Properties

Label 8009.2.a.b.1.9
Level $8009$
Weight $2$
Character 8009.1
Self dual yes
Analytic conductor $63.952$
Analytic rank $0$
Dimension $361$
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] = [8009,2,Mod(1,8009)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8009, 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("8009.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8009 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8009.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: \(63.9521869788\)
Analytic rank: \(0\)
Dimension: \(361\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 8009.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.71747 q^{2} -2.51708 q^{3} +5.38462 q^{4} -3.75245 q^{5} +6.84009 q^{6} -1.33469 q^{7} -9.19758 q^{8} +3.33572 q^{9} +O(q^{10})\) \(q-2.71747 q^{2} -2.51708 q^{3} +5.38462 q^{4} -3.75245 q^{5} +6.84009 q^{6} -1.33469 q^{7} -9.19758 q^{8} +3.33572 q^{9} +10.1972 q^{10} -1.04481 q^{11} -13.5535 q^{12} -5.94502 q^{13} +3.62698 q^{14} +9.44524 q^{15} +14.2249 q^{16} -2.54378 q^{17} -9.06469 q^{18} -1.83561 q^{19} -20.2055 q^{20} +3.35953 q^{21} +2.83923 q^{22} +3.09202 q^{23} +23.1511 q^{24} +9.08091 q^{25} +16.1554 q^{26} -0.845024 q^{27} -7.18680 q^{28} +0.322861 q^{29} -25.6671 q^{30} +9.30447 q^{31} -20.2604 q^{32} +2.62987 q^{33} +6.91264 q^{34} +5.00837 q^{35} +17.9615 q^{36} -2.56474 q^{37} +4.98821 q^{38} +14.9641 q^{39} +34.5135 q^{40} +5.41955 q^{41} -9.12941 q^{42} +1.76199 q^{43} -5.62589 q^{44} -12.5171 q^{45} -8.40245 q^{46} -4.79012 q^{47} -35.8052 q^{48} -5.21860 q^{49} -24.6771 q^{50} +6.40292 q^{51} -32.0117 q^{52} -9.23591 q^{53} +2.29632 q^{54} +3.92059 q^{55} +12.2759 q^{56} +4.62039 q^{57} -0.877363 q^{58} -11.5247 q^{59} +50.8590 q^{60} +4.80873 q^{61} -25.2846 q^{62} -4.45215 q^{63} +26.6072 q^{64} +22.3084 q^{65} -7.14658 q^{66} -9.76767 q^{67} -13.6973 q^{68} -7.78287 q^{69} -13.6101 q^{70} -4.53332 q^{71} -30.6805 q^{72} +12.5354 q^{73} +6.96959 q^{74} -22.8574 q^{75} -9.88406 q^{76} +1.39450 q^{77} -40.6645 q^{78} +5.29492 q^{79} -53.3781 q^{80} -7.88015 q^{81} -14.7274 q^{82} +4.14711 q^{83} +18.0898 q^{84} +9.54543 q^{85} -4.78813 q^{86} -0.812668 q^{87} +9.60970 q^{88} -0.157865 q^{89} +34.0148 q^{90} +7.93477 q^{91} +16.6493 q^{92} -23.4201 q^{93} +13.0170 q^{94} +6.88805 q^{95} +50.9972 q^{96} +2.80427 q^{97} +14.1814 q^{98} -3.48518 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 361 q + 10 q^{2} + 23 q^{3} + 414 q^{4} + 21 q^{5} + 49 q^{6} + 106 q^{7} + 30 q^{8} + 406 q^{9} + 65 q^{10} + 33 q^{11} + 52 q^{12} + 89 q^{13} + 32 q^{14} + 55 q^{15} + 512 q^{16} + 42 q^{17} + 34 q^{18} + 191 q^{19} + 48 q^{20} + 53 q^{21} + 61 q^{22} + 52 q^{23} + 139 q^{24} + 458 q^{25} + 57 q^{26} + 80 q^{27} + 194 q^{28} + 47 q^{29} + 32 q^{30} + 254 q^{31} + 55 q^{32} + 40 q^{33} + 122 q^{34} + 93 q^{35} + 519 q^{36} + 43 q^{37} + 25 q^{38} + 210 q^{39} + 184 q^{40} + 54 q^{41} + 48 q^{42} + 151 q^{43} + 56 q^{44} + 82 q^{45} + 101 q^{46} + 117 q^{47} + 77 q^{48} + 563 q^{49} + 38 q^{50} + 143 q^{51} + 241 q^{52} + 14 q^{53} + 164 q^{54} + 452 q^{55} + 52 q^{56} + 21 q^{57} + 55 q^{58} + 125 q^{59} + 39 q^{60} + 227 q^{61} + 58 q^{62} + 292 q^{63} + 710 q^{64} + 15 q^{65} + 105 q^{66} + 120 q^{67} + 125 q^{68} + 136 q^{69} + 88 q^{70} + 105 q^{71} + 78 q^{72} + 108 q^{73} + 41 q^{74} + 128 q^{75} + 461 q^{76} + 28 q^{77} + 13 q^{78} + 400 q^{79} + 59 q^{80} + 485 q^{81} + 175 q^{82} + 97 q^{83} + 76 q^{84} + 144 q^{85} - 14 q^{86} + 327 q^{87} + 145 q^{88} + 52 q^{89} + 60 q^{90} + 192 q^{91} + 11 q^{92} + 32 q^{93} + 366 q^{94} + 182 q^{95} + 275 q^{96} + 117 q^{97} + 42 q^{98} + 111 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71747 −1.92154 −0.960769 0.277350i \(-0.910544\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(3\) −2.51708 −1.45324 −0.726620 0.687040i \(-0.758910\pi\)
−0.726620 + 0.687040i \(0.758910\pi\)
\(4\) 5.38462 2.69231
\(5\) −3.75245 −1.67815 −0.839074 0.544017i \(-0.816903\pi\)
−0.839074 + 0.544017i \(0.816903\pi\)
\(6\) 6.84009 2.79245
\(7\) −1.33469 −0.504466 −0.252233 0.967667i \(-0.581165\pi\)
−0.252233 + 0.967667i \(0.581165\pi\)
\(8\) −9.19758 −3.25183
\(9\) 3.33572 1.11191
\(10\) 10.1972 3.22463
\(11\) −1.04481 −0.315021 −0.157511 0.987517i \(-0.550347\pi\)
−0.157511 + 0.987517i \(0.550347\pi\)
\(12\) −13.5535 −3.91257
\(13\) −5.94502 −1.64885 −0.824427 0.565969i \(-0.808502\pi\)
−0.824427 + 0.565969i \(0.808502\pi\)
\(14\) 3.62698 0.969350
\(15\) 9.44524 2.43875
\(16\) 14.2249 3.55621
\(17\) −2.54378 −0.616958 −0.308479 0.951231i \(-0.599820\pi\)
−0.308479 + 0.951231i \(0.599820\pi\)
\(18\) −9.06469 −2.13657
\(19\) −1.83561 −0.421118 −0.210559 0.977581i \(-0.567528\pi\)
−0.210559 + 0.977581i \(0.567528\pi\)
\(20\) −20.2055 −4.51809
\(21\) 3.35953 0.733110
\(22\) 2.83923 0.605325
\(23\) 3.09202 0.644730 0.322365 0.946615i \(-0.395522\pi\)
0.322365 + 0.946615i \(0.395522\pi\)
\(24\) 23.1511 4.72569
\(25\) 9.08091 1.81618
\(26\) 16.1554 3.16833
\(27\) −0.845024 −0.162625
\(28\) −7.18680 −1.35818
\(29\) 0.322861 0.0599538 0.0299769 0.999551i \(-0.490457\pi\)
0.0299769 + 0.999551i \(0.490457\pi\)
\(30\) −25.6671 −4.68615
\(31\) 9.30447 1.67113 0.835566 0.549390i \(-0.185140\pi\)
0.835566 + 0.549390i \(0.185140\pi\)
\(32\) −20.2604 −3.58157
\(33\) 2.62987 0.457801
\(34\) 6.91264 1.18551
\(35\) 5.00837 0.846569
\(36\) 17.9615 2.99359
\(37\) −2.56474 −0.421641 −0.210820 0.977525i \(-0.567613\pi\)
−0.210820 + 0.977525i \(0.567613\pi\)
\(38\) 4.98821 0.809194
\(39\) 14.9641 2.39618
\(40\) 34.5135 5.45706
\(41\) 5.41955 0.846392 0.423196 0.906038i \(-0.360908\pi\)
0.423196 + 0.906038i \(0.360908\pi\)
\(42\) −9.12941 −1.40870
\(43\) 1.76199 0.268700 0.134350 0.990934i \(-0.457105\pi\)
0.134350 + 0.990934i \(0.457105\pi\)
\(44\) −5.62589 −0.848134
\(45\) −12.5171 −1.86594
\(46\) −8.40245 −1.23887
\(47\) −4.79012 −0.698711 −0.349355 0.936990i \(-0.613599\pi\)
−0.349355 + 0.936990i \(0.613599\pi\)
\(48\) −35.8052 −5.16803
\(49\) −5.21860 −0.745514
\(50\) −24.6771 −3.48986
\(51\) 6.40292 0.896588
\(52\) −32.0117 −4.43922
\(53\) −9.23591 −1.26865 −0.634325 0.773066i \(-0.718722\pi\)
−0.634325 + 0.773066i \(0.718722\pi\)
\(54\) 2.29632 0.312490
\(55\) 3.92059 0.528652
\(56\) 12.2759 1.64044
\(57\) 4.62039 0.611985
\(58\) −0.877363 −0.115203
\(59\) −11.5247 −1.50039 −0.750196 0.661215i \(-0.770041\pi\)
−0.750196 + 0.661215i \(0.770041\pi\)
\(60\) 50.8590 6.56587
\(61\) 4.80873 0.615695 0.307847 0.951436i \(-0.400391\pi\)
0.307847 + 0.951436i \(0.400391\pi\)
\(62\) −25.2846 −3.21114
\(63\) −4.45215 −0.560918
\(64\) 26.6072 3.32590
\(65\) 22.3084 2.76702
\(66\) −7.14658 −0.879683
\(67\) −9.76767 −1.19331 −0.596655 0.802498i \(-0.703504\pi\)
−0.596655 + 0.802498i \(0.703504\pi\)
\(68\) −13.6973 −1.66104
\(69\) −7.78287 −0.936947
\(70\) −13.6101 −1.62671
\(71\) −4.53332 −0.538006 −0.269003 0.963139i \(-0.586694\pi\)
−0.269003 + 0.963139i \(0.586694\pi\)
\(72\) −30.6805 −3.61573
\(73\) 12.5354 1.46716 0.733578 0.679606i \(-0.237849\pi\)
0.733578 + 0.679606i \(0.237849\pi\)
\(74\) 6.96959 0.810198
\(75\) −22.8574 −2.63935
\(76\) −9.88406 −1.13378
\(77\) 1.39450 0.158917
\(78\) −40.6645 −4.60435
\(79\) 5.29492 0.595725 0.297863 0.954609i \(-0.403726\pi\)
0.297863 + 0.954609i \(0.403726\pi\)
\(80\) −53.3781 −5.96786
\(81\) −7.88015 −0.875572
\(82\) −14.7274 −1.62637
\(83\) 4.14711 0.455205 0.227602 0.973754i \(-0.426911\pi\)
0.227602 + 0.973754i \(0.426911\pi\)
\(84\) 18.0898 1.97376
\(85\) 9.54543 1.03535
\(86\) −4.78813 −0.516318
\(87\) −0.812668 −0.0871272
\(88\) 9.60970 1.02440
\(89\) −0.157865 −0.0167336 −0.00836682 0.999965i \(-0.502663\pi\)
−0.00836682 + 0.999965i \(0.502663\pi\)
\(90\) 34.0148 3.58548
\(91\) 7.93477 0.831790
\(92\) 16.6493 1.73581
\(93\) −23.4201 −2.42856
\(94\) 13.0170 1.34260
\(95\) 6.88805 0.706699
\(96\) 50.9972 5.20488
\(97\) 2.80427 0.284731 0.142365 0.989814i \(-0.454529\pi\)
0.142365 + 0.989814i \(0.454529\pi\)
\(98\) 14.1814 1.43253
\(99\) −3.48518 −0.350274
\(100\) 48.8972 4.88972
\(101\) 2.05790 0.204769 0.102385 0.994745i \(-0.467353\pi\)
0.102385 + 0.994745i \(0.467353\pi\)
\(102\) −17.3997 −1.72283
\(103\) −0.579080 −0.0570585 −0.0285292 0.999593i \(-0.509082\pi\)
−0.0285292 + 0.999593i \(0.509082\pi\)
\(104\) 54.6798 5.36180
\(105\) −12.6065 −1.23027
\(106\) 25.0983 2.43776
\(107\) −9.05264 −0.875152 −0.437576 0.899182i \(-0.644163\pi\)
−0.437576 + 0.899182i \(0.644163\pi\)
\(108\) −4.55013 −0.437836
\(109\) 11.4149 1.09335 0.546675 0.837345i \(-0.315893\pi\)
0.546675 + 0.837345i \(0.315893\pi\)
\(110\) −10.6541 −1.01583
\(111\) 6.45567 0.612745
\(112\) −18.9858 −1.79399
\(113\) −4.52023 −0.425227 −0.212614 0.977136i \(-0.568198\pi\)
−0.212614 + 0.977136i \(0.568198\pi\)
\(114\) −12.5557 −1.17595
\(115\) −11.6026 −1.08195
\(116\) 1.73848 0.161414
\(117\) −19.8309 −1.83337
\(118\) 31.3181 2.88306
\(119\) 3.39517 0.311234
\(120\) −86.8734 −7.93042
\(121\) −9.90838 −0.900762
\(122\) −13.0676 −1.18308
\(123\) −13.6415 −1.23001
\(124\) 50.1010 4.49920
\(125\) −15.3134 −1.36967
\(126\) 12.0986 1.07783
\(127\) −2.16752 −0.192336 −0.0961680 0.995365i \(-0.530659\pi\)
−0.0961680 + 0.995365i \(0.530659\pi\)
\(128\) −31.7834 −2.80928
\(129\) −4.43507 −0.390486
\(130\) −60.6224 −5.31693
\(131\) −18.0575 −1.57769 −0.788845 0.614592i \(-0.789321\pi\)
−0.788845 + 0.614592i \(0.789321\pi\)
\(132\) 14.1608 1.23254
\(133\) 2.44997 0.212440
\(134\) 26.5433 2.29299
\(135\) 3.17091 0.272909
\(136\) 23.3966 2.00625
\(137\) 1.45768 0.124538 0.0622688 0.998059i \(-0.480166\pi\)
0.0622688 + 0.998059i \(0.480166\pi\)
\(138\) 21.1497 1.80038
\(139\) −2.89568 −0.245608 −0.122804 0.992431i \(-0.539189\pi\)
−0.122804 + 0.992431i \(0.539189\pi\)
\(140\) 26.9681 2.27922
\(141\) 12.0571 1.01539
\(142\) 12.3191 1.03380
\(143\) 6.21141 0.519424
\(144\) 47.4501 3.95417
\(145\) −1.21152 −0.100611
\(146\) −34.0645 −2.81920
\(147\) 13.1357 1.08341
\(148\) −13.8101 −1.13519
\(149\) −6.53258 −0.535170 −0.267585 0.963534i \(-0.586226\pi\)
−0.267585 + 0.963534i \(0.586226\pi\)
\(150\) 62.1142 5.07161
\(151\) −24.1860 −1.96823 −0.984116 0.177527i \(-0.943190\pi\)
−0.984116 + 0.177527i \(0.943190\pi\)
\(152\) 16.8832 1.36941
\(153\) −8.48534 −0.685999
\(154\) −3.78949 −0.305366
\(155\) −34.9146 −2.80441
\(156\) 80.5761 6.45125
\(157\) 24.3221 1.94112 0.970559 0.240862i \(-0.0774300\pi\)
0.970559 + 0.240862i \(0.0774300\pi\)
\(158\) −14.3888 −1.14471
\(159\) 23.2476 1.84365
\(160\) 76.0262 6.01040
\(161\) −4.12689 −0.325244
\(162\) 21.4140 1.68245
\(163\) −15.6945 −1.22929 −0.614646 0.788803i \(-0.710701\pi\)
−0.614646 + 0.788803i \(0.710701\pi\)
\(164\) 29.1822 2.27875
\(165\) −9.86846 −0.768259
\(166\) −11.2696 −0.874693
\(167\) −4.78679 −0.370413 −0.185206 0.982700i \(-0.559295\pi\)
−0.185206 + 0.982700i \(0.559295\pi\)
\(168\) −30.8995 −2.38395
\(169\) 22.3433 1.71872
\(170\) −25.9394 −1.98946
\(171\) −6.12308 −0.468243
\(172\) 9.48762 0.723424
\(173\) −0.113620 −0.00863837 −0.00431918 0.999991i \(-0.501375\pi\)
−0.00431918 + 0.999991i \(0.501375\pi\)
\(174\) 2.20840 0.167418
\(175\) −12.1202 −0.916202
\(176\) −14.8622 −1.12028
\(177\) 29.0087 2.18043
\(178\) 0.428992 0.0321543
\(179\) −12.5008 −0.934352 −0.467176 0.884164i \(-0.654729\pi\)
−0.467176 + 0.884164i \(0.654729\pi\)
\(180\) −67.3999 −5.02369
\(181\) −1.54703 −0.114990 −0.0574948 0.998346i \(-0.518311\pi\)
−0.0574948 + 0.998346i \(0.518311\pi\)
\(182\) −21.5625 −1.59832
\(183\) −12.1040 −0.894752
\(184\) −28.4391 −2.09655
\(185\) 9.62407 0.707575
\(186\) 63.6434 4.66656
\(187\) 2.65776 0.194355
\(188\) −25.7930 −1.88114
\(189\) 1.12785 0.0820387
\(190\) −18.7180 −1.35795
\(191\) −21.1353 −1.52929 −0.764647 0.644450i \(-0.777087\pi\)
−0.764647 + 0.644450i \(0.777087\pi\)
\(192\) −66.9726 −4.83333
\(193\) −14.1217 −1.01650 −0.508252 0.861208i \(-0.669708\pi\)
−0.508252 + 0.861208i \(0.669708\pi\)
\(194\) −7.62052 −0.547121
\(195\) −56.1522 −4.02114
\(196\) −28.1002 −2.00715
\(197\) −22.5828 −1.60896 −0.804478 0.593983i \(-0.797555\pi\)
−0.804478 + 0.593983i \(0.797555\pi\)
\(198\) 9.47086 0.673064
\(199\) 16.7991 1.19086 0.595429 0.803408i \(-0.296982\pi\)
0.595429 + 0.803408i \(0.296982\pi\)
\(200\) −83.5224 −5.90592
\(201\) 24.5861 1.73417
\(202\) −5.59228 −0.393472
\(203\) −0.430920 −0.0302446
\(204\) 34.4773 2.41389
\(205\) −20.3366 −1.42037
\(206\) 1.57363 0.109640
\(207\) 10.3141 0.716878
\(208\) −84.5671 −5.86368
\(209\) 1.91786 0.132661
\(210\) 34.2577 2.36400
\(211\) 7.05299 0.485548 0.242774 0.970083i \(-0.421943\pi\)
0.242774 + 0.970083i \(0.421943\pi\)
\(212\) −49.7319 −3.41560
\(213\) 11.4108 0.781852
\(214\) 24.6002 1.68164
\(215\) −6.61177 −0.450919
\(216\) 7.77217 0.528829
\(217\) −12.4186 −0.843029
\(218\) −31.0196 −2.10091
\(219\) −31.5526 −2.13213
\(220\) 21.1109 1.42330
\(221\) 15.1229 1.01727
\(222\) −17.5430 −1.17741
\(223\) −20.8463 −1.39597 −0.697986 0.716111i \(-0.745920\pi\)
−0.697986 + 0.716111i \(0.745920\pi\)
\(224\) 27.0414 1.80678
\(225\) 30.2913 2.01942
\(226\) 12.2836 0.817090
\(227\) 21.7550 1.44393 0.721966 0.691929i \(-0.243239\pi\)
0.721966 + 0.691929i \(0.243239\pi\)
\(228\) 24.8790 1.64765
\(229\) −0.668015 −0.0441437 −0.0220718 0.999756i \(-0.507026\pi\)
−0.0220718 + 0.999756i \(0.507026\pi\)
\(230\) 31.5298 2.07901
\(231\) −3.51006 −0.230945
\(232\) −2.96954 −0.194960
\(233\) 22.6038 1.48083 0.740413 0.672153i \(-0.234630\pi\)
0.740413 + 0.672153i \(0.234630\pi\)
\(234\) 53.8898 3.52289
\(235\) 17.9747 1.17254
\(236\) −62.0563 −4.03952
\(237\) −13.3278 −0.865731
\(238\) −9.22625 −0.598049
\(239\) −15.3190 −0.990905 −0.495453 0.868635i \(-0.664998\pi\)
−0.495453 + 0.868635i \(0.664998\pi\)
\(240\) 134.357 8.67272
\(241\) 11.8272 0.761857 0.380928 0.924605i \(-0.375604\pi\)
0.380928 + 0.924605i \(0.375604\pi\)
\(242\) 26.9257 1.73085
\(243\) 22.3701 1.43504
\(244\) 25.8932 1.65764
\(245\) 19.5826 1.25108
\(246\) 37.0702 2.36351
\(247\) 10.9128 0.694362
\(248\) −85.5786 −5.43425
\(249\) −10.4386 −0.661522
\(250\) 41.6137 2.63188
\(251\) −3.00126 −0.189438 −0.0947190 0.995504i \(-0.530195\pi\)
−0.0947190 + 0.995504i \(0.530195\pi\)
\(252\) −23.9731 −1.51016
\(253\) −3.23056 −0.203104
\(254\) 5.89015 0.369581
\(255\) −24.0267 −1.50461
\(256\) 33.1558 2.07224
\(257\) 2.91116 0.181593 0.0907965 0.995869i \(-0.471059\pi\)
0.0907965 + 0.995869i \(0.471059\pi\)
\(258\) 12.0521 0.750334
\(259\) 3.42314 0.212703
\(260\) 120.122 7.44967
\(261\) 1.07697 0.0666629
\(262\) 49.0706 3.03159
\(263\) 2.45269 0.151239 0.0756197 0.997137i \(-0.475907\pi\)
0.0756197 + 0.997137i \(0.475907\pi\)
\(264\) −24.1884 −1.48869
\(265\) 34.6573 2.12898
\(266\) −6.65772 −0.408211
\(267\) 0.397359 0.0243180
\(268\) −52.5951 −3.21276
\(269\) 26.1297 1.59316 0.796579 0.604535i \(-0.206641\pi\)
0.796579 + 0.604535i \(0.206641\pi\)
\(270\) −8.61684 −0.524404
\(271\) −18.1483 −1.10243 −0.551216 0.834362i \(-0.685836\pi\)
−0.551216 + 0.834362i \(0.685836\pi\)
\(272\) −36.1850 −2.19404
\(273\) −19.9725 −1.20879
\(274\) −3.96118 −0.239304
\(275\) −9.48780 −0.572136
\(276\) −41.9077 −2.52255
\(277\) −14.5571 −0.874649 −0.437324 0.899304i \(-0.644074\pi\)
−0.437324 + 0.899304i \(0.644074\pi\)
\(278\) 7.86890 0.471945
\(279\) 31.0371 1.85814
\(280\) −46.0648 −2.75290
\(281\) −33.3366 −1.98869 −0.994347 0.106177i \(-0.966139\pi\)
−0.994347 + 0.106177i \(0.966139\pi\)
\(282\) −32.7648 −1.95112
\(283\) −10.0408 −0.596862 −0.298431 0.954431i \(-0.596463\pi\)
−0.298431 + 0.954431i \(0.596463\pi\)
\(284\) −24.4102 −1.44848
\(285\) −17.3378 −1.02700
\(286\) −16.8793 −0.998093
\(287\) −7.23343 −0.426976
\(288\) −67.5829 −3.98236
\(289\) −10.5292 −0.619362
\(290\) 3.29227 0.193328
\(291\) −7.05859 −0.413782
\(292\) 67.4982 3.95003
\(293\) −26.3045 −1.53673 −0.768363 0.640014i \(-0.778929\pi\)
−0.768363 + 0.640014i \(0.778929\pi\)
\(294\) −35.6957 −2.08181
\(295\) 43.2460 2.51788
\(296\) 23.5894 1.37111
\(297\) 0.882887 0.0512303
\(298\) 17.7521 1.02835
\(299\) −18.3821 −1.06306
\(300\) −123.078 −7.10594
\(301\) −2.35171 −0.135550
\(302\) 65.7247 3.78203
\(303\) −5.17992 −0.297579
\(304\) −26.1113 −1.49759
\(305\) −18.0445 −1.03323
\(306\) 23.0586 1.31817
\(307\) −17.9933 −1.02693 −0.513465 0.858110i \(-0.671638\pi\)
−0.513465 + 0.858110i \(0.671638\pi\)
\(308\) 7.50882 0.427855
\(309\) 1.45759 0.0829196
\(310\) 94.8792 5.38878
\(311\) 2.59728 0.147278 0.0736391 0.997285i \(-0.476539\pi\)
0.0736391 + 0.997285i \(0.476539\pi\)
\(312\) −137.634 −7.79198
\(313\) −16.7931 −0.949201 −0.474601 0.880201i \(-0.657407\pi\)
−0.474601 + 0.880201i \(0.657407\pi\)
\(314\) −66.0946 −3.72993
\(315\) 16.7065 0.941304
\(316\) 28.5111 1.60388
\(317\) −31.7081 −1.78090 −0.890451 0.455078i \(-0.849611\pi\)
−0.890451 + 0.455078i \(0.849611\pi\)
\(318\) −63.1745 −3.54265
\(319\) −0.337328 −0.0188867
\(320\) −99.8424 −5.58136
\(321\) 22.7863 1.27180
\(322\) 11.2147 0.624969
\(323\) 4.66940 0.259812
\(324\) −42.4316 −2.35731
\(325\) −53.9862 −2.99462
\(326\) 42.6494 2.36213
\(327\) −28.7323 −1.58890
\(328\) −49.8468 −2.75233
\(329\) 6.39333 0.352476
\(330\) 26.8172 1.47624
\(331\) 8.76766 0.481914 0.240957 0.970536i \(-0.422539\pi\)
0.240957 + 0.970536i \(0.422539\pi\)
\(332\) 22.3306 1.22555
\(333\) −8.55524 −0.468824
\(334\) 13.0079 0.711762
\(335\) 36.6527 2.00255
\(336\) 47.7889 2.60710
\(337\) 31.7261 1.72823 0.864115 0.503295i \(-0.167879\pi\)
0.864115 + 0.503295i \(0.167879\pi\)
\(338\) −60.7172 −3.30258
\(339\) 11.3778 0.617957
\(340\) 51.3985 2.78747
\(341\) −9.72138 −0.526442
\(342\) 16.6392 0.899747
\(343\) 16.3081 0.880552
\(344\) −16.2060 −0.873769
\(345\) 29.2048 1.57234
\(346\) 0.308758 0.0165990
\(347\) −17.3318 −0.930420 −0.465210 0.885200i \(-0.654021\pi\)
−0.465210 + 0.885200i \(0.654021\pi\)
\(348\) −4.37591 −0.234573
\(349\) −13.8614 −0.741985 −0.370993 0.928636i \(-0.620983\pi\)
−0.370993 + 0.928636i \(0.620983\pi\)
\(350\) 32.9362 1.76052
\(351\) 5.02369 0.268145
\(352\) 21.1682 1.12827
\(353\) −8.40589 −0.447400 −0.223700 0.974658i \(-0.571814\pi\)
−0.223700 + 0.974658i \(0.571814\pi\)
\(354\) −78.8302 −4.18978
\(355\) 17.0111 0.902854
\(356\) −0.850042 −0.0450521
\(357\) −8.54592 −0.452298
\(358\) 33.9704 1.79539
\(359\) 17.8469 0.941921 0.470960 0.882154i \(-0.343907\pi\)
0.470960 + 0.882154i \(0.343907\pi\)
\(360\) 115.127 6.06773
\(361\) −15.6305 −0.822660
\(362\) 4.20399 0.220957
\(363\) 24.9402 1.30902
\(364\) 42.7257 2.23944
\(365\) −47.0384 −2.46210
\(366\) 32.8921 1.71930
\(367\) −0.474684 −0.0247783 −0.0123892 0.999923i \(-0.503944\pi\)
−0.0123892 + 0.999923i \(0.503944\pi\)
\(368\) 43.9835 2.29280
\(369\) 18.0781 0.941108
\(370\) −26.1531 −1.35963
\(371\) 12.3271 0.639991
\(372\) −126.108 −6.53842
\(373\) −15.3175 −0.793112 −0.396556 0.918011i \(-0.629795\pi\)
−0.396556 + 0.918011i \(0.629795\pi\)
\(374\) −7.22238 −0.373461
\(375\) 38.5452 1.99046
\(376\) 44.0575 2.27209
\(377\) −1.91942 −0.0988550
\(378\) −3.06488 −0.157640
\(379\) 7.47492 0.383961 0.191980 0.981399i \(-0.438509\pi\)
0.191980 + 0.981399i \(0.438509\pi\)
\(380\) 37.0895 1.90265
\(381\) 5.45582 0.279510
\(382\) 57.4343 2.93860
\(383\) −3.76601 −0.192434 −0.0962170 0.995360i \(-0.530674\pi\)
−0.0962170 + 0.995360i \(0.530674\pi\)
\(384\) 80.0015 4.08256
\(385\) −5.23278 −0.266687
\(386\) 38.3753 1.95325
\(387\) 5.87748 0.298769
\(388\) 15.0999 0.766583
\(389\) −10.3920 −0.526895 −0.263448 0.964674i \(-0.584860\pi\)
−0.263448 + 0.964674i \(0.584860\pi\)
\(390\) 152.592 7.72678
\(391\) −7.86542 −0.397771
\(392\) 47.9985 2.42429
\(393\) 45.4522 2.29276
\(394\) 61.3679 3.09167
\(395\) −19.8689 −0.999715
\(396\) −18.7664 −0.943045
\(397\) −27.8298 −1.39674 −0.698369 0.715738i \(-0.746091\pi\)
−0.698369 + 0.715738i \(0.746091\pi\)
\(398\) −45.6510 −2.28828
\(399\) −6.16679 −0.308726
\(400\) 129.175 6.45873
\(401\) −30.2231 −1.50927 −0.754635 0.656144i \(-0.772186\pi\)
−0.754635 + 0.656144i \(0.772186\pi\)
\(402\) −66.8117 −3.33227
\(403\) −55.3153 −2.75545
\(404\) 11.0810 0.551302
\(405\) 29.5699 1.46934
\(406\) 1.17101 0.0581162
\(407\) 2.67966 0.132826
\(408\) −58.8913 −2.91556
\(409\) −12.3463 −0.610486 −0.305243 0.952274i \(-0.598738\pi\)
−0.305243 + 0.952274i \(0.598738\pi\)
\(410\) 55.2641 2.72930
\(411\) −3.66909 −0.180983
\(412\) −3.11812 −0.153619
\(413\) 15.3820 0.756897
\(414\) −28.0282 −1.37751
\(415\) −15.5618 −0.763901
\(416\) 120.449 5.90548
\(417\) 7.28866 0.356927
\(418\) −5.21172 −0.254913
\(419\) −11.1549 −0.544952 −0.272476 0.962163i \(-0.587843\pi\)
−0.272476 + 0.962163i \(0.587843\pi\)
\(420\) −67.8811 −3.31226
\(421\) −26.2734 −1.28049 −0.640245 0.768171i \(-0.721167\pi\)
−0.640245 + 0.768171i \(0.721167\pi\)
\(422\) −19.1663 −0.932999
\(423\) −15.9785 −0.776900
\(424\) 84.9480 4.12544
\(425\) −23.0999 −1.12051
\(426\) −31.0083 −1.50236
\(427\) −6.41817 −0.310597
\(428\) −48.7450 −2.35618
\(429\) −15.6346 −0.754847
\(430\) 17.9673 0.866458
\(431\) −3.90288 −0.187995 −0.0939977 0.995572i \(-0.529965\pi\)
−0.0939977 + 0.995572i \(0.529965\pi\)
\(432\) −12.0203 −0.578329
\(433\) −18.4307 −0.885724 −0.442862 0.896590i \(-0.646037\pi\)
−0.442862 + 0.896590i \(0.646037\pi\)
\(434\) 33.7471 1.61991
\(435\) 3.04950 0.146212
\(436\) 61.4649 2.94364
\(437\) −5.67574 −0.271507
\(438\) 85.7431 4.09697
\(439\) −27.8073 −1.32717 −0.663585 0.748101i \(-0.730966\pi\)
−0.663585 + 0.748101i \(0.730966\pi\)
\(440\) −36.0599 −1.71909
\(441\) −17.4078 −0.828941
\(442\) −41.0958 −1.95473
\(443\) 16.6767 0.792334 0.396167 0.918178i \(-0.370340\pi\)
0.396167 + 0.918178i \(0.370340\pi\)
\(444\) 34.7613 1.64970
\(445\) 0.592381 0.0280815
\(446\) 56.6491 2.68241
\(447\) 16.4431 0.777730
\(448\) −35.5124 −1.67780
\(449\) 8.59046 0.405409 0.202704 0.979240i \(-0.435027\pi\)
0.202704 + 0.979240i \(0.435027\pi\)
\(450\) −82.3156 −3.88040
\(451\) −5.66239 −0.266631
\(452\) −24.3397 −1.14484
\(453\) 60.8783 2.86031
\(454\) −59.1185 −2.77457
\(455\) −29.7749 −1.39587
\(456\) −42.4964 −1.99008
\(457\) −11.9797 −0.560386 −0.280193 0.959944i \(-0.590398\pi\)
−0.280193 + 0.959944i \(0.590398\pi\)
\(458\) 1.81531 0.0848238
\(459\) 2.14956 0.100333
\(460\) −62.4758 −2.91295
\(461\) −12.3030 −0.573009 −0.286505 0.958079i \(-0.592493\pi\)
−0.286505 + 0.958079i \(0.592493\pi\)
\(462\) 9.53847 0.443770
\(463\) 11.4955 0.534240 0.267120 0.963663i \(-0.413928\pi\)
0.267120 + 0.963663i \(0.413928\pi\)
\(464\) 4.59265 0.213209
\(465\) 87.8830 4.07548
\(466\) −61.4251 −2.84546
\(467\) 14.3311 0.663165 0.331582 0.943426i \(-0.392417\pi\)
0.331582 + 0.943426i \(0.392417\pi\)
\(468\) −106.782 −4.93599
\(469\) 13.0368 0.601985
\(470\) −48.8456 −2.25308
\(471\) −61.2209 −2.82091
\(472\) 106.000 4.87903
\(473\) −1.84094 −0.0846463
\(474\) 36.2177 1.66354
\(475\) −16.6690 −0.764827
\(476\) 18.2817 0.837939
\(477\) −30.8084 −1.41062
\(478\) 41.6289 1.90406
\(479\) 24.9027 1.13783 0.568916 0.822396i \(-0.307363\pi\)
0.568916 + 0.822396i \(0.307363\pi\)
\(480\) −191.364 −8.73455
\(481\) 15.2474 0.695223
\(482\) −32.1400 −1.46394
\(483\) 10.3877 0.472658
\(484\) −53.3528 −2.42513
\(485\) −10.5229 −0.477821
\(486\) −60.7899 −2.75749
\(487\) 20.1953 0.915139 0.457569 0.889174i \(-0.348720\pi\)
0.457569 + 0.889174i \(0.348720\pi\)
\(488\) −44.2286 −2.00214
\(489\) 39.5045 1.78646
\(490\) −53.2149 −2.40400
\(491\) 32.1955 1.45296 0.726482 0.687185i \(-0.241154\pi\)
0.726482 + 0.687185i \(0.241154\pi\)
\(492\) −73.4541 −3.31157
\(493\) −0.821289 −0.0369890
\(494\) −29.6550 −1.33424
\(495\) 13.0780 0.587811
\(496\) 132.355 5.94291
\(497\) 6.05058 0.271406
\(498\) 28.3666 1.27114
\(499\) 7.65470 0.342671 0.171336 0.985213i \(-0.445192\pi\)
0.171336 + 0.985213i \(0.445192\pi\)
\(500\) −82.4569 −3.68758
\(501\) 12.0487 0.538298
\(502\) 8.15583 0.364012
\(503\) −30.1901 −1.34611 −0.673055 0.739593i \(-0.735018\pi\)
−0.673055 + 0.739593i \(0.735018\pi\)
\(504\) 40.9490 1.82401
\(505\) −7.72219 −0.343633
\(506\) 8.77894 0.390271
\(507\) −56.2400 −2.49771
\(508\) −11.6712 −0.517828
\(509\) −34.1259 −1.51261 −0.756303 0.654222i \(-0.772996\pi\)
−0.756303 + 0.654222i \(0.772996\pi\)
\(510\) 65.2916 2.89116
\(511\) −16.7309 −0.740130
\(512\) −26.5330 −1.17260
\(513\) 1.55113 0.0684843
\(514\) −7.91097 −0.348938
\(515\) 2.17297 0.0957526
\(516\) −23.8811 −1.05131
\(517\) 5.00475 0.220109
\(518\) −9.30225 −0.408717
\(519\) 0.285991 0.0125536
\(520\) −205.183 −8.99789
\(521\) −25.1286 −1.10091 −0.550453 0.834866i \(-0.685545\pi\)
−0.550453 + 0.834866i \(0.685545\pi\)
\(522\) −2.92663 −0.128095
\(523\) 21.5163 0.940841 0.470421 0.882442i \(-0.344102\pi\)
0.470421 + 0.882442i \(0.344102\pi\)
\(524\) −97.2327 −4.24763
\(525\) 30.5076 1.33146
\(526\) −6.66510 −0.290612
\(527\) −23.6686 −1.03102
\(528\) 37.4095 1.62804
\(529\) −13.4394 −0.584323
\(530\) −94.1801 −4.09092
\(531\) −38.4432 −1.66829
\(532\) 13.1922 0.571953
\(533\) −32.2194 −1.39558
\(534\) −1.07981 −0.0467280
\(535\) 33.9696 1.46863
\(536\) 89.8389 3.88045
\(537\) 31.4655 1.35784
\(538\) −71.0066 −3.06131
\(539\) 5.45243 0.234853
\(540\) 17.0741 0.734754
\(541\) −1.86994 −0.0803951 −0.0401975 0.999192i \(-0.512799\pi\)
−0.0401975 + 0.999192i \(0.512799\pi\)
\(542\) 49.3175 2.11837
\(543\) 3.89400 0.167108
\(544\) 51.5381 2.20968
\(545\) −42.8339 −1.83480
\(546\) 54.2746 2.32274
\(547\) 0.960869 0.0410838 0.0205419 0.999789i \(-0.493461\pi\)
0.0205419 + 0.999789i \(0.493461\pi\)
\(548\) 7.84902 0.335294
\(549\) 16.0405 0.684594
\(550\) 25.7828 1.09938
\(551\) −0.592647 −0.0252476
\(552\) 71.5835 3.04680
\(553\) −7.06708 −0.300523
\(554\) 39.5583 1.68067
\(555\) −24.2246 −1.02828
\(556\) −15.5921 −0.661252
\(557\) 15.1091 0.640192 0.320096 0.947385i \(-0.396285\pi\)
0.320096 + 0.947385i \(0.396285\pi\)
\(558\) −84.3421 −3.57049
\(559\) −10.4750 −0.443047
\(560\) 71.2433 3.01058
\(561\) −6.68982 −0.282444
\(562\) 90.5910 3.82135
\(563\) −35.0821 −1.47853 −0.739266 0.673413i \(-0.764828\pi\)
−0.739266 + 0.673413i \(0.764828\pi\)
\(564\) 64.9230 2.73375
\(565\) 16.9619 0.713594
\(566\) 27.2855 1.14689
\(567\) 10.5176 0.441696
\(568\) 41.6956 1.74951
\(569\) 20.7571 0.870181 0.435090 0.900387i \(-0.356716\pi\)
0.435090 + 0.900387i \(0.356716\pi\)
\(570\) 47.1148 1.97342
\(571\) −18.3475 −0.767818 −0.383909 0.923371i \(-0.625422\pi\)
−0.383909 + 0.923371i \(0.625422\pi\)
\(572\) 33.4460 1.39845
\(573\) 53.1992 2.22243
\(574\) 19.6566 0.820450
\(575\) 28.0783 1.17095
\(576\) 88.7541 3.69809
\(577\) −6.29193 −0.261937 −0.130968 0.991387i \(-0.541809\pi\)
−0.130968 + 0.991387i \(0.541809\pi\)
\(578\) 28.6126 1.19013
\(579\) 35.5456 1.47722
\(580\) −6.52357 −0.270877
\(581\) −5.53512 −0.229635
\(582\) 19.1815 0.795098
\(583\) 9.64975 0.399652
\(584\) −115.295 −4.77095
\(585\) 74.4146 3.07666
\(586\) 71.4816 2.95288
\(587\) −5.39298 −0.222592 −0.111296 0.993787i \(-0.535500\pi\)
−0.111296 + 0.993787i \(0.535500\pi\)
\(588\) 70.7305 2.91688
\(589\) −17.0794 −0.703744
\(590\) −117.520 −4.83820
\(591\) 56.8427 2.33820
\(592\) −36.4831 −1.49944
\(593\) 36.9276 1.51643 0.758217 0.652002i \(-0.226071\pi\)
0.758217 + 0.652002i \(0.226071\pi\)
\(594\) −2.39921 −0.0984410
\(595\) −12.7402 −0.522297
\(596\) −35.1754 −1.44084
\(597\) −42.2848 −1.73060
\(598\) 49.9527 2.04272
\(599\) 47.7380 1.95052 0.975262 0.221053i \(-0.0709493\pi\)
0.975262 + 0.221053i \(0.0709493\pi\)
\(600\) 210.233 8.58272
\(601\) 28.5087 1.16290 0.581448 0.813584i \(-0.302486\pi\)
0.581448 + 0.813584i \(0.302486\pi\)
\(602\) 6.39068 0.260465
\(603\) −32.5822 −1.32685
\(604\) −130.233 −5.29909
\(605\) 37.1807 1.51161
\(606\) 14.0763 0.571809
\(607\) −28.1427 −1.14228 −0.571139 0.820853i \(-0.693498\pi\)
−0.571139 + 0.820853i \(0.693498\pi\)
\(608\) 37.1902 1.50826
\(609\) 1.08466 0.0439527
\(610\) 49.0354 1.98538
\(611\) 28.4774 1.15207
\(612\) −45.6903 −1.84692
\(613\) 12.7874 0.516477 0.258238 0.966081i \(-0.416858\pi\)
0.258238 + 0.966081i \(0.416858\pi\)
\(614\) 48.8961 1.97329
\(615\) 51.1890 2.06414
\(616\) −12.8260 −0.516773
\(617\) −21.5598 −0.867966 −0.433983 0.900921i \(-0.642892\pi\)
−0.433983 + 0.900921i \(0.642892\pi\)
\(618\) −3.96096 −0.159333
\(619\) −32.7241 −1.31529 −0.657647 0.753326i \(-0.728448\pi\)
−0.657647 + 0.753326i \(0.728448\pi\)
\(620\) −188.002 −7.55033
\(621\) −2.61283 −0.104849
\(622\) −7.05801 −0.283000
\(623\) 0.210701 0.00844155
\(624\) 212.863 8.52133
\(625\) 12.0584 0.482334
\(626\) 45.6346 1.82393
\(627\) −4.82742 −0.192788
\(628\) 130.965 5.22609
\(629\) 6.52414 0.260135
\(630\) −45.3993 −1.80875
\(631\) 5.23767 0.208508 0.104254 0.994551i \(-0.466754\pi\)
0.104254 + 0.994551i \(0.466754\pi\)
\(632\) −48.7004 −1.93720
\(633\) −17.7530 −0.705618
\(634\) 86.1656 3.42207
\(635\) 8.13351 0.322768
\(636\) 125.179 4.96368
\(637\) 31.0247 1.22924
\(638\) 0.916676 0.0362915
\(639\) −15.1219 −0.598212
\(640\) 119.266 4.71439
\(641\) 12.2482 0.483774 0.241887 0.970304i \(-0.422234\pi\)
0.241887 + 0.970304i \(0.422234\pi\)
\(642\) −61.9209 −2.44382
\(643\) 20.3344 0.801910 0.400955 0.916098i \(-0.368678\pi\)
0.400955 + 0.916098i \(0.368678\pi\)
\(644\) −22.2217 −0.875658
\(645\) 16.6424 0.655293
\(646\) −12.6889 −0.499239
\(647\) 29.8406 1.17316 0.586578 0.809893i \(-0.300475\pi\)
0.586578 + 0.809893i \(0.300475\pi\)
\(648\) 72.4783 2.84722
\(649\) 12.0411 0.472655
\(650\) 146.706 5.75427
\(651\) 31.2587 1.22512
\(652\) −84.5091 −3.30963
\(653\) 31.1075 1.21733 0.608665 0.793427i \(-0.291705\pi\)
0.608665 + 0.793427i \(0.291705\pi\)
\(654\) 78.0790 3.05313
\(655\) 67.7599 2.64760
\(656\) 77.0924 3.00995
\(657\) 41.8145 1.63134
\(658\) −17.3736 −0.677295
\(659\) −43.7653 −1.70486 −0.852428 0.522845i \(-0.824871\pi\)
−0.852428 + 0.522845i \(0.824871\pi\)
\(660\) −53.1379 −2.06839
\(661\) 1.46110 0.0568300 0.0284150 0.999596i \(-0.490954\pi\)
0.0284150 + 0.999596i \(0.490954\pi\)
\(662\) −23.8258 −0.926016
\(663\) −38.0655 −1.47834
\(664\) −38.1434 −1.48025
\(665\) −9.19341 −0.356505
\(666\) 23.2486 0.900864
\(667\) 0.998291 0.0386540
\(668\) −25.7750 −0.997265
\(669\) 52.4719 2.02868
\(670\) −99.6025 −3.84798
\(671\) −5.02420 −0.193957
\(672\) −68.0655 −2.62568
\(673\) −28.5847 −1.10186 −0.550930 0.834551i \(-0.685727\pi\)
−0.550930 + 0.834551i \(0.685727\pi\)
\(674\) −86.2145 −3.32086
\(675\) −7.67358 −0.295356
\(676\) 120.310 4.62732
\(677\) 47.4088 1.82207 0.911035 0.412329i \(-0.135285\pi\)
0.911035 + 0.412329i \(0.135285\pi\)
\(678\) −30.9188 −1.18743
\(679\) −3.74284 −0.143637
\(680\) −87.7948 −3.36678
\(681\) −54.7592 −2.09838
\(682\) 26.4175 1.01158
\(683\) 13.2348 0.506415 0.253208 0.967412i \(-0.418514\pi\)
0.253208 + 0.967412i \(0.418514\pi\)
\(684\) −32.9704 −1.26066
\(685\) −5.46986 −0.208993
\(686\) −44.3166 −1.69201
\(687\) 1.68145 0.0641514
\(688\) 25.0640 0.955556
\(689\) 54.9077 2.09182
\(690\) −79.3631 −3.02130
\(691\) 47.5370 1.80839 0.904196 0.427118i \(-0.140471\pi\)
0.904196 + 0.427118i \(0.140471\pi\)
\(692\) −0.611800 −0.0232572
\(693\) 4.65164 0.176701
\(694\) 47.0986 1.78784
\(695\) 10.8659 0.412167
\(696\) 7.47458 0.283323
\(697\) −13.7862 −0.522189
\(698\) 37.6680 1.42575
\(699\) −56.8957 −2.15199
\(700\) −65.2627 −2.46670
\(701\) −44.8623 −1.69443 −0.847213 0.531254i \(-0.821721\pi\)
−0.847213 + 0.531254i \(0.821721\pi\)
\(702\) −13.6517 −0.515250
\(703\) 4.70786 0.177560
\(704\) −27.7994 −1.04773
\(705\) −45.2438 −1.70398
\(706\) 22.8427 0.859696
\(707\) −2.74667 −0.103299
\(708\) 156.201 5.87039
\(709\) 8.09550 0.304033 0.152016 0.988378i \(-0.451423\pi\)
0.152016 + 0.988378i \(0.451423\pi\)
\(710\) −46.2270 −1.73487
\(711\) 17.6623 0.662390
\(712\) 1.45197 0.0544150
\(713\) 28.7696 1.07743
\(714\) 23.2232 0.869108
\(715\) −23.3080 −0.871670
\(716\) −67.3119 −2.51556
\(717\) 38.5593 1.44002
\(718\) −48.4982 −1.80994
\(719\) 31.1676 1.16236 0.581178 0.813776i \(-0.302592\pi\)
0.581178 + 0.813776i \(0.302592\pi\)
\(720\) −178.054 −6.63569
\(721\) 0.772893 0.0287840
\(722\) 42.4754 1.58077
\(723\) −29.7701 −1.10716
\(724\) −8.33015 −0.309588
\(725\) 2.93187 0.108887
\(726\) −67.7742 −2.51534
\(727\) 41.0518 1.52253 0.761264 0.648442i \(-0.224579\pi\)
0.761264 + 0.648442i \(0.224579\pi\)
\(728\) −72.9807 −2.70484
\(729\) −32.6669 −1.20989
\(730\) 127.825 4.73103
\(731\) −4.48211 −0.165777
\(732\) −65.1753 −2.40895
\(733\) 20.3056 0.750004 0.375002 0.927024i \(-0.377642\pi\)
0.375002 + 0.927024i \(0.377642\pi\)
\(734\) 1.28994 0.0476125
\(735\) −49.2909 −1.81812
\(736\) −62.6455 −2.30914
\(737\) 10.2053 0.375918
\(738\) −49.1266 −1.80837
\(739\) −1.64940 −0.0606743 −0.0303372 0.999540i \(-0.509658\pi\)
−0.0303372 + 0.999540i \(0.509658\pi\)
\(740\) 51.8219 1.90501
\(741\) −27.4683 −1.00907
\(742\) −33.4984 −1.22977
\(743\) 11.5753 0.424658 0.212329 0.977198i \(-0.431895\pi\)
0.212329 + 0.977198i \(0.431895\pi\)
\(744\) 215.409 7.89726
\(745\) 24.5132 0.898094
\(746\) 41.6249 1.52399
\(747\) 13.8336 0.506145
\(748\) 14.3110 0.523264
\(749\) 12.0825 0.441484
\(750\) −104.745 −3.82475
\(751\) −2.26450 −0.0826327 −0.0413164 0.999146i \(-0.513155\pi\)
−0.0413164 + 0.999146i \(0.513155\pi\)
\(752\) −68.1388 −2.48477
\(753\) 7.55444 0.275299
\(754\) 5.21595 0.189954
\(755\) 90.7570 3.30299
\(756\) 6.07302 0.220873
\(757\) −43.3662 −1.57617 −0.788086 0.615565i \(-0.788928\pi\)
−0.788086 + 0.615565i \(0.788928\pi\)
\(758\) −20.3128 −0.737796
\(759\) 8.13160 0.295158
\(760\) −63.3533 −2.29807
\(761\) 11.8292 0.428808 0.214404 0.976745i \(-0.431219\pi\)
0.214404 + 0.976745i \(0.431219\pi\)
\(762\) −14.8260 −0.537090
\(763\) −15.2354 −0.551558
\(764\) −113.805 −4.11733
\(765\) 31.8408 1.15121
\(766\) 10.2340 0.369769
\(767\) 68.5148 2.47393
\(768\) −83.4560 −3.01146
\(769\) 6.22058 0.224320 0.112160 0.993690i \(-0.464223\pi\)
0.112160 + 0.993690i \(0.464223\pi\)
\(770\) 14.2199 0.512449
\(771\) −7.32763 −0.263898
\(772\) −76.0401 −2.73674
\(773\) −2.38462 −0.0857690 −0.0428845 0.999080i \(-0.513655\pi\)
−0.0428845 + 0.999080i \(0.513655\pi\)
\(774\) −15.9719 −0.574096
\(775\) 84.4930 3.03508
\(776\) −25.7925 −0.925898
\(777\) −8.61632 −0.309109
\(778\) 28.2399 1.01245
\(779\) −9.94819 −0.356431
\(780\) −302.358 −10.8262
\(781\) 4.73645 0.169483
\(782\) 21.3740 0.764333
\(783\) −0.272825 −0.00974998
\(784\) −74.2338 −2.65121
\(785\) −91.2677 −3.25749
\(786\) −123.515 −4.40563
\(787\) −25.9313 −0.924352 −0.462176 0.886788i \(-0.652931\pi\)
−0.462176 + 0.886788i \(0.652931\pi\)
\(788\) −121.600 −4.33180
\(789\) −6.17363 −0.219787
\(790\) 53.9932 1.92099
\(791\) 6.03311 0.214513
\(792\) 32.0552 1.13903
\(793\) −28.5880 −1.01519
\(794\) 75.6266 2.68389
\(795\) −87.2355 −3.09392
\(796\) 90.4569 3.20616
\(797\) 10.2032 0.361416 0.180708 0.983537i \(-0.442161\pi\)
0.180708 + 0.983537i \(0.442161\pi\)
\(798\) 16.7580 0.593228
\(799\) 12.1850 0.431075
\(800\) −183.983 −6.50478
\(801\) −0.526592 −0.0186062
\(802\) 82.1303 2.90012
\(803\) −13.0971 −0.462185
\(804\) 132.386 4.66891
\(805\) 15.4860 0.545808
\(806\) 150.317 5.29471
\(807\) −65.7707 −2.31524
\(808\) −18.9277 −0.665875
\(809\) −33.3895 −1.17391 −0.586955 0.809619i \(-0.699674\pi\)
−0.586955 + 0.809619i \(0.699674\pi\)
\(810\) −80.3552 −2.82339
\(811\) −15.2417 −0.535207 −0.267603 0.963529i \(-0.586232\pi\)
−0.267603 + 0.963529i \(0.586232\pi\)
\(812\) −2.32034 −0.0814279
\(813\) 45.6809 1.60210
\(814\) −7.28188 −0.255230
\(815\) 58.8931 2.06293
\(816\) 91.0806 3.18846
\(817\) −3.23432 −0.113155
\(818\) 33.5507 1.17307
\(819\) 26.4681 0.924872
\(820\) −109.505 −3.82408
\(821\) −34.3763 −1.19974 −0.599871 0.800097i \(-0.704781\pi\)
−0.599871 + 0.800097i \(0.704781\pi\)
\(822\) 9.97063 0.347766
\(823\) −33.1032 −1.15390 −0.576952 0.816778i \(-0.695758\pi\)
−0.576952 + 0.816778i \(0.695758\pi\)
\(824\) 5.32613 0.185545
\(825\) 23.8816 0.831451
\(826\) −41.7999 −1.45441
\(827\) −46.3840 −1.61293 −0.806465 0.591282i \(-0.798622\pi\)
−0.806465 + 0.591282i \(0.798622\pi\)
\(828\) 55.5374 1.93006
\(829\) −40.3324 −1.40080 −0.700401 0.713749i \(-0.746996\pi\)
−0.700401 + 0.713749i \(0.746996\pi\)
\(830\) 42.2888 1.46786
\(831\) 36.6413 1.27107
\(832\) −158.181 −5.48393
\(833\) 13.2750 0.459951
\(834\) −19.8067 −0.685849
\(835\) 17.9622 0.621607
\(836\) 10.3269 0.357165
\(837\) −7.86250 −0.271768
\(838\) 30.3130 1.04715
\(839\) −27.1286 −0.936582 −0.468291 0.883574i \(-0.655130\pi\)
−0.468291 + 0.883574i \(0.655130\pi\)
\(840\) 115.949 4.00062
\(841\) −28.8958 −0.996406
\(842\) 71.3972 2.46051
\(843\) 83.9110 2.89005
\(844\) 37.9777 1.30724
\(845\) −83.8423 −2.88426
\(846\) 43.4209 1.49284
\(847\) 13.2246 0.454403
\(848\) −131.380 −4.51159
\(849\) 25.2735 0.867384
\(850\) 62.7731 2.15310
\(851\) −7.93022 −0.271844
\(852\) 61.4425 2.10499
\(853\) −23.8505 −0.816626 −0.408313 0.912842i \(-0.633883\pi\)
−0.408313 + 0.912842i \(0.633883\pi\)
\(854\) 17.4411 0.596824
\(855\) 22.9766 0.785782
\(856\) 83.2623 2.84585
\(857\) −12.3311 −0.421223 −0.210612 0.977570i \(-0.567546\pi\)
−0.210612 + 0.977570i \(0.567546\pi\)
\(858\) 42.4866 1.45047
\(859\) −0.0563227 −0.00192171 −0.000960854 1.00000i \(-0.500306\pi\)
−0.000960854 1.00000i \(0.500306\pi\)
\(860\) −35.6018 −1.21401
\(861\) 18.2072 0.620498
\(862\) 10.6060 0.361240
\(863\) 19.9725 0.679871 0.339935 0.940449i \(-0.389595\pi\)
0.339935 + 0.940449i \(0.389595\pi\)
\(864\) 17.1205 0.582452
\(865\) 0.426354 0.0144965
\(866\) 50.0848 1.70195
\(867\) 26.5028 0.900082
\(868\) −66.8694 −2.26969
\(869\) −5.53217 −0.187666
\(870\) −8.28691 −0.280953
\(871\) 58.0690 1.96759
\(872\) −104.990 −3.55539
\(873\) 9.35426 0.316594
\(874\) 15.4236 0.521712
\(875\) 20.4387 0.690954
\(876\) −169.899 −5.74035
\(877\) −4.42541 −0.149436 −0.0747178 0.997205i \(-0.523806\pi\)
−0.0747178 + 0.997205i \(0.523806\pi\)
\(878\) 75.5654 2.55021
\(879\) 66.2107 2.23323
\(880\) 55.7699 1.88000
\(881\) 4.27070 0.143884 0.0719418 0.997409i \(-0.477080\pi\)
0.0719418 + 0.997409i \(0.477080\pi\)
\(882\) 47.3050 1.59284
\(883\) −24.1680 −0.813319 −0.406659 0.913580i \(-0.633306\pi\)
−0.406659 + 0.913580i \(0.633306\pi\)
\(884\) 81.4308 2.73881
\(885\) −108.854 −3.65908
\(886\) −45.3184 −1.52250
\(887\) 28.6411 0.961675 0.480838 0.876810i \(-0.340333\pi\)
0.480838 + 0.876810i \(0.340333\pi\)
\(888\) −59.3765 −1.99254
\(889\) 2.89297 0.0970270
\(890\) −1.60977 −0.0539597
\(891\) 8.23324 0.275824
\(892\) −112.249 −3.75839
\(893\) 8.79279 0.294240
\(894\) −44.6834 −1.49444
\(895\) 46.9086 1.56798
\(896\) 42.4210 1.41719
\(897\) 46.2693 1.54489
\(898\) −23.3443 −0.779009
\(899\) 3.00405 0.100191
\(900\) 163.107 5.43691
\(901\) 23.4942 0.782704
\(902\) 15.3873 0.512343
\(903\) 5.91945 0.196987
\(904\) 41.5751 1.38277
\(905\) 5.80515 0.192970
\(906\) −165.435 −5.49620
\(907\) 7.73813 0.256940 0.128470 0.991713i \(-0.458993\pi\)
0.128470 + 0.991713i \(0.458993\pi\)
\(908\) 117.142 3.88751
\(909\) 6.86458 0.227684
\(910\) 80.9122 2.68221
\(911\) 12.2845 0.407004 0.203502 0.979075i \(-0.434768\pi\)
0.203502 + 0.979075i \(0.434768\pi\)
\(912\) 65.7244 2.17635
\(913\) −4.33293 −0.143399
\(914\) 32.5544 1.07680
\(915\) 45.4196 1.50153
\(916\) −3.59701 −0.118848
\(917\) 24.1012 0.795891
\(918\) −5.84135 −0.192793
\(919\) 21.8605 0.721112 0.360556 0.932738i \(-0.382587\pi\)
0.360556 + 0.932738i \(0.382587\pi\)
\(920\) 106.716 3.51833
\(921\) 45.2906 1.49238
\(922\) 33.4331 1.10106
\(923\) 26.9507 0.887093
\(924\) −18.9003 −0.621776
\(925\) −23.2902 −0.765776
\(926\) −31.2386 −1.02656
\(927\) −1.93165 −0.0634436
\(928\) −6.54129 −0.214729
\(929\) 16.1279 0.529140 0.264570 0.964367i \(-0.414770\pi\)
0.264570 + 0.964367i \(0.414770\pi\)
\(930\) −238.819 −7.83118
\(931\) 9.57932 0.313949
\(932\) 121.713 3.98684
\(933\) −6.53757 −0.214030
\(934\) −38.9443 −1.27430
\(935\) −9.97314 −0.326157
\(936\) 182.396 5.96181
\(937\) −15.7586 −0.514812 −0.257406 0.966303i \(-0.582868\pi\)
−0.257406 + 0.966303i \(0.582868\pi\)
\(938\) −35.4271 −1.15674
\(939\) 42.2696 1.37942
\(940\) 96.7869 3.15684
\(941\) 9.96310 0.324788 0.162394 0.986726i \(-0.448078\pi\)
0.162394 + 0.986726i \(0.448078\pi\)
\(942\) 166.366 5.42049
\(943\) 16.7573 0.545694
\(944\) −163.938 −5.33572
\(945\) −4.23219 −0.137673
\(946\) 5.00268 0.162651
\(947\) 32.5681 1.05832 0.529160 0.848522i \(-0.322507\pi\)
0.529160 + 0.848522i \(0.322507\pi\)
\(948\) −71.7649 −2.33082
\(949\) −74.5232 −2.41912
\(950\) 45.2975 1.46964
\(951\) 79.8119 2.58808
\(952\) −31.2273 −1.01208
\(953\) −35.9811 −1.16554 −0.582772 0.812636i \(-0.698032\pi\)
−0.582772 + 0.812636i \(0.698032\pi\)
\(954\) 83.7207 2.71056
\(955\) 79.3091 2.56638
\(956\) −82.4871 −2.66782
\(957\) 0.849082 0.0274469
\(958\) −67.6722 −2.18639
\(959\) −1.94555 −0.0628250
\(960\) 251.312 8.11105
\(961\) 55.5732 1.79268
\(962\) −41.4344 −1.33590
\(963\) −30.1970 −0.973085
\(964\) 63.6849 2.05115
\(965\) 52.9912 1.70585
\(966\) −28.2283 −0.908230
\(967\) 32.3913 1.04163 0.520817 0.853668i \(-0.325627\pi\)
0.520817 + 0.853668i \(0.325627\pi\)
\(968\) 91.1331 2.92913
\(969\) −11.7533 −0.377569
\(970\) 28.5956 0.918150
\(971\) 1.25162 0.0401665 0.0200833 0.999798i \(-0.493607\pi\)
0.0200833 + 0.999798i \(0.493607\pi\)
\(972\) 120.454 3.86357
\(973\) 3.86483 0.123901
\(974\) −54.8802 −1.75847
\(975\) 135.888 4.35190
\(976\) 68.4035 2.18954
\(977\) 47.0942 1.50668 0.753339 0.657632i \(-0.228442\pi\)
0.753339 + 0.657632i \(0.228442\pi\)
\(978\) −107.352 −3.43274
\(979\) 0.164938 0.00527146
\(980\) 105.445 3.36830
\(981\) 38.0769 1.21570
\(982\) −87.4903 −2.79193
\(983\) −57.0428 −1.81938 −0.909691 0.415286i \(-0.863681\pi\)
−0.909691 + 0.415286i \(0.863681\pi\)
\(984\) 125.468 3.99979
\(985\) 84.7408 2.70007
\(986\) 2.23182 0.0710757
\(987\) −16.0926 −0.512232
\(988\) 58.7610 1.86944
\(989\) 5.44809 0.173239
\(990\) −35.5389 −1.12950
\(991\) −5.08157 −0.161421 −0.0807106 0.996738i \(-0.525719\pi\)
−0.0807106 + 0.996738i \(0.525719\pi\)
\(992\) −188.512 −5.98527
\(993\) −22.0689 −0.700337
\(994\) −16.4422 −0.521516
\(995\) −63.0379 −1.99844
\(996\) −56.2080 −1.78102
\(997\) 27.9138 0.884038 0.442019 0.897006i \(-0.354262\pi\)
0.442019 + 0.897006i \(0.354262\pi\)
\(998\) −20.8014 −0.658456
\(999\) 2.16727 0.0685693
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 8009.2.a.b.1.9 361
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8009.2.a.b.1.9 361 1.1 even 1 trivial