Properties

Label 6001.2.a.c.1.18
Level $6001$
Weight $2$
Character 6001.1
Self dual yes
Analytic conductor $47.918$
Analytic rank $0$
Dimension $121$
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] = [6001,2,Mod(1,6001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6001, 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("6001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6001 = 17 \cdot 353 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6001.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: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 6001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.08608 q^{2} +1.06648 q^{3} +2.35172 q^{4} -3.22907 q^{5} -2.22475 q^{6} +0.560788 q^{7} -0.733710 q^{8} -1.86263 q^{9} +O(q^{10})\) \(q-2.08608 q^{2} +1.06648 q^{3} +2.35172 q^{4} -3.22907 q^{5} -2.22475 q^{6} +0.560788 q^{7} -0.733710 q^{8} -1.86263 q^{9} +6.73610 q^{10} -4.80950 q^{11} +2.50805 q^{12} -3.57901 q^{13} -1.16985 q^{14} -3.44373 q^{15} -3.17286 q^{16} -1.00000 q^{17} +3.88558 q^{18} -2.21771 q^{19} -7.59387 q^{20} +0.598068 q^{21} +10.0330 q^{22} +0.337685 q^{23} -0.782484 q^{24} +5.42692 q^{25} +7.46609 q^{26} -5.18588 q^{27} +1.31882 q^{28} +6.91401 q^{29} +7.18389 q^{30} -2.48752 q^{31} +8.08625 q^{32} -5.12922 q^{33} +2.08608 q^{34} -1.81083 q^{35} -4.38037 q^{36} -5.39565 q^{37} +4.62632 q^{38} -3.81693 q^{39} +2.36920 q^{40} +3.91482 q^{41} -1.24762 q^{42} -9.72258 q^{43} -11.3106 q^{44} +6.01456 q^{45} -0.704437 q^{46} -4.67653 q^{47} -3.38378 q^{48} -6.68552 q^{49} -11.3210 q^{50} -1.06648 q^{51} -8.41682 q^{52} -10.9237 q^{53} +10.8181 q^{54} +15.5302 q^{55} -0.411456 q^{56} -2.36514 q^{57} -14.4231 q^{58} -3.30514 q^{59} -8.09868 q^{60} -13.8268 q^{61} +5.18916 q^{62} -1.04454 q^{63} -10.5228 q^{64} +11.5569 q^{65} +10.6999 q^{66} -13.2574 q^{67} -2.35172 q^{68} +0.360133 q^{69} +3.77752 q^{70} -3.80132 q^{71} +1.36663 q^{72} -0.206208 q^{73} +11.2558 q^{74} +5.78768 q^{75} -5.21544 q^{76} -2.69711 q^{77} +7.96241 q^{78} -1.11553 q^{79} +10.2454 q^{80} +0.0572646 q^{81} -8.16661 q^{82} +5.89905 q^{83} +1.40649 q^{84} +3.22907 q^{85} +20.2820 q^{86} +7.37363 q^{87} +3.52878 q^{88} +3.33870 q^{89} -12.5468 q^{90} -2.00707 q^{91} +0.794139 q^{92} -2.65288 q^{93} +9.75560 q^{94} +7.16116 q^{95} +8.62380 q^{96} -9.71130 q^{97} +13.9465 q^{98} +8.95831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.08608 −1.47508 −0.737540 0.675304i \(-0.764012\pi\)
−0.737540 + 0.675304i \(0.764012\pi\)
\(3\) 1.06648 0.615731 0.307865 0.951430i \(-0.400385\pi\)
0.307865 + 0.951430i \(0.400385\pi\)
\(4\) 2.35172 1.17586
\(5\) −3.22907 −1.44409 −0.722043 0.691848i \(-0.756797\pi\)
−0.722043 + 0.691848i \(0.756797\pi\)
\(6\) −2.22475 −0.908251
\(7\) 0.560788 0.211958 0.105979 0.994368i \(-0.466202\pi\)
0.105979 + 0.994368i \(0.466202\pi\)
\(8\) −0.733710 −0.259406
\(9\) −1.86263 −0.620876
\(10\) 6.73610 2.13014
\(11\) −4.80950 −1.45012 −0.725059 0.688687i \(-0.758188\pi\)
−0.725059 + 0.688687i \(0.758188\pi\)
\(12\) 2.50805 0.724012
\(13\) −3.57901 −0.992639 −0.496319 0.868140i \(-0.665315\pi\)
−0.496319 + 0.868140i \(0.665315\pi\)
\(14\) −1.16985 −0.312655
\(15\) −3.44373 −0.889168
\(16\) −3.17286 −0.793215
\(17\) −1.00000 −0.242536
\(18\) 3.88558 0.915841
\(19\) −2.21771 −0.508779 −0.254389 0.967102i \(-0.581874\pi\)
−0.254389 + 0.967102i \(0.581874\pi\)
\(20\) −7.59387 −1.69804
\(21\) 0.598068 0.130509
\(22\) 10.0330 2.13904
\(23\) 0.337685 0.0704122 0.0352061 0.999380i \(-0.488791\pi\)
0.0352061 + 0.999380i \(0.488791\pi\)
\(24\) −0.782484 −0.159724
\(25\) 5.42692 1.08538
\(26\) 7.46609 1.46422
\(27\) −5.18588 −0.998023
\(28\) 1.31882 0.249233
\(29\) 6.91401 1.28390 0.641949 0.766747i \(-0.278126\pi\)
0.641949 + 0.766747i \(0.278126\pi\)
\(30\) 7.18389 1.31159
\(31\) −2.48752 −0.446772 −0.223386 0.974730i \(-0.571711\pi\)
−0.223386 + 0.974730i \(0.571711\pi\)
\(32\) 8.08625 1.42946
\(33\) −5.12922 −0.892882
\(34\) 2.08608 0.357759
\(35\) −1.81083 −0.306086
\(36\) −4.38037 −0.730062
\(37\) −5.39565 −0.887040 −0.443520 0.896264i \(-0.646271\pi\)
−0.443520 + 0.896264i \(0.646271\pi\)
\(38\) 4.62632 0.750489
\(39\) −3.81693 −0.611198
\(40\) 2.36920 0.374604
\(41\) 3.91482 0.611391 0.305696 0.952129i \(-0.401111\pi\)
0.305696 + 0.952129i \(0.401111\pi\)
\(42\) −1.24762 −0.192511
\(43\) −9.72258 −1.48268 −0.741340 0.671130i \(-0.765809\pi\)
−0.741340 + 0.671130i \(0.765809\pi\)
\(44\) −11.3106 −1.70513
\(45\) 6.01456 0.896598
\(46\) −0.704437 −0.103864
\(47\) −4.67653 −0.682142 −0.341071 0.940038i \(-0.610790\pi\)
−0.341071 + 0.940038i \(0.610790\pi\)
\(48\) −3.38378 −0.488407
\(49\) −6.68552 −0.955074
\(50\) −11.3210 −1.60103
\(51\) −1.06648 −0.149337
\(52\) −8.41682 −1.16720
\(53\) −10.9237 −1.50049 −0.750245 0.661159i \(-0.770065\pi\)
−0.750245 + 0.661159i \(0.770065\pi\)
\(54\) 10.8181 1.47216
\(55\) 15.5302 2.09410
\(56\) −0.411456 −0.0549831
\(57\) −2.36514 −0.313271
\(58\) −14.4231 −1.89385
\(59\) −3.30514 −0.430293 −0.215146 0.976582i \(-0.569023\pi\)
−0.215146 + 0.976582i \(0.569023\pi\)
\(60\) −8.09868 −1.04554
\(61\) −13.8268 −1.77033 −0.885167 0.465273i \(-0.845956\pi\)
−0.885167 + 0.465273i \(0.845956\pi\)
\(62\) 5.18916 0.659024
\(63\) −1.04454 −0.131600
\(64\) −10.5228 −1.31535
\(65\) 11.5569 1.43346
\(66\) 10.6999 1.31707
\(67\) −13.2574 −1.61965 −0.809827 0.586668i \(-0.800439\pi\)
−0.809827 + 0.586668i \(0.800439\pi\)
\(68\) −2.35172 −0.285188
\(69\) 0.360133 0.0433549
\(70\) 3.77752 0.451501
\(71\) −3.80132 −0.451133 −0.225567 0.974228i \(-0.572423\pi\)
−0.225567 + 0.974228i \(0.572423\pi\)
\(72\) 1.36663 0.161059
\(73\) −0.206208 −0.0241348 −0.0120674 0.999927i \(-0.503841\pi\)
−0.0120674 + 0.999927i \(0.503841\pi\)
\(74\) 11.2558 1.30845
\(75\) 5.78768 0.668304
\(76\) −5.21544 −0.598252
\(77\) −2.69711 −0.307364
\(78\) 7.96241 0.901565
\(79\) −1.11553 −0.125507 −0.0627534 0.998029i \(-0.519988\pi\)
−0.0627534 + 0.998029i \(0.519988\pi\)
\(80\) 10.2454 1.14547
\(81\) 0.0572646 0.00636273
\(82\) −8.16661 −0.901851
\(83\) 5.89905 0.647505 0.323752 0.946142i \(-0.395056\pi\)
0.323752 + 0.946142i \(0.395056\pi\)
\(84\) 1.40649 0.153460
\(85\) 3.22907 0.350242
\(86\) 20.2820 2.18707
\(87\) 7.37363 0.790536
\(88\) 3.52878 0.376169
\(89\) 3.33870 0.353902 0.176951 0.984220i \(-0.443377\pi\)
0.176951 + 0.984220i \(0.443377\pi\)
\(90\) −12.5468 −1.32255
\(91\) −2.00707 −0.210398
\(92\) 0.794139 0.0827948
\(93\) −2.65288 −0.275091
\(94\) 9.75560 1.00621
\(95\) 7.16116 0.734720
\(96\) 8.62380 0.880163
\(97\) −9.71130 −0.986033 −0.493017 0.870020i \(-0.664106\pi\)
−0.493017 + 0.870020i \(0.664106\pi\)
\(98\) 13.9465 1.40881
\(99\) 8.95831 0.900344
\(100\) 12.7626 1.27626
\(101\) −13.1438 −1.30786 −0.653930 0.756555i \(-0.726881\pi\)
−0.653930 + 0.756555i \(0.726881\pi\)
\(102\) 2.22475 0.220283
\(103\) 2.20797 0.217558 0.108779 0.994066i \(-0.465306\pi\)
0.108779 + 0.994066i \(0.465306\pi\)
\(104\) 2.62595 0.257496
\(105\) −1.93120 −0.188466
\(106\) 22.7878 2.21334
\(107\) −2.83512 −0.274081 −0.137040 0.990565i \(-0.543759\pi\)
−0.137040 + 0.990565i \(0.543759\pi\)
\(108\) −12.1957 −1.17353
\(109\) 1.61581 0.154767 0.0773834 0.997001i \(-0.475343\pi\)
0.0773834 + 0.997001i \(0.475343\pi\)
\(110\) −32.3973 −3.08896
\(111\) −5.75434 −0.546178
\(112\) −1.77930 −0.168128
\(113\) 9.76321 0.918445 0.459223 0.888321i \(-0.348128\pi\)
0.459223 + 0.888321i \(0.348128\pi\)
\(114\) 4.93387 0.462099
\(115\) −1.09041 −0.101681
\(116\) 16.2598 1.50968
\(117\) 6.66636 0.616305
\(118\) 6.89478 0.634716
\(119\) −0.560788 −0.0514074
\(120\) 2.52670 0.230655
\(121\) 12.1313 1.10284
\(122\) 28.8437 2.61138
\(123\) 4.17506 0.376452
\(124\) −5.84994 −0.525341
\(125\) −1.37856 −0.123302
\(126\) 2.17899 0.194120
\(127\) 13.9965 1.24199 0.620996 0.783813i \(-0.286728\pi\)
0.620996 + 0.783813i \(0.286728\pi\)
\(128\) 5.77891 0.510789
\(129\) −10.3689 −0.912931
\(130\) −24.1086 −2.11446
\(131\) 10.5151 0.918706 0.459353 0.888254i \(-0.348081\pi\)
0.459353 + 0.888254i \(0.348081\pi\)
\(132\) −12.0625 −1.04990
\(133\) −1.24367 −0.107840
\(134\) 27.6561 2.38912
\(135\) 16.7456 1.44123
\(136\) 0.733710 0.0629151
\(137\) −4.66687 −0.398717 −0.199359 0.979927i \(-0.563886\pi\)
−0.199359 + 0.979927i \(0.563886\pi\)
\(138\) −0.751265 −0.0639519
\(139\) −0.175209 −0.0148610 −0.00743052 0.999972i \(-0.502365\pi\)
−0.00743052 + 0.999972i \(0.502365\pi\)
\(140\) −4.25855 −0.359913
\(141\) −4.98741 −0.420016
\(142\) 7.92984 0.665457
\(143\) 17.2132 1.43944
\(144\) 5.90986 0.492488
\(145\) −22.3258 −1.85406
\(146\) 0.430165 0.0356007
\(147\) −7.12995 −0.588068
\(148\) −12.6891 −1.04303
\(149\) 5.84453 0.478803 0.239401 0.970921i \(-0.423049\pi\)
0.239401 + 0.970921i \(0.423049\pi\)
\(150\) −12.0736 −0.985802
\(151\) −8.68232 −0.706557 −0.353279 0.935518i \(-0.614933\pi\)
−0.353279 + 0.935518i \(0.614933\pi\)
\(152\) 1.62716 0.131980
\(153\) 1.86263 0.150585
\(154\) 5.62638 0.453387
\(155\) 8.03239 0.645177
\(156\) −8.97634 −0.718682
\(157\) −11.3570 −0.906386 −0.453193 0.891412i \(-0.649715\pi\)
−0.453193 + 0.891412i \(0.649715\pi\)
\(158\) 2.32708 0.185133
\(159\) −11.6499 −0.923898
\(160\) −26.1111 −2.06426
\(161\) 0.189370 0.0149244
\(162\) −0.119458 −0.00938553
\(163\) 0.00171347 0.000134209 0 6.71046e−5 1.00000i \(-0.499979\pi\)
6.71046e−5 1.00000i \(0.499979\pi\)
\(164\) 9.20654 0.718910
\(165\) 16.5626 1.28940
\(166\) −12.3059 −0.955121
\(167\) 17.3447 1.34217 0.671086 0.741380i \(-0.265828\pi\)
0.671086 + 0.741380i \(0.265828\pi\)
\(168\) −0.438808 −0.0338548
\(169\) −0.190694 −0.0146688
\(170\) −6.73610 −0.516635
\(171\) 4.13078 0.315888
\(172\) −22.8648 −1.74342
\(173\) −12.2300 −0.929832 −0.464916 0.885355i \(-0.653915\pi\)
−0.464916 + 0.885355i \(0.653915\pi\)
\(174\) −15.3820 −1.16610
\(175\) 3.04335 0.230056
\(176\) 15.2599 1.15026
\(177\) −3.52486 −0.264945
\(178\) −6.96479 −0.522033
\(179\) −17.7791 −1.32887 −0.664436 0.747345i \(-0.731328\pi\)
−0.664436 + 0.747345i \(0.731328\pi\)
\(180\) 14.1446 1.05427
\(181\) −15.6198 −1.16101 −0.580507 0.814256i \(-0.697145\pi\)
−0.580507 + 0.814256i \(0.697145\pi\)
\(182\) 4.18689 0.310353
\(183\) −14.7459 −1.09005
\(184\) −0.247763 −0.0182653
\(185\) 17.4230 1.28096
\(186\) 5.53412 0.405781
\(187\) 4.80950 0.351705
\(188\) −10.9979 −0.802103
\(189\) −2.90818 −0.211539
\(190\) −14.9387 −1.08377
\(191\) −20.2427 −1.46471 −0.732357 0.680921i \(-0.761580\pi\)
−0.732357 + 0.680921i \(0.761580\pi\)
\(192\) −11.2223 −0.809903
\(193\) 2.91165 0.209585 0.104792 0.994494i \(-0.466582\pi\)
0.104792 + 0.994494i \(0.466582\pi\)
\(194\) 20.2585 1.45448
\(195\) 12.3251 0.882622
\(196\) −15.7224 −1.12303
\(197\) −5.08391 −0.362213 −0.181107 0.983463i \(-0.557968\pi\)
−0.181107 + 0.983463i \(0.557968\pi\)
\(198\) −18.6877 −1.32808
\(199\) 4.47982 0.317566 0.158783 0.987314i \(-0.449243\pi\)
0.158783 + 0.987314i \(0.449243\pi\)
\(200\) −3.98178 −0.281555
\(201\) −14.1388 −0.997271
\(202\) 27.4190 1.92920
\(203\) 3.87729 0.272133
\(204\) −2.50805 −0.175599
\(205\) −12.6412 −0.882902
\(206\) −4.60600 −0.320915
\(207\) −0.628981 −0.0437172
\(208\) 11.3557 0.787376
\(209\) 10.6661 0.737789
\(210\) 4.02864 0.278003
\(211\) −5.43985 −0.374495 −0.187247 0.982313i \(-0.559957\pi\)
−0.187247 + 0.982313i \(0.559957\pi\)
\(212\) −25.6895 −1.76437
\(213\) −4.05401 −0.277777
\(214\) 5.91427 0.404291
\(215\) 31.3949 2.14112
\(216\) 3.80493 0.258893
\(217\) −1.39497 −0.0946969
\(218\) −3.37071 −0.228293
\(219\) −0.219916 −0.0148605
\(220\) 36.5227 2.46236
\(221\) 3.57901 0.240750
\(222\) 12.0040 0.805655
\(223\) 19.6450 1.31553 0.657763 0.753225i \(-0.271503\pi\)
0.657763 + 0.753225i \(0.271503\pi\)
\(224\) 4.53467 0.302986
\(225\) −10.1083 −0.673889
\(226\) −20.3668 −1.35478
\(227\) 8.02162 0.532414 0.266207 0.963916i \(-0.414230\pi\)
0.266207 + 0.963916i \(0.414230\pi\)
\(228\) −5.56214 −0.368362
\(229\) −24.0625 −1.59010 −0.795048 0.606546i \(-0.792555\pi\)
−0.795048 + 0.606546i \(0.792555\pi\)
\(230\) 2.27468 0.149988
\(231\) −2.87641 −0.189254
\(232\) −5.07287 −0.333050
\(233\) 9.24278 0.605515 0.302757 0.953068i \(-0.402093\pi\)
0.302757 + 0.953068i \(0.402093\pi\)
\(234\) −13.9065 −0.909099
\(235\) 15.1009 0.985072
\(236\) −7.77276 −0.505964
\(237\) −1.18969 −0.0772784
\(238\) 1.16985 0.0758300
\(239\) 6.94259 0.449079 0.224539 0.974465i \(-0.427912\pi\)
0.224539 + 0.974465i \(0.427912\pi\)
\(240\) 10.9265 0.705301
\(241\) −1.53946 −0.0991656 −0.0495828 0.998770i \(-0.515789\pi\)
−0.0495828 + 0.998770i \(0.515789\pi\)
\(242\) −25.3068 −1.62678
\(243\) 15.6187 1.00194
\(244\) −32.5166 −2.08166
\(245\) 21.5880 1.37921
\(246\) −8.70949 −0.555297
\(247\) 7.93722 0.505033
\(248\) 1.82512 0.115895
\(249\) 6.29120 0.398689
\(250\) 2.87578 0.181880
\(251\) 6.40614 0.404352 0.202176 0.979349i \(-0.435199\pi\)
0.202176 + 0.979349i \(0.435199\pi\)
\(252\) −2.45646 −0.154743
\(253\) −1.62409 −0.102106
\(254\) −29.1979 −1.83204
\(255\) 3.44373 0.215655
\(256\) 8.99038 0.561899
\(257\) 23.7207 1.47966 0.739829 0.672795i \(-0.234906\pi\)
0.739829 + 0.672795i \(0.234906\pi\)
\(258\) 21.6303 1.34665
\(259\) −3.02582 −0.188015
\(260\) 27.1785 1.68554
\(261\) −12.8782 −0.797142
\(262\) −21.9352 −1.35516
\(263\) −12.3571 −0.761971 −0.380985 0.924581i \(-0.624415\pi\)
−0.380985 + 0.924581i \(0.624415\pi\)
\(264\) 3.76336 0.231619
\(265\) 35.2736 2.16684
\(266\) 2.59439 0.159072
\(267\) 3.56065 0.217908
\(268\) −31.1778 −1.90449
\(269\) 9.64544 0.588093 0.294046 0.955791i \(-0.404998\pi\)
0.294046 + 0.955791i \(0.404998\pi\)
\(270\) −34.9326 −2.12593
\(271\) 9.23952 0.561261 0.280630 0.959816i \(-0.409457\pi\)
0.280630 + 0.959816i \(0.409457\pi\)
\(272\) 3.17286 0.192383
\(273\) −2.14049 −0.129548
\(274\) 9.73545 0.588140
\(275\) −26.1008 −1.57394
\(276\) 0.846931 0.0509793
\(277\) 30.1084 1.80904 0.904519 0.426433i \(-0.140230\pi\)
0.904519 + 0.426433i \(0.140230\pi\)
\(278\) 0.365500 0.0219212
\(279\) 4.63332 0.277390
\(280\) 1.32862 0.0794003
\(281\) −0.490449 −0.0292577 −0.0146289 0.999893i \(-0.504657\pi\)
−0.0146289 + 0.999893i \(0.504657\pi\)
\(282\) 10.4041 0.619557
\(283\) −15.2346 −0.905600 −0.452800 0.891612i \(-0.649575\pi\)
−0.452800 + 0.891612i \(0.649575\pi\)
\(284\) −8.93962 −0.530469
\(285\) 7.63721 0.452390
\(286\) −35.9081 −2.12329
\(287\) 2.19538 0.129589
\(288\) −15.0617 −0.887518
\(289\) 1.00000 0.0588235
\(290\) 46.5734 2.73489
\(291\) −10.3569 −0.607131
\(292\) −0.484942 −0.0283791
\(293\) 16.4987 0.963862 0.481931 0.876209i \(-0.339936\pi\)
0.481931 + 0.876209i \(0.339936\pi\)
\(294\) 14.8736 0.867447
\(295\) 10.6726 0.621380
\(296\) 3.95884 0.230103
\(297\) 24.9415 1.44725
\(298\) −12.1921 −0.706272
\(299\) −1.20858 −0.0698938
\(300\) 13.6110 0.785831
\(301\) −5.45231 −0.314266
\(302\) 18.1120 1.04223
\(303\) −14.0176 −0.805289
\(304\) 7.03650 0.403571
\(305\) 44.6476 2.55651
\(306\) −3.88558 −0.222124
\(307\) −3.46829 −0.197946 −0.0989729 0.995090i \(-0.531556\pi\)
−0.0989729 + 0.995090i \(0.531556\pi\)
\(308\) −6.34284 −0.361417
\(309\) 2.35475 0.133957
\(310\) −16.7562 −0.951687
\(311\) −22.9136 −1.29931 −0.649656 0.760229i \(-0.725087\pi\)
−0.649656 + 0.760229i \(0.725087\pi\)
\(312\) 2.80052 0.158548
\(313\) −23.0308 −1.30178 −0.650888 0.759174i \(-0.725603\pi\)
−0.650888 + 0.759174i \(0.725603\pi\)
\(314\) 23.6915 1.33699
\(315\) 3.37290 0.190041
\(316\) −2.62341 −0.147578
\(317\) 6.24887 0.350972 0.175486 0.984482i \(-0.443850\pi\)
0.175486 + 0.984482i \(0.443850\pi\)
\(318\) 24.3026 1.36282
\(319\) −33.2529 −1.86181
\(320\) 33.9790 1.89948
\(321\) −3.02358 −0.168760
\(322\) −0.395040 −0.0220147
\(323\) 2.21771 0.123397
\(324\) 0.134670 0.00748167
\(325\) −19.4230 −1.07739
\(326\) −0.00357443 −0.000197969 0
\(327\) 1.72323 0.0952947
\(328\) −2.87234 −0.158598
\(329\) −2.62254 −0.144586
\(330\) −34.5509 −1.90197
\(331\) 17.8893 0.983282 0.491641 0.870798i \(-0.336397\pi\)
0.491641 + 0.870798i \(0.336397\pi\)
\(332\) 13.8729 0.761374
\(333\) 10.0501 0.550742
\(334\) −36.1823 −1.97981
\(335\) 42.8093 2.33892
\(336\) −1.89758 −0.103522
\(337\) 10.3762 0.565227 0.282613 0.959234i \(-0.408799\pi\)
0.282613 + 0.959234i \(0.408799\pi\)
\(338\) 0.397803 0.0216376
\(339\) 10.4122 0.565515
\(340\) 7.59387 0.411835
\(341\) 11.9637 0.647872
\(342\) −8.61712 −0.465960
\(343\) −7.67468 −0.414394
\(344\) 7.13355 0.384615
\(345\) −1.16290 −0.0626082
\(346\) 25.5128 1.37158
\(347\) −7.66934 −0.411712 −0.205856 0.978582i \(-0.565998\pi\)
−0.205856 + 0.978582i \(0.565998\pi\)
\(348\) 17.3407 0.929558
\(349\) 18.7418 1.00322 0.501612 0.865093i \(-0.332740\pi\)
0.501612 + 0.865093i \(0.332740\pi\)
\(350\) −6.34867 −0.339351
\(351\) 18.5603 0.990676
\(352\) −38.8908 −2.07289
\(353\) 1.00000 0.0532246
\(354\) 7.35312 0.390814
\(355\) 12.2747 0.651475
\(356\) 7.85169 0.416138
\(357\) −0.598068 −0.0316531
\(358\) 37.0886 1.96019
\(359\) 21.1863 1.11817 0.559085 0.829110i \(-0.311153\pi\)
0.559085 + 0.829110i \(0.311153\pi\)
\(360\) −4.41294 −0.232583
\(361\) −14.0817 −0.741144
\(362\) 32.5842 1.71259
\(363\) 12.9377 0.679054
\(364\) −4.72005 −0.247398
\(365\) 0.665860 0.0348527
\(366\) 30.7611 1.60791
\(367\) −9.38132 −0.489701 −0.244850 0.969561i \(-0.578739\pi\)
−0.244850 + 0.969561i \(0.578739\pi\)
\(368\) −1.07143 −0.0558520
\(369\) −7.29184 −0.379598
\(370\) −36.3457 −1.88952
\(371\) −6.12590 −0.318041
\(372\) −6.23883 −0.323468
\(373\) 2.71449 0.140551 0.0702756 0.997528i \(-0.477612\pi\)
0.0702756 + 0.997528i \(0.477612\pi\)
\(374\) −10.0330 −0.518793
\(375\) −1.47020 −0.0759207
\(376\) 3.43122 0.176951
\(377\) −24.7453 −1.27445
\(378\) 6.06669 0.312037
\(379\) −1.60046 −0.0822100 −0.0411050 0.999155i \(-0.513088\pi\)
−0.0411050 + 0.999155i \(0.513088\pi\)
\(380\) 16.8410 0.863927
\(381\) 14.9270 0.764733
\(382\) 42.2279 2.16057
\(383\) −34.5022 −1.76298 −0.881490 0.472202i \(-0.843459\pi\)
−0.881490 + 0.472202i \(0.843459\pi\)
\(384\) 6.16308 0.314508
\(385\) 8.70917 0.443860
\(386\) −6.07392 −0.309154
\(387\) 18.1095 0.920560
\(388\) −22.8382 −1.15944
\(389\) −7.02093 −0.355975 −0.177988 0.984033i \(-0.556959\pi\)
−0.177988 + 0.984033i \(0.556959\pi\)
\(390\) −25.7112 −1.30194
\(391\) −0.337685 −0.0170775
\(392\) 4.90523 0.247751
\(393\) 11.2141 0.565675
\(394\) 10.6054 0.534294
\(395\) 3.60213 0.181243
\(396\) 21.0674 1.05868
\(397\) −27.7653 −1.39350 −0.696751 0.717313i \(-0.745372\pi\)
−0.696751 + 0.717313i \(0.745372\pi\)
\(398\) −9.34524 −0.468435
\(399\) −1.32634 −0.0664002
\(400\) −17.2189 −0.860943
\(401\) 8.77925 0.438415 0.219207 0.975678i \(-0.429653\pi\)
0.219207 + 0.975678i \(0.429653\pi\)
\(402\) 29.4945 1.47105
\(403\) 8.90286 0.443483
\(404\) −30.9106 −1.53786
\(405\) −0.184912 −0.00918833
\(406\) −8.08833 −0.401417
\(407\) 25.9504 1.28631
\(408\) 0.782484 0.0387387
\(409\) 2.23229 0.110380 0.0551899 0.998476i \(-0.482424\pi\)
0.0551899 + 0.998476i \(0.482424\pi\)
\(410\) 26.3706 1.30235
\(411\) −4.97711 −0.245502
\(412\) 5.19252 0.255817
\(413\) −1.85349 −0.0912041
\(414\) 1.31210 0.0644864
\(415\) −19.0485 −0.935053
\(416\) −28.9408 −1.41894
\(417\) −0.186856 −0.00915040
\(418\) −22.2503 −1.08830
\(419\) −15.9671 −0.780043 −0.390022 0.920806i \(-0.627532\pi\)
−0.390022 + 0.920806i \(0.627532\pi\)
\(420\) −4.54165 −0.221610
\(421\) −14.2219 −0.693135 −0.346568 0.938025i \(-0.612653\pi\)
−0.346568 + 0.938025i \(0.612653\pi\)
\(422\) 11.3479 0.552409
\(423\) 8.71064 0.423526
\(424\) 8.01485 0.389236
\(425\) −5.42692 −0.263244
\(426\) 8.45699 0.409742
\(427\) −7.75388 −0.375237
\(428\) −6.66739 −0.322281
\(429\) 18.3575 0.886309
\(430\) −65.4922 −3.15832
\(431\) −5.90289 −0.284332 −0.142166 0.989843i \(-0.545407\pi\)
−0.142166 + 0.989843i \(0.545407\pi\)
\(432\) 16.4541 0.791647
\(433\) 19.6620 0.944894 0.472447 0.881359i \(-0.343371\pi\)
0.472447 + 0.881359i \(0.343371\pi\)
\(434\) 2.91002 0.139685
\(435\) −23.8100 −1.14160
\(436\) 3.79994 0.181984
\(437\) −0.748889 −0.0358242
\(438\) 0.458761 0.0219204
\(439\) 26.8979 1.28376 0.641882 0.766803i \(-0.278154\pi\)
0.641882 + 0.766803i \(0.278154\pi\)
\(440\) −11.3947 −0.543220
\(441\) 12.4526 0.592982
\(442\) −7.46609 −0.355126
\(443\) −18.2912 −0.869041 −0.434521 0.900662i \(-0.643082\pi\)
−0.434521 + 0.900662i \(0.643082\pi\)
\(444\) −13.5326 −0.642228
\(445\) −10.7809 −0.511065
\(446\) −40.9809 −1.94050
\(447\) 6.23305 0.294813
\(448\) −5.90107 −0.278800
\(449\) −37.7023 −1.77928 −0.889642 0.456659i \(-0.849046\pi\)
−0.889642 + 0.456659i \(0.849046\pi\)
\(450\) 21.0868 0.994039
\(451\) −18.8283 −0.886590
\(452\) 22.9603 1.07996
\(453\) −9.25949 −0.435049
\(454\) −16.7337 −0.785353
\(455\) 6.48097 0.303832
\(456\) 1.73533 0.0812641
\(457\) 27.8993 1.30507 0.652537 0.757756i \(-0.273705\pi\)
0.652537 + 0.757756i \(0.273705\pi\)
\(458\) 50.1963 2.34552
\(459\) 5.18588 0.242056
\(460\) −2.56433 −0.119563
\(461\) −23.1024 −1.07598 −0.537992 0.842950i \(-0.680817\pi\)
−0.537992 + 0.842950i \(0.680817\pi\)
\(462\) 6.00040 0.279164
\(463\) 20.6800 0.961081 0.480541 0.876972i \(-0.340440\pi\)
0.480541 + 0.876972i \(0.340440\pi\)
\(464\) −21.9372 −1.01841
\(465\) 8.56635 0.397255
\(466\) −19.2812 −0.893182
\(467\) −9.36778 −0.433489 −0.216745 0.976228i \(-0.569544\pi\)
−0.216745 + 0.976228i \(0.569544\pi\)
\(468\) 15.6774 0.724688
\(469\) −7.43462 −0.343299
\(470\) −31.5016 −1.45306
\(471\) −12.1120 −0.558090
\(472\) 2.42502 0.111620
\(473\) 46.7607 2.15006
\(474\) 2.48178 0.113992
\(475\) −12.0354 −0.552220
\(476\) −1.31882 −0.0604478
\(477\) 20.3469 0.931619
\(478\) −14.4828 −0.662427
\(479\) 27.1593 1.24094 0.620469 0.784231i \(-0.286942\pi\)
0.620469 + 0.784231i \(0.286942\pi\)
\(480\) −27.8469 −1.27103
\(481\) 19.3111 0.880510
\(482\) 3.21144 0.146277
\(483\) 0.201958 0.00918942
\(484\) 28.5293 1.29679
\(485\) 31.3585 1.42392
\(486\) −32.5818 −1.47794
\(487\) −5.08454 −0.230402 −0.115201 0.993342i \(-0.536751\pi\)
−0.115201 + 0.993342i \(0.536751\pi\)
\(488\) 10.1448 0.459234
\(489\) 0.00182737 8.26367e−5 0
\(490\) −45.0343 −2.03444
\(491\) 25.0489 1.13044 0.565221 0.824939i \(-0.308791\pi\)
0.565221 + 0.824939i \(0.308791\pi\)
\(492\) 9.81856 0.442655
\(493\) −6.91401 −0.311391
\(494\) −16.5577 −0.744964
\(495\) −28.9270 −1.30017
\(496\) 7.89255 0.354386
\(497\) −2.13173 −0.0956213
\(498\) −13.1239 −0.588097
\(499\) 25.1580 1.12623 0.563114 0.826379i \(-0.309603\pi\)
0.563114 + 0.826379i \(0.309603\pi\)
\(500\) −3.24198 −0.144986
\(501\) 18.4977 0.826416
\(502\) −13.3637 −0.596451
\(503\) −13.4428 −0.599384 −0.299692 0.954036i \(-0.596884\pi\)
−0.299692 + 0.954036i \(0.596884\pi\)
\(504\) 0.766389 0.0341377
\(505\) 42.4424 1.88866
\(506\) 3.38799 0.150614
\(507\) −0.203371 −0.00903202
\(508\) 32.9159 1.46041
\(509\) −1.48980 −0.0660342 −0.0330171 0.999455i \(-0.510512\pi\)
−0.0330171 + 0.999455i \(0.510512\pi\)
\(510\) −7.18389 −0.318108
\(511\) −0.115639 −0.00511556
\(512\) −30.3125 −1.33963
\(513\) 11.5008 0.507773
\(514\) −49.4833 −2.18261
\(515\) −7.12970 −0.314172
\(516\) −24.3847 −1.07348
\(517\) 22.4918 0.989187
\(518\) 6.31209 0.277337
\(519\) −13.0430 −0.572526
\(520\) −8.47940 −0.371846
\(521\) −4.19345 −0.183718 −0.0918591 0.995772i \(-0.529281\pi\)
−0.0918591 + 0.995772i \(0.529281\pi\)
\(522\) 26.8650 1.17585
\(523\) −28.6471 −1.25265 −0.626325 0.779562i \(-0.715442\pi\)
−0.626325 + 0.779562i \(0.715442\pi\)
\(524\) 24.7285 1.08027
\(525\) 3.24567 0.141652
\(526\) 25.7778 1.12397
\(527\) 2.48752 0.108358
\(528\) 16.2743 0.708248
\(529\) −22.8860 −0.995042
\(530\) −73.5834 −3.19626
\(531\) 6.15625 0.267159
\(532\) −2.92476 −0.126804
\(533\) −14.0112 −0.606891
\(534\) −7.42779 −0.321432
\(535\) 9.15480 0.395796
\(536\) 9.72712 0.420147
\(537\) −18.9610 −0.818227
\(538\) −20.1211 −0.867484
\(539\) 32.1540 1.38497
\(540\) 39.3809 1.69468
\(541\) 5.18487 0.222915 0.111457 0.993769i \(-0.464448\pi\)
0.111457 + 0.993769i \(0.464448\pi\)
\(542\) −19.2743 −0.827904
\(543\) −16.6582 −0.714871
\(544\) −8.08625 −0.346695
\(545\) −5.21758 −0.223497
\(546\) 4.46523 0.191094
\(547\) −19.4823 −0.833004 −0.416502 0.909135i \(-0.636744\pi\)
−0.416502 + 0.909135i \(0.636744\pi\)
\(548\) −10.9752 −0.468835
\(549\) 25.7541 1.09916
\(550\) 54.4482 2.32168
\(551\) −15.3333 −0.653220
\(552\) −0.264233 −0.0112465
\(553\) −0.625576 −0.0266022
\(554\) −62.8085 −2.66848
\(555\) 18.5812 0.788728
\(556\) −0.412042 −0.0174745
\(557\) −28.4787 −1.20668 −0.603340 0.797484i \(-0.706164\pi\)
−0.603340 + 0.797484i \(0.706164\pi\)
\(558\) −9.66547 −0.409172
\(559\) 34.7972 1.47176
\(560\) 5.74550 0.242792
\(561\) 5.12922 0.216556
\(562\) 1.02311 0.0431575
\(563\) −14.7093 −0.619924 −0.309962 0.950749i \(-0.600316\pi\)
−0.309962 + 0.950749i \(0.600316\pi\)
\(564\) −11.7290 −0.493879
\(565\) −31.5261 −1.32631
\(566\) 31.7805 1.33583
\(567\) 0.0321133 0.00134863
\(568\) 2.78906 0.117026
\(569\) 7.97714 0.334419 0.167210 0.985921i \(-0.446524\pi\)
0.167210 + 0.985921i \(0.446524\pi\)
\(570\) −15.9318 −0.667310
\(571\) 8.20806 0.343496 0.171748 0.985141i \(-0.445058\pi\)
0.171748 + 0.985141i \(0.445058\pi\)
\(572\) 40.4807 1.69258
\(573\) −21.5884 −0.901869
\(574\) −4.57974 −0.191155
\(575\) 1.83259 0.0764242
\(576\) 19.6001 0.816671
\(577\) 5.63411 0.234551 0.117275 0.993099i \(-0.462584\pi\)
0.117275 + 0.993099i \(0.462584\pi\)
\(578\) −2.08608 −0.0867694
\(579\) 3.10520 0.129048
\(580\) −52.5041 −2.18011
\(581\) 3.30812 0.137244
\(582\) 21.6052 0.895566
\(583\) 52.5377 2.17589
\(584\) 0.151297 0.00626070
\(585\) −21.5262 −0.889998
\(586\) −34.4175 −1.42177
\(587\) −5.23935 −0.216251 −0.108126 0.994137i \(-0.534485\pi\)
−0.108126 + 0.994137i \(0.534485\pi\)
\(588\) −16.7676 −0.691485
\(589\) 5.51661 0.227308
\(590\) −22.2638 −0.916585
\(591\) −5.42187 −0.223026
\(592\) 17.1197 0.703614
\(593\) −1.19935 −0.0492513 −0.0246257 0.999697i \(-0.507839\pi\)
−0.0246257 + 0.999697i \(0.507839\pi\)
\(594\) −52.0298 −2.13481
\(595\) 1.81083 0.0742367
\(596\) 13.7447 0.563004
\(597\) 4.77762 0.195535
\(598\) 2.52119 0.103099
\(599\) −21.0202 −0.858862 −0.429431 0.903100i \(-0.641286\pi\)
−0.429431 + 0.903100i \(0.641286\pi\)
\(600\) −4.24648 −0.173362
\(601\) 16.9386 0.690939 0.345470 0.938430i \(-0.387720\pi\)
0.345470 + 0.938430i \(0.387720\pi\)
\(602\) 11.3739 0.463567
\(603\) 24.6937 1.00560
\(604\) −20.4184 −0.830812
\(605\) −39.1728 −1.59260
\(606\) 29.2418 1.18787
\(607\) −19.7260 −0.800655 −0.400328 0.916372i \(-0.631104\pi\)
−0.400328 + 0.916372i \(0.631104\pi\)
\(608\) −17.9330 −0.727279
\(609\) 4.13504 0.167560
\(610\) −93.1383 −3.77106
\(611\) 16.7373 0.677121
\(612\) 4.38037 0.177066
\(613\) 21.4113 0.864795 0.432398 0.901683i \(-0.357668\pi\)
0.432398 + 0.901683i \(0.357668\pi\)
\(614\) 7.23512 0.291986
\(615\) −13.4816 −0.543630
\(616\) 1.97890 0.0797320
\(617\) 25.4589 1.02494 0.512469 0.858706i \(-0.328731\pi\)
0.512469 + 0.858706i \(0.328731\pi\)
\(618\) −4.91219 −0.197597
\(619\) 35.3510 1.42088 0.710439 0.703759i \(-0.248496\pi\)
0.710439 + 0.703759i \(0.248496\pi\)
\(620\) 18.8899 0.758637
\(621\) −1.75119 −0.0702729
\(622\) 47.7995 1.91659
\(623\) 1.87231 0.0750123
\(624\) 12.1106 0.484811
\(625\) −22.6831 −0.907326
\(626\) 48.0439 1.92022
\(627\) 11.3751 0.454279
\(628\) −26.7084 −1.06578
\(629\) 5.39565 0.215139
\(630\) −7.03612 −0.280326
\(631\) 4.31592 0.171814 0.0859070 0.996303i \(-0.472621\pi\)
0.0859070 + 0.996303i \(0.472621\pi\)
\(632\) 0.818474 0.0325572
\(633\) −5.80147 −0.230588
\(634\) −13.0356 −0.517711
\(635\) −45.1959 −1.79354
\(636\) −27.3973 −1.08637
\(637\) 23.9275 0.948043
\(638\) 69.3681 2.74631
\(639\) 7.08044 0.280098
\(640\) −18.6605 −0.737623
\(641\) 17.9220 0.707877 0.353938 0.935269i \(-0.384842\pi\)
0.353938 + 0.935269i \(0.384842\pi\)
\(642\) 6.30743 0.248934
\(643\) −25.8639 −1.01997 −0.509986 0.860183i \(-0.670350\pi\)
−0.509986 + 0.860183i \(0.670350\pi\)
\(644\) 0.445344 0.0175490
\(645\) 33.4820 1.31835
\(646\) −4.62632 −0.182020
\(647\) 22.6735 0.891387 0.445694 0.895186i \(-0.352957\pi\)
0.445694 + 0.895186i \(0.352957\pi\)
\(648\) −0.0420156 −0.00165053
\(649\) 15.8961 0.623976
\(650\) 40.5179 1.58924
\(651\) −1.48771 −0.0583078
\(652\) 0.00402959 0.000157811 0
\(653\) 26.1553 1.02354 0.511768 0.859124i \(-0.328991\pi\)
0.511768 + 0.859124i \(0.328991\pi\)
\(654\) −3.59478 −0.140567
\(655\) −33.9539 −1.32669
\(656\) −12.4212 −0.484965
\(657\) 0.384088 0.0149847
\(658\) 5.47083 0.213275
\(659\) 2.80826 0.109394 0.0546971 0.998503i \(-0.482581\pi\)
0.0546971 + 0.998503i \(0.482581\pi\)
\(660\) 38.9506 1.51615
\(661\) 40.7092 1.58340 0.791702 0.610908i \(-0.209195\pi\)
0.791702 + 0.610908i \(0.209195\pi\)
\(662\) −37.3184 −1.45042
\(663\) 3.81693 0.148237
\(664\) −4.32819 −0.167966
\(665\) 4.01590 0.155730
\(666\) −20.9653 −0.812388
\(667\) 2.33476 0.0904021
\(668\) 40.7898 1.57820
\(669\) 20.9509 0.810009
\(670\) −89.3035 −3.45009
\(671\) 66.4997 2.56719
\(672\) 4.83612 0.186558
\(673\) −10.1874 −0.392695 −0.196348 0.980534i \(-0.562908\pi\)
−0.196348 + 0.980534i \(0.562908\pi\)
\(674\) −21.6455 −0.833754
\(675\) −28.1433 −1.08324
\(676\) −0.448459 −0.0172484
\(677\) 16.2983 0.626394 0.313197 0.949688i \(-0.398600\pi\)
0.313197 + 0.949688i \(0.398600\pi\)
\(678\) −21.7207 −0.834179
\(679\) −5.44598 −0.208998
\(680\) −2.36920 −0.0908548
\(681\) 8.55487 0.327824
\(682\) −24.9573 −0.955663
\(683\) 29.7744 1.13929 0.569643 0.821893i \(-0.307082\pi\)
0.569643 + 0.821893i \(0.307082\pi\)
\(684\) 9.71442 0.371440
\(685\) 15.0697 0.575782
\(686\) 16.0100 0.611263
\(687\) −25.6621 −0.979071
\(688\) 30.8484 1.17608
\(689\) 39.0962 1.48944
\(690\) 2.42589 0.0923521
\(691\) −36.4041 −1.38488 −0.692439 0.721476i \(-0.743464\pi\)
−0.692439 + 0.721476i \(0.743464\pi\)
\(692\) −28.7616 −1.09335
\(693\) 5.02371 0.190835
\(694\) 15.9988 0.607307
\(695\) 0.565763 0.0214606
\(696\) −5.41010 −0.205069
\(697\) −3.91482 −0.148284
\(698\) −39.0968 −1.47984
\(699\) 9.85721 0.372834
\(700\) 7.15711 0.270513
\(701\) 16.7515 0.632696 0.316348 0.948643i \(-0.397543\pi\)
0.316348 + 0.948643i \(0.397543\pi\)
\(702\) −38.7182 −1.46133
\(703\) 11.9660 0.451307
\(704\) 50.6095 1.90742
\(705\) 16.1047 0.606539
\(706\) −2.08608 −0.0785105
\(707\) −7.37090 −0.277211
\(708\) −8.28947 −0.311537
\(709\) 38.0588 1.42933 0.714664 0.699467i \(-0.246579\pi\)
0.714664 + 0.699467i \(0.246579\pi\)
\(710\) −25.6060 −0.960977
\(711\) 2.07782 0.0779242
\(712\) −2.44964 −0.0918041
\(713\) −0.839998 −0.0314582
\(714\) 1.24762 0.0466908
\(715\) −55.5828 −2.07868
\(716\) −41.8114 −1.56257
\(717\) 7.40411 0.276512
\(718\) −44.1962 −1.64939
\(719\) 13.0052 0.485011 0.242505 0.970150i \(-0.422031\pi\)
0.242505 + 0.970150i \(0.422031\pi\)
\(720\) −19.0834 −0.711195
\(721\) 1.23820 0.0461131
\(722\) 29.3756 1.09325
\(723\) −1.64180 −0.0610593
\(724\) −36.7334 −1.36519
\(725\) 37.5218 1.39352
\(726\) −26.9891 −1.00166
\(727\) −6.67830 −0.247684 −0.123842 0.992302i \(-0.539522\pi\)
−0.123842 + 0.992302i \(0.539522\pi\)
\(728\) 1.47260 0.0545783
\(729\) 16.4852 0.610563
\(730\) −1.38904 −0.0514105
\(731\) 9.72258 0.359603
\(732\) −34.6782 −1.28174
\(733\) −33.0732 −1.22159 −0.610794 0.791790i \(-0.709150\pi\)
−0.610794 + 0.791790i \(0.709150\pi\)
\(734\) 19.5702 0.722348
\(735\) 23.0231 0.849221
\(736\) 2.73060 0.100651
\(737\) 63.7617 2.34869
\(738\) 15.2113 0.559937
\(739\) −0.193535 −0.00711931 −0.00355966 0.999994i \(-0.501133\pi\)
−0.00355966 + 0.999994i \(0.501133\pi\)
\(740\) 40.9739 1.50623
\(741\) 8.46486 0.310964
\(742\) 12.7791 0.469136
\(743\) 18.5264 0.679667 0.339833 0.940486i \(-0.389629\pi\)
0.339833 + 0.940486i \(0.389629\pi\)
\(744\) 1.94645 0.0713601
\(745\) −18.8724 −0.691432
\(746\) −5.66264 −0.207324
\(747\) −10.9877 −0.402020
\(748\) 11.3106 0.413556
\(749\) −1.58990 −0.0580937
\(750\) 3.06695 0.111989
\(751\) −21.4966 −0.784423 −0.392211 0.919875i \(-0.628290\pi\)
−0.392211 + 0.919875i \(0.628290\pi\)
\(752\) 14.8380 0.541085
\(753\) 6.83200 0.248972
\(754\) 51.6206 1.87991
\(755\) 28.0359 1.02033
\(756\) −6.83922 −0.248740
\(757\) −33.2874 −1.20985 −0.604926 0.796282i \(-0.706797\pi\)
−0.604926 + 0.796282i \(0.706797\pi\)
\(758\) 3.33868 0.121266
\(759\) −1.73206 −0.0628698
\(760\) −5.25422 −0.190590
\(761\) −14.6687 −0.531739 −0.265869 0.964009i \(-0.585659\pi\)
−0.265869 + 0.964009i \(0.585659\pi\)
\(762\) −31.1389 −1.12804
\(763\) 0.906129 0.0328041
\(764\) −47.6052 −1.72230
\(765\) −6.01456 −0.217457
\(766\) 71.9743 2.60054
\(767\) 11.8291 0.427125
\(768\) 9.58803 0.345978
\(769\) 3.73594 0.134722 0.0673608 0.997729i \(-0.478542\pi\)
0.0673608 + 0.997729i \(0.478542\pi\)
\(770\) −18.1680 −0.654729
\(771\) 25.2976 0.911071
\(772\) 6.84737 0.246442
\(773\) 35.4005 1.27327 0.636634 0.771166i \(-0.280326\pi\)
0.636634 + 0.771166i \(0.280326\pi\)
\(774\) −37.7779 −1.35790
\(775\) −13.4996 −0.484919
\(776\) 7.12528 0.255783
\(777\) −3.22697 −0.115767
\(778\) 14.6462 0.525092
\(779\) −8.68194 −0.311063
\(780\) 28.9853 1.03784
\(781\) 18.2824 0.654197
\(782\) 0.704437 0.0251906
\(783\) −35.8552 −1.28136
\(784\) 21.2122 0.757579
\(785\) 36.6725 1.30890
\(786\) −23.3934 −0.834416
\(787\) 12.6983 0.452644 0.226322 0.974053i \(-0.427330\pi\)
0.226322 + 0.974053i \(0.427330\pi\)
\(788\) −11.9559 −0.425912
\(789\) −13.1785 −0.469169
\(790\) −7.51431 −0.267347
\(791\) 5.47509 0.194672
\(792\) −6.57280 −0.233554
\(793\) 49.4861 1.75730
\(794\) 57.9206 2.05552
\(795\) 37.6184 1.33419
\(796\) 10.5353 0.373412
\(797\) 9.88699 0.350215 0.175108 0.984549i \(-0.443973\pi\)
0.175108 + 0.984549i \(0.443973\pi\)
\(798\) 2.76685 0.0979456
\(799\) 4.67653 0.165444
\(800\) 43.8834 1.55151
\(801\) −6.21876 −0.219729
\(802\) −18.3142 −0.646696
\(803\) 0.991756 0.0349983
\(804\) −33.2504 −1.17265
\(805\) −0.611489 −0.0215521
\(806\) −18.5720 −0.654172
\(807\) 10.2866 0.362107
\(808\) 9.64375 0.339266
\(809\) 2.09291 0.0735826 0.0367913 0.999323i \(-0.488286\pi\)
0.0367913 + 0.999323i \(0.488286\pi\)
\(810\) 0.385740 0.0135535
\(811\) 29.4504 1.03414 0.517072 0.855942i \(-0.327022\pi\)
0.517072 + 0.855942i \(0.327022\pi\)
\(812\) 9.11830 0.319990
\(813\) 9.85373 0.345585
\(814\) −54.1345 −1.89741
\(815\) −0.00553291 −0.000193810 0
\(816\) 3.38378 0.118456
\(817\) 21.5619 0.754355
\(818\) −4.65674 −0.162819
\(819\) 3.73842 0.130631
\(820\) −29.7286 −1.03817
\(821\) −48.2691 −1.68460 −0.842302 0.539005i \(-0.818800\pi\)
−0.842302 + 0.539005i \(0.818800\pi\)
\(822\) 10.3826 0.362136
\(823\) −45.9851 −1.60294 −0.801469 0.598036i \(-0.795948\pi\)
−0.801469 + 0.598036i \(0.795948\pi\)
\(824\) −1.62001 −0.0564357
\(825\) −27.8359 −0.969120
\(826\) 3.86651 0.134533
\(827\) −48.6520 −1.69180 −0.845899 0.533344i \(-0.820935\pi\)
−0.845899 + 0.533344i \(0.820935\pi\)
\(828\) −1.47919 −0.0514053
\(829\) −29.9283 −1.03945 −0.519727 0.854332i \(-0.673966\pi\)
−0.519727 + 0.854332i \(0.673966\pi\)
\(830\) 39.7366 1.37928
\(831\) 32.1099 1.11388
\(832\) 37.6613 1.30567
\(833\) 6.68552 0.231639
\(834\) 0.389797 0.0134976
\(835\) −56.0072 −1.93821
\(836\) 25.0836 0.867536
\(837\) 12.9000 0.445888
\(838\) 33.3086 1.15063
\(839\) −19.2990 −0.666276 −0.333138 0.942878i \(-0.608108\pi\)
−0.333138 + 0.942878i \(0.608108\pi\)
\(840\) 1.41694 0.0488892
\(841\) 18.8035 0.648396
\(842\) 29.6681 1.02243
\(843\) −0.523052 −0.0180149
\(844\) −12.7930 −0.440353
\(845\) 0.615766 0.0211830
\(846\) −18.1711 −0.624734
\(847\) 6.80308 0.233757
\(848\) 34.6595 1.19021
\(849\) −16.2473 −0.557606
\(850\) 11.3210 0.388306
\(851\) −1.82203 −0.0624584
\(852\) −9.53390 −0.326626
\(853\) 41.7617 1.42989 0.714946 0.699179i \(-0.246451\pi\)
0.714946 + 0.699179i \(0.246451\pi\)
\(854\) 16.1752 0.553504
\(855\) −13.3386 −0.456170
\(856\) 2.08015 0.0710981
\(857\) −23.6322 −0.807262 −0.403631 0.914922i \(-0.632252\pi\)
−0.403631 + 0.914922i \(0.632252\pi\)
\(858\) −38.2952 −1.30738
\(859\) 8.49085 0.289704 0.144852 0.989453i \(-0.453729\pi\)
0.144852 + 0.989453i \(0.453729\pi\)
\(860\) 73.8320 2.51765
\(861\) 2.34132 0.0797921
\(862\) 12.3139 0.419413
\(863\) −54.0966 −1.84147 −0.920735 0.390189i \(-0.872410\pi\)
−0.920735 + 0.390189i \(0.872410\pi\)
\(864\) −41.9343 −1.42663
\(865\) 39.4917 1.34276
\(866\) −41.0164 −1.39379
\(867\) 1.06648 0.0362194
\(868\) −3.28058 −0.111350
\(869\) 5.36514 0.182000
\(870\) 49.6695 1.68395
\(871\) 47.4485 1.60773
\(872\) −1.18554 −0.0401474
\(873\) 18.0885 0.612204
\(874\) 1.56224 0.0528435
\(875\) −0.773079 −0.0261348
\(876\) −0.517180 −0.0174739
\(877\) 6.93772 0.234270 0.117135 0.993116i \(-0.462629\pi\)
0.117135 + 0.993116i \(0.462629\pi\)
\(878\) −56.1110 −1.89365
\(879\) 17.5954 0.593479
\(880\) −49.2752 −1.66107
\(881\) 0.275969 0.00929765 0.00464882 0.999989i \(-0.498520\pi\)
0.00464882 + 0.999989i \(0.498520\pi\)
\(882\) −25.9771 −0.874696
\(883\) −21.0756 −0.709250 −0.354625 0.935009i \(-0.615391\pi\)
−0.354625 + 0.935009i \(0.615391\pi\)
\(884\) 8.41682 0.283088
\(885\) 11.3820 0.382603
\(886\) 38.1569 1.28191
\(887\) −14.7381 −0.494858 −0.247429 0.968906i \(-0.579586\pi\)
−0.247429 + 0.968906i \(0.579586\pi\)
\(888\) 4.22201 0.141682
\(889\) 7.84910 0.263250
\(890\) 22.4898 0.753861
\(891\) −0.275414 −0.00922671
\(892\) 46.1994 1.54687
\(893\) 10.3712 0.347059
\(894\) −13.0026 −0.434873
\(895\) 57.4100 1.91900
\(896\) 3.24075 0.108266
\(897\) −1.28892 −0.0430358
\(898\) 78.6500 2.62458
\(899\) −17.1987 −0.573610
\(900\) −23.7719 −0.792398
\(901\) 10.9237 0.363922
\(902\) 39.2773 1.30779
\(903\) −5.81476 −0.193503
\(904\) −7.16336 −0.238250
\(905\) 50.4376 1.67660
\(906\) 19.3160 0.641732
\(907\) −7.92771 −0.263235 −0.131618 0.991301i \(-0.542017\pi\)
−0.131618 + 0.991301i \(0.542017\pi\)
\(908\) 18.8646 0.626044
\(909\) 24.4821 0.812019
\(910\) −13.5198 −0.448177
\(911\) 53.7889 1.78211 0.891053 0.453899i \(-0.149967\pi\)
0.891053 + 0.453899i \(0.149967\pi\)
\(912\) 7.50426 0.248491
\(913\) −28.3715 −0.938959
\(914\) −58.2001 −1.92509
\(915\) 47.6156 1.57412
\(916\) −56.5883 −1.86973
\(917\) 5.89673 0.194727
\(918\) −10.8181 −0.357052
\(919\) −27.1516 −0.895650 −0.447825 0.894121i \(-0.647801\pi\)
−0.447825 + 0.894121i \(0.647801\pi\)
\(920\) 0.800044 0.0263767
\(921\) −3.69885 −0.121881
\(922\) 48.1933 1.58716
\(923\) 13.6049 0.447812
\(924\) −6.76449 −0.222535
\(925\) −29.2818 −0.962779
\(926\) −43.1401 −1.41767
\(927\) −4.11263 −0.135076
\(928\) 55.9084 1.83528
\(929\) −38.0531 −1.24848 −0.624241 0.781232i \(-0.714592\pi\)
−0.624241 + 0.781232i \(0.714592\pi\)
\(930\) −17.8701 −0.585983
\(931\) 14.8266 0.485921
\(932\) 21.7364 0.712000
\(933\) −24.4368 −0.800026
\(934\) 19.5419 0.639431
\(935\) −15.5302 −0.507893
\(936\) −4.89117 −0.159873
\(937\) 9.41013 0.307415 0.153708 0.988116i \(-0.450879\pi\)
0.153708 + 0.988116i \(0.450879\pi\)
\(938\) 15.5092 0.506393
\(939\) −24.5618 −0.801543
\(940\) 35.5130 1.15831
\(941\) −10.9388 −0.356593 −0.178297 0.983977i \(-0.557059\pi\)
−0.178297 + 0.983977i \(0.557059\pi\)
\(942\) 25.2665 0.823226
\(943\) 1.32197 0.0430494
\(944\) 10.4868 0.341315
\(945\) 9.39073 0.305480
\(946\) −97.5465 −3.17151
\(947\) −35.7233 −1.16085 −0.580426 0.814313i \(-0.697114\pi\)
−0.580426 + 0.814313i \(0.697114\pi\)
\(948\) −2.79780 −0.0908685
\(949\) 0.738019 0.0239571
\(950\) 25.1067 0.814568
\(951\) 6.66428 0.216104
\(952\) 0.411456 0.0133354
\(953\) 3.81958 0.123728 0.0618642 0.998085i \(-0.480295\pi\)
0.0618642 + 0.998085i \(0.480295\pi\)
\(954\) −42.4451 −1.37421
\(955\) 65.3653 2.11517
\(956\) 16.3270 0.528053
\(957\) −35.4634 −1.14637
\(958\) −56.6563 −1.83048
\(959\) −2.61712 −0.0845114
\(960\) 36.2378 1.16957
\(961\) −24.8122 −0.800395
\(962\) −40.2844 −1.29882
\(963\) 5.28077 0.170170
\(964\) −3.62038 −0.116605
\(965\) −9.40192 −0.302659
\(966\) −0.421301 −0.0135551
\(967\) 24.5428 0.789243 0.394621 0.918844i \(-0.370876\pi\)
0.394621 + 0.918844i \(0.370876\pi\)
\(968\) −8.90084 −0.286084
\(969\) 2.36514 0.0759793
\(970\) −65.4163 −2.10039
\(971\) 17.6867 0.567592 0.283796 0.958885i \(-0.408406\pi\)
0.283796 + 0.958885i \(0.408406\pi\)
\(972\) 36.7308 1.17814
\(973\) −0.0982553 −0.00314992
\(974\) 10.6067 0.339862
\(975\) −20.7142 −0.663384
\(976\) 43.8703 1.40426
\(977\) −55.2401 −1.76729 −0.883643 0.468161i \(-0.844917\pi\)
−0.883643 + 0.468161i \(0.844917\pi\)
\(978\) −0.00381204 −0.000121896 0
\(979\) −16.0575 −0.513199
\(980\) 50.7689 1.62175
\(981\) −3.00966 −0.0960910
\(982\) −52.2540 −1.66749
\(983\) −43.2983 −1.38100 −0.690501 0.723332i \(-0.742610\pi\)
−0.690501 + 0.723332i \(0.742610\pi\)
\(984\) −3.06328 −0.0976538
\(985\) 16.4163 0.523067
\(986\) 14.4231 0.459327
\(987\) −2.79688 −0.0890257
\(988\) 18.6661 0.593848
\(989\) −3.28317 −0.104399
\(990\) 60.3440 1.91786
\(991\) −51.4564 −1.63457 −0.817284 0.576235i \(-0.804521\pi\)
−0.817284 + 0.576235i \(0.804521\pi\)
\(992\) −20.1147 −0.638643
\(993\) 19.0785 0.605437
\(994\) 4.44696 0.141049
\(995\) −14.4657 −0.458592
\(996\) 14.7951 0.468801
\(997\) 0.871346 0.0275958 0.0137979 0.999905i \(-0.495608\pi\)
0.0137979 + 0.999905i \(0.495608\pi\)
\(998\) −52.4816 −1.66128
\(999\) 27.9812 0.885286
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 6001.2.a.c.1.18 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.c.1.18 121 1.1 even 1 trivial