Properties

Label 4001.2.a.b.1.97
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.97
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.170060 q^{2} +1.77882 q^{3} -1.97108 q^{4} +1.29255 q^{5} +0.302507 q^{6} -0.0406384 q^{7} -0.675323 q^{8} +0.164203 q^{9} +O(q^{10})\) \(q+0.170060 q^{2} +1.77882 q^{3} -1.97108 q^{4} +1.29255 q^{5} +0.302507 q^{6} -0.0406384 q^{7} -0.675323 q^{8} +0.164203 q^{9} +0.219811 q^{10} -5.00857 q^{11} -3.50620 q^{12} -2.21866 q^{13} -0.00691098 q^{14} +2.29921 q^{15} +3.82731 q^{16} +4.23365 q^{17} +0.0279244 q^{18} +6.20870 q^{19} -2.54771 q^{20} -0.0722884 q^{21} -0.851759 q^{22} +1.17639 q^{23} -1.20128 q^{24} -3.32933 q^{25} -0.377306 q^{26} -5.04437 q^{27} +0.0801015 q^{28} +8.33537 q^{29} +0.391004 q^{30} -7.11154 q^{31} +2.00152 q^{32} -8.90934 q^{33} +0.719976 q^{34} -0.0525270 q^{35} -0.323658 q^{36} +8.79659 q^{37} +1.05585 q^{38} -3.94659 q^{39} -0.872886 q^{40} +9.96233 q^{41} -0.0122934 q^{42} -5.13245 q^{43} +9.87228 q^{44} +0.212240 q^{45} +0.200058 q^{46} +6.58729 q^{47} +6.80810 q^{48} -6.99835 q^{49} -0.566186 q^{50} +7.53090 q^{51} +4.37315 q^{52} +6.31303 q^{53} -0.857848 q^{54} -6.47380 q^{55} +0.0274440 q^{56} +11.0442 q^{57} +1.41752 q^{58} +5.57058 q^{59} -4.53192 q^{60} -6.08101 q^{61} -1.20939 q^{62} -0.00667295 q^{63} -7.31425 q^{64} -2.86772 q^{65} -1.51513 q^{66} +7.63543 q^{67} -8.34486 q^{68} +2.09259 q^{69} -0.00893276 q^{70} -4.24652 q^{71} -0.110890 q^{72} +13.3928 q^{73} +1.49595 q^{74} -5.92227 q^{75} -12.2378 q^{76} +0.203540 q^{77} -0.671159 q^{78} +14.5441 q^{79} +4.94698 q^{80} -9.46565 q^{81} +1.69420 q^{82} +6.07686 q^{83} +0.142486 q^{84} +5.47218 q^{85} -0.872826 q^{86} +14.8271 q^{87} +3.38240 q^{88} -11.1352 q^{89} +0.0360936 q^{90} +0.0901627 q^{91} -2.31876 q^{92} -12.6502 q^{93} +1.12024 q^{94} +8.02502 q^{95} +3.56035 q^{96} -1.28324 q^{97} -1.19014 q^{98} -0.822423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.170060 0.120251 0.0601254 0.998191i \(-0.480850\pi\)
0.0601254 + 0.998191i \(0.480850\pi\)
\(3\) 1.77882 1.02700 0.513501 0.858089i \(-0.328348\pi\)
0.513501 + 0.858089i \(0.328348\pi\)
\(4\) −1.97108 −0.985540
\(5\) 1.29255 0.578044 0.289022 0.957322i \(-0.406670\pi\)
0.289022 + 0.957322i \(0.406670\pi\)
\(6\) 0.302507 0.123498
\(7\) −0.0406384 −0.0153599 −0.00767993 0.999971i \(-0.502445\pi\)
−0.00767993 + 0.999971i \(0.502445\pi\)
\(8\) −0.675323 −0.238763
\(9\) 0.164203 0.0547344
\(10\) 0.219811 0.0695103
\(11\) −5.00857 −1.51014 −0.755070 0.655644i \(-0.772397\pi\)
−0.755070 + 0.655644i \(0.772397\pi\)
\(12\) −3.50620 −1.01215
\(13\) −2.21866 −0.615345 −0.307672 0.951492i \(-0.599550\pi\)
−0.307672 + 0.951492i \(0.599550\pi\)
\(14\) −0.00691098 −0.00184704
\(15\) 2.29921 0.593653
\(16\) 3.82731 0.956828
\(17\) 4.23365 1.02681 0.513405 0.858146i \(-0.328384\pi\)
0.513405 + 0.858146i \(0.328384\pi\)
\(18\) 0.0279244 0.00658185
\(19\) 6.20870 1.42437 0.712186 0.701990i \(-0.247705\pi\)
0.712186 + 0.701990i \(0.247705\pi\)
\(20\) −2.54771 −0.569685
\(21\) −0.0722884 −0.0157746
\(22\) −0.851759 −0.181596
\(23\) 1.17639 0.245295 0.122647 0.992450i \(-0.460862\pi\)
0.122647 + 0.992450i \(0.460862\pi\)
\(24\) −1.20128 −0.245210
\(25\) −3.32933 −0.665865
\(26\) −0.377306 −0.0739957
\(27\) −5.04437 −0.970790
\(28\) 0.0801015 0.0151378
\(29\) 8.33537 1.54784 0.773920 0.633284i \(-0.218293\pi\)
0.773920 + 0.633284i \(0.218293\pi\)
\(30\) 0.391004 0.0713872
\(31\) −7.11154 −1.27727 −0.638635 0.769509i \(-0.720501\pi\)
−0.638635 + 0.769509i \(0.720501\pi\)
\(32\) 2.00152 0.353822
\(33\) −8.90934 −1.55092
\(34\) 0.719976 0.123475
\(35\) −0.0525270 −0.00887868
\(36\) −0.323658 −0.0539429
\(37\) 8.79659 1.44615 0.723076 0.690769i \(-0.242728\pi\)
0.723076 + 0.690769i \(0.242728\pi\)
\(38\) 1.05585 0.171282
\(39\) −3.94659 −0.631961
\(40\) −0.872886 −0.138015
\(41\) 9.96233 1.55585 0.777927 0.628355i \(-0.216271\pi\)
0.777927 + 0.628355i \(0.216271\pi\)
\(42\) −0.0122934 −0.00189691
\(43\) −5.13245 −0.782691 −0.391346 0.920244i \(-0.627990\pi\)
−0.391346 + 0.920244i \(0.627990\pi\)
\(44\) 9.87228 1.48830
\(45\) 0.212240 0.0316389
\(46\) 0.200058 0.0294969
\(47\) 6.58729 0.960855 0.480427 0.877034i \(-0.340482\pi\)
0.480427 + 0.877034i \(0.340482\pi\)
\(48\) 6.80810 0.982665
\(49\) −6.99835 −0.999764
\(50\) −0.566186 −0.0800708
\(51\) 7.53090 1.05454
\(52\) 4.37315 0.606447
\(53\) 6.31303 0.867161 0.433580 0.901115i \(-0.357250\pi\)
0.433580 + 0.901115i \(0.357250\pi\)
\(54\) −0.857848 −0.116738
\(55\) −6.47380 −0.872927
\(56\) 0.0274440 0.00366736
\(57\) 11.0442 1.46283
\(58\) 1.41752 0.186129
\(59\) 5.57058 0.725228 0.362614 0.931939i \(-0.381884\pi\)
0.362614 + 0.931939i \(0.381884\pi\)
\(60\) −4.53192 −0.585068
\(61\) −6.08101 −0.778593 −0.389297 0.921112i \(-0.627282\pi\)
−0.389297 + 0.921112i \(0.627282\pi\)
\(62\) −1.20939 −0.153593
\(63\) −0.00667295 −0.000840713 0
\(64\) −7.31425 −0.914281
\(65\) −2.86772 −0.355696
\(66\) −1.51513 −0.186499
\(67\) 7.63543 0.932817 0.466408 0.884570i \(-0.345548\pi\)
0.466408 + 0.884570i \(0.345548\pi\)
\(68\) −8.34486 −1.01196
\(69\) 2.09259 0.251919
\(70\) −0.00893276 −0.00106767
\(71\) −4.24652 −0.503969 −0.251984 0.967731i \(-0.581083\pi\)
−0.251984 + 0.967731i \(0.581083\pi\)
\(72\) −0.110890 −0.0130685
\(73\) 13.3928 1.56751 0.783753 0.621073i \(-0.213303\pi\)
0.783753 + 0.621073i \(0.213303\pi\)
\(74\) 1.49595 0.173901
\(75\) −5.92227 −0.683845
\(76\) −12.2378 −1.40378
\(77\) 0.203540 0.0231955
\(78\) −0.671159 −0.0759938
\(79\) 14.5441 1.63634 0.818170 0.574976i \(-0.194989\pi\)
0.818170 + 0.574976i \(0.194989\pi\)
\(80\) 4.94698 0.553089
\(81\) −9.46565 −1.05174
\(82\) 1.69420 0.187093
\(83\) 6.07686 0.667022 0.333511 0.942746i \(-0.391766\pi\)
0.333511 + 0.942746i \(0.391766\pi\)
\(84\) 0.142486 0.0155465
\(85\) 5.47218 0.593542
\(86\) −0.872826 −0.0941192
\(87\) 14.8271 1.58964
\(88\) 3.38240 0.360565
\(89\) −11.1352 −1.18032 −0.590162 0.807285i \(-0.700936\pi\)
−0.590162 + 0.807285i \(0.700936\pi\)
\(90\) 0.0360936 0.00380460
\(91\) 0.0901627 0.00945161
\(92\) −2.31876 −0.241748
\(93\) −12.6502 −1.31176
\(94\) 1.12024 0.115544
\(95\) 8.02502 0.823350
\(96\) 3.56035 0.363376
\(97\) −1.28324 −0.130293 −0.0651465 0.997876i \(-0.520751\pi\)
−0.0651465 + 0.997876i \(0.520751\pi\)
\(98\) −1.19014 −0.120222
\(99\) −0.822423 −0.0826566
\(100\) 6.56236 0.656236
\(101\) 6.31440 0.628306 0.314153 0.949372i \(-0.398279\pi\)
0.314153 + 0.949372i \(0.398279\pi\)
\(102\) 1.28071 0.126809
\(103\) 15.8711 1.56382 0.781912 0.623389i \(-0.214245\pi\)
0.781912 + 0.623389i \(0.214245\pi\)
\(104\) 1.49831 0.146921
\(105\) −0.0934361 −0.00911843
\(106\) 1.07360 0.104277
\(107\) 16.5449 1.59945 0.799727 0.600364i \(-0.204978\pi\)
0.799727 + 0.600364i \(0.204978\pi\)
\(108\) 9.94286 0.956752
\(109\) −17.9401 −1.71835 −0.859175 0.511683i \(-0.829022\pi\)
−0.859175 + 0.511683i \(0.829022\pi\)
\(110\) −1.10094 −0.104970
\(111\) 15.6476 1.48520
\(112\) −0.155536 −0.0146968
\(113\) −1.60952 −0.151411 −0.0757054 0.997130i \(-0.524121\pi\)
−0.0757054 + 0.997130i \(0.524121\pi\)
\(114\) 1.87817 0.175907
\(115\) 1.52054 0.141791
\(116\) −16.4297 −1.52546
\(117\) −0.364311 −0.0336805
\(118\) 0.947335 0.0872093
\(119\) −0.172049 −0.0157717
\(120\) −1.55271 −0.141742
\(121\) 14.0857 1.28052
\(122\) −1.03414 −0.0936265
\(123\) 17.7212 1.59787
\(124\) 14.0174 1.25880
\(125\) −10.7660 −0.962943
\(126\) −0.00113480 −0.000101096 0
\(127\) 10.0551 0.892244 0.446122 0.894972i \(-0.352805\pi\)
0.446122 + 0.894972i \(0.352805\pi\)
\(128\) −5.24690 −0.463765
\(129\) −9.12971 −0.803826
\(130\) −0.487685 −0.0427728
\(131\) 10.4768 0.915360 0.457680 0.889117i \(-0.348681\pi\)
0.457680 + 0.889117i \(0.348681\pi\)
\(132\) 17.5610 1.52849
\(133\) −0.252311 −0.0218782
\(134\) 1.29848 0.112172
\(135\) −6.52008 −0.561160
\(136\) −2.85908 −0.245164
\(137\) 2.11479 0.180679 0.0903395 0.995911i \(-0.471205\pi\)
0.0903395 + 0.995911i \(0.471205\pi\)
\(138\) 0.355867 0.0302934
\(139\) 14.8955 1.26342 0.631710 0.775205i \(-0.282353\pi\)
0.631710 + 0.775205i \(0.282353\pi\)
\(140\) 0.103535 0.00875029
\(141\) 11.7176 0.986800
\(142\) −0.722164 −0.0606027
\(143\) 11.1123 0.929257
\(144\) 0.628457 0.0523714
\(145\) 10.7738 0.894719
\(146\) 2.27758 0.188494
\(147\) −12.4488 −1.02676
\(148\) −17.3388 −1.42524
\(149\) 14.5999 1.19607 0.598035 0.801470i \(-0.295948\pi\)
0.598035 + 0.801470i \(0.295948\pi\)
\(150\) −1.00714 −0.0822329
\(151\) 5.61907 0.457274 0.228637 0.973512i \(-0.426573\pi\)
0.228637 + 0.973512i \(0.426573\pi\)
\(152\) −4.19288 −0.340087
\(153\) 0.695178 0.0562018
\(154\) 0.0346141 0.00278928
\(155\) −9.19200 −0.738319
\(156\) 7.77905 0.622822
\(157\) −11.5671 −0.923158 −0.461579 0.887099i \(-0.652717\pi\)
−0.461579 + 0.887099i \(0.652717\pi\)
\(158\) 2.47338 0.196771
\(159\) 11.2297 0.890577
\(160\) 2.58706 0.204525
\(161\) −0.0478067 −0.00376770
\(162\) −1.60973 −0.126472
\(163\) −23.2221 −1.81890 −0.909448 0.415818i \(-0.863495\pi\)
−0.909448 + 0.415818i \(0.863495\pi\)
\(164\) −19.6365 −1.53336
\(165\) −11.5157 −0.896499
\(166\) 1.03343 0.0802100
\(167\) −7.00393 −0.541981 −0.270990 0.962582i \(-0.587351\pi\)
−0.270990 + 0.962582i \(0.587351\pi\)
\(168\) 0.0488180 0.00376639
\(169\) −8.07756 −0.621351
\(170\) 0.930601 0.0713739
\(171\) 1.01949 0.0779622
\(172\) 10.1165 0.771373
\(173\) −5.13247 −0.390215 −0.195107 0.980782i \(-0.562506\pi\)
−0.195107 + 0.980782i \(0.562506\pi\)
\(174\) 2.52151 0.191155
\(175\) 0.135298 0.0102276
\(176\) −19.1694 −1.44494
\(177\) 9.90907 0.744811
\(178\) −1.89365 −0.141935
\(179\) 10.9720 0.820084 0.410042 0.912067i \(-0.365514\pi\)
0.410042 + 0.912067i \(0.365514\pi\)
\(180\) −0.418342 −0.0311814
\(181\) −0.168958 −0.0125586 −0.00627929 0.999980i \(-0.501999\pi\)
−0.00627929 + 0.999980i \(0.501999\pi\)
\(182\) 0.0153331 0.00113656
\(183\) −10.8170 −0.799617
\(184\) −0.794446 −0.0585673
\(185\) 11.3700 0.835939
\(186\) −2.15129 −0.157740
\(187\) −21.2045 −1.55063
\(188\) −12.9841 −0.946961
\(189\) 0.204995 0.0149112
\(190\) 1.36474 0.0990085
\(191\) −21.6168 −1.56414 −0.782069 0.623192i \(-0.785835\pi\)
−0.782069 + 0.623192i \(0.785835\pi\)
\(192\) −13.0107 −0.938969
\(193\) 6.12536 0.440913 0.220457 0.975397i \(-0.429245\pi\)
0.220457 + 0.975397i \(0.429245\pi\)
\(194\) −0.218228 −0.0156678
\(195\) −5.10115 −0.365301
\(196\) 13.7943 0.985307
\(197\) −15.7982 −1.12558 −0.562788 0.826601i \(-0.690271\pi\)
−0.562788 + 0.826601i \(0.690271\pi\)
\(198\) −0.139861 −0.00993952
\(199\) 16.8438 1.19403 0.597014 0.802231i \(-0.296354\pi\)
0.597014 + 0.802231i \(0.296354\pi\)
\(200\) 2.24837 0.158984
\(201\) 13.5821 0.958005
\(202\) 1.07383 0.0755544
\(203\) −0.338736 −0.0237746
\(204\) −14.8440 −1.03929
\(205\) 12.8768 0.899352
\(206\) 2.69904 0.188051
\(207\) 0.193168 0.0134261
\(208\) −8.49150 −0.588779
\(209\) −31.0967 −2.15100
\(210\) −0.0158898 −0.00109650
\(211\) 2.80669 0.193220 0.0966102 0.995322i \(-0.469200\pi\)
0.0966102 + 0.995322i \(0.469200\pi\)
\(212\) −12.4435 −0.854622
\(213\) −7.55379 −0.517577
\(214\) 2.81363 0.192336
\(215\) −6.63393 −0.452430
\(216\) 3.40658 0.231789
\(217\) 0.289002 0.0196187
\(218\) −3.05090 −0.206633
\(219\) 23.8233 1.60983
\(220\) 12.7604 0.860305
\(221\) −9.39301 −0.631842
\(222\) 2.66103 0.178597
\(223\) −15.1854 −1.01689 −0.508444 0.861095i \(-0.669779\pi\)
−0.508444 + 0.861095i \(0.669779\pi\)
\(224\) −0.0813386 −0.00543466
\(225\) −0.546686 −0.0364457
\(226\) −0.273715 −0.0182073
\(227\) 21.7378 1.44279 0.721394 0.692525i \(-0.243502\pi\)
0.721394 + 0.692525i \(0.243502\pi\)
\(228\) −21.7689 −1.44168
\(229\) −8.71298 −0.575770 −0.287885 0.957665i \(-0.592952\pi\)
−0.287885 + 0.957665i \(0.592952\pi\)
\(230\) 0.258584 0.0170505
\(231\) 0.362061 0.0238219
\(232\) −5.62907 −0.369566
\(233\) 10.0530 0.658591 0.329296 0.944227i \(-0.393189\pi\)
0.329296 + 0.944227i \(0.393189\pi\)
\(234\) −0.0619548 −0.00405011
\(235\) 8.51437 0.555416
\(236\) −10.9801 −0.714741
\(237\) 25.8714 1.68053
\(238\) −0.0292586 −0.00189656
\(239\) −4.74203 −0.306736 −0.153368 0.988169i \(-0.549012\pi\)
−0.153368 + 0.988169i \(0.549012\pi\)
\(240\) 8.79979 0.568024
\(241\) 7.69131 0.495441 0.247720 0.968832i \(-0.420319\pi\)
0.247720 + 0.968832i \(0.420319\pi\)
\(242\) 2.39543 0.153984
\(243\) −1.70457 −0.109348
\(244\) 11.9862 0.767335
\(245\) −9.04569 −0.577908
\(246\) 3.01367 0.192145
\(247\) −13.7750 −0.876480
\(248\) 4.80259 0.304965
\(249\) 10.8097 0.685034
\(250\) −1.83088 −0.115795
\(251\) 5.22969 0.330095 0.165048 0.986286i \(-0.447222\pi\)
0.165048 + 0.986286i \(0.447222\pi\)
\(252\) 0.0131529 0.000828556 0
\(253\) −5.89204 −0.370430
\(254\) 1.70997 0.107293
\(255\) 9.73403 0.609569
\(256\) 13.7362 0.858513
\(257\) −22.7830 −1.42116 −0.710581 0.703615i \(-0.751568\pi\)
−0.710581 + 0.703615i \(0.751568\pi\)
\(258\) −1.55260 −0.0966607
\(259\) −0.357479 −0.0222127
\(260\) 5.65250 0.350553
\(261\) 1.36869 0.0847200
\(262\) 1.78168 0.110073
\(263\) −29.2155 −1.80150 −0.900752 0.434333i \(-0.856984\pi\)
−0.900752 + 0.434333i \(0.856984\pi\)
\(264\) 6.01668 0.370301
\(265\) 8.15988 0.501257
\(266\) −0.0429082 −0.00263087
\(267\) −19.8074 −1.21220
\(268\) −15.0500 −0.919328
\(269\) −6.94557 −0.423479 −0.211739 0.977326i \(-0.567913\pi\)
−0.211739 + 0.977326i \(0.567913\pi\)
\(270\) −1.10881 −0.0674799
\(271\) 6.76612 0.411012 0.205506 0.978656i \(-0.434116\pi\)
0.205506 + 0.978656i \(0.434116\pi\)
\(272\) 16.2035 0.982481
\(273\) 0.160383 0.00970683
\(274\) 0.359642 0.0217268
\(275\) 16.6751 1.00555
\(276\) −4.12467 −0.248276
\(277\) −7.31608 −0.439581 −0.219790 0.975547i \(-0.570537\pi\)
−0.219790 + 0.975547i \(0.570537\pi\)
\(278\) 2.53313 0.151927
\(279\) −1.16774 −0.0699106
\(280\) 0.0354727 0.00211990
\(281\) 4.95425 0.295546 0.147773 0.989021i \(-0.452790\pi\)
0.147773 + 0.989021i \(0.452790\pi\)
\(282\) 1.99270 0.118664
\(283\) 27.0549 1.60825 0.804123 0.594463i \(-0.202635\pi\)
0.804123 + 0.594463i \(0.202635\pi\)
\(284\) 8.37022 0.496681
\(285\) 14.2751 0.845583
\(286\) 1.88976 0.111744
\(287\) −0.404853 −0.0238977
\(288\) 0.328656 0.0193662
\(289\) 0.923776 0.0543398
\(290\) 1.83220 0.107591
\(291\) −2.28265 −0.133811
\(292\) −26.3982 −1.54484
\(293\) 8.41766 0.491765 0.245883 0.969300i \(-0.420922\pi\)
0.245883 + 0.969300i \(0.420922\pi\)
\(294\) −2.11705 −0.123469
\(295\) 7.20024 0.419214
\(296\) −5.94054 −0.345287
\(297\) 25.2651 1.46603
\(298\) 2.48286 0.143828
\(299\) −2.61001 −0.150941
\(300\) 11.6733 0.673957
\(301\) 0.208574 0.0120220
\(302\) 0.955581 0.0549875
\(303\) 11.2322 0.645272
\(304\) 23.7626 1.36288
\(305\) −7.85998 −0.450061
\(306\) 0.118222 0.00675832
\(307\) 7.42019 0.423492 0.211746 0.977325i \(-0.432085\pi\)
0.211746 + 0.977325i \(0.432085\pi\)
\(308\) −0.401194 −0.0228601
\(309\) 28.2318 1.60605
\(310\) −1.56319 −0.0887834
\(311\) 0.180091 0.0102120 0.00510602 0.999987i \(-0.498375\pi\)
0.00510602 + 0.999987i \(0.498375\pi\)
\(312\) 2.66523 0.150889
\(313\) −4.23049 −0.239121 −0.119561 0.992827i \(-0.538149\pi\)
−0.119561 + 0.992827i \(0.538149\pi\)
\(314\) −1.96711 −0.111011
\(315\) −0.00862510 −0.000485969 0
\(316\) −28.6676 −1.61268
\(317\) 27.9544 1.57007 0.785037 0.619449i \(-0.212644\pi\)
0.785037 + 0.619449i \(0.212644\pi\)
\(318\) 1.90973 0.107093
\(319\) −41.7483 −2.33745
\(320\) −9.45400 −0.528495
\(321\) 29.4304 1.64264
\(322\) −0.00813003 −0.000453069 0
\(323\) 26.2854 1.46256
\(324\) 18.6575 1.03653
\(325\) 7.38663 0.409737
\(326\) −3.94916 −0.218724
\(327\) −31.9122 −1.76475
\(328\) −6.72779 −0.371480
\(329\) −0.267697 −0.0147586
\(330\) −1.95837 −0.107805
\(331\) −30.7138 −1.68818 −0.844092 0.536198i \(-0.819860\pi\)
−0.844092 + 0.536198i \(0.819860\pi\)
\(332\) −11.9780 −0.657377
\(333\) 1.44443 0.0791542
\(334\) −1.19109 −0.0651736
\(335\) 9.86915 0.539209
\(336\) −0.276670 −0.0150936
\(337\) −12.9562 −0.705771 −0.352885 0.935667i \(-0.614799\pi\)
−0.352885 + 0.935667i \(0.614799\pi\)
\(338\) −1.37367 −0.0747179
\(339\) −2.86305 −0.155499
\(340\) −10.7861 −0.584959
\(341\) 35.6186 1.92886
\(342\) 0.173374 0.00937501
\(343\) 0.568870 0.0307161
\(344\) 3.46606 0.186878
\(345\) 2.70477 0.145620
\(346\) −0.872830 −0.0469236
\(347\) −4.66780 −0.250581 −0.125290 0.992120i \(-0.539986\pi\)
−0.125290 + 0.992120i \(0.539986\pi\)
\(348\) −29.2255 −1.56665
\(349\) 33.7711 1.80772 0.903862 0.427824i \(-0.140720\pi\)
0.903862 + 0.427824i \(0.140720\pi\)
\(350\) 0.0230089 0.00122988
\(351\) 11.1917 0.597371
\(352\) −10.0247 −0.534321
\(353\) 4.11371 0.218950 0.109475 0.993990i \(-0.465083\pi\)
0.109475 + 0.993990i \(0.465083\pi\)
\(354\) 1.68514 0.0895642
\(355\) −5.48882 −0.291316
\(356\) 21.9483 1.16326
\(357\) −0.306044 −0.0161976
\(358\) 1.86590 0.0986158
\(359\) −14.7836 −0.780250 −0.390125 0.920762i \(-0.627568\pi\)
−0.390125 + 0.920762i \(0.627568\pi\)
\(360\) −0.143331 −0.00755419
\(361\) 19.5479 1.02884
\(362\) −0.0287331 −0.00151018
\(363\) 25.0560 1.31510
\(364\) −0.177718 −0.00931494
\(365\) 17.3108 0.906088
\(366\) −1.83955 −0.0961546
\(367\) 14.8085 0.772997 0.386499 0.922290i \(-0.373684\pi\)
0.386499 + 0.922290i \(0.373684\pi\)
\(368\) 4.50243 0.234705
\(369\) 1.63585 0.0851587
\(370\) 1.93359 0.100522
\(371\) −0.256551 −0.0133195
\(372\) 24.9345 1.29279
\(373\) 0.507474 0.0262760 0.0131380 0.999914i \(-0.495818\pi\)
0.0131380 + 0.999914i \(0.495818\pi\)
\(374\) −3.60605 −0.186464
\(375\) −19.1508 −0.988945
\(376\) −4.44855 −0.229416
\(377\) −18.4933 −0.952455
\(378\) 0.0348616 0.00179309
\(379\) −12.9514 −0.665266 −0.332633 0.943056i \(-0.607937\pi\)
−0.332633 + 0.943056i \(0.607937\pi\)
\(380\) −15.8180 −0.811444
\(381\) 17.8862 0.916337
\(382\) −3.67616 −0.188089
\(383\) 36.3394 1.85685 0.928427 0.371514i \(-0.121161\pi\)
0.928427 + 0.371514i \(0.121161\pi\)
\(384\) −9.33330 −0.476288
\(385\) 0.263085 0.0134080
\(386\) 1.04168 0.0530202
\(387\) −0.842764 −0.0428401
\(388\) 2.52936 0.128409
\(389\) 22.8777 1.15994 0.579971 0.814637i \(-0.303064\pi\)
0.579971 + 0.814637i \(0.303064\pi\)
\(390\) −0.867504 −0.0439278
\(391\) 4.98044 0.251871
\(392\) 4.72615 0.238706
\(393\) 18.6363 0.940077
\(394\) −2.68665 −0.135351
\(395\) 18.7989 0.945877
\(396\) 1.62106 0.0814613
\(397\) −35.0386 −1.75854 −0.879269 0.476325i \(-0.841968\pi\)
−0.879269 + 0.476325i \(0.841968\pi\)
\(398\) 2.86447 0.143583
\(399\) −0.448817 −0.0224689
\(400\) −12.7424 −0.637119
\(401\) 35.7125 1.78340 0.891698 0.452631i \(-0.149515\pi\)
0.891698 + 0.452631i \(0.149515\pi\)
\(402\) 2.30977 0.115201
\(403\) 15.7781 0.785962
\(404\) −12.4462 −0.619221
\(405\) −12.2348 −0.607951
\(406\) −0.0576056 −0.00285892
\(407\) −44.0583 −2.18389
\(408\) −5.08579 −0.251784
\(409\) −6.11651 −0.302442 −0.151221 0.988500i \(-0.548321\pi\)
−0.151221 + 0.988500i \(0.548321\pi\)
\(410\) 2.18983 0.108148
\(411\) 3.76184 0.185558
\(412\) −31.2832 −1.54121
\(413\) −0.226380 −0.0111394
\(414\) 0.0328501 0.00161450
\(415\) 7.85462 0.385568
\(416\) −4.44069 −0.217723
\(417\) 26.4964 1.29754
\(418\) −5.28831 −0.258660
\(419\) 5.89777 0.288125 0.144062 0.989569i \(-0.453983\pi\)
0.144062 + 0.989569i \(0.453983\pi\)
\(420\) 0.184170 0.00898657
\(421\) 1.97080 0.0960507 0.0480253 0.998846i \(-0.484707\pi\)
0.0480253 + 0.998846i \(0.484707\pi\)
\(422\) 0.477306 0.0232349
\(423\) 1.08165 0.0525918
\(424\) −4.26333 −0.207046
\(425\) −14.0952 −0.683717
\(426\) −1.28460 −0.0622391
\(427\) 0.247122 0.0119591
\(428\) −32.6113 −1.57632
\(429\) 19.7668 0.954349
\(430\) −1.12817 −0.0544051
\(431\) 20.7549 0.999728 0.499864 0.866104i \(-0.333383\pi\)
0.499864 + 0.866104i \(0.333383\pi\)
\(432\) −19.3064 −0.928880
\(433\) −25.8263 −1.24113 −0.620566 0.784154i \(-0.713097\pi\)
−0.620566 + 0.784154i \(0.713097\pi\)
\(434\) 0.0491477 0.00235917
\(435\) 19.1647 0.918879
\(436\) 35.3613 1.69350
\(437\) 7.30387 0.349391
\(438\) 4.05141 0.193584
\(439\) −34.7025 −1.65626 −0.828131 0.560535i \(-0.810596\pi\)
−0.828131 + 0.560535i \(0.810596\pi\)
\(440\) 4.37191 0.208423
\(441\) −1.14915 −0.0547215
\(442\) −1.59738 −0.0759796
\(443\) −7.72724 −0.367132 −0.183566 0.983007i \(-0.558764\pi\)
−0.183566 + 0.983007i \(0.558764\pi\)
\(444\) −30.8426 −1.46372
\(445\) −14.3927 −0.682279
\(446\) −2.58243 −0.122282
\(447\) 25.9706 1.22837
\(448\) 0.297239 0.0140432
\(449\) −26.9809 −1.27331 −0.636653 0.771150i \(-0.719682\pi\)
−0.636653 + 0.771150i \(0.719682\pi\)
\(450\) −0.0929696 −0.00438263
\(451\) −49.8970 −2.34956
\(452\) 3.17249 0.149221
\(453\) 9.99532 0.469621
\(454\) 3.69674 0.173496
\(455\) 0.116539 0.00546345
\(456\) −7.45837 −0.349270
\(457\) 24.8185 1.16096 0.580481 0.814274i \(-0.302864\pi\)
0.580481 + 0.814274i \(0.302864\pi\)
\(458\) −1.48173 −0.0692368
\(459\) −21.3561 −0.996818
\(460\) −2.99711 −0.139741
\(461\) −37.8706 −1.76381 −0.881904 0.471430i \(-0.843738\pi\)
−0.881904 + 0.471430i \(0.843738\pi\)
\(462\) 0.0615723 0.00286460
\(463\) −8.43325 −0.391926 −0.195963 0.980611i \(-0.562783\pi\)
−0.195963 + 0.980611i \(0.562783\pi\)
\(464\) 31.9021 1.48102
\(465\) −16.3509 −0.758255
\(466\) 1.70961 0.0791962
\(467\) −11.6660 −0.539840 −0.269920 0.962883i \(-0.586997\pi\)
−0.269920 + 0.962883i \(0.586997\pi\)
\(468\) 0.718085 0.0331935
\(469\) −0.310292 −0.0143279
\(470\) 1.44796 0.0667893
\(471\) −20.5759 −0.948086
\(472\) −3.76194 −0.173158
\(473\) 25.7062 1.18197
\(474\) 4.39969 0.202085
\(475\) −20.6708 −0.948440
\(476\) 0.339122 0.0155436
\(477\) 1.03662 0.0474635
\(478\) −0.806431 −0.0368853
\(479\) −38.8946 −1.77714 −0.888570 0.458741i \(-0.848301\pi\)
−0.888570 + 0.458741i \(0.848301\pi\)
\(480\) 4.60191 0.210047
\(481\) −19.5166 −0.889882
\(482\) 1.30799 0.0595772
\(483\) −0.0850396 −0.00386944
\(484\) −27.7641 −1.26201
\(485\) −1.65864 −0.0753151
\(486\) −0.289879 −0.0131492
\(487\) 37.8109 1.71338 0.856689 0.515834i \(-0.172518\pi\)
0.856689 + 0.515834i \(0.172518\pi\)
\(488\) 4.10665 0.185899
\(489\) −41.3080 −1.86801
\(490\) −1.53831 −0.0694939
\(491\) −10.8334 −0.488904 −0.244452 0.969661i \(-0.578608\pi\)
−0.244452 + 0.969661i \(0.578608\pi\)
\(492\) −34.9299 −1.57476
\(493\) 35.2890 1.58934
\(494\) −2.34258 −0.105397
\(495\) −1.06302 −0.0477791
\(496\) −27.2181 −1.22213
\(497\) 0.172572 0.00774089
\(498\) 1.83829 0.0823759
\(499\) 25.7541 1.15291 0.576455 0.817129i \(-0.304436\pi\)
0.576455 + 0.817129i \(0.304436\pi\)
\(500\) 21.2207 0.949019
\(501\) −12.4587 −0.556616
\(502\) 0.889364 0.0396942
\(503\) 34.2654 1.52782 0.763909 0.645324i \(-0.223278\pi\)
0.763909 + 0.645324i \(0.223278\pi\)
\(504\) 0.00450640 0.000200731 0
\(505\) 8.16165 0.363189
\(506\) −1.00200 −0.0445445
\(507\) −14.3685 −0.638129
\(508\) −19.8194 −0.879342
\(509\) 29.5680 1.31058 0.655289 0.755379i \(-0.272547\pi\)
0.655289 + 0.755379i \(0.272547\pi\)
\(510\) 1.65537 0.0733012
\(511\) −0.544261 −0.0240767
\(512\) 12.8298 0.567002
\(513\) −31.3190 −1.38277
\(514\) −3.87448 −0.170896
\(515\) 20.5141 0.903959
\(516\) 17.9954 0.792202
\(517\) −32.9929 −1.45103
\(518\) −0.0607931 −0.00267109
\(519\) −9.12975 −0.400752
\(520\) 1.93663 0.0849271
\(521\) −24.0954 −1.05564 −0.527819 0.849357i \(-0.676990\pi\)
−0.527819 + 0.849357i \(0.676990\pi\)
\(522\) 0.232761 0.0101877
\(523\) 35.8786 1.56886 0.784432 0.620215i \(-0.212955\pi\)
0.784432 + 0.620215i \(0.212955\pi\)
\(524\) −20.6506 −0.902124
\(525\) 0.240672 0.0105038
\(526\) −4.96840 −0.216632
\(527\) −30.1078 −1.31152
\(528\) −34.0988 −1.48396
\(529\) −21.6161 −0.939830
\(530\) 1.38767 0.0602766
\(531\) 0.914708 0.0396949
\(532\) 0.497326 0.0215618
\(533\) −22.1030 −0.957387
\(534\) −3.36846 −0.145768
\(535\) 21.3850 0.924554
\(536\) −5.15638 −0.222722
\(537\) 19.5172 0.842228
\(538\) −1.18117 −0.0509237
\(539\) 35.0517 1.50978
\(540\) 12.8516 0.553045
\(541\) 0.138724 0.00596420 0.00298210 0.999996i \(-0.499051\pi\)
0.00298210 + 0.999996i \(0.499051\pi\)
\(542\) 1.15065 0.0494246
\(543\) −0.300547 −0.0128977
\(544\) 8.47373 0.363308
\(545\) −23.1884 −0.993282
\(546\) 0.0272748 0.00116725
\(547\) −10.5144 −0.449563 −0.224782 0.974409i \(-0.572167\pi\)
−0.224782 + 0.974409i \(0.572167\pi\)
\(548\) −4.16843 −0.178066
\(549\) −0.998521 −0.0426158
\(550\) 2.83578 0.120918
\(551\) 51.7518 2.20470
\(552\) −1.41318 −0.0601488
\(553\) −0.591049 −0.0251340
\(554\) −1.24417 −0.0528599
\(555\) 20.2252 0.858512
\(556\) −29.3602 −1.24515
\(557\) −12.2592 −0.519437 −0.259719 0.965684i \(-0.583630\pi\)
−0.259719 + 0.965684i \(0.583630\pi\)
\(558\) −0.198586 −0.00840681
\(559\) 11.3871 0.481625
\(560\) −0.201037 −0.00849537
\(561\) −37.7190 −1.59250
\(562\) 0.842521 0.0355396
\(563\) 37.2173 1.56852 0.784261 0.620431i \(-0.213042\pi\)
0.784261 + 0.620431i \(0.213042\pi\)
\(564\) −23.0963 −0.972531
\(565\) −2.08038 −0.0875221
\(566\) 4.60096 0.193393
\(567\) 0.384669 0.0161546
\(568\) 2.86777 0.120329
\(569\) −37.7314 −1.58178 −0.790892 0.611956i \(-0.790383\pi\)
−0.790892 + 0.611956i \(0.790383\pi\)
\(570\) 2.42762 0.101682
\(571\) 22.9818 0.961760 0.480880 0.876787i \(-0.340317\pi\)
0.480880 + 0.876787i \(0.340317\pi\)
\(572\) −21.9032 −0.915819
\(573\) −38.4524 −1.60637
\(574\) −0.0688494 −0.00287372
\(575\) −3.91660 −0.163333
\(576\) −1.20102 −0.0500426
\(577\) 4.21074 0.175295 0.0876477 0.996152i \(-0.472065\pi\)
0.0876477 + 0.996152i \(0.472065\pi\)
\(578\) 0.157098 0.00653440
\(579\) 10.8959 0.452819
\(580\) −21.2361 −0.881782
\(581\) −0.246954 −0.0102454
\(582\) −0.388188 −0.0160909
\(583\) −31.6192 −1.30953
\(584\) −9.04445 −0.374262
\(585\) −0.470888 −0.0194688
\(586\) 1.43151 0.0591351
\(587\) −9.45415 −0.390215 −0.195107 0.980782i \(-0.562505\pi\)
−0.195107 + 0.980782i \(0.562505\pi\)
\(588\) 24.5376 1.01191
\(589\) −44.1534 −1.81931
\(590\) 1.22447 0.0504108
\(591\) −28.1022 −1.15597
\(592\) 33.6673 1.38372
\(593\) −10.2834 −0.422288 −0.211144 0.977455i \(-0.567719\pi\)
−0.211144 + 0.977455i \(0.567719\pi\)
\(594\) 4.29659 0.176291
\(595\) −0.222381 −0.00911672
\(596\) −28.7776 −1.17878
\(597\) 29.9622 1.22627
\(598\) −0.443860 −0.0181508
\(599\) 2.00944 0.0821033 0.0410517 0.999157i \(-0.486929\pi\)
0.0410517 + 0.999157i \(0.486929\pi\)
\(600\) 3.99945 0.163277
\(601\) 7.75727 0.316426 0.158213 0.987405i \(-0.449427\pi\)
0.158213 + 0.987405i \(0.449427\pi\)
\(602\) 0.0354702 0.00144566
\(603\) 1.25376 0.0510572
\(604\) −11.0756 −0.450661
\(605\) 18.2065 0.740198
\(606\) 1.91015 0.0775945
\(607\) −0.151634 −0.00615463 −0.00307732 0.999995i \(-0.500980\pi\)
−0.00307732 + 0.999995i \(0.500980\pi\)
\(608\) 12.4268 0.503975
\(609\) −0.602551 −0.0244166
\(610\) −1.33667 −0.0541202
\(611\) −14.6149 −0.591257
\(612\) −1.37025 −0.0553892
\(613\) 26.9378 1.08801 0.544004 0.839082i \(-0.316907\pi\)
0.544004 + 0.839082i \(0.316907\pi\)
\(614\) 1.26188 0.0509253
\(615\) 22.9055 0.923637
\(616\) −0.137455 −0.00553823
\(617\) 13.9776 0.562716 0.281358 0.959603i \(-0.409215\pi\)
0.281358 + 0.959603i \(0.409215\pi\)
\(618\) 4.80111 0.193129
\(619\) −47.3757 −1.90419 −0.952096 0.305799i \(-0.901076\pi\)
−0.952096 + 0.305799i \(0.901076\pi\)
\(620\) 18.1182 0.727643
\(621\) −5.93417 −0.238130
\(622\) 0.0306264 0.00122801
\(623\) 0.452515 0.0181296
\(624\) −15.1048 −0.604678
\(625\) 2.73103 0.109241
\(626\) −0.719438 −0.0287545
\(627\) −55.3154 −2.20908
\(628\) 22.7997 0.909809
\(629\) 37.2417 1.48492
\(630\) −0.00146679 −5.84382e−5 0
\(631\) −11.2559 −0.448089 −0.224045 0.974579i \(-0.571926\pi\)
−0.224045 + 0.974579i \(0.571926\pi\)
\(632\) −9.82198 −0.390697
\(633\) 4.99259 0.198438
\(634\) 4.75393 0.188803
\(635\) 12.9967 0.515756
\(636\) −22.1347 −0.877699
\(637\) 15.5269 0.615200
\(638\) −7.09972 −0.281081
\(639\) −0.697291 −0.0275844
\(640\) −6.78186 −0.268077
\(641\) −27.1661 −1.07300 −0.536499 0.843901i \(-0.680253\pi\)
−0.536499 + 0.843901i \(0.680253\pi\)
\(642\) 5.00494 0.197529
\(643\) −1.77376 −0.0699501 −0.0349751 0.999388i \(-0.511135\pi\)
−0.0349751 + 0.999388i \(0.511135\pi\)
\(644\) 0.0942309 0.00371322
\(645\) −11.8006 −0.464647
\(646\) 4.47011 0.175874
\(647\) 26.2940 1.03373 0.516863 0.856068i \(-0.327100\pi\)
0.516863 + 0.856068i \(0.327100\pi\)
\(648\) 6.39237 0.251116
\(649\) −27.9006 −1.09520
\(650\) 1.25617 0.0492712
\(651\) 0.514082 0.0201485
\(652\) 45.7726 1.79259
\(653\) −0.138130 −0.00540545 −0.00270273 0.999996i \(-0.500860\pi\)
−0.00270273 + 0.999996i \(0.500860\pi\)
\(654\) −5.42700 −0.212212
\(655\) 13.5417 0.529118
\(656\) 38.1289 1.48869
\(657\) 2.19914 0.0857965
\(658\) −0.0455246 −0.00177473
\(659\) −5.31430 −0.207016 −0.103508 0.994629i \(-0.533007\pi\)
−0.103508 + 0.994629i \(0.533007\pi\)
\(660\) 22.6984 0.883535
\(661\) 6.24045 0.242725 0.121363 0.992608i \(-0.461274\pi\)
0.121363 + 0.992608i \(0.461274\pi\)
\(662\) −5.22320 −0.203006
\(663\) −16.7085 −0.648904
\(664\) −4.10385 −0.159260
\(665\) −0.326124 −0.0126466
\(666\) 0.245640 0.00951836
\(667\) 9.80567 0.379677
\(668\) 13.8053 0.534144
\(669\) −27.0121 −1.04435
\(670\) 1.67835 0.0648403
\(671\) 30.4571 1.17578
\(672\) −0.144687 −0.00558141
\(673\) −4.55607 −0.175623 −0.0878117 0.996137i \(-0.527987\pi\)
−0.0878117 + 0.996137i \(0.527987\pi\)
\(674\) −2.20334 −0.0848695
\(675\) 16.7944 0.646415
\(676\) 15.9215 0.612366
\(677\) −23.9220 −0.919396 −0.459698 0.888075i \(-0.652042\pi\)
−0.459698 + 0.888075i \(0.652042\pi\)
\(678\) −0.486891 −0.0186989
\(679\) 0.0521487 0.00200128
\(680\) −3.69549 −0.141716
\(681\) 38.6676 1.48175
\(682\) 6.05732 0.231947
\(683\) −12.4913 −0.477967 −0.238983 0.971024i \(-0.576814\pi\)
−0.238983 + 0.971024i \(0.576814\pi\)
\(684\) −2.00949 −0.0768348
\(685\) 2.73347 0.104440
\(686\) 0.0967423 0.00369364
\(687\) −15.4988 −0.591317
\(688\) −19.6435 −0.748901
\(689\) −14.0064 −0.533603
\(690\) 0.459974 0.0175109
\(691\) −0.743686 −0.0282912 −0.0141456 0.999900i \(-0.504503\pi\)
−0.0141456 + 0.999900i \(0.504503\pi\)
\(692\) 10.1165 0.384572
\(693\) 0.0334219 0.00126959
\(694\) −0.793808 −0.0301325
\(695\) 19.2531 0.730313
\(696\) −10.0131 −0.379546
\(697\) 42.1770 1.59757
\(698\) 5.74312 0.217380
\(699\) 17.8824 0.676375
\(700\) −0.266684 −0.0100797
\(701\) −18.6036 −0.702649 −0.351324 0.936254i \(-0.614269\pi\)
−0.351324 + 0.936254i \(0.614269\pi\)
\(702\) 1.90327 0.0718343
\(703\) 54.6154 2.05986
\(704\) 36.6339 1.38069
\(705\) 15.1455 0.570414
\(706\) 0.699578 0.0263290
\(707\) −0.256607 −0.00965070
\(708\) −19.5316 −0.734041
\(709\) −37.1530 −1.39531 −0.697656 0.716433i \(-0.745773\pi\)
−0.697656 + 0.716433i \(0.745773\pi\)
\(710\) −0.933430 −0.0350310
\(711\) 2.38819 0.0895641
\(712\) 7.51983 0.281817
\(713\) −8.36597 −0.313308
\(714\) −0.0520459 −0.00194777
\(715\) 14.3631 0.537151
\(716\) −21.6266 −0.808225
\(717\) −8.43522 −0.315019
\(718\) −2.51411 −0.0938257
\(719\) 34.8793 1.30078 0.650388 0.759602i \(-0.274606\pi\)
0.650388 + 0.759602i \(0.274606\pi\)
\(720\) 0.812309 0.0302730
\(721\) −0.644975 −0.0240201
\(722\) 3.32432 0.123719
\(723\) 13.6815 0.508819
\(724\) 0.333030 0.0123770
\(725\) −27.7512 −1.03065
\(726\) 4.26103 0.158142
\(727\) −17.6643 −0.655134 −0.327567 0.944828i \(-0.606229\pi\)
−0.327567 + 0.944828i \(0.606229\pi\)
\(728\) −0.0608889 −0.00225669
\(729\) 25.3648 0.939438
\(730\) 2.94388 0.108958
\(731\) −21.7290 −0.803676
\(732\) 21.3212 0.788055
\(733\) 32.7964 1.21136 0.605681 0.795708i \(-0.292901\pi\)
0.605681 + 0.795708i \(0.292901\pi\)
\(734\) 2.51834 0.0929536
\(735\) −16.0907 −0.593513
\(736\) 2.35458 0.0867908
\(737\) −38.2426 −1.40868
\(738\) 0.278192 0.0102404
\(739\) 9.86928 0.363047 0.181524 0.983387i \(-0.441897\pi\)
0.181524 + 0.983387i \(0.441897\pi\)
\(740\) −22.4112 −0.823851
\(741\) −24.5032 −0.900148
\(742\) −0.0436292 −0.00160168
\(743\) 44.3582 1.62734 0.813672 0.581324i \(-0.197465\pi\)
0.813672 + 0.581324i \(0.197465\pi\)
\(744\) 8.54295 0.313200
\(745\) 18.8710 0.691381
\(746\) 0.0863011 0.00315971
\(747\) 0.997840 0.0365091
\(748\) 41.7958 1.52820
\(749\) −0.672357 −0.0245674
\(750\) −3.25680 −0.118921
\(751\) −16.9290 −0.617749 −0.308874 0.951103i \(-0.599952\pi\)
−0.308874 + 0.951103i \(0.599952\pi\)
\(752\) 25.2116 0.919373
\(753\) 9.30269 0.339009
\(754\) −3.14498 −0.114533
\(755\) 7.26291 0.264324
\(756\) −0.404062 −0.0146956
\(757\) 5.48503 0.199357 0.0996783 0.995020i \(-0.468219\pi\)
0.0996783 + 0.995020i \(0.468219\pi\)
\(758\) −2.20251 −0.0799988
\(759\) −10.4809 −0.380432
\(760\) −5.41948 −0.196585
\(761\) −6.94150 −0.251629 −0.125815 0.992054i \(-0.540154\pi\)
−0.125815 + 0.992054i \(0.540154\pi\)
\(762\) 3.04173 0.110190
\(763\) 0.729056 0.0263936
\(764\) 42.6085 1.54152
\(765\) 0.898550 0.0324871
\(766\) 6.17988 0.223288
\(767\) −12.3592 −0.446265
\(768\) 24.4342 0.881695
\(769\) 10.0489 0.362372 0.181186 0.983449i \(-0.442006\pi\)
0.181186 + 0.983449i \(0.442006\pi\)
\(770\) 0.0447403 0.00161233
\(771\) −40.5268 −1.45954
\(772\) −12.0736 −0.434537
\(773\) 12.9121 0.464414 0.232207 0.972666i \(-0.425405\pi\)
0.232207 + 0.972666i \(0.425405\pi\)
\(774\) −0.143321 −0.00515156
\(775\) 23.6766 0.850490
\(776\) 0.866599 0.0311091
\(777\) −0.635892 −0.0228125
\(778\) 3.89058 0.139484
\(779\) 61.8531 2.21612
\(780\) 10.0548 0.360019
\(781\) 21.2690 0.761063
\(782\) 0.846974 0.0302877
\(783\) −42.0467 −1.50263
\(784\) −26.7849 −0.956603
\(785\) −14.9511 −0.533626
\(786\) 3.16930 0.113045
\(787\) −31.8800 −1.13640 −0.568199 0.822891i \(-0.692360\pi\)
−0.568199 + 0.822891i \(0.692360\pi\)
\(788\) 31.1395 1.10930
\(789\) −51.9691 −1.85015
\(790\) 3.19695 0.113742
\(791\) 0.0654083 0.00232565
\(792\) 0.555401 0.0197353
\(793\) 13.4917 0.479103
\(794\) −5.95868 −0.211466
\(795\) 14.5150 0.514793
\(796\) −33.2005 −1.17676
\(797\) −42.6855 −1.51200 −0.755999 0.654573i \(-0.772848\pi\)
−0.755999 + 0.654573i \(0.772848\pi\)
\(798\) −0.0763259 −0.00270191
\(799\) 27.8883 0.986616
\(800\) −6.66371 −0.235598
\(801\) −1.82843 −0.0646043
\(802\) 6.07327 0.214455
\(803\) −67.0786 −2.36715
\(804\) −26.7713 −0.944152
\(805\) −0.0617924 −0.00217790
\(806\) 2.68322 0.0945126
\(807\) −12.3549 −0.434914
\(808\) −4.26426 −0.150016
\(809\) 33.3988 1.17424 0.587120 0.809500i \(-0.300262\pi\)
0.587120 + 0.809500i \(0.300262\pi\)
\(810\) −2.08065 −0.0731066
\(811\) −9.88276 −0.347031 −0.173515 0.984831i \(-0.555513\pi\)
−0.173515 + 0.984831i \(0.555513\pi\)
\(812\) 0.667676 0.0234308
\(813\) 12.0357 0.422111
\(814\) −7.49257 −0.262615
\(815\) −30.0156 −1.05140
\(816\) 28.8231 1.00901
\(817\) −31.8658 −1.11484
\(818\) −1.04018 −0.0363689
\(819\) 0.0148050 0.000517328 0
\(820\) −25.3811 −0.886347
\(821\) −8.42549 −0.294051 −0.147026 0.989133i \(-0.546970\pi\)
−0.147026 + 0.989133i \(0.546970\pi\)
\(822\) 0.639739 0.0223135
\(823\) −2.02595 −0.0706203 −0.0353101 0.999376i \(-0.511242\pi\)
−0.0353101 + 0.999376i \(0.511242\pi\)
\(824\) −10.7181 −0.373383
\(825\) 29.6621 1.03270
\(826\) −0.0384982 −0.00133952
\(827\) −20.0369 −0.696750 −0.348375 0.937355i \(-0.613266\pi\)
−0.348375 + 0.937355i \(0.613266\pi\)
\(828\) −0.380749 −0.0132319
\(829\) 21.7687 0.756059 0.378029 0.925794i \(-0.376602\pi\)
0.378029 + 0.925794i \(0.376602\pi\)
\(830\) 1.33576 0.0463649
\(831\) −13.0140 −0.451450
\(832\) 16.2278 0.562598
\(833\) −29.6285 −1.02657
\(834\) 4.50599 0.156030
\(835\) −9.05291 −0.313289
\(836\) 61.2940 2.11990
\(837\) 35.8733 1.23996
\(838\) 1.00298 0.0346473
\(839\) −48.3604 −1.66959 −0.834794 0.550562i \(-0.814413\pi\)
−0.834794 + 0.550562i \(0.814413\pi\)
\(840\) 0.0630995 0.00217714
\(841\) 40.4784 1.39581
\(842\) 0.335154 0.0115502
\(843\) 8.81272 0.303526
\(844\) −5.53220 −0.190426
\(845\) −10.4406 −0.359168
\(846\) 0.183946 0.00632421
\(847\) −0.572422 −0.0196687
\(848\) 24.1619 0.829724
\(849\) 48.1258 1.65167
\(850\) −2.39703 −0.0822175
\(851\) 10.3483 0.354734
\(852\) 14.8891 0.510093
\(853\) 25.3068 0.866488 0.433244 0.901277i \(-0.357369\pi\)
0.433244 + 0.901277i \(0.357369\pi\)
\(854\) 0.0420257 0.00143809
\(855\) 1.31773 0.0450656
\(856\) −11.1731 −0.381890
\(857\) −49.6183 −1.69493 −0.847464 0.530852i \(-0.821872\pi\)
−0.847464 + 0.530852i \(0.821872\pi\)
\(858\) 3.36154 0.114761
\(859\) −33.8118 −1.15364 −0.576822 0.816870i \(-0.695707\pi\)
−0.576822 + 0.816870i \(0.695707\pi\)
\(860\) 13.0760 0.445888
\(861\) −0.720161 −0.0245430
\(862\) 3.52959 0.120218
\(863\) 11.6734 0.397367 0.198684 0.980064i \(-0.436333\pi\)
0.198684 + 0.980064i \(0.436333\pi\)
\(864\) −10.0964 −0.343487
\(865\) −6.63396 −0.225561
\(866\) −4.39203 −0.149247
\(867\) 1.64323 0.0558071
\(868\) −0.569645 −0.0193350
\(869\) −72.8452 −2.47110
\(870\) 3.25916 0.110496
\(871\) −16.9404 −0.574004
\(872\) 12.1154 0.410278
\(873\) −0.210712 −0.00713151
\(874\) 1.24210 0.0420146
\(875\) 0.437514 0.0147907
\(876\) −46.9577 −1.58655
\(877\) 10.7616 0.363394 0.181697 0.983355i \(-0.441841\pi\)
0.181697 + 0.983355i \(0.441841\pi\)
\(878\) −5.90152 −0.199167
\(879\) 14.9735 0.505044
\(880\) −24.7773 −0.835242
\(881\) −18.8531 −0.635178 −0.317589 0.948229i \(-0.602873\pi\)
−0.317589 + 0.948229i \(0.602873\pi\)
\(882\) −0.195425 −0.00658030
\(883\) 30.8381 1.03779 0.518893 0.854839i \(-0.326344\pi\)
0.518893 + 0.854839i \(0.326344\pi\)
\(884\) 18.5144 0.622706
\(885\) 12.8079 0.430534
\(886\) −1.31410 −0.0441480
\(887\) −26.1401 −0.877698 −0.438849 0.898561i \(-0.644614\pi\)
−0.438849 + 0.898561i \(0.644614\pi\)
\(888\) −10.5672 −0.354611
\(889\) −0.408622 −0.0137048
\(890\) −2.44763 −0.0820446
\(891\) 47.4093 1.58827
\(892\) 29.9316 1.00218
\(893\) 40.8985 1.36862
\(894\) 4.41657 0.147712
\(895\) 14.1818 0.474045
\(896\) 0.213226 0.00712337
\(897\) −4.64275 −0.155017
\(898\) −4.58838 −0.153116
\(899\) −59.2774 −1.97701
\(900\) 1.07756 0.0359187
\(901\) 26.7271 0.890410
\(902\) −8.48550 −0.282536
\(903\) 0.371017 0.0123467
\(904\) 1.08695 0.0361513
\(905\) −0.218386 −0.00725941
\(906\) 1.69981 0.0564723
\(907\) −16.2372 −0.539148 −0.269574 0.962980i \(-0.586883\pi\)
−0.269574 + 0.962980i \(0.586883\pi\)
\(908\) −42.8469 −1.42193
\(909\) 1.03684 0.0343900
\(910\) 0.0198187 0.000656984 0
\(911\) −39.9125 −1.32236 −0.661180 0.750227i \(-0.729944\pi\)
−0.661180 + 0.750227i \(0.729944\pi\)
\(912\) 42.2695 1.39968
\(913\) −30.4364 −1.00730
\(914\) 4.22065 0.139607
\(915\) −13.9815 −0.462214
\(916\) 17.1740 0.567444
\(917\) −0.425759 −0.0140598
\(918\) −3.63183 −0.119868
\(919\) −15.5241 −0.512094 −0.256047 0.966664i \(-0.582420\pi\)
−0.256047 + 0.966664i \(0.582420\pi\)
\(920\) −1.02686 −0.0338545
\(921\) 13.1992 0.434928
\(922\) −6.44028 −0.212099
\(923\) 9.42156 0.310115
\(924\) −0.713652 −0.0234774
\(925\) −29.2867 −0.962942
\(926\) −1.43416 −0.0471295
\(927\) 2.60608 0.0855949
\(928\) 16.6834 0.547660
\(929\) −36.6844 −1.20358 −0.601789 0.798655i \(-0.705545\pi\)
−0.601789 + 0.798655i \(0.705545\pi\)
\(930\) −2.78064 −0.0911808
\(931\) −43.4506 −1.42404
\(932\) −19.8152 −0.649068
\(933\) 0.320350 0.0104878
\(934\) −1.98393 −0.0649162
\(935\) −27.4078 −0.896331
\(936\) 0.246027 0.00804165
\(937\) 13.5594 0.442968 0.221484 0.975164i \(-0.428910\pi\)
0.221484 + 0.975164i \(0.428910\pi\)
\(938\) −0.0527683 −0.00172295
\(939\) −7.52528 −0.245578
\(940\) −16.7825 −0.547385
\(941\) −4.72447 −0.154013 −0.0770066 0.997031i \(-0.524536\pi\)
−0.0770066 + 0.997031i \(0.524536\pi\)
\(942\) −3.49914 −0.114008
\(943\) 11.7196 0.381643
\(944\) 21.3204 0.693919
\(945\) 0.264966 0.00861934
\(946\) 4.37161 0.142133
\(947\) −46.1872 −1.50088 −0.750441 0.660938i \(-0.770159\pi\)
−0.750441 + 0.660938i \(0.770159\pi\)
\(948\) −50.9945 −1.65623
\(949\) −29.7140 −0.964557
\(950\) −3.51528 −0.114051
\(951\) 49.7258 1.61247
\(952\) 0.116188 0.00376569
\(953\) −17.5477 −0.568425 −0.284213 0.958761i \(-0.591732\pi\)
−0.284213 + 0.958761i \(0.591732\pi\)
\(954\) 0.176288 0.00570753
\(955\) −27.9407 −0.904141
\(956\) 9.34691 0.302301
\(957\) −74.2627 −2.40057
\(958\) −6.61443 −0.213703
\(959\) −0.0859418 −0.00277521
\(960\) −16.8170 −0.542765
\(961\) 19.5741 0.631421
\(962\) −3.31900 −0.107009
\(963\) 2.71672 0.0875451
\(964\) −15.1602 −0.488277
\(965\) 7.91731 0.254867
\(966\) −0.0144619 −0.000465303 0
\(967\) 0.806690 0.0259414 0.0129707 0.999916i \(-0.495871\pi\)
0.0129707 + 0.999916i \(0.495871\pi\)
\(968\) −9.51243 −0.305741
\(969\) 46.7571 1.50205
\(970\) −0.282069 −0.00905670
\(971\) −2.29787 −0.0737422 −0.0368711 0.999320i \(-0.511739\pi\)
−0.0368711 + 0.999320i \(0.511739\pi\)
\(972\) 3.35984 0.107767
\(973\) −0.605329 −0.0194060
\(974\) 6.43014 0.206035
\(975\) 13.1395 0.420801
\(976\) −23.2739 −0.744980
\(977\) 29.7690 0.952394 0.476197 0.879339i \(-0.342015\pi\)
0.476197 + 0.879339i \(0.342015\pi\)
\(978\) −7.02485 −0.224630
\(979\) 55.7712 1.78245
\(980\) 17.8298 0.569551
\(981\) −2.94582 −0.0940528
\(982\) −1.84233 −0.0587911
\(983\) −0.741091 −0.0236371 −0.0118186 0.999930i \(-0.503762\pi\)
−0.0118186 + 0.999930i \(0.503762\pi\)
\(984\) −11.9675 −0.381511
\(985\) −20.4199 −0.650633
\(986\) 6.00126 0.191119
\(987\) −0.476185 −0.0151571
\(988\) 27.1516 0.863806
\(989\) −6.03778 −0.191990
\(990\) −0.180777 −0.00574548
\(991\) −23.0319 −0.731631 −0.365816 0.930687i \(-0.619210\pi\)
−0.365816 + 0.930687i \(0.619210\pi\)
\(992\) −14.2339 −0.451927
\(993\) −54.6344 −1.73377
\(994\) 0.0293476 0.000930849 0
\(995\) 21.7714 0.690201
\(996\) −21.3067 −0.675128
\(997\) 28.1141 0.890382 0.445191 0.895436i \(-0.353136\pi\)
0.445191 + 0.895436i \(0.353136\pi\)
\(998\) 4.37974 0.138638
\(999\) −44.3733 −1.40391
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 4001.2.a.b.1.97 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.97 184 1.1 even 1 trivial