Properties

Label 8015.2.a.n.1.4
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $0$
Dimension $68$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(68\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.55606 q^{2} -1.84104 q^{3} +4.53346 q^{4} -1.00000 q^{5} +4.70581 q^{6} +1.00000 q^{7} -6.47568 q^{8} +0.389420 q^{9} +O(q^{10})\) \(q-2.55606 q^{2} -1.84104 q^{3} +4.53346 q^{4} -1.00000 q^{5} +4.70581 q^{6} +1.00000 q^{7} -6.47568 q^{8} +0.389420 q^{9} +2.55606 q^{10} -0.567294 q^{11} -8.34627 q^{12} +4.04849 q^{13} -2.55606 q^{14} +1.84104 q^{15} +7.48532 q^{16} +1.83930 q^{17} -0.995381 q^{18} +0.790478 q^{19} -4.53346 q^{20} -1.84104 q^{21} +1.45004 q^{22} -7.12445 q^{23} +11.9220 q^{24} +1.00000 q^{25} -10.3482 q^{26} +4.80618 q^{27} +4.53346 q^{28} -2.27903 q^{29} -4.70581 q^{30} -2.80158 q^{31} -6.18160 q^{32} +1.04441 q^{33} -4.70137 q^{34} -1.00000 q^{35} +1.76542 q^{36} +2.22629 q^{37} -2.02051 q^{38} -7.45343 q^{39} +6.47568 q^{40} -8.92374 q^{41} +4.70581 q^{42} -0.544936 q^{43} -2.57180 q^{44} -0.389420 q^{45} +18.2105 q^{46} +9.40998 q^{47} -13.7808 q^{48} +1.00000 q^{49} -2.55606 q^{50} -3.38622 q^{51} +18.3537 q^{52} +3.72887 q^{53} -12.2849 q^{54} +0.567294 q^{55} -6.47568 q^{56} -1.45530 q^{57} +5.82535 q^{58} +3.90731 q^{59} +8.34627 q^{60} +5.06069 q^{61} +7.16102 q^{62} +0.389420 q^{63} +0.829915 q^{64} -4.04849 q^{65} -2.66958 q^{66} +11.6403 q^{67} +8.33839 q^{68} +13.1164 q^{69} +2.55606 q^{70} -11.2265 q^{71} -2.52175 q^{72} -0.355823 q^{73} -5.69053 q^{74} -1.84104 q^{75} +3.58360 q^{76} -0.567294 q^{77} +19.0514 q^{78} -3.57069 q^{79} -7.48532 q^{80} -10.0166 q^{81} +22.8097 q^{82} -4.12676 q^{83} -8.34627 q^{84} -1.83930 q^{85} +1.39289 q^{86} +4.19578 q^{87} +3.67361 q^{88} +1.38911 q^{89} +0.995381 q^{90} +4.04849 q^{91} -32.2984 q^{92} +5.15782 q^{93} -24.0525 q^{94} -0.790478 q^{95} +11.3806 q^{96} -7.76313 q^{97} -2.55606 q^{98} -0.220915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55606 −1.80741 −0.903705 0.428156i \(-0.859163\pi\)
−0.903705 + 0.428156i \(0.859163\pi\)
\(3\) −1.84104 −1.06292 −0.531462 0.847082i \(-0.678357\pi\)
−0.531462 + 0.847082i \(0.678357\pi\)
\(4\) 4.53346 2.26673
\(5\) −1.00000 −0.447214
\(6\) 4.70581 1.92114
\(7\) 1.00000 0.377964
\(8\) −6.47568 −2.28950
\(9\) 0.389420 0.129807
\(10\) 2.55606 0.808298
\(11\) −0.567294 −0.171046 −0.0855228 0.996336i \(-0.527256\pi\)
−0.0855228 + 0.996336i \(0.527256\pi\)
\(12\) −8.34627 −2.40936
\(13\) 4.04849 1.12285 0.561425 0.827528i \(-0.310253\pi\)
0.561425 + 0.827528i \(0.310253\pi\)
\(14\) −2.55606 −0.683137
\(15\) 1.84104 0.475354
\(16\) 7.48532 1.87133
\(17\) 1.83930 0.446096 0.223048 0.974807i \(-0.428399\pi\)
0.223048 + 0.974807i \(0.428399\pi\)
\(18\) −0.995381 −0.234613
\(19\) 0.790478 0.181348 0.0906741 0.995881i \(-0.471098\pi\)
0.0906741 + 0.995881i \(0.471098\pi\)
\(20\) −4.53346 −1.01371
\(21\) −1.84104 −0.401747
\(22\) 1.45004 0.309150
\(23\) −7.12445 −1.48555 −0.742775 0.669541i \(-0.766491\pi\)
−0.742775 + 0.669541i \(0.766491\pi\)
\(24\) 11.9220 2.43356
\(25\) 1.00000 0.200000
\(26\) −10.3482 −2.02945
\(27\) 4.80618 0.924949
\(28\) 4.53346 0.856743
\(29\) −2.27903 −0.423206 −0.211603 0.977356i \(-0.567868\pi\)
−0.211603 + 0.977356i \(0.567868\pi\)
\(30\) −4.70581 −0.859159
\(31\) −2.80158 −0.503179 −0.251590 0.967834i \(-0.580953\pi\)
−0.251590 + 0.967834i \(0.580953\pi\)
\(32\) −6.18160 −1.09276
\(33\) 1.04441 0.181808
\(34\) −4.70137 −0.806278
\(35\) −1.00000 −0.169031
\(36\) 1.76542 0.294236
\(37\) 2.22629 0.365999 0.183000 0.983113i \(-0.441419\pi\)
0.183000 + 0.983113i \(0.441419\pi\)
\(38\) −2.02051 −0.327770
\(39\) −7.45343 −1.19350
\(40\) 6.47568 1.02389
\(41\) −8.92374 −1.39365 −0.696827 0.717239i \(-0.745406\pi\)
−0.696827 + 0.717239i \(0.745406\pi\)
\(42\) 4.70581 0.726122
\(43\) −0.544936 −0.0831020 −0.0415510 0.999136i \(-0.513230\pi\)
−0.0415510 + 0.999136i \(0.513230\pi\)
\(44\) −2.57180 −0.387714
\(45\) −0.389420 −0.0580512
\(46\) 18.2105 2.68500
\(47\) 9.40998 1.37259 0.686293 0.727325i \(-0.259237\pi\)
0.686293 + 0.727325i \(0.259237\pi\)
\(48\) −13.7808 −1.98908
\(49\) 1.00000 0.142857
\(50\) −2.55606 −0.361482
\(51\) −3.38622 −0.474166
\(52\) 18.3537 2.54520
\(53\) 3.72887 0.512200 0.256100 0.966650i \(-0.417562\pi\)
0.256100 + 0.966650i \(0.417562\pi\)
\(54\) −12.2849 −1.67176
\(55\) 0.567294 0.0764939
\(56\) −6.47568 −0.865349
\(57\) −1.45530 −0.192759
\(58\) 5.82535 0.764906
\(59\) 3.90731 0.508688 0.254344 0.967114i \(-0.418140\pi\)
0.254344 + 0.967114i \(0.418140\pi\)
\(60\) 8.34627 1.07750
\(61\) 5.06069 0.647955 0.323978 0.946065i \(-0.394980\pi\)
0.323978 + 0.946065i \(0.394980\pi\)
\(62\) 7.16102 0.909451
\(63\) 0.389420 0.0490622
\(64\) 0.829915 0.103739
\(65\) −4.04849 −0.502154
\(66\) −2.66958 −0.328602
\(67\) 11.6403 1.42208 0.711042 0.703150i \(-0.248224\pi\)
0.711042 + 0.703150i \(0.248224\pi\)
\(68\) 8.33839 1.01118
\(69\) 13.1164 1.57903
\(70\) 2.55606 0.305508
\(71\) −11.2265 −1.33234 −0.666170 0.745800i \(-0.732067\pi\)
−0.666170 + 0.745800i \(0.732067\pi\)
\(72\) −2.52175 −0.297192
\(73\) −0.355823 −0.0416459 −0.0208229 0.999783i \(-0.506629\pi\)
−0.0208229 + 0.999783i \(0.506629\pi\)
\(74\) −5.69053 −0.661510
\(75\) −1.84104 −0.212585
\(76\) 3.58360 0.411067
\(77\) −0.567294 −0.0646492
\(78\) 19.0514 2.15715
\(79\) −3.57069 −0.401734 −0.200867 0.979619i \(-0.564376\pi\)
−0.200867 + 0.979619i \(0.564376\pi\)
\(80\) −7.48532 −0.836884
\(81\) −10.0166 −1.11296
\(82\) 22.8097 2.51890
\(83\) −4.12676 −0.452971 −0.226485 0.974015i \(-0.572724\pi\)
−0.226485 + 0.974015i \(0.572724\pi\)
\(84\) −8.34627 −0.910652
\(85\) −1.83930 −0.199500
\(86\) 1.39289 0.150199
\(87\) 4.19578 0.449835
\(88\) 3.67361 0.391609
\(89\) 1.38911 0.147245 0.0736225 0.997286i \(-0.476544\pi\)
0.0736225 + 0.997286i \(0.476544\pi\)
\(90\) 0.995381 0.104922
\(91\) 4.04849 0.424398
\(92\) −32.2984 −3.36734
\(93\) 5.15782 0.534841
\(94\) −24.0525 −2.48083
\(95\) −0.790478 −0.0811014
\(96\) 11.3806 1.16152
\(97\) −7.76313 −0.788227 −0.394113 0.919062i \(-0.628948\pi\)
−0.394113 + 0.919062i \(0.628948\pi\)
\(98\) −2.55606 −0.258201
\(99\) −0.220915 −0.0222028
\(100\) 4.53346 0.453346
\(101\) 3.15497 0.313931 0.156965 0.987604i \(-0.449829\pi\)
0.156965 + 0.987604i \(0.449829\pi\)
\(102\) 8.65539 0.857012
\(103\) 15.6616 1.54318 0.771590 0.636120i \(-0.219462\pi\)
0.771590 + 0.636120i \(0.219462\pi\)
\(104\) −26.2167 −2.57076
\(105\) 1.84104 0.179667
\(106\) −9.53123 −0.925755
\(107\) −18.2898 −1.76814 −0.884069 0.467357i \(-0.845206\pi\)
−0.884069 + 0.467357i \(0.845206\pi\)
\(108\) 21.7886 2.09661
\(109\) 0.854961 0.0818905 0.0409452 0.999161i \(-0.486963\pi\)
0.0409452 + 0.999161i \(0.486963\pi\)
\(110\) −1.45004 −0.138256
\(111\) −4.09868 −0.389029
\(112\) 7.48532 0.707296
\(113\) −4.05025 −0.381015 −0.190508 0.981686i \(-0.561013\pi\)
−0.190508 + 0.981686i \(0.561013\pi\)
\(114\) 3.71984 0.348395
\(115\) 7.12445 0.664358
\(116\) −10.3319 −0.959292
\(117\) 1.57656 0.145753
\(118\) −9.98733 −0.919408
\(119\) 1.83930 0.168608
\(120\) −11.9220 −1.08832
\(121\) −10.6782 −0.970743
\(122\) −12.9354 −1.17112
\(123\) 16.4289 1.48135
\(124\) −12.7009 −1.14057
\(125\) −1.00000 −0.0894427
\(126\) −0.995381 −0.0886756
\(127\) 14.9741 1.32873 0.664367 0.747406i \(-0.268701\pi\)
0.664367 + 0.747406i \(0.268701\pi\)
\(128\) 10.2419 0.905263
\(129\) 1.00325 0.0883310
\(130\) 10.3482 0.907598
\(131\) 17.4749 1.52679 0.763396 0.645931i \(-0.223531\pi\)
0.763396 + 0.645931i \(0.223531\pi\)
\(132\) 4.73479 0.412110
\(133\) 0.790478 0.0685432
\(134\) −29.7532 −2.57029
\(135\) −4.80618 −0.413650
\(136\) −11.9107 −1.02134
\(137\) 21.1392 1.80605 0.903023 0.429592i \(-0.141343\pi\)
0.903023 + 0.429592i \(0.141343\pi\)
\(138\) −33.5263 −2.85395
\(139\) −4.73876 −0.401936 −0.200968 0.979598i \(-0.564409\pi\)
−0.200968 + 0.979598i \(0.564409\pi\)
\(140\) −4.53346 −0.383147
\(141\) −17.3241 −1.45895
\(142\) 28.6956 2.40808
\(143\) −2.29669 −0.192059
\(144\) 2.91493 0.242911
\(145\) 2.27903 0.189263
\(146\) 0.909505 0.0752712
\(147\) −1.84104 −0.151846
\(148\) 10.0928 0.829621
\(149\) 6.35536 0.520651 0.260326 0.965521i \(-0.416170\pi\)
0.260326 + 0.965521i \(0.416170\pi\)
\(150\) 4.70581 0.384228
\(151\) −2.66624 −0.216975 −0.108488 0.994098i \(-0.534601\pi\)
−0.108488 + 0.994098i \(0.534601\pi\)
\(152\) −5.11888 −0.415196
\(153\) 0.716259 0.0579061
\(154\) 1.45004 0.116848
\(155\) 2.80158 0.225029
\(156\) −33.7898 −2.70535
\(157\) −9.48698 −0.757144 −0.378572 0.925572i \(-0.623585\pi\)
−0.378572 + 0.925572i \(0.623585\pi\)
\(158\) 9.12691 0.726098
\(159\) −6.86499 −0.544429
\(160\) 6.18160 0.488698
\(161\) −7.12445 −0.561485
\(162\) 25.6031 2.01157
\(163\) −1.16073 −0.0909154 −0.0454577 0.998966i \(-0.514475\pi\)
−0.0454577 + 0.998966i \(0.514475\pi\)
\(164\) −40.4554 −3.15904
\(165\) −1.04441 −0.0813072
\(166\) 10.5483 0.818704
\(167\) 2.56334 0.198357 0.0991786 0.995070i \(-0.468378\pi\)
0.0991786 + 0.995070i \(0.468378\pi\)
\(168\) 11.9220 0.919800
\(169\) 3.39031 0.260793
\(170\) 4.70137 0.360578
\(171\) 0.307828 0.0235402
\(172\) −2.47044 −0.188370
\(173\) 9.16971 0.697160 0.348580 0.937279i \(-0.386664\pi\)
0.348580 + 0.937279i \(0.386664\pi\)
\(174\) −10.7247 −0.813036
\(175\) 1.00000 0.0755929
\(176\) −4.24638 −0.320083
\(177\) −7.19351 −0.540697
\(178\) −3.55064 −0.266132
\(179\) 9.80832 0.733108 0.366554 0.930397i \(-0.380538\pi\)
0.366554 + 0.930397i \(0.380538\pi\)
\(180\) −1.76542 −0.131586
\(181\) 19.5104 1.45020 0.725099 0.688645i \(-0.241794\pi\)
0.725099 + 0.688645i \(0.241794\pi\)
\(182\) −10.3482 −0.767060
\(183\) −9.31692 −0.688727
\(184\) 46.1356 3.40116
\(185\) −2.22629 −0.163680
\(186\) −13.1837 −0.966676
\(187\) −1.04342 −0.0763028
\(188\) 42.6597 3.11128
\(189\) 4.80618 0.349598
\(190\) 2.02051 0.146583
\(191\) −10.1859 −0.737025 −0.368512 0.929623i \(-0.620133\pi\)
−0.368512 + 0.929623i \(0.620133\pi\)
\(192\) −1.52790 −0.110267
\(193\) 5.74266 0.413366 0.206683 0.978408i \(-0.433733\pi\)
0.206683 + 0.978408i \(0.433733\pi\)
\(194\) 19.8431 1.42465
\(195\) 7.45343 0.533751
\(196\) 4.53346 0.323818
\(197\) 2.26210 0.161168 0.0805838 0.996748i \(-0.474322\pi\)
0.0805838 + 0.996748i \(0.474322\pi\)
\(198\) 0.564674 0.0401296
\(199\) 15.3542 1.08843 0.544215 0.838946i \(-0.316828\pi\)
0.544215 + 0.838946i \(0.316828\pi\)
\(200\) −6.47568 −0.457899
\(201\) −21.4302 −1.51157
\(202\) −8.06429 −0.567402
\(203\) −2.27903 −0.159957
\(204\) −15.3513 −1.07481
\(205\) 8.92374 0.623261
\(206\) −40.0319 −2.78916
\(207\) −2.77440 −0.192834
\(208\) 30.3043 2.10122
\(209\) −0.448434 −0.0310188
\(210\) −4.70581 −0.324732
\(211\) −26.3258 −1.81234 −0.906171 0.422911i \(-0.861008\pi\)
−0.906171 + 0.422911i \(0.861008\pi\)
\(212\) 16.9047 1.16102
\(213\) 20.6684 1.41618
\(214\) 46.7498 3.19575
\(215\) 0.544936 0.0371643
\(216\) −31.1232 −2.11767
\(217\) −2.80158 −0.190184
\(218\) −2.18534 −0.148010
\(219\) 0.655083 0.0442664
\(220\) 2.57180 0.173391
\(221\) 7.44640 0.500899
\(222\) 10.4765 0.703135
\(223\) −24.3347 −1.62957 −0.814786 0.579762i \(-0.803146\pi\)
−0.814786 + 0.579762i \(0.803146\pi\)
\(224\) −6.18160 −0.413026
\(225\) 0.389420 0.0259613
\(226\) 10.3527 0.688651
\(227\) −14.5129 −0.963257 −0.481628 0.876376i \(-0.659954\pi\)
−0.481628 + 0.876376i \(0.659954\pi\)
\(228\) −6.59754 −0.436933
\(229\) −1.00000 −0.0660819
\(230\) −18.2105 −1.20077
\(231\) 1.04441 0.0687171
\(232\) 14.7583 0.968928
\(233\) 3.29021 0.215549 0.107774 0.994175i \(-0.465628\pi\)
0.107774 + 0.994175i \(0.465628\pi\)
\(234\) −4.02979 −0.263436
\(235\) −9.40998 −0.613839
\(236\) 17.7136 1.15306
\(237\) 6.57377 0.427012
\(238\) −4.70137 −0.304744
\(239\) −6.48818 −0.419685 −0.209843 0.977735i \(-0.567295\pi\)
−0.209843 + 0.977735i \(0.567295\pi\)
\(240\) 13.7808 0.889544
\(241\) 18.7577 1.20829 0.604145 0.796874i \(-0.293515\pi\)
0.604145 + 0.796874i \(0.293515\pi\)
\(242\) 27.2941 1.75453
\(243\) 4.02243 0.258039
\(244\) 22.9424 1.46874
\(245\) −1.00000 −0.0638877
\(246\) −41.9934 −2.67740
\(247\) 3.20025 0.203627
\(248\) 18.1421 1.15203
\(249\) 7.59752 0.481473
\(250\) 2.55606 0.161660
\(251\) −16.6237 −1.04928 −0.524638 0.851326i \(-0.675799\pi\)
−0.524638 + 0.851326i \(0.675799\pi\)
\(252\) 1.76542 0.111211
\(253\) 4.04166 0.254097
\(254\) −38.2747 −2.40157
\(255\) 3.38622 0.212053
\(256\) −27.8387 −1.73992
\(257\) −15.9989 −0.997982 −0.498991 0.866607i \(-0.666296\pi\)
−0.498991 + 0.866607i \(0.666296\pi\)
\(258\) −2.56436 −0.159650
\(259\) 2.22629 0.138335
\(260\) −18.3537 −1.13825
\(261\) −0.887499 −0.0549348
\(262\) −44.6670 −2.75954
\(263\) −4.17169 −0.257238 −0.128619 0.991694i \(-0.541054\pi\)
−0.128619 + 0.991694i \(0.541054\pi\)
\(264\) −6.76326 −0.416250
\(265\) −3.72887 −0.229063
\(266\) −2.02051 −0.123886
\(267\) −2.55740 −0.156510
\(268\) 52.7706 3.22348
\(269\) −0.916068 −0.0558537 −0.0279268 0.999610i \(-0.508891\pi\)
−0.0279268 + 0.999610i \(0.508891\pi\)
\(270\) 12.2849 0.747635
\(271\) −16.2100 −0.984689 −0.492345 0.870400i \(-0.663860\pi\)
−0.492345 + 0.870400i \(0.663860\pi\)
\(272\) 13.7678 0.834793
\(273\) −7.45343 −0.451102
\(274\) −54.0332 −3.26426
\(275\) −0.567294 −0.0342091
\(276\) 59.4626 3.57923
\(277\) 27.4953 1.65203 0.826017 0.563645i \(-0.190601\pi\)
0.826017 + 0.563645i \(0.190601\pi\)
\(278\) 12.1126 0.726463
\(279\) −1.09099 −0.0653159
\(280\) 6.47568 0.386996
\(281\) −1.38095 −0.0823803 −0.0411901 0.999151i \(-0.513115\pi\)
−0.0411901 + 0.999151i \(0.513115\pi\)
\(282\) 44.2816 2.63693
\(283\) −19.5361 −1.16130 −0.580649 0.814154i \(-0.697201\pi\)
−0.580649 + 0.814154i \(0.697201\pi\)
\(284\) −50.8948 −3.02005
\(285\) 1.45530 0.0862045
\(286\) 5.87048 0.347129
\(287\) −8.92374 −0.526752
\(288\) −2.40724 −0.141848
\(289\) −13.6170 −0.800998
\(290\) −5.82535 −0.342076
\(291\) 14.2922 0.837825
\(292\) −1.61311 −0.0943999
\(293\) 14.9484 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(294\) 4.70581 0.274448
\(295\) −3.90731 −0.227492
\(296\) −14.4167 −0.837954
\(297\) −2.72652 −0.158209
\(298\) −16.2447 −0.941030
\(299\) −28.8433 −1.66805
\(300\) −8.34627 −0.481872
\(301\) −0.544936 −0.0314096
\(302\) 6.81507 0.392163
\(303\) −5.80841 −0.333685
\(304\) 5.91698 0.339362
\(305\) −5.06069 −0.289774
\(306\) −1.83080 −0.104660
\(307\) −13.8028 −0.787769 −0.393884 0.919160i \(-0.628869\pi\)
−0.393884 + 0.919160i \(0.628869\pi\)
\(308\) −2.57180 −0.146542
\(309\) −28.8335 −1.64028
\(310\) −7.16102 −0.406719
\(311\) −6.52286 −0.369877 −0.184939 0.982750i \(-0.559209\pi\)
−0.184939 + 0.982750i \(0.559209\pi\)
\(312\) 48.2660 2.73252
\(313\) 4.05327 0.229104 0.114552 0.993417i \(-0.463457\pi\)
0.114552 + 0.993417i \(0.463457\pi\)
\(314\) 24.2493 1.36847
\(315\) −0.389420 −0.0219413
\(316\) −16.1876 −0.910622
\(317\) −33.6907 −1.89226 −0.946130 0.323786i \(-0.895044\pi\)
−0.946130 + 0.323786i \(0.895044\pi\)
\(318\) 17.5474 0.984007
\(319\) 1.29288 0.0723875
\(320\) −0.829915 −0.0463937
\(321\) 33.6721 1.87939
\(322\) 18.2105 1.01483
\(323\) 1.45393 0.0808987
\(324\) −45.4099 −2.52277
\(325\) 4.04849 0.224570
\(326\) 2.96690 0.164321
\(327\) −1.57402 −0.0870433
\(328\) 57.7873 3.19077
\(329\) 9.40998 0.518789
\(330\) 2.66958 0.146955
\(331\) −8.29438 −0.455901 −0.227950 0.973673i \(-0.573202\pi\)
−0.227950 + 0.973673i \(0.573202\pi\)
\(332\) −18.7085 −1.02676
\(333\) 0.866959 0.0475091
\(334\) −6.55206 −0.358513
\(335\) −11.6403 −0.635975
\(336\) −13.7808 −0.751802
\(337\) 13.8524 0.754589 0.377295 0.926093i \(-0.376854\pi\)
0.377295 + 0.926093i \(0.376854\pi\)
\(338\) −8.66583 −0.471359
\(339\) 7.45666 0.404990
\(340\) −8.33839 −0.452213
\(341\) 1.58932 0.0860666
\(342\) −0.786827 −0.0425467
\(343\) 1.00000 0.0539949
\(344\) 3.52883 0.190262
\(345\) −13.1164 −0.706162
\(346\) −23.4384 −1.26005
\(347\) −22.8403 −1.22613 −0.613065 0.790033i \(-0.710064\pi\)
−0.613065 + 0.790033i \(0.710064\pi\)
\(348\) 19.0214 1.01965
\(349\) 1.02053 0.0546277 0.0273139 0.999627i \(-0.491305\pi\)
0.0273139 + 0.999627i \(0.491305\pi\)
\(350\) −2.55606 −0.136627
\(351\) 19.4578 1.03858
\(352\) 3.50679 0.186912
\(353\) 18.8129 1.00131 0.500655 0.865647i \(-0.333092\pi\)
0.500655 + 0.865647i \(0.333092\pi\)
\(354\) 18.3871 0.977261
\(355\) 11.2265 0.595840
\(356\) 6.29745 0.333764
\(357\) −3.38622 −0.179218
\(358\) −25.0707 −1.32503
\(359\) −12.6213 −0.666128 −0.333064 0.942904i \(-0.608083\pi\)
−0.333064 + 0.942904i \(0.608083\pi\)
\(360\) 2.52175 0.132908
\(361\) −18.3751 −0.967113
\(362\) −49.8698 −2.62110
\(363\) 19.6589 1.03183
\(364\) 18.3537 0.961994
\(365\) 0.355823 0.0186246
\(366\) 23.8146 1.24481
\(367\) 19.8872 1.03811 0.519053 0.854742i \(-0.326285\pi\)
0.519053 + 0.854742i \(0.326285\pi\)
\(368\) −53.3288 −2.77996
\(369\) −3.47508 −0.180905
\(370\) 5.69053 0.295836
\(371\) 3.72887 0.193593
\(372\) 23.3828 1.21234
\(373\) 25.4873 1.31968 0.659841 0.751405i \(-0.270624\pi\)
0.659841 + 0.751405i \(0.270624\pi\)
\(374\) 2.66706 0.137910
\(375\) 1.84104 0.0950708
\(376\) −60.9360 −3.14253
\(377\) −9.22665 −0.475196
\(378\) −12.2849 −0.631867
\(379\) 22.4839 1.15492 0.577459 0.816420i \(-0.304044\pi\)
0.577459 + 0.816420i \(0.304044\pi\)
\(380\) −3.58360 −0.183835
\(381\) −27.5678 −1.41234
\(382\) 26.0358 1.33211
\(383\) −29.9092 −1.52829 −0.764143 0.645047i \(-0.776838\pi\)
−0.764143 + 0.645047i \(0.776838\pi\)
\(384\) −18.8557 −0.962226
\(385\) 0.567294 0.0289120
\(386\) −14.6786 −0.747122
\(387\) −0.212209 −0.0107872
\(388\) −35.1938 −1.78670
\(389\) −2.98528 −0.151359 −0.0756797 0.997132i \(-0.524113\pi\)
−0.0756797 + 0.997132i \(0.524113\pi\)
\(390\) −19.0514 −0.964707
\(391\) −13.1040 −0.662698
\(392\) −6.47568 −0.327071
\(393\) −32.1720 −1.62286
\(394\) −5.78206 −0.291296
\(395\) 3.57069 0.179661
\(396\) −1.00151 −0.0503278
\(397\) −13.2617 −0.665588 −0.332794 0.943000i \(-0.607991\pi\)
−0.332794 + 0.943000i \(0.607991\pi\)
\(398\) −39.2463 −1.96724
\(399\) −1.45530 −0.0728561
\(400\) 7.48532 0.374266
\(401\) 35.8131 1.78842 0.894210 0.447648i \(-0.147738\pi\)
0.894210 + 0.447648i \(0.147738\pi\)
\(402\) 54.7768 2.73202
\(403\) −11.3422 −0.564995
\(404\) 14.3029 0.711596
\(405\) 10.0166 0.497729
\(406\) 5.82535 0.289107
\(407\) −1.26296 −0.0626026
\(408\) 21.9281 1.08560
\(409\) −24.3179 −1.20244 −0.601221 0.799083i \(-0.705319\pi\)
−0.601221 + 0.799083i \(0.705319\pi\)
\(410\) −22.8097 −1.12649
\(411\) −38.9181 −1.91969
\(412\) 71.0010 3.49797
\(413\) 3.90731 0.192266
\(414\) 7.09154 0.348530
\(415\) 4.12676 0.202575
\(416\) −25.0262 −1.22701
\(417\) 8.72423 0.427227
\(418\) 1.14622 0.0560637
\(419\) 32.2172 1.57391 0.786956 0.617009i \(-0.211656\pi\)
0.786956 + 0.617009i \(0.211656\pi\)
\(420\) 8.34627 0.407256
\(421\) −5.99256 −0.292059 −0.146030 0.989280i \(-0.546649\pi\)
−0.146030 + 0.989280i \(0.546649\pi\)
\(422\) 67.2904 3.27564
\(423\) 3.66443 0.178171
\(424\) −24.1470 −1.17268
\(425\) 1.83930 0.0892192
\(426\) −52.8297 −2.55961
\(427\) 5.06069 0.244904
\(428\) −82.9158 −4.00789
\(429\) 4.22829 0.204144
\(430\) −1.39289 −0.0671712
\(431\) 21.6186 1.04133 0.520666 0.853761i \(-0.325684\pi\)
0.520666 + 0.853761i \(0.325684\pi\)
\(432\) 35.9758 1.73089
\(433\) −0.859051 −0.0412833 −0.0206417 0.999787i \(-0.506571\pi\)
−0.0206417 + 0.999787i \(0.506571\pi\)
\(434\) 7.16102 0.343740
\(435\) −4.19578 −0.201172
\(436\) 3.87593 0.185623
\(437\) −5.63172 −0.269402
\(438\) −1.67443 −0.0800075
\(439\) −14.4393 −0.689150 −0.344575 0.938759i \(-0.611977\pi\)
−0.344575 + 0.938759i \(0.611977\pi\)
\(440\) −3.67361 −0.175133
\(441\) 0.389420 0.0185438
\(442\) −19.0335 −0.905329
\(443\) 21.6964 1.03083 0.515413 0.856942i \(-0.327638\pi\)
0.515413 + 0.856942i \(0.327638\pi\)
\(444\) −18.5812 −0.881824
\(445\) −1.38911 −0.0658500
\(446\) 62.2010 2.94530
\(447\) −11.7005 −0.553413
\(448\) 0.829915 0.0392098
\(449\) −32.6633 −1.54148 −0.770738 0.637152i \(-0.780112\pi\)
−0.770738 + 0.637152i \(0.780112\pi\)
\(450\) −0.995381 −0.0469227
\(451\) 5.06239 0.238379
\(452\) −18.3616 −0.863659
\(453\) 4.90864 0.230628
\(454\) 37.0959 1.74100
\(455\) −4.04849 −0.189796
\(456\) 9.42405 0.441322
\(457\) −25.6527 −1.19998 −0.599991 0.800007i \(-0.704829\pi\)
−0.599991 + 0.800007i \(0.704829\pi\)
\(458\) 2.55606 0.119437
\(459\) 8.84000 0.412616
\(460\) 32.2984 1.50592
\(461\) −5.55334 −0.258645 −0.129323 0.991603i \(-0.541280\pi\)
−0.129323 + 0.991603i \(0.541280\pi\)
\(462\) −2.66958 −0.124200
\(463\) −11.6362 −0.540779 −0.270390 0.962751i \(-0.587153\pi\)
−0.270390 + 0.962751i \(0.587153\pi\)
\(464\) −17.0593 −0.791957
\(465\) −5.15782 −0.239188
\(466\) −8.40998 −0.389585
\(467\) −8.08131 −0.373959 −0.186979 0.982364i \(-0.559870\pi\)
−0.186979 + 0.982364i \(0.559870\pi\)
\(468\) 7.14728 0.330383
\(469\) 11.6403 0.537497
\(470\) 24.0525 1.10946
\(471\) 17.4659 0.804786
\(472\) −25.3025 −1.16464
\(473\) 0.309139 0.0142142
\(474\) −16.8030 −0.771786
\(475\) 0.790478 0.0362696
\(476\) 8.33839 0.382189
\(477\) 1.45210 0.0664869
\(478\) 16.5842 0.758543
\(479\) −17.6516 −0.806522 −0.403261 0.915085i \(-0.632123\pi\)
−0.403261 + 0.915085i \(0.632123\pi\)
\(480\) −11.3806 −0.519449
\(481\) 9.01311 0.410962
\(482\) −47.9459 −2.18388
\(483\) 13.1164 0.596816
\(484\) −48.4091 −2.20041
\(485\) 7.76313 0.352506
\(486\) −10.2816 −0.466382
\(487\) 40.4405 1.83253 0.916267 0.400568i \(-0.131187\pi\)
0.916267 + 0.400568i \(0.131187\pi\)
\(488\) −32.7714 −1.48349
\(489\) 2.13695 0.0966361
\(490\) 2.55606 0.115471
\(491\) −7.24347 −0.326893 −0.163447 0.986552i \(-0.552261\pi\)
−0.163447 + 0.986552i \(0.552261\pi\)
\(492\) 74.4799 3.35782
\(493\) −4.19182 −0.188790
\(494\) −8.18003 −0.368037
\(495\) 0.220915 0.00992941
\(496\) −20.9707 −0.941614
\(497\) −11.2265 −0.503577
\(498\) −19.4197 −0.870219
\(499\) 20.0545 0.897765 0.448882 0.893591i \(-0.351822\pi\)
0.448882 + 0.893591i \(0.351822\pi\)
\(500\) −4.53346 −0.202742
\(501\) −4.71921 −0.210839
\(502\) 42.4911 1.89647
\(503\) −39.8272 −1.77581 −0.887903 0.460031i \(-0.847838\pi\)
−0.887903 + 0.460031i \(0.847838\pi\)
\(504\) −2.52175 −0.112328
\(505\) −3.15497 −0.140394
\(506\) −10.3307 −0.459257
\(507\) −6.24168 −0.277203
\(508\) 67.8844 3.01188
\(509\) −10.0956 −0.447479 −0.223740 0.974649i \(-0.571827\pi\)
−0.223740 + 0.974649i \(0.571827\pi\)
\(510\) −8.65539 −0.383267
\(511\) −0.355823 −0.0157407
\(512\) 50.6738 2.23949
\(513\) 3.79918 0.167738
\(514\) 40.8941 1.80376
\(515\) −15.6616 −0.690131
\(516\) 4.54818 0.200223
\(517\) −5.33823 −0.234775
\(518\) −5.69053 −0.250027
\(519\) −16.8818 −0.741028
\(520\) 26.2167 1.14968
\(521\) 18.3503 0.803940 0.401970 0.915653i \(-0.368326\pi\)
0.401970 + 0.915653i \(0.368326\pi\)
\(522\) 2.26850 0.0992897
\(523\) −3.65062 −0.159630 −0.0798152 0.996810i \(-0.525433\pi\)
−0.0798152 + 0.996810i \(0.525433\pi\)
\(524\) 79.2218 3.46082
\(525\) −1.84104 −0.0803495
\(526\) 10.6631 0.464934
\(527\) −5.15295 −0.224466
\(528\) 7.81775 0.340224
\(529\) 27.7578 1.20686
\(530\) 9.53123 0.414010
\(531\) 1.52158 0.0660311
\(532\) 3.58360 0.155369
\(533\) −36.1277 −1.56487
\(534\) 6.53687 0.282878
\(535\) 18.2898 0.790735
\(536\) −75.3785 −3.25586
\(537\) −18.0575 −0.779238
\(538\) 2.34153 0.100950
\(539\) −0.567294 −0.0244351
\(540\) −21.7886 −0.937632
\(541\) 8.64988 0.371888 0.185944 0.982560i \(-0.440466\pi\)
0.185944 + 0.982560i \(0.440466\pi\)
\(542\) 41.4339 1.77974
\(543\) −35.9194 −1.54145
\(544\) −11.3698 −0.487477
\(545\) −0.854961 −0.0366225
\(546\) 19.0514 0.815326
\(547\) 2.88504 0.123355 0.0616777 0.998096i \(-0.480355\pi\)
0.0616777 + 0.998096i \(0.480355\pi\)
\(548\) 95.8338 4.09382
\(549\) 1.97073 0.0841088
\(550\) 1.45004 0.0618299
\(551\) −1.80152 −0.0767475
\(552\) −84.9375 −3.61518
\(553\) −3.57069 −0.151841
\(554\) −70.2798 −2.98590
\(555\) 4.09868 0.173979
\(556\) −21.4830 −0.911080
\(557\) 8.90832 0.377458 0.188729 0.982029i \(-0.439563\pi\)
0.188729 + 0.982029i \(0.439563\pi\)
\(558\) 2.78864 0.118053
\(559\) −2.20617 −0.0933111
\(560\) −7.48532 −0.316313
\(561\) 1.92098 0.0811040
\(562\) 3.52978 0.148895
\(563\) 46.8421 1.97416 0.987080 0.160228i \(-0.0512229\pi\)
0.987080 + 0.160228i \(0.0512229\pi\)
\(564\) −78.5382 −3.30705
\(565\) 4.05025 0.170395
\(566\) 49.9354 2.09894
\(567\) −10.0166 −0.420658
\(568\) 72.6991 3.05039
\(569\) −33.9622 −1.42377 −0.711884 0.702297i \(-0.752158\pi\)
−0.711884 + 0.702297i \(0.752158\pi\)
\(570\) −3.71984 −0.155807
\(571\) 7.30546 0.305724 0.152862 0.988248i \(-0.451151\pi\)
0.152862 + 0.988248i \(0.451151\pi\)
\(572\) −10.4119 −0.435345
\(573\) 18.7526 0.783401
\(574\) 22.8097 0.952056
\(575\) −7.12445 −0.297110
\(576\) 0.323185 0.0134660
\(577\) 0.907593 0.0377836 0.0188918 0.999822i \(-0.493986\pi\)
0.0188918 + 0.999822i \(0.493986\pi\)
\(578\) 34.8058 1.44773
\(579\) −10.5725 −0.439376
\(580\) 10.3319 0.429008
\(581\) −4.12676 −0.171207
\(582\) −36.5318 −1.51429
\(583\) −2.11537 −0.0876096
\(584\) 2.30419 0.0953482
\(585\) −1.57656 −0.0651828
\(586\) −38.2091 −1.57840
\(587\) 13.7166 0.566144 0.283072 0.959099i \(-0.408646\pi\)
0.283072 + 0.959099i \(0.408646\pi\)
\(588\) −8.34627 −0.344194
\(589\) −2.21459 −0.0912506
\(590\) 9.98733 0.411172
\(591\) −4.16460 −0.171309
\(592\) 16.6645 0.684905
\(593\) 14.7906 0.607377 0.303689 0.952771i \(-0.401782\pi\)
0.303689 + 0.952771i \(0.401782\pi\)
\(594\) 6.96915 0.285948
\(595\) −1.83930 −0.0754040
\(596\) 28.8118 1.18018
\(597\) −28.2676 −1.15692
\(598\) 73.7253 3.01485
\(599\) 23.1794 0.947083 0.473541 0.880772i \(-0.342975\pi\)
0.473541 + 0.880772i \(0.342975\pi\)
\(600\) 11.9220 0.486712
\(601\) 26.7457 1.09098 0.545490 0.838117i \(-0.316343\pi\)
0.545490 + 0.838117i \(0.316343\pi\)
\(602\) 1.39289 0.0567700
\(603\) 4.53294 0.184596
\(604\) −12.0873 −0.491824
\(605\) 10.6782 0.434130
\(606\) 14.8467 0.603105
\(607\) 18.4141 0.747404 0.373702 0.927549i \(-0.378088\pi\)
0.373702 + 0.927549i \(0.378088\pi\)
\(608\) −4.88642 −0.198171
\(609\) 4.19578 0.170022
\(610\) 12.9354 0.523741
\(611\) 38.0962 1.54121
\(612\) 3.24713 0.131258
\(613\) 26.4171 1.06698 0.533489 0.845807i \(-0.320881\pi\)
0.533489 + 0.845807i \(0.320881\pi\)
\(614\) 35.2809 1.42382
\(615\) −16.4289 −0.662479
\(616\) 3.67361 0.148014
\(617\) 22.8313 0.919155 0.459577 0.888138i \(-0.348001\pi\)
0.459577 + 0.888138i \(0.348001\pi\)
\(618\) 73.7003 2.96466
\(619\) −10.5590 −0.424403 −0.212201 0.977226i \(-0.568063\pi\)
−0.212201 + 0.977226i \(0.568063\pi\)
\(620\) 12.7009 0.510079
\(621\) −34.2414 −1.37406
\(622\) 16.6728 0.668520
\(623\) 1.38911 0.0556534
\(624\) −55.7913 −2.23344
\(625\) 1.00000 0.0400000
\(626\) −10.3604 −0.414085
\(627\) 0.825583 0.0329706
\(628\) −43.0088 −1.71624
\(629\) 4.09481 0.163271
\(630\) 0.995381 0.0396569
\(631\) 27.9442 1.11244 0.556220 0.831035i \(-0.312251\pi\)
0.556220 + 0.831035i \(0.312251\pi\)
\(632\) 23.1226 0.919769
\(633\) 48.4668 1.92638
\(634\) 86.1157 3.42009
\(635\) −14.9741 −0.594228
\(636\) −31.1222 −1.23407
\(637\) 4.04849 0.160407
\(638\) −3.30469 −0.130834
\(639\) −4.37182 −0.172946
\(640\) −10.2419 −0.404846
\(641\) −39.0484 −1.54232 −0.771159 0.636643i \(-0.780322\pi\)
−0.771159 + 0.636643i \(0.780322\pi\)
\(642\) −86.0681 −3.39684
\(643\) −0.604886 −0.0238544 −0.0119272 0.999929i \(-0.503797\pi\)
−0.0119272 + 0.999929i \(0.503797\pi\)
\(644\) −32.2984 −1.27274
\(645\) −1.00325 −0.0395028
\(646\) −3.71633 −0.146217
\(647\) 12.3678 0.486229 0.243115 0.969998i \(-0.421831\pi\)
0.243115 + 0.969998i \(0.421831\pi\)
\(648\) 64.8643 2.54811
\(649\) −2.21659 −0.0870089
\(650\) −10.3482 −0.405890
\(651\) 5.15782 0.202151
\(652\) −5.26212 −0.206081
\(653\) 16.8126 0.657930 0.328965 0.944342i \(-0.393300\pi\)
0.328965 + 0.944342i \(0.393300\pi\)
\(654\) 4.02328 0.157323
\(655\) −17.4749 −0.682802
\(656\) −66.7971 −2.60799
\(657\) −0.138564 −0.00540591
\(658\) −24.0525 −0.937664
\(659\) 21.4393 0.835156 0.417578 0.908641i \(-0.362879\pi\)
0.417578 + 0.908641i \(0.362879\pi\)
\(660\) −4.73479 −0.184301
\(661\) −12.2284 −0.475629 −0.237814 0.971311i \(-0.576431\pi\)
−0.237814 + 0.971311i \(0.576431\pi\)
\(662\) 21.2010 0.823999
\(663\) −13.7091 −0.532417
\(664\) 26.7236 1.03708
\(665\) −0.790478 −0.0306534
\(666\) −2.21600 −0.0858684
\(667\) 16.2368 0.628693
\(668\) 11.6208 0.449622
\(669\) 44.8011 1.73211
\(670\) 29.7532 1.14947
\(671\) −2.87090 −0.110830
\(672\) 11.3806 0.439015
\(673\) −28.1622 −1.08557 −0.542787 0.839870i \(-0.682631\pi\)
−0.542787 + 0.839870i \(0.682631\pi\)
\(674\) −35.4076 −1.36385
\(675\) 4.80618 0.184990
\(676\) 15.3698 0.591146
\(677\) −17.6181 −0.677118 −0.338559 0.940945i \(-0.609939\pi\)
−0.338559 + 0.940945i \(0.609939\pi\)
\(678\) −19.0597 −0.731983
\(679\) −7.76313 −0.297922
\(680\) 11.9107 0.456755
\(681\) 26.7188 1.02387
\(682\) −4.06241 −0.155558
\(683\) −15.6775 −0.599884 −0.299942 0.953957i \(-0.596967\pi\)
−0.299942 + 0.953957i \(0.596967\pi\)
\(684\) 1.39552 0.0533592
\(685\) −21.1392 −0.807688
\(686\) −2.55606 −0.0975909
\(687\) 1.84104 0.0702400
\(688\) −4.07902 −0.155511
\(689\) 15.0963 0.575124
\(690\) 33.5263 1.27632
\(691\) 12.4553 0.473823 0.236911 0.971531i \(-0.423865\pi\)
0.236911 + 0.971531i \(0.423865\pi\)
\(692\) 41.5705 1.58027
\(693\) −0.220915 −0.00839188
\(694\) 58.3811 2.21612
\(695\) 4.73876 0.179751
\(696\) −27.1705 −1.02990
\(697\) −16.4134 −0.621704
\(698\) −2.60854 −0.0987347
\(699\) −6.05740 −0.229112
\(700\) 4.53346 0.171349
\(701\) 35.3135 1.33377 0.666887 0.745159i \(-0.267626\pi\)
0.666887 + 0.745159i \(0.267626\pi\)
\(702\) −49.7353 −1.87714
\(703\) 1.75983 0.0663733
\(704\) −0.470806 −0.0177442
\(705\) 17.3241 0.652464
\(706\) −48.0870 −1.80978
\(707\) 3.15497 0.118655
\(708\) −32.6114 −1.22561
\(709\) 25.1040 0.942802 0.471401 0.881919i \(-0.343748\pi\)
0.471401 + 0.881919i \(0.343748\pi\)
\(710\) −28.6956 −1.07693
\(711\) −1.39050 −0.0521477
\(712\) −8.99540 −0.337117
\(713\) 19.9597 0.747498
\(714\) 8.65539 0.323920
\(715\) 2.29669 0.0858912
\(716\) 44.4656 1.66176
\(717\) 11.9450 0.446093
\(718\) 32.2609 1.20397
\(719\) 31.0974 1.15974 0.579869 0.814710i \(-0.303104\pi\)
0.579869 + 0.814710i \(0.303104\pi\)
\(720\) −2.91493 −0.108633
\(721\) 15.6616 0.583267
\(722\) 46.9680 1.74797
\(723\) −34.5336 −1.28432
\(724\) 88.4496 3.28720
\(725\) −2.27903 −0.0846411
\(726\) −50.2495 −1.86493
\(727\) −1.66818 −0.0618694 −0.0309347 0.999521i \(-0.509848\pi\)
−0.0309347 + 0.999521i \(0.509848\pi\)
\(728\) −26.2167 −0.971657
\(729\) 22.6444 0.838681
\(730\) −0.909505 −0.0336623
\(731\) −1.00230 −0.0370714
\(732\) −42.2379 −1.56116
\(733\) 35.0887 1.29603 0.648015 0.761627i \(-0.275599\pi\)
0.648015 + 0.761627i \(0.275599\pi\)
\(734\) −50.8330 −1.87628
\(735\) 1.84104 0.0679077
\(736\) 44.0405 1.62335
\(737\) −6.60345 −0.243241
\(738\) 8.88252 0.326970
\(739\) −30.9880 −1.13991 −0.569956 0.821675i \(-0.693040\pi\)
−0.569956 + 0.821675i \(0.693040\pi\)
\(740\) −10.0928 −0.371018
\(741\) −5.89177 −0.216440
\(742\) −9.53123 −0.349902
\(743\) 32.9314 1.20813 0.604067 0.796933i \(-0.293546\pi\)
0.604067 + 0.796933i \(0.293546\pi\)
\(744\) −33.4004 −1.22452
\(745\) −6.35536 −0.232842
\(746\) −65.1471 −2.38521
\(747\) −1.60704 −0.0587985
\(748\) −4.73032 −0.172958
\(749\) −18.2898 −0.668293
\(750\) −4.70581 −0.171832
\(751\) 7.89382 0.288050 0.144025 0.989574i \(-0.453995\pi\)
0.144025 + 0.989574i \(0.453995\pi\)
\(752\) 70.4367 2.56856
\(753\) 30.6048 1.11530
\(754\) 23.5839 0.858874
\(755\) 2.66624 0.0970343
\(756\) 21.7886 0.792444
\(757\) −19.0952 −0.694026 −0.347013 0.937860i \(-0.612804\pi\)
−0.347013 + 0.937860i \(0.612804\pi\)
\(758\) −57.4701 −2.08741
\(759\) −7.44085 −0.270086
\(760\) 5.11888 0.185681
\(761\) −4.38141 −0.158826 −0.0794130 0.996842i \(-0.525305\pi\)
−0.0794130 + 0.996842i \(0.525305\pi\)
\(762\) 70.4652 2.55268
\(763\) 0.854961 0.0309517
\(764\) −46.1773 −1.67064
\(765\) −0.716259 −0.0258964
\(766\) 76.4497 2.76224
\(767\) 15.8187 0.571181
\(768\) 51.2522 1.84940
\(769\) −17.2345 −0.621493 −0.310747 0.950493i \(-0.600579\pi\)
−0.310747 + 0.950493i \(0.600579\pi\)
\(770\) −1.45004 −0.0522558
\(771\) 29.4545 1.06078
\(772\) 26.0341 0.936989
\(773\) 47.8372 1.72059 0.860293 0.509800i \(-0.170281\pi\)
0.860293 + 0.509800i \(0.170281\pi\)
\(774\) 0.542419 0.0194968
\(775\) −2.80158 −0.100636
\(776\) 50.2715 1.80464
\(777\) −4.09868 −0.147039
\(778\) 7.63055 0.273569
\(779\) −7.05403 −0.252737
\(780\) 33.7898 1.20987
\(781\) 6.36873 0.227891
\(782\) 33.4947 1.19777
\(783\) −10.9534 −0.391444
\(784\) 7.48532 0.267333
\(785\) 9.48698 0.338605
\(786\) 82.2337 2.93318
\(787\) −26.9440 −0.960451 −0.480226 0.877145i \(-0.659445\pi\)
−0.480226 + 0.877145i \(0.659445\pi\)
\(788\) 10.2551 0.365323
\(789\) 7.68024 0.273424
\(790\) −9.12691 −0.324721
\(791\) −4.05025 −0.144010
\(792\) 1.43058 0.0508333
\(793\) 20.4882 0.727556
\(794\) 33.8978 1.20299
\(795\) 6.86499 0.243476
\(796\) 69.6075 2.46717
\(797\) 3.30533 0.117081 0.0585404 0.998285i \(-0.481355\pi\)
0.0585404 + 0.998285i \(0.481355\pi\)
\(798\) 3.71984 0.131681
\(799\) 17.3078 0.612305
\(800\) −6.18160 −0.218553
\(801\) 0.540945 0.0191134
\(802\) −91.5405 −3.23241
\(803\) 0.201856 0.00712335
\(804\) −97.1527 −3.42631
\(805\) 7.12445 0.251104
\(806\) 28.9914 1.02118
\(807\) 1.68652 0.0593682
\(808\) −20.4305 −0.718744
\(809\) 26.8689 0.944659 0.472330 0.881422i \(-0.343413\pi\)
0.472330 + 0.881422i \(0.343413\pi\)
\(810\) −25.6031 −0.899601
\(811\) 44.1809 1.55140 0.775700 0.631102i \(-0.217397\pi\)
0.775700 + 0.631102i \(0.217397\pi\)
\(812\) −10.3319 −0.362578
\(813\) 29.8433 1.04665
\(814\) 3.22820 0.113148
\(815\) 1.16073 0.0406586
\(816\) −25.3470 −0.887321
\(817\) −0.430760 −0.0150704
\(818\) 62.1580 2.17330
\(819\) 1.57656 0.0550896
\(820\) 40.4554 1.41276
\(821\) 14.9666 0.522336 0.261168 0.965293i \(-0.415892\pi\)
0.261168 + 0.965293i \(0.415892\pi\)
\(822\) 99.4772 3.46966
\(823\) 32.1619 1.12109 0.560547 0.828123i \(-0.310591\pi\)
0.560547 + 0.828123i \(0.310591\pi\)
\(824\) −101.419 −3.53311
\(825\) 1.04441 0.0363617
\(826\) −9.98733 −0.347504
\(827\) −22.3111 −0.775833 −0.387916 0.921695i \(-0.626805\pi\)
−0.387916 + 0.921695i \(0.626805\pi\)
\(828\) −12.5776 −0.437103
\(829\) 36.7607 1.27675 0.638377 0.769724i \(-0.279606\pi\)
0.638377 + 0.769724i \(0.279606\pi\)
\(830\) −10.5483 −0.366135
\(831\) −50.6200 −1.75599
\(832\) 3.35991 0.116484
\(833\) 1.83930 0.0637280
\(834\) −22.2997 −0.772175
\(835\) −2.56334 −0.0887081
\(836\) −2.03296 −0.0703112
\(837\) −13.4649 −0.465415
\(838\) −82.3491 −2.84470
\(839\) −17.4342 −0.601894 −0.300947 0.953641i \(-0.597303\pi\)
−0.300947 + 0.953641i \(0.597303\pi\)
\(840\) −11.9220 −0.411347
\(841\) −23.8060 −0.820897
\(842\) 15.3173 0.527871
\(843\) 2.54237 0.0875639
\(844\) −119.347 −4.10809
\(845\) −3.39031 −0.116630
\(846\) −9.36651 −0.322027
\(847\) −10.6782 −0.366907
\(848\) 27.9118 0.958495
\(849\) 35.9666 1.23437
\(850\) −4.70137 −0.161256
\(851\) −15.8611 −0.543710
\(852\) 93.6993 3.21009
\(853\) −27.9319 −0.956369 −0.478184 0.878259i \(-0.658705\pi\)
−0.478184 + 0.878259i \(0.658705\pi\)
\(854\) −12.9354 −0.442642
\(855\) −0.307828 −0.0105275
\(856\) 118.439 4.04815
\(857\) 46.8663 1.60092 0.800461 0.599385i \(-0.204588\pi\)
0.800461 + 0.599385i \(0.204588\pi\)
\(858\) −10.8078 −0.368971
\(859\) 24.7665 0.845023 0.422512 0.906358i \(-0.361149\pi\)
0.422512 + 0.906358i \(0.361149\pi\)
\(860\) 2.47044 0.0842415
\(861\) 16.4289 0.559897
\(862\) −55.2585 −1.88211
\(863\) 58.4302 1.98899 0.994494 0.104797i \(-0.0334191\pi\)
0.994494 + 0.104797i \(0.0334191\pi\)
\(864\) −29.7099 −1.01075
\(865\) −9.16971 −0.311780
\(866\) 2.19579 0.0746159
\(867\) 25.0694 0.851400
\(868\) −12.7009 −0.431095
\(869\) 2.02563 0.0687148
\(870\) 10.7247 0.363601
\(871\) 47.1255 1.59679
\(872\) −5.53645 −0.187488
\(873\) −3.02312 −0.102317
\(874\) 14.3950 0.486920
\(875\) −1.00000 −0.0338062
\(876\) 2.96979 0.100340
\(877\) −22.1372 −0.747519 −0.373759 0.927526i \(-0.621931\pi\)
−0.373759 + 0.927526i \(0.621931\pi\)
\(878\) 36.9078 1.24558
\(879\) −27.5206 −0.928247
\(880\) 4.24638 0.143145
\(881\) 23.5308 0.792774 0.396387 0.918083i \(-0.370264\pi\)
0.396387 + 0.918083i \(0.370264\pi\)
\(882\) −0.995381 −0.0335162
\(883\) 13.5678 0.456592 0.228296 0.973592i \(-0.426685\pi\)
0.228296 + 0.973592i \(0.426685\pi\)
\(884\) 33.7579 1.13540
\(885\) 7.19351 0.241807
\(886\) −55.4573 −1.86313
\(887\) −20.9871 −0.704679 −0.352340 0.935872i \(-0.614614\pi\)
−0.352340 + 0.935872i \(0.614614\pi\)
\(888\) 26.5417 0.890681
\(889\) 14.9741 0.502215
\(890\) 3.55064 0.119018
\(891\) 5.68237 0.190366
\(892\) −110.320 −3.69380
\(893\) 7.43838 0.248916
\(894\) 29.9071 1.00024
\(895\) −9.80832 −0.327856
\(896\) 10.2419 0.342157
\(897\) 53.1016 1.77301
\(898\) 83.4894 2.78608
\(899\) 6.38489 0.212948
\(900\) 1.76542 0.0588472
\(901\) 6.85852 0.228490
\(902\) −12.9398 −0.430848
\(903\) 1.00325 0.0333860
\(904\) 26.2281 0.872334
\(905\) −19.5104 −0.648548
\(906\) −12.5468 −0.416839
\(907\) 10.2823 0.341420 0.170710 0.985321i \(-0.445394\pi\)
0.170710 + 0.985321i \(0.445394\pi\)
\(908\) −65.7937 −2.18344
\(909\) 1.22861 0.0407503
\(910\) 10.3482 0.343040
\(911\) 16.8197 0.557262 0.278631 0.960398i \(-0.410119\pi\)
0.278631 + 0.960398i \(0.410119\pi\)
\(912\) −10.8934 −0.360716
\(913\) 2.34109 0.0774787
\(914\) 65.5699 2.16886
\(915\) 9.31692 0.308008
\(916\) −4.53346 −0.149790
\(917\) 17.4749 0.577073
\(918\) −22.5956 −0.745766
\(919\) −3.14612 −0.103781 −0.0518905 0.998653i \(-0.516525\pi\)
−0.0518905 + 0.998653i \(0.516525\pi\)
\(920\) −46.1356 −1.52105
\(921\) 25.4115 0.837338
\(922\) 14.1947 0.467477
\(923\) −45.4504 −1.49602
\(924\) 4.73479 0.155763
\(925\) 2.22629 0.0731998
\(926\) 29.7428 0.977410
\(927\) 6.09892 0.200315
\(928\) 14.0881 0.462463
\(929\) −2.88915 −0.0947901 −0.0473950 0.998876i \(-0.515092\pi\)
−0.0473950 + 0.998876i \(0.515092\pi\)
\(930\) 13.1837 0.432311
\(931\) 0.790478 0.0259069
\(932\) 14.9160 0.488591
\(933\) 12.0088 0.393151
\(934\) 20.6563 0.675896
\(935\) 1.04342 0.0341236
\(936\) −10.2093 −0.333702
\(937\) 11.0172 0.359916 0.179958 0.983674i \(-0.442404\pi\)
0.179958 + 0.983674i \(0.442404\pi\)
\(938\) −29.7532 −0.971477
\(939\) −7.46222 −0.243520
\(940\) −42.6597 −1.39141
\(941\) 25.2443 0.822941 0.411470 0.911423i \(-0.365015\pi\)
0.411470 + 0.911423i \(0.365015\pi\)
\(942\) −44.6439 −1.45458
\(943\) 63.5768 2.07034
\(944\) 29.2475 0.951924
\(945\) −4.80618 −0.156345
\(946\) −0.790179 −0.0256909
\(947\) −1.46997 −0.0477675 −0.0238838 0.999715i \(-0.507603\pi\)
−0.0238838 + 0.999715i \(0.507603\pi\)
\(948\) 29.8019 0.967921
\(949\) −1.44055 −0.0467621
\(950\) −2.02051 −0.0655541
\(951\) 62.0259 2.01133
\(952\) −11.9107 −0.386028
\(953\) 50.3023 1.62945 0.814726 0.579846i \(-0.196887\pi\)
0.814726 + 0.579846i \(0.196887\pi\)
\(954\) −3.71165 −0.120169
\(955\) 10.1859 0.329607
\(956\) −29.4139 −0.951313
\(957\) −2.38024 −0.0769423
\(958\) 45.1186 1.45772
\(959\) 21.1392 0.682621
\(960\) 1.52790 0.0493129
\(961\) −23.1511 −0.746811
\(962\) −23.0381 −0.742777
\(963\) −7.12239 −0.229516
\(964\) 85.0373 2.73887
\(965\) −5.74266 −0.184863
\(966\) −33.5263 −1.07869
\(967\) 17.9790 0.578165 0.289083 0.957304i \(-0.406650\pi\)
0.289083 + 0.957304i \(0.406650\pi\)
\(968\) 69.1484 2.22251
\(969\) −2.67673 −0.0859891
\(970\) −19.8431 −0.637122
\(971\) −10.6472 −0.341685 −0.170842 0.985298i \(-0.554649\pi\)
−0.170842 + 0.985298i \(0.554649\pi\)
\(972\) 18.2355 0.584904
\(973\) −4.73876 −0.151918
\(974\) −103.368 −3.31214
\(975\) −7.45343 −0.238701
\(976\) 37.8809 1.21254
\(977\) −21.0533 −0.673556 −0.336778 0.941584i \(-0.609337\pi\)
−0.336778 + 0.941584i \(0.609337\pi\)
\(978\) −5.46217 −0.174661
\(979\) −0.788032 −0.0251856
\(980\) −4.53346 −0.144816
\(981\) 0.332939 0.0106299
\(982\) 18.5148 0.590830
\(983\) 40.0100 1.27612 0.638061 0.769986i \(-0.279737\pi\)
0.638061 + 0.769986i \(0.279737\pi\)
\(984\) −106.389 −3.39154
\(985\) −2.26210 −0.0720764
\(986\) 10.7146 0.341221
\(987\) −17.3241 −0.551433
\(988\) 14.5082 0.461567
\(989\) 3.88237 0.123452
\(990\) −0.564674 −0.0179465
\(991\) −56.1788 −1.78458 −0.892288 0.451466i \(-0.850901\pi\)
−0.892288 + 0.451466i \(0.850901\pi\)
\(992\) 17.3183 0.549855
\(993\) 15.2703 0.484587
\(994\) 28.6956 0.910170
\(995\) −15.3542 −0.486760
\(996\) 34.4430 1.09137
\(997\) 22.0098 0.697057 0.348528 0.937298i \(-0.386682\pi\)
0.348528 + 0.937298i \(0.386682\pi\)
\(998\) −51.2607 −1.62263
\(999\) 10.6999 0.338531
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 8015.2.a.n.1.4 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.n.1.4 68 1.1 even 1 trivial