Properties

Label 2013.4.a.d.1.14
Level $2013$
Weight $4$
Character 2013.1
Self dual yes
Analytic conductor $118.771$
Analytic rank $1$
Dimension $37$
CM no
Inner twists $1$

Related objects

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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: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
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)
 
\(f(q)\) \(=\) \(q-1.94841 q^{2} -3.00000 q^{3} -4.20370 q^{4} +15.7553 q^{5} +5.84523 q^{6} +3.79858 q^{7} +23.7778 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.94841 q^{2} -3.00000 q^{3} -4.20370 q^{4} +15.7553 q^{5} +5.84523 q^{6} +3.79858 q^{7} +23.7778 q^{8} +9.00000 q^{9} -30.6978 q^{10} +11.0000 q^{11} +12.6111 q^{12} +55.4159 q^{13} -7.40119 q^{14} -47.2659 q^{15} -12.6993 q^{16} +20.7761 q^{17} -17.5357 q^{18} -32.9745 q^{19} -66.2306 q^{20} -11.3957 q^{21} -21.4325 q^{22} -38.9042 q^{23} -71.3334 q^{24} +123.230 q^{25} -107.973 q^{26} -27.0000 q^{27} -15.9681 q^{28} +129.231 q^{29} +92.0934 q^{30} -249.275 q^{31} -165.479 q^{32} -33.0000 q^{33} -40.4803 q^{34} +59.8478 q^{35} -37.8333 q^{36} -388.149 q^{37} +64.2478 q^{38} -166.248 q^{39} +374.627 q^{40} -109.584 q^{41} +22.2036 q^{42} +309.284 q^{43} -46.2407 q^{44} +141.798 q^{45} +75.8014 q^{46} -137.846 q^{47} +38.0980 q^{48} -328.571 q^{49} -240.102 q^{50} -62.3282 q^{51} -232.952 q^{52} -648.460 q^{53} +52.6071 q^{54} +173.308 q^{55} +90.3219 q^{56} +98.9234 q^{57} -251.795 q^{58} -715.504 q^{59} +198.692 q^{60} -61.0000 q^{61} +485.691 q^{62} +34.1872 q^{63} +424.016 q^{64} +873.094 q^{65} +64.2975 q^{66} -655.093 q^{67} -87.3363 q^{68} +116.713 q^{69} -116.608 q^{70} -308.934 q^{71} +214.000 q^{72} +442.021 q^{73} +756.273 q^{74} -369.689 q^{75} +138.615 q^{76} +41.7844 q^{77} +323.919 q^{78} +694.672 q^{79} -200.082 q^{80} +81.0000 q^{81} +213.514 q^{82} -957.704 q^{83} +47.9042 q^{84} +327.333 q^{85} -602.612 q^{86} -387.693 q^{87} +261.556 q^{88} +460.404 q^{89} -276.280 q^{90} +210.502 q^{91} +163.542 q^{92} +747.826 q^{93} +268.580 q^{94} -519.523 q^{95} +496.437 q^{96} +1222.33 q^{97} +640.191 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q - 4 q^{2} - 111 q^{3} + 158 q^{4} - 15 q^{5} + 12 q^{6} - 77 q^{7} - 69 q^{8} + 333 q^{9} - 45 q^{10} + 407 q^{11} - 474 q^{12} - 169 q^{13} + 102 q^{14} + 45 q^{15} + 598 q^{16} - 338 q^{17} - 36 q^{18} - 235 q^{19} - 550 q^{20} + 231 q^{21} - 44 q^{22} - 53 q^{23} + 207 q^{24} + 750 q^{25} - 75 q^{26} - 999 q^{27} - 1378 q^{28} - 30 q^{29} + 135 q^{30} - 506 q^{31} - 841 q^{32} - 1221 q^{33} - 316 q^{34} - 822 q^{35} + 1422 q^{36} - 830 q^{37} - 371 q^{38} + 507 q^{39} - 613 q^{40} + 16 q^{41} - 306 q^{42} - 1137 q^{43} + 1738 q^{44} - 135 q^{45} - 659 q^{46} - 489 q^{47} - 1794 q^{48} + 2214 q^{49} + 1066 q^{50} + 1014 q^{51} - 2342 q^{52} + 731 q^{53} + 108 q^{54} - 165 q^{55} + 3051 q^{56} + 705 q^{57} - 611 q^{58} - 425 q^{59} + 1650 q^{60} - 2257 q^{61} + 453 q^{62} - 693 q^{63} + 4919 q^{64} + 1346 q^{65} + 132 q^{66} - 1907 q^{67} - 3236 q^{68} + 159 q^{69} - 1050 q^{70} - 561 q^{71} - 621 q^{72} - 2397 q^{73} - 1840 q^{74} - 2250 q^{75} - 3868 q^{76} - 847 q^{77} + 225 q^{78} + 393 q^{79} - 4031 q^{80} + 2997 q^{81} - 1946 q^{82} - 4191 q^{83} + 4134 q^{84} - 2667 q^{85} + 2405 q^{86} + 90 q^{87} - 759 q^{88} + 1437 q^{89} - 405 q^{90} - 5192 q^{91} - 737 q^{92} + 1518 q^{93} - 1960 q^{94} + 1356 q^{95} + 2523 q^{96} - 2368 q^{97} - 3014 q^{98} + 3663 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94841 −0.688867 −0.344434 0.938811i \(-0.611929\pi\)
−0.344434 + 0.938811i \(0.611929\pi\)
\(3\) −3.00000 −0.577350
\(4\) −4.20370 −0.525462
\(5\) 15.7553 1.40920 0.704599 0.709606i \(-0.251127\pi\)
0.704599 + 0.709606i \(0.251127\pi\)
\(6\) 5.84523 0.397718
\(7\) 3.79858 0.205104 0.102552 0.994728i \(-0.467299\pi\)
0.102552 + 0.994728i \(0.467299\pi\)
\(8\) 23.7778 1.05084
\(9\) 9.00000 0.333333
\(10\) −30.6978 −0.970750
\(11\) 11.0000 0.301511
\(12\) 12.6111 0.303376
\(13\) 55.4159 1.18228 0.591138 0.806570i \(-0.298679\pi\)
0.591138 + 0.806570i \(0.298679\pi\)
\(14\) −7.40119 −0.141289
\(15\) −47.2659 −0.813601
\(16\) −12.6993 −0.198427
\(17\) 20.7761 0.296408 0.148204 0.988957i \(-0.452651\pi\)
0.148204 + 0.988957i \(0.452651\pi\)
\(18\) −17.5357 −0.229622
\(19\) −32.9745 −0.398150 −0.199075 0.979984i \(-0.563794\pi\)
−0.199075 + 0.979984i \(0.563794\pi\)
\(20\) −66.2306 −0.740480
\(21\) −11.3957 −0.118417
\(22\) −21.4325 −0.207701
\(23\) −38.9042 −0.352700 −0.176350 0.984328i \(-0.556429\pi\)
−0.176350 + 0.984328i \(0.556429\pi\)
\(24\) −71.3334 −0.606703
\(25\) 123.230 0.985838
\(26\) −107.973 −0.814432
\(27\) −27.0000 −0.192450
\(28\) −15.9681 −0.107774
\(29\) 129.231 0.827504 0.413752 0.910390i \(-0.364218\pi\)
0.413752 + 0.910390i \(0.364218\pi\)
\(30\) 92.0934 0.560463
\(31\) −249.275 −1.44423 −0.722116 0.691772i \(-0.756830\pi\)
−0.722116 + 0.691772i \(0.756830\pi\)
\(32\) −165.479 −0.914151
\(33\) −33.0000 −0.174078
\(34\) −40.4803 −0.204186
\(35\) 59.8478 0.289032
\(36\) −37.8333 −0.175154
\(37\) −388.149 −1.72463 −0.862314 0.506374i \(-0.830986\pi\)
−0.862314 + 0.506374i \(0.830986\pi\)
\(38\) 64.2478 0.274273
\(39\) −166.248 −0.682588
\(40\) 374.627 1.48084
\(41\) −109.584 −0.417417 −0.208709 0.977978i \(-0.566926\pi\)
−0.208709 + 0.977978i \(0.566926\pi\)
\(42\) 22.2036 0.0815734
\(43\) 309.284 1.09687 0.548434 0.836194i \(-0.315224\pi\)
0.548434 + 0.836194i \(0.315224\pi\)
\(44\) −46.2407 −0.158433
\(45\) 141.798 0.469733
\(46\) 75.8014 0.242963
\(47\) −137.846 −0.427805 −0.213903 0.976855i \(-0.568618\pi\)
−0.213903 + 0.976855i \(0.568618\pi\)
\(48\) 38.0980 0.114562
\(49\) −328.571 −0.957932
\(50\) −240.102 −0.679111
\(51\) −62.3282 −0.171131
\(52\) −232.952 −0.621242
\(53\) −648.460 −1.68062 −0.840309 0.542107i \(-0.817627\pi\)
−0.840309 + 0.542107i \(0.817627\pi\)
\(54\) 52.6071 0.132573
\(55\) 173.308 0.424889
\(56\) 90.3219 0.215532
\(57\) 98.9234 0.229872
\(58\) −251.795 −0.570040
\(59\) −715.504 −1.57883 −0.789413 0.613863i \(-0.789615\pi\)
−0.789413 + 0.613863i \(0.789615\pi\)
\(60\) 198.692 0.427516
\(61\) −61.0000 −0.128037
\(62\) 485.691 0.994883
\(63\) 34.1872 0.0683680
\(64\) 424.016 0.828156
\(65\) 873.094 1.66606
\(66\) 64.2975 0.119916
\(67\) −655.093 −1.19451 −0.597256 0.802050i \(-0.703743\pi\)
−0.597256 + 0.802050i \(0.703743\pi\)
\(68\) −87.3363 −0.155751
\(69\) 116.713 0.203631
\(70\) −116.608 −0.199105
\(71\) −308.934 −0.516390 −0.258195 0.966093i \(-0.583128\pi\)
−0.258195 + 0.966093i \(0.583128\pi\)
\(72\) 214.000 0.350280
\(73\) 442.021 0.708694 0.354347 0.935114i \(-0.384703\pi\)
0.354347 + 0.935114i \(0.384703\pi\)
\(74\) 756.273 1.18804
\(75\) −369.689 −0.569174
\(76\) 138.615 0.209213
\(77\) 41.7844 0.0618412
\(78\) 323.919 0.470212
\(79\) 694.672 0.989325 0.494662 0.869085i \(-0.335292\pi\)
0.494662 + 0.869085i \(0.335292\pi\)
\(80\) −200.082 −0.279623
\(81\) 81.0000 0.111111
\(82\) 213.514 0.287545
\(83\) −957.704 −1.26653 −0.633263 0.773937i \(-0.718285\pi\)
−0.633263 + 0.773937i \(0.718285\pi\)
\(84\) 47.9042 0.0622236
\(85\) 327.333 0.417698
\(86\) −602.612 −0.755597
\(87\) −387.693 −0.477760
\(88\) 261.556 0.316840
\(89\) 460.404 0.548346 0.274173 0.961680i \(-0.411596\pi\)
0.274173 + 0.961680i \(0.411596\pi\)
\(90\) −276.280 −0.323583
\(91\) 210.502 0.242490
\(92\) 163.542 0.185330
\(93\) 747.826 0.833827
\(94\) 268.580 0.294701
\(95\) −519.523 −0.561073
\(96\) 496.437 0.527785
\(97\) 1222.33 1.27947 0.639736 0.768595i \(-0.279044\pi\)
0.639736 + 0.768595i \(0.279044\pi\)
\(98\) 640.191 0.659888
\(99\) 99.0000 0.100504
\(100\) −518.021 −0.518021
\(101\) −1232.26 −1.21401 −0.607003 0.794699i \(-0.707628\pi\)
−0.607003 + 0.794699i \(0.707628\pi\)
\(102\) 121.441 0.117887
\(103\) −1152.90 −1.10290 −0.551449 0.834209i \(-0.685925\pi\)
−0.551449 + 0.834209i \(0.685925\pi\)
\(104\) 1317.67 1.24238
\(105\) −179.543 −0.166873
\(106\) 1263.47 1.15772
\(107\) 484.448 0.437695 0.218847 0.975759i \(-0.429770\pi\)
0.218847 + 0.975759i \(0.429770\pi\)
\(108\) 113.500 0.101125
\(109\) −203.333 −0.178677 −0.0893383 0.996001i \(-0.528475\pi\)
−0.0893383 + 0.996001i \(0.528475\pi\)
\(110\) −337.676 −0.292692
\(111\) 1164.45 0.995714
\(112\) −48.2395 −0.0406982
\(113\) −2222.56 −1.85027 −0.925136 0.379636i \(-0.876049\pi\)
−0.925136 + 0.379636i \(0.876049\pi\)
\(114\) −192.743 −0.158351
\(115\) −612.948 −0.497024
\(116\) −543.249 −0.434822
\(117\) 498.743 0.394092
\(118\) 1394.10 1.08760
\(119\) 78.9195 0.0607945
\(120\) −1123.88 −0.854965
\(121\) 121.000 0.0909091
\(122\) 118.853 0.0882004
\(123\) 328.751 0.240996
\(124\) 1047.88 0.758889
\(125\) −27.8906 −0.0199569
\(126\) −66.6107 −0.0470964
\(127\) 1539.47 1.07564 0.537819 0.843061i \(-0.319249\pi\)
0.537819 + 0.843061i \(0.319249\pi\)
\(128\) 497.675 0.343662
\(129\) −927.852 −0.633277
\(130\) −1701.15 −1.14770
\(131\) 646.766 0.431361 0.215680 0.976464i \(-0.430803\pi\)
0.215680 + 0.976464i \(0.430803\pi\)
\(132\) 138.722 0.0914712
\(133\) −125.256 −0.0816622
\(134\) 1276.39 0.822861
\(135\) −425.393 −0.271200
\(136\) 494.009 0.311478
\(137\) 2631.38 1.64098 0.820488 0.571663i \(-0.193702\pi\)
0.820488 + 0.571663i \(0.193702\pi\)
\(138\) −227.404 −0.140275
\(139\) −1109.12 −0.676793 −0.338397 0.941004i \(-0.609885\pi\)
−0.338397 + 0.941004i \(0.609885\pi\)
\(140\) −251.582 −0.151875
\(141\) 413.537 0.246994
\(142\) 601.930 0.355724
\(143\) 609.575 0.356470
\(144\) −114.294 −0.0661424
\(145\) 2036.08 1.16612
\(146\) −861.238 −0.488196
\(147\) 985.712 0.553063
\(148\) 1631.66 0.906227
\(149\) 1251.92 0.688333 0.344167 0.938909i \(-0.388161\pi\)
0.344167 + 0.938909i \(0.388161\pi\)
\(150\) 720.306 0.392085
\(151\) −654.318 −0.352633 −0.176317 0.984334i \(-0.556418\pi\)
−0.176317 + 0.984334i \(0.556418\pi\)
\(152\) −784.060 −0.418393
\(153\) 186.985 0.0988027
\(154\) −81.4131 −0.0426003
\(155\) −3927.41 −2.03521
\(156\) 698.855 0.358674
\(157\) −223.625 −0.113677 −0.0568383 0.998383i \(-0.518102\pi\)
−0.0568383 + 0.998383i \(0.518102\pi\)
\(158\) −1353.51 −0.681513
\(159\) 1945.38 0.970306
\(160\) −2607.17 −1.28822
\(161\) −147.781 −0.0723401
\(162\) −157.821 −0.0765408
\(163\) 2084.70 1.00175 0.500877 0.865518i \(-0.333011\pi\)
0.500877 + 0.865518i \(0.333011\pi\)
\(164\) 460.657 0.219337
\(165\) −519.925 −0.245310
\(166\) 1866.00 0.872468
\(167\) 606.255 0.280919 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(168\) −270.966 −0.124437
\(169\) 873.919 0.397778
\(170\) −637.780 −0.287738
\(171\) −296.770 −0.132717
\(172\) −1300.14 −0.576363
\(173\) −4141.92 −1.82026 −0.910128 0.414327i \(-0.864017\pi\)
−0.910128 + 0.414327i \(0.864017\pi\)
\(174\) 755.386 0.329113
\(175\) 468.098 0.202199
\(176\) −139.693 −0.0598281
\(177\) 2146.51 0.911535
\(178\) −897.057 −0.377737
\(179\) −2828.55 −1.18110 −0.590548 0.807003i \(-0.701088\pi\)
−0.590548 + 0.807003i \(0.701088\pi\)
\(180\) −596.075 −0.246827
\(181\) 1992.62 0.818291 0.409145 0.912469i \(-0.365827\pi\)
0.409145 + 0.912469i \(0.365827\pi\)
\(182\) −410.143 −0.167043
\(183\) 183.000 0.0739221
\(184\) −925.057 −0.370631
\(185\) −6115.40 −2.43034
\(186\) −1457.07 −0.574396
\(187\) 228.537 0.0893704
\(188\) 579.461 0.224796
\(189\) −102.562 −0.0394723
\(190\) 1012.24 0.386505
\(191\) −1027.76 −0.389350 −0.194675 0.980868i \(-0.562365\pi\)
−0.194675 + 0.980868i \(0.562365\pi\)
\(192\) −1272.05 −0.478136
\(193\) 1403.94 0.523615 0.261808 0.965120i \(-0.415681\pi\)
0.261808 + 0.965120i \(0.415681\pi\)
\(194\) −2381.60 −0.881386
\(195\) −2619.28 −0.961901
\(196\) 1381.21 0.503357
\(197\) 3160.58 1.14306 0.571529 0.820582i \(-0.306351\pi\)
0.571529 + 0.820582i \(0.306351\pi\)
\(198\) −192.893 −0.0692337
\(199\) −899.836 −0.320541 −0.160270 0.987073i \(-0.551237\pi\)
−0.160270 + 0.987073i \(0.551237\pi\)
\(200\) 2930.13 1.03596
\(201\) 1965.28 0.689652
\(202\) 2400.95 0.836289
\(203\) 490.895 0.169724
\(204\) 262.009 0.0899230
\(205\) −1726.53 −0.588224
\(206\) 2246.32 0.759750
\(207\) −350.138 −0.117567
\(208\) −703.745 −0.234596
\(209\) −362.719 −0.120047
\(210\) 349.824 0.114953
\(211\) −2932.17 −0.956677 −0.478338 0.878176i \(-0.658761\pi\)
−0.478338 + 0.878176i \(0.658761\pi\)
\(212\) 2725.93 0.883102
\(213\) 926.801 0.298138
\(214\) −943.903 −0.301514
\(215\) 4872.86 1.54570
\(216\) −642.001 −0.202234
\(217\) −946.892 −0.296218
\(218\) 396.176 0.123084
\(219\) −1326.06 −0.409165
\(220\) −728.536 −0.223263
\(221\) 1151.32 0.350436
\(222\) −2268.82 −0.685915
\(223\) 895.070 0.268782 0.134391 0.990928i \(-0.457092\pi\)
0.134391 + 0.990928i \(0.457092\pi\)
\(224\) −628.585 −0.187496
\(225\) 1109.07 0.328613
\(226\) 4330.46 1.27459
\(227\) 1544.96 0.451729 0.225864 0.974159i \(-0.427479\pi\)
0.225864 + 0.974159i \(0.427479\pi\)
\(228\) −415.844 −0.120789
\(229\) −4066.57 −1.17348 −0.586739 0.809776i \(-0.699588\pi\)
−0.586739 + 0.809776i \(0.699588\pi\)
\(230\) 1194.27 0.342383
\(231\) −125.353 −0.0357040
\(232\) 3072.83 0.869575
\(233\) 236.307 0.0664420 0.0332210 0.999448i \(-0.489423\pi\)
0.0332210 + 0.999448i \(0.489423\pi\)
\(234\) −971.756 −0.271477
\(235\) −2171.80 −0.602862
\(236\) 3007.76 0.829613
\(237\) −2084.02 −0.571187
\(238\) −153.768 −0.0418793
\(239\) −2593.17 −0.701832 −0.350916 0.936407i \(-0.614130\pi\)
−0.350916 + 0.936407i \(0.614130\pi\)
\(240\) 600.246 0.161441
\(241\) 3758.93 1.00471 0.502353 0.864663i \(-0.332468\pi\)
0.502353 + 0.864663i \(0.332468\pi\)
\(242\) −235.758 −0.0626243
\(243\) −243.000 −0.0641500
\(244\) 256.426 0.0672785
\(245\) −5176.73 −1.34992
\(246\) −640.543 −0.166014
\(247\) −1827.31 −0.470724
\(248\) −5927.22 −1.51766
\(249\) 2873.11 0.731229
\(250\) 54.3423 0.0137476
\(251\) 260.668 0.0655506 0.0327753 0.999463i \(-0.489565\pi\)
0.0327753 + 0.999463i \(0.489565\pi\)
\(252\) −143.713 −0.0359248
\(253\) −427.946 −0.106343
\(254\) −2999.52 −0.740971
\(255\) −982.000 −0.241158
\(256\) −4361.80 −1.06489
\(257\) 6902.88 1.67545 0.837723 0.546095i \(-0.183886\pi\)
0.837723 + 0.546095i \(0.183886\pi\)
\(258\) 1807.84 0.436244
\(259\) −1474.41 −0.353728
\(260\) −3670.22 −0.875452
\(261\) 1163.08 0.275835
\(262\) −1260.17 −0.297150
\(263\) −793.192 −0.185971 −0.0929854 0.995667i \(-0.529641\pi\)
−0.0929854 + 0.995667i \(0.529641\pi\)
\(264\) −784.668 −0.182928
\(265\) −10216.7 −2.36832
\(266\) 244.050 0.0562544
\(267\) −1381.21 −0.316588
\(268\) 2753.81 0.627671
\(269\) 1382.27 0.313303 0.156651 0.987654i \(-0.449930\pi\)
0.156651 + 0.987654i \(0.449930\pi\)
\(270\) 828.841 0.186821
\(271\) −6038.49 −1.35355 −0.676775 0.736190i \(-0.736623\pi\)
−0.676775 + 0.736190i \(0.736623\pi\)
\(272\) −263.843 −0.0588155
\(273\) −631.505 −0.140001
\(274\) −5127.00 −1.13041
\(275\) 1355.53 0.297241
\(276\) −490.625 −0.107001
\(277\) −1413.83 −0.306675 −0.153337 0.988174i \(-0.549002\pi\)
−0.153337 + 0.988174i \(0.549002\pi\)
\(278\) 2161.02 0.466220
\(279\) −2243.48 −0.481410
\(280\) 1423.05 0.303727
\(281\) −949.955 −0.201671 −0.100836 0.994903i \(-0.532152\pi\)
−0.100836 + 0.994903i \(0.532152\pi\)
\(282\) −805.739 −0.170146
\(283\) −3728.05 −0.783072 −0.391536 0.920163i \(-0.628056\pi\)
−0.391536 + 0.920163i \(0.628056\pi\)
\(284\) 1298.66 0.271343
\(285\) 1558.57 0.323935
\(286\) −1187.70 −0.245560
\(287\) −416.263 −0.0856140
\(288\) −1489.31 −0.304717
\(289\) −4481.35 −0.912142
\(290\) −3967.11 −0.803300
\(291\) −3666.99 −0.738703
\(292\) −1858.12 −0.372392
\(293\) 4418.33 0.880960 0.440480 0.897762i \(-0.354808\pi\)
0.440480 + 0.897762i \(0.354808\pi\)
\(294\) −1920.57 −0.380987
\(295\) −11273.0 −2.22488
\(296\) −9229.32 −1.81231
\(297\) −297.000 −0.0580259
\(298\) −2439.26 −0.474170
\(299\) −2155.91 −0.416989
\(300\) 1554.06 0.299079
\(301\) 1174.84 0.224972
\(302\) 1274.88 0.242917
\(303\) 3696.79 0.700907
\(304\) 418.754 0.0790039
\(305\) −961.074 −0.180429
\(306\) −364.323 −0.0680619
\(307\) −10642.1 −1.97843 −0.989217 0.146458i \(-0.953213\pi\)
−0.989217 + 0.146458i \(0.953213\pi\)
\(308\) −175.649 −0.0324952
\(309\) 3458.69 0.636758
\(310\) 7652.21 1.40199
\(311\) −364.170 −0.0663993 −0.0331996 0.999449i \(-0.510570\pi\)
−0.0331996 + 0.999449i \(0.510570\pi\)
\(312\) −3953.00 −0.717291
\(313\) −8381.95 −1.51366 −0.756831 0.653611i \(-0.773253\pi\)
−0.756831 + 0.653611i \(0.773253\pi\)
\(314\) 435.713 0.0783080
\(315\) 538.630 0.0963440
\(316\) −2920.19 −0.519853
\(317\) 2005.50 0.355331 0.177665 0.984091i \(-0.443146\pi\)
0.177665 + 0.984091i \(0.443146\pi\)
\(318\) −3790.40 −0.668412
\(319\) 1421.54 0.249502
\(320\) 6680.50 1.16703
\(321\) −1453.34 −0.252703
\(322\) 287.937 0.0498327
\(323\) −685.080 −0.118015
\(324\) −340.500 −0.0583847
\(325\) 6828.89 1.16553
\(326\) −4061.84 −0.690075
\(327\) 609.998 0.103159
\(328\) −2605.66 −0.438639
\(329\) −523.617 −0.0877446
\(330\) 1013.03 0.168986
\(331\) −6018.67 −0.999443 −0.499722 0.866186i \(-0.666564\pi\)
−0.499722 + 0.866186i \(0.666564\pi\)
\(332\) 4025.90 0.665511
\(333\) −3493.34 −0.574876
\(334\) −1181.23 −0.193516
\(335\) −10321.2 −1.68330
\(336\) 144.718 0.0234971
\(337\) 9165.98 1.48161 0.740805 0.671720i \(-0.234444\pi\)
0.740805 + 0.671720i \(0.234444\pi\)
\(338\) −1702.75 −0.274016
\(339\) 6667.67 1.06825
\(340\) −1376.01 −0.219484
\(341\) −2742.03 −0.435452
\(342\) 578.230 0.0914242
\(343\) −2551.01 −0.401580
\(344\) 7354.09 1.15263
\(345\) 1838.84 0.286957
\(346\) 8070.16 1.25391
\(347\) −518.469 −0.0802100 −0.0401050 0.999195i \(-0.512769\pi\)
−0.0401050 + 0.999195i \(0.512769\pi\)
\(348\) 1629.75 0.251045
\(349\) 2667.51 0.409136 0.204568 0.978852i \(-0.434421\pi\)
0.204568 + 0.978852i \(0.434421\pi\)
\(350\) −912.047 −0.139288
\(351\) −1496.23 −0.227529
\(352\) −1820.27 −0.275627
\(353\) −9043.64 −1.36358 −0.681791 0.731547i \(-0.738799\pi\)
−0.681791 + 0.731547i \(0.738799\pi\)
\(354\) −4182.29 −0.627926
\(355\) −4867.35 −0.727695
\(356\) −1935.40 −0.288135
\(357\) −236.759 −0.0350997
\(358\) 5511.18 0.813617
\(359\) −7367.14 −1.08307 −0.541536 0.840678i \(-0.682157\pi\)
−0.541536 + 0.840678i \(0.682157\pi\)
\(360\) 3371.64 0.493614
\(361\) −5771.69 −0.841476
\(362\) −3882.45 −0.563693
\(363\) −363.000 −0.0524864
\(364\) −884.885 −0.127419
\(365\) 6964.18 0.998690
\(366\) −356.559 −0.0509225
\(367\) −2312.64 −0.328935 −0.164467 0.986383i \(-0.552591\pi\)
−0.164467 + 0.986383i \(0.552591\pi\)
\(368\) 494.058 0.0699852
\(369\) −986.254 −0.139139
\(370\) 11915.3 1.67418
\(371\) −2463.23 −0.344702
\(372\) −3143.63 −0.438145
\(373\) 6689.84 0.928650 0.464325 0.885665i \(-0.346297\pi\)
0.464325 + 0.885665i \(0.346297\pi\)
\(374\) −445.283 −0.0615643
\(375\) 83.6718 0.0115221
\(376\) −3277.67 −0.449555
\(377\) 7161.46 0.978339
\(378\) 199.832 0.0271911
\(379\) −2487.15 −0.337088 −0.168544 0.985694i \(-0.553907\pi\)
−0.168544 + 0.985694i \(0.553907\pi\)
\(380\) 2183.92 0.294823
\(381\) −4618.41 −0.621019
\(382\) 2002.49 0.268211
\(383\) −4747.65 −0.633404 −0.316702 0.948525i \(-0.602575\pi\)
−0.316702 + 0.948525i \(0.602575\pi\)
\(384\) −1493.03 −0.198413
\(385\) 658.325 0.0871464
\(386\) −2735.45 −0.360701
\(387\) 2783.55 0.365623
\(388\) −5138.30 −0.672314
\(389\) 2948.01 0.384242 0.192121 0.981371i \(-0.438463\pi\)
0.192121 + 0.981371i \(0.438463\pi\)
\(390\) 5103.44 0.662622
\(391\) −808.277 −0.104543
\(392\) −7812.69 −1.00663
\(393\) −1940.30 −0.249046
\(394\) −6158.11 −0.787414
\(395\) 10944.8 1.39415
\(396\) −416.166 −0.0528109
\(397\) −1848.91 −0.233738 −0.116869 0.993147i \(-0.537286\pi\)
−0.116869 + 0.993147i \(0.537286\pi\)
\(398\) 1753.25 0.220810
\(399\) 375.768 0.0471477
\(400\) −1564.94 −0.195617
\(401\) 6395.55 0.796455 0.398227 0.917287i \(-0.369625\pi\)
0.398227 + 0.917287i \(0.369625\pi\)
\(402\) −3829.17 −0.475079
\(403\) −13813.8 −1.70748
\(404\) 5180.06 0.637914
\(405\) 1276.18 0.156578
\(406\) −956.464 −0.116918
\(407\) −4269.63 −0.519995
\(408\) −1482.03 −0.179832
\(409\) −6387.30 −0.772205 −0.386103 0.922456i \(-0.626179\pi\)
−0.386103 + 0.922456i \(0.626179\pi\)
\(410\) 3363.98 0.405208
\(411\) −7894.13 −0.947418
\(412\) 4846.43 0.579531
\(413\) −2717.90 −0.323823
\(414\) 682.213 0.0809877
\(415\) −15088.9 −1.78479
\(416\) −9170.16 −1.08078
\(417\) 3327.36 0.390747
\(418\) 706.725 0.0826963
\(419\) −14385.9 −1.67732 −0.838661 0.544654i \(-0.816661\pi\)
−0.838661 + 0.544654i \(0.816661\pi\)
\(420\) 754.746 0.0876853
\(421\) 9475.99 1.09699 0.548494 0.836155i \(-0.315201\pi\)
0.548494 + 0.836155i \(0.315201\pi\)
\(422\) 5713.07 0.659023
\(423\) −1240.61 −0.142602
\(424\) −15419.0 −1.76606
\(425\) 2560.23 0.292210
\(426\) −1805.79 −0.205377
\(427\) −231.713 −0.0262609
\(428\) −2036.47 −0.229992
\(429\) −1828.72 −0.205808
\(430\) −9494.34 −1.06479
\(431\) 16387.1 1.83141 0.915707 0.401847i \(-0.131632\pi\)
0.915707 + 0.401847i \(0.131632\pi\)
\(432\) 342.882 0.0381873
\(433\) 7229.00 0.802317 0.401159 0.916009i \(-0.368608\pi\)
0.401159 + 0.916009i \(0.368608\pi\)
\(434\) 1844.93 0.204055
\(435\) −6108.23 −0.673258
\(436\) 854.749 0.0938878
\(437\) 1282.85 0.140428
\(438\) 2583.72 0.281860
\(439\) 2073.13 0.225387 0.112694 0.993630i \(-0.464052\pi\)
0.112694 + 0.993630i \(0.464052\pi\)
\(440\) 4120.89 0.446491
\(441\) −2957.14 −0.319311
\(442\) −2243.25 −0.241404
\(443\) 9208.90 0.987648 0.493824 0.869562i \(-0.335599\pi\)
0.493824 + 0.869562i \(0.335599\pi\)
\(444\) −4894.98 −0.523210
\(445\) 7253.81 0.772727
\(446\) −1743.96 −0.185155
\(447\) −3755.77 −0.397409
\(448\) 1610.66 0.169858
\(449\) 142.052 0.0149306 0.00746532 0.999972i \(-0.497624\pi\)
0.00746532 + 0.999972i \(0.497624\pi\)
\(450\) −2160.92 −0.226370
\(451\) −1205.42 −0.125856
\(452\) 9342.96 0.972248
\(453\) 1962.95 0.203593
\(454\) −3010.21 −0.311181
\(455\) 3316.52 0.341716
\(456\) 2352.18 0.241559
\(457\) 4968.52 0.508572 0.254286 0.967129i \(-0.418159\pi\)
0.254286 + 0.967129i \(0.418159\pi\)
\(458\) 7923.34 0.808370
\(459\) −560.954 −0.0570438
\(460\) 2576.65 0.261167
\(461\) 2953.91 0.298432 0.149216 0.988805i \(-0.452325\pi\)
0.149216 + 0.988805i \(0.452325\pi\)
\(462\) 244.239 0.0245953
\(463\) 9071.55 0.910563 0.455281 0.890348i \(-0.349539\pi\)
0.455281 + 0.890348i \(0.349539\pi\)
\(464\) −1641.15 −0.164199
\(465\) 11782.2 1.17503
\(466\) −460.423 −0.0457697
\(467\) 3299.17 0.326911 0.163456 0.986551i \(-0.447736\pi\)
0.163456 + 0.986551i \(0.447736\pi\)
\(468\) −2096.56 −0.207081
\(469\) −2488.42 −0.244999
\(470\) 4231.56 0.415292
\(471\) 670.875 0.0656312
\(472\) −17013.1 −1.65909
\(473\) 3402.12 0.330718
\(474\) 4060.52 0.393472
\(475\) −4063.43 −0.392512
\(476\) −331.754 −0.0319452
\(477\) −5836.14 −0.560206
\(478\) 5052.55 0.483469
\(479\) 12938.1 1.23415 0.617076 0.786904i \(-0.288317\pi\)
0.617076 + 0.786904i \(0.288317\pi\)
\(480\) 7821.52 0.743754
\(481\) −21509.6 −2.03899
\(482\) −7323.94 −0.692109
\(483\) 443.342 0.0417656
\(484\) −508.647 −0.0477693
\(485\) 19258.2 1.80303
\(486\) 473.464 0.0441908
\(487\) −4480.51 −0.416902 −0.208451 0.978033i \(-0.566842\pi\)
−0.208451 + 0.978033i \(0.566842\pi\)
\(488\) −1450.45 −0.134546
\(489\) −6254.09 −0.578363
\(490\) 10086.4 0.929913
\(491\) 4382.73 0.402831 0.201415 0.979506i \(-0.435446\pi\)
0.201415 + 0.979506i \(0.435446\pi\)
\(492\) −1381.97 −0.126634
\(493\) 2684.92 0.245279
\(494\) 3560.35 0.324266
\(495\) 1559.78 0.141630
\(496\) 3165.63 0.286575
\(497\) −1173.51 −0.105914
\(498\) −5598.00 −0.503720
\(499\) −4611.26 −0.413684 −0.206842 0.978374i \(-0.566319\pi\)
−0.206842 + 0.978374i \(0.566319\pi\)
\(500\) 117.244 0.0104866
\(501\) −1818.77 −0.162189
\(502\) −507.888 −0.0451557
\(503\) 948.320 0.0840626 0.0420313 0.999116i \(-0.486617\pi\)
0.0420313 + 0.999116i \(0.486617\pi\)
\(504\) 812.897 0.0718439
\(505\) −19414.7 −1.71077
\(506\) 833.815 0.0732561
\(507\) −2621.76 −0.229657
\(508\) −6471.47 −0.565207
\(509\) 16954.1 1.47638 0.738190 0.674593i \(-0.235681\pi\)
0.738190 + 0.674593i \(0.235681\pi\)
\(510\) 1913.34 0.166126
\(511\) 1679.05 0.145356
\(512\) 4517.18 0.389908
\(513\) 890.310 0.0766241
\(514\) −13449.6 −1.15416
\(515\) −18164.3 −1.55420
\(516\) 3900.41 0.332763
\(517\) −1516.30 −0.128988
\(518\) 2872.76 0.243672
\(519\) 12425.8 1.05093
\(520\) 20760.3 1.75077
\(521\) 6839.25 0.575111 0.287556 0.957764i \(-0.407157\pi\)
0.287556 + 0.957764i \(0.407157\pi\)
\(522\) −2266.16 −0.190013
\(523\) −7500.51 −0.627102 −0.313551 0.949571i \(-0.601519\pi\)
−0.313551 + 0.949571i \(0.601519\pi\)
\(524\) −2718.81 −0.226664
\(525\) −1404.29 −0.116740
\(526\) 1545.46 0.128109
\(527\) −5178.96 −0.428082
\(528\) 419.078 0.0345418
\(529\) −10653.5 −0.875603
\(530\) 19906.3 1.63146
\(531\) −6439.54 −0.526275
\(532\) 526.539 0.0429104
\(533\) −6072.68 −0.493503
\(534\) 2691.17 0.218087
\(535\) 7632.63 0.616799
\(536\) −15576.7 −1.25524
\(537\) 8485.66 0.681906
\(538\) −2693.23 −0.215824
\(539\) −3614.28 −0.288827
\(540\) 1788.22 0.142505
\(541\) −2316.11 −0.184062 −0.0920309 0.995756i \(-0.529336\pi\)
−0.0920309 + 0.995756i \(0.529336\pi\)
\(542\) 11765.4 0.932416
\(543\) −5977.87 −0.472440
\(544\) −3438.00 −0.270962
\(545\) −3203.57 −0.251791
\(546\) 1230.43 0.0964424
\(547\) 17507.2 1.36847 0.684237 0.729259i \(-0.260135\pi\)
0.684237 + 0.729259i \(0.260135\pi\)
\(548\) −11061.5 −0.862271
\(549\) −549.000 −0.0426790
\(550\) −2641.12 −0.204760
\(551\) −4261.33 −0.329471
\(552\) 2775.17 0.213984
\(553\) 2638.76 0.202914
\(554\) 2754.72 0.211258
\(555\) 18346.2 1.40316
\(556\) 4662.40 0.355629
\(557\) −23914.5 −1.81919 −0.909594 0.415498i \(-0.863607\pi\)
−0.909594 + 0.415498i \(0.863607\pi\)
\(558\) 4371.22 0.331628
\(559\) 17139.2 1.29680
\(560\) −760.028 −0.0573518
\(561\) −685.610 −0.0515980
\(562\) 1850.90 0.138925
\(563\) 13115.2 0.981773 0.490887 0.871223i \(-0.336673\pi\)
0.490887 + 0.871223i \(0.336673\pi\)
\(564\) −1738.38 −0.129786
\(565\) −35017.1 −2.60740
\(566\) 7263.77 0.539433
\(567\) 307.685 0.0227893
\(568\) −7345.77 −0.542643
\(569\) −12675.6 −0.933900 −0.466950 0.884284i \(-0.654647\pi\)
−0.466950 + 0.884284i \(0.654647\pi\)
\(570\) −3036.73 −0.223148
\(571\) 9557.59 0.700478 0.350239 0.936660i \(-0.386100\pi\)
0.350239 + 0.936660i \(0.386100\pi\)
\(572\) −2562.47 −0.187311
\(573\) 3083.27 0.224792
\(574\) 811.050 0.0589766
\(575\) −4794.16 −0.347705
\(576\) 3816.14 0.276052
\(577\) −11716.0 −0.845306 −0.422653 0.906292i \(-0.638901\pi\)
−0.422653 + 0.906292i \(0.638901\pi\)
\(578\) 8731.52 0.628345
\(579\) −4211.82 −0.302309
\(580\) −8559.05 −0.612750
\(581\) −3637.91 −0.259769
\(582\) 7144.80 0.508868
\(583\) −7133.06 −0.506726
\(584\) 10510.3 0.744724
\(585\) 7857.85 0.555354
\(586\) −8608.71 −0.606864
\(587\) −15552.2 −1.09354 −0.546772 0.837282i \(-0.684143\pi\)
−0.546772 + 0.837282i \(0.684143\pi\)
\(588\) −4143.64 −0.290613
\(589\) 8219.72 0.575021
\(590\) 21964.4 1.53264
\(591\) −9481.75 −0.659944
\(592\) 4929.23 0.342213
\(593\) 1156.23 0.0800688 0.0400344 0.999198i \(-0.487253\pi\)
0.0400344 + 0.999198i \(0.487253\pi\)
\(594\) 578.678 0.0399721
\(595\) 1243.40 0.0856714
\(596\) −5262.71 −0.361693
\(597\) 2699.51 0.185064
\(598\) 4200.60 0.287250
\(599\) 21400.2 1.45975 0.729874 0.683582i \(-0.239579\pi\)
0.729874 + 0.683582i \(0.239579\pi\)
\(600\) −8790.40 −0.598111
\(601\) 16937.0 1.14954 0.574772 0.818314i \(-0.305091\pi\)
0.574772 + 0.818314i \(0.305091\pi\)
\(602\) −2289.07 −0.154976
\(603\) −5895.84 −0.398171
\(604\) 2750.55 0.185295
\(605\) 1906.39 0.128109
\(606\) −7202.85 −0.482832
\(607\) −4910.54 −0.328357 −0.164178 0.986431i \(-0.552497\pi\)
−0.164178 + 0.986431i \(0.552497\pi\)
\(608\) 5456.58 0.363970
\(609\) −1472.68 −0.0979904
\(610\) 1872.57 0.124292
\(611\) −7638.84 −0.505784
\(612\) −786.027 −0.0519171
\(613\) −18252.4 −1.20262 −0.601311 0.799015i \(-0.705355\pi\)
−0.601311 + 0.799015i \(0.705355\pi\)
\(614\) 20735.3 1.36288
\(615\) 5179.58 0.339611
\(616\) 993.541 0.0649852
\(617\) 12841.7 0.837908 0.418954 0.908007i \(-0.362397\pi\)
0.418954 + 0.908007i \(0.362397\pi\)
\(618\) −6738.95 −0.438642
\(619\) −3240.98 −0.210446 −0.105223 0.994449i \(-0.533556\pi\)
−0.105223 + 0.994449i \(0.533556\pi\)
\(620\) 16509.6 1.06942
\(621\) 1050.41 0.0678771
\(622\) 709.552 0.0457403
\(623\) 1748.88 0.112468
\(624\) 2111.24 0.135444
\(625\) −15843.1 −1.01396
\(626\) 16331.5 1.04271
\(627\) 1088.16 0.0693091
\(628\) 940.052 0.0597327
\(629\) −8064.20 −0.511194
\(630\) −1049.47 −0.0663682
\(631\) −11396.2 −0.718977 −0.359489 0.933149i \(-0.617049\pi\)
−0.359489 + 0.933149i \(0.617049\pi\)
\(632\) 16517.8 1.03962
\(633\) 8796.50 0.552337
\(634\) −3907.53 −0.244776
\(635\) 24254.8 1.51579
\(636\) −8177.79 −0.509859
\(637\) −18208.0 −1.13254
\(638\) −2769.75 −0.171874
\(639\) −2780.40 −0.172130
\(640\) 7841.03 0.484287
\(641\) −23594.8 −1.45388 −0.726941 0.686700i \(-0.759059\pi\)
−0.726941 + 0.686700i \(0.759059\pi\)
\(642\) 2831.71 0.174079
\(643\) 3093.23 0.189712 0.0948562 0.995491i \(-0.469761\pi\)
0.0948562 + 0.995491i \(0.469761\pi\)
\(644\) 621.226 0.0380120
\(645\) −14618.6 −0.892413
\(646\) 1334.82 0.0812967
\(647\) −17755.5 −1.07889 −0.539443 0.842022i \(-0.681365\pi\)
−0.539443 + 0.842022i \(0.681365\pi\)
\(648\) 1926.00 0.116760
\(649\) −7870.54 −0.476034
\(650\) −13305.5 −0.802898
\(651\) 2840.68 0.171021
\(652\) −8763.43 −0.526384
\(653\) 3167.79 0.189839 0.0949197 0.995485i \(-0.469741\pi\)
0.0949197 + 0.995485i \(0.469741\pi\)
\(654\) −1188.53 −0.0710628
\(655\) 10190.0 0.607872
\(656\) 1391.64 0.0828270
\(657\) 3978.19 0.236231
\(658\) 1020.22 0.0604443
\(659\) 2160.76 0.127726 0.0638629 0.997959i \(-0.479658\pi\)
0.0638629 + 0.997959i \(0.479658\pi\)
\(660\) 2185.61 0.128901
\(661\) 11806.4 0.694731 0.347366 0.937730i \(-0.387076\pi\)
0.347366 + 0.937730i \(0.387076\pi\)
\(662\) 11726.8 0.688484
\(663\) −3453.97 −0.202325
\(664\) −22772.1 −1.33092
\(665\) −1973.45 −0.115078
\(666\) 6806.45 0.396013
\(667\) −5027.64 −0.291860
\(668\) −2548.51 −0.147612
\(669\) −2685.21 −0.155181
\(670\) 20109.9 1.15957
\(671\) −671.000 −0.0386046
\(672\) 1885.75 0.108251
\(673\) −784.015 −0.0449057 −0.0224529 0.999748i \(-0.507148\pi\)
−0.0224529 + 0.999748i \(0.507148\pi\)
\(674\) −17859.1 −1.02063
\(675\) −3327.20 −0.189725
\(676\) −3673.69 −0.209018
\(677\) 16496.4 0.936496 0.468248 0.883597i \(-0.344885\pi\)
0.468248 + 0.883597i \(0.344885\pi\)
\(678\) −12991.4 −0.735886
\(679\) 4643.11 0.262425
\(680\) 7783.27 0.438934
\(681\) −4634.87 −0.260806
\(682\) 5342.60 0.299969
\(683\) 20139.7 1.12829 0.564145 0.825675i \(-0.309206\pi\)
0.564145 + 0.825675i \(0.309206\pi\)
\(684\) 1247.53 0.0697377
\(685\) 41458.2 2.31246
\(686\) 4970.42 0.276635
\(687\) 12199.7 0.677508
\(688\) −3927.70 −0.217649
\(689\) −35935.0 −1.98696
\(690\) −3582.82 −0.197675
\(691\) 13577.4 0.747481 0.373740 0.927533i \(-0.378075\pi\)
0.373740 + 0.927533i \(0.378075\pi\)
\(692\) 17411.4 0.956476
\(693\) 376.059 0.0206137
\(694\) 1010.19 0.0552540
\(695\) −17474.5 −0.953735
\(696\) −9218.50 −0.502049
\(697\) −2276.72 −0.123726
\(698\) −5197.40 −0.281840
\(699\) −708.921 −0.0383603
\(700\) −1967.74 −0.106248
\(701\) −16056.2 −0.865099 −0.432550 0.901610i \(-0.642386\pi\)
−0.432550 + 0.901610i \(0.642386\pi\)
\(702\) 2915.27 0.156737
\(703\) 12799.0 0.686661
\(704\) 4664.17 0.249698
\(705\) 6515.40 0.348063
\(706\) 17620.7 0.939326
\(707\) −4680.84 −0.248997
\(708\) −9023.29 −0.478977
\(709\) 6595.03 0.349339 0.174670 0.984627i \(-0.444114\pi\)
0.174670 + 0.984627i \(0.444114\pi\)
\(710\) 9483.59 0.501285
\(711\) 6252.05 0.329775
\(712\) 10947.4 0.576224
\(713\) 9697.86 0.509380
\(714\) 461.303 0.0241790
\(715\) 9604.04 0.502337
\(716\) 11890.4 0.620621
\(717\) 7779.50 0.405203
\(718\) 14354.2 0.746093
\(719\) −33575.6 −1.74153 −0.870765 0.491700i \(-0.836376\pi\)
−0.870765 + 0.491700i \(0.836376\pi\)
\(720\) −1800.74 −0.0932078
\(721\) −4379.37 −0.226209
\(722\) 11245.6 0.579665
\(723\) −11276.8 −0.580067
\(724\) −8376.39 −0.429981
\(725\) 15925.1 0.815785
\(726\) 707.273 0.0361561
\(727\) −17204.7 −0.877699 −0.438849 0.898561i \(-0.644614\pi\)
−0.438849 + 0.898561i \(0.644614\pi\)
\(728\) 5005.27 0.254818
\(729\) 729.000 0.0370370
\(730\) −13569.1 −0.687965
\(731\) 6425.70 0.325121
\(732\) −769.277 −0.0388433
\(733\) 2317.28 0.116768 0.0583839 0.998294i \(-0.481405\pi\)
0.0583839 + 0.998294i \(0.481405\pi\)
\(734\) 4505.98 0.226592
\(735\) 15530.2 0.779374
\(736\) 6437.83 0.322421
\(737\) −7206.02 −0.360159
\(738\) 1921.63 0.0958484
\(739\) 14058.3 0.699789 0.349894 0.936789i \(-0.386217\pi\)
0.349894 + 0.936789i \(0.386217\pi\)
\(740\) 25707.3 1.27705
\(741\) 5481.92 0.271773
\(742\) 4799.37 0.237454
\(743\) 16845.1 0.831744 0.415872 0.909423i \(-0.363476\pi\)
0.415872 + 0.909423i \(0.363476\pi\)
\(744\) 17781.7 0.876220
\(745\) 19724.5 0.969998
\(746\) −13034.5 −0.639717
\(747\) −8619.33 −0.422175
\(748\) −960.700 −0.0469608
\(749\) 1840.21 0.0897730
\(750\) −163.027 −0.00793720
\(751\) 36184.6 1.75818 0.879090 0.476655i \(-0.158151\pi\)
0.879090 + 0.476655i \(0.158151\pi\)
\(752\) 1750.55 0.0848882
\(753\) −782.004 −0.0378457
\(754\) −13953.5 −0.673946
\(755\) −10309.0 −0.496930
\(756\) 431.138 0.0207412
\(757\) −6259.11 −0.300517 −0.150258 0.988647i \(-0.548011\pi\)
−0.150258 + 0.988647i \(0.548011\pi\)
\(758\) 4845.99 0.232209
\(759\) 1283.84 0.0613971
\(760\) −12353.1 −0.589598
\(761\) −32306.7 −1.53892 −0.769459 0.638696i \(-0.779474\pi\)
−0.769459 + 0.638696i \(0.779474\pi\)
\(762\) 8998.56 0.427800
\(763\) −772.375 −0.0366473
\(764\) 4320.38 0.204589
\(765\) 2946.00 0.139233
\(766\) 9250.37 0.436331
\(767\) −39650.3 −1.86661
\(768\) 13085.4 0.614816
\(769\) −11921.2 −0.559023 −0.279512 0.960142i \(-0.590173\pi\)
−0.279512 + 0.960142i \(0.590173\pi\)
\(770\) −1282.69 −0.0600323
\(771\) −20708.6 −0.967319
\(772\) −5901.73 −0.275140
\(773\) 15891.4 0.739422 0.369711 0.929147i \(-0.379457\pi\)
0.369711 + 0.929147i \(0.379457\pi\)
\(774\) −5423.51 −0.251866
\(775\) −30718.1 −1.42378
\(776\) 29064.3 1.34452
\(777\) 4423.24 0.204225
\(778\) −5743.94 −0.264692
\(779\) 3613.47 0.166195
\(780\) 11010.7 0.505443
\(781\) −3398.27 −0.155697
\(782\) 1574.86 0.0720162
\(783\) −3489.24 −0.159253
\(784\) 4172.63 0.190080
\(785\) −3523.28 −0.160193
\(786\) 3780.50 0.171560
\(787\) −20721.9 −0.938572 −0.469286 0.883046i \(-0.655489\pi\)
−0.469286 + 0.883046i \(0.655489\pi\)
\(788\) −13286.1 −0.600633
\(789\) 2379.58 0.107370
\(790\) −21324.9 −0.960387
\(791\) −8442.56 −0.379498
\(792\) 2354.00 0.105613
\(793\) −3380.37 −0.151375
\(794\) 3602.43 0.161014
\(795\) 30650.1 1.36735
\(796\) 3782.64 0.168432
\(797\) 27596.9 1.22651 0.613256 0.789884i \(-0.289859\pi\)
0.613256 + 0.789884i \(0.289859\pi\)
\(798\) −732.150 −0.0324785
\(799\) −2863.89 −0.126805
\(800\) −20391.9 −0.901205
\(801\) 4143.64 0.182782
\(802\) −12461.1 −0.548651
\(803\) 4862.23 0.213679
\(804\) −8261.44 −0.362386
\(805\) −2328.33 −0.101941
\(806\) 26915.0 1.17623
\(807\) −4146.81 −0.180885
\(808\) −29300.5 −1.27573
\(809\) 25973.0 1.12876 0.564378 0.825517i \(-0.309116\pi\)
0.564378 + 0.825517i \(0.309116\pi\)
\(810\) −2486.52 −0.107861
\(811\) 18039.3 0.781069 0.390534 0.920588i \(-0.372290\pi\)
0.390534 + 0.920588i \(0.372290\pi\)
\(812\) −2063.57 −0.0891837
\(813\) 18115.5 0.781472
\(814\) 8319.00 0.358207
\(815\) 32845.0 1.41167
\(816\) 791.528 0.0339571
\(817\) −10198.5 −0.436719
\(818\) 12445.1 0.531947
\(819\) 1894.51 0.0808299
\(820\) 7257.80 0.309089
\(821\) 30848.6 1.31136 0.655679 0.755040i \(-0.272383\pi\)
0.655679 + 0.755040i \(0.272383\pi\)
\(822\) 15381.0 0.652645
\(823\) 23673.2 1.00267 0.501335 0.865254i \(-0.332843\pi\)
0.501335 + 0.865254i \(0.332843\pi\)
\(824\) −27413.4 −1.15897
\(825\) −4066.58 −0.171612
\(826\) 5295.58 0.223071
\(827\) −24149.8 −1.01544 −0.507721 0.861522i \(-0.669512\pi\)
−0.507721 + 0.861522i \(0.669512\pi\)
\(828\) 1471.87 0.0617768
\(829\) −15376.2 −0.644193 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(830\) 29399.4 1.22948
\(831\) 4241.49 0.177059
\(832\) 23497.2 0.979109
\(833\) −6826.41 −0.283939
\(834\) −6483.06 −0.269172
\(835\) 9551.74 0.395870
\(836\) 1524.76 0.0630801
\(837\) 6730.43 0.277942
\(838\) 28029.6 1.15545
\(839\) 10677.7 0.439376 0.219688 0.975570i \(-0.429496\pi\)
0.219688 + 0.975570i \(0.429496\pi\)
\(840\) −4269.15 −0.175357
\(841\) −7688.31 −0.315237
\(842\) −18463.1 −0.755678
\(843\) 2849.87 0.116435
\(844\) 12325.9 0.502697
\(845\) 13768.9 0.560548
\(846\) 2417.22 0.0982337
\(847\) 459.628 0.0186458
\(848\) 8235.02 0.333481
\(849\) 11184.1 0.452107
\(850\) −4988.38 −0.201294
\(851\) 15100.6 0.608276
\(852\) −3895.99 −0.156660
\(853\) 22357.1 0.897413 0.448706 0.893679i \(-0.351885\pi\)
0.448706 + 0.893679i \(0.351885\pi\)
\(854\) 451.472 0.0180902
\(855\) −4675.70 −0.187024
\(856\) 11519.1 0.459948
\(857\) 33549.1 1.33724 0.668620 0.743604i \(-0.266885\pi\)
0.668620 + 0.743604i \(0.266885\pi\)
\(858\) 3563.10 0.141774
\(859\) −38799.1 −1.54110 −0.770552 0.637377i \(-0.780019\pi\)
−0.770552 + 0.637377i \(0.780019\pi\)
\(860\) −20484.0 −0.812209
\(861\) 1248.79 0.0494292
\(862\) −31928.8 −1.26160
\(863\) 20964.5 0.826928 0.413464 0.910520i \(-0.364319\pi\)
0.413464 + 0.910520i \(0.364319\pi\)
\(864\) 4467.93 0.175928
\(865\) −65257.2 −2.56510
\(866\) −14085.0 −0.552690
\(867\) 13444.1 0.526626
\(868\) 3980.45 0.155651
\(869\) 7641.39 0.298293
\(870\) 11901.3 0.463785
\(871\) −36302.6 −1.41224
\(872\) −4834.81 −0.187761
\(873\) 11001.0 0.426491
\(874\) −2499.51 −0.0967359
\(875\) −105.945 −0.00409324
\(876\) 5574.37 0.215001
\(877\) 26833.9 1.03320 0.516600 0.856227i \(-0.327197\pi\)
0.516600 + 0.856227i \(0.327197\pi\)
\(878\) −4039.31 −0.155262
\(879\) −13255.0 −0.508623
\(880\) −2200.90 −0.0843096
\(881\) 47724.8 1.82507 0.912536 0.408997i \(-0.134121\pi\)
0.912536 + 0.408997i \(0.134121\pi\)
\(882\) 5761.72 0.219963
\(883\) 18332.9 0.698701 0.349350 0.936992i \(-0.386402\pi\)
0.349350 + 0.936992i \(0.386402\pi\)
\(884\) −4839.82 −0.184141
\(885\) 33819.0 1.28453
\(886\) −17942.7 −0.680358
\(887\) −46861.1 −1.77389 −0.886946 0.461874i \(-0.847177\pi\)
−0.886946 + 0.461874i \(0.847177\pi\)
\(888\) 27688.0 1.04634
\(889\) 5847.80 0.220617
\(890\) −14133.4 −0.532307
\(891\) 891.000 0.0335013
\(892\) −3762.60 −0.141235
\(893\) 4545.38 0.170331
\(894\) 7317.79 0.273762
\(895\) −44564.7 −1.66440
\(896\) 1890.46 0.0704863
\(897\) 6467.73 0.240748
\(898\) −276.776 −0.0102852
\(899\) −32214.1 −1.19511
\(900\) −4662.19 −0.172674
\(901\) −13472.4 −0.498149
\(902\) 2348.66 0.0866981
\(903\) −3524.52 −0.129888
\(904\) −52847.6 −1.94434
\(905\) 31394.4 1.15313
\(906\) −3824.64 −0.140248
\(907\) 21170.5 0.775032 0.387516 0.921863i \(-0.373333\pi\)
0.387516 + 0.921863i \(0.373333\pi\)
\(908\) −6494.54 −0.237366
\(909\) −11090.4 −0.404669
\(910\) −6461.93 −0.235397
\(911\) −14266.8 −0.518860 −0.259430 0.965762i \(-0.583535\pi\)
−0.259430 + 0.965762i \(0.583535\pi\)
\(912\) −1256.26 −0.0456129
\(913\) −10534.7 −0.381872
\(914\) −9680.72 −0.350339
\(915\) 2883.22 0.104171
\(916\) 17094.6 0.616618
\(917\) 2456.79 0.0884738
\(918\) 1092.97 0.0392956
\(919\) 1704.89 0.0611959 0.0305979 0.999532i \(-0.490259\pi\)
0.0305979 + 0.999532i \(0.490259\pi\)
\(920\) −14574.6 −0.522293
\(921\) 31926.4 1.14225
\(922\) −5755.42 −0.205580
\(923\) −17119.8 −0.610516
\(924\) 526.946 0.0187611
\(925\) −47831.5 −1.70020
\(926\) −17675.1 −0.627257
\(927\) −10376.1 −0.367632
\(928\) −21385.0 −0.756464
\(929\) −52560.6 −1.85625 −0.928126 0.372265i \(-0.878581\pi\)
−0.928126 + 0.372265i \(0.878581\pi\)
\(930\) −22956.6 −0.809438
\(931\) 10834.4 0.381401
\(932\) −993.363 −0.0349128
\(933\) 1092.51 0.0383357
\(934\) −6428.14 −0.225198
\(935\) 3600.67 0.125941
\(936\) 11859.0 0.414128
\(937\) −20027.5 −0.698259 −0.349130 0.937074i \(-0.613523\pi\)
−0.349130 + 0.937074i \(0.613523\pi\)
\(938\) 4848.47 0.168772
\(939\) 25145.9 0.873913
\(940\) 9129.59 0.316781
\(941\) 40232.8 1.39379 0.696893 0.717175i \(-0.254565\pi\)
0.696893 + 0.717175i \(0.254565\pi\)
\(942\) −1307.14 −0.0452112
\(943\) 4263.27 0.147223
\(944\) 9086.43 0.313282
\(945\) −1615.89 −0.0556242
\(946\) −6628.73 −0.227821
\(947\) 36897.5 1.26611 0.633056 0.774106i \(-0.281800\pi\)
0.633056 + 0.774106i \(0.281800\pi\)
\(948\) 8760.57 0.300137
\(949\) 24495.0 0.837872
\(950\) 7917.24 0.270389
\(951\) −6016.49 −0.205150
\(952\) 1876.53 0.0638853
\(953\) −7655.75 −0.260224 −0.130112 0.991499i \(-0.541534\pi\)
−0.130112 + 0.991499i \(0.541534\pi\)
\(954\) 11371.2 0.385908
\(955\) −16192.6 −0.548672
\(956\) 10900.9 0.368786
\(957\) −4264.63 −0.144050
\(958\) −25208.8 −0.850166
\(959\) 9995.49 0.336571
\(960\) −20041.5 −0.673788
\(961\) 32347.2 1.08580
\(962\) 41909.5 1.40459
\(963\) 4360.03 0.145898
\(964\) −15801.4 −0.527935
\(965\) 22119.5 0.737877
\(966\) −863.812 −0.0287709
\(967\) −28874.6 −0.960232 −0.480116 0.877205i \(-0.659405\pi\)
−0.480116 + 0.877205i \(0.659405\pi\)
\(968\) 2877.11 0.0955310
\(969\) 2055.24 0.0681360
\(970\) −37522.8 −1.24205
\(971\) −40379.7 −1.33455 −0.667275 0.744812i \(-0.732539\pi\)
−0.667275 + 0.744812i \(0.732539\pi\)
\(972\) 1021.50 0.0337084
\(973\) −4213.07 −0.138813
\(974\) 8729.88 0.287190
\(975\) −20486.7 −0.672921
\(976\) 774.660 0.0254060
\(977\) −18762.4 −0.614394 −0.307197 0.951646i \(-0.599391\pi\)
−0.307197 + 0.951646i \(0.599391\pi\)
\(978\) 12185.5 0.398415
\(979\) 5064.45 0.165332
\(980\) 21761.4 0.709330
\(981\) −1829.99 −0.0595589
\(982\) −8539.36 −0.277497
\(983\) −53978.1 −1.75141 −0.875704 0.482848i \(-0.839603\pi\)
−0.875704 + 0.482848i \(0.839603\pi\)
\(984\) 7816.99 0.253248
\(985\) 49796.0 1.61079
\(986\) −5231.32 −0.168965
\(987\) 1570.85 0.0506593
\(988\) 7681.45 0.247348
\(989\) −12032.4 −0.386865
\(990\) −3039.08 −0.0975640
\(991\) 11175.7 0.358233 0.179117 0.983828i \(-0.442676\pi\)
0.179117 + 0.983828i \(0.442676\pi\)
\(992\) 41249.8 1.32024
\(993\) 18056.0 0.577029
\(994\) 2286.48 0.0729604
\(995\) −14177.2 −0.451706
\(996\) −12077.7 −0.384233
\(997\) −21697.3 −0.689228 −0.344614 0.938745i \(-0.611990\pi\)
−0.344614 + 0.938745i \(0.611990\pi\)
\(998\) 8984.63 0.284973
\(999\) 10480.0 0.331905
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.d.1.14 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.4.a.d.1.14 37 1.1 even 1 trivial