Properties

Label 4017.2.a.h.1.3
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $1$
Dimension $25$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.67819 q^{2} -1.00000 q^{3} +5.17269 q^{4} -0.816148 q^{5} +2.67819 q^{6} +2.66447 q^{7} -8.49705 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.67819 q^{2} -1.00000 q^{3} +5.17269 q^{4} -0.816148 q^{5} +2.67819 q^{6} +2.66447 q^{7} -8.49705 q^{8} +1.00000 q^{9} +2.18580 q^{10} -4.90582 q^{11} -5.17269 q^{12} +1.00000 q^{13} -7.13595 q^{14} +0.816148 q^{15} +12.4113 q^{16} -0.150239 q^{17} -2.67819 q^{18} -3.45812 q^{19} -4.22168 q^{20} -2.66447 q^{21} +13.1387 q^{22} +5.22262 q^{23} +8.49705 q^{24} -4.33390 q^{25} -2.67819 q^{26} -1.00000 q^{27} +13.7825 q^{28} +1.72389 q^{29} -2.18580 q^{30} +3.01241 q^{31} -16.2457 q^{32} +4.90582 q^{33} +0.402368 q^{34} -2.17460 q^{35} +5.17269 q^{36} +2.05174 q^{37} +9.26150 q^{38} -1.00000 q^{39} +6.93485 q^{40} +2.13055 q^{41} +7.13595 q^{42} +10.9396 q^{43} -25.3763 q^{44} -0.816148 q^{45} -13.9871 q^{46} -11.7752 q^{47} -12.4113 q^{48} +0.0993928 q^{49} +11.6070 q^{50} +0.150239 q^{51} +5.17269 q^{52} -1.20350 q^{53} +2.67819 q^{54} +4.00388 q^{55} -22.6401 q^{56} +3.45812 q^{57} -4.61691 q^{58} +7.75006 q^{59} +4.22168 q^{60} +1.57774 q^{61} -8.06780 q^{62} +2.66447 q^{63} +18.6865 q^{64} -0.816148 q^{65} -13.1387 q^{66} +2.58696 q^{67} -0.777139 q^{68} -5.22262 q^{69} +5.82398 q^{70} +6.48544 q^{71} -8.49705 q^{72} -4.43124 q^{73} -5.49495 q^{74} +4.33390 q^{75} -17.8878 q^{76} -13.0714 q^{77} +2.67819 q^{78} -16.8786 q^{79} -10.1295 q^{80} +1.00000 q^{81} -5.70601 q^{82} -6.17640 q^{83} -13.7825 q^{84} +0.122617 q^{85} -29.2983 q^{86} -1.72389 q^{87} +41.6850 q^{88} -6.83716 q^{89} +2.18580 q^{90} +2.66447 q^{91} +27.0150 q^{92} -3.01241 q^{93} +31.5362 q^{94} +2.82234 q^{95} +16.2457 q^{96} -10.1862 q^{97} -0.266192 q^{98} -4.90582 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67819 −1.89376 −0.946882 0.321581i \(-0.895786\pi\)
−0.946882 + 0.321581i \(0.895786\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.17269 2.58634
\(5\) −0.816148 −0.364992 −0.182496 0.983207i \(-0.558418\pi\)
−0.182496 + 0.983207i \(0.558418\pi\)
\(6\) 2.67819 1.09337
\(7\) 2.66447 1.00707 0.503537 0.863974i \(-0.332032\pi\)
0.503537 + 0.863974i \(0.332032\pi\)
\(8\) −8.49705 −3.00416
\(9\) 1.00000 0.333333
\(10\) 2.18580 0.691209
\(11\) −4.90582 −1.47916 −0.739581 0.673068i \(-0.764976\pi\)
−0.739581 + 0.673068i \(0.764976\pi\)
\(12\) −5.17269 −1.49323
\(13\) 1.00000 0.277350
\(14\) −7.13595 −1.90716
\(15\) 0.816148 0.210728
\(16\) 12.4113 3.10283
\(17\) −0.150239 −0.0364383 −0.0182191 0.999834i \(-0.505800\pi\)
−0.0182191 + 0.999834i \(0.505800\pi\)
\(18\) −2.67819 −0.631255
\(19\) −3.45812 −0.793348 −0.396674 0.917960i \(-0.629836\pi\)
−0.396674 + 0.917960i \(0.629836\pi\)
\(20\) −4.22168 −0.943995
\(21\) −2.66447 −0.581435
\(22\) 13.1387 2.80118
\(23\) 5.22262 1.08899 0.544496 0.838764i \(-0.316721\pi\)
0.544496 + 0.838764i \(0.316721\pi\)
\(24\) 8.49705 1.73445
\(25\) −4.33390 −0.866781
\(26\) −2.67819 −0.525236
\(27\) −1.00000 −0.192450
\(28\) 13.7825 2.60464
\(29\) 1.72389 0.320119 0.160060 0.987107i \(-0.448831\pi\)
0.160060 + 0.987107i \(0.448831\pi\)
\(30\) −2.18580 −0.399070
\(31\) 3.01241 0.541045 0.270522 0.962714i \(-0.412804\pi\)
0.270522 + 0.962714i \(0.412804\pi\)
\(32\) −16.2457 −2.87186
\(33\) 4.90582 0.853994
\(34\) 0.402368 0.0690055
\(35\) −2.17460 −0.367574
\(36\) 5.17269 0.862114
\(37\) 2.05174 0.337304 0.168652 0.985676i \(-0.446059\pi\)
0.168652 + 0.985676i \(0.446059\pi\)
\(38\) 9.26150 1.50241
\(39\) −1.00000 −0.160128
\(40\) 6.93485 1.09650
\(41\) 2.13055 0.332736 0.166368 0.986064i \(-0.446796\pi\)
0.166368 + 0.986064i \(0.446796\pi\)
\(42\) 7.13595 1.10110
\(43\) 10.9396 1.66827 0.834136 0.551559i \(-0.185967\pi\)
0.834136 + 0.551559i \(0.185967\pi\)
\(44\) −25.3763 −3.82562
\(45\) −0.816148 −0.121664
\(46\) −13.9871 −2.06229
\(47\) −11.7752 −1.71759 −0.858794 0.512321i \(-0.828786\pi\)
−0.858794 + 0.512321i \(0.828786\pi\)
\(48\) −12.4113 −1.79142
\(49\) 0.0993928 0.0141990
\(50\) 11.6070 1.64148
\(51\) 0.150239 0.0210377
\(52\) 5.17269 0.717323
\(53\) −1.20350 −0.165314 −0.0826569 0.996578i \(-0.526341\pi\)
−0.0826569 + 0.996578i \(0.526341\pi\)
\(54\) 2.67819 0.364455
\(55\) 4.00388 0.539883
\(56\) −22.6401 −3.02541
\(57\) 3.45812 0.458039
\(58\) −4.61691 −0.606230
\(59\) 7.75006 1.00897 0.504486 0.863420i \(-0.331682\pi\)
0.504486 + 0.863420i \(0.331682\pi\)
\(60\) 4.22168 0.545016
\(61\) 1.57774 0.202008 0.101004 0.994886i \(-0.467794\pi\)
0.101004 + 0.994886i \(0.467794\pi\)
\(62\) −8.06780 −1.02461
\(63\) 2.66447 0.335691
\(64\) 18.6865 2.33581
\(65\) −0.816148 −0.101231
\(66\) −13.1387 −1.61726
\(67\) 2.58696 0.316047 0.158023 0.987435i \(-0.449488\pi\)
0.158023 + 0.987435i \(0.449488\pi\)
\(68\) −0.777139 −0.0942419
\(69\) −5.22262 −0.628729
\(70\) 5.82398 0.696099
\(71\) 6.48544 0.769680 0.384840 0.922983i \(-0.374257\pi\)
0.384840 + 0.922983i \(0.374257\pi\)
\(72\) −8.49705 −1.00139
\(73\) −4.43124 −0.518637 −0.259319 0.965792i \(-0.583498\pi\)
−0.259319 + 0.965792i \(0.583498\pi\)
\(74\) −5.49495 −0.638775
\(75\) 4.33390 0.500436
\(76\) −17.8878 −2.05187
\(77\) −13.0714 −1.48963
\(78\) 2.67819 0.303245
\(79\) −16.8786 −1.89899 −0.949497 0.313776i \(-0.898406\pi\)
−0.949497 + 0.313776i \(0.898406\pi\)
\(80\) −10.1295 −1.13251
\(81\) 1.00000 0.111111
\(82\) −5.70601 −0.630123
\(83\) −6.17640 −0.677948 −0.338974 0.940796i \(-0.610080\pi\)
−0.338974 + 0.940796i \(0.610080\pi\)
\(84\) −13.7825 −1.50379
\(85\) 0.122617 0.0132997
\(86\) −29.2983 −3.15931
\(87\) −1.72389 −0.184821
\(88\) 41.6850 4.44364
\(89\) −6.83716 −0.724738 −0.362369 0.932035i \(-0.618032\pi\)
−0.362369 + 0.932035i \(0.618032\pi\)
\(90\) 2.18580 0.230403
\(91\) 2.66447 0.279312
\(92\) 27.0150 2.81651
\(93\) −3.01241 −0.312372
\(94\) 31.5362 3.25271
\(95\) 2.82234 0.289566
\(96\) 16.2457 1.65807
\(97\) −10.1862 −1.03426 −0.517128 0.855908i \(-0.672999\pi\)
−0.517128 + 0.855908i \(0.672999\pi\)
\(98\) −0.266192 −0.0268895
\(99\) −4.90582 −0.493054
\(100\) −22.4179 −2.24179
\(101\) 13.5461 1.34789 0.673944 0.738782i \(-0.264599\pi\)
0.673944 + 0.738782i \(0.264599\pi\)
\(102\) −0.402368 −0.0398404
\(103\) 1.00000 0.0985329
\(104\) −8.49705 −0.833204
\(105\) 2.17460 0.212219
\(106\) 3.22321 0.313065
\(107\) −11.5565 −1.11721 −0.558604 0.829434i \(-0.688663\pi\)
−0.558604 + 0.829434i \(0.688663\pi\)
\(108\) −5.17269 −0.497742
\(109\) −6.71143 −0.642838 −0.321419 0.946937i \(-0.604160\pi\)
−0.321419 + 0.946937i \(0.604160\pi\)
\(110\) −10.7231 −1.02241
\(111\) −2.05174 −0.194743
\(112\) 33.0696 3.12478
\(113\) 5.83028 0.548467 0.274233 0.961663i \(-0.411576\pi\)
0.274233 + 0.961663i \(0.411576\pi\)
\(114\) −9.26150 −0.867419
\(115\) −4.26243 −0.397473
\(116\) 8.91716 0.827938
\(117\) 1.00000 0.0924500
\(118\) −20.7561 −1.91075
\(119\) −0.400307 −0.0366961
\(120\) −6.93485 −0.633062
\(121\) 13.0671 1.18792
\(122\) −4.22547 −0.382556
\(123\) −2.13055 −0.192105
\(124\) 15.5823 1.39933
\(125\) 7.61784 0.681361
\(126\) −7.13595 −0.635721
\(127\) 5.37964 0.477366 0.238683 0.971098i \(-0.423284\pi\)
0.238683 + 0.971098i \(0.423284\pi\)
\(128\) −17.5544 −1.55160
\(129\) −10.9396 −0.963177
\(130\) 2.18580 0.191707
\(131\) 6.39454 0.558694 0.279347 0.960190i \(-0.409882\pi\)
0.279347 + 0.960190i \(0.409882\pi\)
\(132\) 25.3763 2.20872
\(133\) −9.21406 −0.798960
\(134\) −6.92835 −0.598518
\(135\) 0.816148 0.0702428
\(136\) 1.27659 0.109466
\(137\) −14.7694 −1.26184 −0.630919 0.775849i \(-0.717322\pi\)
−0.630919 + 0.775849i \(0.717322\pi\)
\(138\) 13.9871 1.19067
\(139\) 11.8823 1.00784 0.503920 0.863750i \(-0.331891\pi\)
0.503920 + 0.863750i \(0.331891\pi\)
\(140\) −11.2485 −0.950674
\(141\) 11.7752 0.991650
\(142\) −17.3692 −1.45759
\(143\) −4.90582 −0.410246
\(144\) 12.4113 1.03428
\(145\) −1.40695 −0.116841
\(146\) 11.8677 0.982177
\(147\) −0.0993928 −0.00819778
\(148\) 10.6130 0.872384
\(149\) 14.6445 1.19972 0.599861 0.800104i \(-0.295222\pi\)
0.599861 + 0.800104i \(0.295222\pi\)
\(150\) −11.6070 −0.947708
\(151\) 1.53386 0.124823 0.0624117 0.998050i \(-0.480121\pi\)
0.0624117 + 0.998050i \(0.480121\pi\)
\(152\) 29.3838 2.38334
\(153\) −0.150239 −0.0121461
\(154\) 35.0077 2.82100
\(155\) −2.45857 −0.197477
\(156\) −5.17269 −0.414146
\(157\) 4.15537 0.331635 0.165817 0.986156i \(-0.446974\pi\)
0.165817 + 0.986156i \(0.446974\pi\)
\(158\) 45.2041 3.59625
\(159\) 1.20350 0.0954440
\(160\) 13.2589 1.04821
\(161\) 13.9155 1.09670
\(162\) −2.67819 −0.210418
\(163\) −16.2436 −1.27230 −0.636149 0.771566i \(-0.719474\pi\)
−0.636149 + 0.771566i \(0.719474\pi\)
\(164\) 11.0207 0.860569
\(165\) −4.00388 −0.311701
\(166\) 16.5416 1.28387
\(167\) −17.6564 −1.36629 −0.683147 0.730281i \(-0.739389\pi\)
−0.683147 + 0.730281i \(0.739389\pi\)
\(168\) 22.6401 1.74672
\(169\) 1.00000 0.0769231
\(170\) −0.328392 −0.0251865
\(171\) −3.45812 −0.264449
\(172\) 56.5871 4.31472
\(173\) −0.127174 −0.00966882 −0.00483441 0.999988i \(-0.501539\pi\)
−0.00483441 + 0.999988i \(0.501539\pi\)
\(174\) 4.61691 0.350007
\(175\) −11.5475 −0.872913
\(176\) −60.8877 −4.58958
\(177\) −7.75006 −0.582530
\(178\) 18.3112 1.37248
\(179\) 20.7246 1.54903 0.774515 0.632555i \(-0.217994\pi\)
0.774515 + 0.632555i \(0.217994\pi\)
\(180\) −4.22168 −0.314665
\(181\) 9.58936 0.712771 0.356386 0.934339i \(-0.384009\pi\)
0.356386 + 0.934339i \(0.384009\pi\)
\(182\) −7.13595 −0.528951
\(183\) −1.57774 −0.116630
\(184\) −44.3768 −3.27150
\(185\) −1.67452 −0.123113
\(186\) 8.06780 0.591560
\(187\) 0.737046 0.0538981
\(188\) −60.9094 −4.44227
\(189\) −2.66447 −0.193812
\(190\) −7.55875 −0.548369
\(191\) −2.60615 −0.188574 −0.0942872 0.995545i \(-0.530057\pi\)
−0.0942872 + 0.995545i \(0.530057\pi\)
\(192\) −18.6865 −1.34858
\(193\) −11.9245 −0.858344 −0.429172 0.903223i \(-0.641195\pi\)
−0.429172 + 0.903223i \(0.641195\pi\)
\(194\) 27.2806 1.95864
\(195\) 0.816148 0.0584455
\(196\) 0.514128 0.0367234
\(197\) −3.22487 −0.229763 −0.114881 0.993379i \(-0.536649\pi\)
−0.114881 + 0.993379i \(0.536649\pi\)
\(198\) 13.1387 0.933728
\(199\) −10.3872 −0.736332 −0.368166 0.929760i \(-0.620014\pi\)
−0.368166 + 0.929760i \(0.620014\pi\)
\(200\) 36.8254 2.60395
\(201\) −2.58696 −0.182470
\(202\) −36.2790 −2.55258
\(203\) 4.59326 0.322384
\(204\) 0.777139 0.0544106
\(205\) −1.73884 −0.121446
\(206\) −2.67819 −0.186598
\(207\) 5.22262 0.362997
\(208\) 12.4113 0.860570
\(209\) 16.9649 1.17349
\(210\) −5.82398 −0.401893
\(211\) −24.1156 −1.66019 −0.830093 0.557625i \(-0.811713\pi\)
−0.830093 + 0.557625i \(0.811713\pi\)
\(212\) −6.22534 −0.427558
\(213\) −6.48544 −0.444375
\(214\) 30.9505 2.11573
\(215\) −8.92832 −0.608906
\(216\) 8.49705 0.578151
\(217\) 8.02647 0.544872
\(218\) 17.9745 1.21738
\(219\) 4.43124 0.299435
\(220\) 20.7108 1.39632
\(221\) −0.150239 −0.0101062
\(222\) 5.49495 0.368797
\(223\) 7.68138 0.514383 0.257192 0.966360i \(-0.417203\pi\)
0.257192 + 0.966360i \(0.417203\pi\)
\(224\) −43.2862 −2.89218
\(225\) −4.33390 −0.288927
\(226\) −15.6146 −1.03867
\(227\) −19.5030 −1.29446 −0.647231 0.762294i \(-0.724073\pi\)
−0.647231 + 0.762294i \(0.724073\pi\)
\(228\) 17.8878 1.18465
\(229\) 22.7830 1.50555 0.752773 0.658280i \(-0.228716\pi\)
0.752773 + 0.658280i \(0.228716\pi\)
\(230\) 11.4156 0.752721
\(231\) 13.0714 0.860036
\(232\) −14.6480 −0.961689
\(233\) 15.3466 1.00539 0.502694 0.864464i \(-0.332342\pi\)
0.502694 + 0.864464i \(0.332342\pi\)
\(234\) −2.67819 −0.175079
\(235\) 9.61029 0.626906
\(236\) 40.0886 2.60955
\(237\) 16.8786 1.09638
\(238\) 1.07210 0.0694937
\(239\) 25.2224 1.63150 0.815750 0.578405i \(-0.196325\pi\)
0.815750 + 0.578405i \(0.196325\pi\)
\(240\) 10.1295 0.653854
\(241\) 10.1216 0.651990 0.325995 0.945371i \(-0.394301\pi\)
0.325995 + 0.945371i \(0.394301\pi\)
\(242\) −34.9962 −2.24964
\(243\) −1.00000 −0.0641500
\(244\) 8.16113 0.522463
\(245\) −0.0811192 −0.00518251
\(246\) 5.70601 0.363802
\(247\) −3.45812 −0.220035
\(248\) −25.5966 −1.62539
\(249\) 6.17640 0.391413
\(250\) −20.4020 −1.29034
\(251\) −13.0005 −0.820586 −0.410293 0.911954i \(-0.634574\pi\)
−0.410293 + 0.911954i \(0.634574\pi\)
\(252\) 13.7825 0.868213
\(253\) −25.6212 −1.61079
\(254\) −14.4077 −0.904018
\(255\) −0.122617 −0.00767858
\(256\) 9.64102 0.602564
\(257\) −6.57923 −0.410401 −0.205201 0.978720i \(-0.565785\pi\)
−0.205201 + 0.978720i \(0.565785\pi\)
\(258\) 29.2983 1.82403
\(259\) 5.46680 0.339690
\(260\) −4.22168 −0.261817
\(261\) 1.72389 0.106706
\(262\) −17.1258 −1.05803
\(263\) −25.5709 −1.57677 −0.788386 0.615181i \(-0.789083\pi\)
−0.788386 + 0.615181i \(0.789083\pi\)
\(264\) −41.6850 −2.56554
\(265\) 0.982236 0.0603383
\(266\) 24.6770 1.51304
\(267\) 6.83716 0.418428
\(268\) 13.3815 0.817406
\(269\) 25.5158 1.55572 0.777862 0.628435i \(-0.216304\pi\)
0.777862 + 0.628435i \(0.216304\pi\)
\(270\) −2.18580 −0.133023
\(271\) 14.6062 0.887262 0.443631 0.896209i \(-0.353690\pi\)
0.443631 + 0.896209i \(0.353690\pi\)
\(272\) −1.86466 −0.113062
\(273\) −2.66447 −0.161261
\(274\) 39.5553 2.38962
\(275\) 21.2614 1.28211
\(276\) −27.0150 −1.62611
\(277\) −26.7074 −1.60469 −0.802346 0.596860i \(-0.796415\pi\)
−0.802346 + 0.596860i \(0.796415\pi\)
\(278\) −31.8229 −1.90861
\(279\) 3.01241 0.180348
\(280\) 18.4777 1.10425
\(281\) 10.6028 0.632511 0.316256 0.948674i \(-0.397574\pi\)
0.316256 + 0.948674i \(0.397574\pi\)
\(282\) −31.5362 −1.87795
\(283\) −23.3746 −1.38948 −0.694738 0.719263i \(-0.744480\pi\)
−0.694738 + 0.719263i \(0.744480\pi\)
\(284\) 33.5471 1.99066
\(285\) −2.82234 −0.167181
\(286\) 13.1387 0.776908
\(287\) 5.67678 0.335090
\(288\) −16.2457 −0.957288
\(289\) −16.9774 −0.998672
\(290\) 3.76808 0.221269
\(291\) 10.1862 0.597128
\(292\) −22.9214 −1.34137
\(293\) −4.37189 −0.255409 −0.127704 0.991812i \(-0.540761\pi\)
−0.127704 + 0.991812i \(0.540761\pi\)
\(294\) 0.266192 0.0155247
\(295\) −6.32519 −0.368267
\(296\) −17.4337 −1.01332
\(297\) 4.90582 0.284665
\(298\) −39.2207 −2.27199
\(299\) 5.22262 0.302032
\(300\) 22.4179 1.29430
\(301\) 29.1482 1.68007
\(302\) −4.10795 −0.236386
\(303\) −13.5461 −0.778204
\(304\) −42.9198 −2.46162
\(305\) −1.28767 −0.0737315
\(306\) 0.402368 0.0230018
\(307\) 12.8794 0.735065 0.367532 0.930011i \(-0.380203\pi\)
0.367532 + 0.930011i \(0.380203\pi\)
\(308\) −67.6143 −3.85268
\(309\) −1.00000 −0.0568880
\(310\) 6.58451 0.373975
\(311\) 6.88182 0.390232 0.195116 0.980780i \(-0.437492\pi\)
0.195116 + 0.980780i \(0.437492\pi\)
\(312\) 8.49705 0.481051
\(313\) −1.55141 −0.0876911 −0.0438456 0.999038i \(-0.513961\pi\)
−0.0438456 + 0.999038i \(0.513961\pi\)
\(314\) −11.1289 −0.628038
\(315\) −2.17460 −0.122525
\(316\) −87.3079 −4.91145
\(317\) 5.47049 0.307253 0.153627 0.988129i \(-0.450905\pi\)
0.153627 + 0.988129i \(0.450905\pi\)
\(318\) −3.22321 −0.180748
\(319\) −8.45712 −0.473508
\(320\) −15.2509 −0.852552
\(321\) 11.5565 0.645021
\(322\) −37.2683 −2.07688
\(323\) 0.519544 0.0289082
\(324\) 5.17269 0.287371
\(325\) −4.33390 −0.240402
\(326\) 43.5035 2.40943
\(327\) 6.71143 0.371143
\(328\) −18.1034 −0.999592
\(329\) −31.3746 −1.72974
\(330\) 10.7231 0.590289
\(331\) −2.13491 −0.117345 −0.0586727 0.998277i \(-0.518687\pi\)
−0.0586727 + 0.998277i \(0.518687\pi\)
\(332\) −31.9486 −1.75341
\(333\) 2.05174 0.112435
\(334\) 47.2871 2.58744
\(335\) −2.11134 −0.115355
\(336\) −33.0696 −1.80409
\(337\) −11.6444 −0.634312 −0.317156 0.948373i \(-0.602728\pi\)
−0.317156 + 0.948373i \(0.602728\pi\)
\(338\) −2.67819 −0.145674
\(339\) −5.83028 −0.316658
\(340\) 0.634260 0.0343976
\(341\) −14.7784 −0.800293
\(342\) 9.26150 0.500804
\(343\) −18.3865 −0.992775
\(344\) −92.9542 −5.01176
\(345\) 4.26243 0.229481
\(346\) 0.340594 0.0183105
\(347\) −13.1131 −0.703946 −0.351973 0.936010i \(-0.614489\pi\)
−0.351973 + 0.936010i \(0.614489\pi\)
\(348\) −8.91716 −0.478010
\(349\) −27.7442 −1.48511 −0.742557 0.669783i \(-0.766387\pi\)
−0.742557 + 0.669783i \(0.766387\pi\)
\(350\) 30.9265 1.65309
\(351\) −1.00000 −0.0533761
\(352\) 79.6986 4.24795
\(353\) −2.13348 −0.113554 −0.0567768 0.998387i \(-0.518082\pi\)
−0.0567768 + 0.998387i \(0.518082\pi\)
\(354\) 20.7561 1.10317
\(355\) −5.29307 −0.280927
\(356\) −35.3665 −1.87442
\(357\) 0.400307 0.0211865
\(358\) −55.5044 −2.93350
\(359\) −37.3887 −1.97330 −0.986649 0.162862i \(-0.947927\pi\)
−0.986649 + 0.162862i \(0.947927\pi\)
\(360\) 6.93485 0.365498
\(361\) −7.04139 −0.370600
\(362\) −25.6821 −1.34982
\(363\) −13.0671 −0.685845
\(364\) 13.7825 0.722397
\(365\) 3.61655 0.189299
\(366\) 4.22547 0.220869
\(367\) 15.3139 0.799378 0.399689 0.916651i \(-0.369118\pi\)
0.399689 + 0.916651i \(0.369118\pi\)
\(368\) 64.8195 3.37895
\(369\) 2.13055 0.110912
\(370\) 4.48469 0.233148
\(371\) −3.20670 −0.166483
\(372\) −15.5823 −0.807902
\(373\) 33.2937 1.72388 0.861941 0.507009i \(-0.169249\pi\)
0.861941 + 0.507009i \(0.169249\pi\)
\(374\) −1.97395 −0.102070
\(375\) −7.61784 −0.393384
\(376\) 100.054 5.15991
\(377\) 1.72389 0.0887850
\(378\) 7.13595 0.367033
\(379\) −0.138115 −0.00709448 −0.00354724 0.999994i \(-0.501129\pi\)
−0.00354724 + 0.999994i \(0.501129\pi\)
\(380\) 14.5991 0.748916
\(381\) −5.37964 −0.275607
\(382\) 6.97976 0.357115
\(383\) −15.2032 −0.776848 −0.388424 0.921481i \(-0.626980\pi\)
−0.388424 + 0.921481i \(0.626980\pi\)
\(384\) 17.5544 0.895819
\(385\) 10.6682 0.543702
\(386\) 31.9360 1.62550
\(387\) 10.9396 0.556091
\(388\) −52.6902 −2.67494
\(389\) −17.2775 −0.876006 −0.438003 0.898973i \(-0.644314\pi\)
−0.438003 + 0.898973i \(0.644314\pi\)
\(390\) −2.18580 −0.110682
\(391\) −0.784641 −0.0396810
\(392\) −0.844545 −0.0426560
\(393\) −6.39454 −0.322562
\(394\) 8.63681 0.435116
\(395\) 13.7755 0.693118
\(396\) −25.3763 −1.27521
\(397\) 14.4199 0.723716 0.361858 0.932233i \(-0.382143\pi\)
0.361858 + 0.932233i \(0.382143\pi\)
\(398\) 27.8190 1.39444
\(399\) 9.21406 0.461280
\(400\) −53.7894 −2.68947
\(401\) −24.2583 −1.21140 −0.605702 0.795692i \(-0.707108\pi\)
−0.605702 + 0.795692i \(0.707108\pi\)
\(402\) 6.92835 0.345555
\(403\) 3.01241 0.150059
\(404\) 70.0698 3.48610
\(405\) −0.816148 −0.0405547
\(406\) −12.3016 −0.610519
\(407\) −10.0655 −0.498927
\(408\) −1.27659 −0.0632005
\(409\) −32.5377 −1.60889 −0.804443 0.594029i \(-0.797536\pi\)
−0.804443 + 0.594029i \(0.797536\pi\)
\(410\) 4.65694 0.229990
\(411\) 14.7694 0.728522
\(412\) 5.17269 0.254840
\(413\) 20.6498 1.01611
\(414\) −13.9871 −0.687431
\(415\) 5.04085 0.247446
\(416\) −16.2457 −0.796512
\(417\) −11.8823 −0.581877
\(418\) −45.4353 −2.22231
\(419\) −12.0506 −0.588711 −0.294355 0.955696i \(-0.595105\pi\)
−0.294355 + 0.955696i \(0.595105\pi\)
\(420\) 11.2485 0.548872
\(421\) −27.5759 −1.34397 −0.671984 0.740566i \(-0.734557\pi\)
−0.671984 + 0.740566i \(0.734557\pi\)
\(422\) 64.5861 3.14400
\(423\) −11.7752 −0.572529
\(424\) 10.2262 0.496629
\(425\) 0.651121 0.0315840
\(426\) 17.3692 0.841541
\(427\) 4.20383 0.203437
\(428\) −59.7781 −2.88948
\(429\) 4.90582 0.236855
\(430\) 23.9117 1.15313
\(431\) 10.4532 0.503513 0.251756 0.967791i \(-0.418992\pi\)
0.251756 + 0.967791i \(0.418992\pi\)
\(432\) −12.4113 −0.597140
\(433\) −19.2962 −0.927317 −0.463659 0.886014i \(-0.653464\pi\)
−0.463659 + 0.886014i \(0.653464\pi\)
\(434\) −21.4964 −1.03186
\(435\) 1.40695 0.0674582
\(436\) −34.7161 −1.66260
\(437\) −18.0605 −0.863949
\(438\) −11.8677 −0.567060
\(439\) −18.6809 −0.891591 −0.445796 0.895135i \(-0.647079\pi\)
−0.445796 + 0.895135i \(0.647079\pi\)
\(440\) −34.0211 −1.62189
\(441\) 0.0993928 0.00473299
\(442\) 0.402368 0.0191387
\(443\) −28.8522 −1.37081 −0.685404 0.728163i \(-0.740375\pi\)
−0.685404 + 0.728163i \(0.740375\pi\)
\(444\) −10.6130 −0.503671
\(445\) 5.58013 0.264524
\(446\) −20.5722 −0.974121
\(447\) −14.6445 −0.692660
\(448\) 49.7895 2.35233
\(449\) −9.96075 −0.470077 −0.235039 0.971986i \(-0.575522\pi\)
−0.235039 + 0.971986i \(0.575522\pi\)
\(450\) 11.6070 0.547159
\(451\) −10.4521 −0.492170
\(452\) 30.1582 1.41852
\(453\) −1.53386 −0.0720668
\(454\) 52.2328 2.45141
\(455\) −2.17460 −0.101947
\(456\) −29.3838 −1.37602
\(457\) 28.6561 1.34048 0.670239 0.742145i \(-0.266192\pi\)
0.670239 + 0.742145i \(0.266192\pi\)
\(458\) −61.0173 −2.85115
\(459\) 0.150239 0.00701255
\(460\) −22.0482 −1.02800
\(461\) 1.24025 0.0577643 0.0288822 0.999583i \(-0.490805\pi\)
0.0288822 + 0.999583i \(0.490805\pi\)
\(462\) −35.0077 −1.62871
\(463\) 12.6747 0.589044 0.294522 0.955645i \(-0.404840\pi\)
0.294522 + 0.955645i \(0.404840\pi\)
\(464\) 21.3958 0.993274
\(465\) 2.45857 0.114014
\(466\) −41.1010 −1.90397
\(467\) −16.7390 −0.774588 −0.387294 0.921956i \(-0.626590\pi\)
−0.387294 + 0.921956i \(0.626590\pi\)
\(468\) 5.17269 0.239108
\(469\) 6.89286 0.318283
\(470\) −25.7382 −1.18721
\(471\) −4.15537 −0.191470
\(472\) −65.8526 −3.03111
\(473\) −53.6677 −2.46764
\(474\) −45.2041 −2.07629
\(475\) 14.9872 0.687658
\(476\) −2.07066 −0.0949086
\(477\) −1.20350 −0.0551046
\(478\) −67.5502 −3.08968
\(479\) 9.29020 0.424480 0.212240 0.977218i \(-0.431924\pi\)
0.212240 + 0.977218i \(0.431924\pi\)
\(480\) −13.2589 −0.605183
\(481\) 2.05174 0.0935513
\(482\) −27.1076 −1.23472
\(483\) −13.9155 −0.633177
\(484\) 67.5920 3.07237
\(485\) 8.31347 0.377495
\(486\) 2.67819 0.121485
\(487\) −25.2243 −1.14302 −0.571511 0.820595i \(-0.693642\pi\)
−0.571511 + 0.820595i \(0.693642\pi\)
\(488\) −13.4061 −0.606865
\(489\) 16.2436 0.734562
\(490\) 0.217252 0.00981446
\(491\) 12.6253 0.569770 0.284885 0.958562i \(-0.408045\pi\)
0.284885 + 0.958562i \(0.408045\pi\)
\(492\) −11.0207 −0.496850
\(493\) −0.258996 −0.0116646
\(494\) 9.26150 0.416694
\(495\) 4.00388 0.179961
\(496\) 37.3880 1.67877
\(497\) 17.2802 0.775125
\(498\) −16.5416 −0.741245
\(499\) −13.0265 −0.583144 −0.291572 0.956549i \(-0.594178\pi\)
−0.291572 + 0.956549i \(0.594178\pi\)
\(500\) 39.4047 1.76223
\(501\) 17.6564 0.788830
\(502\) 34.8178 1.55400
\(503\) −30.8736 −1.37658 −0.688292 0.725433i \(-0.741639\pi\)
−0.688292 + 0.725433i \(0.741639\pi\)
\(504\) −22.6401 −1.00847
\(505\) −11.0556 −0.491969
\(506\) 68.6185 3.05046
\(507\) −1.00000 −0.0444116
\(508\) 27.8272 1.23463
\(509\) −16.0289 −0.710468 −0.355234 0.934777i \(-0.615599\pi\)
−0.355234 + 0.934777i \(0.615599\pi\)
\(510\) 0.328392 0.0145414
\(511\) −11.8069 −0.522306
\(512\) 9.28832 0.410490
\(513\) 3.45812 0.152680
\(514\) 17.6204 0.777203
\(515\) −0.816148 −0.0359638
\(516\) −56.5871 −2.49111
\(517\) 57.7670 2.54059
\(518\) −14.6411 −0.643294
\(519\) 0.127174 0.00558230
\(520\) 6.93485 0.304113
\(521\) −15.2180 −0.666713 −0.333357 0.942801i \(-0.608181\pi\)
−0.333357 + 0.942801i \(0.608181\pi\)
\(522\) −4.61691 −0.202077
\(523\) −3.52280 −0.154041 −0.0770207 0.997029i \(-0.524541\pi\)
−0.0770207 + 0.997029i \(0.524541\pi\)
\(524\) 33.0770 1.44497
\(525\) 11.5475 0.503976
\(526\) 68.4838 2.98603
\(527\) −0.452581 −0.0197147
\(528\) 60.8877 2.64980
\(529\) 4.27574 0.185902
\(530\) −2.63061 −0.114266
\(531\) 7.75006 0.336324
\(532\) −47.6614 −2.06639
\(533\) 2.13055 0.0922843
\(534\) −18.3112 −0.792403
\(535\) 9.43181 0.407773
\(536\) −21.9815 −0.949456
\(537\) −20.7246 −0.894333
\(538\) −68.3360 −2.94617
\(539\) −0.487603 −0.0210026
\(540\) 4.22168 0.181672
\(541\) −40.9206 −1.75931 −0.879657 0.475608i \(-0.842228\pi\)
−0.879657 + 0.475608i \(0.842228\pi\)
\(542\) −39.1181 −1.68027
\(543\) −9.58936 −0.411519
\(544\) 2.44074 0.104646
\(545\) 5.47752 0.234631
\(546\) 7.13595 0.305390
\(547\) 41.7784 1.78632 0.893158 0.449742i \(-0.148484\pi\)
0.893158 + 0.449742i \(0.148484\pi\)
\(548\) −76.3977 −3.26355
\(549\) 1.57774 0.0673361
\(550\) −56.9419 −2.42801
\(551\) −5.96143 −0.253966
\(552\) 44.3768 1.88880
\(553\) −44.9726 −1.91243
\(554\) 71.5274 3.03891
\(555\) 1.67452 0.0710796
\(556\) 61.4632 2.60662
\(557\) 32.7538 1.38782 0.693912 0.720060i \(-0.255886\pi\)
0.693912 + 0.720060i \(0.255886\pi\)
\(558\) −8.06780 −0.341537
\(559\) 10.9396 0.462695
\(560\) −26.9896 −1.14052
\(561\) −0.737046 −0.0311181
\(562\) −28.3963 −1.19783
\(563\) −5.07078 −0.213708 −0.106854 0.994275i \(-0.534078\pi\)
−0.106854 + 0.994275i \(0.534078\pi\)
\(564\) 60.9094 2.56475
\(565\) −4.75837 −0.200186
\(566\) 62.6016 2.63134
\(567\) 2.66447 0.111897
\(568\) −55.1071 −2.31224
\(569\) −24.0298 −1.00738 −0.503690 0.863884i \(-0.668025\pi\)
−0.503690 + 0.863884i \(0.668025\pi\)
\(570\) 7.55875 0.316601
\(571\) 8.71072 0.364532 0.182266 0.983249i \(-0.441657\pi\)
0.182266 + 0.983249i \(0.441657\pi\)
\(572\) −25.3763 −1.06104
\(573\) 2.60615 0.108873
\(574\) −15.2035 −0.634581
\(575\) −22.6343 −0.943916
\(576\) 18.6865 0.778602
\(577\) −20.0534 −0.834832 −0.417416 0.908715i \(-0.637064\pi\)
−0.417416 + 0.908715i \(0.637064\pi\)
\(578\) 45.4687 1.89125
\(579\) 11.9245 0.495565
\(580\) −7.27772 −0.302191
\(581\) −16.4568 −0.682744
\(582\) −27.2806 −1.13082
\(583\) 5.90417 0.244526
\(584\) 37.6525 1.55807
\(585\) −0.816148 −0.0337435
\(586\) 11.7087 0.483684
\(587\) −41.5153 −1.71352 −0.856760 0.515715i \(-0.827526\pi\)
−0.856760 + 0.515715i \(0.827526\pi\)
\(588\) −0.514128 −0.0212023
\(589\) −10.4173 −0.429237
\(590\) 16.9400 0.697410
\(591\) 3.22487 0.132653
\(592\) 25.4648 1.04660
\(593\) −11.7441 −0.482272 −0.241136 0.970491i \(-0.577520\pi\)
−0.241136 + 0.970491i \(0.577520\pi\)
\(594\) −13.1387 −0.539088
\(595\) 0.326709 0.0133938
\(596\) 75.7513 3.10290
\(597\) 10.3872 0.425121
\(598\) −13.9871 −0.571977
\(599\) −2.26982 −0.0927425 −0.0463713 0.998924i \(-0.514766\pi\)
−0.0463713 + 0.998924i \(0.514766\pi\)
\(600\) −36.8254 −1.50339
\(601\) 27.9757 1.14115 0.570577 0.821244i \(-0.306720\pi\)
0.570577 + 0.821244i \(0.306720\pi\)
\(602\) −78.0643 −3.18166
\(603\) 2.58696 0.105349
\(604\) 7.93415 0.322836
\(605\) −10.6647 −0.433581
\(606\) 36.2790 1.47373
\(607\) 31.8822 1.29406 0.647029 0.762466i \(-0.276011\pi\)
0.647029 + 0.762466i \(0.276011\pi\)
\(608\) 56.1797 2.27839
\(609\) −4.59326 −0.186128
\(610\) 3.44861 0.139630
\(611\) −11.7752 −0.476373
\(612\) −0.777139 −0.0314140
\(613\) 0.702727 0.0283829 0.0141914 0.999899i \(-0.495483\pi\)
0.0141914 + 0.999899i \(0.495483\pi\)
\(614\) −34.4934 −1.39204
\(615\) 1.73884 0.0701169
\(616\) 111.068 4.47507
\(617\) −24.0725 −0.969122 −0.484561 0.874757i \(-0.661021\pi\)
−0.484561 + 0.874757i \(0.661021\pi\)
\(618\) 2.67819 0.107732
\(619\) −3.99167 −0.160439 −0.0802195 0.996777i \(-0.525562\pi\)
−0.0802195 + 0.996777i \(0.525562\pi\)
\(620\) −12.7174 −0.510744
\(621\) −5.22262 −0.209576
\(622\) −18.4308 −0.739008
\(623\) −18.2174 −0.729865
\(624\) −12.4113 −0.496850
\(625\) 15.4522 0.618089
\(626\) 4.15498 0.166066
\(627\) −16.9649 −0.677514
\(628\) 21.4944 0.857722
\(629\) −0.308251 −0.0122908
\(630\) 5.82398 0.232033
\(631\) −27.6683 −1.10146 −0.550729 0.834684i \(-0.685650\pi\)
−0.550729 + 0.834684i \(0.685650\pi\)
\(632\) 143.419 5.70488
\(633\) 24.1156 0.958509
\(634\) −14.6510 −0.581866
\(635\) −4.39058 −0.174235
\(636\) 6.22534 0.246851
\(637\) 0.0993928 0.00393808
\(638\) 22.6497 0.896712
\(639\) 6.48544 0.256560
\(640\) 14.3270 0.566323
\(641\) −46.3459 −1.83055 −0.915277 0.402824i \(-0.868029\pi\)
−0.915277 + 0.402824i \(0.868029\pi\)
\(642\) −30.9505 −1.22152
\(643\) 1.02396 0.0403809 0.0201905 0.999796i \(-0.493573\pi\)
0.0201905 + 0.999796i \(0.493573\pi\)
\(644\) 71.9805 2.83643
\(645\) 8.92832 0.351552
\(646\) −1.39144 −0.0547454
\(647\) −6.13766 −0.241296 −0.120648 0.992695i \(-0.538497\pi\)
−0.120648 + 0.992695i \(0.538497\pi\)
\(648\) −8.49705 −0.333796
\(649\) −38.0204 −1.49243
\(650\) 11.6070 0.455264
\(651\) −8.02647 −0.314582
\(652\) −84.0232 −3.29060
\(653\) 4.79883 0.187793 0.0938963 0.995582i \(-0.470068\pi\)
0.0938963 + 0.995582i \(0.470068\pi\)
\(654\) −17.9745 −0.702857
\(655\) −5.21889 −0.203919
\(656\) 26.4429 1.03242
\(657\) −4.43124 −0.172879
\(658\) 84.0271 3.27572
\(659\) 35.2741 1.37408 0.687042 0.726618i \(-0.258909\pi\)
0.687042 + 0.726618i \(0.258909\pi\)
\(660\) −20.7108 −0.806167
\(661\) 34.4135 1.33853 0.669266 0.743023i \(-0.266609\pi\)
0.669266 + 0.743023i \(0.266609\pi\)
\(662\) 5.71769 0.222224
\(663\) 0.150239 0.00583480
\(664\) 52.4812 2.03666
\(665\) 7.52003 0.291614
\(666\) −5.49495 −0.212925
\(667\) 9.00324 0.348607
\(668\) −91.3310 −3.53370
\(669\) −7.68138 −0.296979
\(670\) 5.65456 0.218455
\(671\) −7.74009 −0.298803
\(672\) 43.2862 1.66980
\(673\) 7.06552 0.272356 0.136178 0.990684i \(-0.456518\pi\)
0.136178 + 0.990684i \(0.456518\pi\)
\(674\) 31.1859 1.20124
\(675\) 4.33390 0.166812
\(676\) 5.17269 0.198949
\(677\) 27.9632 1.07471 0.537357 0.843355i \(-0.319423\pi\)
0.537357 + 0.843355i \(0.319423\pi\)
\(678\) 15.6146 0.599675
\(679\) −27.1409 −1.04157
\(680\) −1.04188 −0.0399544
\(681\) 19.5030 0.747358
\(682\) 39.5792 1.51557
\(683\) −8.66084 −0.331398 −0.165699 0.986176i \(-0.552988\pi\)
−0.165699 + 0.986176i \(0.552988\pi\)
\(684\) −17.8878 −0.683956
\(685\) 12.0540 0.460561
\(686\) 49.2424 1.88008
\(687\) −22.7830 −0.869227
\(688\) 135.775 5.17636
\(689\) −1.20350 −0.0458498
\(690\) −11.4156 −0.434584
\(691\) −48.4024 −1.84131 −0.920657 0.390373i \(-0.872346\pi\)
−0.920657 + 0.390373i \(0.872346\pi\)
\(692\) −0.657829 −0.0250069
\(693\) −13.0714 −0.496542
\(694\) 35.1192 1.33311
\(695\) −9.69767 −0.367854
\(696\) 14.6480 0.555231
\(697\) −0.320091 −0.0121243
\(698\) 74.3042 2.81245
\(699\) −15.3466 −0.580461
\(700\) −59.7318 −2.25765
\(701\) 14.5904 0.551071 0.275536 0.961291i \(-0.411145\pi\)
0.275536 + 0.961291i \(0.411145\pi\)
\(702\) 2.67819 0.101082
\(703\) −7.09517 −0.267599
\(704\) −91.6725 −3.45504
\(705\) −9.61029 −0.361944
\(706\) 5.71386 0.215044
\(707\) 36.0932 1.35742
\(708\) −40.0886 −1.50662
\(709\) 22.9639 0.862426 0.431213 0.902250i \(-0.358086\pi\)
0.431213 + 0.902250i \(0.358086\pi\)
\(710\) 14.1758 0.532010
\(711\) −16.8786 −0.632998
\(712\) 58.0957 2.17723
\(713\) 15.7327 0.589193
\(714\) −1.07210 −0.0401222
\(715\) 4.00388 0.149736
\(716\) 107.202 4.00632
\(717\) −25.2224 −0.941947
\(718\) 100.134 3.73696
\(719\) −11.5638 −0.431255 −0.215628 0.976476i \(-0.569180\pi\)
−0.215628 + 0.976476i \(0.569180\pi\)
\(720\) −10.1295 −0.377503
\(721\) 2.66447 0.0992300
\(722\) 18.8582 0.701828
\(723\) −10.1216 −0.376427
\(724\) 49.6027 1.84347
\(725\) −7.47119 −0.277473
\(726\) 34.9962 1.29883
\(727\) −13.1023 −0.485938 −0.242969 0.970034i \(-0.578121\pi\)
−0.242969 + 0.970034i \(0.578121\pi\)
\(728\) −22.6401 −0.839099
\(729\) 1.00000 0.0370370
\(730\) −9.68579 −0.358487
\(731\) −1.64355 −0.0607890
\(732\) −8.16113 −0.301644
\(733\) −25.6709 −0.948177 −0.474088 0.880477i \(-0.657222\pi\)
−0.474088 + 0.880477i \(0.657222\pi\)
\(734\) −41.0134 −1.51383
\(735\) 0.0811192 0.00299213
\(736\) −84.8452 −3.12744
\(737\) −12.6911 −0.467484
\(738\) −5.70601 −0.210041
\(739\) −7.02608 −0.258458 −0.129229 0.991615i \(-0.541250\pi\)
−0.129229 + 0.991615i \(0.541250\pi\)
\(740\) −8.66179 −0.318414
\(741\) 3.45812 0.127037
\(742\) 8.58813 0.315280
\(743\) −16.3989 −0.601619 −0.300809 0.953684i \(-0.597257\pi\)
−0.300809 + 0.953684i \(0.597257\pi\)
\(744\) 25.5966 0.938417
\(745\) −11.9521 −0.437890
\(746\) −89.1667 −3.26463
\(747\) −6.17640 −0.225983
\(748\) 3.81251 0.139399
\(749\) −30.7919 −1.12511
\(750\) 20.4020 0.744976
\(751\) 21.4762 0.783679 0.391840 0.920034i \(-0.371839\pi\)
0.391840 + 0.920034i \(0.371839\pi\)
\(752\) −146.146 −5.32938
\(753\) 13.0005 0.473766
\(754\) −4.61691 −0.168138
\(755\) −1.25185 −0.0455596
\(756\) −13.7825 −0.501263
\(757\) −14.0078 −0.509123 −0.254561 0.967057i \(-0.581931\pi\)
−0.254561 + 0.967057i \(0.581931\pi\)
\(758\) 0.369897 0.0134353
\(759\) 25.6212 0.929992
\(760\) −23.9815 −0.869902
\(761\) 31.0577 1.12584 0.562920 0.826512i \(-0.309678\pi\)
0.562920 + 0.826512i \(0.309678\pi\)
\(762\) 14.4077 0.521935
\(763\) −17.8824 −0.647386
\(764\) −13.4808 −0.487718
\(765\) 0.122617 0.00443323
\(766\) 40.7171 1.47117
\(767\) 7.75006 0.279838
\(768\) −9.64102 −0.347890
\(769\) −32.4314 −1.16951 −0.584753 0.811211i \(-0.698809\pi\)
−0.584753 + 0.811211i \(0.698809\pi\)
\(770\) −28.5714 −1.02964
\(771\) 6.57923 0.236945
\(772\) −61.6817 −2.21997
\(773\) −5.08050 −0.182733 −0.0913665 0.995817i \(-0.529123\pi\)
−0.0913665 + 0.995817i \(0.529123\pi\)
\(774\) −29.2983 −1.05310
\(775\) −13.0555 −0.468967
\(776\) 86.5529 3.10707
\(777\) −5.46680 −0.196120
\(778\) 46.2725 1.65895
\(779\) −7.36770 −0.263975
\(780\) 4.22168 0.151160
\(781\) −31.8164 −1.13848
\(782\) 2.10141 0.0751464
\(783\) −1.72389 −0.0616069
\(784\) 1.23359 0.0440569
\(785\) −3.39140 −0.121044
\(786\) 17.1258 0.610856
\(787\) −38.7331 −1.38068 −0.690342 0.723483i \(-0.742540\pi\)
−0.690342 + 0.723483i \(0.742540\pi\)
\(788\) −16.6812 −0.594245
\(789\) 25.5709 0.910349
\(790\) −36.8932 −1.31260
\(791\) 15.5346 0.552347
\(792\) 41.6850 1.48121
\(793\) 1.57774 0.0560270
\(794\) −38.6193 −1.37055
\(795\) −0.982236 −0.0348363
\(796\) −53.7299 −1.90441
\(797\) 37.6080 1.33214 0.666071 0.745888i \(-0.267975\pi\)
0.666071 + 0.745888i \(0.267975\pi\)
\(798\) −24.6770 −0.873555
\(799\) 1.76909 0.0625860
\(800\) 70.4074 2.48928
\(801\) −6.83716 −0.241579
\(802\) 64.9684 2.29411
\(803\) 21.7389 0.767148
\(804\) −13.3815 −0.471929
\(805\) −11.3571 −0.400285
\(806\) −8.06780 −0.284176
\(807\) −25.5158 −0.898198
\(808\) −115.102 −4.04927
\(809\) −20.8270 −0.732237 −0.366118 0.930568i \(-0.619313\pi\)
−0.366118 + 0.930568i \(0.619313\pi\)
\(810\) 2.18580 0.0768010
\(811\) −55.5606 −1.95100 −0.975499 0.220006i \(-0.929392\pi\)
−0.975499 + 0.220006i \(0.929392\pi\)
\(812\) 23.7595 0.833795
\(813\) −14.6062 −0.512261
\(814\) 26.9572 0.944851
\(815\) 13.2572 0.464379
\(816\) 1.86466 0.0652762
\(817\) −37.8304 −1.32352
\(818\) 87.1421 3.04685
\(819\) 2.66447 0.0931041
\(820\) −8.99448 −0.314101
\(821\) 27.6589 0.965301 0.482651 0.875813i \(-0.339674\pi\)
0.482651 + 0.875813i \(0.339674\pi\)
\(822\) −39.5553 −1.37965
\(823\) 18.7980 0.655257 0.327628 0.944807i \(-0.393751\pi\)
0.327628 + 0.944807i \(0.393751\pi\)
\(824\) −8.49705 −0.296009
\(825\) −21.2614 −0.740226
\(826\) −55.3040 −1.92427
\(827\) −5.84876 −0.203381 −0.101691 0.994816i \(-0.532425\pi\)
−0.101691 + 0.994816i \(0.532425\pi\)
\(828\) 27.0150 0.938835
\(829\) 41.8824 1.45463 0.727317 0.686301i \(-0.240767\pi\)
0.727317 + 0.686301i \(0.240767\pi\)
\(830\) −13.5003 −0.468604
\(831\) 26.7074 0.926469
\(832\) 18.6865 0.647836
\(833\) −0.0149327 −0.000517386 0
\(834\) 31.8229 1.10194
\(835\) 14.4102 0.498686
\(836\) 87.7543 3.03505
\(837\) −3.01241 −0.104124
\(838\) 32.2738 1.11488
\(839\) 50.7004 1.75037 0.875186 0.483787i \(-0.160739\pi\)
0.875186 + 0.483787i \(0.160739\pi\)
\(840\) −18.4777 −0.637540
\(841\) −26.0282 −0.897524
\(842\) 73.8534 2.54516
\(843\) −10.6028 −0.365181
\(844\) −124.742 −4.29381
\(845\) −0.816148 −0.0280763
\(846\) 31.5362 1.08424
\(847\) 34.8169 1.19632
\(848\) −14.9371 −0.512940
\(849\) 23.3746 0.802214
\(850\) −1.74382 −0.0598127
\(851\) 10.7155 0.367321
\(852\) −33.5471 −1.14931
\(853\) 47.2740 1.61863 0.809315 0.587374i \(-0.199838\pi\)
0.809315 + 0.587374i \(0.199838\pi\)
\(854\) −11.2586 −0.385263
\(855\) 2.82234 0.0965219
\(856\) 98.1961 3.35627
\(857\) −15.5304 −0.530507 −0.265254 0.964179i \(-0.585456\pi\)
−0.265254 + 0.964179i \(0.585456\pi\)
\(858\) −13.1387 −0.448548
\(859\) −29.3255 −1.00057 −0.500287 0.865860i \(-0.666772\pi\)
−0.500287 + 0.865860i \(0.666772\pi\)
\(860\) −46.1834 −1.57484
\(861\) −5.67678 −0.193464
\(862\) −27.9956 −0.953534
\(863\) 2.74592 0.0934721 0.0467361 0.998907i \(-0.485118\pi\)
0.0467361 + 0.998907i \(0.485118\pi\)
\(864\) 16.2457 0.552691
\(865\) 0.103792 0.00352905
\(866\) 51.6789 1.75612
\(867\) 16.9774 0.576584
\(868\) 41.5184 1.40923
\(869\) 82.8036 2.80892
\(870\) −3.76808 −0.127750
\(871\) 2.58696 0.0876556
\(872\) 57.0273 1.93119
\(873\) −10.1862 −0.344752
\(874\) 48.3693 1.63611
\(875\) 20.2975 0.686181
\(876\) 22.9214 0.774443
\(877\) −7.85720 −0.265319 −0.132659 0.991162i \(-0.542352\pi\)
−0.132659 + 0.991162i \(0.542352\pi\)
\(878\) 50.0310 1.68846
\(879\) 4.37189 0.147460
\(880\) 49.6934 1.67516
\(881\) 29.0418 0.978442 0.489221 0.872160i \(-0.337281\pi\)
0.489221 + 0.872160i \(0.337281\pi\)
\(882\) −0.266192 −0.00896316
\(883\) −30.7479 −1.03475 −0.517375 0.855759i \(-0.673091\pi\)
−0.517375 + 0.855759i \(0.673091\pi\)
\(884\) −0.777139 −0.0261380
\(885\) 6.32519 0.212619
\(886\) 77.2715 2.59599
\(887\) −16.8822 −0.566849 −0.283424 0.958995i \(-0.591471\pi\)
−0.283424 + 0.958995i \(0.591471\pi\)
\(888\) 17.4337 0.585038
\(889\) 14.3339 0.480743
\(890\) −14.9446 −0.500946
\(891\) −4.90582 −0.164351
\(892\) 39.7334 1.33037
\(893\) 40.7200 1.36264
\(894\) 39.2207 1.31174
\(895\) −16.9143 −0.565384
\(896\) −46.7731 −1.56258
\(897\) −5.22262 −0.174378
\(898\) 26.6768 0.890215
\(899\) 5.19307 0.173199
\(900\) −22.4179 −0.747264
\(901\) 0.180813 0.00602375
\(902\) 27.9927 0.932054
\(903\) −29.1482 −0.969991
\(904\) −49.5402 −1.64768
\(905\) −7.82633 −0.260156
\(906\) 4.10795 0.136478
\(907\) −33.3470 −1.10727 −0.553635 0.832759i \(-0.686760\pi\)
−0.553635 + 0.832759i \(0.686760\pi\)
\(908\) −100.883 −3.34792
\(909\) 13.5461 0.449296
\(910\) 5.82398 0.193063
\(911\) 25.9815 0.860804 0.430402 0.902637i \(-0.358372\pi\)
0.430402 + 0.902637i \(0.358372\pi\)
\(912\) 42.9198 1.42122
\(913\) 30.3003 1.00279
\(914\) −76.7465 −2.53855
\(915\) 1.28767 0.0425689
\(916\) 117.850 3.89386
\(917\) 17.0381 0.562646
\(918\) −0.402368 −0.0132801
\(919\) −7.50664 −0.247621 −0.123811 0.992306i \(-0.539512\pi\)
−0.123811 + 0.992306i \(0.539512\pi\)
\(920\) 36.2181 1.19407
\(921\) −12.8794 −0.424390
\(922\) −3.32163 −0.109392
\(923\) 6.48544 0.213471
\(924\) 67.6143 2.22435
\(925\) −8.89205 −0.292369
\(926\) −33.9452 −1.11551
\(927\) 1.00000 0.0328443
\(928\) −28.0059 −0.919339
\(929\) −25.0236 −0.820998 −0.410499 0.911861i \(-0.634646\pi\)
−0.410499 + 0.911861i \(0.634646\pi\)
\(930\) −6.58451 −0.215915
\(931\) −0.343712 −0.0112647
\(932\) 79.3831 2.60028
\(933\) −6.88182 −0.225301
\(934\) 44.8301 1.46689
\(935\) −0.601538 −0.0196724
\(936\) −8.49705 −0.277735
\(937\) 0.861259 0.0281361 0.0140681 0.999901i \(-0.495522\pi\)
0.0140681 + 0.999901i \(0.495522\pi\)
\(938\) −18.4604 −0.602753
\(939\) 1.55141 0.0506285
\(940\) 49.7110 1.62139
\(941\) 9.66241 0.314985 0.157493 0.987520i \(-0.449659\pi\)
0.157493 + 0.987520i \(0.449659\pi\)
\(942\) 11.1289 0.362598
\(943\) 11.1270 0.362346
\(944\) 96.1884 3.13066
\(945\) 2.17460 0.0707397
\(946\) 143.732 4.67314
\(947\) −14.9556 −0.485993 −0.242997 0.970027i \(-0.578130\pi\)
−0.242997 + 0.970027i \(0.578130\pi\)
\(948\) 87.3079 2.83563
\(949\) −4.43124 −0.143844
\(950\) −40.1384 −1.30226
\(951\) −5.47049 −0.177393
\(952\) 3.40143 0.110241
\(953\) 21.8622 0.708185 0.354092 0.935210i \(-0.384790\pi\)
0.354092 + 0.935210i \(0.384790\pi\)
\(954\) 3.22321 0.104355
\(955\) 2.12700 0.0688282
\(956\) 130.467 4.21962
\(957\) 8.45712 0.273380
\(958\) −24.8809 −0.803866
\(959\) −39.3527 −1.27076
\(960\) 15.2509 0.492221
\(961\) −21.9254 −0.707270
\(962\) −5.49495 −0.177164
\(963\) −11.5565 −0.372403
\(964\) 52.3559 1.68627
\(965\) 9.73215 0.313289
\(966\) 37.2683 1.19909
\(967\) −19.1339 −0.615304 −0.307652 0.951499i \(-0.599543\pi\)
−0.307652 + 0.951499i \(0.599543\pi\)
\(968\) −111.032 −3.56870
\(969\) −0.519544 −0.0166902
\(970\) −22.2650 −0.714887
\(971\) −37.6026 −1.20672 −0.603362 0.797467i \(-0.706173\pi\)
−0.603362 + 0.797467i \(0.706173\pi\)
\(972\) −5.17269 −0.165914
\(973\) 31.6599 1.01497
\(974\) 67.5553 2.16461
\(975\) 4.33390 0.138796
\(976\) 19.5818 0.626797
\(977\) 19.2526 0.615944 0.307972 0.951395i \(-0.400350\pi\)
0.307972 + 0.951395i \(0.400350\pi\)
\(978\) −43.5035 −1.39109
\(979\) 33.5419 1.07200
\(980\) −0.419604 −0.0134038
\(981\) −6.71143 −0.214279
\(982\) −33.8128 −1.07901
\(983\) −38.1682 −1.21738 −0.608689 0.793409i \(-0.708304\pi\)
−0.608689 + 0.793409i \(0.708304\pi\)
\(984\) 18.1034 0.577114
\(985\) 2.63197 0.0838616
\(986\) 0.693640 0.0220900
\(987\) 31.3746 0.998665
\(988\) −17.8878 −0.569086
\(989\) 57.1333 1.81673
\(990\) −10.7231 −0.340803
\(991\) 52.7417 1.67540 0.837698 0.546134i \(-0.183901\pi\)
0.837698 + 0.546134i \(0.183901\pi\)
\(992\) −48.9388 −1.55381
\(993\) 2.13491 0.0677494
\(994\) −46.2797 −1.46790
\(995\) 8.47752 0.268755
\(996\) 31.9486 1.01233
\(997\) −1.95733 −0.0619891 −0.0309946 0.999520i \(-0.509867\pi\)
−0.0309946 + 0.999520i \(0.509867\pi\)
\(998\) 34.8873 1.10434
\(999\) −2.05174 −0.0649142
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 4017.2.a.h.1.3 25
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.h.1.3 25 1.1 even 1 trivial