\) 16.2797 1.28302
\(162\) −8.42623 −0.662027
\(163\) 2.88088 0.225648 0.112824 0.993615i \(-0.464010\pi\)
0.112824 + 0.993615i \(0.464010\pi\)
\(164\) 6.01318 0.469550
\(165\) 0.0809839 0.00630458
\(166\) 6.01881 0.467150
\(167\) 6.55783 0.507460 0.253730 0.967275i \(-0.418343\pi\)
0.253730 + 0.967275i \(0.418343\pi\)
\(168\) −0.531600 −0.0410138
\(169\) −7.28569 −0.560438
\(170\) −1.63746 −0.125588
\(171\) 5.30224 0.405472
\(172\) −3.79195 −0.289133
\(173\) 0.606282 0.0460948 0.0230474 0.999734i \(-0.492663\pi\)
0.0230474 + 0.999734i \(0.492663\pi\)
\(174\) 1.22242 0.0926715
\(175\) −10.0056 −0.756352
\(176\) −0.665471 −0.0501618
\(177\) 2.13356 0.160368
\(178\) −14.3028 −1.07204
\(179\) −7.22701 −0.540172 −0.270086 0.962836i \(-0.587052\pi\)
−0.270086 + 0.962836i \(0.587052\pi\)
\(180\) 1.40991 0.105089
\(181\) −22.3379 −1.66036 −0.830180 0.557496i \(-0.811762\pi\)
−0.830180 + 0.557496i \(0.811762\pi\)
\(182\) −5.01493 −0.371731
\(183\) −1.13959 −0.0842412
\(184\) −7.76002 −0.572076
\(185\) −2.54122 −0.186834
\(186\) −0.253397 −0.0185800
\(187\) 2.26899 0.165925
\(188\) 7.00498 0.510891
\(189\) −3.15547 −0.229526
\(190\) −0.867364 −0.0629252
\(191\) −17.6757 −1.27897 −0.639486 0.768803i \(-0.720853\pi\)
−0.639486 + 0.768803i \(0.720853\pi\)
\(192\) 0.253397 0.0182874
\(193\) −8.72407 −0.627973 −0.313986 0.949428i \(-0.601665\pi\)
−0.313986 + 0.949428i \(0.601665\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −0.290905 −0.0208321
\(196\) −2.59886 −0.185633
\(197\) −5.40889 −0.385368 −0.192684 0.981261i \(-0.561719\pi\)
−0.192684 + 0.981261i \(0.561719\pi\)
\(198\) −1.95368 −0.138842
\(199\) −27.9355 −1.98029 −0.990147 0.140033i \(-0.955279\pi\)
−0.990147 + 0.140033i \(0.955279\pi\)
\(200\) 4.76936 0.337245
\(201\) −3.94006 −0.277910
\(202\) −16.3076 −1.14740
\(203\) −10.1205 −0.710319
\(204\) −0.863985 −0.0604910
\(205\) −2.88783 −0.201695
\(206\) 4.25960 0.296780
\(207\) −22.7818 −1.58344
\(208\) 2.39046 0.165749
\(209\) 1.20189 0.0831363
\(210\) 0.255301 0.0176174
\(211\) 19.7703 1.36104 0.680522 0.732728i \(-0.261753\pi\)
0.680522 + 0.732728i \(0.261753\pi\)
\(212\) −1.21348 −0.0833422
\(213\) −3.06831 −0.210237
\(214\) 16.8783 1.15378
\(215\) 1.82108 0.124197
\(216\) 1.50411 0.102342
\(217\) 2.09789 0.142414
\(218\) −9.71703 −0.658120
\(219\) −0.449861 −0.0303988
\(220\) 0.319592 0.0215469
\(221\) −8.15053 −0.548264
\(222\) −1.34084 −0.0899912
\(223\) −2.47720 −0.165886 −0.0829428 0.996554i \(-0.526432\pi\)
−0.0829428 + 0.996554i \(0.526432\pi\)
\(224\) −2.09789 −0.140171
\(225\) 14.0018 0.933456
\(226\) 8.10723 0.539285
\(227\) 21.2988 1.41365 0.706827 0.707387i \(-0.250126\pi\)
0.706827 + 0.707387i \(0.250126\pi\)
\(228\) −0.457653 −0.0303088
\(229\) 10.3502 0.683962 0.341981 0.939707i \(-0.388902\pi\)
0.341981 + 0.939707i \(0.388902\pi\)
\(230\) 3.72675 0.245734
\(231\) −0.353764 −0.0232760
\(232\) 4.82413 0.316720
\(233\) 7.70459 0.504745 0.252372 0.967630i \(-0.418789\pi\)
0.252372 + 0.967630i \(0.418789\pi\)
\(234\) 7.01789 0.458774
\(235\) −3.36414 −0.219452
\(236\) 8.41980 0.548083
\(237\) −2.40010 −0.155903
\(238\) 7.15298 0.463659
\(239\) 10.8586 0.702387 0.351193 0.936303i \(-0.385776\pi\)
0.351193 + 0.936303i \(0.385776\pi\)
\(240\) −0.121694 −0.00785532
\(241\) 20.4943 1.32016 0.660078 0.751197i \(-0.270523\pi\)
0.660078 + 0.751197i \(0.270523\pi\)
\(242\) 10.5571 0.678639
\(243\) 6.64753 0.426439
\(244\) −4.49726 −0.287908
\(245\) 1.24810 0.0797382
\(246\) −1.52372 −0.0971491
\(247\) −4.31734 −0.274706
\(248\) −1.00000 −0.0635001
\(249\) −1.52515 −0.0966525
\(250\) −4.69173 −0.296731
\(251\) 15.1004 0.953126 0.476563 0.879140i \(-0.341882\pi\)
0.476563 + 0.879140i \(0.341882\pi\)
\(252\) −6.15897 −0.387978
\(253\) −5.16407 −0.324662
\(254\) 14.5625 0.913733
\(255\) 0.414929 0.0259838
\(256\) 1.00000 0.0625000
\(257\) −15.8607 −0.989362 −0.494681 0.869075i \(-0.664715\pi\)
−0.494681 + 0.869075i \(0.664715\pi\)
\(258\) 0.960870 0.0598211
\(259\) 11.1009 0.689775
\(260\) −1.14802 −0.0711971
\(261\) 14.1626 0.876645
\(262\) −13.9631 −0.862644
\(263\) −19.7908 −1.22035 −0.610177 0.792266i \(-0.708901\pi\)
−0.610177 + 0.792266i \(0.708901\pi\)
\(264\) 0.168629 0.0103784
\(265\) 0.582774 0.0357995
\(266\) 3.78894 0.232315
\(267\) 3.62430 0.221804
\(268\) −15.5489 −0.949801
\(269\) 8.55109 0.521369 0.260684 0.965424i \(-0.416052\pi\)
0.260684 + 0.965424i \(0.416052\pi\)
\(270\) −0.722350 −0.0439608
\(271\) −16.8411 −1.02303 −0.511513 0.859275i \(-0.670915\pi\)
−0.511513 + 0.859275i \(0.670915\pi\)
\(272\) −3.40960 −0.206738
\(273\) 1.27077 0.0769105
\(274\) −9.13671 −0.551969
\(275\) 3.17387 0.191392
\(276\) 1.96637 0.118361
\(277\) −2.36156 −0.141892 −0.0709462 0.997480i \(-0.522602\pi\)
−0.0709462 + 0.997480i \(0.522602\pi\)
\(278\) 1.94326 0.116549
\(279\) −2.93579 −0.175761
\(280\) 1.00751 0.0602103
\(281\) 0.346952 0.0206974 0.0103487 0.999946i \(-0.496706\pi\)
0.0103487 + 0.999946i \(0.496706\pi\)
\(282\) −1.77504 −0.105702
\(283\) 17.4821 1.03920 0.519602 0.854408i \(-0.326080\pi\)
0.519602 + 0.854408i \(0.326080\pi\)
\(284\) −12.1087 −0.718518
\(285\) 0.219788 0.0130191
\(286\) 1.59078 0.0940650
\(287\) 12.6150 0.744639
\(288\) 2.93579 0.172993
\(289\) −5.37460 −0.316153
\(290\) −2.31679 −0.136046
\(291\) 0.253397 0.0148544
\(292\) −1.77532 −0.103893
\(293\) −15.7681 −0.921179 −0.460590 0.887613i \(-0.652362\pi\)
−0.460590 + 0.887613i \(0.652362\pi\)
\(294\) 0.658543 0.0384070
\(295\) −4.04361 −0.235428
\(296\) −5.29145 −0.307559
\(297\) 1.00094 0.0580807
\(298\) 17.7125 1.02606
\(299\) 18.5500 1.07278
\(300\) −1.20854 −0.0697753
\(301\) −7.95509 −0.458524
\(302\) 9.88828 0.569007
\(303\) 4.13230 0.237395
\(304\) −1.80607 −0.103585
\(305\) 2.15981 0.123670
\(306\) −10.0099 −0.572227
\(307\) −8.89454 −0.507638 −0.253819 0.967252i \(-0.581687\pi\)
−0.253819 + 0.967252i \(0.581687\pi\)
\(308\) −1.39609 −0.0795493
\(309\) −1.07937 −0.0614033
\(310\) 0.480250 0.0272764
\(311\) 22.2407 1.26116 0.630579 0.776125i \(-0.282818\pi\)
0.630579 + 0.776125i \(0.282818\pi\)
\(312\) −0.605737 −0.0342931
\(313\) −19.7898 −1.11859 −0.559293 0.828970i \(-0.688927\pi\)
−0.559293 + 0.828970i \(0.688927\pi\)
\(314\) 8.35754 0.471643
\(315\) 2.95784 0.166655
\(316\) −9.47170 −0.532824
\(317\) −23.3646 −1.31228 −0.656142 0.754637i \(-0.727813\pi\)
−0.656142 + 0.754637i \(0.727813\pi\)
\(318\) 0.307493 0.0172433
\(319\) 3.21032 0.179743
\(320\) −0.480250 −0.0268468
\(321\) −4.27692 −0.238714
\(322\) −16.2797 −0.907230
\(323\) 6.15798 0.342639
\(324\) 8.42623 0.468124
\(325\) −11.4010 −0.632412
\(326\) −2.88088 −0.159557
\(327\) 2.46227 0.136164
\(328\) −6.01318 −0.332022
\(329\) 14.6957 0.810199
\(330\) −0.0809839 −0.00445801
\(331\) 20.1711 1.10870 0.554352 0.832282i \(-0.312966\pi\)
0.554352 + 0.832282i \(0.312966\pi\)
\(332\) −6.01881 −0.330325
\(333\) −15.5346 −0.851290
\(334\) −6.55783 −0.358828
\(335\) 7.46736 0.407986
\(336\) 0.531600 0.0290012
\(337\) −5.83412 −0.317804 −0.158902 0.987294i \(-0.550795\pi\)
−0.158902 + 0.987294i \(0.550795\pi\)
\(338\) 7.28569 0.396289
\(339\) −2.05435 −0.111577
\(340\) 1.63746 0.0888038
\(341\) −0.665471 −0.0360373
\(342\) −5.30224 −0.286712
\(343\) −20.1373 −1.08731
\(344\) 3.79195 0.204448
\(345\) −0.944348 −0.0508420
\(346\) −0.606282 −0.0325939
\(347\) −22.8780 −1.22816 −0.614078 0.789246i \(-0.710472\pi\)
−0.614078 + 0.789246i \(0.710472\pi\)
\(348\) −1.22242 −0.0655287
\(349\) −1.33157 −0.0712772 −0.0356386 0.999365i \(-0.511347\pi\)
−0.0356386 + 0.999365i \(0.511347\pi\)
\(350\) 10.0056 0.534822
\(351\) −3.59553 −0.191915
\(352\) 0.665471 0.0354697
\(353\) −10.3020 −0.548318 −0.274159 0.961684i \(-0.588399\pi\)
−0.274159 + 0.961684i \(0.588399\pi\)
\(354\) −2.13356 −0.113397
\(355\) 5.81519 0.308638
\(356\) 14.3028 0.758049
\(357\) −1.81255 −0.0959301
\(358\) 7.22701 0.381960
\(359\) −2.16605 −0.114320 −0.0571598 0.998365i \(-0.518204\pi\)
−0.0571598 + 0.998365i \(0.518204\pi\)
\(360\) −1.40991 −0.0743089
\(361\) −15.7381 −0.828322
\(362\) 22.3379 1.17405
\(363\) −2.67515 −0.140409
\(364\) 5.01493 0.262854
\(365\) 0.852595 0.0446269
\(366\) 1.13959 0.0595676
\(367\) −3.83617 −0.200247 −0.100123 0.994975i \(-0.531924\pi\)
−0.100123 + 0.994975i \(0.531924\pi\)
\(368\) 7.76002 0.404519
\(369\) −17.6534 −0.919001
\(370\) 2.54122 0.132112
\(371\) −2.54575 −0.132169
\(372\) 0.253397 0.0131380
\(373\) −2.13167 −0.110374 −0.0551869 0.998476i \(-0.517575\pi\)
−0.0551869 + 0.998476i \(0.517575\pi\)
\(374\) −2.26899 −0.117327
\(375\) 1.18887 0.0613931
\(376\) −7.00498 −0.361254
\(377\) −11.5319 −0.593923
\(378\) 3.15547 0.162300
\(379\) −34.3867 −1.76632 −0.883162 0.469068i \(-0.844590\pi\)
−0.883162 + 0.469068i \(0.844590\pi\)
\(380\) 0.867364 0.0444949
\(381\) −3.69010 −0.189050
\(382\) 17.6757 0.904370
\(383\) 35.0921 1.79312 0.896562 0.442918i \(-0.146057\pi\)
0.896562 + 0.442918i \(0.146057\pi\)
\(384\) −0.253397 −0.0129311
\(385\) 0.670470 0.0341703
\(386\) 8.72407 0.444044
\(387\) 11.1324 0.565890
\(388\) 1.00000 0.0507673
\(389\) −25.7587 −1.30602 −0.653009 0.757350i \(-0.726494\pi\)
−0.653009 + 0.757350i \(0.726494\pi\)
\(390\) 0.290905 0.0147305
\(391\) −26.4586 −1.33807
\(392\) 2.59886 0.131262
\(393\) 3.53822 0.178480
\(394\) 5.40889 0.272496
\(395\) 4.54878 0.228874
\(396\) 1.95368 0.0981763
\(397\) 5.10599 0.256262 0.128131 0.991757i \(-0.459102\pi\)
0.128131 + 0.991757i \(0.459102\pi\)
\(398\) 27.9355 1.40028
\(399\) −0.960107 −0.0480654
\(400\) −4.76936 −0.238468
\(401\) 17.9374 0.895750 0.447875 0.894096i \(-0.352181\pi\)
0.447875 + 0.894096i \(0.352181\pi\)
\(402\) 3.94006 0.196512
\(403\) 2.39046 0.119077
\(404\) 16.3076 0.811333
\(405\) −4.04669 −0.201082
\(406\) 10.1205 0.502272
\(407\) −3.52130 −0.174545
\(408\) 0.863985 0.0427736
\(409\) 15.1426 0.748753 0.374376 0.927277i \(-0.377857\pi\)
0.374376 + 0.927277i \(0.377857\pi\)
\(410\) 2.88783 0.142620
\(411\) 2.31522 0.114201
\(412\) −4.25960 −0.209855
\(413\) 17.6638 0.869180
\(414\) 22.7818 1.11966
\(415\) 2.89053 0.141891
\(416\) −2.39046 −0.117202
\(417\) −0.492416 −0.0241137
\(418\) −1.20189 −0.0587862
\(419\) −38.8018 −1.89559 −0.947796 0.318877i \(-0.896694\pi\)
−0.947796 + 0.318877i \(0.896694\pi\)
\(420\) −0.255301 −0.0124574
\(421\) 35.1430 1.71276 0.856382 0.516343i \(-0.172707\pi\)
0.856382 + 0.516343i \(0.172707\pi\)
\(422\) −19.7703 −0.962403
\(423\) −20.5651 −0.999911
\(424\) 1.21348 0.0589318
\(425\) 16.2616 0.788805
\(426\) 3.06831 0.148660
\(427\) −9.43476 −0.456580
\(428\) −16.8783 −0.815844
\(429\) −0.403100 −0.0194619
\(430\) −1.82108 −0.0878203
\(431\) −6.10231 −0.293938 −0.146969 0.989141i \(-0.546952\pi\)
−0.146969 + 0.989141i \(0.546952\pi\)
\(432\) −1.50411 −0.0723667
\(433\) −6.73716 −0.323767 −0.161884 0.986810i \(-0.551757\pi\)
−0.161884 + 0.986810i \(0.551757\pi\)
\(434\) −2.09789 −0.100702
\(435\) 0.587068 0.0281477
\(436\) 9.71703 0.465361
\(437\) −14.0151 −0.670434
\(438\) 0.449861 0.0214952
\(439\) 25.4609 1.21518 0.607591 0.794250i \(-0.292136\pi\)
0.607591 + 0.794250i \(0.292136\pi\)
\(440\) −0.319592 −0.0152360
\(441\) 7.62969 0.363319
\(442\) 8.15053 0.387681
\(443\) −6.20495 −0.294806 −0.147403 0.989077i \(-0.547091\pi\)
−0.147403 + 0.989077i \(0.547091\pi\)
\(444\) 1.34084 0.0636334
\(445\) −6.86893 −0.325619
\(446\) 2.47720 0.117299
\(447\) −4.48830 −0.212289
\(448\) 2.09789 0.0991160
\(449\) −0.0172868 −0.000815817 0 −0.000407908 1.00000i \(-0.500130\pi\)
−0.000407908 1.00000i \(0.500130\pi\)
\(450\) −14.0018 −0.660053
\(451\) −4.00160 −0.188428
\(452\) −8.10723 −0.381332
\(453\) −2.50566 −0.117726
\(454\) −21.2988 −0.999604
\(455\) −2.40842 −0.112908
\(456\) 0.457653 0.0214316
\(457\) −16.3152 −0.763192 −0.381596 0.924329i \(-0.624625\pi\)
−0.381596 + 0.924329i \(0.624625\pi\)
\(458\) −10.3502 −0.483634
\(459\) 5.12843 0.239375
\(460\) −3.72675 −0.173760
\(461\) −2.90217 −0.135167 −0.0675837 0.997714i \(-0.521529\pi\)
−0.0675837 + 0.997714i \(0.521529\pi\)
\(462\) 0.353764 0.0164586
\(463\) 3.78789 0.176038 0.0880190 0.996119i \(-0.471946\pi\)
0.0880190 + 0.996119i \(0.471946\pi\)
\(464\) −4.82413 −0.223955
\(465\) −0.121694 −0.00564343
\(466\) −7.70459 −0.356908
\(467\) −22.2445 −1.02935 −0.514675 0.857385i \(-0.672087\pi\)
−0.514675 + 0.857385i \(0.672087\pi\)
\(468\) −7.01789 −0.324402
\(469\) −32.6199 −1.50625
\(470\) 3.36414 0.155176
\(471\) −2.11778 −0.0975821
\(472\) −8.41980 −0.387553
\(473\) 2.52343 0.116027
\(474\) 2.40010 0.110240
\(475\) 8.61380 0.395228
\(476\) −7.15298 −0.327856
\(477\) 3.56252 0.163117
\(478\) −10.8586 −0.496662
\(479\) 0.457308 0.0208950 0.0104475 0.999945i \(-0.496674\pi\)
0.0104475 + 0.999945i \(0.496674\pi\)
\(480\) 0.121694 0.00555455
\(481\) 12.6490 0.576745
\(482\) −20.4943 −0.933491
\(483\) 4.12522 0.187704
\(484\) −10.5571 −0.479870
\(485\) −0.480250 −0.0218070
\(486\) −6.64753 −0.301538
\(487\) −35.1270 −1.59176 −0.795879 0.605456i \(-0.792991\pi\)
−0.795879 + 0.605456i \(0.792991\pi\)
\(488\) 4.49726 0.203581
\(489\) 0.730007 0.0330120
\(490\) −1.24810 −0.0563834
\(491\) −17.4311 −0.786653 −0.393326 0.919399i \(-0.628676\pi\)
−0.393326 + 0.919399i \(0.628676\pi\)
\(492\) 1.52372 0.0686948
\(493\) 16.4484 0.740797
\(494\) 4.31734 0.194246
\(495\) −0.938256 −0.0421715
\(496\) 1.00000 0.0449013
\(497\) −25.4027 −1.13947
\(498\) 1.52515 0.0683437
\(499\) 10.6225 0.475528 0.237764 0.971323i \(-0.423586\pi\)
0.237764 + 0.971323i \(0.423586\pi\)
\(500\) 4.69173 0.209821
\(501\) 1.66174 0.0742409
\(502\) −15.1004 −0.673962
\(503\) 23.4766 1.04677 0.523385 0.852096i \(-0.324669\pi\)
0.523385 + 0.852096i \(0.324669\pi\)
\(504\) 6.15897 0.274342
\(505\) −7.83172 −0.348507
\(506\) 5.16407 0.229571
\(507\) −1.84618 −0.0819915
\(508\) −14.5625 −0.646107
\(509\) −4.93509 −0.218744 −0.109372 0.994001i \(-0.534884\pi\)
−0.109372 + 0.994001i \(0.534884\pi\)
\(510\) −0.414929 −0.0183733
\(511\) −3.72442 −0.164759
\(512\) −1.00000 −0.0441942
\(513\) 2.71653 0.119938
\(514\) 15.8607 0.699585
\(515\) 2.04567 0.0901430
\(516\) −0.960870 −0.0422999
\(517\) −4.66161 −0.205017
\(518\) −11.1009 −0.487745
\(519\) 0.153630 0.00674362
\(520\) 1.14802 0.0503439
\(521\) −14.8713 −0.651523 −0.325761 0.945452i \(-0.605621\pi\)
−0.325761 + 0.945452i \(0.605621\pi\)
\(522\) −14.1626 −0.619881
\(523\) −11.2282 −0.490977 −0.245488 0.969400i \(-0.578948\pi\)
−0.245488 + 0.969400i \(0.578948\pi\)
\(524\) 13.9631 0.609982
\(525\) −2.53539 −0.110654
\(526\) 19.7908 0.862920
\(527\) −3.40960 −0.148525
\(528\) −0.168629 −0.00733862
\(529\) 37.2178 1.61817
\(530\) −0.582774 −0.0253141
\(531\) −24.7188 −1.07270
\(532\) −3.78894 −0.164271
\(533\) 14.3743 0.622619
\(534\) −3.62430 −0.156839
\(535\) 8.10581 0.350445
\(536\) 15.5489 0.671611
\(537\) −1.83131 −0.0790267
\(538\) −8.55109 −0.368664
\(539\) 1.72946 0.0744933
\(540\) 0.722350 0.0310850
\(541\) −8.65172 −0.371967 −0.185983 0.982553i \(-0.559547\pi\)
−0.185983 + 0.982553i \(0.559547\pi\)
\(542\) 16.8411 0.723389
\(543\) −5.66036 −0.242909
\(544\) 3.40960 0.146186
\(545\) −4.66660 −0.199895
\(546\) −1.27077 −0.0543839
\(547\) −25.9434 −1.10926 −0.554630 0.832097i \(-0.687140\pi\)
−0.554630 + 0.832097i \(0.687140\pi\)
\(548\) 9.13671 0.390301
\(549\) 13.2030 0.563491
\(550\) −3.17387 −0.135334
\(551\) 8.71271 0.371174
\(552\) −1.96637 −0.0836942
\(553\) −19.8706 −0.844983
\(554\) 2.36156 0.100333
\(555\) −0.643938 −0.0273336
\(556\) −1.94326 −0.0824125
\(557\) 16.8703 0.714817 0.357408 0.933948i \(-0.383660\pi\)
0.357408 + 0.933948i \(0.383660\pi\)
\(558\) 2.93579 0.124282
\(559\) −9.06450 −0.383388
\(560\) −1.00751 −0.0425751
\(561\) 0.574957 0.0242747
\(562\) −0.346952 −0.0146353
\(563\) 34.3415 1.44732 0.723662 0.690155i \(-0.242458\pi\)
0.723662 + 0.690155i \(0.242458\pi\)
\(564\) 1.77504 0.0747428
\(565\) 3.89350 0.163801
\(566\) −17.4821 −0.734829
\(567\) 17.6773 0.742377
\(568\) 12.1087 0.508069
\(569\) −42.7601 −1.79260 −0.896298 0.443453i \(-0.853753\pi\)
−0.896298 + 0.443453i \(0.853753\pi\)
\(570\) −0.219788 −0.00920590
\(571\) 40.7917 1.70708 0.853539 0.521029i \(-0.174452\pi\)
0.853539 + 0.521029i \(0.174452\pi\)
\(572\) −1.59078 −0.0665140
\(573\) −4.47899 −0.187112
\(574\) −12.6150 −0.526540
\(575\) −37.0103 −1.54344
\(576\) −2.93579 −0.122325
\(577\) 8.55741 0.356249 0.178125 0.984008i \(-0.442997\pi\)
0.178125 + 0.984008i \(0.442997\pi\)
\(578\) 5.37460 0.223554
\(579\) −2.21066 −0.0918718
\(580\) 2.31679 0.0961993
\(581\) −12.6268 −0.523848
\(582\) −0.253397 −0.0105037
\(583\) 0.807536 0.0334447
\(584\) 1.77532 0.0734631
\(585\) 3.37034 0.139346
\(586\) 15.7681 0.651372
\(587\) −3.12283 −0.128893 −0.0644466 0.997921i \(-0.520528\pi\)
−0.0644466 + 0.997921i \(0.520528\pi\)
\(588\) −0.658543 −0.0271579
\(589\) −1.80607 −0.0744178
\(590\) 4.04361 0.166473
\(591\) −1.37060 −0.0563789
\(592\) 5.29145 0.217477
\(593\) 31.3115 1.28581 0.642905 0.765946i \(-0.277729\pi\)
0.642905 + 0.765946i \(0.277729\pi\)
\(594\) −1.00094 −0.0410692
\(595\) 3.43522 0.140830
\(596\) −17.7125 −0.725532
\(597\) −7.07878 −0.289715
\(598\) −18.5500 −0.758567
\(599\) −26.1835 −1.06983 −0.534914 0.844907i \(-0.679656\pi\)
−0.534914 + 0.844907i \(0.679656\pi\)
\(600\) 1.20854 0.0493386
\(601\) −28.5941 −1.16638 −0.583189 0.812337i \(-0.698195\pi\)
−0.583189 + 0.812337i \(0.698195\pi\)
\(602\) 7.95509 0.324225
\(603\) 45.6483 1.85894
\(604\) −9.88828 −0.402348
\(605\) 5.07007 0.206128
\(606\) −4.13230 −0.167863
\(607\) −23.9524 −0.972198 −0.486099 0.873904i \(-0.661581\pi\)
−0.486099 + 0.873904i \(0.661581\pi\)
\(608\) 1.80607 0.0732458
\(609\) −2.56451 −0.103919
\(610\) −2.15981 −0.0874481
\(611\) 16.7451 0.677436
\(612\) 10.0099 0.404626
\(613\) −1.07263 −0.0433231 −0.0216616 0.999765i \(-0.506896\pi\)
−0.0216616 + 0.999765i \(0.506896\pi\)
\(614\) 8.89454 0.358954
\(615\) −0.731768 −0.0295077
\(616\) 1.39609 0.0562499
\(617\) 11.3134 0.455461 0.227731 0.973724i \(-0.426869\pi\)
0.227731 + 0.973724i \(0.426869\pi\)
\(618\) 1.07937 0.0434187
\(619\) 23.0385 0.925994 0.462997 0.886360i \(-0.346774\pi\)
0.462997 + 0.886360i \(0.346774\pi\)
\(620\) −0.480250 −0.0192873
\(621\) −11.6719 −0.468379
\(622\) −22.2407 −0.891773
\(623\) 30.0058 1.20216
\(624\) 0.605737 0.0242489
\(625\) 21.5936 0.863744
\(626\) 19.7898 0.790959
\(627\) 0.304555 0.0121628
\(628\) −8.35754 −0.333502
\(629\) −18.0417 −0.719371
\(630\) −2.95784 −0.117843
\(631\) −2.62007 −0.104303 −0.0521517 0.998639i \(-0.516608\pi\)
−0.0521517 + 0.998639i \(0.516608\pi\)
\(632\) 9.47170 0.376764
\(633\) 5.00974 0.199119
\(634\) 23.3646 0.927926
\(635\) 6.99364 0.277534
\(636\) −0.307493 −0.0121929
\(637\) −6.21247 −0.246147
\(638\) −3.21032 −0.127098
\(639\) 35.5486 1.40628
\(640\) 0.480250 0.0189835
\(641\) −26.9489 −1.06442 −0.532209 0.846613i \(-0.678638\pi\)
−0.532209 + 0.846613i \(0.678638\pi\)
\(642\) 4.27692 0.168797
\(643\) −43.6704 −1.72219 −0.861096 0.508442i \(-0.830221\pi\)
−0.861096 + 0.508442i \(0.830221\pi\)
\(644\) 16.2797 0.641509
\(645\) 0.461457 0.0181699
\(646\) −6.15798 −0.242283
\(647\) −23.3294 −0.917172 −0.458586 0.888650i \(-0.651644\pi\)
−0.458586 + 0.888650i \(0.651644\pi\)
\(648\) −8.42623 −0.331014
\(649\) −5.60314 −0.219942
\(650\) 11.4010 0.447183
\(651\) 0.531600 0.0208350
\(652\) 2.88088 0.112824
\(653\) −24.5466 −0.960585 −0.480292 0.877109i \(-0.659469\pi\)
−0.480292 + 0.877109i \(0.659469\pi\)
\(654\) −2.46227 −0.0962824
\(655\) −6.70578 −0.262017
\(656\) 6.01318 0.234775
\(657\) 5.21196 0.203338
\(658\) −14.6957 −0.572897
\(659\) 5.45628 0.212547 0.106273 0.994337i \(-0.466108\pi\)
0.106273 + 0.994337i \(0.466108\pi\)
\(660\) 0.0809839 0.00315229
\(661\) −11.0906 −0.431373 −0.215686 0.976463i \(-0.569199\pi\)
−0.215686 + 0.976463i \(0.569199\pi\)
\(662\) −20.1711 −0.783972
\(663\) −2.06532 −0.0802105
\(664\) 6.01881 0.233575
\(665\) 1.81964 0.0705624
\(666\) 15.5346 0.601953
\(667\) −37.4353 −1.44950
\(668\) 6.55783 0.253730
\(669\) −0.627716 −0.0242689
\(670\) −7.46736 −0.288489
\(671\) 2.99280 0.115536
\(672\) −0.531600 −0.0205069
\(673\) 36.1899 1.39502 0.697509 0.716576i \(-0.254292\pi\)
0.697509 + 0.716576i \(0.254292\pi\)
\(674\) 5.83412 0.224722
\(675\) 7.17366 0.276114
\(676\) −7.28569 −0.280219
\(677\) −19.4724 −0.748385 −0.374193 0.927351i \(-0.622080\pi\)
−0.374193 + 0.927351i \(0.622080\pi\)
\(678\) 2.05435 0.0788969
\(679\) 2.09789 0.0805096
\(680\) −1.63746 −0.0627938
\(681\) 5.39707 0.206816
\(682\) 0.665471 0.0254822
\(683\) 0.876644 0.0335438 0.0167719 0.999859i \(-0.494661\pi\)
0.0167719 + 0.999859i \(0.494661\pi\)
\(684\) 5.30224 0.202736
\(685\) −4.38790 −0.167653
\(686\) 20.1373 0.768848
\(687\) 2.62272 0.100063
\(688\) −3.79195 −0.144567
\(689\) −2.90078 −0.110511
\(690\) 0.944348 0.0359507
\(691\) −18.1992 −0.692330 −0.346165 0.938174i \(-0.612516\pi\)
−0.346165 + 0.938174i \(0.612516\pi\)
\(692\) 0.606282 0.0230474
\(693\) 4.09861 0.155693
\(694\) 22.8780 0.868437
\(695\) 0.933249 0.0354001
\(696\) 1.22242 0.0463358
\(697\) −20.5026 −0.776590
\(698\) 1.33157 0.0504006
\(699\) 1.95232 0.0738437
\(700\) −10.0056 −0.378176
\(701\) −16.3165 −0.616266 −0.308133 0.951343i \(-0.599704\pi\)
−0.308133 + 0.951343i \(0.599704\pi\)
\(702\) 3.59553 0.135704
\(703\) −9.55672 −0.360439
\(704\) −0.665471 −0.0250809
\(705\) −0.852464 −0.0321057
\(706\) 10.3020 0.387719
\(707\) 34.2116 1.28666
\(708\) 2.13356 0.0801840
\(709\) 25.1933 0.946156 0.473078 0.881021i \(-0.343143\pi\)
0.473078 + 0.881021i \(0.343143\pi\)
\(710\) −5.81519 −0.218240
\(711\) 27.8069 1.04284
\(712\) −14.3028 −0.536021
\(713\) 7.76002 0.290615
\(714\) 1.81255 0.0678328
\(715\) 0.763973 0.0285710
\(716\) −7.22701 −0.270086
\(717\) 2.75155 0.102759
\(718\) 2.16605 0.0808361
\(719\) −49.1968 −1.83473 −0.917366 0.398044i \(-0.869689\pi\)
−0.917366 + 0.398044i \(0.869689\pi\)
\(720\) 1.40991 0.0525443
\(721\) −8.93617 −0.332800
\(722\) 15.7381 0.585712
\(723\) 5.19321 0.193138
\(724\) −22.3379 −0.830180
\(725\) 23.0080 0.854496
\(726\) 2.67515 0.0992843
\(727\) 35.7304 1.32517 0.662584 0.748988i \(-0.269460\pi\)
0.662584 + 0.748988i \(0.269460\pi\)
\(728\) −5.01493 −0.185866
\(729\) −23.5942 −0.873860
\(730\) −0.852595 −0.0315560
\(731\) 12.9290 0.478198
\(732\) −1.13959 −0.0421206
\(733\) −13.7271 −0.507022 −0.253511 0.967333i \(-0.581585\pi\)
−0.253511 + 0.967333i \(0.581585\pi\)
\(734\) 3.83617 0.141596
\(735\) 0.316265 0.0116656
\(736\) −7.76002 −0.286038
\(737\) 10.3474 0.381150
\(738\) 17.6534 0.649832
\(739\) −41.6904 −1.53361 −0.766804 0.641881i \(-0.778154\pi\)
−0.766804 + 0.641881i \(0.778154\pi\)
\(740\) −2.54122 −0.0934170
\(741\) −1.09400 −0.0401892
\(742\) 2.54575 0.0934574
\(743\) −44.2893 −1.62482 −0.812409 0.583089i \(-0.801844\pi\)
−0.812409 + 0.583089i \(0.801844\pi\)
\(744\) −0.253397 −0.00929000
\(745\) 8.50642 0.311651
\(746\) 2.13167 0.0780460
\(747\) 17.6700 0.646510
\(748\) 2.26899 0.0829626
\(749\) −35.4089 −1.29381
\(750\) −1.18887 −0.0434115
\(751\) −35.9614 −1.31225 −0.656126 0.754652i \(-0.727806\pi\)
−0.656126 + 0.754652i \(0.727806\pi\)
\(752\) 7.00498 0.255445
\(753\) 3.82639 0.139441
\(754\) 11.5319 0.419967
\(755\) 4.74884 0.172828
\(756\) −3.15547 −0.114763
\(757\) 14.7318 0.535436 0.267718 0.963497i \(-0.413730\pi\)
0.267718 + 0.963497i \(0.413730\pi\)
\(758\) 34.3867 1.24898
\(759\) −1.30856 −0.0474978
\(760\) −0.867364 −0.0314626
\(761\) −8.87719 −0.321798 −0.160899 0.986971i \(-0.551439\pi\)
−0.160899 + 0.986971i \(0.551439\pi\)
\(762\) 3.69010 0.133678
\(763\) 20.3853 0.737996
\(764\) −17.6757 −0.639486
\(765\) −4.80724 −0.173806
\(766\) −35.0921 −1.26793
\(767\) 20.1272 0.726752
\(768\) 0.253397 0.00914369
\(769\) −7.85063 −0.283101 −0.141551 0.989931i \(-0.545209\pi\)
−0.141551 + 0.989931i \(0.545209\pi\)
\(770\) −0.670470 −0.0241620
\(771\) −4.01905 −0.144743
\(772\) −8.72407 −0.313986
\(773\) −15.4815 −0.556832 −0.278416 0.960461i \(-0.589809\pi\)
−0.278416 + 0.960461i \(0.589809\pi\)
\(774\) −11.1324 −0.400144
\(775\) −4.76936 −0.171320
\(776\) −1.00000 −0.0358979
\(777\) 2.81293 0.100913
\(778\) 25.7587 0.923495
\(779\) −10.8602 −0.389108
\(780\) −0.290905 −0.0104161
\(781\) 8.05798 0.288337
\(782\) 26.4586 0.946157
\(783\) 7.25604 0.259310
\(784\) −2.59886 −0.0928163
\(785\) 4.01371 0.143255
\(786\) −3.53822 −0.126204
\(787\) 22.0604 0.786367 0.393184 0.919460i \(-0.371374\pi\)
0.393184 + 0.919460i \(0.371374\pi\)
\(788\) −5.40889 −0.192684
\(789\) −5.01494 −0.178537
\(790\) −4.54878 −0.161838
\(791\) −17.0081 −0.604738
\(792\) −1.95368 −0.0694211
\(793\) −10.7505 −0.381763
\(794\) −5.10599 −0.181205
\(795\) 0.147673 0.00523743
\(796\) −27.9355 −0.990147
\(797\) −8.38083 −0.296864 −0.148432 0.988923i \(-0.547423\pi\)
−0.148432 + 0.988923i \(0.547423\pi\)
\(798\) 0.960107 0.0339874
\(799\) −23.8842 −0.844962
\(800\) 4.76936 0.168622
\(801\) −41.9901 −1.48365
\(802\) −17.9374 −0.633391
\(803\) 1.18142 0.0416915
\(804\) −3.94006 −0.138955
\(805\) −7.81830 −0.275559
\(806\) −2.39046 −0.0842004
\(807\) 2.16682 0.0762758
\(808\) −16.3076 −0.573699
\(809\) −2.44509 −0.0859648 −0.0429824 0.999076i \(-0.513686\pi\)
−0.0429824 + 0.999076i \(0.513686\pi\)
\(810\) 4.04669 0.142186
\(811\) 21.7333 0.763158 0.381579 0.924336i \(-0.375380\pi\)
0.381579 + 0.924336i \(0.375380\pi\)
\(812\) −10.1205 −0.355160
\(813\) −4.26750 −0.149668
\(814\) 3.52130 0.123422
\(815\) −1.38354 −0.0484633
\(816\) −0.863985 −0.0302455
\(817\) 6.84852 0.239599
\(818\) −15.1426 −0.529448
\(819\) −14.7228 −0.514455
\(820\) −2.88783 −0.100847
\(821\) −52.4951 −1.83209 −0.916046 0.401073i \(-0.868638\pi\)
−0.916046 + 0.401073i \(0.868638\pi\)
\(822\) −2.31522 −0.0807525
\(823\) 16.4214 0.572412 0.286206 0.958168i \(-0.407606\pi\)
0.286206 + 0.958168i \(0.407606\pi\)
\(824\) 4.25960 0.148390
\(825\) 0.804251 0.0280004
\(826\) −17.6638 −0.614603
\(827\) 4.43183 0.154110 0.0770550 0.997027i \(-0.475448\pi\)
0.0770550 + 0.997027i \(0.475448\pi\)
\(828\) −22.7818 −0.791721
\(829\) 19.0009 0.659930 0.329965 0.943993i \(-0.392963\pi\)
0.329965 + 0.943993i \(0.392963\pi\)
\(830\) −2.89053 −0.100332
\(831\) −0.598414 −0.0207587
\(832\) 2.39046 0.0828744
\(833\) 8.86107 0.307018
\(834\) 0.492416 0.0170510
\(835\) −3.14939 −0.108989
\(836\) 1.20189 0.0415681
\(837\) −1.50411 −0.0519898
\(838\) 38.8018 1.34039
\(839\) 10.0355 0.346464 0.173232 0.984881i \(-0.444579\pi\)
0.173232 + 0.984881i \(0.444579\pi\)
\(840\) 0.255301 0.00880871
\(841\) −5.72779 −0.197510
\(842\) −35.1430 −1.21111
\(843\) 0.0879167 0.00302801
\(844\) 19.7703 0.680522
\(845\) 3.49895 0.120368
\(846\) 20.5651 0.707044
\(847\) −22.1477 −0.761005
\(848\) −1.21348 −0.0416711
\(849\) 4.42993 0.152035
\(850\) −16.2616 −0.557769
\(851\) 41.0617 1.40758
\(852\) −3.06831 −0.105119
\(853\) 33.5645 1.14923 0.574613 0.818425i \(-0.305152\pi\)
0.574613 + 0.818425i \(0.305152\pi\)
\(854\) 9.43476 0.322851
\(855\) −2.54640 −0.0870850
\(856\) 16.8783 0.576889
\(857\) −18.1898 −0.621353 −0.310677 0.950516i \(-0.600556\pi\)
−0.310677 + 0.950516i \(0.600556\pi\)
\(858\) 0.403100 0.0137616
\(859\) −35.0211 −1.19491 −0.597453 0.801904i \(-0.703820\pi\)
−0.597453 + 0.801904i \(0.703820\pi\)
\(860\) 1.82108 0.0620984
\(861\) 3.19661 0.108940
\(862\) 6.10231 0.207845
\(863\) 50.2598 1.71086 0.855432 0.517916i \(-0.173292\pi\)
0.855432 + 0.517916i \(0.173292\pi\)
\(864\) 1.50411 0.0511710
\(865\) −0.291167 −0.00989997
\(866\) 6.73716 0.228938
\(867\) −1.36191 −0.0462529
\(868\) 2.09789 0.0712070
\(869\) 6.30314 0.213819
\(870\) −0.587068 −0.0199035
\(871\) −37.1691 −1.25943
\(872\) −9.71703 −0.329060
\(873\) −2.93579 −0.0993614
\(874\) 14.0151 0.474069
\(875\) 9.84274 0.332745
\(876\) −0.449861 −0.0151994
\(877\) 15.5589 0.525385 0.262693 0.964880i \(-0.415390\pi\)
0.262693 + 0.964880i \(0.415390\pi\)
\(878\) −25.4609 −0.859263
\(879\) −3.99558 −0.134768
\(880\) 0.319592 0.0107735
\(881\) 50.7898 1.71115 0.855576 0.517678i \(-0.173203\pi\)
0.855576 + 0.517678i \(0.173203\pi\)
\(882\) −7.62969 −0.256905
\(883\) −7.29434 −0.245474 −0.122737 0.992439i \(-0.539167\pi\)
−0.122737 + 0.992439i \(0.539167\pi\)
\(884\) −8.15053 −0.274132
\(885\) −1.02464 −0.0344429
\(886\) 6.20495 0.208459
\(887\) 21.1724 0.710898 0.355449 0.934696i \(-0.384328\pi\)
0.355449 + 0.934696i \(0.384328\pi\)
\(888\) −1.34084 −0.0449956
\(889\) −30.5505 −1.02463
\(890\) 6.86893 0.230247
\(891\) −5.60741 −0.187855
\(892\) −2.47720 −0.0829428
\(893\) −12.6515 −0.423366
\(894\) 4.48830 0.150111
\(895\) 3.47077 0.116015
\(896\) −2.09789 −0.0700856
\(897\) 4.70053 0.156946
\(898\) 0.0172868 0.000576869 0
\(899\) −4.82413 −0.160894
\(900\) 14.0018 0.466728
\(901\) 4.13749 0.137840
\(902\) 4.00160 0.133239
\(903\) −2.01580 −0.0670816
\(904\) 8.10723 0.269642
\(905\) 10.7277 0.356602
\(906\) 2.50566 0.0832451
\(907\) 36.1105 1.19903 0.599515 0.800364i \(-0.295360\pi\)
0.599515 + 0.800364i \(0.295360\pi\)
\(908\) 21.2988 0.706827
\(909\) −47.8757 −1.58794
\(910\) 2.40842 0.0798383
\(911\) 29.2671 0.969663 0.484831 0.874608i \(-0.338881\pi\)
0.484831 + 0.874608i \(0.338881\pi\)
\(912\) −0.457653 −0.0151544
\(913\) 4.00534 0.132558
\(914\) 16.3152 0.539658
\(915\) 0.547290 0.0180928
\(916\) 10.3502 0.341981
\(917\) 29.2931 0.967343
\(918\) −5.12843 −0.169264
\(919\) 5.14714 0.169788 0.0848942 0.996390i \(-0.472945\pi\)
0.0848942 + 0.996390i \(0.472945\pi\)
\(920\) 3.72675 0.122867
\(921\) −2.25385 −0.0742670
\(922\) 2.90217 0.0955778
\(923\) −28.9454 −0.952748
\(924\) −0.353764 −0.0116380
\(925\) −25.2368 −0.829781
\(926\) −3.78789 −0.124478
\(927\) 12.5053 0.410727
\(928\) 4.82413 0.158360
\(929\) −15.8998 −0.521657 −0.260828 0.965385i \(-0.583996\pi\)
−0.260828 + 0.965385i \(0.583996\pi\)
\(930\) 0.121694 0.00399050
\(931\) 4.69371 0.153830
\(932\) 7.70459 0.252372
\(933\) 5.63575 0.184506
\(934\) 22.2445 0.727861
\(935\) −1.08968 −0.0356365
\(936\) 7.01789 0.229387
\(937\) −5.73068 −0.187213 −0.0936065 0.995609i \(-0.529840\pi\)
−0.0936065 + 0.995609i \(0.529840\pi\)
\(938\) 32.6199 1.06508
\(939\) −5.01468 −0.163648
\(940\) −3.36414 −0.109726
\(941\) −30.8897 −1.00698 −0.503488 0.864002i \(-0.667950\pi\)
−0.503488 + 0.864002i \(0.667950\pi\)
\(942\) 2.11778 0.0690010
\(943\) 46.6624 1.51954
\(944\) 8.41980 0.274041
\(945\) 1.51541 0.0492963
\(946\) −2.52343 −0.0820438
\(947\) 26.5130 0.861556 0.430778 0.902458i \(-0.358239\pi\)
0.430778 + 0.902458i \(0.358239\pi\)
\(948\) −2.40010 −0.0779517
\(949\) −4.24383 −0.137760
\(950\) −8.61380 −0.279468
\(951\) −5.92052 −0.191986
\(952\) 7.15298 0.231829
\(953\) 3.93794 0.127562 0.0637811 0.997964i \(-0.479684\pi\)
0.0637811 + 0.997964i \(0.479684\pi\)
\(954\) −3.56252 −0.115341
\(955\) 8.48877 0.274690
\(956\) 10.8586 0.351193
\(957\) 0.813486 0.0262963
\(958\) −0.457308 −0.0147750
\(959\) 19.1678 0.618961
\(960\) −0.121694 −0.00392766
\(961\) 1.00000 0.0322581
\(962\) −12.6490 −0.407820
\(963\) 49.5512 1.59676
\(964\) 20.4943 0.660078
\(965\) 4.18973 0.134872
\(966\) −4.12522 −0.132727
\(967\) −14.8872 −0.478740 −0.239370 0.970928i \(-0.576941\pi\)
−0.239370 + 0.970928i \(0.576941\pi\)
\(968\) 10.5571 0.339320
\(969\) 1.56042 0.0501278
\(970\) 0.480250 0.0154199
\(971\) −23.2297 −0.745477 −0.372738 0.927937i \(-0.621581\pi\)
−0.372738 + 0.927937i \(0.621581\pi\)
\(972\) 6.64753 0.213220
\(973\) −4.07674 −0.130694
\(974\) 35.1270 1.12554
\(975\) −2.88898 −0.0925213
\(976\) −4.49726 −0.143954
\(977\) 48.2004 1.54207 0.771034 0.636794i \(-0.219740\pi\)
0.771034 + 0.636794i \(0.219740\pi\)
\(978\) −0.730007 −0.0233430
\(979\) −9.51812 −0.304200
\(980\) 1.24810 0.0398691
\(981\) −28.5272 −0.910802
\(982\) 17.4311 0.556248
\(983\) 1.76035 0.0561463 0.0280731 0.999606i \(-0.491063\pi\)
0.0280731 + 0.999606i \(0.491063\pi\)
\(984\) −1.52372 −0.0485745
\(985\) 2.59762 0.0827671
\(986\) −16.4484 −0.523823
\(987\) 3.72385 0.118531
\(988\) −4.31734 −0.137353
\(989\) −29.4256 −0.935679
\(990\) 0.938256 0.0298197
\(991\) −32.4972 −1.03231 −0.516153 0.856496i \(-0.672636\pi\)
−0.516153 + 0.856496i \(0.672636\pi\)
\(992\) −1.00000 −0.0317500
\(993\) 5.11131 0.162202
\(994\) 25.4027 0.805725
\(995\) 13.4160 0.425316
\(996\) −1.52515 −0.0483263
\(997\) −14.5994 −0.462367 −0.231183 0.972910i \(-0.574260\pi\)
−0.231183 + 0.972910i \(0.574260\pi\)
\(998\) −10.6225 −0.336249
\(999\) −7.95894 −0.251810
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 6014.2.a.f.1.13 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.f.1.13 22 1.1 even 1 trivial