Properties

Label 2013.4.a.b.1.17
Level $2013$
Weight $4$
Character 2013.1
Self dual yes
Analytic conductor $118.771$
Analytic rank $1$
Dimension $36$
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] = [2013,4,Mod(1,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2013.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2013.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: \(118.770844842\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 2013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.158900 q^{2} -3.00000 q^{3} -7.97475 q^{4} +7.59417 q^{5} +0.476701 q^{6} -16.2139 q^{7} +2.53840 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-0.158900 q^{2} -3.00000 q^{3} -7.97475 q^{4} +7.59417 q^{5} +0.476701 q^{6} -16.2139 q^{7} +2.53840 q^{8} +9.00000 q^{9} -1.20672 q^{10} -11.0000 q^{11} +23.9243 q^{12} +56.3754 q^{13} +2.57640 q^{14} -22.7825 q^{15} +63.3947 q^{16} +54.6452 q^{17} -1.43010 q^{18} -148.362 q^{19} -60.5616 q^{20} +48.6418 q^{21} +1.74791 q^{22} -148.655 q^{23} -7.61519 q^{24} -67.3285 q^{25} -8.95808 q^{26} -27.0000 q^{27} +129.302 q^{28} +125.987 q^{29} +3.62015 q^{30} +7.15680 q^{31} -30.3806 q^{32} +33.0000 q^{33} -8.68315 q^{34} -123.131 q^{35} -71.7728 q^{36} +175.991 q^{37} +23.5748 q^{38} -169.126 q^{39} +19.2770 q^{40} +247.068 q^{41} -7.72921 q^{42} +31.0284 q^{43} +87.7223 q^{44} +68.3476 q^{45} +23.6214 q^{46} +129.677 q^{47} -190.184 q^{48} -80.1082 q^{49} +10.6985 q^{50} -163.936 q^{51} -449.580 q^{52} -16.4698 q^{53} +4.29031 q^{54} -83.5359 q^{55} -41.1574 q^{56} +445.086 q^{57} -20.0193 q^{58} +371.300 q^{59} +181.685 q^{60} +61.0000 q^{61} -1.13722 q^{62} -145.925 q^{63} -502.330 q^{64} +428.125 q^{65} -5.24372 q^{66} +68.0398 q^{67} -435.782 q^{68} +445.966 q^{69} +19.5656 q^{70} +329.123 q^{71} +22.8456 q^{72} +788.527 q^{73} -27.9651 q^{74} +201.986 q^{75} +1183.15 q^{76} +178.353 q^{77} +26.8742 q^{78} +1249.99 q^{79} +481.430 q^{80} +81.0000 q^{81} -39.2592 q^{82} -903.772 q^{83} -387.906 q^{84} +414.985 q^{85} -4.93043 q^{86} -377.960 q^{87} -27.9223 q^{88} +630.261 q^{89} -10.8605 q^{90} -914.068 q^{91} +1185.49 q^{92} -21.4704 q^{93} -20.6058 q^{94} -1126.69 q^{95} +91.1418 q^{96} +611.113 q^{97} +12.7292 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 2 q^{2} - 108 q^{3} + 118 q^{4} - 5 q^{5} - 6 q^{6} - 63 q^{7} + 3 q^{8} + 324 q^{9} - 45 q^{10} - 396 q^{11} - 354 q^{12} - 13 q^{13} + 82 q^{14} + 15 q^{15} + 262 q^{16} + 204 q^{17} + 18 q^{18} - 431 q^{19} + 354 q^{20} + 189 q^{21} - 22 q^{22} - 179 q^{23} - 9 q^{24} + 711 q^{25} + 331 q^{26} - 972 q^{27} - 296 q^{28} + 478 q^{29} + 135 q^{30} - 574 q^{31} - 149 q^{32} + 1188 q^{33} + 276 q^{34} - 194 q^{35} + 1062 q^{36} - 12 q^{37} + 325 q^{38} + 39 q^{39} - 185 q^{40} + 900 q^{41} - 246 q^{42} - 1053 q^{43} - 1298 q^{44} - 45 q^{45} - 407 q^{46} - 653 q^{47} - 786 q^{48} + 753 q^{49} - 1520 q^{50} - 612 q^{51} + 60 q^{52} + 735 q^{53} - 54 q^{54} + 55 q^{55} - 809 q^{56} + 1293 q^{57} - 1399 q^{58} - 1127 q^{59} - 1062 q^{60} + 2196 q^{61} - 1795 q^{62} - 567 q^{63} - 2133 q^{64} + 1886 q^{65} + 66 q^{66} - 989 q^{67} + 10 q^{68} + 537 q^{69} - 2130 q^{70} + 61 q^{71} + 27 q^{72} - 1471 q^{73} - 122 q^{74} - 2133 q^{75} - 4064 q^{76} + 693 q^{77} - 993 q^{78} - 1853 q^{79} + 2197 q^{80} + 2916 q^{81} - 2566 q^{82} - 3523 q^{83} + 888 q^{84} - 449 q^{85} - 771 q^{86} - 1434 q^{87} - 33 q^{88} + 2209 q^{89} - 405 q^{90} - 1668 q^{91} - 1999 q^{92} + 1722 q^{93} - 2844 q^{94} + 1220 q^{95} + 447 q^{96} - 3622 q^{97} + 3846 q^{98} - 3564 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.158900 −0.0561798 −0.0280899 0.999605i \(-0.508942\pi\)
−0.0280899 + 0.999605i \(0.508942\pi\)
\(3\) −3.00000 −0.577350
\(4\) −7.97475 −0.996844
\(5\) 7.59417 0.679244 0.339622 0.940562i \(-0.389701\pi\)
0.339622 + 0.940562i \(0.389701\pi\)
\(6\) 0.476701 0.0324354
\(7\) −16.2139 −0.875470 −0.437735 0.899104i \(-0.644219\pi\)
−0.437735 + 0.899104i \(0.644219\pi\)
\(8\) 2.53840 0.112182
\(9\) 9.00000 0.333333
\(10\) −1.20672 −0.0381598
\(11\) −11.0000 −0.301511
\(12\) 23.9243 0.575528
\(13\) 56.3754 1.20275 0.601374 0.798967i \(-0.294620\pi\)
0.601374 + 0.798967i \(0.294620\pi\)
\(14\) 2.57640 0.0491837
\(15\) −22.7825 −0.392161
\(16\) 63.3947 0.990541
\(17\) 54.6452 0.779613 0.389806 0.920897i \(-0.372542\pi\)
0.389806 + 0.920897i \(0.372542\pi\)
\(18\) −1.43010 −0.0187266
\(19\) −148.362 −1.79140 −0.895700 0.444660i \(-0.853325\pi\)
−0.895700 + 0.444660i \(0.853325\pi\)
\(20\) −60.5616 −0.677100
\(21\) 48.6418 0.505453
\(22\) 1.74791 0.0169388
\(23\) −148.655 −1.34769 −0.673843 0.738875i \(-0.735358\pi\)
−0.673843 + 0.738875i \(0.735358\pi\)
\(24\) −7.61519 −0.0647685
\(25\) −67.3285 −0.538628
\(26\) −8.95808 −0.0675702
\(27\) −27.0000 −0.192450
\(28\) 129.302 0.872707
\(29\) 125.987 0.806728 0.403364 0.915040i \(-0.367841\pi\)
0.403364 + 0.915040i \(0.367841\pi\)
\(30\) 3.62015 0.0220316
\(31\) 7.15680 0.0414645 0.0207322 0.999785i \(-0.493400\pi\)
0.0207322 + 0.999785i \(0.493400\pi\)
\(32\) −30.3806 −0.167831
\(33\) 33.0000 0.174078
\(34\) −8.68315 −0.0437985
\(35\) −123.131 −0.594658
\(36\) −71.7728 −0.332281
\(37\) 175.991 0.781968 0.390984 0.920398i \(-0.372135\pi\)
0.390984 + 0.920398i \(0.372135\pi\)
\(38\) 23.5748 0.100640
\(39\) −169.126 −0.694407
\(40\) 19.2770 0.0761991
\(41\) 247.068 0.941110 0.470555 0.882371i \(-0.344054\pi\)
0.470555 + 0.882371i \(0.344054\pi\)
\(42\) −7.72921 −0.0283963
\(43\) 31.0284 0.110042 0.0550208 0.998485i \(-0.482477\pi\)
0.0550208 + 0.998485i \(0.482477\pi\)
\(44\) 87.7223 0.300560
\(45\) 68.3476 0.226415
\(46\) 23.6214 0.0757127
\(47\) 129.677 0.402455 0.201228 0.979544i \(-0.435507\pi\)
0.201228 + 0.979544i \(0.435507\pi\)
\(48\) −190.184 −0.571889
\(49\) −80.1082 −0.233552
\(50\) 10.6985 0.0302600
\(51\) −163.936 −0.450110
\(52\) −449.580 −1.19895
\(53\) −16.4698 −0.0426850 −0.0213425 0.999772i \(-0.506794\pi\)
−0.0213425 + 0.999772i \(0.506794\pi\)
\(54\) 4.29031 0.0108118
\(55\) −83.5359 −0.204800
\(56\) −41.1574 −0.0982123
\(57\) 445.086 1.03426
\(58\) −20.0193 −0.0453218
\(59\) 371.300 0.819308 0.409654 0.912241i \(-0.365649\pi\)
0.409654 + 0.912241i \(0.365649\pi\)
\(60\) 181.685 0.390924
\(61\) 61.0000 0.128037
\(62\) −1.13722 −0.00232947
\(63\) −145.925 −0.291823
\(64\) −502.330 −0.981113
\(65\) 428.125 0.816959
\(66\) −5.24372 −0.00977965
\(67\) 68.0398 0.124065 0.0620327 0.998074i \(-0.480242\pi\)
0.0620327 + 0.998074i \(0.480242\pi\)
\(68\) −435.782 −0.777152
\(69\) 445.966 0.778087
\(70\) 19.5656 0.0334077
\(71\) 329.123 0.550138 0.275069 0.961425i \(-0.411299\pi\)
0.275069 + 0.961425i \(0.411299\pi\)
\(72\) 22.8456 0.0373941
\(73\) 788.527 1.26425 0.632124 0.774868i \(-0.282183\pi\)
0.632124 + 0.774868i \(0.282183\pi\)
\(74\) −27.9651 −0.0439308
\(75\) 201.986 0.310977
\(76\) 1183.15 1.78575
\(77\) 178.353 0.263964
\(78\) 26.8742 0.0390117
\(79\) 1249.99 1.78018 0.890092 0.455781i \(-0.150640\pi\)
0.890092 + 0.455781i \(0.150640\pi\)
\(80\) 481.430 0.672819
\(81\) 81.0000 0.111111
\(82\) −39.2592 −0.0528714
\(83\) −903.772 −1.19520 −0.597602 0.801793i \(-0.703880\pi\)
−0.597602 + 0.801793i \(0.703880\pi\)
\(84\) −387.906 −0.503858
\(85\) 414.985 0.529547
\(86\) −4.93043 −0.00618212
\(87\) −377.960 −0.465765
\(88\) −27.9223 −0.0338242
\(89\) 630.261 0.750647 0.375324 0.926894i \(-0.377532\pi\)
0.375324 + 0.926894i \(0.377532\pi\)
\(90\) −10.8605 −0.0127199
\(91\) −914.068 −1.05297
\(92\) 1185.49 1.34343
\(93\) −21.4704 −0.0239395
\(94\) −20.6058 −0.0226099
\(95\) −1126.69 −1.21680
\(96\) 91.1418 0.0968971
\(97\) 611.113 0.639682 0.319841 0.947471i \(-0.396371\pi\)
0.319841 + 0.947471i \(0.396371\pi\)
\(98\) 12.7292 0.0131209
\(99\) −99.0000 −0.100504
\(100\) 536.928 0.536928
\(101\) −1783.57 −1.75715 −0.878574 0.477606i \(-0.841505\pi\)
−0.878574 + 0.477606i \(0.841505\pi\)
\(102\) 26.0495 0.0252871
\(103\) 942.273 0.901407 0.450704 0.892674i \(-0.351173\pi\)
0.450704 + 0.892674i \(0.351173\pi\)
\(104\) 143.103 0.134927
\(105\) 369.394 0.343326
\(106\) 2.61707 0.00239804
\(107\) −1443.28 −1.30399 −0.651996 0.758222i \(-0.726068\pi\)
−0.651996 + 0.758222i \(0.726068\pi\)
\(108\) 215.318 0.191843
\(109\) −184.596 −0.162212 −0.0811058 0.996705i \(-0.525845\pi\)
−0.0811058 + 0.996705i \(0.525845\pi\)
\(110\) 13.2739 0.0115056
\(111\) −527.974 −0.451469
\(112\) −1027.88 −0.867190
\(113\) 1635.68 1.36170 0.680848 0.732425i \(-0.261611\pi\)
0.680848 + 0.732425i \(0.261611\pi\)
\(114\) −70.7244 −0.0581048
\(115\) −1128.91 −0.915407
\(116\) −1004.71 −0.804182
\(117\) 507.379 0.400916
\(118\) −58.9998 −0.0460286
\(119\) −886.014 −0.682528
\(120\) −57.8310 −0.0439936
\(121\) 121.000 0.0909091
\(122\) −9.69293 −0.00719309
\(123\) −741.204 −0.543350
\(124\) −57.0737 −0.0413336
\(125\) −1460.58 −1.04510
\(126\) 23.1876 0.0163946
\(127\) 570.566 0.398658 0.199329 0.979933i \(-0.436124\pi\)
0.199329 + 0.979933i \(0.436124\pi\)
\(128\) 322.865 0.222949
\(129\) −93.0853 −0.0635326
\(130\) −68.0292 −0.0458966
\(131\) 171.536 0.114406 0.0572029 0.998363i \(-0.481782\pi\)
0.0572029 + 0.998363i \(0.481782\pi\)
\(132\) −263.167 −0.173528
\(133\) 2405.53 1.56832
\(134\) −10.8116 −0.00696997
\(135\) −205.043 −0.130720
\(136\) 138.711 0.0874587
\(137\) −2658.78 −1.65807 −0.829033 0.559200i \(-0.811108\pi\)
−0.829033 + 0.559200i \(0.811108\pi\)
\(138\) −70.8642 −0.0437127
\(139\) −1643.72 −1.00301 −0.501506 0.865154i \(-0.667220\pi\)
−0.501506 + 0.865154i \(0.667220\pi\)
\(140\) 981.943 0.592781
\(141\) −389.032 −0.232358
\(142\) −52.2979 −0.0309066
\(143\) −620.130 −0.362642
\(144\) 570.552 0.330180
\(145\) 956.764 0.547965
\(146\) −125.297 −0.0710252
\(147\) 240.325 0.134841
\(148\) −1403.49 −0.779500
\(149\) −1619.05 −0.890185 −0.445093 0.895484i \(-0.646829\pi\)
−0.445093 + 0.895484i \(0.646829\pi\)
\(150\) −32.0956 −0.0174706
\(151\) −2216.61 −1.19460 −0.597301 0.802017i \(-0.703760\pi\)
−0.597301 + 0.802017i \(0.703760\pi\)
\(152\) −376.601 −0.200963
\(153\) 491.807 0.259871
\(154\) −28.3404 −0.0148295
\(155\) 54.3500 0.0281645
\(156\) 1348.74 0.692216
\(157\) −1702.98 −0.865685 −0.432842 0.901470i \(-0.642489\pi\)
−0.432842 + 0.901470i \(0.642489\pi\)
\(158\) −198.623 −0.100010
\(159\) 49.4095 0.0246442
\(160\) −230.716 −0.113998
\(161\) 2410.29 1.17986
\(162\) −12.8709 −0.00624220
\(163\) −1426.06 −0.685260 −0.342630 0.939470i \(-0.611318\pi\)
−0.342630 + 0.939470i \(0.611318\pi\)
\(164\) −1970.30 −0.938140
\(165\) 250.608 0.118241
\(166\) 143.610 0.0671463
\(167\) −417.430 −0.193423 −0.0967116 0.995312i \(-0.530832\pi\)
−0.0967116 + 0.995312i \(0.530832\pi\)
\(168\) 123.472 0.0567029
\(169\) 981.190 0.446604
\(170\) −65.9414 −0.0297498
\(171\) −1335.26 −0.597133
\(172\) −247.444 −0.109694
\(173\) 1836.60 0.807131 0.403566 0.914951i \(-0.367771\pi\)
0.403566 + 0.914951i \(0.367771\pi\)
\(174\) 60.0580 0.0261666
\(175\) 1091.66 0.471553
\(176\) −697.341 −0.298659
\(177\) −1113.90 −0.473028
\(178\) −100.149 −0.0421712
\(179\) −774.926 −0.323579 −0.161790 0.986825i \(-0.551727\pi\)
−0.161790 + 0.986825i \(0.551727\pi\)
\(180\) −545.055 −0.225700
\(181\) 2076.69 0.852814 0.426407 0.904532i \(-0.359779\pi\)
0.426407 + 0.904532i \(0.359779\pi\)
\(182\) 145.246 0.0591557
\(183\) −183.000 −0.0739221
\(184\) −377.346 −0.151186
\(185\) 1336.51 0.531147
\(186\) 3.41166 0.00134492
\(187\) −601.098 −0.235062
\(188\) −1034.15 −0.401185
\(189\) 437.776 0.168484
\(190\) 179.031 0.0683594
\(191\) −1027.55 −0.389273 −0.194636 0.980875i \(-0.562353\pi\)
−0.194636 + 0.980875i \(0.562353\pi\)
\(192\) 1506.99 0.566446
\(193\) −1139.83 −0.425111 −0.212556 0.977149i \(-0.568179\pi\)
−0.212556 + 0.977149i \(0.568179\pi\)
\(194\) −97.1061 −0.0359372
\(195\) −1284.37 −0.471672
\(196\) 638.843 0.232814
\(197\) 515.497 0.186435 0.0932173 0.995646i \(-0.470285\pi\)
0.0932173 + 0.995646i \(0.470285\pi\)
\(198\) 15.7311 0.00564628
\(199\) 721.842 0.257136 0.128568 0.991701i \(-0.458962\pi\)
0.128568 + 0.991701i \(0.458962\pi\)
\(200\) −170.906 −0.0604245
\(201\) −204.119 −0.0716292
\(202\) 283.410 0.0987162
\(203\) −2042.74 −0.706266
\(204\) 1307.35 0.448689
\(205\) 1876.28 0.639243
\(206\) −149.728 −0.0506409
\(207\) −1337.90 −0.449229
\(208\) 3573.90 1.19137
\(209\) 1631.98 0.540127
\(210\) −58.6969 −0.0192880
\(211\) 5042.49 1.64521 0.822606 0.568612i \(-0.192519\pi\)
0.822606 + 0.568612i \(0.192519\pi\)
\(212\) 131.343 0.0425503
\(213\) −987.370 −0.317622
\(214\) 229.338 0.0732580
\(215\) 235.635 0.0747451
\(216\) −68.5367 −0.0215895
\(217\) −116.040 −0.0363009
\(218\) 29.3324 0.00911302
\(219\) −2365.58 −0.729913
\(220\) 666.178 0.204153
\(221\) 3080.65 0.937678
\(222\) 83.8953 0.0253635
\(223\) −800.257 −0.240310 −0.120155 0.992755i \(-0.538339\pi\)
−0.120155 + 0.992755i \(0.538339\pi\)
\(224\) 492.589 0.146931
\(225\) −605.957 −0.179543
\(226\) −259.910 −0.0764998
\(227\) −4702.17 −1.37486 −0.687432 0.726249i \(-0.741262\pi\)
−0.687432 + 0.726249i \(0.741262\pi\)
\(228\) −3549.45 −1.03100
\(229\) 993.610 0.286723 0.143362 0.989670i \(-0.454209\pi\)
0.143362 + 0.989670i \(0.454209\pi\)
\(230\) 179.385 0.0514274
\(231\) −535.060 −0.152400
\(232\) 319.804 0.0905006
\(233\) −3670.09 −1.03191 −0.515956 0.856615i \(-0.672563\pi\)
−0.515956 + 0.856615i \(0.672563\pi\)
\(234\) −80.6227 −0.0225234
\(235\) 984.793 0.273365
\(236\) −2961.03 −0.816723
\(237\) −3749.96 −1.02779
\(238\) 140.788 0.0383443
\(239\) −4046.34 −1.09513 −0.547565 0.836763i \(-0.684445\pi\)
−0.547565 + 0.836763i \(0.684445\pi\)
\(240\) −1444.29 −0.388452
\(241\) 5851.00 1.56388 0.781942 0.623351i \(-0.214229\pi\)
0.781942 + 0.623351i \(0.214229\pi\)
\(242\) −19.2270 −0.00510725
\(243\) −243.000 −0.0641500
\(244\) −486.460 −0.127633
\(245\) −608.356 −0.158638
\(246\) 117.778 0.0305253
\(247\) −8363.97 −2.15460
\(248\) 18.1668 0.00465158
\(249\) 2711.32 0.690051
\(250\) 232.086 0.0587137
\(251\) −536.741 −0.134975 −0.0674877 0.997720i \(-0.521498\pi\)
−0.0674877 + 0.997720i \(0.521498\pi\)
\(252\) 1163.72 0.290902
\(253\) 1635.21 0.406342
\(254\) −90.6633 −0.0223965
\(255\) −1244.96 −0.305734
\(256\) 3967.33 0.968588
\(257\) −713.229 −0.173113 −0.0865564 0.996247i \(-0.527586\pi\)
−0.0865564 + 0.996247i \(0.527586\pi\)
\(258\) 14.7913 0.00356925
\(259\) −2853.51 −0.684590
\(260\) −3414.19 −0.814381
\(261\) 1133.88 0.268909
\(262\) −27.2571 −0.00642730
\(263\) 5480.26 1.28489 0.642447 0.766330i \(-0.277919\pi\)
0.642447 + 0.766330i \(0.277919\pi\)
\(264\) 83.7670 0.0195284
\(265\) −125.075 −0.0289935
\(266\) −382.240 −0.0881077
\(267\) −1890.78 −0.433386
\(268\) −542.600 −0.123674
\(269\) −6249.32 −1.41646 −0.708230 0.705982i \(-0.750506\pi\)
−0.708230 + 0.705982i \(0.750506\pi\)
\(270\) 32.5814 0.00734385
\(271\) −7855.98 −1.76095 −0.880473 0.474096i \(-0.842775\pi\)
−0.880473 + 0.474096i \(0.842775\pi\)
\(272\) 3464.22 0.772239
\(273\) 2742.20 0.607933
\(274\) 422.482 0.0931498
\(275\) 740.614 0.162403
\(276\) −3556.47 −0.775631
\(277\) −81.7755 −0.0177380 −0.00886898 0.999961i \(-0.502823\pi\)
−0.00886898 + 0.999961i \(0.502823\pi\)
\(278\) 261.188 0.0563490
\(279\) 64.4112 0.0138215
\(280\) −312.556 −0.0667100
\(281\) −5856.93 −1.24340 −0.621699 0.783256i \(-0.713557\pi\)
−0.621699 + 0.783256i \(0.713557\pi\)
\(282\) 61.8174 0.0130538
\(283\) −5144.26 −1.08055 −0.540273 0.841490i \(-0.681679\pi\)
−0.540273 + 0.841490i \(0.681679\pi\)
\(284\) −2624.68 −0.548401
\(285\) 3380.06 0.702518
\(286\) 98.5389 0.0203732
\(287\) −4005.94 −0.823914
\(288\) −273.425 −0.0559436
\(289\) −1926.90 −0.392204
\(290\) −152.030 −0.0307846
\(291\) −1833.34 −0.369320
\(292\) −6288.30 −1.26026
\(293\) −70.3266 −0.0140223 −0.00701114 0.999975i \(-0.502232\pi\)
−0.00701114 + 0.999975i \(0.502232\pi\)
\(294\) −38.1877 −0.00757535
\(295\) 2819.72 0.556510
\(296\) 446.736 0.0877229
\(297\) 297.000 0.0580259
\(298\) 257.268 0.0500104
\(299\) −8380.51 −1.62093
\(300\) −1610.78 −0.309996
\(301\) −503.093 −0.0963382
\(302\) 352.220 0.0671125
\(303\) 5350.71 1.01449
\(304\) −9405.36 −1.77445
\(305\) 463.245 0.0869682
\(306\) −78.1484 −0.0145995
\(307\) −2205.88 −0.410085 −0.205043 0.978753i \(-0.565733\pi\)
−0.205043 + 0.978753i \(0.565733\pi\)
\(308\) −1422.32 −0.263131
\(309\) −2826.82 −0.520428
\(310\) −8.63624 −0.00158228
\(311\) −2188.69 −0.399066 −0.199533 0.979891i \(-0.563942\pi\)
−0.199533 + 0.979891i \(0.563942\pi\)
\(312\) −429.309 −0.0779002
\(313\) 5172.12 0.934011 0.467005 0.884254i \(-0.345333\pi\)
0.467005 + 0.884254i \(0.345333\pi\)
\(314\) 270.604 0.0486340
\(315\) −1108.18 −0.198219
\(316\) −9968.33 −1.77457
\(317\) 9532.28 1.68892 0.844458 0.535622i \(-0.179923\pi\)
0.844458 + 0.535622i \(0.179923\pi\)
\(318\) −7.85120 −0.00138451
\(319\) −1385.85 −0.243238
\(320\) −3814.78 −0.666415
\(321\) 4329.84 0.752860
\(322\) −382.996 −0.0662842
\(323\) −8107.28 −1.39660
\(324\) −645.955 −0.110760
\(325\) −3795.67 −0.647834
\(326\) 226.601 0.0384978
\(327\) 553.787 0.0936529
\(328\) 627.156 0.105576
\(329\) −2102.58 −0.352338
\(330\) −39.8217 −0.00664276
\(331\) −2277.85 −0.378254 −0.189127 0.981953i \(-0.560566\pi\)
−0.189127 + 0.981953i \(0.560566\pi\)
\(332\) 7207.36 1.19143
\(333\) 1583.92 0.260656
\(334\) 66.3298 0.0108665
\(335\) 516.706 0.0842706
\(336\) 3083.63 0.500672
\(337\) −142.077 −0.0229657 −0.0114829 0.999934i \(-0.503655\pi\)
−0.0114829 + 0.999934i \(0.503655\pi\)
\(338\) −155.912 −0.0250901
\(339\) −4907.03 −0.786175
\(340\) −3309.40 −0.527876
\(341\) −78.7248 −0.0125020
\(342\) 212.173 0.0335468
\(343\) 6860.25 1.07994
\(344\) 78.7624 0.0123447
\(345\) 3386.74 0.528510
\(346\) −291.836 −0.0453445
\(347\) 7853.16 1.21493 0.607463 0.794348i \(-0.292187\pi\)
0.607463 + 0.794348i \(0.292187\pi\)
\(348\) 3014.13 0.464295
\(349\) −10420.0 −1.59820 −0.799098 0.601201i \(-0.794689\pi\)
−0.799098 + 0.601201i \(0.794689\pi\)
\(350\) −173.465 −0.0264918
\(351\) −1522.14 −0.231469
\(352\) 334.187 0.0506029
\(353\) 2915.86 0.439648 0.219824 0.975540i \(-0.429452\pi\)
0.219824 + 0.975540i \(0.429452\pi\)
\(354\) 176.999 0.0265746
\(355\) 2499.42 0.373677
\(356\) −5026.18 −0.748278
\(357\) 2658.04 0.394058
\(358\) 123.136 0.0181786
\(359\) 2333.29 0.343026 0.171513 0.985182i \(-0.445134\pi\)
0.171513 + 0.985182i \(0.445134\pi\)
\(360\) 173.493 0.0253997
\(361\) 15152.3 2.20911
\(362\) −329.987 −0.0479109
\(363\) −363.000 −0.0524864
\(364\) 7289.46 1.04965
\(365\) 5988.21 0.858732
\(366\) 29.0788 0.00415293
\(367\) −1464.31 −0.208274 −0.104137 0.994563i \(-0.533208\pi\)
−0.104137 + 0.994563i \(0.533208\pi\)
\(368\) −9423.95 −1.33494
\(369\) 2223.61 0.313703
\(370\) −212.372 −0.0298397
\(371\) 267.041 0.0373695
\(372\) 171.221 0.0238640
\(373\) −8778.48 −1.21859 −0.609293 0.792945i \(-0.708547\pi\)
−0.609293 + 0.792945i \(0.708547\pi\)
\(374\) 95.5147 0.0132057
\(375\) 4381.73 0.603391
\(376\) 329.173 0.0451484
\(377\) 7102.55 0.970291
\(378\) −69.5629 −0.00946542
\(379\) −13243.3 −1.79488 −0.897441 0.441134i \(-0.854576\pi\)
−0.897441 + 0.441134i \(0.854576\pi\)
\(380\) 8985.05 1.21296
\(381\) −1711.70 −0.230165
\(382\) 163.279 0.0218693
\(383\) −3271.85 −0.436511 −0.218255 0.975892i \(-0.570037\pi\)
−0.218255 + 0.975892i \(0.570037\pi\)
\(384\) −968.596 −0.128720
\(385\) 1354.45 0.179296
\(386\) 181.119 0.0238827
\(387\) 279.256 0.0366805
\(388\) −4873.47 −0.637663
\(389\) −8212.76 −1.07045 −0.535223 0.844711i \(-0.679772\pi\)
−0.535223 + 0.844711i \(0.679772\pi\)
\(390\) 204.088 0.0264984
\(391\) −8123.30 −1.05067
\(392\) −203.346 −0.0262004
\(393\) −514.608 −0.0660522
\(394\) −81.9127 −0.0104739
\(395\) 9492.62 1.20918
\(396\) 789.500 0.100187
\(397\) −1768.51 −0.223574 −0.111787 0.993732i \(-0.535657\pi\)
−0.111787 + 0.993732i \(0.535657\pi\)
\(398\) −114.701 −0.0144458
\(399\) −7216.60 −0.905468
\(400\) −4268.27 −0.533534
\(401\) −15785.8 −1.96585 −0.982924 0.184010i \(-0.941092\pi\)
−0.982924 + 0.184010i \(0.941092\pi\)
\(402\) 32.4347 0.00402411
\(403\) 403.468 0.0498714
\(404\) 14223.5 1.75160
\(405\) 615.128 0.0754715
\(406\) 324.592 0.0396779
\(407\) −1935.91 −0.235772
\(408\) −416.134 −0.0504943
\(409\) −6829.39 −0.825652 −0.412826 0.910810i \(-0.635458\pi\)
−0.412826 + 0.910810i \(0.635458\pi\)
\(410\) −298.141 −0.0359125
\(411\) 7976.34 0.957285
\(412\) −7514.40 −0.898562
\(413\) −6020.24 −0.717280
\(414\) 212.593 0.0252376
\(415\) −6863.40 −0.811834
\(416\) −1712.72 −0.201858
\(417\) 4931.16 0.579089
\(418\) −259.323 −0.0303442
\(419\) −8553.85 −0.997334 −0.498667 0.866794i \(-0.666177\pi\)
−0.498667 + 0.866794i \(0.666177\pi\)
\(420\) −2945.83 −0.342242
\(421\) −1437.53 −0.166416 −0.0832079 0.996532i \(-0.526517\pi\)
−0.0832079 + 0.996532i \(0.526517\pi\)
\(422\) −801.255 −0.0924277
\(423\) 1167.10 0.134152
\(424\) −41.8070 −0.00478851
\(425\) −3679.18 −0.419921
\(426\) 156.894 0.0178439
\(427\) −989.050 −0.112092
\(428\) 11509.8 1.29988
\(429\) 1860.39 0.209372
\(430\) −37.4425 −0.00419916
\(431\) −5831.09 −0.651679 −0.325840 0.945425i \(-0.605647\pi\)
−0.325840 + 0.945425i \(0.605647\pi\)
\(432\) −1711.66 −0.190630
\(433\) −10183.1 −1.13018 −0.565089 0.825030i \(-0.691158\pi\)
−0.565089 + 0.825030i \(0.691158\pi\)
\(434\) 18.4388 0.00203938
\(435\) −2870.29 −0.316368
\(436\) 1472.11 0.161700
\(437\) 22054.8 2.41424
\(438\) 375.892 0.0410064
\(439\) −10005.8 −1.08782 −0.543909 0.839144i \(-0.683056\pi\)
−0.543909 + 0.839144i \(0.683056\pi\)
\(440\) −212.047 −0.0229749
\(441\) −720.974 −0.0778505
\(442\) −489.517 −0.0526786
\(443\) −14141.0 −1.51661 −0.758305 0.651899i \(-0.773972\pi\)
−0.758305 + 0.651899i \(0.773972\pi\)
\(444\) 4210.46 0.450044
\(445\) 4786.32 0.509872
\(446\) 127.161 0.0135006
\(447\) 4857.15 0.513949
\(448\) 8144.74 0.858935
\(449\) 6345.25 0.666929 0.333464 0.942763i \(-0.391782\pi\)
0.333464 + 0.942763i \(0.391782\pi\)
\(450\) 96.2868 0.0100867
\(451\) −2717.75 −0.283755
\(452\) −13044.1 −1.35740
\(453\) 6649.82 0.689704
\(454\) 747.177 0.0772396
\(455\) −6941.59 −0.715224
\(456\) 1129.80 0.116026
\(457\) −16600.2 −1.69918 −0.849588 0.527447i \(-0.823149\pi\)
−0.849588 + 0.527447i \(0.823149\pi\)
\(458\) −157.885 −0.0161080
\(459\) −1475.42 −0.150037
\(460\) 9002.81 0.912518
\(461\) 2278.07 0.230153 0.115076 0.993357i \(-0.463289\pi\)
0.115076 + 0.993357i \(0.463289\pi\)
\(462\) 85.0213 0.00856179
\(463\) −167.261 −0.0167889 −0.00839447 0.999965i \(-0.502672\pi\)
−0.00839447 + 0.999965i \(0.502672\pi\)
\(464\) 7986.87 0.799097
\(465\) −163.050 −0.0162608
\(466\) 583.179 0.0579726
\(467\) 13178.8 1.30587 0.652934 0.757415i \(-0.273538\pi\)
0.652934 + 0.757415i \(0.273538\pi\)
\(468\) −4046.22 −0.399651
\(469\) −1103.19 −0.108616
\(470\) −156.484 −0.0153576
\(471\) 5108.94 0.499803
\(472\) 942.507 0.0919119
\(473\) −341.313 −0.0331788
\(474\) 595.870 0.0577410
\(475\) 9989.00 0.964898
\(476\) 7065.74 0.680374
\(477\) −148.229 −0.0142283
\(478\) 642.966 0.0615242
\(479\) 13097.7 1.24938 0.624688 0.780874i \(-0.285226\pi\)
0.624688 + 0.780874i \(0.285226\pi\)
\(480\) 692.147 0.0658167
\(481\) 9921.59 0.940511
\(482\) −929.727 −0.0878587
\(483\) −7230.86 −0.681192
\(484\) −964.945 −0.0906222
\(485\) 4640.90 0.434500
\(486\) 38.6128 0.00360394
\(487\) −20142.6 −1.87422 −0.937112 0.349028i \(-0.886512\pi\)
−0.937112 + 0.349028i \(0.886512\pi\)
\(488\) 154.842 0.0143635
\(489\) 4278.17 0.395635
\(490\) 96.6680 0.00891228
\(491\) 17184.9 1.57952 0.789758 0.613418i \(-0.210206\pi\)
0.789758 + 0.613418i \(0.210206\pi\)
\(492\) 5910.91 0.541635
\(493\) 6884.56 0.628935
\(494\) 1329.04 0.121045
\(495\) −751.823 −0.0682665
\(496\) 453.703 0.0410723
\(497\) −5336.39 −0.481629
\(498\) −430.830 −0.0387669
\(499\) −1854.10 −0.166335 −0.0831674 0.996536i \(-0.526504\pi\)
−0.0831674 + 0.996536i \(0.526504\pi\)
\(500\) 11647.7 1.04180
\(501\) 1252.29 0.111673
\(502\) 85.2885 0.00758289
\(503\) 19551.2 1.73309 0.866547 0.499095i \(-0.166334\pi\)
0.866547 + 0.499095i \(0.166334\pi\)
\(504\) −370.416 −0.0327374
\(505\) −13544.8 −1.19353
\(506\) −259.835 −0.0228282
\(507\) −2943.57 −0.257847
\(508\) −4550.12 −0.397400
\(509\) −794.442 −0.0691808 −0.0345904 0.999402i \(-0.511013\pi\)
−0.0345904 + 0.999402i \(0.511013\pi\)
\(510\) 197.824 0.0171761
\(511\) −12785.1 −1.10681
\(512\) −3213.33 −0.277364
\(513\) 4005.77 0.344755
\(514\) 113.332 0.00972545
\(515\) 7155.79 0.612275
\(516\) 742.332 0.0633320
\(517\) −1426.45 −0.121345
\(518\) 453.425 0.0384601
\(519\) −5509.79 −0.465998
\(520\) 1086.75 0.0916484
\(521\) −9926.01 −0.834676 −0.417338 0.908751i \(-0.637037\pi\)
−0.417338 + 0.908751i \(0.637037\pi\)
\(522\) −180.174 −0.0151073
\(523\) 10642.5 0.889796 0.444898 0.895581i \(-0.353240\pi\)
0.444898 + 0.895581i \(0.353240\pi\)
\(524\) −1367.96 −0.114045
\(525\) −3274.98 −0.272251
\(526\) −870.816 −0.0721851
\(527\) 391.085 0.0323262
\(528\) 2092.02 0.172431
\(529\) 9931.39 0.816256
\(530\) 19.8745 0.00162885
\(531\) 3341.70 0.273103
\(532\) −19183.5 −1.56337
\(533\) 13928.6 1.13192
\(534\) 300.447 0.0243476
\(535\) −10960.5 −0.885728
\(536\) 172.712 0.0139179
\(537\) 2324.78 0.186819
\(538\) 993.020 0.0795764
\(539\) 881.190 0.0704185
\(540\) 1635.16 0.130308
\(541\) −20526.6 −1.63125 −0.815625 0.578581i \(-0.803607\pi\)
−0.815625 + 0.578581i \(0.803607\pi\)
\(542\) 1248.32 0.0989296
\(543\) −6230.07 −0.492372
\(544\) −1660.15 −0.130843
\(545\) −1401.85 −0.110181
\(546\) −435.737 −0.0341536
\(547\) 3413.70 0.266836 0.133418 0.991060i \(-0.457405\pi\)
0.133418 + 0.991060i \(0.457405\pi\)
\(548\) 21203.1 1.65283
\(549\) 549.000 0.0426790
\(550\) −117.684 −0.00912374
\(551\) −18691.6 −1.44517
\(552\) 1132.04 0.0872875
\(553\) −20267.2 −1.55850
\(554\) 12.9942 0.000996515 0
\(555\) −4009.53 −0.306658
\(556\) 13108.3 0.999846
\(557\) −8914.40 −0.678125 −0.339062 0.940764i \(-0.610110\pi\)
−0.339062 + 0.940764i \(0.610110\pi\)
\(558\) −10.2350 −0.000776489 0
\(559\) 1749.24 0.132352
\(560\) −7805.88 −0.589033
\(561\) 1803.29 0.135713
\(562\) 930.668 0.0698539
\(563\) −2690.90 −0.201435 −0.100718 0.994915i \(-0.532114\pi\)
−0.100718 + 0.994915i \(0.532114\pi\)
\(564\) 3102.44 0.231624
\(565\) 12421.6 0.924923
\(566\) 817.425 0.0607048
\(567\) −1313.33 −0.0972745
\(568\) 835.445 0.0617157
\(569\) 474.580 0.0349656 0.0174828 0.999847i \(-0.494435\pi\)
0.0174828 + 0.999847i \(0.494435\pi\)
\(570\) −537.093 −0.0394673
\(571\) 24472.2 1.79357 0.896785 0.442467i \(-0.145897\pi\)
0.896785 + 0.442467i \(0.145897\pi\)
\(572\) 4945.38 0.361498
\(573\) 3082.66 0.224747
\(574\) 636.546 0.0462873
\(575\) 10008.7 0.725901
\(576\) −4520.97 −0.327038
\(577\) 6572.85 0.474231 0.237116 0.971481i \(-0.423798\pi\)
0.237116 + 0.971481i \(0.423798\pi\)
\(578\) 306.185 0.0220340
\(579\) 3419.48 0.245438
\(580\) −7629.95 −0.546235
\(581\) 14653.7 1.04637
\(582\) 291.318 0.0207483
\(583\) 181.168 0.0128700
\(584\) 2001.59 0.141826
\(585\) 3853.12 0.272320
\(586\) 11.1749 0.000787768 0
\(587\) 3223.80 0.226679 0.113339 0.993556i \(-0.463845\pi\)
0.113339 + 0.993556i \(0.463845\pi\)
\(588\) −1916.53 −0.134416
\(589\) −1061.80 −0.0742794
\(590\) −448.055 −0.0312646
\(591\) −1546.49 −0.107638
\(592\) 11156.9 0.774572
\(593\) −19688.6 −1.36343 −0.681713 0.731619i \(-0.738765\pi\)
−0.681713 + 0.731619i \(0.738765\pi\)
\(594\) −47.1934 −0.00325988
\(595\) −6728.55 −0.463603
\(596\) 12911.5 0.887376
\(597\) −2165.53 −0.148457
\(598\) 1331.67 0.0910634
\(599\) −5165.49 −0.352347 −0.176174 0.984359i \(-0.556372\pi\)
−0.176174 + 0.984359i \(0.556372\pi\)
\(600\) 512.719 0.0348861
\(601\) 6219.53 0.422130 0.211065 0.977472i \(-0.432307\pi\)
0.211065 + 0.977472i \(0.432307\pi\)
\(602\) 79.9417 0.00541226
\(603\) 612.358 0.0413551
\(604\) 17676.9 1.19083
\(605\) 918.895 0.0617494
\(606\) −850.231 −0.0569938
\(607\) −17723.6 −1.18514 −0.592570 0.805519i \(-0.701886\pi\)
−0.592570 + 0.805519i \(0.701886\pi\)
\(608\) 4507.33 0.300652
\(609\) 6128.21 0.407763
\(610\) −73.6098 −0.00488586
\(611\) 7310.62 0.484053
\(612\) −3922.04 −0.259051
\(613\) 20623.5 1.35885 0.679425 0.733745i \(-0.262229\pi\)
0.679425 + 0.733745i \(0.262229\pi\)
\(614\) 350.515 0.0230385
\(615\) −5628.83 −0.369067
\(616\) 452.731 0.0296121
\(617\) 27619.0 1.80211 0.901054 0.433707i \(-0.142795\pi\)
0.901054 + 0.433707i \(0.142795\pi\)
\(618\) 449.183 0.0292375
\(619\) 233.579 0.0151669 0.00758347 0.999971i \(-0.497586\pi\)
0.00758347 + 0.999971i \(0.497586\pi\)
\(620\) −433.428 −0.0280756
\(621\) 4013.69 0.259362
\(622\) 347.784 0.0224194
\(623\) −10219.0 −0.657169
\(624\) −10721.7 −0.687839
\(625\) −2675.81 −0.171252
\(626\) −821.852 −0.0524725
\(627\) −4895.95 −0.311843
\(628\) 13580.8 0.862953
\(629\) 9617.09 0.609632
\(630\) 176.091 0.0111359
\(631\) 7633.29 0.481579 0.240790 0.970577i \(-0.422594\pi\)
0.240790 + 0.970577i \(0.422594\pi\)
\(632\) 3172.96 0.199705
\(633\) −15127.5 −0.949863
\(634\) −1514.68 −0.0948829
\(635\) 4332.98 0.270786
\(636\) −394.029 −0.0245664
\(637\) −4516.14 −0.280904
\(638\) 220.212 0.0136650
\(639\) 2962.11 0.183379
\(640\) 2451.89 0.151437
\(641\) −20909.1 −1.28840 −0.644198 0.764859i \(-0.722809\pi\)
−0.644198 + 0.764859i \(0.722809\pi\)
\(642\) −688.014 −0.0422955
\(643\) 12912.3 0.791929 0.395965 0.918266i \(-0.370410\pi\)
0.395965 + 0.918266i \(0.370410\pi\)
\(644\) −19221.4 −1.17613
\(645\) −706.906 −0.0431541
\(646\) 1288.25 0.0784606
\(647\) 1284.56 0.0780545 0.0390272 0.999238i \(-0.487574\pi\)
0.0390272 + 0.999238i \(0.487574\pi\)
\(648\) 205.610 0.0124647
\(649\) −4084.30 −0.247031
\(650\) 603.134 0.0363952
\(651\) 348.120 0.0209584
\(652\) 11372.5 0.683098
\(653\) 26149.3 1.56708 0.783538 0.621344i \(-0.213413\pi\)
0.783538 + 0.621344i \(0.213413\pi\)
\(654\) −87.9971 −0.00526140
\(655\) 1302.67 0.0777094
\(656\) 15662.8 0.932209
\(657\) 7096.74 0.421416
\(658\) 334.101 0.0197943
\(659\) −20467.8 −1.20988 −0.604941 0.796270i \(-0.706803\pi\)
−0.604941 + 0.796270i \(0.706803\pi\)
\(660\) −1998.53 −0.117868
\(661\) −23684.0 −1.39364 −0.696822 0.717244i \(-0.745403\pi\)
−0.696822 + 0.717244i \(0.745403\pi\)
\(662\) 361.952 0.0212503
\(663\) −9241.95 −0.541369
\(664\) −2294.13 −0.134081
\(665\) 18268.0 1.06527
\(666\) −251.686 −0.0146436
\(667\) −18728.6 −1.08722
\(668\) 3328.90 0.192813
\(669\) 2400.77 0.138743
\(670\) −82.1048 −0.00473431
\(671\) −671.000 −0.0386046
\(672\) −1477.77 −0.0848305
\(673\) 10788.4 0.617926 0.308963 0.951074i \(-0.400018\pi\)
0.308963 + 0.951074i \(0.400018\pi\)
\(674\) 22.5762 0.00129021
\(675\) 1817.87 0.103659
\(676\) −7824.75 −0.445195
\(677\) −6014.94 −0.341467 −0.170733 0.985317i \(-0.554614\pi\)
−0.170733 + 0.985317i \(0.554614\pi\)
\(678\) 779.730 0.0441672
\(679\) −9908.55 −0.560022
\(680\) 1053.40 0.0594058
\(681\) 14106.5 0.793778
\(682\) 12.5094 0.000702361 0
\(683\) 5200.97 0.291376 0.145688 0.989331i \(-0.453460\pi\)
0.145688 + 0.989331i \(0.453460\pi\)
\(684\) 10648.4 0.595248
\(685\) −20191.2 −1.12623
\(686\) −1090.10 −0.0606707
\(687\) −2980.83 −0.165540
\(688\) 1967.04 0.109001
\(689\) −928.495 −0.0513394
\(690\) −538.155 −0.0296916
\(691\) 28019.3 1.54255 0.771277 0.636500i \(-0.219619\pi\)
0.771277 + 0.636500i \(0.219619\pi\)
\(692\) −14646.4 −0.804584
\(693\) 1605.18 0.0879881
\(694\) −1247.87 −0.0682543
\(695\) −12482.7 −0.681289
\(696\) −959.411 −0.0522505
\(697\) 13501.1 0.733701
\(698\) 1655.74 0.0897863
\(699\) 11010.3 0.595775
\(700\) −8705.72 −0.470065
\(701\) 18707.2 1.00793 0.503966 0.863723i \(-0.331874\pi\)
0.503966 + 0.863723i \(0.331874\pi\)
\(702\) 241.868 0.0130039
\(703\) −26110.4 −1.40082
\(704\) 5525.63 0.295817
\(705\) −2954.38 −0.157827
\(706\) −463.332 −0.0246993
\(707\) 28918.7 1.53833
\(708\) 8883.08 0.471535
\(709\) −30439.1 −1.61236 −0.806180 0.591671i \(-0.798469\pi\)
−0.806180 + 0.591671i \(0.798469\pi\)
\(710\) −397.159 −0.0209931
\(711\) 11249.9 0.593395
\(712\) 1599.85 0.0842093
\(713\) −1063.90 −0.0558811
\(714\) −422.364 −0.0221381
\(715\) −4709.37 −0.246323
\(716\) 6179.84 0.322558
\(717\) 12139.0 0.632274
\(718\) −370.761 −0.0192712
\(719\) 28516.1 1.47910 0.739548 0.673103i \(-0.235039\pi\)
0.739548 + 0.673103i \(0.235039\pi\)
\(720\) 4332.87 0.224273
\(721\) −15278.0 −0.789155
\(722\) −2407.71 −0.124107
\(723\) −17553.0 −0.902909
\(724\) −16561.1 −0.850122
\(725\) −8482.49 −0.434526
\(726\) 57.6809 0.00294867
\(727\) 10135.0 0.517037 0.258519 0.966006i \(-0.416766\pi\)
0.258519 + 0.966006i \(0.416766\pi\)
\(728\) −2320.27 −0.118125
\(729\) 729.000 0.0370370
\(730\) −951.529 −0.0482434
\(731\) 1695.56 0.0857898
\(732\) 1459.38 0.0736888
\(733\) 20347.8 1.02532 0.512662 0.858590i \(-0.328659\pi\)
0.512662 + 0.858590i \(0.328659\pi\)
\(734\) 232.680 0.0117008
\(735\) 1825.07 0.0915899
\(736\) 4516.24 0.226183
\(737\) −748.438 −0.0374071
\(738\) −353.333 −0.0176238
\(739\) 3316.79 0.165101 0.0825507 0.996587i \(-0.473693\pi\)
0.0825507 + 0.996587i \(0.473693\pi\)
\(740\) −10658.3 −0.529470
\(741\) 25091.9 1.24396
\(742\) −42.4329 −0.00209941
\(743\) −7664.13 −0.378425 −0.189212 0.981936i \(-0.560593\pi\)
−0.189212 + 0.981936i \(0.560593\pi\)
\(744\) −54.5004 −0.00268559
\(745\) −12295.3 −0.604653
\(746\) 1394.90 0.0684599
\(747\) −8133.95 −0.398401
\(748\) 4793.60 0.234320
\(749\) 23401.3 1.14161
\(750\) −696.259 −0.0338984
\(751\) 16167.4 0.785564 0.392782 0.919632i \(-0.371513\pi\)
0.392782 + 0.919632i \(0.371513\pi\)
\(752\) 8220.86 0.398649
\(753\) 1610.22 0.0779281
\(754\) −1128.60 −0.0545108
\(755\) −16833.3 −0.811426
\(756\) −3491.16 −0.167953
\(757\) −39481.5 −1.89561 −0.947806 0.318849i \(-0.896704\pi\)
−0.947806 + 0.318849i \(0.896704\pi\)
\(758\) 2104.36 0.100836
\(759\) −4905.62 −0.234602
\(760\) −2859.98 −0.136503
\(761\) −7737.32 −0.368565 −0.184282 0.982873i \(-0.558996\pi\)
−0.184282 + 0.982873i \(0.558996\pi\)
\(762\) 271.990 0.0129306
\(763\) 2993.02 0.142011
\(764\) 8194.48 0.388044
\(765\) 3734.87 0.176516
\(766\) 519.898 0.0245231
\(767\) 20932.2 0.985422
\(768\) −11902.0 −0.559214
\(769\) 37946.6 1.77944 0.889720 0.456507i \(-0.150900\pi\)
0.889720 + 0.456507i \(0.150900\pi\)
\(770\) −215.222 −0.0100728
\(771\) 2139.69 0.0999468
\(772\) 9089.83 0.423770
\(773\) −16563.3 −0.770686 −0.385343 0.922773i \(-0.625917\pi\)
−0.385343 + 0.922773i \(0.625917\pi\)
\(774\) −44.3739 −0.00206071
\(775\) −481.857 −0.0223339
\(776\) 1551.25 0.0717610
\(777\) 8560.54 0.395248
\(778\) 1305.01 0.0601374
\(779\) −36655.5 −1.68590
\(780\) 10242.6 0.470183
\(781\) −3620.36 −0.165873
\(782\) 1290.80 0.0590266
\(783\) −3401.64 −0.155255
\(784\) −5078.43 −0.231343
\(785\) −12932.7 −0.588011
\(786\) 81.7714 0.00371080
\(787\) −5332.98 −0.241550 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(788\) −4110.96 −0.185846
\(789\) −16440.8 −0.741834
\(790\) −1508.38 −0.0679314
\(791\) −26520.8 −1.19212
\(792\) −251.301 −0.0112747
\(793\) 3438.90 0.153996
\(794\) 281.016 0.0125603
\(795\) 375.225 0.0167394
\(796\) −5756.51 −0.256324
\(797\) −24647.3 −1.09542 −0.547711 0.836668i \(-0.684501\pi\)
−0.547711 + 0.836668i \(0.684501\pi\)
\(798\) 1146.72 0.0508690
\(799\) 7086.25 0.313759
\(800\) 2045.48 0.0903983
\(801\) 5672.35 0.250216
\(802\) 2508.37 0.110441
\(803\) −8673.79 −0.381185
\(804\) 1627.80 0.0714031
\(805\) 18304.1 0.801412
\(806\) −64.1112 −0.00280176
\(807\) 18748.0 0.817794
\(808\) −4527.41 −0.197121
\(809\) −24675.6 −1.07237 −0.536186 0.844100i \(-0.680135\pi\)
−0.536186 + 0.844100i \(0.680135\pi\)
\(810\) −97.7441 −0.00423997
\(811\) 34447.2 1.49150 0.745749 0.666226i \(-0.232092\pi\)
0.745749 + 0.666226i \(0.232092\pi\)
\(812\) 16290.3 0.704037
\(813\) 23567.9 1.01668
\(814\) 307.616 0.0132456
\(815\) −10829.7 −0.465459
\(816\) −10392.6 −0.445852
\(817\) −4603.44 −0.197128
\(818\) 1085.19 0.0463849
\(819\) −8226.61 −0.350990
\(820\) −14962.8 −0.637225
\(821\) 19898.1 0.845858 0.422929 0.906163i \(-0.361002\pi\)
0.422929 + 0.906163i \(0.361002\pi\)
\(822\) −1267.44 −0.0537801
\(823\) −18636.7 −0.789348 −0.394674 0.918821i \(-0.629142\pi\)
−0.394674 + 0.918821i \(0.629142\pi\)
\(824\) 2391.86 0.101122
\(825\) −2221.84 −0.0937631
\(826\) 956.619 0.0402967
\(827\) −11898.2 −0.500292 −0.250146 0.968208i \(-0.580479\pi\)
−0.250146 + 0.968208i \(0.580479\pi\)
\(828\) 10669.4 0.447811
\(829\) 43352.8 1.81629 0.908145 0.418656i \(-0.137499\pi\)
0.908145 + 0.418656i \(0.137499\pi\)
\(830\) 1090.60 0.0456087
\(831\) 245.327 0.0102410
\(832\) −28319.1 −1.18003
\(833\) −4377.53 −0.182080
\(834\) −783.564 −0.0325331
\(835\) −3170.03 −0.131381
\(836\) −13014.7 −0.538422
\(837\) −193.234 −0.00797984
\(838\) 1359.21 0.0560300
\(839\) −33554.0 −1.38071 −0.690354 0.723472i \(-0.742545\pi\)
−0.690354 + 0.723472i \(0.742545\pi\)
\(840\) 937.669 0.0385151
\(841\) −8516.39 −0.349190
\(842\) 228.425 0.00934920
\(843\) 17570.8 0.717876
\(844\) −40212.6 −1.64002
\(845\) 7451.33 0.303353
\(846\) −185.452 −0.00753662
\(847\) −1961.89 −0.0795882
\(848\) −1044.10 −0.0422813
\(849\) 15432.8 0.623853
\(850\) 584.624 0.0235911
\(851\) −26162.1 −1.05385
\(852\) 7874.03 0.316620
\(853\) −43025.0 −1.72702 −0.863510 0.504331i \(-0.831739\pi\)
−0.863510 + 0.504331i \(0.831739\pi\)
\(854\) 157.161 0.00629733
\(855\) −10140.2 −0.405599
\(856\) −3663.62 −0.146285
\(857\) 12607.0 0.502504 0.251252 0.967922i \(-0.419158\pi\)
0.251252 + 0.967922i \(0.419158\pi\)
\(858\) −295.617 −0.0117625
\(859\) 41961.8 1.66673 0.833364 0.552724i \(-0.186412\pi\)
0.833364 + 0.552724i \(0.186412\pi\)
\(860\) −1879.13 −0.0745092
\(861\) 12017.8 0.475687
\(862\) 926.563 0.0366112
\(863\) 16562.7 0.653302 0.326651 0.945145i \(-0.394080\pi\)
0.326651 + 0.945145i \(0.394080\pi\)
\(864\) 820.276 0.0322990
\(865\) 13947.4 0.548239
\(866\) 1618.09 0.0634932
\(867\) 5780.70 0.226439
\(868\) 925.389 0.0361864
\(869\) −13749.9 −0.536746
\(870\) 456.091 0.0177735
\(871\) 3835.77 0.149220
\(872\) −468.577 −0.0181973
\(873\) 5500.02 0.213227
\(874\) −3504.52 −0.135632
\(875\) 23681.7 0.914957
\(876\) 18864.9 0.727610
\(877\) −34908.5 −1.34410 −0.672050 0.740506i \(-0.734586\pi\)
−0.672050 + 0.740506i \(0.734586\pi\)
\(878\) 1589.93 0.0611134
\(879\) 210.980 0.00809576
\(880\) −5295.73 −0.202863
\(881\) 4822.30 0.184413 0.0922063 0.995740i \(-0.470608\pi\)
0.0922063 + 0.995740i \(0.470608\pi\)
\(882\) 114.563 0.00437363
\(883\) −45848.4 −1.74736 −0.873682 0.486497i \(-0.838274\pi\)
−0.873682 + 0.486497i \(0.838274\pi\)
\(884\) −24567.4 −0.934719
\(885\) −8459.16 −0.321301
\(886\) 2247.01 0.0852029
\(887\) 37278.2 1.41114 0.705570 0.708641i \(-0.250691\pi\)
0.705570 + 0.708641i \(0.250691\pi\)
\(888\) −1340.21 −0.0506469
\(889\) −9251.13 −0.349013
\(890\) −760.548 −0.0286445
\(891\) −891.000 −0.0335013
\(892\) 6381.85 0.239552
\(893\) −19239.2 −0.720958
\(894\) −771.803 −0.0288735
\(895\) −5884.93 −0.219789
\(896\) −5234.92 −0.195186
\(897\) 25141.5 0.935843
\(898\) −1008.26 −0.0374679
\(899\) 901.660 0.0334506
\(900\) 4832.35 0.178976
\(901\) −899.998 −0.0332778
\(902\) 431.851 0.0159413
\(903\) 1509.28 0.0556209
\(904\) 4152.00 0.152758
\(905\) 15770.8 0.579268
\(906\) −1056.66 −0.0387474
\(907\) −25419.1 −0.930572 −0.465286 0.885160i \(-0.654049\pi\)
−0.465286 + 0.885160i \(0.654049\pi\)
\(908\) 37498.7 1.37052
\(909\) −16052.1 −0.585716
\(910\) 1103.02 0.0401811
\(911\) 27426.2 0.997442 0.498721 0.866762i \(-0.333803\pi\)
0.498721 + 0.866762i \(0.333803\pi\)
\(912\) 28216.1 1.02448
\(913\) 9941.50 0.360367
\(914\) 2637.78 0.0954593
\(915\) −1389.73 −0.0502111
\(916\) −7923.79 −0.285818
\(917\) −2781.27 −0.100159
\(918\) 234.445 0.00842902
\(919\) −25914.7 −0.930193 −0.465097 0.885260i \(-0.653980\pi\)
−0.465097 + 0.885260i \(0.653980\pi\)
\(920\) −2865.63 −0.102692
\(921\) 6617.64 0.236763
\(922\) −361.987 −0.0129299
\(923\) 18554.5 0.661677
\(924\) 4266.97 0.151919
\(925\) −11849.2 −0.421190
\(926\) 26.5779 0.000943200 0
\(927\) 8480.46 0.300469
\(928\) −3827.55 −0.135394
\(929\) 13045.8 0.460731 0.230365 0.973104i \(-0.426008\pi\)
0.230365 + 0.973104i \(0.426008\pi\)
\(930\) 25.9087 0.000913527 0
\(931\) 11885.0 0.418384
\(932\) 29268.0 1.02865
\(933\) 6566.08 0.230401
\(934\) −2094.11 −0.0733634
\(935\) −4564.84 −0.159664
\(936\) 1287.93 0.0449757
\(937\) −36485.9 −1.27209 −0.636043 0.771654i \(-0.719430\pi\)
−0.636043 + 0.771654i \(0.719430\pi\)
\(938\) 175.298 0.00610200
\(939\) −15516.4 −0.539251
\(940\) −7853.48 −0.272502
\(941\) 2182.63 0.0756130 0.0378065 0.999285i \(-0.487963\pi\)
0.0378065 + 0.999285i \(0.487963\pi\)
\(942\) −811.813 −0.0280789
\(943\) −36727.9 −1.26832
\(944\) 23538.5 0.811559
\(945\) 3324.55 0.114442
\(946\) 54.2347 0.00186398
\(947\) 51756.9 1.77600 0.888000 0.459844i \(-0.152095\pi\)
0.888000 + 0.459844i \(0.152095\pi\)
\(948\) 29905.0 1.02455
\(949\) 44453.5 1.52057
\(950\) −1587.26 −0.0542078
\(951\) −28596.8 −0.975096
\(952\) −2249.05 −0.0765675
\(953\) −33387.3 −1.13486 −0.567430 0.823422i \(-0.692062\pi\)
−0.567430 + 0.823422i \(0.692062\pi\)
\(954\) 23.5536 0.000799346 0
\(955\) −7803.41 −0.264411
\(956\) 32268.6 1.09167
\(957\) 4157.56 0.140433
\(958\) −2081.24 −0.0701897
\(959\) 43109.3 1.45159
\(960\) 11444.3 0.384755
\(961\) −29739.8 −0.998281
\(962\) −1576.55 −0.0528377
\(963\) −12989.5 −0.434664
\(964\) −46660.3 −1.55895
\(965\) −8656.04 −0.288754
\(966\) 1148.99 0.0382692
\(967\) 34807.8 1.15754 0.578772 0.815490i \(-0.303532\pi\)
0.578772 + 0.815490i \(0.303532\pi\)
\(968\) 307.146 0.0101984
\(969\) 24321.8 0.806326
\(970\) −737.441 −0.0244101
\(971\) −15226.5 −0.503236 −0.251618 0.967827i \(-0.580963\pi\)
−0.251618 + 0.967827i \(0.580963\pi\)
\(972\) 1937.86 0.0639476
\(973\) 26651.2 0.878107
\(974\) 3200.67 0.105294
\(975\) 11387.0 0.374027
\(976\) 3867.07 0.126826
\(977\) 17674.8 0.578779 0.289389 0.957211i \(-0.406548\pi\)
0.289389 + 0.957211i \(0.406548\pi\)
\(978\) −679.804 −0.0222267
\(979\) −6932.88 −0.226329
\(980\) 4851.48 0.158138
\(981\) −1661.36 −0.0540705
\(982\) −2730.68 −0.0887369
\(983\) 3847.33 0.124833 0.0624165 0.998050i \(-0.480119\pi\)
0.0624165 + 0.998050i \(0.480119\pi\)
\(984\) −1881.47 −0.0609543
\(985\) 3914.77 0.126635
\(986\) −1093.96 −0.0353335
\(987\) 6307.75 0.203422
\(988\) 66700.6 2.14780
\(989\) −4612.54 −0.148302
\(990\) 119.465 0.00383520
\(991\) −13287.6 −0.425929 −0.212965 0.977060i \(-0.568312\pi\)
−0.212965 + 0.977060i \(0.568312\pi\)
\(992\) −217.428 −0.00695901
\(993\) 6833.56 0.218385
\(994\) 847.954 0.0270578
\(995\) 5481.80 0.174658
\(996\) −21622.1 −0.687873
\(997\) −17299.1 −0.549515 −0.274757 0.961514i \(-0.588598\pi\)
−0.274757 + 0.961514i \(0.588598\pi\)
\(998\) 294.618 0.00934466
\(999\) −4751.77 −0.150490
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 2013.4.a.b.1.17 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.4.a.b.1.17 36 1.1 even 1 trivial