Properties

Label 6026.2.a.m.1.4
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $0$
Dimension $41$
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: \(41\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.13493 q^{3} +1.00000 q^{4} +2.02213 q^{5} -3.13493 q^{6} -2.34132 q^{7} +1.00000 q^{8} +6.82778 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.13493 q^{3} +1.00000 q^{4} +2.02213 q^{5} -3.13493 q^{6} -2.34132 q^{7} +1.00000 q^{8} +6.82778 q^{9} +2.02213 q^{10} -3.59300 q^{11} -3.13493 q^{12} +4.28832 q^{13} -2.34132 q^{14} -6.33924 q^{15} +1.00000 q^{16} +5.99610 q^{17} +6.82778 q^{18} +6.79081 q^{19} +2.02213 q^{20} +7.33987 q^{21} -3.59300 q^{22} +1.00000 q^{23} -3.13493 q^{24} -0.910980 q^{25} +4.28832 q^{26} -11.9998 q^{27} -2.34132 q^{28} +10.3385 q^{29} -6.33924 q^{30} -1.95079 q^{31} +1.00000 q^{32} +11.2638 q^{33} +5.99610 q^{34} -4.73446 q^{35} +6.82778 q^{36} -10.9865 q^{37} +6.79081 q^{38} -13.4436 q^{39} +2.02213 q^{40} -4.92852 q^{41} +7.33987 q^{42} -9.18429 q^{43} -3.59300 q^{44} +13.8067 q^{45} +1.00000 q^{46} +8.36252 q^{47} -3.13493 q^{48} -1.51822 q^{49} -0.910980 q^{50} -18.7973 q^{51} +4.28832 q^{52} +11.0290 q^{53} -11.9998 q^{54} -7.26552 q^{55} -2.34132 q^{56} -21.2887 q^{57} +10.3385 q^{58} +2.22413 q^{59} -6.33924 q^{60} -4.29334 q^{61} -1.95079 q^{62} -15.9860 q^{63} +1.00000 q^{64} +8.67155 q^{65} +11.2638 q^{66} -4.97586 q^{67} +5.99610 q^{68} -3.13493 q^{69} -4.73446 q^{70} +8.88877 q^{71} +6.82778 q^{72} -5.44770 q^{73} -10.9865 q^{74} +2.85586 q^{75} +6.79081 q^{76} +8.41236 q^{77} -13.4436 q^{78} -12.0384 q^{79} +2.02213 q^{80} +17.1352 q^{81} -4.92852 q^{82} +1.70720 q^{83} +7.33987 q^{84} +12.1249 q^{85} -9.18429 q^{86} -32.4103 q^{87} -3.59300 q^{88} +18.2344 q^{89} +13.8067 q^{90} -10.0403 q^{91} +1.00000 q^{92} +6.11560 q^{93} +8.36252 q^{94} +13.7319 q^{95} -3.13493 q^{96} -12.9465 q^{97} -1.51822 q^{98} -24.5322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 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
\(3\) −3.13493 −1.80995 −0.904976 0.425462i \(-0.860111\pi\)
−0.904976 + 0.425462i \(0.860111\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.02213 0.904325 0.452163 0.891936i \(-0.350653\pi\)
0.452163 + 0.891936i \(0.350653\pi\)
\(6\) −3.13493 −1.27983
\(7\) −2.34132 −0.884936 −0.442468 0.896784i \(-0.645897\pi\)
−0.442468 + 0.896784i \(0.645897\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.82778 2.27593
\(10\) 2.02213 0.639454
\(11\) −3.59300 −1.08333 −0.541665 0.840594i \(-0.682206\pi\)
−0.541665 + 0.840594i \(0.682206\pi\)
\(12\) −3.13493 −0.904976
\(13\) 4.28832 1.18937 0.594683 0.803960i \(-0.297278\pi\)
0.594683 + 0.803960i \(0.297278\pi\)
\(14\) −2.34132 −0.625744
\(15\) −6.33924 −1.63679
\(16\) 1.00000 0.250000
\(17\) 5.99610 1.45427 0.727133 0.686496i \(-0.240852\pi\)
0.727133 + 0.686496i \(0.240852\pi\)
\(18\) 6.82778 1.60932
\(19\) 6.79081 1.55792 0.778960 0.627074i \(-0.215748\pi\)
0.778960 + 0.627074i \(0.215748\pi\)
\(20\) 2.02213 0.452163
\(21\) 7.33987 1.60169
\(22\) −3.59300 −0.766030
\(23\) 1.00000 0.208514
\(24\) −3.13493 −0.639915
\(25\) −0.910980 −0.182196
\(26\) 4.28832 0.841009
\(27\) −11.9998 −2.30937
\(28\) −2.34132 −0.442468
\(29\) 10.3385 1.91980 0.959902 0.280336i \(-0.0904458\pi\)
0.959902 + 0.280336i \(0.0904458\pi\)
\(30\) −6.33924 −1.15738
\(31\) −1.95079 −0.350373 −0.175187 0.984535i \(-0.556053\pi\)
−0.175187 + 0.984535i \(0.556053\pi\)
\(32\) 1.00000 0.176777
\(33\) 11.2638 1.96078
\(34\) 5.99610 1.02832
\(35\) −4.73446 −0.800270
\(36\) 6.82778 1.13796
\(37\) −10.9865 −1.80617 −0.903086 0.429459i \(-0.858704\pi\)
−0.903086 + 0.429459i \(0.858704\pi\)
\(38\) 6.79081 1.10162
\(39\) −13.4436 −2.15270
\(40\) 2.02213 0.319727
\(41\) −4.92852 −0.769705 −0.384853 0.922978i \(-0.625748\pi\)
−0.384853 + 0.922978i \(0.625748\pi\)
\(42\) 7.33987 1.13257
\(43\) −9.18429 −1.40059 −0.700296 0.713853i \(-0.746948\pi\)
−0.700296 + 0.713853i \(0.746948\pi\)
\(44\) −3.59300 −0.541665
\(45\) 13.8067 2.05818
\(46\) 1.00000 0.147442
\(47\) 8.36252 1.21980 0.609900 0.792479i \(-0.291210\pi\)
0.609900 + 0.792479i \(0.291210\pi\)
\(48\) −3.13493 −0.452488
\(49\) −1.51822 −0.216888
\(50\) −0.910980 −0.128832
\(51\) −18.7973 −2.63215
\(52\) 4.28832 0.594683
\(53\) 11.0290 1.51495 0.757473 0.652867i \(-0.226434\pi\)
0.757473 + 0.652867i \(0.226434\pi\)
\(54\) −11.9998 −1.63297
\(55\) −7.26552 −0.979682
\(56\) −2.34132 −0.312872
\(57\) −21.2887 −2.81976
\(58\) 10.3385 1.35751
\(59\) 2.22413 0.289557 0.144778 0.989464i \(-0.453753\pi\)
0.144778 + 0.989464i \(0.453753\pi\)
\(60\) −6.33924 −0.818393
\(61\) −4.29334 −0.549706 −0.274853 0.961486i \(-0.588629\pi\)
−0.274853 + 0.961486i \(0.588629\pi\)
\(62\) −1.95079 −0.247751
\(63\) −15.9860 −2.01405
\(64\) 1.00000 0.125000
\(65\) 8.67155 1.07557
\(66\) 11.2638 1.38648
\(67\) −4.97586 −0.607898 −0.303949 0.952688i \(-0.598305\pi\)
−0.303949 + 0.952688i \(0.598305\pi\)
\(68\) 5.99610 0.727133
\(69\) −3.13493 −0.377401
\(70\) −4.73446 −0.565876
\(71\) 8.88877 1.05490 0.527452 0.849585i \(-0.323148\pi\)
0.527452 + 0.849585i \(0.323148\pi\)
\(72\) 6.82778 0.804662
\(73\) −5.44770 −0.637605 −0.318803 0.947821i \(-0.603281\pi\)
−0.318803 + 0.947821i \(0.603281\pi\)
\(74\) −10.9865 −1.27716
\(75\) 2.85586 0.329766
\(76\) 6.79081 0.778960
\(77\) 8.41236 0.958678
\(78\) −13.4436 −1.52219
\(79\) −12.0384 −1.35442 −0.677212 0.735788i \(-0.736812\pi\)
−0.677212 + 0.735788i \(0.736812\pi\)
\(80\) 2.02213 0.226081
\(81\) 17.1352 1.90392
\(82\) −4.92852 −0.544264
\(83\) 1.70720 0.187390 0.0936950 0.995601i \(-0.470132\pi\)
0.0936950 + 0.995601i \(0.470132\pi\)
\(84\) 7.33987 0.800846
\(85\) 12.1249 1.31513
\(86\) −9.18429 −0.990368
\(87\) −32.4103 −3.47475
\(88\) −3.59300 −0.383015
\(89\) 18.2344 1.93284 0.966421 0.256965i \(-0.0827225\pi\)
0.966421 + 0.256965i \(0.0827225\pi\)
\(90\) 13.8067 1.45535
\(91\) −10.0403 −1.05251
\(92\) 1.00000 0.104257
\(93\) 6.11560 0.634159
\(94\) 8.36252 0.862528
\(95\) 13.7319 1.40887
\(96\) −3.13493 −0.319957
\(97\) −12.9465 −1.31452 −0.657260 0.753664i \(-0.728285\pi\)
−0.657260 + 0.753664i \(0.728285\pi\)
\(98\) −1.51822 −0.153363
\(99\) −24.5322 −2.46558
\(100\) −0.910980 −0.0910980
\(101\) 17.1239 1.70389 0.851946 0.523629i \(-0.175422\pi\)
0.851946 + 0.523629i \(0.175422\pi\)
\(102\) −18.7973 −1.86121
\(103\) 12.3311 1.21502 0.607509 0.794313i \(-0.292169\pi\)
0.607509 + 0.794313i \(0.292169\pi\)
\(104\) 4.28832 0.420504
\(105\) 14.8422 1.44845
\(106\) 11.0290 1.07123
\(107\) 10.0130 0.967997 0.483999 0.875069i \(-0.339184\pi\)
0.483999 + 0.875069i \(0.339184\pi\)
\(108\) −11.9998 −1.15468
\(109\) 9.22553 0.883645 0.441823 0.897102i \(-0.354332\pi\)
0.441823 + 0.897102i \(0.354332\pi\)
\(110\) −7.26552 −0.692740
\(111\) 34.4420 3.26909
\(112\) −2.34132 −0.221234
\(113\) −11.5838 −1.08971 −0.544855 0.838530i \(-0.683415\pi\)
−0.544855 + 0.838530i \(0.683415\pi\)
\(114\) −21.2887 −1.99387
\(115\) 2.02213 0.188565
\(116\) 10.3385 0.959902
\(117\) 29.2797 2.70691
\(118\) 2.22413 0.204747
\(119\) −14.0388 −1.28693
\(120\) −6.33924 −0.578691
\(121\) 1.90964 0.173604
\(122\) −4.29334 −0.388701
\(123\) 15.4506 1.39313
\(124\) −1.95079 −0.175187
\(125\) −11.9528 −1.06909
\(126\) −15.9860 −1.42415
\(127\) −9.71481 −0.862050 −0.431025 0.902340i \(-0.641848\pi\)
−0.431025 + 0.902340i \(0.641848\pi\)
\(128\) 1.00000 0.0883883
\(129\) 28.7921 2.53500
\(130\) 8.67155 0.760545
\(131\) 1.00000 0.0873704
\(132\) 11.2638 0.980388
\(133\) −15.8995 −1.37866
\(134\) −4.97586 −0.429849
\(135\) −24.2652 −2.08842
\(136\) 5.99610 0.514161
\(137\) −3.06082 −0.261504 −0.130752 0.991415i \(-0.541739\pi\)
−0.130752 + 0.991415i \(0.541739\pi\)
\(138\) −3.13493 −0.266863
\(139\) 14.0439 1.19119 0.595595 0.803285i \(-0.296916\pi\)
0.595595 + 0.803285i \(0.296916\pi\)
\(140\) −4.73446 −0.400135
\(141\) −26.2159 −2.20778
\(142\) 8.88877 0.745929
\(143\) −15.4079 −1.28848
\(144\) 6.82778 0.568982
\(145\) 20.9057 1.73613
\(146\) −5.44770 −0.450855
\(147\) 4.75951 0.392558
\(148\) −10.9865 −0.903086
\(149\) −19.7560 −1.61847 −0.809237 0.587482i \(-0.800119\pi\)
−0.809237 + 0.587482i \(0.800119\pi\)
\(150\) 2.85586 0.233180
\(151\) 3.09790 0.252103 0.126052 0.992024i \(-0.459770\pi\)
0.126052 + 0.992024i \(0.459770\pi\)
\(152\) 6.79081 0.550808
\(153\) 40.9400 3.30981
\(154\) 8.41236 0.677887
\(155\) −3.94477 −0.316851
\(156\) −13.4436 −1.07635
\(157\) −13.4885 −1.07650 −0.538248 0.842787i \(-0.680914\pi\)
−0.538248 + 0.842787i \(0.680914\pi\)
\(158\) −12.0384 −0.957723
\(159\) −34.5750 −2.74198
\(160\) 2.02213 0.159864
\(161\) −2.34132 −0.184522
\(162\) 17.1352 1.34627
\(163\) 17.8366 1.39707 0.698534 0.715577i \(-0.253836\pi\)
0.698534 + 0.715577i \(0.253836\pi\)
\(164\) −4.92852 −0.384853
\(165\) 22.7769 1.77318
\(166\) 1.70720 0.132505
\(167\) 9.99391 0.773352 0.386676 0.922216i \(-0.373623\pi\)
0.386676 + 0.922216i \(0.373623\pi\)
\(168\) 7.33987 0.566284
\(169\) 5.38968 0.414591
\(170\) 12.1249 0.929937
\(171\) 46.3662 3.54571
\(172\) −9.18429 −0.700296
\(173\) 5.77748 0.439253 0.219627 0.975584i \(-0.429516\pi\)
0.219627 + 0.975584i \(0.429516\pi\)
\(174\) −32.4103 −2.45702
\(175\) 2.13290 0.161232
\(176\) −3.59300 −0.270832
\(177\) −6.97248 −0.524083
\(178\) 18.2344 1.36673
\(179\) 6.59095 0.492631 0.246315 0.969190i \(-0.420780\pi\)
0.246315 + 0.969190i \(0.420780\pi\)
\(180\) 13.8067 1.02909
\(181\) 25.0328 1.86068 0.930338 0.366703i \(-0.119513\pi\)
0.930338 + 0.366703i \(0.119513\pi\)
\(182\) −10.0403 −0.744239
\(183\) 13.4593 0.994942
\(184\) 1.00000 0.0737210
\(185\) −22.2162 −1.63337
\(186\) 6.11560 0.448418
\(187\) −21.5440 −1.57545
\(188\) 8.36252 0.609900
\(189\) 28.0954 2.04364
\(190\) 13.7319 0.996219
\(191\) 7.84380 0.567558 0.283779 0.958890i \(-0.408412\pi\)
0.283779 + 0.958890i \(0.408412\pi\)
\(192\) −3.13493 −0.226244
\(193\) 23.3871 1.68344 0.841721 0.539912i \(-0.181543\pi\)
0.841721 + 0.539912i \(0.181543\pi\)
\(194\) −12.9465 −0.929506
\(195\) −27.1847 −1.94674
\(196\) −1.51822 −0.108444
\(197\) −19.8122 −1.41156 −0.705781 0.708430i \(-0.749404\pi\)
−0.705781 + 0.708430i \(0.749404\pi\)
\(198\) −24.5322 −1.74343
\(199\) 6.30432 0.446901 0.223451 0.974715i \(-0.428268\pi\)
0.223451 + 0.974715i \(0.428268\pi\)
\(200\) −0.910980 −0.0644160
\(201\) 15.5990 1.10027
\(202\) 17.1239 1.20483
\(203\) −24.2057 −1.69890
\(204\) −18.7973 −1.31608
\(205\) −9.96612 −0.696064
\(206\) 12.3311 0.859147
\(207\) 6.82778 0.474564
\(208\) 4.28832 0.297341
\(209\) −24.3994 −1.68774
\(210\) 14.8422 1.02421
\(211\) −16.9750 −1.16861 −0.584304 0.811535i \(-0.698632\pi\)
−0.584304 + 0.811535i \(0.698632\pi\)
\(212\) 11.0290 0.757473
\(213\) −27.8657 −1.90932
\(214\) 10.0130 0.684477
\(215\) −18.5719 −1.26659
\(216\) −11.9998 −0.816484
\(217\) 4.56744 0.310058
\(218\) 9.22553 0.624832
\(219\) 17.0782 1.15404
\(220\) −7.26552 −0.489841
\(221\) 25.7132 1.72966
\(222\) 34.4420 2.31159
\(223\) −4.11278 −0.275412 −0.137706 0.990473i \(-0.543973\pi\)
−0.137706 + 0.990473i \(0.543973\pi\)
\(224\) −2.34132 −0.156436
\(225\) −6.21997 −0.414665
\(226\) −11.5838 −0.770541
\(227\) 25.3339 1.68147 0.840735 0.541447i \(-0.182123\pi\)
0.840735 + 0.541447i \(0.182123\pi\)
\(228\) −21.2887 −1.40988
\(229\) −10.9457 −0.723314 −0.361657 0.932311i \(-0.617789\pi\)
−0.361657 + 0.932311i \(0.617789\pi\)
\(230\) 2.02213 0.133335
\(231\) −26.3722 −1.73516
\(232\) 10.3385 0.678753
\(233\) 18.9687 1.24268 0.621339 0.783542i \(-0.286589\pi\)
0.621339 + 0.783542i \(0.286589\pi\)
\(234\) 29.2797 1.91407
\(235\) 16.9101 1.10309
\(236\) 2.22413 0.144778
\(237\) 37.7395 2.45144
\(238\) −14.0388 −0.909999
\(239\) 6.77067 0.437958 0.218979 0.975730i \(-0.429727\pi\)
0.218979 + 0.975730i \(0.429727\pi\)
\(240\) −6.33924 −0.409196
\(241\) 11.6269 0.748956 0.374478 0.927236i \(-0.377822\pi\)
0.374478 + 0.927236i \(0.377822\pi\)
\(242\) 1.90964 0.122756
\(243\) −17.7183 −1.13663
\(244\) −4.29334 −0.274853
\(245\) −3.07004 −0.196138
\(246\) 15.4506 0.985092
\(247\) 29.1212 1.85294
\(248\) −1.95079 −0.123876
\(249\) −5.35196 −0.339167
\(250\) −11.9528 −0.755961
\(251\) −13.2512 −0.836410 −0.418205 0.908353i \(-0.637341\pi\)
−0.418205 + 0.908353i \(0.637341\pi\)
\(252\) −15.9860 −1.00702
\(253\) −3.59300 −0.225890
\(254\) −9.71481 −0.609561
\(255\) −38.0107 −2.38032
\(256\) 1.00000 0.0625000
\(257\) 3.10580 0.193734 0.0968672 0.995297i \(-0.469118\pi\)
0.0968672 + 0.995297i \(0.469118\pi\)
\(258\) 28.7921 1.79252
\(259\) 25.7230 1.59835
\(260\) 8.67155 0.537787
\(261\) 70.5888 4.36933
\(262\) 1.00000 0.0617802
\(263\) 8.07948 0.498202 0.249101 0.968478i \(-0.419865\pi\)
0.249101 + 0.968478i \(0.419865\pi\)
\(264\) 11.2638 0.693239
\(265\) 22.3020 1.37000
\(266\) −15.8995 −0.974859
\(267\) −57.1635 −3.49835
\(268\) −4.97586 −0.303949
\(269\) −6.52400 −0.397776 −0.198888 0.980022i \(-0.563733\pi\)
−0.198888 + 0.980022i \(0.563733\pi\)
\(270\) −24.2652 −1.47673
\(271\) −4.00252 −0.243136 −0.121568 0.992583i \(-0.538792\pi\)
−0.121568 + 0.992583i \(0.538792\pi\)
\(272\) 5.99610 0.363567
\(273\) 31.4757 1.90500
\(274\) −3.06082 −0.184911
\(275\) 3.27315 0.197378
\(276\) −3.13493 −0.188701
\(277\) −9.12487 −0.548260 −0.274130 0.961693i \(-0.588390\pi\)
−0.274130 + 0.961693i \(0.588390\pi\)
\(278\) 14.0439 0.842299
\(279\) −13.3196 −0.797424
\(280\) −4.73446 −0.282938
\(281\) 18.9942 1.13310 0.566550 0.824027i \(-0.308278\pi\)
0.566550 + 0.824027i \(0.308278\pi\)
\(282\) −26.2159 −1.56113
\(283\) −1.92640 −0.114513 −0.0572564 0.998360i \(-0.518235\pi\)
−0.0572564 + 0.998360i \(0.518235\pi\)
\(284\) 8.88877 0.527452
\(285\) −43.0486 −2.54998
\(286\) −15.4079 −0.911090
\(287\) 11.5392 0.681140
\(288\) 6.82778 0.402331
\(289\) 18.9532 1.11489
\(290\) 20.9057 1.22763
\(291\) 40.5864 2.37922
\(292\) −5.44770 −0.318803
\(293\) −13.3569 −0.780321 −0.390160 0.920747i \(-0.627580\pi\)
−0.390160 + 0.920747i \(0.627580\pi\)
\(294\) 4.75951 0.277580
\(295\) 4.49748 0.261853
\(296\) −10.9865 −0.638578
\(297\) 43.1153 2.50181
\(298\) −19.7560 −1.14443
\(299\) 4.28832 0.248000
\(300\) 2.85586 0.164883
\(301\) 21.5034 1.23943
\(302\) 3.09790 0.178264
\(303\) −53.6822 −3.08396
\(304\) 6.79081 0.389480
\(305\) −8.68171 −0.497113
\(306\) 40.9400 2.34039
\(307\) −6.71898 −0.383473 −0.191736 0.981446i \(-0.561412\pi\)
−0.191736 + 0.981446i \(0.561412\pi\)
\(308\) 8.41236 0.479339
\(309\) −38.6571 −2.19912
\(310\) −3.94477 −0.224048
\(311\) −14.3771 −0.815250 −0.407625 0.913149i \(-0.633643\pi\)
−0.407625 + 0.913149i \(0.633643\pi\)
\(312\) −13.4436 −0.761093
\(313\) −1.09589 −0.0619435 −0.0309718 0.999520i \(-0.509860\pi\)
−0.0309718 + 0.999520i \(0.509860\pi\)
\(314\) −13.4885 −0.761197
\(315\) −32.3259 −1.82136
\(316\) −12.0384 −0.677212
\(317\) 10.9286 0.613814 0.306907 0.951740i \(-0.400706\pi\)
0.306907 + 0.951740i \(0.400706\pi\)
\(318\) −34.5750 −1.93887
\(319\) −37.1461 −2.07978
\(320\) 2.02213 0.113041
\(321\) −31.3902 −1.75203
\(322\) −2.34132 −0.130477
\(323\) 40.7184 2.26563
\(324\) 17.1352 0.951958
\(325\) −3.90657 −0.216698
\(326\) 17.8366 0.987876
\(327\) −28.9214 −1.59936
\(328\) −4.92852 −0.272132
\(329\) −19.5793 −1.07944
\(330\) 22.7769 1.25383
\(331\) 6.91316 0.379982 0.189991 0.981786i \(-0.439154\pi\)
0.189991 + 0.981786i \(0.439154\pi\)
\(332\) 1.70720 0.0936950
\(333\) −75.0135 −4.11072
\(334\) 9.99391 0.546842
\(335\) −10.0618 −0.549737
\(336\) 7.33987 0.400423
\(337\) −7.10751 −0.387171 −0.193585 0.981083i \(-0.562012\pi\)
−0.193585 + 0.981083i \(0.562012\pi\)
\(338\) 5.38968 0.293160
\(339\) 36.3143 1.97232
\(340\) 12.1249 0.657565
\(341\) 7.00920 0.379570
\(342\) 46.3662 2.50720
\(343\) 19.9439 1.07687
\(344\) −9.18429 −0.495184
\(345\) −6.33924 −0.341293
\(346\) 5.77748 0.310599
\(347\) −20.8014 −1.11668 −0.558340 0.829613i \(-0.688561\pi\)
−0.558340 + 0.829613i \(0.688561\pi\)
\(348\) −32.4103 −1.73738
\(349\) 8.76047 0.468937 0.234469 0.972124i \(-0.424665\pi\)
0.234469 + 0.972124i \(0.424665\pi\)
\(350\) 2.13290 0.114008
\(351\) −51.4591 −2.74668
\(352\) −3.59300 −0.191507
\(353\) 22.1071 1.17664 0.588320 0.808628i \(-0.299790\pi\)
0.588320 + 0.808628i \(0.299790\pi\)
\(354\) −6.97248 −0.370583
\(355\) 17.9743 0.953975
\(356\) 18.2344 0.966421
\(357\) 44.0106 2.32929
\(358\) 6.59095 0.348342
\(359\) 10.0410 0.529942 0.264971 0.964256i \(-0.414638\pi\)
0.264971 + 0.964256i \(0.414638\pi\)
\(360\) 13.8067 0.727676
\(361\) 27.1152 1.42711
\(362\) 25.0328 1.31570
\(363\) −5.98658 −0.314214
\(364\) −10.0403 −0.526256
\(365\) −11.0160 −0.576603
\(366\) 13.4593 0.703530
\(367\) 10.2317 0.534092 0.267046 0.963684i \(-0.413952\pi\)
0.267046 + 0.963684i \(0.413952\pi\)
\(368\) 1.00000 0.0521286
\(369\) −33.6509 −1.75179
\(370\) −22.2162 −1.15496
\(371\) −25.8223 −1.34063
\(372\) 6.11560 0.317079
\(373\) 32.6683 1.69150 0.845751 0.533577i \(-0.179153\pi\)
0.845751 + 0.533577i \(0.179153\pi\)
\(374\) −21.5440 −1.11401
\(375\) 37.4711 1.93500
\(376\) 8.36252 0.431264
\(377\) 44.3346 2.28335
\(378\) 28.0954 1.44507
\(379\) 25.9716 1.33407 0.667037 0.745025i \(-0.267562\pi\)
0.667037 + 0.745025i \(0.267562\pi\)
\(380\) 13.7319 0.704433
\(381\) 30.4552 1.56027
\(382\) 7.84380 0.401324
\(383\) 19.0461 0.973212 0.486606 0.873621i \(-0.338235\pi\)
0.486606 + 0.873621i \(0.338235\pi\)
\(384\) −3.13493 −0.159979
\(385\) 17.0109 0.866956
\(386\) 23.3871 1.19037
\(387\) −62.7083 −3.18764
\(388\) −12.9465 −0.657260
\(389\) −13.1330 −0.665870 −0.332935 0.942950i \(-0.608039\pi\)
−0.332935 + 0.942950i \(0.608039\pi\)
\(390\) −27.1847 −1.37655
\(391\) 5.99610 0.303236
\(392\) −1.51822 −0.0766816
\(393\) −3.13493 −0.158136
\(394\) −19.8122 −0.998125
\(395\) −24.3432 −1.22484
\(396\) −24.5322 −1.23279
\(397\) −10.8982 −0.546965 −0.273482 0.961877i \(-0.588176\pi\)
−0.273482 + 0.961877i \(0.588176\pi\)
\(398\) 6.30432 0.316007
\(399\) 49.8437 2.49531
\(400\) −0.910980 −0.0455490
\(401\) −2.95607 −0.147619 −0.0738094 0.997272i \(-0.523516\pi\)
−0.0738094 + 0.997272i \(0.523516\pi\)
\(402\) 15.5990 0.778006
\(403\) −8.36563 −0.416722
\(404\) 17.1239 0.851946
\(405\) 34.6497 1.72176
\(406\) −24.2057 −1.20131
\(407\) 39.4745 1.95668
\(408\) −18.7973 −0.930607
\(409\) 0.901560 0.0445793 0.0222896 0.999752i \(-0.492904\pi\)
0.0222896 + 0.999752i \(0.492904\pi\)
\(410\) −9.96612 −0.492192
\(411\) 9.59547 0.473310
\(412\) 12.3311 0.607509
\(413\) −5.20739 −0.256239
\(414\) 6.82778 0.335567
\(415\) 3.45219 0.169461
\(416\) 4.28832 0.210252
\(417\) −44.0267 −2.15600
\(418\) −24.3994 −1.19341
\(419\) 11.8234 0.577611 0.288806 0.957388i \(-0.406742\pi\)
0.288806 + 0.957388i \(0.406742\pi\)
\(420\) 14.8422 0.724225
\(421\) −37.1874 −1.81240 −0.906201 0.422848i \(-0.861030\pi\)
−0.906201 + 0.422848i \(0.861030\pi\)
\(422\) −16.9750 −0.826330
\(423\) 57.0975 2.77617
\(424\) 11.0290 0.535614
\(425\) −5.46233 −0.264962
\(426\) −27.8657 −1.35010
\(427\) 10.0521 0.486455
\(428\) 10.0130 0.483999
\(429\) 48.3028 2.33208
\(430\) −18.5719 −0.895614
\(431\) 14.1521 0.681681 0.340841 0.940121i \(-0.389288\pi\)
0.340841 + 0.940121i \(0.389288\pi\)
\(432\) −11.9998 −0.577342
\(433\) 14.0268 0.674087 0.337044 0.941489i \(-0.390573\pi\)
0.337044 + 0.941489i \(0.390573\pi\)
\(434\) 4.56744 0.219244
\(435\) −65.5380 −3.14231
\(436\) 9.22553 0.441823
\(437\) 6.79081 0.324849
\(438\) 17.0782 0.816026
\(439\) 4.50747 0.215130 0.107565 0.994198i \(-0.465695\pi\)
0.107565 + 0.994198i \(0.465695\pi\)
\(440\) −7.26552 −0.346370
\(441\) −10.3661 −0.493622
\(442\) 25.7132 1.22305
\(443\) 32.9971 1.56774 0.783870 0.620925i \(-0.213243\pi\)
0.783870 + 0.620925i \(0.213243\pi\)
\(444\) 34.4420 1.63454
\(445\) 36.8724 1.74792
\(446\) −4.11278 −0.194746
\(447\) 61.9336 2.92936
\(448\) −2.34132 −0.110617
\(449\) −12.3225 −0.581535 −0.290767 0.956794i \(-0.593911\pi\)
−0.290767 + 0.956794i \(0.593911\pi\)
\(450\) −6.21997 −0.293212
\(451\) 17.7082 0.833845
\(452\) −11.5838 −0.544855
\(453\) −9.71168 −0.456295
\(454\) 25.3339 1.18898
\(455\) −20.3029 −0.951814
\(456\) −21.2887 −0.996936
\(457\) 13.9556 0.652814 0.326407 0.945229i \(-0.394162\pi\)
0.326407 + 0.945229i \(0.394162\pi\)
\(458\) −10.9457 −0.511460
\(459\) −71.9521 −3.35844
\(460\) 2.02213 0.0942824
\(461\) 31.8816 1.48487 0.742437 0.669916i \(-0.233670\pi\)
0.742437 + 0.669916i \(0.233670\pi\)
\(462\) −26.3722 −1.22694
\(463\) 1.86016 0.0864488 0.0432244 0.999065i \(-0.486237\pi\)
0.0432244 + 0.999065i \(0.486237\pi\)
\(464\) 10.3385 0.479951
\(465\) 12.3666 0.573485
\(466\) 18.9687 0.878706
\(467\) −33.5702 −1.55345 −0.776723 0.629843i \(-0.783119\pi\)
−0.776723 + 0.629843i \(0.783119\pi\)
\(468\) 29.2797 1.35345
\(469\) 11.6501 0.537951
\(470\) 16.9101 0.780006
\(471\) 42.2853 1.94841
\(472\) 2.22413 0.102374
\(473\) 32.9991 1.51730
\(474\) 37.7395 1.73343
\(475\) −6.18630 −0.283847
\(476\) −14.0388 −0.643467
\(477\) 75.3034 3.44790
\(478\) 6.77067 0.309683
\(479\) −30.8222 −1.40830 −0.704151 0.710050i \(-0.748672\pi\)
−0.704151 + 0.710050i \(0.748672\pi\)
\(480\) −6.33924 −0.289345
\(481\) −47.1137 −2.14820
\(482\) 11.6269 0.529592
\(483\) 7.33987 0.333976
\(484\) 1.90964 0.0868018
\(485\) −26.1796 −1.18875
\(486\) −17.7183 −0.803720
\(487\) 8.91092 0.403792 0.201896 0.979407i \(-0.435290\pi\)
0.201896 + 0.979407i \(0.435290\pi\)
\(488\) −4.29334 −0.194351
\(489\) −55.9164 −2.52863
\(490\) −3.07004 −0.138690
\(491\) 32.9441 1.48675 0.743373 0.668877i \(-0.233225\pi\)
0.743373 + 0.668877i \(0.233225\pi\)
\(492\) 15.4506 0.696565
\(493\) 61.9904 2.79191
\(494\) 29.1212 1.31022
\(495\) −49.6074 −2.22969
\(496\) −1.95079 −0.0875933
\(497\) −20.8115 −0.933522
\(498\) −5.35196 −0.239827
\(499\) 20.2249 0.905392 0.452696 0.891665i \(-0.350462\pi\)
0.452696 + 0.891665i \(0.350462\pi\)
\(500\) −11.9528 −0.534545
\(501\) −31.3302 −1.39973
\(502\) −13.2512 −0.591432
\(503\) 2.02131 0.0901258 0.0450629 0.998984i \(-0.485651\pi\)
0.0450629 + 0.998984i \(0.485651\pi\)
\(504\) −15.9860 −0.712074
\(505\) 34.6268 1.54087
\(506\) −3.59300 −0.159728
\(507\) −16.8963 −0.750390
\(508\) −9.71481 −0.431025
\(509\) −12.8645 −0.570209 −0.285104 0.958496i \(-0.592028\pi\)
−0.285104 + 0.958496i \(0.592028\pi\)
\(510\) −38.0107 −1.68314
\(511\) 12.7548 0.564240
\(512\) 1.00000 0.0441942
\(513\) −81.4886 −3.59781
\(514\) 3.10580 0.136991
\(515\) 24.9351 1.09877
\(516\) 28.7921 1.26750
\(517\) −30.0465 −1.32144
\(518\) 25.7230 1.13020
\(519\) −18.1120 −0.795028
\(520\) 8.67155 0.380273
\(521\) 6.78749 0.297365 0.148683 0.988885i \(-0.452497\pi\)
0.148683 + 0.988885i \(0.452497\pi\)
\(522\) 70.5888 3.08959
\(523\) −0.834817 −0.0365040 −0.0182520 0.999833i \(-0.505810\pi\)
−0.0182520 + 0.999833i \(0.505810\pi\)
\(524\) 1.00000 0.0436852
\(525\) −6.68648 −0.291822
\(526\) 8.07948 0.352282
\(527\) −11.6972 −0.509536
\(528\) 11.2638 0.490194
\(529\) 1.00000 0.0434783
\(530\) 22.3020 0.968738
\(531\) 15.1858 0.659009
\(532\) −15.8995 −0.689330
\(533\) −21.1351 −0.915461
\(534\) −57.1635 −2.47371
\(535\) 20.2477 0.875384
\(536\) −4.97586 −0.214924
\(537\) −20.6622 −0.891638
\(538\) −6.52400 −0.281270
\(539\) 5.45496 0.234962
\(540\) −24.2652 −1.04421
\(541\) 9.76004 0.419617 0.209808 0.977743i \(-0.432716\pi\)
0.209808 + 0.977743i \(0.432716\pi\)
\(542\) −4.00252 −0.171923
\(543\) −78.4762 −3.36774
\(544\) 5.99610 0.257080
\(545\) 18.6552 0.799103
\(546\) 31.4757 1.34704
\(547\) −3.52187 −0.150584 −0.0752921 0.997162i \(-0.523989\pi\)
−0.0752921 + 0.997162i \(0.523989\pi\)
\(548\) −3.06082 −0.130752
\(549\) −29.3140 −1.25109
\(550\) 3.27315 0.139568
\(551\) 70.2066 2.99090
\(552\) −3.13493 −0.133431
\(553\) 28.1857 1.19858
\(554\) −9.12487 −0.387679
\(555\) 69.6462 2.95632
\(556\) 14.0439 0.595595
\(557\) 34.5875 1.46552 0.732759 0.680488i \(-0.238232\pi\)
0.732759 + 0.680488i \(0.238232\pi\)
\(558\) −13.3196 −0.563864
\(559\) −39.3852 −1.66582
\(560\) −4.73446 −0.200067
\(561\) 67.5388 2.85149
\(562\) 18.9942 0.801222
\(563\) −44.6306 −1.88095 −0.940477 0.339856i \(-0.889622\pi\)
−0.940477 + 0.339856i \(0.889622\pi\)
\(564\) −26.2159 −1.10389
\(565\) −23.4239 −0.985452
\(566\) −1.92640 −0.0809728
\(567\) −40.1191 −1.68484
\(568\) 8.88877 0.372965
\(569\) −12.6249 −0.529265 −0.264632 0.964349i \(-0.585251\pi\)
−0.264632 + 0.964349i \(0.585251\pi\)
\(570\) −43.0486 −1.80311
\(571\) 11.4046 0.477267 0.238633 0.971110i \(-0.423301\pi\)
0.238633 + 0.971110i \(0.423301\pi\)
\(572\) −15.4079 −0.644238
\(573\) −24.5898 −1.02725
\(574\) 11.5392 0.481639
\(575\) −0.910980 −0.0379905
\(576\) 6.82778 0.284491
\(577\) 16.0144 0.666687 0.333343 0.942805i \(-0.391823\pi\)
0.333343 + 0.942805i \(0.391823\pi\)
\(578\) 18.9532 0.788348
\(579\) −73.3170 −3.04695
\(580\) 20.9057 0.868064
\(581\) −3.99711 −0.165828
\(582\) 40.5864 1.68236
\(583\) −39.6271 −1.64119
\(584\) −5.44770 −0.225428
\(585\) 59.2074 2.44793
\(586\) −13.3569 −0.551770
\(587\) 4.72074 0.194846 0.0974229 0.995243i \(-0.468940\pi\)
0.0974229 + 0.995243i \(0.468940\pi\)
\(588\) 4.75951 0.196279
\(589\) −13.2475 −0.545853
\(590\) 4.49748 0.185158
\(591\) 62.1099 2.55486
\(592\) −10.9865 −0.451543
\(593\) −24.8948 −1.02231 −0.511154 0.859489i \(-0.670782\pi\)
−0.511154 + 0.859489i \(0.670782\pi\)
\(594\) 43.1153 1.76904
\(595\) −28.3883 −1.16381
\(596\) −19.7560 −0.809237
\(597\) −19.7636 −0.808870
\(598\) 4.28832 0.175362
\(599\) 8.29688 0.339001 0.169501 0.985530i \(-0.445785\pi\)
0.169501 + 0.985530i \(0.445785\pi\)
\(600\) 2.85586 0.116590
\(601\) 28.6966 1.17056 0.585279 0.810832i \(-0.300985\pi\)
0.585279 + 0.810832i \(0.300985\pi\)
\(602\) 21.5034 0.876412
\(603\) −33.9741 −1.38353
\(604\) 3.09790 0.126052
\(605\) 3.86154 0.156994
\(606\) −53.6822 −2.18069
\(607\) −31.4413 −1.27616 −0.638082 0.769969i \(-0.720272\pi\)
−0.638082 + 0.769969i \(0.720272\pi\)
\(608\) 6.79081 0.275404
\(609\) 75.8830 3.07493
\(610\) −8.68171 −0.351512
\(611\) 35.8612 1.45079
\(612\) 40.9400 1.65490
\(613\) 18.7248 0.756288 0.378144 0.925747i \(-0.376562\pi\)
0.378144 + 0.925747i \(0.376562\pi\)
\(614\) −6.71898 −0.271156
\(615\) 31.2431 1.25984
\(616\) 8.41236 0.338944
\(617\) −29.2830 −1.17889 −0.589444 0.807809i \(-0.700653\pi\)
−0.589444 + 0.807809i \(0.700653\pi\)
\(618\) −38.6571 −1.55501
\(619\) −29.3188 −1.17842 −0.589212 0.807978i \(-0.700562\pi\)
−0.589212 + 0.807978i \(0.700562\pi\)
\(620\) −3.94477 −0.158426
\(621\) −11.9998 −0.481536
\(622\) −14.3771 −0.576469
\(623\) −42.6925 −1.71044
\(624\) −13.4436 −0.538174
\(625\) −19.6152 −0.784609
\(626\) −1.09589 −0.0438007
\(627\) 76.4903 3.05473
\(628\) −13.4885 −0.538248
\(629\) −65.8762 −2.62666
\(630\) −32.3259 −1.28789
\(631\) −43.6294 −1.73686 −0.868429 0.495813i \(-0.834870\pi\)
−0.868429 + 0.495813i \(0.834870\pi\)
\(632\) −12.0384 −0.478861
\(633\) 53.2154 2.11512
\(634\) 10.9286 0.434032
\(635\) −19.6446 −0.779573
\(636\) −34.5750 −1.37099
\(637\) −6.51060 −0.257960
\(638\) −37.1461 −1.47063
\(639\) 60.6906 2.40088
\(640\) 2.02213 0.0799318
\(641\) −20.1519 −0.795953 −0.397977 0.917396i \(-0.630287\pi\)
−0.397977 + 0.917396i \(0.630287\pi\)
\(642\) −31.3902 −1.23887
\(643\) −32.5778 −1.28474 −0.642372 0.766393i \(-0.722050\pi\)
−0.642372 + 0.766393i \(0.722050\pi\)
\(644\) −2.34132 −0.0922610
\(645\) 58.2214 2.29247
\(646\) 40.7184 1.60204
\(647\) 8.70611 0.342273 0.171136 0.985247i \(-0.445256\pi\)
0.171136 + 0.985247i \(0.445256\pi\)
\(648\) 17.1352 0.673136
\(649\) −7.99128 −0.313685
\(650\) −3.90657 −0.153228
\(651\) −14.3186 −0.561190
\(652\) 17.8366 0.698534
\(653\) 3.91741 0.153300 0.0766500 0.997058i \(-0.475578\pi\)
0.0766500 + 0.997058i \(0.475578\pi\)
\(654\) −28.9214 −1.13092
\(655\) 2.02213 0.0790113
\(656\) −4.92852 −0.192426
\(657\) −37.1957 −1.45114
\(658\) −19.5793 −0.763282
\(659\) 8.23215 0.320679 0.160340 0.987062i \(-0.448741\pi\)
0.160340 + 0.987062i \(0.448741\pi\)
\(660\) 22.7769 0.886589
\(661\) −5.15459 −0.200490 −0.100245 0.994963i \(-0.531963\pi\)
−0.100245 + 0.994963i \(0.531963\pi\)
\(662\) 6.91316 0.268688
\(663\) −80.6090 −3.13059
\(664\) 1.70720 0.0662524
\(665\) −32.1508 −1.24676
\(666\) −75.0135 −2.90672
\(667\) 10.3385 0.400307
\(668\) 9.99391 0.386676
\(669\) 12.8933 0.498482
\(670\) −10.0618 −0.388723
\(671\) 15.4260 0.595513
\(672\) 7.33987 0.283142
\(673\) −18.1232 −0.698596 −0.349298 0.937012i \(-0.613580\pi\)
−0.349298 + 0.937012i \(0.613580\pi\)
\(674\) −7.10751 −0.273771
\(675\) 10.9316 0.420758
\(676\) 5.38968 0.207295
\(677\) −24.4218 −0.938608 −0.469304 0.883037i \(-0.655495\pi\)
−0.469304 + 0.883037i \(0.655495\pi\)
\(678\) 36.3143 1.39464
\(679\) 30.3120 1.16327
\(680\) 12.1249 0.464969
\(681\) −79.4200 −3.04338
\(682\) 7.00920 0.268396
\(683\) 6.20507 0.237430 0.118715 0.992928i \(-0.462122\pi\)
0.118715 + 0.992928i \(0.462122\pi\)
\(684\) 46.3662 1.77286
\(685\) −6.18939 −0.236485
\(686\) 19.9439 0.761461
\(687\) 34.3141 1.30916
\(688\) −9.18429 −0.350148
\(689\) 47.2957 1.80182
\(690\) −6.33924 −0.241331
\(691\) 37.0076 1.40784 0.703918 0.710282i \(-0.251432\pi\)
0.703918 + 0.710282i \(0.251432\pi\)
\(692\) 5.77748 0.219627
\(693\) 57.4378 2.18188
\(694\) −20.8014 −0.789611
\(695\) 28.3987 1.07722
\(696\) −32.4103 −1.22851
\(697\) −29.5519 −1.11936
\(698\) 8.76047 0.331589
\(699\) −59.4654 −2.24919
\(700\) 2.13290 0.0806159
\(701\) −17.4901 −0.660593 −0.330296 0.943877i \(-0.607149\pi\)
−0.330296 + 0.943877i \(0.607149\pi\)
\(702\) −51.4591 −1.94220
\(703\) −74.6074 −2.81387
\(704\) −3.59300 −0.135416
\(705\) −53.0120 −1.99655
\(706\) 22.1071 0.832010
\(707\) −40.0926 −1.50784
\(708\) −6.97248 −0.262042
\(709\) 0.0586086 0.00220109 0.00110055 0.999999i \(-0.499650\pi\)
0.00110055 + 0.999999i \(0.499650\pi\)
\(710\) 17.9743 0.674562
\(711\) −82.1955 −3.08257
\(712\) 18.2344 0.683363
\(713\) −1.95079 −0.0730578
\(714\) 44.0106 1.64705
\(715\) −31.1569 −1.16520
\(716\) 6.59095 0.246315
\(717\) −21.2256 −0.792684
\(718\) 10.0410 0.374725
\(719\) −1.21839 −0.0454384 −0.0227192 0.999742i \(-0.507232\pi\)
−0.0227192 + 0.999742i \(0.507232\pi\)
\(720\) 13.8067 0.514544
\(721\) −28.8710 −1.07521
\(722\) 27.1152 1.00912
\(723\) −36.4496 −1.35557
\(724\) 25.0328 0.930338
\(725\) −9.41813 −0.349781
\(726\) −5.98658 −0.222183
\(727\) −33.3268 −1.23602 −0.618011 0.786169i \(-0.712061\pi\)
−0.618011 + 0.786169i \(0.712061\pi\)
\(728\) −10.0403 −0.372119
\(729\) 4.13995 0.153332
\(730\) −11.0160 −0.407720
\(731\) −55.0699 −2.03683
\(732\) 13.4593 0.497471
\(733\) −2.91060 −0.107505 −0.0537527 0.998554i \(-0.517118\pi\)
−0.0537527 + 0.998554i \(0.517118\pi\)
\(734\) 10.2317 0.377660
\(735\) 9.62435 0.355000
\(736\) 1.00000 0.0368605
\(737\) 17.8783 0.658554
\(738\) −33.6509 −1.23871
\(739\) 25.8562 0.951137 0.475568 0.879679i \(-0.342242\pi\)
0.475568 + 0.879679i \(0.342242\pi\)
\(740\) −22.2162 −0.816684
\(741\) −91.2928 −3.35373
\(742\) −25.8223 −0.947968
\(743\) 12.8688 0.472109 0.236055 0.971740i \(-0.424146\pi\)
0.236055 + 0.971740i \(0.424146\pi\)
\(744\) 6.11560 0.224209
\(745\) −39.9492 −1.46363
\(746\) 32.6683 1.19607
\(747\) 11.6564 0.426486
\(748\) −21.5440 −0.787725
\(749\) −23.4437 −0.856616
\(750\) 37.4711 1.36825
\(751\) 13.0581 0.476498 0.238249 0.971204i \(-0.423427\pi\)
0.238249 + 0.971204i \(0.423427\pi\)
\(752\) 8.36252 0.304950
\(753\) 41.5417 1.51386
\(754\) 44.3346 1.61457
\(755\) 6.26436 0.227983
\(756\) 28.0954 1.02182
\(757\) −38.7414 −1.40808 −0.704040 0.710161i \(-0.748622\pi\)
−0.704040 + 0.710161i \(0.748622\pi\)
\(758\) 25.9716 0.943333
\(759\) 11.2638 0.408850
\(760\) 13.7319 0.498109
\(761\) 40.5719 1.47073 0.735364 0.677672i \(-0.237011\pi\)
0.735364 + 0.677672i \(0.237011\pi\)
\(762\) 30.4552 1.10328
\(763\) −21.5999 −0.781969
\(764\) 7.84380 0.283779
\(765\) 82.7862 2.99314
\(766\) 19.0461 0.688165
\(767\) 9.53776 0.344389
\(768\) −3.13493 −0.113122
\(769\) 31.1521 1.12337 0.561686 0.827350i \(-0.310153\pi\)
0.561686 + 0.827350i \(0.310153\pi\)
\(770\) 17.0109 0.613031
\(771\) −9.73646 −0.350650
\(772\) 23.3871 0.841721
\(773\) 29.1632 1.04893 0.524463 0.851433i \(-0.324266\pi\)
0.524463 + 0.851433i \(0.324266\pi\)
\(774\) −62.7083 −2.25400
\(775\) 1.77714 0.0638366
\(776\) −12.9465 −0.464753
\(777\) −80.6397 −2.89293
\(778\) −13.1330 −0.470841
\(779\) −33.4687 −1.19914
\(780\) −27.1847 −0.973368
\(781\) −31.9373 −1.14281
\(782\) 5.99610 0.214420
\(783\) −124.060 −4.43353
\(784\) −1.51822 −0.0542221
\(785\) −27.2754 −0.973502
\(786\) −3.13493 −0.111819
\(787\) −43.5272 −1.55158 −0.775789 0.630993i \(-0.782648\pi\)
−0.775789 + 0.630993i \(0.782648\pi\)
\(788\) −19.8122 −0.705781
\(789\) −25.3286 −0.901722
\(790\) −24.3432 −0.866093
\(791\) 27.1213 0.964323
\(792\) −24.5322 −0.871714
\(793\) −18.4112 −0.653802
\(794\) −10.8982 −0.386762
\(795\) −69.9153 −2.47964
\(796\) 6.30432 0.223451
\(797\) −34.5512 −1.22387 −0.611934 0.790909i \(-0.709608\pi\)
−0.611934 + 0.790909i \(0.709608\pi\)
\(798\) 49.8437 1.76445
\(799\) 50.1425 1.77391
\(800\) −0.910980 −0.0322080
\(801\) 124.500 4.39901
\(802\) −2.95607 −0.104382
\(803\) 19.5736 0.690737
\(804\) 15.5990 0.550133
\(805\) −4.73446 −0.166868
\(806\) −8.36563 −0.294667
\(807\) 20.4523 0.719955
\(808\) 17.1239 0.602417
\(809\) 25.8947 0.910410 0.455205 0.890387i \(-0.349566\pi\)
0.455205 + 0.890387i \(0.349566\pi\)
\(810\) 34.6497 1.21747
\(811\) −46.5567 −1.63483 −0.817414 0.576050i \(-0.804593\pi\)
−0.817414 + 0.576050i \(0.804593\pi\)
\(812\) −24.2057 −0.849452
\(813\) 12.5476 0.440064
\(814\) 39.4745 1.38358
\(815\) 36.0679 1.26340
\(816\) −18.7973 −0.658038
\(817\) −62.3688 −2.18201
\(818\) 0.901560 0.0315223
\(819\) −68.5532 −2.39544
\(820\) −9.96612 −0.348032
\(821\) −1.79173 −0.0625319 −0.0312660 0.999511i \(-0.509954\pi\)
−0.0312660 + 0.999511i \(0.509954\pi\)
\(822\) 9.59547 0.334680
\(823\) −15.5143 −0.540795 −0.270398 0.962749i \(-0.587155\pi\)
−0.270398 + 0.962749i \(0.587155\pi\)
\(824\) 12.3311 0.429573
\(825\) −10.2611 −0.357246
\(826\) −5.20739 −0.181188
\(827\) 10.5268 0.366051 0.183025 0.983108i \(-0.441411\pi\)
0.183025 + 0.983108i \(0.441411\pi\)
\(828\) 6.82778 0.237282
\(829\) 13.3937 0.465182 0.232591 0.972575i \(-0.425280\pi\)
0.232591 + 0.972575i \(0.425280\pi\)
\(830\) 3.45219 0.119827
\(831\) 28.6058 0.992325
\(832\) 4.28832 0.148671
\(833\) −9.10338 −0.315414
\(834\) −44.0267 −1.52452
\(835\) 20.2090 0.699362
\(836\) −24.3994 −0.843870
\(837\) 23.4092 0.809140
\(838\) 11.8234 0.408433
\(839\) 55.2141 1.90620 0.953101 0.302651i \(-0.0978716\pi\)
0.953101 + 0.302651i \(0.0978716\pi\)
\(840\) 14.8422 0.512104
\(841\) 77.8838 2.68565
\(842\) −37.1874 −1.28156
\(843\) −59.5455 −2.05086
\(844\) −16.9750 −0.584304
\(845\) 10.8986 0.374925
\(846\) 57.0975 1.96305
\(847\) −4.47108 −0.153628
\(848\) 11.0290 0.378736
\(849\) 6.03914 0.207263
\(850\) −5.46233 −0.187356
\(851\) −10.9865 −0.376613
\(852\) −27.8657 −0.954662
\(853\) −21.2306 −0.726921 −0.363460 0.931610i \(-0.618405\pi\)
−0.363460 + 0.931610i \(0.618405\pi\)
\(854\) 10.0521 0.343976
\(855\) 93.7586 3.20648
\(856\) 10.0130 0.342239
\(857\) −25.1859 −0.860335 −0.430167 0.902749i \(-0.641545\pi\)
−0.430167 + 0.902749i \(0.641545\pi\)
\(858\) 48.3028 1.64903
\(859\) 43.7711 1.49345 0.746725 0.665133i \(-0.231625\pi\)
0.746725 + 0.665133i \(0.231625\pi\)
\(860\) −18.5719 −0.633295
\(861\) −36.1747 −1.23283
\(862\) 14.1521 0.482022
\(863\) −31.9504 −1.08760 −0.543802 0.839214i \(-0.683016\pi\)
−0.543802 + 0.839214i \(0.683016\pi\)
\(864\) −11.9998 −0.408242
\(865\) 11.6828 0.397228
\(866\) 14.0268 0.476652
\(867\) −59.4168 −2.01790
\(868\) 4.56744 0.155029
\(869\) 43.2539 1.46729
\(870\) −65.5380 −2.22195
\(871\) −21.3381 −0.723013
\(872\) 9.22553 0.312416
\(873\) −88.3960 −2.99175
\(874\) 6.79081 0.229703
\(875\) 27.9853 0.946076
\(876\) 17.0782 0.577018
\(877\) −11.4696 −0.387300 −0.193650 0.981071i \(-0.562033\pi\)
−0.193650 + 0.981071i \(0.562033\pi\)
\(878\) 4.50747 0.152120
\(879\) 41.8731 1.41234
\(880\) −7.26552 −0.244921
\(881\) −6.45788 −0.217572 −0.108786 0.994065i \(-0.534696\pi\)
−0.108786 + 0.994065i \(0.534696\pi\)
\(882\) −10.3661 −0.349043
\(883\) −9.51765 −0.320294 −0.160147 0.987093i \(-0.551197\pi\)
−0.160147 + 0.987093i \(0.551197\pi\)
\(884\) 25.7132 0.864828
\(885\) −14.0993 −0.473942
\(886\) 32.9971 1.10856
\(887\) −4.27284 −0.143468 −0.0717340 0.997424i \(-0.522853\pi\)
−0.0717340 + 0.997424i \(0.522853\pi\)
\(888\) 34.4420 1.15580
\(889\) 22.7455 0.762859
\(890\) 36.8724 1.23596
\(891\) −61.5669 −2.06257
\(892\) −4.11278 −0.137706
\(893\) 56.7883 1.90035
\(894\) 61.9336 2.07137
\(895\) 13.3278 0.445498
\(896\) −2.34132 −0.0782180
\(897\) −13.4436 −0.448868
\(898\) −12.3225 −0.411207
\(899\) −20.1682 −0.672648
\(900\) −6.21997 −0.207332
\(901\) 66.1307 2.20313
\(902\) 17.7082 0.589617
\(903\) −67.4115 −2.24332
\(904\) −11.5838 −0.385270
\(905\) 50.6197 1.68266
\(906\) −9.71168 −0.322649
\(907\) 33.7979 1.12224 0.561120 0.827734i \(-0.310370\pi\)
0.561120 + 0.827734i \(0.310370\pi\)
\(908\) 25.3339 0.840735
\(909\) 116.918 3.87793
\(910\) −20.3029 −0.673034
\(911\) 28.1337 0.932112 0.466056 0.884755i \(-0.345675\pi\)
0.466056 + 0.884755i \(0.345675\pi\)
\(912\) −21.2887 −0.704940
\(913\) −6.13398 −0.203005
\(914\) 13.9556 0.461609
\(915\) 27.2165 0.899751
\(916\) −10.9457 −0.361657
\(917\) −2.34132 −0.0773172
\(918\) −71.9521 −2.37477
\(919\) −9.90635 −0.326780 −0.163390 0.986562i \(-0.552243\pi\)
−0.163390 + 0.986562i \(0.552243\pi\)
\(920\) 2.02213 0.0666677
\(921\) 21.0635 0.694067
\(922\) 31.8816 1.04996
\(923\) 38.1179 1.25467
\(924\) −26.3722 −0.867580
\(925\) 10.0085 0.329077
\(926\) 1.86016 0.0611285
\(927\) 84.1939 2.76529
\(928\) 10.3385 0.339377
\(929\) −27.2462 −0.893920 −0.446960 0.894554i \(-0.647493\pi\)
−0.446960 + 0.894554i \(0.647493\pi\)
\(930\) 12.3666 0.405515
\(931\) −10.3099 −0.337895
\(932\) 18.9687 0.621339
\(933\) 45.0712 1.47556
\(934\) −33.5702 −1.09845
\(935\) −43.5648 −1.42472
\(936\) 29.2797 0.957037
\(937\) 49.5344 1.61822 0.809110 0.587658i \(-0.199950\pi\)
0.809110 + 0.587658i \(0.199950\pi\)
\(938\) 11.6501 0.380389
\(939\) 3.43555 0.112115
\(940\) 16.9101 0.551547
\(941\) −43.7960 −1.42771 −0.713855 0.700294i \(-0.753052\pi\)
−0.713855 + 0.700294i \(0.753052\pi\)
\(942\) 42.2853 1.37773
\(943\) −4.92852 −0.160495
\(944\) 2.22413 0.0723891
\(945\) 56.8127 1.84812
\(946\) 32.9991 1.07289
\(947\) −10.6668 −0.346624 −0.173312 0.984867i \(-0.555447\pi\)
−0.173312 + 0.984867i \(0.555447\pi\)
\(948\) 37.7395 1.22572
\(949\) −23.3615 −0.758346
\(950\) −6.18630 −0.200710
\(951\) −34.2605 −1.11097
\(952\) −14.0388 −0.455000
\(953\) 8.99085 0.291242 0.145621 0.989340i \(-0.453482\pi\)
0.145621 + 0.989340i \(0.453482\pi\)
\(954\) 75.3034 2.43804
\(955\) 15.8612 0.513257
\(956\) 6.77067 0.218979
\(957\) 116.450 3.76430
\(958\) −30.8222 −0.995820
\(959\) 7.16637 0.231414
\(960\) −6.33924 −0.204598
\(961\) −27.1944 −0.877239
\(962\) −47.1137 −1.51901
\(963\) 68.3669 2.20309
\(964\) 11.6269 0.374478
\(965\) 47.2919 1.52238
\(966\) 7.33987 0.236157
\(967\) −27.8019 −0.894048 −0.447024 0.894522i \(-0.647516\pi\)
−0.447024 + 0.894522i \(0.647516\pi\)
\(968\) 1.90964 0.0613781
\(969\) −127.649 −4.10068
\(970\) −26.1796 −0.840576
\(971\) −28.4151 −0.911884 −0.455942 0.890010i \(-0.650698\pi\)
−0.455942 + 0.890010i \(0.650698\pi\)
\(972\) −17.7183 −0.568316
\(973\) −32.8813 −1.05413
\(974\) 8.91092 0.285524
\(975\) 12.2468 0.392213
\(976\) −4.29334 −0.137427
\(977\) 11.9179 0.381289 0.190644 0.981659i \(-0.438942\pi\)
0.190644 + 0.981659i \(0.438942\pi\)
\(978\) −55.9164 −1.78801
\(979\) −65.5161 −2.09390
\(980\) −3.07004 −0.0980688
\(981\) 62.9899 2.01111
\(982\) 32.9441 1.05129
\(983\) −34.0020 −1.08450 −0.542248 0.840219i \(-0.682426\pi\)
−0.542248 + 0.840219i \(0.682426\pi\)
\(984\) 15.4506 0.492546
\(985\) −40.0629 −1.27651
\(986\) 61.9904 1.97418
\(987\) 61.3799 1.95374
\(988\) 29.1212 0.926468
\(989\) −9.18429 −0.292043
\(990\) −49.6074 −1.57663
\(991\) −5.58472 −0.177404 −0.0887022 0.996058i \(-0.528272\pi\)
−0.0887022 + 0.996058i \(0.528272\pi\)
\(992\) −1.95079 −0.0619378
\(993\) −21.6723 −0.687749
\(994\) −20.8115 −0.660099
\(995\) 12.7482 0.404144
\(996\) −5.35196 −0.169583
\(997\) 14.1073 0.446782 0.223391 0.974729i \(-0.428287\pi\)
0.223391 + 0.974729i \(0.428287\pi\)
\(998\) 20.2249 0.640209
\(999\) 131.836 4.17111
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.m.1.4 41
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.m.1.4 41 1.1 even 1 trivial