Properties

Label 6026.2.a.k.1.3
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $35$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, 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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(0\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.00053 q^{3} +1.00000 q^{4} +0.314170 q^{5} -3.00053 q^{6} +4.93238 q^{7} +1.00000 q^{8} +6.00320 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.00053 q^{3} +1.00000 q^{4} +0.314170 q^{5} -3.00053 q^{6} +4.93238 q^{7} +1.00000 q^{8} +6.00320 q^{9} +0.314170 q^{10} -4.16150 q^{11} -3.00053 q^{12} -1.93550 q^{13} +4.93238 q^{14} -0.942677 q^{15} +1.00000 q^{16} +1.79693 q^{17} +6.00320 q^{18} -5.17013 q^{19} +0.314170 q^{20} -14.7998 q^{21} -4.16150 q^{22} -1.00000 q^{23} -3.00053 q^{24} -4.90130 q^{25} -1.93550 q^{26} -9.01121 q^{27} +4.93238 q^{28} +9.74496 q^{29} -0.942677 q^{30} +8.61617 q^{31} +1.00000 q^{32} +12.4867 q^{33} +1.79693 q^{34} +1.54961 q^{35} +6.00320 q^{36} -7.02254 q^{37} -5.17013 q^{38} +5.80753 q^{39} +0.314170 q^{40} +9.99012 q^{41} -14.7998 q^{42} +0.705049 q^{43} -4.16150 q^{44} +1.88602 q^{45} -1.00000 q^{46} -8.83462 q^{47} -3.00053 q^{48} +17.3284 q^{49} -4.90130 q^{50} -5.39176 q^{51} -1.93550 q^{52} +6.57792 q^{53} -9.01121 q^{54} -1.30742 q^{55} +4.93238 q^{56} +15.5132 q^{57} +9.74496 q^{58} -4.34637 q^{59} -0.942677 q^{60} +11.3584 q^{61} +8.61617 q^{62} +29.6101 q^{63} +1.00000 q^{64} -0.608075 q^{65} +12.4867 q^{66} +7.77156 q^{67} +1.79693 q^{68} +3.00053 q^{69} +1.54961 q^{70} +11.1666 q^{71} +6.00320 q^{72} -0.0201871 q^{73} -7.02254 q^{74} +14.7065 q^{75} -5.17013 q^{76} -20.5261 q^{77} +5.80753 q^{78} -5.21096 q^{79} +0.314170 q^{80} +9.02883 q^{81} +9.99012 q^{82} -6.48736 q^{83} -14.7998 q^{84} +0.564542 q^{85} +0.705049 q^{86} -29.2401 q^{87} -4.16150 q^{88} -15.7254 q^{89} +1.88602 q^{90} -9.54662 q^{91} -1.00000 q^{92} -25.8531 q^{93} -8.83462 q^{94} -1.62430 q^{95} -3.00053 q^{96} -8.96911 q^{97} +17.3284 q^{98} -24.9823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 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
\(3\) −3.00053 −1.73236 −0.866179 0.499733i \(-0.833431\pi\)
−0.866179 + 0.499733i \(0.833431\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.314170 0.140501 0.0702505 0.997529i \(-0.477620\pi\)
0.0702505 + 0.997529i \(0.477620\pi\)
\(6\) −3.00053 −1.22496
\(7\) 4.93238 1.86427 0.932133 0.362117i \(-0.117946\pi\)
0.932133 + 0.362117i \(0.117946\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.00320 2.00107
\(10\) 0.314170 0.0993492
\(11\) −4.16150 −1.25474 −0.627370 0.778721i \(-0.715869\pi\)
−0.627370 + 0.778721i \(0.715869\pi\)
\(12\) −3.00053 −0.866179
\(13\) −1.93550 −0.536811 −0.268406 0.963306i \(-0.586497\pi\)
−0.268406 + 0.963306i \(0.586497\pi\)
\(14\) 4.93238 1.31823
\(15\) −0.942677 −0.243398
\(16\) 1.00000 0.250000
\(17\) 1.79693 0.435821 0.217910 0.975969i \(-0.430076\pi\)
0.217910 + 0.975969i \(0.430076\pi\)
\(18\) 6.00320 1.41497
\(19\) −5.17013 −1.18611 −0.593055 0.805162i \(-0.702078\pi\)
−0.593055 + 0.805162i \(0.702078\pi\)
\(20\) 0.314170 0.0702505
\(21\) −14.7998 −3.22958
\(22\) −4.16150 −0.887235
\(23\) −1.00000 −0.208514
\(24\) −3.00053 −0.612481
\(25\) −4.90130 −0.980259
\(26\) −1.93550 −0.379583
\(27\) −9.01121 −1.73421
\(28\) 4.93238 0.932133
\(29\) 9.74496 1.80959 0.904797 0.425843i \(-0.140022\pi\)
0.904797 + 0.425843i \(0.140022\pi\)
\(30\) −0.942677 −0.172108
\(31\) 8.61617 1.54751 0.773755 0.633485i \(-0.218376\pi\)
0.773755 + 0.633485i \(0.218376\pi\)
\(32\) 1.00000 0.176777
\(33\) 12.4867 2.17366
\(34\) 1.79693 0.308172
\(35\) 1.54961 0.261931
\(36\) 6.00320 1.00053
\(37\) −7.02254 −1.15450 −0.577249 0.816568i \(-0.695874\pi\)
−0.577249 + 0.816568i \(0.695874\pi\)
\(38\) −5.17013 −0.838706
\(39\) 5.80753 0.929949
\(40\) 0.314170 0.0496746
\(41\) 9.99012 1.56019 0.780097 0.625658i \(-0.215170\pi\)
0.780097 + 0.625658i \(0.215170\pi\)
\(42\) −14.7998 −2.28366
\(43\) 0.705049 0.107519 0.0537595 0.998554i \(-0.482880\pi\)
0.0537595 + 0.998554i \(0.482880\pi\)
\(44\) −4.16150 −0.627370
\(45\) 1.88602 0.281152
\(46\) −1.00000 −0.147442
\(47\) −8.83462 −1.28866 −0.644331 0.764747i \(-0.722864\pi\)
−0.644331 + 0.764747i \(0.722864\pi\)
\(48\) −3.00053 −0.433090
\(49\) 17.3284 2.47548
\(50\) −4.90130 −0.693148
\(51\) −5.39176 −0.754998
\(52\) −1.93550 −0.268406
\(53\) 6.57792 0.903547 0.451774 0.892133i \(-0.350791\pi\)
0.451774 + 0.892133i \(0.350791\pi\)
\(54\) −9.01121 −1.22627
\(55\) −1.30742 −0.176292
\(56\) 4.93238 0.659117
\(57\) 15.5132 2.05477
\(58\) 9.74496 1.27958
\(59\) −4.34637 −0.565849 −0.282924 0.959142i \(-0.591305\pi\)
−0.282924 + 0.959142i \(0.591305\pi\)
\(60\) −0.942677 −0.121699
\(61\) 11.3584 1.45429 0.727145 0.686484i \(-0.240847\pi\)
0.727145 + 0.686484i \(0.240847\pi\)
\(62\) 8.61617 1.09425
\(63\) 29.6101 3.73052
\(64\) 1.00000 0.125000
\(65\) −0.608075 −0.0754225
\(66\) 12.4867 1.53701
\(67\) 7.77156 0.949447 0.474724 0.880135i \(-0.342548\pi\)
0.474724 + 0.880135i \(0.342548\pi\)
\(68\) 1.79693 0.217910
\(69\) 3.00053 0.361222
\(70\) 1.54961 0.185213
\(71\) 11.1666 1.32523 0.662614 0.748961i \(-0.269447\pi\)
0.662614 + 0.748961i \(0.269447\pi\)
\(72\) 6.00320 0.707484
\(73\) −0.0201871 −0.00236272 −0.00118136 0.999999i \(-0.500376\pi\)
−0.00118136 + 0.999999i \(0.500376\pi\)
\(74\) −7.02254 −0.816354
\(75\) 14.7065 1.69816
\(76\) −5.17013 −0.593055
\(77\) −20.5261 −2.33917
\(78\) 5.80753 0.657573
\(79\) −5.21096 −0.586279 −0.293140 0.956070i \(-0.594700\pi\)
−0.293140 + 0.956070i \(0.594700\pi\)
\(80\) 0.314170 0.0351252
\(81\) 9.02883 1.00320
\(82\) 9.99012 1.10322
\(83\) −6.48736 −0.712080 −0.356040 0.934471i \(-0.615873\pi\)
−0.356040 + 0.934471i \(0.615873\pi\)
\(84\) −14.7998 −1.61479
\(85\) 0.564542 0.0612332
\(86\) 0.705049 0.0760274
\(87\) −29.2401 −3.13487
\(88\) −4.16150 −0.443618
\(89\) −15.7254 −1.66689 −0.833446 0.552602i \(-0.813635\pi\)
−0.833446 + 0.552602i \(0.813635\pi\)
\(90\) 1.88602 0.198804
\(91\) −9.54662 −1.00076
\(92\) −1.00000 −0.104257
\(93\) −25.8531 −2.68084
\(94\) −8.83462 −0.911221
\(95\) −1.62430 −0.166650
\(96\) −3.00053 −0.306241
\(97\) −8.96911 −0.910676 −0.455338 0.890319i \(-0.650482\pi\)
−0.455338 + 0.890319i \(0.650482\pi\)
\(98\) 17.3284 1.75043
\(99\) −24.9823 −2.51082
\(100\) −4.90130 −0.490130
\(101\) −9.00489 −0.896020 −0.448010 0.894028i \(-0.647867\pi\)
−0.448010 + 0.894028i \(0.647867\pi\)
\(102\) −5.39176 −0.533864
\(103\) 4.91339 0.484131 0.242065 0.970260i \(-0.422175\pi\)
0.242065 + 0.970260i \(0.422175\pi\)
\(104\) −1.93550 −0.189791
\(105\) −4.64964 −0.453759
\(106\) 6.57792 0.638904
\(107\) −9.34277 −0.903199 −0.451600 0.892221i \(-0.649146\pi\)
−0.451600 + 0.892221i \(0.649146\pi\)
\(108\) −9.01121 −0.867104
\(109\) 6.22155 0.595916 0.297958 0.954579i \(-0.403694\pi\)
0.297958 + 0.954579i \(0.403694\pi\)
\(110\) −1.30742 −0.124657
\(111\) 21.0714 2.00001
\(112\) 4.93238 0.466066
\(113\) 13.2512 1.24657 0.623285 0.781995i \(-0.285798\pi\)
0.623285 + 0.781995i \(0.285798\pi\)
\(114\) 15.5132 1.45294
\(115\) −0.314170 −0.0292965
\(116\) 9.74496 0.904797
\(117\) −11.6192 −1.07419
\(118\) −4.34637 −0.400116
\(119\) 8.86317 0.812485
\(120\) −0.942677 −0.0860542
\(121\) 6.31810 0.574372
\(122\) 11.3584 1.02834
\(123\) −29.9757 −2.70282
\(124\) 8.61617 0.773755
\(125\) −3.11069 −0.278228
\(126\) 29.6101 2.63788
\(127\) −2.24838 −0.199511 −0.0997556 0.995012i \(-0.531806\pi\)
−0.0997556 + 0.995012i \(0.531806\pi\)
\(128\) 1.00000 0.0883883
\(129\) −2.11552 −0.186261
\(130\) −0.608075 −0.0533317
\(131\) −1.00000 −0.0873704
\(132\) 12.4867 1.08683
\(133\) −25.5011 −2.21122
\(134\) 7.77156 0.671360
\(135\) −2.83105 −0.243658
\(136\) 1.79693 0.154086
\(137\) 18.1753 1.55282 0.776410 0.630229i \(-0.217039\pi\)
0.776410 + 0.630229i \(0.217039\pi\)
\(138\) 3.00053 0.255422
\(139\) 7.42145 0.629479 0.314740 0.949178i \(-0.398083\pi\)
0.314740 + 0.949178i \(0.398083\pi\)
\(140\) 1.54961 0.130966
\(141\) 26.5086 2.23242
\(142\) 11.1666 0.937078
\(143\) 8.05458 0.673558
\(144\) 6.00320 0.500267
\(145\) 3.06157 0.254250
\(146\) −0.0201871 −0.00167070
\(147\) −51.9944 −4.28843
\(148\) −7.02254 −0.577249
\(149\) 9.37455 0.767993 0.383996 0.923335i \(-0.374547\pi\)
0.383996 + 0.923335i \(0.374547\pi\)
\(150\) 14.7065 1.20078
\(151\) 17.5647 1.42939 0.714696 0.699435i \(-0.246565\pi\)
0.714696 + 0.699435i \(0.246565\pi\)
\(152\) −5.17013 −0.419353
\(153\) 10.7874 0.872106
\(154\) −20.5261 −1.65404
\(155\) 2.70694 0.217427
\(156\) 5.80753 0.464975
\(157\) 4.75328 0.379353 0.189677 0.981847i \(-0.439256\pi\)
0.189677 + 0.981847i \(0.439256\pi\)
\(158\) −5.21096 −0.414562
\(159\) −19.7373 −1.56527
\(160\) 0.314170 0.0248373
\(161\) −4.93238 −0.388726
\(162\) 9.02883 0.709372
\(163\) 8.85627 0.693677 0.346838 0.937925i \(-0.387255\pi\)
0.346838 + 0.937925i \(0.387255\pi\)
\(164\) 9.99012 0.780097
\(165\) 3.92295 0.305401
\(166\) −6.48736 −0.503517
\(167\) −1.50641 −0.116570 −0.0582849 0.998300i \(-0.518563\pi\)
−0.0582849 + 0.998300i \(0.518563\pi\)
\(168\) −14.7998 −1.14183
\(169\) −9.25384 −0.711834
\(170\) 0.564542 0.0432984
\(171\) −31.0374 −2.37349
\(172\) 0.705049 0.0537595
\(173\) 17.2365 1.31046 0.655232 0.755428i \(-0.272571\pi\)
0.655232 + 0.755428i \(0.272571\pi\)
\(174\) −29.2401 −2.21669
\(175\) −24.1751 −1.82746
\(176\) −4.16150 −0.313685
\(177\) 13.0414 0.980253
\(178\) −15.7254 −1.17867
\(179\) 10.1320 0.757300 0.378650 0.925540i \(-0.376388\pi\)
0.378650 + 0.925540i \(0.376388\pi\)
\(180\) 1.88602 0.140576
\(181\) 11.6145 0.863301 0.431650 0.902041i \(-0.357931\pi\)
0.431650 + 0.902041i \(0.357931\pi\)
\(182\) −9.54662 −0.707643
\(183\) −34.0812 −2.51935
\(184\) −1.00000 −0.0737210
\(185\) −2.20627 −0.162208
\(186\) −25.8531 −1.89564
\(187\) −7.47795 −0.546842
\(188\) −8.83462 −0.644331
\(189\) −44.4467 −3.23302
\(190\) −1.62430 −0.117839
\(191\) 19.4031 1.40396 0.701980 0.712197i \(-0.252300\pi\)
0.701980 + 0.712197i \(0.252300\pi\)
\(192\) −3.00053 −0.216545
\(193\) −10.0929 −0.726500 −0.363250 0.931692i \(-0.618333\pi\)
−0.363250 + 0.931692i \(0.618333\pi\)
\(194\) −8.96911 −0.643945
\(195\) 1.82455 0.130659
\(196\) 17.3284 1.23774
\(197\) −11.9015 −0.847947 −0.423973 0.905675i \(-0.639365\pi\)
−0.423973 + 0.905675i \(0.639365\pi\)
\(198\) −24.9823 −1.77542
\(199\) 26.5625 1.88296 0.941482 0.337064i \(-0.109434\pi\)
0.941482 + 0.337064i \(0.109434\pi\)
\(200\) −4.90130 −0.346574
\(201\) −23.3188 −1.64478
\(202\) −9.00489 −0.633582
\(203\) 48.0659 3.37356
\(204\) −5.39176 −0.377499
\(205\) 3.13859 0.219209
\(206\) 4.91339 0.342332
\(207\) −6.00320 −0.417251
\(208\) −1.93550 −0.134203
\(209\) 21.5155 1.48826
\(210\) −4.64964 −0.320856
\(211\) −4.70357 −0.323807 −0.161903 0.986807i \(-0.551763\pi\)
−0.161903 + 0.986807i \(0.551763\pi\)
\(212\) 6.57792 0.451774
\(213\) −33.5057 −2.29577
\(214\) −9.34277 −0.638658
\(215\) 0.221505 0.0151065
\(216\) −9.01121 −0.613135
\(217\) 42.4982 2.88497
\(218\) 6.22155 0.421376
\(219\) 0.0605720 0.00409308
\(220\) −1.30742 −0.0881461
\(221\) −3.47797 −0.233953
\(222\) 21.0714 1.41422
\(223\) −0.764752 −0.0512116 −0.0256058 0.999672i \(-0.508151\pi\)
−0.0256058 + 0.999672i \(0.508151\pi\)
\(224\) 4.93238 0.329559
\(225\) −29.4235 −1.96157
\(226\) 13.2512 0.881458
\(227\) 10.6832 0.709067 0.354533 0.935043i \(-0.384640\pi\)
0.354533 + 0.935043i \(0.384640\pi\)
\(228\) 15.5132 1.02738
\(229\) −9.67384 −0.639266 −0.319633 0.947541i \(-0.603560\pi\)
−0.319633 + 0.947541i \(0.603560\pi\)
\(230\) −0.314170 −0.0207157
\(231\) 61.5893 4.05228
\(232\) 9.74496 0.639788
\(233\) 25.2416 1.65363 0.826817 0.562471i \(-0.190149\pi\)
0.826817 + 0.562471i \(0.190149\pi\)
\(234\) −11.6192 −0.759571
\(235\) −2.77557 −0.181058
\(236\) −4.34637 −0.282924
\(237\) 15.6357 1.01565
\(238\) 8.86317 0.574514
\(239\) −29.9284 −1.93591 −0.967954 0.251127i \(-0.919199\pi\)
−0.967954 + 0.251127i \(0.919199\pi\)
\(240\) −0.942677 −0.0608495
\(241\) 20.0936 1.29434 0.647171 0.762345i \(-0.275952\pi\)
0.647171 + 0.762345i \(0.275952\pi\)
\(242\) 6.31810 0.406143
\(243\) −0.0576743 −0.00369981
\(244\) 11.3584 0.727145
\(245\) 5.44406 0.347808
\(246\) −29.9757 −1.91118
\(247\) 10.0068 0.636717
\(248\) 8.61617 0.547127
\(249\) 19.4655 1.23358
\(250\) −3.11069 −0.196737
\(251\) −11.2929 −0.712800 −0.356400 0.934333i \(-0.615996\pi\)
−0.356400 + 0.934333i \(0.615996\pi\)
\(252\) 29.6101 1.86526
\(253\) 4.16150 0.261631
\(254\) −2.24838 −0.141076
\(255\) −1.69393 −0.106078
\(256\) 1.00000 0.0625000
\(257\) −5.05499 −0.315322 −0.157661 0.987493i \(-0.550395\pi\)
−0.157661 + 0.987493i \(0.550395\pi\)
\(258\) −2.11552 −0.131707
\(259\) −34.6379 −2.15229
\(260\) −0.608075 −0.0377112
\(261\) 58.5010 3.62112
\(262\) −1.00000 −0.0617802
\(263\) 2.88557 0.177932 0.0889660 0.996035i \(-0.471644\pi\)
0.0889660 + 0.996035i \(0.471644\pi\)
\(264\) 12.4867 0.768505
\(265\) 2.06659 0.126949
\(266\) −25.5011 −1.56357
\(267\) 47.1846 2.88765
\(268\) 7.77156 0.474724
\(269\) −15.1497 −0.923694 −0.461847 0.886960i \(-0.652813\pi\)
−0.461847 + 0.886960i \(0.652813\pi\)
\(270\) −2.83105 −0.172292
\(271\) 26.2016 1.59164 0.795818 0.605536i \(-0.207041\pi\)
0.795818 + 0.605536i \(0.207041\pi\)
\(272\) 1.79693 0.108955
\(273\) 28.6450 1.73367
\(274\) 18.1753 1.09801
\(275\) 20.3968 1.22997
\(276\) 3.00053 0.180611
\(277\) 19.3416 1.16212 0.581062 0.813859i \(-0.302637\pi\)
0.581062 + 0.813859i \(0.302637\pi\)
\(278\) 7.42145 0.445109
\(279\) 51.7246 3.09667
\(280\) 1.54961 0.0926066
\(281\) −11.4555 −0.683375 −0.341688 0.939814i \(-0.610999\pi\)
−0.341688 + 0.939814i \(0.610999\pi\)
\(282\) 26.5086 1.57856
\(283\) 4.55522 0.270780 0.135390 0.990792i \(-0.456771\pi\)
0.135390 + 0.990792i \(0.456771\pi\)
\(284\) 11.1666 0.662614
\(285\) 4.87377 0.288697
\(286\) 8.05458 0.476278
\(287\) 49.2751 2.90862
\(288\) 6.00320 0.353742
\(289\) −13.7710 −0.810060
\(290\) 3.06157 0.179782
\(291\) 26.9121 1.57762
\(292\) −0.0201871 −0.00118136
\(293\) −0.857587 −0.0501008 −0.0250504 0.999686i \(-0.507975\pi\)
−0.0250504 + 0.999686i \(0.507975\pi\)
\(294\) −51.9944 −3.03238
\(295\) −1.36550 −0.0795023
\(296\) −7.02254 −0.408177
\(297\) 37.5002 2.17598
\(298\) 9.37455 0.543053
\(299\) 1.93550 0.111933
\(300\) 14.7065 0.849081
\(301\) 3.47757 0.200444
\(302\) 17.5647 1.01073
\(303\) 27.0195 1.55223
\(304\) −5.17013 −0.296527
\(305\) 3.56846 0.204329
\(306\) 10.7874 0.616672
\(307\) −16.2855 −0.929462 −0.464731 0.885452i \(-0.653849\pi\)
−0.464731 + 0.885452i \(0.653849\pi\)
\(308\) −20.5261 −1.16958
\(309\) −14.7428 −0.838688
\(310\) 2.70694 0.153744
\(311\) −30.7046 −1.74110 −0.870549 0.492082i \(-0.836236\pi\)
−0.870549 + 0.492082i \(0.836236\pi\)
\(312\) 5.80753 0.328787
\(313\) 11.7299 0.663012 0.331506 0.943453i \(-0.392443\pi\)
0.331506 + 0.943453i \(0.392443\pi\)
\(314\) 4.75328 0.268243
\(315\) 9.30259 0.524142
\(316\) −5.21096 −0.293140
\(317\) 14.7336 0.827521 0.413760 0.910386i \(-0.364215\pi\)
0.413760 + 0.910386i \(0.364215\pi\)
\(318\) −19.7373 −1.10681
\(319\) −40.5537 −2.27057
\(320\) 0.314170 0.0175626
\(321\) 28.0333 1.56467
\(322\) −4.93238 −0.274871
\(323\) −9.29039 −0.516931
\(324\) 9.02883 0.501601
\(325\) 9.48646 0.526214
\(326\) 8.85627 0.490503
\(327\) −18.6680 −1.03234
\(328\) 9.99012 0.551612
\(329\) −43.5757 −2.40241
\(330\) 3.92295 0.215951
\(331\) −36.0263 −1.98019 −0.990093 0.140411i \(-0.955158\pi\)
−0.990093 + 0.140411i \(0.955158\pi\)
\(332\) −6.48736 −0.356040
\(333\) −42.1577 −2.31023
\(334\) −1.50641 −0.0824273
\(335\) 2.44159 0.133398
\(336\) −14.7998 −0.807394
\(337\) −0.0730258 −0.00397797 −0.00198899 0.999998i \(-0.500633\pi\)
−0.00198899 + 0.999998i \(0.500633\pi\)
\(338\) −9.25384 −0.503343
\(339\) −39.7607 −2.15951
\(340\) 0.564542 0.0306166
\(341\) −35.8562 −1.94172
\(342\) −31.0374 −1.67831
\(343\) 50.9436 2.75069
\(344\) 0.705049 0.0380137
\(345\) 0.942677 0.0507520
\(346\) 17.2365 0.926638
\(347\) −0.713534 −0.0383045 −0.0191523 0.999817i \(-0.506097\pi\)
−0.0191523 + 0.999817i \(0.506097\pi\)
\(348\) −29.2401 −1.56743
\(349\) 18.5075 0.990685 0.495342 0.868698i \(-0.335043\pi\)
0.495342 + 0.868698i \(0.335043\pi\)
\(350\) −24.1751 −1.29221
\(351\) 17.4412 0.930942
\(352\) −4.16150 −0.221809
\(353\) 7.32508 0.389875 0.194937 0.980816i \(-0.437550\pi\)
0.194937 + 0.980816i \(0.437550\pi\)
\(354\) 13.0414 0.693144
\(355\) 3.50820 0.186196
\(356\) −15.7254 −0.833446
\(357\) −26.5942 −1.40752
\(358\) 10.1320 0.535492
\(359\) 30.1278 1.59009 0.795043 0.606553i \(-0.207448\pi\)
0.795043 + 0.606553i \(0.207448\pi\)
\(360\) 1.88602 0.0994022
\(361\) 7.73027 0.406856
\(362\) 11.6145 0.610446
\(363\) −18.9577 −0.995019
\(364\) −9.54662 −0.500379
\(365\) −0.00634217 −0.000331964 0
\(366\) −34.0812 −1.78145
\(367\) 0.606595 0.0316640 0.0158320 0.999875i \(-0.494960\pi\)
0.0158320 + 0.999875i \(0.494960\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 59.9727 3.12205
\(370\) −2.20627 −0.114699
\(371\) 32.4448 1.68445
\(372\) −25.8531 −1.34042
\(373\) 19.2257 0.995468 0.497734 0.867330i \(-0.334166\pi\)
0.497734 + 0.867330i \(0.334166\pi\)
\(374\) −7.47795 −0.386675
\(375\) 9.33373 0.481991
\(376\) −8.83462 −0.455611
\(377\) −18.8614 −0.971410
\(378\) −44.4467 −2.28609
\(379\) 18.5848 0.954638 0.477319 0.878730i \(-0.341609\pi\)
0.477319 + 0.878730i \(0.341609\pi\)
\(380\) −1.62430 −0.0833248
\(381\) 6.74633 0.345625
\(382\) 19.4031 0.992749
\(383\) −31.7040 −1.62000 −0.810000 0.586430i \(-0.800533\pi\)
−0.810000 + 0.586430i \(0.800533\pi\)
\(384\) −3.00053 −0.153120
\(385\) −6.44868 −0.328655
\(386\) −10.0929 −0.513713
\(387\) 4.23255 0.215153
\(388\) −8.96911 −0.455338
\(389\) −27.0952 −1.37378 −0.686892 0.726760i \(-0.741025\pi\)
−0.686892 + 0.726760i \(0.741025\pi\)
\(390\) 1.82455 0.0923897
\(391\) −1.79693 −0.0908749
\(392\) 17.3284 0.875216
\(393\) 3.00053 0.151357
\(394\) −11.9015 −0.599589
\(395\) −1.63713 −0.0823728
\(396\) −24.9823 −1.25541
\(397\) 30.6380 1.53768 0.768839 0.639442i \(-0.220834\pi\)
0.768839 + 0.639442i \(0.220834\pi\)
\(398\) 26.5625 1.33146
\(399\) 76.5168 3.83063
\(400\) −4.90130 −0.245065
\(401\) 14.0704 0.702644 0.351322 0.936255i \(-0.385732\pi\)
0.351322 + 0.936255i \(0.385732\pi\)
\(402\) −23.3188 −1.16304
\(403\) −16.6766 −0.830720
\(404\) −9.00489 −0.448010
\(405\) 2.83658 0.140951
\(406\) 48.0659 2.38547
\(407\) 29.2243 1.44860
\(408\) −5.39176 −0.266932
\(409\) −12.9727 −0.641459 −0.320729 0.947171i \(-0.603928\pi\)
−0.320729 + 0.947171i \(0.603928\pi\)
\(410\) 3.13859 0.155004
\(411\) −54.5355 −2.69004
\(412\) 4.91339 0.242065
\(413\) −21.4379 −1.05489
\(414\) −6.00320 −0.295041
\(415\) −2.03813 −0.100048
\(416\) −1.93550 −0.0948957
\(417\) −22.2683 −1.09048
\(418\) 21.5155 1.05236
\(419\) 14.4921 0.707983 0.353992 0.935249i \(-0.384824\pi\)
0.353992 + 0.935249i \(0.384824\pi\)
\(420\) −4.64964 −0.226879
\(421\) 31.3277 1.52682 0.763410 0.645914i \(-0.223523\pi\)
0.763410 + 0.645914i \(0.223523\pi\)
\(422\) −4.70357 −0.228966
\(423\) −53.0360 −2.57870
\(424\) 6.57792 0.319452
\(425\) −8.80731 −0.427217
\(426\) −33.5057 −1.62336
\(427\) 56.0238 2.71118
\(428\) −9.34277 −0.451600
\(429\) −24.1681 −1.16684
\(430\) 0.221505 0.0106819
\(431\) −6.53686 −0.314869 −0.157435 0.987529i \(-0.550322\pi\)
−0.157435 + 0.987529i \(0.550322\pi\)
\(432\) −9.01121 −0.433552
\(433\) 12.8219 0.616180 0.308090 0.951357i \(-0.400310\pi\)
0.308090 + 0.951357i \(0.400310\pi\)
\(434\) 42.4982 2.03998
\(435\) −9.18635 −0.440452
\(436\) 6.22155 0.297958
\(437\) 5.17013 0.247321
\(438\) 0.0605720 0.00289424
\(439\) −5.13850 −0.245247 −0.122624 0.992453i \(-0.539131\pi\)
−0.122624 + 0.992453i \(0.539131\pi\)
\(440\) −1.30742 −0.0623287
\(441\) 104.026 4.95361
\(442\) −3.47797 −0.165430
\(443\) −30.0800 −1.42915 −0.714573 0.699561i \(-0.753379\pi\)
−0.714573 + 0.699561i \(0.753379\pi\)
\(444\) 21.0714 1.00000
\(445\) −4.94045 −0.234200
\(446\) −0.764752 −0.0362121
\(447\) −28.1286 −1.33044
\(448\) 4.93238 0.233033
\(449\) −4.07936 −0.192517 −0.0962585 0.995356i \(-0.530688\pi\)
−0.0962585 + 0.995356i \(0.530688\pi\)
\(450\) −29.4235 −1.38704
\(451\) −41.5739 −1.95764
\(452\) 13.2512 0.623285
\(453\) −52.7034 −2.47622
\(454\) 10.6832 0.501386
\(455\) −2.99926 −0.140608
\(456\) 15.5132 0.726470
\(457\) 27.5872 1.29048 0.645238 0.763982i \(-0.276758\pi\)
0.645238 + 0.763982i \(0.276758\pi\)
\(458\) −9.67384 −0.452029
\(459\) −16.1926 −0.755804
\(460\) −0.314170 −0.0146482
\(461\) 28.3154 1.31878 0.659389 0.751802i \(-0.270815\pi\)
0.659389 + 0.751802i \(0.270815\pi\)
\(462\) 61.5893 2.86539
\(463\) −32.1451 −1.49391 −0.746954 0.664875i \(-0.768485\pi\)
−0.746954 + 0.664875i \(0.768485\pi\)
\(464\) 9.74496 0.452399
\(465\) −8.12226 −0.376661
\(466\) 25.2416 1.16930
\(467\) −5.00157 −0.231445 −0.115723 0.993282i \(-0.536918\pi\)
−0.115723 + 0.993282i \(0.536918\pi\)
\(468\) −11.6192 −0.537097
\(469\) 38.3323 1.77002
\(470\) −2.77557 −0.128027
\(471\) −14.2624 −0.657176
\(472\) −4.34637 −0.200058
\(473\) −2.93406 −0.134908
\(474\) 15.6357 0.718170
\(475\) 25.3404 1.16270
\(476\) 8.86317 0.406243
\(477\) 39.4886 1.80806
\(478\) −29.9284 −1.36889
\(479\) 10.8487 0.495689 0.247844 0.968800i \(-0.420278\pi\)
0.247844 + 0.968800i \(0.420278\pi\)
\(480\) −0.942677 −0.0430271
\(481\) 13.5921 0.619748
\(482\) 20.0936 0.915239
\(483\) 14.7998 0.673413
\(484\) 6.31810 0.287186
\(485\) −2.81782 −0.127951
\(486\) −0.0576743 −0.00261616
\(487\) 11.6282 0.526925 0.263462 0.964670i \(-0.415136\pi\)
0.263462 + 0.964670i \(0.415136\pi\)
\(488\) 11.3584 0.514169
\(489\) −26.5735 −1.20170
\(490\) 5.44406 0.245937
\(491\) −43.0858 −1.94443 −0.972217 0.234081i \(-0.924792\pi\)
−0.972217 + 0.234081i \(0.924792\pi\)
\(492\) −29.9757 −1.35141
\(493\) 17.5111 0.788658
\(494\) 10.0068 0.450227
\(495\) −7.84869 −0.352773
\(496\) 8.61617 0.386877
\(497\) 55.0778 2.47058
\(498\) 19.4655 0.872272
\(499\) −25.1248 −1.12474 −0.562370 0.826886i \(-0.690110\pi\)
−0.562370 + 0.826886i \(0.690110\pi\)
\(500\) −3.11069 −0.139114
\(501\) 4.52004 0.201941
\(502\) −11.2929 −0.504026
\(503\) −28.1395 −1.25468 −0.627339 0.778746i \(-0.715856\pi\)
−0.627339 + 0.778746i \(0.715856\pi\)
\(504\) 29.6101 1.31894
\(505\) −2.82906 −0.125892
\(506\) 4.16150 0.185001
\(507\) 27.7665 1.23315
\(508\) −2.24838 −0.0997556
\(509\) 11.2690 0.499491 0.249746 0.968311i \(-0.419653\pi\)
0.249746 + 0.968311i \(0.419653\pi\)
\(510\) −1.69393 −0.0750084
\(511\) −0.0995704 −0.00440474
\(512\) 1.00000 0.0441942
\(513\) 46.5891 2.05696
\(514\) −5.05499 −0.222966
\(515\) 1.54364 0.0680209
\(516\) −2.11552 −0.0931307
\(517\) 36.7653 1.61693
\(518\) −34.6379 −1.52190
\(519\) −51.7186 −2.27019
\(520\) −0.608075 −0.0266659
\(521\) −28.9179 −1.26692 −0.633458 0.773777i \(-0.718365\pi\)
−0.633458 + 0.773777i \(0.718365\pi\)
\(522\) 58.5010 2.56052
\(523\) −27.5649 −1.20533 −0.602665 0.797994i \(-0.705894\pi\)
−0.602665 + 0.797994i \(0.705894\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 72.5381 3.16582
\(526\) 2.88557 0.125817
\(527\) 15.4827 0.674436
\(528\) 12.4867 0.543415
\(529\) 1.00000 0.0434783
\(530\) 2.06659 0.0897667
\(531\) −26.0921 −1.13230
\(532\) −25.5011 −1.10561
\(533\) −19.3359 −0.837530
\(534\) 47.1846 2.04188
\(535\) −2.93521 −0.126900
\(536\) 7.77156 0.335680
\(537\) −30.4014 −1.31192
\(538\) −15.1497 −0.653150
\(539\) −72.1121 −3.10609
\(540\) −2.83105 −0.121829
\(541\) 28.1615 1.21076 0.605379 0.795938i \(-0.293022\pi\)
0.605379 + 0.795938i \(0.293022\pi\)
\(542\) 26.2016 1.12546
\(543\) −34.8498 −1.49555
\(544\) 1.79693 0.0770429
\(545\) 1.95462 0.0837268
\(546\) 28.6450 1.22589
\(547\) 31.8537 1.36196 0.680982 0.732300i \(-0.261553\pi\)
0.680982 + 0.732300i \(0.261553\pi\)
\(548\) 18.1753 0.776410
\(549\) 68.1866 2.91013
\(550\) 20.3968 0.869721
\(551\) −50.3827 −2.14638
\(552\) 3.00053 0.127711
\(553\) −25.7025 −1.09298
\(554\) 19.3416 0.821746
\(555\) 6.61999 0.281003
\(556\) 7.42145 0.314740
\(557\) −6.49280 −0.275109 −0.137554 0.990494i \(-0.543924\pi\)
−0.137554 + 0.990494i \(0.543924\pi\)
\(558\) 51.7246 2.18968
\(559\) −1.36462 −0.0577173
\(560\) 1.54961 0.0654828
\(561\) 22.4378 0.947326
\(562\) −11.4555 −0.483219
\(563\) 21.8202 0.919613 0.459807 0.888019i \(-0.347919\pi\)
0.459807 + 0.888019i \(0.347919\pi\)
\(564\) 26.5086 1.11621
\(565\) 4.16313 0.175144
\(566\) 4.55522 0.191470
\(567\) 44.5336 1.87024
\(568\) 11.1666 0.468539
\(569\) 21.7150 0.910342 0.455171 0.890404i \(-0.349578\pi\)
0.455171 + 0.890404i \(0.349578\pi\)
\(570\) 4.87377 0.204140
\(571\) −2.80848 −0.117531 −0.0587656 0.998272i \(-0.518716\pi\)
−0.0587656 + 0.998272i \(0.518716\pi\)
\(572\) 8.05458 0.336779
\(573\) −58.2197 −2.43216
\(574\) 49.2751 2.05670
\(575\) 4.90130 0.204398
\(576\) 6.00320 0.250133
\(577\) 13.6664 0.568938 0.284469 0.958685i \(-0.408183\pi\)
0.284469 + 0.958685i \(0.408183\pi\)
\(578\) −13.7710 −0.572799
\(579\) 30.2840 1.25856
\(580\) 3.06157 0.127125
\(581\) −31.9981 −1.32751
\(582\) 26.9121 1.11554
\(583\) −27.3740 −1.13372
\(584\) −0.0201871 −0.000835348 0
\(585\) −3.65040 −0.150925
\(586\) −0.857587 −0.0354266
\(587\) −41.7383 −1.72272 −0.861362 0.507991i \(-0.830388\pi\)
−0.861362 + 0.507991i \(0.830388\pi\)
\(588\) −51.9944 −2.14421
\(589\) −44.5467 −1.83552
\(590\) −1.36550 −0.0562166
\(591\) 35.7109 1.46895
\(592\) −7.02254 −0.288625
\(593\) 12.0706 0.495679 0.247840 0.968801i \(-0.420279\pi\)
0.247840 + 0.968801i \(0.420279\pi\)
\(594\) 37.5002 1.53865
\(595\) 2.78454 0.114155
\(596\) 9.37455 0.383996
\(597\) −79.7016 −3.26197
\(598\) 1.93550 0.0791485
\(599\) 36.3765 1.48630 0.743152 0.669122i \(-0.233330\pi\)
0.743152 + 0.669122i \(0.233330\pi\)
\(600\) 14.7065 0.600391
\(601\) 27.6567 1.12814 0.564069 0.825727i \(-0.309235\pi\)
0.564069 + 0.825727i \(0.309235\pi\)
\(602\) 3.47757 0.141735
\(603\) 46.6542 1.89991
\(604\) 17.5647 0.714696
\(605\) 1.98495 0.0806999
\(606\) 27.0195 1.09759
\(607\) −16.8115 −0.682359 −0.341179 0.939998i \(-0.610826\pi\)
−0.341179 + 0.939998i \(0.610826\pi\)
\(608\) −5.17013 −0.209677
\(609\) −144.223 −5.84422
\(610\) 3.56846 0.144483
\(611\) 17.0994 0.691768
\(612\) 10.7874 0.436053
\(613\) −10.1977 −0.411881 −0.205941 0.978564i \(-0.566025\pi\)
−0.205941 + 0.978564i \(0.566025\pi\)
\(614\) −16.2855 −0.657229
\(615\) −9.41746 −0.379748
\(616\) −20.5261 −0.827021
\(617\) 24.6570 0.992655 0.496327 0.868135i \(-0.334682\pi\)
0.496327 + 0.868135i \(0.334682\pi\)
\(618\) −14.7428 −0.593042
\(619\) 30.2019 1.21392 0.606958 0.794734i \(-0.292389\pi\)
0.606958 + 0.794734i \(0.292389\pi\)
\(620\) 2.70694 0.108713
\(621\) 9.01121 0.361607
\(622\) −30.7046 −1.23114
\(623\) −77.5638 −3.10753
\(624\) 5.80753 0.232487
\(625\) 23.5292 0.941168
\(626\) 11.7299 0.468820
\(627\) −64.5580 −2.57820
\(628\) 4.75328 0.189677
\(629\) −12.6190 −0.503154
\(630\) 9.30259 0.370624
\(631\) 33.4669 1.33230 0.666148 0.745820i \(-0.267942\pi\)
0.666148 + 0.745820i \(0.267942\pi\)
\(632\) −5.21096 −0.207281
\(633\) 14.1132 0.560950
\(634\) 14.7336 0.585145
\(635\) −0.706372 −0.0280315
\(636\) −19.7373 −0.782634
\(637\) −33.5391 −1.32887
\(638\) −40.5537 −1.60554
\(639\) 67.0352 2.65187
\(640\) 0.314170 0.0124187
\(641\) 43.2863 1.70971 0.854853 0.518870i \(-0.173647\pi\)
0.854853 + 0.518870i \(0.173647\pi\)
\(642\) 28.0333 1.10639
\(643\) 16.9856 0.669846 0.334923 0.942246i \(-0.391290\pi\)
0.334923 + 0.942246i \(0.391290\pi\)
\(644\) −4.93238 −0.194363
\(645\) −0.664633 −0.0261699
\(646\) −9.29039 −0.365525
\(647\) −5.11425 −0.201062 −0.100531 0.994934i \(-0.532054\pi\)
−0.100531 + 0.994934i \(0.532054\pi\)
\(648\) 9.02883 0.354686
\(649\) 18.0874 0.709993
\(650\) 9.48646 0.372090
\(651\) −127.517 −4.99780
\(652\) 8.85627 0.346838
\(653\) 23.7978 0.931280 0.465640 0.884974i \(-0.345824\pi\)
0.465640 + 0.884974i \(0.345824\pi\)
\(654\) −18.6680 −0.729975
\(655\) −0.314170 −0.0122756
\(656\) 9.99012 0.390049
\(657\) −0.121187 −0.00472796
\(658\) −43.5757 −1.69876
\(659\) 30.5000 1.18811 0.594056 0.804424i \(-0.297526\pi\)
0.594056 + 0.804424i \(0.297526\pi\)
\(660\) 3.92295 0.152701
\(661\) 14.5151 0.564570 0.282285 0.959331i \(-0.408908\pi\)
0.282285 + 0.959331i \(0.408908\pi\)
\(662\) −36.0263 −1.40020
\(663\) 10.4358 0.405291
\(664\) −6.48736 −0.251758
\(665\) −8.01167 −0.310679
\(666\) −42.1577 −1.63358
\(667\) −9.74496 −0.377326
\(668\) −1.50641 −0.0582849
\(669\) 2.29466 0.0887169
\(670\) 2.44159 0.0943268
\(671\) −47.2679 −1.82476
\(672\) −14.7998 −0.570914
\(673\) 33.8049 1.30308 0.651542 0.758612i \(-0.274122\pi\)
0.651542 + 0.758612i \(0.274122\pi\)
\(674\) −0.0730258 −0.00281285
\(675\) 44.1666 1.69997
\(676\) −9.25384 −0.355917
\(677\) −44.0409 −1.69263 −0.846315 0.532683i \(-0.821184\pi\)
−0.846315 + 0.532683i \(0.821184\pi\)
\(678\) −39.7607 −1.52700
\(679\) −44.2391 −1.69774
\(680\) 0.564542 0.0216492
\(681\) −32.0552 −1.22836
\(682\) −35.8562 −1.37300
\(683\) 9.99887 0.382596 0.191298 0.981532i \(-0.438730\pi\)
0.191298 + 0.981532i \(0.438730\pi\)
\(684\) −31.0374 −1.18674
\(685\) 5.71012 0.218173
\(686\) 50.9436 1.94503
\(687\) 29.0267 1.10744
\(688\) 0.705049 0.0268797
\(689\) −12.7316 −0.485034
\(690\) 0.942677 0.0358871
\(691\) 7.12645 0.271103 0.135551 0.990770i \(-0.456719\pi\)
0.135551 + 0.990770i \(0.456719\pi\)
\(692\) 17.2365 0.655232
\(693\) −123.222 −4.68083
\(694\) −0.713534 −0.0270854
\(695\) 2.33159 0.0884424
\(696\) −29.2401 −1.10834
\(697\) 17.9516 0.679965
\(698\) 18.5075 0.700520
\(699\) −75.7383 −2.86469
\(700\) −24.1751 −0.913732
\(701\) 40.1879 1.51788 0.758939 0.651162i \(-0.225718\pi\)
0.758939 + 0.651162i \(0.225718\pi\)
\(702\) 17.4412 0.658275
\(703\) 36.3075 1.36936
\(704\) −4.16150 −0.156842
\(705\) 8.32819 0.313658
\(706\) 7.32508 0.275683
\(707\) −44.4156 −1.67042
\(708\) 13.0414 0.490127
\(709\) 31.3206 1.17627 0.588135 0.808763i \(-0.299863\pi\)
0.588135 + 0.808763i \(0.299863\pi\)
\(710\) 3.50820 0.131660
\(711\) −31.2825 −1.17318
\(712\) −15.7254 −0.589335
\(713\) −8.61617 −0.322678
\(714\) −26.5942 −0.995264
\(715\) 2.53051 0.0946356
\(716\) 10.1320 0.378650
\(717\) 89.8012 3.35369
\(718\) 30.1278 1.12436
\(719\) 3.97387 0.148200 0.0741002 0.997251i \(-0.476392\pi\)
0.0741002 + 0.997251i \(0.476392\pi\)
\(720\) 1.88602 0.0702880
\(721\) 24.2347 0.902548
\(722\) 7.73027 0.287691
\(723\) −60.2915 −2.24227
\(724\) 11.6145 0.431650
\(725\) −47.7630 −1.77387
\(726\) −18.9577 −0.703585
\(727\) 19.4177 0.720161 0.360081 0.932921i \(-0.382749\pi\)
0.360081 + 0.932921i \(0.382749\pi\)
\(728\) −9.54662 −0.353821
\(729\) −26.9134 −0.996794
\(730\) −0.00634217 −0.000234734 0
\(731\) 1.26693 0.0468590
\(732\) −34.0812 −1.25968
\(733\) −36.0310 −1.33084 −0.665418 0.746471i \(-0.731747\pi\)
−0.665418 + 0.746471i \(0.731747\pi\)
\(734\) 0.606595 0.0223898
\(735\) −16.3351 −0.602528
\(736\) −1.00000 −0.0368605
\(737\) −32.3414 −1.19131
\(738\) 59.9727 2.20763
\(739\) 37.0666 1.36352 0.681759 0.731577i \(-0.261215\pi\)
0.681759 + 0.731577i \(0.261215\pi\)
\(740\) −2.20627 −0.0811041
\(741\) −30.0257 −1.10302
\(742\) 32.4448 1.19109
\(743\) −25.1232 −0.921680 −0.460840 0.887483i \(-0.652452\pi\)
−0.460840 + 0.887483i \(0.652452\pi\)
\(744\) −25.8531 −0.947821
\(745\) 2.94520 0.107904
\(746\) 19.2257 0.703902
\(747\) −38.9449 −1.42492
\(748\) −7.47795 −0.273421
\(749\) −46.0821 −1.68380
\(750\) 9.33373 0.340819
\(751\) −38.1341 −1.39153 −0.695766 0.718269i \(-0.744935\pi\)
−0.695766 + 0.718269i \(0.744935\pi\)
\(752\) −8.83462 −0.322165
\(753\) 33.8847 1.23483
\(754\) −18.8614 −0.686891
\(755\) 5.51829 0.200831
\(756\) −44.4467 −1.61651
\(757\) −15.9225 −0.578712 −0.289356 0.957222i \(-0.593441\pi\)
−0.289356 + 0.957222i \(0.593441\pi\)
\(758\) 18.5848 0.675031
\(759\) −12.4867 −0.453239
\(760\) −1.62430 −0.0589195
\(761\) −43.2483 −1.56775 −0.783874 0.620920i \(-0.786759\pi\)
−0.783874 + 0.620920i \(0.786759\pi\)
\(762\) 6.74633 0.244394
\(763\) 30.6870 1.11095
\(764\) 19.4031 0.701980
\(765\) 3.38906 0.122532
\(766\) −31.7040 −1.14551
\(767\) 8.41239 0.303754
\(768\) −3.00053 −0.108272
\(769\) 2.56567 0.0925203 0.0462602 0.998929i \(-0.485270\pi\)
0.0462602 + 0.998929i \(0.485270\pi\)
\(770\) −6.44868 −0.232394
\(771\) 15.1677 0.546251
\(772\) −10.0929 −0.363250
\(773\) −20.5775 −0.740121 −0.370060 0.929008i \(-0.620663\pi\)
−0.370060 + 0.929008i \(0.620663\pi\)
\(774\) 4.23255 0.152136
\(775\) −42.2304 −1.51696
\(776\) −8.96911 −0.321972
\(777\) 103.932 3.72854
\(778\) −27.0952 −0.971411
\(779\) −51.6502 −1.85056
\(780\) 1.82455 0.0653294
\(781\) −46.4697 −1.66282
\(782\) −1.79693 −0.0642582
\(783\) −87.8139 −3.13821
\(784\) 17.3284 0.618871
\(785\) 1.49334 0.0532995
\(786\) 3.00053 0.107025
\(787\) −42.7607 −1.52426 −0.762128 0.647427i \(-0.775845\pi\)
−0.762128 + 0.647427i \(0.775845\pi\)
\(788\) −11.9015 −0.423973
\(789\) −8.65826 −0.308242
\(790\) −1.63713 −0.0582464
\(791\) 65.3601 2.32394
\(792\) −24.9823 −0.887709
\(793\) −21.9841 −0.780679
\(794\) 30.6380 1.08730
\(795\) −6.20086 −0.219922
\(796\) 26.5625 0.941482
\(797\) 12.4874 0.442325 0.221162 0.975237i \(-0.429015\pi\)
0.221162 + 0.975237i \(0.429015\pi\)
\(798\) 76.5168 2.70867
\(799\) −15.8752 −0.561625
\(800\) −4.90130 −0.173287
\(801\) −94.4029 −3.33556
\(802\) 14.0704 0.496845
\(803\) 0.0840086 0.00296460
\(804\) −23.3188 −0.822392
\(805\) −1.54961 −0.0546164
\(806\) −16.6766 −0.587408
\(807\) 45.4572 1.60017
\(808\) −9.00489 −0.316791
\(809\) 20.4894 0.720369 0.360184 0.932881i \(-0.382714\pi\)
0.360184 + 0.932881i \(0.382714\pi\)
\(810\) 2.83658 0.0996674
\(811\) 32.2711 1.13319 0.566595 0.823996i \(-0.308260\pi\)
0.566595 + 0.823996i \(0.308260\pi\)
\(812\) 48.0659 1.68678
\(813\) −78.6189 −2.75729
\(814\) 29.2243 1.02431
\(815\) 2.78237 0.0974623
\(816\) −5.39176 −0.188749
\(817\) −3.64520 −0.127529
\(818\) −12.9727 −0.453580
\(819\) −57.3103 −2.00258
\(820\) 3.13859 0.109604
\(821\) −52.2275 −1.82275 −0.911376 0.411576i \(-0.864979\pi\)
−0.911376 + 0.411576i \(0.864979\pi\)
\(822\) −54.5355 −1.90215
\(823\) 48.2634 1.68235 0.841177 0.540759i \(-0.181863\pi\)
0.841177 + 0.540759i \(0.181863\pi\)
\(824\) 4.91339 0.171166
\(825\) −61.2012 −2.13075
\(826\) −21.4379 −0.745922
\(827\) −35.8795 −1.24765 −0.623826 0.781564i \(-0.714422\pi\)
−0.623826 + 0.781564i \(0.714422\pi\)
\(828\) −6.00320 −0.208626
\(829\) 7.32008 0.254237 0.127118 0.991888i \(-0.459427\pi\)
0.127118 + 0.991888i \(0.459427\pi\)
\(830\) −2.03813 −0.0707446
\(831\) −58.0351 −2.01322
\(832\) −1.93550 −0.0671014
\(833\) 31.1380 1.07887
\(834\) −22.2683 −0.771088
\(835\) −0.473270 −0.0163782
\(836\) 21.5155 0.744130
\(837\) −77.6421 −2.68370
\(838\) 14.4921 0.500620
\(839\) 19.5962 0.676537 0.338268 0.941050i \(-0.390159\pi\)
0.338268 + 0.941050i \(0.390159\pi\)
\(840\) −4.64964 −0.160428
\(841\) 65.9643 2.27463
\(842\) 31.3277 1.07963
\(843\) 34.3725 1.18385
\(844\) −4.70357 −0.161903
\(845\) −2.90728 −0.100013
\(846\) −53.0360 −1.82341
\(847\) 31.1633 1.07078
\(848\) 6.57792 0.225887
\(849\) −13.6681 −0.469088
\(850\) −8.80731 −0.302088
\(851\) 7.02254 0.240730
\(852\) −33.5057 −1.14789
\(853\) −33.2068 −1.13698 −0.568490 0.822690i \(-0.692472\pi\)
−0.568490 + 0.822690i \(0.692472\pi\)
\(854\) 56.0238 1.91710
\(855\) −9.75100 −0.333477
\(856\) −9.34277 −0.319329
\(857\) 48.2806 1.64923 0.824617 0.565691i \(-0.191390\pi\)
0.824617 + 0.565691i \(0.191390\pi\)
\(858\) −24.1681 −0.825084
\(859\) −12.4721 −0.425543 −0.212772 0.977102i \(-0.568249\pi\)
−0.212772 + 0.977102i \(0.568249\pi\)
\(860\) 0.221505 0.00755326
\(861\) −147.852 −5.03877
\(862\) −6.53686 −0.222646
\(863\) −18.5924 −0.632892 −0.316446 0.948611i \(-0.602490\pi\)
−0.316446 + 0.948611i \(0.602490\pi\)
\(864\) −9.01121 −0.306568
\(865\) 5.41518 0.184121
\(866\) 12.8219 0.435705
\(867\) 41.3204 1.40332
\(868\) 42.4982 1.44248
\(869\) 21.6854 0.735628
\(870\) −9.18635 −0.311446
\(871\) −15.0419 −0.509674
\(872\) 6.22155 0.210688
\(873\) −53.8434 −1.82232
\(874\) 5.17013 0.174882
\(875\) −15.3431 −0.518692
\(876\) 0.0605720 0.00204654
\(877\) 15.2955 0.516492 0.258246 0.966079i \(-0.416856\pi\)
0.258246 + 0.966079i \(0.416856\pi\)
\(878\) −5.13850 −0.173416
\(879\) 2.57322 0.0867925
\(880\) −1.30742 −0.0440731
\(881\) 0.905522 0.0305078 0.0152539 0.999884i \(-0.495144\pi\)
0.0152539 + 0.999884i \(0.495144\pi\)
\(882\) 104.026 3.50273
\(883\) −20.4347 −0.687683 −0.343842 0.939028i \(-0.611728\pi\)
−0.343842 + 0.939028i \(0.611728\pi\)
\(884\) −3.47797 −0.116977
\(885\) 4.09722 0.137727
\(886\) −30.0800 −1.01056
\(887\) −17.9090 −0.601327 −0.300663 0.953730i \(-0.597208\pi\)
−0.300663 + 0.953730i \(0.597208\pi\)
\(888\) 21.0714 0.707109
\(889\) −11.0898 −0.371942
\(890\) −4.94045 −0.165604
\(891\) −37.5735 −1.25876
\(892\) −0.764752 −0.0256058
\(893\) 45.6761 1.52849
\(894\) −28.1286 −0.940763
\(895\) 3.18316 0.106401
\(896\) 4.93238 0.164779
\(897\) −5.80753 −0.193908
\(898\) −4.07936 −0.136130
\(899\) 83.9642 2.80036
\(900\) −29.4235 −0.980783
\(901\) 11.8201 0.393785
\(902\) −41.5739 −1.38426
\(903\) −10.4346 −0.347241
\(904\) 13.2512 0.440729
\(905\) 3.64893 0.121295
\(906\) −52.7034 −1.75095
\(907\) −26.3543 −0.875081 −0.437540 0.899199i \(-0.644150\pi\)
−0.437540 + 0.899199i \(0.644150\pi\)
\(908\) 10.6832 0.354533
\(909\) −54.0582 −1.79300
\(910\) −2.99926 −0.0994245
\(911\) 4.83789 0.160286 0.0801432 0.996783i \(-0.474462\pi\)
0.0801432 + 0.996783i \(0.474462\pi\)
\(912\) 15.5132 0.513692
\(913\) 26.9972 0.893476
\(914\) 27.5872 0.912504
\(915\) −10.7073 −0.353972
\(916\) −9.67384 −0.319633
\(917\) −4.93238 −0.162882
\(918\) −16.1926 −0.534434
\(919\) −29.2487 −0.964825 −0.482413 0.875944i \(-0.660239\pi\)
−0.482413 + 0.875944i \(0.660239\pi\)
\(920\) −0.314170 −0.0103579
\(921\) 48.8652 1.61016
\(922\) 28.3154 0.932517
\(923\) −21.6129 −0.711397
\(924\) 61.5893 2.02614
\(925\) 34.4196 1.13171
\(926\) −32.1451 −1.05635
\(927\) 29.4961 0.968778
\(928\) 9.74496 0.319894
\(929\) −42.2529 −1.38627 −0.693137 0.720806i \(-0.743772\pi\)
−0.693137 + 0.720806i \(0.743772\pi\)
\(930\) −8.12226 −0.266339
\(931\) −89.5901 −2.93620
\(932\) 25.2416 0.826817
\(933\) 92.1302 3.01621
\(934\) −5.00157 −0.163656
\(935\) −2.34934 −0.0768318
\(936\) −11.6192 −0.379785
\(937\) −15.3065 −0.500042 −0.250021 0.968240i \(-0.580438\pi\)
−0.250021 + 0.968240i \(0.580438\pi\)
\(938\) 38.3323 1.25159
\(939\) −35.1959 −1.14857
\(940\) −2.77557 −0.0905291
\(941\) −42.2549 −1.37747 −0.688736 0.725013i \(-0.741834\pi\)
−0.688736 + 0.725013i \(0.741834\pi\)
\(942\) −14.2624 −0.464694
\(943\) −9.99012 −0.325323
\(944\) −4.34637 −0.141462
\(945\) −13.9638 −0.454243
\(946\) −2.93406 −0.0953946
\(947\) −15.2933 −0.496967 −0.248483 0.968636i \(-0.579932\pi\)
−0.248483 + 0.968636i \(0.579932\pi\)
\(948\) 15.6357 0.507823
\(949\) 0.0390721 0.00126833
\(950\) 25.3404 0.822150
\(951\) −44.2086 −1.43356
\(952\) 8.86317 0.287257
\(953\) −28.4616 −0.921962 −0.460981 0.887410i \(-0.652502\pi\)
−0.460981 + 0.887410i \(0.652502\pi\)
\(954\) 39.4886 1.27849
\(955\) 6.09587 0.197258
\(956\) −29.9284 −0.967954
\(957\) 121.683 3.93344
\(958\) 10.8487 0.350505
\(959\) 89.6474 2.89487
\(960\) −0.942677 −0.0304248
\(961\) 43.2383 1.39479
\(962\) 13.5921 0.438228
\(963\) −56.0865 −1.80736
\(964\) 20.0936 0.647171
\(965\) −3.17087 −0.102074
\(966\) 14.7998 0.476175
\(967\) −2.81854 −0.0906383 −0.0453191 0.998973i \(-0.514430\pi\)
−0.0453191 + 0.998973i \(0.514430\pi\)
\(968\) 6.31810 0.203071
\(969\) 27.8761 0.895510
\(970\) −2.81782 −0.0904749
\(971\) −25.8561 −0.829762 −0.414881 0.909876i \(-0.636177\pi\)
−0.414881 + 0.909876i \(0.636177\pi\)
\(972\) −0.0576743 −0.00184990
\(973\) 36.6054 1.17352
\(974\) 11.6282 0.372592
\(975\) −28.4644 −0.911592
\(976\) 11.3584 0.363573
\(977\) 6.98532 0.223480 0.111740 0.993737i \(-0.464358\pi\)
0.111740 + 0.993737i \(0.464358\pi\)
\(978\) −26.5735 −0.849728
\(979\) 65.4414 2.09151
\(980\) 5.44406 0.173904
\(981\) 37.3492 1.19247
\(982\) −43.0858 −1.37492
\(983\) −12.9589 −0.413324 −0.206662 0.978412i \(-0.566260\pi\)
−0.206662 + 0.978412i \(0.566260\pi\)
\(984\) −29.9757 −0.955590
\(985\) −3.73909 −0.119137
\(986\) 17.5111 0.557666
\(987\) 130.750 4.16183
\(988\) 10.0068 0.318358
\(989\) −0.705049 −0.0224192
\(990\) −7.84869 −0.249448
\(991\) −31.7247 −1.00777 −0.503884 0.863771i \(-0.668096\pi\)
−0.503884 + 0.863771i \(0.668096\pi\)
\(992\) 8.61617 0.273564
\(993\) 108.098 3.43039
\(994\) 55.0778 1.74696
\(995\) 8.34513 0.264558
\(996\) 19.4655 0.616789
\(997\) 2.22438 0.0704469 0.0352235 0.999379i \(-0.488786\pi\)
0.0352235 + 0.999379i \(0.488786\pi\)
\(998\) −25.1248 −0.795311
\(999\) 63.2816 2.00214
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 6026.2.a.k.1.3 35
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.k.1.3 35 1.1 even 1 trivial