Properties

Label 1911.2.a.t.1.2
Level $1911$
Weight $2$
Character 1911.1
Self dual yes
Analytic conductor $15.259$
Analytic rank $1$
Dimension $5$
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] = [1911,2,Mod(1,1911)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1911.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.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: \(15.2594118263\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.375116.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 6x^{3} + 7x^{2} + 2x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 273)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.32173\) of defining polynomial
Character \(\chi\) \(=\) 1911.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.78646 q^{2} -1.00000 q^{3} +1.19144 q^{4} +3.42992 q^{5} +1.78646 q^{6} +1.44447 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.78646 q^{2} -1.00000 q^{3} +1.19144 q^{4} +3.42992 q^{5} +1.78646 q^{6} +1.44447 q^{8} +1.00000 q^{9} -6.12741 q^{10} +1.59502 q^{11} -1.19144 q^{12} -1.00000 q^{13} -3.42992 q^{15} -4.96335 q^{16} +0.0394874 q^{17} -1.78646 q^{18} -3.64346 q^{19} +4.08653 q^{20} -2.84944 q^{22} -3.42236 q^{23} -1.44447 q^{24} +6.76436 q^{25} +1.78646 q^{26} -1.00000 q^{27} -10.0028 q^{29} +6.12741 q^{30} -6.15479 q^{31} +5.97790 q^{32} -1.59502 q^{33} -0.0705426 q^{34} +1.19144 q^{36} -11.1303 q^{37} +6.50890 q^{38} +1.00000 q^{39} +4.95440 q^{40} -5.08793 q^{41} +2.91631 q^{43} +1.90037 q^{44} +3.42992 q^{45} +6.11391 q^{46} -4.10864 q^{47} +4.96335 q^{48} -12.0842 q^{50} -0.0394874 q^{51} -1.19144 q^{52} -10.2912 q^{53} +1.78646 q^{54} +5.47080 q^{55} +3.64346 q^{57} +17.8697 q^{58} +9.19324 q^{59} -4.08653 q^{60} -1.96051 q^{61} +10.9953 q^{62} -0.752565 q^{64} -3.42992 q^{65} +2.84944 q^{66} +12.0569 q^{67} +0.0470468 q^{68} +3.42236 q^{69} +1.79825 q^{71} +1.44447 q^{72} -6.70505 q^{73} +19.8837 q^{74} -6.76436 q^{75} -4.34095 q^{76} -1.78646 q^{78} +14.6318 q^{79} -17.0239 q^{80} +1.00000 q^{81} +9.08937 q^{82} -5.34655 q^{83} +0.135439 q^{85} -5.20986 q^{86} +10.0028 q^{87} +2.30395 q^{88} -12.4694 q^{89} -6.12741 q^{90} -4.07753 q^{92} +6.15479 q^{93} +7.33991 q^{94} -12.4968 q^{95} -5.97790 q^{96} -12.5010 q^{97} +1.59502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{3} + 6 q^{4} - 3 q^{5} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{3} + 6 q^{4} - 3 q^{5} + 3 q^{8} + 5 q^{9} - 2 q^{10} - q^{11} - 6 q^{12} - 5 q^{13} + 3 q^{15} - 13 q^{17} - 7 q^{19} - 13 q^{20} - 19 q^{22} - 4 q^{23} - 3 q^{24} + 16 q^{25} - 5 q^{27} - 12 q^{29} + 2 q^{30} - 6 q^{31} + 21 q^{32} + q^{33} - 7 q^{34} + 6 q^{36} + 11 q^{37} - 14 q^{38} + 5 q^{39} - 11 q^{40} - 10 q^{41} + 10 q^{43} - 29 q^{44} - 3 q^{45} + q^{46} + 4 q^{47} - 29 q^{50} + 13 q^{51} - 6 q^{52} - 9 q^{53} + 12 q^{55} + 7 q^{57} + 34 q^{58} - 7 q^{59} + 13 q^{60} - 23 q^{61} + 24 q^{62} - 13 q^{64} + 3 q^{65} + 19 q^{66} + 25 q^{67} - 20 q^{68} + 4 q^{69} - 27 q^{71} + 3 q^{72} - 18 q^{73} + 15 q^{74} - 16 q^{75} - 2 q^{76} + 8 q^{79} - 41 q^{80} + 5 q^{81} - 26 q^{82} - 12 q^{83} + 10 q^{85} - 19 q^{86} + 12 q^{87} - 36 q^{88} - 29 q^{89} - 2 q^{90} - 50 q^{92} + 6 q^{93} + 2 q^{94} - 33 q^{95} - 21 q^{96} - 13 q^{97} - q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78646 −1.26322 −0.631609 0.775287i \(-0.717605\pi\)
−0.631609 + 0.775287i \(0.717605\pi\)
\(3\) −1.00000 −0.577350
\(4\) 1.19144 0.595718
\(5\) 3.42992 1.53391 0.766954 0.641703i \(-0.221772\pi\)
0.766954 + 0.641703i \(0.221772\pi\)
\(6\) 1.78646 0.729319
\(7\) 0 0
\(8\) 1.44447 0.510696
\(9\) 1.00000 0.333333
\(10\) −6.12741 −1.93766
\(11\) 1.59502 0.480917 0.240459 0.970659i \(-0.422702\pi\)
0.240459 + 0.970659i \(0.422702\pi\)
\(12\) −1.19144 −0.343938
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −3.42992 −0.885602
\(16\) −4.96335 −1.24084
\(17\) 0.0394874 0.00957710 0.00478855 0.999989i \(-0.498476\pi\)
0.00478855 + 0.999989i \(0.498476\pi\)
\(18\) −1.78646 −0.421073
\(19\) −3.64346 −0.835867 −0.417934 0.908478i \(-0.637246\pi\)
−0.417934 + 0.908478i \(0.637246\pi\)
\(20\) 4.08653 0.913777
\(21\) 0 0
\(22\) −2.84944 −0.607503
\(23\) −3.42236 −0.713612 −0.356806 0.934179i \(-0.616134\pi\)
−0.356806 + 0.934179i \(0.616134\pi\)
\(24\) −1.44447 −0.294850
\(25\) 6.76436 1.35287
\(26\) 1.78646 0.350353
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −10.0028 −1.85748 −0.928740 0.370731i \(-0.879107\pi\)
−0.928740 + 0.370731i \(0.879107\pi\)
\(30\) 6.12741 1.11871
\(31\) −6.15479 −1.10543 −0.552716 0.833369i \(-0.686409\pi\)
−0.552716 + 0.833369i \(0.686409\pi\)
\(32\) 5.97790 1.05675
\(33\) −1.59502 −0.277658
\(34\) −0.0705426 −0.0120980
\(35\) 0 0
\(36\) 1.19144 0.198573
\(37\) −11.1303 −1.82980 −0.914901 0.403678i \(-0.867732\pi\)
−0.914901 + 0.403678i \(0.867732\pi\)
\(38\) 6.50890 1.05588
\(39\) 1.00000 0.160128
\(40\) 4.95440 0.783359
\(41\) −5.08793 −0.794601 −0.397300 0.917689i \(-0.630053\pi\)
−0.397300 + 0.917689i \(0.630053\pi\)
\(42\) 0 0
\(43\) 2.91631 0.444732 0.222366 0.974963i \(-0.428622\pi\)
0.222366 + 0.974963i \(0.428622\pi\)
\(44\) 1.90037 0.286491
\(45\) 3.42992 0.511302
\(46\) 6.11391 0.901447
\(47\) −4.10864 −0.599306 −0.299653 0.954048i \(-0.596871\pi\)
−0.299653 + 0.954048i \(0.596871\pi\)
\(48\) 4.96335 0.716398
\(49\) 0 0
\(50\) −12.0842 −1.70897
\(51\) −0.0394874 −0.00552934
\(52\) −1.19144 −0.165223
\(53\) −10.2912 −1.41360 −0.706799 0.707414i \(-0.749862\pi\)
−0.706799 + 0.707414i \(0.749862\pi\)
\(54\) 1.78646 0.243106
\(55\) 5.47080 0.737683
\(56\) 0 0
\(57\) 3.64346 0.482588
\(58\) 17.8697 2.34640
\(59\) 9.19324 1.19686 0.598429 0.801176i \(-0.295792\pi\)
0.598429 + 0.801176i \(0.295792\pi\)
\(60\) −4.08653 −0.527569
\(61\) −1.96051 −0.251018 −0.125509 0.992092i \(-0.540056\pi\)
−0.125509 + 0.992092i \(0.540056\pi\)
\(62\) 10.9953 1.39640
\(63\) 0 0
\(64\) −0.752565 −0.0940706
\(65\) −3.42992 −0.425429
\(66\) 2.84944 0.350742
\(67\) 12.0569 1.47298 0.736491 0.676448i \(-0.236482\pi\)
0.736491 + 0.676448i \(0.236482\pi\)
\(68\) 0.0470468 0.00570526
\(69\) 3.42236 0.412004
\(70\) 0 0
\(71\) 1.79825 0.213413 0.106707 0.994291i \(-0.465969\pi\)
0.106707 + 0.994291i \(0.465969\pi\)
\(72\) 1.44447 0.170232
\(73\) −6.70505 −0.784767 −0.392384 0.919802i \(-0.628349\pi\)
−0.392384 + 0.919802i \(0.628349\pi\)
\(74\) 19.8837 2.31144
\(75\) −6.76436 −0.781081
\(76\) −4.34095 −0.497942
\(77\) 0 0
\(78\) −1.78646 −0.202277
\(79\) 14.6318 1.64620 0.823101 0.567896i \(-0.192242\pi\)
0.823101 + 0.567896i \(0.192242\pi\)
\(80\) −17.0239 −1.90333
\(81\) 1.00000 0.111111
\(82\) 9.08937 1.00375
\(83\) −5.34655 −0.586860 −0.293430 0.955981i \(-0.594797\pi\)
−0.293430 + 0.955981i \(0.594797\pi\)
\(84\) 0 0
\(85\) 0.135439 0.0146904
\(86\) −5.20986 −0.561794
\(87\) 10.0028 1.07242
\(88\) 2.30395 0.245602
\(89\) −12.4694 −1.32175 −0.660877 0.750494i \(-0.729816\pi\)
−0.660877 + 0.750494i \(0.729816\pi\)
\(90\) −6.12741 −0.645886
\(91\) 0 0
\(92\) −4.07753 −0.425112
\(93\) 6.15479 0.638222
\(94\) 7.33991 0.757054
\(95\) −12.4968 −1.28214
\(96\) −5.97790 −0.610116
\(97\) −12.5010 −1.26929 −0.634643 0.772806i \(-0.718853\pi\)
−0.634643 + 0.772806i \(0.718853\pi\)
\(98\) 0 0
\(99\) 1.59502 0.160306
\(100\) 8.05930 0.805930
\(101\) −6.85121 −0.681721 −0.340860 0.940114i \(-0.610718\pi\)
−0.340860 + 0.940114i \(0.610718\pi\)
\(102\) 0.0705426 0.00698476
\(103\) 9.14251 0.900838 0.450419 0.892817i \(-0.351275\pi\)
0.450419 + 0.892817i \(0.351275\pi\)
\(104\) −1.44447 −0.141641
\(105\) 0 0
\(106\) 18.3847 1.78568
\(107\) 13.6772 1.32222 0.661112 0.750287i \(-0.270085\pi\)
0.661112 + 0.750287i \(0.270085\pi\)
\(108\) −1.19144 −0.114646
\(109\) 5.64433 0.540629 0.270315 0.962772i \(-0.412872\pi\)
0.270315 + 0.962772i \(0.412872\pi\)
\(110\) −9.77336 −0.931854
\(111\) 11.1303 1.05644
\(112\) 0 0
\(113\) −3.61852 −0.340402 −0.170201 0.985409i \(-0.554442\pi\)
−0.170201 + 0.985409i \(0.554442\pi\)
\(114\) −6.50890 −0.609614
\(115\) −11.7384 −1.09461
\(116\) −11.9178 −1.10654
\(117\) −1.00000 −0.0924500
\(118\) −16.4233 −1.51189
\(119\) 0 0
\(120\) −4.95440 −0.452273
\(121\) −8.45590 −0.768719
\(122\) 3.50238 0.317090
\(123\) 5.08793 0.458763
\(124\) −7.33304 −0.658527
\(125\) 6.05160 0.541272
\(126\) 0 0
\(127\) 12.6716 1.12442 0.562210 0.826995i \(-0.309951\pi\)
0.562210 + 0.826995i \(0.309951\pi\)
\(128\) −10.6114 −0.937921
\(129\) −2.91631 −0.256766
\(130\) 6.12741 0.537410
\(131\) −11.3110 −0.988244 −0.494122 0.869393i \(-0.664510\pi\)
−0.494122 + 0.869393i \(0.664510\pi\)
\(132\) −1.90037 −0.165406
\(133\) 0 0
\(134\) −21.5391 −1.86070
\(135\) −3.42992 −0.295201
\(136\) 0.0570382 0.00489098
\(137\) −0.764677 −0.0653308 −0.0326654 0.999466i \(-0.510400\pi\)
−0.0326654 + 0.999466i \(0.510400\pi\)
\(138\) −6.11391 −0.520451
\(139\) −0.894171 −0.0758426 −0.0379213 0.999281i \(-0.512074\pi\)
−0.0379213 + 0.999281i \(0.512074\pi\)
\(140\) 0 0
\(141\) 4.10864 0.346010
\(142\) −3.21250 −0.269587
\(143\) −1.59502 −0.133382
\(144\) −4.96335 −0.413613
\(145\) −34.3089 −2.84920
\(146\) 11.9783 0.991331
\(147\) 0 0
\(148\) −13.2610 −1.09005
\(149\) −12.5117 −1.02500 −0.512501 0.858687i \(-0.671281\pi\)
−0.512501 + 0.858687i \(0.671281\pi\)
\(150\) 12.0842 0.986675
\(151\) −1.83383 −0.149235 −0.0746174 0.997212i \(-0.523774\pi\)
−0.0746174 + 0.997212i \(0.523774\pi\)
\(152\) −5.26285 −0.426874
\(153\) 0.0394874 0.00319237
\(154\) 0 0
\(155\) −21.1104 −1.69563
\(156\) 1.19144 0.0953913
\(157\) 18.3249 1.46248 0.731241 0.682119i \(-0.238941\pi\)
0.731241 + 0.682119i \(0.238941\pi\)
\(158\) −26.1390 −2.07951
\(159\) 10.2912 0.816142
\(160\) 20.5037 1.62096
\(161\) 0 0
\(162\) −1.78646 −0.140358
\(163\) 14.7756 1.15731 0.578657 0.815571i \(-0.303577\pi\)
0.578657 + 0.815571i \(0.303577\pi\)
\(164\) −6.06194 −0.473358
\(165\) −5.47080 −0.425901
\(166\) 9.55139 0.741332
\(167\) −6.61137 −0.511603 −0.255801 0.966729i \(-0.582339\pi\)
−0.255801 + 0.966729i \(0.582339\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −0.241956 −0.0185572
\(171\) −3.64346 −0.278622
\(172\) 3.47459 0.264935
\(173\) −0.725190 −0.0551352 −0.0275676 0.999620i \(-0.508776\pi\)
−0.0275676 + 0.999620i \(0.508776\pi\)
\(174\) −17.8697 −1.35470
\(175\) 0 0
\(176\) −7.91666 −0.596741
\(177\) −9.19324 −0.691006
\(178\) 22.2761 1.66966
\(179\) −18.7935 −1.40469 −0.702346 0.711836i \(-0.747864\pi\)
−0.702346 + 0.711836i \(0.747864\pi\)
\(180\) 4.08653 0.304592
\(181\) −7.45429 −0.554073 −0.277036 0.960859i \(-0.589352\pi\)
−0.277036 + 0.960859i \(0.589352\pi\)
\(182\) 0 0
\(183\) 1.96051 0.144925
\(184\) −4.94348 −0.364438
\(185\) −38.1759 −2.80675
\(186\) −10.9953 −0.806213
\(187\) 0.0629833 0.00460579
\(188\) −4.89518 −0.357018
\(189\) 0 0
\(190\) 22.3250 1.61963
\(191\) 20.3799 1.47464 0.737320 0.675544i \(-0.236091\pi\)
0.737320 + 0.675544i \(0.236091\pi\)
\(192\) 0.752565 0.0543117
\(193\) −10.3020 −0.741556 −0.370778 0.928722i \(-0.620909\pi\)
−0.370778 + 0.928722i \(0.620909\pi\)
\(194\) 22.3326 1.60338
\(195\) 3.42992 0.245622
\(196\) 0 0
\(197\) 22.1453 1.57779 0.788895 0.614528i \(-0.210653\pi\)
0.788895 + 0.614528i \(0.210653\pi\)
\(198\) −2.84944 −0.202501
\(199\) −14.6391 −1.03774 −0.518871 0.854853i \(-0.673647\pi\)
−0.518871 + 0.854853i \(0.673647\pi\)
\(200\) 9.77088 0.690905
\(201\) −12.0569 −0.850426
\(202\) 12.2394 0.861162
\(203\) 0 0
\(204\) −0.0470468 −0.00329393
\(205\) −17.4512 −1.21884
\(206\) −16.3327 −1.13795
\(207\) −3.42236 −0.237871
\(208\) 4.96335 0.344147
\(209\) −5.81140 −0.401983
\(210\) 0 0
\(211\) −16.5084 −1.13649 −0.568243 0.822861i \(-0.692377\pi\)
−0.568243 + 0.822861i \(0.692377\pi\)
\(212\) −12.2613 −0.842107
\(213\) −1.79825 −0.123214
\(214\) −24.4337 −1.67026
\(215\) 10.0027 0.682178
\(216\) −1.44447 −0.0982834
\(217\) 0 0
\(218\) −10.0834 −0.682932
\(219\) 6.70505 0.453085
\(220\) 6.51811 0.439451
\(221\) −0.0394874 −0.00265621
\(222\) −19.8837 −1.33451
\(223\) −12.1251 −0.811958 −0.405979 0.913882i \(-0.633069\pi\)
−0.405979 + 0.913882i \(0.633069\pi\)
\(224\) 0 0
\(225\) 6.76436 0.450957
\(226\) 6.46434 0.430001
\(227\) −14.6634 −0.973242 −0.486621 0.873613i \(-0.661771\pi\)
−0.486621 + 0.873613i \(0.661771\pi\)
\(228\) 4.34095 0.287487
\(229\) 13.3777 0.884023 0.442011 0.897010i \(-0.354265\pi\)
0.442011 + 0.897010i \(0.354265\pi\)
\(230\) 20.9702 1.38274
\(231\) 0 0
\(232\) −14.4488 −0.948607
\(233\) 6.94354 0.454886 0.227443 0.973791i \(-0.426963\pi\)
0.227443 + 0.973791i \(0.426963\pi\)
\(234\) 1.78646 0.116784
\(235\) −14.0923 −0.919280
\(236\) 10.9532 0.712990
\(237\) −14.6318 −0.950435
\(238\) 0 0
\(239\) 10.1854 0.658836 0.329418 0.944184i \(-0.393147\pi\)
0.329418 + 0.944184i \(0.393147\pi\)
\(240\) 17.0239 1.09889
\(241\) −9.74501 −0.627731 −0.313865 0.949467i \(-0.601624\pi\)
−0.313865 + 0.949467i \(0.601624\pi\)
\(242\) 15.1061 0.971059
\(243\) −1.00000 −0.0641500
\(244\) −2.33583 −0.149536
\(245\) 0 0
\(246\) −9.08937 −0.579517
\(247\) 3.64346 0.231828
\(248\) −8.89038 −0.564540
\(249\) 5.34655 0.338824
\(250\) −10.8109 −0.683744
\(251\) −25.5879 −1.61509 −0.807546 0.589805i \(-0.799205\pi\)
−0.807546 + 0.589805i \(0.799205\pi\)
\(252\) 0 0
\(253\) −5.45874 −0.343188
\(254\) −22.6372 −1.42039
\(255\) −0.135439 −0.00848150
\(256\) 20.4619 1.27887
\(257\) 11.5666 0.721505 0.360753 0.932662i \(-0.382520\pi\)
0.360753 + 0.932662i \(0.382520\pi\)
\(258\) 5.20986 0.324352
\(259\) 0 0
\(260\) −4.08653 −0.253436
\(261\) −10.0028 −0.619160
\(262\) 20.2066 1.24837
\(263\) 4.29399 0.264779 0.132389 0.991198i \(-0.457735\pi\)
0.132389 + 0.991198i \(0.457735\pi\)
\(264\) −2.30395 −0.141799
\(265\) −35.2978 −2.16833
\(266\) 0 0
\(267\) 12.4694 0.763115
\(268\) 14.3650 0.877482
\(269\) −6.80665 −0.415009 −0.207504 0.978234i \(-0.566534\pi\)
−0.207504 + 0.978234i \(0.566534\pi\)
\(270\) 6.12741 0.372903
\(271\) −10.6765 −0.648549 −0.324274 0.945963i \(-0.605120\pi\)
−0.324274 + 0.945963i \(0.605120\pi\)
\(272\) −0.195990 −0.0118836
\(273\) 0 0
\(274\) 1.36606 0.0825270
\(275\) 10.7893 0.650619
\(276\) 4.07753 0.245438
\(277\) 27.8236 1.67176 0.835880 0.548912i \(-0.184958\pi\)
0.835880 + 0.548912i \(0.184958\pi\)
\(278\) 1.59740 0.0958057
\(279\) −6.15479 −0.368478
\(280\) 0 0
\(281\) 27.3000 1.62858 0.814291 0.580458i \(-0.197126\pi\)
0.814291 + 0.580458i \(0.197126\pi\)
\(282\) −7.33991 −0.437086
\(283\) 15.8447 0.941872 0.470936 0.882167i \(-0.343916\pi\)
0.470936 + 0.882167i \(0.343916\pi\)
\(284\) 2.14250 0.127134
\(285\) 12.4968 0.740246
\(286\) 2.84944 0.168491
\(287\) 0 0
\(288\) 5.97790 0.352251
\(289\) −16.9984 −0.999908
\(290\) 61.2915 3.59916
\(291\) 12.5010 0.732822
\(292\) −7.98865 −0.467500
\(293\) 16.4408 0.960481 0.480240 0.877137i \(-0.340549\pi\)
0.480240 + 0.877137i \(0.340549\pi\)
\(294\) 0 0
\(295\) 31.5321 1.83587
\(296\) −16.0773 −0.934472
\(297\) −1.59502 −0.0925526
\(298\) 22.3517 1.29480
\(299\) 3.42236 0.197920
\(300\) −8.05930 −0.465304
\(301\) 0 0
\(302\) 3.27606 0.188516
\(303\) 6.85121 0.393592
\(304\) 18.0838 1.03718
\(305\) −6.72440 −0.385038
\(306\) −0.0705426 −0.00403265
\(307\) −24.0573 −1.37302 −0.686512 0.727119i \(-0.740859\pi\)
−0.686512 + 0.727119i \(0.740859\pi\)
\(308\) 0 0
\(309\) −9.14251 −0.520099
\(310\) 37.7129 2.14195
\(311\) −34.1237 −1.93497 −0.967487 0.252919i \(-0.918609\pi\)
−0.967487 + 0.252919i \(0.918609\pi\)
\(312\) 1.44447 0.0817767
\(313\) 30.5918 1.72915 0.864575 0.502504i \(-0.167588\pi\)
0.864575 + 0.502504i \(0.167588\pi\)
\(314\) −32.7366 −1.84743
\(315\) 0 0
\(316\) 17.4328 0.980672
\(317\) −4.41815 −0.248148 −0.124074 0.992273i \(-0.539596\pi\)
−0.124074 + 0.992273i \(0.539596\pi\)
\(318\) −18.3847 −1.03096
\(319\) −15.9548 −0.893295
\(320\) −2.58124 −0.144296
\(321\) −13.6772 −0.763386
\(322\) 0 0
\(323\) −0.143871 −0.00800519
\(324\) 1.19144 0.0661909
\(325\) −6.76436 −0.375219
\(326\) −26.3960 −1.46194
\(327\) −5.64433 −0.312132
\(328\) −7.34933 −0.405799
\(329\) 0 0
\(330\) 9.77336 0.538006
\(331\) 24.8674 1.36684 0.683418 0.730027i \(-0.260493\pi\)
0.683418 + 0.730027i \(0.260493\pi\)
\(332\) −6.37007 −0.349603
\(333\) −11.1303 −0.609934
\(334\) 11.8109 0.646266
\(335\) 41.3541 2.25942
\(336\) 0 0
\(337\) −10.1490 −0.552851 −0.276426 0.961035i \(-0.589150\pi\)
−0.276426 + 0.961035i \(0.589150\pi\)
\(338\) −1.78646 −0.0971706
\(339\) 3.61852 0.196531
\(340\) 0.161367 0.00875133
\(341\) −9.81703 −0.531622
\(342\) 6.50890 0.351961
\(343\) 0 0
\(344\) 4.21250 0.227123
\(345\) 11.7384 0.631976
\(346\) 1.29552 0.0696477
\(347\) −0.296340 −0.0159083 −0.00795417 0.999968i \(-0.502532\pi\)
−0.00795417 + 0.999968i \(0.502532\pi\)
\(348\) 11.9178 0.638859
\(349\) 28.7148 1.53707 0.768534 0.639809i \(-0.220987\pi\)
0.768534 + 0.639809i \(0.220987\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 9.53488 0.508211
\(353\) 21.6081 1.15008 0.575042 0.818124i \(-0.304986\pi\)
0.575042 + 0.818124i \(0.304986\pi\)
\(354\) 16.4233 0.872891
\(355\) 6.16786 0.327356
\(356\) −14.8565 −0.787394
\(357\) 0 0
\(358\) 33.5738 1.77443
\(359\) 6.39890 0.337721 0.168860 0.985640i \(-0.445991\pi\)
0.168860 + 0.985640i \(0.445991\pi\)
\(360\) 4.95440 0.261120
\(361\) −5.72519 −0.301326
\(362\) 13.3168 0.699915
\(363\) 8.45590 0.443820
\(364\) 0 0
\(365\) −22.9978 −1.20376
\(366\) −3.50238 −0.183072
\(367\) 0.718923 0.0375275 0.0187637 0.999824i \(-0.494027\pi\)
0.0187637 + 0.999824i \(0.494027\pi\)
\(368\) 16.9864 0.885476
\(369\) −5.08793 −0.264867
\(370\) 68.1997 3.54553
\(371\) 0 0
\(372\) 7.33304 0.380201
\(373\) −9.89739 −0.512468 −0.256234 0.966615i \(-0.582482\pi\)
−0.256234 + 0.966615i \(0.582482\pi\)
\(374\) −0.112517 −0.00581812
\(375\) −6.05160 −0.312503
\(376\) −5.93478 −0.306063
\(377\) 10.0028 0.515172
\(378\) 0 0
\(379\) 3.64783 0.187376 0.0936882 0.995602i \(-0.470134\pi\)
0.0936882 + 0.995602i \(0.470134\pi\)
\(380\) −14.8891 −0.763796
\(381\) −12.6716 −0.649184
\(382\) −36.4079 −1.86279
\(383\) 15.7029 0.802378 0.401189 0.915995i \(-0.368597\pi\)
0.401189 + 0.915995i \(0.368597\pi\)
\(384\) 10.6114 0.541509
\(385\) 0 0
\(386\) 18.4041 0.936746
\(387\) 2.91631 0.148244
\(388\) −14.8942 −0.756137
\(389\) 10.4826 0.531490 0.265745 0.964043i \(-0.414382\pi\)
0.265745 + 0.964043i \(0.414382\pi\)
\(390\) −6.12741 −0.310274
\(391\) −0.135140 −0.00683433
\(392\) 0 0
\(393\) 11.3110 0.570563
\(394\) −39.5618 −1.99309
\(395\) 50.1858 2.52512
\(396\) 1.90037 0.0954971
\(397\) 26.2193 1.31591 0.657953 0.753059i \(-0.271422\pi\)
0.657953 + 0.753059i \(0.271422\pi\)
\(398\) 26.1522 1.31089
\(399\) 0 0
\(400\) −33.5739 −1.67869
\(401\) −29.9844 −1.49735 −0.748676 0.662936i \(-0.769310\pi\)
−0.748676 + 0.662936i \(0.769310\pi\)
\(402\) 21.5391 1.07427
\(403\) 6.15479 0.306592
\(404\) −8.16279 −0.406114
\(405\) 3.42992 0.170434
\(406\) 0 0
\(407\) −17.7530 −0.879984
\(408\) −0.0570382 −0.00282381
\(409\) 16.1232 0.797242 0.398621 0.917116i \(-0.369489\pi\)
0.398621 + 0.917116i \(0.369489\pi\)
\(410\) 31.1758 1.53966
\(411\) 0.764677 0.0377187
\(412\) 10.8927 0.536646
\(413\) 0 0
\(414\) 6.11391 0.300482
\(415\) −18.3382 −0.900188
\(416\) −5.97790 −0.293090
\(417\) 0.894171 0.0437877
\(418\) 10.3818 0.507792
\(419\) −6.10021 −0.298015 −0.149007 0.988836i \(-0.547608\pi\)
−0.149007 + 0.988836i \(0.547608\pi\)
\(420\) 0 0
\(421\) 11.1161 0.541768 0.270884 0.962612i \(-0.412684\pi\)
0.270884 + 0.962612i \(0.412684\pi\)
\(422\) 29.4916 1.43563
\(423\) −4.10864 −0.199769
\(424\) −14.8652 −0.721919
\(425\) 0.267107 0.0129566
\(426\) 3.21250 0.155646
\(427\) 0 0
\(428\) 16.2955 0.787673
\(429\) 1.59502 0.0770084
\(430\) −17.8694 −0.861739
\(431\) −5.86033 −0.282282 −0.141141 0.989989i \(-0.545077\pi\)
−0.141141 + 0.989989i \(0.545077\pi\)
\(432\) 4.96335 0.238799
\(433\) −32.1012 −1.54268 −0.771342 0.636421i \(-0.780414\pi\)
−0.771342 + 0.636421i \(0.780414\pi\)
\(434\) 0 0
\(435\) 34.3089 1.64499
\(436\) 6.72487 0.322063
\(437\) 12.4692 0.596485
\(438\) −11.9783 −0.572345
\(439\) −29.1979 −1.39354 −0.696769 0.717295i \(-0.745380\pi\)
−0.696769 + 0.717295i \(0.745380\pi\)
\(440\) 7.90238 0.376731
\(441\) 0 0
\(442\) 0.0705426 0.00335537
\(443\) −28.1516 −1.33752 −0.668762 0.743476i \(-0.733176\pi\)
−0.668762 + 0.743476i \(0.733176\pi\)
\(444\) 13.2610 0.629339
\(445\) −42.7691 −2.02745
\(446\) 21.6610 1.02568
\(447\) 12.5117 0.591785
\(448\) 0 0
\(449\) 5.39643 0.254673 0.127337 0.991860i \(-0.459357\pi\)
0.127337 + 0.991860i \(0.459357\pi\)
\(450\) −12.0842 −0.569657
\(451\) −8.11536 −0.382137
\(452\) −4.31124 −0.202784
\(453\) 1.83383 0.0861607
\(454\) 26.1955 1.22942
\(455\) 0 0
\(456\) 5.26285 0.246456
\(457\) 29.5079 1.38032 0.690161 0.723656i \(-0.257540\pi\)
0.690161 + 0.723656i \(0.257540\pi\)
\(458\) −23.8987 −1.11671
\(459\) −0.0394874 −0.00184311
\(460\) −13.9856 −0.652082
\(461\) −17.6176 −0.820533 −0.410267 0.911966i \(-0.634564\pi\)
−0.410267 + 0.911966i \(0.634564\pi\)
\(462\) 0 0
\(463\) 6.40031 0.297448 0.148724 0.988879i \(-0.452483\pi\)
0.148724 + 0.988879i \(0.452483\pi\)
\(464\) 49.6476 2.30483
\(465\) 21.1104 0.978973
\(466\) −12.4043 −0.574620
\(467\) −15.4278 −0.713915 −0.356958 0.934121i \(-0.616186\pi\)
−0.356958 + 0.934121i \(0.616186\pi\)
\(468\) −1.19144 −0.0550742
\(469\) 0 0
\(470\) 25.1753 1.16125
\(471\) −18.3249 −0.844365
\(472\) 13.2793 0.611230
\(473\) 4.65157 0.213880
\(474\) 26.1390 1.20061
\(475\) −24.6457 −1.13082
\(476\) 0 0
\(477\) −10.2912 −0.471200
\(478\) −18.1957 −0.832253
\(479\) 23.1297 1.05682 0.528411 0.848989i \(-0.322788\pi\)
0.528411 + 0.848989i \(0.322788\pi\)
\(480\) −20.5037 −0.935862
\(481\) 11.1303 0.507496
\(482\) 17.4091 0.792961
\(483\) 0 0
\(484\) −10.0747 −0.457940
\(485\) −42.8775 −1.94697
\(486\) 1.78646 0.0810354
\(487\) 7.81085 0.353943 0.176972 0.984216i \(-0.443370\pi\)
0.176972 + 0.984216i \(0.443370\pi\)
\(488\) −2.83189 −0.128194
\(489\) −14.7756 −0.668176
\(490\) 0 0
\(491\) −24.7444 −1.11670 −0.558350 0.829605i \(-0.688565\pi\)
−0.558350 + 0.829605i \(0.688565\pi\)
\(492\) 6.06194 0.273294
\(493\) −0.394986 −0.0177893
\(494\) −6.50890 −0.292849
\(495\) 5.47080 0.245894
\(496\) 30.5484 1.37166
\(497\) 0 0
\(498\) −9.55139 −0.428008
\(499\) −17.2052 −0.770209 −0.385104 0.922873i \(-0.625835\pi\)
−0.385104 + 0.922873i \(0.625835\pi\)
\(500\) 7.21010 0.322445
\(501\) 6.61137 0.295374
\(502\) 45.7117 2.04021
\(503\) 31.0833 1.38593 0.692967 0.720969i \(-0.256303\pi\)
0.692967 + 0.720969i \(0.256303\pi\)
\(504\) 0 0
\(505\) −23.4991 −1.04570
\(506\) 9.75182 0.433521
\(507\) −1.00000 −0.0444116
\(508\) 15.0974 0.669838
\(509\) −18.6852 −0.828209 −0.414104 0.910229i \(-0.635905\pi\)
−0.414104 + 0.910229i \(0.635905\pi\)
\(510\) 0.241956 0.0107140
\(511\) 0 0
\(512\) −15.3316 −0.677569
\(513\) 3.64346 0.160863
\(514\) −20.6633 −0.911418
\(515\) 31.3581 1.38180
\(516\) −3.47459 −0.152960
\(517\) −6.55337 −0.288217
\(518\) 0 0
\(519\) 0.725190 0.0318323
\(520\) −4.95440 −0.217265
\(521\) −5.25437 −0.230198 −0.115099 0.993354i \(-0.536719\pi\)
−0.115099 + 0.993354i \(0.536719\pi\)
\(522\) 17.8697 0.782134
\(523\) −0.906833 −0.0396530 −0.0198265 0.999803i \(-0.506311\pi\)
−0.0198265 + 0.999803i \(0.506311\pi\)
\(524\) −13.4763 −0.588715
\(525\) 0 0
\(526\) −7.67104 −0.334473
\(527\) −0.243037 −0.0105868
\(528\) 7.91666 0.344528
\(529\) −11.2874 −0.490758
\(530\) 63.0582 2.73907
\(531\) 9.19324 0.398952
\(532\) 0 0
\(533\) 5.08793 0.220383
\(534\) −22.2761 −0.963981
\(535\) 46.9117 2.02817
\(536\) 17.4157 0.752245
\(537\) 18.7935 0.810999
\(538\) 12.1598 0.524246
\(539\) 0 0
\(540\) −4.08653 −0.175856
\(541\) −13.1604 −0.565810 −0.282905 0.959148i \(-0.591298\pi\)
−0.282905 + 0.959148i \(0.591298\pi\)
\(542\) 19.0731 0.819258
\(543\) 7.45429 0.319894
\(544\) 0.236052 0.0101206
\(545\) 19.3596 0.829275
\(546\) 0 0
\(547\) 2.77123 0.118489 0.0592446 0.998243i \(-0.481131\pi\)
0.0592446 + 0.998243i \(0.481131\pi\)
\(548\) −0.911065 −0.0389187
\(549\) −1.96051 −0.0836726
\(550\) −19.2746 −0.821874
\(551\) 36.4450 1.55261
\(552\) 4.94348 0.210409
\(553\) 0 0
\(554\) −49.7058 −2.11180
\(555\) 38.1759 1.62048
\(556\) −1.06535 −0.0451808
\(557\) 13.1292 0.556301 0.278151 0.960537i \(-0.410279\pi\)
0.278151 + 0.960537i \(0.410279\pi\)
\(558\) 10.9953 0.465467
\(559\) −2.91631 −0.123347
\(560\) 0 0
\(561\) −0.0629833 −0.00265916
\(562\) −48.7703 −2.05725
\(563\) −23.7475 −1.00084 −0.500419 0.865783i \(-0.666821\pi\)
−0.500419 + 0.865783i \(0.666821\pi\)
\(564\) 4.89518 0.206124
\(565\) −12.4112 −0.522144
\(566\) −28.3060 −1.18979
\(567\) 0 0
\(568\) 2.59751 0.108989
\(569\) 31.3578 1.31459 0.657293 0.753635i \(-0.271701\pi\)
0.657293 + 0.753635i \(0.271701\pi\)
\(570\) −22.3250 −0.935091
\(571\) 13.0846 0.547573 0.273787 0.961790i \(-0.411724\pi\)
0.273787 + 0.961790i \(0.411724\pi\)
\(572\) −1.90037 −0.0794584
\(573\) −20.3799 −0.851383
\(574\) 0 0
\(575\) −23.1501 −0.965425
\(576\) −0.752565 −0.0313569
\(577\) 39.0098 1.62400 0.812000 0.583658i \(-0.198379\pi\)
0.812000 + 0.583658i \(0.198379\pi\)
\(578\) 30.3670 1.26310
\(579\) 10.3020 0.428137
\(580\) −40.8769 −1.69732
\(581\) 0 0
\(582\) −22.3326 −0.925714
\(583\) −16.4146 −0.679824
\(584\) −9.68521 −0.400777
\(585\) −3.42992 −0.141810
\(586\) −29.3708 −1.21330
\(587\) −9.86312 −0.407094 −0.203547 0.979065i \(-0.565247\pi\)
−0.203547 + 0.979065i \(0.565247\pi\)
\(588\) 0 0
\(589\) 22.4247 0.923995
\(590\) −56.3308 −2.31910
\(591\) −22.1453 −0.910938
\(592\) 55.2434 2.27049
\(593\) −47.2896 −1.94195 −0.970977 0.239175i \(-0.923123\pi\)
−0.970977 + 0.239175i \(0.923123\pi\)
\(594\) 2.84944 0.116914
\(595\) 0 0
\(596\) −14.9069 −0.610612
\(597\) 14.6391 0.599140
\(598\) −6.11391 −0.250016
\(599\) 14.4370 0.589881 0.294940 0.955516i \(-0.404700\pi\)
0.294940 + 0.955516i \(0.404700\pi\)
\(600\) −9.77088 −0.398894
\(601\) 16.9536 0.691552 0.345776 0.938317i \(-0.387616\pi\)
0.345776 + 0.938317i \(0.387616\pi\)
\(602\) 0 0
\(603\) 12.0569 0.490994
\(604\) −2.18489 −0.0889019
\(605\) −29.0031 −1.17914
\(606\) −12.2394 −0.497192
\(607\) −31.0905 −1.26192 −0.630962 0.775814i \(-0.717340\pi\)
−0.630962 + 0.775814i \(0.717340\pi\)
\(608\) −21.7802 −0.883305
\(609\) 0 0
\(610\) 12.0129 0.486387
\(611\) 4.10864 0.166218
\(612\) 0.0470468 0.00190175
\(613\) −3.08480 −0.124594 −0.0622969 0.998058i \(-0.519843\pi\)
−0.0622969 + 0.998058i \(0.519843\pi\)
\(614\) 42.9774 1.73443
\(615\) 17.4512 0.703700
\(616\) 0 0
\(617\) −40.3163 −1.62307 −0.811537 0.584301i \(-0.801369\pi\)
−0.811537 + 0.584301i \(0.801369\pi\)
\(618\) 16.3327 0.656998
\(619\) −5.35155 −0.215097 −0.107548 0.994200i \(-0.534300\pi\)
−0.107548 + 0.994200i \(0.534300\pi\)
\(620\) −25.1518 −1.01012
\(621\) 3.42236 0.137335
\(622\) 60.9605 2.44429
\(623\) 0 0
\(624\) −4.96335 −0.198693
\(625\) −13.0653 −0.522611
\(626\) −54.6510 −2.18429
\(627\) 5.81140 0.232085
\(628\) 21.8329 0.871228
\(629\) −0.439505 −0.0175242
\(630\) 0 0
\(631\) −8.84966 −0.352300 −0.176150 0.984363i \(-0.556364\pi\)
−0.176150 + 0.984363i \(0.556364\pi\)
\(632\) 21.1351 0.840708
\(633\) 16.5084 0.656150
\(634\) 7.89285 0.313465
\(635\) 43.4625 1.72476
\(636\) 12.2613 0.486191
\(637\) 0 0
\(638\) 28.5025 1.12843
\(639\) 1.79825 0.0711377
\(640\) −36.3961 −1.43868
\(641\) −19.7426 −0.779787 −0.389893 0.920860i \(-0.627488\pi\)
−0.389893 + 0.920860i \(0.627488\pi\)
\(642\) 24.4337 0.964323
\(643\) 17.4196 0.686962 0.343481 0.939160i \(-0.388394\pi\)
0.343481 + 0.939160i \(0.388394\pi\)
\(644\) 0 0
\(645\) −10.0027 −0.393856
\(646\) 0.257019 0.0101123
\(647\) 42.4616 1.66934 0.834669 0.550753i \(-0.185659\pi\)
0.834669 + 0.550753i \(0.185659\pi\)
\(648\) 1.44447 0.0567439
\(649\) 14.6634 0.575589
\(650\) 12.0842 0.473983
\(651\) 0 0
\(652\) 17.6042 0.689433
\(653\) 5.29008 0.207017 0.103508 0.994629i \(-0.466993\pi\)
0.103508 + 0.994629i \(0.466993\pi\)
\(654\) 10.0834 0.394291
\(655\) −38.7957 −1.51587
\(656\) 25.2532 0.985971
\(657\) −6.70505 −0.261589
\(658\) 0 0
\(659\) 44.9462 1.75086 0.875428 0.483348i \(-0.160579\pi\)
0.875428 + 0.483348i \(0.160579\pi\)
\(660\) −6.51811 −0.253717
\(661\) −30.1770 −1.17375 −0.586874 0.809678i \(-0.699642\pi\)
−0.586874 + 0.809678i \(0.699642\pi\)
\(662\) −44.4246 −1.72661
\(663\) 0.0394874 0.00153356
\(664\) −7.72290 −0.299707
\(665\) 0 0
\(666\) 19.8837 0.770479
\(667\) 34.2333 1.32552
\(668\) −7.87703 −0.304771
\(669\) 12.1251 0.468784
\(670\) −73.8774 −2.85413
\(671\) −3.12706 −0.120719
\(672\) 0 0
\(673\) −32.0501 −1.23544 −0.617720 0.786398i \(-0.711944\pi\)
−0.617720 + 0.786398i \(0.711944\pi\)
\(674\) 18.1308 0.698371
\(675\) −6.76436 −0.260360
\(676\) 1.19144 0.0458245
\(677\) 15.4436 0.593548 0.296774 0.954948i \(-0.404089\pi\)
0.296774 + 0.954948i \(0.404089\pi\)
\(678\) −6.46434 −0.248261
\(679\) 0 0
\(680\) 0.195636 0.00750231
\(681\) 14.6634 0.561901
\(682\) 17.5377 0.671554
\(683\) −16.9780 −0.649644 −0.324822 0.945775i \(-0.605304\pi\)
−0.324822 + 0.945775i \(0.605304\pi\)
\(684\) −4.34095 −0.165981
\(685\) −2.62278 −0.100211
\(686\) 0 0
\(687\) −13.3777 −0.510391
\(688\) −14.4746 −0.551841
\(689\) 10.2912 0.392062
\(690\) −20.9702 −0.798323
\(691\) 19.5864 0.745100 0.372550 0.928012i \(-0.378484\pi\)
0.372550 + 0.928012i \(0.378484\pi\)
\(692\) −0.864018 −0.0328450
\(693\) 0 0
\(694\) 0.529399 0.0200957
\(695\) −3.06693 −0.116335
\(696\) 14.4488 0.547679
\(697\) −0.200909 −0.00760997
\(698\) −51.2978 −1.94165
\(699\) −6.94354 −0.262629
\(700\) 0 0
\(701\) 6.84859 0.258668 0.129334 0.991601i \(-0.458716\pi\)
0.129334 + 0.991601i \(0.458716\pi\)
\(702\) −1.78646 −0.0674256
\(703\) 40.5526 1.52947
\(704\) −1.20036 −0.0452402
\(705\) 14.0923 0.530747
\(706\) −38.6020 −1.45281
\(707\) 0 0
\(708\) −10.9532 −0.411645
\(709\) −22.4005 −0.841269 −0.420634 0.907230i \(-0.638192\pi\)
−0.420634 + 0.907230i \(0.638192\pi\)
\(710\) −11.0186 −0.413522
\(711\) 14.6318 0.548734
\(712\) −18.0116 −0.675014
\(713\) 21.0639 0.788850
\(714\) 0 0
\(715\) −5.47080 −0.204596
\(716\) −22.3913 −0.836801
\(717\) −10.1854 −0.380379
\(718\) −11.4314 −0.426615
\(719\) −52.5124 −1.95838 −0.979191 0.202943i \(-0.934949\pi\)
−0.979191 + 0.202943i \(0.934949\pi\)
\(720\) −17.0239 −0.634443
\(721\) 0 0
\(722\) 10.2278 0.380640
\(723\) 9.74501 0.362421
\(724\) −8.88132 −0.330071
\(725\) −67.6628 −2.51293
\(726\) −15.1061 −0.560641
\(727\) 22.4202 0.831519 0.415760 0.909475i \(-0.363516\pi\)
0.415760 + 0.909475i \(0.363516\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 41.0846 1.52061
\(731\) 0.115157 0.00425925
\(732\) 2.33583 0.0863347
\(733\) −19.4700 −0.719140 −0.359570 0.933118i \(-0.617077\pi\)
−0.359570 + 0.933118i \(0.617077\pi\)
\(734\) −1.28433 −0.0474054
\(735\) 0 0
\(736\) −20.4585 −0.754111
\(737\) 19.2310 0.708382
\(738\) 9.08937 0.334584
\(739\) 6.10823 0.224695 0.112347 0.993669i \(-0.464163\pi\)
0.112347 + 0.993669i \(0.464163\pi\)
\(740\) −45.4842 −1.67203
\(741\) −3.64346 −0.133846
\(742\) 0 0
\(743\) 11.8031 0.433015 0.216507 0.976281i \(-0.430533\pi\)
0.216507 + 0.976281i \(0.430533\pi\)
\(744\) 8.89038 0.325937
\(745\) −42.9143 −1.57226
\(746\) 17.6813 0.647358
\(747\) −5.34655 −0.195620
\(748\) 0.0750406 0.00274376
\(749\) 0 0
\(750\) 10.8109 0.394760
\(751\) 0.480357 0.0175285 0.00876423 0.999962i \(-0.497210\pi\)
0.00876423 + 0.999962i \(0.497210\pi\)
\(752\) 20.3926 0.743642
\(753\) 25.5879 0.932474
\(754\) −17.8697 −0.650775
\(755\) −6.28988 −0.228912
\(756\) 0 0
\(757\) −30.1679 −1.09647 −0.548235 0.836324i \(-0.684700\pi\)
−0.548235 + 0.836324i \(0.684700\pi\)
\(758\) −6.51670 −0.236697
\(759\) 5.45874 0.198140
\(760\) −18.0512 −0.654785
\(761\) −34.6292 −1.25531 −0.627654 0.778492i \(-0.715985\pi\)
−0.627654 + 0.778492i \(0.715985\pi\)
\(762\) 22.6372 0.820061
\(763\) 0 0
\(764\) 24.2814 0.878470
\(765\) 0.135439 0.00489680
\(766\) −28.0525 −1.01358
\(767\) −9.19324 −0.331949
\(768\) −20.4619 −0.738355
\(769\) 4.33487 0.156320 0.0781598 0.996941i \(-0.475096\pi\)
0.0781598 + 0.996941i \(0.475096\pi\)
\(770\) 0 0
\(771\) −11.5666 −0.416561
\(772\) −12.2742 −0.441758
\(773\) −3.11423 −0.112011 −0.0560055 0.998430i \(-0.517836\pi\)
−0.0560055 + 0.998430i \(0.517836\pi\)
\(774\) −5.20986 −0.187265
\(775\) −41.6332 −1.49551
\(776\) −18.0573 −0.648219
\(777\) 0 0
\(778\) −18.7268 −0.671388
\(779\) 18.5377 0.664181
\(780\) 4.08653 0.146321
\(781\) 2.86825 0.102634
\(782\) 0.241422 0.00863325
\(783\) 10.0028 0.357472
\(784\) 0 0
\(785\) 62.8528 2.24331
\(786\) −20.2066 −0.720745
\(787\) 15.2612 0.544004 0.272002 0.962297i \(-0.412314\pi\)
0.272002 + 0.962297i \(0.412314\pi\)
\(788\) 26.3848 0.939919
\(789\) −4.29399 −0.152870
\(790\) −89.6548 −3.18978
\(791\) 0 0
\(792\) 2.30395 0.0818674
\(793\) 1.96051 0.0696198
\(794\) −46.8396 −1.66228
\(795\) 35.2978 1.25189
\(796\) −17.4416 −0.618202
\(797\) −15.7622 −0.558325 −0.279162 0.960244i \(-0.590057\pi\)
−0.279162 + 0.960244i \(0.590057\pi\)
\(798\) 0 0
\(799\) −0.162239 −0.00573962
\(800\) 40.4366 1.42965
\(801\) −12.4694 −0.440585
\(802\) 53.5660 1.89148
\(803\) −10.6947 −0.377408
\(804\) −14.3650 −0.506615
\(805\) 0 0
\(806\) −10.9953 −0.387292
\(807\) 6.80665 0.239605
\(808\) −9.89633 −0.348152
\(809\) −19.7817 −0.695489 −0.347744 0.937589i \(-0.613052\pi\)
−0.347744 + 0.937589i \(0.613052\pi\)
\(810\) −6.12741 −0.215295
\(811\) 14.8239 0.520537 0.260269 0.965536i \(-0.416189\pi\)
0.260269 + 0.965536i \(0.416189\pi\)
\(812\) 0 0
\(813\) 10.6765 0.374440
\(814\) 31.7150 1.11161
\(815\) 50.6791 1.77521
\(816\) 0.195990 0.00686102
\(817\) −10.6254 −0.371737
\(818\) −28.8035 −1.00709
\(819\) 0 0
\(820\) −20.7920 −0.726088
\(821\) 24.3070 0.848319 0.424160 0.905587i \(-0.360570\pi\)
0.424160 + 0.905587i \(0.360570\pi\)
\(822\) −1.36606 −0.0476470
\(823\) −49.1057 −1.71172 −0.855858 0.517210i \(-0.826971\pi\)
−0.855858 + 0.517210i \(0.826971\pi\)
\(824\) 13.2060 0.460054
\(825\) −10.7893 −0.375635
\(826\) 0 0
\(827\) −49.5213 −1.72202 −0.861012 0.508585i \(-0.830169\pi\)
−0.861012 + 0.508585i \(0.830169\pi\)
\(828\) −4.07753 −0.141704
\(829\) −10.1416 −0.352233 −0.176116 0.984369i \(-0.556353\pi\)
−0.176116 + 0.984369i \(0.556353\pi\)
\(830\) 32.7605 1.13713
\(831\) −27.8236 −0.965191
\(832\) 0.752565 0.0260905
\(833\) 0 0
\(834\) −1.59740 −0.0553134
\(835\) −22.6765 −0.784751
\(836\) −6.92392 −0.239469
\(837\) 6.15479 0.212741
\(838\) 10.8978 0.376457
\(839\) 29.9487 1.03394 0.516972 0.856002i \(-0.327059\pi\)
0.516972 + 0.856002i \(0.327059\pi\)
\(840\) 0 0
\(841\) 71.0568 2.45023
\(842\) −19.8585 −0.684370
\(843\) −27.3000 −0.940262
\(844\) −19.6687 −0.677025
\(845\) 3.42992 0.117993
\(846\) 7.33991 0.252351
\(847\) 0 0
\(848\) 51.0786 1.75405
\(849\) −15.8447 −0.543790
\(850\) −0.477176 −0.0163670
\(851\) 38.0917 1.30577
\(852\) −2.14250 −0.0734009
\(853\) 23.2279 0.795309 0.397655 0.917535i \(-0.369824\pi\)
0.397655 + 0.917535i \(0.369824\pi\)
\(854\) 0 0
\(855\) −12.4968 −0.427381
\(856\) 19.7562 0.675254
\(857\) 6.41561 0.219153 0.109576 0.993978i \(-0.465051\pi\)
0.109576 + 0.993978i \(0.465051\pi\)
\(858\) −2.84944 −0.0972784
\(859\) 19.1724 0.654154 0.327077 0.944998i \(-0.393936\pi\)
0.327077 + 0.944998i \(0.393936\pi\)
\(860\) 11.9176 0.406386
\(861\) 0 0
\(862\) 10.4692 0.356584
\(863\) 5.45273 0.185613 0.0928065 0.995684i \(-0.470416\pi\)
0.0928065 + 0.995684i \(0.470416\pi\)
\(864\) −5.97790 −0.203372
\(865\) −2.48734 −0.0845722
\(866\) 57.3474 1.94874
\(867\) 16.9984 0.577297
\(868\) 0 0
\(869\) 23.3380 0.791687
\(870\) −61.2915 −2.07798
\(871\) −12.0569 −0.408531
\(872\) 8.15304 0.276097
\(873\) −12.5010 −0.423095
\(874\) −22.2758 −0.753490
\(875\) 0 0
\(876\) 7.98865 0.269911
\(877\) 32.6167 1.10139 0.550693 0.834708i \(-0.314363\pi\)
0.550693 + 0.834708i \(0.314363\pi\)
\(878\) 52.1608 1.76034
\(879\) −16.4408 −0.554534
\(880\) −27.1535 −0.915345
\(881\) −33.4768 −1.12786 −0.563931 0.825822i \(-0.690712\pi\)
−0.563931 + 0.825822i \(0.690712\pi\)
\(882\) 0 0
\(883\) −10.1655 −0.342097 −0.171048 0.985263i \(-0.554715\pi\)
−0.171048 + 0.985263i \(0.554715\pi\)
\(884\) −0.0470468 −0.00158235
\(885\) −31.5321 −1.05994
\(886\) 50.2918 1.68958
\(887\) 15.5935 0.523580 0.261790 0.965125i \(-0.415687\pi\)
0.261790 + 0.965125i \(0.415687\pi\)
\(888\) 16.0773 0.539518
\(889\) 0 0
\(890\) 76.4052 2.56111
\(891\) 1.59502 0.0534353
\(892\) −14.4463 −0.483699
\(893\) 14.9697 0.500941
\(894\) −22.3517 −0.747553
\(895\) −64.4602 −2.15467
\(896\) 0 0
\(897\) −3.42236 −0.114269
\(898\) −9.64051 −0.321708
\(899\) 61.5654 2.05332
\(900\) 8.05930 0.268643
\(901\) −0.406371 −0.0135382
\(902\) 14.4978 0.482722
\(903\) 0 0
\(904\) −5.22682 −0.173842
\(905\) −25.5676 −0.849896
\(906\) −3.27606 −0.108840
\(907\) −59.1827 −1.96513 −0.982564 0.185925i \(-0.940472\pi\)
−0.982564 + 0.185925i \(0.940472\pi\)
\(908\) −17.4705 −0.579778
\(909\) −6.85121 −0.227240
\(910\) 0 0
\(911\) 1.45229 0.0481166 0.0240583 0.999711i \(-0.492341\pi\)
0.0240583 + 0.999711i \(0.492341\pi\)
\(912\) −18.0838 −0.598814
\(913\) −8.52786 −0.282231
\(914\) −52.7147 −1.74365
\(915\) 6.72440 0.222302
\(916\) 15.9387 0.526629
\(917\) 0 0
\(918\) 0.0705426 0.00232825
\(919\) 38.5540 1.27178 0.635890 0.771780i \(-0.280633\pi\)
0.635890 + 0.771780i \(0.280633\pi\)
\(920\) −16.9557 −0.559014
\(921\) 24.0573 0.792715
\(922\) 31.4731 1.03651
\(923\) −1.79825 −0.0591901
\(924\) 0 0
\(925\) −75.2890 −2.47549
\(926\) −11.4339 −0.375741
\(927\) 9.14251 0.300279
\(928\) −59.7959 −1.96290
\(929\) −42.7457 −1.40244 −0.701220 0.712945i \(-0.747361\pi\)
−0.701220 + 0.712945i \(0.747361\pi\)
\(930\) −37.7129 −1.23666
\(931\) 0 0
\(932\) 8.27279 0.270984
\(933\) 34.1237 1.11716
\(934\) 27.5612 0.901830
\(935\) 0.216028 0.00706486
\(936\) −1.44447 −0.0472138
\(937\) 47.2424 1.54334 0.771671 0.636022i \(-0.219421\pi\)
0.771671 + 0.636022i \(0.219421\pi\)
\(938\) 0 0
\(939\) −30.5918 −0.998325
\(940\) −16.7901 −0.547632
\(941\) −50.2899 −1.63940 −0.819702 0.572790i \(-0.805861\pi\)
−0.819702 + 0.572790i \(0.805861\pi\)
\(942\) 32.7366 1.06662
\(943\) 17.4127 0.567036
\(944\) −45.6293 −1.48511
\(945\) 0 0
\(946\) −8.30984 −0.270176
\(947\) 21.1016 0.685710 0.342855 0.939388i \(-0.388606\pi\)
0.342855 + 0.939388i \(0.388606\pi\)
\(948\) −17.4328 −0.566192
\(949\) 6.70505 0.217655
\(950\) 44.0285 1.42847
\(951\) 4.41815 0.143268
\(952\) 0 0
\(953\) −0.279996 −0.00906996 −0.00453498 0.999990i \(-0.501444\pi\)
−0.00453498 + 0.999990i \(0.501444\pi\)
\(954\) 18.3847 0.595228
\(955\) 69.9015 2.26196
\(956\) 12.1352 0.392481
\(957\) 15.9548 0.515744
\(958\) −41.3202 −1.33500
\(959\) 0 0
\(960\) 2.58124 0.0833091
\(961\) 6.88143 0.221981
\(962\) −19.8837 −0.641078
\(963\) 13.6772 0.440741
\(964\) −11.6106 −0.373951
\(965\) −35.3351 −1.13748
\(966\) 0 0
\(967\) 23.5683 0.757905 0.378953 0.925416i \(-0.376284\pi\)
0.378953 + 0.925416i \(0.376284\pi\)
\(968\) −12.2143 −0.392581
\(969\) 0.143871 0.00462180
\(970\) 76.5989 2.45944
\(971\) −1.41343 −0.0453592 −0.0226796 0.999743i \(-0.507220\pi\)
−0.0226796 + 0.999743i \(0.507220\pi\)
\(972\) −1.19144 −0.0382154
\(973\) 0 0
\(974\) −13.9538 −0.447108
\(975\) 6.76436 0.216633
\(976\) 9.73071 0.311473
\(977\) −20.4526 −0.654336 −0.327168 0.944966i \(-0.606094\pi\)
−0.327168 + 0.944966i \(0.606094\pi\)
\(978\) 26.3960 0.844051
\(979\) −19.8890 −0.635655
\(980\) 0 0
\(981\) 5.64433 0.180210
\(982\) 44.2049 1.41064
\(983\) 24.4006 0.778258 0.389129 0.921183i \(-0.372776\pi\)
0.389129 + 0.921183i \(0.372776\pi\)
\(984\) 7.34933 0.234288
\(985\) 75.9568 2.42018
\(986\) 0.705627 0.0224717
\(987\) 0 0
\(988\) 4.34095 0.138104
\(989\) −9.98065 −0.317366
\(990\) −9.77336 −0.310618
\(991\) −15.1319 −0.480682 −0.240341 0.970689i \(-0.577259\pi\)
−0.240341 + 0.970689i \(0.577259\pi\)
\(992\) −36.7927 −1.16817
\(993\) −24.8674 −0.789143
\(994\) 0 0
\(995\) −50.2111 −1.59180
\(996\) 6.37007 0.201844
\(997\) −54.0765 −1.71262 −0.856310 0.516462i \(-0.827249\pi\)
−0.856310 + 0.516462i \(0.827249\pi\)
\(998\) 30.7363 0.972941
\(999\) 11.1303 0.352146
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 1911.2.a.t.1.2 5
3.2 odd 2 5733.2.a.bq.1.4 5
7.2 even 3 273.2.i.e.235.4 yes 10
7.4 even 3 273.2.i.e.79.4 10
7.6 odd 2 1911.2.a.u.1.2 5
21.2 odd 6 819.2.j.g.235.2 10
21.11 odd 6 819.2.j.g.352.2 10
21.20 even 2 5733.2.a.bp.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.i.e.79.4 10 7.4 even 3
273.2.i.e.235.4 yes 10 7.2 even 3
819.2.j.g.235.2 10 21.2 odd 6
819.2.j.g.352.2 10 21.11 odd 6
1911.2.a.t.1.2 5 1.1 even 1 trivial
1911.2.a.u.1.2 5 7.6 odd 2
5733.2.a.bp.1.4 5 21.20 even 2
5733.2.a.bq.1.4 5 3.2 odd 2