Properties

Label 6019.2.a.b.1.6
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $1$
Dimension $101$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(101\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.53156 q^{2} +1.58470 q^{3} +4.40878 q^{4} +2.52136 q^{5} -4.01175 q^{6} -1.30202 q^{7} -6.09798 q^{8} -0.488741 q^{9} +O(q^{10})\) \(q-2.53156 q^{2} +1.58470 q^{3} +4.40878 q^{4} +2.52136 q^{5} -4.01175 q^{6} -1.30202 q^{7} -6.09798 q^{8} -0.488741 q^{9} -6.38296 q^{10} -3.27822 q^{11} +6.98658 q^{12} +1.00000 q^{13} +3.29614 q^{14} +3.99558 q^{15} +6.61981 q^{16} +6.15331 q^{17} +1.23728 q^{18} +3.28802 q^{19} +11.1161 q^{20} -2.06330 q^{21} +8.29901 q^{22} -2.96765 q^{23} -9.66343 q^{24} +1.35725 q^{25} -2.53156 q^{26} -5.52859 q^{27} -5.74032 q^{28} -6.10366 q^{29} -10.1151 q^{30} +5.90133 q^{31} -4.56248 q^{32} -5.19499 q^{33} -15.5775 q^{34} -3.28286 q^{35} -2.15475 q^{36} +1.03524 q^{37} -8.32381 q^{38} +1.58470 q^{39} -15.3752 q^{40} -9.62322 q^{41} +5.22337 q^{42} -4.86241 q^{43} -14.4530 q^{44} -1.23229 q^{45} +7.51276 q^{46} -4.95938 q^{47} +10.4904 q^{48} -5.30475 q^{49} -3.43595 q^{50} +9.75113 q^{51} +4.40878 q^{52} -4.95420 q^{53} +13.9959 q^{54} -8.26558 q^{55} +7.93968 q^{56} +5.21051 q^{57} +15.4518 q^{58} +9.49507 q^{59} +17.6157 q^{60} -10.6112 q^{61} -14.9396 q^{62} +0.636350 q^{63} -1.68945 q^{64} +2.52136 q^{65} +13.1514 q^{66} -11.3374 q^{67} +27.1286 q^{68} -4.70281 q^{69} +8.31074 q^{70} -5.71104 q^{71} +2.98033 q^{72} +1.14637 q^{73} -2.62077 q^{74} +2.15082 q^{75} +14.4962 q^{76} +4.26831 q^{77} -4.01175 q^{78} +7.40174 q^{79} +16.6909 q^{80} -7.29491 q^{81} +24.3617 q^{82} +0.278442 q^{83} -9.09666 q^{84} +15.5147 q^{85} +12.3095 q^{86} -9.67244 q^{87} +19.9905 q^{88} +2.91764 q^{89} +3.11961 q^{90} -1.30202 q^{91} -13.0837 q^{92} +9.35182 q^{93} +12.5549 q^{94} +8.29028 q^{95} -7.23013 q^{96} +4.95000 q^{97} +13.4293 q^{98} +1.60220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53156 −1.79008 −0.895041 0.445984i \(-0.852854\pi\)
−0.895041 + 0.445984i \(0.852854\pi\)
\(3\) 1.58470 0.914924 0.457462 0.889229i \(-0.348759\pi\)
0.457462 + 0.889229i \(0.348759\pi\)
\(4\) 4.40878 2.20439
\(5\) 2.52136 1.12759 0.563793 0.825916i \(-0.309342\pi\)
0.563793 + 0.825916i \(0.309342\pi\)
\(6\) −4.01175 −1.63779
\(7\) −1.30202 −0.492117 −0.246058 0.969255i \(-0.579136\pi\)
−0.246058 + 0.969255i \(0.579136\pi\)
\(8\) −6.09798 −2.15596
\(9\) −0.488741 −0.162914
\(10\) −6.38296 −2.01847
\(11\) −3.27822 −0.988422 −0.494211 0.869342i \(-0.664543\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(12\) 6.98658 2.01685
\(13\) 1.00000 0.277350
\(14\) 3.29614 0.880929
\(15\) 3.99558 1.03166
\(16\) 6.61981 1.65495
\(17\) 6.15331 1.49240 0.746199 0.665723i \(-0.231877\pi\)
0.746199 + 0.665723i \(0.231877\pi\)
\(18\) 1.23728 0.291629
\(19\) 3.28802 0.754323 0.377162 0.926147i \(-0.376900\pi\)
0.377162 + 0.926147i \(0.376900\pi\)
\(20\) 11.1161 2.48564
\(21\) −2.06330 −0.450250
\(22\) 8.29901 1.76936
\(23\) −2.96765 −0.618797 −0.309398 0.950933i \(-0.600128\pi\)
−0.309398 + 0.950933i \(0.600128\pi\)
\(24\) −9.66343 −1.97254
\(25\) 1.35725 0.271449
\(26\) −2.53156 −0.496479
\(27\) −5.52859 −1.06398
\(28\) −5.74032 −1.08482
\(29\) −6.10366 −1.13342 −0.566711 0.823917i \(-0.691784\pi\)
−0.566711 + 0.823917i \(0.691784\pi\)
\(30\) −10.1151 −1.84675
\(31\) 5.90133 1.05991 0.529955 0.848026i \(-0.322209\pi\)
0.529955 + 0.848026i \(0.322209\pi\)
\(32\) −4.56248 −0.806539
\(33\) −5.19499 −0.904331
\(34\) −15.5775 −2.67151
\(35\) −3.28286 −0.554904
\(36\) −2.15475 −0.359125
\(37\) 1.03524 0.170192 0.0850962 0.996373i \(-0.472880\pi\)
0.0850962 + 0.996373i \(0.472880\pi\)
\(38\) −8.32381 −1.35030
\(39\) 1.58470 0.253754
\(40\) −15.3752 −2.43103
\(41\) −9.62322 −1.50290 −0.751448 0.659793i \(-0.770644\pi\)
−0.751448 + 0.659793i \(0.770644\pi\)
\(42\) 5.22337 0.805984
\(43\) −4.86241 −0.741510 −0.370755 0.928731i \(-0.620901\pi\)
−0.370755 + 0.928731i \(0.620901\pi\)
\(44\) −14.4530 −2.17887
\(45\) −1.23229 −0.183699
\(46\) 7.51276 1.10770
\(47\) −4.95938 −0.723399 −0.361700 0.932295i \(-0.617803\pi\)
−0.361700 + 0.932295i \(0.617803\pi\)
\(48\) 10.4904 1.51416
\(49\) −5.30475 −0.757821
\(50\) −3.43595 −0.485917
\(51\) 9.75113 1.36543
\(52\) 4.40878 0.611388
\(53\) −4.95420 −0.680512 −0.340256 0.940333i \(-0.610514\pi\)
−0.340256 + 0.940333i \(0.610514\pi\)
\(54\) 13.9959 1.90461
\(55\) −8.26558 −1.11453
\(56\) 7.93968 1.06098
\(57\) 5.21051 0.690149
\(58\) 15.4518 2.02892
\(59\) 9.49507 1.23615 0.618076 0.786118i \(-0.287912\pi\)
0.618076 + 0.786118i \(0.287912\pi\)
\(60\) 17.6157 2.27417
\(61\) −10.6112 −1.35863 −0.679314 0.733848i \(-0.737723\pi\)
−0.679314 + 0.733848i \(0.737723\pi\)
\(62\) −14.9396 −1.89733
\(63\) 0.636350 0.0801725
\(64\) −1.68945 −0.211181
\(65\) 2.52136 0.312736
\(66\) 13.1514 1.61883
\(67\) −11.3374 −1.38508 −0.692541 0.721378i \(-0.743509\pi\)
−0.692541 + 0.721378i \(0.743509\pi\)
\(68\) 27.1286 3.28983
\(69\) −4.70281 −0.566152
\(70\) 8.31074 0.993323
\(71\) −5.71104 −0.677776 −0.338888 0.940827i \(-0.610051\pi\)
−0.338888 + 0.940827i \(0.610051\pi\)
\(72\) 2.98033 0.351235
\(73\) 1.14637 0.134172 0.0670861 0.997747i \(-0.478630\pi\)
0.0670861 + 0.997747i \(0.478630\pi\)
\(74\) −2.62077 −0.304658
\(75\) 2.15082 0.248356
\(76\) 14.4962 1.66282
\(77\) 4.26831 0.486419
\(78\) −4.01175 −0.454241
\(79\) 7.40174 0.832761 0.416380 0.909191i \(-0.363298\pi\)
0.416380 + 0.909191i \(0.363298\pi\)
\(80\) 16.6909 1.86610
\(81\) −7.29491 −0.810546
\(82\) 24.3617 2.69030
\(83\) 0.278442 0.0305629 0.0152815 0.999883i \(-0.495136\pi\)
0.0152815 + 0.999883i \(0.495136\pi\)
\(84\) −9.09666 −0.992527
\(85\) 15.5147 1.68281
\(86\) 12.3095 1.32736
\(87\) −9.67244 −1.03699
\(88\) 19.9905 2.13100
\(89\) 2.91764 0.309270 0.154635 0.987972i \(-0.450580\pi\)
0.154635 + 0.987972i \(0.450580\pi\)
\(90\) 3.11961 0.328836
\(91\) −1.30202 −0.136489
\(92\) −13.0837 −1.36407
\(93\) 9.35182 0.969738
\(94\) 12.5549 1.29494
\(95\) 8.29028 0.850564
\(96\) −7.23013 −0.737922
\(97\) 4.95000 0.502596 0.251298 0.967910i \(-0.419143\pi\)
0.251298 + 0.967910i \(0.419143\pi\)
\(98\) 13.4293 1.35656
\(99\) 1.60220 0.161027
\(100\) 5.98381 0.598381
\(101\) 8.79833 0.875467 0.437733 0.899105i \(-0.355781\pi\)
0.437733 + 0.899105i \(0.355781\pi\)
\(102\) −24.6855 −2.44423
\(103\) 16.0230 1.57879 0.789397 0.613883i \(-0.210393\pi\)
0.789397 + 0.613883i \(0.210393\pi\)
\(104\) −6.09798 −0.597956
\(105\) −5.20233 −0.507695
\(106\) 12.5419 1.21817
\(107\) −13.5858 −1.31339 −0.656696 0.754155i \(-0.728047\pi\)
−0.656696 + 0.754155i \(0.728047\pi\)
\(108\) −24.3744 −2.34542
\(109\) 2.71223 0.259784 0.129892 0.991528i \(-0.458537\pi\)
0.129892 + 0.991528i \(0.458537\pi\)
\(110\) 20.9248 1.99510
\(111\) 1.64054 0.155713
\(112\) −8.61912 −0.814430
\(113\) −15.1376 −1.42402 −0.712012 0.702168i \(-0.752216\pi\)
−0.712012 + 0.702168i \(0.752216\pi\)
\(114\) −13.1907 −1.23542
\(115\) −7.48250 −0.697746
\(116\) −26.9097 −2.49850
\(117\) −0.488741 −0.0451841
\(118\) −24.0373 −2.21281
\(119\) −8.01173 −0.734434
\(120\) −24.3650 −2.22421
\(121\) −0.253247 −0.0230225
\(122\) 26.8629 2.43205
\(123\) −15.2499 −1.37504
\(124\) 26.0177 2.33646
\(125\) −9.18468 −0.821503
\(126\) −1.61096 −0.143515
\(127\) −18.9486 −1.68142 −0.840710 0.541486i \(-0.817862\pi\)
−0.840710 + 0.541486i \(0.817862\pi\)
\(128\) 13.4019 1.18457
\(129\) −7.70543 −0.678425
\(130\) −6.38296 −0.559823
\(131\) 5.95941 0.520676 0.260338 0.965517i \(-0.416166\pi\)
0.260338 + 0.965517i \(0.416166\pi\)
\(132\) −22.9036 −1.99350
\(133\) −4.28106 −0.371215
\(134\) 28.7013 2.47941
\(135\) −13.9396 −1.19973
\(136\) −37.5227 −3.21755
\(137\) 0.427389 0.0365143 0.0182571 0.999833i \(-0.494188\pi\)
0.0182571 + 0.999833i \(0.494188\pi\)
\(138\) 11.9054 1.01346
\(139\) 11.5591 0.980433 0.490217 0.871601i \(-0.336918\pi\)
0.490217 + 0.871601i \(0.336918\pi\)
\(140\) −14.4734 −1.22323
\(141\) −7.85910 −0.661856
\(142\) 14.4578 1.21327
\(143\) −3.27822 −0.274139
\(144\) −3.23537 −0.269614
\(145\) −15.3895 −1.27803
\(146\) −2.90210 −0.240179
\(147\) −8.40641 −0.693349
\(148\) 4.56415 0.375171
\(149\) 13.8656 1.13591 0.567956 0.823059i \(-0.307734\pi\)
0.567956 + 0.823059i \(0.307734\pi\)
\(150\) −5.44493 −0.444577
\(151\) −5.26975 −0.428846 −0.214423 0.976741i \(-0.568787\pi\)
−0.214423 + 0.976741i \(0.568787\pi\)
\(152\) −20.0503 −1.62629
\(153\) −3.00737 −0.243132
\(154\) −10.8055 −0.870730
\(155\) 14.8794 1.19514
\(156\) 6.98658 0.559374
\(157\) −20.9960 −1.67566 −0.837830 0.545931i \(-0.816176\pi\)
−0.837830 + 0.545931i \(0.816176\pi\)
\(158\) −18.7379 −1.49071
\(159\) −7.85090 −0.622617
\(160\) −11.5036 −0.909442
\(161\) 3.86393 0.304520
\(162\) 18.4675 1.45094
\(163\) 5.71746 0.447826 0.223913 0.974609i \(-0.428117\pi\)
0.223913 + 0.974609i \(0.428117\pi\)
\(164\) −42.4267 −3.31297
\(165\) −13.0984 −1.01971
\(166\) −0.704891 −0.0547101
\(167\) 11.1526 0.863013 0.431506 0.902110i \(-0.357982\pi\)
0.431506 + 0.902110i \(0.357982\pi\)
\(168\) 12.5820 0.970720
\(169\) 1.00000 0.0769231
\(170\) −39.2764 −3.01236
\(171\) −1.60699 −0.122889
\(172\) −21.4373 −1.63458
\(173\) −2.20850 −0.167909 −0.0839546 0.996470i \(-0.526755\pi\)
−0.0839546 + 0.996470i \(0.526755\pi\)
\(174\) 24.4863 1.85630
\(175\) −1.76716 −0.133585
\(176\) −21.7012 −1.63579
\(177\) 15.0468 1.13099
\(178\) −7.38618 −0.553618
\(179\) −17.5090 −1.30869 −0.654343 0.756198i \(-0.727055\pi\)
−0.654343 + 0.756198i \(0.727055\pi\)
\(180\) −5.43290 −0.404945
\(181\) 3.83182 0.284817 0.142408 0.989808i \(-0.454515\pi\)
0.142408 + 0.989808i \(0.454515\pi\)
\(182\) 3.29614 0.244326
\(183\) −16.8156 −1.24304
\(184\) 18.0966 1.33410
\(185\) 2.61021 0.191907
\(186\) −23.6747 −1.73591
\(187\) −20.1719 −1.47512
\(188\) −21.8648 −1.59466
\(189\) 7.19833 0.523602
\(190\) −20.9873 −1.52258
\(191\) −19.8680 −1.43760 −0.718801 0.695216i \(-0.755309\pi\)
−0.718801 + 0.695216i \(0.755309\pi\)
\(192\) −2.67726 −0.193215
\(193\) 20.4710 1.47353 0.736767 0.676147i \(-0.236352\pi\)
0.736767 + 0.676147i \(0.236352\pi\)
\(194\) −12.5312 −0.899688
\(195\) 3.99558 0.286130
\(196\) −23.3875 −1.67053
\(197\) −3.75443 −0.267492 −0.133746 0.991016i \(-0.542701\pi\)
−0.133746 + 0.991016i \(0.542701\pi\)
\(198\) −4.05606 −0.288252
\(199\) 8.59980 0.609624 0.304812 0.952413i \(-0.401406\pi\)
0.304812 + 0.952413i \(0.401406\pi\)
\(200\) −8.27646 −0.585234
\(201\) −17.9663 −1.26725
\(202\) −22.2735 −1.56716
\(203\) 7.94708 0.557776
\(204\) 42.9906 3.00994
\(205\) −24.2636 −1.69464
\(206\) −40.5632 −2.82617
\(207\) 1.45041 0.100810
\(208\) 6.61981 0.459001
\(209\) −10.7789 −0.745590
\(210\) 13.1700 0.908816
\(211\) −10.3719 −0.714033 −0.357016 0.934098i \(-0.616206\pi\)
−0.357016 + 0.934098i \(0.616206\pi\)
\(212\) −21.8420 −1.50012
\(213\) −9.05026 −0.620114
\(214\) 34.3933 2.35108
\(215\) −12.2599 −0.836116
\(216\) 33.7132 2.29389
\(217\) −7.68365 −0.521600
\(218\) −6.86616 −0.465035
\(219\) 1.81664 0.122757
\(220\) −36.4411 −2.45686
\(221\) 6.15331 0.413917
\(222\) −4.15312 −0.278739
\(223\) −0.413981 −0.0277222 −0.0138611 0.999904i \(-0.504412\pi\)
−0.0138611 + 0.999904i \(0.504412\pi\)
\(224\) 5.94043 0.396912
\(225\) −0.663342 −0.0442228
\(226\) 38.3216 2.54912
\(227\) −8.45863 −0.561419 −0.280710 0.959793i \(-0.590570\pi\)
−0.280710 + 0.959793i \(0.590570\pi\)
\(228\) 22.9720 1.52136
\(229\) 15.0190 0.992481 0.496241 0.868185i \(-0.334713\pi\)
0.496241 + 0.868185i \(0.334713\pi\)
\(230\) 18.9424 1.24902
\(231\) 6.76397 0.445037
\(232\) 37.2200 2.44361
\(233\) −11.0128 −0.721470 −0.360735 0.932668i \(-0.617474\pi\)
−0.360735 + 0.932668i \(0.617474\pi\)
\(234\) 1.23728 0.0808832
\(235\) −12.5044 −0.815695
\(236\) 41.8617 2.72496
\(237\) 11.7295 0.761913
\(238\) 20.2822 1.31470
\(239\) −7.75889 −0.501881 −0.250940 0.968003i \(-0.580740\pi\)
−0.250940 + 0.968003i \(0.580740\pi\)
\(240\) 26.4500 1.70734
\(241\) −1.70878 −0.110072 −0.0550361 0.998484i \(-0.517527\pi\)
−0.0550361 + 0.998484i \(0.517527\pi\)
\(242\) 0.641110 0.0412121
\(243\) 5.02556 0.322390
\(244\) −46.7826 −2.99495
\(245\) −13.3752 −0.854508
\(246\) 38.6059 2.46143
\(247\) 3.28802 0.209212
\(248\) −35.9862 −2.28513
\(249\) 0.441245 0.0279628
\(250\) 23.2516 1.47056
\(251\) −9.89275 −0.624425 −0.312212 0.950012i \(-0.601070\pi\)
−0.312212 + 0.950012i \(0.601070\pi\)
\(252\) 2.80553 0.176732
\(253\) 9.72861 0.611632
\(254\) 47.9696 3.00988
\(255\) 24.5861 1.53964
\(256\) −30.5487 −1.90930
\(257\) 17.6107 1.09853 0.549263 0.835650i \(-0.314909\pi\)
0.549263 + 0.835650i \(0.314909\pi\)
\(258\) 19.5067 1.21444
\(259\) −1.34790 −0.0837546
\(260\) 11.1161 0.689393
\(261\) 2.98311 0.184650
\(262\) −15.0866 −0.932053
\(263\) 22.2385 1.37129 0.685643 0.727938i \(-0.259521\pi\)
0.685643 + 0.727938i \(0.259521\pi\)
\(264\) 31.6789 1.94970
\(265\) −12.4913 −0.767336
\(266\) 10.8378 0.664506
\(267\) 4.62358 0.282958
\(268\) −49.9841 −3.05326
\(269\) 15.3883 0.938243 0.469121 0.883134i \(-0.344571\pi\)
0.469121 + 0.883134i \(0.344571\pi\)
\(270\) 35.2888 2.14761
\(271\) 2.79478 0.169771 0.0848854 0.996391i \(-0.472948\pi\)
0.0848854 + 0.996391i \(0.472948\pi\)
\(272\) 40.7337 2.46985
\(273\) −2.06330 −0.124877
\(274\) −1.08196 −0.0653636
\(275\) −4.44936 −0.268306
\(276\) −20.7337 −1.24802
\(277\) −12.5434 −0.753660 −0.376830 0.926282i \(-0.622986\pi\)
−0.376830 + 0.926282i \(0.622986\pi\)
\(278\) −29.2626 −1.75506
\(279\) −2.88422 −0.172674
\(280\) 20.0188 1.19635
\(281\) −21.3972 −1.27645 −0.638225 0.769850i \(-0.720331\pi\)
−0.638225 + 0.769850i \(0.720331\pi\)
\(282\) 19.8958 1.18478
\(283\) 26.6561 1.58454 0.792269 0.610172i \(-0.208899\pi\)
0.792269 + 0.610172i \(0.208899\pi\)
\(284\) −25.1787 −1.49408
\(285\) 13.1376 0.778202
\(286\) 8.29901 0.490731
\(287\) 12.5296 0.739600
\(288\) 2.22987 0.131396
\(289\) 20.8633 1.22725
\(290\) 38.9594 2.28778
\(291\) 7.84424 0.459837
\(292\) 5.05409 0.295768
\(293\) −18.3636 −1.07281 −0.536405 0.843961i \(-0.680218\pi\)
−0.536405 + 0.843961i \(0.680218\pi\)
\(294\) 21.2813 1.24115
\(295\) 23.9405 1.39387
\(296\) −6.31287 −0.366928
\(297\) 18.1240 1.05166
\(298\) −35.1015 −2.03338
\(299\) −2.96765 −0.171623
\(300\) 9.48251 0.547473
\(301\) 6.33095 0.364910
\(302\) 13.3407 0.767670
\(303\) 13.9427 0.800986
\(304\) 21.7661 1.24837
\(305\) −26.7547 −1.53197
\(306\) 7.61334 0.435226
\(307\) 6.74483 0.384948 0.192474 0.981302i \(-0.438349\pi\)
0.192474 + 0.981302i \(0.438349\pi\)
\(308\) 18.8181 1.07226
\(309\) 25.3916 1.44448
\(310\) −37.6680 −2.13940
\(311\) −9.20685 −0.522072 −0.261036 0.965329i \(-0.584064\pi\)
−0.261036 + 0.965329i \(0.584064\pi\)
\(312\) −9.66343 −0.547084
\(313\) −27.6556 −1.56319 −0.781594 0.623788i \(-0.785593\pi\)
−0.781594 + 0.623788i \(0.785593\pi\)
\(314\) 53.1525 2.99957
\(315\) 1.60447 0.0904014
\(316\) 32.6327 1.83573
\(317\) −22.6176 −1.27033 −0.635167 0.772375i \(-0.719069\pi\)
−0.635167 + 0.772375i \(0.719069\pi\)
\(318\) 19.8750 1.11454
\(319\) 20.0092 1.12030
\(320\) −4.25970 −0.238125
\(321\) −21.5294 −1.20165
\(322\) −9.78176 −0.545116
\(323\) 20.2322 1.12575
\(324\) −32.1617 −1.78676
\(325\) 1.35725 0.0752865
\(326\) −14.4741 −0.801645
\(327\) 4.29805 0.237683
\(328\) 58.6822 3.24018
\(329\) 6.45720 0.355997
\(330\) 33.1594 1.82537
\(331\) 0.913956 0.0502356 0.0251178 0.999684i \(-0.492004\pi\)
0.0251178 + 0.999684i \(0.492004\pi\)
\(332\) 1.22759 0.0673727
\(333\) −0.505964 −0.0277266
\(334\) −28.2334 −1.54486
\(335\) −28.5856 −1.56180
\(336\) −13.6587 −0.745142
\(337\) 5.39849 0.294074 0.147037 0.989131i \(-0.453026\pi\)
0.147037 + 0.989131i \(0.453026\pi\)
\(338\) −2.53156 −0.137699
\(339\) −23.9884 −1.30287
\(340\) 68.4010 3.70956
\(341\) −19.3459 −1.04764
\(342\) 4.06818 0.219982
\(343\) 16.0210 0.865053
\(344\) 29.6508 1.59867
\(345\) −11.8575 −0.638385
\(346\) 5.59095 0.300571
\(347\) 2.67063 0.143367 0.0716835 0.997427i \(-0.477163\pi\)
0.0716835 + 0.997427i \(0.477163\pi\)
\(348\) −42.6437 −2.28594
\(349\) −20.8591 −1.11656 −0.558281 0.829652i \(-0.688539\pi\)
−0.558281 + 0.829652i \(0.688539\pi\)
\(350\) 4.47367 0.239128
\(351\) −5.52859 −0.295094
\(352\) 14.9568 0.797201
\(353\) 5.04211 0.268365 0.134182 0.990957i \(-0.457159\pi\)
0.134182 + 0.990957i \(0.457159\pi\)
\(354\) −38.0918 −2.02456
\(355\) −14.3996 −0.764250
\(356\) 12.8633 0.681752
\(357\) −12.6962 −0.671952
\(358\) 44.3251 2.34266
\(359\) 8.30102 0.438111 0.219055 0.975712i \(-0.429702\pi\)
0.219055 + 0.975712i \(0.429702\pi\)
\(360\) 7.51448 0.396048
\(361\) −8.18893 −0.430996
\(362\) −9.70046 −0.509845
\(363\) −0.401319 −0.0210638
\(364\) −5.74032 −0.300875
\(365\) 2.89040 0.151291
\(366\) 42.5696 2.22515
\(367\) −0.0265580 −0.00138631 −0.000693157 1.00000i \(-0.500221\pi\)
−0.000693157 1.00000i \(0.500221\pi\)
\(368\) −19.6452 −1.02408
\(369\) 4.70326 0.244842
\(370\) −6.60790 −0.343528
\(371\) 6.45047 0.334892
\(372\) 41.2301 2.13768
\(373\) 15.1984 0.786941 0.393471 0.919337i \(-0.371274\pi\)
0.393471 + 0.919337i \(0.371274\pi\)
\(374\) 51.0664 2.64058
\(375\) −14.5549 −0.751613
\(376\) 30.2422 1.55962
\(377\) −6.10366 −0.314354
\(378\) −18.2230 −0.937289
\(379\) 3.70468 0.190297 0.0951484 0.995463i \(-0.469667\pi\)
0.0951484 + 0.995463i \(0.469667\pi\)
\(380\) 36.5500 1.87498
\(381\) −30.0278 −1.53837
\(382\) 50.2971 2.57342
\(383\) −18.4802 −0.944294 −0.472147 0.881520i \(-0.656521\pi\)
−0.472147 + 0.881520i \(0.656521\pi\)
\(384\) 21.2379 1.08379
\(385\) 10.7619 0.548479
\(386\) −51.8235 −2.63775
\(387\) 2.37646 0.120802
\(388\) 21.8235 1.10792
\(389\) −18.7853 −0.952450 −0.476225 0.879323i \(-0.657995\pi\)
−0.476225 + 0.879323i \(0.657995\pi\)
\(390\) −10.1151 −0.512196
\(391\) −18.2608 −0.923491
\(392\) 32.3482 1.63383
\(393\) 9.44386 0.476380
\(394\) 9.50454 0.478832
\(395\) 18.6624 0.939009
\(396\) 7.06376 0.354967
\(397\) 24.9735 1.25339 0.626693 0.779267i \(-0.284408\pi\)
0.626693 + 0.779267i \(0.284408\pi\)
\(398\) −21.7709 −1.09128
\(399\) −6.78418 −0.339634
\(400\) 8.98472 0.449236
\(401\) −29.4822 −1.47227 −0.736136 0.676834i \(-0.763351\pi\)
−0.736136 + 0.676834i \(0.763351\pi\)
\(402\) 45.4827 2.26847
\(403\) 5.90133 0.293966
\(404\) 38.7899 1.92987
\(405\) −18.3931 −0.913960
\(406\) −20.1185 −0.998464
\(407\) −3.39375 −0.168222
\(408\) −59.4621 −2.94381
\(409\) −7.46081 −0.368913 −0.184457 0.982841i \(-0.559053\pi\)
−0.184457 + 0.982841i \(0.559053\pi\)
\(410\) 61.4247 3.03355
\(411\) 0.677281 0.0334078
\(412\) 70.6420 3.48028
\(413\) −12.3628 −0.608331
\(414\) −3.67179 −0.180459
\(415\) 0.702051 0.0344623
\(416\) −4.56248 −0.223694
\(417\) 18.3177 0.897022
\(418\) 27.2873 1.33467
\(419\) −12.0711 −0.589714 −0.294857 0.955541i \(-0.595272\pi\)
−0.294857 + 0.955541i \(0.595272\pi\)
\(420\) −22.9359 −1.11916
\(421\) −18.1762 −0.885853 −0.442927 0.896558i \(-0.646060\pi\)
−0.442927 + 0.896558i \(0.646060\pi\)
\(422\) 26.2571 1.27818
\(423\) 2.42385 0.117852
\(424\) 30.2106 1.46716
\(425\) 8.35156 0.405110
\(426\) 22.9113 1.11005
\(427\) 13.8160 0.668604
\(428\) −59.8970 −2.89523
\(429\) −5.19499 −0.250816
\(430\) 31.0366 1.49672
\(431\) 15.3464 0.739209 0.369605 0.929189i \(-0.379493\pi\)
0.369605 + 0.929189i \(0.379493\pi\)
\(432\) −36.5982 −1.76083
\(433\) 8.61489 0.414005 0.207003 0.978340i \(-0.433629\pi\)
0.207003 + 0.978340i \(0.433629\pi\)
\(434\) 19.4516 0.933707
\(435\) −24.3877 −1.16930
\(436\) 11.9576 0.572666
\(437\) −9.75768 −0.466773
\(438\) −4.59894 −0.219746
\(439\) −23.0496 −1.10010 −0.550048 0.835133i \(-0.685390\pi\)
−0.550048 + 0.835133i \(0.685390\pi\)
\(440\) 50.4033 2.40288
\(441\) 2.59265 0.123459
\(442\) −15.5775 −0.740944
\(443\) −9.92838 −0.471712 −0.235856 0.971788i \(-0.575789\pi\)
−0.235856 + 0.971788i \(0.575789\pi\)
\(444\) 7.23279 0.343253
\(445\) 7.35643 0.348728
\(446\) 1.04802 0.0496251
\(447\) 21.9727 1.03927
\(448\) 2.19969 0.103926
\(449\) −34.2024 −1.61411 −0.807056 0.590474i \(-0.798941\pi\)
−0.807056 + 0.590474i \(0.798941\pi\)
\(450\) 1.67929 0.0791624
\(451\) 31.5471 1.48549
\(452\) −66.7383 −3.13911
\(453\) −8.35095 −0.392362
\(454\) 21.4135 1.00499
\(455\) −3.28286 −0.153903
\(456\) −31.7736 −1.48793
\(457\) 8.64468 0.404381 0.202190 0.979346i \(-0.435194\pi\)
0.202190 + 0.979346i \(0.435194\pi\)
\(458\) −38.0214 −1.77662
\(459\) −34.0191 −1.58788
\(460\) −32.9887 −1.53811
\(461\) 10.5227 0.490093 0.245046 0.969511i \(-0.421197\pi\)
0.245046 + 0.969511i \(0.421197\pi\)
\(462\) −17.1234 −0.796652
\(463\) 1.00000 0.0464739
\(464\) −40.4051 −1.87576
\(465\) 23.5793 1.09346
\(466\) 27.8794 1.29149
\(467\) −31.2892 −1.44789 −0.723946 0.689856i \(-0.757674\pi\)
−0.723946 + 0.689856i \(0.757674\pi\)
\(468\) −2.15475 −0.0996034
\(469\) 14.7615 0.681623
\(470\) 31.6555 1.46016
\(471\) −33.2722 −1.53310
\(472\) −57.9007 −2.66509
\(473\) 15.9401 0.732925
\(474\) −29.6939 −1.36389
\(475\) 4.46265 0.204761
\(476\) −35.3220 −1.61898
\(477\) 2.42132 0.110865
\(478\) 19.6421 0.898408
\(479\) −1.87421 −0.0856349 −0.0428175 0.999083i \(-0.513633\pi\)
−0.0428175 + 0.999083i \(0.513633\pi\)
\(480\) −18.2298 −0.832071
\(481\) 1.03524 0.0472029
\(482\) 4.32587 0.197038
\(483\) 6.12315 0.278613
\(484\) −1.11651 −0.0507505
\(485\) 12.4807 0.566720
\(486\) −12.7225 −0.577104
\(487\) 8.24621 0.373671 0.186836 0.982391i \(-0.440177\pi\)
0.186836 + 0.982391i \(0.440177\pi\)
\(488\) 64.7070 2.92915
\(489\) 9.06044 0.409727
\(490\) 33.8600 1.52964
\(491\) −11.6867 −0.527413 −0.263706 0.964603i \(-0.584945\pi\)
−0.263706 + 0.964603i \(0.584945\pi\)
\(492\) −67.2334 −3.03112
\(493\) −37.5577 −1.69151
\(494\) −8.32381 −0.374506
\(495\) 4.03972 0.181572
\(496\) 39.0657 1.75410
\(497\) 7.43588 0.333545
\(498\) −1.11704 −0.0500556
\(499\) 26.7137 1.19587 0.597935 0.801544i \(-0.295988\pi\)
0.597935 + 0.801544i \(0.295988\pi\)
\(500\) −40.4933 −1.81092
\(501\) 17.6734 0.789591
\(502\) 25.0441 1.11777
\(503\) 4.23133 0.188666 0.0943328 0.995541i \(-0.469928\pi\)
0.0943328 + 0.995541i \(0.469928\pi\)
\(504\) −3.88044 −0.172849
\(505\) 22.1837 0.987164
\(506\) −24.6285 −1.09487
\(507\) 1.58470 0.0703788
\(508\) −83.5404 −3.70651
\(509\) −30.5529 −1.35423 −0.677116 0.735876i \(-0.736771\pi\)
−0.677116 + 0.735876i \(0.736771\pi\)
\(510\) −62.2411 −2.75608
\(511\) −1.49259 −0.0660284
\(512\) 50.5321 2.23323
\(513\) −18.1781 −0.802583
\(514\) −44.5825 −1.96645
\(515\) 40.3997 1.78023
\(516\) −33.9716 −1.49552
\(517\) 16.2579 0.715024
\(518\) 3.41229 0.149928
\(519\) −3.49980 −0.153624
\(520\) −15.3752 −0.674246
\(521\) 30.5614 1.33892 0.669460 0.742848i \(-0.266526\pi\)
0.669460 + 0.742848i \(0.266526\pi\)
\(522\) −7.55191 −0.330538
\(523\) 9.60674 0.420074 0.210037 0.977693i \(-0.432642\pi\)
0.210037 + 0.977693i \(0.432642\pi\)
\(524\) 26.2738 1.14777
\(525\) −2.80041 −0.122220
\(526\) −56.2981 −2.45471
\(527\) 36.3127 1.58181
\(528\) −34.3898 −1.49662
\(529\) −14.1931 −0.617091
\(530\) 31.6225 1.37359
\(531\) −4.64062 −0.201386
\(532\) −18.8743 −0.818304
\(533\) −9.62322 −0.416828
\(534\) −11.7049 −0.506518
\(535\) −34.2547 −1.48096
\(536\) 69.1351 2.98618
\(537\) −27.7465 −1.19735
\(538\) −38.9564 −1.67953
\(539\) 17.3901 0.749047
\(540\) −61.4565 −2.64467
\(541\) −12.9675 −0.557515 −0.278757 0.960362i \(-0.589923\pi\)
−0.278757 + 0.960362i \(0.589923\pi\)
\(542\) −7.07515 −0.303904
\(543\) 6.07226 0.260586
\(544\) −28.0743 −1.20368
\(545\) 6.83850 0.292929
\(546\) 5.22337 0.223540
\(547\) 13.6969 0.585635 0.292818 0.956168i \(-0.405407\pi\)
0.292818 + 0.956168i \(0.405407\pi\)
\(548\) 1.88426 0.0804918
\(549\) 5.18614 0.221339
\(550\) 11.2638 0.480291
\(551\) −20.0690 −0.854966
\(552\) 28.6776 1.22060
\(553\) −9.63720 −0.409816
\(554\) 31.7543 1.34911
\(555\) 4.13639 0.175580
\(556\) 50.9617 2.16126
\(557\) −42.1488 −1.78590 −0.892951 0.450154i \(-0.851369\pi\)
−0.892951 + 0.450154i \(0.851369\pi\)
\(558\) 7.30157 0.309100
\(559\) −4.86241 −0.205658
\(560\) −21.7319 −0.918340
\(561\) −31.9664 −1.34962
\(562\) 54.1683 2.28495
\(563\) 24.9588 1.05189 0.525945 0.850519i \(-0.323712\pi\)
0.525945 + 0.850519i \(0.323712\pi\)
\(564\) −34.6491 −1.45899
\(565\) −38.1673 −1.60571
\(566\) −67.4814 −2.83645
\(567\) 9.49811 0.398883
\(568\) 34.8258 1.46126
\(569\) 12.5376 0.525604 0.262802 0.964850i \(-0.415353\pi\)
0.262802 + 0.964850i \(0.415353\pi\)
\(570\) −33.2585 −1.39304
\(571\) −17.3840 −0.727499 −0.363749 0.931497i \(-0.618504\pi\)
−0.363749 + 0.931497i \(0.618504\pi\)
\(572\) −14.4530 −0.604310
\(573\) −31.4848 −1.31530
\(574\) −31.7195 −1.32394
\(575\) −4.02783 −0.167972
\(576\) 0.825702 0.0344042
\(577\) 16.4738 0.685813 0.342907 0.939370i \(-0.388589\pi\)
0.342907 + 0.939370i \(0.388589\pi\)
\(578\) −52.8165 −2.19688
\(579\) 32.4403 1.34817
\(580\) −67.8490 −2.81728
\(581\) −0.362536 −0.0150405
\(582\) −19.8581 −0.823147
\(583\) 16.2410 0.672633
\(584\) −6.99052 −0.289270
\(585\) −1.23229 −0.0509489
\(586\) 46.4884 1.92042
\(587\) 23.0296 0.950533 0.475267 0.879842i \(-0.342352\pi\)
0.475267 + 0.879842i \(0.342352\pi\)
\(588\) −37.0620 −1.52841
\(589\) 19.4037 0.799516
\(590\) −60.6067 −2.49514
\(591\) −5.94962 −0.244735
\(592\) 6.85309 0.281660
\(593\) 34.4420 1.41436 0.707181 0.707032i \(-0.249966\pi\)
0.707181 + 0.707032i \(0.249966\pi\)
\(594\) −45.8818 −1.88256
\(595\) −20.2004 −0.828137
\(596\) 61.1303 2.50400
\(597\) 13.6281 0.557759
\(598\) 7.51276 0.307220
\(599\) −30.9935 −1.26636 −0.633181 0.774004i \(-0.718251\pi\)
−0.633181 + 0.774004i \(0.718251\pi\)
\(600\) −13.1157 −0.535445
\(601\) −14.0568 −0.573388 −0.286694 0.958022i \(-0.592556\pi\)
−0.286694 + 0.958022i \(0.592556\pi\)
\(602\) −16.0272 −0.653218
\(603\) 5.54104 0.225649
\(604\) −23.2332 −0.945346
\(605\) −0.638527 −0.0259598
\(606\) −35.2967 −1.43383
\(607\) 34.1866 1.38759 0.693796 0.720171i \(-0.255937\pi\)
0.693796 + 0.720171i \(0.255937\pi\)
\(608\) −15.0015 −0.608392
\(609\) 12.5937 0.510323
\(610\) 67.7311 2.74235
\(611\) −4.95938 −0.200635
\(612\) −13.2589 −0.535958
\(613\) −33.3711 −1.34785 −0.673923 0.738801i \(-0.735392\pi\)
−0.673923 + 0.738801i \(0.735392\pi\)
\(614\) −17.0749 −0.689088
\(615\) −38.4504 −1.55047
\(616\) −26.0280 −1.04870
\(617\) −16.9920 −0.684073 −0.342037 0.939687i \(-0.611117\pi\)
−0.342037 + 0.939687i \(0.611117\pi\)
\(618\) −64.2803 −2.58573
\(619\) 30.4093 1.22225 0.611127 0.791533i \(-0.290716\pi\)
0.611127 + 0.791533i \(0.290716\pi\)
\(620\) 65.6000 2.63456
\(621\) 16.4069 0.658386
\(622\) 23.3077 0.934552
\(623\) −3.79883 −0.152197
\(624\) 10.4904 0.419951
\(625\) −29.9441 −1.19776
\(626\) 70.0118 2.79823
\(627\) −17.0812 −0.682158
\(628\) −92.5667 −3.69381
\(629\) 6.37016 0.253995
\(630\) −4.06180 −0.161826
\(631\) 29.6555 1.18057 0.590284 0.807196i \(-0.299016\pi\)
0.590284 + 0.807196i \(0.299016\pi\)
\(632\) −45.1356 −1.79540
\(633\) −16.4363 −0.653286
\(634\) 57.2579 2.27400
\(635\) −47.7763 −1.89594
\(636\) −34.6129 −1.37249
\(637\) −5.30475 −0.210182
\(638\) −50.6544 −2.00543
\(639\) 2.79122 0.110419
\(640\) 33.7910 1.33570
\(641\) −15.3970 −0.608147 −0.304073 0.952649i \(-0.598347\pi\)
−0.304073 + 0.952649i \(0.598347\pi\)
\(642\) 54.5029 2.15106
\(643\) −33.5617 −1.32355 −0.661773 0.749705i \(-0.730196\pi\)
−0.661773 + 0.749705i \(0.730196\pi\)
\(644\) 17.0352 0.671282
\(645\) −19.4282 −0.764983
\(646\) −51.2190 −2.01518
\(647\) 45.5985 1.79266 0.896330 0.443387i \(-0.146223\pi\)
0.896330 + 0.443387i \(0.146223\pi\)
\(648\) 44.4842 1.74750
\(649\) −31.1270 −1.22184
\(650\) −3.43595 −0.134769
\(651\) −12.1762 −0.477225
\(652\) 25.2071 0.987185
\(653\) −0.363681 −0.0142320 −0.00711598 0.999975i \(-0.502265\pi\)
−0.00711598 + 0.999975i \(0.502265\pi\)
\(654\) −10.8808 −0.425472
\(655\) 15.0258 0.587107
\(656\) −63.7039 −2.48722
\(657\) −0.560277 −0.0218585
\(658\) −16.3468 −0.637264
\(659\) −38.9169 −1.51599 −0.757994 0.652261i \(-0.773820\pi\)
−0.757994 + 0.652261i \(0.773820\pi\)
\(660\) −57.7481 −2.24784
\(661\) 6.02900 0.234501 0.117250 0.993102i \(-0.462592\pi\)
0.117250 + 0.993102i \(0.462592\pi\)
\(662\) −2.31373 −0.0899258
\(663\) 9.75113 0.378702
\(664\) −1.69793 −0.0658925
\(665\) −10.7941 −0.418577
\(666\) 1.28088 0.0496330
\(667\) 18.1135 0.701357
\(668\) 49.1693 1.90242
\(669\) −0.656034 −0.0253637
\(670\) 72.3661 2.79575
\(671\) 34.7860 1.34290
\(672\) 9.41377 0.363144
\(673\) 9.77621 0.376845 0.188423 0.982088i \(-0.439663\pi\)
0.188423 + 0.982088i \(0.439663\pi\)
\(674\) −13.6666 −0.526417
\(675\) −7.50366 −0.288816
\(676\) 4.40878 0.169569
\(677\) −3.00224 −0.115385 −0.0576927 0.998334i \(-0.518374\pi\)
−0.0576927 + 0.998334i \(0.518374\pi\)
\(678\) 60.7281 2.33225
\(679\) −6.44499 −0.247336
\(680\) −94.6083 −3.62806
\(681\) −13.4044 −0.513656
\(682\) 48.9752 1.87536
\(683\) −40.7988 −1.56112 −0.780561 0.625079i \(-0.785067\pi\)
−0.780561 + 0.625079i \(0.785067\pi\)
\(684\) −7.08487 −0.270897
\(685\) 1.07760 0.0411730
\(686\) −40.5581 −1.54852
\(687\) 23.8005 0.908045
\(688\) −32.1882 −1.22716
\(689\) −4.95420 −0.188740
\(690\) 30.0179 1.14276
\(691\) 43.7463 1.66419 0.832095 0.554634i \(-0.187142\pi\)
0.832095 + 0.554634i \(0.187142\pi\)
\(692\) −9.73680 −0.370138
\(693\) −2.08610 −0.0792443
\(694\) −6.76086 −0.256639
\(695\) 29.1447 1.10552
\(696\) 58.9823 2.23572
\(697\) −59.2147 −2.24292
\(698\) 52.8060 1.99874
\(699\) −17.4519 −0.660091
\(700\) −7.79103 −0.294473
\(701\) 5.73694 0.216681 0.108341 0.994114i \(-0.465446\pi\)
0.108341 + 0.994114i \(0.465446\pi\)
\(702\) 13.9959 0.528243
\(703\) 3.40389 0.128380
\(704\) 5.53839 0.208736
\(705\) −19.8156 −0.746299
\(706\) −12.7644 −0.480395
\(707\) −11.4556 −0.430832
\(708\) 66.3380 2.49314
\(709\) 8.08547 0.303656 0.151828 0.988407i \(-0.451484\pi\)
0.151828 + 0.988407i \(0.451484\pi\)
\(710\) 36.4534 1.36807
\(711\) −3.61753 −0.135668
\(712\) −17.7917 −0.666773
\(713\) −17.5131 −0.655869
\(714\) 32.1410 1.20285
\(715\) −8.26558 −0.309115
\(716\) −77.1936 −2.88486
\(717\) −12.2955 −0.459183
\(718\) −21.0145 −0.784254
\(719\) −5.29478 −0.197462 −0.0987310 0.995114i \(-0.531478\pi\)
−0.0987310 + 0.995114i \(0.531478\pi\)
\(720\) −8.15752 −0.304013
\(721\) −20.8623 −0.776951
\(722\) 20.7307 0.771518
\(723\) −2.70789 −0.100708
\(724\) 16.8936 0.627847
\(725\) −8.28417 −0.307667
\(726\) 1.01596 0.0377059
\(727\) −37.8024 −1.40201 −0.701006 0.713155i \(-0.747265\pi\)
−0.701006 + 0.713155i \(0.747265\pi\)
\(728\) 7.93968 0.294264
\(729\) 29.8487 1.10551
\(730\) −7.31722 −0.270823
\(731\) −29.9199 −1.10663
\(732\) −74.1362 −2.74015
\(733\) −16.2336 −0.599601 −0.299800 0.954002i \(-0.596920\pi\)
−0.299800 + 0.954002i \(0.596920\pi\)
\(734\) 0.0672330 0.00248162
\(735\) −21.1956 −0.781810
\(736\) 13.5398 0.499084
\(737\) 37.1665 1.36905
\(738\) −11.9066 −0.438287
\(739\) −2.21135 −0.0813460 −0.0406730 0.999173i \(-0.512950\pi\)
−0.0406730 + 0.999173i \(0.512950\pi\)
\(740\) 11.5079 0.423037
\(741\) 5.21051 0.191413
\(742\) −16.3297 −0.599483
\(743\) 34.6343 1.27061 0.635305 0.772262i \(-0.280874\pi\)
0.635305 + 0.772262i \(0.280874\pi\)
\(744\) −57.0271 −2.09072
\(745\) 34.9601 1.28084
\(746\) −38.4755 −1.40869
\(747\) −0.136086 −0.00497912
\(748\) −88.9337 −3.25174
\(749\) 17.6890 0.646342
\(750\) 36.8466 1.34545
\(751\) 4.65075 0.169708 0.0848541 0.996393i \(-0.472958\pi\)
0.0848541 + 0.996393i \(0.472958\pi\)
\(752\) −32.8301 −1.19719
\(753\) −15.6770 −0.571301
\(754\) 15.4518 0.562720
\(755\) −13.2869 −0.483561
\(756\) 31.7359 1.15422
\(757\) −26.1708 −0.951194 −0.475597 0.879663i \(-0.657768\pi\)
−0.475597 + 0.879663i \(0.657768\pi\)
\(758\) −9.37862 −0.340647
\(759\) 15.4169 0.559597
\(760\) −50.5539 −1.83378
\(761\) −14.7165 −0.533472 −0.266736 0.963770i \(-0.585945\pi\)
−0.266736 + 0.963770i \(0.585945\pi\)
\(762\) 76.0171 2.75381
\(763\) −3.53137 −0.127844
\(764\) −87.5939 −3.16904
\(765\) −7.58267 −0.274152
\(766\) 46.7837 1.69036
\(767\) 9.49507 0.342847
\(768\) −48.4105 −1.74686
\(769\) 46.8720 1.69025 0.845124 0.534571i \(-0.179527\pi\)
0.845124 + 0.534571i \(0.179527\pi\)
\(770\) −27.2445 −0.981822
\(771\) 27.9076 1.00507
\(772\) 90.2521 3.24825
\(773\) 3.30443 0.118852 0.0594260 0.998233i \(-0.481073\pi\)
0.0594260 + 0.998233i \(0.481073\pi\)
\(774\) −6.01613 −0.216245
\(775\) 8.00957 0.287712
\(776\) −30.1850 −1.08358
\(777\) −2.13601 −0.0766291
\(778\) 47.5560 1.70496
\(779\) −31.6414 −1.13367
\(780\) 17.6157 0.630742
\(781\) 18.7221 0.669928
\(782\) 46.2284 1.65312
\(783\) 33.7446 1.20594
\(784\) −35.1164 −1.25416
\(785\) −52.9384 −1.88945
\(786\) −23.9077 −0.852758
\(787\) 26.6451 0.949796 0.474898 0.880041i \(-0.342485\pi\)
0.474898 + 0.880041i \(0.342485\pi\)
\(788\) −16.5524 −0.589657
\(789\) 35.2413 1.25462
\(790\) −47.2450 −1.68090
\(791\) 19.7094 0.700786
\(792\) −9.77018 −0.347168
\(793\) −10.6112 −0.376816
\(794\) −63.2219 −2.24366
\(795\) −19.7949 −0.702054
\(796\) 37.9147 1.34385
\(797\) −31.2303 −1.10623 −0.553117 0.833104i \(-0.686562\pi\)
−0.553117 + 0.833104i \(0.686562\pi\)
\(798\) 17.1745 0.607972
\(799\) −30.5166 −1.07960
\(800\) −6.19241 −0.218935
\(801\) −1.42597 −0.0503842
\(802\) 74.6359 2.63549
\(803\) −3.75805 −0.132619
\(804\) −79.2096 −2.79351
\(805\) 9.74235 0.343373
\(806\) −14.9396 −0.526224
\(807\) 24.3858 0.858421
\(808\) −53.6520 −1.88747
\(809\) −28.5723 −1.00455 −0.502274 0.864709i \(-0.667503\pi\)
−0.502274 + 0.864709i \(0.667503\pi\)
\(810\) 46.5631 1.63606
\(811\) −16.1813 −0.568202 −0.284101 0.958794i \(-0.591695\pi\)
−0.284101 + 0.958794i \(0.591695\pi\)
\(812\) 35.0370 1.22956
\(813\) 4.42887 0.155327
\(814\) 8.59147 0.301131
\(815\) 14.4158 0.504962
\(816\) 64.5506 2.25972
\(817\) −15.9877 −0.559338
\(818\) 18.8875 0.660385
\(819\) 0.636350 0.0222359
\(820\) −106.973 −3.73566
\(821\) −20.7759 −0.725084 −0.362542 0.931967i \(-0.618091\pi\)
−0.362542 + 0.931967i \(0.618091\pi\)
\(822\) −1.71458 −0.0598027
\(823\) 18.7526 0.653675 0.326837 0.945081i \(-0.394017\pi\)
0.326837 + 0.945081i \(0.394017\pi\)
\(824\) −97.7079 −3.40382
\(825\) −7.05088 −0.245480
\(826\) 31.2970 1.08896
\(827\) −39.8210 −1.38471 −0.692357 0.721555i \(-0.743427\pi\)
−0.692357 + 0.721555i \(0.743427\pi\)
\(828\) 6.39454 0.222226
\(829\) 11.6907 0.406035 0.203017 0.979175i \(-0.434925\pi\)
0.203017 + 0.979175i \(0.434925\pi\)
\(830\) −1.77728 −0.0616904
\(831\) −19.8775 −0.689542
\(832\) −1.68945 −0.0585711
\(833\) −32.6418 −1.13097
\(834\) −46.3723 −1.60574
\(835\) 28.1196 0.973121
\(836\) −47.5217 −1.64357
\(837\) −32.6261 −1.12772
\(838\) 30.5588 1.05564
\(839\) −49.7658 −1.71810 −0.859052 0.511888i \(-0.828946\pi\)
−0.859052 + 0.511888i \(0.828946\pi\)
\(840\) 31.7237 1.09457
\(841\) 8.25467 0.284644
\(842\) 46.0141 1.58575
\(843\) −33.9081 −1.16786
\(844\) −45.7276 −1.57401
\(845\) 2.52136 0.0867374
\(846\) −6.13611 −0.210964
\(847\) 0.329733 0.0113297
\(848\) −32.7959 −1.12622
\(849\) 42.2417 1.44973
\(850\) −21.1425 −0.725181
\(851\) −3.07223 −0.105315
\(852\) −39.9006 −1.36697
\(853\) 41.3980 1.41744 0.708721 0.705489i \(-0.249273\pi\)
0.708721 + 0.705489i \(0.249273\pi\)
\(854\) −34.9760 −1.19686
\(855\) −4.05179 −0.138568
\(856\) 82.8461 2.83162
\(857\) −8.15091 −0.278430 −0.139215 0.990262i \(-0.544458\pi\)
−0.139215 + 0.990262i \(0.544458\pi\)
\(858\) 13.1514 0.448982
\(859\) 4.70562 0.160554 0.0802768 0.996773i \(-0.474420\pi\)
0.0802768 + 0.996773i \(0.474420\pi\)
\(860\) −54.0511 −1.84313
\(861\) 19.8556 0.676678
\(862\) −38.8502 −1.32324
\(863\) −0.500265 −0.0170292 −0.00851462 0.999964i \(-0.502710\pi\)
−0.00851462 + 0.999964i \(0.502710\pi\)
\(864\) 25.2241 0.858140
\(865\) −5.56842 −0.189332
\(866\) −21.8091 −0.741103
\(867\) 33.0619 1.12284
\(868\) −33.8755 −1.14981
\(869\) −24.2646 −0.823119
\(870\) 61.7388 2.09314
\(871\) −11.3374 −0.384153
\(872\) −16.5391 −0.560084
\(873\) −2.41927 −0.0818797
\(874\) 24.7021 0.835562
\(875\) 11.9586 0.404276
\(876\) 8.00919 0.270605
\(877\) 3.98318 0.134503 0.0672513 0.997736i \(-0.478577\pi\)
0.0672513 + 0.997736i \(0.478577\pi\)
\(878\) 58.3513 1.96926
\(879\) −29.1006 −0.981540
\(880\) −54.7165 −1.84449
\(881\) −40.3454 −1.35927 −0.679636 0.733550i \(-0.737862\pi\)
−0.679636 + 0.733550i \(0.737862\pi\)
\(882\) −6.56343 −0.221002
\(883\) 43.8163 1.47454 0.737268 0.675600i \(-0.236115\pi\)
0.737268 + 0.675600i \(0.236115\pi\)
\(884\) 27.1286 0.912434
\(885\) 37.9383 1.27528
\(886\) 25.1343 0.844402
\(887\) 44.4188 1.49144 0.745719 0.666260i \(-0.232106\pi\)
0.745719 + 0.666260i \(0.232106\pi\)
\(888\) −10.0040 −0.335711
\(889\) 24.6715 0.827455
\(890\) −18.6232 −0.624252
\(891\) 23.9144 0.801161
\(892\) −1.82515 −0.0611107
\(893\) −16.3065 −0.545677
\(894\) −55.6252 −1.86038
\(895\) −44.1466 −1.47566
\(896\) −17.4495 −0.582947
\(897\) −4.70281 −0.157022
\(898\) 86.5854 2.88939
\(899\) −36.0197 −1.20133
\(900\) −2.92453 −0.0974843
\(901\) −30.4848 −1.01559
\(902\) −79.8633 −2.65916
\(903\) 10.0326 0.333865
\(904\) 92.3086 3.07014
\(905\) 9.66138 0.321155
\(906\) 21.1409 0.702360
\(907\) −27.5521 −0.914851 −0.457426 0.889248i \(-0.651228\pi\)
−0.457426 + 0.889248i \(0.651228\pi\)
\(908\) −37.2923 −1.23759
\(909\) −4.30010 −0.142625
\(910\) 8.31074 0.275498
\(911\) −44.8641 −1.48641 −0.743207 0.669062i \(-0.766696\pi\)
−0.743207 + 0.669062i \(0.766696\pi\)
\(912\) 34.4926 1.14216
\(913\) −0.912794 −0.0302091
\(914\) −21.8845 −0.723875
\(915\) −42.3980 −1.40164
\(916\) 66.2154 2.18782
\(917\) −7.75927 −0.256234
\(918\) 86.1214 2.84243
\(919\) 9.92251 0.327313 0.163657 0.986517i \(-0.447671\pi\)
0.163657 + 0.986517i \(0.447671\pi\)
\(920\) 45.6281 1.50431
\(921\) 10.6885 0.352198
\(922\) −26.6389 −0.877306
\(923\) −5.71104 −0.187981
\(924\) 29.8209 0.981035
\(925\) 1.40508 0.0461986
\(926\) −2.53156 −0.0831921
\(927\) −7.83110 −0.257207
\(928\) 27.8478 0.914149
\(929\) 12.3501 0.405194 0.202597 0.979262i \(-0.435062\pi\)
0.202597 + 0.979262i \(0.435062\pi\)
\(930\) −59.6923 −1.95739
\(931\) −17.4421 −0.571642
\(932\) −48.5529 −1.59040
\(933\) −14.5900 −0.477657
\(934\) 79.2105 2.59185
\(935\) −50.8607 −1.66332
\(936\) 2.98033 0.0974151
\(937\) 32.0670 1.04758 0.523791 0.851847i \(-0.324517\pi\)
0.523791 + 0.851847i \(0.324517\pi\)
\(938\) −37.3696 −1.22016
\(939\) −43.8257 −1.43020
\(940\) −55.1290 −1.79811
\(941\) 38.5802 1.25768 0.628839 0.777536i \(-0.283531\pi\)
0.628839 + 0.777536i \(0.283531\pi\)
\(942\) 84.2305 2.74438
\(943\) 28.5583 0.929987
\(944\) 62.8555 2.04577
\(945\) 18.1496 0.590406
\(946\) −40.3532 −1.31199
\(947\) −50.0756 −1.62724 −0.813620 0.581397i \(-0.802506\pi\)
−0.813620 + 0.581397i \(0.802506\pi\)
\(948\) 51.7128 1.67955
\(949\) 1.14637 0.0372127
\(950\) −11.2975 −0.366538
\(951\) −35.8421 −1.16226
\(952\) 48.8553 1.58341
\(953\) 11.5351 0.373659 0.186830 0.982392i \(-0.440179\pi\)
0.186830 + 0.982392i \(0.440179\pi\)
\(954\) −6.12971 −0.198457
\(955\) −50.0945 −1.62102
\(956\) −34.2073 −1.10634
\(957\) 31.7084 1.02499
\(958\) 4.74468 0.153294
\(959\) −0.556468 −0.0179693
\(960\) −6.75033 −0.217866
\(961\) 3.82574 0.123411
\(962\) −2.62077 −0.0844970
\(963\) 6.63995 0.213969
\(964\) −7.53364 −0.242642
\(965\) 51.6147 1.66154
\(966\) −15.5011 −0.498740
\(967\) −27.2112 −0.875054 −0.437527 0.899205i \(-0.644146\pi\)
−0.437527 + 0.899205i \(0.644146\pi\)
\(968\) 1.54429 0.0496355
\(969\) 32.0619 1.02998
\(970\) −31.5957 −1.01448
\(971\) 50.1971 1.61090 0.805450 0.592663i \(-0.201923\pi\)
0.805450 + 0.592663i \(0.201923\pi\)
\(972\) 22.1566 0.710674
\(973\) −15.0502 −0.482488
\(974\) −20.8758 −0.668902
\(975\) 2.15082 0.0688815
\(976\) −70.2443 −2.24846
\(977\) 45.4587 1.45435 0.727176 0.686451i \(-0.240832\pi\)
0.727176 + 0.686451i \(0.240832\pi\)
\(978\) −22.9370 −0.733445
\(979\) −9.56469 −0.305689
\(980\) −58.9682 −1.88367
\(981\) −1.32558 −0.0423224
\(982\) 29.5855 0.944111
\(983\) 48.4752 1.54612 0.773060 0.634333i \(-0.218725\pi\)
0.773060 + 0.634333i \(0.218725\pi\)
\(984\) 92.9934 2.96452
\(985\) −9.46625 −0.301620
\(986\) 95.0795 3.02795
\(987\) 10.2327 0.325710
\(988\) 14.4962 0.461185
\(989\) 14.4299 0.458844
\(990\) −10.2268 −0.325029
\(991\) 17.3311 0.550541 0.275271 0.961367i \(-0.411233\pi\)
0.275271 + 0.961367i \(0.411233\pi\)
\(992\) −26.9247 −0.854860
\(993\) 1.44834 0.0459618
\(994\) −18.8244 −0.597073
\(995\) 21.6832 0.687403
\(996\) 1.94535 0.0616409
\(997\) 59.0950 1.87156 0.935778 0.352589i \(-0.114699\pi\)
0.935778 + 0.352589i \(0.114699\pi\)
\(998\) −67.6273 −2.14071
\(999\) −5.72342 −0.181081
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 6019.2.a.b.1.6 101
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.b.1.6 101 1.1 even 1 trivial